From de553ce8a6cac89a8dd4847d2d600f0be073f6c0 Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Thu, 16 Feb 2017 00:06:23 -0500 Subject: [PATCH 01/16] add lecture 09 --- .../lecture_09-checkpoint.ipynb | 6 + lecture_09/.lecture_09.md.swp | Bin 0 -> 16384 bytes lecture_09/even_odd_perm.svg | 331 +++++ lecture_09/lecture_09.ipynb | 1151 +++++++++++++++++ lecture_09/lecture_09.log | 28 + lecture_09/lecture_09.md | 802 ++++++++++++ lecture_09/lecture_09.pdf | Bin 0 -> 16189 bytes lecture_09/mass_springs.svg | 214 +++ 8 files changed, 2532 insertions(+) create mode 100644 lecture_09/.ipynb_checkpoints/lecture_09-checkpoint.ipynb create mode 100644 lecture_09/.lecture_09.md.swp create mode 100644 lecture_09/even_odd_perm.svg create mode 100644 lecture_09/lecture_09.ipynb create mode 100644 lecture_09/lecture_09.log create mode 100644 lecture_09/lecture_09.md create mode 100644 lecture_09/lecture_09.pdf create mode 100644 lecture_09/mass_springs.svg diff --git a/lecture_09/.ipynb_checkpoints/lecture_09-checkpoint.ipynb b/lecture_09/.ipynb_checkpoints/lecture_09-checkpoint.ipynb new file mode 100644 index 0000000..2fd6442 --- /dev/null +++ b/lecture_09/.ipynb_checkpoints/lecture_09-checkpoint.ipynb @@ -0,0 +1,6 @@ +{ + "cells": [], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/lecture_09/.lecture_09.md.swp b/lecture_09/.lecture_09.md.swp new file mode 100644 index 0000000000000000000000000000000000000000..4000b4f7d7714d8a4ab35d84fc5ab720a898c99a GIT binary patch literal 16384 zcmeI3TZ|-C8OLi;7UZhp18Xojuoax?xpvhK>>3;Fp7k;;-Gp6OO}5#grn{!6X1l9~ zs_NNkdV5U-HSxk4F9BkN2XE0AZO zCe$Rq?mG8#{^vX2sXEoOFnx5ctZts%XYltfICU_nwOg(qM^kst2EIR4{;+M$%uKah`ImDUd0UDUd0U zDUd0UDUd0UDUd1f7E&Nyxybk=OT&B9@1Jf;PlMT4ra-1Zra-1Z zra-1Zra-1Zra-1Zra-1Zra-2^|Dgg7FVZLI*B*Jm=ly^G`TzB+4dX?40e%8MhOfhE zsKEjphCAUV7=`QL+*OA0XLt#I1K)(l;8A!G9)MHOh5NyW7TgQ-@FBPrZiMUL8u<5> zhVd`>J-h^G;b-t8cmy7X2jElS!8{y=LtsH3u7Jzo+!coLA9xM^2G7D-cmlo#UxmBi z2<(Q7;nm9x<5%!qco2@jVYm}+g-|=HrTXOt{8>z@^_#eQ;=DX#7)8*l&%avZ$_3LRnsv3HYrT8Ax=#O&e;qEw` zc%X;A8nmiI>4@VCjo2CtxYcgP-b%Bh90uh#ny!poEp${=bDB=5%-9qa{PU#nBGPEb zM2GyOx@(hC!J;nV)%gvQ7k5<4i9>HqQ7Z7=ab=#GJ5|V=cmc}gazh&Da*DD}zrd0c zDO;_C!HOHko*VI-ioJW)k^9QQXDHD@7~oLRbx6dk%VZl z*lZ@{YRu!3v+ByoJFS*W|7yzd>kxbEF)L0OGek_pq|(x;)T#&*%DHr9Vw4jM(@Q$i&4Z6>QuQN1&3RcUlq>}jMlJ4&8%vL3yfHfWK>iK3w95!3|?b2jmZ6wwzY z{W+F6M*=tx9k6=@Y`jxJ&E)c9c5Y^DI(ML8P1DF+vYb~!chw8pk#g6Z)=HCQNr$LD zv6?F5o$sC~A_%F{xuc2?LfQrOkCqkvSjlg2AywB5{t)Qxq$w5xUHD z(2iGFPvVc;>~BNaWE^IZD)o{sDZG`D%cXYN8J=S)?FTHspw()}+CpS2=-W7)le&7|s;g>hp|TP?2jwZS@) zmG%Y}g4|7&6Gx~`)n2pdsqEM~7Qc|}_@;Nf8!xdr^gTFxk-j-F*Yu`g7<_M-$IZ7; zvLMOBBqSF&x@uJ!W^$jm={B#2NvAeOLrvFj#7n9|&pNos;XAcKD%k7EF z&6vK~6w6k(Cy~Ww!(9j+HFB6O)jc^i=f`1CZ`UN_C_8_hXG@-OUk7>q-^-W${hDX_ zXW@(R1y}|T?tltR!~5Ve_#MyaFTzvsb9fx&Illo1U_YGW+4~uI8Xg6CZvQfT8e*uy zZ6MF;H^4P;HRygNUCKT)1u_LP1u_LP1u_LP1u_LP1u_NR$_iB7mB?!bKBvg?l*H>7 zzAO4fP{KM=jtAx0iGW3pBv_GPrPq@~2T}(?gDT|R$$E)i8cb{J8QZiuoIq*a8C^38 z`nZw?!yX5gm3{=NgNVh@sZpluU*9uKc|~FvAK`q8Gv@{;VES=VpIpjm%Fr7LIl$ue zEgj}Kl}}EF_{`fq9i;;tsYp~liP8ZMk|fIFv{c4V8lOo~+fI&Xhl)~jdTJ}VbY9!y zF_(~>;p+EYM5GrR9@P79mkOrjPR_5Arjp$BO`h+G+V~nxNlcQa#n|CtTU6o*&rVL} z?Eb;rI4}RsKRJ@a?4j|BNJCmAp|oeo=}nS5iIP(_I=fScP$lh8dZcU(`olC)@_2V5 v-{Xy6f4Z6JUV#rC&q2t(Nsi1`UH literal 0 HcmV?d00001 diff --git a/lecture_09/even_odd_perm.svg b/lecture_09/even_odd_perm.svg new file mode 100644 index 0000000..eeaca19 --- /dev/null +++ b/lecture_09/even_odd_perm.svg @@ -0,0 +1,331 @@ + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + 1 + 2 + 3 + 4 + 5 + 6 + + + + 1 + 2 + 3 + 4 + 5 + 6 + + + + + even+ + odd- + + + diff --git a/lecture_09/lecture_09.ipynb b/lecture_09/lecture_09.ipynb new file mode 100644 index 0000000..4889d52 --- /dev/null +++ b/lecture_09/lecture_09.ipynb @@ -0,0 +1,1151 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Linear Algebra (Review/Introduction)\n", + "\n", + "Representation of linear equations:\n", + "\n", + "1. $5x_{1}+3x_{2} =1$\n", + "\n", + "2. $x_{1}+2x_{2}+3x_{3} =2$\n", + "\n", + "3. $x_{1}+x_{2}+x_{3} =3$\n", + "\n", + "in matrix form:\n", + "\n", + "$\\left[ \\begin{array}{ccc}\n", + "5 & 3 & 0 \\\\\n", + "1 & 2 & 3 \\\\\n", + "1 & 1 & 1 \\end{array} \\right]\n", + "\\left[\\begin{array}{c} \n", + "x_{1} \\\\ \n", + "x_{2} \\\\\n", + "x_{3}\\end{array}\\right]=\\left[\\begin{array}{c} \n", + "1 \\\\\n", + "2 \\\\\n", + "3\\end{array}\\right]$\n", + "\n", + "$Ax=b$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Vectors \n", + "\n", + "column vector x (length of 3):\n", + "\n", + "$\\left[\\begin{array}{c} \n", + "x_{1} \\\\ \n", + "x_{2} \\\\\n", + "x_{3}\\end{array}\\right]$\n", + "\n", + "row vector y (length of 3):\n", + "\n", + "$\\left[\\begin{array}{ccc} \n", + "y_{1}~ \n", + "y_{2}~ \n", + "y_{3}\\end{array}\\right]$\n", + "\n", + "vector of length N:\n", + "\n", + "$\\left[\\begin{array}{c} \n", + "x_{1} \\\\ \n", + "x_{2} \\\\\n", + "\\vdots \\\\\n", + "x_{N}\\end{array}\\right]$\n", + "\n", + "The $i^{th}$ element of x is $x_{i}$" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x =\n", + "\n", + " 1 2 3 4 5 6 7 8 9 10\n", + "\n" + ] + } + ], + "source": [ + "x=[1:10]" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 1\n", + " 2\n", + " 3\n", + " 4\n", + " 5\n", + " 6\n", + " 7\n", + " 8\n", + " 9\n", + " 10\n", + "\n" + ] + } + ], + "source": [ + "x'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Matrices\n", + "\n", + "Matrix A is 3x3:\n", + "\n", + "$A=\\left[ \\begin{array}{ccc}\n", + "5 & 3 & 0 \\\\\n", + "1 & 2 & 3 \\\\\n", + "1 & 1 & 1 \\end{array} \\right]$\n", + "\n", + "elements in the matrix are denoted $A_{row~column}$, $A_{23}=3$\n", + "\n", + "In general, matrix, B, can be any size, $M \\times N$ (M-rows and N-columns):\n", + "\n", + "$B=\\left[ \\begin{array}{cccc}\n", + "B_{11} & B_{12} &...& B_{1N} \\\\\n", + "B_{21} & B_{22} &...& B_{2N} \\\\\n", + "\\vdots & \\vdots &\\ddots& \\vdots \\\\\n", + "B_{M1} & B_{M2} &...& B_{MN}\\end{array} \\right]$" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A =\n", + "\n", + " 5 3 0\n", + " 1 2 3\n", + " 1 1 1\n", + "\n" + ] + } + ], + "source": [ + "A=[5,3,0;1,2,3;1,1,1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Multiplication\n", + "\n", + "A column vector is a $1\\times N$ matrix and a row vector is a $M\\times 1$ matrix\n", + "\n", + "**Multiplying matrices is not commutative**\n", + "\n", + "$A B \\neq B A$\n", + "\n", + "Inner dimensions must agree, output is outer dimensions. \n", + "\n", + "A is $M1 \\times N1$ and B is $M2 \\times N2$\n", + "\n", + "C=AB\n", + "\n", + "Therefore N1=M2 and C is $M1 \\times N2$\n", + "\n", + "If $C'=BA$, then N2=M1 and C is $M2 \\times N1$\n", + "\n", + "\n", + "e.g. \n", + "$A=\\left[ \\begin{array}{cc}\n", + "5 & 3 & 0 \\\\\n", + "1 & 2 & 3 \\end{array} \\right]$\n", + "\n", + "$B=\\left[ \\begin{array}{cccc}\n", + "1 & 2 & 3 & 4 \\\\\n", + "5 & 6 & 7 & 8 \\\\\n", + "9 & 10 & 11 & 12 \\end{array} \\right]$\n", + "\n", + "C=AB\n", + "\n", + "$[2\\times 4] = [2 \\times 3][3 \\times 4]$\n", + "\n", + "The rule for multiplying matrices, A and B, is\n", + "\n", + "$C_{ij} = \\sum_{k=1}^{n}A_{ik}B_{kj}$\n", + "\n", + "In the previous example, \n", + "\n", + "$C_{11} = A_{11}B_{11}+A_{12}B_{21}+A_{13}B_{31} = 5*1+3*5+0*9=20$\n", + "\n", + "\n", + "Multiplication is associative:\n", + "\n", + "$(AB)C = A(BC)$\n", + "\n", + "and distributive:\n", + "\n", + "$A(B+C)=AB+AC$" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A =\n", + "\n", + " 5 3 0\n", + " 1 2 3\n", + "\n", + "B =\n", + "\n", + " 1 2 3 4\n", + " 5 6 7 8\n", + " 9 10 11 12\n", + "\n" + ] + } + ], + "source": [ + "A=[5,3,0;1,2,3] \n", + "B=[1,2,3,4;5,6,7,8;9,10,11,12]" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "C =\n", + "\n", + " 0 0 0 0\n", + " 0 0 0 0\n", + "\n", + "C =\n", + "\n", + " 20 28 36 44\n", + " 38 44 50 56\n", + "\n" + ] + } + ], + "source": [ + "C=zeros(2,4)\n", + "C(1,1)=A(1,1)*B(1,1)+A(1,2)*B(2,1)+A(1,3)*B(3,1);\n", + "C(1,2)=A(1,1)*B(1,2)+A(1,2)*B(2,2)+A(1,3)*B(3,2);\n", + "\n", + "C=A*B" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "error: operator *: nonconformant arguments (op1 is 3x4, op2 is 2x3)\r\n" + ] + } + ], + "source": [ + "Cp=B*A" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Representation of a problem with Matrices and Vectors\n", + "\n", + "If you have a set of known output, $y_{1},~y_{2},~...y_{N}$ and a set of equations that\n", + "relate unknown inputs, $x_{1},~x_{2},~...x_{N}$, then these can be written in a vector\n", + "matrix format as:\n", + "\n", + "$y=Ax=\\left[\\begin{array}{c} \n", + "y_{1} \\\\ \n", + "y_{2} \\\\\n", + "\\vdots \\\\\n", + "y_{N}\\end{array}\\right]\n", + "=\n", + "A\\left[\\begin{array}{c} \n", + "x_{1} \\\\ \n", + "x_{2} \\\\\n", + "\\vdots \\\\\n", + "x_{N}\\end{array}\\right]$\n", + "\n", + "$A=\n", + "\\left[\\begin{array}{cccc} \n", + "| & | & & | \\\\ \n", + "a_{1} & a_{2} & ... & a_{N} \\\\ \n", + "| & | & & | \\end{array}\\right]$\n", + "\n", + "or \n", + "\n", + "$y = a_{1}x_{1} + a_{2}x_{2} +...+a_{N}x_{N}$\n", + "\n", + "where each $a_{i}$ is a column vector and $x_{i}$ is a scalar taken from the $i^{th}$\n", + "element of x.\n", + "\n", + "Consider the following problem, 4 masses are connected in series to 4 springs with K=10 N/m. What are the final positions of the masses? \n", + "\n", + "![Springs-masses](mass_springs.svg)\n", + "\n", + "The masses haves the following amounts, 1, 2, 3, and 4 kg for masses 1-4. Using a FBD for each mass:\n", + "\n", + "$m_{1}g+k(x_{2}-x_{1})-kx_{1}=0$\n", + "\n", + "$m_{2}g+k(x_{3}-x_{2})-k(x_{2}-x_{1})=0$\n", + "\n", + "$m_{3}g+k(x_{4}-x_{3})-k(x_{3}-x_{2})=0$\n", + "\n", + "$m_{4}g-k(x_{4}-x_{3})=0$\n", + "\n", + "in matrix form:\n", + "\n", + "$\\left[ \\begin{array}{cccc}\n", + "2k & -k & 0 & 0 \\\\\n", + "-k & 2k & -k & 0 \\\\\n", + "0 & -k & 2k & -k \\\\\n", + "0 & 0 & -k & k \\end{array} \\right]\n", + "\\left[ \\begin{array}{c}\n", + "x_{1} \\\\\n", + "x_{2} \\\\\n", + "x_{3} \\\\\n", + "x_{4} \\end{array} \\right]=\n", + "\\left[ \\begin{array}{c}\n", + "m_{1}g \\\\\n", + "m_{2}g \\\\\n", + "m_{3}g \\\\\n", + "m_{4}g \\end{array} \\right]$" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "K =\n", + "\n", + " 20 -10 0 0\n", + " -10 20 -10 0\n", + " 0 -10 20 -10\n", + " 0 0 -10 10\n", + "\n", + "y =\n", + "\n", + " 9.8100\n", + " 19.6200\n", + " 29.4300\n", + " 39.2400\n", + "\n", + "x =\n", + "\n", + " 9.8100\n", + " 18.6390\n", + " 25.5060\n", + " 29.4300\n", + "\n" + ] + } + ], + "source": [ + "k=10; % N/m\n", + "m1=1; % kg\n", + "m2=2;\n", + "m3=3;\n", + "m4=4;\n", + "g=9.81; % m/s^2\n", + "K=[2*k -k 0 0; -k 2*k -k 0; 0 -k 2*k -k; 0 0 -k k]\n", + "y=[m1*g;m2*g;m3*g;m4*g]\n", + "\n", + "x=K\\y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Matrix Operations\n", + "\n", + "Identity matrix `eye(M,N)` **Assume M=N unless specfied**\n", + "\n", + "$I_{ij} =1$ if $i=j$ \n", + "\n", + "$I_{ij} =0$ if $i\\neq j$ \n", + "\n", + "AI=A=IA\n", + "\n", + "Diagonal matrix, D, is similar to the identity matrix, but each diagonal element can be any\n", + "number\n", + "\n", + "$D_{ij} =d_{i}$ if $i=j$ \n", + "\n", + "$D_{ij} =0$ if $i\\neq j$ " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Transpose\n", + "\n", + "The transpose of a matrix changes the rows -> columns and columns-> rows\n", + "\n", + "$(A^{T})_{ij} = A_{ji}$\n", + "\n", + "for diagonal matrices, $D^{T}=D$\n", + "\n", + "in general, the transpose has the following qualities:\n", + " \n", + "1. $(A^{T})^{T}=A$\n", + "\n", + "2. $(AB)^{T} = B^{T}A^{T}$\n", + "\n", + "3. $(A+B)^{T} = A^{T} +B^{T}$ \n", + "\n", + "All matrices have a symmetric and antisymmetric part:\n", + "\n", + "$A= 1/2(A+A^{T}) +1/2(A-A^{T})$\n", + "\n", + "If $A=A^{T}$, then A is symmetric, if $A=-A^{T}$, then A is antisymmetric." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 20 38\n", + " 28 44\n", + " 36 50\n", + " 44 56\n", + "\n", + "ans =\n", + "\n", + " 20 38\n", + " 28 44\n", + " 36 50\n", + " 44 56\n", + "\n", + "error: operator *: nonconformant arguments (op1 is 3x2, op2 is 4x3)\n" + ] + } + ], + "source": [ + "(A*B)'\n", + "\n", + "B'*A' % if this wasnt true, then inner dimensions wouldn;t match\n", + "\n", + "A'*B' == (A*B)'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Square matrix operations\n", + "\n", + "### Trace\n", + "\n", + "The trace of a square matrix is the sum of the diagonal elements\n", + "\n", + "$tr~A=\\sum_{i=1}^{N}A_{ii}$\n", + "\n", + "The trace is invariant, meaning that if you change the basis through a rotation, then the\n", + "trace remains the same. \n", + "\n", + "It also has the following properties:\n", + "\n", + "1. $tr~A=tr~A^{T}$\n", + "\n", + "2. $tr~A+tr~B=tr(A+B)$\n", + "\n", + "3. $tr(kA)=k tr~A$\n", + "\n", + "4. $tr(AB)=tr(BA)$" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "id_m =\n", + "\n", + "Diagonal Matrix\n", + "\n", + " 1 0 0\n", + " 0 1 0\n", + " 0 0 1\n", + "\n", + "ans = 3\n" + ] + } + ], + "source": [ + "id_m=eye(3)\n", + "trace(id_m)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Inverse\n", + "\n", + "The inverse of a square matrix, $A^{-1}$ is defined such that\n", + "\n", + "$A^{-1}A=I=AA^{-1}$\n", + "\n", + "Not all square matrices have an inverse, they can be *singular* or *non-invertible*\n", + "\n", + "The inverse has the following properties:\n", + "\n", + "1. $(A^{-1})^{-1}=A$\n", + "\n", + "2. $(AB)^{-1}=B^{-1}A^{-1}$\n", + "\n", + "3. $(A^{-1})^{T}=(A^{T})^{-1}$" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A =\n", + "\n", + " 0.5762106 0.3533174 0.7172134\n", + " 0.7061664 0.4863733 0.9423436\n", + " 0.4255961 0.0016613 0.3561407\n", + "\n" + ] + } + ], + "source": [ + "A=rand(3,3)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ainv =\n", + "\n", + " 41.5613 -30.1783 -3.8467\n", + " 36.2130 -24.2201 -8.8415\n", + " -49.8356 36.1767 7.4460\n", + "\n" + ] + } + ], + "source": [ + "Ainv=inv(A)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "B =\n", + "\n", + " 0.524529 0.470856 0.708116\n", + " 0.084491 0.730986 0.528292\n", + " 0.303545 0.782522 0.389282\n", + "\n" + ] + } + ], + "source": [ + "B=rand(3,3)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " -182.185 125.738 40.598\n", + " -133.512 97.116 17.079\n", + " 282.422 -200.333 -46.861\n", + "\n", + "ans =\n", + "\n", + " -182.185 125.738 40.598\n", + " -133.512 97.116 17.079\n", + " 282.422 -200.333 -46.861\n", + "\n", + "ans =\n", + "\n", + " 41.5613 36.2130 -49.8356\n", + " -30.1783 -24.2201 36.1767\n", + " -3.8467 -8.8415 7.4460\n", + "\n", + "ans =\n", + "\n", + " 41.5613 36.2130 -49.8356\n", + " -30.1783 -24.2201 36.1767\n", + " -3.8467 -8.8415 7.4460\n", + "\n" + ] + } + ], + "source": [ + "inv(A*B)\n", + "inv(B)*inv(A)\n", + "\n", + "inv(A')\n", + "\n", + "inv(A)'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Orthogonal Matrices\n", + "\n", + "Vectors are *orthogonal* if $x^{T}$ y=0, and a vector is *normalized* if $||x||_{2}=1$. A\n", + "square matrix is *orthogonal* if all its column vectors are orthogonal to each other and\n", + "normalized. The column vectors are then called *orthonormal* and the following results\n", + "\n", + "$U^{T}U=I=UU^{T}$\n", + "\n", + "and \n", + "\n", + "$||Ux||_{2}=||x||_{2}$\n", + "\n", + "### Determinant\n", + "\n", + "The **determinant** of a matrix has 3 properties\n", + "\n", + "1. The determinant of the identity matrix is one, $|I|=1$\n", + "\n", + "2. If you multiply a single row by scalar $t$ then the determinant is $t|A|$:\n", + "\n", + "$t|A|=\\left[ \\begin{array}{cccc}\n", + "tA_{11} & tA_{12} &...& tA_{1N} \\\\\n", + "A_{21} & A_{22} &...& A_{2N} \\\\\n", + "\\vdots & \\vdots &\\ddots& \\vdots \\\\\n", + "A_{M1} & A_{M2} &...& A_{MN}\\end{array} \\right]$\n", + "\n", + "3. If you switch 2 rows, the determinant changes sign:\n", + "\n", + "\n", + "$-|A|=\\left[ \\begin{array}{cccc}\n", + "A_{21} & A_{22} &...& A_{2N} \\\\\n", + "A_{11} & A_{12} &...& A_{1N} \\\\\n", + "\\vdots & \\vdots &\\ddots& \\vdots \\\\\n", + "A_{M1} & A_{M2} &...& A_{MN}\\end{array} \\right]$\n", + "\n", + "4. inverse of the determinant is the determinant of the inverse:\n", + "\n", + "$|A^{-1}|=\\frac{1}{|A|}=|A|^{-1}$\n", + "\n", + "For a $2\\times2$ matrix, \n", + "\n", + "$|A|=\\left|\\left[ \\begin{array}{cc}\n", + "A_{11} & A_{12} \\\\\n", + "A_{21} & A_{22} \\\\\n", + "\\end{array} \\right]\\right| = A_{11}A_{22}-A_{21}A_{12}$\n", + "\n", + "For a $3\\times3$ matrix,\n", + "\n", + "$|A|=\\left|\\left[ \\begin{array}{ccc}\n", + "A_{11} & A_{12} & A_{13} \\\\\n", + "A_{21} & A_{22} & A_{23} \\\\\n", + "A_{31} & A_{32} & A_{33}\\end{array} \\right]\\right|=$\n", + "\n", + "$A_{11}A_{22}A_{33}+A_{12}A_{23}A_{31}+A_{13}A_{21}A_{32}\n", + "-A_{31}A_{22}A_{13}-A_{32}A_{23}A_{11}-A_{33}A_{21}A_{12}$\n", + "\n", + "For larger matrices, the determinant is \n", + "\n", + "$|A|=\n", + "\\frac{1}{n!}\n", + "\\sum_{i_{r}}^{N}\n", + "\\sum_{j_{r}}^{N}\n", + "\\epsilon_{i_{1}...i_{N}}\n", + "\\epsilon_{j_{1}...j_{N}}\n", + "A_{i_{1}j_{1}}\n", + "A_{i_{2}j_{2}}\n", + "...\n", + "A_{i_{N}j_{N}}$\n", + "\n", + "Where the Levi-Cevita symbol is $\\epsilon_{i_{1}i_{2}...i_{N}} = 1$ if it is an even\n", + "permutation and $\\epsilon_{i_{1}i_{2}...i_{N}} = -1$ if it is an odd permutation and\n", + "$\\epsilon_{i_{1}i_{2}...i_{N}} = 0$ if $i_{n}=i_{m}$ e.g. $i_{1}=i_{7}$\n", + "\n", + "![Levi-Cevita rule for even and odd permutations for an $N\\times N$\n", + "determinant](even_odd_perm.svg)\n", + "\n", + "So a $4\\times4$ matrix determinant,\n", + "\n", + "$|A|=\\left|\\left[ \\begin{array}{cccc}\n", + "A_{11} & A_{12} & A_{13} & A_{14} \\\\\n", + "A_{21} & A_{22} & A_{23} & A_{24} \\\\\n", + "A_{31} & A_{32} & A_{33} & A_{34} \\\\\n", + "A_{41} & A_{42} & A_{43} & A_{44} \\end{array} \\right]\\right|$\n", + "\n", + "$=\\epsilon_{1234}\\epsilon_{1234}A_{11}A_{22}A_{33}A_{44}+\n", + "\\epsilon_{2341}\\epsilon_{1234}A_{21}A_{32}A_{43}A_{14}+\n", + "\\epsilon_{3412}\\epsilon_{1234}A_{31}A_{42}A_{13}A_{24}+\n", + "\\epsilon_{4123}\\epsilon_{1234}A_{41}A_{12}A_{23}A_{34}+...\n", + "\\epsilon_{4321}\\epsilon_{4321}A_{44}A_{33}A_{22}A_{11}$\n", + "\n", + "### Special Case for determinants\n", + "\n", + "The determinant of a diagonal matrix $|D|=D_{11}D_{22}D_{33}...D_{NN}$. \n", + "\n", + "Similarly, if a matrix is upper triangular (so all values of $A_{ij}=0$ when $j +Babel <3.9q> and hyphenation patterns for 81 language(s) loaded. +! You can't use `macro parameter character #' in vertical mode. +l.2 # + Linear Algebra (Review/Introduction) +? +! Interruption. + + +l.2 # + Linear Algebra (Review/Introduction) +? xx + +Here is how much of TeX's memory you used: + 6 strings out of 493030 + 147 string characters out of 6136260 + 53067 words of memory out of 5000000 + 3641 multiletter control sequences out of 15000+600000 + 3640 words of font info for 14 fonts, out of 8000000 for 9000 + 1141 hyphenation exceptions out of 8191 + 5i,0n,1p,57b,8s stack positions out of 5000i,500n,10000p,200000b,80000s +No pages of output. diff --git a/lecture_09/lecture_09.md b/lecture_09/lecture_09.md new file mode 100644 index 0000000..a1d53d1 --- /dev/null +++ b/lecture_09/lecture_09.md @@ -0,0 +1,802 @@ + +# Linear Algebra (Review/Introduction) + +Representation of linear equations: + +1. $5x_{1}+3x_{2} =1$ + +2. $x_{1}+2x_{2}+3x_{3} =2$ + +3. $x_{1}+x_{2}+x_{3} =3$ + +in matrix form: + +$\left[ \begin{array}{ccc} +5 & 3 & 0 \\ +1 & 2 & 3 \\ +1 & 1 & 1 \end{array} \right] +\left[\begin{array}{c} +x_{1} \\ +x_{2} \\ +x_{3}\end{array}\right]=\left[\begin{array}{c} +1 \\ +2 \\ +3\end{array}\right]$ + +$Ax=b$ + +### Vectors + +column vector x (length of 3): + +$\left[\begin{array}{c} +x_{1} \\ +x_{2} \\ +x_{3}\end{array}\right]$ + +row vector y (length of 3): + +$\left[\begin{array}{ccc} +y_{1}~ +y_{2}~ +y_{3}\end{array}\right]$ + +vector of length N: + +$\left[\begin{array}{c} +x_{1} \\ +x_{2} \\ +\vdots \\ +x_{N}\end{array}\right]$ + +The $i^{th}$ element of x is $x_{i}$ + + +```octave +x=[1:10] +``` + + x = + + 1 2 3 4 5 6 7 8 9 10 + + + + +```octave +x' +``` + + ans = + + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + + + +### Matrices + +Matrix A is 3x3: + +$A=\left[ \begin{array}{ccc} +5 & 3 & 0 \\ +1 & 2 & 3 \\ +1 & 1 & 1 \end{array} \right]$ + +elements in the matrix are denoted $A_{row~column}$, $A_{23}=3$ + +In general, matrix, B, can be any size, $M \times N$ (M-rows and N-columns): + +$B=\left[ \begin{array}{cccc} +B_{11} & B_{12} &...& B_{1N} \\ +B_{21} & B_{22} &...& B_{2N} \\ +\vdots & \vdots &\ddots& \vdots \\ +B_{M1} & B_{M2} &...& B_{MN}\end{array} \right]$ + + +```octave +A=[5,3,0;1,2,3;1,1,1] +``` + + A = + + 5 3 0 + 1 2 3 + 1 1 1 + + + +## Multiplication + +A column vector is a $1\times N$ matrix and a row vector is a $M\times 1$ matrix + +**Multiplying matrices is not commutative** + +$A B \neq B A$ + +Inner dimensions must agree, output is outer dimensions. + +A is $M1 \times N1$ and B is $M2 \times N2$ + +C=AB + +Therefore N1=M2 and C is $M1 \times N2$ + +If $C'=BA$, then N2=M1 and C is $M2 \times N1$ + + +e.g. +$A=\left[ \begin{array}{cc} +5 & 3 & 0 \\ +1 & 2 & 3 \end{array} \right]$ + +$B=\left[ \begin{array}{cccc} +1 & 2 & 3 & 4 \\ +5 & 6 & 7 & 8 \\ +9 & 10 & 11 & 12 \end{array} \right]$ + +C=AB + +$[2\times 4] = [2 \times 3][3 \times 4]$ + +The rule for multiplying matrices, A and B, is + +$C_{ij} = \sum_{k=1}^{n}A_{ik}B_{kj}$ + +In the previous example, + +$C_{11} = A_{11}B_{11}+A_{12}B_{21}+A_{13}B_{31} = 5*1+3*5+0*9=20$ + + +Multiplication is associative: + +$(AB)C = A(BC)$ + +and distributive: + +$A(B+C)=AB+AC$ + + +```octave +A=[5,3,0;1,2,3] +B=[1,2,3,4;5,6,7,8;9,10,11,12] +``` + + A = + + 5 3 0 + 1 2 3 + + B = + + 1 2 3 4 + 5 6 7 8 + 9 10 11 12 + + + + +```octave +C=zeros(2,4) +C(1,1)=A(1,1)*B(1,1)+A(1,2)*B(2,1)+A(1,3)*B(3,1); +C(1,2)=A(1,1)*B(1,2)+A(1,2)*B(2,2)+A(1,3)*B(3,2); + +C=A*B +``` + + C = + + 0 0 0 0 + 0 0 0 0 + + C = + + 20 28 36 44 + 38 44 50 56 + + + + +```octave +Cp=B*A +``` + + error: operator *: nonconformant arguments (op1 is 3x4, op2 is 2x3) + + +## Representation of a problem with Matrices and Vectors + +If you have a set of known output, $y_{1},~y_{2},~...y_{N}$ and a set of equations that +relate unknown inputs, $x_{1},~x_{2},~...x_{N}$, then these can be written in a vector +matrix format as: + +$y=Ax=\left[\begin{array}{c} +y_{1} \\ +y_{2} \\ +\vdots \\ +y_{N}\end{array}\right] += +A\left[\begin{array}{c} +x_{1} \\ +x_{2} \\ +\vdots \\ +x_{N}\end{array}\right]$ + +$A= +\left[\begin{array}{cccc} +| & | & & | \\ +a_{1} & a_{2} & ... & a_{N} \\ +| & | & & | \end{array}\right]$ + +or + +$y = a_{1}x_{1} + a_{2}x_{2} +...+a_{N}x_{N}$ + +where each $a_{i}$ is a column vector and $x_{i}$ is a scalar taken from the $i^{th}$ +element of x. + +Consider the following problem, 4 masses are connected in series to 4 springs with K=10 N/m. What are the final positions of the masses? + +![Springs-masses](mass_springs.svg) + +The masses haves the following amounts, 1, 2, 3, and 4 kg for masses 1-4. Using a FBD for each mass: + +$m_{1}g+k(x_{2}-x_{1})-kx_{1}=0$ + +$m_{2}g+k(x_{3}-x_{2})-k(x_{2}-x_{1})=0$ + +$m_{3}g+k(x_{4}-x_{3})-k(x_{3}-x_{2})=0$ + +$m_{4}g-k(x_{4}-x_{3})=0$ + +in matrix form: + +$\left[ \begin{array}{cccc} +2k & -k & 0 & 0 \\ +-k & 2k & -k & 0 \\ +0 & -k & 2k & -k \\ +0 & 0 & -k & k \end{array} \right] +\left[ \begin{array}{c} +x_{1} \\ +x_{2} \\ +x_{3} \\ +x_{4} \end{array} \right]= +\left[ \begin{array}{c} +m_{1}g \\ +m_{2}g \\ +m_{3}g \\ +m_{4}g \end{array} \right]$ + + +```octave +k=10; % N/m +m1=1; % kg +m2=2; +m3=3; +m4=4; +g=9.81; % m/s^2 +K=[2*k -k 0 0; -k 2*k -k 0; 0 -k 2*k -k; 0 0 -k k] +y=[m1*g;m2*g;m3*g;m4*g] + +x=K\y +``` + + K = + + 20 -10 0 0 + -10 20 -10 0 + 0 -10 20 -10 + 0 0 -10 10 + + y = + + 9.8100 + 19.6200 + 29.4300 + 39.2400 + + x = + + 9.8100 + 18.6390 + 25.5060 + 29.4300 + + + +## Matrix Operations + +Identity matrix `eye(M,N)` **Assume M=N unless specfied** + +$I_{ij} =1$ if $i=j$ + +$I_{ij} =0$ if $i\neq j$ + +AI=A=IA + +Diagonal matrix, D, is similar to the identity matrix, but each diagonal element can be any +number + +$D_{ij} =d_{i}$ if $i=j$ + +$D_{ij} =0$ if $i\neq j$ + +### Transpose + +The transpose of a matrix changes the rows -> columns and columns-> rows + +$(A^{T})_{ij} = A_{ji}$ + +for diagonal matrices, $D^{T}=D$ + +in general, the transpose has the following qualities: + +1. $(A^{T})^{T}=A$ + +2. $(AB)^{T} = B^{T}A^{T}$ + +3. $(A+B)^{T} = A^{T} +B^{T}$ + +All matrices have a symmetric and antisymmetric part: + +$A= 1/2(A+A^{T}) +1/2(A-A^{T})$ + +If $A=A^{T}$, then A is symmetric, if $A=-A^{T}$, then A is antisymmetric. + + +```octave +(A*B)' + +B'*A' % if this wasnt true, then inner dimensions wouldn;t match + +A'*B' == (A*B)' +``` + + ans = + + 20 38 + 28 44 + 36 50 + 44 56 + + ans = + + 20 38 + 28 44 + 36 50 + 44 56 + + error: operator *: nonconformant arguments (op1 is 3x2, op2 is 4x3) + + +## Square matrix operations + +### Trace + +The trace of a square matrix is the sum of the diagonal elements + +$tr~A=\sum_{i=1}^{N}A_{ii}$ + +The trace is invariant, meaning that if you change the basis through a rotation, then the +trace remains the same. + +It also has the following properties: + +1. $tr~A=tr~A^{T}$ + +2. $tr~A+tr~B=tr(A+B)$ + +3. $tr(kA)=k tr~A$ + +4. $tr(AB)=tr(BA)$ + + +```octave +id_m=eye(3) +trace(id_m) +``` + + id_m = + + Diagonal Matrix + + 1 0 0 + 0 1 0 + 0 0 1 + + ans = 3 + + +### Inverse + +The inverse of a square matrix, $A^{-1}$ is defined such that + +$A^{-1}A=I=AA^{-1}$ + +Not all square matrices have an inverse, they can be *singular* or *non-invertible* + +The inverse has the following properties: + +1. $(A^{-1})^{-1}=A$ + +2. $(AB)^{-1}=B^{-1}A^{-1}$ + +3. $(A^{-1})^{T}=(A^{T})^{-1}$ + + +```octave +A=rand(3,3) +``` + + A = + + 0.5762106 0.3533174 0.7172134 + 0.7061664 0.4863733 0.9423436 + 0.4255961 0.0016613 0.3561407 + + + + +```octave +Ainv=inv(A) +``` + + Ainv = + + 41.5613 -30.1783 -3.8467 + 36.2130 -24.2201 -8.8415 + -49.8356 36.1767 7.4460 + + + + +```octave +B=rand(3,3) +``` + + B = + + 0.524529 0.470856 0.708116 + 0.084491 0.730986 0.528292 + 0.303545 0.782522 0.389282 + + + + +```octave +inv(A*B) +inv(B)*inv(A) + +inv(A') + +inv(A)' +``` + + ans = + + -182.185 125.738 40.598 + -133.512 97.116 17.079 + 282.422 -200.333 -46.861 + + ans = + + -182.185 125.738 40.598 + -133.512 97.116 17.079 + 282.422 -200.333 -46.861 + + ans = + + 41.5613 36.2130 -49.8356 + -30.1783 -24.2201 36.1767 + -3.8467 -8.8415 7.4460 + + ans = + + 41.5613 36.2130 -49.8356 + -30.1783 -24.2201 36.1767 + -3.8467 -8.8415 7.4460 + + + +### Orthogonal Matrices + +Vectors are *orthogonal* if $x^{T}$ y=0, and a vector is *normalized* if $||x||_{2}=1$. A +square matrix is *orthogonal* if all its column vectors are orthogonal to each other and +normalized. The column vectors are then called *orthonormal* and the following results + +$U^{T}U=I=UU^{T}$ + +and + +$||Ux||_{2}=||x||_{2}$ + +### Determinant + +The **determinant** of a matrix has 3 properties + +1. The determinant of the identity matrix is one, $|I|=1$ + +2. If you multiply a single row by scalar $t$ then the determinant is $t|A|$: + +$t|A|=\left[ \begin{array}{cccc} +tA_{11} & tA_{12} &...& tA_{1N} \\ +A_{21} & A_{22} &...& A_{2N} \\ +\vdots & \vdots &\ddots& \vdots \\ +A_{M1} & A_{M2} &...& A_{MN}\end{array} \right]$ + +3. If you switch 2 rows, the determinant changes sign: + + +$-|A|=\left[ \begin{array}{cccc} +A_{21} & A_{22} &...& A_{2N} \\ +A_{11} & A_{12} &...& A_{1N} \\ +\vdots & \vdots &\ddots& \vdots \\ +A_{M1} & A_{M2} &...& A_{MN}\end{array} \right]$ + +4. inverse of the determinant is the determinant of the inverse: + +$|A^{-1}|=\frac{1}{|A|}=|A|^{-1}$ + +For a $2\times2$ matrix, + +$|A|=\left|\left[ \begin{array}{cc} +A_{11} & A_{12} \\ +A_{21} & A_{22} \\ +\end{array} \right]\right| = A_{11}A_{22}-A_{21}A_{12}$ + +For a $3\times3$ matrix, + +$|A|=\left|\left[ \begin{array}{ccc} +A_{11} & A_{12} & A_{13} \\ +A_{21} & A_{22} & A_{23} \\ +A_{31} & A_{32} & A_{33}\end{array} \right]\right|=$ + +$A_{11}A_{22}A_{33}+A_{12}A_{23}A_{31}+A_{13}A_{21}A_{32} +-A_{31}A_{22}A_{13}-A_{32}A_{23}A_{11}-A_{33}A_{21}A_{12}$ + +For larger matrices, the determinant is + +$|A|= +\frac{1}{n!} +\sum_{i_{r}}^{N} +\sum_{j_{r}}^{N} +\epsilon_{i_{1}...i_{N}} +\epsilon_{j_{1}...j_{N}} +A_{i_{1}j_{1}} +A_{i_{2}j_{2}} +... +A_{i_{N}j_{N}}$ + +Where the Levi-Cevita symbol is $\epsilon_{i_{1}i_{2}...i_{N}} = 1$ if it is an even +permutation and $\epsilon_{i_{1}i_{2}...i_{N}} = -1$ if it is an odd permutation and +$\epsilon_{i_{1}i_{2}...i_{N}} = 0$ if $i_{n}=i_{m}$ e.g. $i_{1}=i_{7}$ + +![Levi-Cevita rule for even and odd permutations for an $N\times N$ +determinant](even_odd_perm.svg) + +So a $4\times4$ matrix determinant, + +$|A|=\left|\left[ \begin{array}{cccc} +A_{11} & A_{12} & A_{13} & A_{14} \\ +A_{21} & A_{22} & A_{23} & A_{24} \\ +A_{31} & A_{32} & A_{33} & A_{34} \\ +A_{41} & A_{42} & A_{43} & A_{44} \end{array} \right]\right|$ + +$=\epsilon_{1234}\epsilon_{1234}A_{11}A_{22}A_{33}A_{44}+ +\epsilon_{2341}\epsilon_{1234}A_{21}A_{32}A_{43}A_{14}+ +\epsilon_{3412}\epsilon_{1234}A_{31}A_{42}A_{13}A_{24}+ +\epsilon_{4123}\epsilon_{1234}A_{41}A_{12}A_{23}A_{34}+... +\epsilon_{4321}\epsilon_{4321}A_{44}A_{33}A_{22}A_{11}$ + +### Special Case for determinants + +The determinant of a diagonal matrix $|D|=D_{11}D_{22}D_{33}...D_{NN}$. + +Similarly, if a matrix is upper triangular (so all values of $A_{ij}=0$ when $j{i-l?Q^_J>s~ zzpCr1wMgZKMQIplS)fRd?yldU80ZP;3G56lp}4u}L@lhHO&sY&tqq(_giVa>j7{jI zO>E7a%?TLjIaqjkp`4r@O$=H*K-m5PWXc?i@l~$#Hfp{=(DDp-@HwumpDx z2^3IRY5CK}{2_hVb#tGOtkPMJIB4cKz}9v!3pJb3W@r2yi+A`CFa`Z~WYwwH8@U>m zGBy{;H$B7-)eWkzUV(}>JA}8Z@?hGwUL|f;c|?CLay#5jf(l$!C~4JC0;3T)G79W#2I0Uv=Qrq*o?LfplfBQb0yPj@c_0o$+`cwO*HA8K0SL zR-3jP{~}rMs;$kGYdU$1Qk$Iid^X_Po>HB>oChQUpY>s-Wfn)Y(PQx=54*`aHbrty z{9cw}hU;pE<9)zh$N z<5|Ju01C&XB=I*iT^v~iMtxW_0v{ZLP{UJPY|IJq2n7)s;tvL6TUtAgAVH&#ccR8P zp-IRYQdQRwm^}D8;o6CY2l8$}TQq@`_wCrYT~xL^qoXDe8RPL{0T%?H-j#D2N60LG z_95|5-%u}(y9O5|qa!3IBE#gg4a0i1S=Z8%t?K2l$ck$SYd(oee5XD^vkAQD2n|a( zdA2wnMAoOqwE_aCrt+{BF;eqR+Y13fqCYpKzXSldKUHCd1ndNgv~zrE?L~yD>zelv z@%Hl=8k~;kOD+4ZP#aX9tfnlI1 z;5!Xw&^HRgcMahzkmx6AguO7eBrry{(_SLRG#ZqaCl~izOb+#pBfCa;(9_TNy}i;5 zzTzl*@w>m!nC)#98?kUEV`&NQ&}I*Ech>U20oa*OLX` z)Y#>`d_|HPx3mqxM*?!3s%Z9i@cVA^NW}y~&eJ)wh9oxap<$8*7P(H##}@qbAZ9^? zjyh;z(7Dx2*w*V_`FfBP1^!G#P|5hGy#a4FG6?ofr0T)`7DOdP*Q*MpT!`pV8mGJF z3gAcVRaX>nx4#uY{DMDj&bCQZ=)m$1XkTQUP%oyWJdgFEu+mE!5a)M5?DerMSu zd7K;7j4G*#LfH)6z*{adAs7`b9tXvfi^Z)eO*?}@V(D^d0#_|n9cLX`9cvwJov(7y ziaNl}ZS?@7F&53m&;Hl!>kJ|3{R6M*qPe2A2PXk&=s{vxmJ2o$@~~ z2BH6fP0XzH9RJFu9Cc`AWV4N2jB#n2LK7@5i1S7nhWajoO;d>lNF+`a_Q2Us&a;vYXuB zFSD79q>S6o+*gmh*9RYDJO*Fx{=<7=-m0GM*4pgD$9dIT|L|~s{fvP}czntuz^y%` zP3&MBs#(_Q+rS+9gvO=fuZh zzKrsi1rbTpL`P?k8w?aB!v6?TX|(iju5Me^7@ug;;g4%t6f=_%2p;sX(F>xH z+$V!d5T`6?BqE4JlNeqJAQgwhqz+G@BuscDqDo5m3uBVPChm(Yyb)NSu+gg_k;WuU zCQE*45h+Ou8UYa*mGmd7hX|u#qBO9jGsW$OQ4krCDlkBC(~c5jOlTEEtAGuU6&jMR z6}DYwGQ>6*05)Xnl)%7Cp%A*8))Sf2olY+{tN~~gDAp}bI;Boy>%52ZwP#cHy_0*4T>6)nhX>EMM9yo-T~8XOEQH5< z^bPO*qN8$?cqGyy$w8*kCCv5_L*x!h?`Rw1HTeJju$%2*4Me?#uSvfl10EJ15|bef zNezJ*5-~)$huD*tAE+2Y-DCA5)FIm;+#)?jyoSF<91lqvqV7vp6RsfH26OETRF6_% zL)aM-k8A|bdxz5usTyMMOT8gBwMS!%RTC%+qs|Xz{Y`od9i@Et?oITw>Arkp=Q8V} z15qi4?#S&HvMJio(|lM+faIX-`*EC^RJ($g(PmP(q~F~iB1x0@PC6f_sr%Ybv5NIF z?*;Dk`C!GzHEV-V+m5-3`7zx^KiBJDwXZsRoOpC;yYTA$;_Qvh;H9%~a#n5DilqJn zEO8yZ6JldK-Ot8XeCOD_&-!b`s_lO6EhMG1n*lx@4rC0!s>mCMm&gn8W&GiGKR=ar zyLwyh(&~=VF_5S4@X_c~RfsNXr}r!dQ;#i!BwB&g*h*qT8+E_NUd9}AUj21B3qGq+ z7lG4A!_AC&AM!vEqODtJZr-}W#zIw%Xb7IgS!)w)d&mM)RB6CVg|9(leA-o?v}Vmv zPp2|%{%G~cRlp97lKF_583>gyaEQnylZ`;;ZEud2H9k>%JDrF7Myyyg7pt}F8$a#|pHby4&>qfYux{6|-E$J&`x&~DwhB?i5f6(| zjC=Rs3c$~Mu|-7@s2Hu8tTvsv&c$-|fpZk#oes{&;tQlkDNOsFU6P|3pqHI@>+4Fj zNI-E;%eSn{1yZ<~_x1;E@WCIo8rMqBfykv0x@L_2DEwyUsY~qFeJPd38Yx{aU30bt z&j0Ld4{i2%C%5(hMtrfUhn>MRMlb zp~AUzN*Y7+UpM-Fby4sw|2{V##-$An2N=(Mwi|JCn`n-eGcECXz8&_>HP}2wH#P5x zhn$sx+PCXXF%Fl4Ji2>p2X5MCW~7eJTaC(Ts-_e*Z|+%<6T>2Vh>JI0Bl%(%!w zsc(^$;=#%ydXPLe?**?D_eYU-LBcLlHuZo-R|pvme8!0~&~2WW37YN`JB53jUYq$b zA_MW^?7P41Ha~@J=r)G9{yCxzGi*Bog3QPLa^_S-tJ*$`XPWkBNCt9m4$hWW(RCdss%h@V7oN68v?`<`zi# z8el#zvfb8KH6AX& zG=BHhNG2LQijYPV|Q?okXKv;4T**Oa%_m!a+ zKsXDTPg^ay_M?`oWvPr{h~C<)QpoQP-eeZw@V^3+q8r;SmoHUj!zc)b3SPqj5-d(U zP#6htMxE4^mt*gxFs zZnn9?5kre+aNyt|qosWDx8;W?P!6aX8TnGn$I060ar+&MrXraILMb+DR76vXq$y=9 zW|mJfNJlPlDNW4` zfV1MuF1)GZoso4dq(%b0LXlPm^J32+#aWy&L-i0foh4_q(j#cHFDUdCV3E5scu|S%G$)4pZ=IfAb z0!L{NnT1&qHuRu;i3@bToA0!w%+#n__De>G!7C&a_;KO#EPe5>nB&wOyQ2Q)zM;MH zt9~K9k6KFFWYEbno@;n#h3XdYDzst?S&zCt>o|2-lcI0K^(LSg)C%9yk%B=K^glVtt3lbvi1Z6_TaJ8HgOC6$SH@3<`jPx@4ycg_F`UGO<}FFVV}OpZr;hv*~{9h8{foi_4qIgG8Z> z`Tcr3ZZCmKDI0Gpl&Ss2o*ev~Sw6LVtTDC!GB|&I9z?(i;u2cfh~KLp%hI+TNJlA5 z)AwAu2zMtH9=p>WagPOGB68x`)Uq!xLM}fTWJP-Q1}lYbr!%h|1HHv%`OW+8Q7dEo@Emhj; zh7xKTK|8RhQ;N){q7@Y_3hx8^nktz3#hOy!nA_+qO)XjUD#eebQ# zpcB}K4T)gOOnSLw50=XMcPBmOM*1i>S!YicG~SBn>LoGl;d;##iF-MtaVy7YGz{Nf zcF7UjkA^l8zrAszBI&pS)?PMvW8Qdyeylgu=#?d64Czv$%#+>>Z%s|xUj@T>Gb{e$ z!L5d(Z@J;Uie`|)Tiq+?XI<6S31P+c1f|LDIG8!~K$qqr%w{}bLS{d~cMp`hvrT8* z{@!pQsZq&3m3k_oXFST4o;fQ!0S5?iDX=RyT-0f9a+f%auJyIf)es%Bl`86TSl*C% zSq1&<@!{byiW#(>1~;UCVkWdU^(FD)IzH(i?!@M^7# zvk%#g#}%=#YnUO=j+@47YI-Zp#@#(CgY&WrUM&Ti<|C~`iE|F};z+i`*CxFp>>_Ds zg2n)HV8hX$Pn8xOBiJWH-JaF}t9)4bx{fiGh1#;pkOUp{j~N);$M3m_>%UI3XU#^_ zttiyq5lZawSy}*j5%KU5x*Oh(%nUCkH&W^+Gx=UeiwpMrqoR~G^1!jW(f_P(WE>D!;$>N4!xIos}n`xp9EEzChZ~UizDdX63(GUnPfz!;Hj~+FEwgl917+8s@1IwUIFNPZ3Fg%OPJIU_H}0Hl z@n54OO^-PP1d1u~?bbBNzJ&F@u)+R7e6<>*-ZBfaaw5MpD)mlA29R=r^#H}?unGGxYPQ|?(g!@VAEaJ)=2 zLWjNrP4n1Ic=mb(Ucr8SZ?s$~q-`~tjFaEIp3v*Bxxd&q8Sv{XqRIU(R#%&CgXNcS z-}z^4kdVs#dRL>AGfZfx;bgm>S57tq^uG>pQLQkXw|^ch0QrUKJ5MS zl!%o{)54Tg0tJopOvT6K01|KpkY9(b9nE}+EKV|{og*&medZ3<95_(U9c$-aIp>`T zs}&}h0>NJJC$2{Fa_hFczT{zKDl^@soUd~aUa7Jti~h{XJhy4gvd^c5^1^Kr#zKr+o5DzQ0N8+&89ZZGH^r6a#nW zdd9xmr~l5KP#ANKqtfiJX4l_+014d^Bq<^$Whdjp7w!p5|6)R&^Az4J1QEA{6K%j8lxy={UwJf=zi{~hX$=FF&8bb;jU&4hwI-st5Xk(?PIUv&4jS^aQ`(sG(~eAXz%$OekrZMj58 zQASx7$gOB7R)IDLqB5xTlAKQEo-jDFEFC@x<@hrMdNXA!nOI{+ik}ZAsuS)eOq`s8 zVbv1G0nOA9!tNb|w}4vAvYM%dq}HYUB==IQ6SqgWQAfv$OJRqq5u0Ce_3F9}B$U!H zqHgov{9*0eFVgI9fkRbWzOw9~K7$eEg!)&5ZK73GDH95kNPJReTK3+ARC;75y4~I^ zRah+JXhm8|l!rDF=_^6QF3UoujeP-WDFQ}t%PbWIL;4++fU1QPdTsow(j>gGs3)m% zQPQ~P59;VyQI+F#=EYH=F=C^c+QH9pW`*RqB>4PK`6f^hC0*Z|wk=H^3q~Ecv9AHT zmDBZE^MJ8YCqq(U8vI@--B5!R^?)|`(whu1W|7o#Dc0hIa8Xz)A>KtF&6XE^4OxL5 zuA@OCmE%PFFQ@bf*0sRQ>Uy6jm_F-i6-S$@PPQr*!~x; z5)%_W`+sqjRH4!=aDnbg6mXYU~$*ATsmLhASY<@icj;SeA z>fJ@ARKiq|n_TrQ+VPUbca-6oqiD2p=2DvSfG+JAvSlo9VtGfZqEI^V7yIA{EQLYM zh;e_{F-9WSMEPurs${D=&B{4r!vua*A6vRI+v{9Y#}xVPv=#Ms(U5 z;+-sp_R{N#y+a|Tgr2H}YOz|6mwNXx>DRwyKz|Nxc4v9k_Zhc$#9Gl}nYyp8e^(9F zI`LP6_Tk!5m(K4ek^tl}4N_IKm*1MW6}c-MMUa6!Y7RkDkenV0(vX%RPMx1y{3|@1 zEEQogqAc9qkftF)oPZUP4k;_5<{!TajwnK$%oW)yyywlAsv%B&D2gi3J(q$MD*`b< z8zFoR!Ql@h>%&SmHzCaxDx`=|adfxXdAX94(uwO-(J9AC&#(V}0DK{iq4VdeI95cc zY2#VRtSR1tw>n&OPTzIjyAKX1 zJyGcU>z|CACt=B~0wX;&!#m79ianGNNUQcSUF662=LV&s+gBaSUZBJ$oZ@Lh`Y15_77pxXbc&RdKxoP38xdj6X@H>cn>l?3RB!v ziqk3JNMDmzh6BhlCtrEhc?Wm~jZf+tBxCeC|Hn*^6J20lie zaFsJCUdudoaNCPfnJQfKUA^Ot-u?bv7YZEF)znN;no1v^r5A^nCnl2EMvrA!#f(n- zg2r&}+pl?KiZSnzr)1esZx z`Vf_1g0U@$GsEDNrqY%ycectsH$XAHfyFsTtn>EH1zJQQ3DsJZu_Zq0Xvj*6#WRb7m2BXz*$70j zg?t4M^~&^Vzl)xP##Mx12G!j17SiC|3O}Bn`93{kAQ6o#1gHPi(=NE?x~L3JY}fPH z*zV3>%*>y5nU5e%znp$u52{sKpj}`&x)_yNKE-p)vu88vV3l`EoEe!wiC3s#Ejyym z8V|U*v9J^J6T%m-`zxR7rsK^pC~}IcIKY%V)Z@$j-C2#j;UmEJ%n(@^^{^z;!GDbM z+=~UQq*Gv(lOzL!mUYawDWpR9G}?7$Ry6NspYDl5BO$E86n0km5$v5Kqtw(Snkka& z;@st}DxSKdCo339TtQaS6`3&9%Sn>FCWl2%r8_9C2v#ubSM5{%dZh0+`}B4P+b&Qr z2Fr#%nVerWwL*@kuXySV58oCC>~d(luz(Tq-5|8dYN*I@9g56uG@fd8)?^h@a7OPb z-x%owBD46Mb{Ps>r^d#VSXI}I`qsz~`eCW0QJJcdlh}m6BCq{5&2q-D&KwL}7VDg2 zY%L(8(W?W#K#pujG%iN0lx9R`P(5d5E1r4$Iqu1QvKB`7=uLj7yh7MeoK*9f<;}sM zakk2abrC}_4VW{nFClK^S^?9wH;VGQ##J?^tpVS>&+PXMXtYa^Y<&`i?KQu6ZVSTa z-2O({)BzZmMe93(^J329%9ouaiN$d*@*$t;Ia?~EhIl`G&$Mb>*KfXW|55E&TX0%B zpZEx*8X&uDefyB^@tRNkD~o+{QZs=If<2TCBmX_pVsNL75&<@)4;X|^knLpYB1KMeah^4 zd`L~6V8Z!v)@LUSJtsF8I7p%R;Ppbm6;|7ot)LaWsjUf$Dt|D8A#UZ1NpVxKO!p@O z(B*M|r+a2Vb@M(_#tYNR#RU*WP*v>S`TZj(+8Av1o||6YYG*eHBiaANC%E{wEM|B@ zy3i!{j~c1`Mxs6im?p4HK`ETt+%kyTzT@m0JL$Wpef>MT^dXo<<#lm;Gv&us!&9Cu zW4V%|6WOj$*Y8lrKbLN2KdM*};F7vK-7GH87e^6#!~E@5#`!HZ21{(9Ul*>y^F8yq zbKvG4PhsX9qkDqwsOYLsN#0dNEMF!Uy8XQLCSN zHYHcT*avtKB9nHes`l7yBjoKuZF_gyJy%2@c0-Y6Ffn0AcWgW5`0hd-NB8&ptG^9= zpBk8MD1PpMv-zyPSZ#ZR?*)fpKq3(&TlG0(m$R3X<~#szeqou34`y!kw~2`&EYEQk zPb^+I?pir5*{0|@Xwd~C;sIzPg$&s$w7k5zQKzaulUPq6noh68PcV^MZc$ojN)GY9 zUdG66$;g*VZ6xKtkUX&`@Y!8hgLJF(A2di`C~A}+&{K9u7QHlb4MtumPkvQWOzwa* z&U@9AJm+{`JlSc5z{SRwdvAADjl^>b^M)6&j4t7=9}_$#1j|ASAykK_;2Cn_z6VpG zzZbW2N)(Jp-{hSVp9$*gwKZ~plx_BhJ0%SDHp=&@$F6`*jg8wt>&lv{H?|sBIJVP} zn{|wm3M_4Jg8RnH8u5i^@U^~}z;;!Ga$zej^b`CN*f5Gl#9}k!BYV$8b_Vw3K`90u zr0vs_2O}b#l}&S&F3JAPHO)3uVCz5pAAZvjmce%M_A6XC>9o*{86q2zJ|a8HZip!I z5=X7h2D~2Y257%a?ebtj_j4xX^ zawemD<$WzFc@%KnvCz0rHVT`@cj8L;o)9ri0XO>j+g$Ra*#v6rFC8}dFXAdkkY-WT z^02Iw%Ip)ClE@vX(KNfN`U;~(+#{aFtts%^db<~RuX|BA*A!t$;m-$IV%gU-rcz>^ z%G{5!#6z|t@sw~MrRG=?*j{x-$Km_5jD4t}vG1B&y?gdTadqdr@=S}&IM%ifad$f_ z2dH-a;QBRbiV4Uwu4>4+4vOV2s-2ci?1V}M%~*fx>=~cXn)I4OrCLxmp{w5)HmJl@ zYHCUgOSg0rqMJGVE7$SOlXD&*9I~NtP1t9Ky|V{r@XY2;*u;lJ3NlUwxrB(; zyT?Yzf2b{Qmbjbu0x122a_Z(!<01v2F9KbD%HPL6=lp<&gkahJjez3#UkE4$R%W*U zBA}A|tg+27M`tCj+KHibn55kJudx?PRjxU~Q04<9H?3`$67^R~WClA|8fITQW^xX> zMjZ~`UgI8leo}^9kwzOHi!{2KWwrz~mYc2f12L?Dn)}mPBV@u0BJYa~?bA5SvzrMlr zM2BX_hH_-W%WIKYo{2W{dpq6)lysi?pTlm&cKAqkBM4l!a$3&5jA;@#OTxEkLPi$3 z5Ik^+gpL{&*6ECI$9BBTZ%<#g=>lA@cY4ZFT05?a$EOb9uXp?KZ(a8BDc^`egfc0< zcrEDp)h)E}1sc5W4?zN&Oo7-ERe|ijLtm7&P8Gg>igI+`6atB^IH_x0o-`$Rc4RLg zBMDviMK@x#_`dp|nN0{Z5=+y2-Uz`~_oHLxk`~Ae<>l5a2k^E;*FMEV6Gqs__sF_p z4IzPN7T6`uYv6=n>87zQB8P2UH5WcfL?lZ}FjMC@C9tEUgs+Lkc%Q~HU94j!;}fG7 zMJ-AKR=6yey{j8I6AkTCF^sLUb%EI8qo*sKB(y10re$q4?CD8NI%Rf)HX)N{Z0nJx zRChKiwrb&j+bUgHvzA+0(sneT8S;!V2Q0U|KH+})v=T_Z^kjnC4qIvopMNSorWnyMlL^Pn62KEwi(x%r&IM%&dB$2bqm~Gj8dcY+UB3Uh+0L_E+qv_83{9Yh zO$olrEdO(DE)ms(ty4K|lhwzB>js-7Fol`$%F>GS<%5(DGLgDYM6zci+p*-%$bsW# zMiA8hwx;ZGoH`c?)qUWtLVb!A5a)C+&W-UZgc7<9$mtp?WI;Jy6Str&31DB9TFUo+ zgaO}Ay@t+q6MuD2V2K^!l86nJ#<4;eq)J0N& zgL=Z&s8hrib|Iim2I|iGSIJlBL8-fsYCO4O3W=&jaoQ1Z9c;fJHzxA3ra*YG?SjH{3p&@Lz@_ED zU@6iwI?8kd8&~*x&$Id8LQDCBr{I53W{#NSW8&gwzLm%Fi=xg=C@4<7m1tQYb5dWB zO)bY-YIjmQ?Y)~OmZO`sdeNc=pKk{C;ZrLLuZR+tQlm z*4$11sfEgJlzZ2ao_6{s&&!UR0ogj;8zDU|FHWw|V_(>i!vQk2p1L4|umxOHaJTV_FZM)xHBW-HsmN#?MPKPK z2rcHxanReo981KbN1IJ3Cv9icZs#L~;I_gS_PUnW^Wv^3pLsJ^cbT7)7jO1W$-JqF zB$pbpObY55_qoH1&wRu6Ja(0@Au+XgURfzAzWXu{Q-t&Pzwcp;4F8KgjEUpFY+)?1 zJyL`G7-6^8(RvNO`iKgPTEUT6MMRnk1;X2v@&c#o@JjSD5o$`qw1N2`AOgu~HdmF~ zoo82kdpCtq`9FYeEO4bIwD4cL?)Z2R>~Q=Lo2$f=6ALHdNHH>F%Y)8aJii~bjnlcJ28+fd z5nzY!@K|5(Sv46FL24>FMO#cOM2F{;ECOXvSXvu0o(i!<{|2H{03f~*9Ieo zd5PgqK8*)dH(VJRJ<;>yziIcoW=H41cEUFgon8f+tY=i8rEV!Iu^MTq_RoM;w7pg5 zIN)@}BlDnMQ!7=#-MhfZyzxz$zvg!R!fUl=@A(nr}1@`5A&G*gb(J~%~lGV{h zc6YgKJMVrhsCJ_Sql=lNYjt3XnHSvh_$fZ*TK<~_X8g|u{{JszW@M)S*F%Ype7|f6 zJwo>@^~+l{0}TdG0vS}Iy}RWVF_vA4PJKkP3?=xFF2xZpw{ufhPR7(9nyktOG9Vv# zS;*))>?&YcTR5nK!GBnEoF5Z8np}xhLf*_R^-CoN@!`sk=sP7tno4=FwzeanfB^8(KqbrY$KG?Hb}-B46^$9p2%Np8L>!yJ>ofZ#7`9Fj9e_wFP!Thf=G&0sVFwi$PK8k{Z zgLQ#kb$xM(p=Sn&NJpRari?exd36H2gf|Jrr;6rN&hRZ~_(d>FFwxilg9MTg@kPL> z2_Vim1_)W|NC<`}D(cH&Bh?l^^wmgS=Szl4N@iA;dQ@DRLSj-Xenwg$XB*FXrob7!Y5IuG|KGw}apS1>M1;Z4np^x0!-TrrG#C` zA%F9XUVjSZW9q;2*`a^2LoI%v)|`dl-^vg5ckUe=Kd$@trqA|9S)sq4NN{uWPf?E! zD`w0NzJC`$0BG@p3;ml6V*Oua5F;ZK>%XRukE)lw@-k*$mdp(g5!l%Aiu%(IJCu@@ zfN%phvPTj@A$K68DTM?tAZU4&SisW@+WqBdDr0B7NtEFh^lvey{ z{NuyVm&ZFXs2utkROy+^6T%=PqI2(D`i$qItIK=`3~z?Ptl?+%KVFrls}!~XRbW~- z9ocKn+QWHhoj%ma0`VcaVgO`%@MMkNN-Ux4$J%fYdMl9Otma?KHh@I-b53;QJy96C zuTP0afh)8eA_DSn%IpoyI;fTKuss*|uX5#=c378rB+!`lfiFxd=i){qOH5XiqqXE^ z$F@}(6O?PuoE0l^D0ay(++2iU`Jp|lgEW&I=5`!g`=WHp>I2ld5^KBpWf&l9^I`{wYDH67BXuCJU^+?fgYg&2{KzaHcQQ^7;ghFs8{U)m5RcvEoqt1 zZ@}FVzkN|LQNG}+GyJI8+RAvSWjSWymhk}l>bzUiPHk2E_U=J7$UTkrLdP3XRWR3^ zstpq^!-^*X7KD_KEAwd6U)T3ZH7Pcm-7Z;n5S89GS#?jYEmuSiOau}9w<`%3VaRe_ zKW$0{cZKO^eEM(9Tyl4e$)f=1E-q3#GJ5==-R9xt{Lc}0F%If|m=OHw^J*#uJ{$fj>A5V|_ zAC=F%D(&S0wzC4z7RE?^uS9$ahjzSK6mceL+0@qscaw<%+7GfInxre4ZkXNuJ3Q}b z2fzYA3dCzn#4Ey{wvc43xvM;`{v&!o#j~kVkczx{7dH5N345`RK%sG^okjoNuXe-3 zi3J{$0R?yBIc95zjBbL!QDQ*=(w6yBvY1+fak&&Wd%T&f5opugKFaM`HKCRU)gVXA zp1hGNrN+lac2THDz%QCpEJrv`@UUKtK2PBIQ#aQd09;chj0B?6OTRL@g!WdCGZ71q zh-N`gNh+*Vs(UzTpI=;4Q%S#ggg*2a=G7$v1;cjRlZO`g(RaT7(PN%X1+JzN$3aeC zo+aar1&XP)VOsc(4#7Msu2iUmP4z4TzR`y(4!AJ$r2aKqM)7w=iI8TnVn<`+>`q=E z_Eqz5Sq3zF_=^&!A#Uh34t1{Ss_fdt#736K&>(OU&=wOQdJx;XwI8n`Pedgzk?*d9MU*&$$`@b zpx9JeUiw^ps1tIRWfJ)WKmN!W5$8$hzw9o}h271r@O{t|ewz%T;R^f97GM48SKQ;) znz^WVkg~5s0tf8y0G1qc*eLwY2`|FH(*`MpBFoC2It;ODKd5$p;|{TT z@pem%6c`Bk>xtJ6gxk;;g2C3V+;nE*6ZcIOo2H8mZLxEWI12{n0m~)q=FELU+x__p z24&^q-7VKJ5l|M5BFE2z&%DJEd)gAYFLB0q6q7yU|f= zWmT$7cgI?&YiH{R-=Y(fcRSZrZu;gYVdO&98_%z4hbIGOz~HhpRCShrnsnb+5mz6}HMrLeB*F!%Td=~Z#^q-8p0c=XIPt~)qnf3%tzK;{pHN^! z%j&i^1;%eTKOJ05WC{z}cB2|PDJv*Uyu%JDj2dH2Yxsn~_#8@r{(`pWyd z#Sz=_`s*|!_WDSNZ&f?5uJ&cM-v{V06b$g+4@36rxW3 zY1lxN703=GsFX;j9!NJ54rGULidUOJP-g)u{#)M?Z9b7QMn2qD?-oT)y* za+crSkm(kTKIWiv}6htqt&j|yA0SgS#gvCw|64camMmvj! ztj84$gW9jSq0?dy2N#r$+-s|5TSa7aK$J+@EY3`Vp8VDFw(KY1 zD!D2ngz2}5b4x6a$wS$`1RATM=TQ9KO<6=iUggml+mowAtQ;6b*cSTFdtFaAb7-s2u{S z|8&Zw9xDZ$3b(`@iEy|_IGJsJjlw(N5X zV&c5Eo6MtL8H^ur>(uZR%ojh+?uMt#o8#6&6$VZ7-puoqvRLjZjAA+{P7O{fG``fg zas=w{TYX)@pVXsY1BQMOhfcZZyL0vYzL#Z{{`$7+_8OUUF@dPs!JNYhnP_1$(ryq? z$$A2@s<*Sr9|T+SGs}dBC7yxJ-v}&S%$Phv`0MDO+4drsF zV8@Qw(qnZ_&dVP`uu(&?!I5hO6zW!$iF0Wn8`4`)GhJ&|N-I`R+H<%JQFKCwHIZd+*YklfPMcZ)u^dRS^W*e(~o zR1M$wx-<`}xvk^>Je2q`V#<_7b3VhN+-gf!(~^$3@v`ppUQ%z2L;=wk7z`po)kYL* zNOg`|(K$mr*zK4Hx%_uPF){t8V*7sqrLJgVN~dUN_Yau@@(Q3YI6SWY!2k#fa`t4+>4x?>Sk#9RSE36#$cK z4?H*1;@CZw7VmxcL4 ld;`uBg@XO>QF3xNaCCNeG%@|BDV3d#35t|dL{1dy{{b6aBO?F+ literal 0 HcmV?d00001 diff --git a/lecture_09/mass_springs.svg b/lecture_09/mass_springs.svg new file mode 100644 index 0000000..2bec8a4 --- /dev/null +++ b/lecture_09/mass_springs.svg @@ -0,0 +1,214 @@ + + + + + + + + + + image/svg+xml + + + + + + + + + + + + + + m1 + m2 + m3 + + + m4 + + + + + + + + + From 9b28df097f8b74a2aa329ba32e86ceef4a90840f Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Mon, 20 Feb 2017 17:22:36 -0500 Subject: [PATCH 02/16] add lecture 10 --- lecture_09/octave-workspace | Bin 0 -> 1994 bytes .../lecture_10-checkpoint.ipynb | 6 + lecture_10/GaussNaive.m | 25 + lecture_10/GaussPivot.m | 33 + lecture_10/Tridiag.m | 22 + lecture_10/lecture_10.aux | 40 + lecture_10/lecture_10.bbl | 0 lecture_10/lecture_10.blg | 48 + lecture_10/lecture_10.ipynb | 1462 +++++++++++++++++ lecture_10/lecture_10.log | 872 ++++++++++ lecture_10/lecture_10.md | 593 +++++++ lecture_10/lecture_10.out | 8 + lecture_10/lecture_10.pdf | Bin 0 -> 162693 bytes lecture_10/lecture_10.tex | 852 ++++++++++ .../lecture_10_files/lecture_10_27_0.pdf | Bin 0 -> 11168 bytes .../lecture_10_files/lecture_10_27_0.svg | 129 ++ .../lecture_10_files/lecture_10_28_0.svg | 123 ++ .../lecture_10_files/lecture_10_3_0.pdf | Bin 0 -> 5402 bytes .../lecture_10_files/lecture_10_3_0.svg | 140 ++ .../lecture_10_files/lecture_10_5_0.svg | 377 +++++ .../lecture_10_files/lecture_10_5_1.pdf | Bin 0 -> 7156 bytes .../lecture_10_files/lecture_10_5_1.svg | 322 ++++ lecture_10/nohup.out | 0 lecture_10/octave-workspace | Bin 0 -> 86061 bytes 24 files changed, 5052 insertions(+) create mode 100644 lecture_09/octave-workspace create mode 100644 lecture_10/.ipynb_checkpoints/lecture_10-checkpoint.ipynb create mode 100644 lecture_10/GaussNaive.m create mode 100644 lecture_10/GaussPivot.m create mode 100644 lecture_10/Tridiag.m create mode 100644 lecture_10/lecture_10.aux create mode 100644 lecture_10/lecture_10.bbl create mode 100644 lecture_10/lecture_10.blg create mode 100644 lecture_10/lecture_10.ipynb create mode 100644 lecture_10/lecture_10.log create mode 100644 lecture_10/lecture_10.md create mode 100644 lecture_10/lecture_10.out create mode 100644 lecture_10/lecture_10.pdf create mode 100644 lecture_10/lecture_10.tex create mode 100644 lecture_10/lecture_10_files/lecture_10_27_0.pdf create mode 100644 lecture_10/lecture_10_files/lecture_10_27_0.svg create mode 100644 lecture_10/lecture_10_files/lecture_10_28_0.svg create mode 100644 lecture_10/lecture_10_files/lecture_10_3_0.pdf create mode 100644 lecture_10/lecture_10_files/lecture_10_3_0.svg create mode 100644 lecture_10/lecture_10_files/lecture_10_5_0.svg create mode 100644 lecture_10/lecture_10_files/lecture_10_5_1.pdf create mode 100644 lecture_10/lecture_10_files/lecture_10_5_1.svg create mode 100644 lecture_10/nohup.out create mode 100644 lecture_10/octave-workspace diff --git a/lecture_09/octave-workspace b/lecture_09/octave-workspace new file mode 100644 index 0000000000000000000000000000000000000000..f7e8b2b8e46c933bf0ef57c3288b56dd54fd694b GIT binary patch literal 1994 zcmb_deN0nV6n{km=mJz{2nzz0)v>Wv#)qLY@VvI*z=}+C##9;Uz)FV{#z#T6xu6gO zlYzjPOb0T8n>IrVbA?f{g9!{|Fl9g;Co+SB_Wxdewc8!V zeg}KCoz|J04%kk;-V$c`ybOegS*o*6W6=D?nX7rxDiAGhuXSwELV609=e2GUPHrj} zUGDAx_;i*omEHrTn~%GDvjLowoD1LLPlK2$Elbe!fkdaflDkC>BZ6F3iT?zY$|Kly zqYvTyhG3~3LkW=|-^uX+k%-SfsvZSKP^&H1^0aX&~XK6-_y89FJP2H{v244<31 zzR+F-(L1?ma}&__ zo^HbT0$K(RAw3IcAcZ*{(U90Z!t)v5r6oV=UCjlS6F9_XRE$TA&rbd-j6zAp~$Yp5|rvf#>Df^2LjzAo1{f zIVSc7WM0wcNQTBiEbdQfq}D@K7BlGa;!W7RmC3H8O~W)ZTG?>N0Igv%^`3gBVY>Utfo*KlhdML z15rE(;Se^2usaFMCT!#i|8Ben!Vv6PQEeEz#SSxo2R-|RK05@9SlJS+t)k)?a&h?S z8Iu2iu2`Lm^#9*+bQEh!d{O#pIbsKhcM`HwkQGi=CRtHrC6Edxl}9QDBRaagLwY>_ z7(dP4Ghes2x#~r{Z3+|OlFb3mCX*oKA59VQkI~Fc{=eRdMBE?bO0$-Er98VG)K zG#$m{mh5K*o&g;8w*n*P)d5yu2QwUK1*YO~n#JDBw-%POg+vh)=RnBYguH!dW(te^ ztW%g75R!^isab{DIJ$}ou|(`$iL)4@+vR>%>yKXS -- 0 +< -- 0 ++ -- 0 +- -- 0 +* -- 0 +:= -- 0 +add.period$ -- 0 +call.type$ -- 0 +change.case$ -- 0 +chr.to.int$ -- 0 +cite$ -- 0 +duplicate$ -- 0 +empty$ -- 0 +format.name$ -- 0 +if$ -- 0 +int.to.chr$ -- 0 +int.to.str$ -- 0 +missing$ -- 0 +newline$ -- 0 +num.names$ -- 0 +pop$ -- 0 +preamble$ -- 0 +purify$ -- 0 +quote$ -- 0 +skip$ -- 0 +stack$ -- 0 +substring$ -- 0 +swap$ -- 0 +text.length$ -- 0 +text.prefix$ -- 0 +top$ -- 0 +type$ -- 0 +warning$ -- 0 +while$ -- 0 +width$ -- 0 +write$ -- 0 +(There were 3 error messages) diff --git a/lecture_10/lecture_10.ipynb b/lecture_10/lecture_10.ipynb new file mode 100644 index 0000000..78e529d --- /dev/null +++ b/lecture_10/lecture_10.ipynb @@ -0,0 +1,1462 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%plot --format svg" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "setdefaults" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Gauss Elimination\n", + "### Solving sets of equations with matrix operations\n", + "\n", + "The number of dimensions of a matrix indicate the degrees of freedom of the system you are solving. \n", + "\n", + "If you have a set of known output, $y_{1},~y_{2},~...y_{N}$ and a set of equations that\n", + "relate unknown inputs, $x_{1},~x_{2},~...x_{N}$, then these can be written in a vector\n", + "matrix format as:\n", + "\n", + "$y=Ax$\n", + "\n", + "Consider a problem with 2 DOF:\n", + "\n", + "$x_{1}+3x_{2}=1$\n", + "\n", + "$2x_{1}+x_{2}=1$\n", + "\n", + "$\\left[ \\begin{array}{cc}\n", + "1 & 3 \\\\\n", + "2 & 1 \\end{array} \\right]\n", + "\\left[\\begin{array}{c} \n", + "x_{1} \\\\ \n", + "x_{2} \\end{array}\\right]=\n", + "\\left[\\begin{array}{c} \n", + "1 \\\\\n", + "1\\end{array}\\right]$\n", + "\n", + "The solution for $x_{1}$ and $x_{2}$ is the intersection of two lines:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "Gnuplot\n", + "Produced by GNUPLOT 5.0 patchlevel 3 \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\t\n", + "\t\t-4\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t-2\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t2\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t4\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t6\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t-6\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t-4\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t-2\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t2\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t4\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t6\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t8\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\n", + "\tgnuplot_plot_1a\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\tgnuplot_plot_2a\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x21=[-2:2];\n", + "x11=1-3*x21;\n", + "x21=[-2:2];\n", + "x22=1-2*x21;\n", + "plot(x11,x21,x21,x22)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For a $3\\times3$ matrix, the solution is the intersection of the 3 planes.\n", + "\n", + "$10x_{1}+2x_{2}+x_{3}=1$\n", + "\n", + "$2x_{1}+x_{2}+x_{3}=1$\n", + "\n", + "$x_{1}+2x_{2}+10x_{3}=1$\n", + "\n", + "$\\left[ \\begin{array}{cc}\n", + "10 & 2 & 1\\\\\n", + "2 & 1 & 1 \\\\\n", + "1 & 2 & 10\\end{array} \\right]\n", + "\\left[\\begin{array}{c} \n", + "x_{1} \\\\ \n", + "x_{2} \\\\\n", + "x_{3} \\end{array}\\right]=\n", + "\\left[\\begin{array}{c} \n", + "1 \\\\\n", + "1 \\\\\n", + "1\\end{array}\\right]$" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "error: 'X22' undefined near line 1 column 16\n", + "error: 'X13' undefined near line 1 column 14\n", + "error: evaluating argument list element number 3\n" + ] + }, + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "Gnuplot\n", + "Produced by GNUPLOT 5.0 patchlevel 3 \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t-2\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t-1.5\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t-1\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t-0.5\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t0\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t0.5\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t1\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t1.5\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t2\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t-2\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t-1.5\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t-1\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t-0.5\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t0\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t0.5\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t1\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t1.5\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t2\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\t\n", + "\t\t-6\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t-4\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t-2\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t0\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t2\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t4\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t6\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\t\n", + "\t\t8\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\tgnuplot_plot_1a\n", + "\n", + "\n", + "\n", + "\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n", + "\t\n", + "\tgnuplot_plot_2a\n", + "\n", + "\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n", + "\t\n", + "\tgnuplot_plot_3a\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x11=linspace(-2,2,5);\n", + "x12=linspace(-2,2,5);\n", + "[X11,X12]=meshgrid(x11,x12);\n", + "X13=1-10*X11-2*X22;\n", + "\n", + "x21=linspace(-2,2,5);\n", + "x22=linspace(-2,2,5);\n", + "[X21,X22]=meshgrid(x21,x22);\n", + "X23=1-2*X11-X22;\n", + "\n", + "x31=linspace(-2,2,5);\n", + "x32=linspace(-2,2,5);\n", + "[X31,X32]=meshgrid(x31,x32);\n", + "X33=1/10*(1-X31-2*X32);\n", + "\n", + "mesh(X11,X12,X13);\n", + "hold on;\n", + "mesh(X21,X22,X23)\n", + "mesh(X31,X32,X33)\n", + "x=[10,2, 1;2,1, 1; 1, 2, 10]\\[1;1;1];\n", + "plot3(x(1),x(2),x(3),'o')\n", + "view(45,45)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "After 3 DOF problems, the solutions are described as *hyperplane* intersections. Which are even harder to visualize" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Gauss elimination\n", + "### Solving sets of equations systematically\n", + "\n", + "$\\left[ \\begin{array}{ccc|c}\n", + " & A & & y \\\\\n", + "10 & 2 & 1 & 1\\\\\n", + "2 & 1 & 1 & 1 \\\\\n", + "1 & 2 & 10 & 1\\end{array} \n", + "\\right] $\n", + "\n", + "Ay(2,:)-Ay(1,:)/5 = ([2 1 1 1]-1/5[10 2 1 1])\n", + "\n", + "$\\left[ \\begin{array}{ccc|c}\n", + " & A & & y \\\\\n", + "10 & 2 & 1 & 1\\\\\n", + "0 & 3/5 & 4/5 & 4/5 \\\\\n", + "1 & 2 & 10 & 1\\end{array} \n", + "\\right] $\n", + "\n", + "Ay(3,:)-Ay(1,:)/10 = ([1 2 10 1]-1/10[10 2 1 1])\n", + "\n", + "$\\left[ \\begin{array}{ccc|c}\n", + " & A & & y \\\\\n", + "10 & 2 & 1 & 1\\\\\n", + "0 & 3/5 & 4/5 & 4/5 \\\\\n", + "0 & 1.8 & 9.9 & 0.9\\end{array} \n", + "\\right] $\n", + "\n", + "Ay(3,:)-1.8\\*5/3\\*Ay(2,:) = ([0 1.8 9.9 0.9]-3\\*[0 3/5 4/5 4/5])\n", + "\n", + "$\\left[ \\begin{array}{ccc|c}\n", + " & A & & y \\\\\n", + "10 & 2 & 1 & 1\\\\\n", + "0 & 3/5 & 4/5 & 4/5 \\\\\n", + "0 & 0 & 7.5 & -1.5\\end{array} \n", + "\\right] $\n", + "\n", + "now, $7.5x_{3}=-1.5$ so $x_{3}=-\\frac{1}{5}$\n", + "\n", + "then, $3/5x_{2}+4/5(-1/5)=1$ so $x_{2}=\\frac{8}{5}$\n", + "\n", + "finally, $10x_{1}+2(8/5)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Consider the problem again from the intro to Linear Algebra, 4 masses are connected in series to 4 springs with K=10 N/m. What are the final positions of the masses? \n", + "\n", + "![Springs-masses](../lecture_09/mass_springs.svg)\n", + "\n", + "The masses haves the following amounts, 1, 2, 3, and 4 kg for masses 1-4. Using a FBD for each mass:\n", + "\n", + "$m_{1}g+k(x_{2}-x_{1})-kx_{1}=0$\n", + "\n", + "$m_{2}g+k(x_{3}-x_{2})-k(x_{2}-x_{1})=0$\n", + "\n", + "$m_{3}g+k(x_{4}-x_{3})-k(x_{3}-x_{2})=0$\n", + "\n", + "$m_{4}g-k(x_{4}-x_{3})=0$\n", + "\n", + "in matrix form:\n", + "\n", + "$\\left[ \\begin{array}{cccc}\n", + "2k & -k & 0 & 0 \\\\\n", + "-k & 2k & -k & 0 \\\\\n", + "0 & -k & 2k & -k \\\\\n", + "0 & 0 & -k & k \\end{array} \\right]\n", + "\\left[ \\begin{array}{c}\n", + "x_{1} \\\\\n", + "x_{2} \\\\\n", + "x_{3} \\\\\n", + "x_{4} \\end{array} \\right]=\n", + "\\left[ \\begin{array}{c}\n", + "m_{1}g \\\\\n", + "m_{2}g \\\\\n", + "m_{3}g \\\\\n", + "m_{4}g \\end{array} \\right]$" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "K =\n", + "\n", + " 20 -10 0 0\n", + " -10 20 -10 0\n", + " 0 -10 20 -10\n", + " 0 0 -10 10\n", + "\n", + "y =\n", + "\n", + " 9.8100\n", + " 19.6200\n", + " 29.4300\n", + " 39.2400\n", + "\n" + ] + } + ], + "source": [ + "k=10; % N/m\n", + "m1=1; % kg\n", + "m2=2;\n", + "m3=3;\n", + "m4=4;\n", + "g=9.81; % m/s^2\n", + "K=[2*k -k 0 0; -k 2*k -k 0; 0 -k 2*k -k; 0 0 -k k]\n", + "y=[m1*g;m2*g;m3*g;m4*g]" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "K1 =\n", + "\n", + " 20.00000 -10.00000 0.00000 0.00000 9.81000\n", + " 0.00000 15.00000 -10.00000 0.00000 24.52500\n", + " 0.00000 -10.00000 20.00000 -10.00000 29.43000\n", + " 0.00000 0.00000 -10.00000 10.00000 39.24000\n", + "\n" + ] + } + ], + "source": [ + "K1=[K y];\n", + "K1(2,:)=K1(1,:)/2+K1(2,:)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "K2 =\n", + "\n", + " 20.00000 -10.00000 0.00000 0.00000 9.81000\n", + " 0.00000 15.00000 -10.00000 0.00000 24.52500\n", + " 0.00000 0.00000 13.33333 -10.00000 45.78000\n", + " 0.00000 0.00000 -10.00000 10.00000 39.24000\n", + "\n" + ] + } + ], + "source": [ + "K2=K1;\n", + "K2(3,:)=K1(2,:)*2/3+K1(3,:)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "K2 =\n", + "\n", + " 20.00000 -10.00000 0.00000 0.00000 9.81000\n", + " 0.00000 15.00000 -10.00000 0.00000 24.52500\n", + " 0.00000 0.00000 13.33333 -10.00000 45.78000\n", + " 0.00000 0.00000 0.00000 2.50000 73.57500\n", + "\n" + ] + } + ], + "source": [ + "K2(4,:)=-K2(3,:)*K2(4,3)/K2(3,3)+K2(4,:)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x4 = 29.430\n", + "x3 = 25.506\n", + "x2 = 18.639\n", + "x1 = 9.8100\n" + ] + } + ], + "source": [ + "yp=K2(:,5);\n", + "x4=yp(4)/K2(4,4)\n", + "x3=(yp(3)+10*x4)/K2(3,3)\n", + "x2=(yp(2)+10*x3)/K2(2,2)\n", + "x1=(yp(1)+10*x2)/K2(1,1)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 9.8100\n", + " 18.6390\n", + " 25.5060\n", + " 29.4300\n", + "\n" + ] + } + ], + "source": [ + "K\\y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Automate Gauss Elimination\n", + "\n", + "We can automate Gauss elimination with a function whose input is A and y:\n", + "\n", + "`x=GaussNaive(A,y)`" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x =\n", + "\n", + " 9.8100\n", + " 18.6390\n", + " 25.5060\n", + " 29.4300\n", + "\n" + ] + } + ], + "source": [ + "x=GaussNaive(K,y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Problem (Diagonal element is zero)\n", + "\n", + "If a diagonal element is 0 or very small either:\n", + "\n", + "1. no solution found\n", + "2. errors are introduced \n", + "\n", + "Therefore, we would want to pivot before applying Gauss elimination\n", + "\n", + "Consider:\n", + "\n", + "(a) $\\left[ \\begin{array}{cccc}\n", + "0 & 2 & 3 \\\\\n", + "4 & 6 & 7 \\\\\n", + "2 & -3 & 6 \\end{array} \\right]\n", + "\\left[ \\begin{array}{c}\n", + "x_{1} \\\\\n", + "x_{2} \\\\\n", + "x_{3} \\end{array} \\right]=\n", + "\\left[ \\begin{array}{c}\n", + "8 \\\\\n", + "-3 \\\\\n", + "5\\end{array} \\right]$\n", + "\n", + "(b) $\\left[ \\begin{array}{cccc}\n", + "0.0003 & 3.0000 \\\\\n", + "1.0000 & 1.0000 \\end{array} \\right]\n", + "\\left[ \\begin{array}{c}\n", + "x_{1} \\\\\n", + "x_{2} \\end{array} \\right]=\n", + "\\left[ \\begin{array}{c}\n", + "2.0001 \\\\\n", + "1.0000 \\end{array} \\right]$" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "warning: division by zero\n", + "warning: called from\n", + " GaussNaive at line 16 column 12\n", + "warning: division by zero\n", + "warning: division by zero\n", + "ans =\n", + "\n", + " NaN\n", + " NaN\n", + " NaN\n", + "\n", + "ans =\n", + "\n", + " -5.423913\n", + " 0.021739\n", + " 2.652174\n", + "\n" + ] + } + ], + "source": [ + "format short\n", + "Aa=[0,2,3;4,6,7;2,-3,6]; ya=[8;-3;5];\n", + "GaussNaive(Aa,ya)\n", + "Aa\\ya" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x =\n", + "\n", + " -5.423913\n", + " 0.021739\n", + " 2.652174\n", + "\n", + "Aug =\n", + "\n", + " 4.00000 6.00000 7.00000 -3.00000\n", + " 0.00000 -6.00000 2.50000 6.50000\n", + " 0.00000 0.00000 3.83333 10.16667\n", + "\n", + "npivots = 2\n" + ] + } + ], + "source": [ + "[x,Aug,npivots]=GaussPivot(Aa,ya)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 0.325665420556713\n", + " 0.666666666666667\n", + "\n", + "ans =\n", + "\n", + " 0.333333333333333\n", + " 0.666666666666667\n", + "\n" + ] + } + ], + "source": [ + "format long\n", + "Ab=[0.3E-13,3.0000;1.0000,1.0000];yb=[2+0.1e-13;1.0000];\n", + "GaussNaive(Ab,yb)\n", + "Ab\\yb" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x =\n", + "\n", + " 0.333333333333333\n", + " 0.666666666666667\n", + "\n", + "Aug =\n", + "\n", + " 1.000000000000000 1.000000000000000 1.000000000000000\n", + " 0.000000000000000 2.999999999999970 1.999999999999980\n", + "\n", + "npivots = 1\n", + "ans =\n", + "\n", + " 0.333333333333333\n", + " 0.666666666666667\n", + "\n" + ] + } + ], + "source": [ + "[x,Aug,npivots]=GaussPivot(Ab,yb)\n", + "Ab\\yb\n", + "format short" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Spring-Mass System again\n", + "Now, 4 masses are connected in series to 4 springs with $K_{1}$=10 N/m, $K_{2}$=5 N/m, \n", + "$K_{3}$=2 N/m \n", + "and $K_{4}$=1 N/m. What are the final positions of the masses? \n", + "\n", + "![Springs-masses](../lecture_09/mass_springs.svg)\n", + "\n", + "The masses have the following amounts, 1, 2, 3, and 4 kg for masses 1-4. Using a FBD for each mass:\n", + "\n", + "$m_{1}g+k_{2}(x_{2}-x_{1})-k_{1}x_{1}=0$\n", + "\n", + "$m_{2}g+k_{3}(x_{3}-x_{2})-k_{2}(x_{2}-x_{1})=0$\n", + "\n", + "$m_{3}g+k_{4}(x_{4}-x_{3})-k_{3}(x_{3}-x_{2})=0$\n", + "\n", + "$m_{4}g-k_{4}(x_{4}-x_{3})=0$\n", + "\n", + "in matrix form:\n", + "\n", + "$\\left[ \\begin{array}{cccc}\n", + "k_1+k_2 & -k_2 & 0 & 0 \\\\\n", + "-k_2 & k_2+k_3 & -k_3 & 0 \\\\\n", + "0 & -k_3 & k_3+k_4 & -k_4 \\\\\n", + "0 & 0 & -k_4 & k_4 \\end{array} \\right]\n", + "\\left[ \\begin{array}{c}\n", + "x_{1} \\\\\n", + "x_{2} \\\\\n", + "x_{3} \\\\\n", + "x_{4} \\end{array} \\right]=\n", + "\\left[ \\begin{array}{c}\n", + "m_{1}g \\\\\n", + "m_{2}g \\\\\n", + "m_{3}g \\\\\n", + "m_{4}g \\end{array} \\right]$" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "K =\n", + "\n", + " 15 -5 0 0\n", + " -5 7 -2 0\n", + " 0 -2 3 -1\n", + " 0 0 -1 1\n", + "\n", + "y =\n", + "\n", + " 9.8100\n", + " 19.6200\n", + " 29.4300\n", + " 39.2400\n", + "\n" + ] + } + ], + "source": [ + "k1=10; k2=5;k3=2;k4=1; % N/m\n", + "m1=1; % kg\n", + "m2=2;\n", + "m3=3;\n", + "m4=4;\n", + "g=9.81; % m/s^2\n", + "K=[k1+k2 -k2 0 0; -k2, k2+k3, -k3 0; 0 -k3, k3+k4, -k4; 0 0 -k4 k4]\n", + "y=[m1*g;m2*g;m3*g;m4*g]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Tridiagonal matrix\n", + "\n", + "This matrix, K, could be rewritten as 3 vectors e, f and g\n", + "\n", + "$e=\\left[ \\begin{array}{c}\n", + "0 \\\\\n", + "-5 \\\\\n", + "-2 \\\\\n", + "-1 \\end{array} \\right]$\n", + "\n", + "$f=\\left[ \\begin{array}{c}\n", + "15 \\\\\n", + "7 \\\\\n", + "3 \\\\\n", + "1 \\end{array} \\right]$\n", + "\n", + "$g=\\left[ \\begin{array}{c}\n", + "-5 \\\\\n", + "-2 \\\\\n", + "-1 \\\\\n", + "0 \\end{array} \\right]$\n", + "\n", + "Where all other components are 0 and the length of the vectors are n and the first component of e and the last component of g are zero\n", + "\n", + "`e(1)=0` \n", + "\n", + "`g(end)=0`\n", + "\n", + "No need to pivot and number of calculations reduced enormously.\n", + "\n", + "|method |Number of Floating point operations for n$\\times$n-matrix|\n", + "|----------------|---------|\n", + "| Naive Gauss | n-cubed |\n", + "| Tridiagonal | n |" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 9.8100 27.4680 61.8030 101.0430\n", + "\n" + ] + } + ], + "source": [ + "e=[0;-5;-2;-1];\n", + "g=[-5;-2;-1;0];\n", + "f=[15;7;3;1];\n", + "Tridiag(e,f,g,y)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "% tic ... t=toc \n", + "% is Matlab timer used for debugging programs\n", + "t_GE = zeros(1,100);\n", + "t_GE_tridiag = zeros(1,100);\n", + "t_TD = zeros(1,100);\n", + "%for n = 1:200\n", + "for n=1:100\n", + " A = rand(n,n);\n", + " e = rand(n,1); e(1)=0;\n", + " f = rand(n,1);\n", + " g = rand(n,1); g(end)=0;\n", + " Atd=diag(f, 0) - diag(e(2:n), -1) - diag(g(1:n-1), 1);\n", + " b = rand(n,1);\n", + " tic;\n", + " x = GaussPivot(A,b);\n", + " t_GE(n) = toc;\n", + " tic;\n", + " x = GaussPivot(Atd,b);\n", + " t_GE_tridiag(n) = toc;\n", + " tic;\n", + " x = Tridiag(e,f,g,b);\n", + " t_TD(n) = toc;\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "Gnuplot\n", + "Produced by GNUPLOT 5.0 patchlevel 3 \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\t\n", + "\t\t10-4\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t10-3\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t10-2\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t10-1\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t100\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t100\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t101\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t102\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t103\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\t\ttime (s)\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\tnumber of elements\n", + "\t\n", + "\n", + "\n", + "\n", + "\tgnuplot_plot_1a\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\tgnuplot_plot_2a\n", + "\n", + "\t\n", + "\t\n", + "\tgnuplot_plot_3a\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n=1:200;\n", + "loglog(n,t_GE,n,t_TD,n,t_GE_tridiag)\n", + "xlabel('number of elements')\n", + "ylabel('time (s)')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Octave", + "language": "octave", + "name": "octave" + }, + "language_info": { + "file_extension": ".m", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "octave", + "version": "0.19.14" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/lecture_10/lecture_10.log b/lecture_10/lecture_10.log new file mode 100644 index 0000000..088d911 --- /dev/null +++ b/lecture_10/lecture_10.log @@ -0,0 +1,872 @@ +This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian) (preloaded format=pdflatex 2017.1.11) 20 FEB 2017 17:21 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**lecture_10.tex +(./lecture_10.tex +LaTeX2e <2016/02/01> +Babel <3.9q> and hyphenation patterns for 81 language(s) loaded. +(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls +Document Class: article 2014/09/29 v1.4h Standard LaTeX document class +(/usr/share/texlive/texmf-dist/tex/latex/base/size11.clo +File: size11.clo 2014/09/29 v1.4h Standard LaTeX file (size option) +) +\c@part=\count79 +\c@section=\count80 +\c@subsection=\count81 +\c@subsubsection=\count82 +\c@paragraph=\count83 +\c@subparagraph=\count84 +\c@figure=\count85 +\c@table=\count86 +\abovecaptionskip=\skip41 +\belowcaptionskip=\skip42 +\bibindent=\dimen102 +) +(/usr/share/texlive/texmf-dist/tex/latex/base/fontenc.sty +Package: fontenc 2005/09/27 v1.99g Standard LaTeX package + +(/usr/share/texlive/texmf-dist/tex/latex/base/t1enc.def +File: t1enc.def 2005/09/27 v1.99g Standard LaTeX file +LaTeX Font Info: Redeclaring font encoding T1 on input line 48. +)) +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/mathpazo.sty +Package: mathpazo 2005/04/12 PSNFSS-v9.2a Palatino w/ Pazo Math (D.Puga, WaS) +\symupright=\mathgroup4 +) +(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty +Package: graphicx 2014/10/28 v1.0g Enhanced LaTeX Graphics (DPC,SPQR) + +(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty +Package: keyval 2014/10/28 v1.15 key=value parser (DPC) +\KV@toks@=\toks14 +) +(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty +Package: graphics 2016/01/03 v1.0q Standard LaTeX Graphics (DPC,SPQR) + +(/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty +Package: trig 2016/01/03 v1.10 sin cos tan (DPC) +) +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/graphics.cfg +File: graphics.cfg 2010/04/23 v1.9 graphics configuration of TeX Live +) +Package graphics Info: Driver file: pdftex.def on input line 95. + +(/usr/share/texlive/texmf-dist/tex/latex/pdftex-def/pdftex.def +File: pdftex.def 2011/05/27 v0.06d Graphics/color for pdfTeX + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/infwarerr.sty +Package: infwarerr 2010/04/08 v1.3 Providing info/warning/error messages (HO) +) +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ltxcmds.sty +Package: ltxcmds 2011/11/09 v1.22 LaTeX kernel commands for general use (HO) +) +\Gread@gobject=\count87 +)) +\Gin@req@height=\dimen103 +\Gin@req@width=\dimen104 +) +(/usr/share/texlive/texmf-dist/tex/latex/caption/caption.sty +Package: caption 2016/02/21 v3.3-144 Customizing captions (AR) + +(/usr/share/texlive/texmf-dist/tex/latex/caption/caption3.sty +Package: caption3 2016/02/04 v1.7-139 caption3 kernel (AR) +Package caption3 Info: TeX engine: e-TeX on input line 67. +\captionmargin=\dimen105 +\captionmargin@=\dimen106 +\captionwidth=\dimen107 +\caption@tempdima=\dimen108 +\caption@indent=\dimen109 +\caption@parindent=\dimen110 +\caption@hangindent=\dimen111 +) +\c@ContinuedFloat=\count88 +) +(/usr/share/texlive/texmf-dist/tex/latex/adjustbox/adjustbox.sty +Package: adjustbox 2012/05/21 v1.0 Adjusting TeX boxes (trim, clip, ...) + +(/usr/share/texlive/texmf-dist/tex/latex/xkeyval/xkeyval.sty +Package: xkeyval 2014/12/03 v2.7a package option processing (HA) + +(/usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkeyval.tex +(/usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkvutils.tex +\XKV@toks=\toks15 +\XKV@tempa@toks=\toks16 +) +\XKV@depth=\count89 +File: xkeyval.tex 2014/12/03 v2.7a key=value parser (HA) +)) +(/usr/share/texlive/texmf-dist/tex/latex/adjustbox/adjcalc.sty +Package: adjcalc 2012/05/16 v1.1 Provides advanced setlength with multiple back +-ends (calc, etex, pgfmath) +) +(/usr/share/texlive/texmf-dist/tex/latex/adjustbox/trimclip.sty +Package: trimclip 2012/05/16 v1.0 Trim and clip general TeX material + +(/usr/share/texlive/texmf-dist/tex/latex/collectbox/collectbox.sty +Package: collectbox 2012/05/17 v0.4b Collect macro arguments as boxes +\collectedbox=\box26 +) +\tc@llx=\dimen112 +\tc@lly=\dimen113 +\tc@urx=\dimen114 +\tc@ury=\dimen115 +Package trimclip Info: Using driver 'tc-pdftex.def'. + +(/usr/share/texlive/texmf-dist/tex/latex/adjustbox/tc-pdftex.def +File: tc-pdftex.def 2012/05/13 v1.0 Clipping driver for pdftex +)) +\adjbox@Width=\dimen116 +\adjbox@Height=\dimen117 +\adjbox@Depth=\dimen118 +\adjbox@Totalheight=\dimen119 + +(/usr/share/texlive/texmf-dist/tex/latex/ifoddpage/ifoddpage.sty +Package: ifoddpage 2011/09/13 v1.0 Conditionals for odd/even page detection +\c@checkoddpage=\count90 +) +(/usr/share/texlive/texmf-dist/tex/latex/varwidth/varwidth.sty +Package: varwidth 2009/03/30 ver 0.92; Variable-width minipages +\@vwid@box=\box27 +\sift@deathcycles=\count91 +\@vwid@loff=\dimen120 +\@vwid@roff=\dimen121 +)) +(/usr/share/texlive/texmf-dist/tex/latex/xcolor/xcolor.sty +Package: xcolor 2007/01/21 v2.11 LaTeX color extensions (UK) + +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/color.cfg +File: color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive +) +Package xcolor Info: Driver file: pdftex.def on input line 225. +Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1337. +Package xcolor Info: Model `hsb' substituted by `rgb' on input line 1341. +Package xcolor Info: Model `RGB' extended on input line 1353. +Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1355. +Package xcolor Info: Model `Hsb' substituted by `hsb' on input line 1356. +Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1357. +Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1358. +Package xcolor Info: Model `Gray' substituted by `gray' on input line 1359. +Package xcolor Info: Model `wave' substituted by `hsb' on input line 1360. +) +(/usr/share/texlive/texmf-dist/tex/latex/tools/enumerate.sty +Package: enumerate 2015/07/23 v3.00 enumerate extensions (DPC) +\@enLab=\toks17 +) +(/usr/share/texlive/texmf-dist/tex/latex/geometry/geometry.sty +Package: geometry 2010/09/12 v5.6 Page Geometry + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifpdf.sty +Package: ifpdf 2011/01/30 v2.3 Provides the ifpdf switch (HO) +Package ifpdf Info: pdfTeX in PDF mode is detected. +) +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifvtex.sty +Package: ifvtex 2010/03/01 v1.5 Detect VTeX and its facilities (HO) +Package ifvtex Info: VTeX not detected. +) +(/usr/share/texlive/texmf-dist/tex/generic/ifxetex/ifxetex.sty +Package: ifxetex 2010/09/12 v0.6 Provides ifxetex conditional +) +\Gm@cnth=\count92 +\Gm@cntv=\count93 +\c@Gm@tempcnt=\count94 +\Gm@bindingoffset=\dimen122 +\Gm@wd@mp=\dimen123 +\Gm@odd@mp=\dimen124 +\Gm@even@mp=\dimen125 +\Gm@layoutwidth=\dimen126 +\Gm@layoutheight=\dimen127 +\Gm@layouthoffset=\dimen128 +\Gm@layoutvoffset=\dimen129 +\Gm@dimlist=\toks18 +) +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty +Package: amsmath 2016/03/03 v2.15a AMS math features +\@mathmargin=\skip43 + +For additional information on amsmath, use the `?' option. +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty +Package: amstext 2000/06/29 v2.01 AMS text + +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty +File: amsgen.sty 1999/11/30 v2.0 generic functions +\@emptytoks=\toks19 +\ex@=\dimen130 +)) +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty +Package: amsbsy 1999/11/29 v1.2d Bold Symbols +\pmbraise@=\dimen131 +) +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty +Package: amsopn 1999/12/14 v2.01 operator names +) +\inf@bad=\count95 +LaTeX Info: Redefining \frac on input line 199. +\uproot@=\count96 +\leftroot@=\count97 +LaTeX Info: Redefining \overline on input line 297. +\classnum@=\count98 +\DOTSCASE@=\count99 +LaTeX Info: Redefining \ldots on input line 394. +LaTeX Info: Redefining \dots on input line 397. +LaTeX Info: Redefining \cdots on input line 518. +\Mathstrutbox@=\box28 +\strutbox@=\box29 +\big@size=\dimen132 +LaTeX Font Info: Redeclaring font encoding OML on input line 630. +LaTeX Font Info: Redeclaring font encoding OMS on input line 631. +\macc@depth=\count100 +\c@MaxMatrixCols=\count101 +\dotsspace@=\muskip10 +\c@parentequation=\count102 +\dspbrk@lvl=\count103 +\tag@help=\toks20 +\row@=\count104 +\column@=\count105 +\maxfields@=\count106 +\andhelp@=\toks21 +\eqnshift@=\dimen133 +\alignsep@=\dimen134 +\tagshift@=\dimen135 +\tagwidth@=\dimen136 +\totwidth@=\dimen137 +\lineht@=\dimen138 +\@envbody=\toks22 +\multlinegap=\skip44 +\multlinetaggap=\skip45 +\mathdisplay@stack=\toks23 +LaTeX Info: Redefining \[ on input line 2735. +LaTeX Info: Redefining \] on input line 2736. +) +(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +Package: amssymb 2013/01/14 v3.01 AMS font symbols + +(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty +Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support +\symAMSa=\mathgroup5 +\symAMSb=\mathgroup6 +LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' +(Font) U/euf/m/n --> U/euf/b/n on input line 106. +)) +(/usr/share/texlive/texmf-dist/tex/latex/base/textcomp.sty +Package: textcomp 2005/09/27 v1.99g Standard LaTeX package +Package textcomp Info: Sub-encoding information: +(textcomp) 5 = only ISO-Adobe without \textcurrency +(textcomp) 4 = 5 + \texteuro +(textcomp) 3 = 4 + \textohm +(textcomp) 2 = 3 + \textestimated + \textcurrency +(textcomp) 1 = TS1 - \textcircled - \t +(textcomp) 0 = TS1 (full) +(textcomp) Font families with sub-encoding setting implement +(textcomp) only a restricted character set as indicated. +(textcomp) Family '?' is the default used for unknown fonts. +(textcomp) See the documentation for details. +Package textcomp Info: Setting ? sub-encoding to TS1/1 on input line 79. + +(/usr/share/texlive/texmf-dist/tex/latex/base/ts1enc.def +File: ts1enc.def 2001/06/05 v3.0e (jk/car/fm) Standard LaTeX file +) +LaTeX Info: Redefining \oldstylenums on input line 334. +Package textcomp Info: Setting cmr sub-encoding to TS1/0 on input line 349. +Package textcomp Info: Setting cmss sub-encoding to TS1/0 on input line 350. +Package textcomp Info: Setting cmtt sub-encoding to TS1/0 on input line 351. +Package textcomp Info: Setting cmvtt sub-encoding to TS1/0 on input line 352. +Package textcomp Info: Setting cmbr sub-encoding to TS1/0 on input line 353. +Package textcomp Info: Setting cmtl sub-encoding to TS1/0 on input line 354. +Package textcomp Info: Setting ccr sub-encoding to TS1/0 on input line 355. +Package textcomp Info: Setting ptm sub-encoding to TS1/4 on input line 356. +Package textcomp Info: Setting pcr sub-encoding to TS1/4 on input line 357. +Package textcomp Info: Setting phv sub-encoding to TS1/4 on input line 358. +Package textcomp Info: Setting ppl sub-encoding to TS1/3 on input line 359. +Package textcomp Info: Setting pag sub-encoding to TS1/4 on input line 360. +Package textcomp Info: Setting pbk sub-encoding to TS1/4 on input line 361. +Package textcomp Info: Setting pnc sub-encoding to TS1/4 on input line 362. +Package textcomp Info: Setting pzc sub-encoding to TS1/4 on input line 363. +Package textcomp Info: Setting bch sub-encoding to TS1/4 on input line 364. +Package textcomp Info: Setting put sub-encoding to TS1/5 on input line 365. +Package textcomp Info: Setting uag sub-encoding to TS1/5 on input line 366. +Package textcomp Info: Setting ugq sub-encoding to TS1/5 on input line 367. +Package textcomp Info: Setting ul8 sub-encoding to TS1/4 on input line 368. +Package textcomp Info: Setting ul9 sub-encoding to TS1/4 on input line 369. +Package textcomp Info: Setting augie sub-encoding to TS1/5 on input line 370. +Package textcomp Info: Setting dayrom sub-encoding to TS1/3 on input line 371. +Package textcomp Info: Setting dayroms sub-encoding to TS1/3 on input line 372. + +Package textcomp Info: Setting pxr sub-encoding to TS1/0 on input line 373. +Package textcomp Info: Setting pxss sub-encoding to TS1/0 on input line 374. +Package textcomp Info: Setting pxtt sub-encoding to TS1/0 on input line 375. +Package textcomp Info: Setting txr sub-encoding to TS1/0 on input line 376. +Package textcomp Info: Setting txss sub-encoding to TS1/0 on input line 377. +Package textcomp Info: Setting txtt sub-encoding to TS1/0 on input line 378. +Package textcomp Info: Setting lmr sub-encoding to TS1/0 on input line 379. +Package textcomp Info: Setting lmdh sub-encoding to TS1/0 on input line 380. +Package textcomp Info: Setting lmss sub-encoding to TS1/0 on input line 381. +Package textcomp Info: Setting lmssq sub-encoding to TS1/0 on input line 382. +Package textcomp Info: Setting lmvtt sub-encoding to TS1/0 on input line 383. +Package textcomp Info: Setting lmtt sub-encoding to TS1/0 on input line 384. +Package textcomp Info: Setting qhv sub-encoding to TS1/0 on input line 385. +Package textcomp Info: Setting qag sub-encoding to TS1/0 on input line 386. +Package textcomp Info: Setting qbk sub-encoding to TS1/0 on input line 387. +Package textcomp Info: Setting qcr sub-encoding to TS1/0 on input line 388. +Package textcomp Info: Setting qcs sub-encoding to TS1/0 on input line 389. +Package textcomp Info: Setting qpl sub-encoding to TS1/0 on input line 390. +Package textcomp Info: Setting qtm sub-encoding to TS1/0 on input line 391. +Package textcomp Info: Setting qzc sub-encoding to TS1/0 on input line 392. +Package textcomp Info: Setting qhvc sub-encoding to TS1/0 on input line 393. +Package textcomp Info: Setting futs sub-encoding to TS1/4 on input line 394. +Package textcomp Info: Setting futx sub-encoding to TS1/4 on input line 395. +Package textcomp Info: Setting futj sub-encoding to TS1/4 on input line 396. +Package textcomp Info: Setting hlh sub-encoding to TS1/3 on input line 397. +Package textcomp Info: Setting hls sub-encoding to TS1/3 on input line 398. +Package textcomp Info: Setting hlst sub-encoding to TS1/3 on input line 399. +Package textcomp Info: Setting hlct sub-encoding to TS1/5 on input line 400. +Package textcomp Info: Setting hlx sub-encoding to TS1/5 on input line 401. +Package textcomp Info: Setting hlce sub-encoding to TS1/5 on input line 402. +Package textcomp Info: Setting hlcn sub-encoding to TS1/5 on input line 403. +Package textcomp Info: Setting hlcw sub-encoding to TS1/5 on input line 404. +Package textcomp Info: Setting hlcf sub-encoding to TS1/5 on input line 405. +Package textcomp Info: Setting pplx sub-encoding to TS1/3 on input line 406. +Package textcomp Info: Setting pplj sub-encoding to TS1/3 on input line 407. +Package textcomp Info: Setting ptmx sub-encoding to TS1/4 on input line 408. +Package textcomp Info: Setting ptmj sub-encoding to TS1/4 on input line 409. +) +(/usr/share/texlive/texmf-dist/tex/latex/upquote/upquote.sty +Package: upquote 2012/04/19 v1.3 upright-quote and grave-accent glyphs in verba +tim +) +(/usr/share/texlive/texmf-dist/tex/latex/eurosym/eurosym.sty +Package: eurosym 1998/08/06 v1.1 European currency symbol ``Euro'' +\@eurobox=\box30 +) +(/usr/share/texlive/texmf-dist/tex/latex/ucs/ucs.sty +Package: ucs 2013/05/11 v2.2 UCS: Unicode input support + +(/usr/share/texlive/texmf-dist/tex/latex/ucs/data/uni-global.def +File: uni-global.def 2013/05/13 UCS: Unicode global data +) +\uc@secondtry=\count107 +\uc@combtoks=\toks24 +\uc@combtoksb=\toks25 +\uc@temptokena=\toks26 +) +(/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty +Package: inputenc 2015/03/17 v1.2c Input encoding file +\inpenc@prehook=\toks27 +\inpenc@posthook=\toks28 + +(/usr/share/texlive/texmf-dist/tex/latex/ucs/utf8x.def +File: utf8x.def 2004/10/17 UCS: Input encoding UTF-8 +)) +(/usr/share/texlive/texmf-dist/tex/latex/fancyvrb/fancyvrb.sty +Package: fancyvrb 2008/02/07 + +Style option: `fancyvrb' v2.7a, with DG/SPQR fixes, and firstline=lastline fix +<2008/02/07> (tvz) +\FV@CodeLineNo=\count108 +\FV@InFile=\read1 +\FV@TabBox=\box31 +\c@FancyVerbLine=\count109 +\FV@StepNumber=\count110 +\FV@OutFile=\write3 +) +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grffile.sty +Package: grffile 2012/04/05 v1.16 Extended file name support for graphics (HO) + +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/kvoptions.sty +Package: kvoptions 2011/06/30 v3.11 Key value format for package options (HO) + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/kvsetkeys.sty +Package: kvsetkeys 2012/04/25 v1.16 Key value parser (HO) + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/etexcmds.sty +Package: etexcmds 2011/02/16 v1.5 Avoid name clashes with e-TeX commands (HO) + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifluatex.sty +Package: ifluatex 2010/03/01 v1.3 Provides the ifluatex switch (HO) +Package ifluatex Info: LuaTeX not detected. +) +Package etexcmds Info: Could not find \expanded. +(etexcmds) That can mean that you are not using pdfTeX 1.50 or +(etexcmds) that some package has redefined \expanded. +(etexcmds) In the latter case, load this package earlier. +))) +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/pdftexcmds.sty +Package: pdftexcmds 2011/11/29 v0.20 Utility functions of pdfTeX for LuaTeX (HO +) +Package pdftexcmds Info: LuaTeX not detected. +Package pdftexcmds Info: \pdf@primitive is available. +Package pdftexcmds Info: \pdf@ifprimitive is available. +Package pdftexcmds Info: \pdfdraftmode found. +) +Package grffile Info: Option `multidot' is set to `true'. +Package grffile Info: Option `extendedchars' is set to `false'. +Package grffile Info: Option `space' is set to `true'. +Package grffile Info: \Gin@ii of package `graphicx' fixed on input line 486. +) +(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty +Package: hyperref 2012/11/06 v6.83m Hypertext links for LaTeX + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty +Package: hobsub-hyperref 2012/05/28 v1.13 Bundle oberdiek, subset hyperref (HO) + + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty +Package: hobsub-generic 2012/05/28 v1.13 Bundle oberdiek, subset generic (HO) +Package: hobsub 2012/05/28 v1.13 Construct package bundles (HO) +Package hobsub Info: Skipping package `infwarerr' (already loaded). +Package hobsub Info: Skipping package `ltxcmds' (already loaded). +Package hobsub Info: Skipping package `ifluatex' (already loaded). +Package hobsub Info: Skipping package `ifvtex' (already loaded). +Package: intcalc 2007/09/27 v1.1 Expandable calculations with integers (HO) +Package hobsub Info: Skipping package `ifpdf' (already loaded). +Package hobsub Info: Skipping package `etexcmds' (already loaded). +Package hobsub Info: Skipping package `kvsetkeys' (already loaded). +Package: kvdefinekeys 2011/04/07 v1.3 Define keys (HO) +Package hobsub Info: Skipping package `pdftexcmds' (already loaded). +Package: pdfescape 2011/11/25 v1.13 Implements pdfTeX's escape features (HO) +Package: bigintcalc 2012/04/08 v1.3 Expandable calculations on big integers (HO +) +Package: bitset 2011/01/30 v1.1 Handle bit-vector datatype (HO) +Package: uniquecounter 2011/01/30 v1.2 Provide unlimited unique counter (HO) +) +Package hobsub Info: Skipping package `hobsub' (already loaded). +Package: letltxmacro 2010/09/02 v1.4 Let assignment for LaTeX macros (HO) +Package: hopatch 2012/05/28 v1.2 Wrapper for package hooks (HO) +Package: xcolor-patch 2011/01/30 xcolor patch +Package: atveryend 2011/06/30 v1.8 Hooks at the very end of document (HO) +Package atveryend Info: \enddocument detected (standard20110627). +Package: atbegshi 2011/10/05 v1.16 At begin shipout hook (HO) +Package: refcount 2011/10/16 v3.4 Data extraction from label references (HO) +Package: hycolor 2011/01/30 v1.7 Color options for hyperref/bookmark (HO) +) +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/auxhook.sty +Package: auxhook 2011/03/04 v1.3 Hooks for auxiliary files (HO) +) +\@linkdim=\dimen139 +\Hy@linkcounter=\count111 +\Hy@pagecounter=\count112 + +(/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def +File: pd1enc.def 2012/11/06 v6.83m Hyperref: PDFDocEncoding definition (HO) +) +\Hy@SavedSpaceFactor=\count113 + +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/hyperref.cfg +File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive +) +Package hyperref Info: Hyper figures OFF on input line 4443. +Package hyperref Info: Link nesting OFF on input line 4448. +Package hyperref Info: Hyper index ON on input line 4451. +Package hyperref Info: Plain pages OFF on input line 4458. +Package hyperref Info: Backreferencing OFF on input line 4463. +Package hyperref Info: Implicit mode ON; LaTeX internals redefined. +Package hyperref Info: Bookmarks ON on input line 4688. +\c@Hy@tempcnt=\count114 + +(/usr/share/texlive/texmf-dist/tex/latex/url/url.sty +\Urlmuskip=\muskip11 +Package: url 2013/09/16 ver 3.4 Verb mode for urls, etc. +) +LaTeX Info: Redefining \url on input line 5041. +\XeTeXLinkMargin=\dimen140 +\Fld@menulength=\count115 +\Field@Width=\dimen141 +\Fld@charsize=\dimen142 +Package hyperref Info: Hyper figures OFF on input line 6295. +Package hyperref Info: Link nesting OFF on input line 6300. +Package hyperref Info: Hyper index ON on input line 6303. +Package hyperref Info: backreferencing OFF on input line 6310. +Package hyperref Info: Link coloring OFF on input line 6315. +Package hyperref Info: Link coloring with OCG OFF on input line 6320. +Package hyperref Info: PDF/A mode OFF on input line 6325. +LaTeX Info: Redefining \ref on input line 6365. +LaTeX Info: Redefining \pageref on input line 6369. +\Hy@abspage=\count116 +\c@Item=\count117 +\c@Hfootnote=\count118 +) + +Package hyperref Message: Driver (autodetected): hpdftex. + +(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def +File: hpdftex.def 2012/11/06 v6.83m Hyperref driver for pdfTeX +\Fld@listcount=\count119 +\c@bookmark@seq@number=\count120 + +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty +Package: rerunfilecheck 2011/04/15 v1.7 Rerun checks for auxiliary files (HO) +Package uniquecounter Info: New unique counter `rerunfilecheck' on input line 2 +82. +) +\Hy@SectionHShift=\skip46 +) +(/usr/share/texlive/texmf-dist/tex/latex/tools/longtable.sty +Package: longtable 2014/10/28 v4.11 Multi-page Table package (DPC) +\LTleft=\skip47 +\LTright=\skip48 +\LTpre=\skip49 +\LTpost=\skip50 +\LTchunksize=\count121 +\LTcapwidth=\dimen143 +\LT@head=\box32 +\LT@firsthead=\box33 +\LT@foot=\box34 +\LT@lastfoot=\box35 +\LT@cols=\count122 +\LT@rows=\count123 +\c@LT@tables=\count124 +\c@LT@chunks=\count125 +\LT@p@ftn=\toks29 +) +(/usr/share/texlive/texmf-dist/tex/latex/booktabs/booktabs.sty +Package: booktabs 2005/04/14 v1.61803 publication quality tables +\heavyrulewidth=\dimen144 +\lightrulewidth=\dimen145 +\cmidrulewidth=\dimen146 +\belowrulesep=\dimen147 +\belowbottomsep=\dimen148 +\aboverulesep=\dimen149 +\abovetopsep=\dimen150 +\cmidrulesep=\dimen151 +\cmidrulekern=\dimen152 +\defaultaddspace=\dimen153 +\@cmidla=\count126 +\@cmidlb=\count127 +\@aboverulesep=\dimen154 +\@belowrulesep=\dimen155 +\@thisruleclass=\count128 +\@lastruleclass=\count129 +\@thisrulewidth=\dimen156 +) +(/usr/share/texlive/texmf-dist/tex/latex/enumitem/enumitem.sty +Package: enumitem 2011/09/28 v3.5.2 Customized lists +\labelindent=\skip51 +\enit@outerparindent=\dimen157 +\enit@toks=\toks30 +\enit@inbox=\box36 +\enitdp@description=\count130 +) +(/usr/share/texlive/texmf-dist/tex/generic/ulem/ulem.sty +\UL@box=\box37 +\UL@hyphenbox=\box38 +\UL@skip=\skip52 +\UL@hook=\toks31 +\UL@height=\dimen158 +\UL@pe=\count131 +\UL@pixel=\dimen159 +\ULC@box=\box39 +Package: ulem 2012/05/18 +\ULdepth=\dimen160 +) +Package hyperref Info: Option `breaklinks' set `true' on input line 264. +Package hyperref Info: Option `colorlinks' set `true' on input line 264. + (./lecture_10.aux + +LaTeX Warning: Label `gauss-elimination' multiply defined. + +) +\openout1 = `lecture_10.aux'. + +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 271. +LaTeX Font Info: Try loading font information for TS1+cmr on input line 271. + + (/usr/share/texlive/texmf-dist/tex/latex/base/ts1cmr.fd +File: ts1cmr.fd 2014/09/29 v2.5h Standard LaTeX font definitions +) +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Try loading font information for T1+ppl on input line 271. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/t1ppl.fd +File: t1ppl.fd 2001/06/04 font definitions for T1/ppl. +) +(/usr/share/texlive/texmf-dist/tex/context/base/supp-pdf.mkii +[Loading MPS to PDF converter (version 2006.09.02).] +\scratchcounter=\count132 +\scratchdimen=\dimen161 +\scratchbox=\box40 +\nofMPsegments=\count133 +\nofMParguments=\count134 +\everyMPshowfont=\toks32 +\MPscratchCnt=\count135 +\MPscratchDim=\dimen162 +\MPnumerator=\count136 +\makeMPintoPDFobject=\count137 +\everyMPtoPDFconversion=\toks33 +) (/usr/share/texlive/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty +Package: epstopdf-base 2010/02/09 v2.5 Base part for package epstopdf + +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grfext.sty +Package: grfext 2010/08/19 v1.1 Manage graphics extensions (HO) +) +Package grfext Info: Graphics extension search list: +(grfext) [.png,.pdf,.jpg,.mps,.jpeg,.jbig2,.jb2,.PNG,.PDF,.JPG,.JPE +G,.JBIG2,.JB2,.eps] +(grfext) \AppendGraphicsExtensions on input line 452. + +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg +File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv +e +)) +Package caption Info: Begin \AtBeginDocument code. +Package caption Info: hyperref package is loaded. +Package caption Info: longtable package is loaded. + +(/usr/share/texlive/texmf-dist/tex/latex/caption/ltcaption.sty +Package: ltcaption 2013/06/09 v1.4-94 longtable captions (AR) +) +Package caption Info: End \AtBeginDocument code. + +*geometry* driver: auto-detecting +*geometry* detected driver: pdftex +*geometry* verbose mode - [ preamble ] result: +* driver: pdftex +* paper: +* layout: +* layoutoffset:(h,v)=(0.0pt,0.0pt) +* modes: +* h-part:(L,W,R)=(72.26999pt, 469.75502pt, 72.26999pt) +* v-part:(T,H,B)=(72.26999pt, 650.43001pt, 72.26999pt) +* \paperwidth=614.295pt +* \paperheight=794.96999pt +* \textwidth=469.75502pt +* \textheight=650.43001pt +* \oddsidemargin=0.0pt +* \evensidemargin=0.0pt +* \topmargin=-37.0pt +* \headheight=12.0pt +* \headsep=25.0pt +* \topskip=11.0pt +* \footskip=30.0pt +* \marginparwidth=59.0pt +* \marginparsep=10.0pt +* \columnsep=10.0pt +* \skip\footins=10.0pt plus 4.0pt minus 2.0pt +* \hoffset=0.0pt +* \voffset=0.0pt +* \mag=1000 +* \@twocolumnfalse +* \@twosidefalse +* \@mparswitchfalse +* \@reversemarginfalse +* (1in=72.27pt=25.4mm, 1cm=28.453pt) + +(/usr/share/texlive/texmf-dist/tex/latex/ucs/ucsencs.def +File: ucsencs.def 2011/01/21 Fixes to fontencodings LGR, T3 +) +\AtBeginShipoutBox=\box41 +Package hyperref Info: Link coloring ON on input line 271. + +(/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty +Package: nameref 2012/10/27 v2.43 Cross-referencing by name of section + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/gettitlestring.sty +Package: gettitlestring 2010/12/03 v1.4 Cleanup title references (HO) +) +\c@section@level=\count138 +) +LaTeX Info: Redefining \ref on input line 271. +LaTeX Info: Redefining \pageref on input line 271. +LaTeX Info: Redefining \nameref on input line 271. + +(./lecture_10.out) (./lecture_10.out) +\@outlinefile=\write4 +\openout4 = `lecture_10.out'. + +LaTeX Font Info: Try loading font information for OT1+ppl on input line 275. + + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/ot1ppl.fd +File: ot1ppl.fd 2001/06/04 font definitions for OT1/ppl. +) +LaTeX Font Info: Try loading font information for OML+zplm on input line 275 +. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/omlzplm.fd +File: omlzplm.fd 2002/09/08 Fontinst v1.914 font definitions for OML/zplm. +) +LaTeX Font Info: Try loading font information for OMS+zplm on input line 275 +. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/omszplm.fd +File: omszplm.fd 2002/09/08 Fontinst v1.914 font definitions for OMS/zplm. +) +LaTeX Font Info: Try loading font information for OMX+zplm on input line 275 +. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/omxzplm.fd +File: omxzplm.fd 2002/09/08 Fontinst v1.914 font definitions for OMX/zplm. +) +LaTeX Font Info: Try loading font information for OT1+zplm on input line 275 +. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/ot1zplm.fd +File: ot1zplm.fd 2002/09/08 Fontinst v1.914 font definitions for OT1/zplm. +) +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 12.50409pt on input line 275. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 9.37807pt on input line 275. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 7.29405pt on input line 275. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 12.50409pt on input line 275. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 9.37807pt on input line 275. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 7.29405pt on input line 275. + + +LaTeX Warning: No \author given. + +LaTeX Font Info: Try loading font information for T1+cmtt on input line 279. + +(/usr/share/texlive/texmf-dist/tex/latex/base/t1cmtt.fd +File: t1cmtt.fd 2014/09/29 v2.5h Standard LaTeX font definitions +) +LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <14.4> not available +(Font) Font shape `T1/ppl/b/n' tried instead on input line 287. +LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <10.95> not available +(Font) Font shape `T1/ppl/b/n' tried instead on input line 290. + + +Package hyperref Warning: Difference (2) between bookmark levels is greater +(hyperref) than one, level fixed on input line 290. + +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 11.40997pt on input line 295. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 8.33606pt on input line 295. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 6.25204pt on input line 295. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 11.40997pt on input line 295. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 8.33606pt on input line 295. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 6.25204pt on input line 295. + +File: lecture_10_files/lecture_10_3_0.pdf Graphic file (type pdf) + + +Package pdftex.def Info: lecture_10_files/lecture_10_3_0.pdf used on input line + 321. +(pdftex.def) Requested size: 449.6789pt x 337.25917pt. + [1 + +{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] +Underfull \hbox (badness 10000) in paragraph at lines 323--324 + + [] + +[2 <./lecture_10_files/lecture_10_3_0.pdf>] +LaTeX Font Info: Try loading font information for TS1+cmtt on input line 359 +. + +(/usr/share/texlive/texmf-dist/tex/latex/base/ts1cmtt.fd +File: ts1cmtt.fd 2014/09/29 v2.5h Standard LaTeX font definitions +) + +File: lecture_10_files/lecture_10_5_1.pdf Graphic file (type pdf) + + +Package pdftex.def Info: lecture_10_files/lecture_10_5_1.pdf used on input line + 371. +(pdftex.def) Requested size: 449.6789pt x 337.25917pt. + +Underfull \hbox (badness 10000) in paragraph at lines 373--374 + + [] + +LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <12> not available +(Font) Font shape `T1/ppl/b/n' tried instead on input line 378. +[3 <./lecture_10_files/lecture_10_5_1.pdf>] + +! LaTeX Error: Unknown graphics extension: .svg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.433 ...egraphics{../lecture_09/mass_springs.svg} + +? +[4] [5] [6] [7] + +! LaTeX Error: Unknown graphics extension: .svg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.712 ...egraphics{../lecture_09/mass_springs.svg} + +? +[8] [9] +LaTeX Font Info: Font shape `T1/cmtt/bx/n' in size <10.95> not available +(Font) Font shape `T1/cmtt/m/n' tried instead on input line 812. + [10] + +File: lecture_10_files/lecture_10_27_0.pdf Graphic file (type pdf) + + +Package pdftex.def Info: lecture_10_files/lecture_10_27_0.pdf used on input lin +e 839. +(pdftex.def) Requested size: 449.6789pt x 337.25917pt. + +Underfull \hbox (badness 10000) in paragraph at lines 841--842 + + [] + +Package atveryend Info: Empty hook `BeforeClearDocument' on input line 852. +[11 <./lecture_10_files/lecture_10_27_0.pdf>] +Package atveryend Info: Empty hook `AfterLastShipout' on input line 852. + (./lecture_10.aux) +Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 852. +Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 852. +Package rerunfilecheck Info: File `lecture_10.out' has not changed. +(rerunfilecheck) Checksum: F41F49C8B1F4406369908EBDD24F2572;629. + + +LaTeX Warning: There were multiply-defined labels. + +Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 852. + ) +Here is how much of TeX's memory you used: + 10939 strings out of 493029 + 163764 string characters out of 6136234 + 273062 words of memory out of 5000000 + 14225 multiletter control sequences out of 15000+600000 + 35480 words of font info for 90 fonts, out of 8000000 for 9000 + 1141 hyphenation exceptions out of 8191 + 36i,8n,77p,494b,465s stack positions out of 5000i,500n,10000p,200000b,80000s +{/usr/share/texmf/fonts/enc/dvips/cm-super/cm-super-ts1.enc}{/usr/share/texli +ve/texmf-dist/fonts/enc/dvips/base/8r.enc}{/usr/share/texmf/fonts/enc/dvips/cm- +super/cm-super-t1.enc} +Output written on lecture_10.pdf (11 pages, 162693 bytes). +PDF statistics: + 165 PDF objects out of 1000 (max. 8388607) + 133 compressed objects within 2 object streams + 27 named destinations out of 1000 (max. 500000) + 80 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/lecture_10/lecture_10.md b/lecture_10/lecture_10.md new file mode 100644 index 0000000..dd426e0 --- /dev/null +++ b/lecture_10/lecture_10.md @@ -0,0 +1,593 @@ + + +```octave +%plot --format svg +``` + + +```octave +setdefaults +``` + +# Gauss Elimination +### Solving sets of equations with matrix operations + +The number of dimensions of a matrix indicate the degrees of freedom of the system you are solving. + +If you have a set of known output, $y_{1},~y_{2},~...y_{N}$ and a set of equations that +relate unknown inputs, $x_{1},~x_{2},~...x_{N}$, then these can be written in a vector +matrix format as: + +$y=Ax$ + +Consider a problem with 2 DOF: + +$x_{1}+3x_{2}=1$ + +$2x_{1}+x_{2}=1$ + +$\left[ \begin{array}{cc} +1 & 3 \\ +2 & 1 \end{array} \right] +\left[\begin{array}{c} +x_{1} \\ +x_{2} \end{array}\right]= +\left[\begin{array}{c} +1 \\ +1\end{array}\right]$ + +The solution for $x_{1}$ and $x_{2}$ is the intersection of two lines: + + +```octave +x21=[-2:2]; +x11=1-3*x21; +x21=[-2:2]; +x22=1-2*x21; +plot(x11,x21,x21,x22) +``` + + +![svg](lecture_10_files/lecture_10_3_0.svg) + + +For a 3$\times$3 matrix, the solution is the intersection of the 3 planes. + +$10x_{1}+2x_{2}+x_{3}=1$ + +$2x_{1}+x_{2}+x_{3}=1$ + +$x_{1}+2x_{2}+10x_{3}=1$ + +$\left[ \begin{array}{cc} +10 & 2 & 1\\ +2 & 1 & 1 \\ +1 & 2 & 10\end{array} \right] +\left[\begin{array}{c} +x_{1} \\ +x_{2} \\ +x_{3} \end{array}\right]= +\left[\begin{array}{c} +1 \\ +1 \\ +1\end{array}\right]$ + + +```octave +x11=linspace(-2,2,5); +x12=linspace(-2,2,5); +[X11,X12]=meshgrid(x11,x12); +X13=1-10*X11-2*X22; + +x21=linspace(-2,2,5); +x22=linspace(-2,2,5); +[X21,X22]=meshgrid(x21,x22); +X23=1-2*X11-X22; + +x31=linspace(-2,2,5); +x32=linspace(-2,2,5); +[X31,X32]=meshgrid(x31,x32); +X33=1/10*(1-X31-2*X32); + +mesh(X11,X12,X13); +hold on; +mesh(X21,X22,X23) +mesh(X31,X32,X33) +x=[10,2, 1;2,1, 1; 1, 2, 10]\[1;1;1]; +plot3(x(1),x(2),x(3),'o') +view(45,45) +``` + + +![svg](lecture_10_files/lecture_10_5_0.svg) + + +After 3 DOF problems, the solutions are described as *hyperplane* intersections. Which are even harder to visualize + +## Gauss elimination +### Solving sets of equations systematically + +$\left[ \begin{array}{ccc|c} + & A & & y \\ +10 & 2 & 1 & 1\\ +2 & 1 & 1 & 1 \\ +1 & 2 & 10 & 1\end{array} +\right] $ + +Ay(2,:)-Ay(1,:)/5 = ([2 1 1 1]-1/5[10 2 1 1]) + +$\left[ \begin{array}{ccc|c} + & A & & y \\ +10 & 2 & 1 & 1\\ +0 & 3/5 & 4/5 & 4/5 \\ +1 & 2 & 10 & 1\end{array} +\right] $ + +Ay(3,:)-Ay(1,:)/10 = ([1 2 10 1]-1/10[10 2 1 1]) + +$\left[ \begin{array}{ccc|c} + & A & & y \\ +10 & 2 & 1 & 1\\ +0 & 3/5 & 4/5 & 4/5 \\ +0 & 1.8 & 9.9 & 0.9\end{array} +\right] $ + +Ay(3,:)-1.8\*5/3\*Ay(2,:) = ([0 1.8 9.9 0.9]-3\*[0 3/5 4/5 4/5]) + +$\left[ \begin{array}{ccc|c} + & A & & y \\ +10 & 2 & 1 & 1\\ +0 & 3/5 & 4/5 & 4/5 \\ +0 & 0 & 7.5 & -1.5\end{array} +\right] $ + +now, $7.5x_{3}=-1.5$ so $x_{3}=-\frac{1}{5}$ + +then, $3/5x_{2}+4/5(-1/5)=1$ so $x_{2}=\frac{8}{5}$ + +finally, $10x_{1}+2(8/5) + +Consider the problem again from the intro to Linear Algebra, 4 masses are connected in series to 4 springs with K=10 N/m. What are the final positions of the masses? + +![Springs-masses](../lecture_09/mass_springs.svg) + +The masses haves the following amounts, 1, 2, 3, and 4 kg for masses 1-4. Using a FBD for each mass: + +$m_{1}g+k(x_{2}-x_{1})-kx_{1}=0$ + +$m_{2}g+k(x_{3}-x_{2})-k(x_{2}-x_{1})=0$ + +$m_{3}g+k(x_{4}-x_{3})-k(x_{3}-x_{2})=0$ + +$m_{4}g-k(x_{4}-x_{3})=0$ + +in matrix form: + +$\left[ \begin{array}{cccc} +2k & -k & 0 & 0 \\ +-k & 2k & -k & 0 \\ +0 & -k & 2k & -k \\ +0 & 0 & -k & k \end{array} \right] +\left[ \begin{array}{c} +x_{1} \\ +x_{2} \\ +x_{3} \\ +x_{4} \end{array} \right]= +\left[ \begin{array}{c} +m_{1}g \\ +m_{2}g \\ +m_{3}g \\ +m_{4}g \end{array} \right]$ + + +```octave +k=10; % N/m +m1=1; % kg +m2=2; +m3=3; +m4=4; +g=9.81; % m/s^2 +K=[2*k -k 0 0; -k 2*k -k 0; 0 -k 2*k -k; 0 0 -k k] +y=[m1*g;m2*g;m3*g;m4*g] +``` + + K = + + 20 -10 0 0 + -10 20 -10 0 + 0 -10 20 -10 + 0 0 -10 10 + + y = + + 9.8100 + 19.6200 + 29.4300 + 39.2400 + + + + +```octave +K1=[K y]; +K1(2,:)=K1(1,:)/2+K1(2,:) +``` + + K1 = + + 20.00000 -10.00000 0.00000 0.00000 9.81000 + 0.00000 15.00000 -10.00000 0.00000 24.52500 + 0.00000 -10.00000 20.00000 -10.00000 29.43000 + 0.00000 0.00000 -10.00000 10.00000 39.24000 + + + + +```octave +K2=K1; +K2(3,:)=K1(2,:)*2/3+K1(3,:) + +``` + + K2 = + + 20.00000 -10.00000 0.00000 0.00000 9.81000 + 0.00000 15.00000 -10.00000 0.00000 24.52500 + 0.00000 0.00000 13.33333 -10.00000 45.78000 + 0.00000 0.00000 -10.00000 10.00000 39.24000 + + + + +```octave +K2(4,:)=-K2(3,:)*K2(4,3)/K2(3,3)+K2(4,:) +``` + + K2 = + + 20.00000 -10.00000 0.00000 0.00000 9.81000 + 0.00000 15.00000 -10.00000 0.00000 24.52500 + 0.00000 0.00000 13.33333 -10.00000 45.78000 + 0.00000 0.00000 0.00000 2.50000 73.57500 + + + + +```octave +yp=K2(:,5); +x4=yp(4)/K2(4,4) +x3=(yp(3)+10*x4)/K2(3,3) +x2=(yp(2)+10*x3)/K2(2,2) +x1=(yp(1)+10*x2)/K2(1,1) +``` + + x4 = 29.430 + x3 = 25.506 + x2 = 18.639 + x1 = 9.8100 + + + +```octave +K\y +``` + + ans = + + 9.8100 + 18.6390 + 25.5060 + 29.4300 + + + +## Automate Gauss Elimination + +We can automate Gauss elimination with a function whose input is A and y: + +`x=GaussNaive(A,y)` + + +```octave +x=GaussNaive(K,y) +``` + + x = + + 9.8100 + 18.6390 + 25.5060 + 29.4300 + + + +## Problem (Diagonal element is zero) + +If a diagonal element is 0 or very small either: + +1. no solution found +2. errors are introduced + +Therefore, we would want to pivot before applying Gauss elimination + +Consider: + +(a) $\left[ \begin{array}{cccc} +0 & 2 & 3 \\ +4 & 6 & 7 \\ +2 & -3 & 6 \end{array} \right] +\left[ \begin{array}{c} +x_{1} \\ +x_{2} \\ +x_{3} \end{array} \right]= +\left[ \begin{array}{c} +8 \\ +-3 \\ +5\end{array} \right]$ + +(b) $\left[ \begin{array}{cccc} +0.0003 & 3.0000 \\ +1.0000 & 1.0000 \end{array} \right] +\left[ \begin{array}{c} +x_{1} \\ +x_{2} \end{array} \right]= +\left[ \begin{array}{c} +2.0001 \\ +1.0000 \end{array} \right]$ + + +```octave +format short +Aa=[0,2,3;4,6,7;2,-3,6]; ya=[8;-3;5]; +GaussNaive(Aa,ya) +Aa\ya +``` + + warning: division by zero + warning: called from + GaussNaive at line 16 column 12 + warning: division by zero + warning: division by zero + ans = + + NaN + NaN + NaN + + ans = + + -5.423913 + 0.021739 + 2.652174 + + + + +```octave +[x,Aug,npivots]=GaussPivot(Aa,ya) +``` + + x = + + -5.423913 + 0.021739 + 2.652174 + + Aug = + + 4.00000 6.00000 7.00000 -3.00000 + 0.00000 -6.00000 2.50000 6.50000 + 0.00000 0.00000 3.83333 10.16667 + + npivots = 2 + + + +```octave +format long +Ab=[0.3E-13,3.0000;1.0000,1.0000];yb=[2+0.1e-13;1.0000]; +GaussNaive(Ab,yb) +Ab\yb +``` + + ans = + + 0.325665420556713 + 0.666666666666667 + + ans = + + 0.333333333333333 + 0.666666666666667 + + + + +```octave +[x,Aug,npivots]=GaussPivot(Ab,yb) +Ab\yb +format short +``` + + x = + + 0.333333333333333 + 0.666666666666667 + + Aug = + + 1.000000000000000 1.000000000000000 1.000000000000000 + 0.000000000000000 2.999999999999970 1.999999999999980 + + npivots = 1 + ans = + + 0.333333333333333 + 0.666666666666667 + + + +### Spring-Mass System again +Now, 4 masses are connected in series to 4 springs with $K_{1}$=10 N/m, $K_{2}$=5 N/m, +$K_{3}$=2 N/m +and $K_{4}$=1 N/m. What are the final positions of the masses? + +![Springs-masses](../lecture_09/mass_springs.svg) + +The masses have the following amounts, 1, 2, 3, and 4 kg for masses 1-4. Using a FBD for each mass: + +$m_{1}g+k_{2}(x_{2}-x_{1})-k_{1}x_{1}=0$ + +$m_{2}g+k_{3}(x_{3}-x_{2})-k_{2}(x_{2}-x_{1})=0$ + +$m_{3}g+k_{4}(x_{4}-x_{3})-k_{3}(x_{3}-x_{2})=0$ + +$m_{4}g-k_{4}(x_{4}-x_{3})=0$ + +in matrix form: + +$\left[ \begin{array}{cccc} +k_1+k_2 & -k_2 & 0 & 0 \\ +-k_2 & k_2+k_3 & -k_3 & 0 \\ +0 & -k_3 & k_3+k_4 & -k_4 \\ +0 & 0 & -k_4 & k_4 \end{array} \right] +\left[ \begin{array}{c} +x_{1} \\ +x_{2} \\ +x_{3} \\ +x_{4} \end{array} \right]= +\left[ \begin{array}{c} +m_{1}g \\ +m_{2}g \\ +m_{3}g \\ +m_{4}g \end{array} \right]$ + + +```octave +k1=10; k2=5;k3=2;k4=1; % N/m +m1=1; % kg +m2=2; +m3=3; +m4=4; +g=9.81; % m/s^2 +K=[k1+k2 -k2 0 0; -k2, k2+k3, -k3 0; 0 -k3, k3+k4, -k4; 0 0 -k4 k4] +y=[m1*g;m2*g;m3*g;m4*g] +``` + + K = + + 15 -5 0 0 + -5 7 -2 0 + 0 -2 3 -1 + 0 0 -1 1 + + y = + + 9.8100 + 19.6200 + 29.4300 + 39.2400 + + + +## Tridiagonal matrix + +This matrix, K, could be rewritten as 3 vectors e, f and g + +$e=\left[ \begin{array}{c} +0 \\ +-5 \\ +-2 \\ +-1 \end{array} \right]$ + +$f=\left[ \begin{array}{c} +15 \\ +7 \\ +3 \\ +1 \end{array} \right]$ + +$g=\left[ \begin{array}{c} +-5 \\ +-2 \\ +-1 \\ +0 \end{array} \right]$ + +Where all other components are 0 and the length of the vectors are n and the first component of e and the last component of g are zero + +`e(1)=0` + +`g(end)=0` + +No need to pivot and number of calculations reduced enormously. + +|method |Number of Floating point operations for n$\times$n-matrix| +|----------------|---------| +| Naive Gauss | n-cubed | +| Tridiagonal | n | + + +```octave +e=[0;-5;-2;-1]; +g=[-5;-2;-1;0]; +f=[15;7;3;1]; +Tridiag(e,f,g,y) + +``` + + ans = + + 9.8100 27.4680 61.8030 101.0430 + + + + +```octave +% tic ... t=toc +% is Matlab timer used for debugging programs +t_GE = zeros(1,100); +t_GE_tridiag = zeros(1,100); +t_TD = zeros(1,100); +for n = 1:200 + A = rand(n,n); + e = rand(n,1); e(1)=0; + f = rand(n,1); + g = rand(n,1); g(end)=0; + Atd=diag(f, 0) - diag(e(2:n), -1) - diag(g(1:n-1), 1); + b = rand(n,1); + tic; + x = GaussPivot(A,b); + t_GE(n) = toc; + tic; + x = GaussPivot(Atd,b); + t_GE_tridiag(n) = toc; + tic; + x = Tridiag(e,f,g,b); + t_TD(n) = toc; +end +``` + + +```octave +n=1:200; +loglog(n,t_GE,n,t_TD,n,t_GE_tridiag) +xlabel('number of elements') +ylabel('time (s)') +``` + + +![svg](lecture_10_files/lecture_10_27_0.svg) + + + +```octave +plot(t_TD) +``` + + +![svg](lecture_10_files/lecture_10_28_0.svg) + + + +```octave + +``` diff --git a/lecture_10/lecture_10.out b/lecture_10/lecture_10.out new file mode 100644 index 0000000..cb5b517 --- /dev/null +++ b/lecture_10/lecture_10.out @@ -0,0 +1,8 @@ +\BOOKMARK [1][-]{section.1}{Gauss Elimination}{}% 1 +\BOOKMARK [2][-]{subsubsection.1.0.1}{Solving sets of equations with matrix operations}{section.1}% 2 +\BOOKMARK [2][-]{subsection.1.1}{Gauss elimination}{section.1}% 3 +\BOOKMARK [3][-]{subsubsection.1.1.1}{Solving sets of equations systematically}{subsection.1.1}% 4 +\BOOKMARK [2][-]{subsection.1.2}{Automate Gauss Elimination}{section.1}% 5 +\BOOKMARK [2][-]{subsection.1.3}{Problem \(Diagonal element is zero\)}{section.1}% 6 +\BOOKMARK [3][-]{subsubsection.1.3.1}{Spring-Mass System again}{subsection.1.3}% 7 +\BOOKMARK [2][-]{subsection.1.4}{Tridiagonal matrix}{section.1}% 8 diff --git a/lecture_10/lecture_10.pdf b/lecture_10/lecture_10.pdf new file mode 100644 index 0000000000000000000000000000000000000000..447bbe233f131c3f14f9cdfbf95651b3847ad800 GIT binary patch literal 162693 zcmcG#b95!)wg=c9+qQFJ+qT)UZ9C~CC$^oAZQHhO+es%KOyB$7%)EK`&U){UnObL6 zo%-slI;Zxkz1I)B$Q4D!>6qx*V8~||hgM-&IEfgE?2W8oczIzMWKHeNT`Y*0n3))f z{<**~h+EpYm^u+Lh}#&tn2MSj+nboe@bkksyEvH|+QN9OFKPa;KVV1lo2i+V`QC;r z$HiMjdp~Q8YD1{?>q(m(kfbRU%&lBbI?}U~C%Kl8FK6T)*$ibgf9TNN7Rm}+4T_OP zP^&Ram;$+zeaa~aikA$RqVau&m4kU!>!$&=W_4hLL$)rvZBsAj`_?o260*d@@63{# zf%wi*@PH5@GGrr=>s5bRjCf(xoUY#RQN`{~f4{?*F3SL#j)~1sa>5$U*Fi=8p59b-*(`06+yH*@vIwXSQuup#=v@x(pYPf$+GD`8fT~(-?$TBAgszgr+COz zFumy8Vyehgg8&DdJyf|Z2iYOAkqO5_^J{^P@v>xW7QUos{>TkL4P+;mw_LbO(shqwlkuwRNCI}ne3Zi1VnZa%S0|M!zajX3i@G-cI(>N zDJ$&e8(s;=cDDc@(%`>KLxOY54-3U%9u9deR|*FeH$KAfe=g`1X5@@=jYcW>u)!>0*^Xdjyt$-`h}%{=@LB`p=Nc@ncM_Fed*wuAsmsO(4>3aodWnr+N~K;g6QTt)>w1DN zD3hYex-`IIkC=WfF$Tn%AMN#G-OSAvdARRnBzbE`idY` zOS~l?lYTc^Nn=qC=YJj1W)(6>S1i-obzDzIu!+`TZP{kmQDLheZ_WUKOGC1kZNbDT z^G$_6PwJwa{Izx;d8ct&h=CCLnzE89zRXchQDJ4JfD8MW`f!}*lIW^u@-!zu!$Z|K zy@e`q{X97Lhu4vSi@@v_T`h0(+U_i z(s4WNySO$1VU#PfBd|Fm*2#NmZN_eFyW4|tl)crv7EQ!N=c{$LrL7iGIm$a?y zD45UnE0|33JIXHOT%cg>lH%yfH9&JOb|-A0co{IhXv<`N<9J~WNq zDpQWcWoOu|ec?e6pv0Rh`+ZiX6nJ|os>zO7RRw0gMw>-kI~)vu&$HIn!z}aRZmY<0 zhw*Y?B5|VDH>>3i)1c>98$T4Nsf~d{3WaKKf%X%2lQ1F?Qc}LM-ZQ|y<`L!zN&J0P zB8WS6VnTS=m;)DK4foi@ycJYTCoY3@?#RNCMK{(~rI?vJdHmx0!hr*~ zmLM7eIU$G!F|1;sIz2R~CrbHTks@%Ac2O-S`n$OYZJtn~MSuaaiVPLArYHqifrTNR z>l-(7J~avaaIiKw8u#O+DrAyO_VQs(DJV``qS`fFaQo?1CA07MtcginilKUhq&UC2 z?XbyjrY~RN(KH!Nh7QCcu8zmnSqBko{5=L#jF&NDw#MbJ@+MaeH8Bw- zmG=!-B^qw-c#zDUhReGX@a*&?0iDHFr1^O2I0RX<=Y(l;969gWK4r9`wfB!V=QlpC z**YN`7obN<<-)1N{2VZc#MPg??w&J;J|~2uAc2m%)G}vXDPGtu{K|tSJiC{rwkQE$ z9&ja(T4MTPw%$%+{*JPu`H`KYAB0pgA_(C*Qi z8*5+DTSRrL*k{%Ctdzqx2I)@KE3YQf9l2b>4E14gGTG0snRta)h2)tYoX4W-h4cfO zcY5>FjNX{p(WKtpkXcBU;(5x%Bnd`+#$>;Mc`c{(duAM#A-0Vi{ku|E#o4Q%i93w4gX zYn~uU8e}E^HECJc|4Y)UdODaAF=#3nS(zHUz%Zz|8oB&)MBLuV_HX|FUH@|i6AXi* zs+cDIUua`0Z)j^u1fXZI`Fn<|lc_!vqrTbSVdwukz@pDc?_gp^^`ECH8k(ERyV@H4 zMMeMTm89&<>_sh&U5MD&{{9_h7zSZsdk-RQ#=kqPteiwFEbO{43=&TEt`0 z+0@zI)yde@ndl$DOU%PXLdE4T!usc)A>%(cB0~T80b|3z>%WMLpa1V2*tz^YLd0N3 z$4JLW#P*MSSN`Xr{|maYakBi6l`1Pag(nu32`Rw)D}pL-G|Swk<_ZIvm{pErwh;b3wZKv3UDi!g0``kFmfRSr)Dobl_)! z&<#i@f3K3IWNuBaU;(g)#4qJ0@$FLt4abiLR)1GaT~06b(RdQ1=WpDu;*Ek6EBVJ~ z47lLbWejV5gZ|Xl)cR?nGlkF|L!zL#^^oBAA(A=ufGoD(WyT4*Dfw|E zyj+Q0wPv=eY0c{0jB9j^ZE0ze+32VylVAQuMS-bwlXw||M;bI7y*F+YtzKu_N1cLA zFT!8tHr+Jo{M1g2{47pwL8hyHQV1sDOy#rgtX0rmY%Ow(pX|p=05b-w%X+wOSDBPA}i!#(}I~ZX&4J#gFHi@MBJP!SgmI zgO<71B%bRp()QkJS>GLKXu&TZEY_NPG`_xh96$kL5# zvl}Er3h~Y{8kegJB#&*bhycb>br<>kx_ z=$5Dvmo=zdK-TCH12XQ};Bz_7suyLd**A>}T42Qf$#B5Vx)X)^MYz^h+&ZwA{}GG` z_U%-A5vwY5@75K6W2F^%8wA@97WK$y!OFE230LDJ^h?bL&*gcek+9*CVc!`Ms&l<$ zIpH2>g$P~z%#19sjv$zcPpIVUwY@kk>MbQ6s@j>%_?3A7uFT1g`C+(|(RvcbJ-Va+ zWcWnuB&AN3wxTUIzZvTR&DFo@W4_hZL*MZ>uk`#CJj&Ut=ida8>uN6+p*nh^!t@_Xckf3luAZA0pp+k`n zBBL_l7=(ur8Ia^g3nKNG5C>L-)S!bJ6}m-2#jj$ZBje1MBgrdKll&@0p3Se5@j2TH zvsIXx`#d}2^0mL7-1Oe*xOwStKADOm%6HHbCR#~KPc-XUsW-)mzZ5LoVl%ZXi@a7C zC1Lgs52nuX-I?U_J&~t`G0xU&wI2@L*XCm(IQ+9E`nI)DEPwCjv3oaxH*28XV`)=s z$C6slpY^n8$s%(?S!6(c!J_FtoyKO0qEwjslw8?iCZ8do&A>Kg=&K=_`!Tz?20Eo5 z@{Pbyc0sbh=x8C*6uy8><-{h^FIsj*6tYcoq3k6Ob;@^?bIvE9i*G%}#F=s}A;Q&) zPRQp1{D?)u@6VD*F|JgcM%EmL^#o^#EurnQi%`4co93Uz$J4?zvKox9EpXc(@Ff9h zC3>Wpzo(^T8c>7L)j=w`f}tApVQAq|QyiQ!xKC3g4_xesNEkQ_rZUsMV1BG4Y^ypL z&E}cK(p4Zn@%tMoHjLyX=kW0F*qlmCh45;{(bjiJD7xdwgS!Y!6)c&=p!1bhoc{DP zYHZzd>TnGNU?4^UHR&sXs#p{WafTCNQgubE3CxDd8H(xUWoM`EFOu#TT&&Gzm&$%h zj}RrYaj|u=NgAV4+6^5;t}zmnC35E`iOMrfId!&;Z}@85uWZcyY{=J_7QIOZjmHp1 zX(Be;gPQ>b*-*lwoGp-u>zBk7Q#ln=8ks$mBt48145Gc3tK4S5Q;+Le%2DWJ;F~ZP zM>olIWg6%(&_5w}1KbUJ_(xpY>j=Y~tvaf9kqq!iENWjN3oV@8eRd;5>twJ zd|y}1=xqf`ldu{fgc>6ZXrv1zLT-H9WGq?qez|CY`a?r=l+gN~$JiaqZ=(E=`b4XR zoNE$073)e=In{$B$Vl~M!!X;P&t3<{Ro>UDx!@;`Xu)!rc$W}++9X@J_unfk0TSex zVpic41mttW&d8M$*n*iQnGmEMfdDd3qo$1Hjpiy7WWxgXXl^H7tKA&PX_&HVpTcgH z)Ils{0V`Apg4Iu1-w&1zL<`t+<&N^2#UmcrrK1@E_1vb!3|cobC#%<~9|N7sjStd! z+pJ_8Tj4)kSzb{W-k-|{o3?V~ZcL=EuA`(}#et5+Tw6*~cW2@kdB+u@85_{1j&#^l zSLqz|rlv(-Jkah8)xnE!3O1!+C}L3}3R3b@mm3Ukq2G1L)-#@X+$!~ZoI}@@^u%ll zvy{|i2>sQY8XHSfGWOIa#yM;N`szhpKXjFpx-7-Sp1@Xe$Qimmo@Hd7TN4m9a@sxa zRF4dq${IU6lgLFQcCZvJI2z-sqmQjgux-K%hZZS@Bc+VGJw$n{@t5U0+S})KL3KJ3 z6E@a`|De4NaViad)?a*DJez+kd>zQ$;*^Lrtwj zn=pMGW_`8fmW9ifllr-zv6UB18Btmf+2jmh^fZU2EDYFqim=|Qrw%t~y8vSzMq#W3 ztK^NyOly-*lNL|QM+>^}NM$%hQ`QFmTv+(l@XOaM2+ZM@_2}huoQrvdkM_E830<3v z^=D>e$0%c#qneinBkZb}?5g>e5=fcPhH16;Rs>U*{iH4n!C=A&O%sc35?kkN?j*-8 z%lJe4%;A(wVD17r$ZVBg^2>U_vckeh5B?FJP9&!}4VGDi#_ZkRu~IxoUyhu6i~?C+ z`l63re8yVNPJog~j=kxH<~@ZjpSPT8DIM<^O^-aOE_)w-&SqWEk2|J=3GycL$Sa~- zhEP6v$NZa^>R4Tch_mdF(RXLWC$YTKb>1$?#rYDicu(dLKbFC;mCcH1WAUL!>IvS& zzAT7{Bh4X6k!>(5*4Rbw2cH-NdgEo$hB&E(S3Be`NpAo=fBB*0m5ogyY-3~*M8VP)L)+F15hgbH(y7a4o zkmf(akr0KMvB+ZISCTBNmxj-izE?z-fzEgD{Adg;A=ItE8}KfG@Rif$Zd|$LiEVay z+go?4cU3hJTD4RcnZ9`;;m^rHLvW8bl83ZL2aA9eBx>L`Wf$g~%RD6dpB|!J+V&Tds9(h!uS3);t*HMh*vU_9a zb0HLoxFfo64Xl9icRr|)^f?k$7?D1U zkb&X1Lk?sPVXQOZQ_4x;?^2FwYM)Yv;UGl3-xY`@=-Vv^UCdeKBl>9a_qU0r7Tk^% zHq-;*+K%sA9-caTTOOSSx6S>z=%0nNrvr5%qMovO#K``SyQTemN9>-f;T*<}l6&yL z6?8on&eB^*;112Z{GJ-n3kb^IS>I2muT;9B&v1eEd_$A;=c3L(y!*zqWm6+{ILHd1LK<`~Lb?_JpQklvHZRpT$) zZP*ZQx?i5d#FU$7Bq#@BL;}YKlf^GJgmJsbenA=t zfC<&+;tsJrOuoN>$g}$|eY4<8b0QWHU(|R*V2MKTBj7Py(CY>&-A?QV>QNdtu?wyc zm{$VH*WO`@$k4uHk-D|jIv0c6-gX2ZG&dDpeGRq726GKnNL>gZlOPWFq*&X#&zC_8 zmnEKy1f$8y5-Jh)LCSVU8j;QtrexrDD(0phyf0kk90YKp<)dHn_EsAhS2yEfnTFky zDEC=~C#!?Q#x@U<2orA#rU^q5EDQBr28_XGXLD-^!mYv#byN{Iu|k0s5}gOTzjDtV z_~*^d!0%FO_X~U@mja*rSA5L=4~G5U@G%Dy=l@!z8&V&$+h9cMx}fo>fYXG-RFa7% z&?_M3A0*mJVrCHz7sIo%|&jfEBh zgI($^)yc~_yx)9dZjqnX2?6vGLsMn!kd9+Lw+ZS2YH^ua_4BQH64iLyvi)~{23>|g zIfgnXjn_Gdh@fDe)l2L{oo|SJex-e}X8qi&WXiG}kZ=w& z2XHFhh6LUK-Z1$6+U?SG#pc*E+DO|LN0T1gijA8ajNL9QX8HRsr+y>0?JU0;2G6l~ z3d12J?7Bta+5_DGd|QziGJKBdus0W3vC771YIi(Y^4D|c9v_r^;BQq5Uzhi|vj1rbB^*5;ZP(7>t?K|7KE&Uq+FV6;+zufUHT zO*0%~P#P*So)esh#VMdT#AxEM1W6YZTE}*y^cT3fbS;KltxqIw-Q8mSE zy9&zo%hism1z8l?XPeV!8w;KZSkXON2?-lYZzxN132#^y`%oKXi6-A|3YU$sJoNK? zNPfu@kj*Fm(e)VUn+o|Ip$)R{uJ#s}!?(L;sV@!5fpIJQlanRLl`HS3?&eRC@-h@p zH+-1}bs@C#!ciKQ=tirC=A@;3*=tqWCoR+dn@C^nwA(s~PWI2cnaoqvn zc(N`xIaiv_81Q%mHI&8hD=JZp*C29JnASBW00Y5-LCUD0la-#xO*hRiQ#BJH_c>~J zWuSxI|6K%I0u*#!4oWh(M=rUL<=X|DWVAHhrf5tsM4OJ^vr%F!q0F27jsT z{|9my$3LZp|EC7d+*5LxH!#kYtd#u1HVO^ zVSvK=<<@Wcxpr(^XNoF0Wz)Yn@=a59{J9XRz5Td|z3kWl|8ubux*PE!Q6MlkQ!)}7 zE9=nr=>d3V`7=(W_m1KxWx2YM8v48mWdarA4SESHq6$|SU68wGf0;TmD$6}mBu_{(4dfr^EC16z^~49@3eHgjkw3_q&%R}zvd-TYi|;*ZrZt2 zc6)!o{PX$reN^`y>q~H^X+9Wj?ILx=-M>2w^9|AaOdV-nu;19)7)cP!`&&41BpPz|exCI<{-{agd7+#R+!X8e7#>#cdm zSA;473C3OkiFC)X$nsmhWRjg-Ug)-KuU}aZP8?D8&f834b?lGP(x0)hQaLz~zLLuL zq$Ud@vpKPFXw+-?j8;dD zT_!rLtmq`cQ&TNSMeblC*}Z~@HB_f7&9=TT8k%33zz7j*5)Gg5>4Now;56hOX-m-V z%7AmCV7T{v7~w4ojEIi_f2vodQAN8`*#Ozqt|;(ug8tv&Zql!DuKmLo(Cw~e#}f$* z1}baXCFxNy+~4$_eN;hv_Qd1n)|4k52wf*TRIg?euE0Io^|VPYke|t$Z{k&&LUs#Y zP^$&beaBhiT*okR#7M~Ltf-rW>MO?ZC&L@4Qd%{?nj&rvTGY0dNsB}s~SJ#)a!dK0awlZ%Q`$WbIjmx|74 zG<2wROr^h}hwoI;^(v|4rLo_jmdn|eD@u)TmUfD(HnqjIma7QDYr#R2D<`)`@`qld zkr;@}XsVRcax}@sDO2pBM=$D!>)4_SUZ5e9T8BD*C)6$1mEJTiX)ag&VP};|;d<_@ zB$rxSrenJpfYXG8+Vw40okp^FbM8r|Ew`z-ab&)j9(kG+q!%csPoz$vrTlE zgZQR-j;nzHGp5}BZ4ys8q2^F7^HqTUR=>U=+B<$kMHh>bL#O~^<-P{#l}^$}Jt_kc z^C!U&y59l&w9-c}ngICf@YP}>PZUTu5nz`GN@KTd?!3<)G;+6$#jpMi=6B$)fEyy6 zpQ%6W)C6jwwkwo!y=iV}f&;q;9DoEv2p{aVAq19`0)qaLuGIe+t##Qi5|?mRd3=;1 zWLwx0)+a)H#D`$cQ&=QiW5v8f{&S-m88r<*xs0f}fj0tdBeOc1F}%98$X{GXUKf`u z-B|4JsCasEV^y%52U^G^;x{<8 zlv8+0<|y1h$NOQerb{4CM}2aA;J(&rczm;|=x*AI(!E{n*x_^~MTH4qdpo4HkFIB2 zLl35>G!?zeId?XC@YHdL7@YhVZ#p?MOU0U)vx&+CXl|;_(Pns0;DDF3H>}e^oe)fn zh_jc7Kks!@j;1rY`XN8>^X!BVMtfYFuf|-7*+f;m{F&xLF|2;HL`+G{w+U5z zG@2HJDgQwUnySc0-Kr@N@z#6BJ&FTRe0vMyZObyds(T=$;=&tGg( zPNZ3a+vY1LOj;{`w+q7)Hyp2Nl^W?o+j4Wx4rgOL{R(k|R)*aG@0q~Oa5M4N%7oLO z(;c5p)g}EvWv(necGc9pO(G{U);0}yJR5AXZSN{y7m?GRUMQ%IPV-|^;>i&p?g!HH zq3p)t{^I@=w|1i5Tp;5EyeN*^k)12eK#2Avl;RJ>o-t@Vy#FHMur;q5lTNsXQwa9r zlHxf~f!CH>=z0w}nd!VdV6sN_y7y`zkmW~!V*kh#<6qPGGT31?$fA(LqIhA!+^efn zop}oQ18t>Zf7qc4Cpy7;stv9EVqm>F7-XS#ZvNhq`AdB8^!fV){MXa7oT!es(G)P! zR^uF&I7ew_5Vx5FJ%az$t-s?=ayk8XuH>=JYH(lr^V$ch;VK2dP;d@;1is{mUF?9} z*wf?-&GWJ{6A(w%LS1{^y#@9IynSKM6|;GmPVKzf!v2!}fhmj*(&8wO#|3^JRcOtu z6okP?qvs_sp$ZpXbVKdt>enH3^Dn@M&RO$%9cBMaCBvmV-Zz`U+L_lG8^S?K^oCJ2 zg)K@^mjOO+dhW&3AJbhTL^EUu%^{d$t1PEg&7PCwl&*IO=mK+18!?sbZbTo%{##0k zig~vH>TMoZw{2NVv^=|+ zH_LoxVd!Hv*c(xR{XWh;gF#EQx`c=5$9x7O_X z>ch4L6K_XAJ9pWtxV1MD|0ULWqZX0bdX;#|aA5raWm}i2mEZz{$v_5SNJ*AehtRr= zFI4e4lv8fBcux(oS0$YuRTOkP((J&E!jYUgNVkkP`Dy$_$kH%Q`%rdI^^kW@{Lpsa zw&>)|rjb12Zm&^ITqr*gB@@}kWqkJuzx`TCeSx`%76|fhV)_qr^S_g`|FlH^T}=OP z^MZ|u`M;SL-X5w;P5OV{r*p=PDY#hDgLx?o@39n#kSKzY1aGkRV4z82!@}9wN0ILO zz~Sy~z!HQHmyl|W;lD$|B@K^EiNXB!FJP6K3Y*C9DloM~d-I0_^jNz@R@ z{;Yql)$F*x@Lyy#Ec<=rH!fz74mV~uPI~lrTp!B zxTAMV-)hQoF{^13EHdQML^E0(qCGD2jrLk_t-7=@dKXl8t#9 z*Yg@-=`YhGj*<7*i4xhCM50{InyNV~PlOFatNDNU7}qWy7VZe|M)(a5-Ml_@imyz=Tsp0n6?EoP~H#UmGm15SuQi&YDHTG_e_TiNms z^Y+yx#zczjksxBCX^eeFV%9Ff3oKP*PrPQHa{4y->iX;rE*D8>zBnj<)ar^Hl)Q!6nkU{aYB!g^p+?oeBw?Y4s2c z9%D{i!_nFX+8ON-Ut`%hzvl#_rg*lfyc-LGAv$!@ym6Y?)bP-NFEuSQVhG8wLm`@%}1qStU-o~LDHRM*j=0MVJ5f#_M-uTf>)^YeibOkR)6 zaE%?`m!))XX%qLzbpqT9FM$tX-y)bnLv2<~GX}`fj(Yc488> zooL*01<`Tra+PeeGqg6Hk+98xa%EiA?0qyOnjz{sw&1)Rrr!ft^`(oM=;kCB5U}7V zvfs`7`AH4d(&lzI_nS>bxfAF2vm^<#_RSQd&Xuv2i#}z<7l3uS=X4pQE#gjyGnfIk?>9JU{b!$6C>B)Q6NZEGBML7>u&1GRMJ7{SNTh6iFiN=m# ztQV!WQ#^a5>3C$Gmv~gPpzIkeb)WxQ}5NLHe z3VKU4x}ML-D5A{^xU~ZZb~9tlH=Vu99?(HXm zgx8i^^v&Mdjaw|JOfIX0nma-vE|TL($_p-Af>P_0xdvst7@@qxOlwLL&j`6{PTjg; z^`2%;Dq08A(VNoz3|rh?by1n)1FD@J=oV>rydubV>=_Ov=GDN6D*Ggp7`pROslnamAdDo@2lj7;jW!OL69P!pD^(nrkmGkT$=UyeWeBOg!O1dFy zOVTV_RW!P`pr9<$ulD7YYTVj;F&0Z(>6o9&2f$0@Ar@)fDh^78cD9Sd2q~LP-SHaY z=qa0AUaCzDtwy!>*9@(>^Ng0>rm@u|F26)3e;;>AyluOz_qtn?Mh>mkv7gU&4b z!VkY|vohl{bLb}9?j?T|*sp`gIG@p99(2(PVzLJ}W*8HpdH%1r)JlN7y~Y3qyU)HN zOySZ;54xYZUYX6yJPsnnr@j8|cjkz1@4vYr^r>_-ej{>pNA+R)={O&p7k3=00rdp< zUkWJ0W&(e!?j_!}Du)SB`CRrL$uu093eY=_$TT?K6)4>sArVIRg98!Kr@e0_AU}6U zxPT3A@7`?u79%(4+b7pI8U-B}1Z%p{)!q)r?o{_t{Wr?D+Q1hyzk*w9puB**d*Rpu z48EnuN{|W+<;upP6y>&jFEsD~rbpF7W-qOu0nM-amIcUxzK$NVeme}&;v4i zd2h<0b@>}Q=u-*_63wr&R^Koee+q`-DmtFQvz7zG+Xu=aHGq(T`f}Sez60Iu$7~~u z6#Hv!!(1Fs;;h9k5b!R!=h>siU$fh?AIf_g>c`tcD$ehY>o#cMjRe23ZW`3z{N~hF zg}rGb8Va!ym=-A;b_XgL=Jb=oIFA&NgoV-p zG(05tgn;$)fFBs5mS_Z$k_m_&j1qf(das|tNrT4CjE9$^lTHR^N?BQDjHEa(RI)uQ zaSQ0zY>aYwY1$F!5yd$500b44DyQ20 zp(u>9kB$f92;+8bpi#@Dp-miRHTZ^9V9-P+SrG{I)T2dCHPW+=&)zXnH%ajxMmIfK zSsRMO%03$8BJ9TY*QB3u%6oNi63CW2IaqRG66oOlvTp24KgkJ%&p8TALn>!h!uITF z{W9h5i8f0~RAX*!l?w6yRMeE4nwXhbG6_kkxcm4xIUNrVp%I@q;etLM6?G?hgvA2&@5#G zwJ%7?x@DkZKlL`8BnoZ64gVKX)MMEs zW(i7ysRr0cc~pet`X6RQVlp`9`D_W-nHCyPcSoe&P5{GR7CUv0PkoRzak`t|bRe`h znDIqdWT8Jq!>`kvj^{*MBpoJOpEIycV`W`Ruul50N~Q7{7P19Flt|+vL^YN%nGU60 z&6J@rXPgaqVoJ$%%(1ZNM#(OOaF-?v17f4VB<6VW_EZ8~+9-k8Q2OFSi0zQgj*RZK zHj%Wc^b3quk|}7V#t|ZMlSF@;Mh(P}jq3GWBZZ*VX^y)Dl%m+~XG-~*7$>Rk8jS=2 z@OZ+_V(^FRY=DIhddS5|54{D@eSJZs$px4|sI8B1Frg5a)D9S7hxeSDxZ-MmHrofAHf}E`=Z!r*Q(E-&+YqR&lls-2Z-{gl` z>AGBvXxdJkC;;?&+!(#Twyj z1iVT_`C@IVy}yxhuj%zTUCO-x# zRVbXsiwouXlGg$&g)I@#+@3j!DrDk4X9vk+Q5*knk|h=@QDe7ZQUcukaO^Ky4CSuC+D!}lj`}#O_=}N zjQ`on35jes?pb{Tl}mGT;kzZ1zI+WOqKE8j+_$^qj{)qqz5S9uW3=p1_9F|Pon7HQ zQ|Gb0M=sqF0)@{mAAa1qQHihi*Y=bGd{O#?_SAZ22S-lzvU)JE&;v_G{JA<+6e~p^ ztDRZAvU5F}WWNsRP%{+e#r;5kd?QS1bZ=_^)9;RnAhE!gSKBA8CdH6D7+=}ZRV2Qe zS$E{&VpVr&qT}&#YTs~y=7<_Bap5+1qAAzI^W!QPS7Ch5#K*P8mn3K_RoCiU@}A_0 z*+~rVuo00khXo{C43C!dbRcat&z2i(s7kUX|Ba{^0AYgQrrpLuJcV7%6E&Jk_Dt6M zM;Yvv)-Hzu&H9ufPt??$AsexNtg-FGqVO@NZ8Z=6T%jwcvnfv>P$J0}PnYUlt>&6s zigCI^>JluZ3Gv}n_Mo>h)z=i8+-p?h`PHj+rIN6t%$@nTNqAMRv#AI5-cAOfKqz%* zN^<5Vvj+;(O1G9j!0t|1SB)m~d_18+v0UxBy1+FRBcH~&*wCkK4(FRqCDKtkgDR?W zNifBb&0c-OT1V}eA!Xc5A$OzmC18(`YiY9ur_$;Atbb`6AvbVt_(ru|Af3~7=_x>- z=60^iP`UAiYY>QIK9k)f6QvaiHzh*i!5j+{WP@B z5|8Oc?5#rs`Rgtn?tnny$bi)}Yb@c=L39eI=9&j+Al~d!{@owWVM6hSkkDu-sc>NZ z6y&-+QVFhz@B-f7_qsqsh@No*Pw|9b5%Og{+fwD$tQ$bepP9?un7ukur*7$AT~x5P zIo{ae%?plt#7;5;qxRIot5K%-QcpN zDd)WYx54Fs#wEBAqaxWv+pyK8c&u@gdlS$i&t;MzV)y>1nhcf}iM1X|cDxV5Qy|Cf zh0pq1vte(J`0Q2>y~Kh9Q1%;#0hsouAxJ!jasvb$q?k<4npJ074aLP#EV2W*jlbtc zZBTNq0x7eEJzhfB%o)8?KJX+eDH&s`l{)4dXaFT1)e|j)t1nnLO55$lSJCzB5zVO% z*Y8Z#F8Ob{TNaxWzIC+wSNpACx75yy-6Ulmwjjwz1TlMw_UJZmd7QWHU2%qR(y^qLQPBtU$%# zaI@-+J(5~-QbP^cXBO*XcGNWcs-6B6j}iCmxv3$zI?pNrcl~^Q+jHQyodu@Vv{S8C zXM@!;0(>uF?_gQs{393oQz2o9kJsXDP8RB%c4b3HFNtis1;D)P*2z68MZD!vxF*RR zYIFJI`t216xB2i!X!cT1f(S1N2;CO9z*jQXi@e*yI{Sy@4ma*}9If+}O46NCI$mP> z-KqM-q9%D+W++#K9G==yiSk`*>Ry+ zSQ4S{k)=s=j_K`i!cIDI`MycnUi7LH71z6;_k6#kPS1!twV?$Lq^w%5&WyL7ze+_c zJcA;d#RJym4_y!MZMoiHqXHl}{>@{}@o%gFR;K^;W4)yDAAMVYXk3!CBloB?sC*>n z1|{Lq#0-ByQbMxDqkeBT@sO(W^9_l#lG;88hbI9g5u5J(u^oVCd^0wn*Yb1gciT>D z>)s+M7FA`~3ZYj7X{e?-xxPf}mLD8f1^w>mRXrfT0W>w5GDA4HUeeq=yQAUiRlHduM>MF(VQh zFzv@cizN$^=v$C(259d5)}NPDyB&%pT&!82`Lj75+FR2JJJRaph*a^iYE4F^f&1@) zKFpS=SW*<_ZQA$p{B!CEb$uLboM5~82(twlp@|Z)nlD_fJyvZ`l3XG|dYiB85nhs< zGQOSd#9^YnA_Ath%F|J8ZKK(E9qd@ebRA^+_E@BY!Zs7?=fG5`kXlA#w9Dw?Fi8ar z&Ej&ui96(XEI2O`M}wQ*m@|B@&{+qG)pfNrOv6;@u=yXzt=n|mB-F_2^s#X;sSvwJ zKw0$#I7?uX-Qffl42L}x7+GdjByKpLa2!hDxg84;v2t)AQ@HTiJDH?A>g>U*Mx-Zu z%rR4=-|U5J!H|tv$x4AqR^c4)m@+JG^MqU_0-j0cbUZIhF18_-#V@h=beAbFM7YuR3Y?* zJUpkK6$gC@CHA0E{4Lib1AXtNY-+=>sFC0$$e71Og{OOPVRPE-z(N%uJT|<5qa7C; z2UKH*(lSOfl4l7`i^ixBCNzUB-H+fTpGO%CkU0OO4?$1A@H;>+@4{dG*QDY4Hy$Mu zBMaOAmI)7ONZD_2qII8W+yX!;CPs9roFpSHnVg{@fcBOM(pSYGcvQCurhXs15sgID zm8c_Pncs>yd1n z*#4B9kff?Q>(Q!LK)2@WR#B>2=&5d9kaR9iQDjZG>|i+0$de_4&7>Vuhh=|gf~DNp zYL@(bAs+XzXqoWzsmze`SZ_4!s<_!`b=`su6TH4oQE+ue-R9TWa20LUTyAkyu|01- zLvj=rVy+qwI5FO+ym&Qo&CrsebDl@0hDV);n6J@!fbl0H_I()(&tvFgf))g;RTdSW zqoGenrm&&z;X(j|qR1xuCX0oC`Wx&{T9DZ92srs8k0d@^lwE=>P~5!J$FlO0)ySq% zc;15Kgi9wTS^YBXFgS%sNdqZWGd7Q2hJ;O}eN)LiYGuo8tWcaW=)*Us-s_NR!garF zgrH5VwUbojA}$BSnW>7HGU|FX;Kz?{;S4I`yEBC$t}6s&N@spC4Wh0_xJMa!F?GrO ziFEN~w1o%>baO8BQ#rwbowUY~WKEg@#a5kir6IIdR!aSJ2LhP-KeBSGuFF_c->N)x zQ4r2K#RU7LCvj}_$A39P@a?{_@%6UNgT_~zqj{b<9!HTc8q!}<=j5pv#Y=rnIxoTP z6&3{MSVaw54dWwY=@oeq;dF>XgGv_6_iGEbg3S}sR_V||MMW)wdNY^Bid*~yfn-`u zeY1~BzRd~cyBo6@90aSK2|{6p`AVmt$<^Gui=1Idmiz^R)_~K#*~kp@+L5jZ-`u)M zIwrFGXQoCzSN9!&X1}pvg^E_`-&i4M-fR}zw|VUGM=Meq80ghtvuke^>!Ll$ul zL&9-_>E(||>(Z){LzU9hEA5L@KF2uFpE(YCg1@F(+v;vYv)0+Gi zoOP(Kq&H$}I}GpmKzssN$G63qii2ktJ$#Tono-C4f}Me;&WrB@RR0HU=NR1C_ip*v z{KmFz+ji2i?WAMdwrzFXv2EM7)zS2S=H98nZ|dHunt6B5tFxnyFiPL zGdeF6YU<+M^Xla0`sxo=^*5cmErRCwdyN+Toi_1fzM9vDqrt`Fp~nO0Rjmfy1^Kmq z1YqOnncXOW@o2W7mp9hfhBLa=YB?akqqhAF=9U;G^^Q4FM-_u>8l%OMc>Jh&56N7u z628uXjC2~S;OL-i-y(b@ZsFl-s_BfM zaz&$CYq}lo&x-vkh^IR5z@zVnE&T)}d_5xaWrJI|pvwW|GjLxF9o$83!KvHjH7=_! zsS1`pi^How0LBW?SI(tWq@O&Gd~fdlAsXg~j5y705MA#@@v{%F5rmI{Ooe>fj%q@` zG3gr^hkmH`e=jXejQ_Gr{x5g+oXo8M=^t{Jx~{?oBdX6$-Dpu2+i+ezi>h2ce3P8W z!f8`jzli^%h&9S$aNO7XTAO@kaud=pI;qWxUY@fJ!A`QfN}PKc-~Rf6(#@_YV;lfC zG2XK%qAVRF7!VcjQG{b3ow)JllWFdwuN)HUlLw$jy3mj9#zcJxD`{;onEiBIXW`4U zmNkI_%0o%#+2$~hPG2YJ@xIy5-^9VlPx{#$?L_#acx>_5J<(vO;k0k zL1u(GfDHVWvf?^ht^gQ;iUkWMNl_&7jxtGz5S(N_G9@7Ja~)mUL6MJrt_3C?=eHro z`FVZ#?3r-aMX5$4=@9VTmQ}c~96Xi)LhN-ZsKzObGaM|1cPm3RN+x}I8phkO{OWp_ zr^kfZ8TF23+K8W@(UlpK_6siCrm#D$(ON>{qOqEVU$xr39Z2ZFeLc}eC465}I(bLh z`X4Hr8o2Kx2)t}ci@yV(9@u%m5f*&0>h*|#gJT-i^1C9_4Q#;*sL)Df9ei3N*X zAe;P)U*ZTw=}ZXz=4T=TCdZ(MEOhaVG4mFdgvPLysFCVEl}c~{7pzkI7rfm8>4ubg z=663@NPmt z7_-G2wAkURr@Qxrxg9t4}B~zGgW1qdZ(+tLYVrxVkg!Y*CO?YMPrhb@&Iz+%$Hz zF5%6tN0J;){4t(>K*GhpCH`q4{>yaqzbwSREbqT>Vid{w@HVt#P*3`Z&p>5ir@}{Ly*DwN9A8L}U*qv;0YKZntpdoP< z;j`iM%Wmo2K!>YGN8%7Z|Lt*Mz#(l9hcJWSZGHp?Gj3>+yW9?b?0^Aj9Z#oA7=zHm zv^e~c>+;T3rQCs1MTyDqHCI@wg#}NTG)ln~(@DG^+R3coEGae~J0_9qqbW2p749|e zecc_dZ_wFIzO%dNv)5VDkFx#T$U0ZR(st5n6xuhzu#iOnHzmw!FX&lMCLdvBanaD# zg46SwU$>tQ{Wb*2k7#LV2i@do$pI3WqD%l9^S5-3J{4)!x`(+7O7pMYBm-D-#Sq?b zba=OQc4?m*(Cu{?#&TM_8*o}+t2oP_^FYq1Dhb??1q~WzYstpjqd~ zqa?E(AL~*BA}g!!fzY6wG+s4JnO-7-nLiHxOmb`Ir*jY%pIV&mDahdI>5V z6!I82$f=w|q-o77x7L+e{h1#%0z)2a&mssv-Z&TsUwD%|7j^MFXWKcJEzt2!bLp36 zfci-&bEZUlLX*XDBHqRCFM_}pvFa{Av0m_(i&y}U^b=vFj^Nm=k9>vBjkESzmpWX_% zt{HkdVl7q75b?qC0lmNQ(Y+xzU^BZJvk8ai)i8exlLP@I$F;vHJt{P+AU;@2C2DWq z`w7w-!T1LT%H8?BCxWi)eQ9?L*Tt{ShNerzgwnDi3~{AX1#$2;k!OYCQOngz#0kRA+j%nM6q|+!hC6zcfZ6jl>!{E^ z4T7Tz#GMMsx* zt~@^8zdw^F3s{0sRVVxz(Xl)4@*34T4=2B!(Q*k0zQ2B+2>7PIp4_8OTHN0_JwLKS ztK4h=^?e@Xjg6Fzn7VU7OTGv_67|Y8UJ-d>Y0p$PXnA=heh17q<299JpmnF2hCMYj zG^f>ka{7Z{zW>gcii-h9ewsUQ#ZEE8UTmWhF-4z>8rt}N5l_U<{Mu(8t1B8qmn+%XRICm3NW)TFaL)lnZMOX$4e+6(gJuS~mW zlHg|vXd1S?n|7`z14K*3(UwBYUnP^NjV(RCVHjip5{lF!WMJiHiV(TBka z55SE(0&$S`GsT3x7X1Li0~!DYtG~Y}bP=Hlb8Z4G1A$(wpN|(hC~&?IDX5%eNj#;P z3a&QHHY#|wa6A(Jf?_=-ckOBXSXi)ABifQSGFpNAuQW+UuL3n>wirRQKoopsWbI{z zXeJS?A-Wz#WyLI-c9XZz!7%?w{{B~${{G@H*4f(kQ)KKpBl8?gSQwo|q#`0Z-CHE% zwSfA|-XA|RPNMuF0!aB4C_ybLzdNVZMZ&vmPMxtl&x{Jt12ojn1#jdgj^s2=#F|@J z3lGQI2wZO8zop-{%%hz^;^zvJL+UX^z&x1NP*b-h1ZWj)1V;B*o(+%=C)^(eR9rA zWA=h-w}>11Qo>X`+OSU4;mp!QM>Dc!)R=wB$iA6b8g*utp#ISCBMa|f*M_A=%uK9J zD>dtB{{jh!xAGD@I~LLp9_Y#t>_TFcN=BI2NQ%qs`X|@#-zFxZVW%W9b74JfXNh1s z^O&l7w4($;h^6YyKAlPABICwhD`}c8x`jf(3V<7*FcR}9Ko_M=y50DjE|7hL+Cop& zyc4=E)^tg6uX|4Gc`jeZW=M~0)zZfVNv|lAX~NF{WOvhNU~#B%5--sCx0`2#CM6zT&`;jB^p(6gXH0n{HbwW~rmlawUSx4D)Q z*F;Hqu)x38@i*`XUH?b=CblhQRVtIXJbnB%=M8kKg|c%{jmXZfqPC{}>Y;M(e72C# z$d<2JVl5tVCg(N3^MNZK^_xM`TzxV>-;~|T&PDDB162rlk*W8gOTR@o@vSgl>9y2y zF1gD}{oY;1+asaPKA}xKe^(J^c5tm2Q1vf*vP;7^Y(r--`{cOp%7p%C376?xe`doD z>&na`YJbmtjYd8L?ZG`59zh#PK=rNcl-ueEFE11c8F#H4aX!;P|7B3GIv8A(=c{|p zvo)Os64dDuu>Z>?kj|n3G_1ZgWZN$`@Tp}J!v?yq7^bRBg{eSgE4SDxr*-WN9D5pH zyP{idExLKB8m9_zyyng7CCO5C&roC}k49NB!-g?uzCY!SS!x+|^GEHb$s6u?pGzkX z3&Y^23(SrX^efk0);gP?=kMhh9L9JMg63va3IZD3U8qiN0e5PiHJ3L>Z?9W^EW=($ zZeG;B#w^mFVlfF{fh5YWk{Dxi1(cV5hWfbQAG^fv zs=VJc5nY84JaP6(d)C*k*R)1a{ZP zx(AxyAs;nnc=+~SwU%uJUD7W-J2LS~U#q%UJzi@a`)*U)b}v1C@orxz@#jk&Ul+txF4cy97F&L3RI7QJMaM3T9&u z$?Rk^aaS=}S})SCefbJHw#deqDahdDr+H1cam~V7!~hN9e@veD;a)wNH+#o)oeW;U zi9|vfKquy#gn)^GkcKMy(9I1Jpw;-J>?vq193FwhNRwRt`D!wMsdAbfj7L{cLk;78 z;k0mIF=E4o>2X8M1o{0c5e2DIf#182gB)|>4}L&N2=}0b`pcjH2b?Pt)4%RN z{@;MEOice3tNouzS5{Vb*8lLVn4O|67f06S*tt?yesF1+`>JMgXVuF{CNXoQoS!9Sc26T^X0rHk6<+rF@p|&W@r^ev@cmO~&#~3_ zI2nJ1&A0U#iY$*nr7F%TPr#SokF(!W;QNih+&%drujqB-?uKFH#Sb^o;p;|edMC#Z zN4;iA;yuNg@B1;OWnqheujJuEGY?#UI`O)uebB4wz3$=V)Fb+NhaZoL?^-k4Z}8c| z(ti8&~b5j35?~$@}GuK>{vLRmbovWr74Q=DA$uU|__k=Ie7IbG!9e z@tvfU6T(9`uA@Afs{F6F0;Mz~c-b0s;gw`?DuyT@T3vxdeM@_jQ=CWh#_<620@N;h=U|wq z8V%FW_*A7bLxBr*pAX_kvrQOSZChnU*STc@UmkAqnR}HM`uf8hR-lQ-95Z8-YHR;p z@!v15oH&m#KVD3<@w7lR#DCb#32L3lyPW4X>)g9U5Y zuTE}&E#@o5sY>oTtSsj$9+w_+jzibzp=3@M$BN5!NFPH#nk$ zfa!2`UqYB!KbUI5bkjXlUlbV}cS%y{o1c#3#aS$4wkM*Ql~8-KrI5Q*n$I}k?Xv$l zf41ULEt5%2(C?+^C$^5-^o4p@%|&hGwIJ%`m&|UoJ@UD1;C(4*ZR`%Uv%?;+F6Ni?m zbF>6QI$~GSsYS)0Udt|0I~7T~Fj~*1rB0cjqJ`gf<8LR$nH*GT8Umta`Q>S^PC6H? z<7A^gYo_V3UbF@Rc;h9zxU8Jo*yLZnQ`fnz*atckz7x`Q4YT7f?$>U_uOD)$o_^Rq&~@_7q?h=KQx&Ubnr-^oR#K@c??V-& z1u5Z@_NM2A@i9;q!;Ye*u;H$GwJ}&`U3TDP6O!vK!WorQ{atNOk^MiO*!}3yPoCV~ zoX14!?Y};9QQ?LyB9`BJ*OOF|$h7oFB7l7d-A5wjJNb=jcy#MTKEDQbzHcs09uNt9 z{|vb8eBLeC`-O%LUuo7o^vCyn->&$1f9A~y_`WdtaejY?Jv^k%=nH&5-3Z93O_Hw5 z&da{}(v;Jpoo3Aa@QiI47GVw5dCsQB%DzTNA=Dy0@3r|B@Dx>WK@q5j6>FHwI>R@)u>;#Wp3DGM^A~MW& z&YNWKDB6yLjAqdv=p*!=r6few0N52)Q(otia=E(!i2gjw)}X^gXF&nagFo20djMBm64C^@Edh zYWg9V35N!=C}(*U?e-b(vM;h|^tjDmOB6UGL<9Tk3g$zKOQqU?ey~y-6&qmN)8mRh zu^@=eY|_YqE#$Z+k3^$hDNglZG|rIYFB@A2+~GdlszrM&%iIX7&6DMiwktKcYp(n4 z(_Y)$;6{Da&2B8bw#d1oP9w9oTg972xn8JR3LWmVXTDQpj3hppfvAq@H6M@lcIyTE z;}J$H9dhZ2634LB$&oHec(J3JgH{1sm4C3o2D0Wn2q!LB<+uFm!CJLEML7d7ww>6g8Wzc3}&@w^2uD`E%N7S22tRFjYk##OQ?hIWxeRb?aeb&giI`b%+2)3SQ`<~f?f)*U(>}ULDas4HD^(<$ z;?l)Sla1{@#o(hn7+(h)f?3Vrw6D2H?b;8*2E_K^eN^g15&aT^2W}ysCMnRE8ee{F z|G@raelR=k*4Xz$Y(6kCcGF|s=`5!te~wSAKV626sS*7;ni$fEx(v9H z$h}T(M7P(A(A>!QY?y3saDF(*ZVWwSkTnZ83|uR?X3$SgQZkrkIdz(6drv$r7rUiM z+X0w}mSg~@Kp%sxd=U@3N;m{eB_seXATjJz@YW*P4%)vZ7W3|v^vfvvN0`gHN5nSl z&Zl?Thcow{fzy|Kz@#bL1#<<P@VMx=u0;BcM~&!PeFC0 zGenX166FFDv6f5s-?952AR6DJiRhhR)w7U?2Lm-(*48KiflKm*3MkxLYd~xKswTn zh9m+EEnvT8q0>T7QB|dtkZ)+IHo?^!*oKmyGGq>iN;~Zoi(}JRLdYM3^+eFnD@WVG z<*@y!=stjZSxHZXWvFgzfV8j^$K-it_bl8!kmyQ&l_dw|SBR8!@vZRR(j%*%NA3rt z&=NQT^Kq%454ws<;{$u;Vkue0XqVNDyKSd#d%#O;VHGe!e zvJYC~lTpq%Lg8g(1~KLrtsd?7N{~C=bn!8PWS;?9_AccH>j5QqC_}_17*XK6MYAqY zt$L9C5L~5IH6fT!26jCgYMG5V`kJHr zd6o_2!jT;r_~-0TQ6}w<(Tf~j)myg)MHu%{G>QZdv3@>*Y%4q-4s8m#b) zwHYX$OKSC+58+@9gQUu}$!#X@6yfaafn^0;y%G0 zKm+11Bu>y5rnVf637-cV8>`Sqhcnc#|1RM-s7>Bm2;z_tj6{2{((Bw;^JB=LYdaE6 zLza9-k;hP6SiNzK3b?(6{r0X3V@NK8F)oah?&5bl$U;p}(ozov*J z(KR9|1pF#sbj}ST`INK>%b?}}Bh=C8TnGV8 ztBz(EB}1YI`%Rd+;S1*s`fZqHVw~NabbaiOTHeZ{R#e=?(maJu3p`avBBT{dqVu%M zQS}rNHQ?MJH_qVB#4V^+!3Z-KM}O23oYz zu2C!dSHB;$KF&ir)zQBW-5AD6Z9CDqXzsP5&a^tw-;fB|4*q7%M6D=8wYt;AQTACU z&|cu@iTAA!Su;UwS~kn$wz<``!bcz2Y1i_Y2x?f89e}r3q_yuLb`c{fTT5a7O*{;eOB#Wi{x6yujJ~ z1UD4D-p)?@JTZy>n+Bj=m?~&DXUO3yGg^Ipn9`^X!!%~6iyN4v4L90P+Hx!n9nAE+ z7D11IA-X~jG}jzn;{jDgNSnKlmPcC(>nkDSmMEYP|l ze0QI5&_M|(w2GMxy!^>IG>QdfpjmJU*KM2gSB5AZOp}yj1lqexXcTtwZ+2NWta5Po zK1Zs4JzNZABFv0Krj9Bj&D{Q$0q4jwq~ATX4&%E*w1chVs@VZG*I$i1M`T`BQM$woNt3K^7V0EjX%C@+SkPHa9d>?_)RcOYkn2d}9y97m9w5S2t0N zbI$|Hs;Cd%wJqn~YJ|TsFtg*Lb9WU&prSo=KPd4bvG$jz(*iUBDiEsum?3sQmb(6k zyzmy;Faa(Ttzu;^rK>@xhcCw*$P$aV-v7sbA^5zvFq*Uu0i3L z(bzO{abT>H`_6QHKPLh-^9cC7rtJ`cZ@$H{iQSHFFz}1>X#Z(4{zo10-y&d`{#u~^ zkCXA=^Gev6S=j&QypkV(^Gd{01zcuoHg2vr>f+<&=RH_SI{`dkP@?n1gh)eBb3_)b z0p$BZa*V{n27!bTgqTQBk-%Cp;k^bXn39CVl7~$3O02I_)$OlPh1OB0;*P@Qmu+~9 zcs(v(YXZ+3Hyf3;UiN%;OK&+Nb?5AiK#ctW!Q1I<73HtK%P9)rNjjkU$Ba1M%aHf| z24I^xAlc;99Uk-RS&3`NUn+R6+wZ%9^Gzq$e?oKJ=6KF8HOYiNK^0WCwxw+c%v6F* ztL(6rIx2FRy`~4^wx6=kXn?}f&KK}$vot||IWa5|l>E_kmd2+`OQUkG*p_#(e-mjO zmpJP#k&vJO%7X_aM{>6%bHq1spW-l1Xb86TKXytd5_L86dE=E|?L9k$F63IgkgcQ0 zn4Z@5u3kSB%A0@Qb%Z6e8r(wr^XBA{Ee7~|!G)So4H7H}jpi#T@Tl11roa0-zOY zEr!FiWYQVHu30hTfvs^>NNb6EHr@nzN|_N>5#+{}(+o(>Lzb*oos^iuXLbtBD}bI! zfWY#iha00e0Tr6UalAtAwFQsfqTTH2J%Sh9_RkGhHN-%4fuMo zTUHnGQCzy2SW_=l+)L$*DWtLDHB$ ztP1N)(~2pY7(}F7&itg&o1+4+VzUPY7!hd;%xj?z$w83 z2YL~oD}7Lovq$uwPM61A&IgKQOrbS=e(&^Kork+= zhq}Jk749!K>&Nn7eU_|m*Ea;;FuQ`zcmaSmN>P$fY{L6^{pJHBZ{g&HHuC!~b1Kyl z+N%y$*9vnUo4DqrH}69o%>jc~i)U-LQ&a<*Vv;S6q$0D_&3mUOz8k*wUq0&?lWf=1 zm~(B$Be8EbSEF1w6w`G$&Ie}~ANrjhD>6rp`&HpNVM#^4Bdz`@;$TMAI`#t^z0+Ec zY~o4Vf+qPIc*}S6%{*l(zF(J6Ez^1c!YE{fEzM2l3uwY>-fIk@|woUd;rSB%O5JH%Sz-wpVFMN1qBqE};CVBpM>&~a1Tp+UP)FiZY-frSB=+z`dx$W>6E7i##D{rbHLtqRl zAC~xMVO2gUIK0qAb7ZacotjA`d8AM*)17U3jwa!@IOal~HH#xz46YzYR8317fX_P} zj2{R)-VEwS9<;?zIF;zQ+0had%dC{)KwwSeN2f@cUN`&@nbYY%mX8+QbZAW>^J1%< zdNFA+wl9o!(!R-5d0Z=KwI;!Qfi&3=V_$UsMhZFr{F*&>>8gjJjOu$ z*n}f8PK)Dut4pj=rs!3^QWbYFZ~&D32y4}%`4k8bhBF3v+u4dISSc#sx+6qsgO2;d z&?}f>6gZu@O*fW*?6bJKAa+mL^l9F7Lc|4U*fide4#i(7m8I6fXvzOSURqOd{qq@(`s9zijX(28J@Nv749@BkORCJS;4Zz74|Vy^_}hus;m1q?(cnClHp}qFC)XC%vt04CWxP9p;mup^0~mt zBCJ(FHkiwwFt|FKiF0kzOQrEnCa|em5hmG|!_w)u$T|j#O}E7jjn+*!w$keu*!MTT zrUaRAP{6?s<^#`;Cu3K2jcpp4B;u26!+9nRi($7}&8^R^VaEoaZyUXA*hv`|ev@Mc z$wi^tt}boz9>+bz;wE7?-EOpt!3w~1X!hAt9=obc%0*RQ1S$c~FwoR7H=t`IWh}d7 zkSBp1Y-v@SzT7K^eV-itZC}}Zl=CcGC?t3C7@sZ1l)M;swVe7bqOuTEH^t)=*foV9 zxlx;Hv*lSXRM`nwSL1#F*sbh;0gcTH>R1%!gr{R>O|gqOH+iMhP`MhzapH1_WuXyQ zbHe*DeEfpY=W}H;)_43!d{yKHeCgdHV-fR;5z$)K3TF9|=lZ>!mFX{!FO`XRt9xL3 zddh2bvp2M9N(;E`^;1#LCmTdqAPXqlQ9;{LSQ4}MNfqPpn1Ja-Mqn-mvn`X0L`|2U z3JGi%3`vR-3<_P9vCXe#-E5vOR?l4|^`sXf%1ftnmVX@`A16Sj@`SlN)D8Ha&o1$q zgwJPWe^2^7Snyp%b3{zLPa#;ab6A@5hF!7${5|q{9*rS69a9l3T_UYfQpc={RVABp zOf8erJg#1%zD9#rkS@dIns`LftjPH>p!Cb=vo;53`D(rS8sHormDY{6!^o4{;c$N# z!XS_P-Jq9^WO&Dxpv&%<85I-$YRL`#hs1IOIs_O|BSZ5$vfqjlE*ZV(a4}%I_X$1g zZ}g_CBBNEX**p|o-5j>ZayWfMP762jyJc8UR{ZQ+EQ0Vm$hEiIXpGppUgaQ@t-0K? zt16vu2?37zcK`fP#_{m*Rvk^P`GfgP^_BbxOLG$9HEEmgnnKd^fOtg0z_`^-0uPCS zl867vgOT1egJX#sN(sEG<0s!H&Jxr*Ml_a*CG*ySPzgGXst{t=J!U#95z9NTy?H(0d9M0oDzSZykgIp z#=#V+oW1br77Z3k%q zP}U~lujtDeX8Rj-dVx9H^=C^zw;x9PZVrr);*^1;t0eR=*pq!oo3?CP`!otc+d7C}m{yk8a_c+ns?`IVN*8zOYXct8p7O`9Efj7iQv#t+l!&=j-5`ujA5n=4)aSW*y zt=ZX?CEuKW(_~Dz`^uO^d!t`W4jZgD5&eUGLB48FmE86uha6hy?pdCm_hoY!N`@pa ztc40Yl<$cGZ#B~j5QyUwdB?V$+;*4Enj>g&B`p;Tr%F{yEX{E^IA;s!wuk(G>yI1S zHlK7T1wBiNNcu@32ZhjlFS|$^+2s07_*(<@4?kdgu6(*SdAyS?H6n2SrhxP_$gW%#AC>-T!gL*uI*mgfCBHIDPj0m87nx8j0% z-Cx&!y94ga1?a&H!T|HV9(ll1d3)o&%n!g*xocEdcr(}iTONFgZ;b;^K3?tVKgtmV zP+tQ;zg?KVt_Z)>cHdb)K8M^}KFNJunOb&&Z@O?Mc2HjJXmgQYV|!b{zr+l*@pAdm zW)xs~(c=7`52OM{Qa9e15WCSrYCz&(yj6CQ1H!<&iEiV2SHN4KcqwoF@v^FXIyDUz zzJfZXcE5bYyuXDudqlTiCHhWN zY9P5?JKW~*Z|?PKNSf!m?HCW7LCb-xCt^qh`hRKI#7iLjEYhG~P_t=W{; znQz(*|2Z*o_d&|rD84^2a!87t!M?)^z`3CHF6!lmwaZUqU)=lSqTbDqwxW4=Mz7Ox zOsG%eAZLrL?~JrUn_!)Hf45Ft4L_>z=Fr@$rhu?l1;)<>rU95t;n@2jQrD+!GFf z1>?6GdNcDL41WOQ-wZ+1eO1JmzUp@hFa`M*+YO3%_3wSZGJgG3x#JIL#5m|ur9$JB zF;Lu<4PXIFjUL>m@7#zM1Gz!v)HT>+C1JSiw-o=-RfYS`A-F+u=c)02$E0;QP%XW$ znByD@X_a%j-vB$#x>XNIvR8UD31}^MZ|vngA4B1^EF7ocax}^gQBZXZ1h)rpb|Z`| z?fnSgkPdo_(d9fQ+>Q?e4rl|B(7)L&(slQVjnTj9%~nFsMLDhCqlAq`O{a4hbig2( z3mFKj@cs=OW}5NJh}I~}$%@ZHciJ;O_z6wK@rys#6ZHATP#`bjrLkZpmlZqN*3q%(r2Lz9`muOc0$Ca_7ZgdNw7P!`= z(kAh&Y|)gG1;9dej!;oy;1R@yUNw+XrA!uoSKLZWh_=qjl93rrh|t=o@2G06_Zt@a zs}=mUjOtndcvn&#_aD?5mj9g?XCh=`M}Gp;tRGXd5+l@~@lp^WePoveDF4(n8X!stAn8DV zWkO_R|MKwg$sJKr7%;^E_kkmc6egLA{+)*08a1O9*nEDRl4{AIRMHN;s!CLN*tvm`;a5o7r z7>|Bkzh}x1mdT}bHRR`UNe&K7kSnSCMt(F-7>KUSj=bBO2^S$kAEfji1q6rSu7Mf$ z%dX83Ib;V!hV;^L`{|U3LjiUPOl(3TViIaHDrkQXAcJm2ioHB&*^f=b9>HCO2Q|b1 zOt)g5-n~lrAB3C0u1_L?cfsxhKo-duv`7y-y?GP>LL>vkutH#0MhVWqLxH)vNyf0A zX^oe-z;}>p(b_{uu<(zMj|W8W5=Jl5{-qm%M|}<2>RQ`^>XMo7jw3%oGO}U@AQDPy z1SHgy1XN(4A+kYWW#vNuUI9=n!QCF%HwJULU{C2|%-Dz;fMJvz|+9aZO5{f;Ww#xSq8Pn;!Dk=kV;4mnL4Xk?QO9O@(9nRPHVOz8F;C~+G4!qR zvN5wS-89>Z)i;JjX6UR+KcG2Zpcr8t`)r4=XZOcnZWBuxDT}$DJ!-DCcT~R4Y!43` z_M~Hq+0QiJ(hUMFJ6%ST9BV;3vZ2KhK$-|)kqMq+Z<_Cd23{6DZs^yV@NbjA?8w7Y z3}{cpP!z~N%xUCA`Sh8#Od3o~`uOsFc|2i@nlfvLZh;?~OlmE%`R4jQm36nzXGy`X z_EVixxN5zV2>pHp7XdI7; z^?tB{GhM0cWkd@y#gur@3jD`5|7Zc#$;vX){d(2T9|{P3r>SXrz&|V_e!z;0Y4LjR z`K%9#e3D^HNW;n`3CrnY?hGYrV3jSB9TxZvk?>a}cIa*M$LS}H2xP?ax^}W*X;^x; z$W7EKo7VoAXZiN%%yo$}t+4MW9MNbAhm9UDP^QcsA@7u(ETUGVkgdw?>1oD2ycLn* z^%n6w2Rq2AEbY*D$Mya=;*wBTJkt0`cF7yrPSO7}Ttt8BAA^HY$H7|vYjm^ex?P9D zwNIuv=f_0?(0s)qx#$ejvle_N$(An0&7F-;QVGrjwC-w8yP~LS$J_E8QQYumS62_~o>sv0giddlqBn1?&59t;;&& zWoD#Y+&?m3Sb>tha@eQyeso5`vxDd)5k{+r8eluN)VeGmyZU<`-TaFz#CjK;I7 zdODYFYXIK!Im1~gssBuK!RqBNAtU>s%DDa;KaR{TlQtW^{_)8cs1$4*{c86lhmc;` zXT2Htc{wg|Cnu({*cXE(f25*KcPhq~j^$v%ZynE2G3Fw-$t~b}-n9!}uQ_6*k(9eU zY$o{XMp5~-i(IeXWj7$@BWO1%V4^pA_eI$=&)o}b4zhFTg<6%(<9e$2R7>|A4%6DJ z-f;hRvC^mLU^xH#5}VvF6jiK(mr85PupaWWa8qS7On+WwOe@5B|Cjf)!#-blIrEw; ztCCZ8_sK1@PF~AuXCiB0gRZRC@|`u`rnR}tIg#x3@Lq(Tv*>+TlkxeuatldZSud4w zLEo70SFw5m2UA}wMr^Ks*0$$~xa}G<; zwep9T@ZsfbG|y{pb60R~wvEI@2(aw3d2Jx6=99*Qqt=5pre~AOQbx`9o7_-#re%tJ zlqZlv8;tX$8{{A>mcWeJe;|(w%=W7_nu`>O@_#5thNZFIv-YRSYu_uKXGmzY?!6(z zT+oIWWd3g2SvI!byusnMpAqjV$5XJ1d5)@O_X-oGi#y>i`nv&ALoP&z&*Pea=Nbv6 zs0(9-l0JnGu<>+czMN>7FNPry5CGZo)9|p?WsHy@lNCLDn_j?!#4tq{)~br{Jb%Q} zFMZX#=IKtzIqt*WnfRORN}7wRU{rB7P2*E24**1-KSllR@>HWCA<^47+)V6pjJ5N< zD=lT*FZ()WwqI_@l;h|xSy|?<&VsSE<5a7eKtj$(V$cR_Ae3TS@OYE4ruayg_46n< zt1XHv(;%f{ay!!Ly1)1qa$pBRZLugCS`TL%x8o+(r^uVQGf46N`Do=}ovBvyR(D$ZnXpj1KkW&z8;Cxf{tvvs#!j@)grn4k2V{WQS^d4oem) zcmeOCLf|ZzQ1@M(#!G?1+k`D!K4NO8C0E0ngu|K!E(VIDrVbUBX`7CESk@Sq$N_7iZJL{_kky7`0UB5quqjYna{K zOF0ogG0&V$!d*-sL5PO#Kj$@N-OOMGE`NyJ-=6W9-f^@MOpkD?Qqr36-RJ&M#_}@s z&^wT=EPI5*RTu6cIeY=}HK1Sik){oZi1qs~jNN0iDB-pp;APvkZQHhuy=>dIZQHiZ zy=>byvXiQus+-)Zq`&nK=xK}iw~_R|4D~nx7oZZ*^Oih4Ly4lPTh<<-IQ#HWHMF^X9^Ad-qF1bTx9|b#r zbwgToj8nw^0-ro>`;qI@bYTvN<6|kvp5gMgT853iGM+J{weKSgW>JKlUXdlwjy*r4(P-bTfpGg>`_>#%7wXCfFgO3-khaV-W zxC4bzN{{U~fR4`>Q>OnRp`le7K;7mRLZwQPA%*GOQm{6)))1##7TnDDanJLLnoJ>+ zt7hcj$K!44_TqW%M_Ypt!%3RPIDdKJlI)-hN4{cEmJe>8^#@?xt-IVfjP>#))OW2C zv;2N#fSHiiq)_g%zErC-Z~BNlx`nN&&Gv*bg5|X>*cUPp;*Y-1AEDpI4!ydBbP3iH z9*4lC>2Jk{(fZAu-aVxIK?7ecmBAQNu;ud5`!}kLBghXf;e-*9f19I#`$DlxT#p%u z>RoD$2RxSG#AN5$fEHv;?jBsox>lOXS+gcN(R;bFN@fg>T!RTEcdU^HpW7Jv4*d?| zRm}IsV=9dZ>pUF%ad|^LGp$J_P-vJdu|5(`AJPf9u{9}ZOm&4gUIE~_VEB1lcU-pA zA|VImmsX$n#R*&bS{}90I|AL`?{u?j16hn0B_V=VWx@aQ7Fvw`PbdCi+sv+KgNf9)bCOi^MzU^ z{?Sd(Pj-jj1$;G;dU|$83}n1i1{G;(*x%eQ&{^qWn2ar?}f8Gpc+F>e$PdS;}U0dN8}{WBc6>4~Abpx@PLg&z{SN+y>B; zmc3WQk}B!@p#Ixi_9s3Zm8bb%^N3zMdg`Ii%U;7Sy=XyZ{-LfXBH35(8eMZn`>0k@ z^gj2s0~8Z*sQzMdAG2>`h)*JjnSxA2^XafMx)s)eZOGUNP_w6TDVS zu)`Lm79xVpH&%A4!WnfnbSVpvs+}OO7JSvYVUgTBxjI&c8Xv{YKM%u>L!H3l5wR^q zLW7hn;L9i;F_JA5{MoZVc(QTw9_lo+EZz4V*!c>ncLK@L3BtW*IUv?n%HsN_kOm~l zYz8B(|6b0o6VoTKhHy#yi4$c;Yg3Kz?5Qw#W}R6C_!yXTed$$;cK0fm+r0dsdlUUs zpx6dMW01xlS0C#TSC~oKBdPwG_1{Wl(pMbNVWCSd?{sF3)=mBML(YncsOm`HVCvj> ztkCC#E|vIsm#xEAA)e!gqbMR8bN%vmtGv<$Ez14f*Ys+ChR~Q|$!^`^qr`i;mMAZ1 zGmF+r z#me4WLUREFz+GgRQc@2g0^T(4 zRyMp5PlAbmsAKW|((PBTw8be4S#^26wSPVmTVF_23G-v!c7h9Ka*oz~P53Y+JI@Z4 z!g9TQ{f&Xg?N-tTm(~OCz(iZ(tatUQyuEuNZmK z+Mv?|w6-$7xbk97buI?lwc&doEkS(=D*jU-+s9KMpiC6Bb0jfB5r0xM_I+bVO#zKH zc5T+u838NiqaS=oQNGG8`C@bPA`eU7(rlOC-HyuN*7rO^MpZcVu9v+xNzsN{h_NqT zW~T|Vpx=p+#x5&E3-6n_MR!796&gsBtbD)=DTCHZIER#tuQ+ii#%FA{qR(^`i(S5m z$)_?-LY;+V#Qu!?j^_+(dgML!G;1FbIVP3kdVZR$-J!>1Rpu^?r#VE`CYT2p!|I>{ z&E;w%WK`3YHn2Zm0_|NJ*Si-9&)Dd`teR8jFyV@^kxHm7n<3_#;Bk~k!yib7)TxV4 z(u%(W%_-=8S5|C*k0O?nF`9NDlWZIH_`-3{FaMWxsl|_1WW75P$(vEK6%d8r9HG|> z>v0QNX^LX7A*M{DL2-S}4M3Pz%UsGqc35?x3oR>dGHDhwr>5l%EBGNP!YT4HK|hR3 z_O!I=7s4zkab9cBCnjz_uFU%L30O;ip?9)fadPVCcse@k`(V}Y@o!hTAEUmo^F$nCM=`NL6@uBHE-oEhv<~Nx ziEk>#7gSXsH75|Wl;veb%Mh~5_YuOsu|aMH1;j46Hu*+m#WMOTnXIPV-Ik|~%MnxB zC;r&7@*Gx^l_J^;3Px*5uGCjy|MEHK+$YK$04*Ndk7J@shhSSy+$=o^GvM_hvCyhA z+hWVh`5y68?xv4Xmin%+ZMn$7Pa*rh!)CZFbVwkC<3`t_#j0te}hG7jMe8rDHh!vZU-->tJ`f@n!7lBAJzA@ z?J5wIc~A=EIdgcSuu4wuLH>)K9XkP4zfNv2H0=In+G|Is%ly+)9`Gntj;+jweswc z{dLmLy)!TrxZAO+vP6MyFFp{P%iH1c!=rdi7 zdWGJA-lJ!E%Ql7HRsUMc3*BmjeX&ovEaP65OcGw?K1GLEbo4G|4(n$+%Tw6}U6jCl zN{%J6&eiZ;e4%?9J%1G8<><9Y`m)cxA6D1JB&xZ`7ASD6dptX1%eu^Q+uOfCswZ(5 z^mcuk_-(p0bQw1MR0XRPaB>!T97PVPWcwMm2v|zh;1nk$H5Rxhn2Y+k8KcR#fN)o6 zGw&2XHItKFj@Eai=Ifm7LcuEnABb^Elscmd7oVZ=w|+(O<)^YE^9-p2m+WY>7c&Zk zd8c?@_=r-z6V(3F-fwyTIs9-`Yt-hGs|~(nGN*&iaE&P@Zlr(hESmCF8Fgn*1p_v7 zrbtLhJlAsZuph+^;PmkoBMV=Yb@*7c$c0e6HmF#`tspIM^C3rp4Bavk6nH|sW?-S! zI_-AYFjPaQ!%i<7g=SqYrupePeF7R2+xF&$r9t$s0k5uPjcO2I?=?n8E$e;BWHh2n zHVYS+E7wQ+9p?A?qQDh|#plsi=AXaW8c3~sjvm+3 zc{uvvk)B1vKCqKr#%-Rw`aA|t9z$(j*^2QCtnDOT#y%5CWmEx+0v4UPd%;WMP9v72 zEzZbp%$_kuxJuKI0kf{Ji$(k)Aqo0BfwXj9jh-vzXs>ipf;*-6yqydha}RRI)DD2i zk~l^c*;2J6^3DavX9>&AdZ_!9k^N%R78gL zqss$I^=%Gs!t;W<&6B5NQ3$3#rq1g&aJvP_j`sYyPe^rWMZ2a2LD8$KQIhKlwq@l+q8=Czw*p& zN@QeI@Yi1_7>bZOpN~S@FLTZDza=v=n|TK7Qc;82I(M5boSuO4;FTRIqIu4%tLlfn zvaW&ejNsCiKIiAbnyn#jRYcHtN;cfEsEZ0Hdp^ZRFNEp4^nr@dS+9p-Ja@JKgPp65 zMDlHk^x4;1b-!w62jiXB-ampk{iM-D&coJ_ZjDpk!|nMdX*k_Td=yBZ`wMhMM+{9R zsn6oOU_G3);~~O?CU+%Lkj>ReU2E6luZ)LZ&`IsvJ~xI4j2`|~177$rcExp@E)(=B zI`aD=`jxmu+d}i*AEKXt9WB)*sGU4Llue#&Fyha&7|m9t$RFd<-&@3%7l@w~2&4+-?XOoQaL7-R#^s zFsC@Zsl(iKyZ5jGuQ`kwu8?$yrHK=fILJ!W9wACk$WWkAv*T9j&{5t0RL-yU*j&QU zBon#+)laZEUYFbu1FEMML|>eqeYdJ-{S-^4^p{u_`FzdXZeWs8-`Rxt97PFbTLJ{B zaQQ~peMV`N=sV4Mo)$q;wOTH98?r@s{eeHJusZ(lsP+F2r20p#EKL8w)qm8=#P*-N z|3a-y|D5)JUH{MYiH#U%P?e?K6*fYNaEY*Ce`k0~!kPK)835pDIA#WB7Kt!|Kz|C# z3Wj7N2&F`%#Dy4^#K7WV?$Mst@7-JN%g>eS=Pak(?<=1dzR&frq?vvVg$c}k2tdL; zbHV)ha2Ns6RR{_o1Vlt+Bt%5g{UeruLc{nz2FNl@kcdE{J*MBN{J>!UzZx>A(W4K} zi1z-e=r8~%zyPEs{z^ndAdvlda11L;fM;F;dw%0weh@(ZeQv-2P=LR;m9u=-@(7mFMv4v z!0>Nf4grHXy1uCUSI30bP+^{)f-I`PO7#d6ehlgm|5I9t{*|4B`MU!V^vc-|_6=se zc?kGo2lN?Og9-xTLBRV%w?arDEP)1o6GI9F^bi8DEI=cn-1Wi!ZY2N&0GO2{W9>mW zgbYglAmc&{>-=0b%!mv50Im>eTmu3U_4)qlts5O5NBa+b{RsbV>l?bry2Pho{pLmf z+9<1uy#WD%jEDjR79tS=?9nGk8lnsS!WaXD{>UEsy;~0IA^@E8uN&2!>tlNTq5{nA z?(czqF{k1IRcS%^pYjv6AtoR=4Ep;2?kfFWKlmxX)lvM?C;Ykz5zu2?wPl>Peg859 zZ5J@~^?_8I_sp*W&Wjq10sQ<^*73Z88dSLU3&{d~9-)g*pd1ZxxTrwNw!?g^bmW20*PN2wAN&+|^dDt;zo8@b4Aaoh*l*%Sa(WUp*x%Y*Yt_FkzuyP~ z1ic94i4%;$N!G*Pli{IB>{4w$AnG5tuuiqJ%K2V|y6%nRGG-1jlf z(LMlvfp5fVXL01~y4YbK%H_N_mVI_z3`)Ir`X<8bg`m3wj8jg~zp<&m0E>D4d{S_nRloR|DsmqbvOr~3yCMCYRY zB-XiyQS-ZVD@EDy6jV4KEe2nMbOUyOYWW2CSlKVvGAuG+PEJ8EobmOVI7N~^ zQu~u%o4QUx_9Qy|>u)E`qWedH5D}}oKy2E3WVn$y19tO3QdDoxS!tscqKCXGY=-Iv zNuO(R`1y7>sSWIrm7T_;4<=?5tUQvr)B0^Fv>_|-AjcqXX_Nm#RiJ$~T#(R8$#~x$ zQJ}1<*lA2_Z zHw7?oZ&N=;DBk!!EQ?SPy(%Utj!&5;`(}13;p|i$mi%Qi8spw1o7}O!VTC+8A$y%o z{m9hM`GhcFQRVD_CU@a(WMM^8R)i-(Jre7v=%PYa>cdvV z46itD6or`VF4-&9Xvb0MtPs^B6k%A`t0-KKD+(Fivu^>FKqQmuCG9}AWLslf>*nMt zW%T5JCy;AzKP5BYS`Nb{Nl4s#+~x=+u0NncF{D`STlvjSb{^l~_v)ZQ%a?EB(Inim`+|iL6_Ffl*P;`0DV#kEqhJk|uSE|TrE`I6Z1X-EOguD5`8jk=L z&w#%v0GDI2FCCxwL%PVf1V-4>()42nQ9|EsOOl)zG063nBaNcWD$+Q_ z@2NqJUO3Yq{h+|M!koM3H(OmvOYSM0MBkHlm%1@ltue8H`aJGi^bzX%eS@-DuKOtu zJhpG+s-ssV&4Chyo)^>n_a0f!yzzW7y?diS;jr4QNGVHkp1;J8g)LvhobF<((|0vV zcI;jHeZgk72vsE5Ej$4>xbBYhnW%12B=ab4Z zs=s*#c=DPag=L#B$*bm+s_WJt;`~o#0DAcP zyn4gl$z4{Ywaaf3(Yf8zYiD~>s)r{%7R%iB(`@A^Q0g-!AiF-my-RnF*tP{k{&HPr zN9USLTW?1j^-6l2Sju1YKG$4Hr8f<100iQVp<+$^3vnk&b(R8XrU76s&)6hlVk z16H*aM7@-u`5OrZLzTvqhts$wgT`aPyevtNn%;F<#%`P9`TG>oVRqbAew?_u^cO5!d~)K zy}z5_UkuX~1k8->Tu*RwoTLFy5F{Qta*UzGLEDLQmPtM4edJ<1u6tpi z3`n@bFmYo@*QmN@BqJECC$RlH!ap#jJ}fVGdM}E8jZ}b*cZR9lhm_Pv&hOl~yh4S4 zfK3^Dh6_wWjhZh_O&gIrV0{>e*e58aoJ1QT$Z z?f;!{GfudCy&qU4X`Uftz)!bylUhyQOKX17XkT-gvba1o&8$W#*S8bK-^kty3q(8> zmT4MZU+xGAAWhy3xZ+K|OM-os{w|^wUYfjHfifA(aIOEqw8~SwFi0${4f4pex8+(Y zXV-QnvxJqxJtb0WS`0qFsB_3Hz_V*baR3(U_t2Ngb~jqgtLOiUNJjLIaZ_=+-$2vE zS=D?DJDPMydNtyYd0X0(W>;~_lc-?ZPY5K@!H|Z^`Q8(`PMcb*5_W8^-_#W=a(pPk zqz%iP?{ba34js^7l^>~wPIT@Uun_#A&9&npyf{l5yaf?JN547~#5mthSMj1YljL4o zT+_g#OB;WX_E*SBAdtrU#uFfsQm^5nZIsA?PdAEYU{YGn~IVmr*5J$!p6_PMH7sp|_(~?eM zLfzBk#yYHaKW#swo81HMIZNQUW^d;lYJ8vB6-zWM$Y;hAT8J3)1aGLbH$m@3&f(ZPx9S2xAI@~b;!&nvMw_A_ zIBb{9)@l+%GtF_^$a9sy(fSk&!rGl<(5Z;w#$$+SWB-p<@Pn-?Q`=nZ-`(vrxVt@) zbq*QbOj>wqQwoguJ5G*(GMW9}saTuVJHyp0bE?jH#%l0$T@Go7LP=l8S=yg_Bsbk` zq5s^CduK9i;r+nqOOvOiCWn)&CKNl;o<16INouy>Ir+1dd-{6L-3W#r>QH}e3UAne z=R|sI7h2c{SkT>s#ri*DNZpR;=DcTgF7wPshSC@F&@;BgYg~_W+8Gi2kO&h z=dVl5`8N?!)N3L+LRb1FZ1k|_{d`mv3j1jv!MYF0(86!CDJgU-f^|qpPgSB?=k1^n zgEYDu;d49rShSWls<20!(PRawNQ61p5NyrGtuNqsWCU6+lnHG^=u-Q&>r zJl;(qSGFy&9=k4q3G>;0{yEEMw#6h}swDL4GSc$CoMUmZy>_W0e=#*)We1M_jnb=+ z&@s=LF@?r*8sFGdF=;Z3vJj$)$K3qZFIdj_>lxFHUZbh7B7n2SO2uL^@ucejB&QrG z(_`{$49$nUAtka>?AIHtwm^)qL>N>y%BxOLpI6k<6qoHN2wr|Npbiv#B?ZUDcn(Hnf$*qi+Ztu4?)k~U1n|9`b&DU^+8X0&0$z_G|kjj!{j}pV$u5?@rftBc5E7-ly;Z`BkBw#4R zCT(iRXoL&C$3)7;-xo@naXa+2v@U1;-s=TYVHgYCnPwc<3)KY@F;ix0?d!YTF_@K+!5zQCH zfvcm1N+gj}igJa5-2y0_eyDc-a7B(lPk|2AH=DXHPe!O^wosy1yG z2HcU~%nWcQ)Dg_=`oZ zqgS}^85r|;_4$HRe7sukl9f+^u7WPv$>po-@7>in3@kPFEXbnGZG&LC%qXpYF^vS8?+St>TVd6}X z_sX+0t1(dbW`Gk?=8@Q0f$1WEmOCR{45j&9vo;O_8=glktEdV0SUt_INWvhZT@kK~ zYk|h=V=dh8J-+SFM7efbHgmIg-hEb?JQeD&uXd7W-J|Ag+^XQ9oeeBbJkRR7#Z0*7 zvQHIl(WiFZ6fKG8ySi5R6ldcgzFT#npz=bQc5Vk;?l}|(j9_}y+eRgrSrM9bQon!L zNj<#8IX3Oi%7ESJ(;igOHLG1j{jO-k=w*8>*WYXSqG>_24N^DR9lzBJKDqWFxF+*I zdF@s@QT9>u*SS&Y#`dG({7aCC{@ z%dj&~h#C>EhVPT=WFxS@!r*lJI$i?O@<=>Y0~|vajyB3^X1`3W7)yfO&AegVb!)}d z51`NrTWcZ?M6u3&JTMPG&s}MQa=8#hOirK|uY}~+YCg$_0{h4V z-A%t$WizzDQSP1;LAI@W)e&52R-z7DyLmdYJB9kV#!Z_6pBTml#qAwHsm4J%9WB${EO5-qOooAE90~FjvJ-(I zreUE{{;$3x+FaYjpo^Pm)ln-Z@ zg_|LElc=JTnM+7FVaxd{wV12|)=F!5V>;ohL#8d`TfW=&{jd6hcP5cw^UyNe6(BN; zNS9Hm@=so`n-^^mlkS}tIW!SG>`9cT`!bU8O=4J17Mf}9`(5g7hth~|={-(@rhTtp z*`4qRjBNC#%beW8;4~OYpv+y65mE$OZ>P#2l9y)wz5&Y))rmEzLCb9%R5T3qq}?iJ z4O3|(Z8D_8Ky)X2x2-DDrYy!LGa0H)-`Jh=^hb`RZsZ&Hm1_}KvGYoNM zwb{v$j5f`m^x6zrsw(;>KG%UVcv9AN7WUMn}Qr< zEa4(|d;sbTyC=-ndEKu>Y|7f%33c=;+VO_oE8X+%BLuZ|I*>)PxI1#2d`@Dows+EX z8?|S{`Jn+S(7K>gt;dZXZ3d*}ZPT@US{;H5W&=IMx9L3UF>Mhq&evU?A|l&dgqrVZ zV@|WtKxV}~bE$MuEH9UVIg9dN&@;W(;xxo2CelXDyU0>d!F;i?TVSd{*38ZBqRYBX zb)5KSm|EqY`WPdSZ5BTHwl0^EE6BUZobVTpUR3>-_95H|}8rPtsU;1hZHz=f`jAQ`R`=q>L_6-(qnY&D|@#c4OmbU87Pi4=0pn6c@kF zrEd4T87k-#Cs$=;WfVQ%tdS|}QHXKpDacaYj_gXLb6n~Co;1{D(-9ZV4NJynU=^<| zP)jUTVR6K|K1}`Sm$a;B4PkZlq;RS-q&)mT+i2RiKighS7wdaM;uM-GF@ ztc*1I>=s|s+^SS4*im)`Cv5~BOR3&&-wS2SrAZ3mKWsYKwrudvRS~-%F`DXA+ox8& zZSHFnQ7oor%ONY=LyBU{uYh)hlmE4GERPAUramRA>rBE>W|o@jsyl1-;!b$O9LC;6 zKAjx!(ne+RHtv(*4AK}U6Je5rX2qZKhLr@;D4EbZ*$cChu;N}ndw`ubV`z$X>gLvQ zDnl?++AmlceNj+m)4hvj!JSQyT!Oa9Iq`I%>x0}xEt3vf`ywzSt&_lcD*Z99fVsqn za9#?TN!w+hYQ@w33|()krz6Wov?<TF4o? zNLW|op}TzH+V1b?e3Y_c?`j7=6)@kMneGn=t|AJHT!Jp7GP|ZGe7cNc9O9_84v2Hq4$2` zY;>n5?}kVcq7%dQTJK?dc=-!(Ndv|4-{9rHrnLXFKkXl0GIRciEC1mo13T0IUJm^) zc*(%b^#6^Q?w}e;HoJU8N{I{S0$l9zH#fHN7{>hu*5hJsVa}3}fzA*T5=F)S&B+uJ zl41V-5FfJmd9OZs|F%S9Z@FD@HhpsX9@SS}er~+5xubd!`vQR%@G2uk^4|r41SI_v zV-r9jAOL_uK>Y;>gH9DZKIDcA>j_7fO@2!KbshISe<3H96iBO(C>75e-l21;*W#<-@Tpgg_2paFCh zfW+g;HEwwW*kNp78bF8&@^hK`KDZm4eara9IW9Og3iGGQ${6zJGzcq0J!~>k^@Bg^}LV*Z>xq=B3NU*yx z45EkH191%QDfs7BwgPN`&wv9EtqC26GBA;s^gw)T5*LzuX0bef*Z~=TQqGK$W2Hrq`b{b{WVch5%~c4 zdJiE1_(Cca0Du5N0u7Id008>M6vv18R37ttvn0St0EpP%APCugVe%A(U8QO30 z!NfXp&8Jb$2pF6E-|Q+epX&ZD2XOWCZ2xRl27not3Igs2E3)vP^#a`e=ySl7Ks^R< zoej++oc5_aqT4=L?d&mtsNhEges>NTbo=-JHX4S)97J|R{p8nq8^rq2j5r7|pX%#L3AKxfU0t$bDLPk0OnYaJ|@nZ1(x*$*>kZl79 z`6c=%c7k9)o_+IlZn6RTEBtkWTs*w=zn`?wGL(LGesi2C7r-G1bkjtHN{DpyL|k+i zC>Y)E>|zdS>YYYOv>(PI^EgiO-#IP!j!UI@R2!U2^RYZDd3E8L*{}wCob4Eo9(P>y z&XmeM05K&CeWmWh`W#Q!M=i+7>wuECEOaj%t}$N>BmNOfvruD^%rn+6R7%z2?vL-M z2bXk9r6t33{jdt2Vxx%@{&EWAw;LnAe+C9y1Mynj1ybF|hNz|%HHQ9tVSOUf-0L(D z=iX%9W~v&!+>OQAJ%D}SL*t`cJg-Eqh$zl0epoaf#TCOXD3%;q^okfdP()@^s{SEq zT1aUZb)ea9M%Mn|(`A{@WumxRKPs+5@zkb2vuQE|R{Enx)@OE}{@0av^(~8l(MH;` znpuC_m`(IW3%t5%zj{c^&|Q!oj+Ggpt-$KOY?h_5`fE!F`_spXM^B->e&!T%1G+0X z8zny8B@{--`)-k0RMCf{=`*}&{ge6}1^|?oJEV71Ru?S|buPin8%RIzd8l&wwv4&)=2Zlra2+nayi_P@hTF;Y(^W~&GCaG7nEhB0QFPU6hOo<~Bk3WjGzb>@!QpAM zYpIy#nDm5PBS|Ji5;|t$G`fYoq0t$VhJ+YZsB}VtLI<8IJ-4q8&F52vtXh;zm~o_2Wc#R!Ry3+&p15JX z1ZV`GY@ik8SP&ix2f3HrcbmtCi-tknJiH-ztkg{&v~HcxYih}YGk!e%+0v-4Es5E9 zQM~8;0p>J(&{sp&F`l&$L~l8pWTEuQ!Jlen*b<<6+hHT{_V43L!}}99;`oKm#gAus z*Nj@yO~L2uWLV^+KX-BVV*=8k6)P7Z4$=>Y2xIBM`d^b zJ!j49l4zHjb)440I5yq#R@|&7CcjeiGBcDV+=t+-U21Seq~GfT`p=!@ypH@+OdU{T z*AIcY+v3I*VUT0G9JOuq$oFw$QaRcKQB-k8o9M|0mH5W0kX5TtO`DY#b^Hb9PcQ*i z9wpag0q*P#oP4LhE6M%HdP&BOF4+)H%G2S(_ti?V#ns|1&bgK5T~{T41wM#Xk})<{ zP%d-T$)+D=4JQ0iOeiw7t_HA_G@4iY9Wh1^j#>PEckE%a2Upjp8#d6~zGE~(ZVARp z5LTAK(8b(Jiml@1pIZYHM6DE0VdV%KthPganZCDP$Gg&+D{mL3xi_ zuN3p#HWQS^Hrd>hckpVTZ%YISv>gT7u-)l1F2vV?3e$e-T%oecEXw59rD`eG`fhgJ z%s0X6B{msM+emBo?z838zBH=U#du$JD&9Ih)1x37{o#HsP1RN4l}fuAOiq@h(9gDR zm=vZHY5ND53MpKc(4}vk z4uaFceZJkKjKff&*XU5$Csr(+@0L+2F~z3@5%40k7Tl1}Krg+zq|q8E?Y=qYHuI)S z)X7`Zsxa}A?F7ArQ<)`iwnmJr6s95e{+00yYo$_Rw~c!0w#1WJW^BR}Q6_QXrgC^8 z(AtWG(h2m-(#SO&NV8!qJC<I#$^~EQk7%)!K-mE@#uR zA8H*w$?*M_Iof||OX0M4%h`PT_}DOZU~9)4__huZ0~t!~RoNyaAe&;Y(Q4rUrv^Ejz88I+95`$k^g zO{$LOX5F@gb0Vl-Puiq#II6tZJ2Bt1vm$mN3?Z4GfY6ZN`EIv}h6mY;{F-}; z30}bnLuzI>->kTO-@$nHaFw^Lz-AY_?>{1%pqdrm6&Ndmw#Gc2sBoZa?W69-d!5vE zo5-TnKPw*>v?BvxGd62sqk7z@LO*qG%|>m4Pu3^=*Pzr_y=)P$HSUdzH}3%2?2n$Z zdLloa!LV&qSP?^d%bnxi0O|;KJ0Vrd1(Lp~_;T0{nqsYbmYq+g9J94N zSaoP*rV<9C7wjgA`d#%;y0EJF&5pklD4cKwDAn0*?8JPQ2y^oG!a`3#`zWvVro#PK zG>);SfnVPx`)UAGU$(Oj&uC-lwB=C1)C;Tbjj?vB=V#g|s>|AXZ$yT=F2X@=#|^^S5v7WBxL+6Lv}*Uj_NcwH8=$fP+YI&%D0(w>F} z@7BD)9%7V~7!2?^D`-pksV&toks$xu(2IBjjJwB-5f70_(@OHGVTQs_8)O3n;@kQQ zt>>k%eHBG7(u37uZ*naRJe4(Aa60qx1#x6C=0INd6fAnmM3?LbPvS0!q)&i`HCIIB zc-tWSlxFnDsI;#|sf1=TE~^s6SB?gmk!LR6Mq{x}=V0gl(ieUkpBA%55HE`S*~$Z( z!$-z`?htTYAwC##dUS*b^K!k0e1Rx`uhT08(v{z;WR6QNjy6IC?X3?_OJcpgWl>P!y%<2v3vojZRPi8mj zx=pG}eHx|KTmD#Aqq57ZhU(vm^Xf+lO`R}&k3|?`Fvfu^t-H21=US5p#t%UG%;iyM4gn@zIe@v2&hcp}9)Ilfk~r$(;= zU51E0*pZRR&d@iR5mv(`hXqpGqXIw6-Ipbmz=@eR+{vd*T)3XUFZ~S~mH2@)rjya$ zhZq(-A#z<(mk@+L?ygk^KpGVxqGL$`L&H`bvq(i)MvH9RDdt2VXe+4d6edQfmbkxY zhWSu;N-KvopqiK+MFKOgE_;OUxboRYb=K#7fGJC(VsEW4EAvy?_21Y*m3sU2O2B2; zHln6;3xv&tU@1jxm&PcVePSz4f#nrszgz8=)?%W;Q_@Osxy5bR*E|YSyPDG*%4GFz z&2#TJqc8K|r<;eWl8H}QcZcb}BNNEr`KKST&9@Mh@^7XwAJ8K5t6a8>e9shgO;Yb~ z8&fyPisH)OuOOL=HwJl5tgU&VFo>kwhd==#HO6hbrF}GI?+iO7T$wp=6;*SRkVyqK z9@pbSPKR`J5@sa;wR@%Pw))it?$~KxgM&pl{6-SeW!`mkVWFFcUvYDPW;A!&O$7R2 zrs4)FB&U5F~wh${Z6HrlN_ZtUWw#alQ6Pl+mw}d*69_v?89SLY-rA-0-$>c ztQ=J5>tjz!|8@|-+Oko7d@T|=0sa-iPxX(=%3&E&oHb4wXGtIQ08JPp(k|9b0=@<{aUyP2KK36a`yhLDt%XmU1;r!U*Ylj7R^!>uxyGtvs(HJyL>z3MWn zw5`)JI+UWV*+{bXeOy$h^Y46%KrVR3gcbVx2rcVI^k)87fad-yO7yiPUw*5pS zUHGFl?*$f?3+*dvuR!gnu7M9gaQ1Lz-7^9?rB_|6o(6gtf(sLg@-^2#u#halqC59F z!tE4jOO&PS7c=Q>JeP@^<$iQBadI(f>h05(4sil;u%_&;Cbd!@WSmOo$K!mb`#QR6 z_|$C|yk2Apnpq$!YbpvQp!OYYxrg?63E?%Su0_14|{DIm!v`Pw|X>+T?!LohM-tTCAXNHje zpf+#cvS*ssqO+!GQEY7qLGa7IKdPw1^-agZLs$d7N^=uwdC#W$_B>B0=E5Aiu4{hI zZ+PmrxU_Ko=|SY32RMj75qn=dl)>{hK9_^e8L?f zpNTT9Us^?Nx4pF#{i$#CDffGOijrT1u4*Z7_5UF3oSH=IqUhSTZQHhO+qP}nHgDUu zZQHi(?tH0KQh7*K9?uWhb@tkG%`wa!1Q@a2Y!0dwWUck~ItV4&7Air-jo01C$wVOk z#xpkUEhiHVk_EiDn0bGxp2K#0rY$m zw8Sy8V4-}?EX&GINn84PBTt5$R-)(a&}_plrsKyjHF@=LjlH{O;2Im{bCe$;qYU-&$#Zn&G6+NV z8J*-SKs7KgKz*+`pV@3Eb5haMqLJK(6d!lZZx88zvC;f0*Fw>Dw!oNxlClE^kyvUqNt5^anKZ*NrXriokB9*GcNc`;*30HnR6&e+E+!a z;$PGq8<}&9K!3YyJMMyeWPt?sDHT|_y`8;*aWKgTD@lcLwR{ub z;CVCTd0hh2^jhUN1SqS}PMY`qhXd16jrOtS_4-{s?{(g|QIlSP+?1eU?=6uuC-!5W z;+7;~A7ioP)L+eopGv9ozhB+)SOf@Dml|!iZ8D zBb*{eseGk%QCi@>gUl|~T?s!VcDJ5~?PH#&vdBlvC23jsI`K&MzN|WlQnA^X;vF5# z5y5JtODgNeLRFwS2^Zd+KYqpiHL~;8GOG5Kps8~;#6aPOQ?+S~?3EsJLbVOC*G}C0 z-xadBELae#rL3fm_5|7(e6@Mf{Ixr~?&V+g*+C0mK8I*e{F=y&K1HG{wKe0_!9q`* z+w_T3(p#$=4eJcvMZ+c}+-59zh2NH0E1@dFYb6s&gr)x-&0CmiZT_9dB@8wkib~Hp7xClzfP&#%Tou34F2Ck!T3x2io8olmwW-ui zY2EkPZ+;CKb^3eXpVGN%I#$TLIiBPf)n>G6zb1!I(q^39gt|x{_jLc6JH@c(^|Q{N zXTS<`)K4ZW^?T0JlL1FSl&G8HJ9j-}U}@V?=FIeyi`H$Xjo)9omt>8rS5vx>N!ST* zY%!mGtJ}lfD8}Y(#Y{OotJ)>RXWk2zlX^o|#ABl6X) z;%%kyvl5`&OTM@C{EoxDk>!CZDRqrPGPz+I6pQL{ zP@8=roT{1Uv}C-z=APCo>(x@JZ_EJn=TZ?D@p~>%`Y*Ep6K)TF9y%`ChSIndLKi@2 z+8(g(Un(7e~$kTD{?x<-Uf_AVXP;4hpHhs(%7C!9ehOzc;(}^g@ z@7CPT3_>MA@3$IV%QUG|E;;F2&aw>3Jls7BgHLUBW8;%N* zb(8e4s2|TX|1AOggRbr<9J^8CguRT0Yn3RoDC>-itj5;`lerLR$``ASPq2$6=lE*v zZ!$0KMtx^};}x9*8_b@F7aZCvty+u-9N9&34Zf*nB5C`%`BI;c8 z5&+qL)!&pqsH?+q&ghF;X}uML^wN-@O~cPT&(QL}B5I_iadb*$^yKHNTrpi!5*@@I zjh$d5099KAI7O31#LwG|h8#P6tB`@b8Tlz7oT2dAe4l-Xbl|mRnxE@s`+_Tev)z99OIDR;#VM%~osf7x&rr+xCOs z5%yPprKYO&Ojgw>o_D;cAd#WnH@nx_N$pYB< z-Fc{ja}yI&JD3DkcCbwjfC|9U)>nY4KMnw6ZEWNxe@7>ScXmK*^Malu{$ZIL+ZsTp z!^%M92IJr+-4lxUhegkN#9JH8VBazy8+0_M`rb zp|*a1MMS*J*ucnJ{tnLIkk0A_k^ef5_&2#XxdH!xtpWa=<(veNoyo8MssX>n^Zn)4 zhgU}@Z~pAQmpYe!XO-2_z)$LsMtf^l|)p3 zx4FNZW-IMl>z>z9L%8Z#8+%4v)oYJ6x2XDyWbTsK|j`%Aqml4cUaN^N}+D7G4@ zpW@q)RJ`~Vlvw){0=!vNDVR+MJ=Vp5=)0*82sr_}A=FYjyv#gKeP6=~H9uX_xk%f9 zCN3h;`!7P`(3FkRe@l_FpUJe{&l^jAq7i1e#2U@`4 zK>c)jXbc(jmBu*Z@H_9*ZrOwjhu%HmbG}~O2NHLYHjF>i>0<(J0AxP4QdLsWRbUsr z9@Rp+Hd&3|A;CbOfYJX>S~+lg3k$&y4wUjC!#&gYzA|m;0|+r?tZ|vsVD$w1nhh(8 zqxc2|ZiiWcPFPy^plr$~%70~$vdAIbj*P&7BULj$nB6yYw_gLbC)TLjp0`SLB~;K9 z<$NTba%%R5CM(XNeRYh&ai=g)?~g}SF=;4&Hat7$Sg=H`smRZ+9QxfIl>cWEC=;cl zoz*A17|NqMR1t^R5m+6D@75d7#(!xMZx0Bffc7iHQjALW-G zP^~0q!)1?QAbzgbFM8^RGHg<)4RN6CE7#KOr#VgXZJJD5b-{dk&mi>7cXKy*h8GiJ4IHXmS-B<_6`iA2+RGAVs00-&F~G zO~nALR+;Q_TNG4DJ2lG1)_qx z_A(CoXC7naNO&`0*O(F|#Dc?`q;`WV2@t#oeNsitQ?IZ_;WupcdyK8ptM{~zN!q+V zfF|`C%dO@DxIzpfSCjOXDAg>-SzMtbF_{89-$mm%wiPjjW0?Zd&u)akN9k=iu%Q7z z_L~KS4Qrr)3TIS(64)GBKKWELLT?^yA*nDmn1371)09zd4z+4^jp1dgoUAHuKJ@vl z!`-69IOsh4&^-}s`;DLx8m)&#Yb9TaWeL{eJwSFet)Gknv#!(+LP+&~imj#bhY_4q zy=_N46P5dLJauHi=a$iNE~TLDY#^!vIQ=#SjvnYag)RJ_ss8M`Db_x(eF;mgle!vS zNvHpRv#`vBl5j6eO#Zp8EVRF7p zSX2JjzS^`3u2!N$1B7#C39|Yx47@hwlkf;gM}|a1n!AK4k496^_3)+Z_$T|rGr1T$u34YjVN0mpH( z++bfF%W=NvC%`TLx z15?m5nlEZ(W8o=);=LD|w-IN>9nELScEg^nLTAFtNlmB}+5yC{1Wed0pV6j#pD(RD z*q>~2E^1Ed8q!b4ZGyJUQZu-0u%|%PvtE|lo*Wf_$y4D+c6L_cEVsiZ3OCahdop*V z!){#cT;5|3*1?oQedfwMtJpD329mN4v$zot8~myDrN*@XH}uEr-AmBjBCzHzcYG=ydUS+GX2Wl#o%|x(eZ&(lLZj`lhOk< z6D=|wC?cPfAbH~T5Mjj}wNU_80HJ+gKSYiHtR#|nryI{?n5OPmy%>Ki8&Jg~m%$xs zs?#8q+Rr(GGt+?0pWeJu4ejmbk`l8uoZ$JZM>_q~XI<}tsexHlJ!~ha4~QPmics7K zmmF?>1QoY`v$Zt_A|%$EB;Hyke>VXKonWR{+#)EYcrWnjpxY(rUpe}^>zJD5baU1< z7|6c$>Str*zbJxw4LtI* zjFI^pf~y|vJWDFd0!n?6x8vbYF@B6r*c6_qT zaf*uXc8waEcJ`SB<UC1OKvUI1ZCcLw}nLrAn_W+U2Y7+I@yq0Mcq;kE##lj3)L} zMPXQ;iM{Y#SnVAA)~&T&AC;{X3PvoFZQXffJ!qB8;5hrH27r6!NEJ`A5x4y&>D}q* zEk9IAeJA~J7K`r_1jP5|wzjyQACTxqeo`u&1Dew{!MF3+9~tSOF+;kNjcjV4@&lXg zmOTC_OR!SB%8HURs8fI_3iv9GJ>ExnH%`TT*6k#$&Supj|J-r|!$2czqB@o078IUz zJ_sA&hSSvgnWfFoAqckCt`#YQ^N*7~-!l8Jw1$Nb1h?xGvOUTRgY;v_py?~_JJ(OS zGUay}!WeZ@7tI%=B!pFd!60$k&B)889z4U__>U7Cp=eUFxo4%lEf+iLZ*8gPeQU(ZQ)00u!A$efzi zS4SKJBP0zxK4ZMd+ozOv-XXkXI~kVQGRM@BWrhaN$;kDJpmzi;G2n3kNW5~bNa19E z)jgE<^rmOUBEKaoKQVLe(uPi4xhTeAK}5Fm0rZFO3&>ukb)6+EDqG)!LZV!!Ce&9H z+e(X*X1v8bdG%Z5C4XK1)X|cIx87dqZYr?H$)>%yB9TFIM8Gea1;2^ax3yyA!M^wAsYu4@ zvpB(Q27;Q$Tv95jAfOd~LNI)Ral|I!di`1$y}|$3KGHRJb9acoDC_Bh%!qr4MTARD zD*Ph{yme$(LM2$u{^AI?IhZZLT|h}Nc2=j=UU~ASrW44ZIRPFy%KH;In*;%;TRM?C z%3{pwQg~z1GQx+%=B}~8cQp;i8jWk0f)M6Q%m2cgf}92(5yj`FzP0`Z8@sT9sAwP| zrmHlDosNHhjtoK3d^-pbr4Pp{a9vU%&bOe1k;VSQhI}zWjd=$*WJN?LHI4zQ%qc>U zE9Ajcs0;^5o}W8Ph0G%8fdc1M_*jh0(6)Q{0bc}CmN`fRLyxkBqwk@Vh&BE?Mc2J> z585|8SAN@Voa}s5vK-zzA8;h1uFb+DQDir04zq@3kj@1-k#3>`OO7Yc=}R6-esDqC zd8Uey__bS!TT!yQG$YA3fX&dPML}c}QK@L{|JYX4i4G-``rUau{1)0<^<>a0iI_{%nG zdev4FRx!N9p$z|&!e&T#Kx^=m-0hbiQ_h<+I0ZwOrK~FBm7Z~QtwdNOO$oD-A~$l( z(Hj$kJe0Z(zAiGM)Z}LomscNQMdcpnJ^DzTWr_JbQd0nC{n1U#LiZ*%HV8aO>6Y9T za#eFqaLP@2ch|}J#GeyOypHNbFS|X~j6T<|g+2p#P}mcPDIX1C)~M+4t;SLqdya)S zJepYRAV$^~%m2+E|0HZ3{c2oI{?AHu_w>%rFc3=3OYq;Td@5YZ15aFMqKx11FfRqN z94UWOLWujE!X$w1eG#xIKY^a$4bl3EOVWqF+rX;f>xtY&6W)bZ`eC{l9Vi~!C32Xf z5mpz8DWa&@a1y+^RxvY?P}ZMLU)=^Au~j10>4&P=Tsq=(l+wqyWTrJiYI{r2&<9J4 zqio{wmB6%|GIJc4|`*J7@I{7n3e7!aRMt=n;-b}VNVeM*edDpa&5*dXH zTNT2X*H)LG(ALd8XiD((+y$k;E(iPt`|oa79qh#gLAOH{A(;P3H5R5AkFR8bQHznI zORQJlYz+cpX*?6+$3^`=q((zmFUQg}hs&mC@MYckF~&}Z5+su`Nlbbq7|w_IqjSr0 zQaccvn>X>rB0?!N!fYPIJS)L$&K~4xH>!!kl5nu=y2EflG=A+&0R2eH%)uuDv`HM# z7Go7_w&f(0=%a;4F&)GJ_}-;i+KjW-#tX%94Zc!Tc>gh}XI^w|YB#lSsWneByKlpM zF*9AR*IayQ^_5*#z}za`mh=T}Up@!uRyXrtv6*ww`s9a)wMCW7P6tza20J7wj>Ln-Vog~O1wd$Qno3gZnX{L=7Ekpn+)F}7|OW3(ED+KEUG(&cvylRCs)(dt+ z#0_uua^6$6%_m{2mzlm`8Y}%9)@lzm7_0%>>`?~DG(74b-hu=Ho*Fgf|Mc2gqsg;q zi;RjC{i3>voHu-TR6Z?4>+2>NrY0LEiTlO{XTB&|d$JF_%F&JxL!8#e*{T*4mt|FU zEhpVMYv4eQ(5)oba1&d1&r|X*wmFd=l1V9i2bl16(os@`JR~8pPyA!Ll?93LL*k-g zNCMP5ddqjJHDGkwdWGAt0(*x=jnQjvw}T+QEHXC>|A8Np!nCKkqR_V=nz>A?%L#+x zH7Rr1;=7*rl8D%SNS?PBIkU)1s{c*@BL+eh_2X+Lv-GofyRRd-O)kA|CW9m>=94fy zP=?<-*Rn6~+vFq&P5lT*`_=flT93+`Uwzs4tcC;fdC+H3V*HnwSBx#QV6iG+q0K1v zOfagnSzl@I`7ZbvCnA`_|5@T$A6M%K&IL2XX33X^fUvE|D|59uQ0o|}U%~ikz9~;7 zu`LZ`g=>|!C?eCuao+o$um4S7?$F^mc_ZVqi z-8f5+*hNG*Xk3}%I=jl9$#MYRqVb$B=Tx7134mCgM|WyyS*T(GAEpDQ^em*UVK@hY zsKUDe11i@kMOkUz6O4m-R2&J$y_K2GWDn462}Q#PHUEtj94=LR$hLJI9=Ff>o?Y0P zt4wg$VSj=fYvL~FH!ZLYFAT#ZL9zf!0Ml^=X?$fkw=D7`YKm>l_7&tY+bhpEEmoFj zNawxu>cAwloDd_TMtDO{k=L^~pBZPlUETA_*y@2FiRW&nqlOInRWu-q1v04IAxD9$ zl8kUZFuT1i{o`|ev0MG%P0qiA^rHl&-dF`nEme*+9MTrz0GI-jYCYbB-y|aCF)>t8 zSp@I3;=VUFv8(%2GNoaK{K9@|KW8{w%`fhnhd4qio@#T@orA9N zC!)EZ>MEMxr}<)^Z@KCMJJq*zjLWGNdB=E+47}-UUJ>=x%I3V(;*AmZEG)T*9(T2x zgF@nK!C6Ad)U<2~g#D%AXfxfw@2L_u^dkjgkyYUhxQqhT@RGI{8;tdOI;)4w|Ap3Y zdtp4Ia3sJWb|vbIEYHZOL{+^`@ku#Bm>ToP7@{SbBC@@ln9kvdIzCRb_^5djlmjne<-i%=4}a4i2}lCZdF1;*37v@9=}5SQp*F^%T;fd z?|V=)SgWyS>7S2#vdtD#^u@p0pP5es;>v_}yH^PpldB}FiE5u1@e2OocMlaF%f++( z+tk*A>4E+vn@fjCQDr)!83r~9^TwacGVRI!pr z1RG=25X=Sd$8)v8JTdIys8sYzgY{YF17-SwS4q{Gs`^Yn-g&&tud8SG1x=*T0G76c z6iq)pOAe75R4cP02$3D8N_HeNJeJA#_dPVd6u#6+L~ML37h*Um1xNMN7Op)I%8tMQ z5{F_Ht&-r zt2GrWs|E_x1h@>^lWiB9@hxo=;K7&_t zrs_!U&f-u_-y-5?K2kvl_A-#I061Q&&La4yg-YDs*p72-IX{fiL7e@j!+%jrnR<#) zqD>;NFv5S@46Ln3yCgpUh{v63JhgzDe}6I`EfncV^TXS?@ld!pDNLn&tE`A8aIx4E zBFOikC2iiq_#z%(*-UtQjh%59<;o@rc}vwm`f3Ejljnk~EZ-=$b{S8Lyk?){$0lgUGpy@n0P1Z@iU&_lZG!w**9?Q7r=`GtTZcnIXV-pgR zJ3z7z2>!re*~A!-8s<79ffyU6sLYPcFdhK~5>tqWdd^i&?Fy{FbsYypoVYt=q6QbS zy?D&WLnrDDfivJ_gNSI$NW6c%)tBJ&12Tsgr9f8DO91|Yp&u)YrWj;wJ5_It)nd@= ze1&m_CxPuYmmr^!`uV+EV(r6%2VJj(y~omFcf0cHm_idKC^XJ3pf9m3`rI-H(Q9jJ zMqD(q&>fs$zq#=@76DS4G;*Gi<1#y{pw_fmKXdUurLh$@Nm5+iwS>q6%f$lwbNP$h zvhD=ZSL>vdF>>8Qtom22B|Y!94jY7F1K=6(twfz|mBf`o|A=V5FLg^(+x0Ws>Duu; zmuRYd(OGiP<*a(lZ_lCH^uwec09tA2{gk~DvUVS~jQNMtPwTz;sD;)|tq7T#T*HX= z^W(jo!%Jojl@L>uQk8-^{q`V0(xlJ^PkHbBa)fb>c%Z9aXSX#T`GgsbL5Jxh$||*t zXRWgKTwp3vH%Szf=-|oi=qc1i1s(jgrbHltfe~NMJ+KVBv~}jXam*HY5&ob|rPxtK zEUH^kWc}ZKQC;EYmV+qDkfl7q=YMNYgu*~jA~o1#Ipmvo^^(GGIPy;3i1P6XXJ0n# zc5VhuL}I=Zm1FjHu-Gxy_{%e92yBGdP+I&(a;7+oTMGqdD-_0#!OG7>b5@H;?Ip0< zHOc{=+3hXWzz1J`lPK|ZoN2Cd-tK2w)!=yUUR}B3{p<*HV}}=m%eodWM7|VU?7(Wz%By!s}#}bB}|hBAIX16BkBk0qg8=3 zG3?_;mLFV*6VVsg<>F(T56MyJC)5~}$gMF!7t#QyLd$lR=`t=AONXn6V~lpbH#M*N zyW2vcCW&1&Owf#!TRLb*I!m!YR{I6VD(mm3ZGUS$0e>axvxV~LzD^~H_u!pv@`U){ z!z%$NB}{)--a58|3YzhfACjNto<8yT&g(t%m4ZN{!X6cGM;W0GcH*r6Ek+kaC5MDg0xKWm zzbn-btjh?RByRRQJIJfS9w73%jilpNE;`P}X;dA1d4_5!>g&oM&X&-FHNbo>?C-=J zhXQ{Nf;HwnYSiEDK%AKxm;$1wpVkM%eFh?=Jmi_WEGINb(` zQW@O@A}B;&F)#2;8@#Ts)6Sg2hY8N-qdrA{H)0rW`(_Pq@H{bQ z$Ev5XIXaUxIn!8q-C)XRJX3k|H-Z)GDTH>iuj4W8Hm`LcXZUT7|9Jr^0nVprjMCO( z$~z{auYv-HT0ssrjcvR}h4=QZKRybV+LE@ng|m#oED@1zTcuv=M;;8o^UAGdrDqg# zzgb{&aMSX+pLlQU)qL#aT^k2HJXS&2r!aYzQ*ZJOxspbzDKMaPtV*QY>rmkohf{LA4u8* zMf1R+Gt{RC|6z;68e(9U9Eh#R1kW4$qi67XLv2>5A_0*UBW1UsgqDv`I_( zu?90hD4qBi=uqBuy1hPpL!RBFy?OP|?UvRzuwt8DuzEUn(i$~usEn$wvDI16coNft zG!Qy4?(Yc&VIPo9IfNwf3Y#=8boZHcVxV>p$t70?``BMS&QYK6nvqxDsdD=zkjffQ z&`0ZdhGk^y3mI05-$-S_Ud+VthfT3)fzwpYM?#@sXo-DDDtjG;69S;vGvOXRO`4cF zC(lsb5(~(gRhv$>LR#{{_%~U}wymH+GL;m-4ECK^>R03eUsXPPmI7HedrLvxkg?0q zo!Y+Y>fp$hf>%9jphUa4j7@nFS=*ja7MRb+PWD)p#+M@L@lsk@GWpygrmc>T3hfKE6Ax4_l(M?aSX)mFH%HU?CTs=!;;&Tsa}^pQj&eQowLX5=v zIy%`DdI($i%w;8FkE=2Q;VLZtfOHuWkp#-}yd!2(viPAF$+v3?_>95-Q)%;T!z`VYvSYK6LWgwaemS2iHO^l?-Q_B)#0zaDH zX<)YU2%;W|fo!%Q!r$a7ROVBp$KHU*Ig-P3kJ~#r{XX5Cnz_;TPh^G3o`P2DnYr^MTZK11144@mp_c4zVP2HhX*-;yTK{&DxI-GSzMXE{o zw-(gOtE6Z;C%Ndc@PL>K^LnaG1QYU=?V^En|C*h_a$j(3)gVB?~M^E!`I6G2cn*9vs|z~uzO2lFCOV3YEKOVFxYAX z+lAV0mL=pv-0}pwxlPeWG%w3PotQZv6$f+XdQtUn_q;uXFehnK&@A!y7f6QcU=SiR zpqm0le-zk=%IbBpXAZWY^~y?z1dc1iFV>K$ew@2 zkFb{QCxE^Sb;EdBMJoowQami_b0#mO39)k~2s0aqn0_Cn8xtg`)c^CyTt}Z9l z8ws{tW{}VINPI-cDB8&QG8vF*)M}XU^!>~)Nmh1L*Rtu4xlN$FZ0Xptk2Fuy<}a+; z8C!6FU(r2m>n9HL^*QRScXwHc<|nl zKrcgHxLh+Yl0M~Tdcm)Yj+Cg-te^MmOZR>n5(~e+eh2zH3`r;8r^nc9>DdUnClq`r; z?KL~R;droZPrUJ?{6NaB-VdDn=xdS;d(=}CdoHFMZ`Rniv2)iwbtAQ=wYCM`R6P}4 z&g)RQj_l7xaAkg=3l~daaa-UsvnuP4`pq;Je%9fO0VlB!X@}Z^3pxOHP!RUw|UD_6JM4l)U5+M@Fw5qd@C4q)K;R0m8Scyg(J%Ya#UH;3qZSn)TNX<{H`!xuqKC;oafuI5*)!>~>#=-Vx)fC(gqo%~EOLix7;; z7?W+a<8V)j1t`H$kc8;mr~D3b7r8j*xp(PcPeGz#v$3iUP%62!wFCGYY#&bx9X^x2 z){QA$O?(7aQ#end*4_YvA8U5`)Xa! zUlrVyyWDb%@GfwOh2T;BCWvkD8QH;kam21)cU zW4=3BUK)0{Xh)4(vBt^VL;$KeD%654ah1C$r>t@X4O zJF9O3f6@1xCrM~jwqeHma%1;_aPoV)I0Cqj9;XYq&!`!b?;RzdLMfiDGbBYfv3{sA z2v)|X6+;+zg>R`s9g+nUFD=s`sG*`eF(Hc=Freq+n1*4l5YjHjeP2fpc z7NdN}sdegEEaIsn91r}U84&;dXj+~PJ5_XxuT>bCKBGoC|bCPzx`(`h+n; z%fyRQ@U@qa%6#V72`X5N(GZ5lMBMSPdTT~5DYC|p1Lg^isZz{0+*PDHv8APs4&Y}t zy@WX|NAe`@3@;5ip8L5B&{_uejH(EANK8u2yG+by4S-n3I`U_ z`lS&3-b*XD360zMl<`_QjXVIy&b6qFItRxm_Ln(hJDq`u{VPbc9SK_y9LJOvkCCsK zgW7QFB9c&o%3c_*t_&>=siC{gG7+H}KSwfQ&-+(B%2Rj&9o)Pv_uXDi%&f<0=4PQI z5-mKNd!;qV41#B@Zyx{rHSvHHo0MQLf|BkzMCqL)xvC1P0~tyl!f+`|vizuC6Vv)3 zlo=LQ=z_HEEZy3^J~*wD;(?&}S3(n6f4NczbgSj)t<4blO<=2rm&Hwk zlhM^C0u*kKp*kY_SYmoANDur0hZsb~wV-o-ClhK8z3;Qpv;O9?5-{^@t*C#1os352 zS87AOKD+Cr9A3p{S!M?)C3#o;RrhbjJY1UQ!SQ3Y&^Fp)VK~5@d!e9$wfRwcZ@KQ| z5wVL|-_UsXfMp9$9BDvplmfwq$&IsO$U;Pg;aeim#^&0=J|CRX{w;b{-PRF zYL#}XED6!3!V|d@d|O`f=h>9^`2!qIzf5Lif4}0r1BQ1R2Azrla4Q#Oe?$X zWb@^vAG;oEw(dS@3s`1XFl=DyedG);RtjlBU#}Iqv(+tQ z2?4a5)?qXsnWcz%${YFBrFIQs&{k2yS~UFFBt~%^BFX~>p=cOr05Hu?K^`j#xGxh7 zy~d|+*_jQo}Cv) zLH9N5_8+ELZ zJz@Y#e_SD(>l^-AED0^vF}RLhKP?DVFA)vuu7N1S3&wt9F==o5swNmHur-x=rJie$ z#2X$`>(~i`T=|QWjA3|^ZY`v^?NdbLEWyJ8{xadIQ7(~~-RP66Oj~;UM5S)^4$?YA z_--pmiyf(NJ4?NFD01TI3>F0+$YOWmqE9)&%n=n=8X%8lY(IF?BmA=zvSW=tzWmoC zC33;ffwX>%l<*fVmPpqpYi_P%%fZecrGoY#wCF?68=Bbeli+x4zw^%c<1IA&U57ix$ia)1g1BeCOrtvF~G-YdUUh}~|Z zmZ+h$yLrZQZC8o?b(Hm10<(lrayc`jjnD{dIY;zI@LPGRyc4~xMU`|bG{-=$Ddq8w zf}ZbLb&IHbB}jkjSHbZu^4X1;)PCz=ASSNCPQ*L4Hw<6{M@j7=yZaKth$Mv5?_$@u ze>rC4c$!Z618uyi4nx%XA6k?z*2JEMO>*HAft(Xc=6C0$08h9#gyqBLo*Oh zvuNP8wD`U6xx%~BpjYMt8y(v7Q3Sz2JHBruWnHL7U80}P{nIs;&6<3X))Kva_oQ^^}KRAiZfgtlH(#o?>HJS)T~cC zm>_tPRU2saq9wjhA$%^y?$UlIoDu{+(x60ZI~H~>h!}A(MTyF--Z1!lHT)5Mkmyn3 zQjPRbZvw?gr`zFxuEQ)c(DMP3xk`K?rY4?ISqolOQXx3lGaB%eo1Hy>*iSl?>N2>k zvy>ETns$#Oj8k$2UPwz{2fKQKdh5s+6y4aphQ^>x3V%)LRj%mqv6M?23?b2!QQkn% z1JP*3y~_X!^BMcc+GeowA%ICPvSk*%8myPu~BY1XE&O8#F4>Sm784j z3)i6NJaQ-T_e!4cU%62tOGOoWB%wx|PPC;cMLNX}%{Q?ErO!vMHzSy^D4J47V@3PA zm8q(#zUCKXj|4ga?5`PJ-p&vpslB3~ zPcGk+NAj(4$h&B^a7Bv1L@rTx`WR4FK+?fo!v!VyA+5{bJ|}Gx{uSzteqxMmfl@tJ zLT9Fmq{uOb`jd0z{>tHs(7{p<87kp_011ws!4tjZ2`q8o?}N7B z+sLA4gQ8`l!s1)!zqyVvCkl~oju#5?OupYvccJCwKlhIjWp3dS$2%^v{tr2 zk_YV6s-1{ep@@C~BXx7?EA}i65TWq;ARP-P)OZ!~8IEE=lE16)e^a7;0G^Q-_kg*6 zzC!^Rck{bOvjzF!+W{j{>*qE1@Lbr#nQFW4mHBv;fvJ1hGM)wk zOUq4)?V@X>Jr1_WfcL(7$-Raea^}o8X$t#d%L&1*rGj_lRNCuc4Ys^e>vZxhe? zcN()Vr#$!Z*}o-9-NT7%Fyx{B1oH3Uk^K&?AT%{%0X3f&+lcC&#sG9W%970m>Xr8y z4g1dvjBYFoPY5&P|5FWLg)3=tc0-V;k*4R)qvI^~X$Z`i-rrH=d1HxNZHC8IjRcC$tPUfeS5- zi!6=I6Y?>sTI8XkRJ|<~YYz8aQX&=epn1o=yj46&vVj~gZeOR{| zSpi_FsZ+vjIZ*Hmwzl{!6K!ROulopIRIa#vSQ4?Gnfa7^D^zO;qBNPo3J~R940kl^ z>dn0*4By)f=6q$6W9300--w8BZTcNC7ZeoPmp2>VH+sf-CJFG!Rnn6jG~T%5vVyQK z7R=5OX4`_wOSSwIm@h|~Dx)stU1(DA?gcK8D98l*>}ZrEO>DDUM{HkRd_ zFKiAoW=}wFG!KvVCVFlg6)39AsV?MLl7y>CmCEWyGW3|;NmZ{U$bK5_pq6Cr!RF7a z-v-a}cs>F+Q%4C(W+{vUq8hW8DVSKUIXV7jB3AMUDpM=9e!64Rdf?Z+#)J-6rX6qN z?oviI4CO?V;E0M#w^T%4@W0J9B2WK{g^2PAgQ!C}l}(vx(oP z*hMJzAb}X^bU1P?M~FmkSczxh3?I!%5;lm>4weW_IyI(i4MR7f{{mAysQAY$V388D zFm$jw`o%wrQ%!51KAg;&?Q;2zbE5)^OQ{1JR6#Wl5gmKeins#bR2w*N_VzaHIf{!} z0^e45<_B2;&HN9>&LKz;SkaQvcyl}41 zIj;w_N13ZQtt23_BIye;vB!F-MQRg%$GxBEj?kP1pYHENfkKNtN+nAITte0S_O;_mef{<9ia&NPBZ zM(7AIJg>fE?hr$D=Rk51ST(pfE;ZBa)`KRw%DZQ74k*$mj%);C^FpMdkMzA@op0~F z6y%fxrHxQ+#0?{xGi!j_RLpvzV{!`2$_*k+%euF0AvVYnh4WAJ@kaqw4?4tirX#L? z+|^uomuBLivC4~P6#I-5ib3CVTa*~(41k)EDkNlk=u{Vh+_$DykQ1tD`lbl6GV$em zXuWpgQAD2|irFjFh7eBM*(JFJ8P!5m72!{kyNhL~%<>`5lp^ym2NjAR(fC)}l00!( z;;fiaI@B0%OpPx$R~nq6T5@zuBF(sP+>_ zyTph1nd=fWl)xBaLlOS!3G)oJW-7G?rC|ShWfY!x9nk5Hv*0m zEoZ>+GCo{v8%3orC{OpRW9+}KZMVQLL&m$0^^@*@LR;rek+wchx65~_Q(87Pf3|}) zVXDFSWi#X|x)Jc+u`W$f=WuiA z$$T}AZT^=S)CLRAT$-;MIhv9+0m*(chLImaO;hIsB<)$uoIDStP`d}z%|Ip?sbyla z3CRs8)JRS)d_AvQCm(LdYh_8^Ia0IJd*jYL)P}iIRi>XFfb1IwMl%NSu$9zPaaxxh z!uOiIH1|b2s6pyLv<4k9#i)^ZPykt;kTh2G_)AJ(?^-koIIjNz%*IR&UdG^%!vTtA z#e30T8^C2iaH?$Ms~dZ8Tzovfy~If->FexP{aZ?`cv8VEkXrU7=!u@`(5HE=W0f%F zwITF5c;{y^^qax)aO_lQobn1^JoWIwG6T7uMXEQQFhDDc?Bg6GU@&JAL!(5mr=UFF z*~uRX)107;O4H6w*N$LLjx8U{$zBcxHquA~=*f{O~dt zU=Qk_CW2P*0ZEsIEK+8aS>X>elAUDhquHP6#y|2wve zcrOIfcS&0_fK!tKU95&}a4xICQ2GXTPD-j0<-x5EeF}@^8!!qLEe^Tjq~%UU3kW+Z-wHOdQc*e&^!! zDrsFEF9BLmis);9f6K%w9HI+G3SIC5d;AO!bq3(@ar>txCBD)Z@sT#mLE(!Md^=zl zZ3YreAAi}FF1;P7@CBEA*Keqf(~^;%k8i`_@jJkz#uzd6D8u2<=SmpW{82+D$7_Jm zqxN=LG(h-F;z_5A>2ZL+8uS8|<$Gj}(sX@r2J*wTA{M^|;x=13YyHRg<5we;*w4qp4MW<(PN zKzlG?7tr_8GCLR(E2@_0{c5y@52yn&d>;!A6~6{F+v0xH4al>-o9bFaJAP=|$c7rI zh3X9yOx|(hGHK)odsg;!n(Iewa4D}LVVSL?jNK5F(>5wRvaAc1A+*_+k2j-F=>1n+ z2&H(nn#_ZP|I|{I3VVWJzmnH=$C_I#h{lA#Q)XQrI(?MZ7WjjWbkBp0IzaoD7q5GB zog0T{{Rux$ey8ApgO!HuX<2?|*$!S7cy@H9$9r4lU6l6Z{+=PR9xSg_yW<#thMn#CCBZirx&F!<5RBn$xB0 zFB~7ECi7a*CmH}^hb_1er8s|y38C(EzFX?hzlHeCG8YTP%Xia4V*tEA?AnSiwvnAtzo}=3vHv*dHB2=3! zF(cG1LH`PzJ~pa#lI$zR6w=7+{wYH-5`3YK$H?bY%sL2hjdYV+qgkU^EHo83e!A>M zl4}8noFV@BC$)oUZYe82{c#qeiq`KeRcJ;hz!|=Xx`M)rET{pZzQhNx?w2n|4#qIr zq!2@wk~T#o?jN|7*e&aUCRRU!N_E)imKwtvBy!l&`Ajr;c!E$hS>}?9w`3^6ae>)N znTL^-rK^bM);6^1Za@CCONzDZ%L-)E^x*oeNT9NrGR3GNAz}x$QG4-nf3+2R9nW3$ zScal{_iuUs{V3`K-hXul_IB{YtAKvM*JEn2~ z>Qhg8A}$!SGXy=f#?1K{B~B0%8|l~leU4+o7!S8wM4Qoq6FY`)iyeWRoRqpMY2>@N4(PE5|X)e=3ls? z;w% zlP$XIn@|7U;P$zXjzP68S0e}7loE+09EB7*iZ{#z$P+Q22`ty@X5E}pYR+M_1-ES{ zE)2HH!I(;D!`C6P4UIXOL=u*?O{h_wC7z5HRfdv72Gjy7M*U$uji#U$W6+}XWpGe> z6VxmLxVLUDma?P#gP)-=J3p$`4tySc6q>F-_*{!)z{yNww9tB|*5C`MENMxl&VG-! zskMiW{QEMCLo+&j}g`2z3eFABhY);b6JI&#k z_Qv85T5w8#)4hMKd)Bb9!+6jBEr#SC_-wePa$+r`Nn~TdyhYQ8Nz@kitj;qqbeB(0 zytG!qBIIvUeLA!`Ff$))lU1ppe&4!|#!R_yvt$t^dv zF48%&;zsUd0g1oQQm*03Z)&truZk#58k2dYc&CedP$_FTSvHd+P+IEMqP2h7_r19j zqm!`%%S)C6L+eK8M9n&e}ch9cHR*-!E*HV zN!9D&MSYdp*Iem&z1b?00-dskq3jYNua~0(U4@o*!X?xH3B6Yit<=GL<5sUj1gAYd zbH(?!v50Me`66dIP0?EfBJWZdl|y}E$A$p1HYhwpViBR`{VIm7qrhrvC10LouFYST zl{@tYr|IU(sMFU0l=ULPCcs+!rgc89^1XPlX%!iW%$Zg2og;|RQN-+tkap%8vH+nm zJ9)K1gxnqd7I?)@jt-@Vbf+63`=4}bd5IDSYtQru`4J%j9&I~T&5O@fcuo6sEc zi%b&AHRn90H=6u-;8Ch^sXw?4?`Y&AmY^?QJ>_~4TNLy~9IOx?=(3T`lb^IlsIeDHK~?Bhl1 z_V@(TfVI=XK4Q4X$$|pns^Q&d8iE$P&l0rV60Lfo94I)k^!&rp&Ctazd?B%BwTE0r zzLf7cm>$ZbJ-)>Z%FtzhHoN*e#%7OqIRCb!DbTK&eZo4ZtP?w_9y<{WAIB>NgDZ*2 zaaVkum_Bv{z_JAQUDK8gtFc2yIleA;E`QyG`g>GBf2t2d4AUa&ANWS8tkA+XsfTc# zqs2qnCj0}TrY|Fx`ECz>FORoR$A?iHK3g%|OQAu4Kj%zd5|jhA#DARDCT&gMv8jx2 z2ns2GMfPbA1%)v-(V*&v>cqx1(#v#A+{X{${8!AM;5!Vx&~SjbUcDMzCbudaxYP#N zTKv6!B^X^kjgT&x0vKm7TI@q>JxGASb9aXhvQ{j%`~vja*(8^vP3lz4g{sy~p79qV zQj$+2|6Z6SlC=q>w>^dLlpp0xr%8G=UqD^}x3t>zp(v9>ouaNHUTV8?f8l~Gi$oJ8 zU;*7Vt;oAxtDn{F@oE^A`B&*(9@N_}WM<5CC)1A=SlDkG0>Mug{?2pZ1}On=tL zh#8|)2C>)zW+BJ}7#5Z_DJdT!lMXminB_l1bn@`Qu{h^*jauRWBS$^K09#di={XBYB z@sWJNBuw#_IIAbYuG4$k(ZG0d)I?0vmIkMr>lxLwYfB+WaFmuz!jrr~*?oEFr}7*- zH;7)l5Jd;PTm5vW0K;qLv@SxsT1s~Oz^`Bh>`-%_h%N|ZlU zgg1RDd>mD}AV+&6z!^tL^ACWH3NXz!Sik1-jrauXa{X}&r6t?hh~5f);=2IPCE86U zFOSo%745rKCLIJo{w;a~(h$cTB<-5!rZ^GQ+i@RGcWUdqd_{Ij5Ek;m^hT7FP|nsd zEuDdtq2IbDJif|(LX2q=)GZp^02X1g!)(56dF3JIl4B8ERqkI0k>U`i;~vR#i7AA3R15p?QE^Mgmm zNX)mHH&-L@c`uP+w|3GT75kJVc4^_ALrTXu%w|w&mG9@;Y!ga{F}6t@MFW#^y7`|i zu_>1%Y`0G3p1t}OA0WQx+Q^vhEfW6AJD>4B*}jn6&a#J1Fnn{g_yC6;=T(C-tsuw3 zj*w-QoAo!WNHRC#pU#RIQb6QLAvS*^ed!M$~O!(@*!|GmseW z;m#N*<)4S}ynI}sIUTmc)`jlrr#*mCVy6UfE-}(VE+cLEj#Hwbbc;^bS>Y5OqngA~ zZB_l?rSdE5f;+I$2`BS#XS`zF55Ip_;?z0w%X&$??v=Hj=ckLnwBp2zx~vwrMN!~^^__m_UAi}X(|)4+C_vV&>ui2_hbCdvhz@#psEad?mCw|5`mu&J)c9Kkf3|*=QnkOhL-9*dnkzq9j_KrWlV9DhT*TxJ zk&Lba=pA>Yn~aIADZ{dIEIjavj3Wvn#XK|9POnx6pYUBL>k15oiN?RvygE|@SpA?3 znV(0yukOtA%zg z058W5$~Iz8bfR+X3fRXIo-D^@VeGJDY8@3I*c7T;*9ytMLYL;-#}<>9pDV8QdRZCT zApfyg2?R|Tz2S7_DwSHhU}DC5xPH3W=@zOVQHuIs`YqP~rQc%uKi?J;0W%9DJInvl zZ!xp5Gjja5Z|DD^-|93@Fq>(k)oIh+4lV!Z+p^tc>$Lgr_%~JE?RxDs-{oNM)$k`H z7LUvM<76h1gb=Z@&PDCLmd!B7Ft^|glp>Ovih0JV0r1rFuLX@nD2@#5FPdB1AlP5B z8~|2iFehK+m0AV16rsh|N76xW_umo(yuT2PrRyKyVhDHaFiVe-pKUx@> zz#Y1}y6?KVIu^LP9+tn7N=%G^9NF0bGPE_a076a=SV&Dq08WgWr~w&~wUNbvtO7eD za~p#Y1h$4IMwcc+fDEn9AR52ofEerRSlVCE$;j7zfNPyu99+M^(@XPz!3clji^w0bB#9x0US{Ptp z0F0rD%>xP}Gec=%w);Gi8(3R`8-B)Yu8e;9>-+&Yzk}fge&EAV0F03r{fl&KYE5Bn zWB`tY+}K{|{*uK3U~(HHi);7yb+|jXyp28Z7lN^&t>FFk4g8V|4X*FuGlAI5{1nFj z@RLE4D?+;?8+$^Z`oFokxiG%RYt9_;TN4`_+3XuV=DQ^ObG)0Y#$Mah^8U<5{K_2f z9?nNbKtxbVD}J{_{9L0ovNkcdHLwCxaQ+UJ2NvJ^!~VKWVQYMq2mOFg{i>h@?EhXc zf&Gm`y8-yu9O0h|@!i+^o9OampHfhe+l3BG%*z}Q7MTjz-#9#Gwr+$I4w>FVs2>(9N{$TO4Y` zXkl05?(ux7_pY9YjdK&zM>u>P>fPSe zuyfU*YK={-$$)*|{qOmuHQ+-^@^mKWsXr;MlxM;SM$yyM#%F(G+o2jdp6v*Q%eVp) zOW(fCOJ!A}*-S8W9qhZ_>xzKTBar*PokYX)H1y>6HM}tE<7FL9Xba2HDF)XFqjM`< zLt|*WkVLyKb*~W^J21#ieZ~vH0^2r78hmU1!&%rVArVx+eaA6d`}doP!?7JFVKW+k zDb*iUBBS;^j|^%qpFw!{e*~&e`SMcB1P;+xPWgmO8|kSigdvc|yCHm!n9U1^^Ga!2 zPAM+iThAyb+o;;I0)^ugZJhbxGaDlWHL*4^(rG>JEYwbJgJ+Gq1PJOPK@NM2DZK`? zfb9TVjPtjx{9Z|@oN$4-ytXze^4?_TP9Wa>IhfcCkjuHDt?|tJ0V0~6OxgBJ@f`5oQ>ekb zy0E1Txsk7Ig;cZ@%L@hT!&Ynd!>o%U-gcxZ%3@i7vr57B>{ZpIGJG@{b3ilXY8Y(x1&}@^q z-+|i$f20N@T(kN=DXu)Ub@CQwRlY?H0&eCT>yO;L0Xqfs8(JSE9)E5vS0rkW(Qd62 zm@Otii#zId(WySuWw!h&p>~R}+)Jr>iP+`6AO|&7iENBlrB;ocN>li9Cs1 z8A79~rV>Qh{Z%0IYr&vC1ss*IxW>7KYddw2P1pjfVvi=kdW7d`q$twFg!f|h_n~z} z0;^Vf&6~L!d_b)pI2#Zh!mI=)-onv~(Nl3_orZi$Ok@LpevR^aV`6i23PExYt;$C< z$?IXbx|0i6Jkt8EC0$NWUfNW=+G;@3z~yfwqfkR*zSc$18Pw3wvW3WXfnp|kFvC8e|ckJc8Rk&-no5{ z>o_)kgdLg;J#et%dTLL_?tYCl5{t-Eoh8p(v;IUOn~3wB7B;prb|&W!SZk|;I9xQ; zrrQq~XTi;x!9y7;A&sGcDcck9qTQ`}=h{%AN}pQ>*`_yo+l1fs)noM$agl^WFOc$P zWFUf-Mf@Mv10X%&IDc79XUTQ38Ajkx%&{%XA+twBCB)hdZxAj5L0+E#<@CwPAXX zc)ZZCKfL~)_D?UgVZ5}K+-{bOM8JCrKnLC`L-aOXjk}O@1flr+v; zv35G+-D?Vtgg+qO+eRHjXlisOqYU+#VTcsMO>0@ycbR(RoT!4xAt=jp_|)=F6VS{2 z|6b970R&L_-gB+Bub;in`?;Sw4o?OJ*$7mnu z&@|ZKXUWn-pg^U=`=+PDMIjlCuaUEL2UlU8%-nrFbIjU%u}EUa$Xd+)_S;nuQhCyZ-plw6S zr+PTQnL<)zB!R&>iWk*l=TB`ayasx?Wirc%Pect~#iSPm&VE_RRmv)Z@BzPOu(6Xe zdUW-COwGzfV^C|28r)lKeL;Vb9s)@n6Is{2`$@(|z9D9temU8;?wkv$54~B3gnQd1 zp5C2>a#L?$wS^@O1yt=|@ALL@Y_&r_pR>*~%=dlu1f)r6gf_$bkBQ`w44zl#lkY!o z9@bbF)fXZcY-w`^cvcWZc;9rc9j#4n^K;S>UVSB!IZ4*S`acQlQxPxzxIoPPez6oq z@drAHwOXe5rLzCMU&uXBm!$nFUp=mJ|9vavIM<|jSCC@KJzF}F2BANOIiI*#*yN}_ znPc4AV)h2Fl^9K@A$+5?C2eO5tA8SBCy*9VS^M+Ips+lt5LDIu9aQ&m97CYopsXSt zy57?^Gq^*ttsv1((uIN8BkBt`$%}Njlujp=#okraX4dKR?XbA|&^JC8J79T2b^deO zp;-6b${20CabkHvy0t2^#Bwhi<#Rh<@ zPAh3)4_hp`s>3NOZn&WMS7!Vg<`)>YK4l`T?iNioVk8moLdKYP&4|bFzHKkY7bU$E zv0BpYZ49wTDD;B!;MvI-iIH+~WeSuKD3s+Pl^+cfIp7HVEuXqK+1d8-pC@NDP~kF5 z112|+c7QJ^4a0N|2^$CB>KcREpQ|F-K=`a}t2(`5$Pq&e6B_t>995WwYTMmyE9sl* zV+4GM0R0O=;@_O5t2`#vLLv34HYwI}jlT{HXioQ`KkpQKn^m*~Ci1WoU6noXGL3)> zO`nosi2`|v+}0ha)s;{XRZBFBvmv%ex43;5={qpxgu)4)fSuKR&^~G#Qu_r|w;oQG zB|w%!X=nOc)OmFvt7i9D@+o|6tG&rd2)*tHnYMno)MTdue}YHADTKjJ{=HSL%%k^| zmex9LUeYNEkqS8!yhI6NDo5Pp?u~|fV#Qd>N|-YpgX>wfak!5QLA?T{B=@s2huZ(h zpb?ZL{Q8;B9)DjMG7nW)MY@l23TI@F{)AlN^+!dph&8C$bfpNYp|$jig=d{A7Zqh@ z-X?^8cZe+|$Ug|(5=3b9De7`L#H?p71+#Myn~4-&WahX{Bn&b!Gss!XovD4qHtxN% zp~9!oodi2qUG`|FNmAe3utQz&1C@L`8GdyNayXFxC6!ZOrPyNrcV#l5%@^i~@7M_M zx-nBoZ$GjF0gEK_fTr^~;(=AIADRTxRoA~yaTXAXaiVB^#IjXbhl{k*N`qH?-znpt zHVC`6u6w=_lO5`1r-dJ(v@ZvvIU09w=e}-YJXYz8#O~0DEK3WIJ2m>_CEi%3Q8t`t zh8B|PgP)$exwMB5V1v^o5L3*^M)i5Vy2M;m{+uWs{re<|fz>Jd{i;SQD*?kGu!Mx> z0sCg1XE-EiRQmO}eDQnXhy3Z%qK2(XN{~?VAO`Jvjcc*1wEf&R2LS&k<6-mGCF);1 ziR|?wM~SQ6=o0bC;<>Bd9!Mtlrc(;}`erI7;2q*gIl;{yaQ&qIlTe*DaL)p@tdGpK z-D}VopDTl%cMS^d?&`MUkU2*0i$NK^;UeK~%jobo;uS2*^RUk=A~^2ndWUW}(te4W z2An(YCv386jNH&l2OkqE25w3YPS1Km%CE5Dfgg&zOEchs9f3?pFmYOD*Uuy`lJp`b z@Unbuuc%Z4a-88t?Du0wioIUY)|jivBlT5sw_28H5}u8I%knL<>fehZS)U9E@zr(b z+7&?iWbxt1pX723#641r=^rGsBt}wti!TE;^KMpXSjyEGhmPK z_BLN)T{<-gooG$`!7J1hhNKXJu+dYswPd!DhO|j*%UUs<4NMKU*f{P=2l4@RLZ^veeoky_OYD58uL%-xYVga_nVv%6m2@eec`oXlMZ^xNQP2tysjV} z+Q;2&I9d$3e|Yg5KcJJbJFKwAk6JAVQX za5b}0c{4x`G42?*Kyx%Y$iGl-Gz`tY)4{4Y{k#thy#(u*iXTEZtpF~?N|BKX!VWJH zBE9lk;e8#FUWaPi91j)RARZ;G&t#0s@~eZS)}#t1Sh&_e|JZ+;ZP97a%0SqUOuoxf zL%sxJDnYKCaCd;+Mq|_hqc7P%H+QT^J;z3g|1mFt&3ka^#v`shdmSfs4pZFxd~jJH z!x~Mt4o9YJ1>qL5-TQ6}yO+r?SvX5)aew1tXFjMXu6XDQ3ny68sqg!{|2^_oXPVQ2 zz40ZD*4pYTa%-M!-UD^Zl9}f!p?zsr9i@;3MwiaG8xKx#l5Ih$00nRI)9y(sP2N1B z{o?2K3P8c6Nd18d%ryGf|yVh(5D#&y{%=;R}*DStHR>#)Gyl}xZ< z`!$!|>DduG+)KU}(w!6pVu!-|sLf4V&6WSlX&V0)X!g0Hh}9)MqPE`=T}ebX@&>Ff z666UCk;RaPF_B_04$pj>L^r8boajw-jJ>r~0~r7llMU;!Y#t-jg!EI7(5xm$OWJ09 z9y@;`bDwQMPqgI});y)1vnsr>pI?EP<&@cy0B5q5Te=_n&*1h zqgkl7%FRL(W^DZ!KUoJhrcGn)4QLm7O;tr@GFM)Tp5O$<4Lmr#^ybvhcy~-tJm09c z2X0uGI@Z@(nGQcM?c%Zgjew@*B|i3UR*e2qfaZr1$6Q&!pF;l<$jt=td)rVsFn73~ z0xjAiM~+H@Zb`(Ux_6d|&xlB};Sq`9rP+wt`qzfvZ%)`P&`0`+LH(II@ZUv3R#6jw z#feBEXtsdXxN9ODkv@T2iFYpRZs+5bT>I7iI4AxT{Age!)R}YU>kK?r5=GJ1R#;qH z1yItHNCnJ2pQY(N-p3|ZrJ~NJ0maArta*JZ6Xoj5F$XFg2H4-hh%t5*e>Wl+|A_TU z)1c#Ur745=o~2=zy-(W)<0w{`s zL4~6E0|^+sDb=S1W`y>*R~Mfby&9vbP!0gADqu|y_@V8*Kz4ks@Wj1k@bX(o)#G=| z*zlnc6J$aw3%Ea`ewXG6LT45lI6Yc~81*#>S)lBup&($@=TOz?lI-1p6}xbN=X9fM zxZ%Q}M;O8cdS+heo|GBhSLD0Buz|kW5|2gfy{BEh5kFX7t3XWSp?leg?pB#0c|PEg z_|29S9Br9^4BT`~E}VsIw;@;;ck0uNq?2?m2OSZ z^sbWH6kwGKwGu6K4!Sc8 zh_vZ2(PJQzyAkH)dArwD^*9Gb;t|rXCYo}tHl41LS*m%%78FtD`b(Ui?3tHJL&OGo6&67btO9Uiw8cP@zBzY*`dPKFkVCT>3|U=&N=cH~ zu~O-mYX@iC*BsG2B;g=|w-v85WJ7QUnhqAL)x^~l!ef7OMF>z#`*Y<7eol!| z$V~Xj6<>d!%d$s%SLUByZL-ED4$cERX^hGZyZoW4wLu(a8;xnrjn9z#NTuFavVQ2= zw32|Tht;HJuVZ?o>&Z&~BGryuk=G>Ir?NXSoLhBAh~NnDvz%dw=PLxZuBwaRl2cxs z#Kt#xSg>Gc(2}w+zJ&VvwnIEFHY~k;b^dn(%b-+A*&VE%pSYx$JIXiAyfje?*iLD1 zT)2%m#mPHM=;kjJ(Ji2O{S(N$cBhZ|_j|FoHMuX$XEzhP4r{5FVcveu=?i%Dc?yw;Sh#>0KE87=!Qn82XmI9cj*6S^O2bLN#cfeSC z0+AyOZT$tD%||^Grr)9EufB&02*Ly-&!M>7RPga92MHGfp@Y8z)=2&>3P6r5LS3u; zM@Dd}6Bf-IIL(afVGGx1rkS0RCu+TU`K!#Tqq2@!?Ay-M6p}b#Uv|&Fs2u)dd4mED zz;wE&KkgJY_DHj;7NUAfCY#VYq@rLu^rM$n2I52@iOGq5MtjuW<$()ux8`|oSI}^< zk&NEqFh`e%8jbafX+Iiu{FNPb_7y|P^wVX|v2d*_x#He8LW!v}cgkPvkLU(F^f7(t zV8d2*d1JPB)L?S|Y?ISX&)KVzAmk&k%2uroT?UzC05;UNP#Cw|hh!7Qx{}6|v z^T34#!-iflI7+r|&#FUIb>F-inR|p7$GrvU`E=MTaEDj7I$!~D`jBywya)IMt}Y?5 zk!NUdfyc{%FxDcyMjR1WRQH(zc$KUt)OPzp;-}&5+B}9q+p^ua|5&p z_sEvG-P6}gAGq0s1Z4QZPpq-lT%n?6@z>A8s^U&r2gSqR$;_)O-ScEy?#n&7@HCb z9rHDmquwf~0!0mr$j!VSI=`;5fn22yr4S*1=|v=7LNs(JckiM7$LuN$O_dOUQvAG} z?m_`}_)>`WFujNj>UhVJhQ6NI$~U2Z%F-7_nGO+W<|s+omRj3zs03npRbVJOAOF!b z9IDU^&eLcc2}TNs@BgSd;B(*3S!%A?_(3NsqsXdWstAb zlnX5Ze7%uDDw>&^u&g!emt|Dg%?bzpKQFgn|0A~a9FV+OBr+N7%JGeLN zyHMBKEwWcMTa2%021}T(;fS3s+AwA4MaFwxk)Lhe%Tu=KY zK)&;(WQ<@dCK#?&)F#- zg=u&XDQS*BY*vrNbe(ta8Run7V7wW?cgAHwIR-Que_%FETUdyqx#E`oxmr6FhCi(o z8Wh90AEVy2X+!g`gi^1BU$Z^BFKVVU6=0WdOQnSA@yAKoTeDMvzq3cO8d@2)yB#GL zoe@WdwW6EWm46=TA%~TwmQ%Mh+{hba%y*7Qd3slc$fS!CQ2tSxs-rAt{?HcchPIE= zrOZs%?7a?xk3btb5ci>o#ho|W_Ek@C4v7@;q8Ks^A_rp;H)EK6lNu7u{eqKnTi5=_ z^gX`0<7}=*5U==Aowzh!%xTAEBE>3#Tcg2|VjWHvD-mO+j3Yg@S({vU+>Ie0gBcrn z-=M*+NIss7b8SA+7j85*M0wMe4@OPP7;V{M@t;f7mK$-6V2UE$`xBjS2~~Ll z&9uIU`c_MX-6r3miVB=L|*s&Aa5`Z+y8B5Hbd6X$kKq`;!Z5EPZW z;fKi;wX1eB6Xn?Dq{%1++mx&;%BxN6wfu6nMKZ;w6WtDNW&W>pEpx1iG5bDnzQ%ya z-?(X-r#IP6FxjLLKDnaTQ4yS+XbI1DEupl#}|a*0D=4;qe7C zGLnWJig*E6h^K?=MJ!>E*mGpS1MUF|qie+_&0@6+++t+|;ls{m3h)W>e#^8F(WZ`U zD;~0mUj|h#`qR$x?nci|6MyObX2_xk6NThCOprRP^mb%0n=dsK&+x@(;{@`Z5y1qM zFC6M+ux}^fSb|QiCwmG;&g$aCCCovjXOe-*eC(Y9bepQva$wl`1hFI-%L81stLK$2B@d%bdB3~BcP?Ldzv z5*KRou<$N|%h4<)VPvRg}J%tj9U~DVDw^SyWz?}yyy-bvK#)%iBT9WCNPGF_1GXd31W%LBt ztES*Q9s{ebFd?x6iPH|_+o6Of>0ehb)uIi2(UWHmV{sr7GQ`>HF=K&eFVzV42k}#= zAX7>eII~#33$JWWOp8AUu#pn4$pZb3jZrO3PNXwVGOpA5PJmwSa0yQ7Q) znb%Z$sKp*cN~=D>`B!M>U+esVxR%WSOd~~3RSwIEFvl>-rJ_;J1^$_3RFyXFqS3-K zVI(VjlRV`LvS)v?m(t*>nys&om6M1FrIh7Kdf!qUrsq>dgS;Sf2daQwfNvFBNa=!F z(*Bm*lu)C1q=n0pG<}TECGTyA_MuzPDO^QY1(6(eM9y+0k1g30he=DcY}hLpyTjYF zRfVEOEI6|$p3giu`;t?hxLX$(pe#1Eg@=6>{R>Bv#?KW;1+(BF%lYM5M5^!gmf3r> z#jOfKf6hG2IR`xFwJq#^hwXad6%#gfy{MqY|E@L?rw&w;fo=OZh%=EDW#Mflsl9#b zrM5Ie6xg-S{{5v>sb@a52K~mnopOJ&#U}Rje=pCa1`!Y8ZjRR8G^zKZ%NJduL=)Gk zEaVe3e_UQEq%jM>CBB>z4s>Q;O16|q$D}+ZF6po}(5Wo%_n^IB3~5s*CiOlcalpn? zTt^~JFsR)tHIa zt_jG+G>UP+qr8XOjOJC$US7ZNwjbdh)u~zThdvfKP4#28X|94BGTBjWz1}_Y zwK_@{_JU)J($f|5@Uqlb^OyvSM_HQ-MtZS=&oUSK z3)L9Ir?cr){+o?;20O5_Lw6PwD7%W@G&rab4WyhU?mJgafPP|GN~{Hhe?tM00qqss zS#54_7}6;CMY0tRu}jagIPh;NI?gGa(GmgiFW7{MQV8oBVC3*?QTvdM zXA%7aX3|_>=%nPcT^MRtjG1a^v=kF~5l;1T*vNrZmlpr>dYP$^BpAAfhF-9Hhh}Kr zZNh245d+m?>yi-yA5bU_i(^c++di!Sfpy7-;>X6$;@Rg$^qbSvlF*OF3okX1R;$}0 z+dWlwMnXNj9jR2EgXK@Ybj2T*BVGtfj2oYL0C!x@;^sZ4ms|dsa^zWjLFek(jCHr0se$7x3=x<$$z5wq8(#OClS=nI=2?t&Ie8nR^3;JRa1=x~;h< z++eaqaA)#7Gwbm!LP=O_4gwOrWE;ZQ)Pzh15d8WG<~2@}N;IzA)Rh7#vPm*}Emn_+ zOBI0+=*J9gn(lV$*jh{4+E^(Vu$lOe-J=q5LHf1|%@yYI)zvi#D1L{Ie$xapfE>v4 z9%L9A;X)XB-l=^TiYqlyzJNXj84D9KA$3^1opcjhM%?@UkvPW4R{nakK1{r*7Z)i_ z#v0U4N(`r6Cd6AfqV{hrlKfI@ zpH$+4l>Gy0kvZZLQRl*=3%`qD9`6!R1nf>1=>unWzG^?u)^6$~?z?4$05Sefb|6#kNc6eQ<*feOMvG~M=*FPDNKRkc( z%r*m>oA|GQ^7K!dcwRBMIdf4&WcRR)R#P5eHnad|s%zlTUM5aDS9VoHM529qP~aKX zVz9t%dBO3tlvZy=-kl>9ULsO&7Yt7lwNM58;PMIFUW8~y zRPjG%LqOJ6TC+)qeNGWSstWIcH7KH6;+-%}n$1aGx9j=J`bAa6a6v3sIF@7|2z?d2 zX-TW*DVdj?KGBUfyp2U!Tm)CTXpvwH9dG z-7PEE)_J-p zb5k2EVK_1iUy5US>gv<(G!5B+{zil?aO!t4@Y_Wb^cVx4Dg{dN`^^L3MwN=Rw?)4w zLm7fcyoL+S#cPLtm_yOO`>juvD^d4KODQ+sXo3INQ&I#i(pz8f*IM~p|5R|>cFOc@ z3d8qFsln)Wt9@DHr!^^&DeNu}#HnL7+Z2rqsMEGQWO@Aey$=5$mMY}l4B6@4O$Z4y z7v)z4nhrY$$7t{R@F`X!*^jW|rJR56bk7$r&s!M-aovf%qt5(ry1=O7R8E?y>rr5x z&Zmcb2vVKk<0{0ZsX}S=Le;C@s7*vpW(P0Z9lo-cTFZX$t4|L3-+x;~xp)O03j2&S zn_bT>o;rTdJukmRL;HSE*DEK%s6JV7Qrov^u>Qo z$2#pn`qIg|0@7-@-dzvV`INg5t`<6NQZ1%k^c(Lg0&$qQQRdR=MvZl}F|xkCt`Rzp zZ2Qx3R+@vgrI2g%dArlgtc?YF7wg+&ZlR6VsGU{^VExB1eK4!?H@ClzfsSV9bZ1@T zn}t>koziuo`<^3w+yt{kPl-!PrXS0%t_sM3{c*?D?YdNzRaub7Ic}7pd|7VT0%exH zL!0)8Sg3Xcfyrnbt)EXecX4Q%%ZZGzni_qwF{tZPkb>kx;wVY<;qi~>yeTRKiqkV` zj=l&|rfW%B<8DE+wF9f8w#m-JS#;Uz4rr9Y{jht)&+{#TpX76A|Cc_f@9QJD0Nr~B z*;FyvO4srUT6y+%LF~}R+{`PC`#s*BBS*WX53HN3hl$pY4!+Y3<6)@(Yd*tp8-}%J^Uq1e-l7*_4R5( zu2~e=d-Ql)@cMa)gyd07yPKw3H9V+d(1|x?1RXW_$s!3-@N*n7T}(#*&}9V^kK}-~qGqSa!iwvhYe{E6ewvp|!I=Hu`Slt7=9r6T8po z!u!X6{j^iVA%$vNUwxO_EJ$o%5g;UXJE(7al}TtnH60%PO|5QqfOk3|6Bo$Fei0JU zZ(1SxJWKnpGo6)0W(JD8M#p{kzm4JMt^3Rr(zD%GWfdKbOcp>NT+1zL9KTSU9JD=o z;`Est?6ZZ^x;aOMs3i7WK#xDnupPOcu58DJF^7&b#>ne448%AnK|4!u{!=F!3uRuk zE?c3R(_qa~ltW*74MW(*0p0AOS(x&MptPu*pc@DlyyG_g{?auxp_3-zJacX7HUks< z@;&`3#!{B0D#ffmJt{zPg)RGBJA*TSp_z!%aE|TpSvGQ}8|y-`{Cae$DE!4{Zt{&e zNXoINy3fvV6dbjuoBvSt|K>v}i(aMI4dnE9hP(xq3klnV5#&?;Ie?@C|1KbgYwniW z7~T;xHb)i$=cngvXz5EIQdLL%VQqedM zET_Opww)`liXw3y|x;{jIkjP>qlbIzx1(E{U|Ch-zezPBNX!G8G$HO{9jZ7S?WcGIUli!pikDnqW1wDUmhceEmx+jFkYQQz zt|eTC*c$|k_ecFwP;yc(0qUG{I?BzV?eN9!%Cw}1c?jAroOUM>vbwse#sb~f2Q~s?5SbY9c&JG# zsYY2H^eJ!bBchdyw=ZXu4GG*N$*yqDq+M|eihO=>pK(!w$E`w?Ny=4d>N397We{m0 zoZ70TN51@*DfP^iy@5s1qf zyk|m8pS+^GP;3op5NL`e^DJTK2v!a-WuErbdQZRH>lGa5~YQtrL4Ym*|*Z zz_=LZl?8gbIVauot3r^IqBgw~Th#XC{lt7`|9qId{gkgUz#=Y|H7CPOGvWn4~ahoN{mM zy#2^clKVQ>Y+E5Z2tmux}uvAX#V@JJ>9hWoiAWV>+AtmKHxkIcMiOQ)~{QAzf>E6!Zya7#J59=sH1)tVr6Y;h*96<*%VnPrvI zs6eyJf`Hj$bWPTTv=@AaCWyzTqd$A7NUmauK0oN~Np+`x_W6)^^JbLM1BZ4M#F$`E zGTyWA!q;CSnyi?}EqgYxI(5nCg3g%7iTp-P#3f%5UkPby86YK`TtDW?B+`U1A+}55 zfDn7}zIpN{Vho||{i>!b_>cxxKt80>`xM>;MwT_b4PQ!rQ9mFsN(3+OjbU@SHbRb; zfTRo(j!=wk_3#|hrEV7HbX68V>6E$b`+|!T+|B?m6f`LA{5BxuR0DCdlKtZ9Y~qPG z+74j18KC;hGq3e$B0l@8`ishHEVC(IGg>q%hiW12p_2OQ^@V*a-s=5cQ}?}{vc3pV zq0(SumeZ~-C3SKyp}2yTE%}pI2RxQ8Vi{{$r^)de4-ci!{LJis(0(Ww$2hdhX0Hmh zEc9#G7<=|dZn4dYe_A9{jSdiH0KC>wa-Web7tA;go$gAb1vMovi<)M5(|^`OC7Lq{ z{v08zwnkB@IM08Oa;YmnA(xUiSlk+eRD^2F;mSdt!U|R( z_LRri-4q#LlTzS-t$OuJ$7L?|*74byQ<9Vvj+OESA|fK}`t*D9-5~Hqek8r@6q@L2 zAqCw$M{f8UUH=xl?PY@mBYH!Jy@~JC7=j*6haREAaYUro-=GO-1e*2O?)!nv8@J3J zFR&aQi)Em+W|*XXuCI5a2x6!x4EgmQCE05{qfId;$PK?DP?_qjcOVfy6TTWwz)!#* z6}W2vIc)*{rYr)2sTDoUOI4e6zg-#HIkV6KVwH00Nc&_>o|FkN>8k-kgsg$R?N*^w z1jkwiP3x*%D9RCjrMBM9bkYyqJtrw`q?CtyM@`cnCURZ=ufzTk?#V!0`eUx@ojkzW zyq?}Az>|c!6&EP^BrSi#cI?slQx45yV_2e-bg#bCZ1dA{e*IE_ze*O5VFm}+U(H+|V?MN^tN29bZyEn&*?fd>9e3u-QgC1zQE?ImLS6SovpA!#} zh*ntY8)|F;?>g5eJe%dlcz94z%3&?y5L&70noJH+Y^w;bo$1YExz}2d-fCx?6o^zVQfd%RD;YCg-ry^J1)m*9Jo6^X zY?eDt=BmlThZ%kqEeXaaJXgc^E1#5OAKjru`Fzi;dAXuniJ!tsXw7zOeMkZTKW)c4r#(}Un$RU<)7Z5R(AcOjUp4&AGb>^X-xo-uo(iNZLesG;>gJmnTkHSEc*CcFn;f?EXT?Qg$ ztkf`k$Yrw36XYvcLKxLPf&x4>#ZFNU2iqeM2noF7AJ%9O0p1r zzWhy++nQ4uY|)jsI#!zp6+n$1evrisRF4??O@pcDyX-eYI0ELjgLH`xo;!{wXO$0% zM(5jkL!~TISIk$fem(qa4H0b!1-gw?mOZXQQ0|D}or?0<24w8Tvzw)U*^Rr-97%+) zE$(jD5L4Axkb%YbEaEjDQN`)-Xc0d17bDZk*#EwtYRAHYO!U$+9b#5SXG%~3QsA0( z7-{4)V7u5dAj6kYHX2oC^?e<=4RV;uKZq*Y-6X^)7|lqr5G7Ok@~ONyhzg?4R0 zMhf5O@Ck}@cZ;jE=T%N7uMYQrHhEnw6re*D4Jz2KHr8c+Bupq&S*AWvrv@IwV#CqD zt+;X~lM6SZY8AiiRXMDe?Fmh|ef;ZH)^;qk5Oh6BOPJhwh!H#oc(Wc(X7ikTf&DQJ z7ytg_PNDaqdXC1iP>P-#w&E%y2?gsN|EettcCn2gV98%-)3=#Ldg8p;p!bNvo&nt< zXzyMsm|jjfK_lx^aI?}O=sqWVLo&U3o10S4cWh?zmpNx)Lwi^LRv7}LlM*XHcErw; z+el(_>r1SHg=57{P(@^}OzIYPK!y@Q)(@!;-$1#kQGG>++}Leawp*wE1}|+Ll1&Z< zT$0{vxePgh_{jz4YR_Gb>i}OQJKd7p9V*3S!M)Sp1O=sXwR4aX9dgzn{Z!$YflgS~ zXW{J)=7`Nx;}K#!(ftZ@nHTm(9Mm5T=H;lRoYHYKgDu^#+dBG~<9UalI^)-$?uO<* z&}XKHPk&ZQr3eA&6gAMH9LJi)s%c*OUbo#>-ew4zmzJp0Y1uG=GuTRut?+ej=Th)- ze3O&NgA}uIvH1dqy!7v=!Ef5p88#gHTb8=i!Pssq*K7~A76wb{v=$VB}YgY zG8-Cx&Ow??yl|i#IINPX<)i*BXAN*SOA_nM^XYSMUPHoYsiC*swrBs+o^x+!ptjE7 zJ|!$9VP{Ih_kQhggaWg}h4F|kjxgV{oiOgW0xBf$5Ra(aUJBRYheDo&+S^dpo^?4m zDB;90ODmt2K5juK$pZb-M|^(W*&}UgR6l>N&^RZfFF?QvE0+OH#}MGr=<0Cq;&@fD zoNZ|pt-`80rYfuW7)ME-hnu-cg2$HyI`z+AtH+evlrV?ddPxjltc;k_ zFNTM5-l&8Zo*Px6WlQLrWq7o~7=>OF&{X?PzgEbmK$tR>vef$MPj|v6P2_G{dU`TC z5Z0Or0Ga%*`zH>~Z!J^j7)d%)#}dXKF}fqKhHY#N!?cTeESUx-pI!LjboCS~+XTeC zC1)Db6B-t*3)3m(f4aD1naHjv_Y~lGYH_@_Fehn8;7)OafDpbk3)< zh1Uk#7D(UvnK{&{#z4p}fP7j@uwL#k#V7Be)pJ7C8Bnf2ebBbfotiT6%@=xq?TXR8 zE5w3Vupar4t-?rRFqhToUT|R>robe)d&YFFYNtp%WDWFV@jjl&;X!rF?eaBQuPe<} zD1-;-Tl}9gxf_AU3d~S*UV;j-lWJ9UKiO))C&{D0_mJlvy5I@vIc7=XBWkk80{LYK-W?5}Hmxz{LkXp6UPLkWdx5?ATD+F@&wD^S( zhAg8nyQcF0I3QcFLm~ch!kE*;yj)wTct+HHN3N>Q0#~*1!O~Le?nag@I6(FYyxMBN z#j{gp1ljM-QKBmY`S5$ScAoD7F5ieL$0xLWo@Vc2&jgspNS_n|9wM>=x?u8}KK_h_ z96e8{hToO{wEU{h5c<6VCX%irrm%By#o6inK=MozrwGH$OB;#gf~nCierUspb9^Ws zq(=bM{f6f--II$VwSq+$WKgR+SaQ%E%8_tEHYGSCVrnb!V7`xveGu^fQSD9Jl_-j` zamU7tZQJVDw$ZU|+qP}nwr$%s?mpu_tzW2z(x`gXfKz|>D>84v&=jrVLQ5_}zT<<4 zI-=GTHP1l6-;|u>40NeRbGAZcZQ$pnI4E62(8HjKB^JBx3>OCXgIUyCxKyuE(H2Z- zUPET47nT1&<`GA^hD4=`r3>_?fX<@z&7ZgJ*$j`(Q0^34=&IVIld_a!NANY6N;JIm zwKoS*ei`d^|bhBZqF(SAiY1lo2`-r*QNx?|wrWG3Zq!KHHT<=+PWQa;Ai z!cX>;EhLA0CtK|+lEY?>s1g4c`;i-cFMyRwPe&$&`X#eDYH(^H^Ij3DY9;7!rvDh` zDhpZkXSSg}Cy!S=sxm?Fn}fAou`jMs|A-Coi?_21O5zp!C9q(45R{<4rB>JZCg1cS zw5=i%7uwzd3e^Q#dLP^V(!4Oz0bGvWnfQZ-(W*#{G) z$VOlX;ON=GKgGrAj%?K*hkeK>hFuWIUr4>Lb?5#s#x+9|Q3x9>IT-x@^qkYt*pn;P z<|wj{_?o#hv*tFbvtc0P%C}hfqBY#aL0`Hr-U)w9bauI?3etCv#S3qdfT?7&{xv*l z^g&hIVR4+*V42PURdpaINYvWvYSE$N=;k%cjPNeXSi***>EKPZhvUVOu|B@4qB!w1qh$*-j;!pzgh2F&Pu~fW+3o~wG1t^2-Ol%8q=UY zy5sSgyxIL{SoE<+yef1vUPQ39o69-oH8I~qmzM4R1@Q2{f@oP#u8-Kms?%jLCiBL#1P^!dEbCk%{%`EV6& z*DhsCvPZT5HzvzzOJ4_7{{~TxFD;B*yM!o!Xa5PCD6&8lxynVqH3?0%5LtS!^7h|1 z>J?-$Y0A-IV&Qyv*r>XGIx4+kROTnh#h1WWi!B4>HwI5DR;46ZWFvP-Y^i@@R#jCf zF2TCo0@(?zvUL$j`=uVq2u%}0z_C6^nXJ32J3r>&{IKccebNc86xaKB+S@QtKVy|t z@=6ty064z}Z~(cyxD6B_Sktr+UUZddKK{+kTb+x9_;=ps2l!3y656TO>N7I}aZc&( zFF?Tg*9Zy-v*o1((fX4aVe5LN<}$pJ^l>4kR)Vg%_zGDdXNY{Sf9Sm-LOu0h;S!O>_V(M+-k&}b^o#Sc7!Krr&zVR|9%v0 zOY5LY8t0)Y60(P0!R8TwV!c8TH$b^MT<}FBzyWRTg#(*hz z0<0HGx3lMNp)EFuTgJcICWIBG;9Ooj8Ru!JjxW-U8BBmv1u>?x0$y$ej@S&{**4DP zFn|XXvm`p&Y<^(Oc7uEh(BF@p1D$CvY^jdIR3^;}m;qbhh&}Il?FM}fi`VkCPC~3& z-E#o$&4(39UVLh+ok=n^7#vVtF{=yq{6c>OXZ#&l6y*+px|N2;C33~x999aPF}u2{ zewb45`U{4%P-iHG>WV{7ilygU|7>wz!j%1($pQEDFNb-y^76mRzR$mbF9PntpqA*! zWxO!Y>*{@kO(2HwdZBk}Fq()*)*W)I5OA)T=}_UT;YtvUr$I#C=3lF@%ZQ{EHU~zf zU_dxn-Gf>Q>TbUiyw;XGSO~w4Ng*u9w1_045~H7L&R$DSDp;yRXV^Q_A8BF0G$Ekg z$&Gx=gL~4C=zhiImJ3*TAdrC1qRyKd($Sn6c6Vm~`(cP_b1>m(5X9VU#UO$b{8 zdSM7MiEHaI(C0_b`NiPfsH~a+gD3M7!VdEvSeB<1_u&!~R5c83lPJCxb^1 zi0M|qtw=mUDUaY0{>;|;r)UUTducKyOw#`py=KJd%@LBVJr_uEM!j`N_GV?+C|^Y| zg++ic!LC$xKGL{1o?jFtu9Liq4L&Rw974H(6_dF6GR+yvgNU!oH3)TCS+hAk zRGmCFZ^8bZtpdk0Q9krkT>8xq;@CiH1LRgYQvMw5w3P0R*K~Nrwn=UJC>y^FhF)={ znI4PRDJ$Z_hZIKX!whY{uN+;sY7+%H%o7Z+_ce3k{L|83K)Y-VpZ4P|gpiXQmBU`2 z0uGE&hwEo{fma-*Vxat#BN)0*GpT^``df01*j-R$!9~Rgkcm-j5gzw9fze5Kub;tR^Ayq`iGA)br-nzgpr9s^|>_r9LDq{n~iFNbqjGA*0D;1PpJ z3od^!s8UfY0ogYN__A3I8~NZR_O-f4ZMMkeIhOwBKwP~AY82B&rd|Hs#aD{AiB$L2v3wyChNN9(#7ROae^TMrGyS`=!6%d z10zmLo1rgUh#jJX@{+QHRuzN0ee2OA+q{Cx^9Lp*FR5sqmT%M;|;&8hZkL zF%Z@mH1cSD@6U(nP9wo~K}e*UQ^y6~+erjiX9_UT&0{GAlkI8{bdjOqnuPN)QY6$z z4I{#7?f~K@CE_B0=_{02nakRqn$UcGeEDmW`nP}^lYm#ne6j@mJTeA8NN&=FO(QZz zS*`^x6L1e|#S>IZc}YIMgI5AQRw@7Ht{L9e2UxHfBFJ4d`@ft=uEN$~V0jf;V{D)n z$vJ41pVwXw!Bq#-AN&;K8@8Gp^hM(wfIA(D*AF%iYtV_rM+v}myqB&8>GH0#}Oaq z`7(|6srQ8Y)b9{={y_+Tpi?_h%=4NRI)di$4@QC=fo6lKMsqP)GSDDUF^CT?q1d$#?IGt zjt*0ds5-Hf_dP|F?m6j_rf){6G`?!~%`l-*PSy+kvS9xQ+@`mU6E`Nt`_sQJD<(Km zwn9HvWf1fCA6qHHY0L`r3#7+O4boLE^0X11UaR)Q2S$^ipEv1#hZoYzJkTt;5)8k8(HMkx=PhJfwq zPaIuZ$m}bAl2e?2AdIl1oBo8)*9D4qeYEZoYRYI;W6rw2G+4NDkZCBXj8+i>%i~x5WLg=al~z zmU1?4fH!O{VQ~k(=&-C_tsj>j(^`hZlv|L#oz#eKy_-RbBp$7h zdfrjUDPP(q2kDzBr8@zih)nO%r#^dr#517(&E=!kv1#qcQtGGD;$#zSvkNu2>8RER z%Y90lm>ct$zfD{b|My`bjM!3T6Ks){;N}h-f0(KHlDG2f=H*XRKxhy?N0#MI_#RG> z(v-(Npc6&cPJ#Gu0A_5%iRbCoZBM?M)gOlIdOcf`H9Z5@!N*;G{*DO4d|?CZ{%tTc z_j8SgHs5{Tfw*A~%*`!g`fSg%r{;*eAr0xa;p{r?EhyvAm2+1Po1un!G!G|j+X_Vc z(T1}B&JVdljZ%;*Q45A5n1wk@$+zvUt*^9_?~@nO(BeyV@mv8n^Ni`#)ZYV`Fx85Z z^eeGgG)qpOV(oSjVwCWj3B^FvH)}90iO6Wpq={>(pT36Us^fEMRxEviI+f6Ry1wde z_odYOyifbp4~yzTWqSVKMJCNUZJgClJKj|5V~4TB#yz1>^madOQ+VG_;Ys<{FzZm5grb0m~++;r)>i!!F$$Y(@|CuYZ!gQf8Dnpfo(HIPVx!%-UPL;5h9*WFK;eTG z*(7*jH}-g}4K+7~toodsR`(zx#vvvoa^TdP6f;^A?~*_&MXCBqb)^_+((Ba*!R9Vz}62klmCD$$N%gZh^vFN7%2uBYuWi zk%*($el-z@%9ZAp622G{&EaJsf~{s-ANmigI=u@)S0v-}bAb;=G-6?`_YLp#5JUll zJ=E!r8Wg0WaKHLYP#%hr?X_or7Eun;r&SWL?dz1C1-mlG!3ch(VvzlzWW9&C(nf`f zsye8xw3UI5L(gOVfIXPDo(HnNTI7SHAzB*llj?DDV=69jfIqURbD+)VWy*}TS8|_) z0y;%5cetwShu>bC-TxS>_oR_<2JoFzpo5AfR?7{o2K{Tkq5w}#Lpo^u?N>CVH5_fkRqNrNpYEuXe`pFN~%%CPoC*4Rw#DAx=mBAR`?S!|^LiBLfdf)@WQnC)O!655Om zm}^Y#{NJDT#wKPAQjf5!nD>&eCQVM^?v?BaY5ev4#G4RtM$q*-IZ28D0)iPYML z_)l@Q%Wu|gu_L2TTz~#XkmpQY>+t>3KXrSh!lnA&CJIT^B0G|v#pHzeGHXi4zkj8K zpQFVvccs1KzB6rKyLX(uIu+Dq6WAwU%*@NtM>0(S~?wbiJM*Bg;Qf`;$K! zp^EJksdZnlSYa%bQMD4jyZTKs0W-%?o8I%_c&qXVU8!q?iQG&n+ExvRidM5Cy`@*% zKT$pja9&xtCh(x2qy@6k`@e3>RXi22p6PqcD?tIkm~=OLgF5VEyGZ9na=|VrEO&xL zBcawo-F1s?hx#5tWTigpoFm|8WJHEml+e2RNLkGQ|K$Iw7yuH*b zNgH|QI0&A5xfTveV&3Na38ST}^$DR^;RPp4>CaZtxn9<1=sc+z;pw9ev{#>G`EK3_ z)$OTilRNd50dD|a3E6JL17t;AW!B@8$De*7sJoz9zA&q<_+btUGE=4^1^pQQ zBRe(((!}3hcbIrsy<}L;D04@li;Ptb(apDr3n3nbek%ma-O6AwaSVE6t0Vh}8^TgI zNlTQ!)Vi+-Z5#8P-~iVi0-Htm`{70cZqfHckYo80%rJg7nEpWH2F@NIB!GR=0B{mx z)J6AS^7nv&yGzi+tL{DUu{M3Wxen`nN=c>S;IUsc(ly{`)Nt&^qlA(3cJSnRb{>qN zgUeTEh>PzU?_i?h8*8h^+1E_CAi~}K>ZY8|yfP%~q*VS{%MIZ5hL*RO!4Qf@K= z6u(}Nxp<%$W|k_BHAVcelN-%onBcNSH!KNKVs}7B@Kk3SVXP?%bz#MqF?Jd>{gs#7 zF!z%yk~ndm9u@zt8m{b-);(?)B>=Mwx*Z!pu9igv^KF}Z&%yk1;akHbNMI6t<|XR{ zt#1(rX;%>h-71b)(&CYXqddY?sl&bzmV;HOKmbEE2g5 zqJI0CtWV~Y2F;5Gd4q;5#K4k90L=|=Gdw(fH#b<~3ISGE6zmkSu9+Q?1xTaTK3VBhIS7x-B z5={fOzU95d#CS+9CV9F;MaQ+bXvXWDXip~{oAFl8=JDWD>{-3`(FFslq=iN*_*Y~* zr#&O8s2%%&jQ=_UQAC}N)3YnTW`MU19skGNyG_ZiQBv59SK~^`;!l2r_#Yv)`g#CA zZSRvv4{O>5f0S!YX< zwW9_>t>QLWq}aH%8SwX{LGIVd?&HR|<)RtLL|#U1gah*iXXRDPTvm7a=$e7?{6fZ0zl(b+|7-n;Vhgi2bJJYd&M)5Si{ zJmbrp&w~8jO*!R}zxInzqqDGHl56{}RdB|^E=DYu$yZNqUXPO)lNhiydvzPKj;!m> zel2vCIvCQp=giaIyfhvI%iWu#;v)<&Jtg*f?n-z%IqPKR9f)N|WR=(=lG9(~Hg*1* z(Pk;xz(G_-j)ZAUzA=)2?Nd12OQ>~Oz8M4C35t<+#2089<0%fdv5y1%jq@^;*Ta{$ zJW9MTb61paU7UKO=2|CX1!Vn?+e?fsQP`f_Ij`x&+Vy3faZ=RH{;7O}+oIKEd6;0% zPu?27(Za~LuBI?t|J>mAYMQ0M4%wlOAKZs!BkRMfN4W|VGWyjqdh&(;aK$M5s+)WW zT|cR4nq3#k-$np$ww6L)T6|DwK8FYjiBPsBp~l(+BB8uxdf&6ia7)%Jzu^ZwZMjxLTM4#dG)NNoCwufk{d zdwQ55v<$_RN*OJqRm2k@)y_h?+( z`12mUaaRJ90fFy|oQP2_5L>jSrSVqxPHQ0aijxLWi45J0Lz{JxVttox!I|NX?PBnc z0O#$H!!p)xW+~?>X1eAq#W?T*S3%L2BD+ziO_A9{#ed(KG%k0QYf}$|fHEu0%pXp+ z71zkKZ(7FmRp9wg5}Kzn7T&Jbu#YMaTf|N`-a)#Z6M!8Ua}FTW}39k;L~$>NnDqS zekR;CX)JzwerfBhb-8S%0%K#ij&EIhWYux#sAhC%Bh4*$39lS21X_JV!*`lAP!x~D0R@TP{y+qkh-PLay@W`RtyDf z)I$R5rNk%vH1?LG7Y$bHoidk~MVuLv%xZJbcZ{27H#uuWJLHlcs{e<+0J^fE( z9Iw(IA=pO=f?J;bCZH$57V@#=Bq#LJh#PK1ATN@C4mYjKde4<$%Z$o!@IL>Pi+w+i z0mpj|>8}YzeR0HA%BjpvE9tSG^V0cvxq3wAxW)MQQf;$ol}-D&{cwBn9ZlM^LaDrU zBV65w?`N?w^4x26=ydFkF`OSDQ!uv)ccu?2LjsQg4=}8b#^BJ~_}J>`iOqe*zw4W> z!s`o+ym0NR#7Q9qyDy-x+fdEh5#3cJUo6wrXqU) zu%otWT?@~%P)_8bKRcEnnc=MQUN?pR48-+t18^a6G`6 zVnC3SKJR%kv~q6_rXC>TZP33Q_e~7S3Whzdr%1;{kuhQpAV_8lJ3If#`ykh$T`lHd zv6>uUYXEiHzIrM}tgYc`F`O5JSowK-^xo^Me*1hV5trMRM^{VJqE~S8rc;MGoB0@4 zs&692ASyJ@ip?<*YnFwOtdvGl+MogqFt)&n0%|b4FZwP~C&+8~W|Uj#U6aGx)`pyB zkfQVUjDYuY5P!YGx1wmx95|Zs9xw>F*&}^029LTVVI=x5m%7Z}J%H~poUX+u zO|f%gu=Kk6_0uv7WuAqzXh82%DmwFjzmBVzr>K~OuuGwv;eBWi&QZEB1%yM(zp2YwQsQb%w+A)%s^JDKB9{Q)hp{`H$8Q zDiGqV;)gESvzyqIm&YJJblCKFLnd(%F_1@Te}I00tK4~Dkg*ZC)61o!Rz2rxf)D*U%;MDB%%LN;qE!I_Df-8Eu zQKgQN9Sl83)Umb4V{!3G!hJ$;^}AR})EBt!D`r&WL8kc}lOoI?CJNh_NM=vcPaO7# z6wTIQR%@Y+cMt0IeZ3YqZe;vnEE^dx`lZ{roBqlEk42mzDdO zcl9C+ecmr1gUuxuj23=q`-dTsHPs)1Ow;zyT}n0ub$i1ilzWa-!W~qnbn5U9a8Jb$ za6)92IGul-#Id#c|4LSQLslF9cYQYasC-KbfVWwyUj>XK*{IpR-PIS<&Dx zvL+~enVqUYpX|`1-w~3UxizC#&G01c@97FIHw@ zohrL6zB$`q1W<8i)aIsWE2Rv5Z9X)#S0*}ll91!b+GQkIT!IgCZ^dXo;6J}qlGJx? z+vVNgXrkVcU9vRiPN`6d*z^;(NWUXl>LHpz6RdH20&m84NUqsI)qj}EF7uWQXZ0-J zj_cRWM#zOpL!OR$t976rcCQ5xTk-oabR}=gBJ9WOaTCUgEuZV}?xhY-#vZS{Ka@zZ z%~08jWF)N?^aUlppYM-}KL*wGipnZY;Z2Lqn}2`pp}zgD$*RtKSL_ksg{}`zT`RVq$X#}PN9+F8zUw4;@%jH zqbRMrc!>JV*%jpr-fV7b2vWv;;;k$gu8tI8ZL-Hj_ke==9C;L|BW)LMzM^n@oaNIg zG+b>l?a(mIPzHPZXX6|om%7-|h^Z9VSxuA)qwa}HAek$r;ck$4 zA`Kbo371`eA&2fe5jz^9ah!~w;_k^SNboDPWVY^Nh$Tpz>6C$VHLrT|0*VqwvtkRP z%Z7UG?XczJXtb=tftbAPVTW=wNB@L$5>Ee>x=uEK9W8cBDdqF=H6Fssf-K^?Lof5? zgDn_!Nk_;$t1!=R4AZ~j{I?LVUi1Wg4;kPbPX!!6<~M^zHv3~G`OW0|^mK)6d63%y z=h+>JDmob1>xl^o4k`2z#~(g_u#^b=>o2v$VhwEw#4OyiaQ$`B{okVH2WAsS6W?S3 z8|+fGQARi716kd#ReOC-2VZw8wjR;a-8yf=t(Jqu+WF|1iU6a>;w#NH$fmLQqL|o%zo*KyF$c*YZ482J^LuX>RK#6JFRYc`%Tc<$5P#Ax9}TQ znL^a-!L2c)=uL&=iK>Yki9V2goxy=^2Er@>FWQS7V@gPya|KmP)fN9v2Z^Jd9(6cP z8}(7eG^9(Fu8W)|za~vUw9~^DZXa(AXAU?Y^>w{u`s&?B1j3Qdp%ZW!euK2A3C;sB zz!x$jtM(aTJ5J(iG=li|*Wd&}!cX%1bX^0NS)ADxjjHvnlKk|;RaB!-cq0i?Dx!w~ zqsB(8(Kf$uh8Au6$9qu=0ObeI$x@DSh{k-ZPl6MW{yTl|BRIcpI1(Lp0VaKMdn;rD z`rI_UwRAZIcb>0kLaA8UC}_N5{S-PyhS~Bg#ik=^6kmy0xaF5~@1|4vYPr6gm6C70 z+|n3-@01I)wOr70!&#qMd~6d9z&`D1X)n8f-8%yF$DhkKpBm3R-&KN~*HzZHo=qPH zveZqzTWFOJoXk5%K=Z3PV>6v$8jXfpynY0jHkU}d#1)QiJ8o{PQ*y9+QNqazLYR?L zX~^^(Sf31j#G@qyof=i^F%&NsZ3-3`+;ZX;SpXdOf|fi8QD3-JAQqS1-W;j@Vm#?u z3RnY*#zvgL)p*>i9>K@?6p9jRFkw&np|oS@;s@vZmjW_@J!Z!ZjFpw9RGUh`JA+FX z|EzZzHtYH@{aAuYM9-Shy_r)zXNz)vRd+oN9GvbSpX*~Oynp8t`Fjvr^X#gWra`1% z$rFr+^H<%lfq16^m{9Ya>J!K4ee~`{EcNlXv9%K-{-i?A-CvPIluAK4DB(rS?I&@z zEu?0ynR}fD>7&${N3k&e-#mgnzNDFpUZK5lY)T}{=6q=vyKZXhxDHxyZ|~O) zu6aMiRI*qP7wP@z9q?4~_=I1*y{q!POzWWw?Qox82)KtR80p!P7v;*DP!*sPazR+;y;jS!OfrvYAghgRtOj7}^v52ITl8 zDQEQw=N{d@VLAfHlPaHD-%g_zf0wq@xk~>+RdDQa;g5wi9-XAFp)ESR$L5ED5+!4} zS)hkp@`c5-T2;`4r7DF3gKR(G`}@aTdl22>rGXA4g0g1F(M<=53irTkAklsEjOq*)vl#>;sDx_GVtk>uAI>`Q*Vm=80O8#F1B3eWGl^`qLRWRC7n(KmgX_pfpd`bc#e5)ugnD0b z_96$x5<{Jw$J}@Q&;;{)tfVxF7d{&+wXgxQ1kEVu2F;0++7LfdNRfCBZDi)O+eeSI z95-ygR9_**%r@Iyw{&x2Zj(cONcSbdeFasu?+uXYEVcb!D(#B(C>LsmXt)8hZu*W- zXu!A|Z_a6d*S-b9su0uCD3!#Eh=)8mxA*T0C>4nx^{s8JCI}%hGo@=C>+<3;F&I@N zEUK!FZ~iJ{!6syIdRfIuK(|-EYxX{7lTnSmK@C8JOnbi9boC+@s?yClnr%}OM9aRO zx!uf0Z3S{9-usSlrS>RK zs4W$0+MTskU^8c2Q!0^8+`}LO4Gs=3g!Y0i0V1_;`{93BM8Zz#JT(5bq>Rl6=NtUm z8{^_ziZ4KCGq!Y9vb`{^X#^{|wc7RRi{W$;OWT{@orc?ndgDhxK~bRqTS%a?H_vj0(EVl3cqsvK)hjK%l9b^@fpog+AZfyG-XYPEzfIg*=Sl1kIAl;9br8)%ZI{@7kK|2O<^40_%W2;Uy{hb^0%hDqH3M!z4gaq3m$jFR%b-@<`V~J$bZp{sd zGsedAB_mUNt;g*FB8>&Qu)MNnqpPVhjlm=X8*zP~ z{|#8Kw#PJ|`q=N#w1OSBR-BqV=F{JI>K2D;_0zi2%j62J#yL+ZXrrHOt!~ z*W>~ke3t?IG{z|`_voEI4NYu6q<|>u4EVrNaB4-)sGQla6BKt|alNV&GNmZ@HUa1X zEMce+4h)|BTQ(g^i5^ub?9?UhibuR~d&HQwI-HgoEy1$0(R9C!VFqcDr(8MjmF3{f zh`8@5wEd+6i-LfCe0Vaa?*?PlqLDETY&-`rLaAC62)st+P5|^N%s@5mU?PojHtT9s zNz~QF+%a=8EF@vqGwZ;?6*V+^q?8q_z&g18mtc*^N?Z-WOSg(SiEU_yI6ad#=L2Oe zpd0m`>+J*xc6ZU&yzOpaik%~RDD+)dK|Lb}d^0cPSvjcwNbGXhV?SWDTaJobX`1AW z)_|5!$@7t@9NxYotZH8R_V$POY}Qcz5?8Ph(#Y**#VR-cfyDErxXlI*u{lV-z0OJk zRz*khA~8!}pQF`wzorEmVwH|ali&*e9d?qjxajWM|lQ6bBhxE+zfJ?u?=vFGYRc(~MOhPM8}lG9vMfCrnXo*T0lxl0Z)@PK;mK+X|CeNUxjRvmN^Y zXF!<0m#e%T)fBKvIMJ@=KYeK&&Jph|# zp_ZaNHIX-3va~Bvd(yq7%|V`qSQA~FdV|R(yga28uMWKHRa9;E!lMtC3Zgqb1kM?w zXmp>mZ$Y-I3C37J)|j_v9JU2SnghcpQE9sy6~$H31Fx`jS=6#>dp{Fb=f(ay74of2 z-hT?;jRv&Nqz-$Ew#296iNV8bfM1XTo`L{sY8W`@E~loG6kQVDWW9oo_k$)CwY&#Z zE(wt*=x#OA2L2|mGBc*pU}`NGt_vYmEM5EK3#Rf)&Kx!7H`D~C5ex3)4VTgvE4Miq z+cxCg&2vDe!TLDZMHw2c^>2$La>ASPlFiSMM85kx9NDXqS9j_fNgco9H$Y&NW&k+T z?tHb67D2y%*U?TF@k6(+OF;se4PXmQTEjzUSMmJ#kiAyj^#~fOPQ=ckI^WTlMR72a zF)cEwTDh`$ZoZcI&GbGSXzcP}*3P`4hS==7af%hxDxz{UgL3$8U&TccdBI^Ox^Fl5 zgx0Sg$oYmzyF(x)7HnEo;)tgqi$fyJ|P2^ra-*J-Nk+Hh@NRqkOM0Fi?dr4ErWHzTrYmDmKVGho#aL&R@k zPq&p46BxN(zyhsax4nd+bWXi1bD;}+`%Z4TgE!+WIf^FPw!2Y4DQ=n`IA6PJ&wRY0 zFd#1vQy=rNn;=(tTG+qcX(f!qb;~LFQxfR+l@P?{_os){)kb7*pdN2sVjNsOP&=@H zA_Ip&5E1j3${`=W-m1G@gD!adV4=)kj`EPyiJtppFCaHAwk?X-;Je6x{NK_-!?>}* zWr;-B2QMO_%dR5^i08In+VF?_AM+{v8xUWqyh(HFUI(w6qm^BqR)){=P&BMZHaMqC zL;oec07rf(gkMN4+q0<^28AYX7d{?A+HN-{42*>>UlqD(>)~bAn8~yuF!4Bi%o7Hf za7TCsV<*^!nXMAFd=CZ~+Y^0qP-1fY(C(Bx{RiC+wkirwBQU>PY%r4?150%<+Xyv% zQUl3~fy2haMR!t3>470GY0xT0BSNOWgm`6JbO-DScAhd#&1p;S z5*x(VG{(QN+*-F@3y@lq=(}va6j}45 z2oggD!!|I-K3|Zsv`na&Zp83xt>}pb zpVM`m=l$AwtrtlhtyiPx&w8?|S1+CqshdDNOKwBI0Hag8?YpL7jtzgS z5yC!31<)1B=|wZ@?UiW^7iF>du50j|F8wACaL2QDmc=cG0U?hsU&k2p1z3{E_qN5f z;)QCXS7WroA_Eb$fnc0Rcfl2RGngVQgyHw#{N=Lq^iS^S-RSdp2{r zs9MZ|fg^IFJ$FI6hbKgp+UJQxhfLKKD~0l0XGk*`|32N?iew0R)~02xw=b`_Ma5nU zGwF#SpR#@CbFP-DfMwke_DxVHpoT&6rIhFywQ&_Irw1puYqtI=MpxY4?ffqhSXl5*P0PxvaVx%QAgjduJprnEyY6>n zp?RM_4>}bmsHAUQiC3Flt8p}9m{@VB=yvgAmxI!pV_TT#Hsh<3on5IbU4Jmt;p@EH zk`!|R`y9SdwMXM_7^&g?+nc1te2p^}Wn1`5*O*;CJrqDA?CRYAs^gOn9=t^Wlo*8uZdx^HhF}e>2M&Laxu0WJ zGvlbiEX|bIh@3dWrOp*3NmAucVqu5$4^{??gC{wL)ya8JQW_s^a(v%5y0VuaYcK^DWemsp+(H6GjnsP{!YK#Sj@?5!{*rKws?2hi2x1CfG@g z%|x>)db^Of*77vIlZ@42VJ>4p=UpMgBuhC!hQC#RHDdiSMBjZ+t@bEMGBK{_tSXuI z$^%^mCQtZv>ACv_>kt;J*5Oc1!)8aWL=TzGu%mdW0+IzfUTDPrA{5a?^fX5oe8^8Vc56_M*!!Z-@^jjw~=S8Rxawa7ZS$+pQdTM9}pyieM@Bpguy$j33A z1V7ZP`s^EvjqbjZArb8Dr|002&Wgv^qg1#W?EaINg0ozItGrxzxe#BLgNe9_&fybRBpeRe3Lkf z_2LVenE66}C-RRD{%;KcWqPzyibpmnCwR> z+Ijf9UE+J3Rf70r4qnktElvV{2bgZPfdy;D!4GEo(UAQKBqoWyC=(-xE)U=0h9;9Q z6f%|n>e26we5ccItw?Iz|t82eL*q9M^N*CD_&VCH?>Q`?*0}?PVSY?0>lnYf4)`@7$%E0Yk-@6x> zLC&~xD?C(kJM{e0;$Z`&7o?CnDH23fY~NumWb6fZ2+bHau!X&_qK^WC@EaXx)ByoQ z(3oJ7jV`3=2eO5PX9VUwim!GB*Kpkx`O*g$fp%?0AHnW$|D7?*$f82<>4<0R;NQtE zh@Vg!pZ>unDbtp`Hu790LW-bNXE=HwM_uYhSHv<9Fnl_7FDK*YN^y1F7l1tWOO3~> z*`jO0ESyOEXfa0MWSHbNh1d1m_ZzERn|B4|4A&S3R~@C+pErVVURwKJsFr*la$Ie@ zsD7KbsC|a3oi7yUdrRjoXjaMCH43yXHBZ6-)w}khp_-%vC20);YF`{Mso(1=t0HQ= z1WM9Ep9b0aJjg>EVn7+dr^Cj38g5o;!E9cO+)AepPt?eR8a2Skzu_`#n++i1mw{iu zL;gIex)56_hp#8|&gX>Vz{02$+eFzr$AB-hFn(4?doq=I9)7N&r=6Mg4k%m~9L!FZ ze{^=&TI&U^7PQ`4LOU>%8ewvdSZ}&XDafL1%hWeDr3h`?7Uu#uvE^6oeWq|`=~|wP z{iVmx$Kj`;Th6}!^C(6EgiEu`(|9Z&$a9IGZ@sIYne#dL1lz-q!B4eY6S;&niia|9t z-M1nnF~^{+t?6G-%c=bXZ@4ARYnV$<=UhB2WaEp*Kmw$W7=m_=Ry`{Smigz=(6>D= zuHmf(_ok%tIT%Sm;+qf)g{DT@lsk~OOnl-J4E{uU^P!D!Kb|t!=*H1@jv(c8{kmG~ z*S*(OUOoRK!?!c-JuUCsVN*zFzn7CLyRiy&K$BbVTP1ms(-f&p;A{n!$l3QiFo7)X zJ`m!h)=*<(x%PB4ztR*c=akp1f@k!ZFZ6=N+b5ayh|H?;4)xG6_FcWqT@OnSxayc^+NLji4mmG>^8``bA zBk4p6dCd9Mmt-&~!AzrnJP*jBFXo3k-X>D?SJwU4xpI4)N->H3PCrTOYzT}W*IbA7 zx}tqz2Y=i4QNny29*B|VZ(BH<)F}Cik@=c{ywUFS**%)q1Ju7R5RT=@QL#NPy(fdW zg*kkq_V`#kOY}HAlRT(vnPG~=Hs59a?sZOPs`y{xcX*Ch-b3B->i!1LJ$NiF4fw`@ zK??#Zx?i%mp{I?TiEUpbA;x#m?O=OK+aU{P|Wb zw(ctCF4Z2QsPw#KpS+JkQO_y56wkKg;AhwJaHS%#GKcPPe2i7wC!RA|QZB@%fLW;Q zqsl2exs)FUN$1R%3~*LhvwnXqx!8>91Q=qa8x1(VrBvVNAyD69(2$SeF`5@RO4B`i zC_f)FQ3Sgxwl!b2;;H5Q*Dj(bkX(~t4xs$w`L zFOCzA1>*n8mKSP6@UyJJoeN{mCuAe=@;^vYBBBbB%dR!@T2lOU_^*t8Q z>02j3rO{|lxQSg?QnUlg;`XFcWs=jJ=K6K2#I$KZ3=+Y7K>rD*^RP;~66RO11u3?1 z9QFFxq~;La^a2`{c4h+MvE#M184B-`q#_FU%jp-o`h)`~G-ucfBI}9XommsPm(-iN zvtf5A$}|YhY%P#oNA4axSeD6y@dl$Xo-+5QGT=idrW&0*6WATp!#)4>5!2C9pT^p|k66!&eTe8~> z;rYRrx+SX);|4!OMY;xXaz=@WpSGujymg@@ffzL3bxkTrKA|q9;t9FPT$H_N2=;N% zeV{K4oTQgHeDtS1Xr%HoTXWE_e;wjhP(jUCiYM%(jclBu)Pm)LQj1oMEzy06Dgv9x#H`UyVL) zm{+XcEyENHjCtgG+L@p9e!%EG&U2EBghvG~?Izy-yP zjCg3g;oQ+Iwg?-ff!E~Ls_2ts;8j0@4hG+Y_0Dp$ueD}#M*|uzZ5`cuSNAKv6LuO_ zpxuu=kbHWf2_$-2C5?mwj*LAMX|oi`?lDCRZ_#^m-J(=C%ThHk4NO!wu`~!*99(y; zbPvv}=RQTCc6N+tSZI7O9uU?w%0G-~K`BG-mcXi8DOY688gJ4#$OM}u9N*3sbdv;c492&FIebF$qEye(-AI!oosuNe-y zY8{CpeKfDNMB4(c89+>oR+Cj4(a(vN!lL!sB_n2Y(w@UOcr|#~8dTCnR!iPe*S@+w zEqLdziMJ+-rO6w`<e%nUg>~w56eIW`p znI=}=fTlSWh0riM)Ni_kPP|Xd!vy+p}j6PBHhT)LDLSqWH z)rPe42{K-hr>Qc}Shc*ta9*-1r^M4*p=q&Vf^s%4Z9&$N=$BfMdMlwdwL|h~V|(K~ zk$rg%rgpex&uce`gnj&f0iy<7`BQz*5rqTVfUukZ9cPl4H@Mx4`7sPVlSUMCJBs>< zmDQ}}N;gP+a_!}H{VkD9i*PhB`_xUr#`bb;sb)1onE5%;d@#h)%P@(KWiYtg2J~-xftegUi*BT_`vevFU7A}xIkKT^DNNU=< zU)(WMpw9{}?a~%ZvMafE#Y+Le!b`GrdG@xo#`O`Qb!goEXI*p+w%M2a>>nR=`fjQ$ zOEL%5v486YU6{n20Fz|~tfzC1dbl2QIT>B3ew(4K*I2=-RNLb-KnqG%#=W>Y5)?z^$mYpr53J)~p4Oyzf)YqG*lbM@|(0u?X88akbPKMZg0R&OuP+qRV( zH`$hNSm5+((XINMy2o_&I1qpu_h&56*mi+ZSVO5QTd8{tY_yIvt!(5#vWauHZCR|i zU>; zHxSsNDgH1c|1g5naqEEzxl%`}6pLX@g6v&FIJG>h;I^cw*TCTj>Y0iefr>Jw1w#NV zu(N}ockn8G3(ksqP;29AFRm`+BKYxzPdl!sP56YGZ6d$Gg5lpHZP8&xP=CtI)tf6P zLK{8MjmpsPIX!U&llnm`c^cG=i)a}fKMU_W51x-HW$YUafxwd5=C=R{U>~IoXroLc z=)9X7&ykg|jHhO0ZC1BJfya%JF?7k2y?WN(q*Q^{v<@k_$dxK;)S{h2hR)-!dqpfQ zaSt^zZ!+iHB-W`O#77;kA8awP<2=U&UHpP8H-s!_wIlN_Jdq7t^v0drZ67JT^kXDw z%FVR`KO5ITQqI&UtS20Z0hViO8%|^>x~?;lL?H2m-DHrmKde_`-!Z2Hkr{GF(hKD> z(tGc^tA=4w$l!vH&+(P^fHTN+-PR5tPOiamzvoRyxgp?f0&RA@f|%ZS<_feZIm~*s z);D-;OMroNF;=gjc1f=vS|8=oFt^7mdr-(7N?|J9^~Pq!LR9uy=@3#i;E@Y_PjL>H zIXEkMmd0b#&GF|2_y_}DT-zzGZ&&rSvw~N$bHB{o@DtahKq+sM@cd&#|5D4sC*hoz zhT|fR1T=+);PMc7G`(8m+d{&d_e{ClqQQ5D6lU>D3cib;s6tgUQVOjn8zk3pvXqi zP4(b!didg?4~!sqwBciSC&K-F%^{?^hx7gld%L*uo9{v_C2x&xAGJFkGo2no`8wyca1g zUXnCOF(=Z=QKZ^v5exsDAlvcuc*T;yR%5}!OR%Ui{pKm#A#3rUpY~OP)ln|D%EB?w zU0)Fgv4~VnZwlsFxYk$~Q$0_AT>_dC@OZ;_} z^JsI$x{gHmqs5Km4JmXOJGKH(ldWte(<@lGK=Gd3Q$S00t$Xf(M-X`A3-lDS_tI5Q zQ_F*;JBz9LD5%w&dR-zdpfvd-4r2V9&Z3B$`L#^1WVk@upKYYfP)i|~4g?yw#0bb! z0O#jSlCuX1HoTERcxqQTJ(O?&zx|vK(M<{!RSAW(?^VX9FePQhe{jz-&QW520>S1v zDqyG3{|?#0rX98zec*g2Oh0vI30PLI9sVeUOrv;mgZ718jM8MT8dD(|lz5Jo9g|Zz zDJ$|oRRoq)3T19&b98cLVQmU!Ze(v_Y6>wlHy|(|Z(?c+JUj|7Ol59obZ9XkF*Y$Y z3NK7$ZfA68G9WQFFf=#{FHB`_XLM*YATSCqOl59obZ8(kHaIvjARr(hAPO%=X>4?5 zav(28Y+-a|L}g=dWMv9IJ_>Vma%Ev{3V7PAw_}i{U9crww(UA)+cvvw+qP|+UAAp? z*|u$?%j&P+_s*R=ac6$bH$P6q*@=}abM2iG4;hhyGM$i#y^*Q7y`2jk6Fnn0KvhXy z!O+IW(8SVShECYt#su)!%mzb7CgNmj=wfMaCu-u{7=u{OlM1TI{^9LKW?Tr_71kDb}oM*{;w02 zO-%tV7N!6*OB+*wh`fTPl$->BQbJA@AYp1}>SSmGP;fP}u`~wASQ?w!Ih#@e%

2 zHve$|7~9*KSpL(RGyPvIA!mRgz}dmn*z#|hsfV$t!#^%sfP<-%t);W`-~RwhXMnkr zp`FX$8MxR3EbWYKTuuHV@Yil;|1Tj2C;PtdWce=*S7%E*^Z#N%3veHpt}{Qp4W|0e?fKauzUpSb^BqyOa*|Nni@ z{~cP~)y787(AMcxfuQ(gpi&2 zUojZz8UMp*=`3#PVQQja>0)dFFf+9IJEec^s&*!(PBxZyrhnD^caQ)&CPv2p=2Nk- zG`6<;XY6eM;WD)|`R~;K3iK~=1}SkBX(2_L|9zwW8>jGBc^4H=hriVRM<=rOCjayB z4~np`y$8UXj){#KK*z$!^!LI2<-^6o=KFuB_%9ICf1PCwU7RdE0NQ`s{+szv^Z(=b zUnkxF1|w!?Y;W?S|9$a)oBq%9zZc!q)Wg&mW_`up zm?y+4BP-LT9y4!bN>qEGj|p@n)S;|NrMNJl*1p$2BVv!M%HXpul)ia}`@6$)`NHAr zNSgY1tPjJ6qBqU-rU1{EgsQ&~d7He8gXTDhL9Yxx^HM#=`*ulY7fg$tQSEqtN>NF# z^b-Pqri;Z1>h^^yfW)mZ0FCt70m08Wy)hoW8>txxrM~Fml05nB<(Xn=d~{^E_a40e z2$v=|9-55D5YsR9f+)qs)4=Jm$@m-m-Hk1=0$L8w1D|t>W=BarpztyXsbmowA?ij|I(%S1w{tpv>VHDd#6y4&XQ#gX~v!r0NsY*eE z@#V;+eAv-5m*f6!)is-Z?CwYFegW)deQB zWfKIlDqygIluG8T^a$QV7QExP!93$r$gbY!VyAYxYP0tFd^@7f)=gt3K!LIFdo3C6 z55P`&e}srZ8DQ@42pb~A4ZwcK=vyo}v{jQrcr8C;ZQOsO!NFY+`>DNV#0ZX%lf zb{~mfo;gvO=PKQcnT-)4=8J&1u8}G*#`tU}(1bzA=}+G}&%+N+1e#6X*BDm7D>kM^`FMV+^^<^s+&6(B4% zqJyy(m33`T1Vf81)xgfa*kh)#&A3v`mHndVI1j~nnt4K#NUF1K#)_<@w9-Jho?0qt{WA*03_pIyxU17ACMYf8B=l>alalOKq z91%A11)Bg~pdYThzg)eK=&}$By^`oACB%{Zu?Sw_+0HV#2g2{jc6PsE{xIupy?--*}h6}BaG>6090I38~aBuHivF%B}oqzJh_BWAmeTRHyeTodL@^AZt zXiQE?T2F#crUM`Zh~1WEs%E7JCKn?)Go)&}Ux{h;f+mvy&G#?hq^zl}m(;hBGaDa4 zW3*CTknp&W<{5diWXSA04A2JQr%T*n@1+fdR|3X&lj`JWNZwMgpE=W#Mz`2Ol`9fV zAJY6nLtI(B%tG(QINxnc<$K55Miqu@`Qc$9`tC!f8K{FTx7^8G>+zf-!WhOMRVm9$ zhRksZ%Vp#W3g(b>K*xhm(fk+BYKMj?4BBhEuPs41<9AIGQ+uoYy0->=7K0hGktSHK zV^}E#4m3#hM+g{#E-arviEKyfX7F^p%%JC3)?k9BBnfI9Dt8db-6n=i5He3PCOt43 znSHE#rysdD<#et4ID_v)7+W0YcQiijiHnApGB@+iggZyXHYsClczAJ|tv|O563)+g zV_&f)_ZEt}%;zMz^wJ*nVdmO~QAp?!u&%PxrEV!rHtGhNBW&z)bBN?#q^K}02&XPp zu$(R&f$&Uag?InpH|C4-T4hJGJ2Cc~EAE3Hgy=WLH})&Q35}@)7yIaCmi0J^fa(42 zHhvANp;g&q4mbiO(X(K?CMKv0yfqCRsrsBNr3wQaqyJdqpbD7k6Hkxtn0?Q@+je&| zYmjRjgS*k#H06HY>DFA``>KURxg?1S{~E$E@%1b^w)vse=pD35ntu6a^=_89blh6} z2;<`yp=xx%mziiJola%01=LHK%3syaRHo8hs)?jjw?EG0O4+l*i3;m}yR`G#3F$^| zcFA@0?7DE#!Iqs^xEH`M<~R{Hwr>AuZl*x=^;OPoq%I;khIo$9x0y#5wnd6Dya~6- z#pvJDQT!khL=4DbziMYH1R|rh6jv``z z&xo71x?@L~DaY@o&cG7LgiWw4(Eiv$Z2EQvv@qQ&m)#8uqbX>chn70Td+X<9$0C~c z;N^bgVd>=L7orjn_~R2;C*Rf;xQv8vyPp!Nvha94MXu~AF(o)%rC27yM#wph>u5h~ z+^Nv{wFu9BW3<6XC9S+vm94fse}Vf_T(V(Nw7;7J3D!ch-mGDsLed2c%kpAL2JNx{ zmq8ksvzElZoviQmh#}kpPe%ZZFCGsVfPzQSdKIY8~l>&};Jm15;!lxaYGsEc2F}6sJ1gcP76I)OiU}vz;CTV;shVgRX z%ES5}YMxKyP2{~sok0}{g^ zMC$waF`x1_Fr?nt+*+f&Kx-ZV8aRB4FH=Ci2~G}BL<^9CM+(vOx0lE6oyp$cQcYV# zn!or`hCmQR@aODEtrZ#k?wj`#y(kXu5gVzCb<|7jr_>AQDh1JF@kQ1c8ZUPbexN>g5I}D0Rt6sGzTN0YU2}8g6%VRB<$o$;>G6u}` zq}Ln9#3J13!Ni}RCyvd{i{zfUIxHdYYZ1S#i7kVR0f`0Tg{jt#`liS%Z4Yw?3-~!) zBVpq%2W#+B%>kPnPk4BV3b&{h&Y=5LXIQjU0xuw?GA5o4x^dXqc>UIbIY*~9_tSL? zy+TSZ+z{+FJ&MLjpQ$zl!%3CNOAr7`2x8E{BzHm}tVaUgo$%WEE98yHIu5c8*=yp$ zT8+B$8}C#!avUrVQ7ZFO5o*3n3?Cns+Isb2mbxVc%THiej6FYwf7Q~t)sJ9D5Qw_u zS?en>AFh~{Pjd%51!z;wSGr!!EJbNOb!}Vwr{Y{8&SThTxrY#g*{1zHjvODGql|r26@#>hHYazu5}#( zakz6t27Dm^+e5!P<#)WZ4(2Xr&HTF{_Wo#ejGIbw<*j4*PQT7r`mpiVk1YX7+87Sb zs`HbR>CF-hTvNbRpNNDO;!41F0cIo8^fA41vh^zkipZ0KvZc5`glSJ_l(}qmPa3=L z4PQb8Z^!*c3lFcG1KdMCOI|V&2UBALUJP9Y z%}pMKQ~dGcED$siJ%}SO;b!i}N(Swd_UINwJ?q@91_9Yjms8}?UDhmP{hY@5dUi^m zYLC^RZrzs|*k&PED`Xx6v2F;y-4Mb$BJIx%6WyX zcU{tB*-AsCw$9L{%xH$OC{?nbI2k;~bEXD~GSBgzDz~0y&pcx@QhT;%XlFU6=3r&J z8(T#&^RjsSWBf}>bYh0Vmt|(cs?6);YT=%t2=itWs(Igjy)2TJC{9djy-^3trRpb> z3`b)Cr=?@`GQ}#erKHa+Zx1!F4huU)1}_-AD>kWX-y^?=0N#-NfRIw1hJY5@Nb0yG zankvXIvS~V_VFKN#-^Av!?g0?h{^%?B)J2xY?lC!2AE5~Dr%P#4RXs$;V)KH8$nF@ zG&}G?I#XmkH2Z_{YCot5=dzn9NfWSWI zPjaBCW^~bw>mLDp-Ckc>!sV~N{P-iW~ksybdJrl7;A! zLHRy>X&A7NW4IPhpiQhbF?Ws__dFjhB8}vI9Yh0~!PFP~2Y@7b;Woa5eKVxpP{L*= zmVS0p+>P7*>D3Y%qaOqR6fsbmtZv5RiE;QCUNZWSG(#(E0a08tynZCrrgHw0GvUo4 ziL0C2J6EleT_QbgcIIP~z!4d$cIN4zF@eTs3Lks?DG`wpcJ$<2?uC84fw||f6+g4M z5BC8CWzPbRsmiW%NG{HXkVkTIgYU?Gwi-S?OC#o^PW^;D%?&^$*IZJm2&ykHB<#Dkcl?qL+Z;jkQ6EK(TCQm|i zn5HPoglLj92{Vhjq1EE4(t&nW%5g1?b+M<=thX0QIT`(!h@2q#I5f=+OV$m&q^`9h zK%4)^`mlWpni2O_Yie8Jkb;(_XpJJ#qa$xITzh7b5a5U3>>YrR0Q6(>4Y})Ml^=uX zNFfM)ywyN4MrN&dIO8YRIst8xf8W~@@{nduj(tBWG$a3K)EqN7R%e6(ILNTr8!6ax zgZwH5@S(E~3g?G~5{z2c&a%p}D{ySywq*ah;72|i;RzQL@A3fLH8|GXa{@L6kJFn2 zi+c5sJsF2?FsCXgXi}#YgI*5_qlu?CzM86FjGHp;da<^)7v9ngva7(cv4>S+v;+@f zCQGWtUBjN@EYCiIm$4I19|&M5aLE8-wLjMBBE}YdE^Wd(L|ETu9RUcJJ4q-k2FfT~ z6Hvo=Hh6-O-gQ?I;qh%JK=0r`f+IUOlCC=q!1{7~MK%o5& zBt2IS`p6&G7jm8)XxLBKb2=B_nx<=$?~Tw-(Zrd*u_-;)(K5vS+wiOPKFTc-mWnKJ zLgpQWvhZ_)^ci6AD`NSYuArT!76sPrZGEb=S2&v#bg=Oahq)kCR9 zx&hnx7h(R5VF%YW)N6<&3_tcZs+_}F^z1fQnmYY#viGi3pB`V zrWKv__%h3$VNNS@bLO(|h;ha}IH3+9CaB-r^W!;f7Tid2>PjLDehXy34Z9J;sNVdF zj>=7{f4(=Xa&wuGb5l7&9%V zw8_>@v21LQ$Wq5-?m{_GT+xqhmnIJR_{e0(mr_H<%VPxp_S5%{?6Hx_{s8kAD*HP2gJUFIxT`G;0Lt3bloc`dUqhPuAXWj)?mnl$vT-av0I7iYp%5` zR$0rKr07}jcCeJP`aJ4Knr>!W;K0ah5VyOgQ6u9n_{fwXD0p@+c>5 zrDwHU8FQpY&Y$+o5d**F!_xFnl%HYgK~*y5r+J65JFQ_4R@ZE8>lLHW}$V3~Y@H)y)RqX%a}lJ$hQj{sOMzcz_(hI|p) z`5h$g@stglB2IT$3iC)UC-iD%maM&qucBdGrO~3Hb^iyCk3Rp|9R;L}2dkiM4>QKf zLr4|43+s93ftuW(;DaqUe|X=9=)Hq)%t>zbw3sq9A+lKZ?kxkQ|(aL1EOE5Z%Y zcJ4a}UQ9YW6Ks5Ut~wV9#ey!{l9Hqj??|K$B<4ZccDT7NlKJB+B5K3gAH~6mWs341 zZi^4-iZcnQ%RfWXb7IX=48fLDOfSzI)BVA)+lM;}`#0o`J3wiidks;K$UjoLgVMU- z6sh@Rf7uSXGwSaBsc)=mcy;}iwt#b@P=wqO+C>M1?RC?#k5=L?03+B&=rX%=jDmF>q-vt-uQ1(<@jpT$^;xU@mUdHn)*#>U0Di zTtDc>g(mbI#QRNm&Q5l7v}^&XxV_K{t*jAKCn!Y7rw19G0Qz8F0Ag3H5f#Z9hylWQ zmFC6Sk{Kd<-SJQFQM?%=+!jvsY>)vsk*c5a`uwPE4I?Dz$OE;SV5&;uRLuIlsB~Uc zMoR|L?))+0Q+PxSae)Jk?{> z=t2t8QrFI~Wax@1+)WZ^SE=dtQAk+oUefExAFrJ`+7!=oEMnEng@&2X?Lg6gLzoD_ z{(-oJ&&PnU`eOUO#PsF*{f(*1HHpm-7frN*(cQhd6|*3I!mkWYPv>W;dE>0kVhm)X zH47zUt{l}I>&c zF7O^{vcWMVAADimsxI$zaIB0$xg5PXyWh~;0#{Hz=sXBNGb!LC8V3xEUxp6aom|5K zNA1@w0+>o^A90*kw971iwhd_J`u7x{9C3~~n`D(}oVR~mcSFv{6=oKrLs|yn17!7% zBUQ5N)M~qZoRwW1%iIJ}uAlp5R%zm)Ur@FMf17{@qD{tuTN1<1l(UD;#;$BJyi2`e z#P5A$JvQ949vmoGPBs#=*2_Q!%}`PcsEtb}!EvTFs7q^rx#kYGq?kwXn z_s8j3;5^m742h^;@=37THsBR2O1$62wIq*SPqy(IHJ#Oh=j#l&Gb!y8-Jbuh)zTyuIs~lj^drQ+Mo5 zvdXVWl0)rZG4%uo7MGbv49m7Z>BL}MwT{@DUD&8i`&{jV1Gy{5j3R;tSlHAYt6Syg zK@Yr-4i<97QS4XlsSUUbcO4zBEca>10j`h^V57$m(9N+iGMY)lsFrQHl>!rlCzdZX z*JvG?W!UKfquf(F6LjdE+u~yWq^IT0!NWIls05yFk#ga-*bnUe1i7Nm?N0cUyGXZc zgd3sw(I}d6z%)S(%^_^rDzF!6)Mzn5Olf z8PD$xf91BL&WrJ7*pY%u(QetUV>Z_kLdZIUQUTdXKU#%E5Dn(Kc$pGJBet}MCBfAb z6Xy(?-|DrcFVezBC*XgszVK`b+NqhGtFr|Ue!J%Mp9p@*$=(P2w(<+rr7suWzNdg9 z?7kE9YH7hrw6!lpvvrm7^_*Wc;aU&nsKDi%53_l^{&l|szBVDOR~_AfdSm$xmnMju z*rF_+)z+>76?{?HcysMU$Z*f=N3e2I-^H0S-0Q|?^m2Fh18OgOXR)uli_=e_8l_QB z!xCukyWfkBcORr%kb+NR>Ku6@vf!dlYtVK4rpbd_1Fz$wkpr%a@CsUB>SGZ@MlzM8 zJ9X?HTZ8<;0`zL#06alcr~9N{CFej_Zq^3`ZVF1#U{5?XZK-8N9VTma(L~a!@8;tr zg3ut-rkXo86&xfcO9RYBjn=+K?>^kQf*#cyzx5AhBhgtawd3!zd)ap8X%@^r#{%Us zT59CwhM`UjO#(B(Q9Htq7gC@QU{>iX?#^(62v(1p@?TzPg7f0ct2_I3aHRwUlCl-R zW{Og`TjxxZ%hyZ_7?+Kz3?_o6f>Db!5)i)X`8t3cQ|!=IH1^Lbcl zirio-y{-UMmuxZ}ip$>wZguAkg=V!uJO%d>QmuUu5#odp^#ucFg(r(YnThKUU};P~ z!&qi-TzJaj58E$wXLAy+BT%%&G`WT|f-css%$6iAeKo@Ad2-fV@7|0MXy7f9=)W6tWh>@Wk=$^=O=c#rNTh+w$T8)1+#(t^^YB2Dq$C}+I}!Nqu}#LV4gAz zAGExO*lb3=7>U}>y%T(!2Kb^^?T|cR8l3_a2-Zy*(I&`rEKsZV#p1-(S3_~F<2TDl zhTQ4}N-VTqUQ!S~Rt!oIZg}98FOwgu@Ko7ioi1etWdVZM8=cJ%{aYXMrEMn9HYfOK zs_9!~k10GLPSwmsAqT`dz8J`Is6kRfP-%J+`1idRo5Pr=Q=7X@c2wHM!{4y*wTu&5 z91uA&KX^P1G4ah`{jTH|Ib06W0YemhQOLPI@fq?e_4wj3gOde2GpUs_$Z-??yvx7A zSbUyDcF7gBtUiX-9jzx2WC~D_16{jmC}a3y0Xn7x+KPu~70`+qp`lq# znoWPie$X;adXru=mt}FT0i+8vc3k*&^>>rU53nYi`YtauQJ48hw36Fmf&#RIX|b{B z5H`a~+CE^kYi$9~aCmIx&wXgnrU(wea5W=9gUpib462b+t97@MkBus#t&#L@27qKn z6}aH6=n}&p3KpESZYHA2Jt*S46;~1WTddy%Qc#YGkz$rSM#EML;$XgOSjEo)1r#UG4O(KqQ~3my>&XtxX{{`sY#+M86c-__p4I6>IY z=C-U8sI7*#^(|D|IZocSBp13eXawkwe}iY>3SUZ%Mi3#@YuL$-l$L;^O*K`TxduuG z?pEpstj!MIM91)+|sT2Q>X$g+L5p zkXT!K>Da<0F;cxZ-$tpU&F1HTVbiQ`l(vtH<{DEb7z}%cv3X*Y5-F3EJCwh9{PCy% z?7con9XOxl4@&CAsgN|XY&_1_jP3nj-Z#BD%seXDP$e3RG{W5<@%G7;a=RJQyVSVI z^GB@)uDEV?6@Zp7j0iP4e5e)mR(mZm{95JA3(Z!#Xh8@AuCW4px1g_6E!1AzgV&s@ zEbr4qN!UbY?P z1>6%sPV?3lLGl`c=-X^!jm?gq?|6UDxLY1}vcNSeyVQ{bMz#&v zA(zuErjJmsvR5gx3Oc|2d=_RlF|mfXfSzAp^CtBRE@HZp^L{hZ)%ZR z1+GQm=U4k*sM3czJw{;BEXuP`6MfYhlKgbOw=%*E?j(p3X@$a}M3ccf5GA^eQxg7U zb3SfXWkMUN#_~7Z$ZfA8fp~I^GjJ5&Zc2uxD5EhhPZxsWPrCUj4u>INY~u48xj#ml zBSK&QLG~!ObTFs!sBi=tDBQxbFVI=vOzmR383r(0}Q0x{9vXoPui>>E~UxOWcx=%FUA- zo*xE*rv!4oD$=*Dt-jN(dWw_OXW05sl%*2qjjGeAMNF5Q=UB`#512$mBTA@;7XfKd zi9UwjyU}y#2ezgkHhOdLW*rA>y$owTU)Gr|`LC1rKjgeeL5`63uV9O+StEnEdU}uY zJ4T|Eh&4N;+-anvJYj=(y+^T3J2%Xj7nd~o5WM9|nosJNu$*8-Um*|oDjY_Z4%c8b zES zL8D&QUI0qf?9^>(HAu?}#=SzVz{^Sbd2{e+SL$W?yw7sYPen1(IM#)0ZX z^U{7HXW;Jdp2?e)PN~`^w#yGuaE9f_jUm&n{m9ZUOZGAkn4=7lKec&zVAm=%L$o+jGEF@K_F%?kjhBK;h-a}+1c-rtp>Y4|D0O8kPuPC2UnzM>m@1kDAH4%zk! zPK53=<}tn+JMQO^ID7a{Ep+y~gQ6GJg4K$8q!?B|Z5o5=fYs!~7akWud>BqzQ2u&J z`#s5+q4oK|P2)M*zc4c94vsS03HBqVM8t#%!x#b6^m3C$TCBxr)Z zp~9|Sgfq+x&*> z&@=l)BHjp~V>tgI<{hLg5G-&f+=whY6seySx0QJK$S84JF)PP^<6R-mb^Vwr%bQyeQXwn=Xe->%r=)e@5@xuOOo&Gw@wf*tzg#>v z=owtL{H$y`ip50&qhhb|+QvxM7FWw*{u3p*Eb30>5Yg$x(&rBc9HU~ezi~I@;lFTJ zh`Pj?F<{+;4^PkM!EZ1z)@)qM;Vd>INHW=2zG{2>ik80zaT5_h`>xTzxK6{0bc`kV zKonv4dPqtLup((Ggn(TN)_Yr6hUeb{u?jN-9xm5b4f8~_TjscGjju@RQ6BP2QV(Bx z>Wzpre%mZZah%xBQpC29)0v|cZCLMwYaG5jz4{5f^I2DynW+wUNJi_bzcQS9P3*+w z2u@RVm)LDZP`@_0fW*);mAUlC0N3V}MM;Ey?lD9hw8Xsy|@lr%60 zm4%&&{VP~zoZn^FySBYG?%^&1Worvdjs%z9(cNC}sqO6&!#@y8yQ#flGA8cRll6I= z_%5m%ix>%M*md-y7C@KCpiCf)UM|FL!xow1gukGv8&w{Hn9V6~F{YIQhbPOr4zK+a zJE|U`k20x}AJx~4e3{<>ibmqB7<_z>ueQ|+rJo8FcPJ*N{|lcV5y9UO93iV+ z;}ht5No`vGcemm(q^Tp%mMi#}Gw~A31dZskzZ$Y5?Ie`~q9<`c;b5vfvJb57OR;x` zpxt@{;;#xV*2<%REeWo}x!_EQU4Mo_QkoI0UK0>&i!I;*$LLp?4O`KF$RICdSxK}D z@a#M#@W|lMM@RW{ZC)#v1?>(BKW0tkMQJmtEzjaK!D%ZFgq8e@5_2@RFVuddlIFLx~( zP@AM6TkMAGoJy|7psp`4p?iNzTRx#n&I&N0n3ntt9z;pS+L?i)vMx?%cr5?% zp%K3Y3obq@Yp2DH=NtW7MN$Z#b#LGKv9L`;Bu8XlrrUBP0pbJ?h;f-gEVbx#5TJEl@<9c>cRJvbZtX3(2f>?RL4toLHjS7Z z!~_fXN(}m|-f}?yjl`?*82vg;bU1=B@1_rbwmIg>d5${6k@AJM1ey~Y4ePoyv%Ou( z|BWK#A=MT^>#Hu2o~{gsC1qcGBav}SvTcYMd7Rhw6CdJ9P9L}B)$D>Jm93`$2Gmh1 z=d=2hnY=<);4Y%SikN&CI~32PS3d1g07+5O&Qo-_Xcu59Ham3+zqoZYqf!5U0K<5y z(!K4)S{XXDgm~;q;Vt$z`XwM{VkceT63Xh|-xNJsF8gq%HnNV~_TU__pYn*0W`*dC z)R^|5{54Q9e<_j=G$t8_h}{q_N@_Nm#+}^z#6JK>Q9Uu8aXqYA!XNKfagh^` zFnibgF=2*lJ(A9iCL>`d#Xgm_wqczczVBl{lg6z zodJG$HjV#%G>Elilii&Bx_#)!o&9GoYQt=N1^kc!l@M;zaM9ff0Xlb#d7}2ElvhS; zH@p!MPc_oLrd?yR=lXiLRb{VDAH61qPs=t4L)k?;)2c-bT}EpK?k_`yZL~m)zN*L# zv6oT;JbXzhD$y29cbC1Zji$WaUEK1lCsaf~5f#P>c{#HF7VGdcA5zB>m*sfBfc~Y# z=Nk5PBo($72BS<}RN~Lta@j(BO#?zp8qmkMCaYSj50b`+bz>Pue~7APDjwPum7Tk{ zjmhBc&hd)MNKOivztc9ig3>``QZw@J*QbmELCd=i zJ1t6AX>s%3`Np<#*;R03*O(3jh5-#w2rNnhF*Ru$jzidllBAaNEsj)~!>ojqov83) zJIbU6tZ^fjYJtb##%JH(2=m0R5Ug(efQ`?cHkmpby@VI24v-)2BGl3}cYaXlqBw z8@Mvli%vTt`ZEy99t*Kud~bpQw#U+)-*kuaQs+12 z`Su)X_(%^%-ZedRL>GpKtx*iF{CK0b(>9$!F_n*h%XPGzr~UDIE-`9gG|y%mgIKes zx-H$0meLOk!x{qz&lq)*CNYFF`!-itz6h;VG5WEeG!@7`jj<}#Z!5P7r08s&&d2v| zFm(E-SfGRPXrUxwwrZ2FY?;8B*aa{5JfXlwZa70X^K9VshB=p^^l3C)rwy?)fcUig zpmFcU*3+M z5vbawKJ(I+vRr%Jr==r#lE2 znJ#R&HAdEeU3k$%FN=~nHqdc>l;Ieh1v#!1B+9SDYH0e#ASIAhvdt!BG32IbpD%r! zx6v<*D+0Hh^>N8&PYRn5iE6h#iyv^!B%)%G(e?@84~5sBE$tUbbh>-&LtdopGE(R4 z7b6}}Gjc^cUXa6G_IAmsMI92d!f7-+=3S=LLp{{L92W&iBg_qoN07~V7xWO{gWo=4 z{tW4+A+!l>q8&CY5ihSLm~~8LJ()(K|1Q;;xl)z;^Yql!?+4uFY`q`f8-`hy1O}*Y zn>W6aH1@9&>5>u63za}|)mu2Ek5dnVfdb=#xR#x-l_Qjk^@vHz3gpV_I?(NR{x7Elzr3|m zBd^?|05{YKv(wSPNQ-yzRn;+#3yMFd9}vRa_?8bB7e#UgPbK6FHs9|V6vWf{j4 z5o5%Dz~$9I+}mmaV(5!hEQFUjLGY((+mS|s?+H-U&x#uR^`{m+^a1S?{Hc6Y4=o+M+ZvwcLYqwy_nN}Tj{pAQwmzyx zyNHAaF24>iVj@y6M)gUTY!9DYGpnSjAR@U^Hj~*>PZex&~Mo@330O!G)npHG{8r*CZA@rtYBP`H+QKv z3>o&>K>@aFx>+A8(6el}9*8NOr`)6dDll|)>Z}S_bym*4M|Y&7#{|oIR>#-k6f$`Xe5EqSKW19C=+mzCg0%$ zFz%^ZY?oTLN~w=O1PAPlon&934!-EpzFIPK976q;TNd{UC;oViTv4Q>KZGM(X8BW@ zB~Y{~rA#x9GAB!teCF6J>F(A?s7c285cx#p+B^NObq7b_wom&;fdckgKXvR<$S_mDuhe4@G)`-=HpEe1gQ7Q$ z%FM8lB?ca-z5D4VgIcWt1GH5Ty@^faFv7Y)i%&Bx%$)vAz!>7O9^C>aNAV$X9+LIq zAMFrRIF)rdc^SnUy-;C~{JljmH36CS{+XZ*y3S z`g}Fu#*kW~RVJ+#@Kh;1+G(mUqu^t!-lw!#7OXldC>0clfx6mh?;XE|pznsf0*=xE zc7s~N(@3p)Ubh2HN*~e$Hv-->()jae2Z-$6D2(#R=!w8%Y@6F+m43rJ4dXm+$-r}g zh~H=$m|mUl73lNJ)W}^3!cjE zv9#TAv1gD)*JApH@lzn_=d$zbJmd% zAE>7BIp4@xG(Bix(6A$ncr_1kL#W8JMIYZWsRJUrY}83{D_tJmmg8kVXox+gSXh6S zHCfmA(`u<~{23JE2H8#v)1CCvM;l?jG1#FM#!XYO&4Srr5`c2kLT!5F<41y{)wz30M->xyhN|^l7^sa zBM1Gw=UM{2SoJnLGK1ROVTxQVU*gOID+;AX))u)Y)NC+rZ!`9D5=sxe@t$7f1w=~B zS4Nd?5fq+C8LE;V4pP^FPfi|Z+t|*CfpaX~)Wp`zD%RAX=1#6f4{8A4uigsh?>0g(c-Q9+tO=`!N|^i5gnci)O*bBGmpu`t=V~u+4)~mi|s+N zjbF-AY(OpG1QsLIv7;HDbnz00xSbG1RkY0K0ISjF#lZgJ-KB3*~ScXG_FHz;T|1%FwOPunE@=I>&hCn#_FDCH4#s8{bH~GZz2A84|5UQOA zC~LrG@ilS{n06UwVP?zU%|mk-*b1boH9{P7W|g*+Nep{oKK3OICF4RB?40Wf z{f@t|j7$sC;9K8nenxLCfLBPMF#XJI7W!}say9|y^Hs6^(O=JSxcsG20=greKOWst zISAUqfJNGu2rUTS>-G|JGSLJZQC_yTs58f{0sFqDH17@2cdmjNkZ2W3?i275SvgHz zru^}-E9PkC2R$!92@Wdn}HuARQ+)Ox>>dwDeCEj zV|pMLyF_ONUnLtJg0Uq&NsMHNFyA!?!l7xAbM0lf&&kg3XorN6{I3vtB%K}+{4Xj} zp?S1n8%Rcc>9eqljf6KVB^adSZjrN6tMj`59i>{!ob&FUAInF=5y;sZx!sSRqVF|+ zIp03+AQtWV<5d_QO9X-Z6q+Pgk!=Z%BlEc&vrW5SxYpR7>wZnb2j>}r*$`X}8@Hrw zf%2GMuIDU8^I5G}S?2fiSR3wITDJ=jLOVddlNm4KIECtl)mj_cQJ3_HOu0MxCqI|K7iF$U%~L zWe;o#YCtY+YdkV#XfVr{s(R!4vH@4BE_mec>7APd+HkhAyS1 zFlo^t!!aJq2=9OPb=3p4!Aq&*iiq?$S;+3Rs6Hd**t+J$&I4~bn-UISL?3XK8?#7& znIZvF8)A^YtPgtUjlBV>nQyTtcTXn0M~$T0yi7zg87?LvXQieTU-K`Uwlu5Ot43PF z_qL%j>7@x(ZhS<2HxN-9k!t9TdP_0)=kE85ZHRuX34B>1DaJGmP-6oqngNRpNiJia zWJG&M)9TH5>L7Q%_g>@~rgP?x^GS38T=rg)I%HlYB4#y5vma>p$t_5-S4hhyT-mYO z!LdO3*bk>z^;-taqs|nZov`_*R}$rre)QrG%GfMx*hbblr~C) zRPJ6Zj)?;0z>zKr+6^iU%82=Q7t+2~p+g>hi`-+MCa}|=p)EreeeGx)`#agWWHFi_ z>W6Kmc z8RrRU2>~dP)`cJxO_@Ey1vo?Kk|~pYwvirEL=u$GnT#A$?q*R_P%7l%lLJbOgsg5~ zvD=Nju}P=!AWq;Xq;id!15ZiXI%4cpOZqr3`IQVa)WBHvEHgj3{w>Nf) zh?_Anp#{N?A%7 zRs??^+eAa>70%yN2In1+Zv~3v1GvcGsL!umQpNxn-Cm&{Rp*FYnN@4HENSaxXtMdv zaaUh=61zq&k>GekZ*qb{i2Vm|E7C*CP+~Q35-UrwL>A zsM8tTlh<9^rcjJWa=hf+*)ObnrGTz|D#MZsvzUB~QDIjG;fefd$cqU2@GQd_nXB& ze@L^dsZ*h|;hbr08=vU$7aw6!--ZalSFr8pIh)`7Q$hZL*F|z`R>K% zahd-&X@c{AmnPW$uP4Doz{J4G{@=XB|CA<}7}@{-rHKwhClj3}Qk=~S4mqn$li`}R zmhYh!>&+Gwdn$?HmT1WykKN5y+t|(T%HALQ5f0Dl=F<$z>E>4sJ~+<$0;uk~{{$z3 z{(%!b%)rR-{4yFs^Zx}-r0A~itRVaYC*Z_n=`Q{YoG|$ZP5{p_`~xS_v4GXp0j9RL zw(O1o6#g5WSk{BF(A4bsAK*mxOv;H1KtwP7{{v32SEOYCY12ppnxwFm04RVC<1aiU z08mM|v-%a4XO}1D!}8BBkBux~5LlX9S)5u)!ZI|v0&i?HIrpX38kq!ALTzKyNg|BO3Zn0;55ADOY>;|j2jz4G1NP`)GNx}bq+Y<{;#hJ2Zd?D_F8v)ppPCc-f)=%zk zous(fMg2xaG-apr_@$roU6Iwm{hm8AJAbqaDF05uJnJEakiEFD{Ezd#3hM z0xJKyQZaw^BESFo5B zji3QA3uX3tf2`J+nEt&mGBh{+P@DDDg3L2D`TJqZs{$=$XxZtDHT#24r^J=`JM&#D z{L5sjoUDYpEMM}yd%NU&i1KT3TX1oHm%8ywAu_XbfQVTC3gEWL>}UsYrqQPU zi^qv(0>F-4dHYLv*vmil+nmDeWZ&=vVD?L!8UDU|@H_gbNBy7Vgw6jUCz{IIFgDV^ zaO-}}-$t#kE{>kmR()r`b_;$Tzi-PjGd$9;2CKgt*iT?vBxfh=%70VX|In83tj)sk zVjak@6lrRo=~?cAOT+K(*D$@6K^vIm?7v^#Y4bY1IT8pta_qz!3$3SGc&PZ@N=fp_ zhjmEI4@-DrjFqW{q}kUXUVC?wbi(Ej_ZRuJaa9*pseJ&7Ff0yVfH;0jU&~#np2Z5h z9QhrYX02d^u17Dx1gPpcxyZ&lJ$wmsax=31S#X8swDS|o#0Hm|v3#4RKaS#9|4(uv zfBX&kVLF=UXPCmjUaPQxc<_>{B!0sl9L5I9R7#{+m!&0BMT00BADSNEKw0L2i-hvzL-C%RG|xHZ)eIVEKOlq&_4Eta>>%qoE^Jp0FklN(ekSJzCq-Hu$M-2E*UXmAdfiMfr{+g+PKssoM^A*evOU% z6n)nTcSo_1)Y}BiED&S(JZO6wicbin;P=RP5JbGx@7yVAVqhJbPrM>ndB$(`^7a9uMz$C$mz3?Qs~=X z07`LuXs5j2N$i3U30HJbw^t_5iG1L+aIjhEq+gr1e4#!O%pwZLKPTfMJ9?uTY1AD% z1*osH*Em#2fD&D%DxFz=Hw#Z=e0<{|Z?0E>e|V8+jC)B<`pHdkg_fMzOCa-NsNjw@&u z;_|$|Rl0pdx9G~cE3lpjk)1#)-3GcJJ4fpDLs!#Qg2CqLbK+v_6M$pLh^mvT%;b=& zP#nC|mb2M}twX3?*F2uRKRp+8S6OPLzI73I+z>5)ey}xW$X{Ge_ByYT+0*Oqhj}oc zd$)O7OSMqKFW&30OqMksV+aKaCY|Lc+u76-a5+7(&1oXPKnW8)_!ZB1`7+24ivoLXb8_M4`^s~(;lSV=ZxaK-+=l{CWR51qEN zSMdH5q`J^yr<-eH$aCKv_C}6w+{*gy{jIP3dEL=D&h8jSJ;r;wRc#7llS|sTgvSkb zjhizNAII=wO1n29DqaYkYb?Xnqy{u@FYen^6f!!47t|l=g`3shand>~m|Nz~{&C7%T@6z(FK2oex6WFzwT@&lP8L6Ixd>&ipWczKB(& zi$J@hwRRGJ zwXjnGaR&+EU@cHv26URhb#4&#v zvazR(K)-;(E;NymG53vGxY58+@MX#in}xVq1R6n^e@))9)w{?8Gvd2rB;FK{g1(IJ zq<={zY_UTD*1VZCd$CG~{E7ONCZ_M26n^+GF8v|G6qZf>ylO2e`1BgP{S4dO;soT<_oi3(Z)KxX9C#pByXMnIDb<3@z&pJ;X2W z(bSl5hR6RX%(MD?T!sRYJxj z{^%#@o5rV4Noi6+c-eRl$Fa$IX};hg*4{|2G9Jgbmp~(R;N{-JiA~M7NKzTxZAQoi zDV?t*efH_`8!+s?W`UP5oiFQ26{bXs3Pj+FXkLYz-LHr#ot`7Oar9kq((_^J(B>P_ zp|o;B-_bDpTNmxN1P?%2z0y;0l4L@k(nIWg8k zc(XaAD^=wN3vtK9YDzJrSmC5NG7{{TP;|Eb1h(C8E&RUU{HOT<$E6mc2@@iiL&>F% zff@f|%~TqFp~xts;B-s*OsWfL>bIM1$t2GoU|J6+cX}9;Oq9SWDFRc0g-AZ~e7$Y# zw9dl^S=HY1UX+IgIy$-_=t87<6UJn28z9T1bZOmi)bZHZvkM-%V;8_GXQv4}84*GX z^aVLinmMBFr%`-_mbfVxuTtFLx>=RLV|_vdb!p@uCjNP#I*HCW$?C7gLh)CbSgcQt zP^4-MO-x3jwFXkLu3y!|3=X}#4;us$oqi&<{&VjCVu3i%x9U!8TO**yD? zBc%kiJ%c4=2GpXoZAX@M%|_QrU`fh?U?LD`tBtQI9Qg-{v2xmWZ7`J4oFS$Wr`GWn z<}1NmqIOPIiST4rJQ8lm0g@h@fc+lS09!}l63iEr&2^KML>pp}sCq%bLWZSt@rOa4 z`;MpCoLp|j@r!(nEp5>dNDs&ASw`Z}Zem3uE(IgV>xY$3GM$oRl@sRB5!Wh0B8$p- zt6%+#fRu@FOnq^u9qp;|4y$7(`4g8F7TE@StPb514~m(8%N_FDx7wedw7S9 z=x5R)$Sr0-E1t|uflFLIs7GNqz6d1|4#Y@&g3Jhr3{!L_tol~q)?hh?M^7bGFRFa) zjC>j=>>yg%q;IYPy(rd?Dtw+l9E!tE5*H>+2h6wTq|NGDWmA zTGF>}I`pZsu#uC!>w3|ikvx>HO`c>|a_r>L@qMP}wu37ld0fhb_8IhB4PqDUrDoQD z4vc>^@ev*HkyNFkuSwo)NC@BN&258OHDwx$9F~+d7=^Q=Wg%My>JX3SM>ZrEPiuvw zIY9-AxIgY06=*356>My@a{d{vwuFf8LsS~)jrzJ zw*vcQm5Z6`S(7D2JwK%GD^cH{+eQ$p}CxrOladjV6nh)nNJvLiE@PHe6H@XiZm{`KgQ*0#ZZiP$<#oOq-cch>NO=zn_-13+ni)<| z%F^mjHA^pP`gbc){K2KO!#eQ3=Kl0>v0+5bSe}O}6NmFsh<{Iq`S%QA$jcOYZlnU^ zX1#j-AV$5^3B>Nr>jle0Q{VXKbHKQZy=-I>OSbv;r@oQa7oxFt8G^?dQ9pj#PfFCn zZwIu4;I-7u*Oo+PqzY;i;aSWSPG6`rQ`26xW}7oEtRvT$tUT3#EVY3$n2*a}iN2g3 z_0=+Gi;zghjmb4yEa&2(lj)nc$JQ4=hjm}UQqR(!6!gxvg_ONUp%d5QV2be|l$zU3 zxSZrwg>~pbzjY0>>t(J^LwpQ!#vMCL-PNoIzuCt6?)KOzeI_-Aaap9&un=syXkzO1>tmcywd*!YPU9$}D(b_~(MvrCR;XIS%;~ zb;VsVrbfmmg*RhMRwCL1|C_`SP)?ar=S&(DFYW!@NE@IMW}^4IkMepRts=q<_&UW6 z-E-)O8jw=)9W_+{L*iGvqJmQ?0{J&}xIJJ=lGAj%N~%O@4f5dq@y=%n5@e3lC3k6h)1ihTQ_XSkxtvylhyW^DVPm&__X zcWt&{a?O6>Zbwi}O|F5vQq+EHve3j8eG9GmRw*>bOv5C9yfzNWN+mO!WL{&^Ba8;% z?8tQ#f#{vV?X;TteDYKek)Uc-9+jE($njLf9?-uumEISen_>z~39V|ia%&aO^pQf4vh+cLYqZOt-pCgC_ds03=LDbx z$)~J+is_CU19-)Kf!*Lw4Rlt@?s_n1AEV!0sh#4}h(Q#qBbmlD?pjdMp!GVPL0#cR zuqESvSRSApl`xEA$oZ$GASp_f143gnxe8fC13@}?8`o?0tdgit{#tf8c=jG<%--(x z`)D#;DZ-AB`D@m!8p!x77&`M;8#E-E&(MLtsTzLR2RG%~)-lv5aXYptb$+e4?@!p2 z8`UJ{O%<3;paZ?~9n!M-F(~e2mJgAcrVP{qvo{6mCYYz^-b9^icVc{7e585Yk+>>) z-coVY8=HESpSggZ&{SB;Ox>hXh4x%2YqJ&xs+|t)>{Ii;=J--#!pV`WVhu;xhh`Tm{xi87k=4-~T4WR# z%KeldV-g}|c7?q?j#T<1oU|yje(Yt^(`REy$Wk*E$m2)k&y>-StG>LYDv@r~_1#G9 zO20SSFO38wFpx36R9{G?rCAK?ABb(}hOf%y-W~|TgFnVkR_Zozul$Wu{r-I)gL(tZ zezJO8lgLK1B-q?`mP&IODPAaKe-Q||5j`sCq^ZuJo0??qGOjHe{`j}9soq*@l*U1s zG>^k^`At+b)%a^+rYp)VC%qB3vFK!9_>Wb}Q*|Ssj3rS#V-81rpCL$Rj&r+TO-SDH zH-F|)9@GViWg3vjC%U7U>lLGXVvw$Ezy6X_o?IZiYi(w|n}_TCP+W0L(H-w9%?lgU z+S+nDAwZ>G$}g&hb@eVb^(MEcRNAvas*Z6xIqZ2Cb{n2l?M+k@tj`=9HO<7rC6mw z3E-hUkf(NE02N2sCQvk-bV+QMg`mDi#+Co>;;~1O)_0kLkI;+%lGg`Bh|Gm~p7@r) zLE)?f*5A-dE!n3m_e57n#C~aDEjZK=ol-sx?qL(1l!uPIKBa=XGeOqiz!sicCB+8k?^TKv0XOCgds5631#LlL%+5>|+Y`$PS znb9|yLHoVG&`RP`b|Yl#I*^3J-d<(vRV5UzIG_Y2-u8)wB1>i)CctljrKKs+jsG!RXnQ~Q(Dfc{YH6~LnaWoK@X6K+8Egm2_!{s`{&g^(x?C_@$n*&xMQ!
zw5**tI3K!IGMyjq&}GHK>iNixHLM&9(jFjNq;lvnVpfU?}QHmi)^F)*5h0xbDe zv^_LXglc%OPIAs)_^wHwo$}=g6FEqFx-jX(%^RKsOT{5Ny!4hMJsELfpJf9+ch{;X zC1%N37fAOXUtUt>^v_lrxbu;FGiVQ`2-GR4N&_(cW}k?cxGBbZjDi)g*N8h{xWq0G zo~>GQL&U%&hh-k20eV+pBR*qNFzehj_)019rMjKo)4#m;wm3?xrsmUh&IRH$%9pxngU4 zq!esCgCFg`QWGDU{AfYxRrkgpg!b(Xa%Js{Y^wbFk>;2d^MksDqt6TQKM_$oNhw6; zYHZgV(#vr>Sts#LU_{WWp6+Wqbf!#4I?3q%*bi}^A(`I|x6@Z)X(7i4Y%8-8W2Ar1 z@)jGeYGTAfhqU;&bfYgqM!I!~cvM11axgG0Wc40nwt4Q7ou)Vq8s`uRn$+_M20*!e zy`gr)_U^OOCo0zoEkBWl*`fQ7^4h?*SeT$5+LdM#noH$gsLE1xk_PULU;tO z!kgrnQe~7K8$3hXO8o$JszUEzdo?i4n(DzG2$!bEVB;|m{&v%@=w#$$Q*LxKPte`3 z69B~1FWFseFt#eeHggDC<34)8j(q;yfytlU)E24a!A`NLLPalmt=^W{kJ$GT$JAaY zcZyfn2^cyxU_Usr_th3Fe=) z>!6#f612`SKh%6L@51Z8GhS+O8~MOiSJ^;e)s1p3k4nf7hg2KJ&uXDI_hxM-$zhqy zFecwR7A-2gEpt;Zt*5^03IygULkA#Cfz1GL1+B6A1tD2<=sL!OH9f|uBZ4d+`)aT- zmwp7+U4JueyuY_>V<^^G^ZDs=(XKlSrcWfx{UOf(9VN-6FRFi2zuV;Rd!Drlku60d z8bVw4c@CK7D*yLHI~NN0+nBJ9ZiAwq=&4OgZmJyi;IT&bmtz(=D1$onFJ)<(6$-hsELBo zY&LSt!ao5_-WfZRrd^ zOrlwY4UTuld0<4R>ZE6LhlWjZ{TN7KsC(}b?4YCRy%Q&xt#_U7F*E9AW=HMm*k6Z|XS z8bt|AmNaT*>dGtDu5?)7Z%X-mzPXzlgBk2=fEVi0EYCD-udowvs-Ab-o(q`m+Y+<) z<+pDJ0s+)A<2=b1HLwcFd%IOV4{sjaAy@5zuwKtcTf{hSi`w!QV!WW|-V7gwm{{q7 z94eVg-D{TvaiL-^btZ#OHe_8ulPA86T}zG<|Z zM<7nCqW)u)h-^`owQ>*d=SGm&$!F^}Hdh%f0eSTf~-)Qnw}(q=jT6$1aX9 zU>_za2=Oxr_#?11d2)S7WKlwm^57QUBeTHph|20?Murl@U3XcN=_3z!xAV2DEAVr1 z?OPw%M;^3Jv_gF;_|QQWSd)?j zC;F$1Z#Wl#!RvxdSF8MWg%l!k8}|vO+(P98gQ^GoLKLwNf2Iea>8E(e%;~z%kollr zF_7lFXAnOq*Z0SWNT9pGHy(L*g2@#^LvgVb?*X%&b4Sak=X^K1Le;dX{T)67?3p2c zMod8!4pkGMo&Jy%4h=O}B@;v(ZP`9r?xfb&K&L1;Cf0Y|BFD?lEcNH9{@Hx|=P?zj zw9|)P_|(D&aB(PKPeh&Ik`(^g$F-Ky)i_>)o5feU4svJw#f11uM4Z62_^m7mW(l(ZlzhS_r6bNKp(>Xn?kD=4BPM;(6Y>Zj-I2pn}3{K-i(yK`n852iIU~eCjx+PFU$c2;)pT=3-2z1 zkwLWctQ33N5FwJ}&#Nwsm7=NgdIRspn_Fw#0@m;dcCR*8ym&_#6zJX$MwgQ&B_pPP zND&s?BD+lDS7!7-CIoEsGr@=bs7j?#f#%8C`-v<71N1h>0U_cE${|YE39nH9c4l=A zy)TNM=R5JfdjE=v^yD$qD!AM6UPqH z_Z|yuqtV%Sn*u`qrbk}%kJ{uGV4YG9(_F$sweYzFvdlmtMKtsw$L^3Q zq5o35@e>MjKG(P>r}Vg9U7*jS7;at)8P>-l6(U*cMu%)JMP|4gST|g)csO;V_@2Un zpEl7fvJHb}s~XnN4JQAEk>w%Az~Z`5HF!O*f0YeWFzyaO5aS`BYO0mivbR#minOAP z9=s%7VVVt2WL+;*GouhQOoaORqq*l^%p$WiPiheyu`lsD!a{70jc;#zf|0{}VP;6V zx*4{cfV^&HNgef#&aeziU8&8;hbn$K8Vl@0i;0IT=;l5GneSZHtDRE-?^*Mxks7^L zQajcC2#ZE4oO_Q&&Q`RDx8<*S^~9n)Q}M5M9_vn6&EniE2ZnJ=wX8I~9w5$ZFTEX- zDFX#vL)=(_FGwL!1AlWO!@>QdJu<4%XKtWK^PUC2G5XW7YxwZKRr|4PL?jLMN+nMm znroP<;aDY#VFA=>1Q0HBk~qHj0|nnevD=IAx2_eUyg#mePF98 zv`oZ&@9t_5LiCjAX3@q-eP&`V)ba-AOAN9C$`nSw&VLHKQn`%Dtuja<>VxSizf3R+nsBFFKBTog%{Qy_Sb@ zM3md<7PGXimhdYnJj_NMqy5_tM=3bi5HCnafB$yDI1l;7Z5w_q{rRF*Ai^>@gV*uX zhic6)nP#_0c&1NYSI*~B>7v*(((2pLNuD?k>sX%Py z`{4rI+0Bpj8IRNU3(H*hjmP?eS?}KQx)LZQ!`VAS3h3xJy0EDW@bBHh&{|9Av(3qI z20lB*ll=7wPtc{gXWpu%MrMS-TzIkZ3nuC+VJvgdhMwk^t;+9im z5N*dY&MihmY_+h`m5E$#Ur9j*wbFrQ`gOrqGu9pO>6^};MQeNaITLXYrNQL0)c zW@Ch}P;3uHw4t&yTMP9+7(1unP{KCr#xywW&*QrraJseZB}R6bWi{%9n-K$AH#@5BGbq4`^Ju(m&A$RDmEn;UP0U9;(r|aIQ-&H_||Y^X)))g z<1A|CB@$OxJpda*5f;nydTsv3E6vb@@HNuC2|tFqyBKlxkE-7f31@d;W%Eb> z0nLZ=@ibWPc2(Wb|7;hvYXmghIWYp>5Q)naJ$`3jegqlOJJx{Zoo+A}KfWBgp%MH_ z@o=0Z9UiljwdmOmfokN#Ez(olBWxvSPxFmrGgzUM4w!(j#4&K!hR0;Zuce{q2QdST ztVz5~Y8H`=m>cBWT6emTWLgG4(c&TEoAIe0pcbicB#OneQfe)zD>-13NdJZ&)6suc zmD+v!IES+b7M2&andiuvB?_g#*6X(cKhU~uJECY^ftrq1T?3iI z>`f~CsFrT9dNAU)9*LM(-b*4o1hqs-)q%*Z$%Q0+Y1^C_h{$u${iwl z<~cBmF-_L@&$REoudbBL{^TH{s88z5~{g{yvT}6>zm0ZEZWp+{8?6a%g9n%E@d( zg|Mr{=b}KWOOwXB>14>7D*tN38b}5+Q$Hb)*G9IYf;t4#Uc=TJ!_}ffd|w_<^jkEM z#!*3>5mHmCarD*+@()BEJC`M%{!n{EU@UabP{V7t7(E6fk$OD*2Z^J){6@0_uX;tK zP(m`cg?u;kq@eh(WHwzO0D#NRu=T5FPG2t9Ag=n)@tHSt)CuxfHhms1vFH+?oEBUO zC2S3WhrK&Q5}OWPV}V|rkiD#@DCiGI1nsThn?X0Fy=wGHNfI_`tvRK%TIj2U%3&hD z$O#T_j(hZ??$cvv1?jqJj$`H{iK*KoZl#}Jv#gTQxGj5B5ox)8Xbr|*%xF=f-~N}5 zG5<N$WAU7-! zzDcAl0YuY7Z#$XStDh*VuGVMar`!R%c8gG^i-Pr!8onS?kWtOR<&$VRtqttA}x$+5U9_{_E#o($9I&M~E z+Y|$KS>Z-MTWSLh?Qzwr!813A#$KupyG0}?eb`H2(@iE)W>sgIe~!HnDMVm2HBcGg zHEN{2T}|!ef5Ph|=;_`Dl>KrR-NLGDH%6=PWtpbE9>%*?xu#Qa{6UE#9uDOT&sCDz zcy6`j>ceTLpEKvV3n=pZq&P_jk4cZ(#O+1L7P4Kv@XgKmF~_%60h;|__d#m(nWa8@ zlvnY@9Rb4H8?t+5mDMJOrl~3ljE;k9qbKU@^^%34Dz7=Sk4)5otQEnEfv=%ztK_W- zad@HyCxtzzzCkeM7H2iiX7M?rfv> zapa=YBnddm+jh>1yAvUKMCvI5+FHG)p)gN*cj5fMrggaJpWbKhZr+XLaLRBONEM|( zHXX+sBm3rQF@!1mpJboTD2Rt@u~f7r>-ZoNCW&B~=X;zX;{ zH=&u4mvBBLYOYcyg0CW)8Y#3DrTa56IB3QTZ-`sV_{8IWUqd~he5agM~vulKB=g9GWvH#uos&*wSPz@v(HTx)>S))n?{CZKu%^q5%3@4?*u43_ z>!n6&zP9QXMnh;LZ(e`mmLDIi5wrCVvJ_#8G1u=lGATdmP;rxA@>AX)vN117qI(yB zDn&q#Q~x;%$D#acL5wX~5WPYFGJdoKD+@Kf9a7-*561awTpj%TR0rn2hc#_Y=BoDc zK1)F6e2k{>tryty2jy>3MVeR4!#t93;0ft!h#ja;UM0b&GDIyf3?wVHjOUew3hcTM4LD$|7E@F z)+0Oa;{ZBRdda`@e)S&~Xr-(TgVLG&uT2ThIH9AWs$NSw>cCg+LODE2RORI;N;0mu}g45{%9-{5s?q9_LXd&){ z-Lld|ppabtr$JTq$$QS1a3!`AJFrPQZjf9vR$SKrr+`uahv&V`@O}-=5NLb?^rE%Ux)~BHj^$W#S zNBKEW&v$mDz+4j@!R)-nmAq*+Xdw@|i9kIM>f>lJN;_a>1XnMt4yo+!=ADpMMU zYm?(Vg7Aduf)kFwxfn4iP`gQX#TF1UTzs06ffmGPo~O%u-PpAkLF`QY*VdHj_@UY` z>DeXK4rf|r&=vQQ&Zc`aS6=>w{PA_t-^v(rzC^QcY^~C+KdMjyYo;kzzFImW|5Cu5 z^b#ZK@K3+_qZ&tcU18q7Odv4*D+wd*Yh!Jn@?cx?C7m7@Mqy8zmyOk~ze54tdy4`(H`PlU6C;0(JI#-{d-OBd%4%$~}HSq&yr< z6X)?nF&K{gOwAQlZ11~hIZq>gw`a@I0l=99jd2&02x}w)ZoxDdx`*QPsdsB&XKTAU^@PBFO!h5s=PRJY|tha>QyE)y0?0$S<#rz`CM!qfV`aR?5Hoqv?$uErY zs3`)|Vry576jkx&Y7%Fj>VA@_fVTD`)I^9rn5XVhT2FA~o&7`2JWg-3i)r({Ya=|T z(4oLnLa8JmzSKzL)erGkN#)6YDy5Km^goPu0vPN(3BZBv&+!3f9-b5}_qkdPOhmxi zv`3))X%%#7Wa!FPO`jMCLSyKN8SAM3B&=ZZpBId6&-ycX?B4H)NxtR5^942|`{M=F zNgT&yu%8LO9PjCD(RkY!(tB{YIrNzjEi9B+RhSq~WiQ3^86%55{6BiK)GQ?XLJ_?i zuW?MC?^xF*EgyJ2a3G)!FD+7($lsc7vM`7%yn2sz`n`Q|Jh) zd~^k*w0_WTReAu@6?;T@_^MW`*nSykM-;{kAXt#4@|r6%3na6M?{(1FJwmmM^oNRH zIyo)|G~F_tMM|n}f};bHm)onhG^8~%DOZqbNpf^e@ZjLrM@by$UOxK| zAZBSB@B;bhoa&dSOpiWX+UUsrJ*&?$@jg%McNwAq+VO}j*M=Ze{2q+h%d2$1>>q?} zlZ4g%@v)Kzohwhl^$j5i7x)6RSbOysl#^|%(`mJw5T6auU{^3)n|@pT8S$R?vL9nDHfX@5FToj`is)-R*U!xkL@AWfLq$l<~LE&_Eamb?C^HP^w?QAXs35=>6)1%;;nG{A(a1pVhXYkjN_!Hu z2Z$Fmo}uCyENYvr{_r%q!i5LGIFjg&l7jT8r)@uPCjp=;c)|E^&%kRNN7!L8*(eQ` zcZb!)j?Im`f?1#gxyK2a8=i^(M48d60cA!zu;Csi;a(ip-E;zmeQKgjQJu)eirTV!UNym{p8tu&nmwg&>2^Un2+(ZeAd` z_3q(h_1NT}Q|l{LOI4;5I*rKcaq55Nq`dV!u->p4MSpyWu$D*Sb}v)RP}um$)Otfw zXzGyzx21^`#NZwr?AQtdtdOy|%WI_sE`L;#x*$xWj~!51(Zs!9u4=cXueH--wsIhni&14#@s_f_jDtV^3EF$ zM{Lf@*|Py=r$o89!x6Fe73qvVW#ww=`J$wnLX&|9fGFRJ3409hoz?Ntb`~K9<6!bRUUDdTtMDr$scO)`TvEC+UdzYM( znEUH?I}G)Ad-GveEaw%~szwdtZ|fLVCv7kz_0M&Zr12i`IYqUs(=kK!!bTUbT)J8=8-VGmdCWLPos4x=Xv1(d^d&~oV#RgeC|8lm_QQ+aG8E(A9~ zK_RrIrr#Bu6VmI}(3HHW0hV+EtJTHMAu5e*S{ltE`1{uB@{7)QC*ST7Le~lp0C8zS z{mFihP0g7u)5m3JWkpMdr7iVBBLW$M^x`z9aDbnMNAlP6nuw+Gy*6bA9N{Be|Fe#- z8b)I_W<|`}Y#cSfRNZeFxAdp9E$?q(IpE0F)zQ_n?=WESOKzF9$^Ed--Cc2}d zX=ne1tYmW~OeD9&UZ>P!=&bvxI210#3wB?5PQb_sK?^CGcA-HAJ^RvQeM528c3d>F zGbUoyogAr5980P87eAQ@IMw6tQZ?_ldnxArh;@JTu!uE|-+*7WfoRl4q`QYwnDiQZ?{e%kjtV-$FTaQ~b z2VR*37hsksAi168s+Tmaf)1R@3c?VkzSWVJ_WXzw?7xg=MsLj>TNG2TE{&7SlVUi4qeqCCxKczcnVtz8mmHJ5uh}{nK$LB{rd>_O2525**MH}Da@b-W4Ybg zu0Hz?ClLf`ag}Ae+XRQdy3PjFE#0BUIqK&Pm6p8bK@!-ZtdwlJe)^G0DwyC5?-VrO z2qDsVtDs&0*?w^GAYwjn$l}e@s^P>7dZWCXt z?>fKghLTXsat&x5>&7O%QLSdYE8zhB16N=bz@6i|D0VjBP#d7!x*K`*e)rBqdQ)vN zD4`F6fvLlsi1MYo3ytBtn(dWCHSs4RqYpopSk;a^b0<@gqjomqaFn!jyWNAhVd-b& zenf)Vb7emU#(&oQgT9GNFSTSC+2+DFW3`%0@EJG#PtHFEz+b3zAqv*2)B$Hb@aWZR zQD<)Mn!4L1*5plxjte4_l$eD61OIf-ZO>+UaH?~KlCXlZ7A`aSGo+>Xgl@nxZGYuh z^j&FL0RL#{k8cy=g=shP?W&B+C7K#1xto5RgFq%b2H1^;71b*t+U9zY@>T6g6E^k~ zeA>5(@##M(g&pDdMWZcMRTc>jTo7(`My@z!y|rZkWv<>&e>dvRNfAg#G%bzDSFRjW ze9lCk+USjlWe?Q6faa9#6v=m~cT5pqkPfXt+!n4&K7oVmS_(qGK|IuKhbDpK23S(q z7NbMMxDA&_E!ToeBpxY~2I?r8xS5wOr$&`f0Rox;TT5J|%$U{<`5#;`S}~h_Gw%P) z)bS!=V-U{+`hlv6ztUBV~RZM*SRe;!Dmq8B8q*d z$g%PhI>kN&n^4`Fl>B&yoJWVm5KgMfxkLDcv{ ziz7(L;TU>!Nc6Q$S`o4*S^3iRlk680@n+GWUfDX3rP*J@k;N`WPZ~6L!LX!39!j8r ztO<=|`4dUKnOv+jIfY_on+LqXUBpZ;DGS{}y(4&UMb7>aUn`w+8E9+)pbG$_F4h(e zvCV!A!^y597ewZ9in^~cRtbfwz-LU`tdd1WfcY>P=kYLT{nrrY+T_Tl`(O|_sN)hA z2%HmRRrx8=fLhQ{#TJEW6&m-J#FCl^ zs)2yy66J+tY7<{zV6$Tksq&G#i*SW`V`-Hyxx(Redl+ml0EqEYVO5(hhWVEG0LAzu z1rH|TEnS7C*3C~>@K14 z>;46D-JfLkeECfxLAzOc71&qVB%}6{v8nIx(rS&`uIgfN$)Ts_pGubt(d1mQ)${ihOWXCrMkG$aP zoRHarMyVW}iD#a0=9*hW=qe39x-d#tVul72jQH_X0h&%f_M}^;t*qmkG4~z@ zhoyz2dp3%hl99NBky8VlP5doX?L%zzyiSc1(T_y*%eV~-*!R}vSuay$S}3=|zf$bO z`eq)8^JYb3052J-AM$D6onv6TBdzYMgU_{9%y3EjyR|E1CA$2ouwR_IN@PZ^vbgOo zJDYO;We6ObZSwn>@>Y93o>Nl+F&iMP6=3!nnqLlWJf>!13rn@>5FVk>|E)hmwe#u# zUpsQ6{n+tKa=5XA;PDOcaY}WXcGQq~PCYk-8IwN5d#wD_P4aySA*ve6^>-W$qw%0Z zR|VWO?df%C7Rc^*sDdchHR>oKBSLHV(}5Gce>|-|(Ah6MGZeiMv)myzuXttCoT09H zqe>?GpmRYSCSk9@AE^WnbqiiMPrFAFZDR!Nxd{{Mnq&7vAq0<+fnF85&J$OJsu;Zh zVSItfhSETgiEqTlNhMP;Z5hT3R6z(KE-K130W(kb{-F}{r> zA6^Olh+7oQsrHBY%Fqhhk>aBhvn>kTJZ8!$GV69{N&qc2E_HJoZnoLL6ICxj@-2k6 zNkkMeIvemOT7mZF-6d=6M+7%y7COm_e~8zVTPe;1oT!lYyhGqdvl?enmZcu_PdwWi zL(Dlr(hGfheM5f--id97`<2*HI((3UdrS z0%k4CD63KqI9N7~TP8@ZUb#`2wpSk5Y!Tal0QETQ&LLV@w8nj*<O8h%~XDR&F z78%#PSI~Gtno1f_kZRek0QwQ&7H=eta6#9HQ2G)Khb$nC48o z1CT7loe&Zl9rcP{$eWOWIZnH+vExIws`_u2u3pB=rtCMUIxfz6H`>)n~mF79TOwr z2Uja)aS*i3uNCQ?Xun{Iy*OwjX9kh|-YH~MlBw;YR~cGqiN%fX$>kb8-JE!0J!*Z} zaFD5ROgyAJ+S(f?y5q=H-NN}XOGZauUc z(>kZe0$b)9us%5Na5ugudHh+NVwZM2Y97T^-^-PXsWn?>-!hw*hvrHNFi=WTX>QZW zJ5VxaqahL1(5=)<@z=s6db&eeYnL{Bia75uhY0irs_Hn54w$x$_?!6!Ke;fYUh8<$m zUK3a%LzgYBseQE24rBP748U65VGXOyP;Q(i?cd{imY~UBB0^!7?)DFugBj~A>5aaO z12rvDZvCs7qP*rY@jfq~WfyJr=uL$Q5aH%Z4^ABEi2;R6>^a|IMp<+LnZSHCL7Vn5 zM6`FRdcX+3A61O{ffnX{r^*gLcq&DtIbt$D=hYy=#UuKpSRHLrrqA$m^cZ+C_q8&gbOgOjHTbVhIMxV%U`$i+Vy>;58M@kTI^rEZi@_Q#4CGbV2ig+7y zT2PWlZ}Xc9FR;RocltK*q$3D;q3pRCWX3dU6FR@V1>%UE)!STCs>HYKyE(`5f*rJs zlbOTL^6PUN%XAM&J<(%i+*sd;G4a>!gBrFo1wFuM{EAU@mC)CWs>_x{={#dln@A^@ z8(u~~@G2zp?{$v+L<8cXCc?&LOyCqj9?S0m{ZgD6&$bl$xx;yyUvk{KpjzR4cLk@h zwqIV|49_Ir3mbpZtXSi1FHrf;d2D_S_fYy^nIswNzSW)z-^MINj@ODeF87K<1`-#p z)#TBidvJ9~*iG7f*Q9W1xDA}EAX%v0R${Fz^wpNsoOw~)53AFa(W&Fl(Jkc!35;jt z_oLYTxRPU4WUyBksoLSL(!kjT0!t4iJ%aFgIj=FW;2SO)SoA@Q9|UB6r9$vU&qF)n zQrWeXdlov2kG<(H{QPUf4$iA|5pPLCY+dAHM5btIS;#0Ij_0778;@{3^%U1%6eYtkiG06RA@UKtG-&( zVS@Z5CtYv1^gS%+WM&MF7Sb0=!V(7E{JA0|jh3H@w0@wZ8r` zcekz#wp#-R7PjKd`YnZmDx~)siWQtTNm_%79M=|0)2JFl*`kwpliKo|D10G>)5%J! z2J??!EZ(nOYliw)&U>rshNwVJw#$UK+0Nys^)oREa+Gez3n_X2jS{Ao9B2@plG^PSvj{R`Of7gX|v)rq)n%wZ{2w!KL%07D=PjYAeW zIDKNRS}QR3!dDoTaP8~5qmkQzs?EusT^=E)6!IKb%vN{+SeS1IEkOA<1Jkut^qzPv zc%ytaZU{aa6UzB!RHpq(j$^ClM61eslr7L^bQrn(ffLokWb5_=8cQ67yQ5}^S0}D~ z(7RtbBi$y5+q8o8Ktnzo(?Wg+z!h-A#+g!=1dL`KWJxaDpRKFx zFTyLI>&P4y7HeIQIO!S^1ap6pWgcc%%sSB!Pr{er30s?@8k75wLG{y)R*N!7B_y#N z6s!r`{OeoO!Y6W2Cey#SSH0U|CzEBn3$r^^FG-{TS8RmqN9K$OoQiJQPaM8^&2Mo+zD<1DruAGh3C`9@azgXLK@ef~Z0Rf8LzZ*5 zrvi~bJW@b@7(cr`_$-gPz>w~MTjd95DBG+h=w6xR#=Ewx{ z$on*sXE*Fg&ZgVx?&-Lhr-rEx;|WVo47=~wF6DZG*1L4JT}E}zNeczo_16uhc^aNS z=T5jAVB>K6?>#q;IIH>*zRrfdDoYd1C0d9dmKaPsh55g&DSlLpu>` z1h)*fS1%qEjBV?o@V*VZYHHdQLqA|(sAGEblFw+(26Dw-d;a@@j*b>S@9;m=)*hG_ z@$*cUa}}Mr0hYoZDW)?lkz&&~&$;0!GSAKbI;HGl=69q)uMYuEF?v~&d}~gzpq9S_g_5i#i}BaXUImo zC5~POdBVSbL&6e=DHg<3DbG$Vjcx!{$Kpyn1N)*_RpQLCSa8vfv`LVvmzPJWg73>T z3HQr9g*4%$)5qC=08MQwCwpzF3|_+<6y?3|&mU*J@h9Dg_>{u`IwQ9@sB4YoL%mSQ z_V%0*2-!bv$RlmOPQh!gAj4FNlQ50`E>4b3QDd>o1?@v~+}N9<(=_$oXYi5|I3x6TFAq#1q234gO`-Q1^xT!duQ*#S zq32$e^{3ZMWn@y$L9?>xvTwUJE!*H$h_=re9=AT9o2J)29UU#CzDs7K38hh`_lDxf zR*-a}U46IhHk8bTi*RmoB7L8v{Hu9^FpPZhjM@2#Q5A1*Mn#REcY1v`o!1uQq0y%; zX-v{NF0qu*zqymi^SBD6C6>Or$7gK~hsy^3ay0WjGl%aMs zdMnF8aJ!Wic3_(cC)Bs$GBiAMo^o{~=5(}{(v!)RJ_3P5sGG5fx#KY*Wo=i8e}oP@ zZl3Nc{n6q#4}HwtgSQfxWc2t47$FR&EjIT35vm6D;L81^8hvwvpx5P+*M{QIFyGr} zsgMrVmf2)c{FbcxW@VpgRkfiC*S~i)95{OwJ(*O3G(UMW7Ttzidg4peFtqTv*8jX7sa8i%cQmPUwXg}Q>`E{?%C!d~SN zbf-5Z>44bb8p2?2_lkCLyqb^+vi1`MvF6+82`|TNpbV;Ud$4C;eo^ec=u7M#PVUI< zpHCk#&2im#%)V3CbNKLaC_mI zdl|Gq^>U>Wch9zuFX zhv(AQ|BmEVVO~w-)s_Z#Ky#c5G#aQp82&J)5X0;{F*k$+Q2&{YwnXh(s#GS~qNbnS zL6f*rDO2htl%)K@%&<$w~U@t&cNL%-atfcV-4vZjZvDo^B(&HAy}Zi*d5c435fj=!#C}w zy>8J(fNre(gzds-5zI=P3v>^bbJHBdwA! zUVW~`iUNU|PKrk<@I_i?SRAHU!h|4~3v-2yGt>$>#kB^qa*{bP&*AeGb1Dvnk>n7o zR25Re{S8WJJ=D#oASoF4JmbR~T>Arf*C4HH4X$dxuYQl}t#|Pv-onM6N>B5vTTHXv zHBxI3LP-*!o!@*(Mm)h~niVMPq=Izx6Ue=p@b=Xo@_N4DS}FJzMf9xx8H5;INNswwyD=)8G=g~}DzgLV{rUMDU!PN9MdUVB>_Jhr zDgjpF7nwX!b!j#Ldd*JF4A(>#KpdB!+|l0&N?(e3f1<_x)EhJ)?8#pUzmyt?v2To7 zdi6a$b6yjIPCLOVUB=81S7;=)So-^;oKa2m7+EV?AM%<>3YkTyFmuN#dL}sSDM|b= z!aX2#5ch6l*0H*HgSyFWYUSVE_hzZ$CFOZE*KG1q&Oiua=CG<{#9K8`x}3)IKN7ln z>F=a?wn+pF2olZ0%Px!MLY_fiGKrd{e}7UHqqC8t)2~FC$IaH+uE#@brObc0sSCzK zqfA6$Ya1T*#P`Aw9x3r*Uz-vs-J!-*L?4S43xBc>9^hT+e2@ct>8&Y{5t?Kj_8AMJ z=s!JEFto^{%PwytRa8(>>*-hCuwGC#;MjGoj*~pHG^5^F%^%&S z-+YR@z^uH?ce8^b&oBct4F)ieTL7Bl8knQ)ifQ;5FjWrK`5DAU{X`6DpDe0go|%ec zfy^ZvUa=FkQ(-F)>v@zLdL5O(WQ0j&8scVkF+0yB!8 zCNcgwY|rOUNel6MWkvjl22Bm4sp356Kq5ASrzX_3y=Ba_#;ReVF$R81pfi+fsYkq^ z0{M$epnyEVq+PH_stiJfdJPv8a;`OhQshBomp$U5)jElX1n|RXW}U4u@N%1zZaC8b zzdd?Spa{$&H@NdyS~M6c$eu;%IbnCL+5{{(3mrHpOnckUW}~o={Cd2DnM&h)Alg=@ zwEo{TR;K@8v8s63n-I{;|FKkdwt=FTBVc6sWw46Cdl*_?ohgNdEs z|6l)gYVB;|NI)-UZRl(wVq#=xYy!o{2j%4KXkuss<-U2Pwc)rmisW;mK3$|s=fLnW zO{-qnJa*?vO7`~vJUoz;gk%69-{{}PjRin4KxDIoSQ}MEF^$1$?ipW?3_R=rk!gBl zx(V5zfRJ#=Pm6)zKZBYo84wgWNl+nXi=bqn%0e&2#!}Q|4gN#^CYhz6r7=aMEo(BA zrXu|;rq093hNA%#3|6edVNojbjAcAd)0_&N$D%WlsnZw?MZC=G8XACF_NXvTd-H#& zogtz1q6-(FqeaeOmjFMdX6nOk(H<7y7BtW*EvkA$U(kym4U*Du6hEQ{oVpfh;rx z1+L_HBKJ~KMjT2NAXWdw`(XO!Qpq5Kh1Ew9l7hZ)F#+QOJ;0!OxJ<-&?W9zZV3(eJ zJaa}Br~H!e+b|h1e|17bjZp#M_*wr-aTrW+8W0M_isZ@YwR9LG=G^rF#0&wLKo^yK zjZq2FD<<$2c6?H^;FrU?rXiC z$3Hu8;uCB*5g(jXwvkML;%5waF}BzHBCAzbbCWP6kXs19*ul!P-J^{W3e2WFeB6>d zRkjFm1Zqt3q{I@?58{d6hr9IIS`h3rgj;{7FuJqV59(j3JQ@kC6~n8k%UWSYU)7Jr}} zd+Mex{n+b0>HWKVj}6g_;5)4vjVc;2YXdh+!nnO-5WVJVF}3S zjuf}F0PCgl!i)uQL|*h-Sw39K37*opfp_3F{LF&;Tl1uerBwQ8V!|sK`kGjwFjS1Y zK^JZeB;c*)ufX^F?Gtb`k;H;?OH?c zBj8h;;=@*sy*JZY$~0MPwgg{m{=V7IGy|`T-R<36V9jx-SW_8ft>y4jYvzJGKVpOH zl$!2q4C)j$PE&h9QQ82vSEy=pn12R5bLhz6*57il%Xz9LCc;eh8%5m7sUF_gX+%0< zo0Q^OQZpl+QYJD^YX{n9mbKU_`&h@y-@+8%?i^u}?ZG&WgYEZwxQwX86E0gv%Ph=@cv1 z)t}m_v3jFfhXn442K;(&LWX#pS|p=zK1pcV=+%Z>p+1%bvHjuVL-gL##&)BZ* zO23Y_YmchiLe=jh?Ctf6gD+d9yoo{R#0^uO7~^0{Eh62UVNl6@YkoX@|hc z>E7Xgt)CDDAlm7GoS&=0)(1T|?sEc#cyfBF?fn$_Y4cM%>qL2UYO6k9>=4DwF5UGw z!>D*?ks^+;ll;n=iirP{wKYL?`7_yuOo*OFPbwsDb%)T0KVSC(@5$fcMPBfOxqg)W zZ4NRUAkS-jzZb9^=cX#2m#}R4SMO;hvW;2sWMHH8!&9%F;JwzPt)lw=tN!4Mc&Uy0 zZ=q>5CC@!JqaShNq7m)U>oYbIrF_@2U64#MZHv;drfyk-EdGX8QB+=%DqZN#8UKd2 zD*GtYc^R8)H6B*kx4%)``-xLkBW6}xL~EwFm9{$X3RZ${GOKz$-1HI}IS3s8xiX*1 zS6lYS2+zi)w3lMmXhf=cW!Sgy!m`!U-x;i63t~{kg=-`=0UIil`m96q^RU%){^rsp z+W?TO%dB~kZH1g%&NQc^coVTG!Sj4aP25Kn#HA&qR*Gdw~rxwJ$_Dak54&~2N?A>1l06VgZ8IHzMZ1&N-Jd@mt-8B#6kbB>&8D8Ag7NoT3Nf@YE>ZCwCA z4!^torzr9h@;NXfDAN{exdz@&ENBx-hUOFs5pg!lzkhFvb*Qt>#?e|#ye9PT(#J*^ zWWy}@vSZ#r@$U`UCdob%$zwA4AEeX>BjP_m&bhNmz9!2jWozU!&Cq$w z{-&LSgUqz@H&;I;vF`=sz3fLK04mO|+5&hZ91Yj5B> zAK&4)H%hSzD31bS?L%{HRgbHKh3GV)kv z9)NBhx`ZFZeqBdQ_OZtMWRkGEqko+;1n<2=ka_Fz2a*y4`R1&)PXV*d9B97b6$`}2 z|9A3cWM%x1?ET-_nvsB!jp=`qHWL9SBj^8E5&lzy@SDt;nE#IvyvEr@WBIC;t)Q4? zkuli0OoBMj*=?KwhJlHJfjPN2**UDa*xAi3j38%Gf|!)h_qBKT?}yGucHiuV-?UDj z*^bo?^|cxA90rR^yGe~fssU&^aAHsz>zjS&LH_jiUD3E$y`+6rw$FHgTF;IiE zZ}=lZB)|p-fO;P9cK-qfaj$yd`+x&K+;U(r;P_Spe^wAEu3qX_s zID=PVP|iU^c)Vx$b>Iv# zm;e#~Jp^%*J;JKe?!jFbBAbA5{tm==a14MZ-`nQEfb5^K|m|Z%<8u5#XNhvG>iKiV&YOl(!H40~>%_{oV5kp7BkUtFFE)p}OP$(AQVx_h!L&8n^7?1_J!;hXl-; zzQPahr*U*-U<&|m>#N8I&_!Xl01>qii1@#xZmVzxm7R20!zA?5*ws4y-FckmG@w zA>O@zE3RT<9O{0$7ttfB7S8vvS72;zrL$wB*QDMxFK%FWIFj~y64=9XRPX;a_7<>} z15KOmWWvnM%*@QpnJ`Y^gz*GUIGHdrGsA?LnQ1a%W@cuXoA3U+tJU3={wrB_ce~o% zmRc^`dY`Iw?snxX-p^I_!)3fVVjK%g(fA{)X@roeW9dmUs6l;XTSL{2(s^ zK_pvpB|cXg)Y~N4kyF)mo;&PYqR%?lE@@m{be__}PcC}Udj)IfS>=48U6XRtm zYhDp_m%CY*b8`cI#DD(AxE-@PZ`5nWJ>D{F*!vz&6|$dMK2fN{7Z-Hkj(;)mIlD3kFH@6fB2stl#Ih<_On~>u;=zdNSB@R1uKj%Fee=K>v%w5?G zCt7VUq!6aw%{llyAaa%Ia2vd2@(6!ZLZD+V!8mQS#8Vpn;(qR$j>5m9^PA)PE*jbC zT<+DVGT=`*fSB+Ez?A^E^u`isXDza|2?-32*sqX0FkA zd=@;~>8}!DT_xKOKSn4na4ZF9tSQ98sn;Noj@Y*q0Z6KqC0N9`$wlWVjqDLr*bQiYJrNzhs*9>DFv6P_d%4GjPn6gl$DjVmbJit0+z%u|6ve^YQTDt@*C# z>X=hiSQ2`oCzo5pE%lwy2(3c+$~!NlmA6VT_50@eSG#-56;Q`%YfWoiEpK3*gOC+@jYZzVfjuTPEP_b7Zvj}|0Ntw1Jf8;Jhkb(v=ny-|o0<6xKQ=ZkNT3^FaplGe9E8tm~?gLrboYL%I? zzWK!$Z1YnlH})>+=j!~5rs#(RWpn^WfSiVT;Lv$#4Ah3AJkb!!W?UJFEY@S^ZwcmT(Hh4hg6`g%y;VWy)%br)2klHz{hcKIv52|;Qz)umqf-@}xWkk)| zrsm^{3G1PFhXytC5v+vf4dMl{N}4Qa8a6srddn$@H ziWDUH?&1GknpXJjM6Fq|;>9}BeOWy4_Hfq5WBJ~7OqCh%E7mm{Rp(Imm8al|_c8!A zEeAaS{U4pG?kLf~AvwoO)0K}zQ%1`!OHUs7_}|ZiTKBI{&6YqN%Ap$q^BQ#akf1dN z1|ce$yp+pbEE2=x$nk0+@~-+{h21?`LX*d`fw6A5QSlc}P?6^4I(@@#lJMUB9yF2pGrkL) zU74(1TGV!r(+oUEkv{g>6N!)6-i?qC=;uM1jUZ2avBo3*it(7nrR}kYf3Pg}0PA;{mkovu?*Y4- z9io7#)Cr#`L?KdedgPN4s@$ejJvM+i27PJLRp=Fre!2OBF@@txi@tmiytDo^-nnuu z+p5F}-^2F+qZ)wh8c;&#M-NlnyM#02K{w zF;Hpmx$wQ~bolE(R2}Ilod45B$lyWV_h*+6^7~TtALp1XDtznq?Lh3{26^inGr=5X zA=HogzIGgP+sV9E{WMN%OjCEdxxUM}m5dc09elh7m7GZGcXcrox^^Y%1L@y%1X7Bf z)#COs;l}#5o?5fLKz(uf2PE@Gj90H!!#^>UqK(Nh9+=3S?;OcYV=u)Bp@t4tPiYf`wYWT!Ez*cz=X zr#NHwa|s+|eI&MrcdO2d9po7hyXMA?(|P9Iu?X& z<_qtSn|47&p4+#7$GC6Z){^*#aH+8A$|=wBzyz{)VrR=e_=y%$gHx^^7CJ|gtg{J^ zs3*SFgTp-|8?D@UcpGwdEl&mXRFPy71y>lgfj4F))4-oF~P}=4w4RhxT zCI+Tx?wk$;daezdaK#LU$f?oDS_ztsPzOCEIAvf!ExPpxK@mwpK=36V8T@6-6&U<_(7$6V^hZ zz9h?@t`($|M)${`Y|&`$Bxrzu{s2Z7JM}nrZ@3rPI9sF?_Pp-xjd^;7^j|k8G&+X` z=@Lu@(*vRLy?8o)7RjV7rU&qcr=H_}P+X!e{CKua*%}*HwcBlDVg^b*K>zWW#4)a+ zpr1Yli~jZM)_R_RiF_jk>m!jD5Sk(;c$EZ_1|^2~NZL`bU#@~yoTx`WjxRr~YhSqG z5uD}m$w))o=)0xT)6T!*VOL+`eMjZrW(`hmze-ukTY+bsVqqsr9>i)tapXlRh;r<} zD_s}~fzV(COBhSAw(V*3u9=MeW#`EI^S9tQzCAQ4=f+H|OJ$t1Xr;vfTE~V|pin8e z19IS=9EZ0-hf za<%H6;!$_3mvbbpDN7>8R8>#+TB!`1Qo#AmDp#d5tE@++>2H%xPj}BwJc(s1J~q%S zNyf+Rp!=*IC@NZf)JE5SYv2`d^Y|rv8VdFG6!DaI4qI*MpykXAVTomCV?|A%v=f=v z$(;2}X3S`-xTzz8FLa8!X}A=gp1CbUr7%E1p1v!XOd+?OcxqGHY<>t;5Ii}7>ic2S|cPvmU-#*1sOI5T>#9yHO#JB6gZ1 zZ#Kme^!54b0cIkRW+1nAk=q7izd=z0Lx|*uv;H);<1g(QehJ>8$YQyPuVEo1JHE%l zCh<}$BNa|d;Yui`#KInQdtb9qOwfA=v&89gi*1J}$p7l2)H~;= zo=lv^d5rG%#xt1P#O#}bv!mJ(Q5A!-x|??E)Ulciv>LCl$3j`0dp)uJ*Xcn`{q;PL zXm61>?zhK!LLCFyeCeOuN`sPG&-f>po1CoogaMJ8-#Z;$^sR+qeN1xdLM-|xFJ6^a zD#PDi$;9m^d+2M-rRfh^rX0{qrl<`@k_o2?w`L2QioFezi*zz?!{^GF6la4}%1~1) zCCvrVs*4(Kp8i_mFN@R9JKE{2OW9d~jE0cqox>T5az0Y8>ssy$81_gfeti65Vi`p1>?&R%7USk8tw9|d&o!qX|`r$cxf ziq97%o~qa&M`9xQ_=;Wo%$g86bm|RL=y~%{jEJjM@keYCV z@sd7DlP1K@1HW^9T@h7rkI3PbXN`Qy-uqqUy(?U+`2|ND9H}MUq-Zy#|MKXZEBGEQDimX(FwbBz+{BZc z9pGn3fz;!7NgH9=6L=(f z-4G*K|E08=<5@5f-l?VLa<=m$ZuDNmN=ua}9Q9Rq*10Ov-%-b~m<3nVF&&o*QYB}@ zKUNAgsM;}R~{JLa+jGUrulXWq=qv(t@9ny_tJEs{r5)is9u@2B?@W2?7LEE8=NUDfadV$2E9j@x zyAr0+1BLX_FhUQyy8G(z;4jQ78#}0s_waePal3{NBavrJqe!sSy>KJE3M(b zeM&9*e?pt*+_CqR)S-J6{?Scr?5=Vcb6BaauKa1x)ZNejYOjS|0EiJ`SjU<=TAZBf zgaw7Na�b3M<%UINOD2k&rJB<15vadW$!WDiyAAB{Dj_0^S0p_gc)y zRua0PP5K^e3q{sggR3#PT$Cj8)3dmX?n0LC&Y0bE)pr#Ox5<~2M&T#vB)aKVKM?#t zwd0{gsy!olM>N`II849*=4N_$A?HVHmYh_dc`+*Pjf%y!)6j#%(6<)1LshgMsY|NM zbuy*K+_XrDz0Ew=Bd zAV(JDM9F%OQXqO9XN5w&#WJapS_Y}FZPH;3kk6lLbgMRorHh>1zk#ol%^081nh#}g zw7TTB$s$Pwp^KO{sI?5c-~xtYDbGD1=(4jd6?Mq(UBg~yGPK?uA2jl@!RY@Xzk7*p zWN zUHprpMabY$AAH~g#Viu!{12Jf{?;{uZ6v8TfBQI!9sgXp7gARh|J*9ObOISb{2}-g z*_B;t%$RP(172y%U3aRRz3SDC>XKt4|ERnRJK8OMgG9;o#f0GlKQA=Or9vF_@_dnVoHQ&~TNRrT>`Fff z6P>7Z4<*+dol`~0AKV5$;@hoe3OQ9wJ5G`_5fDz7=sO62} zinw(C>p9h;In$>0>*>XGA^BOZrC^Ag6d#Ru-l9cYqwIDZPd}g4VL1uKC){aFH=8KL z(7Xf7g!DmphCZzf@$`K4Re&iI_SAzYTYF*6H}ZqYO0$F8hUgwo*m3H|$~TCN3HaJ) zz*eKvfsk==;5Zyz!MX~9US$5-ZOF_RMvKp_q!d`3*3`fhRNEHb!E~m$8JLTP#EpfC z2S;&LX)_qR-diPIP3b(_t1Hx-JZ`vrq?&rLlYV&=)NWz~WD=j0UI~6p<(|2`ja5`8 zj{ZSH=hks~%nHDouM8&aVTN%&#koU9( z8Han^?BJ0i1NT=+BnvZU;OauJMD|6To682tw$oZ4og?SCoT_BGrojv1@EEs-w7hEV z_%zAuT{VBB`%UuCVQ^7-2W#gU>)4$&*W<#(9h=6pp>Tf3*uHC6dq$1`~SbkV{L_t0jR{9e-D9cX$6eh!N4evet4jk%fG4(`6EbL^nbnXrqkBg-h% zIbR;fY4pdZeEXbkGCkgarqZ!p2b(fwMJ?&M{Q_Z@YaT-rbq$Ot-`_JSvhX0*C6$Zk z{EEZqcLGPnM6dJdJ%HciN9ObBCWWqQVq%1eAqdj8IBUSer}OFdY;bM3Y1M3leiDi5 zGaatUA6zr0*M^yDV4O0czGxutuLVZ-`kZjGHU<3Y?{;!b0B#yuSi&(fLCwx%LeOK(L2H4*u#5s#_-U&5)V(zS z3gkg%j|?~qX}S`jH6~K8E$#PxpGUU~-4CwA zvxEKP&F~2BoCLj_fNtl>g|E9N-qKGyo139b{`M8oMOpMRR3W5fVAn@((W{8;BKWqs zYCuRTWobttCF`v+MrGpW91k^!n9r~0E%2A+V3KFLglbCa^2oN~yy7qD)Wa4rjvy~5 zeh#KhR}7^hz(R)SlRbS2-NFZ;q9LC(z{_Ov)2+t2~+X^R!Q+ z+!L~pLjl7P_!+~BfHc~hd&x5r@?r|_!1nEX*h%@G7s{!$+T9(XmUmmtWQVxDh}Di@ zMZxwZk@4=cf=r?ZRJ8BwE)36gclAayc zFPs6EeExBG6$^Uj>v!7S+(eAA6!bKSB~R8*nZ-@lI-v;en6g@4-rPEQID|EFrGzL2 z{jusJtrLk|N#Ssr9h{F1oGGsWl3eK=EC-3+^NbFZS>^bcnnosv<4ix1xc7LqX4q64 z*qD=d4(D}HFksu~_|&Z=Xj1sqzR_Eb8s13r{H)w1`(wkfczyV$k?0@)lQ(p5B-b#p zIZe{@l?{rV;0ACEj~GvoE6m~5hV=}o;hI*xJj?Z?eq`ZP0FL|ICy+Um`|%~{e3ndP z$7Amo*NJahi2FS{sa*LpHmulbM+>vO;8WzW81#(836uLCn~8qHYh0{69Y`rbcvQb$ zlj74doVMp1vGZBqqE~H27TbM(g;vOm8=8Wp(h|&GsyGHW^f`iJi*s`h-WBY;Lu7Sx zOVe1fvnQgsEPz*A{at{OBXw9`aNQX4>Uh2w5=g(~5j%~cSB(8?D0yU?YF~tAqqb{{ zK8%Ae-@t$GwO&u_)=kipoM{=t^D(ZcEPNHaL^&y||Ds#p7dZYbfY!mZ`I&VS#w3^@lOt;Gxt=gcq0uFySkSmQy}#>`ByEn% zt>Y(AxTXU9C|g^JV7J?eV|(em;Q0(ep?^Z3%%l@$xD-zrldkkq!0b{W^;GVQUyRW> zoJNCc+%a)R+QQuore$06_?>^G(VgmN0F-}z2xQVfyR%I{v?X4Cv0V2ci?;Ua+P^sV z4WEP&8!jj{($5HH{41$kd|V_x`s;neq%r7MsM*ZfTA@p(h*2Q@gYpp@dy>>3a_Rz?SCbP4<4s)IURFI2e*@tuFgM#Y&`p@4{a!GR%ex zpPZw%GiI31`jXljrvx;YaVaOFuYp024+PcD?OVl(13IT@Y%;dSL>KKF!2PJwKN>fo z{-^MP;zw=8jC=e?jImvL13?W>>WLq?O-&=b27rv_nUL%!Tsw;m`3xQ|w+`AOaOL&X zEIGW6ErOzt<{zjNw^r8Esd40xqhNa@f!6p~*PzS@p2*j`&J&a1oR+352w~O*^rSY~ zG2^jCEBZ^9J8b6|p#dver1HEUa7vvphg+iezt+CeTJ1SrLzv;@#?l zTFKL>?`-06%EtMmNoq<#j>+nm7n4r1ihjR`bM$PUPVI6I({D*Bz6lNoi`Nx!w4ew2 zD$?#p;%N0Aol4wQMFJcgfV?}+*I(f_dHV_q@;LVfAc8^3@r2a`3%k25O=ZjQ)4oWiOX9;9ZHUw?ey(TbZaeveZYoImX!PobhM>zr&RgiMZ-N&Iq9bykEm{p{2L8&g zIX1w=7fBNmA2HHbf*C(tH&X9x%||t87ZKEOULpn`{IT3S-0VmZT>Lx5#?|BTX~6w> zPvG)gTpJknDaCN)m@??Y1)&8OG4 zvR;&C`S5N(%B&n&;}|hZz(^!&Mg^uRwAm1(^IUCaq6TmI)W>rTZeok};&WUMxBWm$ z9P>zacVC+2M)uyP!(P;qISP-4Cx5H_jP0BTG*xUpyu<+4vRC^kT@aLy^g72oX{SXH8 ziAvNww8pqKpU1nU?c>?iHZJks#n9}6;VwgA^K@|!kdf-tluE6tM)^a9(SSdc%9)S> zt9#e?8+7>74oOBP_t8-)j_HRbkWhkNr|`Z|EX;fo206$grW+)f$x*E;n?-P)*ngr9 zE`wQ6lVdph8DVH&`~XjsHmQ1R+*L4sqM2-g^AesQj?$IF|Agjc8p?lO1m=9f|7V1h zvykNbJ(vi{jr0b(ZT5{k^ii!jy>SL6vd;8EXiPnOu@kxaEVuSiLI$aU5!T8#++fVo z%}gTX908{4@)%b^8uHBfVw(fB%{-_ao3K52*3EXVsGu8QaL$*QGurv^p_^JA!`UPy zOuhI4GZsr&wefOd-!K1_yoHrQU^n{kgCTw63{aF8A=gh%;Y=|0_`xF7rFZ%MIa;#L zjLtUWY!<}KEUHcJD5|;qa*EwO4>{fCC+oz%Q}_hDYTgU=nmLbnPzg2BA#sEvvAML_ zb)qTHFf5Ngy>y`(9wjw_((9G)pWdN?)c@3^U6k|PlFg~zuB}%7be^MDzFnhW5GACn z{-i;5)$U0$Y3_Mqc?)aHP#{w*cY`(E*AWnB7(eVcq2w_mKnhNy>cO}YH2CG z4JUPl&Og4WxenH`g4P08^m0li1Jk>ZzfGY9y)rjCOhy_3jeNx*)qg-fXf#2R4g@>LT5LS0{L74ym5GCeiIt0%Ssvg4asZk+)6l~G*Ojas z>?OWf8WI`_J~kFsZWgxx?Acg3*ce$jsaaU4zw8tp%>FwQb)d1MBf#tn%rUlg2EZ|^ zs7q=yNx9nEni$*Le*rr*>Xuf{BwyQq&4+wnJk z%l_-$6s+6;Bwy3vWR?J!SQ*>XlGr#JyI48{j7i-7M|UnJHYQfu{~$mBdou?UYdBWU zFWn-^e@X%ZaLoT-!ib&ye*#8q-2Y4VNW#j&$@%|^8%h3qz-UNYPkBua#rLTuOwXZ+_4Osnv<30FH%hC6$vkf70U;Xfd_6PEjw0ju6&Lu!H^1=gtE(@{1k} zq1B8;KUNBs=;;?cWIl6Wv9#2*c{n}NcroP`xYl=7zCg%~-;!0YeAv3vJkbzn9X z2HmDFjct#6e60R{b;K=AG~=Zt8{5eKbI-QO>y71}8W+YRTfQAt)UP37c%soX9_cp`%#a}K@WhP=JjyYM_ukzEoNpYkNE z%}`pP7`45RUQ$VV5xNJ;!D{6;DO6&hG4d-aIGK zMCTUlf84q{8e5SqY~{HCIea_*UAe{b$s8pT+4r%xh9hx5dfV?c+-$#EXRc|qhqbS( zTi{1BS})=zY#QZ1y4X1UI6HSzwsUHTN!#}eT=QE7ur<=)nmS+eS;H;>TyPa#m5i`Y zGOh(f&nFwn?=Cc@a;ear!&Bl_y6CURIjx}%P{OQfcI338bO>vWDhpIDa{RsQ5RwP|qWl(3P_O_I%WZgxwUm*_NeYVki^p zU*9rwYN?-(U;BfP_%eqF#Z}Qbh#}F{xMKxhWmbeNt`(lQi1a$@kze=p|G!tWmC2oOhVD|GA&w z(M_+}Wkavv;zLT5RBQa%@yTtMz=*utuY=fJfNoA=X1Nw6z|&ySnqFs0BkStC$c4G@ zVV7aBJ=``>mqm@~of%fJYB2FQio~!+y-);zE@87*3^EsMvf|W^Rt{CD-jjOc^Xcy1 zQ0QhDI!@>A4-vd8iawqY$0$l3F*Jc1bU<%$e~@y4x8l`U*AOn@h+Ie|ILDZ|(AP@7 zMT+jO%nU;eKdt8yKAylge0k8`dj5S0vB?YqQPXqE0oi)q`R(jcR6~_Zl@_>(@Kxr} ziI6>uV_#}SeUKF%bogeTnU-P^_f3jZ-vH4h+**6ex3{w{|2Hqo`G2?vZ8d;79J8#w z8Ni)HkL61d&t(9|{KLu<@Sh?avlfXSD+xOZ>sOi zrT-s(iE@@#Swj_L=%%TLOc??-9v2n57fiJeOpkby!p=;sWHiE*>|#tdy2u~lw2U*ZxmS}% zswzhvYAr7lFSG$j(`#kTG1V*%nU$|8zY3P@n7(SShIt-zHg7GnPz!G@7QEGM?Tes-Q2>_90{mlg!yBihmARy4qQC2sl(Zs1(y6_O6E16=(d{ zDS&X1KkQ)WHq*;I2m7}3jR3(FTha(wB?QV3UBa)~1 zP-^ugX`hVHtDhP_f4(_L;lXcgXh~Lp$6;DR$?Q=H|j4{%sxWm=)(1CB?qqYEg&Kv+9RC z;{NqA2gl0A%KL?5P*O@N HOTqm=e8<+U literal 0 HcmV?d00001 diff --git a/lecture_10/lecture_10.tex b/lecture_10/lecture_10.tex new file mode 100644 index 0000000..1131881 --- /dev/null +++ b/lecture_10/lecture_10.tex @@ -0,0 +1,852 @@ + +% Default to the notebook output style + + + + +% Inherit from the specified cell style. + + + + + +\documentclass[11pt]{article} + + + + \usepackage[T1]{fontenc} + % Nicer default font (+ math font) than Computer Modern for most use cases + \usepackage{mathpazo} + + % Basic figure setup, for now with no caption control since it's done + % automatically by Pandoc (which extracts ![](path) syntax from Markdown). + \usepackage{graphicx} + % We will generate all images so they have a width \maxwidth. This means + % that they will get their normal width if they fit onto the page, but + % are scaled down if they would overflow the margins. + \makeatletter + \def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth + \else\Gin@nat@width\fi} + \makeatother + \let\Oldincludegraphics\includegraphics + % Set max figure width to be 80% of text width, for now hardcoded. + \renewcommand{\includegraphics}[1]{\Oldincludegraphics[width=.8\maxwidth]{#1}} + % Ensure that by default, figures have no caption (until we provide a + % proper Figure object with a Caption API and a way to capture that + % in the conversion process - todo). + \usepackage{caption} + \DeclareCaptionLabelFormat{nolabel}{} + \captionsetup{labelformat=nolabel} + + \usepackage{adjustbox} % Used to constrain images to a maximum size + \usepackage{xcolor} % Allow colors to be defined + \usepackage{enumerate} % Needed for markdown enumerations to work + \usepackage{geometry} % Used to adjust the document margins + \usepackage{amsmath} % Equations + \usepackage{amssymb} % Equations + \usepackage{textcomp} % defines textquotesingle + % Hack from http://tex.stackexchange.com/a/47451/13684: + \AtBeginDocument{% + \def\PYZsq{\textquotesingle}% Upright quotes in Pygmentized code + } + \usepackage{upquote} % Upright quotes for verbatim code + \usepackage{eurosym} % defines \euro + \usepackage[mathletters]{ucs} % Extended unicode (utf-8) support + \usepackage[utf8x]{inputenc} % Allow utf-8 characters in the tex document + \usepackage{fancyvrb} % verbatim replacement that allows latex + \usepackage{grffile} % extends the file name processing of package graphics + % to support a larger range + % The hyperref package gives us a pdf with properly built + % internal navigation ('pdf bookmarks' for the table of contents, + % internal cross-reference links, web links for URLs, etc.) + \usepackage{hyperref} + \usepackage{longtable} % longtable support required by pandoc >1.10 + \usepackage{booktabs} % table support for pandoc > 1.12.2 + \usepackage[inline]{enumitem} % IRkernel/repr support (it uses the enumerate* environment) + \usepackage[normalem]{ulem} % ulem is needed to support strikethroughs (\sout) + % normalem makes italics be italics, not underlines + + + + + % Colors for the hyperref package + \definecolor{urlcolor}{rgb}{0,.145,.698} + \definecolor{linkcolor}{rgb}{.71,0.21,0.01} + \definecolor{citecolor}{rgb}{.12,.54,.11} + + % ANSI colors + \definecolor{ansi-black}{HTML}{3E424D} + \definecolor{ansi-black-intense}{HTML}{282C36} + \definecolor{ansi-red}{HTML}{E75C58} + \definecolor{ansi-red-intense}{HTML}{B22B31} + \definecolor{ansi-green}{HTML}{00A250} + \definecolor{ansi-green-intense}{HTML}{007427} + \definecolor{ansi-yellow}{HTML}{DDB62B} + \definecolor{ansi-yellow-intense}{HTML}{B27D12} + \definecolor{ansi-blue}{HTML}{208FFB} + \definecolor{ansi-blue-intense}{HTML}{0065CA} + \definecolor{ansi-magenta}{HTML}{D160C4} + \definecolor{ansi-magenta-intense}{HTML}{A03196} + \definecolor{ansi-cyan}{HTML}{60C6C8} + \definecolor{ansi-cyan-intense}{HTML}{258F8F} + \definecolor{ansi-white}{HTML}{C5C1B4} + \definecolor{ansi-white-intense}{HTML}{A1A6B2} + + % commands and environments needed by pandoc snippets + % extracted from the output of `pandoc -s` + \providecommand{\tightlist}{% + \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} + \DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}} + % Add ',fontsize=\small' for more characters per line + \newenvironment{Shaded}{}{} + \newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}} + \newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.56,0.13,0.00}{{#1}}} + \newcommand{\DecValTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} + \newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} + \newcommand{\FloatTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} + \newcommand{\CharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} + \newcommand{\StringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} + \newcommand{\CommentTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textit{{#1}}}} + \newcommand{\OtherTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{{#1}}} + \newcommand{\AlertTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}} + \newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.02,0.16,0.49}{{#1}}} + \newcommand{\RegionMarkerTok}[1]{{#1}} + \newcommand{\ErrorTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}} + \newcommand{\NormalTok}[1]{{#1}} + + % Additional commands for more recent versions of Pandoc + \newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.53,0.00,0.00}{{#1}}} + \newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} + \newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} + \newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.73,0.40,0.53}{{#1}}} + \newcommand{\ImportTok}[1]{{#1}} + \newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.73,0.13,0.13}{\textit{{#1}}}} + \newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} + \newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} + \newcommand{\VariableTok}[1]{\textcolor[rgb]{0.10,0.09,0.49}{{#1}}} + \newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}} + \newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.40,0.40,0.40}{{#1}}} + \newcommand{\BuiltInTok}[1]{{#1}} + \newcommand{\ExtensionTok}[1]{{#1}} + \newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.74,0.48,0.00}{{#1}}} + \newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.49,0.56,0.16}{{#1}}} + \newcommand{\InformationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} + \newcommand{\WarningTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} + + + % Define a nice break command that doesn't care if a line doesn't already + % exist. + \def\br{\hspace*{\fill} \\* } + % Math Jax compatability definitions + \def\gt{>} + \def\lt{<} + % Document parameters + \title{lecture\_10} + + + + + % Pygments definitions + +\makeatletter +\def\PY@reset{\let\PY@it=\relax \let\PY@bf=\relax% + \let\PY@ul=\relax \let\PY@tc=\relax% + \let\PY@bc=\relax \let\PY@ff=\relax} +\def\PY@tok#1{\csname PY@tok@#1\endcsname} +\def\PY@toks#1+{\ifx\relax#1\empty\else% + \PY@tok{#1}\expandafter\PY@toks\fi} +\def\PY@do#1{\PY@bc{\PY@tc{\PY@ul{% + \PY@it{\PY@bf{\PY@ff{#1}}}}}}} +\def\PY#1#2{\PY@reset\PY@toks#1+\relax+\PY@do{#2}} + +\expandafter\def\csname PY@tok@gd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.63,0.00,0.00}{##1}}} +\expandafter\def\csname PY@tok@gu\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.50,0.00,0.50}{##1}}} +\expandafter\def\csname PY@tok@gt\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.27,0.87}{##1}}} +\expandafter\def\csname PY@tok@gs\endcsname{\let\PY@bf=\textbf} +\expandafter\def\csname PY@tok@gr\endcsname{\def\PY@tc##1{\textcolor[rgb]{1.00,0.00,0.00}{##1}}} +\expandafter\def\csname PY@tok@cm\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@vg\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} +\expandafter\def\csname PY@tok@vi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} +\expandafter\def\csname PY@tok@mh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@cs\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@ge\endcsname{\let\PY@it=\textit} +\expandafter\def\csname PY@tok@vc\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} +\expandafter\def\csname PY@tok@il\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@go\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.53,0.53}{##1}}} +\expandafter\def\csname PY@tok@cp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.74,0.48,0.00}{##1}}} +\expandafter\def\csname PY@tok@gi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.63,0.00}{##1}}} +\expandafter\def\csname PY@tok@gh\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}} +\expandafter\def\csname PY@tok@ni\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.60,0.60,0.60}{##1}}} +\expandafter\def\csname PY@tok@nl\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.63,0.63,0.00}{##1}}} +\expandafter\def\csname PY@tok@nn\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}} +\expandafter\def\csname PY@tok@no\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.00,0.00}{##1}}} +\expandafter\def\csname PY@tok@na\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.49,0.56,0.16}{##1}}} +\expandafter\def\csname PY@tok@nb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@nc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}} +\expandafter\def\csname PY@tok@nd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##1}}} +\expandafter\def\csname PY@tok@ne\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.82,0.25,0.23}{##1}}} +\expandafter\def\csname PY@tok@nf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}} +\expandafter\def\csname PY@tok@si\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.53}{##1}}} +\expandafter\def\csname PY@tok@s2\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@nt\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@nv\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} +\expandafter\def\csname PY@tok@s1\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@ch\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@m\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@gp\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}} +\expandafter\def\csname PY@tok@sh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@ow\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##1}}} +\expandafter\def\csname PY@tok@sx\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@bp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@c1\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@o\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@kc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@c\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@mf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@err\endcsname{\def\PY@bc##1{\setlength{\fboxsep}{0pt}\fcolorbox[rgb]{1.00,0.00,0.00}{1,1,1}{\strut ##1}}} +\expandafter\def\csname PY@tok@mb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@ss\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} +\expandafter\def\csname PY@tok@sr\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.53}{##1}}} +\expandafter\def\csname PY@tok@mo\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@kd\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@mi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@kn\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@cpf\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@kr\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@s\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@kp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@w\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.73,0.73}{##1}}} +\expandafter\def\csname PY@tok@kt\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.69,0.00,0.25}{##1}}} +\expandafter\def\csname PY@tok@sc\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@sb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@k\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@se\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.13}{##1}}} +\expandafter\def\csname PY@tok@sd\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} + +\def\PYZbs{\char`\\} +\def\PYZus{\char`\_} +\def\PYZob{\char`\{} +\def\PYZcb{\char`\}} +\def\PYZca{\char`\^} +\def\PYZam{\char`\&} +\def\PYZlt{\char`\<} +\def\PYZgt{\char`\>} +\def\PYZsh{\char`\#} +\def\PYZpc{\char`\%} +\def\PYZdl{\char`\$} +\def\PYZhy{\char`\-} +\def\PYZsq{\char`\'} +\def\PYZdq{\char`\"} +\def\PYZti{\char`\~} +% for compatibility with earlier versions +\def\PYZat{@} +\def\PYZlb{[} +\def\PYZrb{]} +\makeatother + + + % Exact colors from NB + \definecolor{incolor}{rgb}{0.0, 0.0, 0.5} + \definecolor{outcolor}{rgb}{0.545, 0.0, 0.0} + + + + + % Prevent overflowing lines due to hard-to-break entities + \sloppy + % Setup hyperref package + \hypersetup{ + breaklinks=true, % so long urls are correctly broken across lines + colorlinks=true, + urlcolor=urlcolor, + linkcolor=linkcolor, + citecolor=citecolor, + } + % Slightly bigger margins than the latex defaults + + \geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in} + + + + \begin{document} + + + \maketitle + + + + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}14}]:} \PY{c}{\PYZpc{}plot \PYZhy{}\PYZhy{}format svg} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}15}]:} \PY{n}{setdefaults} +\end{Verbatim} + + \section{Gauss Elimination}\label{gauss-elimination} + +\subsubsection{Solving sets of equations with matrix +operations}\label{solving-sets-of-equations-with-matrix-operations} + +The number of dimensions of a matrix indicate the degrees of freedom of +the system you are solving. + +If you have a set of known output, \(y_{1},~y_{2},~...y_{N}\) and a set +of equations that relate unknown inputs, \(x_{1},~x_{2},~...x_{N}\), +then these can be written in a vector matrix format as: + +\(y=Ax\) + +Consider a problem with 2 DOF: + +\(x_{1}+3x_{2}=1\) + +\(2x_{1}+x_{2}=1\) + +\(\left[ \begin{array}{cc} 1 & 3 \\ 2 & 1 \end{array} \right] \left[\begin{array}{c} x_{1} \\ x_{2} \end{array}\right]= \left[\begin{array}{c} 1 \\ 1\end{array}\right]\) + +The solution for \(x_{1}\) and \(x_{2}\) is the intersection of two +lines: + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}16}]:} \PY{n}{x21}\PY{p}{=}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{:}\PY{l+m+mi}{2}\PY{p}{]}\PY{p}{;} + \PY{n}{x11}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{l+m+mi}{3}\PY{o}{*}\PY{n}{x21}\PY{p}{;} + \PY{n}{x21}\PY{p}{=}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{:}\PY{l+m+mi}{2}\PY{p}{]}\PY{p}{;} + \PY{n}{x22}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{x21}\PY{p}{;} + \PY{n+nb}{plot}\PY{p}{(}\PY{n}{x11}\PY{p}{,}\PY{n}{x21}\PY{p}{,}\PY{n}{x21}\PY{p}{,}\PY{n}{x22}\PY{p}{)} +\end{Verbatim} + + \begin{center} + \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{lecture_10_files/lecture_10_3_0.pdf} + \end{center} + { \hspace*{\fill} \\} + + For a $3\times3$ matrix, the solution is the intersection of the 3 +planes. + +\(10x_{1}+2x_{2}+x_{3}=1\) + +\(2x_{1}+x_{2}+x_{3}=1\) + +\(x_{1}+2x_{2}+10x_{3}=1\) + +$\left[ \begin{array}{ccc} 10 & 2 & 1 \\ 2 & 1 & 1 \\ 1 & 2 & 10\end{array} \right] + \left[\begin{array}{c} x_{1} \\ x_{2} \\ x_{3} \end{array}\right]= + \left[\begin{array}{c} 1 \\ 1 \\ 1\end{array}\right]$ + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}17}]:} \PY{n}{x11}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{;} + \PY{n}{x12}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{;} + \PY{p}{[}\PY{n}{X11}\PY{p}{,}\PY{n}{X12}\PY{p}{]}\PY{p}{=}\PY{n+nb}{meshgrid}\PY{p}{(}\PY{n}{x11}\PY{p}{,}\PY{n}{x12}\PY{p}{)}\PY{p}{;} + \PY{n}{X13}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{l+m+mi}{10}\PY{o}{*}\PY{n}{X11}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{X22}\PY{p}{;} + + \PY{n}{x21}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{;} + \PY{n}{x22}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{;} + \PY{p}{[}\PY{n}{X21}\PY{p}{,}\PY{n}{X22}\PY{p}{]}\PY{p}{=}\PY{n+nb}{meshgrid}\PY{p}{(}\PY{n}{x21}\PY{p}{,}\PY{n}{x22}\PY{p}{)}\PY{p}{;} + \PY{n}{X23}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{X11}\PY{o}{\PYZhy{}}\PY{n}{X22}\PY{p}{;} + + \PY{n}{x31}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{;} + \PY{n}{x32}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{;} + \PY{p}{[}\PY{n}{X31}\PY{p}{,}\PY{n}{X32}\PY{p}{]}\PY{p}{=}\PY{n+nb}{meshgrid}\PY{p}{(}\PY{n}{x31}\PY{p}{,}\PY{n}{x32}\PY{p}{)}\PY{p}{;} + \PY{n}{X33}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{/}\PY{l+m+mi}{10}\PY{o}{*}\PY{p}{(}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{n}{X31}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{X32}\PY{p}{)}\PY{p}{;} + + \PY{n+nb}{mesh}\PY{p}{(}\PY{n}{X11}\PY{p}{,}\PY{n}{X12}\PY{p}{,}\PY{n}{X13}\PY{p}{)}\PY{p}{;} + \PY{n+nb}{hold} \PY{n}{on}\PY{p}{;} + \PY{n+nb}{mesh}\PY{p}{(}\PY{n}{X21}\PY{p}{,}\PY{n}{X22}\PY{p}{,}\PY{n}{X23}\PY{p}{)} + \PY{n+nb}{mesh}\PY{p}{(}\PY{n}{X31}\PY{p}{,}\PY{n}{X32}\PY{p}{,}\PY{n}{X33}\PY{p}{)} + \PY{n}{x}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{10}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{;} \PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{,} \PY{l+m+mi}{10}\PY{p}{]}\PY{o}{\PYZbs{}}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{;} + \PY{n}{plot3}\PY{p}{(}\PY{n}{x}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{,}\PY{n}{x}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{,}\PY{n}{x}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{,}\PY{l+s}{\PYZsq{}}\PY{l+s}{o\PYZsq{}}\PY{p}{)} + \PY{n+nb}{view}\PY{p}{(}\PY{l+m+mi}{45}\PY{p}{,}\PY{l+m+mi}{45}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +error: 'X22' undefined near line 1 column 16 +error: 'X13' undefined near line 1 column 14 +error: evaluating argument list element number 3 + + \end{Verbatim} + + \begin{center} + \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{lecture_10_files/lecture_10_5_1.pdf} + \end{center} + { \hspace*{\fill} \\} + + After 3 DOF problems, the solutions are described as \emph{hyperplane} +intersections. Which are even harder to visualize + + \subsection{Gauss elimination}\label{gauss-elimination} + +\subsubsection{Solving sets of equations +systematically}\label{solving-sets-of-equations-systematically} + +$\left[ +\begin{array}{ccc|c} + & A & & y \\ +10 & 2 & 1 & 1\\ +2 & 1 & 1 & 1 \\ +1 & 2 & 10 & 1\end{array} +\right] $ + +Ay(2,:)-Ay(1,:)/5 = ({[}2 1 1 1{]}-1/5{[}10 2 1 1{]}) + +$\left[ +\begin{array}{ccc|c} + & A & & y \\ +10 & 2 & 1 & 1\\ +0 & 3/5 & 4/5 & 4/5 \\ +1 & 2 & 10 & 1\end{array} +\right] $ + +Ay(3,:)-Ay(1,:)/10 = ({[}1 2 10 1{]}-1/10{[}10 2 1 1{]}) + +$\left[ +\begin{array}{ccc|c} + & A & & y \\ +10 & 2 & 1 & 1\\ +0 & 3/5 & 4/5 & 4/5 \\ +0 & 1.8 & 9.9 & 0.9\end{array} +\right] $ + +Ay(3,:)-1.8*5/3*Ay(2,:) = ({[}0 1.8 9.9 0.9{]}-3*{[}0 3/5 4/5 4/5{]}) + +$\left[ +\begin{array}{ccc|c} + & A & & y \\ +10 & 2 & 1 & 1\\ +0 & 3/5 & 4/5 & 4/5 \\ +0 & 0 & 7.5 & -1.5\end{array} +\right] $ + +now, \(7.5x_{3}=-1.5\) so \(x_{3}=-\frac{1}{5}\) + +then, \(3/5x_{2}+4/5(-1/5)=1\) so \(x_{2}=\frac{8}{5}\) + +finally, \$10x\_\{1\}+2(8/5) + + Consider the problem again from the intro to Linear Algebra, 4 masses +are connected in series to 4 springs with K=10 N/m. What are the final +positions of the masses? + +\begin{figure}[htbp] +\centering +\includegraphics{../lecture_09/mass_springs.svg} +\caption{Springs-masses} +\end{figure} + +The masses haves the following amounts, 1, 2, 3, and 4 kg for masses +1-4. Using a FBD for each mass: + +\(m_{1}g+k(x_{2}-x_{1})-kx_{1}=0\) + +\(m_{2}g+k(x_{3}-x_{2})-k(x_{2}-x_{1})=0\) + +\(m_{3}g+k(x_{4}-x_{3})-k(x_{3}-x_{2})=0\) + +\(m_{4}g-k(x_{4}-x_{3})=0\) + +in matrix form: + +\(\left[ \begin{array}{cccc} 2k & -k & 0 & 0 \\ -k & 2k & -k & 0 \\ 0 & -k & 2k & -k \\ 0 & 0 & -k & k \end{array} \right] \left[ \begin{array}{c} x_{1} \\ x_{2} \\ x_{3} \\ x_{4} \end{array} \right]= \left[ \begin{array}{c} m_{1}g \\ m_{2}g \\ m_{3}g \\ m_{4}g \end{array} \right]\) + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}18}]:} \PY{n}{k}\PY{p}{=}\PY{l+m+mi}{10}\PY{p}{;} \PY{c}{\PYZpc{} N/m} + \PY{n}{m1}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{;} \PY{c}{\PYZpc{} kg} + \PY{n}{m2}\PY{p}{=}\PY{l+m+mi}{2}\PY{p}{;} + \PY{n}{m3}\PY{p}{=}\PY{l+m+mi}{3}\PY{p}{;} + \PY{n}{m4}\PY{p}{=}\PY{l+m+mi}{4}\PY{p}{;} + \PY{n}{g}\PY{p}{=}\PY{l+m+mf}{9.81}\PY{p}{;} \PY{c}{\PYZpc{} m/s\PYZca{}2} + \PY{n}{K}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{k} \PY{o}{\PYZhy{}}\PY{n}{k} \PY{l+m+mi}{0} \PY{l+m+mi}{0}\PY{p}{;} \PY{o}{\PYZhy{}}\PY{n}{k} \PY{l+m+mi}{2}\PY{o}{*}\PY{n}{k} \PY{o}{\PYZhy{}}\PY{n}{k} \PY{l+m+mi}{0}\PY{p}{;} \PY{l+m+mi}{0} \PY{o}{\PYZhy{}}\PY{n}{k} \PY{l+m+mi}{2}\PY{o}{*}\PY{n}{k} \PY{o}{\PYZhy{}}\PY{n}{k}\PY{p}{;} \PY{l+m+mi}{0} \PY{l+m+mi}{0} \PY{o}{\PYZhy{}}\PY{n}{k} \PY{n}{k}\PY{p}{]} + \PY{n}{y}\PY{p}{=}\PY{p}{[}\PY{n}{m1}\PY{o}{*}\PY{n}{g}\PY{p}{;}\PY{n}{m2}\PY{o}{*}\PY{n}{g}\PY{p}{;}\PY{n}{m3}\PY{o}{*}\PY{n}{g}\PY{p}{;}\PY{n}{m4}\PY{o}{*}\PY{n}{g}\PY{p}{]} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +K = + + 20 -10 0 0 + -10 20 -10 0 + 0 -10 20 -10 + 0 0 -10 10 + +y = + + 9.8100 + 19.6200 + 29.4300 + 39.2400 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}19}]:} \PY{n}{K1}\PY{p}{=}\PY{p}{[}\PY{n}{K} \PY{n}{y}\PY{p}{]}\PY{p}{;} + \PY{n}{K1}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{p}{=}\PY{n}{K1}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{o}{/}\PY{l+m+mi}{2}\PY{o}{+}\PY{n}{K1}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{p}{:}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +K1 = + + 20.00000 -10.00000 0.00000 0.00000 9.81000 + 0.00000 15.00000 -10.00000 0.00000 24.52500 + 0.00000 -10.00000 20.00000 -10.00000 29.43000 + 0.00000 0.00000 -10.00000 10.00000 39.24000 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}20}]:} \PY{n}{K2}\PY{p}{=}\PY{n}{K1}\PY{p}{;} + \PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{p}{=}\PY{n}{K1}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{o}{*}\PY{l+m+mi}{2}\PY{o}{/}\PY{l+m+mi}{3}\PY{o}{+}\PY{n}{K1}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{p}{:}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +K2 = + + 20.00000 -10.00000 0.00000 0.00000 9.81000 + 0.00000 15.00000 -10.00000 0.00000 24.52500 + 0.00000 0.00000 13.33333 -10.00000 45.78000 + 0.00000 0.00000 -10.00000 10.00000 39.24000 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}21}]:} \PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{p}{=}\PY{o}{\PYZhy{}}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{o}{*}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{/}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{+}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{,}\PY{p}{:}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +K2 = + + 20.00000 -10.00000 0.00000 0.00000 9.81000 + 0.00000 15.00000 -10.00000 0.00000 24.52500 + 0.00000 0.00000 13.33333 -10.00000 45.78000 + 0.00000 0.00000 0.00000 2.50000 73.57500 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}22}]:} \PY{n}{yp}\PY{p}{=}\PY{n}{K2}\PY{p}{(}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{;} + \PY{n}{x4}\PY{p}{=}\PY{n}{yp}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{)}\PY{o}{/}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{,}\PY{l+m+mi}{4}\PY{p}{)} + \PY{n}{x3}\PY{p}{=}\PY{p}{(}\PY{n}{yp}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{+}\PY{l+m+mi}{10}\PY{o}{*}\PY{n}{x4}\PY{p}{)}\PY{o}{/}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)} + \PY{n}{x2}\PY{p}{=}\PY{p}{(}\PY{n}{yp}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{+}\PY{l+m+mi}{10}\PY{o}{*}\PY{n}{x3}\PY{p}{)}\PY{o}{/}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)} + \PY{n}{x1}\PY{p}{=}\PY{p}{(}\PY{n}{yp}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{+}\PY{l+m+mi}{10}\PY{o}{*}\PY{n}{x2}\PY{p}{)}\PY{o}{/}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +x4 = 29.430 +x3 = 25.506 +x2 = 18.639 +x1 = 9.8100 + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}23}]:} \PY{n}{K}\PY{o}{\PYZbs{}}\PY{n}{y} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +ans = + + 9.8100 + 18.6390 + 25.5060 + 29.4300 + + + \end{Verbatim} + + \subsection{Automate Gauss +Elimination}\label{automate-gauss-elimination} + +We can automate Gauss elimination with a function whose input is A and +y: + +\texttt{x=GaussNaive(A,y)} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}24}]:} \PY{n}{x}\PY{p}{=}\PY{n}{GaussNaive}\PY{p}{(}\PY{n}{K}\PY{p}{,}\PY{n}{y}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +x = + + 9.8100 + 18.6390 + 25.5060 + 29.4300 + + + \end{Verbatim} + + \subsection{Problem (Diagonal element is +zero)}\label{problem-diagonal-element-is-zero} + +If a diagonal element is 0 or very small either: + +\begin{enumerate} +\def\labelenumi{\arabic{enumi}.} +\tightlist +\item + no solution found +\item + errors are introduced +\end{enumerate} + +Therefore, we would want to pivot before applying Gauss elimination + +Consider: + +\begin{enumerate} +\def\labelenumi{(\alph{enumi})} +\item + \(\left[ \begin{array}{cccc} 0 & 2 & 3 \\ 4 & 6 & 7 \\ 2 & -3 & 6 \end{array} \right] \left[ \begin{array}{c} x_{1} \\ x_{2} \\ x_{3} \end{array} \right]= \left[ \begin{array}{c} 8 \\ -3 \\ 5\end{array} \right]\) +\item + \(\left[ \begin{array}{cccc} 0.0003 & 3.0000 \\ 1.0000 & 1.0000 \end{array} \right] \left[ \begin{array}{c} x_{1} \\ x_{2} \end{array} \right]= \left[ \begin{array}{c} 2.0001 \\ 1.0000 \end{array} \right]\) +\end{enumerate} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}25}]:} \PY{n}{format} \PY{n}{short} + \PY{n}{Aa}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{;}\PY{l+m+mi}{4}\PY{p}{,}\PY{l+m+mi}{6}\PY{p}{,}\PY{l+m+mi}{7}\PY{p}{;}\PY{l+m+mi}{2}\PY{p}{,}\PY{o}{\PYZhy{}}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{6}\PY{p}{]}\PY{p}{;} \PY{n}{ya}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{8}\PY{p}{;}\PY{o}{\PYZhy{}}\PY{l+m+mi}{3}\PY{p}{;}\PY{l+m+mi}{5}\PY{p}{]}\PY{p}{;} + \PY{n}{GaussNaive}\PY{p}{(}\PY{n}{Aa}\PY{p}{,}\PY{n}{ya}\PY{p}{)} + \PY{n}{Aa}\PY{o}{\PYZbs{}}\PY{n}{ya} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +warning: division by zero +warning: called from + GaussNaive at line 16 column 12 +warning: division by zero +warning: division by zero +ans = + + NaN + NaN + NaN + +ans = + + -5.423913 + 0.021739 + 2.652174 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}26}]:} \PY{p}{[}\PY{n}{x}\PY{p}{,}\PY{n}{Aug}\PY{p}{,}\PY{n}{npivots}\PY{p}{]}\PY{p}{=}\PY{n}{GaussPivot}\PY{p}{(}\PY{n}{Aa}\PY{p}{,}\PY{n}{ya}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +x = + + -5.423913 + 0.021739 + 2.652174 + +Aug = + + 4.00000 6.00000 7.00000 -3.00000 + 0.00000 -6.00000 2.50000 6.50000 + 0.00000 0.00000 3.83333 10.16667 + +npivots = 2 + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}27}]:} \PY{n}{format} \PY{n}{long} + \PY{n}{Ab}\PY{p}{=}\PY{p}{[}\PY{l+m+mf}{0.3E\PYZhy{}13}\PY{p}{,}\PY{l+m+mf}{3.0000}\PY{p}{;}\PY{l+m+mf}{1.0000}\PY{p}{,}\PY{l+m+mf}{1.0000}\PY{p}{]}\PY{p}{;}\PY{n}{yb}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{2}\PY{o}{+}\PY{l+m+mf}{0.1e\PYZhy{}13}\PY{p}{;}\PY{l+m+mf}{1.0000}\PY{p}{]}\PY{p}{;} + \PY{n}{GaussNaive}\PY{p}{(}\PY{n}{Ab}\PY{p}{,}\PY{n}{yb}\PY{p}{)} + \PY{n}{Ab}\PY{o}{\PYZbs{}}\PY{n}{yb} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +ans = + + 0.325665420556713 + 0.666666666666667 + +ans = + + 0.333333333333333 + 0.666666666666667 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}28}]:} \PY{p}{[}\PY{n}{x}\PY{p}{,}\PY{n}{Aug}\PY{p}{,}\PY{n}{npivots}\PY{p}{]}\PY{p}{=}\PY{n}{GaussPivot}\PY{p}{(}\PY{n}{Ab}\PY{p}{,}\PY{n}{yb}\PY{p}{)} + \PY{n}{Ab}\PY{o}{\PYZbs{}}\PY{n}{yb} + \PY{n}{format} \PY{n}{short} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +x = + + 0.333333333333333 + 0.666666666666667 + +Aug = + + 1.000000000000000 1.000000000000000 1.000000000000000 + 0.000000000000000 2.999999999999970 1.999999999999980 + +npivots = 1 +ans = + + 0.333333333333333 + 0.666666666666667 + + + \end{Verbatim} + + \subsubsection{Spring-Mass System again}\label{spring-mass-system-again} + +Now, 4 masses are connected in series to 4 springs with \(K_{1}\)=10 +N/m, \(K_{2}\)=5 N/m, \(K_{3}\)=2 N/m and \(K_{4}\)=1 N/m. What are the +final positions of the masses? + +\begin{figure}[htbp] +\centering +\includegraphics{../lecture_09/mass_springs.svg} +\caption{Springs-masses} +\end{figure} + +The masses have the following amounts, 1, 2, 3, and 4 kg for masses 1-4. +Using a FBD for each mass: + +\(m_{1}g+k_{2}(x_{2}-x_{1})-k_{1}x_{1}=0\) + +\(m_{2}g+k_{3}(x_{3}-x_{2})-k_{2}(x_{2}-x_{1})=0\) + +\(m_{3}g+k_{4}(x_{4}-x_{3})-k_{3}(x_{3}-x_{2})=0\) + +\(m_{4}g-k_{4}(x_{4}-x_{3})=0\) + +in matrix form: + +\(\left[ \begin{array}{cccc} k_1+k_2 & -k_2 & 0 & 0 \\ -k_2 & k_2+k_3 & -k_3 & 0 \\ 0 & -k_3 & k_3+k_4 & -k_4 \\ 0 & 0 & -k_4 & k_4 \end{array} \right] \left[ \begin{array}{c} x_{1} \\ x_{2} \\ x_{3} \\ x_{4} \end{array} \right]= \left[ \begin{array}{c} m_{1}g \\ m_{2}g \\ m_{3}g \\ m_{4}g \end{array} \right]\) + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}29}]:} \PY{n}{k1}\PY{p}{=}\PY{l+m+mi}{10}\PY{p}{;} \PY{n}{k2}\PY{p}{=}\PY{l+m+mi}{5}\PY{p}{;}\PY{n}{k3}\PY{p}{=}\PY{l+m+mi}{2}\PY{p}{;}\PY{n}{k4}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{;} \PY{c}{\PYZpc{} N/m} + \PY{n}{m1}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{;} \PY{c}{\PYZpc{} kg} + \PY{n}{m2}\PY{p}{=}\PY{l+m+mi}{2}\PY{p}{;} + \PY{n}{m3}\PY{p}{=}\PY{l+m+mi}{3}\PY{p}{;} + \PY{n}{m4}\PY{p}{=}\PY{l+m+mi}{4}\PY{p}{;} + \PY{n}{g}\PY{p}{=}\PY{l+m+mf}{9.81}\PY{p}{;} \PY{c}{\PYZpc{} m/s\PYZca{}2} + \PY{n}{K}\PY{p}{=}\PY{p}{[}\PY{n}{k1}\PY{o}{+}\PY{n}{k2} \PY{o}{\PYZhy{}}\PY{n}{k2} \PY{l+m+mi}{0} \PY{l+m+mi}{0}\PY{p}{;} \PY{o}{\PYZhy{}}\PY{n}{k2}\PY{p}{,} \PY{n}{k2}\PY{o}{+}\PY{n}{k3}\PY{p}{,} \PY{o}{\PYZhy{}}\PY{n}{k3} \PY{l+m+mi}{0}\PY{p}{;} \PY{l+m+mi}{0} \PY{o}{\PYZhy{}}\PY{n}{k3}\PY{p}{,} \PY{n}{k3}\PY{o}{+}\PY{n}{k4}\PY{p}{,} \PY{o}{\PYZhy{}}\PY{n}{k4}\PY{p}{;} \PY{l+m+mi}{0} \PY{l+m+mi}{0} \PY{o}{\PYZhy{}}\PY{n}{k4} \PY{n}{k4}\PY{p}{]} + \PY{n}{y}\PY{p}{=}\PY{p}{[}\PY{n}{m1}\PY{o}{*}\PY{n}{g}\PY{p}{;}\PY{n}{m2}\PY{o}{*}\PY{n}{g}\PY{p}{;}\PY{n}{m3}\PY{o}{*}\PY{n}{g}\PY{p}{;}\PY{n}{m4}\PY{o}{*}\PY{n}{g}\PY{p}{]} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +K = + + 15 -5 0 0 + -5 7 -2 0 + 0 -2 3 -1 + 0 0 -1 1 + +y = + + 9.8100 + 19.6200 + 29.4300 + 39.2400 + + + \end{Verbatim} + + \subsection{Tridiagonal matrix}\label{tridiagonal-matrix} + +This matrix, K, could be rewritten as 3 vectors e, f and g + +\(e=\left[ \begin{array}{c} 0 \\ -5 \\ -2 \\ -1 \end{array} \right]\) + +\(f=\left[ \begin{array}{c} 15 \\ 7 \\ 3 \\ 1 \end{array} \right]\) + +\(g=\left[ \begin{array}{c} -5 \\ -2 \\ -1 \\ 0 \end{array} \right]\) + +Where all other components are 0 and the length of the vectors are n and +the first component of e and the last component of g are zero + +\texttt{e(1)=0} + +\texttt{g(end)=0} + +No need to pivot and number of calculations reduced enormously. + +\begin{longtable}[c]{@{}ll@{}} +\toprule +method & Number of Floating point operations for +n\(\times\)n-matrix\tabularnewline +\midrule +\endhead +Naive Gauss & n-cubed\tabularnewline +Tridiagonal & n\tabularnewline +\bottomrule +\end{longtable} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}30}]:} \PY{n+nb}{e}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{;}\PY{o}{\PYZhy{}}\PY{l+m+mi}{5}\PY{p}{;}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{;}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{;} + \PY{n}{g}\PY{p}{=}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{5}\PY{p}{;}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{;}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{;} + \PY{n}{f}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{15}\PY{p}{;}\PY{l+m+mi}{7}\PY{p}{;}\PY{l+m+mi}{3}\PY{p}{;}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{;} + \PY{n}{Tridiag}\PY{p}{(}\PY{n+nb}{e}\PY{p}{,}\PY{n}{f}\PY{p}{,}\PY{n}{g}\PY{p}{,}\PY{n}{y}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +ans = + + 9.8100 27.4680 61.8030 101.0430 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}12}]:} \PY{c}{\PYZpc{} tic ... t=toc } + \PY{c}{\PYZpc{} is Matlab timer used for debugging programs} + \PY{n}{t\PYZus{}GE} \PY{p}{=} \PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{100}\PY{p}{)}\PY{p}{;} + \PY{n}{t\PYZus{}GE\PYZus{}tridiag} \PY{p}{=} \PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{100}\PY{p}{)}\PY{p}{;} + \PY{n}{t\PYZus{}TD} \PY{p}{=} \PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{100}\PY{p}{)}\PY{p}{;} + \PY{c}{\PYZpc{}for n = 1:200} + \PY{k}{for} \PY{n}{n}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{100} + \PY{n}{A} \PY{p}{=} \PY{n+nb}{rand}\PY{p}{(}\PY{n}{n}\PY{p}{,}\PY{n}{n}\PY{p}{)}\PY{p}{;} + \PY{n+nb}{e} \PY{p}{=} \PY{n+nb}{rand}\PY{p}{(}\PY{n}{n}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} \PY{n+nb}{e}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{=}\PY{l+m+mi}{0}\PY{p}{;} + \PY{n}{f} \PY{p}{=} \PY{n+nb}{rand}\PY{p}{(}\PY{n}{n}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n}{g} \PY{p}{=} \PY{n+nb}{rand}\PY{p}{(}\PY{n}{n}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} \PY{n}{g}\PY{p}{(}\PY{k}{end}\PY{p}{)}\PY{p}{=}\PY{l+m+mi}{0}\PY{p}{;} + \PY{n}{Atd}\PY{p}{=}\PY{n+nb}{diag}\PY{p}{(}\PY{n}{f}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{n+nb}{diag}\PY{p}{(}\PY{n+nb}{e}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{:}\PY{n}{n}\PY{p}{)}\PY{p}{,} \PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{n+nb}{diag}\PY{p}{(}\PY{n}{g}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{:}\PY{n}{n}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n}{b} \PY{p}{=} \PY{n+nb}{rand}\PY{p}{(}\PY{n}{n}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n+nb}{tic}\PY{p}{;} + \PY{n}{x} \PY{p}{=} \PY{n}{GaussPivot}\PY{p}{(}\PY{n}{A}\PY{p}{,}\PY{n}{b}\PY{p}{)}\PY{p}{;} + \PY{n}{t\PYZus{}GE}\PY{p}{(}\PY{n}{n}\PY{p}{)} \PY{p}{=} \PY{n+nb}{toc}\PY{p}{;} + \PY{n+nb}{tic}\PY{p}{;} + \PY{n}{x} \PY{p}{=} \PY{n}{GaussPivot}\PY{p}{(}\PY{n}{Atd}\PY{p}{,}\PY{n}{b}\PY{p}{)}\PY{p}{;} + \PY{n}{t\PYZus{}GE\PYZus{}tridiag}\PY{p}{(}\PY{n}{n}\PY{p}{)} \PY{p}{=} \PY{n+nb}{toc}\PY{p}{;} + \PY{n+nb}{tic}\PY{p}{;} + \PY{n}{x} \PY{p}{=} \PY{n}{Tridiag}\PY{p}{(}\PY{n+nb}{e}\PY{p}{,}\PY{n}{f}\PY{p}{,}\PY{n}{g}\PY{p}{,}\PY{n}{b}\PY{p}{)}\PY{p}{;} + \PY{n}{t\PYZus{}TD}\PY{p}{(}\PY{n}{n}\PY{p}{)} \PY{p}{=} \PY{n+nb}{toc}\PY{p}{;} + \PY{k}{end} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}13}]:} \PY{n}{n}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{200}\PY{p}{;} + \PY{n+nb}{loglog}\PY{p}{(}\PY{n}{n}\PY{p}{,}\PY{n}{t\PYZus{}GE}\PY{p}{,}\PY{n}{n}\PY{p}{,}\PY{n}{t\PYZus{}TD}\PY{p}{,}\PY{n}{n}\PY{p}{,}\PY{n}{t\PYZus{}GE\PYZus{}tridiag}\PY{p}{)} + \PY{n+nb}{xlabel}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{number of elements\PYZsq{}}\PY{p}{)} + \PY{n+nb}{ylabel}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{time (s)\PYZsq{}}\PY{p}{)} +\end{Verbatim} + + \begin{center} + \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{lecture_10_files/lecture_10_27_0.pdf} + \end{center} + { \hspace*{\fill} \\} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor} }]:} +\end{Verbatim} + + + % Add a bibliography block to the postdoc + + + + \end{document} diff --git a/lecture_10/lecture_10_files/lecture_10_27_0.pdf b/lecture_10/lecture_10_files/lecture_10_27_0.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8606584d048093b5b120b53a065e5e02f998452e GIT binary patch literal 11168 zcmb`NWn5I<*Y^QwPzh;}QR$o^hX(0xkj|kQVCaxmy1NnS6e;NjN$HlBkZzEA2EDH9 z{>SrtKKF~~3^SYk+iTZa>zo(gv#FKDB$z=g9GKKKd*#=d>;NFZ&e#f*pC7;~2Z5S9 zSpYcTk_sjO0AQ7{v~hyK;H8a`6GRMRVrL4$6cogCbb>*QY%$%^6LjRGsOue?rYj29 zc8xMG)lHAA+JFFIv{^@;ZNq^o|92!La|zk4tTgN|zh1bwjzsiir%9U~GfJD8PTcGT z7u?=lZk}-8Qw$5;JL#@C)Ol~jKcD9Gt~*Dk&Z1N;iGpPbc?06y4Yrw#Ew$aHM&a} zc!eEtUZ}d(*=t;OcRQZCSht~c{VE@f>aG{nSQt)USetu;UT=2>T?UV__woTp^?1g)gf&Y393%+J`CV<9i5B`q#K`+g<^Yt%3m`Z0C& z);w+xBSzSX%!{kgIBUAjwn{>rvVJsv`KoIu;zc%wh9bAd zcbx^W1fSM{!y56>x+w;e_DPJ$Rdy5 zb}P{)oI4pM@i)~RWdnw()pZ=@!e^Y`bnIn2-5IFot3~}BePc5!ti7q={4=vg_t@>b z;@q^0l{)R-&ecRuNirEln#ZhHWZrj#9f%)VV@DMI2MmfEH#=uL*nFkx*;}Zmrt944 zlY)p8S}g163&%RE8r0&=(TF4OiO*WXB!p^=SjC$-IT_Ibb0VoL($+%Y7f}V4J9s~e z+-xStG#yS@8Z$H`*c%Itx)dWTxabQ12S{L$h{iFHg%^_a8 zL_ve{N2&Tw@@mp?&J(8wyZGIY8cO3oW916ula<6buNN2c9+Qj5GY2bu$9%2-GT873Gb(1Ii`(RrZ*yxy)x@rP>lzcHUH#5+itS^=QT${R z1#EUN7)K=4&unSskCew!*7%$4oW{1N-AiRt87MnE^?k(Wo>kvHTQB8dF!mf5gZadB z887zUP8oXb3R|1Fp)W0QMa*Yd%ZvK^6Okdw2SA#N3C-P^Xz_7ux#(hWF)XO-&D(-) zf8q6EQVn3DRL2^aJ2J(Tt|wtg3p4(h#H8wl<~3>4vuc!ciIxwAQjLGDVl?KNLdBH>-}Q}65+56v$KP916J9vol0 zMX~$XM&9Rh({xWK=;4)PP;291e4;|_-FRE4)mH(P?fV>?^_@#^JLb5V@BZ&Kv2iu? z51C`S6o|(`kRaL?LOQYM)l|Jx79^Ie)@(T;=H@zh^-SUq%OAV_Fk32>v+cyMH-I_E z#8|=7NHx%3G9ZJ*$Rl@C8LkAV3ld&CJU-GWs582_WGVReL7+#VGW|||)aNT<>}oU`9u#N(zh5D z3N=)_&tr#*X3Vte4brWo6BDkxi>N*%1WVaLegdK+&@Fl##PYF%U9!p}NX(j{DAWT| zbG5HiiibLy>(4?v-kfpyun=yZxn4Q;iB{U(-DEz)?y(4&x@wz?Q;nn6Hs}pO^zL%& z4OM6oG%n-Qs}Q}t>s-1&*x5XJO6mQp({<_gXxz@{eNfMyR>et2bnE@$w2#+q);A&V z3y=@^{yymBBor!5?$;; zkc4#NH70vUudbdSQ)+HO&Fxcg!o4 zKT08r2o@1%l4}TmcX*Lkb?wh*sU}=v`0BHn!Ofd+;>*<>LMAUWnkik|_sD%m77Uqp z?XiTeRp5=Di!5^%PErUUmL(F(G`NZ)wo6Y|45lA#gbr|fR zdi9m1HPI|}s(|0HwScHsP&Kf!Yj9NE;2m+yy5R`^c2-e?UCOoGg&YA3dClDyHrvd=DuZVWEhH56p`$;VjLohNl@2E4+tABt zb$PeX1-5XB;sj(n!y1QY-@4B=SdZIn^a8DPX=Fn39D-&Bdz+;myT&#Caz2Czn$^;| zb{CFj?UUlq2-{J#?+<``b}Y{)#?x1D45=HI__*-}i#!SQj!3!uB0g>hx-5Nkaja}u zqA4pP%F-S8>(=1NDBZVB`_`GYn=e~*J!{7po6%R=gRCgA%tl`P*@hkJ-h)eXSZ0}C zfMFJdAsf)<@@0>|SED-5`m~W8XPE=~LE6Tv#srV&%Y`wz;LM!GVQOMAnq=p!W8o&) z$NN6q-`%S$HOABK2Z5o{VKR)F^gw`MV~!F>F2a9M^+^jPA|bbjn4e9ZDc%2%Qu;?bi>l8bEFA`+lm>z_mJ#+*q3+m-DkHm?Sd z;zhPo+!X7Ez4#>Z7_pXS_|*r^q5i4Uh8xmbwiC0B7R?n@vDPG3!R)W4dg5V@-$L}Y z*n2y@sAmtQbuqZ}FnaR!n&?VxxPGYhttB$9Y$Y2$;edTpIdzaAr@$X{IQC6#Q*9-7 zMY5;omPGVeH2-*r#My4YGUmo;PNgE7AmV!JAJ*Hi@v&EkwpD8&FGN31 znSz;oh3XrxbwF%uOkNu&?oI@o221^(N;2+nAM4kgR}roaTN+Y=dH%l4o;F%|y}q}M zbI*NlnCBk{CVHu3vAW<73ReH(xpYN7DWc4q744d|fXol)bjCdL6i%8=aO~xbX)iSw zM5d|KGNp*#T^r(_Vp!Y3%1GWt<6V2f5yGl6m2cj-k#(>k9x zW})0X8&zQ-(v7sI-)_TW$y+d3j!i+_dZa6pB8IyXEAJmmGL^rg;9~m3C?CWu?&d4U zrL33?LQ8#=LyM3f?{@qIkY99)os73%f|9%&_Y_$QL5}7qX%)eEPH-1sn5rko*CtDE zl>;{50(L3Obo4MNaUO73JM#34q?*?t=*l=4y%J)rMgAg(k@SA+nVO6;?g1110*c0G z&hGfL6xsFe{3fVUZe$YsJDSr#eNh6!;;#)T@}$1>%r}T_98{aHW$6#g5VT2S`xN*_ zRxI4yahUTy6~qT*7m4OI3rq_hvfyg`3|;k0V4`$D6yVYL+2tZ8^BmDLlSIj~lh#*8 zPZd?|C-~uUV=s}AI6433b0clDUI%Y;LLZNU&P;6TABMget3z~g%Y7`O>wA^f zbpatJ?X*>*f!!RpXGqzrWmr$pL*G(#DSPH)fcxj{wb_LuE;`WV5FIO?`qSgTph8Ry zty|P;qmSE_^G~?VcTCc`VZT_H_#~TUhehUT zeP=yT-3HS+z-O!O!ohAS8qqXG;AxG0iY?M*(uG?(7Nompix@c2a7G*zZ?9U7k_?IE zi4+wc7{r+XDi-=;DGkgitw!xk94Dh14p0Ruo|7#2OJq`6U1p=&TVvv=@htF~DZoO! z?8B!i>}NL}?a`ZrrjSZ}2MP&VSBTb0b5z|1c>NfW?7Jl>+k@1n0*N1IJ&KG}Y-c9x z?l8EP^y$)}Y0E*fPYJ|fI#z9SY%hD$?aQ+mN}wr6^G%7*NaD3dRUbWKLoL_geOX_V zj68yqf8$4#$KgDSo}4MJO3f&S_Ce+C?mc#ASY~-FUxIhn-3Egl?B^$RfQ3J;rI4C7 z+|jI&v4eX*{oF`v+-h`!dqrW5<1= zF3d8=Hp4UY4Tc6Qu%GNqE``49SnVG%-RBb^2irWR1P>ygum~V`(Of+Z_tRXHW_zls z4n-pVO6915wlaeQYLy2QY96Dy4Ne4e9nF0jdLc!q8A>bUQ-rB&Ch+2DrOoD`&>yGp zwTwJvHS9@CP+Sx`AD0d`O8YFXrbpjVN)4{Q=l1nfHBVn;%UKMsLn??8C@Q3q)9t6d zj^>gZuyZGG?KR-4@|9OWSsPG*K8n}N5KhSR#IJhB!Hg)cTWoE$nm99f{3okHJ#m3J zxCPAI&gG!(r6OiU&-+q_F9$ZxSMo!Ys%TPdj7cS|k~X9ag%|0-5ykOk?Xxu7E<$5P zT%D9Y{#A}^1k$6=!OY5ZFKa{RqGwWDAc**e+DtMoVbiO7Urw}de!gqcAiP_5W$mZ3 zZ6f4hJk}1|)@~xa!U1ru)!^WVO{<{SxiLr4wOhw9?L5ztXrJr02BChpV2(=dw!*lz zsZPBA7Tj&M2eAFD&GIIfP~zBDBW!8UrZmx{RNU%CAWaE1KtzM_=(Bz`A-)4&8A_vR z4QX9!>C}&k$;vqG+(aoW2dCBQ!1z8(=2$HEsxR5OQp|gJQq1*8(#-8o14~)#C(u=7 zL(pTj@t9PwvKaj)w3GK{h*=%9EwE*FP|BTk55=sT$XlAiMzu%e?^hm;?18)ceF7F6 zE?1t-Fb5S;)dhc(vT;8^uyK7>bjm0V#|Ix6N>KQQR;&#ZovEA|)mQ@91-E=&97XRA$%31Ycl)CbF+hTUOF}%%r#F(dv=!po9y5kq0 zbl%`s>X7V5&J->9zcj6z!9Zsjeb*{yPeB84ME18X3SM3XcG)W_V+ z-&rF(N$$D`{*)rdj9D%15JGV6{635{_Y0RCCrKfSTe|~&hdwzG?h9}^K|qj632HBO zq>Y0vmAiMw8Xo13+A88@aabi$jIJ1#aeZLzh7}|uQ5@zcgWucj?iIJr3#imue|Ibl zJIa6An>Qa!K2448;fJL1@)19grPPrw1L=0P;VAo%GrHUllr~{U=3+SxB0@B#B$kR@ zN^?{1ML>R-=(BNkSL`$Pd`4T(EohEnA>rf?v}K~?@+Hc9B-AZ!Eldd1^e^-R|L+0X zJdm1)63%KkIJh_-3?8a%|1h236i3|6NmA7bPH+JH{0{>BVl@K7D*#qe5da9lYGMTc zg>xNv!=GPP2|K9MzgU|w1DSyU&cC@3+z9^n*JND(Oa@?8bGL^8Se1;-A-^Y9GJ-+i z?HuF8-4VJ1&1HaYJfcOs2R#%~J0iHv(3DsT@KS0W z6s^p0IaJzkiJoH}wk6^4x^TCiVuGU8`EFL|eEwj*xZKlD06KY<(OdD83y1*hz!N?k zPFGdAYu_EBMI2;C7&}dg;@^FDz4{r^W)wj#K5>c9e1Al8AMKMWh0Eggvj151=Kinu znXaRJKXbT#i58E`;TxW41G zNhbD1bB%x(Md9Acx&8a`Op6QZIeb~jR(adZ{z;C4`R!3-P&|j>A%-u1Mi%vipRXtO zdsF%@%5jme*@{a1=oo{!wVRxCnE9OJ%Wc6O_SW3;>CewytyDMVGc=OB&gVvGWW_u2 z_xJ~rEESz-F}bAq2h46$ebdpoOrA$bU13F}EVqY(45jEWm>ae{Gto zWSCp7?EctGL00Ax#K$?y$J_a{8#|F|R$VfG$w)Kr&ihkIbb78{9_kY=)o zZVOCY*9L9>F+6+)a znHgEg*eN}RmN!$fnFo2C+9Wcj_-I=a35%aF*o3eeAqRq;ElsqFP00?d!sQRu=hB&c zdO|9X;vSLc&nK<7k=gkQbKX(A)7z8Fvh?XIh-HN$w(v2;eiV(d?(M{+;}8sQfU zXeUP0TRAhrTfL~OK(3VURxOh-G)BnD%xm3YCUGTG!;oalZ%(xHaeE4r1{dZtQyKMofp3nKN9?EK${D4mi)%mCP`{9`e-<;zI?2DRqE}n9AV10 zVvHyXY@zzlMJ5;jA-J2pPF6wg=d=)GCgfKTik7~ibaaBDQ4e#Y{H=1+ ztClaXYjTt$GHhV3b?QYWH`Eq|7v>MOueqnC@O_CNeB8^ z5EUwujyj^3?bmcd8&51U`&`f~`B3-dXxP4@{c@W3j??;B4x6Ci)i;EoRN^(S+BwO*#ZMh=%Eb3U7>nz$>kbzQAa!%K^EYtF4_ zhK#wdzH`TYG)r7KhMfr<2sC_pJ4ZCgxj#%iT5r-Dd1bTrm4}RWxPr`aZF}d&pviq& z_J_l2NpMC`+(+-;I$wMVWaCm@yH3rvVeL~+iMT~!(`-$OsUwyezJdhryIu6!Vg260 z;hB@-w91$H;$`0nI792>;(kG9ntUN zTF+Vpcb(wk8Tze;+K;sPs`F5_qB7%|dyv3kMBgWaliPiJiMCu)r1xH;l^+(`v|`xf zbd$-ir0}WhFJ+`0-WD10AY_NdF}}daNBc$pM6~*GJUC-s7k{%me0k8Q<)+JSOM`H<<@c1K zu>j-uK5k!~Bzb>SI|L=QcobfJaIcw9rA%%0&~bExuKB;?bLh^IY`H)EsW+Cmx$~4$ zw=AZ%>2QIJRlh7I%yo&+M7cs?LuEl77nP_>Wj)U~jimTY(f)!loI7o{ealQT&OL#4 zih29H$JaRWT8B*Z?HUOji>_(hkdk33LzFStTL0Q>hl4J?(6##L0a%`{E0l>cS9ZF9 z43%UcJ3K)evj6#w=%{YThC;a5f_+^AwI^rs;AsF9eSAT_{O6(xbl&Iwh=hH~UDzpf zjj8NfHQzc`-@{n7O1;7J*M~LHp#A5-;0QyB4O8yWC~fZj@6F;>vL7!Miq*)w{5v0U z{UDjKsM$iGzywF&E;?HA1uBPSTQ|N_o@eI0G4c##{fe0UvR*Gzuq}0RHX+!=bY8d>mifJsN_w?E2;Z=TAu4rWaY}Zr$&+6x4UaS zr`~-*Gk^#l(Cx-^cgo zY>Y}oQ9k0ZlV*dbu$q;Z)$3GlW>B6_P34@LZFw!Yx-g!qyD)hqoUl6Qv3huW3vt+U zp5YN80cP&K%}*Op0RIU!^lY_45WP))VhfdUEZ_x+jMHs~=uz+*Wt*zx%` zqsHKytodJKKUx)pei?38#^#ln?P2eFZLGD%?uV7w%n81BDBxu3Y)Ahj%E@(3oOz}{DU!^ zYF2_nX;(EkM>#auTMrTPQ1Ai_WU(7?LO>*vOhy&!q2yJI37x*`#P9n+UNUIO$8^p1M zFdMbn?dUdKR0rk5N_YH~5x=oAR0*Mw4cTx`z1<`)+ zCGbtB@+afl@(i-6y}6owJjdX$q!xlDAYW#q{qg!cRt56=&-&>&Mn{}6dRz{vVG+TX zmb@6hURm~HyhD7dnWA+c+F?b99Z&dieZp_J?Tj#O+bqdN31}5)HiphzF-qz_70mKE zqn7vOwPjFiTJ*?Om~mF_9@ve(2t-KVPeo>h!H@019M>Fl>Uh~ax>sO;{$d19M89_w_lGnAqIB6ZB zMLtJ0-n3`t_Y3#)A)};}pXEz4Z9kAVBt|ICRXkMPR@#0mwg6FP(pZ&`R*f2ipD5M zZ3G3x2tpCKEYO6txr$~}pUz~LL@R7tf%=Kq%5q@x<82#SyV~ z#-Bj;^Be~u9bN4K-s)$?ymqhFxwQ%1(mXtl3r2~Qjb2@FXM&y%r|;<%mCHS^SIOXn0mX=w z7`)E&rw_tgdlOFts7~MCr1Y{%-aED4cwY=nz3vPe89*zY?vplf6eIUl*Y$4Q;j&(- zIX6&w=59fM@F+{EC`K><@V!PwG4Dy7(UH7zU1%g$KuwdF-GW~Qr*%DKXPqD zWN54p<9EZ0;88Rg7H&8nuDR;9nxYo52r?EyTFE1k64YXhQnf@|{)RyJRG*QmRWPXE z10f)#pERdlje(;_Y%kws&!-SQl#a>Q514kDBP(RrvHxldA%Cs}_en&;a;S!2B4_+&A01>kH ze(wo|>eUtRZnhtV>QR;A_?5XH{PE!Z^3cR@^XAfy<)-k7(6dXwNB7R4yFI|2`tmi$ z&26_^?JbSB3#fJ}@SvG&UIFlLvUfGO;c)1 zv%$WxEeQpRe;NCT47ugfKcRK2m#Fm83rCcLN-anS1v+b!Utzvr)AMW7*zGM&)_m^q zrm=lo=r__M5kKOL`hpb%Nx1|P zRLOxkp0hJ=wGMaPB2};(Ni>9*zX5&^6h$Sw#34WCqf>*vHZv@d82LO zPB7Es(fNguP*%uA)rW6^^hj|iG_$}Mdm7#mvaUdua9Z>uk?^YQAdW3u;`w)PdkwMG zjgckLDxX>wN43#;&@-TZN76&eK%(GidoiN$X3s=PFT56@jiNoMyzp{F?&FZM1)hc4 zC_qWE^AyRMMa`d1wLtFqvV@hm2vY^j639j%0*50ml48zChr=VHD4QV;j%|Y5LzCXVQxufOZ0K#4o(Mna0IUgQ&m>OtR_?M>$U? z_t3z=+(fJJPgP%+T;GSN6k&B5Jx?0#?yh_b?ffKslu0wcg5-_Pvcj(yD-K?9N4NUe z{@A5H`83-ClA;-2IVt^XLfx?q#Yz02E7Wezf<>6 zl7pC(it`bJGS~HgUCu?Ji$nG6B9A*^daCmV-J6^*x4ag=O1Z$my^F>_J4w{_5+6@2 za$^QuCym!7#?>voRXKAJ&4WmjIne9kStq4%g&t6~m@H!2rPO?)DbLMcB|S+_;W8ct zm71J)cuplXI<@QoybLKuE8ZA{MGo`QHGk#IQLT)OA(6`z`C`naznVFVPG-hvQ^mtg zG(+S4t?~Xm7EddSQowT<`V{ftUOfG!>yHDX=eb!-{~e>>p8qRI>>!@MV+4BOfq%2L zKSb{VH;O?VO<0H1I)EFtUZ?L@^0Xk=NRcVh}4M4QEw2>ief%!pPRr#vMTS zrwQ=TM*pYL#>gDb5!wE+eEkPHGJ}9@Kmaob7aIV?&BG1=v9YuLMIWV|jBG4TM4;w2 z5CHIZKM_Zh2YSiF2L4@rSl>gPnT?(Ew;*a{F9oqQw}1mq_%OdERVRq81_1o0|3gLU z@5;k=;Mfqt26!Ng|4JGksOo=vL3vJ?-Bmp-GJW#`E!SeL*ZxqETQHAR!vK&2-MN?Z{c@8O-oZJ3r9G- zWd}X%;$J`PJV3z1_s@r&>rcrAhr9pz{oCgMf62xEz{7z6E)XYxo%4a{0s(B?e^&ZX z@^Ev&SHli(f5<>MeukHv@O)tBVf(HB#?Ww_Y^M&jd^qX|czBxpYpDJ^aUW3kpL~?H zG=1>Q0}WUC2WUG#(C>et%Ao%t^Kd8)KST-7b^x7;ktNIy0Ac}guy6tBES#L|d0F91 z9xj^0jO;BeO&nS5VCM9HQdzqPmS|G z?La^-c#izL9SFz`e|7PX<^(f>-`cR>XJ}O|Js=OhdUzk8VrK`B|Np$skcOJU + +Gnuplot +Produced by GNUPLOT 5.0 patchlevel 3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 10-4 + + + + + 10-3 + + + + + 10-2 + + + + + 10-1 + + + + + 100 + + + + + 100 + + + + + 101 + + + + + 102 + + + + + 103 + + + + + + + + + time (s) + + + + + number of elements + + + + + gnuplot_plot_1a + + + + + + gnuplot_plot_2a + + + + gnuplot_plot_3a + + + + + + + + + + + + + \ No newline at end of file diff --git a/lecture_10/lecture_10_files/lecture_10_28_0.svg b/lecture_10/lecture_10_files/lecture_10_28_0.svg new file mode 100644 index 0000000..548cda9 --- /dev/null +++ b/lecture_10/lecture_10_files/lecture_10_28_0.svg @@ -0,0 +1,123 @@ + + +Gnuplot +Produced by GNUPLOT 5.0 patchlevel 3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 0.0034 + + + + + 0.0036 + + + + + 0.0038 + + + + + 0.004 + + + + + 0.0042 + + + + + 0.0044 + + + + + 0.9 + + + + + 0.95 + + + + + 1 + + + + + 1.05 + + + + + 1.1 + + + + + + + + + gnuplot_plot_1a + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/lecture_10/lecture_10_files/lecture_10_3_0.pdf b/lecture_10/lecture_10_files/lecture_10_3_0.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5ebf43a2eb517ed27c03d64b0f1dc8eb1bdc8f57 GIT binary patch literal 5402 zcma)A2{@Ep`)@@PAkqOCQrSP=YGMLDCiPi@t+Y z00=LS(oCa28|<0ssJPKq4~;G}e=hVG#5PI4Yh1($WIa88iaM1LT`> zHU3bv0F>|i*&i3>GFnrJ~Y}96Fa(ADs%2nUKo`W0}(toRPk;88P8?GR!#JdJa?;<>pauR1#{?sMwZXmh+ zwcNgFvp&dM6P>n4Q7aX)Awe$%SF$4-rLc}q-?azRSDKb;yN=kww_>{(E$?87(T{=9 z_82P*IR0|yo|gQn80&7+y6O&Xk;J{_jv*;+M&moeNx_Oqn@e5Q@!pBSjja#r+Ep?+^NqWW3IB0gS0MG~;=5#?M>InOd1lQ$$VIh8zXZd_+3wg=wx%^KvOHBQzhQmCLKIvMWnnDFoXFFb;9jTf7QbT{+ z83SZ`p3njM;u2$B>ibFwB9~{5WDlznD0vaHM_VOfXTyW#(*j01PyuhzG9X;)sXNq` z3$GkBRm5I@AJ+Re+5Ug{ot;b$33x6GhCvT3V1(hox>h0dzf}L?U2?8 zdD5^mMB_w^Vrh-xF&`21cE;h(tmpVBAYgdwo1ja6+4SOkRw|c{9Jabc`jj!*CSjk35mNn*2( zyPe)C<_LLBq_&T@r`EXI)<%-&p`{lljkpAPh~bgRh$ z>+;lYg~W5)ytCtGTw_Pjfu>gjJaQn!bKU$DDE$67W-UO0@2 zJ;|jjjhnB)8QoZ(>2VdXx3y~(cmH?@=d&lUJ^!`*+Y?pNsE)nY_Pp1#yylAt!XAG+ zgh{1pQXN6w=zueoS$~V@W%Y&`)M=|Fbf|`(WzB3Md&L|Y)z5wOFgiVKO4{;@YB03Nc zuj|ftmNogsJrjp^KA(7U*e1OqHc9cc6wPg^)4s8`w|v1Q<0V{bXgJ*7TV+Y0d--#I zQ^jza`5fN({p=-UZv&>+P1LZ3@rNmc>5Ml8p-DqK2wqBiJKrZFlnI0zKMw8i0T%`L za33Y-ZriPYN%yERx^rd-{4I2|qtsy1r$eU;o$BeKgBGXsJ;YNitWCww*;JI5=f)?E zS+}<#$g)m0H|p$9T3FPP^z}b&>r0ac*R6auHT`_&3a@QiweN@H6BuY-d2MZ+wBE&$ zJ;z)TvKlEbr`dk(fl7-R4G>S+}1??u;CS3f(s)v+e_%Fv+BcfqA*q(#$e z>GZ1WXW~ltk8$&PksSSse#J`K7pJ+B8r2uC-LAGMG^dtsu7}x6oKA!tJY*aXpjy ztyy)V2TYNA@dHiYr(FYzwa~@ghr9OW)t|~lywg7u-g^HuN_!Uns3AEiHOlg@d;wx^ z@UBrS{HS$6u9z|LY1oPC`vt-Bd4J32g$P51Llg8PD)a}Dm9^6Q@{+zQen!x)iV+!{ zO)$62oa^q5qyks$DV{|hCEc{jgq<*51(#*2SD`_glex6|ql5ftlj#R)22b40DTieM zbG3>u3d`|InHu@f=ZT_k1W!rFm88Dn=^_sv2~>}&fpX48Oq{uR&r}?Jb%eM{|M;Vl z0$sXUGj=nb_mh6ct#AE+l(*}JGu4;QzY!bb!AE!c?3Xh#nO+jlZ->-ufgf}}Ihyb8zAyHP z)8h;0862atd{2kvi03-|)NT=H6Z~yQYcRUShWl;caUSCfOKRCAiSHXjD!=PQaAYS( z^XqT!iz5|1Z+REDxgauc>$7_!_T?9H#7~xfXgr(65nz5&y}WP!P;@2Z+t?tj)cZJI zyPssE`*`k)q*gL9f7@!hm6A*l?!eBXp&!pX95b2+Q6Jl)-oL`-Ip^W+=>Z+b;s-TpCX%I0{a4JXX5vArPA7gZm;yuVEso|kj7_Nd^@k&HUPfa)%s!!0R><6W zPUeWhGJ4FKd4{=Ft+up5$;l#j$O$|x_<2qt?)!Afx$t{)gsK;|3Bw@)1K-*yGuFP3 zLN!74)?Bj724ni*!2RLF;5!o(@TuI2_P<`_R*d^`toZZQ2&P%}=iP3M5@8an4BLpB z{bJ$7+W7^(dfp+yN=ixVEs%p^f2|yv@)>JYA%SSl7`)#-=4&!$oNld^H(K^;N7`aA z?>>ZHTO`6+S4xaG(=DK`(9+JyUbe3fx3atLBebeeQIAl$ny_zLu(xPRx=+4viuv4( z{>i!U#9j$o)NR-nA#(0Kc019Hxv$;B_c+G>uDP<6Y!xQ2VK=iGG~f{(clD8>U|ZX~ z0$6yWxmBN{c--zfvO8X70B^QI9We0?K_HbY^XD5F4pAvuVqX-@ z6dD5x1r^M!=jF{T5(*)tO&2fRd3ZsG84mK16MP-oegXK{=tU%_)OH8$0Qt@Y2vx~1 zKMTcZaa-@nyzxjv`*jb_Q@KYRs`?GD~KVe>vij0ZIp)^TSuGjcdJ zt7{0n;OY_AYs15Lx}x?~-<{wI>gtRvn&lc$1Ki3&K^)@-g8FQD?1n`BNO~baC zmt2s(T(P~hd=RcolSPYdY8(Zc&qI`#KabgYWDDL$bS%@mrsp+~$>;AG78{s37k2a8 z*6TANW90oPuctOQlC7x~tw&siqrWG4?oIii$8}wN;O@;kjboWB!MxixO*-`Kxs^ON z@4bJh?+$Z5XlM1dON*MWaMW-FcQH--y0yP3b}*;+%14ntK*(Uq zMe0I{STIymJLktz_05D!-{LQG715<|OA@a>rBeZ3>Z003d7QwCOmu_Cvvt zYfbk0*li`4is~Ami}5rfkch49yah4KfGqr~5VCaN3b^HG@L!!|cx~>@71_5T6pKVpOwF&-{ZD8#@ z)G%*DD@AoyW%+kD6 zYYK^7Wdhjg_B$hg#s^!EuOGW93C~^udv?oTs@t0_(SMV^(0|GYEal9qU$KG;ki}t0 zG%5g9hQgKA09jWC!&4p1DjcvtA`Ro|O2W~VsWhV8dITM#QSsh5Rz2*0ANEf{0s4EP zZ9T$uF|7Ea64!WK+s)6K!asw2X#^J#1c1UpkY5*|rmCu<3b+72F*pLn;+K5^lno4` zhGK=(zc2`t6;}Vk)DVAQa8)Ra$$!})A%9?NY4a~T6(oX1^M8(2L8AWj0fYTv2ZzD` zv_q=?iJ_1zDmQ#EXc$%o(bmeBR-`ioHdpMTg(a2BI{$xaF2)oW);a&GhtL@q8e@%J QRfvijNLpI|r~&Bz0I%iQ(f|Me literal 0 HcmV?d00001 diff --git a/lecture_10/lecture_10_files/lecture_10_3_0.svg b/lecture_10/lecture_10_files/lecture_10_3_0.svg new file mode 100644 index 0000000..62b5e17 --- /dev/null +++ b/lecture_10/lecture_10_files/lecture_10_3_0.svg @@ -0,0 +1,140 @@ + + +Gnuplot +Produced by GNUPLOT 5.0 patchlevel 3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + -4 + + + + + -2 + + + + + 0 + + + + + 2 + + + + + 4 + + + + + 6 + + + + + -6 + + + + + -4 + + + + + -2 + + + + + 0 + + + + + 2 + + + + + 4 + + + + + 6 + + + + + 8 + + + + + + + + + gnuplot_plot_1a + + + + + + gnuplot_plot_2a + + + + + + + + + + + + + \ No newline at end of file diff --git a/lecture_10/lecture_10_files/lecture_10_5_0.svg b/lecture_10/lecture_10_files/lecture_10_5_0.svg new file mode 100644 index 0000000..9d2a214 --- /dev/null +++ b/lecture_10/lecture_10_files/lecture_10_5_0.svg @@ -0,0 +1,377 @@ + + +Gnuplot +Produced by GNUPLOT 5.0 patchlevel 3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + -2 + + + + + + + + + + + -1.5 + + + + + + + + + + + -1 + + + + + + + + + + + -0.5 + + + + + + + + + + + 0 + + + + + + + + + + + 0.5 + + + + + + + + + + + 1 + + + + + + + + + + + 1.5 + + + + + + + + + + + 2 + + + + + + + + + + + -2 + + + + + + + + + + + -1.5 + + + + + + + + + + + -1 + + + + + + + + + + + -0.5 + + + + + + + + + + + 0 + + + + + + + + + + + 0.5 + + + + + + + + + + + 1 + + + + + + + + + + + 1.5 + + + + + + + + + + + 2 + + + + + + + + + + + -30 + + + + + + + + + + + + + -20 + + + + + + + + + + + + + -10 + + + + + + + + + + + + + 0 + + + + + + + + + + + + + 10 + + + + + + + + + + + + + 20 + + + + + + + + + + + + + 30 + + + + + + + gnuplot_plot_1a + + + + + + gnuplot_plot_2a + + + + gnuplot_plot_3a + + + + gnuplot_plot_4a + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/lecture_10/lecture_10_files/lecture_10_5_1.pdf b/lecture_10/lecture_10_files/lecture_10_5_1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4da25615b7fce4eb0d7858b8945223e8501f4a3f GIT binary patch literal 7156 zcma)B1zeMD*Y{BYK}94*j2o10#zyx@>6Q=%j1U+wHd;hv(nyF(NJytB4FVDp(kY{) z!Os-p>DjF>681nHDBRM?3Qi^|N#=?|!eNeN9*G%7?FeQt z#rT&u>y)(og`3`?0g;i0r?BDHkNi)CThpF7@0|uRd6k zD_TEVdb(Wwh3H`EOW__6a>tLfpDW9jbFz5r_M(u)@N zhqXa;-!FL|ZEbX(_dWRjb)(U~v!Hk7)uj2k*Hc|yr_II7pU^TsI9n&^uy zPr6MCw*h;zeqgL$^OZ-~)A^Ilw)1>@Ym?rF8xk2*iX>+tX(SXIyaS*;^{fsEL|taR zW~xD3`hvnG)eUcJ#o@LCi@}4owrsTvr|Yxwqn?%80@l6q!K75H7l)cDQ{yvpNlS@I z2QEnT%%RYRd7>U>Tq0l6h12+rqaLe^Jf*F0F_`4%zLFUJOnMP+M4~Ag0H{u-gs0K{)aLu)fPf2!(`2&awzMHfeh=CAwOTb1 zi>iLA!!=<UUMC+aaLSdgy<#JRfX4^WZqD zWlb*Yd+AC{8RDKvXRSZP*mJ~YWKuFyDnbV{zH%Cvu$#bDPSFH^Dd7H~rIY#+vPPAw z=9sIg{An!vy@GCOWn@LJj`T&N3#822u@#|`fveO^<_dQVb#l3cO4TB@S*B>h2h4&^ z9I2$2s4w5L4|MtKrfIIJ%9v$VS+4F~#Qg*oG|p8^?L|?JiQ|CZ)lv$onp4U8oJyHv zy*qa*lS?y8TKY11=rYcQIrpY8dvdPu?(9h;ZyJ6~ z7Fh8!8*ea^rartLl2-%Lat@Tbls|27YsKW*(K{+$K;XxXk2JnBkS?vG57bgb!_6xL zF=An-YXP=Nv2zBKIlZ`gr!%3GIUwJ6-^up;Q~cHdlSeP^BJ`w+&Q0WLC3|zOaR&I; zHacT&d?Y`D6g|0N$0{ZLFci%}&=#SlGZYkEb+)(f+ywWJ%bEey+t-N&QZ)u{Vg>0o zE+4GvhK6-r>=?RaIC`xGQ+fOTTsLfG+4l9o$mJ0Qwd~P>hU&bX9XCM@L?6cXP7Fhd zO5>cWSi4t*N~*2@$8a~EMHj=2(?!;0-KR#vGJU}~;dC{PomiptY23BD_Ijo_)VVnp zR%hI??_u+6W18;p3d-7vLYHdfiZVML8~FPyms9vVJ}gZD4=WtHk%V)#*zz=S4r%H* z`c%5`)%wMi_Fjju1UADly8G9-rnio$1oE@z(T0ZW z&zJ#AV|cL3*QQd(s+!ypIW^<1{Ep(;s!4sw(rFNrlcHvb}Mp2(thg=H5+H}$qaw|mF$fb_nO(`>cw1!%kA zqA{uQuDShK(_>pboXuf*LW)Au;@q2q3Oz+x%F^`woc1DTl_)XB(`&@VyKHFR5DoW?9;qH26ems(FF__p`&_h zD=D+2Whrb&CSS`&-m*4y=kqSRUpwW{RMfrS?QpY+m8Q5=Ph*@FifWYb<`ErOyxUbH z2Xx<_DSJZKHVj%UDD&)KW<_t1(@6D}jz;8HxdBIv5687)KAG8I@@*+%oY3NscyOt4 zKa!(yS0aA-DH&R!vRs}|gKzo(KIu+6V-R`x3Ea^P>{2G+aY5M9k zrzLq`|HSr2IHO}*Y4lSsjNZn+Qxfn{)!ifSOo<8xn}qAiEKhGZe0sQ1aJu!ldk?ZT zPBt<8<+0u%>t7ptM;+H^$^*(j2O-`ImRJqer3Sd{A{Sg*#;gwAoJ#lSHl#ZH&fX`3 zBdmV?-{Zd#Dg{D$K={NL2m*Wp`~(AnDDZb7aZ)L1qD+rtdoX}k*V7pe@M^+r z;3orX!jN!$Km5P_c-7!mb}(5d55O3&;sXQ)g#i!<0+^my%i+hwo4W#pI_PK7qlk1u zJO5)IKl?w?{$7XMYtX2+h1%WMCFI-HG`ogJhovb^{g$%SXl zEuHdYQNy(7wfWOanK$z2jG!N0H~ZZatdSe8v{!h)>$`g}@&o(ki~FwRQeyFt?~$*4 zK}|QK3{ ztcGE;GIi7HD!{er72wp_)M`1+VU%q{L}#hP9k8;(2nYein>DSMxdJ`=o;%5oCmCY^@5dVHT-p>4oJbC0ukDXXqrQ(3N%TtNm#b z2EO~R9)#))+E7nFe6%mcRxKj;eqvAdEQ%ZW9LG*U&p$kS_9AVsf`N;@1F0+Z>~(`7 z*VlCmv~`7iQr0Lo+P78uNy&&9&s7tKGkUL;YJmAV&XDg3#@o5fYY0f;$fQNh$)C{g$SfM_+HneJ1+`%uiV_diVNs%e@n(1 zz&)!H;;!k{9GU8AmmgL$H!B5vwKj)-4N7U%HpSr@Tj<0+mV*txJlGwK^H#BP4;{I| zkmn_JB>P|vi4N-$85=+e+n?JS$d1_f?0QeWANaK09CzA{%<$^6G3BjSZ|$6$vu+D4 zEv5R9PkrsYOdsD_wBWT2kz>FyCdkCmr&gC$+I{A!bz7-oWYYT*&XB7C{Y0Ou^UC@w zb)`v5(3oGYHiPb~X=)12j~s8o0jWv+dyQA#We+6K*f1>-pC_VJ{mZ67@|HRFW$)zJ zbeR=YG^TGlQR!ylw6$g!PW#GG#*aG+PT5b!X3;3kz{LU4-W>NhPxQa|~LvINt&46WgE$u6vQ*TwMslCA`f z{31$o?%U9WGuq~+=|#|}e(F?Xi!j%Z1-*&1L(WEqvUa`T4d~Mr+L4SGRV?2;UYd9$ z;IcgOlE@r;V7-E2nVR$x3hj1Oaa2vtSDBtz=D*}wEgrLZb&KO;zXi?Ec}}MerKkuK zhO9#F{^v;~F?|7_bjHWC5RzQuM|8c|WN&FA=tq}k@{taH?6nAGmhjirHLK8wR!tp% zTg==^X;ff4BN2LMh|k97IS3M69H7Gtkzj6Fl6^?)#6LXlf%8XyMB|p0 zbRKl-T)l7aww#^g*fW91&$Az^Of7VYSehL9{Kb21r@6dXRQ-(N71GZ87=C^YB;5fjTUND(!0 zY1OX`mXFL-)J)cm9wRTmZx-ogi*G^{J~H09{n@=q?4f0Pmpj!={~o%uEVR-;9MHC-2W8B3xK&EPKEkv2W5bRO#0^-VI;C^GvMLW^%D8C5 zkhV~IgY=6|6nAyw&egSdgSxVvnUI*q#J0Qu@iMb(bP}1@sZ&6E2fEp5YcwDYZ2Q>#P;tIJH@P;hSt--G!EEcl8w1$`Dz@3c^e-DYV=#?&XW z1nmsBD#;b(4A}AXDQy|GX}xPA3{y2D;hk`37wc&`18r&WyaBazRc z1tXsaf|XHXdbpZpd!*)K_i_;SHrm!-p(0GbQ)2Kl?$uqKR~DCqchj+!=@aar3dpE{ z)70_I8Ia1pQ*OSVsPR;U?cjJE-4E><%<|=rAQjUBAy$nl@X~CEvO|LDr#Fn@oes(3 z>|?Y>C3;o+@kYJ4`0@{>ZNtw*d}H_@`am!m(gn+yLlOC|wPy9h5Mspu*S+#DYj+O6 zVRwCxOJ2Tfb)^>dtfjwPn?RSV`})e@uCKGTDwg};_!(PQkID+u{w%OrY|;bizw5hd zonx6}Lt5%sJNS_D{P9d^q)%Y0xJyz0!FHEnxf>cjnY4lTCSsS-a8#E<$6I@#=P z5AH|FUI}GGV$O1miyt0VZP;A;ez+$}Y{qV4uy;wQHmsh`*Ti)Omsvflhq)&uxtqos z)a}2gI~B80p&cZ}?z3D!cc*v`F2&>0a;Mm3BTZ}5g5qX)0}`VX;&LCk)D@*_2OVK# zg~<)OmZ;M2Q^{3xQ^>Vbq0nQ;<;m<`lb2(80v=UO<94^F1f&ev zFDmYh6pQJxoy4#mDouIT=}EqsET0Y(UkvmWFTbTA>CWKRWbRFIadZU!xS{Mjva;a% z=n!s4%DMeJa=?4%X2n}QSo?ewGPGenYPd;IXdDyXt8gbDcl_TMLWSlhmP3DzE?XTBM8v1}- ze-DlzW*IJh!}N7tGL6g`QcQ~@W^)7Up$d}$-+*Um!)pCCU`Y+P$Xr{}n1TYi*$h0C zrerYh`q=K$LhYz;C@Do>^59dP^1ZkJL-tvdWf|Y>GPDC}ZmpG=n8SDL>Mpx#-RH=D znpH5LTIx&V5Soz8tMAyzb#w}lxsTZO$I{ljeO13%MmLNbmAw}WYH%CVyYQw#ihay8 z&~)PKhwD_9bJyKe6U}3(YR^izQZ?u34$Eec z8|y_XagFu1YPagP2FZ(Vsg^g+HBJJ3FJ(7zAFE@Y0nz89npC1?UtfAWtn-+f z(nC|0a+>BEnG2cQs<}ZCzkxAh*!`yO6lvzAx0UkzG2X_M6a^G;K%3FOTAuCYb-w)+ z*R(Eric4j(8|)5B+zbt;*n=Qb#&voZjuqLqcZt^x?%*E&<#+BO`cI5TfDOMe8i)@p z@EbOX{0T7l37F{r$M%{=wILb-iYII0AFuVxopp<0i;c|SsM+h0M<1NJLQIlF9I#RE zWcHjb*6UR5UEi1Viy05U76eO6`Ny15=xNUN3pIWWz2YM9T#%dX)=Vcybs~mUFgVaL zSa?@otU;uwo7%);*nBsCEa=kNQ;Xi3SHfPI?>?ZljZ$9tO?#(F#PEqTSzb(y>$ACqz|1~xfPPZg-d zg=IWmZz*#Yr4))yXyP8a*73t~=O(E56W3PGCi_Uw~H`1#_^oltI`yzyZD!KN(j`0$>&q5IzwJ z^CQUI0wC~-LJsDv1h=!X#bauGHzz6`6x>lC5dP^;5R`rkgyrCoDqH{{fZ2b7TLO^( zGa5g;LtCIuK)fyZ^>O{9|*+7f@# z^Z$4I4;RD#&m*Ltc`gUTXPJ}DNi{>x582%jzg*5Pl#f9W6)zCXr*2!Ze!_1hPPgyHWa + +Gnuplot +Produced by GNUPLOT 5.0 patchlevel 3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + -2 + + + + + + + + + -1.5 + + + + + + + + + -1 + + + + + + + + + -0.5 + + + + + + + + + 0 + + + + + + + + + 0.5 + + + + + + + + + 1 + + + + + + + + + 1.5 + + + + + + + + + 2 + + + + + + + + + -2 + + + + + + + + + -1.5 + + + + + + + + + -1 + + + + + + + + + -0.5 + + + + + + + + + 0 + + + + + + + + + 0.5 + + + + + + + + + 1 + + + + + + + + + 1.5 + + + + + + + + + 2 + + + + + + + -6 + + + + + + + + + -4 + + + + + + + + + -2 + + + + + + + + + 0 + + + + + + + + + 2 + + + + + + + + + 4 + + + + + + + + + 6 + + + + + + + + + 8 + + + + + + + gnuplot_plot_1a + + + + + + gnuplot_plot_2a + + + + gnuplot_plot_3a + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/lecture_10/nohup.out b/lecture_10/nohup.out new file mode 100644 index 0000000..e69de29 diff --git a/lecture_10/octave-workspace b/lecture_10/octave-workspace new file mode 100644 index 0000000000000000000000000000000000000000..ba49ea896777448b51b05e3e4675e347be091b2f GIT binary patch literal 86061 zcmeHQYdBR~+g@#dJUA}R*ubY2 z76x7Q`|TkQ`veID`vmha!T@3V$gM|4E|?s(FE8i4elsX>L--FwuuqUY@ct*}fntEL zD+rtRt7Ho~n0HX5$tD%T1}yaT#7R7!Ab}8ACrBrP&O`gY!X?I;MdbNIRp}WO?Ol( zYVfT;yaW3L3538pK{^q19tODiTIKs|$)KW^e-)d&2CF(_1vkxB>=PsmLeTYrx1VBw z$T%@e=8Ss=IZ#|xZ@QoXG?g>g(zfHR(6o=a$PYE)*ms@_GZhuuqUc2&@yN6G7*p z$2CDTUb&tObG)<9;lv|o?6ACYZec$52@(b&==#9hPccBqx@@%9(tJgpT70*O(_a9+ z+VR3ezE81FkU$8m6QmPC=V5!tb@`lSWn@f`%Gn#sLty!mW&NAN@%0ly*9G4GfB$`$ zAPP}^AL_}9BkQkvZ*PYca;0H&jb7pL1PO(}dii&~2r3^bks`dS9~wy^m9njNd- z(cfPkK32Pv^b)hwFsv^CSE4XxqggW^PmnMOLDvV~eu@Disb^tHuR#IXT1ehDQ{;lV zN0Q+oXMBGb)(6rD<^l0AxL@S=&%Zn-bzjewK4X{%b>WtWi)*^^c!C5%V4WbH2s#fR zc?%|mpL|6+%bYnTW8MNeQucl}3;5V4NEn2m>jQ5;#Q>3^oFn#rTqb#6E3M<2ay_J~ zUaCH{7C#@4^?~$(c|bgT5f=`h*55&T>wcW>AejswbzWYMku1RD2@(i_b%Jyv=se6@ z&Ry8pRZiY~U^}rizZq6(@5q*{Xu&=~!XN})A9(vI28gCX1IWYl6$Yu-X0Xx$Z=qxPT%`veJt5OjUu?WY(Z zUYFN=4o+wwGcGJTCt=D1iO}d4?go7Q1nUFo1M`4*xEA#+w_LY@G}RBk={vszWQ}84 ze(fjlc!C5%V4WbH2s#gs?L~}EXOxn)dQoxL=43%=vYc6G2Y#MW&~<^g|KEQfX6o+w zpm@2HeC?#tdh9qCoMvd(=PsqtP{+`2m{2{Aim=+Jx5Zd*1LMi^;r0#ujC{yjQ6{cJn-)*=7C~>h*c4( zymz;r>~#x~_kR8iA|L%> zdc5C-1VUh)Ae{(057MO99-B!SWRgk8)>z>Opa!xzA15VYpCDlng02s|{S*U4>XQlO;B(hd~*51H-Js^Bftoz;EPQ2fR2>OdBhA)g10|Lj31XpLR zvrH+eU&#A9w7(ldRFe~H-sAbSupb1|58vze7`f3QQwRLX03Rjs&J;e3;q_hGFdkn& z`5s@mTrmBUzeQ|wY)B=k^!!thbwv~O-|6prJPJRjh5aCye)wL$OD#(Gd&%dKTH*Rh z8993(%lp&U;3L`i_yiF~e2+I=PB9=b{5)5^HF5nxK6y}qTU+Z_0^-oOqk1jQ2Z?}Piy?{^_15ZDib<%jR}_t{+*-A&7@$i(zF>Ib+jP+q1!QylJKpCH1B@9~Dq zDFy_FpAw^;mFt6&$Tis#t7av3f{ID+php$Heu8}wtYASU&hse^0nM zdZyKTJ{j+`CSaynI>=;vmY5^ij*m|eam0`K!}Syc|9GAXH}h=9@8poCInrE7-!@p3 z@|C+O9na5*^)DFu|GWL%>nro8+tdoO<(%g#X@dwj>93+#F})m*Cx}4e@A8P-Q4IWJ z`4Ul^A@)wVhkV`Zu9*_o0-JWR`=r|Nc!G8R&({5a+rOy_=B$$P64EzNC;k1s0#M8t zny%r5^9%pCJmU8MY+tE*r(Tge@`9Yyx9skY$Sw#=)5&?>@C5I7A>k8P|Nm_L|K0w* zBI|DuX#1AjZXTpNYhf$&D-=uEhT^IIJJP zWyfVao*)Ad*aw2)gCF(to}uHZI)SC+%I?&uGY&lhgRKvhqwDZ-{Ev9U^@8P}?H4Mw zC4(DDBS(+Q^YI<9AxC$y-5f7Go**L-*bjo`hwt@w(BAAj%Nkm|Iz zX8vBB=MMWpF#YhoeiypOa_!sPO0GHC`|X`$3QW4I|J6tZ=Oy|cU$|T_{S!Y*KHjuC zkL>8SJpc28Mo3&jl+GW6^Q~Y%2&Nyt*Y7ITrP34XTgZtot+Hy=%VAy6#I!~+e7@^@ zeBpAz^v^WcvFCPes3vbnuRFfks2+SQIA$kx@bmH54}$53@AdnZeW!d@e#|AkH|;*s z8c++<&d&IG>#lfwz6%jXe2+I=PB9=b{6u<+&tGui4!O0o^Zqj3R!BAW+8geV=Rd(d z5G)`3sK4tjxkuj{Y$db5p8wh*Q3r|Yna}rWaPfG8h$DW)AFihu_{Z}kvG9GpwMj5J zu+er)y-ySTnmO?4u^rC0g7q&L`v1HA{L!I1FjFy%{8K?na-1m-WS)+yf;60O;!@S}cCtu^eBbL}K2q_hrA zxXFiuft=K@E=AZUh&bX${NZ|vfqy(tdN*Y`7Y;U)k3UCQ?y)`w$BH#|tZT4Ou>J)@ z|9`iiozHAt_4pu& z_VKxIIpDbRuy*Uk9_$k&{C{k}qs{x@`O$GqG4S2~zGEW%XSpUOi*}myK*l}`b`(vwAAzVg`Vedsy+FGwsRKt3HHed0|cT0<7^Y& zkdJF4Nj{b~*yURTUKeCy4=jCweS!pnb%J>qVSvcDk%`Ee!zE`F5iMH|mqGi*Kb}eq zzQI1h`k?fIXu#u1=Ji`o*DvOi=3-eL(T&ZZv+ZP=%@ynutPhF-0`q`)aBS~4zZ=>? z>fDmOvE8H|_Ia^a++SLP#}gzFtP{+`2m?ggFCmA<3N?|P-(=ISYb3zFnP1*}KCi+) z!TO-|foQ<{T`D=L(n-QE$syCv*K;ORL4HZV;UTjM>=W!0?34dxW7(ktTCTQsx|CBn>w8f+xx~%xu%Zu++lqnePA9C4-dzd7p~)UlJQCAaoY7S zfIoUmjN5AL6RZ#HlVJu3Mh8|l$K%po@X6x^X0CQoZ(((n=j*E*@bL-54@QasLeP1L zuba7hSvHTHz0tNXbaWdOe2lnw^H+SGQP6dPx1VBwV0bW?ocW8|*9>yjhYe4xlS*N{ z;pZjF(l~D_!w*J^0YcDu5V28SW?5cH8r?SBKWSzge7JFB`cDeE_`EO@hQRAX(EY(| zf1)9~DfmVsX|ad3@_br47>ae}1)NO6KEXa2VSqq1U_51MGEY6>0jZ!gU!-2<1qclj zW4CiJMbFUaVX$}HvE$p&(9o#i|9={OjURsLj}*>z+~MfzxYONWxPZkP8aw>9ch9E1 z?rttSotOniR`NKH!%+u-Da`P*c|it;Q*2WOpSL4DL#-)eV5?(Jl(X{3qbuTk~}P%QCn%=TYUw z#C8zvc%87ot_S8#RSCYos|0#CcXAr1J_Vnx$LijvSHX*gm!lhMTcJd1$+U;lNbtEf zsKi}a1eX(Qj>casfTA}OwzhOPf|lE6%VL#OIJ9Y!!q#JjkhLyYGNZ8*8r$V;$C@-j z=)8HG1|Bzqb!_vQft~~ip40VZOJ_A?HJq;X>Pm;t5i7?Ze^&`Qz9FiY_cTGE#WUlb zcGbYOPI{8GuLSH$+BU}bmcl_Y=tQtgC1focxOqFb02WF()?7AhgU#<_PAN~~ffUc} z>63#^Fc|S?U66epnBNF4&ueUgjeYF5N1xy~nU(n-9q@LSx8mKbG8hBi+q(HpV9_n1IWIOBo_@(HD=N+fwTlP*W!aD6^YJco zwWJadsYo60?r4VdCb{-uNqji_!HTaRmJD47T=gG3Y6X*!`S^?4Pb|R=7%4^q_q!{oa?ArvHl~+5U zaKN_PFZ30hwW)Bw^Of}+obTrjW{q(PX5caElWT->5SlD!*4fboPBXOb6Wm7F*R7YW^|lEjDuhSNdo_T) zGdpomp$Gh~xI7_K{o#wgl9RY_14KUlsdbxX3v|Af*?q&e9@IcK=i{U#uxN{@c2X*U zoxRbCJG`Uq!KEdO2*`#qN`8YX-%Pq3Iedc3G^!zOW20CFf+L` zGgUJ)@iH@wGBYVMGsQ78VKFoPFf*AjGc_=o=$TC0OeSF_Q!0}QlF4+(Wb$G%6)~Au zm`oGQll07!!pxJ9%#&WslPt`g`plik%$=6Zon*|NGR&O-%#}{&N)B_TnmH54oM~W= zq?kQLxN+iq&<>Yw%0XKxlYDOsDpqu_(6s3S^Xv<8Gd1hr;J7qn1D{$LwJ$H{y?!$c z<{cDivPp&WhpN&uD%v6S#@9{DUkyJEEp*9fbPE@p)WWYw4UYjqMJ@j-HhB#L#Z~pD z3mTxgCf)Od0w4Tl``mK5#f31(JNq0?Jc3h;?>2Gz3m~RP21$ z-p`-G{jVWY{uuKHl1w_b#tJ`xTsJcvBl!|2X^YW_ttf(8@mYHV@AZIwA@A$Z{%#2H zQ4;S=;e*oiPeIldO`sL7pOlfa2M#K5Yis>VAooI~u?D9D0{chppY6~DiRo|D4{%#x zO}50US&5wx<14g?NbZE7jBpEUt9&CWz z7Vr(!Nq>K@04DVCRf%3gzpx9j7Q~05j)1Gp98(XD>4+DKqCHGp8Ig zXBIOj5HsfqGp7TSv!2Px&EypBbl6dOwKPRrxBC0g~>_5Jaf-HQ_MUw$vhMG z*E28lJ^jo*%gjBQ%spq!JvGcd1I#s1=9&+4PMbMr$DEU3j=7k9%8@b1>Hl?*irt5V zg3>5()6tVCjvpR%AG!6&$OVI4LD;lkC0n3cRH`5&hp&n8qMR->~G{Wh-D%T7=o1wqII()2lCnWVOEa^2UfWiGDzkmMa zF?{4Lm=u2U6=W#qh`k?|317s8!>9Fkz`W($g^gY1P`5F0o@f0V;GKNpbZ7fpcwJue zIXIyKu0=h|E!S;;$Mzydr!z`nrtY2(ikCZ~tT{-=Q>_(ZqO^{(g?fN5njjYy(G63R zeU2ts)x*{xzT+-EM~GDssl0c0c+3fvj?~|k0Mew_9-B!S5IaLAYJyA?f zX)ETev|f`05?r0N&N8JCBR4u^>VQAwZxP!Z8&U~Ui_-mG@_F!F_147o2l)`Gd_5_n zCLhT8r>>dWmcrRx7TrzDtDwYaXXW~!B)IhKtXr=v4-5|#d+2R$hY2@F&$N2ahr-P~ zoAEn2(CaJnr`yyD5K)^U_D;A5QWeZuCFLcc>YaK;?#K(cBI|DuX!{oWb=9BM>??&m zL&sBf0!x9O6&~nWuYsP`7wB0_fu5BS=vn80o>dFzS%ZL{6$R*7AArtk4|LXUptBMK zoplxHtdc-y%>z0s7|>adfX?aybk+)>pUMaNsbip@ss#F}F`%D{0s5|gpzmr1`mRl& z?@9yut{b55DggSbDbQDifIjOD^jSTi&sqR|R0fo3hTldUwDW%*wAbElhn?HVankVL zdiKasmiwkU@nl!D%CTz@T5m-t>r5fB)*hjb11k4N^@O_oAJLkD++yaSDmi-V`c^o}iEwa}w3BqVdl& zR2<5`K;gTS7bzqP{VBYth45X%6;$4Z@ZASg&Y5(RDretD7?*XOidh~vD2y{h*wz$A z#dA`^QTu=h3Z2J9QW*N~4vH;MJH=oWO9`R&oNiS9P6x$Bj}XSmpyfHa2=!J*QR}%F zcaOp`R`)5CQ9$LyfoSwOrVl7&t&XMeTKhu^*`|*u?0b$dCm@lEP0l|? z80jYzvQH;am==NRZ>FF)ZdV#r?qHBiVFC}uMUX^RKb&%@*#A=&AQM?G{h^77 zn-0`MEDu1)GDUcOHNvIK5sv>IVX`4Y7L7}dQ0%o7;Tt-RUxs2;dikX*QQT%imzyDc zWQp)TjR!1HEcOS&pVlD!VvbOOE@$fX=~#6gs&BMG_;o!(_6CIIbp1116rZKrdC~Ey zji}s}j%_xhICm3;#Psb5_tN+p)e|LjyXjj{`>A#aU()qQP)wB3D23V)H|^2--00=j zpqO=p#-CBY5PfvJGjuHHh}JJm|A<8+BvR?P5B;dIUeP~py6F3|+_$06`*|l?zJl)e z<6BYrSGxUS7gRq)f6giNqsZ#rh1x~ZpJPp9CaNbU(97>bpTo+dFKG-lK5n~&PFS0Uu= zpqEdiaWq0gpRONX|Hx?L@&7uAE0RI5&JUj#S*4`DeBU`Zo?TEB!EJ?2K{G?IrgXxd zi>lY2`wx&SUWr6~DQSRZNsCUhzO;b$%PG6x84iG7!`ge=Nfodo>0f_@M~~us{iRM) z{OM@+#{|c9@0aJ1FZTTL;7LpcnUP%)TJo$5bX3+BFW~e-=k(+y&XeAf>*S6*Pta_D zIn~lZmceZL_&MD(TWT(3KAMctVJn!2%YoAm|pYM75_YJ*3j9c_f+_9G&+L=9} zU#J&6e~wfV^{Rr^r)S9@>v#qAOD3xNcMcz&Z?iin8Wsf?2A?aBS#ldTC#C*sr(Oq_ zOIO*|8pM;a5AUr=VHJ>F!Eab(OfSqbIw*fsJcpbYd9^ht`ylE1yH@6I<9;}~Z0G(> zhsr@?wtn>ez8+E|cDCN}DJ-^5vgU>P4u8U>P4(PwN4p>}D9Fdu=LJmIFl(Ff%@!Cq zI&k)MOgXrCoMzv)9)Lxjzb(C?_7kT){*J{8|5o@CZMR+aQ455uy5MTo#wFA9H{EWk z>xPAmF9M`hIgq6yudX`0M{4jn!Kd?cH`x*-KDJw;5m-{y{GUzwU{~Q6(+xil?@?Y2 z`^e^1kYZY)Qmce^fcxr*-Fw%LWh*ZW+5h1}9T_kv^Zd`DHsIK?igSF6VIU|{(PcJ^ zEjbvncfrdza{LBw#V4KO?C88LWUQq!2TthDP&8t*)4%kF*=%3T;SW}rerwg_@T@Hx zE-&4}Cc9Hz$4IW_Y`OIN<`*07IHH=TY8I?G$@Z?9tMKg`hjXyj@7&a<&)FRkuji|h zd7RnXF9oC|yk$eO_bpMELQY;N``pn3D>*M$Yzv(6D4Bi8{HGPaH5+qwA8VMYw0IBa zQIh#K(b;R+EUjo(U6d|oT;A!x-`sRL%bxX>Dy~}0Zhth*qsVd+XJcxGzNeTxr)K7@ z7xOce*<*vu(+nT~#xA%l{5-&CE9Z&jf{5QuW^p#hItSnLaAjMLEpv<*TFWVUSY=bw x?#zi)D_prPZ3nwJXTs_|Yff`+ja4Z>{b>ukH0Mfg;J(#t!#Mr0%wiAD{{UU+ll1@q literal 0 HcmV?d00001 From 07507daa4fd622207b94aa55bcdf52370e0824ec Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Tue, 21 Feb 2017 11:47:09 -0500 Subject: [PATCH 03/16] update lecture 10 --- lecture_10/lecture_10.aux | 14 +- lecture_10/lecture_10.ipynb | 497 +++++++++++++----- lecture_10/lecture_10.log | 83 ++- lecture_10/lecture_10.pdf | Bin 162693 -> 190161 bytes lecture_10/lecture_10.tex | 199 ++++--- .../lecture_10_files/lecture_10_29_0.pdf | Bin 0 -> 10972 bytes .../lecture_10_files/lecture_10_29_0.svg | 148 ++++++ .../lecture_10_files/lecture_10_6_0.pdf | Bin 0 -> 30054 bytes .../lecture_10_files/lecture_10_6_0.svg | 397 ++++++++++++++ lecture_10/octave-workspace | Bin 86061 -> 134485 bytes 10 files changed, 1093 insertions(+), 245 deletions(-) create mode 100644 lecture_10/lecture_10_files/lecture_10_29_0.pdf create mode 100644 lecture_10/lecture_10_files/lecture_10_29_0.svg create mode 100644 lecture_10/lecture_10_files/lecture_10_6_0.pdf create mode 100644 lecture_10/lecture_10_files/lecture_10_6_0.svg diff --git a/lecture_10/lecture_10.aux b/lecture_10/lecture_10.aux index 14a6f0d..d8d4c62 100644 --- a/lecture_10/lecture_10.aux +++ b/lecture_10/lecture_10.aux @@ -28,13 +28,13 @@ \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Springs-masses\relax }}{4}{figure.caption.1}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Automate Gauss Elimination}{6}{subsection.1.2}} \newlabel{automate-gauss-elimination}{{1.2}{6}{Automate Gauss Elimination}{subsection.1.2}{}} -\@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Problem (Diagonal element is zero)}{6}{subsection.1.3}} -\newlabel{problem-diagonal-element-is-zero}{{1.3}{6}{Problem (Diagonal element is zero)}{subsection.1.3}{}} -\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.3.1}Spring-Mass System again}{8}{subsubsection.1.3.1}} -\newlabel{spring-mass-system-again}{{1.3.1}{8}{Spring-Mass System again}{subsubsection.1.3.1}{}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Problem (Diagonal element is zero)}{7}{subsection.1.3}} +\newlabel{problem-diagonal-element-is-zero}{{1.3}{7}{Problem (Diagonal element is zero)}{subsection.1.3}{}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.3.1}Spring-Mass System again}{9}{subsubsection.1.3.1}} +\newlabel{spring-mass-system-again}{{1.3.1}{9}{Spring-Mass System again}{subsubsection.1.3.1}{}} \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Springs-masses\relax }}{9}{figure.caption.2}} -\@writefile{toc}{\contentsline {subsection}{\numberline {1.4}Tridiagonal matrix}{9}{subsection.1.4}} -\newlabel{tridiagonal-matrix}{{1.4}{9}{Tridiagonal matrix}{subsection.1.4}{}} \gdef \LT@i {\LT@entry - {2}{67.64778pt}\LT@entry + {2}{61.69104pt}\LT@entry {1}{261.39424pt}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.4}Tridiagonal matrix}{10}{subsection.1.4}} +\newlabel{tridiagonal-matrix}{{1.4}{10}{Tridiagonal matrix}{subsection.1.4}{}} diff --git a/lecture_10/lecture_10.ipynb b/lecture_10/lecture_10.ipynb index 78e529d..46d4f00 100644 --- a/lecture_10/lecture_10.ipynb +++ b/lecture_10/lecture_10.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 14, + "execution_count": 1, "metadata": { "collapsed": true }, @@ -13,7 +13,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 2, "metadata": { "collapsed": true }, @@ -58,7 +58,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 3, "metadata": { "collapsed": false }, @@ -223,6 +223,30 @@ "plot(x11,x21,x21,x22)" ] }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 0.40000\n", + " 0.20000\n", + "\n" + ] + } + ], + "source": [ + "A=[1,3;2,1]; y=[1;1];\n", + "A\\y % matlab's Ax=y solution for x" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -251,20 +275,11 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "error: 'X22' undefined near line 1 column 16\n", - "error: 'X13' undefined near line 1 column 14\n", - "error: evaluating argument list element number 3\n" - ] - }, { "data": { "image/svg+xml": [ @@ -312,282 +327,357 @@ "\n", "\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\n", + "\t\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t-2\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t-1.5\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t-1\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t-0.5\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t0\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t0.5\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t1\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t1.5\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t2\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t-2\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t-1.5\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t-1\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t-0.5\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t0\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t0.5\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t1\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t1.5\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t2\n", "\t\n", "\n", "\n", "\n", + "\n", + "\t\n", + "\n", + "\t\n", "\n", - "\t\t\n", - "\t\t-6\n", + "\t\t\n", + "\t\t-30\n", "\t\n", "\n", "\n", "\n", "\n", - "\t\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", "\n", - "\t\t\n", - "\t\t-4\n", + "\t\t\n", + "\t\t-20\n", "\t\n", "\n", "\n", "\n", "\n", - "\t\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", "\n", - "\t\t\n", - "\t\t-2\n", + "\t\t\n", + "\t\t-10\n", "\t\n", "\n", "\n", "\n", "\n", - "\t\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t0\n", "\t\n", "\n", "\n", "\n", "\n", - "\t\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", "\n", - "\t\t\n", - "\t\t2\n", + "\t\t\n", + "\t\t10\n", "\t\n", "\n", "\n", "\n", "\n", - "\t\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", "\n", - "\t\t\n", - "\t\t4\n", + "\t\t\n", + "\t\t20\n", "\t\n", "\n", "\n", "\n", "\n", - "\t\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", "\n", - "\t\t\n", - "\t\t6\n", + "\t\t\n", + "\t\t30\n", "\t\n", "\n", "\n", "\n", "\n", - "\t\n", - "\n", - "\t\t\n", - "\t\t8\n", + "\t\t\n", + "\t\tx3\n", "\t\n", "\n", "\n", "\n", - "\n", - "\t\n", "\tgnuplot_plot_1a\n", - "\n", + "\n", "\n", "\n", - "\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n", + "\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n", "\t\n", "\tgnuplot_plot_2a\n", "\n", - "\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n", + "\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n", "\t\n", "\tgnuplot_plot_3a\n", - "\n", + "\n", + "\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n", + "\t\n", + "\tgnuplot_plot_4a\n", + "\n", "\n", "\n", - "\t\n", + "\t\n", "\n", "\t\n", "\n", "\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\n", + "\t\n", "\n", - "\t\n", + "\t\t\n", + "\t\tx1\n", + "\t\n", + "\n", "\n", - "\t\n", + "\t\n", + "\t\tx2\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\tx3\n", + "\t\n", + "\n", "\n", - "\t\n", + "\n", "\n", "" ], @@ -600,18 +690,19 @@ } ], "source": [ - "x11=linspace(-2,2,5);\n", - "x12=linspace(-2,2,5);\n", + "N=25;\n", + "x11=linspace(-2,2,N);\n", + "x12=linspace(-2,2,N);\n", "[X11,X12]=meshgrid(x11,x12);\n", - "X13=1-10*X11-2*X22;\n", + "X13=1-10*X11-2*X12;\n", "\n", - "x21=linspace(-2,2,5);\n", - "x22=linspace(-2,2,5);\n", + "x21=linspace(-2,2,N);\n", + "x22=linspace(-2,2,N);\n", "[X21,X22]=meshgrid(x21,x22);\n", "X23=1-2*X11-X22;\n", "\n", - "x31=linspace(-2,2,5);\n", - "x32=linspace(-2,2,5);\n", + "x31=linspace(-2,2,N);\n", + "x32=linspace(-2,2,N);\n", "[X31,X32]=meshgrid(x31,x32);\n", "X33=1/10*(1-X31-2*X32);\n", "\n", @@ -621,7 +712,10 @@ "mesh(X31,X32,X33)\n", "x=[10,2, 1;2,1, 1; 1, 2, 10]\\[1;1;1];\n", "plot3(x(1),x(2),x(3),'o')\n", - "view(45,45)" + "xlabel('x1')\n", + "ylabel('x2')\n", + "zlabel('x3')\n", + "view(10,45)" ] }, { @@ -676,7 +770,7 @@ "\n", "then, $3/5x_{2}+4/5(-1/5)=1$ so $x_{2}=\\frac{8}{5}$\n", "\n", - "finally, $10x_{1}+2(8/5)" + "finally, $10x_{1}+2(8/5)+1(-\\frac{1}{5})=1$" ] }, { @@ -720,7 +814,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 10, "metadata": { "collapsed": false }, @@ -759,7 +853,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 11, "metadata": { "collapsed": false }, @@ -785,7 +879,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 12, "metadata": { "collapsed": false }, @@ -811,7 +905,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 13, "metadata": { "collapsed": false }, @@ -836,7 +930,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 14, "metadata": { "collapsed": false }, @@ -862,7 +956,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 15, "metadata": { "collapsed": false }, @@ -898,7 +992,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 16, "metadata": { "collapsed": false }, @@ -962,7 +1056,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 17, "metadata": { "collapsed": false }, @@ -1000,7 +1094,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 32, "metadata": { "collapsed": false }, @@ -1031,7 +1125,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 33, "metadata": { "collapsed": false }, @@ -1062,7 +1156,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 34, "metadata": { "collapsed": false }, @@ -1096,6 +1190,28 @@ "format short" ] }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans = -3.0000\n", + "ans = 3.0000\n" + ] + } + ], + "source": [ + "% determinant is (-1)^(number_of_pivots)*diagonal_elements\n", + "det(Ab)\n", + "Aug(1,1)*Aug(2,2)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -1138,7 +1254,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 24, "metadata": { "collapsed": false }, @@ -1211,13 +1327,13 @@ "\n", "|method |Number of Floating point operations for n$\\times$n-matrix|\n", "|----------------|---------|\n", - "| Naive Gauss | n-cubed |\n", + "| Gauss | n-cubed |\n", "| Tridiagonal | n |" ] }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 25, "metadata": { "collapsed": false }, @@ -1229,6 +1345,13 @@ "ans =\n", "\n", " 9.8100 27.4680 61.8030 101.0430\n", + "\n", + "ans =\n", + "\n", + " 9.8100\n", + " 27.4680\n", + " 61.8030\n", + " 101.0430\n", "\n" ] } @@ -1237,12 +1360,13 @@ "e=[0;-5;-2;-1];\n", "g=[-5;-2;-1;0];\n", "f=[15;7;3;1];\n", - "Tridiag(e,f,g,y)\n" + "Tridiag(e,f,g,y)\n", + "K\\y\n" ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 26, "metadata": { "collapsed": true }, @@ -1265,7 +1389,7 @@ " x = GaussPivot(A,b);\n", " t_GE(n) = toc;\n", " tic;\n", - " x = GaussPivot(Atd,b);\n", + " x = A\\b;\n", " t_GE_tridiag(n) = toc;\n", " tic;\n", " x = Tridiag(e,f,g,b);\n", @@ -1275,7 +1399,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 28, "metadata": { "collapsed": false }, @@ -1329,26 +1453,31 @@ "\n", "\n", "\t\t\n", + "\t\t10-5\n", + "\t\n", + "\n", + "\n", + "\t\t\n", "\t\t10-4\n", "\t\n", "\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t10-3\n", "\t\n", "\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t10-2\n", "\t\n", "\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t10-1\n", "\t\n", "\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t100\n", "\t\n", "\n", @@ -1358,21 +1487,16 @@ "\t\n", "\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t101\n", "\t\n", "\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t102\n", "\t\n", "\n", "\n", - "\t\t\n", - "\t\t103\n", - "\t\n", - "\n", - "\n", "\n", "\n", "\t\n", @@ -1388,19 +1512,38 @@ "\n", "\n", "\n", - "\tgnuplot_plot_1a\n", - "\n", + "\n", + "\n", + "\n", + "\t\n", + "\tGauss elim\n", + "\n", "\n", "\n", - "\t\n", + "\t\n", + "\t\tGauss elim\n", "\t\n", - "\tgnuplot_plot_2a\n", + "\n", "\n", - "\t\n", + "\t\n", "\t\n", - "\tgnuplot_plot_3a\n", + "\tMatlab \\\n", + "\n", + "\t\n", + "\t\tMatlab \n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\tTriDiag\n", "\n", - "\t\n", + "\t\n", + "\t\tTriDiag\n", + "\t\n", + "\n", + "\n", + "\t\n", "\t\n", "\n", "\n", @@ -1422,12 +1565,92 @@ } ], "source": [ - "n=1:200;\n", + "n=1:100;\n", "loglog(n,t_GE,n,t_TD,n,t_GE_tridiag)\n", + "legend('Gauss elim','Matlab \\','TriDiag')\n", "xlabel('number of elements')\n", "ylabel('time (s)')" ] }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x =\n", + "\n", + " 9.8100\n", + " 27.4680\n", + " 61.8030\n", + " 101.0430\n", + "\n", + "Aug =\n", + "\n", + " 15.00000 -5.00000 0.00000 0.00000 9.81000\n", + " 0.00000 5.33333 -2.00000 0.00000 22.89000\n", + " 0.00000 0.00000 2.25000 -1.00000 38.01375\n", + " 0.00000 0.00000 0.00000 0.55556 56.13500\n", + "\n", + "npivots = 0\n" + ] + } + ], + "source": [ + "[x,Aug,npivots]=GaussPivot(K,y)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A =\n", + "\n", + " 15.00000 -5.00000 0.00000 0.00000\n", + " 0.00000 5.33333 -2.00000 0.00000\n", + " 0.00000 0.00000 2.25000 -1.00000\n", + " 0.00000 0.00000 0.00000 0.55556\n", + "\n" + ] + } + ], + "source": [ + "A=Aug(1:4,1:4)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans = 100.00\n", + "detA = 100.00\n" + ] + } + ], + "source": [ + "det(A)\n", + "detA=A(1,1)*A(2,2)*A(3,3)*A(4,4)" + ] + }, { "cell_type": "code", "execution_count": null, diff --git a/lecture_10/lecture_10.log b/lecture_10/lecture_10.log index 088d911..9e3113d 100644 --- a/lecture_10/lecture_10.log +++ b/lecture_10/lecture_10.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian) (preloaded format=pdflatex 2017.1.11) 20 FEB 2017 17:21 +This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian) (preloaded format=pdflatex 2017.1.11) 21 FEB 2017 11:46 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -772,28 +772,27 @@ Underfull \hbox (badness 10000) in paragraph at lines 323--324 [] -[2 <./lecture_10_files/lecture_10_3_0.pdf>] -LaTeX Font Info: Try loading font information for TS1+cmtt on input line 359 +LaTeX Font Info: Try loading font information for TS1+cmtt on input line 327 . - (/usr/share/texlive/texmf-dist/tex/latex/base/ts1cmtt.fd File: ts1cmtt.fd 2014/09/29 v2.5h Standard LaTeX font definitions -) - -File: lecture_10_files/lecture_10_5_1.pdf Graphic file (type pdf) +) [2 <./lecture_10_files/lecture_10_3_0.pdf>] + +File: lecture_10_files/lecture_10_6_0.pdf Graphic file (type pdf) - -Package pdftex.def Info: lecture_10_files/lecture_10_5_1.pdf used on input line - 371. + +Package pdftex.def Info: lecture_10_files/lecture_10_6_0.pdf used on input line + 382. (pdftex.def) Requested size: 449.6789pt x 337.25917pt. -Underfull \hbox (badness 10000) in paragraph at lines 373--374 +Underfull \hbox (badness 10000) in paragraph at lines 384--385 [] +[3 <./lecture_10_files/lecture_10_6_0.pdf>] LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <12> not available -(Font) Font shape `T1/ppl/b/n' tried instead on input line 378. -[3 <./lecture_10_files/lecture_10_5_1.pdf>] +(Font) Font shape `T1/ppl/b/n' tried instead on input line 389. + ! LaTeX Error: Unknown graphics extension: .svg. @@ -801,10 +800,10 @@ See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.433 ...egraphics{../lecture_09/mass_springs.svg} +l.444 ...egraphics{../lecture_09/mass_springs.svg} ? -[4] [5] [6] [7] +[4] [5] [6] [7] [8] ! LaTeX Error: Unknown graphics extension: .svg. @@ -812,45 +811,45 @@ See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.712 ...egraphics{../lecture_09/mass_springs.svg} +l.735 ...egraphics{../lecture_09/mass_springs.svg} ? -[8] [9] +[9] [10] LaTeX Font Info: Font shape `T1/cmtt/bx/n' in size <10.95> not available -(Font) Font shape `T1/cmtt/m/n' tried instead on input line 812. - [10] - -File: lecture_10_files/lecture_10_27_0.pdf Graphic file (type pdf) - - -Package pdftex.def Info: lecture_10_files/lecture_10_27_0.pdf used on input lin -e 839. -(pdftex.def) Requested size: 449.6789pt x 337.25917pt. +(Font) Font shape `T1/cmtt/m/n' tried instead on input line 843. + +File: lecture_10_files/lecture_10_29_0.pdf Graphic file (type pdf) -Underfull \hbox (badness 10000) in paragraph at lines 841--842 + +Package pdftex.def Info: lecture_10_files/lecture_10_29_0.pdf used on input lin +e 871. +(pdftex.def) Requested size: 449.6789pt x 337.25917pt. + [11] +Underfull \hbox (badness 10000) in paragraph at lines 873--874 [] -Package atveryend Info: Empty hook `BeforeClearDocument' on input line 852. -[11 <./lecture_10_files/lecture_10_27_0.pdf>] -Package atveryend Info: Empty hook `AfterLastShipout' on input line 852. +[12 <./lecture_10_files/lecture_10_29_0.pdf>] +Package atveryend Info: Empty hook `BeforeClearDocument' on input line 933. + [13] +Package atveryend Info: Empty hook `AfterLastShipout' on input line 933. (./lecture_10.aux) -Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 852. -Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 852. +Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 933. +Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 933. Package rerunfilecheck Info: File `lecture_10.out' has not changed. (rerunfilecheck) Checksum: F41F49C8B1F4406369908EBDD24F2572;629. LaTeX Warning: There were multiply-defined labels. -Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 852. +Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 933. ) Here is how much of TeX's memory you used: - 10939 strings out of 493029 - 163764 string characters out of 6136234 - 273062 words of memory out of 5000000 - 14225 multiletter control sequences out of 15000+600000 - 35480 words of font info for 90 fonts, out of 8000000 for 9000 + 10943 strings out of 493029 + 163805 string characters out of 6136234 + 273063 words of memory out of 5000000 + 14226 multiletter control sequences out of 15000+600000 + 35779 words of font info for 91 fonts, out of 8000000 for 9000 1141 hyphenation exceptions out of 8191 36i,8n,77p,494b,465s stack positions out of 5000i,500n,10000p,200000b,80000s {/usr/share/texmf/fonts/enc/dvips/cm-super/cm-super-ts1.enc}{/usr/share/texli @@ -863,10 +862,10 @@ fb> -Output written on lecture_10.pdf (11 pages, 162693 bytes). +Output written on lecture_10.pdf (13 pages, 190161 bytes). PDF statistics: - 165 PDF objects out of 1000 (max. 8388607) - 133 compressed objects within 2 object streams - 27 named destinations out of 1000 (max. 500000) + 176 PDF objects out of 1000 (max. 8388607) + 142 compressed objects within 2 object streams + 29 named destinations out of 1000 (max. 500000) 80 words of extra memory for PDF output out of 10000 (max. 10000000) diff --git a/lecture_10/lecture_10.pdf b/lecture_10/lecture_10.pdf index 447bbe233f131c3f14f9cdfbf95651b3847ad800..d75909f0f94b76ac06cc538e04ddf87d7eb6c7fd 100644 GIT binary patch delta 119046 zcmXt9Wl$YW(?x>^3+^5)xVyU(+}$o3Towot+}+*X9fAeDxVt+fxPLrv)mL?YbWQEt z>gjX3`}AyW@IAux1X3&&6f;i(3+z{59(Tlkm-8mOW~#`4Elf-BVw5!WTY{07Rlq`v zyz;x}a!9-)_iV6(b1+6x71c@_WXm-8>?7z|Lds_CLigpt(oqKWXNpYZPY zgpwn~1EawPxj|M}|NcJ43Ed}?$*-uL2r_uJ?hfpl{tcpJ=kVylInC&Bo#!2i-zzV7 zV0*7>>-ntRrQohabRKfHuUOsyWU0qYW~O>}jMmiKuX9dLr%RH;%zGQj*iibEKdu~+at-aqj7{rz53;@yd4E~MWpzk%-RKbP#%Tb7=@rw zeXz65yp;w%g%|1t!;>(=i3qU3*w;U=iD=Md>tu9XCP}?ER1(Yf%s08~dmri34Qs$g zt>GdgTs78pQkNAAAP#*4cBoUkAjI~@AEeNXnVXum8eWjMk26xs<`RsVSXPaUo#NGp zgJQKAvEsbSDf1&Ai&yIBXLMguc$(pDtRL;C>YbZhf97Ix1j8n8)X?0BX zU+N$8TZlo-ieQ+}FvEvqbS;giC(-9KGj;{Wyf@<1<(KRzthu=Z1^!GODkcRpnB8hz z|Z(9Bt4{Y(4JVT*N2&Ah?0wHEFsRb*mb;*DIXt3B*l2>9gPZ z)C*T=x{*ca{m&Qmj8iULq{pJLqAgJdnZ5S>{|VqHMXj+Pgi(FB!5mtS!L1sktAQT8 zc=D+Fw$NN1%#qm!?3WlSS={CavBC3nV&sbWgtXJ=!;0$`x;I#dXIT^E_$YoQkg=(O z|GYmfKH>yH0v_#$FS6VE^lk9j+E(>oc@xt$eFdz*HF@UV5C<*Z+hdJeh&icjMHAdl zD|PI9`YxXKAnMAASkWqiux~LW6VQQ{%Bg=aY0m`C>hsu(b)2}XYpJ69D= zLwLBvI7+Z#&NWWjITpNt{~{YE>N6C!?OX_s+*L;K!KT!*ZJQ3b6b(P(6Yd-G;N!6v zqG+fVR<^lY!*ZENj!o~wTZ?XUyV_6;f7Q~d>hNnMqWgE|FN(1L5_NnhO3_qPuaZ^o z@*9~;*RRh92v)RN?&IDJx0wACA~}EH`t#h{G{BhKfrJjOGJ@41+RbYXL4@JVfZL=5 z=kw-a@b#aqrCF-q`KTnXwoFS-X7MAKe-%=ef?RzXk;W`rz?=8ef}Nj!D#AN8M!R=uxFtw4?k+Q#=dn_U^eLhOgCy{v_<^(uc8c2== zCRlnvQ$dM<1+D8)^FfsZ-fib^3&FndylN9%p+*~IXyPY)1PoGj#P{w7TZei#PGRYJ z4I7b_^`+fIE(eR3zGbT2GqF$y4+;Suu>%firqmt8R+qDvc9&JinpU(Vk==xL=h#&$ zdG;gUPRTp_g~v_{o#rVaD>wI%6EG7!u>>Wc%AVRuMH`=e&cs)NScvR{e7f|Tvn<9<0~iKMhX0rA=qO+_SW=(d0`s~HAuoVgutH8T0} z=#8^rP|>A^Md%dnJBgcmZVx?@jj=5BeKgir5qgr}eyu21w6aO2LgEm4W9(boDv*=_ zBaAS@*9?TO;u1gM$ZGX`Rij2YJSRum-b2P>W)KiZJS)7bsscT zklZI|k6%YD>py5w67PRkCFPBcE|;8kP^A06#_q_r5&As*g3Rvt2QY?z>BhFFt5S7 z6}RJ_Fevii^zKV2s9}=SLw#N8&Duq>IWc@lpRg=pfwApSEjjy_kd6q^+@C(HJU|7$ zf~{P1K^{lWlEGulw30&`8~!te;v8&7J8o?_ezN4V(ir*5kyY&ie?;`()UC#AKwIbB z!OKQ-bDCDiw38-TgH4M>4(&LR_XP*dt2l( z;2(&pm?KUBTZ2q8U3bVUbFGr0RteBxxdIf;s9V!?6{DkSv6O6^-IW7HgIz=C5*}hZ z*Q%*1nx{Q!0~%fvlnGDYzyow%YlJDygyR>BABwPRM288P&J!(p+LRDI`=gD5PpMj_ zJ&ak{U*F_@zMlP#pRZu^Z#2PD4OE{9w&U4*t-Z!H`oREit3CWt^h>YI=M)`~Q@$AO}6eni_^G9x~IIJ+E`GIS$ zR*h^TFTat6DI1no&EGLwW1&hXhE^B(!xS;j4&9x)hhc^*lrozMQyE~4P5N#=UavoX zq532mMz6Gg8PUAhimdD(A0{i@NCG2F`5hxdno1Rx-<7Go$sTU25_*ZR=6=OcfGPFGqHCB~5816GTNS60G?kx5IUQvXFSYR^S z{_+W1(BT^jLdtHnFmg7xOP*fSTQf$NaUN3k58AO4d$_h_qxmKvNJRVJZ4*pPQ}Pz1 zY}mdvwuKMnK7wKi43mN*FV#aj42_~=Id30cB9&pzR%0lP17WSUV^lmMU1~KFjQ8is zD%&kp4?Ao(jk1gz%YN47>kBRvWxoWz5!Gc}#bGy}XEO1o;{rZ2^k>`G1+J<)0=Axt z!>N&K9;-g%3@{kzQ0%Lq`=i}vCC1>4#3T@!wvEU zlq&g8i>7~ruxo^)H_)-Tus^-TUs( zE~fn+0H?h&X`Yq@_-v%3_H?0Nz>exy8a(Hq!ZO_JLHY*SBxpTmV z$=$jS6n~+=oey2QW=@`)?!RqcOTPcLecI?gxV-TU%h7yzyZuYNeLi)s(R^u|2?zpz zwVhwiOP*R-OP*?r%^wBt)O@4fUzrTw_iJKC?p5Bk-i?L2?|G^WZ6EtS+$DK?blCkk z*!rU3JO9i2=FH~%ZB0M$dMfnRSbY5OlD^-e<FOZoYz^4Bp>>m)p&^aTlHDcG#Kb zMUuP6>YOg+vl6U3@gw8M`Q-iU+T_c9O-(Km?QU_`tmA8#J4OMa8qZh3vFazEw+rIs z!?4#nP*ct3tfz()Pcj%sAqPc;-{R@Pk2g?h>>KBK*-%`gLll#K+6oZEXt?)~-3&G? zq^^GZHz26{W4T*Uk$%UyLEo88>B5( zLc_n;x@y;AobS5xw2A^u_0!Wod@vilX$6#yAH#~Q-v#f%6wify`#W*I%}Y66Ryi#? z7!E77&*agW<%%4Q>KD<*9$gH$%3d`3172wG|HyBWqnWG z7D&E*ANyRonK*WWX?S)PLkw0L|HcWf-PQOy>gQ?nq;|^r4)Xxc$;r{+q4b>;9s}%? zbPW7n!^fm82hj~|($m+c9t+n@t^+$j0YC2LjBA9Nfs4Ohg3_jCL)j#nVY-IHPUuJP zj&V90ey_y@UVZGpb&2jR_-+JQ8WuXYEaaYN|LOoX>pO$wQM#JBhGQbP*Xy(QfJv0j z2JjfKCJL8I?NK$$Gkl$|Z)f1tqi`)2W+Q~%>^YHWS#Q3%zq=y%&J5Z-7HZ;UbRg-b zHbhkbt~5&4lS05TAG8#6)p^^wui(Bes~sHEpS-}Fyq(pNlg&K%TOR)4(sz3OcDl%~ zaT7qht^4W|z^F0)Ja|xb(c-*MT2gkJ@$I&(cI-6F>9pfG{r)Mp82m}dxA8r})n@b7 z?h^BQklMaYAh^bkrnQF_m~}DB9E*}Jrx^#uo?O zhxeGA=M@w#@ak!u)A^DpbUT-qz8mUStxz=kJ~dtGc{GdP9n@@StqJ&fot>5pWZ4GZ z4fpg!2)MjlOt>ue9H0t3A20p=jhM63%_Wup78+ym?+SdSQ1C3-@fI;G@IEr8Y^bOA zGnn{I=00h4(BV-H^{s)E7-tKiS_)88yb*dxs^PvGyX-hczZLX+ll|B=Nz+plaWS$v zNG{;#?Rocf_)-@7t}EB^z6|zoZapg^XL16Tc3E18V$p zUb$ZA#td8x(z|1<4cA*9?(upgJauzM_pXJm%!gubdtUE+TGHx1=LoUm0FLHGP9%%F z()T@bk)u#$8#R|D+IucX+6UH;pri%W&lOVMBoDsdPCbZw1k6F23(Kc5d^B1m#GRH2 zFQXhLPlPLehFW;ZN!u4j_?BIBjrPNL&#Ei+nPI1kS=6spcN|$`H>avA%!{gpKL|@O zKUaC+a2B=k4EQ-%{yo^l0qoCNji6O&<*1vKS5j`b3F!J?Tty4h4jS~W){}i-ZV9YA z^y(#eWEaKN7y1bHq1^o0-Kg!F%A=X28VvqI48_5P@o-Syb^u2e2Sz*w?3m!X% zSE?kk9bDcfp;}lqL4Fpl;VjtPjpo`&eMAv&iUM__x(83>qr_O7^eO#VwN2HGyj3)Q zU;FDhf55c%`-*Vy^mI zn1G{BZh^-uROXa;eHWS;*9En(#LH2{Z>WtHm=WHO<1L>`dwX z8VFzbEGjXPMslxhIxT{C@FcoLm)NrdpXaQmkdXb$n1SqRF0rHO;kTC-w;Kf`8jKq_Ccw{BoE`%9{0I{-)H90+5uQ@ z$?PxH2<=*IivTVn&q{5j{$|^K>tSj>vdcQSskBgl4f+og$LbTypGIos0(HGb{$q~p zf=Jf!TN1jJG66ZaPuS)N^9rt?|1E-5KG}{Esf{FZF72F}#mgz3O*gj*Mq_wIaE;pd z)=BA#68;>6b~dYIZ{)fQCNbB_A2PPz7-RDD=_Vj-!UZzELs*-)khnQGy-|g-?e0NJTMeC3U{wRl};U5i}U->#9p{j~Q{nF|a zmlEKh>cGqS`LlVPV{%S_&K_DSv%c$QCuUn@84w{-$9Nd;a8lqPVrp1E0sj@n6NOc~ z{%bSaZ#pm);=E#$`6)(W!#aC6q___>na(tgNfLl`E~!H|5G zUO+VdN_{14Yid}}SG_2Ok&C%Q=?@m1mnVwN+i{(^d{qfSlifnRj?8w6G(XTqbQ)BR z6UJ)aEoO4jbv>csw?NAOlFrx!ga6bO7(w6zg)-8)3{xx)b$TB&;8U$vz-P zE_dKwUJW>mEnsx<1rfATw*N5*fKoq{5RGLGI&Mi%U4DI{h;C+>jM5sO$F>2$EFTo5 zf{~yu!sEsIelJ%?E~&f2QYvn8r~^iq)U{~Wwb8Q;E}moIikhhYRd7b?mUOaf)rXOT zlOXs$sQpSaFZQq=2&<@Cp6!7D+K_>1!uC_9s?f0g zm(Io2+eXi7e;q4=SS}?R!X^Ou8x=;$9MnGB$%~>)(vbp9Hup@m5CvN44I*0UiC|h4 z6MrZbDDCu67Dv3X1Nf58W+r)SIi7(mQ$B$9p=*Ir{eE9H zx$~Z>bC%!S0FOXzx6x)7aDb;umrNscMjlf9r& z^9hanrf30HG*5mxCC0yCgTD;6gCec|o5&}y_jTDq!~kQLX!Y!rGXHhjMP^OzM&6$y z%|9IYq9_V&b!S4YBLYAah0qYIX_{@@Cl9~T=y9=H?NHBXixt)AM2s&-c3PPRKBY{* zKb+M_UPjT1PzsgG?^#A~iP@~;>ExFZ0Id*mfF)r4&7WVu28Nf2DX#9TtlM!CYaH8< zky4eTnOf_R2^){C&QYvao-HK#IDcGckm+pkPwB-G9D^&?$pEy`8z^BY6+l=<@5{z_-?`%e+M3^4&IWSk=*?rn8m zgmdi30hTVP0m;%~u7By6#omo6Lp!Mkkl=zQRZEB9jA9uSw)| zb9kvq{Cy?ZK%l5f*A{JQ%ALt+D2z7SfZ+v`gP~rGhM!v%$lQf*)r+Fo`t_gV5V8^N zYShlrtd?P1$~QQUJ~CcCaDgfHOgU{+6JLCx$Pp}GJD~DDfU#u{I?3QCRrnLmR-vXv z>P-8LVZP;FWy8RY(UK^TXyn+!u!*M4j|Rd9?}n5y}nPAk>agU|b@ZIzyZ&OWK7b;swJVXCj6~(zSCOgXW=~3bpJJMn@M8sy`}9J)bWOnntl9g(RKedR z9F@3M>5cwnkb4oAk0yllWp2k_Er1jsZ30TT;5!?(RJ^DuOz=zood>D(32b`9rHFmM z)S_5iwM2fQ0qNNC{oE!W8s;t3#Bxdj0GF*F@!rxOwoay^ErzANR5ql*C`DF=Esa)o zp`mBlZrm>rEl{;!{~P6oc{(7WY)+NjVQ1)W>kIJVt8*?B2qI{d{likCUJcfwnGL2`4~jGkjo5)_XBXihVX`&~8Y z66PjcOIK#x^jxv@3xgwxWDQaMlb?o^^~YGwMY08_>}#c`zZb2`{gHw=yF?!o<7#GCIK0I&SVFaA zTAW&8agHR2y)r)D?$xINE@y2=u+L)2^$wGDG=L?42(|-g$(Y%mCBs zVW-R4v0z#_liYiP#JwNaL#r^$XmLBdWX|BS9}r}d9>!JxfsnRo8N{>!``ZbRpjwR(K6I_hhNd< z@D6lZL39wY`C@-J+l?`Q&qt7y6TJ}5CX&q=C`-~~WJyZ{YDmI~mEYMP0Uk3^^sdqv z_yM*ih-}q+HF8k_6KqgmqRvRTaZjb!W<55}urau5+yhB#{a1V654>H~^m8jDMcXTD zSa@N@e1>7$QP^@qmGSiTnQ*bOC{r~;D5Hs(BBMD`&E~I}R>Wlb4+OZr&qtwuJ5U3T ziWT;^=%U915rlC_dk#_-Ih81|PZ~20(PL7^Echt^74?oNv=0d;VH)sbggJ&C+sbxf z_^JS9YzMy994A|f-^9N7$unGPs5S_WTlzw-HqvHdl-1FPfBfDvnx%?J-Ly%S`$3;% ziIx9+!8e+DrG5Y+D3REr?9eeEd7t!%=!C@wcWhkh&xvvwj|jCg<*%SG=3ftoPk3p+ zh$iL%nZ(QcNAOyct2W1fj}gYLVTO>}VN+@Ng{qoyGmlm-7s{HOr?)Obgr$RW?*}G>+umPIEP`L%t>qw6qcXbplq$tL?7=y z#dJ{9dh2SgrSbdcbU1>gqQ^I#36@_noPG$Dqm2yFGzC$z#XMxiE)9ay=*5lJ2vF>R zj&!yPyJ@Z&2P;4nC#Rb{@ATDa7^ESp-SvsDSvaY{&KYZ`tV?qj7OYbKF;~s?YRZj% z2~)1pPAd65li2*sFKSuGUA=JuR*};k^x9%SwZX8mp1N5CuDi~+b zyAsL7YgW=fon%Vas)l%o^V#qTk7WU9W3yE~vuNZSOA~Apq$i_S5pAXRnjhkhihnUK z6sL=Vv~4P*jN&V8|IQV+pOr)zalfjq<^tryw+@5f7t6-Y-b%`<#ciKjb$AIo_c7ge z6g&3$0^>P@b78LJFn9PwW1AUlA)9B~c52Y2miKfVL;^Z`u?rJ$P9#2=#Bu_Om;`|Z z&??f)BTi8QDWCPJTu+ine#WvU_UrtWj(z^BQnn$_SOo!Zr?w~Dsq2$hC#r}cZKEbL zM+(cxPI#1wuuR~9qZ!gBDq!XSs%+rQ+e62?D(3DRB&oW<2CHt-#3DcL34pppJ`kjM(3c+O zj5pe#uVPcyx_vn&^P%-0Shq(0EDF%dI};sFCnOPD{v(vjBrngW z)-&3f#?YrNCe*3%rtHNy$JL49R$iJ8v`Y8q-kO?5POaPJE*=3hX0Qx%6ZeBn4z|^2|9}A~KQ0)LM+{=-C5CBktli0e$(qLkWyPkr17h^?4h+5BQKLjwJ37udZi?hv@mDlQ z(ChbMcqgWQruk ziN@Fgk1;PJ0Zj?|rRxb+_1BmFSH&)2pxgWl>e>abS zI)4gVgu!Y|u}pu!I|@o&zlnU+G=~}+6p7VoU9&&H*+fDGjHj>svq|nGVJc+2elxDj>ix~ITZ#FZeuj60Dr zil+RBxy&1~-48<2b_{9C6F9F%HwzPpck~x8-<=|ppcSH5% z0Md)5tGivS8mx_OHS~+VIUB5PqUrO5c>tJ9|M2UFtBeZMKIsG^p4P2G;HiDIJ;QaiC?t}Al*~I9Y#cAM< zMi%5LLA8WRIg_jjn3=r_lY<@!7FAHIHC%|+RV(=qWyI=sS}C4p3t2nyg=2n*H=R55 zHz?hASa{r}Om|!UsKPtfmHxz##x5gtmBNn@TbR%*R5tW?)&$5V$gj$>^2@Pg{@!e% z%^oThVdFcVw1Vc?%<*sO%OZ3m2wB2(+Pw8Jq?GkV0r%w*2wz0_X-J1Y9ABhH+1y^z z=krlPMkJSDaI7Nfo_+GVu`eP{VECmN@d zPZdb@F{2r#*5^FV5~|%Xo?f{8`%&2u-O?cBX){Le+;cHm$~n&e_kwl9)KqdyQG6`Dh~X!JBJA1GyRP;xkNDLBQU(0!4Jtrsm;_Ul!g82CQ~qp z%-_*+)DQ&aYac_`A1|tM;MiEYc=)NTd7M93ja7>|l&&9fu2zc%ia z%RlvyG}t-0^7u6#R}SeW^X`;SsKViu><>{hj_^ShKx0UR)~1^W*1%h5+1Yh4ya}#i zA@%Iwj02P`<(l$lDjqm4yEAN4OCk_d|#T3sUH-h z%14n!ql;(}zeRjhWGJIotIjHI` z+3FfCQ(aV-pvxlWfQ55LLO#|!Z zE#C$}rrKmJIBn;eYsxliD^Lm32@=oz`5}q=7I^=xc?;T9@RHYlsZEbS>E93zb2rb~uQ_v?;HitLT<^EFT;8LJX*6`JFLfRp|Kp&#FnXRzU9YJ;V zuzX(+Dtg2!K(VwQd>^>{+S0Db{0vCSa>Y_)B~~X~L>@|aiFTvCpI(O8jKx#rnV-+B zxUi{zbhN}suiR$Ikt2=EJsvUME=>3(2KSj9vX6%Rn8w8)0PA^?WZZq&;CJy;NA;8s zYCW3p_`!t{)(S{h51~@aA9s=?l7(9{WTV=^i9)tf@K|S4*p@G2fHdPX1d7_>V$UmQ z){rTtImcY5F2nHr?Y0NZgaukbV1jr=goX;El#inaa>)EU}z^vyeg? z!&wBm8#`eYH(81QDSl~H27GhI;fmor7SxO`02o>CyJzU z#c}s2iZ8hKFo$GTV@?Eg^|^{JEULEZKTgYR*-zzcWT|_>K^vOF=dL`mmI$=)HJRVx z8@#S7nx{J4hI>IYRT)e-ZOFnUHqYw@D5}ouh7}Did=_rZbvFwZ^U^YHVq~7#U^W(_ z3&o{Aqi5aB?&SV`J2jB|eQ%&VOr~fs`mLCikrvxBhXzUC*WMAZk%O3BFr6iokEz1D zx=PATxHEFIn}Co-^6*AFIqsWjPVOCmgDaf37#@BrZieAL&rBWVa<;5M4v4DB4m((s zQDsz)r&JVTdhVbsn+S+Q^}olT#5{62fn}w&RIC`P_=KM|+AV6+7Vi~DHrQGy)k?`) z#t=)CBp_^E(Sr|Y-$NuebJWQDcnGUrLw?P>pC>qPK@`|Y$RLqX?=xtC^F)edoKg4-{N9wSUR^V zhM8gDrVU-F^e`17H`A_?EqQm_RMRYqf77MWrPDW=k0b%icXkPDE};!g6^<(r$oFgO zYb$5Xzx5~W`uMY?(Ao<_D$9^=j-YHgdu<$-)IQD|7Q}>LJ2Ia9f|V zrpUV#x}f~6AouFJ72>@hjrJU89xSs60Df3rndsePx`zV6?{Lq1)KH=hc{ zRmgOXokk7w27Nn(xrU7uB@oEzz+7gredm(edm zx%2vHYb~g>OG-+XS0JUEhjPpy%ZPBAR@m95;@iY0{+1UW~I4>R+TAMCbg!pFoj2T8Txg@tu+$c%8Aaq z7a059*eYw4_qoIX^60*th6KB9w!ddl2g<-LL>@~%aRu$@{- zlw*}hIr|{$Mn%)Sxl(KhA3Il*l*w%Gj1`PucU!$?=zQP_1rWl+l9!`Sep_7=bbObp zK_+&{N`KuVE)*+vw1P%i7c~AVu7P#a{XJLHKGWz7SV57V$+sYQHIAn0%LOuA#Evc~ zdq5=K@S0MlAD!4WkdHWN7kH`_8m%pq%e2g9G%ATOtl^mOnb*e90NT|#du!n=sUzgi zx0Y;C*vd+iMN0wIjXofRSXeg+zJp{Q3=V=p-0_DTzi(Euolu~m9g*j^$x#3 z{@b>{6aLGjOU6eA3v2&Tv#cDX)u2-OeVk8OW|XfU0udJsoibrBfV;ea!F}6o{!jH% zAk!;qJ9x$$2BlCQa44$oP^H?yo`8|gl70iB9LjXmZ;X7Fy%$qG><23Cr?3{Y%kymG}s&IXoH z-;4c=8G-l2c*#3bp$#VOOG*SDsOsoKX!nzsWv7k`MwcX+n!|FQOra#IUTYDANsBIG zZqUbTjs-6r#?Hew%yLFHFmB>mk=l_9le#X{xq*OU6?WfBf5(S63)a`3HE>$1Iu_V% z3!XJhp*CaVqKo_FS~a(8sPoCfZBn?gobHm?3~OrL9z38?3JBv{D=j; z!L!~yGR{nL8dlA$S)O1_O4krZZIffKPGFeYvN?9AVghWvoAP;6NWQy%e6nn2kDDlv z6a}xJ!N0ipdA_*R<<*nWnwSD1VQ&}y?B`1RENducaWex#g7_BxgN>n*Iv!LpcJz17 z5!bbAo7r*RMZvLK#}DGC6;;bshg-;l(mWS(56amVNap|ZL9TiR@48LoBTTji&kTzd zUh8IUKZEvG7#34lnyCEk5YYc|0;VTe^?wXV@O$w6(T-vNXZHQi^#6fcN6y4nTn{Gq z0{zp4H(&i0D{=EQ_bca(x=foi;mj33K{4|+O0^3@`C`6cz7^J`gmaw1`}}&HEl^t5 zBDu@$u{zYDhGqQwP5aACx$t83&Dz)RA!*-h)apqW50Q*OwDpTX>7Us&zNDxl{Swc} zLq!l`qW2)?Oy@5kaADD*4f8S?8ww(-@KZ~uOG)#1C9&a*2D3Yz80p&2-9*?{Hv(klLO1WK&H;9z#!WB`RcJzS0FH509b;#RgIpKGxhU`+PE$XZ+W-6>4yHaT)741F4d8Lf&4P0-K!SbLBlB zP7dp6rT00T0UUV?$N0-1n-yLP0X0+jSUqmJDr$GZpOKB`2g~hH*I@^Wpfm~SXX)*= zGR6QP8P$n`&i#{4u}uI2;!=qujH|nRlPC7;sf%YC&jghAO$~V0{Dd6|f{}zUXJ&P+ z4Cha!KL}Gl*R=dUtLj?sy{M*s^7{+^q`DkCh^~KpXYs~}!ulif*gZpitI`$fcoxas zcV!oC-^&>TVo*PuQP1C^{o@EB_tF2T^UT(CV$BhzUh>D11Lak$`$m1+DnlCD@EHkS`5e%pU9lMK#SZ zcHc~-Hi{LRge?&4684}Ne4|{kA#LS0?PVQaM{uVe6sthQu$u2F%{_@2pxg3_&)~Lj+PXvsj21?V0?%-cG`fm`$ zs+HRar&apgg77C-9R|Tt&9`(0mG}0SLF|#NLWW_- zrMR1I^&xNjG<-3Lk}IqYFr3FqlIg`C z*5_s=Pq2a-2;s%|R@_|80M*yfG*trexwbc#IM?1bO#=Cuuzy(%(6um8BKx6KXj+cU zCT*1Q1*h$PedXm7-2!J9EbB+|R|e|G&yEF^;glx&df3mzE(+(UGsQlx&@15I;aeqs zgyPgF0~sf=FZrffRB5%ag_OBPpR57jO%@w>u7CZb6l?S=Hi+~InnorXTQHun>*AiV z4M^)kak>u$VaWk$ql!VbzS*Znm$oPp2pxKqM@4?;Ae#cjamK7`;d1^fRcorf(=bg@ zUB20+;BPY_{=={mtpe$EQRaiY3ou3EF?>%2CP`srHG9-qWPH``N#+*&r|B7ic&fS< zaXo?zTTMS3l(eDHS_rfCbi6MH6#q$w9 zcA3D+nR;bW&O@aY)_^pSZX}a@Eskw7=Af!nx*#0y(Czljv;PCW`eW6W| zN`o-=tyVX+DN0V7A$1u}EWO3 zK!ASZRbp3$X)4oDNg!>dXLeD?LAu<~$<1>PZs#q_9@|P-fZ=gOVOWM!$e>WQoMdl2 z?Z*`28Sruc$yYlRES?fg>D=r{DWRRRpM+Ek5_9{5Pc%N!*j4d867UrBu5;=wa?<;T z>9J-tjKT^J@oWSqVYc*lg8Z~Bx8l*$;n(-x#M)<8It!LjPaBGsHX9t7vlSEUb4`o8^>`yxW1xJ!&HI@ z18c|WqCAsyUX&`F7)TE%YoCs@_9_xXb+NTi3`i41D4xv>fBYr2t`$QP_hhk*L` zV4w?lD4LOF?LGZtu}J@?YP}4urybH-okhk~xL}tXU=3wHNhxgJ**c`Qtlrb96}~5tE*SX zN0&m`keYn^F`ND{f5B`8wtOG;*9|+}ywC*YXh-UvK+mDe6NeQjc%h!#}lf zl#TvDfvh`{16V{l`}i}*)_$p@Apa(y+J|t`K64Q3(ay!g6y&~}CB=SkE@Y_CKciO4};WQ(L-A zSH#a=N;|dwY33l1j^fPL1bH3tE6o5n*EzxFH%osIKOh^|pNpHDNKWZRnSw+4kF*HJ zU-0EtqDKs!rFqQ&EhTNuKv`jA9tI`bg@a7Zby)Y31qps7z5@MsfFol7h)Gp0oJ;JN zvmIsPw}w(j#y+(jJ;W_pQ1c)yNv5!rRMfRKfb^~76%@^k#LiLhg+TouQT>QaOKH}R=rcoe zCQ>TeZ?${$-ttb6KYogaP1;kEeqp;wr4RE%{n$VVuikg%b3pkm!2Oq=KboX8Vr(un zuDAV=ETkH-Y1KE6MbchtosEslRM>jyaF@Q{Gk|@klk{jv1k(1!<_0y?N9hPRD^vW{ z7gvFKP?W!8f;JkxTXmWWn;w|FN}?A#`U;CxsBVB9S-$%eD63wTjJ2y@c_ASXB}(qvYH>1=+UcjrZNqUQCX8+eyU~{NQ9S;H*>gl*k6={Au z)Bln6&B2{L(U-Ap+qUgwVoYos6YCS(wr$(CGqEPNt<87qSG!faRj*!E|IzjORd?Te z`}Dc@0DSs?!rH;ONca?;buN{Js4{NbD5 ze2!JBC@BPjTZ?$X5h=ncQ&BK<-Yy3&+G#ecrGGx>d_jd;*a0}dIa_3vSq z79pcE1I>xPZm+pJZ@o0#ZB8VB_5v6d1K{KRsFV~>#ArRy=LbsVrI=F|3mERw!>d1X zsj*ssTggyPR2|>VFPD}ga`ZX}TJM=JL?I-Cad^uau;S_FinabDjvXqvaJM&>Bml04 zCyaOIn^g~2Obn|V2R2vg>5nnTQ$Bg|g)Ih0CMVn=Qp|p8#JwvtL4aj%Rox%z2T)Tr zVHT+-%Nl)$!J>o|HWSN+p{AV|P)C=GQ$Q*u5wM8SfW6gKHmY4iI2zICNp68WhUk(0 zdMt|Q4p+|yD|26-2N9B5Fa=yHPxMgRAg*VK$czbyNBy$TmRW1%!@w#x9dg|pz%&nQ z`z_q`(8nv-vmakfP^%KujyZ{G0zgZ;3tmkC+wd1d3hdN9bxVlWy1pRCZQkLouwCLi zo(hyQuaOKntDX}@nfe77S~7e_C*9^05nY z7?+K>krgYwWvx_ zkS;LoP9k|vc&TIr9trU-2|%)hZeAY(TQa?A@WI|}OePU7AV)FYaambPL&*TE65(Jx zzJj!)a~foTcP@z@lKNo52V}-yYFVip>}11P45rObk4W8Ck&5L-1mui9T zWk}t8`*q{mSmlpcb`kST6*L1m?CBI<$IIo;ml-hebt;N!u>dbG5WtDTDIC~FQB>O) zX>|DIFYOcv3m*HWE!HKT3`KT&c&Sg`i=wGRpHfn{12X6Glr+EV6Mj&^FZw%8NZ6tD zr^WEcy}Q5JQy^T#YT@3)*;2!ifvf)6*XXDpifC_f%Kxeb)4_#W!_4fNJ+H?w#kAqk zkBe{0SUN=m>7d^c5^keI!yZjm1T1wRRVb4*MxDy3#!_rVL8I9^8h@j`4GJd7njWRtAxKK31AlD};gK}U@r?;ju0HGfJ zBfS8x_Nd927!~1yaTwOJtOLzjtvv375qk*iG&tS)mNMPhtOM+(&@RK;HG$T0m%HaX z-KnnFe0J)la}Jm3lp~36mlari&-{IY-$B|*W}*d2CFTRpU@KMm)}cLf9Djrik6w}~ z5>|5c3gN)KbG7_Js;x@m5X%@%9`7R)VY5Vi#%lD7qmyz}>4LEvq$WV$ny(&C0mC0! zRo5$SF%kYcRt8w?_HdUoey`&{fTRx}mn6E)NYlIBsr>sO+<6OZuy;=?RwOPMy*)@s zF&Qp@!*Go`EncyBHv{Wv*M)N*R1ZtBmoiLVPeazY6j%1eXs6?hP zvi8oQtU_)dOH)c6(@O)x6J-R#d2n!)FYn|s;V*I$R|25uR1GF-B)gcAXQ2@CKukui2gt=7 zBWCvrtN_TjAs@h)L|$`VAp!pU*aPC_2uv3%%1?)XF|?7_&^lyl;AU5FH5upP234y2 zKblpnV1&z2>yYqt^5?pZ(;KM9W5hi}iXJ`R$4ifbd5-bEkfx(V1#=mD3~0AD1Hiia zsuTr+GHx%xVcBP>X)$;FE3F}xF^~PV_KM9d?g9UzSKW@~xQrWhx=<^pK5ff5VGquH z=Wvb{bCJ*{PU1u~;HI7If)cOVlhBkXnPKa~Y^bFj5)-EIm&vLGna)JDdXLkrm~TK>Gxq-oyQ$;?vr?6 z^AGRzBbN`JRrX#Nb)+ko%o!P`qV^tHuguST)7n?xo++2{+&24oQpzNJ+wm`w*O!7F zRZa5O6R<~;iYBn%Tzv8bzM{t{P}C_iroqOXoo$6wP>|@R0B#idM&yBsVDRoeRR9be zAIB0Jk-R_Hy0y&YZL z-PBRrkeuAuX$_}cs^A=KtvshC{{E)C19~qYmwa&k!zrfkk98QRbT9P6HWar%&|LJm@V6i`UIOG;(Rjp-`|@ny0}MAz%<>vB+||M z`e8M}a!tdl=Hnuo_`~#UcrCI=ijl5x4W6z+Anet6?C(j{Dh?pabx_Hg5aC!_?a-Pn zJ8&()vNegzx}Hjd;0J262?5f%g3u?LS_AXSR#l7#ip9n=nWu~CWFCUV28Bx zb6auR^*mD=JbNiXa%zebOJtEIHaVRd2#(Vu^3tM8Kt_utM;B5VfP^9L_8Wr=nB0k; zk^}>K9P7%J=^+4v55ne!I-@+?OjG1qIss=0W#g;a8UPG3nV9C*)+KYkG}&ckiI#Go z%)+CQqFCbL47zpb?f{r@th!o&;@xF3DE^5hmVm0o=;h@Xp`wUNV*S#xEg?a4+;4$p zGqS&UO7(U`ej5#8lvi@yVj=+ti82*)nqo~6BgHdH^64qyzA4$YO9}4j0s-VS(cFFPAT@KdZNQ&`|n^K?U)|Fp?l|WZ|t1Pwh2t zn1JL6DT5#jj|Grw2oB%QyCzW@2fo4h2g@ub{;4D_O_7}ETo|xOn34q(lZxyp1H0Gv z!wOM1d5e(UOc0hNO>UX38lq+Xmk`&K``JWJMz34vbQf>6o1wsn6i1hvL#hQcO8P^f z*d1*r0;)fN7Uh#TMK`!Xmq8%t>Lz%Gms`$s)EC6?;0FZ%C5(GO)3OBgKQM`EP)>D^ zGCaH(NIjx=U~A5VGxLvvGLy!>!>*(p?(h&?&UzNcW=YWES#~R4 zB=syL;{qoQFp~tCZvU`^Fi3CUlaw&t8jbH6`*~qAe;vZPzkg5kL4#do@w7hk5!W?^$MCv|n_QvvmOh#g>F-^-u&HQS?#Wf$c2 zw}Suk84Pvv@x`#$zS2bbvnT%&?ELsw*iwW%&z@juCtR$2<4SAT zNCKXZM8-E2}HlW-rf#e`&!)|tOQ3ZworL~mh}11|P~<*1)IrD?-v zx<)|Kz%jnnL85JLKo>r?zI^z~+gn~V4-%`##r5C8bR2{M)1FtOw7`zR`{_-Ncfz)s zRinn1mIi(otQV&y79NVqSndRndnOD+Pr2HO&*#NCaTxx|kW+W=j_F%s5eOj-Yna7M z^5mQ{^+y?DN%g=egVoFV@>{sOb5BW3SH*I^UBH)B1d>u+OXX;!028QYWHe~{EI#VS zgwU_I@zGAOc=s+2vOW;l?;k!7wt5`FW$qHfoB!dxupGH04XA}T%&G%uIOHD-BQm;c zq=vZk=fIT#{nmLuJ_jQ=gJ1^z zWf>%m0g(Tz2CW5P)TN#779f3O83Qle)P@7p*Zan3?tP#0Sy z;w8JGM0sTux9IZyvz;19TRXF_WSY~|f~*UgGn zL`2y6sjJR&81G)ExXYOyj_O8@JllU+ ze+J~O0V&8=@INhY;sM`6Wqc@BiQ+er`xTkukin>*<;;^bWKM1unf3d4<4$7Z7#4tE z&YPb7wYzWP8nz^ZW?V~71_B66GGGBh9+Ph~Us^-+4gH_+R z_3CLf5P6h6nHl6>y07L_SdA+|`{Z6y#IudTWd?l0vV0EsKTUtStltN>Q&KKn^bS)X z?VcqwOG82~J@n>3j#>oZ@G24AA~>VLu2qnWatKrC`cjbR=oBs=I}>gj4Eo~}Rs_(Y zm>Q@;Qxoc8@NWAl8wZj@2H-cmg&+s&r+H@_;OK>T)kI+%l(vE~Xp+X4B`XqLoMLs( zPSBl9gEVh|V%GSH#m?N-aj@@04kJXt6IJmUf05ee1|LL_iXQ^XXu!d}c>btnGiv^z z7Z@?L2>6E|`mi9`o1nKcYn;xi6seFEL_e-n8PK}^ckkvW1WZ1uOVtB+oE(`Q{4X}r zm;T-wYj~W*)6(Q%w00?kK!cM14L^3$&NUz5V6yPD-F1;-WmUBsV`Eiy&Yg(CSp!b2s)?Q!+ziD*|!DOgS zbA!<$2PHgAnknWFg^5_G->1+tqGJ_QWoEBWdM-fP7Yu}<2ZsByJw4p&?#>SNz}_TG zIgv86CTh@$A3p%y3P0xDBWU|!}|RqCzwO5%UW zNeP_qZhlnNebAj=#DbMe<}&6AI{`oA1HpjNxgk1*Yy#g5y$IxILEO+FN!G`Cg- zsWSVMIN}?}TD$|@f-6))45p2CL;1oOFh~9dKYxvBwV-a*;V(rpvNoCS`8kGr*e#@?^wfH0xz+2pv>3FClBcjQ zgVs^S;IM!|5pr!Qd}nL$58p}wcMy@;jN()rx%-DbUy>5ge?^$Gf<=Kh^!;jN6lw}s zXtLNkSTO_Uasb{C{=DLx1JE65V~~Ko zJ|9J2aW8i8U(Qb>@K4VHQodFL2M_n+$McD4twiu}$&xC`H(U0(O?Mmx`}sBBTuN($ zp6q14;_A1kD|!x(>`Rzo<9-tZLx_OzRj5~NWW*mvsnZQ3=nvPb8ba(>_^Q8!1Ym6& z9n00u<9y#W$3z;{s3&IRix$OGT%&pr1|X|m4%6WD@v6$P92zY#q`WvUy()m z)Sz{^gai|^$W_{YfLdOd?C(GtT;~VSS{M__n50Jgr&R`~PeS24D#i!-OyzH<8{6d1 z^pE#q#~euOO*pp|8h+DKa?dA5>Lh?<&1-7HUKsF!Q;btLM+d8_@Br-LP~sD!g-w=l zL3f!$rxW+IDrMh>4CS)&Ka$eGf(cPjkgFPdIL@{q)&=&l?*035M`3T(zuAl>Hs?Zy zxR$)YVdT?r5WgIga15skrK3yZ*2w8BvFxZ;>M8a6m&~(Xe8lv*fz7*D3-N5Es-p#y zisQ{T=bQ#JUiz7M+W>GRbjzhT=|tCC1F>MMl_41tyXi>y(-X?{Y42$>QILZQE;Z+X zjdi^dan3hOHr;wk$oL~dh?9|j6-Yf$dA;)`{d8d~u5uWB>M`^h*|8^2m*uM;ZC9zk zuudFJUPz9pWHI4`4F2s4!cGd|Ke4jmpnRyNoqiHkFc)>FqXJ+RriR=@ax}|PLf$5r zy@@;LCT2}VS63%ygO46Ki_O-*1Dbt!o7^~X5s_#bFL?bb@bTO^U`9Ufv9v~dW0{De zgpX>@$9aJp2w{Ds-$X^;2-`b%-Ozk4i{@ol;;X7Vn9a}^F+ef^IMl3f7(^7RlMQc@ zmE)8LA0K$>Er1k4+f0-W(ff5; z{0oaA%j4WpQJ4lfCTxN>IUK58|J(2cVuDuR3{tS$Craw^ z;qtPCP)QfNy_uQY8XH@E%Uw@le0<{bc7*m5f_zpJVj0n>7~#*cz~-xyDswj9<7t=NSb6v4Jm?`r?bPDpAjA* z{vVEs9sm&ohp*yPwU|COv{J|!XG6b*H}X~tM9TB&mXiF&vDt6OeWqZKyS!XFCcxV? zJXtD$tysRx)>652)8>zTm~WHL!(C*A9mJ5F9BFtIExt9@o?Vc|tw_8npm%Yc$2UX20dbN3R3@;7Et)xpk70+(`6@_S zB%aSbthxw&>#z_=ZXm{!q+}!8U(PvKIu@)ZSLbRmHv^v&dmlNX5cPJ%#WWG_9u$8Sua7BeI4W$CAOVU_nB4Z@y^eUX4gD$=jK ziwOLy5K4;*HnMa+uQ&{zS|4^em5;-;Ye2ql`(7pfvM;r`CFa<46Zvw~Rq(8Upp;QIKXWdmT=jQly5#zm%e;gXmNKqFAfmu@+NB z+NKf~6MzT8M_a-2*cWE{ZBL2~L!kx=m=K?Gs z=N}N+1(Z>E(m6-DjB`zaVgNML88?jNN!-`qvL56RNG-Y{xJ*?jJR;lh&r+?J*ZAp% z6j5rLXzQ=2(kp3KhnjIo=(*}$e;LrR1PqiH(_eu(J+a!bg9dXrK=HUkLJ~XjQ-);+ zKVqF1w;DRbc^)9pm*GxvSm*(UIRH()9o^w|@O5DEuYNw6CI`g=YM={Lcz7rE7hh=R z(cZLOMir7hPAkJjUKr9@Cej#4X|_uesHm%{v*nL0O%9CQ`?(X*yCVZ;PT$q4LNYK^ zGUEXL5@E+!RLU3!s6=0x!TWIH(6nY0!#x~3{B>0+d*<7efK5}N(!GAAbO81~a((b1 zYJchL3X?^=uUw!o3br8#N!Rd~P{yEgN%~txnY!pcPBaRQ^mj=%EJDi3kY4oI>8*+> zIjwJ16$UYB6Kzi8YdcZoeMGg`k!3b_0u(b2I7&W8MRrDRNN!M1&JE~ptM(ql{c^Om zb(ZP6{o#wKko(yu)W^etGa%fjc?eP9jRts81BPxWHY<(}tk9`%`9RDEd_Ls36xv}S zKSiDGF?6&hJ-?w!XoN8n%&*K;tN~wb9=H&#WI@>_kqZaeDY1{l@#v0|p(tfzoH(88 z`sJLXNR6vTtcy9E6KPAGB0YhLB7C@ePD0ExuCYv=E zG)F$;_7WNwfz5a=EHl@6QaaYdApdemJMhuLoaB69lTAfi!sPfxGw@<@&f-_S25j@V zSd9Pkgg<3VG{abWc-%Y05P6HrhR`bK%lS=HSC?nHCH;;WRIhorkX^~1#q<0H^oWdv zw?Y;w<%t7jq1x7W3?Mw;7=&0rHV9R(cd_q0>EtQAo#?k*M>~L{~gj$ z2FcVk!<<67HCJLVhmbl_Zg%w@Nmt{nFRZ9g3Z00|G#@frL`t;#E{IZ2i;|XOTxiFS zM`}o_=Mqmcj2#QdR1iM=(xEE?ch~Or+})=FY^V2`loO zq_m@`Mo?IpQ))2O4{fL_LD_qkfJ3&3QPv;qGgUnXAoaKC+T%^1Lf3_%=qWh6t(?3A zVhBlaF};T4G(V!_osKaboMVn3Rq0=$S3?AGbF`wTO<6D&pQ#cij^loxBeu2#9cbNc zEBVn?I?aVlcPHU=PCD?EG%o}(Ipm{lkb6Y$TiBx~&THr07zaQtClPP|x`TaYS_AD< z9!Gf>&`J_!>Pb7#*=rDMrxhLpvJ74l?#Uo7ff6(Qz>m@OPu7`G5Dgt;!Dv8oDq-Uz z%6y)&&zujpcUjpgLgidtQjIrJpI)??7PV|mdK2ZShJr|63^)Fi#a;` z?khZ{aOtBi*dik*ebhZ7*^`yUwdE|L-3vAi0G=U?=0O}qqra|{|CJi^jJOzNjCe1@ znY-klR{tmzH+jeDJTD#l)i^Vj@bGdWt>%+2sSq&I=6Lcq5yv2pjB5!7UeZH~!sZ{> z;DP1KR@fiF@wLRz+IzUP4wXIT`Y*QDUt4(j(V5&+bIW7}eZE1Ah6mS@e}X(?3ckUu z0q;?T;vf4KLI%r{pDUmsI4lf`H2(E1c`6WwaQXpmi|)-OZoDu_#lgKF-q`M7Y^18Z z_%)>)DOP_%$N32ti_0mMT`CbVnJ!)I|2*KlMo8_D2!H<8wnN4DypV2|22!yifxuLg z1Achbq6kc}tpc@nBsz3KkJln3Ht;c*1u(!T?F<6&IhIHv>mvnZqimfNi(tzlLOD*J zICQu=G0M-=PcbGTOtJLuuA-C=D|vXRAN+(u;Rkb0=lnt$`X~q-gfJhL(2FBC^G}UB?4Y(t05?Rb zy~b*se?(PYCYq;*g?Dnn9@`Dt80d7n_Y&f>op5j_sMG)41|kvA+vhC}qAxsw)LQ0y zZO-M?xnlF7jO7XQb@@RhQP^=1gv}%q6rbz7=7jVjj#@9}w@bRX*{@wP#X~3dj>Jh+Njs6p2@B=PM<@?Ziz_PtREpXgp5P%dg9Metj)T1V6+6+!G zXymP&hJ7k1O_yO;-`&e2nuRt49#mlC7GENBi7N|``>YEm6u%jBiFU1l1$ewv4$J5P zoxTR{4b{YZA=(2Rjiw6 zQzTG%-kU=kPUx@(bF|FtHlWEaG`Dgj*Pf_dFQD6pfWe;b^D(*es}8cLA7T9{a{iZK zM5wzZem z2x0o!1gI_)yCm06Eg+Y6YFD;CXzn+GZ_`4#lc9IOAe#Yg*J;puN!fXo;c>BT*Dk;J zANX8{$Vu_5F18h~tE*$9w;hF~$vHR{;nf4^f|l zFokA=cb>1*Gku~Z_;e_&p-c-Jp9;bI(SJa_zE}i*^9K2>EC7R!?ZNU?m{Q<7O)c39 zE0~!UU2dir_&(DDjZ&yNNEg#OX&b_6cz67)Lf>+!#t=-PC&QMNxOYV5xH{lLA9GQ> z9k*QkwBSvE>8$9S_BP-HUcOe)XDz-HhhWr)7v@L-qi(mW>s&=4>Cp`~G2O~37xf2v zZ@NvO!FK?w<+eh$A?5Vt)ZK7iWo}eep_3>t?eS67=GgQwmjvu_ z=$Ju&F9FI~egK3Oht6&ypY!lPd>u(Vv6j#?X!joHOZJ5EZFwI34Boe!7)3UQXpI&{ z&$z#j6Rq|!v!j3*d`XlFR701%F+iCMi26c zQ&xs#3vdzTno1lVhQp+S*)o0Z)?6<0YQ#lLMU~lvsf{fSyfq<)Z7ITeft9p!`@dM>fLh&g%h%^76X2%;|CgR{cyX2=&u?IQG7NRRTL$& zH$Yq5M%ELlPV#XXRK;DJX7%OI^IK_x5^3f;4Hw4v ztN7@W*znPba-QzM72{B}N)Vy6b>m?tQNncWCfq)d=F|)%V)pg&H|<~fo~_A^y@ktM z0J0FL=eDLT)J?K9V_n;CiBsr`Ht;y(>-H{@RPyx=a`0LH0#m~O6c`N+)Z^}o0ksF? zjG%aVw<7xvdYrxu@_?bfT8EuP8o$DKW`r$z@V+&srf&>0$qX!`i$CAmf%No%T2P`_da?Z%9%7<- zHu}}&$ZA96WF-k8_(SsdQk{y#a(YMR(=Fa$R}o^s`w`~#r!+E|H?_@T5k375YJQQ|Ab#oL>!IzDW;-?~t#+A91|*iE znApU{3%ifN{6jaI8vDN<)dVj~}eeg0JNX zkp{)h+^2C*(9Ze|t%fCnL?6o$1M&$6EV<+%0z`J%I4{sRFV88(KfUt_1OiFRaev?4 z)BCOp7w+q44f6HqiMBB^^+;oN?bPjK>Fr9CN(g1-*d&>lVUP0sfhIsq^C}i%$)M`Ot_z2=^A0#;jszaT~!vEy`7 zb_MMp^-BedN$5z9NF$UNA)}-o9~AEJPxSL^!)V7=zDsMr)xU8(p^QDCauxsFgJE^| zs0fS3-sd&yYMxFc;TerdPBYiKE8o~T= zu+v*qE=<$5YMB^h4K4Oi=t!9JoqO#PCh4eb{@i|iq7z~P-L#f5YjF@H3i=U z!U8(L0^mU{*d8_`;cA_Pcg4N&*bi;jW69ntUp7HSv_DFGr9Gmp<6sJ%SsV1ifIW>N zLgc?Evn&5uEwx5f*|V#`2!}lCYNx?Dsu%4bbizGwk!HO`5qfqeHPIA|EpqfvL*Ioq5i01{3yI6&cee0 z*qONglfn2O?F{#<<=;N;NyE*8_g`kNjh$-;TPB=wCa4@i@M2IwK}et$D^M`uS^^{# zS~hXy%1OV7uzI41q>#V{Lu&$n)rBjBZEK2=`mO8p3gTKYZm7W-ivyN9{*6X2boLb; z!jAlX{uNQ{uoYrlW3=nwfSg$b^(17 z6$Vk+3C7Q{H@nSduvYm}AR1)2Zu?vhWRyNH@l9P~hO2HwovI8vKHI!Rjkz%1hs+v; zyjyzlFK(n?aT@>a0tYp#*p?-1IPo%9$dpM!nRSL-1T~Y>Rir(){S)>N&@BsTbu3?t zZ}}aNc{`}_4aZU@A!!o5K4Wp2gb|U7Iqs@7R8AgJL<|}00!MzYFR<6p#UOXUX<&zTXvOY>epd)PsH8d zqzK*#?QV28)gGCXb$|={{zmUkqAE*Lh%=hAtF!AtszOCm=9x<8n`+aWoI-6vMGuLp zLuFPK#RlfMc!hwEX@zcrY_cVb?(4Bq_hnC0$Aib0=~7w;ovr2@faUxC!Mnp8Mh=?g zreIIiyP66oC2?!TjIrZ48irKvidk#ChH01MX$en#i^JKppv}kEJa}Y`nlD|K@s-qa zHa$K4{qP%dV-6Olpt9#@d_Fkg_l4K&ve}7Xg6TJQ%eSjb7AYCpT`~zxbeZRzypp62 zVJ6{{WZRVSVRbkPqGG35w7`E@wB=OR%u)@u5*#np#uFp4(t z3eI$rt+RA~N-A=_Tj@{oM%Y5&75md=diTcwv>>;fc8P~HKm+zJ^^vLi@uc5YtIfl9 zD)5*aVkYPEf=Q6a{w(mwL$C7crvPvbS#D~>+tCB#go%-RY@(ph+2KjvgfR2G0^wrr zmWRQ}<@>eA>6V**#*J(+&vpSP8O7N>;6((04uwaM(c9VX;ns`SvY3|~)f>J)A>K{J zn`9G7p~U73@L9;%MgSO5eDpkQ+qjgX&tl}8}!jVb(T$LFYP7}i0OzGKc?{B1J{!^d;xT}0}11}=l6Nb{Sz}(t*pPt0n zxf+^7jxvq5t~s{c+qB|#HXceMI|Z?pKBeP8nM-GoumsQ2eothBiqE(Dep0yKWu^ zZLxC%^k(V$_j%QB_AWO3Asf9B(UfCw^f`ez+=D0Pk8`b5R>lG$7(`+~e0KK4lQ&dj zDCM8Ix)~Z?`<3lVZG!iyip@_?I)h;k-rYC=L$v*`@8cIq%F}>vM087P zyW84#2*lZ^`V+jV#-^!?t=1+d*P^yYIV$I>+CI{0-iaATepNbT{FH6f*}eP;`)uh3 zNcDmuWJ4g`Abz2BhQj{)9F~IWS-b5e@}V)yPwXUKQ`O`Bc86Oa7t1~og~l(*rt~}m zp~)%7C%unR!|Ji&k75Ds5-x32p+Q7|gd5cwrQ)9@8!Ttas2%WQ^v`UvT{Cj3T=L6#yAo_1k5S#kd-q;&rhsFE$V{rRho%%{2e)roP zMSMvjl)G1$eu>VNNp0|gdnz2Kb`GW^mK$=&um|Kmtu;`fv~cqeIle?BnUX~C6gf{m z+!-2rQ>050R4vusqW=NCQ)(8~#=*5IFZv|U8bhUNHq}t0Rl|CJF_=A$^aH{pAfLlA zEHp zRh_PM|ADNCIi)3H-)6<|EhD9HKtm)*q%h>Rce-QUC>Dr>364cS!jZf0t})t2KP4Niz?zTiT_o0PH;_u2CgA z74gSwD?c3xOM4Qcjkb4TgllqfiLO1s zR8y`!;gLwwZmBe7_LVlj#bUki8~wmu z$Hm%UJ*v;@kIPfo^3ek_z+=e=1V=3sAxGEq`x#ZzN8G2z=IoiEWA2^tG5DErD@pN? zOI+Qxs}1GgqE?e9kV;tJU66w~zasS8*2y90FBYM)#$y3gD(eWTbHaJG&Tl8nlv>Sa z12>%M;*?~q!&bPkW9ApJAvte_pEQ~lyGsPsIiZYxN)ACg%fw&_z*`hrjcH~*+meeC z>Cx~v#BC{vPT1}_n0N7f`K_R^ce)=V$qQfD>~H;2fkiID{!(P;p_@^xue{rFC~uvJ z9cyn@zdz=b<$sW~4r9zI_Xc<1l?X>}I*GXoZ?&Tr!C&kd1;TcdM#jlLN`NV!_EvDN z|2#kAI()1~pSgp^0Jg#kdu7xm*?p5^p4oiMZ(*Zzt(znr4jf8&3LLpmuQ7J^t^2Vmje zg0XT|Uh+o}qK^~mbd5I}p{=xmbL9G14aM4ju?3W}x7dZNYqPfu6~30MF5``;WXe6N z(r{$19t)qy%t=09w)Pv2eew*$A+smTivC&g;$$Q?(9<2N|kNMkbhW)>NW}t8R9QqYo$f ztlCFd5DAtvD(b~ZmmY;g13iTb^MRj3>)QrOF(B)ujPpkVz@}m)yHTGlry}ziLfV<9 z!t;L{w~PQRHZz00*vvd-e)4r*{70f7HmAj+N1UVU03&SCooppBLN0J_BgPRU_&BZB zs%kuHYH-Q&n<)tucC>va(b^tI+P{?c2FVO7q`R5tBcV;ltpY~eF?%WCAEN7Av*N1|~!#h54p=5bbVJr3LP)mrO&h& zYp|2c05#GBW$||GG)u{0@pe&jRP${etCck|`R;Ay5#3mN2g-wTXzfgNsKItqpnoFQ#YT(kKQnPYzp6oDc1&{aVP+h{nYb0Z81!sT0y- zbHTniYdAir@x!iWUS+fKQxL=AvYh*lJQn8vl%=TwS{qKdoG3mk>QkhLX-GJ3Z4=FhI$0Ga)+*H2w1_bT7M5fUQ;`Mv zHrBnqh!B5riNzz5XveQ2&Da(fxh%2-EPxKiX$vL$EK53&S>Mi2f6pi|^66POfvgaW-yAZxw`M3O*>GC@ zt&IjE7F=7v4(Ph4Hq1+nsUJ>SPcNK!{K!9(7y?JhG?*o6uoF$RUJKSNywOGbB+u2l zd^1d+6JIX?g5Wrls3KEM7{KtMtTRpQ^N`Fu_^8L;5BmoKlLdj!0@_n4i9q$PN^VdL zU~goqhXqb|cI@A5+S_8BnjH*yH8rrKfK7#pzQJ8$?NV62_N=L6#CmEo9 zXKwW2F66l|vSpQ~L z4XXTV*sq2}o1%rNZnB2LT6UXb9NRg!IU-9*yqjn%OLIAuRnEfjy zI*^O(Dk9e@XJ$L9Zo3&CY|HdZ5*uQJ@&M=`b`$R~7vhY_hMjf=X?s(NzpDD*W8niC z_!8xC%$Y3yq;hgSW$w?+aua^{#q>ZB0Tve7UNTAZ7uvp#ddgs8sPC*p#s{<23GI;6 zOQBT^O9ow#h6a>oE8z(KxG9S*Oi|v1@KeDG7e@s!mtFH zmnGn`SsyeNLEGc@ zN+dbf9(Ac=Qix)k1T@GHwlrKSa51e`U}rLWIW@=&BouFocPZ}pW3(o}NQsOR7VFtX zaG=%hLI*}Li}t2i?9{4}>4D~;Koi1O!F8XBmf-fRq6jrx;H&OrFX;zoLI7&Kb>qsj zd>SO|aFfB$*BXw9^#lD)>-Iz?kiTHdLVwS8&g3cf8uY;7BJ{}S9G=~mV-}_|x7vo+ zBsvS!N=Gnwmv@B{-L#bt)S*bCPPtq4NphBBbHaKk;7HWM7P>lsL#(D&U*avd1=r(j z5(ad5_~3oy4Kv^?2ELp_Py?na(vZ?`roo*u8$c@23ggCMX2cnL(VAKgs-{Ad+!iYB zYMp|yxu%9T+ynMn_{y-%I8<&-_~lZ;rA^$nuR?gMYLa&tH;t$^^S4XP+Iq1;q7d6^ zSIgf{*5#p@O!#>+5aII&ntBOA-7J5zY2Z_s?s<>r$)_@bxD3qywgW7FwNpRsxn{N` z#6QcecL1+zIlv`0p<(p}N@;WdlXd7#Zc6j)p5fNE#D$QjyRVjAQYaomCM>EFj&+SJ zIHyDQijuR+oc6AMFm#|ZGUktI`OE`TPR3oyrgHm7_>4K;$RX_QgyG`Mgfd}2 z-(ROsiIQ%g6*=f!=KvU1D$02BUc1Z_D~@K*jPE?IvKoeS?r%s)vc%NcsZLp=BS59n z#|zvoaTG%#l(nO1H0|n+xyG1Q5IS0O!q-QejXW1LpLAAk1F-f=3vSBkjeM(i(NSoo zn2FOaBSU_*>(Hm39`X>hf_>jQrfg3yR9z_h-YlLec`W6_6azZCGwJOkRDx$4AKA7) zKRPy@URKruhS|sM7sq)7tnr#}Izq(}Mgex}YgLYVN(9ELBlX(fW6(pqk{Vcqba2EJ z`*p5VD~i`73y#Qf{fL7CXceqWa%Gj13HN;VDq%cHZMpIS$*stVafRp0-aT)4h=w=b z4H{dFE3e3DbpXTaR6@{UTF^u;!whwK}<4!5Qc!# zlah@o{hnvBSfiZ3xG}q5U>#GbAzb!ap!=3Ej)|V>Luz5phs@H39&O5|b(6c;oh{Vy z|6=PMqcn?_V8OC&+qP}nwv8@z)mOG{blJ9T+qUiM>3i?{GjC?C^ZTr`_Q{=lM`T9E zUp1234vw{Wj*a8zE7S#vpPYpeWgkXor+nH%(~_7k-qPtj?cknY2X53Y1qc_YNC9kH@tq{&T495%yvyt^LsXcDsYU+KRLXRYzUuK{3N0$5<1lUIQdQ_B{b>G1UjO%9*wQrvCs>s+EW$c{^Su0PXo zpgz-sEr$sR>%6!{PWXyu$u@*H;WJQ)G6S=tRlhl6t>oP0W9=%0mKb#DH#}Z-9-80< zALX~or<8f=E1PfWkr1pU1Z-L3Fzm&rc+@uw1mS)E$uDwE6+g%i)3suZWY!@bE`kVW z6n|h19HZg??~9HN4A+0DPY@=ie_qzqfNf3LxPNZeJ&&}%%fU7`qDOQ2Fr3SmYBo~5 z%i4;c)KWnIguM*)))F$~TFPTkHc7#%^o>t(G6D{v>+nHen1U8--(gI8uNVG)e=zy< zX3z`Tn4yTlH=AYURf%bc&D#h))+3Vj!}jKR*a!)X?zidw{32`@~6WD znjO0AbMvn5>k&V!a_vIgnXe}69-!W(bY4UFAuw138>=Ycj~q*h#_QgRRN#5Sm)3rR zSxbKVex9Y&em=8Hb}2q^zZ}!@*<|-wXr5)0H|p*h&mD8Bt>IA#ssPMH$A)B6f#{9n zuZTd2R7^6GAUEk4S1p+*=rO~j9j@~SnMxnl0|W||LHNAAoqhmA30|v_SWAvm-R- z&XHLC8;5o@=Qy2%w}P|x8o=w*yhZL=CF(VU!hI!+WF)A_25qZII4_Vr>M=0!*zb6W zK&Y_9AAp+SqCA>PT1;r_3JGGs85!p0y-qiEy*hH`_v=oCAuG-NS5G)L2moYE*^(H+Y5qmG{y(pFG~ZLrH)gw`wbfs8>7GU^Q5;45a#B9|zTr9@B-Oz1 zYkRx5AEfa@D#-cOJn?;mtD~#0TU&Un4@pccR(02ce&r;+@~iB=pyRBjfa%%Hov-Npl`RC)mF32O0F455Qjj&43)NhS z&n6rDC6@m{HXxXS7*kC;t_M^z5>oH@1*I)*n0|eh-UwLAMh=at7rfGcx4Jog-Mb0> z#MP6Fmp&zA6<-6lhYZc%c-Pq0G(u~m(?Gpi1gO)v%wIxosWRvxnWrt|Rd2=J_PB>; z@>?<1Q=(aEc&*ypkyWs>M=xLGP31k(z2*V!^Sv2^A8@Gs&86RlfZsmGUsGDe=lNW9 z{8#mpRU?HGU4aaJhrj#)UMi$fDx{E5-H)X5Yr7G~v5!VDYI!34PJ?6z>WbinCWDdbP41w(U<>pb%1k2bH=iZ&}iflDk#g z{=uGl8-Th@jj)(Z|H#~?B)m%QnhUj*l|L+u2lX(Lnf`dv0j(azCEoIAZKkP~oiuw< zi<${@ktu0HW>M;sZ+|HqI@wbg(45UrJ_$`DnCu;7)~wZbvRr$<$R?kA$@@(js8LwW)JzJkQV0`1NijOD)wkUA6*|Plv{kaInN@fzSS&w zt*Jlf35&vXLk<1bs`XhZcN~A3B}3KxUa`<5rwMilO|kr0GmBA>Ug;_v88@D6>n!h} zt)_Kl@(aM*Qn*fZy8P?60hFdDwq-#I)E1&_Jic6ZkLWK}ne%^bhoo|0Y!Gg)e+ZTe zFsv!-xXFdobE75_K5PoH>3tacjyyauEv4w6Rv* zt94?f6gkcAB}V#1F;^g2yu*bT+ix-w5aTm$+xjzAfg-*C^y~ikie?@Ri+##}c}Qv~ zz=eQUJnt4?_9FH8HiWe`IYl?G!R9pg!o9-=`*Aw1il_C1w-y>IGaPJL7AC^#8*gDt z48@m0hOu7Hp3_Uat@YDImoDt+3{EDc-g&`ONk>DyG=JXcR%oNkVyDvNu!o@)u-hoX zgRBM@qnFPJKk0kE(thas!je0AZF5ez$f1XOJ81f&_EFub;Lmw<@7z2Y1^N0yy}ja& z`}#Wv)B3QZ+3M(I*IfB@vinUU(xyO~jBJ_0xd?;F8a5>M=}P8NfI>(WSO^I-l$LNp zp}qh*&4CpG7={a7M~mrkCCc}n9p28xb za!X=L+{wnCuAU3kIPNc`udvnU!)Id(B|)EBQjEaGm?bY7A}0m-t5lSXCoaRx9lj)M z*)HO$EgHH*>m%F zvJQ76D+-RkyoN$fy%>B5xF5-Z)H6w8nq#$2)>-3iCrE!1EYYCCZQMzn_CyHL%di+;_&Fz`$7ZdabyRlFFTVc;MC-yR$Rd~o$1z7>3&sl)v7DlDI!5h9* zmsA&YbvN_gNOl>c@{cuP$$g3VHB{!WWjRg%m}uIGXhMqG#Y-R%iO%Y-U%W8VIJAS< z3d6ZWkEW1u?S0IH>c6`@VlB9`HMtOEDLhZ}BZlJc3sM)Auqn6|;(x2KqJHsDU!9oy zwfm-HPWv|WG>^N?@10g|*S$BU@%p;;cHyx2ij5ul4Gma^mb}7wy89mw=vdV5LX;}c z^4j4LVp8@3RUsb7B>`umf-o^B6~Lo{aQ*KtIjo`kpVQXwRP)GOWdnKjm8|kVr)^7^ zO{Qld961RSnG^+s`upo6y)_;R4`vZ|1ed^zhd`dI0Pmcx_Z;qXzLy{V>kR?*3lbP} zbONV=Co_2T2tgcnKJ&|ntK)$xka;IG(^0`}zy)b94zw(<3ET%TbM4~2$3D4`7%_l` zOe-tm%U`z-i)j+x2UA==nDRGNc(_$)+#23Nb{GtGpVmH@R(veH!H?y$%9RHvuxNoG z(j-xVKFFIMMFET?jQlu4)b z%SM04SegwXTwpvCFWsP<5fl)O@gzX-e3W4RhKL9eB>x=s-4_!r=Ncj$a0?QkL;R5@ zDrc^}MTmbGNS_YSdwM605;M0b#cq?hdz#rCVwFMY+*WPy9?vCK?Z7ViHl;C8+I%v; z5IMm{-Y9aBYkrtW9EJ)`w|*k4Riiv5LNE!A;VM+Q0%M)Q9*&o8i4Nm2DFu{*)MjRn z?TR_>k1*6!QXspJ4!ftV&`Pj@AX7M$LVb@>vv^%2B2M;jU#R^X1w#E5588ls#bPCB zRHFtPbGNM6wtZ{TdCQQ#8s$2&RWaNbxz>HE4U3$LnQhpMYTGj5wzJ}U-OSTR#E``{ zZuxeyH-ypeVBEA5T5UPVP6inI2@7mX3M4{WrmRx>TkhQ|F+_8ZEq;-wT=J{n-A&Zd1x+Mpl1t}^+A&hNjMsvJjEa{m}*K(n4+$Di3 zi#C{?)v8U0G_&$~e08kCXg#@FfPkkqd{9N7oFQ$+Jk1wY@Cd|d6O0y%z>F)WHGpvg z;$|llyVK`LnO~I(C4wv=UJLHem=s+@Dqpk@0C?;)#^`_1%btLY3d+v@e<7C%*Uu2Dwfu9i@H1F>yoL z;r9KF2Vqh0Kb!5OR?0QQUA>%aLzhgXXgChC_6}Jzc{C0v*S61Oz0$$=3pP}-Vo;B9 ztbscZZ`Wr8Ewfi5w&V>sE`1@|sLz3SU2erzURbd7%&ecG46Kpvx7j z7i_Bcbc^Iw8cyc7s{^$zK96K0DM~?NqHh8f`hg4~O2k!G_>hfi)2azSv2qe-h?w-= zJxPLZRKgoRMW053r_hhjxm1;iv*fO3gjh2xici78Uw{!G3>}J3n}75@7t)P#&*JQ> z-sSO8)F*srbjGg0*`6C1>A=+tEc9B2195gKbv`rvJlV@Q1(9Ly| z6?jzWKhFu3UGKh^G&>oW6kRizASezc3IWiS#RsMy8?)z%Er0vMY{Y^Q@GlNlE<|YFc`wW;kW*|7SNQuntMWW_uk5Nk z;?A~CzU1xv3hYrleRSFL3Ib3AQtIJ>gd@-8hgcNUw=!trw+Vfx#dBoxX?2TGYwHyJ zy&~cx`dSXxJNT+lX;diHiWI_sPZ2@jVTUx770RPM&w>)ZrjI$eUN&0X5tE^0u6Kh$%Z@?MPE}sQ;eQ2)Z;e=h=4}py}q%{-oI@9 z)t;^WkTRa7KCbhXgaUyxhSQptDktr~2OFdkV$$BwguXewb+o-juzw68D|(4GB@0P= zx&&->qjx#%ndOXT#Q#7LE_AUv1PmZIc^L>KIOmwk}w^bIsrO_v_$?)tfu>OVy8Q6exF!927Y8q zAIMzPnv-BS=(g1bCP)pZxUrZ}uX)($a0W2CPX8qe=Q!-P6;T?X=f+3q5>PjfPB=58 z30Sn?{O~d->LJuqluk?Os$ejc;g$2qlX$X3E-4M7OzoPJ{A?uQd|@Tyy{v`391&T8 zOH8PtNC@*Gjau(pPke497Yw9-AJz;s7pzuv&0C|Db~Gu!w07dZM0*s}2#IF2XaXRD z&cSKb_3+&J!DTzMti@7MAlY-kWJOfXJ(41$&b>#1*Wy-Jp!PDzxl5R3G{LAz`4{-* zuxk9jM+P%f0x}v1EBk+og8vZJ76($#ZS7vMKb#g^7-E9WzHGpnRS<+#rx0Qb@>r*i zSAhQb_A-ULpKloAdZJvZ#uX3MT$EVCeL4!_pu)>;If4!xs>4Qn5U24R0;$IO1`aV0?Yt|Zr)c{Rhk@2jkfIH=uWKm zbg3X3@zc~um`5^&^eIZILq;0-Kk=*;Ov=RtI*`T(#3wv~?XgBRCeVpA5+QpxIglsn ze8O<7yF9{N=n`-!VA-0%s?*Ozq&G-sVIo5uhjXwrKl*#-0ELt>h(1l`y?KaYL;N>m zok9rkcc8blcIS&t11?<|G#q9lOXX;E@Tt1A>F@%t@`3EZk2IGn*?j(E!qwtiM6IJ{ zxyYDnNgXnITg0uMKkGYe?%J)NLW`D0xmzC4UlJU>Ysv1*2A}SY4{9D^uke<1wSIC0 zfioVTzswRL0o-UWz!UOkhR0&_Yhk28ENW`M5y0o-B!YRTq8MP_WEL{ZmQUx^9i z1b^a|@)7g!&QqbX4We6$eMSB9zAwUxmA9{poaGxGOg2)l-47dt%8z`95*Foy43>!H zIHx}t{5g+nZg(r7v)!*kUE$Fh{uy*XUJ){S=_ zaG8b6DcJ|Y3huLO<|nyYD(FR5k6lcjrtOA3GR3N%C|rYTrv7d_Y|B1y>9fK$WD1dy z-Q>>>?~m1-8o3gb+gFg(5R8!S?veTVpfRp`0Q{>Ea1B{8UlcAkrGLkLBq=KzXR5qN zElG6SveO&g@!dT)whcG7k@}AiXMDogm--X^r6#{Je&-pO%uCQ7CdFU@KHVg!SuP&pJ?=3?WbZRD&ZV{SbY-+={BM0si z27vko4ztO|lrIM($W#pKY*8WM$TmF^l+oBPX4x>4KC1P3!oQNWB?a@+ifO&vRFWod z=dI`dULYa`$vYNut@X6&{Lj_TqUX_~`7*>%NoH_HdXtWV7MI*0z6SyLv)GDrSiRKQ z){>`_@9O%>TGK&GHJ*HOp=4~ipkgc9QhV0nmwYpA%V&W6p|&a7^vmG-ra_GyHj2}l zU=DvGb;u&(4XcZ?~ej^@L>{7FRZ^w2D+cUdtQt$g-K49BRmMSkkNwh!4LbzmhU5;KQf$h zxNsB5nsfdw%3dK7NgM)wf0ORiALUt!wcDN7+&_f)V8|d)D8C96H^Hb#dnxb%Ovey_ zL;D`um|)e&*KjBlA%ey-20SU8eIflS5G{!nC~K%aMvy^bbY~K#BIHP6b{9l;k-iZI zG6SuON9z{AF~+11fW$RqB=r)^>^9Em0Sy zW_K%hQ~E+#xtltzOsEz8l1DMhl?gFAhRBxktiZLAZ*8m|%&>X7=4zwUvbaYI>t^)= zuK~ZdAL&a5t}(f(S<0OIs^wd|s2zGnj|UNhqSd1AoDbu6#ExA^bRadr155+R&KG7s>@1dH~4=pK$u`I4eldOe{%k?(Bv=@MObT)H+>?Xfy;dQ z6r&>7I+kiRq)n4x062~-D{Kzrv(b5T+OUkz-qSEKQ6YJxtOEfKa$6+ZLw{(fNA=13 z*JU2%7r!@sp}G5*o_viub79Y0n+6)Dxh}pyQ5&-G{uA<;EKL9379ch@uK#X;VKsS2 zRA!{^+uHO)iAYM;mQh>Hi2^7cbO!$y3>P6H5(Indg0e54kxTcn66>OuK+T8It_;q9 z=@Xhm$Z35JmDE!z@pJm?Wb}2nwYTLmWB-@e`@3JKZytP})YTn*?Tf;db?u7Fs@6!v|&PyjO^(Faf4nL^@W zIRKQRWpSya($^g|O@>6O{k%lHjlHwDc&^#aECrz0oZO8LE{Ucv_`H=fIWNj6Qe8jV z2(MB#oKC}?LqebtRAp0dRm@_IlZ(_DK2(#GhD3Pqhd$bx%m>1Z^100&HpA;-a8y@g z)*S0>saicm2kL1`#_35oQHIO#B4r%2$N$V#>Y8PANu}(~zntGkp-C`0_wVRd^O#4= zuz2|AY~nHuCgX=Ux0!FD4E(zER94SB?5i*p)BlnhYtkH)2?z^!6165R2n%bHAv6&v zGYd;n0JJnVGYi|l|F7~-2J-J=lrwj*bh9F2WoBkd+J`0u=uF1qb0TbC(%P&WxQW*$ zs%`eefq;#Xuy(sPII&#!1@H!~K|g$wMxH8F*p8k{AT^0&P)Ca2$5(x3!DfBE?w?*) za{7I~7xI4XT(lQsy&j$cY`1+CHhrtiXYD`l+PdBSlK%dDKcBpIeXpnOKK%ta*8Nz-RG6e{HBvmW7>vYKF?EL@`%?Nu^cuj4?REi1aN_BrBUgZpRn28%b zYlI-#b;MFr(BD?l|Hej~mJw|ZJTA;pF3brHV8^*6KErrPe&MVYNSTB`!qL6FK=FO? zw^mBd!*P>`Kbra1{8&bu>!ZVN1P?#Lj+%U+0bf{`4l|PYuqW^AB+tbd(N-(R#A*eA zyygbR_1!kasAVp~Z|CeG)BBXb%rk~xjIj;l5Ey)}N~;Pfp1_Se7#V&k-LBum?Wo^`Lp{n0`{vL#D6bfDvoo~5bbDBBMUSog4 zmNjREF+6&W#((Lr^sGQ(zr%y^LafT)MiTX|Y^jQuILb-(+=n2S6(8~EScGj=O0&@C z%h8i5$u4eKXC6?DH~F(P#|r`Ifr^iXWSlE8_}H4`f#{VDWOVp>sYN4n30UYQ@>9#! zedbNjG7qFOb)@oBm%6Vtd*xu7|5>Kdds^6>6KB-w2-T-kil?+aXISp+u6dVuDsPQ$ z6%x@0{H3Fcux$4glwi*DXVDh{(Mvqw+QRuFqSujP{?D69VAk9mg zO3wefG%w`KumW^+)|!eTM)oY_ps{g!rol+PnCYvAA$$u`UEY`kk1*a ztyLzlu%;v=M9an9lmigs^46e1Z;c(pu7HpEEp+)DE!PL{PzBOevK1#b(&8PfMI_B=<=8_Ze`-|(!=l9C&5C`h7$2Bn(k&G zEDQ78pP7f(*~E#DTXKMfEPKg=;^!Dd%8pR{rknMb9{ zFOs?6f`2D{z@q5#?X#KVH&yr~8WkY%NeEG=6I_?r*o70TvF@j z_`ED=_#!FpS^M=RRlP=(XfE(GBx2#2=6U$zLc(vTpOp;J;e&r#8apbo54$<#)WTI_ zViYTIs5zYF60M3RPr;>{?dWl?)V-AHNw8FVD+)OU?teDIh1x?e0x^myOS|QB^idI( zJW@b42$TT8br#-DG27muDcjjdOXB*1GalYjMqvq2fxq6NbE~cv7uK`BxMC?`*&84T znhb&0S3kaj&6KVofOKIMeg4c)l@btrIzyVp%)&#J?c|vrg?e5FJ0CU@dK5(m@n{o1 z)SB$lc7^KKGYWd&%Jk!o8GMep7?D+tT?hMPJI(>l6~?7pv>DTo+@LU*6hmtHAip)4 zp=O95k!kotv5{+S^6S>Pp%10V_kuL725*Ng=*r+H@WO3M=yp!BKI|y>%9IChgsRKX zpr;Dg!=>p3Pv|5-Kl6JJ?{5D!`Q_@H#m+O5X1RCwc=IZ!`(;|O z5LPM@ru}T50%+K?NGbS&`cVyu;J|00@KlhlSl|yy2m2PEP{0&N5(A75w=#&Rd_XDT zz;FeHv0+}q$fW6+*4{cG;W*5U{PX?%fe`>e;918=!u_G|7{YZ2KcJwJ%^Ya*NLA1r zNMN+HwnSX0h{|;)92XQY8e6WQ{VEzrbZ<{)SX!Ph5dk3u@^Ew^(3(thDzMCTSbm_O zXIuYt*SR0ipdY5c^6rJRoF$^4}st6=VT+ zeR;ps=GcKz2n#5LehvH^8(Q`yBIS>U5}8`zxRe-3R8;l!6&bH$mI_WhOhe0$Mm8Am zwJGf4^gIkq8Uhp!ArtEMaLCU)Olpvz0_9IbRIIebATC2K0PP{XSQZ~%l1XY2LK9BC zOnm?z&mE;>Qlj)EKv|iuxCup^sF(|oa(1P5h0az{iF0EwP?gfWLW3a^nP)YVJ%!1W zaDvDe84yED)9@?H_k@B%j|3sOHoCtFaQk-KXWCPo>weF`C*shriYV?ct(F0Qo!^`jQ675BBFrsVIHV{5QiU#d~ zIh$W{*_$hR;8XuitA5z52tKroVjdU2k*`eb8)4nwb;`j`X8Tnsx`LY9;xp0Dcl$Z4LX1s*tx zJyS>xlim?krSk$@fwUlCLo5;SO?tJQqsbPdA%P-)h>YA3T0+SX;$Qyd2WlkC7PDdi zDqqMx6IgP9TEj$qsub>t<7yNJ%Eb@8=f9Y)m4TCOk<1{rICg`jb+MAeZ6_B~0-|hs zaGL>D{$QJz)uJ+F6f0sQw_;?zo*}J;%Z-0}hJB{y>AGJPZx6LStTJYwlBx zKJe5|Kkk(JM};;S@m!RS6N&S`lN6?NCrtZE7bs zQpa--SRUSO)>|Wmt^otGjfNP4sbXdZ1J^zkCvU1jlOJT(k?n7{Z^98NP=X#KW=qeO%=L!Us`&WXRH zMjOMSzeLtHzipSD0YU zBRjAT`j>;i^f4IOEGhnRFsUdL&Ox%G??#l?jE_DN57ZQ5reFby?52XATda!W( zqmF^O{wdBW0g2NNK}>L?w_cHWouc6K#BL}enH{iUzE*aKKoN_?F-YLvd)Jnu>Xg?& zKg0EZov+MJU)rA!X&PU-vJf=RB^*iV9@%l?LG>gU5o9*zt6J4RvdR%j29F$cHPUr% zEtFSTKKrK4W3smR*S-89iHoOp{)BLSL~Z%z@cwdN1t9quf%H!3vBfm)Dcuw!)_#Mr z$c}%m9Q?F7_{e=my={R=rK~_Qj89>t&f$i4_xhJTb|o~s#sE3~y)H*Bg`4^Ps=PD` z8hXNwbCk_3slmaF^OSbQ7y)|{_%`i-!;HQtCR$Pn*B@-)K$C+{}aF7Vr3|Fod{FigzfA!*XlyLpB+=p zb^Mj)+yLA);byGes%*b?M&Ya)Wd=W}9#KKA<)->NL^N6%*Jn&`;zth5GMa%-89|AGza}yH3 za@PK*JMZ&-t6R(R_Icy-_3Ova78DK$;8q8Q)YW)`k^FU?(jf;_2}LxO{=8Ob;Mpf` z?;`+oC{F%5o5Oik4+%_C2G4r~@HC!3zx}lR|&KynThKax)C=^@7X1$SDXonlp<;ma2zLX zl$EILEf}TJA)N*Wj`WPtB3njnw!uPT3fB~J53w$C5e`mXd8xq_a=5j*m1)-gjnO-M zK#M}G7Rg)y+a+QDala|4Cf&D(=g%d2K~w_@JgNm3DWarP5t^@YsLYMbC&$>TXvcOc z=U6fxkkGDQP3-L~qp8#Sa1o&jC_No%;J09l64`;u6Q8&%)%}e?Xo>np!SSijL9Dh* zl)5wTCaEY1n!q4rzUx&l(*frl9^B?HkKQCQS2xo^A#=&rIe#7=ktnLa4Rf8dt^ZK0 zhC!=kX6v1~OadEWZInRFpz)5bvD$M7^4)zmfL?MesMkIKFw&vU$~&M0l;@h9tA*A- z5iuU4cO|AZl&*`sfca#qL55saDKXGdwrjtLR1>iv9kWsn9>_E!KZl6O-GUo?b+fd_ zp3#%Nx9#l+WpfGHm&faa2HN;28CatQ)-AP3=-UB#ZyRM<98(yzt1|Xu=sD}3*qqk-F|*>+_e)0ZqK%=Q z>uH`xv9@vLa&xx^54?E)e(aFCTHtw~HGAy(+CM~bt4M+ZR_spFetzKp&Rp7e61zLv zU+=sH*LA^4_dbjD0!e7$I5Csr0MBz_DAgj!z@^z_2tz8QNU)^?j#yD~pT#IgPxe6Zv6E;fiU`LlqBo=Q{S1k6K}#BhqQlVmmPo{Vs{lDirsc63c3*}hAgx`5={z% zL|)lSzZ9F%f) z>#a(L{-K^X)-+z}NPGYMdi06oPj~%&({DPh>v3IOwW%=+ltpveGa>@hn10;JV1T%>@M|S+$gxy7Ujtl`pr|o5Rb)A1W}lcAq^Hq7GZjf zNsk*X{K@U6DUMV)3~Um8^c#&pb(&BK=dsKcTTP4+w~o#t!b>*X0f8)YQ^;EicxjDa?h|6>?z)DFX-bAWB+-gE6cYwjp!N;Ydw45kvJ&Kd4tV?Zl#(^S zGFtY0Kw2}feG7-7?w=H`T>2cjbhvjXRDF}5l>CXGkby}7pk`URAgy#{DJAV@WecVD zB?Qsp$tZbd`uPSNI*S;I6#Mz~#vJ8L;MQT}z2Xp&f*QZ-80^LM*(`PzR(2!VnAupy z2t!=Lq6dwy^|u~Rdgsb;{sCdM;N`oKeWENqDVRQ9+0=S~1t;39s z-rEp@Ui(@7t-$qnj?$~ib^phXOu8^KstIE`_``;_i}4D!CbVgGrH@dnAQ;Ruyfii3S}SZ=`9H*JC(m7~_>QDINvJsd|1ckurZW z^$A64*e_g#?)Sa=jK&>6xW}U@9rY8nDkrpV-o}<4%1w^*-CCV-Cj@z8g50Rx6~>SA z8BV_bV>L;Mr{HD}b6Y*4HX z3(J%ZisD->E~`qrI_u)TZS>;FA@0l{rbVSmlS@N_U3bU=kYqkB)T(eBp*)xjz>1On zM+L{?QibVIFZ@a*V`Z(C(LCAJPwee1!jf8Rmp4q%tQ_oZukR#I_#$RnEqA@h2`wPo zGxKdQZu-^a(B#)7d<)JPg$Z#1aRIrmaz!00j10OB$}hb`X87AAq(;QhxQs~$y%r5D zMWI*{6lXrzBAFQn(g==6JdJ}HKu%42-c$5YL@sTc6eyjR^al#}gjrHc8o?)+GCH@S zE$@#d46aN*b2c5Srs9Tx>G4DcZi7zi&s`d}Bmo1DPMzKK6@CEztnY)tJOQ)qYF_|1 zcfh^CV!k}B?d!-e{?yo54j=QTV{EN~M(ZNH@l+Y5FGkq&IduARq`)#9;7Mb?1bE>z z{pQlUu~RVe~OX{HtkF}dL9ZZqeSJ(d0MR^|H^~vob76TW6kZP+qXthrT8;|)5t)HcvOW4 z2WQ;(;n$#Ki1+Y!%M$esK+=J;^Un66UH`~+aqx4)*sagY_mrJy#l(?iuIJY`*`Ga* zumjtS@3y6km)h$n{IKL}`&73;VeykEq%>gxw5+~g)SJC4OKy|6kBEep0E^FH`)+XE z7Q8CVi5f5ujOmW(P4wPfNwy_aj0RIcmB+`Y%Zudhn3Vh|D?#Cy?2<2+e!WN&+F3hG99(sW^MMG{45Eu@xXvcJd_~K!>B>bdYsGq{4ctj5 zG~!%&-a7;3x<<*etl1D6hN8t#WdT_5I7J{z<_ZxX(8I>85>Q+jvwwixqggj|ng{+a z`&&SF`o=f4JW5ui@}2w#U3&Fn?ggR6LD%tpsdJrzBkeoazT>dvZyRG?@2KJ<;+xM; zoo{l2FC6jbTmYdCmFeRdX)}c9J?=EcmX z(RaOmJ%T)fRxjm7MzOecp_Sy9y$RF3%b(AU1>2|^`Z14FpNH=E9u$v=(jnag-2;OI z?F0RTsEN-A@trXVJy2Nj@t(XA59ERVM&2|GfTN9r&4i7Yjiv4_Iz?9lGr)1?Dv0&R zSzC&cCQJKcm0#N9g~6VRhU;q~Ky>9{Su~7;j3N{*Cl^S`>+H+ezZGO~?$1gYI4p3v zi>PqrB1@D)DSo9YY?-j9eqmY@4qAGVD)(@fn*vfyWNu28KCmu1eFw%9RbdLdX5|w) zV7MD43FWnosrQ7dOOa_eOFHo#(0$)IwNJUs&P6O+}*LXJ4!EkL5BzH zgJ>oP1hUw}Kky9I%>x+ob|WXjZ6!k(_Koj-K$;?KR&cGART{T#WZ-T8M100!XNVMC zqT@KM)PLY~Sg5$pFpM)@UktP4LvNJfg+i2> zZLg7j3pyL&~fdDCBXBOObVLJ)Z z*uo_`;-|0D2L#TMYh(s!iv3XaYJB7;QN_{OBAFESg_#kzP#ObJh-~$ZN-&>yuyUgq z_ZstHmiK5Jec&77^?4j+f!5q+ zkpuWjqdeiY9B%}vrm;#2B^eB8$ls%9`lVLi7F6iM7e+jL14b957uK~I`-YeZ2|NSG zEMD5!M?&3^3n1=z*MFq!aCrwh)Gmpk2oG+Z2!3L!kq(Eh5AcB)9dR7$$^wTMm{0T6E@Q<}3y9=(N5Vm>#>B}kIub0Y2mG8DNIjp%KORO%A?PBQ$$ zas|&%5YHwDIQdwtd&1r{LHc#Lp+@j(^H~F56%tarixWEcc=vk4xfnfRs-CoD!U>)c zX4P#_#z$E;DP$_1L1wjERBxl091s+WuLQHt@X|lxi?o&9fSCAgE4?%Oi_6Jeh7qau zn8Zfp?@Wn#LXVqOh*@~)+;sl!%{AVel}bnaGyv_he2zk#OjJiXV5@qc*?duAToG{i zh}+$G;;A`ac_2}pXc>nCVho1n!fC%Mzmbu5;|u z%rf>7lYPVvNb3ZW`wENmrpR)seKG9SGb<2RA01fCKG(k|)Hco!5(_rW~rGfEfbVn8x*P$?qk35M#3 zk{?JE+C`7$|MgW$2#^~jw7K&^^&73vIu!hRtA_3^@1OMh@?M@^SjA&p-qU1XTMjaO z+1up?_%Xu>5=LQi`=y3r@|4P8+SDac{8AWx%qx*P^|@O_;~Tw4jkR37>%Dq&hR@x9 zng^wjBA4XXrOh)}0;7m~l5O0=JNC1n;n~^%^J) zs5pEJ1h&nKOSOT$f1hr6`pxE$>YRj-ci2`xLS=uXWjbV|qoyB(yOLD|59-_vop;^u zZu=^G$yHN5k+gC%+AKR%Vfm$^PM`rkWcl^RHp*TZCS%K0Ll9XRKCRAqI8pkvAj2yl zKB{(6MmGeLs1`z~sda~lm&VvAHOb8YXxvkYmE}rxg?r*}_pE;+8y${vRwhn8<|<+l z6zF#*9vzi$>+_F0cM=$t^r>rtBs}l;;@29ePd~in7PuM=;}WpKrsd~CC*0$*WZqGX zA&G6|#&F3VcBU8&R8HRwdc|RiJLJc+behVkNpkUV>OcVCBGZ3!z?VAzKLC3`gulF- zcD{dmEao_HDwCzDQ8>kplPB1u$sDuw_#2Ls?vkZR9Pg6xPL304WFp52<7H`r4ad8T z(s&u~FyieTZ>zy^HFzt>TZAFfEj>7PKi)hM101tB-gKi?y2*|=jxkF&T5-&1qckSa zXU5S+9K|t{^M9_FAaZ}F+-2T+?Z~}v>WtN8pj*-n3|%OQjM6R z$Du>C(oh+PXfZhr2M_W~g9~v`l2sby$0REbO!P|wZ^lGFCiwMIf*JjKjOQ4~G1iPe z;?rkEZy|bm&`m733(;jnCrQxBF{TFxjKyebM01QP#7L4pq`^nMlDATP1A5x+fh}BA`OaU0S=^IR7yNG%@NX~Ie*-RR`|pzhniLf>ATS_rVrmLJJPI#NWo~D5 zXdp8;lP?7-f5lWyPs1<_z4uq-m?7fXPTa0YI}C|Ua74Y09gqgxb^!jraFQ0$uA7F6 zL@VXfe)e;chvvQQ^vBgI5Ja9iwRGl^p$bse?dZ>;rb2&-uq~uS`oC4NAV*X zW+WK{O0yKWTVY`7(pFeH1{zQ47-_gK`jrt#>#RSBd5`7J!^cgb_2Y!@grP*Aqud{I zrMKrix7O47{oPHw-=4JQ7I$N#qiEh=NnR=N{^hghs$fqjxYCC5X(3cz`n6G~)iRo3 z_Jt5}f4e4y>#gJ@X&C5wl6RNkg#dbXS3`(jQ{YJycp`;AAmAqv@c&OBOd=3Y5ztrJ z-g6dxB_ZGQ=fg)QgpSaAOIZV8Tr%Rb7}#gYXzfqEUxo21z7j6igi}h89EWPq_VabQ z_$m6#3(Z|A2MJJf8=d-xeAg6TPEAEX3T19&mp?uNLIW{4F_SR`DSuj7bK6D|e#fuq zN4d5P&V6jTQYBlKzSnqhO{OtBgn`aL4Vqk^%xY%IYVghLMNKM4&=#ujPev@D~eHMF`+O4V@OIT$p%Oj zEuo4>PfnqPELL;r63frQl8KO48FCf^hlp9A1IBp?$pz+8q>RV2h0qZ*J7^^&xyYp> z2Q9p_31n137-Hq3h!miK0G)*T0@6!H4sZm91JJMn62b;eT7O|Oh@!RA6c{I=l7M~# zCJ;$84h)O~v*1v&&fw!!posB72_TNr!YIHo;06_R1fsBqj$S4Z-3ZYb%`i?<2sQyM zCKMS3H6n}w5gA5QAdiH4#;^%7mMtR%S1eaFDlsM!9F5nExr7ZhD~Hmv-e4OWb^#Tb zUIGFu0(W^B8h?OFIE+=2D-nhfs6Y*C;4Ts-u@)0cc#Mtk5D8_SWb?sm978AJQ%?gFu$h211v%GtmbaJCT)VK5g2S1?7C zT!HKHlQi%J11n48$VZL=11mD;XU}MGMuS)7c}as4I)AG2VO^BtR6e2azDtf?WwWZH zm!smQ7-!t^WPQZ!6aV+)Qqhk+D@VT-<14E2x}x&ml>a(wSXA_%qQ0h^tezHMsGQ`} zws|w_Io~CT@`p$ycS}^=R&@@EieWYy-R_V?wcL(pb%`N4?FrI+yl%(8otB?Q`3?Pi zbW&tj<$pLEL9P5IAJI`InmJvu{M)%2mX%MmzxV!K-OGoA5%jfd7kWp4H`)j)qw= zEq@7NWKsury{_xYUk8Jx^=g_;u8U!nmeVVCR~G*BY?wc6)RJlpZ!$QWeX5(s^XV+- zj%4sWtMUf>!P_5Szx(*{FDLmg+56d9Hm+clVp`QNuCpnYreyF#);(C)+Uq2*hSOrg z>ex=@m*ZjinbX1Gr(%3Ou8O`PLBr?zx_^QJ#MVFU+R|ya?GBXB%YTjwaLutEEJAyy z>78J$pg(3e`DO*td79l6qgy&^+le~>`RORTsv5PK=6PdmdWtnt&{M-pjgPznX*T=o zIvW+kE;q^oE#wL`%<-Fm|Ja0IWXdxdXZ#a8s z-U!%KhqYX>9{Wgm`fFm}$JN;P2X2sj*lUBdLZ@QBezpDLR9If8`bo}z<{a!~a>DP`{{IYuQvsHU~ zS~^q3_F8`{vgx|-GuNdg=5fm3zqXYm+6u<>MFcRyy^7Rf63_e1!8Ce;GM2E8KVJ;;%7Zm-+PC9+JPX z?2{R!Hmj*m%g0f2yCN4>y3}7L7v6(6`)$8emyL-^7-f;I;EM3?hnAG%z zk23Y$eQ}i2A&ndEL4R1Ju=Tra1?-9-k?Z<97CgQj&JOz{dSL&vTw)h)w&QuMvx=DKqc&SL*@ts%@Y}yga6fo9d6iciFXy>7@b8DZ?B8cD&Q7cO zyU&1+lD~Nc6S3KY&sReJg%7q)TDO_kt2SFk!nx`BBH8Zo*w(c7NHJ3pi0TmE4HVQ9HWo~D5Xfhx& zGB!7p&wLdHGBYtbHj@F~Xc4q#$ng(D{y zbpjf>SlZi(8My#?0GdEkfGW@dz{~<*VPay2BL|4uJ9s)-np?O4sDDhT|1AV)*ch2w z+FCjRH0*8c-7HNk0DNw4ZbEL(t_)7D0u28+sRDrj7YiW3%+dx35LHytmR67iP)RDN z10;cVKqn&`fRd}Rjim`d&e8;E=M1C{;PcN6o7&sic>bTT|CIIbpo~gtI-)viwEx=>|5l6Jnb@0J+L;4XUH-w=$jS77 z1^-qn8Cm|Pn|}aI|97~5^UVL3mp5{8vh)DxGBNzCU6}s${15f>|5}NN*n4=H zSvi;h%&Z(704`Q0pa06%#MQ|OXy@{8{QoKCfB1j*6%gnFG=W=Pwm0Down}RWt?(5u znyrMSot-vRr(I?S{X5ljt&3tgWMOJ>aEW`ThMVt>Kz}e3V9dXBu`PYqOkxxVL^zt5 zj3y5Mxs3Z#LRx9=Tf6zDT=3cuu73rgfn#f;0C630>yojy8mL4w$(EISRx9IJ#*ZS& z9Bo+M(GQ8d6~D6ZU?)lalM*#k=L-S2M_YqDYY|d-Wi0rzy9ySTAGCvTO^#z=QCJb+ za1f?b(0_2DS7tAeie=kyitNT~c)oc44Q{P#r&7gS3-RYCLHVVryF$1C}J7wMD_YZAu%XKj8LCAbxq- z2H4l6v{fFyoa`CvU!BY@dBI-CJs#pfxt;g~&;P=)K?NHfaUfgqtq~!dy<~)>z7o8#VUVpNEgTg)v zWl@3Ww5;sHTRK^y#i0l=P_rtQ zu);wzy`LV|3H+a|&`zwnE!~OQ2aR`-O5wMhx7!9SA3d}$6a<*O@qe6GX@&pjX*)Yc zu?I^d4;jJPg0Wx9vR3bm%!DEkhc_SYU2+pxm}AfDP=Xws{@v~xlt;(0vPH=G@=bQ6 z*+Rh)ZF8Av_UzQlm!W=9E@y!P_p=N(jfuny&a+uZ5N*=_ zLBtN0dLaA}+WHs(0=HN=pS4;4r#dQhFK@H7BR= z;BGXy;RPK3)b8wM>979N&m_d+Z;~cY$zJzr6AX==c%dQDGSo8^Hr;c|`B#Z?tG4TqhzLkY%X{c-@^rH;YNmS#Pip zj%6YSd|TkNTYn@^xG*f&Kg2;>Q@9)!AigrQjB7zAvtY_lG$TbFaa558kf|w$Z!ZTp zP>Qb*P4UNHj*QI?)JV2?21PH=rY0%XwZ9p-EE8e788_p6F{kCf-B*;?RnhMpPwy_= zH=O6qD?&Fu3bjI=i=ly8wcc(sVqFcLA*txeup~~^1%DQypNXJxSPu!&V-2{Mpq6#$ z&pi}K%d~;V@0I%K6X9$bH2EJs)&*o7NLn3JdI`l!N84upk<()RbAUOYMffa3EP1P+ z%2d^AdNKm*r5Q?cZi;@~koane%b-M9y9=40{SYDO`fFX&1}QGYs?}+?Fo)Xg8CFfh zThQfw9DlT?r``Ku7K>6-Sznz&cr5-T5g4V%?%#6Vkh;ECrAC`8?N9(;e4_-8CZY3D z8C#2Y4!a!jx8Ul`2GNhJJ*6f$!e6!N6y@}Y26Wxz2JY%^ea1`=KIF@r(-pmL8l3WO3|L~B?1(>9ad&VO_)6b&D-ZhFD6f)f6@Px{ek8e#ne zqy@F2)$QT_C~ddU&ul}N9@c`X*(JAgem^^9Lt&V@U5*G5D@JNN40<` zxqsL;0mzmgbIOhkQ}}R>AVSB!0jvAzHy9g*6|y=}6N@E%85~-0=qxQI&Vp2;{%%}z zgw9vT^8f8X%Ob^;|hD%)2{4Qr3b9sHC z=Qym|&=W#2DSxU~GQBV^*KA}p^kdj`t?g_t%!e^&guC@u=|%0(aS@(FE>-3rI9+nfTxpK}NU$$((hUzi6{Of+1k53mZnB#&fhG>Pjpr zdr%r9M(2tt8D~(Et~kaJGaFU$Nz;eDAKsL**k2L1n;9i8a(N=Ti8P^*r|xU}I%YY^ ztCT8%|9P<$mQ}e#`cOxuw7i`&et)M(wDfML{XWk6qY)JS^V-lAGUO2ES+Zqn<`F+r zfmbvJ{Vq_qDOeirOpW>DL96~R$#}z|ccVOOXk#;q=6$6E9j3|66^51b`7ruaW;Dqy znEd=R8HM{`>*fnRw>fl$5UiVt;4GED`LSyqTqR|df^q8R1Nuu+Piot40Ti@?@zLsB@5rC-+P@ zc9vV}#VQ9C17g8HYoo5+PpHogo-B45p1$1Y5CkQqgI*X02810bjpGbYg{yU=rTlSW z?+S_<%&*NP*PccXG=He)AZTZh7>Vg=3+_Ly49}OaaLz zNOgM8CaJ&ObgXPBr)LG^W7;3gH+#@#>#aN)-i9OLd?8-ddVex8*|1&%Nz|1zCXp=Q z%qpW~U&CXkM;2Irb`EOqOOddJ0An)Npbwh$8rs4oa_(iuFoyH{P^3CSS`5lX?Y7u! z%%+)su)OQ2%__jet>#68ZaeEeJE(*_gN+Y-jryd+(yfkE2>Yyn_#1npWEKwj*97@q z4PAm5<@}x-VSn>jx)LEPMV~S2!yR^7g7d{*Bq^c4Ha?wD{88}A0%;_BwL>tn&VUJ- zoy8USrXLSB^w|v1r?3@tcd~#cf+1u^YRfcjGt!3soD63sJtJd=t(e~wu6|k-@{(4W z%5S*bEC?UF<)MmijAbGHK%)RF?88>DP1bn)a`iujm4DuqZ+#L&s?x+V;O@~=IpHTd z6SJd!HM@O3cKC@uQ5IN)Mx6T7=8*4g9sgC%(!3qX5+6nT;2r(F{@HqF0Pl*LcTC6EU^Qm_VH~l zvEJ{@lYg7{Vwy^oLT2>um2hYCydB-#U^aG2=!Om}Mmjap2C`V2UKd|#3{Trj8)tCR z^#=g;E0UP%PmM4-r=L_-u<6vb*=~ z!>w%PT1lIfEQfhuPF2QvrrcLOtL5IDtS+>atZDrM$dR3YrKKn!&u8+t=Gr6(vy%Az zAS=fJbV7RKufnElW3hCGv;zDKIpCMr$<6JUFiY)T(4etK>UYPUSz?m(TMSc?@qgcz zx`@*Fbzrfiyv2wuf5M<`77Gpc%znNIY(!Z!nX0OpE5s1;UD*(yrJ9PrJIdw}4wYcM z##8M#2#u2nga?E1lhpLq{g$taV}Yjr&<|VkudK+*WFc5R-L)E(n9P(PyTR(I-wy$1 z40Nl}@(Zud@Ea14xgbL0QtmRoAb*Yhgry!2b9Rl1$)<8D23;4IolLt1JEC!+A)ImO zuad~J`VU{>CP)UrF9|dUWCY1jy5Xuhigjg`$8P_Y2kAdJ%3U-X)5wX z-L1~N1GMF{svx!GM?dD4JeQsQS+glygrCSlkczbTclnj8Ku1ajPm=CsDgwiek%fGN zoyWK<8IbP&;rbcb@se`lnNRugc>x+}js0foabY`50{I1oQ7}{_<)K;R!GvaH)AKJ_ zw*2-R5dnA!eyI9|49tPv3V*d2wS6xrl-(sU21i^Q!g?2c^ZF8BvSM}lHagvt$czLm ziNt1=6W?~2M0Hx8W=OrDn)Dyg>Y!GEX0Kn z`g;G!8qY%i^9=ufQ*rb>8ocOY$W(*9-80~}>1=DTNB6Fy-bRPgT7QByA?@y*O&3bI z@WFX!h`9*QQ^&0cuzBc2qYcX;Cb2)0-fTB+FVUf0SQR3vMs{NWUqWp_9*uLP*F)Pq zX+I=qQ_4uU`P>MVc~2cNiEf0=cfMa8*LN%C zGC@cDk{8iy`Gaw+(kK#s;rykFF3%xtxCWKpNF!_I+G;)4O5}kzDLO6JLz_ROv**{4rI&lWh@KKa>tc7HRPgV<7tI0YDlHyL~I z+2-(C9uGN-`Xe-85BKxY`=s`a=s`w$s0F+W2kK(RUi#a6TGLu>cE{Vcn? z@B8H0wNsR!zklI_-~zwI&B1u?K)rb7>*VLJL>E*gcW|WRn0h+SJ&K`joh)__V$mMa z#`LcS^YEX9eAgn%tVUx4z}fs#dRrGfM@QFAdD0g~>XhE|EKCFk1O19)l@=BvKT(rz zQ7;nbrM|SUG*Xo>Q8y{`lDoT9HGCSjPqQQ9Gi%V?WX942As-LC@n#~}P*7W^4 znm~ATVKMYtbG|-=7=d6$vgVym!zeY^g_`mW*I-}qj_BIQLQt#pL{UhK__gg+Y?)fJx}qSzUw@v9I8BzrYVrcTkb|QA+0uES5YD^a zTW1HYsR5s9LS42$ZI6UVa;+Uuvk?aLCS(}Y9PpxBC~!jw_Ph(jIWQNn)soUd)?e}2 zf~6kx;-5Q?cp@!VAac|1AJ@J^{UN#7h55;d2 zmPSTh?v28FLEkit4bdCsFslL1p^|i=>H7$WNf*(=RPMsfN3w|N$GDIQc@wl#8yHUB z-6|>Q8o20OSK&l2sp5sG>ER})4Zg&(P)NS!2{Ocurw_W z>uJi}?y7R)80NMe^Nv{6mw#L}v;{^97%oCGABFa1kcxMKEM8{(`b3^*?R0EA)9sVY693I`V(F{bCVWDwWC=0mnb-gYY8-v8h$0^???fA-8Gvp=2IKftx0D70R$2sRc!i9W2#A22m^MyZVN@a7EIbb$Zc*Lzg zTxf6~|28|W=p*A{#I&|bu74|jT@t@eLdamD*L~>d%cB30L!3vr>KBKCB!F7`)}X+% zZyDK8#+biddzWrnUn~Tt+w|Y5s1BUxV`;hoMRZ0OF`3HnHeeV*;dniMsQ8QV$DKl-^<0bIjcX2Hr|2>X`6K^Go{z9 z%Js>_L>N4ZlWKy|fuvv<+(l&|%FkX|l6R}b%5KK|OV_HBth|@*dKVGMdFjXUdQC&^ zPw2+tv#v_EIfnqK-+#;cO11#Y9hI8Rn$gmr_vtlHB&j{L3@El>C$zbI5PQ&!b zEwes)YHd=;qK1qudg3zLMXtXanV?gneFv`DeTK3@%!k%L%73cpR~y=Q%LSM3B2`5n z4hW#k*>BWgmLKJ4_eS{Jpbg8xDm=kStSH|l*7|xox?J zTWgeVDrfYnH-Ga3_eaQ`x|n%2HBwZLcz{hu?JC8-eGgwNPv=fR=s#|^gxQOc?(i8P zR>9JkqMx(ahuN$_Cu4OTsvNkw;5Q0Pgfd_(S=1~PS1e7=L(|26GFUTn@o=5MY{ccc zaE|R7#xCt>x7&F-+dCIumJcs?XiqZe@ctlHy;TWftADOG`X;XD41*j-?ZdLeayXP^ zDXF}V+6v#QGK{;;kNGo13nDX0OxPHE;)fXF9lLFx%}h0Goe{ln;M9e3p#%{VDIM1n zg{621u>TVOCZ~?y_;oK&`vgqY_f3m2vvhPUoS*td!MSB0x&8O65bkmGuUIDx?jA2uFMMXmZqzipiFsJ|*r;1?!LQ z=i|~xkEJLR5F za(RRn0JEYF;f1G3k2z!dYUJqj;1l2S;(wjozYj-)&l0vpE=d}V^Y}{WMofPOa4}QX zF$R0^)&*XNCT7+oZ8@G>8gcWyi!r4{t&tl|4-eDC_Y;iahfb^tmYSBuKi$|dQqujY zay=I1(33QyQY82wyKNlYPX!0raIi$aHhNe75zLx0u-syCqHJ?2ZMji2YB*%$S$|k+ zi$ZAGC2-ZR#RFzFhmhKkD{Bo^`Jig@k<2IZJ&Cmz$kUP6?BKB0Wd~pu)I~sN)*SiJ;Pm!Ue0hQi7aaB8+Pw zUf=If$yo9z#JUZXoa{xvhQ1p1bALccj4dd7Rt$i#)8BKG0O%4b_fR(SlniN(&}kq8 za%#A|8++%vN&i|!siT;lyl7mzrRCU_{7%H-bP=jED$w)D#iX}dtp z8OM?RL?^m~xeW(p;DA z7x-b?g=!%SHB*=M@=yq}v)52dBd!{;%+D=&((QZ26k@*w4kEJ@QO8rhTeK@<+93qP($-Re#zBrF+F%L4KQ6 zJ+j=+@YbBaR7i5FFoS z6>6icP#9NrqyQcp}yWbYCQ z&%GX^fAhn);z-%AF@Nmvr9lWiPkAQjx#`UhLdjxpl-WQ6AwsCGMNdLEK^qXLWw;a~ zj7*v*;_&9x1?|V^3$SCqLLaji?K)x{vG9rVH8{o3`rf9!{kX8)56=I5xrDc)ww!mL zLjc%O4HjFdytrWTfu7-(X5UMpm~;sw>8WuYwBKpPuGrAJ-G808q_n52TBy__^R9R; zMdwA$zfup-Dz`oTfKzIcehN_lVcf8!HgoLZk58_-c*UL{HYe}pq@w5P?Tt*i%AydM zk%q9cG0WHlOWYIC?deRLW<1x{M)}PFb+Jb!i2{slqE&=T27*6^UqIHJl6HPuLTMF| z{vcD8^3d~!T7SNaj2Rs({RGiJPkTuGWGE4MXqG=jF3SC3!GsE-7w_0>v%QFL6ys99^1`5ZJR>rXK!dJr(_`B1ePm%`7+{K9JY z2kj4rRVB821Tijy-LmQL%Ml`Y3%>$iT(;Cj!Av|i;eTNMs~5W*O5!7&BA(IQKVGly z0VOsVk@-Vm3Q{(4ANW+(jHUkUx!!RbvmH&e`Pl3$=^HQdN+cwz8lXXhVRPsdT9=?< zA}wrd2}UZfT$uqVxyFw4^x|;ZzLn^2xB)NHTiOX~{<#_Aa9WE|QKq1B1-NX;CRH8` zETrwou78{U(OPa%AXRUrVI{_SpY9qz+t5>|n2%{(+M9TIc4WLJRoc%#0gi#lt~SW*je`7Cdu0nq23P=oe~wemkfpUh z8XKI|2cGU%B6Zb)!BslthFS2xh5E)X|1@ZphJS1%7KmK2uGoEckI{;ecQLSf0H-92 zBGup!6rz?v{x0AJe&UScuPsy&EMKlO9$4|5PLo(`aB}y|<%OizC^`Vvb7T$OSfYo0 zhAzK+{Q0_8s=1L3Coth}$Pj%Mt=MUrY zj(;q|O~LZZq?Y=kjC-6u`YnH(t?ebQZf8=7#5fTl)i+^0g=4CkyXaYr)>ZINYl_@0 zzG7_}Lji{-)X)_J@QfS*7l%a|zy3tzCf492$AN?%(UY!Xn|Bj4M1WiFC0#EL`^lfK zUe1o<8C8K)J*8tFsZ|}!ObM(M6h7ye@_(RezD3KvimZyxT#GILK?27j@v`5(A{=BG z7-Xho_mhF`(OmVyV!{5%mVdl}Kw^1?uCHSSPswD>L#ZaIKCqUjS$l=%Et$H{nHJCv zOtMznb6OenbW z4TE9YnT=V5fDj4Fm52vX8FeQPxIY&`f(T@!pKu=pawedw?vS$0A4LJ-jep z%kD-Gp_%kB6I^kBLW`e4ntw;L0N5AIt9&<4Q-O8t$Yffk>(UM$K_=`IRIqEW$mGh> zvD+Mm1fJ)h8nh!`>o&0@5KT9q6vL*rR$D$hMM(spv;#9-;q?d3Bt>z4F@Ak*kQ=Y+7k{Np4$Pcmr}xJFz>IQ;Ot9fRx}xJS z7qI)6*63k{ATfh9> zK>9dT?+86v!G8|l7<)*yoYAkBh!`27`iR1hT?r=bj;Oo)zn52sdA|DzDBz~qK_^-L z5=mvRn%L3(+HE3q>XW%b^#yniXBd>)&J~La#9w24j}N`0nb{wI8!(b;$JnnTp)`tr z^?4anKBl$j4d~zflFd2fSzaP1MH8cIS`{w$lkfF1b|eaSS)~I;ZH>c=dkCIE<<=g{`IaY$zrFUIT>c2! z7FXdvh!Dp85JMS~2p-4rwm3v}w%j)JeDQ2&$baObUgv_`d})|d@J$}ipvSpzXKClJ z|1L;FaMe-3iK^Zk-~+{vgODIv)8qwAaf;XcwZu`7pPc&E;u#^pJRM#^=!4Ci*nEUj zi+Tvt6p+9)Jzh&R=kAEhlVT>C(i)wzf1;NTTj}5d4cg9eCUhJHw_T|rhQ6UDCO<%v zd4K+v>UQu{WwFS7m|U(sacmbG62eacw*>{YLaNE}WDe)&qUbtW59)G@np}m!6?#(Y^o@}GR96)7;l3Ep9}&4fv|c<{YW0nw8(T5e zPxxw>28l5UmYesjR9j$EEC;G5l`nEdZ~E{zE84a@a5w-gu9PKnVwxa?CciGiqJJ5K z#;#u9X(}dX@Zqlumz2v=heZhXT&#RR5Rv6NC}Fsvo7$_{#`DQvJ-JV*w{nJaYLWRrJBY&bn6oUvS3Pw(m;(F&Zd0I;(aNU)YrH>QS`$Fp_ zkT^Bxt*LD9zT41u^N+ENN1e%n@`EnWN1ad0fP^J6Xh}Aq;B6)bvMAHmIWE6Xa>&AL z()=cx7=o6uDRpSkF$vCC=zrAD1H&h~ zQ#z{FWDfAmbQrypuqg_>_Nj9rCg-8kjC5EwS(16K)IZeh!2&=A+CmW~3>?`KaV$$E zWqDo0T%?%$8FR)NwJkm4zM3iH_fbS1_@_;H_OU-6Rbq3rzV2b#XTP}sWZ)Si z%A%>7z1~mZ{I_rW^|7udp7Uq2Y-~zjpi?wotVj0X&)O0Qd}C6a(0}C=zhQUS>7l z#`kC+jwrw0fq44$bkW^zNOKe4MZ)5v>-sY634pvjC%r}UXe73)W6DL1` z2VjMhNS-2;3p(~_Tz|K8a*`0aStYB#N?u>u(`8h$ZAd*`>w9Fvb6wjWf#*>aqZwR} z&?LI6^dlLLfSJNDyaoe>wBNXn;T5?v?{tkGgw86}4JSXu!NHxCmg zNGDv079vE3eF!Bi^Ol==ayI`Or=SGL1`PJXiJs10Cs+}3_JJKEReL#UvHE6RXyzP2#!LKQA=8buyu%rC)(7YOMin4E&&l0~p2h9zDO6~C4L`!Gl9q}04_;IhEl%!pn2C#pz@{PhoZ4gH zX2W1_GWP|{P1A}kvVh1Jsj<@;0KqZg*QehXYc{CgC5X8)Bgkg2UG%gC``@tL5=7mh z+K00@uz#q<$v^>LQLPS`Qt}{Bpu*V$;*gAJ>x@or>w;@| zzFZZ8s`Ka6xK82FYet@q)LL^dco&NuVrvQROuGokR%w8i)~C+3vMo-QrArTbIHPl4 z8yoGYPFq{|?^CXh| zkxqK`iE@uA4X^Jg+Abvm4cQjGlkdo*9ZAgk|38niaR@dDg(UAXO%eS4@n`iIq6wTNo)4MN*y4kbsHc*;0GA?o~I1 zZGXG2xAi^xW^U(lRzHRcw7*+w^L^Wgz^xdlpgkeGXVme*)i{z9q&WH|^9w(_+S9+c z`o^~GDEu`7(%|sV;6=mB^>FAX5k2JiT$9axhxQ7g=f(_fUpi1CC z;-rVDtk>!2IZ1xHL>#X6hEyR~CxZ>`DSzff3H9(ym_-A>wq zhqSOy21Y!e&FJW^f^?~XRU*5MNZ2kGNt^y$^`$2ghnJ!4P2Dh(U1D zYN`0$IU)VSaY^C7M~afqQ2bN>5+<#o~G%uXiD{@seg&mmfi1_T+@ z)_RRA)8%K0Jw;_73qoo#FZQnamBxD*@L7(Fuy|lbry??h7lh9>n zHoY-~;wLGW-Ydk^dPJf$A`e54X4M-0C+^h#s4%j)(_sRzs#hci%+`W%&QrgRB+{k* zHy?4io6||hsvrfgrB*`HBg0)%A5KuxL`W*WQzTPzJVD`&YW0=kk6_+p)PmwlBXQgVEc!M4_SPbV1IhL;H=6IQrF(W zlWS0#_1iwj9nh2pQA^xEr&K8L0su`wvcHI-MTx2sB0_02i<{b24D&*X!RIH3E~UvQ zaWeu?Ukd0N0(z$H8fwX~?K;~sZl8NyqMozvjpYP>>zJ(I1R^mra-c}x)1u-BfKg1Y zz&&90c~;e{O?O3sv7;}zqrQJ{D9Jv5+fR@DIbdc}DX(+1t*S`Et&(&4)CHsTDiM5# zs*C}m$;p$`VC?-$lSq2o6gv5$gBR2c4P7k7>$@Ipm7x?uHWI$-E%3Iy5Luz&Un$jR zk5e7qr3@-yt6Xo{2wL$zong&kWz~M!*n?rW{;ojdpRIEIVcQq2Aa;ME)Zyd?tL4J2 z8z`h4k3@=W!9!av>h|}ToZpwtvwn?fRj;4q50}K^q!!gP(O;w8pINNkP0|?SiyD#m z)cqvcGHL#ML{hV-F32zcIk`bhmQzmRRBDmz9VQPwkS!&Dhz}5bie~MTOf~S3P9qWz zc-{!kg_9{(#AMx65Tkz$<9~#8jflsOk_l>9I@QVWO7A=B{dXRaRIh{ z*;czv(c%W@<6AZ@gZM=R)RcM?iyME0#51q^$y&K=2Ao`M7=DsUKHWEYV#MdsnvWaa zytuVg-h<6?>Sri0Kpue{IFQ!)i_}HiOfO8&J9mY&%tGu47e#+&8=1`^;m&ynz)_?b zx7jmnniGoF?;g9 zi>Y|sp|5_^+~upEY)CCO1;Y(XW}uo&HgRgY1Cpuw`;oMRDS5f>sWnfcv3P2(>>VgmP$(7Wm)4>V{5&`>*2p;MbTiv^ zizrC=fpMkRRkkm}`?H77z&P(C3z;}ZA?FPC>sKDKH-9$RgP5M`Cp;8`fU%NGqCb)= z6AcK(JDYC4`;9G9XpLJ;(uO~_=T_eLaGhti=&j{8-9CSKe@&OWtKuon#C6G7My5lT z9ML=`S*!To*esZSmFK8hku>as4y3ppdj9CAqT)pT?4bLuXUt2eg#RzeOY4l0jr+J0 zsw)*r7j>-GBJO;`qqmnL(lT!CY)y9q^o{CfvYtrG8ry)4+e#Os*l}n8CR-_ov8;y(iO}PKHjiaU#kSnpK1b_GrkgjX-jG&}f05M4?MI zbTS-_&6jLNyXf6#S%=v}UT;?=XDDUl{czDTVVN5!8|S|}M?N-brUz=doEq}JAt6f ztZ*r2OrPK`ooq$aX}3d^ljW#yEE=@?9wB>-4Y`7Oiqo#w9xfT`nUOAcz^|)^ehDk} zI&5SNLWwC=%LMbNLOnXzBUmuyZ^as%3y89kIlkQ5c)q3S&g7OLdvJ3@QT}tl8p`}? zn~Hzqx%jZ{at1fKI1Nt)_Abr9{_KYbMiDSfvr#YYjyK-+#@Mx7ouROK1h=@0{X%md z;eX-$HPx!Ka6+DG(AKJP3)Y#XpMwa~fdQh$tQ!@&ms{eRY4+gmico>5K1p>OS7n)I4BFeNbQ6&X0?T zWBc3;^_sOrp8N+mzkqnuf-XWOP3rURZ!=}hU5c%49JZ4XW9~cbhQh^P9{gcGZqNfB zBa-zU?52am58QPwQD3vpvO%1QMCiV3gW-3H2OQd7+zv_8{5!oKYQ6HPzw?OFHfn!U z{@FhRl$6lFQ-X-GcoNK)=TyCsP3o9l`5SZe5D|L!BEX_R#8S@$hha!&6W2#N!#wt` z(-gz_rt}=E8c%#Bz5|mFQ@~60=HS?Thf0n~7N&j=fZw?5Q)Ug;&qvuC{lsNl>s;)x zkU7x16opM-hyV>^#q9v91T@Q5dLe)9n&aBh&IGbqr}%kmgAiAm%KGud79A|fb{noL z3J=h#sn$mFfYjus2ENK%9qK!QuS_tdKt9Z{DmpZ4D*=QBE!-Z7VF* z^BgqzwAN5Fl z!f2aT4ijEWv0MB{e=VY4yb)U5XIU&s^&M8g>xPLe6Z4VAWYElnM+4%(Fr~hMxvh)g zZy}!n@^=VSafiS5u}90Y*b{%X5BpdZ^e zeZlLX>#!;z+TdB%G0?U_$!VxXMuyY|E*Mxdq9M!>{D0p(*tjIMNfUpzbqD70vg6>* zMw<2WLT&QLOKts3o0|Q!?%j27#Uu*am4E+{gwjT{R2OIdrgzcD`%45jlCAJtH3Hbt zt03$-y^XBKhOKqrudwS=#JjcH`C=vRT`o5dWd^#u&Zk%RLsD4umESJHp~8@ud=&>G zLRzdh$(*g>tCzK4Y<}xvxBpIaz)jHffsmLs2Zep>j_U>Cex- znNs;s_O7Vn_^H-DTAT`JgTcpzoqMB&BwC4?1_9(V%QQe*l>(NOYH4pVQP`Ep$Ps746M|8cK*>!FQ5Yi=U|`hJ zY|x6}z){MmutI;+j}v6En7!agLO!EgXU6A7A`}+E*Cn(F9)o@V)|A#Al8zzmV=}TR z)Yy_Qn$o{4Xhn{!*2l7nOS{_7XJger0}cG zi4pzR%=n}hP%Mp4Sw5{ip?yPjGGE@%Bk#HK(9+{w31n5IghTZctNB+h3*0tWQ zfzx$acjnw~2M2q*5LUk*a$U6eaL3nEk^jbUsj9OBJ-n&YV*0iv`18t8LzU9gt>(;0 z4B~%}e%RSWItXqg?U$tzYzxKcUs#H2?H>7r7q;eiR8ln5csc4jpoW_8fc0{W{cvef z$z13ppcsfMQPLwi>{{Z+Y5?nQyNRqspr!&sU~5XwkS6Fu{hq--l@E8d!8tjlScvxv znuW%^ns3vQtbyb#_!q2d!J#d=PMdonMU8)2c&(`-B+s^1hAs zbA=R9tE%{mW6%b6X?^H=C*M+zn?;})X#Ii>KHI{`*stvu3&C|xtv5{;ElQm?!9v%{ zd}R{vzPjDVA0K=cdt_&lgQG7&L0)_*SMw+8{Hk2x8;{Or_qZx;l)@$oI(ol9Mh1U) zMADNw+gIPH6emHhd!F4Yi9}W#gBi!&5n>SfK~j#Y96V1m5+~nYRff~$=}!Z)_7k7F zcGu{6NKDcLLWj`;rq+8HJ0`v|}ab_~3EA+chcDS`qhHhEms zeVit0QpD{Yu3^aCy#fI;#^}87RIQ0mx|J>DxjRB&Hm#IIV|ltInC=V8#N+Xn88 z7HqPf;&M0zpd-L0c`Q649Uk-T1CqxE>q|t4lK#j#TWs{uHQr)6a>_^+e3?2GHLie~ z$24eA*=W9$k7dA)+M~)Ad-X(ys_W>TI`5Pb_g`={(S>x0byPCZfqoj1VC{M?MU?XZ?D$-_aErzhW1UtasV*_ zi(evhJw4wdA?gHp2g5OG3B04XWLA|6LAbbQNA@v#8x_s*o|aQ-ZX>wvzvhSV($e@? z;#~(M?7*J!OAD74q8fiGOPtKvQ^;tojsvX8ZPi;r+D#jQ6>aI^sw@r?A)JDe@mq8B z=0Bivt**6Q;jJj)Mc?=xIAZkTtfPcII1`7EWe(YR%tna4%QKTw7^4VT zsoD_yk|p1c(=EaUw#d>p97%%X6Ll^rIX(OFhHhDrzQdoOBdr44VVkR_(Wn(hDc8IwWj3 zj{N9(cvjQvt$PX?pP)D9u6yMnRq#q2q~Zz*R?qV{U~qrHN+7`J7QM7tQFq|7yy#J_ z=KZG+-l;*U1>!U~Ro(~NTny+bLYwt)r3niEYJ^1~n;LY))Ie?ah|r@Az!?MtD}N*$ zSnib0iw(eQxuBYHRb0AOq^5U`QockEyOQLre{=-pTC&V<)JaFZTI!475@zVn5#+y0 zeF9u)^u~XZC;C^XtrsC|fkfoRqcNI&v)_Au9w}_(opv;g=X$&J^Ju+C2%q0oR(!c} zdw0^9&n5_sxR%G6FnR&QWtIELJ+V*hpLb;2`6s$n@5!LBsF__Eh zDA?`sV~t71^1Ot74QdHyD(UZ-SB`y)-4YEIf{$q}_~DdFWc&T_thfY1P}>#ZpC>6e z_o{!SsPo`e&-4A)vr1#f;-Z0CUJ8U7AF&u3$;kf)n^a5=b-JF_S4)GED)+wH91RhD zBnArFxKWjGa3Q^=DV}ASnh=$@VEm^_fFlw#*Gkm3>#3h|M!dyAiW?!Au?TSj`8Lg7 zdZK54btsoCn1Xs6`MsG?O*^-Hca`AvFISv$hAesQ@6=)v~W{9YSN2=U#utfmCJ$ zJlC3(w)X&$?2E3CQL;5)NRdjjPDgbPUdgbWEBsQP9aNCw$iEhDhTp58#=cUi$A^cA zA`A7~&#FR|QKq)vVn!$J_D*ZWE&a}Jz~kZFMh_hs-gD*qC76gUm|Aa8(3OB^;x83& z*7Znxy1wt9rB~uYov6g@K)8P;w~k)~PUTv$U%=2gdrj&F7&xxglRjxl) zO@L$uu^)xY7)g#jIxxuGxFh(93#x>lg8jXxOkuy2%btdk+whHqh)#cj5n(Fvy%Fzr zlitdk7YfeZ%2LI4K|$(}lgY0w!V?9D{DMz%coueT^MqI-srzjjd7zS}J^_S@unmqf zaD`3GB!}gfBSnLvt1~DP8mRr`g#Hb`YA{#V#h8`-V<6S)zbUi6a#w3e%gwX>47S6Z zDSk~NAme=+pB0!d;6Q)yjF$ozCC^`vus3}p?6eJ)B}fdRL|*okc&O@+IAP!AG%oQG ztR!4)X$D6PfbeZ+j5BA%RqckvF$i^!qF{lBx)|})OJfL`{F}f-;p}q<5|NN_7(Q6E zOYqi%Y7cMeDAb-0nyfL#D;y3Ffj|R0&7u3W$F~NRZ}~=;Q=ADzeiz zb(k2gn%IDj#wVsVF+WCy5KRQV?AzF=b;0}y(%||)<{&d#+hD!_+!@fzvU3-$r@M2} z3X`iufb_e|uL4eCNL9OT0;p9XqkspXfh(yQU)44d1{|B#GA9vwi&E4K?7;sT_{aU? zd`S(B6?1!}@`!&|QpJ_Wl)GqE$R{;ZcPWBBpg}FsR3ooN4KRA|!QKqT1DUvrmT2HM zTR5uPoxTjw_Bw*#<&_{kY1M`>nF!{Akp3W5+vwpqWl*EBs{%#2{H_JG)Vu|0mRx=F z#eXXz$t(C3bCzT%hpGgqg3UJ-dI$h>!1s4f zCINY4vra1q3CoC~7R?l7p~vMEm>kS-^I|_y3w`xSnD?JzwSiGn-9Ww|q3ne3>XGpp z3YpJ~r{;~;Xq-+THx9};8q>NfW_h}{6zt0l#zkp!?*T5>G!h>I!l)&Ibg-e z@1ALfA*k6O>iu3}S>W{FKtHaVeba;R&2WD?c>3@~wDaQpPWVX@u}WX0`FtG~{OrPJ z%cYxcF!M710?T-YMje1X&Zl4f)t zME;-G+D{pA(GIhaq#YBvoWLj{2R86Rc|dCU3{$svzBV<9gCN;#S|TXlPam&9d_=DY zLe${zp@#L1)F#jfsY<;k((LQRk_&&6I)M(>EZEFg-1}8uT^8r91jW1y@ttj z|4c2HcXgQ}#iepBN56T5>T_7Lcw~&-ajIn7qP9^0l1KEfpmz;7*@P`_)HA-3-dYVV z;Kp69G?j4`ZtVyqJSCy-h#cnCcSNBEt*Ehz?~%5Op>8LZ>GTDr?T4ol<-~vGM;?Mp zfpga!Y#}7{nv}N6gU|Ds@QhCCq72{BIai+DRh&}@^Capj!^ld3yB3yz7yd1y_C1f@3+_J6du5fkHZ^}rEPouYky(H~JKxcpbH^cp#4ie3(RRNBWS;{+}C|`vFjq~p9MEg>RnQoY$Hlu5ROYS*D4m%ZJ z;YCgujG6s@I2jzTm()P2h#HnR>~bLY&v&+cTxxgW#4So9$boNBFo)&fP)3o^Te>RN z$)w&!P^Ot+^Y78pjmCcwGE@urLWj4sAEmPvlbV{b9lojFadMB&6~s^!{YP1f*HpPG zVRV+60@li&Jy1(g60{?AERh+q#=`#2rb@Z?L;ruQCUAt z)x!@4uy$o>ZSTOCZgTTyL*?zxk4T)TOtLeKH|Jx{^5L!5JniYF2;g%D6hU^XwDspa zrfn~a&e6gQBy3O~&kCAHW4C?b#ez2VutAKCGb3&UHY1x-7%s?aFRs7 zt^Ci{7ntGm%nEGMcp zgKF5QA%gj`FEsw6SjC%x)LtdO@F2C6($1&M#Q52(#9r6|r(%=s?m8iSY>HqLrg_wl zn@atWXTg+gco%Mcpx601hxJ;~s-4E4x7+pjGL42{zd(NxJf5-qn~?VQmHFbB3t^|gatg=SpfM5P<_ll-VbvQory5b4MRk8WJ z{YzSR+Z4vAel=xb49xHq@$FJ>%9odlc|rYVKB>WoMnY>dtM}sZr4)AHOJ{20 zrxwX4WbN^Tzk&CzAOeeXnR8&W2ou1cpQU*6(rAC-VQb_y-36D~O$Y#L#CXK-Te(BY z&fK8%QxqZP=Bnc;9tLTyk;kxl4(_Ja6*I=nz}n!gJb>*T4co zCdv)4I|}}bn!o2b_(J-Y(Dv3pf{ku`Ke|{No9%OcvsUA~4d&qC75)t?mtr*3K7MmXiv;Z27UGjlAIQn@Y}R zxn(Ss7-Opmmh0kn)3{~e?0K-m8Hs1I0@P0)2V7>7)Wh=h$i!xcwEIYGE^~A9E&9RP zpw(W?a_?PnLCH-V>(UHJBsn8PI^W`VvTT2=XYT^O2N4^ zyMU!p8Y%BVnc~_`mcJ*){)W|5Te(uAUorVpDDTJ8)hf@3qm*UnrSX=sNZP6X|iXmOvGEZ%3_RyHJS9)_ZY=4!;PXA8%2 zRlK@&|8e`N%;BrEXN}uNB)8te^{;zZ#)N?DBu-)iyLi|+ogoaD01G%=l5(=l6@>M?)rae~s~ z&`L~4%ttZ>9WH*EZ1QvMy(>&`S~cN4M}dIA68o*;0AahDkSYR*X#-KrR+)Qiby&Lx znEBdB9ciV?hwzoFaJ-^&IIid`cGD&Ipt3j-(Uk{(u*ibkp6UT9?w0ja75@(2SJ(>C z!M?-es!~Lir&L%yDt%xAa`k^_Wt#etWT{zmtJ>>wV{hMGfK#Od-p!~?wuPxuN%E_yBZYmzmr`L8Ha2@yx0@skb|GTfBQ zc)vA4g{_*&z0I2heZ(e#4_^D6_OYGbUhbHu^$*-IxdgEU0;Du(WwC8|1hlfNKg?2I z;uO8C^VpcSG>%XW&vkz#AU~jy*6(vkCPd3^{v|!&@4wQz(rZeTeVl9YwGt(Aw5&EA zxqI9C;k-n&X{XcE@W6=g!aDfmU(P#YDs#||icYW1sBOrftO)*VE@~N_D5qf$Jm^%$ zoDEM_@JNl?DG}+Ay+9g@vWIYbJsXIw=6D>AQqY3$OMHXDEGfme?4d^Kf~ z9GqiLn)gSeUpf%zU9}b6yiLZQbyRkoj^)h-xbFlX#v$eMRO+5xiITTD=zI6)&3S0^ zpPl>5ilS;Z$?`M4Wc5xAdiiAGyLdRgHfy?#NJ&Y>NP?3+Ae2AStf1`(lg^!jc>^l; zyVtFGV)m#?w)%faq&h}o!SJV<4dupb=%rA}bt2U$9!WAXIpHx%@Dwje@nfLEMXQh5X2RudpMzAj9{Lyl zT^D8NJDVHA)I&DRZaBh3^-%n zD;!k;+2!{>J;z`+*Y-H3u0e;fR|yT`#v7IO(Y=3Y-<$~$8qWN9YPT>QRW0UqcNh4f z71F5m56%3JYL}1dP9qOCOOkA>IHDiN=|+sm!N-s1C(Q+y=c7SMIPmkF97S+R`SN-} z=a;pzgPI{|no%4qOM5C9cxd&cb9uxsC!Lbew9H+R@rjYkNRhVezjl6MKF`L~gO5p= z!z_PEjJF2pkJldg^tMy0P4Hz_*Q@iun?8|yZ5vKu11Z{VozRMG{Ki^e#98&dU}a78 z8u}FQ#DbKNkY0fg)f>(2CFf>rzmaA%c}Lofe}-uev;+`rnQ`*lR`Mc`RaNLBX$3(h zlik9h1Y#_ck=_XrC}a+^yZe(YT(j=Y2-|-vt=RFa*=6?=C*gFo6sp8O%U=*fz#w3I zVxBTy<>pBpkS@mK^t)UF-8|KzSH^Dfj)IS?%(1zj>(C+Kcu0Ngho2Ja)p^D#AFK9e zN{Q4{{MxuG6~&N6k(@9zzmn=gPG<_nnL|jhL1JilH7OfKsl-6QT=7Hk>Qf(SM=F1G zC5(j(!niUgtp9-_yR-3`j3n7berE&BkEsY9oh<=5_NMyIVgRW6aC+f_;vV1_F>1zo zxu-uV$!stb`vwAGm?_k3r-EA^y|N^=C+*r#qO5$;m=MvC+U62pOpMNY`zx;W-p3R8Z43$ptg|4bSI%z9;b_73zsYJs|KL-mC zm6x#&$K!Pf69<9~UbQxvcr%_W6?B{BjN(T@ojZtETJZ{Lb?V_%dhiov>SnIzr9shX zWt=;|lezKA!KbuaHmq4fi1sVGA<(vi@(!nn(H#RvXLD%}OD@%G?|*;q^gzR!`j%QKd7jTa6eGTN*JED!B?v4?V2bxsQFTe zVit1H#Zwwx;cub#uUk;3H8X{u|;lC@nBFBp@m@p{ZZm?%Xz zf;upco*e^HT%GU8Ry|V#HyaT!prfP@N#~#SMS=ps!R}nWM1Sk3rCT6&_&}NCFn1`a zIYdF%KwuXvdxA|61n2+mun!rY!%2QGoE-?QIzt1(^4~1&^Sa{e7ve&m86JJ?8L#%I84nO*js(Dl!5|9=8_*rcEjv{3aKNvp}(4l=x} z%OM4?^K^jer}FeNDCWx#@d6|ROI7df%8ql8#=AR}vT(V)_HCr#Er>p!*X4wPF(@Cd zqV3wXY)S5@_W#CYIc@3dpc>yGD)FU-k!zO_1@P=Y;S)uch@w}yXt$uwq@k2yF$Z2EYgbb>3z^}b#XwhYwI zSS6Lb(gh_LoL>Vt7`eQ-4HO_))3gxYbd_no0e{WSTb+x9_;)@Q2l!1MlG>>@8Z$Ej zan9);FF?Tg*9eLT#peB2{ydJ&ytB zDt~4D)+X1TtxZXBX)|j~VF)XM%JhJvaKI>vbyL&PKeQ_VM7BJ~RnXRnlZblk5iX;a z=P|(m+4SQRDYq!u28^k@sq_zoRML8sw7f;q@8oJ|)bYlh+!?}VO(?t<47l0!^ zLwB}~GdYaG1BzJ^9c?~8FlM(wK84ZWkDc=;(?P^a1BIzfh8JT7Y=I;8yyvwW^nW!x z{-2*s5@OZro+EH?KCEc+;!|7gOp=+w;DFkSd0mLt7uq8@A~)R4 zVdbD1^Q)WchbcvGAuyzcIz#EdZaCzmSbBc-&zAQkOxcf_9B@x2In1+_m;Y7vef|x6 zQE*QN^+YEwhRyk*>g2I`3sz{h3LMW=<{y~sMF|%^v@l8^W@z($<>SbfZ zv_EelguK+KJofq&aDNa$1FoOh6<%qSih=S|o?z%c&9nmATd3q3vAdwil8cHFLpDaK zMSvv1cQM`KoAqPUf0FF${Iaj;@|AY$i7z;t@_q_&gm^CQYu3hcdkmCm+~<1UiXQ)| zzZ}kS$*gShf=3)8Eu{Rxph{J}1Z3X~!;j5+*vJ#l#sln`tQUn z#Ak@zc0DBe;8Duh3+Ri1u*RT~=im4Ke7Np35^NWQWU2*qT+qF}WS~u^00Z4TmU0N$ zt|mbj87i)61Rolv^Hx}A+Y1U)+wN@ST>v& z(JpW&B7fZr28vS)#0;K2vfR$an`^Zi`)2utXY0h3Q}n5n*RHg6I=t>Xrmrido+NE{ zNPtCT1dXyt7`5>ggLkOqx0Gt)X88|(uIE4b=}rnUjcKe-fChq0*5VJDn%K)xDXuX7 zmiDeyUqXV{Y_P_%JV$)E*UL2Or`{9pQ@>->`F{r?{DDsGL^026R@extrwNQCI|9uH zQH|Duq6nc&e*JBzis*F*O|BHzPx!<8du?2lONFUwWhyM4aZTGbac;s6nfSFqoRsg< zQcOqWW*+JL_~(`YCglHjh$>BrBVc!7wRsiaz*ZgbyBQcnmi7%=MIVLjy|R7a{H-zj z0)MGlP~5uMburw%tT~LGujw2eX6R9M;wkTYN+{iPG9^vljM8a*)$E($!eN}O7y4x( z0S~xMZyP7>OpN!ZLar;OI8k=OKh|Xs^YM=A_VE*if{Vj_d_cAx-jL5dfZz=5CGG>v1< zYa>rCBky)iN)}tAlm{(CjP2=999>$d>??kfQydczM%dBK0K(_%0;Rh?S`UD_3ToAu zi|#KC7Op&08cHgowdN#c>NspT7ZyIavQBYO++S?1dYW&iz-bKmBi?A3XgoNiuYcR& zNM^J#k4_vu%dFQ#_r(3L=al~zmh!f5g28VlmUh=pnAGKO=+)hr58dpy1zcT^TDsM) zY#3TPqr%ugjBf|1A_GkNHF99HWjma*kgjO$AWE*Q;-z9?sM8||wvP`n(=&hy+}N8H zrRQ(C+CzkBe_+K)*uM-nFshH3#(&V5u8u4crW|^%x)W=}&p(5TpV^zQZXyQs@S^M$ zD12WJYS;hw(}B@Um*F~Rg}+zt_9WG3*I-Suq!F$N9QA~S*R;F?Uvym7sMhCX&7J80L!@V1M^-gQ0qyYc{m`?eh-A4Rc^_ZV}UGd!;=!1MY@2W!i?b z>$JC^jl)*X-8gKA8tPF!owe;M5FJJv%Kke)p4 zypV<(U#g4ehH*2`m`+XoJ%9;Qtt3Ui5{pH%!;y(Z~xOah4<|ok(6%}^RQxNQ12qCXO1*tL6u&FF#t6*Ad7 zWk!VqTGO+t6T9JMn17b6MfCT32^haA9D_Ln*CTP9CVO%&&P5P57of=#6ut(x)viLc z<(_)@4SfF3Qhc-<*PBSE&(PF}11Ms!BAWy+{Kf%~wV~#wkX4_P)A}An)Hu|XWPG`@ zYjypVP+^CdR)i6NkPn_ry`*^&M`}Y5Qa|@ZrZ+TmHE#)8gnyqi4oXsD>Vr=PCMFNn zF)5CVJqFcHshGTH=uW2)-g2pPvhQFrpC;Z@q7Lr-vX4BupaS`mw9DfHR_?3=94uF>P8Qw}86)vjkptjal0XhylkM#%kWZHTj$ogtg2#JPh zX}C|S$H|SUxWobe$fC~qV=*sVW~{xE`z##TDSElXRb4;)_S)i(SPjY&Eg~dPlSr%5VZJbA#4Y`Qh&_JfVsxx&rKlL8=IKXNlg>+!GFb2IG6lF zNav>YA^VsYvN+&-$8sQm&U|p1j z=D-YrpSu|WfQWgX5gWVq(3ktLL7yiOWy%*HZ;eXQMxHqig6CeYg@clqxA}g;Xqjq# zLTFZa!O2qkvsE;%m-QJsFKR}3`lti#)h9W=n>RuY2Wr~nPJI=OHw<1$xo*P)WPc@H z71raD$De*-=)2%qzHsZV_+bu9GBc(kMg1taO;y-5BYQRk(!}3h514pZy<}LeC<`ay zi;PuGvCTKYg)om|zcqr@Ze@tL1UkL3^^pVMhOpFK$_hn@TK5&9ZDXDj9K)@Lz;@B& zez=i-pHfP>IArV>m2?gG`ELYv<59xMc{_OWJUb71@WJJ)3&h2DjZX+s@r{jjFh6*7yDrK-G7L_&EuFn!l2UUjdVr4!EXQLmGKeidS~Dm=aa5ckBoAswG+S5gi zHCvuqADqY|`|~fi2EWxns$up@Fpc%U8KkW|){L9hw1czGmLwY|O@dmbZL&!5aT{~s z?@5E)uan)!jd80*f3E*gv|tFur2}MuUOl`CbCwC2YVbvxnSXdEVkFBt7^h!xM?5KF z6|p~+Kj%lKmr@X)-?Ki(>?fGm?4k|tU3qyzB`r!Guv@0tVjpLo@nz0uLH_Qhyvm4> z!y@$PEUdTG+P+&AoN$;173!Rk?x(x0)^Ry2y zjpx8}_a>>t2!8`iPluL(a z_0J7%ua;idVNr_rP_LaxYMcgzvhj0pZ3|ng@y!?skV)9Gb{m#6%#{u!D};y3 zYTc^kk$>{`-C5)Q?z8!l>b}~(@O<7M+uqT|5yXKwSWC%GKZ#ZN?4ECdkQHKQ^1xKZ zu{=fO!k&_+Q{BoY=BL|l>XdRiJ?8&KZ*wxB#+}D?iqYxUO(7EDOD+U&UY@yHwDW75 zqn59ylx|%lME7!cO+m=VIKICn;uA%|?{17x=YOjMQi^w-|F6J4TN8D(jY34|1{&!W?iJ%+@)J`W_Vz`8ki8^yd82_#oEs- zVXhYW`&yvz{$1Z8hQ0i%bL9k zJbyzbp?axc;qCq#_EqCy1MGC;9i%%>b7c5Oc;WEX=P59abMPNwEQUl-v+WCbRFT_g zy{q0TA>A_JdlQZXpQ^^iuz$QVgFR*-JKHVghM%F)9?VTB0dr7t8p&|@?81lx{6;8m z^-YvNFk>--1XcN$Ky!&fMVID+aiwEqBY#^9LLnn(x@;f|3PTA<_D_;1o`1r0LlcnB zgcS6+m*?8%v>vJA!yT&?F%K8NnDqS{-)eDX)OMG z{%Py1b-8S%0%K#iPH$a$WYuwKf6eLOoSEQK5Vb@H(j3R8U+%sv>YlO0q#{q|c7IQ= zSgbs|a#T_YnT~y}e+`UE9K?Z%<3Sv|kWuRXxIr7wQb6gJy2$sy6Rm9ak|#-ddP*$cx4yET7-I;EAjtqbTG9Bp)g{f`*AO26vFYkKM| z(hD%CDW5q~jP7U)E)$~I%4n<=v*iB826IGkxo5fGy3q`bFGMAS4%eFd3F&}6{ZC^Y z@6sM&*hfi%Tb}(UpeMl=^0DM3XS7nl4L2f?H;IYkP3yAWb0yd^qY50nuZc>r-^YJ3 z#_^tG`fEZ_UmUTuN-A^HN_woP6wGbHo!Nuxkia8`Cm2>oV@TL-d~9{}#OA(|(E6sE z$oc{!FI>ACaZ+djdDMHzth%6T1`K~)4>cw^e2KfK)Vh-xWcOra*AT`9A`g%MkeTQn z2G~(swXUVtSr{ks5af;(NM;0Uy!TC^iGhS3j{FX|prPb7CgH_TyS(S``fonYMPF=X_Z0|=7Y!p=@e1z&&UI@GJh z94uDT18hy8PPiS##!+>CSt9!P?D9>NJ`tk7zXHD;6#Bn=sp*HmwzY7YxrhVTIk)9Bih!6 zoM(`t^Y)B@_i_+_y(6}wXw82eIhyev&OLyy3F6@DP=5b6jNPX zXIMWGB$51EtRgo`px*Lnp_suicORu5D~U>&jIqf*f$z|r zuO%kUuybOt^t$@>(=rQXpGC50K<`s3I`eGhmO)T;;6);J&x>I{eLtM|`fQeMJ@rOy6> z^B=7rR3OAz#}8ewXE(8_ERR8a=&~$Gr#t{65@0sCFS=0rDh? zK(yER!t90EW(1JHE8c&j@65{MAD=Xl-9w$6dI{YK^Iq}+B{hX@C^$9y{PH12XNz@} zm*7fX?o_E`WCugffI7DJcq}eHDY#Dvu6|c*$@&7feWi?wJg79^V^W0q!$c8VQ>pAp z`iaB-(EJ^il#TL%E*y{=X3$dK-7@l(bTUh>)^U_(0#bkUWRD;XuUJP@I9+c< z-pu7Q93+Q~kbfo>MJdRuu;yp^dGJc?qC3gyxO5I$$=$2zxIvpQN8(<-t-o zG!b(0Kl5(hgkjJ71!SmSNm;oRS`(I;B&G zcNq6n41p&^)`@@f*>%cHKZ~!Hu0hJ%;@~+g3#&X1Oemg=l3$y>h*;}QXe`GeTU0(^@MTaPT7L58>%&PnaZi7(822_S1e){!Xi9F35~$c-vioTiM1#h{7vLV@ME1`-UN(H1yP-tV4zp zBy%9VS($%DbgJyP_~z_F5I`lE|28*8TPtViYxAL^zB18ykc1vb)-EH#;u3sV_$WpD z14I5&Nm1XmZI^d{ql)=NcFED4JEua&-D%R&-qIsMUdZ-6Y-mIi39W8Au1>+YxcC+x zXlV=lil|RxY=8_k< zTE>4uy@iOrb)_-Of!Ca)^-bO z@B%scID*$HJ4Z4jgLQ&!vsX9kOTW-HKkI+{mg%6PU~M)3l0!}~Jf9>6p=rjPxF&^Z zZfwM}ZA*4S37TniJPPw24=bqv!1ZuMnV%u_5_3?|+^%)nDmh zKFurif7vD$}p~Fo6Dll9Avxjal#uPyO36# zqQsiQf0>?(Y%N67>Q1MSlAu(oOD`S6_r&JOzn38Uxt>`HzX)MRlYl&Z(gAKm@i3|c ztD8Hn;=q5>QyOCG;Jg1jl#b@85(#cwrl_N`I)lJ&k z#a8Xj4atOm5IF2wg2|K2jS}JLC4C&7l4XMO9{8FIw}aqga=ONBIogLjyuNs_HbJ$r ze!TI6g&#iER*zzgPEyF@2I+q)5j4}T*K(Wfp55eX^L)kk!sRzHnG2E+K&RqwP06O$ zY#b_{JuQB}*0UFF^hA9?jITx zQPk1L;jno%GYyrn?Y3#X-pj}HkyEF_!x#V)^OIF(!*xWM2{CWiVvN?6%<4EoA6M*Dzu~D*4yOvAieV2xa^fVdLXSq~ zU~!8l1Vrc#tp87@*GGEZc~&KYIc*$20&lBY#m|kHS=#VmBXP9kwy&xA2mN8Fat)jn zHECFE(+(8_M^S$>*oGUM#?Z;U(^^H-|OSgZ>-hR68GKTkAS|0OQWIV=L zLc7!_q}Z}B-7GG_I)}PP zeeE_FRUAIIb-$xJ8E4I@v@*6RXb#3<4kCZ`J2q}C zx?Z*2^)i0|@K&Ek`JT$H6-$hPy|no3dbt1e%=8^MH1C>fF}VLD|7?T8O5%dO88?$C z%QdF95$HO4817gKob!O0f5jf4AHA)q_sb4w3|$S}b2Qf9zEfF`-&k^`6l{wrk{BM` zhOZqsggAVHO7Y%}ZT-4&q8)E9GlPG!R9#|q9tS@x2kAseU~c~hn`#xS zWIvkW1VsvePzWtLaLyohPA&z)NDnUfJrO?XeW)KiKnn{bc$~ zP>l{R1(9MVR8HM$rjB92VO6sK=b#S!AICRgXgc$T!p&v`$0!NTi;442F2zHD0TvMR z+tYuVr{2@&+fv$XP;qVgZwS9F*P6zq6!NOLE4}RTeVq{_#TM8c{9WTgo21 zsEOz=sP<(hOh86_`l~~6f9)g_{WA#Q0wlkpsrRkPYLt`WEr?!_HE?;eOv6BQGb{3b z1Q<#=;l&|G9?4OA;Dc$Qaazj2lEiC;uKa&evKDkT5tmy}mbb-coDgA6Tlij05-19sm0IPzf@>WqHY1xVPzuhmQ%Ww5fK(c--N=Ij9y&aWPO$ z$fcj;*?Vz@OWs-m2gVcuI0*!2gFOCjy&$*JzMw|0UcWu1{`}4Zo%l*Z(b^jPnr43h zAUaiy2AIs^ugHc5e0DuN+{wF)j1kbF5#&U}pRbV?UE;X$`HR@u_uv7C-7<9+h+gaqMp5 z**jzff*f|l6jNUtT#oX7>v{mfgQa6dr0{4OIYW+ZRvK~7%1PO!zK^+FS=(!9uNEm< z=Vt(~_;(EhKbGp1aNNyN3kH8o;VY@rZlD| zbIicnCQpD(Kw}!7Qd9vI5b7~Q7R|TpRJ)F7_gRNRmXDoy;#TDUWB-4L@Xa6b0+ba= zwDDc;R#T;r5OWqp}nq~37Ms} zG5F)Z*4_qh2jDFvu^hW>M%1w2WYxHHHq}@M_*w@qCTI=&K&)AEI}xbb@QpeZeQ$nd z5ty$~5LO-6iP=<}a(kB&un@Lsdd=TZ(!3E~6&uTD(5=iO`&Di90%p~#6OI%L5U=5E z-KHe~3PzI^Aw_?rW?guYV(AtINOdm^@%WjV@FYtNlx!s{7WxHf@jn^#{8xn`7hP#O zw^R(FB#R=X+?l}a{ha)=IX4-EDT(d}6x^aS;oD0>{A!n8SAWYzm13H`vz{p5!ja`= zx^#&>G1WRB@YTq{sf&Uk$D0a9G7GnC9@dUFi9aKtUr>Mh`F~aRMi1m2;OXG@;>b@F zBLd&93W`qZN5DlmM0w8c zD)oSkM^uVxD`wBqlAb(o{gfgGjc9hs`?ivm#W8<0GAu4(RkK`up#-Mvut-+#?{+CJ z%W4=y+<1Rtba{AN;5iHJq1E|`ZIwpZgx*nnA@-{0fWLv%ZMG_Ja65XFG?)kON*|@R zQ|6|vpplMX(f?_PA9! zK1p_m@CdS+VJu`9&0)3skS?YuoaRGmj8Wgl@LE%7mm5^zF``_QUXd@UG z3%V(W#bl!+c7eQzy%0W#m*~T?XFJE$pYLO8bitA7rK(I) zmGLxza_A!?aa(-@Li4KnPGOD?i9?6eXI%`+D(^(rse5i$F3;5x_79k~R5#jTPV^6s z7$SeB#5DgFx<71O#7K|eqde$t_^sYq3Egg-z*^H2pN|yh+XE6ah`2vLUtW{m($BG> z|DcgSVdB3Pj=t|#<_CUCr2L*p^b_sIthB_&%^2yR;kq#1A0%NwJ!iJ^wHN5pkhE6j zS|ZfOPCSiSpWt!frzTQ!mbDXcxkjz0;D3LhT@u@RmVu9^(sJyZn*{MXSz21d(p+|S z4^4?9p)Uo%eVsiQ*{=WAE9@>NWn}~Q73{0)1QLuX3rl1KwLq%`y9Z_N4B^pThH=r3 z|BCuSMPLR;UCWD)!!X)sVLQ9%AHsXY@kTatdGaH2*Y?g&|6Z+Y!Y=R%F)Yr z!8M8xBD{w)GB^)vo|6JuYgBynV)c=F;CVq4IRd516@;3RcnD!5(nqrauW7(a_wp?oV=f{>!GN zbi}0AK;beGZJC{cGaOzYr0iWM&^#vX{f&W%^T}7CH%WhQC9&A^OG?;G3 zo4CPn3nkQ*dpLFt!90G=5rvmwa=jykt}x;%gI&=6(tlF|Eq znt-o!N+#1!ReZ@jiX^{;TcQeC$T>D5?h2f18%79j;2r-K9+ z-gCpI8Pr!W+>xAUg5rOo{%p6XN^#>B`i=e3%`slzL|mN3bk8RrV(&y01FR!HxLM;6s z4>Z_m3FfVfnx2<^Qtq0Ggoe<0D8eA?o&v5$;4&bc2*Mm9atPQrAvZc}*oZy?jug$K z&!YK`aon}t)FppHXvekK)?t#S1Yj(1MYoR$4xhYn6ETE8Muj5cX0%G$_qgW1owp+c zwJY+%YqB#NA`e7){<>x?0TlT9i$bT`+njcrVs3dJRZ+pl*qe{;A&z_Q7g`H?a#3XN zHSciI?JTCE$b#WT{tHhBgz_@>i7%Xy$stMy7?GHw_u_v~QWI16XL#}BAA&p#t@A$5 zLKFjQGyAe$#OFfI$UZ@CwI9(K8zeq{8=`tIr;RgqI|&1$gqcwlyOht>5AGE|`vmi%J( zzJP;jLDfAxYA4rAzBZ(kHVaD{q|{T9pEgAYn|l*qGbcaq-H!OAJUQ6E$W-c8;xlZx zLaT>2{v4tzztZ`ggMFswN!5#j<#F(JAv^2S~?wpA@zV zPyk`rF)VZ-D)iajZ20^U#g-dMjQ`T0>|b`K>e~bBut+^|-ajknTqfv(?j?v(Bi!my ze?5QZMeFQqQiDsO050z-DzIoi-*-{mMQ3#^a%tuXI)^(~CQw7ScKYA8xP4PXkyb`_ zDnT2$?|`-%kZaz7F_ssqPI-UF6QAkyg(mVKti4{x<%gMAO@3FFWv2J0*fO-iS-QiCAgBS=C^-Q z8NJjadfD&F=!)eD5(^{-(C8#49w{t~SNl%$0Q#hdS#x7^8Z#}zvi4OJ$fh1IA5|0n z!dbNdjN&ue$2)e~lXj$&;qc=fw=@u+8TsD2#{_Vbza@Y=*uLwUpqeKb&Hmu zK@_8CJ^ytwJ;%M}-z+{4C)tU~C=OgP696Z~JqIU{$M4^kymS3gcVkT3T{D)wJfcZl z51NXQ!ex8``V*4W9=V^zmx^=)^iNK7HxXC7V4jRA&`uPH8Ss!?i!mqB>qLKbW)Cni zODP18AEw1zU%#gUYAVU=mPk;GGIYX>e<>Yv|1M%xxUPevs~R`$rma7Q72UGTYTc$}PDkiAD*M%E7?7DlHfQNp@lod^dZqD-yv7FR`(jrRl~- zI@x4Czh9kBoBZz1SbaAENFgctm{yE<9(46+(SHKKrsb+i5NGccFI|6xKU8DhZ^uUz z9v|qBy^b$i-GotY{7E*)K(g4IO5E^n5WS zEf?D5hPPw5&gGF)WT@#jFocbM?B(BK>td|KSK^Q+`||eOD@OxK88Xw~zrAQ%^p4>k zBX#>GIYQ6b!rzO zkxwz8ik{PwoxDy~0A{5eiND zw;vt6X$TG+NS}Y1uMV1>{R8T2*Ok>LpgP)u7?t8#i7 z40U=9HiLdf>6Oa+tHc)AmWHIW?$|ZjyR>gJeQhis<))VUD`--GU1HC*;GsUpcQbDJ znq}Y6fmj+#NgBQcpw8-CX<{zGFnvW52p-eLtfm~kIsbo{x1d^0h90l5NzpJDivkXS z(%9~I_+Mc??(U&L>Hj^P+98NGGms^utymj-<+>&&t(M z2;a91?o4<`zO1E1-Rei4jGLsAeL>2uQ+2*M>!Iobwr|BXho9U@=UC*Z+7Wb~QJ+wO zS{jkc5wU*^o@REk#9*Cyx#?QQ`d>)vp$%dmsTX?Yyr$J!^QZ%O0NP=n(ryy4GWS9^ zcQGibD2{vQz>v_2HQ_zaV51>n(skUQk7zyFAzCk`=sCZs=0=y+1mrcC-DK}l9L&Z` z)ZBB+fNF1rxJNlQ9_GYCDRfwq^b9_?wDCojqP&N=O&1XGVwutYv}@=PB=J01yyp{_wwljKa@{ock=tX5YTmCIsobVhk(3( zZrXpp7E2=fFqLNzwajb(M271dx|miAx@(g1n!kLL;!6(P@m)nzCc~H^HNY*mk9)>C z$ofQ@?(XEjA|Ap;J5)(Iu;m17))5B}fyn3{#kZ z&brRjFQCs=rOjwvq1a!&${hj5V9O-JLD#8$|8qEX11a5TKJmz&SJ<)H4@IXYW-)&z zzTPy{}qBh<*t+(E~;H7$Q1b^gsf1yGNWm%1Br$aE%cyKeQRZRSsO zvCM_%HiEcuMyb=g%)XE-iOFRW6U8~@v<-NOLfAi$8Q_}p9m0qcytM}}2A0qDB8%3Z zF2U|?reISWOvS`U2y|PyIus4Nw%mX5W9g(o`2!$xD)g@SiXLC+vvq2Xk!&+DcS$?a zQevDoESsIwRewH!K?nLI45n+KFW>}obRpPefMZ+eEayvMU9Y;J@P@bs#RY!j6il=X z=^!#)+x92P`WQsKFNvaCfI;kMt1dk}6MGm33kCzy^wh4dyn(DC-WPoZ@alhWVi5wZ zq4k1h*ps~^BQ*4)eG3@KnTmf)5^QzB%q>F31O(EAnrIJtYN+=s)9aMnm)uQ&JWDAS9Bb;-U6y2 zuKDK20Yof?%DR0zm9Kpb=(1i$6GTJuJQIbrJe386+|1$&8@wBaBrkt%QIxHd`27#C zWYI`qM?ichG(8W-njXLc0nTzCSB75!R$S`lCG21V7|nz&`R>{xV*Kd?)Sh6RC?GP0 zG&CX`A0kyoov+vpw@JH6ZiN<~Cq%n_WR>;{v2eddf8Hwo_=T9YEN4shwFW9l9NKxH zDw0(yL8g!#(emH4*;Rk|j9LGBm=Z8BXk6fuEyuf@eiCz^hca*);La>HQ5uo`X&{)s0vce_|hPA!h z@wF%WjjCWR{^i!FOl-7`a1rJQ5wTJd6oZVxlYJzhCYQ-Mbq{~%=YwuZ0>gz~*~_K! zPfIcfbBh00LloSuZIoi$T=1;ef9P@6RNjlgN;H_D!WD}L zmS=i895u)E_c5}ZrjtA3v7c6`7F%uL3Xh{dh;KP9bD4iv>`t1a%{dd8O8Xh^GKftw z$?Ka@p_<)TFD{NUMiwjGHgbw?wDxD_*jq5l~ms1cTMJeu9-O1nv z!TGm8pXFO@r3y-5t&c0{P)!lbU1n&v+su-;g*!NSC}vH1MJl#~7X?Fx9Ik@FVoPw6;W4 zAzSG+^Z{WTki2$uA_h49py;kuO4s3YAyL*4<7r-+vTfGlUGSPZVvQuY&ich-l z#*rlwL+?*U@Tq*(4y&<|U+Ub!X$$hQWRwns&#dVPHLF$UIWb~~Yq+nvKx^!`Eah1; zu}LI_k=lTLgJ=HG^WF5j|11buYr*V26=G6EeGSP@7@+WS7k{cP*-1iL`3#o#klm&7 zk`jO8CM?sQ56UUBu6EtiEAkUGbW90g`Q?m;>K~1$>Rs2dS!sOT*9JkK=e3sNo#&{s zCY&M4Jb=D1b=Vdm$$js1<8zOR6rJ2;)-I*l(Oc2FhxEM`i!^aa4_ugrk-T7v^Bw)* zsMyE}0#`(|m$?;!Ownf^rXXO67Id5acAtODue1f8x1cZR+iu`=zK76(Umrc5hZ=CR zm^0v?0cknp1*WUK0)PUvP65|1R&HU*dWHfHwZo(HCbs`CrUzO0mANzuB_Fm<26K;0NGBdDp z6oAJ*1FuYDcrc5aPvlR^R=N`fypkWW1WcNEii7Tndx>Y7v|0FvsJFwEgvUAVUCvcS zBey*F7Vkk*e;#7fLBZO38+&gRQlx*|8BeR%sTmG?0nY*I2y$}H30vl=ddx zS+FFq4>NFCsiEf7qE9DLjli{`K44|9LnwFV+=KLJ)l;Bn+uep~6&qsDsTzN40ad$9 z##wa-B!t*Kk84EXvAl`hYiJd(JI1tpT;8dry>^0&BM2?Lppa0g=)YVP-(y>SOS(T2 z76V438081cMYTub zSIL>Z#-A7mw{?d`)vISQvV+!B%)$ou7(wIJY1<-@55~Z(U5WOpO#am<;4&9gM&O>x z(LaV*yX9FE1 zCZVWbFN+=*aDT0CyIo;CFsqZJBS^Sk#fz{ur_Whje`HDbzN;AsvTFN%Lh?^nSgt1w zoO(OBwXouPS6q7|-hq0i;JVA!3i@<2@ev77X{024oed?f?(ra)W*0(8a*9|rmq0A*$&PB41=s@)ri!or< z6U8awZmUE(Nc3ht|NcNA^L08M(GD2pGT4yuTNA%j`lL3r)u^9iXv5vZ2D{yBeIK1* z+IVefV;Ft(<0?nTTX-msMOr3G_>XB~F2ZnDfLRj%)n^ zNg{)mwrG|+H-!9$M09oQgmvl4tl0(?@)sv03RkIX)vPo{`!f^SfZ#7^`ox zn%p1a>+-Mod*ffAD+#i4)?_m-+mY1#P>jZcl?zein|hxfdI0OMfg!)kpN_LnvJR|U zS&P2ei5q`5a`n$u<{3)}4Dq%cvr*Q?YJFV+Y;gb+F(f#544!emJhejIreUBP){!}3 zhYg6SNENtz$0dqSy}3_%u>%QJ=m|8qqg(n7kvP-e|KLIPumzgM43o@SIH_-W^LgXG z_lbj^3||f=L^{jfogv>AH30kvd5?MSF_Bh(g-(C?S}ae7R~koL*#_5t2+vs8az!jz zo_N_`VPTS-T1c&s04%i}Ku1JaRpx>{uYY-F*LtfoMVSbMKwK}i8C&G7_GnRu&4l+> z>2#_=sX>ZrgUAW&55)Qg3*{5j^3qCxfC|F^gt^T4#PSjWJ`Jzs zE7e0lRjTaX9%7!k^w58in0MScMkASKBox$(7-~l%5~L@8KY|^|wVB1(C;|*St|@e~ zWvkWAd`a<)ih3Nqi?){$V_#doDO8lVG|^V7D`MteshVTrZaKOy7*3`i5}=Bm@xg!D zM1{r&1i_4fTM`O*_bGBcJk>*(t(MXbpf(H8@j4f6{t^*^Nk~do(ILz@Xj{GMv!UqW zvUdPDfnZsO@1Q?-%(&|*F+#SE84mE82uY1fZfVtOl_0f;M)fV%TWK+QKP+a z{XtXQkE2n?OhM<4#tcjn4IZeGnjn9$my8f7(~eIyv^YU?+Cwm64BPDW`k-uzvtM5D zzjeL|-67KFU2q#JpH{4=rLbFUA`5tRN$=e0J}}Z}lT+0VUdO4as5d=yrJPy;`k(^O z)K%JJ_8h>Q(cV#2`kmtRD-58Dyg3^yT0<0Y;{**a6{cPUWWcQoPYPvjWOI`SnhpUq zm%-=(7q@Pv0a8K&HZhmN=m8@GG&3}l(0mjHGBGkVG?xMC0VscZV{~TSmUV2al8T<# zw#|xNv7XqrZC7mDX2qyD72CG;)%)JQeS6&QU;XuuGsf9#tv%OVYp%V=`EkgI6qMC89>C=&fUS>)XWJ$`3HlFhKBZEmcK#(hVK9L{MqSfZfXM{ z|MTJkw6e9c2HH6Nf%soU}Eb4u=>XWU}S4!Z2nhij`V-9gdBeX1^`Dpppp5XZ9q38pxs|C zT7VtU!P?x>@y|QJ+!0{vU|{3)rw2~90CO87D`(@s2>h{|*#1q(&cXIig!LcaA20=5 zM<+)k2Xi|oz@MxNqT>JH>11Z$^jB_2^FMBYt;wHAV_PHVze@Vs_Xp;W*U7-##u4BI zbaVPEmmz-;U~KMaXJz32C-)yPI|uW>X*fHY+nD}~0WH7*XlmeKYz1_5`~&j``>*c& zt4_dwsoucO&dUAo-L`*6{U--=Cr6-_2|XMW^PikXPJeQnn%lrJ{52|4HYT2m=({M{hRzh;K&4+#TfTN^8PfHBYnjzNFU*6B}50OkKqW%~a+k^c`Q{y!1; z|3u#ZKXLzEqyKV<|9{W(ze9^VTUp5&SOfpw1o-D21CRmyb;;QLw`c=vb1V1%DgNIh z)q(#Y`9H!)IT`$Eg^-QuA2}H58UJB4cN8~w0~#xsI~kb)Obo34^yzQAs*N$w!OGkQ z_(y-wzgr2QV`60dH=l}`xsj#KUyWz`hYM(9{O{cVNc1;z1~C~CF`;iX|NTz=J5J$` z_D(A9c7Le-M=7$l#{aqa3q@Gi)(zlE$HdMKpkwA_`E%r$nE+g@EZ+Y^#=n7>{UY>j{anigdz0~_N%1NNVWzuZR74i0~G{rk-S zDf*x5zegPibORc}E&sMP;t8@y%}8^q{gN{@A*%JWmkE3**si2Or7+*G+P23xHEfHk zLjSEMn7(n6`=iZ$;l%EJPnvpvq!-JIq9+A-k%#9^Le-a#x=!A~L9-vgpj(2NcB+3K z<#{>EEL#KLK zTbjp3bUlgbrk4r$Rw&#!&W5sbtw?`NCyNq)hMY|w1;KPK);~c@k6cxSG|7mqag6kN2M3I+(q!6SI4nUm0{XP3(p+ za*LHz7Mc;Ro75pkjH6aK=jU2arw^Z0(L`~L>dM!xgRv)FB}|_jQ?8$a1?zvtZGlw$ zX*#M=1LB;nMmwEATu!DJw}Z&wN>rTuiD|K^k{6?z~Jg&KzNyNfBjiR0}z%X&fLjJ;dRSfa|W??g?V z{(<`QpvLWsRja{SHJzA~{{w;waoi`{^-7a2lLz0}MC(0}zIIPP8L4P==U9KDEoC2x z7Nc&b*D64&9pU5N?$R!OZ@QX9@z6mXHCh^9S5@i8O7&8a{j>#39^il3+qA_lub7P{ z+Q^eEY6I7%uOoLPB{^B(S^P%RwzW7(vYB=4mrW`B=ZKy#Bm^{52g1(TrtkE++55My zUwPtR+A=LMRrpDMQugf~A*VsMVzq?r#!aPcA?D{mC2Q^Nx$MKIg?4q}nI~Uj&rx*O z-@sT9i|LalPqYN%4orWia(*kWHOC(@T)D6~_1yFAX9UV@|5UYdmR6vJ-8COyHW}KY zSS>fp8Rf{$fN!WKW#8HAjNmp2SMTCoMPf&!Bcrm@-kLf*0)ANFja{xA{Mghc&V7yj zyrooULZM@|H4F_(CwPlO-|txlqG;jOyKCw@fB8I*8N}mt z%)K$_Zp{d?DLgK!Z)x6_*8pEzD_zUdP{>^KfSnjI!?vdJ=^6rx1))ZltwHqj@Ag3N z&blQ$5Sy4E3LAg(LRj!@GddMe8af7*7j%;c*BiSa={hWvUndkYF0=MHUN#VTCxqY{ zZVOtW;sA8s%4pJZXw;H<{sx;0+$ifN-~O}}0=(7Mo6AuC__0%L#p#?0ufTyh@t`u#E7mQh9@ zgX`p_E!RT*cQDO!$Bt`6m%}@&Co0beV4+!uH*S6;y#w-{9E8_0g-iGbXkB2&%HU@~ zRF)eUNeRxQ;IS~Ec&Ur+E$v#d^&8EY_}0U2MC07)RSj*mjlmP{X0BoEQc&uq;#W0F778F);l=xXc&~{P z9?DbB4Cl3~O3^a|FyfjhmaO*=PYrQm(l!HQNHl-WAA*YO-})dfcET499DYuH)hH!4 z)H^7+#8+#6)5oMbstRTz8E$&Is&iKQ6euSf?)UuGf@g^3>vVL^jP#T-GB-YN7EfRX zf|NR4?&=UJWN&tn$?Sml=n3EY7(9-=@@-7_m4_2OEPfl>Uq4YAdWM@P(_+UDOakmA zBAtI}UQ-!?*QKWr(&~X%)7CBg*;Vl}x-=piI4iE>_VH?Wz!YVzs2mEvsqjEBo@z<4 z>-*bR2+aF6>yEKRYU%g5SY0C-Owoh<8dGM$4+7fee_)ZNtxafC)@VJS^s5hfd=LUKx~#SuSGumJD<&IQVw` zHiu>$28L+~8nmW;2-Ybmm5)2mxJAr>txr5J&>n^CPYCHDROtGh&q2I zzbcN4B)nt|R1_TDb3XGJ0UF;@k=UyW!?_chvI|$W@(7f5ZN|hpR16H|##{K2<()4> zZwQ$l-@MdP5Pwcj+dz0AVD<#tuXl!yHkk8lxZ=Qexx`)xlI5(4)KRu$64H_e#|Qex zpPEORG7CjV(%m)0i6}Woa&5t5GroUO+lC|LObH$y)sR&%tyMK<{rs##;a{RS9)2n- zrZl-bS}fAk!dKA}eg2)6zrPxXIKXe%NLSRNof=@P8Xi?;nf$od|1?H2mN42I@m^>* z{8}DGhp(bUlzuNW=@05q(UABnO1E^_MMkVep9FJ<1--DZs}?*nCl}me%4~nhngqdi z!@w&!I9*G;qI<@+EylJkosn(F*W@YUp%Km8wFsY%lJh*`%M(NP5(Bd`ghhQ#i{`N- zr=pY~JCmjWP>6bB-RWd~$?7>5G^LmZn#5ON<9a21Ai*m!t<20~GsL0oZz1l&ZepLCx(p$?;bLR0#8wP@2=t&XnKv zHBP(t^?T`3G+pjW@hk-u8NuhK>z%U_`MOfHGXuo?;hrB&FH)te4i(P>8NH|Lq7%o< zeP%J1-)Kk;$uKr_W-nzON;@X6a|FLY>rA6j*`O_apB@~Z9d2gN;Awy2a~0xCXLV^0 zJUlb?XG^abvUW6$-Ei68xwxE_7o4NLju+*<9aW@Lcqx`F3t+g=`qp5FavZi{PhU_m zZp||}C)Y2z=nls*>U_WS(|)$F0HFC@zJRn8k}buvmJJe3rEf`AIY$1e%dnbk1CZ;a z6Lww^s}H^gmlmAIgEfDxf%e7in4M{vfMrIA&Snu_%aHhm$twOF8!n)Y8t8c;SzHK{?_v(jAQ)-Qbay|<)sC#x# z^;=}E(JS8irn?VR-}gwy^QIxvRM4jW}CTzsa-dmEs+bd9ptSrxaTU}J5WyG)&_ zHBGsM#ydF(;T~c`Z9s)moEZI4Zp!FLk z7bVOaPR)N1_Qyxm&N1OkKv@ni2ZYO`i?=e^l5~)X+qnEJde^E}k$r5BZ>;Q|N~aOV zH#^53b$Gs(i)gNli5`x53G~~(x%^QH8v26RFMO2bD)_BD%lZU@HE|237t9*vcnouX z+*?{yLYU*AqDJn^?aov9f38vlZZI`Ms#@@U%ea5em>@7(kNNMC^~8FhAhlP6`g-ES zzN*5V6W;9T;5?@@_h2;pb-MWXe#!)zSh08Xg`vn>GMAq0kwU$*-b7CcZPln@ZCiju zYw4By4F}yGbTg(Rc-WeHpQ;Wj9&$19IH+m27K>+B0W zVb3t+hB!fuQ?fM;WkJ~aoX6`aw*K6>YJ%Sz#*QqfQ-piTCdhYvxN`l(Mdek>EM~7& zG+T#kJ!Hf!b{C}! zLm&2>Rn)!IK%0S$TLt;T_*c>0>DB1?;J1Na;s-EQh2qxE1TYdQ&py@#u<}uCtKS`B zKRmH2s7K)*nWn(Eye@*#QnVhC*jFF;@l-nsV>Bs1Y%(|&k(w!{EgN-6we#CS++Tm3 z{ESe*4<|n0LBa>L1s(WvLBUKyXm4{m-kaE^?|bHXEkdAkG%K71l-j-(DW+GB zrRK7JpRQrM%J`kbX_bGZ8ARAUou{d}B?Nz57Sv+AKV}K0x)F6fZx+2iOcCJr6-RMt z9L=TNtE7kwL#D5NE|Wa4-gBT6(>Z@C-bo1x|#tS=v38**MLO@+KjqPC7oNsj`sO(eO?%Xe|#ns z$Y!o4;2mFmj~mb~MhnRgsWhVwmco?P5_&HQ9^~1ln{j5P!t2+#%>mD5XC^+NPe9pPfuEeK-ngT8vLIt{gOQ*w`MaJ`~8`@sY`T z0cWLDHXT#dk=_06tLe-ZF6@UH{Wj&#m_$(X)f%jEFeRq{u6S1PCXtt-yVrgEklaf%Fo@`hYNaK96tLVXBBrJc!gY%(TEyc%!=8|ZoI zrkRQM==SBaq0ff5@jG`i2i4b(yd!HihNrSlXWy(jHOZMtqeiYn;t@cAC5%4>m0S@cJsTIDY>kK11?PmI>48_ZP@*i)9fCK zEHwxf;PcmqB-=}03LHAW1t+JG1>g0c4yA{QtM3}#$PlIcLX_1>-sX5@I>T;ZCNL_` zf!%{5hB6$t9bMAcR8AgaxPIS~z2)~|XCe-UAZAHtY}-{^z8g*@6S{HE7EE#kcjsH2Pla_G(9Ol_SphrSxbbh7gLL%_Zs zb)M{qy`Fj`lQuSiO?m&xlG(z3v#9#;I$9j5nLi3iBN) zNXPAf)fhT8N2E>gy_P8<5$0~^KqGzaH)(G#9yK*Nx^8%aS|T)mSBE%7|LKyG4&0R& zE=xGLin?g1Lz*7q{g3s8A2U|X<-e&S@EH!{*<$@?Rlq@AW~sGd(!FF=;sa8D$n5z% zoUcZ>)D9Wu)@ANV&ZG`vSfv~X2*>Uv+jbZSX82#GkBV&7#DxY4;e@HNY_ddX>PY*Ftmz)jbyi|plhIw)ooJWN^*QM36^~>~5FEX6lFfMi^ z77*4w=02YUeMU3WXbZVoCbJV)(}}xcbL3=wB*(vv+rSjm^jXvnQd5Ko7W>vN+AJZ0 z9ZOCi0Y7kHVAk+aQhw)|iq`YtSvM&0^5mgOBN@7sX`01<1HGfI|2q%d>sPf^+7c4R z(iSZ~ugrq%M3Glv6VHO`2|We(tdNnX4n~m@g^vt8%Wv1)gW*b#Rhr@!J$dlhhw2b% zB0DPUIU-bC7Y+D<5|{OmMr$QYF6Z6=13^smE|+22IklxNS>LalEh7~#`& zgAE(Jf{)^V63@choDc0>e`bkTz-tFdP75RX8OB=}+iJi_I}OJq;S%_&^F_fLx3kL6bjA7cg= zq(K&Pa8z9=ups7S421I~@H0|z>6WN+Z;hO3w$kQ*V9)hbY1GNVn>`*R!u}YOVYbeS zWX#3i06KZRD6igG_&e}4w^+*X($i}N2UUS8J9RTF1Yf$Oi4FCbElv zdNQ07QD^9ej1%K`ct5KZc4OKb=pF_2zOY%AlAMgGr%J%*?CdTa!O$*exI-s=Hk!v3 zK`@hlmyZY0`##bQQgNdodz0ozu3-=A&~F{Aiq*1Se;6F-D;74)%mRFx*T`?%nkK>G zWPBXPz07q}`$}Y5yN{F#`b_zowX|fy0I;VQ_xpB# zan-0mAfXMtyyVfYN_JW0^msW+@DYXhNwyv=we0~o36uO7ui=V}wuDF*o;_1K#TXCS1k8;_x7_`97_hWY}Y;I%)~Ptz5QRdcXstrIcBrvDgJ^z^6mehLv7w zYh01<>E-|Gh1pl$P-<&m!3kMXiqr)d;FQ3XJ~uXztGaL2M405s&UOvHYJK+hf|tKd zc^CGZUP3FW0YUwDc*c7;@GDrcwas#QDk66mvKw+qLQUDnbG;6<+wwnu8>a-@d(vOa zs1X#aK@fsi!RcZ95j*;jP(pyKRcAkZZQR5c1weK9p5{zUDc=z`J)ef!KVCNLgG;q+ z`_QW=Bsz{LQaE!-CdKvMjWckAJBzV!KD{>r3pcW5F+Y*Oh}%Uhp@qs%{+?9h-4 zx$E;gDVloXLh)^IjVo1e__pjVSlNQ0SJY-g zUn4iD7O3u28woLfgD8RPMI5eic7wC~U?e0|tQc$@V|o)2a#U%5mWhLha~Z#O6Qi-~ zvNMH^QgS|vAAT$FxC8k<9&@-=qc6hK|N3%pf>Fx#ga>Q0&e?7O{DIB2EN{9?-%uJzmZ6q_D%xJ? zt0>07U4H8JbhQ!Pa0(%=bmv|pAh}gvQf`Ld3F&<{{H7Qg9D_YpoKU&gZpV>=O0~1F zJF12b0J9c<)GB%AMA8cw^SSjqV``sP=yUynKzx{L2_eg@j7vx%FcP}haFgy?O$*7;kL5o{7j>NUJ)2Of}6_UY-!O$3(sz`>@2bFiMr>At&MO9EzVG2wLYJce%C8F_ z7o6mP??kTwI{q2fc4__EGHj!UGY%gcL(g}Ah0|%(LZo)Le({@d#`+3L5Gq13(lax5 zRy0IOI;xn`bKu~z{4QZ3Jl$_3!?choNw>o78{cF_D<}7U^?$ELu9(L>m0Q_gh|KLH z&R_8$ya-7tf}Y{FZcVKsxkKEg>z;E>>^!6)B~vBv1z))PBJ9rxE(D5GB3Pm&fr)Q_ z8H+47OT!B@wyDMUJr4>mi%#+K~i`=KRNzfo? zg=&!Bq89t)^$nkQbN|WygH_=hPXPyrWG-z8GY-77yBP$2vPc$={Ids6pzkb2gVNa* ze}K4hdqp>^N@O104UAigt!3E*#AY9V*?PyO#^WJ|u~N||-&YOUjKrAC-~7S#*T~Ce zKU(R5&+KIS);Uo0sIp3w!4N&Nqs$^^Ab8d7?0{f#;<7O6ErM=A*7LD*ocA6&5nWFS zen)5V$0(Df*`sU2E(4{*f~MMO;jX=~p3gjr)dUqae#>bh?vv?PBVG91NC| zX40!vwD?^kgDRv25}8*zizK*Lyz<(FQwHc%SZf$uU}0MM!OPsuUmS$zP6Qt3ysJF8 zcqio56-t~`_TIL86jV8m5q8A9I0lTz&!$+ule50t{G@h_7gvz+J#y<#1UmU$zytCj zN~yL@D>U^yW0pP%#~E6l@9GPGy%ZS~S#qk>UB;hOP4lahWHwf#Y9;yFx7ax*WEeNe z*Jw5C3kB~k6ryoz8NkrkzHa1q9v^yc1sj&v$_ujB0wP0tO0*P)=fpTk=YOz!JjIyj zIB~EfxpfQnXQ{7K!e2)5KQ0#k5V3cPT%@Fb(76JpC2ry&?o1xS(?uSCtj%Y88uFQQ zAe(G#gtGniO>x1>C{@T!@ul(M!vVjP2#X3PI6vWl&^**zC{5ObJ=OlG$wX|?Q{vkC z0*ex?$8d=g6WneKZbv10d>kTcQGzb_ZkkUcMb+z-2F9~Q`A~H-E1XLdU9;w5mCXFr zo=L?AAp}3$>+AYe7(Cv8blTgA|8ag|4B507+S~4`&wbMA^zYggQej5xuNo4A7XE?m^_z&aclR)3-7Lr2JGYP4XOL&vRVUcUfpSnyD-Pa7N!uH8ip76J) zPEk&l;g74D0hJ#!F)&xirPm$jtf%Z z9$Z;i-Xf1Vr%hL^g&^q>XY@yhrw^cEw9lH%XIOL;+p3O~5U= zfOe@Xi~Tv>Kkw=Bl|A#sQ{*G$9x7-N^#<2^>Yxa%HI6f(m|(p@(-HTPSt4%Jt`O!d zj;wQs#@12;A5B}^GcABi*o+NQn3{PlnM_Xn{@HD`-S^{vv?-?j$CnlHCXqB7Tj<(7 zXS6;^A%bM^-0@7}S_u5?Bh%=vPXsc9dy^Sl`{2MXC$MPrEQy+I7# z%j-4l);uZfdothMFPH(Xx2Q3Xh>a87*KVAuO1U*o@tA$w=AO3v*xYez%bV(2hsEpD zKIk-DTiM5dw-7Q*we==bH7(NmiGv#Mr6*vd=Y*c@#_L(;alyUWWmO%nEI-Ty3m0o3 zdoboeCcY^7y>7EAHH?CDfDMdP`eB-S|91Sz>x86w6UIoN1W)u%(ksj{Wlvazk@%XG zF<|Do42f%>ad0`bbR&KA5H=p!P_{%msSXb|fSg!=Y?A{qV{xs9cAh>E`GD{ld@4EL zTw$+e^ebu*PJS@6veU6y;XMwQU=brStGgz`Qjc$I>yzA;?NA1!zo6dVN3P+7`&V2W zWT=*!XZP)Sr2|uY2~HaYWTts98b~$srot3+GqbtqtGP=!k#6&5xTMRS1@*T|zgzNQ zeUV0gJ-}d}{FYk8fLrd?X2?PPPGcKRB}b*eKE zQ`D!C8{J%{o+zcI{RCnOA*fzEaoxBXt>g25jy=P$lSlfd5R9XDXc5C*?VLwS!nvCA z?J{7E#3Kd$(rbtpn@VG-4Cf=4f#^m=Lg*UC4^A4jF-lx6#iUav2WLgdS%~Gcw$6x* z=JdKtKn>l|SIT`Qy^MpDYjzyN-O931;ftQ@xWn`X|K2VHo`bH?PyacUOPp(q4+P17 z9nfK^N3Ak6g9u)o5Fm%3Yt6*3fT^GNrpMxWg+qYTGE4$=@dsfBm&IRHnZ_}Fn6{1f%#1&g{a{{Q7!S{~mi%xL zr*Ha4QDd_KXoPR>Sk|wdmAB{bw$B<-`!^DFuT@DlEk10!jaX6XDm;=T+yM3bqBDV$r4zyU9u^;e-cWUq&o?a0 zU+=+f<#*4E2EHUvzIEL5fZgoWdeO@5S3k)Th0w`G`0u#4wkV4|M%N6|7+T#SQSw$? zVS~MEpq&n(kvbl*(fb|0PO-^?=_XTY75i~!9*u(uSz>QYoJyDHs%6Hm?{TfyDt zO-S(SnGiQ{izZj@IU5GcDSCc`132~#Q-@1Qz@;RtV5VX)B|&2?YHl9+!L35y&GP1@ z*%WGS;3B3}I-qc+=Sx+?jZB(2jhqxZk}HVMwSQ1*_npe)>Lrzbdr23{f^Am~u5ZpT zu`wxT;;n0xI5MWo6J1k0v{5FWEtJ&Ta$?n&j{0oWgU0tyvPwgrHYZk96vFhmEY-IR zIW$!wax0S{i&?OV?^O^^L6%c4vA>pX zENUuAlm~l>SAHeii^@89IC2}Jz3A!=RgJgKIOZ_!O2}+~>)BWPc5j`iN}t(k5=(<$ zy8v6(#}kE1Dfh(lF~@eSV><@Hj~U&i6L1qEc>DFqp7`ao;?don|7e4)wp@9S7n0O# zI^7n*74q@eM`pl2U}abdnXNpT$U3=s(I!z+ArtA#Z>C9+i@x>YY8yZNbIP=+LhOO* zmjau{zOjgZVn1=72@t#nb1HoWn7h-PWu1+gajeal;z5yDe4iDPGA5{9)*%m=qmE^p zB8>zTU6q6!iUm%x?!;RFS9vU0FhO71{HUe4E4=z4dk_FY=|AN z0!^|o{>=zC%0k)B=5)9r{1vP4L%-{0f#KM5*%I~B3tA|+eQsGdCx`$CafP7JcWgy-e=8`Ko5#!le8~BGhyJz_Z#i z)R_!`1tNj-{XIctyunk>_e)lgurL zROz9$@9AwZ62%5VmTBNWc8ANzxt!Zlzo`peF+!>9j$ z=o?wNbicnoS{IMbi*X82RD?E|ckQ9KH_t>6O>_N_dAJD=b+1I064j`ag(M7ithduD z=MsM8LI=5C=x&3Va6Ez*<`_i^WNCNXBz&~dO;q7+Lk+Q{dEnu6?q3Vk42a!hGP@IaAYktw07?#YE58fexd6zR*T zkvj7`A`kqT$RfkFO7gXpb3M3oP69xp-iR3rL2~J!M`n~ zD%YlTguTF;QHl_j?xH$o)Jj|;G9)y}@_2u)mPmMSr&Osnh<#tC7%SPT{|V$N7$Gy6U0Co^ro2u$4SSAVZybCjYF z&Wx{D=%?eK)R>WnjA==HE_8r@iUGQ}DY@xw#kDnS6vuA~U6K=zQw4B72``4xkS1V< zC(A&#-;3HPuYrrTr&*KOi5NXYd6WtAOic@=25!lgk4eZ>Xu^2%Jj1rj@y7%vGl!8l zfZ6Z8uv&!+xzGAOWNS>U$u(HFcv6E$vgm1%d|&~-eP(=A7Ky(0dQ2dH2MQy}T=g~d z2E{bSxlr*#2-_$7RzIZvpH0M*QCjbSgvLfcP0T0hSoEZp#D5Jck9LZk~o3*POe~Rq~&xq z6SDaDygUqV9xl|FpYpMSPHk3ShUV(_7s&(@W0ie014A&kquqCSSc{%RvSt)Rd+jvZ zu&F{?-LjLirf2RDuGL;jQ^fK_+Gbv;B$EUL9YFcOmRL^p+I#zdRVI;ou^k}H4}Rqj zSYSF8WEd2kPA}k875RaHUEql*C4Ggh(8STyS7L3OyNXtLx&Uc(vRuP0ES2}P3$kIE z)T7j6ev?x!)R*}~A^SiF=!3JX+NGrFnwstF?pIF$dXjblae7Q!do)!k0OdX|1A5`9 zkTn#kwCS6Su-#RErz$zNz%~Tc|T7cVg4^3k`~tO=5{Q zC?1Mf^ViT4)fHGi6lpy$-43ZUH?i)=XiG88m5+BkY zkw*8JTZJYk;*!gwc{WS)(J9mM1~2MX0QwY!w)GBsxQr7Yr@DbF=ZJggfO#4xQMHny zdE->d$xH)9Sys+;@=XO1rS_GI+~Hn^tQ3K$(0BEeP1>KnSUx$?_@4aKR{>L>eQ!d& zok?qdv@@sENP7K5IHngnGnI3^QC2vROI-H>JYVTW4V6sxBQt6U7Ze2#2jm%LFmUI# zG=mf17oZ-OxkPSYqT0ONYtsjAtQ{HjUA;`BPjHwK-9)I9!G}|jOuFBN9yBENEh3Z& zx*_Hg_JqEMC9p#fRqxYtFHH2Ol;2V*l!vE(VXFo|;bk+{WK(BjYOa?aLY!%PBO((y zqa0{1D7KS- zJ$k>0GN5{?j4^@rHj9X3(lO&_-4_@AJpIm%Jm!Oz)F-r9tNX|!V@m?}!}`z{=GZr0 z=Is2FL8wbSZ$GlbK}s7o%^=_Ju`sivDECo?)<2_lm0way?;7w>ISZInIY&G^sno4B zVKiN5&!;!=H55o4x2Tz>PM9X}TNN^Ye1=@2Tfn9KwKQeNkbj+EZ?_(@3Lc=MV$_G>~@+>x5fQ!{OUM;|Mno>p0 z2^j|`p?y=UzL=ysTc#^aRw}8)HVoW%E0@@@(Bl)2J1Dcnwhscmz_DyghrZ{3!_l%3 zAMUxjYn1e}%ZAq^65NcGuz3d~K)HDJj-kH#JHvlMfL- zVu!zqVOxWxomsNA;Q#a)F%}_z-)cz<7H0gR$W9)}hz8xMj#}f)TuD;o>!iym@YG@5 zJFGNP&FPCTgTY>wkUww}=uCko7O?u_!Uu@a%y<_g^ z7ZK}YPdt-N416j>zy9Z+2WC(?5I#8Acbq3{s-@fuE>}qD3frwkcDn%Ak1OPtkmBX;C7y>Ze>!9Db zZO2eSFr0yPI^q*M2yxL>j!+R*%Pjf72*eR8<3es}LTG_j`Sk>Chu`I&{8iHprl3$A3mIs%)z3xCfI1eYu)K83% zaJN!vqc5_uJ#iU-lp0ke>QEhpDT$4pi@ zS6)uzsSQbe0^CFV_CNaj0UjeQY*55yn6`kW0}?9|17Y7~lXRG`VAH?js<)`rJQvVYzh zgLy!n(?pwMfgFJ@Q^dA^pDrSsz1XR31m5(}s!vS9zVhIU2hO4zP)Yaa>IbCi@|$?9 zhIdZ6THVm9*uARj}?u3vzxck<~T`Zhk6_! zR?a(rN`XG}49{`K4qqJOq|jU@U{ZWECYCSnpS0Jtx4yjf+FkBT6h0g;O16+beINd! z%41^)>jftmqF4(rn{LJ~L4kMj>PNDH1@SI4ta1_(>b;K2ct5lAiV@505JAgtHOKGZ zNyTz&t_k{;9aSaRVA9(X`PLeA?o?fA^2acLo{UZ>3X`qPfS*wYO{)9>&2hcDChD2& zwu=5KAX|qU^lJz#OM)FlJf}YO=|j{0!jV{tUyq+vmkF413B8d-R?pU}pHQh|cp!6I zWaJ9?;0Vt)x^FX;oVrAfN6Mj!N-b!ea0`Yd2{vtSPqJcU3A=C9L1^4Q3a1>b6Luee zINvlN5sc~-CYEr4Gard9V*T74F$D&Gq_86DbK5WLF;2itB(ztx)ie&GLC0AdyBM=z zmiw2Ru}&D@C^(tJ6i~v*zk1 zprTE1F-eZPY0FW%G?)zt3J+_31b9xj(->T=>S(7JV{VGmsP51`3=X zZjDABk6gwe{%Yo`9I-g46&~JwS3gwYdZ5Xg6qe;&lO|M{@6=^??w?18HK4ofo@(%EkWXqPD!^|eHxXo5Wo?9wk;KxdTE2WL2M26S;MLhrR z@~RjZ6I|k=b|_#=JA7V5Iu+m)MvwlzPaammHjK(L(NXM!s8W`Li0lw7n#G3i`hm<< zJ)Et($Uc&_z(4;+ykYe_cbiIo11Y)$5(5InJd2e1WLoJ!Cto8QRdD$szcYOVHmf@9 z<~dZ3uLuo9Ok>U&N#OhTIy9fx&ipH>Ue4fwQI4xfYqhQmjH%e!^$%^%JjExWH(Ytm?+2QTLI$$9p`E@?w zzN@@}@SDc7Mv?8qsZ_LooPt9w>Fj|@ekfM@yC7mEiQ0)S+6_Ial$bCPTGtWXWd!OC zzT!QJBF(8|dQZm#FzchuxR_d4eyTtvZD1uwthx(FOy#iqVAg)wP*)*K>rrM7elaI2 zD})kz<;tO$&CRa9lTe>-s1`rRiJBsQcuZ*zf#3+*HE`b zQOS_s!26O1Rvoj&p1AVJ$%qUmxXvekKF-D$rDnsfqEmredlVp>Tyi%{DV|JG1F2H+ z$%~vswMGyAMx>?1#v9qfpAj-@qOxPv^K#-TNWymtV?b~X+h9FUY=Ko05Hy$FE8|$< zgq$nc)#%K8j82$;H-9OLA7^~sk{En_#rFOp`*d1({bD$u66MuP(TxVFrp*tFLDFxG zB(=(ce`Ljg5e4Ch0kG?z<$iW~yGKo00jWy!OjwtH0@xrBSJC*^eXrj|GMv(~+#ZZ@0~%LY`{lL_(@es@qm7y~$PCU(vW_tJrivsV4urx; ze7!iHX2Fzyz8+f8K^*}>l1aaJZ-Sl7i#K*o9%;X#{7J#DOwmj(+<%}B^^)M~?)sq( z*6gb44W4g7j!gxKB77BLOpgjOO#%S|nl3V=;!cQ(8!XE3b@_Zovte^Ei+a{{Nr%D# zcZ=#!=brA~c0|@YL>yNBG+M@Dmf$!9t{yHgBl^~@ej$~q zt0u00nBw*=Nl!YCaB-8Ka;u6Kl{SoW%)oF&>jgs0Vk1>wlO@*zeiyxs!Y}=ha|lR& z#+C$+8Tdw2+#|-BSJ>3z1zaO**%en9I%cF-ibi*;;Tv@J{yC9Wi58}y8rG@L)ty~9 z!&G{ z@m3$co*-o|{?1KRiW~;yeEHaUoF2Dh+g3;@q2$;EyYHzdMY^L8!kjlknCpZdcG(ATGkt{&a?)a13yoiLb zHGpu?0@zkfH5kYG-1N8{bxNocz@@Pp#Q0(rgYVcU-X5KNX1f5&p5>m@aji8%FR+f+ zwxt*DYWp8d&2gPAeo>n*t;bwjl$>L0H_fP;2YzACtNI^ zmoTl1YBT0oiTzncXE4M2TMrf{D8z@UR%Bfk^SM*D$#CC!Y2wD?O|Sj2YZZVkl^N-Pjn{3?*Ip?WM-P$N?9;4&pO z?mYCL&z-KHpbX=Xl-3Q_WFv7z6P-y_CY_k-LtpcbOfsa*juxS?>Ys*?or4`ww)te) zW{IZMCSzGQMhyR70QM1o3GVfK!ctK&QonBkG)g zeSC}3h2O8BNHS@>Q6h~Xz4wY`TYDCmug zD}n>y^30K{9LjWZAI!XhuJ!QhkD2bU9W99M_Xg14A z%ge+&i_)Q?;P!$SJvkM+5OeZ0tPNkgi;lqfojF}fX|nh7b4*zW^umw$Dz*dqUNV$> zcNUI`cg?98Z*$5v4}QoImNXKwwRo)flJ?x#Zq|_Am$p9|>O5I+7GUuj#%BI=5dZ*f zaA!9H_L0ng2U-Of;bzE_?#J()EMzx&`np%U6)esnIO_aMA93wn$qFc^IEXZ*3z3XVEaYP!(qN?= z3hXwz{wV+n`&aJ_fnCpzBs z08}u4lzjv2@c;_ZoOwmCBFh?KA+{^p)1syhs0G{XgqWhz1Q8Dmq)1Z6NS=<>>d*_D zV?I7ii6?#;?$cZ8Xp0?TIJF@^31~h zym7a}UZGdGEHiLWg>!2Yfsi{1Fx6S(c;r5RuN$X6CvIAWI94?quTa5dGW9Z)aP;GqEQ@EOVPB)fXqoR2v* zFcVK*ja0)v&E(`_iU(=+2Mv-QNS`ad?ESLlw6vCw*uAAmO%as9~q)8HUm! z!6e2|a-MNTlGIEXM4JLOUCPpBvG;Vwj|4>S$IkYRzu{a)lq&fFk{MKUSs9Oj^a>y} z21I8J0?Sl4?kqwGRum^Uj588zHu|*;1j=LxBEiyief&z&Y`&pXu<_yAhj^Y7GQ zpa*0|cyGdmuY_pID=xYXiLjV6z~+#)>KWmjq@phVRMM1ojo`7XeOCG+nG4|7)qy$2L=HZCo?)TXTn&t1TeSZS_d{OVZnjI96TO+lpN3iad zEd^>pOnzVQlt7MpGBYH;L8U44YLK`+Nj%hQbap z;#sP9DA=jJODujSc~As@h#D^d@M#KmzhS8<+5detp~;5nzDu|$E$_a`2=9I3TM0`p zizk0ce0_&_vORluPfyBZyRFwJb3E#E8HuFf0_HNI>nxN^cbr|B(gLt0&tWFf;VKVk^!EFXftFbzw^jFO^8S8uI-5TF zT5YEY3hY`eCQ*A(1z;U8>5M)p{UD;_1fraB7hU&o-f!3@zd4j^A-I6DkdserieO1S z*kYWl@Ms_<`tg&0JZFGKae8WnGYcsu(EvDb(T~JJD#PzyO-DU*moJrP#oY@MDMGBt zIV7UY>EMS(%0Q4AUQp%>9D-vr%l_j{=P_xEWwlUAYyNa2t?BT}nQ+TIS_&S~?)n-jIHZDK_ zfNf4i=Sb`pzfmsmT7<>;=@6mRXhgK8j0#mH*v^KL6lIjrU3xtS>=G=3U$VWs7!ios z8c@vJZXkMpilfsj_}1YnP)Nge3@0kE;Aws2Ckxii&@%@twlOrVxx2(Rfenc0q3x6t ztkF6=RvR(V zz!@VyZ+^22m|=5X;rJXyfoqz<6l;i_qch9u;r+Xb1XSLE#mx+9j~UBp<8?((!33vo z&43>Qk_D@n2v5O|PecT=c(MiRARZ5sP&SMJlI^RR1#9nw1ZM`zNsE!|;@b(}r}q_I znJfc;nex!ZDfa2FvCA&#$OC$V5UZQq1^wz1X~Sh+0{1AoShQ|!_`V!O0kKjV!RPqd zRi`(e+)4W$!MU?(l=C~7_AkyU2^nd-Ij!UyGbDGYCyYlDzGmAk-6A)6vF2Cy14n5o z*sK!OYh^BA^;W6L1;YOmOZaWisGt7e8|B!47Gog5$5>LOdE=-_$r!uvj#t7LPmy`V zA5s#qW;KK>G+1ptpU{c^{9y&2c7><@pgNA;liX%zsXx78y{Qrr@M z<)cEbPci`zh85U7-U1=2+vTw}LF`vOF=i1yhw1Q`^TVIPd3G|$DF+1q>=+4en(Jt0 z2%fdD;r89>4iZlq6D{<&hz{=N#Qt^oD$- zG*?#r(N-kZG5L$oi17taa_tPDMIQfuO))2y5XH8>%J9o{c{Gzn$m)Sxr;e3sFAx|$ z-Ul%ARbgY68&?5GcXe5FcFVB@ItGBr z_{`NwjbT1czuA}S=PDU}$fA&cVNFw<%~VL*Hq$Y5cbjphVOl-7rdw$pN>2oiW_|^m zkCKxevOa8OQP@<#xr)l}7Z7}ZWc*9nTx2(iS?$D^@i4cOrBf9ul%Sy6AJ?dPSMwf1 zFWn1jY~R2{q`R%Bsbs)&`ro4cUlj1~8-zb+nSAU|aF2lA$!rM$?~fmUMSGIs3L~tJ zmY%0_M=3j2X$XnnAw<|IGdnUp6j`3V1fGwPN4Jz!-O$KTWSRk&v7$%I#brtS+*_qmSR$YZsVVt1i*l*GL+ z^9#|QSBWJ>5#i#Ec1zTMo%76RO=(xO-;wed_w%y|9%wLstmVl67&_hU1`Dy=YG`(w zS8*S*px6C@e}ZS}r$Qt5Pp_~|Igr5XhgFn9So0W8C_;{va|M$I$-k*Bn1)Y9ykT@z zVJm9Fj1#VuZ=JeIqMS&;)~~$Ot>(Y!A{Hkx=^VR(ultqfM&dVrcmhg1x*(DV%E2uh z#to0&Th zy6%7qJ-2(mfn`iB)Lj?*%Z3aS8m^Ojq!&)RM^f$$C)x5rU!YO_>EUvPUJA;Z`|-Ic zxM1(Po7_u=?TDR!6zpsZpwfpOc>-hI)_L0I-E2*i*q+C0=-=DAe#>myQEwAqxhz$den~3gD9@%zOlf*tN z^NWgTD#2K63HCKXF^B8abdx)!yZ;)SF-Dtx`Y!65e&}z1vuL`O+mMZ^KlLQLMkXB0 zhEueJv)|PT7Lc#IkGL3?L*V4GMcKO-&u}r3ZtT)7|6QS#d*xI&GgpJiw*70 zt=aBAsPg~V{lOtWu@x$^Iq0Q`&e{_a9|xA=SN#}gmRv{i>K#QiHItd(*QN!#W1*-| zk0nTh1pyL&LYg0nHH2Dgel=zI>r(s>^E9&p)HMFr2gpQeW^DEHMTML_QFWe;fJPM) zOWlqt7Lb)L6I@NfM#(jP6+AaZ-I7ubvsY;61Lun@EF14$`%~7Mh#59h{!-aro3?4z zYK`s7@mvjtU?VQqshJ8L&r2u1C?dzZ0DN$84Nez-cmgS!4GeT$tV;Oq$r@O^e%;_pp(SBpOR%j$SL)@6}pwlRhKi zO5=F#3}ZuZf5Qoz2`jOqkiF^V}6o^CkU#|MlDK zP%;nm=7Z}8e_)NiYc`a4F489C7K>28#1HaW{-$y01s^Th_9zK@W=L?EGWCdOV5M`-yv+_G- z13c-pa8d?j+*D@tZ$$tb+s62O(A2?;rz>bvjvZngaOae`h$pOk#7kN-KoNoC;0Hin zB6NJ#e-g|iTKG8Tm87styzn(vXgq7B&a=AW#fbUcR|ocRbM|-``y1saKiVeQ!8{Nd zITfym_oL|W#|qSF%`;|Ez7rwjMNdPfoW7C$E9CAXqdI)TnN1r<|eq3k@+kQ1% zByms^&?l-JL!bt{LAm`Vrr?-|yotb_cNq~Rf98}mrV`Dy{U(l;9u+bhtz^>T_H4}H ztZ{VDB%T99o;oz+u>g=xRH{1?K`Eq=dLIrQk8O{|UXX-@oVUI%VPR7aE5h4p+p9Fm zX#Oe`Hw+5h9f5^@@}w{+608w)6AQtue302)*2I(^YM$KoGb<=xX@16b@;v$OEK&!U zAe`-lmDIEm3h?4=D69P6fx5`NZohJe}HJ52| z0*5LwF)=hYF)%GKH777ICn*XqO>bmGVRU66C`39kFflhUGBPnSF*G(YFqax~0+j(U zm#}gI8yYk+3NJ=!a&vSbGc_;@FHB`_XLM*FF*!FllQ9J-f4x~-Q`@>0e$TJaV>_Kx zmSoHJ%$_|16nfY|;gqz{?%}~CB6ym_sqM6M|N8w&zC^xJ!ePz>$V<1i*7vQYB|FRw zi9?vjiC`gGmv|mSD~T_)91zBYAWZ5>Ax0!8Ead2xF5x2Z33D0YQqOVG6H0%?ghzzn zg1A0f-y^Ohf5LMZwkASyNnAnD?GP7QgU}~f=sNlzLzjboED@LtYg~`9kqoefhk0lN zN03mrSjPk=grS5nnCy7^K@zNh9*)+BWdZRx{&6_QeL=WGJP|k}hIuYbV3_BI9>FvT z3o%QYZG7VSLO)<2bhO_gk&cfA_>81|P^Z|b{v@Y(2(KSp%& zYpn=9N>=$hl}*!lohRwY$RDC5M&6%%Ir!`R&B58>HFGeqh~^n_iy8a-$piU&4CBW@ z78|>O#P|8li0)-mwaS6ph#o}i|EPF=pA!gLi5?hB2hwpKE#m3kYQ9i<@G@7+&!A;Q zugev#e_+_)K1wfDPF~U5G@5=>`9j_0xAA=5kaJs754M!AD=F2x+DnU$ydiEE8!=zM zF5EqeVI~914*59x^UtTjcl`e7>mlI#IE0?-06oo$1J)3BTkvG)+UUtZSokqL*o&VG z2k}$iH_?Kwqg1UlF2$2^lCBq~usaRyyo#;Z+6mzzZ%uNS|Xo{3#NyO?}E_&RxWd2~EsPU!XfhSVAh?VCV` z2f`w8C;^;7r@V$!j_uSQJ)<9JM5AmP$J02SZkBk?RT^jC=q;VnX|hOGbVgN4^&Oql zfBRqSd$po5{YDpbNmn$X$x6}nKpd!4+o#(&nbGf?Bv)CiZKNs9Xts#5dz#byXF@l0 zvzn*J#^ohL#4jvmtY z^q8I)&@bqOUK{9ZxNmVr6nI!?P2=dOe;Ju3%VkvXV)`p~?&2Sc-X)t<^VDT(6@#eX z(WPn9+1uqxE#pFcrhZ`GEPmMXcb_WN$Kua|#~vpAU6?#Rn*6o*-#4E=UR^|sMKp_( z)A4??nDtYt3;bB(3l6f^*Ef7&=nS-%xfODc2(v9 z9{@CPEj)FJvGLre2f*~GOqWxn%eg`J6TNDs%<~iF#d7645=CWs3~fc0{O`FTcdC_> z&tFbITs5iGm=92i8y#}P1CT%MQ;ql(f| zqq_!HaK7nvPaQp6O_LdpAQ%$g-6>!{RT=r4gFRI1eqO5hz(u>{za+OLtl&k1ZrIht z6cm|YFkxZnGej0)V}ij%6p^e5BHV^+;&CCaqxMk8E%60C#y!MD@0p3;e+!hBB8W-g z(<>4(J9=?QH3FD~o)s%3^c$y&MluG0zEy+Q^?6~P5;spmQ}|Vx{w=0OWq5H^x3$H> z7ntHW(U9Vhu`$JMPlHMVN2BV}2?+vv-9ofmPAgBgcby#(##PgOHpZb{Pj9-pjbz%~ z=0?<=NVfebQ+lNP($qK#fA9)Xoc#1CPP1I+9^U&#^fW334+r#BJj?GhTyX}9#G~4q z?;I`VD77u+uB}|38kKUqn(VB+{UXrT?zXkt%DLsZzq{`4RlTiUwzUi2QqQ>Ud~tKF z7{h(YG=V4@6D~K;**!Ge>9?4&b;~v^TIQ8)_&XJBNCgw@ zw`)Z;x%gJ4KS&z2f5PoqdcMgQsOwot1u279Gf_QPCROWV6l@~Ogx@2gJSIwm%S9Kd z`k}vT+C-U!JggRS*;v>+*{dh>VJ)QrAJjvxKdo*9OMhV9x>E^-KjW4|oK>n=FsO=g zOI4r2%&&KG8@rS%o0Dq{*)WEItVt@U^)8u?FY_qPUz6f`L0%o>rQ|JpjdvSM=8!#07LcVSyO8}tzKiFZ zRK1->YkjxZI|XHq(9?Js=Pk9}`8RDNTQgt_ZkC0zH8M@BC@yA|?7Y^WHSHdzdm3x> zF1#@ZKCvQ=e{55`%IoPJL(KqY6qmYkBDR&bWHfFRQ;n*N70s5#V@Ok|7g^Ac11PDB>nSH zrxY#7~QBha6C8(+u+XJA0Q~$J7o)2?%mdq6Wl&NiDIbW;Qp7D@~`pEnj!7K*x zlL49&0yj37&v*hMe>XQ>3NKS>dSxInH#Z6|S0Gz4ATuB_T?#K!Z*O!UF*h_IFd$M2 zFG+4@Zy+%@H6Sn`QVK6gL?Bx{H!w3cI7CE7G(j{pH8D9hGB7kXMldoqLq<3 zJ|H|dFf%qdL_|h3K{PZqF*!CeFf=trFfuknMmRD-HAXo;4P6Q^Ol59obZ8(nHa3$m z1u1_e(m79+K^VpH=L}p#0RflG6)uY6hN6flqPXunxZsL{+V~kvj32oN=a-jC@k^)ADds!JTrIh^Uh2}#9WF)|>!;1JVV@JX(MZpHnd#V!x}y>2zEfz8mPcsS;X4X_FNp-(Y2>WP0X zupPE4o{YOT0DE9i@$9K~-xR9EOu{RPpNn zmmh-@is`=|o`F+}*Y7+$4VU1o;>~Z@#^551z$lzkyuVu<#D}t%oQDf=6)r2jHhAI+ zJ-2}$%{90V<8T9RGV5nH0h0{<%x+V`ZMdWO^@;s*DE;^xQVe=1sXFVFq@fw78tJjW zE!Qe_wm6lPChj@aDNX-z;(2EtNalfL?l*S>x0<=t%xh}5T-%y=ALm0f#RjYrD+1MvT?G^ zX$Kn8Xw?QaI_Bze*fsZYO??Zsa2b4G#SxRqIQh`A7{)-6koN=5hH`nv87jr`TCAR% zBHE0JEyBORVvj|F<_Iea8Xnrt9m>g)kAPXEw1V(mV&JL5gvpSNL2lLnbQp;usCnIe zkz-0dT>$^1*KVr-+Rn+XaB{*ruD2m2f#E)=A}41*msSQ`N^LZ~)MdMi-sRU-lZsaA z+xFyrDE;fQ&JBR{>)zCOCVSNtjoqsJwXU6307}SGZq+X&Xz+U1q&*Um5iQTG7PsrJ z52M`O6Y-5BvwHqs^$530sHHq$rnAgX{o32dgN=G(X1>9PiP&`myU}Gv!K3Ne?8L~b z&w12cv()m9p>r&}Ko`cZ2MQfA5)7mH9evZ(Y#lD%+6Ta9bp`&8Bfpy{qV=g){RHFU z2&)YS)=P}$db4bf?ZEK_W8K8&y~HA6P5uSNW45B%W&bvFRkk_=IMw-Mjr&TlJt8}q zNIbNFHrO~HYt~lDYi9PZTrp$2o1XN%r`aN3s!x^8t>)=MkKZ`j=b-9$4~`+`>Yd} z+_64$IWt?o%>R0Tkx$KQ@hPO8P?d8_wU@r?w7KS%0^iDytz1v+_gIXgFFVXKmfa{u z*1K!EsDxd$BcBbG!hEBZ&2F;tTc5nB9L?{Ep+l~Z#3FVBvt_CJP6qwS=;j)mL!6oI zyG1}9WurGU65c3O9oQL_z-WgJ6G|}seCIk_=}c3sA~R)5ELpcESo|?_!7@`oyv6Z; zAJ*;sT&btWZdQud_p4ZL*^A2}JnP4{?GcgGCnvn9FGV^PbXIM7P|0h}59;9q>@xR? z+OSEIlHCm#Gz=!lV%g;O4jql23kpqd4k!RY30=<}1#eH$HXZ2j9tw~yl&=DI~z__uT{g`pwT}9U3v(c{k#>v_1)8oG-eopiT); zUWVI6eC%e7`!Uf}pjjn7{ZVFos1v*qHy+UXX@q%{lb}r-9}?PTq(v>u&oD;&4v*h@ zXes_WZQ|pYZFCo5*M_!k%Awxd%x4X=5THX800l5>w(F3qr`GfKdui1bYuD^+zc(kg_UuKec8bvojqq zxjHR!^qM@U@y{o)S;~cZ`q4D|YRov3S6pCo4n&4PLM7kTI39AcrNKMWQB8NvYpO7d zG}|o`I^bXgdSA4+ALm$(_5f|7E1f1QLCM6)+CbJToo2x=Z?^s@P}7@(M-+;+K7t*m z9HtROqNJq!zx&Rq4z!LjPe~FVYLY=bXp)m6yT={53F~;qCm)Pb_~^{zd(#is*}QNW zW%5TCk1cz!wyVX>J;)Q6J{J!id9;Pl5XcEZG>KuAf;1SQLA_8a=K-Zkp+j^_>Upui z7M^s4!pW8ahRCY2)GS(J6kx@cM)Yp)JS;^tB=934I^bwLPgiP?DYCgMM|BmTIPJ;m zH*g^xXV=v%e!w}CQ@9kv4G1X-{`ET%Q8v2Kg#$Mz~Cbw9ZhuJv{S8Faf9%q z8th*5IqXsnrSVg%CxA+J`Yd$)dCRmAcDjV4T?`_n# zL?Gsr^D!8v0ngm}Z-Q-gno(J}9GJ+lvI*p8RV9Qbw@&~#z@;W(^cBuh zol5-D{^oRhQWffHS&DGO5}TcZ=9Oyq&V(RH8e!pwg`;dgen83b3>j^fF2oY9uIKi7 zClOoX0|r!_w+Ujd=2byuvzw;6xTvz~=cb!7Ee}s3NcL{y)%_`WZf1(0?$R34LLyB9 zf}HtF(hNC{yw9J06|~az&#!lvcYf}C}LLR`NAo4U$)8NFl45H_|U?zL~9Wa|RO@Co9ti4lmhFhWkT16O=#>8*3b;qdCtMhb^fX7NdFyp1=d2Q3dXt|}o zStT1qe2y*|{bO`4_^`i@JPhsb4N7#6ed?YeNgCy(lIx+0fZ3B7@raULq2+)%8vCK+ zL4diEmEllvwopn#JV;g}kS;O}8D*@>8l9E`1D`1oKL<;?6YTrG(>nYsQA zEj2)6+4t z_-Me4%h!R66)&j(o#bqb#4a9M7z}o~uR^yl@91IcouyS_MmLPApBS1tYnOBa>!n>t zpXv`T3!6ca4R5kKUwbZKH!%1r49Z#j{0R`HfM?Bm#vO4sb=Dn#7l1cW?r~>DgOPF@xzuAxL?hjV>Kx05@A8brF0h-bW8P)A>iL(pP?r{&ym$m+P*ZF^3+~t z($Z++erY);FmN^f7qNYJ<=rS`o})_y4k2mJJqFi-%HsoQRdU$qC9c!KLUh$S7X#4T z;c}$RE{R-`&8zuzxJM@Ruq-ql|lPs3y0>fykJiK5b3+SVB?acfme^gia&PM@K%T;NQZ@=3O5l8gi z?v@eI$fg)YH(B(_btFY#yjqN}C;-5Yr5y<~tOysK$O|b%W8Jk==Xg`up={Sxa0Q+) zQ_E6@8IV@Ra%-hpkWb?zna!C$%>eKI({+GN4VY!^n9WnZ9JfocFX9>3G$%-{lBZDr zHEu(GA5d0_yRBxa&(ldUuq?TsBQv+r9<7Q9YiY$igyTj$Xg9XnVS_SACtA>OP zXE2hZy@EIT9sl?z*a}Ud#|$nPV`Vt-Vpw6>iYk|1;j8;8$S)ld7@-}q|NhS%E~j5l z-Ew~hk|Wc0?l%`}up4(_px#!XXytDdFL!*|Mh#)Ki;^)~*4QTN#+H=jBDotix@T>( zf!k<5os7GB$u5rX``c!^RV!1l{*?*6!O)3RJsxuI4Bhe2lTp-gR->PoWN|*j=q(XC zx3~Zd1WQI~g3)?)#N7L16c`WZN zJPFXGkWBD0_3y;5&GzWBa=(ju!0Vzsq&2wVBT?^Y7OQREy;5=ie8l|teg+=X`^5SY znr&VPL0i8}AN2tAL}0!n`g}d!Ps93uyr16>+DzBXU+3-_LKW@Lc!L=7wT5932Y%RW z0c4!Sg;I}sNLFbWaM8lb)=ryTFG{RE@Mz8|cL8|vgEKivJ-tPHm-Sd~CN)szw5rUIIl)Lvams}hF02nWSjE`5y!-4ddS0|=4TN0Vii$_AE-oUSn zpcH16RYEsIKrg}Z&mFtEX;txf8qjg?mT(m_>m&v%aK~e`Ice@O(_`htrU;#xX+tXU zgb>N?7e}q5I$vwG_y5q+7G#G;iQ158`bN$aZxn}QAot2xf%a4fTo8r8eICGw0JbeL zqP_wE)NjgTO7>@R0di~IG2oE|1AoEYW!@6p21YKSJKTPsOeQfJs;=vlXU4?w02#RW zs)6?IOC-#%t4ui(x=nSeUC$+5gL`)9>yTU`zmT`wCaN}v?G?YG)(T$uO|T}ojbq}7 zlaSL}(=-b=RF5x}agghP2xr}S0U-PqTa)PACs~NIQQG@z$vn_>St}NCc~Y0l(r761 zL@62iEWE1BE>N$O=*;y?q)1Bnyz;=z`;u*FQcKHF$WbK4mP^lRHFc?V&18VkBX?`) z`;=7+GdONhE9LDfm82)OD!L@pn%fiFDpiHxwc()2RZ`oc1;TI8NDL)p0a~h+bezrd z2`Uu(=&?%%k-B!MLYHXBq&DGBz=V30dNNxk$JzwE8EDcmkxl;zX^{MNNw3czVb zLhT01*PxXu+nRrtZO?BmYZ_fBW56thigBDTAorrZX8tQhEX3DBQkV38r`4{n`p!qI zMmioT&roEUwH0ayO$Hfq1uzJ@73~Q3lZIPX)n?yNXa;pz-)FInjc}CMvdD8Y6lB4a zKe$Wbtt8YM&S$v}FxVb25JLOJkE-fsRdx&)M65p0B)!&6`D#FABx3m{7)JL$O&I*UmLkzO6H9L=^>)pg5kNOE{g=JE;2)@+ zD&>41+FRO?pq@d;P=aBEFOEN91Xh%SLV##Dnt#9kaXl!NkaSUfdXgn%U)&ZkAVPb> zhhQmGTq0a&!@NiSxK)denSq~LLDbsB8x3tIvp$|Ry1ue3TG~L~kdUv~TpH-CdVY3i zQ?y?QwUkZ9ZIT%T9Lw=eddJBWS_Tcrx-*jd#+K4IhXTRVokym_9_{7SAWV?6-}ndi|K;Mlq^=vO-KtF0u_*dNQ67hbjSM zM-*>4fU+rB-g8sRqq-S5550J`O*@rg4QXGf zo-}Q%`r9D_fG2J|S=X*GHh{L{;hG!C#dt0VbB9)e-30HQ#LaRy_0i6TGnm(#m`m3q z{X%7_t~hbi(z;6_Co<77i*!04YPRd>uG|on*O^%?{u7(w&#ugyCrCUHO2?0~mw;Qq z^DSZHOtZB}#!vOCG-gkBp*#yA)|*s;KNx?`sQLH_C?Mgqv#1%DNxFek4Dsfc<~>w} z*O6cBehWCA?YcT-wn6oN@NOiK6F`9C_{tU+Sl9e9++{P&p^(R-cxA=hudh*?eGd45 zwpMjG>QsXhn`ArFf!297wAmU8wp72c_-xHCkQh390iJ~ad47=>)Acc)4vn_cynrRn zQ=T0H;I?q0M+v;S4|Lv3tz`bqmpZXs3+c~%S^q*cTBD#c5}HRIg)cwm5I^KF@iP5E z^SY|erb-}drTKHyvkmqOykl|S4YOs0Uj3rh(&38XkvW1M((<^F*A;#PRe0UJ0))|5 zv-dS9sRkEbY*YRAy5I=9rGV;7_q=7Jo^oIoP|bMdfd^ze^k?>M)|POH61{OuU2&UI z%yp38hkH{P5S?;Was|K^ZK1d#LatO9M430=>-m?>*5 z8TgF=9YxwkOH>DBqvX>`l< z)7_!@?f71BdI8M(|Aq&=|Ih;`%l`+S+5UxWK;pRlAQ4j7E#ENSq9~YqGF56qDNXm^ zIdQiSAS?*T-w+}9{SF3cRH@!TJ-_@ju+K^X=QWW+f9aV zq=(ZqojIYDY?0x1kzB7DyaU{GvuL`;Ylg4YTM>w0KxaNmSTVVVuYTB-Hd@_3{n&P3 z0ErF+v?Ic$iOhz&YBTBNIdW5zWeBr9^ z;k-)Yr3V_2{Ti9fn9|_8(H2J@6wcJ_A^H`(sc(~KLe|C!y2sxS)Q^P^#Ec1Jx zGv`{v$5U;&+2G@ICU4w?f}1rngpb1L0ZWMpi6R6^=oV`q2AU*3B9en+4C%ff9PYsu zEJ@^O8R?G+JTN3&%E;)nI85Ri2CNEmNi+F<6{faWU(rZ_K3liwTDy%z*Q@{Q$Hq5c zy>8dzRp2tGamD}3-=?N}mRML!xhYMk)(iHOLBM9GIb%#sxP+g}VO<52Kkc9Teov98 zlp0N_*Je7^FzN+#`Seh%SX=#hH}Y!!@Ifo~Fc18PPc>PBj*$Rl2WVpdR+YR1ce;%llM%pB1xCiXU}d3%;wpR$}zxoSS+9CH;F8)MH>C{}QNj-e>7DzBoXoJq5HDc@Y6b-Sn& zk@+z@<{bTen=F@WO(x3cs;il|_CnY+vR-f%?r^$s^|Vyb_4e&hlx_F=Rb>Y-pE#mi zh(2O>Ua-HND>*_VJVc)Zyqb^89E{&u*B?2u|EADM$?N8)@g0p@zXC6|Qj0(Jo_)^CIan_>7xlMK%a7J5H^Nm@N+a&d`*`Md zj`K?GkztViEz5FQLU}&!9pwsOC^ai9Pp(o)JdG{= zt=3vr_ZH`(5KJklZEb3z z!-PM?6cBW4@4dTOEaunrf6MiYR$aD0I{*Z}2~u@(i+1h&6#;XlCt3w$QX^qAuN{HG zW6VovI@#DlyPzH6Yp%Ey^`2t%)-nm2yHa7)cWC70+b4V7=;DH^7fE#!o%GU1y=Ut@ zRZ`oj25r;tKhHc|v#S)Y;T3AjlPMS3`?8uT_}lxQtg~9A9Qb!aGF%9Zq{<-rus)kM z+65e)jI^O*k*Vl`AOWuse=TtdKt zqsReU3zRE~?pc)wV>f3s&lXdrgv~E8X@#1JI^>8$5@u4J!En>KWsyrt zGrVYwz5)xNb(oS$jMK#}uccp1%Y#f_2$@jb-Y&Nnpxge!oL|rP5ds$*b{aw0m||YX zi<72^E$ZyP5sMpBQYE72HFS{LWO*vh5tChEvhYn~GYUFBjFQr6hKxD~a?B&&vcPrgECwZnffbl{ZgszFcp%*!>7J z*OdiAe0%D%S8skNU0hzO`c13iSlhT?Rs6P_+p({%ve{}ctaXaJ+}l{)^|^g+hSbBR zycBG6J`R3QHojTN$||KR47jrg5A9*WSZF@~lslw{j4EVjBQlR}HxBibuw7NKKGhY~ z<*o(X*J>`XLO_U|3W5*ODfeG5w{9G^b?^0V{x~Cdjd0IXWewTa2I@SMt$Gac0!&I~ zJWvl8|6&U#^|Fd30^Fv4(tA~ry_O_=Z{~ECMC6SHZBlLZ2hsxE6IK=%ZMhkE{ywHp zw|u$A&N$BUTnI%g6h%0%%RB`xopn$Zit+&@105qk8Y6q#7oSDn>AK~Al6R!vyi<36 zYo4i-VEP>6wda=tIoP=KhzI|c&nc(jiBe36=6sg+hRcfi`kZtBFjPaU>7sj8}#5wHV-G@|WSG z6|nwANZYH{sd!kA zvC3C6Z7h-cL^0`{+@C`c@w_%BC0Yacy=29(AbIbZ*RMNW9f?64PjK40{DgyFV*B@Z zo(0S!`|)I*mua$pAopr?&Bp3dq_iuq`bGDZjkD6(>{Y}%nVV&hL|cr;H2?DIMeeT) z?{YeRpP?URy|DFV8CLBYT0J{ZP*#~YhstVo9-aL-%jNA%%x{&$&@1F&RvA4&4JV~y z2m9qwl(cQO-b5X7?6hq@AN3Z7c9VL?TbB0xMOJHH^Y~f{w|_D-z?UObQK;rB^pjhB z=5|EkGYUd7#N}`6?ycqTXT%b@It`b z9gQ+o;eJzqqWyP&DW*uplP7&(zIS%Z3a_Im@mU|B$nRT#?E%_C{b9fdyV&_kGBHBZ_7i~&Y8|Jpm&P)_s> z^tg??5r|e_(ZXw~PFqy~mvfsgfz@bY^ZR~&$ML@NEf9jwbAE@D)V`Y_0?lW(NYy|u zP1ng_6|?8DS*!1Gc)HHjgBhpx)nDk~Z)qe*H2>;921fb#(=d$Jv5Aace>fq0e4!lE z0|*&uu6E24JJH>L%{8$~bG-d&oKN6Qp0nHwrTUcG_v%#_sM~7=9E9_oh5Pfhl1d18 z;JObP`XIq?ZkPoRw7fgF*WhoiTs#XpPQE)Y`8*T0)vFs#o+LU)51b^f4Y6@oOgi$Ozgbp3G3w^j>_mnddW+yN! zRWa%bQZ&jNAcb)mEhdQwr>D~Nl-d^#ZCIfCg&}5zMj$1Xgy_j6x$m$4_AQb!WYWTP zbR{cCkj2P45xt#fS{^c<6Id?t+7>nH|sC= zVv;nlt=-ba8!_O%r4Cm&AV|IC6|T2)-iMEBa*XdTmt&ZU+6`KtVL0p=3KHt{hQQ4b z@mU`>6%!{hQ(>8DGF)L9GZmLY3U4ZD90EBQ-hS*z z7`APnKDgBe*pAx_>o~UaFsi^6-I{lnqT8AuQyEhmixB5|lxrP49^4~Z$Pmdw{H?*Y z9;^_WLX-rXI3$xKQiK@1rW%Zf;;AHpa)6Ep;{@Y=W2pIuSyP8N#(L--so1cYOsXm< z)JF#esRqf6NQF44Q=BRTpXsf@rFaG#39&`wp4wJQf*yAOh&qB}U#C|c?njd9=@sHm zQ}zM?8~_Dy`@dV&f0rt*|6QtB{u%#yM%31e-)uwod##%jh4oB|I63B21sk^Sgx+Al zuw)e{G%pYJ7-2OrwY3Tcm9HP*LD%-uEBFirCrK{q>HT^~-s$~_+9ChWlmXfez>7rr?<3+BoLP7jw| znFTxfer%fhGf(q^;PZ}yGLR}+l(D@!+kVV=dSlJglGRz-+N8q(-%48Y)04B4%cfyz zRrg!ukR-o?|KY+9)j#g_~vrurLlRAqYJ zFWGYrciV4!r@;MS5c!EuXD6%x6QIz`D{GFnwxe}+{}4=y?nwa*J&VFlFogVV3kOJm zV)C4$voI%PET4j#UM*1k;lU5RFEFW-`6^+U0ROq`cQg2pb zGSd^4em5B!@w(KddvfNBtcBCl@~#V^v&n)lwkikxB^G&;;e0YL)+*&V)%KEwZ5A)* zT8?$vk5wUE#JHF%1OQPcO^g!LT)|{Ml5sOvfySJ5G31S_AlJ3P!k!-^yA;M1#QYQZ%&6h}60 z(07X#hSs1x=@wLuVSkvd5MXASqPcG}7NUa36KN5LKhj{Q0xWhiKrT&r>Mw#G7ziOv zEy4srZGT0A35U6+cfyF6obRe5OQFlIS*=ASxYYK9kT@Dk7Bhec2J@F@-B3XpfvJ!- zOoi4afT@9O?$bbOQkBII!4i%M94l8mikT2>w=9Y{!r2L`Gll;SlBzUp`3=IuzexIK zTkOp>NzPtc2v`b2T5?1+*52y7G-Jq5#W($BUa=uxCzi3BAVvjxGhu>0&{rBnA4}<0 zCsI(2cH`M z|r@5uixCU9ImgGVTq7K9?&xQx?Z* zM`KHXujTU+O%TY4kUlxieFGD^b5T@c$s=B(U!+ zKQxYO1_B;NsFZ??%@z)-g67hEQ-@t2G@NU`)XUn0BWb<4QC_b2EV0tqlc`!dvZqjm zO?~F=A$e_UQg@lx)O5%;<`ITD%$oIQJAn>?Z)nXcWxQA5VnathL z>}XX(PE8r@>Yqr4T|#Cutxtx!xJJaD)h;$~BLMHSfb-Q;61g7S^M)j9*Or!&Pb+2v zg*r+^Pr0`Qp!<`rLG1SZgYu7YI*u5J(M7MW?#SNhi}=1{*PbZBk{8!6f1do9lbdK_EsNgh#(@MP!H)AWJSBJD8^ zSn}ds{$z8$r`OkYKCa@#zNxQUs~<`5cDkN5Q0l(asrhLf--t1h2&W|^dmOK}3}7aR zu9kP(9X4DwRZHMjOq>c~lHj(()>0ykL);5BmRs&z&ga)}*lq1SPD9#_X(Qg4>3Jh| zVuN@SyT>Jw6E3@2Ui|qIH!c@5-u_U@6hAyY>QD8$8**u;nJVcku&`#t$1}OZzNU0P zGi-A2G0m4Z@3z%y!p`3wEGNw(YXJGK=3dkXds!+)Lg{-ml5=<2eNdP-`t_ng4iCcm zS~S_0lSxgAm0GX0MegZ1g$$;p#(o_OIKNzK(awrlR58^nf@#KFj@nzcdK#xJX_FQT z`CHu|K?j6dhZqLqHIY#cXb~ zY>aj^+_Wf(Crdm`gvF5G*2fpkJgo%j?Mgg9aFtsLdupjt^Kv zqQ-CPJnhu|w{ZU)mW%8@YZy3&0cUhhM_=8=A)8kg3(Cuk7f+;Y+V2iFLpL}OTZER=L)Xu~w*h67SLuBgZ&-anQS zXc*B8PS6>i$QweDoU&JYy8OCLBS_^7OQk!DcW3(a9mAWeD%K9?I|sZ)@o}&CX?9TT zfV_2?+Wjcbsjj?tC1npU;U^-vgs1KQW*sipf4vM)HqQS@QrlYcE*t*{7mu{AAte}9 zsirzcZLVeGOH@_PfiU(wnzq+B045zu9Wt3PAbWmRpmR z*DLv}FTnH~BF;52>ABaw&m_(vrxlgi>#%8HL>MYizoLXw!S9BDvvHZ#D!CY4C}jG5 zoy>?VZ9$O*hXq@80}qs-5G`laCc_lAY{PmGrmZ%_0$^`#Lst^qJ=(!WB}VNN?RNE4 z4u7YByz8y-mIqw)wX@cp#hR*$ZEn20=CUw#q0em^p^~GAtwJT>@UZEQKapB-(LfD4 zWS8k-cGk7{shq9?&4p&vbx^O>=7RlUqVl_fy@zFk z14J(l0Ma30h)>oNZBG~Lo%iIz$F7L%dIZ6I>Nm(et3`bjP`Iba9slI>%MUmx67KNh zjneL?p9T|N5)isCZG*37ZIt@7M|2Gg%O7pt>pIyKDVJxupme^*4R}!Zi^ojyvCdMi z1wY<&d(I=6fDPH&*suHL?Fd^#%;6d#btgi30OT&2I5K!MAA+h!oHcg!VwZ!TM0cbF zO51rMdITd&VewqJfKL@m97qgo^aHWZHB zSdSj;xZh!80w6g5KS!1Ge`7f(8*}p9Kccece>|ZNTGtev=zW?jYG0}OAt`t?aiaoA zN=WuZRNxj75I3coI+&@tLk)I{|nmx8sBQt%2Kr+jraA_LoSpsH-DZ z3B998`%@|FMKT5_iaGC?2i~n9(83q|*+CDoTanf%;h4YrD9yLRJqit5+J&?Mx-HKO zem}Gs2twl7>yW+LZy(}`R7SG&&{`^5wovf?Ql6^#g}L8n99;n_CQL|Zp&7phTdi1; z#NLDTvOx0}wm)9e?RP1bak1un7tZH->F&%X?MZ7>qtYdQ*J?2-4?X|~`LbA{Vo6g} zw(C472+V6B)c13)bAjy@AEq( zM^zL|TaA~K`ub*z$p+Yos@Vp}%-xA-Cxu-$RN&xrxUhOwQ>^RQ(g;Zv0ETvHWx&(} z5*Q24o5acRwlD4+-#dKHQF3iVJp=kO3;NpD-p3uNDy3@h`*^R&UzeBZo`&P?=cIu@7xNS37ZzufTrs^WfFdHsv9dqs9Zu*cGo+7PeKyG5H~k$H`FxlC3lQ zNBJp9x|)kVokkUOTajK3rJAL_+V&+$*U~ga&J3V+7sF*%fh-wpHsgdQBKJ!REbZ1# zt32?Pc*4`Nb<)eXI!oSjqsged>UOiuZ5uX1=;kI((ai;QM?iDaO{`68rPWQ6WTkc35-uT}LGo3U+^ z$bu!wDYtH1s>W5sQAiq*vL;fxR(v6YED5`6$Ck21%<8uJc!>m4@Rwg+gZB~jq}##o zQG#~ywk}f9%Y-}-7v>sb%9xw6fM36QM6v+X#P{cl!`#;h$doPu;+jO=O>j@L4B{G6 zMU$Blsc4H)lIRxP=x6dmgS#0`VX0cQgGz0>mCD0tZETbVnT`Z74IgsyYi=u8(?B(z zdMF4NT;f9gGE+FV1``D?5d3@Z?EHQ03!sU$7HD3lPA4(sOGXS=GlM4OvuzXDmWMEbOo10Nu8IK?V0ToR- z#C;4&r%C4557D;eHD$*PcNa8wAGDXlPYKkUR-O+o3%zc{^}nu$J?+JxFE(_7Ql&Fm z0+w9$sBWaU;_ADMpZKBp1h7u;OS4snFRuFdAp5jqP7TGogUwx+z=PC3h1vjiu9*BV zsOifO@9Wdso9lP#>K}RyJA_{oA2r$x_c|m`1?oPVPKK9HM_!Mh*R`7TmlQVvktmzT zFC4~!OviJDeSC2ywp=l-)+>PpowXh3Fn1)VY4|&)%+@XQ^!UZc>*=O*0jgEa z9_^V9xc60uzaZWke1lK^pLPtBknr`0$X5*>5khWlS2uWU{$#4y z2CR;M15jYBQTi*mm5U8h7LXq-JU_+40mz6mJccp#K9sKg_>Ca^jO2)_6f^eJlLn2+ zKft&Q!?nr8`Dp(o68=AmEf)*he~_wwjyg>Czys2Mg^nytK8!aPG@#gB8G^ZzE?4 z1(c7P!Mnq05tFe&*z0?HP_TuIS&;179OF!+RWiPG;+bSPTzaY+SL#R;R~x1Pgn`lW zY2lUS5D;hhJq~2+qQZ6-G{DR}ivh)R1tP3N3;{rNvYJ7`ujRdgwdw0}TFLD(qpDX+mT;_^gqgu zvILTY-%2w7A68GU5H8z4Eox@ka1Mv=a_GS$-r$h!o0Ys zkC;0b>Aoz}j3OHbp5L~P@Rx_j7DR}d_rSxrOtVYdZr~ss6zKtlXZFGBk zO`4z6>{|WfRsxK#&6#yx@z}RSJn4+r6O)!q)GYzk>JRoHVS^9##G94y{mB^=o#`9z z)V4KnKgSUGIaDe?&JOl*11Vs~J1%lHY9e!Q*VcJ*Uk=LVOU#Ymk8WwBvS*TumU%$7 z1($y$5Q;OH5dtjEMFE1QC!j~H^a)I{3zk+yCa{%gQ5t@g%5Z^~Y|;mpd_92~MpXJ1 z_tyF+r_@adG_+zJYlD3G?WGeP6lGW^6H>Hfel@1Fwg{O1BZdsk>nPQ~JBgd@oIqfw zyR}ymPznTiwGcKcY2eG`L z!dWbrdMw-tlZF`Z2R6yzskP?E`uy@$gZ!s$pJ}gtwNJo3WM1kb4J26t2XC@vpFXlV zohVT1j2kW>4&$S8p;da#N{Ht{ahPMkOc(jQaxe}iyVgq)#z+#AYL|IP=fN9_=}qcR z>e+BMWzZXb`tWH7)#N3q7_2>`#`>G%5{&V3f3IcyR>ISp)=Zzjf)ncnh# z5qkUa)5zEPTOkvKs(wj?xrZ@>MGRZr(w9;g{jl@E`)Si)a(&QMoxxtSYW(8K{Bsgv z>5Z4(1dxN$L=NMr45I*MiP+?5Lz|kVB~L58G^zv_0n7-dPc@7R7P~Pa*A4d#E7Z2I zHEwAfB5Xqw$;pj|CZQ*6oX0GIf;50#T#aeWEe;~j(8AKID*d`nx4I!<(JY-ZWvN=v zA>I@qhF|K#LAl4|$F6DN(VEu3Exbb)T+y^#25=82MDwE|&5qm6p`d~2*a8}sU==wZ zxwz_)*$Z;KesUrS*W+-6uK*jkj zKXzZ)y{?o$RQ_FRI&#Auo@Qyu8!m%dIL&;T06;&T6PhE#!RNptc7HO1MyAHQ!F#B? z2jKY!pWha^c#6IFoF{9QALK>VxuY!aB(FuI{}7G{TL$t_!L0Rxp7&<)6GfF24__}j zzpMj#0J;o25Tsf$GSH5CDKS!mq%g%42@{ty~v?04`{%i9At-ixRc0Le{!g*hWd^(1uW;*%v2c zq;s908`6WKt7{)Y(4btjJ~hi(KB7WdT8HmbJURtwosGgLQB0+qEH}vW$6rN0LW+k) zyoQeQsuvLH+6yYJb>-IY3uDG$$m1Q^gb^p3hZEq7Z&DXxZh#B+-4nS&UEg#!z<>-R zlq-Xjy3~bCu3gt6tcV2zRBk(w>GKRqTtv>kUs?Y3%)AWP76!!%xpHBCJ(Cf%WLR#72DCob zcb7?(fc9S(Ywp^8DQTg5EK*H4z`QpRPo9!*G#Xu+eaemC_XWiT$@~=!V-c7B0v@(h z@I!umLt264D!defXUp41cI&uWZ(FU!h9&F{S43k7=8x# zEm)sBuvlyEmHkki`2u(ByWsN0Q7j^^B9sZ$zB_CC-x;5yuQw9qdQ@8vKt63((gA}t za9uO>Oyqi+xDn!`)g#70(UWIGUf@2z8#h4PxXC`0kJe)5sWP+Ctu(uF} z?szI9n&}mX#mXnXdw&0D;cqH%d$LaVGEG+&&sONDuOajD3~qkyUHYy(kGrd>a*P<& zh(Ow5NL_XCMT7w!3X#_lCn(V@3K=lVTd5XCsfVzAEQlFZ8%%x>gh67jGSZUd{)TGj z)&(c|*y#=>Pu|$FL*!|}9RiKNr5`T9V`Rpx)+!MviMs9<$W2mh0S%Fi_YA0ka~JJ4 z(P8~6BVyG_=*8>sCex&z@9J$%Txl!Dtc3-&K8+|kPojp|)TQ$H@~d4z;N->#>E{uzHyAJC>OA8wsr zp4gyOZ#RMZzYg=q0i)%kW}ckTQm?{K#C`IO*Tmk~IKYG6x%Y#; z1uD}onO~>O8lYfA8>vBQ=y}N90~EMGm<&{2 zsx*O0Toq3TW(R-eR==mpIipi%?9hp5=2t5du zKm}Q6MKOk16nmJyS4l-Fo3_LBEo>+}AWC51uj;@+NjTeF?Z+81&b+ZjE*30|ZW2;4 zF}>a$lF52t{Z*fqYvyTm07M{}fFc#B71dAIjD~1Lw=Lkz1>5`FxDX>yQ{zJDR(|qW z{+FqEa|@e1g!$N_vAI8K_Aj~ylDgXIjxH88kMP#@CK^q>hbX%TB-b8o%{XZYQ=!#V z6Zw>8h5jbpPZkg-Bd`PGL~E2N67b_ybm(?;AV)qaJ00M1;q8w8nBA24iW$lbZrE7DLF}mD_ECDq^>I1s) zR?{8(kF_2v03u7mX4R2t2!xwHg%NSj)Q>f5@yNy)jrNFJG-q5t{32vn2=xx8eqH2Y znhHqvew%M8bx)E~01Ns@X?_EL)C+iGXky=1QKL4E&o>}gciF_CUM#-=)r{)uE^co+ zs2;B1DPRu`i)#6vBhluSV0KvtTnt|GYTOQynNM5jN7uK-IP z65HYaGV5s--11kI27P->cgMn8{lZ)L0RVSV77lRjSWt~`2J$PTHyk4uFo%@*p3205 z7)iI8y8srWPMgZCVwwQ&1IQgWVJ50V1r!GWvb zJ`FIqXz#zCxi2>KmPk-%%fJDzS3tT;hS0DEHjwRq*uke)OpO}ozhjxJvJ|I-Q~=f< zaaGP6I+?f*wEp(RcRJei3(_^tza{XSx2l(=$~3&gkdeF^<;0B|#$EW|D;l%aGwT+P zJIqoxJ@LPmPahXYz|R(0oFEuhZ@O)Cx4teuDlj=s@F9dO%&8RxHF>(xoZAEM)xB%3 zZjayoZUb0He2zVQX#7oBWxT~>69L~rq&HMM;4PF5^5@Ptfh)egNI8;_|A&op3=TBt z)@_W5ZQHgdwv&l%Cllk1Z9AFR#>BSGiEU$|Gv7IN>ejt=|MkD_+FjMv{q$a|Z>+7Q z*6esJcg3tYmz&RCmW4KxWkVzvTz46A!=3$__}#m`r)vHh5fQNTbhHQ)qFhxV zJQga*&=&nNs#z!i$XckDs*ntGapgOD+t0vLp^6(zo-y{W-k-L!{doRQvB_M8jnH|6rN_?zl76bb#8NeLwNP z2czaqOXiPG;e@@0G;zDlEZOaB7T!u0E1N~ewNF1`rxv*wb46La{50?BHlA5H%NUR$ z!uQFuKK#o^i)NpguH(UTc+p50L)gT8(+~)8F!E3(Uxv9sB8+N(v|UB*g@Z$|7#XsQ zzn@JO&y~)zgYlS(>gZv-&j7cjBbzY?{_dG<4>1B z@)0?e!Sr4T2(Ov0oG>$(95hieyjJU#wjWSQdt4m<**q|o|Aq>| zShv=g0rx2{i6z{aadS*{srm(4_C;}&dL5iTw#iid>loaQ|C%;+5Ux5 z?u)wVt#vOmu`u+Si_WRxL}OqG4$gW?eh(8R8|mn?oBM3caDJAw`5m3Kx#{BjWq9ew z`^)h?*B8OG(AQ7hU8h#Rqh!Jr4!_nX7>Yb1)yg>MJRv_pfVr?+zeJdNrl$+r|2fv<;@mW4k=0>$^|T6vHL(}`Er?StNxZ?*T& zC!Wzy+kylv0#{nuz~Gaml_h^@h@wH<_WKQs55D?wDN!sEi_h~ZlO%kcny%4j$^;pF z%u|`_{=kTF_2R`HUgn^qc8E;`Ic{;2D)qmzVJdeI2A*Z538ZbrSV5+ zlUoAd)4F!r$36$Q&)(i2CaJ=}224&=D>4*$(DwwOel**LLDaNWly{w3{SwH-Pd@di z)W%%DpTh|>)tqBxj#6vwzb*PV<;tpfVR73o`?VPaov4ZPaZnN&4#~;P@ z6*p^js>}1&#o@|yJc2B*HJ{kxKOpC30nk84e;my(Sb}#C2UiE@je6BbUwdy&_w@(F z(wGb?IGgxqmsaa$sEXscm|MTa1}$M6Of@>Vieu!0ocN%1k<49b8zF9zxKgWg)WdQQ z+ogF8@E<2r4`tUB*Qp%NS{f>BLdMs!OHs3C1aImLST_8<9h{Lh)x6e~n0ni30<}Op zLnn-$nly&%;vh+_H%cb&{;kH44*nux-|e{oVdn6ti8EEqwc|W)YeeBep#{S66fbqE zpg|3Irv6WPHR&YR#Rr26v?1{Js^kW^B7qXT%H*ztiZY&}ahV~PI84nRYSwho9Q`Dk zRieE+eDP$4aHT)rzUz~Q8y+%1ed_?+JeCk=*7v8Hu-)|zG!{h%$6b>Y`{t+P`0*A? zSsh5|W+l}h?Wp8$mFF||`MVr`&Y!M$R>@}467_rQ1LEuGO`qroRXnuD-V0*RKr*NC z*2u@Qq0fb|jfn@$_BLnCMvjfVXkZ`~9+-TPS!V^Ng(p1~8nPWHbpi^kB?ZuC(Hm~} z7j^6#`NTKKrbGh^7y5*%gEUxaVYI{kgF<CNg*Jc+TSpExa^%~pHCAgcJJyhx_lHyOG~up`@9TdT#md>m zKV|XFtyDb849ra1Qb;H9sfm1K*%HT!$%eHc!oorawT)i|O3Mro_j^9y4sF!M`bSfD=pQ+^I0M45o$ zYspaRUGg`af-qwg&rxXQ;}`3Q`MXzvIxFMt{Pf;bsiB>@VSe<<`_hf{`9nU{3&8b- ztyO3yzaUJUDql6%YBR{TmQGE18!9LNl@c!HV0K0v9|L1K>?BqK7w(o<6N6*kWe-U) zA+_G}J)>d@=5q&!jV{1Zw^ANmS1k^y|1w){ehBHH&o&LZ#$dp0v*Wg6>-V z8t3Wf^9=V*#hdB{K5>T(Xe{rX#J9AJI0ln-n#rI2ERv@`Xv9}yn)@np&%KQ3X^gk_ zCGNC}LEf z#bxrh8CWslBI5LN?a?7O&&7>zfqYhK!j*<(4dw>#KccZ;_6jiReatDBb?rhS#%?WX zb3gkMG2I)vkA|P~EEqX(&4?2jW9{h|HY1z>gGq9k_E`t#Qts|a-A zH{njIucM4Tspgr>rTm6HrC1|^s=@VxlXL0@A=n8AhO=m=dFAa68Eo%ePSurN*33ZOMTukjD_e2H%&~ zi-eU8pJQ(LH?8f2_1^D-TAjo5l)}8g+Y%*;DIPt7G`ZOB6D$Gh{qc2(p>L}h+z!>} zsa<xE$5-y*nTSA?n$~KBD?d9%7c>xJ^|XK)17~2 zuWAprJD4L4mn5jy7MH;5qfVyRjYZ)N7)PJu?z{(`1-XiBiirC|VAKdOu2DE5MAf4; zQ5>P4q)fnoze_&DYZH{%lTh5tfpQ+hs=?THsgjN|J;pRzKo;ZPexe~ISRClj;BBjg zI^zF9w@wJWGi)FPr~0VFF}a~l3O4=ad2xrhFDEKq6CGT#G~1Xi7)Sv37EW7BaT(!A z=&Q02grKa~G9`$=*q;KpmTC9T;d0V1pn3O6*dv%!mP;&pj@T?6>2&1n&jvMFY-a8^ z?^&3;8F6lPms65I#wXSvFT%#uN$L(KhBTut05 zIlf+58tVdX15V~aWtskAS|yHab{iL-agj`mW)NK&CnGW;rWT0baYm=&Y#kn#YoKMlh>XfHeY@poC8n`#hk z+{7^jzS&(%4^L!<;=0o0p!{;t;x2&|!5c;tjkCzTfE0QnCr|+%jk7^FF&RQo?_3-u zs{ty189h}fwKJ|`siMVWDl0TTP};{RWU$#$1&rqRr$){}D?$qD87CNmjLabB{KD14 zyrjmGuNn>!CeoK+P#N$pf#n`wchqJRj(P5fkpp$9MGB-r zBOwRPjBMS~>ZM7#kPA%t$U*oSu~C^&`I`(yXSnFG1x$X;{k!bmSW`YRa@n}pp!gE2 zRljBKL)$M_9^KnLbHBtg^{roJ4EjgSW( z8>`sIfH%}{@Foci>QMF;fH`IaBh%lh_5v<_)jx*(dA1@kH03B~l=zG!zH2m&(SWwM zaNc}Xk9Eq(gZvEaD1=0a=GpS*$Z%Kcf;4mttLgI`c6fv{FJ}B5esSP28Sdn`v8cmb zc4i|5)_LR!Z36)xK2mpf0qQ4SEQ}8f$y9M*b<^gFznDqeHr*=M@N?a!Nn;0wX#v{) zbW~sPNxvz|@+{!ZQ4RgW?ZXw=?$4LDBSZT4#%E2h_yq8|Z4rpLCn4?`1t10~Uy-5% zH20-hku=rq!LUckT{NI~SCLtI{4;=Zf=G?PA6?26)|fXUQ!vp0_O$3%0p4|@+Gl(dX=bps)%YxUI6Uc1=5AI z1wG4d5Yt!@MJHp7e~3{!n_k8(YGv>8_r3P}SxBb_ z=I4Ps(>S?ZCngWwop#izb|>a5GBL;gKjBBziV94t2SXfnpG^Y&Ibohe-};aZ3)CM= zhPccjYuFFlrqr*Q@FD9?QZmI1see{<4d{$`Dpg-Won5W$SqjV(X4x{y-0wjge9qoSu*2B((R3Oz+J zZa=51NPNkib;Mp9(&9*vUIY0t`V+-6;FR|L-DAHU#(K~dWr4f-5q>Coy`7W(X<`!d zHyx@@L8`F*oDr9sEHGMib&%4i^NnT9UJpMoNe6zkpSnbb^ol zl>@Tu(IqsB4Q-%VcnRNqi@PpEjNx08v{MAen`>wkZqaW}IS!mMNRK`zntpwJEEE#% z8jPSYlS-%&3Lw_jNtfKyFJ~W>=&+>`dq>>49xFjt49>VMxaG*&EGJdmIY0(&WXRJe z>42BGUh5#_PT2Xjgmk2MBOHH)0>&!bFH)5+#bhpzaR;$W}sU=Y3*dfT~!AxpWA&)p`EAUpzn8lPgJ(`>+sMO(wMywX)A99`h^m!G zB;Y-5j|6)CC7w;{et3;VSd>TqKhM8ZfO0QLo|*K!VIXk?F*Y(xB&c>wc(0); zwiGd`)B#JpGW*L^Rr?D}flbtjgwyx3i#CEqf*#k;HKC`C>kXiy#@j)_e(5!5r1p%H z8HBkXRrqE)TUF(=?_!DybdmvN{vjid|03jVuL0C{4n!_Fb(_!PYF6?Jx=xkAZR>3( zaK7pI>ThVS`yAidg%*X#2e_i@pDh`?0dv(Lvr2oMrH=AkR`2P7xUI+RQ#z2aw6g_5 z`YbK5I%lROqGI5$o{J12Ls}Y*OZk?9tHY~krpSzc+lSDa|0!g2-sTq7pw0>|{~PF~|D15{`wP-f*Db(S}PtoAAlqTJ=~yMPbR(t^Ml7Ax2O7SPvH%@8(3G>|Bls&g)f zlI^1@&2&ISx7%4<*BmOBX?@U&){Z{uPAL@!6{A3VG5lLgCW9f|nl&o{#2QbzjJAYV z<8_div^jAlQEqG*-GKBwbn$BCaj_XfW~a!!BKWB!7#u%lxCv$xNP!uAzBJYzJP{jn zBMN_{KBvwS(mk#`q-RWOAfL3}QSQGMgAEt$0YAW-)2gaafa=2C)P{DU{7yP&Tru$s z3|x*Ggi@Gf6Z+nW;-p|z_+$iXkC`*$k9GHwGc=vq{pxq!X?k%bQ^SaKtC^ov8%dWD zT4gX15%f+^7h{#~E(XsQtIIiUdci+#m1iB7lWORsR?3wKvBB(1>(}FzE?q-6Q{#@J(gTQ{iUE9h@iw0w_^?o6m(69NRgm<8O9}?mgg}_cI)4T zjbv4Re#$YXe7nY=qRidozXtK-l7EE{v9-!7$epbS(dC-`4KqWy3o@76h%_crhm`Q$op>a{X8?S`~Edn z|G2i&*Jq&R^$;V4=Htn$%i@WCy?nQd3{Rdkn{XBNglK^avrxc|F(}8yGx~3*Zx_XZ zHl3&x*b+5MVQE~XOg7Z4UVcF5JykNc$Qq%bPx_7S{q3}4ZQsiZ?HsNi&e)FE0zhLrQ2j#8Kf<|qG{<4GJt=xjoHm*78)#pH0 zYrycu^2vtd1l^FXi0ltnQlWY3=AHASz_mboo$or_FS9ENbIZa!qz=CHllYtv>K^0ms4N6XntP zWNkTgAg{BX5^1w$89sQAf@&DB7wI_L>#xp3-UG#eYTKP3U)!zQP&v~I7m*I%B^8<|9zJzhF4F82F@A$(3l1(Mxg z4`+JwsmJF?9JL^fHgDMBb{#iH`kBW}ZbkST{ zYkeo?l1ZK^RLcyff4oMM@LQa6VNRPRkSzySP$DX)r3@kGo%hH0zdHffgL;wsZSfP% z#k%hH^h8CnE2Vf)I1~BNDbi+F4L?NZbo-AKqQy2HTT>{!IVvU}g6v@yHsx#1woL3d zfUjE|wrx-0pOO3Y)o-dLHi`OP#;T3#?cRTX?Tdz85i*Cz7)l(Oaz(~zb6x%E5^t0( zd{L-S!ygPB0Ovf!S+xY3Pe2I1amS!+xmfcBD@Wzqbc85xFz~(`c?UC%f~J$U>BS0; zeH2ywirrN)dz?3$5Ou{{c2L95i<-k?3|BtxF&+^V9MK+V($|`?@W}qTO2i1^Om9AB zotcTOxK+ibATJe8WWqi~HELgGPG_pw>@EJYQP2K~V@;Zgt!zDes3~$P zw|1wyR3j)FyST7fS08%DTDoSkMnr|RKVLy#Y9DQ8wnBO+^?;eY#TKB9^Ms-Ch_{OO zOg2h(O14T~JAh=8O;Cv`F9DtYsoCx=tY+=5G#*P9Ad8TKD1Q@t3bDJufD6DMezgwlv7ewG4vAPdR*=wqO4;Dx{_!`eW zwS`F-X1Pn9dua(KIs_%9 zHZ*@nfuDi%-LI;u{*Ajk-G6`b;k9L*W z^PNiA*YV*$kA3rD&XZh$i2U(Ge6~1C@?zZOa_X0;>OxHI6rXco*A$}EMop^iAFncz zicZvZb>4ea`<1;Aeoh zK){W~#K7r2@kNOr^;7=_1&5ShoP^%0MmWolG8cF~Ej3skUn-U8*6_sj@>0<3=4@!w zk`Z#r}Bk)IMxpMoy{%@n1;`1WPeQp z_m%>e(OePJ9#e>xoLp8G{9%`zKYx#WoJC_vO~;f6%M{CK7T2<>;Z(|{9MQ_AG>>Z( zYpl@`{7RQ)aZ5a;YF6TYA5g9{{;0{pTfPL=o3Bt^!lTl4*zQ!Vce*?SnaUYElU)Qe~WU;f5Uv^Vt@GAz0 z@GQ3a=Z7+mhKK*u($!epTg+5lDvYo-Cm~&txB0CpCOr*EL?jH1TVE&ekr^s``XApL z>rXQ|6}zJqBd9rj2yEgl!K`CN75OZ!e4j}aaOOZ|vXmxjYwrW$Z0Jg5M_f!O`4svvH`bbkD5WL}AW)iV zQLawTJXVpFS_hvnB5cMtD?NeXOJ8s4qwt86Snj3SBmvKY$XNV#!^J2Tv7;MpN37e?cQ#&87b8I-e4 z7#Y{#4zv3WKD|Jj37r$DZRszQI5ae#FH@0RqBP;O1(ijerVQYDo_dr20d0Yw?q{Qx zMKgrsll`sGhg1g-S48VPC07n49|$S9G|#qQba5mEX2Kk35&@T}%^PhOS*Usj1e_9?39*L0%3l<3ZcCOFQ#+ zDYBhlqFMX1P6oc6mZQ225MoEWD#@~m-_Q=cB0ZRQy~7&Sm{k@NqiH8lM32j_f*l?Jt_OMlj-vTgn$slq;3ln&a^BP8Trk4g~+o)7w8x zXJ6`-*T@mJspN1tGmBv>(fT}kI{{s_ zGA3={B8Km;uItxx&S|sT{A8el?rBML4W6e|o*)=R{HIw(u^16ZGWwm2Ao;U&#~(km zZ9eHh8g`Z%iTr~~7~H)Vl(wTSir)h@hDXt4TDbjby7_g)dYMARGR#;6Y_}LkN>Ga~ zPSpx}X9k2CNuQ3qM=)&M3nVCG9JioNjh1~_?6Sn|5-5X-q^9=|V9t6;6AawdLTJ87 zEjVH1l9mM%(1ZZo+HS4|-{<1e&TpXU{Fv%gcYv20J~}_0ur!~Ssd2m)E-5WOi@%xJd<9ivR z5c*31_?Iio=Oyu{`pz5s`^S(+%Lk>O8%xV}@O2m7#5RETVo#ro@)FzI3i&B+s6&t| zh%uuG$Bz*QJnc&djHGV7vLJP1gj9pYee+S>K?w+h>?XO1?_Ggxf#IjV@h8Zt^zGC# zT=)#?l-~LD75DiP+3XS9dZr@U)pC?Z0zBSoVQVQcWmsK6gh)?ixYr%PVZCL%L`|ppT@bk``1;YTM%PK>-LmU zx8sP|fX-3g4#mI)d4)c~ChzWcowN#JRPoiZxff7ZMBJ@}5afZ-M4e3G+KHr+^9g~= z%Qqq9ScIt0WLLi&ICS&T-DxOx>z3P5;S;2EjOe8e2*}-L(w_vF9B++v(Fe!DxN0AE zzX!lU2wD%ln)?if-$Mv)hG6KuC}B-s_B#idfqjYZ1Vy~~_r6`4ynLwM3I;S{?RTls zU;x~*hDtkf0c;Sd(Sv)8og2~OVAtr}dWO5~WK0+RRub=eYVcn;maPR7|GifT@QkPfKa z-H0PgyFUWBWP)B}^tg|Rx8lP<1KPkO4S?&NLOl=P*cgNB-fU&eT(pz=U23>k^mGQt zK}Rg2xsZXda-ZLDVP+XG%ovSw-0XyG3@1I)gCAhEY(^685f(p~{{)Ld;k_VZK;t>a z6G0>1+y;o?#~bl>os}z`Qnp03RGTAKQXF^yb7fQuq*g7JBixa&78jwfb+%$=#SkI3G44C8 zTSIK@kX9xH;K4{#S&~M$G)bLt+*lR%Wgw7Dy_o z?;Jb~Ge;{Jm>33nbI~CMs9NHkHHdUR!tB=UxBL@RQ!{(`cn&V8b#9Py(2|xXkjgJ^ z5EC6dw0pqG+3AN3n>R{`RrETOLK|0@PoSmP|u8BY>A z7ib6=K8pQ1i$&adF_;*?=}Dafs=p*I^}bA4dRf@O zZ;4h1$F6|yU&zicVMP9CL4sue^b=?+Dg7HjjU=3q`w59_qL6k z@Jw{jT(Y)7Fh+nTjwY^Grkm@!f?uxyPy*Zg@Rj=3I`jVJ!y_u`?V{xHwi;{X1ou=(EM-*#Ic^$^Mk2nSmEhO7;gkP|5Bv;+W+#d@fX(2 zXW2YUtY&e@7ngBy%xLxKlj9-3oJJR zP`;*zS|0S!%8lTWcP)KL6Uo&aV6ThAtKM7PACIzBwruoHYUyBHb!|*M!_VtMVM^9KYgNkh*1b~B6jVBqqzOy~kE5%Ir$w0ry*FzhLbcEJ~N*!7F~y{$FC0bK*hxND)Upk^$`D}36ofpu-P9=%3|hdYE~`Wy$W9r?UPza#bc zl?b9CJ}`AZv2GZEd}mEx;kBU0?F#ZWA5@k^_YDl#47G+Fv$E+zUsp^}d`qWbS3tcQ z8iI#Ltzx@1zp3y1eF646p<2`Kq(!PDzMQ@=`!(T+N2@y|NqGkIt!)^QFPWKcXEd^s z^@r-;`UjV6OZLbWHN|OQY0vL^x9s25uvDCpVcLN5bRd^@PfZf$kMQy!Qm6iC7SUs~ zTE-{Mh>T>afx}DMA8+nSr0n1NxBITo6u>2fKuk==vdGW~q(Q zPVfArzB+nL#iP+xVvrA#uWr<=nwbKfk!edU;3;KchaC+xiA*wd#|;>*r}pEGPUXgj z1DE(~IiV3FG-M7qc4=cSTMYt#FuO{K#q7Xn5ih(<0t+mnt({0N$Lt%DBfqobb0lh9 z5=estZNnW_lJVCmtx)?7T0fk_e^#uk1a0N)D&||4e7+89ludH$7;Mx)gIs{wrjXJ^ z+OrEqeBm~HkFp5A<%ce;pOKz^`gM$jKhh{`QRh#ea)ArDRiA>FOTgr4QCyLxm}k34 zDzzmfQA6kb{BaP|f|AU=NDb>}KSb=K@;n$&Ur!YC&JMwe+m}y^Kddhb1yms(UvY1p6V`T#{Z+S>tgWCb@VUS?Id37qwb0`Co#3EW3;NT7?o>Gx@Iow z=%U#6H>d3R_=XmDS+;w4xW zp6J7X>#FerLo$qlTLDeF-^Y6rnGCWyo9YjZj)gv_QS+Q2UtOzF!I!yp_A6up-*T$S z>6Xl^!0(dZaUGg%TL9KFJ33Em%8XZ==aNI`N3``0^vYc`$Yc69Iy4i}36P@gNBZX> z7v(=%57NJlx;B2fkW`FoeM@HOLkW$?LCEw0h8y#I-n6d~KC-BI>3Ha>DgHWb61QfQ zm?LIE-3O>2ce7u0WvcJCmw zLtDHAoD$%i!atI5Q zxN9OotU*G0pgu?&3aq6P1tuGgn~=>QWS>*y ztzm@W!mljJljoqnwwjlLsqq-Jz&9m3Q8;7Hgc9!{y=bWn6Evavpvqf&&*Jh@ z{}Nxc%{ZhZ?2jnleDKvA3fJq$yH4;(G;{Azhglb8mW6iV%{l98zCSC1RV}}QW{lZ; z&+N`Ej1(E**{N7N$H;BTMy(eJPuLku9aMPaoP!c=`f!Xko$jr&og?Eq0oTZZNf)1S zNPcZxOJk=X2MN_Wg4HXXkc?z*USr-NYx7{ zqy2*e_Rw#Z^#`HSsaVhBA+%|=ggddiQ!%HWbIa}h z?|LUEuY}cVF7s54NnQ&m6k-9=|08&Y{QxXne3ME;&g0mA%>AA<@_3x!~h?JGaqH<^FNP3g5gJK3e zru@P&`WQk4;Be$j4h&-5lSS4ssc-O*b03#TuyuZxkC5>nEm|m1Miy+E0A)_J+v)Z$ zz~VuY#c}8_wS51f<)wm$?p;%x9Q0;2WA~@I`8PadD%SoypqObe14jvmxIgx2fJYCZ zpivf9tn5?%$D-=j6_;1yW@z9CaY=jq&a&Rb3~z5JE|~#Z0m)!fE$7*2O~AkvT5nlExs>|3S(;6EI?SQ7CLM<4?|@P~*~tr7b*-dlO|O=oi5 zvwU92ibIHuEoWg(H?~Y1doMpc%Viht)%Ou%JHw{diUWhQ=T<2}pMGDg5cBha!c?Oz?OEx)jVjewMQvKOcg zS3x7rI2eq`B-D-8V;DKbnh-E^dcU?*0GjbpdrJ7&qkx4Uu6wB=QF-T8c3pR>ghvz* zE~xB|dMt6CBHc#&2$|5mA8w6Kv}kAHvNBkd3xTpFJT*<|*0A=; zn-wLa1?Uxx;KXuGHcrfT(n8&hH*UukiuF^WfWFbs`Hd|xkm9tUriHXL)k_tBw1)w6B^nT z_$LwjUi>dMmqfnG#%Tuc0850ow?3-!%2hNo1IExGv;94?Rd>el*NOd)HgqF&RVCOo zWe7)Py2udC}1el)C{iNIJaEEa?{20HiMp-9fkylWQ(nf&C0Q2T+3lBU)W zdNlg}cWB@n{kx+uY1&|n67Lx;%4{=w=s!0)9_*tjM)V7`5eEtug-JA6MRp;w!Y_Ut zC7>bOGvor=}q#z~(ODP2t_A-OV_VN<9L0<&xm$UluUBUDlxRd!F(P}1#B%s&sb z(NdrGOR-BT)@SDAd4>q-S`6qYoMLL_EkN(4LItM!^at`s)8jl8EW?ivk5T|gbryt$s4`82d zI&9jR9g6)|ApM=h779s?bOCoxRPb4Ahf#1_mCe&FBoDChV^a9&`LHX1$;ER2EaEeu>YDc%^v-CUqcC;<3leY6U&>-#4untxl?-U zyQ_vvymLqlJmMMtIxBRi~34om6!Jq&& zngWGTV|=jtjM6xW-c2F6xDc_v$R+9O;m^cZ1Gm0qqo+fK(?-Hm?XM5O^%A2kf{y9T4o^a!A6dEE|%V<(#sPNn;gC z>YtpI$Rl1G9e&?8E^i={gC=KAX@s}9kxscjw>oMOPEUzD9V`FoQx2dlU@v^y4~ngS!zI83PUJhyTC zCst(?_7Jw0&yw?nBr=#JS^Oxu)*@LvU1*bTv}3=D!=Nr|_rgFig>*7N3?gVU`tOM` z$MHRzP1I~S7ZcH=_UG;-bW!|~x)-Jy(vMpjPL)T02$o>-VD8k5fHC^wtKK9913~@VI>pS;Ne*sQ@9}hd_S3Fn_g%>c5sL z?ctRxd@6rM}LYg(UX($!VdbTiX6(}W$9{9|AA%x(Ew0o5ocm;oLelPq;h z>a)^H`{u*W>=kIR2DldT3&gRF>xT)&N4x9@59!2Y!Cf4rTG>b$5`OaFn0uiSy^8z< zqyb6sP*h>MKY;$?wR$xaqmKTsO$6cXy~2j56}PK?2w!%&%egBk?8H!=N#01T&D$nk zv#K(Zz&I_M9L~6ohwVgCE+6uT&3T?os^Y4G$pSJk3~@if7D_8W2e+GA;;W>RizZ4~ z;vzvQqg_>`?GtT>vYvGw;*gZrFwD;%ALpx)xwFfUJAh{uBACyu0lNxIK|*d3p4^<} zvSPUoi^K!*u*!N}g@fmd$X%?MNV3r1V$ZtR8b4@W_yJBU!Bk}AO=SVO^Yy+OrwD^` zmcJJ3inLOjvS8K(*17Xya*f<4-7k3t?@VQW?Slvs&Ub3uF2=&=u}t2DaSp!cHyfi{ zGrrN&mOv4gCnP+^boZ8&ZnQRAh|^y&8jk0fnV7sx+-^2Sp=IQ8 zi0M^-3@DG=y~*n~2-`LJbKR#G^Yb|fkHZX~pJGmra8gh8Ry(D?FIe{7P|?**Kv7_P zuPtizj|`F##X*ccN-Rau^B+yV#1IJ;d)y5g*#QRkRLW~BEBFI(`B8LO*PacDD)|9YyeniB3w z+&_{XHn7YwTZy-Vl4Ld@>vwC~>)+M+PR-qC1)z=MwHUq5MD3eKiULO%tR2iQI5jNo zYMiN%X?XHoLWr`e7~xa-O?ON}N9SMZ zKUug;9PN6)J2zv)M|e{&?RgaON7Lz!;9}(|UW#wY2(NPs+8>hWF;E}=TpUXb|*O0$q%n}g!Mwx4DT&%8Ht9-8-FG`2=VFJ?}MIG_GjQnr< zE-Fi}k=9<0H6K%d4aq9vf7?Gv{WJy66RpRp ze4-`Gg$7^#(c@P0$2(UkE%}puy@|GGjuGN6c+ehdbbBm%o;!I)SQCDXn8FN*I;+kX zFvZR{t(zKWA4eDx#dpZICK$mubKZ9+8vVHvc!QBCSZ9W-(`>t{Onpz%>Qj|<8GZt@ zgc)z=5AJhXs3HFBt-Hxue)@nFw^%iXwRs_o*dNvkE>ucF_VJgOZA|@S!IW_nJR<9# zWQa0KPMRsryxR~oZ2|shxn?A4#77nR#ztLR28D5OQv9cnaKsxCYQaNMcIOTi{K{N) z*SdK8K|YnT#T$QHy$>6$SJY^&>!~r~5!2Pb{+@n)2=#FZob!}4r?LTuJRVNP! z3Vztb{rEeLdj*jT8T!iK#2dw);6=Z5m^oVZx5#}8$VQ#3J+;A_K0h+p@VZ!7~icvL;l9+17d&oX?sIQlpt>25rFK+r>SE{`)YC2Z!2x`lWrDrbAFkN z{1*UBK(oIai^rJoJie#fq_~i-Ha0>+PT>-7fP?uMG};)!O2j(nBnZdED5{%@m}A8S z0!C1e3iO>*mAiqk?sdok5y|i3GAjo}ZRzr#9v33MgbrXiHVBBfn33@E?q5hgegbC* z#wZg|UXTO(3@^v0izvb|w}0kWvW;3WUb^-Sa}Oj9yk|%!%}V|L@6$EE8V?27stxcO zTsL;>db!IMLm;7JouDtJX`}kvX9Qliv$PS?VrX5$$v5roe`7=fQp#d;%}zRIVTYgE_tpk+j_$|8c1aCtj%c|yA?3xoUD zQXohe7>}qs!PE`Y+vj!J2*tf_W(oDoGZnp4R>f9`K0 z6fhvAO2V^g!+nwK^^`wh#rP+(6#4oNZ>Pj|=w=HdBxl`~BVFO|j zv8JT=BSu|5x|?U6|P?BguI|~U*zB{Ij?Q2qMxsfe*jIDIVCNY z^S=r}<}m!6Dp7EspEpF*M1F&!^Kag2S(vz z+*2L<3)o*+!Au!L?sTN7pliT=P&8kG-52qH>`Q%|n}03loxV=}Ae6tM^AMCsm|^|& zJsQ%XhB;{wHE$qgnk&MHPg>>7c<*u*x^8{ohNdJ0Pd>di>FV>bkTou~}cLq`@eZ?|b+PU;nixX;)y0uQPI*UVD_?2Crl!g-Bv zKb8~8)qn6nZipTGrV(QGhFL5h5`V*3iv0@twoo~dhWYJHKLG|9~5^+NP zg<}OGcCwIN31A$lT5ZlU>W-BfTsplt$1Tvlm7c8pyl7CZk~dX`L1ra8OM=}?no*!l zTlE}jn*aT`;M>@cAJvNbwJGE9uT+vf;rKSn<$ojL`FfBXl!jl>eeZLek6cX@de({uBb%$1)dRPULdtrd8M1!l0hck+<5vZ?ca@}%m%-3+h7 z%zw1i|E-^}UxnTgYc&A#LAiZ1bNG@II(l(lc?xz=43_GQ@;n9?LzEU{(|!_uY2RNX z$ldnvGwV=5vQXbDJ-MeLTpN+jf9@E&2&yfo5Gv6CeBC=U4e~XPF z^oz5aw7MhfMha{fhC@LXw!R&5xZt+m1T}~-k7oSqm-A-6M zVW;291kUsKRZS&r4CrS3sboqx2{BW@C@^&jo{*{5y!MF2NwJblwXbOhGKfwXbMYrX;bx(SP!G1{L<};M+ETn}Jb0t$ zjY#&mmKu6ibLguUtNa5tGG|BdlZU%KTeIAuhapCp?&NDYsKabPlOZ-nPEaNkCmpeo zjaaiI`5+jR)%(aUZ z8KvPy)lVP$wJT#35vIh=WpSkc2m)P2-#@NQlgR3;iMu(358W$86}ak?#Hv{+QeSJyVLYt4BhF9fk6aDOr2-$H^L;U>#) zgpxf&WU|q`zh=4^6}-bvld6M!Z|m~UE9E_AC#vsNJARNQO=HO~i(Gkzn44chVX8;% zN}3Jn&5l2Y%QRXCEUVCo3KSSxM)^rodgF&702FUB9pm%LWM*@d%_{CAKu%_?Wy-b* zX+8{pvuaJZ)fNddrGKCd!oTHdU#Xr0>#Fp5rUGfSdrAuJCO1qj=56*}TpUfN2dng0 z6pM6p$IE&mYi;Ezpl8sH%Drl)kERk{Jt=BwGJNk5me$C|Lf_(Bw&9MjJsv`wsbQDX zG0kN>gdKpIbjo0~731f*fa-Yow2pv)p|MnPNJ%8W!88J6T7Tha1OLdcTal8JLH!wB zq;*0;q~}c@q|N>ve~W<>IQ=()|RxVIm}fO+5G!nJF}W7o$(OSwMWp5294Jduoj5Z^F~{6Wo`4L5>yA zpl5cRU^t3LwD^L}N0Rm%=8}UbEGo+ONH-x~FQ@meGk=I;pDj!qg)B;xuX-!Kxe;}l z+ECt^+m&;03BEO=0&gnSE4IZkW<#A#fS;!F##5J&Qj271y5wb8_$&K}WbDq6gw@Qs zf`oO|13Gi&$z<6Ib|MPg(kYzT`70eqnPkh<%yleB-Hq^1 zc2H?|=6`%ZK1?v1WpPoT4@-`AB#V7!Op7V2(S_` zCeEOUe`M>0O!`E}MAb5HJR++!b<&SOSOKHY;)#Yo z)LUS8HtDe?;OsoA$XBM-p>VE5+Uz!XHb>#bqimOQ8)-$^PT*8Q zv_KOm{`HdG+Z|!vzxOc;n0;z*{Rpr++NeRWfxO#D-;WaUir-ck0fTDU8+0pf&NPJi zM}KMM8??7kd_|s`f0rXOpA{S#&Fs=u|K8}hgdv=g+CgTK{{8|?D&fKinSi_~3}40r zVk&O`$o4L>HKquEag_lKRb_gtHO4&4L-50)Hbf;1s+W1cIi2`r~I@Uprd8q3JR!@KmlF z+2TD;u#n_ato46ip;Y~&*14EES9=%3I2j798GvkKx8`=a+d7I;v9d-by-d6k4X8}Q zK6T?q#av>GVq@x)0W!vF#3APR=YEn+O~zemv;Q-^@FhOBcNL4V-j zQFn&N{~E><1*B@(CqS@vQxFQYxn8pGZeVHSiO}j>krPvO7G;n`XD}TcM>N090hY^^Np?i8%-)(kz(I%&)xpRTt zTBP$n7auqIc+Nh4glD0}+!~C3lvz3!&I)7nS75KGA zfX!@`SGub`x7q$3X`_qR+dWHpRC1hXuR>Y@d|@p?t}@gKLX$js^_ex`>^%R;2m0Qk9Z+<6|zk+rIf6@PCW!B$#g%=45X=GVOacjrYgsb>CNFRJ|)E@GdMtr$OBRLDc6Py z$aT4vU{Lu}TW+3g?y9PK?9(CB51}Wf-+tFs=*sudX{Ka-G_w`k;eT!und)2BO{FrO zxo2#fyK*7pfoql$s&{=rA@{4EfmBWGLKl;R^Hx2r*!H_aTs~yq zw%N;FSsxHJWo|RUcp24-tR0Y&MP6={L(K; z{!|^+@13Yaj@| z`(r-u4LvM3c8hUX?nbi8osj@4&ngw5+ecLI$9*J_zkI8Y3BR0dr|T&@A{VVlaTFbd zZkXL{^mOL56AZ94eVgZ$KkSZ}u_uvRpZbdA)lR2qC`l4oASpl-b;Xa zzHVy#Ab&;poPYC43l%oRG4QBkcfp4z@Gg!Z4*9)u=??me&1C%DQhcFGJlp3IQFcba z3daaFF|*ZS40lkzW4qMJ4NCrbmNT#Tlx?1N1uBhMhT@p%eu*ibW#pa>%wyp#!|a1+ zWB$n7wUZIC$F73Wlm)I$b`R*(=@l~k_}=dS@{pygmVXDKNFpPD)3$Z+fhCeZLN^|q z9_}9P(<{Vc#Jn-`Y+cb?vFf?XlI^}-przNlSBoFW4<8n=lgX)?{gPsWvwlCSijvtq@z}kYf}MBPNd+*21=e8FYlqTw>pC837IguPMXg10GLr%Z(PHhjYezm< zSp&*VG-97|%h)T<8Y9c&9C#ms%>;koi!D6aZdDg(`_>XxqQF&`G&w&GD2j_G@ZJz0 zG4JL^voPg&qOTk`taiD*PIrRa(_~2z;xpW&azt{0D<@Qi_aUs4d4 zUVc1!oqP~0!m*cZHvCE%3JFOIG~U`VVx2-c5|RzL=~aw zI=@30g{McPlpkBu5~qC6Hz27sq!tjv$3%A?8osT?>L{AW6M)bl_Y*x*JPM zH2 z3^7B2p)G!tApY=6Q@29MY<#CZYI4Q#1C7tMRK|0IkCDKqa~pE!1V*Buk!{6>(Lu-= zOGk`Psm}`8a=Ri(QVN^V#H^}?ri867?thwOL@dbY5@a`?qO8U|q3H{QwA@boxU3^H zUO8rVXk0{#L(ZM+TEa5~9%El;kM#S=@e+-akZ(j3mwCe}dz?wuRRvrLg(rkC>P;ln z@>i{lw)sMthK8YZ65Ml3wz$~B%v_Xs5K;f7EQzq{)vp5XT5)?@FoFCaZIxP^OMm(m z+N>O&nma5Un7g+`0*7xHRmDy6rDf(pF9Z1w5rQf@(Om5BOoe9);C$J=*!OhRfX(!4 zQD5O3lNKg^rfe(N&faoUhpRSer)~jCN$;flucFmwhf6H+arxGvZHs8p#DI4@(V(d{ zwDL>e)UW085xX;AVPoFmG}|6W5`V!~#wZYMGIlws!)QcQF#Je?Y;5dscb;+|f+;+h zGRvT~Z|STVO4cpQr;-tDsd*E+2i#9d{q$u$^!W!4U#CpP;NYqFxePtb3>PXe0o$Do zE06|#VQ^$@at(+IPckuX!P3kgWRew~dFeAsa$mo18^@9a3xOGYTF8-Z*MDC>7V`${ z3biP-Uj|y6x9!J^6 zZctAeiUYry1{bl#3UycHeSe-c95j2BkZR0_Lo5>(ze9FBDk1I1!4TC?{S}dVDV6Z= zdlJZdNVD)aJq$!#0}=Nkwx>-4nkGZ7H9AJMlH4+sqib`sB%KMj?$?MHb9?FT0*VI! z1+3Pak++)_$Ducf!3tlX7rYPLU%wV){C# zTT9&KRIk?W32THy@7sb}Hxj?xnpd{NiOKWl4HO>&Xx_=`zf+KAaTOg)0G>3*;DgF| zhx(=oxz{g`sQ!4AiGR_4a3!$EB_aM6jUruqn$OR<+i-4w6saxYg`@didkZ6O`XJ=T z;JWW)`S*o~8bxZ6veJ%Gi$Mr!5#O*q<>T=KKX%_(1Ftr6kVG2 zvqrJ1o@izAxYGkn71Kf8q}Oc{XzUw%c!~+ zx3yIz+l8E9PJgqM^6w}wKJ-=FBD~dtU(5bbarcSzb|WQk+u^~Cj>Ih;aggJic-ebVjjK$>4E>rmy$g{5)MQfrKihUZ%-&ky~wr@S)JVik{4hE^qWzR6Q0z9-uf$U31@O|h|_)@}7lRt_-e1GQ+a}N$kr&mHiR3)cEHcraVAFH)SUpoFu%40WJ{% zVi}x3vwvJs1Oa`sz`)7ZwFjsJVwmZPthLy*F?S)1M!ld(--FO6v-sxd)QKTipe(WI zG<=yAZyfh$j1w{(s0ObDW6e}U_p7X*3gg##e-lmH1V=C7UF>u6J6aknisk@;lGcvd zs15r=J5>^`(ig{~UP!<#IBoXAF)g@DW?QlnKYw%rvZ}^RFENBU!1?09vYqw)WGAcK zQ%Flim#sbaY4@`;57Now^0Dn->nBe4FW(`k-0g`l0r)a)dHRd^D=+jU- z?a`rsZB?sFIoi^Zhwh$-q&{f1$|0_O7w;)G*PUVmAQhE6Mor*-$qp4mbg<{%rEv6KsTz{l+ zwC#;Rru5@=?Zp`l6j@5+$D`m~s+Cn$eP`(=@*rG*H};sjdvgc`mA*y#Cnm=RWs#h$ z=2DfjrG^L|LuHZ55a~{fv+68N^K|^m<4?AZ6W$hW4x>>6B6N!HUl%IJyhz{oT!k`7#WkDeS!flNKBK;qJ5swttH4S)Vl9Yih- zE5l(@ANc}7#^(Xf_xmGtM_uh5G39I_q8)_0}?A= zp0vF@>2D5YTXo;3e0rw_S9)zR=79rCPRd5!7g(0^!nI5XzV>=f_Jv_NoY1pbLwy@g zLJioKXKu2oE@Pm&-XzFo@oPU<>`SDBY7NL_p4)7V<7L5SeSC1YU?eFB@Xs39E#GGQf<= z+J48^SF-2DXm;EFCSoQmtdO=oDRcM|S6o0Gt)1+C%zv?Lxq&yaT zj`jDc^GP-Y;>yhX>iU09bOoeQ>C98Qu>5}{-CB9?eA#fv{dHNkQV(-C%1BsGeXjc2 zOPdB)>71?V5XDXw`H*g?6q~ou&WR9v_$oV{W=9f(z2J_wxK(3tv%t;-6`TO@5uxqC z&V^yju-lnCe1GQ%MYMN`HF=t(3mEtLYqnx)02)?TDGu9kC_h2AwSLqh+na~jd_n1| z)pq%5A~ok`e5iX+tXM%5vt|uIBAw~PxwKtg&-IYR@NB}I` za&i8d5r3*YK~pPIw)%G)EqEWV_KbzZs+Q#39o{L5vBR8;BpgLYOSP$q>779UN(vLu zmvp4h*N#}M`Kj^_;Wd$w+XTnAP`z|5lQw9PAu2&Ah(HaRDb0=;8h+MU+cH<#{AH4hBD}J;pq!@ymc=UCj>HpZ zGgt*|sLy&A896}DPQnn(O?R~15r42wB8NZ8zdwostHN-PIhPUF`tYpkd!?Bi7Bx>r zn4^5iAw~=FJ7}b0oWTWVB~Xx?cwDQZ1o5?%s3##-S$&j3H8MV*cv||G<3?{# zt%M=WZf=rxf?}-*s-hptCwE4hl+Qj9&7~7OGlHQ<W6Ve7kh&GNDQY1#zi@` zhrfK$4M0T`ouwII1!f?Y9DJXH>qSXEZ-qTu)C^}uNmjP@3PJ4a^j@#&*wp&oS-~sG z1V?R!3mkA@I}-OHJ}GH$JAVeE<-dL^c~a-L|4Bsm?KH?-Tke=uz$1%vkA!|_T_Z50 z3}PD!A^%=OJ!MlqpkU%KuKRn}><7K{D966wT6^b(d~}1f;25j10mvfNm<&BJ^6K4U zikH$;%)nO|;rH0xv=7w@k9WtwCE@!EYo5y`we`%mPrFwsX|l8Xw|@q*8CDE^oAbdu zaN~S>Xt7g4m_~&}&e}4RW2GTN_1iASej@KxUCyOC?m&CqYo(M|ICgNonfGIjv#rJI zt%E_$>u1+uab+g50!{ldh9~0+%qyP&lHh2~=JmmpD|djd%?XfVR+$+#LQcU@tVzn! z{Po#uljGfwTAE4laepf}FMA!$@~wt-Dyf&};soJifr~MMJT|1SDmiPW;}5=M_Ori> za8?Oi2(^ObGK^LvcqjsC<|MJGy?;qd?cZp!Kylf*0h<|>gVh)~P8E`@-;k zXv6=QIP&Fkp<|Ty52MTS`ZUc6*_tI@%#gt?MH75;j6h(}WQ;6QFJ4en(Ym@ni43!l zTOU<@k^iXaW-7VD`!2)oB=`vz4^mR`?f;zx4L3iT#K zN_ebjU4M7Jnm-v*!Ad*xpb6dzivAXwB0|i25K`2_$=G*Ic8ztOd3fRdjk_b@gb97r zTUmfPStu7qtTw{Xny`6YC8(Xa*6QUm{!B7;yp@ti$baxm4SeKLu4q_Zl4GoZ~&W!#MVp^s)nf`sAqk<}S&?P<1jv~UJy3@?pC9bYL zAQpm@MfbqKw8_^F5p)=oE`!oHkIg(Qm;uD)xBFQsA5#1y}Nk-K9z_`1sqT9um1gja%POD4L?wlUC?^%el2mrT( z0lNbI)YUfzGBp)iMe)~*XnX~56A!;M94bFp3pUf?vhD=+Z+2DKu(uzDmc`mu1!z_7 z3V#fq<+0TziTXF1o9&i$`i+C7Jz*iHZE;L)!wPcU6%P|lbQ)m`X54&xF?@yb{H}y4 zN2^v$@^F94)T&fBkU_vwdhNK_c8vsB$w2g(uAUb!idx(U@@z}J@@!WCx7>O?ceAc` zI9adeKRlnhLE>;~SZ(K~uZW?_+gces!+(ohFz1F1T7Kvt3J6Y0CpPI^xN#l}M%`qy zxdXmUxIHuvHy2X#@oiJz6t|PWy~h^75;y=qs8TC52>?bCbXVQUu&wqD0a<3PiX`lo z=d4amPOrPgiME*Qw0G0$mQ0>Tl|P5NamgRjjE<)m z5>B)S3C$z=X~%I0v$UqC=l*j-DvMvbrBJgMARNT%itGv+iJ+_kE9)NsYk$B`rxSx1 zV%sQ27fMTI5hK9C??~UKy$d5(2pAY|CXBtRx~g1#DLKdUyA2M)$~_ z*Lc+mD*1eMSE_E6qp*H~Y=6k*P3mbp>=jrj0W#3Pu>dGE%mjZ80vf31ayF;L-n(w) zDsTe7SCaH2pvP`u1>-^?Ds$2 z{rTQpe;abNS0Ux@$(S8^8-RkcLR~dt5xfz}aL2vTsD52mN2rPJqko77cf;sliD(Br zC}+|zODwY`E}u!88SF1Mf0sb7_qd$T|33j*3Z?bQ{epZ|RNGIr5@}Oc5$s$#LQLy( zKho?fIio_@R*`?6;aWz$)|5i^W*rm(m2);MDx%&}DF{O!U!=cjOz{QsZQEeXs!?15 z2sLtkO``C>(Uo=&4H&{yfxd)QnQ>f zZ3k_)BcX$8oEXcHwjW$1ZH0{H$`V6KZIG;0&m+om&m3^Th$op!$EqEj(!AygZj)yu zygke~ahCWre+8iDFYdhI?Oo`w(%v!gH~mHucY*a`+*IakOj#mqU^Cn-zZoL7j`deO z!Nc&MFC*9Bl7DFYWBRMD#Jt(X?m72_wcb+Ajtn)%jI=0CYyv4dRQiel1&cQTKT4LP zb@?efPRrRuy2aLZCvs>BAK^5oSam;TV%o1&5lbbEne0*UT^-`7O<~HW&744`rFyhl z;p@Ns+un>^nBEODDoQr-Pv+n0jyQR{{*xD{T};WMcKX)MEj-qOM+w96`J!* z7y(z*kLd0TK>{X;)n}Db*n%><$89l%QVx_CaQ|Ao0At_13vwJ=w*3~ADFH+6ZqSx- z|Nf|PGJkX$ZqUl1m}-&G2+mDhLPRhf!n>V#2Y`uP1igpJz7Nq!OnGNY;7VemXgQC~ zztI?d;BMbPtGv-rL4+!c9$l;FWKZaJix)`=&)963vMr7XIXCu|Sslx=Ga08&;mI&` zP0?`;kZH#E^i_KD_E*;{eP>ej*|TbyC>JTLFn^}&5T3p`xEE9{Ey;A5fAkl=P8Owb zd)n__xI`SckD1ne|FNPr!87Wd)s|6vL|(loa0NB$kZgc!NA9)Jj;Z;h!m`&B0w!}cLHRg>F>yp@ z^nW2O&Fu-G5V4z+*RVtCS{Y8kGjt~D#4oKWRsPg>5RUMC*{HOO0m?yowkEQ7mkaP_)(j- z4Ga*2g=fPGE^-OIRtnctKr?k4>eXiYgMU1x*N8&*{lPAy;_E;9Nj%18S88MI4#J1q z@mpR8!sp7z`u0li<>nb+HM($bh{U~eXebEmu=#w<2rV1GX$7}w7OTmp0)vsI>H2AQ zVRUYX(vhs!y(dghr9S0@FA8|KkF;hAVRYfoo2&hdY~Ve_pYNoyfo`)m$!mh9x_=vz zuN#pX9~^p=7&?+Nao| zu}G#VQ&6-v%3cudoLW37wnP31R$oj`nfY%A@lPJ%E?Zqf3V#Y1$H}l&b`^3qI>o*+3E(xthji>4b?Q>+E zIJQdXMszBzc26J8`1irVFKIcCa=v=Z(#-Bh>Kpmy4b${}rnK)M{ zuBeYn-KpWy>L!{bSrmZM7j>4Rd#_r+HFopt#1%9DQu$8>dwzt?$7SA`el-I_e#{6E zeq9gndD7|8@*eQTatWVK$+V6dnVmPZ)NycSeuaEb{6IvWxky zuR+ryPn{xFV~FC(&Q@a5YkvTy;N`AO4=wy5BpVpf&x%$#SoeOCNZmf#3_HsSE5aKE ztvnjicsjKj;X61Cz?%BSW-&^bBSz90p#<^<8X9XQB|Z@{Tn7?{X^<;Blf>fXM>+MZ zR*~lqE5%U}ha-aA;bv-!`nlVJh!K{ggbl`%MJs!{-2PlN)K6;Hj(<(4mwQ&Y>+8s) zC@ z2NblKA?BXKP2o=q^na(EZgvR1ZiG>A9`9e5a)4p&QqhREe{*)0SFJC11uvZkO3vvRdz!Kd%!Y;tmMJ>2{P1=26V2i%L*L80 zC4adUp_$>cOMl3dWN!uhE5xWs2Vo#UP$ZSw&y`J^chfvAmq^M&LYGMqhw{wDOr}5? zNKvge?ZzYJdJE7Xx?D>?2Z@YG(Y9x^s}MeW)FvCXx-8_Qe58@PS{~^MON?;Om?~PQ z;hk*VAxnlawn*fQ10^|jf9TXUQ>2jHwacC8_kE+{5r6reY)oa~(;?1?Q1u@BHvAHH z=$pi37=4^tJ^{pW(N%*PY6-`Nll`V z>xpeX<$sil3SFY+*)U|14@#e@u7kK67a_`?9nE@;cjNv3){a*>pQgSf zdht_RbJ5JA23n3sqP%N2Lk&!jY59YSnwdXreNzA;(?t{y17C9g(R94peU|=_-@C2|Aw^o`vqkkNpV4EzQtt`MA#8_58wL$*e|5BA( z{5ypor4+NN`!wY)Pi>R;ckFaVPhk>b?0_$E-b=D$BWo#!nw)5O9-?E2povC#nU?45 z*TVE4b;_=wVM8Lw{g!&Vm4G#V3Sl$##=PwCXP##8Cu^VSiHGj4^kPSkj&8mY@gO!A zTz}&I=vEllUoZgX1YsDxb}fFm1gz;|I^MqLlc#T3tl25NRnvo&QFixg2QLfd!Dp?m2ZjrApZ9GBY0X?eyy2yh5+V zQi_uypA!N!HJAF60U`r2H#CGH=1q6s_SxOD;mb^|bhBZqF(SAiY1lo2`-r*QNx?|wrWG3Zq!KHHT<==k>{!%{1 z)WT2plr1EOd?#D&E0V)zj;Im;7yFSLeJ_BON>4{7h59A4IcjifA@g1lscI$YaHjtl z<|+$W^k=rAJ|~Y?JgPE5@SB6RU9m5&QU8by@r$>!3QFP?`z5eoco3AJzNJ>z`6l1= zA+)U`5*OOu0SeUxT6!PaN4I}nex55M(=J~+t%xW6prSI|?LZAHVR+gaU$LsUYogSk z=1V?``LDe$p5o{l=Z)kEc0?FXM48PmFDCcm)pO`JQmE`XO?3@fvbHng1!Gb*UXR%a z6Q#&TU#p#Z0)gv`vvk?IR6(w~@I{&OM92fu&cIVvfah%m)na+OzRdpaINYvWvYSE$N=;k%cjPNeXSi***>EKPZhvUVOu|B@4qB!w1qh$*-j;!pzgh2F&Pu~fW+3o~wG1t^2-Ol% z8q=UYy5sSgyxIL{SoE<+yef1vUPQ39o69-oH8I~qmzM4R1@M3Hzk)u{LX~GE%_b+? zKVe;6_9=Lsrvpqsm8X}1F<-uj7a$o}Dtd2Mww!}BUfrpbh0Eo&ZzBb7f%N&j&L<3v zf%$M1ZPzYkOR`6`|2HPfX-i)RRsRN2jxQ~YT)TuQfM@>+n<%nC6uHVpzcmR>wGdf) zuk!ZaH|iB+F=>Cw(P3iYe0bQXx_&w;yEnIU39b~^`*_;h zFi<~Zl~nRd6_fxtzXossxxBay6d+jBv=Cl&m1#cy&CP#Xor{F{ci!d)_)YE-+Nsv+ zGcy8lPU-G1K*0Ie2nq<~>pe9kxj@IMh0J&=Fq>z)5^%I>R^@T=lQs>ULF z9s|x*%KCq;b*>v*o1((fX4aVe5LN<}$pJ^l>4kR)Vg%_zGDdXNY{Sf9Sm-LOu0h;S!O>_V(M+-k&}b^o#Sc7!Kr zr&zVR|9%v0OY5LY8t0;dAdjfWu)>KeC>B3DVhRB44O6Dy{ zi@V+W>c)U6cLJ;zO1HD;ZlNtUh+D?L+9re*rQlp%JQ?R{sE#kvjTuaUQw1@mvjSdj z1diAY-PtzI8-6tg5c+H8Jc%yxr(3eew=odca|FKnrf!c->B3zz|0;D|l%dF=*$ z4U2!*^0iJvtXkc30Pf9)6-i!vYO9?|GBp?+P+c*r3-aITo?P~ofLN)U{vK}6o> zU#qaoh@=%Z2S%k}KsZ?4gIWpdZod<})|NY12)~X=AuPwVh$NyCqn~QdUQ13YSgJ#3 z*gMl7X<@)LA)wyLjeN_4d(w~Se#PXL3s`s{kbxJNQ&ZS=HT1x+;iDy4!Oy3`+bVxe zJ9orQq4i_j?Oh21F?cO2f1qRyKd($Sn6c6Vm~`(cP_b1 z>m(5X9VU#UO$b{8dSM7MiEHaI(C2?g&*P@cs3;xbT2D_SJ#v>rU_`s$@hzx`0^>9N z*TeoqbQuMCCMSbO4~Xejz^zC;K`D>m5&q29`lo0JT6<|SB}~%)6uoA|=*mfE9m}xcM^8 z8Ono*ugf(Eby-=nIXzUJJT`B^{++D?$1_nr^i*8>%@5+(KxzZzRyk7s9PG4|?v2-U zc*V9!ZTcu1zYK<6aiy6ai`OYD;=+d%M(M*0ZN9G@UAJlz1v$(U46pY!bK?Bd(qBNk zYz&|F<1K`clN^=9UY`OEj8K1v>t}X>R~)5cp!}307`jh0setnOTXK!qT~K7fMa2k^ ziBW73AW869OgH~#{n+%IB>OtQ>?^u_rQLes3(BUvpF$iVo{RgMwYJzE17#ZbzMi+F z$A9WChjUmmEt|aH5raqzE`KnnQc)`b**69FvRMrq`QRn?wYo=bw#a|wIhOwBKwP~A zY82B&rd|Hs#aD{AiB$L2v3wyChNN9 z(#7ROae^TMrGyS`=!Ab4q5~sNOPirDT!<2S*<~N*a3teK8Q$7&P)|eechQ=}sfTc0ov_np4LG-rGq8SZ4|_(9L5h z1(WS+5Ok5D;hKc=F;XPdM-3ywY3=~xCMDt`faxogSeeV(o|=Eqe0_ZRYm@r7fE$y5 zSH*m?1pGWQ20ln`(uGYUGDTUg1uheC4{F5|R7-hDKEH!k0zFnK|K_e4-qr_Luo)uA zT{Qc@oJX$0)?r|I6%L?9x>D>( z(q{h?VICPyqa++kZG6Sx6=Lx%sgk%^{)3P)GU8UZe8rU817!y9LCPqbdC;FjHo)Xl=nSFlb z@5OML-)}l+celHdVJwWdJqx5@e(Z<+EsGoY7?yvuZu*-w+Eiw?pb=Jr6fepF13$58 z>c^bdMjl*7UhNu`EH*|d51NL6?deY(U0TTOD}ItwoPQvUu%ny)gwNLnig$gq?h$Ir zXjNm*y1z77xN?wbD5;EA8k3Z%mu;sMwnIG~bQ^(*U_6-e{O;JUFDU z+u?smX7n-lP8>dqtk*=h#Qm@5l>Zi%ayD;*L2v&oY_AH!O{VQ~k(=&-C_tsj>j(^`hZlv|L#oz#eKy_-RbBp$7hdfrjUDPP(q2kDzBr8@zih)nO%r#^dr#4~@O z|IOv2*0E{r$5QI2(&A(jY_khBxap|Y2g`j*o0uE(n7>V25&!pLA&l5kWfN?XmEh(M z9DkUp`I5Kt>*nQ8R6uADK1Y`2PWT>9kkXXLJ)jds*G_@>ZvbX&!-?nV)@@I|n$;hM z>v}y~k~KX8*TKhKe*TUK!+c=_?EZgkFf{jbjfOVgecpipML@d0xM2>=%`Ia3Y|pf( z=7_r?4e7Sw>^ki&DC5wTb5{(pT36Us^fEMRxEviI+f6Ry1wde_odYOyifbp4~yzTWqSVKMJCNU zZJgClJKj|5V~4TB#yz1>^madOQ+VG_;Ys<{FzZm5grb0m~++;r)>i!!F$$ zY(@|CuYZ!gQf8Dnpfo(HIIa2)Jqx{airD+!S!=bWO_q0SMwI2Mff>?5du{q@r-Y`bTz;oDlTz=KeDKEpv~uH%8a#Fa-W3)Iz=vbxT@=i-(H*D{}`(G zq>*q2@SRhjgNh|q%MGmt{cFCW08dRrI%xdlj(w4RDztFmyQgIepA%t!2j=95Fse;E zQ=DuvNVOHcMWQfRtO=Ss9<=`*pss-a={7iXx}*;8_J{fJl~V<*kmI)h>?N>CVH5_f zkRqNrNpYEuXe`pFN~% z%CPoC*4Rw#DAx=mBAR`Fyjg6d|A|mR41yN_EST+JR}$Kc447+7?)=}M^~NS<3{sOs zeDGgU6wW2zVA8p1{Xb{;m%SaCYOKOy?D%oaD+k5wux1jz@u4#e)w4eKRM8%WH()$p z`G3a&8tci$^I=NtpzPv&4t|SdObvA{kfd2-!3KqI^NG~jhWJl^aka~D)@`vPqfcCa z{zj1JOkL~n{n9^md!@pq`ralANz@`clAgung!nRRO2)r`rG%fO#V~iJz2m+!ZC|^4 z`Tq*#9$55Mp-t*vitMUk4scVFZ+)OFjRt<-WR>3hs8K>@&+bT@m0I_zV+Nasaz!7eB)cY;JCq1Hj&b&G9>`W``K zr9SGMBj9IbM21%63D26N1436waA~tJUn%zPs?NCMe$cFcRSJ)-q%`a0y5_Ojl@(8Z zbkxH#1i`u}3(bHT0zP*${3F8Wc}A>l+e2RNLkGQ|K$Iw7yuH*bNgH|QI0&A5xfTve zV&3Na38ST}^$DR^;RPp4>CaZtxn9<1=sc+z;pw9ev{#>G`EK3_)$OTilRNd50dD|a z3E6JL17t;iU1iqelEwrfW2+utebNAM5@Xaw_h0h&fPuS9 z(8H_lJ@BzMeY&|0>wQW|rQ+bRUo_G+;Ahlu?8c*nk@I%&Jz-TmsOoX)&5CyVRFPDNpZcMmy9>QdLQfTmJzG6EF8UXQtWpcrPB zDvmXOMf|Xn8_i&t;Ic(GED2I#cR)t)RA(AttSJh0Va1m*b{aJOm6zKv_meA?2rwrcH&pR*5r)S=PLPxA?1f;!xY?sl&bzmV;HOKmbEE2g5qJI0CtWV~< zGWmJB|B{J<2;2Q3S&8odDe?D6e~*!tM}w3aJY2F;5GB zn+{=2*gjwAAGLd9o?_&EuFn!l2UUmlZ|4!EXQT?%N5m=a9`wZ7%O z#Kd?=E+%=pLq*56w`j)eoM=xc9h>o1&gSvpQ|wv2_R$3cs-%TRD)?7qJEuJ(s;C|N zfQO3LC-euVfRA+`E?06%T?rWe`| zZ5DJ{w1=}QYqlJU6(*BRXUOoIj=B$5YDnS=%red9ch>absMsdtn1ExEp(PT z7}B`s%+ubyG#&%X-J7K1BMdNqJtg*f?n-z%IqPKR9f)N|WR=(=lG9(~Hg*1*(Pk;x zz(G_-j)ZAUzA=)2?Nd12OQ>~Oz8M4C35t<+#2089<0%fdv5y1%jq@^;*Ta{$JW9MT zb61paU7UKO=2|CX1!Vn?+e?fsQP`f_Ij`x&+Vy3faZ=RH{;7O}+oIKfWOsqQ_G+4?zz*4=jvw5IWh3jut4FyC6f*kNF?#Za|8T`9`>LCK2wgv^ zXqsIY$=^l*Z?={~Us`-nXg-Gs3W-p>hj{KpQsXqpmyMr;Yn$6xj&H_@gG|DfwOg~C zVXkx-St2}KR_j(RkCeB6@6HT>E=`sH=dYh2}HSRpFQ;bf(ZvG_^y5vIe z;^mpEML)l`K5F@TO6k@`LUb#4(-8dg7{`ZNA~sPJ^zOy5=m!IPd{iLD82YyHTf2k=aAVf8UujE_an{QxAlIGAqo?A5OLv z*T}PPTE_HM;Q3E~5}Kzn7T&Jbu#YMaTf|N`-a)#cu8EB ziGC*BHEAqKz+8zI5LlCSQC+v}X(SO5vhXGA=|^12V~d=kDj}RD+ssLcfp0|PK{PtB z*2z#Y#7eeKr9|TMXjJ8mm9am;#v)Y(*$cx4yEOrSI;EAjtqT|#9Bp&~{f~fL#a}hz zH9a*JsRbCcl+PSVMmO{Y=Lr#PC3Mz`S#rN(gE=C&+_T(o-Dn2J7ow6u`)iH;g!G6# z{ZC^YuhJeN*hdM1Tb}(UpeMl=^0DM3C-l;Y8*W4(FOq)_H?7Nh&y`@yjLLBEKL3=9 zeLs$W0mpj|>8}YzeR0HA%BjpvE9tSG^V0cvxq3wAxW)MQQf;$ol}-D&{cwBn9ZlM^ zLaDrUBV65w?`N?w^4x26=ydFkF`OSDQ!uv)ccu?2LjsQg4=}8b#^BJ~_}J>`iOqe* zzw4W>!s`o+ym0NR#7Q9q#KhId?*o@+m=UHOVgrPaPp>8 zhdG=17*?upBE=voG|r06F%fH)g^;Y2MpD|K0t_&=z=;BCFuX7NE>S1QYxriATj*Vr z!`s$|oMw=s^Y)B@_i_+_y~4MmXw4jdIGXVuFbKHWBYiLikGdpbB>FFxy3F3?D5cG7 z6jGgCW>`NFB#``CEF(8cAm8$7WDS~9G2O;o_RZXLoZnsO3qu=2b{{1lD~U>&jIqf* zfbTGzuEi%!v2$Xu^t$@>(=rQXo`th$K<`s3I`e(zp2YwQsQb%w+A)%s^JDKB9{ zQ)hp{`H$8QDiGqV;)gESvzyqIm&YJJblCKFLnd(%F_1@Te}I002Q$ksS;@N7S*k$76BvNy2?XaP_-bNz@m(?ki?gNAbm4&1FoT|=@by=-?3R(Qq?1{2wT`1S6OdwmB)bQyd&WAL z!0CD+@@6id;UL*(1Z(}PC`!48Itd%2v8*`w2x)9x%u4{RAv9~W(E+n2M%a6a`6T`P zDi4yxp$V6j`B^QhqerWrLA(1uJAAwBM_Rn2PHU)Ki!y=S>j#I)N zRHt<6@D6ZK#Sm~pWR*C7pIxWK^t1SC;S#8{Ee4*`varfy&xGQ^DDkz~i-@(}gw8_1 zS44pi{pzx+O=&kljWaDOg5x7)DQEJ87XPnKi6>O}IF6MS^N1yFQlg-knul-#Id#c|4LSQLslF9cYQYasC-KbfVWwyUj> zXK*{IpR-PIS<&DxvL+~enVqUYpX|`1-w~3Uxiz zC#&G01c@97FIHxMVVx?wExtM1U<6QcX4K}UXe*@*eQiE8v{xoNcao6f$l7HjSX_b+ zb8p3HKj1&VRFc$pZQJGD-)N%VkzKMh=T50miP-cLw@AMuS?VF0K@+TTdjfC9c1W(- zLDhel$}aPk3}^K$-j3_n%|^(DNkg8FdaHGy9(Jz<5L@wo`!IARZ_6U=$Lnzu#)&PT z>+kNR4o}7&ue?8$NU_aO*@|Q&trqkJCBC2UkBL79)%1$WDox={i_V*Wf9;{Z{jSNX z)Qub3SBVVf@;$-CUrjGGAK5UajU-&?!Sq=H=W#1+JjE0_CJNDqp2=wI&1hOS<|K(aR*o5 zCTGh|p^@SnBPI3X-WZIdD6PAAi2BXh73B-wY;J1^QpSAZtt=R>juc^Svd2aDfP(oP zc@(H4Z5M97qHueh<|h^Z9V zSxuA)qwa}HAek$r;ck$4A`Kbo371`eA&2fe5jz^9ah!~w;_k^SNboDPWVY^Nh$Tpz z>6C$gbTzMf@&bwyMzdlIqRWPQ?d`DT<7l+3!hx8)>|uv;G)Mo0bP`VgmAXzge;qA$ zN-5>@@iiX8%7QH7x#Yk0WwZvi#Z3x6H z+_P}~b6Gju?WC7%M)H9

9;g^(C)R(GL)B8@x`X0%>rfj$8pCDurgSg z$_t~s7DyGYj6n6mw%z(w^d?Sz8$4}37;;Qji^KB{Nl$Z^1$o6NL{8^wn0N$<*U?#j zs_7eQxx-s4OMir&A{7K+MmORES>3Nydwos^Uw10D9?{a> zI&Z?QmV?FG`RJI60Hep{@+jpVKLqw;jH@R?l1z0|2roe~9@|NJRfN_wQ(`Wt451@E z`|CwYvQRF{C#kg_@Elkb*dZ(I1PpI~H$fmLQqL|o%zo*KyF$c*YZ482J^LuX>RK#6 zJFRYc`%Tc<$5P#Ax9}TQnL^a-!L2c)=uL&=iK>Yki9V2goxy=^2Er@>FWQS7 zV@gPya|KmP)fN9v2Z^Jd9(6cP8}(7eG^9(Fu8W)|za~vUw9~^DZXa(AXAU@jAN6&; zWcupeM+Cx=&Y=@<8GeJbs0q#kFu)fwBdhiqVLMLZYBYlQ_t)SALBdb+`*d9cmsyhnaU&iV|utVNd#@v}5Sv z2j}~j0y2R;X2%VTm6fJ{RGUh`JA+FX|EzZzHtYH@{aAuYM9-Shy_r)zXNz)vRd+oN z9GvbSpX*~Oynp8t`Fjvr^X#gWra`1%$rFr+^H<%lfq16^m{9Ya>J!K4ee~`{EcNlX zv9%K-{-i?A-CvPIluAK4DB(rS?I&@zEu?0ynR}fD>7&${N3k$}{@*-;J-(!wi(a9< zacoK?%jSG(7rSn1>$nbDaBuI|5`J+%X5Ej#L= zOyneWGLuJfw41AQl^^LEJCx-&2#Sa=`2<>|DX$O*tXVy+muKg3kBSPvKJ{pcO=RPp$PU%kDn^1Mvz zp$qRQt0s^odsDt{flLkmZu=;>3EoF@Pu126t8L$>3(7=!aZ9N6mqt5*pLr0J0_ziZ zkT(aq_jM3|;cyUxBd`E6d(}2#0Yk7*$__Ps__0Ns5zput_bqCS*DUEHPFoV zg`nDkEXq1o?mm$Rn0>5X4VQ^|Y1k_x)oxn$sP#-B-RbnV-P=v99%li;(?G}9ENm*M z@=n{_b+CVbS!OfrvYAghgRtOj7}^v52ITl8DQEQw=N{d@VLAfHlPaHD-%g_zf0wq@ zxk~>+RdDQa;g5wi9-XAFp)ESR$L5ED5+!4}S)hkp@`c5-T2;`4r7DF3gKR(G`}@aT zdl22>rGXA4g0g1F(M<=53irf@szc8F}j&BsRyT&7N2IC2@Sx@wEjql~BsjPmWf;(ZQk zFsDU-q-pY|m7qZlZ~py8;?>wQ*&|4yK(*+bJB>l!e($VQ+f!=1%^Ab^B_dS7w&A_v71L!F$*+;{!Z1oL~Wq%?^a zJ{v2wumQ3J%_!&w&54uR5I<5#k$4VmWahNnM~}1|H*CLDUm?ZJHrrjdbaP^ElS6$- z_a(u71y!~04Up+9wf$Zy?TYm%7ixxRxB;_n`i@U%z_=T4&S`(wz6HXn5Yy5qmBfpG zh=)8mxA*T0C>4nx^{s8JCI}%hGo@=C>+<3;F&I@NEUK!FZ~iJ{!6syIdRfIuK(|-E zYxX{7lTnSmK@C8JOnbi9boC+@s?yClnr%}OM9aROx!uf0Z3S|FB;NauaHaMrPpB;wYTBK(RbVq`TvIBMPTa#F z0u2rhFNF4jE&(F7Z~NhYSVY23={z+4wWN&A2j?67+8g8ITZ%70XEU~RRkFP>t!V@+ zxwYE$>5JiX5lh>f-<^irhI->iKtWNV09#0)vNzE#^R1F9#x=W7>;iRdp9;T!a{NHN zVPMPmDGc!$%~9Gd=S(zZO@}SdeY;Z*ze4B+qYuNSL|0zWgcrcU`OZ0#n_rSj)2@`@ z8KxU(lBWK*L}Flrvjzh3bVp{BU5{=$L#?kjRm@} zys~DatEn=MwklXu6G0OqiF4_FDzVK8s^?kj7_h+`aebfv4Op(W$26b%*zeG^f*rP2 zoSHo5)8BXM7Kdv1dy+Iu4EVrNaB4-)sGQla6BKt|alNV&GNmZ@HUa1XEMce+4h)|BTQ(g^i5^ub z?9?UhibuR~d&HQwI-HgoEy1$0(R9C!VFqcDr(8MjmF3{fh`8@5wEd+6i-LfCe0Vaa z?*?PlqLDETY&-`rLaADR6$rdW3jX99ah3*TV&*Dj>~zn64^ zEv@cjws4IxxeQT%A^Sldf-{D>%CrY`0#J_UC^btbXV{9@a z5u|is?6hNMsG!5AjL+*xBneCjLVcS){cYtvj`*qk!9{mNXt>k-Eg%7dMe9xHcshp=O;e>q+eX`wrJLZe}SnmCgyz>zfJ?u?=vFGYRc z(~MOhPM8}lG9vMfCrnXo*T0lxl0Z)@PK;mK+X|CeNUxjRvmN`FtGpf66tGD+(XQp0 z>i!W9sLc-jB}3+aga?MbR+`r>_DO_^Z;E^$YIN=KYeK&&Jph|#p_ZaNHIX-3va~Bvd(yq7 z%|V`qSQA~FdV|R(yga28uMWKHRa9;E!lMtC3Zgqb1kM?wXmp>mZ$Y-I3C37J)|j_v z9JU2SnghcpQE9sy6~$H31Fx`jS=6#>dp{Fb=f(biIu-J*Ox}MA-;D;e&ZG`|inhe3 z;)%h-Yk*&n0-k~ZYHAob=PswFlN4PN-ekRkjrW5l6}7wvR4xgTC+Kc9(gyw}uQD^H z(O_yV7_JK;RV-cm;|r$pO3oZL<~P&?rV$J7;|-V67b~|p7~3}F-OY1Aros9+*hLu{ zt@UqzizITwoAQ#)&yYmE`#c=ktCClD>KaKMzv4GQV3cM6IMeQYwT~7-zkk=!P8ab* zx2{V;0+|h93rt$WLuXg<{P>W)R^9ao8mdmj&Y?Qr(U?VXFp@DXGO1d*vUzU4miW!| zJ{xH4@?h4^yrG8J?7DG^71S!Cax{Z-_-OC!i#j|sN z2^ra-*J-Nk+Hh@NRqkOM0Fi?dr4ErWHzTrYmDmKVGho#aL&R@kPq&p46BxN(zyhsa zx4nd+bWXi1bD;}+`%Z4TgE!+WIf^FPw!2Y4DQ=n`IA6PJ&wRY0Fd#1vQy=rNn;=(t zTG+qcX(f!qb;~LFQxfR+l@P?{_os({)YV30Z=fD;U1A(uJy1KaeRt!0o1>LoomPg=@=!FaM>aU8OGE!9y#Pmlekg=r zNG;p5sTBr=CT|x$9zoh}Hzo{>g)Ltdx@qg-W!9L`C@IDE_#2AFV1cm`u9*oB#` z6198}1{m8DeR5D@a{SQllsx?h-43=Y3Qr?2zguiDlNA2Q1Fg=K8up!Y62(7t%j0l5GRA-gt=^8w5|l;Jo) zc*27F94z(HVwGSGnz1=K?og0nlfQm9$@XnPElwXrTpt@>8q+!C(}va6j}452oggD!!|I- zK3|Zsv`na&Zo9j#ZR^(U~P+FRDUmSvrLB?0PlR+SkuHOw>*2A5Gj=}qKo&-@fTt}tA?EP@i+ zR6pyO3Yg~?sh&#D+KEIDv(I|6s#h3#JWFmvzW}3CyY0JwreTf^f2$F~K1K!5 z70T&FGwSV?X$%)-vG}fQ@SHCFCJ%7Ovv!unErtOhk1t=x81n^KlF0YA#kAsuYNJo#a;?C>4_kp zvVG=ru9m5QW!(?v=S?cHnp?RM_ z4>}bmsHAUQiC3Flt8p}9m{@VB=yvgAmxI!pV_TT#Hsh<3on5IbU4Jmt;p@EHk`!|R z`y9SdwMXM_7^&g?+nc1te2p^}Wn1`5* zO*;CJrqDBgOeR+TW%N9@cIZlELgnv8?qWpATI)9mVs2VBXog@7tOpK%kGY>?Rx{(M z!7R;`*od4s!llj?BuP@`Phw$*^bb}Bi-RXQhSkY=Pf{8mZE}3yHoCHxA8RlJoKHxf z`?y9|Xr6h7`ry~2SlBv~XkK=kk|=)-1Rj`CA`I1kJ_b{nLnKG_G-{nr2Q#eu;~xv{ zmRl4O#CD1&uvkpEPfETTlpzZ^Do<$kKB`sy2CSmqz8VL@I7OIX?B?pBw26cH|O~TPFwn*`q*G&9Qr*sOE9R zEey_oFgQhl0w1xn0IOrh(Wiei5x6~?hE0|BR6}i!j0_wa7&S*uxX^+ty=sC*zS zy+*+jE=;z5(KlFVeK7P-EGkT(Zui@H=YP^DWemsp+(H6GjnsP{!YK#Sj@?5!{*rKws?2hi2x1CfG@g z%|x>)db^Of*77vIlZ@42VJ>4p=UpMgBuhC!hQC#RHDdiSMBjZ+t@bEMGBK{_tSXs* z_R0fY9%fXuRjh8_5GQphy{*M#*h~<(*%~C+6^Np{6gWgwch=R4qI=IQU$ue6CN-n%l+PfqiQ2@xt zF`WcI)T{dJ8;gzZzLFsk?Cq!L;E~RX$Je7&xEk#Klb3?CTz{*)TzI(Z)a19oRmjve7YyY7RboVGT{ej5~;Je!?s z(a$G#Rs1j%>4ziXZZ2!`YwR>+Ijf9UE+J3Rf70r4qnktElvV{2bgZPfdy;D!4GEo(UAQKBqoWyC=(-xE)U=0 zh9;9Q6f%|n>e26we5cc1#*OTifn2*y+)?c|#)Q1irG6QK_#hnR{ zmW>;;BwY)EO}9W#3#)6tKG>KMc1jo76wZDO^6FP_J_8akFIZ)O4U`L257voj%*w#+ zU*EeIm_g3Caw|Mkay#^Y{L0)p@x z9cR=50YlK3V3Lh4r0EB;g@k7W<~@q9b_LgP-4*%L2N!{MZABl!?r{H|G0VuJLh$K` zXY1hK$u5YWP#d5A!6qrwmb^CdTqQz^pj2l#dLTz#>PA<@G7vC-d^&Y6C*$Wzadq7n zfIRj~jmN6lqHDq|oJjm=F-G8InB+Bu*Y(`@8>?KKcLn4O*BA#^9i`TvH-d0pTKit8 zmV6#^Ty49kew(+beTJ)@FBIo{OXn_VR>{~k3bZXXPr?AzyY`}?nxq3IX$=BuUmP&0 z-|H%?B5J$@O434qp9b0aJjg>EVn7+dr^Cj38g5o;!E9cO+)AepPt?eR8a2Skzu_`# zn++i1mw{iuL;gIex)56_hp#8|&gX>Vz{02$+eFzr$AB-hFn(4?doq=I9)7N&r=6Mg z4k%m~9L!FZe{^=&TI&U^7PQ`4LOU>%8ewvdSZ}&XDafLKY|GR)HKhn`+ZN{nII-nd z?R}dPZc8*p( zD+reP=h4u&Juj}|tp)d{r1Lo#NkHP85DSH-M%t7+khe^H;t~x0M0xX}jc`AnGT7+G z(RPj?<#YYITI<)n*HvCU|0BbG6_FcWqT z@OnSxK(!Reb#o$6?x8l&16SI6j61 zYrAe)xI>)t<5bt(hQl?jwG(5wMoY19r<8Malt|sNq7=#07uT|jfCIv#N6=AX9CA4` z5=dFO{g)hyWgFV9yCdmD3VF==)t6*2D8Wple>@M!p)cl#JKiQz^jFsX*ST_goJui& ziTzGLN$YF~j33urhxNLmePRcH+xAhyd>kH#k>+n(IGfZc`HGSGnt;5~?(^9_n%4u= zzb+7t<;YR7JubZ`gSUk_e53aGSUXGfI6RX)sB4*Fio`bGW&Q4TPG+k3U*dOoj#u78 z-SO)F2G2csEG-TA#(+T!0xG&+vbdptr;VG5ZC@lI#&^)|V0%j2Aq$pGHEaDpmM&X~ z-%E3WSlMWJa?8+Ap}MWc*SosiF^oaoG|-c6Vg@n`{dz0(yW1!-nnTinBMG=2_9BKN z{y@r6RF^GKcPP ze2i7wC!RA|QZB@%fLW;Qqsl2exs)FUN$1R%3~*LhvwnXqx!8>91Q=qa8x1(VrBvVN zAyD69(2$SeF`5@RO4B`iC_f)FQ3Sgxwl!b2;;H5Q*Dj(bkX(~t4xs$w`LFOCy`js@cX%9a;uL-4b#!JP|Z&L?Ce@bW)MQX--Xk;|?% z@>){-boj4~edDeg^!SE5wCP(XL8Z}XPq>L)S5mYC%HsBHNuKnxPW zd_eyRrt`2$x)SDBumvf$aUAvf*retV-Sh$)m3C$V;j!bjwHXTUlB6Pk3ir$D7rOd{ z11B_R*a{-+iQb)A6SyPjCg3g;oQ+Iwg?-ff!E~Ls_2ts;8j0@4hG+Y_0Dp$ zueD}#M*|uzZ5`czdRO-=z7uvDR-oOFJdk{Pp$Q~l3vbbT zbKRm;H_K8rFbzypH?cGbR~%e-t#l90tLHvNpmuhQXjo``Fdh)rHOfWCZ5rHI5hJ1s z|CJ?fjsS=wx!?Xl>NIBdI*XX~)&;|W9FL+UxcH2yKWYMhy{bD(TsB98U76O=;PSKp zZ{!H2FZFY>-3q)dX$(3`<;t%a4!UX`i6VV8ueC(m0Y>!#H>~c-R_L(nVHF-cr}Tx;`y<=dX#kCW@uW8^z_(*y_w@<~F@lMKtuFC@2>~ zBy!Ip2^o5S*>Ny_+eY5(bZj_%Aqq8_CNEbJn*iU!`99+|xbhWBH8epF=-v+|@B8ZU zVd$nQoX$ai-6Zc?!-8?Z;=19&L_pUWgzQsHyjU#aeqm?aT*sj78IO}&_Li3c^@wjt zH36AW%?-V?latMiK2h|B;gG&UV+yv_hP3htGG38?r>Qc}Shc*ta9*-1r^M4*p=q&V zf^s%4Z9&$N=$BfMdMlwdwL|h~V|(K~k$rg%rgpex&uce`gnj&f0iy<7`BQz*5rqTV zfUukZ9cPl4H@Mx4`7sPVlSUMCJBs>mbvUGX& zwzbCf5utTx-2G==bPcxIm;3A=A9VU|sw_(~2i38E>jhny#GC+=Wd^LLbB=nr9&14&g>%M=wV5pz~=4$e;Bn`KK}{ECjwWG<;_49dOC+yRp-2tzt4gq+`BJ<#(EE zvcgVt_3o7d6)(XWI-Pt!3~%pNZ!gY&+qRV(H`$hNSm5+((XINMy2o_&I1qpu_h&56 z*mi+ZSVO5QTd8{tY_yIvt!(5#vWauHZCR|i$LcqomQ3KJ_$u18tow2LZevXbsPW+^KR*TXN7waXS%?kF#5p| z;tFalJfCHPEw5PFjP_D9uS_rVT5#|#ez5;O1UC@ap(*|_BmXdh({by83As{7suYW1 zOoHrPLO8WNtKhbzsMo;Z2i5kk11vB8w`QKlG^6C00>|or44AKOe5&Ln;XxOm9UJbW@T-ER<}Zd$BmIO zbjgyvde+{gRDssC4k@_El`3k~qMbs9&f~9pMJz3G4>dAxGUwbR)~O!EM;)&pY%#Ip zJjVrH{DLbtge+&ZBl9ghkqun*#+}=3A1S=_V(tGc^tA=4w$l!vH&+(P^fHTN+ z-PR5tPOiamzvoRyxgp?f0&RA@f|%ZS<_feZIm~*s);D-;OMroNF;=gjc1f=vS|8=o zFt^7mdr-(7N?|J9^~Pq!LR9uy=@3#i;E@Y_PjL>HIXEkMmd0a$)6Mbc1^5U9UR>KL zu5VZMw6lU&vU9)8-0&0Eq(CWelJNXvL;q6C!YARJmxkjajs!G?hT^v1l-kz`JJH70 zelFc3`4{16BeHQuyxK*%IESExx?Wqpunb){P%FZGAk`YlaV_q)Sut&1(-vlTzL)Ji z)OhxBl6pSTM&`EX*nBKczCS>M4bGfNZJpt}%)3nF8H> zp{nm!A@hW4l;+sN4gIt~Djm;+HQq2>sUezD#NE6XDJ@=qk~By$C(_ALq}pf^3;&xS z+wt^x#gf2QW5L2pu&6Tq<|*4DYw@3-_Emz_Q7*U2!ZFZYUl9kfh*V8)3g%hljmd1N zdaHM!apZfgDlU4BjeLXTtz@=XSdKYP1VBgnXW8^%71qM?eS@FD6Tu`ok0{lygkK4@ zF`1VXp7&3GhrOO;1;JDymiJ>xYk$~Q$0_AT>_dC@OZ;_}^JsI$x{gHmqs5Km4JmXO zJGKH(ldWte(<@lGK=Gd3Q$S00t$Xf(M-X`A3-lDS_tI5QQ_F*;JBz9LD5%w&dR-zd zpfvd-4r2V9&Z3B$`L#^1WVk@upKYYfP)i|~4g?y1xWov^Qvm1ZOp>z)2{ycuL3nCc zI6ahb0Kfg557A8u6;%m^wC`2Mr!XaD#eZs9Rg@V0yH_7eP0428aX#G3NK7$ZfA68GaxVuFHB`_XLM*FGBG!o zP#pp)f4XCIW?i%;9NVfmPi)&}#je=4{lvCy+qPA4DoMq*jY__H-`lrukK6sLzy5K? zID4(N=bCHHwf8tb4mq)+3caw2y^*Pey`2j^GXoP3KuuXg(a^@m(8SVSmR{N3))4U5 z%nnCRF6v}z=wfMaCuZnk$^+0aH35j38Ut8Ze*nzf+}v>F08x7fPbW)r3l{*@Ukqwm zTDt$T{1XB&^88QF-<{5u=5_#zzb|g4Hues-rgkoWA^xv7s+gJrTr5lhW|lUl08s_S zAJX!Y04hm&HGrh4ovD+d4M5S=$i~tbAZuxCYUgZ94KTBJ0@(b=0$^-!XJYwJY0eCP zf3bv}0fqo)2UBCqzuQbbj7=T>anS)BOr2~kot^)_11y~Z=1zuoE`NLAVh^yiGq!Ox z`G>$?yP5sJgdCjg|3=vU_5B4?w0CxKHg>XfZ~^?yswgJ$A3R+w3|;=o?QHqi4X`)+ z8);&1?D|hh|N8#I{PnsRTG}}STueP&fBwm3WC}2`bat>Y^!%IqFPMXq<-assoh|Lm z|BC?~z{%9y(8a`7-`wVwc5saUjEc0KnLU7+=|Aiyt`7g{b2D}Nw?S0@%nbEk5{4%Bb~c^>e-l$P zI7WGUm%k|iRR4D>GyK03`Tv2$|4#(|eW237}_YV)}1BRSQdFYrB6M&;B1S zQ#+IY&i$`M|1xJ(l~WbfP^SIg@6>|g zb8rCYS-4pL9yu0f05=<}@Bbm=zd+3YwU#qWcJ$8GHDvL2c21FW^87?OJTW#p(sv6vaDYdf8wX3y zYxvDC<%~Gl#nZs)p~?6Y^39Ds{>3PPv0I~}Bg5+|rjgWq+s6!ie2wk94*{8h&#M3{T^{PPwIs*_K1^G5uO)mn9-#`jHgk&6yV;>WQdqi z)k1NP?kUu3fN>;Se<#YEnN(?F}rhX?4|LtMe-rPELzZ&5sJc~BZYD* zCjD(?r+SGZ;I{GDHYev7-*g?`Qllk(W(H`33B|Y~{C#r5fBXz3PYA&VIm+QZA^b!V z1~mrZ{}5Yz7tc3jk@JSc75A{3wMt#s*o~S#mxelcROj){rrq$OmR{T?;0ZyMB>s#2 z_IHaOvlsv5bo-+zL;Zn43R20$-l@TKN9rLG9Y(`mzfGWYC&K5W!?i=^!CWn=(y@~U zYK#nlo|^KVe~sF;632NPmIA=Lzh#F*K`9qateH1O%nq)@Kv(`mT56`qyYz#$V`pWC zbUWwNKbK16?-4y?Obl$L34&d;&)nMQ!0quZ^0kW5|H8Qf{btm~Wu&bKWDzG-2&ru(9HD0xMj5J?D*CdN?lP{Nnq zL_w^&K;1lp3R06{%3JJ?bwCU{{3BLOP$;tBJi0WDs6B*%UG&~jt6dz5gqqRdj zwn4K6Gyi7zomjjlgPM`Oj!F1Z zKgL>Lm{N&6 zJXy_$vZl$Mh3pNCeM&05bb^{@sbWDS8~gD6CLqn3?E zL5dwkTI`8v@zzIE=jjl5IKb*TFFzSwEumyC6t_7G@GLWdZKU6}g~AGK_b)0rB!8O= z=PwB1X>yJ};@r;kHE0x{iV}d&M4|w%gQ(}zc58H>@_G4XF68N!ao^MqjJ9=uLs>A< z`=-GJfEi3#0xaf8mu~YGeg%}MMLuH0jx2OLIQVYkE~i#J28MYV8nl*UDAqYB+Z6Yw1CW=a7Joz`5NQfem&gWX{~FG#Wc(COR1_S&OMc5(L0VwB zXxvSe(c&3x#g)5yWhBa`4pUMCDh7s1^F93d+TOR(4}@&5?>_3Oh=X%;b`V|&n0+CR zo84g(O_sb{?l`bLZgDq4VwbIWLR7U7sE`iG`?QGaFEDDEA2 zY^Dzy`v`=*S)t>TI`S&!jhg11!LJ$=fmO=Wv6qTcDzk@^l@cv&0#$9X*IyZhhwJf( z!vaRl^d)UN>4ElY5z#f)DbEK(FO#H`i4*;ie~KN(-YcW&2~?GdGaqGV0zjRrnv#A- z>y?kW$%?lbkYet!q8AVJ)PI9#=jDT2&04J5k|Nk|8TzDzWNJ%P_0HRO#M(DxGO_Og z&0Zp(n$axXO9<$xxGp2Vy)fpkGP0;ZST)wQX`MQADM<@)Flz~#3e!w)x}0sU+Pvn2 zrk2t|lL7^|ZhvPEC;B91RG8hbg$iWQV;N*QTjkst_aM-dT%N3^M1RYikrEw-;u2pr zL2=*;!Zy02)C~LzZtb*7Nw^WDMp&YP(wb{^rTSr@dER?y&`+PL<@QjHZ!M(61im=e z=$ezn-;=779Vjsb_xfypl`d0rtaKT~aC$A#h| zfYuL%BC>Kw_EhhBc1SeUfmJz`ScR7!qgwJUK)#D^_+?d`0e|=gTt-L%FV>tU+Bc6= z4(2sN-eoc#0k=n$^0+lKe_XOOw2rtqv)~mDT&#JCx^71Ml;Z^N8G^SSP0pfrkf8;7 zqlq6yDIy#Q#*vau#sp0=jhhWv+=JZ1sTg{`s|vprP_NEVm^lr@7O2Z@kyBwQ?`LTf zW}H!s5kZG2wtwC(XAyIn=;Z=@IpErz$sEUE!v~7R0ockLR=P%wW~0Guj|Mh4v*L0# zp*M=*JsjAz_u%y3cU`CY4Z>uow8z7^UPTx+ynAPdta3IOR33{U)5iC^7rct$bUsIq zOyG0FCm4%YUK#K|hH0`u%?Iiea zBq8|GX>Wx!T1~U0a@15=F+`n>P6@X`uo2|Z#@b5L=dVLdIR!zaJo@o5Q7tJUQJ(-` zvFrS&fPa6UX6)$mJ}Q&ngaW1}1ebYZ8pSP`zJ%aWb65Jf>D+_BPE@5bu{D)SMtl3s z8s0RYnGP-qLM8O`8~pi?Hn~m}gN{HyyP@<(;8y{Md#cQQEw<;Um6bii6-tbg2!pIQ zB#kSmK(Ty@+TKt>pO%Im89YNDp}zr^+#+Z2=6{`wn=9{eEDv za6*!np(ySfKNW>4K|Al70ijS`{IdBKi)JN0ny?Fs}z9; zOn;q-x*q({I=(wL7>v$q>4#J!i9RSu{mqDhzQh<%O{9C;mjfM~_k8{ljP|fWkKoZ? zg-{DC?t!5=40%WP+M6RvxPQTy_$9HU7B#$M2ased^ZRkjNv{vxg1H19wyx2yri+@F zLR=yqYR;q0>Q%KXE$p|QX))5-6Ru{~^nb1d)VKvOX~|IRM)v3Az^^l%MI=g)$WOCs z)t??0CSYl~kFlloh`sC$E6*+FqQB3$hN$<97bCA68Am-3r)hA?cIKe0h`L`3_`Jn8 zUz^v>2>Qc0kmYqt@UGc~_-~JY-@b5D`;@bYJ8G9KG$7lK8uN%hM5?IujlC31H-FcJ z+!RyN(p-Q8JRZSFcals`V#+>fEQN@^iI}*rqNu z1Nco?)S#`XYt%CNWgKWn`JC{TMCT@v0b}_yosa@rpY=q@(OcP z7-WtoK+Q`DD5q3{hmV^(qclc?1iC)6*{EUIfw%`ZW`T~X=RVOe!%E64}wt6E=l9`Jtpu$bf`Ut~$ZR^<ABIoaAWSs~BQ=!u%nT?O=8Q*M3n0e@|bK+#*C!k$hQ!*T$N~|@B6yXauN2NN;--?{NzlWq`kcT|5~V<9xI%!56EB7riRvY%Mh+*V1MWW4>eBX=+0$H7bz z0ztx>$<(okSTJ6flxcR!Tt@iT2gkDa;VAOP=PlGpiubZ)WdUw&pkfn~K@IKcp_BIOG*wvXK z0IOe?{}ownt=}6f+dO+qnDt?oU1hl^4e7iaxE@Qd?u@hze$X~6EXvaB8f0vs^C9Ew z!>g_?Pk-MFPgqZk=I#`)6fjqI)`j=`joTUyuBssh>X^2VT(awelBrBmv`b z0()G*f+{$u+X9UaOs0>VYC>Ron(Tq!)8%@kTm7g}ena+w)O`8~hE3{eph(<7;-k+= z8e)g5TTb+xd6Rbu5y4CYTMiY5U8g@;JjG^RmVffPpukh2rSB0=V`iwahSWkh*R>kN z9L$Tm&=M-tr5>HOy??fEW{J__mPx5IiJ*wyDbM8$=qs9qW=H7F8o7gnx^DapyE7Nt zGX=qY{1&E=mfwm_u(}dNi1_zTu~tb@>^KTSN%-L-LyM-*vdRbVbhN%t?}ib{w-+xh zT7Rjq)ok+|Ug$j?gI@*UK0j-1GFFi=R(I$K_+*#mrb~Q^TX>h%&KM|p7KDwxbumhm zDg9*OS%10TAB|Oet<#pa=_`Q8J=KQF5Ia!YE)t{SxoN@=m$_|*Hrpy&BZoh(85j0B z>o7B(W#W!e<$f3KP+7Q853{|8V1m!k3x6?c@(DSKPr8Wca6NW#AIuT8g4YR_niE0t zH%hQFvDbu=aT$wE#v=r3@JGX%;E2Nx5{4KcPI++%(CHUG%iyplk+LWfG^eSxtqQ)b z58UM8yljr-9eE?Qi|_3TVENa>$6CMzYm$c^ozxZ!E{nUEn8E=G{f$-KdL?T-+kd0x zTWxeWIr6<#n|1T>7fwfru|FqeS!{EnnDPm>OkKR*RMsD?0-ShT+pJ~z7#Oref@?rk zTzXj)L#{m<=AP;HKkX#-bfHiolQ<;4ycsWvX|nV}r$`98d|%azdodji^-hBO-`K6o zNzW!V(k0>Z_V$-gVCdGeJfRc6ntv_hOCVS%DyM=OfY0hfGTr1?_U_gxb`i_5t3*7u{9pyd6;an&Eclj$vO4Lbach&at25nK`_h=1w$ZCFW% zE6Cz?z5LxEr3}JD7arTo*;HS4PH|Sm5`JN3}hA=HueMw%7F{=4qHhN zxW)}UL`nyJrTWEIUN&tAIDgQO|8>8zZd@do*nwVla-_kE;PDP>Q&^osa+(WmLyd@c z8(I36qT2NboZ&^=RsVn`o@b>%1$c=U(Lq4;A}e%D zQH!5h-LYdYPds#Olt0QCiY->>;aqaNmd%TFOQ`l(MZo@ErmiLZ8NS|Ac%fRM3mJ%?2g>~~8W z83=lV*AHf%XDXVgFkf)LCG&Hy`v*foHJ5^B0$bCCwL^N?5( z1l8q#Su``J`h&3T{W9A5`L^8{Qm$=3fL=Q-*>ysh%9T$#BccDtB%3d!vG`c<+d#ne z&uoTHrxqf_7S(?Bg3UQNs=`yLE=~E+hXMbylGzt-6n|iodt4mUIng_XmU4K6{!SL`$qg z-Dp3@W>HhmofD4I$C|HDbsK_yNrxFjo&1P;kcLZr6vWgWq9mRVNrdLb9nSufv9NHd zQiw^c`F~wx=t;FjHV!_{b;8D7tmeMk-Yhms+2sO3#J%A29^{{?*yEiNl}mgqH`I<0 zYOWlKG1to;z339Xod~L_sD}j9i#NPbh(8t+nkxEIv~&d^OSU|`U@CHBF{Y-4S=fVC zvu{XNibSU63d4eG4zj2FS$FrbSA1g_g}!GU4S!!>2Xr(|u;b`1P*2oHs4WLbaTHSB zfcqgaGwH{{p!bK|!;%3s^{{r>7kB}3sKk4`tEUb_aYl@N9DS8m`WBzGSYyQ?g7i+p zdc!JB3mz^GxWLY&a_7PjPHYKh;kRg*ml)kbU(gvGLl8SZKPz7XIp;Mn(7CnWm~0c^ z^nX_l&oky9>;tY+Nf|VlD^x41>@~cZ4FmltP@zB2?(SjE8|?u0E2o@$m>YbE<_9Xi z`ES1J4BhXhX!+In{V*Uw6{uyPO7>RB(Ov0WjO{-q*cH&4wr8`(ToPX3p2ZGrOX_vinA?XKB`rZ3qFn7)=4!EZw zkQ}F5L&&kH;1N*@E(YP!jwS)7bUe63IBB1oc}K&)%c7r36;sagH@^k~@-r>R-A&nZ z%+P!{g}4uDTf>=m=UnQslx6h<`c@%?P5*vL9MFV24-ahBll1cz)@%YZxOcI zr+Bnx64I3-bG$hG1Aa0~2uSD%599`zP$yss6GkCfsfD&aVF)*fM-+4}E z&E$G{ce><8&cT37Ju?mpz6HEX(OqKjyEbn9NTe8DCsDM6o_*#DR?y+ z8W5j@7YFx4xD95el5{Whn*9!T0K@H~n|ExX*-@4vCvJJlGM}SV;$f`vAEOjU`hha? zL(TM&37gHZ`-ahk|3?J1@bv_M3U~SQii-m9gZMpAHz3Q_A!A5KmVLr#-hb(HYxMP@ zcrK$>n9SkcKVcir#6U3_LRC0cW`5qmhL$*4R}E8U5gc4jz%4wKxA%i|j1Dq2`Cg=R z>${v-^~}M~p&#|gRZE!X^1lz4qw)tx3V(YMU4^EWK+p5owx`#SJ|OPX_b$38bsy7` zk*g5`!IvMti3IS23xnd634fJoOJWjO$03U^(DK1dZfo=ZhyxWU5GK6Mp1w8nhs_Oi z`^GOe9(#e;ZzCwjHm0%UCjVt?7CgdLr55bJqRlaLd&lqFI&^mUWK;aXTf_+>l}{JS zf&=gBX#qiyBASDv@alyV1YDqOQogtm2$WFitm-?V~;VwsET!N+c&q8jHZ!k)Mf=dj7t#VqR& z3bsFXgEYqBF)j}oI2YhI0p z+tiDid0}m`?ACg8y%c}v4hQG7EYmi{2Ax)8vCzYnVhm0_BN!Sx?p9&<>9O}th*4#| zf)GbNAS$%4Oj~hmQJjlxDUHMHCDt;}g_AYeqgQAsM`M!;{yJLVd8IT>)X^nsg^J-x z_r^3MX&WDLZ-3?(o<8bmV=33$h~JVE*=%bojQtld)eS4FTroctNbARs1AZ+T9vwn> zdBzE$b*#T!o}v$XuJc)!jo7BI%)Rps79~WV@fs&Kq|+YUfm-bJG*r&23|;<@c_FPd zb-zyr81E|8Q_b0eNIr2)-G-Y@3Jb0yv#K9LC_%0d?tkV@I6VGb#>ZK}X<d*ODm>cBs+pbHtbB><-hS3ig zk0C>jf`3SH7w$i198xM&_n;JUEW=L>%w9lM(Hj}sD<<#62$Zhq3CTb`mpcS!QWCMB zN9kmT7^*+BdvH!6{4#3Feyf7n{_?kW=uUKOiE9@A5XTqid5H`MtchLw^x_Nxd{&7?<@jGoxF513#05Yyz7^ z7ww_+i0oDCj-RYymLa=>0=jOWh*x$6?bc8cH#j%6>pyrlaGX5y&lK!44@x!?KY=E-&%; z>VGlO3H&^7iS11L_FJMwG{epwy8gfwZ9qzxaMK~^U?;GtKX$8jQohEwf3mwLlgSNp zsgiVd&JXRfV4mEGQf^(z1R~~O1cUGTb_2V;KpOjz9Jv1tGqC+0HTD^?dAj%3gG)_0 zzs@BAbAZRv+g<>hCw^mXTSNP}baT!Roqv{lC-?LoLUy&j(QLM^O~xQ;MANhU42Sk+7T#-+c#c^|*Q2XrQ&CM7t7J18@PA;# z$VsJkc@Xnfx9Vt@nZr>}2wx%RQcJB>j@rgQqetKrMzX8Bom&V(u)%>7aznw(Lg(sb$$#oMmZc zu@rl^bc-O?Yu%2Ja(l3%`CjdRPk%9HAlj@C7#UF5QI8z<$luuxU9LB!V{aL!tyjX@ zWwbA}9EbA0A{h|0mGm@~`;da96C)QTl1Q}Q5@Gf{lj-KtwjOf(#1SGy%;pc_WO6y| zBa;49ZKW7{gWN|)VsXDXe~;%r*By>68PLp+X|2#mlGfIF0kMV<(x{)lZGYa5(e?X- zJ+f}?+I70XlWT0ln1wVwL@I&g#3D;53PXOs_{T644l=QE#?_)b((_!h<= zP6o9(T0%b6tXnn@=eMw{FzZ)+gE2Yn`E8G&I=VAZ+Vgj21t%Hz!W4$5jdii&H+}ah zr@1SEgMA2mCq3c8fJN17oPS%ZPXwtw&@t&}?Fux*NIu3+orWK*AtJpxG; z0q-J5Or!Mvob3C9V=r>82A}BJGo&;Pl#!lmbi&- zNzUk?V@;Vg3zOn90)HAu7#-Kd$4y7>OAFA#8G&PLBztA8(i3Adu}*ik-MbP@wZi-s zkO+{pA1d<-(kdKCq(_^Tu4yZ(I1Q5}-iGEbFZ`>fZ~T39h&O_wsH3-Nola+xLYVll zU$+DEEqB~<6k6>CX2$2?rdwYaV}MqcEMsn&2zLKB5i$Q86n_G*Pc^Vl*`|8sD(MnP z$_4eG2=qBA&nLwGZ3mHH$+Fe^D1``=C-1BqFMMbt*%g{mWxB&{{Vl&nt$qsW9w)_y zT&K3hz%q*YkIhs~Q}Y#vvbQdn=*JcU$tC;SU)5GQzLTQ+tV^+L^J6<~#fiz(;FBif z1!@$QTnL`6o_`4?^s)N!g=u(wePCh!{1ehq`S7}82qc99Ht;L~_H)x4#j1DT{iVtj z!)8|Cf8gEQqpb89-!jTzX!nLjE7)*{kMwVVb~}Yd>3YG&9CrOY$0iS zHWuN~G6Is?WQ<{v&X5oF96!;x7+;WujK;x|H?w$p}ZNmOo6fDWGE7sk?Mb4^rLE*_Pm8(StxP$gX~mo?gRVKtUd z_-!?UCJfE6$v~gCCe>6G!wk5sHnxpAwNxYWsE{IyTd_+VR1wWWR#L5Ud|ZQof)&T= zO(V?vR{0PyqI8*79=K`7<_086^yB3T997i$EPve(RqY~Br6kAO6Y<0KP*LTj&X_=f z06K4Bw*9@&UrwH2kE~+m>3j=|=M%@AFP}XlMbkb`S`MWt4Xq$~aCiulHe4>Up-2 za(|liBxZN?9jbqSv`tcD$Zj`_qa~-B=ecev`27smn5Z_ zjr8po^Ni@#z~)%3oj<`PRYr6%_VC^i0C_k-*3_iW~hC(Q7@R2t~I+7%|sME)x6&8Zdl4u^3|UweFb`O*OMG@_Z%_Y-uShR0 z`N30vozi!Qt8UrGtny7V%zN|5yVg3)l^lQtB8l_kPonBnleawZTTZZuEzI_s&^w_h zpMOd@CBo(<{N6DygAk=7X+`$**u;ltK!s?m3*~Wmf`hQ3j*~?h3A}Pi!F^Jd8ogLwPFx1Q|}! z&RFTrA32Nz?OprEmtyx?-NrM(wfZq|fh@`j?BST}wvMYbPQ5PLT6V+|k= zdT_Zy=f0~)_MqoE44j2q8WQBlX>E@Y6iRoB?aVDcIf)xqx6gM)k0(XUB#|6b+;4PI z-^qoaB3G3_TUx$mh79$e@qdUv5HNfWjQ_s&e7rr`l!z&abqQ2bf;L=o?_+SZ%tjE) zaQ~Ejx{C<&tVWg=(`=A~BnokEbkMHk7J24I2f1DD?SPqfK7khDoInaTrv|(c3LvyhNB5w&oQ%*5&sT^o%He zut4B|1wXY_5`WN9pBdyxaXf{)v5vv8l-494Dq$31_qQP7vtS@R$Zq(f<&*81tt|^e zKVfic36m{D4^RFKn4ctg;dP|wRkeZq5AE5!XUrEsbJw5cgwi;-i$zrT?p9GxWMjxydTl(#;sv4|^KaBr$$~;o zp!{H~tbgbFo&7_qGf4f|P7szyKMRMgFkOnW3`@@EmT_uI{6WC3@I{rAabc^paI_4R z**X?)ViaGlK$=~wH}Hzf6}%mS?O12@sq|SsJx!`WBsQPy%#&jot= zHxh!LWn4j=pVHNz%vK9Rc}~fKUU@6#j7BMM1AkKxc6%Dsq$XEAU5V50%dmBCrjWoH z^F28uq*z@x)flp{+<|g80j@E#Fnzq+(F(k7*jjs@B&&|%0d(=bi&?6xW-Ku7W#*qC zh>@(J=Qx7TjYdiZZ^}1OwFD*|A1tN8wGs9__3ZLpj@S1=8=4>Zww26~!>)%*&eK)7 zbbl>V1=V=Py0h|Uc0E7Qpvc%ISLuQiph&cSj;>PQfE7ZKHJWBRpjMa>KhuHFOVcqW z#Q(r(^j0{WucDvfOo9V1_#`nc__D6QQ^L2D>@Hq97^1zmdu?mqfN`NN`jvpy!Fq4@ zoP>PgZ0!FT*>Xyo9Hnd1m6w0!H{MA}=YO_JexX-4@_v-BJ7YT55vt%n0TQ1a8D(_H zl12+O#=!y2;#kOa6p3sSAUi>q3=^~z28dbnrG8~+Kol%F zzm=get>lTu^z=Zxq1nw~Z8K5*BIxJ+kdt;X8*^?*An7KvL7%uHAyJ3b+0NRCDS!T* z=*Vv2LmM5q=aQfQK|4U|SS-KFk90t+**ob`rNxD~>h^4z%i4N!&V0JXhq@DpJ`15^ zyT=hB>%z~aVd%~^?in_0nZZR|tE^<%Jeztp-$YrFlQ)-gS4B*vbE7JMe2^t4O(-V( zLnC#YZV-s&mls3eEkJVEiz$A--x45Gfk_f*H^}NO{dIuBT;p17KIecg9%xK{5V;*yc z!-D7`N|ORUmWpK7`$zamQ_8?9QiZS=VlnYR7&knT1A@5rkb!4;dMLH>o_|`gG9m+8 zE#w71m#Hq7CKpp{v-}w1LdO>onb;NONNWur_R(Z+>A;yhZ~E~gB>qnapg`J+z>q*! zByz`08}=ama`G;27CpBxn7tf3IA1amX=ze5R5CE=P3%XYF^Z&lfcw3hR%uDUh7o+S z?i^+I@io{@{3WpN21^`s>?}Q2R6g7(EqtOyQ?JsS(Ppz zt9@NSN?QLG@Kn73m{Gk%JU*+|t2SdY-{dG{Fa#P2rcYVb&Cw*z5r6ux3md&cuF@~# zQT<$hk7M_z~ZS>Nh)HC}L6Cid4s2X)NSvy#y*b4ohK7S)7BNf`M>A=EGK9x8q zf|$^tyERbjTv@6~OMotVT!JrMw*6zuip0XBog zrhjs-N23vFIe+UdNpAs5-TolI1roEA@1VIzO&UgNPMGmUIjIz)42VnHC5#gSc;msV zvr^zluHq5vEP94VnKV|~wtx>TT|=Vc0~|>ga!Eli73jDB`R9QJR33yM4)z1r+2k9C zjhqy*YVqT&BXYE|-$9!N!Jg)kn%R1iW#4ozM*Pxh9us#T^`%#pfdCa@f^e{lRgusjWX4Vj~2ej*yw#gE_Ym1h(- zJ|apX+ZRw~toB+xVhKSMNX$8WW%@CYa0!jnktmd&g7sZ2GcANzhbV zHGlAwoP4F~BxrzLym7<8ynH?zsnnmNu2qY~AKYAFtdrR@62Q;8B$qwnK68t;*e){) zz733|)$QTfKv&@VgvS*i^m(Dlb|Hyv8#Y1{LYR9});5Lpp2+8U?X0`wEVeqYL`NJ+ zcrSQL8v%kEY0;_|r>JYVI|b~K_HjFXzkeIVs@<7uF+Ic=ltO{147n{jT_UW;8( z`$kmsvLm7gU=$P~ZYwX}LC->7yjWRD>#YMxa|W(m8=WGiinG(kogm)%x^=8-cz7q= zy+RjSh=BxkwH5!I`i_>J%%@)+H#IdDlnpJWdln)D!wGviXee;Si@`Fiz-6XGxlDmTpDk)XbVwhW%TemmF%EBjY%?G( z=~#XA%?oEm-Bej`aQzcfZS6xMPSZE9QoUhxUHnnQh(bLE@~Y|}F*yh=2}PIdSSAb3 z_q}ZIDDAiAqs86FL~Fd1ic=$wDSuYpACw{kmU-UOtUdmCrWxVIY`~1fL~I;?!GF@; z)Y- z&@kUkRHn!Iy?2Z_9;Zk;0h>huCvR%jdrK`)Tn<##5W^W?Yvg-d(8Y5N<$sy9F??Cw zZWLyFyJ3IhEZTI1BihqO4K36Qxm{I*b3m>x4=8RZENh|zL;{xq&G}Qy;qr-is(+uq zO^+FvN*RN(WKQ4CyT5R`b3_nJM^w~r@R4!eU36e8wY-L8omc9ys%kxGgGd{OH7Pb- ze_x7HR2c^_`Y0^^5QR$~)_(-g z2YZw)(OsL?>37Nf*7{rt#e$`V8K_tbTx_zlUdCFq9_>ScU*dKHRDS{8=C6x4HUoxj z0-mq$PglTrx{@zuTSf{(`yj!~9F&xu0lrW<=z; zHe`qtm+Eid;*Z2j_7lJnAkOMje=srSY(K(&lGFFDCK#M(Lv6>dSuziq@4)qR|6l|C z6)uHPY*j0P>AepZtbf;w>34WpUEHN?C$r;n(L~BA86kkdCL?yte!%X8iSkB z?3zEBOG-XM?*^J~k7#f&yO)~)lN&%F|$Rd6Md+2BxpxZEQjFZ(G&au4A}jA~U>(jek>5P$Go#qBuGd|ONbOzryU zx-k;!B@iXWS!!b^)$MYXed$E?w=ZKOP2yI20?$)#Q77Lk-DVN@660$GchT;p`~!n; zwV{Rn1bJ3&!^#3q!8DaN(u{_OJ7LtuYS)CNNc1U_!LKPYJ2TVl%f?a_0D-dswxxAS zXENAfKl61MwtpG4ewp%O&96NY8yF+d0e=NnNBAzO#h*8Ckv34in7{QawM>YBK%0+$ zik_3#URfKL-E}mzmc;L6Gig$n<=EH9HfR?lgL?^=ghB~n4A=L&JF>v$%T4;BEe|t= z17<`=c&(QahO_I4-PADeCYH>x{L97<#i3m1$VIRHEPp|}{XB)6d0Zc!9gUJpf?taj z4m|~Dy9;W*1QzkB(axceCCy=x6;Lnc2e;TBqVvYiH zDb?R~6@Q{I?=Th!3k#JISp61{Ad#Io!}M{Ier}W1LU1J2{aJrWz(z!TG*~Ou+u}_u z;ny5Z8>SbN!f16EYAh4Okt_+VhKe*|iYwZbq*}_$6lZRq1KB&HGcQR^3%M)ZLGo)S zH~WyTOP%b3WN83h01Q_~w~PqfH|7jEH&jl8CVzS872#ONstOfQK4dMlRGTIs8S~1I zdGo?--eC;xW#nzV;=%)ix$F%B2RRtlQ}vQyD?wpI_3ug*KxA7piedOI>iQHBk4c&W+(+2BaC*ff|6K;7OA1Rk&USWX=zmq0PuyByeXDB0rlo7mh zR)2~b8lUB7bju0uiP_PWQk&YJpof9(grE*1p+bN@5o35IHB|@d*Q=LeB>3vCT(tlI z>C7X$D1w6|B*(BcQXO%KG)U zN|{fJ(If)WM$$tqP_p3DMw7I`tO5c~l7CM^Os^g`J zUA-`F>i{DjmJL<2>%>0OJ^@BPNkQYutI z6L3RxGEf3%n*}5GSxe^f%8wJ!fSlP*Zj@eSGAe<{4!6xn^Ymjh8V;Ae_Cj>UxoNLe z!z(gxv{rhXU3yOB;#i!Ju|vi8AAeluCU6CdRO0DJn&&uNJUK#LxbMAPQo{6gF-xi$ zhJ+x+e>|%JX3X@xm}-~R*d1pxzTMJS&Ghh(cp&7nm zXzat;^p=_%LrS+?A>) z$4lcL^s4+_lYaMwBCErmfPZqrhb(z27gYh;X1%_3v_PD|ajOWZU1PbWCL$KGV!0fQ z;pWU&!Meah&BKh@jnuhD&{6Gew3$~~?^PyE^IYpAhe&WxKZ;Th3h)Q7&@JF3jBR5B zdfE(zcAankC_)bynHQ^u*gTJ;6;X`Q2xRLSHWaZSnjd2}IVw!4%ztW!Jp!pA2uDRl zI>`*et8toGY4f-IdLAJl)h&1nhPlYx98ZX<3-leMggI7XGwoq(3vwv?x*4~N2WXAU zV~U&b-OE50mXDU&+z!sPV0sl^fl2v=Ewe;L5saJx|BO&A@A`F{$Nxkfh0Y6;Yd^z1 zW;;@kc?Tk*E$X>I?|)gW9MVlRumxg}HrFtX>L8Q%FPN~gz_}jhZkc%PM&y_egJ4PU zS1W%r?%u!c8y*BcyCJ|+=vl&cqH27vBt)2Rt~ACqQk@3|oGf>m1fE`~V~1ONp9apO zHo-tE$Ti*L7Ke;j@}g?w`<&H~`VYFM58K-&I?#KA$f1{1mwy6-Rj1!T7vurkJ&G(t zp}YHX!$VjLysvt5j1{VG%LOP5mRNl|TI5CJ5QF!o?F?Z`G~F zzKI3)dHO@)hcUQO4SeMZ9oe|f73gRZjkKC?;sl!!-GwA9Tvw^S3Gaj7>dBXo0mOBj z|B$FGsHA`I`w41;jn27>{Zp!iWoEPSA;+u`T=f474u2H!>jhI#ejZJ+mh+L5bwMBP z4uDxvGFNjt{?N>xQ8p_)l-w%{teCDk4ny?r1$vW02pAuJ<6B$th`OLaefk)3y{R08QwY6aLz!p#p(h*G@MlG()?jc-mUXJJl zQLKIp`+tKKTow~4k9MYIMoS6@5P2DM)n?XQmeCdg&F}Fym&8|!^pL2UF-6<}ePQM8)gvr<*-63Djj~6+Q3S@c3M1V?*66BQ)O+@ttRElWt!*}Tfstv+3ykRx6zUw;jV1j~pM^Se?RDJZH~N27sr%+kPS zH=|6UI#&!)=lI>gX*cPM~qWwD{EtK9YtH0Pl>ZI;*6?8U~76!`)vaJ zFncXshIx791Av=K#o~u>KPhz9%;A_Vv3;=q?L$b*5G%g$^wcNMsL(y6{~dcml>lWH z)_(y(mCx87EP4;;Kkn`=JK5X+#BHLll1XcyNKP%eN3#-R7EsHwz*Cr&vSl#JX4GpU zVNYV-n|=}H;19qZ53<}<6j@oQ$14ICRO0^`ciHu=%Y#qAjfse@gfS$Y)>gntqr!q_ z?6`*8qc<}`#seFGdI3?HC6cTki z1aBH0&>-Sq#MAFdUhafqslfkhLR1~9b}N{$h-|~(jkeETG!3VAf!M;(aq-CDNq^@2 zq?K=%=Ei7?Ikr*O5-pPv?XDFDHyB&uj_x;??A$8A_hi?O^?z9`;lWsJD_aBs^nYs0(b{0A2IL@7kQrZd7V8Dq55fr1m zj=gBD2=T8U?sSb;O(WSlY5OD$9e)^j_Cj}Ze8fyQ2*z+(14x-&HkY%w#-eW+#Ofvh zY*%sD8mD1S$SjxT^w^t0W!@qoLo~d&`wZgEY@18jznS7zS|vMQ?aiZ~w8uxkdwtY( zTUU(QP{{;Cw5oYI981Z;Q0yDee#9|N7eGvcpjJU`xW^F|`YNyiiGTl97=N(AwKL&! zs=0p;Dp3;8BPM@z)`LOPd}!~fdj_KW`Y*Rf zljH~wLY&Xd6ET-dWiEf8(Ibi7*6^NYDw6q}@y~Loq1_gl=gs4~sP5`4YM6NmUPa~; z9gcp9$4B_w;;lC6P+kFyAF0L{REGGOtL(LsOP^!~ZHjYs?>#Yp2Y;&)X#UtZppsxC z!?Pi>)ENVnK|E^y!C$5v&3d<$FVEx9EbO3^*g;mJ(7dTRWLtlqugyHlKKC|1lg>u6 z@V)}5-Rh2@tvkb*!ly|l6@{HuP~5?@?~x#j6Wlkr+ae3W9fG?A65O2x=Z8xO5Zv7o z+}$mK#WlDFcXtl|b57m+a3Aj5bk|JH%T#yQRQLC@Zo8%_GCzu%={@5^@qWfR^{pU< z?a-FVIf@PlbAfIBYkc?ztaRC{epuhs-A~3>9y%d zQ=~MPc+SIa{jfItM3r-F+$?aEBIP6RZ{BNh<;}0PJfB$N)K4c7?;-ZW+x$@;5Wp1& z&OzJ1j){LkRHn6$RJqBcMzt;bv&TFg2b8_X#_CzAVZ`o&V=pkzvK?LZIs+hY+x_UGK9R}F;ft%0tJjyxfO)Y6QbE6E=sOWM}!yw;T z5)Xt73+__b^r!8QScSH_OWidUZn}WMubbh#D^1yjVBHy5h(7c2&(;uWhQl8cFxC|3 zFSN6gAo!JHRv-LKlmjFeYjvd0S_H`9j~Y>wi@~c!bSKe?%5feQAFvSu7Tv0WTP(DO z+sT-=#iP$l4FTN~i!qj6HWER^aDwz z&=-~VR4lo~x34n%DUAf2sebzVvlzQ%&r3Q(ELU9I z+t#dDbgG8(z^^kMYXPgJ{%i{l02o)AEXUP@%|Dl)YCu%P#{)U-u|^VI2uv~1 zG`bSD7LN3tKLJ0~#Qqc+(HsT}x1&qPq)UIcYgiMGeB=`JM~u@6Q>t7C0%{6fB-6zP#7d_(+JBxsHnwfw8F(*Z zq146F{*3xdPKDNvMHl+BiQjNkZ~3${g8Li2qsYk!l#_@&Dk~}(aF&uLEBlu|=;^7U zIIZs+dy&%XlJm3X%W9W!Lrfiwo`i!_@`dYT1(7f^$#M!(J-yr$Sj>}GD9bU==G+mmYcf-T6C5O43dKHfbXg_t`TIZQ_${yT3E zPeSqfXk|%PKIP9bpgFBiQl?=-Zl|?Z9NFVW3DU=}mcFAa8&4%C6gCHA{;m9=NB|go z*N*(0^p4i1N4z|2Va2b!UPNl6Sg~tut!%Z~Q8C?N6=SuxN}gIn4$AHtteooxO*%^O zr&BtjlZv7P-6`rA6_`>0^lrF_ullTAG~o-!qSiYMOEiZ-qyBZ_5DH%l?GEb$6dYlB zZR4lZPM>+Uriq%<*PqL<`D1jc=URnif-}XLq7=X~R;tq%_b7>X7hYZ34{U!QyxQvKgI4zRi{h;f@P)s=5Kbz;AWU>{64zt>+KM zhMW5)Gf##5$aUK3gj{#6ojSj@0dkaRmcPwLJn=u9u5z)3etO_5$>s2$TbvTKhcQ-fJ zi}(QHCMpD&)Ph=k)IDR#f$emh5J$%It zuijZl|91}B4Wm*=`wsY(Dm<_9cHtI=tv7>*Q7TKzJ@DF#`5VSU%C8)xsLcIa&=Y9= zvzd5BYcQXcQ@qeBa&%T5QnhQkM{|XM&|ZfV>p>y{$K4KU^xr#7_8Vz=_X(3>8X!Ci zjEpi8K;7i*Cnqjf+d1iQFE6Kl32F~*Q(fRXBVd#6$ zncVyU{l|qC>OG04CsFAZ5p(xo&p~5aQuqqesK&&44((g&o)6Jv;4%UE*Zd%{nwuW_NjF;8Up3kOi?q$>AI~ zIfBj4Wr9eFk}Y-ECgA4ur!LYjWcK-tFi_*g?(wK#mxM9Ea;UD;;u9omfLv#=uEYF+8>hnQCM4siPL4z5XB9*IkTI9W2Y zP-X8P?+s@+MtSOX8pxZ`w)~NsifwhZZnK3`W=tYP(XtC6PH!33zXa-7_A#@a1r)(zrQwYLUNm7w6$#q_WZhcqmS&iOCBeIxscM<+6_TXTu+X@V*JsO0Yq zQzuE5JqH!+9P_BQhyct#Rw-XUJk$f@=-cnxDQ5!XO)pIlal*(OqoeOH(aH%njy!hC zh!*C-9bXQG?HM@r}SkfGwa;5TGgc#{vEU7h#9j)33PIFISC8V zMD`3HrvCkDmFs=EtsF}Bt4=~nL$YU1z=q3pcpg1Eho-@QL<5paagAZZrO~?^*b#<~1}YMm zH3fTh=Hy4OOW#DVk!SUvnmqc-Af+mu;j`%n_!8BlYZof6tkFE@s8w+9fBq(i9KMiN zAaYPkXVy6N#T*!gFUDF6Pg_f6L#R@wGmfbAl@`A^AhXB;t2nAKoNtx-llHzHd8I~8 zFsBz4nZ^~_7ZK}VUbZZRbL7mEx+sw~S)xu*L|0ms zsob6c@gX2|+WxHNkj{=7MpElJiudacN}PeIHB*7zue``_jpHN-d)_$oIQ7TbH+Tz`xS&Il+H@H~H zSoep$PYX!nN*kZ&FGY!|*IBmzmhJ2F;-iwJ&`|0b znBd%-nVq!maj5T8)UGTValCW1dTGe7_s>Z0?0VZoROQ8Eu19=@gDYO(&#FHd+M#GU zt?Qf<_!u4B$kq$;CvmXuK0hTpteR?9OW?B;f8)aF2==w=jcT0I{r-K_B4c z0s3CvVJYP?f51@(3NoekBLEOhY+z13VbMraK_}BDohr=#>^3|IM4pM z{J*{4Bk>`lIKM1C$n&qkyX}Q>52h3w@0?|Q8X+HT5AM)TvT7SdSJ!=bN`>i!F0J%x zy){yCf*?@a5-!Tw&+3Q6l>S>1M>kz9jMw&Y$N@pp>6978(Smp*L{sLGqa62FT7V3@ zy)yf!68v$BjE_rIl!OgTITt6D!IXqdark_VeFI)p-o%pqg}(fAFsY(t77{h0-_bJR zS9ZbO!ZR%w%J4TG<++LyL%e;yzk?XNcK1|`t+UxPem2snscLGscWKPqO=x|Fu70f) z{NxGxkw!jxTHg&@ASc$)46Iu zv%`YKMQ-ikA0}#(?vPmx{qZHOlSCf<~cR_xi>ds6u*6k|7+<2 zeC}Ro_eNgw-FgNeqtmyi%QFmEvcLuPk_MAqeE+-*B9xmyzB-K&IMSbYSsZxlyQ4Fl zZ^-V<`7q3;Q&RW)%!`hGWdkKVkdBtN8!pH6-@%DBTmjs-Iysp}=3fP@pJ%i7MA{Xx zF}tZPQof~_)0+f@go7TfyMs-7^fXgZ8Oh_(LM$hd=#exeZVJp4Sm>+$d;QJRijaz; z^6Bd56qzifx_B(yfW8FdfdEEMTVBbqNKF;4Vj5*?q!^E8V!jQkZy72l= z1Q@kz<0dR_AatYed6U=QrS>qV;2#x6s=`hQFD9^*Kl9VmaE6p<61$VO*}^i!BZSL~ z-(Ii<2lx=y=&@oA6d-cRAG7hn`-WEu>>{Y1>GFTZ?JA^(1GeAg!9i#{r>zj#_q4`L zKL!Y#z@v&QcHvYbaQn~Z+kvRW2NE# zFo;i*3jWfb15jFVX}abVhM$Hh%J}QNGu9mtL;Nx7Um}Y^g2MWSQSDd4(D%6%3{yzf z-vHcHF^s@3nmN$DTt{&N-Kf3~{#vE@TC}wTp;`W(^I}51T^ZEOR{eJ+2)cyR86!n;d4+6{%-?-sr_c$q|9FEteW=oI8hA?PBi#V^6g(Z8d zTl4*lBtUI86-D8h7GH!c4hsoGd|V;Y1I^&8bCn}QAC-UP-Qo(2xGh6xqw1Df`NULa zZaPS)J;PPab{lJ1miSZOD6yzKOhxMQ(mDp)p$N3;xKUd08@pB>bc_yVQ#w4WE%;+` z$H~NatR>8Wcj)rN*PM#RP4^wH>sB!(;U9Sizz~nmwz0wI<{43%*YaaF!n7G5sjogi zrfm=ZNvcV~G0V|$dQs3G&81s$rkJwKS_U|WdUz(M>*#cD8aGr^Bh0Y}H(fAql3eNy z+O4?;ihT%9_mDAh??r(b75w1@XftTbc95{OQfevOybm|DQ7j{Sd)`g~MG5_-S11Ao zuv*51I;UA;I21e(ZhILfO}#i7T^ap5yA-4#d}8gScBR|quh zsJx)@`^@)_Z@&j^;JG~B#!O9MdTZW5Na3~^@^4Fi_7w@BB-YGRZg}@y^H97_eX>R~ zsXx?mQx^6<4bCtctHqoUN!A2{h08>Lk$J0=Fp6gRWf$nonM;Fw!8wn?ia8a&z^57J zq)9adcQn_%0xaRZ?~W0A^V%^IgJ6{38Z~X}m>$M-Zjt4jE(t#JVT1E~;xHm5x6X^o zYw3)33)gJh2ll(w);Xe1u!uHHgiIs)-16g8n)zIv4a!{I^T~ReB}!%VYRAF^Z>9(1 zoMsPi1r*S(6U5rz;=^iD81AeAf?A}_lC^K})#p*1R7)G3$FJe{oSReMe_C{Q%)F|g zp(aTJ25^@%%lhV*Yu@hg4JimtXDO4f_T4}VE>7D;5^57pDGw^+?b z|0so|QB2&}koac9j((plUd?NZ|v&;zV-M{we3wE zc_1z=AYT=8VYra=;@AfpJAEKVuEq_`v@TtCvi??I!_nU4o`&Olz}G@vx9k+ZRgnJU z(7z@;?>*-Og)vroH+hT9Ps2~J<#O9Q*1sUc_V4gd_qBMam#|5CMz@{V`uPq6tQnSV zd3eWQJ-g2zZ1EPp5`Riv0xDWlj=wuLMOH2neCmAH(cv9~o$Gj|PqjpQ=eYUxCB#ps ztS{3R?uoGpNqad@W!)#$8J`J9gS;#pr70TO&kmr+dEW z!ON%#d|%<&_^a&vscPehW~z~8CC{RaN$8x63!sUcG-cbmy(W9hq|!R=7^GOhRql?-%oZEu$nYe)czwx!-XutszNojA%%cwKdQY zo*|7jOyJe2!Wy0;WO#!my00Ok`P7*4&@VK9_`zE(eIO#qswC`La$?$cYGs5p*qR1O zZQ}T?wwOJ$c~$zR)qdD)ifCQYltaLqqr>!ZsU_9SEP-U#E#QZ_Or-dJj*A|}r6%4E z)DQgwb3{{I+*ilbj01~YSkW;T-%ia!!u^EorHyXb2&)L77(nY{`TkodZ`xw2i2C1JbfFw=OE49)~BRp9GlL9L+8PNf=4eZ86+14;$N zAc|$UHB^En0LiH~_v0yU=bz2>N_hbVkz}I18LeW&27|%5ucaBI1_I>^^yTk|lrNH+ zY?7vaH-h-^hU{H^p}t?e&ew@gGs`8hlR6kmc@pf#q#D=ea~5~?D)nzcq#q-)F>TNC zD|uwvhJbrea*H--usC0DA`xOovvYTF(HoQv-no0Iw|M*4$eiwyEyi_QTUD+-B*$BV zLy=COWgnV3j3$y5HRPs{om)pcWnc&gK!LOMt4M|&hB0JnG>dvW#_yo+Xl&R@T=o!ixtn^7;rE5(0!s~{Yv zzd3{}Cy=ePYchz~ksG|qJl*=&4}H8mI=CCwy}nq>o?|%=H9}-W7|QCi=Af4M46}h} zR^+#97}MGNM=I9tur41aO*V$;hpMPTYUv5@?rHe$fd**Z;&zHQTc?-DTpgfVaZMFJ z_X)uhuA=IWj|&tTvt8PS&#-i6ea2SHmHm^vP7aTs2!$tTM6N}MU_jvGNse7W2t(oI z;^*e#;ZCMnL?Hh^hQuO5BHt@70qkgEgC-<|#-ZuyWDe#~F|pBbvq$4l216id95U7} zu5MuN{|i_EbMf%ZCS1a}fd9XOq>t;sf`mS|W2%C~I-)B$`C5!7R6Cq$e$;4UHlGcmvTB~BX3 zxn_b48mXj9zUY`@T+mnwO}MUD>{9*&|FBrFgcw|0Y~=?@F|!1eIPdLl6ejBcmUAb` zUXC|=YKBXuV8lJa&>yb^Bn^L9f?l3_>WN^bkpT3$W71!Cuf`+)0{TH)I!&O^my*rO z{PB77^zpvGwe$c6Sc$~Y%L^{OXUY?}8_u`Ja`@-t^h2a;NB9`>H=Y*BGDCd#oDAjW zLYD*mG{ngXr~G+h&`sN)NC5@2KyML`(tW%@Y2)diTZJ))o0H~lzxOF3is)_e%J4+n-t2fwdnc0OcryVy z>cQpA(M#@G0Utt-sF@DHBDaTCVCq zl-^jq%ls@7b58O+uJ>(E-SmvD-z3R8FTDbS&^(vIfSq#S{f&vG&s-wfSx_ap4x$Da z%DSG?`WYUy0dm6yc_r9R{*I?OF{i{n5e#cA>L%fq1p`P%5@6?GQy-Lom^mDmwvoKs zNOnaeoS^|$n7`_}m%xM`WpQc|+Xt@|lkf3SC7^aiAm3hL-;d7MmDMTg=5~ZJN^~fr zB;$>Vn>o4J$`%l`2>dnYu45!Ibv+fd0nM1Zktlsp{zSBwb}AfpI9x|_ailGiO^@dq zkrb=i&T=}$YlHj`C)|c{-N7%`P&iSTwLYk-t#J1^`HEPR#vMpby`a~spBiDX;@>iP zMbZ5_`&aL!>dLvnJNBhT>7xV%=6963Lfw^P-cH;<9pk65UU&_@)hO7F zk@@m`*;1&GWBPez0B5q1c99HjcdG6v;NGW|u+WaOVIb;}7jtF{A_}%*IBt{QY*)iI z?`PL6C;h6tJM~Pr8Un7ftNzeQ%xVx<&bmmqSbErM)-rktgX*VNZgAt3@(E(aORLv? zZhhvrk7L8$=+VP$$iuS$n^`S>7lPJWHl%wILq9h8DCBujo=pHI5Qzstr0_;~-HxUZ{jZh^)j?_g%`0XEJ=HsAt7z+A6Rbw@|HSLc6Hhx&g`SUA2~JpXG+fenPDquMBZj`vP1K^ll3{rz-`rkWfEFcJ{3s%l58(+LKsK61CB;tC%QPM zKo9G1Sc9T&#W-JAR*@QT!$f)h3jL4V^&%KN2Y$aX}3RZ oD1E)`^@iv3qE2TW$iPKLE&1m*0tE&imw*5t8XcXqiVWI+0asz>oB#j- diff --git a/lecture_10/lecture_10.tex b/lecture_10/lecture_10.tex index 1131881..633c945 100644 --- a/lecture_10/lecture_10.tex +++ b/lecture_10/lecture_10.tex @@ -277,11 +277,11 @@ \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}14}]:} \PY{c}{\PYZpc{}plot \PYZhy{}\PYZhy{}format svg} +{\color{incolor}In [{\color{incolor}1}]:} \PY{c}{\PYZpc{}plot \PYZhy{}\PYZhy{}format svg} \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}15}]:} \PY{n}{setdefaults} +{\color{incolor}In [{\color{incolor}2}]:} \PY{n}{setdefaults} \end{Verbatim} \section{Gauss Elimination}\label{gauss-elimination} @@ -310,11 +310,11 @@ \subsubsection{Solving sets of equations with matrix lines: \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}16}]:} \PY{n}{x21}\PY{p}{=}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{:}\PY{l+m+mi}{2}\PY{p}{]}\PY{p}{;} - \PY{n}{x11}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{l+m+mi}{3}\PY{o}{*}\PY{n}{x21}\PY{p}{;} - \PY{n}{x21}\PY{p}{=}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{:}\PY{l+m+mi}{2}\PY{p}{]}\PY{p}{;} - \PY{n}{x22}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{x21}\PY{p}{;} - \PY{n+nb}{plot}\PY{p}{(}\PY{n}{x11}\PY{p}{,}\PY{n}{x21}\PY{p}{,}\PY{n}{x21}\PY{p}{,}\PY{n}{x22}\PY{p}{)} +{\color{incolor}In [{\color{incolor}3}]:} \PY{n}{x21}\PY{p}{=}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{:}\PY{l+m+mi}{2}\PY{p}{]}\PY{p}{;} + \PY{n}{x11}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{l+m+mi}{3}\PY{o}{*}\PY{n}{x21}\PY{p}{;} + \PY{n}{x21}\PY{p}{=}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{:}\PY{l+m+mi}{2}\PY{p}{]}\PY{p}{;} + \PY{n}{x22}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{x21}\PY{p}{;} + \PY{n+nb}{plot}\PY{p}{(}\PY{n}{x11}\PY{p}{,}\PY{n}{x21}\PY{p}{,}\PY{n}{x21}\PY{p}{,}\PY{n}{x22}\PY{p}{)} \end{Verbatim} \begin{center} @@ -322,7 +322,21 @@ \subsubsection{Solving sets of equations with matrix \end{center} { \hspace*{\fill} \\} - For a $3\times3$ matrix, the solution is the intersection of the 3 + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}4}]:} \PY{n}{A}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{;}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{;} \PY{n}{y}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{;} + \PY{n}{A}\PY{o}{\PYZbs{}}\PY{n}{y} \PY{c}{\PYZpc{} matlab\PYZsq{}s Ax=y solution for x} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +ans = + + 0.40000 + 0.20000 + + + \end{Verbatim} + + For a \(3\times3\) matrix, the solution is the intersection of the 3 planes. \(10x_{1}+2x_{2}+x_{3}=1\) @@ -331,44 +345,41 @@ \subsubsection{Solving sets of equations with matrix \(x_{1}+2x_{2}+10x_{3}=1\) -$\left[ \begin{array}{ccc} 10 & 2 & 1 \\ 2 & 1 & 1 \\ 1 & 2 & 10\end{array} \right] +$\left[ \begin{array}{ccc} 10 & 2 & 1\\ 2 & 1 & 1 \\ 1 & 2 & 10\end{array} \right] \left[\begin{array}{c} x_{1} \\ x_{2} \\ x_{3} \end{array}\right]= \left[\begin{array}{c} 1 \\ 1 \\ 1\end{array}\right]$ \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}17}]:} \PY{n}{x11}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{;} - \PY{n}{x12}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{;} - \PY{p}{[}\PY{n}{X11}\PY{p}{,}\PY{n}{X12}\PY{p}{]}\PY{p}{=}\PY{n+nb}{meshgrid}\PY{p}{(}\PY{n}{x11}\PY{p}{,}\PY{n}{x12}\PY{p}{)}\PY{p}{;} - \PY{n}{X13}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{l+m+mi}{10}\PY{o}{*}\PY{n}{X11}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{X22}\PY{p}{;} - - \PY{n}{x21}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{;} - \PY{n}{x22}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{;} - \PY{p}{[}\PY{n}{X21}\PY{p}{,}\PY{n}{X22}\PY{p}{]}\PY{p}{=}\PY{n+nb}{meshgrid}\PY{p}{(}\PY{n}{x21}\PY{p}{,}\PY{n}{x22}\PY{p}{)}\PY{p}{;} - \PY{n}{X23}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{X11}\PY{o}{\PYZhy{}}\PY{n}{X22}\PY{p}{;} - - \PY{n}{x31}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{;} - \PY{n}{x32}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{;} - \PY{p}{[}\PY{n}{X31}\PY{p}{,}\PY{n}{X32}\PY{p}{]}\PY{p}{=}\PY{n+nb}{meshgrid}\PY{p}{(}\PY{n}{x31}\PY{p}{,}\PY{n}{x32}\PY{p}{)}\PY{p}{;} - \PY{n}{X33}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{/}\PY{l+m+mi}{10}\PY{o}{*}\PY{p}{(}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{n}{X31}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{X32}\PY{p}{)}\PY{p}{;} - - \PY{n+nb}{mesh}\PY{p}{(}\PY{n}{X11}\PY{p}{,}\PY{n}{X12}\PY{p}{,}\PY{n}{X13}\PY{p}{)}\PY{p}{;} - \PY{n+nb}{hold} \PY{n}{on}\PY{p}{;} - \PY{n+nb}{mesh}\PY{p}{(}\PY{n}{X21}\PY{p}{,}\PY{n}{X22}\PY{p}{,}\PY{n}{X23}\PY{p}{)} - \PY{n+nb}{mesh}\PY{p}{(}\PY{n}{X31}\PY{p}{,}\PY{n}{X32}\PY{p}{,}\PY{n}{X33}\PY{p}{)} - \PY{n}{x}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{10}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{;} \PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{,} \PY{l+m+mi}{10}\PY{p}{]}\PY{o}{\PYZbs{}}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{;} - \PY{n}{plot3}\PY{p}{(}\PY{n}{x}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{,}\PY{n}{x}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{,}\PY{n}{x}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{,}\PY{l+s}{\PYZsq{}}\PY{l+s}{o\PYZsq{}}\PY{p}{)} - \PY{n+nb}{view}\PY{p}{(}\PY{l+m+mi}{45}\PY{p}{,}\PY{l+m+mi}{45}\PY{p}{)} +{\color{incolor}In [{\color{incolor}9}]:} \PY{n}{N}\PY{p}{=}\PY{l+m+mi}{25}\PY{p}{;} + \PY{n}{x11}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{n}{N}\PY{p}{)}\PY{p}{;} + \PY{n}{x12}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{n}{N}\PY{p}{)}\PY{p}{;} + \PY{p}{[}\PY{n}{X11}\PY{p}{,}\PY{n}{X12}\PY{p}{]}\PY{p}{=}\PY{n+nb}{meshgrid}\PY{p}{(}\PY{n}{x11}\PY{p}{,}\PY{n}{x12}\PY{p}{)}\PY{p}{;} + \PY{n}{X13}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{l+m+mi}{10}\PY{o}{*}\PY{n}{X11}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{X12}\PY{p}{;} + + \PY{n}{x21}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{n}{N}\PY{p}{)}\PY{p}{;} + \PY{n}{x22}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{n}{N}\PY{p}{)}\PY{p}{;} + \PY{p}{[}\PY{n}{X21}\PY{p}{,}\PY{n}{X22}\PY{p}{]}\PY{p}{=}\PY{n+nb}{meshgrid}\PY{p}{(}\PY{n}{x21}\PY{p}{,}\PY{n}{x22}\PY{p}{)}\PY{p}{;} + \PY{n}{X23}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{X11}\PY{o}{\PYZhy{}}\PY{n}{X22}\PY{p}{;} + + \PY{n}{x31}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{n}{N}\PY{p}{)}\PY{p}{;} + \PY{n}{x32}\PY{p}{=}\PY{n+nb}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{n}{N}\PY{p}{)}\PY{p}{;} + \PY{p}{[}\PY{n}{X31}\PY{p}{,}\PY{n}{X32}\PY{p}{]}\PY{p}{=}\PY{n+nb}{meshgrid}\PY{p}{(}\PY{n}{x31}\PY{p}{,}\PY{n}{x32}\PY{p}{)}\PY{p}{;} + \PY{n}{X33}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{/}\PY{l+m+mi}{10}\PY{o}{*}\PY{p}{(}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{n}{X31}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{X32}\PY{p}{)}\PY{p}{;} + + \PY{n+nb}{mesh}\PY{p}{(}\PY{n}{X11}\PY{p}{,}\PY{n}{X12}\PY{p}{,}\PY{n}{X13}\PY{p}{)}\PY{p}{;} + \PY{n+nb}{hold} \PY{n}{on}\PY{p}{;} + \PY{n+nb}{mesh}\PY{p}{(}\PY{n}{X21}\PY{p}{,}\PY{n}{X22}\PY{p}{,}\PY{n}{X23}\PY{p}{)} + \PY{n+nb}{mesh}\PY{p}{(}\PY{n}{X31}\PY{p}{,}\PY{n}{X32}\PY{p}{,}\PY{n}{X33}\PY{p}{)} + \PY{n}{x}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{10}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{;} \PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{,} \PY{l+m+mi}{10}\PY{p}{]}\PY{o}{\PYZbs{}}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{;} + \PY{n}{plot3}\PY{p}{(}\PY{n}{x}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{,}\PY{n}{x}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{,}\PY{n}{x}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{,}\PY{l+s}{\PYZsq{}}\PY{l+s}{o\PYZsq{}}\PY{p}{)} + \PY{n+nb}{xlabel}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{x1\PYZsq{}}\PY{p}{)} + \PY{n+nb}{ylabel}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{x2\PYZsq{}}\PY{p}{)} + \PY{n+nb}{zlabel}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{x3\PYZsq{}}\PY{p}{)} + \PY{n+nb}{view}\PY{p}{(}\PY{l+m+mi}{10}\PY{p}{,}\PY{l+m+mi}{45}\PY{p}{)} \end{Verbatim} - \begin{Verbatim}[commandchars=\\\{\}] -error: 'X22' undefined near line 1 column 16 -error: 'X13' undefined near line 1 column 14 -error: evaluating argument list element number 3 - - \end{Verbatim} - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{lecture_10_files/lecture_10_5_1.pdf} + \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{lecture_10_files/lecture_10_6_0.pdf} \end{center} { \hspace*{\fill} \\} @@ -416,13 +427,13 @@ \subsubsection{Solving sets of equations 10 & 2 & 1 & 1\\ 0 & 3/5 & 4/5 & 4/5 \\ 0 & 0 & 7.5 & -1.5\end{array} -\right] $ +\right]$ now, \(7.5x_{3}=-1.5\) so \(x_{3}=-\frac{1}{5}\) then, \(3/5x_{2}+4/5(-1/5)=1\) so \(x_{2}=\frac{8}{5}\) -finally, \$10x\_\{1\}+2(8/5) +finally, \(10x_{1}+2(8/5)+1(-\frac{1}{5})=1\) Consider the problem again from the intro to Linear Algebra, 4 masses are connected in series to 4 springs with K=10 N/m. What are the final @@ -450,7 +461,7 @@ \subsubsection{Solving sets of equations \(\left[ \begin{array}{cccc} 2k & -k & 0 & 0 \\ -k & 2k & -k & 0 \\ 0 & -k & 2k & -k \\ 0 & 0 & -k & k \end{array} \right] \left[ \begin{array}{c} x_{1} \\ x_{2} \\ x_{3} \\ x_{4} \end{array} \right]= \left[ \begin{array}{c} m_{1}g \\ m_{2}g \\ m_{3}g \\ m_{4}g \end{array} \right]\) \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}18}]:} \PY{n}{k}\PY{p}{=}\PY{l+m+mi}{10}\PY{p}{;} \PY{c}{\PYZpc{} N/m} +{\color{incolor}In [{\color{incolor}10}]:} \PY{n}{k}\PY{p}{=}\PY{l+m+mi}{10}\PY{p}{;} \PY{c}{\PYZpc{} N/m} \PY{n}{m1}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{;} \PY{c}{\PYZpc{} kg} \PY{n}{m2}\PY{p}{=}\PY{l+m+mi}{2}\PY{p}{;} \PY{n}{m3}\PY{p}{=}\PY{l+m+mi}{3}\PY{p}{;} @@ -479,7 +490,7 @@ \subsubsection{Solving sets of equations \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}19}]:} \PY{n}{K1}\PY{p}{=}\PY{p}{[}\PY{n}{K} \PY{n}{y}\PY{p}{]}\PY{p}{;} +{\color{incolor}In [{\color{incolor}11}]:} \PY{n}{K1}\PY{p}{=}\PY{p}{[}\PY{n}{K} \PY{n}{y}\PY{p}{]}\PY{p}{;} \PY{n}{K1}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{p}{=}\PY{n}{K1}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{o}{/}\PY{l+m+mi}{2}\PY{o}{+}\PY{n}{K1}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{p}{:}\PY{p}{)} \end{Verbatim} @@ -495,7 +506,7 @@ \subsubsection{Solving sets of equations \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}20}]:} \PY{n}{K2}\PY{p}{=}\PY{n}{K1}\PY{p}{;} +{\color{incolor}In [{\color{incolor}12}]:} \PY{n}{K2}\PY{p}{=}\PY{n}{K1}\PY{p}{;} \PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{p}{=}\PY{n}{K1}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{o}{*}\PY{l+m+mi}{2}\PY{o}{/}\PY{l+m+mi}{3}\PY{o}{+}\PY{n}{K1}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{p}{:}\PY{p}{)} \end{Verbatim} @@ -511,7 +522,7 @@ \subsubsection{Solving sets of equations \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}21}]:} \PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{p}{=}\PY{o}{\PYZhy{}}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{o}{*}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{/}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{+}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{,}\PY{p}{:}\PY{p}{)} +{\color{incolor}In [{\color{incolor}13}]:} \PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{p}{=}\PY{o}{\PYZhy{}}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{o}{*}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{/}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{+}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{,}\PY{p}{:}\PY{p}{)} \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] @@ -526,7 +537,7 @@ \subsubsection{Solving sets of equations \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}22}]:} \PY{n}{yp}\PY{p}{=}\PY{n}{K2}\PY{p}{(}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{;} +{\color{incolor}In [{\color{incolor}14}]:} \PY{n}{yp}\PY{p}{=}\PY{n}{K2}\PY{p}{(}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{;} \PY{n}{x4}\PY{p}{=}\PY{n}{yp}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{)}\PY{o}{/}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{,}\PY{l+m+mi}{4}\PY{p}{)} \PY{n}{x3}\PY{p}{=}\PY{p}{(}\PY{n}{yp}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{+}\PY{l+m+mi}{10}\PY{o}{*}\PY{n}{x4}\PY{p}{)}\PY{o}{/}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)} \PY{n}{x2}\PY{p}{=}\PY{p}{(}\PY{n}{yp}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{+}\PY{l+m+mi}{10}\PY{o}{*}\PY{n}{x3}\PY{p}{)}\PY{o}{/}\PY{n}{K2}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)} @@ -542,7 +553,7 @@ \subsubsection{Solving sets of equations \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}23}]:} \PY{n}{K}\PY{o}{\PYZbs{}}\PY{n}{y} +{\color{incolor}In [{\color{incolor}15}]:} \PY{n}{K}\PY{o}{\PYZbs{}}\PY{n}{y} \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] @@ -565,7 +576,7 @@ \subsubsection{Solving sets of equations \texttt{x=GaussNaive(A,y)} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}24}]:} \PY{n}{x}\PY{p}{=}\PY{n}{GaussNaive}\PY{p}{(}\PY{n}{K}\PY{p}{,}\PY{n}{y}\PY{p}{)} +{\color{incolor}In [{\color{incolor}16}]:} \PY{n}{x}\PY{p}{=}\PY{n}{GaussNaive}\PY{p}{(}\PY{n}{K}\PY{p}{,}\PY{n}{y}\PY{p}{)} \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] @@ -606,7 +617,7 @@ \subsubsection{Solving sets of equations \end{enumerate} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}25}]:} \PY{n}{format} \PY{n}{short} +{\color{incolor}In [{\color{incolor}17}]:} \PY{n}{format} \PY{n}{short} \PY{n}{Aa}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{;}\PY{l+m+mi}{4}\PY{p}{,}\PY{l+m+mi}{6}\PY{p}{,}\PY{l+m+mi}{7}\PY{p}{;}\PY{l+m+mi}{2}\PY{p}{,}\PY{o}{\PYZhy{}}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{6}\PY{p}{]}\PY{p}{;} \PY{n}{ya}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{8}\PY{p}{;}\PY{o}{\PYZhy{}}\PY{l+m+mi}{3}\PY{p}{;}\PY{l+m+mi}{5}\PY{p}{]}\PY{p}{;} \PY{n}{GaussNaive}\PY{p}{(}\PY{n}{Aa}\PY{p}{,}\PY{n}{ya}\PY{p}{)} \PY{n}{Aa}\PY{o}{\PYZbs{}}\PY{n}{ya} @@ -634,7 +645,7 @@ \subsubsection{Solving sets of equations \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}26}]:} \PY{p}{[}\PY{n}{x}\PY{p}{,}\PY{n}{Aug}\PY{p}{,}\PY{n}{npivots}\PY{p}{]}\PY{p}{=}\PY{n}{GaussPivot}\PY{p}{(}\PY{n}{Aa}\PY{p}{,}\PY{n}{ya}\PY{p}{)} +{\color{incolor}In [{\color{incolor}32}]:} \PY{p}{[}\PY{n}{x}\PY{p}{,}\PY{n}{Aug}\PY{p}{,}\PY{n}{npivots}\PY{p}{]}\PY{p}{=}\PY{n}{GaussPivot}\PY{p}{(}\PY{n}{Aa}\PY{p}{,}\PY{n}{ya}\PY{p}{)} \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] @@ -655,7 +666,7 @@ \subsubsection{Solving sets of equations \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}27}]:} \PY{n}{format} \PY{n}{long} +{\color{incolor}In [{\color{incolor}33}]:} \PY{n}{format} \PY{n}{long} \PY{n}{Ab}\PY{p}{=}\PY{p}{[}\PY{l+m+mf}{0.3E\PYZhy{}13}\PY{p}{,}\PY{l+m+mf}{3.0000}\PY{p}{;}\PY{l+m+mf}{1.0000}\PY{p}{,}\PY{l+m+mf}{1.0000}\PY{p}{]}\PY{p}{;}\PY{n}{yb}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{2}\PY{o}{+}\PY{l+m+mf}{0.1e\PYZhy{}13}\PY{p}{;}\PY{l+m+mf}{1.0000}\PY{p}{]}\PY{p}{;} \PY{n}{GaussNaive}\PY{p}{(}\PY{n}{Ab}\PY{p}{,}\PY{n}{yb}\PY{p}{)} \PY{n}{Ab}\PY{o}{\PYZbs{}}\PY{n}{yb} @@ -676,7 +687,7 @@ \subsubsection{Solving sets of equations \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}28}]:} \PY{p}{[}\PY{n}{x}\PY{p}{,}\PY{n}{Aug}\PY{p}{,}\PY{n}{npivots}\PY{p}{]}\PY{p}{=}\PY{n}{GaussPivot}\PY{p}{(}\PY{n}{Ab}\PY{p}{,}\PY{n}{yb}\PY{p}{)} +{\color{incolor}In [{\color{incolor}34}]:} \PY{p}{[}\PY{n}{x}\PY{p}{,}\PY{n}{Aug}\PY{p}{,}\PY{n}{npivots}\PY{p}{]}\PY{p}{=}\PY{n}{GaussPivot}\PY{p}{(}\PY{n}{Ab}\PY{p}{,}\PY{n}{yb}\PY{p}{)} \PY{n}{Ab}\PY{o}{\PYZbs{}}\PY{n}{yb} \PY{n}{format} \PY{n}{short} \end{Verbatim} @@ -699,6 +710,18 @@ \subsubsection{Solving sets of equations 0.666666666666667 + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}36}]:} \PY{c}{\PYZpc{} determinant is (\PYZhy{}1)\PYZca{}(number\PYZus{}of\PYZus{}pivots)*diagonal\PYZus{}elements} + \PY{n+nb}{det}\PY{p}{(}\PY{n}{Ab}\PY{p}{)} + \PY{n}{Aug}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{*}\PY{n}{Aug}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +ans = -3.0000 +ans = 3.0000 + \end{Verbatim} \subsubsection{Spring-Mass System again}\label{spring-mass-system-again} @@ -729,7 +752,7 @@ \subsubsection{Solving sets of equations \(\left[ \begin{array}{cccc} k_1+k_2 & -k_2 & 0 & 0 \\ -k_2 & k_2+k_3 & -k_3 & 0 \\ 0 & -k_3 & k_3+k_4 & -k_4 \\ 0 & 0 & -k_4 & k_4 \end{array} \right] \left[ \begin{array}{c} x_{1} \\ x_{2} \\ x_{3} \\ x_{4} \end{array} \right]= \left[ \begin{array}{c} m_{1}g \\ m_{2}g \\ m_{3}g \\ m_{4}g \end{array} \right]\) \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}29}]:} \PY{n}{k1}\PY{p}{=}\PY{l+m+mi}{10}\PY{p}{;} \PY{n}{k2}\PY{p}{=}\PY{l+m+mi}{5}\PY{p}{;}\PY{n}{k3}\PY{p}{=}\PY{l+m+mi}{2}\PY{p}{;}\PY{n}{k4}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{;} \PY{c}{\PYZpc{} N/m} +{\color{incolor}In [{\color{incolor}24}]:} \PY{n}{k1}\PY{p}{=}\PY{l+m+mi}{10}\PY{p}{;} \PY{n}{k2}\PY{p}{=}\PY{l+m+mi}{5}\PY{p}{;}\PY{n}{k3}\PY{p}{=}\PY{l+m+mi}{2}\PY{p}{;}\PY{n}{k4}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{;} \PY{c}{\PYZpc{} N/m} \PY{n}{m1}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{;} \PY{c}{\PYZpc{} kg} \PY{n}{m2}\PY{p}{=}\PY{l+m+mi}{2}\PY{p}{;} \PY{n}{m3}\PY{p}{=}\PY{l+m+mi}{3}\PY{p}{;} @@ -782,16 +805,17 @@ \subsubsection{Solving sets of equations n\(\times\)n-matrix\tabularnewline \midrule \endhead -Naive Gauss & n-cubed\tabularnewline +Gauss & n-cubed\tabularnewline Tridiagonal & n\tabularnewline \bottomrule \end{longtable} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}30}]:} \PY{n+nb}{e}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{;}\PY{o}{\PYZhy{}}\PY{l+m+mi}{5}\PY{p}{;}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{;}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{;} +{\color{incolor}In [{\color{incolor}25}]:} \PY{n+nb}{e}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{;}\PY{o}{\PYZhy{}}\PY{l+m+mi}{5}\PY{p}{;}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{;}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{;} \PY{n}{g}\PY{p}{=}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{5}\PY{p}{;}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{;}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{;} \PY{n}{f}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{15}\PY{p}{;}\PY{l+m+mi}{7}\PY{p}{;}\PY{l+m+mi}{3}\PY{p}{;}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{;} \PY{n}{Tridiag}\PY{p}{(}\PY{n+nb}{e}\PY{p}{,}\PY{n}{f}\PY{p}{,}\PY{n}{g}\PY{p}{,}\PY{n}{y}\PY{p}{)} + \PY{n}{K}\PY{o}{\PYZbs{}}\PY{n}{y} \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] @@ -799,11 +823,18 @@ \subsubsection{Solving sets of equations 9.8100 27.4680 61.8030 101.0430 +ans = + + 9.8100 + 27.4680 + 61.8030 + 101.0430 + \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}12}]:} \PY{c}{\PYZpc{} tic ... t=toc } +{\color{incolor}In [{\color{incolor}26}]:} \PY{c}{\PYZpc{} tic ... t=toc } \PY{c}{\PYZpc{} is Matlab timer used for debugging programs} \PY{n}{t\PYZus{}GE} \PY{p}{=} \PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{100}\PY{p}{)}\PY{p}{;} \PY{n}{t\PYZus{}GE\PYZus{}tridiag} \PY{p}{=} \PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{100}\PY{p}{)}\PY{p}{;} @@ -820,7 +851,7 @@ \subsubsection{Solving sets of equations \PY{n}{x} \PY{p}{=} \PY{n}{GaussPivot}\PY{p}{(}\PY{n}{A}\PY{p}{,}\PY{n}{b}\PY{p}{)}\PY{p}{;} \PY{n}{t\PYZus{}GE}\PY{p}{(}\PY{n}{n}\PY{p}{)} \PY{p}{=} \PY{n+nb}{toc}\PY{p}{;} \PY{n+nb}{tic}\PY{p}{;} - \PY{n}{x} \PY{p}{=} \PY{n}{GaussPivot}\PY{p}{(}\PY{n}{Atd}\PY{p}{,}\PY{n}{b}\PY{p}{)}\PY{p}{;} + \PY{n}{x} \PY{p}{=} \PY{n}{A}\PY{o}{\PYZbs{}}\PY{n}{b}\PY{p}{;} \PY{n}{t\PYZus{}GE\PYZus{}tridiag}\PY{p}{(}\PY{n}{n}\PY{p}{)} \PY{p}{=} \PY{n+nb}{toc}\PY{p}{;} \PY{n+nb}{tic}\PY{p}{;} \PY{n}{x} \PY{p}{=} \PY{n}{Tridiag}\PY{p}{(}\PY{n+nb}{e}\PY{p}{,}\PY{n}{f}\PY{p}{,}\PY{n}{g}\PY{p}{,}\PY{n}{b}\PY{p}{)}\PY{p}{;} @@ -829,17 +860,67 @@ \subsubsection{Solving sets of equations \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}13}]:} \PY{n}{n}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{200}\PY{p}{;} +{\color{incolor}In [{\color{incolor}28}]:} \PY{n}{n}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{100}\PY{p}{;} \PY{n+nb}{loglog}\PY{p}{(}\PY{n}{n}\PY{p}{,}\PY{n}{t\PYZus{}GE}\PY{p}{,}\PY{n}{n}\PY{p}{,}\PY{n}{t\PYZus{}TD}\PY{p}{,}\PY{n}{n}\PY{p}{,}\PY{n}{t\PYZus{}GE\PYZus{}tridiag}\PY{p}{)} + \PY{n+nb}{legend}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{Gauss elim\PYZsq{}}\PY{p}{,}\PY{l+s}{\PYZsq{}}\PY{l+s}{Matlab \PYZbs{}\PYZsq{}}\PY{p}{,}\PY{l+s}{\PYZsq{}}\PY{l+s}{TriDiag\PYZsq{}}\PY{p}{)} \PY{n+nb}{xlabel}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{number of elements\PYZsq{}}\PY{p}{)} \PY{n+nb}{ylabel}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{time (s)\PYZsq{}}\PY{p}{)} \end{Verbatim} \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{lecture_10_files/lecture_10_27_0.pdf} + \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{lecture_10_files/lecture_10_29_0.pdf} \end{center} { \hspace*{\fill} \\} + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}29}]:} \PY{p}{[}\PY{n}{x}\PY{p}{,}\PY{n}{Aug}\PY{p}{,}\PY{n}{npivots}\PY{p}{]}\PY{p}{=}\PY{n}{GaussPivot}\PY{p}{(}\PY{n}{K}\PY{p}{,}\PY{n}{y}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +x = + + 9.8100 + 27.4680 + 61.8030 + 101.0430 + +Aug = + + 15.00000 -5.00000 0.00000 0.00000 9.81000 + 0.00000 5.33333 -2.00000 0.00000 22.89000 + 0.00000 0.00000 2.25000 -1.00000 38.01375 + 0.00000 0.00000 0.00000 0.55556 56.13500 + +npivots = 0 + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}30}]:} \PY{n}{A}\PY{p}{=}\PY{n}{Aug}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{4}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{4}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +A = + + 15.00000 -5.00000 0.00000 0.00000 + 0.00000 5.33333 -2.00000 0.00000 + 0.00000 0.00000 2.25000 -1.00000 + 0.00000 0.00000 0.00000 0.55556 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}31}]:} \PY{n+nb}{det}\PY{p}{(}\PY{n}{A}\PY{p}{)} + \PY{n}{detA}\PY{p}{=}\PY{n}{A}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{*}\PY{n}{A}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{*}\PY{n}{A}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{*}\PY{n}{A}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{,}\PY{l+m+mi}{4}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +ans = 100.00 +detA = 100.00 + + \end{Verbatim} + \begin{Verbatim}[commandchars=\\\{\}] {\color{incolor}In [{\color{incolor} }]:} \end{Verbatim} diff --git a/lecture_10/lecture_10_files/lecture_10_29_0.pdf b/lecture_10/lecture_10_files/lecture_10_29_0.pdf new file mode 100644 index 0000000000000000000000000000000000000000..20bdd512f2f0927f20e0b03273421012f667618b GIT binary patch literal 10972 zcma)i1z1#F*EZcCC6Y2oH$x2F-QC^I&?(*Bt%P*9($WJeAR*mINQ0z=|Dcc0`@HdA z*LTjGv(LWw+O^g?bFQ`TO|2p!#SCQOM5Aswti46!0I&hTW_D--0svM8ODAi08vrL1 zQbPj(0IX8B4(^t&(A2@y-BQBR9Bg5UCM1OB=I&}~>WJq3DqZhm0vR{f@;;;8ypg+P zU5dtHF9saK@C%MEw?=37!=7ON&^gqzTgsRnl}dZaH!199Ndo#9$qr->?8#2o`GTmk}Zbt@~kw_^*>SK2$)j0NvDLRQVSf=}zxyjH3Aj3Ne>?WRZ*H*TY#X_^JxYuphy&Efz`0g!t~o zq2i=**xlZx#uav^n>nWJW=`{In`L6|k?gy$IyD8!(qnOb?{U=CrUPjo)oUd3t0tSf z?aTr2stPO7QV`deiGf?_>1cBIA+V(a*4~D#)|O33@g%CXf}+}MI1o4Zfd;PMr#jME zN(D1j5i=D!IHNmv_?a=zBtb4ZOFJ7)1jS$$3Lye}7?QLR=AJbtFhca~XI(G(KcW*Z0SkbqO4(aXK%AO&((Vgx|R=c2V=8(jV zn_x+Ier2yM>}@UWz2>CI%#O2!9T5dph;pL_auM%S>=In2U2@k6rGLcyO02)XhwFbC zWUG>vPwcLU`E~513Avmi&rgrb1QTaq#@$V2a4YpJ-xPBy-aZl})PGT(Ssh;Tfh2KbXz;RZ)xLh2Y&MBz zs(2*aouB2cd2|66O-a0>?dpWxkU&Oz%PG@B9OgHp*xD_)3wltor zrPOZOB&58%xzoWB8+nsetH^HHPtUv_Hki{hsmN2JdrwUeXj^kX$#m~4>1*JGnNjTp zc8YhYF=@{r)@d^OQEbp&!Li`G(`r!(=Jpz!OY2VKHNefS)$bU2OZDVg=Eoe~JZ@0) z$c-!0W&c)d37cHD_0R^&Dt;3a6~Vo{ou)lX%?;nrjVP@m;eEijCAULv3-I_M(Jgv; zOKv2~cOOX7o#9OP3<}W=CIUawtm1JD;Qh>!x@0L>LAv`i9H+eGtKe&^$fYV-cIE;F zW-1l=sRi4d4VsbWAoi9d5oVZ@EfG1FDgpt{mLwQvRU zHV+v?Jd0J(>72qz{D+zikOR#l-eMt^tr0fVM_#)Y?5KD)Y$68d`Gro6QGYhpn5#-= z=SWXZj#EfHs(6x^KZgo`YzmG%fZYi|`rW zn#0Pv`*AcYoEPx&?qpAB+3}}ehhTT$OW(VTt3+{kL0N9!+bRFc4Xt7p;r1@)wYs@^ z4v00DJACzv&j|sUeibLO@h3ly_PGOJ-tipxz5ID(%f%FB>JpbO49-F_o)lI#S7Ocx zImw>DZfJgN-aKKxssS3 znq5AvEB5tA6hlMDSwurqDf)d)YF2&b|cv#b3>F`?5 zRbcC_e4FE!eIwGBUtv#68VZkj`O26?CdY<&-k|1HA52Zo=ic!o(4uoSB0X<5hMk}N zaTjKxa)<<@kFM*&==%6Qz75-~4NY_kNhmW)rzraa<^$F8NuV*(zga zgkb}#usitjiK zf)PYGb#?{ybG)dVGSq9K+BW^igH}xCm>)=^>`IwdwsU_t(5{uM_8*DVl;fj*Dw>ay zWftCMl7hc2c)xjatm-qJXK0Zy!AhCy(betCubM@QSa%G@Ry}h@o-X44mJbX4=G;9z zj3%OEA4NWC95J4q5$WTr&KJ>fA-)|}3r-v8O|5g?FtOAFl2&8L_4mrXBgC4iOdbue zI}c{y%B7?c2<^o)24EnLqmZg$AFyL?Qug;uo#P@X52XZ~Y%XO3==|VmF%U?EMTyWZ zBdKJW+2*d>kug9PCP4)OL9kdbh`C$XqP-C}1fumD5Ag8PEg*bF>}pgHHUi_gJ%9)A ziE6zWXpaU>Ysn41S4|6>>H6G)P{;c+Iyk&g5rZilRh#Xz8al9^FaRE&Is{7*Lqe1y zys^M!w*rng=Uy`!$$y>>mmtApjy@wkIHH#wXM=ylxB|24}6jho-X%)^8MgN6<12Ks=R?n+OoqTG;O8{sURc-@x8`LSG8qQ^4d5$5=`WU4ah)%X z>*fTQgnO`~FRzRbzB0&0l38pjub;1L29kJ@uiSrM&do=yT#rpUl^fjxp;<~0-iSUP}sBaT5opJ))GBB|NC&E&$#{o-=;N2wt&>Yb>O61Fx2i zVn-#)o7l}H5}rp8buDNrODCK7l~o#x#MJN+q0ZjSYhDM1_)<7k^Nr(dl!`O^{M@%{ z111S#b_z2lmh;)NIyhXu9}h(|8sZV*vANC|a8(CUZSa9poGm@-(O6yQ2|;{MFfrml z5)^qK67$!b)+$~Rv56@>#Wg6&V&E2g3a=I}qBA4Gn$WJKq2Am^ZK6r)5&UIvwZ&kL z615fq#y$>d0IeDbL_pNtk)&>}#aHYH>dE)EIW`lE6>2(NJ=NR7c~czGLJb2E(vaDs z7O{`ZHro44T=WGYXr`R^OVXEkYY|bb=y&%v7_?6?ES`RNs{1H ziQTmF8z-~Ma?#h=Hq2d56b#Qnf^6VY(fzrRIx;&9m)s?0t8^m`-*u#FN*k zooJOnHVfFwSPHbtvjLQ+)&&g3TV?LB^CBV_{8xePuzl%hmQEIb1q{%q$57)jzIaTb z5e5ek$o44km}UPv68RN-NP4?N2M>)q00IJ!0Q6urWrJn_tm2{oAb{1}6nck7BhZ51 zcUCE|llwoUt(e)E*#KOBq8X?V^!Hb1pualtH-ZVJkC}eDkWj*X=`q&CN1_T^4B!gEZx8!uI83*fJc?7 z{bN?#(EOt+{}Igb{5`Dy70f+$^E>JT0=Pk(oc|Wx9qRfSXli!6ic-C=sW z0!$SO;8WJcT#=D?kEElY5X`0|_0{-m?t=zo*cauP{6~S_rW4`C*x+c0RGt zO$(eK%)%ri?U4vY^2O;-SC#uSwruWv@;^V_I^3475R6<%6fzK~f?1Q!A@PY=NE~PO z?vyYn$w9_W7k31YP&Ua+RlP5S(CJZ*!otRQ$Lmmi!E3Q2#Ab`q7V!wTEp`)F^1h87sDek}vt;q)h)M z7P&RvH4W(25JaJ|3dmTQaFt(~U5)A@I9SeKkoG&lXqis!+DOj{_o@&i@pTOOBo%B5|-4Zrv>kBl| zqtDIXpsmO=`=$}ma1LPIdfJ(i*;qC&c8TDZqk$ZLP_4qkMBAo&DOLku$KK+g?cb1V z!MO+*Q#eL6_32`Nm$1uBb@MP?gudJ!^`f-yyJ2;(Hw>o=0o|(JhoYQ%( z_gQXI)_UpCNt`LFO9R6Ngm9TeAun&Kf5V6W=Z_UiH!D)#-4?G^f5)>}UNvd>z!`__ z%!dcepJV%u9TXm5$HSHDu=-AP+4mO`?_s2Lh@F9y#IO@Q1S)k{au}I**`mlw=~A3o zUpeqdE+pE43hkm4UH%I8+BwvzoGbG}rHt{rROwZgr(t>-N=bY0q33KUM?nVOFa$je zD$@16Nj*rL&Y+4w;+-Y6?k@iAUdy2)GyQ9^ya1S zvxRS#=Ev)7#5;Um!yt=wuYs-?p00)K@0Cf-p4yt+!PmjxzwzXmk|w9arL zoU^Q4-h++tX|^m&gIVc_H}n&x+NLw@nK!q0-~AE=v)o=D^_q|BdmYx)`rWiuAd}Mz zCf^cq2!sYG?=K|2zqn0YO43rlh}?5Tmy`Rrfp_WMRp!OIP5K79o}@+I;I7GfAB2Egwz@+%RA8w^zyRl?G^`38dj8ezh*qrYwscSY$5(YJb>x zX}|9)uA83JuAZRB`x&z^c|=eqJ2kBwr7V*;s3BD)iCr`ZYZmwQCH`~uQF0aH@8xbp z8WOA|^-NaTZu}034M{)lEQ*NwO$QVYGR;(~f@<)wB9Ew~qgj)>lm1{P*`AHPkE*mOA5}FdgU9OXmX08Mz8FTVNgEf{gXwr0e7{zgEb?xN*iaGGp)P%>uzsmm#QeiK2iLzFDFfr?$X{W3dCME^ZUrTI-G*bK!~54NS7wL3KUU-lk4kn{ecRrteOmSS`APDgJzF|J zTS;J!B0_-mIjMqvp^uzv=Z9h|_(k$B4vy^AE<-#B@#64!h*dtXI4~A!OtJ9SjxcUD zz2+L=WOZwCwLf2U?>EYS2w}>gw%~0vE4J{6p^?n3W{fb?V#4Q-F>m(y9>pEWdf-Ay zN<*-tS&#=%6-=Ywrpbu(BvI8{S_zEu`fkode@?H?jjEr&u;hSy^xEZQuHLi* ziMlCS0pf5#@ZhpPB-pWs-^FWD{l-K0=Ii7Cw8Au^Zyvpomr5) zeR}m8VoudB(Mm{Y&WS>EuaTHrty`13ciIZsJ9kRl4MKaX)~wB=CB>ybU=^5ZIV$o_ z={Q=oKaDV6wx$7+KtdO(M?dMALdC&RC#Su=YMAoAqnJ=;u1(Q6S-YzLeOp5ZMe-d5 z+iZo~-s^}$sx=G$M$=}`W~b(WX3=9r*4SrAdq{i8^J)k538Fag%kYA-D^$iW&BANN zj7`hg^q$t?Bcv;pNW&9PgjuBliIGh(_#`tyKx%r%Z{5Xb#niI)sUfnNsc%q7wt><* zvRHm$v~hWrt@&@P(MaS9fUlVFw3Qcx%(p&dlQinRdpOA?l77y@r&sSVdO#LTHtv6B zH1Qm0Kid<`%Nu+uG*zI;Xn!>{NcL%X__Y9V5u8wGr1fqJ)AUn0tv^BJ#W&QfFEK)2 zFwV6mN?|8=vX1tBn@Xg0$UH^KxR-K(3gxuvnzIPnOvbg1o~J--;q{{K&YqPv@8m8_ z?R#w|s;+qxZvb&i5KU<%r)~}gGarqONs4OK1fx!IP}N4w>*X3lQ|;x{?{r{kIFI?ma&KJ6wD-W?=Tu z-JbVUZ`MGO8}`}vt<%|;b%(KJk!gpH8SWvXlH2FlnW94Yxjmlri|=Qq-9M6ie?o2@ zXmuOr*oCP7mbCiWhgt+Lg3daE51T&scHgAQ>>RTr0Z zp)oKYOPp8712X%%U!JS&t-QR#_4*t?5GefJl(>&al7)$`R76ymjJ5OZps9|o=`d74}=fD*c(%uvuoyZCmn)TU^armpG*F0Jrehap3yu%LU~TRa%vV1&44e@zj(ez0uT(J;JM4QZDSwr-n$Dm98Fbr3U)7 zjI)_UAL6%4UESIYoamd7idd!fqcZHxD7>z98T8vtcM|q4_`Pc1f2zKl+yY z&Es)7{k{q5F5iOqJo_2b!;;E2Iwloy$Qh1upImGnx)h|Ik}dkZGDb6nq+HKEL=n@j zrWlxW;kA%1AzB8LV+7kA9bbCV1n0i)ykLh3nHp=xb`iTFqZadnPjHa_9PA^SrU1W^i!@x#4z z#B`8q2Ata4G}d&POlr+Q>=KyD#-B~{>lMw%oy|FCfM*s+oq)l5ySR!O9pmN$SB=~m z+nH8GXT6B%Z>kf%*|>+bD%RyK#;9mCZ;jO^VTHHSg<|Cno{)8O0@Z>`s^Zr-aJseY z$9D1&Z{%MJ>5m@yXH>+>i&foFKRlJ4{qgw{>#dVM_-49eo(7b8pXb=V`SxckYyNwP z^7kj#eh>BjY03T=6t|y)$@S>Wzwc7E(0FsHeQ{{?W)!%6HR^(}<$e%5K!?aGP~MOz z4+v3yo4OemOkdK{#6Mlrie;IfouNRj^dR&leNXA4*jL@ZqCqzrR=bDn1fdhw7yw#K zKODQX@N4p)ZK2Nzu#R)$>NAG3n8UY9J6bPPOqlfmLMXJ5o4K~yvm_^tOoQIR^?!ad zQ;vuZTj44$S~bNUt5il-rH)=M>TOt**-VU|RjkfCnCq^D9UqgIUTp}gPtDv;a86g0 z&ZS*-{&cVlHx>7)v~ZysXpi_>yuQk@9f3mhP?L7Iv)yzLV;R2hMWI5M$~y_2QlnCR zMu{keL=Zu!3lk9@7ko?q9O0|dkuPI20_FY+O)4E}g7IGte45pRnr?Q_#S(fpP&Sn7 zDI9=|*5WJcTaKNbntLd=Cy>0}6k3EA=daXXHrGX(jXWFZ$Wa+6#;r817>09K!jK_u z>*AP}W%BSUDQT<^eGY?(AY+1H^Yv8*4y7AB=(DegRpXi}W1DrfXRKCk0AbB&8Y~Ov=m>;Y=CT1muqI zj_Y^4U8~Y}-6w+44HwHyp+48VD?^Y*W(V%7bvJJiYm!M<#p=t7?+czd`b4unv}rv?D(t!aDf3SKA^hV#MHG60C$N?((v`yEL09?|DN-b&%j#p2awtbU4Qf0=UvE&8v*{ZJqLs6uc-X zd~51@qiPdGJbpKOU1uD3$FC6>ojy zO0q1GXsMp$&Xw%ObC;MoDkFU5UX%t60qX78lDJo5IW&$%Inl=`T74)_I2)Q&&~8uA z6(9tsS`!G?r}&^A#0ANQd{B9aFCC@cK{erraCTF)3({1jUMq${&VZQebMZG$gdA(4z6_y;^&}A{m>LtgeRq{oGOJS`^iD}n4F>ZFx+B%S8L32* zy`wE^T2V~D=GvuGsdk6&QQK1fb6R&~WEE!!CEI_~X%%wrjn zX^T&3!nx0pnjrT&nnfDNl+DW$Twa{xKbolmlVt`nUMRj+N|cLjuLxYKSqEB9NsTB6 zZhj}}YTEYJ9;w=ps!6d%fn9bn0#t){U*6Di`!a$gJf9YMP-KT0{U7{s#~L(Fj_R!ifmbZ=~mO^Y`U!`ry& zey)l8s=()a?NQB3zg2MwHG)yJ=w9#2{LhQ1mXejY@$w{e*4au1RK_(Hu*7m!&Ab}Q zaJ!8a0ZJ+|Zs*hBf}4md)HHJ1ynWbDqA_QbbmtCJ1`om5~Q3^po42_~8XW8ge&<@2+c5-&gd047l_CGCDa+%KBwZn``b% zsPX06DsKP~O_)6P8E-&F#52A!xo39usWhHSgWvN@Wp?~drtk$Ir+5k0Qz!2au3a$m z)~~r4A9l>{_5<$FA&E9Wq+=V3?ma8afp1q6$OEt`{fAFO2?a(^{SyMWub)HIxx5=k znO}dM+aB_oIzfOGF)~f6(stto*N`SUzs%h_9y|p=;7Rp)j&@qdLq?wlRAie^ z<=&RiB!G`bQ&*M}!7Mme4z9}dQsaOTs;*ZNtl1}nVi=QYCYVm^I#(g0 zm7CWgu=e?h8FuKWH=~W`FFBnuTvD;}H(MKq=p4W5m=DTv3jH zk0Oh&$Tt3+pangLY9-5FM9R#Ls z4&!**T0BW0WRa&l;1LjK#moeXC-yI8ISn+EoU0K-NY1lz-eju9XT5i)hKRT zjMIga_yrZEH2f$?q9CtGNs3t-Q*p{!V^LKz>IG(u1uRyv(N}yj3t7St1*x^+9G&%; zviY^2=+ExJcqd@i*+6&}yW8XcUQmBrL!5c`iV#zH`RKL^wkz4WPMgLbPeXT6LV=L8J_S>FO%lOMzvlP!n8gk-fqVbKfHS^%P35TMN!>jHyZp%Q%*I2jlb^zE z?DZ0yO!^Em%g85!jL#%dUGIa+zjr3LxW&VOe;!ugm0^s%yi%Qpz(;KJ5`TTgE3E|r z5}#)tutuYAhg=W8q|*9?*0zxqV|H$C#yMPFA* zoAUK{V`}@~;+L%LYJnR(Q{r-N#i$9-kHE~If*U8V&}DP$2LIcLzfALo7U5$5V?^L1 z5AkPB|2LEHNOMS7x|zG$I=h2if3Xmckdmn*l*Ulh7L}CHVwAA7Gu84?hf)lGmrI#C z+B*0E=zbRg9?R%|7dn_)L-`B#za_x|u(+CcNxCzp{_xd(1OKm!W9 zKh4;>y19$nn7aN^fP(2?c_5JcR}25HZon^t{CHh7YEA#!(N$c* z79Qr%4UPZzYX4#kf&bho`TIo_H-)|iVC!Gj{xzGwNW*_s@^-bfLSq8}InmhuJ^&yt zE)Fh$72r1pWaHq1D(mq8IQ@mOaj>&PJ^kM?Ha4hr{sZG+XM?Kc-{p9DfzS`azhfL6 zj~4z9j0;L+{s+bj$rMj)J<)f}1SxGf87;682k*cyzR!}=X`oJ%*a&tFzb^oPZARCB{3yqpuQdtV^ F{{a|IK2-n! literal 0 HcmV?d00001 diff --git a/lecture_10/lecture_10_files/lecture_10_29_0.svg b/lecture_10/lecture_10_files/lecture_10_29_0.svg new file mode 100644 index 0000000..eb8af2c --- /dev/null +++ b/lecture_10/lecture_10_files/lecture_10_29_0.svg @@ -0,0 +1,148 @@ + + +Gnuplot +Produced by GNUPLOT 5.0 patchlevel 3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 10-5 + + + + + 10-4 + + + + + 10-3 + + + + + 10-2 + + + + + 10-1 + + + + + 100 + + + + + 100 + + + + + 101 + + + + + 102 + + + + + + + + + time (s) + + + + + number of elements + + + + + + + + + Gauss elim + + + + + Gauss elim + + + + + + Matlab \ + + + Matlab + + + + + + TriDiag + + + TriDiag + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/lecture_10/lecture_10_files/lecture_10_6_0.pdf b/lecture_10/lecture_10_files/lecture_10_6_0.pdf new file mode 100644 index 0000000000000000000000000000000000000000..53b6aa063d77a6f5534dfc5123b02bb42dfbf727 GIT binary patch literal 30054 zcmXt9Wl&sAvjzge-Q696ySqEVCCK8726uvn;O@a$9D=($Ebi{^u9x?#y1!1>)Xu5y zex9~Dv(&1R(#&k%I1#Ap&njOKILKJZ987Hx1O>@h6an^@Kds0(KbO=I$jHc8q^<3K z0-Qgeb|yaok^nOYa{z*{FoMfZXMhP1!6UQ2eYEnd#hH3>LA$(Yt!WhF?wlr;jx5l| zeC`N;iH_F<_fNmH1=lIKN^T$$ot&9%7f5(7vK-;^_{=pTU8b4ebk@vgAKg0AhNf` z+j(&JDzE=+B=V8gS@hG-VQ`^NdBalPSj70_VZooYlIh^?aXtCScDcAkvTN3t?!CV* zdc#`SuZEMfJBKf4!}fG^dZYZ{fj0+ioZO-RNO|?;+u6W{Yv#n6+1~rsjr7Nr?elua z{>80lM2`03``s1E*4gBPR>Or^rm+8&uJh|z@pB`4@pE+%;7Ryi!#C>Vjm7w5uPSEv zLG455!$hRxfv>{Y_Nm){Z;SN($zkWythEK>55d>9jp>b#yQ*IQw-b@~x}u}U*Yv$s z9iNWf1DNrn8`9ASACg=d08aY+#okTP%=?MNH0cA|%D}T@5ugh7{fJy?=l1Psb?;UA z9{+7;;|=(1^zrWhdbjaD=Azfo0yEvPKzjdFnbWR%T8w=!d1&%9m%MjVoqVyUt<6KK z+ac+ib#w!L&nzTT<@qK&TKVkreonG<5b;(6tgqUb@zj#xO9taA=TXfQ<`iD&MdBg!O+ebqFg97z1mrQ0;3tC-x3}4T^l` z4>J6O>wIQ_Hl|7&m@W#wuLZBKbvaSShI+@S%p2SPz8C%DxAxqRK|M7P5xD->TXcW(kCFlJ{y?7Mibw~jwkKwoN%`R z(eX7K*Qfg+u*mzlfW$6Oe}z|Au~jltF7CGF-kO12DqK;;l)12r)9lx6uckR@Mh4Y_ zvQEVlzwd9#N7k7p_(Vi%Jq1N#?r-{pb9|d zznQnGPZmbqOrXoo(E?3&$ornS&69rnK8jMZkvMvcX?%JbLjqPA`^F8f-qE5P@$>xg ztZ~Bq0sRQh$;r{;qw<{)9rd?Q(lhdV`#maa*^h2ylb*gd`BboKdK1(N4E*_^U{WR0 zaDL?_ENccD$R^c}&^I1*LO=X)jMH29dn+RJ>gMdxCw{OHxD{smH{Z5tq3|+urRQ(6 zw%tz=rLXmod?|u8BjQ0jq-9KtLagI50 zH>0N@pSgck`uowP`{d^RWI<5tHjsWx|IH_mS!?X2f4}0q(Rq)o7<7{H?G98udJ^Gu z(t4Es@cg$3{8hxa?jym~X5-H80`sPy#=co7q{@!AsgvG+#>G5yG)lIVc5E%>-oO0* zxK;kF8KqX_QN&risZ{@Bku7rfI-^IdVbnFdI`=hO zB$X>>L$kL%Cc6_{`H^?CrIN#cM8Wq4{4Mn6X`R#dnkaHNo14B9=2xjyIP)<%RqlB> zL(mc2U~H}J@8@-TQrwqi8+1R|*%>M1@_Ih*ve3DYD)e%+c-4cDv)#cXllLALV{v^6 zzEsM8k#2pD92EK(9#u6qF!&Wh@-Fv~w9@bJq=EYWkDCN{6TVVLL-|(ZF{z68a`dA0 z1pQ9f^IiUP(*$j2VdVMnMn8p+pSS1z^T8`9>_cCn^sMePCQ6D zg#bY9`K6N>0a~46k~YhP*AXt$XQE|4V;%hDq^=dP zTH5)MLMkGWpZR7M%F;Mv&jc3)K3`pVFv5KYDgiWbLQuApOG4ni^#|>=fcZUl(<5j- zZhV`W3A!Lk2D;JOS))AOm$k&r9Od_Uc)gB(Mh~;wuc!b$VY^^$UeMYyx^NwNU(EA4 zZM~uQb_hE(8hGAg``}WYRKAtR+cZoEyDHev!u2;B4sRVm7qOc-@?BY|MqGdYnPP+l zdxJ5h7rVN?l9|7P){m~Ymis4kQ?IZ19VgIb2A7V|veMxwrBFn-JpkElJs)wi{C>vn zv&fA;t%#3&TllN_9wFqY_c!0;^zk~SM!L*p+WU>|FP#7!U7-iB%D)K*<@NMkuL!mK zy`~fD>|av0+T@;_+?O2(H9=EoY*-OQ%j^rXYC$D#$?HRZfi4v}$Mc!m_2b^AzZ!yB zHR73*>Sv%+wkHk3`+m=(h)a#9kv`~}O^M;}KZ|cNBzA7YZci`Pg6hv6a%vJtI#}P`W zF%i5<6ztg$v9faUQtV6dq-^JzD?ocb#AU|%erLzwyIYzWTC1Y}kZNce!C^n(($@hI zRb3J)T&G)7Mu>~L6+h?KuZA(MiCG~A`!6z?we7dtFkHZ#3ueUqWi%Ql%`W0cmdvv)!p#(cIJ2)}r>{&ZtVQ)+2fiR;4~jw^%E zyJbJnvI#Pt?+Hx!)o=*;t~kMyn~{D0MryfK*vVXuG&^hZDns|nF6t}6xf7`An}L~W%rMIa$hU!P*@JO7-V_PF_~bP#Gdzk3eU+ekv$ z3#JxEaqmZIld^tX&K|MyC3;TSEuY7Rf3Ojx^z7fE0tSEn%Sra7sCS~6&oC$Mwn$hz z0+WBji&W~syR;H`5S!2J;tM2fqG}m33WU-;kP?q&4?b#4PhEO@ri^Z2nuyXFoWrpJ zvwf128d{2`5T76W`-4Iag|z-QTZyFUfgTuLTHm5Y-^Rc;q-d6nCu+PhJpYu;E$Mj2 zsv9E*H$nKLU-yl6PU3Mb2u4}GOtW-m1`ZZwQXVLuFkVEK+lRWmPdt_s2=GXHAe9))E>w2tFm0up%QI2?{uXIC0fZX0$Rzj za9Rb6U>G$p?c}RYxAhdZaFWIn{ixmagiES=DB$S#Ql;t?2Tnnv$^P30FH?3$Td%MT zJ&+!@5d)_S_Yh9&y3p<4L02L3-lLY^FQXGSNBq%!xZ<`37Da0XzP>Co0s6=Gd1lRr zJ@w?a2bQ)OL4XlHp~gLx`6rs;ER(2OROhn zeu4Hg8t-l4JdAj*;!;XXK>oTQ2&R=Xt@fMPSFraDXg;!!xm~<+W>Qt~Cha`4>hF5) zP@(n^7lAmkQgh9zNYk)T6s5=jyIGoT^H&eQk?1jrYTYo;Xp3d_=tK;xLpz;JBcBqM zo=;V^l9!NmB2~g<@;aB$8)G&q_}T#dS(H=d=6Y0HqhY0p`4P-W{H0$1_g`WP84^M=NVtb0yjz<5 z@Mk!G`qXr^68AWo)91kIE064Ys;1?H8Mxih! z0G!MO!JZ0CP+^6>E!yIwJB!mm1bwy<(<>$yQ>_H8Ag{WA<_=twK@{a?_u<2f5!^Dfxm?)I^!?BTR179s{!1l}MuT{l+hdBwW)fCjUcHV_cD+uANydcBl zRMS~r$roQ%>ivI)@dDS0bYqm57fB~i5ynADJCMZuV3?y!gwQ_>Ej&|7XvI@dC= zY%%E-iWaJv2hf$w?~%=~f1{mmRxg-ci@#;Ia<7}&?-KhuY3$s{Zlh!FEK-zI}onqR6#WG zJ@4vNv`*tbt@wL?O)sPh3q-N`E+a$=9l(U%9;^ob@-Qd}$cgw<*u>`tMeL{|g@hjA z;RVS@9%(rP`QXAn_v-!AvH8Kt&Py57;R^dlyxf^3pVAw~w?q?N>t8KK4m+|C>WI7Y ztkCY3yHnKCbM9?aN%a&aa#gCCnc+A;Ay-hTko4j_e-O16YUv|WU@tRh`JnE(y zcL^YJ|BVv@x=D5`d3?z9KJl`0DyNN;r5;c%nfvQ^n1~H0?-jT|IYu&Jxt`F(@HFNv zuDm5f8gA$nVi4JRou$BEq!MUPZTQdzXXypW%Ud;ahB-l4G>qmn&AiuMg)Rj!I>{H~h~tN#x*v}BWV z{#de>xZ&|HW2)LCZ0ADx{1eXAl9QeV>(T(kVD5JDr^L9bnPo0-i43+d9l1uQCK%j9 zDH5*?*q+qd6qnQHLzowd&EX3iQ}t+kCwpY?ZA4rTYBM+ZzpEM4XaT|`;u{9WCIg)lZTx?ck8@a z!E|!hF(U6?TqnKK470`E;39y@WiK$;COzIj{HONSoK3PE~rKC@(l_4vPJ6Nm3-kocmmKNg#4C$4l!MOkNA80mX4 zh|mN^w6Q%n)PGw@AxT+<8$-o3Fh!c3I1`WSfyET{EsD0ktw(lvq5Vv3cQ1bGC>Uw4 zWGzy10i=ZGWlS69YJMfVvogJQ`7x6WxQmd5xl;$LDdLNxWoYaSzM(7N@9Q-I86aZw zB(64EOfY-qB1ub$Ux{WC$!CpJr5Q1@WMwrFMH9=vb3Xa=nTw;hm&CyJanwU(t3PN^ zhzptG0D}_shX1_B7LAY6&JF;2)C4`d0?0ai3C2LeE^ncdF#YxQH{`QVDP+0Kqk5c{ zL)51cgR3E^e|18zQ@AD`@Yd@9PlAHO6=B0!U`S>CeR(1yMCW~2CahD{Sp5`F6sOM? z+!0>J@ILL!k=6sXL9_Mf7}I+Hib*FVz4evuo*#ItqW;%rXo{{^)}ZM8GGLl%%Td&F zT%Gyk?S*Ket}s(QQY53EgfgQcQN!lSTqklO{U8HbQ`W3fSWBN zXlh^d?D<<}pgI_qSN2??`j5@{2)m((yl*t?a%~?( za3YBX=)f@#X^-rX_?XQHZ*)v%=vWoRCq|=66&{QQpgR~m=BLLJPt46ES=u{<)0tSY zIl4N6AG3xYKx~0Yr4fhYWxND6dsxo`GHZFy>FegVnjnTL!R&jPJ|Aiz)GWSb;xeh^CU!;*YcN z*7ZLwkC?_Ib>H~vtVYKUTEIC>bL37EtH6l7)PJhhTJ?5a36%W?a`Q;pOyMbqX-$rtgF7rFcso)(WZ|97?4QkikfdQ+PehyEwUD^sGSP`lfx=F=7(}@i)g5s7n zyp`+cU^NB(5k6+6y0xRaJ;OUTP3zvV!MXvB8h=A)(=z61^!7w@$*Se_ug96P)#{-h zk^(jYqN7=8qcatqGiVg+i{l*QWXB_yk%>RrjkzR;>L!0HL z#HJ#jER4`Pn+5WAi>*wV6wtbQ7yZ;C1p6?7y7NIZcmkUKud1Pcp>-4t8R~@rsL3s1 zQ8}pSQiS5NAj_Jm)46Q4JjL9~!0q|diD-{pCYLB7)wONZz8Rfi7aJGhFjOGibr6+C zQOYxy&*zxd9r0z#nu+;dKv)Ltv%BSUlID*obk)4jmj$zETPz_7j*Kym@2C~B?Ffn} zZI<;1UO&1y0d=*Ck6QaH?$9Lue4Yc;Bnki_C4;d#Su@`0gXttDt@XQeOy|OCKXGpQ z^Q$mWC-+p;#DUMFcDs0K@JfD9fe(S@9x*PcXm04cL`9nZooVD`J&K`Xz?vMSpYT4yAJc~$&D=!I zmgGu8yN~<;vQSENB`F3FujSErCnS+rUK1%~Qk3S=82s3t!Z4&SBGRk!rs~2t!_$l5 zRb8A4vPuu&-JG04O0C)9EgA+hXRrSrFkqvp|3Sr5i-t2h9Og87y6$`)E z5cXMYR!*1+aS<^&uDkQHM~O$=CLsItbC*%_2sVrZ_08k*3v4To6yArXR^4FJGlqsh zVr$07D^a2$JC#ynaZIYSPraFy`U4% znttWXR@@<*Ij z3AgG>aGTQaV)78ip&EC()+CtS@D{;PZq$-oUz#94#O1flOOPPxU|ssS1BJ|t>h`cP zS~{7lnEeBP2wO@ZcDKRU2mvHeXBmjmHscx|_Xh2(n6_TOcqk(#9P>`%uNb#Fp<3!J zM74JA`j153$8Q)a-XBN-JzbN;onGRy2saTjm(Hn@NjM6UbXzdPJQd@#h`xp?#qgz5 z=(ieR=a%UuBuRPF9BYR@CBwX?8Ld_a7^CA2Iu}s0H)NJ}Q-R7kz&`rY^AH>vMr6j5 zohIq0#WGWfyZYj#qUk?_HF=PzCW2+{ku+(wSk%H8udtCzak!{|7x_Qq+1nP} zye876SC5qC_xWt~=+lS^G7kvG(<|0sbVZnN6%)&lZiKcx0?H;ZqBq!xVAYHEc#Fiw zt^#mDLw7&iv@r-y=7N{+4Ie8@hCoW-)YQ* z-CqA#cfeSa{rl`hHJoPEHeQBFtGTAD2E7cIr zR8lLlaM@1nT^L#syX(${i@Dnt!o4O^q$!WJM)&zl_?Zc5i_tG!kFhK1UVGn^Kg|GO zp{}0uOJ5O+Z@>RJf{$Q^wBa>jc!_7Z(iMhwWzR0!qU=>f&2E$C_gnAs)i6BG8K~U~=Pr zHaS2kSWPJ9BwH_Mg!SY1j*ol>%AhB_CJwpIZixze3sw&BkwQky1%~ z<}-n`4NLRbq^J7yythR%0Nii!;4cyIoHo5oZLj%B-+b(YZAN`4`LIXRmA#Jj_Gw}{ zqeh}q#^4S!G4O9AuE zoB0`s!BF(Vdeo8Yt`binPlD_c-gw3cn(7cM$Q!c74?@~@6minke>szkoGAENPSqs` zr|&tS7-+}d*bL@M=1y7)De`qU)?5lCJFmaI-@&fJUhmLAKkuHk!QLXCI!l=I_n%1r zRO_d!oEpm>**F5e&Ye=wiG8#^(55vx0f9<^k=8X|853%bz?Fc}AAKTe#K;3G}O1IbsZi^0kj)=#3Xw+jp!hSvdF#Y8Vp?(O}nM z4P)p<=x-nLBIaG?-Z^9a5Y)w+bh*|HO@ownv*G4}-S^%GI=u;jGsRObz#U4mfL2x|c)|QJvG9qXR3QY^!Xf?IVYB3>r1Ers zg!rwy%;%fPQZF1nIeI!=@ddX%dgVD8@_`M=54DO}aQ?uS%B9cIwb=t2p=mKD%wIkX zieZ|>{hs`ktPG;m*JCgAK29mNvj!RC#HZK~w;nclzA}G@qLafg=!qoD*yQKW8>!uu z#|t5OuqyrZix;9LL*&o1?)8RbYK`qXuz7VQ*op#>3O}&-ZYd8C* zkR2N0{0}}uI!isk0%q1a+vq@{U3@r&6-CI_&Q?@iZRtQk?IK_-9pkP82NvaTcsXx% z0xWWV_$^d(EnIh+oS7dKv)X4$LSu+*l)OWDQf2}%YVgMu=x-&F99EzkIgKE{rK#&1 zU9~D(s6>u!eem z-Hh_Zm7EbNGL-rHaZ_u6#&3ND4?#NlJ_-JIOt?iR_vsw+&kFpM#v>RA z<9VKB(sA(5@BEjZ`iTJ4S~StoqYE>Pm4CWsD78l3n3DprJnX752lYB`6q1dS#~O#y zmLiA=(p@ap3%qIng7xV_s|e11W_$?$1PZqt4;XFW^P3-*h# z8QkCHC-!2YMuB?3J%Q2Nnld2O;qJE=M16(PRQ2+2U5r!~4no~yhjqEnwp1aAuzu$NJN+aY7`=j5B*qP~ZEOTfP4Snq$ zZ4@A8=FMh^6k{szFE5k+CfxsUvm1wyNA&PUJU;54ZbPsLkf(l%8uAykW*(?ji*u;VR>n#0*wd8p$0qRULE6~V!+fyM037TS74&hrFUxFO?)wx7UuMF5_Is zAiJ>4Y`BDe9>$y7O>7M=UooNM(_v%Sf zPs^{D5gPfvRR}%sB$*7y^3JvC3{ANBYv@Bg8C5VO3uThm1B#p*X$pUYYK8_R!>A5E z^Gh6K2LzyY5%XukY>Ie6c8$&lna$kbKqAE&LBKuQKrc5m(yOz?%B5Bn6r}K}FMWAi zcWe5CW97u)-8I@%*CcP1i&AU^dH7IDON!Gx)7!bA2W8|Is)((axQurAfD#Z4?EKs2Bf^QET<^ts-2{nMD4> zTnyJ8{y?sYV*8bwnWoVd%6z3R*{XD@$Ccl?fE&h#DKi-f=WfBisCHO!)Hpt2I7a1? z6bQGt=%rXIR{=}7f(JEcBt+btIp16VsT4m>v=mOm4HCpB{7tY2xpP!Qg9Al1V+JS5 z=C|Dcxxq2!FENlG5&gU#F|i=Be2pdxh9J`ml5Dk1&2pg^JMh!azf^`+A{RDw6wZNV zr;O?iMR_SlYJU{$gK6rN&2nc;a3Fl_TuoCZvb{5wF~aXRyUfuAz~f3l_{T*rN4>n} zn))yC?dnFEIHAkEH4Au9>^RX%TA=nX1S@z(*7Xk$JoS4lBhz3dWkwd?{E(G6+6t_5 zB-qGpePDKC92oXlIaJ5;5A6%b8vwV?vSfY0Gv?YX_h0Nu72iYQmzpr1u$AKxze7_^=)MkXy_@GfDMnUczcp9A!0{zI-426gb`I0hjFNC)=kHLG_ z0Jv7a5X$t5+6tNWhDI(>bSSKBRi|FZ8Hbk5l6?mvAIJmYd6)Q+?5Fi*Vl;H2KqN$Y zNTCPKy&xoxUd^I@Qw@Rs(qYzr2Cl>3YkaJcI3mlQs1|;u0+~6=v|gwlR!?V>(_G6G ze#cX8&AKL)F>^3#r>J;lu-+jgnZ<~aR$&xzgIAZUhCyzG(4R*AAD*ws`FB? z(A%`2XAxghdBm71l0<%a)*Uw@s!fV6KBBByu5dk#e~V6DfGpLwT-a`eY%AyWR}$!K zWC``XD4>Y>BQak3o=jw&MfZXVo)4-ry5NiZ@#~UPYZ!x~EADZWG7@sVk+36;p z6a{CPA-J%BGFMdM^5#ioO+pEuu)70y`fIsmhCK|ksDTMSL2{Ge(Z*Os6CbJwC;B`0 zu&+@?w4}Rlg|C8f5?U!x)LNPXTC+Lw?n9&&*jfG!MGH2k1=_l-K=p0$?97q zx4S)6hB;KRjeWmud7Um5U8uZWrTZS5_Pt7@mTchw@duE;cA;cwCQTqI>d>&*^Ur}Y z5FydKA9K1b+&^f3!J!%RA{hq?BC6nPW0*^E!&o_q@w67JJA(w->aU$dm?k&2^ZKH+ zyGq}VmwLIzScl^ZKSZUrT6#Mhg zyk&uZM#-?60+?2I%@riI42_G~VUIJE=k06f;PM~$&+qs;#?wA4<{Cw4!Fbx6uR1VC z>Ta2;sjH&ulLN=~#&uEY9MZ6Ic;2ZF8TxB(D5){(9HUc~B)jY7aS&IQoV zQ01J8k5AcyaviaP0DE?Zb1s?MGoEgBnFgF)1Y#d!B2#fr$lV1gaVQwSls^dI=CF^H zd!KO_!BRAGjlB-pEb~(eX_&#q8t^Jq(6|f#`cntkUuuE6iP%>Lrb&Hyk=R0`CBhIT0b4Nr`f%S5`r|L*)TL zOvArsrT4xezuCMB=#lnq-Hqm^OmO+RQ=2&`Y!ok9_NiKz9xBXFU-Yo`3)&QpIerXk4`tjeaiCwL*{+mVx z2(M$v8<&>&u*mY=jl%zoW1VtRmhktps~(eZiS~OsliEkiYd_9#RsqwX<6_+Hmga!B zeHwuT#8FRk>9~jCL&pF+<_Xj=lCd@#lK&%clgGiE?OprKzgoS@|HQh5&Hf~sSTLV*>f@bq^vUW&ak~!$ zV}BkZDF;{kW}p1Hutk=FZ#AGgEc81A+Two=I z(S<^5B+53>^FIGP8W?+C_y!Vkmq{}DWcW-^K+9c~N+={T;*Mk<{O2Z97zH!0EUG!E zw1O(27UHdRlCQ;)ZN@BAg<3m=<2}0FE+G3q&^x|aAN{{XI=?#%kuAG)z~I|XlQApq zNb$*}E!&h8FV`yS#@rFPVbyM?&$0w7_`=N_0it?Z#Q~nNe^!gJd!P0) zW~tj2IVTla3N{Ehd#6R$2yb;hYG1#3Il9j=;{7kd(%YS*8DeY}e;d~{$U+>IGWHA= zvlO>YWodqE$P^a>XVohq@em~_xN;O%Z<9rK*GNJ5ZoLiPrOEwk76U;DImHXioI$vS z^;|bSTEZQaqbINWxXs66-GiD{-w`aCO)8V{5;X(H&u-1L)Krn5J1 z^aB$WabI*z&%Un+zpABOSr$6Q>V0R%NkGi9)M|M=VcYwAA{#)pf1)^dIvq4-$T?}o zG$7nqrX{qsf@LE-R_$e^q&nNeO{qF6LTO*3b`rdhH&gKR?Y;D%Waz?0odh0dQ{>5{ z9kSmPc^mKyLn-EHb3*{32_a~WUT9}trWJh78RY9+Onfk`Tv51wfwJ5oMigC#i;paZ z<-EF=X5*-|>R2oD z^apoVlrQO~^Gc}o?u{3$!aJ!m+&0!0owDeHArYy59IP*6i;)oH`kT~_9Lr>;v5HXI za_7u~o`YnJ|gEl89I~S1|OCl7sy4sPMDlbiKcQ_xY z^a;xtzOk{w`;&OTVdfze@SAl37?>vfM*)T8VtoU~*K9p8Q6NN{0Uq^gzpvf@v2a?Rz3XJiVu5j} zVhse_*#c>;$tLG2n!iRFrbu8&=z6w%Az=|{K@kuUgI6Jo4QrT4UpNpxX!XJmD{C$; zLIK@;*o1ir(=LkhR34JRTI%Zv65HK3V9;b=2;?*HPd&8vPWaN-kT$T(2mkFQ+Fkj_ z7~v)J0^aPpAP>LQ*UWfplagCbd8pFSgqW^B_Q?zxc*G%|z?S#zksCf3$1m^r!{ zu8EA)LrA>`;iP-&AknG&7avoY_kM;9a{rYsjVr} z8Uh_{ANa3xf=v%wZ?K?zT<>4Jzlju7UQ{W#RM%vM&;i1)cT$}a=xhzEMrbK%t469y z!*kHc*)Ck<8m@!-7i@@d%kgFCJ%NtQfj|~@h2K09;m&qciQoQ}I5Kx@Y#Sh4A`vA) z1)b#>UHG*_K#4XrbQvWj!qVb6++-N8YIeoM!i>&py?+K=*Ki05oY?gxJ4d@VxB@#eU} zq{7t7{&wl^nYM3pk{t<+MBF;xSf_#d%oxATLCWFXab=kMg?ZbiXd}@(6(^}M=|RaW zqz17gZ!p*ennp-}N_U=vb?}a}HHH3-P@WJz-o{YIvkma?o_;!Cbu)VR7$jJuFyc*Sg(C@Qi z;Z22JKT0Q4jwDuiZf#-Dn72dY8V0*-ORC6X20GFrd7E*hKtygqzX~8Z^CjWz;j+y6 z57`>iii}Zsqjdk8#F(g3#WbjF%cxp7F`A3gpn5N$J5mBr9l;o5mg`*+E#vxkWRG7* zM-?c|P$^03p>vgn)2DXT3!;am;7bFM>z{oOG|FjdghLt&1Yl5UB4|@Ea15T$dQROZ zjWGA~+`j=%J!N5C?Cx~6i*5x}%vLw+>L&F&^~o|Su;?VYHD}JD>VCoyK5ou1P=MiAy{f7VOBepcfi=aAM(mlDv zd+cqD2f3Z{7Hm*P|JzCX>3_yMD`GilLLvD`70k3mX? z;P{-~W5eIh8)NGtg&!s|eZ4i5C=BzRNQ~&%FS7=zkQ~u47J9PSD-dUrA2fRUjxUKs zr6g7>UdVN1%C{*xLW1XDQ_&q3@LkiKO}v6CbMOTLj}}(ULNW`1o^eW88(S$>1+ADu z*eY5F@ybx$v}y@uf54bOsR8!jYlqzXUBU162<=?x5|6nlC{fvIfd85LNC&+g>TKOeXwJ{t7B}iztHEO7Lqle4|C}i@;ZWEXTly4oU$C@ z#ec2pb$r_-v@armoF{9d+-W&hQ9s!?7@}E1~ zTecYv1PLddJe@jlQR+acrh9Jhex9;UXzX?_KG=UgH0!4mY}-g81cx5QN!*QjQEv@5FJpz-7%&_#k)4os>fwFUI?a+rSKP3^G z0*uJCfvR-ukK#~IEPKKL+8*U|wB$Z*%k`&~3o{KD$*cmliE{XF)QCr8L@keJ8}Am7 zf03}X)vOV;T8^TUKc~SlKRNl2Zfg zk6;M&)aV_;AO4II(zxUvONL(3FgLBW9;u;6*q~2^r(&G3nAUtHgP(FvS4goRWWDck zrKv|iuSrz@!i_VY)|m1Q0&{ zvVe`%>dj=vIYj%qFI9XXk6h<#%>}!+R>L%&{t^Qan$&tpp4G?1{5|pp+C~y9BUB2x zAY?jcvBrl1#6nf_yuqv8_+;~b&@+x(^iko0)r$pmOS2)8N3Wp#k(!hn2I}Fv<{m_o zT=9sR^5R|g245tbOiLL$jj63qHf=e2^H8c<%8*eiG?4@g1i`JNlQO84*IcN;SxODV zpn`0j8U=`wze=rk+C*-Nwh-$a3>{FI3HKagC|ZZ5AQV(A!obr^VgeJXrtB{{!F&ge z9z(#;?)Sik$SG)_@c4NnhE}N$V`)q$hbCHz1KIb+BE3equ(se3|4X`x1ckSI9UF@P zflM14Iv5V+FO>PfMGv*4({Jz&i4FQy=qn^HnfIi3Xi%UKevcFgh4pkn{eEvAM<0C& zt3|#N3A{k4%Q6|;t5MPYTCZV)AO^y$Mk6xFooqKttEC%`mhuWMxbu1$F5VB}KOlNX z8~-CAlEc#RgK=#&2)eDSTva$Y{pu73k!ymU5qBf7%=YUX?m?j5R-vWU&34qH`+*X# z**}9e%(AgJU8yo%AU0|VSr=lFxJ(F-fzKd*T62SF>*XWRx+1ODOV6`Wq~ z&oXjSsAb;hJ_or7-*{<^kfc`p^lCM!Z&#f!FbwH@sN?$04{gy)$R5fIy&T6^lJ=0p zB4k9AV_Q8l?3J$ZV_drGuRqE#@+PRe;HwIcO-1~>9vB>shbK%XPT+VAPU&}khi5Gr z=$3owS2VcWfZ;oggS340N!xdQiPXDw*%Q1s4ty8%=^`E`uB4(BvE z#8J{F5(9_dDV`qlHZ*mqpAMn#C`#*~wRi=UN&F-ZFyQEuCjcR4JgrUnba1fP0DnFV z<$vfsBOx&DTbc++f($RCay6|cneR^|Jb!k=i0oOnoVriH2F-by^ZqWO`S=>-67+4s z3O5WAE+63*N;_-u1V_tVk`1{$a-eG**_JH)Q9;XHdoTL=N;Xfsi9f5kg_}s$CW?7@ zfh}z+vD0J!x4Xqo`Ag1Qxu92|v}l^aOEOws&d(ln@yQ=pFZXMGE@XL&5eJcK8UlZC zqv=M3jmKr5BG6!}QG4(D9}&iVkROnO2@xM|AzBD^)cmJRO{7p(w$hio@$$$2opC)! zN47RcFED$B_&B+GxNBoJp*g#AF`A6KmLoX=ZM?>%=e20BAzt#RWp01E@JJd5;_ZcZ z2qGrrr^3V1w|8Mbh3Bg}{yUipjcNdE&vd&>q`c*4+aFGYOV<9pL64B}+?xgNY)uxN z-eAY$0=CY`4FA4=-bF&>9Y@y8B}6q3MCe%Yp5cm=q+HMqq8T!Dun($UBY5Stq6Fb|eQy{7auxG!2G;SY^Mlh4S0+fwXg7g`6?Sawy(@1dVX-P6J~9!q~cc_L}DYFgi%I?>(5<07E(-;8lum0uCWb(9GM z;(4sI&&-r4<~sxfw-|1)64a^2<$Z6_udY|Isg#J7j%A&01w#G^U1N8?W={&}fEJ;aZn&{h+$9I{(W$(sK z;5r8NWOIFKVaLenYCX`fS~9jKDP~S5tAgdx)(}=6>U3P;+0lck7mys%(FT=W&zM;K z3xECx&KD>ey-Lad>+P$<;#it~gF7L(v$(U!;vSqJ!GgOk?k>R{g1fr}LLgXhcPBW3 z;O;?!+$Bf8^Sw-BaDw)jjj8t?6?2cabNh`=E94=JAmz=2FCGlV^%E z@QM@49>AvwZ7}|0AD^xpN*37R%rru^>+y{^M-6132KSlv4U!bYc+w97hD+GT$VL;| zo1+^Jh~l<)8_GcZp5TA7^u;R}S$J!s(R)oA#$z}j$fC=k;Y)uG4qweZp->uxI>r5g z!X_^9pd=$hla%XR5HL-aoQWKh^2$LLWxWI9(V=c~7a_MCFDgZuR6kzX!^rj{{zF~P zLmf30v+gIy^Ek`3bVVS>2d12CN-gAmN{IWzT7MJZMa?FXn1JLSj=?F8EIMgRE9o_w z{A`AUzA&zbVDLAx50}_lV86~wRxu6Qk=DL1UpL~o#_?EPLRVevhwVX~jMffss^4?M zY+L$jUeR5Qe3chik~QcFjGUX8e^JW`!+Sy<=?zHKz`cc8un@;OEM(B4J{JKg{aoPa zF9utaxO73^eatV0%&AHnZdJ{Pvp!{050*S4(qs{92LYy-y{^%RP~%8Fz%M8(?)ZK4 z`}|Uq+K#Q3#BAR15F+jxcHkE&n4)n`OMVRXObp|EM-5n$c-dC}u=p?pZ>ZhmF#aly zr!l)pQ8RxXvWaiscJ;)%*bhTDB0skma<^|pAHQTx=DrK524TEr(l0CWxZHGK$H+gt zfV-WCJBcr<5AVaa$*~*6g07^C5$KGm{2u+{x*vrf`Y@D!MO=$j&*I{KODc2?cfnp0 z&L||=a#SC0G2>n2#C~hASor65?C;G=oXA1gC6=4w=9XICy4hh4Z5XdV-Jh-x^@G)#A zLV<5xxFi%8UDDH^5iJKMa-m@>svbDk5Y`t@>?8H?U7l{M>sx;K@v{?XZ2vzBEJ)?Tw)X z=pu8#j^rB2BGnp4hG|w&p4txR!5hQx$Cpj=0V~$ zL`44I@f^C5VYMgKXe|h0h#|G9iFZNsnN@0_)Ks|hV7(7&;^CoKz%obqYqBt$)Kog+eI9K9A!idUB7L`eXL7r+DC&qUdEmzMncjcTY}8Q^j{a zn<9~W`$AfEA%&}!23F`J5NJ^MP_*5O2d`ga?V}xU@yoj?$ZAt)qqFxQ*z&56h^@BE7Xrx`#)9V!*2E2yZrQYk&1r51isCe%9I+Mw<-$ z`TlU&dX0AQRU5PN2y{mr@>Kvf{Re@UG(;S#QtJR?Tsm|7k?fF0^htVC8R(D8A-I+H z>TP(bpSskRzHlqkZ|Jbut)au7q`qpZYi$i>L)rACM}>p=-mQb!e%()9A54ldgXI0H zmi!0U%j=af?!cFA*wEZz8(`^P5OTM_Ebv41%yLxxY-B*cjG=C14eaYU9AnM3m~hHK z%Db0R5YvGXCE%LE`|N{{1b2ZijEfBh`HXE(f`T%u4ZUG?DxFy7r;u>Rt{Hjfo`!qN z2Zw>P3f}!ncjA1bv=vW^E3T}Euat3Ip;gKsc`Wx8!`v5FR~J&@f=*;#!?3*zH?Iy; zU({EZ_w;`QcS$6_FS4)+Dr?O>`SR8h03gUyt)?EFQR`p&MGUddlruWmGDcuUzg-ma z%8TQ72o39sc;$9_c%2fp;h$@Q-%nCjTT+YGPuYmPFO$>&R20TGCf2JPw%{9FgA>wzJ& zvM7W?g8R#Bk7zc-!$IAsmT&bN2c$jT8VJGy`G2Oo$-8_Dlt~adB#Z7|U(CrCg>*+j zG?_24$DGXMSyeD;ZrcJf^{^m7jyTgKI^2d?Me#iLR<0{LFlR(OZYc4zwPq;QJg+w&&{_AcSO~F) z0b-30G`8}BHF(FUO9m@TZ<-T~9oa4EVe*A$a!VAzPXB8JTO&GFQB`*QWVh`Qx@pQl z6sfDXBg@mn?bG@GmLBY#q$xK>M&?iz4*3;y?D{<9kpU0cOHX~IOe{E({wu^eaIy*a zHBt~BvFV4;K7|w+wYTEjlMERMKce+sz+-YHjfM~IdxySa-$t`a8r=5RfGmnQ6-z^W4I+NHe`z*tq>stv~W#d0_N2EUtWxrFp$o!-V(686BUk~Vy9DJpO zGvGP~c5V)R$lK^(3r?tFQDAs~yKPhmedAM>uTED3lZiQu{lX$#k)k#6#^jUiX3G72@Fsg`eK_X%)MON2h*Xi}=jXDOmu-G}P08e` zy_+A}5k>Um9f0G&7=r=j^>8J2OLX|17blThxx2$**A09!I!8n$RWaZ zTFsah8)|zPloyxfiB22t80#}7?$jN93iKn;73tRe^2pbG6L)|jP)YtZ1KT0|yTs*D zzUr3$vJV}{oOD}_GIo*+)o?)n3R$xYsbx#?ElbOh%>8m|d1?+3+v(_i>iZ3&(l80{ zx6-AxBb(+tF>PZf$5c^1RoKlgA;Dzq@)b7sFyKRzjqeBsCwT#k7RCTslay%x)QZ5g zVMG##w{bx}BYCT7#@2aborCQJF`F`aL(Yu_hEI&Nypsu$I`Pn%lbV_+hXw+0G=ubC zqJvdc`0P+I$uKcrRo1p~?XSWw3T@zD z_;(WZqnxQffs7@WCqjC7X1w5#6;cUbJ~|{48jcjmM3;P6pk@N&+tSU|(CT;2m}lPj zi0ku0nYYdt5L-)sj22ETiZffDaO_UM>15?^M5SPwEjdjCoUC-k!p>KOq)V=)VUUat zDKn@3N*#+r=vH*8I`CUs)a#Srz5|1FYiJSTw#ndk`+k&Tv?1oUPZoDFh0VFj;|i$9 zFl%JR?*2R~o4;>7PI-gB>tJ$2u}vq3hZbb;V?!8aScK#!2Z#{!UNv>^0Z`6X*qVlg zqBzpy9+ItDh8c1<#O6)@bz*4TRBV2JXgqlPlDo)k@hRYo4}YB-7tu=$hT22^_vIwS z?p(-y_ZRqDeeJQVfGE-Js)Ip(sLy05J~DS=ukXm3zOK1p`y3Tc%FV@9er#ql!<2P#r%u>mWWEL%I-h56R$T%Jcp*uwY7%TtC&F_Ku}uiFM$ zoV|`SB{OUwcHS?R0z$vJ+?B9=e+}>G18m`Dm^(p+J5dyCl!_JKtrplD9WjI-58~H@ zZ*?EE3{Jna@K)uT>g%vsjN=f?Ek8hq_S4~2C9yvPp5SMA-AC+Y`=;xEemTv&CmUD= zie}3eVEInxd>kb6I!?en>|-I$%2vS(`K}mGisGd#e|hH|nON9TaBR7eH(@FKSv{NK=V zB)eidEFRmB=lGxkzVs4cyn)d= z>ZfLzU3ho9*CGnLZD_DGh_)C`FA1 zF(-e+v{F6iD58tBNg*pDg$qQBwnX8xE68}iIxOCcgxL{m#MDdsx-Q@zF8sX07uE6Z zFleSshg9rijs?QxWlX*_?tUKQ9Mcyuehj1Or$FjN-V-=E4{CUfdfgBr)=Esi z*Q;pP(hYbgBx!~;QEHmli?>)ZbE(H$njaEza@1SCvEbkf87NPu-9mAD;x`fmb!T(I z5c7tFBsAwG_sVtO$2w21eEu5FcL|R(i@Hb1&g^HHt*Q52w|5b45lZ5*Q$V)P{%t<} zi$g3lG)MItUnI8v_S7|?3dK6NrQtL`GUYfcWekE0=!gO_>Ud;-_C8aS3peLtVpr^Z z+klPRcfPWK3KomXI6$yi)FBp&HpU(?!B@8XBAh%l^$VuqI-xDeqN=nV+gWnJvgwPG z^-iTUf{j--!QEJ$CAV{|7ID7vfufiMhR_r(y^kX4-O9yjcj=|-VjG0fm<%#c#aSrm z$-6yz(F1#DDyGzozLk}@oWQJaJ+z%HIrc1hqNeC3$XLE*4{ z&dpMoyfjFjMt5>^z*VTmQzhQQ7S4^aqD~Y4*0O~5yMt32++q{`W0OF6hj7ZeKgx;% zTTke!^l27H4otQ}`q>c@5jx0tAuJ=uc~~aa!yxadM?3J!-kjo~YZ;`XEoriIqZxQO zJz?>tMg!%`pm>b`^^iYpeKgBJTKI=w@IBP^DoY~s+&2fObuBHPX<+8>W{BlW9Ohe&<0lHQ7$ShTzLv;}G_Pch+n#?a(KazR*n?b96xiMv0uwwH^=$FV}+gm^-Q zVDdWe4GMq@#rZBMg*1oXgIZ37^bG_<}}I;Ig;JkWb~2pzgb)e;o!5)bpEetRA?T! zhac}K>3Ww^<2zKuW3vicB(LkZ=X`+pw_wSs2VxM`qV|qJ!J~Wg`;ip7tlTcKQZ7oG zJCjq!&nYZZGWKH`A>wC@s3Fr|He#s+Wvw6iZGj^CIa;9oQq*IlzZIT%-09Qky08@f z49;pSqi%-p!4RHKtK!08^qdbg~ve8!WD;mvPei`#*AJH;XI6XU%HPnp9FT83lKG5cvM}l)p1K7nreISPX<$cflrl4yEPAcs&kD6m{E~yb^@h{ zjm{t0qO;B)!;=eU?mq=vq-Uq~yGJB>a@HV}V#b10+clP9GZ(AVg&`z?XcAeV|~1{qDt zLz>3=2T%7V_+}-{$#3UGvS;B}xQq^+9p2&_P{W%Q;=Je#-jRt}s{9V$AfVyqiIh{2 zXH5PRoYk+W0*U(#3lW1^sfRfjXhL?Dw+#L@^|>nWhN$`hZqx2xirx5;6N`e|@4X4! zVL_Ct{3KN+OUaf_p@V{C(?w;p$}SZz@mP;s?3^wMZzH6?Q;0si)3(JT@jR6IBJ)DU zk^&x2O&;ptGK%xrdQ7DUU!SVB_OQR z5Hfz51RxE)z|3lA4OAAW&OrC&*5!MVP_*vsy@~gsEFCnY_9A$fGdM+&%Xxc7&9;au z6sLfcc4IYeCoz?qp)aGoqTh31ubK=RS(tQN*W=@|90>`B=+m6e0x?LL?Q&5$I*CgfQW{uatu5p4r zE`llU5)#-zi@a{{uwmIvFey#V;ZL^bU#9~fc3Lk5AHO_++{tHJZdmY$t`Zxw$pQP} z%O|Y>4a}~oA7^c-8Yq}}dZZ|p{Xaxl-a{3q2;A#j;@e#8nsO7I1MfsUuk|xWkzP6qV7)LUL>Q)5tO3YBXd?*c&fA|zmCUH98675=r;&D^a zE35Zn4>h-3z%6t#jlPZ5%sB6bSayTaSf*4{Lw|p7_KudU``J_-%^~%drf)$i!L3Md z8mG6kddMn99Uyy~RpB>?W!+kijF0%BLC4sd1>SFlk%3s(F4vJOy=}L`zu}pm#e_l8 z#kz^rMZPG@y|Zs54DHomi;*fBj^C4GJTgizRtzPKGZ z`9?S*)ZHaB?H76K#KhS7i$|AcBAku`tIYk{4&xUeG$AGmT2Jo`QT`;UV>WiuH|yH_ z#bo^VI-sB4kvmil&aS*((E>MbB)sUi>={fFMg#Ra0-T1SwTkMH-dWkaJXf_@d39#k6c6xp<_ z33@xB<=96KOB}a==Dd!NcZ}}7D<%$4IQR%3iCg;o^woPMn!vtMA4``nM~UDn1kdLo z<`W;L_{HEC-($+YK41nd4H3U5!-B!5T==5@$BTAfe9~{Z-2#>t-40E`3UqkVaNq0d zvlQp>GAvr$OmRtkMulpnv9d7^M|Dz{L{o{+1vx~X2AFFtfnEDxtjim=NFk$Ex8swXw<0qAOCWLGiV+v} zOJ;AE$6%1->L>yOX6zeD1mRzP9N<;OEJNDSqmlF8+=`s2$^u6*e#V{c%H@I4ULHx5 zozMY;&URAF{k#BpOD>(Y1OeyXA0#?b#Nzd#`$+C>&PSZ_gR2UB`sw_4r!j9qEYTYE zZ#_SJyBcb+i(xb<>j7>aaT^akn4r4KEyVQdjmR{U^9$QWFu)0_g-5HH-FDwuU91BJvM< zN?d$gFdgjj053gi?dR$&4Iehh%BwdzP?Xbx<-cxLYMxt`4Qvz-5|mQMab@p-4r7MC zA}lS%uyGON8A<5vMa82-UNOCH)toK$swKis!IE7@u8u7UJToCjsV^k_iHMn2WF;nC zbsVZa8@6$3fN@FNEouJ76W&r^ByMF>hf&vrN3$@e9`_yRAH3t zdKY=V_!^JmgO^STSWC z;~x)1&6`_5Fx9p^=dOg+euyjb8%^QWku?C-VF4b4$`2=|nH_nPf|i;v0L?td-hvo^ z6(3y+YXK%P?!E7*MT9gBk^s!cR$_ugTIA-n__IsO?5eH=ypDFkx{YJs{RR1fyKvdV z%$K7RE29?bCYhSCu1#m;$xMYy#N2V8){ih$^7IX|N!Y(Z(V{{2?FFN%a(THF_50flPnAh%$^Zcue99L@B)VJ~O6gZVc5YzyP?<%ecR4p%kPRHnrMj z4UKdV6rOP5fH>VrSRsVYq()@eG(vZhiHlMhfTN2Z?wVfc>Ak4OjGk*J@SnPjiRN4C zRF|i!4w09WB83+W$y-lxEELaf@0(1sxI>vokAdq%pVS}G$Y5L6x@vNe7are1XdkJY z0B+DfBsAFy^vb;k{m|1$(0yM9<L+sm%F*03a%SC4;tp;T~k7HdqUBrc@L zVAI0FJm%6pBF(~`?P5=og1BQ<>@$g(TjOh2zGZ#q3Jb1zNm?01G0wrwxpBCKToKBk z4`UapyhDuR?|bIM5}>1ZtC!<42A= z7vw&QV(~y?`_&J5Y`y*|P{dFUj>%waAxIGFV*!o){D5o}{%mHbzA&DNdkk~*7C-*= z7H_hERO}C{vrE$VH~3nM2>r-wJA;}t0b^97Jq$swFbi{Um4)HV`}3B?M^ByDtQ`Ei z)d!9O^Ql)1bKJwI>vwWc0t`k;4pJr1NT}B;nAFJks1R#%O@*8;)dS7nQshBP#%SH) z$Pf7kp^0_RubDkau)lXGbj?nse}a-kE~x9d9e+FunO*KkAPFL1DWkPU2^|-jzrL$&0Gp?(<*(vA-sbFc&({Y(!uJ6QKIkN`3EN%i zmk1Y8Fi~t%Mkr4sL`h#=DxQ<<>gQF5F%HZ5fzKQ z$gS1Y+#5_hwc>C314 zhBLdZ=%=gk?(Yx3F0UcG@4v;IZ7#YxxOgk{^i=(Hdka*)1=`28ucyxgnaoRLg_C+8 zkH7DnpFGU9hdc@0KLNUn0+3B@P5umn0Qv7ZfWmXsgy+AIxC!ha9(JDR63=P&zXL4% z4yhpF?kuI^3<;+I5D<7KKn|cGD->+>X3VV2 ztN_lxf;2!1L4N;a#`QNd08rJ#-V^|QYiMrzoAFyiM^ngk*#4>qls7d28@{%42WUe` ztN;**2f)F>1!sxWB$<6;zk9$fF z2P_Jh<@(VdJ@vJta0jhS=;)&E;pC_5c9z?ACWq6u+gRo;KvY~oOE$NoPE*Co&&hDu zn?gHvpwUO`q2Myq&%0jciW#zrnB&d}(=cZ8x^Ec| zY@EV=w8|k^?kH4~fS&>~&bl?8P}xf*rA(q1$1IK#aU)Xj23?hU%BVvM$q`~*P^m98 z`fFnDO%#)9Q?~}o1{T@jSH3 z&9jfZ+4|TPasDkaf`3T66~|4rO?G$D&jn{=sr`F`DtlsxGq$sk2av>kna@}~jBrv<~?T%9GQCnT}rN^V`OlmWejpiNu z)5WECvpKRn68mZXx~lg_I>O|Hl{qtD^E+%@>6|&UhByt=7KgoJzM6Xb{ZV1-`^QPR z$QU(WrWWI4>Der1X6B3DyH~Z@_}s$Eo)2+(aAZ%1UgNW7yTb9NPXzT(t}dCBRM_W9 z6b#X&o)Zd6QaWTAWHVBYBgR`F!*Q$&awlfhNDzQ7m-B9wOG5P)>J*qoY(+f71rY(k zr10euX{%Jl?TkY#Hg<6?#!G#DF%8b+Zt;G=g!*r0FPXW;8LpDIaguI(gWC=hq+%^c zAL?Cw=(?jA1CLQnhe2OUCP$6oGk8H_(Q`+4h$*g010Jb#QTu!=rRtXGP&IFvFs+#N zxj91k`dHsviUkg)99lbHf>EiYe2z-P?_^bu~0c=x6P3Sa7Jnux=pwTDv9n$}xzetxd4@$3*4aci*d~6gS~Em!*URy&Uapg;^Ns9eV%s$<&+WBY*_l9T0-K8D)0MUJlzKBEqE|Yi6YV+;R$8#>PqS`)9Anu^& zFM%DcrjaHYA?BP?_N@ue)cY{H_L-2KC zt_E7|OSi=hX2m)eRkiy`lL>O ztdF+#WR58@BN@uuF3LQ^_kl>8A+ui z89YMGmxsEKjZ+utl89JMw?6H^$?TYtNw>6lV#<#*%(uW&VVXtPQ)~Hov9k!)j!@kA${KhC?ra*mr!5|oh8YywM#s1Br$DhnSWH5TI1ept!2c-MZ>;hGpmrnJ8tH| zFSVy6*`Ur;vT;dO$d+6mv0*)Dc$c1B(53M@=ygHJS^H@7qQ|{ic|u_f3N6?eaDgv4 z?xKDz4CAry?)I4JwqR7AdsNSrF_%4Bt3kR%jvj`-BpETK^K&RQ52IXge1mYMqNq zboC~lnp(wq0|ovZL*Rn>WA>@sYVP@2lK;11W65g^5*5L8j|7G$u+oUxW9sAzyVcY? zoJ~6&7b}Css18dfm!Dy?+n29AW_+Lt)iThtbv>W1v7~$?e5$PXuSuIHegUt7uYoIx zZ?||P)LmN|F*gsZHTeSRMD^W;xybX%L!WFM?SsDIlPPOleryAkh^_f~|wT~lv+gswUvlHN(nC2R{$2$sBy!mcvSr~%Em zC{b?rKEa=rKRQJVDv_IG9 z2v3}@uZisM=cD)CVPaOo3fg7Wr8s?)Vy;2HWoIbSIaYO2_M7&_eEAMMSSPq^B+(7; z+-J0XThamo2@ycP#b+UXzR@|BEmddwgw^1~>G^}sifGZRa>=D^pK^KQ@nd?+aiK#^ z2Dc}wQddPJ7ehDcN2)MgLgAP-oam<+i`kpFzG1_b#P@h^@UxMIht@L6{DBrST_~t` z!T8y8H+g;N(L3>utl;wK?m13U13(XNmh%GUTsR z8Mrd$H+vEY6~&kLk)p$hAP@Qdl`1IsE7mo5Br=aBq={`L zJnx-xeV?Djaz?Nh$jnm~@)pmHe_s^*@~C)ppL6u5K2Y>mP;rci3#wb6aYP>pVS|;b z8lRdPYLdcoa(uZhV~0t!w#T;i8>RJbD#LP_R<_AVB-265fIfG;whD*g(c)%_4Kplm zaAIwtPJwl1*-$(iOZUgVH2j0UXhLprR+@lG!Z{+3{X2ZwYsfc^L7=t*ha*mzeJx-W zK~iazOjl`~EhocFQdpdA)CApRWAl7PRZO0HV_8HizTT#Cw>)+eD-%|*EjFr48FX|W z%jQdmGH>pXMpmBjJotHfI_ z*q#y3|1QRz?uS;}9sp{;TXxrm3y&yfmZunYSu+d4U0$)z3v{`NnHLl$150xqdkiiw zp6<{3=kM8tV#jFKP9`gmu<#F@duHvF$aNg*V>p>DDyBvm8?;OeGJB@mXmlja1rEH{ z$P#r_mLbk+4>)A_FHRdu*|fO3*ALidC+dPv15uh`1JGbBK$pvrsMU_5YZBhXoLe@F zu~fe*ZkAzQYu^|9%6LRueLya7=J>1^2IXlCAENLyoK^9|a;71w(vDLNSv2HIS34Ee zL8Xb@w&t5bOpfJ!qNXZt+SehHvyCR!wB@I7^iNdPheG*_MumGrdcztXfP>SvyEU4FO~K|C5VQ=r%x{v4v#HHH0M8%wpA*u5C7!zj!Jww>fM=NcPuThl(f=)t zKQ8BD5q@)42b(xsIQ?k}c%B>o{^8(a1#qxE_mK-?CHUv( z56Zu5{QswL^0NIg=ny-EotiE9IbbE=dHVlzSpKb~&o+`jbngw=$? zW|M!IBiR1Oqyw>LKtf?cG#fx?YzTI=1F*5MfmpZzbQaFe_IyByF$Y34cQmxO02@28 z*g2Zh|Dncj9qmk9j3J>l|M%7Y$H>F>&zPNmOfxYR$qE_O|E$Z) z_0RS>I~qc!vEy$mlM2|=^jTKV%Y(9=9c29f#||cAYX%wTzim`b&W4W8zopC0%f-Wu MOieAJD2e=k01b!_;Q#;t literal 0 HcmV?d00001 diff --git a/lecture_10/lecture_10_files/lecture_10_6_0.svg b/lecture_10/lecture_10_files/lecture_10_6_0.svg new file mode 100644 index 0000000..73465c0 --- /dev/null +++ b/lecture_10/lecture_10_files/lecture_10_6_0.svg @@ -0,0 +1,397 @@ + + +Gnuplot +Produced by GNUPLOT 5.0 patchlevel 3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + -2 + + + + + + + + + + + -1.5 + + + + + + + + + + + -1 + + + + + + + + + + + -0.5 + + + + + + + + + + + 0 + + + + + + + + + + + 0.5 + + + + + + + + + + + 1 + + + + + + + + + + + 1.5 + + + + + + + + + + + 2 + + + + + + + + + + + -2 + + + + + + + + + + + -1.5 + + + + + + + + + + + -1 + + + + + + + + + + + -0.5 + + + + + + + + + + + 0 + + + + + + + + + + + 0.5 + + + + + + + + + + + 1 + + + + + + + + + + + 1.5 + + + + + + + + + + + 2 + + + + + + + + + + + -30 + + + + + + + + + + + + + -20 + + + + + + + + + + + + + -10 + + + + + + + + + + + + + 0 + + + + + + + + + + + + + 10 + + + + + + + + + + + + + 20 + + + + + + + + + + + + + 30 + + + + + + + x3 + + + + + gnuplot_plot_1a + + + + + + gnuplot_plot_2a + + + + gnuplot_plot_3a + + + + gnuplot_plot_4a + + + + + + + + + + + + + + + x1 + + + + + x2 + + + + + x3 + + + + + + \ No newline at end of file diff --git a/lecture_10/octave-workspace b/lecture_10/octave-workspace index ba49ea896777448b51b05e3e4675e347be091b2f..8a9aba219ca289b60d17145c92d4a88a046dc12f 100644 GIT binary patch literal 134485 zcmeHQ2Ut``*Iq#Zu>m6X3L+vX9c#|oE754INi-I)BR0gERbx*Kme^v91q*733N|9% zML|?VMLAgk8i1pu{b1pYR_|zod=TCO_dE&{uclPd?_q=Cj?%jKqf#c_l^>nqi zwH_d=B$LUys{WJ7UhAm-nLc*TtjS)lUcY`_S=Cbir>pu;^=d0;rrdvwmBWUrUv=Kn zPo~6EXuYLhp)jja*vv*@NuZ^AL)WqFU8P*qR)OmO$VJvg^^bv^{;!m+M{PYN9@nFG zBeM16?4!o9qoqDdeMJ4AZb0HwpE)Vby0A{NLO?5?su0xvbe%JS!KKcj2G#%R-f~!f z&!Q+5CWg4$JUWviu+B1>f?LJ_=K+PFu{`V0_xZUoP1nMpd0rh~yx@6) zvf%Rs=YcVxa5eR=d;Ds&&~wJB?;bD9hZ=SBwxvDK>O|9dsBWe;=||Hn;ry(pP6LM)fY5aX1YbNP1gq>KVv|Vv9WQ|;4ZPkbv-xFh9OyyjZV8={yt< zX|7}C{y=y&AnQrB6PfTl)z-n!lz)Gs>AK+Ke{+5a-|Se!+2+2m!@SY*s_3D>t zdi@LddV)exaJ{^#7ft0OXK~=y7e2}tsy6CAt-kMF*gEF&Q`wmZJWo&%3Qg4oA2(y5 zB>t`~M{b@tJzw}}s{g#u6G;%bwt8sPhzmSVP$(rlVUs_{qNzMY%-CS!e)K1y%aM6T zXsMp3kF<0R`s) zdH8*O^qgil?h5n#GO9oHz75?%juq=3zsA=S6bRP|=RwVY!gh9MXsgY!Lf`$tweRms zg@eu-|yn{C}Tjuc|aa=W_kT~{J=fIcxb=N&mGc0 zcWKVDTE_8wJwbtRop2u13@EavFWj^=CQ*nxJ-*OvSTcNi{!oC$MP8?c^5FY&&I4mW z5mE4s#oDE@LiVYrPvZBd!*?ArW_;zE#@7=Rh=S_`b)xA!__uOfwPl5ekkF;pCz(Uy z!O`aA;*l#Nd7hv!6q>FNK7Pi4V(^QkeN&>-1=Aj?@(!F7T<(R3aH8i#jpcsyP3A9plq ztxFH6T~XACH2)>qgKKYm+yX_8$uDmWI*8`Uw4^HB0UL4hc^ zPEaSB&VxfyO7S^)uCS$&b~B?jNnm)@C*X(qw|SnRFcg}u4?cdzfWmoB|1%y-a)jR7 zm%noPE(e?rcbd0Jo8K4a`apef9*~C(zu#yf+kZ>2$_c$O`cVp;N?bf|)oA|rPq;pK zo~Rg5h&m9y-M+QM>D$7>w5vaNdvFWFteejEGr!08T}V&~PakxL>01OVh5}-t9Bs)WS_CR{HYq z8O!5~X2eu8aJGiRj`c5K((PNuhEW&10ytW5UseHSK#g6D;1=0)kao5!|ZeD=a# zp_5&*?ezTfP%yu$@xGnBp0PAfysg>!(&o`u*B-e?3T^hBo!RZWKQzsZako1b&DRr5 z3XO-Q^DKb+ya^QDQxz2e=Jn9_kx;&BR2_}Tb=>dl=&7-`{7*O<| zS@*S}Pk_+c=FoEOynN^sojj%M4*ok5Tpy?p&I9tG^Hp-#Gq*$`tlwa3Z`%Y|c|Ybv z;m8AgJwbsexK23p2b{>fGAyF_7HgO7y7?imnd_He?~ zs_A^+g~Cv1x<2^$83T%**^84E+L1!uxwYN;AJ_jZV8={yW} zvL8^d7@%KA?jdM zUkBHxahXEfzFRW49SnuYhP$jr3;cKPM1Hts3@9|6hnNL*ug+MMCpb-Nm~QWT5X`D< zuYJ934!=G@VQ9QQG(A7W@xQuwuDPyNo-kKY`KRQENieWugn?H)e_mMRhg-&gLeqK3 z%jmV`pnZWbpz6hbM;|3Yo{#02pGNWecum&@A3tM2A@b0q^~j4RcdiSA{e(c<%qw8u z{cx3A;}iJ43kfRWN#u)L#(>8066_XtaOn6nq5b)vs|GABfT2!9+&UET-|yo2pqcql zUfl04vTpgc(*@zv&5zp+JCF~)KlhEErO%&RDUUCXYi9m5>A&by!GvU?w@Lk@X-9Iv zqngt^&px?)--QXG;CZ2$c~Ls<{=Yg7yb+ouC_n05c}H;$Ods#rb%HXM=Lr&}D9smd zGX^w{muencCeQUcC%AXochK-kGAx*s8M|8d63-J%2#wPN4qN&jnztDPidh$iRL-`{ z7qmAn^L5Nif$(at96KcQ?@zcsP#>HJ??zvvA69jV)og zcWJsV`1s$PA1wRYO*=PQDJ(r!*stT}JTU6MZ+PP3D||gcp(was-qeex@-b^(}_slwS+dIsaqq{COM zCoj@>;m>#RJmGnwVn8A4z^(Q=;}yB7LQYVn%bU!9g+;}Bfo;!b@_iQ)RKku?~lE*{*l3~Lao1QXz2AAcOC^gRJ@GX~1U{jPQW1S{vu!ZK^;)b(G4 zz&ba>mn(u!@;pJol;I0ut}9LBLH`>M=ZPazg#87d>2&$!CQL3&|0v9!*Pm#b4)}N( z1B&u^2wt&Z-@cYdyn7snX`3Qgl7Jkr!>=Gx;zhiBHe zQg_6_eus8T;`}4|z6*t*aeB}+{lDvY<4-DIjcJiD#8*z*a7;TMp8M78d~)Lho+ms{ z)C?$)25!f7IQv!B^h}}UuM;a}xTL_T(}OR_y(4&@pg_1zI1g$D6jK5kMrB1@6P`!^ zy6;Y-NNBUgHSX&Pyq*!|!RJxV17kpuWfYg?8-7!0eE!BtSH*3pHE;88p0Z@Vo}fS! zTqmd#P3NIz?{@9hok$m|g`1`4`lN%lijb~zCo)=I>!{51v2$ik_ImaD^=mCvOMO_E z9h4OUTJhgPIH&6L`n9fHJbsY1UqdAo(4T>&&RAIms{f-iww1F^GGis$(*KHhBRL&W zmhSN;t|!NKp_uihx{G)rsE5|ymL2{R7ptfakc$p-)~Vco%#?UY9E#X3{RR;i&nLFa z>t`l!x+3S3GrLUX6Wvs=mF?wzy^|IgyLTbHyIf24*8Xy1r^^5)A8dl)`N8L1wGdv?I>grx@t!eX&($+!V#&P&zJ9QkL(cwHeTU1Y zPrgs&`zu^WOYTjfJ_`B1o$-I0 zPq;nxw1n)<47@=sc2th}#n``G>e2;gWxdi~dOd zA#OwcZOCu2-A<0j+tTgpgsUa_-J1Bfp#Bzw+tK*S z>QDV-t4wA~@00jL+(tf}IV|y~ewbIyAL0^!h+7ffhIqAP5C6(!mV~z^+=6fm!dnq; zPPjSYEeSU(;~#TFCi*M+hki@^Vcg5c7jaACMdA-}3&KVIB>(XI=ESSyAL3?&o08ux z=sYb5Z!Sl_+fp7`)42X_d|T0Z%<24+f2b2P!X^I@Z$Y@^AL7jjZ${^BLjE@EUHzB+Z zjZ5P1@5UGP(~RQYjQnjv{x>GSMgAHPUZ3!K)Zc{gI)ob&ZbY~t;RZC08Wa~Z(v>O2 ztp(xlA79i#1LCJXou?k1*M#sogc}oXM7Sa02Gp)W{_7L2M|c&&wFs9{`+vvZC^o;< zAYJIo)kPmNnVuZ+DuinhE|Ui^y*-1^+53t>kM%EvNvxd)9?Zr7>OkTTbtT0Y*QGk7 z6Dhuk8xn3n@vb5NnSHK4#a)l^Duip1zGdX^GeG}~KwT&!Q&q&EziH&B_+4Xc=RWAK zFaZ4*9N?y(qrV0LNKG_nHd<^EVB?B>u3w z_#J7CfZvsh-%%6_^c|>x*OJf3PZ?EyXese{6(ycWPl@w{KJla{AIUzaYN%;DhHAo-+KkaDcV7l*n%t?Hpll7Hy0mhxlv zzA8%eTUUv=KH)V8uSNbEDi4x>IG);s*CE`5##5K@`V<#c-3<9h-@Q;ArTDVb9xfYS z_O_u?e6gRt67d>zegkS7k}ix0HzvFe;UUcw@qw5Z;V_HtDwx#odG|mFkin>J#38@P>ppCcFvZP08P8biU?FbhA0(EeJO) ziSIy0U=3w4>-g8>i{ouTac@X*Z%led1SMm?X-<)vCKg3N5HzU7W(l}cZZccGA zR?_@Rr5B1oJcx^?zS`go@32#lfCE;xdZ$r2h;nvjt=i>WM`-i#`{cKBq zx1;g2qqa>+d~rSd`|(9xSyJ5F(D|)M4_1U*6W*5awuHAM+=kjVbX@e)mT+6bZK=N< zji(jO1Ajlh@5&#J*M>gVhWwEH!+FV;a69tbj{1v!+Y@e2d0hDOnBjKW-PJ}xV?nM2amD;NFjj-c2u&U=L zDokxGYJ}IovQ&_L_}W>zCMtQpw4%0AR~5JRRrDWqQSoYCOZ$!YB6tlf=F^9-oyGW6 z+}c;sfAQM=-(f3m?JM#x)fHfTD(=5;)8N=W0iKPUt_8oqw;^+T-$ zUfWR49+JLKKe)MUPMEx#c4nsNHr+ro9(-IAIfpV z!T!e7-E~)jw{!&c{_BWvZ2Gp-6y-%!Bs!q5*;Z>=>o*eHNH<07Ap!I1y^$C~! z#&Omq+=Sk5LjCIyF8Pi9YZGon{f(%jt}xwWWWQ;u_P4Z^Dtu1|PX!gUGPA-oEW zt3Hjh9@X+leB<0@Lb${?;>IO4K{&V7rkWWe!X>`3zX9O})UReq%@EekRVQ4Z@Tw&> zMEHK4l3F6{Uzz%A5l{7qr~f}XL7nLk&sE6J%EY%8;gtxN5iaQjd96dZq!W>EJinw9 z#0{yxq;KR;(l^$4Nqpn`s#1LPh*!yP>@V?+{VP#_8P)c^q*^kuX6oXxwG}#`8#gV}BX(FZqqSdRnUH%b0Za-g%5&1@cW2jbB^jp~(6FQV?HDl;^b0xpuS0~uN?0kabFPoR|s*^YQR(7W6%}V^n zn#TuJV=C61iu)6Z@AC9r+Hcg?Gm5X|H{#NK^1eDL?KggIVu{~$FRA3333Vl{m+z|+ z)KA&@1Z!(0eZQ|xM80u6X;jmjEnqEa0kt2}xQc|*eq-FF^%DJg#{OcUO!k!Khay1y zA>qpDUGyrg`P{Ki@{ zEvhNgrkb)UN{pBI-F!CfyWU+V$Wsi(SDH_dr)B%x~f5Os7bmqP~v!`|1Sy*ChQ&e&f7iNaHE}n+%1tUwlaQlOJ9u$iKul z>dJ`XU_|<=O}aA18d!T?1Iue*|MxYusLc;w!}@pqz&$PhJFs+ZSTZMms5Zuv*TB-X zIbC~xxLR7e=A#<%4`0jrSN%a<@fujX=KTNicVu}DEb8*Z|4a95;NM|+4J^%fbWiTX z)zIQK82>x4;&YZC+M+Ia4J=-3fA|_&%#ROW!}@pqKwa?~Sk%>ruc5_w@)}s$S;;@N zWzW^w^BP#y_jM(|HzwX=z}WD=XG`A`l-n{28KG)7`V8weVeEm=} zz^~8w^|@LHPwD={zq|(4{y*2iPIObh(t+KIQ0=jM_E5i4!NFerN&(Xr>Q^!t8LD4N zCHHh5B(N6*{i=S&!;bChR~&fFQ@`%ev(qtjo+x^MBqXx8MNt1M^vruG)Mn=oCj2b5 zk3$27@1f6?$!cI*Kzm%k&pj*LXXj0Wh->OsDx70}rBH1^GMzUGR_}2+|&MJalo2_^5gI$i(A<^>}Gh`I3VBKJC}~bX6!E*U>t?F#bFJ_p|DgO@Oh!T zfXAgcpf00Hk7eVqfCZv#9Psb?m5qap`MIG?9PTn51qrDCi^6|9A25$1U?;^vtU92WFUbcn4mNlmf%1&vl0y0T&&^9>98lk7^MU4> z_nw!;e8Bl2l=OCmo==qKrMJaF%!hZ41J1)?;7D;uMP1W;dlE3eeW4ZR0bo9F5HOE@ zsW$7Rz}}V+B-l|L=3<_ap27ujePE|~kM-eg^O6_`yay(&4?m&4X+1ekd9jD)-%Xv7 z?>z$Q|G4lyc(c>m|-B{2^7n9w2wj8mi_=0oXqT3jE*c}ZNS z-?l!?FSS14_=2d$@g(@*{6qP@0dQX3Ab2BAwG}4?^fO4XrF@|H3Su0vHsppt`vrxKAQ2u_Yym<-zjG%QqlIGhe;cfZwSLY?#_x$7Y64nIW z5Sp_<+!AOXCm^5Y$Kh@BQt5mU_pRbOjcsY)it%~-eo0&(aQ&9%C5%%f&A(Bk!x-9M zN&8lDeR$V=C~scE@&EPxQhD=|m=9tc$WP&YuOGyGC>@8=`z0|BXy1RoRNlPA(%wFb z=H(axdAvi)_k3 z%1h!;h&zDaDN*^`@=h;|FnLTfBjH;-zw%q={Sh_P&y8Ob-z^Jyu`xbcDp1F z`25vfQD1Mpo-Uma$hWjki}@g4Ph;HHy!ATnedi_2|2wq5ilcpEydcg?;`KD{8_QnD ziE${sUlQYheoOl$F%E>k_kO9oc}dI%F%Eb=dylTq%U(~5`A|9z?>aAu*V8!Pmwz4i zzVi~>zHE=9{Ykt)`w+UWefxD>>3n$Gyd+*f(ESggyz994otMNou-iM=?g_Ln6!#}U z`$iDs@OS4WF%Ed1vnBU6#C)Lh6Q5=GOXbZ=cpWaq0q4U+LH%6aSohhi$$qbH_V}^W z#?I0`$0iJ2_S;tDq@&Zv&Y3mYOI<)cK?SNOGu=^<)sC#{l@E7!%9H00SOs^kpSkF1 zlLdS26`e;<%z^a>f~I8dDu6HY6yI3u6+qnlYJ+RUJ|H`NJ23)_B# zhRZEB@5sLmv*CE_hQ=B2g_mx#{j=j?eQM7xqX&h+gdf(fHJX(Pdm4=Du`N6ig3TJP zQuIoNz}!oBE*?yUCcpPc$y=5J&YPbfeXt@K#!kK0FMLfF)EskS@lyYbP`qS8)Md+L zh?|t{H80~PY&y2B(VR1x5Z14%x54cw=#@OgyHR2`xGgaJ^?}wDm^sMlx17ve$h4o) z=;W>>$SZQ#Vi|ZJ8fDDi_*u_nSZjFR-997}9-CQqJvS#C(w-aqU^y%WwoMtBlWSD~ zi|dY9zJGTrBu$8T)o$`Fc1oYnl4Ufu!QbzJLtZjB05cWBpLIj%^D9WKX$UNl$_l`g(s(y{h!_{^izjp9ZDu(9e=>-?k} zkUo3b7o7eFT;bx*unW0R&3%>8sL&|rAN#`kSMw}5sB?eYKM z(|wr`)ajG%^UtTk^WqoQPW8`%Unh&P3rAgpC$&?DG+mnq6JMlMYd7ElG@b2vz5Ce$ z=-$-l+vM8G5Rz^c+v&B7A zLH+AG6I|zXm6C{347UO!S&F$zNB<nLG!#izIc%WHR|SVOM9LP zC!18-p;!50%?{r1rB9~VY|vCH~lPj#{($;-f|eH|4=skRP& zrYWkM&M(vS`WL{~F_)jp&OCs?wbetTMqGdgJ38$NeijRr9@jo}pi2_8I%QJ8(ACe z{J|G4J@H#SEF&MrS&trdbJI1@U7EA3mT^3Mdj3#=#l;l(u0zI*uUyl>(dOjhkt-sh z@0>H9QEoA?B*XNZ<^958|E}hVTPsC@&yl`nRrjaC_u+d(7P;JosIErl&#wl8d80ap zaUM!Ayy_G1!~EOebhy*JP1@mbDsl0=Rih&y%)04pKl6KVaYLu4E;sJOsfC+Ptn^KT zmF=&*vNG8N1@o&K@7oy+(eC6rDV!>yAiRc|Ybv;m89}Fv25n)sq6K(<5N(g1+}5$n4>Ssa4a#aqGSneU?3d zv4)N>1{B0W_v%A01o*1@&Ary|Y{G4bY`Dv6v~U;9s%)=)y=@K*>=t2HJ zYOfqSB*#GT){OQ?4f5cs_tn?^zV3 z!l-+npBvM3E%cnR>bu9w@?m73I#J##CG4`VJNVYa8*qNsQ>TGL3m|gyi=a!N<-!-{ z!|%WHPlD@uZk`Q8vf$N#tS8k@WWo;fdV432OM|M7x=*X`dlx>M>OU{^L=tp4GS4Wj zOFkH`%`IL$;Q`$FWMoYH>uHcR#PbWAn%SUr@8X7P<_KhxWVt+#wC(PLD4% z8^VEL+jW0vIQ+5Ik%tA4 z(BndJ+skQS;vIYT%Ed!)f3+o@yBOVp^Uqda_Z=Dr%ltRbwf!*!&aTok z7=I=ma)K&d-emqO%rz)(cfNHVIIQ`s=6ThO_w%aVmY?6wfIB<8JGoCy0gHj73{JUb zLU`T1(P7K7pz0>ez{!E#v zs?F2+8!KHEx1n0NS$eKdI?JGm|1pD>2U(2KGE4whQ}4RRuSUbtk^8W?GYeG|d9L?MnjM$ArMZ-#r_L#z#ZO#>Pp5yTn5Akmfp8?hhb*vttcsoBNQn zIPmKWALWB<%aNNWPS1yk85>O8kNyOWZ*=jlWDpJU4?V6qD+Gm_0e;h-M9<3vok|mZH|TYdZT;28g~Oc?{?JP(kB=`Hh1r_YiuIi-`(QdpgI@f zT(@fDx_zDuIkUWeJAU9EWKUnXX=zL%L==2uv36-J__uOfwPl3|41STcZ%TAJTydS~ zW*>hKTK_Qlb&qwKVAJ%+Db<$dLBOTuR|bs9hk(Z6-5VZHhne*icEgX~28W`Q;&bv` zaGulujK`83*zo&}7P9@fK=^k1)()p{L*T6~jgN0hh12aX4Q$*m5&Q((o@UNUFpq7$ z`0Rzf(B{!s*B-e?!il);jkVT?z-gbeO83w1!_7w~HukUcAkHegkyB(Q^q*PxwV_V{ z=zNtN_RK92zMIy+_|RU}8b0>>&reTJg_GGoxoUlv2tBhGCo8lgVX&iB`0N=e(7E5f z!|}_~VP$8t*a^Q!z^J|su217KA!b3{t1}km!K;hsn(JESL0(3$EeGujph@eI7ftS5 zhhVq3gG0xs!QDmHEx&fU08RQYI#nmBrbX?Dak>KC^l;8Izd0@Zh)=_<730U^En|5xr5@yY795`Dw6F*4{8DAvq zfx4FCa)R?7z%u)wsK@iO!K&N3dPO5s!L9Z>;}yB7kebk>FSz7^EGR5;;*|^t|K(Ed zMwtMndpGa59v2JKeLI`p^NEJuVY|%+s{GBbQ`C0Q!3!|6)}*PCj`yK)y`erG*E|5b zwJy4+AQ(2(d_K2s!z{RKT|dFf`7-E#zj%QOg&H1(Oe_Bh0!RK6P1 zLbYe6tJkpkY*2#5Kq=ip%m1zX>&aw`;fVM0&{s0_xq|R4IdKkH-L+8T$$6 zsekyTp+7tPhvKF;4jbdU|L{D;8;50h*rA-yE@VH)Hod&hro-iZHlBQXd7rJvK6`q3 zpN&6t?T(&RQJGm|-6y*0A}L}G?MS)URv&QpnCv-YPTA{Gv5$H;J!eeso~&K!2iDag zP+ykf2TYS=Y?cpUR`Gf)+5v8e-<-m%{N+q+drn1L*B$NENoW;_D@I{|#n;q6HH{rt z2=x9JvsqidZ4SQA-4l;*@?utLzX0)mOVH|kg~y|p;&Hv@%r+aon%Uh0zeW5Y+Gcyd zLtI~VGgkFdPW8ri)+T0cT(&SPFGBm}rmd`fv-LJ+oAuq!tSo#7+Lk++^*H_`vx+W1 zF{?LaH?v-L`0&f>-_RyT>}9yO?>=TPd;2h(Id?y^XXYMYws6KlX8TMy#B9AGzGy!_ z%xq@wBh22EA7ys+h@TPfcZ}KSCH~A_lLaul`2yP94X0RJVTJA3s1vMh@d@@<=pg>( zBD9Lnv45kOldNCJSJ*bzJI&gYen4w{_6%!}*n;+G%d@P#EdZ@|+d$TSdIzmf?_XK_ z*iE!nOV6=(pAfVLD}%6YaGu$n3bglJ1=jxZ30g}nCAN2>-SQLK-Oj-b|7Z!?^!sQN z+g)I|r3+el6j}@OiwsZqMB6J0ZLD<&!&_9vA28I4#`b#WP^hlbk2;CQsBY#=m^}7R z7ydVsN&e&`wdiCw8?lqhY?`7y)C}z)BeXIDvQ^OT)p+pHcQ-z{3=c@SBJ=m)ir zksqR;Vq3H$THyISnxGZqC0aSfO|+M(J&CLs*Gy_(Hl_2Kp|zm)O=^3!LR_yk+Dr?y z3bL2mU^~_d?P|imBwNoC@p{&1J*ZzI;R>>=OPxna{k^Hb1zA~JJkL#Pd$q%MCiTB; zgY8erP9Q7dHq=(wVn6Zyv4jsGJivzC-N-2qSbq$}FxL(!%VLc8!2 zwBL~3H~`z*dZYF1jyAI!+6BGPCQ|z;S?`{R>(l!-Q@;z;uHFZax9E>HpdZ@LUCxGE_M-`iZzJ2p72C7OrjXq<5znVf zb|+fJ1GMs==i>Y7PR4#WCt-U8wS&mEn1aX0pj8~8_L8aCe-v8TGqP6G5Z{MZrZXMe z^U=y8s67QIF@+o1VzLKku>SJu9%%K^DnCN2_>SytIv$QzWZM2*zW|A$ zFC_6thP}$}YFn(x`Q*$lQ@Q$k4KLe29G7mZs!vy6eM;4T>KFYkXvM9E#cNdQLPFi5>-i3X0HlNMmrS@Iwy98|2XiCcgT6?)4y%XEr+3kz@WB=?F z>PeNIf*q7KlcUvBqQ#ps^T)APsZUpX&E8rU`^wSat(N&7tX1kQWgKSDt*mS>_wneW QedJUA}R*ubY2 z76x7Q`|TkQ`veID`vmha!T@3V$gM|4E|?s(FE8i4elsX>L--FwuuqUY@ct*}fntEL zD+rtRt7Ho~n0HX5$tD%T1}yaT#7R7!Ab}8ACrBrP&O`gY!X?I;MdbNIRp}WO?Ol( zYVfT;yaW3L3538pK{^q19tODiTIKs|$)KW^e-)d&2CF(_1vkxB>=PsmLeTYrx1VBw z$T%@e=8Ss=IZ#|xZ@QoXG?g>g(zfHR(6o=a$PYE)*ms@_GZhuuqUc2&@yN6G7*p z$2CDTUb&tObG)<9;lv|o?6ACYZec$52@(b&==#9hPccBqx@@%9(tJgpT70*O(_a9+ z+VR3ezE81FkU$8m6QmPC=V5!tb@`lSWn@f`%Gn#sLty!mW&NAN@%0ly*9G4GfB$`$ zAPP}^AL_}9BkQkvZ*PYca;0H&jb7pL1PO(}dii&~2r3^bks`dS9~wy^m9njNd- z(cfPkK32Pv^b)hwFsv^CSE4XxqggW^PmnMOLDvV~eu@Disb^tHuR#IXT1ehDQ{;lV zN0Q+oXMBGb)(6rD<^l0AxL@S=&%Zn-bzjewK4X{%b>WtWi)*^^c!C5%V4WbH2s#fR zc?%|mpL|6+%bYnTW8MNeQucl}3;5V4NEn2m>jQ5;#Q>3^oFn#rTqb#6E3M<2ay_J~ zUaCH{7C#@4^?~$(c|bgT5f=`h*55&T>wcW>AejswbzWYMku1RD2@(i_b%Jyv=se6@ z&Ry8pRZiY~U^}rizZq6(@5q*{Xu&=~!XN})A9(vI28gCX1IWYl6$Yu-X0Xx$Z=qxPT%`veJt5OjUu?WY(Z zUYFN=4o+wwGcGJTCt=D1iO}d4?go7Q1nUFo1M`4*xEA#+w_LY@G}RBk={vszWQ}84 ze(fjlc!C5%V4WbH2s#gs?L~}EXOxn)dQoxL=43%=vYc6G2Y#MW&~<^g|KEQfX6o+w zpm@2HeC?#tdh9qCoMvd(=PsqtP{+`2m{2{Aim=+Jx5Zd*1LMi^;r0#ujC{yjQ6{cJn-)*=7C~>h*c4( zymz;r>~#x~_kR8iA|L%> zdc5C-1VUh)Ae{(057MO99-B!SWRgk8)>z>Opa!xzA15VYpCDlng02s|{S*U4>XQlO;B(hd~*51H-Js^Bftoz;EPQ2fR2>OdBhA)g10|Lj31XpLR zvrH+eU&#A9w7(ldRFe~H-sAbSupb1|58vze7`f3QQwRLX03Rjs&J;e3;q_hGFdkn& z`5s@mTrmBUzeQ|wY)B=k^!!thbwv~O-|6prJPJRjh5aCye)wL$OD#(Gd&%dKTH*Rh z8993(%lp&U;3L`i_yiF~e2+I=PB9=b{5)5^HF5nxK6y}qTU+Z_0^-oOqk1jQ2Z?}Piy?{^_15ZDib<%jR}_t{+*-A&7@$i(zF>Ib+jP+q1!QylJKpCH1B@9~Dq zDFy_FpAw^;mFt6&$Tis#t7av3f{ID+php$Heu8}wtYASU&hse^0nM zdZyKTJ{j+`CSaynI>=;vmY5^ij*m|eam0`K!}Syc|9GAXH}h=9@8poCInrE7-!@p3 z@|C+O9na5*^)DFu|GWL%>nro8+tdoO<(%g#X@dwj>93+#F})m*Cx}4e@A8P-Q4IWJ z`4Ul^A@)wVhkV`Zu9*_o0-JWR`=r|Nc!G8R&({5a+rOy_=B$$P64EzNC;k1s0#M8t zny%r5^9%pCJmU8MY+tE*r(Tge@`9Yyx9skY$Sw#=)5&?>@C5I7A>k8P|Nm_L|K0w* zBI|DuX#1AjZXTpNYhf$&D-=uEhT^IIJJP zWyfVao*)Ad*aw2)gCF(to}uHZI)SC+%I?&uGY&lhgRKvhqwDZ-{Ev9U^@8P}?H4Mw zC4(DDBS(+Q^YI<9AxC$y-5f7Go**L-*bjo`hwt@w(BAAj%Nkm|Iz zX8vBB=MMWpF#YhoeiypOa_!sPO0GHC`|X`$3QW4I|J6tZ=Oy|cU$|T_{S!Y*KHjuC zkL>8SJpc28Mo3&jl+GW6^Q~Y%2&Nyt*Y7ITrP34XTgZtot+Hy=%VAy6#I!~+e7@^@ zeBpAz^v^WcvFCPes3vbnuRFfks2+SQIA$kx@bmH54}$53@AdnZeW!d@e#|AkH|;*s z8c++<&d&IG>#lfwz6%jXe2+I=PB9=b{6u<+&tGui4!O0o^Zqj3R!BAW+8geV=Rd(d z5G)`3sK4tjxkuj{Y$db5p8wh*Q3r|Yna}rWaPfG8h$DW)AFihu_{Z}kvG9GpwMj5J zu+er)y-ySTnmO?4u^rC0g7q&L`v1HA{L!I1FjFy%{8K?na-1m-WS)+yf;60O;!@S}cCtu^eBbL}K2q_hrA zxXFiuft=K@E=AZUh&bX${NZ|vfqy(tdN*Y`7Y;U)k3UCQ?y)`w$BH#|tZT4Ou>J)@ z|9`iiozHAt_4pu& z_VKxIIpDbRuy*Uk9_$k&{C{k}qs{x@`O$GqG4S2~zGEW%XSpUOi*}myK*l}`b`(vwAAzVg`Vedsy+FGwsRKt3HHed0|cT0<7^Y& zkdJF4Nj{b~*yURTUKeCy4=jCweS!pnb%J>qVSvcDk%`Ee!zE`F5iMH|mqGi*Kb}eq zzQI1h`k?fIXu#u1=Ji`o*DvOi=3-eL(T&ZZv+ZP=%@ynutPhF-0`q`)aBS~4zZ=>? z>fDmOvE8H|_Ia^a++SLP#}gzFtP{+`2m?ggFCmA<3N?|P-(=ISYb3zFnP1*}KCi+) z!TO-|foQ<{T`D=L(n-QE$syCv*K;ORL4HZV;UTjM>=W!0?34dxW7(ktTCTQsx|CBn>w8f+xx~%xu%Zu++lqnePA9C4-dzd7p~)UlJQCAaoY7S zfIoUmjN5AL6RZ#HlVJu3Mh8|l$K%po@X6x^X0CQoZ(((n=j*E*@bL-54@QasLeP1L zuba7hSvHTHz0tNXbaWdOe2lnw^H+SGQP6dPx1VBwV0bW?ocW8|*9>yjhYe4xlS*N{ z;pZjF(l~D_!w*J^0YcDu5V28SW?5cH8r?SBKWSzge7JFB`cDeE_`EO@hQRAX(EY(| zf1)9~DfmVsX|ad3@_br47>ae}1)NO6KEXa2VSqq1U_51MGEY6>0jZ!gU!-2<1qclj zW4CiJMbFUaVX$}HvE$p&(9o#i|9={OjURsLj}*>z+~MfzxYONWxPZkP8aw>9ch9E1 z?rttSotOniR`NKH!%+u-Da`P*c|it;Q*2WOpSL4DL#-)eV5?(Jl(X{3qbuTk~}P%QCn%=TYUw z#C8zvc%87ot_S8#RSCYos|0#CcXAr1J_Vnx$LijvSHX*gm!lhMTcJd1$+U;lNbtEf zsKi}a1eX(Qj>casfTA}OwzhOPf|lE6%VL#OIJ9Y!!q#JjkhLyYGNZ8*8r$V;$C@-j z=)8HG1|Bzqb!_vQft~~ip40VZOJ_A?HJq;X>Pm;t5i7?Ze^&`Qz9FiY_cTGE#WUlb zcGbYOPI{8GuLSH$+BU}bmcl_Y=tQtgC1focxOqFb02WF()?7AhgU#<_PAN~~ffUc} z>63#^Fc|S?U66epnBNF4&ueUgjeYF5N1xy~nU(n-9q@LSx8mKbG8hBi+q(HpV9_n1IWIOBo_@(HD=N+fwTlP*W!aD6^YJco zwWJadsYo60?r4VdCb{-uNqji_!HTaRmJD47T=gG3Y6X*!`S^?4Pb|R=7%4^q_q!{oa?ArvHl~+5U zaKN_PFZ30hwW)Bw^Of}+obTrjW{q(PX5caElWT->5SlD!*4fboPBXOb6Wm7F*R7YW^|lEjDuhSNdo_T) zGdpomp$Gh~xI7_K{o#wgl9RY_14KUlsdbxX3v|Af*?q&e9@IcK=i{U#uxN{@c2X*U zoxRbCJG`Uq!KEdO2*`#qN`8YX-%Pq3Iedc3G^!zOW20CFf+L` zGgUJ)@iH@wGBYVMGsQ78VKFoPFf*AjGc_=o=$TC0OeSF_Q!0}QlF4+(Wb$G%6)~Au zm`oGQll07!!pxJ9%#&WslPt`g`plik%$=6Zon*|NGR&O-%#}{&N)B_TnmH54oM~W= zq?kQLxN+iq&<>Yw%0XKxlYDOsDpqu_(6s3S^Xv<8Gd1hr;J7qn1D{$LwJ$H{y?!$c z<{cDivPp&WhpN&uD%v6S#@9{DUkyJEEp*9fbPE@p)WWYw4UYjqMJ@j-HhB#L#Z~pD z3mTxgCf)Od0w4Tl``mK5#f31(JNq0?Jc3h;?>2Gz3m~RP21$ z-p`-G{jVWY{uuKHl1w_b#tJ`xTsJcvBl!|2X^YW_ttf(8@mYHV@AZIwA@A$Z{%#2H zQ4;S=;e*oiPeIldO`sL7pOlfa2M#K5Yis>VAooI~u?D9D0{chppY6~DiRo|D4{%#x zO}50US&5wx<14g?NbZE7jBpEUt9&CWz z7Vr(!Nq>K@04DVCRf%3gzpx9j7Q~05j)1Gp98(XD>4+DKqCHGp8Ig zXBIOj5HsfqGp7TSv!2Px&EypBbl6dOwKPRrxBC0g~>_5Jaf-HQ_MUw$vhMG z*E28lJ^jo*%gjBQ%spq!JvGcd1I#s1=9&+4PMbMr$DEU3j=7k9%8@b1>Hl?*irt5V zg3>5()6tVCjvpR%AG!6&$OVI4LD;lkC0n3cRH`5&hp&n8qMR->~G{Wh-D%T7=o1wqII()2lCnWVOEa^2UfWiGDzkmMa zF?{4Lm=u2U6=W#qh`k?|317s8!>9Fkz`W($g^gY1P`5F0o@f0V;GKNpbZ7fpcwJue zIXIyKu0=h|E!S;;$Mzydr!z`nrtY2(ikCZ~tT{-=Q>_(ZqO^{(g?fN5njjYy(G63R zeU2ts)x*{xzT+-EM~GDssl0c0c+3fvj?~|k0Mew_9-B!S5IaLAYJyA?f zX)ETev|f`05?r0N&N8JCBR4u^>VQAwZxP!Z8&U~Ui_-mG@_F!F_147o2l)`Gd_5_n zCLhT8r>>dWmcrRx7TrzDtDwYaXXW~!B)IhKtXr=v4-5|#d+2R$hY2@F&$N2ahr-P~ zoAEn2(CaJnr`yyD5K)^U_D;A5QWeZuCFLcc>YaK;?#K(cBI|DuX!{oWb=9BM>??&m zL&sBf0!x9O6&~nWuYsP`7wB0_fu5BS=vn80o>dFzS%ZL{6$R*7AArtk4|LXUptBMK zoplxHtdc-y%>z0s7|>adfX?aybk+)>pUMaNsbip@ss#F}F`%D{0s5|gpzmr1`mRl& z?@9yut{b55DggSbDbQDifIjOD^jSTi&sqR|R0fo3hTldUwDW%*wAbElhn?HVankVL zdiKasmiwkU@nl!D%CTz@T5m-t>r5fB)*hjb11k4N^@O_oAJLkD++yaSDmi-V`c^o}iEwa}w3BqVdl& zR2<5`K;gTS7bzqP{VBYth45X%6;$4Z@ZASg&Y5(RDretD7?*XOidh~vD2y{h*wz$A z#dA`^QTu=h3Z2J9QW*N~4vH;MJH=oWO9`R&oNiS9P6x$Bj}XSmpyfHa2=!J*QR}%F zcaOp`R`)5CQ9$LyfoSwOrVl7&t&XMeTKhu^*`|*u?0b$dCm@lEP0l|? z80jYzvQH;am==NRZ>FF)ZdV#r?qHBiVFC}uMUX^RKb&%@*#A=&AQM?G{h^77 zn-0`MEDu1)GDUcOHNvIK5sv>IVX`4Y7L7}dQ0%o7;Tt-RUxs2;dikX*QQT%imzyDc zWQp)TjR!1HEcOS&pVlD!VvbOOE@$fX=~#6gs&BMG_;o!(_6CIIbp1116rZKrdC~Ey zji}s}j%_xhICm3;#Psb5_tN+p)e|LjyXjj{`>A#aU()qQP)wB3D23V)H|^2--00=j zpqO=p#-CBY5PfvJGjuHHh}JJm|A<8+BvR?P5B;dIUeP~py6F3|+_$06`*|l?zJl)e z<6BYrSGxUS7gRq)f6giNqsZ#rh1x~ZpJPp9CaNbU(97>bpTo+dFKG-lK5n~&PFS0Uu= zpqEdiaWq0gpRONX|Hx?L@&7uAE0RI5&JUj#S*4`DeBU`Zo?TEB!EJ?2K{G?IrgXxd zi>lY2`wx&SUWr6~DQSRZNsCUhzO;b$%PG6x84iG7!`ge=Nfodo>0f_@M~~us{iRM) z{OM@+#{|c9@0aJ1FZTTL;7LpcnUP%)TJo$5bX3+BFW~e-=k(+y&XeAf>*S6*Pta_D zIn~lZmceZL_&MD(TWT(3KAMctVJn!2%YoAm|pYM75_YJ*3j9c_f+_9G&+L=9} zU#J&6e~wfV^{Rr^r)S9@>v#qAOD3xNcMcz&Z?iin8Wsf?2A?aBS#ldTC#C*sr(Oq_ zOIO*|8pM;a5AUr=VHJ>F!Eab(OfSqbIw*fsJcpbYd9^ht`ylE1yH@6I<9;}~Z0G(> zhsr@?wtn>ez8+E|cDCN}DJ-^5vgU>P4u8U>P4(PwN4p>}D9Fdu=LJmIFl(Ff%@!Cq zI&k)MOgXrCoMzv)9)Lxjzb(C?_7kT){*J{8|5o@CZMR+aQ455uy5MTo#wFA9H{EWk z>xPAmF9M`hIgq6yudX`0M{4jn!Kd?cH`x*-KDJw;5m-{y{GUzwU{~Q6(+xil?@?Y2 z`^e^1kYZY)Qmce^fcxr*-Fw%LWh*ZW+5h1}9T_kv^Zd`DHsIK?igSF6VIU|{(PcJ^ zEjbvncfrdza{LBw#V4KO?C88LWUQq!2TthDP&8t*)4%kF*=%3T;SW}rerwg_@T@Hx zE-&4}Cc9Hz$4IW_Y`OIN<`*07IHH=TY8I?G$@Z?9tMKg`hjXyj@7&a<&)FRkuji|h zd7RnXF9oC|yk$eO_bpMELQY;N``pn3D>*M$Yzv(6D4Bi8{HGPaH5+qwA8VMYw0IBa zQIh#K(b;R+EUjo(U6d|oT;A!x-`sRL%bxX>Dy~}0Zhth*qsVd+XJcxGzNeTxr)K7@ z7xOce*<*vu(+nT~#xA%l{5-&CE9Z&jf{5QuW^p#hItSnLaAjMLEpv<*TFWVUSY=bw x?#zi)D_prPZ3nwJXTs_|Yff`+ja4Z>{b>ukH0Mfg;J(#t!#Mr0%wiAD{{UU+ll1@q From 3780f0c36732e6e6d24aca6beb2e1b1dbcfe90a1 Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Tue, 21 Feb 2017 12:51:57 -0500 Subject: [PATCH 04/16] added HW4 --- HW4/README.md | 37 ++++++ HW4/collar_mass.svg | 270 ++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 307 insertions(+) create mode 100644 HW4/README.md create mode 100644 HW4/collar_mass.svg diff --git a/HW4/README.md b/HW4/README.md new file mode 100644 index 0000000..f9c6f19 --- /dev/null +++ b/HW4/README.md @@ -0,0 +1,37 @@ +# Homework #3 +## due 3/1/17 by 11:59pm + + +1. Use your repository 'roots_and_optimization'. Document all the HW4 work under the +heading `# Homework #4` in your `README.md` file + + a. Create a function called 'collar_potential_energy' that computes the total + potential energy of a collar connected to a spring and sliding on a rod. As shown in + the figure given a position, xc, and angle, theta: + + ![Collar-mass on an inclined rod](collar_mass.svg) + + The spring is unstretched when $x_{C}=0.5$. The potential energy due to gravity is: + + $PE_{g}=m x_{C}g\sin\theta$ + + where m=0.5 kg, and g is the acceleration due to gravity, + + and the potential energy due to the spring is: + + $PE_{s}=1/2K (\Delta L)^{2}$ + + where $\Delta L = 0.5 - \sqrt{0.5^{2}+(0.5-x_{C})^{2}}$ + + b. Use the `goldmin.m` function to solve for the minimum potential energy at xc when + theta=0. *create an anonymous function with `@(x) collar_potential_energy(x,theta)` in + the input for goldmin. Be sure to include the script that solves for xc* + + c. Create a for-loop that solves for the minimum potential energy position, xc, at a + given angle, theta, for theta = 0..90 degrees. + + d. Include a plot of xc vs theta. `plot(theta,xc)` with + + `![Steady-state position of collar on rod at angle theta](plot.png)` + +3. Commit your changes to your repository. Sync your local repository with github. diff --git a/HW4/collar_mass.svg b/HW4/collar_mass.svg new file mode 100644 index 0000000..cc18c3d --- /dev/null +++ b/HW4/collar_mass.svg @@ -0,0 +1,270 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + + xc + + + + + + + + 𝝷 + + + L0=0.5m + + From 4a4ee8b39b30e3407210e9f7cdacdf81591c2d3e Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Tue, 21 Feb 2017 12:54:00 -0500 Subject: [PATCH 05/16] update HW4 --- HW4/README.md | 2 +- HW4/collar_mass.png | Bin 0 -> 6794 bytes 2 files changed, 1 insertion(+), 1 deletion(-) create mode 100644 HW4/collar_mass.png diff --git a/HW4/README.md b/HW4/README.md index f9c6f19..3cacedc 100644 --- a/HW4/README.md +++ b/HW4/README.md @@ -9,7 +9,7 @@ heading `# Homework #4` in your `README.md` file potential energy of a collar connected to a spring and sliding on a rod. As shown in the figure given a position, xc, and angle, theta: - ![Collar-mass on an inclined rod](collar_mass.svg) + ![Collar-mass on an inclined rod](collar_mass.png) The spring is unstretched when $x_{C}=0.5$. The potential energy due to gravity is: diff --git a/HW4/collar_mass.png b/HW4/collar_mass.png new file mode 100644 index 0000000000000000000000000000000000000000..f9b2836afcb34b1e0e10352776471d9c40f4178c GIT binary patch literal 6794 zcmZ`-XEYo@yWXhLqXZFxSS46B2%={7x@`2m`s%%xAc(&D>Wk<^w5%GUtu8F0MhhWI z^r+YOo%`qhxIbpzGVgodnP;9kGiPG8HI>MS8HfP@0GWz1Sm$0g-M7Stc=!F%R=7F< zK=i`l%^Ph87z_aLn@>-%(@u+~eLsF4yg=fdS^DjJ4)g_yvSC2FnF4;svSG$^t2ez5 z!8DW(A6QUf?;tOzcu)opi9Z-j@KWKW(Z@gM<~mo}SI-UPlsUQ%_?727CN4}E_M89^ z_TfQE3Gqb;-`St!2?5a{B_O|W-tPK3(cRzxL>2&eR{buNf?a|ml@KrtNFG<)A^{|u z049bgOYW6oz}I+HRXPC6)`Kt%1rZsptjhy{@IF5?A;5OpT$%!)9uii73;2M`GP%}y zTz+uf75D%E{SqW6@1)MRAOq4%rp6>$+FhdO8kQIt=cKP2=OQ<<4#;oyH$!C~rSbp( zZpvyay;?DGbf4~A%j=6$D6eng&O5^ZfF6eHl{>&!-;PE_z!(mo`QU)JlA$n=F6?Bg zOSq{RfQkZ`p8FYI|LGE9yk7+u3$c3g0|jk-&;%|_fRN`CE~guz>%%bZIl$|fXqumI z$Tz-`bG@UQBP1*$*eN11Dr6dy7c+^3yHW4=1k*>^u|&S`!#zHv%y@*y`rIore2_&o zMgkQ_&&JqG;4c4~QU*v9E4!8q1(INte4eu_i|a(ZWC0Co4dQPwcszZgn9o8z$a}kcDE-$M$@7KC%GFbrJ{U_W+&RVxwyeAg(UPA(DG5z zzc4JSn9$WSp993ga|VLHP5nLcGi_&ICS!h=^lj^B++q5KZ4l=zK?sdZ)SWWRBLh5* zcjDdYk5rX`P8?}emQkA8GE+c%iI;>%uRw9lnLh7)($6B# z@-@rg6MNg1UJru#JEB7JZr|OiM6#mz*Epy^pEXMKO4O{u8#P>pP}4M?R=Jm2jXEc} z+ftL_f}gYAXGIv4%<0t|)stAktVq^K-Pzn-|I+-``K$MLVNI9{OhiV+8EYRa9}ArX)+Atb#Ry{@h=#S+@m&62$mSV>%|WQkH~*Wf3cTx*2&*|68}>&!mP z&fw+Hufb<29jua^18EJ2b%f)P}R6YVPKbzm30*{wD7x!6xe_`(urC*>s$A z^7O4rnzxCL)s9h)1v~9X1Txd8(itK>PyH?lE(uRG95lp6 zUyq88x`SFXYV_Xg70L2GgD5zovn(V$q~+EaS0q9p;)Vd1V1-nJER`&WwBU&fJ^JZm`csA* zhice}aIHwl7i8zW|7kN;s%j;B8`+!1DCqArBycLUQxn;)vgFA$ikMD?Yi+_e6OAtlaga;y!B*-Krc|$7S9JxrAPNwm2kBIF(ew0Ww zsM^!W*KG;<#la79QGANr^_*Q-UedzXDDJ+ts`@sAeM2?r}-jA1gTe-eL!Y;zDp5~n%w~5!WphXawaY_xu z_^P?Wg=bN;Y02ga!<5FPA{p{RfR~H^;*+qSookW&>RAuQl&@|61Ng&*0<5jZXZ9}a zigh)*NUG`_dhkz=(KM*6_fyGdYjm1^z?M=mb5)4RkEdrNna)ki{Sm{E*F62R)C>YWO`s%8BS6KZo|Be?kjgwwpG z%;m4!$!ZFlkJ9|^;~lk~E=G-4mtVR|i>e^S^+)up250s98gd%A1L6b5NShorWLLhj z6zl8XzMs4L+Dl8{b~aU$IS)JLNIeeOxpf$rlG+Q{BV(#gL~2X4UZ$i-x<;a$Jd?Nwq!mxUuYVy_+CQdfMV5vC=O6mFbJe@a0V3LPiV!;_Bk> zPPk7Ce8TI~G2N88MD)n}*8S|2U9_uvm#^RG;U?um3Y>zGc`<1F>~Md3esWbQJn30d zR1y)hl1#oo;(B9g>Q9;4cyrSFKwLqbR9z739qOXlyJq$YB^`?%(dt<5 zGXB?a(lK&H&8#kc0=nRBzsNdrcc{Ne9VtsK5HBF?#0$+f8#3hJ(+|ep&R>nLFI=b& z4Go0?_)y91+GYFo_irZ_n6i!r01&_d0E9&X0GIc!ux$XqTL1vqu>b%hvH$=&x7=39 z>-zy5D>WrB;4V68r0d=ya#J?+yqC)VZHgGU^u0pprJ|ugxQg?bQsk+4AXFa!c!aM4 zmV^4u@8t!?Kb`gN4^^7n_xO!zXy}Dn^Nev7WLi5SMJ(Ber>__NV({6u_3<im1R>&j9Jer zI2zcPkZ|u>UX+lkJf>RrwndwkGAacr-%uM`g;0R*CMdgFH{^!Rk8I3-3F%|ITL&CA z=89ePmgXpNt+Ep$ZA2#qlkMHC)8bd|2Bn;2do5J0HU^Dt-)#PffIN1ry#AEBv1u#v zoQZxaw0E~eu=4Ep2z5$Q{_I3`$Mf0n|ju^5aPr{F7|_!K#-J0 zp?RJ;g*4Ui`@x-E-95^2Vgdq!liB6TJOmESD^63bre&>uPgA)F2(i$=fsCdJS4;j$ ztE(_p9Y~!0hAQ!~?T^_+54kDMX?D!a843V}-dez4)51y$$nx&aE>kM(LtWzuO z_K3dPrB4N4;`op)7tMyMU13ormiGhWkWXan^Vs)_2wid_@w?*VlDNNQDM z6QEm}C;5F$IM*%}_)g_>BXjE77f!3YX-}x6eG-CIY4P?z1v$4<;S#J^+@NBtNYDU= zcWA+P55A_RyFQgV^|8&i*6~7F1K;LLzfxAz8S=g?*#=f0PxHq7zVI}&DMIvcAa9Hx zf6nqELnSco-u;>AFH)OLOlv)uQv4{C5i8abk6lLqA^4EpTx0|Y_xncuc3=53>FKV+ zg}4DM1ly&pH`ocOS?F*S(tNsKC;SOK(e)!#p%`0K>alE*kI@uT%Cc2f7}V_ z-5(n@w?Ef{v5>=U5!wsGD{JYQVd&I5QKzXYmlP(FCB{ttWBdJ`LIzVMGTI{I8Z=KYe>JUiw18aC0^ zp*KdTh@hgpu309Ek9=s0af{JJO3C^E#5&iB zdQ>0&kR&`4dA&we(WAv@{;$3AC0IDw;Ag6|T@;YQaT#^te?yXgGJ)YjfT+Tr($^wm3 zd>6z{@SNcZ`E2#;!!qZTLu%&v#;&ex-Sg|U_n{^iR&l!*T21!gSV2tWk~JP1ds+I% zdk4+Blf2H$GCmyQ&Pyx<2M2^ByS&Mbicm(%X;Lu}#5lLGqT|8rR_1zBI?sY@jS*6t zao7U04SYFz5i*;&;qzkwK>rB0m}}Z@uay!gKSGhcuj$cs01YmyU445~Hb0Z4JegZE zgz3&7xCApx`L8Gbb(2IaY^FzmMZ)aCF^Hyi%1MkL-L5Aadc6AjASv&D5F4S`gthr@ zBfg%kp1D2ITSp<9y13;ZQtyh&b(+{ejZhYekwg5o0&tH)PlGh*_FFhGdq>Z@OBjHP zy#c@vn(r6d=ys`{Pr$4BH^HO8b6uW;+rs({A408$ocVWV$d7Lugj90*FelyXH|Af8 zD|CGW{;gqqaN+v3;f&Zm2Q%ZZDnjaBW*>c3J=)rhC(3CP9twV}JT1-wNrb4f%Ss)m;uQ=@H?QE?>1KKnwPZ+~6hLqOJuiC4Z>|r{mu3!Q8eVtNgm{27 zP1*2faVx@+2wp)w(3AqRl=zyw2S2mH&Ij0&LkLJBduZM5^o96R`r`hhZ3u`#C9o%Z zXxNgfk!d&e9=h7@HbSJNcU9&hpE2bI1eC2ahiR@GO=IK-wn*XyKvU})K5Vi$WP5R@ zC@h>LOx$*W*w1yWCnIPIERuFwS)s9(LSri4uE!08Nh=pUdHKpNnH@wz*t0@i?DCy$ z%&wzd>hZ{7S7X|u+SB~)_2+?0x18FKg|O8RS1E?Rs$iq>Pu&g>%L9A4cq$;({G*dIsEv&K8WM z+o6s5&J)s{{xbgM(U*CBUD2l`O*OBy?w>ZLR#zTS5to0$b^)Eu8A(@ONqtJ#)m~&3 zH-6+{Ns{u38L?o)AMkExC#bXai4y*8zSh*Bw4DkF6WS;fGxHkGiXl<3=f9#-S!>7h-f|bF0WM1f$Y8SViH@3ns2@8+ZmEBG znbC=}xp`}YVRI*wC*vj;e$qV~^6|2FbkflE-nD&(W}6!KE=jyOJy+@JyFoq&mpr&& zKZ#hz0Jb5drIYpn6V{5f;74;)Hj6{N4kV_KH5uwE-FTgTb)`2xBgf6}NJ5TdFAF|M zl9_8k{&liMPPSa{zmdXAc08%6&fg}ev1Uuiqlx%NH3~=Sh_bJf1qB?*>X_6*GL!%7B`U~Y zizxjto&DBqOB6vB?L)Fs(fm&J>gtk>N`wENbkuLf<^ShqO+KgBq}7I8yjyseKmlbw@0gya!gl z6FSYWRUfJjbBJEo$cQsC{jQf0f#iv}mx+&S_Rq;bc(`DTUb*WqWnRIM-r4Yw&*dBz z2UuI%dnkQDwED%`ak;sQ*B1t47&kg6)m;yLKd-%e!#_ouue+z7`NA!O_sZ#c5ORuV zr?eEU_oAbNkfMUtc}h(0Y+=@;zy`Sl9Z|N)F#gqsu3TjHQ*82VvdCyy?C<>iEO-6n z2p$E8z%z`gHX_WQG)ei%H#NwPGirHeUsYBg$GuIG5>(dvuwF;ubr)50xvg?KIZis~ zkY^jOO5k;aBZXLXbG;lV%iiX|HdW#CyLApp%+|${ut4H9YhF+gv?@0>aO{(6HKbn+ z&7j>iOt?5M399*a<|o)I^9+4Fb2q8(r`~qzD5oN@uqQ8Xh9ZH^rY=tXX~w@a#`c2D z%62*gJCYK0_o`zhM-552cXb!1duv|u#Z(AaDJZc8QW442Pc<94y|;VlS%t^xXl$(?$~yDx(um2BfJx2*6$Tsf%!~iQ<~I+%T&Is3d#K<3}}|=tUhPNaCUrfGzeL z6ZF1ajD!1zYH4@^wK@nOPW)Mhlj}lQOodeQ9&X^9$7Qt=EJm0jcvk5ox!l>LD^3G9 zen|{~BiyJPOY95*U2Ye%!2+2Ofg>4Jlh331R5B2KilkH<#!##8&ILSmnC5syy-UTj z*UNWbnM5(p_~4{@;Q8;(IQ^$;F0rsrrki~%-LH}@v^=R5duzyIj6~cs zb7;3Ax-`sg+)0~n?NLoEZ2{1&@alP7R4Oh`L&*;&BW>qWKIDxLMrzarwaHeEBNbQ90 zpkIfv=AW>=-UMK^ik8_{v;b;Iud4kIt0E1IsX}23ZtsYTstP94$VnLfch}QMe%7yY zkG#GRm@3__Jzm5qO_sc`#YRJ#A7Jmua^R?SA3n4g9xo2roBn z!eW5hReE1#r2@zolp?gzALO|e=4@J!XNpN Date: Tue, 21 Feb 2017 12:57:11 -0500 Subject: [PATCH 06/16] update HW4 --- HW4/README.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/HW4/README.md b/HW4/README.md index 3cacedc..ed5ca61 100644 --- a/HW4/README.md +++ b/HW4/README.md @@ -11,17 +11,17 @@ heading `# Homework #4` in your `README.md` file ![Collar-mass on an inclined rod](collar_mass.png) - The spring is unstretched when $x_{C}=0.5$. The potential energy due to gravity is: + The spring is unstretched when x_C=0.5 m. The potential energy due to gravity is: - $PE_{g}=m x_{C}g\sin\theta$ + PE_g=m x_C*g*sin(theta) where m=0.5 kg, and g is the acceleration due to gravity, and the potential energy due to the spring is: - $PE_{s}=1/2K (\Delta L)^{2}$ + PE_s=1/2*K *(DL)^2$ - where $\Delta L = 0.5 - \sqrt{0.5^{2}+(0.5-x_{C})^{2}}$ + where DL = 0.5 - sqrt(0.5^2+(0.5-x_C)^2) b. Use the `goldmin.m` function to solve for the minimum potential energy at xc when theta=0. *create an anonymous function with `@(x) collar_potential_energy(x,theta)` in From f29d2cd48cf2333e32379a56402ef6b5a19f580e Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Tue, 21 Feb 2017 12:58:13 -0500 Subject: [PATCH 07/16] update HW4 --- HW4/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/HW4/README.md b/HW4/README.md index ed5ca61..0b8a5f8 100644 --- a/HW4/README.md +++ b/HW4/README.md @@ -13,13 +13,13 @@ heading `# Homework #4` in your `README.md` file The spring is unstretched when x_C=0.5 m. The potential energy due to gravity is: - PE_g=m x_C*g*sin(theta) + PE_g=m x_C\*g\*sin(theta) where m=0.5 kg, and g is the acceleration due to gravity, and the potential energy due to the spring is: - PE_s=1/2*K *(DL)^2$ + PE_s=1/2\*K \*(DL)^2 where DL = 0.5 - sqrt(0.5^2+(0.5-x_C)^2) From 72ca990cf5c532001f3317577e52f1f54ab1a1b9 Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Tue, 21 Feb 2017 13:34:12 -0500 Subject: [PATCH 08/16] added suggested gauss elimination --- linear_algebra/gauss_suggested.md | 71 +++++++++++++++++++++++++++++++ 1 file changed, 71 insertions(+) create mode 100644 linear_algebra/gauss_suggested.md diff --git a/linear_algebra/gauss_suggested.md b/linear_algebra/gauss_suggested.md new file mode 100644 index 0000000..6b1f6b6 --- /dev/null +++ b/linear_algebra/gauss_suggested.md @@ -0,0 +1,71 @@ +# Linear Algebra Review +## (Gauss Elimination) Suggested problems +### No due date + +1. Solve for x when Ax=b for the following problems: + + a. $A=\left[ \begin{array}{cc} + 1 & 3 \\ + 2 & 1 \end{array} \right] + b= + \left[\begin{array}{c} + 1 \\ + 1\end{array}\right]$ + + a. $A=\left[ \begin{array}{cc} + 1 & 1 \\ + 2 & 3 \end{array} \right] + b= + \left[\begin{array}{c} + 3 \\ + 4\end{array}\right]$ + + a. $A=\left[ \begin{array}{cc} + 1 & 1 \\ + 2 & -2 \end{array} \right] + b= + \left[\begin{array}{c} + 4 \\ + 2\end{array}\right]$ + + b. $A=\left[ \begin{array}{ccc} + 1 & 3 & 1 \\ + -4 & -9 & 2 \\ + 0 & 3 & 6\end{array} \right] + b= + \left[\begin{array}{c} + 0 \\ + 0 \\ + 0\end{array}\right]$ + + c. $A=\left[ \begin{array}{ccc} + 1 & 3 & 1 \\ + -4 & -9 & 2 \\ + 0 & 3 & 6\end{array} \right] + b= + \left[\begin{array}{c} + 1 \\ + -1 \\ + -3\end{array}\right]$ + + d. $A=\left[ \begin{array}{ccc} + 1 & 3 & -5 \\ + 1 & 4 & -8 \\ + -3 & -7 & 9\end{array} \right] + b= + \left[\begin{array}{c} + 1 \\ + -1 \\ + -3\end{array}\right]$ + + d. $A=\left[ \begin{array}{ccc} + 1 & 2 & -1 \\ + 2 & 2 & 2 \\ + 1 & -1 & 2\end{array} \right] + b= + \left[\begin{array}{c} + 2 \\ + 12 \\ + 5\end{array}\right]$ + +2. Calculate the determinant of A from 1a-g. From 543fb4befaf120a39c88cde7fce8a17b07c6798d Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Tue, 21 Feb 2017 13:34:49 -0500 Subject: [PATCH 09/16] added suggested gauss elimination --- linear_algebra/gauss_suggested.pdf | Bin 0 -> 87205 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 linear_algebra/gauss_suggested.pdf diff --git a/linear_algebra/gauss_suggested.pdf b/linear_algebra/gauss_suggested.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a78b2778173adb57f91a5eccafa5b843897da538 GIT binary patch literal 87205 zcmaf(Gn6n&6r{(tZQHhO+qP}n_WWbpwr$(C_w89E8*C+A9dy+93#!f~RS*%QWu#+; zBAs6zS%+d|Ctx73H?o4_;en!;F|{*yu^`~!WFz=rf}$6*v~e+YBA^$uF?2B%F*UX~ zF@@segK~CpGBvb?^4L7ln6leqKS$taLi(`uc{qSBLqrA%Ib85Sv&6F$g9OEmEnBF2|1!!f zsZs>e8dd+`$*xv%e`5C5F_ACcJF=$(Ay%8zg}@@+MzYO}c916h$+BCsX20Xo=b=fv zFjJ&?fOUqqZ+-G?-8E5m|1wvVdAv5fDV`cfs%ozcGH#XX*yo4JF(k;dYkCwKUUEt9 zu#{OTWt7WU^{WjZ9j8c48D$s!u8=2IqBo32r-=?Pm20%p{G}zbj zN*1ug(jUrZcxhk&z89*Wq&^o|QNR!bGD?X-3QPsK4Ftsm8=P@K$tI?>TNPlX3}dHI z>!D-=R`j8effzupQ?A}E!swxtO+M^`LuRhoT^TX3(Ky|vC%Ys>NLVj(j)sC*ED5a{ zy$7Cg>P4IH5-ZXpdeE}mEb!=q3*gmbjJU4~5^J!#f9}Q&IBLsUYuXbO$^d{JVGouj zs(y930WEG3Tv`rUT9gR-k&QMR_@oepDPq6EP6p0&5dFs_>%4>pfl85WB0>ORFpRNk zhtkp*s$vbH5GRdn^>HD4!*Qx$h;uo;kPv5C{*v`V6KwKR} zVz4}gTdqBhnbX&*%0FXdD`Q^2-sQ^;YFI63@Io!P$!BmYdlPCUv?QwuMH#2shc>LR zO>p2c@5l8v=8(ViZI_)s=H9i`^fR%^vSm{BIPRc{S7*E3q0RUt?)3X?tIE?(okk{6 z*`_k=xCLg>1X4ayqp8b-zIGJdr!!K23T0|%^1o61&;3t~Svdb6o*4-k*%_Jt58X@z zObpD-4FBiKOz?j#0TUz3f6xD?{{P%Jce*NQ@4fQHbZI*Vb^WLR4&?2fsQ(;#8OI1E zT}gXa%HikY+|Opu)7M+Bj8o(HhBd!+K69o*Qe`=FR2FvzPzjDeZA`TcjSm2*C@Z)( zG6FSpaYk@1XFzOZXee-ClF~M&#i7*=KoWx^=p$geZVkYsSuK9xEC3rCnjVN$01E<$ z%P&I~uuKm?lz=)iEWJ1Zb-?H`zTn8fNb17!@W~Jih^AI>Kr=q!AzYl^>}r}?t-o_U zGt=+PGrLv{B!Rh++137mku@v>U?%W!21+J?6dWGDlr=ysFoXeAGgCto0EY$uO8^&u ztg9reYd~{WV`&r@?UJ~WE4#Qj_}SkeQEhD@e;Y`Ffh`zF2f!bgB2SCiGB^C1V}^|C-+}X;rkxh*&pT8-uws- zpW5rj?AYA!5x@I1$nojnkH6Q`-4vTMK!-+Gd*?SbF@k}iE%P@JcHIIDEpKzZGq@;3=Aam)-5@cr|3Bn-lP))OY$_IMji^Ynp&M z05rfk2!L0XCgUIN3%v4grRHBHzt;ZQ(fK|^Jwt;t;HRcG06!fBA064PKtNR!_Wa!0 zAJ(s~kiiL9hIV#`U&6Ps0>bYE9dx4u!2PfEPvCK%>|e_d%O4Eo%~(hlcffTwz^MQ< zh#4vP8a&hd_aC$IpQ7~S%&gqRFrLKI9qf-hJ+ikocb)&+7d*P{zJ58&U%Y`eI;FLI zK}S?eRpv@x=O=wnb=3s;g{WYfTYo(6hj__{d)zf2#Fyi_#vgAJKuk4`&Y$7eeo-bZ z#Q7o6{--*|eKGi7;9K#7{{m13>+*?9iR#5)Fx?-AWY9Fubd6vd0Gk|LKx9)>Bs$O( zIQTjTCm>%nz6u+-*RL=V05kIVzzZ?R{`u)8c)f#z*n3yvHV=SVNnfQuiJl!m)5M=d zH4P1b+0!3!BTz=*A9bT&1l*taF%U!7Fa85@>K6ZDAHCGc9m}7vTH2rPi9fFM-}q(i zEL^LAt@Tqp@$X+dMOHhPw)bU|4@2yW@ZZDdojur}TEL@!`0<}ebR?(8Cxg?y10cqR z2Pa^)4$U?`!p6qWFYW5JKKU#^&EI<5U)oBVzNCgs6^2e48mf$8-e=xO|gay2*6ZDHT=V?=SGB+e(7IL{^&n_=~`4B zWS;8w2>MUax!8wGfcw&gQW-8B{>R0+oM`lTEeB81FeChgs)4tJB5hNEKQ=BU0?7{z z8O9pX5_f#aG|oBaN)Lq4j19X;K!R@&f=JEAdsZvicyai~P!z1&Y}|pf64!k>vLVJ8 z!5^2+h4!Xup!jIOOOwxM1FGeNb{}jVoQUfo4ed2-j!A>m5TC6rj# z)|0*`gm!VIg7m*w6Qubs%vhh(VY^p?&)FtsiQXeT1KijLpSWBulvCDZHiZ=*y<8N|n#LCWB?xyPEsu!K z;J&_IRHz+k4r~}^9VlL}x0PR8`}M5CuZDp}njY#{aYNZKmtOuiLuA_1!*0Y_FKM-} zk>_t!z1*4$!9W;}esh}quHqEsbNu6Y+}FVXOWqQ;rgab0CKFFQA4Z}dlVqsSCj+5H z37t92(pAr{TwYlGME#aH`it)R){rU#1$=KDZH%DlH|xys3YIsv z$WTq}G?_{D?(Dl8gI=SRVkV{Wp)*h1mU$V69(0Fc^t?!VJZsonX3z2TB$=yi(=2n( zzO|r#M$u<jj);gF@Jo+$uru=WEF>dUa?Uu3y^;Stkh3oUK!!99%mf|#}SLKjBq~rYxjKU|H(ZL)))mWM$VLs z60c!oomliHm$ z!*OmhhzF?35q}?)oGCoqvPq;Q0&$Ooj%;(K^$##Qh*F>%PUaiaam zT?%EIc58|cZv- ziM}r%?l3GR8jjQe^*10ee@O^~YH^s+;(+C-!&HM5#?v_}D1e9g-IS9R-L!90_2MjbV%bmhHu9 zNkGVM)Ez52bmndRYGS0VSR4qH*b4jj zL-j$tPId@?5N{mo@q|bC!L%{Om?Kc9^gP%QLVR?@j#UnB`fZG4isDoY?^m}a8Q|`O z)7OE;KM~4~9);ML`UfrsrWW7GJI<51nFpSm?kl+SEC1D$*)sRyQ6jBY_Ri_4xTUqT zkIo=n%1DdMlRKDrFEPV(`dx<|!K9~pyeuB1Y~2Rg?YSm2D&(~k^`u?j4B&O~V(#Mb zD_nWjE{Z1>HUQp9_L8mJVQlc}(cx6gBK6 zft%Kj?5E;1_#8&yS#s*Yx3^4;p2S&rE3PXjV5Xwz6{lzblhAP=UY+G(Z&Dhf_o#Y74%m5r9fu`+#lV|?j z_$uK!7yv=(c9N>$K&}Idb%ZiI&fzl)awb07YH;Z@KpCqrm?@Kdlb6nA2{-m^QTL4% z*Imi?VbJA$m)&knknQj@*7CYSN;O@?Bp>v*EeSxKH5k8=)_Yax^&}B%K_^+Qi*8TJ zivM&uW~NR}Z*0ortkJNBb=5w#=jSme%)8K9?pOgRud6okJAl3u;(aLw`syI1!6H^n z`r3T#$L61d`)ko9aQ4I+2BU*LOJge%f83)_dWEK`LjO2D*>vY5NudXzzn+580-GZ4W$b@NybYRw6 zG$nM&L&eTi#KZv8W8ZbUkKbfTwkdV+(C2L8URPbCd(;ZTY;lup|Ge7kT2p4reE7~i zK3W(;xJAPx{`#NaKg=#|M%Di`aA_ z-Nwd$uOK*|4Y&^y+g96n5lU|>)CkA<4fR3PF3)o$9g<3ouAKu$sI?ajI_29iN1Siu zCe$)3YIB+sJCoGcA))QF0@^MIAWso-_n41*)?%phL6GwA%G2K28-skr zwi?M%eEWhl5SN&n=pfqVMiHxI;MIGCgzq~ib6wF5jb05eEGR7~>k^lYKH8C_IL}J^ zxgtSCI|iyMSMn-5X3+26Qs6DY0O|!hwb-f=DLuFjUif9Zp3X8FD=FC6|H{x8$E(am z?2k)%Yp|G7q(Bl|%Phw*x7|SH-le$I1=*gLokH`uMmXm#i-XMtVg)t|INk$mOp2v` zg}~hKc`Sk52;D_YnUy4Awp4^&36fV^*V+oxgWhI_61Qq{*U^F~uAh6iJ}eDZ5l~oF zvk3<*O9@14Z?<+HEm#mf$>(v{u+6n5e%9pX0vlfu9%tav_F70dByZ*=(=O)Y1tv1h z#^OxhI2(2N;pd!;mVDx}*8%}->Q*K+9rff*b_TK+qTMHP&d6dgr`voTFNX#@HJ7qi z!<*4;w&ByPBz4Yx*9a$44`$$To%H&S<#+1putx7ly=?l!i1CnvkTe8_jI_DSdi-FD zt)>|YJ~^}9lvIr_^j0%@?Xwg4updh@=?1mNR!VaW5#s^k9JggY@quf~$4fsqPv$)` zoikm!M!p?L{?zVv**QAx0PyPUqORAI4m;{q>M1T=b>?fD=IayEB{>KCAbec>%-$~$ z2zLfPIuR52taW0k6n-qy7Auj{yA^WW7|4r@yoyHmZscTmEhwYzC0xbG(CL~8oXIlz zmAw4dhdtQS8(eXuJ#l1K-2~0P{}Nx7W`K+SswoIL)=}wMD_#p1YV7x5-vpG@ZAp4& zeL>spmXS_ltSzYPXePVf(|2q^s z;SP1#;qlGzJh>hoZc`Kz>2FFvpt|`pi01x^g+o=DDQrtb&eLu3xrVueg0JJ)Tc{|d zI;tW0qnMrxq2R$vlQjb9JPgkZ!wFm~NW`M=Ei={HObVxkym~F z;@1(d<5s!3GxVQj+o^+#I3g?6tQX29-z~ja&YR>T9cA{}@Sm*Hq>r26RL+x}mv4ax zjoSuD#Hk{U1>(9-m~@%VmrbN;=vfI)Y~SigF}hd`&-$JKC-~NtM%J%v3yr0;fO0P~7?WW9 zxF(_*%-lnL5EAtin&H(#vQ>?N!M@)1*g3I~f+tnm!+GKQs)6HKH~plO1DoL>QA!!N zhEIvN2uCT!d`}mHY;=ci<|phb5K9&ju$Dze(@s0w^!57{kP!A>Kfsi*#~ z6lup+1x3t*>*qAy`FT|w(x{Y#yJ@!OfcGkkXQLea)sxqh#+^7xE8wlA+!56seZCw)V= zg?OI}IukG@nJX2RDEzcWYl|;}-VegtpqhlS^mK{k>6h9% z64~$3VDV6T26pDQG6f{F+>I)vfnQ5P8KB3+s{H_~;)_|sIl(Bo7W8#vA={py!pmSB zqVj@lfo>9bBekIQ7@mPsoR`%}dykt7%w_(b`{$~2W2X$GX~3G)$S*bcs3F1aH5Eub z>l4bCIvJ($=g)IbR>QRJO4(-ehWzU-w{$<5Vy&^vb6Gn7{H|R8L3g7<0$Gn<04&?C zpn6b+PjR%;?+gV~K-vJ9$xP-cdR)64XXC7o-XQ? z2i<~a8zEj|9oTm$`Vo^@v8&YVFfp-z9Q@qmh39mhH=q#+Ak{eI7he$+WPU8kcpIzE zQIta~#A9F*6T)F43EFTt|8cvtP(`aFg2FM&39kLpKcCaxmlF1cyfiAt{A$5_dumM^lzTnswB z|1jTz^K3lS%F&~_#ZoRsaV$4aA;nr$K7|lMS}FwO)6cgmgvTK$(;q1q+RnLVIhB^* zncP#-M9G7kSk?~D;W^Q{$*0cR93#JENg;b*OfL{U)Lq`=hKJjT^f9hZ@nXLrf^U&r zy4igt&O@16G}C?xpsK~MYgcA?E^)gU-zcfQN%c4cA3mwR#tG02UrlpxuhI{!Zc2PN zY7xg6BYI{ex)siW_C$qwyU%C?#=nxR71(pn^mQkh!;a>otSOkL-Ie6fZp%VcDuxb zfkn@}ltfX%XyNK?j5M0}Z8ejAnZDEoXqiKj(`3WZAE?`nWUf*JeLLd9_Zc~{vOJzZyu zTixhHFWK{SWedlwAtA-F#p}z}5}82ekoJ_-z0$1O%XxU+PM|BaKPmwMnwrt-H!woS zUpP9RkdIuuKt^Hwg^0|C(NL!5in$YPe(4!v7q#3gCMUElDjoHv2fu+3~d;2T=47AyOFI7Zj7&|1>(J`G0Z3_~qMk}?zM z97wHiZPxTx!)|A6 z97UZ}**W`2x|yD|pO;S|8>k9N8RPcF7p@oVkdZpzhS4+$Ku7D`lsJiEH?Q3J^R(qO+!jpiY6N~_V(A#DTih3tvOg;_ZSV>W?Xkk#M4#AUhAC8i z{BZ>|(&{gR&=K9*G3V6k+&Iq#tMq_u3is=4YU7YE_dj9U(>tn4*;^6o#P`3RVC82_j_I{!eee6UfD^;iCKr5}+yS(~vD~ ziSPDHO(Oeawydp0-kDXLFFZy1iB;V4y)DRv18yN|HeZ^KZn<2X*fIkE+07lZzkfp1 zBQTS3k-?)IEZj+Je4_Sz06@nX{1^Ru5*ifhPt}ihR<5VN+-fSRwu4D&e5!uvD5<0o z+54@h8oWD`u>?ktOPWpv?YYVV9I10pOX0xC2;H@u^!(qSnC~nRpmYJKg*$L@lp}3R z*G_~~GBovPWBUl2C-(b>tb|5^cj70E6Occ)Kkb9g5)B+qRfPz9`XitRPsZj{tI=Pi z{j9om#z-Toe*fFGBXFs=#MLi$3cd(wF2Mha0*n0jm*t-&ndLUdPH|baDb;gJtte9!Ou6zZDZ>oi5(x zS1%(igyt*v$7}rX6FD_Zywe|-S@lcEr~hGDlWqo0)yG~bJo&s8gT1tkxSK#lWkPLU zCr~CZms)!orew4VubZud>UA19#(EvM+`*=!^9B=OsFAKk!}ldT)C2p#z)`xgsncdZ zs;dovkTfsP83eAqT)gpWYoO<*a_UJD05HJ6TlnG)0eb{^Du*L<6bNZ{u@FyRIIrm_ zz{&xnSBZ%i=o$inA5=>g&%-b@KgRTZs6bj z5DzRQsDH3nh_pQSi-O9APl6+Wh*0AIQX}XtSBoT(DKGmCcb;?|?1`qGnNUFuYI8_w z1cq0%yK2rGo2;3}-fOqKk7K+j5EYlNxc}uS9U?oe$WKb=NhFDsxy{_}SrXuKIk8H6 ze}Re)SJNiPe-Y&1*ptVVV2Wp@7U|lvez*=(1x+aeE}({wu>4I#p17hw80tk2d(hP| z_hXR!VzC$u-=k&8miL*Kfrb0pl;U{XO~mIP7HLv>9wJ@gIu;oJKZ@MPr#czlG&hO3pGMcJ4>yTG`&TYRy`XhH7*Iki+HCBR(E8L61(E9A%{!??j znV0{LfsH#!9sX6+o%c`0$Y5Je-??F_`HL_aYAVN^=RCG*^yVmq6>yDOtJZ%s^ZMTI zwWa+C|2u3z(O^AE95u1b+X&|!PVrTxXV6^~0Ol;gP^k74+g*&}T&lf6r?xRGdxd=qX?*W6nEV&4qJ=f%7~SRqTVd&I01B)^!A?Ts{*Ik`4a9#|Rh z@=K1S3?#IIuMtVvXm3F(Z!1M?5CT|YTvGa7f58)hP`p!hRh-Lw1NdDsuH$^KBKPow z$K0Bhrms$7O096(;!z#NE}(LG4`1rYPD_@Vn8QKGvr_dYe)Vz}%xoYOeT;H1GiWoV?>b z+CBLVi69HTYqn}kO?6R=#W!5#Qf&q@igh-ydLp@!7(q%1D?`fQKc}o zD7lqzK@?{B%p-mAORKe(DBTwOF(bTc=}J-lfDG-KOlL%-pfzR#`pCmLeQCYa(@X*Z zw2&}*Q6v1o6}wxG3e+a2Dpr*hkF$443-L3mE-W>m2U4gd+|IuHfOd z1sS1u&Jubp4ft+s=lXC?K~z4!y&xczVANZuacP7;qWcU!b2YK_Oa1F!?!4C+TAN7I zY9{~Nn+-v}LG9k%GI~NldDMWB$}*^si6ln9fXar9<(= z)$-`y?_x_uz^|?gJh&%t2EN*oM~QMx;-0em)Od;ZrAUYf$}QR;Y~+=duq^Sp1``Q= zKxWt)Bq09f0lUNm-&Xm6u!2t0Zgdzz(yo$)4c;9cVAox3YJ3ToS#r@NGMl6m2#3qNA{|he64-@UhxPbn7TsG+q@vD=st>(o zS%JyUb~ntPd?3uWH(yKgFhyCi)%&v3!3KhMw~SXjABTF!v*LHoYKNwK^=1ctYGws@IYTE}(| zR`XD&g61t?ETl-d^1I@`+A4$z5_fN!fzTaeJ+PJo$>)QPPO`S>MEv}PQ^fYX#B|}S zK&dOa$WsQQ({v~7zat3EK_s;-$ixkOc|v|=trp~>`3vN)*K#-h%tW8DOu>wAEJ6W1 zu24`ZPJ+`k2spCP5u)ZLM5#61lD}rup@s?i2e&1{1t4aTXqQjpt){YO}~EGSvqxcLp%kU z*sl9Q%RXW_9EI9m<^)%)@T4g;%b+vK-*4!|Lf;I{+?gKer3or?@I$03IGkHo=Nh=%i%o5ED#1^aRsyK0BN{dU=v0M|L^| zQe6_c+JDL_BIfGh#ye%}j%u$fUHe^O;N(pa6c%Vx6TsPr_cQ6*J;*3~c#oD}B>Fpx z0{oRYdK^MuVdE$V)6fgqZ0#kBiZshncXO5hkek(kO72>^w|hgeV|I_?nrn8A^z$v;&>q&sIjL@Hu}Vh*dd*YGX&{CDu8qFbNr74-~$JY(N7 zD(LE{z9oKh?ugH&S^+U2;M+#%hGDX=ak?dH+y5*Mk*)QurtK!&)hv2$PKg z*7~_RqKEw!ZMz98ERjIO#m>Q!Prq2V7n!cy`H|~rBf-Ux)?wO9i7%ki7ewBKG1to@ zYVaXweQv(b@lf9tt{($f8OfvBzH#oj;1+@(BgnRMZ7Jw%Jzj5(2&u?W4*&eHW;c*^{MJ2xG>i+2_1p8my}lU}Zt#Aw>r?ARzGm zc#iXe6-s7gu+_;=Tw^dZ1QYuvkGlU!0VJ_U3?0VfKlxY70u%}dg0_WN|(3vv2sUMfx4T=LcT(eJ2C5uMeP)Kmkd5uBIY|e#>IeS*UbtW@oncE%U^}}vk3PxB6W&i~JqHaDGsMC)& z)wTF^EIkkI^Uhp4vtwoyX>d-zq@YKp&kBS17?IByCB|_v?LqiH8A7l<(wKADT925a znmf_AiPnTg$?^H4fZHaLo+al49jddKs7C!>A?bVND;A7nOp zDTkM|5%|8;1tu|(_);>R-@xQu7$+eYLfWfgB#pqqOdyx$8g1=?riTUaxgSyDMN|K8 zM1pJ3D(ST5AVI>>QcFN-t5OgK>NV}Ywyx~n)GE30yWISdn0?+HM&BSUpvBmH5<|C6 zOk=)qf)icq`LM>Nk*^g=Z@|B7`3cknJh#U#oyXe1w>1+JOAHaEvF-;i3S;llJ!zd~ znK=&yXCrVW*^Y?+Ur#~f=LmzSs#Htg`23l6vliXu`G(J*iZy68d zESaCOY&D(LCO4S9btEXmUOph_OUi|9U~RpShf0f6Ct*y8(z_$Yfd8Z~eBWSb)uq-?muL%u8Rc>i1HvM^%mY{ z+!%Ykl=QIWr)9sQ|04vM>41CL5Q5>v``cdDU7Y&Exb^E@i97$KRc#jGGxyPVtWf`l zSas&14;L4j`;g%Vs66SI%RNIU6;S3eu)LQz_Yx9M=`QLRJT8YqHeS#WPiQiZGYQ(z zs@*28M=PsDL>PVJ@tM8x@EPqOhdy+BkaI=wmm(55JAXq8CxVZtJr0tu!4bY&PceN= z-qL?&3&;BKZDeaMYad>kS$S%0xWxoD-RRk=TX4W9P6piR)*Ib2_D=~i7x;P(b$-Trb)Gf(&}^f62p>`>(V|| z_)v^6Od5`;kI^7(>B5h~FdHvQ$eIz{U_f*KDsozzEtqKR8vIet=saA%CbG!BBEDmjThOv!^;dE$+CKehxZ1YegFv$UZn;1=R-` zbMa)#okKxuSX{XDQbK|5z4F9&=0sBpspvX~RDUEK0Fq0suTW2~f}bnG_^cD&3meZD zuiw-|Ve!!m2BOcg^~M2H{PrWXzX%uDNlrrPwG*)}o3@z}&@4W%?HiN9#pvQ`iL%8B zny=u?zL%%EZ_G4Dk-sHv1cco!ao}z1FyY?y$y@daZ8X#fJ3)Z*hZiFEmU9SX^Q=7r zf8_>>7~1{RM={x{6{ABcgdWO2HryC81O@YAB&@N;03R<_q8j=@J?It!MbK3;&1HX7 zfOflvn8$jQmgnkw>Twb0jvqDF zPpr&aOfEUnT=L%z!mx!%CUD(%?lD@fi$dYOET;#n+@#G zwjVjg*!~+Nup28zz?u5AZcOfFF2};^koFY;&+pT_=w4I({>hv05Ve`V;Y!I6X$TJE zwgd)tqm>1}4A>ImF!T5xPZGV(5xQFtgI|UJw?P$&U2n^jo0#6(g-88a(!6Zo@*W|5 zoz*zu=OA)j6OX2;0-vrFamo~*uN-#25&46hO>g?dx@T6Zi$4KDW7K~QVQ}fjN!U(f zkSK}gY;25(7kXZH|#&xffd?z+Zp=^Kj!dQXn2&Ym9>1_IOJt%o#_7&<7}jW=dhB}L_`Cs9l8;iZV==!Sh&AinF}G31SarL)Z4Sz*s)ih zpWx*6o(nb%F-fMbloTGd8gW01TGA}wR`C)9F@EB{3bqmW4m+)d()1CbnZ$(DiCM`Q z(TY0?kYb&M=HF42O8)F8<)^Ed#+!~wCiL8 ztQjzx0WEE~S_Y&_dJ>pm=oCu|9`uvfuNbOox(6h@tI3itRaWTcQIcX1xeauYjSAw`B zc+yd(Brsyy`^t=BS5Ncv0nU8C0U2`9Xp?f}&w1(9bl^bDJ>*<3^D^j#fg8U>N{k+T zhwLsi$&J4KXXq9&8Ac9Au4Ajcy5cJp^XMbNnPxm{I?LmSjD)VtbKM<|9%M=gT5<~T zb@$=wiTX9jVx&NQjX{_J5teG&IxQjwxhivgW+=d=v^cL(7_5v$s!WfvUT-c-6;>`Iz5Wl_V4oxkn;IED$I(0f19&T%9yKto*Hq!tT6RYgO0*lvr~dLmq+ zl8~_W1vWr z^#iEOUq+GD2a>~x=F;)qO+&NTD^{oz~?c&v)`2!ge@G=|Eux znvXKVa7xz2SDP$rm~U=g)Ka*udS1pq$qFT`;GjNaIapjJrQeHv0-Mm^WAWovnmzWW zo8gbWSS9o~j`&+L@T}SLnZ%nzAXYo`UPJz&?M*;-CQM{}@{4B&bJua!(7lzsRb10| zNBXZO#?NH{Dt#YH%%W8{3IT8mG&Dh(1!Hz7p&r^jzJMMN!MSUA^T*Zkif5eOepKCP z{WHFr!y^s6sdRCh7qvrL5I;Z<2MrM2V+A+qEE;-#(1n4Ecy*xv9hD7CmqEu9#`%r!z)f9 zovs-r=0rajyr#5A%pRaM_cTvQ18I<7&tA`*t@QV`Tkp!ElA%&7|GJ&g-C`d6vZ}PX zxV%2V-~_l!FDmmscKU+!e?cxY7OL_%Ez2v8&VVc$gkrT3`(PV&oZ8gxe9@0^$Kf7h zbGXj4phK!Ncga9G%fnzqI4#~#HZFqR+w}`$-9pj~yfbUuZPRlG;cAlvOM2p}OE~=D z0(&OsK>4T;B_z3p&2}KW+ost#H=TZzBTSuozU2yf)O8MR~Vk86oD@{+m}Yy{z2F+j zU;*DkIxcDA`nI2)LP%)s#T1-N!hS*mlZe+@3nZr|z6csHPnV>*`rzO5B^>x6-;C*Ng4( z-k!&kseh5A(P3qdQG%l#>n5ZpJ!bUS&AoedxLELWz&%I{gZ<`*AF{96 zyDzGC9u5RoOMJg&Foxxw)xm(=V^{XAeL@%{w)_<>7|T7uBF*o2lS-bf0}fpL?bJ%- zQmA2|>ndrO6e(3Mg|%7Bi{))23lO>>S7>kdJkfOMUn9KIWjVeoJZD!}i#a)eQeM28 zROWn{&f?t_slH75Wb@SilAAM=*d)FlqwOY?A+9?MlQfyI_S-I8?p@|xX;Z;rX<;*+ z@9gDH27?dlr^JnSq2(BW6%@+AU9&<3!Q6^k6Mf&Xx6%zBpGNMvs=xd5qW472io0r_ zF96aPf&75HkW4c#s!o;n8C5Z%AMzlRV@V(Ba6BeQLPGaZ? zH%%C?e)4)+E(Z;E#IOfyV;;&PT(H-iA+h|$t`eDCxO!^=^>k6PITGCRfxQYpPKit= z7b+Ur$};6TFGA%2oy>1n00lX|ocuiT66WsAw?V2KbM)y$aApn7cMb>YjX!DxHPMSa=k#y8WZE za(zNFjCNiKdv-f>n`Rj))mCRA z0ceu{`jQQ8&jkKZrkM4Jk2}|%-+%EerDS(`9?FLk&kNffY9OFW{Ek#*F4D)WVqF9} zaWYj9Ep1~`9diJ!h_z>IPeHj*<*h?(g@5G){H8J0MB4p+qE(edfs65pR)Ni3u4d&5 ziTtkTb=(#>*(Ks$OHj+E&XJE?qI(i!^#Q14kf23M9TU9c^QYDm(h4+E>nwKkxsU-y zx|~moBpm?@bYt^E#-biBX{y?413{vO=xX642>oKg%llE7)x=B}qpH?*MeZ%#jV@Dc zZtGZF64&FCG=MK4_PyLd}; z6^md-Xfs%;8WVnpd3^NKFK8^1-F1auV+D6rPQeww3^WIpmExCWGR`@3<+ySirW8!A z1d}DIWBVN$u>)nMQ^t4b2`hQT<$x#T2K+~Dd31lemv@^>T&em&HJZH^jrSsqC&yN$ zUbV}~RPo8NplftV;BaHhp|LF@<8oC<+X>+n%#byRYi^cYC$7an+P=|Ce?Y^JuU6w0 zvZkz+CvF_jwgSn<0^;*1Ej?KY6yqWyn^!alA7CDXh#YV+Jsb$270173{0I+g1uBUf zwKLPOn3335Nc}WG6)|nyb!sjzw|N?`fF@$^&|G1F#U>&s&b)Hs-oO(pRk&OQxu4+Jw--> zS{=>749`9Bsr_1+1`TZ&!m-e(#WZejP7}P+B2)io)W0ctk)j#7f=4Kt^H0pS=M5l&7tq)>Xl!hC_4|S(O*8RGMYqo< z@GN$$iP>1QhNSvwo|W409fJGu1gY)-j5^sFl5NncX`O6#Yi~(#Lt7zFUq1$__9I9h zfAN|-V&u`o!gJHgayc|cFetiQ*sDmvk1rcCr4NRuY^c^2H3R~IWse3+?)+h5BM<0= zC#ec_z}X(G_SDK|MwD1wZeCV1lNwg{uH14Gj$x2alx6@nZV<2fTS*?(kE8Km3ru}{ zbvNFxvKsa9w5g;#3}iv4XqIX_3U3q;vRRBl$yDa%)daV}Y>3KV99Ofr5BpDzH1;kD z{-|tD)X$uGMyPh4jA#*?T}b{Y?i5k>nv>PLdmnwSm?kzg0}^lD42O>qN79bbXy^Aj z$7X{Uf9j<8Qg2-c3uq=hbxjS=A4*ZYDz1~h&I}NXU#K!W6(M+y_4{@g1PGCwSr%=E zk%?Ozq$q0@xb3xaKtib0!|t_op)@Pho-c|GjCFmQ>?; z7xg=KPNq|;6F(5DlE8YRJOvY>ByFWft(=qHT&30VlN`1Uid|~o3(C(Efcy1rIH>8M zB_3v5S^;+e+!sK8XOZojgn`kU#3N^~wBdu1gHp+>4SXpbZyTDeBXXoU#=k7Nti2@# zc46M5V{eF6x_8BKqCDxl<=%0q;luR7FvsS~aD689@$qZ*N7$SP-4HmRnMZ9^h{GVl z?-T;}42(?Hf6Ca^cyp)w=gq@wJ7mew83eN7ylF{_rVB8kyd>bNITM}*%Y%V@7wmQU z13K!B;Mp-#SQp|8BMyfo=5$WyHhno8(O$C3gP5c{mQLE8YEq{AJ%Y8oS+W;vgfXV6 z4ZpfyYnNv*&AjHoJ4c>)M@4POo3IwwLq2WG)@rGumdPk;wS>!wF*8BEtK0VX1y26H z&P_a+vo?Kj5ZMD>B1$-L^-M({xZRjN&N!yh_hJ`$+-Zxlo6r&l-``nx{y<4Yi2qei z8rSuSQX|az%BjZnL+{A>fmCzuXXr?g2IF7?f{8dIMsi<(hS z={@*DFF`tzW6Xj#QI!GyJ8)*S6A)lqysJ`+B!5%`QSF09^kn)k%>^*S(%rnpCPl6Q z*?2zI=pUj($)hTfll>v+LpP4D)rNa2v?(VUE+hWbR+udsRkNJl8Z4Y&A;Wmfi*kK6 zyGEPtyh#b)Ne%gsXW}6Pt!+6hm_j&b52FHRU1k_+0@2p6x{4!7slFj5fiF-dBmt<; zx(^g)u%Au(>w|pp+ou#%_pikQxwNBSUTlZh*93JV|S zd27>ky@lESx=Df-69(nIKDBxb)}Lt`tsVbCFq?9;=HaCj5h^6i;F7hIkrHfc03o+R z^5ZxdV~w&GLNE~UgOD@@S72&chN~o28p9>DK|Wx8AQzjQl)?m##{}AVgnBO2TbJ`h z8|mfQ79}^*3~u!C8v;|tB}Sag|K0Luj*8`6W=$$X6+#HRrt}#lGn)i8AX@}yv7mt2nRaOq8a8-Annnvg1LEpyLB&pXURxJ%`{go!MQ-o*ExxPf-VmZ&B&bB? z84IcuR&Jqb;&d%l+GisPGCIi& zn`lN<36^^B>w13w-*-LXfML3|Cr{D~VBnLj@$hC>q}!1hmZ8p?&DCil8*7?a2`J*B zu9W;>RW&?}Ueb9b#A&f9D{db+{)-pH_!s)Pn5$hr&S}oE1V{<_zX$T9Fi|(sAUE0S z;!6QYUIp;c%T^I`Fg8p(SRE+Dgvt5CA6BRQ#PZ6(@g{8$7%%-pqWw9}iQ6og$RQN@ zEkk3-TMnz+i{gM4)@CiQQ{fl2YMQAxP#D1zsVz-VNM*NVw;@tZ%v|EdqVX1xZ|!2` zZM}Y+EsK>uJ!h2nke^H=kRBXg8-3UXDm#u}ktd9)V;A8#OPDEM zZ_w_%Wif}Fu3?`I(G~{G0n%GVM6^`tGtV$YR(hi1@fglJdtP%n#u;CQeh;sh{?vl2 zey(=oWGHkPLLPQsdTCR_P=??M%p-6)5sCA2=Rzep!K5-mzswsC$*M9vD`3I*a5Z>K zXhTefpjZFps*c(5iu?e40Yr3X}Wi9Q0!HJ@6M$K;8qH zPFo3nqQtpdJ!%3SMt-tPKAg<0(g_NU9_4mxOXM9Yn{rrqNCb_oRb(Ap04%mW+fF;C zU@VpvafEf{i6C9jYFI`1Y%=<1x?pbZMK9cN0XP{t!uAB{rNTyB$OQxa(TXhE%|E5= z{m{Wju&bh7(bB_>rFFMSJxW;htWZ(%v&yQ1)e@ay3!1rxz2coSD29P!Y16zo(|C*c z17SA(5?lju_^+3uGL@@-t;(SYf3f6cF;>C#hkAyZCvgSWFIj|U(C%7~{XV6CmLeg} zGnI{=(}J@}f!`N5wCg_d7(=@)RAh2fW525Pkc}0u{1gywQ>iCx8ScVtry2~ogo+NJ zj}?+;uAKc6`Nhz?r2y4f=P7KCZ-iq~w?Kw}vPi1mL1aPlPYUXNOj5E*LpRp3as!S( zh{SQtw`%h7mi28c9()1!?m$64t18K^=O+26RT%Yc3rMLRYz z#Q}44x36sq^wx4A6kxWwea8)bc8CGc=fVZGQLnUX^i{X%d-eSyeV<=M6zu_xnL4p; zBKM9R1)U)XE9os2(lrsu%}d&rB74x`bnRVP32z!w1a04h&@RWbWWee0qW(7opP@n7ODzoT2G!~ z@aY~A5QucY3?VK65GphL!}reZym&JC;V1IaM*i^Q;mX;oc^SB9gHGs5sbML(rv}wx zEBQdN1s@oCf`Cpp4G;VIx#iS@KS@P#Tc5S;sJV?LoWvEV4GVRRzTzTVp3s!-E`-Cw zYmFxYY^qT>j9E)n8;clal%tOgqSNE+G9UhaikIeT&e`jrN7 z`wG>+FLpTfm#YBGbvG$@x}3W?fr=F22njt=@;pS)y&%5D$5=-pWpHEed zttUs7-9xx{8yq5v@luE~V7+$cGhQJpuMi^t6^uuEiR!4>bR*+Ul{P~acc;1TA5y;DEn3$2(5 z(>(bOd*;}%fCB{8kC6%kU^9vGOWvuPOAu){y3zNrrq!i zvfLI2-(ltZXjX!YTq+1q$$aFYCS{xoZ!#(@;( zI{8(m_Pp!tl%EGdwtf;xl`<1!ZV-_QJ;v>W41720Ns}j*b?HNmI(tz2Ti&U;x0Kd1 zFI}Am35ClD)9;HHeni{^%GwHngU2Vx#f}5;44^ z%B_h)*cn`e-c9WQGHJ7(V&E+{!03tG{f}-{eEvO?cv@i3QjcTD8AxD!Oo1jfK{>L3? zs_El9=u(4geN{tU7gi#%MWsm|!hS(9Vq3VY`8Nss0j0UQibvWF_h2}GHGR;hDd!Kn z*2w%p*B+3&C_iMCY3p1b6El@bZ^_;DHVQb}nteB2rVW(aQu!J zS)?Fh?ACX2aWjfm8bdi?=6zH;{6h?~>f|@YDnTrAy*60rR^n9#vdr*y?T%Y(1gy+;Fep*#Xjg zvy{i9wB&8M>7}aSwC!2!&hXd-elka)&<+p>r6GY!-9#_wulI~6I4D*32=+l;>h8`4 z1%!=7#Vl?2W({HoK8>$yuoj;m3GXVk^IK;AXTE}06RksymH3iK=yI zjRK9JfZmoW<}OHA)>|l;3qOM;k{;%0v8pR`#lMfP{9XQp5>agS4{!H159^dPp;LUY z00#)Mn*=66W${6SZ-}3bLSxK^JOZf61V*~(eQs>Z{{=*u>Hixb%FfR4A2IYFAj-f- z&-9<={{lpr=vW#4-+-vGQl{t2zqk9X?Eo}aSJ%HcaQ%PUP+Td8^V|M$qU1LkRbuw8 zt*JSWx#^6JIkmSF5;t0!wVt=%o8l`_B;^Sdfnk_qAb%knT=n(zjZQ$vD9ik=qOR4| zFopPAOaN3wOiWzdBqZp`^6Dc|$8@&VK*yl>9O^;57@XZ*oq*~X7$5r-fr|WI_)1-i zG5dy)^8lRaRUVxH8UV_oe}N%LH~ld;czxyK3Gcb4f7PmDgG6bEyNC0Kj z+FCen>1kWr+nCf^+1eQVGH6k7Exz}PjZF?SzE|k3)W&*jguR0!sHgjn(t}<^ zE@UuQA%9oaI>v7HrUJus$FQw5Or zE_mSQUtZHIUkCAyjSUK{O~CTs&b(hsV=GhR%lBQEU&8{(FTv!G-+ilND)VDNCdCE^ z`sT0B3g1a%t*G5louQopw6~r3UZD%$nfU9^z8+fKN?uOrzP^Fsd)|&$b*AQea1Ksj zHum3t5RK&>uh%a0Zz#2&xVWf>fESPd4M5^}FCsJ}qu=;HK!F?l?%yYFn0Jqp zv(mTkRj%dN@7C)22UvZFX!94iM-=QExChzgjn&Av)tSymm$rq^G4)qW{YUoWweM#% z6}Ru`3I1(n;vN64o9>s%r`L1Ux6gIP=HFkkwtoYDw=Ii#C2wjOr@nGees^Dfp({Js z{H^>lR7`Gjy?*KB>0Im^9_EaFc>SnuA6`d$cg}xRfhK;hVtm~qBLcX(FxGZ8C;KL* zf%W$H4m?W7MvfnKdrEw14|?H#Ka+l-f7b&52=P^WXz$cpOeRODFRE5 z^to#K(3TRS12rTvF9`ZjXWym4P$(eG?qy3U0LCRBFFr{@*U-)7!3@`XYMMz^WOOpg zp=~igDc+C>B*UUiEa@u1ODL&6Qk~=HamGwe&CwfYi&}@95rLOP;fLKgI`9kB$#&-c zaf(k98!C?Z+t8IK=%6VStW$-(w#*CNZL z9fYw&Wa<@MvhVwjI|tj${0Mv`H=4o5E1Q}FPAfuYVan>ILiv!DboKE?DcwzL`NtQd zuWbt$6^Ycgg=5N~v#6b^G?TxBxX9wKuwtd%up%S)Os$CGfXHv;S*pf*>(^G|jy~-t zVzp?|1Z8JJhW3FP1O9vM?|j$NwrDne$OCs@$p-;Qj=0BEPZ)C9e8=8+R#y|$F5Sxg zwAQBG=)jnnnBNj~HGlH0ssD*GpLDc|6-GK*$HFVIu3aSC)BKE9eSBP4LbCT>MEF;4 z$3tsX3%Q0_Y=0)QEs`9YGQF+WykkVHc>^BUQm#=Nt@rfv<>`w~<4&Viv)np^0a2%Yrrr_Ak=c3fr)ExVAKs>|h%hlKEf!C7 zbCZf(lKjlray()RfT`(Ji64;94%-ZSBYXnKOP$~KL$amZ0f)U``!5-q$PVIm7rGua z;1(yXUl`skp_b&FT?pPOOfYU?hC#yJOSV1U1#+ezZau1+6$~Ilj@2>b`tpm=xGT93 zh}2&KnS^ox$tkva3Xm5w@AH&-2dJbai)vPoxnmXaWP3p|5n4jK$DV^z$+vLveLKDQHt>j1-H!mO1oKN&>4@@r} zmNmP*&f|+to^qU`HDXYZOeM(2lwKSb@QaerVlQR_{xMAGxl}pr$_|t)QL`42(;%IA z`e=3%BLAx;a_$pLw`~lDNbX<#9UgC5K55!+jYTB|uFVbWL}Tk=)X@#6l=ufZ zB%n|ase!FQRP0`gdF@vJa#sDPFttT885vI?AVqzXJy%aTD#FqD^Myu{r$j9!UY)wl z+p!=6@}R=$;0^^?IS8u}r^M{?m_-wYn(0tuLr9>PuU^)l1+p8M8Xa5QNLDy_teBR* zqxbFWC(X~?6_?G_x-mN}r~15PV*Hi!;D+HYaaD5FR>D$JWM45unPX;*o;(R3^-LK4 zL=EwhKTF91UBpM{u=W@rhy4cygwhK*-yaI4gXHq#hwP5pA&h+V3boh?Q?{-G!kz`b zd?)t8eP!fLW;tCbaHKRt9OlKF(CNDJC@)IB(w}rFqC8>XCI5&ki}_Y5ZEdj~m$n;c zfq~N6YTv`MkSG4{_{r1xh2IbcstpZ*SzkLW4Q&@G{FZ|_jPt^GvQDzk);cpcNg~KS zrPfQyC9rp*(ZiR_025pv$M+IM!6+@mT zZjOB=HYyrv`3Q80tq`Kzy2m2Wa>JNr4+mZAJXK1y7btkCxIzQ!``qV5X^SirZG8`W z>`|YK7>?%3-1WgHoYUa5fGgG7`&cv^x;6 z2^3FeP@*QyK+9h8U$w!aG(=$qaM#x_rQVh0WD+24md|sb+AKmds?ctw(=M4AeDLO<%?18)23Ii+ zKB|nrwuW5uKl;7T5i7_yud{^65?{+vJ;JRsWFc4R-HZ?-=4w%viS8*fxL>+o=Jj?d zU^)-Q#0NAC%%GM@wn>Wd1nL(n9gmPna=}vS=5fkr^Lc8`9uMGV4o&&IXZHyu#fUVi(3_6;`vXW3<)8X|7!JYP{JrZm;qe!@wmhq z>E&N>@Qbg2nN{`}P2gs2n>zhf*>Aj(qlal{I{^7{(eDhE(4Z(eOK@ zwPObdVm^@Yw?T$KbxKDm-mwHxd|eM(`W*hk)MrjqH_Gh0<;sN_l6Q;#WRb_=vIHPY z_L4Q4;sHb7n<>Dr%P`jscfwdTWJLk}XYs*iY}{~Ft#pS{JX8FrnS7fGHzyABartiu z#^??+-!Ay)c83b&etJ_=HJYhtRn(UeIovN%wIa}|2I?>pmDQ3hEq>-skDY9Iq5XM`oYcIF1Ucv5Oy;qP zv7BnPii~-S+eTp>GS%kec(0@U3GTSfYx!*RlX~wb+Hf3qK{%1y zGk)VN^qrK|16_#s;11#`wIME;Y3^2M;*SQ~HFjxF61n=!ri+euJn`!OTJc*0QJB6P zP*@W*$#_d0I2_{A5A`W*n1%*?eCIcplA^z2B{Vl`!}Ma%=-oQ*&)|t!#k!ljNLW<- ztbIj=QO-PVE~WxMONWewO%Q!eCyuwt#GYYLa3zA-gucI-SwU=dCB3ZIaEUwx;=A$u z-NNAxZ-QR%@i_O}A4pI5M~M&yIe8J00>{RwzhX`oB5a#%_h zJ!DJ9M!f&WEci8`xc9mNPvv5Q;(36TrC_ny#$e`!eF(KzK}CwK(!{hFp*)^<*(}l{ z%&XggF({uS7j0E?>Cxf`P6SF@GJGiZqko~{#EXW)8M(E~D7ouq<8@!dD6W269XW7B zzof9;hXV-34kL!i-0mv7s^dqFhFMWTYue^@m=t@{k&6Injzl@sQR(%#e-bnsXf^Gk zx1O}y)L*v5KR|AIMCRd|jhVA5IsqM8>CD1){HbIN^qp^!kkr0^Sn2$j^EHRc73FEt zstoG?TVM)yxgTJdMS%(h=bb+7ma{=inCKa_h5trQj7|jmJ`cDZq#-*T=yA$=gz9XZ zAOpO~O4~sE;$w2i14ma*)~C{z+mNL)F-cNf%ySc9Y7wyoXe(sFg0?D3|1m0+M3hB- zs$YgJA6Mw)DMhcv9P%d0WSR_88lhXX4=|ScV=Q?qTAy={pede^)L+3I1rI#JPW5yL zDOZut12QSb(d+%nUQ5L0od?rrppg^=(&Ywn9=DvpOT_Vk?Ya9 zgyD&r*LM~=WG$Q^nZ?u1ZL=(F=QllNG%kHVf{Q%##HPUlfI5Ek6uC5Vj-fdBW{yHl zg^>9kFo~&k*6)vhw@(Apr&Y`PbwRQsR(fI8p9WdrUo;Mt84Y32g;`-kbgb@>CO}UH zc9rs4(==H8O_}B(pid2#Qq|0?wAmUO{g_BoXRb^%yOBf3Z9$AX=Xu&E2l1n+lD?>- z0WQU%JM{Sx(gmOIj3laVId$xq@G{cL;jYWodzrI{X@pQOV`|-AawOiwLyUIR3G(#( zZsqu&5V8clZrjE84Q+WA6doO4hF^IJDG`8<)7AyQPI`Z8cK~7bgnXpdS4Kgkxi`pW za$Nw0e1)v<9)F{I^Ii~qz^VtUR3TPjVsHQB6?oF|@BS2K?k?TTy{1kv!s{aQx+RAx z;uPv1G28WI-wdPM;`8HYjUWjc4^B0tgT~59xFtcSOD;jW#)BwMSpp+PeeHJ_@xrX2 z+3hejfxRag!g_YKvo)gFcnhnL=El$DeQ*)HR+Vq<21OyW+i&_&hIX`IiEg?TAPW-W zW8?=~BeX{N6njAVdHj~dW19)q6m_{=wC;p#Zi08gCUeAfMTfWg`#8?Y%tO(*`#x+R zUnm9~SXgeOF3vMyP!3HmgT#Hxt!M;sxyL^UkK|JZOz>_cmWv)mDjZhhguG?-GEwnb zYfjg;9rQA|L=*4-lCZ*Lzt!o9?aKz(jDC*f*031~+{i5EVv(^$C4+8sv&8f;0^XfV zXY)uzXagP3VQQ7Ld?|R&+;L_dBeRLV()(~+7QVr6!>&slkCNoB_9A?S`a`L?C9_ic zEH~-ipWhXyHu`WmwNLnt_98V2Jk+P(CA{4g^pC|IKT>tvoB>tN-3KJ+uq0gXkZ1w& z(OOLE{0P=3j(IBgrAkiN%b*)L&XP_`Cr4h&`9d-qRf~S7w#kkO16TAOJNBRq3@cWt z%MJud@qa8nwwPKjBkP2uh3ID3qwMKn{xY!}TzX8D>d2B~>2*q9xDpPPI1NlU+Z&t| zaHCUdN+6|-?G!T(ZgB3Nu@fHYF2CIToQer2Aq+N@jq0aTx<@o7TwrWQSVl64apZV(aYaWFG4LGnnAdn0GynF3dBEbb?O$V(ix~dwtl!_e)vdRmh z^|TD$*OY~o1V@F|W3(hG1U@Gk!LxAwrM2a|=c#~CGTkS&wrc@gt?Q`XL)hvO!p}9P z_#240YeQhtq#rD=6jqMoOyQ;W6+{iCSR3kr-{+DNzhT9i5hohU$Qfu&IT;XJ<^aSp zSamArSG{j)*Y>r5C}o1AqJ8!a2(iA>s&L~%h2V@iu!K66HZ-0J!K#GQx{O^q(R3WQ z@_flW3x^rkJNf4-4=t0WH;$l1li{rs0>w1l=VkN8rPY!K-Ky z(mQ^Sp5gRK96gjLb3}CE)$$~Xs z&ytntYY&m7On5S;Jtg?)O(YN!Xji8C}tmG zd|7dX1~U8>3nSx5D*Km*2ODNX0_WHr$VplDrlVNsXLO&JZQlXWNdm_8~TaS;hs< z9XO|gGcddbR((3X34`HMAD3s9-^GWh2hp-Zln!yY&u2cO4x=IH*uPbCWop36+$N`< zgfoA`aXd#r3amLe;9;K3-QU!XHE5^Es6(Dn0|DU8t+=Vo(S@wrU8riA=Gkh6#64*a zfN9j|!y`Zxu}6z_sX4p;?$Z4ooSuCgJNaH+E#?xFJY=gAMJ&6O-#|5|)L_?Hr?$Ty zHT2cRs97T0N8FUS7&9~q04MU_MWVAr?`lR}%R&J#SRgn&pbRGkn&kCEP&)YpHpPfM}70%YV5uqNBW-fZkB=AQL21s6N0ii50AxBkioNN%r~qCIIDe zfL*7_iC!f^B5}yv35=W`DDW#NUj#n8Mao-8 z3RtE_T=ZxsF&ee%wZ4PP!t=xO53+BFiZFa4e7!?lBHne_mP0yLl|l|{h;WVxDBI8w zlHeR(j(Q7sk-KyXcgs|)J~^WYj)Q?UVZ>$T12N=)F24Niyqe5kRtfA`iCvgrxpj%v z0P++bysC5ChR870+pUxH?%Sd)8ylACQYdK~&`{i};Fv6K^sFFBG^+egRySJz zF%c!Y#a%8~%!=&1{CZP|ifJl0E_!J1QV@^tRiW4%mb*Y^)s719MT}nyC2Q#x_`v%i z7n3}Cdo)LZ#m=q6J9yu|uA+GggA38H`9fu)A4p0_#zU3&{2`{_n9cIK%%25u#&J$Q z{w~c+|GNWIi4ZPf%#&IWmo{0=8p$B8eX)~u* zJ1{wzd)(}Tg{B~W>Oj~V^1xB!V^7(xnYj^R3VL;y8D!4LFoBSE+>Vu2+D|VWE&CoF zA5gzs=jY*`Y*Q+){@$Yy(b;0`wIaZNM1LkwUoUov~9Ozilo?48H!WE zZurY;1$*S(L?Y6X1=Zx@WV$|?8RMCDwIbe5s_jQTG$cyr*FzhxrmFW##%F3fu(@X1 z4h8sPO(AW++$guCTx*{54mQzw%a8&K1>&%D!lL>n)^$2`Vd8;RcrBu_kNWVUH;y^- z+_!RPJA9UUT)b&1JStWUxU z!b!j`eU`ABRkBLyT}^Vhv2`3=IuwC32PO_6y>2I0<;5!$6EHz(ykS7crA8%@+8*J< z=t1f2E^X)2L5&^tD^Xo0B)kSev)D!|=Wv&R){d$~<6{&PJW`HAM_Nk$?#S+I7B_o% z5Oa$e@TL+--ef}?kIYbE)1e=0kI8zk1XI1dN+*n;eVM7=k8wgp(JOUub4Dg&;w=Rx zU}%6ig5!lP^onmD*Jc0;RUS!pM{ih)eYr|Yu76t;5a~8u) z$H`P-)iP2K-v>nCYy%iJ7~dCzCNo}RcUMr0)^N6_A)*%HVlVO7_m4E!rNh5mU=Wy*r$Dd~r}Im&8D;Z6lJTP-_02wITEpZG{y?ZNuE zA458g_bxZac^J-QuY#4_2WbIn!b`NB3fN|&%mis#YM~#Uja%6MC-R zBVvsAC4&XNwEj&6+MmIVDv(tW!3M3M&r!n!$oFts47fcfK5jdI|^;mb~pC9;!tvuu<1T{swi#8}ebSN`=(rxI*?>ngysnI~Y+579PxJnH+vhirWM9 z%=@_xng*V_;i3XtJiSXoJ$0he)5JER#6U5ugd>i-sU8>B7eq3(5S4~RE=74>x5xTf39saN?zL{%L*M{((zt3GNxBa2+P&z74^{10cN_G zY3Yz=UPjPGXjYrSI&Ql#2ld_GU^a)7zi(TnE@hU{WuBu?ZWCdGuKzjSFFHg7@~43!*J2ZSO|i6ru>6;W0#e+X^60 zH5J7~86{U&Jf8kG;NATcMg6_y(gHBZvU7B%-Rzd$#Qd;wZkBsJR7e1VVTfh`}TNi%p zp)aHC474Oi0uBv5pWG5;o_$ddqqh4@hv%B`E1O6irnXXEZs_oORmQ@q%alo zyigV>PD;jWQr%Gn4;tkFE}KPw3oV_FLP+S?a)x(vxh1L~f!eJCl2YX3@0Z~zr#Mb5 ztI@1wWO=sXgc)WM4OLgF<4 zwBW|eepzVprL7xf{%ZSkQkW{c-Yj&pa$KUFlr?-jSc;VjLyJ3JS`A~jj@7x zWNK1G_rv>fUjT!CNCelQzbfLC-O#Rj18uUPjYpcZFkCW8&Elbns0EgGqboNuCM#F| z1gWx^vLgJ)hx0E((3zwTz17DKH&&3T165R9!m}7$gmjRx^Y4!OF{eW*-dvmMY@QfX zX13$4y!~luiT!c{`l;92G@}x=XucPX1-!6}7#vR%9dRK_?)^T40SD3_&X>Q9S^E?@ zLh87K5}pSW+zI5<3Bk%Me)J-3Rw>qFg~pKW*l`%A{f<`|(06}+qS*3l92jyjq+7V; zKQnYS4@nVysGyDdUL$p`_))AQFe(-Zx0qwit1*0u6Zewv`&karC@rdra8;ee^&(-&NUY)q?P{w1 zQzV>mV%7%vwRTH^=~JrRVt94Mm+Khp7&b;i(Z*;gV9Am!yBTNH|FaiHi2% zW=I1=8zoWmJ9cBEgQ#VSE&!q+Ql)(x1Xb&%mYN zJpx3fx2{JFt+|?IluX=jSc2Bn+ocwNRo+X175xCb@c(wAHFGSn=o8Wcvot z{!zlZ0j)0g(7|xXBspQMf6RNQi$%{yRor42=VAM;G(=groM|IJ^7H&DJ?W1!F>nVd z_6$?aF<3J?qedFZBdu?v-91s^8QyEFtw3*SQ|ae<3<$n);t0$6_=90JWLL`_X5@t= zad@M^{U65ODMpmG3%70CwryjzZQHhO z+qP}n-K%Zew(Y%gk}o+s`7ie6yscEFo|0Z3X5tER4-M=rCkh=v@|-sy6(BTI0c>l(`}%Ol+9dNHruQ~E zxoe+>gs07yyeho29bwmH&_os1J5FPplKSN*C!U+%CPC0^<-ZT?O^r^pXmQ=L#;nS{&K4BmJQ3xs6r_^U0`87 z{#Z?E!vuy9#<<9X;=MlJJ}=QQSJ}4xD8*`g+6%BH`OtXZNXjb|X#6v%_J_*fJiEMs z z=S?8As1Qwz6j7>`wUq-lvTNWSQ$Wazm*^Xfgxt6`o$!=S4*iYKl^>G%g)q8&&GH9^ z2?Az}0BoVMXs(7MQmWCVRd!jxx1BAy4e`hr7bUtATAiGI8pa3i;%@YE-d~RrGSp+3 zprg9imn`k!IDXIuh3WWau=x* zHvZvY%~D@Byr*~uodkg_3np*dI%eUJ;p>JSdYfv-Tm(|wICKc&a}+Gfv~* zGN~Hg)gtl;yq}<(CKJ?B%(|Aa^)UK6Fwfgq9Av&?&<1{AZ?b?|$tCNCm6jIcbQ3+o zlxjI1cWyjmSmZNI(!71@OrPnzhpu~VGgf}RAkg;Z1+%k{8Op0zvWBfC!o&ICqE+amVupr1*NqdoKHIA=dPFnbQ85eNGTHQnu zf20i7A}BOoGV_(QZr~voghJLXN~hBu%Xi`>g7aY*t!MB@+N*XL^5z=lyCbf2;ZG%k zT(6$K!wRf+2{Gz#E5!pPAI?EvTta=Pzk|&;;nHzi5vqgtR@Ld36w_^(Mj&e|#<79B z121_F_K@)D{FSA8pch@=PkFVToOC+{DVgV<=x<8qU4VB!V-$Tbz%X(xennZED5O^W(~NoQL&e!$3LtgUB^ z_)H+YM6rlPr(Rr;Pn^XfNYP=D7*kwAXxP-rwb6}%=_9Wb=XpSu`Y*QC13(>Fj@3J4 zD5Cw+wUm~JRdH|nOKpCdt3Dn?AMmgcj#{f>`blf!#Z-UQ!i>lhacJDf&DotycrqRi z_;CW+v|&pk-LjBsh*HF&f6%*SMPsiIj;41k*Y(|+Q1(BWsMKR@j-pS84T5P7B>?ew z595SJoN)KAT4@jYi2j4PTq0_PFv%?1#VAxB}my1yTD*K!w?Xa`*B6h#_ zelX%W*RBQd!8f1y|t)wg>Ugv?oWfhL-O5Sje6!wms{}wS6$*kv#_tMVoa_KI{ zb!)*$$F?g&!T?v{bxS$dk(3`5s=WK76BAx2yTa6%s{W+2KdMfPZJ-N8HG4cu`Y1bX zKi1*d^rCTl;$E!bsWH-D`ULMIuofN{^@)rWAu7v+RX|b#2(-}Qzl5>r8n0`=aIBh3O(k|L%rcUp_ zK)HX1f+CEjo%>^xEicuO#THR!x#%@M@bSk)kZSKM-wo5ET_Bl4u&(T+UNrWr*z%s+ zZ*h75P!A<69X{w|2Irdbn0A2%aEbUfG5)f0kK%RSECX(5i)MTKcm>!^>LAjx>E_`- zMNYQokv)Dx2UWm5Bdyw@CkM&^*--gO5gKH2ltJlg6ySxCo(l?zn2)V<=o2zWmFEIN zrj5xICDt%lY=YjMF3G$>Teb zZLYXni;UeztK&Qs63yJQHHe0SNGHGUBkM-lPyfL)@`+6Gcy`ewM4Fmu@Dv(G#zeOK zi~w|V0ZK6T>XN76;tkA6E%t}z67D(A2d%UR{0HKL_9@DbP`Vh52P1=uYwdv4S}j%L3fux zUq7J4K?nL!`c912xBp$Ij=R2wrC7p-+RDi;g1&b$@lswKY0)cgQN6s!MyT9? zw^L(P`=Mv+u_N8LJH{`a=1oyNaM6AWa$i!OX*wueNMvpsR+)E4URFnc)GcQ;l)s$lTwGhYBoLD--Md@>@0}7I=dEGvb@rywW0^;(9 zjRN#|@?dsF>T&Erru}04o$ZM$$&-0MTp-}ZSP}Ggmb{UzLvQI4e@<5(s8{E2CACy_ z?!wWQBIrVDa*eD;q*;oZ35DV-jZuQeQwRAbp+V*b8ezyM4kA$kX!%0=g21RBE%TK*bO z9z`~qX>8u++}l8?HWbwNOl;9rt7m>}z{5i?Bfo>9D$7@y#@LybDAcggHF}s_6QGpz z=AjON%0izmYE;q1?Xx0nq1=h+D%4uoY{wQ_Nk{pha)0SzSK}m`t*|rGv%J4NsV{;v z*1b!A#bZ}up$cp_aDuUC#)=nGvVs22)`|&6(5nqkNH?-ETj~B$K;GfnIW>1nQToHX=#pKn!PlU#K2P=ZxUVlMl$eqpv}UBaO4lgM zf3=Jw!;boLGZRd!lxm>;uwkwzI>0)Lw?OiIU>b2A$YwZM zvyE*@+ZL{9%I77n=6O-80H)D|)tZy{(cmRz{dq~0to{}meL`<&$(4$StoM7>Gl7as zP@>VglFbG((hnA^B4a>^O~ReUwmB%=DKDMTqUnsVw7N7 z-Q>hyX*_tlfKeJbS%nwlTc_6qNk}udh%A-F+sT^S@f{b6GfN2>mOzt_!zf?S3Zct5LDdMKAY1uv7HNYe6Gfuw)q46Wqc>W&Ph(>1w+USm~4Hg*wAM(_lO8)o8;Zdk~sLmvb)&7Gk;d?xXj2}`9$a#u>0beGi5&rh=Y^YQEZOs zz?f>cmP8P>gLHlgdN;RF1q)E0$-fYpZ}rs{3fP3jIwz@-xALXZJU3hZnn;RVU1W$7 z_OPTb-)7W0`SxVu4f~BuxrA^nz|w|Y3K8EUq?6T0;DlB@MSw4-!a?M{1p~Xsx@^gd z%?(XK>@;N?!XQx$!LWqCfNV6XfO=6%!?`P)<*k*I!V_hoq;36i)?`Q#Pmwy949r?p z8)#RI;9%A6*s&G##&h3C-kP|bH~vd8)h0|Gu2|t@h)9&zCBpv~6U%(@@ zCw0{<^^T{GoT+D%S*c!QJXk8{_v*=)EwDHagxj?qtgw;@TRuyY2tbh4e$M(48=vXC zkc}^YEI40~7EKHS3$lCs;iL0KbI=KbmS6<^sM>`eUCXH+|j``nXp~h5?yUYAbbeMjlS=rm0}A2CTD7s3wxhr*xUpe z*?She&ezthH2D4Cgi4&t&SHRo^7bMKrM7-&I(;CO1H9&XNbs)G$`5g zjZ;Lyg0(*yns!(5SZ4*|@dL+x40{KF&`vd*XsQN)9gq2IIDY6HPlyRMQag?za$Wfm z=0KxiUAQhe{|OaYS6Fh8V*{QBG#PPLfxE6)JSNQkOrV?(#!RnTb~E@1lg92Nd3vuI zJ^+af@I0nEU~FZX3hNal>erFQ=fDfy1Gp9{H z?I1KHOCiC9?4@8by7g{8@K4hf9^!DmyTxjfsiLs6c1;3U40k9_)e}EsCTY04{%9mI znNy(T$7u{s8&U>*QjX=6#i^jA-odqsl-JsrSdO4Ft}c2bKcL1*9=*Gpu8UC~9BpBf z8*AiZyG%PtZeA}gCURl*v_WVh7j7atf~~z+EUB3s#^8zgsWR}@*s-moPcciWA!r=&Su-wweKXlbGh7;F?~5!W|rN|!!mcf z2Sq2OO8}!=+v#2AaBHZ(9{IVw?ku9uO92?^9>s)EF*uP;#$;wJF>c=+1w+%=L4ql3 zZ9!-|?J$&?G7B&s>cq=(cDR>5f)iJ3-*b_bnL^2OzEuPdU5g~+>i(6z6)a6ppHt|J zoY9Dk1Z37D)j=2fLxE*o?nF*|(O>{PGv!OwZ=9bsY6w+*Xtjai>fTg^(eT4rR-7-A zkzRFMLum++hBTcB+^{-5XKF#L0{)>hFSX+7pR4G?5JM`zq!T#dV+asqlNHRZz^-I* z_X0iIek`*k;hXu_w#P=`J7tC z2%INgC9S}Vo#8}`*=Mb&qLnmlIpV+!%+ z8>0L4hrt%8XNQ7nY3y2*w9AaY4l|de76%G8pO8$2n;9#M)_o4LvmRI1{?>nnw;9xE zYYoJZyip7Xx05uFh?heZKQ(4VhiGoqpp>b`cLM(iNsJh|)voaWeG3X4bPz=?b zsNBY~bTe;ECFz}a$`Z2ehml;*`kjmO-q{aoTUrw~QNU#Zdb~W<{T`TD+0M=&ySbu~ zD~25)4LIInk}$c;KPaM&5Apt1=UderxjzQ?L2W29wMJsmS)7@roqbu?u6`wGzQk*H z2-y;X0BOtEdE+Tp1}T%A9<5I&1x5%~3Xu#U8O~R?vJP(|lE(Y_eENt?Cyrb6cr1di z)Rxdc)M(dL4K5Rf!LB=&7zUOb#gnlo4)JTZ_@|>to?qYv7x5i~NUkzc$*`qn2)#{&KiEZF|Dw~X6U zkfBf0`=+&GM&!dzmH`82h_m%MlAA#trS$dZqh}zA^SZx-hqdxsMR&uKu?hz=!IFo# z{j*<(cL?^j8@XzHi#oe;y<|l-E|&RP<`wmqd`N0 z^b-h9hL)y2-9X%e75_<}KC?_2m{dDLAwc>{h1`+$?Ajytr4tV`$?_&-$)M~qCL5~V z-Ox2~BUKJtHQZK;U>RoqC&NJi{)hQ>h9R4^PM)nHmJ&1!DHlDHnWKe`(;ECQiuBE6 z)v3-<;Zz5=bjR#w=)pmg_BEy_gxwH2=1qimc=n1AhVXuWBbo0y_NdU-*22g}t-I2A z5v#($da2jv;T$dGpKhZGO11EO`C_64Fq?BVx&^(+go#}X)BQO~qxL?1K%Y!s0fGxf zbWa~ProT1SGK*FtHXjk%0H?j7@%e~!jsN~BQT6G)3q90_AMV%-u(~F?IHceM3&3muqGl-L;Y}Ho?)3JQh?FyB56K9( zfES^hF~2kA{x!uGbcA)ux$zV^9AG86u|Gnf+{%;J(z+K8U9d0}8yXGU)5 zF>W!lJ|P|Z89}Li3Av4~%)1wyX%@hFJOxDHSuUwvSc7%hU?n))p=$tMbJlKI1+%HwMQ}dv`pod+T8EW zmJ7Hm&SSDy<-JjKex2_(;;aIz-n<%tjN@-Yl%VX-j2~Gd^mO%`nU+(XYfstpuuv?G zsmhmR*%CN^CU@x6I;a^WVAunW62c&A?4BUBNKw}`^yWIe?$5!KM3?}7 zvSk|ZQi~_DHF_Fy3CjkZJ-6O2O!ks?R35Y@|MYtNSk$!eA`_kI4s)uF|8SoA+?uS4 z2%Q<#y%C}?I3Smn$K4HzZcX#Mc0q8#A>%xcpXkII>*s$%+3_4cbD`_>)gX9q2{@_n zYrH=%{fEwGcxx*t#&k zlXy|Ch(TuWG{!JgbdUx&rGI1ndk_7q-~RSku&?RM-~1QbC?c!L_=fPYBhtZt7S3Ut@7hW}Yui(1UJvf~ zUy7eyJR13mmF~%kYK*8enUt0->gIHRb23o-#&9u?2eCkW65g2ETtI}-Sb&)eS`7~8 z5SuTBhR;uV?GjS87PA~83zR@4G`gHuBmvP?rUhn+*JclkfiKSlIjo?UuPH zCvN6WySM)}v#e zZ&sXfSIuZEOwh7tv&^>smF+K{ZImui%2 zb@Ezd@43~E<&Hzi`0HDkK7D1^h)vC?<4!0G;SseXU3mCNC5m}%(}xB5o9S~pL4ZGF zblr=L$tZC4u}vnD+@{yRALtcwzlZDZ-$OJn*2~rB1cOIK_wknUHr{8hF|B(@uk(ORV1du%Tb9q@Dg_( z_R3-Paan3C>DiYK>u6f4Fg#+^b6v&1RVu{^@clAWaZi}Fu5t5~ ziIwT);3m>4dT_Z*Uu1$>_=f+3TZRk@;?zn>?Vc~`kDAyI#iuuY)L%E6`|x({TY>%T ziJE~&>Nf;2bElWuF#-%5VCYp4XcA8mloru`8PJsHLuQm%-ww zmLfD;<3Is@__&+A{@If8SK`Td4oJ%^!eL`i7%gJ%zLj5Vk#=S9($kIaO%D@szyya@ zzmov4a4xanV<9mUTi%(m_0n3bY8;+!Twm$Lm{&v-Wz0$YvQ%2=+An~Dtw4mWInlgl z4E-#(t+K3$z+5j5B^Ub)1Cb72cM(dO)cwv zeJK~yZ6@42w(k4>B@ELtOQGuH3h*pP7ljW3it6ilgKZS{)&MWHrQ0v2wwFE}S;ZEO zUzIx2?xDz88g?HOLEUENV53xZz9LvdnNbdfO7`Ez988Q)QOU9AfbzbZ+)Y75z`k{J zEHRA4zqN68^&i5T2yriDt3aY%{zb@g*Fi~?cV~+fR{-~i@s}x`*WLF}M0l+XgoLjt z&=3ctwo!6Wpb2~&!4`wy{XSS`;YwOtz2a*F@KM~p%3%lgaRf=oWp9zYLIiMC>^Zp~ z{!(kFPffM#UKJ4Fm#4 z+#lcLJ_C9&Br0xKSi~XsDXfu{=`8tNGeC-xE~B`$CaF@^ZUJqytsEiymSCwpq%_@N zyOp(`0;RJi)v-WUex*jG```g@I<7QHFUhR!22TFZsk}B{t!1?~4%5W^$JB6&p1xdi zr(H9~%8Rrb>0;$+73ppy`+4G;I{dS*?%blGv!Rth=*0^k$h&}!AI@yRGBTniU9N?= zPZ&?q{6EM*k$PEyp;@kC2oxn1NP8PMt(~rj+J*LZKS-`H z2dnf*Yhr|j!$SzN1~mo7isaDD6Cm4;@ccHU>Hr%}nVB6Nu=m?+V1@R#I4Cdx{8>xb zeK%wy5U_-}O}NSY(Sq<&pBm41k3qiwbO*Op#W4t44A1<6{j!M7GJ#M{f5iCxRO*Sg zzyj7F}T3Z%t%i1rQh{*_}IWa7a?Fpyd<@BWTeV%!s2oRp>_t}D{rw$ z-g!-HBhx@fn@I?a>EdI`l~JGzy~1jC49OXVR)mHSmWJQ3yD@#S#bIXT)S;dTvA{LV ze1(oll=a*!?bY)#s4&r)c)Nc`G6B`Hm?$E_4_r=*O}L9MY4zRAev~Dn8tUuMjR={z zylvQY$eFbAk+*PU{msHgL6{+~*jVsqKhk3*hBLsB-_B@KF7FsD&> zt&n@%R`)9r%&<{Z0>iZaG-Tr`tsnqw@CZG4cZLOIR`X?90Jpn)_B@DA&aQFJU_G-8 zH~#@;h0BM;o{MNuj0%}=lS?r*st+|A_nR%LDD;_;_T781)&QTt76fTl5X6bti-Uoy zl+sPB?N25WGph!Rl~_bo-^DFa31$&L&X<_oyuDK&KbGh zK4q0t*b!83klEJCY#mTqC+7Mx4k@}<-s#Bf;v3s6>4ZppW=Y1hDLH1y0RFpB^&R4ub|_-(ij+)|IRPm(ppJi3INQ!IZ&kXBPpJtucEAO^o( ziwrit6Tb2X1<&>Bl_oV$opg4CJ-m~j2v6h?@mcJAn3DEFi^n_3#3?7+*@xxIrA_WF zI`_+eX_i1?5Us)uZa15NuUKRVote%@ZLKsQM2tfiS5j|8C*GrK*?Swr>8fZ;cWa-S zl$0~ImT~i_2sE z2V|p*oTt zfLiKVUSYv?DPTY1A#`@sq2u{ToXtqHYVHjB^z4s1VOAH2{Ir!Mw8dKMaEo`j4+AYj z#mi)Z=INR>bxX8V@D_P63qC76e!Z%|8mb7ZK@m6_iU{O@1$|)f=8WE1$N8=RG0I#s z65jO=Rg0)w9@+b~Ut|J)*ag;E6a!eiV`el30&J&u)3#`0X0@ZHrhqTtsk*aadsTN( zl*9WOtZ#fAD2f?(fKPY9A(m`+eLhO}BbX-_E!D%9ZbWuE@h*CalfXA^+*XieT-v46L8|pV&D`$ztW1_= zn}<_Hs@^u40cz)4@bSY-YAYz|%6jeIXjt!wAdf(*-r(r)N38^-n9v(q9}0r^pJ?x_ zqq%?}FC>5mU^ODxcQ8e*fhHp9J^gV!Kc>~+`KE)m9&gouBy9+2CQz8s6XWriKiFlc zPNPDjFdc=Ju6rF!h)2BUp-yDFCzP>APjZ%rd_<4pQ6ekHAO99w1AH4XS|M}XAzjXt z0xYt*3f|Nzvy-ad!Fx#XjFZqN`O$7k8`qqaC%5k$$_-75xzJ$P<+ z`WJxL(5md+5Z4MMzZ0ZeTR&DLfqO%f0v=w#4+ysn?`^HDEDRmannav0o-p9YWT=+Y z@lh(}wY}||r2a0UVl&e?M4>Y$V9@A`B#|FQ->t~rmD($xW^baC9j*F6hLD4|;1$zA zPd@P=4M2YQsZcWT;%)T`6f6z58LR)vz@z)%pnVfRTx9=K{|)-#`9S*;LWwSIHg;X& zz{XEYiCAsdkMS5{=GVBdhigso^MHZlJ#$T5%pCCqKGQHFeec<9SUM5!x2<>k>n`K?RI% zok9J4U;qONG98bJ>AP0_VaFrEGou%XLs;OT(d9goS#}_*^VWrl7&b5Iji}WSfuqF= z=Gr(E0r%9@n55i)L17_@XX>zVY*=emOwCbJ~#~ zdGL%wn?0R>dIj zpfnMflWP^E@S=o01aLR!jaI5j1l@9E3y>0_Xu}PR5rX9I#ij3PE|grYi|gcP<|{i8 z^^8la9B$LOmMQn!x< z=YsA75M9A0(hhp>ysm+N^S1%;w1Y9Xg5%4zcPcZ7y|ziFm%(*W0?2ki^>$DZ5vIs_3?oy*1Uq z_5(lJH7;0CMhu@1Wh$MLwgAFwF7Q~$&I@ZTIQI4vmP*P_$0BIW;+w=$xmhPkebBK? zVxXHRfL-bt=A2gABbajv4mlVd6PWVKTz(yTeVE3l2r^T`aEHhwQax#!0pHQ3K(?K&_DQgv8|rGu*nAg&p*F5(UYm}4)dg;3jWF}F`NGO31EhRpYlHb)a^Fp9*{sbm-so9NlMe>Srs$1g?>D;HS{E_%=j%P1Ov*z z@sdkqXTjOr$Y4n;-{_Pt)uD_clN_#voafYb-n;>z2>v>l{7_DY$nOa@fRd^(n?lHj zK}?#YTLu=5V_32OEF7#MmXSV~2~pe2#MUSd+Jjxk22gcK`K-XramEUL6q15RIoG4r z9eZlBxJ7Q!S~X5yRMefCp4FVLcYx?hMuOVXRr|<|YDkfxe%g5#qJ1$2F4C1o#~Dyv zrYWrXnOJ3z`W^Z=bfKI??$S8?lQyFG`%~S#D6vy-f4#z!K=6YfMmB_GOA#-pHchi~ zB^=OsBZHVVo(>hRP(L%{?MoW-tSpk@1@!Wzz#%cqSf0q1 z#HQbFw+6;46ItK~nVPW#@n6+iCrnNB7Xha@zY(}XHKtx5Az%QbotqB6*%ebJm&?fH z<;}pUtN5GmmU<4tL(iui)PhI*{GeVoNth@N5cGi5X9$Ad(pS|G5*nfiX~moQW~e2? z6K5<08m#I8X%!S@fhZ&-k5f_>46}v>Rt;=ze$L}ysIaeA9_VVN9n?5HoN)?aF_L5O z{_1M;3NMk{0MrrdsL6zd604i*&u(EQk9WNq0R zRn-@Zg8W_-xZ%oNwH)qc1_oy3Qa)`mU&;BnLhBH-uvyWhZz7t@#2kz=`dbig?PGpl*IR*wXJyOr zM_k8Y5V_~}%k8fHXn^<}swI@C2C9!jZH|kx2R-Okoj6yY%X+3?kzl&;42G_Y%INr- zb??{Dsr0_~<`C0q;s9jO)j3VXB}%tuq=4&Fcdo1JMd0b99qbPp@kb-RoCix~L(q#9`U-8ceo}5r)fR?id3mZYCei3TsJhRQA{lS3N6l?etV< z^$mGt($dJ%=D}VX+=DO=*p5ajb~n4&qStvSYR!Nn?>=pQgc`?(x@jen7P0A*!>;L% zdaNmHn9;d}JcCBMJP-fpoAkZJ}oy*|WMn3kKOKr96gLzHT|bVCqDDDMx~Lq-v|Xye%SB5FuC8_WPu z2tCO72|p0Uc0J?xV5uK5sL0Fq1YRHR0)BUJsnO=q;g6#?VfdYpqLM59ZEklLrt4fK zZpWE=bg~`fMz=X9p#@|Aqdy@{ZG%MYecc`9=rJ0{*G)ZXt@P^#PT;A-mFzU~PC&t+ zi%*|cE5x#&qS?T>o2*9Mxz9_R!*iOTv%^BJz`5CW@r6=p)Wm4E@bCuKd2mP9_Y6&$LzFa`1Ip+Syr-b>r%=N&1qjH?YEqIzc7FcuZ9CR zWF=r)TYv;fjq?s+>}>cz+CTn${c9yy!KB}|6l*i_9=~^FeWbIXL$b!3xz8*?kIOon z4DPmD_5c=EFn;ahm4d9IwO=_*!I5r4E?;HfJGhmUZ`EInpaHYf`8a|MWM+LefT2zQ z&xw|tt6f}3CdB+gZzX5^LB#`mmlZPlfnqtCz>L-jx}e;0WZa2Ad7SS))_4(FD;u4p*+@=L)gV8 zl&cI|;oB=_(a+#{sJoDFyB^9v*a|ZI`RSLkAEB`}1cR8qu`?vW&xTI! zp5u*;UxyEM8BwWq+E1$>dM|TF%7lB1{3)?HwmPxt9J;G=q0$5IWzTHg%+1>FHBbYb zh4));kMrxZyXxyBf`E5?CGrUms2Hb#Y>OiTss#Dq6Y3=WZ?Sw5z5-z_3XeDVf6`f*UPb3Ephj2)ma zJZ|KS6>v$u3!NvC%-Gdwk(@HkK2`>tgMNFe>W>T+XorAYGoOv(p47-Cyq&fFAN=`$ zKzRZ?LrW-b?*9<;j0B7vEDZlmOazQf;OWeMCt|*5I_c#0--So@}~-u z2=EJICXNG*OQ%bdAPUq#i=f>T>Q~W5J}mjW2o1xESV!@LYV-38G;pJ%Xvqiv2=7SS z2fcd#_UQR0jq~hsp8CFWoo>mW20xh75MqIU7D31w&E;?lK!gGBBei0MA(o(sV8}Kz zs8=TnVCc`~IiOH6=J z`XdlR6gr*xN0A|lQr3$gB7jQ~WI*H-^@kA)aKzz`00SCG{T1?XbtYnzE0ND%)1vF; z_I39MzB6)ow+5hh0s!3S=6#oV!mXs`vQjyG#H8kuLEIk}e6Hg(497Y1TAJNCG zMivc$faG+5Hu&6bGUsA_f z+}s=@UPv*xoHZB%LJa4xiX=i+6CylKHkTj*ST7X}@#|i9Q2py>cTq0{scfrYYBmsQ zObteGd9oGng6UHOD8;;`q&8xHnB7f?WTTJt)ip;b(FTgpWc;wth`<{KLBhWR5+`B8PA1C^7;Iq{I(C91$fE zNEa0pSeiQhUcEV_`ew*QDg`eSnz#37jBA z8)|WW{Su`1*x-R+2BUQ3WdaZ2(fktY-Tpg|JX`V{K5WE%K}sU98Cz)p1B~JV4n&@V zs}rz9%pm{>gO=I|e_~t#2OLG{RaZheNLHvHcV{`eyFn!%Mx7BjW}CszX`%`X4sZhpN^6Xo&) zW2j}=1cl|dD@Wfz`s%RI6tpts`U9nJfl69%C5^AF=Fb&)Ph}+|I|%}t0xr`Ma*zta%itIk5UW>k_qx&D|e@me8`75%Ooq*Y@TJ14; zzBYBTH!oXIQ(fbNprQ)l+I4qbTtC+}2)bV)>PFwAf;47UL(85|v})&adz#evD&EKr zpJ1ffbbL0)t^(h$L!l4v_6IOGnF=PW(LS*oM6{xocd>`N`fe%vv zr+UeVkL6t#yJLw7mc<)SJZ`M}2KR$hY{-5dUmaTYnV}nfS@6H6O?b*E2#Z@*Q{GSe zk*g$H;Dsl-niWK#pM?Wc&A3!eHFLv1nOY6KH@7=M?Z`Nvv@lI=zqr&92s7HqO6*b` zzT#)y_-su>`#ieONya$SQsV#2t+-VWJSZDyZ$fU~KBG&s^yJMY{UPS{UwzUSN6Vfo z^s)J+F}(lYy3F_n=P{kqN1Za%Stl6lbZ^)m`Bsje&r)%*-R|=THwZ-ux+n z$V>;YB97y|6;rBX<50J6wSp~t5SW>iN#bzLX_$n=p33qmNz8mG+fm@IDs#dwnS6|R zot-&St{ah^^Cg9I{@y-ytj7*Ho)jV;I>wa+l9XTP6%Bo5jy0YjF_||(f zUz5oD-e@5!(C!=K>1`SIf8kEktBK86!J4?Q(gDc$8Dag`sn;esC|oMjnv{ug%TOpo zlOMKfaP}CR?wL>74r7ALV8g>RP2;YNwsJ6l;nGOolGwFi=oW3#rr)t>dlZ96*)+PSzQQYi$(=z4J+ScD2n-u6n-6K>! z@U{Ey$xnWm%UR+g7RX6Hu;tNn1<1>btKV zwXLRUjSo?^_35K)0ku{GTWY#-i`dsx9gn*Avq#6wmU_M_2I`I`?K_lP^Gi+d?ha~C zZ@XP)Gs;gQ^05m!ijtWYAx{%6Bi}0v8WvI4SMYvKwN1Y;+D&>$lSwz8tQ{&Pkx8c z=+q$X73FqH8!?vlHb+=mpTtT635OHw0kXIgi$q(u!74AyJ=gW4`qaFOfBYTIQH2xS z8$C|jiqD$+k`p=~Elcz?Z0}vJf}Wy=tG%jStu3;j67BXXujNh+TOM4`_>+R3`RdzX zOa&#+77?$+n{PlDk;q{GB(mwH@NSIW)`pad(pvzs1e!MHj$kB&Z#RC7oG@S zWes$Vyf$)8Y{w!lCZ|}1^I3Y8i>=9va~T=Ar{jzf+s8Wmv)IU4sxNjE++_a$5s+E` zS3qXtWd1J_{}VJZva$X*{r>|pGZPc*|8qcAHd9Al#{#3H0HX;9Ro)_24EaBdokNf= zO0aI*wr$(CwcEyS+tzN|wr$(CZQC~fdnPyH4esC#YgAD=$}cK&Eie&uMKU2OWKE)H zaYrc%GK%T?iD0CJLfAzuC9vQf@nXG(`g54Td?R5+VI$@5{Gs@!+;&_u;aOyU56a)gR+WTuCUkthc%`X?y*f>B3O4xNpiLit0TI0OHl4)JM9 zL?amF>)ZF z`1lwhk)U0_<8tcTWd)Fc!~&sCs|N!|4F#2)gDP=Tglg zhzuGrX*D+!jBE^HXl`f%vHVK8%7~}STbPi=Y750Lo=p#U4l4Gp9}|MjiYp?cd@20J zfHZ6@F6&2=$ap8sz6+`EddlN&kGM~x2O0IJ_V0sqfD5uEv87juU6xDDbd)(XDw?P2 z5A*=xiX94kz$8`&5+4FOf<0(o@8j*&MIK-EpD;9NKYth?9e1Q)Fel@JJ@h}gKrrRurk_s@;9lt_nqD`Q(Z~WJK}j|OO|0xpIj$bkB>+SeT1@DM`Em#-z|(X! zK*MLEMuF6|NUXB5NV20LbHTiQ&)sR-3_ex-iG-%k`tH5XWfCxZca6uxl)da$sWv*CZ{kx^mMTMv6@b@cjd^FOk0 zep7BPV#Y=hr)K^ZW)XK2%SQb5t!y!0BuUKPCF3ShtRJ5AIp#n^%uGS^-k7HA#nz%;jy4%SNc55oZS_r#C819Rz_uPL8?~$v;$EiZVOck+@1R}rkwiPi zCEXWeFCAm{y{4aBa3T-6544zy)N4_oQomhMeBLNkvzEBA^O1;<8rs`5R^yhM@ZWWD zJR5AefOOMU<|2;NGJNfo`+6~HRo^V#w%|D(yrm`!@ukV!Sqe{^)1yQ})`F`gqMGslqx;AzA!c2_d+@(=g0rs8cAuQSB_s!hoRw`xCTVUbBQcdj-zt$j8#eMgHV z3rb77KYuP=lp;bBNNkH;h7@-fc;5sZG}zse5KSd^TWhEP%Cz8Db59!W+H7j*3mwwK zao1uNont)?uBi{*x1sm!6+E*RzTVnJ;=_vEt z+XSsfRNy)PY+m^dhlW7zRL?O<=|i%0 z${uxhYNe_fbo3pnclb2ved+j4N8aw*nOcchG;Y~=)AS= zY4?SV@c^t!@Yyi-7j}ylFEEA&FY%oT?l(AtHl*z9e}jv6mD9XZ?vtiYn^1QoUUEE&c8+FXmqu0>+I7{y1Jji+MVt6Xe(RKxaJWPikD*x z^I)1c*&qLI;OdNnmS0Ct|Ft*L&jLM?~cy55@zPq6oPegQq^^v-m4&+`wqTK~A)yGwu!rQdr!}=G7 z3|YUT>6|i_TXli9K^mFeQfMqUfgfq_UzMtahvE3y$yAC^9eyL#_OJ_Lc{hFC?s&A@ z9w)NK{g$9q2G?ViE?tP5fVZc^4r@@#n-oOe+~b!KDYRpBwdfeA3H=GwWU8FKrZ4-C+p8e#;{M3q<5x=l6=A42)b2nIB_fwCs6KR#}9z4)lf)nwaQ zy{D26u*GR+dgPl5*jf238QR)>Nr|-t$!?|e`?xC^9!?zR;#T;=St;kvOC_^&(;UJn z#y4Chb$764sh59V)+KLlAyLB{s*G)!h^<#l*W7H~9?P>CbN1K_-bH7mLe)h5HILd`y_XNHa(RhMjQ2=c5Nno+Raubt~xeN$t`O}$zyV}jiNjmoYTlW zv(pRfT`@vAZ}4^MS2_ToT(*qai%Lv>YmL)-Xe-itGNd!n$K^B*dv~<=yDt@nmYe8K zX{Br5$LH!lr=Gs%XUkQ>Zs+RYd+^Ya+G25{)0)13)U=e8Gy*ddY*S3RLdC{A1AVQ6 zpsgH2uiKnJuQ$6UOj{(u4GquwNZiy561SPaQIMa z!s1`?^mV;2GK;&YGYff{!qQWUC0m-dm;Fxv-CZP_tu--pX{e)7A;7Nnx7{)JEwD4^ z9|YR;WiD?dqMW+^d?VVmu%^9?xPEY#K(4H4dpY}{sY_HFX`Z}?(ruD_L~Qn&RDLF| zE1KAGb&!z78Ye9hjsRM&c|L%6`!Rev))DD>a(j@(eE_ z!Zx9t*?lO;-(*^46HO3{7oOxxW~iTE+#vI^d^t!JP$*Ua?bcz-7h1XhFgzWqdb#A|<|7P%fw*xoVTzL3-h)*`OE#%7P-t0xc+Vqq?umn-u zC2=;$msRWj-6ff6e~4V#0003U8ioHKd5H7>$U`juC7u6GK>y_-4lZ_%|2_V{f#^Sx zEf?4SuduewR5M$rl|8bn3yf-ehrPWERTt(zZ!O|~-r7Lkfgn)_cgprI-NvuyjjpeM zes?N}YI20m)g7lg;_}tyB8(I zD?6H{QOW_DmH)^TQ_t!j)#&tl86*&EKl=H($wS$-pJCCv5X3v~ret|VQO=A$IFRb;?CdLFbhMqF z9h@11{4AVXtQp+vs^5VMdz%AD`v$i*uz&!5z-oVAxMKtRNB)0Rd9MTWlLsfVHiT<- z1^Ijz!C}Anh%lu5iK;-DF1N`QBf4Es;xB6V1L>`q7jc6*L8wrEVWf{%i z24d-hn!29!cl{orBPJh#+S9p!rnhZ?O5=#po7j;Xni~ESWP-hg2`EJ&=4RjE@nZq* z40JX&J2t$21mQ|CS}98X+BqE?%vGCO92|gUB7Wn(!eDOgbFk;J`@w*Cfc$SqPow={ ze%TrQmZ$xe3B}$$HnuiE<=|^_`~@&d`{NL~7%4?Hi264cz|W6f6o&j{9Hz5@P+^VF z;*fkdD&u`j|Ar=7j?!f#NHV$FH2GCEqDYA7&^mg7CWcEF$ z`z7{ud6@eoq~H9eXYpfucBlJ-Z2e2A;jR^YSChzY?5p@@wbSY6p<+lb-DbH~RHEa=3&22Gz$wWba)6BHu3r zO$iRiz3Kt}yKVoqZTu1W$DO$qQC}hds4wy742$+x>%{Mds`PGh7%m5&e!C?@00ZtR?Dy#94&VYP0{YnNdLUdF9CW+=`)pG!2jqou8+X@W;H>$CebVJcb~`0dVdWZTRsL>y;u> zsIuFdiFl#TH?h8(8sj_eEIzwj*Mx$PTMTTYOIJ9$xZ`ry0;Y43yY)o z{XrgS#hG*ltQUQ`VCbWD!`bW>tOEH>i3B3psBmJ20yHUx&qdc3Ex>(ka(@p^HeV+$ zpThtQuAD@Y%q=Y09#gIorLbMSwyPajNgGgML`mBdR-tafcfo;@JDE{nc9WO2^Kr1_ zkz_dx^pNo}w&<$hqe8$}3_cE|)AOllHb(0Df3qGC;E zhSrHUvU+ET^CpB4P9tmA((Vnr^F9JG?{MvjJ}qJRnMlcm8!@2lh)VivzEe#{nX zYr#vpP5xS#Ad0b+n3wL(w@VZltK#ZxacAQA9Yvv>%d-n*_^+fE_hqzgGos-j9pf^$ zlhn!NLt-Ollj@~pJS`(Q%e10xyE=``#s0MniSpom9hw_Smnb;`1pKnATk8)9b}Q(} zZRx6reTE{zZ{gIId!?eVbfD`CO4ykIIbU4Q(_A_T+GkWC3QH-y9I3v+h|6OYul2;P zR=^&psYdI5y|s}iS^4=Z^SYv(RP=J8vZ%W6kdT>aHlp%v` z1+ohGFI3&`#u1L-7>A_-2*NK8$ahOZKIzszxz0+`H_#1p+f zhW3pf62(~^T7o*w_}4HYJ$(72lFhj+SY&~BS!Fc1RmGB6JJzQ7!txug^H zyqzE+tBFfu(W#xwfU1-x1Q-38okk7vOx9qFqdF~sI;#`hZ^8rn56gE-Z3AnJcg&WV zf&~rGve~alP8bQ8y`4F#@9sQD9TaVDZrKCb${Dw){k6&1zG*3k0x<17LLSL6p93p# z%_|l!zFKNZV+lTfFjjJjoYJmB%`!|>Bid%fA`{M@ z`w??@Uo##eZ_JoO)E#l9#kD8nZj+==PSaJ2F=E zOGE>zrf1LT3Nk+mvqMHacdGwpsl8D@1XygTVNZar5HRs--?JxRF<9Q4Mbyskp(7L5 zjyxsEXkg6&r-~JCFxh7_rBM8W(TI`YHa`%Kto2IG1)Bkn;}X2L9COmtGa4b^RG~b@ zo3xlm;j=o>t8Doj0Sp0&R796AdPr^BULV1^sucj znP?=W*@1mBrQ+u_hlBBmN(f?+{#A%7qTYh%BZGMERzyro>$$*3b?p9|#ghxb+l-wW=dvM=-I>ZC^ zAO+&cPkx5{r$i)Cl9#f2HLNQ%j{ubVjU6=J5DVuuR3l%j%P3sqsYAVevmfO;W*6~2 zF@mGHLS$Ix5V)cJ-tX!wEqX!@O7jT=HHO~^jhtYOnWcvL z?xTaWk1jae%-xzY#^>4J8LfL}k4VElVzD_M6Yy_E(~Ol|)Fbgahe$A-3@$}ZW&0xo zk>c095N1Y=wxkH|N9)qo*7kX^tiO&fQt`?$lJarkD#c zAH2NOHvUNRFH#>lVJidQ^jOzw=b3o+LLtdM^hhjxSoKY)UgHRnjF`wDd+!@Md;;O`9+)MYD$q(I;br?I`$hJhjgAZmyR|fHR6Nwn9nN zPI;=IfQ7dNeqm#(I9@g4lg#>$NTPMvZuLF88kjdvy^cbx*kif~oWuNJ+Ku6mu{5lt zk-$ZP2V-Q|pLff5`nUDfRZKVn#H#bvW1N7Y zYau+_zn+|H9_ItG9pW(ygxJb~#J{j3dZNfj;*!N>y!^fGZ%*2&oHhv@FFNCAbv$yp zyM}aqQ{oDlf1EVQ`_)Q(=^X2ab2!{|{3@+1&F)5+RL`O5#Bq+FpKgfuvP;@(`z-i{ zOz;_M5kiJV$P`R`SI!>yQ;aING!xoho9tWdpwJ_Tp8}Q_pQPS=`D;yfTPqw?PwD!g zW!VCj|Bwvf-%nd|pHeP{l2svEkg&5gF!H3`Z+>RCaj6cSW!bFb-|UKrpO&KLVD`lk zrRO|8lFfQT6uRMI39Oz341y!Y`5d!&aE!&6WsTGs;o*4Hh-G=-3r>A(PAZ{S8Y zzScwfl~TIjCZ6Jf>h#0KAlB>$y)tw3$Vp{6vlje1BW^J(();h4ZSU@4adX^^d`}`V z_>CewmALXAcLj49c0ELGt&q7)Qfg^#P@-nN(Y-e4?`R zJHd+hRF&C|`Qh8PQF_3$7CqRAkz`N;zRv5 zjy=@bQsdvjRzlpI@XSd;T0S9rVHC`NL8FAkW!iFOH_P~Vu29}nTht>J@oOAjvmpIO z3j^O&o1GqRBza4bFp<}l1k@j1ozhacBRFztZK!5t|K2cp_!pG6JSaR5_J^>ZWkRqn z(?YxE|JwG!qC{Zr$9*^wo-$1T?7nTC2UF|$^Q!QKUe)7!qqI-(*!1x}P)mOQg{nF# zq*PZdeZaOmT1EG|l&hdiMp@!(d;Kb_h{16bHrbJctnc}bp|XUhSDt2-AA>1PFW>KUp{`Kq+D!08us zm1E@Pi(Va8mNkkw1Boq{U&=W?gD+^xRDRp9U7982n^fSXj9GA>gu=YO&q(HnRXE-% zkzzEFJ-EBf-DNgC9zT@A;8(eAQK+99$uDnlR<EO883cda~KZ7w0 zuw~-=WE!$kFrmoIR}Z3S6#ksAdZf&3>8#Qd7Gue&)E|tEjnvzeN{7CLs5`DU+hH`27&piN8GyGhsZ(r1tRme`<0PN65RXPfcfq9$29|_7gsd_B_MV;UU~gV% zN&N+Oxj(YXPx*FWU^?~FXqq1qDPy(aZSZitO`01)|5<9IJm&*bmoTX;F1bCnRxbIT zz|W`l#%Egi|3zSo6;j@tG=7-b%SSs}B>&mqolp#gb#hlERr^Xh+4SlO*d6|~83d54A} zfGOGJbrDaQ20xG@#pQ!;Ipc((qRVccd!+4~;{WJUWm|fyY%j&{{g+}48R%>XXS+`NU{H7-56rM|9DszkKtkl@2 z3C|eLvXcqNxeQ9)vv5X)4*ZSP>KrHo{S2ek*i_dos)8=COUuJ;_r%;I9kKU&ZY}u9 zhWU5pj6`#$8p_8Q>=35xct2#WZ;8s7!rEaxdKN{D#>Pr!j!Aw^L3p!3YWGP8D(y$5 z*q;p+hc@vMfm3h@ixqsPSvkODNR{FuEtNOtb9Du$eRLl6yoOd$Sqb*`@^PHryB4aP zT$Qp?u(kTLhf8|Uv44azYKl#kwHO1A0Y%atgmYgLa&0xT@Pqz>wpXZ^*S?x$jNjR64ixu)gg0i9M!8DdR{Qhu2WShTO8+X^D~;-n8ibmS6SpLONWOOVb#c7HwH|8EQxzyeqi2T!~vXw z^@E&y8!M$FZKUW@Co_6*S&p8nh-A{NCksq;6dGha$@*xpoOrJe%* z2J-of4=h=LSD`TG%7?01>U$TDh+pZyoA^osnFF|?Skh%o$E?*XsOXXE_X@~6>GV|G zzO{sP4$@Nv$iSxDCL)CTa7fSgRbD@Nwx=jA`IcN}3CbPO&b3`&!rAO4x&NB;3 z?q1!FyB(n`bKZg#=#)tSFKdi(qo~uvR4;=YO^U_Y?t^1^mb@+#9b1hAv}GohJ^5Zk zX^F%mnr)rrDScuPB~QkzJhvD*nzU`0bDRB3_scHTQZ_Pb%`WkY;R85|uo$E3NFfl( z{?ieeT)!mAhFLS%Y+@uUtI#$?$mGU#TC^EE7$RWyQ(hCvQAYAD<6V&`IjUR^_vEJj zrca0>iU4LTI7J(s(nKrW_(z3~cGv?pz`@@iFlQZyj$AIYqJ7zuBX!%!AcB)%dd+VV z;D>g@~@^)hd2ZcGJ??%Dd%1XP|zNebvzJmgJN_hD|P6g8pMiP5@ya>;i1*mM8Vc6Z$^i1O1Ws@ycL1XbA~ z(4#Z5Wc$%UsQ9P^F_0FG-y^)zp?7tcs^1>B;h9EVCXI!)lanYYy7ok|1@@zOVOJyE zZfl5*$HKSp>U(~$Y_DmOa8xHw_3_2OO)IF~8on2Zrhhy(7v4KljzJX-LD+piL%4~u z_HpzqpH99Z)Q-5iI2??m4d%N@FqOU8?S=Gb^zm(`k174nIFBfV@pOK024H$`Aixhm z3JaeWwzF}>$%**r5=R6rXY&hPD51L>%Z&SqM>t|bEX$rHCMnQ;5kX!cT=9$uXfRmU z)w6C2ooaV!Q#sH^n4P3JTtqco3t#s9&B(j&+R0mmKQtXLCV#}w&xBBf0}3s^nlM^` zH!$|9vij2cgE@7vukQc$-$}^!lls#6Un0XD|1g}6E3tpbv1TfX0lWS9N6`d? z6s>@zJ7L30q-N-;fqro+7TQKa{;HB@oRqK@+f~%FUX9NiDxbe)wyccTLH%2gDwphq zmR50CG|kPMmqwJiw?(SP(%Zg;NPDD(N7ny%WbH3*De(5bM3OFcgd)8XemUXex;+SU znjrc6R%8RE}4z`*U%8S*|L`{n>QaAY3lxO<)eblxe&23O-tmsPE=tlN^c>nPkoH0VE&)A43g8JTs|QUM z!i&19D>H&yF(p+x$$^9Ts&vGRP`1f1r_L!P2J%Et2R7PTWr!&U7N>@J_~{N~!+|9; z1BLIg+%3M?qQOQCthWEYQ3ZQo`?RS2wUe!()>}hS`-^5QtzwJ`d3~%7Pdb;wnqhVO zc68d*CH|#)VKD$EiW_{@*3Ib%nr+!bvJqC25R4M8eqP<+`95Ach?xm-3kEj$8?R+= z-7i6twde|+bPszEP?LAH57B6!SOO+12sh#Xg~}|ZV2PtNz z-OO$-LVP5hbbuE2)antEx-JcN@uw8=+rt~+eq>OI~V`jp}!o$L4cT{KyS7$X<1}ckL<0?{b zJ}VPcCobNi;Swl=_=3hXTd`7L@CG;hI0qI8LVNaBvQMui#8@nWt$Fk#3VUJrwhTT< z1Uo+SDx-ECPI-F1UrlpJPj?0{wbJwk;nm9>HiE44y#!NnTKpy?wZ%59o0{SvrA?=6 z-FqXI!PkfOHVty~nd53Y^xZ34A=BsZ`~e|YYU2vcIE~t?_O5uA*R9g4r#cfO!Bre` zI-?_Pk1XLwp}4{LvCntphRTB(j88)LR7&nj>C4Y)l=2qjgd-jdq%)!=OVOLw;3Lat)^~O_p%1C4kq>ny+*!80}lK4M`xHWQ28u z8pLO8{fr_@t)zsEo`>*awkEas`yLN}->AoZMJshv_+7!Dp=C;#t6I9xC!7B;8 zPzj{WEP08LDHf>#5SV;>p(<~P1J^&a8v%o((m&i(KSJ!X+4`{FCa_%<{QRPfe(ACO zyB&q!n@kbQuiX=Ol&C;86U{m%>@y+n>zP$)a%BA1FOtax#PRo~o)&Neo^Yv0 z?9)<`2*mG0$s5q>;a&?bG~zhJm{Y7{uPQbKx@pj2=uFpx zQa_nLxl?S#Q3M`Jln805@5|TZG!{{@A8+U|3&K2$mRnVDsc7f(#dV|g!hh8b?}%pM ztP&_@0AM6(a!?g)lK{wNo(N!MHF%uY%&%*4otZwg$PzqOEK`c zOy3obdsLi_VHCdopF>pK?OVMTPYtx|Bhd(Sw`5HR2PG`8QfY&~Kxk)d`wWiTl8UFM zy(pRFlS4r)d%7jOi0a#5#l}T}=dS^>#i2_u15Z7zWk7AP00H8fv!i#BC#*DL$_){m z0BUxiHy!5n;ge>Lw5aJ^`ou)d`F|v@|Aww(`>qHiE40rB%QxxQkRR#sBF$Tx2r;Fe zipObcV@uSl&j0Sm7XSftp;5dNK4cqYG7t=um$f(2{FWOjb6~dA&G-1v!M7wnlB5a( zM3+3_kP*ZF6Um|uRXWq<50rV6N_zFEa&m6k78NYIw}OGSR55e5FKw?a=@a^ZRLFB_ zYfu7soVT@t5Fo{2S8>i;s+5JEq6Ek_?7enAs{R^5 zZXyt|;T%gR>ml70lm>x7=oU{6B2HcQ?DDsT{rgnUQSUhb8O((yi(d{VoS3Pw<$-RB z_L@_2nj=~l*l6_s5y(`T%out4i7azn*>)zQe;SCrzHACv)P`u4{hSuwCfIB-b*i$zg z-5^PZLLJU-OxZL`Zm|rfH2QEjOA3!g6%>DcnE{aF*5QGNbmrzCJH~EK4l+IDe5*MJ zW}I)vhlG2>l&Ue(J9p)yd&3dee{eaamT*?s3qO~6RGL)-&r0b;4$|}`^*L`-;+hLS zULHEv)C%SzGSkmb`e48-CjIPV&E4M^&_jD82Nn}j^IK@91oHYIgiLy^VT-W&8B~ZiW&MY!4{qcQ zlQo4WsQGlp9H*N8F6rq+^q;+r7^-1Y`rvHaHSiamYWlPU9gjvEGWZbV?O4leb@{h4 z?P$g9rCqmT^^Pa~oa$N2L(a-cAW?|tIiy?22?z&?;P1Gi$C!(AJN8Tbg;@Zy>@atz zD88V&(b>@kdWw8M2F{m>fZr9h9sc?c+lVA5bc`xh)UZ+dZ6!ZQp@8h6z@GY=nzzmD zHtOmf7&HELEv(RYU9~W!~0NhVTpwP-avOs}Q%(9=r zjGay2Xy-66zvt%}4V~FJXnhKImBw-0G1!l=8qbGV5h>G_V|QlT_e2aH@Kw7hW-Oh| zK}@sj7XY$RFeHTZhZ4e7W>7@+KT^4js4T-I*ct&?TZebK>Oy>$XQZp22?jaV>$m(J zEju;J*{&F-`9xHUet0GW_ZC?`um-cfOf`(&9jKwsVO8RbNw=+%Pp3}bIyaY>jBlvp z56&5fRz-qygOVDzE|Dp8>DxFiFgWc_>{-mI)lNl9eY93u3M1cm7Gf&X1qovTNrM&% zskVokW0#E5uHuUGlP9r||5b17GQ^7lMX;C&Q{b(9dCrek*}nEW)FDX3Fmas8U?+>0IjjC&{%)*k!cy0yk& z>yGja>f*^cO)bAv)tq-ZJFf*;g;@-Sw6j2i;2{$sWgf(3q*bV^x(r+Lgkw`^UlGHx zk|9xy^{lkBlAl%WvUF&WD?u`Wft)4-dqm*VYPUkDgrRGHip8RYzuntb;cgj2BFNPU z*-Z)?in}r3jUZgC^YkQB67%4W$dg{88~Gq4j<1EyZpU!0e{L?sUC2+3E%=9HWU5EI zS323)!1;Q}b!A87QZ9=wU~lBU`}1*FKqO{`3RIG8$k|4e7$7qn9{^)hE>rwn+UT{B7E>>#l7eK=M3$ii`eZN9)i9El)JkP-pS$qw04^ui6#~)(* zW5W=$hxDlP&RuqshFA!iKUD~4Y4YiXc!hR?EQ65wJhz2N(U)@8YJ<|ljZ_EXK_XXp z^ryXQLslWGiz$I?gPLNwR}1kA{iBD0j$%jypXSTnX+Yk|f%#8Or~l7pBe-RaT;iva z5}Ye*kNUYmrvyfQ<{y)wFlD08=H^tcW#_t2R>rlsNTLlqvGPRo z=ytdL`jkEYS&t*u!gwhmRh~b;J;jIBhui5r>zmN?uEO1AmHJ*ebm(w#82pKtqm3+- zRd8vDOJQ_}c;ws^-apSK-udi4C#oUL|H!n1$=Bl{QGb^&rmsTl_?11=>7#-i89JzN zR*-wN5_%_-FuI;g7d^%@X+oX*P!d!8$?B}kr!lry%A^LxXr`^;zZE0~e1j|A#TfnA3HJ6LYm3nigoEOO>$JnEaon#m3 zxMa95l%{?G=I-O*$BilMS5mA-F=NBnE{G(9>=&p2lF4Q>2#Z=kZcOL7!qoH;H(Txp zg@h20f^mxjyYNza@X?p2Xf!D!3F=aB=-s;gf%gzd2xuowmoP*H&N;@v>hKmFNf$U; z{_l0P;F;>T-a>}o*3gfG^-2xHM-Wkm&@I@hY2Y~-Z9*9T zo*6%h6J`^b^xA2pp1TNKFM8P0-sWz$2EccZq6huXcS;QRb&G-E8E|cS8sF+Y3T&z~ zbax+fN|R6Te=rzS&SMhyA2G6#rK7V{!b^=UlWt-jFX*k2@}Os%q<;llCx>8LMor6g zO|ydg{O#r+`!GYk`F+akoU`quF~$vXH^~s!7+HdCDWqgCPXUg!FK00QMxP-u#W;HX zAGcUkhS<$gg8CQO=IgOwjN4WHg^GcD?aU=%X`&8V39i|YR(y*#Ar#E;)z-Q|W*HN( zB)~zu$q`%DC1o5Bh)5QeGoFT?k@AafdoEi+sC;B6q$a`vsu9(L};wJJ5q3rhlyD{IW|FO3pebW9QM=>vcjD z8oA)Gq|KP;>JRhUo@-MHw>}(rf$i{8G)B)INu&l|!C}vPu`y0sx)*rvpQR+gfNZ#O zr|N~Zm#2HC@IL=*S8Z^YFR7bm;Grizr{&kMtyXKj@bK-%-XIvvb2Wx@Bl@w{hkcWV z&oY>ltg8BbSPGyiE`;!Xuk%T|dh8zXP11(Mem*u^Dv>v-`qpI-e8n&+#j=i8YLT+b zRe#)?Wg%+l_L?ahKfkZHIa=8vP@|Y|mK2WF;)=g&>#xVWsJV)C#F*7UWOxxV>23#D zgAQ}kElX<4xc+!Wp`wBH+RsFTFn+hi`D})(vtHYyelVaBKPW9FFUT8&EW$)K#D@(r z3D%&5usEwtvdc+a8JmzMZ>$_0?%|<%=V~01V&Gdx*oxpy%Z5U7w^zS)QMCdO2;-|j zxu5>iH;W+{XEe96^7U?aj_yZ2SJ~*Hbg*5O*v+3Li`iqS3n$pARqPL**0Ana)k?ro ziI3t=2!{J?jk*6?mg;pQdDOeTl`)f&gZ)?YAA8cBlFluu*(i@|pb|5nfIsy1rk5;K zb@&91o2WAfvtYCH^OrSQ7MDa9tn|{D?Qb>li-$_XG}%kJ*q3(|gEe`M%s-b#Jpn zOhc?N1?o!N43x?DvqsBqDgZ#eb>oS$5fTgKG8 z6B=AI?!a~yLHL|01ID`H2>fLMqp!UQQO_L9#aA|aoqgRgAt9qu=jUI>tLM$TI`hjI z-GAs-->VyVeSZF1`Ud;XIO4nQ7&_2s*t^;oh8kqG2#%1tZTn<$pLtybSz7)L zz7C@}zt(#EJkEo$np;Qt@n=PdC)8i&yF+v9eAM-B%o1Hn=(8E8+v8(~F;wA7IcE(; z|FRHd2CtB3q!&uzr(46aPDlHaNbdc(lnv|?P-qaKw;$aTvp(XE54`WcVDoNtvtJ{+ z=<-nAF}bIWXV)@A8IvrZsIm8qv%}yxJ990gj>2G@=B576g(vhb6K(7E44tObE9kH| z^*i1p9Y7SAlfX==YJqOmTr4TRnH*7#@?6cQo}$qJIF8LS0A=vDvC6Kff41AcI)P2R z;;pBS*tJ)TZ-(_IB8m+&8BK%lZy8-wM*Z7uCRKn*f>F=%b$ar%`hL%!jIZ8w-5+$Y z#1E1q=(@lvz3jqemnze;BHAr*X(iNS#c13@1B&3JNnj*jnwuDqn1+JY-Y51e^s%y3AnU57%d19x7JN;UW{nUC5^F5 zk+^?Lst^m{dIzJ7Y`B&uItk}OLrQ%Ug7r(C7QN|a5{P`3Xbei7Un{$MkV*mJIiq?Y zy&$;^6F!pRu#1dkZPCO^QpG7X@Q}y%-ZN#!y!uR#D#IZF*B(`QH8p8&#yq)Gmg4rM zHKvbLqW3&`Sjemu`%bzcImxabD9QzcLV4ow^Oy>QkiEIjn}#!-qZND^ejLnaXdQ2+ z3h`GjeVe%1dxfuXB@%B{K25`@0hKB_9_D<3@w>Z=t3xwB00pMpAwkiPKl@pO(MNuc zm&Ak~FkJM%3{tf{MB_nQcZKD*rdfrC>#P)=Y)D`kb3}iLzfIUgO2^G3AmNfj@EXHl z%kF`UO-IoVM4=OMg`~2Ty`LOz+45YT3M)O1(FVIMTvNC1pN3j1C5Ks=i!fM=YuQ<( zu-q=fGFla_kd`6bN5Z`Nqlch{ze@2Vo`Z8W31XC2?1HK3Q92lL;@9Y&t&$)F$<1Ji zQ`lAq&_kLWFto{#U=g=$+4`$nA+qP}vJ+^Jzwr$(C zZQHhOTm4OXaI1Q7C#lLGNIgmRUh8rzR(DfF-^DxF+ng8bvOP!FYiw36aQi&MyEgv3 zYpqzu4HF`Z^e5-)$=@!4un4FW$0V~n%6^V&lAhCBuCqsrJ2sljm6b`MeT!rx3O5i# zpzce)v8Il?r{_3?c_ml_w3)0zQj-M(h*6KB=?!lu7!g1YHpcp<=fI9WoP1Fxt}o+` ziqi?QA12Mu<11!1ocQb=8e$ZzZ*{ z(5RVm6&{3RA9{E|3QK&6=s6=vkfPAVH}@5*dvPUBLrEZY#aGY1?j%enQFAb1!; z;1ud$0--Dyc$;lGsc5|UKeUBqcJuaX*g$Wlw#UF7uRzcpt{;?#l)+q=PD=FHLEf_= z8T3>t?`{bIb&Ntq!49YfD>IP&i4Dw+0BIuW)Pb7g$Text5kAAf7z z{A$)Xr&T}IafLj8u_#y%)~37RL;{HZX7}nuQNs6T8I9cAUHe&|!lfZD(kTMEDBrIq zS6--OOEEj@6e%9qZyBV~bSc1gFw;VG z6Xr5{by3_Ym(ZwMOhA1v&ESJ*;sfqI+YpI2`zuzy)z=qQv$D2}(WsDpaGJyOrVJtw zhFSBE*U@LV&o_?KZOXutn!Jrk>k{E_`o?^9k>MZjZx{1y1= z-`8eDvyp{gHidA$R$*5r1G;7QP<)iXIWSVdd(wi@k+tMrj4cEzE1;QxKbQ~w z$UB}Qz`A^+9qW}hy`z2y*IRzqkKgp{t*tqq=6v1@t(^iyi7eAsiPV;1Yk7`N+beL3 z2@bI%U`@R%VApIMjKBZ)NMEl-noR!W#s6wng_(W?kf|oIgoCwkmvair{x)iyAxAt< zcrx5USoL_zyM4#w5Yx6}L)ys_CuFIk+d`?ym7pd;Z^V##;=Ko?X+qKqr1Oi zcf{_2Q82pPuQEyJVjH(U>8L}z`m|(&kcubqFEVn8vb*gOWqflet1+a~bnul;W$p`U z_5;LM+HUwE_CcHRen*WP6}NYAKW@y_I_zCQ(m|bxyvk9j!$+oo&?=!A@|aO`bmFtb zLci12`Ta?S%=zPD$xT71er25zOYD{S#`bGw#HN=C1=lngY;18!L{%oJV?Vbjb7M-t zfy;fdGO?fx=iqguWtgCjtW$@cM>ncyrdG$tW^CvYhH4Odq1C`xTDn2Be^qVOtSnn6trbE)Ib}cM_v=MGb;pDY9ku zYLMyrE5KP&ElPidLH`Og@f&9>2~&iCunt@GFd$+m1L+7d#D>Jy*2Tlt`X1D}v^7n9 znxkmGh_H!`zqg1s>gi2)oEEoDqL}2wj6Yh(vu{U`>@@dAm#{tW!PkUO*~y+S;=iB7 zBShfPLGx|mGf!aB6oIJKN+yjE>}~|FksM@6A+}GHZB^txVxsZY#gq}tqlcE2Fu0K0 z;M^#PCg`)z;_AYZ$t=_$ayOa}R77md!n{)z~H}K|#Z3lllL0@7g)#=D}_qrV_g<4Ctf@Y$i{v zsa-rMkFE2+HXRi$m14&FDag5KlzVD;Xv3jVJhE!kXD|R0uU^Fh={^fM zI#|%6VRN`ahB_u`IA)AC&6Yt<<+9gio{g)xGU34nQ1E=(CxGB#zpLh**zy@rm9pu` zsz4c~j2LA02gvsW{{IjuMNA#_%px@GMtd~7Y^iR#E6yoauOZvSgPX|d=a=%Ai1kO4 zmp1Zg1ahd>>{@TG3WzBe%0~UIHH}Tk1Ot2?uHT|?7BCF1H-Fb36si^&j*Uc7r4yU< z!0ePpA-0-A7UvIo@D2m$ier zNon$Cf>`L2xJTotaiY%;^5KJ4u#6N`$`YO4*db%)2K%C+LQzKD3BitZkuXapF2m}L zULZ{P73I#9qelI<$}A%QTBVnk#knVQ6dzA9af)A?x%+yhwz=U3Olw$m=R#W9QfXt% zyx_V#kjM`iznMr+8Ch&C;zzhaXh3AtxELYEQVqCICkuJ3Ab_deLD!Z++wXR{WVtF- z6E>YjQKEBzIVTS9E(TM`e9ew4RyO|iiF%ctnSLdgXs^`~T@Z9;HYumUrOUWW;_S*4 z4ZLev%3E-qy48^Eq9K;g8WUpixd!PW)^jA|ieR#)uW$4CXSm59kE3}<0nBt(W?;S& z%pov*DqP+~K!?SMZ-%5R`~yRlZe-GwMG$>hrqgqc2HaBD{yzT>2ORuk=@*&6Fy8K8 z&~v(A&n>MRA9O*jOAJ$N(e03+_@kgCt}lq0z_?;R941xqrmwDpv!myVk~V@mw9ojDJH+WFYWDZi@~yNZZ*K92 z`9*}`bD#VTrPhq_FodHk<2b!Ta*Oj&4S>`N z?RK+l9tgYDD6&a+&X$xmGAcl>g)x5ruyjT_YF=4sakes-n#}yD9Rjn5(gQJ;V#`@k zP4;m*Go?wceqnSNG0sluhe~tY>Esc*!QgTeN%%Fleio8%hSmz&Mqc`vR@L?rwAHZ>_2c5CE+6E&G zYt#`)NPeb&`I!uH#Zf@6{#1=m!b*RR*S!g=|CHz1P%K6@>|2A$Pad5qHYaY(K*=tR ztKw%nz@?rs-NEb=-ajxKWsNT zxlB0+ZC%|j1nt%I?9DCP(x8&`onNy+u@=k)ggTMabyntOs#|y%e#?5b$RUPvE^AVt z<`$H;haU9#ny$SWzP{5;J{?Ms+D3Q#qMKVjXb9b7sfE*Yb|_h()^=-rV|wo|X<2n#UucEvO^9k9i^Pttv! z>Xcgs@boquFZ%e~$d$aGWJA$*vX_0g6P$4h9pbX)t*_=y$IrXct!GmC;?dU}5K}Qi zyMrA9_+FNnVhquM&xLGA)j=)ksmNMP$(8qEKe<^C%TEaKX$)czRG+Q)UvA_mHHo-`~^{7>mPxN9lIt#EvgikxrSkGO49uge{~E@;YzNBNOj7pEw#EkD z!4T%78akyIgHbBUMp4_|yMpz z3(c@(8}k?94~9*LNZ4W_(ZGd;>9DiXPc#%NM#1BRGz%VPUG3~(^HkxDJfdGgJ9Q~Tzf##uW8mwdU+n}8d8T{VJ2 zgHZeNXHbI$N@eE^m|3TT=9;|9IJjH?00bA@$R(A$U^GJXQuPiMm{d*^727pstd1I^ z@qFQ{nwyNQZ`oQ>KCMuSK%v)UQ&Z&a7g^suT#Y)y#`5Ot5(Ccl8;>Dib@p`d7q`Oc zIx+sEP&YsaIf{t2QFh8Ulae( zupI7LMRdWB8D|^Cm*L@ydrxrAo*fv{Od$r@m|2D(8M+ZS4*&*&S&lz%qV77Q{wymO zDP0b4Z^Cb~F)PKH@<|4j_=vn5h|}yHQap_NyY?JX@z0rn3(#|Eg zN(^d7_q_nZ9~_hhE|T46XRVK)9raU{)=3fdU8?tk^@P=mnZ4ya^=sg^flQ6Zja6@C z&J08w3A($&I`rr9ng3;By$68jgzvSq{<=7}Cg05Uw%uqiZ_v0IxHmg1qR2lCS%a66 z^p4Z0u@%cZR(k8>`%a!6pQ+_aG@~%oqEP{9rgjPj8zXx;v*S^gOn=lF^DfjiQ<;Qv zHy$@nr@pu>*wB&Bm2tY}@kFEt)Bkuo7`eJ~mDiks1T8Bcw9#!Wu{%JD=TSF7T#vGG z!sR5Qr)tdIzi12@kMuQ2vHz**Ff8kfIndPi64ox>7{bLlg&_qnvm;HrcF`1w9j)aW zLTPG?X;(>)p|BJc6r_Xe{En*bHA${BO39RAJma%X{&Q2+)e3p_7+i`IefRbKM+Gp& z7UXS6E`i3^k$1PLg@*L(fiU*OS>sBQ;xV}A{?bl@l4gy*zE|6$70g|)@Dj^>3)NH~ zrHQ?!40*T@s|biwjOIigV5oukwb6BF*p;ItD2-kDR%GLAbQ`w4OthL$@_D<`8EVQY z!)$R%ZLfuexLIGes()5@dLH?h>8Z4|a& z>=P+8Mz$kN-&a1#wlhqvz^CYJV%?+1kpTKYi!U(yQRN-(&Cmaeqcff(z6}WN(0>gS zwNuuF+XN|Qlm(*+J`tdJe-pZOD~R$N1FWqgx?19U1;l7y z@UD?wzJNgzcG9FU z=F)-`SnKS$Iprs(+MZ;3l{K%%Q!ER7pY~KJ`>Z5vyhyw%_wHSPd69Ut&+{U*qfcY< zaf;m4eT|vjv;ZIWs&7hq|KyVk^RTHFJ1d@?fh(shkyrB35iqtA4FJLUPnkmvN0U)B>{f+jLGRxGjD>Z7jXsu{ z{x7JH_Y1y@wo>y#0$q-L%W+D?&9TS(KQlHxql}6H#9wtJ4L-LbiI(SlKUT}{71d@h z+NGVV^}~HWO;kJZ1EL$=13=S1SyW2k&eYv6iM!u1M&N2?3ouXID;qns2LI(g&cW9a z!jU)^bh{9Xf!J(0Fd7E0s?D7daD;5_@dRjQe#KT7<##Ysv-f4xApaC$>!m66`Dl04 z3}=l&;sUS{n?dYZSTFH({IhM67I{LE`Q99!Y7IN}asig$VO4lI6MnPfD6{0#-1+dK z`H0hnjTX(R#_ggts~ibTQC4);&f%q$iK>-TKkdGc5WO-pn39{JLqzlE&M&sX0int2 zUGBEn>ks4;wo(!@OD$9^))8++x=l9?{V-(i&&Elm@&)F?xjn4nF9+K;vq=d z<<*RoKiQ@r4R@TCBP#zz?P<(OY*n1{`vY<(|&PzA(^K@TgkX&_Ep`=C#$v{$4X! zWZWJWXL|p#bAf=AyTmAbX$tgSYVOu8+CE)+S4VCKUQkBn>lM71qx3_fhOGY1|%&fT4lESE9;&SjehfUJCf(T*Bm*B zZr8`l^%aO$6EmZeaDS`bZ(f?>FE3c#SReV2@-Z=56=RrvB^^fEds~M~LFfO_(p1;i z-z#Vrhc^NAN1?Phf4PdYm5{gH?;2qMHtY~}LUoZ-@fgv_5Z1R>HKGq$hFwwuRF#nm zA|ujz8E6tw1P*XmkGJ6?FFuoAcwdpW-j#&>CQ0&Ffmjvx&&h z1T->FBrJQz?}%H}QfMEIu5I{7Zr!a-S#KtJxKfX~2K{=M$@6cJ8jZb1Y){03^Apfw&+=eNJh1t3LgA<-6brd1^i9 zi{+c%SYOw-V|cTc#m3DqKWtvM`X{M;R8GU5SOQG%uSK|So#$63P*?sx9d;Le_3`YM z&_m_%3PY4f-$e#&5{JF(-xnvm8gdZ0{B?fB$ID^%EA8EMB*{u9ML%7kPBCOOq8vpJ zPeewatuKMMtJZwVw4E|%DNT&TZMv0Fn{<8UANqC7vE#dsy8^&~wTw?u*Ywe<-~dEE zg@Pn%m@90s<>`}Igh4#xHg_s+m$f%+BWAqX@YS6X&PKev??#XJ8|by4c1Sdd;^~C| zbNW>QBWe8ky(qg4f-9(1#bmLFXsMW^%=ks91(2Hkr!=KY??-wBk%}$Oa()lXzT}^}4~E25pjOP??+k`CdOX0~ zwyu?F5K@4sj2w`2#GB9tYfCMuD~eT&sGo5c0P!K3Be)HVX=ZWDux>uk<%zDGEmJvj zACd+)+$n8^!_YM#rv#cq&){Nq5oTMy7kOA%WFYV`j!A!a%hG2xTvnDCP2ES#EUuKb z^L;3>vufef>^9FgYY(5miP{S)rUzY6YGBYK>-I1 zsGeOy?hHYf#Yr@?<_t;g)a;p+^|uR_4hhD;G8aHo)ZVI(B13>aRNc-XcYF_J`g}nU9!1AQ4W*5*BEPaDRW++-h_8)4f#`Zsjk#=vXF-F zWICj*aK*(=L%z~NOPLi^@>&M@wiMx;WkZ^RtE;c_dkMD2mR??OCY}VQP>I_1c72X# zcv)nlkkr1MmA!Wfn$YgYSkzms8}#*#qIpPmZ?*B9=@$9s7+@o6(Xi@I_4n6FWuA1` z52?T^1i5)0w><;0^7LzdQs=u6+erTY9&-cA8Fw0{Z`~h`vym2Tv930c4dHQj&!-x} zM*biaM$Ubm83bTOaQqm7etUce`4m7Iznwrsf!+7V zvP7Q^%XWqb)566F%c%9KNF7RA@x_r!$XP56{prVAQ<1ihzHyJXNIjGIRW(`vOhE4s+<7bky%Y!72J3D{pO`8s(x+GMDjPD-91YCw!+-IlnIRd~Pd*v+-qY_TX@ZPW z21)9SCH`f4@Bn9CuZV_)2_tN{%bbU}yID1ggBMWwb}2yilg2b8dWU2c=Q@uJKe$Iq zIO?p^^|T*K4?W~{nBg;BG>zY%dkXpN=5g2`AnZ-mv^RKnU45fB8w%;)-ZI`FD(W~& zw!4YqgoE$wS{b_DMYqYCWhhCSBfG&KL}+yDyROU%&5$Jt0xWTu#Q%$Qs0Nfw+N6P7 z1bjB#UG_VWy)C%beyn5WHSdEf9xa;-EH~&yKo&Zc?V8EK@YDa#2*-}H-_q~1)JcZ9 zY!0ALSw^ODfEUwhbecYucbn#IVUI3>)I+5)1KVwkbZbx7EK@A16=QPoS$LV~U#aNI z1{gqbZ#5630^_+7W)k_gNU#5>54V?@&2BuRX%dq{m(>1(02wnP|FjdTXkG}yzU_UGO| z5xN>!d%?;i@)7PRX|D;Qp@fyx-l(>22x4qr#0}MQ8=3p?jzM03nYK-<*8~l`?qN?m zM5FrclbK4E{?m}xHlYy{S@}7wFZ+{j2#t{A3XM=e1berwO_5=2beY=M9z#gWSF_DT zrVN+6Cd~y&rHMRrBFoR*dk$V~4z#lS{Nz4!mR?@AM1}POve)%+;H>C-I-)7=0dR1j z1xV9fj8ko$z{`7EGPNUeguq*~N{@&IYK(P3)1G-jtP%mKiJl&RF`=Y7jHd4#j)QhgG9b6z4;Hr4rUM4H>2obx-y97W+js0}?08`cd@- z&D%Ns^=4KxZwX6@ZGvWZ!`9x6L-Ie#~maRP8DEN2^T>z3~Qz7c~}j z!8p8=Z3p;HQ3O9MOQR=L3DzaT{o(i9{kk2~5Xo8!FRK-JeuBw$3}r&9nK!1yJLbMa z36(#fF&@2V{Yjy5c@LSCdg9dWZx~g9*I|=%Zm#9(xJ@WVim22+MJ58DE;a|=; z84%SSn zXejREIR!v_4M;h->QI-AHvkJA@XJw;5g;JXI&qjYE=6HU`3{%ZNn+!^X?a0-B?u+F z?FZEVs!~oBIxm^x<6({w+o*?~g+&$W#eV4dy*7>lhZPXj7^-6Z5V}9oc695fdqzak z33G+=p@b;-2$(uTY|m(mU>6su-GLI|J^9%$~TnRh(LP3fdVckExTgyA=`{hiY;BL@SNW z<2W75O^ayTI@0Id0#APtP^(hC7Qkk<^4l{s&84)64EUgRY1G?Y54q;pYZcd;&x}1m=Q|iQ*^A}LB3ztG zn{Hd4RdKd~Z2nz6i?~Pyg(HVK&H*mqaC-jL-tY)R@6dmkn%2hoOB%O^Y~M>LYV;<7 z;(MJR3UYb&9i~0jN0JC+s|Nmr!?Ro&HqC);C|rrFT;~NTW-cv3_wU4(c;iGyZ|ukk ze;u_oK^|N9=G$@rX&=w`w^|V z`yRL8LwEK-*H*Ti5&qLxc&?fm-;GZD>z&IB9|YdEM<0Z1ssU6XAZ< z1tQSzo~;|1EVs=fu+$?YO00`BE?4W5lpFi|&M(~+9Mw0OGj z)Gd9NE*pRH7XCUu7|pwdz=kY%~xb&`(62xBGjaszmz6Cnw* zXX?j`j{J&8cEXzTemTab&s1?I68mQN8r#-SQUbi!VvKTjH(fd}8<$EB1w}s4*l?3XKXT3=C89((NM@n0&UT!iuHlZbSJKL?7M)pd zj{TIJ=a7Ywap;L~wxxr%Y(%~;2sPNeJO1JU3?%EY3-e$IM~i#W!_*_KgSUn{iL-MS zdjW3z%VH0K?d(euy+bT~z+F9P=61xlq0>_0+;7+gh|5*p{%Bv#H9Mq#$YR)+&UY(M z^!hQ=-WaZ^4i4;Z)?SX;kwReKS5zM`zU91Y2F*N^6xA^tF_d|&6#YR9n|RwUkL_vi zJgvla@=y@~(+3@)+k>4NwsI%7EHW-`c)Lid3(ME~QMlb-8YciS1auxYhUO2!`-uzk zGI7Enl^}w;2!K&ss``ZU#?stuzY-MAxy15$@OBuZ_NLvZOX5+SrBVKI!UaU{FL{A9 zq5uNpgSMVY*TL9EvU)>~)QM)>$^SSs0-=GS@z;BJm+h7u>712kjq4{nQVSAEbeR(kVR&KZJvP?+oB`4*Yu-=~)V&DO8Z1 zoLm|}iO0#CqV%L0iUttnMuj8Ldg2mB*vXf=vW%r0f|C`x^R5?++lt7i?y+_drVaCa zfmlhb5;)F^Xr_c;%1ad3ZRZeK_g-?k*u-pD{lITa#<8gl??BBzFWBWTvW8(0L_aP4 zB6>;!!M4q{64)>SLodQ&9*Lx=rl@Wn&kcDBfWnN$A%+hZzZ(&cHsC7A^SD;c&OWq} zdsq;gumq~wT*=*3GIAV1FKbdbDugQ@+2|w(Du3cv2Mov(s#6AsbH3$r8`nmq&_Sev zCpJEknnHNf-@)U!g8}A6&ifzk$Vwb`3BJX)bPdDkW279F6Rim!TUP)LFat4J-Ukmy zZ-WFt*CF@~>&=YO8u&z!#fw-2_VfsQaC>No$-oQ1qfhRc4&5MCe7Z#L$YqCXB3iIl znOw9b1AdgB`Qm>yy>pBogCt4klqe}C;mnA81o*N$ucM3+>)AuG)hO}4Cd)L(eFgY zgC%*#v^pE#8j~~NAJUFfTi4X*l%Xg|{;kaiZkb=$>yu4i%f}&Vs`}p%aJ5~`gzCyf z5f~3>4SY{79rdzJ?$q7XM+y2kx_1eAOBI=zZxBg%8qbt$qr1};7#0H;p8QG(7}QF# zlVYC#qBxc@<4-X7EzDv2w zw9^EG8hBU`MFB&DrRLrQMW#wKocUN(ctaD5s4a}Tj871xZ^JJSHu(t#Oudb;6aE?A zSp8`O8SCgxO#Nij663h=1bo~OUu&bYO-n4+D6AWlt~IfN_2fy7Oa( zDNw-PES^v2?I!m6^1x5%xl}4ERKepA`p(!|m+jHDl){6WZai&`9%)~@G|t4puB}7P zZ#5GvqB#i%0kKl+Z7GP%uld8#B;{ZCB;ahS-Sw2qGAF?PJyGkO7xIk1YwJs-uKwLb^f)KF{pG^&zm&y=uY6 z-q*XEcq;YGlEjNUb=p-@_5o3Ds_6992|DZ-XM-Cg-KdgoVAuT;qaid(F?$^?6D(wW z^5v*OU^ONJipX1Djwt!P23&Dy!HciF#ox!4NOyfCv($y z=zKL12jR8Z(g0eT+Gu;n-NLAX)ieV8)}WM~B>Wj79Nc~sMf{X8XPL53TZ9Bwv<`EU zUZVqWszT2Q9ZX1XzR7e>M&wr2SO_0uMtefUmb9&G5Oaf{GCE|d*-z&~MAYUUW(JJ? zRh;SRZJyIyem&u!CH5t^pP zZ9QY;X9_My=Sw9_zmyiGv!3(%SqORJlR=sg$`DuUv%#k?ib<@H^QMPhZApU0zL){U z#KM!F4g}~+X7pJJ-<24|u^wjVD8Z?V?K|1~0xaaucZzaaYmc@!ZSQFM^*9?5{FN7t zUe6q%HFE81Bjty{SWJEh4R*&R7dgqc)cFE7s$sw*ecHv@Q!*I;FV=(V0YM%vNI_}T zm|%R&1LnPZM%Mn$_$uaNQ^Y*u21QJ^z&u; zGeo1qSRxaKM{cNg%7vg#wq-V5ruRE4x!I!riA~+kYo#{!q6>I2wS~;PXZ=E;=v-6S zv}PoA8`a^lN=<=lie~ohm(%b5XHSp?D~WDvXnO?BZ>1AcctF8ZJ#)vpNCV26@$UZfoOWVHRMe z@1o4>L&PrS`Pv>U#F_ny<+#%&I=01dJ;u}WLa>w1%oe|0d?pW^$fJJI`Zt|yI}f2| z1kTAY*qP7Bk>gaCFD%2VmxeX;=Ho(Wu^hfl2}NjL&U9 zIb3ReCqe>?#l$og?`!2bn|w9!^f`+8w~8vOZt|;OuenyC5Iz!*k|+e;=j}{c7tecT zu(yteDHqOiSu0#DJKZlh(Tt`pEC?j5)*a`YbeXPh_D252g5?1rhPf|xamjrg1>J1e zDpjr6blpLvY3eI-R{1q*`RIz$^R?&MK^*j+Si$Xy4^PXyVV~*+NNp^05=i4W$+1#- zd+^naMs)>PgHhDZGuuXKMZciLG4ep1Zu8PcPq-ZpMkPlHX<`F9e3jX6je9E6tr*ST z$kIMj=__ckdKGXwmHURy!FOZk{qoq^=Ni5_(LJa5P+*&1-Ehw8`65W}3swoia6}}&MfK?%`?~f>{dFa_j{HV*~PK08I01~tP#0v%%eXK00 zTs<-qta|s|0CgdV5{THlqnLeroK_$=OtD-%+?-#&F~1hDfz$wIUqr6iOEg-`- zH`N?n1XXK03T*w(&K(Nse8SaVDtE5YDJUYJcDeiLH#em7Klqo6e6`G}p^e5awsM5t z(o-nph?dVY3boQKa$-C43U8-`AoF9k(4szLh2hPeohr$E%0LRY{6%0U%j32^IIeuwxQQ}$c;eM9r)@>?f+cj|cn>Ae+UmT`t z>N>B5zxS)Ti-{y#+2ov62n<_A@;lqbIxL}+I(7V_Wuq559rxsmmVNTNSHrBIKHOrM zZ4jmM6O_!?PiDh#!BSU`yBW#X-n3{whI@pin7-{QnSbWlpxBfII^v~b2RlQ>zX8Du zv5Mu)^UXmukWmCZP@r*3>e8rFs?X3Wreol+`Vo{1%I(g5_L1E>HSh6-2<-ozy){-? zATwrcV|U8I;7i9D(`9Uw!|=Q&6MO!Le8txUsZ6V1_YXy%^Zfn1um~w9S&S5-B{8(_ zi|!D(DPNs~ z_d@NpcsQdNE$Sr=DG@3X=RD#xVi_A1+m7g#$gBU!tZRuIu5Xb29>wSWypim$qm#!- zr_q_|lQ9;~D_$Y!$ zjLKNg9_%8>(gBy;E&I$4@jtnCbfTgkt+so-MOh$9`xS5kcLRpz zsy+|jOB{0&s*>OKPZJhuiuoWVk+G{!E>6>`p{g?!^$WBB!YEx|3kMBmisxLJ_gI*E zaYv%(LNW&7I=-RUsYta-J*El57uL(cc1tAha+Fl2c`=eU;P9%`e(2{~$#}^b+ROBx zpzTq+NRqxcGGUhYcf*)#U#z!mH+UVf)S>#6ibppo$o;C+S273tIh3Ze)^{=cl^u86 zi8wr))w$051&_oznPbAB9i<`0GkLE*iI{qPzH3AJ3}RT}&-%%}LN7sktFxdg(hNqa z0yLSQ1k+q{n_ma-?3Aq+n&iaKWj)m6imE zoFAYvNM9Q3^#TosiWk-u%ayv0UV{@F+Swx)DasU5^w1_n;&TIy+Z5b#%R+WV>+e6? zpubjUhJ5+4Ic*wJXjs)-Z}>>R%Wu#w=-7KV9rgCv2^;P<-kPjmHC9Bn9&UnK5j?S+ ze1ijtGPh~0KegszK~VCreDb2Zl^`(Zh|sLGj4_Y1Lv`L};+%NEyqd^JO;PsL3|&yM z81o*yy11Gd$LYAiOAhX|eftuO77g+G(!;&#$WI5{V;I&8d9eeCjTYvFmC#Xw9$Suh zByegV^QvCID$fDg;A16VG{Yf?e}it3Px2bz^@FjaCA|n5yfI4^YcdEqvRbZb)`MPSo1GUuqMeB4Z% zdd)Qb1NYmYIxvAU8F83IE_{X11cclAH`tb6NkC(dU2q;7Y*`NZ`<+>0prXkoQyCNd zqYji+rk?s0Os2k3c>VB9UvJJK<^?J%L}l1&H=~e%x5nS_^Jm{Df_T6vX0&bTpr0qQ z9~_ujFj!fcPty{TE&YrH2QB9(GJ*=AY>gN4Ce4$}Puc=Mw@7Wj%Dhu-?>CcsE;DWa z_(^#IeF=rm$FAKNF9|{U245;2o)Cij8W99z(wjtEk-vtc3no^ zUmh2Lmz3P`dQLRth(%>OsYrXD2HuYiv32Gzz{x!|M3H}K&clfaT}htHhZP51IMvU` zj2O{0nkCz=L|CKL=xv|0lulx2k8t_7UQLLk9MBBs`21vl2WNVA-bw@fg#Bbn(eVgQ zaume16bY~Yf=l>6ivJ%@I?n&YNyo^>$?(4tIwk@}R#wjc-TgmGI#y2h|9?lf7mu<9 z{$KJ4TY)-Z8=j$p>1eyCTAF~ZjA^i;Q@Yux!D%+*8BC}M?F3p>Bu!89CT;W0s%_Uw zA-3jDb7YD6h-S^s;f;v%)?2oM)<^fxhwrJ=Y4(}h58vL|msd5dyLV|BLR?5MhbR*# z4LCdk3QlzVgLerFS{eclxG4n+HAy&*y?QJh9E_Ef9jCB3%9u9-k|#hcH75MKyr`fB zO)@amaE<}&Hv!m5vL1wC3IRr9_&>@Z9Q~+rG@fjNj0OmS4ni_fMsu+e_amkf9MrKS zXIOHwq*`G!uZDjBNNM3^2oV(j7ziQsL7V10eo~k%v7A z?pts*=shSk~R#foJcePl9Fq}okPc;4-X-DR3O^lIgy_4CRtHgQ6f3# z8yrIfL}D#jIt&oKPJHRh+0e5P*>i`{iH349h==Zd6Ck z9pd*Csb9G)wfP=m4azl5h)L+>)h>>8TPn=*VOl}yVBozCaxhay#VRsv3AtVlfbP#<@ZJsRK z+C?~<(|Oa#g2JV8P}%5)-*txS^Gw zn$p3*Zx+lU$0=7O1lG73%fcH9M%2TM5l9dP;RA335|VhWe|Z&I3sY)@3Bd%4=3j88 zW}(E2%7x#0kjy|sgfZJ}AZb#F6EOIa?}Zie<3bbd?-rS5H&znCnb305Gy(n-4yK$O z9bB?rgXa-R@{6UlQfgS$Go^0_uv;!yZ>#%av8p2>D17U>zD0W?66St=rP@E|SCzD=_;`ZBKfHv^ zQmsdNqw8li2s|9#o^$IqM}x1{UGRU~J=crY%)eZ8LLELOAY?_)X73HY$L|uKcd}s9K^cd6%62@t#C!W#d1eAoVQQevHDB>9Av&Ciux+ zpq~<>^K_+cM_0_Uwj<>ea{IadmXenSw3I{$h1?*EqPuoJuPyuRxcbJfUfM+p3S~vd z?Q9dhbDFHuT|I#8ZV#k)PtLuVzSLBOM=Z8V*IpySpuy|g2F-=BV0X{vG#!Ge$+h$A zD)t&!Bxe{+sjqej??e}B1NS<#HlF2LE2Jj)kqlN(W-MYd;3=eDte|}1cAU;La&lfS zXDp&gkZ6_e;!dimw`x_fZcl3XR`^tSyBsV{8jaRwal;AZJ}fo(Rs3MMTpx!xZFc!? z6s>%FJm)sCVr^-ifE!s|(M~hh?af&yn69v0=|Qix*g*1_H!520>ftelx#@0mD&(7) zzJ#rbTZLv+FGoAhQ zGBf(*b7L)g*C_1&pT^DusEM`f<6c0xfFO!ADTX4VlvEOmfOMotFCmlw2@nDaC4dNm z(tDRGy@(W%DjkuI6p<>uiiikOrGL5K{oa{7^L{h$JF_$U?CyW}oIN|U&u@3;oTGg6 zyg;TV!~to@LfdRQSSq`bs8)G=$rSz8`9+Yb&QYf-x6P^HNQN#OR&XeO02{#O49^e{q)y!_1Qw%P4mixDdEeqc#640i1?8OWwjHTdjkAd|-68rIQHF8_ zb9Kkky8bdj%+Xe11*q4DbO(uP&!qOtXJO%Xa(eY*rA$7#WMk{%}fLUU< zVt8QdYKeHhYy;m&=x|X}qvzW4oWX9=n48Ib8AcZWQP;y1o8NqhK8cIhDS;ePjQXeN z3|pkkOXGCSKk(E~$z1dpokWR@OsDnlL?&IBiHO=T@|ciorHJ?I!OL!xHrelVfA&SX zS6#j%eYD3KpArxe;YWvJsxY^y4;z?0xoi7WTNUpg!>mO+AUqNC^_7?HkCRADdgJcM`om}OX~D+B(OQ~`y-8K` z?h=CE3~c8lw|Ho$(rG5rdZv(i|13qGgEU7Z?`BSHUj|@CI@R@&OtK z$wN`SKCR44i+AX2pBfvZjKTF~v+HlRg6H34$~kcHOn;L*7a(3Zk}DB6z5A9WVtW1H zldF+^Ntz!@KoN@clRv3beUra3o-COqdS+E#o1+FVpmj4dKS1(ESz?PK%R{PV!%t$ov4^l8}HOK6;1Rf3eS&X4WP zdshg0V!jts^qi|$E-r55Y18&8-vx{5J4=jR;$?x2Rrvn)PM0?YJ>M$3Vkw*V6VkE=TXK`ntd1&k=Vw#P?&@_ji@;I8MJ84l}Sh;myQVy$hSV9e3bIsI<@ZJ~c>Q@F%G*i_z~WKVPzx(hVGksPt) zwZ6Nx1J;H_9x1wFtw`i!npOr_6M!dly4Vr>D=RyKGmJM3Mcjw=!4Zi96d za>m$_Wujm)7)T5ZzYEmBdU+CEF>XS4>HfYFj!00lB4GhSN>UII7y*Jnz+fm827!u# z#P5JWcgQ*|BIZ9y3|y_8ov|1IP{qp84NC{qF;F%UQ*n26w6-D;u&w|h1ACksfV}+e zj|jjB>*_`}4S7|o27~^K z@c|I11oXcJ`(`B4ZCc{G??m}~nJKmS8lFw}C zcjn8m9q-dKM{bbP7?d~M9rBY}jV=k?o`_DO%`-uNzzaeOt0HMTVYY#`g8C`8DjfY# zVQ%KBV{n7ExFkU1Lj=LeqAMn$-p)X?hll z_8QFL7nP_=!)#sw&a(x$#NH z(Z=15D^DH#<{8ox*;BnNwN)pmIKCXch`J-?(Mpsdq%;vHC;FAVLNbC;e1@u~K_?kb zx)TG%iZ0mMs28(TD-k&<36DBSV?)IWOpVFy$`OnKl>wOX3Kjk0J2OUyv*({^@$P0G z!K;VC-dj7~4v*rJIizh*vx|n*hBhYn&)2*8>`s?4X)(VElI6Qz=DdcXE*&wu#ZBfG zD=e!>F0U+0)&#^VxAXuAeJxY0r|KG&NJadI~C|~&boPXe|oU5x)-5Vs@RaJFQ z0+?}Cah*{C(;e6V9{o8->nafaZ7g#-qYdUl1q!rFcwZ2sI|zxZEb&ydu^N+5(@WlVq;`-jO5$9lrCB&2+?KJmD1+~hg7CcNibqK zn+;^0q<{YN=Lton%}7<^-qJ5;JbBoIhE^mQc;C0xY6AHLSInJ$ED2VuQmEqxnTy3fM2}nsB6+TKp;%!bM*e zZ#Kdp_MYcg=+u&CKYT-qI;O7eC-T-v<`hrRgRbl@1_?rZv`;>Jvg;QZbIqK)Q94gl zwP#!&$8b_?;R%?6@0^ZKK1gciCY61)JZ}_rE>1w{bh#lKF@RSzC7I=TzmZ_OCdFwM z`i(U8u_OXpQS=cjRVJ%R0PU`?BoBqOo}GO=bMbevvpT_utX=CTv!sW-15V3*kR{?qZ)x3RsrB)=fut zHJhL2*JFXm2*!rz0T$&FYO`w+DM6~-Gm9suvA2HN_)-`Tzj_1KJ0+| zQ+$`Uw}oJtA{hxXvQnHM5*XfBAP@eO@Cc2%uIM zig`r2ul~-W6kTZH|K;b;#kM&hgKck)*0aS$cT^$X=>E@O+A3D<@2?+E72d}^_{ekF zDI}}>v7N=zZ1VEE5LNF0h3$Nso5uQq6w3bD264i#D^2N7cOBZ8hu^k)rgPOVu&tK9 z>^2K4y??Rm0a-RaE&iRfD|~;RH{{LHeoUvk>{dL^qW^VlVs=ll4>BcJg4FKSE&YY5J_t@nFYocP>2boUK~rruio^Xo0=pu(xp^v6~E)$7JC-t?HnE&AIT z{Ot`rTZ5Uaf&DzfFmrHQ{h3nzdSl6p*LP)xs`&hw?#ub{cqbifdi76r3lZLB)9$1Q zf~|!1^snbT<|?h%uKn;W;x8r)ZA=!(2acpae9;{;uUdXxn1kZ}NJ(;lHFE4m#N@^` zxilCz?@Z`LRb6Sh@RLRkBx?Sf`)UB~??l6xj0?O`uX~9Qk=iI|?%oBP$-YvJIkbNs z+JA*10ZB|bqrc+a)rlT>&`ikY;H8_qPV88V9!eP0 zIyVj-%_<%qNE789b82K6c_Xazc->9wg|oBC*EIZiBkhrBT`P%@Z6Uq6NMGH0JzM+FNDI zYHPpen|C&pZDzMoQKpC@L-j3Avwzc@i5}LL4)~CO!9E6{KmY{DoDQgudx9m8=zzum6c_*nfXVyxh(rWhf`-ey|)fhW E9~*eb3IG5A literal 0 HcmV?d00001 From 35dbdeb9cc03d9f912cee00b2dccea4182c531cf Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Wed, 22 Feb 2017 11:42:29 -0500 Subject: [PATCH 10/16] add spring constant --- HW4/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/HW4/README.md b/HW4/README.md index 0b8a5f8..7f04a9a 100644 --- a/HW4/README.md +++ b/HW4/README.md @@ -21,7 +21,7 @@ heading `# Homework #4` in your `README.md` file PE_s=1/2\*K \*(DL)^2 - where DL = 0.5 - sqrt(0.5^2+(0.5-x_C)^2) + where DL = 0.5 - sqrt(0.5^2+(0.5-x_C)^2) and K=30 N/m. b. Use the `goldmin.m` function to solve for the minimum potential energy at xc when theta=0. *create an anonymous function with `@(x) collar_potential_energy(x,theta)` in From 46f626edf1d24a7dc9a189eb6c4ba024123f8242 Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Wed, 22 Feb 2017 22:01:53 -0500 Subject: [PATCH 11/16] added lecture 11 --- lecture_11/LU_naive.m | 27 + lecture_11/LU_pivot.m | 36 + lecture_11/lecture_11.aux | 28 + lecture_11/lecture_11.bbl | 0 lecture_11/lecture_11.blg | 48 + lecture_11/lecture_11.ipynb | 685 +++++++++++++++ lecture_11/lecture_11.log | 826 ++++++++++++++++++ lecture_11/lecture_11.out | 4 + lecture_11/lecture_11.pdf | Bin 0 -> 154124 bytes lecture_11/lecture_11.tex | 656 ++++++++++++++ .../lecture_11_files/lecture_11_6_0.pdf | Bin 0 -> 9079 bytes .../lecture_11_files/lecture_11_6_0.svg | 149 ++++ lecture_11/mass_springs.png | Bin 0 -> 5031 bytes lecture_11/mass_springs.svg | 214 +++++ lecture_11/nohup.out | 2 + lecture_11/octave-workspace | Bin 0 -> 178581 bytes 16 files changed, 2675 insertions(+) create mode 100644 lecture_11/LU_naive.m create mode 100644 lecture_11/LU_pivot.m create mode 100644 lecture_11/lecture_11.aux create mode 100644 lecture_11/lecture_11.bbl create mode 100644 lecture_11/lecture_11.blg create mode 100644 lecture_11/lecture_11.ipynb create mode 100644 lecture_11/lecture_11.log create mode 100644 lecture_11/lecture_11.out create mode 100644 lecture_11/lecture_11.pdf create mode 100644 lecture_11/lecture_11.tex create mode 100644 lecture_11/lecture_11_files/lecture_11_6_0.pdf create mode 100644 lecture_11/lecture_11_files/lecture_11_6_0.svg create mode 100644 lecture_11/mass_springs.png create mode 100644 lecture_11/mass_springs.svg create mode 100644 lecture_11/nohup.out create mode 100644 lecture_11/octave-workspace diff --git a/lecture_11/LU_naive.m b/lecture_11/LU_naive.m new file mode 100644 index 0000000..92efde6 --- /dev/null +++ b/lecture_11/LU_naive.m @@ -0,0 +1,27 @@ +function [L, U] = LU_naive(A) +% GaussNaive: naive Gauss elimination +% x = GaussNaive(A,b): Gauss elimination without pivoting. +% input: +% A = coefficient matrix +% y = right hand side vector +% output: +% x = solution vector +[m,n] = size(A); +if m~=n, error('Matrix A must be square'); end +nb = n; +L=diag(ones(n,1)); +U=A; +% forward elimination +for k = 1:n-1 + for i = k+1:n + fik = U(i,k)/U(k,k); + L(i,k)=fik; + U(i,k:nb) = U(i,k:nb)-fik*U(k,k:nb); + end +end +%% back substitution +%x = zeros(n,1); +%x(n) = Aug(n,nb)/Aug(n,n); +%for i = n-1:-1:1 +% x(i) = (Aug(i,nb)-Aug(i,i+1:n)*x(i+1:n))/Aug(i,i); +%end diff --git a/lecture_11/LU_pivot.m b/lecture_11/LU_pivot.m new file mode 100644 index 0000000..37abb26 --- /dev/null +++ b/lecture_11/LU_pivot.m @@ -0,0 +1,36 @@ +function [L,U,P] = LU_pivot(A) +% GaussPivot: Gauss elimination pivoting +% x = GaussPivot(A,b): Gauss elimination with pivoting. +% input: +% A = coefficient matrix +% b = right hand side vector +% output: +% x = solution vector +[m,n]=size(A); +if m~=n, error('Matrix A must be square'); end +nb = n; +L=diag(ones(n,1)); +U=A; +P=diag(ones(n,1)); +% forward elimination +for k = 1:n-1 + % partial pivoting + [big,i]=max(abs(U(k:n,k))); + ipr=i+k-1; + if ipr~=k + P([k,ipr],:)=P([ipr,k],:); % if the max is not the current index ipr, pivot count + %L([k,ipr],:)=L([ipr,k],:); + %U([k,ipr],:)=U([ipr,k],:); + end + for i = k+1:n + fik=U(i,k)/U(k,k); + L(i,k)=fik; + U(i,k:nb)=U(i,k:nb)-fik*U(k,k:nb); + end +end +% back substitution +%x=zeros(n,1); +%x(n)=Aug(n,nb)/Aug(n,n); +%for i = n-1:-1:1 +% x(i)=(Aug(i,nb)-Aug(i,i+1:n)*x(i+1:n))/Aug(i,i); +%end diff --git a/lecture_11/lecture_11.aux b/lecture_11/lecture_11.aux new file mode 100644 index 0000000..cf3c530 --- /dev/null +++ b/lecture_11/lecture_11.aux @@ -0,0 +1,28 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} +\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined +\global\let\oldcontentsline\contentsline +\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} +\global\let\oldnewlabel\newlabel +\gdef\newlabel#1#2{\newlabelxx{#1}#2} +\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} +\AtEndDocument{\ifx\hyper@anchor\@undefined +\let\contentsline\oldcontentsline +\let\newlabel\oldnewlabel +\fi} +\fi} +\global\let\hyper@last\relax +\gdef\HyperFirstAtBeginDocument#1{#1} +\providecommand\HyField@AuxAddToFields[1]{} +\providecommand\HyField@AuxAddToCoFields[2]{} +\providecommand \oddpage@label [2]{} +\@writefile{toc}{\contentsline {section}{\numberline {1}LU Decomposition}{1}{section.1}} +\newlabel{lu-decomposition}{{1}{1}{LU Decomposition}{section.1}{}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.0.1}efficient storage of matrices for solutions}{1}{subsubsection.1.0.1}} +\newlabel{efficient-storage-of-matrices-for-solutions}{{1.0.1}{1}{efficient storage of matrices for solutions}{subsubsection.1.0.1}{}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Pivoting for LU factorization}{2}{subsection.1.1}} +\newlabel{pivoting-for-lu-factorization}{{1.1}{2}{Pivoting for LU factorization}{subsection.1.1}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Springs-masses\relax }}{5}{figure.caption.1}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Cholesky Factorization}{6}{subsection.1.2}} +\newlabel{cholesky-factorization}{{1.2}{6}{Cholesky Factorization}{subsection.1.2}{}} diff --git a/lecture_11/lecture_11.bbl b/lecture_11/lecture_11.bbl new file mode 100644 index 0000000..e69de29 diff --git a/lecture_11/lecture_11.blg b/lecture_11/lecture_11.blg new file mode 100644 index 0000000..f6400af --- /dev/null +++ b/lecture_11/lecture_11.blg @@ -0,0 +1,48 @@ +This is BibTeX, Version 0.99d (TeX Live 2015/Debian) +Capacity: max_strings=35307, hash_size=35307, hash_prime=30011 +The top-level auxiliary file: lecture_11.aux +I found no \citation commands---while reading file lecture_11.aux +I found no \bibdata command---while reading file lecture_11.aux +I found no \bibstyle command---while reading file lecture_11.aux +You've used 0 entries, + 0 wiz_defined-function locations, + 83 strings with 494 characters, +and the built_in function-call counts, 0 in all, are: += -- 0 +> -- 0 +< -- 0 ++ -- 0 +- -- 0 +* -- 0 +:= -- 0 +add.period$ -- 0 +call.type$ -- 0 +change.case$ -- 0 +chr.to.int$ -- 0 +cite$ -- 0 +duplicate$ -- 0 +empty$ -- 0 +format.name$ -- 0 +if$ -- 0 +int.to.chr$ -- 0 +int.to.str$ -- 0 +missing$ -- 0 +newline$ -- 0 +num.names$ -- 0 +pop$ -- 0 +preamble$ -- 0 +purify$ -- 0 +quote$ -- 0 +skip$ -- 0 +stack$ -- 0 +substring$ -- 0 +swap$ -- 0 +text.length$ -- 0 +text.prefix$ -- 0 +top$ -- 0 +type$ -- 0 +warning$ -- 0 +while$ -- 0 +width$ -- 0 +write$ -- 0 +(There were 3 error messages) diff --git a/lecture_11/lecture_11.ipynb b/lecture_11/lecture_11.ipynb new file mode 100644 index 0000000..c290a47 --- /dev/null +++ b/lecture_11/lecture_11.ipynb @@ -0,0 +1,685 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%plot --format svg" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "setdefaults" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# LU Decomposition\n", + "### efficient storage of matrices for solutions\n", + "\n", + "Considering the same solution set:\n", + "\n", + "$y=Ax$\n", + "\n", + "Assume that we can perform Gauss elimination and achieve this formula:\n", + "\n", + "$Ux=d$ \n", + "\n", + "Where, $U$ is an upper triangular matrix that we derived from Gauss elimination and $d$ is the set of dependent variables after Gauss elimination. \n", + "\n", + "Assume there is a lower triangular matrix, $L$, with ones on the diagonal and same dimensions of $U$ and the following is true:\n", + "\n", + "$L(Ux-d)=Ax-y=0$\n", + "\n", + "Now, $Ax=LUx$, so $A=LU$, and $y=Ld$.\n", + "\n", + "$2x_{1}+x_{2}=1$\n", + "\n", + "$x_{1}+3x_{2}=1$\n", + "\n", + "\n", + "$\\left[ \\begin{array}{cc}\n", + "2 & 1 \\\\\n", + "1 & 3 \\end{array} \\right]\n", + "\\left[\\begin{array}{c} \n", + "x_{1} \\\\ \n", + "x_{2} \\end{array}\\right]=\n", + "\\left[\\begin{array}{c} \n", + "1 \\\\\n", + "1\\end{array}\\right]$\n", + "\n", + "f21=0.5\n", + "\n", + "A(2,1)=1-1 = 0 \n", + "\n", + "A(2,2)=3-0.5=2.5\n", + "\n", + "y(2)=1-0.5=0.5\n", + "\n", + "$L(Ux-d)=\n", + "\\left[ \\begin{array}{cc}\n", + "1 & 0 \\\\\n", + "0.5 & 1 \\end{array} \\right]\n", + "\\left(\\left[ \\begin{array}{cc}\n", + "2 & 1 \\\\\n", + "0 & 2.5 \\end{array} \\right]\n", + "\\left[\\begin{array}{c} \n", + "x_{1} \\\\ \n", + "x_{2} \\end{array}\\right]-\n", + "\\left[\\begin{array}{c} \n", + "1 \\\\\n", + "0.5\\end{array}\\right]\\right)=0$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A =\n", + "\n", + " 2 1\n", + " 1 3\n", + "\n", + "L =\n", + "\n", + " 1.00000 0.00000\n", + " 0.50000 1.00000\n", + "\n", + "U =\n", + "\n", + " 2.00000 1.00000\n", + " 0.00000 2.50000\n", + "\n", + "ans =\n", + "\n", + " 2 1\n", + " 1 3\n", + "\n", + "d =\n", + "\n", + " 1.00000\n", + " 0.50000\n", + "\n", + "y =\n", + "\n", + " 1\n", + " 1\n", + "\n" + ] + } + ], + "source": [ + "A=[2,1;1,3]\n", + "L=[1,0;0.5,1]\n", + "U=[2,1;0,2.5]\n", + "L*U\n", + "\n", + "d=[1;0.5]\n", + "y=L*d" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Pivoting for LU factorization\n", + "\n", + "LU factorization uses the same method as Gauss elimination so it is also necessary to perform partial pivoting when creating the lower and upper triangular matrices. \n", + "\n", + "Matlab and Octave use pivoting in the command \n", + "\n", + "`[L,U,P]=lu(A)`\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "'lu' is a built-in function from the file libinterp/corefcn/lu.cc\n", + "\n", + " -- Built-in Function: [L, U] = lu (A)\n", + " -- Built-in Function: [L, U, P] = lu (A)\n", + " -- Built-in Function: [L, U, P, Q] = lu (S)\n", + " -- Built-in Function: [L, U, P, Q, R] = lu (S)\n", + " -- Built-in Function: [...] = lu (S, THRES)\n", + " -- Built-in Function: Y = lu (...)\n", + " -- Built-in Function: [...] = lu (..., \"vector\")\n", + " Compute the LU decomposition of A.\n", + "\n", + " If A is full subroutines from LAPACK are used and if A is sparse\n", + " then UMFPACK is used.\n", + "\n", + " The result is returned in a permuted form, according to the\n", + " optional return value P. For example, given the matrix 'a = [1, 2;\n", + " 3, 4]',\n", + "\n", + " [l, u, p] = lu (A)\n", + "\n", + " returns\n", + "\n", + " l =\n", + "\n", + " 1.00000 0.00000\n", + " 0.33333 1.00000\n", + "\n", + " u =\n", + "\n", + " 3.00000 4.00000\n", + " 0.00000 0.66667\n", + "\n", + " p =\n", + "\n", + " 0 1\n", + " 1 0\n", + "\n", + " The matrix is not required to be square.\n", + "\n", + " When called with two or three output arguments and a spare input\n", + " matrix, 'lu' does not attempt to perform sparsity preserving column\n", + " permutations. Called with a fourth output argument, the sparsity\n", + " preserving column transformation Q is returned, such that 'P * A *\n", + " Q = L * U'.\n", + "\n", + " Called with a fifth output argument and a sparse input matrix, 'lu'\n", + " attempts to use a scaling factor R on the input matrix such that 'P\n", + " * (R \\ A) * Q = L * U'. This typically leads to a sparser and more\n", + " stable factorization.\n", + "\n", + " An additional input argument THRES, that defines the pivoting\n", + " threshold can be given. THRES can be a scalar, in which case it\n", + " defines the UMFPACK pivoting tolerance for both symmetric and\n", + " unsymmetric cases. If THRES is a 2-element vector, then the first\n", + " element defines the pivoting tolerance for the unsymmetric UMFPACK\n", + " pivoting strategy and the second for the symmetric strategy. By\n", + " default, the values defined by 'spparms' are used ([0.1, 0.001]).\n", + "\n", + " Given the string argument \"vector\", 'lu' returns the values of P\n", + " and Q as vector values, such that for full matrix, 'A (P,:) = L *\n", + " U', and 'R(P,:) * A (:, Q) = L * U'.\n", + "\n", + " With two output arguments, returns the permuted forms of the upper\n", + " and lower triangular matrices, such that 'A = L * U'. With one\n", + " output argument Y, then the matrix returned by the LAPACK routines\n", + " is returned. If the input matrix is sparse then the matrix L is\n", + " embedded into U to give a return value similar to the full case.\n", + " For both full and sparse matrices, 'lu' loses the permutation\n", + " information.\n", + "\n", + " See also: luupdate, ilu, chol, hess, qr, qz, schur, svd.\n", + "\n", + "Additional help for built-in functions and operators is\n", + "available in the online version of the manual. Use the command\n", + "'doc ' to search the manual index.\n", + "\n", + "Help and information about Octave is also available on the WWW\n", + "at http://www.octave.org and via the help@octave.org\n", + "mailing list.\n" + ] + } + ], + "source": [ + "help lu" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "Gnuplot\n", + "Produced by GNUPLOT 5.0 patchlevel 3 \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\t\n", + "\t\t0\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t5e-05\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.0001\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.00015\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.0002\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.00025\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.0003\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t20\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t40\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t60\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t80\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t100\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\tLU decomp\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\tLU decomp\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\tOctave \\\\\n", + "\n", + "\t\n", + "\t\tOctave \\\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "% time LU solution vs backslash\n", + "t_lu=zeros(100,1);\n", + "t_bs=zeros(100,1);\n", + "for N=1:100\n", + " A=rand(N,N);\n", + " y=rand(N,1);\n", + " [L,U,P]=lu(A);\n", + "\n", + " tic; d=L\\y; x=U\\d; t_lu(N)=toc;\n", + "\n", + " tic; x=A\\y; t_bs(N)=toc;\n", + "end\n", + "plot([1:100],t_lu,[1:100],t_bs) \n", + "legend('LU decomp','Octave \\\\')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Consider the problem again from the intro to Linear Algebra, 4 masses are connected in series to 4 springs with K=10 N/m. What are the final positions of the masses? \n", + "\n", + "![Springs-masses](../lecture_09/mass_springs.svg)\n", + "\n", + "The masses haves the following amounts, 1, 2, 3, and 4 kg for masses 1-4. Using a FBD for each mass:\n", + "\n", + "$m_{1}g+k(x_{2}-x_{1})-kx_{1}=0$\n", + "\n", + "$m_{2}g+k(x_{3}-x_{2})-k(x_{2}-x_{1})=0$\n", + "\n", + "$m_{3}g+k(x_{4}-x_{3})-k(x_{3}-x_{2})=0$\n", + "\n", + "$m_{4}g-k(x_{4}-x_{3})=0$\n", + "\n", + "in matrix form:\n", + "\n", + "$\\left[ \\begin{array}{cccc}\n", + "2k & -k & 0 & 0 \\\\\n", + "-k & 2k & -k & 0 \\\\\n", + "0 & -k & 2k & -k \\\\\n", + "0 & 0 & -k & k \\end{array} \\right]\n", + "\\left[ \\begin{array}{c}\n", + "x_{1} \\\\\n", + "x_{2} \\\\\n", + "x_{3} \\\\\n", + "x_{4} \\end{array} \\right]=\n", + "\\left[ \\begin{array}{c}\n", + "m_{1}g \\\\\n", + "m_{2}g \\\\\n", + "m_{3}g \\\\\n", + "m_{4}g \\end{array} \\right]$" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "K =\n", + "\n", + " 20 -10 0 0\n", + " -10 20 -10 0\n", + " 0 -10 20 -10\n", + " 0 0 -10 10\n", + "\n", + "y =\n", + "\n", + " 9.8100\n", + " 19.6200\n", + " 29.4300\n", + " 39.2400\n", + "\n" + ] + } + ], + "source": [ + "k=10; % N/m\n", + "m1=1; % kg\n", + "m2=2;\n", + "m3=3;\n", + "m4=4;\n", + "g=9.81; % m/s^2\n", + "K=[2*k -k 0 0; -k 2*k -k 0; 0 -k 2*k -k; 0 0 -k k]\n", + "y=[m1*g;m2*g;m3*g;m4*g]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This matrix, K, is symmetric. \n", + "\n", + "`K(i,j)==K(j,i)`\n", + "\n", + "Now we can use,\n", + "\n", + "## Cholesky Factorization\n", + "\n", + "We can decompose the matrix, K into two matrices, $U$ and $U^{T}$, where\n", + "\n", + "$K=U^{T}U$\n", + "\n", + "each of the components of U can be calculated with the following equations:\n", + "\n", + "$u_{ii}=\\sqrt{a_{ii}-\\sum_{k=1}^{i-1}u_{ki}^{2}}$\n", + "\n", + "$u_{ij}=\\frac{a_{ij}-\\sum_{k=1}^{i-1}u_{ki}u_{kj}}{u_{ii}}$\n", + "\n", + "so for K" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "K =\n", + "\n", + " 20 -10 0 0\n", + " -10 20 -10 0\n", + " 0 -10 20 -10\n", + " 0 0 -10 10\n", + "\n" + ] + } + ], + "source": [ + "K" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "u11 = 4.4721\n", + "u12 = -2.2361\n", + "u13 = 0\n", + "u14 = 0\n", + "u22 = 3.8730\n", + "u23 = -2.5820\n", + "u24 = 0\n", + "u33 = 3.6515\n", + "u34 = -2.7386\n", + "u44 = 1.5811\n", + "U =\n", + "\n", + " 4.47214 -2.23607 0.00000 0.00000\n", + " 0.00000 3.87298 -2.58199 0.00000\n", + " 0.00000 0.00000 3.65148 -2.73861\n", + " 0.00000 0.00000 0.00000 1.58114\n", + "\n" + ] + } + ], + "source": [ + "u11=sqrt(K(1,1))\n", + "u12=(K(1,2))/u11\n", + "u13=(K(1,3))/u11\n", + "u14=(K(1,4))/u11\n", + "u22=sqrt(K(2,2)-u12^2)\n", + "u23=(K(2,3)-u12*u13)/u22\n", + "u24=(K(2,4)-u12*u14)/u22\n", + "u33=sqrt(K(3,3)-u13^2-u23^2)\n", + "u34=(K(3,4)-u13*u14-u23*u24)/u33\n", + "u44=sqrt(K(4,4)-u14^2-u24^2-u34^2)\n", + "U=[u11,u12,u13,u14;0,u22,u23,u24;0,0,u33,u34;0,0,0,u44]" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 20.00000 -10.00000 0.00000 0.00000\n", + " -10.00000 20.00000 -10.00000 0.00000\n", + " 0.00000 -10.00000 20.00000 -10.00000\n", + " 0.00000 0.00000 -10.00000 10.00000\n", + "\n" + ] + } + ], + "source": [ + "U'*U" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "average time spent for Cholesky factored solution = 1.623154e-05+/-1.166726e-05\n", + "average time spent for backslash solution = 1.675844e-05+/-1.187234e-05\n" + ] + } + ], + "source": [ + "% time solution for Cholesky vs backslash\n", + "t_chol=zeros(1000,1);\n", + "t_bs=zeros(1000,1);\n", + "for i=1:1000\n", + " tic; d=U'*y; x=U\\d; t_chol(i)=toc;\n", + " tic; x=K\\y; t_bs(i)=toc;\n", + "end\n", + "fprintf('average time spent for Cholesky factored solution = %e+/-%e',mean(t_chol),std(t_chol))\n", + "\n", + "fprintf('average time spent for backslash solution = %e+/-%e',mean(t_bs),std(t_bs))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Octave", + "language": "octave", + "name": "octave" + }, + "language_info": { + "file_extension": ".m", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "octave", + "version": "0.19.14" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/lecture_11/lecture_11.log b/lecture_11/lecture_11.log new file mode 100644 index 0000000..10423a7 --- /dev/null +++ b/lecture_11/lecture_11.log @@ -0,0 +1,826 @@ +This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian) (preloaded format=pdflatex 2017.1.11) 22 FEB 2017 22:01 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**lecture_11.tex +(./lecture_11.tex +LaTeX2e <2016/02/01> +Babel <3.9q> and hyphenation patterns for 81 language(s) loaded. +(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls +Document Class: article 2014/09/29 v1.4h Standard LaTeX document class +(/usr/share/texlive/texmf-dist/tex/latex/base/size11.clo +File: size11.clo 2014/09/29 v1.4h Standard LaTeX file (size option) +) +\c@part=\count79 +\c@section=\count80 +\c@subsection=\count81 +\c@subsubsection=\count82 +\c@paragraph=\count83 +\c@subparagraph=\count84 +\c@figure=\count85 +\c@table=\count86 +\abovecaptionskip=\skip41 +\belowcaptionskip=\skip42 +\bibindent=\dimen102 +) +(/usr/share/texlive/texmf-dist/tex/latex/base/fontenc.sty +Package: fontenc 2005/09/27 v1.99g Standard LaTeX package + +(/usr/share/texlive/texmf-dist/tex/latex/base/t1enc.def +File: t1enc.def 2005/09/27 v1.99g Standard LaTeX file +LaTeX Font Info: Redeclaring font encoding T1 on input line 48. +)) +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/mathpazo.sty +Package: mathpazo 2005/04/12 PSNFSS-v9.2a Palatino w/ Pazo Math (D.Puga, WaS) +\symupright=\mathgroup4 +) +(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty +Package: graphicx 2014/10/28 v1.0g Enhanced LaTeX Graphics (DPC,SPQR) + +(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty +Package: keyval 2014/10/28 v1.15 key=value parser (DPC) +\KV@toks@=\toks14 +) +(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty +Package: graphics 2016/01/03 v1.0q Standard LaTeX Graphics (DPC,SPQR) + +(/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty +Package: trig 2016/01/03 v1.10 sin cos tan (DPC) +) +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/graphics.cfg +File: graphics.cfg 2010/04/23 v1.9 graphics configuration of TeX Live +) +Package graphics Info: Driver file: pdftex.def on input line 95. + +(/usr/share/texlive/texmf-dist/tex/latex/pdftex-def/pdftex.def +File: pdftex.def 2011/05/27 v0.06d Graphics/color for pdfTeX + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/infwarerr.sty +Package: infwarerr 2010/04/08 v1.3 Providing info/warning/error messages (HO) +) +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ltxcmds.sty +Package: ltxcmds 2011/11/09 v1.22 LaTeX kernel commands for general use (HO) +) +\Gread@gobject=\count87 +)) +\Gin@req@height=\dimen103 +\Gin@req@width=\dimen104 +) +(/usr/share/texlive/texmf-dist/tex/latex/caption/caption.sty +Package: caption 2016/02/21 v3.3-144 Customizing captions (AR) + +(/usr/share/texlive/texmf-dist/tex/latex/caption/caption3.sty +Package: caption3 2016/02/04 v1.7-139 caption3 kernel (AR) +Package caption3 Info: TeX engine: e-TeX on input line 67. +\captionmargin=\dimen105 +\captionmargin@=\dimen106 +\captionwidth=\dimen107 +\caption@tempdima=\dimen108 +\caption@indent=\dimen109 +\caption@parindent=\dimen110 +\caption@hangindent=\dimen111 +) +\c@ContinuedFloat=\count88 +) +(/usr/share/texlive/texmf-dist/tex/latex/adjustbox/adjustbox.sty +Package: adjustbox 2012/05/21 v1.0 Adjusting TeX boxes (trim, clip, ...) + +(/usr/share/texlive/texmf-dist/tex/latex/xkeyval/xkeyval.sty +Package: xkeyval 2014/12/03 v2.7a package option processing (HA) + +(/usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkeyval.tex +(/usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkvutils.tex +\XKV@toks=\toks15 +\XKV@tempa@toks=\toks16 +) +\XKV@depth=\count89 +File: xkeyval.tex 2014/12/03 v2.7a key=value parser (HA) +)) +(/usr/share/texlive/texmf-dist/tex/latex/adjustbox/adjcalc.sty +Package: adjcalc 2012/05/16 v1.1 Provides advanced setlength with multiple back +-ends (calc, etex, pgfmath) +) +(/usr/share/texlive/texmf-dist/tex/latex/adjustbox/trimclip.sty +Package: trimclip 2012/05/16 v1.0 Trim and clip general TeX material + +(/usr/share/texlive/texmf-dist/tex/latex/collectbox/collectbox.sty +Package: collectbox 2012/05/17 v0.4b Collect macro arguments as boxes +\collectedbox=\box26 +) +\tc@llx=\dimen112 +\tc@lly=\dimen113 +\tc@urx=\dimen114 +\tc@ury=\dimen115 +Package trimclip Info: Using driver 'tc-pdftex.def'. + +(/usr/share/texlive/texmf-dist/tex/latex/adjustbox/tc-pdftex.def +File: tc-pdftex.def 2012/05/13 v1.0 Clipping driver for pdftex +)) +\adjbox@Width=\dimen116 +\adjbox@Height=\dimen117 +\adjbox@Depth=\dimen118 +\adjbox@Totalheight=\dimen119 + +(/usr/share/texlive/texmf-dist/tex/latex/ifoddpage/ifoddpage.sty +Package: ifoddpage 2011/09/13 v1.0 Conditionals for odd/even page detection +\c@checkoddpage=\count90 +) +(/usr/share/texlive/texmf-dist/tex/latex/varwidth/varwidth.sty +Package: varwidth 2009/03/30 ver 0.92; Variable-width minipages +\@vwid@box=\box27 +\sift@deathcycles=\count91 +\@vwid@loff=\dimen120 +\@vwid@roff=\dimen121 +)) +(/usr/share/texlive/texmf-dist/tex/latex/xcolor/xcolor.sty +Package: xcolor 2007/01/21 v2.11 LaTeX color extensions (UK) + +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/color.cfg +File: color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive +) +Package xcolor Info: Driver file: pdftex.def on input line 225. +Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1337. +Package xcolor Info: Model `hsb' substituted by `rgb' on input line 1341. +Package xcolor Info: Model `RGB' extended on input line 1353. +Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1355. +Package xcolor Info: Model `Hsb' substituted by `hsb' on input line 1356. +Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1357. +Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1358. +Package xcolor Info: Model `Gray' substituted by `gray' on input line 1359. +Package xcolor Info: Model `wave' substituted by `hsb' on input line 1360. +) +(/usr/share/texlive/texmf-dist/tex/latex/tools/enumerate.sty +Package: enumerate 2015/07/23 v3.00 enumerate extensions (DPC) +\@enLab=\toks17 +) +(/usr/share/texlive/texmf-dist/tex/latex/geometry/geometry.sty +Package: geometry 2010/09/12 v5.6 Page Geometry + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifpdf.sty +Package: ifpdf 2011/01/30 v2.3 Provides the ifpdf switch (HO) +Package ifpdf Info: pdfTeX in PDF mode is detected. +) +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifvtex.sty +Package: ifvtex 2010/03/01 v1.5 Detect VTeX and its facilities (HO) +Package ifvtex Info: VTeX not detected. +) +(/usr/share/texlive/texmf-dist/tex/generic/ifxetex/ifxetex.sty +Package: ifxetex 2010/09/12 v0.6 Provides ifxetex conditional +) +\Gm@cnth=\count92 +\Gm@cntv=\count93 +\c@Gm@tempcnt=\count94 +\Gm@bindingoffset=\dimen122 +\Gm@wd@mp=\dimen123 +\Gm@odd@mp=\dimen124 +\Gm@even@mp=\dimen125 +\Gm@layoutwidth=\dimen126 +\Gm@layoutheight=\dimen127 +\Gm@layouthoffset=\dimen128 +\Gm@layoutvoffset=\dimen129 +\Gm@dimlist=\toks18 +) +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty +Package: amsmath 2016/03/03 v2.15a AMS math features +\@mathmargin=\skip43 + +For additional information on amsmath, use the `?' option. +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty +Package: amstext 2000/06/29 v2.01 AMS text + +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty +File: amsgen.sty 1999/11/30 v2.0 generic functions +\@emptytoks=\toks19 +\ex@=\dimen130 +)) +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty +Package: amsbsy 1999/11/29 v1.2d Bold Symbols +\pmbraise@=\dimen131 +) +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty +Package: amsopn 1999/12/14 v2.01 operator names +) +\inf@bad=\count95 +LaTeX Info: Redefining \frac on input line 199. +\uproot@=\count96 +\leftroot@=\count97 +LaTeX Info: Redefining \overline on input line 297. +\classnum@=\count98 +\DOTSCASE@=\count99 +LaTeX Info: Redefining \ldots on input line 394. +LaTeX Info: Redefining \dots on input line 397. +LaTeX Info: Redefining \cdots on input line 518. +\Mathstrutbox@=\box28 +\strutbox@=\box29 +\big@size=\dimen132 +LaTeX Font Info: Redeclaring font encoding OML on input line 630. +LaTeX Font Info: Redeclaring font encoding OMS on input line 631. +\macc@depth=\count100 +\c@MaxMatrixCols=\count101 +\dotsspace@=\muskip10 +\c@parentequation=\count102 +\dspbrk@lvl=\count103 +\tag@help=\toks20 +\row@=\count104 +\column@=\count105 +\maxfields@=\count106 +\andhelp@=\toks21 +\eqnshift@=\dimen133 +\alignsep@=\dimen134 +\tagshift@=\dimen135 +\tagwidth@=\dimen136 +\totwidth@=\dimen137 +\lineht@=\dimen138 +\@envbody=\toks22 +\multlinegap=\skip44 +\multlinetaggap=\skip45 +\mathdisplay@stack=\toks23 +LaTeX Info: Redefining \[ on input line 2735. +LaTeX Info: Redefining \] on input line 2736. +) +(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +Package: amssymb 2013/01/14 v3.01 AMS font symbols + +(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty +Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support +\symAMSa=\mathgroup5 +\symAMSb=\mathgroup6 +LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' +(Font) U/euf/m/n --> U/euf/b/n on input line 106. +)) +(/usr/share/texlive/texmf-dist/tex/latex/base/textcomp.sty +Package: textcomp 2005/09/27 v1.99g Standard LaTeX package +Package textcomp Info: Sub-encoding information: +(textcomp) 5 = only ISO-Adobe without \textcurrency +(textcomp) 4 = 5 + \texteuro +(textcomp) 3 = 4 + \textohm +(textcomp) 2 = 3 + \textestimated + \textcurrency +(textcomp) 1 = TS1 - \textcircled - \t +(textcomp) 0 = TS1 (full) +(textcomp) Font families with sub-encoding setting implement +(textcomp) only a restricted character set as indicated. +(textcomp) Family '?' is the default used for unknown fonts. +(textcomp) See the documentation for details. +Package textcomp Info: Setting ? sub-encoding to TS1/1 on input line 79. + +(/usr/share/texlive/texmf-dist/tex/latex/base/ts1enc.def +File: ts1enc.def 2001/06/05 v3.0e (jk/car/fm) Standard LaTeX file +) +LaTeX Info: Redefining \oldstylenums on input line 334. +Package textcomp Info: Setting cmr sub-encoding to TS1/0 on input line 349. +Package textcomp Info: Setting cmss sub-encoding to TS1/0 on input line 350. +Package textcomp Info: Setting cmtt sub-encoding to TS1/0 on input line 351. +Package textcomp Info: Setting cmvtt sub-encoding to TS1/0 on input line 352. +Package textcomp Info: Setting cmbr sub-encoding to TS1/0 on input line 353. +Package textcomp Info: Setting cmtl sub-encoding to TS1/0 on input line 354. +Package textcomp Info: Setting ccr sub-encoding to TS1/0 on input line 355. +Package textcomp Info: Setting ptm sub-encoding to TS1/4 on input line 356. +Package textcomp Info: Setting pcr sub-encoding to TS1/4 on input line 357. +Package textcomp Info: Setting phv sub-encoding to TS1/4 on input line 358. +Package textcomp Info: Setting ppl sub-encoding to TS1/3 on input line 359. +Package textcomp Info: Setting pag sub-encoding to TS1/4 on input line 360. +Package textcomp Info: Setting pbk sub-encoding to TS1/4 on input line 361. +Package textcomp Info: Setting pnc sub-encoding to TS1/4 on input line 362. +Package textcomp Info: Setting pzc sub-encoding to TS1/4 on input line 363. +Package textcomp Info: Setting bch sub-encoding to TS1/4 on input line 364. +Package textcomp Info: Setting put sub-encoding to TS1/5 on input line 365. +Package textcomp Info: Setting uag sub-encoding to TS1/5 on input line 366. +Package textcomp Info: Setting ugq sub-encoding to TS1/5 on input line 367. +Package textcomp Info: Setting ul8 sub-encoding to TS1/4 on input line 368. +Package textcomp Info: Setting ul9 sub-encoding to TS1/4 on input line 369. +Package textcomp Info: Setting augie sub-encoding to TS1/5 on input line 370. +Package textcomp Info: Setting dayrom sub-encoding to TS1/3 on input line 371. +Package textcomp Info: Setting dayroms sub-encoding to TS1/3 on input line 372. + +Package textcomp Info: Setting pxr sub-encoding to TS1/0 on input line 373. +Package textcomp Info: Setting pxss sub-encoding to TS1/0 on input line 374. +Package textcomp Info: Setting pxtt sub-encoding to TS1/0 on input line 375. +Package textcomp Info: Setting txr sub-encoding to TS1/0 on input line 376. +Package textcomp Info: Setting txss sub-encoding to TS1/0 on input line 377. +Package textcomp Info: Setting txtt sub-encoding to TS1/0 on input line 378. +Package textcomp Info: Setting lmr sub-encoding to TS1/0 on input line 379. +Package textcomp Info: Setting lmdh sub-encoding to TS1/0 on input line 380. +Package textcomp Info: Setting lmss sub-encoding to TS1/0 on input line 381. +Package textcomp Info: Setting lmssq sub-encoding to TS1/0 on input line 382. +Package textcomp Info: Setting lmvtt sub-encoding to TS1/0 on input line 383. +Package textcomp Info: Setting lmtt sub-encoding to TS1/0 on input line 384. +Package textcomp Info: Setting qhv sub-encoding to TS1/0 on input line 385. +Package textcomp Info: Setting qag sub-encoding to TS1/0 on input line 386. +Package textcomp Info: Setting qbk sub-encoding to TS1/0 on input line 387. +Package textcomp Info: Setting qcr sub-encoding to TS1/0 on input line 388. +Package textcomp Info: Setting qcs sub-encoding to TS1/0 on input line 389. +Package textcomp Info: Setting qpl sub-encoding to TS1/0 on input line 390. +Package textcomp Info: Setting qtm sub-encoding to TS1/0 on input line 391. +Package textcomp Info: Setting qzc sub-encoding to TS1/0 on input line 392. +Package textcomp Info: Setting qhvc sub-encoding to TS1/0 on input line 393. +Package textcomp Info: Setting futs sub-encoding to TS1/4 on input line 394. +Package textcomp Info: Setting futx sub-encoding to TS1/4 on input line 395. +Package textcomp Info: Setting futj sub-encoding to TS1/4 on input line 396. +Package textcomp Info: Setting hlh sub-encoding to TS1/3 on input line 397. +Package textcomp Info: Setting hls sub-encoding to TS1/3 on input line 398. +Package textcomp Info: Setting hlst sub-encoding to TS1/3 on input line 399. +Package textcomp Info: Setting hlct sub-encoding to TS1/5 on input line 400. +Package textcomp Info: Setting hlx sub-encoding to TS1/5 on input line 401. +Package textcomp Info: Setting hlce sub-encoding to TS1/5 on input line 402. +Package textcomp Info: Setting hlcn sub-encoding to TS1/5 on input line 403. +Package textcomp Info: Setting hlcw sub-encoding to TS1/5 on input line 404. +Package textcomp Info: Setting hlcf sub-encoding to TS1/5 on input line 405. +Package textcomp Info: Setting pplx sub-encoding to TS1/3 on input line 406. +Package textcomp Info: Setting pplj sub-encoding to TS1/3 on input line 407. +Package textcomp Info: Setting ptmx sub-encoding to TS1/4 on input line 408. +Package textcomp Info: Setting ptmj sub-encoding to TS1/4 on input line 409. +) +(/usr/share/texlive/texmf-dist/tex/latex/upquote/upquote.sty +Package: upquote 2012/04/19 v1.3 upright-quote and grave-accent glyphs in verba +tim +) +(/usr/share/texlive/texmf-dist/tex/latex/eurosym/eurosym.sty +Package: eurosym 1998/08/06 v1.1 European currency symbol ``Euro'' +\@eurobox=\box30 +) +(/usr/share/texlive/texmf-dist/tex/latex/ucs/ucs.sty +Package: ucs 2013/05/11 v2.2 UCS: Unicode input support + +(/usr/share/texlive/texmf-dist/tex/latex/ucs/data/uni-global.def +File: uni-global.def 2013/05/13 UCS: Unicode global data +) +\uc@secondtry=\count107 +\uc@combtoks=\toks24 +\uc@combtoksb=\toks25 +\uc@temptokena=\toks26 +) +(/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty +Package: inputenc 2015/03/17 v1.2c Input encoding file +\inpenc@prehook=\toks27 +\inpenc@posthook=\toks28 + +(/usr/share/texlive/texmf-dist/tex/latex/ucs/utf8x.def +File: utf8x.def 2004/10/17 UCS: Input encoding UTF-8 +)) +(/usr/share/texlive/texmf-dist/tex/latex/fancyvrb/fancyvrb.sty +Package: fancyvrb 2008/02/07 + +Style option: `fancyvrb' v2.7a, with DG/SPQR fixes, and firstline=lastline fix +<2008/02/07> (tvz) +\FV@CodeLineNo=\count108 +\FV@InFile=\read1 +\FV@TabBox=\box31 +\c@FancyVerbLine=\count109 +\FV@StepNumber=\count110 +\FV@OutFile=\write3 +) +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grffile.sty +Package: grffile 2012/04/05 v1.16 Extended file name support for graphics (HO) + +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/kvoptions.sty +Package: kvoptions 2011/06/30 v3.11 Key value format for package options (HO) + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/kvsetkeys.sty +Package: kvsetkeys 2012/04/25 v1.16 Key value parser (HO) + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/etexcmds.sty +Package: etexcmds 2011/02/16 v1.5 Avoid name clashes with e-TeX commands (HO) + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifluatex.sty +Package: ifluatex 2010/03/01 v1.3 Provides the ifluatex switch (HO) +Package ifluatex Info: LuaTeX not detected. +) +Package etexcmds Info: Could not find \expanded. +(etexcmds) That can mean that you are not using pdfTeX 1.50 or +(etexcmds) that some package has redefined \expanded. +(etexcmds) In the latter case, load this package earlier. +))) +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/pdftexcmds.sty +Package: pdftexcmds 2011/11/29 v0.20 Utility functions of pdfTeX for LuaTeX (HO +) +Package pdftexcmds Info: LuaTeX not detected. +Package pdftexcmds Info: \pdf@primitive is available. +Package pdftexcmds Info: \pdf@ifprimitive is available. +Package pdftexcmds Info: \pdfdraftmode found. +) +Package grffile Info: Option `multidot' is set to `true'. +Package grffile Info: Option `extendedchars' is set to `false'. +Package grffile Info: Option `space' is set to `true'. +Package grffile Info: \Gin@ii of package `graphicx' fixed on input line 486. +) +(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty +Package: hyperref 2012/11/06 v6.83m Hypertext links for LaTeX + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty +Package: hobsub-hyperref 2012/05/28 v1.13 Bundle oberdiek, subset hyperref (HO) + + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty +Package: hobsub-generic 2012/05/28 v1.13 Bundle oberdiek, subset generic (HO) +Package: hobsub 2012/05/28 v1.13 Construct package bundles (HO) +Package hobsub Info: Skipping package `infwarerr' (already loaded). +Package hobsub Info: Skipping package `ltxcmds' (already loaded). +Package hobsub Info: Skipping package `ifluatex' (already loaded). +Package hobsub Info: Skipping package `ifvtex' (already loaded). +Package: intcalc 2007/09/27 v1.1 Expandable calculations with integers (HO) +Package hobsub Info: Skipping package `ifpdf' (already loaded). +Package hobsub Info: Skipping package `etexcmds' (already loaded). +Package hobsub Info: Skipping package `kvsetkeys' (already loaded). +Package: kvdefinekeys 2011/04/07 v1.3 Define keys (HO) +Package hobsub Info: Skipping package `pdftexcmds' (already loaded). +Package: pdfescape 2011/11/25 v1.13 Implements pdfTeX's escape features (HO) +Package: bigintcalc 2012/04/08 v1.3 Expandable calculations on big integers (HO +) +Package: bitset 2011/01/30 v1.1 Handle bit-vector datatype (HO) +Package: uniquecounter 2011/01/30 v1.2 Provide unlimited unique counter (HO) +) +Package hobsub Info: Skipping package `hobsub' (already loaded). +Package: letltxmacro 2010/09/02 v1.4 Let assignment for LaTeX macros (HO) +Package: hopatch 2012/05/28 v1.2 Wrapper for package hooks (HO) +Package: xcolor-patch 2011/01/30 xcolor patch +Package: atveryend 2011/06/30 v1.8 Hooks at the very end of document (HO) +Package atveryend Info: \enddocument detected (standard20110627). +Package: atbegshi 2011/10/05 v1.16 At begin shipout hook (HO) +Package: refcount 2011/10/16 v3.4 Data extraction from label references (HO) +Package: hycolor 2011/01/30 v1.7 Color options for hyperref/bookmark (HO) +) +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/auxhook.sty +Package: auxhook 2011/03/04 v1.3 Hooks for auxiliary files (HO) +) +\@linkdim=\dimen139 +\Hy@linkcounter=\count111 +\Hy@pagecounter=\count112 + +(/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def +File: pd1enc.def 2012/11/06 v6.83m Hyperref: PDFDocEncoding definition (HO) +) +\Hy@SavedSpaceFactor=\count113 + +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/hyperref.cfg +File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive +) +Package hyperref Info: Hyper figures OFF on input line 4443. +Package hyperref Info: Link nesting OFF on input line 4448. +Package hyperref Info: Hyper index ON on input line 4451. +Package hyperref Info: Plain pages OFF on input line 4458. +Package hyperref Info: Backreferencing OFF on input line 4463. +Package hyperref Info: Implicit mode ON; LaTeX internals redefined. +Package hyperref Info: Bookmarks ON on input line 4688. +\c@Hy@tempcnt=\count114 + +(/usr/share/texlive/texmf-dist/tex/latex/url/url.sty +\Urlmuskip=\muskip11 +Package: url 2013/09/16 ver 3.4 Verb mode for urls, etc. +) +LaTeX Info: Redefining \url on input line 5041. +\XeTeXLinkMargin=\dimen140 +\Fld@menulength=\count115 +\Field@Width=\dimen141 +\Fld@charsize=\dimen142 +Package hyperref Info: Hyper figures OFF on input line 6295. +Package hyperref Info: Link nesting OFF on input line 6300. +Package hyperref Info: Hyper index ON on input line 6303. +Package hyperref Info: backreferencing OFF on input line 6310. +Package hyperref Info: Link coloring OFF on input line 6315. +Package hyperref Info: Link coloring with OCG OFF on input line 6320. +Package hyperref Info: PDF/A mode OFF on input line 6325. +LaTeX Info: Redefining \ref on input line 6365. +LaTeX Info: Redefining \pageref on input line 6369. +\Hy@abspage=\count116 +\c@Item=\count117 +\c@Hfootnote=\count118 +) + +Package hyperref Message: Driver (autodetected): hpdftex. + +(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def +File: hpdftex.def 2012/11/06 v6.83m Hyperref driver for pdfTeX +\Fld@listcount=\count119 +\c@bookmark@seq@number=\count120 + +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty +Package: rerunfilecheck 2011/04/15 v1.7 Rerun checks for auxiliary files (HO) +Package uniquecounter Info: New unique counter `rerunfilecheck' on input line 2 +82. +) +\Hy@SectionHShift=\skip46 +) +(/usr/share/texlive/texmf-dist/tex/latex/tools/longtable.sty +Package: longtable 2014/10/28 v4.11 Multi-page Table package (DPC) +\LTleft=\skip47 +\LTright=\skip48 +\LTpre=\skip49 +\LTpost=\skip50 +\LTchunksize=\count121 +\LTcapwidth=\dimen143 +\LT@head=\box32 +\LT@firsthead=\box33 +\LT@foot=\box34 +\LT@lastfoot=\box35 +\LT@cols=\count122 +\LT@rows=\count123 +\c@LT@tables=\count124 +\c@LT@chunks=\count125 +\LT@p@ftn=\toks29 +) +(/usr/share/texlive/texmf-dist/tex/latex/booktabs/booktabs.sty +Package: booktabs 2005/04/14 v1.61803 publication quality tables +\heavyrulewidth=\dimen144 +\lightrulewidth=\dimen145 +\cmidrulewidth=\dimen146 +\belowrulesep=\dimen147 +\belowbottomsep=\dimen148 +\aboverulesep=\dimen149 +\abovetopsep=\dimen150 +\cmidrulesep=\dimen151 +\cmidrulekern=\dimen152 +\defaultaddspace=\dimen153 +\@cmidla=\count126 +\@cmidlb=\count127 +\@aboverulesep=\dimen154 +\@belowrulesep=\dimen155 +\@thisruleclass=\count128 +\@lastruleclass=\count129 +\@thisrulewidth=\dimen156 +) +(/usr/share/texlive/texmf-dist/tex/latex/enumitem/enumitem.sty +Package: enumitem 2011/09/28 v3.5.2 Customized lists +\labelindent=\skip51 +\enit@outerparindent=\dimen157 +\enit@toks=\toks30 +\enit@inbox=\box36 +\enitdp@description=\count130 +) +(/usr/share/texlive/texmf-dist/tex/generic/ulem/ulem.sty +\UL@box=\box37 +\UL@hyphenbox=\box38 +\UL@skip=\skip52 +\UL@hook=\toks31 +\UL@height=\dimen158 +\UL@pe=\count131 +\UL@pixel=\dimen159 +\ULC@box=\box39 +Package: ulem 2012/05/18 +\ULdepth=\dimen160 +) +Package hyperref Info: Option `breaklinks' set `true' on input line 264. +Package hyperref Info: Option `colorlinks' set `true' on input line 264. + (./lecture_11.aux) +\openout1 = `lecture_11.aux'. + +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 271. +LaTeX Font Info: Try loading font information for TS1+cmr on input line 271. + + +(/usr/share/texlive/texmf-dist/tex/latex/base/ts1cmr.fd +File: ts1cmr.fd 2014/09/29 v2.5h Standard LaTeX font definitions +) +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Try loading font information for T1+ppl on input line 271. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/t1ppl.fd +File: t1ppl.fd 2001/06/04 font definitions for T1/ppl. +) +(/usr/share/texlive/texmf-dist/tex/context/base/supp-pdf.mkii +[Loading MPS to PDF converter (version 2006.09.02).] +\scratchcounter=\count132 +\scratchdimen=\dimen161 +\scratchbox=\box40 +\nofMPsegments=\count133 +\nofMParguments=\count134 +\everyMPshowfont=\toks32 +\MPscratchCnt=\count135 +\MPscratchDim=\dimen162 +\MPnumerator=\count136 +\makeMPintoPDFobject=\count137 +\everyMPtoPDFconversion=\toks33 +) (/usr/share/texlive/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty +Package: epstopdf-base 2010/02/09 v2.5 Base part for package epstopdf + +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grfext.sty +Package: grfext 2010/08/19 v1.1 Manage graphics extensions (HO) +) +Package grfext Info: Graphics extension search list: +(grfext) [.png,.pdf,.jpg,.mps,.jpeg,.jbig2,.jb2,.PNG,.PDF,.JPG,.JPE +G,.JBIG2,.JB2,.eps] +(grfext) \AppendGraphicsExtensions on input line 452. + +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg +File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv +e +)) +Package caption Info: Begin \AtBeginDocument code. +Package caption Info: hyperref package is loaded. +Package caption Info: longtable package is loaded. + +(/usr/share/texlive/texmf-dist/tex/latex/caption/ltcaption.sty +Package: ltcaption 2013/06/09 v1.4-94 longtable captions (AR) +) +Package caption Info: End \AtBeginDocument code. + +*geometry* driver: auto-detecting +*geometry* detected driver: pdftex +*geometry* verbose mode - [ preamble ] result: +* driver: pdftex +* paper: +* layout: +* layoutoffset:(h,v)=(0.0pt,0.0pt) +* modes: +* h-part:(L,W,R)=(72.26999pt, 469.75502pt, 72.26999pt) +* v-part:(T,H,B)=(72.26999pt, 650.43001pt, 72.26999pt) +* \paperwidth=614.295pt +* \paperheight=794.96999pt +* \textwidth=469.75502pt +* \textheight=650.43001pt +* \oddsidemargin=0.0pt +* \evensidemargin=0.0pt +* \topmargin=-37.0pt +* \headheight=12.0pt +* \headsep=25.0pt +* \topskip=11.0pt +* \footskip=30.0pt +* \marginparwidth=59.0pt +* \marginparsep=10.0pt +* \columnsep=10.0pt +* \skip\footins=10.0pt plus 4.0pt minus 2.0pt +* \hoffset=0.0pt +* \voffset=0.0pt +* \mag=1000 +* \@twocolumnfalse +* \@twosidefalse +* \@mparswitchfalse +* \@reversemarginfalse +* (1in=72.27pt=25.4mm, 1cm=28.453pt) + +(/usr/share/texlive/texmf-dist/tex/latex/ucs/ucsencs.def +File: ucsencs.def 2011/01/21 Fixes to fontencodings LGR, T3 +) +\AtBeginShipoutBox=\box41 +Package hyperref Info: Link coloring ON on input line 271. + +(/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty +Package: nameref 2012/10/27 v2.43 Cross-referencing by name of section + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/gettitlestring.sty +Package: gettitlestring 2010/12/03 v1.4 Cleanup title references (HO) +) +\c@section@level=\count138 +) +LaTeX Info: Redefining \ref on input line 271. +LaTeX Info: Redefining \pageref on input line 271. +LaTeX Info: Redefining \nameref on input line 271. + +(./lecture_11.out) (./lecture_11.out) +\@outlinefile=\write4 +\openout4 = `lecture_11.out'. + +LaTeX Font Info: Try loading font information for OT1+ppl on input line 275. + + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/ot1ppl.fd +File: ot1ppl.fd 2001/06/04 font definitions for OT1/ppl. +) +LaTeX Font Info: Try loading font information for OML+zplm on input line 275 +. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/omlzplm.fd +File: omlzplm.fd 2002/09/08 Fontinst v1.914 font definitions for OML/zplm. +) +LaTeX Font Info: Try loading font information for OMS+zplm on input line 275 +. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/omszplm.fd +File: omszplm.fd 2002/09/08 Fontinst v1.914 font definitions for OMS/zplm. +) +LaTeX Font Info: Try loading font information for OMX+zplm on input line 275 +. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/omxzplm.fd +File: omxzplm.fd 2002/09/08 Fontinst v1.914 font definitions for OMX/zplm. +) +LaTeX Font Info: Try loading font information for OT1+zplm on input line 275 +. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/ot1zplm.fd +File: ot1zplm.fd 2002/09/08 Fontinst v1.914 font definitions for OT1/zplm. +) +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 12.50409pt on input line 275. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 9.37807pt on input line 275. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 7.29405pt on input line 275. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 12.50409pt on input line 275. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 9.37807pt on input line 275. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 7.29405pt on input line 275. + + +LaTeX Warning: No \author given. + +LaTeX Font Info: Try loading font information for T1+cmtt on input line 279. + +(/usr/share/texlive/texmf-dist/tex/latex/base/t1cmtt.fd +File: t1cmtt.fd 2014/09/29 v2.5h Standard LaTeX font definitions +) +LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <14.4> not available +(Font) Font shape `T1/ppl/b/n' tried instead on input line 287. +LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <10.95> not available +(Font) Font shape `T1/ppl/b/n' tried instead on input line 290. + + +Package hyperref Warning: Difference (2) between bookmark levels is greater +(hyperref) than one, level fixed on input line 290. + +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 11.40997pt on input line 294. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 8.33606pt on input line 294. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 6.25204pt on input line 294. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 11.40997pt on input line 294. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 8.33606pt on input line 294. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 6.25204pt on input line 294. +[1 + +{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] +LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <12> not available +(Font) Font shape `T1/ppl/b/n' tried instead on input line 372. +LaTeX Font Info: Try loading font information for TS1+cmtt on input line 387 +. + +(/usr/share/texlive/texmf-dist/tex/latex/base/ts1cmtt.fd +File: ts1cmtt.fd 2014/09/29 v2.5h Standard LaTeX font definitions +) [2] [3] +LaTeX Font Info: Font shape `T1/cmtt/bx/n' in size <10.95> not available +(Font) Font shape `T1/cmtt/m/n' tried instead on input line 473. + + +File: lecture_11_files/lecture_11_6_0.pdf Graphic file (type pdf) + + +Package pdftex.def Info: lecture_11_files/lecture_11_6_0.pdf used on input line + 487. +(pdftex.def) Requested size: 449.6789pt x 337.25917pt. + [4] +Underfull \hbox (badness 10000) in paragraph at lines 489--490 + + [] + + +File: mass_springs.png Graphic file (type png) + +Package pdftex.def Info: mass_springs.png used on input line 497. +(pdftex.def) Requested size: 89.93611pt x 152.576pt. + +[5 <./lecture_11_files/lecture_11_6_0.pdf> <./mass_springs.png>] [6] [7] +Package atveryend Info: Empty hook `BeforeClearDocument' on input line 656. + +[8] +Package atveryend Info: Empty hook `AfterLastShipout' on input line 656. + (./lecture_11.aux) +Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 656. +Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 656. +Package rerunfilecheck Info: File `lecture_11.out' has not changed. +(rerunfilecheck) Checksum: 06B2288B56AA590C3216AAE67971C54B;297. +Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 656. + ) +Here is how much of TeX's memory you used: + 10920 strings out of 493029 + 163179 string characters out of 6136234 + 268780 words of memory out of 5000000 + 14206 multiletter control sequences out of 15000+600000 + 39052 words of font info for 103 fonts, out of 8000000 for 9000 + 1141 hyphenation exceptions out of 8191 + 36i,9n,77p,460b,465s stack positions out of 5000i,500n,10000p,200000b,80000s +{/usr/share/texmf/fonts/enc/dvips/cm-super/cm-super-ts1.enc}{/usr/share/texli +ve/texmf-dist/fonts/enc/dvips/base/8r.enc}{/usr/share/texmf/fonts/enc/dvips/cm- +super/cm-super-t1.enc} +Output written on lecture_11.pdf (8 pages, 154124 bytes). +PDF statistics: + 117 PDF objects out of 1000 (max. 8388607) + 92 compressed objects within 1 object stream + 14 named destinations out of 1000 (max. 500000) + 43 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/lecture_11/lecture_11.out b/lecture_11/lecture_11.out new file mode 100644 index 0000000..41c2cd3 --- /dev/null +++ b/lecture_11/lecture_11.out @@ -0,0 +1,4 @@ +\BOOKMARK [1][-]{section.1}{LU Decomposition}{}% 1 +\BOOKMARK [2][-]{subsubsection.1.0.1}{efficient storage of matrices for solutions}{section.1}% 2 +\BOOKMARK [2][-]{subsection.1.1}{Pivoting for LU factorization}{section.1}% 3 +\BOOKMARK [2][-]{subsection.1.2}{Cholesky Factorization}{section.1}% 4 diff --git a/lecture_11/lecture_11.pdf b/lecture_11/lecture_11.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3e2c8282f6df7163590d78759aa2ad6caa034544 GIT binary patch literal 154124 zcmcG#V{~T0x-}ZxcG7V=)*IWlZ9C~W9ox2T+qT)UZTt4#-#+7>argelIe%{bsI^vU zq1IEgYR;#~E7a&50OU830883^4Sf z7S_%tjzsjL)&|Zd!X`#`#wIYlyf9AAjwS{+Fm8V~)ivz)0Z2YGHM3H{9Z~9ABN#s7 zG4PsT-jpa0KXB3hh|9vQs_IX0e0hfuyT}*gdv1!%5%X6Xv5&BA!-e#Z3Hc{XFn>&6 z$E=ub|4!um0i!_d=Ex&c8fZ0yN(FAHPP*dm$d!)yykyEs?xFl4GWv4$#?}%^L;}_{ zp%|2CDDjhBalTcBFk+^nj=-jVX`Q_YB!-gb88el#0vykek2F5%aYX0K0h-q#9VrqH zP^c=~C+n_A{Tqa2 zh=2I?acZHnGSkX}lU6Naa=R*rP*5oZ{JII$USAgvvxDR3)4}qqhO#^36yVO$ zJ61_%w60O#s(c_*-dx0^$3m+vk10Vf=Jx^by#qHowUm^rQ<}{(!LT8()?~5v>7sxK&+qD$ZPspC3NF^Yp{7Z zq*OP#{>N*Y=xFA?7@@&JrSfSGW~n(8Z1#}%>@Bg6maQPzCha{fg}w>dZ9%N_5~gNO zSP4$V(i!zj1&%08U(b^CL-vuWf*`BTaV>ByF~kb%=4Xxx;vrK8V)^iMoTk14f6HwY zbodI>($fPkn6E?Tlk({&9GUnp;;Pr?9GM9Y-{q$^h?(-O%m}wf$5;(CWKQD^J5ib;Rg{6DwX3TP#&IVlyd5< z#Xt$T&5)=t1`f&s7i<-4q+^~NqbomvNwh0{a0P$iy1;aYVN@T*xoN1}=A_U_X{f6y zm)HV8{D9e(#n_ZVbv6}$r^9l}nZvJ2#(4ZbNg2**blxxY~$h(aMrGbQmk<0!h z;M9&9y^b;67XTk3?>X7PtVGLGWDLS-2tj|*EjJUkX-Pp!R^1@GfwN+ry5dwe6&4UE7)618KVdXui&_ zHznO0@?J#j&jeleVC7m~s93yUTbDi;ggm)=qe?dyCgB@2ylgvEKy#v>PIdHK@NoA5 z>Yt%OE0GNtw(ql=us+n1Km_O3w6EDEga$2mX;fd zShru_M$i&rAttlCwqIN{eH3fOTE18Q2WMDK+Xz|h7RriCGIXzDgIr0R0-4=dTjV9+ z>5z!coJGmC9Q}FXl;(qH;T>TqGo0pdppsxLCzyP0pp0I!cjq zf@bW^>y_&>SI!KifLv&92Xfu{ln0B3GEa8$5ibRrry)gS#osSoTF#%O|WzA85-e}aoL z8Ubpb?%ihZm40rQO_YKexkU0)iWnA=mPfA<`1bc-3F~MwhMN#CC@~zS0jsLkreIJS z)`H361Sx2Q?_mN_S4 zk>}TP%-u5m(CO}KamgS#w>-!#>VV+!*vq2%O)1gg%36^S!zsr#Z_K#=Np5TMZBZ(Z z_pX~83juulX0TXc1Z>9;pa5t5hrcjO5hQs;b2y3G<`TgLM{poRCytCLO^fv>wiZ=# z3{zD;aZaEHGJd}^2xjO2k|~@~aRn#yuuI=-@j!cRWy%vs3MP^DuPJd$m~z$a#!yqv zCW&u_Pl^bg>vijHRI6}|eb0uqN3ocu;3`wE7b4M)>RxMv)=5)5FaV=Q9=S zACZVxOB|85VAjBE`5+Zj}qnv~r- zJ5u+t8dg`O=4xbVNmm32Gg|DR~U|;WEFaAmSnS z887BLvuEbtPwPQ3=j)e4hvYD(ixkwqMa?6o z^AjWTgExz7m^D})XKFt&ll2U!Jk@(%>g1plV7KKK!qjAzp5j4+HufjpXKIhQm9{ggXZLnX*ZSJYhkc32zF^iq4Z8ak zojqi@T_n4@X$)2#Jv=GWbun14cg|#4&|&oSYHGgxUCHGOy7xKc8#I;ni|xmxx~fg` z_vsL+QRiZ32mz2B!SWGx@LC|7%dMg})$~O&WUUt>@G#{{XubLtZKa7JxBJz|=))l< z8YFl5-D1aVAw=wGcAEI0s+b;$OHaNf(AGj5N;tNLK_xe)#hT9Dl z(Y6~$C#IOPk9@?9;!8;gSze&8Rv(cO5B=Culakn+5d>hIdwsAYH3Nak43K(RkTNwGJE;`pW30Gn3kH7{JgT$8D)$0Z78z91 z%S-yRG-J!}okI>B?oT7T<^;a=ML0V;7~Bq>e@giaN!dF~)>awhXFs_2T}t`GQ&8L} zkU%sTi{uCX0cjS4wo=jG6j#F1dlyW#WM*|4L3Zy(;4hRP(m42z+=;ELXOSj=Z4>(y zGdiQ3vH=^dNyVVVZz+G?UE@Zpz@d7KDlD(rs0ka`Y}^ZbW?>j&)VtbN!I1AZ`w>#1 zRMZjx8+?YAvMXs^eE`q*i!&i!t*X(x+FmYT6D$_?H82M))bW-E#I?1TT(=InN2-Nh^gpP@Y$ zZf)7f{c9tM33@rSe$t=mPjkN~Paz!n=Iv<73|uNtioJwj;+7dH-of%BpfZCk#3$U+ zC(i&ZTreQ(=xi-a{4_prVkc8Nkgj1fqfhw^#mf>l>KRIw%&ZMP@_@ailwy)Hd`yki z-^dD1S*l1(=oiJB&R9tu^_P-7qp#@Yg|HQ~(2+Z1);qaE)4Bfpdx`7s8H%`}S8vzU z+L1-`h!D{;W5?+cnDZx@vOT+LTdL^0GI49evkl%C;JYt}mkkpO+d;1H?EDI;=8%q# zNzG(A57svG^<>g5L$UefwHJaK9B!-;m8*M5Lkg6U)CGJejK4mR(;=9d{i{|ilo(U0 zhy->YbfvIJ_@XCc8-a7QOfx@rM7DzXar5tDk9Vc!!s7h(w-FioeQ0nP@8Z*%@7q^n z+Y!rr7f2~=l5IpRt8=>7VM;Iw(k{~fTHSM{C^I>K@!a&Z2?$2D3Tr|zq23g zVWQA&7kpR+5w^!+4&Ken2lksJOW}FxkJ9PxK1b^xmLCckQsPr~l4Kju(rQ;zT zBBnxL0h<&FLTUP&4u!v?AKzwvtdjDxr~Y~1b9yzXy0w2IUw3qwUE)#Qu^gA77M6=trO@}#{+BUda zLa8a!I;iSwt_gRodPqGb(xsC2l$Ei670sf{dZKa7K<^i(osL)F9oF~=@8{LD$Uz=^ zXmFvRRhyqTXK{U|k$&*Y3u2c{9KO1UPThlC_2oY#V3ojptp+m1zcM z+b|s@3>S^+Ts%2?U-5LTXD{^J>#QN~@e8H9%5Y+Q`h4HkBk1>RmH5FIZ^!c~htT3V zNFxxkb9MRP3DjOXsS2(+ZN6rU+U6HYJAXl_T5N67HfN@d$o^Gl9rFO@FvhUuzEiVQ zQ1Bs)GhT@9| zX1|_GJhfgx@#@TO{)-TKTkY!-=GsfX9H+J6f%);*o$5Bt&FWa#dQIba!o7P*2luJZ)+_2d8Iw8J@I+f)aGR z0iu7bl2~DYffRxN<&pVUlYYY86RqLqHtp6G!aQ{%J#x8=L|eoN=C*ukVYZ$uX%+eQ zBK%?CINR4=R4%F1-ZC=-c7#+?YtZ@c@xrBoXxeD{>?Z-&5RjNU*BOCzJP$`=*_(4Q zpTO4p7o)UnFNeXL-v*wJy_?6an+vU#UP_;Ov=_AA?Q;tn*QzMv)IlHf!91&JHsEiM z&ewdt2vz3)KFG8F2O^M-h53KItlL!6vRhz4^SQ3MF(MB=H{yzpV)-$QwMSeSMofT( zsFBe;mu}4BcYE*Pm^tys*vMR{HicmQ)r)TXRW^gEo;b2IyA~PtDFK;?Jh$JTIIU3H zib;-Qn|x7x*d6|a_Od{SVq239fx$Zggkzeb#B+85sI$jBaUY8(r>2dcHAX0V&W3moStuckcvRKf^y8hZP3i(Te7#4 zl={|>%k{}SekjiA+pr;gre#iPLxROZ8O>oge~~~N;huY9&mEf{=i5ztaD8yEXL<{T zP+2Dq(H~-7U&KW}BE>v>!X~~7W<#6o5J&AA!Eg6$fTaks8|cVeSBxy%#eG#qYZu#y zI|9(!HW^VUP2<@*mBOV@bMBsGwqB>!&}^a&dPIb;qzYC^PA40IG>baq@Yn@1oL^r41x<296L5S|9;gab0 zTz0aT%fZ3f{Y%NsfkiK-qU`Ry(u13)4*hvGAhuqfXjLJWc)A`>5tS*Equebh9|s9c zXqvR@ZPri~0Tl)4XCk~2?L0xghjO3 zUSb=W@wmY(+|8IGb4rPjx`6@F_~aYU-CtCls_BI=(lJ6>_;4jf8ZrKJg{{8Pl6t`b zWh!dMZdSHGRO)lq4bIC66O=MvahOt*5jTFxUrRoauTg=nc(N3BU_5+7&5+U9DidsE zJUp4>E$Y(m@r2t2PDAP^e3JpLc}ICyOpUEC90x$BR#@R!XW);nI}vHiAT(THyakF|F-&5cDFYnqF0wQ zv@|hthM`w-F?9ZCim08V&0k{VZ~V^^j4<@_$|CA?f4OxNSpyprB1$@X>%TQz98L5X z8TCy6COiH21b`j`oxQOs)xWCA80rRD#tB?((oJ7EhWXCl^rOw|-&=miDs z+=#UPu`*?0VJBi{2I#=hi#gi4*b}ib|DO_yCQf!Pjz%UKVWK|h_Hk)bRE}b)GFMEk??*)RBOgOEsb~AO@v~p*jW{r#>!~SbW-@a> zgB}6l?fG&4_QQsq_v_N~?ne~K(1}!E4(t2Yf&;$TUDd<>`Q>e2P{7yc(*m*=Z};v# z?8o<5mq&n~eW&Z|%i)Xv#C)aITbv@#*5=fZ&^^PjgKOhL?=i_pH@w-&`s($F)F$@s zm;FA`+jPu_)D>?s$i($yi*_`|XX$faSNqSFl{{`wr~5s_P=l9MgMd=tAodXKJ-m0q&>bo27p@oN9>_2a zc;IY*6iarpc@Td`c+_#$C-(6J=3*>O_K8COPFXd%J=B{E3NKCmxM>4X&JnsjX2UbW z17==ulPKPyAO!;OJa}Z@2)%xzN_?$%0eiV4##iO$>}4~PIfyi2+_umGu&L+kc1?rg z5+dz(!zvbO&8wU~a_wL=7yU&?xNjX5U20l+(| z+Z$_+<^wI^X$W5Kevv3lZ*#E~K=+Sg;v#LbrIDasyd)fad=vX;G5epF9emecf07_i z*yFARk1HDAA>8l;LdIl!dn|w+OYQ$S zWP5>bL_;6_gL3b{*FeKD$kFIA@yyfn^H@bvqB9Ld@Pc9FV%RmF!v%j-Ni#@bxvM>? zLrm^LW&Pe)64l4RQcL#F?*Q%3<3|q`WW*wSDQ7^l97_zuYVX|7W!b{>SZL%29|Kd? zX&E15gBUf9Ge8n#oPDvpOl5N~yIp4#BaX>_6;CCS#ewiZ39r}xm_$nb!TXcYLHw?a zGB74Ch$u7uuxQTP+*^wsf+{u@=G!@kf`k#EVP@&Uat6(=loWv%7A+@Dwof*^v+Q14 zoLa;|xRUJ8YOdU#8KV)yXhO9nOwSQL>djSLP9tn>Pc9i#i96XHx;m@a;IxDiMmCa_ zTSAp&1^6ZE3)~saB%}ZQ9$HVzVnR|45WQN~g;(y4c+$4ku>94v)LuNOORP1nE#%ct zx8ee?U@UxTY_q|BaAP%xcJPGv$^yNPHggETBfY0^jJvTMYLs>tU;QaOOK>_FE)L^Y zASYNpKc>|0um2?DqL}Dh{Ut8(#%uX*XjecknKkVwslGG_6Ir+v>v#lr5jRY0bCw7r zpVTg+Q5+!Zo<^*r)qYyVGX|daCXrfN?BNXHHNh8Lrb!EY29_O1>s~aD+?wa$Deb=V z^8mOciCq;^DMMcdl`sC`gIDUX^sDY4-DyQXpi=al&Zu(RT=x4DQotq+i z6ssGDnUV}(e=(eSUwcz#IIP_F#dUwOe8@CY-7cTfG_zRwC_|&snOPQHnat0wC`9rIKrAL*!-|*uuK!~i=Qq-_iy?a9H*hRU@d8tveY@c;W zXGtm#;KbdeC^2(YXo8c?Sr$-fk}C^CR-Rv$WLS9i^T~!&Ybg?KS!E~_ZHQk(i8`pP z$h3$QF%!{AQJg4gcT&P^FcPhveSu{m0SXhN5*7is+{j^p%Cd~qcRbs}65hkQP9-z% zFTWNvE3%tXQO#jl&j0zd;sg_he}y}v#J{~*s~CrWB9^aq;A>?+<%&-WzUI%r&lOnN z|KjEUM{5WC1Ec=}_Wz)>XX?bu*ak2l1wHc)(JY97vFq3Ki>tI7%n>F%0SyvRh!3d; z)3kc?WK$-!`@TjV^YFQk%5F*>52M$|Fq{*p)fO-Vr@UgY^kdT(pay|4pFMU<+VQ~a z8Y^trO@u2QU(lpO)X%iGRT>0rHl)qGkOC2TB0>zD(AB>4K7N$-xPJ$rwxc`FHS5oc zcC7UEz@rK#557+iemZPEDLk#*Ho1ePErW~AH}nl5;tcH2QKoa-<<&K#pG@}fXw)BA zKe|BWbI4m|kD#;}Rufa3iqOdHsS}ehEB@~L1g|qr9)vssbr{n|`J3Zq%qvRgvZpSr zblaxFnbIIJUc4$67i0KaYS6V^}Yn^EzP+uTQ5U>^I2B$l^p7u)&{#gkii!)~WDW|^sxBy@p z1R!$9`|J#!mT##BpvuMI&zVn0g{wCS8PAhXpsKoQFThBJr@<#a4xf}asHtLzLr61L zuc%CD28ZWX|LX|6`(kuK^K*(*_84$!o8V>AVm1etnL)O8Wt!9_hGoZ{t{1>A^vTKt zUIFMuI+jQ+aiXo$zjR43aD-?Zbc&~VKPVo~`<#yT8T3%`zUZh>->Gp8-zIuGDUXNn z@{&!sZTaD^lY*tkECE^8%Aw*Gh#wM6UABJI3<$4Knu$&77V?2`$P__wBU?+kCuv99h$;4h4I6LDPHuXTd>0(Qwlr7_-s< z@LW(3v?wJDv;7J|reQS==3<#L@S^*J+{s%N0qip_HwY7yYspQUB;%x`89VBH**2SI zI9ZtJW|54LxU+Q4y<@eUIQ>F=)$-b` z9_H+F+?WH{RKp(y1oocvdN8)zwI4s@5$rZS*y*wtfAneR_sG)$QLp}(L4^bq(=S&Y zG`C>Yu+|zGG$rElV`A2^ve0 z5+V$&*;};Qv}QdoKP^2jJtL%oI<4YaMB7B`mkU0bi>u;()of^6#TU!*I28Z>4&d=@5TNk|Zx95ztoT!!zns@9^er2#uGKQ#kJnSS?^kMWM^BjS-(J4AsEVMxQe zfb`BtfGA!yq}S`D1e@xBAd(~Ff%F|Q!u8|TxVtUVyg7AIz=0G*gH@*6Tp>||%&z03~0f#M40nAC<~KE8uGl)1MO&1sT`$N`h|9R$J4gRvw|db(9bi7o)nXXYs05Ii8m)1c~aBeNb{R=2iczt~0gAm>zm%oG4@hxju{Q zs81^W75VkaJ=#Pbubaj&%{$GA@Zv9-Ni-p2U5Mc8H?ZnWSzJz(WTP6T3TmD7;PVc~ zl$w}1@{IAlx7R7zri)Z-))5JHqJAT^PC zzXBwTu^@*rV0^VG&t+=NRHZ>CB^W?~O7F8Yek|T~tX%X27nsce!L;kH4pbq4+wUR3 zeI5k5D*VJeFcX=eL6jzE_iE+ywb7eS{Q>6>8;X|~&SuJQm!G$do zt)g(kwi8Pe+h-|AOcTMGM!=#kydzJ|O6*GIFG-C95Dx9 zXqry&fCExN3F=ClOG;&tl$`-B?*a6$c=4e>g9jA)iu$UwHVkB3RzQ~YRC06`CDyc~-rkbE1A|yY_l)z-+B7@1 zlz)KirR#hlF`D#F+@A_tpWo*2e#?5WK_%SIS`tu{FitP|HC_hk@z}mKYu}|-Gv3M$ zh)hcjDjNDi+CE0rv5aPkb}ZC{UBt0m#2Z6-0MoQC_@WZK8$>{)_XUy3YnE3lrH7-0 zqhUb9ft3jo2$IZe>)nI3gJ%0){P{ax^04QZ{`W9EB!acM0fs}zp_M~O+U?nt)3NOq zr{_^b)n27JhMocgp)}+AIK*q6I~qT(1j}%*vRvnIJ|ZlLOyROAWtg);)Tdi(KDbk? zY>5Qhx&J)AL3`+2ov^c`r>CcrnldhDW7*O*6m8ytgnz=`{QlkE^3ZE(C#EZFHM6W7 zT7@jhplI||&0$Vw;p#_#V~het%IB5vWyHPI^I~`FP7+U3(?A6V?N&^MuFvWE3}<$7 zb5Gl&u!vY#qxW(0^Dmdg(KX1Nj9aFcLoa3NWa>~z^ppYaCtL01)a82DTQ^dJJ4QZE zv5HY?*{gUrB{mkGH#+ODA&KJSFF)e=QZ!uDnRckhiHyUQ<>D?Kdjd|b8O%;vcw*-( zmGkcCfOKC;yJ&X0?h;4t5brg3Sw8Pq{%I|1sHDSmBYBem>EH!l;ElSn!g*_pKevDh_{9x;6CxwCGS}0R9qo0E;bvhSF z3+mvnYIn6h-iW0B-Mi~Q)SL8CSHO3*^i4-x$bkJgdAxy6&>}1vRV)ZK#d;38+27jimvS>T7w1eGX43I^ z1f3&>2zpz1{s2K_1Y(2VbCw3TNL=CxWJ4m->EIHm)N!YRmJ;*F%Q)yG{&Q-htJ2eM zq?w%br&dH_ycPq=cY+WPxid}GbiAgi~BGHG#hwZ{jBp-4dvTo(J81Ygs% ziTE@LZSUMdV0dOwb5U`qYX^9-Fa@7-m4+Rl-$3#W`mE4OPV*L<$a!>))Ufy;LNMhg zS888L={234qUmJl@^88{=n^K1L4`_)^98!ib1f2JqNBHoJrBJE^-?J?Wi;>$2c(h3Ir1-B>U1IEc=X^!o5n2u}rFP$HFIb~zZQz7n^K(Gg|UUjD6mHHL-NuA-C zR^xe@Ht~S{^Sg7e1XIH8in95vMV%#=vtR{Tw9NdH>z>sRxw=#9H>z9bjLgk!Kgg@s z5B1<_WJT5?;XvUSm2mwEqSGfQoJm8CqQZ)cmu$8#?`Bib z7gr${F$P~6nZlBUPH2BJr;63H_A zQdcpM3oko_!{3iXCy~_F%?3FQXhlO@?omD#*2C}nntjlCl28X%AARG_$!REw}T&?&h|CcQuY7%_-k z_i4g=lgK6_j>(O)-pRB9LyW&V24vD6H=u2dQQY$=L+*#f2i?t3mKv!2AdKF_O!Xf* zjH`#PHUw4ehvyV2{yfh^`9$Rgr3&e z1UwcPJsl@X1y`!16lHxtw$7AEmQZ`J#DPxNl=?v3J%<}YvV+ujOq=el@Op<=lp8IMzIQ~A6G(U`6wg-t$+tZtWS!?LCeR$(e8A1nIrK0s zwrZ;91lTm)S!?ERm-r{X4i|`h$$v%U=4}fmPRH!>eI41VKi^-CT%t;+y-_bJLuz1- zO6WF-kaEyEJnuJCNT)r&|L*LE&THdFlPtAO$uOvP#_ycRX_daTQl2QYEjlaGlyr&W zCY-*Vke6}t)iS8glzN1iTv{Gbuq0fP_VtP+Tigx=d1dF8ZeH|`DwHHhtRgkdE-vS- zfXbkA%u?owfTD%YGY@Ca4McJ9#ynwkXjomN?zjampj9H%1 zVK?QcPnGymCZ>N4{t3TE9yF^|9T(1>^$gamaeHn1!Ha#Jyzff>p{ife+tYT7i|V5j zO>5iP@P_OowsYzDQI40felr31sOY7izgdRrq`J8`?wn%@+ol{LPhVw$uKB&3qGvZS z^R~z8_Z!)b75m$INN(abymtcQ+7%EhTm_b7eWx+@msI1gd9xu>%o}#+sxht>dB8rP(HXmPQMZ`AEFy?KML?}ikrY* zS8xJMH|ZS(=4Ffy_p07>k`cG4UXqZ8mpCK0LUG;?Pd2{H!_&b5g4btTZql19$4ZQs z=H8!vJ*aN85k0KCexJ5Jy%F!!v|c^9)U+=c$e*gXSE#LOI|P0mwCX?XS7cGQlOnlf zUWzfjS%%c2xxj3=2bTd?iVlkK~gBD4V1UQ+C~sy9(UUOGF)jwIWpwHu+h7IVXn zUN!+?Jx@rs47+at8ZFnz6liU=^r02}0T&U+(+XSN^q?YwR~5EyV*ATUEWR%2F7;T0eQ;ZC8vD53AaZT}-V_k~?p}AB)a_vU=G_gzBr3buP7T->6OJAd`vkZD zOnTr9Y-Sr+PJw83uNk-pI4_BPaBn8dr0u{d#3Ty4%#N~Oni7bcDXuJZZ%#KgVvmYv<+KaGX3^lvJjvEd(z5RxIPz>yF zU7RSdY9FJhm-NnwBc4h$2{`XhvOBSL`$0x8V{Q*H1Wfh|16V@Sp^y-W+YnlI=g>IB zM`ws#B$8riJR191erm$SU{FX(uUvGEau}=hNC|Hcccdgw z@PoWz9$R94!aPs1!@4}1ohg`}PqjDMwigC{At)Okd14HGQMXt81cZTC{E?_w)C}ZM z1z|JhuB%I>@2!2n1NG!kIMJP3MTSD&N+b%?1Sb(17*ME-cJPT# zM@FoK1Xho8q;m^%{`h;>|Jw%S>k|DHu{gwA=HGcf7PkM!^Znn%S_zxK`YH^)nuYN{ zwn8y7!O)AFSeThR6ESiy{1sL$oSo!N9EI#`?Coq#{>q{3F!Vxp)^?6c_6A0O#b05Q zUlv9tVvYvxfAwD(11BpYz&{k?zeM7{HdnE7{A+L3|H4)NGIKXRfB`D-`BRUR&1u1+ zz(2`UKxi~a*P|+j+^;v>rpn5EJ$L|j`Rf$2_WSvnSNii3c*pZ)08$i@Fp`;o2#<~1 z&3>@yf}MRY^AaziElJFsG0?Ma6l3PS?(=JEPl6q6KNd4&vDIF80A#Q}w7u1=IuRGH zy9$Vg02M;UJTGUI(d~2Oxvv57(%aY&&Aa)w>-($I*M{0qb3=#19p+Hkx<}dcNP>ds z9%=y!6miTw(qeL2X}M$@<4(mRE%RAK6%BwA^Vt`-(h1<4_{wJ7q~WQke?B(7E;3Vr z(Zi@49@;eeT^5!1P?_dlw`*qa_IWf2#0Gb9wSRAhF{1TM9~i@5dXQlYl9yla0Ua35 zyGxFA#+^fEw99xjH!VbD=cPY&&&Hb@&NIsW2G*Zb^1>V@7VlX-Y(WHVj`>Uyuhwyv z?4JGphrAa7SaK$vV{1xhUjCJZuUOAFH6=xJS0|6Rq6iQ?-$4E=r)9G%YCZ*tz5LJT zm)h`jGkR0@Zh?8+BU#chQ=KIb41iUbhCtR$k4@ww#)E2K6Ok+n(;Yuj4m%vJezL{;-A0ge~A+R|J%fWZ82m9u>Eh{M=!M*qYo(29?@Gt)OKL-^ik@=Xs3Wh z#c^$g8}X|{$*sfOnBt+?`2VZvY`?e1HHizV-zqCKsxgTj5cFVz?4Ek!} z+K-j|89I7L$}r38*_kr-&9t2~=e;HOJGVCE$8T2aC>Xxz)j98Md|nt1?Z|R%dA2b0 z&9R+~W;>ESzAfxxvAlLLnugnyy5zB)ESr|{)Wd6RVThK6+br!0a&UGz!5E$^%hRHd zh5-Eudz!zUJDa|FfEF=&#QxTeQ>2lWDNX+mMn1ksV1X>^#`GeZODz&Q%Yev5 z*I_GgDgQ37ur#|R{t;**!3swN4q^rvm;o=zXy1+eh3j)Fm%B*>hm% zxupmeqS38s9o%f%?X-Q@;-fY$4Fs3*H~NGxmVhk>XBcH;;~ggK--G zD<*bJ+1_!2N9|EcKCfPewA>}Ks$U@1=nTVI;j{DDS~pk{8EY77o$qfw%U3{4bo#=y z^?8~$Tf%2SoHjGK`t||loxnBzb(%F(F7vu`r-9;fCVbpre_F)0)9}HSqte37kTX=Y zeD-P=#%#b0DRm1K3e!94U|p{(^iGx^l7tZO&Z-aV9~(@0CEj|=Hw7gK%Jc)t6r>7S z0PDjvzAyD+l!O%ixb3}G-4tSI``NPaGJk3en-_TuseByXcwukuKb5q2 zb5Bbl&MS7Eg7m~d(#NlVci~;0TEvJtQ*IphoCJv_-GvRSA<<5IoH(6({utomlISRj zdDcPAR8#s<`aYOS@Yc69?ts>;4f^*xD03UTCwmyXV>pa1Qgr{a;74l>?SCU+1L8Tu z(9Nqio6P%}YCqO6{i7mcgaMK|I&Q=17*rZ`q`?UkS8F1N{g%qYpL6$9AjRh?%E8MyxZq{dRW7qu86f z2xbi$;`Vw4egSuCzfS&R++6TEEpR&AY8|tIez0nqy;SD3vNX9GWSu$NL7JNOT!o!i z4>~-i1}~X>kBP>yj7ux@RqN0TF=d}#DJx#D!qUz*2VZY9Bjp>YgnW1JKLEjh^73c< z>n`@s@INZle>OF=oN3-}< z_;MYeI5Ti@bGd(?RWXShRY=4RggY$CTj$3@3389BWSmp4Mk5cX$^E~?#~d%%z<#hw(M=r~=uc^>+( zed5f;iO)xoZWDzcm=C?-ydMQ)pf%l1wzQ*~C04uA$Qo&?)zTM5M$Hu<#~E)8E=4yU zMG+QA$e)QDH_kpg7CGoi93?DC*rT+bK;o?QWY2ihi<&4hP*?^h7aRaLs$a@g$LG5=#NgS)2GtUN<%`8wp2L)BD_cLX!rhCdJ^E(eh}*8onEl<;iH6o)DZb=tJ-fVlu9b^OeqDXH!y!^TT;fvnecbk{ z*RyYw=gWZ>p`%}HUme0aDsaE=vrf9T8V8mgRjG4g1{Sb4i*G80AMd6jFF}ARkceKY z0il~fg7!G{fNVDC6A;T;9cF>rhFW##R`Pxr^tbB*U zF(0=k6saUWU1}l>ix1Bv+7o2-j$_@ROit>c60XKYzXNH%o?D% z3HN<7>_&pXM{Kz{dEPFHLkIG{XTYEC=N4zst%47M2#*j2E(b`pM+(@*JN2Za_vZXt zFEpvr?4a-}TK%68IN|Xj;bOf~=ma77^rq~{BhE*F?tZcS?YQFa=;VdhOVlFRH{kC;2rb)v)9vl8JjzbC29^%4VsS!cY()Fu9)3%j zB=Y(ga^{+_dExRho;6E$_Qp8|mte`@mjyTP;!q1X$;yiESL{4~3-tera(_QHd4{$p3NB(TD5f&HF zv2Q{ex1-@x3PI?h=3rD84@X&}fCS)0Kj0-ib$$%l!S!U~d2!@^!TnWWFepevEThvz z_SgDOu?3EAF1pqgcOq|g$jrnU8GQS4*iK>swk@|~C==z5Y7?nV<5UX5TbLHxDY|I8 zk^djY&M8V17|OC`+qP}nwr$(?E8Dhh+pbr(ZCmqZ_4KTn)&0?b$$yfYn{)PwWP)eb zw8HX*dtvC_3-Sm#or!1{pa3vixSDI#l7SpfiGi(Afx39>x`yaL=XvO6b73i?-x47D zsOS5ArTR$2jr53vvuMO2)C)GOKxNMKwz?sPA%V%HqZ&Psjwo!%=A<3mj0bvNcYuZh zc?Nl_4RRA>gJIK;4mq2Sx@QhxX9GHqx&o*g2ASYwO(Qfu48KlF^72yYgd4EyYe^&W z3`A;YVZI7bA4&~kwfc>Z8r{-0MpGFEkI^V}$2mitQ#CjeLZsA%cc7TzOmx@Zmtfnu z20iql&?wbd-m3D~ZAgi*qA8U!f=CMfnPS(UV$cAp7_SN0{bU$S8Y_(WzoIxs0Mv#p z;exmGXpHA=U5%k7S3%p`f{u6X+je2m|yO70;4~`c*t0)|Fuy5Lwo;=jfx0rAmkJ&qkWx(%1X$u(g`zw>PP@hC0eC`RTZ3=vNBfD+TL71s)n>8 zvk)z`wVih2Gv~6XTvMB>igk-WwYZbVx<3m-qU+n9^+?_mbOLTv!07Mg3GuLrvvg93 zJiNW-U%C~>8(s;%Y1RupRr0iS-=i+W_s9Qrb!fbuEa!GF4;;5-0f$H7g%tQ# zdYGlMW~|fT{oODbrLHjjJn^K?_O6z#+u8!URfr+Ox$t0S5A}f-i zM>8F+D22{$##YiCL|hzMRs+m)PvkOrnfw`GU*qR!^&eFQi*AOW``Z^jL4z#2+{a>> zQ(PHBcD^fFO%#*Ky3v*A;n<{U=V|IWlvj=2CUd-UX#L?4!MIEf^YeDcPdp$hVWS^I z)fhrPuD7>#FH#vWD{@jWR!_LXNiL=c>6zEBCz94}H<|bN??p}sNV!+s}7%ie| zWjc*~oiAe@hSU|lGqP|Hz~QFLLJAX}YmCQe+RLy3<0IB}LYpdTbtl4D|I%M7W52{! zmQI~WXT9`Sh>v-4WeY+698TwccR!*}T2bbintc3{PE)IVGBo4B;p6VI5=)GUGXEvV zNCS>A1>9XX{mIhZDETcXmCnm08O&P99TwKCu3&)8{PosIHIvQL5-I`>V~YFz=73%> z4F-1F6n0hH)n<@JF+hbYm&A{cC#O{QHKP2V4S+8`rO_{AME)bWa-F$S(QIz;mbvB| z>B0hhW0`veNsxYlW%?eEa}EB1HlUnEo9?ElR|D0QTQFbBGEgM;PjMxk9Cn3|-rNsx zr(0{^f3vmzn>#2Q@2UD5DD2AU+C6KH$9l8c<__7*lBzO6X^fO) ziizraT^%kr?ma~$sP9@xJ+8jo?7cf5H^deI2p#xY$qN6tfF+*oD+m!-HaSBA(lnC;>qj@9I84<1@|)MoF)9XcO!)WVs=3|Pd>|up(Kwo!SDSd< z!t^*Bb7($+SL`usbMwWQ-nyD7{39dzG4{>!#uH zEhrEoSv=$C=*Ov$vFtTexWW_~=T8n^)khmulw*jv>M5(&9=Opspkh-YEmpo<9Oxhf zA^sr?gaJ6Pj~$nG3X7%bY?VPm7}S#YQz+6W<^9V5M>+Hw2YDXe@cC7K`RfAWSWLK` z!sDO0qb)Nbw(p&+g(IQH>#uy6LXlR?_t~Ni@VYE}7$+jF_E*0B7~?OL{zXB$Ln1yEc_9j()oY?m4f~bIXrsh2<>t<;M$+%wQCI?nT^6tDHaFTXRcc zO!})+yyEc$UW{&{!RzOct#0_;yeo3}su?@weRlQWEw!(D`cp27=p~bG+aAi=u*(x9 zSX9Dmt0Lh$zam#?Eopa_;gUD1oja&eWb4zm7D#a5f@-cWR7SyOKY(H+N`oQRw1#R^kk>13P^3j7N+E(UlO4#M1V> zq3ORswJ(4lt(XGiB?0 zm}VQ}*Z+0Za{kwXz(~Nz#`+JQ`H$x=CIU7N7Uut){R43Rb4b9>!Tvvv+KO=jRYAVN zrX!Fb#+8DJpPi3!aZh6~=nsb-9hWR?mY~#KASK-6+? zZuPx=?0)v0`(&E8zI2>e8>}9PWS|Iw9-pBGi(gb=0DA!P@O2UIwyc|MsFS;13Nu}3i2E%a1H2&V9p>Qt(b$oAF~G% zkl)H5L16B_R>MDz4B`l;xr^kN0tZAfc?KZRhWm3fw+#m8DBAAaC7kX5GXBUsea%WO zV0&ypM`u7Wh*2>=i;QvtD*EHu7%X6W?bm8}xj$(P@Tc7~K=sJq z*-nv z6CbCTdmI@?pr5zjZ`>c~mv0{+5I{Q|7RUg$HB7+qC)UpzZ1dZ(*Vmt87~5dfo0^{> z;Pv#h&L6D}s_Bnlj_*(Dua^;?t}CY~DsJp9?Jwx$&r{T8+y9z)D|=-7NLE zweu(F*YCf$N;#PKod?qG4>CDp6g>|dq^li0SAt8@Y9zJd-)&$ zk~=pd+ku_F5SYFF&_RSYx`54>F90_Nj@dc(<3rFpjUhocxxGzVi?I68was6WuR)Oa zpBTa)F_51>TcvN%@9sPym--O+cl1YTR6jY9zx;drPLMy?ALfm}Az$Kb`49nP&u)E! zzh%_}hkNr{BzA6vEi=B#C*yv7hJ135E0U6V3DTrT?end$;YqIV2mHl2{XT;m6 zPGuEv%!ThAa#JHo(o^Q0hnKV*O~yyxx6p1TR-YF26&+9bwmcn9-bNTlE@hA{!YPzv zGr}PP+;K-?>UD|kw)*E^UH>e$IWbg(tXoqHkhL1Y7?1gdlBGJA)09%7T@Z9wG;RmN zx86x({?6NT_yD|!; z7=vl(bSCqPg%6cgFF=i!AoJWc8$60P?wfdll#r`xGb!A+CgO%1yxiQjHv3^l@} z4g}xzdm7#GaMGqM*D4K_b|KB#*yqKWyiyOlV1Tr4sUV=(so(u4M-CxQ*e|JJyeV;p zcGD#3Mz0DotO>h9YoN#mX)$_Uy3fo=e{dqmsv`@9^2Qsg5(u~ZzM#bpT34m#9_E0P z5LZq5KXNX2a8XfEc+gdi%RblS&K!%CwS9vGnBJ?`#z`mrnhc54s~#_mS9*XQ8zJlV zP$7$`X%9h#u8f>k1(MPN{&qbc>2&}zQ^)1*Hb~MMDiUJvN^{*3%syJeRGu4aH$Es# zkS9vwjWvf|Ga2FuE3X`4X3$ZtFSS%ry^j;`YM^W0C}|Z7!E%z%$xD_CZ{W<3O(g5f zuV95*l5lB7p~PB%PJa-`%9^g~H~y@JRHJN|I<$Z-XIUCkqt?5E{=|#44ReO;zAWR~ z?;2nhIwvO(F{pQQfBR~TysB_k7jK*zTI~pPfaz@qbK2!%*^eP2{AV2ABzRFk+M;VTjw zFXHp;Lzq8iE!^P85*!=TRWy{yIyyIWd=0l(3hmu>8aA2h-h)&-4WL%2N696zhM`M= z>wZ4mKsNpjrCXRCV^#}jdnoiC8&swi`mkW!NPhcXB$O3P`IbUcah?aQ8;HtfxSr&$ zz2B{6%&ckMBtY#ttG4zT%EVA9?{)j*sb6Jeq7{~#A;}NTf!%p84f{q=%{jL+_J_la z+C!%_fAGVDP;uyLhrC~8GYi+Z%c$ukCl-9DH%fav8&rp*V2efHG;D%BYtG3R6d2== z?{PD#g}K|MI*NJj&|j!;UvFQ{&yF#-nF6h1P_g57!;tGQtEd-!D?+@mtfsjEC3v}6 zmaIV}vqXP{w7x=aS8A}?3rBeQQ^(=9hhASSf(9oolli+@<|?NR(8VX0J_d6H`ku%e zp~jieg&>crsBwSBFq}d_PAMxDh8NB?+qqCsMb{Eln)Z(M;xqEip z(&V2>N}OabfC#ET0WZ(XwK^Q8p}aO^e1KNoXhhTa3f?v^X11Z=m;*u9?XM`7CU71_D_FcS+^a@~ zrh9k2Nv^ZRWP>o9Lh0xY)2zy%LVIYk{5CD2@w_jX6N8sKN+Ei>dAZ=phHw$}Rp3J1 z2&5!&d^{F!;Xfe^{!$D3RzZt*$-rTYm>nW~s9~}YwHhF4qQ$uGbp#VX{%p9uh)jy8 ze<{1xHF85S9TmaSh3*3B7^of={R!{-*`3l&VR#&8_iFWHNDx-Y(d!*N^EE zK9rH5oIPsh+z6S&zp_7Sba$vb{xBabz0XVafcG?}p=3^ST{m?UKE(4NljYymepN^pxbwr1+t z`?XYiH81r6J-0r0thidLt{U5(*;q#_1SJXI;kzRc8}sH(R}Y$yz-W)plpi0?zn00^ z(M%E5G+7V^5Eq|TXDuUKRq&eYBTNa;x^(zdjihzJ|T`aBvu<6!EcHB1VBw ztRZ~qZZZu`Pd~LWcJbImswq(uht`Rdo^A<*h_QF^ihBG>0&OWe64u&6Ht2(#111K1 zMonMSnQoyy;AAbUkOEmeL_}G(sFF4mN=u7aI9Ek;9ij5JQn1CP?~#B(Ng@O|xL z%;GF}LGH2Iv1Vufp&GG!QGDrnoIIa|O9RDVewxEAn2Y)6&$&Yih4Qq3oW@+VJp=bc)%8k?|7E-I7m9&E0WF@ym@$ttOj0i{siR zs4l&*8ogc~tibQ{%1?znMWYd^V&dYp>hDRNR7-iUH-&tHSSf{6--LSRi-&9ORjiju2RSE^t6)~BKjEDd=}_|_ zln+?AJIfqeM*MQQJfX!{MSmF0FV(t(Y>c>dsS>6M5vhhSESY>^ogIOvYF(d~0(y0I z#G%)8(s^a|=)Z1$J|SO%$oaXna2xbD$oD}b%!N5Le6La^UvOoP74H<_Y=bkEGCkoj zU)Z$ncpjK-IrBQK{b^c_n|A$C5Ti?rOHRDAqmkQN=hs7O(q7*f&OL|{lH}Yc=?vTU zwF)+QdLGEogS2M$G>zi9Xy{t~3`(7gKMi$VQa2z+T6w>wtC&5<51@ymOfoN;7+4j$ zt}8?5*<=@AjK3YqTsj;a{93M(mZq+ggC_eMjdZDty7sFJQ;q ze%=qZ+`24QcuFI-@n;xctMy-)K#U)}Ot||4MEPa@arixPG!FIE^cRb*$jaDg6v0dy zPg1`BIHCYVZQbvkpr;sDfqhgv9QQf_=2YI2>t&7*!*kC}i@M3yu^b>U)f{!2EyxvV zX`2?s%86-P)|`y{H1}VV35%&g5ZoZBxn)zEjOH3QVCBj0PLQWBs-343W=MW&WifH4K z??Gb@wWcL-*+|u0{ufUW9_$U0eBi5kE&^D+-98-PzEUU3%|n%=23_f*h|FR`1+-rJ z?d$L~!!vZB#KEwp{pcdqQ=6Ge3nHdM5tp9|Gx_|?E_nQE@qj-M8-*H$C$2;l&%{Sv z13;KuDt0{*UxM5f7#gP$UVi?y3RH6kX|ct*d`Ps%QuWhPf*>FLuZm(qjAP%f*<6NO zgK`BQ-b-ZGImU6Wyq0^e+6x%2D4G1Fu;ePEr#^wtb=~;pR#P@Ha@#%+^t*2fC8?5O z`+*WmU7lv9SdG=i)}mE;HgkPdTcq`goI_0iybmL7RJssOlSdXb+J#!0L?li=jSD2* z0NQqnD@(nXVqYwQ63c#9wf!RfJ1b6n57C4t(3xZ_h$n>?17n&uHAVIq?!EMJ^OOVA zay}9~*13*VCKoMEBrxGfiJY-mOBI_=A}joDj}lh6bXU*r^Aj}i#yv!H>C?g=ku9pmA)HkS+6E7fH_K*0E$9hfAt!UwVn08^dq^p=d+ZI`*!q^Eq*t&wLh5PYC$U0ROc>aDuwAROJiU$_HLEDgrA5 zySalnSQ;}NaB10%o8Rw<8+SjlDCVxfN=iS(*D13u=lR{wi1A}oLO9QP6I*@KQ;y@& zDsl2=)G~qY-yUbtEbNl^)EYCSqXzZuNs$8!R{{Bvmd;RvG1&U9aobgy2A=byXTF;uCy6abBKl;`{uefNEXz$(bwLfW~Uu7cT;@FC!l zIsBwCdvrv1;bmiMu*h9gd#uDL_c1z54ZOh65q5=-JDnWVnV|q`#NIO4*T(FG^2Q^N zXoQipuzXB}WQ@b2W`4miK{O?ek?e1!tu|oU>hjvy-N+=wDDTf*MnJLPx3)&+QC(Uj zTO9yJ#)Xhz6T1ap!_jT&YVd%6duO6VIp1K3i>&T$!(HbuZ&ZTzZ!J%}LK?dZV`aD4)xmxtzBoj- zZ`B|LB?0v}2(d%OLVqXm(3Via+9K|wWL$G6@|CM#wwmd{5vz#+l_ z5;MbAVy+_`os7->JC0~ONZep8C)^em75$*c?NF&fD`XFhgiMwhYWOm%GtV%W)6s}`kuzl6#k zbtX)Yo33fQv=fH5gA)#6aTr_x!K=?_EPw=#Lv8PJro~F^DyB8 z4HDfmNTVAZb@QfC0v$-9_}WBIpbvIqJSj5S~28+dCT6>a(6&IAm)Zx!~uc=KU0_>Z!DzqC(!*lIE3d=vqtIYkI=H2lq%; z-gVLVhtcoIK4!7(ihPHd`K7c)eX*T4uL?eW+MOFQAJ;pV0L+~Ud~7-?Yp;#>Iu=aR zD~=MHuW~oE(SJyb!gKA4olX+r^Y{%fm;4k*K5Id5&Y4$3UP7^#l3sb{yt@|PEC^C{ z1UiU2YPa!3|5(fc_RW9zDfBm`e~T3e3Lng0BilU8a2fIwi>!aRDpuD|y(V>#gFPrp z(+BCvz6pPAPxaoemhqzkYF2B#vqy6B@=Qlt+)G*<3y7qHCk3+z{*@%Nxu@wMFI2{! zJh^bn)mLFV%pQCdZtvN2FET(&hKFP+Sa({alh;_%>@9EV5N*n@-nIN}eA*7Bu-@;@ zmz%-?g90_}A#Pj}4>S+EpKt#)VndAP_!5f2fu(r_XwQC(X*?Gd(RFbn5dwC(;E9eh zvT+`2q2D$YJ{FOwFQk1cWEB{WygBIs&;b8Kd3l}Hw8dJr-jEu|Cv0iQo3mXs1l9?G zlzb3VY$ckNhV-((S*e^y4MVxle=tT)gCoaZ>m%gjw0gq-M-x?d8+lUyAWr;Pi{5tV zS5bOwlZ_jtfrRF7rC*I>e5VYkNtzLSqIxAdj0zb`uECAF|6}yRCGF>Y+|t(Y%|7cr z_@?zuHEKijMx*mJ0C+lD5Tz7rZwYu;*n%<6afm^L_SM6gx73l31jG+4vxn<;&PtC| zLB4+u{u5os_ejf&Tc

KcV82XGxfPDpQv2GDyu){;%%`Ib zzrv2H%8H3@eh@XKZR=CWTfq%TXRiQ6*BNmFSYpJ}jB|r7m_Q-emeV<;mhT(7q{P&yHw@#9#zd_aoUHDxZXo1Wq4huS;| z|58=2(=By}{(d0Q`#OG3untcM+#RJrN+v*dL(m^egzN$G49 z?SD1=`$vG^j1%KkV?WmgL~UU|(g5fs*riGOE}8_nniajH=ulyLb%SifN+P>R>g0A0 z5xpEKeC!d2P8o3nVn21T^D03(+DxLBj7#hLZdWtUA~)B0rp_WRlV0$cBCC`>PQ)A% z#AyM~w`|GiEk7?l-=u0gESR)vBJv`cXc5W3k3)BRP<3|5Rzig#gNN&21wUt+%26bO zoQuvy;3ThZ4GUvb*mwpJGr(`}oG(Yl;c7S>T$CI5RLYXz>Cy4jG4ar_@H-Ds9sV^_ zOqVQEqO5nrnk3a$DfUi2M#3>UM>JYNyL+Hvo^EzffzsJxa?iy{ z8AqJf1CaNg>wiRH)i>3`e$;1L{;*4w(tjq?KR!L5X?Khqi2n^rSyfQd$+;`(b5(}- zCU}0s1WkEK8*gin|KP8K+m80r{-ju_jWbSsqq*!|9~jMd-DWYdU@(f#;J1jf}Z8Yi4=xci6t<`~}Kh95s`!ic2Gt;ZVcj^<2~&R zDC4deQ9PMz@ep-=hvOljM3NoMy&2!~y`p}wE?fJPb*IHi2pU!ZMoN46QiDw_$GUQ{ zqiA&r%b!}@qx8;mLaoz|wjxzRdZFTA|JiJg#oIP)=ePoV(n9~OM8f&rAbd~%Fla+_ zL!Hu!NjKBkq0Np>nV$oHF35h?j(N<@g153Nk3@jWXyHIA+E-4G_?bAb>u@fyj7yaB zY6qt@o(@Ta9;Pq-`BrI%v!#Z9=x9P^5YrC$)uBwqe!LpAvIN*479eKT?b6Cy z7rd;5KlEG~C?u&umR9bxCi?M^i}H7hdA*o^o`zA65>+>LF$#WEeOMOu!+CmQym1f+*RVXAEElH9_fwbnY$ zxLLz`W_{Hlt(0mBi-_VJwoWe~v$c*2Ufr<0^wlDPpHl&0dHfjH3*!d8h~@sub1=K$ zAu}N7*5#BAIL@lsj*Zf6ovu{QJHe=aY~XNgl2=QmD%)(-YLTySR+kz+$;wLmYMDj{ zKsU`K>QzK@KQUI(BZ8le&54bXKi{qW`6jdqHX(W0<%L~G~K>R z!skipAs)u#rI%08p6mgGT;bGezb8}-=_LguRIrr{_fxTn2zhgJb}}BLXZW-AD3lp+ zZVElMD+At*Ag!}@X>M2g8-Iw`5B$H8&i~)|%>NL}|4HZnvc>;XA^#_xGqL^O+5ab< zGco^<5t9EcoiFXKun|gxON0#vxWH2q&ivh;0RWDMV`gAxkq9FQ3ZS5@U`Qr{P)bBf zT!>*w3@RSx9_@Mk-o4en{9LJi&T`KEzVdzH`&ArtY;)K;g~aygmtea2pur zHF!`LkWK*uBp-eOQRuS}6u_YUk)8-6RLJ0aV8?(0<|>@@YZeCvfD#j^e+}q2HOxs! zi1#lAAqvV%mB_xnVSQUQn7f)_dzbK@1|D)iI$BRG62SAdBj+Qa!?iKZ80176Bm<5fLdZSbzr*L9d+MVBcWYo2P&uc3_`@ z4X7X>9t3;-4>B&a zu+Gm_!;H9)FW?H1#x)=yQJ>$h-n!B8adg1Y*N^b;w!WdOtZRG<)^A?qudTA0*c%WK z$cQLFP$3c#z#e^qq#?TCFN`rj=#T87|GU+oE&{+g|GH7#xjv@%FDk&??*1O=7jr5e zP?Z)$z$rgb8)5>2E;RumjIkyGs;z0ru zB$5T+@c(fdR4b~yNlx7M%We#c!SrKKX$`^CI%WQ4i=}D69Kh8D}fVkPrD^E?@ zMO#(aBwl~Eq`J61EdOgif+vu^nx&I$jvYI#rE|k?o|*Xba0A64WOm+)skDi7*EH$e z+I5<==eYFPnRJtxTarrfxC(^}B~!~Mz{kpdxt3v>0dsN+g5iR%*TgB3^pV=1{MyuY z3bH5B5m0|SX&&7_0)&WI)dgbP-Xp_}#2L7o2a=+Cd(KK5tq?urLt#5qH%R(ii^I>i zyGd=}fUN919(^z|qhRfs%$?S6OQ8)}fd@GTaZ8^@Ho*>FKZD<$J|`w!MzRk7E` zq`!@Afqd-pr^=ykHdZs!%A-iIA8+kOC0}dP!`&#s!CR;EJ?ifDP*Ezh5pN1);NGTw zj8MGsdsr5sB6?L!QXHQ$OZLm`RKnS*IxLxIGaBRGB%9o^xnYGoIw5M69t{;@=SbVd$@U{-)oNXKi4+;DZQ|1hV_ zZ6I6Pp%!0PnN`G}6iwY~vTPkbPFGhAXZ#l9Y4@UgzdA^yjd0NtZ}knKcAT2E45)NOpYd-?J>8Dkj>S# z>fqyG$7TidWh~Rx)81`YHG9!V%Qey%CBvL-P=HX1VUCJn-1QjjN7c zku*n26nb7vi{E=>Ig7^g#q{ot{)EG7^CG1z#lQR|{w!?y8WwaHQ=NXRNwQ<_((enl z!zV+g`5AYIbjRM2_Ws$nO%Wt58Ye_w@|>;m;Bnl-9Gg>oaITAQJ~^LMR#E-UGr*JA z^e8Obd`aFlr&L|H0TAaVm4WOLWJ);^kzHRTaYLD9Cjip~jfD_ixa}eLz3}P{dnb2U zkv6WsNkr%NPp_TrNvWP*^jIu&+fTEVqd=+8lz{B|0QaulIbz$E5c$h>nH`;Lu5G;? zZPY92abhX+=*b;(98Qrky##yQ&Jw%bJGogrc{Eo}YpI~tM=T1+Gbx6Q$_K1!D~Nh2 zLw|216bw}wQyxy^nhY9`0rRpXJ#Us|H4yp*LnN<6969J6h;G0zWC;=}v^HeVJW{V` zUhi;H=z?2-5j%@tRE&q_W++eSGjiDy-)S#v^(8}-kGfl|dBBRAG$T-+1G72?H97Kc zt0`|szBF!%X*m-vFJj><-8FQlwGO+|^p@Y@dB8xCk(37+%1Ezjv>uM*t&zc}yM5(jT5&RHe(SoD#L@wn}UfifWB3d6*W zAzh>Do{@}Tu%5v7?+E|El=`x~*z3J0`ZrPmHr^SgavxGsBe}eDngE+I_6!%8 zh8i_rnwd2scfk5G4zW*AOg;a3YC_Kkf_1-5jcy3BZxI#k?CmypwiismZFVSy3efoYYecwvxOSR3S#X>ZH5QqHdJOlAoy zg?mb**0daaeo^O;S%7EPisAq)*6*P&lkIM_{Hvb-D2U*16K7rXG3;d8 z9qHYOKjvfQK$=~}DNmyE53m+UqJtp~mGiqNa+@}@Q6=oyT)(L+R^<3lf=L^ex7g(x zdmTEU!74ve4V~!RFJK`sq0P1DA-p(C8oUJ&Ku5ni6T~>*PFL}!HkagHTU^t?qe~lq zkoH_dd3$40(4wnMTAPt7PkEiGCSO!w>S@kyPp`w@m!L63}y#Cs^z2vITeE>ogV_X>#u!IA7hr5cd=FbCf*X!hu zse564pA?5|9Q8Dzx_sQq&X=svlK_h6%~>&Jr~DexzmzPVM5*0>v8Qtt2aL-u+$2EI9=TPJO%&u6XVL?7Kp3p+Xm=}0Mor5WQFB+GAYU|I|s4P{N zE8pBI0`=>;>P=G#TqOh*3}5AYO0!Oj7f?oIrf~7PSnj5fu{$?;jG+^MIfCKewO$Sp zM7-%hNgESoyJIUN%2D`Zkm*acw54bK(w>5nqZZ!=K_R9OA;0E|nC%ri8rKrxM({2lcgQ{hs2Bb7uQPV8xADs6MB= zAs#j#X`ICzBjdN~XSQ&7W?NiQ6Bf@h^)lKN1;JtaWVTk* z7@BF0+eV(N{EgP95D?bx9D`0p40j$wOk0PS;9~p`>&nzNSBG~GdkyYx&t#oLMt9Q| zp4yZGBmRz)BcM!X|92|ZruEKn^~#*8bDpsp{9M;V+M!U=*KwBi=N`#TcROg4yK$dP zhAq4w7=3B-wAAEqa@B-lC)(3T11?F;7Ch$wwsJ2&uelq+&_f;SuT9|%TkxDnAMHX* zhd@iZo3Pk`M+~Xk5#5~kjLv1A`y>2*besVd3HOpJ+$H9V6?yPahbm8>-sTVQkul!# zAzl%%mLj8mj^^@b|8M9>GIAlKeDCm+>hMdlD@^=x^eF8=PKWlMt@KFr>S!MLZ}^L zSdkEqT{tYbv7${Hhk+Ni=FnbuCH&%K>~BUfb+n@Z?%xbTKrVkY&;^mbh~y4DQB<#vx_-}87kg$MxuYV3r>#&&}cI!VKD4L>sOP^nQ z57@1C6W#Z%c!(}|8^2vy7DIDAm&m8U;GgRT+6(OatA#ARc>d5 zh9$vHSoM%?-Y1gg5{DUjf`-6u+eKvOJ&l;9M$jtwA=CrC`%*!C?v2$AKNLizETGUe zzA`Po&5uy$Nw%OWNfx6HC6=#5!7S(P3Wb_Nx2R+DQQqSTJ=x7o!qJd^4B8`u+ed8{(2CB)qbTO4;O`0(GM-2r0bRgLM~~Xjdlsqi1_05cS1a| z#H8u6hhk0Jeb((ttkw38M;#f>fvz~o*NwP(j>~i{tk>y>tkX7I3pB(GYXOlnQ zdu35tEju0T)WWvrH}MWKdSmhO&Qp3G_7OODoqPIN)&JB>9e zIj4AV*v&6Cpv6asm8#uqJ*&5XdTqq8IS!jk{sFh~s!d4^M~+TzMOU?HyD;ER{H`y1 z8R!wx@k!>`eIil2!mUx7oAcF8o8&Xv?6RPf4q1OW|NShD8S|Y@_C5Y$nd{^o?so>p zJYIdi;2a;X*1KfwTcE3;OLlVk>h^ngH4XzyjXevpXnPxBhJ)59_)E(D@n>%G-Y=Wb zi!7?;cI0M0P1}Z!f~8&Anl$Gx6kL=j4zqCDC@YFNlCUn=AU)m^7No5ij-H2em`f+L zqSGrTeM{xatK8t%tmb)1qUEEV23~AMH}$2%Zh5P>e!&f?VO_4{cd-}J+XXqN*4sVA z`LU4C?E&6I&|6VkKa)rFx4h~*0ld(UDtdHPGdB36rXqN4%|Y!=#Zbt08vMnEcq0;N z2q<4p*7IsAYeH_9l&BG%l;LA4ibCB&{L1=q>-T8Eb`5=U>bN%cbY+-06Xd<}EX`^R z)V(?2gp@@jc2-cj2%y!@2p2Zb9 z{aG2X2YuRuD!OL1tEm4KZ5X|5kJb8n4PP`Zh_*rMCcD$Odch~x9t789{wJ^fN++uS z$yhCjE68VJ-A!g6d3$avP@EXACn3;j7p6lKP^p3Hl|RC3br_ReuiNzvTUA*8EP}fF zkNlUeEx2cZuqvW?m9W*$?A4eZidezyr}H;Cch;l0k0gsRdMK}c)Dw;_(R&$o<_S?F z;??kdQk`rB_E#93PG84MU|JrDmujF>=)%!PInC^snKffcu!p%1tcPx`xcUJUT48HV z#DOT*xvwYY;pe#TJti0C|eCvFbEoFa9dkRMXg5QyIj!NxX_r}oJ9iu{oVHv4B7ZI)M7u@66(MmFm7aT{v60Jrm%r&@_R zZ0+Xh$nF&C;~IBu27F=|TNL+q0Hqp7>2$PA5A&cgYjYU}l5r%+SIABTf|!PdD%B!P zm4R&~37QVQ{$+Q zjswx1?A>;%NSm@4o6KaWwtZuFF4G@5&NCtp9craB)7)CAOr^eBWi^x^@sG+60)umB zrJwx;@|aTA<5L=$4<`i=(xG~^w`zd4D*`$P-<9Km=4Q?j5g8=(v&=BWmDT1aM>5(p zCh4_*WM!#2?(rSzx=D9ds`3=sQsZN}AniTFu;V7o?6Ixqd`>&<8s{0hY)&<7b_7K@ zW|Sw!06ngRHM|;UrI9~5JSi7qwc=nkSIo}!Dbz7WM8kaOs*b8FoHhkH$XLQf?)U)I z7j{pWZSuNbiP)62vlHs*RkY&`eO9{vdW;a%*6BbN&EoFJZSpybz1rPL*KO3E4d;gj zszB?4PPHC4dbSymmbXpU@@aJlE|?GW5Z|WrsK>NLytrI`+HSZ!zL51+e#%_VB0@*M(dx$RUHq~+Bn`3H~ zd+B40K(<->=G(bmMy??5B6GrDIC)d`TREhhT>|=J*ar)0leCqVDC2EZ+f`%VstUyV z76&pKLK^Z@HSaiBh4*m;_V|5`gO_nKqtoTQ%jntR$OW>969yHB$1+pezZ3E9A>Md| z4LnI>;StPYwVWTnsZZJ9oRc!TMtzILWi)rM^xBV&pLLB&xjvjwnp0f-x|F)#?`Ei= zPn=wpk(E*Oe6vQT{4d7NAxIElOV?%Fwr$(CZQHhO+g-M8b=mB)ZBIqKm=_ZC6=o2cw${&rharx zg~{5R`Ha`x>111E+eA(kL=guyR@JnD4hMhXu+!)s8%5NSgAg)nBTYX0#g}yVDisQL zlwH9|TS2EXs@I#hBH0RQk|Owb+YYuZTl_Os#O?=-ruww@sZ}4_yBb9l%c+?P$Uh#T z#c>svKs&-IB8;ZXV}h$`k4fq}lQ5K7WoEkSE?T{~6Fx8pao16g$NRjr(b>F>dt^9+ zG{z}JnB<_@2`9Yar9m`Gru5DZ!mK2$xK~e}U?w!TmTa>ocB=mrehPH13Qii*c;tkT^OqHz$Fv_V6-sjyZnsm0~?W zRaCAv*nohDw*LmWz!7Y3ZxeA&_xCddPtOtLE|A6&-~ug3Q2fS!p^&7)0|Fr4V|#l~ za$Y`vw07IfYIr|7ZZ2w1I%;{F*tnwu8T*Qe2LY?Y0*YTlK?0NjOm&T=2?+ooP!Iut zLhshsWeX@UUhTR0x-i#(Aw~O3zkv%c0b9ijZK<9qSQO9!!7V%o0fdME2pK5}9VrQZ zg&z>9Z&(oz2|$(0o`N_4UBCb|AULu8CTij>U)}<_848!&K6^kN0=s~Ok`j*H8;5`* z>@{Gh#&BSlE5#WDb{EkEUKoQI0Kox@UH_7QNseNLTcseNJv}|3m)i+I5b)%jc6hhPV8n@pdko?Z z-~qU}1~inx3GCv+{6JSfpa;O;nmYps0SWy`y^z1F6H$D+*YiSzI5@Y3e+cc#{oVo? z*lE=nM1hZj4}f?30et~4Or*frruVwA;WL~?|INx3pjA{DfcImF|FLioPr)@s2>=q* z2W#=aI+jygwNP#<;;pTI2Na|qb$==acm{}`o8BOQxK-4++pv$Ho*;p}xCDJ;4zEt= ztii%~o`EbXe+CQW?><{O0~7%i3Q96EDi8pEpa5TinV>$XjMvU!e{TQmd1jFJF5)df zghz~j0u&%I--9pW8{UC{6!7v61wZ~=-yMVKNI)Dyf)oM3YmiW5KkjbLm@seFv3&mU z74ZE~5oP%Z0IwGhb==l0LpX>I88>}_-vp&vtRyrUI-leaFh>id} zlrbeDQiGU^OS^C(kY74_^^N~mrJk(DXT=Xwgc*z>&^7A4NTqsBIv%NyMSjaNnigFpC1$C4r0b zWam7l2w$J`?G9KTfOFs#`fXZRqKlvv6}Iv!VfPyT}cE+QQHay(V2fv8VM z%8Y>ivAEFwEaeKOr0Q#&8_=2qNKONc9`XS( z>UX9|f+s9CBx73`oi(&qd&X@YAiutM<7=4?FjZJMV$_4;R{UN-h8v@;*Xc1OB%N3AgjjuS0kn^NK35X(eb@B7sdkmTEYaJ8nX ztQZJ-B_3#H`f?HnH#1`8n!Vky}vRG zS#&d%A4Xv`Lko88!X>9=-}5m>C~LMC5kgZ}Vs{tDv2ERMf!pav?@dAyR6uOH1A&mT zQLz|%n(!=M7Qq&+MCesDC}z&Dky6D2jxJyi#&UEwWWt(W5%o&5f!8vY)V5v8ouBW< z^i^O-Zn^myx6G0<%#E{)o5vDZj}U@>wr=_< z12eW!bx}?VzHtM|oME=txy06FFk{(Ii5F&paD>GP&1;|}?dG<$*^DTG9ZIai#}bx; zR`Ysq5Ze4UXqsrygAkdeqthFF8a5D}!4nK&R*L1qFjh7}@yYx`s%>00$$hTT;Y#YO z@C*d)ZnjUoO0lW9%+<$bBxb%?OBt~Pe5#)J}mH+ zDBqvdq56d`IZ~hcsx!yvaz#q4@tvu=Pv;7T!ZRWWxG@@QZYX$=m!2IGIStfSUws3sWy4i^m9?n_h-ewoWKG6@GIL&hjW~y? zJX7rbE92)jT4mJ!EA`}kY3DP)U)*a^7J1q(8-fs+Ed_EpRf-j9#1>98$#}-MB?3Up zc#yd_tTeIEmNVyYb|f|65pzEICS=hqNOf|GUMa?VZ#h3NsP((}tY$)0M?ZhECe6eA z)Rx*5zD90zk0&n!Mtn+`Jr%wuUCp{CTpz{sL71Kz<#Eu(?;zIH22{k1&L2oF>%=Gm1& z#Fw+j;Vc!Pw7mB9Ae#dScz@!I=3cv@+`mTmf9TipZc&_T-W?np4P&WF7BgBDxE#5^ zHWtB#IKcE3A4#NTB-30v#-V$2OdA8$lT$VL=LfJDT@?lGXd{?M@lj6kd081s6c~~R zK0*kwrCct`fK2$W;qbL~EOOpBF7zcU)Dfc`52xck)jFJW;QKAI^%tqjpte6%Y+IW- z`7l;&^%HGEBS?Ri;-AkOXona#Fl`fLn84NyFmdWJI`y|a zlSTaJj|tu8@5DMw_5?@WUi!;cfs#w81L-Y+RFlP`>bh8RC+9xF2$n;i1t{E=&etfm zI^Tukg7Z5Yd8oZD0A7V7*{9rmM>8}&B_b0C*fvkn*#6|_-n55vA*~H>gp%LB@Pc?G>v%7jax2)1Q{VV zaj}Vu7a!_&J%2PU9{XHR*R{vrd!D2VruCkE8P`ccIoa(cZ=T1EZm-=@v-|^^n0Bx` z<(zdQKPR81Rv0}J9vP0i$3Lf~Xqf02q!}W5r_*_w&Zg1Fub};17J#yuT(+~(yzJLv z;X2U%m0N?LuTKVGM6I)b-X7F99F9f4=?B^xL}0dmp}tb@Y=vo6f6Q{$XV7GO*z`bRpiVjUe zu}#i1Ogr9YheV}PBIkvhK8jthI@Ypo#`a;#s@BtuMTS=iTgYC1t9?gN&zta7J99p( z>FH0hAcU?kxh%Vwt%vU^azXyuTj)7&uT}mc=pmpTGf7((`0+WsyAn_de*L$>1wN)u zOCA+`wW#v02z#e?p01h7uB@f!Ok|+*e2mo&s)j*E$S2{TQ#1w67JNkiqT4Bm#U7}|k*Cn@6`{+uq+$?M|C zDhW4VN!!GxQ^#vE1ZP^F;ZCICR}+lfC5ow%^kPiIyj+L_PddJ8uU+^Sv8p zP~yqIKPFoNW5d zbXl;kdl5}>$#Qa;l2bFPI1E3%3I9kHbpkykaN;XZd&=V!^`j6WF~3(PQ=M%1>zA%y zIU8ie9(cr?jiaJ{09|?DO)5XWbawt>`=-9aIyUpwJ z1jcBN@76c-SJUl6P#8WOg{_JC<}BHPBoQSv950jDykvk@V{lE>Xm&4I>vq|i%IR~ z`i6GxL)Ykh!o^RGwgW{OwH4wZrDxEW7hZG$yw3DxyHrnljK&$0yvy!|l-JiSRy?Xl z`WNaU6c8f^pZCc#NsJVi2YqJSO!fP~bjL z&@J`E{3q4>E4a6krK2e2dR#Ynx(LxWcr&KV{^s~a!^?@IVy3s>^uy1RU$aeTxs)V6 zoBevZW9pDBuW)lO*D3_2?5m~XOB0wpZ?r?bHF_1QGsJX34-HJVhTh1m(0ai$nPRtn zO%RYg9C>jGKA7pSzx>O@Rrvc0(9N+kY2Qj?Ce$RxbS;&IPeI~^n81mT>Bu|(xdpQrjff|}(<2GStd7`GOllZ&u8b2iF=2d=p^WLku$4`WEugn2` zJtnS01Plx}U$^I*)11y%nvsX!b-+B+P+jABSv zI#AKk@{L~*f;G8NJzh9jcJdGWJn2mao)>9w-%QmEaK%JSKNDQGWz`M7ndEmfsa|Yv ztuZ&IwRz-)zF60GlAh*$0%!fd2CBM-5_&AM&!m!NRmDZFsBEp5B#w&p_R|OXsTffY zWL*m$I61X_8gb5eS)c<0rV~~Pz+jKuJ!5^jHs2DNv@^Mg67FbQbhAvuv4vIH8KoYar_th;%}ghejISf(I^AmQiGSrp zXii$8e)rK--~)|b>4{A5qI8H>jOiJ7fP>_X zS=hWFkX5@^H|c7kgCV)jk||zr^53e;6yVYy`R?E}OLV7*Pz{P%v^Sl~gpcw*IvP7V z8#Q-#t4fFYzy!6R>#QX8D2=ntDRN?R{Lm-3{m*}~w$;9AR;^Y-rFHZUX zdxwRco+gMkPSAcqNrm~b&b)}j$#n>B#YZ#vnE^R1%XlSqHR!tUI|myTEynuybtUAK z#%ByBlc*q01nRyUGX&aFs@=;?c=B;7>haYI%F=T08!&fav+K2MdXq|XzA(A7sk^Q! z2!M{s8qq2XrU+LvOw&g752s*O437(@S1E_m)ZBdfQ{B9WdpnZa8sEx(GMb`@iKalkPda|O0XUXMHR{FB^up0W7@#13l zYOXTcZh<2cM}ew3XD1#C;$H7Ixnh>&>N*qbCOT(eMwDrNozC^5!PI^eKi9KA0a8wxm z4b%#+MV^Oow9b?{j+YV(q z5YS%S$}Fc`>W!lx&P)nszza=z+4d%xE`4ap`~(a9Oa3%i+L1`0ICD%~f0qyiwr91J zly?1lVJ&vI2BvIc@f_U|1-M%yKjizToeb1*vS{@jPwt|O!2rW`q3Y-}kPmFgCb`*HrUV_#i z`E-ARn23D{-+0YzDb6iwsQze={-R=om`pub^2+75~C^|DP%6sO0O5cK&cj z%Mqm5{0{D`P|}YTUtr^K;!O1OFROqg&UEw*-poFP`)yqgO*+jgUofvdizmpeXm%t( z!|AIejP)c|xl+kSZ_DGSXuxnVvpFf&u*gre^7r?MSK37cYnXSdu3>^fuJ6Ij(af#8>JlAkvg?UF#nrmB*Zwi{ zccyBaYE#!R^UqX644|G(k}ry|ylL*Th@CG>joMy3ly9h!+qTKyxl~*s70bmSbUBT~ zOW{s7!SL8WJIK1stdoWXr?ZZF>VM@2kCU7dV)~=d045Gi^&c`Js46?o&AkhyO-(HA z0jxC-PMU^FI6s312&pGAb2UzYra`2cCc&;jLn_*-kIv(lye|dYu_)mgUn_k_foBq0 zB=UoiVtp`KZ5LwyR)lUEgU^_{Z{kJBE{GVk-_^))Vn1Z_6G)Q`VyzbK+5G9kNTc2L zxv6=ftQ){nqeLBY`$OMpRgZbSZOx5Y3>9NKuZI|!iDTIE#`5&{Y#v_HfLFvdKzbur z^?8f|goQrgpfZjpLltiwdOf12_~&XW4|knGFVkD9%>TlwqYR_PDeO6xDXqX=HxC=s zZu!ITz}c@*)Q{m#j_c&BSZ>ZB2C&qj04&$vHdtmeKmP%&Kxr!$hE|8JEqG zKXBFkS^BtC3%Lq-4kzwOkphD`P4(*!Wv=w66{=jj{Uzh%l)2jE;ygp<{UuoPNE? zlub5k28HLQtD5uWabi&)ZaQCxP~Vb`ZN7hxI^&Dkk7|>w+k8;@UVdztb-M;XzN8A( zg}o3C^BrjpstyVC0FC!~8iL#j&3cay_Xz zWy$K?w=j0QCua?F>q3q=aPmJS+m_9(-e>q!a{Io_OxQ=ai?>wM3q%3M3&E%F-ZLe< z$g15rz)XGaI^uH~4+Ffl=e8|wolNgsNvUHUlF9wbs5nF)liKVX;548Ag(Snp7xmU$ zS|5+mhFc7!yO@u;jxsa?rGGmMAkpUH*P_#cO-S9o8@mBI+4hBdp@cT3$PWEXu+w%xQr8C1Eqy^a+<_m5r$XTg`- zCXS}d8@nyy0mk3T{KeP|cs+|B28@B*(WaCM%73NwlE4{TG7^33XTsV%>b zFt=7W$-|!+s{4eSyXbpe!hW_Ti&AOV9 zd!8^8HKyk4j3B9jcCIN_F8DULYmHCpJNow<-&!E9b_zfmi+>FyAORPW=ynb zK&cR6<{*(=wUsI)471u%xo=V>|5y`W)S7(dJ@^BdHS=5k2ic76Kgni{|FbQZiJj>e ztMqp4Bpv})QbsR;LRAF^ zp@dQuP*4y7kP=Es2r-dJbR;MuXu%sXypvvLGdK6^-dEC&_k{mNZ$enDH7d*_3f)4C zP&kT$^iZ)M$~(^}F4PBr1gSN#5<*ha7%L()0;LfW4JaPSjD^S`&J>7379f->YJsP+ z2(*GAk;oA!u1&*C=}>c1P8<;5QGS`aC($W@VN|tqGk8f1MDe2 z17D(eNFreR=ClzYCbm35QU(Cti#R2gQiUv5;x-Tf6Ela#KnMg9r9VorpQ@gdpsiOm zl3l{6`<=;|wA8bRtvikDorcQ)_Ifa5HhzTx?C~zl%DNsr&2#7$Fv_ApP0FVoH7;z8H006F} zQB)P6;Zn!^~f#>oiOcl6-1q$aSl-Plq8Va{@WIjR# zqF@ey8kxC2Tf)fPm=HjmaBMlXTRk2uUA(u4~D5HJB-96H2opd6`T zCIj78loYX@qQP9G$)NrzRDC4~4XixSnYQnGWq;4@Fa7=WQfT2O$l#9(l5c0RAU>wLEY|8iGgn<$+5oVPl_|p;2;dl1c(Ocp**o)d`wCLVS|KY^j8 zKQTbkoxeHkRO^W5`o_k@&ZN}$?8OFDc9J6sk2X1~D=dI?v0)~}tA&9yZhJsbcnmo3 zTJ%0J1$81Nf)0=ZrUC*F3|5dYGZocF08{SXMVD*tCB}Z=Ud=y7VKLR9Qy|xNpqaWm((X}er z9DMjXes?FXYfjHXqQhXBF7$Yj>XY;fP%3~d&6$NGDUbKZ(2HsnpRP9#y;%<%&!Kuo z7P4J8&uqnwr*I5@wFhJUNhfowgbxAN%ZKal2MZ@nN<(WnC3nfW|j08+~=CRion53~@%zkeaZSK3PAbq>H zxlME~s4wf+J#{jZ0UkKk1S#$nP^f&VHt`6= z;n;T3j&A4M_5Sf$%Ik?QZZ6H?&ta`b=XMj*oIDjx7Wc z&ErKjmD}BpUtcebVK3)@l}#g!yhSM*;E&-{lG5M7p87@#MX1z>xl?*POELEkgRv;thx8sIWuPFc=m1d%DVA za7!d(I(T%H185HHaoMlX<^TO_pZzbm{H!Ieh3nt;o6V)@X=B5QqBqEjwW$Xv%_F+2BROMW`j z@~Jz~s(XJKnF$-5=Y$R7-RZVWdN%abokBF+hF2Z#s>N+Y;OUzyB35eNuKTAy&ZhMr zCkq?hA)e*Vsa~+QTpB>L|7vZFflg%1jThy-w90oe~pp3j&<>qA_ zJqUKxRXX8p7TV%*B;3W6TLTXL^`xB;@2l}`GCq>*=sgg#{hku;LW5nNy{u8CxqHaL zSBzn)UkAI)3zU%BE4X}dO40k6{@diCxLKHhv%jz^d~S;k{tKR7aD9m~xzv*JVkw|F z?j=yjpyyv1NW?;KdaX*Ii$A+fk!K{%zi#vC&J=Rv8E>Ja9L*s-q;oA{!;wMM)kjnP zi_|!Wj_Fe1x4Z*FoN9*>si@K8>vy-#qmDkjf-K|?{n5R!zC4GBn>vAX>qg^TqvLGu zrvLJK$5?2he~xRE^l8$snE1g+$HK(?S;JBAwO}{>k`nnD%jGpFC;* z0(u*86DaQX?dst0fv4xM>`nBv{BcT33!!FB|5r zgwEv*c@mQ~KwhL$I;sVpV7w3MWHMR(R+pAHVbS_+HZ^ub4^KLUFEjXHx_a6HoilY% z#x-^G)0Hkz>yr!TgVxiw4NB#ob!Lq66rk0vhdM$v-<@pKId1W)B@d&VK31 zmuy>uj|yv)yQSHN7!noP0*d6-KWbWn-|5O*bn%HFB(VK~msJH~5`G#)JlWT{4)ToG zm)V}6>iKfd*W2He@YT>q4`@rAi)^p?YAn|^b25Eu7-zM+8R-Z!ZPb}~nrZuY=em^) zG!#04oF1=Z=(VG-OP8*)2FDBCHMFNiM>5S#*>%Qvm_V!FTQK4DWrx>VX!)x5_jrG9 zueM}rtjL_ULk}lPOjdG>c4MMJxR%+x@FMM&l}lAgMZdQ8s7wgMV4Ed1E#*_^@WQ01 zRlT{3HHomz*mSnZo;AeyOOu}}`h=_tuP3KM^lH%)V{H?y?%@~2v;tK3$%A;&Z1ChBJvM4DJ{ws$yQP-vLZ({dng0YXZTq@m_4AsB6fL+$d{wOcHsmBt?isAhWi@zREeUI~ z-$;Ye-7aNWO2ldwOl!tq&~cp4wDdx9#pNwED9(GmvC3|%%yNLl9^X3o?m&@04sM29 z2FJdN*yr@JpXUAW|u}cWN zE+;(73pso`6o{U=26ydyjmaphF3~4wPWq>DXFD-;u$J;-5^ju5&GN>~80`Fosv6kG zw^?JVVPgBG;qHxA{$VkMUj#i1jN^AYe%5Efo_cRLy?PZ7e>&Cm>__SfmR){4#Nlpr zwgr-X-_w)DKj4Y^>OfwM>u^rOD3*NXI(cbVupwWx#X&uRf7<@yzhq4Fy@=LICpU@jz?@UTl zAF?mUh1^X`s2SicWw(sklMi(t9p>c^l2}Jui}~rziiB3)3)gIOqxdRl&KHv51zhE8 z4Ne4`dOL5ffGL&7p5|r|Eu6O?U-=flyDq7fR94|K(S&lM&OTQto|l8<^vp3VGlAJ^hEIV3^L+6%lZu69nW)0KS@?x{S z;X|Qj2vuCtp9!dpC(L3PDXa7 z|0CSerqemW>}G~;tM$sSjMa9t)%G_7*ZS9Tvz613y{Q$R#daCvfRM<{f_Ldf|pfx!0Y_|n440%U=mz448ir4isi zSLfe=fU{evyVFtm54i*=1W3CE0H9eKn?OKBP*GY+_pilMNDr0(uo;*Oa~%LhH`bO$ z7N9YWOn}>*0JVR52h!jHAJo9e-rVY~E+^;gCpRD$dv4+=e|S3Q(iYIks8VPj>b??y z5fMxkF(5IQQb6rK-+>$5{Mx@ekSvYvr!o%h-@X3C=xN{YBvksNmCN%@JU_(92q;4< zs{=49;4IC}5$1nKW@>Ks>q&sOIX}PUFY`xo`X=WGIO4}q0+b0f`|;@7SR2P)2LenX zdTxcQr4t|z$myY+n}EBezuwNJ`3aTi!1z)={1L%e*V^#-{u%wmkN;_hUeEj)BEm(c z<|V%HcaS!Bl!h<(Q&c*|ztzRj0rUfG4e+x_&ROuMwCc)#2H<;WmLHd`rLF1ilYjMF zd8LouGy!>4Em5)T?MC2plg7;4$ll7*98SUUEnJ(JeDMe9hm9Ib^V>WNAm-<#-Ty-7 zM?Ia{$+7Vf;FMwE$65#D=jk)Paz=h^A27nCB%?*GYy7=a2a%FgV z0@C8--v0ZC^2q+JI*ax>+NKlvp;lWCQO5&D z9(}GKu(p*?Ym0n(*(v|_oZ4PK?;yC3>L`>#@NnzIK;q$eyT}@lB2E{Q3je$MzyUYe z#8W2E<7wrFWyo+Segu~1)xIhGxX0&kRXv4+4UBQJ@tAyBNmWbDArMspb={D1S!Kg` z0TU2(k27_-u%d|ZrLT^nG0MivGA6O!Ef3W zuunFg3C{Z!(vVG1am~$S*`&S*Qv|cATE#BHPlr0R^FH|Err9)<%x0#ZcTCFw&nk%J zzqQz4jdYf$PeMEQ9tF%BxF{l;x5U|&sjHf+x8#qHM6Q5RjE#_A>K!z+XKMx^*%lQKZ$4*pk#T;k;|rDFDr-<%fgsXlIo>crHy@F_RF&~I=}Wsdi=ub7GQFxLuA<+MXF2Pixn(x{s2y2(~MEHZdF zl|W`ch@VXx78RRQ=0PwRlEl4Nv_3J_hAy6>#_f!IFXGx^K?SLl6&MX>v58S|g>ACA zCH3v1TTEz*=Gz-mtbR0@Fh2c2?1A?RQ#-}Zh}E18+}G6qwqiZ*;OH}%Ql~y5TQ@Kb z`560_;{nuz*Q-Yn(s#^%l6>0^1JS0@PJZEpjkXdn@(1W?JhDg1Qe|VBl-kTzm=6I+ zaEhId68ZgBo}HxehfRj&NHKnv4AIzk2Nw+2iU|_*;KtudE~i6`PP*}s*@D=xg$b&1 zNL8kR&y?qs(J>+S6u=gj3Q~vrdeA+L8&&61uY9ievs4u1)Ore`vuGS{lqN>Oms(41 z2xHxEgpbo|Juh3R`%A4(GnE{Jwq|GmYZsXKXoC?#s1DF`FHymf<)rfPyx^Ix;6xa& zq=iFwkPZ7R2=C^FSDC?WdoOnRK+Y|4=SZsob0Dex34GyMR%)N* zP$h;yqBhrUiNc5Xnh`BfS^IzAm<#Jc%2R1)c7aET1=8>P2bz`8WWEO-v%n74Xq7Wp z673oxZ!$`h)^WwfY?D3;cZJtw`$Va_N$c>f)%0DEUb>Bfv|G_+xW21TII<9vhnLAI z_>O;gjnkIPL6}?}+k&+4uz6uLpw8^1gnVYgW7c&_&IP_YjW9{(#G!_U6x%sKOxW5V^&_8L!47z@1YHU zOd);;zOQwthz|=L!hbFXx zF^UG%m3daVFPa!6;iYDI%O-;c*|aomRVVl(3AT(Lp{nWZT?UYqfbDcq(t%Xw!Hk$u zryH48!Op1x$YQf61U&PCyH#+u)iLZcl&gSOhxOUPWX16@={RCMFTh6{<>y_Zm8OMk ze~K6)?@VEApTzc&-1i-X#cVNmo|m-gndxg{vIzrhZk3|HBJbyNC;ZHP zLTmi`HO*~sz)Uh6`O47t&&t;mqbDap`CP``o@M%GO$QFgL*rc|VajdFyy z-9sUaB*PA>uZqDF!7Qg~iKwbW%DDz=zQ+q0;%z@E3%O|<_34s+0PIxfn1rEHc}0?825Lj)%=b(RZfOFf^}~0v9VIk`e&M!#Cg;Gv6** zf;6%XZY8>L_<;}I>Ead_#GO}AfsS&-pF_5}c!#(nIXeB+QKR6V7bGOlQqj&=1iIv8 z0CCDu;L;%3pxazx?g(54eb)$`LDdSXAy)W`D1D(UoA}3eGD%QF4@+4I_mQ}2(e6{k zqO8Cy*ctm?KJ~*GI(PuMgV%J{9`-3Gm`XW~YwTXZdJ(bt%b@#lt5(}*y>JGuF*tr{ zMSv^zoBYuq=Y|EG345~ThS`EE+RuXKmINQl)P@ULDLhd#5Xe8Rd1O@OA5)uU+_Svo zrTYEFra@&XY@jA>A)EnMl8dPDlNNn-9aB!$PGBE-Ef!9}J0&I8R*MBavmSvdn!Rs`Sh4{}@H%BEfC$z^xAGq55k=2pXW6M0P^ zK`_xC>s*>dNMdkfNjjNoQD46XGb1pEVj()Z8B<1OO}ojh;Vt+^M>JXE8GcYz=?!)j z7om61AL+?I zhDpdjg=WNrnNVbp7Q8TR&yvz;FrGLjLP#w@X5{@hZF}Ntx4>e4OYkoaovQdHBp*1I zxvk$zI{PO|ho2qp9M;jsWMplrYoE6rxsf|h4tGgsNZewmv=q@SEI$w@UD$`g z1HkK*l;9$bx;WGG$y+45FCL{BeB(aXr!{qBrSy%x87W>1pI&-Qx=wjA)}I?DWDYHY zyj1Z=e@}UhBX2wBlm9UxVSq3$$^x`qY5J}JvMpnRXCTEAnEAOXj6A~NKG8|Cv~qNL zGR&&M4U3M8>S!Zw82yc+*0bjptqqzusJG~FqH)qXjY2^kyMIQ1 zlDo62ZatyEgQtX|SA*$H}?$oy;WCz;!}ZHI3KoqtLw0 z&?Luwn4*nd{>qTb;6sdRXT|T$pcjz;m;2{COHA4D0vjIntR%g|qrgO3mpcC_1Iu^v zIiTY1;k|>264@R0xDG#Z!CH^ixWZncvXRKaZ3mAVwLVw3&e9FLZtn_TT}#DYl(Tp| zGGprqd)yldL#$Vokmr%po3BrgiNyJqb+i0?^C<{7v1xJCLst*}36~Ap>Vde#({O{P z$}(Y$3eq!Xmj7AqbL&;!)v8y@SW%{*qzLN`Ty<=Hkd-kKUa%Qop{XlA*2S-W;JQdl z4gJh9?hE$elBuX5EU)@~ddoCN;*^BzHGq?j;qUWzmWh-^zIs;@#*ot*OMkU6hx`aJtlgFV54E2l_H z5ueMlTF28i-o!M4cP(z1J+m~$dj~ZYN(IhiAgx$^d6!r8TvR~R=kR)OFiT}?8N-8n zMN~9D6oOFYPca5)*IbBGML6MH$(`sBuSPhr&*b{Fh~ywbJwVkNQG{}hJQRxc7vN-u zxsO!DEP^U9a9)wOh13jbySFd$1tepiyH+srC|^AITug~v>5~<7+c)>de#K$soA1g= z{G-(S)3&>zK1!N)E3X8Ro`5^98Q6XvRVEdHCw#>WA)dm)ZJg`N@}~AQbwZIw_iVZ9 zRwrh8<2MuS{w=SD`UJ!xsT$OoliGVP8K!KMVLNZKc}5sMm;6O$LbujiHy60IKMZ7% zG#MkAc#v7u)4n@CfV+>-%#b}nLKvYR50w-G%!_Mau@O{a%2ULy_^3iRvlf$-5g4wt zG7&7!{6~q#sD#0Rr#E<30@}H+b7_G{m>lZu)y7VSikX68u4bKvn#q@w_-vs%GcP@r zShOf3eB53N3I`&oD;}@S&f$CyF>F%xFZ!`DKx<-y$m|8aciDmyme)D* z+z#=#qv7FLn|nuzcxMBB$@9eo_XJ;xvxYOP?|#RA*?;9$am6wd;Cc6s?-1FPg7#z= z1>fe>P1^_Dhd{W)_XjF?VGmfStle3Nz{dnXF4|Ja)pOx}RH}k7Q~ZTw_zOJDP9*GemVwvo?qC-F*)==z$w! zUD@K-z;{4RG#YpvODQe=d!K$WebW3>Nid31tnI>OG#tn zPnl#MP$A)d@eH71a6IpFNl&g2fu~~6MmI+E`aDgh447yeB7!e#(K6@ zH7A>FB#4Zk{B`a=%x`8HV`{vG5}ev}+qYBeV1XX9^|oB4yY+`JO0sNm_d6V88(#LO z^q2hUgzd%h*^Z?4Ty9Qeti4?UX2N;z-0tD8u2!Pte|m6g-;fhR`ss< z$cs@44Hp_HS7dA?(*W^Dp$uq)t~sScv?2E@-5H}SIdo~&jXF<_8+C>xTN*_S2 zoF)e;^iR>YaRMrEhgR%#Xmpz_>~DAjo-FF$&L1Wy);Cy*DE=PD`oYczUj3&k_u3{E zEv~7fH-Mtj%7S{abo2+^t{Xt*}OK9S;{F5M32)#w8($` zvu>JRzQ=1BeCu=*H48qf#J-5diP#FY9NBO!Q&~?mhq7uhPUpB2(>rWD(Y?Bwyfyl8 z<*nYNMd-{G1EnUYs3Q&JG#9)fExV0Az$ld7RVQxpkiU&3oH0auyZs5j1l#((!uu}4 zuY*ch{bDPW4fBdRDN$eyBvsgU z23P2GNV=%8QVq6!b^prqV4C7t$cJt)U%?IY5ruu>zf&C!JG#v6t2*4L9p&!QEP{4| z@l82XQ_lR1`te%pBNK0m|$OB!vz_nio|)vV8hx_aq|-6@~-iv5EG7NMcXHxvH>Eu6>XmQ$B;w=U&S@HFQiL&|BjD|Wvu z4##Z3(JrEb1_-&2lC5mWnuPaEo>**nF@Bzw!yYqbxlW1sF?jcm-rn`eg?-g+H6DP# zIOeGxso6BQu=Ny5k8nRns{l{PV{eVNvh)^l3dlcaJmxG5;YC;XXnFuwL<<;hMg0lR zd)3T>#A~*6PX4hZ3GG|*k0sP`wDj6BcH)puxlOiop0`s5DIPpbs+Km@{uksD%o#rh z4BNZYVSez1${Au`$C+1Hq01Dc`qB5pa^dw(GCN5&NqS;<) zSEk6rq5{@8EvG8o;WW#yWSoJiGg3=lMI4z)_8kN7ZL@a;u0O%<$QqIUt`PbofO{0k zM{Ai@!-BR!s@o0PwKl;RdGrm^fv;@Z+NQ$gVPbraDr5bd?tf52gQn z4+&UltX2V6-^h_#Jrtr!b%0{;(~nDyHz*$s8M>uBmX*!_l~K;h)*#Lf29H>jl#GE# z3Z3_h|1C z6#eC7(cZEweHe9yO!p$r6nIr(evShJuFCUX56**qcur8~ zQE~xtDWA!`wKlDDdy9hL!36_W;6hiWsSPB`U;j{Jj}Eu8=9Z|{f_Z<{%XV1cF$=u2 zT2b_tw4jm8L(Q@~uvrD+`k|6y|82ff`w>n%2gClAd(7E^tlHeM0N*%fILfhAc^DGL z!Dpu5A&6Q(FnXP@ixwksUr`B#Gxrf~^L0+DjH z7~Y1e)v0=#eo^`=Nsn`TzX*Ibr&wGwMxzwhXR-m5Z*N_I3%3h3D3Ehk9%UD%hRo+M zG{2XkV(WU}k+c0){VAMiw_0B%RP603V|UJj5Bzv&=QN4$w9Eobt5suZ(O77JXa+nh zN!}jjBkzXQ5Q-_1a_!9; z64vmqcqKGP%lW}->g-bjXcc2dI@|NnR|!w&HkTRyU!t%F83SrDT(JOJWNVG>YP;SN z@sT%PC?M3V*9e$N4pr2CRSGBLh`brB!-9|~u4!~pJ*0IYe|ESv2{b%6ECi~XG4(WZh-gwEs&fI0?3IqGLum3wOXkFVAI>D?_{GMVQPs}ThU?KQvRqRb#s&~C z=&C%hKjSwz#7GXs zVVU2EkU)n8wOflVd+Eqdr*YFv?|(ODMi-P{o-hO&6;!`lm-_zV)K24I<7;9m6on*K zNaEk$5h0zQ)Xo=492tsBkb%um^p`F(6aqs?kI8>Pq~PAg^O&4@La-9d`N+pWjPZZT z`fI@*xW*D|5`b!+nF-0z8r$FW+Ec&p(P#@!#{}aT0P$iY^7ltAW87Y z&h{8|*i)YWzPr9qz;tUKjLCP;ReT$BLOs9&vEiP|_w3TA*yE$bHST&YniKqd;A-;@ zLoN{>^odG8-fA=P>m6=yEGSfjhd5=f>cc!jQvD3_0cQbUjY&TLy>^J z_pDRsCCGP_$IGl{kM5km)w=(sayn}i#NxXK2GfThz@~Fl+Gf}5?nFH7$DG`Yv($ct zh3TLEyU55KZ*)LrYz5mG9Edib+}zYQs559s7j5{t5*dDmZUr@HNOrfDMI?u`j9QsAKxXF( zv?2z*U?hhS}{VI<_3u0PTI>5wNFk5qZDA5UU=#S78NhwxdeaRkHz!<51 zbs`WMLtVq5_bxG{6d_{bgv|44yj@N1dIhZv~o@(&S7@?Hij1I>#(z5_P}-l-r~9xRuGsV138e z>hD->^qF$8hO|#GwjYDQtRA-|h?lB36ZsA1zb|cK;Lj-cgvc3B*5Z{mP$Y3-ICE>q zSDJO;D2FAl>_t|E!5;?=X&8- zZ8-2r_YtnC<;JPbB$CvfSz`1CB)bCxCH!yc(^;t!M|fs*+yu0ptGCJ87w#3<_%+Wh z)hCi;;SeV;ajKFB?;wpoBd`v+@eBFqi`S2-hM<wtQbqH8lqE|**DHEcM*#enp0mnBfXD4U95%0ZA!uFq!N5M5GtolT^ z*ol_>3@Wpp-crd2>>dROS{LYY-Zwq_CntK~4e5ITLPm=8W%^VaHz{K|D zqqwV3R1n36Rti9G&Cbx`^%|KCDv4=h68f7<1#_Wnm$UaVO87|Vx<=)h$cEC42_cBt zJg`%>m>nJ|Eqk z3x&(LQt&kzDv36|TP$#J%eN>_K6o%u4__r+vMU7n*U4it(riy`NShl=UHP=SmQ~sQ zAe9YR>;laOKWK10ixc&1bZdPtqEa~xHF(SilE9KyC!kkuLaScO0X>~Z3}SES_4x=V z8r*Goq&^B$DZl*5TogC>r?OxddWwCa?uU{oLERzQNYUwXD5_sJ5a*nYmULWYHNLO5 zFYGtEs>-l3Gj&77NSGatWKNs)gwftZDB5PFYdav=L;h#N-N4~FXpJAyMQllRY|<@P!)cwy+Pi4V5v1YE3$MrKQ=bba#NBF)jYpExO{c7g+&*5-fZCRUlbxl`+H*~oo90#n9evALMJwE3s| zZtj(6a;;#N)|bz#z}Ic+dN&S1F*V4+}tkBGxilNQXe@)vHboYoEf3sQ=m zqWy_HBySPYME^k`7s5!GZK?l~cqlLiv-v~pNW5LFaXYl)K?=Q|b=6MsGPr7){fNyp z(s=j2Ds#X$<5qeR?tC&QD{?hbMrdIw`k@ap3q7tMSaTfwhTYpB5{t{e)UlYESx4%HVWfW`={Q>F1cC{DMV^VP0@ch*M<9y%6hD~|T9%BV#@9i!)ofh2*uhY71u6 zh^bn$r-v@OEUuBJ#9AYq^ReJl%(lRWn?CpaVn;8Et4t=NlfG*ojeK)1_a{%Cy?sUQ zUkcp#`Ac^Kx?XI{wGc4`HONk_xKgxjS6%eS^TtAuG_>l}H{#^A9eBmVGJuHZTGn!< z^oDTTi)B75Y)#GE+7!0orWNRP7iz$Q7p?gf7uH+S=bgb{pZV+x_d`qU<-K86oQchQ zdu20{Z`l^1$Xu!7S`DC1_K-6dc~;dtVR!cmX{HyW1wO$#XY(U$Z*?NChVwJX=Op?k zKOYepV{9lFi(zySq!Y$A2Y0NxfF+Fv(s*bL4fR|}mriaa8%_?31*M=`U#@*A5C^-C zYOkft;kQlelF56$O6s7`KbWi;yQ(x?TC1*?0CQ`uSY~M+L~()-xV+RR(c8?!ZYNtP zRHQPrO$~0KWs$3kZiR}TrJ?P;=HBu}W9zk2A7t}uW!MIZW%Ri?v6}#^k~0i(ihAoD zf8*`f`DitPpWiA(1MW!XvoU~DxT@W)5`Cs1=ayn7pYAeDHZy$wLjh(%ZC7nX-^Z^p zsL^x$`d%mz2I|^Imv8Xj^pIhZs{pQU`_)bu3wY)Q2Q@45 zrhH*n4?)sO($0`k#0Z<1``dodK}7U2q83$pc^F-+lu*2O3{=7Rt$@vWe?SyaG{}vmT;TJWQ$pe$%&w&fOGPx%kw8th< zMbqKxUde&MRl4>`!L;XT&8H#Gx%>D)PPzYBoCu(E%0J#Jeshr`4GP|aZ+niSM1wmR z-bLwAbnuZF(D1`bRCok2j*}olx(Rfl;ZH6!StwVP!}h-=ulO-|6a-J;x%;uYc&cOQxjBy*y{Aa|9EGh`>LLV zZ(uo$l3eN~KeME^A%RiJ!O6pi>Bc2T{AyBb?>RsQxXS_GvpzbxD@4~6Rq7#P`wj-F8)2Fk-|JefRCxe#u@mo@VBdXfEh;J$86N@Ma%;aXyk$={j$IDk$Yzsot^$y-bK1ArL&uVc0J?O) zlc3&Efv=cB;Fo+ZYR0_cgg$)!lS7;djmmsMCw#ALf?=6iLQo_+jzSf=GIM0mys>Tn zy~?*{t(5(FgYC`-TCn-=5q-KFh}xA+j?~^O%)hBrH|+Sw+cOx3AivF>%3C`^yTp%p zj96KdUiixRu@8bea3m6%@rQgp7E)tIMyNimZBk1kz>?GE@DrPZ`sIb%UR@CN6IzBA zTSEqKGNh!(pb3J^N8eBcDB!xZ_XttfpoA2mW>y;y=N(%5fl&L9qSU`ABwjt3uD@(3 z2Y67!7 z>*G>>35l_nrvDlzch|}mV;E7T!Nl7-W+1p0YTO{? zZjeut3}@nX%}vG7^~{4SW&kRCs*Z=DC2eHm-UrDi z&RoQqSDGQ3$2D{ayx_5}ywId}5r=?RD0zR6Hs8+^LFhiCA^N<#MEng_C$thX4P~MI zJn`1XEN=~cy$b+pu{{W_x3!>XTA5vPvw5=otp`RB#E9rFHGhnLrwdDs++K<7qhL6c zfz|YO>9?n3V+Z z#7$G9+dTo);mCqAnbFU4dRMtW zWJthkJY*?=82#@l3Nqyu%zi-kTRNaCe`C^G{DU#Q79n_ zsRB2SX^fJ^IXsVF8;koTMt5$&I=XVjM9M}Jihr0n;@O#HdSYz90 z%fpu1%uy8!gqI{uvl?8N7x0fv+LvMQ*6z+Ld>SjIyVHmwBJO9Y3@?wxWla+Y*4d-3G*wp-V$$KPa*6y5{?JN^ScBByLr~+q28%<2A{PG&&1w~Z1Zh; z=77lLM>Mw2rg*Ror^0zl&g)}!213$HHUmm~aL&4UrlXYKkkv>i*6 zTk@v(&*^>b0K)c{*5~^1NJ=5_QJkq?H8FLU{*!)~00En$#_~jaI+z{6SqIZ@?w+FX zjiSr?8Bw*M#|a&5cQi%&&=>_~zohG<2D4*M;_JtmQ2Hk$+beEXjmicoX#eKEYGSaCk)J_o7RnApJp5Je?QC!Xo?M3N&0C>4Wq~ zbJQbZ-0_lX|1oGrd18H#!A3;v$GV>P>n%Q679m5BaFXCM8BuezpH-mwmGM4JE~Hh< zJe~tu1BBr8=wNF2eQjydE`eq2MKQsUyU@D$elTK=yEZAn9GXhnOwdg}5y2B?d`Zs)!PYN(_#) z^7iSHlhGlB=NDB-=1SO#)V0hXM$H)K$E2N;+*A(msIbdc|KIR_mmSstyMul0kfW0m zwSSOi9uM?kvS<`~8J5BKK9y%zQjQz{6}0Q$%7ee_9CD%Xe8``3Z}_RAuE|m8O8H3} z{b*Cf_#IF3#Ko0(r(37Bma@r)ATv>bF7+!*Wx}Ds>`Ebl>sawI6NkG3ptU1>bUQfN z1~c}>0pA*XR9Q7O;zU=LS?E`02dK2G27a9f_iMhFO8`f{>CeDgRy2kOyq)g$KTh0B z`syZ=*-e(D)k#0iLThqAEwjl?0gVS-4WbaTxJuPrphW~St4r`vA$rSFo;9Po8M!9vP+`qb&dpYoL~waT#psFz;h=9ehjR4vXDzmBO|P^{G$cmE zw@!SO*51uuTqLToCq<e+z>QxgfXfYqC2kN6Dw`cRca3dsh4vP_@b0&;`KHhQWkW!;~9eP89xfE1s7VKufVFnd4G z;4R)FsoYeVj^hzU$}vQb6%F)Wi6eX{_h!D}YgP3%QI)nDSY3bg^^7T!v)*s`kGu}I zjC`D19{r2Sl5oFQth97UO!`&?kf6ufJ!#467wvTwN>as@D(2F34RI?JhiBI9KC*!> zUbJ9S3NKeGV>XtbMiwi9MznuB{(zA(M@%zEl#{H&O-0_MV%UYs<%d7G;T(6sK7qFw zrOS3rQPhxNttccKc{1=#q#Upli*o>>$d0GRNsfpRiy!b-AK){Pw6Ehr9;ujE%sxqp ztGn3_KYLD8f961cJ4xm%XEA6J;@Sl)0UpUaJ^F16#9NS?p*wS#O0m^=8o`>Fhajuo zuL$8;_Mw|0xh!F9>#IKsSk1#5MQ2Q2!vFJ@_V_S5ZEn&its;+X14Oumi;_a0SD0%S zx)PzaeoKcBqP29a$IheQv~$QR7|huhKf`(fdW(X(A@amvv6)8eQHJOY(#4ogFHut} z(ebFK%V1q6|iQ)(2shk&hj)4{W5&E;`nc|(P7Br zD?!43F3swz(=+)bwq}xYyvx$#;WkFzNu~@wifFEGEzkMeBik(S`t-*&aNWDoC6_L? zy?O1GobbMvJgJKG?I6pO6|NK#1!B+BW$}{6wU(-eG!&c}&?R=G2{UN`yI0o_>& z4i*BRgNP~Q6Czj55ik z98Se=rWBOxWa*N-qHn2@VKz=>a)Bl6B{I`*R+uOX}b~5=5=)gQkRLVgVR!mkO3Q{1E zW&X51{)_anKHZ>t@fVF=(PowdX-N1>Sx+S^qOYU<2#N=favsEu>oqkCBf<_%BA+=k!Jmjutg-vM(LU>9X= zno4?-cL_RTFJd5;es@jJTM0^Z{pw-@^htBj7wepB-yV$#BOCPEEl z0iRp$9D;@0nntTw0_w}Y>9D6L472tBLQ|9uS%xERcn>bHt_4c+G0%JgOtt+}WPi2O zeh5SqFhjg+dMqM)_>lt>W-(giL%9xJ|B;)-iYH!j>bhqQ7+jGvo;ao03ZngOFlk}Aym<9aXn=vEhwgsNmIdRhcU6rM6Sz$b;XViI zCryyDk|KY_J|OxN+-XkZC+*M{;)elsVDxAKQ2#F`bzB-}E8E~w>FX6z{mpnp?|rFQ z4b;bn(T7C4Y&-EHGEmgaHd*=FOf^BA+5t$Z=?zwU!G`s~LRp7L6{7pgHO>agD`$Av z?7D(R514-5WnX^ms?TnQaj_*TYQ{OHVH+LFm6c&;59yR^=V;;p?PT-NL8c;~PLDZ1IAbv`>KQjjU>>#=pvLw-{p9>)kj?rHiQq zI@~a0MPdu)2&7sf7M!?}fwInW4B)V;B_cH_9BwBw+#{^AFdc6Iej3Pgyih@6U9hWOUHhNYu)!)`j$KC6jxbKw(#vp329+@L-Wou+vgCzPJFY5lFMv8bRkZsx!6Htx=$OdHe=8?WwP806mNOmVb#+Suu^}(3x_SC^ ztJ0FK@|JkTH(22VI#X@8o>4!G7??LZ_tgnewahn51jYgBKR4)u0mdv&YS!DySoN%m zougvdF0Bk6WL0%YbJJ{GbS!agAG4To;do^JC0#Tm&R=Hy>2gB5uH<3aTn1{h9K*e+ zw!FeU$Vh6>hMZC8adU5jnhDkI^gl1T#rirci3GP|sj%}$u_jY9m0l1Aub8=hAz>1Z z(CIPHtEZHuoLSFboXcOh7*@iFmrle+R$vKLV0rwB@OS`;!)NE*CDPiVg_qNAG=qO( z#_I#|tl_5V48={SyYqI$8;;W8smInt5q?A>dS6_^bSvY*A_vcaa0|0giJT`CzeHmBx()-}l&1sPm`FmEa!W63~5jmSf>9EdK8vID5 zZ1-6~epw)_f9`v?HKjHN6EaR=$_u0OaXEaf8kN`&gcH4Af%UYyPvWVu1p>N~(SadF z9W!aNuX%2Upzn6?Bm$LIc#KDEW6I3rs`@3Xvlj77;3$*B6 zFLN9?wY=Rtm$>zb%>W1osu#Dj7zFi?`Kc{1KYqiG)B-U1^bH#!$OhA? zaOINRmw6kXM0K~5otni5om@<(XY7tsPgjz11IvSCgjvd*_tyIxFZB^iwe?uz(mi_( zAl;T?*m*@^v!u$97uic%=S{I7QACPXk30_vgHu18aGG|@!acm%C{x|xIq%2lG)7fw z7E+Y6Y%#SOmoFs^t5=^kv-q$9 z8XT{T6$2qoIaOeQLY?ZkN6`VCa}6$4=3My?2x{mY2zN`M6*T4mRHy%Oq)#^I|s#3gNZM}zYobkT#r3jsQ z4Um@r?!Qii0;tL0ua_>%esHBkIN_(J$lyBr(sjV&8gvwTT7$qhMv;*w%GmZ)RYrKT4KC}C84W}vVsG(*OtADZao}Bi2nEf8X+hyA0`Ixb z;ZNty3AH2uSLI&_^G-qkX}~w>qy3tl{_v7~TNNcwnvbgvC8QYVLRep6GDvF#BROTe z_#wW?ni@`f2tRM5^WQ+bl&x*AeMKA@KLIH5kkOh!wVZ=;nu{)5kKvc&~2 z$>8k4y*rSt^y=Ggr3uQN>Bq>-`Ef^a3hFQRyS<+(I*xATu4HI&Pj$3;FEQ;chuf&i ziD5gI<2Q-oie?m+G5L#abix0<$4Y-!MDw}aeg|aY;rH=fgo3%7P+|nb_(yhwgPSOV zkgmqaO`gM_btbn@pD757ms!^r8f+J9>8|1rQAV?*%i-;T!%N)KUxQ3rJlQ-AYwY9e z`-f77MK6M*3(DFM3VE`NkIN0Nq_Qe+Z&$;MRsx**`40Sc7dWicZa4dno&{>^MI1&u$xA~PmEr1zha4_3P>sjWP6V{|4uRkkJ##8o zw`*sr%I2^tQ3&CdJq-Hm9yPO%miISD{t%Hsa>C4W{Gt*cUR_~tB(Uq@q?o{3_oYhY zX9|LN$W492k@hqgo&&6G8AVn&ENt%sAZ-Gh;5;a^`SaU)($-zwg=GCKOV>Hv*y4Ml z<2{IySQlEuwFu$$Gmb3XGyFX=HjR=};DgwgZEuwM^$N=_7F)5tB(cS=wVcvmoQ^=y z&7VrCEo#)-&n_9q$k?(GcjVMjZsuba?OoBJxk;HktjxYXToO4KlR!ha-Cddy4n&L(D?M*opFFahxwexNV&zb%b^O{y))d* zgvpF56RnyRUL@u+nHY}~H&Qt}hko|s%75w3EUP=ob@5{0y8Ba6_<}^7i?3tweuKsp z1aL@+BP+5<5g4?vP9!fzBJ|M&h>9YnB5U@{4aZX#FeM-PvyPNm^Hw+fYB(rro`6&f zF2u3Ta^yXNnKEIW`szCqC4_Pa2+OGg7S{`mkhOW{G!5DblL6T@xLu6JsY~2oKdpO==}NwX6{PLD^nZT!++y~h@*Qf zI&XG>4Xm;Q{ML8QwIg(-g~sn(ehTwhbu5G%rjK01RjMu`ZiN7=DhpPP+hplBrDR!0 zUFs4!bjkCunC^S5R>|ta_6@F}2j!bybj>UdAS>+cNCA2YfM5^h7M-BoTnNLzxGik(K+bJVJ~a|cmC zaL&(dz(Wd3_S!|?HC4IvJfx&s@_uEypR-FI#M|A!TrVjOPXGGcHY;V6YDf5MY&G+OIR>bieG55z!_ zCuf^$%@eT~qch5FrUKb>{+w*NNn6Zja9?OFtRb(_kpvQKab>3-P~SA*0fYd6?%j>l2mn&)F6(|ct03JkvM=h9Ot z7#B0+a!jYv)&-3|eYKm}zp=E`n_^&%;CH2%M$-AIShA;%<8DZ5N1i73a6*hi$AkzR zdatt#R4OUl84Ku6sSK2eacwo0w=Xm^XnL@hAg*mRUF#}XfY4#f^=Cl(M*%d9GVD$& zRz6eP2hdIG{zRC;$4yD>GdMVKJgObwPLYB+YHQS_>9EFHt7_|b1E7JXB<%e2YWISr zEVHO9fXWs{j(7Z~LN(xiX)f;27m6_L)}qpsjtQO-P9vo+52-(2{Obw42)kH3PXbm? zHt;GNxn;{ON_P$KS1exYpWs+H;LIT0u zz*EL>fkNz)42|^8;hF5NPI*J-D;|x~{iHfMwp+S zw(bz`Tk*+!qxsxZsD*HcS1amx^qqaQ92o*cmFG78lcsnDWlS$@rZyRcc{5HJYyD?B zcsY1#!3HCbumrf%C;<{4r`i`FfP@3Q)JpywPg4RZeqI!R9_%NeHlzGr#imm*xs|la z&piC?O#Mve7?HEs1Yr99KFM9fNvTE1{?-bu?MLv6Z}9PhN{+3Fi&b`#b9Yki8!N4T zCG-nR2 z%)pCXcgL(#GQp6Qxzh2fpU+y;v>^C+acI5&SYYu2XWOP|mkVmc7&%O14 zZ;xui>PI^WF+E;XHX_zR70|17!!Z58c%f^)1Eu=t?QQR-M^{PzDvB*tFV8*CfFlU~ zb&^U(*vGKJ#*bS`ognhCcBw0uC<+X4yEtQ&`XW~|Eh6p?kPpA0rB4f+yOUWqkMEe64tF#Gd)@lcFmmXXCWeEl$|5Q6OO-Ye___^SgN|NX48cxG18BVty- z7aKO78|F)N$u(D$Ub&tPe|>%niAGCw>RLrYc)f2v+pn~7YukNWyx9s)otxV!!jJJx z2uw2Mk^6s5%!AK;F^BP5H%j9Bm8DLANCBtDDOB8MDa(*2uEYQkhTo_+Rbw%oA%+Oz z9-?55gf#P)y^sRN=2T4y@}FCbJ@i>+hSh0Ibsg!;+Rf?~=ff^E2phP!M{|dwMMOn@I68f$$;862375Lgn|XGRrTOBR<<#b%g$9WM5GTe$^n{&6dT*v zX%rSZf!+P_=A}xQJy>}2(^d(zVx}CCi#AXJ&%!T+^+C`+pDNuL<|B^+khW-mL`S$Q zpWF4&#&GIsgJ%FpUJ3WKff4ty-JrA0*0(pAfehDK0tk^KdQ z=(avo3lE!Ki_u51%W)sq59VbwCC@fhne$_~k6C5Qbft+;K-2#>T8oi^;s3?f`adu& zCIV&-4(9(STZ@^KnThlNo2_N+V7IeKhqL8&OG4fHKX9#VYPUwC|IV$}CL{m3-LLDn zWzVbXk8;hUOY7&F+bT}U$l>c79Tgs28B9ye3ygMvNh2z%7?_+I05C2y3?(H)a%Ew3 zX>V>sVRU7>fX+%tfsJLr{&5fkBLjmFLQse;ZVxWaEbVpxiWtg2Tabzkj4X{!EiS<2 zYuoD`npj!@9y>cbAiLQ*7r8ngmp>B9>?|N18kzqgYn1^QdV|2=_Tf!tXu&}i_vz3BmY;XhG{1yYm+}z0g2e6vRyxjx1-j>PL`2{pPHL-_I zKvhLVNlsS=jDT9Ih5&}SkpW;r`YYM$;BfvywzaxGe5}8;0HFIL-oW^cH+kk?{PXzV zXsrPTCLkG_SX}_IvePs-hUdRS*~Qsuy#81GrpW3cf89R-r(baVfJ1yZNs@chk1 z{-r$rhhH}xIXPxgsr)O4{JlYIVQyt_Xl4ed==vTiFHD~J!}z^XV`%=C2me8z^5=%? zfA@FQ6hf`C`NMA? zt&@{0bEEqs`^ne(t^VuEl#%6?i8WkRzmDw?u2Iq!n)(reKBMZdJTrq)sZ_@ZR4@0o zYe}RHr;&M%uXFsZ+CT0XI+z2)dbriSk@~eIV~b%9<<88BB7<7f9r!OntYmnr-tbeO z_OFIt>jG3BYGq9W?uu=9m)!f0s#TC>G%?*#k?2HoB8p}n!$xs+4lceKsjuzRj9k7< zDn2p)8OF?8P$!nv^seh*Jp9+$2Zxk~-VN?99aU?usDO9wfKryK?{7<5Q(MU}w@w?4aC3e~s$XhJ9G4;|djR7J~Vc`$m>y}yH*y=IoKB0&i|Xu2eF zn^X(13}>@M!ajeCA}97vgW`2vQ!7h_SeNsGd!Cr!=P=D95f8XZHygwcX!x+|GWtW1 z70}eQk@>O@-|?RDkJMRA`MRKufV$6Mk!ouoG)fZ~gYu`8{syaYxRi&-)l({D%yVQx zV#SyVV2@Up*0o7v2syi^nZMqMB2wEyHuRpZ?IA$Crviklm)uhU*Xa@FS43g%FqgUP z==itm%Tx*>3%|zR^j2wMIBS54+T?gw<3gkor=tiV#2PLJ`A7$S>-S`Jr;06iV!JwR z$}gF_yv2#KMioTV8!?zR9#e^o{|EM#z8&;YV!=888UnK}zz^+*!TzQR=idUf-lGb? zn^^+%Y6pjZ(YZ~xsvn|9IZ1(f*Q=oWth-Q^#`&jHrciPDT$jMMq$XvR%iCMp4Z{Jt z**?fr&R&G~F#5wIw5u8gyVbT9w{|dQroVY3>g$6=n?`M&E-4Q=7)=zcWmB({Ic7AC zm0V7g@^3G(ASz`~ZU3z}(#Jr(3-&v>+YqQVypc9IHtTRqu|h5~i{D60E9zNU8J%B@ z$Ju+X$izX`#b<-5o82rR2ZqE7`q?odDs~O?zs9gDB9M~(ey7*j`?Mnj#TBvajD5XaD|(3+HdvtzgF^PgksIH5 zkq_(sdk$48!+`kHbq}Lcw31Q7u*~I% zd4d2PEm(!IdjK;84>S(&qVS72*qsV1=3a{0m`QamR)v;tiFP|_oUzTzA_))f9)&v( zAy1;@l;YVaIhG)Gj3iu)ubCZ>`OF&w$B^U8LPE8deaCg_@*B$MepwTWN6z3)p)CB??ObvCpIvtYPIH9SGmA073K_ zBGV%foI|D_QI>a)G|hJWHI^uRJ1h!Aj*R5lClrQXY|5&2KB12By@MzvGFtw_1XKUM zq@U@~8qj5IHt${ylBR0%T*Q2eZjs{3`lXxX3Rbt2dt#*3Wc1*#K;mWbP0`~l10%Wo zdsLowsW(beyvoyoD!$xl6^HcU7suIke3Z#g0D(!Q8lV*}bGl z6Cy?GMgeyTP?&R-cUNyqS zPP#nV(Hj69TVfFFH3^~;R}ri#*@m;3uYQd{myy^mZg;D#OB*>^d8ZOoiJyS!`!|%5 zK7=l>y0W{w#PRZeQeC=OySHrHRuA)uZpZuNQNaJ zqukO$6CAsof-5SI{F%emadXB1FzFJsy&#s1UfBS%jPVE>>_{>6<_*u!1=E z_NHR&Zf$n8J;b@YxMDqZyQs@ON9KFj|tlaC6>FzJz+@c4Ns9#IDm9XrZiNlzuK)M~cX% z<{TK%eN)BBxfJAqdI@GvC>_5{vMA{Rl-9G%v{n3F1iA5aHC4erj<+JDO=@2<**}m` z=JUaR4Ad;btM=NbuUYC0Lq?8n&KPTVauyit3iJL=%KfK6AZlFo8yuz^E4cfNDv^VC zIA${B4sxSsM*p#bk%6rpz+M(V-Y4xRkJa6@H6|N{pU{h76IAhEbk8zbjhNmXu+*8^ zMs$Egfz};}S#r&GJ0%%G)~=Vb)g%L{S`c3`V=uRs&XX;a+i>^405w3$znknE9B27% zhVA=Iy+QDo`8S0spFiT(UFOwy?q_PDlI$sOP^L7jX)(y3NkvP^3vXFpx*7#k}Fnca%J6qrC#8(QdqTbA(UB5HE68ExBKPO(N-nkv|8E_#$~q zYFaLvPrFSu9;Zded+?&HpF77ZUc#t=cXA_xl05CU!BV9c@@$*RNB68xB+8_@qKYbx zDi~P5497V{28H@n@j6og-s>TUb*wD(UC1n7xJ_5WFozYHIa4tvVs$2PQdu6fVql!a zNwBJ*0+iQL5A!3%0||jh0;!y750hXQRPIT@dV?#b@xA^2{8S5zBYtqH35l4dF{EIZ zT}L?vc+VW{nqo=4P-5k>ue=G*j&OK>101he)cY3huq9HK^=9O{G`2`sleRV8;PmgG zQ)FYccPakQ_uSr;3eeAhWgR>O*?QpR+2^UvU#lL+&Kzf@fvJxJM>k@@Tz_x%a3Z_s zOC!9I;rgUov_1UccCFcK1g03zeO}(2DdK=>k(UwgtdS3!`iJO;{`7Pd{c%xKx_XDV zL=`D5vkn${OBOw(e;+-gX{*@^i#e)s?AJN7I%$LaE)Ykt4~GUpcyO?xeKBTTM+Ys`7KNLYb>AmEY;n|Z8*xGqRn#*jsHfN7 zn6!WDhGqK{or6Ip5Aq_|p`wlPX)wccw^#5gDfr81_E(x9_waG%4ozCm{j9GNy!S56 zr1~1(_sWyI9V>9To#eB|g;s~o)%T_ToIPIdJLW^T0b}vHE$K*P+ucs5Jc?=5=OsOy z_%(v0!z)L5VtmxYrV}ns`@mxaJ$ndw2r?3RSyI9oAYlmy4=KawjS57ye~|&YHCe%ST7De<<=no#bgI=5x&xuv!V~Q6D)KH9TqZhqk<(oTJEA~ z=RQ6X`OOle@R;Z+ieJ{J9Xm_NJ~LEuf1KJ6orhKC;ct(n>kj3TD)N+|%`&EtSBV;N zgrW6rW$2jIDaGq5SOchw<{t^BO#d?Uz~xm#^BL|Z46XIVnuge(ZmZo)XZoF^$f~j} zVqfss<)<&{5rOE5?rI^u5ftdiV)1= zgy89@L%J#i`1yURnS_nFt=80^vot)kV##^zqVB z%kQOamo|}UzJ`kOwhs-~jw16nHZ!-OOkB~_zgrYSIY0So057lF;GwSIN!3umsBt8Q zB=E0mT*hjD$vdA2)lRHsOrNSiA(6T*Xm15ipa$_QN^6oC%F{Z;sY}xJVjPfhjCIK;JHsM8)|0Fm;mROw9>kpV z)8MI@(w`%V-JGjeN!&Bpe?xlCaR81!#L~HgZepSyFRijawhRh(*MhgCr#;z^BhK!| zLHgW8_wLzayu1tjB6%uSN4Cwi>`%3?|2EenIECnT-guHG;`}JD;SU~t?f7zFzwg85 zlb-?kf;ZwG364PTMOch@UEQbQFx8s~8sXoirR3bs@yUnJ8Yfe|g^m~Pwe!kYPg~;k z=5_#hy$)1~0vDI&fEjOvE1}%~(z0sGbawr+=J5b0HrGVm`aj?u}iu4 zVCKZ6t3*%O$$tI(NS_jr*Dftye;pd9B9R`0@ZQ1u8882pfS4DxbkX(3d_#DN+V39N;@0XQm zBxs~UI(s4=!V^M!uHnuqG}2b3HG>pmPXvW<;;})<%#TZ^Q_D>JDhy$|Y%SWSYj- zmkXml2|LU!`t2?IG8lC}$K5+bDgt|z^owch&@cOwVb04U4Gb%(emEp=IU@q7aC&Y#qW9! zv!snOPCb_lJWg3{GJ))v3_68%DE(rh7>Bg`$nA}s2r~V(IXv6Kr{9Nd_Jhr7@?rMk ztit$17%2Hz4b%syHIq<^Wq*VD*nj1dEWh6V)Y^R`7k6HxVi*b4@t$JW^2mld_;=z5lki))G-*d;aj;_!Zvd+M+7irOc_SbSjq;ZEpF{Lh%~ z`faZi!(59n^r`kPN&e+2QP{~Q%t3hc||wTGhx1y6TneKLIC zC*EDd`4|gh_-hD++s1Tj1+KM$MP}5n)*6bKHX~PQTPR=&qQ$Y_SQI2O@TNUJ>6oW`*8xN&SgHGg|daADnDt&ETW$B|LR z50Q=+f%cn;u9&=f1+4MZj(B#oCEgZ{kd(}}_E0P3oe6z|Pou4Qe%uhSg)b%fg}&Mx zpAWR$&QI=YX}xG;dyIZNnb!ENk5%4Awc&p}3H}NTlrh_roDr8E*0&CvA)46IuYQ3d z`4pke4FB?H*y9$_66f3{b~Ty3JRBpI(FNM-XSv}-4SX_ZV&g-Y{Y_BG(PDPB+Fgq6 zLE|$$I^rg2n(O2*@SPdbf~Z+$qxB*IsW7TvW^Az*XjB8!6F8dgVS7b5KjO>i+7Ww> z<1>f*%lIJqu7s92%gA77mR{eX$e!=klwdv!NYr-~>zdDWWTl~N^4)8LU7EV-JSkyi z{+5v&gDTdJ;}yV5dwr?sY+nq3F;2RoUwJ5Na2gIR)c3ayvqDq)Q44Kx4M}-@CsK@i z^dU|jyZ1c*>vTQAV#uAqrp1+LX-juq+hy=%1R2? znqOuUqQR8$h1D49^=9)tgMUffUB?F*n`e3Q@2{!SDS-ZY%6=oiNA2fSQ^Kx0M!b2U zM@FqWjbvILE(MfByLOGn#$4anCD!?b&wW(s`3R@dcWvCCE^9q5+Q% z4r<&14Hl(p03|&~CEa6E;RI-geJ2g=?e-|~_pH%)%JFFgDDq;|PgSe=Ogtqt-}#0Z z7lY%M4`Z7d=wccS+9i{}j-sQ(Fv)>>k1?r}bAvc$l2mRX!~u&U-Ay?6_PA>==+|wN zE*j~dr9Z4Kh2>%+j4544aBJ^P!@zO6G24(MOZk)Fc4jsEm)huBNG5Q;M}86TTr2>H zg$1BxTen&3R8ZDttvE%Lz3}cgVY_W0VYTq0`pUUEz4xY>b}N z^DyOaekk)`pO=qvj6?}RUe%((l>=9$&O%F^jkXv6>_SgdVrV80_4`+o441%uHL06E`iSL>Ew9 zB+n<|i41-OIfA8m_2LeRaI-PgJO(}|fx(PpX=#TE^F-cPx^guilTZavk_Vfz8)O2a#ezV z!No4ypCek3xgyXLBXUFYVFqYZfRcM(bwXcnCz=I)voq5;Mq#pX@)mJEZ_K>GQ6yvI z$KAX?nuRCg32Vn9kBa%lofJ)c8G8q9U78k4UMM0zTUpYmYlJq+df017o}Kx)n(;Tt zDZ`P;VZw-YZ4Z=&Nf-RB9(5L6I&e6>ES^QCG2_zqA%pNICT=y=wc-ZcE-C6kKoZu+ z+y_ux6<$!pLRh(w*l-h;@~8Y<(1|ac`X~NqKeLti)(a=6Kuj>%o9@ihOOFJI9IQp4 zSq(>v*zS@y9%3|6%GJKIJNX~2`!Y0!dUW}_ccPMr336M@h2fgSe>_VlGN>?9zTS4f zRM)YxCTAVZ%V+FZSgkD@w!l@+X@cMfm$x1~e1Hp5*d7AvG8a{m>yYMx}V?YF5RF$X$y33?<^K4c87yP&`d% z#89>buBn5+)q{GMCO{mV=_GLw$-O#!gn2js7uYE3S>J15q$jG(kqSQh3qA1eI54Q5 zH|b1-#8erQfE>SSYKrt57GO*^dZNN`22mZ5$^jAU;SmvSqLfOd8M z)$gu8xTyL# z(6Y%3r`+LMd%FVF}zw0MeUlL3~mHI4Mm$n5p{!0K1^3(ZiUl=mtD2XFNk!F->! zsfrI=i4uz7K!OeaqOTBSTGCEtK!=FoglLR&+8>DxoFh6l+5pzfcsZ(ueQshe442>W z9y)C7Xb=*Xb`GOBBpEToyiyl_nl@J{#04N3?``;vr^-J3vEw zZ?nTvI}Pss+^}9X8xW1ApwyKGlti<8k}k=GiWWw(md+&e!)$7A@F3d;N}PF(1Fas}#`gAJAiddxW6mL+6txK}>q{*yS0=W1uID9B&$lfV zt}S++vD%UMt1*vTu8m8i=>7<@_z$%hL^%*Oc1g-2z5GFNM0moG25bwf;Uh?x#OD3y*Trs9ixWaZz?JL;CY0Dw0;JTWdi=goQyS#zu_d;cEaS+sA z;^bDt5e?YkZI<~%EFn=Nt&>?H7c7kvVeE!NdQ*R5$6g^}Ak{Ce zkkK->;wUItnOz%>A}SKFpS19oGl6a8ZMK-A-8GVUq(FD_ck;T!7X*1$Q>H<`qcw%n z4#)}ryDKW1XtEXX?^}e<(kGG2bGdm5$Qz$pCu|uuY&vz%-OExjMo3j}?vd!S1Tr~> zD96^tO|Kt<6D9uedwb$K1|G&#VxDxh!0*`_^2Z!|7^SM)t}3T30G`70?w^OBs*4?F zd+g*_)NGk)=^n)MOjB}B#)p|J>Zs$k<_)&y-3Cdm=ZShooC-RXJ){DB7_od~;{a@q z&x76cgk!b7zeQFeBs{wq<*Z<71Rz+ts8X*{JM7l%G_oa#Ba4#!T>*YpER)4;QpR98!0^GV5I5 zfxtZTGJX>(=Xy<|l7U}{kQ|A@^~L_+yKX)eICuD8kv&Hm!_+P9u|LVMJAuOB0#Khi zucEni(s1&kpa>ToGnDDNIu>sk@?cHmud3_15sKpj&1a7{eDJ{}X3^+eV9>hDLZ^Nj zsL!nL7R_UHUj01Yg(f;Ijl&|2p>ywMYG_+u`%96kep~VkZ*cD{6@m=RGkyWc9v|Xq zaT~3zIzj_CQ_pOp@VADzK(ESUHc}q$jAMC)i_i?euh<|jWPwfKRRRobTmnq~2fFa4_B z(qNg}rjSUqX9(p#{9|Ynl7$djo<`Z62rr@bZ>p{o&gw?CwB@mL;*H02mYF*JTZsYt zydx2V@qHDK5O4a;OHG3iPQsii>MvhG#w$dvRd|@Z?*boB}Tq*E9-Zl@B!Uag>ws$3% zo15Yy6CZpJB;tBhg%zs49=JQOD13jR#%&IIfa-GKX$a0Wn=(7^3N2s%zn{4ghCwC8 zX@p8E0xvz&KRujY^!Cx$xDy|T1zp0gFo#fV?131I++?Rr;ck@RQS&ilI zcW-nIzpt2=#q&MQG-QVva1+k1wK>kD`m6(uQL!?i_t*6<$#Et2dve*mPjdM@$iY{M zk({+>ik)>IFiJww$W7dhzRnHJ8xmQH1*Tws8yJYY=ISrq5lbw2KXgw(+{$X3XR+NC z^VO7Q@3-#tN$hDi343gzez{AOuYGEmTC;<4KXqrrs}b*b;jj4tv}X)`i}d#e z!I-@{u%0~{#HgNs-7Bw7JMwecn@#uf1U@8KL1Nfo?ehC!|Yg{>bVrXhPw87V_r zmM>H-N0yeq=lsd}AbrBP^;}@fVXjv4R8B=|{stEe&uWu|J*3BDiQ+L7dSR(W*h6-CoDF~d`4Xyocq zZoxLub*Ko&n@Bam%0B(f%mR20yz!Go0f@^bB~qT2?fWyar;xxN4|#WU;O}|%Dr7Bg zIHd`0cJt}a*w=|If|=<_5Q$h6{Y!e+YzQ}F5-pl;z<>1ESDG5DgPxHl1|N0R&Ux(TN2;9u0kYqt&H32A=Gy^U*R?uW|VxQjNvoR`jGaw6*ys;<4!C?+P9S&Z;kxi+=+Zb-!ck4H5?kDS4^E8h@}L8AG>Ny1E@ooF=Y=Ax5LDQ~5h21umgPl5v{s`j=bYRQ0y)k6^SkT^tizrNWg8CqpOo;`}lkI zE~w=Fuo+!As*Tln%`K3`8KZiL8QwM*Azi)Jz{_XFD}n*hA*zL~9q*nv zYlu@&G7_G+(fWn6mR$B0|7?B4c(Wos&7h6H*sD$*26&ppuNQM&zs zVOI;NN+#R2mWa(ks5;D-;DIbQu(@pTtX&Nr*PCVG#Kl6!ZL0naRtwA5;CwZR)92s; zA|p-cCeCCKU~01zIEWnF*)GR+E_dNq4@%pW-}c**B54Kq#S->5ek2hoX)1Qo!HK3V zK0*u0m3ExIHMot=T@Sd9nAamIs|DBrA+v8&;)4eyB9h`P0gW@B8JC&2v&X9=Sl-B) zp^g!Y`{SRLL1KpgtkmS+dhK%PvdhtCa+az#sDEg!(IvR11TX}&p=2mCAdqs;faoG5 zf8gGyGgo=gi*X6`e4jgvNiJB`KPj(=AxTHfA9flfPjftnT{Yqtuvo`VY!>Vjp{luM zmmpqQxo1Jy6cVmtE<_xOsbQ;1Jn&F6Hs|eqKlXIo__P`e0h2O@qqCZB>r;yvK1fuG+G{Bu>(O}NA z-UPV?%!*i5toGugBAOOoxmJfu4o5A=M@>xG<%g)7Ul20oM(J9ia?&Y#dot%9+#p9& z^l{ZPWe&xU4wU85QP^;9l=VjDWhOzjrNuKatI{y+XMutz`JLmwYt4XW zFVf*kvR6lUVVz<|r}HvtBhUesNFmLzVQYlmLwmhj7U$FS@`F!F^95CyciwrIW7vX{ z%k>j_op5nTyJSwY5-OW*#X`}6Bg*>SN0zFwX>Kk_Ol!ToQ3WwJ?aaDp!vJ;G6gs^vy?oQ`fY@S&MLY_41*#y3QyG7@+T z+lG_A3V57*lm+D{$QP>>kN_8)zR(eyn_t*Z_9nSn+`bfMXfR_(gC>F=Ye-JXSm<;* zEF8>ucXj&oO)Bm7CZ`_Coo2E5=DBpYW6yPIZ1XA>O7dl6=<`jXtD+G?Z~#ee4XNQ^ zLhAocwNKk`5dzXi+Wor$`bUkqhxj9%|nBysPlW?|5w%7{SG@BVk^suzY5=7qNq&m!bG~{AXxYE=r*0 z`&&Ip+bxeT$uCMn))~JCxVoZ0b|F^e^IQ%57G7+2f)t$j`y;RQWxZ={K?2C%czcbb zWf|{JkGZ{u_&vbpTsR!x?FxpBiGy=`7mG;41vo>0gmII=`R3cst;aNX+Nb1o;IJPnlIn=`6Rm3wu$Cr6m?o(sDuU% z^^ahTbhS}JG<+JkmPhvZ%JQdnWdna9*hGrKCM_~EJ|wALXQx<^l*VbMSFft2YWIin zn;CW=8YSabT_W2DOaD9mg0^+GQn!hhi@#5{v*hNbY<2K4@x-su8PjSpZDx)KY7Kmw z(RVue2J#h+)?~`{SemkXJ_zSPF&(V)Jt>u^tIz;A=9pF>yiq?Xuv|wc$v@bgDCCY4 zGzP0I=^OdQWddyzNI(-_Imz)uezqbv%dZ#^EoH$|R?Z zD8nyZ$!jFLE(N&|27b+wx*_VSNHuY(C5S2}@}(_iA>I%&@=J`5NrR~(g`_!*`<&Vz zwB6(tyU|+K7<4_%w$i9vbb65RDvEMRBah+wG^ATa@I@I{t%5~Ifx{p64T3H?YiaL= z)y^AdcbA11imkn7L7%IaQFiq}U#EXYLHfrJ^S6EM127rS#)RR#-zY<{stwFxVPZq< znLk2=rvXFu-ms)=m@0bQC>}=2?`QidOaIcUeD3LPluEP*<}xYz>nu=Ge3-UL3|F*d zM0)9zwse%PrS<1!-YJZU=ju%PnmW1K?!h8VQ4AL1^ATveL}!PT`5qgW=_80J1Jw~X z86z}(#!9_F8=KzjTF;xtwNafgF>ZSG1ID*`>o5V#=>PGk92n#;fkAxv`_Wr>dYMLG(MbPqkC$ zw({DpXBJ(ngSWw((%IB4Q7)tJqeh^4+pPsiWy*2hTj{~EOR$_3i85($^vcE&G!D1= zw0LLD_aS45FldW0FSj(T@XuLoTjuTkE%ii%nozuQbtCWD=g-qNfxb-nYVrglkN12t z8fs98jpAo3{U=!}ldZJpObsG`rgTg=nAM*><>Z54(NV{KD$_2(g@N@UCRBsxXIi(i ztg*jY^k?G;SVexjzfo^KDwu+WFkt(yk=6xN-%YtaS_$;G9Qprue0#VjOMj`$9Oo<# z-cUJSSjebTOdfqC<5RCRQd_Z;m(?JR^eb^!!Up-8;&~rc@x_=$R^jEp3AVCpV5lX# z#sTx?3u4C=nt~yJi9^&%CeB|tnz^z$c(-q`aDKiy5B;T&`5Oa{1`+wQSmNbg}94JkT7&q6PZ7`fX`opRJIzRYbW6PsH7%aTkf+`1M|qzAdx-xsJlE&JISe6c_k ztuU^VUc*P4jFeLSq8t+E)w%b5-l>5Y(?Xap3J%RQ`qbUAc)l7JUc$%QTMT-@+ps^A za?mEpR5L+pSIGW8$xWxvwAA8kX~pG!=cnC0s=>Q0dTuSGgkWe)LsOAI;P;xI)a8}T6@Ymt8PPKpI zR#2izWPkn=*}?2aqCNX0HSTfcEVYCY% zUs`zJ^Cg)DR-88rg?R&vVN@`JL_rI;2W46BB!a(3aU2O*^*w{xD)AAYZh3H^z*jqw z0Kr3H%&Av~` zZ)ZXv%62~CgK^bT9X^15A8E*G=Fc9d%ay0O>d|BHXYP^d;k;KZBC@_fEzZtErk+-~kUt7(YqM4VGZdB|N)2&rjzuI0DG*V8ArNGEUvIf2~wfK{v|H zUOLGArS22xFU8`H4EYPc3U6>U10?l%KD0X@p$il>5{+6Czd=neB%OzxzfjnkfftTL z)_F2;v%n&gBLd@3A~dF%sAhL`6naZa`&jUK=MGJ8AEU|3ui^zfMfZu@g$QBs)Ua+8 zg|%-~3~|OOwGOZ3 z>JD?E-vbgb*Kjqm=3)Gn4qX{oHCMI5!={=1+`K-<+rqgJIcUc4ttFueWv#h721kE< zUV&Im#TqWNuoI8_)wAj|F#iTJbs&4Xm-QRg9~E>a>6L6(i2Y6kYWo{TuxO)N&ce#d zY_W!l<9p^`=Y87ZJw9aEi9m0g9Q@%G%gWaB*Z=~%+A7;ZHCA>Qj}jJs5ByEmhXK0gGIV1A=D$R@=8jsmXE5+${Znne_AE}*2%MQ`4;!W7nX}@$+?!jJb#}0v{ zhmKDG$-BXQ2aixYIE4d4d%R@L__+toiPk+%vOFmEy6IYBVE1d~l@kWCTm&u6xB1(; zvUpu>a%8wzFoqi4BO*X)6z@IvztQ;XQG;Zbu(=I=jkSIRsB@{;E0g#j~MjX zMlb#8+y|~R0^4^RqAQg^y9o()4@klB8$Z6fV#-ot2Zl)Tub{mo>?sM!;6R)MlJUG1 zl|SmjQ6S)Hg}_5KH&3nYWfjm`!ZFf?UO9T(Bw9V5zy89Q?Rxae#@+YZO}J z=F#M!@C_vFK}Z-pWH-t<)wM4X)s>&pjX9XdT;9Zo68-v%YV?I|KaQJ7*w$+tb|7hf zL13NTcUH|Kw+AZhdR8&%1Hr`}Mjq+(fLhiPZ-^jCagC_)XF(PEqbE;F@mlm;tfHMB-dL#J-q9zRGjM7BEbB1FAPIoaCpgAK5E8Z%H{l$ zfU`vJCx$m{eG2A+ga13$Se0n5&0cqf(aSav&uqlAd>RPwv-ojz6<3P2?*0aYP`TzM z%3+^9oW|+F+h)SRS3UHEQ)S%%kq}Z# zbo9lJ(3sf+9pZvjkj&eaqqEyzcM&wd1YQc>b&qvaj5j4xc%WfPVjsXQ*W5pS1npx zatOt)pl~f>IUl(VUn+vWVLBexD~~RWjT4j0xOC8fJd`dx?f7>#LekSyZZZCEfAiLM zF|&A^dQ~uDk#$Q@K_$ka`UO;T>zz%EAg-THu1zc~a>?ktKKab&y!1Dap8>Gvb>#NX z;`DheRbHr|TC0>HD7}5z_Pu4i6^Q2BKTZp+xl`9<9ZOEg9+_W$m6a!7iP6Iv3v^34;`B!fh-c}!qC5A9RdgKoXygZ}FCPSI>m96HD z>Z4qh!Z3#@q#WrFd13Gdr|FGuxr!I8@dbcrb7e;JV@- zv8Pel`+Gc`&wD`|oXNVLGRAWq75%S2DR3iVACCM-$d+E?R^$ZxY!Ae0)`5e5MwAw3 z1_Of_?oVT2WQHWNKF5&AQ26d?pb$;!S;PbNWYY*jkyTj}4!05Ue25sq^w3gZhOV8b zjD?Ut6eKhP=4yHc6=e+hp>SjEpi`DG5S6Q# zTDzJto9uKq=&E3jJGm|gB^ua|^j`by6<`q8uig+0oN=Qkskpxre^>4zwiI{GufF>Z zmEQ5c&C_PHqdFrmuy__~;ES6-5*QQ^fW4o6P6DNf{)5fy%kdC)a zs#}2j*uK+%!><7&)PNKb{(}lFo*Bf-fj!&J)89>U8 zC2laGoY5g|O1R~&1Wv`?3WLw`om%a~UOcY4i=XneFiy#G$b}9@6LW|*b}R){KTE?G zQ56I7No+BvnZ9iiM)~lOG6Ud?K^@-F3IkX_j|-`+owbXzxfH{lm<(n34GeLbfvp|* z3=p?4iLnB7MK8qCodPA;-6!KDYlIJn7_oCaMKi0L)Fo zVIIwmnX6frNtrQ0*iJ=L*_MT%Lx^FTAJ#lVS-EdvJ%PgrD@ zY0?%@R6He$$-ybqc6k|%>S;oD0m2nZ!!+9e8}^V=l9D97IcMNQ+{6 zFy$zxzZpRLZ+&9s>Or#nvPOKa73?5XeYGt(F_*+ zT18TQej%{(zrv2F&d$%%bdI1gRe@xkr3Z=~o;9X$HBQ0LN@J-jSGzE6voDxL>Knp@_8jP#QDUgUhqU`1wiWM#l`l7{LFrP{s~MiWF<(O+*4BY zxpZ{&9y(wW(}X$^BIWN{nx%$cfI?YDw?)|z!)(z|be@Hj_Mx!{cS#lq_C=Veu}Y;# z*{flDJ}uXnZjT|y=;S&>Gh&@&+2!Yhl3fI3)HcuGd|jJA5C4B$oKur90Jdw}wr$(C z`)k{_ZQHhO+qP}nw(ps`Pc#2vXIHASl4Kp2V)|4fu&{qkTzk9`gjb7kZh#S0TYoq> z)SN4)z|lTN4wbu(&QTpR-n(c$j%QV6jUvW`3RvbvkC!$aF>t%bC$$e@$8FhMJZkk} zOS!AL<0aQA4~&2X*!B$J>RCRM>JLg$B{$Jv3FHE@t9h*QvHWLV9J7*poXEQ^QsQ?0 z^s=?M>%3`Q`56k-n`oHLSXsGj4-UFa1%?kQNg{N>Pe1ZZ>+D?dAy~2kE_0kAmwsky z8{P}(y*u3#L>5K#`;d$C$&l-F3XV``onlCxb2|1rRHQGQUQv}Q01y$-7y>lLBVh>l zcc0>w8gyD8Z7VL6rHfFkfhjOjd^Pew6W&K0&!nJ32W1}`x73P@d%RAP7Mr`?rUBJH zo?NQN(eXXp>Y6}V_Rsejg$rwME?q!Ev=#r&f#B!&kU=IdVcxIcrne8cR;|zm) zr%F#k7XtY<@}5754mA86^Hd)#aiveYBJJo0=>O?TXoV#jqrJ>TDQCv`E6eo9f?cXc zJNp25jKCMup;Aioaq?O##Mw|b_cRj$`5U}!5d9=hU`3r8#{C|G31Il8_%L%6 zA3a)QqRuki)qVDf63MGrF>U+S=jCdfjvG0yX7QRfnvMYg)QUAJ8dA9yw`#NVr^q=~ z)aVgo4UtWS1k|)%EQyzQeg)}7-d4gj#gSCdgCtwB@+##+j0Nl>Jxe) ztX?{Q)>2hSLchglmJL8+4|AX08>2$Oe$h%AMaiH_@WATB(O5TUOSZ>2-;Tsq&0gzN z07_Vv^><^qRAR^@#YLGEqi+?;vY)6~sC7B?1(hJYp95SfY*O4q$#HOz=R*LZ#v0m{ zf;EvL0lcI`o^!hK>4QKS+nF6`8qfeoL2b~A+BZY`^Y1UalxqwIcWV3#l{alEx_hcG zaZt-2MA)vj$&*QK^1i(;HPP?5CAY;zcE1mG5G|4lL&|}e3hLs=!;2V4!WsxkIuj39 z-1&&QFeH;W-?s34ouyeTb5Onh{`lBi5k5>nl-(lbA6=N7AFk`ZKx6V5-wpJs%s2#7 z`J_0A=VpoR{Me3V&a?F-0^DmRKqN0F`sLk?l#(KH@(6Ei^(R-DkisbOgOlO2Z2O?B z@ky*?7ZX%U0wHCd38-9q@EFYto(<{LgSxhF$_kI#3?or#W|RsCUa84OhW08d;ofBr zRCBK6_T5-l)y?)C$MdTSQj~H6^$DD|s`7{RdZznOE_62bU^s;d@Dzh8dnKslia3Z9 z=ddZ6igT`ipEf3)@YRbtkEEl?C)l7RFI{r!MgjTm4|-v7f$l@5J%i1l<-fWAd)2+c zcM$k@4x^s!aT5eVf=JQFctOLb(-L;`N2`!I&Oar|y@5Pk3w4SBDrgDh`Rx*ScwC-- zQg{Sm^c;ItLrb^IEjw%Y@NXA8cCV4M&!q0Y7x($Vd*H)~e|!idi9R*QhU*L&J<4}z z;$d?<<}@Cj1Z3(SS_xteMyaoi~${i!9DhH z{=vSb(IXB{FpAaVqv^YLxbVawmHDtQbh~R7{mXjBZ7yr$OwzE;GTyX!ZE{ul=X~py zt#OCdKNtXNJ3U5@3wGBuM|txhpJ|WN#+io9_91*mIGwNDe}*G#f(}kygdgP@n>5`? zWY6Fvx?p3?t7C^QNFCU7kL)tf&3iS*#;|zP3P!5Qdk|PS*T1+g0wJ`iN0m0qj#Ih2Q{n2AT zM_U%Y=nRGU#1r=J1%Lz77% zYdA+93Oi(6Sex!-pSzJ*%Yt6`>F-2kT06|b+ZB!U)2E+=soXQ;KQ;LZd=-Fo=mLos zg1fV?v%?QDI%yYo?@1Pi!4vX@Oj$t=ljF0&2O>X|Je3ht9UKnb*HJ1H`kRBx@#^Fx zm6l@8GX|yk$>yLtKBi6jX;F~ycuq)C`~j&$g&6rc?AH9?I;oY_rQ>L0;<{KY%#8Pe z_kXzAn0C3;IR~#_HUec;%?HQbb9OpcJkfH4woV}^`IPh4A=fpWO$=$L1N#9VVidV} zRYS8b5^%a-He9Tr$5$_~2000tQ?>)?3g*VP$__S!hF`i8GgeiPQ)njm?dkB3l}`@v z^rhR0$>3o2F51~@(`hppaY;=5{Rrs>;L4xDo%=>QVY+ zY5577E7q%SAVQJkxzjf~e1G)MJ>F@cfd8^YZpvzhMQd!w@)Hu`A4BJ7l_^|`VLQp^ z1+HBcv$)x5{Brz{pkfVy=9mG+UdSf{kAiD<*|WZSg3F-uT18X^nn{g~l}trm51}*g zLRb-;N$>&gWtp8zE1U>r3Fc@=npcO`&w(23R5aA2sCO5&u=fDcS7GSTmt6iOiWZF_ zH0tIR45kFuCHAnh$xLjRZG8)*Nxhf#6OO3K+|%j>3fr_PzF;kCM0-idJH0A&4wjO3 zN-iV@y2)aLQ+2=pVWy2Lib0eGset;xpg2oJGZM|*7PTWo>SGc8^3-}OGWJq_Ho(0OpeOUrBXn7ya9ncUzYerx+Ii9= zR&GlTIsrezcBQ;wJ)>>O>R9zNxHfonsco4sT^(zCPx*rzt`i3L1J#?tuRCz4%&j>u zJJ;N2{*vq9dt+G3oweKe!WO)RhZr0i7*hCO{X-$6%-6CJMy(~E)>Jo`I5ury&aqEU)u zp*MYJ+eJ2Dn6sK5~R=Tq;EiK6Ohh`Xdp9UWJMgj9A=+ZfTu!GYGq= zBoP8(ioY5o$K)8O&TV8IFrPs zK)k=g@m{9HAF%~bokr{8+xP~@sMuJjFC)uQS7E`>1?ym(;MQxM+D}T5FRK+6ZbaE`1xD~)h5LWmdiccu>Xj% zMd-mKfSh6tw+qLC-Tok|nf@wNc}d?%VzXe5PUk|G7?`IbqO&Y}Wko%Yj&z9O22Xe@1XP zo>pshB!Y64g_Wcq`eaK)d8p*jl6#>)r{6?4RK_?_3J~+#50-DuHB+z%g^MSj-ZIrE zSv>H=#g=CZ?+rv#-lHk8Mg2IF6tp{4;Mex6bgdQ=JQ~ZV@9JDzJ%5;>kfChgFJJoS z#eB`m+HzCTm&`!5MYs`}q1r}d&(VbI9*1B=g@h7*#AJ&Gu&DG0@8G%C52mVb*;pFj z|I{a+p~VwHcEu<2b0baefeuijUL=)_1~=C~O61*fUp1R~ec+%SP8i8(hQW`bO&($1 zC0wG9BjTo2z0PB)LjWgn#y33~0?&FYbox->1<@fp`!2}jRFzh|0It1V66B>}iOr|u zk^XfK5P3B%|KI5l%d)3Wy@q|Kb*5HPHG#xhx67!bz|d^ri%e_R4K<2l6zk{sv+Hq- zUo)zyC-t_0%96xx=2-eJO`H>9E*`q5n9PgpvIp3ugVE{O+18?;b&=?!_W4v#evLaF z;I2tz9?wElfWRM)qhPV*x`A2=dv&K=)1pN_<}XJZ6G*f3@0XL!%nVQ z7F2~net229x;q79qX>0@ z?n2f*J9J8kEhKd!Sx?EK){ciJw}iHAR6(nr=>G9x@9i?WzeoT7f0HBLHI~OPg?+{^ zV@LCse%FzEA5b~RRF?f(q`*ME-orofu}=mm%3Y<(lix>K3|Q{phs@=)IT!Ql1pgKK zwC9~6M-e`S^$j#*PzC9afuKuA^)PH2P?bNl6ND{DBpq3w!_<%QCU{-#5bdr$jK(Jv z*k*z&pKw8rtj8~p<4cJh&}3oMqUA_XlUWX~0Z4u#X%xaV4Yc^qrK}KhPR}am{_{5B z9zuW5jF3#s#(c=f>1^FVey#J09%V_$E~m>-S!P_=|T8b!5;9nxXeGg7{T1+A(Cws<`hwuG{nq)%NXcuDY?+Kk0m z&iohJE7E+bImm7kV%rGt3IXV^87&hI>F^q_^32}PY&z(th=~V=A5@EhlJI&6m(eZcv3gygaa)xWf56Zy%Q#jL*f>a3eGm7Xms#gL@ zH#G4*;{yAoM^eDb6YJb01SXzxemJeWhf@hP!*IVIN9R*ih`p6ZyuaG}&;sa7Rl)Uj zT=;)*eNmQ`Ou5!ZgJFCTJvX7r#`73r&U`Fp7Ak>_Wg?zksIK+Z`cJ`z_TqV3XD?f& zyM^jiJEE^{!;$+|BHfp~iP6rlY|d_&bX4A)-g<&|{@eUXT?AAi3Jy_~&dE>7DclZh;p(Qmb)|8|S7 zrkF#~yUdpP3vdD86oDH5Q@PY-en1jmF`?0D!yK~)=1D&5V6tLom!ZFF5$6JjgSf$3 zZprf;E~UQ@q?7vve|Wv34J;ebrw(%3ajEY8s`ylL97w4Z%JCi_riTDOFmF#?mT`;i zmv^g6STDctZDkdT1PBrf6x^wzXHtf04lQi^dFSe^^D#h6F{q*8Pj}`R{cnP-M(J|ybTz$D&w6e~1gD!_(mqpSkv$KeJ|<;sT^-0JTV9k=$bBw6pjupb z8WX|BDy{H#V-c}C2=s8RA+?$$ZOhsjV!KN<-BYJJLmM7Z2EPxzGS4|JO=}wDkW{B< zKr;osqfO<;4_GdvtlY+aF7vtA4r)l=pUxmH`nBfrc${2+&|?gE01JKqH5U;w5{h{V zk;7{L0WH2kN=J?Ln`uDym5~R<^$i9PQ8{#1 z4Be-Anp#&crPappiQ^Vg1C7?h3neN-Y^-uQ->G?81+~WS?RcPDts@G zkb7-6dLh~)BXKFVN2nn&Emgz1?T4XJi z7u1Kzwn*LuDqqR$3Ip94YLa*3ho|Y&ovkw32eu`aBqZ=dV5Zzq_+loYL7MQrKZU3~ z`o_}3Vs%tvMMP5TPM-jTpY>K#V-U+F{KmGpHEyegkKH6Fbh+Sr{Y-!;MhfD$oe8)iCRFPwb?E~G(W^t6t1WD@u)2>I zg$sCA6kOS?v?wYK)?UKEsV9|XHI=kW`bY!id@D79S<4iU%{#Sg)w`6(-V6H5Hi@9P zU-0=q+UVx4{Keya5936g9ku+Zu3Or}4DZaDr_`En`^rap4D34V zWs`*~N+cDHHN~yV?tQ>_S2k%_IV~dR|45rGNP^-#DX4PSa)y#^2{n$$+6ieiq389L z)d1?k8gTq)6ln9s_#eJdxrp?iSv85ZB-rJ{0TMW;eR+2!{HOKYZXTiRUh(&W`>I}5 z2FwD*Nvl|uQ4T5*Y*VV_Nn9-SFaJ@#`OPpnJJ}jRkdS_~E#N6vuiq18tcSi()j#{B zUcIs@^|w~N+li$vHM6cdpI}+PP5J6%1s_0=%QL<{<9v{B6Y?r*lv<)Qca~>|<1mjp47+3LOWR>aAFxej!hJT1qL0Qxgnpe1e!y=*iN zm{*mF%a3&5>`YiA7R2KpsHr;V+mOUaI-#q~15%bYWKdukTC@NYujN6Wf`YOO+64|m z9Jr!(TDQjKz`B$80#7Q^5D{a6E!O+#6F~BbadA4~S9-;7Eqm3s*3i}YGG>zq-FtM1 zY;K5U`dRI_T}z@lg%1OpvW>4-8Jwoy#z4Xw{O8DkUBNFzolKKX-V6wn(FCQ1mc2$+VfS|I!xt#-bIYv?_0 zIT2i?v-Kl#qw>U3Szi0SxYAtJT#Xh)yfv)BX?r_s(TNt6Z2&@uJX!iw zl#yG~vn8*v`T@0m_x)gU_rGxb6*3XN?v6+JNJVLouCr}BO+A)y9BWBz%bwDPs@4!| z05Wj-%7i$;1*gj<5fAK7_glvkuh`j_T`42~GIXuWG-F^)WE{o{rLxFPm94hUdSp=? zc1784#4<-*6Ax|{{=GJTUba5RC_y*s%=ZzLN$k(e_rJqg9v><^e3LplbmLy3Mt|A+ zK@*i9j) zS+=QF-OT8$RI!C-~5})?=a5e>_lNp^5K;}<|CKLs~jsb4%*N|n2o(FbZ zc|9iE2P>?<8Q`C1%Q1dL0sV;9(((Y8ZM#Lvn*lpdb65ED^zF4&{#rAhO#=%at#fbx zQ;M>ctZh@9&`D2RdN_?3A2DkGtiu_;9zm701^=9bSKj7mZvk+-*=d@HF{Rcpo!KIN zN=}B9<&5-k;MMp~o+Y?xUVtFHHJhQ9vv4}j$WS=Pjq}v~K6@cWzfUwgS}~IP*1Sq+ zx-@_bo4AhrNt}u_VUdBJ$m}`rc@kOE1 zXed3?mG?&tGkF<4G%4pLfV`WE@9ldi=E&m%DJC4k^EWy!Xvm?*>}s^bq72QV>JFL5 zzTyRKRxS+tHtg?Vy1j8c@(OF|hLcCf{2W>hd~-34msY~A{|FBWK@L?9E4u?EvP1A0 z2Kuc0O8bE;ka~w7@dyS{ksCK;ZdOWOt!3-}1P^KNmG!jmVMI`grD$L8l#FDOMp}Sg zlnvX>dHIBWp_o+L1}_=`Vl-#6_ISlMLyj}!oih*~VnHUn2ic%{1JFf8xUNM-MDoo& z=PuTm{@Y*{u7k&OC#1k^Ffma7+{mN#bFdJuJA(+*4JMgpkT@?l;12SfP=(_BFG(Fo zOST_91OW#=<;2I@gR5~fWcL_Tt8DWjJN<>Xg;pwbA0{>mMQe69a*CUt(wW**&wcKm z=&}l^^|M!Iw}qh+J~(?*MMbx1Q(8QBt+z9_Kwl*yA-0CZ2i8IXvL5%ovS1U2nJQ;{{=j7)J7dMtd95+_dCAOZ z#u7Yesj0OF55-X9jyTuyjdRJK*gsf_+;I;gr5AC9)M^iVH z8NYu4$>MzXevp(KaKZKIEf0UcgngkkGc9k-MJSgHx1*lb3XOsO!iS}fYxKFhDEQkZ znyfti+av3#7OkEBn&sWr1)UYaCFnI{GBURE^QYgk&bs9vdfdBrm2Q`p2=}l|%$9-?d6PAMn3^5{G&GxQAnK$7EJ0oa9-^Bb-^4!6%ZnSg= z4}K;mL`Mvh8jUJ})0wru!}#p>&CRy?Ad%6T!3a24V$5Wk7qG3x2Mf%pYKopl(6O1M z5-A@vG5ZnPd~^AZ0wkw?ATmUbXrUPTQWea_fVB43Wz`;KNCv*SFy=KuqJ{C)C>={RW_DR`Tv&)DvO+v-l{V zxSV0wjJp(mK9@$6mk0~eO*M0!+XJF6KC{jOqTL0pZZ9*$(d}KYM42`y^L&Y%ReT9;E<5`}_)3t^5~Y{Z_*A%$E^)68ziNpGJzGB3 z297p=K=7c}B^fyy>OsDH_G%4JAvKX=Jf8A2Z?Gj3sto7sJ5z$mN>9o|s<-KNMr!fe zs|Ek}%DU4;zKo5MHh1C@Y$apWKUj@SpKitAjLkGLsjLKu>Ug8Sc$Tdn4H!1}H%Kc% zd-A`qR=<-xR7`>erkiqoAi(OvgQW=iUfPaDM>8h~`so+sQ6&$MepKIZ$1$oon$8f z1G0y(n7&NY>y&S?HBpGijhSeM4Sp?hSm-#s>$O{?`cTQLfmxyGv2QvU<~OU-Ya zEKQc<|0!d$Niw?LMiM9O;P0J|ec2Xu+NSonDr}Ru) z*Zd}e*4G_%@6_`xEx5-!tv4Veq}>FILTA1H8DwfLL64$V3U^*wt2KahBf=juzi;0u_rlkBu3N_jYX25PbkTVvGmR4h zmTmh0Ugs-&7rE5ox*g@YyO*7+B>nU=l{1G=!FD^fc&Kd0j5;cpt1?azycZ}>B^cV7 zZ~~*tS3&U|WY~K#J?CVQh#O{7E8`)FWq{WJa(5@Vh0soH7MpFy0?3$G!4s7-!s8d< z0H@*Pfv#RUD*9>o>4>10Ii%*Aqq}=TCMg?wnz?`_`%7>5m8e6TiKn#^vJ25o(xOsO zCR&I)`H2Q9<`j5U>WMhPInrevy8NP7c^}krigP2){h|TyK&-!I5U(K=uY~++H(mg_ z{AYY-A3NdGLH{p5SHs!^PMnB_(^P2Cu=6KJ9Dta|hONbs?6;r&0wm39A47C`VWp{7e+I+3R@NE)82SGDG%@!}bs|7xE|l4&j?DvY zx9!TWt`E|-d%yU*rS=VcDwuJ``KjkC;EZi}9oMXnX){~OrgaY486?&9FJ%OR(3+5z zEv#;dL7;uGBCm5I{NI4P>n1QRDj^red!%jKYOh8~-K#cI=y{GT_5G7eZpg<!G+Y@lgRstP?<^-Rl5Xm3eS2aAhw)U;6kq)~hs`u^FGgl^A z%PaKhR@;Nip1H7wqGcOy;J^VM-)1veJXvbh$Mkh9w1f`dODE2maMg}6tMN-fi8*Fw zM1%o@n@>{s8KLs+;_mH_>is^M6jbsOf~Pt2^zbHThy%O%`5G`rcrP8HXv za>PuL#<9Kf4jy1Y9ych7ddc%y__9$*ya*3H5)1~>M9@thYeBZMAJCEd8DuAIx2p1? zrE6Iqm@QmD?2F%~)K9ttw>eANE3`yS^cd=ei~>S*AdYEDz>XNv{7ZUW;B8DObuziJ z#Ofu7f-y!RlQIUxKTho>SS*{4^)$r>JR zmetnwJ^5Q+J3LYCgEVHd3xCG#sHu>36w52lyfpyDQpaY8@$|M+;`l4OqfLiDnb!E^ z#CfrTttjDSj4kkVYi{HKK#n1XQ@Sw=P0blmmM@>nh#EPwhyPi-gM$acyr;AzdKoP4 znmQVOYToul<%L%GPq1)M=##?b`-LEr)6r~D@ zKm774Z4ErI_4VrsvWMDDlia9SC_r}cwKypUx*H9DJ1{;Z&3R*&z*C>FCXRW2u+l#Rq)_gahcF zY?XALu0w_Nju#23>>s54#d%6z%AbI&4vNTl+wdkE3}#fFSk0RTe84H@5+5#x&5#r0 z0a-;8)@Wpc+*O?xOQkyGes||UY%zl?ejAoE%?Gnx>Q;=IQD7J^XTFj_eD5@F^RXlu zAzr$8{1=y2=Aq86TU?5`h=o!WvtLeB0~yUXcu>44*=lbfJ~d`&Qt`TN?OXNrMR z`&ND1I9g2xMSmoCYmiz^zq>7em2lkD1yWa?~50zNi=|aY~UqrGp^;IiSIejr>U02FLH56$#bA*{? z+UM|iWMK-{y=M$gfTFaEJ_Tuf_|n|S$Lfdb8KTsgzb0Bw{YjXg_K-@`bc8qd@VWh! z#5UD>8mholU=al2Ql>1$+}&AQ5-e9`j!)G_y%b|mid*MtI-HT$1(N;9%pv|O>tnKn zL4UAG3;4ahEIpKw&5%gfNd2%XX-p#qpw@`g@VD?{r|b0^MMe@V#I7RxjeZo?D0Vf@ zPmHSG539uW3p&UAv4eB}toA1^+9?;Qht6O;3gjE836?o993Kv|2$f6FI5e2=Pqz*w zKH2HmSYagFmD^3=L6uWyR4B-#C@vYEC;^ioTn`+jOe0a>)VaK|7DK^~@erw`>VN|@jh$Vl$9y$pzl(N1(v2$0(95t4(!u4(XT=-4t3sg{9%hIuJt6N zNhLlhq8tlXo=3-uwDJ!~O|GkyRZ62>xObg%DGgw|$r*SH4vQDJg$RB10Sm>vnfogZ zN?p0B?4EX7PV!?qAxoYQrZu~<$bxYf1ABsI^Z>a=zrbLs7S;71^E zrrinw6VR|wv*Hqx2><NL$6m)BDGDDLb7`jm zAj~M)0f=%bb3yd-`O%D|b8NYn4{{wgvcO0+R1bsI25fz|ag&Co$g& z^IAGOkMXtBc_k}dnV@{a96+`6efB?`QGqz>V{`#6Y$q}U>Y?gtu2XG8H+;0ko-ifVj!=Ea7^l18Wq&SqLHTbC%d%5x}GI5#~p~dW|2YEb}#zc)4g-nB4 z11T}rxNXVaYl2c2@}0InX!%kR3As9kbhlWAClR!T&Ew=6CzL$My-@x#2QVpMh%&ew za~_xUBQ9oMlJFFx_9|8Cdx^%ParTOdp(Jzrn6U#(FZs~1YtLi`4UC^k19~_KHz(@{ zK~U|53u(bVzzmZ}`OaPILLv|X$Ha2WHieQX=pWh7;W;XIfvGpU8$G-!RiI>~-K?Fs zbmJbQY2E;(rLQCXbg+Rj*$cC7DD>WNoXh7eo@Iaf40spf1+%={luCq{pND!K zH>84YE2m;_s#7$$iq!ND;HzKj@)*KEJ4Ej~O7U?(&>Hrc{(Ev$3)v@nhqUPa$O69M zOa%UoC3wrp%ivOLPLZURZR;Cewl9ub8os?^`fctrj~p-oKBSdWT)IK2Nf0@OugT&q zWJu1T9^wAxBv5Z4=fu4A?Fo)YiIF@`2e+M1$LE-{{{){ySUAgBGxkn&2zn7!;&F}A zJ*Y~a#8k5JgAw1ODyvOd#DurAbD=&wNpgR&`H`9qbx#{5??&ujLz6`B7Nj##q(}?K zr{kqyz?MaMk%&Tf3qkG&71&^p<#2LWQoNjb^L(y0UM+!fCbQwiM1?9RtYc4L{T+by zQ}l){VtC=H@NSDN;s_`?AAyNKh3XV~75`Lg1b}8Iw0#awg(OXU(%Ip?TkP4rj(|0! zjd#VoVnCD#=JRA$0Q=vVthNlgHl85^`XS}$w@92zT~WRtoUe9KK%*cP;dc?tg9cvO zhj$E~oV0hlx{L90y{uz4szCFd7o|27DZ#7flIpNa{H$P%1Xb!8Xo_NdCkSr_TO5J! zf;t)&vRd0F83#TF>p@VWt3=IM?}u8?1{vQZ>LjGBFvRv8<5koqS3`S8s5$R^ zYG>l)rNOI9zOW5Tth5(=JA*(m3BV?Boz!kxOO+ZgrH)-A?Q)sY51rz<6YQw$((<#h zAriD%Vbcxv?WgTB0y6TGgP-9Bf7}?pF}Js)9ow}9Pq}(4kvMcYJxp%Nh@LE+5Yh_t z`6^;A1}J-5_^J>JDnzw*qU#QwiQ`f; zF?r}REU;fB&^-{PBQfAy?bCLwKT&TS*m0Q4dcn*B%{;5>Ds_)5=;de@K&}tBYNPM3 z1E!Df>DX9TdVivAW(bLFTkYUABM$<5rm$u>+lEq58*dMZ3+4}LS7uDN{(ocz5gJgdA}TH%H#X` z{)FtAR0}x?JI(C?5os&gLU{$~Q-;PU+Pc`0(CYh?FIn-#J4)P%7Kh973~vdN#2!>$ z%(XAbUdQj-_o(z$t@f>QD`q-O*agB%cZIp~w*;jOIo>@yBnft9fDT_H0i0G=0H$8E zL~XceqP&tuutv!3#szXSGm6xdDq|2*9Hy#JU&R}ck-Vr;$ZW7r1p4|xb=iry;l#C| z7GXdGku1Qv%MI8&9HnpytB_5c@~1^ZYl?Nu+#PLe1K&-JAb+5*$67^zuGk~M&o4>w zI39x=mvdwSar%uwAjsgPuLOvf;F%^`vb=;oFwIh5Fv>0KQbgBlwSuYLXU%y`BJ-!u z9w;?kYWFtj%c0-Gtno$*(MpRv+kGIEcSR;eU8~Ev`VlNny>1rgyntAeu*E_KiAkeO zK@_J~G!^pe1>Czoe|~L*o7sre-wO7b4nWG2=^q*3(2K)a>C3a@u;!-byyCuid?t1C zN{O1lRvPeLPfy9V1IdtNj!nCLD` zlE)Nzut-OJB-xt-8VzXdd1;965OiXOuHu(JXDeVpAU;IsSIeGSM}WXC^sFJt*|Wq3 zMiYA&D;BPpfhG#-o=QmeZ+#39r}tz3F-N?5wXy&(<>bl>?I5xIeVNSB5G+*JjyMB0 z+_N4{17*ySi{?WUI$;W6o7}$tbp5pL!3B#uyMUhrr01eN7t{%Sx!#LIN0eJ1mq=fK0Oqz4*Q+7!+A}c_{D*_`w6!%g=3)X z295qiZFONx#vj>1J&Tqa!k^Fsg{ z6z9Ui1y3hHdL;x48PdfG^peQrkD{E5?0Ks`1#eIp-?qnhVWjO8s~IWqjUC+uwrV+; z>}yj6PRDG0OZ&XVokb;JMWA_5o89JX_|7w1MLy3fflp+h4Xlt<)@so0?vu%@LofqA z@+4@14C4RH_Ns}46h_aLXYe<=KsC!=4B8Iagzh^;L3}3TIf{+W-geqp*fTw}ng{T+ zEdDIH(AcIB(z_v5Ys6AJz2kCwEeNO$5o;%M0y-a20G)O+<}qeN9Z3DH*Xb&i@y@Kv zlJ;W^6ZD&pH}l|v48rR?X{GUV=rcky`MnW_8^}OPn!ymuEzu|gX*CrAj$e@*U-%ro zHGE>;2EP}bqRPrOyN|YW&pCGlO4TUVhJrAdSeN&lWiQaN22@Dk>e@Fc-O>m3xLRIL z8B|LbEX=}Mskzb~w*^wGwtFR?WFN8BoA2kuTjjebK!NHN-apjIdRSvISTp*rr_tp< zCQp&f_`Epmwgymh)L5IuvL+OW*TrOQDw$lC;%MLv*%2~6iSb|9V{Vy1HvR)b!s>dV zN?*1EP54)2#bFQ;fF+6jW2NFLlUQ$rR}>{b%0K1rJkk6sR;4#v*Z}Md1?9N)-p`+a z=xAutZ&3eG@J1xbQ+)K2=&vNeFs_b3k;>rW8t|-rPxWs+of~lc-$vv!He(7@8Afy6({Cq5F+ zIEr+iOYY;XuQMQKAM|Q^h1po@s*SaZm4BWKmc9n1ffLOJR`4xNGS^)K8vh|t#iyvl zVI_v77QdAX&Ad4PByI(5XbVkrf(K%VDQg4`i9hqa0l(wl-Y!7M*M4yujv<`iYUrk- zq*;37-7(}Fq<`~FQP}L1w26w?U8#uMzn>tr*Kfj`djBTaoJ*H*1EYiBU4UsbX5s?W zcoC2UYAZupu3j!c6zKlHZhZwg_Km`tc+)aO)(k*N|I98{sD9;DTY zrcFVnj%5hMD&&^vlHB2T)#V)rb>4XH(wq_X(E@)Xmf#2TfFZb0Jnj!O96mfPY) z+R;*p0vCia8O%aTYVygnlk_N5{paZGv=JaAUbCqSi{xsus#lA~sZ{qGpu}0!%S6TpmVh5;3< z)zvog_HKl|5&q$2Ht7MzgR~6XMKW8Ren$FZ07ZPbWvtMS*uNlU@^Ohe5!B~Q5ddnA z)usg8jjcR{KFkv=U1OkseHr|pBinB;wD;8HSY z^=D-V6>=#M6~UH4dfN>=?90O6V4EnHm0w<*L}0>STHBhK@K;0sAl~}vU23CEzzJme zTs*eqxg_kDKq`+IRhStoPR4?-wx$RFK6V#CaAaOGQo>5usL- z|1}%f_qGbaMfOR5bHy!BP$_^#)0`bUG*5}UvIkIX0g?KwzFM}Y3A>Cmvli|ybrxZW$Fujc3O zkP)5Jl0?P6rLh|bpJ*?O&qw>NG=zhzWac?7Av{7pyuhj~{WFOGB%V5@VW*ZH<(7vZP4XSub zZz|f@$%}549t_-*YUJ%GC2^iUMGUF9O=g!5U$`wDh%@NJmhzj;4Ir|yXHHAaRGTKw zI{q6u9>y+~CBA1^tvT`gyJmir^)aK@J;;a4a=pV50MDCeKj*Bj(ll4V%l*6gI9Vx= zVt=%S7r5g02=q6wfzIfgq)G%_a^dpr=czLeELI%Kz2gj(CvR2lAju0SbJ+;~D0-e` zLkIi{d3M#*BBoqBh++gqzDRRgxb~xv*kZT|Lx0^rfi)?Hf$xg6?wT5f`pXNHMZV zMPtYh!N))KvFi-*@QUPv2r=f&#eLifCVrs&lOeWUoMh&KiTZifXmAf9om=|Ck5>TJ zjFnm`LyX_lJ7YKH0Hvk?RF&T3Ir~R6alB1DLjk5ocG#)h&p6VJsGEEB>&?TIeb#Z} zZ&&r&2(ON`I$SC^T;Yem(LmQgk!Dt^b+kY31X>>FzKVg`d`{hY02($FLA(8NjCx36 z7)(%6BD(rI9#xf?6IJ4mjDE5dty)a0=8j%Yl5*83MQ;|1q+>{)UNDu=gh$7BdzYfs zOQDw$ll42DueP{H+yGDRh}uE{)S}_Sp{V4?Dg+6httr}0EQgAbih(|#LkRmAa|0!+ z$1EocJvAg=@{a+4Ap?bUpK|nUjn&>e%1wIi@RQ{2jpDI`aR%ebh*&UzP!13?h}KK5 znMx>}M?+5Sz}O3~H-!J`YlnW3Buk=+%G17@0Xn)3Agb1Z25L z#A)&!=;!~0_KDR%PT!L+Tuel%$uKcH{Qm-(7-r`yJE24ioe9Y@494u!#P^LS&5-&X z_T%kbBHixQ2IBr+osCa^R0^BBYlc%Sa1VSybMdhnSYV~AL=;-b5o*soV+I|V43@AD zzv;w%DwnhCGpa3w^9v97Ziu9GAkCnFL?=)e*BT0bcX16uK2jL{JfbS7E0R*j+upl6DB;eefI zoM%c1&Q)(mW9E$Z#`*h;>UhqI!(44!%>1St9Vfv3bpn^v*N?B3Fi&1l`fTs<%3$)O zAKUS0#zmF%4dU{g-IaU#+%ncM!WfFw*NeRXw{kyKM!l^hzWp*INU8Blcf_$5Z61;g+;b{CbX{iBZ%`!okBRh(Ek?qPFM$TD zu%mP^272YXfBFw*iIyro>;(C681{k0A7&yyS?G`QF_a@pEuHB_VlG8LtFplyRUY!g z@yB>4k+!p!MKHxW5!a+o5HOsMWkAeZnkDU=BT2OCtgdL~SO@EyAPAsdoa|5%MXpm? zcs&ksJ?!wuz~$5(T`mFwa*I&@yFm;YVy%T}bwB8TScySjN3moNu8BsEv7}X2kQ6Z1 z5LA;~L%*DPHwr&XXQU;GfKACEwI=gNt{nt|44!3_{iTWne(|YhA6x&)jci^kdZ>=g z2qSb_%-M-vbiEG*IlgI_P3~be+x#9s^(QuoNcgLDUeheVdC+*#GUbOrM-9;Bu`nre zg6aZ!!8TK#zi9USRysYVFxxy{sgI1T#(-NL58$2%r zgg)j8)iv|&B2qa(?qYMPD7*=tE4$kISyM?<&T|fo?7m;~|0|9ioWw%Fnbih#W_I*C z?&wl!oNKmz`M#|qDXI@tU!Vsoj;pJ?jX%k^p` zx`r1=jK`cS43)JcE1wP!obol2GWX;+s87J|(`c&JrED$l18OV? ze?R_2r;2*MJ#~n~pi+f-0`g7uop_%~C)`gPwc1$$4L=k;z>1?hvjf$I`<87Iu%qob z$k)r53*j!wr=~lKlFJqlcYVKnjvS;$cEhxCRW5X$pnFGi4W+O&Cl7Zmy}`lWTL5ryn0Xv49f?yC)I_;2Sml4QZ~v0 zxTT34rdm%Ypw8ux$m6j$-%wSlw_ zHn5^gC3wNYB}O6U=|!(|5#x}&UcrCt&uuvt;BWx3batt37tv-%NNCbrI~tM%L6BGijao@Sb)tZ2_>pSKzZgky?0e*ln9t_l_>0l} zGBos2qD^xQ8=(K6oiX3RiZRC4vLK%Q%}mw+P?iV7Y<)a>i`R3Ls@#yUQ$B5m9%$j+ zmr*eBP8oinvn%C7#Z>l|I0IQZZgz4Q8FpH5P-(?8LPx z+}bBhkk@RXu|(k~SG+?Ho=ud>sE}BryiC|0Ll~kBWK8r^mfMz-RO;XGWj*Ql;jr=P zY*ARpZu?6^#fuQ3XlJeY2{%O zyI)3Oy$73?tW1r1_OXB9Ah@t3mws1mB-nMOyG^5Ay{Wwait654rc@z88$ZQXvmY89 z%Ao3fXi1nya!ja8hk0?b8KPXw5;|)%BMIGio6}?1*M~a1t4!)fOACT40rfeqmLi=t z);ou(iHt{P0siwQInIR;dNz3szQcBcToya!O`eF*sN)$?>_`2!P#O-nSY&^Wk6FW& zhT@ZJi8aQMBU1`W`jNvD9(6%)GkT(T&A88K3>)-4ZkelEpvKv&!YzQrJp+v3o^e}P zh*)rN*MXB#)4<0NJ3u$5@OoJum?Y#+w<#vMiPNC7QOa+mW(|>kv6=bkygz;v7UXn^ zo9tLaz8BVr-_w=sF%L0^UN&p(1e*ogUH{k2D!!nS~oR^P#C^v;3Tj@x%zjI>qtdzEPTTSH^;+@u7{rJ=<8Z+oX zV8b}pZ~ytER_D+KXmmxkHOV=(O#llJaYJN=HKYZacg#-aMc^@(kQ;1g*qQv9GV5N! z1ItU&kW5YnJ>iqw;mO|85H?K3CQgwgeK)sW?tr#V#)VndA9S#%X>MK?lp$1XF#`HO zm%4cLMD`b|)Hte2v_dk8jdc_{U@+g!$X9bZ1s$NrLDXmXdtexN^_T}Ve09d&Y_L-L zW_I)*yA*c|dcKz&CBL?C3y-b{x_fCHH^~dOO(Biam>pki~`f4U-8LDr)I|$~j#{M8=K!4J> z;b**Wd$$v@xn7eK++eMsG>ResIuniR{+zq`fKzDx*`_3D+=21qy?a(+;C;XGza__a z|Aif~iUZsB^dX#IXo7yU!09W}Upa`?Ymh>vGR%AYT??znFZ_^!YF}|Nu=mC(_|hW6 z0cp0#SG!zI-G4*TH@nc%kVrBzIP<<)xZK#{XHR@;&<$X)WZdG*lo(Eqam^Ay)7DVy zf@AsFl5)U?=r%WDU&y6&gM5g;{UZQZK&ZbENEgu2v@7KRf2act?f?ul8I!me9?Xwd?x47y*^eDGrFkFkLmZ}+KvbrvQY-eNbWTGA^yL@ zZz()Pm(_^Dd$fn?*GQP`!_=`~Ca$4T{az5bWms(*hQ(_QV>>s}CoXnQgfIX=uMEhX zAl8$Vhc=GDse~l{(mpp#ZkKQGd)WhBN3xoHV9%=_))aa93f^pPnE#@{i{y5I$tbG; zaNGv(d#iDpJJGCn(FFVEFlYs615(-3U&P~oep<358cvi$6;wN<*2K$sq~B96{EKaM zp(qqwS6~FUvX-|7bNr|Nn4sj2N$SM&_v+l!^tb>CLGEnv;Zx(bK!Lun<&W+j)e|v?q5yg^LauE*ZA{f7X*m7xG zS0KEG^@-tzAD85m!LKj-RUVsTf4A4~kMZR6_hhiQuKG|>UPA+=4;79Cag~Q?A=O1! zkEQC>LQAv(ggpK&gQbz*1-4pP4=XCd$dg2^h7Bq(YlYhFz;qutQ**MOy`PP zYK!B+ux!m3!RQf`4XJ<3&mx}XQFOxYiZ-H^>7Ba+%%J9uKC3vPS6vSQ1P5HpxXAo| zpkU(mokJp!$h2M6>dA$;VGNuv(1!qY#gotVmCsYaT7x%3I@=OH-RoKK7vga`K6^IW zDSLuY*3EUI8lBObJ7u(+oNjKg|Da-Ge-+4$gZ;dj+8n?KAK6sd`gn}terGk$UyHRn zPV)3)@h)T@(TsIgN3%xaySw54B_!%Ho+hizKxjn{XE+j=iB<0A$N*88c?5|p`T~uR zM7XOTvl{quWzWZIda-rt^`vRS8h)E7jnmPDz**yY|H7NwhPuE~&640;^URG}fs zb3vmVLPjF~4NYl+5**9ND?>sX`*zDfsH^wR59iW*O$nA&1WnQUBCF&l>gQEj05#2m zxUNa94@kPaHF%?XvWthHZ=P!|4(Pi~zPhqQfOgPbicUK7h4p9{U@MFX6WpRGA$hu- z(rLbY#EbEDcNkvQ?h&QTv=5r!O)Swp^D)d5<_wW>52q2|r)ME3X6%2D3s*^niBu0a zHV#jfMi?~43HO=#vxMz%1JMS>;Q|E&6m+N41D-}c!%mo=u6~a%vPgqaB8I6ENxI|2 zdI4bg#4t6TLHYVG_v7E>c~@;MGHGeI^$5{=LM1Eof5Fn?K}tK1_XGmQZPhg-N|Y~y z^2U7rHgUv2VJVNbb%{d1D+Mo9QUED(cClGOvl|>11H`*B6FCuR3O;R;uQ)1xqVj0~ z+>yKQ@~@pR1PhYyTH19oACLP;Tn{oQ|_?*@Mt61;7L{U~WH-Dy@^YQ-#N(umwxkZ9^ z?X~;Y>m3rc>1Ku}M$qHt^~yIhj50A-L>+_S&m&VpC}a3Gk>%gnf`p5pYONqM!%%!! zwGHD=EP#1A*Y%1&RR?)i6TT3L8Xr9IrRAg4f4RIb-2+c<51J#Jj_XIE6djC#$Z8`g zB(i@776a+bgv?|%8^$>?@9@w2i70>SRC|CN&(=>FV(;(sC0D;a%*%D1Q6luLuXJUa zJ-a7gEiADcNRt@r&9ONY3+23`yaRPBNe{3&{Ie-d4!R=b_IkCj?GSpx{DctbfJ@lH zY9$2S6=a|CJPm`q$I-<}_+piONkCA~q}(sGo8rX_L6^V_P(tBKG>eVOW#nX3IG<#g*VOngg0Rf6o3>Y9|vTg2f~yzg|VZ|gzRr_1-{YG(hQ{Kj4!^T zjYU2jx><{>=mG)HIRoE9iwuAW%!lk^Mg(>5jFQa(S@^bY_ zVzPRelqFJO*V*LkXMPGun8rW@SZvl{1g_y=gkW`zI-jufqXIAHSCc}e zKikCcu9lvR+_O(*>j$dVLj!vhM;&vV_apbaQNQzx^q^XI<~?0f_c6IbC1b=DVyE`8 z#|0{HLOUrHwutB)G^A=CUc{dIgDeBVx0V+UkpVc6P}7(&!_X*LiIq!IoFle=yjD|J zg5B#bJ!Gs^z2e#F9G;g9$>jgy#%xas1jo~$^|G=@Kzs}iKxWSm1=a)Skh*Atbl`mP zYHt!-Sz^Gm2P~M^o_HFX*+#G4JoqBqCdgfzx=(EfQ9fbua_yp7BC2(d51ZCsX$0e5{pi=yiTjgcz1eUB~FjON$S>O~TF5-?$Y zJfT`47IYvsEzb8*4(ct;B)GnQED+gu(ItGmyil_!*!BJYhvF5#V;wMOCa4Y#vyH9y zm3aOho?)o&7Ag%HRixQeSI=jsnw+W%>oIiSEsBu+eWSh>MK!Y@m_ZB}5o<3&%)c!M ztuQo7EQPOAZ)ESo<=QO5hTJnUm(gTnRG-x_UXPWBW<)bn zXDh=7x$GcS2lbA7SfT4(<}+Lk-cz*I5y}TVS`U~EdxJV(It);?a3T+K{~>`E3ey&6A5wvO zlWB>aOImi)qe6{HfHY$nl)U6I+$#^`GjIx07Se=#Cw&$iu^O^$`O8zhuZRs@ULoSY zM;8lBn{46$0o!jOn7kbv*EDqD7?{ZA6A{enR7XrjleZa3p{ovTOy^vd<*Ws7hhCw4 z%25DlN0`a|!RhR6(+!$V*|k$mdqH=leF4c2v!|)zj%;6LIpEKa(;jU5^f(RU(Slpd znaF__HyBFnCyPTbtWXr~IVPzn;Z4$-Moz)#A7K6#R zL?-gb4pnc}C66g|i2j`N_2M4i#oeqX**_)#AO3%)bGWQXejBR`r0~Z&z0h2cStpG7 z*E@$w%Z49*yhpWkh9TZ)9Z( zK0XR_baG{3Z3=kWt$0;bUE7u|Zo%EzxVr==xVyV<+}$;Ja0u@1?oM!r;1Jy1T^{G$ zx^=7Fs;_$Wv07VmNFRNSKId$EFLGi9WqLsqJ0qZ&ovkxHGXoPhKvhXy!O+^;(8R({ zhF-|d+63@vW``pu7j^_1I$PM;iWoWrxdG}x6MzWN7{I~;VCLfDf+GhA+u3_KT9}zT z1E@YRsA*~G{$=?q1YqRxPtRwjlZBZrfa3GT6=-c|Zv(V-{)G5nCn^Jh0B3U`z|_JT z2oRQ6(3F%D2T+O2sRG1-wm?TiYk-1_k+p>}K*qutXzK)|2AJA80<8bB02tfZnpphR zniIn(mY@^B5a47FG`9Fm1G*an?f-Jo0qlW}HWp4!pYH$*CxDrwp{?`h44mx%7PiLL zE+&5w__Uka{Y}W;(e5+C=F|5HreNpf>}2d{Vebt1tg0X)_79%U=7!FH)poM@bOY>6 zKO;@-j9va}>2KdB%%|7c(8AUU;0$zk{;QS|5MW~AWN&Tg@mc#5%-+%BZyGL67Pe;p zVn7FQ1ezH-npgv!oIYVbvHzORzxo9Hm+lSi?X5lj&bIqI>OVPHI6DEYO&Q>rSw3qT zJAc+Tv#^C@{A;U7+M3z{n3?`zH*vB5r_UAW`1gRQ{@OFtpCk-T>};()046|FI7T@; z=g*P=s{ftJ4F7i`{~t*Fe|DNZ6hZb|Oww5!r0sfr?_~#u1 zkOBO4$^5rqLmLZgkN+wB-y_w5|KRvPp-4I#ehxy=*6dRZCI+T|7%iN{EZl)63Kq`B z<^WSe>(43uZCAB50XkY+*aAP*{Cki9dS)i3fAguBTNqo}{xx>?f4G3QCjUL1|<(*YL>_4gfM<=p&CjYtk3q?rC&K=-I&& ze7IQIeg21ve*-c9Yb|T&>}cT*(Ee=uGxM+J|Ks`BO84JjL~V`jO#a#{%Fc$iCZF5u zKMjAmja?iaKUMwv#D6yZ&-LFM9SC#>8pACw*ctPDw@gV-b*{n69vm0Z?(1O&9}KoH zu2(6@^RKe&_Dc!dZB`5{IgcThZ_+VwqO*sA<88h1 zJLIz~dt5239KJgN=Q!=UlKl6*2$>`B>_bie05HQWbv^;&D*nS#ykfs5&t9_09nR@J zI43GA&o}uGX8ybg_Uj1x-#d<>h(h-g-x`1_xwXb8gD3JKb9db6Mgg^w!2P9U5FV05 z=Z)4?VjS7npYc<)Gl`>2G2W4m6VsY7ysPj5{&2s$MYm$XBP6M= zqYn6Ce7GK9!YJtY(X-5REzOBYn_#L}H$%V$(<2&fZZD?fZ1#hW&U3~T)!&_|HY0(( z$P@N>#5!R#Z@MWghC`=Blvd$RUicW@GT}0egO4sRgB6zH2E@EF*ia-lM^l{%>is(m zLE1=8Tu87Z%yt`+`0HTI#tjQ06FP zlInB}Clv{g-|YLS)H7n?$5S|j5VgC3&Lypc7XFqjaZF&A^DWO1EesXkriPiEzSH-c z(!w`7kzZ?K8UqUW1;#X}FZXvFuAh~IufjYez23vmUa|e8@ z7bN*DLV}sC#Z(!xYx;d9e!u;oD%Z8caVJ2{YC*m=Q<$A%*4m#JMB0V7%f)M#J{>X7 zGoF4-TnyO{oA9x@EP+-5*#ehK)(?=GEnA`2)38Q!h#2St1yj_D2s7rebdKWL*^DS4 zzP59ozhKRqoB{=xd^4E(rt0I{5!C{YwWBG4sP|&SyzK?L?AUgyoGj?R5rSw$T_N2z z@Jt!^LC)i#B9m{1>UIB=r|_UN6wYO~Mq*pnYC`EDUptGCDX+Ibc{>VCf%{4eXQ#bk zJ>(rN+@lQ8LBSX=X)N&9q>A<1kdE&r)m_9}xW|<)$-odVz;kufoKn+TQ9yam<#v9D z^xF-?+Rl3*XxibKul7=W1K%ma!Buo*1vyS}N{k;NJaE~x1v~^NxemGp zb|3g}^VAcssM2@H??l}AV6y19#%G@YpptObk*;uvnAE{`MC9jntcj^jfp&mMabdtU zH)k9+Wz{IDgAAhbI6o<3V&~F!&O2(#7x71?Fzoiox$5&%S)PVFYn( zW{I%w7o5fa$|$U^Z}@@i?&D4sY9Hje{dA?uGQ;!5}bgBH0PcuhlnLQm3`Y z#oQYe+Q6tR@z8o;B7MEuwzE%NOwLa{xDff(?)aNQRQ>&^USSoYMS<+?T*$4GrmSTx zR6Fj<8w4GGTeIM#cnq)~HbX3Ndo{W0aEzPH&BQbBtLIOnQhIfPyNaQrksJ95tT z$ppi6#Z<_^lKwm?s9zPCKcIQSv&D#hLAwB3lq*XJxI5B>)fXUag`N=^jx)SVjVXuh4zdmxy-}T&eJruu|t5~zNRVzqAj1&5G^OX2uLeoa5 zoa!B9(vgPdH`qzC@A*+Zf5;`2qGlY#o^Wz7$rJJ*ikhQi)B@X_(8kAqmPq>jty7V~P>oLo(rfCGN?VPJ=f5V= zYTqSHQji7f#BZ*WLcsP4IjAekVX$_>W@yM4|>n~7}7S)wrQrb6| zkP!&cv!~5SB5xGJ9m%S)Fn2;Ad3eX?AUr|i@jru(O`gsQ$)Lb}X+wr%_=85GhwxjB zoLz6>E|_Mi44#S+yQv z9D7zl%UCPP=tkm47ypIqYM0D=N1r) zTehGy0Mz=ZoG5g&#jmt=tZNbb{-TW{eW^0fXpA=vMn#H{OS*AWHolJntVAmI6 zrp(=bg!^;*(ho7G#0a^REk7H-42ZD{75R1;Yx=BT+@y!A`9n;q`@v7M^yAi*nU<{D zv{OaXAjJb7$F}eM{MYfNdx6bSv+cWWZ9{)3{rb4`*CmSbp!LmEIr1;dW-=H$x!|t# z!$sp5FuQ|f3u{>^m7^33+GYZ10#I`iKouO~T0|$KZPUIBSp49tB;56l6X!B4)T6+@ zT51q+$buepjk$!VN&&U_*`{m(=XIFF+<164uS>GwcTCTbacODGwgDs8Ucd6tI7?*x zrrw`i3&IF7P~^FV|M9+-@xvwQa<}Mq+4COCLgvqVhRuv_>KO(O>XYf~Y8B>9DRHG9 zP_!SN&8~C&KARfbi|K%r4FM$DDfc$rKx1{myq{N*m%U`c&K)vmaSwmwR zm4DEGvg)5Q-5qUN4vP)$77|Za_lMmI!M}G6ukHk)I8Vtf(oPo?{j55ET{ zJxHfnrQ&n$!qDskI$4N_08|YYCVdBCLEKh&neWd+PCalNw#9iXT0MJ|%=Xp5^umf% zI!pM9B2B8UTUxfmSC)<_=41yYxmNNj6aG4^_(itIt$NYT;BY&o)Q#CFmW&X)lo>uj z_(9&0R7_d2Pja-@mjMpI^r3>lsi1$Y0(I-Q9}HH!jkM_?c`MBrCcUtHEm9CDGV8qF z)te{IuaH-BIFpIhC^_caTbj*pgjbC@0ZVc(M})f%<@w>daKQFL=I&sMrV(>O)CH4x z8?r&9^DEvCk^phi4267^_qQZ2w}2z@$94N`h}B?Oi#g68zf&erCg{ zkoVHIOD8WNFCZP##qCU~5n$qA#}R4Fb6U#qysq5^kkrE>>X8N+*~UUfby*T%}zwK#Fe4J)^kFQGzNH9W#&K*Wb(}jyr!YzYi!VZmjEk z8OjDGq(kQ!N;&OMz=bHBEj&XDLyebpKs!Gc@t-1c%$#+x+v1m;|7mlK@U4#?iK}-2 ztZFi?>a-VaX_H(m@$10f_T>=+KyNMx-2Tyn;%9h5@`-gZXVL>!iuJb<3T zT;t-gFD1aWR^(%!9f!y(lm_`dWx)K8OuZYbof<16Afo`Y{r^#WCb5F3{-0t7g>$UX{1I)MwuiNF7nWJ8aZX z1WmQeKFvWGMTJDM?V+2(@1Ht@h)6%5TKJM*aS!=42IHog5jQ)s65=5jwN?>+Z1(y= zM*t)gp4$;azoqLTVf%?E&ooqon{<>cyORIAG2Dh*Q==VEA4#?eepKt;6iAf3Bp1{SK&y-K;!$H-k#{4(r9)0acWKxq{LcU5r? z%x!lIA8dm`Q!sJYty71-1&|NdcrfS2r>3_TAG}Wc5J%#FWqqqTa#7gt9b+F3|tY&igA?nYh!c;jc0j=A?kso1Beao6@tvCu~Qva_XdX) zbTe=TI%aC5;1aCpjSW9qdlR1fcW#zYXnbQp!N=J$kym~V)s1QoK%@nwBo-KtfW4ZA1Ei46>23gi{bSXTy|Rp?p3z! z(V!3~BnJu(9~p_@jFe-nEbA%ayTJY4N$?N2MN%-BGiG1fXM{Ned2tvd3W5~*iK&$e zo*91AN~!vWGRSoQ-Iw8Rv=u|z> zDo0R?{97fXNH}|C(|ukcFw9yts`(ibu!N4NU<4~{`i+;OBsz)hYC;w5WX+uG&AV)` z&>Wo3_l&l_vb82YVDLk&Xj@3!U-2dBTH@tsJR^l_=*UOk8S0Oy897PteH!EIpDc~P zIFSsF$Vka4p>%JkGcJwVd~3tP(Ftby<@7ee8R|O$TA$W8`ntGnb6{d2o@(4)5a|x> zF_tZ9=W=-1Ony43C<;<4Jk3XUw-|^cSR3ha3oo~u>nMFD33*l)A(sF3Sa~xPBXqBV zszLdP8DsA*5Sgwp=v}Uq(j=>-4i`&@W@CAdf#U1o=AiOYD#^>!>HNDSruV(HTz0MB z-okM(^#~nC%uWnJgSBO?3P^aHm(obQ;W>h+SpsAwLVT$T&<4J(J0gHSuWvgPEL?fCx>X zL-!ptsUb`V+npx(#wYSc(9&s zXgtYxzhF%R-hD)CtfLYxUd7vH_SzwSL1=-!QwTIr(d(b(0$s!zegfm2x%iq<`@f*k zEy^e%2-e3eTf9Kd2(=bc1JkZU_M?=Q&AUe-g?}Sa^?zjuYBF}JvVJO_=-S0O87 z3($?vmzr-VMCEyBk6gW!`T$o(W#1VV293syHU9$bV$ZhoI~EwLVQu2#D*&crj|l)R z&)e`qC9)FttY7MCYCFU}L{(QdOgph1F}Cee$qb0()tZiO8M6;+q|y~1KGx@|;rL)> zi82a&$l%UP($brOF1&9|C*$g{W4hMz?h!xCCNE4Dnm8yH_Zxx$;Q_T0GxiMlHvcO`mQa8WCWA zw+>GmEd1E;{mq4*HcIL8OF9!F;DCbZQAy+D$Iuz$#Tk)k*g7xj5DzqF?>uc^eE;+e zj(RhDJg5M(ey}ZaVTfp&kwL;jV6v@++=(xdedckQb(WyCAC(wkXWy!jQ$@gFbVmut zStZpiu?z;WBFryW?DJVGZlrh%F%$K=9TVx1E!A;hCa2fkR|O47?X5CFo@UqhJok=~ z<}Z#F8|FbTd#?txzV@V8eYodgX5d{EloSLS843G$KM9li;-wp`#C*S=`W#MNxHcz? z>Cfq0RO~)z-?P>0@v-)3U2jCKBpl=j_t(E$k4)jiCyv65rVt#=*hd9L8#$)TWu~nA zMh32^mAHe~KD~3saO%MDL06;k2<=pb6fmF(GWo!>EW1*@Alrz%cMN5=rR+rd-H6tn z@c4%M3$utSeUnTP_bTiwCI!TCWp{r4uo?rkOo17lAT9?Tb%@eZkeHF``<<-NLBu4+ zvd+bi!(r11UMQtR;c}6!xsZGK>+oVLd0xx=H)ttG=2r{O`xsI)tEe%fE@Y+nwZUfh z#OSkSS4pBC7MH@u2lGntK?x=O*o!~O9c%GW?%;cD!1s%B^OwUFiy%niWu+EP^Rtjt zeu%`1i>~|O$9I10c+^Bztx88)0L4!ClnbPV)OQciD%~A3l;UX=bPFmUo}GIT>7@kR+7OuZ^nS zIaryr2#xjtN8^K++Ap#X0fPncwL-3;QQp?z=9)~RZ>>d*d4fg1lZ%=wW<{-iDoTS# zgTi!LW9xkp5mrpa%HtB7CdLTWDQzT-`6f>MGKuS1CM5%lHmyfaQMe$WRJfJLG1;WG ziCxC=c(1V= zmMHci4r?vAf1*-0k{Z!N*vUkkPj)_lU}~M(S131LQF724CibCrYFdsceyxqX(ILl- z6N_j3?Hv8djjj=@kMlM+<1csna+I^;=7-{JR>G8hfAKWWGePPV+u6C^S}(!+hI zT6>6d<+wv>aR;9B?bwKncKEhakd%!OF^5_iMUJB~S)I8Woa;pNBoyZ5krkwadsvl3 z7nf{@t&a&hZ5Rz%Z%r*rGl~ZY;rvNp{aVNHZ!cDU^1wXzGX@(9fOC^5y}msj9-@f z;|?NjHGrh-Xu8y5(Ws+j3bwpBzb9l~3fbJ4ZHOkZ?d3E|T6J5U_IF2eN)*V~or}|N z*NpgQnrlVjpU^YJsw9rSDZDFsbiYE<8jSmi$$Rb5gAQvhu_m7$zAo6(+SEYoe^V@9SP%@*(Q2yP00i5IUR!XS@4CHaD{HcenEl@HIq@A`H)#u; zES&dnt;>_Nhp>stzfKVk|BR>%<8X1$_|3Ar7!oJ~vU`kch&bLB$U|jC;6vjl66;fK zJ7zpXhsn;V=zK(*2TLKdo*><`X!oeEg|t8`--AzLhCKaN7#y`jYFr*S4l!IS=tf=M zS-sz^@_La%crW%4X^P?2MchsUt`<_DEp7hjJQo^=%y=eye96(HT5Ftczv5BRezYci zm3ob<@K18331eKy-@ad{H#;t#t>r{6fwBD+s7WplF60AGIBo2?v*g$a-K{vj88%3$ zuKU$cN@-+Dqagz$B)x8Vubz%9P1IE05v|?8<@IvQ(2G@AGmzPhN;_5$n_kJaTy%AG zF|m2ZwP(;g&kTOv?*JNH{$z7NHi77M%r|AL*#pM=mV2&U)Xg*!KXeeUl|-S_BjgF0 z^-HyE4JoFHLwlTO*gp0Exowu-aG{KgH0TfO+Sj^RR!Z%$ANrxU^QcnOnmG@wP9VK2 zydMVys5~tY#Lw;o36Mm)$M;q>A_<9%=)>9S8Xrt_$Y>f%vNcimd&BFO&^*+xL61;* zc|DxZw@%tPcF}+VLW=J=S$h|Yd8Jac8w{!*-^T1;YS2d)YHjvhyoZ9pKPsq%=uwZD zeCLv}u8$fq^4%?p(Jf&;E7IrCpfS3R+}?`=ezkxL+CRPCvq+uxsib-3!Mq((L}4fc zaq)$Pg47W@)NdJ}Q5#0n47ORv=9mmal0295&X`FEF$44)NNn?;H)|yYu4V62BXRn^ zazIP+plZ)GFVDVw}g7jpwAeJF8oJnlc3`)k6PWUwF8JSJ*^M+$_7{{Le|Ar!yEm0&W@5HJmI%#zIBONw&o=J zt$=XcoBAkSO|Y9g0GVF0vAjkRl25|fS8`Vd{U=BR1oc8u5RNr^W>vodjn_tMWRBrC z&>kdRj)9V~tBqbF2W=cDN%Q9l;`|%61UC^-;edr26qFqly`|cQ(C-_ui zf>Q{YZNK<(d=yRIhVuQP@({RRyYZ@X;bMw&Q#`K1s{+)vcCo@&x{w?WZ0%R#?(gub zu!^e*Y2!?Z4t3$A4(S>JI7M~Vqa8~=Ph7d91m52W2uUSQV2t*2O^{QAAb?8cZ<$)m6q>E7`lg? z4=dbymLyLQFO2>~)x)NtgQb(tlWZyn3rZ>8$A*NGS=U2%fI;am)}=XG{OB9{_F5;z zIX}b!GSiIUsR!QhP)>Y&h3N(IgE)o}#e6cSyjZS*1t{nzR?4-|r+ho3PaKaEsC^6- z6n}JzRt$ymoL@IrJK>TA_L7<9e2ZuJu`vdVlthY6xhQ;?-UJISSN-+KI}oumcthvB zkJ!i`+g`J#9Soq8)D*cx=m8EVdzbzdi&wDh`y^5}>Evz#h&aLmM5_CWuR0KuEp*}-al>S+}3m!Jh|WQINkO-%rxfa zjFZib>yn?VQ_{kRsiotvm5qSD%<ZnZCLC~O6h1i4CU9h~G(n|gn%*us@rp)baB3l0~ew6O(Hd8h6> z_n@Mk@P42F<3jn>csNa4P7F79^YLv|9un>>+jhqJ%D~&#a!g&1U8bpzbHYgGJJ1GD zAW?@!ONoh^`|^OuVuf5kpJA11iq|!%`=660rBi5$Y&#pH-h@+}%mq#tlM_e zN4?0MqRhk*AN}I15d`~2Y$xV=U%E32U-L7Rp@CBOq(L69gnjhc6jCcX#D4iN<%39$ zlXT6A^Gmk45ID=~Syxh%xt;OCi(RJ(_tf;YXL<|7MW}bezv$Jrzk*1z)Ul|15xcG( zTFe{-Wn&|7D8+a&<%R$u5H5r$A95A7viLKCbk(_wsQc2J>rhOE7;{^JAQM5HdQmAk zmKRvsIhUIP0Xu4YpqWCL$h$~>Zj)CgArlzocZVRF%|QSi82b=mlo;a@SzVO&CiKOT zL;+B%&D?YHBksG-CC*Pu4mxy$pTS2iX0S%&oV8YJR3#pg69}?IlSCl-5ISh|5)HK8 zu=DaF{=w~81YOArhpQ0GVLv0%T?Y<;S==?a`-h@gVm}C_*ao^L!#j?sezQl+N-~j+ zYW^vjMtR7#i(MZNoGa6z)U*IGrBTQ@6B4E*)Za;awU9MgJ7v+YJwwCFJ|*0ZZ$jEp zg(lE`B}^NEZV~&T45x|>bZQKf+GVv9IGK)oWU^CM19lq=UWd)+SpCryB_%-eo!2Lg z9!$6Gtnb^PJG5D4(~SI4HQ%%nP&AA=B(Az4X2#?AE$Ve>-#Zaln+jnIzGFUeZv*#g zPk^=FtkQXU)!-1Ly_KiDwi?Te5@_~W2bqY3Y91FkXp;JJHF3UNS#~Fw3$VlBU`8{eVdSdgRisyaZUEouA zF{b9jwUCWz9JfNlr&U2Hfi(Qx7^$FnirAyeGy{;2nm3_!hpKo&HPIek5gYm^zpZTz zz#a18W2HeIeB>>g#JjHeSOKrf4XjRG7fh&u zgc4DLr)Y#Rm!*0P7#fCnf<-cq0Yjc++BWvBv~2qLkb)N-iA76z@XMI1pelS|`gba@ z0<`oA=xJ9b8xiyQr2=I^_=l9CZ(!G>6AAnm_}3v7;mAmLn42Rknh)zdw{?vl{lh*g z5`k{?Xcy>B>v;q@*8qWxKEWq%1+>Y+PC>;}!Kov5KI&wt>BMj63D7Fp(OmMx?2vv3 zRb;$K$e`=9;;XqcD=NX8d(24r}{=8@=@!(LXL4rDv`wx)5KmeW>}H z1)*fIbuTB$9}z-lj;pA)9K^VUuRNkhaUwkAB;V3kA&XQr%_MKH7~fnxD|=N7ge}g% zCW$vqG~bT@o@iB@O2Wn+R8I6`zF7h)=Qq*_Ey*o3Ony76t`?@b-b{%TxwST+gywgFMM+&2LisKYs6k>>j?xtFLh7PHV zsh-IY$pR2jqar*l79|TiI7cp0G2H830#g$<@DVm`9ll5ZK&nMAywInH#1mdAqFh4? z?DcbqDtWeDDAAx@F^jtl_Io+%Vo?m>~yca(ch} z{PK5?o91G`PACZ{(v--pm!yc=bi1@26iFLLad|RBhZ1~+LTZ~OJ?JRJQlQEO*o%&_ z&Mj;)YlH0-H#Y{or)>CRy0h|m$dqgs*riK zQyHh-Q6+uv3$!bdD%FNOND`R9kwtW6_&q_zI=ApcZsulkHf&~TrZ%QCCHgwoBJ@&N z-_<4d_gT*@WbhRo_oo--Z?{=V7wxB~deM&-YgZyi^eBItts#EdWUh$*iFo2p5pv}c z=|oa1rY{(}Wo53cL?_u`Z2J8++%au7cJeLUol6oZV_-2IOg8al>vrkYe`ix?$14D zd}Lervb-s=?Dx}I&w-SYC+QfnxUO7U(E&?ymu z$iSbfOl^ehPGE!Qq#H6|!p~(j!yT zk*|{NByPOmALx*+aw2-RXiI}?3wS?ZZ6YF%8`CYK{XYT&5Ww|Lxxy`Vbr80t>cfs_ zg}{O*eJeqK%4yTsMtAQfkq#!Tymo#}ymTbZEakEC#)cUL(zP06qaod`W0B(7A!i!zVXYdbLemw|LWp*;fJRC@=Ass5 zHnlj#B&NF_#vYJ&*B1Sy*r)(g!71Qor(A!9pPT)*LW|+!j*4}Dz=&TN?L$TSl!oIH zH}Z1QDTcu|tgbDEOwOx+;hp?WpxMD0gq?!yhO`^z?qIWcZb3bFBn~PWEiZUj5**7{ zLFP%w-`QV5-h_gAXv)Z3u=n_kDGlGB_zz~#1eonkESihTptkHoWV{GYmtDPleHem0 zFD;0^1uvPRN@km5!A0_3Bcf8+FKQe9KXbt5uTEV)AW-d0YH?aG|{$WKwPFwS_0f;N`5R zp9twm`AepjF5u1^iXrgMSSLb@!hLJ*ZM_)`s*c{W{GrWeYvYKC+#@&$_YNNZaCfsr zLA1GeqFB|=qAZQHi(5jA;-<3D))#%#fD+Ite1HZA>LFwiy}?*C zR+jMJ#j3Vcmq1CE3K%IJVu9UGd5r+)T)2)ymfdJuMp-VBv?mD@<=>hZ4dLQlE=${1 zKk9MEIe__AhW8jb%u)sLf0-7Ae?`QNiU~TMDiF#jG4evUHk{g}K6^Pv*Cmnxc(V)p z84h9WUfr61KMwOf%F}=md;8%~LUq4S-bdpB;>*To2KT^m9&&o+2w{KI=;#%(laj4a zxByce72|-1gEmx%&9BQC-tlvLhI5;!%A&A{5A|e5=C|_YoA$qUCGVAZW(*y7YB699 z+4(L4OS#UQf`{>yh1e6@1)<@{+ZyO5#|BGps;7lSxblWn;&2&7u646hPSay}ECCUT9xo)OUqO&hKa_dnR+y{I zJgvH+W4)K}WYp)>9u1mRb+Zo0nd$dUFC9Fcq^+>naI}i!*fT!9XLcYe!^W2K*RvS& zv801^a`K!YRl(9M>7Hx{ov&Rmex9@TA|@CU&WWY6bhrGg0N|fG;PDF2XyV4(53TuQ zNk~D|K77LzBy#Gx-M2(}+7Wkv_HT#BC;$D4TVW{>4B~x+Y~a$&$mvpt3V*8Ct>U3L zGK=a&Yj!IK;#2!PP_aZ8Md?LY6Qm1|{KEJ$(0i{C@gzuMAGh?H*sGL6vM zhYaSePWZshjayzdu#&(FBJkbKd+pw)ryf0yx_1p~T1a8Q7(r@1HY-2U{7(2Fniz3Hq{3vRY=rLWEh#Dsid=Ot! z++#FS3_UR5Nc*~+5m|gcK9VL1_PsurG*ZFQ z%>(StJu*euFREh&tu3F2j0lr9I@>7szw8|3JG+>vyxnT)-)C3lryyf+YWv5g=4<6b z{d@_y?x0~#GBV<|SYgjuck{J)=>7@A?!bG08$b_}aO?j?gefK6 zaMQAUi>*#Qf;g-Rz6{A%xPa+uy541%zysHZI#5z9hX_yQ&*5qt2X$Cg*^I!U?l;rH zzZP;wp64E{xTpYq3QibPEhKl<8v7OzC#svN65H0x2$UYNvM7RSr1`qX8jkf^u4iW?`k;T9>6aWIVytu)1d$1+@hiz6 zHxKD*9hJA+5jQEuSe$UheB+Nl6gn-Waj4fKWSK4>b%_mQA5F>!9KSd`RXuXnOkiCm zMX3_~fF~W4S`~FzCCg5z$Fd*o+yzQDe63^*atgU@)J@#fMR=97uJP#nfWWVc4~If+;)p^*0pf0D^&GUx|2&R&i8sdO&h|*{kSV`$e8zG zPc?eVb@Ie0qBTH0dp}#D14U^mko_yVp1S47i~jX?+MQg63#aQIcYDg?n%UD0s7xO` zrpJL5&FkjYG}7%oGujw?0YCnT%L_PF-lFef?ap4~#$k{QGAY}^zH~y(WyVP0ZiYt4 zdqo*Vo}jd4MPmcr=&uR?@&1v)x3k$IUpMkBVV;z0&>xn6|6FFRv*f z#ulaL_%YR}Q86m_B0;gJ0!DTCfl;JaZdf}3RvC^{ckeU9ESI}2PNGI=U;9Bl9dFJ< z^WoKYOc4aB5jC*L%{VyFjK42_Y$%jZRp5ID_eOgUbbak6{`}-0z|dzv6Se(l-eT&t z+H1{l)|PEdFbXL#LAd3RRLGNy$o8sdVd1?57l}&0mb1KjRRh`x>H8=*cd1J>Q~QSLfY-Sn zU4!*u)iMydtqMn+cSE~<4H1_x@1WL$s`W>~uCzgDw@Qt3Hke6)5G3-&vIJkS&P)r= z8Bb`;hTg>8u8V46_%^NtbR-4U#$FICN%>yV5%QN0kEp_LUR za$|#Io^hVp5l{tX`3SbU8YX($rsN#OrUn+kZ@Svv*jNZo0GQlK8`}_=oB&+_)*J=_ z4C@~>2`H1Doo#OnK&Z{_2JWQHOb&3Y4?~58wej2hg$%^t{0l$3n-hCd$_DVz2TvzJ zt<7zfAG4?*{(BlDB|y+W4gOktQ8KR%8wpEtd(u#@?I)~XzboRp4`Q8j?I))G=kgPp%gY>e^7r985}{Nr1HdfaaEa2G*d?&R@`v=%0BvUuHS}zeS$F z+}zZ!e%Gzv>Px>T1~*3#%}fPhe~f;z7RS!*Y?Ym`IYRx!Lpu%z;J;tS+C}N&O#wWlcVQITL=tNq+DV-~2>&{ufGB zkNJrc{`!68`BgVpG^3{01h(4iV*~s-j0Kbc{^>Bb{;4wuwsN9={iXZq6RQOLm3`<7 zNw8;n+k^tdUhH#ZSYZCyG{2#+ya8iLWp`s@0#3)!_`Y83yP{$n5df!l!rs&8{auy< zz(poL^t-3b%D~p#_*!&d@$2$u8~IK7)Q|WX&K49_6Ht=OJo)Wa{zWDKRrew{aqH?^ z`cbE3Y90CYx`&U<&#%GmPl}C*ffX2?`up%Y#>foF;aBhe%Z~XAI`ouhg$Ya!?!@lD zvfGH6@uT|n`|*7$b=ub-zJ{@m^~+2vB?rbf;s<`^hyCM#&B@L2wfwAa_G35y+wikm z4jf=BK-``ps!e=D5OvgyQg(5x8FVw|CrdGu!0jR`u`G zbCOOT?G1F9EBkah$6JpO|FJJjOM}GlBWCN154?!>D{5 z$~Uoa5U?(LJnv^aOUC@aL^QBnA0)YmgPg5r+?&g2K09!sj{&rylF@|OL>m0(mW`P73)^I$oH_QixYXTa`b%|wia8xUE0{_t}Hi0T>!QZ?q*O9*1NCc4a{0*O2av$$KZiEXPF9~OeN=8l(2o08Xt zF-M}V3G7wGGUgE%V4@>@VWE%C*TA=&%M4tN`J?0B7WSZ4*-#9J*REkRQ*M$ z2Tp^wQ*D$&5PlJbDCtguU(s7?RMH&Z>Jt8VJzl$z?I@ zphm9qI*>rlEIUcuOum6BZ-9A-na7s@s4%}qK)uhANDp#jun#9zbmHk~+ zO>DfjZ4aWf$qI!he25B> z)b4xXVsaI@kc?b&|0X0?y?~st^vpTIUjb|53#I!0clXtkn|_!(5xU9 z!>#?&W=Ex(nQpgr1t%1&1i4$b;P#aWRWSg<%uQu1L4cNUi^0NUXP<@G^b!Vi%kzoFgiPzp{NGR`ISC1(s{16$Hq_2}6 z0CKL2SQ(6z?r8p3qV2<-sS`YjYM2R9_D0p|x#@N^>SzeqFKK zxUjEz(9>Glv@aZ=M2c|%pMBo7fbguYy68^?4Nxe38BgKBN&?5!|(aY)iAmGolRn?uY>%Jm*tYRX<6{fxuei4*Un+)l;ho&i z)yCjkEqK@?uBxZ2c3<9vkIw4tfmf;R=J9s~jHzh?>8Fj4m3a&{^BTAt@l{0kBk=%5 zwY(qtnSj7tzE@IOru_-Qlmqn72I zIW6>Jq-1xa`=&LEcP;x=-z$n z)r*xXKZ(RzJdsa#JKl-{pwDw~Ta`jyUSQxB3Jo)!9ytU`%(>&}=k5J982EyE*Oo|o z0~z1|fCCxD{j+K=q05*EIX(EYzdoNGpVt5bN%=M>3e~bD9g59S;Y4aM?pgZrfr8H=D?vNoMe>n}v z36@7<7#MXqNfjbnM9RWL{+huQy{315DhSh!@H0rIi7sR=-`ID3A0DN9QllWx*NhT7 zB|jh?f39w)!XO-g)W1~u+!d!du?V@}HB0V&e14$+awEUzGt5<}a6JGSy;_IldPye~ zx8ZFA_l61$rdq`wfZ3hGgg2(m&5o9J{7NcPLRPwNvo{zm{2u7?N8?P zIZ^;Ab_bXH7mS?U9$m+SsK7t_&(0nwdA&{_->4qajB8D2Y7%$eHTbu7|5W@zya*TU z-~q;3ajrIM70-v9bM28RRoQt)sG{Dh9UFG*!vre3eO8n#52@U6B#pdIXnpRTiLC=$ z46lpWEifa_-=G{Oin3ZR#WU16+24{J&0l|W)k2D^iaKs~3irxl7bB(gaBr$dsd-RH z!=pARY}K3v^7D#J!Nnx8PhfB=1qaA(u_a#w!cvf*DKGC0iqrff)MMIn z!|?TMg*lyvC{Nj;jDdyob>iMHz~!<}kzI4W5-{JGgs8?q(HpgrG#aPMODT4^2lQL5rvUPxqmhlJz9701K;} zCo~zQ_pb6i{%zg(QjtXvfUU?$1;7jsk(D zj{ceW@DL~)8B@gTQSm={MWG|NyjljlkFpa|rVy3dJG8XwX~rS>>_m%sOyLKiR$A)+ z>`VJt2OnHBe@l+KP2s?|j_JFkMxdS<{@D$}+#H+IEs6CCGuFzXrD1*A2>TuNDhht$ zts_jxEC@aMs2#4^X22q;jZ1*tS+fqjg~R$S&&8xhFV|;n2Qa9gK{~)r zzps?^fKHvm#J>Mj>onaAgjVr_v@i$xf)j|G2ooKD(1#ORzbSe$eeF=OH(FHonnePb zmucX~i%^iI*0(U9D_N0rmL|5dP(`zj;ip2VNr64ih_VG}YR&fLTWxM5?nbwik;O$( zS#2VoJZt9Kwv>O6rDrkH%gYLNMlOEvbxthr9cYkF90d1KpQZ9@C5rb%7o{ovV0cNL z-oaA{Yy}^I5Vp|EaMjN53pfVrTVv*3mR-c(cmWFCK@Z#)n>dV}9-uzmKwKz0b~P)< zY^wxYl;f2nkg|(O4nZxSZSC2{U%&r0}tK_Asig1RP&A}OH7STLErLADz-8y zc2Lkjz0=rKiZTSPDzPejzwoTVqhRua7e+J)`BAlb5#VTvG?nOhe%=VM@BXJ6FMQ1c z#P{zpKXEQ$BkUTiV2HrG6{(`74=K@!d$CSW1Wd2DCantZf*w2xH&7rCT`w)gHb=c? zJBF`+ne6%C?JT1DXZ=v}or$PQja_F`V$nQTY`JP|vJb6n8VDdonSQaz@W-q0&8lEa z`%T6wX%kJyecPWFQis3vYQaayMk5Gtz%EVX&Pe5r3E&?Q|1_zIiu^ax+f2=h+~e%v z%^UbU6hku!ly4o4B&lvJY+}Zf9v7HY<#_f1OEHA1TrP%jk^%H+^?OEuDrpMmgIxAkgUL#ZNjP|2Xr)n?3E+;Ept~9l{!Mg>fHKevzslh;{#7{%D60{5%GGGgjrCISl<+((x<)Q!n3n_<5UoivF zs4zffWXP!JZUiH~S;osYNK_rBF_&dy;xHp=KSMVe05Ng>@FFm863?gvamz#ooV|1V zG(*QKf35!F+pg+7Jo*>DxV*iCP0)3Itpl_vBJE!>Lus?z{2Ho0{|E}!cVNhdyT^w* zin*=4UF1_hVepZ&L(uDqu}UGNY}cSDYAH9y>8$)%p(nKv);=I%5S?rX;1AL$4LEe( z<|}0!;))ax2o1eS#4Vy-Wv2nOOd5XZ*Jv4jM>tYtz5&c*9<_UKQ{g)>Oxw-3)Rsg2 zXQHS>Vz2YhohY9}87F)EjxjcWcm!jP345rJwroE0zF6CumuquyECDh(gaVf&d-6OAB#+>!!}iTM+aqN!~Xr4a>Z9~erZ}`vhWFO|JEfkgO)i&*IuX##Xq$I{D>Nl)%I{)c zvT;6|maJD0{E)=PVo(ZLV+HMKvK~t4gYO?4x)`RCT#tCm!Nj5f*J&CxuK56>&g``a z5dKkn{!UiGJ9oGU{k{bRE!r}Mh?ouXF7-l=X-Nwsy9c+8_1lkmy%5(CV{YF0>kP|m z5)>SM?N?aPoy}f@d@Y%+bl{UIe&L-UZj#K02Q6%rziwoUfN$zZaP~Ft;s^ zKxPbLluad{w3w*qi=m?v102ZRgRr{zDJB%UR7Z9Nxlb))9cYlVTFR=m;| z50x;>nbJ^mp*lfbx}WG^7Jh{lZ=Nzr1)cz#UToi0T@UW*!sQ*=e2<8m0aizC4_$LQ#*YMQ?)lh#V+evfZYm*WPHt}ek76U=mWl8Fv2O&b%#PC`S(--j* zTn1A=YvA1$+xyPXk%5QMGhg8U`F!;r&80;Wi@RQeh`;paBOsN*snPS=y*0^gMOq{m zC-WOtkg5hMz@Fvv!qZ(x%fu2u?lK@HbaFNpZQ_uh9rbfhhN|t5xz$+8K};LzB2dc^ z#95!Ghba9Cn+8QM^Sw5#4P>wn8 zN=ha^(c=Z<3bhCGB_fBK11YcfBIlb-PY-1pJ1!V{55jwBYRmmh@zm^M*IHzkf3)rm z8($6R_6(pAXvv((A@~Zj34Jfc2&yY0QcyM*Z2LR*UCtW5tSCHSKl!JzsyqLTLiE1T zZ|vU9Zk8A@(E44$G)}ZQv|;T<>7vf1NTIZ?SQX)L;a_Vu8pQ)RR`E-FVw>@k%W%FA zbz`B&XT}Ts0x0M5lPs&GKl%pt3S1SY-q&OJrm`?!XTJ9R7CysaM>5iM?~@!*@950wKMvO+?=Qy=pK>Lgyi#erVLNKl>yDb93EZ^K-%GPT=^Z2CCJ;XwXH$#Qn-7 z2$QK(EU#1wcG?D&7X_;7!=sgOi6(4X6Xg6^n;;zqfbTRc5C&33I{fYiZf!WCQsn#| zgnbxyi$~V$cqj+rU3>TX3k-Pw4T2m6DA{);x5vUWTYE#p0#d%zq$$--*Y?H`t#THm z7l2M=mhKF(j=}awZYAli;4F~#wCxfM25QzcI;(Ao6X^xTeZ~Sn;l-6cKce^&Z4W`{ zrseS__vFf0%{4v~`{VECQmc&($!vz>%}h*A9dJ_vMb6MrJl=RSg9Ap}QkU)Np5ZCw zv;!Rf+ITbu{`r{(*b27|VdiCdA_41eE=8qFV2X>ICCWrqmZ3dojt`FX)LRE?B_6o0 z{Ptc%FOMK1`WDAO&adOsVqXvcMby`XJx&ldQPdcKF9Xb;=3m3vVUx1ntb5H%!~I3B zr2Yh_!O$kBN~x{pHj?IHh|8|UW2Nvd9Y*C_%(GzpT>@%F3QpVenp_vu*VH;CW!Jq+ zeGk18dz}W{0Boo-_UY1qc!}iWV={C42im+C{P}{1zKbcnBW3Y?Si-wA1FGLYY|k(( zbZ%vC9H1AP9--qB&NFJs>VW`wJ%wkzlV1o}Q(nnC3#~+bG7O#HN<=M5a-z3ssEwm* zmXZb$RzfSt+RMLzke6gft*Xx^J=B8%0s`adnI`G7@z#biXk}iKWMV$RVBJAdHdUve zyNhsl@{V%#XkY`28`{lSseYY8w}|;&hDTY=W>TAiiK;IdKec#fw<6XJ|B$vtn_)m& zZz;IG=pWVkRFSzWWnx{Cpo0o~U?$V-uULw5;gtbiRC2?Q!X4FU7Xz~<3P;)duvs1^ zoc3mhAAH<-HCL7eBmTZ+^b4lQ$gK%oJFWLJrb~Wm{BLHwK0`m@s%qa?&pa7ZuIUeCI+3q&MgIS3kdO?9!ba;Pd856TJ7qx*nEmeL*1Op|u z0EPMCI)8L_B^lvqr`)`nSVvg?J?0uz%9cc${H!@sXBQyIgV&@Zmn_^N^k>e3h2u(e zF<<<9+3<1k2)!MX((sVZ)Bm6dJjr+13KVgder${|01qoLfo_t0l8?egR_3rF^z5s< z{+%L{rKKoHGZEBqIeatJIfZ+|JnTqRz?ue_CB4X~OPy$ANg{JMDjSb~M-Jr^F^9LY zb~76i?=O^95-TxTg>QV{Li`Zw!M=yV*=?%#W32Y zqXKx#J5}%Dw~$a6*ueDwAG2W`r?-h}el=%yYmx!cOfD;=$bpRJ*enRmV0?Z>NK%gU z%t8U4bOC?O@Qk-yVy6Yq=kpq~Xlf>CP6ny6|jr*|zj=rPM%?Fg6bw4%fz&DuNon)IklrdAVY59SIOteCb0 zET-haj63Z|j<;U~r_G8(*u#o%+sp5BN;VgYu!SYAm8(#%foxvuN);qMs5-a@M1As! z;3CBLZkE$!JIIrILwXLgW*@fZH`w8llq-@gFIJGA6DfW_t@>$6JIinGzS-q3l5r$M zI;ipq9z#D~!||oj?RFKyj^~XN$>_KJ2YN>{9$8u9i@-;FiU6#!ahkh^Ug5w!H~-6^ zwTwGFZHz_OWg!pNTE!;qtnI{XgyEy8@akbM*0cv5+b9^1oGrch7K;Xt!##K-d$HFP zPx`YsNyfo@l3Qdz$DpHb?R_2>tj~8b&q1@~tOj6pO^=(^f5P6XI{Lf;aw*e~U;9Lztv;dT z-SO3axFprYAB#EX{t=jP_Y9Bk_WB*0J~aro+Hp-)YCjXteBZn^_aW?vWcm*a6BdMY zh4>pJRW#v}WzHBX!f4=?8CsUa7kbn;!E9W;r#)>$yJCYqlsDf>$r;3yY7U~)?~b@_ zV8RJY!T#*XC#Z~i^#bL?po0KpvSdo;4@!#qI_|7xPxFDE_39~ddX}svfX#I*wu+)- zYnacmD@Eea$MXSRYkO=sj<0QDkGURrZ67e=csxf>3 zM+Rl-oeQh;nWc90SqYv^XHBciLD_#Dk__5u*P!J1H+J1A2>! z)5;n(N)q`jxpr_A5u;b_**OkdTSi4t_PvRt{h5{}SMu)LCopWoUAXmZ5f6*j27uZD zF!{~$>qlG*m;RJAw{vbrv{|&LReZ2U@rIItI&L${pXDUF^`)HoisB)<<)ldaFfHq8 z`K%7x>>hj&r*;KNP^2p-MJ7(ey`6D>A8}g(hzUaFPI3l4ZSpqn2%N^jDdX4}cpMm! zDCvDaN5|Ko?AxUGiSR?<>*K%`@X4!vhS*EU&zRz)6HXlj@lX^@GI`g?miFG4=5^;4 z=tKN6s%T7rNfULBV%2aErVbG+a{oOXW=^sNp#93yUDWXEyt!<0B~ncvYw+Uq2lz^T z2(KFc;YD!ZPFHHNNk<#%-xbQacLZKR#iV|4+JVwm*_DEJS;A7GxILe>Qfg`4$Isi- zeLsc{WhkMC%)!<%UcVKD&+fA7epr6~Dq6`VVxG_Q9`OleI}aT-g947O?7?0sYhE{2#?!1T?gHrN7oi9M6Dcs7QNxZ1w{Wa}Z>R-BufCkDBSjYL+Ggz!cA zTJ0Sf^sUD#XZ{B9r8iDCgXNxV)ll_c;36NmdM*Pv`!~MK%W)A$e?h$ll*(IDh(`^F zR2;H64pc-vxG-ZAsHvGqBm|C+wB;M*O0|`pjfA zx0jP=W&P6;Q?Ec{U>@O&o<{Nkt)up|oUJ3$Gu{Zf4};iJJTj5uzK~{a%oKHMniaOB z_fU;PZ>Dx$pF-dHGV#uHaf5*3v-!enL5+B^1|*IpTBK(~^F6Q6o%meHu{){o2|5XF_{>1r#IND)?J$-o~>GHU7c=vq3;E)V!ePi{K!@(s;Tr+a;n?;ys3d< zJUNHWie;MK!_kr+#3WlKXZ*p8VV07>t|A3@?PG9G3U1@X5Bjcck^x zqo6LCKgZ&HI;y2pRi3~3D~Wo-F)vwBLQ|jJdYPj6_crUQK8idzjYt6i$k4J&{oty~ z%8j$ukpJfC`fp-v{*BERe3hz@z+nVQ**;S5V9v?=vY`)D^(AB?bdc+xM3{9$v_}tE zKNGcX?wIwJw~Odl)}@k`#Bygqmx44K*TS^tLen0%^>Ta1+WJgyLXNDlpSCm~IlfM< zpfO|tm_P1wyJs<@Vez77V9QLPWzDUK%X>?PeW%6wry9SapjyHP@F;l-?h7D+{$ZTGJZ0?igwbyr8_kbf8al5?NHT`2x-k2RV71;W?lNlj5on)V2dEUWp3Ls#Hk|fbp>N634B0OO zXC2>`$2)Kk>l8q-Tt{Rh_dtLS06j(oInI4NlrYO)5-WvYYJALzFP9O#?t(BdrZfTZ zUX~*m5-Men4@!9-M{K^Ns~kn!G(k~XX7=0DP?RK!5UK3N+jLGkpUnFuQFa!Erl_Os z)S8O%Z^_Xvq&j};b)foV*0Xv(tF1w|C6gM6u4MWbDiZMjuFeF&&~O`ccGsoAlza3YM3P{Ur*BYFB~3GQR^&yJOpp3 zM-L;THZN{9=us8yH%ri%HPkSXf6R#6<~I79+9XpEAX`S-SK>-7p6f~>>KfmSM<<-4 zyzV_&wegQ9Uww=Y5T|Q#;WRmP4Ja_*wDd&y_b0j;B`YsP)okNk2PEER9SgAZ9G#Zz z$|DWW53pB%szv&3;<*bPo2e*LC{G%Q+Ns0$3^={RW~x0Bok*O_&Fl?>B7 z2lZ##&PASnubp^ZLF&3oNnBCTaFo5bhS*p?QOUoi@*#Bm5iCy`nlRbbBhF%e>kbH) zO|A&mq^j!#K6~(%R)gV5|2rrdoZr z`;hz1^cuDdCC=gtq~#3HNDz33bBF{E>mvBdHP$-{ADiC;@f1a^7g^PV%Uyalad z;$`XHM35QubqOeH?bnUji*GSDQm{xMG<>gh;M2Z@+Yo^D{cCiF+9GsU{Y*g-XH{CW z-+=WwA?gqlcdul2sDQ+_1xhVe{yaGnOX)2oQ~< z8NJ0J7G;tKZ<4!RVh1Buo?|!-iMsB(ZzWZ&+hXE;+{5r|z}bRGO8_JscbD~zh`ca( zk(SLO=Cx!KD1I$YnuPiD#6KV#ooT>-orK=k)H@u_0{IR4#IVEHGIFPOcyrP2kc~XA zl$uhno=64}L)*8ZIUh-wIOgDiMC|P8p*lBqa$(MdFB4md_DS1!tvve?rkR>j@2kiJpS-@rcuFb9vHLP z?om7;tEmrzs#Ub^7X%^j_iucAB1)xF%IninHDc>7IX=oZ_r1=Y>{Irpok<14V{Qc? zOa?x@n^s-oA73p@8In8jUPYxe2PA*wgb$EhX@^Cl!9Q6Ttv4(~027z;?#2KU;b20C zvl06gI|4Fql%eBn6@3_O1!Y~*awNhYEqE(G|Ls1aLo@p95;|d%f4V{fhr9B9^nzOH zp|~H6Q64oG^-tt4I1K#YuEc2i>&E0ki`q;wWMjZFD@?5?P&&FrL3(Hjo1-WNq?c%0J znTqXf7z@ebdq+d4U3qb8S~X6Im%ha?WcXp$;|t}sx#j|t4zTP-J?<~)hKE{4l|EtS zSqf?A|IMe20ttm|3+p%%kb2$>7mJ1t?$6w3ek)8=2Q^n9)ON3N`{01u=+TyI*xjmn zO=YoH%5t@E@rs%gBgjGJl=jrl4Lm-FV=q9+#l+ko-egU9OKAGA11RlAD4rn7D;l-0 z>>7c_@SExIwyjR^yWbG7Ze=9ONN0<{S?ls@Mb!f5byUl%4b(D@d=_Hd6v&dJayJO5 zg+{;6*EhbWCLIWmmFeJ-_d8sN)zT0aEEKel9z875xiO4Y)T~&H?vIe@CN5LLXMYPm>NAvxL6|likVlOX z9k^I7D6H#4#Jd!!|M((OdWOA2uMjry-KjwVW4e5A$7x(Wtf)OX_@?y zM2^t<_iZI~9Uw2@l32Z8sid4_CAh?Z zDucfwnQKd@G2~z*T=pcIs*@92mOoZ8^2#mQ#nC#5CWOU6rGH*Mszm9++rf$>)~z>2 z=311FWD#LwjAr2T;_$_+hpZT#gmikx06~B+fV_Rpb&aj)i6-pk<<|Y3?fooa>?YH8 zn25cP>FwzwW3H}FY-Vfr?l$RDdEzabgafZ-Nerv0%H=S#1#tOy?XmbK;u0jn<4z;P z@#P5g=N1sf2rPHso08+BXEtx?ZWbq?Z9JGqc#_nx9G<-TK>j9<`R`AL_JP5b4_^6 zqP^+3=N{$Bg8b-1{IwL@x;XQ0*w5efcxnZe41TLG}RH^s*grd=47JS7RUIA+az?TmPEibHfM^c|$iu#?Rd% zx4N6{%=9Q%C)pB!D+^(e^8$m25nn`!4Y!}-n5B5oiM{WFb<*xi#OfY7n^E22-(hW1 zA$Keqc*j-_T3nDz!MjoyfjA^5=;|Hm9miO zAP-0f+rVMz^T<8Wkna)lOGfo7AOJu1b*Sh0S;#p4So%#Up#lbB+R)gGNyBXZ?Z5e> z7bM_Dg8L>={jI+YxSKE8?>kfkM{r@ezz9F;I`atI zED0VSR+7t@N|Eabh`d{qdHRT{@{?C!gh(cAr^C;u%nU( z*h&bf&=sVbWpI0rg1CF%{quBA;_$q*?7~?ptayr*lCUNY%faqQ#4LVj1hL9nO+zZIFv zKrev^ezcI1S#Z4}$T1^+;4{TA8(keOncJNSExPAb2$u&gT$c>F#Z+lUX1#W2Fi)38?t0Iz=(cA#-!!IRLSpZ7+U0am7M+TSW>-QO_cx9fl)TCgC$S?*n)tw zu&PFIcAc5O+-F?zJ21Cs*F?=VE41xSLJK*P)0pYdWwn4X} zO{*%4xshX4T;PRIH?S}K1_m`VqG*ptImY?64xbWFfoG8Fwc_k7?ZX5O-qMS7_F}Yv zsk1?zZAzqtysrY+A;l;!Q$m<=zBf^h!-^NZ%1_I&pu4NncwGkTT3i%u2WlBx-z@@XQ8n9;VsA^okH ziWxsf<}+SRaI@&RC6CgD=W*9|1*^7+H&_nROLpJl>1Qa*LoZ!>^DDyoCs77B3g^3{PpX+gr$k zE!d!%L79K0GXei-2Nf`Q+j*vgaQv!q0=CCrmI_U~r63|LOfwQ&96yf)JW%8$2GGSM zrc(j#$Lq*3HwwQt4N?ZcpbAEJy(lJHh#warr7pW#Y@4QR5L~j5w%AdG*A|Yt7@f&`f$K{nyxD}M7f^QXYRtt^sIVBEhYHh>96e7Jq07|5(-iF=Q_>55k@-gc(hMZt zTIYMv$W>c(E^UJm+_(Z#D|c5x`KzjM3&|W}CIRy%6Se_J{mjhS+u|@q4nE6TdW`Zb z#@v(Q;PD+mlo`$vdO2O}p zqx%tf8Jp)B)-uH0Aw!9xZYa#*jxsfgkYD>-5)T0qJ-G>9qqD_}N2Gjsm`~b-WtTXz ztm7s1tS4gR-9`vVT+G?a^bjVXl{orXy84FlH`wL#okGiE?MiPO6WXRN7SyO@C`*4M zeHp9iZFHzI+F;ct>+fEoEgUO?QbxRFv(9n8?3bqEqc#FN!{V-;t>D-ZGWCK!GE>Dy zSP+4#5^lAm^XXFBI$r_3Ts?hE;?mmmeN&RKx7UyxkDt30Q;6(7rnehx8rg#Pt5P zqE_@=Z+mxci6;e$3+IJms$jFckgDwgbnXr3#rkHb+6Vx*n%eq&xGm=`Kc#~#E2i?y z^h4ZKrC5D2MLgFUR;8k-4aar$ElaF-atxahSBF0mt(71#0*hog+7nXZrXrDfAG)SK zlOrRStSn%XeW{(G)*6dx@LUgb~$QJbUPYlEo!m{kNOEiiCF%+xChPlT?OEK+Qt0};H1pJY)r z@nf$@^K#`0?bt+(j|y=6hyV_DJff-)d3~DWulrI1tC^k}x|GP~p=~*#+8dqq9-BT3 zyaxLDovy#!s}g1w3`owXzl*6!v={qLL54FuBsFbjuY&`hV}jxFljZXtZO*Z_C_533 zL<8)HIk6pKLWu8kB8?}&bicx#QA;aOKaUN%H@ zZ<7n%0Vz$y1;Kn6rZknisSCWxS{l7NOyTTm2&q^?k+X)xV?4^T zI{px%qyKPdclEz$ASB+cnH_ENRU?Q@c8+wst>mwd3m4H{%9n&uyh?x8a$iX5MECLCrIf&_c$p+DKIko4j3ugRFB1Gln-r{?*B#)sw6un|>hxqXE4 zx>DbS(n51Q&J1k0^B1E8P5fL%z*NMI$6XwYw;`kcIlM~j{D@pc!Y`G^jcXjs00l7I z$2$3v@hi0D_IFbSkOj5xVXa+5$*uIeYi~&9Sc%7{PJwGaiYfN4ueqSm@y;8OQ%944 zq^7=N{spNLX~t85`5(s4F-UYET+@Ry)*0KjZQHib*tTukwr$(CZF^?t?%lg}f846w zRH~9xzH~aNN>}%nx1Se(en6MTBd&k&JE@$t=LZWke4K(eOW(QGRBYIuO1K*Go1Szy zQj71F7=WSateo6J-Sl=ukud;>L&^rjNs#h_T+pa}+SfsRAo5^Ew3SfSyYtSI*TFBPoz}S_>Fa^6EpP z`)%FFc zJ$!u+e0EpcLQzSxag-POXKZ>VXGM!P`(V%8DJXpy$l4;aUxdwxhcvrxaeZow!FV)T zs|W)@4*V5A$Gh4fgb~cumdWn9Z4Ml&FD0=|%%Ql^DX~l_A_qr(x&%V3@bn)VE}+|+ z#Q}DDv(O>d>*ccpigPV^p$6u|a1i(zI7h3p3vWVc4{Dh46aQ5)eW1ZOKh`M4doNp{ zJiWJ$?2Nb+@`YM)Ct2)Oh0Y)E`<iRXJa zv&VT5#K7QrBH|m5{pfJYpXSB`#vihs;81+}95XQ@Zm(l3fA(xFCtI2_QRiM6>#zC? z07i&4ew>YcMxdM4&%NSYP&b_eiB_j%{y^vK6^~xQ3pr4EnruoAi)O+AsG7ypc%!v+ z!?QVAWA?eMp1K%{D-=|Mv~Y#I-YoTnT~n{~8|Z~=6W7yEW!$)bzxI)wuNLh>5?IMR zMML{e`>Tgwb9%_OIb?x!%d}L{Y7*L8QKTOQu`u{Lir{&#C{nBZ3lEL%ag&*QMGY0f zF0h6SyoLtim55J5nM-=O*!vqbBymdRyzFgP==`IT7@L_9b~U!g(_uS6CmAd}96?Kr zXH@<57M!!TWj^^*lNI)F!x58vbBv^?uM_=gRVb3LG%wAS7C!L<{)OeoD+kwNfgRQL zmaJZA!wfIGS*qmZ@e?N-G#sB)gYY4pJ*YaimKdh^^H-mW#W$6CT7xj2;XeI*IjrmE6VktnsZgtM#xLwjty7 z@!f1E25Do9+E)SzWe_uS=TGiq=pIK@wrtT43NFMF?4n%=+G`-FLD;XeSSc7U0^=#o z+f~N)4%(m_=NJn1U*g<0RgOre!FKUh?$EfTQAvf$vewU{H^HjZ@rO0c(R1l33M8MX z$)R>&d+rf0XCyp?oV9O&v7{29u@@{_`%gR>xt}kR!srxvllk~V!Si)sPxB5(8>RpA zA`>QK4&q9}2&ql+D3|(VuRW6W z79#tZPh@>xBUB<{>)LwSJ4Mwg==JLCbbS|hhl7GuR*4{u^mY7H*|Qe zu;^S0Ge__Es zHZk9Nf?4?5u~&^8zV@b0=y^fw%fN=z`~qz*31-_DzL9UPm|<(#tRG z7oh46wBNhG=p!-Ya@p7|I18pg0V*$+Se2K?dV`g2JPI`lcj!O~RHmtiS7*ZkhsY;C zm`#CGYbOzG%dAUH+_)0$Y1!|o;)Ofpo|}9>efC zD_vJ4cyd9qO+PuC0W!uCymMHd(Z-+V$+4I_{4r$gaG0p_7BaCDQ&n(~nzkCUnFj9SsVmVSX(%rv8enSvmjX;saW|tm zpZPOMfLY0le)b4;;Z=lHjVjHME0!mkeSv&`n^;FunS<=JP*9EQY?E5})oENwfq2D2A8y4B4@cloi zKyY8TOf@Xjp8GF--pkVZ={h3kEBXwY!--R@j?cG&M~!f1+s71gm1XHBjlFPi1!V7f z1DcH+bwX{ehfNUU1yh_xIs<946W?hOX6Zp^q+>av-2NfKxqM&aJSP$#ok7!$%^c{6=2UT6iLcB15WQ?Fx z>4_Ngi9lh4B~_^z=L;+qP$R0cnBH;W6#LID&{kjvMheLeb}S6B4Xq)GUGOou=%X4M zb2{1}>!<}2cBB+Tq0+(D(l_s%)i1fo2DaCIZ9#}dZ*Km#ee%N!1pAz&<@!~4h!d+h zpgo+tpXMfub+iw!>Rc<=#nVJR`pE$FVPN_0SquA(ygf%NNWy@0wF3(anxzy4Nuk2X zi7SA{Ngovm=eB;*%nQ{L40v_!%qOqjP1wp=i+P=)f76X+BZmw-e>1Z1oE2&<-gA0>;sde zJ8p0Fl4Cn0NQt?Lv%^PXzP6-UkQCq^UJjbz{Y&L$o7t=*zN`~d4@{Hi!wp=$=t6)V z591RLxeNi_3}Y_~MNSm&9ZOcG$4#*PBZh|3%}!);ZMImsvxp|ErBWxUM}`mC__X;f zf41;@HqJ=YhcFWoVj@3FIfQg`eQ$^1Rl*BcZ%^cbZon}(mz5G;q!x7m!_57;n8`sP zd2wGT?)Qn(-l-OyMp&$sMXu8z^^n4breiM1?a+!(_EHV=xsf*)NX)kK*Q?1ExI{6- zP{mQRBo#84H9Ml&ZWnxlIv#?hu44zZi{-uV#g<_OL_i?{|Bek_U5c$pO{E&&B?uc8 zeu0Bq?&gzA_W zQDML~zzOqhNIj^pYAMG7WYA!}X=TUGZ9LF9lty=`lUTNSa(f`^0T&b~E>dZ(LiA^d z3w*4RP8te-ef9Rtepu@cydbolK$N!DcYAyeQROOc~XK!qmAu*E)^YzmgWY z52Dyq+Q~SrKIx?&#wz2sX6Sxn!LF9eZlMXH461(ufbQY7N~d* z&>i&SGw2$Dn8q0>dlN=rXv&o!)A71B`hZ&W<@yw{BHb%xAYC-z4RGT=C7M2B&C397 zUKkhDkgo|B2{!~Xm2L?83JoQ4WykrAUt;^M@a1Yw>G*?GWA?i2J%pr?1jcK51s#Pm zjdGx_gq8qZ>llcTyT5TY>%v=TCkdIY{BSh?`Xi!ADFFuEFB0m@9^NGa7UQ=OrMa5tCHVCOb{+65c6hzfRjoOEQZbq*5`knlTbF@a^B; z==a)SdF4nN5*Jyxi?F0GeVamu{vg}|0{{q*vndR&R*ja&Y| zZfBirXS(7gr4dyn-lnmCjOUQXe+F8JtiF7fRV&j_kuXlx@qA%&1htK3_}Y}}deck1 z)U;&ylm?|Jk%H((o$>aVhsb8e75@#-(>p+sQs1jkVhtBBJI-`W_V)6gMzG90f+^vN z8u4^lxTDq&{F&#m<-K3wq`kh6bcPDAZ%^sPF0s|JA5{Pix$eItgrF<66Jsh3EKKt7 zBhMnF#Ka6BuNi##8)ARbB2`l~bRovl^ZcP6`e7pwxBP6WW-Gaol}Rip9;f||EWM)M zlPI%$9tn`8XA#WEI-TL`*URy2zTO{-ge(%e`TEz4pZJI=8Hmh{)E7A3(`zY#~3*MU|3(x4csk}8IqWeTVR`5`uLB}o=pf+c8Ec%VJp|H ze)ol68z&YJ3)DENc#fFW#;;NoPLnc#?Sy)s-BJ5Z(OqKb3-^jx0U60%Uk;@Z zuxoR{{c}#Pen5Q9@p^7uYM~F&$6nY?V!>F)xQ{{ecA~Vv;u$PbvH|A|n^2v1;ud2S(sV+K= z04aLTA|2>(?J+eCkEFKz3F@=1EOw;1U4~Q=ol&&H1q74J`m$GAM&!A*R!_?JLlh_4 zHW0mQ0hlH$QR&?M^HvTRU}edh@FM;nEqIS~6b#S@L=ySB4vL;UJ~f~{ix2!1)#xN! z?Yhf6C*{4X$f^7M#dAB-&^oGH67GjVnE&74nnxy{?IyG_0dwsqldO0lXxuP>js6;0 z2e3zPtUnlD+JcrlpRs<}35E-W(eH=z8s>EtW4`BsdG}vdSB1gYXP4D<+W5{k<+*H^ zO=|x(E5C$1WsaRfq`dv%_SF6oU?J&~MUT(L>m!m$m5-t^6?!r#L9uF5scT>$*R|h6 zXRXzQM|VkLJ@u~fc?Z*Xo?KtrLNBLL6u|h`EWULFCAN&lZOD{914^R0kE(;>#E0G0 z>nD$$VlL(w#$mHYO_7%CLc45Eal@LyEM?i?^r`Dxv@=Vvy1C6reC^}$1VkUY6)Ojm zE1KKN1QSyOg|c3){=x2gyf)A4pL&@gWV2wFY#Z5ypnGJ9^q}c~Z0ie(EDfYSJ(`Hh zNjU}Nc0Q!{Mi!J>`Lu{m=svfu*|ByR{%BpyIaP3+392J{RCsT!YZ;$UP>-qz^A>g) zOn1YK^P2Pf%MoX&*Q&arSMm>MORpj1Zw09PGkXBg4P`z{jRt{UcDg^pe(#@j390u* zFckv?fWyF(!ZTQ|!s&oH3^Su0k3GnJJbzkq12o-fm!@5%5m?3rlm}%4u1s6>nIpAl zVUd9^X_m~aV?P@v#UWv5IHZb(7Q!QcoI*P+(vt*U-ZTDEN`R(`iM?oArIbl&P{Utd zwUay%%V4%|CI640nRz5!>nsvv@K+r|BR~1`BmHB^R-dJ3_^CIzn zkV`R4(TUF0$ki-CX%uC1ph9z2K}dps<;RDhd@EWrYSK_I)E$>1RejE&`#<4OMZa$F zd9>{m#?oD6esHg(=v2#6W`MF_X5%%Exu_le8Hjptm8A2tOVD$?W zNIQqWGPc2QV|ou;m8%{EJ`VYD+!`blCT(JW>0i$xxCY7ujnRB_*i3^Ei0)Lk9Zn{& ztYaa!a-yj=kwfY+Km!jj{e`Wr@jEIJelhYgr7tVE^wUkGqnCeyz&(S(JaOqjo3;_< z!l@025R^571dn1GOJzP{26(tPT5b#U3OGc0tPGJ|Cc2+_gsU_$@{@3{m|%qntvYT_ zrFdp3``DeNMAZ(M|5aTVB#FlF=hPO^0!e!TQ5CX#j`VS;hX1I3=*xZTewz+kJDEZ% zrSB;6wk*Z(hcCuOzF5Juk7W*plzjJ^^xSvgQ(&qezA$^PeQsFqzR~;(G?;ArL(0b& zI!urcRn(NMvkQCQ-75R69lo{Mi0IS7?o*z&p#`*?`+Z!3`Wd*5OYhcVb{J!xV-iV- zj+qGzbLK6)8db~Z_xev`?r=76PZ-OjNpb7Sft$s96NRLj|JQgFGEa~=zX zuFqCQybZnQ(`9;&c;6~XdvE2tYUBfj*+mWa+*AsEf7>csjp&3wJMgS*J)3$DN>k($ z&*>o|&`}CWpRWK|he~i(K-@CQ#YUO!k=GXJnzx3FI94uX7o-Kb6XYVE`?m-+yk)JA zKakzWbeeoW6S9taR}ndu#akH^zC%v~ajdNumYPh`eS(lw!eA59bY@$yoo)t2$u2!(@uqYYBs>j%@c} z6G)hmmpt5PH>R$SE?Q#`$C2ka2StY}NnfbX@^Uc6H#cvdBsWiaL*J`Z$e;yu$s=e= z6q$3Iv|EQiZz$Hmd9PxggakeK_uIQ$i~O@j+zw4Y-13+Je`eAbjvFeVFJafzQY8UI zsWKjGM_6~sMd&w_n>TiamQkY=dwGqi05aJvk%QMx6I~v!%UBq4eVED>!U~MS4pBD6$PzU+D)E{Mjfdo&5AwC^fCsAWYzZr4 z^GxD1lT@qs3$#vSz%8)c!HV2xe_9_--9=9pml(}G+S1T)Jmt1IHDox}vegl+O{K(1 zxdI4zTpf5S<#6KDkI&D5BGIfnry#rYcMsXD!gdmN%8Macp))ZEpL&R~h%xk7&}7xN zoh5MANmKqO79q?3$RcE*gQS%*wl;AzWx!*nr)U4KqyLT~WM^k$`rjl%JV;s*GfPKf zdpueZOMORUA!9=uBV$M&9!LjAdt-eoNZ0i$Cu21&?PTWaKA=COK^>fbR(7vdkU)_9 zC^oZp`?&icP`KFo{J~rxWNbrr-{W4s+C8$f-#sGw(oHGzzJ z@c>v^eI>=jzyo0MU>t58{na*F0nl>TQ`OYeevID^fNF0)!S1onpzDHxPIGuSd!6aP zJm?mW()N9@OF=+^wJdu9C_}N)@T!WfZ&j3WddX_afn&i0`($RMOFJ}H`S}2h!NH-O zKp6om^<)4#dQbuWLYqUpEu=GkFs2kT0)X2(0|emB==^z@#zh4By_w6`*wn_3@lg_rs(h+NaPiVDA=k3_C8QOpc>#+w#ie9HkdhtbA13`-%R>9vkU+xD(Oj&{yNLwSZ&T*g6ZF%1WP@ii#bm&bI*DkHuhDDJ@Rc4tkbIQv!9m+Q*}E@4*EsxaKJqU6Sh>)x0z>zw=J@#uZEqBNNw|~| zj9+8N)1P1N3S7e2k(JMVXQIjhTD-_Y=^|4w_tZe^*I@tJSKnuDJGidO8Es$QxEhbl zW&`nz6TcMczh{TE2>nR=8Z(9tG=ful>D~mq+$G*a#^dvrTpzE;1{a&{aYGJ`vf_|7 z9#9qoV6=1s0If@cS@O!Auc-B-Y-+ToD8G4pJce$Qw&|i0BORmuOJtN7YlMXy0Ry+6R$W z#YKHUxVKZhfJx&4D;(!YtYXF1Z|Vm8jdM&{WLVSbLK&uCFM4pW<@+O*rbfaY5N3eL z2xX_tKubS3B$i_;h?oCew?n075}^+2n^xg77oHy%8YE_Gz3X^QLcILU&z3a2l=fKp zmlWVYP|ys)u(baoLcDp&?Xy8zZI*PigRe~lrwE4R%bPYeTr znup^*A7Hzumn2fIc3RKN_%1(cP=|k|#Y&SDMeTi|K1#7kbrR(fD3VcjP`Qx#*}PrHgvN%ryNCFp`Pte~UN5F3?bGBn{>Q4d z^(a|Ph8>L7T0_SQh?>baq;J?5&3uDNFe%&EP5azNdcs1Mw7fe@gN_-oL%QUpBh-ZQ z(W-4W$RCZ{4Rv-(d9rM(CLx5I?*-u_Mzq9QsK`s1U0+kPiYME5Dl0RN96TQ*i^6%% zNat;N>x7GEE;kv=N)Y{ZMIc3L`K8|#Z|gE;O90$CUw`H7-M+ptYYLO&v7z4TX9sFq zsDO|iU$KH`!-bxQYDlq|Ibva*m|E0s-MZemI-*0U!;rZ4-kmE7mN|ax9)a+n&~gO> z4EQaJl6GOn(#LhZQ_Y||9`1v(0l~>HR+X`#<6$jVLK0+dDHDfWC1i-Qi03-X)f6Gp zf9!1+JNMc68vLsAI`Ztlvjp?CEl|HI)PF)U=dj1IF&N3s6isZ$Y?XlX(7B8dpHP44Hq+2V}vw}ACMoZ%L9My^#%dm5ms)9Q6y@XqEpSE}`;t+~M z?8lXzObnhCLK5YP*@djTw9S>;$EqNGRT7@8%KUyrfF<#MJ{#Et*0YWbwH@bPSP*Z8 zYjBJLGQ&_lJ+}-Z@+7+bx$hzc)6xno^I8qUO+$SkmngfHvs>UI)-!8Z4)(_ZGEnu@ zk_zSi!%UyK*E@P2tPOnG6Md`|72zU17jkX}bZ*cayHLscRD69{fh9?Jv5VAPm|q&? z46AqHE;fv`NzwSuYjn8A%I!_PdO(nRm)=?_Sd|XA%kgioA*#RQZkhoYVzV z+pnmRFG>gK(Jn1lHM9M5l>(&q#ftnoVV%buT8~m1aBTwPEpJJkKEcpIKBJl`30%@( z#e2Wf{FMR{F}vkyh2_&cXu`@RG8CV&e+#}FBS}cQ{Sg+A=RGIT9IMMJ^c;3B%#^2@p5nGR^wXqelos zMTq^^KyL2gk%fP=TC7OoUQMPS?!5k+Cs-G(|2B!i26+4Bc@Cj;3u>wCMQf72>ciYl zN+vtPR|FV@1?}kZv&tMs$GFBgn&SoB;F}4c=bxV*(O7Zl!+L>Q$yyQRA1;xV($_IK z`#Zip&}UjO;dE0KE1$#UBog`zvO*)6+orUP65<{|+MPZsXOv~+SgpJPVY3$t2jpiH z2zPs7L-$CLj>8s-MePZm>xQ_aOc;^3V802Hso0aMLz5AR1=Dt|?y?Ln!3QmTgVEfC zm_7jQq5E`P8EuL(I?OP2{YFu+kNkR^vx7t=af04|d8+KG%Xw+TPq;8?50v1Y&nf9} zrQFH17Wa*CuiC{`y(M-V*j1&3sQl9-+FXl$`<~$W#cb`FpsZtS;D27fBKYKm25u50 z)t|pqi=H5FsHU6C< z95N)m=dh_ZgUHZecz;9k2xG{SX!-8zT00R&cNu|1t($$7mO`DUEutaw7vX*vi7UFA z1!QkCMD9M^K5fgiPAYLoJQtjJ%P~O{#`DV&1``oo!om*<7M5_;PpxqgSs;T5GtX) zoUhpdT8TJ$=w+6Bb6T{ku1qUli&u&3gn1dyd!H{UX`v>^ju-xvdu(ym4-6;ds`|{H zII~0+E@k`Jh@y|7{wW+DLa(wy!TgEe#IGVTi&##6Xmr)~ColyeWols69le{&^&_Ah zKCH+OpwzTIUObr)U{I>>l%Od<3pd;!@yw9i4!uB3C%B2)&cQI`{l-Ky+EptxB-Bf&CluLF@Y&SOdk)aGOt(r&80RZ zb_C?ni?}uBJ@jq({kNFVi)SlH$!q4*5&Q}dU6Wi5a)(SDRCWO2#iUY|0|UF_(lkct z*ij1k(%*LTaC$vqYiG|hIpOMk-By8Gw~HJm|FIkE@B4VUV4~B}U&s(?aCpj+OiyU!rXHNnqT>gPBxAw?e+fAN_)r)b8ZLRai?}4&=;1GEpqp zj2Ly@oyKa=TtR8VPScWPd(<7w;bE`9^)oO`(WHw;26DcOs5Ksxv=h8 zuz~jiwGyqSKb`93r#d$ZJ!#7<$1_g@!cj7~Y#EI~qX+Io_}U?aXMMDVZ}0`BCwyn$ zo@C~_)@yXgc-d@a{ze6lL5>$AjCiX{A^h*gA;hH3TEi-rPW@sZ<8}YjmiE@Etb|CA^KaP7p zfZbNfNj*KNt>m@lzrf6?_jNj_Kp^3Kfb4Ugv$fXbY)|-54m>lu(=Fs5Qw5W!xT4fd zqKGjs4j~Tw80a}ef5u@Tlt{@{5dG{oB;qR4BwOk^O0XD5-CS~Io~jhGRj^feHBuzy zd0I3z1+?jrHh`)2*bek8&|EKtv%6)8))WlAN^!UHG9V$3Z)b#FfUa`iQ$Xfta;Fab zm*`VnW7fnk!re@o{8UxxgX)mrMH}oG;?O`!4n#F_0dZ)>EE2I8w!cRIyi-=XLJa{~ zKg-J*B@^V0mb)|Hxd8}P@~t-!64y@W|E2PbQUKuw%~h#u?a@~_{8Iswqfy{Gn{o7K zU6|};ZampaJwb)J&-h>XSlYliVZ13!g0ex7gb8E)OQ$g&=&_ zV}NRN*lRxDs^pj z0v-puRkq#qym&}lqpFx>i_up@b$y*Eohz4=+p~M2b=r{uIY&DYarSw(cgabvdhdT*5fR3`(1{I zyUh*GD1r9t91S~|o=y^9DuCMF(gv1-mZkvmkHf_Ahr0;Syt5o($Vx%fziRU{my?C2 zRk`Tye{c-Ym-2O6EidiY)SfMnv1^vuQBOlsyCpHmceN)YwDfLkZajS`N$2)0gJ%*G zmhS?U2Qc3MOjPQOPdi@3R|0Xw3EA!ZEpRl?qb9k6_+?KD?hei(=&^Sz+^Wmxi6mE% zxYu93H*^oK7mSz+Wid?^g_fLo!B+0}-^P>07>e}_3|FT!>(^h}K8%nw9>(VA%0Ba0 z8w*8>h6FGk*W14*k1hg~1d&M%35ZI=uXk9wwKm?&kZUz-_AAnI8_w7N>1;yoju4+B zh8YE$jrUz%u~`&;3?WscC-`S&w`UYd_fFiG6@}uwP`r0hYj592e5QEGq$tmU^Vsxy z>bwA&s7N^qGZApN_q?jMPd3mxYEvqr();3n4DDh$5glt5uWAI;2$PVrofOTo?OMe; zSP_Ztc+_gSh#vf}a1#{-;m+M;lVUeB#oKg5_T{OkU37VfAI$UvOs8<-z2X1jq>co?Aex_ zRH+#S%da5?7>BM+A7cR+=K>qGE*p1xA@rOGO|$hbIC!6Z6E3Z~EwSvR%TH&B2e)UZ z(Xlf%jPYQfcY+KFM7s6Hn6xWaX;pO^4)>L6!#?p#0#ijgho>Sv{UbY<@N%gH&fB+m zK9SwO(PeIf?(Wn@FPfGkre~%)uxOG(7Y=s+_SR%6}vX&c&xoxG2vS1C9YV|JVHERbvW^gtP5v@*- z+?!VF*ola^jeZAKyy$Umypd%!`8@uhe`FffoJJ!*L7I>55G>S_FrSsOD|D^*6aVp% zSFdfukdssYoa?`gCbXcKjBH$+GuUUc5C|lnQYB~dPE4N6-wu3;H>(`zPob1#<(>HC z7pv2-K0`Bu44CYq?39)jN-!R>yFa)jSIl_M5mbOaaq()?zx#BmhyI7slXH~GULkJ# zzN-5s$EPtY2$8+z$8fjhBkt;KnI<~=`wZGpD1&O=Bm&V+rWLNZV=0;NW7fTk`a~eF zs#e)8Y9+9is7tDOEXCdVGbG4?%x<_#!_XsX43N`E&D!yi;qSvDxVB|olobx_F|aW- zV-Mi$MD;dg!itD5PXybk_ckCc&8>i?HYd=d>J3$?WN?`Yvf z%)iveAO5}T&>>V3T*FEsvP2Y7NOdxZI-HHU=wSeJZiA303!ekMP)Im70vKE$3TL^X zws#YUgcZ1sx*h{m*Aj4ebyq{KaPaMqp#;mmKLkL79=P^U z@E?k`Fwh@6{I7(+gV5~1fnB{7VA^xI%TW~IX~0pqe4df2H>$;3trQ)Z_}NfzCJeL= z8_rzwpbmq~cs48Q^Q2lVd;t=#hr)@TC(aKC<{ezvy87-p?{>=Y>(+e6ZkLZMCR zHXauIDiHzw_Wk7;loo{PaRmV+=0)P5I74OTX@bU8J$-8^RL33LGKiHI%JN3La3h-v zGs%V0IWJLXC8P=9WS#hcX9vJ0BKz+es-MW+g-thwP}rm4NU*y@$f(866vmnq26AWl zD#nYovV&2m!WT|&JE~wiqLjA??E5=K@;y0{4rwM^Z1~mnFVif@m1Rh5EpPNRL2HWJ&=;P+W7ux^M72A@+0YMt5kE zP|1Z2Z*y#Ha59#${T2PrIkV>5pWpF>@0!UMAWz5Vm=V3xZ@*Sjd({(C8nDZ>uCJ&# zPGE81-pO8FZoLnWB$QzL-`P3Q16`s5+*M#G!=WwVuIiV~YY9-zXU22mEH0_XX3tj7 zOW9Ow2}|r}RO_e8I28_nVEqBKpeAb6DhJ?nTy;4~dTL^LO?%6fl69`ruvnp~JAcXz+HpYN*`r#cF55r2 zUn$s@fch#@koMlDUQR{xs$^~!L$N9xRFa{c<&aBO#6pMRD_60v{6A{|W~yF43a5m9Q)ZmP^&+_rGNV)$rZiEVVxCx)N7yoohTcrKtnK0*jlX1!^Y@^G> zTG~^Clf)uh3bHj1hIDAn8*QWZC&36~9;~S@+HuH%befcrdHeDy!-_&|)n?jI4?d6O z16@Q+h#cRwHv*)Yk|}ztgOK$*GzHaY1ETEQzIDKhQnZYuHCbGjXiqx1H;&`-8#GPWtDfjWBsB%CP9DqT_dh z%M`oKxoIdCB^g@kwfNp27;i9R9E-d9&ZHulOi9;#EyiCAbw^=>%@n>>#nVeT!)VZ6 za890tAr$9(&{H}6T{wA}5lXcUeVfw&PAEiMwb-Ht36FhxSR_fP9?Ov$@3_bE%#?D2 z?DEZpmk(pEm0VpW`1yeO8+;x$cePljmOJc)Bq;3bc)COyhcH1<{iVwF6z#T`=Uh8% zUUx;1M$0T1Vu|A+f;7vueEf_d1X3{es1AdM!@|KW#O3%h$gtzg?Gmg<8CRI8P=u$&0WbgGa#pP zu~Br3-({Bav}a+Noe=1&l4MEh5SVl5z<5sLWx`%Vu}@xN7N}u045KCgk>Ch9+zIbB zLrRMRzzQ^Ayjsm2DOIJ#K$`c3ZsL@*EhZ^IA(Qwrc;ZVdkv8xID68(Dn7HvC;nvqg zOixIfj#}X3aGLK{SPw>FAR2SCWB;$LtIuA>IXNd=Q)S?e-6dzyAT5|8}XFx&t$gx2A zOfy299CJ1mORUvZaJ?1s|!!WxxTO{l_N+Vo1mxJnjas!!?V{-uI zECrD{r^~*$8OgM+AN2rRC}=D!pb5WSD5+ht&4v5f%Fp}gqDCw(9CEzP8`~@C=+>YG zDdpE%ry+tYC7eT7kV$%#=|ckI-4&t0Rae^2~F;Z$$qANi#qnS%%SMeDAAsznjFa`%ipOR@a>JdbI>)C2d!H zJ2kVI-^bjkZx!bLZO9BLeEbH~+_oZZ-8tG?qVscf(Q$XqZIc&yro$XA2P0t^6`h%U zL}!6)cQe|&^L2gW?AmZ!!U>1*kW1A-mP7oli?GO5)ni%?G;CqPr7%hR4H#P9~PihY$5HdCbMHO4ldcj$+uG|W!j+)2q3M)Kb8YR;jl`*eNzcj5oXo$L~65B8vJBB;}<7^ZE=C` zVE*mK4kEfV>1Z4|_Dpe#dy8ymM_98`QY+%auScL}`jcam<{C=}i+(BAQsUo%GVUx< zhG8^1PWTl~UMQB4n#~b7c5Q4#RtOHF0m5xrymKBa?6aakK!X|M8G$j61@BJjidY~8 z{Y~LAh7n>qL*YeKJn`YUIsSNK{cs;FJguAeP6%mT-1^1l1{?C-CBVuHBBI$japj@Z zT=0U3T)1q#DyfU4xIjZy*H?b*f|yK_EH--a&IIT#CLnd(4Em!c>3c{jaLpeWoO-fG zC)34OeR!gs`>impDjf9@7{iyHT_)$k+{)4(uRTTfdmRNH-Da5m0EaL;XTHDQwlpt& zrq^X-_^jr=L$|KM%nT|xAC7S}7b9K>CXk7|UsSDmG!GmHM^X|F@gL9&HwG+0ez{bB zNPhP+aScxT>;U5WKdF=icXz9%>ih0@1T#U9f{JCVK@kdJx9u<7Z-rqBIM8P4+sX$2ciLW9phg(M0Ht(N zt;TLvp^okG5}ya-MG$YRk@z)UyoBv8bjOK~N*?%?o~1A_QN{1!ECubiH;_Tj`rXMK zUX!a3N%N6%w{yby!W1zSJa!tjsht> zR=W?%XN#1o6b4?!FFL=QuO~{hse{OX2AEMH>OM1QuvWNP?5%sOX>g&UR&_1)eFtAE z1kEnEW!?=lWolHXtMJx0aZu4S1{a?{IJlB^g~&_#e(SbJHk)SzL`2+;^ljVo#bbJJ z;P2Lk>lsc76Vo5o$9}17?SB?X>q zur9$6;toTRYM1z1rZU*1Yd$zT<`}d1k5sgoz8zRBymKQYAOwP7f0D z@nuB*JdBbDSBECgh1o?dNwit*K``{{vyGdrR3_}?o2*&BAXr65coH4J*8nt5lIGr~ z*&VrPdJ>?UZVWY&x)unA?uG`Pz!bCthES$dEu2=(K+4~%PU(?Kg)7xqqDVO zu+jEtwkonpF0RiYcV@h;m>S{AFD0h;vC4uyX7f(r~!f>g~nzFz>paNi1z@YW+9!G3G(rR$vY=3g->CEr~Kh zG7uz41OP{t#7$f^GGg@nWKS(^E26VTi9IJ&j8ES{3`k6%a~y%1JCP6KO>Hcda$ZR;xZMQG$ID#Xbm)F0x1gI8x@jXoJ1{}s$3 zE(`EBiIwm?E^}b1fL1`Y>fnC=OMABFQFJ!H5I+<)q?<0BC-$sRy!xkSm?h_Pr7}f! zgHJI1o;vho9f|ZhC&k&~=#oG!)tFF3AKs^KmR7Fk1HS<&wI}XoYHr!8^ZwTI;n0(uhb`?|=tixPC1`Dh-LtJd@XZN9(IXCkp2(V6xX!(r-ufTv}gg!&nt z?40=|-!_Ag4)phTQUO^?s7!k)5U7Jh)9!T58u_=}0kAg@+LT*hBK37D89j+ehKHLa z&=g*ZkFxb}b9aO$jXzRk9Va7VJiO>mTE>8k3dHV0ogbz|OOw-$>0;U!Jb!EMNJWgR zKqC+P((6|JQ!5%9N41)7qUnbBO3Hj-?aDJsP_Cv!r)FPH9?{~R;IkC}nZ0=w-LK>2 zYE5=sf{dnGp(fS=Wg1gKRzQE$4W2zkO5=d6uYABwVY7Ev&Cvu|M>rhBN=B0BwE0v( z&3iNpD8D$E2?j|ZKiIn@7>@Ty4M<-G@-${VU$E18VFnmGB8>u4v<$=CQ(4zk{-=v# z&Zv&}#csd+%9;&ybRMrNcU7&)vf3n$E66d0hXpti?a)0-9GY_&@2#w1l&N!Q$G=;o zRrdl+TUoqP|N5CR0?`Ld$INUx6Y#drb)VApqUGBMf{IfVth^`98+n%{Z|N6Ay^>wiUm@)k8v?&IJ!SW_)XX z>ZF+hI2U!?_lqL2fOI^90|FJCm0#PNF8N62fnf7xdW0bPI*SKL{iGrwIOzShJ2K=T zb2Ct46KUFs04t#Kn>Ndgz?yEsq}Cp0Doh3ieHPJ68&2c2sW;++e7637^l<61VVY9a zAn(!<=1*{Yusdnq39St~&ioO;eSHeY2n(qR#D7n1Y!-oJ@9w{G$72SZ{|7xC{eRcf z@jE%1+Srqk(<+%cS{nau6`c&sjSU@t_XK~1agM*|r1X`H)$m-*98K{|-E58R?T!E8 z+3Fiw=$jam)5_V~7&#dl+mqQE{re50rl(<|qoHRZr+Zg@7LX_%vScWNcujZ%vM8VXNR_yo=lp*zXQ5%Bp(pC7Cc&619L@3D@a-yJa&fvkQ>@NIO4G~{$Gn^JVqvFw*Ox-;+3Yl!v-6I_exD~ zfi^kR|7zsC!`a~8K5oR;*sE6XP_=`^7Ar<=TC?`vB@wDMV((d_qNS>jt<+q_vi1uuJ`@#-1l|vbN)GhobS2M_tR(W|K{(HdL{0I!94sadFlM# z&s&vpbP_6L4Wh14wyvd zL<brnU~$l}PRU;NZGoKR2ztLIn7Ive`RS$7E3bIm=r}@)VaVz^uttLabRK%X-?lt6 zNui`qb?%*8$kiGo4J>k8zxK3&`6m9|);13^9Avv&`$7M}B6lU%+=6W$Bsm=5m@Uh1 z5_}(9@*~~d`0%fb0_*v+u?z})U>+&sSd>UD1tw?pW#6Ajb)yk!*wD9yrc#$bx*N|X zdh6czpvOy3x6iW-?rqbEPQAW3zxnrZuZIh@H#z;!XeEUhrQBl62ZNw@?$XyL>TYqA z6B(Pa>Ut#l?)HiFF^jazL{pJ- zNjfvanBw%pS3@@Kgtazb)=b2jZ?a^FZN4=VB^-9um)Iq9Oa+$nMA~jl(?~6&YcAl$ z8uCK+aes-2kda!RK+fHEaWx{><)2%Y*@idNxu0EqXuoiKvPcsx$6JBPD7L)yYIm}E zCv>xBt6#pK>W1?AthzU!kFRUx3VFE)x{`YgQ!^Y8CV9!`(Gp$CT4s^OCmfp4G{?OT zlB9w|H6x!LDR*%){Nkp+BxpmIc?)f)C*l$@KX3p#>ckg?*DT66H|05>dLlfOSQLHl zai9ngdz<4E8IDvQ`t! zeKY>xEU+lIN-u1L^nLZFv+gs1xJqLV=}#k(w^MruxDX+{OAV61hjPXdKIWI`&&woy z`3PO0nR`(sI)yGCJAcw{QOW^20#pvHQVnT|JyLh3Fa=HpHR2T`v0F?bLc6xw4Av zJ#0SJFq)zxwT6LLe+<@_zi&=WZI@op4_1oz0pgtRF!jtHi1A@9C)@q5xxrs0>bi-+ z;*GZ5Kcn3!pmac&zG+rjQ%AJ6pBfxHu8XN%_UcFSBZQFrXC3#0v&#+KCOHf($eWcf z@f{_5BO-E**3i(~nNzF7D1+O2v;{N$td2|O$;xS5b$DZ1Xm{xh=$hPzM};p-fA0w+HQL{MGw!J2D$&&2 zA!(A11$NaFRI&1XU$PPaS5#OHDV|LAg#MIv)S3sQ3C4~u{A7-w!Tao=Z=S20%K!nSB6qI6^*q83{L88DI}Cv@&d&V=k#(7G4C2iR5*Bi*MQzP)@TiBCC;JtL7#xCx(^}47JxALzAGQKCtXUNNmm(2v%^9!Oq zE+NzqD@4?+Y9HljM?(y3wyEixvWjbF+>3&t&Q_0g4mnuONV1ubha2x+);e5|JSnEl zk0odrwsY-4%(}WZus%!3bS_0FEponb<B1NFgRpZ}X>(LQlu zPXWhb=i!7xaR7#H=ZDR}Ye#=;<{Ny`QF`B68$0!ps5@Z%+b5X;uu+@9A8-<|Qtu+^ z?TXrB^zXG?_@|~=dQ&!3%qO5kW4n@NyAQrCnMkjx`|Xt`YssB$Q9H%(!$F#pe}o%B;KyW9CDjPP>#x@f7=t$0!zsjr7LLeL^0 zlG&1y-UcHs7R%GAR?(ZtdtH8Kt5`wWm1 zB6UbQ75B6#OMv3KTp^|-uQHRNjR3u%{ClX9!e$)^dsqSY&WF8lNc6E)UQcfhre*&q z@S=`ds$~Z>{)?N#Z`+y}T5P@Z>3D+UBYp6%8DqWY9F0a@q=T{-%XXJI{pp2+=_6yi zXK^3&@f3f`S9TbPd4G)3R0)*HwV3wa+Rm%6>!_o>HA1g}EKd(@Hvj(KW-n$l3eQT_ zmHgvWQ@p2&y&oYrc=+hMcV~|pCkHy36AB9kb}M9db3giZwiANEa&-3r%-Wr9;AK`P&7y1V1c#OCnl8s@^^mx;2i* z!1kAXJdM}1Mzu3xTNj2xlMyhz(aDx+=5^HmSXXz7f*o$`bX=OjuNPQJMV^q-b8tV`Ivn`m)j zV|cf?$lAs9M)-Ub@88I4>THCpsl6UH zf>l{-%vJJ33}iB#&2c|uZH@32Jtoa;Y!-Awd(gUEsx9Oy7jAF`>OE>hf%lx}8C)vu(H)5?fZLWB_PuF)s=e||IUqf-t~l3 z-LZ+W!EO0*^v)r>!*aV&>CwR9MB{f%^8wBh8D1;(GduKih$jZ&xFi=Az9<#sqBZ)s zEc`S=r>+z<-oqa1$oBy{&!#^{(`S!fa{^7Q?V3}8rt^~!+|(PsEgA#eEJJ z(|$eZu9A{*Mc`-rGvCKn>(O~eqn-Uw00%s~f8`gkt%5F%ca@4^+lGRV-bh(^4r4%3 zdeTSQL{_IDuhRY_tGC>jPf(U)QjRlWG`sd;#||w-*_1AU;Fd&XCwM1L+nKL|Q9xh5XpwH-;5mVDbbhkmR9 zF8)3Hz*>H`q4j7v+VF-7u6ErT*m|^}YoFD2q~29a#nJEg>3vu$*Y3wJhkGao#)c7jyBKC ztFqR;P!HR|T#CHm@K`YU*p`RqDpi+{_?-cW`+M!d^Q#yp0v^if$kpR zAbS}Q7_8_(D{bi$;qmW~R@xe54+hDBz&A;YpdjQ;5^}SI#lIDvK{wIAI{e>A2V}3R zpsA&x4c1hI>S{uCb!By-U?oLuh>nsxL{<~5q@=43`oE{#?DHQ(97t9P@*k!7|M0!> zPK`jdf>~pZIvE5DY0a_1VOa4E_IyRQ-0TrMzHV_&uIF6E&%;SZFpVGL^kn=bpFa6z zzoLFor$$UmzEl>>tg<{~s^J~e#G`?Vag^TiCRJK2;m%|xuej{G>D1Yd7SFA`Rrh-Nc(ggr9;kA4FvkdOqXXH3`q?$}&F01EJH>GE83Ot4Uwt`s1 zTmZx}e#-mhr{&Ca3(;{h6}hx?iZpIwJINXAW-*FJ)f>&NMTxSb`1I5Z*EHLrBp!)w zK?%I9JBZX^sE4+$r}$pAZ>5D;n5osSSQfnYR{ktit#SS-L#\linewidth\linewidth + \else\Gin@nat@width\fi} + \makeatother + \let\Oldincludegraphics\includegraphics + % Set max figure width to be 80% of text width, for now hardcoded. + \renewcommand{\includegraphics}[1]{\Oldincludegraphics[width=.8\maxwidth]{#1}} + % Ensure that by default, figures have no caption (until we provide a + % proper Figure object with a Caption API and a way to capture that + % in the conversion process - todo). + \usepackage{caption} + \DeclareCaptionLabelFormat{nolabel}{} + \captionsetup{labelformat=nolabel} + + \usepackage{adjustbox} % Used to constrain images to a maximum size + \usepackage{xcolor} % Allow colors to be defined + \usepackage{enumerate} % Needed for markdown enumerations to work + \usepackage{geometry} % Used to adjust the document margins + \usepackage{amsmath} % Equations + \usepackage{amssymb} % Equations + \usepackage{textcomp} % defines textquotesingle + % Hack from http://tex.stackexchange.com/a/47451/13684: + \AtBeginDocument{% + \def\PYZsq{\textquotesingle}% Upright quotes in Pygmentized code + } + \usepackage{upquote} % Upright quotes for verbatim code + \usepackage{eurosym} % defines \euro + \usepackage[mathletters]{ucs} % Extended unicode (utf-8) support + \usepackage[utf8x]{inputenc} % Allow utf-8 characters in the tex document + \usepackage{fancyvrb} % verbatim replacement that allows latex + \usepackage{grffile} % extends the file name processing of package graphics + % to support a larger range + % The hyperref package gives us a pdf with properly built + % internal navigation ('pdf bookmarks' for the table of contents, + % internal cross-reference links, web links for URLs, etc.) + \usepackage{hyperref} + \usepackage{longtable} % longtable support required by pandoc >1.10 + \usepackage{booktabs} % table support for pandoc > 1.12.2 + \usepackage[inline]{enumitem} % IRkernel/repr support (it uses the enumerate* environment) + \usepackage[normalem]{ulem} % ulem is needed to support strikethroughs (\sout) + % normalem makes italics be italics, not underlines + + + + + % Colors for the hyperref package + \definecolor{urlcolor}{rgb}{0,.145,.698} + \definecolor{linkcolor}{rgb}{.71,0.21,0.01} + \definecolor{citecolor}{rgb}{.12,.54,.11} + + % ANSI colors + \definecolor{ansi-black}{HTML}{3E424D} + \definecolor{ansi-black-intense}{HTML}{282C36} + \definecolor{ansi-red}{HTML}{E75C58} + \definecolor{ansi-red-intense}{HTML}{B22B31} + \definecolor{ansi-green}{HTML}{00A250} + \definecolor{ansi-green-intense}{HTML}{007427} + \definecolor{ansi-yellow}{HTML}{DDB62B} + \definecolor{ansi-yellow-intense}{HTML}{B27D12} + \definecolor{ansi-blue}{HTML}{208FFB} + \definecolor{ansi-blue-intense}{HTML}{0065CA} + \definecolor{ansi-magenta}{HTML}{D160C4} + \definecolor{ansi-magenta-intense}{HTML}{A03196} + \definecolor{ansi-cyan}{HTML}{60C6C8} + \definecolor{ansi-cyan-intense}{HTML}{258F8F} + \definecolor{ansi-white}{HTML}{C5C1B4} + \definecolor{ansi-white-intense}{HTML}{A1A6B2} + + % commands and environments needed by pandoc snippets + % extracted from the output of `pandoc -s` + \providecommand{\tightlist}{% + \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} + \DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}} + % Add ',fontsize=\small' for more characters per line + \newenvironment{Shaded}{}{} + \newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}} + \newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.56,0.13,0.00}{{#1}}} + \newcommand{\DecValTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} + \newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} + \newcommand{\FloatTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} + \newcommand{\CharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} + \newcommand{\StringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} + \newcommand{\CommentTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textit{{#1}}}} + \newcommand{\OtherTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{{#1}}} + \newcommand{\AlertTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}} + \newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.02,0.16,0.49}{{#1}}} + \newcommand{\RegionMarkerTok}[1]{{#1}} + \newcommand{\ErrorTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}} + \newcommand{\NormalTok}[1]{{#1}} + + % Additional commands for more recent versions of Pandoc + \newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.53,0.00,0.00}{{#1}}} + \newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} + \newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} + \newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.73,0.40,0.53}{{#1}}} + \newcommand{\ImportTok}[1]{{#1}} + \newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.73,0.13,0.13}{\textit{{#1}}}} + \newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} + \newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} + \newcommand{\VariableTok}[1]{\textcolor[rgb]{0.10,0.09,0.49}{{#1}}} + \newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}} + \newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.40,0.40,0.40}{{#1}}} + \newcommand{\BuiltInTok}[1]{{#1}} + \newcommand{\ExtensionTok}[1]{{#1}} + \newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.74,0.48,0.00}{{#1}}} + \newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.49,0.56,0.16}{{#1}}} + \newcommand{\InformationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} + \newcommand{\WarningTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} + + + % Define a nice break command that doesn't care if a line doesn't already + % exist. + \def\br{\hspace*{\fill} \\* } + % Math Jax compatability definitions + \def\gt{>} + \def\lt{<} + % Document parameters + \title{lecture\_11} + + + + + % Pygments definitions + +\makeatletter +\def\PY@reset{\let\PY@it=\relax \let\PY@bf=\relax% + \let\PY@ul=\relax \let\PY@tc=\relax% + \let\PY@bc=\relax \let\PY@ff=\relax} +\def\PY@tok#1{\csname PY@tok@#1\endcsname} +\def\PY@toks#1+{\ifx\relax#1\empty\else% + \PY@tok{#1}\expandafter\PY@toks\fi} +\def\PY@do#1{\PY@bc{\PY@tc{\PY@ul{% + \PY@it{\PY@bf{\PY@ff{#1}}}}}}} +\def\PY#1#2{\PY@reset\PY@toks#1+\relax+\PY@do{#2}} + +\expandafter\def\csname PY@tok@gd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.63,0.00,0.00}{##1}}} +\expandafter\def\csname PY@tok@gu\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.50,0.00,0.50}{##1}}} +\expandafter\def\csname PY@tok@gt\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.27,0.87}{##1}}} +\expandafter\def\csname PY@tok@gs\endcsname{\let\PY@bf=\textbf} +\expandafter\def\csname PY@tok@gr\endcsname{\def\PY@tc##1{\textcolor[rgb]{1.00,0.00,0.00}{##1}}} +\expandafter\def\csname PY@tok@cm\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@vg\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} +\expandafter\def\csname PY@tok@vi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} +\expandafter\def\csname PY@tok@mh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@cs\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@ge\endcsname{\let\PY@it=\textit} +\expandafter\def\csname PY@tok@vc\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} +\expandafter\def\csname PY@tok@il\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@go\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.53,0.53}{##1}}} +\expandafter\def\csname PY@tok@cp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.74,0.48,0.00}{##1}}} +\expandafter\def\csname PY@tok@gi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.63,0.00}{##1}}} +\expandafter\def\csname PY@tok@gh\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}} +\expandafter\def\csname PY@tok@ni\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.60,0.60,0.60}{##1}}} +\expandafter\def\csname PY@tok@nl\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.63,0.63,0.00}{##1}}} +\expandafter\def\csname PY@tok@nn\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}} +\expandafter\def\csname PY@tok@no\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.00,0.00}{##1}}} +\expandafter\def\csname PY@tok@na\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.49,0.56,0.16}{##1}}} +\expandafter\def\csname PY@tok@nb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@nc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}} +\expandafter\def\csname PY@tok@nd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##1}}} +\expandafter\def\csname PY@tok@ne\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.82,0.25,0.23}{##1}}} +\expandafter\def\csname PY@tok@nf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}} +\expandafter\def\csname PY@tok@si\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.53}{##1}}} +\expandafter\def\csname PY@tok@s2\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@nt\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@nv\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} +\expandafter\def\csname PY@tok@s1\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@ch\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@m\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@gp\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}} +\expandafter\def\csname PY@tok@sh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@ow\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##1}}} +\expandafter\def\csname PY@tok@sx\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@bp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@c1\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@o\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@kc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@c\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@mf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@err\endcsname{\def\PY@bc##1{\setlength{\fboxsep}{0pt}\fcolorbox[rgb]{1.00,0.00,0.00}{1,1,1}{\strut ##1}}} +\expandafter\def\csname PY@tok@mb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@ss\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} +\expandafter\def\csname PY@tok@sr\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.53}{##1}}} +\expandafter\def\csname PY@tok@mo\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@kd\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@mi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@kn\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@cpf\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@kr\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@s\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@kp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@w\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.73,0.73}{##1}}} +\expandafter\def\csname PY@tok@kt\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.69,0.00,0.25}{##1}}} +\expandafter\def\csname PY@tok@sc\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@sb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@k\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@se\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.13}{##1}}} +\expandafter\def\csname PY@tok@sd\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} + +\def\PYZbs{\char`\\} +\def\PYZus{\char`\_} +\def\PYZob{\char`\{} +\def\PYZcb{\char`\}} +\def\PYZca{\char`\^} +\def\PYZam{\char`\&} +\def\PYZlt{\char`\<} +\def\PYZgt{\char`\>} +\def\PYZsh{\char`\#} +\def\PYZpc{\char`\%} +\def\PYZdl{\char`\$} +\def\PYZhy{\char`\-} +\def\PYZsq{\char`\'} +\def\PYZdq{\char`\"} +\def\PYZti{\char`\~} +% for compatibility with earlier versions +\def\PYZat{@} +\def\PYZlb{[} +\def\PYZrb{]} +\makeatother + + + % Exact colors from NB + \definecolor{incolor}{rgb}{0.0, 0.0, 0.5} + \definecolor{outcolor}{rgb}{0.545, 0.0, 0.0} + + + + + % Prevent overflowing lines due to hard-to-break entities + \sloppy + % Setup hyperref package + \hypersetup{ + breaklinks=true, % so long urls are correctly broken across lines + colorlinks=true, + urlcolor=urlcolor, + linkcolor=linkcolor, + citecolor=citecolor, + } + % Slightly bigger margins than the latex defaults + + \geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in} + + + + \begin{document} + + + \maketitle + + + + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}18}]:} \PY{c}{\PYZpc{}plot \PYZhy{}\PYZhy{}format svg} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}19}]:} \PY{n}{setdefaults} +\end{Verbatim} + + \section{LU Decomposition}\label{lu-decomposition} + +\subsubsection{efficient storage of matrices for +solutions}\label{efficient-storage-of-matrices-for-solutions} + +Considering the same solution set: + +\(y=Ax\) + +Assume that we can perform Gauss elimination and achieve this formula: + +\(Ux=d\) + +Where, \(U\) is an upper triangular matrix that we derived from Gauss +elimination and \(d\) is the set of dependent variables after Gauss +elimination. + +Assume there is a lower triangular matrix, \(L\), with ones on the +diagonal and same dimensions of \(U\) and the following is true: + +\(L(Ux-d)=Ax-y=0\) + +Now, \(Ax=LUx\), so \(A=LU\), and \(y=Ld\). + +\(2x_{1}+x_{2}=1\) + +\(x_{1}+3x_{2}=1\) + +\(\left[ \begin{array}{cc} 2 & 1 \\ 1 & 3 \end{array} \right] \left[\begin{array}{c} x_{1} \\ x_{2} \end{array}\right]= \left[\begin{array}{c} 1 \\ 1\end{array}\right]\) + +f21=0.5 + +A(2,1)=1-1 = 0 + +A(2,2)=3-0.5=2.5 + +y(2)=1-0.5=0.5 + +\(L(Ux-d)= \left[ \begin{array}{cc} 1 & 0 \\ 0.5 & 1 \end{array} \right] \left(\left[ \begin{array}{cc} 2 & 1 \\ 0 & 2.5 \end{array} \right] \left[\begin{array}{c} x_{1} \\ x_{2} \end{array}\right]- \left[\begin{array}{c} 1 \\ 0.5\end{array}\right]\right)=0\) + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}3}]:} \PY{n}{A}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{]} + \PY{n}{L}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{;}\PY{l+m+mf}{0.5}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{]} + \PY{n}{U}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{0}\PY{p}{,}\PY{l+m+mf}{2.5}\PY{p}{]} + \PY{n}{L}\PY{o}{*}\PY{n}{U} + + \PY{n}{d}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mf}{0.5}\PY{p}{]} + \PY{n}{y}\PY{p}{=}\PY{n}{L}\PY{o}{*}\PY{n}{d} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +A = + + 2 1 + 1 3 + +L = + + 1.00000 0.00000 + 0.50000 1.00000 + +U = + + 2.00000 1.00000 + 0.00000 2.50000 + +ans = + + 2 1 + 1 3 + +d = + + 1.00000 + 0.50000 + +y = + + 1 + 1 + + + \end{Verbatim} + + \subsection{Pivoting for LU +factorization}\label{pivoting-for-lu-factorization} + +LU factorization uses the same method as Gauss elimination so it is also +necessary to perform partial pivoting when creating the lower and upper +triangular matrices. + +Matlab and Octave use pivoting in the command + +\texttt{{[}L,U,P{]}=lu(A)} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}4}]:} \PY{n}{help} \PY{n+nb}{lu} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +'lu' is a built-in function from the file libinterp/corefcn/lu.cc + + -- Built-in Function: [L, U] = lu (A) + -- Built-in Function: [L, U, P] = lu (A) + -- Built-in Function: [L, U, P, Q] = lu (S) + -- Built-in Function: [L, U, P, Q, R] = lu (S) + -- Built-in Function: [{\ldots}] = lu (S, THRES) + -- Built-in Function: Y = lu ({\ldots}) + -- Built-in Function: [{\ldots}] = lu ({\ldots}, "vector") + Compute the LU decomposition of A. + + If A is full subroutines from LAPACK are used and if A is sparse + then UMFPACK is used. + + The result is returned in a permuted form, according to the + optional return value P. For example, given the matrix 'a = [1, 2; + 3, 4]', + + [l, u, p] = lu (A) + + returns + + l = + + 1.00000 0.00000 + 0.33333 1.00000 + + u = + + 3.00000 4.00000 + 0.00000 0.66667 + + p = + + 0 1 + 1 0 + + The matrix is not required to be square. + + When called with two or three output arguments and a spare input + matrix, 'lu' does not attempt to perform sparsity preserving column + permutations. Called with a fourth output argument, the sparsity + preserving column transformation Q is returned, such that 'P * A * + Q = L * U'. + + Called with a fifth output argument and a sparse input matrix, 'lu' + attempts to use a scaling factor R on the input matrix such that 'P + * (R \textbackslash{} A) * Q = L * U'. This typically leads to a sparser and more + stable factorization. + + An additional input argument THRES, that defines the pivoting + threshold can be given. THRES can be a scalar, in which case it + defines the UMFPACK pivoting tolerance for both symmetric and + unsymmetric cases. If THRES is a 2-element vector, then the first + element defines the pivoting tolerance for the unsymmetric UMFPACK + pivoting strategy and the second for the symmetric strategy. By + default, the values defined by 'spparms' are used ([0.1, 0.001]). + + Given the string argument "vector", 'lu' returns the values of P + and Q as vector values, such that for full matrix, 'A (P,:) = L * + U', and 'R(P,:) * A (:, Q) = L * U'. + + With two output arguments, returns the permuted forms of the upper + and lower triangular matrices, such that 'A = L * U'. With one + output argument Y, then the matrix returned by the LAPACK routines + is returned. If the input matrix is sparse then the matrix L is + embedded into U to give a return value similar to the full case. + For both full and sparse matrices, 'lu' loses the permutation + information. + + See also: luupdate, ilu, chol, hess, qr, qz, schur, svd. + +Additional help for built-in functions and operators is +available in the online version of the manual. Use the command +'doc ' to search the manual index. + +Help and information about Octave is also available on the WWW +at http://www.octave.org and via the help@octave.org +mailing list. + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}22}]:} \PY{c}{\PYZpc{} time LU solution vs backslash} + \PY{n}{t\PYZus{}lu}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{100}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n}{t\PYZus{}bs}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{100}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{k}{for} \PY{n}{N}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{100} + \PY{n}{A}\PY{p}{=}\PY{n+nb}{rand}\PY{p}{(}\PY{n}{N}\PY{p}{,}\PY{n}{N}\PY{p}{)}\PY{p}{;} + \PY{n}{y}\PY{p}{=}\PY{n+nb}{rand}\PY{p}{(}\PY{n}{N}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{p}{[}\PY{n}{L}\PY{p}{,}\PY{n}{U}\PY{p}{,}\PY{n}{P}\PY{p}{]}\PY{p}{=}\PY{n+nb}{lu}\PY{p}{(}\PY{n}{A}\PY{p}{)}\PY{p}{;} + + \PY{n+nb}{tic}\PY{p}{;} \PY{n}{d}\PY{p}{=}\PY{n}{L}\PY{o}{\PYZbs{}}\PY{n}{y}\PY{p}{;} \PY{n}{x}\PY{p}{=}\PY{n}{U}\PY{o}{\PYZbs{}}\PY{n}{d}\PY{p}{;} \PY{n}{t\PYZus{}lu}\PY{p}{(}\PY{n}{N}\PY{p}{)}\PY{p}{=}\PY{n+nb}{toc}\PY{p}{;} + + \PY{n+nb}{tic}\PY{p}{;} \PY{n}{x}\PY{p}{=}\PY{n}{A}\PY{o}{\PYZbs{}}\PY{n}{y}\PY{p}{;} \PY{n}{t\PYZus{}bs}\PY{p}{(}\PY{n}{N}\PY{p}{)}\PY{p}{=}\PY{n+nb}{toc}\PY{p}{;} + \PY{k}{end} + \PY{n+nb}{plot}\PY{p}{(}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{100}\PY{p}{]}\PY{p}{,}\PY{n}{t\PYZus{}lu}\PY{p}{,}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{100}\PY{p}{]}\PY{p}{,}\PY{n}{t\PYZus{}bs}\PY{p}{)} + \PY{n+nb}{legend}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{LU decomp\PYZsq{}}\PY{p}{,}\PY{l+s}{\PYZsq{}}\PY{l+s}{Octave \PYZbs{}\PYZbs{}\PYZsq{}}\PY{p}{)} +\end{Verbatim} + + \begin{center} + \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{lecture_11_files/lecture_11_6_0.pdf} + \end{center} + { \hspace*{\fill} \\} + + Consider the problem again from the intro to Linear Algebra, 4 masses +are connected in series to 4 springs with K=10 N/m. What are the final +positions of the masses? + +\begin{figure}[htbp] +\centering +\includegraphics{mass_springs.png} +\caption{Springs-masses} +\end{figure} + +The masses haves the following amounts, 1, 2, 3, and 4 kg for masses +1-4. Using a FBD for each mass: + +\(m_{1}g+k(x_{2}-x_{1})-kx_{1}=0\) + +\(m_{2}g+k(x_{3}-x_{2})-k(x_{2}-x_{1})=0\) + +\(m_{3}g+k(x_{4}-x_{3})-k(x_{3}-x_{2})=0\) + +\(m_{4}g-k(x_{4}-x_{3})=0\) + +in matrix form: + +\(\left[ \begin{array}{cccc} 2k & -k & 0 & 0 \\ -k & 2k & -k & 0 \\ 0 & -k & 2k & -k \\ 0 & 0 & -k & k \end{array} \right] \left[ \begin{array}{c} x_{1} \\ x_{2} \\ x_{3} \\ x_{4} \end{array} \right]= \left[ \begin{array}{c} m_{1}g \\ m_{2}g \\ m_{3}g \\ m_{4}g \end{array} \right]\) + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}24}]:} \PY{n}{k}\PY{p}{=}\PY{l+m+mi}{10}\PY{p}{;} \PY{c}{\PYZpc{} N/m} + \PY{n}{m1}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{;} \PY{c}{\PYZpc{} kg} + \PY{n}{m2}\PY{p}{=}\PY{l+m+mi}{2}\PY{p}{;} + \PY{n}{m3}\PY{p}{=}\PY{l+m+mi}{3}\PY{p}{;} + \PY{n}{m4}\PY{p}{=}\PY{l+m+mi}{4}\PY{p}{;} + \PY{n}{g}\PY{p}{=}\PY{l+m+mf}{9.81}\PY{p}{;} \PY{c}{\PYZpc{} m/s\PYZca{}2} + \PY{n}{K}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{k} \PY{o}{\PYZhy{}}\PY{n}{k} \PY{l+m+mi}{0} \PY{l+m+mi}{0}\PY{p}{;} \PY{o}{\PYZhy{}}\PY{n}{k} \PY{l+m+mi}{2}\PY{o}{*}\PY{n}{k} \PY{o}{\PYZhy{}}\PY{n}{k} \PY{l+m+mi}{0}\PY{p}{;} \PY{l+m+mi}{0} \PY{o}{\PYZhy{}}\PY{n}{k} \PY{l+m+mi}{2}\PY{o}{*}\PY{n}{k} \PY{o}{\PYZhy{}}\PY{n}{k}\PY{p}{;} \PY{l+m+mi}{0} \PY{l+m+mi}{0} \PY{o}{\PYZhy{}}\PY{n}{k} \PY{n}{k}\PY{p}{]} + \PY{n}{y}\PY{p}{=}\PY{p}{[}\PY{n}{m1}\PY{o}{*}\PY{n}{g}\PY{p}{;}\PY{n}{m2}\PY{o}{*}\PY{n}{g}\PY{p}{;}\PY{n}{m3}\PY{o}{*}\PY{n}{g}\PY{p}{;}\PY{n}{m4}\PY{o}{*}\PY{n}{g}\PY{p}{]} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +K = + + 20 -10 0 0 + -10 20 -10 0 + 0 -10 20 -10 + 0 0 -10 10 + +y = + + 9.8100 + 19.6200 + 29.4300 + 39.2400 + + + \end{Verbatim} + + This matrix, K, is symmetric. + +\texttt{K(i,j)==K(j,i)} + +Now we can use, + +\subsection{Cholesky Factorization}\label{cholesky-factorization} + +We can decompose the matrix, K into two matrices, \(U\) and \(U^{T}\), +where + +\(K=U^{T}U\) + +each of the components of U can be calculated with the following +equations: + +\(u_{ii}=\sqrt{a_{ii}-\sum_{k=1}^{i-1}u_{ki}^{2}}\) + +\(u_{ij}=\frac{a_{ij}-\sum_{k=1}^{i-1}u_{ki}u_{kj}}{u_{ii}}\) + +so for K + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}25}]:} \PY{n}{K} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +K = + + 20 -10 0 0 + -10 20 -10 0 + 0 -10 20 -10 + 0 0 -10 10 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}26}]:} \PY{n}{u11}\PY{p}{=}\PY{n+nb}{sqrt}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{)} + \PY{n}{u12}\PY{p}{=}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)}\PY{o}{/}\PY{n}{u11} + \PY{n}{u13}\PY{p}{=}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{)}\PY{o}{/}\PY{n}{u11} + \PY{n}{u14}\PY{p}{=}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{4}\PY{p}{)}\PY{p}{)}\PY{o}{/}\PY{n}{u11} + \PY{n}{u22}\PY{p}{=}\PY{n+nb}{sqrt}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{u12}\PYZca{}\PY{l+m+mi}{2}\PY{p}{)} + \PY{n}{u23}\PY{p}{=}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{u12}\PY{o}{*}\PY{n}{u13}\PY{p}{)}\PY{o}{/}\PY{n}{u22} + \PY{n}{u24}\PY{p}{=}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{4}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{u12}\PY{o}{*}\PY{n}{u14}\PY{p}{)}\PY{o}{/}\PY{n}{u22} + \PY{n}{u33}\PY{p}{=}\PY{n+nb}{sqrt}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{u13}\PYZca{}\PY{l+m+mi}{2}\PY{o}{\PYZhy{}}\PY{n}{u23}\PYZca{}\PY{l+m+mi}{2}\PY{p}{)} + \PY{n}{u34}\PY{p}{=}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{4}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{u13}\PY{o}{*}\PY{n}{u14}\PY{o}{\PYZhy{}}\PY{n}{u23}\PY{o}{*}\PY{n}{u24}\PY{p}{)}\PY{o}{/}\PY{n}{u33} + \PY{n}{u44}\PY{p}{=}\PY{n+nb}{sqrt}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{,}\PY{l+m+mi}{4}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{u14}\PYZca{}\PY{l+m+mi}{2}\PY{o}{\PYZhy{}}\PY{n}{u24}\PYZca{}\PY{l+m+mi}{2}\PY{o}{\PYZhy{}}\PY{n}{u34}\PYZca{}\PY{l+m+mi}{2}\PY{p}{)} + \PY{n}{U}\PY{p}{=}\PY{p}{[}\PY{n}{u11}\PY{p}{,}\PY{n}{u12}\PY{p}{,}\PY{n}{u13}\PY{p}{,}\PY{n}{u14}\PY{p}{;}\PY{l+m+mi}{0}\PY{p}{,}\PY{n}{u22}\PY{p}{,}\PY{n}{u23}\PY{p}{,}\PY{n}{u24}\PY{p}{;}\PY{l+m+mi}{0}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{,}\PY{n}{u33}\PY{p}{,}\PY{n}{u34}\PY{p}{;}\PY{l+m+mi}{0}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{,}\PY{n}{u44}\PY{p}{]} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +u11 = 4.4721 +u12 = -2.2361 +u13 = 0 +u14 = 0 +u22 = 3.8730 +u23 = -2.5820 +u24 = 0 +u33 = 3.6515 +u34 = -2.7386 +u44 = 1.5811 +U = + + 4.47214 -2.23607 0.00000 0.00000 + 0.00000 3.87298 -2.58199 0.00000 + 0.00000 0.00000 3.65148 -2.73861 + 0.00000 0.00000 0.00000 1.58114 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}27}]:} \PY{n}{U}\PY{o}{\PYZsq{}}\PY{o}{*}\PY{n}{U} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +ans = + + 20.00000 -10.00000 0.00000 0.00000 + -10.00000 20.00000 -10.00000 0.00000 + 0.00000 -10.00000 20.00000 -10.00000 + 0.00000 0.00000 -10.00000 10.00000 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}37}]:} \PY{c}{\PYZpc{} time solution for Cholesky vs backslash} + \PY{n}{t\PYZus{}chol}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{1000}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n}{t\PYZus{}bs}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{1000}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{k}{for} \PY{n}{i}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{1000} + \PY{n+nb}{tic}\PY{p}{;} \PY{n}{d}\PY{p}{=}\PY{n}{U}\PY{o}{\PYZsq{}}\PY{o}{*}\PY{n}{y}\PY{p}{;} \PY{n}{x}\PY{p}{=}\PY{n}{U}\PY{o}{\PYZbs{}}\PY{n}{d}\PY{p}{;} \PY{n}{t\PYZus{}chol}\PY{p}{(}\PY{n}{i}\PY{p}{)}\PY{p}{=}\PY{n+nb}{toc}\PY{p}{;} + \PY{n+nb}{tic}\PY{p}{;} \PY{n}{x}\PY{p}{=}\PY{n}{K}\PY{o}{\PYZbs{}}\PY{n}{y}\PY{p}{;} \PY{n}{t\PYZus{}bs}\PY{p}{(}\PY{n}{i}\PY{p}{)}\PY{p}{=}\PY{n+nb}{toc}\PY{p}{;} + \PY{k}{end} + \PY{n+nb}{fprintf}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{average time spent for Cholesky factored solution = \PYZpc{}e+/\PYZhy{}\PYZpc{}e\PYZsq{}}\PY{p}{,}\PY{n+nb}{mean}\PY{p}{(}\PY{n}{t\PYZus{}chol}\PY{p}{)}\PY{p}{,}\PY{n+nb}{std}\PY{p}{(}\PY{n}{t\PYZus{}chol}\PY{p}{)}\PY{p}{)} + + \PY{n+nb}{fprintf}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{average time spent for backslash solution = \PYZpc{}e+/\PYZhy{}\PYZpc{}e\PYZsq{}}\PY{p}{,}\PY{n+nb}{mean}\PY{p}{(}\PY{n}{t\PYZus{}bs}\PY{p}{)}\PY{p}{,}\PY{n+nb}{std}\PY{p}{(}\PY{n}{t\PYZus{}bs}\PY{p}{)}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +average time spent for Cholesky factored solution = 1.623154e-05+/-1.166726e-05 +average time spent for backslash solution = 1.675844e-05+/-1.187234e-05 + + \end{Verbatim} + + + % Add a bibliography block to the postdoc + + + + \end{document} diff --git a/lecture_11/lecture_11_files/lecture_11_6_0.pdf b/lecture_11/lecture_11_files/lecture_11_6_0.pdf new file mode 100644 index 0000000000000000000000000000000000000000..40e3f285bc346d547a3c8211b26c74614a6db81b GIT binary patch literal 9079 zcma)C2UJr_x29K7nt*^1=|~A7B!u33?_CKHn$!@KssyArL68p8LKT(Xq)1VEZz9q~ zP*9NGd;#yh|Gn@2Z>@Ju+I)Lv_RQXMvS)pJICT}31weu#WSljd6(?k1fDpjl#+gh~ z5&+ahxH+I40U}sPp9}y10F|9wPzWUU+Xaq7C?ag#?GR+r(qvvJBm(YA=98Ihs^xAZ zN;!98@)2R$>2td2T3AZ$Y&3%5vql2|xAN%BlUwJHs?XkP9J4)6l-RF{AL`Fs&H!G$ zdVH|AynX5llRn>c-nkXa-t|SJJqL2~Y0UGc%Fc`3<*%FD?V%y(XZvGR0n#mt%jBoO zdfxbjpgo!&938G62KSAY-#bpwm-;j}(53KGsN3^F^;p{)`@0qjhcC0!-`{D>-B>*L zSOy#q#-D0zNk3!%y!?4k>X*mO3edxk0UjocGXvZQ%L904B$cKf$>a3GQG`*00SnmoL!(a~UD+q4ZHqlw4`SFcAz+5(A5Uwo#PH+iqv%$Io zmL^2RN_U0ou@L4`P)SGMeQR5O)8a(VL+3N-$gnnh(g86-l%~kk5Ya&}aPYm+9F8dh zST@?c5YaT>%4z4a45Rh79!FmJWo2}SOFBq~4(4b6{)^MwrCjovXw_L?&22Vaj+;g0 zW_IYR_XMyaOCsU0g%cRL@Li(HcQ*mjt_we$aPxD?<>0t7ZI*9H3~#Tpc+r_H@C)M( z@}{6Q8>BleTS-==@;TQSnn+*973TKIB6wPAevZreL|yy3g*sulezh^+Inlyg2=0RM z{KpxjV@F+7+SLGGbPTod@yL@hoS%Cts!9#o#WDB+((Ga~GJVS%@ylnMO)}rlKO_@> zfhByGUn{FVA@X6C3-8fxYjwieE82M+v1T-Ng=0l1>Lr@1I!0|Fg;@%6^<7c`=j^v7 zbr7L64^fin95H^@jY!Y;Ozfk|SMlF#<&Q5JvoED5lyt8xl1t%n6NK_`2*yjXH7j!f zW3}6Geke!m1&2Q0A)LXFqT`|k(la}z=jB3_QsOe)ey{n4z(G`MJm^X1}p&S;8Iy zL#w*p9#NwA_6cxGdC>5o^Jc23Z^`y7NQEsv`$#nvpv_3+M;%pZecDf%dQ18?tEcKt z3D4vBgit_c;%ebYpktr~jEMJ1D%meo4mUdpYUbeVC$d2bGf0kRj*QdM&s%p=YPKY3KS8w({fN2<^%~^N|SYEbY)Ll$qlvH!|Ueb62&duj=$|#bK89{wP&4 zbiR&!>1dC^+hFT`EpPoKRK>Zf+Of3riH&Q7ZjK)s6Br6}$(VJH zyOO1h@F*Fr-2+8$i`-I`=ABhyl_K@eTZki+I*su^Kik`)y==-@Tv{ebeIz*yD%!`vDC+m>=`%9?9x!5d<(Q)|N!=FRGeZzhq6G{SYI!Xkh{q^^iT5C2;N(W?e?eV$J z8-}P(3V8KV_Bq4f@N&1rM3H0C>%nE2j^ZXI>4Ea$PQ^AkLF~1ZHyla)0Q?&t4jg)D z^qx29N>~LJKHR9~5>l|z9XBi)h026F`@Qf*ckeAi6*!BXm2HYmTlzHCybWKVCaTR# zmLU^X6B@ZtFUcBxwV|y71Y@>%Nk}>3xi%SRX6x@ihz%a`8J&}3UaXz)2vL$0d@$v&1 z!p-iFfQS8c5h^d@1FIx@ps;ZhASrnPU@stC2wMOE z732UQ0MHhW{lrF7tl;-2P}$uL^|#vg0zv{p0LY)w7+VSZ`a>D?FJ%Crp|1x50Mvy$ zATAZ_!jTAUKcGL`0ksfzPH=g5AAkiG5(0>bzyM${6kv5(TLG&RTipwAu@U$k^;MAW z-X4D&$M60x(LX0*fYpkGyLowB=(6?w6IKJDklvT0xR|X1ww5B|zLPCNUq$|+${*9z zM|in=BW)30fD4o9|7}*H*z*6{jKKaH)_>cKT&VfIYXJd7g}}o9*qyAJ`kET9H9Ttl zne9%OdSmbk*adv0Lzt4DR?c$xOJ}iXG-rb8h;_SW1gOSlxSo>SnXryvBqH*wq9>`j zMud^BttN+{oSSR%$BeQPh>Zw^USeV@TfnYV2nS|pO!}bpb8gzX699FO*uUpTp@(y*`2=8+)Ys4)Ts$HF_#I## ze?SVe9GZ9~@T(x?0Do2gXW{1pYp?2=o33$#$+=Rjo13DF4U@ZPqCjWAVHVD;sa5?? zcxXzp*V)#wLwM2(X$aTUPgE<4;R7s~YSFqS|qbt){t!vY}-KDKJ{!4;mKT#uqK?7H7Uc=)m+MM_FU3rQtRVLGHwW)99^B!+1 zhNOtfb7&rP_EMR9y{5jgIA$K$dpmz6q_Df@1DQi{2;p;lJla?TCx_)SdEssoGcZQ0 zgs|}E%JcqhBe@$J5hJ1vuE}=EpNHJ}^0XUVYp-aN#nmchguhO*du4V@oJ;!F zgjy_a$=R~4t;h!*P;Rs!z4kq^}_9hOl zrs8`|Gdsn(##!Y+QV<}E>YPY4lqTA{q!h4U9hlmiU^#uq)e$EAwLiu|uo+<9bz?IB z42*e^aR22;%X^6!9Vt)DqhBFX{#A1PL4;K*T}9p*S8sl-*y!x5P!AnNzI}EiN8#ifDt;h5cQsgdjRn0*O&%_k#_)|eFyko^X4(dLx0#1vpos{e z!zo1^^v;$EEp4{5U1rX=k98Vaj?3HSe9tqtIeRz?8iSyB*Mh{Es4Nu zJ0z=GKkq5$)Mygr5U2-r;xXrvIkP42ZyVKKxqfG?aXa*O3yA@@&hg%AQPG4>yz$~) zrz4Z{-rQ6LVjA!4m79>qi8aV&m;a>VtQhN?$uY!`g>fAkGQ!eqYKX+@5u;7boAYiBww1`1y>0V4oZ7s z?jN*wFx7qc3mlE4|2c$sIC$k{oj=v`BNvu0Shf8}wu5RveruPIKM9MfArImxe~_|uB};Eth~r)Gi~ zLv+hz_8f=}GZ9QG>HcR^FVt=4$DN9$jxLf@psc3Zm$nN2z0!-eGexH@`AI0lt%Fui zp)MNwa$MWjxB<5qbJ*?bmcZpvyk6zrOg6i59uBYY^Yg#C2@B{eKAraxsS!OZ#*43E z*)R(k528Ryy_|Y7ReoRHY=zxM1bR<3Wj9T0kAnJsQ@daeRTeXwQTfN$wwy+ooL7jq zGtqJirFZMQ>m83YQ4zEJSu@-&?YC4OwD^9T&X9;#k9J;K>JnWV9IEQf0?N=o+LPG5 z;ZkQ1>qc@f;w9u^i%l+2a>Fy6%7m0L2R!1y>s6sOolI*V@pb)Gmss#FErMs9Kxy`A z(thLT$wqq_g*n*IIwG1j7VEcj;ryI}oMMU)Dw%N`+a>*zYb0CQvJ6ir%V*#C&oxRl zb!{OK!$)gnc`ob6R!duRO-pWFsgRe_dOCS1+tH3gpV9N{p3?7A0+JNY_=}MmYUe;&iQ5?JeTTU!B;>ficuaakC{vH*L-2d4N1jkd0kvv zRIE*Dh=SIggaD726C-Yib?CJhwo3%-&9y{Zc}11VjoNyjwHvT9m(!bctu2Ms_cG0{ z)mb)A2jBaULubO}K zE?KdgScR0Bmo#OeV6$c`yJ87KN=4n6bVL3lTWu15+5P$|4AO# zK)O1{`no=zw0R7g)T2`OH$Xm6W;1u^oByP}LqIfh-9I5PYtCWKS$CJXO|bcp-L^k4 zX?Y-Wc644W@HlJNm4#&17LR9|hqZ~d#Ag7~V7Bb?5&Y4x6Gc-r>HfY+MaCvpGJ(Jz+D9qI1s z39)K|W_yW_Ui;F@GO3Alw;Ad*cjsLr$I~j9wC9OL!DG*S>hlP_o@f`TiGB?py$NrO z7}R#D4SR}8Dv{NJ zYtIhudndi0A4^nrJ zg9)}2Atl2DXDGB~0*~yPawMPdxmUM!S6GTk@(^~oMn#3}6MLxx3@BL~}3 z!m{;O5Id5pgdqK%bc22uTs}&^?zPqvx8=b^>K3a2-4BZv5YL}+GHNr0E~Y8WWbaw1 z)pT$d!j_ZFlnBE%w0;;DVH$z5XK0g?TGQSvZmcA&tFo5t^pH1oW{Lz zw=%dVLAqW&KbApUHuBX(EkSLtpqRr%AEn>_gFvU?-FoCsz2r!C>h61#gP&m|pOm;1 zm((pFT*)r7ilemCi24niy;U$Um$QB5O|`$?L9mO%eZyKl3Gtyc`sB6VXh9^M()EU@ zybhL_=xbHzgDf*irG%s}#8pX@>zxz$8f(pZ76#zc!(RNon+K`Y4-EDfV;poe&n%*o z5-o(-e?3)@;zIGi=pXQXwAREe5PI);w?tFb(PVE|s4GTZj7h{}=xLCBT3=$Cnq}bg z0$d6(zN4}#$#+i*l}NpZrAAc?IFE32tE?fU24161b5yy4)qLbPPZh{YzigSDC#Sz` z7FSN^ysmqEhyS`7LO-;?;M!>Zo!XH)H3H@L+exjvZ7h`smw6;NN73Kw&CPU8 zgf4&G`5N%lo^`&gWHf8sYQlRXOi!COGq31->vXuz>vfl7-fdJy=3F+Kc%ZU}SUu8LtGx7QC*u&;4 z=S_QPmSvspj)y+vxuvp{J&Q#tp`~e(s#AsM0#wH`k|)0wyYzF3cv`~_a;a-8rN(;; zw;INmpO(T2`-`#-%Cn`Xs7u_hRktano8j%5^5QcQ^Ny4MAWeCmjA*;{!B$A=d%HPB zAiH+bwH}>b$c|P6E>Z6hG9*)At%~+z5BEUIda(rDWrmO0bTn~gWqzdh#SUbtA?XcUATb4u+E2D3Aj9rOx~W(j z)r+vcmFKy28YPJzZQmGWb7SfU?UlLr&xB~oxDRaV>fH`_^E8Lv^m}J~;&x`+7+?QsHNMQ1c5!qO!9&20Kr}aD3-^!5 zZ4U@p=zTO7^uUvJO};PM(%Ikn#I~`AR~;tU`V^>2pZbf+WUj7vcCZ{BxJh#S$U>IW z9oDwpMz_-V3`e&@7SU&J58I+o_yhu4nfL?_>8Q?(nYL)^O%_^Y+jAY3goxe0}E8G7)V7<010Q27;V?<%%{3LO()jc8{>OOp$)Kj&-7bYM9o7Av(LNCCkG4cuO{hhJjCr zizGjC$dSCUnPDPK+opZJOO;(*HTWue9~#4eUK}T(XZYNun`l_vMrlq<9S21lqucQW zMB3SgHJj5_o>vltG&@o|iahqnm&G4|KDK_|hC{fA=Pjbet$R-?mL9>FM2ZV7xI?>g zc3qH@&47}ilJT?EHrdy`M~lI~T=C8~uOD5*ga>N%LwYFZ7kgqHGw^Go^KkGah z>^$?F+t=Hl+OF{>NSh>78LevXy2jYCAjp$0>7M(#_WGCpRw=W}6_-74k~}fpd)e=( z8*D1r`0SPVwU$iT*unab+Rq4I+dbTD;sr6!} zRTAQD9x0vo3R~C=mhd<+LX{|U1PC@K} zQrkT%>EOH?as8_St%^C=>n;l|zuSQ7a!xiZ|<$;B7I^IHVCkn#Q& zy1*T<47KoIHRXTP*#aOTVIhEk2viu$#EXFeAYriZAH2323hv@$E9d6mf&d6zwv+R+ zz2L>ggkhJ(i}78Q1%$znOF#kcp^9*FaKuvQ*lsQ%0~Es57y$d-{-U7zXW?QxSV9^h z47lK||IT4w@b&+;#_#UDZBUn7y&;w*zp&ILDi8NUTr&Uvmt~xgUMK}eIPy;eXu|&} zgFwHh@=tREE*w^Uy zkZ=!2CtEK;cccUF?KQSSp3!nTG1HmBJ z|M-7mFl>(Ie`6pqF|5b_Sx;D42`e4?V@f9Vw!h5l>IFv!2h0)t{# z`(JudNI3QpM_!(dF>vxjT-fR&{_E%v4qU@}fl JB^_n5{{d2U*RTKp literal 0 HcmV?d00001 diff --git a/lecture_11/lecture_11_files/lecture_11_6_0.svg b/lecture_11/lecture_11_files/lecture_11_6_0.svg new file mode 100644 index 0000000..bb1f18d --- /dev/null +++ b/lecture_11/lecture_11_files/lecture_11_6_0.svg @@ -0,0 +1,149 @@ + + +Gnuplot +Produced by GNUPLOT 5.0 patchlevel 3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 0 + + + + + 5e-05 + + + + + 0.0001 + + + + + 0.00015 + + + + + 0.0002 + + + + + 0.00025 + + + + + 0.0003 + + + + + 0 + + + + + 20 + + + + + 40 + + + + + 60 + + + + + 80 + + + + + 100 + + + + + + + + + + + + + LU decomp + + + + + LU decomp + + + + + + Octave \\ + + + Octave \ + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/lecture_11/mass_springs.png b/lecture_11/mass_springs.png new file mode 100644 index 0000000000000000000000000000000000000000..259a33353fa69e0a9aae47f2b0c210b637748773 GIT binary patch literal 5031 zcmZ{GRan$twDu2&5D}Gb=?*DrhK3)oN-ops#Dy<63Yl;3)zA`z9 zLo`z%GFX?Jl(*36{)1?v2|iNXRO(n39f=o4M#jOT8^g^Y`6ns7caH+mT<+D5 zjG?N#buFteNFuqqjydf>0zfzI)$%RS^{)M+Dlm2rXg)aLtDw#Ir$YYy(J9hY1Qdn= z=BGZ!S9_hp^mn)5VtSyJh@+x|$3Fpr3li|wfjHd=T<;@wW&oMU2=W!BM;kqlxPnP% z2nY)BcM1qi@)^by#mz#U+{pI31F6I8m_oUIK*xVb(w^Wlvv`HRA7Ijmlq!s&W~J}N zcUP1lkz*r|l3z=Nu@Mcbd9$!XB=tf>nfM2^2kMS_@cMLUhm z0^;wp`U87@93J_Yx3Mn~GX^L0Y^}unL7mwKaNgh}$mPOrAxuwRj>#;Sc{V% zKu~Cd?>67>J7j)Trev*5;U8Suus`DPput2fXm+UOvOLr6<<2B`(g4_#8bb6`97-4R zWA&Hx%V881ct6uKf$6~54s`@v=}B}!l-!5`C{?j7unIte|=eNpN(f!%)P zg%kL!Jq(d^6MUl{%3Sztjf0fG0g5(2Yg#LBRC5`_%u{(kD~M`;)cc#gE&EMUs39Xf zBg6fAu%Cmlzo(96r6OLor8v23ANg_ zBIGTcNi9yTuXRs9<@Z-D>oh@ak%)}rWYT1gWQAl*a#M0TTNqz#@fQy`d*hIiopFMZ zC7K-Fq9>&1kDe=5MN<}UqOoW=I;L0}tybJQP-l~EooszF>@_Tt-Z!{2a5402;Av7j zvovRaYGd;HAjNPF%AY4;Xm{Xp&^1ktLyoI6Kfi3HFtJ9b+Rgmci=<-v(u^{r0v}^{ zgQx=QqSSm?ftSkf=cdV{Hk^%>GuL~*Hoi87n|z!2o6MW+6i}2r>K^J5YO8|$WxQjR zW0+&!PFrSjX1Ym-N!FbH+Xg8$S&Qq$3*<#%c!_G=SC=@KI2xz}RD4usRBY6p|8rWk zLAXKDl#+9>n3}ZuW!*_21FRp$X;Eshl`Bx;RFakNZ}iTG0)gtQn0y&m`Sq{8pIQ5x zcCmKCz_gB1#Cyc28&lBp5W$dZd=UQfLnv_yan{2;8g*(69R>A2+G~d@_=rf&b3{vK z$DHrK=AW{a%OAEgdo$>TeBTTS{u5qwp0m67IkFJzI^`nfRAc+}m4zMn>no1{iQ;Ti zN*^Ns7-vcGA44!c^a zoz4BXT}}bj7ju(Mi%TomUx8hhn1mAT@bU2uTua7flVwAMD&iagx_NjTcT;`C2-*V; z-OI&u#Iwaa!HdEVBWS|q$Ct)WCm>RKsMs93K#U@W-p3NMhU0}jkKnKJGsM(Rc+GK9uYSH$gDKJ1G4<7z2)gNcx$!y^eys|c{QRyw(=Bq zaBe_v9#Gm_hi} z&Fxa`Xzp~K4@>QLh@E)Ehz-prC%qe$z~wEX~Z$T!<{Q%eApV!p-o8`Mtc5=M4wJSxF z(`OEuE~z=+KXZAdZ9o18@02L8-Jm^3Zud4|t?;OCPBS@uNI+kJ%EAJZ{LW_8@!}`O z$$gsRQtU*w^{L18t4`P33E~90PcBl+ZQw437LVbJslNHNPtO)s7k+m*d4F=6@Txne z`e7**F%tfH|HJYw#?`&^ozLi>O_KQ}r^ob+3jy0FfA+WMzOAagPk5RTmO#j;CYS4* ze6_LoW3NFKmN2?-fj5T z5cNaj2fxTy5h}YJyMs=PQ@ZD$!r?hf^5DI=vRd6Ibq9k@XsEQX9Z1PlXz-ppN&uFs!o3=Ith0Rn}I zZ91j<^>?!q6C9!k1pq$|06>NUz{TAbavK2N3If266#z(O005O+_Gew0yTrZMnrh0x zZA8LI=UqhT1~K-$L&*O#)j=olokQTI4pkvoy+;MYdH9h#=je{cqOPm}^O?iu$kiT0 zD82@T7|h`lYJrGN25S@TEw3Kv>Yg7F2XN0k;{H@DGU`o^;N=3i4d+<{{Ao*9Kx}zd zD9C($9JGGaK#62|p;tWjg9NxA!`!bTS}zM8&pymPKOPZE>j-JN&F)iF-oSLH_h7a_ zqHc?AY;Tv$^d!c&U}MMJO_~a?9n9s!V|&3<`#QEA zY0TdR8N1)GAXO|(uE4vT(U#$HTjqd=>a5S?JJZq=qtYXLolr`*gtv-AzaIJ&!N8^X ztvf+}v(~Jzj^oOpy>C|25;?kJplbbG<8wW2oc;*B0M*&QUDBVh3>f4%7hS>7R^`pC z1D=fSW>yDQR|Z0R;Z0oa*!Pv`tJN}m-g)FIV?dlH zVkGE%%>70mF(5uh51#k$c0DgWzRIALnIoo-DajaGDhDSX{06_UbOHLwQ_P;rr|2D` z<0p6+HugJWCl8~du`CZr!8386uSF}$qRNr2+$+D^LTH4ZKykG3@~;P^Y13@MD!dib z1Ii;t`WU-myxhvGmV3KTB|06D8AZbWLAvC)@G$y_M1`>nm?k` ziW0OQ2IOhWPTO#J786AJ{7BYqSh|EmXU*4pUh}86$_Wqe{;gB;TANlL8AOJ^oNr-c zQ|=;r+&pV;_nx!CTZ0F*Kltc}_qG=*AIsv%H(cYy^eSr6vTpWfPj55HOVWr)0mN(H#e=(-g-qQp-uz~eTU+NAhrDgh0+6^Cjhx;%ztGZb z{L}Qzw-h@PgF1aI=qr1`3AN= z)r7r_C{^0j;A(N?nGTPPyLz~74Sa$LRNSTcU12q!_BdQ%HI;zGd;7C5siD;NXR&!% z;V5%17IGJ(W^~?u{S=-4fUSj9ed`057srYGudOZb_W(|$x>4DlksrzPAadOn5N4R(1Xh#EE_CqqLv@EB5vgw7 z)F<;xuP`;X3$~$jC7UiM79N8Wg?7I})y=i|0j+KWeMjpz@Pk<$nnUMJbKRU2AxYhd z=!wX}-R*x7ttPu6Sp31$D|v>3mXwxX{57>=+_%Zge|}WXqWS7a1CW%##(C6SD<3|p zcvJhv9ld31CITSwBHJW3RA5T~d>wE3U!VC{bm%?~{VUJfX1D+Oo`;=gRz#U^RzP+j z+5^zOZ_-q%;Z#cbeaz8X$(al9S)Vp5x7$S1XEA9RI)s_mM1@dze=qy=<5UKV(OK|EP+VaH>@ z6?&Q-q_7{C$!Yh+T#_-o;HkSZWA_CGK}%&#eVE+w`F&psYiCw6`QQ4PUJb;=e;96Q zm>VMti9ev-K$TmR~-?*3+Y2JT-a0Mb)(g!VD&rVWKBJAhL2GxGPQ$826Gr!=l>+u=zpb~RsXI%s z^g}3lrEP0e#tYhb1ff30H)rfb_DPGKU%IGfUqUETqUL~DiE0AN zo2%7!VD@jVh7=cqIhZ#kzhC=zSodf=S1m3JNtkmUqSS0Ut&U{bgHso6GiAK(rX9|_ zve6Xg_PwnAjvJ2tx3k{th&9O|an-R(4l~qjM^m6TMvR@);t z*w{t!rRbN2{e##h28=~XCNEU69lMX`zyhj!`|o(EQ8x826Oy7)kR_L|E0R5Jr>WKT z6eanQ5zRCImoV(s8!r|9Yf2nh-M2uTX^3i1n8c3=N@82bND)w1!nc>^d|yS}#J f7ZDI-Qqj>@{m*%j<<`1>#{<+=UMSZnS_S_PFkFO! literal 0 HcmV?d00001 diff --git a/lecture_11/mass_springs.svg b/lecture_11/mass_springs.svg new file mode 100644 index 0000000..2bec8a4 --- /dev/null +++ b/lecture_11/mass_springs.svg @@ -0,0 +1,214 @@ + + + + + + + + + + image/svg+xml + + + + + + + + + + + + + + m1 + m2 + m3 + + + m4 + + + + + + + + + diff --git a/lecture_11/nohup.out b/lecture_11/nohup.out new file mode 100644 index 0000000..838862f --- /dev/null +++ b/lecture_11/nohup.out @@ -0,0 +1,2 @@ + +(evince:15386): Gtk-WARNING **: gtk_widget_size_allocate(): attempt to allocate widget with width -71 and height 20 diff --git a/lecture_11/octave-workspace b/lecture_11/octave-workspace new file mode 100644 index 0000000000000000000000000000000000000000..2e1bdfa519a4a95dfba5dc55851ecd65f7eb66fd GIT binary patch literal 178581 zcmWigX*iT`8^$YHQbe?o6j54eQz1^t79mRtDSL}3DTyQ^OQ9%{O7`$a*6e%secz24 zGs6rsZIV>p=l!7L@P+X__kCU0`8&@m1KZoyZua{Q>^r?|`LbopP7q(qmMw7+|2SFS zzIE08-_p{O9r4}&zqnIZv2jZ3M{UHw1h_JfSFgIA z06|<2N{|?V%Yl|VHgB#Wz~AH%`GKqs92C zcrmWUKW#9-+zgchaWl^?GZ0D`y(RN|92IYi?N_;V<7Q%bjLZTBk=2sgRN*A}*8UKX zl&*(owUTi~;Sh3)^B&kX*I@X{n5e+A9GtI--1Q@m3Qvoh`oV3bh`4VqBwsv=wU36w z1T}}jYq`6H^>!BUK9z7Iei)9?#h=HFa^dnq-NRRqhN~|Beanj;g1~9tkCi+mTI(;=ZIi=6zwquv_Evr9WfvFLiYiC?Ci0sh!6y{xP8QyRrB`X&R*VKe5{IrW41j zlWu17&tiDlw8?IZ2^_LE=C`NZg45KMT~ofr0{+Qj@XE#CJ!d!qT3F4I<*0L3Tg)bOet{Mdu_9Y;0!dM zm@(tEoAI-#c0lRFG-}e*%yzyTN9I_^p!}R7kEy#(R>U?|27ZZ{Cz=Gc}1< z15?6=>|O|OE_OLco`F4ky}z>WG#t2din^~&;g(U5G0hH`c1=hY+( z?HOl8d~HO^TD7vhE0Tj`U)&CCiUU+%@Hi=SVaf9L}>iu2CtPeTZ}RJh`mGZT{y2ZL%h z%tF`y{+>kTY?%BpaVsRAUoP*v&qDv*L6Cpi@ATz8$W7D`9M@rCac@~iK*Kn!8~0r= z&Y&Y9sA}&=^-(C*wH(cHE5@?M<@b|Dn20a<$j0bre0!)y5@{WB;_Ba;Lri~^ap(6Q$`T$*=3Emu|_ZdW;c=c2K+Tx@5q&zw>%?_E9(95v#g(5!l!Zu+mwkP!r(k>K z#$TojDt5ko`$RxJ$G;y8=me>RJ$wr zcpJxfB70y0u%9yjmPo}VwPmXW50D^{emJ2sViG~-*>~K(^yAXcYb1}A6ezgrM_u=s z!2YAnd#+|MVcHwuQztrw0jVUm(_T90W%tFVS5RSc{ZQyR=_$PH=l$?NhJt&RoBke? zAB9oh>Z~1;6s%k5yZ!4+71*86*X)>_!s$P4+IwG5;>5-Drb^lrIM>~~_RD-6mT%v@ z5De_ZY=GLeO)E#xv-YRi%g#wiQs3>N&&*;X(&e6E+$>t(wnf!lBSAGuJl^^xQSX9% z18lr{@g)5FhLaq_uqj^gvg|(b^EdLY#B(ZQ#7&jH+jZglb-jyHTSpM4KRHUaVdM3J zqNt7kBg|Hgm`#jygX7X|hx{``(2Q!UIzwYY-kR%Yut-0oYWMbR-a3xUUH$tu&CbHX zLNeNG^L4oDhz&o9XTl-kXtqHgXk@0yIN+xvs2WQTC6b8l0X zLI*6BcNu3BbHms9sK{b98bCtiW)`n`QD$qm*~i4{dcxszyt8VDg_)Y)`jU04rvcTfCEK9vK5BH1UaJtndC{6OQnwjP88 z$`1SRF>yrZ-=y%?&+wNxr?*Ukj1$iC7CzyFNIqp{3R$awxaZ988C8bi-cTydYk_mH%&T!kc} z($=V4vK_+N5?`x!i5c|0IzVYX^Z_2d{PjchD(uRizIkuUBvL=slEU(sFg{!9^&x=h zcP^>ST;g+Xe0J#Bj)PrLepAq*szXKKy4`LETxYQDki!Z=?OBu`6=;k}%U;!1<4zx$}jDSABn&x8)Kysh!;u8e>`c)9T9 z6_qeCTQL#xo{b|yS8wc6Xu`*5kjka8Aziazb(VO(zK70Q?e?yPtx8R%VMQTkRVwbc zuVTV;XuNAAEWgWenH#BBp6LF_^gbyR&@vZqNFR&ns>R963pb?TdzT+dpjd zFBaMuHFV)rHvg(0yGL=Bbgs~9U9*xzk!1LS7kWo4W^;(DU_@hIz!w$!;PPL zSs2SQyK=2`1_rs0Dml!C&~D(sO)(mVQlZn%@Ao@U(RIddv-%V~6&_u7B(dPzc-M8} z0|TB#M$SjGspv~c-eC535+)hBp^C8-tUj!!b>`|2L{xvYI?@=pFZgBqc0&^WQ6E+h z%+w*jSln-XBMrG;tMx>x^DsByEhP1E6p`9dEd}N&2nsl&yKcS@UF*2Sl^;(+e#$Sf zhN$nE*Hw3}yHA0?++)ve24tA;P12ZH--@{trMWMkjiXApQ`ba)1P-N=psY!Q#EPp~ z|M^y;i2H#^==N^#$^AA@`4)j?tLE2r%+gTwL?BsQp%b3b;SO_yQ*e4L(dNR{g+@)j z^8Lv&fSfj+}Z!!ei^I^?UXtLUQfJ4bS%GLO)gLP1-T3&uYp#=_xkG}9T>#_2&{vcUz5;mW*w&a-C;*?@ee(F&&9IgIqQs2Y| z+10--<9!qOlz*uPEXLsCt=0m%G7BB9;c`j8==l6I{J*~vJ(wN3R9Tt&3S+!~%i?pY zk-WYs=9q5{^b?$n=QdQq?8o?3zj-QpPydpL+1G{5+=cU6!d>`OIBz0o-vRUbft7xZPQ+NKK2B%Tr@h^)#;F}eFL*jgarLVVqWv+~3&YkOgNmdU;?+SUA z8fL>^D)Uv8VK>B$t=x_~cEdD|Wq3+%7PIxKA$&)sFqBrAbKZ6u$$v{1j@@7&M1HGx z6Gs#d*tpSh)h0pNm0-8P(T`#8!Rq>rohZ6=;*%E9hn|>!IkfHSAY9*F&;}T1*#eCAFbL+8wIKB|7x>_;}_Lsm{!$JKh zxmLG)Zmf+I8#=Au3y-~zpW1g# zL3&S==MA$a91$F#okkk657)R`mJDENmxRb#AEIvsAFU1LX@ySuNiChLOtkZ_-@f5} z7aX_cx06qFq0M7Qo(3&y+M1^JS!K`lt(`bDg}@uh%w`(3cr+X)fGAaEkhC9IR=)Ig!bHS;~OsV|kAw ze=@<_t5G;+T7!x@vV&p}14TyF!>#H>x2@UVz{i~pmTZLf_!twn&eV%cInfZwnl8BS zHiM_)DH7@=8p>1R{RdR)v8ct0-C0tC8{BOtp6+5IeSfhDzsoqH8Ta1UEh1c%qa;?9qVvhe%%78V+#YsXDy^7+s{EvGQw1^4i)?#; zWR``pm%U{U!jl*+GS!H>F#(}F=O4cFAz{Vq{fSr7KVyY^in>^L3y!|G(=Rva$AZ91 z{~tzOSmUUgYf8+mS!=k$Wp53jnfqV-izq6LX`6e39A@$Cn?ThhQO{U0ob8WWYw%i5 zfgE%)5OTO|$Vtp6Wt5}M3hZ$>ZdpNGp*-M@OX%quT-)(T+4M7U-@Qpgv>(3s z8nxWbnnvhc+rmKXB;NVTU6Zk5Zo^-Ai01-K~lczNQERF@}JCuD2IA6UE5mo zVQv7CXI6(v7gb?lK(irHW*XKR{H}dMeYo14Eb)w(D_w*dWDJ&@|{3c)R^A#INA%@9KAofi{8PODsvvR-_il2x-TFZRhsNI8ZSyR&c0cfN@Ml9PTdDTTk7683 z-^Axa{)l52u7^d-kzsJk(ex*C4CD6k6bO?^+}6KA2K zL^R_se?OL1&+H+SCtxY;tUpflcaNGSX|Hvyxc4m}MC@J{zFyIqu|G`+ z*m!-%8ls=SR~IBHCJ|h7jrMWZ-Lv?5>xudr2|^c^4Dc#_9LEFo^ASHDRzp0@{P_6P z5X2fz4~bgN;HY9*Nc5qx#qNXMG(_8U={4;dLdkf3zm{(iA{H|0x6sP5Mf8zM?ji$fbr@LC?DMdi8hSOuH5(qPFZtJ5*JHlG>!I5F5ilpcCmM;mkYRgMZQDC4oO{Lg z$~R2Ie?WD!(M3XU3Tv#)s~UmruG?I`%#Roz$ou`0I*B63Jv?>lJqW0@`53=r02?MY zWUmlv!QX$Y<&rT5(y5s{**}Q6ORjv`*HvVgP|9?9?5NNe=2xf}q@rZ<`Eg5af^Wuo zEu{1mAl$@q+G4y0sUwugTw5lbM#XM!k7i>7Z8>jBYBP>_O9iy*H^So1_bxgLK$Tiw{|ee}bs#VF8lexP&X9K*5?@?sX;vT*r^OL3VyuXEv9pr z1i9}Yt?V~Uqb)2{@zo6~L}M1h`tzyytsXd)^|1l8g2_>kTTsrgD$$c z2>#+s)qXgQy+sWh-PETsyXD72qtX}@WmShgJW2=q5Yr@2J zXJP;FvUJ^=9{ks0M~d6R#?!DrJ8FCw(7Gs~`n$Ow>kn1sMe>a!@}9B4bK7>*y43wM ziJU-}ikkOOY9n;Q%gck!=~y?KTBbckL)Tu3O%Viluso~!c+2J)7>fHpvo0LKo*0Hk z;PnA`3I0j_);|o%4}qO)EBf%hM&77u8^I^?x+~U6_M!gH>H&#?9vqc;8T94DBTj2S*Vw%S#556Jg zpRWI5K`khBbb;WZmVLe7RxtX}T|I2wU_OF%Wp9VVZ`OfpModBDYb`?OGWT_cu(6mL zD*Z};4a*0-{Eb9?XyP(|@!$jvpIZweBgn%z`!h65CS(L>D5I60_h+D-g>NjmNr*f4 z?wJ2eN2|T)zn|{W$lN@4LCU=e-`79e)BCm;MnQ6M1{Fqm@!vhGc zwKaM1gbBGMUz3VTVh%Fu+`v^r^ox4`+q2bONMEXKoxM4Py9*!th-pRwj(0>-| zFFw?{M(#!d$8Y}Jj0|uskb0DKQ;^(xeTQ0TI!1fFT9*GJIDbQ8;9_DMA}n9+5SH#m zTf4aw$2{Tpl--o{3TNP@+R95y#hs|gT5sS{I07k7h10?Wx74g#??=5;g9)+e$Abwo z$WVOo^%R5911H^rmhGN~uA$XLjYBWa25tYca+tW!##wi@dGhf%{FYm*Ne1k7*L<^2 zB<5E04+~v>{djfNIMZ}-6nw%TtFNq?L5Q(L_qF;-?8&$;J>!#$ikiNT*a<4`@OM{@ z)sTqy)p2IO>J-Au4KrhFs_{8i)xc-#B;H+nd-?=_E6QK|%TGDi0J#%w0;hvWNS{&l zyha{Dz_kazeJ#czZ*rnOV2Xqwr8RB3*Qa32+H_G-t`rj)(xX)|Jy7~{|FU!k1u^@- z80}@0Ax&8_&)>ThC){)+Vy$R+&vU?fUHU9Ce6u!XeVfMfD&vlM-fmdV-nSPcbhy{f zIO*d$Y*3BQeLE*i!OJb&4T%SbAmn~2xaA%LRrbl}`Xx!2AGj9FH#&*&E2G@2ya!>N zb>mIF92IRzxt*3D8HiapAG@63q?>QtE33_zChFwN;i95ud}@`W#C{)v#Cex`&Y@;3 z=w7;_`m-Bavg$VULI!fHB77_)%W(MP8xzq~Ha4||pDrYHQPhn4gA<3z(0Enf&{)%h zeV=nD4wUv_)#qjX3(q>SkVyNPmO6&;H!b&U6q`Y`l;!CJFO1wK-v3ZH4G!W<;ZN4E zvAun~%gU96vTn+yS-XB@wy(Rwl|;Em}AY&J(j1+r0bHa{c|UEo+$=x~LR* z_D(g-^Up-HxT{gZJ{t06%_zE;XEogaISmi2Q~nh&fsp3GoUW=^xT$Soo()Kb?U!@8 zE^haK2bLrp739MheEkF73N2@fqj#m)#fN(E|qida>5;c63`uZY&>} z!GDHDhm$(l@H_f?!FoLd%G}$&t8Six)b`N$qPKnU5EPwad(GnZPW}U}>=}HDH46W@ zjo^AOQe?MZ&O`nV=U0YBT}a!QbYeK50r&T*`meMl!*gBGuk3+rBpK`~NRk}H&C*L7 zH3_|Hv+q{A^W!G?2R^PeXkcLRh=ommEeTA^)?{6$5g5m|KPg)Lh$?fV6^?IaaBJG5qf;aesm=qR8J}k{o*c=?d3_Y}{NY?%=lgM> zQ=(Ov)C0-)sndx{6_}qpU@FYZhK$(t=a)8-@$y;qJ=2~ZlpNFU{YU$R)joUXOWrf! zZL|F?wQ~wdFE;b9Eeoz!<=}SIHx8JL(_-!GB*X{z4O|>auo({Hq>~ZNg?!zsw(B$%~9B#zxHTx zZ!Ox_s+QZl>w|&vihHAc!+0dJE=<0Wj{R!YFXCNh;bZYE#E$4Ub=(|6A)D%e6XdC| zMS^ELRa>Y#Wx*#rU#RkXC!PxqFBmD&k)rJ?M)e*A*NX1jrkUw@$JpAjPKfXc9D{f| zR?cGQi(k9`lb|B$9^F%Yi10}w&L0;W?n7|HU(H&b7JR$4an*BD3pyC?Ud*F}zn357Lcy@If4$v*L+ zg1P1O$I-NG!Y5D-6c(pK`DW!>H3=3KHKE!-QhqmJGHTBw47}Q&KqT6!>eFek6Tfb1Sw)v{F zhwdou6z%ELlJCYLm4-sgi;JFL&nu_TcbFqwsncqVILD z;(j_e30vvjpH@w!aE*`Teg2M3+?NOwJJ}8-HtnxZDV@f{m}^pWJAylIJu71{G>w$S z7uIfsPZL|h`g(}CPnQyNz@QKJXY!%^Jqe_8n z$?^)T8amEi;xdhErDI68tZ8Xg3%I$;^zP@=5$dV+_L<`#iN+;jeB;F8=J10hNn)s-QG9l zxK|w{xSi;;scDi02D=B*@h|dK_)|K;fx7Eyf}>!a39)7#X@i;IkW^>V2+pr4^3iG~ z?%Q3-Qt_}P$Xz{DmUw!U;5{u|HoyDPb0Kcnl;BT|tznfP^2Sjq>>YUj-V9tbR(=+Z zu0VT;s8SB02fL{!HEL3Gks@etXKy(jH`?4TUCg3j;~vk{YND?vTRl7Ltric3(ADFG z#Qc72UikYe;@k$(52t-nA;VO>K_h##3DW2Pu}GP%*nju_SaA9zrut3?9ojX4w$Tv3 zi9HOkGOdR4qgWt&)vP(Yp%pJ~i&~$ICHVFIH*SBOiMiwCzno9ci2kR}IrvSN4O#2k zkt#g3xFHvpCP>t4DUIZ&Of5G4Mu!W|HPf+)bXYQi=tDJH6E}xGkf45?`dt|o^mGg2}d$N32VKI#|Za)RrnV&_{Oi=tvk>O0q?iT=9`&lHR5*@{%DDz zCJhN^l^|FIzfodU4Wr&(kXd$N3~2`q_K>+)=vvRHiRUB1>)yV%%>5$}Zk={A*hKJ- zFNKn-)}wIX+<7;$W&-v{a;ZjMb&|L1CM`r57{rzz?f`geZ*lp zjubMCrm555_$uyKNpO6ZEvZlyD6G1n{v_1qi;j zRv`IrxYYV`8W8fZ5Lj4e-pmtH;mOed-|jQ4I%4P_R&dl z2NueQWo!vQzh}!6;amPBtf>sBEtjT1h2^x8b-NzI&L3r534Xa?Uuvd#ZWxbWk813W z&mis@Ydnlng|;%TJ{$QKJc$av@-KtPLzpLiP4i$u`BY?=>k$?PPYjl-^HE@6bXI!u zDsg|xSj?=eJxJ%)e34K1_kZWQBDb~lV_SMjMt|W9^jC0QI{mg0(jkIl4DcPpHKN5ctWdVL@_6DOOgL8*ax*c@>9i~LR+B*L0v zRy=A#r{cwgPu4_#-M8AWZ~rK~4I<@h%RAA+mXYJJron-|)}OYr4nvcQEzU&W`I-9A zE{X7MZE6g7^%Cn~^h`B)V8sLuc3zAkzi!3P%-kBu=Om0j^zXiRg@M)|ar+s%CfKoK zmZLS3&>aeIN0t-!sL21)J)|hGmYasMdX?_X4KpazTG)GYCy~GKJ=FBIz7a{pI2ydV9}ldKmu3B^ zf``nu3ywtItgT(O=&=tSp38D}eDEN6mWUW7W(~p5YA#-0-!=@j#|MKA)0^=1H{Ur$ z%`se(6}oox4Z(d2K8ZZ>Pe2`u zXkQr#2j+Qnp55+(>}rm0d`)z`l>K_=MZgq7bH<-dWHDf(n!e+N&kTlCPuWLS($Q46 zNOByk#jo%^d}Tx)P2q#7;e`|;Z{*)ov{jCcoPcdXKSOCS=CE7tbz=&9g8%vTUCV{( z*u(i=!CB-sSJr87C;W&nR|WV#OrbfxF~8QDjY9*LLzcY-h*|r*XoGVp9xorRxc#FJ zVU1j|T&sxZ+JEieWZh-Bcpr1G=$-__F7t1oQ$4N@59|n? zh2q}8eJUJvU?eN}UVcU7p43X61dlhu<4@WT|KwJ*1&c9PUTH#W<&!%v)g!U|-iVV@ zU_Y89rQ=R&kYQw7C3|yaHL{rQwr5U^BHXS${6pt7a!+(ynFLH?dd|n=p>7ZKoS2_j zR?pFTL&U_;jnE}89M+AUe*>}j=_DH>ujcjd(mCaUNw^l@nT#muhvhyai9n)%mox>X zbkvsP$2YUHnK4W-JuVrE6ZxjzyC!10cFiD;&s~3LbOL@Mwwhj>SrDzfa?6{@Q5^X$ z;z~~YfV(zTiNXMHXp||tyYCAT@AFSX#KSJ>R zzh~z2S9jp$1Cy#Tf)B)ew|=3`Uyi!$3~??EA`dY3RIN{(4Vq$1p0{^)1d#7Tu^vV=Y;{iR#lM&w(EsZrA*IfLL;IREv_z!ch-l7=cCbVFBdua(Ws zBDh^XmbLFc8rJ9DxstGU2u(-A%sC&lXvmwJ*Nu zz8V3?ma?^u_dgN+>o%?TVjl!3V=f;yQ(&@PL1OQtY1n>Xm*)|F(%qmJB2D4rxMn(~ zy7*)o{}NyC7+6L__wll=ON04X^)*aA#AFq3jiv?&>PPLtTv&xyQV@so~^Id$k8_R`(8n#i3w zsHxuOnMTAQM`qWn9`Mqh>a~tBU|n=HR`Ui4ksl{hC*m3K;^W*&+0~6Gk0ZJ-TPI=k zMDN-=0VaO&PE0=h<)wy9 z*vtQxOuW&B)|YOFj}raI^U_7x0Fg0BW~vzfweE)(U74L_I)m3FjoaP|^)Tan;L&<+ z5HfwmvXAv6Gje0^W zJIT0gc4BflF{fNKK7FgOlY#csV(DSG9waL}`e=M2xa*DerT;EbaBXSN%y@7$6#iBG zari>y3pVc$mvOv|!};@O*}BtMocM8Bx+e!^x5w_x4vu5tQ1UnDjZAPKp4G|TLgdSK z+wc}ncVaN5xjSK&iM?z1%hHUQu-l{QL0&t9UTyBX`C+5r+%kOEehmduYhBMZZtQ{W z`Sh-LD?g#!kQ$V8i^yHPy7%j#%Ov7&O}NyVR-@*unD!k#B2QgCJAV93J6yu)+_?3$tX1XF8z+1 z(ARSzTlo&nVu-6~Gy5F{LFF|ZZI%oqYhD)(oTMRPv$4VNonxq%IwsRs!iMwk)H&{x z)ey|>ALH^Ifbos}KhAr10y}kurC)X836E;4%}gGeSdVTtK550&bk%!{EHY}!_bWDC zXP{umRD_V_6jnu=j~}d?By>RWKY4C;HiZ!LT>6HB9>+$=e>lEP>~|j=bxM5v z4tRqn-4md@JIkvhy>d?7uvd<>5t?Yt8Cf(hAGZV9I(+93M&+salVXL!)b!lRkU z%lq$`U$o&P!;tgU71rJk@aa4Lmb%;tig8p}_?vw6HLrfqdc6g&?xvp)H=o67X<5IM zCPc0?xVnhvMKd;zB_6kHC*j=j{Qtr>41v1ykHyNzWX#$w`>Q_n5|=H1I3~Xtf%CJJ z^U^6)Y{~VnAQu8{+x-`Cef7KH^rdQcr`E2q#-L_3-8Nh3|QRRE*7^vG>lqkt$;`gHi!KaD+ zfPB@#Z&@Fa}#;Wo&tS` zQW|(T`94|`{k-m-xb118ZyNawX?B=2Bj8bNc9>>29JE*XKV6lMup8~&>up%T@d!cD zDk`3h^Tl#HPlM88CGyRXV**`56`6yp8YN=@e+Wr?+4HOgyig;IKK7PRv_fyUm~Ve;<2czPqp+)q|Sx zU;W!*pL~)mO8BJf)%F)po*BmSuRqVN^zFl|{x{kSM4bz45?H@qgn~^6jW1mEV?vkn zX|U^QHr%*NcL6qg=H#VlL>Yh_E1|H}a}0`RoL$1DE}h@UBC2 zi{Zja#TkfE4TnThdlC9A^o#9(1RpkPlH}qca`mx$touT(D#E*WPwtwzT&(?cM7y?o5G_V?9y?CYB1>leP*lwjo_C3|H)ZxhU)he-B0+=KNp0;@ zqSGik=68ql=n(8~Cg^MDR@@J7z%LnY=C?8;hmqdmTT)5nk+lUj zDg5d~hDy2Mt@bfQ`02$s)t14e)cC(mqXcJ~sSY~vU=St$$qj`T=A(Iou94C4G3*WO z|H0fli#d;QZ-d}*m{+!M&-)dI4bn-~{yNRz+Om`L<-KMk&oj=flp%7Q9pQ=o4gK)X zmQM}#>&EN9lmquN{4w?+^@8adI!>v?q|`heh4QFytrg)jX2fyx7c~ze@(pijPj4p3 z-dPS=gl=tLy{sVZ774@R!ZOnb3lOrrCV);K$8N_e*B`coZ$t5s;)xnU?&FqBuRDa^ zxbG7zrkM}3Gio~4I~WL;ceBX!tA~8{;h;o!B2N=gqw(l{4y=2g+;=8&RdXhNVmyQ{ z-uEG5b$)UreC>5RbVHhP+gCOH&BYnCt(d4RQ6-_eV{_OWx6jB8yDt*++ygyv7xSO@ zF%elcc|lnq3%`pE+njH;frGv5@bTdhM5iPwh+Le4&W=~x&KlLD+w8vBh2lcY^h@V@ z5&7byGJV2SA`hiSi+azgM21BEn|IxWF5p@)z{ov9KR#J{y>ge~Oce6;3S1digJ`ZlYT&4`w8<72;V$-}Zj=fIV zULPVR5gI*Z;Gxli=gULm2UA9&`DL=+>qjDyThY(ELilQtrw6yy+oYjjn}qjPqc|9D z$o~3Iqze)UI$u2sBjK>)tAu_cub7};R=GcA1U1`t8d3CfV7SLvt6*gp)Xh^mzq>Gz zvn;|chscv%n^pR2yI7BmPQ$x%gf6kzQ}OVS7_Gr*m3{bBTS3*9qq$o_1nddah!f z=OEJZ_%EmZnS{%j#9hUGQ&{|V%PB5!2(G(JuOy!yKyE}q`oiT7?2#+o4`w%ZZ!UUs zgUE-S9VIzCukAs!r|HGYFDzI#e|M=pHICK1r*4IF^+VT3k)z}v2_@AMho$mLaKMm< z$L>!TGR~%wLSwqYwK918pLr&j^pSk7tdH=Sh_s|P6FGuon_pz9QJ}X}Mc<(pi>+nh z1J{ULcm8?xdmLt6h|oWsF;iX$x!L)j4mbN@cwgFWitrCB+I|HdAoj;Lsy`4^pPt0w z#*~^vZj;DfYm_BFHw%$m>Rs>kvrt$Q!2Q~iiY65;1xKRqTblZn7E*^$$HmL0Ei~hr z-u+t?jdu8ZUS(}=o5B@A?U<+`I(oz3KjtBF+%n|+ln(!4c;{0a2iA{a>+;y@w_S~J z)*;(971ki)hW+LI#$hOTkTmUyKB2IB@a(gRQ8a%(a^GvN0GcNr$TU1A>g{TSbrgMK zFYpfG|GXw4o432)hlhax+pfkhs)RnF=)u zB3Gi>p1t+p8w{;#?VkEd%z@)Fvd^-KJuLx_*zan&VC8o%t0DAn=5h9@Yjh)oJRLd{ z*u**AeeCDxHp1VSD5?KwTLsO{5>jp*lV}QC9wJNZ4;8z4i099@LrOJhq}gf~1zSpG zbdNQmVqEoheQEXzly5xa!paHtK(n)HY$Fx?*WUI++5Ag&PjtNkpE<*soA=O)sH0CL*nh z88~E=X{PDng&SF)xs`Tx!B(`vAz^MDO_w(|sOz=i6hCc{GDE??bEP*-1zNCRX|U&9 zF5%aT3E#<9YXa?di<Av-=TO2{GEai#Ov!}r9@E; zB7A^9{#EuNjbuEH8~yf7iH*GA}zy|UvTLn2q3J$IrS5g+PK6%P#KC!N)N zFrgYNKKawvttaE%{65W?VOtVX?I2g!gC(E{RMxyyK@JXU00{WKJ_q549_4Sxw{J zoL==;<^;}a>@y!D-fREh>z|gq4ERmBrZm2$ zi_H*EBJ%4>W?}~JSMrE_te%esk@t&;wk!~j9)*^CYH@_#0Jd5*@-01YMQaKD6Iav} zl*{XuPuumN#=(gz-iifVKI1laWGA*<{rRPX*zX7%lw>(i;l7Hmjpu_Nmj=;)?dYs_r!hD1j$!;qH-d71|4jWQJ+ zzk{9r65Or!?*S|-knxw}oE*82*njamCZ*3usqDW3 z{Mf|(uk{d{*k2Hj5?8JJT};mk{UG*Ob#6MoOIT5h zZ)VT6A39G$El^vQ?-d2_0#;gf2-G2{Vac7W)P;rQr26H{r@)Z*d6?2wiGM|^=^DzP zG2QA^RA)>fa>AET6W@%*lV5L*?x(|OCM50O1vYLp+|apjk;th9Ox~6EtboO~%Eq5n zy=YX_zhXW?N9@hKUm8STvvVHbv@(Xs^PKx|VS!9W#5utjayj};&1nrkB z`lZc=X-6Q>A0lr$^tyN>$AtjAQhxAe7xA82AO6*o>o&oFh3tj>@-);t2`4S7vk`k- zG{Ud23nf0sG(#SBNHxuZW=2Y^FB)D*y z?EYn(b*S?x?~U(fAdyki*GOB7ZGe54|6 zyQbtq92Fau8{Z8lIHc{F)9nkt2;YKt=*0Z-c4CfWDR3Sp_M87`M8vp#fTQDO$D1i- zNI&0narP(!LR{x|kQRu%nv7xijy5XH{7e)2363iICuZvo;yq{_T$Q)wOh2AKmztDj zb>op;(N3*(Bw`;X;N%FgZ`QP+CV2HZ!K0a6me;=15s=ch&2hRPYC_|lmvac;J4>ta zyg9*1HC;0sj!|%`dN8({s6T=^Or!7i#Q$GV5n&9k#rIap$zbaX=g{A9=y{!Gb zmf@TG@Pw*#=$>&t9y~QZO|PxOH;#*=JBb|P?1zG-GaE*cB|95Z!6I@ZH?Ac2l{O>y zZr;i^w^DF4tmN^XFUK9XWr@Yfy?E@^bHRkz-*V<=^F3nJ!*0#zxB1Bg=gQz&Q!q`& zmz(BV|mO>gVMj^9^Ow$71pFsLQNq_&mtQB_F+?=#_&E7*N; zn1bgnDocyj#QuDf7FpPI7Ml4zscNg+;qA@ujl& z9@%?m@4fe4k4-X5_?_QhuCA_&$K!tP`*Ysobt+|MY*hXXK;_lfe-c%4fk?$U=JpEa zT1nc&Gl#38RMM^cl=K+P3Z=$|N}vu^KKs)rvHW1fN|@!x@0 zop`O5&rMM5Uj*sBOx7~fhD2$$A(Z(oG#bcUkDn7NFyzh z`g5Id;L+uO!gSbAk7fu-bRU8T$6lUZLj5@Q6t9ID=2^ao#-)GlU4S<>+Cs+HFn=n% z94+iS4aO30F9=~Sq-gBb)(!0pSc>piv={S*@@VZJuh3`WGN;h`b`E`*P_5X067*Y6 z)kpq* zv~!^SIL818NJ?HeEuMwkq(`f5w^PC0LZdsfA`58y_c$zP`@rR|PQWefbG>+SAg42B z3f`FxWQk%g{qD_yQ;bh%Kr`{#R6HN%^2un}G$hl(&%pEfen$=DX@u(u)Gxpvk-78A zdA&e2aOAAP??uS?X!i33K2I6di{uuo7y!@5qKKjhno@|m=hd?E1;Poet4$zSM z*zCbQ12H$0=Xo`kVfUJ|T~_TNlrn@FF;?|pPpaBosj3^o782vAg)4x~>Y;s|SRXiw z20!V(+X+AI#k}Mcu%Alp9ZWkq4(8`h_qSRTyXj&qsk`~=C6LZ$w9nZT7&yRLj+E0W2yw3U=g>op8%Gj!1$pZSrGVfJJhoH42jK9-l z0vv=Je>_aZJ|NrT$sC-62~^&CTc;P`^@+SD8?8yWc=vB!|H3Rhy{{QEI4}yEdmJ&x zE;d2YHLAAL`IFF*9P`Iwu>pGitE@fws2ql`t)>Rk^g@lo9F-eS8sxaw8Uz&JJXG-N z$BEy$@ToD9I5e;g%EhOj8d~6U^@`eY9rMddCkw zG~E{qNL_*QHYp2DheaTFPFbw>nE=yN1;#&pE#UTgwLNB}2FeP!+)6d(Ako?-zwZ1j zSgg;5bXb&u#R<9o3z+MS&sWK3m{1^Ua{%Fh|lcw3iEM1Wn1Sq3Clww298)#2#7|fob$(3y4*!1(`?B z!9ZFBMWewN@Jnj?F1x=7I*Q88OTU(YC0m|<#Iy^tzds8sW19vnkKBvGUd|WOx-(&| zcrJGmEt=WD_jj>qTjfY6q}T)n%y%P4fyCUm*LVbY1*EgK_qw4bPMNJFu?hkb)|J;X z7U0`OA_HA~PQ4a4e>wMj1$4cgEw_jo!6+i8RJRNJg)&o{8^Uu?%xYdgWj6%((o*sb z&QF0x+!9-@=^~uC`r33P6Yozd`7MTev!LS}PM-335Xw6eeY?_o;d8J5+jY4GC^*vc zZRlJ(?Eaq3y@$Eq&~+M-bnJV-w;NztJiH81!v9WEl2?HCs6i;fWD4{p=M@B`@%jr2 z9=M(`2KpL(&iQKzFn-mU`;Yz%h?~o8y!$l^`p<{sbTkqn=ET&ufrcq4%$_^;@Mx7 z>V0Vik=@4PFBVH+mS^f8lHLG`x2^tK-EIQMeG}a?HCb@&RxQn;8$aMS|NCf#dd#P< z?OiEIYJ;an!h(-%=fUEp^)=#}1lZ0oZm(LN0Ip)r;{?3^jwiUfCg2<&cA|u4|N9cm ztyP{hxPm^%-^onD7y`6i`o(I2_XUM35R;#13kcQtjJ82)(E53inlrS2Ovl5K*M`B z)L~9`E2J#Xf{*IR(PvcXkCI0+s@t}}u)*Mli!tW?oF5yTa#Vukt8g}9)U|W64_p6G zTm%ZqYl4%V-Jt#Xnp4l+UO02%lP?`iVjeZxgcI}mqZjT+J?a?;dD;1a((Nf&eCy58 zi#@~Kl*IGZmDv9yiJ%H?OM!*2%h~#;ksFjfVitH|49?tGvR-wbgNE&i{d4FO(X<%- z_6-_=VPCl(70laG*vdq)P2zcGTgv_s1LguW=90KoJ7E0lETK!j4=f~k6U_d_fpY!h zuXV}T6J<}X*T=l+a?0$OLPjO{vei``l^%deqr-26mypZ!VZ~$kLlh+S{>;3sIt+B| zOw4o-X@cQF--dt;(;~W&fNF<~G6hM;v2(O=1 z%Ng_QrqwX*eC*hcQ8&Pea`~&@yMg_Q3#X!TD^!Fh4y=1lfg3ANiR9ZRmW)0~o*@7Q#kAizDFMm@U-Qi8qhG^LdUA(n5ju(GZanQB z1HsnKH|wfnV6>FTGI+Hcl8nro=2d&4aoO{N7%y_bSU!w$DAoaWytw}u_C>vKD}Q17 z(hl7+=@)fTSJO9?Wm(_T1=C-CZ(6W7^hfW~mQ2J1oK&#SRP`BzN1P>&Yr;*?S|>Bz zy)*#6^scY#Fn29xp2rv$u?X+y3^RfvCxPbr1&Y>w)B%n%+qKmbz+9sB>`q}RNN-pE zyz93JN`{w0#Nr9yqr@EDbCv)xtFca}JH~;q<#=vju@aIJ*8RT}{sbzK8rH~R^hfCQ zGijKn!SjL6vl~HEK(lM4w%m{NSh-XFp?_oW%E0`PfMzEMzTpnwwH*Z~@g(xG=a?T> z`%mG7=`?I#$&?S#LZ4jd9reYOMX;ai4Lq*44Ci9^&`({0hs-;pLu(B%u0ZK8T{i~x zcYoVa2;(_&n?LdI)oJklOhdZtGXR}+6SacBX28Yr;@|rh%OUs%m5wv^S~cf0z7u`z z2cgTOxAbd!V6|cBNT~84JYf#ln0vbfHGU_*XfC$E#4Ac(_ls3|xdBX_Tjr%9e0TdsngJu8Xk5se+nKc zFR&8wDu6C>mP^;h0Vt09KdFDc0E5cR_U^YauU$r{Gt!ArV!2R6$RXy)azF*@P} z;AjC1E2J|6UdC$SjkjAtyLhxF_x%#=^Lq-ai6AF$H9Vx++6T6_Ub?rz z5|9^%tTJMb4M;xISrtw|uI{{!_wPv99{1%Yq8ta$OKKlB-I~Ds1Z{#EejejqYDt}W z*91{B?5*vzRX}R?;Q>f5gEf#F$Km~5KRz&<^lU5Y-9}>h_2Y2xUd_GT@OgM-dp*h? zef3E9_M(px=o4|Cu5Hm6Le5B0VfW20aA}KgT=$Fv*QW*jo&Cts3H|l+49Ns|luXG= zRQQ8t{Lec~r&eHZ=Bwj-n@YGd3FBV;qae367Z5QY1O_xkgZapNJJxxKM&-x^EF5`z zSC+C1qTZf|p@7(Tu@X-X48iNm#x{Q~^IGn0r=ZN#muZtsK z`)1YY_2xX(r85s$s3RYT&h5BT!8F|VI^{EAi20K>wliR^pN>c~xV|(nxqF-;}SjIt_A(zpEe4jX+=v*&9QA{Vr)Qg)YrT!&a2 zy`d&+f$tlX;_5S9u(0MbO+JWRidbgRfAWiPjR~HK&Mks%Y-qDE&Tm)7mZfgRPQq5T ziEK>HFns^T$p6%~4F-SFGM(Qlg~L2HCr2??vg^Hmac5@&f(BXiWL7`JAfedt5#0i~ zuhDT$WB>2J&UQU}{Qsg+VZFfX`H+0(P3(22NgxEW>Z@neK`wpewG&DS(3s%;g2ZGL z4vQY3?CYNdvukZ$`9TxVe3urN zrD^ah@tAl?oeD+H65{#WIpBAUEBV^nXju5(Yx{v~27m6ts7U)F?6k?hNdK1)9IP!H z&rvU9(s**e{X;A4E0XK9qu$ecVLPchs29W@IdBDvYjK}0wt~TpA9*dN*#G6@ z*>GRz1s9qD#jlE0klR8(FVa#4<$sTRH(>rErQ)jV9_IUOe%`#dL9_&S2Q3bb;+(ci zd!cH%e;Hnk*0*tEZ@`{(p-$-22*`E3CJ1DIgTm?vg<5hvhr6pkwT&DGMolt*Y25*s zAoblpF|Rn!MEVplCxk?Yp1ZE`!Z9!mYQvlr0k96575M7N|CDv581o!3r> z&O|x=#E@)wHpa{>rjGdl#W&7pVsMU6dK>j&+Z3)6|H;^PTYxao9!Sue0>zf|JJIHN zUMVR5ZP{Sr{VSFc-Ty%J17?p+3ClW+gCxqLx^^z1lY@ zP?tVSaCwb=dVvQ5IU)^X@E~6$c(SGfH1b{cMU^{&{wU$!xgXO|@PhDAW*xa!o%>4D zn6I3OH0wLuQwyW@b%yf?$6)AI=-#`;B~WHQVA+O-cRTbO@DT}21 zw#frf>-#*eTMqqu)`LkhhrQr~fD%vke+zK>SGwj|_bM3V;(h;8ANwGGO7wDWOabB7 z1DkZNWl;9laC2Upf@X&LoYTL2!07e~4ld+k{h8406Z|+1Q{zT%r=|%Y>?}0!Q+yuw z{fGL3=O$q|cc?G#9`X`Ov;Q*~nE~#Vx1E`i#qg!gU|5q2&tVq6cIRjD`EMj1sK*%z z!#!sXym;OL4Ps=bX*LsZaK5-A({Bk*(#iH+MZLq(#=49Z`H!naN?Pl0I^bIOw9l?{ z74Q^Yzi)&7=KS-Gn}zr}|KUm3xEDVLjx?8f5?N>A#mexeyhJrH{U#U8Iok~G?5;M_ z#!IlqCfeS41$Fwg)26$ryhD`Fql5LNxI8|=i>u5Gxf%=D0FuhTb#fa~(LU#G3 z?AyqZ8P;$9PTmR5l5t^tMI&I6BXjEUd+eR`-1(GKuncSL2gkc+Fegi&$+|E-i0^Oo z)i2|{u=jz)CMc*LYBCe(#Yie(^GYwp&~ghrXqAm!8*YM;29B$>#&{i^`6m~z(*UNN zdG7{n7h&0WZt>&IS`gik$s+fk1)4HPHhpXKpTCnCrtsmp@5!6dq@$zQlUB+uNM8mG z+Jmp?ao$--r5+Z*^HRDyhm-38)SCxdhTT?>f59wu>wqZg(E*c5<#+l(^}vdDx7M~-BZiIAn*25r82xHofPEaHie828L z2#mu)v6t|3O(_yJb5wa8PQ28q3_DN>^OhX$R|_!j8Z)c*dSf0W&F}4p-Wh@%7RT=% zP9yM+=Uf=4Y(G5RYMJdZ9tS43+4GHx<8W%s`gAaI^x{`m4)m^b9_v{3jjzY%U~2VAHBlm&FxRW18dJ|mAc zrAh2UHTH^?B;vkJg3ckEifH71o;rBrpL1V5=nV8*-1oxg>ZVJnkjpZ#ydtJHDw;=* zXa#4!UmF4R)I(5V2)dwbR5&#~`wkyL~+9QA04#ZOk;ov<}tb&S|%2=fdLtb8Hp zuRV3sV?7xNJP#7vLgXGa3V*waFMnqrw;UfL!7?p5cC<^ z3me=aK%&8AfyAaJV6x%ae~9PsV8d!3!3E@xsQf#1cclb$M_CH@RBGU`R<~iY)C}xM z4b$!6eEn?ikNOf3@(dLcJ3A`-q2%DWQX=-eB=Z{Pnb$|*n4Q$$jAQ9%y7)nIoFQ90^S1n*2q*`L2qw2+=ZR zEY}Yo>skg!qgHJb>=Bbz$5&j9d);PW}7HW!cXma(Iq?lV$@h({~I5@P&nV`rdc+-&yTK zk90IZ<-Tt+OZ70!uon<(5@SwYlUw$MPdesmBE_I}-B}1yFOK_{unPm%2#v`{rSc=+}M=8*+87a50nM`#^h= zrCs1dAKat9+?r>@966Z$mJ{dKV=sQs+KG=Ke~>ed`D-nh z$uGE`%wGno;INAN&O8X+H)NT)gnXwEkx@;9TJY^PtShv@KFX2}rH)?)>`Q)Mc3kfU z8I?oZu9jukM@<@a^__sn*S?AcaLj}K3*j_Px^WnD7brHoIth)n8g7=?X29X;v1aKF ze10`Pxas{9^M3aQuWhysL517Ac=ERjn6$XS=RmOn9GN;iw4B&$pe;Pw`KlSnYg6O~ zABI5Om3Mr6Ar-)1*_=~*qX9PKj80PF`9j*|Q=Jzd^7sx2$(+t<2C{}jQHd=J@F+W# zrsf#-qV#zU1&h1DBwh1y8tM)Pm!^74XvZP3Du3|FNz_Ni3%>1R?y=W4)r{`RDDW2Z z`>-=ipr5^hFLE5z9}cw8kKp^x9?Un^i+x1jmj?TmLoo1GzUXF@J#c({_T9}0eWGqT z*G9}C-#fZD%k!oL&bPf03*at*-6UxPIqVJOK0Z}Sbg2Q{4IWLrx5Au1(|e0~dgMW9 zTFF%^$5(2s(rL z``Y-%Ta}H48e749?w#f6$s{T{2>E%si9|gP&vCVpp@_!2@-kAd3d*z9c{@sx*ap(evYx6q#^dOLOZj=9VVO zY($DTCgI&*3ip554~XPa?@#>N26v6`=j@Tz!anc);jJR%Tckvl-&bA+VoxfD8+WR( z7cTo(=Epep6I_q(RkuUZgM!w8b>x%OwcSbhJ_~;(E~|81M2@9fzsMQaudvIL_%8PU z^ZSzsdiuB-*p)qHcnokR^*aH9Es;op0s-nJh^awOMO(&vwQB(R%h{_oZkYEv z70Z7NzkUk-sP87U0#+1Fccgl;r$Hl~#h055=EV2f42MfVb&uqLQ%oGp)zc)@KIwwj zPa>XN;zZ7Trt}MkQ{E6=P_OXMyblr>!UVOdM`7(wnNw6>KfHZLvr3LR64qEGF9E6(wi(^I3aqhGmg)ZGJY`T#(L~SI(VWrWzbA6PTE`ozwI5iM;2r{pSXNeXCvt@~l`e!pA+kBZ4WI>unQ z_e!*Z^X>}zW{S*FBlvxv_@(M$kL+exZ~$p%CqyKuc@1t%gS^D>rtr`xOi-kb{<$#? zdG+oeU32jL&~nJ2L_cbx-u($Vo{PR(!p~_u2VVZ2`1RpJEo?Y#5_h~GhiCN8x2`E6 zpWG~k_Hj}py!`27KdF%qC5In^@i@*cQlVR^9V;LqPaZgl{!_EWONy2G4ycsI24p}k za4=tZZRI)w9cmjP>~Cuz*pur>(ye|NFqShe$9)MCt9pm-BFBfD-um6Fe>UpL+-H_8 zbFrVe+%bf@VL038)4voafUa}j?F#a|47Q`o{IEaF%T9KjihK^VgWL)d?)8F@sF%1x z+XBq}b2X7k9RfmfkKJ17EOLTh_x!sr9n?Z`*@=z4@1afx?CPuerAv#C$ zpYSuBW0$E1JjT<(TThuxa()Oxvt-oB(vfp6w61)4$_EIF$vHWj4RC`&eoIyhb4yPi zX9)^S!_RNx9{Y`x@K~V3;L|Sxh%!e?`(mE+dt-na&97nDZ*)qLZ(4$76R&mfpA32tm18-r?tU?G_boPRj(j5#qZ zg0atN<&TarF!}cCBB5yzide0vU$ysw`+*VzON_ z9M3POdtY%`r-LSI@eQ+uESRxbo_%y^61+27KEQ!IAWSUShBGF^zjLEWZ+6C^~Z(P`Bt*|X+}2YRySIPe&zf00BzW-tRM;GR!Poq z*uB87SKSh-USgkzWj*iW?;^-O-u}Glzj3&_lTk>xzX+nMLm77H16~vOPS&6m2`=qF zM1#AU!B^!%`7`exD0%N&SBZV`i&ZSDCrg?@!7DuH=KXOXE2%j4dINdZ3)gLXi;E%X z^JS<+f96t?YizgNEZDq_@hq9Z{CWT%xyfWG^mGipSI(@1Q+|Qh73ndTajV>45c9*X zVt2+b9q5DJ7ejlGMhVbtR^wE`i|5Iq-s=JzvrsVfYS^Ts4Sd9H?#H}XfDyq@m412U z@NkfBvy-U|1W6D0FJR9y>w=N~JA--ne3WB-fPWf#MW}h?cSZm&m{8}#cn%nHRdCg- z1V+>QZJ})KFz(8jVK_Ac!Ci&7d6CEPG;#VD)wMy`3z0Og+K>oITH8acPBJ%d*QeT-)f=sUv;{d}X?3hTvq;&z%Q(o9B7(_kYZu!0} z=4Fy9zsSiE<6eN*?UH_;BOov=zxE8DW2@nnH{g_$E=gNamDMKa3esl1WIa@&f&JYlY)GE1kf#s+>&}hq(s6 z5i6ahW@vC%`MinG(LzxN3P<*p9eLE<=i%r)Q8@C?A7Tc!0Zu%cai)8L>hFow_5bVhK1ZmHLYHF zWOAjVE4miW>UY&ii*~@hv4H4R*HJjFu%RSTo(8Wb-{}R%cf%3ogS*<3E3lM9aOtIJ zgXpP=vwEm6edAKLC%ZZaw90DB)3|>{5d=LHun(kCxub71IRqLLoVV$xk@w}UuD*WC zA4JD^j@X{4fYT>tmNuhefRu;vS%=jM2x)rIAIt23ol{GRSKH9f4B&Q$#mwSwhSkwA*nH>bb-EjK+YR<5 z>n8{he6Y*3g+3jMsT&fPjghBRttBwbKLKp^DJdtodm!2-`&>Xh<_%rcd#6$faGqTC zZSCa_m=`anPQSMZgN-uXafdtMtH7Nf#rPbPzF8m>wJd_=#i86R?RMzN z$liT95eq^N?F1I=afMzd{kntvlUxlKz6)>TfZObGTANNboP5MTOND!5$}dwkGZ9aK zMNWBTnlb8KExUnYN?E|gs+FdO9J`y>7n|b^mSJUm;^cXSMKHXw#Br-?269%OI*2CD zLy;b%5mQzvys0nW;K0`rwH-ec;f8r_d&Pc{*>u=Wh!%PH9K>b8RV#0U@0z`%!ZqA|KE%Iwr z{5^7k5B}%3cdZSmi#CW&H5MUc`^!)%_BAz{&3t2a^Mmv_3|}=Ta%yac;qeriFh2AnwyW1&cp70v zS{7P!SK!ns1IyGl%pD&NxcSj!0TMJOk}8Pj;CPMFDwpLLT-oU3s#jToo{vjOAzX>D z<~i?gfpb*uTyVP*_ASh7j|s2I<-qg9+!Er*XFI3mc)^Uj4Wt!nI1`b>wbyK0NY%Lr zNs1q}GeYu#hu@HnMrRVXJN}Sx6)XW?SWy|%w|*F-c<@EscOGuuy?1q>YYc=q;$o!k zw1GqQPT2UN21sx#|7vk~2IP*^c-@W&1ogSBwL;WIny=>1PF|UWHIq+=bB-^;X){aR zrV9=5^^*MBnKqmadM;;nRl7lcWlBKnS;Gi!~#E?MR-@Oe?Px2J^M0U@pOIr(|euPqE`>`8@5 zkA?#ctHZ!boD()cSqXIJ!%YULBiPtfGylkH1k3MrO$RWS!=C!DOf;(j{DTffa8fTo z&-nvIkFKI#{jS=a7kkk1=Ug*bej^8vFM?T&uMg_!eB^Daao-LR8E39lGnm#q44%%Xb*Oi%sJWq;QTagx0qF^f&WQL^|uw67ENa+}DX z9M1udZkt7M0qkpV`ShP`IS5`0QvcyrA&V zpH^%IIvu5iP0toE=*eiZy|@CM&83E(vjaeo+KpG~MBO8PlG|%y87ii_nl;wPKw`;P z;NWO0T(}u!%-e@t=xsT}kEt`zC{_A;IW7+*Cmr*XDRJ-7J9aabx=QGw=FJH4t%BE` zFOFGp%qwL(Qc-@!MKV)$1}lC_*E4YkmY|EG3r^>-tba(fNb+<2aNq(`{9K>4Kos_YEsN0jL&PH>-jMc z&uD(@U1*wzW6z``J&*$}?I>6nMUA~YZ!$L}yzkRT${fz5TfuxJg_OPPAow?1`y^^E zf#VsWhvC?BHqkN6S4*FR1D$ttzaYoci}zgUPh$c+(D2d_v8V?^uSvYWB;HNib+ zlMgn^T~IGjwQPTlzvl^oejl&sF^KQ9SYAHe0TgbWG;DO;FzBLr!oN2kf_#-rpY1w8 z_dz-$f$!}=;9m|g@k3pTt8A+SxqCWEm)m!dFFlxg@?|MZ&58j7)8;qpd zLEod*C-hzvRI)cDF8*DC+n;w+mY6%iFLG2f!nPXvJD;6s#{EiuDkU*jw6^anYQnPe49Vf9xQKG4k_6wCokyf$v+^JED7Spzx=d zOSfwl%r``=n(6Yu>hYJO2gzr^zq_!0uCNz4_s&Qw;B)SSG5hPod(|LUuNYT^_kHb9 zhB!#V#xG)zK! z`U3NRxL4vx_^pUe^!KPe|8@uBTwmbo91v3120Jn;X|7u<@Gh#br62k67p{G4A~B!B zyZ~)`Zs;PgcODxO8fXT_&K;@nLzq*@ja0dEasaMnOO8{|CWFz0OjS|`a@hk~9=t)_ z;v69~pXpO4n5jQiY^ffD?5&u=XP%2-y?T=2;aluI@BFyKK814tQCP3D$RctBFWHD{ zAg6!HCt3&d>wnKZTh9)_9{+X5w?4=TyP!U)!bZUBn|sBMHopzz)D?&>4g~|XLkf#2 z_LkhsZ(Y_*Edh<9!=bM6$OoHPT;=;b0}@@j?SiHejA1@*-av+XTfkVIT?0>YwlCt#(p80P1dz&C)gNg z61v-mechKdCDI=nA%ebyLHhR?h)39e3rnAb+DOXN>!;fwfyGfGC=NLvJTeW(X{VvF z@KxPEsU8p|F zUNAU|bJ(cL9buh3+|v`UT}$)@{V1a+YP9WzP+@U!(6g!ruAI9lYST3VDFwP!BButy zDyz8bQYiLItWV77i)O>_hb$d;yq3=2d&%&7Mg3}M|ffN4QahDJO0Xecmd>S}M zx)8fuxygrp!27RRUga;q%ki;K??~rCEzw*f8~0x=@Co`J&dG+qT+#!HM)MH#RP|_h zU?n_PwyeKn*#_4km-ZuavCJN+rErqhz@NA0Ho}C^muy`AkwiTLR|&>yX2`8`Uwpqm zNuC9H-`H*G*pTZyW6$?%r3{RMJ-hb5EaB%vOTQlTRJBwI7nHD1^678ueyJkzKLebN z3v-YsJ>t3UEr92N@YrsR=vLUgsxFv^`n1&X^Ng>ju=ht?#<4EjgE(g> zQPtHC1q`WY=d-(^H9(GnymSVRdsQA_v}ynwN|&4k;zpnO|se$;R0fJ4^MQ{Zq1doxs< za8KS3E*YKFGPqDG4V&oK>j$ao(FD}PEk|EYrZUWnm?^qbUqrqMYo1{UT@4&tevrPf z+7AJz($&IbkdvKsd9Hn^4br|5Y7Dz4;QHgKOwC!`$5LGPjft=VJT@bTjOT_RD%nkj zRD1z?Hw3+v&)`1Kk3OYmt8qV*5AjuAye>v`B}T|vFmL=(w!Y0Y1o+5xCY1WI$3*@t zJ1n>x-1MmC876QaT`9+gy?r}e@_qGK75lxkx6jPV%P+xXi@)D-+@pBw({{vD>>)Pa zFk|=L@dtkH?X3yAYRHRCY&5z$1<9;;e(>U4Dp!8yOUPI_n3j@9x9lS)da5qJzkL+< ztV!M-{?ZA26TiCYvG?w%?Yb&gIEnk*+E+W*`+({`*`c3%Ltv@S!+Hz#>N;_6b+>a% zK+ncGdINQfG^>ae(#Lb?cQr(^`BcE%`_K}}fpI9kE9kQmF$gkO`s`UI%E5z|a+8uF z2x{(U1g?vhLskCiJNNM%PW9~O87XVzuQq;=C@-G_iE5cw56Y&1xv9DE= zuk<9iZgV}vs3k5FIiCN05ta$4g=Is} z^YhcVN5P^=d;W3}Y|^|q&ubeA%EU*#zsF*3cIlbT5&I0FzqfH@lofE0AYW zm_d}k+X|lxl|w=z#=&UCvsyvu3usYm>Z_S z?dEfq&vdvS<99#vkLFo;p0K~@hrW`=dyfO^oJ+{TP_46G=!aiow?`jxkAaA7O9eIF z@14iKE&BPR|2Wf3B1c7l_$REBH=W19{!PojGqkvm?G3k`UD!A*BnF;5jCnW#-J{>n zNA`kc^i6w7^fPXHJhn}5!*kGp?q)vnp~>k*dkq|r`@tCaAWtd-;=P5Grgf34I^jn% zg*_DAbN4R4U|WV0+}{G7wI*RsMn*HFWDaiqEcLR(^WCL~?Q#5p%P?+VMhA(wAMnwr z_4EJx0tbh@bCJKNDB~3&AT)$~So!Hz*k?e^P2r6V-2fz+7Q7aRT&QLDef9d;3MjYy z_;&_%>@7uo5jV_B8M`hKPhuWvUb(&oPnq8fno4Zd-M$yp%(V6##3@EfEq zocyb;JqKzgEaK0ZaBm6iP5Hlg{;Sc6Os2>DmUHk=!~F+c@U7?U-oG$>-t6iz1(Uf! zW$S+UQ>$+9b{}Xz8a)dh3M{#Y}3_)uE&S(#?7GUlr*fLa53HRApD1CeA$P^118pqujFb}lm$IJEAgS3^AwbggCldPWt%G{8p2 zfw|%t&wsAtpU_YE*&h*@+XgFHRw^skJK@9T_qjBh8sOIC9ooG+2gicEKJqj5!c*rt zgC@Uaa6aKl+j4UfqBW*&PNwUuEp@= z^lSm!82U-6l-hgPSIbI__NZwiz`@AdLp0dCj;ebySJTu85*6ndRz{Fx%XKHw>}fCD ztUVzAnR*uUPfy2&E}`Dmn9Vb~hx>j^T<*4(jDu|R*Vl}yIG3*9w%4Rsf*-$s+<#Po z^YrR7`od-0$86Xnd-8Yzh%PFhcwb)yrA{#(vQY?qr!c(L)xCrvfyb7KxR>r^olWqQ zfo`C$k}~f5vjmp5x89~SdS>(j&!6RyK-3ioj8j=g zK8tYv&{T7iIOat~C2l`im;*U7m(wd(Q0KBLq%QEDf)d+9*AJ!5LanY?KJ6>a^9QbO zFh3l^-dfjs$o(#Oz8fHR==&U){@hIsr)!2*|5f!3FXR<%9~I)o-}ih?V7k}4PAE#T z_r8lhM8S(?y~~b$F!;C9ulIZrSWkT`wJy(wa_(2lArd{1yY=+l(<|jL@}7_xHjVjW zaoxX@I1kf2I^T#-M_r)0bav7J_F3z zcs)+`aqB{Vxt;8*4&HwlHAEi>2cs?~!h%^&+z%{!(8CM)aX;<+x~A49;XK*#VcKsU z@WoO~QW<&pzeB$`CjYF0f3mmlea7?HYccK~cIj!b`0%7se>VjlP+s?CTSFa+s`Y*` z_TWZcsVNxpklT4g<@~pL+`AQ{@{ae?0I;8rj0^i30h1r~)@(>HKa;`mfZw4R25!|* zlAdXXvxa|O+TOu=?}5(W(fv*ku6mlMP-JogcKUdU#nW+m> zdey>?jZK4UtQVsV_CuAYgUD&$&w|uHcKI6#sDBG88a;o|1eX}DMh9}BkH7IR(cN?f zj_<@p@I_(n@>|S6F7nQfsqa73E|`Q?9xiQL^-iF)(z4AwJ_m=^4nC4cPIhA)b(C0J z4(7W~YfGd?!}ziavm^Eoxo9u<-NYQ2+uhf>X=D|^VAtsPi+mBeH^$NrU=TdgFZF3+ zUiD4$xtC|&^rOzs!+8`ruCZZX6OB&{L6&OHt)meMD zH30QiORB&S$`Z)G7BeGwcM6=^>L*Nao}4&tLw}j09CCaU{}Ag=Ko^mxy%72#Ukyq0 znxA9;r_6TD5a+tLH$~fxvR7~)?2mbQ)GLKNK6`2l<6fa*FKQ1<%%L?1j}9qL!S3^W zx0%ARKVVkgDo8HR@8)Oc>>C&_8}b#U*~uT9)Db?|^e4j1;;4mTutjSfP_ z9^)Mku>lA(GVWOYR}Z=J57UD(TY;!1skK>o5vH;~W~<1cK6Ry$DGxt)M4pU_xlFUr z9&j=FD=Tt$6~jYiqK6?U+?K9|%?^rMsrZP(Mlct%VWe@r6&xLIoOrO44-wqb{*;?z zU|(g~N>MWc(^T)*9be&ISMyP&x2Hxy`s)y3#q7hj~2+H1K}fh#b`=Ivu5jJp4FPhMt=U{5PYiE|H!d42peMaKE%jRTPmbdK5`d1CgJg5 z_zC;hjf%CdkEbB-1O0HyBIces!B`IWd(Sci_&nB_h5*9Gn_|@2jwL!N=}=9A`l@U5 zBlO1`-x!g;f(La?Z`}~dH~49>XYRF?nPs*Ys~ss2KP#Z zRGJ@;WA6C#q4nKTkW%^d*R=`n16p}nFQn6;+^C-V-AUxW|L9uM!E?ym2i@E)W4zDX z*F`f5e~08;KZo&j$aGr_{)X{S(?M4VaeJ4q%iiK zTJ6+L8W-S@_d&YDgjryId4tCJCHlQ{Kh|6gR)9uIw{qC92eu~<6!}swgNNt@nbZx; zcUU<#?{nhb>fMiIBzxnK#F%r11vy2vM1{A{{XxBBuZW)#?}O)$nteUvgPf#4-^^ZY z4Zw|O&hKZA%|grG^y?t(_ucg=i)sCh`^z3qUgVpb1Ip}g)2sP&sPm9my{koE{ld@` zRdWw~73X<>Z*Bm%zc-#_7{Ok+?h`)&&n{TzW453rsfN4!U-|_6Q7>mv1(T6{Q00mU zeY7F@ zq;GPYHv~3b40*mi4>8KjE=FHbADFRlO;MVLryK+9BG~h~Lpye0kr{hqy^5=ww^ty` zL{H>3a?7sS=UKjpZ-R&7RoJz$dfcB**eeJaYK0`ea*=83ZuoKi)E~0I zIWYS~W5`Nf4Fc^4m%z9mOmD@(-cjTS5PsVZG?*hp|33|=HN`3>a+6L zMK~<+J$%;YLyG$=j5Y93}J!rpe}!LJ&@LvZnsPojj^JRI@}y}_|L2fFmZLFveE;xkC0 z{m%vG(-^qUdu&{QtLfN>kk@}p`3*`)o9ogrSDhmgC8nQ304|4y+s!T5 z0UEa?uh0?~0msxl-c1+aDpT&RGwOs_FVi2+!ujLw<~l#svq~tLCpDq%t^k4U!sc43 zEJz`2%wO^7gSlaTQdw%u*Nk;d@l{8`sEF|Uz(mZgYVixU%$CiTn#vcl{W#{oBsGk?PjR*_S3-a@(t1N&QZocGe`KYhwZVDU! zLmy|qD~(!n7Do4`+-cIWpO$Q%^RR^g4o#ze+m&_Txwz`4z%>Wb#XpoBjK;xsq(LR! zt`{-}*x1k6cfx(~K z@AaI4L^pwy!+H&HmWonXsAmA=3_OmR<9ua9(-X=0u@cnd%f8Fv{?}-BEizf&ERcK` ztQa4Ky$MRN6Su5@pltsM|7z?Dshiq|8YP1!+huk68k|>7_5A2PJ%sx~j&WO;E<=sz z^<3Uw%<;`x(Xvuv4>0-j^T#4R;Aay1GWvQG?5l>wmo_4w@`Ai5(QG^9n|~IV=AHt^ zwvfomUyBe;dnGbcjR3vWk0?rL=7C99;_P@9p3f8Jvo2rk0^*g_m+EP0a3%h-1@|x9 zbIjY;$)tt(Vds^r%u1-UX1OvgpM!*ylo&~zCeuoWUWI(WgfIZqrCWC_&Nc_DO?mc@%rUq^Jk$G3IRf22aSwf zBABS^wi#T){a_AZmmIKHGADI-Hogn$u;Ke6mnp zCzG`& zMlK1ZqV9SN2j>5j&fdH9qymOnBQ5V^j)&ND-}s5Ce7DsV59p`hU}l}k8ZFts=c1qtH6AOj%YJ6UweYy2GeF~H+!eza1YH3h-bGE}}3uFYx*psjLcZ=>(xw9 zTF|G@b6BrK|1na`t`s>6*9QF4#H`D}X{&;BO?(DyLU*~}g*E_DnrHYit2yA0vC2ENyBxww-?rfJ=I?YP665c<)h6S$W7SW{yLDd0(pLPk4G04;S|NK z^dyRL7#%rzEazhfeB(K|dyr-t9*Kx)?VS4$2G#%Mof$@M-15Jpi(A-lCw?{k>gE#M zlr*W=`-i;w%iP}tNmk%b^hBfua)=$$iuRY$M+?g%eR>shV^pU;&O0jO_p7)WxVAL` z17|cE&S76zFIW|0dD+lYbxwK=Iaaw6l5tGeqM)q*d?(X&+%I_aag`YJG!);EyRkch zeZ(Ps#;oofP;?O`{T$VaIXY)!md}w8Pg$BIAv*~f^`vjVBM0s8OCe>+V7y`NDFUl>A-Xhm;}KxEg>t9eOokU#aG_lf`H@wuF}SM#g{{~gH5pDTs=hGLb&$}$zm*=wutxcong&O03I zz769dBP)e6vP&UlW#=Mg#FJzcQdtR=5sFY|p+X`ViBPueoxS(o<2G-bloEQc_pkSO zj^lj}&vD=P@AtjF=XIW+^XVKY-!PVO=S40!r)aZPEfFRy4Nv_Q!~6I(8iGhR?aCO242g@3!nKM47k7c>;b@f<1` zwL0~<1sbjkzHCLE`_0oe(R}H8m@8LOF#6g7C(Z=Ab24;-mu*zb%-MPPof$b(K7f0y zf%!kW*pITWgkThlzFIjT4!MqIK_X-L2di^k@cxwbyyyV-+$(5@(eq*7bC0m_Dc2-W z^Lr|(rH4Emi_i=Cddnbi#CYu@|0G<|EBhV7H-oxuq3Kj65vZR3rXJOshRD(N1NvMO z(4WFrdTST`Is1icSstPu8Fl->3++V^Js3bcxQag1Gcqnw=2H-U*2>G_Hu8wizWsVZ zyBGR&$vq;g4i4#Yhd2i+dwenpn}}|8G$Nmg zEwspFtGE)Xe@}?Mr(1>-bxm(9E3lW8TB80M#}ZJKUi1A`m;zG6MK>HzPC|@C#Ur`2 zKGb{O=lWOIfuRWfk=L(%L8!}%RP(<Z=;Wp#`8gK zS4tN2ll1J&Vo&FRX7&yL4FZtvc5wu>SAo#Rj<1P9Db7hnOC%3)4@NGYRD<_(n}EI% zdxjA>PaKVq%O${OTXXsz^1CEydZTl0F2J=5IfV~4Yk|;2X%~&}Pd-UqSug(;=+%9b zqyB{eci&$a@kD*$k27_T4?S|lrD#vvt>gT0?%#7}tzu|TyxqDt-wpjHck^hJu}4a% zH>?4;kAkutSoe=V+dWT!$>Y|8ZFAVS)ph*_1?Di=_WLE2_0<8N z_4fuItw9)0yWuTcy9C~Mbj!ZU7DL?nE5E6}Q3$KbH@j1SzGP12IwRCS1vbX^n{pr* zVrk#-)Gh&do=5FwekLHt(yM*Xycnk2p1sj^K_0rGJ5SL>A8ama6E$R)q5N9e7dnMD zh)GbQ*Y!khs;8CvO{~IAdI)<7qP9jkD5pSNGW(>3?-YEwr03k*F$B&$vMjBesH>8%w^q*J zz9nhH(c(fi=zaJ8usucu-c3*?w$y-Op>JNyRy731ZgrPmEr;C@RhJg>eo&6NGv&RA z{W5=#9-Kg*(SN@W1$aeA0DGly(Qqd2n`l0lSga4iP7eFl=W5LB=T^qCZgoT37f;rh ztR_gG*r#Hk5DT5p!wI!5-Wc~%bjrskPmHQPPVNtF=Vgy+8g>E0*$8tG8Se>OYBJPjzv8I;QkaUUt| zruoie5`yHe~HbT1iuW|Q@@R|$6oYbm4`?>a#jD+dGHQHm1NL;nl~Vs9e>~@kN`iST2)#PaO~SPZkz>YEfw;H0ZOdk- zu!{co1>%P_^oOvAJP)EuC2I1bV~Si=+5GuU>DuDFR`O zW?`?FCZPL5owVN@^c~Iyd7ddiz1L77vX!d~Ig0&cr9Ya1_3Zv5Ur8{BxBWexx{3hJ zHm;%LJh(TqPtiK5y$ntUzrxC7`(f}%u#+A34KWjke5D6Q;k!znygSZybk?Wjcjn(i zU8uiWxn3Lcbr)F_vWvk*>+Sspn?u(FsaLk!Y`Uciv|6;;YHD5aV9lqb45GgGLW8U?f7xnBukoS6*2FJu33 zk_(r$AL@EW_xrr&3c$He-f?iC0#tYWl0(QxpzZP}scRl{P_wZcIcK^G8Z<29RrAx} zcwT+KQwioE?rD|nj0{6xl}MRK7xGB7jr28YaNqj-(D~oC+CUrI%$hSW1%toSzcZk& zI-GGUCedRQTpn+p&@x*9l5a)+hEh1MlRB8ZO{>HlArt2WVB9K{pRnmPwFEu)*8T1$}Ovr2M|Y6bd2uTutl zVqT{B<6tXt={!stTD8$vlrL(lCqw=j?mp~AU_m+*wWY8XvP=UXyOGcezdF4u*k>9VUDe@TjIygf12N z(#GBQbk3*4=qi=-Oab!p&G{$`#v8!2j`wL4?uE-LB2N9E12aR{q+pCbndrk2Gd;j<?ZDxC?$bl) z|78kY)pK82fGm$1=NEI+@HAo5#;Um&7*5#A)nfliq3=xW6MQfICF;x`n^=Go^ImhL z`1x>McqLwaeGa(_tXUBf$P;NTbNN%#0XCFFtxl-F{;1&cCw}UOGgp(ND)IUKP^4}p zm4m%3J1c`iXOYvg`t#1cpG#ozSSI>H$tVak$dWux9s=cUg_APFM2P+v`MC1_1kj8g zkk2+71CN?r$%Cllm=4rmKKHo}_Re?*b0Xi0I$!W3rC}`?vvP>XqhDQ8jo~Tz!A9tv zyeBYsyBoUhwkFS>uYkmv)2-d;%cV^G&D;Jrubzxe?xI_ysoUJ7+V-|eMCAtGfdov`vQa(Ppc02DggYjnXW z=$9a^t0`T8BZqEl%v#66(HHNZeT*bR0P%cIGV*a0I5V{VV6KEqfQ0{~))4S2l`?Y3 z)k?1>yCCC7l3(Tu_9)x!^mL(4pQ!XN`wjX|oUf7md`p4+lSb!tOX_*J7GU(Z z;uz|rWxL$6aSkAv1l!?Zi*Pc_;XN7pU3QMp=bn6s`J&TrAAd5z`*_T|@v9H<9`FB# z>n>e7gtHl)JI(kBa*UOACe@tbWvocf(iH+6mXe5*C#!;gceE7v=4PPY=h_+r=JcmJ zf1M=V?gg4a_iG_{#^C(Ni5puP<1qGfr`BGl2`<)6lI#n|?wT6t4}f6}Rg_g} z6Z~_pbXAWfLR{{&71!W0^mhehUm?T2prx^l;2d%m`vi=hU_NC?H1Mlm5fSK9y2XBO zHvx?uPk=#77c}?$_p}#tm9OSrwQufBfVN>rRW|Z<#cytkuq7imDt#?3EvN!wj<1u% zB9C%h_K)lz@nM*)QQJ&HJtNg)D}0i;jQzPJRjI*5=({agucz1uH(t!hvLpYeyT*Cr zlo#p`&PMLlIRE6(=ZF7c7{{Imo~K99SE)8Ed(mhNc^cFYu3R?3zt1Y8^%rxh#1-15 zA=C}y+<0o@39BGh<8iU}P%|i)-vK3wphM%UzzPvvJ3;`NZn2&zrQ_1Nw0;k@2so9m|p6?4spe-5BopN^Zl>J>m zX>-3@>MC+NAFSki{y!(#W@s&@odX#<+mD(@u-~|FLM!582T0HiNz|Z!NP8%tAYN$* zh(|{w?2+gH*L__v8uuMOG&_T)9Sbn3I_+fXJ&QfJw!$7AW0;S2i&k;Zf~1hR^ou?T z(8qq|Vgzz+)H5XX2%-4BsLGqPTVnsXqded1KIFI6+?VAFLymgjfU7Yx&gBM!a=Xvl zAjQh0V+#EyvU*MWO}FZy@!n0%!?nW@K72#&J?23u;x8E6i>Kk7z~=KJ1$jV^c&=;)mg*U+$&Vp_;&X?-wp0zgiPZTaR)^{NK zn1z3?Li5OR7!i(C>4EEX2iW;955RvRkqJ%Y$QkQhr(!$W4-dasjNP}GM8AvESU)53 z)Zhep*qJG)mOFHs>H+qKJi7TqD);}rRRyGjf?Yu1G?`4F!N|&gL4D_epzSX^9 z?cWcYR-z0EQP?+gO6TWMPXVKqiPB4$183s#= zpiXh@ffP@9ep!{Z92iSUxHH{L0fje6$w!{j^N`%9F2SI+`a{|ERzHYsx`;oKY=!1@ zIc?GLA~4PL@<>9xWc|(;RaK@5c+T|lwGDDhMjA<+R&YOBC*U#tCHV`SNKVtrmwcBeS80&zl{#QT&W@Zr zZ->nfu}M%s5tLJjJ)$?H605SVOu_C6M(%g7u%GONkmhBUYT!HWe9mih0oICYQ)d__ zV2S@s3ZM2YWPa%USBKo2Up6~A;FK>Xr&%)I!%!ROQSXo!y@(yZw)@}%e zjzFFI-do{Q8L-@=P0Mh39EL8}%=+cGfxD~X6WQVspplX?+rsbfj4-dzJ8smenA<=3 z>2!j^tE(zRedM#w96e*n{}9+jL*;oVCt+RZ{@tWH%o~c6^*Lf6hA`dX>nyxuVCgo# zakQ}?`w(4Du9c6$u<{gx8TPiX9o764Ix&fT>?^)ms2k@$;?@&A-V8z%OG`_so1vX!XH_o3~#`jEF^H|yK5VDQp&Ce{dvM6u$S^R=yglGQ5CV{hVMS z=`OH3)!4hvx&ob?JRhgf&yjQa-@2^L5=7~}8hr5{`E;Hk*Ch_yf#tsQ9naAxXpkY# zCx>|u`rt?snRhsEb_c||Wldt9Z^z+hM-0e0g_Nsc@AF6VS+DoG=+EZ)N4uY=2TV(S znI(wz5N}mKFkOLuXY1!FCl!a`$e;mj(1$AcNlXsP_&5pw{PMF_*!#dl+mwsiZ3^PI zIrz8Bs(|(r#~JZJTD}VQ8*0^^-pMGuo8$A(X zPhCvC>(v9htITE}l`zM!pU}wgGz%6RZ`nTiSPc5%9D%-^$bl97eJAsN4(jiFA1DHs zV01&<^6TX;C?m*lsoX`KvCYuM0NDKU* zHBeshdd3>(P46#$+`Dcapj&;}MA&x$c&#rO_hGJGl;w?lkzWrqce@9M)D(mG^RsHX z*~6gpBVO_QChBF^W*@n!Oha$#U42f!Zdex?vmmb;fON0d7dIW|pi@JtWCgjY2Uv}n z-r)0{5!&YU;Q;Ek5*K44L~C$9kF{N+Bf#}}pQ`U>sJ}MUarQT&4o)$({TF>8E%Pa54esl9jbv6H8Y{Xt!y~Yd3wwbb?}87l_rAe3vlY> zCJ7TG=INvPDZdmTPuxuQSEXtzT%XCacf=mO@LQ5~A_bp;cgxbs6nz9wCk%wN+K|g@ zbo)y~!x(TISZvRs-WG`bm3;)Hyf zsF*kDo}b{fT}f$z8UZ+nn^!ZD_ZKE-x_sII^)jZzGhrq5pwxX@DER;W+vTevk?LKL z8JMVNjJa^5(U4CZ0%PDk64y`ntQgh}T5sJ&PT|?p&Euok4|r64M_smQ0RpdExeWiA z0B-j)x8MF=h6wx11n03CsQv30)}_=7I;nvl*)WI9ui#2A(mMm5GtYMi&^KV@Q{BN^ zHV6J`56SXzo?N)YS1(Ck0lKbNv^g<<<$Khih%Oy@t{-;JGsjJXJO88CUD%VPzFpe- z4D)ZVW3NV!b$o!W6UvSzDl>4t;$07aau2wyvzo^S%)yoWujWplL>_&J=5oX)@>jlm z5@uGK2d^`1Lu8T7ILD7M5=0*Ym){Og3GQ=~$gln${qhwA6M`B%KF~Pv;0J_M-h$*2_Ir3SmFkrDD_3w?o)ZboHBu)RKKp@14KH zUt5(|E9j4jcw)c7iTR;?#`zO_V#sv~v}x{wRk&3#=-EiQ1Wbv4Bw{fSdZ3`rZNOsz z>@ObqYlXVyHrX+yaTCmy95JE{M6OuX1CbU6ugY#;ja=TlzMxSB!w(Vr6~yxs6V?UHQ7!Vp+L`sDn? ztpbcPX7v|ZN}=3Uk?<*R0s@8lwmmN5b8fq>5RUy>qV(oHBz1jo#23!QYfZvA>GYsW ze`ml758dl~1K#VXtO zX9#-$l&rJ!(8nPieC{~!Dt?bw^o~8b)CI)+Qm6JmMEF+O!6K}?0yG}Y!3Ublz%N4C zOTc~+PI12VUPGTOg?#tT*9)`gOA#=CF+Tx6?zSbWUm}8S{oc7tUdUA}k(G3^ngR3c zo}vZl7p1(Yl#p$VytD$MDlh6ym#ke3)Q_Q`y(Xh>gmfC_w_?X=dx)T5@@^u}7Ttd7I|+{^9bJCW_5xF3~S(0YQc%$$nW$UCVY8Rf_d`t~-OV599vz1va~-2TI#SpByLE|HYobF1lw;gd7`w{fq@Mf*kK z&+930oM}C><1+z++fl=Vc>m<6-I-BC?*BLD!Y%tBi{QtoymX+X7BV8EVj6^Nun&qg zIKF=z*hOPhXkvQcLSg5@hh#Od_s0E^l}i<5n;4164mQB`JFYLvX9jT(E5CX!eH;!s zMjT!Bc_L=8fR*JucYa`!I9K{|NHx zvi_U;=dcK2ue2v}0tcY7MI~8odlBkiyq&D3S%gZ!UvW7Q=qvRD5yrYiB#mHTcnAkm!P$Z`u5PIWr))efgQ{7d&sH`286QaL;z7 z`X04b3sebg&I!ImfAP%Y#tY01|qBM#KV*LBzLoR|XB#qJlzX%%48 zlk(9M`Gq_@ad!VsuEK3Dg&keIUkQ`yQvN``1cmCgSI1EoBU!y^W4JK~VN<;A%9y+Q znV&ppRyG6L1(qW9+=rGRi?7c;e`Xn8J{{J(fVq_`I={=5nvm0!<w#dA27~ z-Sc1^Qla69_okC=x-*rSAF+*B6K?aKfgjHgTr}|Rh2oxZ)w+yI5TxyNBGMs8DVy0= zDzzHOzEVefXmx}2`f2-AZsdt|tyBkKuEJZ-CcOdoyWQ?HWo5|K_-1;fjO=;`82nIJ zzd_OkJsVWl2t0GB_dcFpT3LagdralQUK7A9a$(w5dI@L^n9EvAmtd^&lgMKN_Sd^S z%DwVp7W=Q3D!P=1ppUv{jd3y#hWB|Mje52WCXEW)hyIMiUQNWrYl|7EWUVEP)b~J^ zBBf%^D9%}BJISv!zC(4_yX0R&xj+@`;9};D`*aSwhC{x!aJ=)dv+F)0@^^lzKcO!K zIXjIjvD*Y#mA4)|{NDg5#vPOW&l~w8J-kMoasU4vC!gn2#l38<%lqKoB}ge}N&Yq6 z4jxCcpA<9B!RZUDXX7O&K!7FW$`1O^Lj>o{`|*2nxgRVM8QBGwv(~l~>?=Xp{KwIg zI5)M&sr|~td|Xn~3)R)CIuMuf5tw06*L$hMV~&J2Zt{|Jne7{ee{1~I5@81z2(!;S##u5OxBHD9K!zf z;?(rVukkstcO|EAJKqE9H)!u%okV}xnC4FWU=E0_iAU?J*MUt`qRi{=A>bnGj(>ft z8$^ChthFJ3i7zXA^wqB^=>4#a6G6Yzj3jPZ>#>I}Fkwtyh395d@ zV(+t0Dp~UZyywS_=oueW>Oub;uRXg&9vq73V9>?9C7KWelPsZV?WdX--mgID@>^s?(VG?TqU^!TP+qM z|2kHo_ZpwR4dxGIYh%aSwviWU7;-rSbCpp$U3YT4a^ZdYYU$tr>f=|VBuMtp!>*oB z0I5O;@Gm{M{}^*g)dyk&<*?t(??F4itWW}!u+xyyZGXd@hAHW{uh<9a(2=qq{iZZG z7%nTm$pyU~Kl`ZrBamK_ok`=k2u|ZhhZN^fUt4?ld`b=P<+kfSKkwomLFGsMj_^~6 z&W$;zv4GsOqN&JR5sOfs_h8zhwgL{A<%YLno>M;Yh@d8Na1*JlZjX;IV{UGmE9^=W z+)GU2es7Mx@U2){;q4L__GjF`(3=g_O;y}F@}+WTFjr$$4tR%^w zM0oS&r_z6sEug=k&~%Qh9s*wq-44g+m63_UjoOR=({)9*#JVN8etGa1h>pSQzm5HY zlHD*@dYd~UcpQWbO)H!y%R!)R+xNK1GQ2puT<%;)1l7$;p=roz|6&!X$YQz-imod> zH0MzV<9|TnfOA=fF9mu&TcFfz{bouW`l2pyxW|*C?{U=9FR}vt->04YO9}ReaCaSs0cVk<9&3fdqIt*RV5Vqnh|nlxI5B9_bz>f^<9TuYOe-*ET;Z!^{tlfRN6da^qL1&v z%xN{`#2P9WoUlH&0*N=)_w}_8f^7UjUNYtun9TEP)v#UwHyRnQSSrjNzWdPZe;#=z zrf;PhpVdIxTSlHA_#WThIB+-=^Juf|gZsH1Gr^La+N~PjyA~wp9c0vIfUsh?u=$|^ z4E=Atx@(XAeY4)pO`1%gH#{mUaI*>?ojh>c>UkcxvPC52Ej7bwBeG@cnOP8*tF!y> zunY9dl_r10z5%}_q5L^QCU~&B^|GUm{8L%mJhEU0K1hiBtYPn1;-zlij<++=W1J#m zzk>5WD;rHYa)bFe$yCoh9e|GNtMDrw`(EityytMQ{5IN4gAx7G#Ir3;s>$8(ir;u| z{1W;C5C5?f!xFn7`tvzl;0}KlP;t9H&yi^Pb#h70w;PhE_!>UlxHsg-$4DB_8xM8lxUl*T9P> z^t~55N077ENGi;i3sy&LRo(@z!m)aidY(JTk9mEFAQ6K6@#y3x%D3nn7GQ}c9UZ}( z@l3P6753G<7&>sRa20eia;Lt0>;S&vQ>5yc=NM;vmZ6QkBQ!#*W~WvMK|9)kcdc&{ znglaF^mUQzo?IdS?^Y+U@BehsdkN1Q()PAgUVVBZ_Z`tB6MnP{+<98#*vBp8>#R{(BJk& zP%T8|DZLMD%LdVbstty#!w|?Pc3|=r`sSTjNK-|}aSr*rY=nN-c+dR z^t+;dGr6r(hTIbq?b2x4)=7BsN5)cDnh2LqO*+_wBWIs=X355)3UYHTwu$aU)ElzS zuy{{Gfv;9$u;DZ;N3l`UmmrtQl<@oKKs-=zB!*FmR0Crt<+i?h7Kk~YT07d=29j** zO})G5mpoI~TcHGX~n`S={LQ|%d)x#RyHX6wn;MSp#X zH9_!X3-GR<)OUzzga^Z!!VD{eFg%$LmuBfZ((Tw%Gfw z^?l@MSgIe$+ay*mquZ0uxw^C0N%7|`t705)lrmk$R`gZN!nF+V(qW+w{m-ZM-=N!jCkeY+vtM;Z^8 zpB{(C5I>TEGW?vgZ%y=U%|j1YK({LD26;Nt7TtV{&^$DI@LU}7`#IYxohV{pG5xJX zo6#H?-wvr`?H+^VhnCkIRVF}lJoG{v?%`*O{{{>p&nvX*3`|htbNBhwjLI5$al zJe~pjEEg|Zw=>}RXX523p@I2t$30JfuX0d(D@%LwAo5HkKU)ahs)7^?MW0Y9zWDv-VQJ*XaH+g86`lcha;D5U3*>x8FwJcweuCd( zW-I^K4N{l0+$FD;V&6*NO+{h6_qlf8tUEUbriXku4-jg>{e`#n_?ZsSkLo#k2=7m| zY9`H=qqE2%xqLJj^G%O9;%{EM)D59g(!AmS@3$!zDK_074P&RM&pZ>xb8ErbIQ>fw zSf?>Z11Sp+8li&gH$=jym1oaaLBfltBnFNMZef`hrpPPfodPd@tNBjbFw5 z2sQhG-K2&pcv!3%CzQ4fTDHAkG_j9Zx>uql?fDAu^Qyb<&dfnli#9R*U>c;o{B!&u zo?DG)w|&Ys@m> zCSi$tBAN$$x8xRzVV3d)hxpQGxIsV7V{l;>>|2EEEHepE>*UIR3G)o85|vHgZ%o7A z8IJ^MzAO;_Jd#9?bN1Q$o{xNAc7c9=Ua?)oSJ>Gf=DLAC&+)`VSK356p;WtRjSuxj zo40k|r_q05_$lW$<3<~VuC-T+boYU*)U)D%1MT4Yg@s3$7jt|bcQhJM|FQ%xk#7de z(DX&evzi6_u3AqN%;Ef3&;74X_y5-B!QY#Pz0XVW$G!0MSjDgG z67(}m+!c<%eLvGQ<#{`A>{-jt{W)8TTr~E`#a`Yjpg9|>we3^_Ata){X@^EY<>JUM z9>y6kZcE{d_nk)HWk`ZW(-5@u$)wbJV($y*`P`!QanLuBp1;x-4~AE$n1}8)gVvnG zzE-JmNTa_nmzj&c`Qw(ssyo9#$CrGIabF*tqJHgRyEcXSl(iSFspH_gD{VQ2Jt|R# zDnhq|FlS+_-*a|n3itBcdzX-7w$J+B((Dou94A5!cO$nYgQUZW5p@D$+xg`fnl2bk zw^hNnlgIRRn$p}PG*lSK>DR|?|pmWpuC!^YtX#{Mj?rsi^y?fev#(xa8|dEh_qa5~ZK6KFsEtxfr| z8ze7EaOhMv!D{YoQ0tgg1Ploa87dA9npcux+P$)}eq_@UoU>Qh2Q@FWBY9P@s3 zc^)bVnP>01B0o>rozAIl1caBa&$*?HLE1T%>O=+XU*FnEbd8w>YoSwBO{i}dzvLO$ zHfe@k;$<;U+>2@N+k0JZ*az(xlsIyH0Wz0|-QxW_;5E;OmeSc}Fcgp(kTUgxy23j% zZU)ovP^(j1qjtjdclbFCk*n{VxOoowC_e{D`$dT>@Q?Nz z`6baVctHHS)h2`bFqJ<`&vq-oNyY8==y!^cyLFuh_wAG<762aFN5 zKmL^<|D9(xH44wUqjF{U4x!7e&!V4XuU8;1WA4nY4}~z5^NV-wdpRsx87lT6e>~f#`ts}aO1SVO=l+g& zJLI_Dy{`A&9<25q2&2W!&cWgV{V?>Q@qVb%jK-Y(X9|@web@^d{oBA|hj|KAixRH5 zQ{!Cj*uc@MLja$TzApsuUhPFX@RzXF2A^9Aqr=|(-lrTCw4%8k3(FyTqh_77v5UBI1L-z1v!hR*aH<(OW)j$yq+@! zk2?~PyUU^P>b4aM;gRkM`wA<-y`k@g(Bpo{KV9m7?nxT((l^*x`L~0wRtZUzA`v!o zt_(}E62V*MMf9-@yq_25oV7TFzGUkH4uvxdaMpG{HYyAEy{FelzJ6JP5=v6q&kcR> zCh^SHFWd`J9JL{`mN$ZP%2fp==2ocP7jY{09r`It1tNvSdf~sPe#3?m*vr7~cH$28 zB)ANSxD!p5z)2wRS|9383Z(g`PjfUv<#DF_a_bYo_S9dhxgYtl{9}%yn0Mf8PfR|4 zvjKXN6e|NM=YZ~_-`PO62&m+KZW5F;3tFFjXnh4U!#Gm4g^bE4*;uKy`7 zqvaH&+n+vBq)7n1;!hij=wJLYYapoN+zHMT!L^KkmSBsUd~*)}J(6D!uL@qmxwC+2 zKYMl|m>CtHHV!EQaq+&?$!+u*jQPLfT^)fY0Wz&D++Q@SrivWl!Ca8HWz}=FeE3@+ z+W50%7ie<8p*e@qa}l3!+I=h4w_3q^ z#s7McECF1lsaSncuaVSnlg`8ExM}p(C!Nq4`1vegvJ-PdvfJWx5*?Vgym`%LOs@w# zr|I3lpikWN9PiQRsMFsiUb#cvSpjb;{>DGK)daW5hJVm#&Vcxf;m<~Gc<#LT_nxn3 z1d303>8as;eoK0dsvGkk8-F71P^I8}Mei9TwBiyW;m-fVneiI)fhOOx`XWK*Djwy=dZ z7xVqacJ80K+u+0E4g1$zW3W%gGH*D#2i#KciT-g${ot0^6GFujh$_eMh9I9vr*-cq zOW82+Y-nA15!(ri8XV$Bzm>pc*D6hBan#Aa9(l#It zPks*~_)=#Cxw$SNm+Q@&gY7-=v}r&^8Ta{Oma7#P4d#Flqo6jjgT2h>=h~0#5Ml6? z(SNdJIM0#C#04Tpo{+St8ixK;u}0CmMOo<2jw;LE+qVjbW*>8}y_^Qm8#SWj$Wx(c zezt6)T?c2+RE$lxPs1f2K9>E8qtIj}gTXfHdGBV|4c0hQvtFJ+b?P&M^w z;Hxh9HWTmt@hbY(G|qH$>R|r%YsL>o{GJZ>JY2Tj--jF`Qj;E;UeE}3mFkbfybjM_ z2g!@Gu%+o1wD-FgCQTC4m3q*>S{|Rg{Tb&G@!ktHzp(G-jZ)wK9PGb&XQy4FRttZa zzdUJqi<~;FrHJoBp36J=2U~!>RxZ?EW>|23yivHaKGg=7ev(YLTP(wBM`QdT@&O3- zuUM2FaGu_1{FwK+59iQ#nbK<&pu@;JawKR9Xtf`&k~%HHO|_Sfh3}_;e$vzXEj#9_ z2A@A>`dSJa|Ar?hqC3Gp$VWaM&%vCpjqnuva3;M=oU*VVAx3n*GUXcbIR=g~JKgUG z*NH1!oENGfNAlOggKAg!PvW7H32h9prus{JFHe9wLvnjg!8qn7?tY{K{Jt||Q#=ph z-+kbC+P=OG1mmJPh0f=DISco0y*?j< zI;_vAQs2+w74Tcl z{+9&yzb_JP-y^rILG0!GraAchg3o{fbFEJzX_^AiA16>iH#CKL=4Xd_KE=o4`E93q z+X{JD>Wu%L*Bu!HRozzU`}W;HnU*2SK|Ti))4BQ4WteC0Tu$ zT$EpA|NKsbx5J~ncoLb3PwQC0UI6LQ;DC$EU{l4LA}%)v&tKl(?~gtL=I9(7 z7Q;ahcWbT+KjR4Wq?&rR=s#!Uym(@b9rt@wmWMJ|I>Br%;0u*g7u1ry)$1Z1!#*#W zMhgbykZv*M>1!c(jXKe}u=FhmefiCKFQOQ-FZxu5UB#Ys$%gRz*O3#lU(ZHkx*MEG z@K01l4~UIRM8x8Kpd@`Z;rQk#Y%~nyEyz!Uv;TRGW!&@Wd;OR;YEJ>0 zi}8-4L8aISbf?>fy9jQ0WrL3h;dC zNMQPr!ZHCmtDS0ngmRs}k22H?W4*T=ocwdV>`TXrW z>^YeosM>TEYlP)H8^4~OLf*w8uC#~BxL*<-bGjoo5BsQ&#)-WjgL~Dg0zZOQpu|eE z;|cygDa7anLj>x8YG{JP4d>ITSbpQ<3fLR-a7v8%9rlvUDhKsHEQEo6^V-LFAE-?= zjncIlhFlHS8CT5RR%h<)oh{D>bB{guSE##k^sFzK{>2_|fxo+~spZf(Z==^TjJ?wK ztx*g3yn8d#4&}x4!Sq+gNnMvIs2#cddH&51G{t{S)(u7!X*$XkvQoTnld+{Fj?NX;S=93o({iQM% z;RC6_`LHtdt6uBfr(29Y$6u{R)Z-2;Qsb;=%Ph@S6;% zKX#o0|6`XKs6R}>&o|ulrZ$+1u6 zx^~x$YB78f)?v8z1v%~q8u&YM$047LNY$j%3Ot&u4Ju(na66qqYB4$q#|H#nlG0;e z8Pz_~xBq$}KT%U8D>M!M{VrzP*y}()$?uoet%NC1C9%s zjC3NmWJ^cU(y(V1k`CrC%&4{tNA5zf=!%P0OSA}9BfMcpGG^cU&rM~8pKbLst@ z9#$e2b?uL3OJNKou|C;~lv;$> z5>rNYCy)~+S;A-CKLnMX4342&=y(0ZboiP}H~i|kmq~frq%;U#o4f5_s;Yr>%atL1Kl%!a<95RE z{Y2s0M5{}_3f}S_?MeNsFgW!7C(YJ4*kqWUSdHlhlVhFFqczcoWhfn_Wibm`1&1d^ zt}cU{yA|C=7W&{ep$yDIEN?~C6j)?=gdly1SZ;tf9PW+W{m1`?--0W#cb|m&I zSt=8x8k&LWSSn%v1m;)$+XVWpu|H?uug6W(9iVJ6p=5_S!`>5Bfsb$=oZ@vnWYkCm zpVuVgKaKEx8uaGP&7WNmSoZS0EA~}tUpP{FBe@?Q%nPz;k1c_x*_^bU<`Sr{o+NqD zh&*HME82{4xZj{W8lcWH2ret$4^nV%XWSWG>icmDtUQ@E5b;d^9mceLUh32m+XzF?Z^5d`O{o`WB3X*{?pR@ z^nMv~j&Yu4Z*c@0^MvkiBQsFao$MF*p%_l=B* z?1r&F#+tJFA3yF9Vn)Sz`||M~yfCjYY`*|e2Y&rnTkivJv+`@rM@q5xu-@eb`a#8o zbP1(Q*x#(w%W*(_9CXre_R!s$0ul}5H}$eBpr4t1+jJWBCOz@%Z@FtAF;h|c`%41E z@0yGDF}K6oU&_BMI436N#aMpJ#kutEAA3`hukh;fq(I%}MX((6{H6S72FU(!jJGS! zLk-;l`+y#NKYORWiJ4h~N0Dvs73=a~S2u`J{sQtK1-8hPntFllb@1Oe;XYs{6~oG8 z-VZtR9J6P1%OL;PbB%cCdB|I8RWQRjUQXbspc_j$^z;gpG`CH`{ReN)OX26|ear7_ z{FOY2NiV-p+A<35Q(sh!ZXkbvJNxIe`Bh*~>m0Mo?+1f&_m8TZDpkH z^o)n{8_X$&(Y`{?3;#utcdcxR&`C2romV&s&bgBY@)arY(Z!xP+ur~!Q3?H)({r%# z`)09$D$cVaNouP5(eJO>duR&tq)z64NGcPN?;Tzqd)bNzE9!zzdt|U*GUEP^0P87m zlOz%T%|S%zm3-fSUx~0q_cTLD4fE6)6<=Ay2rxW#_9)k0KCnBe8eM+12xc7)`9m4s z!N%?c3mwBC3_R%Xi1uBAuAp>^p0#Qix9qwv=rRc_E)Q-w*;PYrvVkQN>JP4qKFid| zM;VwdrTav_437*APHZP;L4LF9*t80M4wq`pzZnm}#JJ$>6!Iwj#%g(=eMBCr?2YNP ztu9DRlRI~ZW(9(G?=PP5$9tFcsb|L)7GaS(v7kJ21`J*n-x4uL9eqWdtQCDT2K@!P z!w<(HLD)jf;{nc*k?ME!j8{Rw&-%60%{aJw+boAvCmsSye&0;PT$4!C8{fi^X*iqT zN&$P_KyYa*dVyTN6DsrL`KXi2b+pmTo#}@~gPA9q{VNc4^HwkK_bH%QBU`b^ss@LM zY1)qOP1w^`VMK75g@S8Ue(BGU-^RCX{+bqjK^@FBe7J|TWrbX;7q3X~Okoe^ zi(;1)^vV3VnQ*PHX%xiBMB)~Z+q`FDo<}EH2Q))U&l+;k_X{pIXV70`aFIvm!rv+I zswh|6(?UP)3+7|9A$T8cjGz4awF^qBCBwg{4uWsbVyI6k?(IwHQ?7bcfl|R&74_5+ z@R+gdNm;jF{uS=LfTaRvPAfqm8;uw6NgyF zuHxQtw5n9_K>sMv$x{2Jvy4Ibh1-U&hwEXuF7UaU4{|Bw+XWjOQ1{F2G7ZK#&aR-p zcU={GC!|%VKQUn5lX86iJjDoj8xkM6;M@ViHj6?z3teUtG04Amdk zA6Uwk{g0yaj>qzC!+2${tZb5BWOpVxUD$M=9A1a^MGst%yq(z>0OISV0wIE~p7KEboJTBai%n6L0S zzGl^fxhR?QOs27TzvX)+oW!3EW8_A+`s&a(7av|ai2iT)|K@1~#0KHTpzi65w~=#E zAS#f#Hvl=KWnX2G$GlMScVzZt79=L~(c9Uq zfFiNB<6X{L5Vy}wzS>g@VuZ`3BPE!#r4BuO2=lZLCx~f7v6t&VnUgm@cw;{}Q+nuH z$N<~|A??!sVJKVET%S|J_nOY|&fTRY5TN_(I5JOw{@Re@0^Ui;x!vYcg}o)aC%%!~ z>FI<|3}jy$?ApOpaVn;Pwi^0WS?b@SkJA00Am6JI+*6OtFCPqR1UJ==vwv{junc6? zP{4h*;dP6$d5>(6iK3PA4f_sGP4^6G3XmuIRdu1PaS0B+Q`PMAoP;m+6O{weD=?V*aP{40X(B0j0*$j<{C}W4gYo(gaN1 ziP0ZJdm;Hozx+%4UbvMXq7hRx4W(>9c0DjJ(KAa%NiEa@&okb+>|REl^KzPMq+}&f zYS~ttv5mWVe7#LzE7I;wK5i$@f^%B6`%J+YYSgtvAS;_!=8^qG| z&d_^+Iyv8vI_~r)WTIFx;{%2DxARW#RAX<;hxSUV+C3otE zCui?4+w^1ZbIXS5CvuF2?bI8qhOr;FV35UdYX;aGTNBF&70_w7D5ce13{=ZLO|^Cd zFx#3I)x0+Ycit*qq(om#;H2QJJ##BG4bh)6rNNwKJ?Z5)@>4*1*zpzjk20v@GfIrW z{6>evj*WwTIq*}5p4BvH0fwwkH}|NUz+6K(oge+XJ7lr0DL&Xg5jEWt-H!gm@A)=2 zaeowXxkNQubP{A1?$!}kW1h06&haSj9Y~7FO4eQ=KkC1tA0JOFz?Y#YX=&X5|0N0Y zo!&?O7fC>p;L#P39dPP0$2}))P-(@iL^teBUCKTlQx0kcBwH6>bR#GCnt9a$^r;(Z zzKK5H0zD>|#Pp_9L1>y>z2Vvfq*YmDmku<+gy^Wv!H5yiJ`gGtmfi#o$33}^8`Qyf zvJnwl?8$X&PHf{omJF98TX8z#yf~HW}WZ zKHEE8lr@`#L7hLIOW0fT>HT4P2IQHI#f27yA_v23Nx6g+In&RcIW;w5?v-(Sno|pV zN)8bZ@*b6L1YLFQhLLX6e|2aUn{f`F=-FT$$NSLTUl+bu2egBTnh22~eKk;ByHKus zwis&5U!7Bz9fx1hW7pvjaw>!>h5*$0U$Tx6{c4BefOo!%}|8A@!C$iRA zG=C2Lb6UaCN{a)?U4LAivtBs_9VA%>R`^_O%iJgv(iwz$`%BcNSB4>tI=R9)wgIk$ zXbSww$cN+vmX~%hC2;sx*4|mJN)Ss@9@dP-oTFBO>jm}};J0jL&!w&c`)al?Q|Obs z)gl-rgy*-1)%lp7Rm|~kg=Cld4Z*%LfvrKZ13bSvbsyqf0@hIFey1kvOW%me6@9q? z><$KhUs|ld&OQG34cK3?ez`MS_5<>JS|w_3At$<9!2ZL)>v^~<(QxS8`B6|MXbuqa zm*Db^+mQoXsHk}{%*nZ(V_947fQ;^TcT;|Es(Sv+0`Ove=w3MEg1gdSEFGjCdL&xBnFC{a+uMm5dHvVFy@!3{QGCa)$_>C;0Bgpc-~{x% zOWE-6mK185TXpKFhS1KcHr)7%vGG*+^ZG9T=o8AS&t^nT~O=k+|a5;Ui9eO4t?AY z70v63+2Z@x->}d%@Z$uiCLQh~j4Z>EE2gnCMoOj|_gr+NAE;nB0W4^ZCY zT6e`9(N>{vGTz?{vY8_3Z}&p<0a1r9SIVG;fme|sx&~CPCOHLR9{}0szY)jY&%n*^ z=9@Qk+TcUboUlhW<{LNy&XADA!igu(C%URI=SuZ?xqt?H7TMy9d*1Y5@8wgKV!t`; zd1R^EBgGtmkeUBf9Ok!bm8Zy%_s9H|%eGu>4tdGmrC&<%y=J{OGln|)Gn;73yUr0H z8&)2`%d`wK7FJ>zjSb*Z9L-1Z=tS$P@o?$01Z(OEbg%14gKAw`*2=nrsxva!rdK8#$? ztw#sY2f;6MnX&Xm6&xP;FWn?y4hm|IOWQx|16T8ZVKJjapdVo{VKRh0Mn`rAzb$=( zuQfqU4}1uiH@I<4$e;_JI=qq+`Gx+>m$%I1i$;M+?%=_V*KOFRr6VPCvkkoGrlq}7 z>LFkDcLZBH-k-HZYOm&E-|=FN%H$d3%U`MGt!f#7mK#JVH}U*|c@;TD#R*smljHa2 zKn_!SNOR8n2r!$SNmGwNe?lI!Jgs~+$cxE5V%6*gO1Ept+!NUIAk}c_&1x>#90}WF zx14nceAeH*TGKvY?Al1dMI$}-g@ zKLm|}eo>)@I{KmwhfSmn(Kpdrd1Aqk7rB~051O;%zVeO*^~?lvIr!4z&R?bJhx-fm zG@WVaC$@FLfhQ6Bl0!8(_j-VhEwd$9AAMH`&uZK&8iVo7cZhtOfJ-yNp1&fdu^-$s z{Q~O3N*>YOmgQ~xPr5F0)GEYBFJJX7DX7!VYU4(dCD zFN&?)&_|i(b=Lp=fhpL6YaoDn@jUShK_$`#2#OIE+ehB*?pJb+;Cb||)%C>>ZO($| zcGI`FX_H|3UDy6jVKZF)=+gbcbp@Uo9o9aJ{P@TFU(cx1PXl8c-^_4I9@I`P2AAuP zLuisnI#GEyy!sKIr-fY8bMK6~sj!EDp{noH#%?3bUahu?AIF^P3WJ+aBJMkf|HbkM zj6(*;l9Z#(3~&l7tFK`GCMWRhzQGdqo@wySoY0;J@}g3QBJ?HIt_6v;>fqk*Imw65 zpM!z1H@)#6>QOe)BXb91;=xpVNQ(e|BfVH-urh+yQ$aC4(30&{y!N;2g!NF!Z^o9X_*j5BKpS z;;Aa4ZD4*p`04>3?46;V7L56f{0W2gkqrATNLkKP@qM`jGbO_fp9`_~ly39!H{^K~ z_2~f`pxY_Bk0TbIzLb2gM7cj)YC&`L*ReD)K_C3^}WlRO>_y^ z$IKGhYl`=?lV+Q+dJMTr%~^v=TVv35hGP97>LzB=8r!0|3-EJ8AtPP57ddZH0b!m? z;A;0;W+DxH7XBX3{j{Um_pbT-6e0iJtFC}{ zq!RWo@e&m<#G2RQI>>9DP{Sn0*O*1CnIzUlc#a{8FF| z^Rr1ykobPsDj5AlRfpDJQ(Tz_g4&40_4EDUR95ayg`5Si#|*hcnD;JV4CYPH$KL5- zV}bwYW`3|;8MG|x2BEv3%9AsOpih_TMlbrCj*^@!PPMEDxTaM9C88TD25l3gwj1Eg zqoc+L_3+mV^`$Qh&%(gqyDZHdCy-NK71o0}^nqXLB}V`K&HAgN{SQ{)-!(SvPp=5L z{+P>s_RtUBl*yBIhSvgZ$m27d!pH}@pnY;RAA5*M_Piz~n_&{SwawFP*5hb8sb zrr`nnQDovVa8K;&;vToo;H?hZ)me9CA8`coCBr#NPz@+pY1BM0nU@28@R zws z?LyyWkLKiQFXC}H7VBu3ZGxPS%i{%Os5^VgTMr*ypM{H$6*PJ~7vSI@w+6{9%xm3w zobpMf6i5Qn1hT6qKw&}b$uQ;)U4Q<%kock?x!~`(@cIJIG(NnPB%gYaz zTtZ!;iKq>IP5wvzK0FXG0Tu1qZw$K{LHuIy5hLCh*yO9( zzqMKL>WD3Ond<@r1>suhiCzd|vAu0pI{^*XLvvJde(MfST%VYqLk?h7!U}RV*uN@7 z{9$#6(iBemxc3wAI*c)2&8`DNl_nl7T4PQ^+2+_iifWv1eV(3cMP1{htK3KIoAJpw zwq30@0u{7se%>C%kzfIgI5t!C1FY%H@`fRYk29x;_*Fl0 zKf9V%UQIxd=zomS26zv6kW|=wW&!%Yy!#=6b6BpnX^%VlZbFn?8jf?lhbM&KP-4^% zh^8WmHD^1pPwhp+`spF~cFaVT2zg2zTV}m(C8(?J)l61BssW}4?B-Ofm@B;0IkkyB z@Q)Afxm_T~Ieo^oINGNL->3STv6x?WjMwqpKp%toM~0?1j4N*JsH!0#w$P3>cnHi4 z|MN@nEQa&O>C#L1eW3rz5x|7cf7T(wM7nG{2weT>FNJ&(%LGNnJrC?-spr2?BG?Eq z7P|)SadV*TBEFP_=Stb5-S0JI=(`IM(D%^p1I6rQBGsd#aI1FsftBVWBpt2S{chO_ z*KO`dQQFRfLY?T>$z9}WY*b0T&KbuXTANnWjYXg&J^uU_`d%E}F3j9JHU#g|*I2_R zW~T@cPhDRk`FK1Vp?JVovJ@#=>J0C%zV7|1-{uDdaj{dXo@iX^=Ft77)hgfC1 z6?OxILzkZqLkWN2%UR@N1Xf>;zh*uQL_f=QsKd}VoIG`M4)bHosqZD%g3}>_TB^-q z1%1};J{6zmW`Mr*DLdys0#LTU-`Yg(P!BDCb`|b8J4>pnP?=c7F}I zAbd6JVy~NkZEcb{Xl)Wc-Sgg}%qL(Ug6BP@D}%uFWQ9B@9CiI?C)JXUN5gOCqCN^8 zV=Rv+^ z^H<)*uL}_nb$`IZyMGRn8GJk@6Oh~NEzi#6(+?+ij)yXtW8b~V+j9p{51-$a9VVA) z!Ja#jT>FA$XkjfSv5IMd)eD`Odg!O-iE6c$%Ik%(PK~ldI9Hn86mB(olm}tm#HEe6 zfArok=RS%(W&FM3F~Zu5aLrq4)W{pTd!%QSMmO=C*yvpOSBw0|`!e2fE$9RFd-^dM zeMh${UO5w|&qGBgvGp|a?@UWPIt7vE7(PCgeC-F`4|At=4kG6(dEkv@8v78q?%9~V z_&or|$0TNLs}dn$^0Z;}QXAOF4qq%}O@){Ld374$-qAy<%D&)1VT_5b*DaYKcej!=t9n|0a54e#&=)&Bh1egASTF_wl zC{r-j4m?xJbfvRx(64{|Ff$i&HhDH&wIt@C)Vz3PzHt)fYNmb*I%B_U5v@+wu3Bp0a|@#dhQkO3_?v_8SKE zM=9w?;}e16$V9?p$ec=>NX`XT->S5kUxB<-jrXS5k52XQ zS}fI@}4oN%M_w1#T0Ki?w1uji={u;N`1hz@fKKsg*eg z-)QKM`;ZR-b&i7UnmmVh3G(4cr!Gi{O8%H77watV|7W*7@W|`Qw{pI0#XWN zT<^88U*0|{UnnLW)NdIdBP=h%?-Byh#i1VLv3vczkQ|M^Fz@QiJ<~8hv{8Gvpc-ti zD2Sin=z_pT@$wDg2G9x<4^fYTxI4#Ki+l|H zV^Gov+eZEw=dQz%dgS~1-H=M4?*}&3UfN547h%fr`qWJ^>^l{7$`BhL0~VILHVxd1 z$KJJ~(5e}S@ngrRH@?-w?>7UxzNnwh)E9*Qx`%r*wf3ii`9l!6N+)yGyao1O2J;Ky zzRFF3t-R174#>CAONCCqi`TiSa<^*6B{xIdlP6Cmz}OG9TKENpbZnH6_O zWz0Eq@6nid?#}}8U5TP=Q+O|EdPd*jiTy-W%$KTknqh&pIHl-4{=OKO)1T7@LA}Mk zs+%VjqFYJ5WUyb5GSk9^dS?tOCQo0ygS_jG5m~Pn$nDX|W@vq`JPZao%_fT2Yop-a zl=ZNR0K?pyw2F97mjCzvWo8pu3!#*XD8%z*-8GbMn15c*!dwtxoB7l zZuVr?@PngM!EddQt1|H=J*bmV4BmRXJcZcrOR+#kb4Yd)gqO9WUwrZd-aj7+B=N}Q zVcUD2k&0Z}6^Y+l$m8)|mlz#JZa8D@?<(!RY zFkI5%aJr9k@G4#03%gFRRjG55UhaZWcCy>Fdc*MIT!|7L>Jr07RgBM+=CK!`orUP# z5CoXqjZ@!7PD{npa{^|4P;YG@6s)!YrF1l2`jG=bYI1iX=|>9m3>}kVxE>8hyTeqO zH(SB3gtp@R8uAJ!#Jp&e27oK8e5?_5Z8A4u#W37AKE0wXTkE_GySvT98mN=~t9=r) z>RkZkS09GzPa{t?!1?`C%xk_ZJo(ic`|3i{S2p+aYvEi)Av^t`4gBP9W9Ft^1P9gq zlUZL|;UTqdD8tPv_>^?EMCA(hLTa*(IdzS~C()|5>bLDcLl$s{lqVFX8wJ-Kt&kU8 zRVb+wIRZbAY-T>fT-v1ts_Ts@)36sbH)$m?1$K#Vu1(|nE_d?Ya}U!Qc)sf6aIG9U zzqPjcI%c^*rq{q^#)iHhMlWHX*i10W>J%fc?}NTfPEXNqV^Hv*^+(s$4&Y;@b_!g< zxhm2(QXQYSzE4?RZwbg>_{O~L6*mt_(y=*B!#z+N^D6Hwer|UD&;HV4FNo)>TrGz5 z7P#?ccr^L`BE0?*Z6_Br2#ps*qI*y$9iWt>Id=?mqt0ie;)1m9=E9QPBKg#lHaHh4doeM~5`=V~ z>gwTMCpnEs{ZeT$%o(th3I=t8M&$>~%3Dk5-?B56Oq~J&qr84HUF;EyZiyT*B)|vR z%+D{0r-6o?@@(q&ZlFfy3?So^k4t#$4b}=q#rBFT!PM|BgYwKGT_i_BU`3RlMtv8Dbe79 z{)O!UZ|=So@CrO}MB6wA8v9QRy5oF7PIW!FmU0Q6@fhR|{#XKf-D1D2$Ad6+FYcc$ zYY$ZM--xWlys|>dVJ^mjNnj&6kQr~?2EVQ{hS)9F!ig7lBR>Snq24`GRvh_yeziAv zwg+cG|047Aqj;~1Tc#ZMJ&t+al<_yqBZWYDoSHvRs{$z2O+@ICE7@zR_#l;N2y9Ek z=vY`6AgMv_ozS&$V7l~TOHyJmmTXqbb zi#P6c{~Lok)^H!abMxT(xwT?nzXMv{4crOCe1Q9Q^j64FHzfbJ)^Nr&58lLmIHhHQ zyt*OkSOxS0>E5MVldHqM{+ZR%)mQ%Tv3ou7zC8A8##l$pydDL=Gyk|RVIG2pGYpu0 zuouksZOx<28hGc{#>ISM8iHPieGB-x0#OP+vk3wH@F1Dqb8T=Qa(xGKvbM{?Z@?$# zi&_(8Q!S{MGfaV~Ud%CtnNf&0&8BchUkTASzVWlJ!%(Dr!MjZf-{W2l%dgSblw_!Q zK#&ak^E7`L$K3h}uX$n<8bW_eSwx7iSp=&ad4jh$0X6YhL|%|8_8Dx%TkAdO9?o zWS^3C&j4d4ZMt+iV|b!po*gGjKp%P|ov7&mEIsADEc|F3oOQWAiVmai(8mAecl13O z8+pH&V;a{gg*DK(@f#4ueUy-g>5k`HjQ;CaHwI4X*E-$W8ufS{X4jQMtZeaR*@{5`S z_8}i>Drm9A{ojPdU6w>bZUye%Z2)dU<%m>N9@lK;0}7> ziM*v(!3sw2kx#V2Xoh5dSgEADv8dMu%fqyBn)sY$nh|f*;QP8ouVATd9eogc{Jy*^ z1HiB|B;6)m57Vo8^`FAAkD{YX%;P!s{QmUa{c&LeTCU#Vdw{uogXJ#QPk3%~$S`o{ z=NCis5s#Uk^guwH(nPSrFqHcKvxvlV;*+PVQ!4sCrh1w}O>8=VS0y&>3Gz;(xklpV z#Fs#9f;5Vp9dku%DlfX_24TaV>&aN#G~AA8_%Hh{Zmp583aEb$cODvAE>8GIAT%wJ4>-N5QtLNcs)tsm&T) zzw`ZBfOjp#zYd%pfrN`UKMpd_!YPM^LFUm(DEsx7~~v<%+y_Cde3*KbDUpFp$U^?_>$zaQLEjtQvuKhwDXkn7$sY?$cH zh#=QKEp>(05-*kaIVB(G1jLAu7_PGw?aximB*m2e89v zX<|kdFlTL0iD>RJ6(%(@5xZIUsb*E@mo zT)t=OCi0t;Qxq7h(BJ!(TfvxU6y%F(cQmH4@6!33x8-I6P&izfW~AwclRZ?QjIA&i zc~4I!?mYHKt);MiyWI~}yMF8ns9)M@Y1>6%e>n%due@SA2-?0ackOvRKxE00V%7rZ zu>HVq{Ac<=eC?sw3SBBxUx=&ZKyF*Dr+>Qi#vmm3TVJW7ZG$%s=dG#;HSm<7AX*B0 zRNgjt5RUV9!-DilHo4(k;7c#%j9TsmV&{s)?@V=Kl=CTVX+5g4^T{d_;ZD=fXwqtnSYq0;D_6_V4=-E@ckY9 zALTfHj%FUlny63f-1}vci(Is8271Xq`Rd`k$DyDB3$uZ2MQfC^*<{IPvG;F>s@$5X5T3duj<9;pb&1Sgjg9*%E zUXoFGw21m-Z2dTG4{}Ed_EDU;H|yE?V$F>CrVPHee!Q3dyf0H79x@N~FJnhZ)Fz-b z`De|u$H*7DO<8@$1#>rYg)%$1Co=7KmkdJwXA=bn!*BZqc(Wa{?JbV?qx26XH#NRP zGqKJ3_gTYX%OO~=Iy&3$lkXyD zz+f;b$(dsm?#6j#PZUjpb6!#(XMPLN{%(}Fzl-z!&R-Ja)n)MJ{`*JyNHg~45e*ud z_MmPj%(~mR08(cH3&(MfpR#$(V$TOjnwe|>BGK8kbgk?6F-Im|1HdR)FaJeSAO&*ST8rGb6{kvAVT zui<%X+vh+bf}EqX)by?AYg?g1x_o8v0Os%b76*@2OarM?zl)t%I?NDkC)Fa`K$rho zq>L&7d+yisi(gKGh>7|pfw*L$Ux_xfINf?b%?lL-8gnY6N?UR!FSTXUeBM z7KAQFFl}0nmO;)&^S#--!pKea@VfYn_3seG*FOyAM?S#1zYu5tWAxFJK2kp1@B_}h z9@9O{wunB3Bwqh=+%wZMZM)(AIOfgyl|($>O=*l+DKWn&7_Z~=9{2hoP1c{X54FI_ z;`j+_^x5tl=;*(Ud4~2>ZHa2lCCnKy2dJUWmdk8%qB*q@`krw1CUTF#Wh~Y#y;BeJ zymT=&JPVMbLl>dyzYI1<-B#SG&=qyNaT_nR4+XghdrE?6xH58 zTCwk9+>=y3VFb9^>%xg{^ud}Jv!KK9B;5P7^raj*a;Ap-gjK_8NHF@3o0oq9c*{AY zJB}P6RG zYdg1a-dL{dD7SN~fqbEjWoP6DeR8v0;}8o1{;(jQ!3oqE>ps;6boK-D9$jM`S2`qH z<#Lyg4#4Z(v)4nAd&6p%eI~hZ9z;Jk3GcUKZ>E!QBH?Z(NZ;hSO})K#${WPF8E<4u$HSHDe~zgkKOPCmhUI;L7T2h10n2a&S*wB|qK(6vt_PbNDWRK_gSx@5NqVE_&OQ z)_CoJF3r!pIdE`Sf)f^E-p7PIo z_A=;0GaMLa`^bU3Q%i?qAA>@n$NTPo(|NUUKheW>!v*u;y14;5yVKzLuf!-7b3Q5w z{DZx#*mLpuzP$e=0Ui!kovxs1gkb%Or0hWS4VLm;RJfM~2I+lt&HKZcPv6vv#Ph*= zzsRH!_rTK)$6c=e#k?R{aK14<4}XS}Rw&|e@AFk)dBg_&ulKt%lu%Er*p%xzeF6Kp zuHQ@5S)B#P*&_9OsN24A+1uAap6QS@`{zH3iy(V=ZbV3C88%cFLjLsPJafp?hd)vU zY!3ZxduUk)$1Nj#=!2WR0i&2#pW;qit{R44I#VO}1gr2IxSzK?@&gRNp9=5k z$b%h<)3!~xUrN?Ko7al-;B+bZD`BDps9rBUyw5TZ#ZHDAw^tY7)&cJiarnG)1d|J9 zq~^i#8A2R?^B|lHP@ZQ+J=^p;9hYPn_RfmF*>kEZ0S(319nJEnYh8Fgx?(>;tjlZjL8HRMt^@=dDHkHWbE&47>S$CjNJ=S=)>8fI>T^XN<`lv}JD z6R@|`ncV*7=!r>SDpDJD62-hZS8iOVbsvmBlfKL)JPA~1JB>~!mO`lH)llDu`EcE2 zFN*yc<{IpuJiai1d8r$Oi^0c{TW7TX$eFVRth%I|3m#;^g{1$Yo&^trZQ8y2pW{ZL zSiRGo4*TRfsoit$uMJ~Q&-c@d?4^)kKEkTQj5@`H!Jru4BW*+Cym)odC#JL~Sl^HS zu`ity0er|4(PVmFQ!@>l*K>5gaiD*niRA**+iplHy+Cn(8+)_P-VHCux!pL?@vrXn zRM@)NO(R`f~BlwPZld!Gs+EScHcZIj>_%_A|!fjw4t z_>K`H&zDdlPU(CK`AIHTYE*TY3*C)8JSTzsotpubr@jn9ZU6^Y8|eyMesgm{QDhGD zYARCl6;p7_>Cnrf64W6BvRS9Uy@#o4(@be|%o#`e2ED)>cQyq_x0b=Fe9xz)KhN^FD?Hb16f993sR+7h>{WcD#)}1Ikd~mmr-Y3 zj1>?F!Fi57{=2e9RulXndq%Zwjo))Zk=<0_93=Q`-3@B%0rlAnG(Hz9U@*+7<3z$F z1PCV0+ooX7vQPbm(iyzJr>Bt{qVHw;_Vf8|zIixz{?uwPvm*dG;z?`em##3(8jhX`D9755rdXBhyVGPf)YBHh{aE+HV+G1?Li)oFt@j=a`0|n6(rF=IB@SA`b>3{-X@3;z;B)Lz$)har$+xqQGCMQ z>tZ?8N*(lb^#0vRajF8+$2y8zdW7W|L?C)Yonkk%NzJ7>4HmnkoGob&f6#Dd3QZ7h-wuYzK4Gl7= zmojo~mFqwF0siUQgO67Rp~fPY_&)A~OlZ8%GUFVQ&Czl>2m9uFnw}=yyq^NL7kAj- zV4q;sqqF<(F}I^=Oi&@2EQ7hkFHa*P(NEUT($|K*PdcyF;eO0D*GK=Z8DCt&dp9e| zEkE=p$Gt0ih41l|zK`$!IgP-#Yn&2;xOY`pGUmFEy1&&fLzQtg_HX2hi#|mEhqf0( z@3sxk(koMDg_#FFHA*FB-s8$kQQ79I}g;oNm)ByT6UP(TA zp5FoCr-b>cvZf%Q@7WQ-zdbPQNC>xHUj#ocud;{NR$%+f@lH+jRSG|{KQ(&_drh*- z57b61!?_4~`cs%|^;#4&qOHWzPqzgFbk+-%njio~7UHT-J$XPh6b$d2a6#aFk z?yrsBq0gl_Zf;u}`Duq%I%)Cejr^M5tCL4g@}FFKarYi*9Fxs{wDJ>l$9oGiaj$Nx z`imu2e+5QZ1I9cL_5u4rWhv5Fcc@b(W&aHGU>xw6`iuGksCG2iB<;n+1^H_0Sw_M~)jexpJT93Z#k{Jbm|c7@ibA<5TDw05!uhgAd5x zBoWBd5XL+nslUsq!KM|cwT|GMd5GLHx(Q>)R|_CFFK4eSxd6oZgWP);X28wOLZTV- zUh#)A-2d?=!?9eAG)nS0=neQV8Y0^ZOCJV4DFph%EshJ_vujK6a8_a{st5OAHy*5U z6{^CG13vjXJ+tsBXZYoFk#_KkWmW$0q!`TNlJ{p)xbj08ev@n?;AUKO zF;=q%p4U(=)OjK2c{S2dPB{(e>Za>#IVYfeCt%@B3+|u99cc#*U7$p$$#|Z(0_v6T zQhPbgg1uo z_5+_%%17aiQ2b-w`wd{VF5H-kJ|VjiYS#qGEO5@D4m&>F0vgX=Kl4R@b*zSpD}sN3 zZ6l+TpBV2Qgz$M%^c}c)HU3KSNPqx^b8o{`7Gaq*$966i{mhfQN~t!n;7%!k5%eKg zVH_9x^J0~sfmnOZ+Afw`5tWEuK) zvt*oF)?#v?yQEpuDqsfW``J=U7>dEsWNsTQACgv;IWp%XX@9;BUJlU#LrX>k#ToQWHqPZ%(j2+ThwdbAGvq= zOYI_jZTa3Ci~iovDz8m+wA*1IoNQhebI;A3WOeUObpwA|?rcb1BG^T#msmC79>8Qh zjYc9GQg0N@G!M^$YqH?s9nS$cY>@tVEU+0)6TY!6dmt}D^TDX}v@LATNc0sgrGmS0 zji~ISF))1Cc_nG96e9I<&OezN1Cq2s%00q3{1BC6e>{qNL%9#mOx-`B)c=c1rDHox z_`lsRo-F|OKz2?CTTlExiMfWK7)Acl8`?j3Kf516^y#qTGHA_nKMrXhhuGn*`{c>E znW<_%qK~{%CreeXlbDMp-z{5QFv9+yFHtg|_3B~7khn<#_Z3NreMfTtqQA!eq!&TO z91;VIh{BwZS3UDot6?z*I0l?N6L0mxvWfJbHRj<(oEm=BVZQCE9JOsEdk=h+(TY8R zenJBWQY+Dn9*{Aob?xz9gyajqd!KWlu05qZ(OD6Vy|yQ=Mxw5Gwp>o{Nkuc1pL1l8 z>A?OXp`Qnna37fV)$^>TE4~NiH>EQ$r*-u=$1I&s8{};Ws69T_2l|(!(=_SO-;(Ng zwc}wkG!HF*64%j(&`(0OWQF*gO*m0WJ7O=L43|+5evWG;TSBBExF@Q3vA~1-?C_q> zH=Yv64S!GakAig`9KhtoyY+eaCj1igFCb67eBJxT#$fRKcWqbxVW{gf zKc~8m`jYD&I2h$N-t`iOg^=QQtYqGD^{jkJ(E0e$7)$sd0X$9oamIfWT0qi++3%a9UA=kO_sZw$a&=?C*2{sM^ zfhgEPQB!w)EH>XJP*I};{#k0TKig(*^l`+7wy}t?cf|Oz`&J8783YXOzWGP~&;SeJ~tD9W~Y?(7^7-jXswNpEn-Y6~MUb}^NL9iE8 z`nMZ(QD2J465|veEQk57*?kIH)Zr$=+CwlW*Sw&Y1_jpbz#l~SjVc+nI`kf)1 z^Lm3R`g7pr+f$wrW0=zzA{qGa;}C?{T)W6kqE{wesAhbHyQX) zzsb7bq}ubR1MlfOoWx_}uvB=lL+-~E@ETG2Y|Tx;9jfc*CjOYKDK6-3m-zs0ALaS% zuYQNJdG$c%N$i9C$wqg^7Vn`iuN6PUeUHYNopD;?EFAwZ#3RN$1Kmd`_OpgNFs`cS zcI84nEO;*KeUwLi(CuglkNFT}87}|kLH+Id{(qa6h4|;PqY{jb7eMAqtyTLE^f%Ex zwLTPqeJ$or)Bca9@jW8>_@*2BMioYEQz+75V5Uzr@-+HS7E`QKk(2ZJ_J0q*apF8t zdZjd4#~TEwrS)Y`V16P_@LD1Eu2rzRtM^6JCstl1xm5U;%@F7^D%tB z2rBu9kOR}*Ej;7S)(w6vT0(>3)8KZIIWo;H33mK`y~w~l@YwOjfX*cqQpYqf<_T+&>fjQqhg;wAYF#Tz=i#_pUKXYlHRY3EPjaHEZVPJk*lJw=` z0GxYd;6RS=3GR~)gV}525Vx&PAMjR>4IuOHDJf_uTC{w=~UBzWCENhjZq31 zYJerzhedX{x4x>G#g|qnB@GC{%A_h(gP4c^_ikba`w4%noDSe1fWny9QC|HeaQ-T8 zU>IBnha<@fiO6bkuUulmGL1crI+oPgvH36)8*SV+I}DzDihmF8wSbab20anmI8@p* z%GTiLrQNGHH_z=1z}ek(xv>{&l`P14-r~G=|L9S^S51(0l>A}`V>e`N`cunFmx4yJ z@V`{#_Wd${tD0ee96tYbfqe(;C$4uoI~r0AHg)%`&Yy3E9J_Fh3iSO6-)oCoEnWr# zuOnZ$kD+cZJ}1NYtr}`?e(^k%kI%aq^QlhtMc_LU$#-O67}ORnBFIssaaxu=k-J*}zs<+qt4{a8XYmkygH!zwxKx_y z?t*_$bJfS&c&@xzivRQbKp7b3J)5^cj!N$P-~;J4*fVByY?~^n4VqQhRC96up~{t8 z{2es~htKQfNgJWRFTh;kK+p=fM)l0es1U013f`|mtT$VQ7mMdV1npl%y%QaF`6 zyp4e_r&SX^64dQ|-95RoD)9MFY%rJY1Fs{xu{R3)!MiD|?-Vo66ZCCDxyIN7$0eo4 zOoV!VQ!a%o_88aFRE2-D83)aPNKcSK?&E}~bv#QC_LejUm> zoq{>a!QcAHI#KXR*=Ds~Xas~wY=@I-BS0tqyvG^r**GcAHNKdM?}@~#9W>YvmO&g9 zdz%jX&gpv%)QN^cteDCp?Os3RU7A0g0qa8qSTXDh_xj{Z- zb5?5|&{(+58!(XtB!m94*(P0}vf9}+fqqp+?Gqokd*;DBZ9L4vZwx-m@Z`~2wL_9h zwPY&h7YSn@{m)yV-mLpfB@%sCXUt?cv+TOTix4grhPrITK&M|fZxxtv=~t;#7sKPS z`KRqQ!yw!Jc++2c8qA)%r16TC!YjUP1;UK zw!%Ah?fJhoeGpVV@O!@$`uD&6o><9MX7z76dcR~HPeQVcHKMr~k(EHBYOc znF0B0Vh^Q|KgWKr{h+f0@}n0_EuSm&!|q^DDJ_m4U>6u!tt&hQGI<%5R~w7qlKH0w zfzut}m9yzvsND}p;4C@y40(XBhUC+dkt-!m_lWn;wpYN!&p2`A@Gwx$dRu3r?s`14 zSElyJ1ej0nzcq3?3q%gSOdo$c2-?9-+-0c$J@1OSG*LGVI|kO(cg^6n5x0-jJVOkj9OUYTN?bW9toF^Y1%r{_Jiy$qwzdkmr}Nz zVOfrakY&)Za#X4roT!%r4!9SC`WcA>n~lE1<#+VXhWWiaa~i*oSj!`R|vRIxu<{dTp^3_nnLNQ{Qvi zAp7Xs2j5Xo)Lq~{=5en9w*MAB94OcZiQb*G=XoY!=0Nfx&)5PeIa96a8y5$)IyIQ`)v*lSF)xh+pGclqV^>mI6`}bZY$mh{vg}7M|?@MTN)**0LIh$2y_W)?U ztMJbrtOFIeL3bv20{eW8Y?U#WEX3_7*|!zv`9*)<$h8+jbH8B6UYu|1PkEeqMU8#I zt?;gugE4R>FRIKcn!NfTQlt^3DqR(8pbRZ%q*A zA0n^gwf{{)w&D@hCkHWiI&kNQEpk_V&M3s)@W+1HdjAu)Cdg0Wcrg$xIfK1l!R8#l zCP36Fhi~(mep8BF`sT8%^=r;=Z9zw3Z^DF?Df~W zXbKX zj-NAOh55iTW^}9sxjIZ1HW9zt>%hB;yUaJF8CbhhepNBnK?Dz%i@ft79O6}^%Be$L zYs=lqYj>vMY+1N(>gyp;qB&c5Eq(^`6o!p$U3E}C8z|`gtqVF_+~QA4l)@(+Mt@(1 z5u7_VU6-&xp9^!w&mGbkFgPdI!@WEPSpza7Q5l#=RFB|8|i0KFCu4d0$MY^7uj{89i<4k=H{;0r2;@gT zv(=}K`3{z&CyfhjC&6z^xPQ7=E0}bBx~;@F0jDXsvwqc1!9y$6w2wz-Vesu6SBuG9 zn27aRiqb+Zghq|wXVU^u_}m^D8&?co3GB2Z-@<`uE1%r{mIm0uH#5_GbOLPTt*P=K z4nuEFr1(EP_YazqHzPUdgArV7Tl}5@Bh)4P-+Ra4eLS!(O$d9bD$t7SjrzI0@9D5( ztWm4Xg|wcp$lH58LjU@V z9CDPeJmNfu=So2v$*vfjUrSg|Kh?p$z-M0rI{$|BgH-=R<3r2+;9+DGHsyu=Z0g4! zbmOD(!QGc0)FLOX^iEDyGx`yWTc~3EXdga6WYR8qUAPu5zf5afq*7Ye__Y$k@PbnTN>f)V5l)Dv26{ zqnt`?ia0lJd!(+~GWi=gnMhw0zl z*tb$AY?5YE0H^oS4qYh0>w)WiyNIGJ&~Ek20`}QwQy=}H6%UVoZ?sXyR)KBAo9eO?*n_Ph z?KAgn9Et_2EWcr%HB85%&_SRdF8aPr*6yB#JEdy^Px0&AHc@tiF3u< z3AVLm=^2n@b86Rx^meEg+;~B)*bJ4A8Ci3VPr?4I_Q3$un>-IL>p68{|6ky@{+aXW zD|tadrK^t|ut!NtMbQ6{xN>UEfHm0s5}Z<)Ke!z+6Ga+DIPfz6%Q}^7f;kA*3Y} zfSeJv%_)u&=BQVey_nNxb%VyZv(H;Ykk|I^s8oyc7_6@rXhu;M!9I=cHGk2sz><6~ zl})G>#FosgWX3UvP|x(xj2r!$McP|vuqS0nZRfcjrVw~`;n?{+f877p&bH=TeS+=j zTi1Ol`oPv`cB6y`c`wq8LQl|#`{nX0V`k)I-CE21u_+aGx&1V;v^ckIZfW`>@UIc5 z62H`c63K($-uJbK_!F_eK`-?V`dU@$ygQ|FuJm=N-Y;Mm`tt=ZWos6U17(%$1l8~u ztfYDy^C3^QUaVu&DdgY?yT~24InoPfx9-~I$TJ02x)2=bH32zkt1=Icw8NWEk;8K? z&0uccS$Zrl5t10ncetw{-`8XP&xuF^y607{Bru|0Tuf0?VbK6DECQW+Zw^9-tURMH z>X?6z9ZxZFZG%yc6A=r@t@SZnl1@ecKy6X7QXz7EYWJ7e@2AGTW|k8NTdFD`wfW)4 z&j-h${JT@pBB8M~;t2^h2~pp6DFzbDta* ze=5p_IwKR4s$n_$+$v0m_vPaCNl~C(ah||-)quAN3+^y%_fL(368mvP_5_>$9R=nf zG3_n>*q3_x{l1v zcI=tP1eOL+T&$+xNScL;XpVw=Ytz7QdGRsJLO84n{XW}iG6v5}N&_qo7Qt!HZCf*( zPya=PwfKID4o;I!EUBz(Nc@$zL8^lshsXFRM2W;HWd z{`!w&j}Mg^yGj?tnlb;3(&pz|%tIV+Bywgjm1GZ3f1DQQ<1c$@y3{ zRB}W%0}ezU$h&Oaf*ij5k#wedXw)vt)!mW_)n>XM{&{-=&!;xq_n0GRU)texL3{*` z-@CbG(h#}mN2u%u!jZdb-PSpYI!t5m;rTrCS>#M!l4YYPfTKT4R9(-EVXk>}T)YRl zVEH>-(yk4l4tC%~c3m%|OE@XhI-n0Zr1Y{1eKR}{yK}b6Bo11s|0MZKAx9$n3h$v_ z?29bWJ#`&@apwl*RGEj76YwxyrA?z7Jg5hbxHC3Fz_-LcZbm#;IsY@>%RdXI8kG#6 ze)d2w1H~Es{XLM{u*LD#R4J(cu87b^E}v8VkHuMzVz|0|p63I51Ejoo{Jmoe^Twr5 zHQ8DxpxX2HwTuVXLB}Y3AOYvLNs>k}dz3oyD2JW1`FTK4BJW(-?xbZE1(! z2VFm}7+|mQ5eE8cyg%JF$qq6O8-pXo0@f|RxW~rlJ zvA6J=@yHCR4_(~I+_GegMh%<}*E z)w%&<<_({0+x7((K8w_BL0&aWUXcLn#w_-BuUr$_K>k>hdd6z~XQ(%I-W++g4*3X5 zm-y0=2UoYc+XUyx%V%F0o=4thh4pDMK)+_^WA9mCyiW3@&t7~VT@44cuf%N2K%Gl< z3$3owFvzwVPIHB(W6#c6?r_Ttpm3Im%T$_$&RqlA?{WVW*;j7-;ARo1CA^yo{ebzr zioARo%qiLCdA;bj9fQ%s9KX$EW+3ASr_E*|^utilxL3`Vfk$7J(9@^Aa4~Z-`Nq>u zka^xJ7KFN}iIb(E@;dqn7r8@4P}kp4r*X0RX$y$2WDmZ6oC?hPwFy^Nk|8rCudR1y zKa6>IaET^hpP7^Loh8KrADBMUcVV0 z91R5_qn=Al$V3l)*lTbN(H^iZ7U_VLIO6;j+&Z7!Tahe%3YvJ?W0J;Sj2 z%9qX$U)SWd(?*gpt8}0 zOQ}2BVYr{?aQu!Q^xtfnY^=6}6JmQ`_m&ian~iT44ZhA7%3{u(b?AYXvp4h<*!n?c z$8ELeD^=ja`A{h)brfhlmw%te{$fR$l$-OYPwGi%>snxMy$ZAR%iJ#+=o9~)DPi6S z!}VdG%xxy&{tl6jX8mFK$C0pfrvUYRlUl7gvtcl={a1A5+z^a&E%SD}g6uTt!O zov9JIq*=QjUivTwI}LUmtm7+%oaMD$*RdbMSHZSt{-pyfy_a!(cMUmj>%W_XKV^W- z$*@x&Xlvk-AmwqB@5o_t4RM<@9DtXcX|(P|xKB2!ILnMYst0t(-d^BIgPw&bSzf4t zl>RIc{yiOV>mol7)z(gUricc1%SXd-Wk-K*m4c&Zcd^3^9=t0ltBUfsQHlmqbRHN*bGr+tw9N8hjP z;wT({u&=U%yA9~32XEw}@Ax?H*#VpFGZ1q*g>v>yASkKTrmXtnzRZrfvJ&rK*F=u3 z?mnImbo`9T1vm%c&ndPgnB96dTIixgQ_;B z*;V{=H|CCHiy!R(uH+B3pK!nT-bC%`s)m=436<9U<4aUI~m z^iY4@wV8ff;V=HY2X?wF(AJ57O6aJjcLsnf?3 z=#1Cn>@TImrm+Jnti=Pc5qdwZ=@`z{g!}fKLXP8QrbQ*^XU(8fu0Qrl4}IVMxB8Pd zJqGoATuCjl-(efih{QwGm3W6wo*XDlfNiC#R;EFPddq=MJ&xKC73yL)kNH)wmX z`h70=Pty%7op&4OXRp zy1zO+uA1A%xRJ8AGMD9Ih?tx~F2{qVZqrYXP7QH;Jzotn&2@qBoCbpMEy0`_6k zonWrwtAc%B+kfqwoPpkYW07>hY2=fLQJ!B-h24ea7hAni?`NuC_s_t-hq$JN>pC+K zD);X6*XU5>{_G9OQyPR{VkOz%u+QxX2gR4<3_q9*V@%Jd?1$eesS*}=-jQf)dR57s}1B<3{WM=P|p@%E__#&HQq0` z4NCvEqeE`W<<_Gzm|G1UCt8-teemg3qjL*Q9*pXyn>pgwBQ!O(%>(%gl=oGP3u|Vf zXq{qJGieO8vt=4gu2jSEgZ);_mTY|$auRSIA4l}UqLRo(!A0Z z;b6=$*7+paVs9ZmwUF_7%uB&){5^GCPZO~{@jR^+@YF5u>__AoNF3W2+*^lSg0N=U z8cFOmU=7}tHaP)rV^4SAkwrf3L9-LZHWMJ$wI#vA3we-MAzo=Wlfn1sm4c6h1(2%6 z=E;Zi(S)fS8=F7aBWv@~aJ4B5`t+0>1~*N^m-87nyYRkg{!Mg`$yf{Ic)9uC-G|o= z>&kyY&SP+ghjNWeeiRZzrY#IGC-u;=p}&8(FZd4E@g#i2UX-IB-<5R?LomY+``t;o zz|U`4l&>8Lk*ew8HFQPrVQM(#kz_wyS>wDOEHVHhQkDTF$YX0wut|A^{gS(fCAGXv zi$F@G!TA{G?h~jCM_3rK&qdc?a`^2ih$-JHp7Sh(Kf$ToG^2x{Q0l$)#l|%7t@j$-aVd(*hh7u2DT=Dlq>-vL(@ zegsI!cS3i}^{b-YJ@7C~*t9;w3z)Ybvvkv+1SMIEF&^aoFUj)>ww@n==T$Ecy>=}D z&$nZnr?ZD(rw6B;8)qrpPwenMzg`B7d1h4N*k>#)@>t;1g;5wOcDVc({i{hL2N!rR zW&k(y--y4c;g(I?YQ%6or20xxb7DUELicXjuHqo@d!u(h zKcEAgQ=pYHd`HNgItGw~*vk2TI8 zDsM$SU90{3Y@q`7%fH~bcX)XSoCmDg_`adPXXtj6;%yh0?(SjT6qq*MVn-5s_$hd$u3;`VxU zy$W7wCT&wc)(k#<)okng`(gW@k&JV(!%!)0-`Shm4O@2%b7b$D0A8l&4k4Jcv*NqE zjo|&_QkverlgP(Fz-ewPOB-;m*PXbg*ae$plr(iSMxk^ty?~Ls9^}G24JR((yyNSt zzX5U_nx&(iejs8DR4|&$cn|uK4Gp`@lJgx<^05j4XSOlxdJ8m4buY@6) z%~F&h$UV(-`(R0x3J+Os0~LKcxZNIc$>`|^N(u^!%lJ+~u|b0$9_l_dGk&?gv9Upo zzxvPn7JSFIW77Zafr2mZ|9t!(KmOO}|9Ag6KI#8F!z=&ozxyAap#gsKKkxt7Gn@nI zz&w{6>PiSWq*%#tI1_+9HK%a00RG)`KKK#4>j!3Q7cXiI!#P?Fp$Lm}e{5)PLebNB_)%?}g~G zPdGdA6&7@i^FVJM7k5|^vNpQ^C?B}}rV-{B%C=4849A*z3&@L(z$e*}Wto*|kW)M) z{p-dE3{33Xtd!LRdkoZt>_h6|WkvG1X=n%ZE=1c0NKQb>_xD}uSMs2VN7V6`;1sNQ zHRP#vWy28XSqCokDjJ+)xhQOgTH9RWvUEi|aJ_HUrdThBUqYJtaUZ83Kxoft%cqsl z`qOElavx@z6|Ei~$j<|Rfp$i2l}@T0%i=}=)bk%G$L}Z|6ZSuu0Q@3QyP{-&*#dU&FmwHfwWj}b^Z?fMV&=2(cdpeo- zqKB4RT{y2Gxv30PhnG?b^q&Pe}nvq8wjO;Zw#{d{c{ z!fB4Y5Any@c%;q5DeOp{kGxQtP2C6Kz4gu-=y54#i9dOZ3^>D4?2L4yEo6*5j|XA-F94*!Y-bdeGkruPQl?*XLp67C*}2; zTHce@DM)O&&mr9s2nXZ7#D{cD!NRL8yQ%QraQjrGlfCNF3LJO3_K1R-WwEAP`l|CX?{8a5~6XA zNkK4P<4MlK+z_&n)8dM*CfC3V)gQvfd!0a&+DBauy+)NHF3Jw+rKCi`?U6KQRoFMQ zlACbv!c=dnwDU&}`THVr<_zAWcf~T(Cv}d%g+&g#VCfM^-`4XhPksdCvo+q|T*FzX zl;-3M0qn|RC&zV6%E&ppWL|BfJ zY8pFhI{$e59fJKmDj}1@9pK9Nv;I{`FF5N{10uAm5}^Ia@Po+Ra(=3 zi-oko{En)zJ4}V7ThN8sy)cd(8z|)Mh)#!)9eUG=`&*#b&zZ+AZVDtzPvoWUZ->IG zHZgk0B}Tdm5uuGna6IFADT*~25XJTM^}lAYwfWuf{MG-s zKK^T=%)$B7M^f+GVm6K@jozZUkcjVfeEaf70zAoAcJ%pDN0{EJ%NKQq5T8Hn8s5n6 zO1v%^K3v!W@AUS(6W!5CHtKJuo3S-RX7qrsets<28+c|fJNFUIwU(*J8U=)%{XZCHTtz?7*2s!dNwq_^ z|CWnp$g19Vw&FeOyIf!n<2sY=Qwy7&#l&gY+lk9CbGE5*IWa)++BKy*qLlI=4CwPf z!Q`^y2fsWL^>D~$X{`hvFqBU5VV4QpX=#@V!%{FKO~;F`G{HkB&f|MqYe>tfya&Da zP)jtM5}@=L0+Fh7X}`C3km>8aZON+xa8H{jYQ`Pe*OKxvtC%G+`hGY28lLIoZ`^43 z@G}`+4RUOq2*ZvLmv31#LOpPIM$yMWI1)Vh*0d${`pD`dw*DXgFuSbHMdz-SKoa~M zPv+bxAZZ5uoNm&SAha&eW3VX+iXJ4cGA#DO-bZ@xbiQKu#;lcBLR%V`q-^Y*HyN&p` zIV9@Z+FDgb4`AU>-bKUTQVw93pm~LRGc?AX8c^nDRw*4IK0hzVw?P*?x*4 z4r5u3gtfnfZiOnJc$C;);_YdL_YS#Q*$p4hjPOL_F2H$^NpP^|5nqL|-?E&U7e; zgavRh97gS@gmS3nVkn*k23#4JFsmR`^`^OYqmxw1I=`#N8Clt-YV`nRWS4D7GFf;Q zK(U3C9nW|LZ14sIYR>k-`KtqV1q{8A_t&YF4n1i!*0*>s*kA|cadTSD{zj5BHhto@ zbRhZeCTbN}GzJvKCHeQhv_g|ZKSylC5L6jk{_VqAgSF-LBH{W5U{H0Poir>Wi^muqx5~ zjK-y%-007^$|YS+=*726@cb@;`2^R#PQ?Z?`@V*;7d?vYwzN`(27NG4S*??B%#*0R zwAi%&Od)J}rLyZ=PaARK(b22z^MttA276bpQli%U!y*9hb3!ZyJxkp~(AYUMk-Cxy zGPVaM{cko9dB=|fiXw4v#-|}TA-DmSijD?{j$qdRn!9I8Hfpf(#@1Ai2Z-um7}GJq z6tXFIfa_3K3;8!nTQ-dyb$OXH5)RGvu;O-Tn}l>b;br~3N$c7qEUX`qITE&d59d4TF zy|)%@f(Lvd{M@mv(79B+a)v&K$SCYnAJl0jWc>3a?b#gio#(wKwF`QL&PKT_3+2Pj z1FBqpt8KtC`SQ8;n_;k={jSf|aGVV@-532A96|Q27n)J* zp8~g7+FGu=tuQX6^tSm|0?_{Q(-o2%2C?4$&EaQ;;J5Z&?O;pn+^u=7>2zZPz{=S0 zMa^f>$g9*e6KW%uf-;U;kL3}+??FRRxutL?=Jh6x_woP3{_20eN+>AiAXDYGuoguV zc686TRUmstK}qUid|Eqn#q4$BAbGI8ZD0Hcratn`!1m^mZE5gjcHben(qh6?z+ zR6o((ah!^03+`v6QZ!r~QphPQ|B`fzB(QZk7QpqRlc;TW%|E)Sm?W#pZ%U!-hH!(W z+Obe=!rjnkWy=>!ZcdKsx$(D<2B(C558hXjum0XE&K32b?`(UvdUF<8FH5(pFK#3% z)=sdDn&CxL~$Vsf#K?s1q=7gQvq>ZFv8 zK(CNZwe5EFKAf8d?+(}`W4OEf|T7B;y9nH|R`Se^qb~dCRICI|iK^NHa>3DrNv65^8qV&}VuxGeLC z^qnG>l|#d@^EbD??_wir2q&!>s9a!p8?Dx@$~qF#@piOPubx=m%IH*8>H^IJjK{X3 zRwt>M{;y#un~WO16TEt~3n+_KO(@E$$)Zq4WW%|5Qd3a55O=&6R?5Ccx}&Si=%Ug$ zXEFS`?KJa@HuXZcc7pq>`C{m7pIR5e405^?oz0W(Vp!oXw%-(-4Mut6_tzqk30W_; zs@_shA~kpC{WT9E;qI=N4NhX0uBEU{R#EKr@)}t?Ci_TRN%Bu=>8R4Pc)`J7eBvM1lywCnfB4tkwB7>5 z;9VP1v4;G$p17C28av|2w|is4Crh!b_@}`5`^YK~9Wg&9qfiI7AM{y1qPO#ZwIcrK zpPz&L=PA@Vx5t2CXRUi2sUS*)s!bZ`VV`{xdb*aXlw|2H>GW1$cFSDgk6gtFwC|AW z>;2b7N)>dhN3zhfnfdhWr{G)=%l7uN^_~JBH;p4FGcY?suktmydYt@puD6k|Kn-*8 zCAHGwB65p1>+#{Y{bcvTqebN|LgIsCnK!Krl3T8yR8DP5M=f?sThP4`P~8%dVRy2Y zNH}s?`|D+rgFalG(fqi-`Fj4iJ7$ZnQb%l+XY&JYQ3tc+JCkIiVtkN8xq(oeHKS3u zfo!Gk|5CR;$skYO8azrbLJtzZjWj=MQkRYD5(BZrZaVHwxpsCWeC^3j)jC=Q)a>d- z-Z}w9Yfo`hUUxd_d&@It&Q(ly?xHK{n~x&*_&#jwnjsjEW(r>PS z$yIw<3AI4tK9k#VbpI4N?3q!dvH%@b5D~q(U*hx#lFLi^FzG9rNhXdI8N&j z-f5U$85H`;R7MUN$Ozu%Z-w-5F6NNIW)f8SOMfqVaAV(pybyV2h)~@W;&zT0AwE<_ z%$m;!NPQERo7&`ExbSE8Pw;iTzF(xh?IeSpS%wrXcRL!Phg-X8^ALKHr5!8xtRnN^ z|IynVfN}-TbM+cvFM58ap)3b}TFJUB{_X^AL%Of~)ys(5@Qw{(^cXbo3J4xsuqXWo zZf`xZoK1q)bSDP+Ff&)eXZgXW0fNTk_7pDRxjKb&eCX*2S)9Gyvv;ixdWQw5zUh3hU-Ra~f{e7W&WCjFlJ!cQKZ6vRjOk<)B z=acI<4WkbnYX_Cb28V4kYl()7^ou_H^@kdthY@lvWOlppgZlgya(bGMvfH*8o<+KALHk6B*?2vrT2fVmRy0 z$WajD!+qePxQ7o7reI8eEJ&<;fGj_)a6E;x?$E9Y$`b-J5OyW**&WpF9EzC~hLNxx({02dd9&|UvnJSo|M5|m0c27&aTh&v zXogK`ysr*v50G}*KP`%QPR?nTu@nC~2GzpPI)1MVz>*%N04y~CN1n{z==^vn8h?9D zj46#Y@m~Ly&VnqF3(B8gzaNDO)3_U%Zdv5xz$VV4cwH_J_miNLDupXekA~%5Hj@n+ zS&yKTqeL{mNFtsLl7DJ#lm?ed$@^Z`8tJBHxGSDvx<{%S82ODA&Qm0jOO?ic0e|vH z+4{eEVWv3Z!Ni%c5524Og?bb6HKCAPvMzmszMjyX7-+Tl-cNYGv7QS*Q4c|haZmm= zkHgEF>V2w(tz_v}edt-y400xLi1pvGJP`Ez*t2CYk34^HNbgcq7zm8D9l1D_2{9=` z8hW)w0(=BnW#O&Uk$;p8%_-yl}>Ez!wa40e9_!ZMavZHn8zY3Tpq`uML! zH3v#uH*4%q_K~5BMjgJ`85ldixw;{)jtDNkll2r!B?^u0f3u>?;apzO)&PoG!sh5k z$^NC7=<<2>HN_T?@db}srkz9ZTs(3AL*)V3mh+s^rnnB|+)6sjD*{2i>lf>1%q9ex zP}B9S4TBnkN6FV^WEpt*ND1bSfVg|Kj3;KT=nI}cp*I|aV+~Jrhllcr`ZZ7cv!1gg zZLfQW?Y9Xs=gH=mvZ)Qy#HJZ`Sd77PbYkAiFC)-*?Af`KKU(3!yC%o|w}#15zuwZ1 z-BmzW-?XII+)BdVY}E+R%7wPnhSQVW?c}ER&4huz8Zg=FqPEJ|24d`YX+*J$FRsG- z%317Gey{p~-&>&`ZfN#EP;d*m(WIky>uM2+yd|+yV-1ybcGKzkpcVFRHM?Vq#cyI`&3zDNy^wNqnG8 zBeEg$pLRc=B9nl}qy^c8qQRxJR;QguLFSy!b2mD?G0&iB+5GC+hW# z{_Z(3Fvff@pe?wSyxw^%DCTtspVWLF_)+A9MW2=2)299W3p*>;bb!sODF&v-6dO*Pb7e zWgr})Z+AE*jKmZ%cMesLg86>`6A^#Qz`>G%)dJ^CI~)0wcDMMG%+@W>$XETFljRry}#ITUhc@BMF|p zb+>7=2dRZI>0r!O=lRQwP6cFiK1 z534@h=p;#^X_-fUrVNR^V24^sZYNysEQNN3yGQ%@@Tn+t_!Mv1cCuS4gt z%eGB2!kzWpJMvtEQ#U6%lZf(MFAT5{yRe; z(aG|JEwYa+zJBBq=!FdLXRl=p&?En+Fg;2_CIgPihS5*l?;=)mr|%1!d?w9NspCyVpe)<(UXy$LMY5>J5s;1pG0!DiM)3D3f~GGx#GjIyC--$Wu#9Lc;+a{DIeL8AoaDtl z+6c|g@B@B9op9{yv#GL(Oc*PxlNO7qfF{kEz>B@D5O?y}nZ8?(AaDK3M+KW0qBQbr zKJ|D37&{5^U)o$qjC^a(QP~ue@51lQ>zA^~7GE2KTVKz@kLd5>+Gi8Vc6q%_1vrVa*R8GKscTBEd2~R$!dT0;x-sava6-=NNeKDpaz)iNp`N&hrCt#m`axROBlU#^ zJRxkj_-Z(HBk?QU`eJIXiTu|q{D05m95BdESz0otLk{(0g97yCZEVqYPeEOAN-WB_ zhq;5uM6xuFT*Qv|GIFyhs2wu5tVY@8u*$b zkCy^pf5Dym2fBe$WOjL;x`Ct!465Jf#d)|kOYaJ1?P+Ou9n*4a1A3S+^i5A7Eax-p>1z?wup*R|J#g_glVwVXSGcDdlm z`tPU4$)DtaU#rSqam;A0%WpI2#4HE*o6S~lI-u&O(&y(k70|x^M#CIE7Dg^xJ9yRH zi1R+fj#1ls>^`TPDzWz@>_Km+@>%Pk%RflL@|YvxY}|V(ZEAo}Z=&9K8Qn)z)wXEu z;^`to8(-_W{x%V>sbKHdf4bok`xAp3m~ERFEDjApkG+lMP}paJOi#|4>u(eD;m1%P zRc`Yj346@#q?%?+>@)Xk{J7OhrfU74ADbhD(*ILQ9B&?(-ngCuFWL$7Ed6EABekI5 zf0n`FTp7{1#JrhNuZ)CTW^d??%Ldni`7{l|B4R$SdZa}QncsJlVt!iJL7+*I@vdv= zk$9%_S`4oX9zLU5A;)K6SVY@%_YEp={rP)&$VFXB(R1T)WzBR9fXR zvc2|3{@W>52r}K7A{X?NNgZ`b+>ev>q)bRVZ_TZqu;%S~QShMhfAjkIuT?e&wbNCu z{O(oc-iKXuE_+7-jh<2bI>WHE;bbQ?*?N zn=h=9TTSu<8vbr_Dg|+hn0_l+`ECuX;5Afx{w1w^*&yCsPC4niRbc8G=e_o z%MNeU8}+P;PbWXdGdw%)Bj)JS*&gXY5;W5I3Sc{7W2 zJ{jD{pdGC`4o=Jq=T3V$k*&0MBMZ(95E`mOd6w9raeOlIb$&c{md@?^$eLG2-c#Sn z7C_cL_;%fn!kS7 zwT!uOY*&gPe|7y|#okW1BS1U7oYhWd_@42|AsZ%fw?sIlb{n}e_2qu)zgDtOvFAqR zYxGPF?4I=(X@dl>nCISwnPf0m*7)3)LYUPHdVeri5!k~R_#$GuL5h+3kKVx{!p>VH zn`W0s-tIe;_?ckDPNC1hIyP73_LELxIuXYnfmy-vv`aM6=ojc6%}suCz7m;j z2lBRV83roXeBSMXzU1Cv1qvPNFcMgJ<-+HeCE&^z|2!=`9CiX%#qNynP{$w8&!JIE ze$oD-H=2wj({0wzZ1M+)bg=GcMd}IimAvY^jQWi0&Go+>d^6y8{OR`4>RAY`ZMm(3 z9U*g@ySCi^l!;x7Nk?=CvjFxBHQ&vyA|9rehuVEAN!o7-ss#2Dn7T-*M0u!z#Pi9p zJFgTIJ6TajiSHF;;8gb0M*B=~;xGNwqUNqGQz>+k z>`>zlp>q+W)i%BTl2AKwqfVA$Ll0<6k22Gc8TyQv)BM@u%1C=Aubrk~6`8fUeuM2? z1DuuI_P+a6)BmRP$A7Jd|JCCh@bMf{zO{K25)SfA=q?X}tupP3(ftB)s^C&3zef)2 z*ZHh`JgN>9i|&kZ2sc2#XRANI!XR?AR>l+ayW08z`wSKf_R!@GshyM}AE zpm~e4Lv(NmLg$~N3E`AI6!v)7p)eO3*!xsK+OwGlwMa>B7$ zwin(-`CI93>Le|L>v25jM|x-Pb8quvKY*D>QJGpK@nI+#y%dTWEeQ^hGcoxf$NkFm z(7*_>d?{9>^fiP$dqXodCprkBl zsIG?84B`BR)~u(!5E);)vTeLkuY2I5^ruQO87?_I`#6Sk088dkJt%!k?r)OU-pWu2 zlDx7m)qVw#5PQRavsOHu`zV#`soO;M@wQC-<1dF*8Toi~VRr~eyLK^SF$^o}E*QP4 zBGe8qS$uCx^O3=hTzqh+Z%`MzAiefB7(O0{=akPK zG&X!8gt;@-{8trmmN@>eygnZ``n5DP8L%szUa2IDx|&qv#25+wse%TBt5eL_%}RUo zGMrKXjImeYovir9)tuT`<=}gkS@_GnaTHm}JpHJpNB&BD@JVOBps3{db2=67V zk+*u)N}54~vYn%Ru>*cj4RQL?_kc*NOG}Uic1~o-%rd=f1-_uSS3Ftc$Tqu;@hFIc z28j-b@`v9^uMbaZ%8@jf8vJ{}D!T(@Wp`}mxQ}|k!ZxFVGj&kPdZWLNwTg(pnSXg? zxd7ZHO(;B1X8-@RKK^Un%)yPA`O^~1o!A|D>EX*ST|}#-?ksyG>i$!n{1gf8M9Tc3 zenz(gsqqqOJ$H*RvkY+qu=ML1$PZgr+GfADct<9^ym<_r3*Ub2Q5x74KdHxMMPC9P}gn?=! zp>kkjp>s?ImAi?Yd%jP>&2Lv@q?C$qKT|y&D3Aiz#kpAyxW~g=S$}rv^)7O!Q|;te z)G=bryziviG!g4P+!BW~ia|QQBA$VcFhoZzyDND&*S7a$4 zO97F&Sy9bz*+_OxN{$-e9RQ6pFYP^;3gC0mhpJ1cV;tq~JH{720tWu8g0p`s$hK)$ zQT~HZn}$v2d_V^#18X!o*4z#-W5R+-|>5l&#`Od z`nA{Bc6ftUQrs8Oznvs#e&?&2Cfrwg^$jNYwnKO=+m~=5fDL85CcdM5uG54fTBoHL`0FKl2Hi~B`HB92MLn1YL$_z!fMqg8o!f zNNy7SS+>`FW>zE+H#)z+fMA?$V`9HlDK&#d2c7=vJZdC#Q9C1C^}2B=#%1Z3el_yQ zlB0U)2o~~<*EfrX!;rIxS+2Ia4~*%OyQ~S;VP#{9@t*U8xD@7YUe4fwp(DQO8$Ed_ z*LO30$2%fh-g(!ZVwD!WAUCitWoI)k3#Z3FSsa3`+Hv!tbh#kYo5e8hJdW8eIf*fg z1y~&0xXGiG1a;AIPdIOuq3$;ty`NW!eeKwR#d>K%*GR*AuCR=Rwe$U&lCP)Xq}T%% zMWT%hW>xv>aumK7Zj2u=ZbFW5hOtblG0=Foc3jav9wy8V zxVyZsf=@>S?Ltlu0Ef8k#soz@$a6@2+^*OM0&@pf7W$`=6zm&gpBPVMogXwRaTtKv z-ZKd{vY${l;j;L|0>QYLQOheilu0m?)wOk}2Y|uoCy#D1xfBhz)b6yCcZoejAc$= zmSe`zJ^SS~-Lz@0)bBSz;$dd|7A}OGq zBD=@1WE9#{>pb3VG{J|rVcQ%zNknGE?lK1NVTdtE65Ag+g)=FwW*jmk91FXzcde}j zl*h&#Uq$vqw+N0JwIx7yH6QuXAmLH{Xkw*XYXS43SJ&R^MC0Jkwz(H2LwG=RVt9r> z4a(>4q}*mfAZs{HOs|npGd=F2)s<1a5~b;?>pl!056Bg19vDOGLJji?!o$rYah0E? z(-Z1;Jh$=U=?9h=YxnDCbMUC<#quHRG0ZJ$doUY6h_>m^eyRNEf>*ES7u&l!fbKls z>2q~0h?>*wuyp|CcO@l|_Yki1J1U9#i?UVN!@%$a$uaH4P0iLXxl;$ibJ)tfAt>>3BQVQ=889!VS-zyOs)Mi zY-ufAj(t}M`*ivbS8LQk=ic!5di(od{ba&3J)gOCRX7(rTr91I8QP$%RPzc? zU@`vN)Wtvk))g2%)P35LKM-FZSG`=YyB!t{nFyhAB0T*(zMv~MNw5ubD*e~fAv)2i zQ;?s~%cOiW)_&238i(dsC#focdFRS~gM))0D}76)lBE=BM~-O5q)tOwPG9eD<~po1 zIMPVnl>#4`ZDMi_a`CQiwX0BaKW;oxi@8Z|h8+Tjp9TyKz)`PVCaw0Ju;T@TcC&Rb z@UoV)=${&f&QFQ~&qLa=(txct#kddtiZ|8P(GcEqUN~p;whFC}o!>{xMtJqEE4gXX zb)t@NtK<9IqmZE!{@6>c3-rDnecZU5jVG`8-WakUz^WURO1zmQ=xZx?dAz3&%w%5T z7sUZE4OQ>p4b4W^Z*n2)1`U|4^YBUj^F(}Y>J-Eh&%X9 zosy6iVNFNN)dQ|@sTt+{1U-;Y!ZVlDJpSe9-Y3tsd&OG%oD*evL~_+pHSKs zaUE%cL-z%yqL6~P)P@0S$%}J4$C3MBEos%b9z0u${)eRb4JN8tVwu;VLjx@yD^N~)x#YS8HMLJcTuoDoCl9@7xozj&!I0zs0YpI zGDti}eVkSthSJ?=_jFX-*}V(|o3{M*Xq$v*OA*by zt&Py0^xy#Rt4{opJ-x0!=8Fux`|sza3;}~3f6k60BN%reNHFO z6?2UH$r~)&Vniu&xQy_dH8Yo_w?ZzRzuEcs8BnBi&8l#00Jb_8_-*F3p->I|oawqJ zES_KfJEJ`cJLRcq7t*}oq*ld1^FQfj`=j#|UW_2Cmok4DM+}aQdd|yJg#m%9P|@CK z!J7}BN2Z*fMaoivMZ4H6)Ny&kq|}p&@{a>9HOCGCchKE+uI}RAue)XJD2*(U0RxTi^VVX0_PNp4Pi=Uzn!%TiV**ZZ<&BCt)dTCV#SXj)E(7V*4hiEs z?NHZ3CpUVw8b^~--nbE&E-HyJR=hh9Oxyo%p$O@PZ_k%1)@jO7asT0nt9*oa{Z7%& zOCCf9w{_=@loLJ3^U}bPY?cF&)H`zhch*B_Pr;IKeZaqy{o{YG6N$m;Dh9#_VVj{; zZ*55UXy$0Cb} zydeG22f{D*eED67M;A`&s)xJ#*WjV|Yz=>n$DvOu8(_iIT zw3Xe>n@>@X8;RWeFA;hsvx_uiPhJn8ZC&1H?gvchxT?IoxuBEqE_ z(t{h!n%C36kx}(!TdD7>7A!oHNo7vlJH1su33=QYfaUpol~eC(fa=uNWa`asTwZnm z-Q7BhX>Awj=3Ay<|AQNSq>fSaURrzAd1DAK+<6=3SdxpzlYe}w=l*4MxR?_heGCub-SnB;uLX+|0(jIVxE(pBJ*A2OIU)CM8qVQY`Kci=9W$43tmdf#TcPq)mT z^?~0!pP6f86|njgKFs3m0TVHon420iXcse*rmawoDSZvpg&y8;kI7^5k6k97HeFt5 z4^Bjjw)A7ycNc>f1C2kYWC2QlXZT*xQiM**uIix?uJ9}3yHMr&7-So*Pm!OD!B^KU z2|RYhJu5-fs?2o|^U`ZQc{GQRkIdaKMeKLx8A|Y@J1#SL%qQ9@5J`J>}iKkC<#9b<`1ft}ZHHJn?GN3m1Fe;hr= zuw+RkaGs_cZFJsX3kmRwWWCIy7_j5ZAk-mt&mo)29N$bt&e}Mmlg1`PC7Ss zjmUz#yO7dFuvEi_7vGm&nSyvbF7l$l0{&*{4?9luK~GR0-)Q|OKcX3PYnXKw*l#S! z+bz1_{(sg3AM@7H&QX9JMdzg2Bgap(@dCs?m2!HE*YsB!jPN3SHp;XfuLUjw}s_N1T zj7_RjQZtK!M+-YPYE7zVEmE3wy; zLrB|qts<+d3^J)+P!$LC!k#RX4h3q#w9LFtE?e zD%sPA=Yfapqmb;24e)$I^F{yR643wRz3*r=!O~{Ak?LL_4|EN-Lfebd;km=$SvB`s zb>_MCRK11qc>E!_tiz%4M{W$pY33_Bfoc>FC1XeIX4ZKJ`VG`9?26tkqos~sH@zj%aHmMadUJ)`WZI8%&%@peO2PG0 z@C)6pMpQd+Gxi2+F+Mpc@(b4L@K<0-HfEw9m30VcE?=IJ3-hQ3auVh1M|CLy->eS z82+tTPVuuJTYqM-xTW>uS^2<&M!DTEuQ7GPi{>5Lengfk(-F+=UXCov>&9ahA3D`( zdU2nSUpaeGC2H5Pr6_fj;r?b52WOwye`oiP|FX{dnA4Bj zR+PY~tE}tgo*^)ss$}e6&WHY8`DN1c#_%Lp@pDIhD>RpHvpHs(1ev73i-`|o!1v2m zs%9aA_4aA~PltC8m@~QFyUSXSd%51ZSLqTg&Lb|-Y>h;p;BE+yXlOe=sM7J{keCEr z8}%c<$GY&Co8B(dwRYgypDjN-H;E?QKh>TJjN-%d3fD8`JHhrF3+3FAewYxr zgoNvWM_Y*mH|jM5d~a6)H~E|o>je^AJkGY_FFuT&WV`fxn-j2b^Z84LQ@wD+DdoV~ zquuzcP@E@-s|h(D4G0(%7h~|(2Y(}~mVvsfS?u1kUR1j=VEL8MbCf(|P#Iw!#bY^Y zOGn=}Lu=BV91Xi%tiH6(p-QR>qRSrVa+<3Et<9!T5LGysrYZ9{&ydmhg)Qr%1>$o2 zY5*m1-!nL2pc$aqhejI@_6!i`KeLPOnkxiD{*r!V=r!v!*g+i?k#xKkJwGp8G>KOuW8~Bl(7q!2_LEocL-vam%O(z0V)x z(v}!SpVZF3(;-#pndq`bQLYu6&bE2x$Bf{&pkCLV50kO(#2Q^)T@Ks}%}Y7B+K0)# zD%I+>b6`V1?{HpQ6pc#`&d*~1O*yvD(}>4arbLMhF|Q& zIi&7@^~vrYbUr~-$MPxys)j=Nj;S`_L{oSE8z~2<^?cqe|6&S-yXvlnupsu5X&5+; zjbYbEv#KDUF3i~SR#(Sw0wyHhR>^qH;I)bj$GgON-2Z2m;4g`849qd(>C174JDV~N zVzPwqd{3Ur{u?#uUid}!Fl{bo-qnu!n%ac>zqw?MYLby-f~hPuq8&vhWDk9cs0Y~* zDdz6hKH%>+zshbgh6h<*ZA_))VoSa2@SI2k?51hlMOw(i-gMQRxZ^qaF3r4W$LuJ6 zcRP~go7fCHTmFs?j*g*Ojs>qOF~4O?D=yme>;}@D>ol&D>xV7$YM1$f2C;?m_sRQn zWazoVJ>k8r8d)0`>ApT}g%6S}wIf_Lc-P18fbdQ~6tgSd>2BBsk;iV@p3|L1G04#3 zm?q^)dNs@~AG@?+PZcLi9bc<0-mWRtOb47F|Bm3}O>q zvwB3fJNx}yjymBUG?{7G9{P0xW@01zw-021%V`&-n|uTR!S;{;xlY!KJ}FCYBVljA zZwrgPH5lhAd!y-MET{{}dHA!AfmO+ZU~zmK&IW1N8kVL*V!=z(tP4c8(m+e>;58Rm zlz)5bazG~<9bF!|lMn|^n`^g)4M(xXZ*0JnuO4kSbu4xd*F!XCPf0yl#UaGU-n5RefZW^q_A0)btdlD4krap?P%!DpLd4a!c9oX+SRYk}Eqr z4v&B^X>lLvZ!XNF9T;rN?8gVf79H)^hCnP(B9Lq_iZ(AbhpH02A?J>+)k0t`@|>ym zX(N1uPlKM3pX$zl{Z6kE-vj+1LOQGR&S?}Cuct7WP>rF;6y{j%%Yms`4kyyzMmb!p#R=ovDXd;W(6e{sq5x$-FE)W12mAH)A{ zed0f^=l@;LD{wRXj^`V~-&@OX`aySF8zvsGf6g6R0>>M3r=>)r@M`t1<@&i%I9)u( z(oFarOoh1=pw1VKeyiBmx)536$7$b`dy!z9y?!PScO!DkS$&J97=+or46^>0YN9V? zdN+ai|Ldxh>8QA)4!EZ%7W5Ahe2M6niITkSP}pTb^QUwMes5-_o0+!bQcNC?sKN-$ zADCa-bAk-RCY*MLvOQ?7z`8w4f9_T}sGs3}>@bysqAWJX9A-5r|A{G3heTxWlnBtyGn9dep*`qt zCAa{;&861}y`tm}H1jA30%FE!?ylVohgkibPTm@YYqAdpoS7=YDTQi1O1=V0(mD5g z`;S3cq>AQ6hhW@C`Pr;~mC$!f-FWZMJAhYfPDej`QHC3Psy6K%2zKAiow>eD<lSe0lNRlt9Rzo~Ia!}0 zqnMg|q%6Cj6XonxryQRb;w=Auw`GnvD71<2x6y5cx(qJ#WNQb@W`3DVdbtq&X5C(o z@Wpt3dIE*t8*qg4J)^xz0X!D}8J?n0gV#8et<7%40(rao!A7G7Twa>8{>;&boGn9X zk7_eO?Lr7YTie8c@crW->urV5U6htu_K(9m?{7~JZ5zUm>gNXq^5?r^+ z?Ts!zz705kL|}@Ur4oFvC@T3AKA^q1)6bQ}Lcxv9#wn{ajtOe?7eBXj!OXjmOXYD* zV5If3$;7@L8A-1qMHQ>ybDxW01;H^Ae#E#aEL;m}e)#lQ1Xc2R7 zdSls)FL>ffS@9isH0#TUvCHM?bT{L^Zchb1<-E3Oq!Er+esgo!^pfBw#WJO1PzT;G zSR+*gRpFNpF|}&Z-M}prw@2tQk-aUhe#<|#9i_kRzwdgW8TGDsBe{*p5FCi^9-M4P zHm>XsWliJQucH;*#}kR~Pmn8Ci1XtZNjNC*aUtlQO4>8FuMR6}MY5K7x$`b~8FX_ke;E>l5x_6_<8Fq)F zs4o)u_{MAy((&G^pP{YbDDE_1^)@H`-cn)ovDd^Jv8M0vK^pBGcrm`f-09kb$<&v2 ze>gG+~iY-TMI~mkm?b%jZMA=96`~pgdf*DVW>L zY6tcQ@jOo+k@0GY__4K`GURyj;NJHabzmm@VaR7-0SXQznI}utBhR^3pT`#~kdw>6 z{i|vt3bjRd-Ab-NW=9!onx0P3p+5S!*7*b8-nL=7Cf*2Z3a@=lSci~$=Yg}f@4Dgn zWX+0yNIN_#NFO{?*$S-3s@_o~*`b^<<*`RJJ($z}+B}F@KlN&AqsY~QS}h7v5A#U) z#@;sKSq0(ut1{0{3dwvecGoS>$TP5C<1Kl&gpa!7awX%c()`|iN*Ch%yL-lKJYp#tsE3YLdE6RCHGj!;{YQjv@S4P&0Bs%$MF%`?w9ZHN z$z?_6`B9|K-s*jcIN$!`%KFdsyaK-)zG}Cwr@#p(#iZu^VI1k+5w5z?4esZTx7Yrc7+WxPPh6<5SA=pQ< zpadsQYfZ-;C4=tOS<0>_)6kcj%);;{0qngQ-zyQiRn2c9^+}w?D7z4`MZMY@7&7T| z14M>kUZLer@Ma_2?Bglx-6ZDW^)>k?3B9UL?q||p~!D*f28FNG?LinoEape)@sIOR< zavX;TCoY&*MGrw2x2@=@u5mo`na0hYy93=?c$i({S}|Upjc3)g3*$W^+?*6h5UXNo z{w%QtM#Yj$A~bvO?WM5EeT_4~!_j+HY^@Yz25o~Y=_2sU^T;Ga$IGyNUUq`!b~AGL zCAxC?_o9Q&`1KmkMr7q{`=a2 zsUqpV)t5BPXgxu*ohcW_ee|*(%nl<%&ICn-*eK{vE9fnLBw@lSvex$qf@K_>o^YwO z4;E=dvhH`)!ae)qH>@9fVOw!jn?PI=+#kai#!_J*x;5+Ru`{1>6n>hX<*J>NI+8OX?tOTBY+8m7N_CSC3)^h3*+vuuwIVTWw;69@iW z*sz+9+bTE;m$r>xi;PSHK2g88+gEy^;-msQnadtkmjmbMKaWCFOTCP~XA=dHBUy$<1Yrs1JbjnULZTKXL z@yg~@4|eu8z*i!BR0IRI{2};Pj&Xu}mXciYr9+@nMOGDN*2EqakgUMMo)%h;qfXnnptU4*L+9fWT8 zd}R*8gM0g!bcQOihyJ9epLHmdTqVy_)RW=Jcc#LpH9c6Zs{WM~GvNJS%g_WOLvCyF zt2?Qu3H>@MWyO4IgWUy>1EyR*qG<4-#f!mSP*J{+etzj++JFAf>+#>~>k8a1Z+s?4 zUkS|O@rH+Pwc{M!x8>`kUK}^?<1lRP!6&Yqe|PNaM)!xY_H{NDm_nz;6U8+FRHCEd zJHB^<^>D_y^AW9(utnY~_6QkSi+sq6Yzz2_oh6p`-VpdKNiOky^+dHp3VH((2=uVi z|2C0DIP`Yr!u=Nocwatl_QmmDLQhs`;XB<2F=2PK-trMVH!*<&Y&!ZO;SF6*@RvyG5IXsQ%HTl#g9jB5O#A9wbX4%2FI0*@_?XP zJjWCwU1{C~yB>1>?oMoj@clly&1;oNM-%B-ryLANjh|WD-CG2qfbmYb$;;Zg?`o(oUTJlymNv_Mq&Mn|{jM%0Rh& zKGI(+4g}j&le8F`!N}%dljiec;(aAsHc$FN@zrJvg^PVK9(`L)Rg{?1T-^07%xV-B zUO%YbPw3T-#Pwh1+tr7YvW2FNvt3}VS(ST~F9U84Oa(?(HRDLr<(#aEO!%wob>JfX zC`OD`zsP5)#Iq@1NAgq0@Kn>Ka??*usNJheYR}5XG?A{e$3NEKtUdv=XspHP%&gr` zZ(M;%@YgMak+}b4_w)a+bxGV$-ah4cZ8!lMb()S}MiB3Qd(>HXYyf&5pQ|E;wW1QO zKI2ru0Ca7c4Qbt-k51Wc`U9tmfluunV>sUs{7B{Bywfla&mwXK-ZB@0h)Ye^;>9xH z6{KR69F4_tQU0+-uPzJ_vX;~9$$%S)iu<+rmO<;)_wsFo-ib=lbMc2t7d8ueggh#* zCUj*=)@N16QSZbjr7vd-h`GqNEXtTFylz9GtK&EbcPuC0xbK>VpEv$y-;b_k}>oJT~Xco4JY8EDpu>M`xx{hd|^J0RqY)7_E679w-4Ir5BN zITrlnKW=z$9Q-S}{i;}Iz*YIaenWmH#_yEL*OhFBE!%`wgWNlDWW07ufc`MjUtaQA z=^z6`uAiiAQVqdrJo34W&_U9BtFKny?Sk!(*0&WMYQl4lO)utlG~jj-H3we~fAr=a zm>Qd$gkH%T+)bic*d;(_GhvFy^i}>YDZRn}BIm3Br@C1I_TA@R)tU6eB5SZ~!npw$ z-0l6*ttbWk%37i+b^AevZSc&Q6YcOeec_lm(*SN4Oyex;F97OQA3b)NF$i|8wK8Ow zgK!3Z`Q!1ka5ebE_A7aWzcn){Kvk(3Hj2(JE$9_s?61;*e&Ie$YTM0DD?AM$;k{Dp zc0`_o{bwhJ^OIN>S=Gz6uNI!FWIn(6i^yW1J@q~L&Zp`mm3TbP_M0qRT8^nES z`m|`wt@$zR*Wfie7(9&^IPC6}k9UB6^lfQ{A|m6|N}AD1qJ`iE4N=*twV`O`p%&#| zU1)euZ0c}$1Gt~yG&1}=h1YBa%ersHW3Y46eC#cvzbCL`t<{7K?~M#C=?U)9UtJSx z3*uaejA4Niw^BhzMUr;Q4kF7~R*dOGbU6+-c}(9d8AH$7-Y*O?#klZFO2oyo28PNq zNnUj3`1(WIwYpYk@HwD18RAg97Q%>Z~@EE3L_|L`#bwlQ_%*-?5%El34O2$`@K2&Rez)?sJ)Q8r3CjgdP|@5 zA$%jVoP|Fe3W>S>>C(nvGH&V6=%l^Sjkb-CrJb}1e|Y)({QK4fFY#otT_Q2}^W>{F zq&DpV8?&D*Qu_5U;a1Z=Z`_To>;jVg!X3aBDStfIuNH$&)k)?P{{IghBT@$mo!L7V z*WpqR4`lzbH;FN|8|ij@{u_Lx0=@KJ+Jz7q#DAF;j_Y$3fNjq0bNlXA!2(IQyZu)k ze3N-_UD9m~1Dt=F3O;Ee<}z{8zCP-pL6fORdCv#8-6<0xF^+-yq=!ZM^Jd_%vw3KC zg#_OOlue%SCc*U!4TouelR#Eaqajr%6WEmWZ+|wU8 zadC0Z5d1RAcQaZ^80K?Fu_>t&6XCG^J0W<%uw;XnNd4%?qB!pWSK&b z^ZKtmt_|S6M-N_7^-aK^3qmJq+H}B}_Dr`UCBd0L!z%0OJBmM?O(>^Zn?fL_}QjMBtHbqSyMD*sn%9`k1C+V8_P z-a^9P$0HP2e}~~dTN62EheeP!EwTE|KY|TbBU6d*dcddEk$qUH3!?M=AN^!o0K>j* zAESvrIMsQIA4!?oXgtzSu|qr!Ym_&7?#h>A^v5FcOQjiT-y!;O2jd{>Sr*pOCH251 zJXs% zqJac$Hbc&75m`|2m5s+Pl(_Hte||Q&We9(WG0h#F|M%h_{Ks|rZ~aX4yN@k|?TV_MnpbVx!j4VDu6 zwnkv4I8y5o<}&ZEF~vVu}h6285b7j$S#BgO^XyM9cU;MhMN z-Z;?I4vq0+aab^f*Ir6zvc0Z>SD~|`Ulg0LHN$0cBqalPeGDJy$>_zStc<#z&%1Ho zi_>0bH3?s_UzLg3Y9_p&yYlRrE}?tn(sq)`s6%__ux9wZ05#LoJG+twz<;}as8&M+ z_?}Qoa$q7jxxzP|OPu?JhMtK}?|9atZl@q;TIe(uZ1H=uKRPx0TExStWa$>HQqg3aWTQBeV$72H|3}d!vzf3&rvGv#?3!5hb2eh<*HR zC-7i05Ntj(aSDVl+n(}0>a|6gtOw2g=Lx?7<5T4Z+9A-gFGHROgdZ$nK!&?06L+mO zUr4YU0M=I>F8$Jo@K8Y(ksCWzR#Y#b?pZGPg*C)iq&8u z=U${XF@&8`7C}NoofsHFBfY+39)Ft--)!wDgeKCu-l?5M_%iCod9C#+Md&|FOYbagEyM=!?ca@I zn2{#>I8~q*jb)3I^gW2|UpiH58v_ztKR@;02hj(Ny%jK?Ma)sdcrrDZtEcg-(0YOu zF@Jfv{oW$aiy>?`>OWkXPULO8XtxmH93=Y5yT)syNf`OEx|ff(2z&1DxfOCJ0z13mt| z`=kDsi}zpgn=7z+KYJ?eNjy~K-r#2@@-DnM1>>Cdx4~Mj(&#US61021V`YlS4WTQ0 zun0rhhXG%JF1kN5Rj5 zQm{Um=p4Ae2RYbCRz?=>_!ZEdpmB@xx7Nv8u*-;{f493I1pCjpb{OYld0x;B zFQ;-attQ9CDU6{{O4l#GYqQX5(U#V{GYsP?Eb88vG~(gGFQq)YClEfDf>d8 z6>YZia^RPGWOWb{5|*n#4hsH5ySPV)d1!x%MpZi+?ot1Q5Brf6OIEnqT8EXzf?VA{ z&Ebb%-QR|N{n$4wl_b#F4o2@qg%}7u=D*@1`%mzzR)8`!arC$K9Ck}MOPA-BqeV;m zq0n%GJJ0qxEy}hXQf0Om@0zFt)~;VI+zTCWTwmQ@>~J(*w29Hawlf!-baa2{7M0@T zm6N%R5zRoaAJfQ9ISTY)TIxvfiIe7K_q)CBfcsly^5{?H!!;GVQ@aJn;b!3G`Zu;t zIGyk&;>=P982IU{XAym{$+11mo<#nW-_8$`66eN%+lOA9_TxBad_C;QakLORrDD%x>2S7J0Ne?gwP7{Acou`~Ecbb<4SodFLe*Q0Ankx{v z%1ys!+KA^K2)g$36Mc?1^f3=;TTrcKw{eBw6b#2ye&N;c!L6>6ViC>*Anhrcl^fbg zoNG3QJaVHzZ=KPk=U6(PIq>mu*~BQm(Y^0*q-zM-RgRDJ9?3)2tt_-IbQQS6K03f+ z_cR`q&8m+gbQST(7>4_or?B9ba7v~p8LzqJo@9JHioqe?5es7d*cmk9PA9YgL3^a! z#-xZGU>dTI?i1$eBnieM-IaU>*oh|Kf{Ov`5(~mQneC&F0R`ZPALDz9Ou=}^L;&*~GP|nIGelr&DlajMf zW>v%LP-8tkxf=DnbFXAGPoSvWyU|0^jmY=(!t)=IL>|W7s3WfqWMI6#)nDe+ZXhD4 z1Sozr;nzXa+pzcvErocKlPsK||I4}-e|7_0X6k7uR;`3_2_ETCuVVc4XRF{}rLzCt zKmLD}4v`b2NG%pFO>l6p#;kWN5P28{$Iid}M20&bMdbUNIx*dSm)zo;CGg1Wxa+fn zgu|@vvo2TCQM38oF5ATxFgmgO<%r!7#^2v^2I%`R{T7prV_OrjK6j^j7Zrhxy$myZ z)W%`1bNC(CpLCchP4U(M2e?ZAZJz-#=Lo;Jd5SJ<9L*~1ioRQ9!*6oq-eF&YGyK3u zG(Nc#mg@>A&ub8U+$GuQT-_1a-AGQMI$Qu%QeV`Jib+rtT>kySsI}WTvrKuJ&{mkslCvnu^>%(Fgv!uI_)KPyvmUk}b6~{g@eGIvz@@ z0}o10*HiU_F#k@=Ns6}}1)Th^tOyjtT9Lu@LI9yhZa=Hsk<^X+Pcy!kOcDBjK1SQ@ z3&YqZ#RR=cx}b3TOS|*KL1gx6O>KW(jD~ZC2mYvb;`uV#w7J+4?5B;|cB#P)4E^z1gr55U z*Yf!9AO1f-ffaZ?t!;0KoA+vbJCU2T-0bK@_-)&6YKMQ!g*4Hz zBbQH&Lb+vq!fIM7Mod1{vW=<&g(tcND`z^e!M*T~K9SeJRVcmpEzKa3eqaBvFT4h} zhFv`zW0a1*gS3k*2OB`bMnK-oBnB6bJnl`h>4We!&r45;yf#Zl&e`*lQz+II!E{fi z4+E9aV_CWuD;ep2KiJHG30v#X+1@t1dSO+Dnx4qtZar^hEz*JtTz=8lzL&#$YfazK zaDp>88`NAJ6pxqu#h~HtQrciW7Q;4p&3)$m!P7%EGPSfF2YmLyx6JDdHRDcn54i|1&&7p*z*=>q-BF9FoH(Ile$SZaG z)zuMSi&0P6i%u}NLM&fJM6t;*;ZuAd;5$pqLj<*=%rwVfN%>=EYj!QR;JN2#JxcK4 z$=BhJ1gGKdj|b{ZW)qMVbCAn&rW+)zKWr88t;bhl&V!bsL~d=&jDy2}U=Y*;_OPU3puy z3n@u(;hW6O-#a>?XUhqJ`N15pHYoAc{Ot?;Yt`!+1h*x^Cfd1Kp$Oy$uF1uDR)U}c zXF`^26{zvLtZsVbL3`8{$2ejhQr$Rnr{i)79>@K?xn5&9E%=ZooVpJEO3Dm1RRXtC?(JL?`~cnUQzC_DGm%r;P~jR?H564{5m%KbIJ^!=M84Oj zVQr^CXLxWkd_TC|=&^qfrthNYBR|i;-aR>WKdAEmyTAJ{TOj{qKPj%;-?r1I6Sd>} zN4$;>Lk$PbZHLM#eD>g_L$FZ~z7TEe#i<&Mu>qvp7s{P?7qZ zj@R!|hR(d7f|6sm=z^^(aM4xU?7{dbbj*Ld{q=YY{K*TqcJmtt_h9l-4W-XW8>#g* ze}W7fdP`SWwTq#}HR8}=ib2$uuW8AA)sC5h>p7zDqfv3!_|1oeuVtEPLn$=A19%_# zNG=2rdU18m)Ht_#lwUe2A@1A;ukMC9C+iS7j`3}2`nSk9mbENa9P$}T-i1W!WH(^I z!Luh+GxIRuTFZ^$J7gHKy!ChgZz4abo0lZ%(1}YNud|HTiTqy4-2o+TwOA&c)W%BO zYqBAkQ=o+ehjPQeJE)V9O_%rG!o~#Dh|ZN2T+hau>&2>a?v*$-C2g+PS%A7+Do=0h zDZ_0jw^n~P55_vVZPOLIa4*I1vr&&pG+Lc#D{iO(|2dh4{EcBW?usv6;A%v_rsrmb z;?>|IeS{;BxU~FlSswrWrvIZ(Qm9ACx&jlJn_BB}m#qu9uKp_iz%)kmN5(E{{3hY* z%%3*eC=$Vyl?-Q98vy+W>yz;lL;>*V=XxXHmEZ7VW~f3tpsG?EcMe7pLEeqRsRAF!NR zXbl4SuM+n<0*QJ1jY5$t%H1%Sd+GNiYX>eJEasl&%fv9_8M$k;lX#i#!t&g2!iOvp z7aYV(}Cgs za#np{ZLWdR+e#O`U#DUyb(92eb0=uh2MoC^_uxDWyG4(SFY3y4%SXM7#Vs#R7+HI@ zgM!D!a4ymi+}vs^y23qxA-hx_ZEBIxD0!BW-J}D~*Or(Uy&*V0a?PBMu5Dnz5Nug( zwnXSpo=q{{UIGJIBiTIxdf+v8RENdT7BY(J+gzvH(RtUe?LRM1A$@T1UBAR^!q;n- zl*%-Txmo*Vwsv`d+@o>w>8-W+S#zPAn()8r2C25+-9_+6|NHA-;S*Sar^n!(jX~H6XHmQ zN`n;5Ar%@CQ3)ABVwvZ8o~Oq=ea)X*-@YoPZL)|_4CmiP-r(3D z1hbxP?vynz!2A+l2PKo|_&|PkiOk$0ylej?+6+rkx4E&(=XEPW$D1}2wRUV!94h!| zUJ*7P|feBNPPwT;CY(9uBntEu@p*&nLca8CL zzaZFA61{(Xn#?i&N5F;%j zJ(?1zEB?0dt^QDxipPw^6a={%;c>y@Ej!L2$e!=mxMqF<8g{&V`@+2dXStnRK2*E9ET}q0SSL*|AMN z%dG|0H5>`vPJJJKvio7n%&s_?|C)D=KJ{F2$LC3>I5}gm=F93?Gx(Fx({)eOIF%Eq zd-v4Q7V3H7Jr>??Rz~DPLP)YB=gBmj8^7Rk@QHT3b=GIUSVax!aW2~`Ay5TArg?V%{6uLZFg{8mKe$S9TMe8wIPZ0IAoWFpE6|Uxs1YMovJOiz%V8fs zqe{^y1~>8YIw&aR!(u13WP3&q&N|Y(qi{(jUfH6#!BX`F4jx%KzR)!RPM;X=k?>Oz z9K9Csls78@j%^xWn>Q>O%K~4#Hq*Hcdv_{~x=Ee4Z8MYEC?wd1i&r0%Hr<{D54%gf z11yW+tm?!wgN|h4VI}vx=@mE7iife8W8i5>F?;iMtyuvEweo5?J+H?&AKQ{AIVm7N z>$UIcsaaUZv8CGaQ!Va!dBxbTvJH<;nWC}nT@1|Uld2iBDIeE2cIBFHtOUzF;UkS| z>fpu@74xQ?hhTl-t@@)Q)bm{9?Uh1?P|s-@8%ZWnzbh4;h_urgodAh%Z{2O%oQsAI zUs9i$7h#yfW&iQ>b3n~@bng{so1!;SQ1LvrSGWK!pvB@WlP zK<&;{v??xHmJd4Zf?{>5)%aCEO~|i=I#031vP?iNAF`*;dGQO(qh0Z+#l z!@dY+}L3C`enuRtR{4QArY~rAeXxTecE`#)Ebl(<1qunY_OfeC!;tcAAKjh_Z~?-zq)8m zAg54sAk^`vwPacaK~2{2GoK(1tk2GUK4}H@dsJ4Z=P_!X+kN=`L(`~p<~3idZyL-) zy&gvdd=940VH0q6ID06z7?x{^?XGLdg6jb%dehO(hxMbegww#r9SXgB9 zW;peHh@V1IW{GGX&UM-1_=S4>a&2pyVnkde-da9aWa9n;h$%Xr^yKti+$^?R&POL5 zOupXUxmKnfnETZ~X!+E@08TaYkaJl`Jt45-#lc*h8$Eb%_)7+gjj}CVNS*7l_t>o3 z%gknwvU|14qdOXGZb_E5Yf-=J<%o20WLM+z45y749F0v6A^p0V)4_IuPm@E7&dt{1i;b6#0(nu0%QzcG2qP3;G{ zWFJ1WDF#G=*T;Rse2mjcq&JAQu|v&w4M$QOvDV891+bmB{)qz zNXD5v0;e8X*c~m=jMfLb1d%%LsQ7xsx}5`_gQw@=GXabSoa0hkrZA}leS%Kb%LDa1 z;N_iL2U*m^F5469n+u9@meJxo-8nwRFGsc~w- z{&$5icITqc96OpI^To59t;M-mo?|-8-!1?Hh5U9dTa}A^JG1kZKGvZFbK=#gz;tYG zcq8BVu@p|Kg^vhZUXF`Bl-3Tmc#bEBM(!MUu^OuE+_`1*voYgM#F$K}B8+Ttd=!*e zf}QumI0mKVQ0s=in@3Z>yZ_Ti=HILROpxo!IhT}JjTXlx26=L1!zsVKp_`mS;pA#d z=I*Cy_$JtB=`G%uP`@$B0xsm>eCfkhHWE1yAyA=LZ|;JL#bS|R4Rs*ND<~3?Q3`fx z>y5lFwZILj^&!iSRKWhzYW$y~lTguXUm@SyV6a!+!f=@$08huMd^nQ9K-pE3N?rBa z@X5ukavwWAVGk~jI_VgV&3PL`GcL!#huJ~{=I|9m{QI+`6|WXRt%qW$_k?^XTPb&4 zDYXuE#2n2E@##P#WB>8N^U5K{=cfgm5#)rRdV#RBz&o6TXW)gGg`e+ zuuDm918=)Yk;e10!C+hZt{~BH^lgolHS^8@@DSK`tHB#?RJ~cHf4&XY7p3ZKJ9rD* zwt57f4@yMWQ{g_3uhoFzytd3@Sm9bjhMPOtI)|O5d+h`hn-Za zq3+`myt$go4UVKbxDWV9-CL>7Jy`Wn0py>*5;9@p3v|A93#HFTg7ZP)yOZMD!1Ugw zp=Uhn@$6{zho#iLgEDoZP2vZNfv;Tu)=$)P0DoMc_FMYnGr)v}d@l3z3d1ns=jxoT zho53}?Dd~ln#ZEe&N*jg*M#C;-4pIdFXlkqX#VT>^P<5i)-~F=suG{PySvukHU=u5 zs5fMD&@qvirem#*S zv>ou=`V{q?1=p&q#MvA3Ky~QPBcm@Aqvm$^;K!>P;N)$U(;MIA!B9i*Q8rpF5Sa7q z=$bdhkUmy(+Rj^57<@|8c!+reXezbnIvq%c&h<0r?47~D9VfK>0;$hoozb<2E*wh% zljh)*7&8WFJ=1nHI$RBx2Y9V1(@Q|l8GH7xiOWarxUp{AsC`b{6PMi|YV8d+rFB)} ztMVXOW4J{lb#I(+?D)wWsr!%z512Y%B_t0jIObSSr}poAp4Zs?vZ5O6&okCKK1+s4 zs{`j-?a#qe5%)Svx^qz2^xd6+hDKQMpmoEMW*_`4+x`0Z`U;S^Is3x|+bH0eefsK| z?!5l_@y8G9KfxjsEHuZvdc@}9i9@ezs|QlgQIv^~_*@o*(G}*Sx3s6ipm@vA8$zyO z?6RMZ1v}Tm+Z&5KR@KJ9fn(#^qT{L8RrxbXkU^%f_dpsp^?UN2uo*Tnl4O@&?4<>VtCzq=XgW`@J*Q z9HsVcMSgagz5G-SI3!zkZFhF>|NikOjOIVjBoiKwP=A!F8w(e!97UGQOGkH^rD~6I z1910#BmOm9QSh^dhR#lb1~9afQ|?MG!@F-j3|qUb2@|rdCQAynp#+CPU9M{^3~7{M z>>PRp>W^-lv*vC)oS)=waA-<1I=v6@|4N--$eB55@4|O^=+Y);)yxwEKC4SWc}x=W z3P{}gU{(Q+BIn+vyiUgYq$Z#CjsT3w_PpObwH}pDeX`NCD!|(+$~R}ZFmMWUK+N-r zx4_`uWNxdBRJeNZDdz_JR2;cR##}Eu28LvJdDujzq2`2XhOj;lGWNE*yNZWk!j0Ay zmoytt$gt)>!|iCCm2&!~VSXCSUc8iR?Ymrf!sFewV|pS++%G=4Ze=-oy?dWANh1#; z%w~)+uPFi1M5RkQw(*$uP&m1gKL`iAO&<5*a2TAJ6EN}9h-}n%rgnHA7-u%JA{}1IuYoHi@sP{g9Kio71Mhw|c{9G7y8q#d|B^SOvZ11= zyz}X+QV0@e79(|TPHIWoxhu}aV31>XT(Xtg_hNQrtJJDu9P>PI?wYul@Uk($Mt(va zbq>-jlT~t!nCE;nL!3GWAvW3mhld;ofwDbn$NYK0cvGlfJ z4t(i)JE?GQJ{o#3#0^q6!RS2iiLybd@OiYEez!y%j@fK?cHEKY@c5kL;|)`q!EXGD zq?5JUI7~n;z_Q#84=L;}SiYzlr*kAk?)X{(+pi{XGai@?)JFSysXR{zo@ARm z`%hJAZMlgvHb0X8TvdTilN9&@)|Q~(*Gly~)pS_sGk?Fuu5^sMBmCeCbq~9O_QW(9 zxhC|PWay;PaT=Rnzq!jR^1tQ&!M|Xr{jYYxgfnhGK&=Fc6K4me;u#07@NHvT zA;{S1%~?$^_(_r1nfncOuKZ@M;DlNA$k_RX;UQmy&GXHtcO0)k3wxD&B1W0;`r7h# zQ@;%S6j}e^qFEG-)xYQ^tzCxeU!EDUEI1vF3vN!Ytg8W?B@1qy(JFzEY*R%!>R#-; z!%wt&#w9@262-Vq5e8`Tx-XtJwFpI?4nHX3 zn*_$)Gp~jWb3nZIL27VZ9j=7XSaA^&Y8MwO?4xiY?SSU~fPKIW#ohzvO8zqH#52U_8U4gWwIajOk z(dRP%FzVjQD6PWvJf+tA_BMjG zkLBnX>ba>8y33SfseKwCB58d!fq`aj(yvFvB;(^bnOkS`CBXxMR*P#Z8^J?m^t+Y! zYoKeCo8G&`1gx>y;+Ef8gS&1jcc)oYf?Mr$_j|XmA=i1SAq%MYuR!NLN{Q6EVKJk@ zdW={tB%HhDxcFu^=&L{cnr2#o2hwzKMUw+~Pq?VLmb$0AI%A1p+T=J$vyxhJa?@kb znjzy@xs7^0(XYEeVtpyKzcKmp{FYa+o1xft=nHj^YX86ggBf7L&5zCk{86Q_GQ?4N z{LovtC&}Za#lt{cI4vM+a&RGjzSTBt*g*z$&rJ3JA&FFocW)e8eeNV2IJ#%aJ?cKr z+BsrA%0V@7MB$EBsZ0*_+{LZ6X)}Uw);guzmIGfw-o_~kn$F+u9cVsw?HHny%Cq;g z_oiU9#36y$?hI7RI2YfP9*DE_O};u+B;&TDwnZ7c(;=N{)u82Afx+hn{q%}DKXQ}M z%I3puFL0{XzT|`@X`p)k&~9(9dLOg2TRHD#LH2LfzhQgW=0_!68u2KymLGaC|gbCjsjUmlp0)YOnn^hrbx`^A zg8A++Qnty7@wplwhs#)6J`RM}b_P?zE2?l&;xwB#TqW>w%>k1O0@VJ9GfHlwE2;ab za+}A0@XtVjF?$}*qJA%{xbOCMfLJti1URUS;);XMiwagu3$6xjhU87JYxywjSy0J- ziyFu})+n*@RyHgfR-B-IJ{b>}1TC$&-+tsr&6?KXFZSD8}%yo7M=mcVOFz z%hh8BMF79>>*B!jAW#TCAT`Fl2Br(>Yu>)l0#SLhbQQyS7Ic!08dfkDE@#L&U~S z*_J7>`1Z6&tntVG^L_p`mi{mQ#e`1IdCMIVsdKI*c5GlwjE0ey-K}^&7en~5qz_9r zxj@pSp{r|)AL4R5{V-$d{=o?vpP!{I$VR_-7e=674311ZBkeY*4n{hiUpkH2Pv6wy z-<41OeznzPXM1%#b#BkLsqdtQM4+!gD-OQ zU85J&;_k0|mMfnt#bLG9u^(dUV0*Q}ZqG6|`0ze&lFp_y5J`8Q&J^*2S%<%VNShyq z!j~;qeqvD1QP!PsH8xF$&X4Od_%o^V<9>b_v6*ifR>`2PW=t&(NIrNpjk>4%y02&G zZMjl>KQ3ry6W;^aSUCT~mbd-;KmISzir#Hwf?;?-$1|z(xaw=r>IT(3V19hb^&qDX zvJ;j3q_Pu0bA~j}t}RF8+(C5lk_r< z$DXL>DX;YTS{Bi*=jSL(@b0O~hKV0%n{n4v!y%crvXp!)yn21P=cFm2P#LlBiuZs>ymNAqes@_l zeiGTUNs)Sv(wh7HypcIc;JerC(X4qk@GgAzqalxr;l|-5%iM|@VD;JH#sJC9%By7*L#r##Z$F3vV*fwn7Jt|@`M4J9t*W&$```QDCWfDGjj0;!!XEg&@&Wf z7)ezIdZWDMCDcyrKfk^A82Tr0m@wCTPxVOaJd|^foHx~~3BzincG>VE#N1fE?BUBO z^tyRjWfeblUXRlL*H0(bU{Rb(cfXRm0+n*(l1-Wd~spEUIMEqP9z2W_Z2RAW*j46hd+ZG9jX zYV?nsljbW&%gH}Y7nPyzcjmfaenYkf(#K0^PUNKadA0M&J+qF6!7GCnE^vzm#a71% z4Us5}J`insXGJ+Y7g#a!NLvER)f%1+eO8V$yA)OipG-ubna*+-a#CUOfrK1C#~1MF zmyz;hM2H@Cg+cg{PN}%=0v~!BodR%T=mtDDP zJ#5e3o};rb9$e2v8ogamhu*_&-5&1BM>|!^Vl{zm9M)-P89O!z-XCaFJ)%+wgN#bU zUabj2=2+7aw?7o)j{G6>tp>JW{q=zN*JN(unL&b*xpOkW@U_FZMB@%j9`mqZfP5;h zg({4n2Y>UG=*Q!_KQlGypcHFusn)nQ&B-Vb=n^uG4zIgav z%&!M!t;+|)7ctP6Ic#qtenE*y3D#7-p$Nc5_rSP&_^@|Bd z4U|kgIYm>jhB|kC>U*`tS@1!zQs9fb4m$086guvrGgLKXu3tgzU%G5RY;fMbdsrXF z|6-3t1O^Qle5B<~G;r$hlEneMdtEp_b$JAi9eH?l*UES}nEz=~^w%Wt_boWO zF2(`%-fqpCKGBythiFlXb&4bK=|ptY2)4ozZhwnoBMXtY_+f~#WFcPl7_cGRJOR2F zEZQL`9@_u@@lToteYTZ)4swm`hVxtMa5ZP`bq%#txcDi!DInnmeoZb(Z(Q4shB?hw z2j^$Ox#ejgiNUWRe8)%i`S${;`+<+W@sf3f&8O8~NiHbFhNby2%Hzu5qNzjs+?7Q* zUFyyxmt6ta$mRHcMFq8QN?aheO3e?0=Op=c2O{oVUuyX&l!5bZY!~MU@`vkpo4L$m z?&0vv#eS0)7vjdFuf0C(%!L4%5xLLPThU%=_IrcH@vznCwD9wv!%@7seWSly2l(g> zdG)}p7$yl@418#J0ZeaN4jRQMgBhl6qdmlHao;?}@XS^Oo9EVzd2g!WSVeT>PW57( zm-fnMRGJ5#XyH=ya<_qEsgLKiR=w<91b`1LQ$VX_cEQgHeOJ#(-UEp@zI{bRJ21H-S-k7fBf@-(R=0?v*0@JfkC%qjL zg9j6CxYQ251Bo|O%eMs-fV5R>(+=u;PqpU+wR;^5IHI;l1%eXcl<@q3Pgi`=t+e68 zjD5wp^rqdQ(~Er3sxY+`cpt&TrU;Es)cuBIB$7%ET;f3P!nrY$)V|(XRTJX*m*rv3 zUEMmT5e1Olw9hePTrvu(Z#^?wE}lAnPU6J8=gIx^=qqK`UW!~qN#%Q>wf9_+cVPO*Po zfHjFR9`oKZV7TjR^E9ar7#-^ox^4%xj=$rs*uGT>ST%g&rlVtX;N81epM#A_;2=^U z$~B-7Jsdwxh>p+4mt}hpJ(J||d6pbLtt47rFj6Xnbn`_3HWZ*s-VgSwyy=TYN5m>N_ki|&V0#-xrNx-9hV(uT8OVWCdF+yk3YEVx>|TSzWOrdu`G4}sLX`u2E-Bu9Wd}^9WObzVgNf(JSZUVtrn?&aMWbi@Vua)!ialFIMiBr#%VT!%r znK=bH;QnMy)OO7RV8lgj{K$D1wOT$F%D30!TF#Dv7h6+7dgy~~O7pXEK&Uo{DKj5c z>O#|9iu%vL`mH0RU;bMLm|#BgX-af;1~gv~s2ix&4$2PiLXJO(#OQfb!_&eO@qRJ) zyYZrNAb-&BaZY0a7+h$Ux-i)Zz9voeUg{PHzT7WYPFR-@>gTf62MAY#0Va&e(%2v2 zmx<%6Cysr1z7X~&JBv!!C&7q&RZiN?rEub9B~u;ZL3Y!~l_qkv7}p&n=e)iUzc_sq zy%@rPf!Rk?R(Drm+1u@WoP~FgZ?@XC&a6vtkLzGcmQ@`t9L%vaZdDytpDJsaPMyc~ zrD~UfT~;oHSGMGD6+;Z>;JjuV-3)nCorYVDi2`-Gq?HNYQ6M1y)5b@>@i4|}y%}G4 z1ngforBhiW1Lk?w)SMof3G$s+jJK|-ggjZ1pC=mRLUs4vv|T>O@Myc^f)KA;Xj`P( zlz%#~)>RJCXo8%rBjhAasrydU@A_|~?icNvQ)n?dt^?m3l4~srO+@AhO;4#)Ef9L9 zR?J7S8WltyMowQ>i9;jwR+g5OQTN!aTfOdODhyL zGPtX}pD|k22bGFMHqDkw#$B1)txQXNLB{i^)UKk-n0vfyd-jV)Y?M01>uOsA(v9X< zU5f*dpWkqW@q1TTpqQe5tS%9In%MtGe+K^R3@~B6M)5Y?<^ou}#HvH(U>kMryxK<@ z{tl=eu=(+>+!&Bh+V|dxS|6EQWBpWwIv*%p`KE}6cr&ijK7GUMWIgbV3)(kG^C7+p z_7SYf@Wvq-D{>ckGGK(BS7=dn1zbAYJX7XM6invSUc3HqChSrSvw6~-29c5b<`4ZE zi^_%L7K`$g@Eg|7bnwg2^y=r`~y8DPRH%W@;p!PVfc5V3i2 zb3QiXy07DQH{lo;=O+UeQ|ou}BY5sIicrV6T`lu;4vx>)+@W{B3`hGPaK7tOgXt$V z1TD3mz$S_3cGpyrLHoJWvpP|3Ebfc7VIFDuV(f_1uRxIUyBihZ};&@XC+8lx36 zs0UooY44;R3e-7VSEa{pl^R%u+WcM@uI1%`xap)SQHNKceR(Ut{HI)acXiFjDcc$N zLZ`W1>?QSk8K>))z(dv8>1%o_VOAx22gkXOJerA0a*+~x(-`QYc1(Txwlb*Bl`T2h z5{>%VHhdPxV{p;jQR}Zz`hQd=`t9^*fPDs-pwN1Elcs+woDlwrvAZn-PK94Ntfe1@ zColO(kA7W(2KDixAGpfkwPi^C*85;YHkBwnjN%twtF$Ytxx4170?7C^5eIv zP4j|kyWm5{`gNdUGB2~W>j`w7J(MT7>@+5)o0x9*rM?G^%~#%DSOuDU9+=s>HDPfO zbxuB}gW}Rlvy8qJL5pNCeC)odG5!yq{5=k<*4c54)C1p38&r0^GcNX0~8r=~f#Jp#o4DSJfV6nvUo8 zxoTv#rQnErH@74^H$wdAdg1gX8?p4s2cuoozWJwyl6RV~F~DL{g^A$BDimzq^2$yy zA2i={j_1-%gzCgc`C8U-a3E#&(9?%=AaLcwpHzY>@zO|xjE2;D%wBubQ&m0@7VR+; z+nrqwp{F2s*yk6(xm2}#>Xah1oB5#2)3K`m`}rR|1p4j$Kn9qwpk=*c)08@VeO|}u zMtcY3X`kOA9-jm+f-Kh>9xVj*G4+oNq@%!hxcCu8`5GK$dFyB2C%G^!ZoN5={0VFm zOX-{vl>v@dua)LbN&!a2=jZxg3(!*H@aJnvC79uC7+W3SiI=v`4OpRe6vXOgXN1jp z4ty_Go^CR11>5i?rX3C^apZ`O$)nwp@Qdzw;q=Z&Q0|;n&@r_M9@I*CcDwX{zWRaA z>=*gdGQfmZwR=NssC^}C2VJgOv%em$E^jqaskgweF#df}2GQ`@J@CyTuNpYottRJp zAOz=tV93tIT+EoX zaNB`*3D6K!8Yp`u6Zy_|^Tu}v5dc-VjUpdz^OIzBD=ND8*_hYPyMCE$k2vr-jpeqiO97BQ4J z0-m}Gx=O2+!cR&u2Ylu}#&OF<<*v)+VMXEb+u8g%7~Z^Ccq(;2d`OE`X4a)-aMHga zIm9ComQHuu!ZqSm|L3b8@5Fw|KRpA~{qdeVhj6be1m&mWrToV_yQOS*{Nig(uWm4MHJTxlM4pJQW7?w_!y)$XsW2_JKyeO=dh7q;< zHzmrXqus%Eb2c9>hp&yYU#88qhmm9KFGTQA&v&icB()?z7%BoBW1R2SLhgpNHwAUM z{qy6ucV557UzPzTwEf&5dG%})u5WjGC}qLG%rk>**9F$%l(h@xm~YB)=d4o2lI#W; zVHjM$Z$lAGAA6q3yPUdzbMyEE<_*c{wIr7Fm{uOxEVvNE-*pqz_@-liO*Ib8 zv>H|B^32?CR}9^TCC75FDs4)@4~mvuBn+|lH4NR#@~#A??nsZpR}XP#|7dA zMI~r|tj4}uy%16kI?U&8dJZAx?^mC=QG+L*9dxrCmk+1UVMMq0Mu79@e8hHC;wroY*zr)A5$EiknJ?K-sQxJE@o(v?vGsSDb0W6S`fF z7pgSFgXP*m=kC|S;0BwIz7du1V%*2*<-6)|`8A23Z}0Jh>ucr+T-a6zho;Zq?c}}z zOJCU)RU|U68JpeLDM6msa>JbSPT)*5*10e!1^o`4QaYwujz2&7`pKAj-tl5k>c)zy zLNJ&5$tj~C5zP$`dRcUrpsgO$r*dK<7O2GSIP2L8|8=PS2KqDbKb8R|s9v3WENx#s zEPi{|XYa)h+;%ztVhv9oXuMUc5xQ9e@1ylUw{K}dg>|}eC91`scCUHqtI9lF5+o3= zIFh=*)P2?^1?qki(YC;6Ue-~-Kk3CNg&|e&fq$cR@XVtA`SCy2xBZU)xC}5MOFT?L z8f$Rqtid}r`s4wxf{k32M?BE_Z@>x3ejHS>Ztu%@fgr# zBanEm8P#uy%g4@3gW_rKB~v^~anx!Ni8ikG{`v98byB~j|M3hkLGAr;&it$nTowAU zRzs`<-4~`GX?pq)Pi*C}QuM0Edv_o~fGZeM%yVpf9O6)@tXbPiyA`@WDJ+AaK#;b% zsAMs`5ch=Fi%j#3=>PulKi;SP0sQe9p!UZf5tY!M`WP27D}&~1q{F8X2bO8BNrYxo z`#o`*3|xAked2bTa(MEHKl+|=4pcl?J!j3dWSE)}->K3agYpeRd~fYy`sc?V-#Psj z|27$50=Ma?4Y`qpa5z1AmCJ@)SU9-LaPs;N5T5pveJgJh?)>1ZQ!%9-*JQ68Y$a2M z^Q9_BOfPH#8>_ve?phV~&yT-NU-k#`=VgEiSH2Fa)#9y##Vf8}ysQ@hC&Q#SYO5txCdVgU38TiXGK<)cYRlTsK@DzTz zVJ}oBQ2^H-*PV2hZt0&Ne_0>&JNo-)fC=uI!B4(+TkVGLwWBF8 z*=uTKZnn!z|0mR^^feKxSXoge}gERMA0`Rt0~fIc#ie^%zO_2yix)iBUw4I`X6iuK= ziK3kp&7x=&MN$+Er$~+>4T=;fnoiNT7lv^Zt)+;cqRkY^Q>0AMB8s+9G?t?I6iudR zDMh>#@liCDqHq6(QnZPptrUq;G>xJW6v^V(-uB%{9x?f;hr*0>h2 zZB-AuC-%#@*6&sO3q#TVms-PLujQDk_-!N_ed{t-djDg}FyWW#Z@utq)g0forPx$+ zf3N;FUw%!SPw`vlnd$8Qx5WJ`HBD4fe@V?R+5!CE-}>BmzT@OE-%*j2hyEwujg(o~ zS6PvbJkg`qPo~L7v&!t`+_+is(e#KNH#U5Bc8NXW&zkSMeU3r@f3zO>pY`;zE~}m( z-5y<@l&fiaq)gZERUZ7G@zCq7S?wYA2-4+9*_ssx9Z5YMb=kyi{Tuz#?XoMA_z4m@ zQYNU&CN8=>y-f6~Ilt$XU^J_&%k`a4FVp4dWx5`{{zuD-EdT7}37^PWv&Kg>oAwa- zzL3OE(Twu<>`Le)zj?|KLm*$kt0az6}!KELg3)AW+5r} ziNAcJpx*Q8`YgWn*Z;Ij?Eg`yNc_Z3cq%PGG5 zj)dQ5Y@*kWB5*IxlQYP3d&c5QH$IWVYpLXbSbUQS^J@FAeHu61kG<^~e$pgp7 zKKhf@kJcUE<$gD||Cjo|(LVn@S zv^YtbV6S+aS@Vt!TC?~BIcRc(Pmo?uFVp2no{1c(CrJ1N37;V0v%}vi_gm%J`6c|m z>{++6<~0k69>Jb^THZ-LLF+#1f3qB$c<6TMe#!VEa&)B2)9Xo@$PpxbI+A*V^m{!QZH_`x`=>sYUsH2hKh-!1pwj)(tNpG|(O|0KJ= zIZuC=IN0RrH@AnK9oBrdu4awHS{Aa(9Av)NuwH-Il!-oD`9Ade)F=K45_>FUt54)v z*fYL}KB=eKA@;24`Jl;j(8_G}*!Uy)>ZM2b%TAxPi^vnC_g^3SJ#nz~Nx26}I|&kd zH0+fxT0K2qJ!N`3$ati;gYKV{f2%&xBk>V^;`evvu~$FRZ2;Ysh%t!bH z69M=ujTK@OT9QnqICi5wk?UAi3M6M1^Mnq`;HS7gl- zMcQ()E~`xVq#VtLPnYYfOqM%|T{`xq&#u0j79Tq~U78%dTuqi^X>$LqeWFkI7tQiR z=l|BSVjp%$-Y2sjOCa(+%hF%Je@s$jAz3CTvBZC7m{Ugn%!PHI$ANgM>}%esV5kkt3Y*@yie z`M%`nag#Djug5=&Ps(I@x~I%qW+r|Kzb9Ur-Cq13t^Ywe;-4Tpf25wYr$>(DjZGeU z>`n1da%mK}T5)0QLY_DGo^(I;hsbbj>f@AKc9zKl)E1c`rACP?SA zE3@O%?GQN@auB4+k#-QIw~z4YNaWZe%MUv}vdl`?C-QW@HO(Hqp6C%I^`uO&hfm7~ zspp{O&6?$xjAx=x_&sHs9p$yf@}A`v z^0PS|Y0H5<@@$svdg_TCnjEPo$kB&fPd$;NA^Dp4N6B%}+Dpp4kQGNS|9!QWR!{6& z6TfVhWl24e?}dHEL+XhiHgOQUJ^pCa{4K@K9HLbNj)hOWXC7< zKZ+>h$f{gI!Qi9W4Nem15f`T3TPbh)1KPhb8beh9Ms_tK~7 zk@}w3YogCWQs0AQzL8}nHgfcKu(MD2J@#pKd)Z;*kL0D7{O|1tx*o|3J+Ex?LE6<5 z4_%L4KhXU2=+pT0e35dG{Ex;@i=#)M_@g7ccChl$OaDjX_;2;ujT<)pNxtaVD}Gx0 z>GEXU5k5P8Qr`=Ibo`Jw*yaDfZ9lvG6TdWM*A8~=@8Q$qr?;O?e-Zs2zcf9p(UHo|v-gXX`s3jghJfPZavC!15Ng}$#QORzS-2e3B1o3P4+AI&OT z3w)Q~F!nq0jr&j39sj-TCiopCSY?R`tTGEHv+7M)sLQfb&B6c{UvtWLJ;jMEWa(S8 zkYn<9zAj6i_|2a5oo~YOzhM+hZuED|W|jF^Wj9v4C$q}BEbKW1fYt737Lv{IZY()s zpYVwtk}nCC{c4&&l5ZkM4k2K&@}14fhY3rc$dkC}d1?*0& zVAV_ZwogtL`Nh6uZ~NqAk?-|=*q7?9PfjHHMPI77J~@%(mwM^m_2i_IZ!a=Oe(e?L z+pE(ruRwyVGerug4nBS3fuy2aqUz!cr)3qrR@NNjH(vV7X(C7ezZS@;B;Qd=(T}D1 Jy{xSG{{VxH-Q)lO literal 0 HcmV?d00001 From d34ee7155856ed1f53de836cfd03f1c9a9763bf6 Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Mon, 27 Feb 2017 11:51:22 -0500 Subject: [PATCH 12/16] updated lecture notes --- .../lecture_11-checkpoint.ipynb | 699 ++++++++ lecture_11/det_A.png | Bin 0 -> 20397 bytes lecture_11/lecture_11.ipynb | 163 +- lecture_11/midterm_date.png | Bin 0 -> 26061 bytes lecture_11/octave-workspace | Bin 178581 -> 0 bytes .../lecture_13-checkpoint.ipynb | 737 +++++++++ lecture_13/lecture_13.ipynb | 1401 +++++++++++++++++ lecture_13/octave-workspace | 0 8 files changed, 2955 insertions(+), 45 deletions(-) create mode 100644 lecture_11/.ipynb_checkpoints/lecture_11-checkpoint.ipynb create mode 100644 lecture_11/det_A.png create mode 100644 lecture_11/midterm_date.png create mode 100644 lecture_13/.ipynb_checkpoints/lecture_13-checkpoint.ipynb create mode 100644 lecture_13/lecture_13.ipynb create mode 100644 lecture_13/octave-workspace diff --git a/lecture_11/.ipynb_checkpoints/lecture_11-checkpoint.ipynb b/lecture_11/.ipynb_checkpoints/lecture_11-checkpoint.ipynb new file mode 100644 index 0000000..e2aa425 --- /dev/null +++ b/lecture_11/.ipynb_checkpoints/lecture_11-checkpoint.ipynb @@ -0,0 +1,699 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%plot --format svg" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "setdefaults" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What is the determinant of A?\n", + "\n", + "$A=\\left[ \\begin{array}{ccc}\n", + "10 & 2 & 1 \\\\\n", + "0 & 1 & 1 \\\\\n", + "0 & 0 & 10\\end{array} \\right]$\n", + "\n", + "![responses to determinant of A](det_A.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# LU Decomposition\n", + "### efficient storage of matrices for solutions\n", + "\n", + "Considering the same solution set:\n", + "\n", + "$y=Ax$\n", + "\n", + "Assume that we can perform Gauss elimination and achieve this formula:\n", + "\n", + "$Ux=d$ \n", + "\n", + "Where, $U$ is an upper triangular matrix that we derived from Gauss elimination and $d$ is the set of dependent variables after Gauss elimination. \n", + "\n", + "Assume there is a lower triangular matrix, $L$, with ones on the diagonal and same dimensions of $U$ and the following is true:\n", + "\n", + "$L(Ux-d)=Ax-y=0$\n", + "\n", + "Now, $Ax=LUx$, so $A=LU$, and $y=Ld$.\n", + "\n", + "$2x_{1}+x_{2}=1$\n", + "\n", + "$x_{1}+3x_{2}=1$\n", + "\n", + "\n", + "$\\left[ \\begin{array}{cc}\n", + "2 & 1 \\\\\n", + "1 & 3 \\end{array} \\right]\n", + "\\left[\\begin{array}{c} \n", + "x_{1} \\\\ \n", + "x_{2} \\end{array}\\right]=\n", + "\\left[\\begin{array}{c} \n", + "1 \\\\\n", + "1\\end{array}\\right]$\n", + "\n", + "f21=0.5\n", + "\n", + "A(2,1)=1-1 = 0 \n", + "\n", + "A(2,2)=3-0.5=2.5\n", + "\n", + "y(2)=1-0.5=0.5\n", + "\n", + "$L(Ux-d)=\n", + "\\left[ \\begin{array}{cc}\n", + "1 & 0 \\\\\n", + "0.5 & 1 \\end{array} \\right]\n", + "\\left(\\left[ \\begin{array}{cc}\n", + "2 & 1 \\\\\n", + "0 & 2.5 \\end{array} \\right]\n", + "\\left[\\begin{array}{c} \n", + "x_{1} \\\\ \n", + "x_{2} \\end{array}\\right]-\n", + "\\left[\\begin{array}{c} \n", + "1 \\\\\n", + "0.5\\end{array}\\right]\\right)=0$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A =\n", + "\n", + " 2 1\n", + " 1 3\n", + "\n", + "L =\n", + "\n", + " 1.00000 0.00000\n", + " 0.50000 1.00000\n", + "\n", + "U =\n", + "\n", + " 2.00000 1.00000\n", + " 0.00000 2.50000\n", + "\n", + "ans =\n", + "\n", + " 2 1\n", + " 1 3\n", + "\n", + "d =\n", + "\n", + " 1.00000\n", + " 0.50000\n", + "\n", + "y =\n", + "\n", + " 1\n", + " 1\n", + "\n" + ] + } + ], + "source": [ + "A=[2,1;1,3]\n", + "L=[1,0;0.5,1]\n", + "U=[2,1;0,2.5]\n", + "L*U\n", + "\n", + "d=[1;0.5]\n", + "y=L*d" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Pivoting for LU factorization\n", + "\n", + "LU factorization uses the same method as Gauss elimination so it is also necessary to perform partial pivoting when creating the lower and upper triangular matrices. \n", + "\n", + "Matlab and Octave use pivoting in the command \n", + "\n", + "`[L,U,P]=lu(A)`\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "'lu' is a built-in function from the file libinterp/corefcn/lu.cc\n", + "\n", + " -- Built-in Function: [L, U] = lu (A)\n", + " -- Built-in Function: [L, U, P] = lu (A)\n", + " -- Built-in Function: [L, U, P, Q] = lu (S)\n", + " -- Built-in Function: [L, U, P, Q, R] = lu (S)\n", + " -- Built-in Function: [...] = lu (S, THRES)\n", + " -- Built-in Function: Y = lu (...)\n", + " -- Built-in Function: [...] = lu (..., \"vector\")\n", + " Compute the LU decomposition of A.\n", + "\n", + " If A is full subroutines from LAPACK are used and if A is sparse\n", + " then UMFPACK is used.\n", + "\n", + " The result is returned in a permuted form, according to the\n", + " optional return value P. For example, given the matrix 'a = [1, 2;\n", + " 3, 4]',\n", + "\n", + " [l, u, p] = lu (A)\n", + "\n", + " returns\n", + "\n", + " l =\n", + "\n", + " 1.00000 0.00000\n", + " 0.33333 1.00000\n", + "\n", + " u =\n", + "\n", + " 3.00000 4.00000\n", + " 0.00000 0.66667\n", + "\n", + " p =\n", + "\n", + " 0 1\n", + " 1 0\n", + "\n", + " The matrix is not required to be square.\n", + "\n", + " When called with two or three output arguments and a spare input\n", + " matrix, 'lu' does not attempt to perform sparsity preserving column\n", + " permutations. Called with a fourth output argument, the sparsity\n", + " preserving column transformation Q is returned, such that 'P * A *\n", + " Q = L * U'.\n", + "\n", + " Called with a fifth output argument and a sparse input matrix, 'lu'\n", + " attempts to use a scaling factor R on the input matrix such that 'P\n", + " * (R \\ A) * Q = L * U'. This typically leads to a sparser and more\n", + " stable factorization.\n", + "\n", + " An additional input argument THRES, that defines the pivoting\n", + " threshold can be given. THRES can be a scalar, in which case it\n", + " defines the UMFPACK pivoting tolerance for both symmetric and\n", + " unsymmetric cases. If THRES is a 2-element vector, then the first\n", + " element defines the pivoting tolerance for the unsymmetric UMFPACK\n", + " pivoting strategy and the second for the symmetric strategy. By\n", + " default, the values defined by 'spparms' are used ([0.1, 0.001]).\n", + "\n", + " Given the string argument \"vector\", 'lu' returns the values of P\n", + " and Q as vector values, such that for full matrix, 'A (P,:) = L *\n", + " U', and 'R(P,:) * A (:, Q) = L * U'.\n", + "\n", + " With two output arguments, returns the permuted forms of the upper\n", + " and lower triangular matrices, such that 'A = L * U'. With one\n", + " output argument Y, then the matrix returned by the LAPACK routines\n", + " is returned. If the input matrix is sparse then the matrix L is\n", + " embedded into U to give a return value similar to the full case.\n", + " For both full and sparse matrices, 'lu' loses the permutation\n", + " information.\n", + "\n", + " See also: luupdate, ilu, chol, hess, qr, qz, schur, svd.\n", + "\n", + "Additional help for built-in functions and operators is\n", + "available in the online version of the manual. Use the command\n", + "'doc ' to search the manual index.\n", + "\n", + "Help and information about Octave is also available on the WWW\n", + "at http://www.octave.org and via the help@octave.org\n", + "mailing list.\n" + ] + } + ], + "source": [ + "help lu" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "Gnuplot\n", + "Produced by GNUPLOT 5.0 patchlevel 3 \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\t\n", + "\t\t0\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t5e-05\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.0001\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.00015\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.0002\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.00025\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.0003\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t20\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t40\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t60\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t80\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t100\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\tLU decomp\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\tLU decomp\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\tOctave \\\\\n", + "\n", + "\t\n", + "\t\tOctave \\\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "% time LU solution vs backslash\n", + "t_lu=zeros(100,1);\n", + "t_bs=zeros(100,1);\n", + "for N=1:100\n", + " A=rand(N,N);\n", + " y=rand(N,1);\n", + " [L,U,P]=lu(A);\n", + "\n", + " tic; d=L\\y; x=U\\d; t_lu(N)=toc;\n", + "\n", + " tic; x=A\\y; t_bs(N)=toc;\n", + "end\n", + "plot([1:100],t_lu,[1:100],t_bs) \n", + "legend('LU decomp','Octave \\\\')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Consider the problem again from the intro to Linear Algebra, 4 masses are connected in series to 4 springs with K=10 N/m. What are the final positions of the masses? \n", + "\n", + "![Springs-masses](../lecture_09/mass_springs.svg)\n", + "\n", + "The masses haves the following amounts, 1, 2, 3, and 4 kg for masses 1-4. Using a FBD for each mass:\n", + "\n", + "$m_{1}g+k(x_{2}-x_{1})-kx_{1}=0$\n", + "\n", + "$m_{2}g+k(x_{3}-x_{2})-k(x_{2}-x_{1})=0$\n", + "\n", + "$m_{3}g+k(x_{4}-x_{3})-k(x_{3}-x_{2})=0$\n", + "\n", + "$m_{4}g-k(x_{4}-x_{3})=0$\n", + "\n", + "in matrix form:\n", + "\n", + "$\\left[ \\begin{array}{cccc}\n", + "2k & -k & 0 & 0 \\\\\n", + "-k & 2k & -k & 0 \\\\\n", + "0 & -k & 2k & -k \\\\\n", + "0 & 0 & -k & k \\end{array} \\right]\n", + "\\left[ \\begin{array}{c}\n", + "x_{1} \\\\\n", + "x_{2} \\\\\n", + "x_{3} \\\\\n", + "x_{4} \\end{array} \\right]=\n", + "\\left[ \\begin{array}{c}\n", + "m_{1}g \\\\\n", + "m_{2}g \\\\\n", + "m_{3}g \\\\\n", + "m_{4}g \\end{array} \\right]$" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "K =\n", + "\n", + " 20 -10 0 0\n", + " -10 20 -10 0\n", + " 0 -10 20 -10\n", + " 0 0 -10 10\n", + "\n", + "y =\n", + "\n", + " 9.8100\n", + " 19.6200\n", + " 29.4300\n", + " 39.2400\n", + "\n" + ] + } + ], + "source": [ + "k=10; % N/m\n", + "m1=1; % kg\n", + "m2=2;\n", + "m3=3;\n", + "m4=4;\n", + "g=9.81; % m/s^2\n", + "K=[2*k -k 0 0; -k 2*k -k 0; 0 -k 2*k -k; 0 0 -k k]\n", + "y=[m1*g;m2*g;m3*g;m4*g]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This matrix, K, is symmetric. \n", + "\n", + "`K(i,j)==K(j,i)`\n", + "\n", + "Now we can use,\n", + "\n", + "## Cholesky Factorization\n", + "\n", + "We can decompose the matrix, K into two matrices, $U$ and $U^{T}$, where\n", + "\n", + "$K=U^{T}U$\n", + "\n", + "each of the components of U can be calculated with the following equations:\n", + "\n", + "$u_{ii}=\\sqrt{a_{ii}-\\sum_{k=1}^{i-1}u_{ki}^{2}}$\n", + "\n", + "$u_{ij}=\\frac{a_{ij}-\\sum_{k=1}^{i-1}u_{ki}u_{kj}}{u_{ii}}$\n", + "\n", + "so for K" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "K =\n", + "\n", + " 20 -10 0 0\n", + " -10 20 -10 0\n", + " 0 -10 20 -10\n", + " 0 0 -10 10\n", + "\n" + ] + } + ], + "source": [ + "K" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "u11 = 4.4721\n", + "u12 = -2.2361\n", + "u13 = 0\n", + "u14 = 0\n", + "u22 = 3.8730\n", + "u23 = -2.5820\n", + "u24 = 0\n", + "u33 = 3.6515\n", + "u34 = -2.7386\n", + "u44 = 1.5811\n", + "U =\n", + "\n", + " 4.47214 -2.23607 0.00000 0.00000\n", + " 0.00000 3.87298 -2.58199 0.00000\n", + " 0.00000 0.00000 3.65148 -2.73861\n", + " 0.00000 0.00000 0.00000 1.58114\n", + "\n" + ] + } + ], + "source": [ + "u11=sqrt(K(1,1))\n", + "u12=(K(1,2))/u11\n", + "u13=(K(1,3))/u11\n", + "u14=(K(1,4))/u11\n", + "u22=sqrt(K(2,2)-u12^2)\n", + "u23=(K(2,3)-u12*u13)/u22\n", + "u24=(K(2,4)-u12*u14)/u22\n", + "u33=sqrt(K(3,3)-u13^2-u23^2)\n", + "u34=(K(3,4)-u13*u14-u23*u24)/u33\n", + "u44=sqrt(K(4,4)-u14^2-u24^2-u34^2)\n", + "U=[u11,u12,u13,u14;0,u22,u23,u24;0,0,u33,u34;0,0,0,u44]" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 20.00000 -10.00000 0.00000 0.00000\n", + " -10.00000 20.00000 -10.00000 0.00000\n", + " 0.00000 -10.00000 20.00000 -10.00000\n", + " 0.00000 0.00000 -10.00000 10.00000\n", + "\n" + ] + } + ], + "source": [ + "U'*U" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "average time spent for Cholesky factored solution = 1.623154e-05+/-1.166726e-05\n", + "average time spent for backslash solution = 1.675844e-05+/-1.187234e-05\n" + ] + } + ], + "source": [ + "% time solution for Cholesky vs backslash\n", + "t_chol=zeros(1000,1);\n", + "t_bs=zeros(1000,1);\n", + "for i=1:1000\n", + " tic; d=U'*y; x=U\\d; t_chol(i)=toc;\n", + " tic; x=K\\y; t_bs(i)=toc;\n", + "end\n", + "fprintf('average time spent for Cholesky factored solution = %e+/-%e',mean(t_chol),std(t_chol))\n", + "\n", + "fprintf('average time spent for backslash solution = %e+/-%e',mean(t_bs),std(t_bs))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Octave", + "language": "octave", + "name": "octave" + }, + "language_info": { + "file_extension": ".m", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "octave", + "version": "0.19.14" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/lecture_11/det_A.png b/lecture_11/det_A.png new file mode 100644 index 0000000000000000000000000000000000000000..50f6ac16d1f2fceee6f8b39a8f94e0f07f6fb92e GIT binary patch literal 20397 zcmeFZWmJ{X*DnexA}t^wtw@NJbc0BDcS(0kcXta&w{*v*JEgn3bJLsN_u0Px_r3Sa z9pj8~&d2k7aqRu9z1Hmcn{zG zAK=7=1e9FTj#s=rQg=MT&?N63h3}Rqac`-lD?iY(!JAjr&dY_ZFcE;z!p+=5vX?@q zPFRdhxX;_(rJbTs9r)5y^YYqp)&KSaEqKU^qtb*^|9Zbq5D0Il@jIa#gWIeK=WCUq zE!~oj5!JcpbIhY=J%!{2og{c~D_fN4pb7kts|(_5`l+2sGx!ztB_{C1awJ(g!I8n9 z8iCM?5a1zyMbQTP9QXFuZ5Z%b?7Q414eSe~|GfoFiaHp?*6hSOHNeTSKZaX-Kt|j* zdE{|%rN20?&9D<2Z`IKI(}e80i9*#kqd@sl7k;#HySl^GLkuPhkL1XQJjTHkWMoqz zmYYZAeH*e8_9e^lprb-!YgHxwyWqe%b-$U+-wC4$J(f(XxK4O#;u6*JS|@DW1mf@9 zR)jN}Q}p}OdEAbNf0vZ8m59S5%vP_+C@5fwi#JL+a*=H0=XAB>pOu1&u8aJ92u8;$kyk(xc> zl(NY5otP6Av_nnH4RX;|n#;I=?!8iWq?@uF7tk(BFR_NA%Mx)5L&j&GOgNq&bC*5+ z({m0J#Ybnz$Q(j2m0`;scS(lk@J5Mw~Aonm6iH%=0HM){jf2b**VpD+sF zU?qE?hiLVZ;K&&2h-dYOPuEkruRj0zaU&%+F0JXr(I@v$4uLw( zu{)h7V53o|ZGC3;-{LN2rNvvQ-;CLCeH0y)KvJ{1OW&_g4chn}oF?YgB!$fwg@uKG z{ZiesToz%2qbe-UDBp8I&cHo%Qk4g*wA+;)nU)$mw>*9)XOc0`bN;O?C&kv!*^6|j zP4eY#ZelO}l&WU~fVy{0cPD_7ZR0uP6e#cHh8BACj z18Pp3EM_=M$2KV}v6olY{Cci+c+w$FnVhUbgp(gZs%$($muq;SbCcn#7-`)yyzQ|p zAm~VUx@`Z&zRX3lctQOrqouLz_sLRtP`jFo#$i#3^Tv$}JdJu3nS?}G<&po#FV$f~ z)WwU^j@r0OlGk@M=M)#p#K*nw)I7YK4ymG$9JmQN5Ms2yyN23)J3C+OL)!A?){@cX zw*TxXwOX<1$X?l83)gHlZ5R=^!XmX$vYuV#)NF$l>}c4$oWoR{Mr>ek)AV`lqAnR4 zSny;JC42r<^0>4B!d4;;nG+9%s@ecj zw{${KQkzp)aI7ph5xwK6_yY}fXdXHDl4gqwK?ya(D22uJQFYc&Na3FMqd|PY%xRXP zJ1>0ZpCTRS?sFsgjSCTI>$_3APuF}z#Em6UClt9+sfOJ;a^HnddhU>PR2#vrDNuxr z8}E<&*H0xunf|30gS%f|@!0Q2tAByot+(Q2BS7zh-I$ZRO_i*u{q(nA&$I? zj*Pk){A}Xu;u1p2bWyU6YI!AcRKiJ+)&TErVDtsAq+CMRy6Bku4Kj^CG&mM-e`P1kLD#39gA9OScTJ38JEX z?ANULOVw017K2MhuULmG!If2={3`U#)vjH)MQyvDeNDrI(Jx&^b|yZEybHpzX^76B zFkt~}?zyAC)S(r5F8?#$7j|7ozr>+pPJDTck? zQzvr5`n`zm6dP1+SSr_6@%hX%)pl^%kjT=C>E@lx^J3jLm=NN{{Ksnrtv|`ka-JCl zoNpUNSOm$2Hd-z!a`ZZc>J6?LMR+w|vsw|7Xp-#5)zA&h-AR$wWI5s^B0oL+g|zlX z%<_svK^+@T$5BNnK%`%h@mRe2c0ChBcFO(x z_LF|-Iz(3G+V_+1QG}vG4chl?hog+}l0!d}w*^hK&@6dlF|eRVdG-G!zVLqYK&9wN z%rff>FBw^8P@`#(1Qi^uJ{_ND2Lh&a8%Do}!DWVj-^3r|+=G1qgRwuy8!!ctK;S2> zr%|cUB_kc1(Fvqav_*7PnTJijAc^-bgh_LaTy*j@m%zVeP|O4 zaM`XLT`c6^4W$3yY5!vM$6A4yfY)syqAhuaHtZu1Sju(^G3(q^E{_^2TUm#r_4?#g;$^j10oI{E_(0M2Xw+(*ah|nJ4V#pqxGOzol!WDtk=L> ztTj2(p|;$<-QjEoDpq)`0LonZeSaQ?Z!a(h3i~r#cttJ)#-5$FI)Y+_Y^62{MR=z8 zWSCbV`~A*lS^dtIn-TaAhQn~+O zB%Wu??q^${NU?|@PH2u0G-!5;^xTS5f$Bu2{FN{e&0*+bV>Gc__75po;9cVqXkw(+nz zJ!4c0B4I^8E@t`SJRQO5j7Dsu3Mi|nZU$y#)BnCFdOu@LzDn$lP9U0^8oB#Nu&<36 z@bswce)`}4bk`I`0J9)oUrCnGVR3o&#*q|Fzn4DN1i}4$Ze~RmXEVXW47nYzV}#|4 zY#tYin)){I^Hvkxpf0VJVJMWDp*m{X(t`o1C+{90gZOjvcG2p+N~Amko&Lc^Go1dkJF|MnwSdR0`2|uK!D;v%C z+n766dYWW|!CQ3#k@Baeg?;QG4{FVlp~3VsIYarT=4JkFk5bbf>_JaF6$CdA(Hgmy z8kUYW2WlGPrhZB4C3UWKAL7Pp66ak?t%n-ZbD0RUGCwsR*@+&m%kx7UiYhKt#TZJnOsBWZ8K|i+d<>Lk5Fwk+bBS`c5X^gc z$!8LR;ulg8sfoc+=nQHnQ%W6Ybf*1tWZs%E%)BLyvce z?1_7SB^dgGC;}SDJfN29hU%SLv!>>uq!a4Z^SfC+-Y-bi2XbB(RHVJ+%>T4ASREFo zj%?eKnC%d_w6HH3Lx=EgiHbV}LDPpEvm=F-hfe?4@N=sFW*im(mIlyVaO;_>Zzqq@ z_CbrHZJ&8mbObzy8sZ~n1YDI_XJ(X@-U;RUC=^ELCnYwCti8(3r-&h6Kx>Bs4uO0xV()Upba*VBC{T;Gsu0p zRx}sXZH?f}>xf3b+{XRQTAXudiw0G_pEp(=-QH^5?7SU=mtKP>M)~WF%RJG$h0di- z0!^l2wi^^b8`f_OIyNzO!uQX5z2*oN{mkK+A!HLc=k~^Y>hEyq0*rOo zn@Q>Z+Cl$dbdYybOY4W82f|1fV}rHq)RQD%b#VUvvMdH&cSTi^q~1cf{l-H996KHH z+X=r`dDr2VhGL7S1Y6{y-)B>DxV<=cl{@d#3UkWy{Z1O=Pf7xdt6SSV=~jj}f=-yZ zFrtyI?&k@$T&#rOA-X6~9?f67Aw30df+qlHHg@msNiBO$UzDWzJZ7GiU6o;8fLE!< z@Hr>XrO6?F2BL887VLlZ-G{+N#j-7eDIkC;q#?%^s`OWCQ~DQ{F3k-VVxnkf!CHHa zaCylng!yJtzwhy{$w+=}N0-4EWUJJoQ*+&@aEqb22lM>Jc}CyKJ3P-!gKi5`HMNxV z9d4wJ{H*}|&`KP4*O%6!bW0#`-pv5@y)5z8foSykRqon`b+tOEEbMTFf>8m)bfweq zBL!nGTtzcv%>CzP=yTg%{k#W*w9&MKS?V9eN%P(pS6lf8BKRslimFZnG4&a|K*aZgX) z8Dh5jB-t676Yog0lYVcW3X{iH$mY3A0T?OsM+!`C9t_?kSU*AuC-4v9=7}h7x!%dh zf$cG%J-^kJxK62<2@#CiNbkp3Sk{38aULy3Tt1e!TEKByk?Sfuz9u;(_v8v+hilnd zLqo&V%q;H$q~Dvc<{slnVV+P2Y)w9UI#kb`TdwH9NXG8%uN>x1d( zVUERLNm8`lsZ6%uvB75@teUOlNY62K#%CSmVXj?PHk^vNtqL4ViXnpRJ?60JWKdN~ zc1zNh_XwJ*cCYdlgYGTgvqz$0ow8JYOe)A=e-D!XPKvRgj6>y^tz#==oA)F?KN~Z8 zM!>GadWV)secdsd7;D{;ebN`_;T9q8kHJu{HA3`KI2}!RsXSgP-4Nvdj76c?KVsKK|^sStbCH^kxXh#oC^-gHtwH-x!2VXR)sR>O6t(-z@ zx&!CTyNy#1v7~H#BWatx)67K;La4ok&ds!_>`z-20%%EE(t!8cS~rJ_65+V8plS3Vy2SVJP=sezD=c_V-%wub zuwzl4AIm#DzUk17tF+M|=t-KU5SEE}=v*rGF?c>}8_I;~Y+8)u_p}ErQJa)`CvU#^ z`$BrO8c#kAZ9S)ccIU`!kXkPcVad27+`X_%=+8^h4(vb9O;K5&&&K6+gaicOg?D^a z$g1V#9e)}R_`@z-g?l!T2G&*eqT*Gi&!go_f^p$0CQj`2T5U0>e37X6g5Fb~nf zDFNpns14E)yGG8)%XS`&oUIHl*CQ1h%TqYEudK_>KaG`u- zzgCX)9izyl+7SN04B{l3-_K(FwtM8nb;`Ks%$hiIT18b+d#@{1Q_9uV zCmU0sS5ZV*9aB9+tQrj*6k?6ZCfU-}r< zQk8{#>jLi=&5MuHe$Es9`jr&vx(sBA?*5Xp@;^xP%yyvY@&R+x101?e6{&Ld6<; zL%m4LTzmakwcKj}7|*0#U`U13fzK$trH9T@tY7I(x)po&O_T}NnO#PH+u@A_>On4O zy`;bP$1lHKx?N}^Z&Eg9(gqfA8#p}Y^b9n;qN<9FHzge5BQ-vLS>J>gX}0^(Jy5J_ zaCjSpIaV7zB?Tew+2U>rx-_&}47RA;m2UD|-N^2zXtqB_HWrvUPv3zka8z)A8is5X zru1*0Aj{D#e${|Prh&-R``MQ-$MT#HzGZv28yx+Som}K#xzebz{GA_&bRY2tR6?{qEGNAiZ`-%TTtlgmnY77G@jhmCyI;6J@SoceL_>Ku z`O_D}C7;gIHXjgrm8RLo=jTIe+ET*wxs%rJt_H>e;s1ivP7t0mw?^eaHMk~{DDh^hXj$2|CTS5%61C|7Dy6PL#CMIJgwwh}?a-c|4K zn!legCR46{bzeoz9pcbR=CAIt$QqhN6Op#~EDs`JC1j#nS)1%~?50VN)U9^eJ%4rC zGWui9Zh4Dv)}8uzPWwGr(EC{09l5}Rp3XHvq+`amTces|`BE0H>>;8h8zNHK{yI`4 z^sC(1#lG&Ly;EI~3n|syjFQ3ed=*1Te)yi>?dkc61+VGxVpTuKG)Xi>21{GX-J@!k zi6t*;SYM)m;HxoBmZhnPgOhwfKLj07sPj}r1LH(r(d)(*qsGXLgzyW-Wx)$Ij>N8#qW5is!<63LZ00FkrptVG z`s>pHN1SSd^>AC^rw_(;L?9aK)A?z_q=K)LU(|!BrBpzsv}NT{Z&#}E$83D&vpIl z^Wfxx9G3@cCt3AH%hLV0_`ElkLPDp4s&4E-P3@6SJ87KDa+RNT|PWHyWx-2>#?AdjgfFhQe z`8~V4??TwjI2cbg4zQnL^zTB3eXkKexK1MquHo-HcDti}nycfcvUcX`aLmnL_)%rB z=@>4e4H|$)sa~IatU6DF_ROgW84~b&)u%tTb99S(;=NdHdkzv_cIcOw#LFADH#`>y zMr^}qeILm0L`~8k-Z!njk_~4Vv~vF5j>x6G+nZz!(Z=Qck-d_{!tgBkJBe>{w+k+> z5F#Sv(b}@M3PG>PJWj7a>AIulag#;oq}fAkgwznZ+M?{#jg&S(-!NFKGoId%q?n&> z`L;4lE~C&ooz*>%>}E%nR0g<-?!JGLp(3j~@S9^#gIo7EXd_v6qVm}HgO4uCMwmXj z(U#$+TCHyxNP4Hc>4T%|7hZ9pT_L1KuJ?2{2=S9}gXcSJ?wBRbSWj+mb-K@3s}Xgv zmE^3mlKg#qJX!CJqU&84nF?O%f4al>xZR9yfV5p-{UOc0m&DIriRBalc<%|C5dYCn zbN0;O5qfG?5Go)%V7508Em-gvJR?Iar6s}t!ss<06w*UcFw|Wm$}PCKo7;x+2pm7J zZk$=Iy;Q@$-b(>Fmm0x&%vw*ajkFnG6S~&HJJ5Zgp4pkZb91TC6x49wbB6xlx6=J$ z;sLegkq4%iyZAhagO^z)_=`I4#eW)9iL%GN=2?+XS-98@VbMN`zF;?Xk4@r}+S`q^5J9sT$ojEG zFn>eaKblyhKN!)KiVciS2adU*NO|-=Ywbujk8d@Ow)iK|`pgQz7xyx2m2cdUw!JJ2 z)dE6#0;kenrdb}Pp5MqM1vgta{+wK*ll(KP@vxNQnn_`)&gjHav7@LOGb+iFeqyo} zcT0Rw(xWPrW3x~77`^I`4MnB0@Z8d)sMKL^k>6>~TUfuqYIx-DG}2|{X2L|8I>317 zUTlNJU+P({t*yOO8+f0&q`_12=X3k$Vs&DVui|cj?g!JJzUK4R!ZjnD)LWEjlF={l4jy|O#oX|UF3*|yVsl) z1I=eO%=RsJ*fcu8V4Q!p6db{DcRy&qwoNOolFBRC+9A8$p*YvcEqhZFSJLBGw&S37I`>Eehi8mM$;fhBoN}CR!8_q} ziuBU7%(;NI_A$No43{N>`c{1R@2Rk$@!;*C#zpgf8yk=Xd&_nAzC|ND&M=g0b${r1A)t9Mb~bC{SG5C!52b)e;x6@%N8mbOpyYKqoQ zb`Mzozg)W z8>{#_^8ryTqoCS^4AZvlN!tr5i!t@E?281-f9hn_x-fy*O^oQWeyqODgV!WGH!n2r z-lF++C9$1W7+7F)MQ37#3J78#ZT8{vDQ(e3yCV%l0AApxb3y@$JXcW)f6 zr9JesPRKJ;192vAm;aH?ZmR5c0H*e%!X^z?G$1q^9JW|f{Id?(iomtUo?|f}pI)AT zU#DN8-`(c#-9GVqc`rIyjXnF|B`xVFA7R6P*o!@M8-&O|w+0^? z*RHIK@?NpF@)!{g#Zjmk*Ft&#(;+8G17AvW*w3XBhmsd#*GYH@`;9|L6{*Un4*2hk z1IWas01|eYwq9JNpHsAIgh~%P<;+4#y6^aEK4FGxzHE2xK7PB)0)#b(8M(%4D*J>h ziDTQjhqe$PH`Am3CXN(a7Ju-!7(v&Q0mx&*!^iVzH6JTeY-9@MO{c$Ikp9Y%Wp6^Z zHH_lGTL0_khz3e9An!)w&j(Knd)aeVPAp`;j!hmF6PKP}T~?1xh4e)ZtB1szFAni- zDwLPI0NXR9$4|d9ck%CO%HD?f%>lC2|4ZSm!)IO;q3ACI$jZ?vLP^$Xzx zL+FuR+!S+x>5RxoSs>3<^EZ%oXRD}Ao`-N@Y#$zs`@lGzB#=AJ$sMGf3ArdK)zFUW`V{OVk_zE9El1KmzVecVNxd|ua3 zm}G9)->r~g{-gRmA5dx{8hVH3!@6l8;ABEF@^q!EmQL@;;(UOt+Vf@WMVi^wj37=Z zyY4bZ$*E7?J3y1MuW}gM$f^b!;4pSAYYbp(bClK~7??YH20xhAO? z#ow~7pSSig6jm0743qqOb9Y_5{^7i03ZeZm2q01H1rRB)ETW!S(}1`WH~`o~_t6?F zH!`O9+mvNWESlG2-H81x$A)nVP<#et4#VfYAjZhjIRxgT>5`HFUOrG2@( znoczL4+WO>IbjxnlJx&kXPrKhT`-MHa_awPf2``!;J7SWey?W4PE2 zdh#ebAn<>_rNq8>e@HD{JtBLu;LmS*EQ1?fu-=4D?KiD8?7x# zQ}};S?slbyh?~$bl~W?LV!)D+2b|jJzGw!dimI|XwD$Wbz(#~r3M`CUTLqV|6<00Q zs|}T^x#YbynZY#yM=B9kMt9RVc@BwxYMun@l1l&s7_LWoIxCh)3VpQ``9*gJJJw}_ zbk}fK$Jr$q42GvQj2Mfe!&lqSE}&{)b4UOJ$imIyQ}N~ptT1mHR_+&=q1ZqeGag!Z zy?sh;Bca7aS~a8cutkkPfeDaL@^`p=-cmQW2LQRQrkK5Izk6dm8OFq7YNa;*V?kWz znog3IEc*eZpzIuTTL}~_H70GXt>mTM|AVYb79X08-P8p-ktOAB(BepXlMEC;r$+-$n zr^}5~Kv>$;QDAC$t6yc0iC?mX(@_5+ZZDZQRLljJdmZHXb)0z72{bLuJe{3cW7FP8 z2(F!QI+P~J@JcA}owKv*1DjbKbygc9;i)H9?#3BBZbh5hs+WJD*`e)!J|{V~@j-JZ z-8`b9jUf<9<^1xWNVvJU?&@*`-YERS84_T1BBR#a4Memqz)wuV{A9gQEd2JVt#fy0 zzmwc+XDyYluYO`sXnWx?gt<2M(%oCefgz91sq);nm8a6Hw@|^fvo_fsP@vG#9pCMs zJ>Yvne>0sr9`lVwKVr4%uyYJ$Jq>JIO)_l+6(?gv$1uXy#xuTwo@XUe;)dp>G3kPn z#9BDyk2HVhOd*h_Uuc6$$Jt})3Q#AzN?(2K{; zAFzc%bAS^Xw1rX9CJeZbQ*(^M(|>`M+SZ8sJ2+}-g`d?VwP15JIO zR69kJD?4BM?mj-&zwyHVaUmr4P}gy&p{5DvvT?%1;bmz#B?;+pL*%(bxcxlvK#mm! z9}VWc3C6hnix3v_3INq&EaVj3gNp+vV~Pl4)6vb7$f`4)e?|5$q5KFOitz0OAh|xO zc-l0~VXwWUF0{t8>7B2Y@Ta8+5aq8*zEl*5VShJN(J5M)npX=I%$PBeLIIN&W2Wx_ z@c7?pp}&EO<6h>+j+gAdE6Aet-3V}mYCcnu<6g8KGR6&S!ujK>d$Q()*>mVaN#7y( zx(_pTF$!oSRK{LVA!GfHm+ic8C2U1=szQD_%zJ(jpH=nrk0DhFVZ6!|Qei{S~&^}zReLld6%{s9Bh-IcdV!MdH zVn9plPeemhM&g*yfBr-s(Zjy()h~{J->s|E+Df!2sO6+cuHd$ECJ@tZ8zR;PgDYmx zy^YVL9WUmBVEkjFo5UQzefZh1{vEhyJP6uUuLeTbVyn zEN$C(jpCz=Bgjx$`r^W(^EJ=I{P4|#0BfF7XHL3p_B-7Aj$~RjRrCt(_3xPP5`38P z79BRC++4=c3#L(MYx3$y_#hZxtSB8+oW0pA()j)orrVtN1>4x4Y+4LR4Xx88;W?<^ zOVo6S(-d#fU{U+;ZIrbK=f)=>hQ}z2Zs0OZd%?f)#GKp6Qf(e_yiJ#c&8iqyHIEOMK=deDrsS*5a-TKrxC<56z7y2a(6m*U&VU z1B7|+O{5DidtMulTjLlQIt~WemKflasFdj^Y^l`qJif3pSiBlnQXIX{X8TXp%QTEW z7Xths?`LL&B~r~d1^W$!b^pFlkdbvD1F6rj9nxt&!Z*Y#89Rwo^L7IaCcE!T2pD;W zku2gh-`iD6;?36)L_#X|Qlr~O z!kTX`#-gFj?qCgpsa$7=xo#T_s(Pyj(Ajlxikd=ObiemKhdaB5%T3$0rMuq6D;^!7 z&Ix^G@OE_-?`bPteOzr zZbxaLo`)j5k&pWw!5+n>L5B~sifVEL_YXJKkX@El??dX<1H}9PFSAUy9%Z>=%gM;Mwy5+7VAX@8;d4)wb9^%r$E+gBN1d`Gp^_5!e|IP5!>Ux;Qv z*sFa;;3XaW*TA-fP-Lr$q)74!xR5ZVO^SkshvA_ zd>2*O@oi|p!uwsgvk9Hs^HpkVZvu2)-n)~l?xCUeowpDa+l^N|oP(uz&h@wSWX6Y% z53AwHB_mNnh6>=Dwtm2QMqC~;K_r`}vfdVPnsl`4Rp!UaPvEo7DxJyl<^*NjeH)8i z&%{cj-g!N{L|JVCE{2Jp^_h{9e^RiSKnEpNVhzR?zx_j`z#v2q92Ft`>0i9{0{f>J zMnu*a(ik>d6Oao1rKdncxThyxpTLOo#xjbRD7;racVBgZ?7WduriV_(#OvHz(G@0^ zhTPU9h!Kgg+B;|Ae!JL4@K?3hhQazXkX`~T>Vr5#2ClfY$DLu|K4*8ackb0haij@! zsmvp{K9d`Ir|xx@PtgrhV`37^&CECt^tyN7r}B@82nix|fNdezO(dj0=8pD5>nk^M ztdF&Zmx0=nZu9M-nZ}jv_G+Z1yBz}L`HGt4ix$(a%21p~;&@+GeO0o}7&zs?2myg+ zv)M!q@F$MAIL~WAVREO2qq^ULJ+<5pr@tqh@XZdUC`SQ{mwT?jw_It@yf}LCbFI7~ zSrZRq{8nkI5P@d&|J$MY_BqxTXtlO8rG)fEOv%)IdYe3XGv<~0k}3n$wYi!9sjMi8 z{*<#z5Tj{*7jY15lVdlWB7|SsWQ`_CYw@|AA@d26pxAb(SHEj=_FRKu*KWb6>+Zoz z^F7MkTKvCe2eF(-D|=ZRB|x4h+roho(LaO%uusa|dkFh+t{X=H1P${fj`nVJ`pfoY z!#^+rnz_*H(5zVR{KQ~C_y5z2>4AJh1T@ENqUF2@D~dZX|NWAD9*T4@lKLhyQ!Gs55@iOU4ugyny0t#h&$TI+39A7+&E7xKJbC-T8C*)L>HVN z`+aPDecGXZDyr`=Nn!HN27d0=2iY`UVeyz+cV#d^Y`T-4<8E=f&~<&D4ri%{nonxC zE)QoS%USkM1aVPq`YSbGdXv%`EWvHK<)#k z06727y3WY`B6gk?rL`g3t>%)hT>Yoxbo3{(Dp|np3;zj=obC5?IAQVWGl^mp4Ox{a z@Z$3*BpEp9IJ^^f#`#7nN1{hcxYC#^`3BH;LJ~goKy!?_WfOI?6P#FC^QY+5cY05T z^%5pPiTq)5l2;4i52x1iV4U?NPmG0G0)`TSzBdW(takKhK%VGOk5L}Q45%2EeZ_fA!5@oR(l(xhoio2 z`nuT(3rPVQ6C&3DgvIRk+HF8==qooWCSx+t$BY$|W3ZNT-|7b4E?*E1qYDa2{QD>S4iE9MY1Cc! z=AG$$)=gt%#|>>DU8_mq*GjhrRH9#PSo0ECh*XdsllGV0THPGhS;V4%NdS&Z8;-Ws zkR*y`hWWkC?#NVsdI-#pqz}K>e2OtWbV2ZGW~XK5d>hIlX&$%m5%3;hQi+8u?G|PO zhQ4@>c-yUvG8`o&B$V?FW-_=tfXN6cHe<(4iAjiW_(Cn&xd}qEaFR4e&;^9_ePCkx zNP6FQN3hCgJvddF=u+L06U~hYr?e#OzU!11U4KiSYc``&F=ZYakif`F9vY zKtH9LtR^?c)E$bKr`?(uox%N0LL)^Yb;Qm>m0`OpOYgspJ|tr9l>B;Al4I_fzIAM- zs8*dwOnmmQ6>TC@35@W>BTboA6s6yWpZat8arr>BA4}0k@3Oo&T#@6 zMkzNy=~IdGB!rZqq;`SG`Jnf57$!Vevs7-u9?$FW;L9r3aJ_FnCCDc zQ|w9rPJX)zMJNi#dpUl2`SObuTQJ>UC1A#U3n(=iDe^KB=(NO@9^@I9y@LJN+)AeD zpHhLJGhrV%{pa`}dK+$V32dpkwdScI5ilbLI@i~?lz#9S9+RVfW8U~a4kzG?^LA1N zU=!nO(Us_wnFCnGZeJUAIi+E$W?v`u7j z#v&NXeJjt-JN9S;aQJezTxTFqp!@i%5P8r)8Nn77q~{qMM>Q7jg_^_GST}IR|Jo-1 z7r0<#{h@E1J$_@zR?Gcy=I>*R-$sejqNR1i%|-Y>J^jl%653fC=%MSi*ggpCt6aOl zKH*jxRnkJR{vDHI--mfgAiEh0sxn_*+Tc4RNTl}G*OlPqY_yUwWx#^GghY@stdOtC zK0%nIuaRxg$RE+4YZ}w?3xb3VxB%wTr8nfulDZ%-R$Ip{UM=%@parZ@y!U%oT~n)6 z6(W@fs7-4q959!hvMEqZpw-lhK{*M%l~bb%VmO6`s)a{I$Sas`wFveIp+M;<&W*wc z-9ci%=8>2F+oA+e{LwS@8T3*N zQYNxV?gVj{ZzhP&T}&~&4*59Kb>FOVStB}ov6yS&YBe_VxPK#+C_TlQQm@a*{e}Nz zX*X6@vBnj1p?iru*0Xzu=egD5b^%hpD|$q){}?+(uiH6BqCRr3PT*O2dN2INfRZd8 z#uL&d!^{`!(5x+-(x@?nmV?|+V|r=a{k+avY(oO@`1p_f5Z$4*l^7;*|98mHAp)n> zH?k-0@k^(k{>>y{BiHkU>19Snb>ezcMsE;rDxuq`?HGpUZAm|G-kNE_4Izr>lA%`D zD0eB(b^GdeG^x2k*8FI?q^MP<`Nn89#ntl>b;e1=HZi&-;IA;i{0k6`ke?m=#VIp4 za%eroyR)U#2;PR^i`C6t2}8maa2BxHyTSSHy=YJ_7#z`k?J zR*;HR6lzpnx40J8F6gd47pbF_T-L3fUAI5@#Aiy)c4d*i=U``}KIUhCvxoZng;iXW z&vlg2vS%E$dH#7QRO6)fpLlc zx@bV}lkoqXPvPime&5%O;ko6(Y{P)!atXw`inX8Tw676f^6tH)st~;A+pSU^(_?sk zr>k)&iHcXQ)}za*U`NX9&n>6l)baNa!9VS^s`~D&j|fbl|w_t32WlW+X)oyw%R@d-PUn)J;6j;Z4tz(?spqoylNNpxx4PJE!BGj z=BIzjH5`_oO;3)!7T(4-0(UyZ$hB{9fNni;pwQHUuAX|U@nmYSMC!?W8gICOG!?+k zBRsb%ME(JT&him#Q*#aF7Thzb*q#ul1m%xNlA*n~t-Cn!*KS$8VHDN1zdQ-@!d+`f ztGm=&cQ$b~$cVhAQ54g(V|1pwxHtyy-ci=_I)vek=GWv7_Z?8JZK8N@?dEllMzsu5 zu8%AOu{*3n70n1U85Zcom|kxzBEu4_xpQ2L?cu8MrDSSk%}>TP>e@566K)>+M+2Gk zgRSei#oL>$%pdJW2)ciNHw=DTgCm7M1&Ki35H_qG=91D_;86(Zvagk$Y%DfcYyfE| z06V(bm35D)E#cnR=DX%>Z|R?;mp17pSzv<DFo^YY5y{7DYP&8~n$8OMo5t?Lbbo_#@Ci{CDM|_R3#m5`Jws+6ct4Hz z_pF}@HI8n9t9RPAJWkt;pVvU8%MQ(fcqB(>(x$0NVLQu>8$GUB;1_0>pVqb>3P8qY z3aKHlU?bW*x&gm5CK&$*j@^yX$=)lG@obDWwd&t8ucn50j>G#hE~aWGD{ax8b$wPR z+hkpCUd^LeMZB|>>^g0DGt|hZ1IBL`@IkWL8=c~}S+&KmS$s5neNV={a8gf*$Gnyk z4cxSd8pS1>I6H6$s-m2OC*2sQ>qY9+VI8v?a@;btfyEgV^;G6e;f}5Zyu0W2MfP*c ztP|Sk)@a;^2sk(lD%k%EfXJSxJ({knsg@YqcUY2i0dl6zf{vg^-Qpz;JZ~oO=(ys~ z<-JJjcRfQbs8PAt-|a1JeI&EK-Nbp^PjpT5I$)`QL`ITXxqR0IwYT7-{&e9G=K^WR zzPM!2-p7FSu0yiZ%yn%nbYYN7#{xqk`|Fj zT^as_xE8Jd_40PodvGJ8R9@$+}6tDSTp|!%_aT%b6u(pX|z@}croo~xf&b4{sVUGZIa>pAmdjdLfy?{ z0^O=3K-|-F#Vq9?K4@;2SUc|%PaT1Fr>Z>lFwIRNp5CgvHcwW_zaogW@sh*88=1W_W;GnP02JNp zLU4qHiS5HOkD>yTmTQ3x)32VSDH%9i-15wNvpIfG??eE`wAXPSaFlBmRsl!`R!!wt zo$+|=3IGI)0b@C;6WZIyqyj6q@+a*U=-zwXcC*9$C?mJS6P#FE0DpznZz~Nni34O8 zo*>Yc%)OeKu7P6W($}sxFnQkhVZ{LB2y!i8TjL?TXAn@OW_&Xz!v)Y;N4*8U|p<+EScxp9R z6my42aPgLb?H! z+RN!F8nRem^4&u#PThvHQeO6z8w+U;tW93PfNU0@kxAOY!44EM@XL-v3f4_*@xKfK z`CzF791Y(jBeHJml>_xmNBzNR7CW$M2Mh(S5Nv)RlLrEBk7d!N-pUw&6uKskf@HbW z&h8k3YZriQ-TZ87_H#4EpX8pI+wA{cE>8VpD3GuiC^);$I~jM4bnz!C1@lM#K7X#& z!#Y0%?hD1VP8WYfC&OX|2+$X};92X!y#Wfz*kmBRxSdmcwAo#NzDd&J;op!$S^jB7d8xqKBOsImYsQpL04tAx2;IbSW!DC- z2Q%1FO{IzNLdMa6VX0mB_Upw0(?jxiu!1fbDCkgKr-W#%>fLr;&@IrC)yTkhlaTS} z_d=Sq1iE>humbqA9Zky4TNhf9~sgwhV-23C(kn z+h(^ruv!f~yD-!H1r;hpu0+wAshP)fpAsrS{e~~>pHH$Ly%MW`>NpI|`}At;!Q;P| z2l7p%p27%}F27g1!XT=yu|emkOR6fPSNY8gP?J%@5ehcq64GD=3NW&4=rqP_@Xdy) z6!hPX-fZt|3wb21HzK*ZBheka{l6ywdw1OQc0Yww_ih$>q<%a$5b8Z=d(!J1^|K?# zWkMIHhn`IBSsyB%-Sk4gqGz+G^OeaOZs-+ds^aaziduKkGcy@~879zq#A}V4qV6_| z&q9em4zkM}%)ZR1@wtGeYVdE8yJHiq_(pwaIWNKh!4 z>|kJ7+xV?b{s#nkcA6X6TYmVldcp-sqCZ$Ni*H~1TW2^`&96+>(_a`EyA%VFk%(I% zm0BKk_UP8WU0>UAQ65eG54$TO5l*-LSREVQV1A@E2Y1w1gq^e!3)%EmDH6h6;D3k9 z=I_`Z9Fa3iuEIRu6gZUO(~KYs_j6OKIMI~F$LMI*i~&1Uh|pkoyl#*tiZR|~t5N9` z3OX?}9H(I=i!8lLg0a$;v%41}zj)VsA^N1TknbYX+|6C(hcrp}99GD5(KlBH{&u59 z^3Pb2`zszMscO-yi!IoD4I8D_Ko9~nmR+Y{GwWnib9q=(KYdFgrAR@+N5O5U-?P8w z2HYQC+6v2#ce(($bAxu1x@BVB^2tXRWF4O~CZ1tlxwMWFekQB>C}fLZw%rR4I}sw= ziopJ5KeruXWEW@}O+0er2-O+A0>;!*y6{H}1m^~V&Q%^^ zR&dnSGUeYE{$AlA2s3Iihb22`ou?&S*a=NKjVt~oq@_bF>(tnBYSkHTQ>J!x$W@0# zjZ%MvkR31{nMdtj@4{c^6`uygQh%~v&jjUml2zC8GQCEEr^#$8ULNj5|8%vKhq0`^ zv!UcB!ga9YEJQ(&7pJ+OmHDTrGE<3sx2h{p%!MA^dZ`sco%(2Ht3-Km^m*^u&(Wm^ z$80!%Fs-wMG@S!F-Z`egcVb9=s`GTOutPw(NrBM^9ZW?!BeL(QydBilRv55fm&)#O zuR=gBJ<9rEGZkOb6o1cBTyGx3(nBc12K${0GUrw`j}j)^#D-Kl_K=bc!l2!GACmzw zOZ@!8?Gu3gOcLC+b#P#cg+T6WqQL4p(>KmD2?B^hJ;m2<&D3UWH|F>RTI8=P+*5-C zI}$OF@oiEsjjzvQ?#3KeW;LY6a?*7E6OLe9u!60-y3)}2t$T~Py63p=x?O4n=r!`c z0|GW!1UQPy?WCBc*3My&a3FdE#d=tD`c(8SX)jz8u$g5ln!3lGs zfk?!xID(qY22SWm8S{>&)ys*Z3V#r`qn94P`G_{oO zYomv@#I$4I*B8+mg+ez0C6Iu0#yX2sof7FNMCYU@E&61)LqPgJuZ8XZTf_~OZ5zEo zXx_;+U3ZsC$@`FJX+PPOl!@FysE&-rI~h;4`-JJ$#UMQAT*h+xJxtQokBKIsMkTDAt;P3E&Lfz&}U*EId{MOqtENXW}yJ+Q=@U4Gcxy#~#fCsbDV zMI;dHHk3y6|s7Q_u>+R;cJ|jlHgtlcfA6zto56TAUcM{<^Vz$P~V1j{0WDY0qd9z-0*+N(0k~VXUEB30AU)mc?oN?xw>StZa zsvo@!=5HHsyo&+46{xoiZIO-olScQVjp#b^`_EjblL}k6`_;n(0>yUhZcHPjcNj)&{XwrTZ1#?!1Sh zqO8YUy8R8!w{`nu{D98_>t3B(u6SrE`_H zi`&cBc0<6A)Yl=xy0=xAjL`cmiX|Xz_qSn^PmU^>Jd%*q84P^ z0Vk70;G_KbJS6aBCBRCj5}O&0|DA1UCQ%4gg9I5W}M2 p2-GF~WCs8oKPV0W(Eo?Y5eJs*&XTWw)3;ywn;BUdR$X&_@L$;4fLj0n literal 0 HcmV?d00001 diff --git a/lecture_11/lecture_11.ipynb b/lecture_11/lecture_11.ipynb index c290a47..41f1870 100644 --- a/lecture_11/lecture_11.ipynb +++ b/lecture_11/lecture_11.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 18, + "execution_count": 1, "metadata": { "collapsed": true }, @@ -13,7 +13,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 2, "metadata": { "collapsed": true }, @@ -22,6 +22,51 @@ "setdefaults" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## My question from last class \n", + "\n", + "$A=\\left[ \\begin{array}{ccc}\n", + "10 & 2 & 1 \\\\\n", + "0 & 1 & 1 \\\\\n", + "0 & 0 & 10\\end{array} \\right]$\n", + "\n", + "![responses to determinant of A](det_A.png)\n", + "\n", + "## Your questions from last class\n", + "\n", + "1. Need more linear algebra review\n", + " \n", + " -We will keep doing Linear Algebra, try the practice problems in 'linear_algebra'\n", + "\n", + "2. How do I do HW3? \n", + " \n", + " -demo today\n", + "\n", + "3. For hw4 is the spring constant (K) suppose to be given? \n", + " \n", + " -yes, its 30 N/m\n", + " \n", + "4. Deapool or Joker?\n", + "\n", + "\n", + "## Midterm preference\n", + "\n", + "![responses to midterm date](midterm_date.png)\n", + "\n", + "### Midterm Questions\n", + "\n", + "1. Notes allowed\n", + " \n", + " -no\n", + "\n", + "2. Will there be a review/study sheet\n", + "\n", + " -yes" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -137,6 +182,35 @@ "y=L*d" ] }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans = 5.0000\n", + "ans = 1\n", + "ans = 5\n", + "ans = 5\n", + "ans = 5.0000\n" + ] + } + ], + "source": [ + "% what is the determinant of L, U and A?\n", + "\n", + "det(A)\n", + "det(L)\n", + "det(U)\n", + "det(L)*det(U)\n", + "det(L*U)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -250,7 +324,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 9, "metadata": { "collapsed": false }, @@ -297,68 +371,58 @@ "\n", "\n", "\t\n", - "\t\t\n", + "\t\t\n", "\t\n", "\n", "\n", "\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t0\n", "\t\n", "\n", "\n", - "\t\t\n", - "\t\t5e-05\n", + "\t\t\n", + "\t\t0.0005\n", "\t\n", "\n", "\n", - "\t\t\n", - "\t\t0.0001\n", + "\t\t\n", + "\t\t0.001\n", "\t\n", "\n", "\n", - "\t\t\n", - "\t\t0.00015\n", + "\t\t\n", + "\t\t0.0015\n", "\t\n", "\n", "\n", - "\t\t\n", - "\t\t0.0002\n", + "\t\t\n", + "\t\t0.002\n", "\t\n", "\n", "\n", - "\t\t\n", - "\t\t0.00025\n", - "\t\n", - "\n", - "\n", - "\t\t\n", - "\t\t0.0003\n", - "\t\n", - "\n", - "\n", - "\t\t\n", + "\t\t\n", "\t\t0\n", "\t\n", "\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t20\n", "\t\n", "\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t40\n", "\t\n", "\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t60\n", "\t\n", "\n", "\n", - "\t\t\n", + "\t\t\n", "\t\t80\n", "\t\n", "\n", @@ -370,7 +434,7 @@ "\n", "\n", "\n", - "\t\n", + "\t\n", "\n", "\n", "\n", @@ -386,7 +450,7 @@ "\t\n", "\n", "\n", - "\t\n", + "\t\n", "\t\n", "\tOctave \\\\\n", "\n", @@ -395,7 +459,7 @@ "\t\n", "\n", "\n", - "\t\n", + "\t\n", "\t\n", "\n", "\n", @@ -425,9 +489,9 @@ " y=rand(N,1);\n", " [L,U,P]=lu(A);\n", "\n", - " tic; d=L\\y; x=U\\d; t_lu(N)=toc;\n", + " tic; d=inv(L)*y; x=inv(U)*d; t_lu(N)=toc;\n", "\n", - " tic; x=A\\y; t_bs(N)=toc;\n", + " tic; x=inv(A)*y; t_bs(N)=toc;\n", "end\n", "plot([1:100],t_lu,[1:100],t_bs) \n", "legend('LU decomp','Octave \\\\')" @@ -474,7 +538,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 10, "metadata": { "collapsed": false }, @@ -538,7 +602,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 11, "metadata": { "collapsed": false }, @@ -563,7 +627,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 12, "metadata": { "collapsed": false }, @@ -608,7 +672,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 17, "metadata": { "collapsed": false }, @@ -619,21 +683,21 @@ "text": [ "ans =\n", "\n", - " 20.00000 -10.00000 0.00000 0.00000\n", - " -10.00000 20.00000 -10.00000 0.00000\n", - " 0.00000 -10.00000 20.00000 -10.00000\n", - " 0.00000 0.00000 -10.00000 10.00000\n", + " 1 1 1 1\n", + " 1 1 1 1\n", + " 1 1 1 1\n", + " 1 1 1 1\n", "\n" ] } ], "source": [ - "U'*U" + "(U'*U)'==U'*U" ] }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 18, "metadata": { "collapsed": false }, @@ -642,8 +706,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "average time spent for Cholesky factored solution = 1.623154e-05+/-1.166726e-05\n", - "average time spent for backslash solution = 1.675844e-05+/-1.187234e-05\n" + "average time spent for Cholesky factored solution = 1.465964e-05+/-9.806001e-06\n", + "average time spent for backslash solution = 1.555967e-05+/-1.048561e-05\n" ] } ], @@ -659,6 +723,15 @@ "\n", "fprintf('average time spent for backslash solution = %e+/-%e',mean(t_bs),std(t_bs))" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/lecture_11/midterm_date.png b/lecture_11/midterm_date.png new file mode 100644 index 0000000000000000000000000000000000000000..4dd066395aba013c45d83b088fc22f810120c608 GIT binary patch literal 26061 zcmeEtRa6{Zw=Dz`Ahjk>1tM;n3*IsMSIah~$mzO~NjQ1G=0s>J=Qd9{70!kDD0@4@u6Zp&@v*l6n zA803GDHT}o;SFmX3jU1iEcU}$+0NA2&A`zF!pzpr#)RI<$kD{a*2&z?`5dZ400QC* zgp}wv759u2px^fux2*k#qId*Sene9awRHId<|xzUoJ@g;v^K0ZUZ|U~EhhZkZs-Lz zk{0ZQHlC4|+J0rPPv@8_d@wDpA~s9;NAp+nw)&P68(FN(8niZew*8%Vbz2w8NZ-$(N@@K+@FjEhDJJFkcv&$3 z&u_MZJM4E;LxkX_Sf;`v8l@eVZg(m#<|_R%D+QV&;vzQ7k!Wp-U(S1a;jY|H4HqhO zRPJa4WK);rz^~?R4mU+^2ER=hGuPob2vFVPS((^TyOpB^sx0enJs(KO_-3TWH;F+O zq&nNY9Y7b!uq@TnhDhJ}zPlll* z3_!SEpQKu?w%X{gz9zg5OSFo#)8{)pDcsJm<3R~*hn$fVa@3p+3CL%2^;e_Y2D44x z*%yzAiHf==P!T;6-p@JJPl)*%5_962S~~i_R?K*xm)~#X0l1WuB+hok{yGvVX-~mD z1`9;^y;);p$0VY6xFE&2yLo#_?%z#RZuP?3%Dc0c@F_~2eNrRLJlWd0UnA`oU^&)K z5G?aku&~~*^GLC03z6`Fa2TK|R`OMi1A5z2B+Q-`VaBjv(`Hn;U}^o);h z|3sp}2hhn=qx_?X`?jb7<-Wie(2Ul2<<5Xe<8bx$VfI#ziG8=I)Rb(7Bvv($s?q(C z&PR(wP(z7**Tu;*Pa;}O)HuwB%>?O7yl`@Q{L|Lk?NlEF(c>sLYOKUE#>*K4CH!$Q zjW)*_N>pY$0j1^cZ)uiK7}lB9T;B(1|ge9JLUTfHLBKfjBTw^`Q)!hXrVx&mI> z30^VUR#jDzsUW$mF`;AYBQc$OxX($KD)_J)o33`?Ci?-=NDZ(9a| z^$|J>z99g^%j~wdwm(5*M2j0GY_$`Ec1*|hl0^(W2+cwY=bwo$`1_hQ3Gb&~4c^4$RVeuOD+sP+{&LOlQXR%c zd3htN^}Ev%ZC7~9%ZkEzB?HtMDAQm@{viIa^mI<3aO=j5QLm_++F^{R=3EmqQ`CZ! z7TA4-cciTK9<@G$wH0>|8x|(u3iN(t=xv$@ZFG%mh8gF~%DR?y}lWB;UO)nFDXv`@b${^~66y50^>-h}#Vl#p?iZd_pdhNWp`rRN-`6&zACi-4*(& zqJ_wQsL}x_92mSx#)csg^XrxN9;Z{O&wdi>R`Cvb*Y)DtqxA~$ug~@JdU1Z|_loiy zi#A5j+Ids%duhu$qQ>afJ%I;FQ%2e6)NO{^+2^Qq&YgQ5ceo~%v-m~wnJn@y46XzM zZO_0U`TnyS&%FJ|Mu+QpIiqLIB8NqR^{yqG)|x*eRdvc~qds$OsSb>lE5@9<+)hi4 zXZW1n3ykl!HD11&kAWMJcJx-KK1fkSZQ^EP7 z58zT$$^1==e}cjF@4epwm(!ftYOBjg<6(f z(?jzn{ypvjV>T<&O0p{`+3mzm&&!}f=MJ}&?YQto*ADFAmkNHN79a}`c3f>+e{B&1 ze!EsS9zd|oWVLnPqLt+h5ZNZ)X18lMQCRedc>BW{%$^lMS@&1>m&(i*Q|)7JqYTT)WUo`%7zh5LBErk3 zzHM`B?=h|!k2xGY$DStl39x%BZ*k1_&YqS__z9t|+o}7+g0w zRvTnOZT0jBn3?#~nRsFsAy=MswjFC?Zte6qb(i@4Y|P>mwtU35y$N8FT+$Yff3MpC z({bGlfi3ZKJ~LdL+1h9P)^vw0z$4~itmP)EA?l&AKKaeFo(RGm7>n)tvW3@dUH0}C zuUEI?sUJ(o;Ke9EM&(YKN9Q0(mw2yVK8eP2S6E{_!Dq`x8HtpVCC74fb2t~YuXW{> zxwDkaw_GmYBS8H0i?tsVzTa+g(^|FI)Uh9Ej_y~<*#?}y`f|$QYq`0EMEAs`?*VK< z*3(;Z0G4sALvVWOvf?S|=+2KjgWU~Zj|Tn_xi7ckN0ZhgGKA} z=_S#2eZTm2{dj4x-E$$cZ`%OZ+@g8wJZm<}YV^RW``0YCH3H5GJptBa6`-cto7E+< zl)%euqsw*kl+$1EoRvEbc?tS;C}*l8u8*bn%dM;CU903xfix9_oBG`Kc){xd9Hfy? z6?pr)R&02B>2@tDTg%1!>DPxY+p=JD_SR|?!TXdh4h<0u3ckalb8Ex~JGTn~h$k-B zX1+sPBNH>A3dK?+?W$i~M0Q^#zehv#^X^9$n+z@uthZNSMPNPr@k(ejC+iuDTTSzI zN!b$d8;1iw7So(xngPU})3Q#yap}IdrTjt_{zk2DFeN9${1fV#;Mlz&)Z)lyMf{># znZ{tR>j`Pp6NDi`_L&ij6n|+OObN51M-Al=E4Gq)t=*a6ost`il-FLucXhNk4i4^E z?{Z}{z8xi}<-T@I^+Hotze?=WD%X+nUY`e+WJbMh!?EyU5otuko$UqhLxr)H93xl?cDu(#WP3CDge*1!B>0n8( zs=Abv0m%b*YA1$>kMEzRM1s=NUbPej11ZFcVeLP!0?(Tu{+D>g!OA~>^M5}-3rqji zzI4%JOp2f&jODK-rNco7z5KoPT@%UiGPaa~R4$E)p@ZUHAh;~h<|(aiHlQFN?WiA%iX{Zaj$|gsO?cG$0jZO;kSaX z0UUe9SI1OiYJ-3fl@SWR;?;tC#DVw-?Q|O{|0InR1tewJKuE``U9)auV(h0E*?!`m z-CwaQ{&pAKnlO0PI@)0D3Ar1d-BX^Jks>rv$ec?=M_qY`%7c<^tKw?e97acnp#NNQ zNK#Zp`3kTMjRu-?c~5k>kdoFkg!nNXYsz|6tIs){>NWA z*%dVUx{JK*Y6&cJOwmgjDruqzI@**iXOE2*o;rYB~^*S?D8aJ#U{d!^c=jYIxA( zKg{SZAamvp!r1GaG)|$08Z(bzLM?GE%Pgx;|`mao_U zQBF^dmpOwXOeK;tzz6QC^BuWV>h^dOlPneWS?Szg80omK-^yE0jP^qJhO)3PY%UIA zJ$9#Zr~h8DnR{w_AgTj)uc50X`Nd2vJ}bzc0F&|0xzJ6H+MeWoH`I)6lOdoeAh4kO zX2nB^7Qxnf^8lxhm1&bLxl)ZkaPKl$#zk(KFg(9~33Ww^WtL!s7N+t57ms@+x#!eANMy%|-)E<5fe2TC+UgnE`Ciuc9 zmCzgQiWC&YeS_?A86rcSJ>lGqE*nTP!0~ock|d)jPx6o|A}cFCq~S}clmJ>UuEGX* zg^vC;n#D8~HU&>sqRK;CV-Y26JdFd7*f?w8Zm30C7 zykCEK0)w5#cew?#y8m1&MG*UZ2PJ+gjXeEpuiV)AtB^p@eVa$OYpjTEJGdq>?V7M? z0=j1Q8jfC8t&!(#m0zeH3=lRT_8(h{N7fe?8!E?W!)e>fB_z zpqGE85_J0PrzfbK8Z?`@zv|R9yQ8e3I@sICFz%YDtf4C@&o&y^k)0c+eI!4tn4&Cc zU`qU=WBd3Qocv7DGOwlu;ZhsA3;Y0ukM??zN~&=Rrtbc)0*srZ!bj3r3ni-aix+OU zn`fVuRdppzozc#?452Psz8aY4@-ROZsV*>O9hs+C}R3nfAwyBtSEt(84) z4t#Fe%}h<#^-*EV=sCqK{C=8jlN+;=JUNwMoNW02N0f7SH0Js7mdNm!mZl4|X z5HsZWtFo%=A?;QesU#Y+Osxm4oEDb)#f`?{MbFWtGbC%tOYK4X=-94eholTwEADFI zshb*%b-y&P+OFz|$nGX9yOr6_A#13G@qvAD_0ata*PR-aZ~{X16cugA4XJIpZzC9O z4i9otknM+GP~#5SRNL=f;yJ0*a{%QS-~?YDvgfU}uY+v&Yp!+Yd13Z_kJm;Um5ZNd zh@Mt8XkjA9dyVMP#z~f6y04t15PFyd*elv=+%_Zgf{uvuqZZ=2xkaxloiIf-6V)J>G z>fU5he)S!nUjzXKUtuAh4rdZ3{8XASt3T|hY`G>Id~mYf7+PUO zu^8Q}kk#e;$!(16irLZ@(+qzfsSTH3*dPqvts^@u46gOXR(m(7^+wHlZiMw(W^ex3 zr?)R&2SHAD<6eOwI@0=|P|E>c(OT^_wEAYBC#pD>l@eDjjC{{dH%ff)eklN8ajHnx ze7q{G_m~}F)}m~2-Ti)+)i@D6)T^c}b!JTLgWr$|ux_ZjC)Kr{O%NpYTL4EydPuw* ze?BT{4->++^0sE4&l&o%YWrQgzVn*4+JGk+#=X|PY5&U?GSOfIoPPT4qs^Dnb>w)5 zoXfQ8E2xtv>+Smd*;fGKdTI^(xfRc(xwaP3g**`n3pg@t@iG}tbZ=AdllXbD*N4G_ zG+JcvR-L2)D{*9yTh=qy+vo{N(!B1TtN<(hw_xN5=xfK0RKKg7Pr7`v6;EHkBh(GO zZ-0v(Uk5H&wB9W@?c^!*j_2_UJ3sB2Y|mPmMV11H`ijs|mxzeUQAr^jsRd6>h8Lt> z;9c)db-hjQUs>9{j##$ieP+vDQpU*C?=2lmoS&LpP7x~kTC&@m_Vo;xM}A=+9kvRD zy*YctA!0X>s{NF;9tcjkx}9v?X{Wp+a{u)>ek}W-;51>?0%-F-dZcXfJ!3L~N47CM z|7BKke#1QF7TL{S;c}~2aJl3&+R@empG-f$R&(!E3$$x7QF2@!87nOURrpi`WxbFu zgttxlsUEp}t}strdGETZ<7vm?mNPgeMl1771v_nrwG&IuLz6_K%cG6hACRlCEP00t zu6ixxE1N#vk7FX5DV;egHc5p@M})$jfZe=!^yMFNQM93(j7yjt%%*|)G&~A$yubg` zkbn~Q4@J4G^dHwOWZ+`|VJ-9N|Noc%zYG3b6l5(PL4Z?2!2y-NH>ARu+)Em-qC20{ zwINz;9rJYrZ|ij}t}j;W*o5yZeEVfRW9;qDcEXaQ`(sIDIg-LoY|RK0f>CJz3hENu z=KWUKaM2s1_nkTuez3yx<$@{Yw%$D{t>A0@vzcDj)6&fD?*~j!;-3N&)1Ke4PBC2( zk~}S#E!gy2lcB}o<&6lIrc8O8&fouP5*Z0ovbm*2gI%;ZV zRyJf{0;X0-4YFWvz`}w{GK;1`o9SK;BaQ4fsgl+=Dv2$(AM&5a%!7KXbKS?QEnWy z?BOyglGB89ti6SXM`+NTgV!=7BQn7@F{{(XpZ%PG5zlVBKewj);dVaADk=2A+{zt) zMkd)_GXW8Z9{T}mO99Q9qh1@6gO)9D_GWr-{ zmV{Aj9LlGSM`qAO$HzBcZ1;AkcIAsh_tsHh2XGlj%y=fF<7(4KXTRwcj@Xx_#q(FI zrsu%GVU|qrmaP5mot>SEc_E1`o0Vu@qr5npp3Y`tnoSXH#%YKL@lvky&|_} zh-53dB5Va^_B&E|tcZ_ZF6dCXf$&C(<88LpiApOhLiY9ekiGs0 zb#%JQDx1Bhi1f4=hK=P(N+VzI5fNwh$~sL`JM2En1Cj^3`IRCC*<@wPGf5*p$|%yv z-!rXI@?v?x8^KSY80U;h1=+mnB1OACVx50X3D;@-TzKf?<32QDat)T5Vox_CR+#pJ zf2{|+fykdX^u2G4TjWE$a0Cea-Q>I9OrofQ^AMSC_q7NTLapnN1ygq`{Q>7sk0gHK z#29^sqQc+2fddvq&@H7{BhOZ-#97sJCzx2WDNOqsN#%^6nYegF#2r2k!T6DaJX=Sx zRFq?@1_z;656n$-8lz$_At2AWPks>{rSJ2;pa#dNE3f0{{n`H9)6=7EK~FL35_m*; z{&h$_aB~|e+BqO^8%@1JJEw_S=xL@kKmmy;STDNVioe4wf= zNgiwl|H|^LYhnz=^}6B5q#wUyt2JuEPg0UQOdY1QZNg&kQb&sEhxA>o6HtWAf8PPj zsLc;@9&!>}TlvbOO?i&)m|pfgg5xPZ<$lxk^9uemkA#PWWmKQ^ePyj{^D}&|e)puD zD?MTPT*43fAIS4gt!$g^DGtuso6>f?^%Pii9$3b__E_+}n>$64gDXHRuH*LUeP*D!ObjrEG;)=iC;Vk2fe7R_98pku=>v_{m6ikxVj(qDG*-v7!KIGfz)Tw+RYSW03UI)z<#>uwbb%eeP29Kgs1_ zPC7Bvr3>!b@aBSo9{fYp8km)I z+_JMi10-e^9=UJzHcJQcC=*kbN9*Hz1)O|!N#!_CQYd5`@P#Mja5I`uP`!nz6!_Oy zqN537pHNAMK1q|Zj_Q-H)Q$H;jp*sJe4Lbs-&XaMotT=Q7cJ?F4ExeH7h>K~1R@(X z>~1B;LSOP?(f8%hHV(!$b-(_d$f>S!fzTz1FnYZ(fKQ4wu{`f9u*3wGmW`c&udvTW z+k~!BpKK~phd^n0;56{c13JgsTJgYl(@#dS$5^U(U3)EqY4&|vmQvg*U{uG6id!k4xJzkm@iGkxUs(%jo-(r-Ab(npcy#=dQ# z{Da8Qzk2~N*CV^G31OdyR*_wh0E4c(pgZMz7hrO>cgFg2{}G%j-J+a`5C2$z%)b7| z7o$H;`iRxIh9hVdKXR}qZup^*Q${&PWw$$Ge@}^d zw;pQYo<~_Yd51JTFxJAwbI0^%Fk<16^%8xa$BT?dECLr=4sk=$od=|wMDu{a(~TYy zQ0+2^!R7q<{1W&a*`h_57)p2D!S{CKqjNuf?rky_pdr`Ca1>#RTkbYJ%OAP0Z<2FO zJ${EgNX;)@!rh-@hENvWR~tmyQ`Z2>oeksP>p8xq^p2t+7GvI3v>eknU7g^k_hVMK zziFbgt(%+SU=nA-Fdm%|_IWSDLAK+wmO@D8#auA~9^0&h>l}Ph&G4}BJScibD)IxebSO_XWV~KWV#c|$} zrDue!p|LtI$SX)~c--d}gg3_g?(mGLsXebs+1poXF=Cr@3L-Gqu$>=NK4ZC#=@x#OCb$9o5?KMiM*Z?`HTwtgskX#u>+lTY5GEPkffo#pdR@ zG(CN&Z-%WDO*^gcU=Vn} zzpV%wf};@T)ln08zJL4Vdsg^ISn5PIz6 zI1tPF&c|E7gVDI=7QN2Qm5c4XOR=Y`1NY%i9jC#SivS)pRH+N>^D#Q_w;LjK1;NDX zps9RPf56Z$r`d0SqF;452e61U^OMr|gNUXOcNmu$r9okda0xN%2AdS=_WX`PQ7 zAa~E$Rbf+?mlzs4`03rH5s|$1PezT8F>L(uNyEb-e(rFi9ZhrZINO@~9km=(dTmI& z$>s^yG}{qHR5E(<5jI4lp~gDr1WJ+vaoslL5ni9Ot;&Drn;O_mRYJ8i@Zf>labW&{ zFJ}T@J_tO~9=u5~u{O<34a&#GLcR5T1kL%?{WAg|3V4LWlT5*IyNoZ69qk?n?LMZZ zc_<#nz}HGaaHkGP@&vs}Z#%5=^$1IX{OUkam^{ulvIXS@`t|01vnRJa+Vp9dI$)jH zf1qXK&AB_XDO=DN!gmBQ3C;aOs9fiSe5b;iCS7f}E=UaJ4((b9#u?wR`(y9#SlX#&hz{d-%m%5U&F@y(lCDDH1xygdi!ak8N z-nxAGe&(Ou*r3M(eYsvB(*YSPN?uj$GTGOTf~o`a$=@8k0-w6KsD{^0nivS}*NeHExSZ#YuSO=jH$_Ae}#;B;iju zhj%q>*3r%_2H|bZ^PLqRM0*|wU4ad>QoCtDUn>E9&G+TIDzeZ`tJ0j}Iyk!>l69Ua zzUn#1&_NLlkifIXshULf3%?6mS*M;t_X3*l>+V<3XD02BzhbropB9l76u$W)Y7^^l zOD8CPoY%g^jUSPW1Lx$s?1+ zRxz3wA!B5;v*0H|9`C{_I7Lh-o3D-eFSIHv6etN@bHX7l9X>+}srgl0pWGgq%%GG> z!@i+abU*jgat0YVQ|rmta)3*q6ikmig-FTQBY!H!ZiV0lhWkditW|8rY-A9yG+{*c z^*WV_FBTbhs3P^vl+*i(Zq>1?9HXe;8V0-*_uCgGH+i@IyuIS-L}ArRA#4Fs+3;XR zKyZ3f&4kbJj+_1SoFLrl5hDuH)=>Tv%HoV=thj@7G?9tk>Zb`e=l1V^v%EjHtHO#5 z=)0Etdu;|$KgUafP8~sv95{Z09#g3#UtqF^+W+HLN73&0n?ZkzQOC0c?ARJf0q zF2qG1C?^$~bk~()-tPT1Rq8*~qIaOZEPPq}BjoCL=>2TILF>gNFZo-3#roVA+WTe2 zx;bPj_Y1H>{Sc3~aJL(xCxCEPe0+w5tMvwK61VNjaW-?{Bvu_qzv>4>X`ty zOCUUbvZ(6+Zz$Ia?=y}Ke;})YK@uFSa|5fP-F9~($JbE^50zOgrsLDDqDb=|Fg4(z zA}06?@Y>FyAi1PV?bb6eu<;TzPxFL|klcxEsc-$kcLf;+iJZ~1g;*f68vwjW1YUq_ zLBaTR+z}=Mu07kT7qe#|&p(U`of1u#Q5b6uU73#5mHx!o!U}{tZe8ubp>sfH>%vE< z4j8@X4`*em2I2YjD{t(5fu@+%*)Jxa3xu83wP+Y_jV>c%kQ`IH-rWGNGYCGPz<-4j>KhDgKyx4a+* zJK(#PAqit8j)W6@GzGlbC>KwKeE}eI84W&(51wKUkqh4R(ql_`b`&#&W(=ojrM3}H zxOXKAnYSXG4}2qJ4Rv{W&SIQIRzcv=ooSk7C>VztDC?4&_typ+ z&d;|4P8;JphCa0hgF^-bpkCy+2f(J^Gh@{;bEYbJO&5#rOFB&=t5yWFvaD2Uz;vq; zQUfRJ4`4(OfuXT;n*UK^=EdZohq&3Pb3#RRJplx>VeQB~yh-xZp6oqAhACsAh<)YOOnfWDTw9pH%SSkH))QJE1Tz(GMLAv8x zm%0DJKjxw9=}q~SM`nwRVTq#7i{bmKLzcW7lwAXqhFI(3>NhKwIEw&UBF;pdq_9z@ z9t1n0nybBV>}(R8FlIr51aF|~bKeiTPZo`0eWqa5=c<_Ltasvm5* z=N+I}lH8QXAyW7ekPr)3O?XE{MJcAhSCTJD-o@y1t4@6II8ZyEvWJ=%g5uVm4$C&yW%v`$Sd6-sMXtUB^*=%dPr+8-&T3A_sudP9pS${8unP8@O8|70>wz8~T4gB2!Yru? z2sUisI_!Z#jq7O-SPz&$>sSj)HRr>H>%h)lzPq$Y84p}P4EbZWNo#U}&#ylblARrC zmyCFUuf7@NxnYm-x~HoIATQ>rkVSUPufi1A_?W@DYZ}5Ar87T z!Hg`%;&~hHdcY8p&nV1c422Beshe7wZZg8m)58Xfpn|jz2G}^^HRQ^L-GCGGu?+!% z&NeL5h9<9}K1`|ba$VA3!9T(1=TcKk%GGccQ%{t|^>l#c7^UnU-~3ACKQu-b`^2xf zr@TN(<05628QjWqyu9C5#Xq~q=%xF>`_3Z66m1ae1!jZ61g|;%nP`|)EQcnFM%A8%u+`ur z5HIV8QQ(lu$)9%fq$y7-Ibe^wkM1X)m@VtKpOMpf328==9{rt1`hC8iW07&PH5wSq z=kWi7^XO>g7}SPn2UwJs5AbjF?O(HOxGJu^LTXG9X0Pzur1HVki!rTD3l(t+ec31g zl%&Q|0KWEh!`w8(zy=CK2Ll`NZ1ou-{K+CI5N38%8>J9 za81T-{f}2!|3!%$Hj_y?R=VN_S9^E2hMtheLbN{ICm;-sUnL;^_0b{>8f>_77!m9! zIt36v?b6+~Jut+Wl-C{`_e!|Q&=L{}&eRI^vo4k%TUb=|cjL$vOl;d-Y?bIHt4eZvce!Jhxr=MPoK4w&I}48Z+a_Tj5#%#4bkeV=tx-;<~L zU%T7^K}1}ys)Yu7uKCf@0HlgYHY4^vSZCsaxhoD%Q1XUG z_}`icdz*PG#2)F$gIi7Td9AtxhB@V_cWbD&qY&WnRU6GMUHUoe{=3!&=Ky`^oG@i7 zFkrslg&}^jqf1SKwlvh3zR&+0YqNbeYPM?mJRtfas0%nT>d5G0 zeH*}JX^&kF{){X(DxrKx@`;v#d0MlTKj|gJvxMHp|1Q=fWaf;nx*AJ5`~JIw#mlXn z<2jp&ym3)8x+)7fZ#t44rp8uv8IbS#yyAkklH+2L(X3pP;n>Y;@qVvmg%!7s%|8!sSomWAbTn;}a`1ADlUzQA^EpzYR?mPQu0x$~(Jpw3|u} z{pR~T+_HgRY3+hRx-tw*ooGCLLIrP~C~Ey~mEUU-UsmE6W3m8XFDkLrSU!p0IKgJHz0 zkF;VujjE!eM0io)M`Fa{Uzjo4felVK<3Lz=h4V%QzB47{QSWmCcP46Z@p~LEPGX(P z7j#Md{$iwY;_tRV`#r|FCdA)d>S8~i#B8_Fgo7y(7BGRalKJMvv;>$_4CT`naY1?2 zc)laydUN{N_c+lkO0U6<{9XR6m#gO5huQO?0>)RZz1R{fcv(jK0?y*`K|+P zy--(_BXAu2NZUx>i&*T}Ydaeka?+K7-0UN7QYqwY(B^<2EFf5oF&<3K2|zs^6RD|? z#=Mu1CEK%CdhMry_tkoL)wBQZ&U17@?T7K@A(Y-2eH_<*iC866{JeX2_5v|1IxKiB zt&ihLkp9)XyR8KEn41Kl5F}u9sIs`VfRQ*q&4MDkX^Pq^SAd~f$9!bhWt-Zv|4uh3 zmoO0F{F_*4GtT>;h=unFuw_$~H!et(a^H{HBE|{j3pee#=vi+8T<-;EUTjYC1PR~p zlv-Q}i5=r>H#`4AQYUJ!AX5Q=BuB#xe|-}-qvHyfb5AEA;3m!~enn)^@eKH+^}B+s zz7CXRrYIv8oNj+>tbATEpu5xSv-tr#$-C{_ij&4~lf2H1$GkI@Tw559qU3rl8+yv{ zW8kdW{e~r;IQP`vWT18IX?G)3ZpY8;toL|nC<4n83#BAQ-;cv~rmkmdBdmhX`hKHZ z+Eu)I+W)pCUR(jP@owQtI#ef?De_h#dBU<`gY!{Du((7DLvgVmGre zR2(=yAr`g)X@#a;JXRefb6ID~c1A8w>;_l?ul+evQR3 zAx@rV;(vqtH~Mz?(;oSkJYlYIG`FY48TP@?j z7sFCA)Fm!(^k3hfzdfoTpGWtF2Ks}VV`lhZUDfH69u`Oi_>91>N|$0-ou7xd?7V=$ zPK&^?a@)EJ{K-ckk00r_C8b@2ft%}v5uSm$6T~;$;hFWbJW&R!2LV|-X9;WLxs<_E zc{pr7qD$809uo=t>wyX86a4%xydJOCG_rlD#WY4Rtxv6AcZ)I}_)(Se%jD8{Xj>G# z`f@Q7)Q+N}R%aOiCY$9CVo}TzSb8v*RNfU;x*eCQdKU0LEY%_m8|)9|-v}|FDd$C; z($NvV=ISK+s>$a(%TP#B&5SHiR;MACVo0%bNx8jELY>8kPIdtQ!IX5Urr=+C@QG_& z%uDY@gNuD$PS$w+-tb45!y6GrE%}*63*3#VY-=hy{}&tIk8; zbR>nJDLs)*TTBJG5(jtC_RU)sdjG)KQ%sLuVcQSJVAH={uHLk_-sy&0iloGk!)V*S z;K(j5rO5p@81B!=jH21eeHm*i37xx4p{qZ2c9(E(>KXgtLOb8IY$jJ<$4;Of$CdVv z2F!vMsc1S^*AxYA1&lr2czal9;~|gxyTtT-kZl9b-n@~i;SDm{?s)-)$#m}NgtN^9 zd*c3v(0qBLKmO8;e;O@lJi(0wu+1DsphSq_9NYZqLMJZJu;E#af=wyk+o_ZY_VBU) zq}65=HANEoQ39?8MoUpx&9LUXr5v3J=?aEn{+N_l389uEs+gEb-TKd^2W$G4$R13M z)q}Ill~e|Qzz9r%OF~*#!hVkP1OorKW^{`eE)hIxPh|aKICp_ISrCpI-%4kgRcD@k(K(GL^ z)0Ike@q4c9IUzi?ye}bv+rGhd#%ndQqb;=yMJP0O%HlJ@b*4RQG!mx^7Grrxc(rCk z$r-eIE#jcA2{eVcHJ0qsP;J=1fFYO6!jdKfmH}9^EiAZAsbN7I2AMmyO1JnSk2lEk zkJYHxv9Wh!zOcl9S=+MHwhzHAi?nElzZm+}?~JwaRM$2NB`-ge`>IJ&0zVS^NX zUkK(gq?zf^Qw@S~*Z7QeYCd{g#wvahW+I7|UW>jAj_D(EPyeJLuDmDOFm0sJsmJ!u z%*|xCA-wHi@nya15qv2{))%`z_Z`vH9hSEX!UCVfMSgrmGL$+n+FvR&-sr&&-_*yL zh~i(AK^JEjHDUAWw}AZ!7b};=oi3zBb5fG?#bVs3JE2J8Q8-%(A^4iJg<_Po; zOv&F@G=*(wML+boua>iM&KiFG;YS5fG5YbJ>agd?)uUX>^*nxBI5J79Y#IY#icOfj zM)k}WQt)XTWBfNtY`$sF##@#+xPVl3oV`{&@xpAu&3!fOvc)?(wjk2xnfQ7@Y=p(C zRvQ*tnJkn{jUWk%;elp&GDjc;h=eDB+t6>h0^vkN&`_yu3MeR3Ez=|6y1 zoZUj^{|>Hh|F6JR^d}Ro;bI$`KM5AkLvB$&?qo~)A!?o6n0FHm41)1z_6kB~)8tY{ zJ<3=b8-DniN1}L5Z#@@=$bplwn#V~PXv-e8$xo0U-i^&iln8R24~v+hS>4a?6wyQW z|D*^bVJ#dEfO1-b9+y2=p#=K9p&E7SoyDXrDgcyvWX8jJvuRzUjoFwo+N8ux0=4~* ze?&cyEF<(=3x3Jl{S@kyu~TLxld)9|4?;e0K}LZMf<KhA+WA>)KTqo$vF(5xX-UwlUOx8Q+(*feSG z*Da!cE$uplNK}N6aPBSKXViJ4OLF#^Uct}XqsBjIblk|L&Jy2O>3cQWk5O91l@wKD z$B(wtsI+M`DH<94W%l&N$n9uBXQnUV-@O0{F5NS`#~AMlvFJzyIq{p0d9iK$QJ}iukbg?aA z-k z_%CP(O=iMzQl_SFuwRnx$40%|<2?k%FEi3)_nyM{XD|Dnu6_I{e2z`!PM*e8l_VIa zmqYqX?n+kJEpE)Chyw`a%YI?6V6y;S$q1Ta)5!6)H_UA z9RI21&tM;p=Bu>GJBue;@?7q*Fp`-WK(?68m&3bXeK@!4?lTgG7S*Z}do-spfrZ8P zb2)x1NW>^^VD%VVs0**n!eDJnz_@cM39PmV!@R3mvASjxO@n$#&RLuNIj9_CnJ#Vp?9;ZNOx0zW#Dv^s|i`;fZ z{YLWP56vXCPebl47xd4IBf;8Rg*ixwMpz8eFU#|{rl}uLXk^16Ah5%{LVudWu}MGa z{y~6@y?Hz5$b^7EF`^a~s^dZ{0Pg$hLjQDq9GOv)2{^=n_=zJ7elW=*9igubPhFog zTF&;$lNJpITjmD{6f*ElY>S!GdcHW?obfgI0DQ+&5Pgu-clp~94uX- zBJ>_}{tO`$nS%lui-jP~5i)!KX-4WN=<;&A5FG--5IP7pl&wYQwFb}P#52fOn>I?* z=O}&vGH|_pT?$b`wg>{E7veK2%C}shh@KZ`DIwiK26T3v>90KBGmaQVMkaK7Yed%R#;mc`qwf3g@L9RjTD zE9C?@xWt*NrOHD>RB^qJ(G{HcXlOmI(Q!UboL`4;o4ntmE(0gObaXFs4y5vFAPJ}W zg>*8!pD(bG{(ch^_$HEE(+=;-wwxLM zxj5Uv5;|~+PGAoL!c2nX18IK2v(;(GV4rHZF}F4o0R%g43#?_Q&egaZ!@Q_&$iRshrem<1kHrn7+?qLcf3=ucSl zbB8AQt~T*bvBphCCCy*|Sh6)pfMS{}lmi^tWe`;!Vo0QK7I~^5D!%G_qw`Z0!fVmZ zC0>xuQCBj6Tn9%~e1qpxI(eF34UD@wkmspZnw&wKc`DM)^A6J;H zu5P7GTy`#$lCtKD?D}$PRBnf4o2cUnW5T%OW^LE$jY`E{Gn`(ecEva>IZy2Tg`{Dq6`AgAHpbV83 zspI>wcI7ksjz-N73bt)->V+>@a!g-ID`;&r&f(=8JkMz`eML)^tbO@wmNxf)E|Yv; zo)F{xPRFeaZ0Gi~bTnVD4FEhS)b$ZHWuBsYg?>l$vqIaD^E=Er9bH#Bv=8G?^q)gZ z@?dK`!UIcpJ=ia*Kj+&oTN>!kc>o};7Z|bCv|T~0==JDgx`$IySsKLwC(0w+0dE@I zl4DDarey?oe^-x)$B_Y8fz5u>o-6qqpHXP2#CT;^8N;KTd!njG;E!$e$rKHXw$|ScV3WNRn6UiV=#vl<&7G4QfcCN}C>ZE~{o5bVk zfbP%zde&j-SCvEkB>>+@lr|E$zR2rhx;JOuzte%BN}@NPj=DW9#>&0`tY);gt-eim z0(*IO()-d{QM7KJ2UW!$^qeg+aI_)H6ISJQMLyi)i+hwc0*yzjNcm&jqxwt6 z?O`NP8!6ZZ_Q5dIsrKPdsXmER+$>rJgeqw&x_%uQ1do@9L_6={@QJeqDUj6~8g@Bj z>0HmeV%5H=m~*7D>XV) z#1C%$B8=g=b|(Z~`XZ|&e|x-{r3r^j)uchfdoDy>O~@_tCj8}PL>KaY z(hZELywb@JI#F!TMw<<5v{k`PAE>aC2A$R0n-iY<+aO^Nr@`vea;ZCWfn$N%E#HQ* z{xCBAV2$m3{4P3Jq^rv#E&3mX^y>&1N3a$> z@qCxK(>t?!65s-44A()j1B?0fe3Z`GZ;7#zufEObb(4nV`H5g#JG=|ze~n3I3n#`*HkXSyjI+1=A;Hf?6Gu7WB|8Y_u z8RyC4SsARp>lv!EGKCxM2b zd#9|ORM@G(RtvTE>fhr+UL2rK105-rNR=6N#~KKtB|1GAEJIqx)&E@rtr~65tS${o zzmk{`ZBJX#t4@oN1B$pq7bK$23`gTAMe;#pl?bf0^45BE-dlj@tGXmB35XrQd9}=% zS*I~qKUl5Zs88x$vxiaj<{@-}sb;PaT^pn%^v1aO#Xcg4d}sLph}xN*BR6ks4p2b5 zr?aT!FO9LBfg_g1u%h?PhFzHW=XRWMD=pxvEMYV==m$`c3&>C+Zum7980opQAoTuy z61%^6qbBS}dv%k@$5W91OAwIgA{q6Xd@>HR5V`X;ekswxl8=g-5;GUXSx@~(P9O;r zzkHk#;rHam^NF&b@3VthGUdpiTZ}-B9N;BKs}8H<1vc@W?`z<6@lf)s!Ck71cs;-KmFbVu@CQ<0+BmvXgL9QXP7DIt4@wSGl>fNw)5`WLiHW|7 z{zte!Ag!-8PL{%h5*jRTsyx=V29+d z5Mwy!Bah^?XYRMu=i^)7cFvBZcgbq0zOtBl6n+}7BT7`wU2xzxpqe#~c3x($r-oL4 zeYM%rJ_eI3emS@Hl<2CtPjmDlP7TYyV+}ZvNbGGL0CGi4#ur)(ua5KzpK5$IKE-1r zd$*%#&Ivd6DA9SWfbGLixmm`F%**@9Y1I7L=5qCf;f z%C6R@T;=FjrmSyHd!cp5=2qk@-VMI|0E-<50zV$MhpCv7#ZP>AB#U-MNg9XXOl2dL z>$gUBS~>zOp`e?b@2Ei}>f-p45)DP3mLi3csx%sF-G%kLATTn@ZL~V>qnCZa93K(TQ!P zgsyS9J)(|yo1jmxr5g0vsNB3vex6P+eSqI_^c(YcMO(*~!P-!Yt-v%?WwGl+8b%YA zp=Y}O<;PPNDDNrh>>q*6y4_Pw&Ij5Shu@n=i*|Gg%aw|=6hH9WH8!{-rmlFbxldi9 zZ>xfVVzYI*tAqcs3*nrQlTzkmPL_d}7Jc`y?T>*d8XkY$D4-`-vS{VWLQ;=3Sb!H_ zs?6T7Q^s_8IDJo?%!N0<-qF~4i4ew4<=Ok(RjB5o*6D9Kt{5c5Bb;?ZC089_wy+_| za4PP_C!cvq^-&x?Kfg3S zgWAxhU9}(@Vt;4jM6SDATd&(k=1DJsV0W!UA}Z0`Q;$|DAgvhTYZXY%*$gORTs$(zVO% zoQ&m4zHv-p^Mnv-?0bB_d1|~-ck{SZ{W3?j@jH)9DK(AZvX5uJED=kC; z-Qp%HLQ*yO!z?O!GX61)N&vYe70LKd;!ttly>hsr{@ojMq`Yq1rP@ z;bEFnqqDr7?sZd7G3u&+qshz1G(%a0;z+{A%AMv(In$a8n0ps_J=V)e>j>$sIo87K zv8Ru;bKA{nn!Bj2%*Rq@;ZTr!E@)d8F85SPr}Ki|V>q6sw6d-Av`*{`DtkOkudYfh2d%8Fv-s-OTmCK~gyQpL z0ZVV?A2HG7(99!X%k~Qt)QLCwM*(h)#$VQ#YA)temj8Uu+gzjyQUc?)u0i7sT^)_( z>5D8j&--%)g#*hKC*5luRl=zJik|FxAN(G*&4AV7`(JhGqSm*uHD}=xf987JyM!2T zXfjfy^`X0ZJs-v@^ne5rckEiXjVVH~ZqC6_F^aG{&McU5gxE^DnH_+bD%xWUb5RiYd}<1k;~E<& zl%6ceKvfk;5m70xoU*OGp9JCzkG)C7f0dS4_NPa9I}I;)N>a!*(ElE!Kcm)Xv}A0k z-5I1Tk$hEeK9!SMmgn;>^IG)%!H9DhT4*Nt?<*3eGu@1?LK0U@_=bk^3u+Ehqc3ba zx5AbWg-M~AO91hluTF*YIeeWjv~9~J7Mq8TFF2$X?jxhHq5)NQ{b#>)Bl=!xZx_jnQrCI)s>E}QwXmmud`FLSkiL2K;+Oye8x z%KGq3;8kK7AQ}ev9YYahZ~de_j9j1$ltjafsL`z|8KbR-+AT7QFQ7<666j($SQbAi zw7$EXa^Yus$%sIb;0!28$qVy7y$Mc#6tI5VYR>h~1UuCB8FXa>UMqLY+s4I#67V&| z8ufxxgRtH}l(bej1SNxycqpY!R`g;Q#W>rgPfG21I@v&O!`w~jz;#+I*rWi|xTnW1 zq%W*-!p|q{OqnJe6j9*=niK+Td{oWdxp{sj+*K-!vv)D-pthh>-S6KF#1e2!ODs0}{KKZAyNZrj4XA($%3>?aH`I{U)B!8e6 z0d+LWHhljUYUMoMH1{=NmCBQqQ$l95HkGq0@%fi#**FG)^4JM9JYyD}d}g#lZ&64X zx$>$$nla1W>Uj59&G^?u`23W#4dZPm;hz_AyO`u@4vR<|ns483vVIo(&_zAzsi;eI z7go@oh1U|pLHX+NO0m;6Q_x89O)BUGclSlI!-XrH;|TYus7 zoCdr*@V(sIb$Fhb{bH%xK(phYjJ?(S$|(xCmvgRl*3&6M;IB zmtp9wB**v3ymNlKp6eQG{F^^yS}vl9O)p1J@k!JB8A)#FL&*4^# zSL3q8UA#pkhj)fhsK(Vn?H-HBVgJF6;3U~5h9NyPc5=g5QXS~<;bR(OudY}{3CH5H zME7l-;@pO)0t#m|S4?6@2C_of2)WEV&9B!dXgF_k$IQn0(BOsC;&Q3fB3rkZx%o1D zuIWH@?3h@jUO^5yBWtdfV;{A@WCIeM}t`d~)sPoImkvfD5fSJy~9z@%)<74aGE72M-<;vAJP(D`cI zJ>pr!P;8>@cu!n~!kNWu&?e9GNe4->LrqJjs8+#eo6PN-&jbwqjPlK4WJKwzeI}@e zheM9p6yEUr{qaIio^eBm-M&3p{sZ+hMGFf01BxQ1hq_uo4s?HJr%|1hzPj8r@{Ln# z=_eA7L>arfY683INAKj{PYP~uVtiIRmfru8TJliNu{_0v#0n!&I+=1M4|~?==~)&N zqL%jN4A52v$ZDk?3LSz|eX8aaPDFX?PBL=7*4FDieI&zc-KTkHSA~;oIObX3^7(}E zd77oBS_?~e%WD2DMQ;U_NL36Dcl>fW?>#WYg3e&cC4)jPhEi6>#YgultGsetcrzN? zqpgv0a6Dv-Ur&_qL*BFgph&SUbjRyhH^tvuSARH@#nbw*1a5*dNnIpQ?0F|-GyiwT zt$V~Nd*allFu~?}#i4B^!veBmBOi6}+H)>eDq*)Gx z|MH)i;@1_y=dj~nDg!!Hq$X5>od7XazPsO{zuNjZJNQoYo1AAE&J9*Lceau8n3Z9Q ztdW#xdi`;n^E0#EQ4RQ}{d1t@SuA;Fwi;W8;!5dMr2!$pug>2~7^{DMZQ%Ak=CeMa zbV5MbK$&~A?sw24UMH#NQwTmqXC*DT91tkm; z@Jt?CtE2z00ZK{_5GW8u3eS;1*Iz4;nZ4`DKz_?YMgQh={`4MnRq$K%wH{t_Sp9ZP z+DdQbQ3kz~?lGcQZJ^HSpRlrvUeNd2x(H6ah# zdco?@oE5s}yE{bkFrsJPWJgu1`Vq;q690{hfGJ76i4Mo{Tm+?gzpeXz7jEVq3v{g! zunXs^q*>te+lDdRlKQV*!~QQZ2Olu$TSsk)7qI}IO+En-W@ffEUBgXsX^Z`ZB@&T# zPJjQQPlU#DEqqILO>)O_AV}ne0@;Yx8lVko;?{1q{$8G8 zbK2uab@Lba$;!_ml)r;Mm}=V{u-vEs!xd~J^LF!=xp31w$+>)lj}PfdUM09{5(`C&ZQ(zVW;Ve@tc3-iFlN;k|~aL zyKe?M9Da_T%fk{Ak`1VL)FGjI+WQwheo~*U$H|J%XJ-$43l@@zk9AkM_qcy z)ilXewG0SiApm0Pv2-D6m_3i*{NoXLXVt>ssgkJ%4O1G;$gj+6?F8#`bZM*a<3{C+ zq|hg-BtFOuFy0!*GF~X$C6O7>CB(sTh00kWs{uvPtA##>zG16J5EQ`#?#QCiL}0Q* z?aJ;je$D}v0AmbOF+vAEHsUJWSRiFb3DMR7ow@N1t(bxtM)-PaVPTwA;p{aGe58c~ zp&}fWQhyLPod@KObnY^=u2)(k${+xCPOp}>g6G@w`PqpQ_ueS*?wWP8*C|elt)pJ?tZ>r zYCI=P8&_;B$FB#^eJMr;{ni7*-ZB))PTD{jZ*Pt}j#c$|Fe|+U^j>=1I#PU0J$_xz z{bM_5zH9G0Ry5{w>4kvG?gIUF$iDh^!rPSc6-HrE!KIo1BKqe)jn-f%@7*cN0)%jB zMMgSs3Hfk<<~B6>ODdzp(qFGAj7>jGfs@o?5-k@D7g~;1?jG7071dLP-UwOibYj{Wn#9gG0EmA47Xdpp#0B+NQwu&^g~GJ|J4g^~mUhNP7Q6KDkj*KnCt&eHi(9u+3H z!zbzXD|K<$E+tARC>}@@Vk46Mb{e&0kI)ts`wQRbiKMjp(;}QVpWBRH5+?+?UIj5$pB~9$xVoN63^t&j7GW(?bbCC{ z=ZSf?VeON_f=el!1)g^kOrUa?$A*xEa#Q2uqU151QEK9_QzgKrcy!ADDf6eQTM#6~ z6iOMSpY!GP-g{@0BQ`|QK5^`+qos!ab)a$CuUsatB2G}W%Yy~X;+etHf}vJ?3G?v> zWxNaFg{@~NOBR{W7b{f03r!Ij2}G*`#7lBN{GE(Iyozo)P-UIGR~DAxk`m2m45lm^ zjZZ^l5XXw>R?ie1INZaGxZGm|AeKj-%p-0Lv z+jhr-1Pb~JTIdK~Fi?LA`Z?Y)JyfCY9lhD!XO3fklTtOjIzQcvi4(d~98$&t44vrz znGAjQbY0*}QZh(>2q5g!hj`7n8+)z0k)+1+juYei6M12*E`Y)^HtecE+QAoT;wIzw zwf|lgwLUZHhZ#US4T(We&?cDD|E>&HUAA*?(lu9ReTqyzuF(Zk8ud7ED6hwNqv8ju zKX&-hn-rKe?c1}<72u}7GdcX=uhV4@LjFpDpA(4%gD%<~;vSl6Z+qrjvPZ*71r4&5 zB~2fO#Dklufiu9e2#bm4v*3Bn8Hfx1J_&-^3J{?|nVl3oY3qr@NeKD{j0PU^6QJe< oPa-Qx{I^@A0vUMxe|a;$^{>6)KwCq=HR9#em35RV6z&KA52uY_4gdfE literal 0 HcmV?d00001 diff --git a/lecture_11/octave-workspace b/lecture_11/octave-workspace index 2e1bdfa519a4a95dfba5dc55851ecd65f7eb66fd..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 100644 GIT binary patch literal 0 HcmV?d00001 literal 178581 zcmWigX*iT`8^$YHQbe?o6j54eQz1^t79mRtDSL}3DTyQ^OQ9%{O7`$a*6e%secz24 zGs6rsZIV>p=l!7L@P+X__kCU0`8&@m1KZoyZua{Q>^r?|`LbopP7q(qmMw7+|2SFS zzIE08-_p{O9r4}&zqnIZv2jZ3M{UHw1h_JfSFgIA z06|<2N{|?V%Yl|VHgB#Wz~AH%`GKqs92C zcrmWUKW#9-+zgchaWl^?GZ0D`y(RN|92IYi?N_;V<7Q%bjLZTBk=2sgRN*A}*8UKX zl&*(owUTi~;Sh3)^B&kX*I@X{n5e+A9GtI--1Q@m3Qvoh`oV3bh`4VqBwsv=wU36w z1T}}jYq`6H^>!BUK9z7Iei)9?#h=HFa^dnq-NRRqhN~|Beanj;g1~9tkCi+mTI(;=ZIi=6zwquv_Evr9WfvFLiYiC?Ci0sh!6y{xP8QyRrB`X&R*VKe5{IrW41j zlWu17&tiDlw8?IZ2^_LE=C`NZg45KMT~ofr0{+Qj@XE#CJ!d!qT3F4I<*0L3Tg)bOet{Mdu_9Y;0!dM zm@(tEoAI-#c0lRFG-}e*%yzyTN9I_^p!}R7kEy#(R>U?|27ZZ{Cz=Gc}1< z15?6=>|O|OE_OLco`F4ky}z>WG#t2din^~&;g(U5G0hH`c1=hY+( z?HOl8d~HO^TD7vhE0Tj`U)&CCiUU+%@Hi=SVaf9L}>iu2CtPeTZ}RJh`mGZT{y2ZL%h z%tF`y{+>kTY?%BpaVsRAUoP*v&qDv*L6Cpi@ATz8$W7D`9M@rCac@~iK*Kn!8~0r= z&Y&Y9sA}&=^-(C*wH(cHE5@?M<@b|Dn20a<$j0bre0!)y5@{WB;_Ba;Lri~^ap(6Q$`T$*=3Emu|_ZdW;c=c2K+Tx@5q&zw>%?_E9(95v#g(5!l!Zu+mwkP!r(k>K z#$TojDt5ko`$RxJ$G;y8=me>RJ$wr zcpJxfB70y0u%9yjmPo}VwPmXW50D^{emJ2sViG~-*>~K(^yAXcYb1}A6ezgrM_u=s z!2YAnd#+|MVcHwuQztrw0jVUm(_T90W%tFVS5RSc{ZQyR=_$PH=l$?NhJt&RoBke? zAB9oh>Z~1;6s%k5yZ!4+71*86*X)>_!s$P4+IwG5;>5-Drb^lrIM>~~_RD-6mT%v@ z5De_ZY=GLeO)E#xv-YRi%g#wiQs3>N&&*;X(&e6E+$>t(wnf!lBSAGuJl^^xQSX9% z18lr{@g)5FhLaq_uqj^gvg|(b^EdLY#B(ZQ#7&jH+jZglb-jyHTSpM4KRHUaVdM3J zqNt7kBg|Hgm`#jygX7X|hx{``(2Q!UIzwYY-kR%Yut-0oYWMbR-a3xUUH$tu&CbHX zLNeNG^L4oDhz&o9XTl-kXtqHgXk@0yIN+xvs2WQTC6b8l0X zLI*6BcNu3BbHms9sK{b98bCtiW)`n`QD$qm*~i4{dcxszyt8VDg_)Y)`jU04rvcTfCEK9vK5BH1UaJtndC{6OQnwjP88 z$`1SRF>yrZ-=y%?&+wNxr?*Ukj1$iC7CzyFNIqp{3R$awxaZ988C8bi-cTydYk_mH%&T!kc} z($=V4vK_+N5?`x!i5c|0IzVYX^Z_2d{PjchD(uRizIkuUBvL=slEU(sFg{!9^&x=h zcP^>ST;g+Xe0J#Bj)PrLepAq*szXKKy4`LETxYQDki!Z=?OBu`6=;k}%U;!1<4zx$}jDSABn&x8)Kysh!;u8e>`c)9T9 z6_qeCTQL#xo{b|yS8wc6Xu`*5kjka8Aziazb(VO(zK70Q?e?yPtx8R%VMQTkRVwbc zuVTV;XuNAAEWgWenH#BBp6LF_^gbyR&@vZqNFR&ns>R963pb?TdzT+dpjd zFBaMuHFV)rHvg(0yGL=Bbgs~9U9*xzk!1LS7kWo4W^;(DU_@hIz!w$!;PPL zSs2SQyK=2`1_rs0Dml!C&~D(sO)(mVQlZn%@Ao@U(RIddv-%V~6&_u7B(dPzc-M8} z0|TB#M$SjGspv~c-eC535+)hBp^C8-tUj!!b>`|2L{xvYI?@=pFZgBqc0&^WQ6E+h z%+w*jSln-XBMrG;tMx>x^DsByEhP1E6p`9dEd}N&2nsl&yKcS@UF*2Sl^;(+e#$Sf zhN$nE*Hw3}yHA0?++)ve24tA;P12ZH--@{trMWMkjiXApQ`ba)1P-N=psY!Q#EPp~ z|M^y;i2H#^==N^#$^AA@`4)j?tLE2r%+gTwL?BsQp%b3b;SO_yQ*e4L(dNR{g+@)j z^8Lv&fSfj+}Z!!ei^I^?UXtLUQfJ4bS%GLO)gLP1-T3&uYp#=_xkG}9T>#_2&{vcUz5;mW*w&a-C;*?@ee(F&&9IgIqQs2Y| z+10--<9!qOlz*uPEXLsCt=0m%G7BB9;c`j8==l6I{J*~vJ(wN3R9Tt&3S+!~%i?pY zk-WYs=9q5{^b?$n=QdQq?8o?3zj-QpPydpL+1G{5+=cU6!d>`OIBz0o-vRUbft7xZPQ+NKK2B%Tr@h^)#;F}eFL*jgarLVVqWv+~3&YkOgNmdU;?+SUA z8fL>^D)Uv8VK>B$t=x_~cEdD|Wq3+%7PIxKA$&)sFqBrAbKZ6u$$v{1j@@7&M1HGx z6Gs#d*tpSh)h0pNm0-8P(T`#8!Rq>rohZ6=;*%E9hn|>!IkfHSAY9*F&;}T1*#eCAFbL+8wIKB|7x>_;}_Lsm{!$JKh zxmLG)Zmf+I8#=Au3y-~zpW1g# zL3&S==MA$a91$F#okkk657)R`mJDENmxRb#AEIvsAFU1LX@ySuNiChLOtkZ_-@f5} z7aX_cx06qFq0M7Qo(3&y+M1^JS!K`lt(`bDg}@uh%w`(3cr+X)fGAaEkhC9IR=)Ig!bHS;~OsV|kAw ze=@<_t5G;+T7!x@vV&p}14TyF!>#H>x2@UVz{i~pmTZLf_!twn&eV%cInfZwnl8BS zHiM_)DH7@=8p>1R{RdR)v8ct0-C0tC8{BOtp6+5IeSfhDzsoqH8Ta1UEh1c%qa;?9qVvhe%%78V+#YsXDy^7+s{EvGQw1^4i)?#; zWR``pm%U{U!jl*+GS!H>F#(}F=O4cFAz{Vq{fSr7KVyY^in>^L3y!|G(=Rva$AZ91 z{~tzOSmUUgYf8+mS!=k$Wp53jnfqV-izq6LX`6e39A@$Cn?ThhQO{U0ob8WWYw%i5 zfgE%)5OTO|$Vtp6Wt5}M3hZ$>ZdpNGp*-M@OX%quT-)(T+4M7U-@Qpgv>(3s z8nxWbnnvhc+rmKXB;NVTU6Zk5Zo^-Ai01-K~lczNQERF@}JCuD2IA6UE5mo zVQv7CXI6(v7gb?lK(irHW*XKR{H}dMeYo14Eb)w(D_w*dWDJ&@|{3c)R^A#INA%@9KAofi{8PODsvvR-_il2x-TFZRhsNI8ZSyR&c0cfN@Ml9PTdDTTk7683 z-^Axa{)l52u7^d-kzsJk(ex*C4CD6k6bO?^+}6KA2K zL^R_se?OL1&+H+SCtxY;tUpflcaNGSX|Hvyxc4m}MC@J{zFyIqu|G`+ z*m!-%8ls=SR~IBHCJ|h7jrMWZ-Lv?5>xudr2|^c^4Dc#_9LEFo^ASHDRzp0@{P_6P z5X2fz4~bgN;HY9*Nc5qx#qNXMG(_8U={4;dLdkf3zm{(iA{H|0x6sP5Mf8zM?ji$fbr@LC?DMdi8hSOuH5(qPFZtJ5*JHlG>!I5F5ilpcCmM;mkYRgMZQDC4oO{Lg z$~R2Ie?WD!(M3XU3Tv#)s~UmruG?I`%#Roz$ou`0I*B63Jv?>lJqW0@`53=r02?MY zWUmlv!QX$Y<&rT5(y5s{**}Q6ORjv`*HvVgP|9?9?5NNe=2xf}q@rZ<`Eg5af^Wuo zEu{1mAl$@q+G4y0sUwugTw5lbM#XM!k7i>7Z8>jBYBP>_O9iy*H^So1_bxgLK$Tiw{|ee}bs#VF8lexP&X9K*5?@?sX;vT*r^OL3VyuXEv9pr z1i9}Yt?V~Uqb)2{@zo6~L}M1h`tzyytsXd)^|1l8g2_>kTTsrgD$$c z2>#+s)qXgQy+sWh-PETsyXD72qtX}@WmShgJW2=q5Yr@2J zXJP;FvUJ^=9{ks0M~d6R#?!DrJ8FCw(7Gs~`n$Ow>kn1sMe>a!@}9B4bK7>*y43wM ziJU-}ikkOOY9n;Q%gck!=~y?KTBbckL)Tu3O%Viluso~!c+2J)7>fHpvo0LKo*0Hk z;PnA`3I0j_);|o%4}qO)EBf%hM&77u8^I^?x+~U6_M!gH>H&#?9vqc;8T94DBTj2S*Vw%S#556Jg zpRWI5K`khBbb;WZmVLe7RxtX}T|I2wU_OF%Wp9VVZ`OfpModBDYb`?OGWT_cu(6mL zD*Z};4a*0-{Eb9?XyP(|@!$jvpIZweBgn%z`!h65CS(L>D5I60_h+D-g>NjmNr*f4 z?wJ2eN2|T)zn|{W$lN@4LCU=e-`79e)BCm;MnQ6M1{Fqm@!vhGc zwKaM1gbBGMUz3VTVh%Fu+`v^r^ox4`+q2bONMEXKoxM4Py9*!th-pRwj(0>-| zFFw?{M(#!d$8Y}Jj0|uskb0DKQ;^(xeTQ0TI!1fFT9*GJIDbQ8;9_DMA}n9+5SH#m zTf4aw$2{Tpl--o{3TNP@+R95y#hs|gT5sS{I07k7h10?Wx74g#??=5;g9)+e$Abwo z$WVOo^%R5911H^rmhGN~uA$XLjYBWa25tYca+tW!##wi@dGhf%{FYm*Ne1k7*L<^2 zB<5E04+~v>{djfNIMZ}-6nw%TtFNq?L5Q(L_qF;-?8&$;J>!#$ikiNT*a<4`@OM{@ z)sTqy)p2IO>J-Au4KrhFs_{8i)xc-#B;H+nd-?=_E6QK|%TGDi0J#%w0;hvWNS{&l zyha{Dz_kazeJ#czZ*rnOV2Xqwr8RB3*Qa32+H_G-t`rj)(xX)|Jy7~{|FU!k1u^@- z80}@0Ax&8_&)>ThC){)+Vy$R+&vU?fUHU9Ce6u!XeVfMfD&vlM-fmdV-nSPcbhy{f zIO*d$Y*3BQeLE*i!OJb&4T%SbAmn~2xaA%LRrbl}`Xx!2AGj9FH#&*&E2G@2ya!>N zb>mIF92IRzxt*3D8HiapAG@63q?>QtE33_zChFwN;i95ud}@`W#C{)v#Cex`&Y@;3 z=w7;_`m-Bavg$VULI!fHB77_)%W(MP8xzq~Ha4||pDrYHQPhn4gA<3z(0Enf&{)%h zeV=nD4wUv_)#qjX3(q>SkVyNPmO6&;H!b&U6q`Y`l;!CJFO1wK-v3ZH4G!W<;ZN4E zvAun~%gU96vTn+yS-XB@wy(Rwl|;Em}AY&J(j1+r0bHa{c|UEo+$=x~LR* z_D(g-^Up-HxT{gZJ{t06%_zE;XEogaISmi2Q~nh&fsp3GoUW=^xT$Soo()Kb?U!@8 zE^haK2bLrp739MheEkF73N2@fqj#m)#fN(E|qida>5;c63`uZY&>} z!GDHDhm$(l@H_f?!FoLd%G}$&t8Six)b`N$qPKnU5EPwad(GnZPW}U}>=}HDH46W@ zjo^AOQe?MZ&O`nV=U0YBT}a!QbYeK50r&T*`meMl!*gBGuk3+rBpK`~NRk}H&C*L7 zH3_|Hv+q{A^W!G?2R^PeXkcLRh=ommEeTA^)?{6$5g5m|KPg)Lh$?fV6^?IaaBJG5qf;aesm=qR8J}k{o*c=?d3_Y}{NY?%=lgM> zQ=(Ov)C0-)sndx{6_}qpU@FYZhK$(t=a)8-@$y;qJ=2~ZlpNFU{YU$R)joUXOWrf! zZL|F?wQ~wdFE;b9Eeoz!<=}SIHx8JL(_-!GB*X{z4O|>auo({Hq>~ZNg?!zsw(B$%~9B#zxHTx zZ!Ox_s+QZl>w|&vihHAc!+0dJE=<0Wj{R!YFXCNh;bZYE#E$4Ub=(|6A)D%e6XdC| zMS^ELRa>Y#Wx*#rU#RkXC!PxqFBmD&k)rJ?M)e*A*NX1jrkUw@$JpAjPKfXc9D{f| zR?cGQi(k9`lb|B$9^F%Yi10}w&L0;W?n7|HU(H&b7JR$4an*BD3pyC?Ud*F}zn357Lcy@If4$v*L+ zg1P1O$I-NG!Y5D-6c(pK`DW!>H3=3KHKE!-QhqmJGHTBw47}Q&KqT6!>eFek6Tfb1Sw)v{F zhwdou6z%ELlJCYLm4-sgi;JFL&nu_TcbFqwsncqVILD z;(j_e30vvjpH@w!aE*`Teg2M3+?NOwJJ}8-HtnxZDV@f{m}^pWJAylIJu71{G>w$S z7uIfsPZL|h`g(}CPnQyNz@QKJXY!%^Jqe_8n z$?^)T8amEi;xdhErDI68tZ8Xg3%I$;^zP@=5$dV+_L<`#iN+;jeB;F8=J10hNn)s-QG9l zxK|w{xSi;;scDi02D=B*@h|dK_)|K;fx7Eyf}>!a39)7#X@i;IkW^>V2+pr4^3iG~ z?%Q3-Qt_}P$Xz{DmUw!U;5{u|HoyDPb0Kcnl;BT|tznfP^2Sjq>>YUj-V9tbR(=+Z zu0VT;s8SB02fL{!HEL3Gks@etXKy(jH`?4TUCg3j;~vk{YND?vTRl7Ltric3(ADFG z#Qc72UikYe;@k$(52t-nA;VO>K_h##3DW2Pu}GP%*nju_SaA9zrut3?9ojX4w$Tv3 zi9HOkGOdR4qgWt&)vP(Yp%pJ~i&~$ICHVFIH*SBOiMiwCzno9ci2kR}IrvSN4O#2k zkt#g3xFHvpCP>t4DUIZ&Of5G4Mu!W|HPf+)bXYQi=tDJH6E}xGkf45?`dt|o^mGg2}d$N32VKI#|Za)RrnV&_{Oi=tvk>O0q?iT=9`&lHR5*@{%DDz zCJhN^l^|FIzfodU4Wr&(kXd$N3~2`q_K>+)=vvRHiRUB1>)yV%%>5$}Zk={A*hKJ- zFNKn-)}wIX+<7;$W&-v{a;ZjMb&|L1CM`r57{rzz?f`geZ*lp zjubMCrm555_$uyKNpO6ZEvZlyD6G1n{v_1qi;j zRv`IrxYYV`8W8fZ5Lj4e-pmtH;mOed-|jQ4I%4P_R&dl z2NueQWo!vQzh}!6;amPBtf>sBEtjT1h2^x8b-NzI&L3r534Xa?Uuvd#ZWxbWk813W z&mis@Ydnlng|;%TJ{$QKJc$av@-KtPLzpLiP4i$u`BY?=>k$?PPYjl-^HE@6bXI!u zDsg|xSj?=eJxJ%)e34K1_kZWQBDb~lV_SMjMt|W9^jC0QI{mg0(jkIl4DcPpHKN5ctWdVL@_6DOOgL8*ax*c@>9i~LR+B*L0v zRy=A#r{cwgPu4_#-M8AWZ~rK~4I<@h%RAA+mXYJJron-|)}OYr4nvcQEzU&W`I-9A zE{X7MZE6g7^%Cn~^h`B)V8sLuc3zAkzi!3P%-kBu=Om0j^zXiRg@M)|ar+s%CfKoK zmZLS3&>aeIN0t-!sL21)J)|hGmYasMdX?_X4KpazTG)GYCy~GKJ=FBIz7a{pI2ydV9}ldKmu3B^ zf``nu3ywtItgT(O=&=tSp38D}eDEN6mWUW7W(~p5YA#-0-!=@j#|MKA)0^=1H{Ur$ z%`se(6}oox4Z(d2K8ZZ>Pe2`u zXkQr#2j+Qnp55+(>}rm0d`)z`l>K_=MZgq7bH<-dWHDf(n!e+N&kTlCPuWLS($Q46 zNOByk#jo%^d}Tx)P2q#7;e`|;Z{*)ov{jCcoPcdXKSOCS=CE7tbz=&9g8%vTUCV{( z*u(i=!CB-sSJr87C;W&nR|WV#OrbfxF~8QDjY9*LLzcY-h*|r*XoGVp9xorRxc#FJ zVU1j|T&sxZ+JEieWZh-Bcpr1G=$-__F7t1oQ$4N@59|n? zh2q}8eJUJvU?eN}UVcU7p43X61dlhu<4@WT|KwJ*1&c9PUTH#W<&!%v)g!U|-iVV@ zU_Y89rQ=R&kYQw7C3|yaHL{rQwr5U^BHXS${6pt7a!+(ynFLH?dd|n=p>7ZKoS2_j zR?pFTL&U_;jnE}89M+AUe*>}j=_DH>ujcjd(mCaUNw^l@nT#muhvhyai9n)%mox>X zbkvsP$2YUHnK4W-JuVrE6ZxjzyC!10cFiD;&s~3LbOL@Mwwhj>SrDzfa?6{@Q5^X$ z;z~~YfV(zTiNXMHXp||tyYCAT@AFSX#KSJ>R zzh~z2S9jp$1Cy#Tf)B)ew|=3`Uyi!$3~??EA`dY3RIN{(4Vq$1p0{^)1d#7Tu^vV=Y;{iR#lM&w(EsZrA*IfLL;IREv_z!ch-l7=cCbVFBdua(Ws zBDh^XmbLFc8rJ9DxstGU2u(-A%sC&lXvmwJ*Nu zz8V3?ma?^u_dgN+>o%?TVjl!3V=f;yQ(&@PL1OQtY1n>Xm*)|F(%qmJB2D4rxMn(~ zy7*)o{}NyC7+6L__wll=ON04X^)*aA#AFq3jiv?&>PPLtTv&xyQV@so~^Id$k8_R`(8n#i3w zsHxuOnMTAQM`qWn9`Mqh>a~tBU|n=HR`Ui4ksl{hC*m3K;^W*&+0~6Gk0ZJ-TPI=k zMDN-=0VaO&PE0=h<)wy9 z*vtQxOuW&B)|YOFj}raI^U_7x0Fg0BW~vzfweE)(U74L_I)m3FjoaP|^)Tan;L&<+ z5HfwmvXAv6Gje0^W zJIT0gc4BflF{fNKK7FgOlY#csV(DSG9waL}`e=M2xa*DerT;EbaBXSN%y@7$6#iBG zari>y3pVc$mvOv|!};@O*}BtMocM8Bx+e!^x5w_x4vu5tQ1UnDjZAPKp4G|TLgdSK z+wc}ncVaN5xjSK&iM?z1%hHUQu-l{QL0&t9UTyBX`C+5r+%kOEehmduYhBMZZtQ{W z`Sh-LD?g#!kQ$V8i^yHPy7%j#%Ov7&O}NyVR-@*unD!k#B2QgCJAV93J6yu)+_?3$tX1XF8z+1 z(ARSzTlo&nVu-6~Gy5F{LFF|ZZI%oqYhD)(oTMRPv$4VNonxq%IwsRs!iMwk)H&{x z)ey|>ALH^Ifbos}KhAr10y}kurC)X836E;4%}gGeSdVTtK550&bk%!{EHY}!_bWDC zXP{umRD_V_6jnu=j~}d?By>RWKY4C;HiZ!LT>6HB9>+$=e>lEP>~|j=bxM5v z4tRqn-4md@JIkvhy>d?7uvd<>5t?Yt8Cf(hAGZV9I(+93M&+salVXL!)b!lRkU z%lq$`U$o&P!;tgU71rJk@aa4Lmb%;tig8p}_?vw6HLrfqdc6g&?xvp)H=o67X<5IM zCPc0?xVnhvMKd;zB_6kHC*j=j{Qtr>41v1ykHyNzWX#$w`>Q_n5|=H1I3~Xtf%CJJ z^U^6)Y{~VnAQu8{+x-`Cef7KH^rdQcr`E2q#-L_3-8Nh3|QRRE*7^vG>lqkt$;`gHi!KaD+ zfPB@#Z&@Fa}#;Wo&tS` zQW|(T`94|`{k-m-xb118ZyNawX?B=2Bj8bNc9>>29JE*XKV6lMup8~&>up%T@d!cD zDk`3h^Tl#HPlM88CGyRXV**`56`6yp8YN=@e+Wr?+4HOgyig;IKK7PRv_fyUm~Ve;<2czPqp+)q|Sx zU;W!*pL~)mO8BJf)%F)po*BmSuRqVN^zFl|{x{kSM4bz45?H@qgn~^6jW1mEV?vkn zX|U^QHr%*NcL6qg=H#VlL>Yh_E1|H}a}0`RoL$1DE}h@UBC2 zi{Zja#TkfE4TnThdlC9A^o#9(1RpkPlH}qca`mx$touT(D#E*WPwtwzT&(?cM7y?o5G_V?9y?CYB1>leP*lwjo_C3|H)ZxhU)he-B0+=KNp0;@ zqSGik=68ql=n(8~Cg^MDR@@J7z%LnY=C?8;hmqdmTT)5nk+lUj zDg5d~hDy2Mt@bfQ`02$s)t14e)cC(mqXcJ~sSY~vU=St$$qj`T=A(Iou94C4G3*WO z|H0fli#d;QZ-d}*m{+!M&-)dI4bn-~{yNRz+Om`L<-KMk&oj=flp%7Q9pQ=o4gK)X zmQM}#>&EN9lmquN{4w?+^@8adI!>v?q|`heh4QFytrg)jX2fyx7c~ze@(pijPj4p3 z-dPS=gl=tLy{sVZ774@R!ZOnb3lOrrCV);K$8N_e*B`coZ$t5s;)xnU?&FqBuRDa^ zxbG7zrkM}3Gio~4I~WL;ceBX!tA~8{;h;o!B2N=gqw(l{4y=2g+;=8&RdXhNVmyQ{ z-uEG5b$)UreC>5RbVHhP+gCOH&BYnCt(d4RQ6-_eV{_OWx6jB8yDt*++ygyv7xSO@ zF%elcc|lnq3%`pE+njH;frGv5@bTdhM5iPwh+Le4&W=~x&KlLD+w8vBh2lcY^h@V@ z5&7byGJV2SA`hiSi+azgM21BEn|IxWF5p@)z{ov9KR#J{y>ge~Oce6;3S1digJ`ZlYT&4`w8<72;V$-}Zj=fIV zULPVR5gI*Z;Gxli=gULm2UA9&`DL=+>qjDyThY(ELilQtrw6yy+oYjjn}qjPqc|9D z$o~3Iqze)UI$u2sBjK>)tAu_cub7};R=GcA1U1`t8d3CfV7SLvt6*gp)Xh^mzq>Gz zvn;|chscv%n^pR2yI7BmPQ$x%gf6kzQ}OVS7_Gr*m3{bBTS3*9qq$o_1nddah!f z=OEJZ_%EmZnS{%j#9hUGQ&{|V%PB5!2(G(JuOy!yKyE}q`oiT7?2#+o4`w%ZZ!UUs zgUE-S9VIzCukAs!r|HGYFDzI#e|M=pHICK1r*4IF^+VT3k)z}v2_@AMho$mLaKMm< z$L>!TGR~%wLSwqYwK918pLr&j^pSk7tdH=Sh_s|P6FGuon_pz9QJ}X}Mc<(pi>+nh z1J{ULcm8?xdmLt6h|oWsF;iX$x!L)j4mbN@cwgFWitrCB+I|HdAoj;Lsy`4^pPt0w z#*~^vZj;DfYm_BFHw%$m>Rs>kvrt$Q!2Q~iiY65;1xKRqTblZn7E*^$$HmL0Ei~hr z-u+t?jdu8ZUS(}=o5B@A?U<+`I(oz3KjtBF+%n|+ln(!4c;{0a2iA{a>+;y@w_S~J z)*;(971ki)hW+LI#$hOTkTmUyKB2IB@a(gRQ8a%(a^GvN0GcNr$TU1A>g{TSbrgMK zFYpfG|GXw4o432)hlhax+pfkhs)RnF=)u zB3Gi>p1t+p8w{;#?VkEd%z@)Fvd^-KJuLx_*zan&VC8o%t0DAn=5h9@Yjh)oJRLd{ z*u**AeeCDxHp1VSD5?KwTLsO{5>jp*lV}QC9wJNZ4;8z4i099@LrOJhq}gf~1zSpG zbdNQmVqEoheQEXzly5xa!paHtK(n)HY$Fx?*WUI++5Ag&PjtNkpE<*soA=O)sH0CL*nh z88~E=X{PDng&SF)xs`Tx!B(`vAz^MDO_w(|sOz=i6hCc{GDE??bEP*-1zNCRX|U&9 zF5%aT3E#<9YXa?di<Av-=TO2{GEai#Ov!}r9@E; zB7A^9{#EuNjbuEH8~yf7iH*GA}zy|UvTLn2q3J$IrS5g+PK6%P#KC!N)N zFrgYNKKawvttaE%{65W?VOtVX?I2g!gC(E{RMxyyK@JXU00{WKJ_q549_4Sxw{J zoL==;<^;}a>@y!D-fREh>z|gq4ERmBrZm2$ zi_H*EBJ%4>W?}~JSMrE_te%esk@t&;wk!~j9)*^CYH@_#0Jd5*@-01YMQaKD6Iav} zl*{XuPuumN#=(gz-iifVKI1laWGA*<{rRPX*zX7%lw>(i;l7Hmjpu_Nmj=;)?dYs_r!hD1j$!;qH-d71|4jWQJ+ zzk{9r65Or!?*S|-knxw}oE*82*njamCZ*3usqDW3 z{Mf|(uk{d{*k2Hj5?8JJT};mk{UG*Ob#6MoOIT5h zZ)VT6A39G$El^vQ?-d2_0#;gf2-G2{Vac7W)P;rQr26H{r@)Z*d6?2wiGM|^=^DzP zG2QA^RA)>fa>AET6W@%*lV5L*?x(|OCM50O1vYLp+|apjk;th9Ox~6EtboO~%Eq5n zy=YX_zhXW?N9@hKUm8STvvVHbv@(Xs^PKx|VS!9W#5utjayj};&1nrkB z`lZc=X-6Q>A0lr$^tyN>$AtjAQhxAe7xA82AO6*o>o&oFh3tj>@-);t2`4S7vk`k- zG{Ud23nf0sG(#SBNHxuZW=2Y^FB)D*y z?EYn(b*S?x?~U(fAdyki*GOB7ZGe54|6 zyQbtq92Fau8{Z8lIHc{F)9nkt2;YKt=*0Z-c4CfWDR3Sp_M87`M8vp#fTQDO$D1i- zNI&0narP(!LR{x|kQRu%nv7xijy5XH{7e)2363iICuZvo;yq{_T$Q)wOh2AKmztDj zb>op;(N3*(Bw`;X;N%FgZ`QP+CV2HZ!K0a6me;=15s=ch&2hRPYC_|lmvac;J4>ta zyg9*1HC;0sj!|%`dN8({s6T=^Or!7i#Q$GV5n&9k#rIap$zbaX=g{A9=y{!Gb zmf@TG@Pw*#=$>&t9y~QZO|PxOH;#*=JBb|P?1zG-GaE*cB|95Z!6I@ZH?Ac2l{O>y zZr;i^w^DF4tmN^XFUK9XWr@Yfy?E@^bHRkz-*V<=^F3nJ!*0#zxB1Bg=gQz&Q!q`& zmz(BV|mO>gVMj^9^Ow$71pFsLQNq_&mtQB_F+?=#_&E7*N; zn1bgnDocyj#QuDf7FpPI7Ml4zscNg+;qA@ujl& z9@%?m@4fe4k4-X5_?_QhuCA_&$K!tP`*Ysobt+|MY*hXXK;_lfe-c%4fk?$U=JpEa zT1nc&Gl#38RMM^cl=K+P3Z=$|N}vu^KKs)rvHW1fN|@!x@0 zop`O5&rMM5Uj*sBOx7~fhD2$$A(Z(oG#bcUkDn7NFyzh z`g5Id;L+uO!gSbAk7fu-bRU8T$6lUZLj5@Q6t9ID=2^ao#-)GlU4S<>+Cs+HFn=n% z94+iS4aO30F9=~Sq-gBb)(!0pSc>piv={S*@@VZJuh3`WGN;h`b`E`*P_5X067*Y6 z)kpq* zv~!^SIL818NJ?HeEuMwkq(`f5w^PC0LZdsfA`58y_c$zP`@rR|PQWefbG>+SAg42B z3f`FxWQk%g{qD_yQ;bh%Kr`{#R6HN%^2un}G$hl(&%pEfen$=DX@u(u)Gxpvk-78A zdA&e2aOAAP??uS?X!i33K2I6di{uuo7y!@5qKKjhno@|m=hd?E1;Poet4$zSM z*zCbQ12H$0=Xo`kVfUJ|T~_TNlrn@FF;?|pPpaBosj3^o782vAg)4x~>Y;s|SRXiw z20!V(+X+AI#k}Mcu%Alp9ZWkq4(8`h_qSRTyXj&qsk`~=C6LZ$w9nZT7&yRLj+E0W2yw3U=g>op8%Gj!1$pZSrGVfJJhoH42jK9-l z0vv=Je>_aZJ|NrT$sC-62~^&CTc;P`^@+SD8?8yWc=vB!|H3Rhy{{QEI4}yEdmJ&x zE;d2YHLAAL`IFF*9P`Iwu>pGitE@fws2ql`t)>Rk^g@lo9F-eS8sxaw8Uz&JJXG-N z$BEy$@ToD9I5e;g%EhOj8d~6U^@`eY9rMddCkw zG~E{qNL_*QHYp2DheaTFPFbw>nE=yN1;#&pE#UTgwLNB}2FeP!+)6d(Ako?-zwZ1j zSgg;5bXb&u#R<9o3z+MS&sWK3m{1^Ua{%Fh|lcw3iEM1Wn1Sq3Clww298)#2#7|fob$(3y4*!1(`?B z!9ZFBMWewN@Jnj?F1x=7I*Q88OTU(YC0m|<#Iy^tzds8sW19vnkKBvGUd|WOx-(&| zcrJGmEt=WD_jj>qTjfY6q}T)n%y%P4fyCUm*LVbY1*EgK_qw4bPMNJFu?hkb)|J;X z7U0`OA_HA~PQ4a4e>wMj1$4cgEw_jo!6+i8RJRNJg)&o{8^Uu?%xYdgWj6%((o*sb z&QF0x+!9-@=^~uC`r33P6Yozd`7MTev!LS}PM-335Xw6eeY?_o;d8J5+jY4GC^*vc zZRlJ(?Eaq3y@$Eq&~+M-bnJV-w;NztJiH81!v9WEl2?HCs6i;fWD4{p=M@B`@%jr2 z9=M(`2KpL(&iQKzFn-mU`;Yz%h?~o8y!$l^`p<{sbTkqn=ET&ufrcq4%$_^;@Mx7 z>V0Vik=@4PFBVH+mS^f8lHLG`x2^tK-EIQMeG}a?HCb@&RxQn;8$aMS|NCf#dd#P< z?OiEIYJ;an!h(-%=fUEp^)=#}1lZ0oZm(LN0Ip)r;{?3^jwiUfCg2<&cA|u4|N9cm ztyP{hxPm^%-^onD7y`6i`o(I2_XUM35R;#13kcQtjJ82)(E53inlrS2Ovl5K*M`B z)L~9`E2J#Xf{*IR(PvcXkCI0+s@t}}u)*Mli!tW?oF5yTa#Vukt8g}9)U|W64_p6G zTm%ZqYl4%V-Jt#Xnp4l+UO02%lP?`iVjeZxgcI}mqZjT+J?a?;dD;1a((Nf&eCy58 zi#@~Kl*IGZmDv9yiJ%H?OM!*2%h~#;ksFjfVitH|49?tGvR-wbgNE&i{d4FO(X<%- z_6-_=VPCl(70laG*vdq)P2zcGTgv_s1LguW=90KoJ7E0lETK!j4=f~k6U_d_fpY!h zuXV}T6J<}X*T=l+a?0$OLPjO{vei``l^%deqr-26mypZ!VZ~$kLlh+S{>;3sIt+B| zOw4o-X@cQF--dt;(;~W&fNF<~G6hM;v2(O=1 z%Ng_QrqwX*eC*hcQ8&Pea`~&@yMg_Q3#X!TD^!Fh4y=1lfg3ANiR9ZRmW)0~o*@7Q#kAizDFMm@U-Qi8qhG^LdUA(n5ju(GZanQB z1HsnKH|wfnV6>FTGI+Hcl8nro=2d&4aoO{N7%y_bSU!w$DAoaWytw}u_C>vKD}Q17 z(hl7+=@)fTSJO9?Wm(_T1=C-CZ(6W7^hfW~mQ2J1oK&#SRP`BzN1P>&Yr;*?S|>Bz zy)*#6^scY#Fn29xp2rv$u?X+y3^RfvCxPbr1&Y>w)B%n%+qKmbz+9sB>`q}RNN-pE zyz93JN`{w0#Nr9yqr@EDbCv)xtFca}JH~;q<#=vju@aIJ*8RT}{sbzK8rH~R^hfCQ zGijKn!SjL6vl~HEK(lM4w%m{NSh-XFp?_oW%E0`PfMzEMzTpnwwH*Z~@g(xG=a?T> z`%mG7=`?I#$&?S#LZ4jd9reYOMX;ai4Lq*44Ci9^&`({0hs-;pLu(B%u0ZK8T{i~x zcYoVa2;(_&n?LdI)oJklOhdZtGXR}+6SacBX28Yr;@|rh%OUs%m5wv^S~cf0z7u`z z2cgTOxAbd!V6|cBNT~84JYf#ln0vbfHGU_*XfC$E#4Ac(_ls3|xdBX_Tjr%9e0TdsngJu8Xk5se+nKc zFR&8wDu6C>mP^;h0Vt09KdFDc0E5cR_U^YauU$r{Gt!ArV!2R6$RXy)azF*@P} z;AjC1E2J|6UdC$SjkjAtyLhxF_x%#=^Lq-ai6AF$H9Vx++6T6_Ub?rz z5|9^%tTJMb4M;xISrtw|uI{{!_wPv99{1%Yq8ta$OKKlB-I~Ds1Z{#EejejqYDt}W z*91{B?5*vzRX}R?;Q>f5gEf#F$Km~5KRz&<^lU5Y-9}>h_2Y2xUd_GT@OgM-dp*h? zef3E9_M(px=o4|Cu5Hm6Le5B0VfW20aA}KgT=$Fv*QW*jo&Cts3H|l+49Ns|luXG= zRQQ8t{Lec~r&eHZ=Bwj-n@YGd3FBV;qae367Z5QY1O_xkgZapNJJxxKM&-x^EF5`z zSC+C1qTZf|p@7(Tu@X-X48iNm#x{Q~^IGn0r=ZN#muZtsK z`)1YY_2xX(r85s$s3RYT&h5BT!8F|VI^{EAi20K>wliR^pN>c~xV|(nxqF-;}SjIt_A(zpEe4jX+=v*&9QA{Vr)Qg)YrT!&a2 zy`d&+f$tlX;_5S9u(0MbO+JWRidbgRfAWiPjR~HK&Mks%Y-qDE&Tm)7mZfgRPQq5T ziEK>HFns^T$p6%~4F-SFGM(Qlg~L2HCr2??vg^Hmac5@&f(BXiWL7`JAfedt5#0i~ zuhDT$WB>2J&UQU}{Qsg+VZFfX`H+0(P3(22NgxEW>Z@neK`wpewG&DS(3s%;g2ZGL z4vQY3?CYNdvukZ$`9TxVe3urN zrD^ah@tAl?oeD+H65{#WIpBAUEBV^nXju5(Yx{v~27m6ts7U)F?6k?hNdK1)9IP!H z&rvU9(s**e{X;A4E0XK9qu$ecVLPchs29W@IdBDvYjK}0wt~TpA9*dN*#G6@ z*>GRz1s9qD#jlE0klR8(FVa#4<$sTRH(>rErQ)jV9_IUOe%`#dL9_&S2Q3bb;+(ci zd!cH%e;Hnk*0*tEZ@`{(p-$-22*`E3CJ1DIgTm?vg<5hvhr6pkwT&DGMolt*Y25*s zAoblpF|Rn!MEVplCxk?Yp1ZE`!Z9!mYQvlr0k96575M7N|CDv581o!3r> z&O|x=#E@)wHpa{>rjGdl#W&7pVsMU6dK>j&+Z3)6|H;^PTYxao9!Sue0>zf|JJIHN zUMVR5ZP{Sr{VSFc-Ty%J17?p+3ClW+gCxqLx^^z1lY@ zP?tVSaCwb=dVvQ5IU)^X@E~6$c(SGfH1b{cMU^{&{wU$!xgXO|@PhDAW*xa!o%>4D zn6I3OH0wLuQwyW@b%yf?$6)AI=-#`;B~WHQVA+O-cRTbO@DT}21 zw#frf>-#*eTMqqu)`LkhhrQr~fD%vke+zK>SGwj|_bM3V;(h;8ANwGGO7wDWOabB7 z1DkZNWl;9laC2Upf@X&LoYTL2!07e~4ld+k{h8406Z|+1Q{zT%r=|%Y>?}0!Q+yuw z{fGL3=O$q|cc?G#9`X`Ov;Q*~nE~#Vx1E`i#qg!gU|5q2&tVq6cIRjD`EMj1sK*%z z!#!sXym;OL4Ps=bX*LsZaK5-A({Bk*(#iH+MZLq(#=49Z`H!naN?Pl0I^bIOw9l?{ z74Q^Yzi)&7=KS-Gn}zr}|KUm3xEDVLjx?8f5?N>A#mexeyhJrH{U#U8Iok~G?5;M_ z#!IlqCfeS41$Fwg)26$ryhD`Fql5LNxI8|=i>u5Gxf%=D0FuhTb#fa~(LU#G3 z?AyqZ8P;$9PTmR5l5t^tMI&I6BXjEUd+eR`-1(GKuncSL2gkc+Fegi&$+|E-i0^Oo z)i2|{u=jz)CMc*LYBCe(#Yie(^GYwp&~ghrXqAm!8*YM;29B$>#&{i^`6m~z(*UNN zdG7{n7h&0WZt>&IS`gik$s+fk1)4HPHhpXKpTCnCrtsmp@5!6dq@$zQlUB+uNM8mG z+Jmp?ao$--r5+Z*^HRDyhm-38)SCxdhTT?>f59wu>wqZg(E*c5<#+l(^}vdDx7M~-BZiIAn*25r82xHofPEaHie828L z2#mu)v6t|3O(_yJb5wa8PQ28q3_DN>^OhX$R|_!j8Z)c*dSf0W&F}4p-Wh@%7RT=% zP9yM+=Uf=4Y(G5RYMJdZ9tS43+4GHx<8W%s`gAaI^x{`m4)m^b9_v{3jjzY%U~2VAHBlm&FxRW18dJ|mAc zrAh2UHTH^?B;vkJg3ckEifH71o;rBrpL1V5=nV8*-1oxg>ZVJnkjpZ#ydtJHDw;=* zXa#4!UmF4R)I(5V2)dwbR5&#~`wkyL~+9QA04#ZOk;ov<}tb&S|%2=fdLtb8Hp zuRV3sV?7xNJP#7vLgXGa3V*waFMnqrw;UfL!7?p5cC<^ z3me=aK%&8AfyAaJV6x%ae~9PsV8d!3!3E@xsQf#1cclb$M_CH@RBGU`R<~iY)C}xM z4b$!6eEn?ikNOf3@(dLcJ3A`-q2%DWQX=-eB=Z{Pnb$|*n4Q$$jAQ9%y7)nIoFQ90^S1n*2q*`L2qw2+=ZR zEY}Yo>skg!qgHJb>=Bbz$5&j9d);PW}7HW!cXma(Iq?lV$@h({~I5@P&nV`rdc+-&yTK zk90IZ<-Tt+OZ70!uon<(5@SwYlUw$MPdesmBE_I}-B}1yFOK_{unPm%2#v`{rSc=+}M=8*+87a50nM`#^h= zrCs1dAKat9+?r>@966Z$mJ{dKV=sQs+KG=Ke~>ed`D-nh z$uGE`%wGno;INAN&O8X+H)NT)gnXwEkx@;9TJY^PtShv@KFX2}rH)?)>`Q)Mc3kfU z8I?oZu9jukM@<@a^__sn*S?AcaLj}K3*j_Px^WnD7brHoIth)n8g7=?X29X;v1aKF ze10`Pxas{9^M3aQuWhysL517Ac=ERjn6$XS=RmOn9GN;iw4B&$pe;Pw`KlSnYg6O~ zABI5Om3Mr6Ar-)1*_=~*qX9PKj80PF`9j*|Q=Jzd^7sx2$(+t<2C{}jQHd=J@F+W# zrsf#-qV#zU1&h1DBwh1y8tM)Pm!^74XvZP3Du3|FNz_Ni3%>1R?y=W4)r{`RDDW2Z z`>-=ipr5^hFLE5z9}cw8kKp^x9?Un^i+x1jmj?TmLoo1GzUXF@J#c({_T9}0eWGqT z*G9}C-#fZD%k!oL&bPf03*at*-6UxPIqVJOK0Z}Sbg2Q{4IWLrx5Au1(|e0~dgMW9 zTFF%^$5(2s(rL z``Y-%Ta}H48e749?w#f6$s{T{2>E%si9|gP&vCVpp@_!2@-kAd3d*z9c{@sx*ap(evYx6q#^dOLOZj=9VVO zY($DTCgI&*3ip554~XPa?@#>N26v6`=j@Tz!anc);jJR%Tckvl-&bA+VoxfD8+WR( z7cTo(=Epep6I_q(RkuUZgM!w8b>x%OwcSbhJ_~;(E~|81M2@9fzsMQaudvIL_%8PU z^ZSzsdiuB-*p)qHcnokR^*aH9Es;op0s-nJh^awOMO(&vwQB(R%h{_oZkYEv z70Z7NzkUk-sP87U0#+1Fccgl;r$Hl~#h055=EV2f42MfVb&uqLQ%oGp)zc)@KIwwj zPa>XN;zZ7Trt}MkQ{E6=P_OXMyblr>!UVOdM`7(wnNw6>KfHZLvr3LR64qEGF9E6(wi(^I3aqhGmg)ZGJY`T#(L~SI(VWrWzbA6PTE`ozwI5iM;2r{pSXNeXCvt@~l`e!pA+kBZ4WI>unQ z_e!*Z^X>}zW{S*FBlvxv_@(M$kL+exZ~$p%CqyKuc@1t%gS^D>rtr`xOi-kb{<$#? zdG+oeU32jL&~nJ2L_cbx-u($Vo{PR(!p~_u2VVZ2`1RpJEo?Y#5_h~GhiCN8x2`E6 zpWG~k_Hj}py!`27KdF%qC5In^@i@*cQlVR^9V;LqPaZgl{!_EWONy2G4ycsI24p}k za4=tZZRI)w9cmjP>~Cuz*pur>(ye|NFqShe$9)MCt9pm-BFBfD-um6Fe>UpL+-H_8 zbFrVe+%bf@VL038)4voafUa}j?F#a|47Q`o{IEaF%T9KjihK^VgWL)d?)8F@sF%1x z+XBq}b2X7k9RfmfkKJ17EOLTh_x!sr9n?Z`*@=z4@1afx?CPuerAv#C$ zpYSuBW0$E1JjT<(TThuxa()Oxvt-oB(vfp6w61)4$_EIF$vHWj4RC`&eoIyhb4yPi zX9)^S!_RNx9{Y`x@K~V3;L|Sxh%!e?`(mE+dt-na&97nDZ*)qLZ(4$76R&mfpA32tm18-r?tU?G_boPRj(j5#qZ zg0atN<&TarF!}cCBB5yzide0vU$ysw`+*VzON_ z9M3POdtY%`r-LSI@eQ+uESRxbo_%y^61+27KEQ!IAWSUShBGF^zjLEWZ+6C^~Z(P`Bt*|X+}2YRySIPe&zf00BzW-tRM;GR!Poq z*uB87SKSh-USgkzWj*iW?;^-O-u}Glzj3&_lTk>xzX+nMLm77H16~vOPS&6m2`=qF zM1#AU!B^!%`7`exD0%N&SBZV`i&ZSDCrg?@!7DuH=KXOXE2%j4dINdZ3)gLXi;E%X z^JS<+f96t?YizgNEZDq_@hq9Z{CWT%xyfWG^mGipSI(@1Q+|Qh73ndTajV>45c9*X zVt2+b9q5DJ7ejlGMhVbtR^wE`i|5Iq-s=JzvrsVfYS^Ts4Sd9H?#H}XfDyq@m412U z@NkfBvy-U|1W6D0FJR9y>w=N~JA--ne3WB-fPWf#MW}h?cSZm&m{8}#cn%nHRdCg- z1V+>QZJ})KFz(8jVK_Ac!Ci&7d6CEPG;#VD)wMy`3z0Og+K>oITH8acPBJ%d*QeT-)f=sUv;{d}X?3hTvq;&z%Q(o9B7(_kYZu!0} z=4Fy9zsSiE<6eN*?UH_;BOov=zxE8DW2@nnH{g_$E=gNamDMKa3esl1WIa@&f&JYlY)GE1kf#s+>&}hq(s6 z5i6ahW@vC%`MinG(LzxN3P<*p9eLE<=i%r)Q8@C?A7Tc!0Zu%cai)8L>hFow_5bVhK1ZmHLYHF zWOAjVE4miW>UY&ii*~@hv4H4R*HJjFu%RSTo(8Wb-{}R%cf%3ogS*<3E3lM9aOtIJ zgXpP=vwEm6edAKLC%ZZaw90DB)3|>{5d=LHun(kCxub71IRqLLoVV$xk@w}UuD*WC zA4JD^j@X{4fYT>tmNuhefRu;vS%=jM2x)rIAIt23ol{GRSKH9f4B&Q$#mwSwhSkwA*nH>bb-EjK+YR<5 z>n8{he6Y*3g+3jMsT&fPjghBRttBwbKLKp^DJdtodm!2-`&>Xh<_%rcd#6$faGqTC zZSCa_m=`anPQSMZgN-uXafdtMtH7Nf#rPbPzF8m>wJd_=#i86R?RMzN z$liT95eq^N?F1I=afMzd{kntvlUxlKz6)>TfZObGTANNboP5MTOND!5$}dwkGZ9aK zMNWBTnlb8KExUnYN?E|gs+FdO9J`y>7n|b^mSJUm;^cXSMKHXw#Br-?269%OI*2CD zLy;b%5mQzvys0nW;K0`rwH-ec;f8r_d&Pc{*>u=Wh!%PH9K>b8RV#0U@0z`%!ZqA|KE%Iwr z{5^7k5B}%3cdZSmi#CW&H5MUc`^!)%_BAz{&3t2a^Mmv_3|}=Ta%yac;qeriFh2AnwyW1&cp70v zS{7P!SK!ns1IyGl%pD&NxcSj!0TMJOk}8Pj;CPMFDwpLLT-oU3s#jToo{vjOAzX>D z<~i?gfpb*uTyVP*_ASh7j|s2I<-qg9+!Er*XFI3mc)^Uj4Wt!nI1`b>wbyK0NY%Lr zNs1q}GeYu#hu@HnMrRVXJN}Sx6)XW?SWy|%w|*F-c<@EscOGuuy?1q>YYc=q;$o!k zw1GqQPT2UN21sx#|7vk~2IP*^c-@W&1ogSBwL;WIny=>1PF|UWHIq+=bB-^;X){aR zrV9=5^^*MBnKqmadM;;nRl7lcWlBKnS;Gi!~#E?MR-@Oe?Px2J^M0U@pOIr(|euPqE`>`8@5 zkA?#ctHZ!boD()cSqXIJ!%YULBiPtfGylkH1k3MrO$RWS!=C!DOf;(j{DTffa8fTo z&-nvIkFKI#{jS=a7kkk1=Ug*bej^8vFM?T&uMg_!eB^Daao-LR8E39lGnm#q44%%Xb*Oi%sJWq;QTagx0qF^f&WQL^|uw67ENa+}DX z9M1udZkt7M0qkpV`ShP`IS5`0QvcyrA&V zpH^%IIvu5iP0toE=*eiZy|@CM&83E(vjaeo+KpG~MBO8PlG|%y87ii_nl;wPKw`;P z;NWO0T(}u!%-e@t=xsT}kEt`zC{_A;IW7+*Cmr*XDRJ-7J9aabx=QGw=FJH4t%BE` zFOFGp%qwL(Qc-@!MKV)$1}lC_*E4YkmY|EG3r^>-tba(fNb+<2aNq(`{9K>4Kos_YEsN0jL&PH>-jMc z&uD(@U1*wzW6z``J&*$}?I>6nMUA~YZ!$L}yzkRT${fz5TfuxJg_OPPAow?1`y^^E zf#VsWhvC?BHqkN6S4*FR1D$ttzaYoci}zgUPh$c+(D2d_v8V?^uSvYWB;HNib+ zlMgn^T~IGjwQPTlzvl^oejl&sF^KQ9SYAHe0TgbWG;DO;FzBLr!oN2kf_#-rpY1w8 z_dz-$f$!}=;9m|g@k3pTt8A+SxqCWEm)m!dFFlxg@?|MZ&58j7)8;qpd zLEod*C-hzvRI)cDF8*DC+n;w+mY6%iFLG2f!nPXvJD;6s#{EiuDkU*jw6^anYQnPe49Vf9xQKG4k_6wCokyf$v+^JED7Spzx=d zOSfwl%r``=n(6Yu>hYJO2gzr^zq_!0uCNz4_s&Qw;B)SSG5hPod(|LUuNYT^_kHb9 zhB!#V#xG)zK! z`U3NRxL4vx_^pUe^!KPe|8@uBTwmbo91v3120Jn;X|7u<@Gh#br62k67p{G4A~B!B zyZ~)`Zs;PgcODxO8fXT_&K;@nLzq*@ja0dEasaMnOO8{|CWFz0OjS|`a@hk~9=t)_ z;v69~pXpO4n5jQiY^ffD?5&u=XP%2-y?T=2;aluI@BFyKK814tQCP3D$RctBFWHD{ zAg6!HCt3&d>wnKZTh9)_9{+X5w?4=TyP!U)!bZUBn|sBMHopzz)D?&>4g~|XLkf#2 z_LkhsZ(Y_*Edh<9!=bM6$OoHPT;=;b0}@@j?SiHejA1@*-av+XTfkVIT?0>YwlCt#(p80P1dz&C)gNg z61v-mechKdCDI=nA%ebyLHhR?h)39e3rnAb+DOXN>!;fwfyGfGC=NLvJTeW(X{VvF z@KxPEsU8p|F zUNAU|bJ(cL9buh3+|v`UT}$)@{V1a+YP9WzP+@U!(6g!ruAI9lYST3VDFwP!BButy zDyz8bQYiLItWV77i)O>_hb$d;yq3=2d&%&7Mg3}M|ffN4QahDJO0Xecmd>S}M zx)8fuxygrp!27RRUga;q%ki;K??~rCEzw*f8~0x=@Co`J&dG+qT+#!HM)MH#RP|_h zU?n_PwyeKn*#_4km-ZuavCJN+rErqhz@NA0Ho}C^muy`AkwiTLR|&>yX2`8`Uwpqm zNuC9H-`H*G*pTZyW6$?%r3{RMJ-hb5EaB%vOTQlTRJBwI7nHD1^678ueyJkzKLebN z3v-YsJ>t3UEr92N@YrsR=vLUgsxFv^`n1&X^Ng>ju=ht?#<4EjgE(g> zQPtHC1q`WY=d-(^H9(GnymSVRdsQA_v}ynwN|&4k;zpnO|se$;R0fJ4^MQ{Zq1doxs< za8KS3E*YKFGPqDG4V&oK>j$ao(FD}PEk|EYrZUWnm?^qbUqrqMYo1{UT@4&tevrPf z+7AJz($&IbkdvKsd9Hn^4br|5Y7Dz4;QHgKOwC!`$5LGPjft=VJT@bTjOT_RD%nkj zRD1z?Hw3+v&)`1Kk3OYmt8qV*5AjuAye>v`B}T|vFmL=(w!Y0Y1o+5xCY1WI$3*@t zJ1n>x-1MmC876QaT`9+gy?r}e@_qGK75lxkx6jPV%P+xXi@)D-+@pBw({{vD>>)Pa zFk|=L@dtkH?X3yAYRHRCY&5z$1<9;;e(>U4Dp!8yOUPI_n3j@9x9lS)da5qJzkL+< ztV!M-{?ZA26TiCYvG?w%?Yb&gIEnk*+E+W*`+({`*`c3%Ltv@S!+Hz#>N;_6b+>a% zK+ncGdINQfG^>ae(#Lb?cQr(^`BcE%`_K}}fpI9kE9kQmF$gkO`s`UI%E5z|a+8uF z2x{(U1g?vhLskCiJNNM%PW9~O87XVzuQq;=C@-G_iE5cw56Y&1xv9DE= zuk<9iZgV}vs3k5FIiCN05ta$4g=Is} z^YhcVN5P^=d;W3}Y|^|q&ubeA%EU*#zsF*3cIlbT5&I0FzqfH@lofE0AYW zm_d}k+X|lxl|w=z#=&UCvsyvu3usYm>Z_S z?dEfq&vdvS<99#vkLFo;p0K~@hrW`=dyfO^oJ+{TP_46G=!aiow?`jxkAaA7O9eIF z@14iKE&BPR|2Wf3B1c7l_$REBH=W19{!PojGqkvm?G3k`UD!A*BnF;5jCnW#-J{>n zNA`kc^i6w7^fPXHJhn}5!*kGp?q)vnp~>k*dkq|r`@tCaAWtd-;=P5Grgf34I^jn% zg*_DAbN4R4U|WV0+}{G7wI*RsMn*HFWDaiqEcLR(^WCL~?Q#5p%P?+VMhA(wAMnwr z_4EJx0tbh@bCJKNDB~3&AT)$~So!Hz*k?e^P2r6V-2fz+7Q7aRT&QLDef9d;3MjYy z_;&_%>@7uo5jV_B8M`hKPhuWvUb(&oPnq8fno4Zd-M$yp%(V6##3@EfEq zocyb;JqKzgEaK0ZaBm6iP5Hlg{;Sc6Os2>DmUHk=!~F+c@U7?U-oG$>-t6iz1(Uf! zW$S+UQ>$+9b{}Xz8a)dh3M{#Y}3_)uE&S(#?7GUlr*fLa53HRApD1CeA$P^118pqujFb}lm$IJEAgS3^AwbggCldPWt%G{8p2 zfw|%t&wsAtpU_YE*&h*@+XgFHRw^skJK@9T_qjBh8sOIC9ooG+2gicEKJqj5!c*rt zgC@Uaa6aKl+j4UfqBW*&PNwUuEp@= z^lSm!82U-6l-hgPSIbI__NZwiz`@AdLp0dCj;ebySJTu85*6ndRz{Fx%XKHw>}fCD ztUVzAnR*uUPfy2&E}`Dmn9Vb~hx>j^T<*4(jDu|R*Vl}yIG3*9w%4Rsf*-$s+<#Po z^YrR7`od-0$86Xnd-8Yzh%PFhcwb)yrA{#(vQY?qr!c(L)xCrvfyb7KxR>r^olWqQ zfo`C$k}~f5vjmp5x89~SdS>(j&!6RyK-3ioj8j=g zK8tYv&{T7iIOat~C2l`im;*U7m(wd(Q0KBLq%QEDf)d+9*AJ!5LanY?KJ6>a^9QbO zFh3l^-dfjs$o(#Oz8fHR==&U){@hIsr)!2*|5f!3FXR<%9~I)o-}ih?V7k}4PAE#T z_r8lhM8S(?y~~b$F!;C9ulIZrSWkT`wJy(wa_(2lArd{1yY=+l(<|jL@}7_xHjVjW zaoxX@I1kf2I^T#-M_r)0bav7J_F3z zcs)+`aqB{Vxt;8*4&HwlHAEi>2cs?~!h%^&+z%{!(8CM)aX;<+x~A49;XK*#VcKsU z@WoO~QW<&pzeB$`CjYF0f3mmlea7?HYccK~cIj!b`0%7se>VjlP+s?CTSFa+s`Y*` z_TWZcsVNxpklT4g<@~pL+`AQ{@{ae?0I;8rj0^i30h1r~)@(>HKa;`mfZw4R25!|* zlAdXXvxa|O+TOu=?}5(W(fv*ku6mlMP-JogcKUdU#nW+m> zdey>?jZK4UtQVsV_CuAYgUD&$&w|uHcKI6#sDBG88a;o|1eX}DMh9}BkH7IR(cN?f zj_<@p@I_(n@>|S6F7nQfsqa73E|`Q?9xiQL^-iF)(z4AwJ_m=^4nC4cPIhA)b(C0J z4(7W~YfGd?!}ziavm^Eoxo9u<-NYQ2+uhf>X=D|^VAtsPi+mBeH^$NrU=TdgFZF3+ zUiD4$xtC|&^rOzs!+8`ruCZZX6OB&{L6&OHt)meMD zH30QiORB&S$`Z)G7BeGwcM6=^>L*Nao}4&tLw}j09CCaU{}Ag=Ko^mxy%72#Ukyq0 znxA9;r_6TD5a+tLH$~fxvR7~)?2mbQ)GLKNK6`2l<6fa*FKQ1<%%L?1j}9qL!S3^W zx0%ARKVVkgDo8HR@8)Oc>>C&_8}b#U*~uT9)Db?|^e4j1;;4mTutjSfP_ z9^)Mku>lA(GVWOYR}Z=J57UD(TY;!1skK>o5vH;~W~<1cK6Ry$DGxt)M4pU_xlFUr z9&j=FD=Tt$6~jYiqK6?U+?K9|%?^rMsrZP(Mlct%VWe@r6&xLIoOrO44-wqb{*;?z zU|(g~N>MWc(^T)*9be&ISMyP&x2Hxy`s)y3#q7hj~2+H1K}fh#b`=Ivu5jJp4FPhMt=U{5PYiE|H!d42peMaKE%jRTPmbdK5`d1CgJg5 z_zC;hjf%CdkEbB-1O0HyBIces!B`IWd(Sci_&nB_h5*9Gn_|@2jwL!N=}=9A`l@U5 zBlO1`-x!g;f(La?Z`}~dH~49>XYRF?nPs*Ys~ss2KP#Z zRGJ@;WA6C#q4nKTkW%^d*R=`n16p}nFQn6;+^C-V-AUxW|L9uM!E?ym2i@E)W4zDX z*F`f5e~08;KZo&j$aGr_{)X{S(?M4VaeJ4q%iiK zTJ6+L8W-S@_d&YDgjryId4tCJCHlQ{Kh|6gR)9uIw{qC92eu~<6!}swgNNt@nbZx; zcUU<#?{nhb>fMiIBzxnK#F%r11vy2vM1{A{{XxBBuZW)#?}O)$nteUvgPf#4-^^ZY z4Zw|O&hKZA%|grG^y?t(_ucg=i)sCh`^z3qUgVpb1Ip}g)2sP&sPm9my{koE{ld@` zRdWw~73X<>Z*Bm%zc-#_7{Ok+?h`)&&n{TzW453rsfN4!U-|_6Q7>mv1(T6{Q00mU zeY7F@ zq;GPYHv~3b40*mi4>8KjE=FHbADFRlO;MVLryK+9BG~h~Lpye0kr{hqy^5=ww^ty` zL{H>3a?7sS=UKjpZ-R&7RoJz$dfcB**eeJaYK0`ea*=83ZuoKi)E~0I zIWYS~W5`Nf4Fc^4m%z9mOmD@(-cjTS5PsVZG?*hp|33|=HN`3>a+6L zMK~<+J$%;YLyG$=j5Y93}J!rpe}!LJ&@LvZnsPojj^JRI@}y}_|L2fFmZLFveE;xkC0 z{m%vG(-^qUdu&{QtLfN>kk@}p`3*`)o9ogrSDhmgC8nQ304|4y+s!T5 z0UEa?uh0?~0msxl-c1+aDpT&RGwOs_FVi2+!ujLw<~l#svq~tLCpDq%t^k4U!sc43 zEJz`2%wO^7gSlaTQdw%u*Nk;d@l{8`sEF|Uz(mZgYVixU%$CiTn#vcl{W#{oBsGk?PjR*_S3-a@(t1N&QZocGe`KYhwZVDU! zLmy|qD~(!n7Do4`+-cIWpO$Q%^RR^g4o#ze+m&_Txwz`4z%>Wb#XpoBjK;xsq(LR! zt`{-}*x1k6cfx(~K z@AaI4L^pwy!+H&HmWonXsAmA=3_OmR<9ua9(-X=0u@cnd%f8Fv{?}-BEizf&ERcK` ztQa4Ky$MRN6Su5@pltsM|7z?Dshiq|8YP1!+huk68k|>7_5A2PJ%sx~j&WO;E<=sz z^<3Uw%<;`x(Xvuv4>0-j^T#4R;Aay1GWvQG?5l>wmo_4w@`Ai5(QG^9n|~IV=AHt^ zwvfomUyBe;dnGbcjR3vWk0?rL=7C99;_P@9p3f8Jvo2rk0^*g_m+EP0a3%h-1@|x9 zbIjY;$)tt(Vds^r%u1-UX1OvgpM!*ylo&~zCeuoWUWI(WgfIZqrCWC_&Nc_DO?mc@%rUq^Jk$G3IRf22aSwf zBABS^wi#T){a_AZmmIKHGADI-Hogn$u;Ke6mnp zCzG`& zMlK1ZqV9SN2j>5j&fdH9qymOnBQ5V^j)&ND-}s5Ce7DsV59p`hU}l}k8ZFts=c1qtH6AOj%YJ6UweYy2GeF~H+!eza1YH3h-bGE}}3uFYx*psjLcZ=>(xw9 zTF|G@b6BrK|1na`t`s>6*9QF4#H`D}X{&;BO?(DyLU*~}g*E_DnrHYit2yA0vC2ENyBxww-?rfJ=I?YP665c<)h6S$W7SW{yLDd0(pLPk4G04;S|NK z^dyRL7#%rzEazhfeB(K|dyr-t9*Kx)?VS4$2G#%Mof$@M-15Jpi(A-lCw?{k>gE#M zlr*W=`-i;w%iP}tNmk%b^hBfua)=$$iuRY$M+?g%eR>shV^pU;&O0jO_p7)WxVAL` z17|cE&S76zFIW|0dD+lYbxwK=Iaaw6l5tGeqM)q*d?(X&+%I_aag`YJG!);EyRkch zeZ(Ps#;oofP;?O`{T$VaIXY)!md}w8Pg$BIAv*~f^`vjVBM0s8OCe>+V7y`NDFUl>A-Xhm;}KxEg>t9eOokU#aG_lf`H@wuF}SM#g{{~gH5pDTs=hGLb&$}$zm*=wutxcong&O03I zz769dBP)e6vP&UlW#=Mg#FJzcQdtR=5sFY|p+X`ViBPueoxS(o<2G-bloEQc_pkSO zj^lj}&vD=P@AtjF=XIW+^XVKY-!PVO=S40!r)aZPEfFRy4Nv_Q!~6I(8iGhR?aCO242g@3!nKM47k7c>;b@f<1` zwL0~<1sbjkzHCLE`_0oe(R}H8m@8LOF#6g7C(Z=Ab24;-mu*zb%-MPPof$b(K7f0y zf%!kW*pITWgkThlzFIjT4!MqIK_X-L2di^k@cxwbyyyV-+$(5@(eq*7bC0m_Dc2-W z^Lr|(rH4Emi_i=Cddnbi#CYu@|0G<|EBhV7H-oxuq3Kj65vZR3rXJOshRD(N1NvMO z(4WFrdTST`Is1icSstPu8Fl->3++V^Js3bcxQag1Gcqnw=2H-U*2>G_Hu8wizWsVZ zyBGR&$vq;g4i4#Yhd2i+dwenpn}}|8G$Nmg zEwspFtGE)Xe@}?Mr(1>-bxm(9E3lW8TB80M#}ZJKUi1A`m;zG6MK>HzPC|@C#Ur`2 zKGb{O=lWOIfuRWfk=L(%L8!}%RP(<Z=;Wp#`8gK zS4tN2ll1J&Vo&FRX7&yL4FZtvc5wu>SAo#Rj<1P9Db7hnOC%3)4@NGYRD<_(n}EI% zdxjA>PaKVq%O${OTXXsz^1CEydZTl0F2J=5IfV~4Yk|;2X%~&}Pd-UqSug(;=+%9b zqyB{eci&$a@kD*$k27_T4?S|lrD#vvt>gT0?%#7}tzu|TyxqDt-wpjHck^hJu}4a% zH>?4;kAkutSoe=V+dWT!$>Y|8ZFAVS)ph*_1?Di=_WLE2_0<8N z_4fuItw9)0yWuTcy9C~Mbj!ZU7DL?nE5E6}Q3$KbH@j1SzGP12IwRCS1vbX^n{pr* zVrk#-)Gh&do=5FwekLHt(yM*Xycnk2p1sj^K_0rGJ5SL>A8ama6E$R)q5N9e7dnMD zh)GbQ*Y!khs;8CvO{~IAdI)<7qP9jkD5pSNGW(>3?-YEwr03k*F$B&$vMjBesH>8%w^q*J zz9nhH(c(fi=zaJ8usucu-c3*?w$y-Op>JNyRy731ZgrPmEr;C@RhJg>eo&6NGv&RA z{W5=#9-Kg*(SN@W1$aeA0DGly(Qqd2n`l0lSga4iP7eFl=W5LB=T^qCZgoT37f;rh ztR_gG*r#Hk5DT5p!wI!5-Wc~%bjrskPmHQPPVNtF=Vgy+8g>E0*$8tG8Se>OYBJPjzv8I;QkaUUt| zruoie5`yHe~HbT1iuW|Q@@R|$6oYbm4`?>a#jD+dGHQHm1NL;nl~Vs9e>~@kN`iST2)#PaO~SPZkz>YEfw;H0ZOdk- zu!{co1>%P_^oOvAJP)EuC2I1bV~Si=+5GuU>DuDFR`O zW?`?FCZPL5owVN@^c~Iyd7ddiz1L77vX!d~Ig0&cr9Ya1_3Zv5Ur8{BxBWexx{3hJ zHm;%LJh(TqPtiK5y$ntUzrxC7`(f}%u#+A34KWjke5D6Q;k!znygSZybk?Wjcjn(i zU8uiWxn3Lcbr)F_vWvk*>+Sspn?u(FsaLk!Y`Uciv|6;;YHD5aV9lqb45GgGLW8U?f7xnBukoS6*2FJu33 zk_(r$AL@EW_xrr&3c$He-f?iC0#tYWl0(QxpzZP}scRl{P_wZcIcK^G8Z<29RrAx} zcwT+KQwioE?rD|nj0{6xl}MRK7xGB7jr28YaNqj-(D~oC+CUrI%$hSW1%toSzcZk& zI-GGUCedRQTpn+p&@x*9l5a)+hEh1MlRB8ZO{>HlArt2WVB9K{pRnmPwFEu)*8T1$}Ovr2M|Y6bd2uTutl zVqT{B<6tXt={!stTD8$vlrL(lCqw=j?mp~AU_m+*wWY8XvP=UXyOGcezdF4u*k>9VUDe@TjIygf12N z(#GBQbk3*4=qi=-Oab!p&G{$`#v8!2j`wL4?uE-LB2N9E12aR{q+pCbndrk2Gd;j<?ZDxC?$bl) z|78kY)pK82fGm$1=NEI+@HAo5#;Um&7*5#A)nfliq3=xW6MQfICF;x`n^=Go^ImhL z`1x>McqLwaeGa(_tXUBf$P;NTbNN%#0XCFFtxl-F{;1&cCw}UOGgp(ND)IUKP^4}p zm4m%3J1c`iXOYvg`t#1cpG#ozSSI>H$tVak$dWux9s=cUg_APFM2P+v`MC1_1kj8g zkk2+71CN?r$%Cllm=4rmKKHo}_Re?*b0Xi0I$!W3rC}`?vvP>XqhDQ8jo~Tz!A9tv zyeBYsyBoUhwkFS>uYkmv)2-d;%cV^G&D;Jrubzxe?xI_ysoUJ7+V-|eMCAtGfdov`vQa(Ppc02DggYjnXW z=$9a^t0`T8BZqEl%v#66(HHNZeT*bR0P%cIGV*a0I5V{VV6KEqfQ0{~))4S2l`?Y3 z)k?1>yCCC7l3(Tu_9)x!^mL(4pQ!XN`wjX|oUf7md`p4+lSb!tOX_*J7GU(Z z;uz|rWxL$6aSkAv1l!?Zi*Pc_;XN7pU3QMp=bn6s`J&TrAAd5z`*_T|@v9H<9`FB# z>n>e7gtHl)JI(kBa*UOACe@tbWvocf(iH+6mXe5*C#!;gceE7v=4PPY=h_+r=JcmJ zf1M=V?gg4a_iG_{#^C(Ni5puP<1qGfr`BGl2`<)6lI#n|?wT6t4}f6}Rg_g} z6Z~_pbXAWfLR{{&71!W0^mhehUm?T2prx^l;2d%m`vi=hU_NC?H1Mlm5fSK9y2XBO zHvx?uPk=#77c}?$_p}#tm9OSrwQufBfVN>rRW|Z<#cytkuq7imDt#?3EvN!wj<1u% zB9C%h_K)lz@nM*)QQJ&HJtNg)D}0i;jQzPJRjI*5=({agucz1uH(t!hvLpYeyT*Cr zlo#p`&PMLlIRE6(=ZF7c7{{Imo~K99SE)8Ed(mhNc^cFYu3R?3zt1Y8^%rxh#1-15 zA=C}y+<0o@39BGh<8iU}P%|i)-vK3wphM%UzzPvvJ3;`NZn2&zrQ_1Nw0;k@2so9m|p6?4spe-5BopN^Zl>J>m zX>-3@>MC+NAFSki{y!(#W@s&@odX#<+mD(@u-~|FLM!582T0HiNz|Z!NP8%tAYN$* zh(|{w?2+gH*L__v8uuMOG&_T)9Sbn3I_+fXJ&QfJw!$7AW0;S2i&k;Zf~1hR^ou?T z(8qq|Vgzz+)H5XX2%-4BsLGqPTVnsXqded1KIFI6+?VAFLymgjfU7Yx&gBM!a=Xvl zAjQh0V+#EyvU*MWO}FZy@!n0%!?nW@K72#&J?23u;x8E6i>Kk7z~=KJ1$jV^c&=;)mg*U+$&Vp_;&X?-wp0zgiPZTaR)^{NK zn1z3?Li5OR7!i(C>4EEX2iW;955RvRkqJ%Y$QkQhr(!$W4-dasjNP}GM8AvESU)53 z)Zhep*qJG)mOFHs>H+qKJi7TqD);}rRRyGjf?Yu1G?`4F!N|&gL4D_epzSX^9 z?cWcYR-z0EQP?+gO6TWMPXVKqiPB4$183s#= zpiXh@ffP@9ep!{Z92iSUxHH{L0fje6$w!{j^N`%9F2SI+`a{|ERzHYsx`;oKY=!1@ zIc?GLA~4PL@<>9xWc|(;RaK@5c+T|lwGDDhMjA<+R&YOBC*U#tCHV`SNKVtrmwcBeS80&zl{#QT&W@Zr zZ->nfu}M%s5tLJjJ)$?H605SVOu_C6M(%g7u%GONkmhBUYT!HWe9mih0oICYQ)d__ zV2S@s3ZM2YWPa%USBKo2Up6~A;FK>Xr&%)I!%!ROQSXo!y@(yZw)@}%e zjzFFI-do{Q8L-@=P0Mh39EL8}%=+cGfxD~X6WQVspplX?+rsbfj4-dzJ8smenA<=3 z>2!j^tE(zRedM#w96e*n{}9+jL*;oVCt+RZ{@tWH%o~c6^*Lf6hA`dX>nyxuVCgo# zakQ}?`w(4Du9c6$u<{gx8TPiX9o764Ix&fT>?^)ms2k@$;?@&A-V8z%OG`_so1vX!XH_o3~#`jEF^H|yK5VDQp&Ce{dvM6u$S^R=yglGQ5CV{hVMS z=`OH3)!4hvx&ob?JRhgf&yjQa-@2^L5=7~}8hr5{`E;Hk*Ch_yf#tsQ9naAxXpkY# zCx>|u`rt?snRhsEb_c||Wldt9Z^z+hM-0e0g_Nsc@AF6VS+DoG=+EZ)N4uY=2TV(S znI(wz5N}mKFkOLuXY1!FCl!a`$e;mj(1$AcNlXsP_&5pw{PMF_*!#dl+mwsiZ3^PI zIrz8Bs(|(r#~JZJTD}VQ8*0^^-pMGuo8$A(X zPhCvC>(v9htITE}l`zM!pU}wgGz%6RZ`nTiSPc5%9D%-^$bl97eJAsN4(jiFA1DHs zV01&<^6TX;C?m*lsoX`KvCYuM0NDKU* zHBeshdd3>(P46#$+`Dcapj&;}MA&x$c&#rO_hGJGl;w?lkzWrqce@9M)D(mG^RsHX z*~6gpBVO_QChBF^W*@n!Oha$#U42f!Zdex?vmmb;fON0d7dIW|pi@JtWCgjY2Uv}n z-r)0{5!&YU;Q;Ek5*K44L~C$9kF{N+Bf#}}pQ`U>sJ}MUarQT&4o)$({TF>8E%Pa54esl9jbv6H8Y{Xt!y~Yd3wwbb?}87l_rAe3vlY> zCJ7TG=INvPDZdmTPuxuQSEXtzT%XCacf=mO@LQ5~A_bp;cgxbs6nz9wCk%wN+K|g@ zbo)y~!x(TISZvRs-WG`bm3;)Hyf zsF*kDo}b{fT}f$z8UZ+nn^!ZD_ZKE-x_sII^)jZzGhrq5pwxX@DER;W+vTevk?LKL z8JMVNjJa^5(U4CZ0%PDk64y`ntQgh}T5sJ&PT|?p&Euok4|r64M_smQ0RpdExeWiA z0B-j)x8MF=h6wx11n03CsQv30)}_=7I;nvl*)WI9ui#2A(mMm5GtYMi&^KV@Q{BN^ zHV6J`56SXzo?N)YS1(Ck0lKbNv^g<<<$Khih%Oy@t{-;JGsjJXJO88CUD%VPzFpe- z4D)ZVW3NV!b$o!W6UvSzDl>4t;$07aau2wyvzo^S%)yoWujWplL>_&J=5oX)@>jlm z5@uGK2d^`1Lu8T7ILD7M5=0*Ym){Og3GQ=~$gln${qhwA6M`B%KF~Pv;0J_M-h$*2_Ir3SmFkrDD_3w?o)ZboHBu)RKKp@14KH zUt5(|E9j4jcw)c7iTR;?#`zO_V#sv~v}x{wRk&3#=-EiQ1Wbv4Bw{fSdZ3`rZNOsz z>@ObqYlXVyHrX+yaTCmy95JE{M6OuX1CbU6ugY#;ja=TlzMxSB!w(Vr6~yxs6V?UHQ7!Vp+L`sDn? ztpbcPX7v|ZN}=3Uk?<*R0s@8lwmmN5b8fq>5RUy>qV(oHBz1jo#23!QYfZvA>GYsW ze`ml758dl~1K#VXtO zX9#-$l&rJ!(8nPieC{~!Dt?bw^o~8b)CI)+Qm6JmMEF+O!6K}?0yG}Y!3Ublz%N4C zOTc~+PI12VUPGTOg?#tT*9)`gOA#=CF+Tx6?zSbWUm}8S{oc7tUdUA}k(G3^ngR3c zo}vZl7p1(Yl#p$VytD$MDlh6ym#ke3)Q_Q`y(Xh>gmfC_w_?X=dx)T5@@^u}7Ttd7I|+{^9bJCW_5xF3~S(0YQc%$$nW$UCVY8Rf_d`t~-OV599vz1va~-2TI#SpByLE|HYobF1lw;gd7`w{fq@Mf*kK z&+930oM}C><1+z++fl=Vc>m<6-I-BC?*BLD!Y%tBi{QtoymX+X7BV8EVj6^Nun&qg zIKF=z*hOPhXkvQcLSg5@hh#Od_s0E^l}i<5n;4164mQB`JFYLvX9jT(E5CX!eH;!s zMjT!Bc_L=8fR*JucYa`!I9K{|NHx zvi_U;=dcK2ue2v}0tcY7MI~8odlBkiyq&D3S%gZ!UvW7Q=qvRD5yrYiB#mHTcnAkm!P$Z`u5PIWr))efgQ{7d&sH`286QaL;z7 z`X04b3sebg&I!ImfAP%Y#tY01|qBM#KV*LBzLoR|XB#qJlzX%%48 zlk(9M`Gq_@ad!VsuEK3Dg&keIUkQ`yQvN``1cmCgSI1EoBU!y^W4JK~VN<;A%9y+Q znV&ppRyG6L1(qW9+=rGRi?7c;e`Xn8J{{J(fVq_`I={=5nvm0!<w#dA27~ z-Sc1^Qla69_okC=x-*rSAF+*B6K?aKfgjHgTr}|Rh2oxZ)w+yI5TxyNBGMs8DVy0= zDzzHOzEVefXmx}2`f2-AZsdt|tyBkKuEJZ-CcOdoyWQ?HWo5|K_-1;fjO=;`82nIJ zzd_OkJsVWl2t0GB_dcFpT3LagdralQUK7A9a$(w5dI@L^n9EvAmtd^&lgMKN_Sd^S z%DwVp7W=Q3D!P=1ppUv{jd3y#hWB|Mje52WCXEW)hyIMiUQNWrYl|7EWUVEP)b~J^ zBBf%^D9%}BJISv!zC(4_yX0R&xj+@`;9};D`*aSwhC{x!aJ=)dv+F)0@^^lzKcO!K zIXjIjvD*Y#mA4)|{NDg5#vPOW&l~w8J-kMoasU4vC!gn2#l38<%lqKoB}ge}N&Yq6 z4jxCcpA<9B!RZUDXX7O&K!7FW$`1O^Lj>o{`|*2nxgRVM8QBGwv(~l~>?=Xp{KwIg zI5)M&sr|~td|Xn~3)R)CIuMuf5tw06*L$hMV~&J2Zt{|Jne7{ee{1~I5@81z2(!;S##u5OxBHD9K!zf z;?(rVukkstcO|EAJKqE9H)!u%okV}xnC4FWU=E0_iAU?J*MUt`qRi{=A>bnGj(>ft z8$^ChthFJ3i7zXA^wqB^=>4#a6G6Yzj3jPZ>#>I}Fkwtyh395d@ zV(+t0Dp~UZyywS_=oueW>Oub;uRXg&9vq73V9>?9C7KWelPsZV?WdX--mgID@>^s?(VG?TqU^!TP+qM z|2kHo_ZpwR4dxGIYh%aSwviWU7;-rSbCpp$U3YT4a^ZdYYU$tr>f=|VBuMtp!>*oB z0I5O;@Gm{M{}^*g)dyk&<*?t(??F4itWW}!u+xyyZGXd@hAHW{uh<9a(2=qq{iZZG z7%nTm$pyU~Kl`ZrBamK_ok`=k2u|ZhhZN^fUt4?ld`b=P<+kfSKkwomLFGsMj_^~6 z&W$;zv4GsOqN&JR5sOfs_h8zhwgL{A<%YLno>M;Yh@d8Na1*JlZjX;IV{UGmE9^=W z+)GU2es7Mx@U2){;q4L__GjF`(3=g_O;y}F@}+WTFjr$$4tR%^w zM0oS&r_z6sEug=k&~%Qh9s*wq-44g+m63_UjoOR=({)9*#JVN8etGa1h>pSQzm5HY zlHD*@dYd~UcpQWbO)H!y%R!)R+xNK1GQ2puT<%;)1l7$;p=roz|6&!X$YQz-imod> zH0MzV<9|TnfOA=fF9mu&TcFfz{bouW`l2pyxW|*C?{U=9FR}vt->04YO9}ReaCaSs0cVk<9&3fdqIt*RV5Vqnh|nlxI5B9_bz>f^<9TuYOe-*ET;Z!^{tlfRN6da^qL1&v z%xN{`#2P9WoUlH&0*N=)_w}_8f^7UjUNYtun9TEP)v#UwHyRnQSSrjNzWdPZe;#=z zrf;PhpVdIxTSlHA_#WThIB+-=^Juf|gZsH1Gr^La+N~PjyA~wp9c0vIfUsh?u=$|^ z4E=Atx@(XAeY4)pO`1%gH#{mUaI*>?ojh>c>UkcxvPC52Ej7bwBeG@cnOP8*tF!y> zunY9dl_r10z5%}_q5L^QCU~&B^|GUm{8L%mJhEU0K1hiBtYPn1;-zlij<++=W1J#m zzk>5WD;rHYa)bFe$yCoh9e|GNtMDrw`(EityytMQ{5IN4gAx7G#Ir3;s>$8(ir;u| z{1W;C5C5?f!xFn7`tvzl;0}KlP;t9H&yi^Pb#h70w;PhE_!>UlxHsg-$4DB_8xM8lxUl*T9P> z^t~55N077ENGi;i3sy&LRo(@z!m)aidY(JTk9mEFAQ6K6@#y3x%D3nn7GQ}c9UZ}( z@l3P6753G<7&>sRa20eia;Lt0>;S&vQ>5yc=NM;vmZ6QkBQ!#*W~WvMK|9)kcdc&{ znglaF^mUQzo?IdS?^Y+U@BehsdkN1Q()PAgUVVBZ_Z`tB6MnP{+<98#*vBp8>#R{(BJk& zP%T8|DZLMD%LdVbstty#!w|?Pc3|=r`sSTjNK-|}aSr*rY=nN-c+dR z^t+;dGr6r(hTIbq?b2x4)=7BsN5)cDnh2LqO*+_wBWIs=X355)3UYHTwu$aU)ElzS zuy{{Gfv;9$u;DZ;N3l`UmmrtQl<@oKKs-=zB!*FmR0Crt<+i?h7Kk~YT07d=29j** zO})G5mpoI~TcHGX~n`S={LQ|%d)x#RyHX6wn;MSp#X zH9_!X3-GR<)OUzzga^Z!!VD{eFg%$LmuBfZ((Tw%Gfw z^?l@MSgIe$+ay*mquZ0uxw^C0N%7|`t705)lrmk$R`gZN!nF+V(qW+w{m-ZM-=N!jCkeY+vtM;Z^8 zpB{(C5I>TEGW?vgZ%y=U%|j1YK({LD26;Nt7TtV{&^$DI@LU}7`#IYxohV{pG5xJX zo6#H?-wvr`?H+^VhnCkIRVF}lJoG{v?%`*O{{{>p&nvX*3`|htbNBhwjLI5$al zJe~pjEEg|Zw=>}RXX523p@I2t$30JfuX0d(D@%LwAo5HkKU)ahs)7^?MW0Y9zWDv-VQJ*XaH+g86`lcha;D5U3*>x8FwJcweuCd( zW-I^K4N{l0+$FD;V&6*NO+{h6_qlf8tUEUbriXku4-jg>{e`#n_?ZsSkLo#k2=7m| zY9`H=qqE2%xqLJj^G%O9;%{EM)D59g(!AmS@3$!zDK_074P&RM&pZ>xb8ErbIQ>fw zSf?>Z11Sp+8li&gH$=jym1oaaLBfltBnFNMZef`hrpPPfodPd@tNBjbFw5 z2sQhG-K2&pcv!3%CzQ4fTDHAkG_j9Zx>uql?fDAu^Qyb<&dfnli#9R*U>c;o{B!&u zo?DG)w|&Ys@m> zCSi$tBAN$$x8xRzVV3d)hxpQGxIsV7V{l;>>|2EEEHepE>*UIR3G)o85|vHgZ%o7A z8IJ^MzAO;_Jd#9?bN1Q$o{xNAc7c9=Ua?)oSJ>Gf=DLAC&+)`VSK356p;WtRjSuxj zo40k|r_q05_$lW$<3<~VuC-T+boYU*)U)D%1MT4Yg@s3$7jt|bcQhJM|FQ%xk#7de z(DX&evzi6_u3AqN%;Ef3&;74X_y5-B!QY#Pz0XVW$G!0MSjDgG z67(}m+!c<%eLvGQ<#{`A>{-jt{W)8TTr~E`#a`Yjpg9|>we3^_Ata){X@^EY<>JUM z9>y6kZcE{d_nk)HWk`ZW(-5@u$)wbJV($y*`P`!QanLuBp1;x-4~AE$n1}8)gVvnG zzE-JmNTa_nmzj&c`Qw(ssyo9#$CrGIabF*tqJHgRyEcXSl(iSFspH_gD{VQ2Jt|R# zDnhq|FlS+_-*a|n3itBcdzX-7w$J+B((Dou94A5!cO$nYgQUZW5p@D$+xg`fnl2bk zw^hNnlgIRRn$p}PG*lSK>DR|?|pmWpuC!^YtX#{Mj?rsi^y?fev#(xa8|dEh_qa5~ZK6KFsEtxfr| z8ze7EaOhMv!D{YoQ0tgg1Ploa87dA9npcux+P$)}eq_@UoU>Qh2Q@FWBY9P@s3 zc^)bVnP>01B0o>rozAIl1caBa&$*?HLE1T%>O=+XU*FnEbd8w>YoSwBO{i}dzvLO$ zHfe@k;$<;U+>2@N+k0JZ*az(xlsIyH0Wz0|-QxW_;5E;OmeSc}Fcgp(kTUgxy23j% zZU)ovP^(j1qjtjdclbFCk*n{VxOoowC_e{D`$dT>@Q?Nz z`6baVctHHS)h2`bFqJ<`&vq-oNyY8==y!^cyLFuh_wAG<762aFN5 zKmL^<|D9(xH44wUqjF{U4x!7e&!V4XuU8;1WA4nY4}~z5^NV-wdpRsx87lT6e>~f#`ts}aO1SVO=l+g& zJLI_Dy{`A&9<25q2&2W!&cWgV{V?>Q@qVb%jK-Y(X9|@web@^d{oBA|hj|KAixRH5 zQ{!Cj*uc@MLja$TzApsuUhPFX@RzXF2A^9Aqr=|(-lrTCw4%8k3(FyTqh_77v5UBI1L-z1v!hR*aH<(OW)j$yq+@! zk2?~PyUU^P>b4aM;gRkM`wA<-y`k@g(Bpo{KV9m7?nxT((l^*x`L~0wRtZUzA`v!o zt_(}E62V*MMf9-@yq_25oV7TFzGUkH4uvxdaMpG{HYyAEy{FelzJ6JP5=v6q&kcR> zCh^SHFWd`J9JL{`mN$ZP%2fp==2ocP7jY{09r`It1tNvSdf~sPe#3?m*vr7~cH$28 zB)ANSxD!p5z)2wRS|9383Z(g`PjfUv<#DF_a_bYo_S9dhxgYtl{9}%yn0Mf8PfR|4 zvjKXN6e|NM=YZ~_-`PO62&m+KZW5F;3tFFjXnh4U!#Gm4g^bE4*;uKy`7 zqvaH&+n+vBq)7n1;!hij=wJLYYapoN+zHMT!L^KkmSBsUd~*)}J(6D!uL@qmxwC+2 zKYMl|m>CtHHV!EQaq+&?$!+u*jQPLfT^)fY0Wz&D++Q@SrivWl!Ca8HWz}=FeE3@+ z+W50%7ie<8p*e@qa}l3!+I=h4w_3q^ z#s7McECF1lsaSncuaVSnlg`8ExM}p(C!Nq4`1vegvJ-PdvfJWx5*?Vgym`%LOs@w# zr|I3lpikWN9PiQRsMFsiUb#cvSpjb;{>DGK)daW5hJVm#&Vcxf;m<~Gc<#LT_nxn3 z1d303>8as;eoK0dsvGkk8-F71P^I8}Mei9TwBiyW;m-fVneiI)fhOOx`XWK*Djwy=dZ z7xVqacJ80K+u+0E4g1$zW3W%gGH*D#2i#KciT-g${ot0^6GFujh$_eMh9I9vr*-cq zOW82+Y-nA15!(ri8XV$Bzm>pc*D6hBan#Aa9(l#It zPks*~_)=#Cxw$SNm+Q@&gY7-=v}r&^8Ta{Oma7#P4d#Flqo6jjgT2h>=h~0#5Ml6? z(SNdJIM0#C#04Tpo{+St8ixK;u}0CmMOo<2jw;LE+qVjbW*>8}y_^Qm8#SWj$Wx(c zezt6)T?c2+RE$lxPs1f2K9>E8qtIj}gTXfHdGBV|4c0hQvtFJ+b?P&M^w z;Hxh9HWTmt@hbY(G|qH$>R|r%YsL>o{GJZ>JY2Tj--jF`Qj;E;UeE}3mFkbfybjM_ z2g!@Gu%+o1wD-FgCQTC4m3q*>S{|Rg{Tb&G@!ktHzp(G-jZ)wK9PGb&XQy4FRttZa zzdUJqi<~;FrHJoBp36J=2U~!>RxZ?EW>|23yivHaKGg=7ev(YLTP(wBM`QdT@&O3- zuUM2FaGu_1{FwK+59iQ#nbK<&pu@;JawKR9Xtf`&k~%HHO|_Sfh3}_;e$vzXEj#9_ z2A@A>`dSJa|Ar?hqC3Gp$VWaM&%vCpjqnuva3;M=oU*VVAx3n*GUXcbIR=g~JKgUG z*NH1!oENGfNAlOggKAg!PvW7H32h9prus{JFHe9wLvnjg!8qn7?tY{K{Jt||Q#=ph z-+kbC+P=OG1mmJPh0f=DISco0y*?j< zI;_vAQs2+w74Tcl z{+9&yzb_JP-y^rILG0!GraAchg3o{fbFEJzX_^AiA16>iH#CKL=4Xd_KE=o4`E93q z+X{JD>Wu%L*Bu!HRozzU`}W;HnU*2SK|Ti))4BQ4WteC0Tu$ zT$EpA|NKsbx5J~ncoLb3PwQC0UI6LQ;DC$EU{l4LA}%)v&tKl(?~gtL=I9(7 z7Q;ahcWbT+KjR4Wq?&rR=s#!Uym(@b9rt@wmWMJ|I>Br%;0u*g7u1ry)$1Z1!#*#W zMhgbykZv*M>1!c(jXKe}u=FhmefiCKFQOQ-FZxu5UB#Ys$%gRz*O3#lU(ZHkx*MEG z@K01l4~UIRM8x8Kpd@`Z;rQk#Y%~nyEyz!Uv;TRGW!&@Wd;OR;YEJ>0 zi}8-4L8aISbf?>fy9jQ0WrL3h;dC zNMQPr!ZHCmtDS0ngmRs}k22H?W4*T=ocwdV>`TXrW z>^YeosM>TEYlP)H8^4~OLf*w8uC#~BxL*<-bGjoo5BsQ&#)-WjgL~Dg0zZOQpu|eE z;|cygDa7anLj>x8YG{JP4d>ITSbpQ<3fLR-a7v8%9rlvUDhKsHEQEo6^V-LFAE-?= zjncIlhFlHS8CT5RR%h<)oh{D>bB{guSE##k^sFzK{>2_|fxo+~spZf(Z==^TjJ?wK ztx*g3yn8d#4&}x4!Sq+gNnMvIs2#cddH&51G{t{S)(u7!X*$XkvQoTnld+{Fj?NX;S=93o({iQM% z;RC6_`LHtdt6uBfr(29Y$6u{R)Z-2;Qsb;=%Ph@S6;% zKX#o0|6`XKs6R}>&o|ulrZ$+1u6 zx^~x$YB78f)?v8z1v%~q8u&YM$047LNY$j%3Ot&u4Ju(na66qqYB4$q#|H#nlG0;e z8Pz_~xBq$}KT%U8D>M!M{VrzP*y}()$?uoet%NC1C9%s zjC3NmWJ^cU(y(V1k`CrC%&4{tNA5zf=!%P0OSA}9BfMcpGG^cU&rM~8pKbLst@ z9#$e2b?uL3OJNKou|C;~lv;$> z5>rNYCy)~+S;A-CKLnMX4342&=y(0ZboiP}H~i|kmq~frq%;U#o4f5_s;Yr>%atL1Kl%!a<95RE z{Y2s0M5{}_3f}S_?MeNsFgW!7C(YJ4*kqWUSdHlhlVhFFqczcoWhfn_Wibm`1&1d^ zt}cU{yA|C=7W&{ep$yDIEN?~C6j)?=gdly1SZ;tf9PW+W{m1`?--0W#cb|m&I zSt=8x8k&LWSSn%v1m;)$+XVWpu|H?uug6W(9iVJ6p=5_S!`>5Bfsb$=oZ@vnWYkCm zpVuVgKaKEx8uaGP&7WNmSoZS0EA~}tUpP{FBe@?Q%nPz;k1c_x*_^bU<`Sr{o+NqD zh&*HME82{4xZj{W8lcWH2ret$4^nV%XWSWG>icmDtUQ@E5b;d^9mceLUh32m+XzF?Z^5d`O{o`WB3X*{?pR@ z^nMv~j&Yu4Z*c@0^MvkiBQsFao$MF*p%_l=B* z?1r&F#+tJFA3yF9Vn)Sz`||M~yfCjYY`*|e2Y&rnTkivJv+`@rM@q5xu-@eb`a#8o zbP1(Q*x#(w%W*(_9CXre_R!s$0ul}5H}$eBpr4t1+jJWBCOz@%Z@FtAF;h|c`%41E z@0yGDF}K6oU&_BMI436N#aMpJ#kutEAA3`hukh;fq(I%}MX((6{H6S72FU(!jJGS! zLk-;l`+y#NKYORWiJ4h~N0Dvs73=a~S2u`J{sQtK1-8hPntFllb@1Oe;XYs{6~oG8 z-VZtR9J6P1%OL;PbB%cCdB|I8RWQRjUQXbspc_j$^z;gpG`CH`{ReN)OX26|ear7_ z{FOY2NiV-p+A<35Q(sh!ZXkbvJNxIe`Bh*~>m0Mo?+1f&_m8TZDpkH z^o)n{8_X$&(Y`{?3;#utcdcxR&`C2romV&s&bgBY@)arY(Z!xP+ur~!Q3?H)({r%# z`)09$D$cVaNouP5(eJO>duR&tq)z64NGcPN?;Tzqd)bNzE9!zzdt|U*GUEP^0P87m zlOz%T%|S%zm3-fSUx~0q_cTLD4fE6)6<=Ay2rxW#_9)k0KCnBe8eM+12xc7)`9m4s z!N%?c3mwBC3_R%Xi1uBAuAp>^p0#Qix9qwv=rRc_E)Q-w*;PYrvVkQN>JP4qKFid| zM;VwdrTav_437*APHZP;L4LF9*t80M4wq`pzZnm}#JJ$>6!Iwj#%g(=eMBCr?2YNP ztu9DRlRI~ZW(9(G?=PP5$9tFcsb|L)7GaS(v7kJ21`J*n-x4uL9eqWdtQCDT2K@!P z!w<(HLD)jf;{nc*k?ME!j8{Rw&-%60%{aJw+boAvCmsSye&0;PT$4!C8{fi^X*iqT zN&$P_KyYa*dVyTN6DsrL`KXi2b+pmTo#}@~gPA9q{VNc4^HwkK_bH%QBU`b^ss@LM zY1)qOP1w^`VMK75g@S8Ue(BGU-^RCX{+bqjK^@FBe7J|TWrbX;7q3X~Okoe^ zi(;1)^vV3VnQ*PHX%xiBMB)~Z+q`FDo<}EH2Q))U&l+;k_X{pIXV70`aFIvm!rv+I zswh|6(?UP)3+7|9A$T8cjGz4awF^qBCBwg{4uWsbVyI6k?(IwHQ?7bcfl|R&74_5+ z@R+gdNm;jF{uS=LfTaRvPAfqm8;uw6NgyF zuHxQtw5n9_K>sMv$x{2Jvy4Ibh1-U&hwEXuF7UaU4{|Bw+XWjOQ1{F2G7ZK#&aR-p zcU={GC!|%VKQUn5lX86iJjDoj8xkM6;M@ViHj6?z3teUtG04Amdk zA6Uwk{g0yaj>qzC!+2${tZb5BWOpVxUD$M=9A1a^MGst%yq(z>0OISV0wIE~p7KEboJTBai%n6L0S zzGl^fxhR?QOs27TzvX)+oW!3EW8_A+`s&a(7av|ai2iT)|K@1~#0KHTpzi65w~=#E zAS#f#Hvl=KWnX2G$GlMScVzZt79=L~(c9Uq zfFiNB<6X{L5Vy}wzS>g@VuZ`3BPE!#r4BuO2=lZLCx~f7v6t&VnUgm@cw;{}Q+nuH z$N<~|A??!sVJKVET%S|J_nOY|&fTRY5TN_(I5JOw{@Re@0^Ui;x!vYcg}o)aC%%!~ z>FI<|3}jy$?ApOpaVn;Pwi^0WS?b@SkJA00Am6JI+*6OtFCPqR1UJ==vwv{junc6? zP{4h*;dP6$d5>(6iK3PA4f_sGP4^6G3XmuIRdu1PaS0B+Q`PMAoP;m+6O{weD=?V*aP{40X(B0j0*$j<{C}W4gYo(gaN1 ziP0ZJdm;Hozx+%4UbvMXq7hRx4W(>9c0DjJ(KAa%NiEa@&okb+>|REl^KzPMq+}&f zYS~ttv5mWVe7#LzE7I;wK5i$@f^%B6`%J+YYSgtvAS;_!=8^qG| z&d_^+Iyv8vI_~r)WTIFx;{%2DxARW#RAX<;hxSUV+C3otE zCui?4+w^1ZbIXS5CvuF2?bI8qhOr;FV35UdYX;aGTNBF&70_w7D5ce13{=ZLO|^Cd zFx#3I)x0+Ycit*qq(om#;H2QJJ##BG4bh)6rNNwKJ?Z5)@>4*1*zpzjk20v@GfIrW z{6>evj*WwTIq*}5p4BvH0fwwkH}|NUz+6K(oge+XJ7lr0DL&Xg5jEWt-H!gm@A)=2 zaeowXxkNQubP{A1?$!}kW1h06&haSj9Y~7FO4eQ=KkC1tA0JOFz?Y#YX=&X5|0N0Y zo!&?O7fC>p;L#P39dPP0$2}))P-(@iL^teBUCKTlQx0kcBwH6>bR#GCnt9a$^r;(Z zzKK5H0zD>|#Pp_9L1>y>z2Vvfq*YmDmku<+gy^Wv!H5yiJ`gGtmfi#o$33}^8`Qyf zvJnwl?8$X&PHf{omJF98TX8z#yf~HW}WZ zKHEE8lr@`#L7hLIOW0fT>HT4P2IQHI#f27yA_v23Nx6g+In&RcIW;w5?v-(Sno|pV zN)8bZ@*b6L1YLFQhLLX6e|2aUn{f`F=-FT$$NSLTUl+bu2egBTnh22~eKk;ByHKus zwis&5U!7Bz9fx1hW7pvjaw>!>h5*$0U$Tx6{c4BefOo!%}|8A@!C$iRA zG=C2Lb6UaCN{a)?U4LAivtBs_9VA%>R`^_O%iJgv(iwz$`%BcNSB4>tI=R9)wgIk$ zXbSww$cN+vmX~%hC2;sx*4|mJN)Ss@9@dP-oTFBO>jm}};J0jL&!w&c`)al?Q|Obs z)gl-rgy*-1)%lp7Rm|~kg=Cld4Z*%LfvrKZ13bSvbsyqf0@hIFey1kvOW%me6@9q? z><$KhUs|ld&OQG34cK3?ez`MS_5<>JS|w_3At$<9!2ZL)>v^~<(QxS8`B6|MXbuqa zm*Db^+mQoXsHk}{%*nZ(V_947fQ;^TcT;|Es(Sv+0`Ove=w3MEg1gdSEFGjCdL&xBnFC{a+uMm5dHvVFy@!3{QGCa)$_>C;0Bgpc-~{x% zOWE-6mK185TXpKFhS1KcHr)7%vGG*+^ZG9T=o8AS&t^nT~O=k+|a5;Ui9eO4t?AY z70v63+2Z@x->}d%@Z$uiCLQh~j4Z>EE2gnCMoOj|_gr+NAE;nB0W4^ZCY zT6e`9(N>{vGTz?{vY8_3Z}&p<0a1r9SIVG;fme|sx&~CPCOHLR9{}0szY)jY&%n*^ z=9@Qk+TcUboUlhW<{LNy&XADA!igu(C%URI=SuZ?xqt?H7TMy9d*1Y5@8wgKV!t`; zd1R^EBgGtmkeUBf9Ok!bm8Zy%_s9H|%eGu>4tdGmrC&<%y=J{OGln|)Gn;73yUr0H z8&)2`%d`wK7FJ>zjSb*Z9L-1Z=tS$P@o?$01Z(OEbg%14gKAw`*2=nrsxva!rdK8#$? ztw#sY2f;6MnX&Xm6&xP;FWn?y4hm|IOWQx|16T8ZVKJjapdVo{VKRh0Mn`rAzb$=( zuQfqU4}1uiH@I<4$e;_JI=qq+`Gx+>m$%I1i$;M+?%=_V*KOFRr6VPCvkkoGrlq}7 z>LFkDcLZBH-k-HZYOm&E-|=FN%H$d3%U`MGt!f#7mK#JVH}U*|c@;TD#R*smljHa2 zKn_!SNOR8n2r!$SNmGwNe?lI!Jgs~+$cxE5V%6*gO1Ept+!NUIAk}c_&1x>#90}WF zx14nceAeH*TGKvY?Al1dMI$}-g@ zKLm|}eo>)@I{KmwhfSmn(Kpdrd1Aqk7rB~051O;%zVeO*^~?lvIr!4z&R?bJhx-fm zG@WVaC$@FLfhQ6Bl0!8(_j-VhEwd$9AAMH`&uZK&8iVo7cZhtOfJ-yNp1&fdu^-$s z{Q~O3N*>YOmgQ~xPr5F0)GEYBFJJX7DX7!VYU4(dCD zFN&?)&_|i(b=Lp=fhpL6YaoDn@jUShK_$`#2#OIE+ehB*?pJb+;Cb||)%C>>ZO($| zcGI`FX_H|3UDy6jVKZF)=+gbcbp@Uo9o9aJ{P@TFU(cx1PXl8c-^_4I9@I`P2AAuP zLuisnI#GEyy!sKIr-fY8bMK6~sj!EDp{noH#%?3bUahu?AIF^P3WJ+aBJMkf|HbkM zj6(*;l9Z#(3~&l7tFK`GCMWRhzQGdqo@wySoY0;J@}g3QBJ?HIt_6v;>fqk*Imw65 zpM!z1H@)#6>QOe)BXb91;=xpVNQ(e|BfVH-urh+yQ$aC4(30&{y!N;2g!NF!Z^o9X_*j5BKpS z;;Aa4ZD4*p`04>3?46;V7L56f{0W2gkqrATNLkKP@qM`jGbO_fp9`_~ly39!H{^K~ z_2~f`pxY_Bk0TbIzLb2gM7cj)YC&`L*ReD)K_C3^}WlRO>_y^ z$IKGhYl`=?lV+Q+dJMTr%~^v=TVv35hGP97>LzB=8r!0|3-EJ8AtPP57ddZH0b!m? z;A;0;W+DxH7XBX3{j{Um_pbT-6e0iJtFC}{ zq!RWo@e&m<#G2RQI>>9DP{Sn0*O*1CnIzUlc#a{8FF| z^Rr1ykobPsDj5AlRfpDJQ(Tz_g4&40_4EDUR95ayg`5Si#|*hcnD;JV4CYPH$KL5- zV}bwYW`3|;8MG|x2BEv3%9AsOpih_TMlbrCj*^@!PPMEDxTaM9C88TD25l3gwj1Eg zqoc+L_3+mV^`$Qh&%(gqyDZHdCy-NK71o0}^nqXLB}V`K&HAgN{SQ{)-!(SvPp=5L z{+P>s_RtUBl*yBIhSvgZ$m27d!pH}@pnY;RAA5*M_Piz~n_&{SwawFP*5hb8sb zrr`nnQDovVa8K;&;vToo;H?hZ)me9CA8`coCBr#NPz@+pY1BM0nU@28@R zws z?LyyWkLKiQFXC}H7VBu3ZGxPS%i{%Os5^VgTMr*ypM{H$6*PJ~7vSI@w+6{9%xm3w zobpMf6i5Qn1hT6qKw&}b$uQ;)U4Q<%kock?x!~`(@cIJIG(NnPB%gYaz zTtZ!;iKq>IP5wvzK0FXG0Tu1qZw$K{LHuIy5hLCh*yO9( zzqMKL>WD3Ond<@r1>suhiCzd|vAu0pI{^*XLvvJde(MfST%VYqLk?h7!U}RV*uN@7 z{9$#6(iBemxc3wAI*c)2&8`DNl_nl7T4PQ^+2+_iifWv1eV(3cMP1{htK3KIoAJpw zwq30@0u{7se%>C%kzfIgI5t!C1FY%H@`fRYk29x;_*Fl0 zKf9V%UQIxd=zomS26zv6kW|=wW&!%Yy!#=6b6BpnX^%VlZbFn?8jf?lhbM&KP-4^% zh^8WmHD^1pPwhp+`spF~cFaVT2zg2zTV}m(C8(?J)l61BssW}4?B-Ofm@B;0IkkyB z@Q)Afxm_T~Ieo^oINGNL->3STv6x?WjMwqpKp%toM~0?1j4N*JsH!0#w$P3>cnHi4 z|MN@nEQa&O>C#L1eW3rz5x|7cf7T(wM7nG{2weT>FNJ&(%LGNnJrC?-spr2?BG?Eq z7P|)SadV*TBEFP_=Stb5-S0JI=(`IM(D%^p1I6rQBGsd#aI1FsftBVWBpt2S{chO_ z*KO`dQQFRfLY?T>$z9}WY*b0T&KbuXTANnWjYXg&J^uU_`d%E}F3j9JHU#g|*I2_R zW~T@cPhDRk`FK1Vp?JVovJ@#=>J0C%zV7|1-{uDdaj{dXo@iX^=Ft77)hgfC1 z6?OxILzkZqLkWN2%UR@N1Xf>;zh*uQL_f=QsKd}VoIG`M4)bHosqZD%g3}>_TB^-q z1%1};J{6zmW`Mr*DLdys0#LTU-`Yg(P!BDCb`|b8J4>pnP?=c7F}I zAbd6JVy~NkZEcb{Xl)Wc-Sgg}%qL(Ug6BP@D}%uFWQ9B@9CiI?C)JXUN5gOCqCN^8 zV=Rv+^ z^H<)*uL}_nb$`IZyMGRn8GJk@6Oh~NEzi#6(+?+ij)yXtW8b~V+j9p{51-$a9VVA) z!Ja#jT>FA$XkjfSv5IMd)eD`Odg!O-iE6c$%Ik%(PK~ldI9Hn86mB(olm}tm#HEe6 zfArok=RS%(W&FM3F~Zu5aLrq4)W{pTd!%QSMmO=C*yvpOSBw0|`!e2fE$9RFd-^dM zeMh${UO5w|&qGBgvGp|a?@UWPIt7vE7(PCgeC-F`4|At=4kG6(dEkv@8v78q?%9~V z_&or|$0TNLs}dn$^0Z;}QXAOF4qq%}O@){Ld374$-qAy<%D&)1VT_5b*DaYKcej!=t9n|0a54e#&=)&Bh1egASTF_wl zC{r-j4m?xJbfvRx(64{|Ff$i&HhDH&wIt@C)Vz3PzHt)fYNmb*I%B_U5v@+wu3Bp0a|@#dhQkO3_?v_8SKE zM=9w?;}e16$V9?p$ec=>NX`XT->S5kUxB<-jrXS5k52XQ zS}fI@}4oN%M_w1#T0Ki?w1uji={u;N`1hz@fKKsg*eg z-)QKM`;ZR-b&i7UnmmVh3G(4cr!Gi{O8%H77watV|7W*7@W|`Qw{pI0#XWN zT<^88U*0|{UnnLW)NdIdBP=h%?-Byh#i1VLv3vczkQ|M^Fz@QiJ<~8hv{8Gvpc-ti zD2Sin=z_pT@$wDg2G9x<4^fYTxI4#Ki+l|H zV^Gov+eZEw=dQz%dgS~1-H=M4?*}&3UfN547h%fr`qWJ^>^l{7$`BhL0~VILHVxd1 z$KJJ~(5e}S@ngrRH@?-w?>7UxzNnwh)E9*Qx`%r*wf3ii`9l!6N+)yGyao1O2J;Ky zzRFF3t-R174#>CAONCCqi`TiSa<^*6B{xIdlP6Cmz}OG9TKENpbZnH6_O zWz0Eq@6nid?#}}8U5TP=Q+O|EdPd*jiTy-W%$KTknqh&pIHl-4{=OKO)1T7@LA}Mk zs+%VjqFYJ5WUyb5GSk9^dS?tOCQo0ygS_jG5m~Pn$nDX|W@vq`JPZao%_fT2Yop-a zl=ZNR0K?pyw2F97mjCzvWo8pu3!#*XD8%z*-8GbMn15c*!dwtxoB7l zZuVr?@PngM!EddQt1|H=J*bmV4BmRXJcZcrOR+#kb4Yd)gqO9WUwrZd-aj7+B=N}Q zVcUD2k&0Z}6^Y+l$m8)|mlz#JZa8D@?<(!RY zFkI5%aJr9k@G4#03%gFRRjG55UhaZWcCy>Fdc*MIT!|7L>Jr07RgBM+=CK!`orUP# z5CoXqjZ@!7PD{npa{^|4P;YG@6s)!YrF1l2`jG=bYI1iX=|>9m3>}kVxE>8hyTeqO zH(SB3gtp@R8uAJ!#Jp&e27oK8e5?_5Z8A4u#W37AKE0wXTkE_GySvT98mN=~t9=r) z>RkZkS09GzPa{t?!1?`C%xk_ZJo(ic`|3i{S2p+aYvEi)Av^t`4gBP9W9Ft^1P9gq zlUZL|;UTqdD8tPv_>^?EMCA(hLTa*(IdzS~C()|5>bLDcLl$s{lqVFX8wJ-Kt&kU8 zRVb+wIRZbAY-T>fT-v1ts_Ts@)36sbH)$m?1$K#Vu1(|nE_d?Ya}U!Qc)sf6aIG9U zzqPjcI%c^*rq{q^#)iHhMlWHX*i10W>J%fc?}NTfPEXNqV^Hv*^+(s$4&Y;@b_!g< zxhm2(QXQYSzE4?RZwbg>_{O~L6*mt_(y=*B!#z+N^D6Hwer|UD&;HV4FNo)>TrGz5 z7P#?ccr^L`BE0?*Z6_Br2#ps*qI*y$9iWt>Id=?mqt0ie;)1m9=E9QPBKg#lHaHh4doeM~5`=V~ z>gwTMCpnEs{ZeT$%o(th3I=t8M&$>~%3Dk5-?B56Oq~J&qr84HUF;EyZiyT*B)|vR z%+D{0r-6o?@@(q&ZlFfy3?So^k4t#$4b}=q#rBFT!PM|BgYwKGT_i_BU`3RlMtv8Dbe79 z{)O!UZ|=So@CrO}MB6wA8v9QRy5oF7PIW!FmU0Q6@fhR|{#XKf-D1D2$Ad6+FYcc$ zYY$ZM--xWlys|>dVJ^mjNnj&6kQr~?2EVQ{hS)9F!ig7lBR>Snq24`GRvh_yeziAv zwg+cG|047Aqj;~1Tc#ZMJ&t+al<_yqBZWYDoSHvRs{$z2O+@ICE7@zR_#l;N2y9Ek z=vY`6AgMv_ozS&$V7l~TOHyJmmTXqbb zi#P6c{~Lok)^H!abMxT(xwT?nzXMv{4crOCe1Q9Q^j64FHzfbJ)^Nr&58lLmIHhHQ zyt*OkSOxS0>E5MVldHqM{+ZR%)mQ%Tv3ou7zC8A8##l$pydDL=Gyk|RVIG2pGYpu0 zuouksZOx<28hGc{#>ISM8iHPieGB-x0#OP+vk3wH@F1Dqb8T=Qa(xGKvbM{?Z@?$# zi&_(8Q!S{MGfaV~Ud%CtnNf&0&8BchUkTASzVWlJ!%(Dr!MjZf-{W2l%dgSblw_!Q zK#&ak^E7`L$K3h}uX$n<8bW_eSwx7iSp=&ad4jh$0X6YhL|%|8_8Dx%TkAdO9?o zWS^3C&j4d4ZMt+iV|b!po*gGjKp%P|ov7&mEIsADEc|F3oOQWAiVmai(8mAecl13O z8+pH&V;a{gg*DK(@f#4ueUy-g>5k`HjQ;CaHwI4X*E-$W8ufS{X4jQMtZeaR*@{5`S z_8}i>Drm9A{ojPdU6w>bZUye%Z2)dU<%m>N9@lK;0}7> ziM*v(!3sw2kx#V2Xoh5dSgEADv8dMu%fqyBn)sY$nh|f*;QP8ouVATd9eogc{Jy*^ z1HiB|B;6)m57Vo8^`FAAkD{YX%;P!s{QmUa{c&LeTCU#Vdw{uogXJ#QPk3%~$S`o{ z=NCis5s#Uk^guwH(nPSrFqHcKvxvlV;*+PVQ!4sCrh1w}O>8=VS0y&>3Gz;(xklpV z#Fs#9f;5Vp9dku%DlfX_24TaV>&aN#G~AA8_%Hh{Zmp583aEb$cODvAE>8GIAT%wJ4>-N5QtLNcs)tsm&T) zzw`ZBfOjp#zYd%pfrN`UKMpd_!YPM^LFUm(DEsx7~~v<%+y_Cde3*KbDUpFp$U^?_>$zaQLEjtQvuKhwDXkn7$sY?$cH zh#=QKEp>(05-*kaIVB(G1jLAu7_PGw?aximB*m2e89v zX<|kdFlTL0iD>RJ6(%(@5xZIUsb*E@mo zT)t=OCi0t;Qxq7h(BJ!(TfvxU6y%F(cQmH4@6!33x8-I6P&izfW~AwclRZ?QjIA&i zc~4I!?mYHKt);MiyWI~}yMF8ns9)M@Y1>6%e>n%due@SA2-?0ackOvRKxE00V%7rZ zu>HVq{Ac<=eC?sw3SBBxUx=&ZKyF*Dr+>Qi#vmm3TVJW7ZG$%s=dG#;HSm<7AX*B0 zRNgjt5RUV9!-DilHo4(k;7c#%j9TsmV&{s)?@V=Kl=CTVX+5g4^T{d_;ZD=fXwqtnSYq0;D_6_V4=-E@ckY9 zALTfHj%FUlny63f-1}vci(Is8271Xq`Rd`k$DyDB3$uZ2MQfC^*<{IPvG;F>s@$5X5T3duj<9;pb&1Sgjg9*%E zUXoFGw21m-Z2dTG4{}Ed_EDU;H|yE?V$F>CrVPHee!Q3dyf0H79x@N~FJnhZ)Fz-b z`De|u$H*7DO<8@$1#>rYg)%$1Co=7KmkdJwXA=bn!*BZqc(Wa{?JbV?qx26XH#NRP zGqKJ3_gTYX%OO~=Iy&3$lkXyD zz+f;b$(dsm?#6j#PZUjpb6!#(XMPLN{%(}Fzl-z!&R-Ja)n)MJ{`*JyNHg~45e*ud z_MmPj%(~mR08(cH3&(MfpR#$(V$TOjnwe|>BGK8kbgk?6F-Im|1HdR)FaJeSAO&*ST8rGb6{kvAVT zui<%X+vh+bf}EqX)by?AYg?g1x_o8v0Os%b76*@2OarM?zl)t%I?NDkC)Fa`K$rho zq>L&7d+yisi(gKGh>7|pfw*L$Ux_xfINf?b%?lL-8gnY6N?UR!FSTXUeBM z7KAQFFl}0nmO;)&^S#--!pKea@VfYn_3seG*FOyAM?S#1zYu5tWAxFJK2kp1@B_}h z9@9O{wunB3Bwqh=+%wZMZM)(AIOfgyl|($>O=*l+DKWn&7_Z~=9{2hoP1c{X54FI_ z;`j+_^x5tl=;*(Ud4~2>ZHa2lCCnKy2dJUWmdk8%qB*q@`krw1CUTF#Wh~Y#y;BeJ zymT=&JPVMbLl>dyzYI1<-B#SG&=qyNaT_nR4+XghdrE?6xH58 zTCwk9+>=y3VFb9^>%xg{^ud}Jv!KK9B;5P7^raj*a;Ap-gjK_8NHF@3o0oq9c*{AY zJB}P6RG zYdg1a-dL{dD7SN~fqbEjWoP6DeR8v0;}8o1{;(jQ!3oqE>ps;6boK-D9$jM`S2`qH z<#Lyg4#4Z(v)4nAd&6p%eI~hZ9z;Jk3GcUKZ>E!QBH?Z(NZ;hSO})K#${WPF8E<4u$HSHDe~zgkKOPCmhUI;L7T2h10n2a&S*wB|qK(6vt_PbNDWRK_gSx@5NqVE_&OQ z)_CoJF3r!pIdE`Sf)f^E-p7PIo z_A=;0GaMLa`^bU3Q%i?qAA>@n$NTPo(|NUUKheW>!v*u;y14;5yVKzLuf!-7b3Q5w z{DZx#*mLpuzP$e=0Ui!kovxs1gkb%Or0hWS4VLm;RJfM~2I+lt&HKZcPv6vv#Ph*= zzsRH!_rTK)$6c=e#k?R{aK14<4}XS}Rw&|e@AFk)dBg_&ulKt%lu%Er*p%xzeF6Kp zuHQ@5S)B#P*&_9OsN24A+1uAap6QS@`{zH3iy(V=ZbV3C88%cFLjLsPJafp?hd)vU zY!3ZxduUk)$1Nj#=!2WR0i&2#pW;qit{R44I#VO}1gr2IxSzK?@&gRNp9=5k z$b%h<)3!~xUrN?Ko7al-;B+bZD`BDps9rBUyw5TZ#ZHDAw^tY7)&cJiarnG)1d|J9 zq~^i#8A2R?^B|lHP@ZQ+J=^p;9hYPn_RfmF*>kEZ0S(319nJEnYh8Fgx?(>;tjlZjL8HRMt^@=dDHkHWbE&47>S$CjNJ=S=)>8fI>T^XN<`lv}JD z6R@|`ncV*7=!r>SDpDJD62-hZS8iOVbsvmBlfKL)JPA~1JB>~!mO`lH)llDu`EcE2 zFN*yc<{IpuJiai1d8r$Oi^0c{TW7TX$eFVRth%I|3m#;^g{1$Yo&^trZQ8y2pW{ZL zSiRGo4*TRfsoit$uMJ~Q&-c@d?4^)kKEkTQj5@`H!Jru4BW*+Cym)odC#JL~Sl^HS zu`ity0er|4(PVmFQ!@>l*K>5gaiD*niRA**+iplHy+Cn(8+)_P-VHCux!pL?@vrXn zRM@)NO(R`f~BlwPZld!Gs+EScHcZIj>_%_A|!fjw4t z_>K`H&zDdlPU(CK`AIHTYE*TY3*C)8JSTzsotpubr@jn9ZU6^Y8|eyMesgm{QDhGD zYARCl6;p7_>Cnrf64W6BvRS9Uy@#o4(@be|%o#`e2ED)>cQyq_x0b=Fe9xz)KhN^FD?Hb16f993sR+7h>{WcD#)}1Ikd~mmr-Y3 zj1>?F!Fi57{=2e9RulXndq%Zwjo))Zk=<0_93=Q`-3@B%0rlAnG(Hz9U@*+7<3z$F z1PCV0+ooX7vQPbm(iyzJr>Bt{qVHw;_Vf8|zIixz{?uwPvm*dG;z?`em##3(8jhX`D9755rdXBhyVGPf)YBHh{aE+HV+G1?Li)oFt@j=a`0|n6(rF=IB@SA`b>3{-X@3;z;B)Lz$)har$+xqQGCMQ z>tZ?8N*(lb^#0vRajF8+$2y8zdW7W|L?C)Yonkk%NzJ7>4HmnkoGob&f6#Dd3QZ7h-wuYzK4Gl7= zmojo~mFqwF0siUQgO67Rp~fPY_&)A~OlZ8%GUFVQ&Czl>2m9uFnw}=yyq^NL7kAj- zV4q;sqqF<(F}I^=Oi&@2EQ7hkFHa*P(NEUT($|K*PdcyF;eO0D*GK=Z8DCt&dp9e| zEkE=p$Gt0ih41l|zK`$!IgP-#Yn&2;xOY`pGUmFEy1&&fLzQtg_HX2hi#|mEhqf0( z@3sxk(koMDg_#FFHA*FB-s8$kQQ79I}g;oNm)ByT6UP(TA zp5FoCr-b>cvZf%Q@7WQ-zdbPQNC>xHUj#ocud;{NR$%+f@lH+jRSG|{KQ(&_drh*- z57b61!?_4~`cs%|^;#4&qOHWzPqzgFbk+-%njio~7UHT-J$XPh6b$d2a6#aFk z?yrsBq0gl_Zf;u}`Duq%I%)Cejr^M5tCL4g@}FFKarYi*9Fxs{wDJ>l$9oGiaj$Nx z`imu2e+5QZ1I9cL_5u4rWhv5Fcc@b(W&aHGU>xw6`iuGksCG2iB<;n+1^H_0Sw_M~)jexpJT93Z#k{Jbm|c7@ibA<5TDw05!uhgAd5x zBoWBd5XL+nslUsq!KM|cwT|GMd5GLHx(Q>)R|_CFFK4eSxd6oZgWP);X28wOLZTV- zUh#)A-2d?=!?9eAG)nS0=neQV8Y0^ZOCJV4DFph%EshJ_vujK6a8_a{st5OAHy*5U z6{^CG13vjXJ+tsBXZYoFk#_KkWmW$0q!`TNlJ{p)xbj08ev@n?;AUKO zF;=q%p4U(=)OjK2c{S2dPB{(e>Za>#IVYfeCt%@B3+|u99cc#*U7$p$$#|Z(0_v6T zQhPbgg1uo z_5+_%%17aiQ2b-w`wd{VF5H-kJ|VjiYS#qGEO5@D4m&>F0vgX=Kl4R@b*zSpD}sN3 zZ6l+TpBV2Qgz$M%^c}c)HU3KSNPqx^b8o{`7Gaq*$966i{mhfQN~t!n;7%!k5%eKg zVH_9x^J0~sfmnOZ+Afw`5tWEuK) zvt*oF)?#v?yQEpuDqsfW``J=U7>dEsWNsTQACgv;IWp%XX@9;BUJlU#LrX>k#ToQWHqPZ%(j2+ThwdbAGvq= zOYI_jZTa3Ci~iovDz8m+wA*1IoNQhebI;A3WOeUObpwA|?rcb1BG^T#msmC79>8Qh zjYc9GQg0N@G!M^$YqH?s9nS$cY>@tVEU+0)6TY!6dmt}D^TDX}v@LATNc0sgrGmS0 zji~ISF))1Cc_nG96e9I<&OezN1Cq2s%00q3{1BC6e>{qNL%9#mOx-`B)c=c1rDHox z_`lsRo-F|OKz2?CTTlExiMfWK7)Acl8`?j3Kf516^y#qTGHA_nKMrXhhuGn*`{c>E znW<_%qK~{%CreeXlbDMp-z{5QFv9+yFHtg|_3B~7khn<#_Z3NreMfTtqQA!eq!&TO z91;VIh{BwZS3UDot6?z*I0l?N6L0mxvWfJbHRj<(oEm=BVZQCE9JOsEdk=h+(TY8R zenJBWQY+Dn9*{Aob?xz9gyajqd!KWlu05qZ(OD6Vy|yQ=Mxw5Gwp>o{Nkuc1pL1l8 z>A?OXp`Qnna37fV)$^>TE4~NiH>EQ$r*-u=$1I&s8{};Ws69T_2l|(!(=_SO-;(Ng zwc}wkG!HF*64%j(&`(0OWQF*gO*m0WJ7O=L43|+5evWG;TSBBExF@Q3vA~1-?C_q> zH=Yv64S!GakAig`9KhtoyY+eaCj1igFCb67eBJxT#$fRKcWqbxVW{gf zKc~8m`jYD&I2h$N-t`iOg^=QQtYqGD^{jkJ(E0e$7)$sd0X$9oamIfWT0qi++3%a9UA=kO_sZw$a&=?C*2{sM^ zfhgEPQB!w)EH>XJP*I};{#k0TKig(*^l`+7wy}t?cf|Oz`&J8783YXOzWGP~&;SeJ~tD9W~Y?(7^7-jXswNpEn-Y6~MUb}^NL9iE8 z`nMZ(QD2J465|veEQk57*?kIH)Zr$=+CwlW*Sw&Y1_jpbz#l~SjVc+nI`kf)1 z^Lm3R`g7pr+f$wrW0=zzA{qGa;}C?{T)W6kqE{wesAhbHyQX) zzsb7bq}ubR1MlfOoWx_}uvB=lL+-~E@ETG2Y|Tx;9jfc*CjOYKDK6-3m-zs0ALaS% zuYQNJdG$c%N$i9C$wqg^7Vn`iuN6PUeUHYNopD;?EFAwZ#3RN$1Kmd`_OpgNFs`cS zcI84nEO;*KeUwLi(CuglkNFT}87}|kLH+Id{(qa6h4|;PqY{jb7eMAqtyTLE^f%Ex zwLTPqeJ$or)Bca9@jW8>_@*2BMioYEQz+75V5Uzr@-+HS7E`QKk(2ZJ_J0q*apF8t zdZjd4#~TEwrS)Y`V16P_@LD1Eu2rzRtM^6JCstl1xm5U;%@F7^D%tB z2rBu9kOR}*Ej;7S)(w6vT0(>3)8KZIIWo;H33mK`y~w~l@YwOjfX*cqQpYqf<_T+&>fjQqhg;wAYF#Tz=i#_pUKXYlHRY3EPjaHEZVPJk*lJw=` z0GxYd;6RS=3GR~)gV}525Vx&PAMjR>4IuOHDJf_uTC{w=~UBzWCENhjZq31 zYJerzhedX{x4x>G#g|qnB@GC{%A_h(gP4c^_ikba`w4%noDSe1fWny9QC|HeaQ-T8 zU>IBnha<@fiO6bkuUulmGL1crI+oPgvH36)8*SV+I}DzDihmF8wSbab20anmI8@p* z%GTiLrQNGHH_z=1z}ek(xv>{&l`P14-r~G=|L9S^S51(0l>A}`V>e`N`cunFmx4yJ z@V`{#_Wd${tD0ee96tYbfqe(;C$4uoI~r0AHg)%`&Yy3E9J_Fh3iSO6-)oCoEnWr# zuOnZ$kD+cZJ}1NYtr}`?e(^k%kI%aq^QlhtMc_LU$#-O67}ORnBFIssaaxu=k-J*}zs<+qt4{a8XYmkygH!zwxKx_y z?t*_$bJfS&c&@xzivRQbKp7b3J)5^cj!N$P-~;J4*fVByY?~^n4VqQhRC96up~{t8 z{2es~htKQfNgJWRFTh;kK+p=fM)l0es1U013f`|mtT$VQ7mMdV1npl%y%QaF`6 zyp4e_r&SX^64dQ|-95RoD)9MFY%rJY1Fs{xu{R3)!MiD|?-Vo66ZCCDxyIN7$0eo4 zOoV!VQ!a%o_88aFRE2-D83)aPNKcSK?&E}~bv#QC_LejUm> zoq{>a!QcAHI#KXR*=Ds~Xas~wY=@I-BS0tqyvG^r**GcAHNKdM?}@~#9W>YvmO&g9 zdz%jX&gpv%)QN^cteDCp?Os3RU7A0g0qa8qSTXDh_xj{Z- zb5?5|&{(+58!(XtB!m94*(P0}vf9}+fqqp+?Gqokd*;DBZ9L4vZwx-m@Z`~2wL_9h zwPY&h7YSn@{m)yV-mLpfB@%sCXUt?cv+TOTix4grhPrITK&M|fZxxtv=~t;#7sKPS z`KRqQ!yw!Jc++2c8qA)%r16TC!YjUP1;UK zw!%Ah?fJhoeGpVV@O!@$`uD&6o><9MX7z76dcR~HPeQVcHKMr~k(EHBYOc znF0B0Vh^Q|KgWKr{h+f0@}n0_EuSm&!|q^DDJ_m4U>6u!tt&hQGI<%5R~w7qlKH0w zfzut}m9yzvsND}p;4C@y40(XBhUC+dkt-!m_lWn;wpYN!&p2`A@Gwx$dRu3r?s`14 zSElyJ1ej0nzcq3?3q%gSOdo$c2-?9-+-0c$J@1OSG*LGVI|kO(cg^6n5x0-jJVOkj9OUYTN?bW9toF^Y1%r{_Jiy$qwzdkmr}Nz zVOfrakY&)Za#X4roT!%r4!9SC`WcA>n~lE1<#+VXhWWiaa~i*oSj!`R|vRIxu<{dTp^3_nnLNQ{Qvi zAp7Xs2j5Xo)Lq~{=5en9w*MAB94OcZiQb*G=XoY!=0Nfx&)5PeIa96a8y5$)IyIQ`)v*lSF)xh+pGclqV^>mI6`}bZY$mh{vg}7M|?@MTN)**0LIh$2y_W)?U ztMJbrtOFIeL3bv20{eW8Y?U#WEX3_7*|!zv`9*)<$h8+jbH8B6UYu|1PkEeqMU8#I zt?;gugE4R>FRIKcn!NfTQlt^3DqR(8pbRZ%q*A zA0n^gwf{{)w&D@hCkHWiI&kNQEpk_V&M3s)@W+1HdjAu)Cdg0Wcrg$xIfK1l!R8#l zCP36Fhi~(mep8BF`sT8%^=r;=Z9zw3Z^DF?Df~W zXbKX zj-NAOh55iTW^}9sxjIZ1HW9zt>%hB;yUaJF8CbhhepNBnK?Dz%i@ft79O6}^%Be$L zYs=lqYj>vMY+1N(>gyp;qB&c5Eq(^`6o!p$U3E}C8z|`gtqVF_+~QA4l)@(+Mt@(1 z5u7_VU6-&xp9^!w&mGbkFgPdI!@WEPSpza7Q5l#=RFB|8|i0KFCu4d0$MY^7uj{89i<4k=H{;0r2;@gT zv(=}K`3{z&CyfhjC&6z^xPQ7=E0}bBx~;@F0jDXsvwqc1!9y$6w2wz-Vesu6SBuG9 zn27aRiqb+Zghq|wXVU^u_}m^D8&?co3GB2Z-@<`uE1%r{mIm0uH#5_GbOLPTt*P=K z4nuEFr1(EP_YazqHzPUdgArV7Tl}5@Bh)4P-+Ra4eLS!(O$d9bD$t7SjrzI0@9D5( ztWm4Xg|wcp$lH58LjU@V z9CDPeJmNfu=So2v$*vfjUrSg|Kh?p$z-M0rI{$|BgH-=R<3r2+;9+DGHsyu=Z0g4! zbmOD(!QGc0)FLOX^iEDyGx`yWTc~3EXdga6WYR8qUAPu5zf5afq*7Ye__Y$k@PbnTN>f)V5l)Dv26{ zqnt`?ia0lJd!(+~GWi=gnMhw0zl z*tb$AY?5YE0H^oS4qYh0>w)WiyNIGJ&~Ek20`}QwQy=}H6%UVoZ?sXyR)KBAo9eO?*n_Ph z?KAgn9Et_2EWcr%HB85%&_SRdF8aPr*6yB#JEdy^Px0&AHc@tiF3u< z3AVLm=^2n@b86Rx^meEg+;~B)*bJ4A8Ci3VPr?4I_Q3$un>-IL>p68{|6ky@{+aXW zD|tadrK^t|ut!NtMbQ6{xN>UEfHm0s5}Z<)Ke!z+6Ga+DIPfz6%Q}^7f;kA*3Y} zfSeJv%_)u&=BQVey_nNxb%VyZv(H;Ykk|I^s8oyc7_6@rXhu;M!9I=cHGk2sz><6~ zl})G>#FosgWX3UvP|x(xj2r!$McP|vuqS0nZRfcjrVw~`;n?{+f877p&bH=TeS+=j zTi1Ol`oPv`cB6y`c`wq8LQl|#`{nX0V`k)I-CE21u_+aGx&1V;v^ckIZfW`>@UIc5 z62H`c63K($-uJbK_!F_eK`-?V`dU@$ygQ|FuJm=N-Y;Mm`tt=ZWos6U17(%$1l8~u ztfYDy^C3^QUaVu&DdgY?yT~24InoPfx9-~I$TJ02x)2=bH32zkt1=Icw8NWEk;8K? z&0uccS$Zrl5t10ncetw{-`8XP&xuF^y607{Bru|0Tuf0?VbK6DECQW+Zw^9-tURMH z>X?6z9ZxZFZG%yc6A=r@t@SZnl1@ecKy6X7QXz7EYWJ7e@2AGTW|k8NTdFD`wfW)4 z&j-h${JT@pBB8M~;t2^h2~pp6DFzbDta* ze=5p_IwKR4s$n_$+$v0m_vPaCNl~C(ah||-)quAN3+^y%_fL(368mvP_5_>$9R=nf zG3_n>*q3_x{l1v zcI=tP1eOL+T&$+xNScL;XpVw=Ytz7QdGRsJLO84n{XW}iG6v5}N&_qo7Qt!HZCf*( zPya=PwfKID4o;I!EUBz(Nc@$zL8^lshsXFRM2W;HWd z{`!w&j}Mg^yGj?tnlb;3(&pz|%tIV+Bywgjm1GZ3f1DQQ<1c$@y3{ zRB}W%0}ezU$h&Oaf*ij5k#wedXw)vt)!mW_)n>XM{&{-=&!;xq_n0GRU)texL3{*` z-@CbG(h#}mN2u%u!jZdb-PSpYI!t5m;rTrCS>#M!l4YYPfTKT4R9(-EVXk>}T)YRl zVEH>-(yk4l4tC%~c3m%|OE@XhI-n0Zr1Y{1eKR}{yK}b6Bo11s|0MZKAx9$n3h$v_ z?29bWJ#`&@apwl*RGEj76YwxyrA?z7Jg5hbxHC3Fz_-LcZbm#;IsY@>%RdXI8kG#6 ze)d2w1H~Es{XLM{u*LD#R4J(cu87b^E}v8VkHuMzVz|0|p63I51Ejoo{Jmoe^Twr5 zHQ8DxpxX2HwTuVXLB}Y3AOYvLNs>k}dz3oyD2JW1`FTK4BJW(-?xbZE1(! z2VFm}7+|mQ5eE8cyg%JF$qq6O8-pXo0@f|RxW~rlJ zvA6J=@yHCR4_(~I+_GegMh%<}*E z)w%&<<_({0+x7((K8w_BL0&aWUXcLn#w_-BuUr$_K>k>hdd6z~XQ(%I-W++g4*3X5 zm-y0=2UoYc+XUyx%V%F0o=4thh4pDMK)+_^WA9mCyiW3@&t7~VT@44cuf%N2K%Gl< z3$3owFvzwVPIHB(W6#c6?r_Ttpm3Im%T$_$&RqlA?{WVW*;j7-;ARo1CA^yo{ebzr zioARo%qiLCdA;bj9fQ%s9KX$EW+3ASr_E*|^utilxL3`Vfk$7J(9@^Aa4~Z-`Nq>u zka^xJ7KFN}iIb(E@;dqn7r8@4P}kp4r*X0RX$y$2WDmZ6oC?hPwFy^Nk|8rCudR1y zKa6>IaET^hpP7^Loh8KrADBMUcVV0 z91R5_qn=Al$V3l)*lTbN(H^iZ7U_VLIO6;j+&Z7!Tahe%3YvJ?W0J;Sj2 z%9qX$U)SWd(?*gpt8}0 zOQ}2BVYr{?aQu!Q^xtfnY^=6}6JmQ`_m&ian~iT44ZhA7%3{u(b?AYXvp4h<*!n?c z$8ELeD^=ja`A{h)brfhlmw%te{$fR$l$-OYPwGi%>snxMy$ZAR%iJ#+=o9~)DPi6S z!}VdG%xxy&{tl6jX8mFK$C0pfrvUYRlUl7gvtcl={a1A5+z^a&E%SD}g6uTt!O zov9JIq*=QjUivTwI}LUmtm7+%oaMD$*RdbMSHZSt{-pyfy_a!(cMUmj>%W_XKV^W- z$*@x&Xlvk-AmwqB@5o_t4RM<@9DtXcX|(P|xKB2!ILnMYst0t(-d^BIgPw&bSzf4t zl>RIc{yiOV>mol7)z(gUricc1%SXd-Wk-K*m4c&Zcd^3^9=t0ltBUfsQHlmqbRHN*bGr+tw9N8hjP z;wT({u&=U%yA9~32XEw}@Ax?H*#VpFGZ1q*g>v>yASkKTrmXtnzRZrfvJ&rK*F=u3 z?mnImbo`9T1vm%c&ndPgnB96dTIixgQ_;B z*;V{=H|CCHiy!R(uH+B3pK!nT-bC%`s)m=436<9U<4aUI~m z^iY4@wV8ff;V=HY2X?wF(AJ57O6aJjcLsnf?3 z=#1Cn>@TImrm+Jnti=Pc5qdwZ=@`z{g!}fKLXP8QrbQ*^XU(8fu0Qrl4}IVMxB8Pd zJqGoATuCjl-(efih{QwGm3W6wo*XDlfNiC#R;EFPddq=MJ&xKC73yL)kNH)wmX z`h70=Pty%7op&4OXRp zy1zO+uA1A%xRJ8AGMD9Ih?tx~F2{qVZqrYXP7QH;Jzotn&2@qBoCbpMEy0`_6k zonWrwtAc%B+kfqwoPpkYW07>hY2=fLQJ!B-h24ea7hAni?`NuC_s_t-hq$JN>pC+K zD);X6*XU5>{_G9OQyPR{VkOz%u+QxX2gR4<3_q9*V@%Jd?1$eesS*}=-jQf)dR57s}1B<3{WM=P|p@%E__#&HQq0` z4NCvEqeE`W<<_Gzm|G1UCt8-teemg3qjL*Q9*pXyn>pgwBQ!O(%>(%gl=oGP3u|Vf zXq{qJGieO8vt=4gu2jSEgZ);_mTY|$auRSIA4l}UqLRo(!A0Z z;b6=$*7+paVs9ZmwUF_7%uB&){5^GCPZO~{@jR^+@YF5u>__AoNF3W2+*^lSg0N=U z8cFOmU=7}tHaP)rV^4SAkwrf3L9-LZHWMJ$wI#vA3we-MAzo=Wlfn1sm4c6h1(2%6 z=E;Zi(S)fS8=F7aBWv@~aJ4B5`t+0>1~*N^m-87nyYRkg{!Mg`$yf{Ic)9uC-G|o= z>&kyY&SP+ghjNWeeiRZzrY#IGC-u;=p}&8(FZd4E@g#i2UX-IB-<5R?LomY+``t;o zz|U`4l&>8Lk*ew8HFQPrVQM(#kz_wyS>wDOEHVHhQkDTF$YX0wut|A^{gS(fCAGXv zi$F@G!TA{G?h~jCM_3rK&qdc?a`^2ih$-JHp7Sh(Kf$ToG^2x{Q0l$)#l|%7t@j$-aVd(*hh7u2DT=Dlq>-vL(@ zegsI!cS3i}^{b-YJ@7C~*t9;w3z)Ybvvkv+1SMIEF&^aoFUj)>ww@n==T$Ecy>=}D z&$nZnr?ZD(rw6B;8)qrpPwenMzg`B7d1h4N*k>#)@>t;1g;5wOcDVc({i{hL2N!rR zW&k(y--y4c;g(I?YQ%6or20xxb7DUELicXjuHqo@d!u(h zKcEAgQ=pYHd`HNgItGw~*vk2TI8 zDsM$SU90{3Y@q`7%fH~bcX)XSoCmDg_`adPXXtj6;%yh0?(SjT6qq*MVn-5s_$hd$u3;`VxU zy$W7wCT&wc)(k#<)okng`(gW@k&JV(!%!)0-`Shm4O@2%b7b$D0A8l&4k4Jcv*NqE zjo|&_QkverlgP(Fz-ewPOB-;m*PXbg*ae$plr(iSMxk^ty?~Ls9^}G24JR((yyNSt zzX5U_nx&(iejs8DR4|&$cn|uK4Gp`@lJgx<^05j4XSOlxdJ8m4buY@6) z%~F&h$UV(-`(R0x3J+Os0~LKcxZNIc$>`|^N(u^!%lJ+~u|b0$9_l_dGk&?gv9Upo zzxvPn7JSFIW77Zafr2mZ|9t!(KmOO}|9Ag6KI#8F!z=&ozxyAap#gsKKkxt7Gn@nI zz&w{6>PiSWq*%#tI1_+9HK%a00RG)`KKK#4>j!3Q7cXiI!#P?Fp$Lm}e{5)PLebNB_)%?}g~G zPdGdA6&7@i^FVJM7k5|^vNpQ^C?B}}rV-{B%C=4849A*z3&@L(z$e*}Wto*|kW)M) z{p-dE3{33Xtd!LRdkoZt>_h6|WkvG1X=n%ZE=1c0NKQb>_xD}uSMs2VN7V6`;1sNQ zHRP#vWy28XSqCokDjJ+)xhQOgTH9RWvUEi|aJ_HUrdThBUqYJtaUZ83Kxoft%cqsl z`qOElavx@z6|Ei~$j<|Rfp$i2l}@T0%i=}=)bk%G$L}Z|6ZSuu0Q@3QyP{-&*#dU&FmwHfwWj}b^Z?fMV&=2(cdpeo- zqKB4RT{y2Gxv30PhnG?b^q&Pe}nvq8wjO;Zw#{d{c{ z!fB4Y5Any@c%;q5DeOp{kGxQtP2C6Kz4gu-=y54#i9dOZ3^>D4?2L4yEo6*5j|XA-F94*!Y-bdeGkruPQl?*XLp67C*}2; zTHce@DM)O&&mr9s2nXZ7#D{cD!NRL8yQ%QraQjrGlfCNF3LJO3_K1R-WwEAP`l|CX?{8a5~6XA zNkK4P<4MlK+z_&n)8dM*CfC3V)gQvfd!0a&+DBauy+)NHF3Jw+rKCi`?U6KQRoFMQ zlACbv!c=dnwDU&}`THVr<_zAWcf~T(Cv}d%g+&g#VCfM^-`4XhPksdCvo+q|T*FzX zl;-3M0qn|RC&zV6%E&ppWL|BfJ zY8pFhI{$e59fJKmDj}1@9pK9Nv;I{`FF5N{10uAm5}^Ia@Po+Ra(=3 zi-oko{En)zJ4}V7ThN8sy)cd(8z|)Mh)#!)9eUG=`&*#b&zZ+AZVDtzPvoWUZ->IG zHZgk0B}Tdm5uuGna6IFADT*~25XJTM^}lAYwfWuf{MG-s zKK^T=%)$B7M^f+GVm6K@jozZUkcjVfeEaf70zAoAcJ%pDN0{EJ%NKQq5T8Hn8s5n6 zO1v%^K3v!W@AUS(6W!5CHtKJuo3S-RX7qrsets<28+c|fJNFUIwU(*J8U=)%{XZCHTtz?7*2s!dNwq_^ z|CWnp$g19Vw&FeOyIf!n<2sY=Qwy7&#l&gY+lk9CbGE5*IWa)++BKy*qLlI=4CwPf z!Q`^y2fsWL^>D~$X{`hvFqBU5VV4QpX=#@V!%{FKO~;F`G{HkB&f|MqYe>tfya&Da zP)jtM5}@=L0+Fh7X}`C3km>8aZON+xa8H{jYQ`Pe*OKxvtC%G+`hGY28lLIoZ`^43 z@G}`+4RUOq2*ZvLmv31#LOpPIM$yMWI1)Vh*0d${`pD`dw*DXgFuSbHMdz-SKoa~M zPv+bxAZZ5uoNm&SAha&eW3VX+iXJ4cGA#DO-bZ@xbiQKu#;lcBLR%V`q-^Y*HyN&p` zIV9@Z+FDgb4`AU>-bKUTQVw93pm~LRGc?AX8c^nDRw*4IK0hzVw?P*?x*4 z4r5u3gtfnfZiOnJc$C;);_YdL_YS#Q*$p4hjPOL_F2H$^NpP^|5nqL|-?E&U7e; zgavRh97gS@gmS3nVkn*k23#4JFsmR`^`^OYqmxw1I=`#N8Clt-YV`nRWS4D7GFf;Q zK(U3C9nW|LZ14sIYR>k-`KtqV1q{8A_t&YF4n1i!*0*>s*kA|cadTSD{zj5BHhto@ zbRhZeCTbN}GzJvKCHeQhv_g|ZKSylC5L6jk{_VqAgSF-LBH{W5U{H0Poir>Wi^muqx5~ zjK-y%-007^$|YS+=*726@cb@;`2^R#PQ?Z?`@V*;7d?vYwzN`(27NG4S*??B%#*0R zwAi%&Od)J}rLyZ=PaARK(b22z^MttA276bpQli%U!y*9hb3!ZyJxkp~(AYUMk-Cxy zGPVaM{cko9dB=|fiXw4v#-|}TA-DmSijD?{j$qdRn!9I8Hfpf(#@1Ai2Z-um7}GJq z6tXFIfa_3K3;8!nTQ-dyb$OXH5)RGvu;O-Tn}l>b;br~3N$c7qEUX`qITE&d59d4TF zy|)%@f(Lvd{M@mv(79B+a)v&K$SCYnAJl0jWc>3a?b#gio#(wKwF`QL&PKT_3+2Pj z1FBqpt8KtC`SQ8;n_;k={jSf|aGVV@-532A96|Q27n)J* zp8~g7+FGu=tuQX6^tSm|0?_{Q(-o2%2C?4$&EaQ;;J5Z&?O;pn+^u=7>2zZPz{=S0 zMa^f>$g9*e6KW%uf-;U;kL3}+??FRRxutL?=Jh6x_woP3{_20eN+>AiAXDYGuoguV zc686TRUmstK}qUid|Eqn#q4$BAbGI8ZD0Hcratn`!1m^mZE5gjcHben(qh6?z+ zR6o((ah!^03+`v6QZ!r~QphPQ|B`fzB(QZk7QpqRlc;TW%|E)Sm?W#pZ%U!-hH!(W z+Obe=!rjnkWy=>!ZcdKsx$(D<2B(C558hXjum0XE&K32b?`(UvdUF<8FH5(pFK#3% z)=sdDn&CxL~$Vsf#K?s1q=7gQvq>ZFv8 zK(CNZwe5EFKAf8d?+(}`W4OEf|T7B;y9nH|R`Se^qb~dCRICI|iK^NHa>3DrNv65^8qV&}VuxGeLC z^qnG>l|#d@^EbD??_wir2q&!>s9a!p8?Dx@$~qF#@piOPubx=m%IH*8>H^IJjK{X3 zRwt>M{;y#un~WO16TEt~3n+_KO(@E$$)Zq4WW%|5Qd3a55O=&6R?5Ccx}&Si=%Ug$ zXEFS`?KJa@HuXZcc7pq>`C{m7pIR5e405^?oz0W(Vp!oXw%-(-4Mut6_tzqk30W_; zs@_shA~kpC{WT9E;qI=N4NhX0uBEU{R#EKr@)}t?Ci_TRN%Bu=>8R4Pc)`J7eBvM1lywCnfB4tkwB7>5 z;9VP1v4;G$p17C28av|2w|is4Crh!b_@}`5`^YK~9Wg&9qfiI7AM{y1qPO#ZwIcrK zpPz&L=PA@Vx5t2CXRUi2sUS*)s!bZ`VV`{xdb*aXlw|2H>GW1$cFSDgk6gtFwC|AW z>;2b7N)>dhN3zhfnfdhWr{G)=%l7uN^_~JBH;p4FGcY?suktmydYt@puD6k|Kn-*8 zCAHGwB65p1>+#{Y{bcvTqebN|LgIsCnK!Krl3T8yR8DP5M=f?sThP4`P~8%dVRy2Y zNH}s?`|D+rgFalG(fqi-`Fj4iJ7$ZnQb%l+XY&JYQ3tc+JCkIiVtkN8xq(oeHKS3u zfo!Gk|5CR;$skYO8azrbLJtzZjWj=MQkRYD5(BZrZaVHwxpsCWeC^3j)jC=Q)a>d- z-Z}w9Yfo`hUUxd_d&@It&Q(ly?xHK{n~x&*_&#jwnjsjEW(r>PS z$yIw<3AI4tK9k#VbpI4N?3q!dvH%@b5D~q(U*hx#lFLi^FzG9rNhXdI8N&j z-f5U$85H`;R7MUN$Ozu%Z-w-5F6NNIW)f8SOMfqVaAV(pybyV2h)~@W;&zT0AwE<_ z%$m;!NPQERo7&`ExbSE8Pw;iTzF(xh?IeSpS%wrXcRL!Phg-X8^ALKHr5!8xtRnN^ z|IynVfN}-TbM+cvFM58ap)3b}TFJUB{_X^AL%Of~)ys(5@Qw{(^cXbo3J4xsuqXWo zZf`xZoK1q)bSDP+Ff&)eXZgXW0fNTk_7pDRxjKb&eCX*2S)9Gyvv;ixdWQw5zUh3hU-Ra~f{e7W&WCjFlJ!cQKZ6vRjOk<)B z=acI<4WkbnYX_Cb28V4kYl()7^ou_H^@kdthY@lvWOlppgZlgya(bGMvfH*8o<+KALHk6B*?2vrT2fVmRy0 z$WajD!+qePxQ7o7reI8eEJ&<;fGj_)a6E;x?$E9Y$`b-J5OyW**&WpF9EzC~hLNxx({02dd9&|UvnJSo|M5|m0c27&aTh&v zXogK`ysr*v50G}*KP`%QPR?nTu@nC~2GzpPI)1MVz>*%N04y~CN1n{z==^vn8h?9D zj46#Y@m~Ly&VnqF3(B8gzaNDO)3_U%Zdv5xz$VV4cwH_J_miNLDupXekA~%5Hj@n+ zS&yKTqeL{mNFtsLl7DJ#lm?ed$@^Z`8tJBHxGSDvx<{%S82ODA&Qm0jOO?ic0e|vH z+4{eEVWv3Z!Ni%c5524Og?bb6HKCAPvMzmszMjyX7-+Tl-cNYGv7QS*Q4c|haZmm= zkHgEF>V2w(tz_v}edt-y400xLi1pvGJP`Ez*t2CYk34^HNbgcq7zm8D9l1D_2{9=` z8hW)w0(=BnW#O&Uk$;p8%_-yl}>Ez!wa40e9_!ZMavZHn8zY3Tpq`uML! zH3v#uH*4%q_K~5BMjgJ`85ldixw;{)jtDNkll2r!B?^u0f3u>?;apzO)&PoG!sh5k z$^NC7=<<2>HN_T?@db}srkz9ZTs(3AL*)V3mh+s^rnnB|+)6sjD*{2i>lf>1%q9ex zP}B9S4TBnkN6FV^WEpt*ND1bSfVg|Kj3;KT=nI}cp*I|aV+~Jrhllcr`ZZ7cv!1gg zZLfQW?Y9Xs=gH=mvZ)Qy#HJZ`Sd77PbYkAiFC)-*?Af`KKU(3!yC%o|w}#15zuwZ1 z-BmzW-?XII+)BdVY}E+R%7wPnhSQVW?c}ER&4huz8Zg=FqPEJ|24d`YX+*J$FRsG- z%317Gey{p~-&>&`ZfN#EP;d*m(WIky>uM2+yd|+yV-1ybcGKzkpcVFRHM?Vq#cyI`&3zDNy^wNqnG8 zBeEg$pLRc=B9nl}qy^c8qQRxJR;QguLFSy!b2mD?G0&iB+5GC+hW# z{_Z(3Fvff@pe?wSyxw^%DCTtspVWLF_)+A9MW2=2)299W3p*>;bb!sODF&v-6dO*Pb7e zWgr})Z+AE*jKmZ%cMesLg86>`6A^#Qz`>G%)dJ^CI~)0wcDMMG%+@W>$XETFljRry}#ITUhc@BMF|p zb+>7=2dRZI>0r!O=lRQwP6cFiK1 z534@h=p;#^X_-fUrVNR^V24^sZYNysEQNN3yGQ%@@Tn+t_!Mv1cCuS4gt z%eGB2!kzWpJMvtEQ#U6%lZf(MFAT5{yRe; z(aG|JEwYa+zJBBq=!FdLXRl=p&?En+Fg;2_CIgPihS5*l?;=)mr|%1!d?w9NspCyVpe)<(UXy$LMY5>J5s;1pG0!DiM)3D3f~GGx#GjIyC--$Wu#9Lc;+a{DIeL8AoaDtl z+6c|g@B@B9op9{yv#GL(Oc*PxlNO7qfF{kEz>B@D5O?y}nZ8?(AaDK3M+KW0qBQbr zKJ|D37&{5^U)o$qjC^a(QP~ue@51lQ>zA^~7GE2KTVKz@kLd5>+Gi8Vc6q%_1vrVa*R8GKscTBEd2~R$!dT0;x-sava6-=NNeKDpaz)iNp`N&hrCt#m`axROBlU#^ zJRxkj_-Z(HBk?QU`eJIXiTu|q{D05m95BdESz0otLk{(0g97yCZEVqYPeEOAN-WB_ zhq;5uM6xuFT*Qv|GIFyhs2wu5tVY@8u*$b zkCy^pf5Dym2fBe$WOjL;x`Ct!465Jf#d)|kOYaJ1?P+Ou9n*4a1A3S+^i5A7Eax-p>1z?wup*R|J#g_glVwVXSGcDdlm z`tPU4$)DtaU#rSqam;A0%WpI2#4HE*o6S~lI-u&O(&y(k70|x^M#CIE7Dg^xJ9yRH zi1R+fj#1ls>^`TPDzWz@>_Km+@>%Pk%RflL@|YvxY}|V(ZEAo}Z=&9K8Qn)z)wXEu z;^`to8(-_W{x%V>sbKHdf4bok`xAp3m~ERFEDjApkG+lMP}paJOi#|4>u(eD;m1%P zRc`Yj346@#q?%?+>@)Xk{J7OhrfU74ADbhD(*ILQ9B&?(-ngCuFWL$7Ed6EABekI5 zf0n`FTp7{1#JrhNuZ)CTW^d??%Ldni`7{l|B4R$SdZa}QncsJlVt!iJL7+*I@vdv= zk$9%_S`4oX9zLU5A;)K6SVY@%_YEp={rP)&$VFXB(R1T)WzBR9fXR zvc2|3{@W>52r}K7A{X?NNgZ`b+>ev>q)bRVZ_TZqu;%S~QShMhfAjkIuT?e&wbNCu z{O(oc-iKXuE_+7-jh<2bI>WHE;bbQ?*?N zn=h=9TTSu<8vbr_Dg|+hn0_l+`ECuX;5Afx{w1w^*&yCsPC4niRbc8G=e_o z%MNeU8}+P;PbWXdGdw%)Bj)JS*&gXY5;W5I3Sc{7W2 zJ{jD{pdGC`4o=Jq=T3V$k*&0MBMZ(95E`mOd6w9raeOlIb$&c{md@?^$eLG2-c#Sn z7C_cL_;%fn!kS7 zwT!uOY*&gPe|7y|#okW1BS1U7oYhWd_@42|AsZ%fw?sIlb{n}e_2qu)zgDtOvFAqR zYxGPF?4I=(X@dl>nCISwnPf0m*7)3)LYUPHdVeri5!k~R_#$GuL5h+3kKVx{!p>VH zn`W0s-tIe;_?ckDPNC1hIyP73_LELxIuXYnfmy-vv`aM6=ojc6%}suCz7m;j z2lBRV83roXeBSMXzU1Cv1qvPNFcMgJ<-+HeCE&^z|2!=`9CiX%#qNynP{$w8&!JIE ze$oD-H=2wj({0wzZ1M+)bg=GcMd}IimAvY^jQWi0&Go+>d^6y8{OR`4>RAY`ZMm(3 z9U*g@ySCi^l!;x7Nk?=CvjFxBHQ&vyA|9rehuVEAN!o7-ss#2Dn7T-*M0u!z#Pi9p zJFgTIJ6TajiSHF;;8gb0M*B=~;xGNwqUNqGQz>+k z>`>zlp>q+W)i%BTl2AKwqfVA$Ll0<6k22Gc8TyQv)BM@u%1C=Aubrk~6`8fUeuM2? z1DuuI_P+a6)BmRP$A7Jd|JCCh@bMf{zO{K25)SfA=q?X}tupP3(ftB)s^C&3zef)2 z*ZHh`JgN>9i|&kZ2sc2#XRANI!XR?AR>l+ayW08z`wSKf_R!@GshyM}AE zpm~e4Lv(NmLg$~N3E`AI6!v)7p)eO3*!xsK+OwGlwMa>B7$ zwin(-`CI93>Le|L>v25jM|x-Pb8quvKY*D>QJGpK@nI+#y%dTWEeQ^hGcoxf$NkFm z(7*_>d?{9>^fiP$dqXodCprkBl zsIG?84B`BR)~u(!5E);)vTeLkuY2I5^ruQO87?_I`#6Sk088dkJt%!k?r)OU-pWu2 zlDx7m)qVw#5PQRavsOHu`zV#`soO;M@wQC-<1dF*8Toi~VRr~eyLK^SF$^o}E*QP4 zBGe8qS$uCx^O3=hTzqh+Z%`MzAiefB7(O0{=akPK zG&X!8gt;@-{8trmmN@>eygnZ``n5DP8L%szUa2IDx|&qv#25+wse%TBt5eL_%}RUo zGMrKXjImeYovir9)tuT`<=}gkS@_GnaTHm}JpHJpNB&BD@JVOBps3{db2=67V zk+*u)N}54~vYn%Ru>*cj4RQL?_kc*NOG}Uic1~o-%rd=f1-_uSS3Ftc$Tqu;@hFIc z28j-b@`v9^uMbaZ%8@jf8vJ{}D!T(@Wp`}mxQ}|k!ZxFVGj&kPdZWLNwTg(pnSXg? zxd7ZHO(;B1X8-@RKK^Un%)yPA`O^~1o!A|D>EX*ST|}#-?ksyG>i$!n{1gf8M9Tc3 zenz(gsqqqOJ$H*RvkY+qu=ML1$PZgr+GfADct<9^ym<_r3*Ub2Q5x74KdHxMMPC9P}gn?=! zp>kkjp>s?ImAi?Yd%jP>&2Lv@q?C$qKT|y&D3Aiz#kpAyxW~g=S$}rv^)7O!Q|;te z)G=bryziviG!g4P+!BW~ia|QQBA$VcFhoZzyDND&*S7a$4 zO97F&Sy9bz*+_OxN{$-e9RQ6pFYP^;3gC0mhpJ1cV;tq~JH{720tWu8g0p`s$hK)$ zQT~HZn}$v2d_V^#18X!o*4z#-W5R+-|>5l&#`Od z`nA{Bc6ftUQrs8Oznvs#e&?&2Cfrwg^$jNYwnKO=+m~=5fDL85CcdM5uG54fTBoHL`0FKl2Hi~B`HB92MLn1YL$_z!fMqg8o!f zNNy7SS+>`FW>zE+H#)z+fMA?$V`9HlDK&#d2c7=vJZdC#Q9C1C^}2B=#%1Z3el_yQ zlB0U)2o~~<*EfrX!;rIxS+2Ia4~*%OyQ~S;VP#{9@t*U8xD@7YUe4fwp(DQO8$Ed_ z*LO30$2%fh-g(!ZVwD!WAUCitWoI)k3#Z3FSsa3`+Hv!tbh#kYo5e8hJdW8eIf*fg z1y~&0xXGiG1a;AIPdIOuq3$;ty`NW!eeKwR#d>K%*GR*AuCR=Rwe$U&lCP)Xq}T%% zMWT%hW>xv>aumK7Zj2u=ZbFW5hOtblG0=Foc3jav9wy8V zxVyZsf=@>S?Ltlu0Ef8k#soz@$a6@2+^*OM0&@pf7W$`=6zm&gpBPVMogXwRaTtKv z-ZKd{vY${l;j;L|0>QYLQOheilu0m?)wOk}2Y|uoCy#D1xfBhz)b6yCcZoejAc$= zmSe`zJ^SS~-Lz@0)bBSz;$dd|7A}OGq zBD=@1WE9#{>pb3VG{J|rVcQ%zNknGE?lK1NVTdtE65Ag+g)=FwW*jmk91FXzcde}j zl*h&#Uq$vqw+N0JwIx7yH6QuXAmLH{Xkw*XYXS43SJ&R^MC0Jkwz(H2LwG=RVt9r> z4a(>4q}*mfAZs{HOs|npGd=F2)s<1a5~b;?>pl!056Bg19vDOGLJji?!o$rYah0E? z(-Z1;Jh$=U=?9h=YxnDCbMUC<#quHRG0ZJ$doUY6h_>m^eyRNEf>*ES7u&l!fbKls z>2q~0h?>*wuyp|CcO@l|_Yki1J1U9#i?UVN!@%$a$uaH4P0iLXxl;$ibJ)tfAt>>3BQVQ=889!VS-zyOs)Mi zY-ufAj(t}M`*ivbS8LQk=ic!5di(od{ba&3J)gOCRX7(rTr91I8QP$%RPzc? zU@`vN)Wtvk))g2%)P35LKM-FZSG`=YyB!t{nFyhAB0T*(zMv~MNw5ubD*e~fAv)2i zQ;?s~%cOiW)_&238i(dsC#focdFRS~gM))0D}76)lBE=BM~-O5q)tOwPG9eD<~po1 zIMPVnl>#4`ZDMi_a`CQiwX0BaKW;oxi@8Z|h8+Tjp9TyKz)`PVCaw0Ju;T@TcC&Rb z@UoV)=${&f&QFQ~&qLa=(txct#kddtiZ|8P(GcEqUN~p;whFC}o!>{xMtJqEE4gXX zb)t@NtK<9IqmZE!{@6>c3-rDnecZU5jVG`8-WakUz^WURO1zmQ=xZx?dAz3&%w%5T z7sUZE4OQ>p4b4W^Z*n2)1`U|4^YBUj^F(}Y>J-Eh&%X9 zosy6iVNFNN)dQ|@sTt+{1U-;Y!ZVlDJpSe9-Y3tsd&OG%oD*evL~_+pHSKs zaUE%cL-z%yqL6~P)P@0S$%}J4$C3MBEos%b9z0u${)eRb4JN8tVwu;VLjx@yD^N~)x#YS8HMLJcTuoDoCl9@7xozj&!I0zs0YpI zGDti}eVkSthSJ?=_jFX-*}V(|o3{M*Xq$v*OA*by zt&Py0^xy#Rt4{opJ-x0!=8Fux`|sza3;}~3f6k60BN%reNHFO z6?2UH$r~)&Vniu&xQy_dH8Yo_w?ZzRzuEcs8BnBi&8l#00Jb_8_-*F3p->I|oawqJ zES_KfJEJ`cJLRcq7t*}oq*ld1^FQfj`=j#|UW_2Cmok4DM+}aQdd|yJg#m%9P|@CK z!J7}BN2Z*fMaoivMZ4H6)Ny&kq|}p&@{a>9HOCGCchKE+uI}RAue)XJD2*(U0RxTi^VVX0_PNp4Pi=Uzn!%TiV**ZZ<&BCt)dTCV#SXj)E(7V*4hiEs z?NHZ3CpUVw8b^~--nbE&E-HyJR=hh9Oxyo%p$O@PZ_k%1)@jO7asT0nt9*oa{Z7%& zOCCf9w{_=@loLJ3^U}bPY?cF&)H`zhch*B_Pr;IKeZaqy{o{YG6N$m;Dh9#_VVj{; zZ*55UXy$0Cb} zydeG22f{D*eED67M;A`&s)xJ#*WjV|Yz=>n$DvOu8(_iIT zw3Xe>n@>@X8;RWeFA;hsvx_uiPhJn8ZC&1H?gvchxT?IoxuBEqE_ z(t{h!n%C36kx}(!TdD7>7A!oHNo7vlJH1su33=QYfaUpol~eC(fa=uNWa`asTwZnm z-Q7BhX>Awj=3Ay<|AQNSq>fSaURrzAd1DAK+<6=3SdxpzlYe}w=l*4MxR?_heGCub-SnB;uLX+|0(jIVxE(pBJ*A2OIU)CM8qVQY`Kci=9W$43tmdf#TcPq)mT z^?~0!pP6f86|njgKFs3m0TVHon420iXcse*rmawoDSZvpg&y8;kI7^5k6k97HeFt5 z4^Bjjw)A7ycNc>f1C2kYWC2QlXZT*xQiM**uIix?uJ9}3yHMr&7-So*Pm!OD!B^KU z2|RYhJu5-fs?2o|^U`ZQc{GQRkIdaKMeKLx8A|Y@J1#SL%qQ9@5J`J>}iKkC<#9b<`1ft}ZHHJn?GN3m1Fe;hr= zuw+RkaGs_cZFJsX3kmRwWWCIy7_j5ZAk-mt&mo)29N$bt&e}Mmlg1`PC7Ss zjmUz#yO7dFuvEi_7vGm&nSyvbF7l$l0{&*{4?9luK~GR0-)Q|OKcX3PYnXKw*l#S! z+bz1_{(sg3AM@7H&QX9JMdzg2Bgap(@dCs?m2!HE*YsB!jPN3SHp;XfuLUjw}s_N1T zj7_RjQZtK!M+-YPYE7zVEmE3wy; zLrB|qts<+d3^J)+P!$LC!k#RX4h3q#w9LFtE?e zD%sPA=Yfapqmb;24e)$I^F{yR643wRz3*r=!O~{Ak?LL_4|EN-Lfebd;km=$SvB`s zb>_MCRK11qc>E!_tiz%4M{W$pY33_Bfoc>FC1XeIX4ZKJ`VG`9?26tkqos~sH@zj%aHmMadUJ)`WZI8%&%@peO2PG0 z@C)6pMpQd+Gxi2+F+Mpc@(b4L@K<0-HfEw9m30VcE?=IJ3-hQ3auVh1M|CLy->eS z82+tTPVuuJTYqM-xTW>uS^2<&M!DTEuQ7GPi{>5Lengfk(-F+=UXCov>&9ahA3D`( zdU2nSUpaeGC2H5Pr6_fj;r?b52WOwye`oiP|FX{dnA4Bj zR+PY~tE}tgo*^)ss$}e6&WHY8`DN1c#_%Lp@pDIhD>RpHvpHs(1ev73i-`|o!1v2m zs%9aA_4aA~PltC8m@~QFyUSXSd%51ZSLqTg&Lb|-Y>h;p;BE+yXlOe=sM7J{keCEr z8}%c<$GY&Co8B(dwRYgypDjN-H;E?QKh>TJjN-%d3fD8`JHhrF3+3FAewYxr zgoNvWM_Y*mH|jM5d~a6)H~E|o>je^AJkGY_FFuT&WV`fxn-j2b^Z84LQ@wD+DdoV~ zquuzcP@E@-s|h(D4G0(%7h~|(2Y(}~mVvsfS?u1kUR1j=VEL8MbCf(|P#Iw!#bY^Y zOGn=}Lu=BV91Xi%tiH6(p-QR>qRSrVa+<3Et<9!T5LGysrYZ9{&ydmhg)Qr%1>$o2 zY5*m1-!nL2pc$aqhejI@_6!i`KeLPOnkxiD{*r!V=r!v!*g+i?k#xKkJwGp8G>KOuW8~Bl(7q!2_LEocL-vam%O(z0V)x z(v}!SpVZF3(;-#pndq`bQLYu6&bE2x$Bf{&pkCLV50kO(#2Q^)T@Ks}%}Y7B+K0)# zD%I+>b6`V1?{HpQ6pc#`&d*~1O*yvD(}>4arbLMhF|Q& zIi&7@^~vrYbUr~-$MPxys)j=Nj;S`_L{oSE8z~2<^?cqe|6&S-yXvlnupsu5X&5+; zjbYbEv#KDUF3i~SR#(Sw0wyHhR>^qH;I)bj$GgON-2Z2m;4g`849qd(>C174JDV~N zVzPwqd{3Ur{u?#uUid}!Fl{bo-qnu!n%ac>zqw?MYLby-f~hPuq8&vhWDk9cs0Y~* zDdz6hKH%>+zshbgh6h<*ZA_))VoSa2@SI2k?51hlMOw(i-gMQRxZ^qaF3r4W$LuJ6 zcRP~go7fCHTmFs?j*g*Ojs>qOF~4O?D=yme>;}@D>ol&D>xV7$YM1$f2C;?m_sRQn zWazoVJ>k8r8d)0`>ApT}g%6S}wIf_Lc-P18fbdQ~6tgSd>2BBsk;iV@p3|L1G04#3 zm?q^)dNs@~AG@?+PZcLi9bc<0-mWRtOb47F|Bm3}O>q zvwB3fJNx}yjymBUG?{7G9{P0xW@01zw-021%V`&-n|uTR!S;{;xlY!KJ}FCYBVljA zZwrgPH5lhAd!y-MET{{}dHA!AfmO+ZU~zmK&IW1N8kVL*V!=z(tP4c8(m+e>;58Rm zlz)5bazG~<9bF!|lMn|^n`^g)4M(xXZ*0JnuO4kSbu4xd*F!XCPf0yl#UaGU-n5RefZW^q_A0)btdlD4krap?P%!DpLd4a!c9oX+SRYk}Eqr z4v&B^X>lLvZ!XNF9T;rN?8gVf79H)^hCnP(B9Lq_iZ(AbhpH02A?J>+)k0t`@|>ym zX(N1uPlKM3pX$zl{Z6kE-vj+1LOQGR&S?}Cuct7WP>rF;6y{j%%Yms`4kyyzMmb!p#R=ovDXd;W(6e{sq5x$-FE)W12mAH)A{ zed0f^=l@;LD{wRXj^`V~-&@OX`aySF8zvsGf6g6R0>>M3r=>)r@M`t1<@&i%I9)u( z(oFarOoh1=pw1VKeyiBmx)536$7$b`dy!z9y?!PScO!DkS$&J97=+or46^>0YN9V? zdN+ai|Ldxh>8QA)4!EZ%7W5Ahe2M6niITkSP}pTb^QUwMes5-_o0+!bQcNC?sKN-$ zADCa-bAk-RCY*MLvOQ?7z`8w4f9_T}sGs3}>@bysqAWJX9A-5r|A{G3heTxWlnBtyGn9dep*`qt zCAa{;&861}y`tm}H1jA30%FE!?ylVohgkibPTm@YYqAdpoS7=YDTQi1O1=V0(mD5g z`;S3cq>AQ6hhW@C`Pr;~mC$!f-FWZMJAhYfPDej`QHC3Psy6K%2zKAiow>eD<lSe0lNRlt9Rzo~Ia!}0 zqnMg|q%6Cj6XonxryQRb;w=Auw`GnvD71<2x6y5cx(qJ#WNQb@W`3DVdbtq&X5C(o z@Wpt3dIE*t8*qg4J)^xz0X!D}8J?n0gV#8et<7%40(rao!A7G7Twa>8{>;&boGn9X zk7_eO?Lr7YTie8c@crW->urV5U6htu_K(9m?{7~JZ5zUm>gNXq^5?r^+ z?Ts!zz705kL|}@Ur4oFvC@T3AKA^q1)6bQ}Lcxv9#wn{ajtOe?7eBXj!OXjmOXYD* zV5If3$;7@L8A-1qMHQ>ybDxW01;H^Ae#E#aEL;m}e)#lQ1Xc2R7 zdSls)FL>ffS@9isH0#TUvCHM?bT{L^Zchb1<-E3Oq!Er+esgo!^pfBw#WJO1PzT;G zSR+*gRpFNpF|}&Z-M}prw@2tQk-aUhe#<|#9i_kRzwdgW8TGDsBe{*p5FCi^9-M4P zHm>XsWliJQucH;*#}kR~Pmn8Ci1XtZNjNC*aUtlQO4>8FuMR6}MY5K7x$`b~8FX_ke;E>l5x_6_<8Fq)F zs4o)u_{MAy((&G^pP{YbDDE_1^)@H`-cn)ovDd^Jv8M0vK^pBGcrm`f-09kb$<&v2 ze>gG+~iY-TMI~mkm?b%jZMA=96`~pgdf*DVW>L zY6tcQ@jOo+k@0GY__4K`GURyj;NJHabzmm@VaR7-0SXQznI}utBhR^3pT`#~kdw>6 z{i|vt3bjRd-Ab-NW=9!onx0P3p+5S!*7*b8-nL=7Cf*2Z3a@=lSci~$=Yg}f@4Dgn zWX+0yNIN_#NFO{?*$S-3s@_o~*`b^<<*`RJJ($z}+B}F@KlN&AqsY~QS}h7v5A#U) z#@;sKSq0(ut1{0{3dwvecGoS>$TP5C<1Kl&gpa!7awX%c()`|iN*Ch%yL-lKJYp#tsE3YLdE6RCHGj!;{YQjv@S4P&0Bs%$MF%`?w9ZHN z$z?_6`B9|K-s*jcIN$!`%KFdsyaK-)zG}Cwr@#p(#iZu^VI1k+5w5z?4esZTx7Yrc7+WxPPh6<5SA=pQ< zpadsQYfZ-;C4=tOS<0>_)6kcj%);;{0qngQ-zyQiRn2c9^+}w?D7z4`MZMY@7&7T| z14M>kUZLer@Ma_2?Bglx-6ZDW^)>k?3B9UL?q||p~!D*f28FNG?LinoEape)@sIOR< zavX;TCoY&*MGrw2x2@=@u5mo`na0hYy93=?c$i({S}|Upjc3)g3*$W^+?*6h5UXNo z{w%QtM#Yj$A~bvO?WM5EeT_4~!_j+HY^@Yz25o~Y=_2sU^T;Ga$IGyNUUq`!b~AGL zCAxC?_o9Q&`1KmkMr7q{`=a2 zsUqpV)t5BPXgxu*ohcW_ee|*(%nl<%&ICn-*eK{vE9fnLBw@lSvex$qf@K_>o^YwO z4;E=dvhH`)!ae)qH>@9fVOw!jn?PI=+#kai#!_J*x;5+Ru`{1>6n>hX<*J>NI+8OX?tOTBY+8m7N_CSC3)^h3*+vuuwIVTWw;69@iW z*sz+9+bTE;m$r>xi;PSHK2g88+gEy^;-msQnadtkmjmbMKaWCFOTCP~XA=dHBUy$<1Yrs1JbjnULZTKXL z@yg~@4|eu8z*i!BR0IRI{2};Pj&Xu}mXciYr9+@nMOGDN*2EqakgUMMo)%h;qfXnnptU4*L+9fWT8 zd}R*8gM0g!bcQOihyJ9epLHmdTqVy_)RW=Jcc#LpH9c6Zs{WM~GvNJS%g_WOLvCyF zt2?Qu3H>@MWyO4IgWUy>1EyR*qG<4-#f!mSP*J{+etzj++JFAf>+#>~>k8a1Z+s?4 zUkS|O@rH+Pwc{M!x8>`kUK}^?<1lRP!6&Yqe|PNaM)!xY_H{NDm_nz;6U8+FRHCEd zJHB^<^>D_y^AW9(utnY~_6QkSi+sq6Yzz2_oh6p`-VpdKNiOky^+dHp3VH((2=uVi z|2C0DIP`Yr!u=Nocwatl_QmmDLQhs`;XB<2F=2PK-trMVH!*<&Y&!ZO;SF6*@RvyG5IXsQ%HTl#g9jB5O#A9wbX4%2FI0*@_?XP zJjWCwU1{C~yB>1>?oMoj@clly&1;oNM-%B-ryLANjh|WD-CG2qfbmYb$;;Zg?`o(oUTJlymNv_Mq&Mn|{jM%0Rh& zKGI(+4g}j&le8F`!N}%dljiec;(aAsHc$FN@zrJvg^PVK9(`L)Rg{?1T-^07%xV-B zUO%YbPw3T-#Pwh1+tr7YvW2FNvt3}VS(ST~F9U84Oa(?(HRDLr<(#aEO!%wob>JfX zC`OD`zsP5)#Iq@1NAgq0@Kn>Ka??*usNJheYR}5XG?A{e$3NEKtUdv=XspHP%&gr` zZ(M;%@YgMak+}b4_w)a+bxGV$-ah4cZ8!lMb()S}MiB3Qd(>HXYyf&5pQ|E;wW1QO zKI2ru0Ca7c4Qbt-k51Wc`U9tmfluunV>sUs{7B{Bywfla&mwXK-ZB@0h)Ye^;>9xH z6{KR69F4_tQU0+-uPzJ_vX;~9$$%S)iu<+rmO<;)_wsFo-ib=lbMc2t7d8ueggh#* zCUj*=)@N16QSZbjr7vd-h`GqNEXtTFylz9GtK&EbcPuC0xbK>VpEv$y-;b_k}>oJT~Xco4JY8EDpu>M`xx{hd|^J0RqY)7_E679w-4Ir5BN zITrlnKW=z$9Q-S}{i;}Iz*YIaenWmH#_yEL*OhFBE!%`wgWNlDWW07ufc`MjUtaQA z=^z6`uAiiAQVqdrJo34W&_U9BtFKny?Sk!(*0&WMYQl4lO)utlG~jj-H3we~fAr=a zm>Qd$gkH%T+)bic*d;(_GhvFy^i}>YDZRn}BIm3Br@C1I_TA@R)tU6eB5SZ~!npw$ z-0l6*ttbWk%37i+b^AevZSc&Q6YcOeec_lm(*SN4Oyex;F97OQA3b)NF$i|8wK8Ow zgK!3Z`Q!1ka5ebE_A7aWzcn){Kvk(3Hj2(JE$9_s?61;*e&Ie$YTM0DD?AM$;k{Dp zc0`_o{bwhJ^OIN>S=Gz6uNI!FWIn(6i^yW1J@q~L&Zp`mm3TbP_M0qRT8^nES z`m|`wt@$zR*Wfie7(9&^IPC6}k9UB6^lfQ{A|m6|N}AD1qJ`iE4N=*twV`O`p%&#| zU1)euZ0c}$1Gt~yG&1}=h1YBa%ersHW3Y46eC#cvzbCL`t<{7K?~M#C=?U)9UtJSx z3*uaejA4Niw^BhzMUr;Q4kF7~R*dOGbU6+-c}(9d8AH$7-Y*O?#klZFO2oyo28PNq zNnUj3`1(WIwYpYk@HwD18RAg97Q%>Z~@EE3L_|L`#bwlQ_%*-?5%El34O2$`@K2&Rez)?sJ)Q8r3CjgdP|@5 zA$%jVoP|Fe3W>S>>C(nvGH&V6=%l^Sjkb-CrJb}1e|Y)({QK4fFY#otT_Q2}^W>{F zq&DpV8?&D*Qu_5U;a1Z=Z`_To>;jVg!X3aBDStfIuNH$&)k)?P{{IghBT@$mo!L7V z*WpqR4`lzbH;FN|8|ij@{u_Lx0=@KJ+Jz7q#DAF;j_Y$3fNjq0bNlXA!2(IQyZu)k ze3N-_UD9m~1Dt=F3O;Ee<}z{8zCP-pL6fORdCv#8-6<0xF^+-yq=!ZM^Jd_%vw3KC zg#_OOlue%SCc*U!4TouelR#Eaqajr%6WEmWZ+|wU8 zadC0Z5d1RAcQaZ^80K?Fu_>t&6XCG^J0W<%uw;XnNd4%?qB!pWSK&b z^ZKtmt_|S6M-N_7^-aK^3qmJq+H}B}_Dr`UCBd0L!z%0OJBmM?O(>^Zn?fL_}QjMBtHbqSyMD*sn%9`k1C+V8_P z-a^9P$0HP2e}~~dTN62EheeP!EwTE|KY|TbBU6d*dcddEk$qUH3!?M=AN^!o0K>j* zAESvrIMsQIA4!?oXgtzSu|qr!Ym_&7?#h>A^v5FcOQjiT-y!;O2jd{>Sr*pOCH251 zJXs% zqJac$Hbc&75m`|2m5s+Pl(_Hte||Q&We9(WG0h#F|M%h_{Ks|rZ~aX4yN@k|?TV_MnpbVx!j4VDu6 zwnkv4I8y5o<}&ZEF~vVu}h6285b7j$S#BgO^XyM9cU;MhMN z-Z;?I4vq0+aab^f*Ir6zvc0Z>SD~|`Ulg0LHN$0cBqalPeGDJy$>_zStc<#z&%1Ho zi_>0bH3?s_UzLg3Y9_p&yYlRrE}?tn(sq)`s6%__ux9wZ05#LoJG+twz<;}as8&M+ z_?}Qoa$q7jxxzP|OPu?JhMtK}?|9atZl@q;TIe(uZ1H=uKRPx0TExStWa$>HQqg3aWTQBeV$72H|3}d!vzf3&rvGv#?3!5hb2eh<*HR zC-7i05Ntj(aSDVl+n(}0>a|6gtOw2g=Lx?7<5T4Z+9A-gFGHROgdZ$nK!&?06L+mO zUr4YU0M=I>F8$Jo@K8Y(ksCWzR#Y#b?pZGPg*C)iq&8u z=U${XF@&8`7C}NoofsHFBfY+39)Ft--)!wDgeKCu-l?5M_%iCod9C#+Md&|FOYbagEyM=!?ca@I zn2{#>I8~q*jb)3I^gW2|UpiH58v_ztKR@;02hj(Ny%jK?Ma)sdcrrDZtEcg-(0YOu zF@Jfv{oW$aiy>?`>OWkXPULO8XtxmH93=Y5yT)syNf`OEx|ff(2z&1DxfOCJ0z13mt| z`=kDsi}zpgn=7z+KYJ?eNjy~K-r#2@@-DnM1>>Cdx4~Mj(&#US61021V`YlS4WTQ0 zun0rhhXG%JF1kN5Rj5 zQm{Um=p4Ae2RYbCRz?=>_!ZEdpmB@xx7Nv8u*-;{f493I1pCjpb{OYld0x;B zFQ;-attQ9CDU6{{O4l#GYqQX5(U#V{GYsP?Eb88vG~(gGFQq)YClEfDf>d8 z6>YZia^RPGWOWb{5|*n#4hsH5ySPV)d1!x%MpZi+?ot1Q5Brf6OIEnqT8EXzf?VA{ z&Ebb%-QR|N{n$4wl_b#F4o2@qg%}7u=D*@1`%mzzR)8`!arC$K9Ck}MOPA-BqeV;m zq0n%GJJ0qxEy}hXQf0Om@0zFt)~;VI+zTCWTwmQ@>~J(*w29Hawlf!-baa2{7M0@T zm6N%R5zRoaAJfQ9ISTY)TIxvfiIe7K_q)CBfcsly^5{?H!!;GVQ@aJn;b!3G`Zu;t zIGyk&;>=P982IU{XAym{$+11mo<#nW-_8$`66eN%+lOA9_TxBad_C;QakLORrDD%x>2S7J0Ne?gwP7{Acou`~Ecbb<4SodFLe*Q0Ankx{v z%1ys!+KA^K2)g$36Mc?1^f3=;TTrcKw{eBw6b#2ye&N;c!L6>6ViC>*Anhrcl^fbg zoNG3QJaVHzZ=KPk=U6(PIq>mu*~BQm(Y^0*q-zM-RgRDJ9?3)2tt_-IbQQS6K03f+ z_cR`q&8m+gbQST(7>4_or?B9ba7v~p8LzqJo@9JHioqe?5es7d*cmk9PA9YgL3^a! z#-xZGU>dTI?i1$eBnieM-IaU>*oh|Kf{Ov`5(~mQneC&F0R`ZPALDz9Ou=}^L;&*~GP|nIGelr&DlajMf zW>v%LP-8tkxf=DnbFXAGPoSvWyU|0^jmY=(!t)=IL>|W7s3WfqWMI6#)nDe+ZXhD4 z1Sozr;nzXa+pzcvErocKlPsK||I4}-e|7_0X6k7uR;`3_2_ETCuVVc4XRF{}rLzCt zKmLD}4v`b2NG%pFO>l6p#;kWN5P28{$Iid}M20&bMdbUNIx*dSm)zo;CGg1Wxa+fn zgu|@vvo2TCQM38oF5ATxFgmgO<%r!7#^2v^2I%`R{T7prV_OrjK6j^j7Zrhxy$myZ z)W%`1bNC(CpLCchP4U(M2e?ZAZJz-#=Lo;Jd5SJ<9L*~1ioRQ9!*6oq-eF&YGyK3u zG(Nc#mg@>A&ub8U+$GuQT-_1a-AGQMI$Qu%QeV`Jib+rtT>kySsI}WTvrKuJ&{mkslCvnu^>%(Fgv!uI_)KPyvmUk}b6~{g@eGIvz@@ z0}o10*HiU_F#k@=Ns6}}1)Th^tOyjtT9Lu@LI9yhZa=Hsk<^X+Pcy!kOcDBjK1SQ@ z3&YqZ#RR=cx}b3TOS|*KL1gx6O>KW(jD~ZC2mYvb;`uV#w7J+4?5B;|cB#P)4E^z1gr55U z*Yf!9AO1f-ffaZ?t!;0KoA+vbJCU2T-0bK@_-)&6YKMQ!g*4Hz zBbQH&Lb+vq!fIM7Mod1{vW=<&g(tcND`z^e!M*T~K9SeJRVcmpEzKa3eqaBvFT4h} zhFv`zW0a1*gS3k*2OB`bMnK-oBnB6bJnl`h>4We!&r45;yf#Zl&e`*lQz+II!E{fi z4+E9aV_CWuD;ep2KiJHG30v#X+1@t1dSO+Dnx4qtZar^hEz*JtTz=8lzL&#$YfazK zaDp>88`NAJ6pxqu#h~HtQrciW7Q;4p&3)$m!P7%EGPSfF2YmLyx6JDdHRDcn54i|1&&7p*z*=>q-BF9FoH(Ile$SZaG z)zuMSi&0P6i%u}NLM&fJM6t;*;ZuAd;5$pqLj<*=%rwVfN%>=EYj!QR;JN2#JxcK4 z$=BhJ1gGKdj|b{ZW)qMVbCAn&rW+)zKWr88t;bhl&V!bsL~d=&jDy2}U=Y*;_OPU3puy z3n@u(;hW6O-#a>?XUhqJ`N15pHYoAc{Ot?;Yt`!+1h*x^Cfd1Kp$Oy$uF1uDR)U}c zXF`^26{zvLtZsVbL3`8{$2ejhQr$Rnr{i)79>@K?xn5&9E%=ZooVpJEO3Dm1RRXtC?(JL?`~cnUQzC_DGm%r;P~jR?H564{5m%KbIJ^!=M84Oj zVQr^CXLxWkd_TC|=&^qfrthNYBR|i;-aR>WKdAEmyTAJ{TOj{qKPj%;-?r1I6Sd>} zN4$;>Lk$PbZHLM#eD>g_L$FZ~z7TEe#i<&Mu>qvp7s{P?7qZ zj@R!|hR(d7f|6sm=z^^(aM4xU?7{dbbj*Ld{q=YY{K*TqcJmtt_h9l-4W-XW8>#g* ze}W7fdP`SWwTq#}HR8}=ib2$uuW8AA)sC5h>p7zDqfv3!_|1oeuVtEPLn$=A19%_# zNG=2rdU18m)Ht_#lwUe2A@1A;ukMC9C+iS7j`3}2`nSk9mbENa9P$}T-i1W!WH(^I z!Luh+GxIRuTFZ^$J7gHKy!ChgZz4abo0lZ%(1}YNud|HTiTqy4-2o+TwOA&c)W%BO zYqBAkQ=o+ehjPQeJE)V9O_%rG!o~#Dh|ZN2T+hau>&2>a?v*$-C2g+PS%A7+Do=0h zDZ_0jw^n~P55_vVZPOLIa4*I1vr&&pG+Lc#D{iO(|2dh4{EcBW?usv6;A%v_rsrmb z;?>|IeS{;BxU~FlSswrWrvIZ(Qm9ACx&jlJn_BB}m#qu9uKp_iz%)kmN5(E{{3hY* z%%3*eC=$Vyl?-Q98vy+W>yz;lL;>*V=XxXHmEZ7VW~f3tpsG?EcMe7pLEeqRsRAF!NR zXbl4SuM+n<0*QJ1jY5$t%H1%Sd+GNiYX>eJEasl&%fv9_8M$k;lX#i#!t&g2!iOvp z7aYV(}Cgs za#np{ZLWdR+e#O`U#DUyb(92eb0=uh2MoC^_uxDWyG4(SFY3y4%SXM7#Vs#R7+HI@ zgM!D!a4ymi+}vs^y23qxA-hx_ZEBIxD0!BW-J}D~*Or(Uy&*V0a?PBMu5Dnz5Nug( zwnXSpo=q{{UIGJIBiTIxdf+v8RENdT7BY(J+gzvH(RtUe?LRM1A$@T1UBAR^!q;n- zl*%-Txmo*Vwsv`d+@o>w>8-W+S#zPAn()8r2C25+-9_+6|NHA-;S*Sar^n!(jX~H6XHmQ zN`n;5Ar%@CQ3)ABVwvZ8o~Oq=ea)X*-@YoPZL)|_4CmiP-r(3D z1hbxP?vynz!2A+l2PKo|_&|PkiOk$0ylej?+6+rkx4E&(=XEPW$D1}2wRUV!94h!| zUJ*7P|feBNPPwT;CY(9uBntEu@p*&nLca8CL zzaZFA61{(Xn#?i&N5F;%j zJ(?1zEB?0dt^QDxipPw^6a={%;c>y@Ej!L2$e!=mxMqF<8g{&V`@+2dXStnRK2*E9ET}q0SSL*|AMN z%dG|0H5>`vPJJJKvio7n%&s_?|C)D=KJ{F2$LC3>I5}gm=F93?Gx(Fx({)eOIF%Eq zd-v4Q7V3H7Jr>??Rz~DPLP)YB=gBmj8^7Rk@QHT3b=GIUSVax!aW2~`Ay5TArg?V%{6uLZFg{8mKe$S9TMe8wIPZ0IAoWFpE6|Uxs1YMovJOiz%V8fs zqe{^y1~>8YIw&aR!(u13WP3&q&N|Y(qi{(jUfH6#!BX`F4jx%KzR)!RPM;X=k?>Oz z9K9Csls78@j%^xWn>Q>O%K~4#Hq*Hcdv_{~x=Ee4Z8MYEC?wd1i&r0%Hr<{D54%gf z11yW+tm?!wgN|h4VI}vx=@mE7iife8W8i5>F?;iMtyuvEweo5?J+H?&AKQ{AIVm7N z>$UIcsaaUZv8CGaQ!Va!dBxbTvJH<;nWC}nT@1|Uld2iBDIeE2cIBFHtOUzF;UkS| z>fpu@74xQ?hhTl-t@@)Q)bm{9?Uh1?P|s-@8%ZWnzbh4;h_urgodAh%Z{2O%oQsAI zUs9i$7h#yfW&iQ>b3n~@bng{so1!;SQ1LvrSGWK!pvB@WlP zK<&;{v??xHmJd4Zf?{>5)%aCEO~|i=I#031vP?iNAF`*;dGQO(qh0Z+#l z!@dY+}L3C`enuRtR{4QArY~rAeXxTecE`#)Ebl(<1qunY_OfeC!;tcAAKjh_Z~?-zq)8m zAg54sAk^`vwPacaK~2{2GoK(1tk2GUK4}H@dsJ4Z=P_!X+kN=`L(`~p<~3idZyL-) zy&gvdd=940VH0q6ID06z7?x{^?XGLdg6jb%dehO(hxMbegww#r9SXgB9 zW;peHh@V1IW{GGX&UM-1_=S4>a&2pyVnkde-da9aWa9n;h$%Xr^yKti+$^?R&POL5 zOupXUxmKnfnETZ~X!+E@08TaYkaJl`Jt45-#lc*h8$Eb%_)7+gjj}CVNS*7l_t>o3 z%gknwvU|14qdOXGZb_E5Yf-=J<%o20WLM+z45y749F0v6A^p0V)4_IuPm@E7&dt{1i;b6#0(nu0%QzcG2qP3;G{ zWFJ1WDF#G=*T;Rse2mjcq&JAQu|v&w4M$QOvDV891+bmB{)qz zNXD5v0;e8X*c~m=jMfLb1d%%LsQ7xsx}5`_gQw@=GXabSoa0hkrZA}leS%Kb%LDa1 z;N_iL2U*m^F5469n+u9@meJxo-8nwRFGsc~w- z{&$5icITqc96OpI^To59t;M-mo?|-8-!1?Hh5U9dTa}A^JG1kZKGvZFbK=#gz;tYG zcq8BVu@p|Kg^vhZUXF`Bl-3Tmc#bEBM(!MUu^OuE+_`1*voYgM#F$K}B8+Ttd=!*e zf}QumI0mKVQ0s=in@3Z>yZ_Ti=HILROpxo!IhT}JjTXlx26=L1!zsVKp_`mS;pA#d z=I*Cy_$JtB=`G%uP`@$B0xsm>eCfkhHWE1yAyA=LZ|;JL#bS|R4Rs*ND<~3?Q3`fx z>y5lFwZILj^&!iSRKWhzYW$y~lTguXUm@SyV6a!+!f=@$08huMd^nQ9K-pE3N?rBa z@X5ukavwWAVGk~jI_VgV&3PL`GcL!#huJ~{=I|9m{QI+`6|WXRt%qW$_k?^XTPb&4 zDYXuE#2n2E@##P#WB>8N^U5K{=cfgm5#)rRdV#RBz&o6TXW)gGg`e+ zuuDm918=)Yk;e10!C+hZt{~BH^lgolHS^8@@DSK`tHB#?RJ~cHf4&XY7p3ZKJ9rD* zwt57f4@yMWQ{g_3uhoFzytd3@Sm9bjhMPOtI)|O5d+h`hn-Za zq3+`myt$go4UVKbxDWV9-CL>7Jy`Wn0py>*5;9@p3v|A93#HFTg7ZP)yOZMD!1Ugw zp=Uhn@$6{zho#iLgEDoZP2vZNfv;Tu)=$)P0DoMc_FMYnGr)v}d@l3z3d1ns=jxoT zho53}?Dd~ln#ZEe&N*jg*M#C;-4pIdFXlkqX#VT>^P<5i)-~F=suG{PySvukHU=u5 zs5fMD&@qvirem#*S zv>ou=`V{q?1=p&q#MvA3Ky~QPBcm@Aqvm$^;K!>P;N)$U(;MIA!B9i*Q8rpF5Sa7q z=$bdhkUmy(+Rj^57<@|8c!+reXezbnIvq%c&h<0r?47~D9VfK>0;$hoozb<2E*wh% zljh)*7&8WFJ=1nHI$RBx2Y9V1(@Q|l8GH7xiOWarxUp{AsC`b{6PMi|YV8d+rFB)} ztMVXOW4J{lb#I(+?D)wWsr!%z512Y%B_t0jIObSSr}poAp4Zs?vZ5O6&okCKK1+s4 zs{`j-?a#qe5%)Svx^qz2^xd6+hDKQMpmoEMW*_`4+x`0Z`U;S^Is3x|+bH0eefsK| z?!5l_@y8G9KfxjsEHuZvdc@}9i9@ezs|QlgQIv^~_*@o*(G}*Sx3s6ipm@vA8$zyO z?6RMZ1v}Tm+Z&5KR@KJ9fn(#^qT{L8RrxbXkU^%f_dpsp^?UN2uo*Tnl4O@&?4<>VtCzq=XgW`@J*Q z9HsVcMSgagz5G-SI3!zkZFhF>|NikOjOIVjBoiKwP=A!F8w(e!97UGQOGkH^rD~6I z1910#BmOm9QSh^dhR#lb1~9afQ|?MG!@F-j3|qUb2@|rdCQAynp#+CPU9M{^3~7{M z>>PRp>W^-lv*vC)oS)=waA-<1I=v6@|4N--$eB55@4|O^=+Y);)yxwEKC4SWc}x=W z3P{}gU{(Q+BIn+vyiUgYq$Z#CjsT3w_PpObwH}pDeX`NCD!|(+$~R}ZFmMWUK+N-r zx4_`uWNxdBRJeNZDdz_JR2;cR##}Eu28LvJdDujzq2`2XhOj;lGWNE*yNZWk!j0Ay zmoytt$gt)>!|iCCm2&!~VSXCSUc8iR?Ymrf!sFewV|pS++%G=4Ze=-oy?dWANh1#; z%w~)+uPFi1M5RkQw(*$uP&m1gKL`iAO&<5*a2TAJ6EN}9h-}n%rgnHA7-u%JA{}1IuYoHi@sP{g9Kio71Mhw|c{9G7y8q#d|B^SOvZ11= zyz}X+QV0@e79(|TPHIWoxhu}aV31>XT(Xtg_hNQrtJJDu9P>PI?wYul@Uk($Mt(va zbq>-jlT~t!nCE;nL!3GWAvW3mhld;ofwDbn$NYK0cvGlfJ z4t(i)JE?GQJ{o#3#0^q6!RS2iiLybd@OiYEez!y%j@fK?cHEKY@c5kL;|)`q!EXGD zq?5JUI7~n;z_Q#84=L;}SiYzlr*kAk?)X{(+pi{XGai@?)JFSysXR{zo@ARm z`%hJAZMlgvHb0X8TvdTilN9&@)|Q~(*Gly~)pS_sGk?Fuu5^sMBmCeCbq~9O_QW(9 zxhC|PWay;PaT=Rnzq!jR^1tQ&!M|Xr{jYYxgfnhGK&=Fc6K4me;u#07@NHvT zA;{S1%~?$^_(_r1nfncOuKZ@M;DlNA$k_RX;UQmy&GXHtcO0)k3wxD&B1W0;`r7h# zQ@;%S6j}e^qFEG-)xYQ^tzCxeU!EDUEI1vF3vN!Ytg8W?B@1qy(JFzEY*R%!>R#-; z!%wt&#w9@262-Vq5e8`Tx-XtJwFpI?4nHX3 zn*_$)Gp~jWb3nZIL27VZ9j=7XSaA^&Y8MwO?4xiY?SSU~fPKIW#ohzvO8zqH#52U_8U4gWwIajOk z(dRP%FzVjQD6PWvJf+tA_BMjG zkLBnX>ba>8y33SfseKwCB58d!fq`aj(yvFvB;(^bnOkS`CBXxMR*P#Z8^J?m^t+Y! zYoKeCo8G&`1gx>y;+Ef8gS&1jcc)oYf?Mr$_j|XmA=i1SAq%MYuR!NLN{Q6EVKJk@ zdW={tB%HhDxcFu^=&L{cnr2#o2hwzKMUw+~Pq?VLmb$0AI%A1p+T=J$vyxhJa?@kb znjzy@xs7^0(XYEeVtpyKzcKmp{FYa+o1xft=nHj^YX86ggBf7L&5zCk{86Q_GQ?4N z{LovtC&}Za#lt{cI4vM+a&RGjzSTBt*g*z$&rJ3JA&FFocW)e8eeNV2IJ#%aJ?cKr z+BsrA%0V@7MB$EBsZ0*_+{LZ6X)}Uw);guzmIGfw-o_~kn$F+u9cVsw?HHny%Cq;g z_oiU9#36y$?hI7RI2YfP9*DE_O};u+B;&TDwnZ7c(;=N{)u82Afx+hn{q%}DKXQ}M z%I3puFL0{XzT|`@X`p)k&~9(9dLOg2TRHD#LH2LfzhQgW=0_!68u2KymLGaC|gbCjsjUmlp0)YOnn^hrbx`^A zg8A++Qnty7@wplwhs#)6J`RM}b_P?zE2?l&;xwB#TqW>w%>k1O0@VJ9GfHlwE2;ab za+}A0@XtVjF?$}*qJA%{xbOCMfLJti1URUS;);XMiwagu3$6xjhU87JYxywjSy0J- ziyFu})+n*@RyHgfR-B-IJ{b>}1TC$&-+tsr&6?KXFZSD8}%yo7M=mcVOFz z%hh8BMF79>>*B!jAW#TCAT`Fl2Br(>Yu>)l0#SLhbQQyS7Ic!08dfkDE@#L&U~S z*_J7>`1Z6&tntVG^L_p`mi{mQ#e`1IdCMIVsdKI*c5GlwjE0ey-K}^&7en~5qz_9r zxj@pSp{r|)AL4R5{V-$d{=o?vpP!{I$VR_-7e=674311ZBkeY*4n{hiUpkH2Pv6wy z-<41OeznzPXM1%#b#BkLsqdtQM4+!gD-OQ zU85J&;_k0|mMfnt#bLG9u^(dUV0*Q}ZqG6|`0ze&lFp_y5J`8Q&J^*2S%<%VNShyq z!j~;qeqvD1QP!PsH8xF$&X4Od_%o^V<9>b_v6*ifR>`2PW=t&(NIrNpjk>4%y02&G zZMjl>KQ3ry6W;^aSUCT~mbd-;KmISzir#Hwf?;?-$1|z(xaw=r>IT(3V19hb^&qDX zvJ;j3q_Pu0bA~j}t}RF8+(C5lk_r< z$DXL>DX;YTS{Bi*=jSL(@b0O~hKV0%n{n4v!y%crvXp!)yn21P=cFm2P#LlBiuZs>ymNAqes@_l zeiGTUNs)Sv(wh7HypcIc;JerC(X4qk@GgAzqalxr;l|-5%iM|@VD;JH#sJC9%By7*L#r##Z$F3vV*fwn7Jt|@`M4J9t*W&$```QDCWfDGjj0;!!XEg&@&Wf z7)ezIdZWDMCDcyrKfk^A82Tr0m@wCTPxVOaJd|^foHx~~3BzincG>VE#N1fE?BUBO z^tyRjWfeblUXRlL*H0(bU{Rb(cfXRm0+n*(l1-Wd~spEUIMEqP9z2W_Z2RAW*j46hd+ZG9jX zYV?nsljbW&%gH}Y7nPyzcjmfaenYkf(#K0^PUNKadA0M&J+qF6!7GCnE^vzm#a71% z4Us5}J`insXGJ+Y7g#a!NLvER)f%1+eO8V$yA)OipG-ubna*+-a#CUOfrK1C#~1MF zmyz;hM2H@Cg+cg{PN}%=0v~!BodR%T=mtDDP zJ#5e3o};rb9$e2v8ogamhu*_&-5&1BM>|!^Vl{zm9M)-P89O!z-XCaFJ)%+wgN#bU zUabj2=2+7aw?7o)j{G6>tp>JW{q=zN*JN(unL&b*xpOkW@U_FZMB@%j9`mqZfP5;h zg({4n2Y>UG=*Q!_KQlGypcHFusn)nQ&B-Vb=n^uG4zIgav z%&!M!t;+|)7ctP6Ic#qtenE*y3D#7-p$Nc5_rSP&_^@|Bd z4U|kgIYm>jhB|kC>U*`tS@1!zQs9fb4m$086guvrGgLKXu3tgzU%G5RY;fMbdsrXF z|6-3t1O^Qle5B<~G;r$hlEneMdtEp_b$JAi9eH?l*UES}nEz=~^w%Wt_boWO zF2(`%-fqpCKGBythiFlXb&4bK=|ptY2)4ozZhwnoBMXtY_+f~#WFcPl7_cGRJOR2F zEZQL`9@_u@@lToteYTZ)4swm`hVxtMa5ZP`bq%#txcDi!DInnmeoZb(Z(Q4shB?hw z2j^$Ox#ejgiNUWRe8)%i`S${;`+<+W@sf3f&8O8~NiHbFhNby2%Hzu5qNzjs+?7Q* zUFyyxmt6ta$mRHcMFq8QN?aheO3e?0=Op=c2O{oVUuyX&l!5bZY!~MU@`vkpo4L$m z?&0vv#eS0)7vjdFuf0C(%!L4%5xLLPThU%=_IrcH@vznCwD9wv!%@7seWSly2l(g> zdG)}p7$yl@418#J0ZeaN4jRQMgBhl6qdmlHao;?}@XS^Oo9EVzd2g!WSVeT>PW57( zm-fnMRGJ5#XyH=ya<_qEsgLKiR=w<91b`1LQ$VX_cEQgHeOJ#(-UEp@zI{bRJ21H-S-k7fBf@-(R=0?v*0@JfkC%qjL zg9j6CxYQ251Bo|O%eMs-fV5R>(+=u;PqpU+wR;^5IHI;l1%eXcl<@q3Pgi`=t+e68 zjD5wp^rqdQ(~Er3sxY+`cpt&TrU;Es)cuBIB$7%ET;f3P!nrY$)V|(XRTJX*m*rv3 zUEMmT5e1Olw9hePTrvu(Z#^?wE}lAnPU6J8=gIx^=qqK`UW!~qN#%Q>wf9_+cVPO*Po zfHjFR9`oKZV7TjR^E9ar7#-^ox^4%xj=$rs*uGT>ST%g&rlVtX;N81epM#A_;2=^U z$~B-7Jsdwxh>p+4mt}hpJ(J||d6pbLtt47rFj6Xnbn`_3HWZ*s-VgSwyy=TYN5m>N_ki|&V0#-xrNx-9hV(uT8OVWCdF+yk3YEVx>|TSzWOrdu`G4}sLX`u2E-Bu9Wd}^9WObzVgNf(JSZUVtrn?&aMWbi@Vua)!ialFIMiBr#%VT!%r znK=bH;QnMy)OO7RV8lgj{K$D1wOT$F%D30!TF#Dv7h6+7dgy~~O7pXEK&Uo{DKj5c z>O#|9iu%vL`mH0RU;bMLm|#BgX-af;1~gv~s2ix&4$2PiLXJO(#OQfb!_&eO@qRJ) zyYZrNAb-&BaZY0a7+h$Ux-i)Zz9voeUg{PHzT7WYPFR-@>gTf62MAY#0Va&e(%2v2 zmx<%6Cysr1z7X~&JBv!!C&7q&RZiN?rEub9B~u;ZL3Y!~l_qkv7}p&n=e)iUzc_sq zy%@rPf!Rk?R(Drm+1u@WoP~FgZ?@XC&a6vtkLzGcmQ@`t9L%vaZdDytpDJsaPMyc~ zrD~UfT~;oHSGMGD6+;Z>;JjuV-3)nCorYVDi2`-Gq?HNYQ6M1y)5b@>@i4|}y%}G4 z1ngforBhiW1Lk?w)SMof3G$s+jJK|-ggjZ1pC=mRLUs4vv|T>O@Myc^f)KA;Xj`P( zlz%#~)>RJCXo8%rBjhAasrydU@A_|~?icNvQ)n?dt^?m3l4~srO+@AhO;4#)Ef9L9 zR?J7S8WltyMowQ>i9;jwR+g5OQTN!aTfOdODhyL zGPtX}pD|k22bGFMHqDkw#$B1)txQXNLB{i^)UKk-n0vfyd-jV)Y?M01>uOsA(v9X< zU5f*dpWkqW@q1TTpqQe5tS%9In%MtGe+K^R3@~B6M)5Y?<^ou}#HvH(U>kMryxK<@ z{tl=eu=(+>+!&Bh+V|dxS|6EQWBpWwIv*%p`KE}6cr&ijK7GUMWIgbV3)(kG^C7+p z_7SYf@Wvq-D{>ckGGK(BS7=dn1zbAYJX7XM6invSUc3HqChSrSvw6~-29c5b<`4ZE zi^_%L7K`$g@Eg|7bnwg2^y=r`~y8DPRH%W@;p!PVfc5V3i2 zb3QiXy07DQH{lo;=O+UeQ|ou}BY5sIicrV6T`lu;4vx>)+@W{B3`hGPaK7tOgXt$V z1TD3mz$S_3cGpyrLHoJWvpP|3Ebfc7VIFDuV(f_1uRxIUyBihZ};&@XC+8lx36 zs0UooY44;R3e-7VSEa{pl^R%u+WcM@uI1%`xap)SQHNKceR(Ut{HI)acXiFjDcc$N zLZ`W1>?QSk8K>))z(dv8>1%o_VOAx22gkXOJerA0a*+~x(-`QYc1(Txwlb*Bl`T2h z5{>%VHhdPxV{p;jQR}Zz`hQd=`t9^*fPDs-pwN1Elcs+woDlwrvAZn-PK94Ntfe1@ zColO(kA7W(2KDixAGpfkwPi^C*85;YHkBwnjN%twtF$Ytxx4170?7C^5eIv zP4j|kyWm5{`gNdUGB2~W>j`w7J(MT7>@+5)o0x9*rM?G^%~#%DSOuDU9+=s>HDPfO zbxuB}gW}Rlvy8qJL5pNCeC)odG5!yq{5=k<*4c54)C1p38&r0^GcNX0~8r=~f#Jp#o4DSJfV6nvUo8 zxoTv#rQnErH@74^H$wdAdg1gX8?p4s2cuoozWJwyl6RV~F~DL{g^A$BDimzq^2$yy zA2i={j_1-%gzCgc`C8U-a3E#&(9?%=AaLcwpHzY>@zO|xjE2;D%wBubQ&m0@7VR+; z+nrqwp{F2s*yk6(xm2}#>Xah1oB5#2)3K`m`}rR|1p4j$Kn9qwpk=*c)08@VeO|}u zMtcY3X`kOA9-jm+f-Kh>9xVj*G4+oNq@%!hxcCu8`5GK$dFyB2C%G^!ZoN5={0VFm zOX-{vl>v@dua)LbN&!a2=jZxg3(!*H@aJnvC79uC7+W3SiI=v`4OpRe6vXOgXN1jp z4ty_Go^CR11>5i?rX3C^apZ`O$)nwp@Qdzw;q=Z&Q0|;n&@r_M9@I*CcDwX{zWRaA z>=*gdGQfmZwR=NssC^}C2VJgOv%em$E^jqaskgweF#df}2GQ`@J@CyTuNpYottRJp zAOz=tV93tIT+EoX zaNB`*3D6K!8Yp`u6Zy_|^Tu}v5dc-VjUpdz^OIzBD=ND8*_hYPyMCE$k2vr-jpeqiO97BQ4J z0-m}Gx=O2+!cR&u2Ylu}#&OF<<*v)+VMXEb+u8g%7~Z^Ccq(;2d`OE`X4a)-aMHga zIm9ComQHuu!ZqSm|L3b8@5Fw|KRpA~{qdeVhj6be1m&mWrToV_yQOS*{Nig(uWm4MHJTxlM4pJQW7?w_!y)$XsW2_JKyeO=dh7q;< zHzmrXqus%Eb2c9>hp&yYU#88qhmm9KFGTQA&v&icB()?z7%BoBW1R2SLhgpNHwAUM z{qy6ucV557UzPzTwEf&5dG%})u5WjGC}qLG%rk>**9F$%l(h@xm~YB)=d4o2lI#W; zVHjM$Z$lAGAA6q3yPUdzbMyEE<_*c{wIr7Fm{uOxEVvNE-*pqz_@-liO*Ib8 zv>H|B^32?CR}9^TCC75FDs4)@4~mvuBn+|lH4NR#@~#A??nsZpR}XP#|7dA zMI~r|tj4}uy%16kI?U&8dJZAx?^mC=QG+L*9dxrCmk+1UVMMq0Mu79@e8hHC;wroY*zr)A5$EiknJ?K-sQxJE@o(v?vGsSDb0W6S`fF z7pgSFgXP*m=kC|S;0BwIz7du1V%*2*<-6)|`8A23Z}0Jh>ucr+T-a6zho;Zq?c}}z zOJCU)RU|U68JpeLDM6msa>JbSPT)*5*10e!1^o`4QaYwujz2&7`pKAj-tl5k>c)zy zLNJ&5$tj~C5zP$`dRcUrpsgO$r*dK<7O2GSIP2L8|8=PS2KqDbKb8R|s9v3WENx#s zEPi{|XYa)h+;%ztVhv9oXuMUc5xQ9e@1ylUw{K}dg>|}eC91`scCUHqtI9lF5+o3= zIFh=*)P2?^1?qki(YC;6Ue-~-Kk3CNg&|e&fq$cR@XVtA`SCy2xBZU)xC}5MOFT?L z8f$Rqtid}r`s4wxf{k32M?BE_Z@>x3ejHS>Ztu%@fgr# zBanEm8P#uy%g4@3gW_rKB~v^~anx!Ni8ikG{`v98byB~j|M3hkLGAr;&it$nTowAU zRzs`<-4~`GX?pq)Pi*C}QuM0Edv_o~fGZeM%yVpf9O6)@tXbPiyA`@WDJ+AaK#;b% zsAMs`5ch=Fi%j#3=>PulKi;SP0sQe9p!UZf5tY!M`WP27D}&~1q{F8X2bO8BNrYxo z`#o`*3|xAked2bTa(MEHKl+|=4pcl?J!j3dWSE)}->K3agYpeRd~fYy`sc?V-#Psj z|27$50=Ma?4Y`qpa5z1AmCJ@)SU9-LaPs;N5T5pveJgJh?)>1ZQ!%9-*JQ68Y$a2M z^Q9_BOfPH#8>_ve?phV~&yT-NU-k#`=VgEiSH2Fa)#9y##Vf8}ysQ@hC&Q#SYO5txCdVgU38TiXGK<)cYRlTsK@DzTz zVJ}oBQ2^H-*PV2hZt0&Ne_0>&JNo-)fC=uI!B4(+TkVGLwWBF8 z*=uTKZnn!z|0mR^^feKxSXoge}gERMA0`Rt0~fIc#ie^%zO_2yix)iBUw4I`X6iuK= ziK3kp&7x=&MN$+Er$~+>4T=;fnoiNT7lv^Zt)+;cqRkY^Q>0AMB8s+9G?t?I6iudR zDMh>#@liCDqHq6(QnZPptrUq;G>xJW6v^V(-uB%{9x?f;hr*0>h2 zZB-AuC-%#@*6&sO3q#TVms-PLujQDk_-!N_ed{t-djDg}FyWW#Z@utq)g0forPx$+ zf3N;FUw%!SPw`vlnd$8Qx5WJ`HBD4fe@V?R+5!CE-}>BmzT@OE-%*j2hyEwujg(o~ zS6PvbJkg`qPo~L7v&!t`+_+is(e#KNH#U5Bc8NXW&zkSMeU3r@f3zO>pY`;zE~}m( z-5y<@l&fiaq)gZERUZ7G@zCq7S?wYA2-4+9*_ssx9Z5YMb=kyi{Tuz#?XoMA_z4m@ zQYNU&CN8=>y-f6~Ilt$XU^J_&%k`a4FVp4dWx5`{{zuD-EdT7}37^PWv&Kg>oAwa- zzL3OE(Twu<>`Le)zj?|KLm*$kt0az6}!KELg3)AW+5r} ziNAcJpx*Q8`YgWn*Z;Ij?Eg`yNc_Z3cq%PGG5 zj)dQ5Y@*kWB5*IxlQYP3d&c5QH$IWVYpLXbSbUQS^J@FAeHu61kG<^~e$pgp7 zKKhf@kJcUE<$gD||Cjo|(LVn@S zv^YtbV6S+aS@Vt!TC?~BIcRc(Pmo?uFVp2no{1c(CrJ1N37;V0v%}vi_gm%J`6c|m z>{++6<~0k69>Jb^THZ-LLF+#1f3qB$c<6TMe#!VEa&)B2)9Xo@$PpxbI+A*V^m{!QZH_`x`=>sYUsH2hKh-!1pwj)(tNpG|(O|0KJ= zIZuC=IN0RrH@AnK9oBrdu4awHS{Aa(9Av)NuwH-Il!-oD`9Ade)F=K45_>FUt54)v z*fYL}KB=eKA@;24`Jl;j(8_G}*!Uy)>ZM2b%TAxPi^vnC_g^3SJ#nz~Nx26}I|&kd zH0+fxT0K2qJ!N`3$ati;gYKV{f2%&xBk>V^;`evvu~$FRZ2;Ysh%t!bH z69M=ujTK@OT9QnqICi5wk?UAi3M6M1^Mnq`;HS7gl- zMcQ()E~`xVq#VtLPnYYfOqM%|T{`xq&#u0j79Tq~U78%dTuqi^X>$LqeWFkI7tQiR z=l|BSVjp%$-Y2sjOCa(+%hF%Je@s$jAz3CTvBZC7m{Ugn%!PHI$ANgM>}%esV5kkt3Y*@yie z`M%`nag#Djug5=&Ps(I@x~I%qW+r|Kzb9Ur-Cq13t^Ywe;-4Tpf25wYr$>(DjZGeU z>`n1da%mK}T5)0QLY_DGo^(I;hsbbj>f@AKc9zKl)E1c`rACP?SA zE3@O%?GQN@auB4+k#-QIw~z4YNaWZe%MUv}vdl`?C-QW@HO(Hqp6C%I^`uO&hfm7~ zspp{O&6?$xjAx=x_&sHs9p$yf@}A`v z^0PS|Y0H5<@@$svdg_TCnjEPo$kB&fPd$;NA^Dp4N6B%}+Dpp4kQGNS|9!QWR!{6& z6TfVhWl24e?}dHEL+XhiHgOQUJ^pCa{4K@K9HLbNj)hOWXC7< zKZ+>h$f{gI!Qi9W4Nem15f`T3TPbh)1KPhb8beh9Ms_tK~7 zk@}w3YogCWQs0AQzL8}nHgfcKu(MD2J@#pKd)Z;*kL0D7{O|1tx*o|3J+Ex?LE6<5 z4_%L4KhXU2=+pT0e35dG{Ex;@i=#)M_@g7ccChl$OaDjX_;2;ujT<)pNxtaVD}Gx0 z>GEXU5k5P8Qr`=Ibo`Jw*yaDfZ9lvG6TdWM*A8~=@8Q$qr?;O?e-Zs2zcf9p(UHo|v-gXX`s3jghJfPZavC!15Ng}$#QORzS-2e3B1o3P4+AI&OT z3w)Q~F!nq0jr&j39sj-TCiopCSY?R`tTGEHv+7M)sLQfb&B6c{UvtWLJ;jMEWa(S8 zkYn<9zAj6i_|2a5oo~YOzhM+hZuED|W|jF^Wj9v4C$q}BEbKW1fYt737Lv{IZY()s zpYVwtk}nCC{c4&&l5ZkM4k2K&@}14fhY3rc$dkC}d1?*0& zVAV_ZwogtL`Nh6uZ~NqAk?-|=*q7?9PfjHHMPI77J~@%(mwM^m_2i_IZ!a=Oe(e?L z+pE(ruRwyVGerug4nBS3fuy2aqUz!cr)3qrR@NNjH(vV7X(C7ezZS@;B;Qd=(T}D1 Jy{xSG{{VxH-Q)lO diff --git a/lecture_13/.ipynb_checkpoints/lecture_13-checkpoint.ipynb b/lecture_13/.ipynb_checkpoints/lecture_13-checkpoint.ipynb new file mode 100644 index 0000000..6a5dc68 --- /dev/null +++ b/lecture_13/.ipynb_checkpoints/lecture_13-checkpoint.ipynb @@ -0,0 +1,737 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%plot --format svg" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "setdefaults" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## My question from last class \n", + "\n", + "\n", + "## Your questions from last class\n", + "\n", + "1. Need more linear algebra review\n", + " \n", + " -We will keep doing Linear Algebra, try the practice problems in 'linear_algebra'\n", + "\n", + "2. How do I do HW3? \n", + " \n", + " -demo today\n", + "\n", + "3. For hw4 is the spring constant (K) suppose to be given? \n", + " \n", + " -yes, its 30 N/m\n", + " \n", + "4. Deapool or Joker?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# LU Decomposition\n", + "### efficient storage of matrices for solutions\n", + "\n", + "Considering the same solution set:\n", + "\n", + "$y=Ax$\n", + "\n", + "Assume that we can perform Gauss elimination and achieve this formula:\n", + "\n", + "$Ux=d$ \n", + "\n", + "Where, $U$ is an upper triangular matrix that we derived from Gauss elimination and $d$ is the set of dependent variables after Gauss elimination. \n", + "\n", + "Assume there is a lower triangular matrix, $L$, with ones on the diagonal and same dimensions of $U$ and the following is true:\n", + "\n", + "$L(Ux-d)=Ax-y=0$\n", + "\n", + "Now, $Ax=LUx$, so $A=LU$, and $y=Ld$.\n", + "\n", + "$2x_{1}+x_{2}=1$\n", + "\n", + "$x_{1}+3x_{2}=1$\n", + "\n", + "\n", + "$\\left[ \\begin{array}{cc}\n", + "2 & 1 \\\\\n", + "1 & 3 \\end{array} \\right]\n", + "\\left[\\begin{array}{c} \n", + "x_{1} \\\\ \n", + "x_{2} \\end{array}\\right]=\n", + "\\left[\\begin{array}{c} \n", + "1 \\\\\n", + "1\\end{array}\\right]$\n", + "\n", + "f21=0.5\n", + "\n", + "A(2,1)=1-1 = 0 \n", + "\n", + "A(2,2)=3-0.5=2.5\n", + "\n", + "y(2)=1-0.5=0.5\n", + "\n", + "$L(Ux-d)=\n", + "\\left[ \\begin{array}{cc}\n", + "1 & 0 \\\\\n", + "0.5 & 1 \\end{array} \\right]\n", + "\\left(\\left[ \\begin{array}{cc}\n", + "2 & 1 \\\\\n", + "0 & 2.5 \\end{array} \\right]\n", + "\\left[\\begin{array}{c} \n", + "x_{1} \\\\ \n", + "x_{2} \\end{array}\\right]-\n", + "\\left[\\begin{array}{c} \n", + "1 \\\\\n", + "0.5\\end{array}\\right]\\right)=0$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A =\n", + "\n", + " 2 1\n", + " 1 3\n", + "\n", + "L =\n", + "\n", + " 1.00000 0.00000\n", + " 0.50000 1.00000\n", + "\n", + "U =\n", + "\n", + " 2.00000 1.00000\n", + " 0.00000 2.50000\n", + "\n", + "ans =\n", + "\n", + " 2 1\n", + " 1 3\n", + "\n", + "d =\n", + "\n", + " 1.00000\n", + " 0.50000\n", + "\n", + "y =\n", + "\n", + " 1\n", + " 1\n", + "\n" + ] + } + ], + "source": [ + "A=[2,1;1,3]\n", + "L=[1,0;0.5,1]\n", + "U=[2,1;0,2.5]\n", + "L*U\n", + "\n", + "d=[1;0.5]\n", + "y=L*d" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans = 5.0000\n", + "ans = 1\n", + "ans = 5\n", + "ans = 5\n", + "ans = 5.0000\n" + ] + } + ], + "source": [ + "% what is the determinant of L, U and A?\n", + "\n", + "det(A)\n", + "det(L)\n", + "det(U)\n", + "det(L)*det(U)\n", + "det(L*U)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Pivoting for LU factorization\n", + "\n", + "LU factorization uses the same method as Gauss elimination so it is also necessary to perform partial pivoting when creating the lower and upper triangular matrices. \n", + "\n", + "Matlab and Octave use pivoting in the command \n", + "\n", + "`[L,U,P]=lu(A)`\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "'lu' is a built-in function from the file libinterp/corefcn/lu.cc\n", + "\n", + " -- Built-in Function: [L, U] = lu (A)\n", + " -- Built-in Function: [L, U, P] = lu (A)\n", + " -- Built-in Function: [L, U, P, Q] = lu (S)\n", + " -- Built-in Function: [L, U, P, Q, R] = lu (S)\n", + " -- Built-in Function: [...] = lu (S, THRES)\n", + " -- Built-in Function: Y = lu (...)\n", + " -- Built-in Function: [...] = lu (..., \"vector\")\n", + " Compute the LU decomposition of A.\n", + "\n", + " If A is full subroutines from LAPACK are used and if A is sparse\n", + " then UMFPACK is used.\n", + "\n", + " The result is returned in a permuted form, according to the\n", + " optional return value P. For example, given the matrix 'a = [1, 2;\n", + " 3, 4]',\n", + "\n", + " [l, u, p] = lu (A)\n", + "\n", + " returns\n", + "\n", + " l =\n", + "\n", + " 1.00000 0.00000\n", + " 0.33333 1.00000\n", + "\n", + " u =\n", + "\n", + " 3.00000 4.00000\n", + " 0.00000 0.66667\n", + "\n", + " p =\n", + "\n", + " 0 1\n", + " 1 0\n", + "\n", + " The matrix is not required to be square.\n", + "\n", + " When called with two or three output arguments and a spare input\n", + " matrix, 'lu' does not attempt to perform sparsity preserving column\n", + " permutations. Called with a fourth output argument, the sparsity\n", + " preserving column transformation Q is returned, such that 'P * A *\n", + " Q = L * U'.\n", + "\n", + " Called with a fifth output argument and a sparse input matrix, 'lu'\n", + " attempts to use a scaling factor R on the input matrix such that 'P\n", + " * (R \\ A) * Q = L * U'. This typically leads to a sparser and more\n", + " stable factorization.\n", + "\n", + " An additional input argument THRES, that defines the pivoting\n", + " threshold can be given. THRES can be a scalar, in which case it\n", + " defines the UMFPACK pivoting tolerance for both symmetric and\n", + " unsymmetric cases. If THRES is a 2-element vector, then the first\n", + " element defines the pivoting tolerance for the unsymmetric UMFPACK\n", + " pivoting strategy and the second for the symmetric strategy. By\n", + " default, the values defined by 'spparms' are used ([0.1, 0.001]).\n", + "\n", + " Given the string argument \"vector\", 'lu' returns the values of P\n", + " and Q as vector values, such that for full matrix, 'A (P,:) = L *\n", + " U', and 'R(P,:) * A (:, Q) = L * U'.\n", + "\n", + " With two output arguments, returns the permuted forms of the upper\n", + " and lower triangular matrices, such that 'A = L * U'. With one\n", + " output argument Y, then the matrix returned by the LAPACK routines\n", + " is returned. If the input matrix is sparse then the matrix L is\n", + " embedded into U to give a return value similar to the full case.\n", + " For both full and sparse matrices, 'lu' loses the permutation\n", + " information.\n", + "\n", + " See also: luupdate, ilu, chol, hess, qr, qz, schur, svd.\n", + "\n", + "Additional help for built-in functions and operators is\n", + "available in the online version of the manual. Use the command\n", + "'doc ' to search the manual index.\n", + "\n", + "Help and information about Octave is also available on the WWW\n", + "at http://www.octave.org and via the help@octave.org\n", + "mailing list.\n" + ] + } + ], + "source": [ + "help lu" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "Gnuplot\n", + "Produced by GNUPLOT 5.0 patchlevel 3 \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\t\n", + "\t\t0\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.0005\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.001\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.0015\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.002\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t20\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t40\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t60\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t80\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t100\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\tLU decomp\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\tLU decomp\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\tOctave \\\\\n", + "\n", + "\t\n", + "\t\tOctave \\\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "% time LU solution vs backslash\n", + "t_lu=zeros(100,1);\n", + "t_bs=zeros(100,1);\n", + "for N=1:100\n", + " A=rand(N,N);\n", + " y=rand(N,1);\n", + " [L,U,P]=lu(A);\n", + "\n", + " tic; d=inv(L)*y; x=inv(U)*d; t_lu(N)=toc;\n", + "\n", + " tic; x=inv(A)*y; t_bs(N)=toc;\n", + "end\n", + "plot([1:100],t_lu,[1:100],t_bs) \n", + "legend('LU decomp','Octave \\\\')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Consider the problem again from the intro to Linear Algebra, 4 masses are connected in series to 4 springs with K=10 N/m. What are the final positions of the masses? \n", + "\n", + "![Springs-masses](../lecture_09/mass_springs.svg)\n", + "\n", + "The masses haves the following amounts, 1, 2, 3, and 4 kg for masses 1-4. Using a FBD for each mass:\n", + "\n", + "$m_{1}g+k(x_{2}-x_{1})-kx_{1}=0$\n", + "\n", + "$m_{2}g+k(x_{3}-x_{2})-k(x_{2}-x_{1})=0$\n", + "\n", + "$m_{3}g+k(x_{4}-x_{3})-k(x_{3}-x_{2})=0$\n", + "\n", + "$m_{4}g-k(x_{4}-x_{3})=0$\n", + "\n", + "in matrix form:\n", + "\n", + "$\\left[ \\begin{array}{cccc}\n", + "2k & -k & 0 & 0 \\\\\n", + "-k & 2k & -k & 0 \\\\\n", + "0 & -k & 2k & -k \\\\\n", + "0 & 0 & -k & k \\end{array} \\right]\n", + "\\left[ \\begin{array}{c}\n", + "x_{1} \\\\\n", + "x_{2} \\\\\n", + "x_{3} \\\\\n", + "x_{4} \\end{array} \\right]=\n", + "\\left[ \\begin{array}{c}\n", + "m_{1}g \\\\\n", + "m_{2}g \\\\\n", + "m_{3}g \\\\\n", + "m_{4}g \\end{array} \\right]$" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "K =\n", + "\n", + " 20 -10 0 0\n", + " -10 20 -10 0\n", + " 0 -10 20 -10\n", + " 0 0 -10 10\n", + "\n", + "y =\n", + "\n", + " 9.8100\n", + " 19.6200\n", + " 29.4300\n", + " 39.2400\n", + "\n" + ] + } + ], + "source": [ + "k=10; % N/m\n", + "m1=1; % kg\n", + "m2=2;\n", + "m3=3;\n", + "m4=4;\n", + "g=9.81; % m/s^2\n", + "K=[2*k -k 0 0; -k 2*k -k 0; 0 -k 2*k -k; 0 0 -k k]\n", + "y=[m1*g;m2*g;m3*g;m4*g]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This matrix, K, is symmetric. \n", + "\n", + "`K(i,j)==K(j,i)`\n", + "\n", + "Now we can use,\n", + "\n", + "## Cholesky Factorization\n", + "\n", + "We can decompose the matrix, K into two matrices, $U$ and $U^{T}$, where\n", + "\n", + "$K=U^{T}U$\n", + "\n", + "each of the components of U can be calculated with the following equations:\n", + "\n", + "$u_{ii}=\\sqrt{a_{ii}-\\sum_{k=1}^{i-1}u_{ki}^{2}}$\n", + "\n", + "$u_{ij}=\\frac{a_{ij}-\\sum_{k=1}^{i-1}u_{ki}u_{kj}}{u_{ii}}$\n", + "\n", + "so for K" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "K =\n", + "\n", + " 20 -10 0 0\n", + " -10 20 -10 0\n", + " 0 -10 20 -10\n", + " 0 0 -10 10\n", + "\n" + ] + } + ], + "source": [ + "K" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "u11 = 4.4721\n", + "u12 = -2.2361\n", + "u13 = 0\n", + "u14 = 0\n", + "u22 = 3.8730\n", + "u23 = -2.5820\n", + "u24 = 0\n", + "u33 = 3.6515\n", + "u34 = -2.7386\n", + "u44 = 1.5811\n", + "U =\n", + "\n", + " 4.47214 -2.23607 0.00000 0.00000\n", + " 0.00000 3.87298 -2.58199 0.00000\n", + " 0.00000 0.00000 3.65148 -2.73861\n", + " 0.00000 0.00000 0.00000 1.58114\n", + "\n" + ] + } + ], + "source": [ + "u11=sqrt(K(1,1))\n", + "u12=(K(1,2))/u11\n", + "u13=(K(1,3))/u11\n", + "u14=(K(1,4))/u11\n", + "u22=sqrt(K(2,2)-u12^2)\n", + "u23=(K(2,3)-u12*u13)/u22\n", + "u24=(K(2,4)-u12*u14)/u22\n", + "u33=sqrt(K(3,3)-u13^2-u23^2)\n", + "u34=(K(3,4)-u13*u14-u23*u24)/u33\n", + "u44=sqrt(K(4,4)-u14^2-u24^2-u34^2)\n", + "U=[u11,u12,u13,u14;0,u22,u23,u24;0,0,u33,u34;0,0,0,u44]" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 1 1 1 1\n", + " 1 1 1 1\n", + " 1 1 1 1\n", + " 1 1 1 1\n", + "\n" + ] + } + ], + "source": [ + "(U'*U)'==U'*U" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "average time spent for Cholesky factored solution = 1.465964e-05+/-9.806001e-06\n", + "average time spent for backslash solution = 1.555967e-05+/-1.048561e-05\n" + ] + } + ], + "source": [ + "% time solution for Cholesky vs backslash\n", + "t_chol=zeros(1000,1);\n", + "t_bs=zeros(1000,1);\n", + "for i=1:1000\n", + " tic; d=U'*y; x=U\\d; t_chol(i)=toc;\n", + " tic; x=K\\y; t_bs(i)=toc;\n", + "end\n", + "fprintf('average time spent for Cholesky factored solution = %e+/-%e',mean(t_chol),std(t_chol))\n", + "\n", + "fprintf('average time spent for backslash solution = %e+/-%e',mean(t_bs),std(t_bs))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Octave", + "language": "octave", + "name": "octave" + }, + "language_info": { + "file_extension": ".m", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "octave", + "version": "0.19.14" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/lecture_13/lecture_13.ipynb b/lecture_13/lecture_13.ipynb new file mode 100644 index 0000000..c687623 --- /dev/null +++ b/lecture_13/lecture_13.ipynb @@ -0,0 +1,1401 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%plot --format svg" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "setdefaults" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## My question from last class \n", + "\n", + "\n", + "## Your questions from last class\n", + "\n", + "1. Need more linear algebra review\n", + " \n", + " -We will keep doing Linear Algebra, try the practice problems in 'linear_algebra'\n", + "\n", + "2. How do I do HW3? \n", + " \n", + " -demo today\n", + "\n", + "3. For hw4 is the spring constant (K) suppose to be given? \n", + " \n", + " -yes, its 30 N/m\n", + " \n", + "4. Deapool or Joker?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Matrix Inverse and Condition\n", + "\n", + "\n", + "Considering the same solution set:\n", + "\n", + "$y=Ax$\n", + "\n", + "If we know that $A^{-1}A=I$, then \n", + "\n", + "$A^{-1}y=A^{-1}Ax=x$\n", + "\n", + "so \n", + "\n", + "$x=A^{-1}y$\n", + "\n", + "Where, $A^{-1}$ is the inverse of matrix $A$.\n", + "\n", + "$2x_{1}+x_{2}=1$\n", + "\n", + "$x_{1}+3x_{2}=1$\n", + "\n", + "$Ax=y$\n", + "\n", + "$\\left[ \\begin{array}{cc}\n", + "2 & 1 \\\\\n", + "1 & 3 \\end{array} \\right]\n", + "\\left[\\begin{array}{c} \n", + "x_{1} \\\\ \n", + "x_{2} \\end{array}\\right]=\n", + "\\left[\\begin{array}{c} \n", + "1 \\\\\n", + "1\\end{array}\\right]$\n", + "\n", + "$A^{-1}=\\frac{1}{2*3-1*1}\\left[ \\begin{array}{cc}\n", + "3 & 1 \\\\\n", + "-1 & 2 \\end{array} \\right]=\n", + "\\left[ \\begin{array}{cc}\n", + "3/5 & -1/5 \\\\\n", + "-1/5 & 2/5 \\end{array} \\right]$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A =\n", + "\n", + " 2 1\n", + " 1 3\n", + "\n", + "invA =\n", + "\n", + " 0.60000 -0.20000\n", + " -0.20000 0.40000\n", + "\n", + "ans =\n", + "\n", + " 1.00000 0.00000\n", + " 0.00000 1.00000\n", + "\n", + "ans =\n", + "\n", + " 1.00000 0.00000\n", + " 0.00000 1.00000\n", + "\n" + ] + } + ], + "source": [ + "A=[2,1;1,3]\n", + "invA=1/5*[3,-1;-1,2]\n", + "\n", + "A*invA\n", + "invA*A" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "How did we know the inverse of A? \n", + "\n", + "for 2$\\times$2 matrices, it is always:\n", + "\n", + "$A=\\left[ \\begin{array}{cc}\n", + "A_{11} & A_{12} \\\\\n", + "A_{21} & A_{22} \\end{array} \\right]$\n", + "\n", + "$A^{-1}=\\frac{1}{det(A)}\\left[ \\begin{array}{cc}\n", + "A_{22} & -A_{12} \\\\\n", + "-A_{21} & A_{11} \\end{array} \\right]$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$AA^{-1}=\\frac{1}{A_{11}A_{22}-A_{21}A_{12}}\\left[ \\begin{array}{cc}\n", + "A_{11}A_{22}-A_{21}A_{12} & -A_{11}A_{12}+A_{12}A_{11} \\\\\n", + "A_{21}A_{22}-A_{22}A_{21} & -A_{21}A_{12}+A_{22}A_{11} \\end{array} \\right]\n", + "=\\left[ \\begin{array}{cc}\n", + "1 & 0 \\\\\n", + "0 & 1 \\end{array} \\right]$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What about bigger matrices?\n", + "\n", + "We can use the LU-decomposition\n", + "\n", + "$A=LU$\n", + "\n", + "$A^{-1}=(LU)^{-1}=U^{-1}L^{-1}$\n", + "\n", + "if we divide $A^{-1}$ into n-column vectors, $a_{n}$, then\n", + "\n", + "$Aa_{1}=\\left[\\begin{array}{c} \n", + "1 \\\\ \n", + "0 \\\\ \n", + "\\vdots \\\\\n", + "0 \\end{array} \\right]$\n", + "$Aa_{2}=\\left[\\begin{array}{c} \n", + "0 \\\\ \n", + "1 \\\\ \n", + "\\vdots \\\\\n", + "0 \\end{array} \\right]$\n", + "$Aa_{n}=\\left[\\begin{array}{c} \n", + "0 \\\\ \n", + "0 \\\\ \n", + "\\vdots \\\\\n", + "1 \\end{array} \\right]$\n", + "\n", + "\n", + "Which we can solve for each $a_{n}$ with LU-decomposition, knowing the lower and upper triangular decompositions, then \n", + "\n", + "$A^{-1}=\\left[ \\begin{array}{cccc}\n", + "| & | & & | \\\\\n", + "a_{1} & a_{2} & \\cdots & a_{3} \\\\\n", + "| & | & & | \\end{array} \\right]$\n", + "\n", + "\n", + "$Ld_{1}=\\left[\\begin{array}{c} \n", + "1 \\\\ \n", + "0 \\\\ \n", + "\\vdots \\\\\n", + "0 \\end{array} \\right]$\n", + "$;~Ua_{1}=d_{1}$\n", + "\n", + "$Ld_{2}=\\left[\\begin{array}{c} \n", + "0 \\\\ \n", + "1 \\\\ \n", + "\\vdots \\\\\n", + "0 \\end{array} \\right]$\n", + "$;~Ua_{2}=d_{2}$\n", + "\n", + "$Ld_{n}=\\left[\\begin{array}{c} \n", + "0 \\\\ \n", + "1 \\\\ \n", + "\\vdots \\\\\n", + "n \\end{array} \\right]$\n", + "$;~Ua_{n}=d_{n}$\n", + "\n", + "Consider the following matrix:\n", + "\n", + "$A=\\left[ \\begin{array}{ccc}\n", + "2 & -1 & 0\\\\\n", + "-1 & 2 & -1\\\\\n", + "0 & -1 & 1 \\end{array} \\right]$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A =\n", + "\n", + " 2 -1 0\n", + " -1 2 -1\n", + " 0 -1 1\n", + "\n", + "U =\n", + "\n", + " 2.00000 -1.00000 0.00000\n", + " 0.00000 1.50000 -1.00000\n", + " 0.00000 -1.00000 1.00000\n", + "\n", + "L =\n", + "\n", + " 1.00000 0.00000 0.00000\n", + " -0.50000 1.00000 0.00000\n", + " 0.00000 0.00000 1.00000\n", + "\n" + ] + } + ], + "source": [ + "A=[2,-1,0;-1,2,-1;0,-1,1]\n", + "U=A;\n", + "L=eye(3,3);\n", + "U(2,:)=U(2,:)-U(2,1)/U(1,1)*U(1,:)\n", + "L(2,1)=A(2,1)/A(1,1)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "L =\n", + "\n", + " 1.00000 0.00000 0.00000\n", + " -0.50000 1.00000 0.00000\n", + " 0.00000 -0.66667 1.00000\n", + "\n", + "U =\n", + "\n", + " 2.00000 -1.00000 0.00000\n", + " 0.00000 1.50000 -1.00000\n", + " 0.00000 0.00000 0.33333\n", + "\n" + ] + } + ], + "source": [ + "L(3,2)=U(3,2)/U(2,2)\n", + "U(3,:)=U(3,:)-U(3,2)/U(2,2)*U(2,:)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now solve for $d_1$ then $a_1$, $d_2$ then $a_2$, and $d_3$ then $a_{3}$\n", + "\n", + "$Ld_{1}=\\left[\\begin{array}{c} \n", + "1 \\\\ \n", + "0 \\\\ \n", + "\\vdots \\\\\n", + "0 \\end{array} \\right]$\n", + "$;~Ua_{1}=d_{1}$" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "d1 =\n", + "\n", + " 1.00000\n", + " 0.50000\n", + " 0.33333\n", + "\n" + ] + } + ], + "source": [ + "d1=zeros(3,1);\n", + "d1(1)=1;\n", + "d1(2)=0-L(2,1)*d1(1);\n", + "d1(3)=0-L(3,1)*d1(1)-L(3,2)*d1(2)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a1 =\n", + "\n", + " 1.00000\n", + " 1.00000\n", + " 1.00000\n", + "\n" + ] + } + ], + "source": [ + "a1=zeros(3,1);\n", + "a1(3)=d1(3)/U(3,3);\n", + "a1(2)=1/U(2,2)*(d1(2)-U(2,3)*a1(3));\n", + "a1(1)=1/U(1,1)*(d1(1)-U(1,2)*a1(2)-U(1,3)*a1(3))" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "d2 =\n", + "\n", + " 0.00000\n", + " 1.00000\n", + " 0.66667\n", + "\n" + ] + } + ], + "source": [ + "d2=zeros(3,1);\n", + "d2(1)=0;\n", + "d2(2)=1-L(2,1)*d2(1);\n", + "d2(3)=0-L(3,1)*d2(1)-L(3,2)*d2(2)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a2 =\n", + "\n", + " 1.0000\n", + " 2.0000\n", + " 2.0000\n", + "\n" + ] + } + ], + "source": [ + "a2=zeros(3,1);\n", + "a2(3)=d2(3)/U(3,3);\n", + "a2(2)=1/U(2,2)*(d2(2)-U(2,3)*a2(3));\n", + "a2(1)=1/U(1,1)*(d2(1)-U(1,2)*a2(2)-U(1,3)*a2(3))" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "d3 =\n", + "\n", + " 0\n", + " 0\n", + " 1\n", + "\n" + ] + } + ], + "source": [ + "d3=zeros(3,1);\n", + "d3(1)=0;\n", + "d3(2)=0-L(2,1)*d3(1);\n", + "d3(3)=1-L(3,1)*d3(1)-L(3,2)*d3(2)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a3 =\n", + "\n", + " 1.00000\n", + " 2.00000\n", + " 3.00000\n", + "\n" + ] + } + ], + "source": [ + "a3=zeros(3,1);\n", + "a3(3)=d3(3)/U(3,3);\n", + "a3(2)=1/U(2,2)*(d3(2)-U(2,3)*a3(3));\n", + "a3(1)=1/U(1,1)*(d3(1)-U(1,2)*a3(2)-U(1,3)*a3(3))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Final solution for $A^{-1}$ is $[a_{1}~a_{2}~a_{3}]$" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "invA =\n", + "\n", + " 1.00000 1.00000 1.00000\n", + " 1.00000 2.00000 2.00000\n", + " 1.00000 2.00000 3.00000\n", + "\n", + "ans =\n", + "\n", + " 1.00000 0.00000 0.00000\n", + " 0.00000 1.00000 -0.00000\n", + " -0.00000 -0.00000 1.00000\n", + "\n" + ] + } + ], + "source": [ + "invA=[a1,a2,a3]\n", + "A*invA" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now the solution of $x$ to $Ax=y$ is $x=A^{-1}y$" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "y =\n", + "\n", + " 1\n", + " 2\n", + " 3\n", + "\n", + "x =\n", + "\n", + " 6.0000\n", + " 11.0000\n", + " 14.0000\n", + "\n", + "xbs =\n", + "\n", + " 6.0000\n", + " 11.0000\n", + " 14.0000\n", + "\n", + "ans =\n", + "\n", + " -3.5527e-15\n", + " -8.8818e-15\n", + " -1.0658e-14\n", + "\n", + "ans = 2.2204e-16\n" + ] + } + ], + "source": [ + "y=[1;2;3]\n", + "x=invA*y\n", + "xbs=A\\y\n", + "x-xbs\n", + "eps" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "Gnuplot\n", + "Produced by GNUPLOT 5.0 patchlevel 3 \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\t\n", + "\t\t0\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.0005\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.001\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.0015\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.002\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t20\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t40\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t60\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t80\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t100\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\tinversion\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\tinversion\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\tbackslash\n", + "\n", + "\t\n", + "\t\tbackslash\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\tmultiplication\n", + "\n", + "\t\n", + "\t\tmultiplication\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "N=100;\n", + "n=[1:N];\n", + "t_inv=zeros(N,1);\n", + "t_bs=zeros(N,1);\n", + "t_mult=zeros(N,1);\n", + "for i=1:N\n", + " A=rand(i,i);\n", + " tic\n", + " invA=inv(A);\n", + " t_inv(i)=toc;\n", + " b=rand(i,1);\n", + " tic;\n", + " x=A\\b;\n", + " t_bs(i)=toc;\n", + " tic;\n", + " x=invA*b;\n", + " t_mult(i)=toc;\n", + "end\n", + "plot(n,t_inv,n,t_bs,n,t_mult)\n", + "axis([0 100 0 0.002])\n", + "legend('inversion','backslash','multiplication','Location','NorthWest')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Condition of a matrix \n", + "### *just checked in to see what condition my condition was in*\n", + "### Matrix norms\n", + "\n", + "The Euclidean norm of a vector is measure of the magnitude (in 3D this would be: $|x|=\\sqrt{x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}$) in general t" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A =\n", + "\n", + " 2 1\n", + " 1 3\n", + "\n", + "L =\n", + "\n", + " 1.00000 0.00000\n", + " 0.50000 1.00000\n", + "\n", + "U =\n", + "\n", + " 2.00000 1.00000\n", + " 0.00000 2.50000\n", + "\n", + "ans =\n", + "\n", + " 2 1\n", + " 1 3\n", + "\n", + "d =\n", + "\n", + " 1.00000\n", + " 0.50000\n", + "\n", + "y =\n", + "\n", + " 1\n", + " 1\n", + "\n" + ] + } + ], + "source": [ + "A=[2,1;1,3]\n", + "L=[1,0;0.5,1]\n", + "U=[2,1;0,2.5]\n", + "L*U\n", + "\n", + "d=[1;0.5]\n", + "y=L*d" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans = 5.0000\n", + "ans = 1\n", + "ans = 5\n", + "ans = 5\n", + "ans = 5.0000\n" + ] + } + ], + "source": [ + "% what is the determinant of L, U and A?\n", + "\n", + "det(A)\n", + "det(L)\n", + "det(U)\n", + "det(L)*det(U)\n", + "det(L*U)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Pivoting for LU factorization\n", + "\n", + "LU factorization uses the same method as Gauss elimination so it is also necessary to perform partial pivoting when creating the lower and upper triangular matrices. \n", + "\n", + "Matlab and Octave use pivoting in the command \n", + "\n", + "`[L,U,P]=lu(A)`\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "'lu' is a built-in function from the file libinterp/corefcn/lu.cc\n", + "\n", + " -- Built-in Function: [L, U] = lu (A)\n", + " -- Built-in Function: [L, U, P] = lu (A)\n", + " -- Built-in Function: [L, U, P, Q] = lu (S)\n", + " -- Built-in Function: [L, U, P, Q, R] = lu (S)\n", + " -- Built-in Function: [...] = lu (S, THRES)\n", + " -- Built-in Function: Y = lu (...)\n", + " -- Built-in Function: [...] = lu (..., \"vector\")\n", + " Compute the LU decomposition of A.\n", + "\n", + " If A is full subroutines from LAPACK are used and if A is sparse\n", + " then UMFPACK is used.\n", + "\n", + " The result is returned in a permuted form, according to the\n", + " optional return value P. For example, given the matrix 'a = [1, 2;\n", + " 3, 4]',\n", + "\n", + " [l, u, p] = lu (A)\n", + "\n", + " returns\n", + "\n", + " l =\n", + "\n", + " 1.00000 0.00000\n", + " 0.33333 1.00000\n", + "\n", + " u =\n", + "\n", + " 3.00000 4.00000\n", + " 0.00000 0.66667\n", + "\n", + " p =\n", + "\n", + " 0 1\n", + " 1 0\n", + "\n", + " The matrix is not required to be square.\n", + "\n", + " When called with two or three output arguments and a spare input\n", + " matrix, 'lu' does not attempt to perform sparsity preserving column\n", + " permutations. Called with a fourth output argument, the sparsity\n", + " preserving column transformation Q is returned, such that 'P * A *\n", + " Q = L * U'.\n", + "\n", + " Called with a fifth output argument and a sparse input matrix, 'lu'\n", + " attempts to use a scaling factor R on the input matrix such that 'P\n", + " * (R \\ A) * Q = L * U'. This typically leads to a sparser and more\n", + " stable factorization.\n", + "\n", + " An additional input argument THRES, that defines the pivoting\n", + " threshold can be given. THRES can be a scalar, in which case it\n", + " defines the UMFPACK pivoting tolerance for both symmetric and\n", + " unsymmetric cases. If THRES is a 2-element vector, then the first\n", + " element defines the pivoting tolerance for the unsymmetric UMFPACK\n", + " pivoting strategy and the second for the symmetric strategy. By\n", + " default, the values defined by 'spparms' are used ([0.1, 0.001]).\n", + "\n", + " Given the string argument \"vector\", 'lu' returns the values of P\n", + " and Q as vector values, such that for full matrix, 'A (P,:) = L *\n", + " U', and 'R(P,:) * A (:, Q) = L * U'.\n", + "\n", + " With two output arguments, returns the permuted forms of the upper\n", + " and lower triangular matrices, such that 'A = L * U'. With one\n", + " output argument Y, then the matrix returned by the LAPACK routines\n", + " is returned. If the input matrix is sparse then the matrix L is\n", + " embedded into U to give a return value similar to the full case.\n", + " For both full and sparse matrices, 'lu' loses the permutation\n", + " information.\n", + "\n", + " See also: luupdate, ilu, chol, hess, qr, qz, schur, svd.\n", + "\n", + "Additional help for built-in functions and operators is\n", + "available in the online version of the manual. Use the command\n", + "'doc ' to search the manual index.\n", + "\n", + "Help and information about Octave is also available on the WWW\n", + "at http://www.octave.org and via the help@octave.org\n", + "mailing list.\n" + ] + } + ], + "source": [ + "help lu" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "Gnuplot\n", + "Produced by GNUPLOT 5.0 patchlevel 3 \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\t\n", + "\t\t0\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.0005\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.001\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.0015\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.002\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t20\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t40\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t60\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t80\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t100\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\tLU decomp\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\tLU decomp\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\tOctave \\\\\n", + "\n", + "\t\n", + "\t\tOctave \\\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "% time LU solution vs backslash\n", + "t_lu=zeros(100,1);\n", + "t_bs=zeros(100,1);\n", + "for N=1:100\n", + " A=rand(N,N);\n", + " y=rand(N,1);\n", + " [L,U,P]=lu(A);\n", + "\n", + " tic; d=inv(L)*y; x=inv(U)*d; t_lu(N)=toc;\n", + "\n", + " tic; x=inv(A)*y; t_bs(N)=toc;\n", + "end\n", + "plot([1:100],t_lu,[1:100],t_bs) \n", + "legend('LU decomp','Octave \\\\')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Consider the problem again from the intro to Linear Algebra, 4 masses are connected in series to 4 springs with K=10 N/m. What are the final positions of the masses? \n", + "\n", + "![Springs-masses](../lecture_09/mass_springs.svg)\n", + "\n", + "The masses haves the following amounts, 1, 2, 3, and 4 kg for masses 1-4. Using a FBD for each mass:\n", + "\n", + "$m_{1}g+k(x_{2}-x_{1})-kx_{1}=0$\n", + "\n", + "$m_{2}g+k(x_{3}-x_{2})-k(x_{2}-x_{1})=0$\n", + "\n", + "$m_{3}g+k(x_{4}-x_{3})-k(x_{3}-x_{2})=0$\n", + "\n", + "$m_{4}g-k(x_{4}-x_{3})=0$\n", + "\n", + "in matrix form:\n", + "\n", + "$\\left[ \\begin{array}{cccc}\n", + "2k & -k & 0 & 0 \\\\\n", + "-k & 2k & -k & 0 \\\\\n", + "0 & -k & 2k & -k \\\\\n", + "0 & 0 & -k & k \\end{array} \\right]\n", + "\\left[ \\begin{array}{c}\n", + "x_{1} \\\\\n", + "x_{2} \\\\\n", + "x_{3} \\\\\n", + "x_{4} \\end{array} \\right]=\n", + "\\left[ \\begin{array}{c}\n", + "m_{1}g \\\\\n", + "m_{2}g \\\\\n", + "m_{3}g \\\\\n", + "m_{4}g \\end{array} \\right]$" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "K =\n", + "\n", + " 20 -10 0 0\n", + " -10 20 -10 0\n", + " 0 -10 20 -10\n", + " 0 0 -10 10\n", + "\n", + "y =\n", + "\n", + " 9.8100\n", + " 19.6200\n", + " 29.4300\n", + " 39.2400\n", + "\n" + ] + } + ], + "source": [ + "k=10; % N/m\n", + "m1=1; % kg\n", + "m2=2;\n", + "m3=3;\n", + "m4=4;\n", + "g=9.81; % m/s^2\n", + "K=[2*k -k 0 0; -k 2*k -k 0; 0 -k 2*k -k; 0 0 -k k]\n", + "y=[m1*g;m2*g;m3*g;m4*g]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This matrix, K, is symmetric. \n", + "\n", + "`K(i,j)==K(j,i)`\n", + "\n", + "Now we can use,\n", + "\n", + "## Cholesky Factorization\n", + "\n", + "We can decompose the matrix, K into two matrices, $U$ and $U^{T}$, where\n", + "\n", + "$K=U^{T}U$\n", + "\n", + "each of the components of U can be calculated with the following equations:\n", + "\n", + "$u_{ii}=\\sqrt{a_{ii}-\\sum_{k=1}^{i-1}u_{ki}^{2}}$\n", + "\n", + "$u_{ij}=\\frac{a_{ij}-\\sum_{k=1}^{i-1}u_{ki}u_{kj}}{u_{ii}}$\n", + "\n", + "so for K" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "K =\n", + "\n", + " 20 -10 0 0\n", + " -10 20 -10 0\n", + " 0 -10 20 -10\n", + " 0 0 -10 10\n", + "\n" + ] + } + ], + "source": [ + "K" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "u11 = 4.4721\n", + "u12 = -2.2361\n", + "u13 = 0\n", + "u14 = 0\n", + "u22 = 3.8730\n", + "u23 = -2.5820\n", + "u24 = 0\n", + "u33 = 3.6515\n", + "u34 = -2.7386\n", + "u44 = 1.5811\n", + "U =\n", + "\n", + " 4.47214 -2.23607 0.00000 0.00000\n", + " 0.00000 3.87298 -2.58199 0.00000\n", + " 0.00000 0.00000 3.65148 -2.73861\n", + " 0.00000 0.00000 0.00000 1.58114\n", + "\n" + ] + } + ], + "source": [ + "u11=sqrt(K(1,1))\n", + "u12=(K(1,2))/u11\n", + "u13=(K(1,3))/u11\n", + "u14=(K(1,4))/u11\n", + "u22=sqrt(K(2,2)-u12^2)\n", + "u23=(K(2,3)-u12*u13)/u22\n", + "u24=(K(2,4)-u12*u14)/u22\n", + "u33=sqrt(K(3,3)-u13^2-u23^2)\n", + "u34=(K(3,4)-u13*u14-u23*u24)/u33\n", + "u44=sqrt(K(4,4)-u14^2-u24^2-u34^2)\n", + "U=[u11,u12,u13,u14;0,u22,u23,u24;0,0,u33,u34;0,0,0,u44]" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 1 1 1 1\n", + " 1 1 1 1\n", + " 1 1 1 1\n", + " 1 1 1 1\n", + "\n" + ] + } + ], + "source": [ + "(U'*U)'==U'*U" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "average time spent for Cholesky factored solution = 1.465964e-05+/-9.806001e-06\n", + "average time spent for backslash solution = 1.555967e-05+/-1.048561e-05\n" + ] + } + ], + "source": [ + "% time solution for Cholesky vs backslash\n", + "t_chol=zeros(1000,1);\n", + "t_bs=zeros(1000,1);\n", + "for i=1:1000\n", + " tic; d=U'*y; x=U\\d; t_chol(i)=toc;\n", + " tic; x=K\\y; t_bs(i)=toc;\n", + "end\n", + "fprintf('average time spent for Cholesky factored solution = %e+/-%e',mean(t_chol),std(t_chol))\n", + "\n", + "fprintf('average time spent for backslash solution = %e+/-%e',mean(t_bs),std(t_bs))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Octave", + "language": "octave", + "name": "octave" + }, + "language_info": { + "file_extension": ".m", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "octave", + "version": "0.19.14" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/lecture_13/octave-workspace b/lecture_13/octave-workspace new file mode 100644 index 0000000..e69de29 From a1f55bc9f717ad66bd8f75c9439052c73ea431d2 Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Mon, 27 Feb 2017 11:55:30 -0500 Subject: [PATCH 13/16] updated lecture 11 notes --- lecture_09/mass_springs.png | Bin 0 -> 5031 bytes lecture_11/lecture_11.aux | 28 ++-- lecture_11/lecture_11.log | 117 ++++++++------- lecture_11/lecture_11.out | 12 +- lecture_11/lecture_11.pdf | Bin 154124 -> 191934 bytes lecture_11/lecture_11.tex | 136 +++++++++++++---- .../lecture_11_files/lecture_11_8_0.pdf | Bin 0 -> 8728 bytes .../lecture_11_files/lecture_11_8_0.svg | 139 ++++++++++++++++++ lecture_11/octave-workspace | Bin 0 -> 153 bytes 9 files changed, 338 insertions(+), 94 deletions(-) create mode 100644 lecture_09/mass_springs.png create mode 100644 lecture_11/lecture_11_files/lecture_11_8_0.pdf create mode 100644 lecture_11/lecture_11_files/lecture_11_8_0.svg diff --git a/lecture_09/mass_springs.png b/lecture_09/mass_springs.png new file mode 100644 index 0000000000000000000000000000000000000000..d0dc65cb340f830eb2b8dd7145ef38908fb8419a GIT binary patch literal 5031 zcmZ{GWmwc-(Do0P5D}Gb=?+1?KSHiutRuJrmB^U0)}>9q8AU2Y{zlL4l9ir8trafMFnETyu*ENH7B?hDgwN zMiI~zqoF|sFm2(W1|Jg=gXCRs0O9>-j0Aw~q$T(#bGDcn>96ovxk zr{2a_d!5he?{2}x^gt^CM_C7te*y#-B;c(Bak>$>-bd-o05TEb0$vg>ZX=j{lIPJ;7yWL4>>?VA6II81@egPZ;BC-)(9x*mGLa4N9dRDv_36+KK`3;H zCxOj;vq=!K{B)7KJ$`05Wuf0Uo{uE5pf(%sZsjkxRX5g(xFP6-O?M1#{e!(uh1YSQ6=A#)j4d*5afG zYN=?0?>67>J7j)@P_kAg^A9d<*dK9t&|o4LG&@vtS)S?ka%Yk|X#nhr4Z(WK4y6nE zG5SmT{O#zD&807V<1HLW2V)m+9f^Az6C3L@Gc_5NmW%YKs-YRCx7 z2sT2`7}T586TODNCR%&w&g$-ZNPehyXmB{cCQJ$;BqrpHw2xGbgp*FQbI?#LrLK0Z z2zfovq!y>v*Se>l{QIkxb()~IaCpXX5@`}gl0p(DsVOO)EtD^&_=^Xey>ZCM&N$x4 z5>1Y7(G$}1L(dhfpec(t(O5Jb9bGJqRxR!vsI$qoPO?53MhwfO_YLk0Tnzmhc$(PG zEX~=U(wMY9NHLs~>cd8RlW!A$lX;V!0-7qHdN1`+>Q)8$%Q(j> z$56+-owm%R%yg3uldL)Yw+&LNvKH3~7pRNEuo9KJuP(7Ju{2NzsQ9SNsMx4G|L3%7 zgD``lDJAD1F;!{x%es>Q23S9g)1uU1D_5YxsU$1k&*+^u1v0g-V)A8d<=4OVzGm%j z+Qr%l1JXK5k?)b8ZcIUTeBKNR{(HXYJZE?Db7UdLb;?D|smAu{D+@dD*H<3?62;l3 zl-@*s(aw}q{9w~e;|F}>CO5B&?NY6OI*K-`ctS@qOGJ~Wc%~Akh^G|knxP@1x^xBA z4bEuiBCMwL%U1hV+g67fG4VvdsLQFPiCouZht6%Q-*tVf6|BFu*NpZgHrQ6lw_)pl zyN&xK$1tNlOMR0zjl(Yu+bY9%k<&urc;dOH(erJsm`lo2GA44!c^a zoz4BXT~7Yh7ju(Mi%TomUjbd0nD`Ryu<`K@Tua7flVwAs3i2EYx_NjTdsBVG2-*V; z-OI&u#Iwaa!HdKXC1}Fs$Ct)WCm>RKsMs8`K%7bpy^kei4Z{l+4d<`&GiJ2*Lc_kTXSz_5WSr#b*BXuJZ8A9WyE8=!6A9jWPaJ3XZTM26NIvGwunxS6K zC#Bi>*`Am+OgSbv3n7M`70KDke&;XjBJApE+2L^$cNNLMz)x(NSgmV%*<9|zyCBxI zXmdHpkiwuYjpP>O<9c>hC+uzKTA;Xk(miM{&^i|di8@n;w^n;i-=Z#=SHlZrD^Fnu z=LYoV{-wQj=mu*{ilOh8Y7t{4(rlKl^o*ltE{^6|wWMW0ouha_7dO|A#Er7fZ}g6_+IJ#<4rHo5zCmMNF-~S-$&ZC&xQmyHYec zedcP@B{k>!XD+X_?Z^M%oe~AK8?@)h?cVyY6(04?X(pu)3Fr$@Sy*6_-r1}=Ui`#3 zxleOkik--|KJ~bM)#-XWK^#x_$wg|p4cx`h;xT+N)iDj{S!tV|zuTM@Bh`M8{ zAC^+#BVnKSKP>NJT-`h0d5`|tB$-cidQ8u_;JFA-G+Y+ zQ-5gu;1~WXOl6m2chG5Z>bnEI$STGZF82l2`c?irxnlGRd^i?9qTRmUX?ouHw|(T2 zj8O~xm;a2f?JVQS-J$+0d89NsPco0712^!4#gH+FfMLMTo4L!;_4zZ6p`oEbK%g+8 zO{a9f{%&_-f~)C40l=3708k+SaB+8p+6I8Pf&j2%1prbR06^uI{aIJ$E^zO)rYZ!u z4UZq`yz>a%)QmmvQ0@PT%AgbY&LBXjLzM|u@6kOG2dqTbWbe{g)FBEm?>TIaTxMpDgW2`4|R+$jz(ws>rM3I4qMpwii6LuVdSh z#{6B7vHJ}RRKddJ3cSi0Z5bZ7We#|#%z970Gc7$aDm}8-388e0f2%n3>!EiM3|xxe zx)bO-Yt0JlIIaxb`(`yQk)taHs@BgnKG)O6=?};ASDF3WCH)D@fI*FO(G?7BRo=`x z;K|r-W_4g?^|~%URGt+JuMqRBOf=ApK9gL@F~5$#sl}%IPFiXVEw|H`kBL0)n76sl2F@!^ue8skEstu&{xz~1-o)09eP5ZrS}nupoky)Q`p0S_ zM*`2s+;8-e1L9-!;Ca7p*Yncjs|;G1Ib!PQl8m9Ha&W@IZ}1CC7oeX!*-TVES?>@X zH^IZOvELChc^DamWqCjfo{9Z@EmBbyS&nMuUisY?Oe6FJildE}e?1^gn`R4E=B=0> zfQ%UFW9)|Uax1S|?(II6=yX7BOn&~8vVe<<{6OYzXZX1`Ur+n%2CQn2z}eg0Xrgxn z<0v=tr2YebZXDyA7Eq%|a*J>3y9u$A_jo^FO8ed}Y}36XvtlH+HY?4t-;@g1{1KH_ z6tDHrKTlhB+J?ikm>|OYN0M&C(j^=^Yrfv|nm?sg?)mWU-#R74+B9Tj5Eb@vzJ-kq z(na>TdDh(SJ!gZL1`lX|@X-&iZA5B5mc@~8xW&-R#Yt-ew{~(uha_#op|? z7|-K;c?6a(dzXLQAvp zQxlj`d5jvf;MEc8fSqf}C<=HSsqp>RPcxdC8*)sxH1k+IiXth>-Df5sXptj*T@N4+ zg;~GKj!<>*jyO@~^_^xOsCQXIj0X^Md-8FYyN-vrX_sJQ80etAu$fn6Is}(YK~v?3 zufcQ%d^1myNytD%Pg6>QHu+}Kd{mU%PgS9twv=&xT)G&o1>ZioS<7;nKbwQ%HFI?7 zbg51d@7dTPb~k%H%#!h8eUH;Ov0eiKEVVk?!x@8u$oVM94@e$Nf}BEJnY1WwZFV7^lkEuf}NqFnw<-%r6w)ze=a^ zCHk62x6ZV8Z*JSjH-qDDK3|qyXWhDbxAiOt^sOF4k~r5rx9G0?o8vNO$Zegg%Aq7) z;jiud$Uh_=4n(CaSSfM&C>~gaO{WU4TWjzQ3V#YZ7oMLCP&0N5%^PZhON99*RKWaqd2!i)w-i|%RR)pST>koT@jKHCvn|(AQ zp5efHU&pouK`V3EmtIfM#%A;jjU|!q*Jrwig&KDqob5{LQzyf>ZvB<3#?~)|S_M04GA-sBF*3mqav>T(<>;8KyUZ)ugZs9en*z-62Rss#`bp z$@~%#s>*i3Hk7Vp)8)j%V{oF-?pvs`xfVB|)oq~fX#EC$Fsnmz=)7sJo0BXgsXGxh z5mC6i{V%-LWH%U#KX`g2&rr~k-13XRrdEvmHfj0KkIGpzU;U^*iZaMJkD6=c!$)N= zYMHr zLv5<+IqXUGp6_MACMrURPesrhkh8FF=|7`R#CiH@X&waju-+A{r*T5(zr4BZ{YYbBqL`(d7H_H&_fEb3_MFF+5#?3tG5IL6*d@b*(&U0UeK*1sq_IPu5%5@fdK0 zo@NIs?8jzu+I=yXWDF~K>JDM-zMvpzsjR6Fl{-Ga??Ykj%t|KzTR#)gKur9H;g*KE zF`}?oNzUj%Z^0D42rA{rStv7Gk5q5@<^9}xdKAG^llNOhT}vR;U=jioIq4x^kuONB zCywte$z-#lC~FU%N4+F_LL$PLs(TI|2HzC4c4z4{tXec-bU#`tU~l%@dJCGmvjj^& zgpgO-wnk>Wpp8Qk>SKIz#!h6PwAlIje=GDz6@ia*XA79mKS~G!OkhmRz2LtF+7nxKRvA z<2OdI%!Kbq$4iZ}DSw$z6pex`xqMv_>}fkqt*)m~ ziAb}!8SnFxu|b@DXMj7y*)NA}gsUtb^mwGHglRFr_FGmoQ&)4_u3=zqlj1jZ-$;2A zh00vchpN#H488hFq4%w+meh)Z3h7fdEpG_SToAbP){E|U3luv-*$83%3SlD!_prGG z;JKiXIKSX?{^#N_At5PIQ7J(|e!>4VqF#yee-WHrtsQKA{%-=_-etudf$_fzZk|$V z4th48imq>6tQ}nJ6kWXmA))8qLXv{Kg8V|2-Piv$L;wF%wQRg>-T(^LuCHzQg#`qe bly&q~{xcqAxwWp} not available -(Font) Font shape `T1/ppl/b/n' tried instead on input line 287. -LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <10.95> not available -(Font) Font shape `T1/ppl/b/n' tried instead on input line 290. - - -Package hyperref Warning: Difference (2) between bookmark levels is greater -(hyperref) than one, level fixed on input line 290. - +LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <12> not available +(Font) Font shape `T1/ppl/b/n' tried instead on input line 288. LaTeX Font Info: Font shape `U/msa/m/n' will be -(Font) scaled to size 11.40997pt on input line 294. +(Font) scaled to size 11.40997pt on input line 290. LaTeX Font Info: Font shape `U/msa/m/n' will be -(Font) scaled to size 8.33606pt on input line 294. +(Font) scaled to size 8.33606pt on input line 290. LaTeX Font Info: Font shape `U/msa/m/n' will be -(Font) scaled to size 6.25204pt on input line 294. +(Font) scaled to size 6.25204pt on input line 290. LaTeX Font Info: Font shape `U/msb/m/n' will be -(Font) scaled to size 11.40997pt on input line 294. +(Font) scaled to size 11.40997pt on input line 290. LaTeX Font Info: Font shape `U/msb/m/n' will be -(Font) scaled to size 8.33606pt on input line 294. +(Font) scaled to size 8.33606pt on input line 290. LaTeX Font Info: Font shape `U/msb/m/n' will be -(Font) scaled to size 6.25204pt on input line 294. -[1 +(Font) scaled to size 6.25204pt on input line 290. + + +File: det_A.png Graphic file (type png) + +Package pdftex.def Info: det_A.png used on input line 294. +(pdftex.def) Requested size: 375.80544pt x 202.3582pt. + [1 + +{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map} <./det_A.png>] + +File: midterm_date.png Graphic file (type png) + +Package pdftex.def Info: midterm_date.png used on input line 324. +(pdftex.def) Requested size: 375.80544pt x 171.71808pt. +LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <10.95> not available +(Font) Font shape `T1/ppl/b/n' tried instead on input line 328. +LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <14.4> not available +(Font) Font shape `T1/ppl/b/n' tried instead on input line 342. -{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] -LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <12> not available -(Font) Font shape `T1/ppl/b/n' tried instead on input line 372. -LaTeX Font Info: Try loading font information for TS1+cmtt on input line 387 + +Package hyperref Warning: Difference (2) between bookmark levels is greater +(hyperref) than one, level fixed on input line 345. + +[2 <./midterm_date.png>] [3] +LaTeX Font Info: Try loading font information for TS1+cmtt on input line 461 . (/usr/share/texlive/texmf-dist/tex/latex/base/ts1cmtt.fd File: ts1cmtt.fd 2014/09/29 v2.5h Standard LaTeX font definitions -) [2] [3] +) [4] [5] LaTeX Font Info: Font shape `T1/cmtt/bx/n' in size <10.95> not available -(Font) Font shape `T1/cmtt/m/n' tried instead on input line 473. +(Font) Font shape `T1/cmtt/m/n' tried instead on input line 547. - -File: lecture_11_files/lecture_11_6_0.pdf Graphic file (type pdf) + +File: lecture_11_files/lecture_11_8_0.pdf Graphic file (type pdf) - -Package pdftex.def Info: lecture_11_files/lecture_11_6_0.pdf used on input line - 487. + +Package pdftex.def Info: lecture_11_files/lecture_11_8_0.pdf used on input line + 561. (pdftex.def) Requested size: 449.6789pt x 337.25917pt. - [4] -Underfull \hbox (badness 10000) in paragraph at lines 489--490 + +Underfull \hbox (badness 10000) in paragraph at lines 563--564 [] - -File: mass_springs.png Graphic file (type png) - -Package pdftex.def Info: mass_springs.png used on input line 497. -(pdftex.def) Requested size: 89.93611pt x 152.576pt. +<../lecture_09/mass_springs.png, id=80, 112.42pt x 190.7125pt> +File: ../lecture_09/mass_springs.png Graphic file (type png) -[5 <./lecture_11_files/lecture_11_6_0.pdf> <./mass_springs.png>] [6] [7] -Package atveryend Info: Empty hook `BeforeClearDocument' on input line 656. + +Package pdftex.def Info: ../lecture_09/mass_springs.png used on input line 571. -[8] -Package atveryend Info: Empty hook `AfterLastShipout' on input line 656. +(pdftex.def) Requested size: 89.93611pt x 152.576pt. + [6 <./lecture_11_files/lecture_11_8_0.pdf>] [7 <../lecture_09/mass_springs.png +>] [8] +Package atveryend Info: Empty hook `BeforeClearDocument' on input line 734. + [9] +Package atveryend Info: Empty hook `AfterLastShipout' on input line 734. (./lecture_11.aux) -Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 656. -Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 656. +Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 734. +Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 734. Package rerunfilecheck Info: File `lecture_11.out' has not changed. -(rerunfilecheck) Checksum: 06B2288B56AA590C3216AAE67971C54B;297. -Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 656. +(rerunfilecheck) Checksum: 41743ED7C91140C56E53FBD51DB19D65;568. +Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 734. ) Here is how much of TeX's memory you used: - 10920 strings out of 493029 - 163179 string characters out of 6136234 - 268780 words of memory out of 5000000 - 14206 multiletter control sequences out of 15000+600000 + 10955 strings out of 493029 + 163773 string characters out of 6136234 + 268999 words of memory out of 5000000 + 14228 multiletter control sequences out of 15000+600000 39052 words of font info for 103 fonts, out of 8000000 for 9000 1141 hyphenation exceptions out of 8191 36i,9n,77p,460b,465s stack positions out of 5000i,500n,10000p,200000b,80000s @@ -817,10 +830,10 @@ hare/texmf/fonts/type1/public/cm-super/sfit1095.pfb> -Output written on lecture_11.pdf (8 pages, 154124 bytes). +Output written on lecture_11.pdf (9 pages, 191934 bytes). PDF statistics: - 117 PDF objects out of 1000 (max. 8388607) - 92 compressed objects within 1 object stream - 14 named destinations out of 1000 (max. 500000) - 43 words of extra memory for PDF output out of 10000 (max. 10000000) + 152 PDF objects out of 1000 (max. 8388607) + 121 compressed objects within 2 object streams + 27 named destinations out of 1000 (max. 500000) + 85 words of extra memory for PDF output out of 10000 (max. 10000000) diff --git a/lecture_11/lecture_11.out b/lecture_11/lecture_11.out index 41c2cd3..481e738 100644 --- a/lecture_11/lecture_11.out +++ b/lecture_11/lecture_11.out @@ -1,4 +1,8 @@ -\BOOKMARK [1][-]{section.1}{LU Decomposition}{}% 1 -\BOOKMARK [2][-]{subsubsection.1.0.1}{efficient storage of matrices for solutions}{section.1}% 2 -\BOOKMARK [2][-]{subsection.1.1}{Pivoting for LU factorization}{section.1}% 3 -\BOOKMARK [2][-]{subsection.1.2}{Cholesky Factorization}{section.1}% 4 +\BOOKMARK [2][-]{subsection.0.1}{My question from last class}{}% 1 +\BOOKMARK [2][-]{subsection.0.2}{Your questions from last class}{}% 2 +\BOOKMARK [2][-]{subsection.0.3}{Midterm preference}{}% 3 +\BOOKMARK [3][-]{subsubsection.0.3.1}{Midterm Questions}{subsection.0.3}% 4 +\BOOKMARK [1][-]{section.1}{LU Decomposition}{}% 5 +\BOOKMARK [2][-]{subsubsection.1.0.1}{efficient storage of matrices for solutions}{section.1}% 6 +\BOOKMARK [2][-]{subsection.1.1}{Pivoting for LU factorization}{section.1}% 7 +\BOOKMARK [2][-]{subsection.1.2}{Cholesky Factorization}{section.1}% 8 diff --git a/lecture_11/lecture_11.pdf b/lecture_11/lecture_11.pdf index 3e2c8282f6df7163590d78759aa2ad6caa034544..9fa1342f31dd6555dcdd93dcbd92be2fa02e7535 100644 GIT binary patch delta 113152 zcmcG#by%FwwZ&7E=X2_ulF0hk9ZM**)T)xw%7&EG8dF&=$Ar_O+zso%hzKko+ zPj%L)HMEFcuEpksly)bvDDiu#`r#+9>y3UDrUiewYgeilGh-!bTC2|^KVKuv)(mEr z;(J@^5*y?dS|kv(60$zkFKA*>nZ3ZhyBGE#tMZer)H>om4s=fc{3$SE3UoRcG1gJz zSTUdR?nz2A+sclk>}t@%M0yUi(2Ah_VZ1^?laDVOH-y`=8T;OZn$4jg_I06%vD6=b zB4d)lKoh6OtDBw6>{P6wMn?PV8r4)^dt`4ewU` zWKZ3b#4JYU%y6=q7EjHCLy+O;<><(G-RSpHn~A~WTVEtIYCyF-k+<&@Vk=UHtv7{KY`J7Z;IZo!(lp8^#nzvlqmThL?fU*Oe$s z{NPLaYxY_T171yC(I*!n0Xc(8(ZIwG`*=@+dAC-BjS`VV3Tc z?zXK|!mHhIt|Li7R<9A*!`UrTr!PkF?x-p|AZ zAA2j+4HAjxS}@k&(e`4t#J~EgAQeCH&G#wml<1;==@i+*!QA-^#KOe>pKt$whm$8k z4Udvo&fdhz0-06E#{3@?v2h@?%39c1S$}!Q$@@M*?L8ftx{Nq7tA>(^^QU**Tu|Vt z|98x>b8th6u;bE#N6Yqh1~+-DpWCMt5WMr-(;=_zX3N<{*b!g6l{Aq^@Q9kR^jk5w1Xy znN|_gU{N-mdO=B@v%CAPJNlqRoQ&74&uPd~=p?yRmh-a+_)LZX1N;|@Z;9{t!I?W; z8y3Kj+1gpEthu^|bQ*E8I$ZLpNh4p=(cB5+rk-b(UO&XUjTVU9u1(Kx%7uFyGn8+X z@o2qNGK9wPcef;FHno3~u+A%9;-?Te&(KjH>{=eOscP}2I1gMnZ`EJgKZtK2xNXuN zW4$tvT4&|rcduwD74z}FirT&=El+TV(_E;WpIIs)K=;bGuO;%8FT__prW)GGj@Qo3 z{@wMwvf@)tnUfLQ4-xfQw#=CGol_+l6q^%hbJVi3dH((YN#5_&Ch6ZqZq5Uj*H7UK zgd=>S3s$3U6P5yaD%Z@p}^s~ zYJn|drl_pNAlzmdu327liqr?c>YFvi9x}fv^Aetv?sC6SH9dom^|3)T9OR9-948q1 zz!CR;h>j26fHju*qaN7ElQeHE*J2Cc?0pr=5@7~92T`)vwZxB{z zjsoDcLsEEQ3#&g*J}{aZJ0>EU7xH3QJ>w4gZHhulhBp63a4V))Mt8x1>CB1!>4ea- zG#Q*rbuV!t!rJRu4LWfxl5aF#mlG;pBHjJTpY8J7)j?$X_1lLSNjRhs{Fr(er0$cg zdQcr2m1VbIJE(+F+SM(<)TBr%`-e83VZygR8=ppN)%qB}zT9|RxVX~zzVCkCjnw+! z`}=syjKcb_RD(V@iY;J&kx2PC_n##bhcXq?pGlPIJ6>o(kL&)oS;@DKq(rjGFEa2s zQ;Sos@6NcMemUeQaPpadt!i6c`@{PFS~zqk?l!EpSji_LKTM-ks6Zt2a&ifSivc{F zH47Me$az$lnc)rVoUy*oD85h8qHw4#cc;y+qQrAerpbzbA~^%ugV2;JN!oc*SYvQh zuM$A=PRlW!_ls4J%y6}FG($DJUf4$;4>^N{#+BdF^P-~muPpn{CG^=hg?4ovYbg(_ zv2&p=5<8q>r7SZ%hxCqxD)OCBx5tQ{jk8fBP~GVCbkJ$T88sJjY#HShL~UlIsQWcu z-=uOnI$s^_eV77;WjdRUj-qv~j&(Q`+bTJaK5lox#s}Qq6}F2Vy!O_Mmx!Lry}_IF zBEPB(sQNSK@zYG>VXtp?zBMhK7$T%&bmHX0s_Q{ELL%oVArG;(7MLwNr*(YKv;SFd zaepTJ-4%{qkN)Zwc>KF=DVyQA{V_TSPwO zLfakEk=^Rh1{G<8zr8WU1oUFhVTns2llm;Hw=GQh$|*}*#0|s|-pzT8cV^*pZ_DWk zmk?z>80FN1jZwd5-w^Syrn+iO N|cfu!*Z(ePa?%{;b9eiHEVLjFzBQmL42^R!E zpB-ri4>Vn&3-scxe-^MClI1x2>dm)LSV$Pxm)Dy;v^bSs0>&puJdY=Bk&NBE8$6Nt zpkbhMk~={2M4s?!dyc#QTK7n~Y3T?u@3}E!>3w($@`NaO_1H9B_t>`IC!YB(#7n$Z z7R&mp~5Yh}*yOBc2KHN*&E+CGN}jD4n$BGpzDk zS~)x%%e;gcqVdi>p2wT94VSV@{OpKSeR)#b+wl(T04>ac_yPxM8|lF!MVU1@#qO z(bCOMw9iAVKFG{@cw6Mb2hHAo3InOvv)@Vd=0$5Kf`1!Z(aY$`nA3xPxD%qH6K(R8eFH$Pxh013H8c^ zq2Igf;i7rbHDxOHQasZ$B#lXhv;Q5y5YuP$%NJj)aF_VVAgq0sXyAQFK$BJtO5 zjcC|CqbUk69T{q(fcK+W@E`F~_#j`64sfS%<=46y4d-lwhUHolO@qyk!+eSmftV9! zWk_iIc4X}bn3RU5;^N}D^*^5=13P#+EsKgi5_Br}|3FXnKNmc%pqc+1SWd0UhYnyuy#n}Th% zyB`}ZBhb&38}79gR^YBS%aqH-BnhwP9F;t|{x+IZg_v9&hg(->P2!U`iBm<@f6-0c zMnAEx|NIUMQMz)S_DOWTIR4p^9x?j)<9Q|3Jqo>?^z&@N-;MCj$IS7P8y8EE*Y{iK zD%s|P+@Z+EjosE5*;n1Ya#<4ULLspCXZfsTo*r+y*6a+kxMR@ds=n1RfeYTGkIv6O z;gQCMgREthy{ z-w~I-`HmSX>`|}AbggG(%O^{wlKwe!bAKs?l<`}R;<^p_hLw;uwYIg0nO`;MMgt5r z)ZL)1CZCwepGdC1ee>yia-ILV3ER-5ghgwi_YWbJCRbQG?rBS z;kgxo^zrFJQ>u{L{lNum6|WopIP?IF6 z8?JU0(OarmD}w{(Po=>+sr?j{?NBs`TH0;qm)TSoN7nVJioH#Kw)Q7+@4y26aWl(| z073J~4W*=xYtx@QpQGi4&}R!e0_u4}{HA#jb!;;NsB?G_kF1zZU1-{QGD48i3)iD! zQm+T<*of30C`_B=*;#%t??-g)wv2k3E$_G>w%F0LH=DP=p=SkU+XgBEgh;k;L)e{< zd1k&*A(lfFTpsG->y2e+XKx}ma}S#9;{&1tG$kPuF6#sn+qr514~O<&ZJj4Pylpa1 zKcMkxjlM5$*g{IKl*LdiwcLOQM}mkromp8m*WPT`au?{MN5@dfp!Fkwp7U45U_*5UDNO zk|aBRBp^$^{9~E)ptBukwPIcfQ`ASLdbKmjj%z%{xg{w(fJA;I%MNu&7_EzzU)}ww;B>y)#Kb@+5Rbf50 z<`+o7GV`bfepD5F;iAO1Nrw~X1?-D=e^?$)b2$_!?!BHSagp}0c50~ECB)P6*$+d7 z^94o3EgYmSX-UpUP*Sv2WWE)RpGO9@kGYqr4H}4IaYClPR;Tj_ez3^>ZT1 z?EL^o8Afv%+(@=09O4oJ##g3h7Z(?26XH5Kiwlz3_UU;ACqxu7;jx~?#%KPZLE|ss=gj!U*to2c6jC0vZ5uaKkr8Yr^}$7`ob(2ucO!3Uu$KIRYd!1dvy<&S{!DD-012b zztyI0Gi3m`;F1e@Ls`3ctaTc2(_lMfQ@NmstO9i=S)p6usr` z%5?!Z5=Oyn+;c?Py3LGB(`R<-^Mjx$I+I0*f;RD>@mg!B|kSZz@D{@;kNKQJQOiB|oU&%=1rQS6Y8^ z)J&UBdvUh#2)PiDwHT?Ka0b`+o`?7O6t;M!U0TuU6)uZ!W)BW)r#!q%bN2WM*Aufl z>fc7X9~AB*#c&Kz3t2^hEdo=&IB)agrLdZTWifE~DRg54yrRq{VQhJr02#TN9cr$ zC_XoauC%rPo^*r%#nk)%uV(*y{BfnMB|-x|h4+=ExTtg#TvI z^MkPndy@7mJ5qMF(`SHf(LvG%XFhTNvRR=vknP;xl8sKj`LXSiiC5+I6kcFIj<~hZ zS-k5l8$wSyp>k%<@CfP|1x@&Zj6pMc9oOe;>$<@&o9kZtb8`;HhkUj?a{Bxa(#MD% z{V>)GuX~=sm_OO?X8$(s$Y34crm2=9q;S7erF{U`!|i(r;d0xCAkJSfM>^+Q&59)ZNy!k8CIB-)3cShT7@?6mVbI&Q1gC%-&)1U_qaTR@L|xz zUa&og{JnEy?{wxLWSHFaK}u4I1N9Wi(jCb}`@m2abIJE4ssV#*h@EXJ5Fpl=QsRq! zVY9*{ey~0YYMPXy(z*fG%6c1Mj}BdJC+N{a!Gb2(l0xZV>*~Ol+G$2Li(mNRGw`+i zc=rAunW!0(sy6>R-F=}(TuXcY)h8n0A(cy_Bqz7R>1iMS z{V0m}ia|vZ+Xju>RY`MsmLc-&C7MRckY5e1+&u4X#AuXF

Omt{>-ODyGmPXGg0EKk4l87nN!`=gzGDPp+^2jmj7V}G}k5gyUy6M_Lii>YZ$ zEb$B`B)wyc$2T_FC{Y-IulG)SS4nWVjTh#NE&v=-deY(ZyvC(+dI&b`j_F)q2Fg~C zqo*ahJ`Nx=<1A15tBox5_+UDBC-8QHFMsFahx0q1n=;72febiJXFJ`j{1AUWJYS;& zGW0@=;7uqz2kvdF%$Ss9GeGN%Xv55%CwPXw_TlL^Esn#rJra6ESPM*|&Gn;~@;{|r zUZI=M_~z+f zqVZ2xdhjX9{*y1U#J=ITKWnI&kwmEtdd+D3)Q32Ezya!hYq@whRjgXSpll=z(Y!_n z?{AEJ=6f~o_<$`3H<@{TDxT>{{se=}tNEMFzfZrLw8h463@_msd>~b+lRpnJ) zo~=y9RgVe=%vu=%i{Rcu`Z9}sG!}Fax9QB}VgsWWX$`7bFQ`-9mSrYO4OC}8(S&e9aZ_%A&Fm8^fqCDcQXj%$KO?{sNJwsu+KEf1p(106nhSa_-|&} zmhMfwE0g4kvh8G;# z)EB(4ufYJe1GkKtAg*fz0Bq9uD4YMLMTR4-iP>h6BQpxlj>(eM!BF5Wgf14SsztRX z7vq;2s^QwYYcMSpKMFE)XApQkZIHkYVU_c$?$-VE=?%^#Gk}DI6o%EwWGEF;;!U~E z8MS)X?v(JgT(~M&tqweaAB`|z23G!J#;2#09@1Uv{d8aIki3z+{{D9$?!UWze3bv- z_W8(QW4U<(3xh4n_~hw_5>)o;MA0?i?y{9le@?K0XS;dF5u6G*%Ql1L?hlF)gMZu% zY!r2gP8@hhYR9ZVBvEB1JUM!`=0~ut2Inub1dj*L`vHsILeI#*lkvEKKf&PIbF&1^ z#iubz)}BS(;=wOp%;^s#fbYETM?QS>&rhuRBiQTmO34&^Vh({P_Q;xGki29P>9-Y6 zLuT4*OOH?ylvpL}gge~C_>@X17VZ)Qr(J;*;twtHzZTs+ImMl}?IKF=xUJa0VTngQ zU%UAne^XHcfsw*jP$-;Hm_R|uz>O?HU7I7nY_OInEmU>`&Aoea5GHzH(Qzq556%rJi zcY98o+wKuXJohVp`BsFF6wRA4at=|UoP?+`dyjEbGg=G7ziaRE%c`WSUU*GwX>Yihbrx#>q}UG672J>D?gdEOF_V z6V9I@&#SazHJ0QaTBYr7GX&DGlY33a?Y3do_0$J_XoMjorfV?5KLP-*_o{R)(gJLQ zuzAYAuV-!4dsIg4P@*lwu}lbelp!6m@FFJ zViB{LG&A1690bYu&FA%4V_hQa5S5rLKvk{5$X;e%L<387Ful5GJgNEWk;TMrFGbg6 zWR=lTAP{TJV-Exs#Fl}bF?gl{q8#l20Kv~QQsj*^}b5Fa- zVB0$|rb3qYU_{R@VaZw+CZ|M?EvSvL48Jh@BJVNi$-Wq$;9PKr`Pcj zn5?b*T&1Ik+a}_h7v7lX8t|^~Wh)w`tUQ8|5=c)(UFLMeBcd|FlXLmgk&%EOB!2~WkrPU)o$yV+IC^_@qebGf##=Jy zwAmjCod=`;1hrzVTPC9(MN*Ln;POr%O(u@nPD^j9)9#N{=$%o{}AN*7A=Q5 zU1+kWe8zn0U~edIQ9_1$R$I$2_>6v&cP2Xde9j?9$drSmK^jrKDyq1N4c=<3F*QBG zfE-9HEB6#;s@$n`f=AG`I@9W3vFAo@g(w8rEz8xkU(nx-r{+7X95wMd zY9~Pm3jnGfm;)?*qVtuNZnFGPCI}0)QWb9NHbd1o#S8 zE*Hao({y@m55a=-&BG@J$b2X`oG`wdq6;}RK~h$a)AK7v2^qLOnKhkC$W({`9cANA z3Gb&CxvrBWmB3|LT?cjdRUu6WXh(&q7r~!}sKBc{!peJ!V2NfqlUeONC1j>O0H8vY ze?2^aQcDwrAmhSCA4?468dfY9XBW!(Z34gmh^L@3RRA@6AePu#y`=qnV|yP08njnB zuC@9{7+WY?J2$BW*g+UT6q5U|KJWN69R{t{F}n@&WOvK2WF+czd<5_Meq(euc#X)bU9zsA`PhY|!wD6k%qmY-Y#z zt*2hj8j4S{mKIius%ZHDQK|62!opW2Q&IF_HbysNgt3c!gc_$%-H)xT+Muif7Cf$h zBz8C`pLhx|Ht6ITxg3F>qEuM|Y@s`F`(G&M0`zZ>dGR`4QedYzBlKwuh5xZUBm*7% z)~lKO`RZe`M?&Zy2FJqY&~$@M-Z}tzd7!dd`~stA^XKKrdUDbX=07M3K?aw9R#v;h z9hgEeQKmTcULgYvGXp5od#{qtbb4+c)|y64As;#)x%~8Tw44Lj4KV_Q_>(7 zS-mZ9`@Bbv#|}lKTS!=1@Y|P-N(0_a^oY^bm*l;)udFH6tPm(_^0K|;gB%RgT5%WL zX=wlHSg0uS(G=*&^9K42-?!6E@_f&M`cDoOzyK0iBh@9~O2Z&Xn znEEfh25v_C8N$!U@iLgnwCb>;6`4No-(V+yxDa`N;xj|zy>!1>aS7UcXWMkX6q^d} zw(p!G`kZ-E#6ETtrL{vs3MpZ7`Hzl~Zdf#mPlji8UMY@y?S+GDWBD82#)?JMAuC@s z{A*5C&hDRPU$e{JrnF9GkT_(eqN1$aDQ_{dc5D&2A4I1TFRti+i1B{9n2MpO>wFfx zj_h1PVqql}(HmLqeg;E|4`W^f7Jai&%)==1`LNuL0%gwX8yc3e^1X!4cx(8B0emB+ zVG*Eeq>DY2YWh`KcKLoNcP}k%a4qnl$6Qv|+w=a)U>$7C0+U*(1g{15+TVC*>ydNZ z9piO6AKH*1@i$7U4`C)DC1-K= z?d5n<)-{e7f_`z&SAHD^tj`b|Pd=vS>C3=H_A56nCqGzGK2r=7v!OqQ1ATQPo2rX@ zX=V24IAUF$4iAN`7guRGCoIY#@Z(pPSn-JCEG!BV6dT5!E`LaIJ5K|QYzle`MBa1l z^1HjP;GE}x-qO(6yXGcB4&2Q*_VKB4b2aA{yc-q*uMFF~?$J|dfJDl-u51;GUr#d0yR5(r61}ciP`CkK^dAx3SU%29L>m6RR(E+rIy? z|1!WcMUNJFNh-qU;^gG9@WRDEd9FQY?*7Eta7XCbIAdu?1tijUrr3ISHg+)FU5-R< zLKj1@zT+EDton0f?$K5K8fKVZ+&V8^JAPBNF~+MCuiBK&nm6YEbYwrCup|0P1 zxlOmNlPE2+vZM*I=9Pr#bVqbvN1UA%?+x>M`*><&w#68Q-)I|Rye3~QZ`YtFA(Mln z)L0@G|7zpxzA-7mA`j4g8n-N&z4>%dJ_#z0w_U9-Ea2=|skCv6FhY&$q;uhY??{7SHMy0yXl4_`O4kkW-HT?_^@C~L*>OyLu7^pObB zhn$z`vSl3HHcr;bNiH(*Ozb6gAj!e(Y8Qcnev`@HZHB!vV#UjB^%iu*{%C2+T;P(kz>n2Fj;ldeQ;I9+xuqY0T*9~AfRVr?-+7g^@2Oh2 zB9!n75fD9->h{0E*}s{5`(idzS-nnuTCAe*<0}msIsl}Tlvx}wHiPaDFY+a|dud$n z0a1&k%wiu_lV%TwVNcZtJ|XA(VI@K+=kK)%QhP(8T=6Dn{i}oV#J0AcG_9I|s1}z1 zldRcY$rjq`Jp`F>)Yx3vY3NGEpifMdRFX)@4uCygS4N0VZ2>&+YlqB-Kyy|f&~>f;)E8bGr)qqyWC!Vsis>Am5$g5F8oOS{wnM6Xcn zC#=*qDLQiWnmWp6_tN@T+ghbW5CF~gWsLInnB zc!zCjUqS)hS6WNzh4RbJzPnt|e$x{?Jck#C2B;eJ8Rzx!LJrDp)3XO#Q~=co@dH$M zHg`~{VLi42V{m{gjAn>{vvr*iIm3aP!d(G!LWWzQ=>v}mA_?Gq)C=y^~+l%DP30tsS- z17guKY~C75L-83Q@~oUanDxc#64_n5;)bx;cMu ztK|q`bNAdn<2|XW2%d+*0X_zvzBQw%OUeL?17&3$A+bePEUbi_LJ2mw(9;h#Zc$mf zp;;Yi<#9o;piNkaA<4Ox!Pb$21-ycS;tPY5Ja0}mpmTAs$ zjaM_j9Me#cFnY7HJ=S-e8OzD_38DSMO%forLbM$OP}m_*g_tV+BhJ;>On+uP;EQbS zg(>nGhxF3XJ4sN;+19~3CZ90bi)ju3N{A!9Qadmg+_iNfvBg$z1^v3$&OgJ#0t|{& zOo2S`GCD^zAz=<;&|w3=W@g_(DL%i$p#y*-AiLvAp)#iHL(FA%L zbVS!&-3q`Hw3+pEwLGPl{yAg?^gEStue-}E=$!OAqT@hSok<|0nCz@;TpYsqS7H%F zjR?hQK5f@w+S>jm@__&hP^L}A^d!Ko${0Y4vV0FR>|84HafZgk6952r9GN%~^yAxs z7_-++20}>4$X?pnNDWE26T?4e0}hf%4?#8xNjJv0^-xFqFE~+i0)RCb`+OCteYCC? zr7(G&>FW6I9D*jD|(ga;24hAm%-D z=YJB;{b(*Wgt`Qy3=aTbq(klZR->v5!tj#>VkckR4`!n>+p(8!tO|Z&&aaQ713!&| zo+dk0ii0xRlkmv5SxOze8$hS?Evu6!rnmUrCeH%^keK_1LjTvjWnpyWS@e)BmYjhx zlvQ{5*5!8p9K|ylJzHSoT>>od5#B=pm7Jg0be2YGh;9iNi-c?qc^LJ|34#jvX% z`Q=of#RYTSb=k`m4b&mx))EW=kc%CpLCXX^U!l;xG<9JO4tI~6l7e7Sian||qlvMU z->9S0o%BGjGuVnvq*SipY53iuL7+eXYX$06{?8VM{ue|-%p0-)@zn-5*MH^J1~)u6 z7u&zRhdSzFhw6a}n|sB2WV#DO^?z2-|CHMQ-qno%l>C3%;D5&78}UEw_J6Fw|BV0t zG2;IPLZttTHf(=kh{Riu5^Tt5;MqC&-v8_ET(7QzqX-S6-@%zLTD|nZF+y-k00>ptM{23I#aE+EEqp|2ff$PzkHiu{GdZ9*h*An<8}LZBQ$C>qjR!G>lu3L z(KAkqj%}xQjBQSk0;`r%tWc(h)BgRa78I^;yn5}@(0N>}mn_9Q&T1s&lAn?(JJmYK zClOfcCm^YQ*es32*RuZBrW~Ov1g72g1 zIM%tf6g{@2J7fBni_gqGWs5<<`wo>mzgK-;&vhF=mbVVAh&Z-t+|7vCJ60aC^n=$k zjb>($o*$P{a&NvN4_Lt3kcJ|)bv*rzGhR??7n!x+awid!=3)Pd)Ds#hxt_=4df@*Q z$-b<4JrShZ+CuLju71VyMdmm63=O0`igRYRbxL*Ig5Yz>N2EtQwsQF;&5#VgeqZ&& zBVyJ+3&%1T6}uH8xZTlja@CzSes_YeB#vKY$hjZk!qMlwi(Xlm!Vafcz%X+>hh#ao zc*;_5sACO{WOdjrX`r^ZGQ;}atPK_+c@W#fMFwHHf5==E&0p4f*jJ5wjTgf4_`SLE zaM{-|s_jIjl|oKFIxpu^P}mxady}*H)nW|Wg~}gHQsyBl`gf_hoGUh|xiOzX{_H}w zH1Xg#q}ebS`34O3PY=9x$mRnI^Ci@QC+FEc=xv7HY8%cIw^{MY&r zNa|=SEadq+5trlA!gg(=xDkX3jAbGFw5&GqL$B8X#edtp;molp5~J)imWivEtw6f} za+_Mz}$`Db!(yhkbLSbtR~Rhwbi=PwXW)^*e0 zl)0M_c4_-8c%B+B@ZdrJ6fV3FLH@k*%Zn8Mjg5tCs|ZQF zWZt^8gvHxW2ugQ;J~{yzwKPuk^u(xvpNlDou|C@4v`UD(#0?N~opV(>@08n)3}g64T#5=KMl;-$coWsx$q z3-W6Or0-`U51^XY2w>z>%KC0|x(MTy0+%{XxZSs`?A1^VEx^7o5xqCjI|pA?E%c7vlGv zJpcFe$@d)p@%bbV_y7C(BsVV~*S|lX1QiW#+F#Bd`*WIGUL>CwvtGhpE(+vwAG>zR z3hn}278+=_zFlR!vuC)cktlUl)9Y&*VmW%VQHHZzF!sR_LBoY)@LE*PL-W(wK6rAa*}?B>8tp1o^bV3)bk=lgt$lcdtm+LLoPA|6jDx#Qf$0 zLh5RXjOk8LHuYtjYuNYXWBhFL7&~?AZ!i9496domO{Jc)*Ucqal}ak*@MrGGCl?o4uaLMwt(|~K+)Y{+*>4gg^13ybOCoOZbh^*3Bj}s=A){MYS zgaDcB@|`3Y7DiS(QILOe8z&;bJ)aQPEErE>)7vM%8~-6{n`{%nxG^`1^1ONE)k0%c7?}dia5y#e zUzH=hp&0yt&))Hvir+jpHFbiYaXE_1l&0}K>z%ocTtx{?iwqZbil;;B3bJ^}JdJ z;+%1s)ylr((7i3;X%p_~N;U;$-iBODBL7k>RnTM@Cb8pNm{v8nycn#_y&pmA&E|FM zwk>7CLqW%Dr3y*6LknioxxC_?zqcxDZ!9$S88xyQTs1|go>r~gtL4V^)>!Zqto`m7 zp=6kB$G~(~%IXC@YRB_@6*a|NpJPb(xFbQ`bo^=mq=fbcx}V=(XJ`!;?1`2&VsZM2 z6otbw7mr_+2Wzb2#?@Z_8BTVlB)!Vn=z{Kfk4-mibxrZDB2YhsGYI`NsqV4CMN5_HS!)IjQ8FYrBd< z_7Y>bQR{jvL^6bSX^cm^c0)xm$Pc=H3bm+ zBiHys&=7vBkN;@C7%?1qe%(#%do%>uU%d~}F#fpL`ITceCPXFPtdG(|tkgl|;xRuImoy+rHN>R&^fM|N%c)%$WWj%)n ziyQd>V|Z+GBBoS0f)!u$WsS3fgvkxO(r`}|bzR@fzo;`HWT}uSj z6DGU}cyG`wfHubb)s{I#;=Z-2@FRx*K&lZd{~u#rcG;lZqQfS$u#*A?bm$P#d&gcD z+6*O{i2rI-@8W%uO84yBXOZI8V|hB2$O>9TNF!FqwA5!s6+CnThct1w5D9l`*nmiT$Fh$&n*9m9k|AJm8}n;GBpeQ3 zM3LWWnEp^_!njSOI5*1U)n_}-NfgBz$(Hj*w6f0duGc>#Ajm8hxdYyewEd&zm%dM~ zxSn9ep_@84V(DO7qM&S%8y{yI6VKSIvjL9fVknw}mt5WEeX@-9g%_VQ+Q4IaU3eh33jvDTTJ4?_X~} zQdQ3v6y_@?RUB3#=#9M}uJTuUR+HJ!g>#$^k3?z=q*&&tgp(=5Esx`sox(6$LDNK z8lMxLgzIk=mQV~Qp%d=?@c5~lSt^lC1ij#b5;ZS>bEy@#Wqa|j@xNZGzE0Yo0h{BV zr~2(fB1Q~L=!R$3nRRG}KhPy_L42^;slJ^zC69hwlt3wbD5LBejJp)A_vzOy+G%7P z-ZN1^X$&f+l$Hve)O8AA(zz$#^~f$9dkfgcZK2;Nj=@KX7i!b7-aYBcg^kzbTc4d2 z*#2Wir4+-37_DbjC0a(|4BrjGnitvsi@2{2ilb}#U6K$I2#^Fzf(3VXPl5+`hv2$E z7H5GWN`M5HEbi{Gz~Tw+!5xAuwzzxlehSf?jIC2JA3+^o<7~b?$h0) zx>(%yVR-B*pEU}mSo<$lnp7GiOZk^Jc$9OX!tQ5#k7$xHtUcgf>Ww94iHf;<$Rzz_ z2eb|c9wPp{GTbq2e_S&4>DQkUU1t$UhufN(?7VU|;q+>!TX@6Zff^pH?LOpBnsJRN zrG^L$z+y{P)kR;53`-XQwzS!8f)@oPtIq{QqU%P{;L}db>x~r->XHfd!N63q*+Ryw zPzhHsj8S~yX6$Fp+j9gIA`(ej&G`l4NKzNn@NVc&L_BtDyZDFC^)byzr%$iRmEsaF zG}kEig)c7g>s8wxAlL*<2e?H%`dsfCdb0AGa^}Sh!q6#i-PQnuP1vnK#R_BkvF7-i z9H@sucEX3z73G31*ynv1`8ZEO9kGsas`6s-S!9iQ!)#YhXK%6-vj9z6!apJ>QEBW^ z%AY)m3%4r#7khl9)ktH;G)IIfrzHoXeGcV>YLUiqTC`1zTS+5N7d~G69<@Zm%)%wp zU-jiZ0s02yR0e}6hw8{Q-84e`EXSx2qSR*jH&ae0tcPC{#RioJl#h3B1$I{?UFfA1 zuN*bLu6+H^hS82h_w-xp*xWTDpcZwnwRX+9P}1l>RwVQ9`SzCUd#3|vEO+|&*gk6W zh9eo9XMJr@1*Z0WnOw6*R;I7&Ms+pf3flprlC5S{8O`pQ;^(}4km=_0Ea43{hH)N#B(h3~QT`_P>9ilO2y|o9{F{cq-(Tf^h5} zAcQC?Z>{yG>LHO7rDWyZ2owIq7w%`IiNko1Rq!!F9}!SU4oNYN zZ;z7hY>5QqrP-+a_K&>&Yj^Si*53S}Z8fgWRFMJ~+DgTbi-q+GN*X$Gd|O1n-eBC7 z2R@G89#kesRdQkd#V@Qi#N{|sY3w;ReH-7R5PRsF@kGmxrD<1swb5tq;{~g&U(=f+ z&*s?+8v)6WI`r(`$IfL0gBs*=u?C-n6Uu28KyO7x-pd6kgJDt?UJl3YwnJl^Qj& zCr*XyNY%NV{rr@nbOS`8S=pTLc3yBjQ2nR?gD9t-R+%Vb@cji1e4?E7su%nZz8bc;5rFz5Y#~|KBmf|B`++b9Gu# zAJnf#=BpC6)6Zd;#W30V^;s)$Zt~)Kx4kf&ioFPC0D+Kynbjth)N>Y#b!^tYxyazX z`D#a&sv7{jSOjMrCfUM0AJT_x}jY&(4{lBPx~swB?Z`ttX&S^O&m;rT1-pW zua$&AXlU5X{;085>rhQr4l&S=W}ub)C+Fzo zhLZ}fw6W<~3=n)Ec;}79P$29wBkwy@8dg~LEx;&guvp3}b8cGbDx=KBEXsSp^PY}jzOvL_T z%8yp#eR1!yD~qebJfhdVnpEoJN|jOZ_VS|BLrmE-=_vkD2YU|%4ZZqj^A%D9&51nL z`RRk-@1DZqW=i7mAmmDI#2eCXV+(>qqgOuL@%g?cux|^jCk?>Pq271&sP2^Zy{S2S zBtPLDP2dkX6%rGvNT7rzy-*mJ?KJo45#y$&v?(ScrcN(j<(hiXyR=aQ(+aIRt>Z1% zAozM(oqOq-ICFU6S*gZ=y3q8hto9TZH(=Z$G0xyN`jg^X`9xJm7Wu>8V`IQ{7=G>p2w7X zN{0GAEi4~FP_F0n!|k{foHSfg6BZ920u8qnfu4$E(gOsY2BA4C1Og5o4lLz;=U-mfcxU7> ztL3P9%sTVLup$dB?6>-lb{)nf`HoI+O=6G4gk)FUMcJ|ZfJvG?f)=@Gir-IK8R9Mm87t=EL`$;%;XAhtB!tztpEjKq*uA38r zictPl4$pd@M%sQ+Z2ZKNzt`3Ahp?W~WV^Wkn_%JV(7bJDpAUx{eUyK42_I72%Nn3r z(?-rrCz)FsR=L-9!yuc8r6o3t_bosP6`o$}&IG75mUW)Hxls;g~ptGf` zV~tWYD;KC~HJzyKois=&Ru6Vow^U)@+;JwB6?576l`(<-ob|2J_$4f~ZU)cN$Xvx~ znQpDW=a-m^P#+Av30n#@;RK!s5y$5DV&&P=s1DU>owk0dEmrey^w+3&z%;xq!)RC3 z8lN+)R;5`ON6VD<28Zbg^aD@UB)+sOv6C17F>-1!-rqzBKIF7*Fm|!Dp?Xi_usW}D zaxyg|nlvnz&z^Yyn7PJ0jxUbx*a{(JI`AvIV4hWRsG+6XTLdDY@-|&fMusL=XKueP zqln3e$eb+SkJWL5V7w*b`|+=Fj61x6Y9iu0i^I0-r^8hVyQz-p^m(AWi+W&?>q2~- z#=ez3KBZIi_kq&lsQCCQt&c)|Vs^2Mabo9mGG93IERrEtGKK3Q0nTh#Salc}h?_4n zKJmMiQ9C{QBD!G-dtf|-_nn}T{@_E6WkLZTX$x!0R zvUUT)*Q1y%)#4hPazL==)B(?PWdN?AQ*(e6#XH&WF)}N0_x$@8Iig|lFooiY3Kxzo zbmxg{kdSBvg{vph@Ho>`A?Y!B9GyY-{{(gbLB?wqz8ddn=b?6AVq(fv#}`& zIh0b_l9ct?d_4a4ix57&j6<yKe_@39}i&fLA1VKzZ68g}Bf}Re2O}m~5lCXxS2jl_3tmQ4VF2`KhL-hqeW$HZ{E_Zdn91>Lx0HDs zjNBo;a%b%!pl3NRXCm7@|4!G@tu%-p=M52ys=&1vT@yi!v zfBz}lye|au=5U;-XPQV<$E&v2W1nC{*;TI=;nsOcC5f{JXmPW$qs+e-FE6x zUL(d{N=>S^m|A&+c*$2JbE@hWqidCRswbK;X}sC<+qEz;<{Rbi*L%wfok%UBSbgjbEM=*hx9$xPhxB5=hdA*>C*)cig-M7X- z|E-gD2?_Z$Gb?U^VC#ycO0D3|n8KjpQ<1#Bju`ZhtKr!_#kX($5N|wX3^Zc^9HzF^ zQf21I6m9mTa2D!p!sAGJgJLEL}XAbfy+2?Ci;7=}SAiBnmn>jJ$^QNj(Z{kRrD>!S;@c?H1H9a;gn{r|&T3 z81yLF8_b@zkeLaA@HBfhr;t5BFlm-!w$S@hmAHqveIY}+f90rrb!_21h$)(%-w`D~ z{^3i*iHz4(4-OChpnMT?K9b*AAmTcmLxNFdg(;x?T!YLi>OTkxRKL7hyvF~KG*9(M zK3HX)K6lOmN=<0{K|g40cydjxlgvJEYSkZXcRwnGdzKbQmh<}%&-(l%c z7v&l5Q<1c_p>39%JB>)x`2;*<@{v#I-MLLKdQ>H{8B&i9R?Py zSym{aCDgn?#Fl6G#{n44w)rtW3N_Ry{kR$J*mjzZEDsAFF1olE z7HwoSY}&X{Y(yK9Q>_+(vnw<_=$9$l^Y-eJuFOi0WC>Vrh}uN9%t`KwG(x!vU&Upb zcVo63s`Y31T7S#%R-y@AiA1txP76%Odq?-JTxvjjjo)h)HByq3shZ35TycKi6rMR2 zrD`~>^37xuP{CsP{dC)*Dy!fNt@X3p*`(;{Q9i;@DSoeT_}GX1@O5X^wL(pUk`=8k zjX!}G>z?t%-+FxC>kx`>l6bilcvVgw<7GE0JGvDnypp)lCaa)YUAM(Psh#{OIf=kT ztY7=NikhUc>Bf^oHA|ATuc9+JPxFhr9<>n%-?!dM0}f7JTEp}cPer3s4jvLqQEzK3 zNur}T1kmPZwd*!IBbnbt3Ol+ew_QB0Ulg4u>7%d15{ytcZ*>extb`m@@e9gFo<`tD zcG^G(i#dZ+t#Mtj->DNXIhkw>$WCQ4iW$N6>Ln|GPCM;Va%g4|p*qzqM+m^x!?X`B zE2DV;`k-f#qDYE-J;=yQo=t}uLzz3#*NvMjPcDR714^aXCi`~=c9 zMV^$;;O)Ib6~^-dLk=D!vGiD5s+b<3%1aB|62gu)<*~l$=je`JN_9zm))0C3l-2mv zu+V(`x^r_L){*~pLH?-hnk$!q|PNb)Vn6pGr;8w(j{i)*)Dv` zDGsmkD3e!Sizpm)Cq`$SEA_VtB;MPV=W*2JWLq=BhazDcdvTPeWFB65L5|z7ukZ%b z@ZO=RqPuk`KWPne1!6-qrCh!Azxo%2m7I*P$|dS#qx(H;k`%S_>w`yLAKPyp^Cbd} zGd!D|_ujTw7$b7KY(zK`(GRY*QZLvkxkGncT!a1b4X;iq= zkb&F9gi}dbPvMimBl!bg1>~morFTA1B0ZHnAk=P8QhSw=a`Jpx=8p96u+1a=g!&|^ zW@25R_NnamaVY}GX}tn2VShvO@Jb=EvSK*@bMV2SQ+`IEWt!NtsHDfiOiO%KSaryb zfvCZ|MzWR1myBH-k1$_gEF(^|2JM|OLv$GhjEn+LCg_JSu%`EQvtUcZTwcJJyS`zs zBI68te#)cj)0N-*$+L-5K1teNTQXS3B{V)juZU{R<6He#1NqXZ;5Uz{puH^d_Q<@j z3ImnW-q`g(72CY4`zhESC_Bbkv|hu}&cul_Qt6J`aiqCGj{qrxlN`S`d9FC_Crh@7 zeR-eO6AWw#3{Cz8iz*AcKm4@%Xov~G*meCes;-+E3LB0vsX8p0YsEm5w zjn)%<$EbA=k)d+dIt~!-bSvct2FT-MRQ2TXJn=KD5mCe%|3&$-E%fsOfTwHCI9 zP-rdDpjQ>6ixEIkyGYKfG`W;3^fm5>*~}(BhOkEuL*e?u>dug_!K9%-%tmL*}xswWv%uQo()ipx)lIS1e$zvI7jqMb{g)m$k=P* zmvT0ng*Ytl6`e@No8g8A7fs(WfYLgavv-Q?z99^`djgNhv|gf67mH=*@v1p?MYW?d zOl@nbAAD(QFe(*nD4J}*X;il661&T8>o20g;CB2p&KX0|HTRqyZdLv`*z?x6ZGTQL z7aIdnk>6W@19CHb2X>KZ9M4#B_@@(_Y*Y5^#9E{T72l1z4>SVqf@|yq|*LBIdRnWHLUqtJO zd0~Rloc?&fe5tF}s(_vej$>Hd-$)fjQD(b!-l%JD^wq71<^d$o{+zOnWcn`0(fz_0 z2mpB_iRrm!yF)VF0X?IR=@k0n27!FXV~hAzVC24YpBhXf?t33x$e)7*>-XWPfEU8) zPzS0zmoFiZvJt;#+PGhWQ&bBNdtZZj+R2Zbk=5Zr zl`o509qhLbbC*N^6?q!k_YA!!wLy(T;gI0yB^!#(BXIO|B#q|DH!uBS%BeM8ATC-W zdGo0r0^MVJ81)1 zznscFNpq6&l=|NnOUwFdWTx!MDb1+w-;9;jmp1Z@`HTGvnTgFI3qAe=m(gy1`n()k zn=j!uPj`2A5x>HCKlh&44Da<%-?~`d#y(ObqlpM1hprT;G-r@WV}D6<^p_UjL4Jr9 zpwuBN|0ME5N0RQ=J%L1>iMK$y)0gOfK$Rw)A>8IgqJm8|XE-~&9*Qzh#S?`NT*YL? z9vf21-bz#u%C6I6$Td-sPgYfX5!JBVcp_KGkX%)j_^f_3@s?%_-}IQBqRu1P9)3A# zjvi#bE!FtzFLTSL$8R?2>JmrJ3$%eawsT_Gs8m`kb+(=Mcx9gNZ;jI0M6Jfe_7XGZ z?M?keqcP&meVhzLyyJFSDhYQzI*1r;cMRPmSN2cDl9l*gw6o3cQ+HI(E0EWrYWqS^ zhAL49qlh0~y`jkBANqysQ@RSdi7ke8%a~Z6)wDzjO(p$JMNC1|zFVVvcMwqRh@dFm zfTfvYx!)Piubgvu^hg<;kGc3EvW6^m) zRlQChoa3HtMXtAjs*>T!V}K6bmR6RpM^ z?_dJ??Ux}DoL629ysq#qfjUOqgj>oDmk%GB$Y;eK>o z&;dhuI_gIOKWS6Hpa?&ieDO8mY&OhgEVj5`YGuNiaNp~kgsbrqIR{NrEtKRfl0$Xu z{7jj%YuVm%MiQ&C^ecv1r~K59C-TC;&Tork*XO}l2;P%qk8K=JYq-xvLIc%5$ zSEq@wn;P2g79;4iP{tT+8c#%7m@%W-2UlpP-K}*4W~l}4rd%cE#ysI-g2SQhJ4xj5 z2g~THMO)vv!0=PK4-1?s@4XGZRC3!Vk@V?e8pkau;@5)}{|?ljZ5{qsEGoVlw+soi zk_h&}e_^~V8j^}z7Y{BPImdDMk&UE~Y4b!Wig>U7?v{gg@1S;v@bz7Mroyy(Ons{`C>hCQ=6pIh`L1EH0i|sH|2uUaJ>VBOFj9B6BA!}=F*sJ? z$g<`XHM{ZF)q)7yHvXoldYm&?>X~P7`-=w~%4#7UOke*O;|}}}>t3<4sYKYSRr=EA z9g5aKHA@SOS}8kh-^WD!@+{)dZMqJ8rSuXFQwpx>|AGJBxF33$f@6VKktAusr{M9j za`*NNjWD@P{-B2 z0^Y-*`$1^zPf2H74B}6oJGtXCs2C~J{lon`khHJIGJYF93cuH-UgsK)N)>g+O)NY1 zEJ1tR`750^+8^A5KzeYG#Y=5O8s{WViuVd_Sw@EXhCly#rv}yuS<~yq@x2_FWCs3T z-1&MSf(=Q_J4Wg>en4txD$85m1t)C7nC!q3jb}#t3(Zi?Rdw53!YJ~2R;pQLEbbgF;)X* z;3^HbbrDK?Gm2STmG+ zH+?Pz9AX>exo)-oq=Et**QnwaNCIRkT`yRmIK(L&|dfbViJ!n!x|C#sUYW$EucKJeigtI?1RtT(0 zd)~X<;kj@FJ=RpaAZ+5*ENRZFnOw2)ZT4!YzH>8hg=e! zJ0wmpDVDIC)gxt&Xu(B;3~t0kU!5(uL^l14S)P`mLDUtJiqILiHJ3f``E02T=ac>% z1LObdgNK{3e~$mecD+G5a9v%H{_{AGes7)L*DF$c^_NTWhM;KE7jCdO8E+sAT_YHN{hoTq;m z{jUKkVo&-)CI1TO^;c^}Pe1?1KA(;i^&{>;0#z&wq9_-#bgns+FGv-w6CIla^p>7dtzKm_0MBbPa@ zHVwdG1;m}tM<;e!w4mD_V>s%TpjhD*6UHo{8n&&t%o9j>d@jv@T0#pHbC z%BWFlA>e%8zofajn3@Wts?1*v4r&dar7mW(sJ=XH!^cl1pI}Hx+iA6n)I5!dj<&R zwQ)6jUWox*L(W=P2=6ETfLj9Ee6t?~@ zqpSB|v@MzJ!Y1G%HGJ$(a%!D{=w}lEWF$ijYfo^2cHO27t%lLI7~)h_iE< ztT)|kkuL%p=e53j_NUvnQ#;_H)P=rUTfA{*8&f5+tKOxA>9K%mYS#1K4I=IM9Nt5< z(i*j{O~L@rlD0jJv(y9EquF?^UPtPN{qrF= zA$hW8Ef=T!W{;~=b&YC9B9JGhVN||E#xWg z`Z*619oMwiHq>7IC|dxh{Be5FSZrEKs`=`yDsRF>N`l1f;<9gugZ)w8190c|;5GZk zomo{^?_F?>nyGM1FtPN()^J%pXnVU`xyVwF_bSOlc;UNKyoW|3T2!OUS(m1zHD*98 zn%s=aI`|C)vdQSV%vTXDGQs3?b^MyLauzQ&wK@MuM{_>PQN+TUgFp;fThDJx z89D?Mn)gUMn>a(+JWv~ATR%W6*|9Uztm4VL##n4*n!0jP=|BCfxjE7~Bp=_a>Nwzf zFhy~9AdQ(YXQ%O()ZvIyq|fo79-w94A7H<~n!LBcH&roHm0_hD(Q9@>FM$3b9Oeu? z5?JsWm}_YGK6~ViS{qpSU3nj*6V=`6LKu;(JQmRi-@k-XAyjddEfLfSe zpcG%hC_0z1$xl!#)2)=HXIO1;g`k8jp+~b`e5G&nY~JWlC_egNdb&R!5L>V`0JX>_ zd->j%-&Q~Wv2rzh8%F%+9j6`+y}XrR6=NPT-}Al(MaORwOjG#Z3_!%7{psn$Rg+Y! z^X~pB^mQD1waFB%1p-DLs-$blsqT+|RcLlKCi;8Rb?@#iKPoIp8h?%L^ky4a)!^V{I{Ybylq07|b?r9>9Im4!-tHwB>uXsFY*Vx2lSaor+Gcw+ZoMLm* zZ3z4LIa&7Tqm;ToJ*g`}rxR53h5^fyl&uoGS8e5tz}0%{$-o7@6oBCbPn#j?pWO?x z2{hU+)_s*Dr9vAHq&Jub`y1a1q%-fI9?c$)>h1Qk^jv4ZJkFsW0KCnv-By^?VkJkl zhT*^|@&)KqL2WIRM$84uDB(BV!^NMX5l53%u3U_Sg4>8q_?xoAvuScn0P|x^L&(qJ;JUgM;)FVmL!@K9A8g_BCkP1;GPui1jEy{w0^{ ziXlgwqJgVoO5NDt>oeT9rwgdku3bQf|3k25;$vVJHTA;?!A|C9E$V|&R+lPbs`lKd zrzNev_V%&o^j+PMKuLC+Cfxb4QwV{K8e1%C%*pjjc+~VW;$PXT1Q$P;tO97DWJD+f zPGRn1=8?r}TEb?bGXvO$8ev#Iz#NG#!5Hjplu9NkU1eLnb@6f;uB-4GXYyHd=0=Vs~sWMl8=1+yVsofn;E`Zuv$wuNhO)a|aa zL5Xphs;ti;<)Mpko^ukQ@cTj8(SBxi?t3o$b}CNB_?^yqxMXeoI8$)x_BRznF4JTs zM#KRqLfgfix;s>ty8Uhnd!yy0rdRt{aB8L){Vn`rzN0)3RproH(Ld3-yH(;6mp$z| zJQK&`egScn13nhr7~g9Sre5qYiRK1(sSL@h(dLq#kwd2DLN&mr)@>`OSIJF@%V3uR z?)>&8{yTVXvjA0qaC2>kC_Pv{@BZBgI0!BbgFkI}Yo;NYI3lJw6YvB@GLkCjgIUUa zH`u1q3A-dU^Od3jNN;kLZ3}67^B?VJr%(R0fSLPl#O{JM^;CCljbwJAej94j{xZc} z`{n~MhWffszCemz=~(HX(yGGB+2kO$B54pho8%+X1@|+zCtKrFn_a#SxUThGDq3^G zSjCigR1>#NXGZc-gm^xOYN;1JL~OpF3qPPjho0t$=cz^R!2KOghOe{Mg1kg`cjKww0hUs1)2%ywR9s6K!1O?qfvnd7;=LcM2y#)6HCEGwZ4+#E1{R{Qk zY;7}4ihT$A0zQSOO;*2?>?fEIM;r-03uCTU-_#yLAYvwomcN0dU?F>f{R?_(HLi+X zuv-ITddJ<0=%*7*1_2-}o=R$6IU5BtURVWYW^=U3@g34Qi&CW8~P%flzwNTDRUzvt)OcOZk=G7+U}RdBNYdACXD~xb8C`Zpa5^ z+Gl93L9`S87{m@Vh%ZvUd!T=*XfOj*ODg&WIG6_nx9h`WKw{P6b!mGCs?X> za9Fdm$+Ckw6naAWcjK`ll-b37k9wX~jGs6S7l1ch_7YBk(ICjEIv6G~DVeF1>|ToY zPGXP;6}AfKp=|>3#z0mtGN966tc9KPSQOkSkWscFP?t9aT2MoG5Z|c;d)&5XF0@t}k$*~mo~ zPeC{!UZcd6T@b8&^Rw3l>}j)gsGbYX1yJtyNRJP&TJ=qSCe{p2X6kX0;B!zrKxik5 zi#Gv<5^)36O>jcO=vGxF-grLK-g+$GCZek*N6S_*09-~M<8;36?)>OTGSyy|7RT{A zUq53FS3_`V>lJtc2ytLWUA5J=$-~f!TOGCz9a=^!QPOI@h=%wHkg4RmKw32ufTCSU zFpb`EH3!+P3^pi6ADn7r{=RVd>Ikm+|Lq5i3I5lgE&M;!h2ITLqH!dtqm9X){I4(W z{m+%>0(S)Y`TnB?4Ay;+z^$~K)Dr6S>i?S7zxR&+vb^BmOYT37_HUvu{+EaUH=lnK z{r?-%|NQ3vH+^osyCIT`YX7-~f}k+i58;1*k30B|>3@3BjOnVl5b->0Jk>jUU-fb> z-`1%Vs{Zl444b+tvq&rjZFaWA!z|6_ij_BC-E zeZ&2Fg1|hynYC!XSLxkfa)3G(VtSS^b&d7ch5JzJvd9vlGzgR;BK62z0Bn&fq zqCVhxH;ayUm)K#iBV_vBKI1FIlWx>#w4rpM4VqxASOQ@EOq#@o-_`vH%b{_9fOMTl zT*K~sKCtV33@6?f%@_I(jb9^w=iqq)TX<*xgJqC-+y=Hjcn9 zbF0Dfh=M6T@x1zml}}Fpo;X$9I;+ZRRsWapCy2W{^r}eDkGM`Pbm-%IK_!ccPf3@4 z9;wLQM4cZ!kqV#Q8{wrPqra)ageoCFwQ?8_?OxfLBFw~pdy&htgfs@kW6b{4W)x27 zx&!#908EM+&Dr7iyKAPFr;UtMbc0=hDLMOb*T+)c8+#%76Gp0I*7~|m%1F-pE*9F& zyK&+B8=8{Mm*U3CZ!21%VqP7S^IsYsfh-Cg56oJFqQD&Q7EXq!937!@kB2SoI|22RWO*KC zc^+=EiLvSq8jshdkZc6H;V`({ae%*o!C6T=Gh#%favUC7&XRtJ5Xg3Wun%b+$L6;kggLyuW=A}l6^O# zC6kqHMXDjnAS9&KlZ3UMldc5w&VpkNdn6@^_LHYc$YX*+9IV7BrdlPLK47>+VRC7F8X*J>+&d8sz(XVBwt1@o0we$D-Xed&BSnydh zY!d%M?5P3pSnwI`9U|V!xh!pkw#+PV5D0pt2vrqCh)ay}bnbp+3*n7?qNT5}YC4I( zZ)@6q)s(wmleZ) zzr;_GR$3}ImMDh*EafG~=XMu;`f=_cbW_}0v_eC@f3jS}-fCgj<4Hu>v#76c$$H@k z-Ha|K4c#yPF{;l4=|j@mQ6<6U%RjsLe}~=vxhs~3C*vQAWgKSiRwIEVZ%{{mW|ZY0 zW>L8So*qkSxSAk`UWtuA&E~ zSDKm}kxbejDcThEdXF;&ts5mbCxpbI#3Gj~`D|i`NVb<4+89NR#E5{?Yi`>MB zMXct>br6bt%#}-jX6*3rfw8M~N1S5AU?`s|U7mSeSo&-oD&bX(hp|UCuEv-w?p@Vw zMu*8Cqg6_y_{-^3RZpm>@&~H;=z5F;JPCdVE*g|rwk!+MZiS1N4AqkGa8WOquFHq! zd;v7p>npeKqOJwvCz|}4S4dffo%B4hO68r(lB_zt z&+peqhJp0HvO|ge6Y<1BQOs`J9z)|?kL^uYVXJ*#8@l`35*z%NejJWnbccriN_|7f z(a4ZeBt*2ur5-DX6~6{9t^(yJ|=C@+k-IoO)HIKAJ|rIyh>s}@lM7_Vbv9gOZy zQNUjcNH279(ZJ)g+2iD?0i zwfb$+e}XjFP`P9`S@Dw(gVibMZDeVTa{~**l7~6(_eXslDj!lD`30Mp6kHhcZQax) zJPR8YciCAiO@JBh9&X+(>c`d4ojz6!ypqlP_7JPe&LreBzlbA8JD`CV_vT`HgFb_r zoY8>~ebC?M9T7(FF1(24bBraBe5R3hE>fNSW-dgn@@dNpP;|#KZIqtH z1Gl8)de8Pvn?_G1Cc zMFq+$L3-$e+x~ZM>)e$k+#p!{GU_@d?Hy`K-!6IE<(Z-M*n=vFtXX5%ZIR}s=c7?2 zE9})}zJd>V;_kaHrhbq~wjMX4j2kv(y|e3uT7o~%eIM0#ASVuVkfw}tyR_)>Dz1tO zT<~TuWkYf1BQWm?lH>nGXb(lnq5EXm-aLx3MlBI*Qq+!xeK@WUcaiMBTLN9+t?Oo! zo}d);JWmn8Rk>Yoo4?>=M@>%3lQv#QAeZzGydvmSQPPfNODjvJ%J zq8>76ct?rVU4-mf9mUToA_@#8OkR4h5V1DLp(|5po4xOS&@DLWSRj^ub#Qe1Ygy_f z{k|^t@?^$vLWhu`wD{O0d{g;-(^@9_>G)Zv$gk>;B_U^z^mxBi^hQ#C{<5Wx^Yr7M zc^Up-l1OD50YG5#^T!L~_UAqY&9m(vnibTU#bV@h({y%sd#8FOal$H7#yy`tr)aCL z-brxs?zBJcXP*~qaSJ33*z-=7q_X2Hl0;T;E%p%FXgK93QK%iI`w{LuT7U&;p*J?N}@DAKt6@6~XM zzw%28?fg@5F=6c7N2P|q%?+V?ch-u&F(b?!Fh>+73wA+HhEEHd{PNJ&P+pJPF6VhW zLDg&5w5 zDrZSOT9kmC`Fb8n) zXPCmYCWhRwRsb8lO(;#gq5EC2X;Ar5`3wE&pBAmaSl*AxVGE&x@e)~6emAWK7n#@s z{ACv-<%Ew_8`U4`$g8Z>=qu_1n5i>Ubt*;#Vj;yor?TikLnY1on%~nJmfS!7iis6{ zJZJArKVdI!{a|x6m7Ec52W}G7QGwrK8`#^%oSU`NJ*W9=k|lG&NZxbdqnUA=UF&01%>N3s!@FvAoOImkPEN8bedkla&yN#De24}CN6zFM@Fc2(wOr6S)o|9foSBQ zE;pa`jKX}tTRK}{?VZWJk(XV+o!8FZ@!_{T-w!9{=B6MhT)wd#D34_A6CtkSP-SIl(S;W>nVo)eB$xXeZ}C=X03&_AcJ@dz^AxH@Q}J&X z_RsK%i0ZrNEDcLv*aG(r-Ej_ttbUw)@1&%6+N_oO*>azZ<=NEh?sZa?_uH}VEg$K( z?(M03>tY6c$Vqc_e}AZHqlZ}B!>m01kR?Zdk7R?M9xs!$Rha4Jj1TgWO3vaR(&dp? zSTxG{w}Bfz@3+8zBkLW5bBUUE;n>=-ZQHhO+jg>(+_7yZJGPS@?AW$#+dg^T@BONt zI;U!W%vArFnl;s{d-c_QU7HUzxnkvNBRn+WC4*klhm|UnS~&Fq2L~0UPhXn95Xq`< z9M0Sp)F986orq$4+2f2P77TAQXR&>7r19~$CyDh0x9JA6SXrqB&*AyC80o)Qb}~L${&1>oJa?n6s9(> z{dwhs+=M8&)VyT+wBqb-$j5zjKaYXnvyo#K@Uh;EKbF~bfUB+36^*J*|3zJkES~i> z{`#uny2vt=moov*bW{sj z$wHkj)B$8Mj0BG91SXCIAa;|*$2(u>RUQghc3jDDmzZ5t_iagu(r_fzK|(RMVc1Mj zPa~tIdk z=KhbV(}GdIF;gqD2NND?L!D%Qt_8>`EZXJ}b$aaVQn)P=aenQN-|6>ODs0V+Lx&=X zdnW$GXW_H>jS`W4o|ChRHr0OeHE0(F zE?B!GG>$7sD@HdkFy^DA^G$5&FA$X>nL^yHmkcvvtJ$~*9JW4>qSS4O=M#Z|P+zHZLPU4a(myTwHxcVOo&1U0>5$tT$)T;)( z6YbQcjs0hlLvLvqZ#1)ZOifk~$#C}e6yg~3@*`tXOZ(L31CjO{eAbnj z9aR-(WwbW)vqd5KEk(JmD87;H_`?`D>E0kn{eBjmOI2`(FKf88H#KYuM&f@+CGLI1tK8P1O$ z77FrBN~z`0T%Iw|jU5ity5H@N559QLh?eK%BN#?pjTpa!k%)#|NyV6Ss;Dc5Dw zfvjPF1zXWwbZKa-a2e{U2%729K6&5mQDgEwsAxGhKYvNBPM5cE#Bn+YaK#c(htOP-+e{$By;T1X>(YKUJ;UhFDS9bNu1&VN*%8fWVxTwynPPc^Tn>UA`f1JFBhlAJwN0} z#eKYDqj)eO{>{w)ar2;m*|!ry6xn#M-p^SCuJWzWN9^XV%n+G7=0 zy=jOdyCsZfhn-Tdx2Jf|T2`zQ5e=Ss0B2zHxs`GqyB#5@jgCjp*@yI=di|R1uR-hi zROTjiKCa*;@^ph}o;Qa4k_P;TTizz9AfD$liAH)bZeC-88&>;d|gybzKsp7F)hZu7SY`NDY zNg^76@A*FHv?#^n54ar`NX@xe=ybK$C3=TyymA8P;YM-Ha1bKNzGdcCl4LB@zb<`P zp5GBek9xP$ayrY-5t|o$!U`J4W?$jUdW}{90cv9|&zuK7CpL%P z2MXaF>O+3B%R*^UZ+Vap4ZE!mH*`nWPLhnc(zlZF;pl$kGr?U27L4AbW83HiOnpR2 zjgnbZ)`}oa1}NY2V$Vv-;>tZ}T-1ic9tCPL%j_k#k*ZHbzKr-p>z)nFhL;#mMzWG^ z)12xLa!0zN9#f7fK^}qDn~AmzgszI#XqA%ZB)UkCm1{N1XKr*CeA!$zmhjVD(P3jR z_!6@+uU(p8yrB#0ig*KAeX+jI?(WCDtg5KJ`2mZF{~1gYk|6^n>R9&|49m5T%FB~>|i{z4>i0zRn;15UCwj$=Va_X+8fHZh6p8M z5r0PLp>RqOMnYjzWI<$h3R>jk=D|8lEOK!OWI?eA!q9)ma049t=|=ICoI^->s1&a9 zCH53fj$IB%zrQ=LeF4|GHS5m{t7jUe74mq7KuBQ4{yToQe)_w`;2mE-W0qiqlb#o= zV)mZQ)ObAwpoRtcHxaL}kbFFdgu!PwLnsOibeim^36LjQZ&^lH`(Cf@rR>{9Pb334 zylI#vd}|nGThfm&ZTA>_9N)eoME-Jr-l|G5cvB(kl8zeqewXJy9vvCa| zo7@g)8pD|0VEpO-ZYx{J1iU<9$q{50{yWdq?OpE$GD13rpM9y?VX<$phg#+d(mQG5 z=|cmY)4A28>Hw;xb(o`4Xd~I!2CbEf22krLkuWN|iXVAAE(^A6^gPn_H@aLTHq5ox1PdN-I_qStWAl=% z;Jca&ffZKl-Xyi*cL=3Szl=#DX-;J(qn;~meobyB9|b_t$l^4q)i6@P3R8elVW;g` zBv}hLk}s|_n9J8f7N0N7Tu8C?YMpU-hM6bDCWo@4Wky~`v5T=%+M(NcJ4;6M4KXJc zm-uf&Fx5jxSkYI&$>Svde8TM4FA{Fw&(h~>!`r=rR<8Gl4Xo1Kw?_$r&$nHTMo*XK z6Ky6g)B*a<|4i>z*++Mh1fdf(<5^^dZgtZ37Mp9x^rh*)2j79@+5ql+Z;6%h5@X<=k$I>p@ zV*u))w$%^00A?&%>#ZQjF+acEHZzRUZNrv&7LtMLv$HcYTa}>?JCsz_*skx7PAZPA zyyjX)X&(RoY3prv7~ni&=oBu+N&RZDexg$gDldljGt zr4Sz{PZ66)F|iG2Cr=xgRWYCjpIE~@6+rJ3o1g(E;_3}4ZGc-oyxAvVz+-=}EzIwc zmv}2|8pEhnX5C3yFy(1u#zo;H+la=2qCeu2vPBU`M=m*yZNmWgtdDZYkhsHKgb{tA z7JaOnanJOt7{pos@(HLe#h7WVc7Bs*#+A>=ijp>CaOQm zi_X!J zq>|YCJ%+r<^voXD`O*i9;dkXaRs#@sB7*`PyO&Yq%aGalH4>-WN1KUmn-3gKd<;tY zwy>&7Peh1*_O67g7aVN|wk8Om;`vz0>Hy24rs7hHZTLPGe_Bd@HZoNwg`h*46eost99GLDR(T6N2ZPva-42FW9HN~ ziC8Gi{i~EbMA`C|Ol$eIvdZZOm9@;dh=9BKo)aDnzVhzP7j>`}-1YW-EfHV`LltvO znSi#fxAMc#)N@!YDP8(})d7oaXl$JR);ZN*f{Nq@q%mdIoY;8EzZxjO7Ee2NwUrm~ zihQf=czxbJ`(ySZUxa<=Yi`WH_nu%e)|@&4sjam9M!s7AtX*KO9Lz0kQE_t^7jS-Q zA)4#(E!#0J*V|!|2g!T)7_&vkz+^*FQCU-3DtQ$Dp?kHgsa!a8Ap)$TR%54`tJ_7W zmsT5koZ>$(Et>s%^)bP4W#j)gKVAjR;vnE{^|}Y7*ogs=MjF-RCE>0j*)$7o6OgHSse2|-Ky-Ra*n^f2$-yKTWx1vKAKxSMSDyk zV7syg~MUrhR2NWwfS*+tTCxQ!zHmGmK#>)9IGCIC(3Wn09{VT)SqqSn>q zm<~8N3|(XUo^xD)Y^LpB4N2tCHsC>Z!jVJK5{f50vi%B9ajobpC8< zmL7pF?S#!*69C>7Ui~@jRYjRlZKRvX+L3*w6eIquXc|*9rGceUlBF6~G8FLj-OWqh zCpG;!DHd_C-E=;gNp&|zv%B05&zcC-sLA8;_#6te=-!~>N3GtoQMTniogNB>__*Zs zXOA?E4#C<2i%}!Mhs&g_-qgfD9O51xg%bP07jop2tN^p%7To=A3Hy7JC#c=q+iSjo z@B~}VG)NoOMy7~FqqiBiA-6dDzN%X>-N@T$wG%g6=s)Qcz`Y^_u@Yo9xoh?U+X`=Wy<-lV{8KhgExu?_(hQ zm?-~vA7GrRD~73RfOG2h@TQ&P1^OFDK|CRk59y}Wsp4;Ok*m$W;^obMZ}x!q#;CrC zV~GgKLSxj=R2U^_8_83~{hh<6u3d%N~G-K44`Z`$7JKpBuzM_8%=bmVVbn`bql) z^NNdc3?~Uc(xEL?9_<+=zAw?)iYNLguB}f>I+c4ApD}r50ZWj4OphNTQ9##W2a#xu zw0RBe&~k5|{MlF#95)|X2lt>gzJc$Ev;{2Q&_z)` zDv>(-`Y@QoKAr1RCec~ zp{SDS1mkCRzvke?)WccU`JznJA$j>Q2JqD0$+WdHQ6{Tl?pngbLe9d@QqSn*rrK7? z+rFWP-^lH5QovBpH@nEwWKJ& zxdY^f7ScOZY7|d%Xu{NKJ&U_)>=#Da!mxR+8Bcp!HVU=kx>@#XFO{u@ZnFy%0C5i) z8*K&cgx8&&4tWi!RRoOr+)T5zSMyNZkTM6lGd*|?#M-9xGU((^kBDUOmg(SvEZV}J zX*QhF(auWMnYR$&2yAToYAW(<-`T6b$Jm11EV54pO0ptr!d{lG5uPe<=XlFCsT0PE zl&z9f$xatS9?H@#UFAiMi?Ri|09phWBpq&6@k7jvBJxWyK~A<8 z>2wxnF!}y`5ej1pH*J}^o5q?0k@cGT6KPiJ{njn$%VRcP870WntL#=hU9{a3f2|Pi zKr^v7sW#E{((FkOy@<-a+s_ALI48{;S4#)05V)4}Lc*?IKw9AR3X8S50mr`*|FKgg z{-Quu!k&CmTq6YT4}cEyS{~i08XqP%AnYIaiW$F?7t|)7(k>;HSM({iMQ2G5X_X){b;k*9RKp=Xl zb)uy)$Cd-lK!Ho-P~?fI8G!ROsY%7CUqTyEMd)Y&KJ&T0_;q^%>Ts@?ouAhf_Vr>0 z`gmto6#ZQq=RJ&2a#8UPP1Nv>xcmipsbehzZD;BEtq9Mv>Q{k=^qa`ZN13iFbZ~%c z68qFTRrKHI3<5@(1sAJvGn_4P5i-V(3VknKD!7DYtSfitd^2|Y&w(x>ZX|BR?ar+Y zI&?(LIVqb4qh57my!7@{^zhO3%*{v$>a zSWQv3VPyq`@(<$;l+)B5`HH+5a5G0jiaz0KY@^x?977>(OxR{sh9g_wa~(`$5psKS zku*5zw^n9l#E?T6F@Sl_934#fOoBHtcPSIaQ^E+@0U_D_uEBUDkXkNhs3fLPO*Q7y zqEw59s}zxbhgLT{ZN-{Po}V%JshA@)RJtuZHD zb9``$q7V!CjdkeFwbg%Sig|Y0b znp0e!5{sq!Hh@Vuha0zV1)DJn;38cxtKAa*dB#E5KIXl??aFPey*1ixY#&Q1ARR{e ziKenWv<-mI`@s`_g+Sf?d)M9b`ukGhBWZH=ZF~mLN%L<)QrA%wB@D*i69pb(R^#uN zZ_mCFVOUShWSR3_F1j_&F6V8m z4Y|m#p@e3GFymL!XhMQB-yx*(gvK1O3L--L28k3&^;f9L*3c7P@QDfhb|K|FQcNvT z0Y$^2>wGQI0gi)trMh1|uA=Y(z^q2;;Gc%{gCY^cJ2ceZtMnmr-MSPh-W^v^7j?Va zye}d!TY#E@>&cg#9vzVHvtEbE7df()-#16??=Nxzb}27zWG(JH8h9@l0S4wfF|(d} zI~Y_iUgN4?USutb!>Q$-myH1*+K_(iNVPB@jXg9}FBCXm^~emc|4awJ^<(pLdjz09 zg4+QNxLFMRJy~h{gOE3U*LWX+J=;7t9v}kfFMvFdZxKTkvRnt(+j|fky%!~zToh09 z=8!z6J;*;Rgf~q+&){7YH_1I7;9Vp)b^#RNxk#QHfsbbR`V4hfE71BBH!HKaeivZ) zG%0akOZ{<2o*g%38ei3raZo;$$Tr|zRCVGz4q*6G!vl{j#!SEtbKg1cBSF+8%yDhX)o_<$#{}MjJ`s^~5mV zI$9SA$X}WlX{0V%N1fsb2NX@KzG_xW8?vsZ!3l$Q$iL}ME|B(Xo`DX?t@XrV4!i+4 zGKY}{UY=qI>Yj%NUN>R^I7^5-IAApd{(y6+pVfA}#0E96>1TtWr4aYxPfaKp<856F zWPs9bp6kid2Bf?!e8_fR2H`$YCYqGi)MA~(w-b21NtKS!!lkR9W)pbSd2n@TmwYHR$gWhaG5oCMQk}a zCwm}i(#?B>=w;cA#yTN#iEs2l$q`v^Oi>V6cl=5D2=WaR@!v}gySwnW7zo~<>hHSn zFH8o1BlCUazBA4SLF0oeK#9iz?}HCPN5c0%rS9!y+qVQi2Q>;8I)1VVxb-@40qo9LOxoa*F{z+DI?0U|i8K zD~zuQYll46gtUQWTxT87O`_Z&Cgn~mWB1pV(olJUYr8EeOd2|qC{Q0k(yZu421!g- zX(C<~TZd*wjrqmIAD$?<0LuydojsY6)(}@%G*Q+NZfL8@Z zDUhxnHO4^@JSas;5+59&8El($2qnBW&Hr zjc38sbDZOpS|nwfNQ|s3`K52me^Hmg8Dg1k89!9GT&V zB-6vAduvIs0vm@L9OG(w)G=a5z`}(F^VPTl*?fRsj(3*aZSB>+4ZJIvS1eZ7cQecn ztBSEvCPgqvbCKq7?(|S3AloLHnQhA`3gj$7M1XCr%(-F&lZ|Tx5oRoHg99c!Pz~75 zz!ryKBRk09BFam^2XTl2qx5E~LJwWNJW%I$$jvn!amu=x4?2)ijZ? zn*Lqs?_qyET7PX#|Iw0rCkQRxEuH|QVj3~=lR}e$QI=d>szUhGR?;zq zcvb~QKFH-C;-Q-Wgfa?hdDP->iqMt}s5@Hwp}L-nw}$lD1+q#-ll5!Y*ST{;h04W` z1{OtOczXnnlff@B<7uy-U>LSkAd)eMh4bUiiD(aKo0L~9U5_FFN65*_^a9nMnE!>9 zPJo@L7VR^vwzJxXvQgq#D6lURJ6)nZGDHdMQQp+>(r6I@^n}8f>26nJ58pIVk5Ddc z;Jf5r1+vWHHX3;ZRpt~iPr!jcBm%h!%+}yD63S469>bv!w>F1*3xbskP8j}ql^Fj8 zEuqIH;qFGb7q37!r{3M%+JJV{!!CjATAkYBE_6a13Q%Q=W4CLYre4lr`~{WVaOnn$ z-FiKtS+EEP_!$s2KnS%UuA&wHBa>oSN2ocfJ4a(_O1d~Zh+jl2GxGJEHXS%UebN`O z74t#eq+t1;#1uw@h6OI}n%QUp$(=gz&G}?Fh%-JugiQ(B#>LTf!`_8Y9uS-v#u?U_ z7`FYBspGt{5NVLJ?%KPzf@fu$SIZj4khgx&2HmLx@;?|AXJJ%v!MJTgtp51DNBxOU zU$Mp}?|<-U5s2n8;QBQ!fiWy`D_Fu%nY!JKbZQ&LLlRGd>R?D4aw!O=rovxhx2T~o zczwCKOys!u{m0hZl%>N=U_R0feV6I^B||rHb&M=y}{)>kzV-Ze)!ygXx0xJh|A6+D>XVW z=7D(Pfksl~jH>>%4;q5g5txM!X#%T@SLY*ugZ}{^HD(O@yRCE!9 zytTeG^o}TY!GIP7?~xM!bIN*@b?Xm7_xE!iRH}0$?yP}PYs7j~rj0e0-l+1Lp@CdzsdJ=@LJwBGe)S z?$3NTya*)#L?S5+Wzm>STuI}j6iDPF#{Q)Blh@8S7wodL)2CVeh@-DCpZ$DaD!4^n zx^ZJKo&JlX=7&e(&DW*jQLZSw4ai5TfM+veMz{Qs44_fZA_&M3`j}M>23N3;O)i8y z!caBfhA|uD%q;p5kb87*>-#(y#xGet3)YF26ZHT|RT9i6ZVs@w5K`uT4`DBG z3{e6EiG$IEF)^lD(;4hYqCnsQ>wA!5uZdztj$tQH3?-F&aCh6A{oCnf*0Eob3%Ex& z`C3)7NT}*nsg+Uak_xb;fETin;ZOi7e^jq>bgw_lJhojP%z_J1Q^`xjp?e%* zn6)10>9N}S#4hwy1BnqsP690jL4h2O52m-SyD(ZjfkFd8_g4;O8SQaz)nC;;Ms(J1 zmhz4MU0qSAvn!%n&LL$9_fcLw2MSk&yGQw>+r<~3DVG-qa!DImDO*YNYn;W0KSl$n zie<3ym6CQw4O=_>p`csW%^H=-%F4M1Z%!kvV{Lft;Xu%UE19amLE#iB!F~~=lW0f< z?$XEQ@yJH5DAlbBD658TZvN6qiQp2oU6gNT|6J#+*Ast^(1ZM8IM!WW0aMK~f+^Nb z(ZlH7k+1IS_cE{}Sxtnw;AESH=sg3}SY9NLFie_&RVKe14=L&_mSEBc&;@fgYo;;9 zstF>C{F3q|i?_7yX@_M9i;FZ#q5px8ePeyqlny&k6cL7-RP-Qct4@qEhhJ43fOK(` zrTEe0Y4Up2QACj2!)Zd>q>O4Kj6mtL(y8S;+z~4qVG%uo6Uzs@y%xBOLnr{4aZPng z8O5k*BV^04vO81U3<^nVT(O+P*%_Q<35)Pl4&N`W9Bx$yD}l7;!*t z4|l`M4BH`Y0{4kgAP-g9=I7Yc|M~)z1~P)tl6Q!D<{TM=vgk76eLut)u+$CR+_I2) zA42SMk3wiQFcVLngfUvY3o`-h*bR@D1$nK|X%diknOfDG`d^CK$o?QjOtk`Rpf`zd zwp;{n$H{1OSCH2mPe&+m4P6Fy+MK=|m+uMNpi+MeKdAh%6$0Drl6#dpqL$$%BwpJC z%%beNQzq!bj39^lmZN>CXRL56&&O-zy6G_VUZ}b{^BQ0U4mqAt@{<6>Vre_@>ECev zrUJq@&y|{rLz*c>enz7`ILQ-@%&4%lF0wC1fNsv*5g;exary$rEk zDOwpX;TH3@uHe$jMF7y>G3DwZvDq0?rRDpVCcrO&wN3(o&;Jr8c|%LOFda**HGmwT z9&Yk^>dc}3VfNzuOJC=lKy*V#=!JBzn^*E|juIZ%lO`~ywS!bp=tP7e5?;xDhwi*? z#@;8iB%*+E7W-Ei*ett}7AGP0Y!|Hldln|tGrWZ1hqATZ%MP3kj?Pw`_cy49y=p-k z)6d?F@t^Lq|7(Dbla=d#TQ=9_*9DP$k7+&vv0=6*E(V_h@8&AHi8V=wS&bC%@_8rWy9e^8=6I587^zcvnI)P^ ze)g?nYNz&c1dC9uD=ll6?Q-(iQ;Ztux_R@^`l9w+#gf0189=<3&vs3kkKV2znLVFP z0?ljPt?BO6?rf{!b<&qV=XZP3YhR~NSLSxn>SK}(-^+&{oW%0#Bx474eFaQ$qW_1F zsGM z_zjBo+wrCijNIox?OU_3`_%G+^Iy(ex5}G?5!b>G*zu;$oQd;J6;|#=_ zENLKj$%Rp+`do{~DgJ(IiBBKrL^_jho_&FzuAq%)8}qFHitVQ{MG026L=Sox_I>?w zi;NboB~i@?HFP*Z^`1ly2a0bm$P8L-nV0+PAO>gLZ`f_a89X9LPAx2BJ?WJjuJli^ zxizlaouv+?@^4UaT|pvDo8VBn=t+Sv*Au~Vak;@8PdD&!@vZ%Tybc9~nK{jf2n4Os zT85MWl!=-3KToKQMb;&_AWY0@hW{}ch7sZXm^lAGQ(6Hh0w@y;W72FLAviNL6B|pC zQyA*c9R~~B{|JEFwz{~QZ#MAZuDj>1wAkU`Q7G81w@k)P#@ZE{tY4AhQEdO7YJ2_| z!rRAr&#TZm2h!wk4#bvE;va(6Gd3{+A_0u#;`rd)(ohF*1y{_P`@jLST*J=NTGiqL zWyQ0_+o+bM1OB+Wy6U^4w~wB(4~+gsEe8$&(vTtS*%(8ILQ+v)N>EA$QIw&w1}gG@ z60|VU@o&hAs7|30+!{l*yap)(PUqnSwf)`)lEu52toj-p4Y}P0yVwkvs`*A@@o=vL zrIaj-lBE8T?gJ$qNM9HP8hSDZ@;U{KUFzw1evd+AYPWq=@_7571L$=2zqQG~o4;_} zo<8CRp@#cF7#o@0z|(=~sxEfZzlyV>JKI40?*-~Ivi842zlaX*5Cwo91+eFUCj5`S zO*>ZCsIk|9fftMs++*!)1TFjngRo{+@oyL|`LY4kUm+u{*x&O9-|Cp_TC3il-%B3~ zLx4H43%W0*gn*Eogp5yt)|9BC6p9(y)v-r{OTC;;|L=fi|8Fh|@cfLFtWCfY&{yHK z0EO+5p~Ly3!1~wxQa6Vga*B%5Y)aw#wcrO2t&zi-p}Cm@u%gSSgpP?t<2T4R0u7GN zrv)GrXyV(U4e(C;J*~m$?$&Y#_F-uLvE0h|eg0}7^ZjiW5y|cO#^_iNjJd*@0ZeO~ zoegBqZr=UfzqBy9ie-8I=J5G#bqM$bOrs&4K(mJE7&tK=!ZuG?!q+~eQRdbL7G>qJ z&E@MD0qf30B4#UI6>Wq;tm&0Ooja|xfs=fs5+|K*g0C6__Mm`VRDQR|!r;FDDtk0b_ z+zm-(66U^1GOQov@d+y>@a~uycmXE$F&rdMj5t?VF^K>4n*H@l4U-X+6t9GM&NfT( zsGH6v%}k$DV2pp4%wYuA%Sl5%*1Bs08c$Be>I*6gp8Y9pn0Mj&En&p@0wFeRw)1@= zSRpbu%Vl=}%@Jdq|CQuE8@wZYK5$BdF=xZo(y~L)86r$I3c#sWUk!a*Ee41u4g$xn zA$U2fUyR-Dxn&Yvv@y%;Mc?3=`rgf)rxYxX3R*-%QifODNFa<;cSq%hsa|@PS%c5w zsLA7fi9yszqtw49J4KWIiMxmByp{v&XtstAmRLmV-z6caGw!6^iNL1>CC^9;Su}e( zt|o!14C8)F`lHP^LbK`f{Pw=v_nZ@i5U&G%~kzPe+VAvf+5{${O&3{eI zVywJzK2!Uuph-(A7d7g8fZ(xgwhHRdV%Km2saU^OQ>sq7n0|1ni4C|tWt6u&x?ZA2 zIF?x??%y;2)8$vp?v;)S@wJ=E>fXg{hZLfB6#z73Y@{?FXyU1%=$V`={@2mRh;-FO zvngTfd$Fu`LU3hji~N*e17t4Bco`z@>|LEh#acn!N<_oF1$OA=$<$r8A32tD`@}`m zoh(|n|KC&W)!geSmkEGjs9nHKUt|x2#8YRYDJiP=6hh^C37mb|jU--^moZ30^m9j= zD1>%bPE9a+Jyy*f?{$ZX$9e-jsf4aAC=qEcn^1~vQU5+x=AC(aFi%s@-L{XBtuGQa zgCis?=^mHKu%BnfV9GTMdj(Q(vlq77LzRJvN|eQgJ`F~=8y^69Ec|uXM5AHYHOoL7 zoIS!ANwxGVoRmgwzx;5G6?T}D6-om7U;ZpM@jLx>mLAW<^`@!BJz%JiI>LaT0U{;s z3)!{RRo=>Lz3C$}nktQc|1aVL9bBiZkyOPv1h(=IZ#tj4i;Io<ZqTtd^M0&27E_$ahgPWEy zh)Dghm5j8LgOs>^k>2ffv;H-sz#3+#X_}C*MRK`yU2vpY_&S*`DT;WpR#fVMwijhH zwXR?w zW&i<~U};waW9T49WpupkBuyx_{GuxV%gIj`3Bl&co@#9RT`?Qh`y(rSs0C_rrOFZP zv~<%zxN6hOZd=Sno2EwoE9c{a^tBw!uoHh)J6%<@IJMHHV79wNPYiEGR-3`NP)kW7V!Z*ni^x!wDOy(s< z{pF1y^z|CCQ`2Thb4bHO>&1ryvaAJ<^?pISFxi>2kMxiLiUwp>Q6k&xco6b zJM0OHi^#7jF5S?h_5H^lu)5AD#kr+>qdrU6Gm@KJPws?~#M^^mgU?}KV2Q3DHN(Ku zs&#-!Q(4I=%Q^6XR1B}U3ojo+6Ai`!g zNqua-bZxp(mm2rr5I01hvoqv4QQ4Vqy;O93(cJytCW2tS>!ySzUU5*F7cOOCixnGC zNM+GhTOF!e!_4A{B>0LcfKSgkOUv7Q&J>_ZNXwT3d%ip`C^J9Bv*G)KWKKH@iKrCp zdFg89PL1yM{J|5O7Ip)9N>K-n83j7Kj+hGE@)ue)QMkF+)w~|1z6h(uAs7`Us0lLA z>B2D#m8`6dJB>{kM_awnc#&m*aa4o4bYYi!AJ{2~-U8L2M!763Te(gzXm2{LYQ}*dJzfs< zhe!b85zd0|vB(4u7R`Imm&Uv4?RO0IQnwrWtW`I!4XIy4W0)#B)h?m$vmYm1c2l0# zBg$SF1D7(G4>`hBpD@BZ*9JlgFiE+W)ss!rqE~Sox|Pm>JgVzEAHRyp{DUgoirUECWD-hU#{! zFj8@q%4XX2m-E}!LpaJ|kN|(q^!Okv@SFl9 z?%IR{Iq2Q-oY;|S1ya}3=)FA%b?Gr*8NKrsnwshO8zk{PGGXt4#ou8$$8pnB3?46p zy?7`A!JhtqGCsf;i)!1dq1*thC#e3HrSo@EIMJYS>5E?^yEdHhgjL;!7QodaH?P`- z^SxA-N-{4~f^KD4-vzI=%rx=XDWf#`_l5SC(xRQelrPg`xtJus-_*B@aXY$lrjyM$IA9lU_289Nkr4;F&xZ={QwaWYWYkCR}z&k8QTjtXyK@0+PPzh%ueWiL98*e zTmamTsFpIu90<_dmNI+N5CcDK2BmProo#Z(WmnGR+L!Ba8yP^h*sop9)dF@m zJ>w;u8BIywFj~Cd=3*_?pT?$bub$F4AI?6f>9RDWL&ZGxD_rXo6)>-TNnjVv?Q9Qc zVtotU*9sEt!7~8)VPRXwY+(>axDc2dUUW@XYVm~pJS@2#AZWeV6MUTLt`9xg^}L`E z?Ez&hi>7NP!vMC@h0y(Pk!ZXTY=9m&;YI?phEy{WKo|9g7sE{3EMcUT2RUM za?PlJC}aKaK3F(V2S;8Ci^k&)-Nl`$ABP!*GnAwf`Z^@-?ftMIhobF9IWo2rLf#+1 zG;m@nD@x&8l_w-4;{t8cjKVHhpQBXf6C6S6+(ch{WCv3H1r9)$Oi`X7%#ez8!upc7 z1(OAN1>6Ads*X>dBlUCZjkX>%fzqUTCo-8mf9GB&h~qk9DRa0Q{n`QnmE>wZWz;d$ zL1H2N6osv|!JK>It`EU9rwoBkaLbel=B@9{6YGYzIX0s~*@Fjh|B~og_$0BksTb2` zcDMw7GEa#c4yL1mh-&xEFLU8U=&4{hDGluP4TzWn$HfolPvpk@C?clx3-XIu5uiP zG6=xxP;nW?&j8#8eX(Hc#4AMyUuntvv9S*M{GsqQB;qtv5vK8lR%!*%uC6*t&EWR3 zvb7qSfnlHw`<9p=!eCA%jMu+p!%`jQp(1#!cHrpf5&_z2ScNF%&1=p=I(EmW$V@=- zgkbJHULqT3;V!*!rv#5oT4ve1gOh;+j0b?TW3pbCZJqsHDwA~lTX!MC_$sN1OFv!; z_Kjyt;uk|>tT02zFTY%eszVoY78o1&o-=x8GWN}N*S~d1dC7A&jo0k@BW(1I3c(7? za4g#Q@Z!I=7L|D{u6g;wiMrevk3(PR@a>0L=0x^Y`g=|eembkah~WX= zUMvL1%3}T?S6Olv5=F~B4b35u9Rp2UDF+Z?yoWi$@}L+5(%HsNi!BS=2U5b7R>-7J z?raGBOD_6l_D(U;AcYd=YITwMNt6=~!Op_7*(8g`t6g_R#*6xx<2{EGUF&OHb$Z7h}E31 zh$@;UH`80Vj?Lm{K9X!`3!rnD@C=hVQzwSM7yQ|ErSSd6w%FR<&E2zuLW@MePNnpy`a>*NBsqBQKC<=0BIwdKt_Uqc)H6Kj(#Br@yWTE}@G!zA(XA{0} zg&_mZ4A>O6Ra_d#aM{~Kn4t*@de$|{n2)7vsRVkt6KIh;FQ}ilp8mR{mjO&ZM$ct6 z>GCMD;r0M^uWfVE?J%XYA+YX3iq{GF27#5NEt}%;Qappjj7^wOJ3u89iCzj&Bm0Od zV+i1MEUd{*W)OrU$56Ohi_-%Zqb6YQyNyIqpA!{be1v{Ao2wslHSPcsO!gP!c+&@x zl%5MfEFM3D!4f*naBf?L1o*?G-CVt2Vkz)mKT(9-n|hrYo{0c+L>GtIW)%KPNZRy&=_7Q-wj5ec9~A;%1mz%=1Ok11 ze8RSacsF$j3={roFU z(?C0!8;OBeBq^o9Sl1wb@x5;#cte5c?nYzJvU}l~`WN0(S}ZpNKDxOo%9EzHBYjCD8}p(( zQ-ajn`!iT_jq_A~QK^&Ycd$dv_(4{nh}MCNt4OKd$KIGp+`Q6wS!F1Y0QBvG=Iq}k zeA?(YvAShm^#sVm)4!L)NuT)^u;vo;_Z>A&XF$86WB&s1N4&%R>~cr)=)TikV{`)*bEeHG#|B)1$lOwrjgbNm?)-9Rq7 zMsewXxsOM_Gf;U^j>zc20RxGWWr*kic&(QZ=?<0L2=&7z|%N$-0nusf;Sd+EX&B3o@1M%2(^+bWkp z-1ChL3BwuJ9M5nOiVAV%)9V*SL$j{?Dle>!#C5|<&ayf{B-B-bl?WSRWoBrdnb6Qq zjBnt(RkOOVr-Il1?)=Ad*=C-T8O(JD}S!^GK@i)x;)GqKNUxe&`x&=(}HWM?8}$b4-kc?GdMOyDr{o zm{-P`XI6i;7=5Q}{E7{e1<~v4`gd4HQ1Y6cGyvIH*&sC?kRLqkt(dTY9PqivCDsRC`9xW6|Iv1C#94o^UmN#PAlCkr$5T-F^u?U zy=BjxK2eB1Tq2K*|*PE#{bi9 z?K)O8&CGhlZ6h)G0XYbKL9xK$?c-uLy4kBP@q9s&|CnFE7C@5bul7GGfga^VV!lwv z#{`uQ{B~NFnSxb z+V1Q$*h;IgNs9UO$CL@d?6HyZ02 ztIZR59e=PLW~^{&`{-tM0md=xKwiWBwxJZ1^d*#;@Z-jm`QKj7L`mm_-(7WeH|pAj^Od!y;o$gdvS%R#9${Ln?I_|KPXe+ub3F)R z4rmNN3%s~qcR{xI_In5oW;SZz1AJ{@770)!>wob3!y#{VS1Y)p0?SL-At#&ZxSN}) zzXfL6X|m~&2lOjewu@8%1WACp;!-WpE0jJ64~6cUthKhPM9sS$jc3p@fsj?8FW_lR ztjS|a1`CiCu9VE*%@A!CbMKg3l`Zc1HJ(@SevyNX@G#Tp+70m%>Y|jIF>b59#wft}j8lFLw`VK+>`NNp5Xw z$_Lf8*Vb|f&GO9Lo%nN!#2Kx35TCIqRexB_zQ%0e9v9ej&4|T)XU14T{J3C~}(Au5}y2O|B6 zq1nZ~3(zik-|&hErJIC&y|UjPc_>x;8G$UwaaQe7)3hi%IPxKn_a%Gd+{9}IiGR%8 z-wm~)>zU9%m#cA(b0GN6nr7{XN9cFOCuW#Rql~gd z`zrnI$=Chj4Z{Y!nD5}MB7)P2kd@;XFOCQ;muY5+ImwMGeo-e{UJc0!hf7dn2rdR8 zGLSj?n=&YM{|9RRF$F64v4!Xs6n{+5lyA>O{|AVDth^8dM)`%)r8n1v!#%Dl45Y!2 zWX8_UpyPogy)!`OFf_;CkPeB4xs1ZMhsuijYKFbj+5N@8yCD|hy#|Jkd0hD{<+Jh1 zl<b6RkeZDU$G zzI)Y9n|zceN8%|TlPGscp#2<{nqfSVQgVKed)suE? z$Wwv04s30GFoHe{1npa)a zN2%`UR>~RHd6ouDIDGYWD8HEO@V!Jubze1A=VAnWq39_E!U-U^~#gIt~B=zY*aOpe^ZsSm)ZLI%48Mh=`K-+WQUcY z9HH2ED|f?*I%=cDHD+3+naQ@mD?EMA&H?xjd@u?zn`AJ~fvIJv z#wH1+^W)g^`M)QXr+;*A&}2%g5jY4h-@+F-@RzH95|!fM)R3oypvF=~#~lj>7;;ic z2a?3^92FjZ1%$?NbRy(oBNn>**uts&wQf}3IL%lf923)~;0;l~Ou8I%B3>fCeomoT zGX&!AY~h2g&fDZzj7q9|*CBlNJ*)E9TeO|%Tpo8npnr5SU4PG#TfD}QbsEH}@icdm z$fHP7yY6fL;70i1PAQ=sDCPQ`teJ=n{#fAD#p`{9 zUD{L30kW6=$1MzZ4EozW6WkB*u2Jy{%L@nJ(|8&9tBc;uP>iPn-QPn`7aLo+iR?dB@`=jpYo zc(Fhi&$)&97G$qoY`;mBrC)w?^#<3?ymba+$vG>YdL?? z4wB&|hx@0ZL*)IUhhnN@ICd3uY@;B~W1+JLbFHg@l7CM&ks@(ypd;l_&-1jeeMsg6 znUWK$XJ-9&i7EuHDBDM2G5r-f9-Brxd~Ik&nMWR6k1_GnEwfjr>v*NB1gV#OF!mTz zQ&L!LaT#vs(_b*-)(MO(w^Hs2&g-h%%y0!GJVbR(xKLIS7tn`(4~8Drn3}S9*oOn_ z^7u0vB7dVTmq}<(_e+|=Q6~u5Qo{zOU_J(&{j}jt0k!Pt>#Iz2K3D>-j^S=`PPSX~ zj#}tfK4@0`&-inrH(z`GtohZrAUVkB?&s+WrArpM7U|K0hajtvg+KR`t8o`L9YzAh zjSp1#Y7)cp9S(GUT3Gq>&t78*DxuKrX=+e9~+!LP_|*%ZTn*W81V2SWkZ)zfGx0y*haZjL-O~i zOeefgfEroEys9J8Gb3Nx*x8xu(_=sq|dIwXe=?s%czWIxUO}r z!A*5`w`I#k(~far-$*KfqA|z=RLvQOu77QuPi>~jVbVa;NV)8mQdc@#6!Sm-V29bT z9ky$go_`Sg@3zD`?dOY~zB+yFQ0(I_(SLZ+B*~S@_Uy_bwv7ZztE5c!Ad@Yy_u#fe zPpNT&!r(%Ya!I$ORbam+afNzQD|c+wC>pY6ZJ&%uHIDx1QQzK=c;VuS{DdpU-N--nP66MC zL-vp%abH1MeOIsYA$E|W-5Nnp)C&!EE@DfgxbuRO_eJFOa0M5e1CDh!_@@vYo>ab{ z*-ZnmR$A5~Q-!ISeR=YQ?j6RJsi zduZfz{%*SXrT587_VC{iQt!gr^K!4@C;vlnH~jugc2c7u-^wzP`!0>cHC70~i^4=D zsX2(VMzmrsKPO)~{{Cv#DBA=yX_aQ2NH1>5xwShxU(Ei167)u=f2-RH(rG_=ELXC zG?!SOUMqvfd=fXD#PTJeSSDE8YO8@g_;Oi4N6hX5*B%?I2K+?aSmTlGm`_&P?|Bm)5tWN>W>{ZczB}&&OO-#b+B444U{1% zU$4Wg9s#NH}VBUyN9b{U#HsH+7TV1 zy^{;l_|+(TS74c_LDvMz9FmLyG2R;SfV_1GS%ZZevwypyB7dUZj!eV`Wl$aN@tLxb zX|&JoE7T%qmN|DLQO2F_u6t;9RgK$&#icnGTtX?dDk$=XyTVWfeUXdWdwntT($7%E z0>TOJy44*1GkZm1PX-WQB)AQ`d^&&^n&Nv>J zdyI|Jp|oS|s()d^GX;9Z^#uNcm64;)K}iZ)w)@IimwP;%4X5qW;m4I@u^-4t8o?X; zp98vLLNqKVYL_*!n zM3J0*Fb=HLwD}qybQ@FE8C>(I)8}^=vjrIqsZCQxx^G(n*=1ObVx$z4qUXHx#xVv> zP4(Dmz3!oaMSI}{hq5i&XW>RDC1{*d#$_Zw^BAh42>&s3kl*-wW&I84xb5nzN5bKV)im2GCyG) z2#l%TcgF*bW~flvnQ2qX@Vt~X7UiK;On+bnSs+cy;>?+lqxYrBFh>`4xrZfHS@o#I z<@Ff%?*oL6o!S`bac^S3aYx~e?^`e>`mj$pVCz`tX33*jv6#DYPvJrCR{L%>AOo3m zj4Xaf$S#18nrltLgU~6t$1^B|+-^12CAilYZm{*&nAE7d=nk>`BFi*`N{{Jk9DnRh z$O>v2q4n${DwaNw)i^NT6ZHO~o9YA>2R<>xjVOpk;6k4r_pWZ<90!MI_O5$TX#KRe zN0Eg=gtRyL=ja8a_v}956mYLro^itv*G&B*80)M(0^FO%m;=_r#-W)knOMh z`Mnng`=HBgZG?td17q?#TTumJ_x1sKdi78UURixbOh9$rRFBnVSKu=^vz z(`)iJZKFHl2&lz8?~i(uaH6Sc8~ zzXo3pMQ$Es#)1sPe!ZRYqP>q=bswWIB6+UfaA6pQWb%$!SMUke-ZAB35=j#m($?1~ zEq`_7awDKNEUpbLKW|YtboI~TMhlEd5vZ-yN~4I$wofZl0fk8MkAJ#^+cNu$$x4Ky zpa$aPpG2?K53OyCaaet3tHs>SB=7UfjJXCg*m|7qE6?d*&bixOHX_(mLw5OXNfK^D z7sS)rHq;4)guF`b{gip62i8s=Q3}woBKp)4hKRpAp(1ru6Fv|k!oUo{!Wt8djQ*Gk4lrJ>zmw*3udyvzr_?&??zSP#6ajXc7E{mv64Jd7m2b5 zyni?RY^ze>9Wa!jj;9mS>JJdB`=0Cdjs(J@RYvVC3-KYE@qa<{4nbpqLlpi&Obr#b zOGQSJ$cSUFtW0B^&%+rF-%IaN^!?;JirMJ~Y7?kvN$tv8RG`P5z)5&X=6?8=Txq-` zu~Dws64=U7Ylvuv|2YO0QG06!XJNkU)UAb2;bBm9+EB2h;c2r)L`$IUC=SX#*S8Rep{T8|2N4m#7!9!pl>EdzhW16z=j$mbUp1T|f6hTS6~`u!o^vLr|4pnz5$XfL zjaK1f39J!oig6V)Z}OXn?|M>3t<^#?sf09gypu5X`TJ-$I-_(Ek6VS%MU_c|y{nH@ zy$fp227gl{kR~3da`{%juWOl52xGgy#F^>M1+UD>Bh_nsi?L2m3n@h+Vd{rl&NCWo zzX=B4A8^htR`P3f-|4RwOTov9U>Qz=b(K!XN?JZQH~$eUm9`XTSWd`$P{t8hz1B+L zeJwky{QVt!T@?5AjeLeU?%ODHB`kC{uZc1XmVXPhTdD^*cSZVZ6S_+;DT2MNUPo89 ziV;=i!!8^Y4gs9twU|CBVeDF_?mGbpto|O+Vg}-Vc(u5I!=9DXul~+nftrKohXX11 zOaq@hNGsYgT{|Q5`2zt445K7LM4Ch^$``4tlI>KHzCmGQTwmfEoA$x(cX-3w3+1qm zvsw%)($P;Q4RtV0XE&ACB9fr)4N^q-fnrEAZZRBKl_Ls?2x0&U8_~60Ih{bm@zA5& z5p$x_FH^_tG(^j+DzKigjjqQl`*&+4;7q@}Uaw2C+ThiW`Zc%JUJkU5aKsc5NPoAD z-y|khYI7CNZmM0R5EtG#)MHQ%y*$gC@hX(VF#mA8>tSrliVr+Ur%SzkvpPk>bMfrX z6IU44z+1nxSnG~qyK$qY@2q0CxaIbSO^9Fxv2z1Ao_GSU02z-kw=8&_%RGHp0yCgq@97S1NTIN0iY`!_ zKThW)c{@n%pXET9oKC$rM^a!X9Nx1blwDF4C?yx{{>d8CM94Rk_#^Q#tpeU*&2!12 z(o!PKS|=_QeAcGg>)L#^mVX=0ZomiA(5YUL#K)LFTWMW(GA!9j4Tr&=jxx@e9C&7AN1x^jX$B z2ghxk*r(|2wkrXK6JitjY`QLQ(w=ygHq;3jjA8@5#L*Lv)sT7Xm4D-TkICm{4&@pP z+v{aTpWH%r^;8g{J<}MWD5P;gJ-d61kKSU?G$4Ww3H7q6*?KOXkow7fq`DKd4!%&}kdyz2JvF5bXkgM}0JidPMBJkQcf-&ag64VbA@TEE! zWJEemJXzo3sID*(%X$>2g?zA2YQ!l8dM+!4+Sz0#<#a_hzJGdIB8e}p$j#|HTi1sS zV!`uWPDS`YJLfBQt7NazBuFlg!KsZLtVyJ3>$KvZw>ImF zTY}DW4+Ht+9)BB!0H$C*tDz&O7(Skfl1sN(L>O!Z3E7YbL?N+7%_YdE7oAnZ!sC0Q zokKOE%Pr)kGu0Bg+tOzCAK~Dw#9f{2ybi@!rqf~Y`DT3Z`h&gm0SRK{&-!GF1|+?J$@!bL9}{_mwlu43IQ zH;)p}>UHA;47E|c^a3hs22rD8lHNE$&5yHE9|d{hjA%i9)?SqV6VTK;Ru>UuxoDe z4y6?FvVX`y>UoW}%-Wv3^c_qQA1W$HT0(|o0OBq${J8^mI9u%`q07A&O{^a>K$Z`Q zDs;fY1WMtLVKJ3<>osal%xYo-HB+PLN|)}|sYv=91s)i`Guu9#t!A}`c5$nZVS3}> z*9aYPjdv@1!(sZkU!1(HF~j>_0&UN&;2tuQ>VFzuc$(wh|9vmwFF{!~snB}M6EF;> z)fKQK>KNQN@r4sjFU2-(E{ALRi(xEXKuUrdOJYDI50Z%IxP}>WLL!%$2S^UV^fJf{ zmjT~TjqFFY0c4U&ntea|Xc6n?QgpTRcjCxUigr<~Go+F%xkgV?cuA^{!5I$ZIu(s* zoPVdiUwFuFkDJB>X)4hk;AGlw5@ZajA)}N*5s>72Lzkeh`HJL!Otvm+LvT&_F`-R88O)3yCD3eOm zXOO0%8P+f^tv+1!zAkX>;mbH7IU2J*%T zE-NYo6B*Dv?e0pPuv1CLaM%W{6eGhfd-!)3i|qo}*L_H-U`y8ExA{aDlARIjJAVSS zzeZq8@UP{A#_%FCrF(f|DXl^*Kd^*#e${|fxq9>_ij5qs5`5rQr^K>)!C!m~p?Eq> zXGxLdn276F2uC73f#b8{8~kq7^dZBzo@#?^o7BcY`U}A^x?|B^x<7!?`r*6PQVOyaZjb_{jUT|Qfu4|;6*J_$V~^e669-9dw1$FEM)!(ONqvjgxWD(7|O04 z-`XLN-StgV6l@3o$amPy6h6GK;i!m5-8E{#PiVEYP@Q%8q73B+ZUXsnc7G6xuNbsQ zja6(E(;t$0mz!HeCP^(B3DNtGI9XG?#-^~<8$6lai>fmDQixEaeMVgI#F7Di_!FO# z^Ffva;jvog9L%<=jyU83a!LKgY$x~wqI0J5?T+RGklw}172Y6wXtp8mbCiR*kAt?C z6}C|SYgHb`S0|K|Z&t;=>VMHoG^}5}W?edG*YN2Cp+T#do0M z=|4~=-3QAmdYpf}V&v9?a^vDrRIQ2*)_gRwzGr;-=eFSe3edm0P9)C3RayOe-b}R>=3i4Eoz&2PJ8s_fc=%#Wl&;cUYhh_F-NoA1XK8+sZ$7e?ue!}RMAnu~ zkE$jNOz$bHx4MbF)qf9sI=+KK!>ZIdouhC66+=s}Yg3ZSvwv|F`lbfA4V)dWWDXr?NsNy0(SKRB55 zruOZU9x=XHs0T8N((iAS>cTg`^$I4Y&Mrikk{eHI1x7XsB22YiO4j3!}q4j6T9D<960Z6hxg)f>Wgk}%$t5@A8uLgpwrkn za4qh=igp4*TfxO~mmVnRf22qB^ozfLi5cd_-Li8UuYYbM``xD%u;-w4DUS7@b(wlL zxZ|vU`)I=AwOZUaxwuIl$R5a4%ZLAVEnhOc+6N=O#)QAtHL9{trLZ3jc4dqLlShP9tZ#yzAszEFw zdxW1>!GA|O|7Jb{C>Eq)nnOEiS!8Qy3wZa8K*$I5phy&Z>KCU!y zQk*x9*N~D|Es{GLa^W87qU0nS>jR9d)y2AyIw(m=%lp!Io?p8;Oa{*#f$zArTH>`P z4$N{bp$7)9NJ=hLYObWkd3F&*ukv(X3*1Iu-hZ5TTapON`-u#JC33am&VD&T&>}8G zJ8Cs~ zm*0W~l?5@Y=;#6fPEmIT=$>d6T2^+r5b~^;z>nzn_f4O&bGX&tjx^7LZ6-Z7^_ehE zXkpj!Kd3ea&W;;g$#Nfx%!h`$mD4mGzrMqypSH8z)n3`lW(z&xhrx6O1v-f0L_C1uz&T-kpY12&mV@*Z;bshMeki<$oCaZQ)qc$+%sOs znoatpos0?pe4J})Ns4uFkwu;egZqpT?>B?7yg9j<2L>KtAIIl6O>Nzd@^d6EGfBV& zMqN`;mp1;552U}g;BIU|RJ%Zp9X%^qbN7;a^M}3w|f^Cg?tbYWmd@PvSDWDsxbQaYp)YMt+)-D34=HHWUH22^lPFOd^h7x`0+n3~k79+GF(^1p{|ck4`9!Vu$Y$-XLcynO97dJR=sIu) zksT)|*V4?;F12FyVSmK-{ug#Ttvyvc^TSMlH}a#S`**E;y+uUCxV$w96O=b~pKY8@ek-#D95|206rJ!3n~4?#*+mkB z4EfxQ;jLcR5EuSqUq&1C4_%OA6EdRgy9&Ignyt1yoo)y(mMQXw-2j=Doa}DY@sUb` zn7`GsQA~+9_>`EUB!7qm7+&hncP7~k)V!4$Qy*QI9G?~8iQ=igr?AIQ&W?Eep>L>d zMrjDyD0d`vc%e~Z*6aEczh%z%sf%l&iel((x}eQp$J^=;kl7Wla*|>xCW&&vxMV>H zKx>;l$y9`ky4^CO5r32`3=bIE*5_OXW9WjBmm-MD$weZIK7X7rj!RJ($x+%wF;Wl6 z8UDFSOST971`8ty{uz&;=I=N)OSN8)U9i$b&Vxi3 z{+C1Xnvk9Jd=!>3*HlxhD2M}zSOnu_rhkV)#0ppiOBx-uXQp9{fx9Do z65r&aXEw@qFn@cWdND!8l;pzzE3rb0Wg(-yEVY1dV@E;KIrMcg!Awd&I!zAp>8Pyu zyQOtQGSqEW7S$sCBI^JCdC+PRxQ=xChKmuXwwO^$a;$QbJhZ@b;CRKe70|*O`5y8G zi#ZkyAE0SExs0JtIO3m2Hr(oBoRxPABl1!?Oip|8`G5M*qi*o<9`+Xmo4d*{Io{K3 zJWQSSEPCZyW73&i5yruHUqfXtH10n=i6S^t9OY|q(G<|@ogKtP6xd{gS3EMX$|eO@ z*7NH_fi$?`dLY(HsK6;|S`|k#xqivNyZWRrfCuD!PBHFk=B;8s;j|~(3Ul-4rK{K> zOIz7Hj(_2iWyg&O$X@uX##CmFiQ~A%h;amAQG}&5u~%rZ2|tc3#OKrU8Z!5lK#!`2 zE(afg80~nG9}YCD>KJUqtFA;ORhVff^zj%K7&3odVyr-7cu8yQ4y0{np=fiv>=$sl z2pg^FVMQD*<$3^qMZh_}&dy3VC^&3C&NF|Gs(&#J@er^@WN7%1n@WZEUFQ_5*}MmQ zl8&1Cfst&T8zPA!&eoR5dR-HRmccv2eMkA=h18`a?}|khH6aL?$GmOfk659kg-h?7 z-f8nt*t96g4`Fp8Exa-uTDAG|!U-FYJO8am*W2 z$GBYUFKLC6iV#2t2_;;0ss0!cp}S^KpH1&zi@<}_3>R1>j2>u>yEgrf*q((czf-vsBAHY#rndO|@^9SBz-P-B zBA>*!2H^I1f6wRRy5k|6XMcFHqqm#Cl9K>urXF2#zQ5@bB^fNX!{ZoC*oEQA_<`pC z7bFUdlq5)03u|Dc!I>VK@{BtUrZD-JF+ zA^+H*Ku+uI64sVhu@uA&YY`$Hac_#ZA51PGk60m>HIubmE}mgq1A`Dg6^C|nzet*H zyE$Y-A;kCQfEH-!Q5d)J6EbEfvakMRh5;&pj^d@H?`j7f6)~-X`XEikS9$DJC+)Co z1l}VjGX>$g(xu>e?0@2q^8}^{o5ZLT>5PI_{ybk>H`KZBt1or8Ca1O$gR@&VEGyH^ z*7U6abhqkn0WuWVH#m%Jt)t^gie4|X)<_fZNG4w~P;7ZNfk@v**}6x`Ij`D;oN zvD3gN&#TC`1ri~MKI?94HUK>pd1F30t@Kw(e3 zY&8%;e1-yhZ-79WGqd?sr{(J>Cl=XzeQ;HO!LG&?UY>=jGO!93$+OvMeIkZKQ2rcG zA`c=6^WZ-{ov0e!s>>U7LGVRGZ!Pd7JfuE~vu+W=K#TehwXaq+OiXcPMIdyxDV*M^ z_aYQULx0>X6R#=fL<#nZ-^h_#I=;VxSmRS=Eys)_P>*-0F6-;fEw~i5r?n*3YpIT$ zd^W~#81hpDH}GCkO89g9M2R_I@}IGD&#h|K{5U}nz)ni8%^kZS<%>G1XszK6ZC`52 z0MPFDR|w&tSDs$!KJ`kAFvehFw63O*9<;KkP=7_@{r;Q#B!rjMKUd#V$jA2q2B6m( zTik0Trq}s_uv`^NJ+N(;iJm7})y^;2F?B+%BZr{$fFX8{K|B2HBAVK8H5sQV`*m%W zl`qXAZnq{W5`;Q_|~x0a)-A3Gusc-=i{+uSxaEeVY6&zRoKN^ zxzc^p8g$9CJo(VflG+fTruPJN#@LDD*{ltu*;s`oi+>Ewx+Zq#RX}FZ{`zsLq3Wmp-fzJIOtE1p`tHugO5ea+GyOFyTqmA@9xwJhW z7Lc#u56a;tn911X2!iz%i~E1)+A)DMG#dhqz^rV!x|*7u-P_NC(BQ>JD?NF-6@Qob zn0=7n7RntL>0Hc@;@!5BcAj|hOZa0KpF%|_^VU1=%PGT#z^U!D85jk4omW0I+WB>$ z=C3qqi-<~Z&BR`ebPf%1LPoml2E{zxT|gBq?BdtXt;&5@$LsuU(ZyKbL5cEwY=S%I z3EQW)7u+@n;}Pb1kHnNoij&u10e|$7xGWb~$(DBf&314V^E@iNkY=Y`>_PYo2#n%I zz3}UmdI#A5_f;(H4H%Ks&*j?9BoL)^oe$wL4br;JgI!<7nUVw;Pl6Uq&vnmq8reU_ zH7Izpst{9p11e^dl|K2$D@;@qbF+txl|r}fv_2skCOVSEl3@8(LJ4S(1b;L#9F{a7 z-_tVz-f?w!>0RA3)N1Gr%h_0J&Y6kf()f&s*60#+f2zn(X3v}s@KZEZ5}YF%nIx6I1v;5&UkmDO0BsGH7i22YK0hGn*OtA3Nnn?bQu=q&{fcb?+?|FkQS|qrv@@MFU;dQvBi+{fA!G9EDb& zYhH83^LYKQ+wu2D!xoDtKFkY?XNp*eOl`V2%A!`x7c8GR`wB$GOf7sZH0NN6R3QbS<=t8!NI5X z6nqwhHX{e@O|ou790G;x^aMSh^=Bdy!UUxUH&m#8G=KD)xmZ|Z$k2{L3^Axv4vLw`5 zQJLy}q+;1dp9#thewnO-ZdyVy^7~u0uCZi-%YTTy_92^Q6kEL-J(N$Ias2-qRG?Hr zNm=W)jDYyBNRm+uBgF4$E>zz8snjtFpCgZd-s!Zgg;<${KwBMj^o$aQ`7Ccxe9D3a zIG^(8;zd02V?R3K?WPKbfuDl)W4Ap2usq}>lCx5I&w9082JDVQ$uEM1CFTVSJ}lwa zYk!{*c)JL-w0;JEOzV=)QNKMz8g=+S63w}lf|ILKE^Rz6x^Y|07ty*+ZFs*VxKJ>I z^uc$fYeyZN2XN4bHk;!gZKmRSc|CN1j=QAflK}okhSAR%AVmnTFdn>Zo(4ez`x7z~ zJ^V1SHM|sH6mtUi$`gzQG$x&mi-l~OynmLMB8d&Wt#sxS5@C*}GqBj$n}44f`gkg# zc$wX_XktVHQ?D?AX%7L-ydFeneYO$k#=`07wu|$s%EGp}y_ne3Ht0I*%m^gmxtY%} z)QN&@c3n#Oe@ZAN(YvoFhE7YsS&}aflC}7*HC?~(LGT->$b1N1%N?U=Fkf?A>jbMMTSw~g%;Qmf4Nwp)KM!4RN1himre z5J#8if;_ymTv9kY6I$7;1SiH%XBpB4F~u*RY_Aqdz;fD6oQbikixGi%3b zX0i{>!wyQ4YM;5~;JNLbJcF=S(SM*CQBVha(lrB6|8J`35d_R~KA|BYtr8cb>G?ox zL&||)t2|1v#rU;|87O^Aaa!Js#NO&x_tb17?=G}PJU-DKPlg1XY}c;C3R(vhJ$G95 z;OFmc=3tNc2tb5mJZ|I=n`}B{mrTEApW*FDcjsJ#SdRrnnUtTi*=%1pV}I2D5Eh80 zKA!Syf8c{t(T~ktf*#~Ba>;K?0F5or@^1_=ql@;Ra<0&BAq<(nds5S@c7ej-nF{Ft zAjKY%4<#U6>J44CHO8>XG?L|?Caqj8H|#A)D!irr7CX`tM>|YyaHDDIAFmf%mFNV{ zDnKF;$kq2Mi~W8iVjyT$?tjP6(O0M@p1)ta;!pNtRO22`X1EV%`3;hFNk?8~Y~b^~ zjc7rF9pH_=ej`yNV_?f`M59x!P8PZ#1oMGbg7-D9d=XxyR0jq-3ZmOPb}R^4h;#T_ zfEa|X9#`=D?rlNCV;mit+Vpc4^F4qj4H?tkvT2qI!E4(d2_;9kTYmuK-YXq<>Ao!p zv*IZBGjb>_f6+j#S^~k7s^yu=TQIMH=}2?=$s0tqveyrA2N#HtxJ73e?ei*q*+hU4 ziJ+$Oko~7ojih1ra`E|O7&H5z-^d5^yNgF1WA2eraUXp%mb9{<6NZ(!ztNc~OI6v* zClr|a$F33XpXT0KCx1yd^jMfz!6Y~SJ)s&Nh&t*NF;LJCiLG4%)zkK(x+dvS919F> zk2Bye27Cx}4ioS|FU?f?8WtkPn|2Q9y_>k6NJ$vD^9r#Y+CKzs;Je|cZRlL_QITnQZg&hq03u)t<`D>=F^@uC0Drt^=={Q!nNuS>dt0n0 zXWmpCP^*(%jPmhf3dTtZ$3xs<>Qe0Juz5aNK2Fa&Zep1hMLLNtC2U9dQl!x(wDnHyk;4iMg!M!Bs&k95q9Bg1eHfp=`Y-MY zR6@>*uQ+U1^*-~@uBkcg;Nz<1rxuToeI3#!Y8$cO+kaH1U3}3O@u|wJCPh41t6mmY zbTP+}^k$KYM-ZZ3CJ$1C?F$Kus`;tmyvx`Mo_(Vbm3gsgs-g-eAIe}1vEghREf#)_ zjd+tQI@+79{c^o{bdAb$CbeDsD4~41-|x^Xkp=O3+u*P;!(OHi@7sp2;FQ(pr)#17 z01e;STL*4!=ZPe3@h(U*&*cmNhSC$`{f}^u_#y&;2>eRR$SY| z!W^?FkVZ)MSt?cIPL^NbOp!VtgaIUe0>cn=+8>g~C}CG4SFZjwhIIp5I*DiO4u8r& z!x#Q#>uOeS@{eJv@tt!mwDj%xdKM6MqWA4UJ0svOP%UPBYJEAa-IDgJwl$CO3%w)4 zAnEu_6EePUqS{67cbU=A#s+AJ^hT`OutTNO+|%z6!czO>~BwmWl|DKbKBq(X9 zbJQ%UiE!D-+W_3tv7|t3-eCpZ;eWWY{73hS=i%3j>Wj$9x*<}V>Fn~Nr~kHreWpip zH2vK&)=9W&FpZ`Zg_aJ8?57VZep2xJ0ValjjdmWFyl(ZN%kD^b4Xag<5om4E4^ca~ zDw!movj@G4434BuA7NHhOmKF$VD7!^E|`#T-W11cbk1KdXr{oYXKoPYh&B3ey>Z-okO#e?XuGm zi;1#;rKq%l5&J>v65T<*;D3y?$j#|i0yTVzBP5(@Kv4T(%PzY2KZEvaj+!N|Z_V7# zXEbmGph>n=HAJ3n6uA$k-rUqC)=t>}ICd<*P#LS26Dha590RkLDs9n(9%lAz*QkPM`m&_MY7MSh)O1u6WhH)?HQ`rQqTD%)7*=uIyYbN&|DuE-JHbl z@r2!sEW}j|8FhJpn@JJJ*deaQ2_=^-&aT9BV0HC*NcQPx1}Z^@w8em1;tE_^USztU zOdnmnM`3XnMug~+bAd#F1rc~d3kvaw+KMrL=S~9$1SZuj zXVD4ED&!tnJ}Yujpz2Ey9ws!6-U5=;={_&*+K=fJU6|JA{-~TTWRk(gb+RJC3!Cb~ zsjRAG{DJ-`IOzYKNkxCP^MNFh2)B^=9U78GV$lMC{9Uwu;kQY-KP{P-%B)YxLyFw< zd+g8qqh1VO^dek+=N-?lzuj@x+8^+tReH}%8#mdnJ zalG;=anetaZ<4ZlBIvUPo)ouDw!Q7QGB*=lT8`(~z-O)7+nqyj1bb= zn_(457u4p6r^$bm*uSqW0ZLroeHynI2mRt|WKEAL?&A)E~?TGMgx^p)X) zJG`bv&?e$KkOcBBk$3=*(uSo31fPQJkS8F_i84S5%lupplUem}bNl+op;DFmbJ6E; zyHQI$9m|uqa#S_rEuqfTYj9KuHsEhA7HKON!BbA$vd@3??l!JMIo4}Yt)#J^@*XPC zGx6__k^jz&a5b_{o=*wa{`)1f6dzqf`$69_ zz<~S^_o`*fGBQ-VfT0VuP$ZGZJN|^Jh`$*YGkuFTya~#ZL@*w?V4}`RJ8tIT{iH_V z>0Gah?F)aKlL~)tN>`szCVETuus14D2FrX_-dCwIa6ZCeM5wsU8Nim?!KDGBC%7#U zpH@VvK3`(=5W^0M4+ykm>8`>h!WM+w1FkXE@Hl>XV5tMq?H^mS^W@&-ROK-yN;D!) z-zHU<$t~;Ix%O$3g4ZU)QU@0VmvQ;R8%71@Coz9-+Y*ex_1M{F^IId?(r>bqPW{zD zO~mP$m&H1<&@5v$c?7gSC^ng_Bk+3>n@(ASG!95d($zrG4B8Iclx$7Gr`6@H!<=B{ zEFb*TiHnAH`21kbvA+bDPa_AWzU8x1&{TMN-CF7z(NV?)+3jCF-k(?h8=9^et|*kL z6_}SXmH`t2GcuFWuoSaF`~#W-Gc=cBAp#YbTb2P01T{4@Hj{CO6a_IhGc+)hF%&0% zt$1ZnWNnir?(U5i?(XjH?(Pmn;qLD4ZVe4I*0?s_xHZtYySr__-|Wn6%+9af`B4$~ zNjZ5k&y)8?6eX#OI-{tCvzeuovlEDsm5GH9psA*vYGLcFz$oVIU;+4R=0u>R z6bD+Gf^40gBuqh;d;o1r3xI^BIe?9S4ZzCF%Zoq>5O;R*2HINNfB-aqF=*-O8UEAq zPYA%w``>hod8sSA3Q7_oLw9(oj`vf{+|=oEiC~c8%uzdt%D^%TvjZkDtFD`z0U;olAbb7v^j(>fB!Bm{xKyKzhTNe=EZ&eiusej`MvM~kyQ`^nyT#GP49&*t)qmn0o)M{TIvyX!|c3?ryeD*8jp$Svdn(S^mv#;qLP9J`YRazXn9}&z+(DOTyH`*~!5hU}0&0g}|)j4EkFV zK=c2mGSmN@$o~Tp|Bnd#KO*n{pSb^3qyJ-x|9|)Szd}p7J2)trI$HiK3Gnal7=Qxc zpO?)46>REg>)`$0h5y$`ZOeb-_}`((f=vGoLe$CnuNW*$EdOS-b(6C7vb0dK1)19b ztV|vLPU&BEO(zRWpo6V{ljUDE|20SeBP$EbfAMM9*qYlr{WEsXe{)$nS^QV(e+Bv% zab{&*OZzsiF&yj}iM``?`?I$Qk5;U5$+F=sD;FC!}_8-S6Wh4t^k z{pG{U&guW(RQwkZ>wlgVO+i3gFM$5vw*O}S)BOMb{pZQ>zraX;I+;6L{Bu{-L8eX? zf3Men82)jay90rLRsGk-|84r;&;PpUmX=MA0MV2GwV*@1AEkF-JL9wk9o z6b~*a0p^*FiP&9e&0rV}r6;FUsYj0w)IY~YhKG8uq5Jm;=nE3zDfvxt1JX}O(?H%P zz`G{%59k*U&g5!%B|w} zQ@cDf`v`6{_CD{*pR7V9F`PFsjPtv|NEERL8Ifj7jpFa-r^Bbp5exTxSZ2ZBWi1bW zXM*vQrGYlv*GRu8CS{~d)6b@jvn2Y(0w-s5;RM!@f`bs|dnI=iq^0hRvoS9=y?)wm z)P{_3G63j*34$~LZ({wlA6?OqdkLS_Ol}cDHIoYcnjnPmmNf|2nxMh&6toIQ6?@2D ziqP%1CbKN}VVg#8^Bww`n$7yhvu&sbe=Zuc0V*sdAHP$PPO%drO|?5Nn#xZ2-wd0F z5!VWTVOCjgP*rjTj#7ODxIs&>kE)gA2}U2rsAY(M+ary~a$Rnt2`RHBtMi{_`mk}b zpv1islhrrU2FIBnZ3J5|ivmCUR`_q^c~Iz6t&AFHiFo1qBol00q|`vxaSRMTvsM^E zUM%19QaLMp;7`UJQpZbXTB8!V45}pQRqmC=Pq6G#ucEjF8A|fl;hAp1Y`%q?N)#9A zYO}z9e1yRf<%|_2M}!06b~;d{--Z)6M~F$(&q}qw2^POTWwqLOSC~7+Pi_#fKvi)g z3a`WD;=GtVZpJMIN>m?0oe|gMOZd-~2F+7MlA@+zTEijJ5xi^Fwvd07x#OpK$U5>; zmo5@o^*aY9$-Yc^h4Ja@qbiqL29K=@@x&T`;ecMxr?z=e7cs*P7`HuV>}ecUn0Tdr z?N9{<$o7TM}WA82lrpGo(UTW=@Ck`fy(tAdLXKZH4^1zo@g55y4(U(Y-Ah3M;mM zLg!1~$rc;EW7e5!f#N%L`*Aq_{nR~{bV|J)9V$osvH%e|p_oESOhh9-oG;5@a}qdMw`}_N>BxR#Of-59^9Ox`4aETJ}rI?fK%IRC5kN0$}p) z0zK}&dyKg#B|a&P6Vg&>fq2AEKfb2YtDxE9b6@e~2K%oP>m2;*vZ90T8|#EY8E;L3 z(z1%7%CL5pS#~5}%u92E=E9GA@ecPy>oKuvSxw%uk)FbgLlJZji0`RSzEtLa47TGv z&`%HjE>oG?q>}KRjC+eJ-I%glP&9Z{5wc-ODvdeH7q#rOxCT698j4gu|630@khUau^sN0z-8}u|I9nCr9`E~p_ z_Lqe-FE<6LvAXebatchugSJB4s$RU6-j9H3Md&=+g?fkTD@9*EewhhZKY=L0EoQ>Y znQm7q*pQwFAb!E>XXf|{>7LUnNML`tt3q#oCr=sd<`r-= zKFs?KWtwXc)#KYK#<`qm$0l=*DlTEyu0iXH?A?1VW^_$Nz=XK)7$Rd|B3*)nK;1J|0y|sN&-rcr z5`ewvaw@Y0cPcw5L{KnF#01eJ@}>pGvgG|kuLJAf>Lh|kT`mb{cB zKq!`ohn$Vgzr7HDh)s7NI&M+9^2qKAWxH^oLT3r;tgbd)w93Exg|*UR5TQC};T^fN z=(~bv7n4QEHfW*cWBok|yNV1m2KStJv?UxBajn>^uvaFe<^ZbT4*OJb;cY3XHbz{V zazfwMHIS@G>lpbD)gM1=Zx2?70@YP&x12u(oyld13%lQcAy`2HESbWXV`H*hi0=Y$ zx+h>LqmIC*aH+!O-n_+n*k!d?d4hJCAvojD3EsEbdttxFjPTR1~l$;=p27kTOnl!6u0hglUx#|8e&? z?SBUL?nMq6Y=+kajEF?`oAKotCE^G{gQ@L4pfHLs09SSooLiyJ5St5}Vi?tLS>1lq zR<%fff^Tz%gPBj^>fY4lYS&|I=1?0+Y&3?L9{>~$i!As&*~&=7&w%l+i5?I2;0HJo zA=MXl=03bG`nG^H^RZit7K zc}e!Dk0C>$a!CTp3sbqa%cfRnnu3H%-6b`(>}h>8qI!0<)4$?F>s4YCV(1)j7E%u~ zqtD1B=G?%)Y-F6Hd-BhR<^vXEcS+BG&}g61)uYf~l&IP?_>*QRed?J1BIq;M@42&~ zSzL4N&zEl!5rmC&C_5b;1XV}@p^pwG5HqHf-_kPUw^Y9xIRQPIN%9osnw(z9)R|M~F!+b|1st*>!^N9c+% zPOG85etRL9=QZr&$=(h`RTBoEWojyMtbT8VEXL6=Eiziv9iF#~EcsAUUmmFZ5;8Ag2&}cdv1YHT zMPAbXaa=q#WOhG|*pwuNR{zI;$N6sAbLa~P#qXrx)ZWKwO326tO58jL--*unOe~6= z96z>ruQ?%&wy3@9AFpuvCC)ru9wEZ|a$wUV;hpP@5zWlcBvSz};`)tg5Nu&LykI{W z7nB8gg@+kmU}2TgO{x-uMpNv;ah{x`DvzxYswf4uz`!YI$#LR@b9;nR<4 zV{=z7aW!XniS&8UO1o1}n@9C$!5o(EI;?E)6GIQ-zuR;Mw-?HP{iPY`1^9$=HizQT zR2lFLHFsk6*n+a5Q9ZvbdHbfMj|%SvjUfPwnGMk^AHBUI|1^BO7o!PfJ;bAoO8Pgk zrEezz+s089oG0jT8+ty%>F#M?zjHct)Try&T3DEp^57k}*RU^dwo5&f*r<(fqejo# zbjbgZ`rOO#8&UgzbO2Bc`B^ilv~@V8>NRK@Y=(GuH!PyXikd<%RZ=GVw0zy)iBU?q z>-;8n94~3#9*0#Xc9^mKCFTm)Q{%+5j+9WM(2@Qa3kB&xa_x-%=Uofrpu1aa;nL2JEZzT=V(=GXBga#y6MDhr=c)?>l|~G?LXlu zryN|a?Yq#ZIcbXZ)sDp=j!Mv~?iG$#R}3iJrmhKp!Skn`xf86ow_@_UfxSC`_xTPH}aCbCS{y!c*ZGSNfiv$0MVDK&iEhPH*x@D(8+lb^_lVOhV#*@}hK^it`90p!S@)I_J4%)C&Os8?Z zB8a4aQHw?k6iX>ldgpyXxqR4$PI|#wX|~9+Z5ht=#zda*J8SWcCc_Foir<7ndRb5> zrqWFC1%rQ-Qq0v_0{rWOU?6}$&c|dKNY-sEg{O5A&Q>QW)mbdc@s%dq_$|gZY36=w z4AqJKh>CCjIQ`M7%2T}~L;5@aew1fuY0Eu-)rCC=BD0na+$(I;L{}h38K!lh;pI|V z!6hAgsX{YgCXbQxY+7woE_bSV!~ga*{Iyt*2+ifA%4eAd``qJm8C>khX@E+VqvMnQ z5xTC${jHXA>+#OIjCi>W^-TR5cuv5B3AgCzxL|dU9Xu9gP*qNb(L!_Kr@`$R)bK8U zq;gr+%h3F#WK43CT)DW)7awZYGfxb#Z%bnd8`A}`=J z@6s^Z?0vlI8AHqsDC5s{=Mt`1r-)1)!Hn9J#Ch%@zFPBdrdSH85O#oI45XKTcK0Hy z;tC2cass)A34Q&9R}0=Qw?`Z%T1Hi_WS`B&lJw><7p|aT!QD@NINw2~M69=S?pmd!h7!#0_JwURPmLWSeNqz&u%NqfW-(+@B&c%d?XguJr?L|w0h z_VzbS6t`^`oyzRQQn_z&UaMSW_*lLHo(InnWvfIj$TfX^*Jolf(>L;7Kbtq|9Ea6v zA(V6-kfhiJG$@{jE~@W;ZLfFWyWp9UoIn)6%)S3AD50j8T~79QV1Dg16|w3^U3haWbHF!}af$IxAK z6-|OuzS&zEjk^j-ZF8bLZZ-NTR{f$$0esNbZUmJ!ohP$Oa2CSs9>jFd?1zlN=2Q@_ zs&0SJk*x~(#cjoZETpN8+C&TfYX?3?PrDvV#{1Yx748USW{B9u$gFUcPFHK~BSL07 zuWPga9j|6wi$FiK);x{DS&jD`M8gCz5@C%%9xV)+)h&*|KhkbQMRM5JAZOuZdGbvDtg-%O1{>u}( zwy86%XU6c(0;sQd@{#!<5jN~np^(CS3Y7B2fZsE|MT9yCF21CY96U~6cJKMpJPiFm z-I}oWz@R?af`H2D3yXLO-RSswoKq6pX))_?6;EVUu~)4NEIi^L_0gz4-TBO81K{iwdsi~)M?Pt2 zxyKI$FNHxo$K=RpYS1wt@@yEjIN&Oh8GgePBNDze8FUfyRIv|eJOBNGQ9aGG>`_Q( zSqBTlQb^DaHwm$Db2Sp9SJP$`8)4@egPe|(Ry#6(0~~WFM{ulL;8(NM!cnG-^i^h;*aCczK&$^@AYkH0(OY5$_~4#;GQ{TKhBHH+m_*ZLn06E;ty- zXp6pPY$v}Kf%hmH<$v?$zd-8nigaZ4_6kdXQhXXEJboT5_e(*j&BlwYUe2rrMW?wV znL!d#M&bZlNXay$Uu_{&pR$8T=BMhguGIFaf9B9g-)hy~NM-$?WFYI|@=!kVXynoe zw87SUJU&gp@2$6ps9uBVVPpt3xO1N|4R(B>%r}|vNM}WYdZTlUHH#<`+)aoIzvfPV zuop25=u55b680qB2Vwfen!=XEZlpN<7>e}!5fb^j$ztc6S{wfk{H&d=T$$!ajA z#OnqmY>5=-!$L8-XCoLzIO9Gkf9)}|PjF{N-X6vAqq3>Nk5=MgSa0rUTMJTuT29Qm z=oMDfgx%#@%&Q8tXE8-+LSLUjMd6NLdE`b>N2Ny`OasKhB+0q(eEQ`i32~`IS_a+ESOaggutdqI0?6%yU??6#uaud3oKARr>ZNS9c62%#E53 zUIETQWpcLXRKd^lP-N`PfXnrN4ocZ@fOtzaf1H2Cth2@7bl9AK71mP5W$Jn%+fb)K z{cFK8<8K%SBR%IYW8a^bs6{IJ_iBq-);%h`0c$N3*RsBmkx^~(%t@0@7V($*F;Jx2 zf?2;}H@ef?3NJv>$<+u8UtlHHk{v2{)j`@x<-uQElOxBv*c}8jg!Mju((2T*ipRR? zUU!@5>^^o2G~G6%U0o=y;FSbT1eW799(bF~HsStQ}7C zQPUbayGNgKHk29Xn?{V&Ud)Qt_UVR0Sl8+9Jv_xqrSKz3HWNV@P%Y>B9-xwfhFg|sr$Zp zt3wGPl+GY1^$RDikn&6WxG3E7yH>}=XSd$&pdXqbvM^Vo{2u0ia7*pz{b4i4+yKm@ zs;~g0Fjie1cNS-Aj;g!9#k>@-xGBcgWm-;`O%G5I>!6SGXWc;LyErL@wW)Y!PpdH0 z(bi38*99?m-D0#vLW~*er1JRwjv%%Q?oN}x3+ujujJP#MqDIR{rlIQe!?YiR>%HxP zouEnCF&H*9!ye^-#xJHDHXO0iy|t2Q)GrX8lxTFQ@N5EqJI6+F0j{7d$H+;iDxo}8 zFi*s~jcfJ8&N5k_4h+J*blVN+qGa|I8DyhTc@&njtTah3+A|kvqVk%hDikgHT(OhT zm6LbKZLl$7To%qEzkt2ARu1(XUPS5j*^fGvZV18)e$eHAB<{povUrTES5t4Fp|NJT z#1x{)4Co}}U-x=dKvBzc?zn0w8^vuE^+v*wNw$MV{J>W(P z{3AbOmig#^a~fKb0xF7N-f3(=#IM4(OFdyLhzwJlJ5w;wsoSzC0>Gnq1&4)@ks%a5 zAug@=eMGziR7hj^>Pn^2yS4-xj-ifO$cjwz!|1|7Z&x;8(J_-b?D4JLlbCPYvhu{4{qQ*0zBYFr-sZAvzE*@_MP z;)desek|Kk3_0m4zxHCx1zQ8Srn_9brj&Y`LVdcX8$9&eZaiQQ+2-0`X}-5>Pk4H< za2hcwO~J>UQ3r_HvnvVp)cRj|dr_1kv=QkJ!H5<8!lo}d!`2Fq9ad1~@3o2Zc!|9$ zv=Uf<`IOt!z3wEi<-**a4^`^I>$24g%aaZ398uH^>aRN0SZcB@DG-~b^}3@5QX^sf z-pe#>$g<|ITGf9iQ+kgeLYrL-8UyP;b~ZopOLPFz(wFk1nceoOYfj+vtaR)U;y4Md z{Z2Q*3IE98EV}(0E?PK17Bh&4jHz7(v17cSxlCj@qU-4d}@L9Or0Wc5TPe6Q=IK%_DC9j!ZtGN(+Hulj3$R_vt6*fIKHXN+PL`6syp+sAtH`P&tOZM9;X z7n2MY5z}A?XA0lG;Z@iN_JUVqCAx(TE<1R|Eajy^e@touUD9FMK3vJZp;?hl1n@wS zETMSC@SOZY-bAAN?le@tii8=OxTWyakw=)A@;l_KWz?Dwwavo!(ND)0@z7I$rd6ra z9a0~Q+JvniI@5uw3PpnwlqLRmZ<-ZC(O|!~aYJh4U0&fPA;SBdVfY>|yTwYiO`UAM z%u$8n)~U+ZgY{Pw2c}2*2V4{_F9kSu*3=BogVnBCA~*qTWAS6WpmJjhvg46g>k7Ck z<-UF2iJ}90?bVU=0o)}xc8Gz0&3{UwZW3?)%%u|4*f<*x47EChzUd7(ZI9}|6tcm3 zy}YZtB9f0DM1fzm3IP{xdNB<7GwbWHe20sWhDJMY4eu$xe8Y4z1F9ojwx_C#*zu|q zB{{28l&vQL%ksBkaskpQl>IcDWro0!3$+)O)=8o=A&}vVsYc_X!cSO#L;N)`&5}Tr z9xBDx&S{QVuz=`cW;3Te)&-D`E^ zPoY2AGqC^rRPnlDa7p^4EqZ!qA2c~P3|6#v5&3!z*4BEQ@IVm?^p#s~0EVRAcg6jO z-Zo~I&qOr2>H&nrgu=UjdERw?mL$krugcdb;;vvI;YO3LLW!pT2+LGilr6R3R=jTA z_3}#M413)^^{tf16nytkBQ;W29P1NO-Z<$R?Ry#4V8R7<&(;7-Gr`3g;#-UC5tvP#? z1u}c;8N?Q)uP#P@Q<^amezvI3l&QgFA~B?JDu1ZV1AmwYr_7cZ*kVnl@Vd4~>AQ0i zPwyctsC&kgX&^D0?8> zzkOFJV84i^XA^3FanD6bLdIjHhtYwb80g5G7S1WO_lgJfiiL{WiA+)HR53}?K$Z_B*V0eii#owYVTDhAdzz8~CfJ^v1#Njsc<#*L>O>R~o z6N>K7u@U7Z^iXGDIf((WNBA#pP(os)YzXZCT-v^kgPMqc?}!BUrTg;VRoZ)sGS5Zo($*ilAIZxH%-r+otmg|Ix(h8V@oV6~DX|;w;7K2D9OH6)Ed!6Q7DH^r~Ldy za+3SYczHc0{b0&h$SFNSa=y{k2$AfXUOzxX4_)oh5j$4w5l$x2_b+_< z>T)VbQTa_BHc zCx5gZmkw5KVe2wB&YU)HBzT8p7$GaYb()v3h9A{JPnu(Rurp8hX%HpJ4+u?viCNqT z2d86DdzmL@PU?{ycat?`b)Xx1LXL6+q`U3McYh>#E+L)e@cUFnU)MnIIRiSZ5`fMI zYUaz#TXBHKKR^bZ@Cr>Peoo`)inGyTr`9sN`z2cnHqWGgE=w7)zyJ*CQPC8v8c1)~MFWF^=vd5}$wM}B@}`m^ zI>g(kqgA`O&oPHt=W_4?S&yE}xrSh7~ z4-r1{vPM(tN(e*E@BO4?MKiidzp$k${cR%~V!yO+|L$tVSrpz`y5xp%>4yxmIS&Cb zfGpi-fP18?mjw(r$rBkmwy=>Us}vrB-R;v|j_r(PG`{sj8KO#C=euBC4I3!|7ZOGl)J85X}i(-Xqn2z!UPu`^sG$CuLS{5A2MH;lB z zXP0Ui#;PsIUrfUF%!T65Z?DDJiYhn>$V4tU70WnmR9~PRH@m|{hXXy5`oBpKU*sa1 zgMUwACg_WeF^$=LyaA7Lheay3K8S=C@7Y#Y1?KRG&Yy3}?klS>h6O(xTZ#0stwL%GW(s6Nn!}=YJPJR%O-~CNA zJVfoQDIx>JX)(OLB$Ml1(5#;<19jdzOfxy?)`Ds#}ZC86jpv`uaF9B7bC~J(UNnYnZ3da+N_A)RfsD| zcaQlxex4@d<4-~}#Y>=o!WO2IR#YLm7c-glGGj=8QlcsJIHw-gFvI3J#uvQ#cCUAW z;@49eGrlZ=NU*e<1LD{A_L;s_-a6plas5I%N)ILi)pVgI<>)-^)`c3SKCo}bE7kt};Ex0m-ri@~a(5vE*-Z>c*FFI9e12$DoQjC@%#vPjFf??{{g8!|Csu z%FVi0))>?fq(iBq_}T}K${TCXlnFN&`vbvJ{Q1Ep@*R2PD`Jr6AB|Pfxv&vgtjchI zS(uq@n4Vecy6FyV(Id!taKZSIF<<)ogbfb5%T6aGI|6d7uT4(~BK2dA4HageEY`I~ zjq*I7sLCJ?vw3M8^YRKRIC0em(W&`Py?*V$YhB;PyN2j{8%|NmKqXb{f2s$Y7O-By zj=R*e!QgCtu(XkZ}Vp+MzAJepvp zb^(Ugg$(;z7tVkpQf3sR!9^{?_}&+dAeM1^+^_(BywS_&x9FL)+I!Nt6FD4X0wLh@ zh&YALXXlxN-o}JN?Lz;=4pTILSe2hMSB|^Ig{wm2L-dhVYFl%YR2SoA@O%B^_Y3W@ zWzJNda7r#TSDkMGO-w+ellcj8)}2CXG}p`(2h$<*2`83`9Y17M52~k?g{}iE*8#)q zRI7=YF%$&Yc^w7j6DSpiq_s(h+vZEm^HKOY|89n5AxSb(h|YrAAuG3kJnc^P2gFbt zi)xn?taC`TXsFg@&xsT!jF2@8kDoE)yq144EN&8dH!jZb!|u)EPjL_D<{CqAfrF;^ zt~Ic$xEN05ad+GEUm#y3VR~~oiFBf)V5jL}o*)WRI###yW)f5J0ab3{5`25s8Nc1( zVp#mPlMB{t_?+w?o35~bJ-B_cqJpm(+cmPCNmO`0R8`7Ud^|xji9rGy)^Qt@`~e zzvXuJTTsc(pR{|Z$WF=0U69mDuG3g2ge%LO=#Ul4W?`Sd;ds!0$2orfI&hca%SI>R z*&g=0DrbgyCh(}{8$d5dhU1x_M++xtXVFyaIVu4r)l-fT0?C?nXPCIM*|nvV1s}WXXc!Lkc5qvo)9ADOOJo-?ff8}t0soZu*Ozs{xRwgs~|QZHfDF}Z+mk- zr~(O2m|_g&4s7N&HL12oQjDE&N6gx>a=PyC-e>e8Q^Fki37XB=jOpr&+vv7Xd4;Ze zh8F_&h!XsdUw+>;ZSQhJF6DWONB3&5#0rkt^w7G`dzce{a;y&&4adu!D%KYYqvxf@ zHuq3$eC$tsA^b_(zfnmbQdwaJqf+{2jl-bm+^!=aig4-f6&E}&L13%8Sd!R(Xh0fd z2;4q{q=>6Kmx>En@q;~1=}L^u9~kW7IQ>|B(wK*uYY+L%&Wy!9oeoIN+f0Ky^$*GL zmd>$alO5TAFsjqUd@8RE^RP-f+UC>XhM25kT_W3-eeF15hJUyi^%?Z%{*&|PO=*!c zkCsd*%_lYih9U4&g*zq&j^00X!1HHZzama@Y-4J{=EO@TcX!ZM8O>1G$XGKyLg8YQ zFxy18C^6#FbTfZ4n!gY#+1zY%&@PlQ1rPEQ6)dE%3#AFB#g= z?yd8)P`(ahetC{pANULfFUpQyaps$`HIRy-t=gG{KOnlQ?sf&yuKvVs($^ZE$cygu zV@PLzq)|ZN3q-qxbq`i1tF? zi&0QeQQb%1y2)`#<%mXC))7604d-0GQU5~AMO-x3d`Jt zcMYDVMtzk*62tSac!rI(80N1!kMOAI=1od(pa!dypH}e)#C&k$0B#&eV8*4YbfS{Dv@ckH zoTI&1IXN5TFt13oGT~V^xE~JEN=s9WHf`jO2`B`(9|ll{h}&3oQj+mv?`+)+MVK7^I|%;q(oyM8@%Ud_BW*kkofv0{F*7_ywm z`NyiFY^7w6-Wzc`!*CjMc*uH3bL8QFn|GoP2*k6TiS+HEwPDh)o|N9<$!ir>>hq{y z)AQ>*>Bl5B!$si)X+e(hk$U(~Xv-a#)E3v+ZGXaS^l2pqhB=Piy#7p|bBqHsNbt_EzP(q=jXy&wi$lzPj zn_DrVgSQ+5mvjH<@z#Mdp-!i!ylFbrNYn2#pk}-7L4!ru`i19IMOxwc4vETF)NRY_{q}Nyaaa1X0S${-Up|bUk3v#JN213TqqF8&xQf!R*mwZe zKmHvDcH0Wode3w@>iaKy6<_RKO)DkR$w(wEo=x5;M{F?Tj0$-<)mg%HD;JbAPTsJf zAj((?Z@$Oy$6H5yr}v!*`oUy!DO#Ocy5%j(4mmGuRC>g-STt}LaWOQ1J_{DMr&7Q~ z3uA)8a@MCBNc45^-~iyh{9+4vmWya&tQbM3tt$YJ1eWNO#`y~$ z=RjeuW#qH0O`gRRiiBA;48=g<+Qj!C^kI0<(%&8fbOPBO(K-$Yps=>trhXN~NasZ| znle}|t0#WJJiU}g^Y(LpM$mqleUVAvrL$+uYAsGe&7g>sf&WH59;MJALf?*McJw{Q zSo}w-_QjxRO_QH8Bt!mDzgnT^)0k(qQXU6#qWN=c((fidK$-svCo{u$pk(Zagv3J05SKnKIZb(bM2YoS<1{Yg@8jn>rB=%+<-|RSw z&nhwS^`3^jvj%}@z##BU6RoklRMDA{e+79%AraU9F3m>1LmJmMz)h69o z(llRJJsszg-xSG>UvpqV+{g%3-4RpwHu9%uroe&P)+qLWGn831S@W}Fk42+xje-@U zI8g~i9pZCWxC-rFj+lDMhf*cKPqppf(GDy6`4tQ!IS_e8c2@y|yFX&pTs|;T9*P?g z;b_`Mh$`UbNMWM5bZ>BxQjw75;EDVeokEJ_CUgafvFI1rxG+TnMZ2R=Mc7B_a+>h5 z0S8c;LY_l^B^_N*$wa1@kcQSy6_6ZFdl>P0Y+CWSmbR+8W&6$al>tgUCQY|-# zc|yviN;zK2>GW4B^C9V*M=$++#u@C3p*$pqw5z6tUGSB~Y}<8ne2)fg77H! zq4ST8HDUmm7L?umGe*v!{Y2+uqXhRry%_FB z6Jja0?%?Q;ame?v;Y=kM$GWIptudGHg4FX!5l)l0H97NGc~wlMFKW3lBgD=?)KdFO znn}vy?M`moqire-cS}SP9F*zulDu9PS@3K?j36WF!{PXRZqbUI`bU;uW^UN z(-8qS4!dY>kl&u_NneAD@w-a5wor<$#-MCitUvQc zl@M$lK{(cg9H}#xH-j6#Ea=MC54}UeYZg)5z;4P1+9!G(y$c;%?zLZmJx*zVsnh-G zVL{?cyZF;MFbY?-i7`LRS|Gqw*7`*I=SccHLmHkZKAbhsEQMB2>fqyQIfwejKSSwX z=ru_N9EQB*WZEThl3QoKIyce=!V0>v3y^)#F8)kW{+1gl@uif1d)ctinnL;hhW=Q7O8H~V8>#dp7622LhSd_RDO@pJHaQ%Z4Q!+Ce>P14 z%PR;ri8AsyqL#iqVdRxll1%HujTm>^dfJpyZla@fjSE3p#;}Pv;_{KAG?C*j(|eLB zG@)|n$h2^5uv^`D$@{?4_h7%iqw|cZuESo>aK41lCupagzqh056+gyb(X5GVqj(;} znZ}sy)2A9^7c%Aoi+xpSbgb7&e^CAxXRjm44RPLjVeWu8Y0IZmzXT+w?VrR1>>tx# zEc^||c?lQDhM_?S(Rm1{0jaH3-`iWU_DyHUH`M@OTFmE)XXPBcn%K0Nw3Z?R=kzdzhp#0z6$hso z|27!C^3hRFEk>!kFJF$z4Pw$CD$&6^Bub=3L-PEROze%jOj$DIfACCVle}9GKQSQO z)IEH|uhW-C*N9n%GFo|QUl5na+AiZI(x`MA5^+bE;ymp%9by7g!&>`9F!b=d<}3;|M#!yye4h6LjE zR}*le)CvEyMZMJVe?f7lGjPuduRF2!H;aB@E(U<<8tlVxy7_HMu7R&CuEiO&Y{o?o zIs!-Sr>G0iEGbyrvx-ypqnQbZ7H%C`uCZ-4D0OMEmn1l=%B*3ELG!rprnvYlDrFTI=J>8UNazKje59W$B7NuoY|<<5e?W9X+VW^VM16{mej*Nj z+HQ}b{!5UuCWk*S_cwEV9*O-GaU3*l#}@$F$BTH4=e)Z2EV$(MY5naa13Z&;iihhW z)y3E|g7Ifc#L$IA;S6IAHIpKy0ORbWnz3xJ%h$sJ;9AmcAYb#BLbyLQ;G)R-!(SO! zSbygS_*_*fQh4sq#r#Andi8m?bTMm(z!dt9=7x&FnHoRmgh`XSiPUwav&krJSw{#! zT%5P8la<|`ihXtS_^sh@lsd*lU1u`%+I60GXhZF@eF*7nSlQ9%0f2_4*bfsOiC7h&U+cw{MTz{j0zJamIL-=9+8Gz4sv{lvkn=Ft#%^5w){*reUC^=LD!Is>vHz zTN@Z#*h$kU+SwQY{<>M9NlAqqO$?kZ>}-V%oJ}|ZY9_`2VG|<&BO`!;gM$N_e-t2O zXYb)?VP@_Op!kbHNkv8dU!H$b0EQm_8Tni3WMO6tAp85_YGQ3?Z)0NX{1@W?x=_i) z1mJ9L0x-3(HUS99$!kc+iUBCZWK{rSCblMy2G#(17ei|cBY?Dpk%_I72_?YP&Jke! z9|pk4&equCpV6FX|6&O^0So|6fA%Iu7Jti3+>K1^{|Qk8>`fePES#MFegiC=0A`K` zw$6Wd;A{u5ur;!FG5&|ZU%#o{zl7`^?fz!i{Ehtulecqnb~19buy+Rh?J6%U`X4-< z%?+IY>Fs3kHw>^d{hMiQXXNtFNdLzE!u*Xo8(7#n0h~?To&V`&XaX>{e{iz5Ht_h{ z`!ATiqs6~8T%0Uy&Hjr4HNert%)rsu+QiA}FU();f41{qa{~UC=?(1dtv&v&w);2h ze{!&Jb~3RxrG;i-{M*yW`EPGC3tMQqe~yZTt*IS=f&M@I#xC~%8FMvp{C7bV|C|}h zza$Kd?QE?*0LCV!&~&nPf6jkf0x16PRHprZC-VOTiT|Gn{QpGW|9|5Cca8p+OZ@-$ zKL2-UQ5S1#SpyrBe~SSB`NjaG0slNQw*OnUfsKW=$Nwq+zh|nM{0GVZBaDQz!QWK~ z*qZ&7gPxZDKb#g$q89EZ#_|@q&_f3F-P1Av2>$>;yj@n0Z@|FUHaoE_8F2+$re|e1*JI?3P77-d_A~q#4Y4n4QZ6p^ueIy*OAp`WsM7za3!!bE;r#0G z_Gb)De0XAP zbfoVNY~T=wDmM;_l*<6aH|3l#+1W$i@uA7+3+&C6CH}=Qfv#Jvq9eoeI;N4>Y{%R5 z$8H$(6xOzqe^R|rY&Vl4Z06G3#KE=Y{olVm<^`;0SEfm0D70%mAIn^xuC_o7) zy{SLnfpTLPXL=D)_PkwCPY_2bQcLie**#wP(;#C1wzNLtWR}zmYUCa#t|Txo*f66* z1{eQR{)(4lE0Z>2Mp+ZlExM;rw*k_DWP>1cW>Tqfe-;X)7pDzOVbE+sy$;AFQ#X--QcyRdkbFjguiffKUm&DtB>3Ar=aP*Yh&+EPaAk| z(yO8c9ZCKuRBB>y$714jOIzhDL|)g;$F?~c-}t7R@Rk})iE~px8)PWzHU9ePDZ?|k zEIueRf7mFi*Mz_mQ5g6bsQ*K3@qIk^ka^A3YSt=cVPiK^`dk{);BlQhhIPBa zWi5?}bHEd=e!q2~L?`Um zqy3G2=HXl|vBHU?8d8iTp00}Gy|v1X0_#N^f4UsNtG{KJRZbxnS-6=iMc5X)LtjVs zR6=~F$gA{&s$+L$hIl9E%s-bx@b48pr%McM{TT$cXqUO)@9q%LzIE$`cVow}%24Gm z{!KA(c#4n#){fp5eh@#Kx(ipB2cDvJc<6crlM&X_gKLp;gSklF+jtLYNhG3Ak}};E ze}XeSm(DI#T5o|jZn%DJdEs^FH$-nDy*H?0?II~p4Rv5KwPrfHOTJNQo;Sgkp9RxY zOTxOp+a1Yi8ll$1y#db(M?*?!uf02aa%%Eri930-WstU`O_cv0_sv0=Z5A;G$1fHx zZSywhMBf9ZCn;jC~+ zB>{98mU*2jaCIGn>T8;rmI66r1hpoX%XXfubm`OapLDPklAgMOgj<(`oe!L6(iRId{CT-=M{E- znQyh?&`71L#jie$2M>RIa~hF11K5APO*-_rDS2gn97BC;`<4p+}17wuUin({Civ6pH8q#{)K z?EB;VGg6MuhY|7{Z6=`qe-&*sW!`#9P=fs@_f1|?x9l(+j~YFkp=335C*6#JkoCa` zH2mV96IJ8;MuT!6ZoB4aK;LB@vAJt(2{q4DjQ4tI?4fms2mL@PS9rUJ?i5-kZg@*$hEnwe|&}~RQC&3PyVB- zD0JBqpiGO;fWZ2p2@+dM46|L%dCE&KSpT5OjBKthB8vv7w}6S`S6DiHXbiJn6gt5L<-M=6GsO^oVxN9OP-OtVEbHT5RGfSM?n28ymXMh|)c-lvcF!X#g}3wg=k2(U`ho3GmZjOu+H z$U6bj%5X5t_0ZmnUI;Lu+G)t;S+*Xf7@HzdspT$Bo|XKPe-WEOUTB?>TcF(t?R>$b zqMT57De$^OTLr@lu0qp6vl&3j4SG$J0~1c_g6U!TpzJfk?3Ge&e-ME7ajDmt{iA^v zn*j*9xzeQ2z>`EgNKrjq1>aeulA8D29&KUS8ii^J#JCS30H~g2C6o#=_uC$Cq~t@! z8uc85scKS!e+qPIM8AHohAt8qAA&}u-)WRmjz$2>eJ+EWy@QU|twno3f%=z3yCVk< zNVQ1TxrGcHT=}gB^i3iNNTuKyUM@L(g+`c%86l`k?672}MQS6jqT`XzMJBP{csUW9 z2#&`H6(Tl8fgE_6JVJkxKi@;lxm>W{UiO+@vXU>>e;<6!WTMci1WY|Jp`#Frw5(o5 zt7FPwZ>KEV^A&t6Rx@pU&~_X3jT~IXtjx6U zf%9XEV-nd^bjwp9GkWfIEb^#(afOmsnH**p8b(F^(X6(t)wOHxKWwkIag{g}Yx2Bs z=)wmge^$A~Sv3yS>3xpGumz9ys=%H5nnWSiJhuZ@_7(yH<5US_v1Y&jxP!w`rfm|D zKt>i*TGWdEmJmjGud!9tseJRhBuVHaQIM%Og{|CktK0S=+;ui+DwGS$JEZqBTUsZR zU8F{jde=|ixvZ@7;+fT{Vz);iKXinjx~zBye@6w*PMaJK8mU3T!S|j}Vl2;we! zdfuvLr{ERktr(z--|tb-T=9>6OU0hW)EPJ+x@HC+(tW0FwWw43af?=nxQ0pQUZIBKJJxS6) z5oQJ)9a;wV1tCUe*L+=FjL4Jzi}#18fB0y0xfsaXZ8`TFKo^|x3VydmUspevn zu1pQI{e}RmC8d_;W6~9-`Ly40OL?gq_er+koS|zyCO6|L^_>BhL)%-S&hdBVi|o1! z_Yg*D*J_3!pP)egZ-I;0g~!`yf4=^Vyo55Y3j8!$oYJOlU5P@*kvRLRxb#^#FWs#O zQD@H)SWca<+3AN~zrC9=xo=b!q>AeW6`1IY*K*67{eWg2O%XUELcu6n9HTr2Lxa>I z?+JnKhWo-&AE79J3BM}}k0q)t*p0lVGyW`Bm;&FPQE&9`}2cf8>nc^f-nP zo?3B6%^2jQce?HNzC06R;~JfeGVDzA0~Hv#-p#GvE)DPbPD&nWLVzSRYveU>3q=^W zA<%mxXvo9pG2!F$Hlt|5>DyqGDT`l;b1N(%y7qr%tc5QlZ})kG`*mz&LuENtSKi;p zuNuf0bAKmUDb35JC7~wIfB7oWxA{!+a?5HFG%f8)Eh}8)@!V={q%BfJe~{e?Yn6KvWjxA$XhX z7iL)^t)~(JKacN+(};ZhrX}x4@I#r_9rdn*y89q~3 zteIYNlY`W~UpK)Xe+zVk|#Hy8O3mqPC`Hpy{$4I|e1}rnnPCrOzjZ=y>Dvp3{p_vgG6Ze=9LDmoBYn@iJA94=vD!@X?Zs zh8&rar%!L*?vSASzsVAB0=D1coo#j~`V4=f^$4ho@*zEt5$D!ddvO@i!3o^CUu6Sz zVIb%07$#92FLLr-4nG+8m$?sz>5`=Qw>kW(X{6~IaF9o@9A06*>Fp-u+(aJ&pQ`2tH!2_@oYz5klO<}&pOPD=mTDKD^WBC;)vi6b z53GK0(A6RL|K!>l(TNBZZt=Q8LT~-gMh!3`C-$Z>utnuh z%t52`Pd@G#?-TWR8jK|yzj|nSGZB0u5u0EjPgd}K%S5#Ry*a$?9)t<}tsPWLNDJm* ze;j%UJAV50v-%Y`nxU~5deftudyTgn_>=f`o|CBr`?ExRB-0d1iQVs~jTIN+{RfV-7u_GG)27JVfiTLJHUUkHDqx*mMK<$lfP-|!f1EMt zR6yV*y^oYR%n(?QI$$E9UkX2>Gw@tifXme9@kSKgH!AInu=6*{nw>*k2k>xZYc>O- z)jOg4BI4}!m*9cuLE1UbWSrRsGu2Uv9HwY03U5G$cT#(y>POBb#;_{HHPQ4IZ5}YU zh<(u3!)W0Ni!4YxX*2A#oxnDce`8PaQhtP@d3p#R(W0E=%QqyaDb~wqo(mfqT`Ame zZ}$Bli7TPb0V>lDqznB61WVr`0(^xRtPG7eNC2)ucz8kfG|A*kZn8=!NYh33?}UEf zVYWsF`5)7KkRX%D!bs;_mkw*Fzm>iRR4m!P6lIEk*mY%WZquYd@FR6Ee+{3wt{K)R z70NWAPl3;0J$F}%Ynd98vDZ#5H@3E(lMXauuCBxthNa?8@P}qr5@B6)Gmz9g!<#P%fO#{YcHqr})(tfDk93D8BMf8Iff|$n)j6j~3 zPD^BPHNL|>c2arE-g^#Rp}Dv)xDaFS&OiNGn*XagvGF*~r=Ds-3&pMxq@##OtiZA0 zIGS0#HPyJMI0d-Ke1)oOs^T$9L`bSN8ikM$rA-k6f3vPu%Pp5MU=76N-OCGxr0?Vkfrh7 zz!|is^!B_!_235noK4p>UPmH=%3eLj%?_Dm6^9kkT}m9Se|^@80aGkt>RnFriqjlb6Nf6+S3FKgeNL#b`R$Mw%<*g zf$lsLdyE1vtk9fAfY$3fN+iHQmFT9x;60R!HqzEl1xoq`GI1WB7m@O2Fc}tFJ93ljKAW z8`IC?&hXj#BN#o)pe;|D$0iOKx-cOYHq1W+%ATK(lkClJ6fRK&D6vN2=cz6jJUe=h z1Y-Pcp9Co_Pj(r`8ZT_b#RFuaz!5fJHaL;z7s=w#e_gM7P$z~;T1~6!(?vcm^fJ;0 ztszz_$As+p5&bJ`gA%?ROkX5#lXanRg})lxgE9T($z(CC0G{$reodB=P+VbRPvas1 z^T7H;?N&jMp?(!GL?)t7lD{untsX0UHX)a-mjQ>{c8NB^Q?sAqB`+Vq2yLUDrJ3$L(#003`I}%> z=w1UOUwF9)+z1fG9^8XiatFiL`3C5RT2!}~Fps9T4A zhjI<@oBC+0H$9CNHI4L;3hzf>(=u>(ra+OLPA4ocv#qPP>LF|US(tRSq=kr)wOHa( zSVw%0J{>FezP>vo+{=>}a>td$@uzqke|5lC7yjHl-%{tjHJa)qd6Tqqb;2EUbZb|pSsmUp+{e!%|AzV7pOa{G_$U63N_-JO)0~(Vz2fw`x_Kgv(YRuI;VGkA zvN%_qgWwWjeyXVh6b+}$g+AmAqb{-%W*i`6Ya^n!geJ;C~Re2j~ew3OE zlBD-rd$G#u^S7*|DK;IZ^}mBEj#mA7aY#L0r<>Ln(u^*tCJkj~7nS67e+7=z`LTXz z7go!TvV{MQ_D2~Yc0!-WZ7v1TjFZu#;nZoW z_5jmF-7BoZ0(tScW5s?M&IS_j3tj#hwBVVnC^sZI0NMD64DQE|Ft>svVVwZjze-zD(Z$gyT2&Azdbw36ij3dzuT-76vW@N%Qcv;x_7P%;; zA7}Vhz`TNhaMX>K48z>1nS{Zi9UQJUQoXKnE~2CFlB^;YJ=##=H5vz_liRQgweJBv zIPAJ=CLg#Ej06sH0qnimNBa=Uy!e7(()-AzTi~WN|C?KJk$K=ffBIx}_M@wyAcz)= zSq#UIFbRcSY?2~Qp}uKkm8fiku#w1!k?GAC0`gV%sa-;dv}i=LQFf4g_#khof2*O2 zLh{5pE%x}x4;7Oc7W;W%ZrHl62L#Mw+C^zkL%>LGGgyrV%G);_ zvy!#4BEe=6=RoZOf0&|SW}S4hK_-S;%G+E911DkD!gk6Hs*KxfNq&%BGAN0mS%e$< zp*ihNxORI{%lSYV$C#abiKk3#_{6xKHglZfPQBh5%u78qvVlf7lJj1<=~B6_9CW2D-q} zF?COe;M2mUWf!>Z^ZUe@C( zFR_Q?FF&ov2mk(&W!|l*t$C;8oiE%+Rq;VPsxvS6a|*Hk0f=q*Dkf$0FV$Xsn9V8^@Qhq_3oj_Qc>H0x^0{W_13wupPI7EXg5pD>y zP!Wp{FG=?|S)}Da@&ZbJXrucT4f$fjKLabQIqcVj-VpGFUS8uC@UuxTs7RLKW zpodx(3_B)8prnO`6L``FciRw?@4zg>>dv}lPUYM}W2713WZHBBKTS8QSN6y`JDMr* zTYoHngRkx4%T5oK@{_u?P@0~^O;z=dStoZun{pieVA9nG4q3%Ae- z%exEGCpAz)nGzR}n3sD!*oEsv&X#)g8sK-$MJ{^#; zRV@@on`1@ywm;}D-&vmS{1em$pA;RQLemGhvM!)(i?FWSj~o3FvM2M9Ko1#vidx#1 ze`J6u!8FF}YFAiWz+$7Ehg=dq2mN3f+SUw6wLhY960Di#8U!*lbWhp7Y@*ewK`xlb zKR`YU4F;QNt9qhwqifz-BVtq_gol;7ev8{euiCA`67E^wd)Lo1#G)uF!M{-=3**qY z=?{L2+1BmhTw{Y2b6eD!d3v;Tm0{_xEFkc)}{A1yoRBdy<- zO^Hdm**twh8LzAxERWg*obYTsSC~0%chztos?ro^o_cIuSR~5RZyqAKwblxce;xuM zz)d(FoZHaJ%`Ew#KWvfT^!O94Aa?g%TWWMP$tr9T;6QX3$>qu91+`b`WP5d^(_)>O zcw2gWj#Xa3-?4E$b9t#C-a2G=B56jO^rhWo?L>O3_oUc#sfz4?br zvm%9peg%au)(?Ei7Tqlt@9cYxf7DFLLp2kRvBwe5!Nmui(HmmeQ9X2fV;n@>O~dB62x+c zsVXbnp-VNJrlku+3nBBSM8M36btbz7?!Kf zveR>MS*om|W|U$P$e`?|_(+J`aV-MmZz2zI`E5mn_je7C8$Dp^xoRi)|Zu*jGg=EsBrCyj=wz+b%Ra`5DMg0+eouio+Si z$Xbh@er^_jO5{mrH0Ha5f8`7I3x~E1N&4u5AbwF8#c$y|#0PD9*v7{NY7-!Q2mHKl zE4t^>=F_Sa6&L6~u@fQpcOwg{7V@5yYiho23&zbXE3{Anxvu*lU3qG?>6%-Ob=y(U z(ttq+D)D};%~|7m!Nh%a8Zh{z6z&yJLW7_AP#tZ3ME9|b*mrxLf11er?XT__wSo~I zXG-rxjL@N&J)08&h3KYCdH6rB)EWgSY4wn=yBnkC`1fUIYfSRXXClR55pt~CM7`+AObcUC8 zz&)XPxp$@Nz-w=Qf04#siiGOr8YbfX&2?uxfp7=z^@j2VB>OmJkc5}Ca z6^(0E8mGgeO=}fI_fsx+-%uexZ8G&)ik0REXV$r(xE7W_lf@S#twRM&5qdD&)Io0v~=(A_qNF)-e5j;w{lg2p*HmLx}c7?n>6i8f@kri z3Oqrkyiv~NM2$gUp_PEh%B$b^f{#}rkb8qaf3`T&GM-HAyxNbQBGM{SI|0ZXhA=D9 z#w4NmOE&pW41*7jwdV@hL>WN}_NBBizvhz6@`RcVLhFJk<%+4M_0=q=kGP4Utx)YZ z53X4oC9^<@E$f+Qzj3Ct%(Fu%1M`E=hIzwtQ5$l}pxo_=Tk^RB(_6=!NW+?A#4(mpF|3J6EXSxk0_Yh=`i#7+GVHCxF6z(?Iqx435Zm% zuY)j6&Cz~Lz**_L@$elc#mDsxjW@i zc|WKwkS?yvz4Bfs$(iCfvBGU(kf}cve`8!|#Y@jdDrk0I@ERTSpj;L_D_QNenPiXX zZcOhOlxQnnwH#SVROLgDW?bj8OIr$q>S*WshO(FCOi^F?A4MLqrT>A;z_ZXnU{mkJ zy7YoGPVcklt)g`PLcz+=Chl@r20Dpcpmrl^Y^?jHhMmfip-OK<7X2uh1;?~le)3saHP>^RKFb)Muu2GA$_9f8 zgo1wi{VScXS@;e<49(wxM&*I6Ap1O$*VjJeG9QU3iSk>q~V&(Uur; z$ROEmD_z2bQ!I$PCF{d_WY=qZu~{Td(y3XAg3f4ie?gm|Zvws8 zIO?&tTQT_KA)%zE{q{P}az7;@f~sevYF!tQ5JEZpzyh3(F3Jr8o&Z;%jzSc##8!qt zdM5=Ov6b5_SX*9xf7e{}45yZJT6qdNo(5eJH9x@J>Su}%qVNlCNH#vbYz{{D0y;z8 zuVnJDkNMsGHirM}kc(1~f5@cd^D)M`yP-12TQh};hlKnoYfD;@7j_ltS6_znLmKt7 z-r1!f@p+A9m=uu~XzERIzs3#GoH4WcB+~Jl8!U+GTn?K^iZ)w%%e$;xi*H|IK^Tyc zy`|JE<<4;b7;J>@julWG$TMvh+$Q3PHpn}ODQB@S)uyIG!TFeIf3&o9*t7-Dr94HZ z!c5+t&ly@SH_63P96b)`gDHcdN$96rBCf}y%NNXpGbJU|wZ|8wNP4>jUq-@q(&X2y z15nJ67l!zKbg!aKeCH8nvLw@k9f06IgH;f)pEOH4{+=NqjhVNs1D>vsBsc1A-1JE?zsy2&GxT-{7JV9uKf*1|A+-etl zF*^xqi*7MG6_*B9>maInhJ19Nq(;tC*sG+144eoI zZtdLK18d{H1nFVGH7iwDNm3GSH`P7!vSV^}MFuv+g4l`PV;jt>jH9T*pbM#Dw~C#P z3fQ1rq)TF6_f{nvWAk-#*){?idki}ZbL>MHQq57*{O~X(A(KJj+8yytpIh~BFL2|A zp2f{ufAs|qd}xrHU3m;bj&eYkm5$4-wW*1!o5&E&S$t1lU8wXCErDQuD%h`;$WAD1 zh{SXje~>RnbYgRVye+Q*Zz`PO;Xs8g3(q7)VBZXCSx7ZpWx~`!N+x?0artS+;!hfV zWa=tBk5?OyY$OU%01?U#v-I3hkbH0N(Upw9e+1yuSEH?%SHgG#rldp^tETSXd@_I{V9SJTu7l zgL~@zeh!I171Ra~uEzHQ9gwZt9ws?MewdWYMHmoKV(v`-X|IW@eZD7JmyeF+IwpItqc_?It4PWhYzE#0%iICKnoiE#~%1NUH1G2Cjsbw?LffKhv^m5iZ z;9;u%kjC_CVl-;9FX~@h)XI@nJk721s0dlOXoS|_ zi}^sDk83O$g1omIzcMJQxIW9vdZkTZf0pOwYrh8D8~~(6d-$)NAtn4Au&nra+S;~V z!>Bfl%^s0jat@?qZ0?-)L`V6p$pPOU2lHf~3XwQQV zKJL27s2SxmifC#Ct$SN@W_OCsK`l!rCf?$D&r7k?Kg%g(SIiq!v_a}7K8&7we{B=9 zC`eDnCelTYVqz5#E-8M3rKS1v{09`3WL!k7cF##e2ZUnq&j%j0X9!G*xK&-xjPo`@ zo=R2Fv$L+lYUnlH&Ldumt46bEUgl<$t~+w^B%m!XXoMKvUpQcvEJN;s!--owR7;9P zBGQ)GUH4!=a%@=oGhz3G_eZ?Tf6qDJ^{8$uF(>QCILtalD!0$agt=TJzrJ<-qxf9m z>S1N>o(na0T_j@)KFEL&SZGf^nnF&9nuPTLwH6IQ-KeWSJ0cMu_);!bi6{$XYbZLh zTv^U;w3ly-M_BA*B%kx69l1$zNx+a0!kN^&gQxpX8BB@tMU>VcyHRYLF5gxV=4IV&pw z-v#D+_yf5>A&gU3i;Q{Sf9fa-6dI~&5C9cKB(UV4E`I49?#gY?*ku$w7y`J;VJ{zJ z40VyCP~Fo*(IE?Lr3QKrRfKY3AGF6Azt@FnM@Po?o|@K_O1}oL z2$b?m=g-zCD~a~;f6(Y^2E2b~jj+qpU|tqWTxbQaMXx;a_b+#Fc*&{wgEjVMj*xm_ zNDWzp7aB2T<%qm3JV`1BTGNHPRcIvmylyk>52CIJ;tBdvOd1He2z=KDK{ON3ZI4Mi zOAo?T2TKV0W}e;r8KLAs{Bt(bno#Mu-AS9-3??0rpWTy+e`B><<;X-|xl9x6T4(;f zAz;DMS4ww|p-7O!jqS#yc#k!csD+6_R7J&5!d|Ho;n9sV(^#F0ODi7#L zBJ%ykgo=hz>!fP}nk>F%vd`Z$I#o$h*vv(w-$j+0Rs<&N={IdN6L$V?plM+%Y<8qQ zKaGF#@0;S0f6>O4s&&Cj`&2y0uB?F^BfapAZl@Yt7xXna~?rL_Ghze3QH8EljGsxO zxIwAiwMueCi^Z2=$6{;zIC@l|(58RYpm9j9jO*p?6=ad!@7sRo^0tRC2od&6p4z@v zn%ulieXdmU&_jXnY%bae7}0{liA3ot`bi~M+rZPbRU~CmqNB<3aQYfoBj?Hb+T7|h z(i!u_f7fj0w4l8&?cJc`%?o?&4lZwNG{|z@mSGa9vs9k?%_L1ZEDi^VRcDYDAJ}D} z3-EouOulrCzh^Q;!VW$o@lr&?TLf(mj8`TyBaF&WxKdbU#L8RyqCP`+!wx1;_Wm>- z2|h-4zw|)SY~K#!q;d+Pj)^(m;+~tFGdKSL>rlb@huE)X5L~0>ZK-m&L`%IBK!DT> zp&?GA@de01O{0Wy5Vk{CfhYI0+RR| ze=)|I@f?w&MZ-RHZriGG#y5|NHu zWZySXAp{o2D<$vph%`vU^7U?uNKN-%T7Z5g3%9=A=c+U5Nz3QOzQf)iP zknFEOpM^LR!&E=A4s?b9gq-JTq$vR$e^glm4h^-)9*=>W-mnmdgz2lMdf}kO@KyK2 zj`NAHQ9n3-DOU7`v`e=$y3>u+H&WTpys5F8#TBmkXU{hHzW{p%cUpbmlqADX(z`(J zoE82uHFAi{u(sKWNK1Lf+xwL!K=-v>As14cfs6em&heu-Ar;I+*LH$|q@;Nee@+-H zb=hGgu=MfBo&RFR-mbRAUzbmOS$ zlZ>>AV`dB4C7hn<+0_^ zu|qS+bHw;i*3EZA!{Ru8aQBcem19YsxQNy%+RcZl|4AH3s!Wt=s5V_Dh+}~^BM|!&-exi~vG`!DkpwGrQgQlnvX2RS|9bOdU z-ui)SyS$|KDM&vaKQw)PG?%`k<`@i=WxM)*;)TeNvJr=iE%3Q1j!5I!M6gbZ z+-qikpR*?I*{)~64^rbZ&V@>qm%0ntT*R)tw-X#&@i_f>y9h1x4@a^x3?1-;p zD`G!m&o=|VKVGi|PXCfh^7g|TTrsedpqLsOU))1AF!%e(Tjm^xe|97$w`$hg?*FC` z8WZ_7eNv^oj%~+8)umVm=e1YN;ygUEq4~449?RE#(eAcT#4-$7#X?ooCp=R_8Y}`V zy3k3}ELa;zo^a8$muvc_`zD!Lawf*o$@hYti{okZ>ln1keI+u3qcsqoNj|{e#@PCT zj}?D<97z!+nG1@_f9u>~^h_~RB}*VS=(R(BFgV$k{SpRNn{5Ftx!LhzIZ9MKEUIVg zcIBBTK-L{&w1Zj7T7cn;Zds_Tor-%k9+1<5E9#@x2yX)744VlJT}Mt^#nMauxedN- zQvTs@u{8fgk}J)NmVoG{UQP-zp8+}!Duzfra{BB6o+|7qe_K&SpXV(>|ATaO{Ev(ASh1g@eQs10Psq%|&Z@t<0-B#L|KAjh(=rhHV8c;YVA zCYAy!3%s?XfAn(TX7W-Q*bgqVgW3m316DG=&dlTbTA3ho+}$jk%Ff^0_x)#s-9~1E ziUgT0U2i#Vt{Zf=fy_~%hi=!L)AUM-Ru3$2tP8QUQSq~=w?>)H4uvi&d>l}7K~fm- zREE7*(}kYz0zVQM#hANL3T);uH1Rb>hcit%!{Z{sf4=WHOI6qBghB8@my)OS9P!Vm zHU_0=O6|YdPt^4Mg6Qz1Ik94|RsA%Z7R0Fpjm=a67sE1-p=T z{Nuo0PMmjT#>ND((qSgGlL+eOm~%6;7}QLsM)ZHwf0s9Lal%O2(^ry$lX$8V{qe1y?`r!- z|I?<=^T8;I5I4#C`aNffvY#xE2QOkbnw*QlinbcTrlvF{Eh-rvOS>_b5o&)^;2JWR zv=vR)RVY?m)`fMh9}5rnN}rDgyen*JE`ou*d{LI5h5r0ypBEje(>njs-p{@jO1b#&p{EU;3PL@Tp5X{aJ$XX`I@SrFN|*5b*ImVTq}wTGvl z;_GGIH8AJcqqfyZlLq3SAX!R%oWubQ?ej~$)3Z(rjC$H}P0DKW&c&Pwr~>0UTn&=F zA_NQ)tBx1#m&WfnJ1>Yg9fK)Fo(q*xe;Obr`tpx>$!x{n!Oo2x`vaGdSa0H&f9~I^FFQ4?x^MJ0%HGpB9 zwpa1V@AXiA4#Fcr$p$)P9ZiQ`4au1>MQ$=n5k(wM~uG|K4bOTpP!O+J~fKu=1YRL^F?OZD<9QvH*i zw?tuwp!o`Kk>mmwGx;<0xZIX<>?#FiDk?mpP1RUxfvB+JyGI&Qvi{PHbo`%WEb%K3fPeXQHWPE~Hb2zckPfA^Cr`4eI^ z;q#n9cvw@oS-9!ouQejf=u&Cr3;{AG}0 zyKJ+{T+<85e(i-YPub%o;GK1|nmb+RgK=KHAwX^Vw}Fo&C>H-x>J{0brjz8LYmtd% zD|0raQgVgv`IN$#58(Sii9~ZEPee!`PR>z+F8NS_f_ZVX1KiL~^VGU$JdVgMj>MVw zx`!CSdXv&2jhV_WtJ4aIMdEJJ^10jhu^5YKzlE^exoyc{|Q{V5i?i z$ZN~0FEvEihe%0~eXa(*+pxJd>13-Ia6cb>Ks`%yfdFDXFJ zge@U@o=kBWwZ+<=c%LSFYmIZl^O7H@(Jl0LkSVgGUB(h(s zImmp$>U|GgQTub>t{Yw>?Qy+JgaDE6dh?5xk~cO81wgV0d!G;9%@jE?bQ7GN9Pl4vPa_vRyi2JP#-(KeGNpb+Yw z+Bsz;&xq)>7eez7|8T^y`M&F#Q5eOst|1ZTK`fhfHg0%rbRj)-Y(S%HQ6bXmp}1h( z>#d3vup%Sju>iA^k=TS#?=3IcKDHPU2b}orLEiVNWD!N4Kpo!RcU^CxaT6$0!98Oj z%GbyoCna=C@w$)8W`OJ`j{W7WR=foEeJ0#*$Z&KGk^dv0nptu1i^ePeynq#O`RL2Fg-p?l>-C#=117pfc|6BYzu#D4;f9Ij7)~uR8vlzm582 z4!SX8tnEK1HkW^6lO4{btl7Gqp!4VfIQ0zYLi~tkO_-fkfz#*9%>}m_8T}$HuCp8N zh(_;Bnx&cF-$oWkF2wyr{lz^%oVW<9X-ncte$-IL6;cvs^~>nUU=D{O=O8tQ?CTOL zQfNP2?y&z4d>2?h_t&dV8>Q&QHK1ES%_l|l%lqgDd!|Iq9b*EBMv6>Owc;Uu`yD9A z%Yivo3sfN^z!=KRE&0g!9sj}M^Dx~EWBJ5iQcHbgtdg>d%}=nw=$f`Fm2=sDD2Gu{ zXO#-+a?`3+C$cQ-wehpG)g`s_8#WSH6y&LR~XT0vteaQYP}guVj*x7wy|3S2Yt%thxlSx zlOC4SWQ%0wi(KOuWPXWxx(uOx=x`*7z?txsu&QwRC&N*5^4g!`UA~5U)N409x}j!f z{nto-bvpOqT?GTd>Scbc2LQ5$lLkFwvSNXcT&`!_aTnBAM02DSA|$=?_l$7EyqWdL zz?>geqv}x+JaD;{PFJo)zM%9~ruaJqW#s^OIWDZ=Kz?ghhjcA$jyw<{MBJQ&WfxK`2j0WzwP=AAK++2(f964DWx zw*N+_Y$%WOh@drb#sCy7={-hTfm{Txuw;&Zui~!JmiKVAjqly*Vglc{PWsNN3S>r5 zsru&@V=O3}>7DALrf28`05nXVl}-fY$2hT$q+Q^2in8)QK|f<= z<{qXbmAvLmpQ_KSNs7Q&(WsiV4>gFLL~t(D!5+Ba$r%nslL7S|niyl1PYN;df>~lZ zuR|hGDuOc>SlOn&>scnJt@J|B^Tuu**msH^dg|yXP#I=AZ;2B%p`JJ1^+)L1I=X+- zVVK3VZ5O9l=APDgNIlZ@&+&sHoBfuN_E6~;i?Dvwy|l1>%&vEE9s=g+>qRDh@bN-oo{>CJ3#f$9 z)N?6%MG3h#kNCO3RNsG1(^{e~UTpHieOg32=X_)*WnLQ*IHm~Tntj;p5h*!fHlg-^ z5tcFiScsesLKx@A_gBM#82KoUc{tVYwwzq8FaI94Q{W|?^AeIzGKphwnCTR4QgIlL+uWC@2;mt*5W4Hh3phW_B&!$MQ);t2NF3B zm>pKGc`HRlk@lf2c|A;;l}xI9|Db0;C%iB8xCvmBx~@2UDKlM-%I0c@EZwrTl}S38 zv@CmQI1a{&{D=w_%T$VUWXt?8+S(?gWW`-Yq2D455l-#kZKoLXa}K(930`pQ*&SJJ zc!ec~!(azRS7ItBxQU=S?_0lb5HUF1de90%W@5G{A{r9Ct%_FMArcBMn%;`ir3&a4 z?f|42W=>fnzz{asTfmqVWIA%zBCDRH@#*Nzs}j8v!EL#}0u8H{0ex7acukZu_1Sy?u= zJ@VFu=ZH2IT&S|s6J>~qRz22BMr`-4KM03qMc;!iJq!*0V7*omh@mrQ zDZjt>;H#?zNL`>OsA8_&dSud7NaH+I&+GQ% zC|My0ye7tH9c`HZYN1|Egaa(iXad59N{}a080NVoN-&u{3uD2K^)!t-S~^Cc91Bp( zpE3;*J1$@6)x$VM81Ap}k!t#|Wgy$X2Ch^+kkX8v_9d{Ny3su@MJA5#lcJnO^5sBE z0%@cj!tq8W@TZjfcB0;JXua6&!^`GZH=(#!{6oM^=sH=hTwZ?}zWGPY)dDJzq~AMB z!=;59^C}axy{f4=YV)`Kn`f$-`a$HUZ6ZD{r(VO`x&LfXg^*um-i@l@{sphz{oK6o z;Tb|Nty#7WE-1xqLp@ufL^h-xT~WY|J>vF}&w0ali$hV*ef`LqVA0-D|Gmkf-)liF zfXH6mO@?ke=m!!Oh=$~5ZUI2s!-ROKsQcZ%uYYR`eS6kfpjS_}?G}u15Zt?u*F&fo zkeJo?bw5{iLfSD22|7esvRH|$7p{#}j?TD#5qF%%gTXzGT+-0~>ITAHZg1)9f_S;F zLYwn5-m?|`st+GUDznquGtJWILPXjKgbV%$X=g-9j|}2p_*6(VsVjgsS6ABmHhe?o zr!RkjzhLCP5q6knq}n({z5{8+&;(Qv(+z(v*F3kh2Ez~dY$QuUKJ2_St-Obh-JBro zbS`3t5)8F?*BDlOuy;vycW zJRiH*;tDt@>Lap|=D^Vg| znXwU=0Q>i5>BHSn&&jcDBot8xHLzwOX+_6Zz^$QVG!IQTWgde`dg9eQBbS!CoydNh zyN5FSqKmPP=BLhs=g|kdifl>p1e6PgS*tH`2Lgx(GWLHAnfM`gabi+X?^G9~2CwpS97O_w7^-ru$ z_s|JcGKOUsw>PI_3Z65LDcH-)A$l+EY%TDCFstd)H^QhyM~)!hr=b zi>DY@^<3GG%XVt|@k?v|xZBLoq{dk>yi6dF;0CHv8}4xVpd9hwI@H;84}xL$4nFMS zCzJ;I>--1PHDsqGdUXf9%*%S4{kgocFbP<+#=rc70`tkGEazo~f5DcC+G>!+rKW}1!9*!}aLP)=P2aEK2Fy5JSBz9H?i&j8uV9zjcnAv%{1S6}aE9tgw~DN@PTfCGg{OyoVlcLKJDVsJKUN(ePqfpUs` zPXbg_-4@!MuJdNo4}Uuh6@yr5(6W3e#9wxXXYh(zkDMHzKvk$ZpSALFMaZ#T5A@v6 z`I)=snuQG4#(S94DjDbOiR8NRyb~}p=ef;AJ!Y)(RyE5rSnN+KU&M)k2)K3yOlAP! zzjvT_eyeq%URMDz>!^thqCrYj|)oMr|s|cvcuLzG>r8ao&Tl2gV zCw72AusixA^o~fyNV^?7j#Zl469yUwKdvW^m?yys?6{YuebTeOd|!KYd@OP-@&NO^ zg6TWKrzQuOaFemhGx)U=7OKa!D1Fl7?YQH5)~kY#NFI!}E7KhWVaNO%I-{imFQ~%c z*rxOXC)*%-6K7g3B?PrZRxY$Xmar~6Nk5-O9QB+|=wyZZ1uWxCFZHC@7Hs(z91#a6 za-zpC8SEH+9z>j=4~yze7!Hf)od70x&9YIaIrT$Ky7-x%tpiWQzt1t?eh8b^DN_i6 zjA$lmGP+$b%hYT0cX{gR5X+_BngoffeSf2AHUaU;E?iVLOXuxFcZEm|YML5`>o+yn zwK?SJnAvc77xl!b##zIiEJi5U9haWuHX`DID=W~PeEN5xHUN8=(}!>o z4x%d!X(xv%@h#k|N~>)S@Kt=VrLk(*44Voo!}raO@7Emg8yMRud77h+-`UJzqR)&> zhVF9|e{?*>ef@*+WT)uL!w8TBg?v@qaQ%d@TmQL?u>G z8m2w2Dba4$c_%={nCFLt=K~Jkqu(4zyOL~>)`ENN#)Hd;{KZJ+$6K^pw)dX08O^pO z@*8wzclWb+pjeA>G2YUcV7txlK$^!~mzfU=F}5ckH*NOQ|Isg+_rKcFvp>dHe|!u9 zjS5Y|V~2oicl5%I=UBZ)t`HRs)un+t<3C-#E&5jbW?S(cxpUtLj<$V1z0YS#wYI`TRP%nMR*1+Nk$dV7Sk-8LJLZpx|dn&Ue2Di4ax+TU3z z-@(+IdfMMHTtO}*W7`^=+`&~9cR%zjRXE@e$^B`# zZ{PxJ;w{Bq9UtVK&4B(=+apH@{puJW8QmwJxw{LKALvp%QULbYv5KyKQ0YEa4`p4< z7Z+B&e_e!x^$H(SH@W}7$1m1nMG{Ces$|lrCj2c-)>Z-uuuM&Z>z&sr!y>QWWf(_O z9b)?E9e3EcOepo&ioUi*)Cc#gqpZSamIO_6IQ%&)H5ipcmIvo=;B4U3_$cS#^jCX) z6CL9ry>pamQUFttV@dS}4AU=VQ$ZS@Y7q~rTmln|=6Ke|GD}q=M2Jo^45aMQS%^tE zIx)qc`|MUCp)^5f`&9xfb1qBSs673}isw&AMr4@zWwnXppwfgCvg~Oe2L{Tf>4TLY zI;Kjt>rN(xl5zT(t!EQL(=Pl7@kv-D5$V0*#}36MO#*-5sN*taRrRprMYYMl0INhEPkeR?wE zcsh(2dS^q8wI=S_bjkrww!rdK2CX(>5^ePPI9`#iV4%uu1I15F6`gW1tASY1gK+vQ+}xC*CCF4Sq&h z5m=r8vMl2w^l;lla(F;ONgnLmx?!3sk|_1D(&^tvSY_V6R$75VjqQ64$Ug$_D50`Av%}e_jnQ`vM;eW#3_ew znZm_nK>_c~REEVu<1`m#Ln$6$p}B+3T0%()mcc?OHD?t?^i}rOE*Fi%FP9irA819P zHs%!%0$55yqnfvxPO`)px)10VLh3SCP^eAuj3pAl0`cJx&LQbz(RG`pWh}{K@ZSOz zLEYKoVS-wNG#9#pDB9-HO+!V|AUVeqb)qW5%vUYImc;l<5K>aZw;^>fVboD( zCW0vJ>MYZ%A?FY|p_pfAGH*Z!7L#GTCC5920npMs#6_a3q4jN{5Xr=FP{JbX!Y#;G z_`C38<>JWAk-}iQNu^YiFbWXZ?D@i21~dr6q@{85^kCV4AVbFYV7gHDbb`R_N$*Kq zNhdJ_Gx=dE&IjgWEN~~;l4~%6kgL`^1FJ#ju$ItJHMi!M*qKQQ+rz?kf`y9TehG;p^I{46XNk zJCVng-JE!ZL)diwl}si|f{1^DXVrfEjkKZ$co0^LiPVL^AjVfUa0j3n$MxWP0OrNTxB`vZQA_kTD&HFz&y>IW+ z{j(?_ESiD*IgKv*srI2i@0|Uin$LF)IDsby=z32@wiF97tP@n1luC>#{8{nIM_0TG zCzwldMqIq~HhLY^dOh4`?-SHHo8}U-ug@@OaGl9OpnEFiVlswB`j{3Bka3M1!1&ia zb>M~GN`f=LPPJsqVrx(3je~CSEX@gSgz*4{SFwMr1|!Ey<)`rtFCNv%iJoU;`xO*2 zoAFpIQR$JC?aRwuV8Qk_c`VUjBIpjVoPwT?8M10WkcbK*S1#Nn^({AJLIU^3a%VLH z1PAlSw8Z@Z2*F`!l!`{%5P!}VK)JCrHRBLs`Sl~T;P|e!vq-W;Z}eI5CEy+dnvm$4 z^(!~+mA>lHuFC)GS|E(oYLi)9I(KIDARz=}xezP-uYg8uY&fpVO}_2AGKaqrhxh^s z>AruPD2IFG*|Wx?FLvg;1*C5!@()KAgNVvQMC?>q5pK?5~=t6mxb7(-``b zJZMimR+mbyGh~*Vl9y-ddNcWk7Ep@1zIm>p;jz>0Dp;Q{I4|#cl0Yt zOf!$P0D^v}Y5kdT$yd4_@?@QmALdV04-;xrU+T=e-7ZPq^snzB6;vnh2~R2g`&=z( zwFDrp*;q&09=T-k2rn_6ipDVdJjOyal0Lp-PoW;r-n;}BSgn8dofgkhY?3%}ewgd0 zu0Ze?f~#08H_*0a0`9ZzbZA#kt>h^t!W^O$qw0q>0f+LfLyBm47^U(JW8;5;rbOaL z9`EBFQQ*|h*?9_T+PTJV>rd~$5#Z)%k&Q-D%z56Z`6H>$UeX0B?{P2!k)RGo8pIeQ**M=Tpv>xlING|J_m?FfaW(tQ3aAlbn;)kEzcm zy;N(Z%n7DBb>a{KF68_w3-Fh=>;OFHs<25>hHs7$m4Qv*4yu*ekx3Nlu^Fvcnbjz+ z9WsC#;J(|Dp;r?k?DaG>!}gZ-f}9oL7r7*PM*_RTSV7u5k3Lr=38dk3pZRD}v%peD zh_`RfUG0SeXd`ze(C4YzgI7&oF;RJbL|D_KO$4ei8<8@i1JC^2;Lp}8{#)qDH z5$6;fWSBD|S&&f<`~nt{Y~)cZ`<&#iNV~fLND3Y*MAH)fyjRDD#5F_ff}+9OXST?; zJ;$$q&{ZJ?-qj0%TK0aOGYJo^%S}HidY>$YVt5kHy+kYLo9_^pE1s&Yf}{%X?a-Xo z`k%jn@BLrj&wasIm~zs1p&GGBHP+;32{KKBqrkbkggX)LguBToiP(z%fQvO7!3<@9 z`o+i#rR-NSwi27Yu!}yErLCMv?w5C6F`K7$AN>NlfQnFQfcs->>sz5mX7=ooUYNJp z692FnS8t}P7=U-`)IDM0fiQgX1Wy50SVztZ`Qe6Kl%EEta1-}!F*Uan`Ys1w9KU~+ z&-?3bej8YELTVk4>;7J90%hvSJh%WTo|-ETYe#wP3PxOqf)Tlh9fTar8;U%S6ydWc zzrfUmad##-X=U>s5IVX$byJN`0p6?mdMwLiT&dsJ<;I8kLrK_v9D~=;uZnqtJEm-0=7Xc;9}}7z-MPu}TicKWt#`m%#uqi8rJ> zRN9Md_vkB~X=XTequlN-FcYveJLr$O4s_<*)SS#t247#-a;zHv9&X9UUzHgCt9i{P}m`MtLY;BeVJa{bJ+@X?Q5a8ErhSqla1lL<~5v-a=8^dD+{WE<^l z>r<)a-_QC@QTa`>#V6$)mV!9-rSI}Ed9%dF*csm6-^9+oXnk?@Ukw1tgB^^2`n;Sk zzv3A48T`l@9tPPwpN-?~bN~jmIbVS_R(u2!-CKR|d=u>Ug8Kn($-c6Q7PUYE?->9q zA#9A3SD&A5Gi#A|R7M*~d+DP6uygT`SiaMb$Slk?RDKSb1=Vj6`6_bM#08oDujnLOscz!SSSqTGgNb#F2V~W@mp$G=#{|Gl2;MNv{!rG*U?rhw zMir67)t(w(>Frj?s%Q_JyFCxUO#Ob3n@DPF~5&kM4>lk5ZmVQI1 z@7P}RZSe{02%Q6bDrlxGP-MAb)93vkj=9n;lr+R-ir)cb3_h6z8% zQ;w-K-uK+X-(CNWuf;y}*_#N1Y1>C@v7G_6R1i}gjwu81k4TUCsm)`+A%CTZp#UP% z#A8tDT{#l47H!bVa<{0-11n<({W{=VuThI}wZG;wgfyjI{A zPvdhC>19F-)bH+_3XXuezoxE_YPefXf9bDdcV+s0({PDj+1wwz-GDk{T_u3Nbq`z@ zd_FAKf2#p(?t(!4QRm)-g{Qx-E097n!ZSVge|DGjxi4lYUVL`B!xFje`TpGdWRNrZ zbs^^jhoswl^wfOAIPr5K?Nm;yKCZ_ekLa;)qEM;0L-Xv~wWDEyfR%bnMTSv5d9XqG z?3%FlrlhhVIaNiDs=(GAw)l!eyXEwv#4V!M6@#1l_ZH~b$H1yiZ_jznF{h?Nv{BJ| z_M@0l8y{k;CB^iW?ba7m81|Xk|6(f+mW(E8um~tF78VW;X0{BWe-P{c8KyE|DcmgV z%*4#ZPNuf7{QR&?>ORgE#7s)2wrcJUuuO`?tStW*jInV3!)5;kV_dA<#Qy`v!ZZw& zHki@b>L?={gwS9}Sg;q_sjUM!ZT3l84Wqyn(n=SfZn`}8ciVNIk+(MO3fvNu zE?1?E3&9JQ60HU(O0>X(qDi5OFrX2W-F9)tW9Q+OVT0J_=%JR3Gi4J)RNz_1(WirR z@kHTB-G@<;VPcc1eH{JhaR0HTJy^SoJzy)KQK(pEQ%T!rT9ESa$Sl0~+rgb#wArRS zIR0IFTf$(G5yFh~AWJj^4J4F6!XXKMg@=q(3|&Z+jR^w#D)eRNfd z9Lo4=h)+Db&I@vtVs%#)X#TZTsZUoo>2vkPrTN8>-Y&E7*H-M)L)6Csa5nvVGH(Qw z_#qVLibH)6aveO#Xida={rdpa^N#6B-xtz+Rq9iynqN5W`JYCr|L}CVKaCdR;TG81 zqq}97(oIUdBH}=^e-pC2;E#Ew3lFFz2M0iRFM9V`5_Aqy-Jp<5tfHfY1Zx35<{&p5w({zI6ZpOw38E{}w${cFg{4QIY9^QkT zp1hZN^O^&@0m(hup9qbAHU5B{u=D7x*1N40feLH+@7aQr?JZP?>7@8I9D)uiM zSgEbMnrg{eV;slYO%Sv@{aN*Cg!}0~eN3aCRTGoM%3~rqxrFP|5Fa0wqtaAr;dP#W zTIX_3UyP}@^+~&=w@U0OxA!yt$~9phQeul~%^>@Wi}8Kum%9IwKYIk{!yuwN2I_!8 z+fS@DpLtBCW!5vs=w~|0O|W^Ir_rLRArhnY3tN-Lh|xYH94@xQa*A@Za!PWt2onGQw;=vI z=)d8|&ivo-BUtECN>f1|-OF;*0Y~qIg>I%UB+iMhEv_xzWsGT##tUo9BWao&K1X*C zT^LT5M8&I;r-o;MiNaKeg!=-)MSTfy`g@qibCToc#%5_LHAtTsAyg(ws~AZog9tja z03<6T{xP!%q_7ahR9^&=SPa2*N-N1gz3rn47|bgJdjH5PsVRyG!p|+ffKi9G>Yeun zoY_!&wSc8r6+&+h$Y}?z++rS^Aj%e^PwwI)b?HfkbUn^k8xp8@dJt6BhSGL|a45qu zZKk)omw}#d2@+QIz%$I9KG`VuQWC2Eg4EjV^HcL#cIXoH@$(lyLa_FTiJYY0ecAr1Rg&NNNvGnQ{V~5GYj%y{BYSWi*CLB{UC>Xf;9L1o z^)NLg+P>h1v;&}1@OkN%i@r2Bry|QiTgx36?Gt~ZC=b$zqL-$>Z|q36e-Fqb`0=qS t0t;*5Xzu3jYGLB=pVfaJS2uSPS9fn$3rkoQ9u`(EW>^Xe2_;F`{{tO%SoHt^ delta 75630 zcmZsCV{j!vw{7fXVo#EZGqFx=+qP}<#I|kQp4c`fwr#(;_o3?5cdNR(yQ=?nZ}nPx zb+5xmHNjGl$qS3pGSacak)e5-||j8Ct?|bHmX~o7kE;n-ejzG5``4`lx{F z8g}~tWZ#+ESt-!YX!WfTOkeR>L`?`EO4Ns6c<6t{Wf4|Y^(Q#Kd_sv`HSymRDv}%!)+ts;*f=Z!~*Udn1dwpGe ztWJ*KPY27d8p;Pafta155ZxoKJ3^UTWw1q-POd9QhSa{ zqvIOw^z@Og!{$&cVps?sYg2A!#^$mUM)xIfk$ z+v=U?F$MVs0hEt1-w=k4UFyK8lpnSZk0;SpjUp&#_iiGOePX0<5&52Vhr9;j_A{Ss z^kvrZ46wBV@+4%+LWvT}7$SkDd!{x;&-?y;$D|y!Q^= z7}QcyZcgbo%LK!Qyjqhf8d&x%lb=JM`&I6?tTUV&SeYJ}kYqzJ%$LBA`y$AYGC&qG zP63L+5sx{H9qAnZ~S%(S>PY`1sgB~#@T4{yvA+xN4r4*v@u zE2?QTWFYaQVOAr*`8Tjy=*I8XVDoTDseW?(ulF?3(ae1bQlo`R)zci@QcD=b>>=;j zTT&k_TVaSz`g?jReKU&tf>_rjT?2bpL3X|4TF_cj zs1^3j?_84~hfJA2Du$oqHT4zvTW_ObBUYG}o*sB1{2a2Lluv=52xQ`}#MQ4YxiS+R ze#=koP%{-+P(!$v`{Ox*?gkl|Sj|uXiqirj9^*4U^#V|qu^yjUax^usD zyQ2_)4!zpyTN(gw+ZK`UV;(y>=~FAHvloLT5H>@j!x=az3tezjtdWm-Zj7${0VXkS z^dXh}Me737orckU6z8U4a+{MvBV}Q3rd(nR0PzE6TNYze2G!ZLpF5qFQ_dXz)iMV3 zL{XcV29f3=E#_1MtJ`DVt%2KFqk+~ELV~&AMsO1H8?eC3nxK{=@g{{n{{crz{!nAX@3bB>Uwel5Q{uIltE$#HSooKp`S9=a=?C2QKF(xXs#^=d7?a5yNfEM^n1v|g&ixTw2S_CnK#nO?vQ?)!4dpC3Y2jigvWTCX#tiTsRJ?u zew5M)hcvK~$Sq%#Ybn6Ur=0|~k%WYi%l;(r)Q%dXo-xA@fEX(8HQC6lM9Wib48~~) zMSsyPHxs^TNkK|h(nHn1(V=!pgrDrKYw=wyi7Xd9ge+jJT()EikQw_?4 z1!g)FdM=oRB*a+)cBvzsioM^|UbErEwV9V?`T~d`=(fUK-P)#uq>$EIPXI{yn@<^A ze;)*ZjeQa9_O#<@Yd@)7*LG(2M4s+Hnydns$z_V^@MwI(L;fTi_DBF^3Q+Xz-7Jk(@%*Y=BxrjKH+M9c3g z;NT3qc^fIa!$MhcNrvtg9 zJXtiPaS9-2#aYIa)CYD7V>H1xUsaovzafF5j7EUEr+fF=d!^so7c5rb*Y$?hIJ6KxWNh<5qnr5)RohPfQIYueQ^&3i?$&!BkowR5|HlvTH%@uzpTJ+dDsSu2KD31x=q!6@F zj(Gt(kL7I3oMe_6-mXTz@Kg;pnkbX~99J#*Guclg;SAyg+%zz@>h*W%>{`{{xUSjL zY!1Cow0ErbmDVc{FX>Jz6#M}|R&ygcq0i>nuc)-a^Onf>Z$0L2oqp)@aI?5%kepi{ z6@_g)N(fp>A=yYSPOpN7}*mElf!@9uELIwU+A#zw zAQ=DUFUnQ~OBvA|PNufGL~_9u9LUs(CnHMNV*QPyMU@iER9!%v8>E5qv)>sED{KJS z6v3#Zl9PGZrSG+5prfuT^$9E$i^$q_O575zLUp?-%#^cP;#=X9B2wpi-MSmiDgx7H z->Y%$Q7pDOq}tT`g-Eos#+84q{Hl||C@R!;dbs7`e5P_ebXmwwSHf+Pxn$eV^ORr& z^fsesu4UrV^8p$Ulyv_;ZJdSSe<*$!*%OC*@axe<;K0ckFN)kG=af5Sb2-9p4eV0^MPOE=Bchao~D;3m{5fW&^)nt~Q z62OBu_9xzF>W;XTwliyH_jb$H`Z~ym{fNlE;MP73y89KKJ!QCEB>!~N7_2;cdQoKP zVzOTEoXN6a!0GAL)_w)Jk;@l$?{mmE0yUNPOYFy_{?wQh?9=_AMw^S9Ap}5kgvdwM zBWi(dF1Lx^)X*2pkhNWiAi`BBq4(-rw3j7?-tO0+U<`+vXpr0$bc-Fcg%Yu&+iCs; zSCu8}e+Q@bQohQd+(4Gsgu6*SFwF%MGYjun# zQ5G2qwL#LCdwhlHda8(?9B2t`f>8mhpZs_F)7<~bO9+H#zBoREasDQ%h95Z&4YkBy z$G#L?{X%wVMn%i$ctn&NHJh@KAqF-&;k!7dAW<80+;?w8>}zE2^y2I^8fBO+SlsCA zGL7J3=M&Ad3}Eq)bvs%*gOJ9PYA+#}v}Hz$f3Um=sLEsu^^LIf1?C$-L;iVmQhSnMvSSk1{hf(C`%QK3As|N z>5P@uQ-3MRGx~{MUI<$;3mthdX1|jwG@t9gzn8iJXDH%_UVYrs>P8mLBSS^cj2)*( z;Le|9(ldG0<+vzifpLX|&GN@X#u=^Blb2&J4ti-cldJ00^Zs47;8k-zO;AFrj=`gA zeoZg;29k$0jPCP1Di~@a@jv+ocO$!bJ4%x;qi&DX%=RF_pRAdl>D|{LEY+3%GmKpBZpO9&25`uEln@W&Uxy_fOlyT^4 z65q0+?*`{3*hcst;u!1y5XV@UIR5u1&dP2bfc}}IXMlixgo#9QW}tD(H2HJ6Mr*cM zCqQ33P%s5sD~;5X_>lDTaerSCpmLO7!tei!Us~bd@Xv9Mm-sjyt=QJdV-9o=z1%aB zZtxe37v(J~H|HNznIF4r&gfpScY<@tv2?@dhC&_+^tqQ}>;%kPMOid58GR+7`rm@Ys0gRJ{OR?FNc?n6ARnHZtv{;3Tfuhj*iJKWVsL4HuDW+ z(yc>r1>|)Xf*Ks|tdUi#d&olylu^`$d?$>qA1E16%*+ARD;7$OsntXRyAQfj*d%;0 zlW|R;xmu=KA3Gvj!TfjycX7wSU8%Y7_yGOw9}NAzG`Ng+3F$5O9jkF2Kg#_UNGWVm zY(y+;a=X{#q85%i!>J**?-iIpq8nTSeh(l(6U`xS0a!aJk{=|$a~|yDqQXFAh3edp z0n$siR~Zn_8kyCT3FU%joR||k^#rs8e;XFTE0lMr^fucJGKVOo6QCV{kyBx>fK7@- zp>+LChazCilxAsru>y9pS9Q@3D?%vYZe33`(Uu&>W$SK}t zP%_nVomA5&_LP4?eY?cuS=hrBb|78nvamKtzcau_G`nrvb(lk_Z9{4#l$x`wgR9Tx zn(@|ZhSXD|T&ieKSsD9*tLPSgtS6e*4D?*F>~y???y$#4ct5YEMGo@W!$OJ#t=j#4 zI7=F`Ecf!*7aOU6zMWoIpFF$B3Ai+7Hvar<4JDY7JL>rW6&f-$tkkbTz?cM>33?bE zyK}07DFn_a?M8S5u6nIX)}^h9rFjPyp^5$XD6_ueEd}m2f;1L^Ss7gxfj4dFoe+NI zE9kf4KZK>pL7#5E$z^Qho>S*PdLCp?5O;Tbn`5Ha#81;1ou4TQA4uH3rSSH0ctyy+r z*6Z#8O1@eiZB%5-9U`h4HkBk1>PllaA#V8`<*ht%pdNFxxs zb9MRP1=3MAsS2q%ZN6rU*6trgJAXl_T4HU|K4+%=gZ-=CI`#p=VT@tRW2bhhu<%0| zcf1NixRiUrKVCit@STKGDTaeGhMqds9X|#FZ**Y~1nsd`2n1@^eX9kC*FIMhGLB*Hja%Q z67fC49y2dTkR1)QH+E*<5T9%Lg668m#DwbKfI=H=&(o%LaBzB6l;cZFC@8@u82ku` zQxYoz1{z2a1Y91Oe>LkT-aXM8Zf?_VT_Md=C()x+xJa}|j$m!emlfsc$&yx+Z!aPq z292|Q?M3I2O6@H(GvGu@CAS5i1ILS&3S($v=yRR~+(N-(>)mDq*6}?ZiDhrj#e9R> z?q7`3bG#h}bAbk4j=h`5ZJP^iRo+UUdbAgev_2hk3mVs|sN>YZAM+tRtLZk7Z;#H` ze11sP=KmSXSsCL|&=Li_sezknT6PNz=)TvrH%8=P=SEyH(Ja4)vG<6J!ifp6e`sX3 z%w-s}_}|_;IA%@!H8wIAs!JtUfAyx@ewEE+Y9Nm4%Be$ve@a9lBG2o$Cr&StwqlZ_ z*d|{TAND{zp}j2Bq1e`BLt^kr1ml>dDD|3Mz&z`W^QAwUvu5H^$N+*AhTsr2lFen{ z=7+(sA8IGA1$f`;9%;nW>|OfL6yJ`!L`6=rB%Xd~ToPwaW%(Bpo)YY(mu?)6M>p%N$8}tjcKZ;uvv9 z0@~UqBa5VIyxOKxx%6qyJ(A7V>(v@tOte7{Aq4X@@k&vqu+hrmZ8iA7`1||}cy#O+ zhfZ_Ad>*czH-3!zQ_Cc)LR1kH9gJ>?6-~J5oSJQ~j@RZJ$OD7(wV~V{RI#Q#R^&Q$ z#rQJFPzQorC)qMT#-aM|DW`hOOcX2vLJ1aCy*4yE^WC)+f9>2{F7iT$22s z%TM<5I5;@FU6tG&SoC5m%kSQ+Jh^%5F`icg;~M0NRu$riryKAU(U`J0D%^t$aFHQ| zrb(;cW(`%5(155QzmpJ+7=JA(u0t(`Q3O)0l|({0FdmTPsiGq8ML}BA;4Jz1A}ylN z_7dC3jK>dV<88(kn^Q`J)(;GbCZybW?YdHRsb&Zd<{qizT(AF)QS1<4KqVVW2;QC zk@@gsj=!i&zsD0{7c>p6pZHA%xaJ+@T`@JbzK}!N008_;Hp2LD@NUzFOY)VsX3ai9 zgh&YPXFn$N1l({luOR7RXr{la9E|h`HwlCFpJkq~kR%?l{?iLsn1~W}n~4*p-N z`?nu9?7Ux>mUq9RNrq0O`f^#{w-y|JirrN|?4MuW_5}xieLgLqc=LAe?!$k4kNxos z^tbPFdwn^437D9#vI4%vEAnh@P7Mj&GYmVpH7)cWlZ;APbyunaVqJrrjT|D7;wM+!*&!u5jE10Ak`2$~as zYROJE4;J8vh&Imp#6Et&T!O91K2a3VC95X4hjw#8;jPIZKW!k&IYPI`Ysn>5*^;7Fzz+Uc%@m0AcXW7hT4k}$3uRUx4V(R(2L(`z7lt{b7 zu$o0$^D4KGTpJjI?xMfwi14kWqD#)}$A`)8sX2OL(Z81uzZNOJ?je0kEKmBgv`WL+ zzi||Ty;K{DDP-rJ9iB-Ks$t|O5wFe8jRk07KD>YdC||Gk9~kA|hXhWT8ap&hpwm>T z{?hHdgW5eX2Rwyj$Jm{)wK2u{6Z|HW-Ocxl0`3t%&aZ&Z@7Nef9o~6RJDY)^JF43o zYmVjvtr6)+-X8u@s7!Bjag`wVk7D8??XqQ2;NH9>9DIBe`)9HHpO>9{*I$2=p->AGzg1@Sz86>bh)SlF# zCih^nf%{6L`k2^iDFFqY;Qjgh7$Jg;*kmsi4Cp}1v7{jEj;{SYmMwhGg(iN;F$iUy z*6}ems8Q2+17tzQ*%!;pG&Ya&+jT}U;@F&5@iZb?TqsY}hz9+SN#wL&yuS$@#P7-} zgJR=@iLw$7i|2gIeYDu2sN&M#zMXR^NEiVcW|p2TXRz!_$&vWsF>=ym`((pA%N}JV zX~jSe!j+T&R&(W!tXPd$MiZ(vVS0|3Q6H|73L0T+dveLxD!j?=u+>?`MyDmzaI%r? zyi%%UD}bx0A81z$lZ^iJdsqW0iwQ{$K=f)^7g4!4@=4oT!_xK7Qb)<4F0t0Qwvcx} z-HHpMg0b+WvCRhi!Hv}%`oR?i^-HGJyTX2T>+(OR*CXarbd%9vn(3h{nT2l zWtLLN6x%Oz4cYCaJC0i!CHzO3ljXq$wo(h}^$W}$rhD=3jaPF_+|PFib|jp0Cq4vX9u zr!ApH-qh>}pJ_9v85cL?=OR^c&A$u0E5W@VPLa;ZWbc&`Z>3s@MvbY?Q?W&sttY3s zA+sN7W$xK86xX!?voDTyXI%5yAHMf99uu>k8}a2nh6ClakzR^VB0bG#Y86v_`KI9H zU+ps}??qIK&ZfDu7hw5U9Be?x1>Vzu$}DqEwek!f!BC4b!(2a-7GxZA7*8Uav%k+~ zV`vI_?ebhYKE=LgE#wSBI`WIklR4hqFAe$|O$~j;x}fJlU}5?DvxmrxtK23Vm5+C<}dv zUqgvHxV+f3nDj^14<|)&qU7C43A4c{^al0?mW4zZEX*o+B)keEhXpFja#FwX98XI` zPwRS>to(m~QShwDZfa!>hh+u-=kLlBEI9rZ?#$AFjuNdBT>gnTzPf?0mHpH!J}t!B zzyDtbO}t~n0Ru23`ljP1>U+Zjvvd+I#`bQ(rMz`f=zB(SjkE&mOxa z?RXG%jTJWRCL)xMFK9BL8fMzss|*4+8`EcANI{6aen1VJ(AB;3K7Nz~dpy1a(K;|3 z=UVh0lMo|6`p8s)OR*?S5;Sj{S_ zw1zwk^WnR;(RIkCJ{U=S;D5zXd}3SBvBb~q?r+~VQmArmZ8UHP~j*mIv_hna>mjlgWpj4;52 zjD;?sJ$o`(<`791uRf>WCmqJvY&hG73~ve93NaTJelF|)t0@(xB5x#3N+)1zlf02x zS0^z@&Pwh40Q-?!R{563Cra0+UkEDLG)ORDQtO8b;=n7Eo&FNOkT|4;4(AF z(XL9Dy2J!pcHZfF1MI?{tUM7FKwhNdh}4oM+PebEmIQ-Fh_=C}cuMwz6A*mP=~$n^ z4;Al=kBao2n$~{W#7rmW^AKKMvI(~@Km237Ej?!m$g)=s6}Q0rk>Tod^rL6Mc!knU zY|^$+4unIe2uhmRS}VL*n*r3ViRw|tsx(w%n2kVUGSWZ||5fZqy6UwK8@$gJo6eDk zy{kW7dvpu;&T~Z5N;djb%5RP6xuaM^1;Pi7YOBO8X@3L@f-Z#vQ`rPbrJo1KQ8b$jXGb;;(%mW8Qk5;lU+piR48dlR_E|DpREWSU;o4i#Kz&Yb` zhcW@8UQ2G;BpW9m&Dc>F$hO2|@>h&_g=rW)}mAh7qO*Mqs;q5b%ofMmDn$xfHE z_^VI5phun#gnISY3>q|`gnqgDprsYNmbDIOWYC;~JD?f5Nq%b0iA}E&Aj; zYQm`1lpF33K#O!KuONDA@<|(y*Iw1NF=uBwpNul2>mt$|!dWi-WG<u25i0sJdXjmK zAX<0?b3QX|A_d4F6ZjvZ!iO@XV_!h~WF|tDtQykmbx}f0bwUxzk?}zLjTqti^J?7P z7Hi&|x+vg63!=j-(`~MhC_S!fuQUTC94q1WZxc(5hwFp{ut}vfzze6im$D7XB_Z%A zw)AIw2Zx*0l*eCMs2*bAoPQxI#E4wV{}g?_dsP?yW>~o28+0 zAte0Zi9b!!zfY6y*(b5mM+P~s_yDpysA}==cfUMpwV1% z4oVNkyc=BWyV81$>0wvKi9#n(8nU^L`lK>mQC^=sVoc=myJ-y5ebS8xFaDu#L=!UB zMM!@B1FJriB^5-;HmcF8;MU0xzV8rBX-Qcl&zRqPd;LSHB^!pz3Jd)rRwgEgV5%tq zuZ2~}LlOd>ZTi<`Xu0d@NOYjy+v~Pu+a$#oA+hoksFpo{J#WP-#ziBJ&l@6c=uGpk z7U{<2mP)ZO66{&rt1vezq$bf*Rvu->4|4<09td%W>Z!rfh_$1VW%3@2*GM?6qdBi^ z4h0T6yCwvU$uVoyR|@jw$l@<^D?Wy>feF`e_`T%^=0>LJXrjfINxPz%v7aOCN%^=fkyAU zG=41p=UBP;2_Yzl0Sd^p>!A)(DS+4SDZqUm48AJ-#5^z)m8e0NIfJmGAe1eH^j3!dRajJ;VMcwym%EfcMxaN@QTOEcSN85l6Oncz$#aM2IZk*9Vg zZl%gqQsaQckOg2Rp8Ak3^N5J*+Sx~!i;|5`tWvd6Z$ze2l3QoezZNMVRH4^4+-CkN z?HsmFlf6b^-SbHIpk=GSYHyZ-{MgdZuwOo1PB~_{jBuW8JD0Z3|-+R?F(! zZJ1BbedZ8~q6UP;&1If5qjIW|SxrVa4Ld)r8{!CfKsTXWgb-OzOnT}#TJA9A6WV0I zZ-qkZCD8BR45cBXBjXTeMd4dCG}=>q{{eHA!;hV~T($nkYqNu=bLh&%WcKyAvcUTE zO=s_FvvbdOD6Qde0${D)(k1<7?<6sHL_0*5Nzqvmxdm*u-_0(tRGU1Vm$Th`D|%p= zNN=@XE5ZtkUlRaz4jD zFK1Y;k|QJwQ1FOA48o#8%JjwyH`c8-8`%kPpq-V_($^F=|m|MnqGCTTVIJm`8iq1T7l| zF)k~hNO~zbx``5N+EH(B$=*Rgtzme@`($sL9b3vjK=;yhy^t79`Xud7g|E+VbNIYv zKLBme2)DDB1QaEVGfG{@%b`6VJGN%+|ESfDx3L4F($j*AhrW=vkI{52V_0Gwi!|XE zaV;0|$50<2G_4E2sKo9Dk$%wofyv~z$g7pnBTypHFreeY%LEGqOXj!t?!nu^vVAZ9 z1|~=z_PFYQ4adIfSO)o&l$vj%~L%y^bQQ_o~b>^%NKgr5V@9piV9p&v53XwDhz;3X6z^H~Ac=JiEFijjloG zX5KQr9C|BDr%;DMW26pnKiO(8r!6I4M~(7 zfB6$9l%eCH&2+##PGlagESLPzu?G@xa?N0M(IOH%U#XmT#{_2hN!rD*({-0Ra)r5IHT4eHXmfB=LJrtOL5bWU1G=KweOXd{w)v^Y!^b8UXCxUH_%t ztdF(=xvQmbI^seG>d(pJ19E~MY0;!&L8vL#bI|wIRV>wWAXEV~Gpc~BJgs9jhG~rV zQyj}snzRO`My4JP}pH4vS*727AyQ{_Oa38}bu~uxYo{A4QN`NXM2f7oopQIrI z8FD6bqgqz7Z0w35_S0o?I04umf=h%x5ap?(kA7BFxF-QPrjP&o5%b4RN6Cr{_Oxkx zArrcC?p#eGUShhaj8sk0S#k0PLau1!H2kiOdoCyKVbs~oQ@Mkhhm(h#=NG+!h;eu$ zX~m!l>K|fLodEiLvc9!HOBJoKl(2YsRr-Mu2Qpa5iT1w0xFXP~kKcCZ@+?1Ynqs-)_KeZy060{gdz7vIb z$en4bC#O7s$DI_k!B%e%<LLs5bpcr5laiGHT(6A9@O+CF(jpoq-i=Az;- z*A9qc;R?PLDvdiJKoFpOqdqIFlGD7!CQ3eC6E*zL4!yU7eaI8v% z{vw(`WwbsQ<)CD5on1B`jyuumlN0Wwp+<30<;6=5+m}y^Dfo+_ z04!X7qKqMj^)KK%s}_BBN=@6IjzkU1ivLO4wCv+MuJ?sRip;*$RV?(v%MRi2_v6q> z6ty+;`gn`d?IwL`d6vmpYR{=&O%he2{EF4dyAHHxLluZ6^w;`=Zx_N>=c7NtzTEJD zuRDBx1wZoGZfR<8MLM_mO7Ryh${Qc|`}gjUVm=gQPYCciAGM`{XK}pvs(o=kvBCgy zvNT7jDu;IkwcPGUQ?E#d2H2xI6*wL=)gt^2Y-(PzN$;<}Mhqg?eVT|qB(h0A#^lCX z?_}CRp~hbw1G8w48__q$DDHWbq4z@*g70Q1%M8?h5ytFcr3H)}#y7y$7=o+zBXWwA ze4gi{|IP#Ynb$XP$cx+VNStvD;OR3bbFggjQ~nWO{An_gkD@E4feXH_L2|3|W4q6B zG7gT)UoPG;{EN9s4ZM0A;T2+86ca@7OvFc+C!2Ku7&|DubwW>TYyuevijjdEt%4_2 zT86qlAX{(BBul70Sn5EhYf62f?vcw4CD}>pwqp1V0&)7`i^z4J?Rgz4>Te>swaPqccyW5hB`+tN_EJ@L0*2V zRCxk$!|0Dn4n;}Zw5ce?(^qMU)Lcge(Vy|QQI&|*q#xx&hwQJXbx>Y;AQF@dYYD4H8*eqY?|+^ zH4C;&1Cm~c3&pC2y61t5dq#U#k z&-*PD(&^9dz^;DS{B~}1$uis2OoJNdpI!5~ZPJ%k$`j?b#b?Euk}lEQgwwYZ@-j|- zS_U;)QjbuROUnZamV`^ve%?`Ji`zk9uk75?EsH+UMUn(b)ug65B^A7tFqw3Y*~%Qi zxv6tX?+VT7LeDUD9OoWgkl7gs7$SNc{%e000&&o_y0{Hv$Xhqn&)DS|9d=WG`ZS3z zWn%i*kl%=Fcxb*lF|@W_jc+Kv zVmp_P9~JnS>o*gCkIG*9`I}{!E~*>gy>ZtZOZYbB2zkaT3v4ZLIaSYYVCHR))gOrB z&WiJGJtQ}A8__#~`EgD5GRF8p?@ze!5SyyMUp(TzkJ|Nst^1Lft%v?X!S(g81Hm7N z{6YwZH-78=CovaG{dzDq;Wn#xfqL?z37ik1kJG;t!k6gA$DabSo8l&@*9{U#faNZ| zqrkk3+38W;n?W+-9^Fe4+V~Q0Kw3zmrz|m;H(?+IDgjm&{8EmJiF2 zS_~J2?Y3zi4O%OX{dtOg_fjNK3qb8H#cr#56Aj|6vs2rRhuk zqaJ6l4{57SV;|oeOs=ipn+j&%-RohKwjDy>vbzD8L}M4*sfGAr!qr1&pWqId$q1T( z&uWLrEflTkHG}koCIx9v>iBwnnY!n*-`dSR|0c4#gm2Y%?%B@&!yNm_LrL* zlZ);}z>_tE%S8{7)4T*T;+U zs`fF8dQ0z|IO40skU;YOCc6_`w;yEmHs79oGT?BOp3RePU2&5>%W^C6ZlEVb9(jzCnLEVv(JRuJ9 zhI?*_^$GJl$qwuCY<8t$c|FzLdRUGYbuVN)}Z!xVu#bl16O_w(ku}j#V*viD{(WGyEPceY z(p?#1c?}SOUFPbj<}5+>h5X=CfFS+6UJ%GfFc%gX3VAD$Xe<-lBv?>DkuLhdCk7oE zu@W*w1MZQ|E!_Dda5v!F2JGt+Im+^FKSp6n_)!Cn>c9EkDp*sB>$W;UkN+Byo4u;RBo+MGrtz2l{AG&!-1Mv!+;jG zbs3xX#PlpFTD|Kivo}IBN!%a!P-ifV6!O!uV%1Ql)81oU-UtIzIDjdpxNdju0aKn7 zXHs;c^K|9rdFaFTi8Buum{5Q!-7bnaFdufqc|QulKx?|2VrfS;ORRRKkv-B}r=>57 zf|e&hjyv8KQifqXiYhFSSTGYmZYXK(--s$M@XiiUW(E+kMn@Z~Q>TQwK@Y*GuWstnTdndP0fisVkVnl}ax4q~(AB-ejcFVt{uQRD-@s z9)LMf$1|u~WiCd0Q=N?~E+!XKe)2?eybS)Tm2Y@z>WFlNS(W#jKm3%2jWKTuS#EMf zx3X=as=vTtC%F{0_vqU~tX{RfbJnWj*G3In&uP%HWyq5bFyL3}3tX);g)xqU8$`g& z05ZpjubwH!a4-1)!;U%rVYF!F6Y_ubci{#a&ze=GGOb!<}kyflWy$F587>M zL#VA*;E<5jhg@r$q2Cl<`cOC9TUb6`-?_|XASW;}3Za-`uiyfbqYyqYG_fTfcbpLu zq_Wk&KQ3In2{?_M&je~icj=sE%f1hFr>`LpB;lg^GG97?>*MvLyQx5)PPD8;4MHSp zepjvGAAKV~YE9Eal3^T>){V!YJF?NHqnsS7reUUBe<@OulD8D?UM%g=x9~>Z{+W#3-#wjZY}=LMOR3Sb%b(|3xrpM| z)ptJ}BDKQ<5|?4@<8@TOo_(V}UkPPr9|529_OFsdHlo7H~F8 zZmNVI@1~+I!9XgJiC$^|VVfX=_PFe#=5+b#0gce%Ub_xqx!YzRROw8}v)w_V!z(}S zV6nhod{!9>w4eT3`3*&2J#I}XQb~Ne)J7VX9G*!4I}&B|j^o^6OimgiHo5C7+&LoH zqC7CtwPMS+SwUOV69xyo_dqXe41*TMM`$p+zQTkOY5v0U^Qsf2wE=XP*l&iOo(?QK z#Lb+=c60aLZ3yWI%o<_23HSXn?M8wjM{Kz{dEPEc!UpocXCR;M=N4x$tU?Y!2#-|wMPos#k=&RWA^3(+AcJy((PdIE87B|kT?;4LLR@##(3kw>17fZVyV z{Cm8T@0gT@*Gse`2KV$K>`xE#wY;VSZ>F4?uXOso&%>o6%wg=I^+WCmo=LR&TVn@h zE=op&dM=HjmJ=fvL pO&8h1_50t*LrvGfJ3d$9&#|chKmHBGJ1|1a4!;b0dn?cK zldXZJgR3~)Fc}-sK7c8dPX1K0LZNM6jO*UtUfsh2O)rmU<1!<^dOuESaTHh&-!12w+pLNBZsGA)!GjT=+zrI|yli0v*%k5ao zB)OxyBx=)mmBNTtro|45KeXK_67e3u%t`sBGq-|}ohP&*3OZwvPEdYuK$xma<)XeU zezCrdVZNGJ%bL1KU&m?4dQ(9OqwgXp*09IxZH3xU{gu>^y^~1zKHL)?B7a5pK-s_dD8iOlCI;0f)vCJ8l*zf^P^yZO|Mha6N~~c-q?85K?>*u(>JVaMQM_d$uew zBo**TR<+txG>BhzY3U!cp)uJhS7XE1FvQ+uQ|?Vc-;xRA8<{S5MYLa&4h>yg zxy*_4;a1B(`~^;chO6?QS(5Gl$t>b=;KA8A{7@M#(Qr6sDpGU2NwInweDX_7bbmTSTG_P1yov4g)jXO5Kk;A<` z2|%Um*_?Jy+7WOBZ;;3C?dA@0w~n=Nl#kfIzUEuJ79tp24!mm84LMfyuyEUK<9zw?}!9CGD~JoS*88}y5cZOYO*+Jy5gpwvBQ^U z@nD(HLGE1?kK2_xL^$l7$0n9wQ~Y^j2PL;qBtY%rKhy(>dnSS4%NYtJA1;BtO{N8> zpJl=_p~NVV(stio8MzHch@&&kARd1pFO;UoG#M-}fzN8fQ`G23Sr}SU1735_eU*15LJ4MpI-QErF zky4O;q^1}>r_<0Z8xKj}vwyoeufP>$qRM;9HdIIYl??5sllEZYW|;Jnok9onbWVb@ z5_CgEG_B3=1DHKu8>(agJS^bCF|jAOUa$7(1yT_ZCruDnv|OzFX%zgFIde#TdAYMo zWS+yz{$bm^amfw7=|ggFNfm3%6$+*^{nyOZpQvZ%(0`Y>mQe-h=UFCi2{=}N+|l}# zv1rj<6?Us*m~aW?Nm}>|#{{z%RnW=em3!;Xe1Uhkw)FfDZu38M^#d4L66O1T168&D zsqwIVj@4cu5toNoZ&|C|*P2w7{8 zee1@{1+xJHK?i+Oyv#SsZ$V&lzkawgV9n5;$Jh%)PT8m50znLwMZpk{I>}_u`qo7t zh7dWo^y2w+h=I)$9rn4uVrIKB2lQuTE*!-)^=uWZou3>9Fo)z3dBz;FHZ`4n=&q@% zRQWD>?4Hm?&I5S2FsW5GZ7vp!OwK(z+A38oT-FT^uOY!u$m1B_hu@9`jbtw2!sI6~ zIli(9D&JavM>+(FsT{L1zsgRLOE7qPkyrLSk1`S+W-EUmJae#NDhT-8%A7wCY`FZ$ zLnsh#!Fio7{0m*1X@}rQtl9R=yBlrvf!@2?27-1bWP&ta(sXNSJBe!i-f`2aoXOs6 z8_zZ4IecpI_9(xUiM4cp22{@oM7QHw_*r3@9n7^cvlz;xw=%&a7DwdC=qeJpb_(0# zO4!A-EK8`8zE##^TL;}-^Q@~k;jDmFJnp*buB3&yG)9X1TWEDfIBe@%_yV&z^~NGh z;!34s3nP+zZPLaZ6$x5E)#d58VW8<3s3@soe~=Z$Z~^Q+(5{eg8_1R8L}~V-S10Ra zXt1BNk3F*2+yaV128$kMDaL@Rc)-{fRRP0DB4x)DlIDbRUt%?qx>mnmO$9@4 zA+&33D2@%MI2hD|-eNd;=o-c9hHceq$&XZQk6>apRl2r=WBPaW@;{A|lQ zk&P*Fmxlsq-Qg5xdOc0I(Q@fq!fLbLV#D`unzC4L;jr=go6$0L-TKUX&HI@1X8D<@ zEpf%wo}kjKsxk@;TVHQ4^W+3cKS?{mX$Sqir&u8!rELu&>WRtj=!im*7av*tC%Y^j zJ`OJrlm)U3pEK%$)3P z0diuhLgEVYf2sg65e8KefRUXkKvwdfa61=g?ti?2CYCP$s*V=m@?Xiu=)aQjf2IFg zojm>{(Zew@0Zc7TTmZ&Eb4xoohJW!UWoKp&VE+$n>gw=6rhgK0{wF^Gg(H{l7fN^cFT@DnSVtAwPP zn=w?QSz!WQo$kHXLA4yVFf};5#Jf|)%Xdd0f1C|8=G(p4k-BRkF^UHw98XTg{D{z7 z!Fwqotu*(m-Fj0hcx{N#zk*Q5wKb84xQ@Ja$=p~EQly?@&CWfmm3A!SLzQ5PF)Z&K zfJE6&SX+Fslc3W3iI%1Pg#g^AsX>{u2raxa7I@iP2Mf;+-bJ`3$2G7htO#^C4A(Ab zf4I;sv*%C4wrw~?apN&OUpoH=x7Pe?XrC`l%YV3>uD(8df)4wviWH#-hij36BgBtx ziLC^pIdmkbfAO$^!FElN=rVcc%u}(|35NNKomuuf@R<5R%@q-Yt9C z_#NysJCQ27>HI zcAKOJnbJDejSp#&gZW!14fSk!kaOawO9`_IjL~|53qc_!2gjJCotkA;n9h9@EAUovGYmGl#9u`ViH;GLun;B%KY|p4?f5QMsIY#KlB7PU6H0PE-hRTJUN-_MT!z^#SgP_E&MnNFG z9gpxy)t3my%62>^Z3JvKhCx+0N~)Fz&ZnHFE;19npbev?K`V!ScrNqEVyvGl*8JJP zG^n7Qu6aTiG+5-?rICscrE5vrLmKkhhsZ5j_SI-te@fTPGNk4Of3}!d16!bEd|L(~ z2vxx^JJc!;CY+T#Jog@D)*Ogq)|Q70xhBMX(nH^#hpT1|-Fwr!dOr{>cQR!wO@&f0fg-nc-AJMH`mM!U1x;_@{u$EQf>X287L z5ui)@;^SGW3nqQzf4R>CaBCK-&h1FJScLgZQYmYWqoX#;d{FVB?xx}*m0gnA54Nl? zy9s(-vOz7}izXd?*YzAt2+HK_lawEEsXb$s)u#k9b#b?XS{@rc3|R^c{eoGB+WY*- zxV6SC6Fx_--6GPvFzi8*nU3)3(g<5v_}3^h{ZOsrFdm~;e_NgrL~ycGEn#$j&Og~> z1z@&*3CU`AJG+e7{b6UDR2p##d$cu6JVHlb>5Fu*ucf^p*AbV(Td$ZOoDS{SPMeua zWBS^=X}etig!U`PYI<42Im`X}g|Vq+2r}q#mjB|jtnMcAB-He$*SUKsw#H2olr`A} zhL8yjnrzNze~@hFTJH`0n>#KiEhn=r?s3vEzm>Xf0h=20fko%OJn_Af#9&3{L&BVk ziUCbKwGgUN$5=$4TcRl`%AU{-zR z(wIlL|CG|5mfEnFNqzt~D(V>_g-V{Yk!jd*w#@(381?7(tr&ZXruFf`TKzHT$-C}< z@SvxnjH)ktC0s`Se3ax$ej2U6KP*W+c=L=be;N~xd=~D#Ryo)>L|Bc7x!MUgLun*& z(<3dNC0ER?+5G7{&bo_EKRX?q+O05f%CkVM`-IKy6p;qaZV%r z!)=`&JFT)-=e#s_)pBqa7qi*xNDT_+|0j#G*UO9Yz*-8x2h5ISJL?hv|ytWZ^i ze`+656u*Tu+aKm`Op*%2^VFJ<@`)W*i+9T-MKuF78<^sHe6YkATpj=&!tO3>cyE;F z8B(0G*f)BEUWkpK)dk{?*J|DAz7Ak@j2wQJq5;-#+dqr@>S3Tckl{_IVVgnLTlPU` zX(0PkD`C=_lst;g2owLdo+c`%`^(#=e>=}TC#7G&qh*4olr{xqw}d%>?Mc%W56Wnv z+}X896eOYMc|;?=_k*IPz{s5th|Ky$n(cgOosK~kryTVg@ z25_T7E-ubxF;iJ?%G|`<53+F&`US%o_`SC5B!)-8A8Rb2@3M?w zJ#Ept(cgBm!LTryR58~&37XQMe~UK_-*HGY8+UJcGB2;hI>A?7%DVXiI*!!Z_|ZteFhOS;z~9M(S%#Yi zCMLI)*!=Lhor&J{aPgAq5<5l}EhvjLH2(Ol$nwWF~O6K|Lyu<<00lV~Oy((UagZ5*P$A z(@g-k?OA=+0XEec2bdC#AZC7bP{s5N9rZ3rG`2Xqc`(mb4#Y*sMO<4F{V2Py2Y5z# zN&WCgC}PcuD_(CqMXrL$thVPafBlevYoTUBO|;$oC%#R$L?0w3aB3K=A6;)-AS-&V*?wDC89rMdAi`D&@N|-(oinui& zzL+mSPvD)Y{+dQpVe1q*GAR>x4d$;OiPCFc zHDjo6P^z*baCY7ve>)Yhon5bKb{ntZ?H^ZKRBuH&qsWPv+~pg{dlDE%zEvSS^f`Mz zzg{vVbMQ6Wr~cdZf*p~w)5dsRUJvyhHVbO=Bcyp@+AOPSkjE+sd5q6L_D=lV_)m3e zzDi?JOu!_f8u#BjyN``@ez3vrqFPoLf9Y|K{SEW%GNPb{o~-)J z+-00d=p;J$fH^KO&G!D9WJ*Y%SG$rJ!*by-XbT3UO`)53Rat0=`X|Kj0|*&nZaDVK zmElWdGxTh^?fv;ZqQ3&$D(El7cf>fztQ^%(F?gS=>4pf&CT;U*!re3DPGC=Ps^LxD zf=%D^sjMtne+s`V5RYR9JdIr&1kie$FP?A4VBtZ*?Q)4}M11U~u5swMJ&~3``dT{- z;bxXm@^DsEDNs4)0$Pn025D1kOkv~lQ56<`6d;9D{6;Vfb)5+4 zQ4T|$N#2Wuda@2i{FAVjh?9aLUIA6kMG&W0o)jqAfA<5EFwpyz5t<;Y1_wPv`O=k` zOK$o7C(;sQeDSshCyIR@51koEolED|7j5}>vcOTqQ}6z&${*#G^60nm!@nskxN3Tk zM7@CVI?fHiJXJDO0QDbHm_j_E!rdJ1?5DH1mRBJ}vUi(KthRD9PheOyoEoKYTm)UyY0c*haz=H=up-n?cEG?wn6MaF6iDhld*5;pLGY z>A}B~(W4;pApKF#Vb0h3e&&9g%}&=HMwyTgJ>ll@5jIkS;Z4&)`OsHoxWRYB1UrY~ zf5E6d4dXN_Yj-pv2ggDD7_|k93)gLim?Hmw&-eL7`^SXmYDthK zGp`*bGxpsdoolrqMHUu=I2a8DB&0=Ye*htvuR&D6xT`1fYomlm81sD$T)3a2#=xo( z9oY|m8Ywo|Nq9#{$h`QBGh|=loWUrzCOq~qvJdty(|d{i-o*FtdTg5XRe%M=STgHA zeELOS6?f`t>cyE^VD1|$*>Pvx;9(VYmTPAZzTf(VV7(5&)l0|EeIy6r)>oI%3M?xmYiPJIuS3V?dq&(A<7?TyH6!W9n((3zsly z3ekjT+QjNa!?Oo#5g$Pmn$Qo}9t?-=lIlPad&>~?#dGGiQbslD+^f({lVU*=ACvv+ zcf>ztX^drK+!TYAv+%#(u5f4fe;BF@4uyeE zqGMuAu?VS9rUKe7w3N9;v7POga~P(Rh1Az}E1p(671lD;01<DT8+$wi?>Y;)rIyCCW_$RsWJ*R`3*>lKfQ6V!n*T4U-heZuCr8HI?LtxFuxB7 z^F@~SNy!YTf?|EgHBqT?f2KTcjz*{NFFiAGn>}oanp2dqBJ|8cEfdXun(wps{>ZK{ zeXm`SS)lu?M*Sm4A~vB~aW)-kl{M#C!xDcrwd8(w_^lXVx8td_@iSKk-$>hUM&?zpLcpEyg>$S)vPa41JX8R#Tb$ zivN1px+1_T$L`?&e@0qdm&XEZhcKcVT(J%nUxNn*I%nrX7+?ibw~OlT$8>!wHq*^Zvf8 zdIN*6|Er&wMiUnsGwFy}UOvu``wK&!GIpG=nDN<4aG>?je}9Z6IcncV^3_KUGhjHl zL{t_53E~u+Q(-ld9`+}ZqhagF>Xw{0jLT`+DH;31@%k6IyZkyE?YwHpfDkdqd0UBD zv(VDq^@T4G^3W|%4_(F0b@u;|`)N0f%ZU{0BYlv@{Yu zX4L8@`_xGbe|@CjG=*`-rS5T!$>c6mw@szdJ-SR1j|YZIt}T^s53M+ZIgiHza@Tpv zrDUou%5H1Uz_W&YN`ys$qm+je{9!+dAU~0y0)pBaDq}8Dc_-8pBce5GEZx?)Qz)Jq zDg$3-rz)l1IcA@#G0qIHVpfya5yj4vea8pBw{LX=f3W8pxthgG{-{E!Kpo|QJ}qgM ztuz+eC0)D)yV%JwiRJzTvw8c3`G+)<(~S`WkpFaE^fy$`=~cy}xQ@(BT| zV^*jRu(CLntiyy=D&rJye83$m9>PzH35DEK$C{fz{g|gUHnB%H1`iRUl9L!7B??|t z5Wd}We@XY)hml^=jz1*R8A&9wKP|1C*C$SnD;rp=X)@G^7xu8A;-F9)*w>kawhuR{ zGwxTPbkYcjVK~!;I+f-i!}_q3_|Zx}cf{8Kws+G)j+adgQ*c6mmiIA$WqXVAx$tKl z`nSLGZ+L=>`*LWwyE9iiZ9XkK&X@ajpV2Dke@JF7-z;f$OMe=o}0ORXq5w z2Rs|%=pe3mr0E3ePnkR0*UVh*?i3JsIt&J&bS|n{TLMKtukoyJ7Y^0ec9B}O8Sv}A zHsYXo&I8@nsG|3h(O8{4D>UB0+Nub3`Bao|{Abmz`G+mf3^)6o|Ndft{{y20=+^zVV8b(dy$Fa*Oon^!r0EYBroCK zyU6i=Br>ZQF^9JmTDn!{m+7VUNiQ7kfAG=+=g(22tj8=;j=yBt0-tYdpdAk03c^5~ z@284xhE@|kaKq5wlvHhX@VT7a_pACtk#5$nszRfCc}#BTJRbw{;%;)vA9B<*11(yt zX=t*cU=d~m&PgY@hI~(U8nJ~LM3m*#Zv+fUV!ORViRTPT%23G_?Mz~&m;0lQe|w!i z1}vM+HujTtA_#W>Qu7>~HBVGlPh0&!eiGjvkkV zE8OUy^;ahH>ND!ccKEmCE6fvwMUsIPbD%U$>s)1Ug_GH}naS|K9LfpE>DlLEs@>z+ zb>sFEPP2v>*#bQU)_*vc$R`&$(xJ~fU;6gJVEo>i8E6_%F1Uo;O=E(s-tcZ6%co_SV7^MH_E>=&;o1Ai(}ffyjY3GU|KlMpeoEc@B#tH&bb?@P!;AY}GYSweguP_0E%t-H(&&tw z&>;q-8PJLHff&fJlV8_^xgBFjMqE*yU{&vK5U{p5tGF_mYWr}5e;Un*h;Iu>@{x!6 zBW|{N_n>V{4KN8LAIIn4FkCm3^#A<3`xFLUtnp(f-sn_)vYdr@27wz6^QYf#m&-Sg zibq)Qz3H@&etZtCp5lb+5b=?{3>0SdrEOw36e3Rb;Va zeneSc7pQmk0FVKN5(9hRYm_fYC*4!XrfSaP?{oZCys(uyb6B8_A9aC)FNfg`mpG|y zo3CBni1FZz43a1$}M2HC>Fi)YH(f7)AMu3)$qMX~+sM8xz9 zwgq6ZlXq)P5hn?0IemERbzRT>8PZ!8niWu1N|)<^@ZQ#xJ#~(;i>dJ?Vh9QG(=SBp z+wWLUle?vfiq*~<7PE&M63Np_cps&!G)6G*_Lf(ys5<) zMSi2I!yP79e=^W~K4SLCnL-Gz21JIFZCG6q&$>O`TMXX3BIIetUO6jL67*8lO$|6F zy3G-2p8-X$XKz>C;n=5OvTSZ1VQ2PsxozhTx@Kj>J8)#tn}Bf-xZKhg3Jd&RG6wRJZY{ z>?WP+g^~1GVeKf0|H=$|BoWGH_ZXD!2}kO!dza+>8660x^i7}aI`>x~C?kBCPPE1^ zNPg^bFdVhtmRW;L9DK>upA7DC^#gJ5z+5-eQ)-^OJ|!X~=e%{5_ zA}VpWe@y0r1d+qnNHvf*C5=1-#E5BCuEY72bdn>-2jB3AadDiyf%p5royKqIRV+QP zv&gV8HIfO`QMvvKB;2WIE~T$kcn^>^>{-xwp{QmLJBb`uHzL2)3ppud=TcVu8$1h~ zW`xQW;K1fPc%|gFGGbuZ-F<5R6)l;`$$DV^&@7{n@67&zO(!A$68mQ zGK*dJ{Tb%jY85u-jlE)d*rCU*hXduj;~iyb+2&lz5=!r8k&D?0H*hd15B{a|=cQ6O ze}|cij>!vdb$evj`yJ~B$m~4sD*6&}p~E>nBb8EkJ;E%1F#}vDWA!Kc^?LnfSV3BN z`eO~bmf@n4S~!>~Lzml=x~P51IMhLqAYhcRZISfw8S<;KrV#v^cbufiBMBk91Kb7$ z0?`$h%nu^Zc)+wr`}dB_M_OX($KpGle{h`4@bJ68u~!HUO(OO&ElOk}n9iU~i$HPr zN^^2^Ud4Og>LIxO`SL;6avHCZc8$rkpO`9Uy}qSM@f*ER2rYCAr#<&xZ}W051Njnc z;=G4BT%S^$!FeQ`@Yopg%t!*v9>4yds(`Lqu8uW*(ylPVQ_YF7rI^V=2+p1c=2nb|SibmlpSYPsD(20Wqbcxv75rDUtq-EG zQ;Z{0O444)L~{>mw{Pg*uR(nIyt>h$)E!C>tXNc$Y`)tx4i41r6monX42tplq`OVk zAfN1$$4pB$^EMLN+0(n9EnR7HefDkjH|bbuEV3JH)^KT4NYJ(f1|EePmhW! zH8JZ~i%N4DO}$THYHAdDUeBC7A9%5ogr<^CdzlG4uNoDtegFin$!FxGsY>3cn%zNT zRYpZHuIhwm#yqr|C&zFU{@}R@Fbqx#BN)+z;2xJV$p=FRWNAyz)q0bRaK#v z@imrru;w)tR$CBFszy$sQ;0L;xSQQJ*7|y}PBi&yslEAIC{~~7f8Z}8i}v&lDioZZ3tNT5L}(tX{*t_JdJ!FaNFw4lC7VIlrVKIu(t(Wpr8c-e?(C}6hu^k(RzAvg zbarAnT5^yD$u-8^OUKvc8{__}{OoUuRV$dma@~ z{;PWg_`MA)SUIVhe>}XYy5){mE%)`Ji&3w(aD~t`1$capc5yx*Fsv7`;n`f5K9MD; z<=|Q;uip|4NMB}E=Ri%s@3P$$x3EAY&Z#h3oFp;1Mf-a%0a0b*@uav_|2-DXXhlCR zK~$Yb3+9k>G?V@wPz0H6o}rx$@uPy?d9~fQGhNz=n@g0tfBHP`63;HU<#JM$x(5Sg zt)Kgyk*a2PcPn1oY)<;}11XLgHgslmw||#?+TWyEI@KAaucy#d4|yA0A5Z^Ufc`x# z?u#|;**V*PY8aT)ZhMQ2HEhn_G

#XkF6z*h%i^f97<*>oX^U|F$Yqv;D4u$Sq<3AQIm}tNsekjC-b#aNOIjz`+Ek({kA` z3C$XJfEpAV{KZEMD2*&;@co9bL>&CS%G;dQBcY%z2KvX*JmZkvT)MIZ|pfv#07 ze&M5+ZqI#NulRFc6obR$M>eC2eW{tcTB7mo{eh7U`4<{y!Z^6m9txygd6uzHT|v;W z0uDZAe+-Kez#SCG2)fNoYtVfh&Z*lHdfV1*24b=qRjl7$7e&-ZSe8;XtV5jn(R`ye z(Ka2I&-C?fFGU?wCQMwH-fxQ&?dVSbPb-_;>nDGu1G4)5F69N-qis6Th{FoPH!D%q zqTFt)qW?ViG$4}0)^fkaa(di>>pV2U5gv7>f3@pU_Ym&B8fVT!Yb!mrvxeDrT7h!! zguklJX}5?`GpST{s{mIf@tn_z z=c=^HZtwO9W?qb12gx9R0#Raz+17(1?kQV_{B>7-HdqT!uE!4&+tQ ze;P{`1hV2|3kvk9E|({2O@}898VXQVucuq;K#mRA6>nNoIDXtMbeTQu)+KOXKf;q) zjn-1crL9+9kPPl;QKo5Uf+*!50o2pCNWQc@H*QU#LZVc|+$#rQT4;bC2zNe!B8%$seD#LM#VyCVbh! z6rt8zyi|+lP)>G~W>1%N#3s$e==~@LXe(~3VlTfxSi)GnLmT8``Q~ z5aYv=g=sR@(rep2?~ejbPvtwMK2p4n1@;{unD70*DOb#&>A#acsIP0Rl2vIae+Hv+ za-402vq9$tb+;~`VDP2&Fw#1p4zAqxZbKRa&Gj4=nu+bF(cWGVNoq-MVKGEv8zVdX zZ^CdyMe2yH6-(5_7e=Kz;l2G;$Rq<0w|1C+UrgUHme)i4W(rdr&+zw|246&JJ_U&#xtWn>jVjjNY|e>(mJ;8l4c_XeCXNjg`g{mvzAgn^2a zgOkMKmt&;ke{B!;bzrVEe?^>~^wr0bg!^tT%jDN}DU}^iVDnE>jJJaT>&c+(IWV6m zAr`bm@I*jvc>~hgw66G-i_1vivdt%iX&or1g{Nw-^;POG)I(T)*d!s@pvmUQM7ZE& z8t|%!iBk#@4oZ)psXn8HfR||`?j!Jv(7bM{8Vp8*Fb91eZx4bpe{6HLn1KZ6v_Ko` za`g0w9bgl2IPOZ)TsOEPu_v;Q`*=AJ3+y6$Y@x0HP3Ssh+g~_SCjb;)qpZ4$vWJ8F zsd0=H>l1Cq@wrU-@@X`(nLK)JxhfWb&{^x9*3(-7Evp9g+@>Sqx&-}_+%lDuv~Sx! z8~O$$O@?VjmXa7&e@9!ILlEJ3%2QZ9-r6Gd5~@8X6+-Qr0$-USl4zU1@VM-LlX@(9 zW@iZ&bQjOPZXN;;X8Asj{jj=Ww7D9I$6?tDIaIeR{Sb_}wTiAbR6-TL57uA59<{mg zX7&e8R)HZy)DBuFTeiy`G-})XE=9c;QI0@pOBi~%aQjWue}TopDv!3p7V@8~#}*d) z@NEj^Lqu~ReyMbr8xl3Q9w$u>5l&9Xb?&Iv4wv@A&mG)EidTcr8_QvM58jU`REN8v zu9L>-ueq7yqHy?naf{~y-% zQ?B)Q>=r$5e@B`CJmRkhP`vfqASTX}?dyON8=Sb@H-*QNA^^Kx{E`ay6$9%t1P{}E z>8!_kjzal-&8#QqLdHz{3y}QP+6EeCX$UBhamTl6ZZ~YP;?e+E5-VT$XdG23DBKfN zSP%)Kf5#ugUGC#M%4Y5}$MN$+P8ChV6({9+2VP|tf4Va`m@M};-2e7Zwwl$Z|9b}B z(1B<+f8QedcVIw@KDhARI9Pwe~)i4VT2R+&*o2SaSL>h#dyVPYbEJ@Onx`Q z1#mc#A!a{>`|_bH8HtEh^VixdOArkwEu23iX9a$qg>CEUBETVOg`;Z;gW52Zmy8xc z1kj7^e<*-Z9dx+8LMyBkgrXIht7F8T;%R;aD|{ssuk}!o>+xmS_1RN^cqz`>ldX}N zekIMt%9>A9dNO21AqG$Cr~D{m z7sRK+5yqILPrAE)~~`3@$|m=JZLSnUv<*(b~-#F-wu zf6vQ|F1^qPQJ4W!c~!`U@Fiv*pzGe$ziK*0zf{1wO7v$Yej%SiwGV*F*&~CTe+emw z6{YX#loD3)XmSk&u?pn8GuFWdYNpackn!??Y|zlYHHN&9rjps49q@urk!mE(BBQnF97X9-*t&G&$ z!~6I^0a`ZkLfE&p6j^F!>N_@hH2>Ivh#-taUDLGr#{8EYJFNM7DPd@>cA2`4gx0co*3&O%;PuP$^?y$Sc7~u$aH3;fIN=Oe=8Sm z2=Gw->O}2A^B+5KAg3eK6Dd{Di{;1!it3FZ$8tE9#(}pSO$9P$FVH!As(102NDo-? znotB{|KRWHMzZ>WvHgs(Ek7`hWgvYR>C}Xg_}aJ2-qV2~VvjbTw6seN#D)6d{{d4z zLZ`kj89GL*n{=c2H;F7lnf4bte_&^?RYaL_?UQe{fF798&O)nM;#2WnW6w2&<_r!( z`)H>)u~%(yxJkGl4_}&Yk3L2kXQGu8uO`Run6wsFufpqRD%~r}I#Ge??9MS#0q!M- z`Rq0Wk?q#L=MX9uZsLygXCC6Q48j?l`a}M#)HuV7{`L9_eyutumo;)q$@$pW5>D4eIB6`t(Mn>?b0uCovS1ybBv7OxgsKN) zjIxSN9OCGY*TRYfo5xScRT30uotYA6y?d zO4^)NMu87WC6;Q!*iS%ziIU(H-Gs^jSPB-Kld2&T5C58{dhyeY5m9 z2$??-X6`u#%qLO&0&1)kNs9S$xfBndP-DUb!aIKfv;#Yd0WvwO4xPXIYf=}AzIJbF z;iaJmL1?_49Y@2Re_Iu?HTdz%&lBV#dn_Lxa8}TBw;V$W1K0YsH4Wws${hp?^otC= z0dW6SwR|!HNvrGX`T3i){v<$KQ;NkEO`tF1?8$YPFmvS$J3TMkg-17bO#MV_WN(oR z+29E2!|Jktc^S)(>A)KvRY6}V|GRfi#=O)@;xEh1`3NO8e=|Bg+&mbAK5KRT!`zK5 zouv0suyXj<;RtR1Eqv_q<4RD0@<%ejRgsn6FZwUUAP^fktZC(2%!4-ob6gp2&+sUr z_b9t-^bu8{y>b@@-o}($;$svH;H10xtQon_Nc;VBAxr(3nBwp|Zt-5nprpqZSw1i! zXHnL{YS8C%e@`zr!T;jHUk|<3;Do9Z6PvYlv7>bd5hk?YJ1G4O)kTm;g0)-Xz6cP5 znql|2;W{TRi+VP($>)+}Cqvo==w)^P>Wbtr?&QT@)nF0;DiN@n0@oHyzwPXuF&BV z&|0NlB!r8!Dm@;(R$D@Y(S&Vb?lHKK=oeCa&C-j}|KPrmsCloHF zKP9q$EtEz-apj&zM^Zh^w#-`7n=AqyfeJFXsle)mX&AdvfpK z`Q>+{zpl!YH)PXGS0(ypg{+03q(Mfs^(zrIG3(`HX;Qh ze|q@8xG#Zm>IlB3l=NAOyfHe-t`!Yt6zFEvQbZj*MMf^7K@JP;+QXb)U(RUTt!3+4 zq*zGBN89CnQrGxr^>j$98_GpWi6s8hxY0ix(mnLh;NNqcvuU_=iIB-E_1cE%o=6%b zn^8XFqIM8j?L!!=(oTs*VDK{;e`r#6!DL}h!ot<8{C>m1x?1spV1V&i>C8d= zX4t4*oRLNqy*`?9r9`wCQ7BgGp6blkB2H*OQ!hamZSyM(V?9>w}y6*9J-%SR0 zmQ}e4(oCyCTrysxw4=}sroC9aUEkHnVrvqXB#oBH5eGKpgpZEFIY7eUKyxbMfA|y6 zt~rZEKl07gB8{nVdW5sDnNh*N6;p(vCc^!iW%Rdzor1^Ny{aiqcl5q}_D^O4QS^Nc zSlr1OzWV16X!nUKc2zRuj}b(t7)9h!U|#kkhZQrodLb^TvnVz(f1@Un9sJd5e_C85WWUuw5(~$;c`YWd(r;Z*q?JcfsLz&NVI8PZ z#Ld`l`I`di^;!*-q3YGCjM>!l#nPz)#asTl{{s@4#buerQ<7?jWkmN%j5k83PsI5< z4sqQE`UBfBOQzms6jl-qYA8suJeVJ3N^l#IqnrT>CgjV=B;z6xqwyZrfAJ5P5?kz! zgz_pfG-moGBdfeN;`+ViRsGKe{<TIkdC-OX#nykx_H2CphvY6v-k_w){(nf5H~Ex!8@+7wxz>O;BLZZ=>`LdI5Vy1$GfUj2bp&i(V;& zT*5AlWz5qnDN-&!cV0>=SG~r^|Gf$59y*{knG7$*hgG?v8vMuiyxG?XzrM~qvcvu` z`nDW@+cqv3PajeV4f@m0Uso?Oe37=9B{=v^FCHDTiSJ32!tz8}f7aX7&wpcvx@O3VerP8)Vf(`Z?`c88p#$gyMo^z25*UdB^1pZA4DeJe7hTb#sNu+Y8H6V@)s{ebZSf7} z4tO^Rut965G+Vwsf48#>_uP=3A45ql>=(H@4H2KUnF4ceH#kL4Juja{?)twb*#}2k zI0KIA@6_nZie#NB#FZbkDM3!WG#A8w6_b8GicRy)yk!^lxJ&FkJfXD+X_q)1^#5lY zF~27u{Im)(q2D>pb|KqN5Bc7)8Nq`gETZ)#cV?zt8b&HTe>PXW;X23BCPJjw$Lu9K zL}Nx*Vg|?7FHN{UP?hq`EZ+BU3U-g*t6*)A5EJ&}USIzXX|UO!?!L6xx8=(G0dO-f*vzq2>HmutsJCXE31K1rDX%Qdbu>_1wHLNa$eq<_ z^gYC_QQZj!f9Y&@?#1EPPU2wez`w4sUS)Y>cok)HH0CKQe$rbU?7dy;rUrWtCNsAm zz&?@>H{iJp=YVdCYh{%s<(}#V#cxDlMwjpGFFmORBJB2bWCHpu;lGV@oo~97OmKDj z?L zfR|MC;+4X!?bUH7|L*qf=`Ui68<^R+5mgENRpMEwXCE2a z1WAp^rZo3C5H{)lL5(EyUp2AS>#>%!c!d7-rb6E%p?-O)%qI4|qBT zyU{5p$9bP18CKxt6Mt6bzz7i(24NoTFB&3m55?hRGe#{F;!e3;f5q*QsPjE1E3Wid ze+(UB*rzvDta3=(F{v^d9Bc$i8|+xs`HEQJnJ(Z>!t*nm5GO}WbY$b*1?9fsHyG$x-q(ngUtAfelr=Lzbf_`sRm)9I$>jTy&_W*_|YebL2{F)fMci6u4q`8MC$qI zSzfu8*~<@07nYq)hS-bnDOc@IZtz^Ze|Cs9cUv35Y{Mub;M@jFLr$KLSGo%T!Q=6~ zz!|mCW9#@;SjA)x+89H>a4Yj!1g4~-e^I{zFXbJ~Ib-u%g|#E`!B+zpi$Dc``!ZJ@ zEOTmYgQZLC)g@orj}d#|N{v_*^6|#;k#3uAN1`SL6`8k9Ppz3&K^(2Y2};b_e>HDG zvDks3O>pv5BJk?hIk740a}N!huAs7b48T3qeLowj`n)j6M$;-QG0!r@Y+NbT)xQM{R?G-ldi@r+a;|_A{sV(+3VNEpB%ak~t=N(Z)qEtAlBA{E4(@Qs=PzyyvW%C#Ws&YnJx1H zSF$x$Wn=zRcJ3HPYuLOTQl-+BAY3~P$D&5jXAmV?L})o3Nr6psPA~@zRis3$6gYO} z%{#?4O$@pB0Df2#&pir)e?|t7w~vqOMJow5{|t~pkN!;Cd$@^Z(AYPS!?5PsX|AT= z`8MOD6_-25-vKHv9BWg^Z#1)?9WI+TDR)$V?oJy%DM^j^v^{uD1(&6f5{!&ME!FWS z-|Ekb8=e;RAG$$`V@?=QN%OwPvc-}z8Cu?0oM7^druFphmC$Xff1bV&VAz5y%V?tx zAiwEwdf_WXbagmiSjg&bSdJ{`++>uViTxfM))a$PBGD2g$#WjtHH^xmyi{PldWll# zfH>X{vAY}?7+T*-BTB}!VR>z{LjsT6%Bbck5=>odCR9nDV28iaGE;1&_ z{;A34TMgP^)R}OPU0tMs8wu*Fyga{Ms+N;#p3^-?*)LsqA)Ysy5LtK z69|&A%oRsb^8(-A;m6UGtgI*rj+Mv(CO$;>2zVK3`eEOjftol zLZ}*e|3o}^0!I&ZWf29E!ngO`x%d40zB6pmR!S*%$IjPxsPGSEFM>ltcoG| zi4lA0>I}S79t{(N%>+3>_Y4C63UcA_+W*mDIPT}SfB(AFp9Mye7M;&oHsnOm;jjrx ziWz+6wK)P%p?F1zF?b{O7Mbb(d1gV>&B@+d_dPby?M@kKixd&R)>b*>V08uc$X9w^ z`8i#jwMs<)^i`@EMz179=g$ zUUr*3=}I@iUF+o?NzJSKnOXp3`hAAQAe#nUsC7C?;7s?($`yBRP0P+71*sb_SjaF$~k0(0gA0$fbNnm2G&}I$h`XfF;~YFx~bPHfbuDPek96*gceJBvBHJ ze^-g)E(fpT$f-2mp6?le2Z+OkZmxp~ljF>=Q$rDlYpoYZK`){dV_OATJHmd$lOHU&sz zo%6F(lry@D2eA^1TI!Mk99G0FNWx@Ne`w9p@!17~k5d|q2uCT)pkNd$m2uxFxdWW+ z2TG=Msq_x4g8KHkXb^{bWnztuqb8l@+&Tmi6YA#;V&;{r>FM9cKVI)1nv5O~0%VLz za6xEZK3;OBUqm{}NI^0mem_{bteo?r{jOyrz6e>;}spBSwoafknBAbFv zWDnkc*;&c0E7=s(5t}F|vP^GRf8&L`HPJTd#B5G;BRe1?Rn|A^o6Z=mmC3>@QVx~a z*ey5iZ0p~PJKPs@P|azRf)O1)YeP4OWl@vBtIc5_evL}mmh1Ed}m@nxkp zx8Jq$P2$tfKzA>IttI4;uYhJuT1`ILwkwbMK4!|bbRLpm=ka&Efi|V<{BG5=3U@O7 zVrFyl-BHU5|Bd{(z$%N5F4ga(!_wbX#JQ?f08KcEXEBnllwNt z(SP{8YG2+&S@frG-2}<;{_^-lC^NhvNW~aq{Y}|8J0gf7F05j9PdI-y&7HqrGJ+aC zGhKZP2HqOe@2LL~Oj)G6aQE>zdPix0SSDLXlV_G1$NBsG{V7Z|UWhom3Tt5s6Uw_j zI(81Esj2`uK*qnG-`-eyEq_P{EA;ON?!*$O+$u;-}wNR$r~W(f|<1X{AcUN>I*yoyEbBAMS{K>iaf+-_i3s`lc z5cc|xCYO1K_=$~{DJektBYigC#xwTo8g7jnQLm(twQjbjDPYJhAVGG2DpI$K#%q3V zlN@4WX|f%~=5bEV`G3w9_)%cAvr{LArf;u@NfVtJAXr_vcT}WLDStE^yXq0;G6`x+ zd*=q^!te1hnAl6%^Itxzt7!uPW9IyKF~L8aGw3{GQ?+TkaH%@YJ&>$sR4uo;HX~p=6 zGbxbRE9?B36oe_m0vd9t4IO$0F)nYZ#c4eR#Q%@7nZj-KZ(`xIFfe}_-x$p8I1TR? zHl+R#hv}$wMSs+G;qp~kXkKhC&78(2nTwyVkTW}}DeGly4dSrKK@rB^G+g&?0kJhr z!9Q#7bFIZLC81;ZI(|^lnyxe<*=6!N#Hv+vM0TM7)>P4IvfL(@Y^5fevXKdM>my43S+&bX&R0!QX=;9)AIyP^@h;OP50F?yV4OB-H@FgjUXTF>@uz6I1-v>C#Qt5wI=FQ3pq$2}SrEuOAB?N| zics8+SBWa0zF&z**@=fA`X0}Db0@FYkDaE&v7{kzWr0z;V(iZ=Rc+7ViUJOE^tS`U zP*QJOqJR9Xs+})9B_-QWex_ae&eM1!+`Rre^-KzVM1~Z6Ya?Q^PQq41Iqu{y!a1ub zpJuKz?c2gqe4ZekAE%i zElc-fzfgN)n+!_8ZaC#&IT&D51(AedH4$3-*Cf~#CHWiR2< z(TPy2#V-;*eQh}5H78V@t%GC7aBG3I1;JYREsT5&LdMN`k&(;9wyf|$(F+Lg0nhI=u|V_HG2 zo%P}KwHpQ}h-m=tSfm0&$SUAKAPEiu>ROZf$d*zBqx8~8^uoX(D`qMD)*CKRWbR37 zpPAzRx|RBqIK@tA+5j^A{D0-0*Bq3s5S#p3g{{C4dXKSuehQO~sE&IOm?DDm zfB{so5R4;^JUP|qhVGwk^{(d}TG^vj>C;*h@8G+Ou8J0)Ez`HR(|<$RUG5(_8Bgwj zkrc%NJEbjK7a3uiD^|ce z+wmW76=XGjEy4)Q$bX`y#YVX*fWBJoFwF5W>0M{t3RUuZdvA7LE~zi}MH@=5Pdm^s z96<~F<&`EOzcAT0KOLznkVNs)=5#{7A++DqRkw9lK@{lk9CutByl7AXB@N&`A0E>FzR6+_*;zQr5e3zeCxF^?yNq-K72zxm?X>lGk^Gf`iSFZ4gxEiN|`Jio4NPngI$B*bHj>W1~NI0O}(gbSGjGaAJf0b ztpYUw71ICKo`0lk9IY52`$ISM=%d4oVVYuS)DN%3IYJOk?%(ze@dx&B7C-RLQ%9Ma zlJXInfcrKZ9(Eb^i=^y2ie9H)Y(KA`wIo=ziOw~uDk9IkeD z<`Dg3&4dh-3FCMCzkA{O;6`xBt#&CR@YU100Es|yvVY4J9kfbmg!4L)fCMo9iuYAx zMqI-%h$FosgE)|uXZ7ENpfR+SSx6`S?ik+}&Qmbf%o$f)OX{uKtF?3DyA}v+4)^kB zaH7%?Sz~8NEG&^}jM@FeDow9OGIBu_2LkeG_;L7;W2uLmq@ZH$T3bE*s?CGiYX zfLUQE+1wkJC}>=PyugoVrBWHa8XnNhYLG2PWq&w{(rgNV^h5O_uYwDF`c%9aXT|bB z32hbuBI6y^`rNMzV-8oA!sh@IdXVrffr#*pyamp*YwqotfiUcvKoE(=KH(*DHmdad z!2^wi2NC~a7j1kh(ec`P(u?Db)QXQq>d znJs|g^TictZD(%-v~~W3_+KX~1Azc%b0EOf!Wsw=mRHb}loJO~iOZ=1#DTUzM?-6X zf{T&0g)uw#L>jCVvt5w42)fO~~HS?lZ#X)AtFc zVCUrQWb9~R?+o~?svsiv51!8EhR%Q0cCz?%1MEycBTej#UH)q6Z{H`(r`Org!qy4k z40Lz?tCkTEe_&$aWN&Tg@mc#5%-+%BZyGL67Pe;pVn7FQ1ezH-npgv!oIYVbvHzOR zzxo9Hm+lSi?X5lj&bIqI>OVPHI6DEYO&Q>rSw3qTJAc+Tv#^C@{A;U7+M3z{n3?`z zH*vB5r_UAW`1gRQ{@OFtpCk-T>};()046|FI7T@;f9KDV0IL6;$_)Q^BL5#q{C^_w z|B1Z+f8zeTM*rmy|Noxne}@)xv9^{ov;qE|1o-D21CRmyb;Gqe;6&C#4Ox_CJGkL#^wN1L+j5e{cTsZH32$WTi60W z)%<&qe*k)BCZ>P$shC?BTiO0KcJ_a`fVL+8PW@A$zlk$S2nj1niPHY}8};uvg-_+3 zRXprJsr^SMvUVo_x%dl3NXX6|;6=~O&H|ukWn%t3aG!j*SlNC4hl+m#G5>2VYv}A~ z;SSLLZ2L3wujc>b`PWMK-(W;-jqObS+AGS=e}=XupWEv{4S%_fT^t=hRsH+Ke>VNk z_1_yE2y_P;!!0k^8S{L%Oi535uEEM492e2<>tO~T47M+>S1HKzud?g*O9|WLDmQqo z4rXYWZB`5{IgcThZ_+VwqO*sA<88h1JLIz~dt5239KJgN=Q!=U zlKl6*2$>`B>_bie05HQWbv^;&D*nS#f4pM9CeL27$sNw=Jvb*SE6+Fi4`%+n2=?m; z`rkW_p@>5F65kqtD!H}BCxa*QA#-=!=tcpxlED3?WDp*bMCXmxRbm|3*q`xJv@?mL zOflY(juX?GFubeq0se5myG6HU#Kms)Q_;>h-1{xoD*}hu=>W8N{wjc1pKPcWiG4b|Ju>kE!~UUeG=zpQ4Dqm=;HDT+D#hAG~CoghV6 zhn4a&_`(k&lzs|Z!H-6ATx=opf6KGPDf65rd$O=IA^vzHB&n{W4)|ewxE^4_DCqdn zv&?fX&51~xV5(O)L%;>oBN}aPFQ(*d_JfYjbH)_a-<_#8BZ0lh6ZUw-I$<<#x+yG% zL#ITPR^d)w_!!+X;WCVak1j8R6_()!#Jn=tP$V};Q=JLw{W}an+DJ}Ze@L(+%yt`+ z`0HTI#tC{oW9fdo6^EJI+0&%Vj2Sq z_yxu^s4w?-RleeI&|9VmOT9Vm?euU~BC;+maS-T{MH)C6$D1s)e>N$nidnL6l&wd> zxObCx=;HC!mNZCgQH#6;r1(NI@ev_)xY*VWa^YVBkab}jR{Nxpf3?GLCqT_=LB2Ipn4MzQ+MgFh+J(2v#cP*79Wl={o_f_rH)dG&SqbY%?_hQ4m?FG8**mkO%Ea<)we}ZU4T_N2z@Jt!^LC)i# zB9m{1>UIB=r|_UN6wYO~Mq*pnYC`EDUptGCDX+Ibc{>VCf%{4eXQ#bkJ>(rN+@lQ8 zLBSX=X)N&9q>A<1kdE&r)m_9}xW|<)$-odVz;kufoKn+TQ9yam<#v9D^xF-?+Rl3* zXxibKul7=We*@ns!ogK^WCb}+aY~FIAv|!|v;{l_C%F-POobm|U)eKim~C)y^xyRn z=M|Abnz$%t0TjfE@14xp<6(6A%Jnj8r3LAAWA&5xxeylFx6rR=A%*X5opZ@Irsm<6E9` zGug%4*yMHC4{5cMm6{xW?0@apl;;H=$Au*cius7*>XnXPjxEW(W%Wu_3yF3g_;2&n z6R)V!e|O05MBMmbvgo(QXP*C{l5p0Mu5gH$)WLQ{hn`so`ySXoZY=*Rc*UiOyQ3VZ0dmx zGd(W{I%w z7o5fa$|$U^Z}GwHb|7rBq`duw6kR zASWD`1i)E_FPbR7Y%1Mrgz-4A+zxNsVvU0%EAEB#-oYR+Z6etT%dgcpSW>68$Hm+m z723e4Eb-8KU?P3J+P1S#T};kTJh%|~f7R~zn?Y3l{it4H6{1Cf?Co60t&*m!Wi3=Y z?#dek9e!K0;G}pAupc%^&jH{cBi7P41it3sf2a=i zawmJO&9ATS2JtN%)aePBD3)0K`jy62pvklIMk8j7Z+1;M=c-^igkAe^{4_s1a?bV1 z1jBU2RLH=R{yZtDUlo}@pn1Zx#fW}Ey8v61D@zEtJJN*J7a(kfo)Hu<@rhM+y(ee8 zcG?<<`20Cmel>Wy66|wfuZX|De?D@{-}T&eJruu|t5~zNRVzqAj1&5G^OX2uLeoa5 zoa!B9(vgPdH`qzC@A*+Zf5;`2qGlY#o^Wz7$rJJ*FZDs8A@A?is!#3 z(Q4l%Oj3{q>%?!al0v}te+oIME6ZW9cEDAgQoLyPjB$!CblIPfi?wjO(EJ%X^d4fP z4A-0iwo!)L+D>n{St@PoF~R@#>TzEkpa$J^z0fA1O8IJ=b!6|rUcK459(C9D7zf0UrfZ%~AVfDF1>oTCf; zVdoYQi(9s!Gyv54sGKNtv&FBpb*yU<`~IShB7Lbc&uEM{4Ms(ZkW0F8Q#QV!(Ion- z!C==HVW!O8euVpT`_d0Fr^E=klr29SzYK`63l;fx7;E~hU)-dJtNBArs{6rDv-IQE zm6?{T+O$(ef72kv10Kh=@BIAN@uho#%~7-MyKQYle<=O>xbxQ~it?cK%~Uz^FUw{! z7&^J&uJyx3;}|fzgJcV9St*sH6bssB0%!tIa}hul9O7C;C!=lCz6)6V;HxCu^^Ftf zGAz`iz`j~)5OK(Y9(0Ylgs4gZwfNblYyszWn8Vz7e|R>pOS0j2OwW;VX=%&00VCI5 zzw*#HOJx0~-k)3x!U!=?%<#u5420C0VLWf_cq-?V|Bs2pI4EWy=1}89WrNfvCo#Q zCQVSwmwRm4DEGvg)5Q-5qUN4vP)$77|Za_lMmI!M}G6ukHk)I8Vtf(o zPo?{j55ET{JxHfnrQ&n$!qDskI$4N_08|YYeEw=(zZ({FCZ@<9n!_^e@v+nVB%oM5oyeGTFUUeuH6NY*7v;1(fn-a ztU@WRzB!V~8knaA>}JDMl<rE>>X8N+*~UUfby*T%}zwK#Fe4J)^kFQGzNH9W#&K*Wb(} zjyr!YzYi!VZmjEk8OjDGq(kQ!N;&OMz=bHBEj&XDLyebpKs!Gc@t-1c%$#+x+v1m; z|7mlK@U4#?iK}-2tZFi?>a-Vae`%9kEb;5W-}dDZ13+&s2;Z3)Eo2n1H1Y=hfh_cC zRrIQ9-JT4;b2sQ{eZ);O^Na>C@Dihyvf(|6AsKP0CfS%jB-cFq=NblV(J!8$3s6~j zhcg}^12)+%(}u8bpbx)LhiNahIt-g3HmSLrI($L!zsB)Y0CS2-#j?C$e;c*UzvVQy zGRNv0oMk-N@A>gg^v7GuW zM+`nd5oGY)46n0adN=jP6+YfICQ~eD5l4bIXj@o?A5q@sa)|`Rwf8wz(CCvma$Q7MLws9iO7Q|^T#DnjOlm#snxtQiY{;4w@ zUMsA=0Z(AWhBO$elnTa1z)Waga~XeYCf$yevVmbydp%Z0FQg=GA;e_NldJVky*x_D zEecC$ zUX{1I)MwuiNF7nWJ8aZX1WmQeKFvWGMTJDM?V+2(@1Ht@h)6%5TKJM*aS!=42IHog z5jQ)s65=5jwN?>+Z1(y=M*t)gp4$;azoqLTVf%?E&ooq zon{<>cyORDIXu&URB$H58$q&?BID`^L~g58$W7pm}GtZ`t2 z$dFSsBNVzEWL>b1!`+wk!s-O95h@K+73X4TQO40sPC!Mp@gSYMWCj+h(7j5z(Z|SL zQT#IOLerN+#z1Km0e4k#4$N(L3mdnnV1Zgs^d_4Q(Ffbh8r9nRv3}dg?Ep!fO z?#a+#z!B|^e*%nl-Co}nM+okAK6WGa${CCu4OG=9K@hPQvVA$Q-<1kGkCGZtW;)Cl z!Y5chJ!l{tmx-@U`XcS12+^CiAV6QL5QiMaF$`nicnuz;TZJz$?BTFaf9Nv@g(LFI zcoZ$Tli1>hlz_0r6nfnEAe*)cUhlRVe_-;La%vS0H_lxzWppJfO**kd z%BW)~J@~ET9&4;$&<76txwF_Kyb5;6d8>qqTa#7gt9b+F3|tY&igA?nYh!c;jc0j= zA?kso1Beao6@tvCu~Qva_XdX)bTe=TI%aC5;1aCpjSW9qdlR1fcW#zYXnbQp!N=J$ z?lOHH2l@)3wPq+Mm zwF${{|4F-2eT(7s6I^y%1@2Y0?a`nRCnN_74j&nb;Ea@GtSsv(;=928-bwHexJ6Ph zm@{Ty+Gm7019@>6BnpBQ`H88O3Z5B$(@LrOe}*#1bpPF#;cm1QL)z>QS#ykuGp^?c zdh#QUH-+9R;a>@4C0>(e4O%y7-6JYTP>TFpC8J0W`=yIZ5z+8sqDqERDZ7kqnN=NXaRobZ@9LE{)oJYs13P31<4`^ftj6 z>N^2ipVl|}y0~p~U}7PjYTRBB=??8NmMv-La(LKGembZq3Q{UO%|~~)7>FZS8|iTi zFSncPD19agc~%x7mjCrwc{3CvbgzP{e?j?(8DsA*5Sgwp=v}Uq(j=>-4i`&@W@CAd zf#U1o=AiOYD#^>!>HNDSruV(HTz0MB-okM(^#~nC%uWnJgSBO?3P^aHm(obQ;W>e~4XW z>LEW1vB)?~3_X*{k2UdV{)3sEl7I+JphNc^G^rs>2-}?|{(>^6XmQfp5(E}5nbS0$ z<)PB}&cQJ8Zijdk^Oyes3DV1k_IR+KZfHEocfVjw1Kxc^YpkOZE?&jkX7<`4enDt~ zy;BG@P|@q3e$1GdCK+XuY7E%M#u0!^tl$Fi9 zMV3-_1w07>Q`s)soZvrx9w=Xi=g;!e%WJ%MboDL3&191X?`bU`8#+l}(>+9vTr~ezy)!8!Y_T@cqq&o;FJ9@=H1sA>e?5 z=}}4J5(nfabYH>*WFhI4M^>+GC`hZ*Z4g5j*;dsjuji`e?c#MuLiWf_M}*SxaVPJ z;9V4y6a*R>3Hx_H36uKbr5mioe7~Oh98O%gHYbbe&*@xL>^^AUv(@YIvG!Pj>3$l5FE_dM+HS2Ii}2IrmXu$2Ck@;xP#X|y>rHJ>cH?pSEKO= z?No&nFrW!CfBC?(EW1*@Alrz%cMN5=rR+rd-H6tn@c4%M3$utSeUnTP_bTiwCI!TC zWp{r4uo?rkOo17lAT9?Tb%@eZkeHF``<<-NLBu4+vd+bi!(r11UMQtR;c}6!xsZGK z>+oVLd0xx=H)ttG=2r{O`xsI)tEe%fE@Y+nwZUfhf5hmsWmid}9u}9v#|QID@j(eC z{n(2?$sKF)Q10M+Y{2)6ar2kM6^kH9;$@{4P4lymRDOuWii@uM;m3D=?0D2fR;@}$ zS^&jP_mm5yh17Qs?Y7BXXlpI49v|=D%F9KkP+5Xnoajc;;d9hDY1JxAEi3vfrq1qe z6;^%Ye--NZwPhbZk}hdxr|gz@pSL*~T%M35l+Le>s@^$RnY0Lv_5erYgO}PbvJU}+ z1@W~)uAx!h*5KxvOrmeCMU8oaMZc4ank!~St$iv=gGYnHbXsHUeGw5>OvTFM5}PK* z2-PWVB#ikcPW&>7>sclx1B*7TM@~_=AfQyZf0f5E*`&3JUB>Zv>@(Q%xrI-KQ+}m@ zLpcs`nYL30FVHBRextQoh^A3q;f%f6$~rxsyVRc2&~Sc0bR6edO!uPMKPKu<#vk2n zvOC3DkvOJIK;h7b_xsaLefj;S{W2p4daJ<(1V=mMHci4r?vAf1*-0k{Z!N z*vUkkPj)_lU}~M(S131LQF724CibCrYFdsceyxqX(ILl-6N_j3?Hv8djjj=JRq%{kXh^X=G( zjCT08Q;?L65HW{Z8AXnxGFhFu8l3Ay^duDK<&hPngL_z&L>HHAhpmqZI&ByYe_3x$ zE{VTYl?qJZ?ln))KE;$R=W!p7JSiD6!+^O6tZ?8}07~=-(_!;pu)ek)cVE`QdlC|MAT5TGZ#ly92IK;obWHxTeK=+ z5LBgtvGZ(lJo}-kdZsortf62sf2feYWlAa?gNM)&$_=87UzYph4kB(ffTZkby3}IP zsH0>Gw!ApMCuCj<+1!|Ih$gY^q{jQD4oYenIo&@;rU zB#yo*yeoQize3VW9}sekJE8D%|B^_l<7C9W4FWZQck*oiUaXL7DR~I7f19$dU$IsG z(b-(U0l5Zb?V%t!dqSkA5h;!$cz;`820HBY&QWAN;I25`@KX&$HVZP&@3#zOq;A&o z-9^)jG@&|06W66IeTyZ>cJ3 zL>e1zqievc^pq7QwH<4sthw*&UR?4a>aDw>dc#VObJOoqmLuEzae?#LZ66;fKJ7zpXhsn;V z=zK(*2TLKdo*><`X!oeEg|t8`--AzLhCKaN7#y`jYFr*S4l!IS=tf=MS-sz^@_La% zcrW%4X^P?2MchsUt`<_DEp7hjJQo^=%y=eye96(HT5Ftczv5BRezYcim3ob<@K183 z31eKy-@ad{e>XcWo~`9XE`hQA6{txr4=&^bPdIJtxwGWh2;HqXz8N-1sIL3fP)ccJ zN~0kIBP6|Ud9R+1EKSr@-Vv?cz~%LF%g~EeSTm5>jY>OK51U@ewOn*{bTP4c#fNpKsJHsb<8(qtJwp_`<8pIUDVAqe-b}*5U-U)q0=Me37PdvwQLP3 zrinv)oM+fR_5itUmfmoojEgkr59`|3x>#09?Xe&Fp||s>Qq!6_53Eigy(_#Q2Lz}* zEfB=d?gR;tM7ziLRy86CiHzvO+3Fe}OmxU-8cVV@QTBVo>zB|x)UH8~P=aR9m zj~X%Z-7SjIEnz(?(&x~iF}jZ2-irf%wSWuSKfT_wNS*enqlZ) ze==A~O1Ff1%b?E~iZ1*|X_KJiERR~i7R>K?pc+QTJAw1!?X})!dS+?dR`>lX* z+?)C+T}`l?I{=wpva!5I5t2{B*;jH`e+K<0NCO1*LQxQoHF{=MzX6TcMrve^;WyA8 zBwdbylCi6eULpr=94ATh=L+Kd8@1#`U$|#EQn+2vu@imh3P7S=PeS|d7?mgZRAPct z2$^la_;P#{P2Ps`{h{&@xL>>Rs&nCDigQyuuEMJV)V6l9!dJSG91d*lSK{vPfAFfX zimM4}<4lPTb>XBA=^6n#wb)E7`lg? z4=dbymLyLQFO2>~)x)NtgQb(tlWZyn3rZ>8$A*NGS=U2%fI;am)}=XG{OB9{_F5;z zIX}b!GSiIUsR!QhP)>Y&h3N(IgE)o}#e6cSyjZS*1t{nzR?4-|r+ho3e@`5b6R3R* z6%>DTidGDT@|<5cS3BX71@@Ae<$Q~0_^~ktiN?B z*A8JPA#aA_EZ)FN40<6xI31bqf6mnQs0xy8=~(3&+L@lYrz!J~U|X1@r+>&#a!g&1U8bpzbHYgG zJJ1GDAW?@!ONoh^`|^OuVuf5kpJA11iq|!%`=660rBi5$Y&#pH-h@+}%mq# ztlM_eN4?0MqRhk*AN}I15d`~2Y$xV=U%E32U-L7Rp@CBOf22VkuY`T{*%VSMI>dhY zFXe+sj+1oFiStXgxDYtY>RDG(lewMo!i!y}2=~Uk3o9j?ag&1>Nfglq> zoO)3yIhGe#f7&^hn*sqlYI~rWLYTJ%KhoV_xKM1AR2D&E0JC3M+ zvq#KIGLemH{wbP9dC0blT^|peE7PIWv;Z-sQOGzG5~d{7-${G5kTqF5WznxaL&M5G zCESf~LfTPf7d6C9!$6Gtnb^PJG5D4(~SI4HQ%%nP&AA=B(Az4X2#?AE$Ve>-#Zaln+jnI zzGFUeZv*#gPk^=FtkQXU)!-1Ly_KiDwi?Te5@_~W2bqYe+rc+@{n4~u{*xcR7jm$&E!XHGZg#V zuqy99U`unR6mP+OKdyMlWX$GmkW7{vF;q0IIUFui z3r;R_A~Q;d!4AUVgmi)f{Rnz}6g2oo;__rV;Q7}{$LyLo#Y58)gvdzUFZn%cD0*V^ zf1iryecfH)Q+P3^=EJp+jcFXWLc^z3K`4PV{M{I-pm~beqsue{kdK--p>>C`ssfVZB`UyXWv?T$vOfE z%%V(nJ?EC95_*QqQPNeg?9c)t=02FyCm(bQPMAH7VuT(psx=@!I5iR-&#j8r|9FHb z?K2H^u%+X>eBnn}&W=fxEdKe@)s%RM_RHm4Yu-eK(V9~hb#5{lCMy2z<#EyKe-Y6AAnm_}3v7;mAmLn42Rk znh)zdw{?vl{lh*g5`k{?Xcy>Bf9rV!IoAMzj6T69Zw0i;!cIZOQ^Bbtc0TH4sp-UT z=Lyg%+0k6`#O#oM2UTRow+JQJMwkx2jK|}$oaUOjkfSh?ux9*qDGqD(g@_^A?(RwKW^14 z`+y-8N3o zT?!t(iw$WP^XacSH&Ofce~`e(J+`O4J2RG=sBJO(x-VgN9ct&bf4k$n(?OX>3Zr$3 z;}l*LVu*w8rdoQ24ylW&p2-l&0uWK7B0Mb?B?~(^M=nw^-0NNfQxi7u5jJfdzDNH+ zszoon(5HsP6J9BzTtf=%^>c_SdA40B(V$&1i@OZutOOkdD#hZbf4b?~h4h<%k*sma zG>_Io+%Vo?m>~yca(ch}{PK5?o91G`PACZ{(v--pm!yc=bi1@26iFLLad|RBhZ1~+ zLTZ~OJ?JRJQlQEO*o%&_&Mj;)YlH0-H#x8qJ5f2Bco3o7_2?IZoUn4Nv^Eh`mRG6- zpq+{-x>hty(3iCOjjE7&v{M!6CW%xZo#X7g}LvH3~ zayD#cX{I)&GbQ>u*CO;%Sl`tp_V-!OEM)K%9rvdfA<+j}~iJB1iNn zf10f!e%WNMi2jLq;!Y8A3WFVLE)8Mb=#TFjtq`kHxPXh$gBX3Qd;EL{E+kGoC0>7etDd7^EB= z>FQ@2kKXxrf4CcYLV6KQ2OT`rFO>M~-zso`eSO?7(C2WTQ25H+V{_RTE!~}8F-Na% z5pWVX=HAei0fuI4NmViK&pl>*WLx;MyeYBl_tRP9fhwN7;^$1)6Pr~2s0D~BvMmOl z9sHfZ+6p^&w-SYC+QfnxUO7U(E&?ymu$iSbfOl^ehPGE!L!DaxRBch?4;7wXD4TusBkz@C}^1H{@gFnWG83fX`8e^j&-K}Gh;@Kf* z8t-AP8m2{iWEb08_y!;AW>>e}$i$ zfBm*Xi{ayrigkX#h+i4)Lq+WE`V6%8`K|OaQ4k{TfFL+oI9LrZh=1Iuk*_xOw{4d0*m4`$E= znC(t1nv2Syw(LV>ya-O0UA=sL7=k@7e=Uf<1uvPRN@km5!A0_3Bcf8+FKQe9KXbt5uTE zV)AW-d0YH?aG|{$WKwPFwS_0f;N`5Rp9twm`AepjF5u1^iXrgMSSLb@!hLJ*e{H=P z462UavizaVW^3b!iQFSN2=@*i{&07*L_xHfB&tGSVN@WI%;mVe=Esy&;Zf4F!_y68KzJNl}>A- z!9+)5q#(L;sSu|r7@vmR+H<%{`@T5G*+`TCJ)EMzFyjnw_jk1a`s1K^sFwo~zQ7I? zhF$&U`Nxm|kf+Jc!{7%T@}0g;Ar1eRE-z6Vlay-|Isuh(QI7+~gW6Ohe`xKeF!>*z zy~UohDyNGYBja97#?joMPqX3t-%0UOJkDWq-mVx8VK+YNf~Gp@vxLPTQ$jbAxIqgJ zC%3UK%gDo~L!MLces6(hu=6e+1SeH4Av@EJ!^o3?7zBwLB0c}EK<6{W?ySv1L^_|u zRF54oMD1OimFJj^JZb?EeI6X*Ine5`u)z{2&#w3)S%g$F`ybtgIt}Ta|u-jmufEbZo_o# zbr}Bjo8XDcF_GybN}FBWfU5ux^tlfnqUbD-$++WeKaM0N1XlWfe}_;=ov=H2+(kUN z5#9pf@5RZ>3Ld@Ohm{C0N53I92TL;(m`dYNW31V0kP0}OqpwA+->SlpmcMxw8b#AZ zFGMwwOQPg|hd!AXzU&bmNF`E7|5N*GZ1m%C z=cff$;x7kLu?bp7e*=1&7+1-Rj2aw$)u==Bk9b$s*VHpHf6(w*L?UMwX{Sm?HWM0Q zElf1U>?yc1HwHHA%HZfD5rvufSNbvQ+XED#@Co(?R#VBy&b0zS-P#SA3-8%4=)g_C z=}tr2h?$66Ic*C5MlreEexr)XEPp7ilP?){)FQIWV0{txm3WOF& znU8EJk&9|+49bx3(+&q z1aa6w_QX%Abp~BocJQ2~4+F4dT3gSl&~ZN?52;j}If_o6$B>7L@& zbyNcTLCRz))PD)AN$OgJ2gI+(N9#(wdVwHX_3Ex0_XuCy+a>rwQFv$@)6wAH;^uLRjNowL)r`PmAjt3~-DkJ_C@`#mub6=(Hegr%EYQjPf2! zgO;m{<1t!JqQe*_@3Dsh}BeT09?48+I^K|kMJJy)`7Z4${+K(

=K?;mHo((PSBtNy0mo+C#-_wUUug)%$y-$!9FpZahr$LBic z^f5$Q!Yj}5DrDQZBR|3%rB+*rn!UUMQ!j+bUN{?w;U zky6}iDquBcJ-x}PAk){fr*0}lsm)}?6PgzJtHj7?z z`hU!_SgFTO_DCqxR0b;J`WT~Ls9~)L|i8fiS;dEQ{UqXtid0*S>5p z=(n6?Ajb(v$|KoVYoITQHF7-O+AnxuQh#^#QrzJ`3;IDrpH!zQPQPLhn)VyKTxR2C zccqG6RuhLbpWADFc_{@>_Q*R7%c|aKVuMfBIA3+2_i%BpzyRb-eiN|ijPjf7kUs_} zZf(N)fPz3qB6#KdCn(})3nyE!BsSA`GM52uBW0T<5_@YeAbmwBuy&vIs1Y$_yML#~ z=HvOfbIbXuR~BMz(kJ}=T;QW=oTsK6uIz8ov{NM&NSucXKn-?`Ix|i23+DylcJF4K zf~iA*8o=J$F@rl=;WFAgG-1thg`1L2DZhikPAMIyd{`hx>=2ko6>9b4XiWuICkhz> z(M9FdGb5*07lKK-rwdx+kVp{H`G2Jy5-MM=IjFqXSPNnj{p6mW)VoERTkbOAJ#@eq zST*w3YJwBDs~kr?+FQ8T5gj3);;wlrw*F9Wrm;fbt5!MBgfdVe1d8@*r5{1BXIc() z9zw`%FJ*XdyDHMw=GW;zzY*xGSJa>ZN1Lqu4_9m*ZQ0SD_aGM&(d8mV>42;cfrRfxHtqlNw&8%=_WI_%=11ED^8({+{AQwOl zXbcbr8UdJpnE_0koSblE03lmDcL#G*GbaG$UkoZ58ruJ~{1XB&bpH>}-<^);rZxcb zzYi`zD_c8jppDaCi2vt}NR}&3np*t z=;UbRU~cCG_?uN;SoGgKoy-iJ{>klV{?`q#HTfH9Y-{BFPf7ps{e}7KbuuuwaRfL4 z-JJe^$z=!x7@IrVSsA$h&HWe5&cXa&G@KpHZA|}@0WH7*XlmeKYz1_5{0s9J`=9Ro zXPtomqk027J1h5p?Y8|_)c@vS?&JuxGNFfKV*Z=c$mwrxQ*#?QhJQvy!p6iFz{L1( zyRoy~fB0O04*zNpo=} z_b zzecJ7|4s70g^_SF_}dBr8`HmXFw!&r+i316YVHO!mN$1YG6R?xSpDtOzw9bD#y|&u zD{~v*Up@cTN&p=bBjbPZDVv!aS=#*5c-DWrfHubemHS_b{>7X@LsmdiNt)*WzEl4d zC;wM_CuMiLztsL$DKfUk|9kNdilCsa8^Du}iH!|F$IQX<_sB6b0XToKc>gyU{{_VK zpKBQdCkJykfY#r#8JYf7{Qvs>=St^)zrcvt7}*;CGc8I^1~$fj2kd_v{&5>QJ2?E+ z^hD>DcW0JL3w9x`pph_>*lc4lq|wRDL8bxqj%Rk9J5tMoG2N80{$a zAZXQjr)T7G$4`$G{Ubwz16?u$5>AQYo!s>u?(2*`AzxisW1bEF zFtn?cw4``kM%I#;Zh4u2Z->HvjbU#pDOC$awX-Plrpem$P!LRKQ_lYF**HU8XM!N= zYz{nj?u?C;W5q0Z&Nu(UtLoD&SXT~lmS+)VkLy|WKjPo=)c$x+ZXeFx)ri==&aVzQ zn#OfP7`a7@D+$a9)=cViTIxEogGi%>kiNcYC8fv5@zOIVmt(D4ul>*yY6Q&%%v%6uN zO->;bO}L&rLD&YaMPEnuSVDX<&$IBIre%9+l4L96#4nRl@b3{lWrz)Eqz;6gvrXOY zcC+_y-njO}zp`aoW-9X&|Dx>KKSoZ0Y{qN~+l!e>+(yjJf=bZZ-*-8HPYLblz%x&{ z!kVM#ti6S?AQsVoCrub{3dZf9PUes*tTx9VHe9{5IP={1?PCN=@ARrzIZMjZ!tR-m zt(XjMQ>>MmWsR_Br@_}%lCte?w?}Z9gsXM@Tti|*q$8uU)83vsItG4P;Ei5w7$j|J z6KB6ge{m9}n}!b|@{5H@Tfg=?GIl`fNs8Eb{UIk+>Iu$&YI>dKAJzu9K87m&`uMpV z3fALXsrkXvp_5~c<7c6c7q%fYzmKy>RX)i{Vl-P)=Jm1I21D5JYY9U#IU7dY`ThoVnLwZWqaV; zg@!%QyS-+A84tuJDoK8GUH}uGbw;NQN?pgG{E}|+@Md!lBvprH5@%dK?RZGSRN^tr z6VAluq!PNL0%4Sg0h$jFHpZSWnl6N0_}OgN3Lz!1#0_rDxiPIL4>D1qo_HHYZ& zkxTf9jY8Pn2&!l@O+Q^m?~jN4(FNzOEtmWpeUd1D$v}PKJ=lSWo4c=!`w&Z6xv-zGpW~u?QklU8dvO8>c6Cw< zChblc$>Hwvm0bd642up$u`9XZ9Mj`su2djaJd&nWh=%Z{e+8nIzic2g3OkcYfB7_8 z-i{TD2@i`AN0Bx)4Uxh}*PRn}gdBr6Gt3u%#-xAu3&vo=jMbQ+1PArctE{?q*?vSG zHAX~3$#S?>hDie^t2__Nl~O4|90wR>%*wX*@TH?5xeJ-}d-J=f+ zIV_wLp~*-gkw5gxAb(pk;T5Ny=yTG(7?qs77k-zrj#S-jN$nqmuQxBJrClcwP!omJ z_@?Xiy#q4`|HE7S{?ooNBwg_RUa&@grc?Apj%oBK&Af8&MF1DkI6G^m3G3<@9il?T zG3VrQf=JMK9ABT{!C=Dt3i(?|m-qz2H~Z#k_pYj_TkyloRFWlh83?E zKWWenuX-B|_C|=h)E~rp*|+no7Ys_Ib{u?ulCDQ3#;!Ka=yIC@0ij2)b(DRKoO(r%<<7ZwiodgeA+1IpyUc2LY+3Qr|lK9PjnnJTK4GwbWw;oX)Si>om!fFM!2$;|KlK04X2 z7DW*^`Jt~@yY3frJ0WUrhJ@QF>l_^P{!RdvX-vf$ygvMbH{5(8L-%XHxnPnl2g$*A z%mLlz>zyuEoiP5TBTgD5+|+=xMa#f0C)mjJlCQ0e8Ew>mZ|-*gm;i$z^E=vRQ^xHY z$XQMxWWeGq=>|&2q8~qqpQSQsrP-5vfoW@SCYG?ZGwD)mB)X=OxHKw^ zHOL=-mIzi#2J_BEHi21M&%dB++uaf0jJ2mGkBcg6+Y#pVS)OjSsQMO+vbg z)A~NT%GKcFSS8Bhgug53mOWaMN4<=rms0*1drIf<4=6y~gyaMvwJ%IMuF>H@a)e)O z8K3K?>X7bx0YdN#!ttbKameT574+^1>Qi!myR=h{-Bg5Ws2->gB{xP(!V-O!9#18G zYg?zm{UO=d2ZY{*A;ZZjR(y~ql9rB@7uUymn zC^CBwLlIzw{#9-EKsdFEW=Og9_1b}OykvshqW7BtAAr4R=5(btA-lt=Fo_=TM5`@- zFNLLCkM?Ysk^z{oY$dCRy9>kSh+t4BhS{d38)y~nHsuen_RGEcJ-VYRN5^+ke$I)j zmX6srQZ!lVQMK%{vv7v0v%-NT6wUT&nSdUtew(Q_m;aO+rME?x9r)qRLRSy#d$k`B zoE9K~aT}(RJDHX}je$SLNBd>1i;8D|8;{$Tn~LB$xjmo4`{PCyWr9z($BHDZvZAvy z9!tqU%T+k_eFl|b3aZtl40B8YdA5Bp)ypxYrikQcI9<68Xl!_<#z2xFj@axWarj*n znFBl*{Dzcwx%s84nzm+--yPn-z94>Y%7r)Inkv#>mFLeBst{i>B@KLU`}9SBSDag_ z?jB1?J`HI}sT)nR8mlJ(a%Bm=PA7h+cvMA7k+OzFa5y@P8lz$&H%Dd!YX26FoZj#B&Mq}i?N|1GxK(t;$H5Pz zsJOW{L3YvDxdpR{m!?&SDQ(rX_l8%|^92UK;$b!&;64?{8QoLeqkW+$VEUcjAijDS z*C;|$Z?REDYEH;GbW`)GUP{u3xWY(ajFfKxfCREj0mSLIeoAD8b`p?(0SgP;B0EG| zt8Z8W)g_4If3j+b@FB*lXxaljXp7(RZK;03#Vx!()VG~0W6GnsNZ`6-@I^jxr#Ux} z-eem;h>0Byz&w4Okb_LOmQa-S1Qu|R5$vvkq$7)px&^0#Lqn_g zg;2f!5I`bjm7I zV1~RdmJ2ftlt8d=)B4G+b|^(xru=#Tgl!*o1>9#unMy9K+Mrl%U!D2&xjS5louF^W zkJ&F#dB#+6i0gmTv0em&$x>8lvd5cKPg*s^7tLO2V49#?HVo;1LY%QDE$^4wN_4-) zW7W&Q8OLr4Dt7GME$_0%M~WjSb7J@RkDLX!e1UcgDHWCf)1Q=NpcYz9dxHW0u@W?;c=;wUGwT!X0 zWXuRc(VF7N`BS^q`3XcNaMW}x-%tCd+k3nR4ek%ZEOl1~kuUM_O`Bu78e#B+7IQu| zuVy40t<&;<>`#Ce3Y=Z$eSv}!c2Y8SQ?IM`-ts4Q?a@xx0Uwlk;Ua0rHIJt6tsmy% zx9tzC!mJ8oNw_7R`L2_ZAln`-bJKzaS4||a^}`5-*hU_;VVKh&k#)nC`>hXm)40Fs z=@SFQ7n=4D7koQj^Jq&%lBB!#gCqQ2(TNFD2P+qUpSXNkCvHTwNz==qvDOl+!l?%J zPoIdGcE_hikp%FW2}oR>+S6^16ZLXmp60}?ZxcIKG^hk-vMz}grw~Uq_07a7fFZNP zMeCq^W@;KB`OKfn%3DB1r{SMgq=b5NB7j^O5j(<1w*4Q?XJ)S2HB_WdX^?%>1p;)M zpza}m_5N}ME1bVvXvXeMeT7fl!0nLaV?c?viG?y|hO#0|9_e){$aLRHNs{z09)ul2 zxP(5E6NYF4Q`x=~pk>X?#F}Js(qVkV4|!QzPX5e1t=}82X`HC~w&2BN?805W!WJM} zOz2J!enU1w{nU*?S5XltDYT*8fO5a<&tdj|)==^r^njN&S9Jcz2)_6)+TZZc+ofPI zEr09`vdXn_w;JG!T@}!kN))%&Yoi=GAMIJPVvqoGt3OM68)rW!OgZ_)yc!pfnvg*M z08^enB-K=y^L~Q9KE2w> zU-QMU6XDg4#pgPc=JzUC_#1LrFI~rG=s+Iuqsd?gPRaiJg+z5zpd`)uv?%mdmRQdB zMI&CbyAGddgjq^Gh++np;rKs0V;bcs3LyP-R+ zPL1rrofqJjZ05emBs(BS>!zvNEfG(69)?kqF}sMNDrO1Lh!_%MuA=!0H?7b0hv zbO_lPHuEQINqA6nK$rC0b%X{5XS2u8TWTDNdkQ<~Gyo`jI+)SMQTB{*2qAY`dH7EB zb}_6v$8XB>QgGb1M}f$pseCor+3$+GUw90o15ubg^#nR-fd-UE>L zvgF7I`}>yxwhrA0XM1YqNDX*sN-A9-W*r@yMKUUVuyKU{saaIg>jBEPd6$smWyqq2b?OanKUfUP;XZI#)yUF|)8EIa%sQdjg2 zSTMIvRViCmcgB}_VI4PGJZn(>ONT0cq&(7O{iOwKB?m3N_mr=Lzq7W?N^iX1EAb27 zj_sENu>)aL$oqA%5$h6tePzz)V+&}c2leVaFS|0Bxs}uD#YlX*nF_#whu~p{hS1i~ z$pF3!FA%xw4tk5!Yw{p}1KE{4*}6YM16fZ}e47@fSIdVNKWju*lS#_Hv&6SJyU!^s z5e-OMgKT?%u^~Mq-d3x>ZJ366FbD`3^z|&0>$2}{DTCJ0NhHeAfneEjNllhqz&pDk z-^=hR*W|+58aoSjWKyu%C|#p7`Aj@hR&C2$C^9O)lpmI)&flqjj&~p9Ewx)P!b@J% zgs`IvZ9ep=n%_!gY^jl46%FENOtgSerWERXnFph#?mrYei?VNx4A?~uDZcXCsE0$B z_-7x4<+|+9r<)8%`P^dv22n9PSqrYsUiQdcC+B2C0KeJJFU`E1w+XZFh#qY%J6eJT zz-*tc*%Ed!mEDVfkC5X!cM&wA>2E&Uw0vXmQoz0Fn{rjOeaQOI$1xzukF4gc!apEHKYm+r2CaHdqztWJz72@G}VCe6YzQoj&85sU3n#lG%)muV)+$}mX^y&Q2}I&dS;)@>EW?nXsfClB zOU}}v9!sG=t;NoKPLjG(K6v~PK9*zqN`wB=e;~(yD{`%itSWQ)S~d&FYVTW#b)1*v zgT)pIQ3Hf`9(gc#jxv1rBo*yi*vA^eQ!k^o&@DHt+i<&aFWpsHnsSFy8 zw~-ouGL*xa@LTgZ`2P@d+o|IX;35|Hgzb6($qTE?1p>7oIPx+R1#hauMYAN zUnk0hqY?SMH0RZC3Ffe2FF0qkeKxfC4aKFE>?GWKH3YrpNVordD1jQt$t>`(zC(iG zcYy1I*qQJiTNu*~)k1kSu2HjFo86L}5XIz+h^)mrHJ9>SZi@_go!nlKwP~?=j%CrUkk z-C2h_2A(c3q2d(pD5t~_3>{BEw>41qD4)HL5^Z9UJx!ZlM5N=zKv#VDA%Jn||J+1MDHxVXZ z^3uv_AuggH+9azih)Jh(7*sfBPmvK zMa}tg9k&KUk<^5MHxuR+FEfHKud)}QgX${22lbvs^e z5#yuS!UDJe89!&Bu*Pxzm@2IMII4% zos~;{GSyyMeb>cp-{Sfsmb-&UD40`|ijvI^_~<$PA72~}p*~Mm`-N~wPtIl^7a`2zgFGmq%QAee zO{Tu_rk}i@pz z1niEA6H-YCeiZ!IzQ)6Tuo|c{{RDn5WRzzOJIl6MRe;huC&KLYrvT{wS1F&Jbw?NW z73~2^pVUy06^IE@#A)S%Q5E9qXEs2st;&)i0xcdV$*w^B@7!az&iwY2$%Wd)n?F{v zujM8q_EuXo++emn8ZNTvqheoLoe`$+8LI3=y@Y#>$m= z(wAstGK=SCn}^h1@~j*$XIAO3l`p#X%K1F%?hq7x+x9(aD-r700!JD}qh4(+{n1}L zlJ%lE-^)<@2q2fh=}81*O;a-Slp`75zJzP8cv~otHmpj2*;g*j(!cf=so9||h~#cu zi?gQdNzA-->9esg$&{ToW%yz*?M0HNsNELobybma{;jm&5O0VRZl;({F5una-Wn@NLgPuY}F{V|L>dZu!|>z zmm*LA0%2-@yI11ut7~^Tu3~l35zB z(;Ths>vJi*)lANMm`sDt0G00G%BZf)Z$G5PCPMu(Zp<6IEa0mPvy?mxM=L)moL z(Mg4W_Sg$?KXRII(mZ%2xfL4~iW<1|&*WahWm6CXEwB$~GZCLdB8XwYPWr{|I(~yg z#U+cc46m2vbST)q2<(2|zlcU?W@%M2+v}r1@?BxAb&swSQs`F6M5S|et z3&-X4peoN|rQ!rnzN$2%C_IU|k*L&LAA~wmaUzlblh6g)$(q0uo1>PkPGU!|fC#6aUhGl%Di| z2X!c`i{rCr!2_ABNf4iHmycwDIMhz$2g9rRbBeQN=78o=}O->VP3LbV(6jU>XZOWR;Qvj&Y>?nb0fZQ@diceL%R-*#N3U zY|EUwJ7LX#)-Sc2S%u-J2Q|svPafibaYnj86l&QKHYa%y3xNgY5d`I)^W#WooYY39 z57e^rosg(ZLG8N;U}Py}1bo#_AjCqZH;{vs`Nn^It7TaYMQq?nm;8;;fB8fz* zz8>3jlj+N!|0Gj%MGGjeExKCFjexbCTcRrE^uBQ_V`shB>CanOF5FC(f)`SMX2Ase zSvv8~(T+LItbpN#W#LPJG`keEXj*39xOy(7n;a1B|gMtAic$@$aDaP@Y862-C002w%Bp&-dSw_TIvXan-Id-I?%_j@31p_|KOUj7-`xj>^ zH9ZKc&$95j2_D<8Gy_Y}E?P~???-wFC+C5t5ppHJP5|69NaeqW?i{jzAF$hTOAQu} zhII@v=gB3XJ9AFjI_PY$t4uP{I4k>?-s+!UzHdjbp_bWorH`Y7#fxx!SVqXeBBfX* z%Hs==f(sA6Y=ZRR zNO!~lZ1MMunO4&ayRgooqdBXWw12{E=^+)wGCRIWoQ6P1-Dwnmt{R}x41qQvV%jI5 zF&7C~>n55qoaEZz)8Z_WI#tC}vGg4s{{z`_*b^~Nj`iizv?S&gMhu?Yq1s%cDdtwY zW*QGPT(V@^w6*XxU_)m#vpO9ys!OIRa)<) zBcL7Qi0uK-p^9pM01_N{b=lg9pN9`bwcDdJ*py`oKUz5~kRgJ>QK3A{-eDh&CgAq;df>+NT#B+@tzp+=H9zEjW@5IFvMZ{ zXT5$3ciY%?0+;~RcPq(&L3bV%rz)7rXL_ayZ-D(iQxpjb6K)N1#(|dUv<{9I7YBed zzi97&Ln5yV(4j)N@mTNjaTT(8x1M3VwpHyaY2c*M@*$YaPJ4leZ-O&A(zF0pDP%Qg43u$LtT9$J=BU{^YlxjLiF;=LX%j3 zL~1H{Duw@MmyFCMV?=Ly1x7KhmoW{P_7b*l?M0#!Zj^HHyD_W7kiY}^0c3LuVhpg9xkjC&#tRBOfg4 zO<0ZmELprB+LazYYV-(P-RBVmYZ>z86dm1IJh(?Aol>VLY*X`8#-gqC18g?wjhwa? z#!}HwPi2X3kv2_l+=ZHb*)%G8lixeBcE+Qf)6#j^W<#U~(3 zWZnu6!$XT3M#Q}Dstd0HJpt54uz#jWPD!cp!-@`^%NA90b2giR z8l)4}?ES8i(E;gA+n8Gg7wqI>d$#iMlMK8 zn7P6rfqno_aINjFZbjx<4cqH~-0|>k@y{WS+cMpUL~wm(@8|O|o?Tpynzo$Z-6iy> zlJ7Q1aXo6KjWuRe>%}u^1E~G3&6TF+yW@ZIr1jBL38btz_x_7 zp@|2m7(KuC658^@v@lIc%#OLmRos>kIp~KDF zBN9c6;_<^wJ{|w~n@}ExE?Y>*Cs?PV|L>Ll-dXKIWt$81t>cAcyg}78j7^;rnX_px zG^h=#I0tQYY8Q{T5EPFcSme)Y=~!pqxI_h8^zc*gKz##Sk;P92J6jb9<>lWY*mokZ zh4JPF1_@)m@C_IGZQ0R(p)#3iy_S%z?q7Q#V3XD8ax_mO>fBZ3jF(PO@H_3QL5PD$ zXLvE@8ag@B2nk*qeC*>5gZEj9axE8S(VLog)fBj(GQxW&_xs?v^m#TRzDka%x#R~} zlHH=Hh24VXW@5K>RQQbZmn}cCzcZy&vk_i7R%lrd8KdCMkM+HOQ_G>CjN>2Jm2R(( zXuJ*k|Jjf$P*mma)ZV}jmD8&7ab`Pu93&#CeKTjFJJfJd|CP6GX_6(Vn>TfeAI4dw zam5;iPniUgIe(P87p+>cy)PwuQIahqp?9h43_39_4FsS~>~Tgx^Z) zf*d5~7gxEMx#bosmW*!4!;srocekc6rCNjsZYdht5>-NQc$Ax+tEs{Clk#$a%z?zt z6ruuN`Za(#1&>?@J*q-8Q5*gH=IA9ZvWX-UsUMbQJ)TwT;SS1U68h`bCRQ^~9MdON zb``$-w>$BFL9#B5WPw)kxBd-BLjHuPE-&$YJoSJxv!6nnox@lA zi4;WK`Lr6|$OpVpSTWiBkGNGKok`ED#mqJ}x%CR@WIi@Y`V+!Sgl!HQUp!9oEGOV0 zKS_(eP!I$2zqwbRe`!o|{%U{9QWXJ%8Eq_ZMoSET+rhx@V^N0dXHeEH;S^#X*z1A8 zaBZv<9^3~(jtbm<{nkl3DdBshq12e=oAm90$lTZYJ{uJ%TC!r;OHSCB?OwBlT#k}| z)_(@SzeM)PW&05~Fy1n6G&rf^UZ4GjL>xiV)uCb^i|v}^8)uUb4-H8=WGYcQJfi@7xvbRo8~{a_eTJZkui0<~i9(U4LBsK-W+Mit0Dgd(wr2 zhbeaX(LCq)4hgAGkfz^8ilN3dB@Uay(9#elCyXqjD=Uq=Q9um3+_(hKa+*Xxe61;Y zg(;y48I!1{v6tI5HG7Zj{ilF!bX^NpzjB9vnp5c;xd!>U2OuuH|j-vO`V!3bWdcP>na(66r#A$({FZKtm%GRgmPRLz|R; z4CdKnQz!~5Q{ZomA#e@4XuZ4BFG-X2QONr8X;0r*u|cD;AGQ-JU|x|T567Y@GeOz0 zgL0XW!uyqBoEKLXlskAb7L2|3LLEE~h+QTVwPsS*Oxdp9#_p)r`;i7#o2%1IU})}F z1aKj|>of&8>Ucql0`~BozdgT9_%}O$%KLT1KI{bttlAXSsh*%ww$kH>a`fop(wqsU z*MVX$%1mXo;$~8R?8OU2|JNrs=;cXQs8&Tk^Kmgvm$@{bPvvPKIijnrLC@JUKd61l zQT>9Rqu*s#cAJK`@JLY@8>2f~je66$OuPj8Xp8v{_)rk{sBW=cxwl%Yn=`V1IM+u& z_C8&LzliP(6`F~o;5<`}bnmYpDIQQf!z%Zw=;)XFWfl)=dnM26$DuO1u}?P4M71Zs zsU2~ZVxO8wLow05l1?~tB|X^U%LY+si2MA<$iIhAsgsaKuwwmM|B;KkQ2|AzO``kb zJPA|Tmy4uhbbg%CywfZ^tpfFb7ps7ET&p(JRb?Sl=aM8wV%>mYFYjkmXFnL4^&YK+ zv_;8kJW}d<<-6UfHCttT2AvZ2oWIlO`-U{~zAm`5_Ym3pBAGiBIqfgBD2d|ckHGuG zH!qjuQ@Z1ON4E!eu$kpB+yTuALzi4|L1aiKDwDhWQZ)5-DKF!_?{zbOJ@NDuPC=w` zyPS`M51=47Nx|bgAhBFp(M%{z8jm`{;^K|3r#(WgY65C?nR-h`@9zoX+zo@R!%TX> z5FkItxhew(x9OU3Ly*^GksEozG^tr{)Po{g8D}JJ9DjL{9t9JVFa^_-GUq@$^X-br zcPM|iSS2t4gQ+oiUW+n+EeQT~LQ=bLt{ZK$oCF;vg}08!5cjn>uZ5I316C;&+nv%Q8+$-YOXIBsO&MGmBvF> z2X*BSShCbO-KthY5t*(#b(h}}rZ5Ra_Pn{8Sq#lN9?Ur@dGb85*tn`e{h8$P#t%$w z_0Bb?5uU_hNTa+88O6D$R!D{aaPK5}KqOvH$~|J})9UjQpbrfDEs@oAk0zVt)K{DI zBNN}U2nih-&+C|fg)#!xk1vicu(7E44b|!1qH3gDs(fu_EwkJ-6^oP#YJg&2Ol!^E z7Ye5>gjKU_{k|gH9BUw^F&>m>y2(DA_Oqnqw;*p}q`ThSgpS50SE0WqW>K;Y1VF2$ zJ64nF&897{en4KHUSAm_rmmRb6+JVa)sy@b=1XTQ5URC*lQ;22VBu0MRIMrS{7u(i}R@J=w>iR|P4NVcj3jX={T99zmtM`lEdpZZ;9eapti z>oqh6T`@xPC6XVLg+Ipw)rV}L-{=7qO**g4MA7O|Nq1b``J5*>io0Ekvmf!$df*&e zvVz$E%rBEDKvcs*bWsg1ZE4O}a(L{eD5oo*wP%KZp4Yfn^#;+T-EB=XIw|iHps0#R z?0|sac8@6fwNQJg3W1B;$Gq6X72z4HAZ4`-4udl*){*ofcB(W=Hip89J)-+2i>;8z z_Y%=gsFAoEBC_*P4&f01ac?|DRS2KIS;_a|O2XHgdRSd46KICForYW5y0CfMebPN( zU!b~wcK+)0UGh>fy74Va~lIt+!|Q!@~Q>L5PscsL}ejbdGKm-idM| z!Z+icj=6_I5&6(0*|*k2fl~xDFZL9t>bbyNm=KnV?C;R+EdF2bW}xrxT?y8Wzk3?g z2P$x#5_;NG8fxAuCxN43bTxP{GIbSzcx5lYy3|UL$!``4N9n9@w%Oh@0#@du<|r zF8IsRyn&UoBcX&o7-lT0-(fV z$_d+?Bt zvrYEAr}|^I9t2G_E->-@YrYM+dixiM9m*=QS#7AWbVM<+#(dG5>)$xho2dLrb8Jc z)c9ptBez->@Kl0}&`@@|#<}>`pxMboqb}=DrH3f@OZ%=n>PcLR{U^ljE8zZ^fsFpA=1NNE_;!}#Qv44H^2WJ28zlmKb>KAxM)a!#&Rr0t_uD! zC&r9iK=361GPUWdDQj71@W)d#gAFHGCY$|&iFMvk550zIpUH1`s0{}*sKFcoFO9`V zugXm$Gg_b(!{izzx|BKR9cz0`ZyI$&E9)skWV+6Pe_>)&7^a*SlmFZKnBkaTrJ2Ya zC5Uv6YLw6!#u#I8R&jcN9oljF{B(P%ty3y8=+Al?>@=hEClGwB$0~W$_gof`yP3^x zI$s)oEEX)AT7P4~1n7d9)>vC4Dbcv*wQZ1%3IA1UzByr;zEYoNGLt*#kw6%x9jfcK z4Nrxy0Lr6g&T?s{XR4}&J3ow10(KGd=uWo?LG+Nc2KshJ9Ps6TZ^p%u>}(V8f@vB2 z!&2_}+TPv%EqI$4sNZ?t1SH#0Ej5jQLoqn_VYf@At(@URbwX8l7y@ z6Gn{k6B2B$w_jI{cDI$zJ&`uxWfxK9)ls_#G2n5xy1c+I&@%pskFr9gytL#VqcET} z|IYpkH*IFv27|{{Dy{GK#H2Ht#mCBR7%k31C&c(VS4Jy;!&Is;N{#*-7+qa?W3L@^ z8bew};%F;aD~q zW*8p0a^EZF+dODwspn<&ciR^s$K zIMi%Zf_#|y3CbU;0S+)yn^I6FIM)6ClPTe}(g-2oYU6y28IU}{8`jFB2owu5o+z_p zewRF0VT1K0LhK5pyahj~)Ui6E274Zh zpj|U<2wLs03?Rv3Da-tDM$J-SCbzpjp81rJh$b^yvk;oAH@9i+e{_yMcV^{%@bZx= z@$yOqxQZ9+w{wF1;KBz~w66KFdnkr*B)UCsIG zQtP}o8MOhopA8We4ExP}$lBXrCp7I`4iqVmSGqn9ejWca!_9c`FxHz{O{nz1e&1YW z2PE|cmsIR6Y@f-8cGNW3^Z64Ga@}v{>a;J2Zi1o4{3(mnJ{^WffA(Fi>U%tDX@z(B zy)<2b1)yOI7gnELd-sME70GAzXJD_IQhuqyy+Xmaopw9%>+p8pj)#1& zf9Yjn_mcQBuWmQQyo~_VBYwV~5@tvt=UN3PolVaxQZ&9rYP|Qgs$~t_FEy7yvq^j` z<*JXXi{iQranQ8<1rPc#>r#~f?RO%v%r}?nJ)yj4sv1(t#OxHS+Fm{NZXTZWHT9Rq|y6Qw76kq<(&u1rJM;x}VAVD%{hy{v&IR=m2TKFFQV#F}| z7Qh4qqv42mP)v#q##v;2_Ggk|5{RIamizv@A1Q5jefMMKGP>VwfaXWOH`t<(DOi^Pn;*-~W^O5!f?I4+P6XEBivTC*x4{9b z)4iBypA3CD+Iqz{l=zGouHc5RDP>be2-%?l7*gPr>~9|@0)s?U_Q;+Vv2w?QMS(-H zz4*-D@60z`n$+!*vR}$IY=cO6>~-%m@{KEK;l5cO(Gsa`{DtC0kkDeH5;q5N+aXYh zGLH-meI_4-n&sG9y1aw_MUO6!k(){96@-p1dRi`xcFWl`;xC7jdxUa97Kd4L|PPU0&+Vihfr#4(Qikx0VqC!Rek-;$EKog)h zia7V>Uh;RTL*991FsLJ%9RL2Gg)mI@C1P(t@3-fah?99spYU9aVokKd1bRS6jNNgC zk8?DZD3xkp`vanCQ@5DWiW?;zP!!IuDfDS01!>KuQ&+*ViuiUu=(h4+B<>*9)Psq2 z?EEdq!J@{R-gXXK%8zeLsQ3@p;1M5ZXAE*$ahg-_dww$l(%(3qQH2&O2+iXo@t4#i z1QZoEk)@h1lOH#*-94@aW1E1lU;!U5!@QA4)6-k3jSQE@{Dp`VZ)<1AFH>Ib2ddOP zD>|)12YxhD5x$3!<7C}l9Y1JDcC=c3_%rw*ikyMy%(0p-cg)XO-*Jv7scEWuBNU2q1_CiF4*rI^n{9I zH}MT+@P@hO5)xU~JEyit=&?IJBGyz>OA$w%AM?6{V>WP3b=abYSoR8qk}ZBYl^o`U zg|;?C*S$*VEbeJmiyGToimMW)=;arB8cPi)z@m{+otB68#89@)i}m^ToKa&k#m-`# zM^yFFgD-k*)ajYKBL4yrhbwk@!#KTfL~vNI7d*8Pwl7=vJpuD7rddX^M+>H027@UR zeC~G_p}Rk@Y}WUf)vL<0tbRbTu!@bj22G_Ss3+Ys*U~4{A!bh z|C1;Gjw3{md{fYg$RD#=`hzL^vN0M8hU-0LOHJh^Ku0ePL0$ofy!l0Lh8njk1zY71 zALq!gmjiBy*T}#f^=;eLoqN(^7_dy-h^$#Dq_Zh-QT?UW8QDj3kV>>69W}Cm#AxQN zyB2f@q-_h$G&dIrS3+ZJL`o-4JQc~XzW$7n;k#v`;xQLS=7C6+a7UH%C!w1A0s=GV zv!1pvyl;;_!52V}#-Jw6mQY!RX*CFMY%w3PTS)B1*6LS1$Mu7r@WR>mNxE*+G#GFc zQju@&+}01V?%f4^8CcG`zPUMrGUnpcNEw2Z1z5|}=Stios0Uh$aav7D&xg{hW#!sJ zy14Uo3Hc9>k+Y&6oV^_e(Tnw(P*#O?%s!KM!$G}#%-(rU!TB1DzRjQJInb z{M`(Ydw&BJHmiAjLxFr_6W2WBM}v*RP!efazw6Pl>jJKjF0PULxo;lKPaVG8u~aOcRRLh~Pz@0EWU!A98z3-i8zhbjh8-7{Zp(Pcid{_+@tIDV8p%S1K7 zj~bYaKYs5*{C)pVhIx?)!Rj1?&05iN4bz;k99a~R0#UA#W;U-uM;!mf91zxV9j<(q z&}aBvBj8GY9#c{l5fv7Dr2q6penEL6!}2m&#-g}@>Au;`o!dla(Rnx%YB(-f>gv4; zW9ScHLuR_!QVtOGuH1JwvW--tN#bo(zVlwR=Ml@#qQf>TB{5w_D$A)J{=16Adq3v} z^KTUQ&o=Ngdy#9_7V(YJLgWVLWeh*Yw{C^<07)vu@XqnbUJ(b{wupf}GTjBUA*M}k z`t~b($G6{~+K*)XU&=)T6kn%h{I#dH;qCnZIwJR!ua#!}eL@(2&Dr`*b?nsz;mjHx zR~=jgL@fJ$4rFrf7^Rf2?q6)n`C)~HD#%vZYSSSM2qTaD;8a1QUS7O7bRGP3iCi4n zP9w)r7q~t;gQtAQ9ULd$-t6|{-nWf?atMrRG25ou3Tl&f-vP|UxUTBZqy!Y>`t*>2 zxnvjVN_>g%Ys>UEaAB&?nn>VW-$zlO^NE-}p7qJ~Vmj+Y^vX)=ACcb=7X&{FZmF_P zT2I1@teTpeHo&;Tm>MixO&oqC@?*C4tSE5I6br86Am~B)Zmr^Bnc0wf--{90JBC27 zniHaS_c~afeMUwvt!uoY_w%fj%$S!0sGaPw6y^F->aBUSpK~;KfaopzaH^w@F$f3q z7X_YoCN`+{dxZ+4EoR@6hJwOX@x$2}A=?eq?6u$%qC!60CHl=B;u4L#{vo136KQB< z`l%Gp-m)V}pKjdA@&vsW=L1V9XB_M~{EsabVpF`@`#z4sC}FgLKr3Me5flPez&Ju+ zft`h*s^jQ9D5d>E=43IyZ1h_BN8Ym96^fFyBI!d#B`32d`^QjY#ZQu)tt0QGeSRt9iY4rvXw(i!W`%t+0rR4dM`2 zDDOj(e~>XsIpt-_pWt}JZ`B)G0H2g{-@mKU3a#Oe!3%x-{Ac*@Qh!C&P$s@GQ?!?i zQXsfZv%|C>Ynuy3RHy{3i5=u;(|B)m*>AD!nDQ37yr}?L#js*}z5gJr1W@SOE#OT6Y*&PWBa3{$%p*0|tv#g(xZW zEqO*3iTliDQTQ@5qy&I-=K#;!8^okz?q`RL3|JDt7P{GIfLW0VHQ3+G*!Y)X;}8E9xwE zwIIZCb`|4^7TwUE4y7n{{^UBWi5PL#dqRuCS>__oQx;m1>KF7rmzIT$EaZJ{|2=ku z>wb%J?YDtrc}Vx&vtH!0lVsxjoxQHJ(n@X)y_73QwDM9S5}uk;6gIMi~|I z5eF{tN zXEV#nb3J%~tBjBSLMTq72dNgFd~h>j790AA-z~14zF~?gNQ|G-X@hE=8iiN;XunFx z`2Knc5@?ofQSx(D`)Xz^C&s}XN-Ini|Jbi|>pcysZYTph>fZZa}K z40RQ^XfO5U2}8~8s*Fk`+;Wv(@5qE5PoOHQvUja@Cdz@&a+Gn-p(LGi@a(xMAC7!q zF4W;+7JdiN9w&X~K<-wF#ejQ8NqxU;L};Qx%?9fV0dOW*hsXKrmc3?$SgyQf4}52j z@7nPPmWcqLRH|pQs9@~y+8Z9x^(NvGNn68PtK1}MbgC$rmEKx4H>8^Yas*O;Ln-@> zmxLgSWb?U_xTl?2ecO7wk-($S!mC$@(~@wC!;>0LLuyZ_iUR(VCf(1gRj<-tRQEh0 zlmmjX{^(-UkmH*&#f{D+nc^`iR}2&Llzid(fW`+Hu5g> z!~?>?Kljg0oYChqnTs)kYkxg9={^-!Pj{pF^rOCIbT(NpwlXR}#;ZTehb+;5CJ0+F z(cGj}XThZOGv%5|V+3|3qVJtR2;4bK5u_H-r!mRP3dY@nB4jBlKm9_|Hp7M43EeL_ z#1t->44EOdvDonYgSrI@=CCy*HlFlq+Watt$vsDS{n1P~$C+emSNBdvw(nI1l9Rg^ zRgcfM*31)5 z8ty&m&-1qnpU9M^%(Bx1KJg$r_GR~~P{d!v58BS=+Owad0?36oXJwOuP=Cks#HD!F z5Y#}zGMUR~5T$1v!tkZAHAV-}0xMgA?AlDCV?FoZF*?8@dhZJsk=*M!wWy(s=17*8 z>KoOmGN(>?`V?F)Ci??d2z8^!WunM!_B@ON)IP&Tq43=x{%i;H+K)~3QtH6z$6s7H zABk9-XVc?LYcwEf`S@an-4sL`BQJ(F2DpE)g2~4%Vpj-Ag}5S>eq)*zYcl=>24Az+ zkuTz*JFOq9uO**%Bq)6v6*b4568_ne-N{m!eWdvjCq6^L(~pAZ%X-n_VTH*z5^Ds6(?fTI-Yton;9MM zNBuCV-S{76s?YI#q9Q9T7sV#UfS{bHgE@iMSl6AXOtk@NQ7Y9b52iG&L&y1nvgkBR zkAR1=obER7=jyZKRJo+B{JLTeI2C_5))Ij)Lp_2z(Qi7>rs^-of2{`{J*-hbWNm1P zwfs)nivE=tbMJuBK9VyKQTi8Z)qT}L%}l1ZbI1D-n^O5~?sM&ZM0>CIP9yv%; zg!Zi|&1e(zs;gD)&Ml%Aplflu6%;qEcm-uO7s%CP6hU9vDt~Y&9{o7B_Yd! z$2bg-S&Xd{5BmFzeS*#K$+?=rgdinjXg-ISv3H0Pe^)m`#40bHqq1yWTZHrNefohA zZQoPNbjHXC{7)Adr+;I#L_o3$bCHK$ig@tD!1jQIw zt4wkNf4M!$%2()FWN3$0J?X?;Gus^3ip)%;gL~T+`D^9If(78G)f)Kqx(SwsW5 zm*?@Njfy7v)}_fzjb0uCBfZXV@5${R%h6!2k}O)-ET8P7=yGN*+i5kmKNHNeZaIFB zWjG#sMyJn=#u`_mn`8W1*i1|KU253Rb47GKAvou>9^Pdqjk)zq(JZzj&$rcC&suFC z6=UeWkSflHr}Md!1F-aSAG%9)({ig;3PgLUs6f(s^a&76_4%S<9(bC88a79ww2RI{ zsCwj-dEtieNaz?|_#ppYdUASF69}=I z?z*QUNm?|eIJ#} zu^4h8r;19Bp|Z|w7D$v1E8$WIc=d!YLDq<1Q?s?J^kl|ihx7lkW*rC`mzT!J!I_cP zH&d`j`HGB(8W2jtq}WS~DbpK9&C2jeY692MGTx2G3e^5igi z*OS<>Eonm}&j|ix z0B2~TyBb0h|4|uzx(S4E(8E?>L05oyRRs7dOBjkf7E&<{n-8dz zdxu*l=nK;hw-YTyb1|1#3?~)>@#rMh2&Jf60!&(FLQkVks729nZAnw>Z>GmN(1KI@9vhJSBqSpq2y5xlSbDSxJ! zw2`EtNw5TB8*wm7;G$A>`Oubg6l0-sLHC@dv-B_-`>w|^85VmofT8kTcH(AU|6hMm z#vW4R}%-I`~>xUFGIs0DA5Z~aK)WlAdUTd)jjgr-wR2d*qwhG80~V@&3> zlbdtiTIM`qiiKw6;XiJ&Rs+LUFprxF)7LkCGM|%JWsJ+%pRk4UL%R~gv|t73@1d+d((ASpI&k|uVOk_V;3)$dAC-b>E@!lI!8Z} zXx6ca++S~J4uyR^sNz{BOPq(+AcT&^6%JPGj`z|0xT}KUt>{8=fPATt8rKIfMcy)g{0ljkjh>0i-(!=Bt zST+Iq_ywBrl=L29^^0WNAT}f!h=hO2rC>KP))g80%Z(Idog!UtZaO49`=|>64LLkF z{S8mBBHwP&rus<+@Oa7q6nz{SFxyCpCg8eYMR=HEl3QJZRj9NmqUYrozP9b(dLIw! zB04(f8OLx>3(_-VI&5SWy_N9oK5$rI@7uk=s zKx)p%SxRiJ<|Vwxg?qj7NJVe#IeT!-NGg-_8iQ>w-!+j1QV>{#>Jnkkl^JShPtLkr zX?sj7+;1p7O}cJIQ*-2(IKzIALY7e$bIX`!gR&+c{aQ8ii9nYKrGuMD!;;L-q9*Uu zFlU|Wdied@_HkTkkM*Rc_6BhdHar=5Qz2i<4m9j~Kk>z7FLgoU^<=4xXu!jtx;p>j zHG>@=j&V+ag|_oMUj(~5coro0;ETq4aphSwSRFC&=Fw1fQF~)_bSuYps*6CV4Q7`K zBTnza88c;@)=aD28yR?wwF>&=!cwOPJqOI+LC`Qw`{(ev)Qp0p>_lYRrew1#*R2NJ zsoZGYsUA8$xFi%Qn9mR?X~H)OzVvkDoQyGW*XaNd57M~V%@I!pQaRML`2l>RRgFl& zuOwAHDyR@>{ygXn-iBO=GG6}pFYhS{*3e98y|~CGFD}dMg{ZW}uJo;n@}s>Wn=5>k z)M)a>2c2)qzV;%h*C+E9o+D*U(WI_l*^JWk%cqfodHR3HhatQowTZKn$BBjwM74Tu zSz-gK+4_{;cZ*b5)(=1aeBRt$cR;xyf44=EmO6{DQjbZ#hLvwFB)+wr-Njy;&+9>c z{6y{GusSspdBb|IIe_3yi#ruev%M^BZ|KM3BYZq$*ENiG{6IdmMSKsx{4idK_|uNG z;M*KF7CWgz!KyXGDw-j!&Q4QQ(dJS#TRs%nX4573P_4kTjqKJ_wBL3Yj;R5im^y_T1#_^llW~JIrxac7CStr5wXKJ%cuC)HwB%CusDvb6Q3A&(>7>`d^Xf?|81SApN0N2wNaMINLV@xLN?mrk?vrzk-ZM?KPkaw zO#fC3A@U`Y1;W&y3C=;Vatrlea0Dh$D)$^wyCJdyTyG`GOw!fPUZ5ae8+XvSzTYV0t-m9HcSZg6FlvLC3lXoZMep@jpB0^yUQQGW2O5ikk|OsE!Hn zKFTucrl%8~8wX`sQRxUK(+f?e6MI*HD}Ljptcy=kFj!#{RR3~Mi4}SpR=M%HKfBu6 z*;!J!;s%mG+}p862zRJ#5ueX59ldYRR1upVl)C8*2lij}T-GCl^r0&S0dkGexw~TPWjeF?AdC$7D zSA>`-2q1=txnM&1;-F;CR}Y7-*=;0vs;SG^ly?2x8H`G>%S^uj;q}-1r5R!I(nlse zSZoA*BDx^7vodKIY^`fku~nIij9M6`G+5Erd5`_6plq?zRh!Q$Tax2aabo+=O0+Y+ zVshg%O>?;0o~OWMH#CY*ziaY-iUUh^&mq*LrYnL<> z2^Jj}?rLK73`WS{6FnJZ?7Tbpw}tqeA#U^66=jRhSXDsCx@9CGw*g)?DOTu6yehI# zHfMNW`=4AKPxKr3s;8jSDBh-!^>OVUhG_`e=7KMmnt@!KFTSAUq#4`KK;9W|0;5yc zt*x8dph*r~6?Lb7%NEI()yi~|BKjILOgZNkPw6R%YqL98QKNe78uN7@;P8UbaJ`i_ z|8nqRx^6GK@vKYB-Mf*s7Yqg8G%?-h0@Q^|3k0`GfY>8gCtR4<{25#>+F z5`p|AO20wSmN960>sSK`G?yCTMuxm&+ax|{4@?3R4Ao!9gTG#VgqE>$nz{AN+sCyB zm&>7j27*lNJP{0g2<=OMGw-K$i#L?=dmSjzIDcc;{5+Bk3XtQtlzPH9cCyMJxYVvC zd-3zsnq)Vc_d+=~@VYf@dg6-ergmux7c`dX?2#nw}8ZL;+f18D6^)qNn|*sV=C-Yb;y@GH*I>ErdR+WkjZK7v)3HW zDOQq#+myb~oRbPvP6PsyT;EeyF6{6*V1jya*m?Y zeKE#LSJdl}H2a0& z8S#-{`_E$wXt!{A+bdGI@$K*bp?hGy^!LYb)Bu>@5S2sA#@7-A2J@qG=zt8s zAZ`%&Us2P^$^BoE7sLtDMCDL${Ot4(LH>iJK?cHn5|VsUU1^r`=OaR5~7(~(qKk%{>izXdaqmACHjb(>0 zm7gFfVN9PA%0f(%Ns^W64KtQq_cKI}(~j+n-<83J=yR3G)7QusL7KQStp}V6ib;u{ zAWZ%cMC(x1GD$pd6FAjE5`8F|D8c2*qqcPjZmTnl41cKbNgpM-6w$*+VUiBqK-z;K zM}WX-fKVb;eTf;plesH2mO9m9&6Ze}x(FA2rG;496yd3W3h_hHeGx9&G7!R9l7za* zk7CYz7#X{*9>}j;zSG#85zaN<6BGSx_Ej$I)qZ_xSk_?lv};0RR1ZQc>!JVD!@F9x z-SsM#zufWy>!41Lhid6);pXmYY3lIbFDElwR5y21S9fn$%g?A_UT$7KZd7`D88und F{{lFE+Mxgd diff --git a/lecture_11/lecture_11.tex b/lecture_11/lecture_11.tex index 22d4064..318852d 100644 --- a/lecture_11/lecture_11.tex +++ b/lecture_11/lecture_11.tex @@ -277,13 +277,68 @@ \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}18}]:} \PY{c}{\PYZpc{}plot \PYZhy{}\PYZhy{}format svg} +{\color{incolor}In [{\color{incolor}1}]:} \PY{c}{\PYZpc{}plot \PYZhy{}\PYZhy{}format svg} \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}19}]:} \PY{n}{setdefaults} +{\color{incolor}In [{\color{incolor}2}]:} \PY{n}{setdefaults} \end{Verbatim} + \subsection{My question from last +class}\label{my-question-from-last-class} + +\(A=\left[ \begin{array}{ccc} 10 & 2 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 10\end{array} \right]\) + +\begin{figure}[htbp] +\centering +\includegraphics{det_A.png} +\caption{responses to determinant of A} +\end{figure} + +\subsection{Your questions from last +class}\label{your-questions-from-last-class} + +\begin{enumerate} +\def\labelenumi{\arabic{enumi}.} +\item + Need more linear algebra review + + -We will keep doing Linear Algebra, try the practice problems in + 'linear\_algebra' +\item + How do I do HW3? + + -demo today +\item + For hw4 is the spring constant (K) suppose to be given? + + -yes, its 30 N/m +\item + Deapool or Joker? +\end{enumerate} + +\subsection{Midterm preference}\label{midterm-preference} + +\begin{figure}[htbp] +\centering +\includegraphics{midterm_date.png} +\caption{responses to midterm date} +\end{figure} + +\subsubsection{Midterm Questions}\label{midterm-questions} + +\begin{enumerate} +\def\labelenumi{\arabic{enumi}.} +\item + Notes allowed + + -no +\item + Will there be a review/study sheet + + -yes +\end{enumerate} + \section{LU Decomposition}\label{lu-decomposition} \subsubsection{efficient storage of matrices for @@ -366,6 +421,25 @@ \subsubsection{efficient storage of matrices for 1 + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}5}]:} \PY{c}{\PYZpc{} what is the determinant of L, U and A?} + + \PY{n+nb}{det}\PY{p}{(}\PY{n}{A}\PY{p}{)} + \PY{n+nb}{det}\PY{p}{(}\PY{n}{L}\PY{p}{)} + \PY{n+nb}{det}\PY{p}{(}\PY{n}{U}\PY{p}{)} + \PY{n+nb}{det}\PY{p}{(}\PY{n}{L}\PY{p}{)}\PY{o}{*}\PY{n+nb}{det}\PY{p}{(}\PY{n}{U}\PY{p}{)} + \PY{n+nb}{det}\PY{p}{(}\PY{n}{L}\PY{o}{*}\PY{n}{U}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +ans = 5.0000 +ans = 1 +ans = 5 +ans = 5 +ans = 5.0000 + \end{Verbatim} \subsection{Pivoting for LU @@ -467,24 +541,24 @@ \subsubsection{efficient storage of matrices for \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}22}]:} \PY{c}{\PYZpc{} time LU solution vs backslash} - \PY{n}{t\PYZus{}lu}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{100}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} - \PY{n}{t\PYZus{}bs}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{100}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} - \PY{k}{for} \PY{n}{N}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{100} - \PY{n}{A}\PY{p}{=}\PY{n+nb}{rand}\PY{p}{(}\PY{n}{N}\PY{p}{,}\PY{n}{N}\PY{p}{)}\PY{p}{;} - \PY{n}{y}\PY{p}{=}\PY{n+nb}{rand}\PY{p}{(}\PY{n}{N}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} - \PY{p}{[}\PY{n}{L}\PY{p}{,}\PY{n}{U}\PY{p}{,}\PY{n}{P}\PY{p}{]}\PY{p}{=}\PY{n+nb}{lu}\PY{p}{(}\PY{n}{A}\PY{p}{)}\PY{p}{;} - - \PY{n+nb}{tic}\PY{p}{;} \PY{n}{d}\PY{p}{=}\PY{n}{L}\PY{o}{\PYZbs{}}\PY{n}{y}\PY{p}{;} \PY{n}{x}\PY{p}{=}\PY{n}{U}\PY{o}{\PYZbs{}}\PY{n}{d}\PY{p}{;} \PY{n}{t\PYZus{}lu}\PY{p}{(}\PY{n}{N}\PY{p}{)}\PY{p}{=}\PY{n+nb}{toc}\PY{p}{;} - - \PY{n+nb}{tic}\PY{p}{;} \PY{n}{x}\PY{p}{=}\PY{n}{A}\PY{o}{\PYZbs{}}\PY{n}{y}\PY{p}{;} \PY{n}{t\PYZus{}bs}\PY{p}{(}\PY{n}{N}\PY{p}{)}\PY{p}{=}\PY{n+nb}{toc}\PY{p}{;} - \PY{k}{end} - \PY{n+nb}{plot}\PY{p}{(}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{100}\PY{p}{]}\PY{p}{,}\PY{n}{t\PYZus{}lu}\PY{p}{,}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{100}\PY{p}{]}\PY{p}{,}\PY{n}{t\PYZus{}bs}\PY{p}{)} - \PY{n+nb}{legend}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{LU decomp\PYZsq{}}\PY{p}{,}\PY{l+s}{\PYZsq{}}\PY{l+s}{Octave \PYZbs{}\PYZbs{}\PYZsq{}}\PY{p}{)} +{\color{incolor}In [{\color{incolor}9}]:} \PY{c}{\PYZpc{} time LU solution vs backslash} + \PY{n}{t\PYZus{}lu}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{100}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n}{t\PYZus{}bs}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{100}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{k}{for} \PY{n}{N}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{100} + \PY{n}{A}\PY{p}{=}\PY{n+nb}{rand}\PY{p}{(}\PY{n}{N}\PY{p}{,}\PY{n}{N}\PY{p}{)}\PY{p}{;} + \PY{n}{y}\PY{p}{=}\PY{n+nb}{rand}\PY{p}{(}\PY{n}{N}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{p}{[}\PY{n}{L}\PY{p}{,}\PY{n}{U}\PY{p}{,}\PY{n}{P}\PY{p}{]}\PY{p}{=}\PY{n+nb}{lu}\PY{p}{(}\PY{n}{A}\PY{p}{)}\PY{p}{;} + + \PY{n+nb}{tic}\PY{p}{;} \PY{n}{d}\PY{p}{=}\PY{n+nb}{inv}\PY{p}{(}\PY{n}{L}\PY{p}{)}\PY{o}{*}\PY{n}{y}\PY{p}{;} \PY{n}{x}\PY{p}{=}\PY{n+nb}{inv}\PY{p}{(}\PY{n}{U}\PY{p}{)}\PY{o}{*}\PY{n}{d}\PY{p}{;} \PY{n}{t\PYZus{}lu}\PY{p}{(}\PY{n}{N}\PY{p}{)}\PY{p}{=}\PY{n+nb}{toc}\PY{p}{;} + + \PY{n+nb}{tic}\PY{p}{;} \PY{n}{x}\PY{p}{=}\PY{n+nb}{inv}\PY{p}{(}\PY{n}{A}\PY{p}{)}\PY{o}{*}\PY{n}{y}\PY{p}{;} \PY{n}{t\PYZus{}bs}\PY{p}{(}\PY{n}{N}\PY{p}{)}\PY{p}{=}\PY{n+nb}{toc}\PY{p}{;} + \PY{k}{end} + \PY{n+nb}{plot}\PY{p}{(}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{100}\PY{p}{]}\PY{p}{,}\PY{n}{t\PYZus{}lu}\PY{p}{,}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{100}\PY{p}{]}\PY{p}{,}\PY{n}{t\PYZus{}bs}\PY{p}{)} + \PY{n+nb}{legend}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{LU decomp\PYZsq{}}\PY{p}{,}\PY{l+s}{\PYZsq{}}\PY{l+s}{Octave \PYZbs{}\PYZbs{}\PYZsq{}}\PY{p}{)} \end{Verbatim} \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{lecture_11_files/lecture_11_6_0.pdf} + \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{lecture_11_files/lecture_11_8_0.pdf} \end{center} { \hspace*{\fill} \\} @@ -494,7 +568,7 @@ \subsubsection{efficient storage of matrices for \begin{figure}[htbp] \centering -\includegraphics{mass_springs.png} +\includegraphics{../lecture_09/mass_springs.png} \caption{Springs-masses} \end{figure} @@ -514,7 +588,7 @@ \subsubsection{efficient storage of matrices for \(\left[ \begin{array}{cccc} 2k & -k & 0 & 0 \\ -k & 2k & -k & 0 \\ 0 & -k & 2k & -k \\ 0 & 0 & -k & k \end{array} \right] \left[ \begin{array}{c} x_{1} \\ x_{2} \\ x_{3} \\ x_{4} \end{array} \right]= \left[ \begin{array}{c} m_{1}g \\ m_{2}g \\ m_{3}g \\ m_{4}g \end{array} \right]\) \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}24}]:} \PY{n}{k}\PY{p}{=}\PY{l+m+mi}{10}\PY{p}{;} \PY{c}{\PYZpc{} N/m} +{\color{incolor}In [{\color{incolor}10}]:} \PY{n}{k}\PY{p}{=}\PY{l+m+mi}{10}\PY{p}{;} \PY{c}{\PYZpc{} N/m} \PY{n}{m1}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{;} \PY{c}{\PYZpc{} kg} \PY{n}{m2}\PY{p}{=}\PY{l+m+mi}{2}\PY{p}{;} \PY{n}{m3}\PY{p}{=}\PY{l+m+mi}{3}\PY{p}{;} @@ -565,7 +639,7 @@ \subsection{Cholesky Factorization}\label{cholesky-factorization} so for K \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}25}]:} \PY{n}{K} +{\color{incolor}In [{\color{incolor}11}]:} \PY{n}{K} \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] @@ -580,7 +654,7 @@ \subsection{Cholesky Factorization}\label{cholesky-factorization} \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}26}]:} \PY{n}{u11}\PY{p}{=}\PY{n+nb}{sqrt}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{)} +{\color{incolor}In [{\color{incolor}12}]:} \PY{n}{u11}\PY{p}{=}\PY{n+nb}{sqrt}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{)} \PY{n}{u12}\PY{p}{=}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)}\PY{o}{/}\PY{n}{u11} \PY{n}{u13}\PY{p}{=}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{)}\PY{o}{/}\PY{n}{u11} \PY{n}{u14}\PY{p}{=}\PY{p}{(}\PY{n}{K}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{4}\PY{p}{)}\PY{p}{)}\PY{o}{/}\PY{n}{u11} @@ -615,22 +689,22 @@ \subsection{Cholesky Factorization}\label{cholesky-factorization} \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}27}]:} \PY{n}{U}\PY{o}{\PYZsq{}}\PY{o}{*}\PY{n}{U} +{\color{incolor}In [{\color{incolor}17}]:} \PY{p}{(}\PY{n}{U}\PY{o}{\PYZsq{}}\PY{o}{*}\PY{n}{U}\PY{p}{)}\PY{o}{\PYZsq{}}\PY{o}{==}\PY{n}{U}\PY{o}{\PYZsq{}}\PY{o}{*}\PY{n}{U} \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] ans = - 20.00000 -10.00000 0.00000 0.00000 - -10.00000 20.00000 -10.00000 0.00000 - 0.00000 -10.00000 20.00000 -10.00000 - 0.00000 0.00000 -10.00000 10.00000 + 1 1 1 1 + 1 1 1 1 + 1 1 1 1 + 1 1 1 1 \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}37}]:} \PY{c}{\PYZpc{} time solution for Cholesky vs backslash} +{\color{incolor}In [{\color{incolor}18}]:} \PY{c}{\PYZpc{} time solution for Cholesky vs backslash} \PY{n}{t\PYZus{}chol}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{1000}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} \PY{n}{t\PYZus{}bs}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{1000}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} \PY{k}{for} \PY{n}{i}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{1000} @@ -643,11 +717,15 @@ \subsection{Cholesky Factorization}\label{cholesky-factorization} \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] -average time spent for Cholesky factored solution = 1.623154e-05+/-1.166726e-05 -average time spent for backslash solution = 1.675844e-05+/-1.187234e-05 +average time spent for Cholesky factored solution = 1.465964e-05+/-9.806001e-06 +average time spent for backslash solution = 1.555967e-05+/-1.048561e-05 \end{Verbatim} + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor} }]:} +\end{Verbatim} + % Add a bibliography block to the postdoc diff --git a/lecture_11/lecture_11_files/lecture_11_8_0.pdf b/lecture_11/lecture_11_files/lecture_11_8_0.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7f562c690445bbd18c791024c270af8abf6cd77a GIT binary patch literal 8728 zcma)i1z1#D_r4N>AR$QCpwcx1%+N@ebeHtdFvK7w!XP0rAdR$0cS{JOq$nklA}K8? z!qER2y!zey-T(JIzjLPcyVpKzueJ7>wV!t#7EL(?9uTh}0ZaX6#R-7`00@9tITDDA z1Nc;-u6A&HfFK&uCIA2cdIYX! zMbgm2vs{@aQWkI+Ltjs3Y?-EpIHy=)%vRX5T6xtRHu9d7GcRzag zeleSm>8w_0IPmmKJ!4;5+c$b+leXwv#=Pg8m1GL(=O6qp-pa=YK0bNhqj_e~_=q_0 zUQ;@QZ^n%Gf)3^{3_A-q=EI%Zr<7F^7*2`Q&K6pSx{p z6DRPlg{R4ANE!qNY-9yAMjDVFjx$Xsp!SawPImp$&tqy$Em9<4cC;3DClJvuhvz*; zhWSTenX~Tc4{Xn>sK1Pij}H#|sY-;IE*}(KJ!piz>wN)2xBJ#ZH^PRpods-q@sWQ4y&g#bMi}N zq;mo-DB+-2Ie}2r`+=a*;B)$@5Movq4B^z*_G6$9*;qEc@1CDi$V* zK_Z{=257kJL-l!SGYW6a+)%vh@!`OfFc)A*~; zj@KC-iRA9b$j#%pIaN)~85LIsvK2@5EU8ev`0-<;IqP(Owl(l%Wz)Q;IMGe)dCueE zv5ZFtDHc_Ua`%+yy0Kjsg2V?Y^;u&+g}KjiEGBMax3SUVG`n4=gJU&Py}5do`lph| zPE6rVES>KAFX?Ac&!M-q+b#3LKTGSmw3Fl+ul3WB>}8y*z-9nQWeUh=uH)dE+%oG@ z@h&Thc^MLGo0`24FHJV-W@W>1wIPwBkCY7ZluohCttlQ_?#;B~UK2kUvsQ`75pjK` z3|Y@hzWAuEl77mJAJY{vF^o{qf5B#0Zxzu?o1vS$Rl~4qoIEzYcqqH%r$XRI0d1x> z6!cbl3TaNdjkGOZwz_NYnq2=)wt0t9aAIh@o%}kTj=s&jEkcIj$rhBRsAP-gE(6g~ z=OS61unuI2M^8juP1sCYc^iKvqISC_6W! zy=n7^sHOqgcx()5vgMXih_37MwgF zvYAohTST9ytW6Ot+oaD$PR%iiF5bdjLaA9=oGodZd#$$YV6G^*?v7ARDcG>ZiHA`4 zRjq{UI93k?oK7|R`*#&5edqfU%f8z76xx)~HV9+_>BG1y zj=1vUgl*Ms$RLbN9xhoJ+TD!()RX`4W~}M{r(A=()NUl+#iPJozfKj6+huBI&2_ZE zkdta9T6dtk`-k56A93Ig>=^n}Z6KaGkM@j{l%Jzo-8Hq4;P8+TI{)CIg>lebWkbEh zwImib2s~AfHpNKLvGbbe9z4{qCbyuj;C6hdgl-Wlp-OOx#Vzb-mWs@@hSZa9MCa2A z+l)x9BGipuOO2b)p8r^$Jv<*R#Ws?Sy8i0NPESsBkMxs(grrI#!|@?=)5zN~PO=uE z5c40BhCKmQF((#!{4|Dm8l2drZ;jrT>_e&^HWZtJP4FrpM>rFvqn=t-~dsC+)!uvQDqguA8`+QXA=^HD=q>mFY8GD}7nRE|@^%`+VZs zm;&2AzCJ@K)_4cdw)qpK56Y#nB%8=UB8#r#VNPg8cvJO!3AJ{kV~2BNB%OD=(=8y4 zsn-m(sY@1(X-{HO=CB^#%Nj5C9-{IvA^8o>wHHq`?%^QI#uUQzN3?2U-Y)6Y?7_Y0 z%5N>mI@;9VEVGfw(eD)%P9Nx1fjnm-7<*xEb8T$cSEGBhg1n2yNC-|{COotq43?K~ zM2zMPSa{WWP(%|Lu3Z3QO&Ju7ahy_O`Ia2Bk2iU3LNy`w1cogxT5tV)6xyfKW3-sL z7;F*3!Sx#s+Eox20Jf8fcl-LO%7T9Nl=ICl$B|_II(-R|kTKR&g9e$r$$+;`Hl$B3cOj`b!z)k1_zCuCE&uz^7?x2fb9RY3Tt)UkCJi9G@E0#=%ks z<^wQ6LqLF_pfEr{00MY$DJ_fEi5B++U~=)V#H;85^K$#!JbqpO68&w64qB^+rK_hK zMwhkkZ&(=s_wc%$1;$!gw3Hn5p@TJ4TTuoh@|T&~P*0ebhc(m_fN`1j->ecsxBqKD zApB=q|G)hJM$NB{0|)>S5(NHZgRo@a>!YhzQ|Y;pW%lX5t9Ns)SK)|}XdDYEIo4fg z9;})Ot=qCe!0X*l*=2zM85=SwG6)+tSz>)x6*Ud3!Zk7}`3OMR>y;awLXxSL&)9{# zNf~aj!PN^~+1%aQV9Wj&t=j?HSruOnKTob36qcwnSX?2+$q$-)?EKhlJ|DN`{ECGn z4xr!X`=q?94?ibEdoH#`Zq81`5h0$07zrR`eW#mTgOA4$vKEK8ntq&axwYtf)LaOe z%{#c$Nhh8{T_7<#CN`=YvxM(W+oEC^WpiyH=d--}J&GhY;w^uAlSBQpDWpe_qHLm#M zVox5d)``8N2;AWDsz^2|S25v_O5%6^=%tO6yy|1;vY7HgmUP5(F^=!c1@Je5Yd$_@a2_!4zlydh4=hr0Dv zU=`R`sYGJyQz)T~=9{l~og`sl?5Uf`ggf=g{4AWG3hR#&>sjC9ajDYP=~V#P2xZuC zIA~KA>=GPhYFS4oYHZaj@$xr54}Dh#zcpGH@(H(1h)E2CP^3j}MnU8S*uaH-)qzaKMRKVwUka%#={-EexDyjn(r9m&!gy!RYnYZz zMo@sA%Kw{n$)j?juPRDS`L2t3#Ur)WlW`U|lJhf|L6lj`%Jt83g4J$SR`uMoB0tj` z^%zDq?=tj{B7Sl@v_{muQlHpVi+&2XXdHP5t#ady)iECc|VsRbv@qjnSiRa zTH->suJxeyD5TZ^RIUES~OG(-03V|Utec&*6BWVAy3wgX}dUW zRhSO3Vr16BkL3?FF)86B5IP~v|klRd(a9vDzoeyQQMjKLP1G2FJgJwGqbj-Cy*%pv=}cmb}5Uv z*G#&>jArM9PwEzuWH_k!BYvAEa*(E3W0z*U+ttH$huZq*0KUOfa_d|MMh}{)l;oh& z29!x6q`qkRdp%g@j#GSEm9pzMB<)_jaY|x`hhbT_E8%8?vn^Bmf)&em@QLuN^)V2~ z3+>S~3I8!t(AhVJgnO?^#mf$gOQWL>2IUIvt)G7c`Qj0awH=O?UH&~vrEz7N(WG?av!tKpCxq1;9SkfSVu=#yG^KSh&H|s~{ zg%UF~WreG<%;5cU3Z?)H2RUYzpG#@7n%_khISSJ#`nK#xR zWylLCa}j@ZeAapx=iqQ;x7YH{f5CHPUs3vb$&-2VRyl2ot-ecy zeqp(V_Zs8j*eLY%(IaarI9T$+c4ZPfU5H7%(f7wyanAm8la05h;*hYlqUiVJ2i+Uv zbP;~vIOC$;UL$7T?|zcG_5tqHc;?l;f&4D#(^@~!_;#)8zGw?EtMb@f^+3>5B7{#q zqv_WHx6&_k$I+3T(R=a%^rMVjif`E=Dzs3hrMa_uY%lDeXHO{Gu^Oa|EzIYJR=Dqq zAEZj{Fj=vwUd;wv43)Iy4)?K~8(WW5``WFDAMENZBny8yM%}ZX5_OnO+x%(ka1iZ1 zKuim7gatwpajQumzCl@cG~5aIE``XZ?uc4O25Fh$C02uLnm*RC7R}rq4<9vx$T^m? zQp4!zicu!oej4WPrD{hNJd;lN57}e1dlbS4-|Ah(eg{91lIoja9PHZAc?fOuTK;JA zyrn?Ak*_e}p=g8y<5#XihV}7nW1W%u$7dyri<3&Ww))98@me8Oso%7JAR-b;KAXIl zF)Uoh9-9jvc4RuyI0_PS)s+L?a#E>dX(kI$){J;DVQ9q(O2J8CXGyjy<;#_Lw>P5n zBcblaYQ8MY`K!n3Q1U}t3YX2$18nSk$p43LY zi&#;NPWsBPDVPJ(*EP@HwcYhyT^BV!Ef7o;-wIN}6C-g7F8T4JQ+XFVDZ%%9 zsaZH-uYug|>PXApyK?=BsZ1&boIc?Vc%7eDvm04gbdx^ z^Kt|uHH#@5LMWm}6C!6GxA?+*MP_+sDp&W*Giw3{xAUh7AT=f=UEfHQ>olb25DAI$ z@^tU^ZG9wEbzlvRA97>GHWqsybVQSe&9k-+kRnCDOyGR#KZ>ezL3B7;$bR6t$FZh5 zw_lT23RU|x#l8_(tlZRgl-|wA)rj4H zKHZet4A^dMg=N@wEw6{JU2grmkCi4RJ5KZzF`a>n)L zX*(q7vaEd$-7iYngsaP07Y~AqUW`fIFfL;AV$AboOQRe0LQaw(%e%C%Z2E90kSx zx#yA>eNh?j#`b#cc{N=R z>y`IN$l#)?)}8)PxO*nIhC|C22xj?B8Eczo7a8o7_6B^iu3@!?*LRc|n-T4r|v@}-_Ga?`HR zh)bl9gm;eH^l8e3qlmgBdu({5E0G1S?$Gp?QBWFILt<5FzG3DA!Z+%l zg(PW83*hcJhV5)Sd{aN-w5+h;Q<;?|k3mRk0$#;c=p7d02p5dHJ;xH<_vQk}+sQme z9?q|Ak?KQpp6Ua#0#@5@jZI{Qw$RVE!

WXo;LHGNkZ`Qgm$6l` zMlV)iH&)$b{ZzT7O{_Uc=tQAVT^XdiHu zHitC@GK!yyJ>4SaeB(d=&}aK%Q{yzDfAaXl5QDqntGI-=jB-Q#c{QnI3>&g*BZqnCH*7({>HFXaomp|8JnfGv+q(H$=%bm z$lJ~_lIs-uHlkH^vmGu+gt#hbnTmU6!P_MpaeI!7({GYD^wS$twj{rnE&T6Q^Rwb8 zS%R60&h36wX1fX2#rj)VKT3_I!GCAD`2?kga7jXWu{1oKGhjebAaogB-65G9T+wSbRAlPuTNPVV*e?l3}_^P%huA8y#ObpXM{*J@Ql@xnE z))Bkx)3Q@!a9)lVi~p#U%n7%Rqe@{8hQm0}W1hY{M927;ooTkHVNXch(4}i!d39WD zC#M}7>yU8Tu8R{%%YuW_>}_(~?n74(TWP6hMfo7R7N zXK>xr;VlK$ecWXH{fB2BM;_<*5g$?(e;gTRKv%jLOs@LZ6+Zf@tr-T_${_I!BN2rAhsQs70pU zaVu!2!Ky99+xlMKID=BH&d3F@=g%ec1k?zj6wJqXGZ9H zE0*GQdXaa1ic@Z#I~J1fB0IvLqugKyKw<&Quy!~?Hhcm#L`=_bI4|ogEZpCY$CYZ^ zF3qb7w(M)YmUVl_44aiiaL0z6Sa2@rt^`w#MLgq4p~agv#u+}QlY{ELHpcJPUH)Ve zr&%Y!;V0J_u{H1&Vy`aZc3+Ps>ZX22V=eD3so%~T*Tco_ehXXkVdviIVaAKPIedoRFZC$ zV(=Qd{&`9>A(kK9XLI%8U0#C71A>(JXB_xgMhqX!&u(uV2F@ccT&|vPlK=F^l>#LH zn{LD~V1Ln#f}qI3XV|1%g;61EX1u3LU$IfGdfN1x+;gX`+5$w^_#wZ^ zS`dbd{mpCsVpB0xuN>6V+QY#O4)eHVVlj}qr3;$MHCB+wlU$FELjOFJ}&%l}7G<`?110|N2`0X%{begH^FL;wKd7vTSk`BjEn zIy+cPyV^NJ0l>>~(w^2B=2(PZ__B$aAEwR2F95y-WG&s4pbmESXmS~SnM+6q4t3E7 z2>%+7X(;_}V9Y^NworZmhSmK$%Zp*O|Lu)mm-DiMU$WV{XdW5ksY_JG(i3{gjsGvt zICyx%W$i6Jemg+b@~<`s^vjfgx*KpAkY6{7yeqn}?BHq#;4^S=m3H-X_zhfYHgK?k z+k2vka{&;>ivM-~>V=?5_1|ycpI;c{SL=U`{wEFw|I#ER{CAB)0+==QpA$pi|87A* z7#&xFEPoHz zzZWm2)bMLf-gmIUcn32V?LP$tFHH5}Z>;|1^nM3i7G1qZuXq5vwWWgx3;^N<3GzY! z?DlZDn#Q69$3MmSYZp>u(Gs1pXHW z1Y%2@3%KrWfvEiN3u(E+5{|aqxp;e1)mUXv1LW`2VMzr0i;oj`N>Vk0;#H1AggU QVF3s~0Sk+~h62I=13AMC=Kufz literal 0 HcmV?d00001 diff --git a/lecture_11/lecture_11_files/lecture_11_8_0.svg b/lecture_11/lecture_11_files/lecture_11_8_0.svg new file mode 100644 index 0000000..37a1c3f --- /dev/null +++ b/lecture_11/lecture_11_files/lecture_11_8_0.svg @@ -0,0 +1,139 @@ + + +Gnuplot +Produced by GNUPLOT 5.0 patchlevel 3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 0 + + + + + 0.0005 + + + + + 0.001 + + + + + 0.0015 + + + + + 0.002 + + + + + 0 + + + + + 20 + + + + + 40 + + + + + 60 + + + + + 80 + + + + + 100 + + + + + + + + + + + + + LU decomp + + + + + LU decomp + + + + + + Octave \\ + + + Octave \ + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/lecture_11/octave-workspace b/lecture_11/octave-workspace index e69de29bb2d1d6434b8b29ae775ad8c2e48c5391..8c437bb6e55a5d1b6115661b3a20e86870909d32 100644 GIT binary patch literal 153 zcmeZIE=ep))iu=hVPIxpU`Wg>29gX6|5<=Ua%xV_zyJULGXmL6K+FfkHXuRW)ST4Z s)VvZqpa4)UCy*#Ej4v)J%FIiLX#g3JmQ#{Vk|uVbru4khf}H#k0D5999{>OV literal 0 HcmV?d00001 From 05acb2ba6965445500df5e7397353ef0c9574eea Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Mon, 27 Feb 2017 12:02:53 -0500 Subject: [PATCH 14/16] updated schedule on Syllabus --- README.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/README.md b/README.md index 73ca14a..c7011f5 100644 --- a/README.md +++ b/README.md @@ -79,10 +79,10 @@ general, I will not post homework solutions. | |2/16|8|Linear Algebra| |6|2/21|9|Linear systems: Gauss elimination| | |2/23|10|Linear Systems: LU factorization| -|7|2/28||Midterm Review| -| |3/2||Midterm| -|8|3/7|11|Linear Systems: Error analysis| -| |3/9|13|Eigenvalues| +|7|2/28|11|Linear Systems: Error analysis| +| |3/2|12|Eigenvalues| +|8|3/7|1-10 |Midterm Review| +| |3/9|1-10|Midterm| |9|3/14| N/A |Spring Break!| | |3/16| N/A |Spring Break!| |10|3/21|12|Linear Systems: Iterative methods| From 903cb54b88940623b481de3d97d3e56f6ea51e60 Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Tue, 28 Feb 2017 09:31:16 -0500 Subject: [PATCH 15/16] add lect 12 --- .../lecture_12-checkpoint.ipynb | 84 +- lecture_12/LU_naive.m | 27 + lecture_12/chol_pre.png | Bin 0 -> 46613 bytes lecture_12/det_L.png | Bin 0 -> 40288 bytes lecture_12/lecture_12.aux | 27 + lecture_12/lecture_12.ipynb | 1123 +++++++++++++++++ lecture_12/lecture_12.md | 674 ++++++++++ lecture_12/lecture_12.pdf | Bin 0 -> 169270 bytes .../lecture_12_files/lecture_12_21_0.pdf | Bin 0 -> 9752 bytes .../lecture_12_files/lecture_12_21_0.svg | 148 +++ lecture_12/nohup.out | 2 + lecture_12/octave-workspace | Bin 0 -> 11 bytes ...oint.ipynb => lecture_12-checkpoint.ipynb} | 0 lecture_13/octave-workspace | 0 14 files changed, 2084 insertions(+), 1 deletion(-) rename lecture_13/lecture_13.ipynb => lecture_12/.ipynb_checkpoints/lecture_12-checkpoint.ipynb (96%) create mode 100644 lecture_12/LU_naive.m create mode 100644 lecture_12/chol_pre.png create mode 100644 lecture_12/det_L.png create mode 100644 lecture_12/lecture_12.aux create mode 100644 lecture_12/lecture_12.ipynb create mode 100644 lecture_12/lecture_12.md create mode 100644 lecture_12/lecture_12.pdf create mode 100644 lecture_12/lecture_12_files/lecture_12_21_0.pdf create mode 100644 lecture_12/lecture_12_files/lecture_12_21_0.svg create mode 100644 lecture_12/nohup.out create mode 100644 lecture_12/octave-workspace rename lecture_13/.ipynb_checkpoints/{lecture_13-checkpoint.ipynb => lecture_12-checkpoint.ipynb} (100%) delete mode 100644 lecture_13/octave-workspace diff --git a/lecture_13/lecture_13.ipynb b/lecture_12/.ipynb_checkpoints/lecture_12-checkpoint.ipynb similarity index 96% rename from lecture_13/lecture_13.ipynb rename to lecture_12/.ipynb_checkpoints/lecture_12-checkpoint.ipynb index c687623..1332b29 100644 --- a/lecture_13/lecture_13.ipynb +++ b/lecture_12/.ipynb_checkpoints/lecture_12-checkpoint.ipynb @@ -768,7 +768,89 @@ "### *just checked in to see what condition my condition was in*\n", "### Matrix norms\n", "\n", - "The Euclidean norm of a vector is measure of the magnitude (in 3D this would be: $|x|=\\sqrt{x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}$) in general t" + "The Euclidean norm of a vector is measure of the magnitude (in 3D this would be: $|x|=\\sqrt{x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}$) in general the equation is:\n", + "\n", + "$||x||_{e}=\\sqrt{\\sum_{i=1}^{n}x_{i}^{2}}$\n", + "\n", + "For a matrix, A, the same norm is called the Frobenius norm:\n", + "\n", + "$||A||_{f}=\\sqrt{\\sum_{i=1}^{n}\\sum_{i=1}^{m}A_{i,j}^{2}}$\n", + "\n", + "In general we can calculate any $p$-norm where\n", + "\n", + "$||A||_{p}=\\sqrt{\\sum_{i=1}^{n}\\sum_{i=1}^{m}A_{i,j}^{p}}$\n", + "\n", + "so the p=1, 1-norm is \n", + "\n", + "$||A||_{1}=\\sqrt{\\sum_{i=1}^{n}\\sum_{i=1}^{m}A_{i,j}^{1}}=\\sum_{i=1}^{n}\\sum_{i=1}^{m}|A_{i,j}|$\n", + "\n", + "$||A||_{\\infty}=\\sqrt{\\sum_{i=1}^{n}\\sum_{i=1}^{m}A_{i,j}^{\\infty}}=\\max_{1\\le i \\le n}\\sum_{j=1}^{m}|A_{i,j}|$\n", + "\n", + "### Condition of Matrix\n", + "\n", + "The matrix condition is the product of \n", + "\n", + "$Cond(A) = ||A||\\cdot||A^{-1}||$ \n", + "\n", + "So each norm will have a different condition number, but the limit is $Cond(A)\\ge 1$\n", + "\n", + "An estimate of the rounding error is based on the condition of A:\n", + "\n", + "$\\frac{||\\Delta x||}{x} \\le Cond(A) \\frac{||\\Delta A||}{||A||}$\n", + "\n", + "So if the coefficients of A have accuracy to $10^{-t}\n", + "\n", + "and the condition of A, $Cond(A)=10^{c}$\n", + "\n", + "then the solution for x can have rounding errors up to $10^{c-t}$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A =\n", + "\n", + " 1.00000 0.50000 0.33333\n", + " 0.50000 0.33333 0.25000\n", + " 0.33333 0.25000 0.20000\n", + "\n", + "L =\n", + "\n", + " 1.00000 0.00000 0.00000\n", + " 0.50000 1.00000 0.00000\n", + " 0.33333 1.00000 1.00000\n", + "\n", + "U =\n", + "\n", + " 1.00000 0.50000 0.33333\n", + " 0.00000 0.08333 0.08333\n", + " 0.00000 -0.00000 0.00556\n", + "\n" + ] + } + ], + "source": [ + "A=[1,1/2,1/3;1/2,1/3,1/4;1/3,1/4,1/5]\n", + "[L,U]=LU_naive(A)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "invA=" ] }, { diff --git a/lecture_12/LU_naive.m b/lecture_12/LU_naive.m new file mode 100644 index 0000000..92efde6 --- /dev/null +++ b/lecture_12/LU_naive.m @@ -0,0 +1,27 @@ +function [L, U] = LU_naive(A) +% GaussNaive: naive Gauss elimination +% x = GaussNaive(A,b): Gauss elimination without pivoting. +% input: +% A = coefficient matrix +% y = right hand side vector +% output: +% x = solution vector +[m,n] = size(A); +if m~=n, error('Matrix A must be square'); end +nb = n; +L=diag(ones(n,1)); +U=A; +% forward elimination +for k = 1:n-1 + for i = k+1:n + fik = U(i,k)/U(k,k); + L(i,k)=fik; + U(i,k:nb) = U(i,k:nb)-fik*U(k,k:nb); + end +end +%% back substitution +%x = zeros(n,1); +%x(n) = Aug(n,nb)/Aug(n,n); +%for i = n-1:-1:1 +% x(i) = (Aug(i,nb)-Aug(i,i+1:n)*x(i+1:n))/Aug(i,i); +%end diff --git a/lecture_12/chol_pre.png b/lecture_12/chol_pre.png new file mode 100644 index 0000000000000000000000000000000000000000..67d2493ece53665959de7ad49f5a0af566b1490f GIT binary patch literal 46613 zcmcG$Wl&u0wyxc{TW}{30)gP}4j}}0cXxLQ?(Q1g-Q9u*cN!;XWN0ssJ20RTY!f`VBGJvG0 zkdj;Gai?ymg=F&E)3_($Dh!kc;|~~=Q-26LyeWUA74QMnVUM5&W9+TsimZmLxqx}+ zuBOK(+@bqdv}Zvi`T`W(20b#qsUL6z*Mb2gcvDbN>5M-RP|~M1W$t_1&}^K`J)cZL z3t8?9a0PYIr=i%iDixvF7(Cm7q43E4jQ@HWGQUKXs*gJAt{2yhkuIcemlEx)9He<_%WlBkCHKc5u^LaF@cgoBCy zhsG{5{#=)Y7(w0!DI_We>ef;pBXa$44N$y&BLo^ww3#sPWa%B#FQnin-e7$lvORTu z>teF(%+24Tf-N+}n&~h06%LZhfkBv=nVEv$8ts*$nr7=zWzcCd@@)!TAnd!LsC2!f zY`b1?HoTl6ef8a}YVr1*YwF+PrsycqoiaB;w%z?_K6g+)_iL{Aw;)V-1M~}p4L~m1 zFUylFJjF|~TlZOZlk8f!{tmO~CEF89Jz|_^&bX|;CQ_#P^$_?$mI{iT@Sd|Kq10gp z&P`PDSQ^%g(Y04lUWVB4lV``%J?Gt|{|QpIP4dc@Cz#C4CG=637`kx}o%9Y5_o&^~ zAKzZQ@J>lLw)=N3T_@2<_1fCIWect%G zZU-+2KECJ*yelik;^&3(!!G8)b`pmsK#@ZwX3{%Jj+LQ|{bDT7H+U@39r-+D3XpZn zsU-28s*xczNm!)TG2~iIk}M;Sa}&6&PX@#f;CMI?o;1+3w6}`W9B{TQX*wRWk235g*ap-er)w3^>(?8w&K4WGB+-wM`gOYXm-&t+*i!w&~ zyhlDe+t@(>Z1$-$e>WROn}$VhmrlG=b-MyVogWhWTthXQ;Q06qjdpyoPAuD5`DsoP zB#ORsRJWC?-8?tGb2MJ<7K|y(8oilo{RNrAIa#cXo-7e@YiX-T!#nkxPQP2!u9o7* z(liNmo4oJB2#4ndm)7WOLZPRd5JB^k(?HgKKoR(Hi{pYG(MWhIOjKWp<6el`K5&wS zkG*|H8A824@RN2D!O~6jJT}3|hAzK##L9pPOlkz(kmE&@rK9vd&BE~tbcp<>iFO$r zBmQoVpGP}Mz}0D!T0%#Hk1?%4IBghF%fuk9)7dfTP(`1>dOV65C=OWPm->%kK5Inl8;13t6lsd`i&PNMmK!M4_+hM@NbRXdvl5iFBUi#v4qiw^-a5` zg&()0FYa_-&dZ-|uA$bws01jAez<&CUT9+E1M~-*d55~ZkKQae{TQNUmVLA$vEF|8 z-ooZ{cYk*fN%QnjaPid9ViHtXQ9*mBMV&QJU0$X%4G(x77OJG#SJP$Yh#5R^s3V-IGHZ{={r+{%_+*gA~b8=UdIHL1{g) zRzaK%wt3iy80CXs%&+TdR;7uWIbGtFn%s>RV~}ptt<>K@8Ve8yPQ9oeuBM9kpNqND zOJquY7o|gz@uyzW#1_`@*BFw0O?+(H&=Y(shrr3w zmXZkNoBYSMPzzia>oqkz^J zZ;}6UV7u=lCGZhhjVkD7dO$kPA_|AiLadF;Ri?XMM=6=cM2V{15qL{@sEGxlviQ>rgK*3dT7JbUGfoNsMvfen!ml^Fs zu`Hb!jYgiYuqMRiXD(f$`J-uCDKZM!5iT`BVuXPSkhm#M-rmxST+1Vs$c(V8cqQH* zbED%%b-GGeH#HF?98*ICPwN>~O;*+E2i81X(CNkxpkb3xRHt*2n|QA>HnxT9FW&T^Ojb<(EE|{N+3p!5ZC}ZMm|P z1nYSR?%A!XM;43728camwMq*XF5uK3XT zwTIhc^_yw5Uboy~hs0bnOU4 zy4zD~#zS7&GbQfziO-?+gC#|7Zj}j312~E7C2Ue{E(`KOI`)sqnOD2Zk}(a2#q|u@ z)<7NAAMGbrcr_Z37AGxigy_T8-ld!YPv(!wvq52`h4fw=a~d?3F{cw)Q0?vk{9ZjC zX5CG}mE1m<*X}&?;Q7xa#iewynPllBa&4jZwfMCMl!_QBWK44BgnwnLpR(=Kv}Fj- zTyE*hv(9K^H^2S!4TylJp(-ogyXRr`sKN2Q3V2#6s778LKk~|f0FjKfA`~I3LAf5G zRyndP2X9dnzMzH|E5ca9qy)70TrWqt+{;`k5VBhL((kq@R$MNyUKcy5d>v}*qrN$^ zRLc1Eg`Tt0JR7C0GgAJuizG)QHiYGV^u$M$aR=`1AdN6#*X-8LqHsNzfRmmp=BmRE zIFvR9oKm$4IVm=6F}PFO39i>es|Cc2G?_S?-4@hB zz*8fe)$Bz^?j*3Zi-UTM{zReLmajn?PhX1XfhA9su;$jG>&8QVn5ns4s#yD=sh{|0 z>X(mCu><}TRdlzHv0;cg5u2^!tgq`J^(VMc$Lh%_3#|IG$ecU8n$!Bs481;)l+QI> zb7-9Jh!UWdDF?=`->n2a-c#y(;=PyWQ_fgKqXPVhD#Kuasy2RdU_-jO$XP(o(+J^5 zuo0!$iQiJx4}g-p21%j!pF;w&&!u?3D|o(V>5Xvv7-7X85V&C6pnx4Vb#?*51h~ak zB%{yALYz_;iH#*=!?`-iQ}aOrKIh*1oOL$3V<3iLpu*+)0y1+2px&6vY+seA*8Ty;Y zg?`}ASL=}y`yMGl{|}|!gBy)f;}?@Ehhh}k-Y&Tts8Ln@JNFN3qt0I4?V*xGsHgD$ zDuDaQzH2f@gcC1>7{Kus=QaWgV>zqdA?s;L>Cq4yI`%`{rE_DP)dNdb7K173;F58b2&Fbq2X{I?tc@!OJE?4$B6+P53e3E z$;9ND8vX2pc0x2UG(+BN?P*5PNa>(iM4cDF;nn6scUZorfUBluLk|w)v+Gmw-)ZGWs^` zuMQN@r+ea!ojZXy|GONLb7-Vv87eJ$TrK+jrC$2n)Ft$Vxy1!MVJSJkPpOd8eDRdI-wYpu@A`h?F#dN*T{`NP+rJr5a zBNea5_uuyQpn=H=3*gwGx!n7M>{{2(H0bLewCfiVP}UFJ=pI{j1T`V2=qTO*Jp`h2 zbb#m|9gwdW50B_O+R!`1@C$lI5d#>GSBQ`*VytJaVwQ|Odb_594rbmb2zj_JfF6qU z2u0U8%L zi?u9n6@YWUJ6qqM&9AKKw4%3K>zk{nfJryfsFKyS(jMY$8?lGf%Dfo}ecr&TxF8>C*kZq(Ro1vHtP z1z1oa*1wUm@|zmJQedNFF&3v-XB6_cPg#ak=cA?oUwlT5NxCi9Jsj@y?I3y#vFE!2 zeVjYY3=zbc)>}W5e?UtFEprDe5C%Q60Fa)iv3WLi@T$r58ilZS1)ik8_@l4`%VKKe zcM%NmE@^oAO+c0#<3}k9_lNsA7gv+!N_TbUK-gw#q^ZiPOyeWf_DfyzRmDU{$n<##!-r%2gK;-C8R^1= zU^j{D08yJpM0As(%%fQ|74Y|J_+32Oxc$qDK2y;o5V`ZFQ>uLqq$#b3$pf50x-gAc z`f0wwtHrU!fMR+EvBG|4ON`lh4brUYJ8VRHak(c4*`YSNbniP5ubrj0Wd9`VlhJ!7 zu_T;7rUKwV=f9eJVuNigcDAZ%KnQ!%&1Dlb&ID4UY4ZP~|ua;uhWOWwV|mI$1c9>^G#DeXU< zue0lBid{dDE^Ru;+HV}GTWex6h`Ei{ho%wfa*NTA_ITayorWI|@2r%N2t)kQQMt~a z-pJ5^npD#Cq&;dZ-fg+(@eTta>duS39^VKYJkseO`KHN-uR*l88dE16VnZ`z>} zzp9k*a+Q(abBJx{mt)Fy9m06BPZ{8@(xSKLbcC@m2-mhGdO4|7*KbM;}C%dDut%qIo;A^DU8+^<13YZ5L=sv_g z@;>?QG7#k^RxD1od`(m`(F>t2p1nUm4;{*d(y`}1lMEM0`Z7VSxfIEdI34O$SC2X3 zU=nreI=k~BYJ|h$QEkB9xp1%xIFaiv&Xun}SvuziiQpodx1Mjq#~h-on70wUsQ)d8 zqc`<&y-@q;rZS`v!O&{N>(vShnqhnT0zjDaE_9y_616n!+x3YXITpzWb^&hE=*JeHr_bbFKf_MjxoB>r>iZT9 z6d(le)=T>Z=Q2LRQS4-kkEQ9YtH=cN~y~_Ox@Y zP*$%WY$xjcX}ps~N_Raiz2myygteZBJ5vQj_!>^>f|-2reBO$8bk(GG{aIGZnE9C! zeV&d@a`ymcKJaUVM*zf)2KK1-<8RLj#;$XB8OrigjhWKwiScWCdNtWk?yC7Rwt@jd zF&ark1H1{ITv<+~9Vw0%Bnz#O>(iyi$*N*I6Gao1!a8aPR^?-=jW>1I&LZxg9Q^1V z@07~tOB6Z^#}tc&VbQga?$)M5H5RK5?{4cYY1p}0@sLXvTZ%KTman>i4^*X&B2^=N zrl!qG=8YxO2fyYsY&4gCXE$Qs&a|R@+jY@dDB-}H65L@SI1z~zOtV(yGBtDTI9%#sY8mWGk+pWt_`j<%Dc*`tAaUskvmmTQ(D zJG75HF-b*u8l={`ZhHQeYMq>ssF=pnRH8a_m-CN~`JWy3@z+x=KCtbcTFzNGm&}*Q zU);vaWYwSXEk>c7zGc(mvBk4w)Z805d2akrDHm&e(hP^GaD4goyd(ln9X5tQl_H8y z55%L!qB)$Bcgj)3MQFH(O7gPwNfCagu7Cgl&%m75FK|BAmPzYI2|9lPe;^ba?FYomn-PX!b)Y+TiT2XT*``J1deu%;j5@{noj#B|tGiAw|3OR_ek zMSHU&siHKxl&d+}XPYv!XpYnlU6Bu~&E0sV`TWbNt(;`>z_8Mru$Z=ULQNIOB-vwe z$JMyoq$_97bdnEUAqsb6X{m15ZvwhxOHwT{1sF1@6 zFMsq%BGk%k)61a*OfFM8G}5OZ{uuS-Cg0xm{2*)UuCW$zb_HHvEvFi3ja2z;@?z#6 zNX1lX8S_qvV3D2=_gd(o!a<=G^qGSWW(`+r_OA=ynPPN-Yv8F$DaX|4UmLo=(Kq7v zZ9?$J6Y2tr(7A?P`5~zUaesEfg~VN?ZVE0bz9IQRO|Eg2=Rzo=SB8ajoUN#}M_`un z&d!p*y!qvzQKWt`cipABTWjyS-K3HV&L87pjk9=gt;`>Hdb4E?$5&||6efPB`N;L2 zoVy7fxgMu9tmU3>olnEgWkceVQSe?rV|A(v;h8~WQGNdbFLr{@?sxhWC0ahfrm|eO#h}r$lY8`0Ob7W zK%4q7pY8|+_U{~|fS$1Xq>aF{`~UnEG??t{iCS#a-19tNvOZC%)&BTUxAtWV7!el>M6p;lbp*`}N;YlaBuXGoEB!z~9#I{gHFk(F3`^ z!-P}MdkeYUdJd$l1Ug{=K1hjNw`*S)8X|!S6F8c1rJ902Ur_v)Z(nCB#J8N?;!1o* zpm2lr*@K`|D9rzXOuwOXFZn4xA*?At3JoE2z25RXpSlWchHQ9;*mm=OCxgXcxVcMB z={+u?DAg8RJ?j}!)!oUk?H=IJ&Fay;@8c0H4XmJ}9eEBI9mo{#X zxQKk9PaNnAKQ^TA)npG*J)C)TmDW1Y=W5zS4`rN_AG3X*=@#w2qD)qYK~>YmQ(%d? zoV`C2%nfu}LJ0u~)(APlVMrFBJ7@Hi;ziAgm(tK~v&IOM!^R4DAy(D$&C(7H}=&SG#bUWP{lnu&Pu~WYmi{I|F7|fn+LOs+`>$LUn@AwRJ0~n^y zyuyrC0-zRfgISLah>Ex{95Q-5iK3Pf0%WQ^&se(ujHoMP^4v6;O(;N1l^r%KBd?Qa zY*!7WTOUIhZ`HU}1>z5~;qOPH+3(W}k>8cp?S0MTij|whI)?|SP=U9R za)K&+Uso|8)@wYU_Z5kq8vzm)`EtJ5FK>qUyH$^8UoVAg=1G61)VRhlF%Z>su@-~{ zcz)M3_zQxWI24EvpWV2oQo;pUSy>=nMX_7}_ld!mWZO1e0lKf(I07%{bX|4s7&1vi zz~B&NqwV*heT(<6Ljv0;84az?Us21469=VGvYkj&=>cw{@ADh6T{(ze(K7*llhka= zShI9Lp5Xy5_s8HI)nCI1NSFUT(=^ z$AgT_9dz`)1016jPAnqrsE0wo0UAZzqFc8iRC`={SS=A1xq>x9zsDagh8i^fL}9K} zY@t5aivT?xVOIvtmLxmoZXnW7RaM}#&@T4|tSNS(VZ(5Z%y~Ns(cN{`COO}0$8_e& z{M}`pW%UvHaely~##*k3@9A^aWop@k^FlfQo1I(mZmd^qDB)q%DB2^;{cc-m$$XHK zgi@2Xgs}INJ36UnEWb=z4~|Q1trhpm2LEIIUlh0=_Kk`Pok%BeTRmt)WlV8M&4^wz ztIJl?9otItOo1=J-fLHc*XX$|eKVSz7a{YKWzyiP*p3*y{v&Q4V*0%7E?&^=?&O@` zu6gqELe+TM5k#bV+}Ns(|9D0QkbLO#5#6Q-^eDcELQ(A|G=Q(y?j0*0bS*dL1^BT< z-m6{QCss2o>vpRXzoF8LcC0)tT|aQ|Jmq)(=Ii~{r9yeuA9aQXf0FQrL?J;;J-fxT z5m+af{AFddFcW-6(_eu;G6UHQ^*EQA?t8vxBh$zG6c%gQ@yd!eNDoznV-7Lgi9C%K z$@8ZfBc2}J_t)(1(IqbWiwotHf&;zxu1SjOZxbIHS+Ct(Feze8G>V;?ONR0fzleno z7HXm1fH~Nw{!jvr@7T-%pSvu}P;i)+du+s`r0Qf(W{Ry-7943@2%IpdY;bWl=$w;B z@iU5im1OLo zy*{f@=iyu{GsOLyNjVEtqN@EW6k$#X{SXd{%oSV2RNsGoM1*zyol#J|eGWS?n-&vZ zI$U{PJlm#lkD_}i$iHyFZzK7W?$`ix`MRl__^DnVlq^%Z;tomjm7Y6Sdyw3L_~6F7 z?RV1EYS+4iQhV%^)#8o925WVMcjF{DF#xL?YbATjma8+R#vj{Xo|8{CY1|1sT>fg!t@G>*ZHd84gbRJV9+i5n+J zAmpe9KK&h>(JL_yy^elAYr6Ir2L%BAuF?Z-(qC6u1 zi{n!Q7^yi@h+1fIV-GqCaSW`eRsBUkLMsN0MGUfeLeo^f`*|6yebL4mq%|_gixRjT zVr6U^b0ye^dtNFyATi?+#+cmvq|eAx^9O5L6R_A|Ce>;ySG<@nvy*MZfCYt0?81Vi zW}NjWo6*e&XERZw{@NNQ9%IS`a~5nRF1}K=rLzrFhr&Y^TIU9GJd}CzyWbW{6Ijbc zeX}Yi(lj{gQGfmq(nfRC=UV>F8BV)mu9n~Zm&Sg^T)B>KQP@_%1nQcHQMZ#zx03Ij zX*fjGOFYi}%$R!-l;5G-6(0Y>6u%9d<%vP170=QxeH#gw4%XuSZ*)*<(L=_u_9wj| z#!BzqVUntA=j2Mljh5l|jNdJnwPNbGp2^wPtVr*VhM7_d&IwQP)=skDxt_Fd5MuYv z3sW+rqjx`Y{dz`&9M}z;Ou%@n1u(30i;f&`N|D?_*x#jMu|J?Au&j>2rzNk_?Y!kNqi z-S3Z^zw*g?Q^~b7LHYW$2nuQJFl*GWgauSkQM*iLimP2QQ!Df55mNfBD{` zth}Lv9 zr?lY+eT!RzO5mjXS)o?#eWNykC~;dF)=Kk0WV}J?Q$^k(Mv>I!0#Z=iCmJTZ;_RIt zZrp5vmMA-9Ycv>`9s<4J0S40Bso;_uS5ff3C>BTdXq#_cQ>XyIpe+u+a)nOSjj7DEiU&hrQ)vd_G@an#bl}a)n0G3!mCC3vW~8ZFVmj2# z%4q2Kw;vb;Mc<4XE^zB=R`cAmNTZ_HOkDHn%Kn46TraCyN$03dvXDLIsM=6>4Wo{C z7HY@IzA86qA3MNl$5`x_K|L&^5jc6`=c^sZ+gMmYfNl-rw7qh4+?^MnoZ64V`Ikd) zONTjrXwj%3r=BE`fwfYqoQNBDQ~Lx*QwIV9qP&C!K)c1>=V)KqXzSjGcL#{9;cB#F=`@l zPNKj^Yg$OFS&G5i=j2vA|7TR5>~sq_Ts1w%k}TVgx!NT$x+YB_81Lp2n%!S6!z`_p z+Gp-t6&#-n*#Zw#a1#&59d*qPA<>Bv!V|DU-V=*Rw3FwmmsC$`+EEbTOGU}TB=s{l zfE7e``#f2==R6H=NGtXSBWUxKe(xrXBefGJUFW>yDz9rl7Uaq+A!u8I-BG?%T9`nw z2U3*j0n|&ppj>AkE8im0USgpsL_iKUmC;wTeJM9+J+vVV*?RyW2h4_Z3D#%^RRwu4 z5XzL#bG?o~x~J#*uo?j)v~9{Q1^+u6>>YvE`N^VgRFD6msnbot`Ey;y*(_D{t4B(( zwYm*0ktU8Wl~wfNjgv?r%2)3%kN^-2qWRl>frcwlPyv!3I03bk+xR4S?Xk6XKv9-SeEujl4x zts|V9E@Mz{K7=n(H(a9aeEb$fF}4>ks$bo)bI#U>sS5dW1&9O|&qgKY!hNi8XAj0_ z-R2_fk%>=6(NE0Rg-Qm)Q@!XmRDfh@f7y=ZcHsPIzmS!%-N9=5?I@*Q%E3|FrwSu!|t2|dWxT~`)+;e z11Eb%QFU0P=6%@|LKuGdAYY25kB?%Azusbj`Q$aKfX^Kp^mL3JZ%hGbn|)I4 zaCDb!N(awe`-c(htsd2VgeLPW$@o0ECUoX;5{>cC{oYc zY2#y$C}g#)o`-^8veEnZkw0E#KJ|asv-5&vOs8z11ia87=0Nm>)%3X|oWcvM07~+w z5&_85^f8nn9LRhi6iZUBuN8Vm>wCA2A!nYqleV{MOEuZT)c3HY#djE*dam4hn9zWC zk2$304U@>&@azyhEMzFnsR?mS-6~?QXAKk3giRTNb2D~`{f_iPi{S?y%+^Ut zoG(BRh5QHy@IJH!>HhFa;x|Y{v>$RM=wbrHlCiFM1eU_t?DUZC5&$5Yd1Xet>7mf@m)+5oBXxs*Zj_D6oc%k=j3#kvoXP&W2kInWqF z-L=9_z>KPOMD#VJ@(Kma1BA}p%(Iu{kX;jg=}Fp6%%ZZ{WvAnx^5Nx&b9_#oaLA^po-4g4Lv+MfcF#C z2I_Z%+FmSv;WF~aweGEcaRJm#A0@Fb@0*k+4c=96&yrrWpS`v)2ZeaSo|IQq&3~h_ zT4!8!i;=yLRH#R)?qKtFuN#N$=5@bQqt6Fo%lSeAX#IukeIX%+tnXHF%f7t7f;3tO zCU5#YAfD|;#MzFyi|$AEnEfSb=c`LvIqad^AHqI<=!MO&o|lLnGYSyNw0bHvY^PiE zxZ=ebnwmakZl`j0EvLOY{RaSk>~#0aDdW-MVJnldLMO)Lv82~t??g0o%GD*IWGJ3M zxin?BzvTyR^LR#l>0fT2XrdeY2#etYxpSumEHM#)s3F6$7Ka5be5W6%A>??kDu7%Red{=*qc{xKb)NSiZ@Jd zq1We}=plq$64T=6Wq-12R=86WENVS-Wq(OMMm$vkQ7h#zW?N~li(6kw3{?w&xtX=f zuB$~S{MkcRl3~*m?lLaH=vchFEJS(W>F+7Ta$Fr{3Cm3@?e6f7XM^_nGi?@;A3tGT z)qFrNwSmWj6T*Hx$65TUX5|7@rB$Dg#{cPOU~M>UH*0a2(2PPic4HRI{rHZ%c9Y=y zj6A0?g9$vr6;`WEz*2c<@*cvtjVBN4+|~K7>;XRx{6vt+XJI2}gLK?=EV2lHPg?2R zSMCT1;EvLweTZ9uc|iZrgY9D5>Mbq$ft6&M?Z4m}_P^oUu^S9dHuWt|HNgs1YGXH7 zG6O*#5nA8b9R(gkInk6^fIwVtkd^1jQ8L_PNwk>Dg}2A@=Ksn-#g4$kFA7|`-?wQ?-pFz7F{?lcqaAKJnfK7zLZ{FQI?|Y+a zp0i&?*kUf+rF?Ei*qK6OF#+kr`x!e)KB{h$J9&oDLON!;X4DK)dwehzkXD#*S4v`% z#)!3=U&wCUZ{L9ByZF1`B#j3QLLF$>)>F`U$Z1$4%F+7~paFmwH(Y6H*)JKBdEtQ@ zQD3_Fl7JYQe0S{Gs`laDiB)xOT92+T?j#Y02WF~7xwM(;zdQ2rOQJB^mZ{f=cLD@y zkf#A$PCIt8yQTY}F{mVc?8EZOh_^P_eBhze24OIb&PEBheV{^JmiM5taKA*se__7Q z+PPE84`FjTBt`{Y zFV;`Bp*|bMy5QNt26MLu=D-5x7`8#S6qx8sMcyLSCyA5fC^5L**A#Ytz zuycWLEt7WUmQKr~eWcTzHE$uxG&%SxvMK`Q2pN|3z`4XFr9iR$Ig3xc-f~KO?n_(I zq`DVVTc@pDIT#bZ&<#K?v@%a_m=SwK`9j3K2YQ-TcPp}?Ixl7PiV0~Gaubj`7 zDHp$M9ZTzK?ns!earw&X8k2o=>F!SQn1~Q_gu+W}7{^jE$Js=(e3#O6;SNwg& zEuX!pv@6=~l!|$aDz6%E$~JN;jqGG`!0%vOV1 z=yS-kXq+|`T6tYvZ0X@^6f1J$XPLYza=ljx7M2GHmR;(`w4K&k)7E_vK%XejEanbT z%oq>k%j5G?C2mLTW(w=FUGXEPzzI%u2hTOI(Gm2>uUCEIDB6g`CA)uv)Afd4XDt=u z&?V_@y^t-QbY=bmw?|KRGIdg#1VCz~r`24G;4gIMGi|N{O(1ej6tN?!9XMS?1I^PP zfjJj1aqQwxMD>pvS$4H+x=tP zK&~e4I|c?yN&NLEf-;Rq(?rncqUl^PKfA*B+*CrfnDb}yb|<0I<4cZKsS)b=%9;nR zl`i~+BO6Z>!M}_J#)^$L!=}^8YrAO&&R3fQ;P{JzGpU=;1lzL!kr2NYW3)(W3P~^bZsvelNRo4<%(%9LJk8b$;?RPHRbk}^8vZjX` z-it>r9bm=tXDFBpwsAUtx;CZ)bHQB;4VdZDh(_)O+89ZY*N(^h4(Y;lzQ$?%1QdN8 zjlX-un%MUUOPV8Dx3Bx+*;;lw@sDmcf_Dy@jhXA9TSCvfTDZd}#vjV^`&F)|lg%2kENp%gA$h4uPjx&MbBT z8^rtq-Wd;0+T%M;^YJOs-cSOjr#T(l;@g#6O?Rqv+9JmwiYrVz%)enp_*Fg;- zx2~zLUx;_SCbS-;_bj6bH%Ox~$;ngG{s#vf5>So!1N%}LLK!SRljq{&Uc9tR^rVPX zldN5}M%|8XPIPC`^YZFR_WOrQyOv;ZGOvLFur&5kA5J@y}; zSR%X~)z_9=aEbyh=^5|THGe;^2;c1v_*^`UOAZUJox|HJ?EkmLj3s7Myv!?vh4%b# zpN#zBbUi*f-5ff=_5wg#A0tZl+0AHeEXQW|Q%QmvR56ORX82<=>o= z@&Del_J20W{Yv@HD%uSc^VMz6W+~VA{#Og0eo!iV$`p-Ap-;q|4@Z_>S0~N)d*zt- zNd1NpjoIKwI)Wf0107h-Ky~C<`}nW>_~W=^z$lGs(CrxsL&>#T>@X+Eu)%qMc6M>P zv$HCI#J=?fk~q|GemAA;Ou3`M#aP3gvO&sR^qJg>ii(qqt2b=Zj{{4hX#$h{FF#7( z^1Gp&VW4=s!0*9aH!VLPB_FpzI8=fRQ^J|YW#UhilP)~p`cu8vS^9&8e9FwvVHg@B zG47GIkAJ~H!J8Cl6Qh7jt5%FwKY|1}$VbPxSc?(ZktHQPXMNb;m+8Qj-fh6dc5MRk>Z2kdUAh99@fG-v!Akxf+ zSvaas`amV<7c@bWPp8NMZdDK5>V{2>9JtkLG{+Gs(Ye-}s1ro8h<$&X)6-IgQn?Fu zasCJ^N4sh1{iXQ7E<{7Qt?l` z*xiA{MFP=pPTKi8vb{X&HE6IHmq>QLZ#Zc8k>8r4L|437CI7l3nPAudlI&E>(ir-R z8jTb959IZF%Hnns7)>#6J|(X1nv8!&RfjNGXp@m;bEcS0nyNNIM`XoQ&S`wFL7Jx>N{1JM<_OBO(@_< z-m``JKD*M8^Yi->hn4cV$bP0IDeu(zNsry@=TsgupPp*N z?-yWdWS$=F<|wJ#Zvs(T1HK;m#W0jSfk@FVg!x61=7vu}c5T-PkK^0H;4&?YfVjP2p_hn1czAyNN_wafWv8J%aUB7*;NJ)tyP#dlSW z|IG}E&n7=c+RBtln+r_RGJy5yqPaXj?Up3i=;@1T;q9pX)&3d%d)Rf&;{&sBzBDH60v58h(Q*z z@*%2Xt~dJa5)6v=it32;N1pIbU|0u#n_?FhXW3NR^Jy~6vPQi5Tw9@HxeAw{Ur2mo zP&4xU3=!MGOlem1fTQ$Pb?@P9F1Y=Mj=>uVVcvoXb}!$hbzz^fndP*m12p?)o&l4#Ki1F=jlCG1xYQRd)A#AqxdYD6hw_*lOf?@=^4^mEVt<+xRewvXX?#!dj9H=#30Fcs7Hv*@-;u zl^;#*h~P0J1gOORQ?X_4?6$*CChBZyxFpAoGlH6m6F{{BxXboqn`dRq^yLhsPOE){~`U?+i#na4u({06Q zs7CYm(n@aS(Z4qCU!Wd8u;YVMYG_NR&13remyb|rf6~?C%l1G3`mhm(%jdVJ8n2)} zOaP~SQkbyT^Y=}$BO1onCqR=?9iAPoXVr-cr(9W*dS1c zE?-ibrm&e)n0^|hz?U8fGqi#B%`S^Bim3oK6v^Eh+`nMZH>I&+ogl&4SAo<)SwX(B z;?sv%TQCzho!)k@`^Gd$ql=}SUMc}&nj}Ep)?zCOrItc9bbum`EW&{0RXr& z%kaqq?=U1K^kDponakG32bgn+o#J9df8TxA{*ugmPHVg(6w_YEp?%Vu-TuJ%Ea2V4 z0*E++-Hjyu*rJ{Gx8Mni^Y~M*0sO_G-q#a5R3s~!05d`1b~#c~90N3p4`o!gSC6}! zHBm=1p{5(=Qf4W?^S@RIiKa-{N(lXTIa_GVANS%L&axFO!dn+T>9nrEP<*p`Nz7YA za05sNEWyVW6Y^s#p(4-Lm3rr8g>0rCi1gX@5C7(Tgas?qSf~_4sC|{`6=2It>S*5= zGo0TpV1pQU!0f+k0W4vs{W+o>c1iA%Ap5q9gwrNb+m_*9&-J}N$NzWZ%Y4!8=Xp%{ z*DbzmK#yyb2U{+)`tYCfrC*j?J&P+~^;&b#_ZE0y%bQJ*x8?&5_C3yqZ=rqq-k(A- zfSa)HP06Tt5ua!`EosCNeBXJCu_BTFZ(G@+a_OA)t)a87V6sPy=;Am!j^?Qc_G3Bl zjk+qh8lZ27w_ye(coMgp+1h)YzMnF7keF`v2Uh?%VZE>BINAH#WwFbrC;dJi*ZH zCXRk(_`3j_`r1$cMAM~jgwYJNpmKv*mFLZq&fVSOX0j;-(Ab~AM+y<~>Lq>5&!&UR`76E>ATz2x;O7#p@H%&z z%Qmk|#vh)()&EgO+hbvg=fay?qO*DpVf_BlMQ@6ySM#UZ7bf+0vG$&1x($x6p>-Mw6$AQ03ZhquyR-Cqr>> z8=LK8ZXC(n*R~5z%VXS1RIJpHii6rg_ z-M{!i?-(bER9gLY7u+E?m9O!^jCnY_eRhXwp;#~Na3628{9{UZ2Noy2FMwzQp@uiN`3FCuj>3fb*`G9Gt=Gs+Pn8&d#!H2KbZZ0RgjnB211?p(T;`r)#xl@+$kA) zP#6)O4O+NBLob?9+~Xgyzi3LRD*2kbNQN~J*8uB)dq@@i&}UK$eOjg7_TR)5^>*$G03X#hmAAisv>ymthCja&zMC=HpB z4-cF2>I|2NI#*5fjt~B*knQ8jsKmKMd8-gj*`54%0ky-a_pt@`koAMq{0gecpHugm zL!gxroYbGY(WD3KuW{Akk=7FBw|aWWK7=8=_ujQqQkU%CHM)*VlHhe!T(~F>I=(GM zF(s9dqaMS*i~Y~Sr{=jV_6GN6dp zn(K)B>9Unxu)+7^&?tx}2olMYuw;c|e_Ei$y`6(c2q;4q3!J`>5aI#kt|jK)aBK35 ze`LU*n;HW7>Cf2%#Uj-o56e4rg8mRhD@e(kYOkl&$I@*kbc%U6x6}E|`3tsnV|dyi zk>2wEJu|Jb&6e%F@ZL7HFss~Jd8|geq*iO%!Wpw;s#vt`qTKj9pVgHkWc7f@zZ!3K zK;w-_v*^ZC)QQ^0M8#U82!wR;e)-O1#hq$yis3=;$e7Ujirf}ywb+-R{b2bVBhtLI(2;>ymqy&BrN+G1)L(FX}GMG zXaf!y;N?zO5dBlE_$M?^*6wjbo>1>PB~CfXyUBzYzrxpDcB4;#GMxThRx;583>FS7 z89pooR0+Ay6l9X;YsZRel8MC@s9&P&ps+{H=@^Q#3ZbsKAsBEx@5f|=)})ABVZ-W?U#0ZLt&hE<5eg z`K&@{9Re~RkV`BpVjUr39X=e(!*EuqxEI1hRq|}`wuqHaNb=XMq}m9HwR*>G7h@!0 z{;~siKe*mITST{J5_e|)%v);|b(GfwWZSGdyHZKcaLC5-iCo3}@{ z5Kx}I-g59oy@l5-6O!PW>Wvx%Hc{U9Id=rSzo{=O3l;5{qTs*vbG%94Ld+umt3AUM zEsyMr@}Kwd^w_-lKf8kG=rq~jKW^j+T_9`i{y(|@XD|V3mLzoY3xxrP0T;A7#=mD7 zw(AagSQ#V26QrCbN>VdbVV*FiHX&F~{1>kPiO5@tU|%a!U}*nc#t9d?AzI)?sUiN3 zBi5)Zj;NH_6%8_Y8HJpURh{amm_oh5o8tH$jfsv=p+C(gfAZvg5?{W&?tM*XuODO7 z4sMCUC&v$}gHi4l0vajJ6eiU!?`%mQyWp1dpf;7A*~IkUte=q`<)X;j=8YN*c6_#h zlL-1*gh+L#5>BU%@b6iVta5vI($p!Hqin#1?gl9p$B48e4-yK~9E7<3p*Ey~i>+k-8pQAVm?LY53y{*&n6X8ii(aOSUipf-_80Oz$QnqycKT~AI*povxXCcclh ztp1nUU7vP*sR*jDB*yhFst8la=K+qC;?E^{3uzEtZzu32$dA+pn8jK?3l%RA5}{LY zts{k^Aq76iI-?#tz(hJg@+V#S?dK+>l`+ckz!Zrp{rD zFRzFdFaFkG;|!dD3q&>)ZA!j7Ru+IjC4MVTtS{;FUM!sKKdxeWxBJrG+}zA#68dtv z_wrkxf>Y$>pifZtMO6ei5sM+$xbY|L{N<^G;&CtcCA#BrZjCtnC3x*Qh_w9K3uC6k znfZuQiT;Ul$nTl;`7!OKZ;kK;8Z2l9Q{~t1_fimhvex{5@$q)f4`AS)CFg_JgsgDl zpV$1l)_flrZ{z$>HeT+I*CrmFaQ*I<1iM~99FK3&n?qhgUY_P&puioHsK}n@+K-$E zGc?cle$Tis7YZ*-axWbZFF_qGqPKAa9b5X(cSPr4Gpw2Wm-Pl;#%CplZt{+fm)SVK zmpIhtom}XvOx4FbM!z2Wrx&^x`P7EB-+oWJVoZ+}XDzn3OMXvSeov*re#p(|DENaR z{3-S$_P&>XXZn7YoAxiajAt)5R4s%5z6|Rwkjr73S*(K*GO)2Sl1I!9&Ok%5?NpKq zFBHmWT81K-MU)t;-x*vHd|r|ZG+YLdgb(sG8Ght|-kf80Z$=*3lKlQLbX?~1Sw`+t zEUNO99}ZgD{iie;i%|5lrBDl33ZZD?BO)R$^2p5>(CSl|r0SZ-i=PA&M)Gee+(>kG z(~|hlr}8!p5x+9OuY^{c{+v~eGJc>JZDIF5L^_#CY;MVS;oM*4SXh;5K1N@(rF`o8 zrfXCco%-=ORZ1yLEwgsrf79UiMwt9Klkgz!C&w3N$T!>l2$!tE$nxE1ZNgpmnEuE*j5`E}&TFi;h6$Dj zT$lB7@O9)e$VbZzZyeW8En=E|5iE&kX*pgDu8s@`o&heV@B5R)Yo-haV=#Ul#2Bu% zdQ4Mp-)jl5cZGDlXpeOqVuh_EU@LBp~QasQ*prh zJ18^fm`vc*z##OZHse>R5tFV!SuVV91#O`IIag7jbg^Pi*RCoVC4SztSgdrs#zYu>-uI2i`^abf;-j4YAj! zZe%ac6y)7H@+Q@<{_JQz z-D%R@qhJ2bgM55ydf$G%&yl+`EvOE(9Sh>oWUA>nym4KTtEoAI()1}zVI3TMhcSPL zpM#idX143h6IYLZD@W*}tsmyWQV(7&I-Il*Mfe?RxT!!aJjEWIu~*vHNEAL8sn` z#HkQP+5W-lakmM>1c$*ySdG*rX7=gYYH85^jqNs_-U$6r+25F9>Fe`Bu`XPZ-@Snd z_>oQb=Ye6S7KYBx0VX}pj^fOMkoOZAYf(Jb@TrmT+I3NSNSQloz5PnpO|#Hxjv{Xq z5LO#-cynfp>SqRvuJv{(XBNlE#4#fTyu&g$U_H*HkOGv%dLLTe`Z=^ewsFC;`vIe<*{+WiPgmA)E=DL+J|2v?VL`rdh>g&+J;KaLh@PDHa4GlN&P3hmk!pSLM)Lw%G z4NXcK;hz^nnwX6F&wRzmsi`af?iJyml$8zsMiW{>etsv-Kii&^)W82cG4cQX;s3QZ zv}|602@j8MKA9SK!YeFD*Nq4t@aI|G-@HrXai{i9Ow;oU%dF@KyuzJwm}hOWQ!826 zi3leTNzTd1`A`#uiiTUSLb-mCzUOx{tM|tnYEg@L7P;T^#q)a)?^{7I9j^up=!K4* z^_g496WOGd@)?|_?_npaUL;Z-PQLxnPUh}+$wMjcdi~ILd86sQlXEE5VYJAl{*g3M z2k=z#;%n#ZkEV-Fy~Hb&YrEA`Xzu&{4tZES_m9lOE{GtQ#VdjV9ffGwe$p*bARrQ@*ZlE#Z&~_s z_QH?XMh6A?W2*c(Yvz37uHxuJn@i=&*&z41&zZbp2zQ^6bev=!FQ+IC?;W0@K8t;f z3Om#~=l7!9IA=ANHD2mi&A64d{w*oBf!FP%Vp)^CVeg#8e+vnHfNweMvN@vi=79D< zUv6RuDw$(i#fp{xS065kl?=8L@2Mo4Pk+F3#Ng*|K)4njaAT3}T-@sYa?7#Y-X?N0 zI9lr&6g)n1dz{g~#Z&jYfmHVOHtkrWteYNj_s=#BYa$BbCW`f2B@7y_)t57=UYeL3 zQ|Am0^~nO>0beUA<@YMX3Jghc4ty&WYV8FPOHqu13@$=}AL%aQ!xnU_A}Xc=Qt0ZC zOc`@ZwPgvL^m3mw1dnN1cBd&c#AGo5`}F&5Y@9*4q2G_w#d^DNAIHrgzgL6g$;|!O z>nP6mD92XiYO#U<5`5Ru3e}$brai6`5r6$y^qg5YyD*iC)Ohb<2|4Z$*IG?Kmp5H% z=KxboPFp@sMW@oAzH}G3IL>h9c@hc#nI?|Nk};V5@D2pGD#Fas&{4A1lU!hGe2yRpYlz8+Rj9As3gywOT}@pc@jj%Q)G0$ALzP8xm1sqOV~O-Lw3Ir zo=--)z5~u^QtCzdx!n`8(qbeiIp1nTr*%_GdOyad`r-}fQf>D-5oa5@31G{7U@*tF z6=3WV#yEr_6__ns{xqOBnEF=mIaDrrNz_J1a}obJlvg0S!I{FP%bSLSeH}cv$znxa zY7Z3!Bh!r$e12*3ZdbX!IN+@xROXNqyjlzOF~&2U(141ZiZE7Yy{eK;47!GPcS#J% z(T?_Jf6Az_`VPzT>KVjb2!+6=JzEy3k;IUWP>y%H5m1c7x#*qk|0^r_!y6XLEPNjtc%2vK>O z{-40H}Rk1Jw-M6lU8?x5vQhfZS|;zrmV;A--+MR;897ljntX% zI1uCITwVB^%Hd{xIb@N!1(w5$U>r+n9I*OCwOl>00{RMU9U0&5#X%&4{Yb*s-fZPuB-@oH=S0!-15N6TyS3)z)w(e>N{%i z|F~pqG1!gy;aHwOGl7S)t!)=FdK%iPUT33Wg5b4ZM`C6kL;OJ>-$_O%>lh{Z_&0wA zl)f(UM!}C%8%l9aLL1i>4Q=f>!S`LA(t5rhW_=we6t`l|7`jaiLB|+-bR3bF=yZRU zg-tX_*;JdT8E86lGG*+_gASljqjFw`{heE$Y>3&qk%B)JeLMY3{d%Htd{#uJ1LfmT z0F}mN8P2ip=+G!X<5#U}Is-B0xA#6`uJEcm9?-+mRK@R zYgN`ZnH+xy#7{5wOuuz* zMa-YpGHm^mkM)o<`ux3;k;Xuy!EptJ&)1mUXtP;v_3DM{;K&je%!M)yI2HZs=mW%1 zEtY#7+C^blLcVsoxPC^SeVuNlps1wA0JN5MK63?u)@sP=Y_N((RpiG=O(ixlExB8~ zbHA^lhS6nI3GiYs1!SaYN6t%!t#ws_f0BB%*V&b;o?14xhWmE3r1s8YZ*%vEVqxcC z^n+>lGBgvy$=9JSrx^Ed@8Jg+No0;gK( zm|HQCiiK)fW+#aA>|@%VRqy7hPia(|fpKo=G?YQXT{5QQI;!$Xy|LL6L)ICVbVR^C zb?3!~GMkzH;vebg;jt4o4s~yq?z%4teAngmo=jF7LsTJ*Uvh3+v?w2{*Snl+`$P{5 zZO&RY{!E>NTEZ6hK9ZV!SrxDr>mSWxjsdUneOixUtE!@wC|?R86O3zZb@IC)q-Z>@ z9G(&*EtQOM@DB|gUl{Ag<$x_8a>1OC7!HV<10l1oCh7`t*w!8$JC&hz;~aTmBNk(a zhyDN#PlYYuA7EI;Aira&yh*=i6S=-!eA_`JQxAntNMKQub8KW&vrwr?uTi#e#TkKs zJ2LG5$;splc^IB4qg112Vf{o4B`1SI>~L0b#(Q6QJ{&qCzPAvU3AD55HwIm%1^MJe!fe%}%U; z<$<#XsD9Q9tvC9#v<7-rlUG0uYLPmw7U$z!iYm(j(eY{3suany_wb=T!J@)=R_&tx zO_3M4#a}E6iLMekk#r>guh@u4! zKkR3PEiq;U>cyP0maBiDhfrh0x{%7RS<>0n?B3N#Wg5J|U@}7yNJi^yWCA*`cMnhB zdAsZh5!;`>wKnPUDBnvO1A0e8bH)$)KVKkyOt@&y)i5!xldGpUI;$+GO=GZi*!70) z_a%6*Zf%xx@J{Mrid*feqf&uOqIG3Fl-6*KX~#+sQZ-uXh8qlrU6cvi(;^egoJ6Z- zeimzpgxX_8As|v0zf;yx6}?-eFd-~4)*KWfVG8OV^5ke_v7ph8{4w4|>V^b+bU45H zW#WZwnD}K?L>a{$1L5w86>hfdJA<;AX>Z;tVUb!ERthFT$&XsIaPSr~jjZt#q%z_u zg{+=6)cC&xpJvb|r6(kh|{A-l5z;)^cDXScRyX^E}n+HgcagSm;+ zf<7jYS0ASvKVHUZhY{?x`e5rf?cEETt5bdq+MR)+v;HzM{yB8?$noBot)|=pH>OwH zqJ$uZzvxFloSI_owB&gz^`lqE0aTLF-QwOaBo|;?f4; zIquy3qZ4a6sZnzQQARK0%k?ZIxOO#}KgdtpbZY~PJBg`G9$o4j_1{_m)Ku@Gl2ij5 zhJN0w-&b4+8}y|;ROR1f4OI)_o|<*V7|?;j&sJ5R+0@S}uQ`^0+_Z1TERC5N$jh*E zSuN|aFTrf3X4>Mit}A7qKj)YjP6ZeDKAH_661hNBv5ivEyNBp@9+vr$B zgneE*0>sf`Vs8s@)e?%!S~AOTIP_lb*C?(p)&g1|8ep4_e(iNOj2|g~EI-8VmTY4( z=E%3G$O2$CInHQhq^#kwwr^+GP6!4|*_-zdS_Zp1HN#)$kx%_|_quXUGXPKpV1ID{ z&lF~yFc`t=?*g^4BT(o~`fN5XV8zS>I6@A@#;(_FQswG?({=lxy~h29U)M~X9022Q zsDKf;kF}qpfbvjwUUR0sIranj&d{?yA_*`)PxA#nh3G`Q8 zzgW0(|Ja>QnA;Q_Y3f-P`IyvR^NUhHEXS^f79D8VQOgFXnp7X2Y))H~=(U{ow60tw zFU&-j)YSYwz~s9Jrr(duz(liX?J|?$B4@U>Z{6 zIRmiXETiMIVczwSQvgH`7ovrBWm}X94*nK zx;gMQ8|hd$V)@u$P83YWyG|w;v~TJ86f;1@<+Dv}|6CavTg2cCb~%u1a2UlIYOJ=1 zfKLI?=U&MpR2FCltBO6M5ClXG=pCFR>; zh(%oQhayRI|Kk4R0us8P<}*=9CP(%pj!gJmqLXNPsux>Z+;O60DGOuypt;0n(d{QeUTX-WuTv?#CzK z^S`e7&AwUDt!vY7R$~YxMx2)73zXJY_w{o_K6!i&bN)Rd!rr}VL)sfujtouP2Bo9( zEnVH{6|)|*nk}6rA+F7$Ayv#5x(2w0BCwu>qwMLW+h^=FM zC)Uwu*3EHz+K^cEeg<_bp;J>rwh@Gxzk=@_1Z4tan2@j-A|1E(M(JHu@IM)F*N2mf z0se>{4%~??b?rN|5lQHcYqnfN2wnbJz(+I~kPBsi_e*j;d)C z)kw{k39@jui)>2XfnR0cZIlE&JVF{vtQ$M#CCJM()e-RGOpyfT z`uF#Y$Aw|E{TtG!flHYiGW-t1F;6JzE`rM*V-ufVpw5$hp1cJc7TIHKVpWiNi z)!yuO{b*^*`vr8^sgCnU_lAc}ramdJ44I=vx9r!iexhgt0}4h#lu}dZEmneM{j4!a zd;aqQJPO6RcjB~E2dvuZ?Dne*{^1na?}&K?TR`S&bnkyhClDG3*Si=3;n}~LUL5k>QmrG?mSX5S@>KKN{8WH^#*oWYEbu@HYOnD$tDC+$< zsnw&uKtL<&^n^yX7@@eL@j|i z-gD|#kS`IE&F?wLFb)RN3OB}LdXVrAWcb}79C?NYD?;&&ZC-b}u#7D(Z5no>xm$I; zufLg?Xlz5g{sH-+BLC_)$O(wdOnS^UefMV@(={fWDxF77zfdRH+8|^ecW=$rg|>Q* z%$P^j7JsUZKbsnNm+5w7C_A@7D2dm{%v$#J$oph;zQTfNAGk1+{6ZEP5fyrAU; zpgR^}bC*^@5QwcWXk6#0Y*!p=+|`Jy@DP#@g60Rh@tm+)*qu2zTe(jlBlkIh+jXNe ze#n~CoSe5pYZ-eo>bA$9wx{F1Llz0n%*eNDg;R;&kp+;2xBQ&E$3Hmd0Ff3fs zK4O5Yh3)a>Mii=5$O7%AOhm<3s3H*bsw)?~$ymh8aWtqC*2$p1C!Q`T!(8NWKWUtO zyazqqvryj)s`%97G(4`O+G4O%|EArGeeSqBAy-mwwMp^%U#UpAO(v!kJqWE@Y1tB^*;tNmS)&&EmVb~}!@Y|GR+XXhN@C9|gfg4O4 zit(Wtr>F)DFikk1$d5b%Ese>6^_0cdRhzCmF)up#b>Vex=2Z=O$&sPN8=t-^b`EP5 zL4_^JJWgnAcCpWg3%)1M8ep-qW-d+3cluVHjG)ijWdL#7%syTB9uxBl3=$O!l>xHT z8$}Jm#bR}^=Ng(Pa)?;MkOh>U>xXsl(ncSW!>RV!o%(t#Z~w`Mupg(grQs0gnv+)@x&md! z3@t3#Ww0+U@o4966^Vy=YpnU zrcbg_ANf|b{D+aZo4+iE(iy)qQPj``y;XlJXDagrlSgB_e8b;|P@9ioGj2?J;(%hr zc4?%ffT83jNBU1|?15*=N!_}3OLT$E=?|l{mruHy*)_*wBfSdvcaN-!bb+;XEsJs553E@o>eL}c(hX{0a zr-nWG6-4ODRSj{nfY1R7P){Y?lkO7 z3$YSn@q5`rW#@HpT2RIh_XjfB;DutI;px?XvvfMXAJKT6QbOrg>i|xE0K^TH% z5emJ;qT&_p`*yFjM-nrt_DYeVwdFi&1uAo!(mXRR~tOcQPhiz zgx`ZQ@5U8`9H0C%-iKUBRy*?5&-+~7XISp$hfNaF73GmH0q#Evyd1x6B;10hSiYCm zDG(mVa}Sidjhq<~j*J9={d!(2h(31xN4)f0>K&6y`RKG8)TNHh=}bFQEzh^=*z~y0 zpaU`Vn`X_=KK@tBEyd?$xL`9GQkHX|0Yd&gr+g~w_8NPUsFb}W8GdUzA?Tc_ys0iqbq2w-gcn(*rk0G`7=L?^BItUMKxdbW>G&l$HW6R?iC^O0tk^jA*Y-{z72cxI_#7a zFvC==vTH%UYmR4xUTkdd%)h5+OcdlWrC_&J7dr=W8&=dYhJPv+ z?$R5|6#&>(RuyP4eLVC${F*@*lQ-6JG?}<=l8^yE{44^J%Qf}6bkn>aPP}Xvup`)8 z)%VGnwk-aLMFp&XP(DEQx5;7yPqTc8{`b8hf|}uYfd|!&+a=iBy-v;t!ul3ll(qY< zhW;k5*R@eyY2l+`SgsxXi8@|GBGNYl5XRCY);ge@xj_@SkKzR}Kzi}CKT)wh5zZbhsLvap6Jp!nZPIPQI@a64I{%rh}> zp;x)yUKefp$tABLg}IRn2u%L&D}1l%q_S{$j`qQ-wKuf1I*_G^{oGpi4O#_83$H)( zxIgv1j#y#>0FAj0_7CzdL-wu_GMTZLIwZ3L`-dN~&IYrcopX2VB?dyt6qFNy! z5vT9}>5-7osa(Hc`e+Y1OkE$(`H`-2}e9r4dqb_7&_ zaogUz*{s#Qrgmu`Db_>J1r-AwR&|y zS6qi7#?B2YzIv*ja-$Rs^7QA))}N`m-%*AA*l*S)mJ0+(;o~CylVh|v zwsDh#=!Q+aU0hiFEmCf&gi63(wIT)ml;b295!0q~ZTXYt$&M%i6l$M#b7D-F&JYLt z?+V=_!E+gE14Efgfu2U8AJD|xHouqM#wR*qNFv4Ig&Gednnf8#K5Ywa07B;3B$Fr{? z+s~F>Mi16vMk51|TKxPcu<(h=OXGxlxF=7o$4Ys`dvr(7s`8c87@2NLUJF1O{ zwkCVrRKJRe{kS?l|54w(M)J)i9h3x$+bj#}vs>;Z>iK&}VEr~@N9x%EP!B)E(^~ai znEGS3yf1+ZTjM@;NB@gjoF5~vw4prlAiO=er$ZzR1lFUZ2AjFUFgrWDg(AUJnV6Ov z=JLD7?~CTm^5vUEcFxSt-E5N4!F}&H-iqX_C}yoR82yVn%*~VqVDriL#(KZTK&6;P ziKB|nXMcXqv}GOG8CYU$enDHaog6=uR64}>O7EbeU%5)9_$6~O2?4h~l$v>&pZ4S+ ziQlroo@V^3B{R0qQ~ueqXdy)w7wEvPxu-1@$bK-c)OVr6f4=ZR&gLpB=wjj4U|~GI zy~+~qh<(ekdFU?+(1&hjD8@NKLr|!fbGnr%&ZxK{pC34sHb%Y`)JLbtAPxc@E^Wcj zNqOHj??=q~3ZUNlTuy&8&Leal@7fx^7(1z`Td>)#ScDOS2XiM-7~k%DjvN2w7L`{L zLt2J{DvBct3+c2`~dvo~@{Tz@O9fSWh2PsZXrH3;9`e$Ob4#CV18594-_TrdZ`- z(ijH0j@1dH-PVkcxNic@G)*19b{LuT>t43scEmyL`+%+fCwh=SDf*QjbgC)-FYMrR zp(TC37BODzO?m)Q4X5)Lh{O3AM?ItsU6M`--`sE9^Y8zI3*_vvs?n;{sKGt?ZD_;g z)F%P^7FXjz=QrHUmNot=JG~n3EMl%{ZF+wu2tVbFmGJofpVXzn;}glr`T47EZ}POu z6*0B?7)wiZgf#)U6nTdz=eb$Wi7ct-7fS3A;RF$$cZzUhRVudQ7c5io<*yXdG(s&t zw$O*W`!^B;G7BZ>($-JVJ%-)iiILdXNII7L5Yy1?nWH$KT5IN^^ z0diZcb9~JX%h}lP0Zpz<*;)~jrqQuu2()7%6M^F>u}8SUX_|Zt#8GH;s(D}R_7pk03)#8G2a997a*6e>X85}Xl9VREZh^|LZQafrBAl|8vaS7i1(Pio3%iraf) z{F6nRlX?!N`jLPh&9U-8gjuZoTy_0Ckn^lA8hxGy($FX| z$U3bad}Q{5HPld#@>(gdaBbBpj5p>b`e399-e@Tb;X6i&9b}1u^(Mc{@qJ zHRE0=+<_{5O{K3n^)tdU3_>aC(|93q0`vIwF1}dqvJFu2>K)BIjePa1SuiE$Zt-$qnJ<4mv=pmvQM2cU`4tkcl=kyYX!9?$sX+N zF6F~35zYpj);`W=3k6}mmhqSXM3GPeutu!lImWTB9D1LO*QVh7E7>w=mP&Zyosn~h za~aY%nZE?M?N;9xU-ZZH)nPym%Od`o_Vbc0ry{JV9VUUCAN#^IYzO>~e2)R>7&1>f zxvv#2$@z2~e6qbAMyVwS1mGr-iUwG?6aXRT%r@(EFd$qblOO<4f1wK)#!ZJ`yG!5h^?a*C}nk`P<}IX;nFc zUIC_;dvs})3W$GA5dMym&BzA=6n|_j@0$G2C+$2NCy!W0SOb8~W_M7%-f43h9`G`N z!DB82I_lCq^+0n*_#O=a^vSe^f2?gkcKOZ(5OBuU9CxairI7#_$yoNVSWH4V?n@$Y z6MDZB3y)8}TW;YoE2`(nvQgg@v=^{c8(^u8ZqNL{FIbF#bkFB=tLaMQ6|iFK)yRH` zT`oPkj&Z6tg0w%Eshb1vu%GsUhq(nVA)>6PGzz2R*?#rsWA#G80E7*QAPC0~?wJuF z6z63|gX5mx*=ckGIg4@>eLdjuIcF{2YxGTFfh=naW`g0}tkarVPi_b3T%&gFRQFP_ zr^EL)w`s_6<{#N8VE%3N0@=*IB{_u*-OzWWu4ks7{Nff&quZpKfyxBP=ujc5>58%V z{hIe;@NtjlYj59`LagEtZTSd35VtJdyt_nD!dq^dx8cZI9T@M4fhcvd#Z(Om^~e@h zkiN9yt~D5s!M0xTz6doBy`xyRgP4#Twy9(3RxyoS6d zWvMKjLi+`6D#nmaMoq^FA!!ZDFf4 zH2;nScscj^wi$qlNt`(Z!z2oKGHXnCZ=A>Y7 zZ~v9NS~_a`b-#VwpT<$f=d2+3CsG>OALfkvy|fOP&0ow2ySI>x-no7fl+h)7rdjTF z1;8c%j=ZWeXoH^O)5RxV1bH}lfe!xz zt*obKvWVQyHc<`nJLQn-U?ByAeAh;-T4Ib8Al91E5j^{`lFNRObe|odp{W4zs}rbk zDD(coEfesFjjPv&l%3D`vWSEVK#x>MKYQZS?^HPwcJB zYg`g}8UF4Uyc?w z6&^z?Q+&!<6MCLnp3m@Ap||kuV+?y^9)7XK(fe)Eb7PLTPSi`&LO~q?ayw1Xr7Owz zq&Qiean*82w}-S;^QvQb`uG}j8gvj!kJd68D)x#xHAo$6p!y+FQkPOHO&l)#Y5LB9 z3`e|+Qj0}=Qp|ZFVGCC4p{KS0wggYH-*iA`CYyGmk?6+|=Uf(@_Vat(7&aUe24}lpdB;2 zOcZ;k&4`(BXn@2@DE;cK&9P7~B3*L0P+t(3_pEjmiho`!Waj}>E`qww&R zKNneJhQD-B`UPvT65s{tsC)PsC2ANkQ8LUy+956D60SKxlNksX53ADo2?vzCU)9w_ z@ACMnYib6aQdMe5qw4!PH%}i1Y+m(|l@J<)jR-0cFm7m4wI9%!V*u<9SD=$K1V|`s zU2zk?jp5{E5@ZM3>q3pKoe%N$-#^01ZX!ap$2yj}yn)-2#^s!r!1EQa4XEgnvcz zKS>?&_OctkoqDidH1T$T>O_4-@{Jp`LA(vWs8HalXuTP%%yxDsIYqVqiX5YV1D<*L znpqU*GVLw6&!8O-X3{8Ki`IQ_O63c7r9~H3>cbio+JI$|8t=}Qb*YDoLE)dfbbgPC z8sM!#Vg3K5GoFHv4QI$m3zgCk643ta^NjKayfC-C!wm(rACpr_ z(vb@x(PBXSJf>agWcLg5Un0>%e()E3^b*KXDN9$Al6KPpf0yBTo-G3-U)UxKW#`Vf zKHMp#T(+hwl1+-;4OtyzkkUzC)v?S1^jSzF4GG@GR_U+&){ziXJ&cq)9CAUKx5e+p zkb<0w$2%>ekla1V{`AhJj;&~ye97j{MI&+4>x|CjbnNo@;RCWBBuybsKn7yeZOfD>f#EVew^qr9UGqM;i$MeFIDK$=a}HwL$Xi0qnx9F6#<0Ij5dZg#Kr6&zIH+U}n33K-iUU;O!2P;i=!8;ma+ zpCKunSK%Y~4e;Q&R}aoU6Et;&XL$#J&yEL`U2GPD#R?ueUKBxNS9sDO&p#FIJb7Dc zPZf+`Qg%upJ6^YP5r*=-Bj5HqkRf+- zI&!a~Z79oi=CzeVDN#u=5fnShvkHaF4F?&z`$!I~@!`ZtgCFaXQwhHrd_c7$eb3yf z7H$2Z_VZ`OHG+=>2Yf;el0&-BekF6UR9H;xF*OA+0=~=&MHibhUfh>WNdp^hOCzNY}Wf#g1kH zhF2Wy&1doGRy3*c8``~j-6GO7L73_@itVoOnqdbTYRcl{l^f;1Htno2Oos`$vUZMW zej4Zsd#+i1`8=nhV${`OMja~xD+3Ur^*55!X?sY`wl25Vbe|CT5sFA_dSbHh~Jx8TNpiC9^e!yP2WiHeFVNZGHH# zHQa%J-!={&>j-5NXg&RI>UW_To8QMSahAL>G5cD9(N0ho0VOulzy)u zC2-eUT8t757Z!NSZ(3$8RnV#Xt&)Z%$Px5Y^YSq@+HZNe54}2UB6;$}D3u~b6I3-#anD2^hm21d zPMk!bS-B%`5iO23(>ll!3fsz)}LaK6r39#}+Q$;WE`{3v_*M7fGsq$SweSgGw zwS1*H%ju_X=#tDvxF}U-z3wIi===tLe+O#YchqS`lXpc*o-bAh^!YDS6-^s%{gwPq z@0KcZcNW=m4LlEEfV&A{W=~dbd;|H+eI{2!o52QbFrm|yLC-R;ybDG!5a~?4H>bEEH6tINUY;`+h=LkQ1?6r} z1qKfVeUOIDeTSCWeco(mVd*?P**o=S;&Wf@h!d3iMh>TX$2D0CdMgb?*TmNY=JY-J z7)|7xakl1@!3ka#+HLS1ECb)vYqsvHjOaOGOfc>_on2yGd7rfCxQOPesZGcl6_=}u|$lLlr^&N8T-uG_g%e9_MPneI)oVe z^1Y_d{kb3C$Nd-F^UHXcm+Ly$InVPv&vWKwrmHr{)OPWuA3x?U~86bVaHJ4AKY8sq%55XKCS|^U z0Qt#%a&T{F&xJ+|pSGBlBmX_$xJ*^lJeMV49@%g?e)4`Y{Zz(sl9r{Jha3;v(Y+GY zTC!sN&qunpPvy>-U|sLDB>O%ms%!3eRb2GGc=UdNwzDz3DQV}dY&!M6|J!cT)bihm z#SiC~q`ekhaq}j081P@0fA4aN&H#6HO&y|9yILuT+0w+an)(&IQRs{{-0VR{cl~8` zAD-Ol`j4GZf0%7wmxefv+n;>YYDDy%tN_u?7X`m-nCvNQKtEo(bCGsjAi)_0Ge7d7}sVrpSq3TN`o($G(&D;F+a+?-pmd7K}PZL!s` z<9W$lhGVev2jj!h_OW*E&uw3m`mrTQJv(*Vao1K&M<_yy)h;$sb@Gm=NVvBWmrKA) zy89IOm-i_UGYnhJ`zhb>hu*v1dCSMAX;O!I-;#TrT5vLlv!gpwN)!SQC$0SvQM8d9%zkeUw8w1onBlorS$m$7AAON6wY?m9`5F! zJClc(%`K)$6b?7b?-y?+1k(C{JuHZKt#KQhL1_Eg_~}WX&iq;2)lFH1C6Z7lA5cRe z58i#HEPwRvrB-~np3KhNMQPu?C<%{RpU$bQ>R$G>Urn3QSWR^H?|KU49PT8Cukn~| z_~S2p>{i+6TIB&xL4M=R%iQy`j>C6?Hhmw)9&_$EiSQj&x~lRl#w|>x3I#7d z86|JZ9O#y1U@Oy#t;=LMYe&{hHNuCwlNrSKJ%@U<`bsteZ7c|dnN{4Y2kEC)gF|q$ zFFyuy>3{9hI4rx!>~$FxjVV@3JpHzz`EK=3h$tNRidJw24VDT58R*h#4%&I;3%x#4k{xdo@!7FinN{mR&b+1WjoGBlSPO+ zjVtu5fNmVtwt>|iGT_^*Y!N$^ZZf8sUV2ck)k5m)HNjGBPRMkVk&#g?nN03h{ezTl zpobm?ojXCMvJ3Lm4ttg{ck8w?N7hw6xfJ5D{$9KIlV^|_8(!=~ff_`Q_iszN&kSO< z@oPKs27YA~dDL}Y?b&#n3RAe>>vU#LGD5le+y$B%*7(EsC%ftTk_}a`eGTml{z2DT z-KE6w?9#{{m#o2qWgY?{J^ewlP3dz(uDql8&_$#gw|as`w~KmdU9DnH<1E|J*9N5x zCKSBt-(y+Z+!^6&^NL8JN0%!Pb{2P!%+W&voF>uwh88@A`Ra@5@s1tArpT2*r2_fa zvxATx0Rdk8);?s+(Phuvsk{0l?Gm^-*+k)0!?j!<~_Kei+@X?wNh!sZ*tC#lpYq7k=ah(@kQPP6II z-Fxwl1gX|77OdZ(4!2Ng;GQnb80r|hrCQpa;?qEKGaa+Ho1J!(8}H=R{@NQ?u+QpL z+bZ_dvT9#PX{vy6@nC|$h8fd^r!+fb)!E5}ZEjm-}*b zt(VBKRFEFS;a9|y_l+5Ael%oPk_&%Y>_$1_d-UB+qG79@rXBj{8yLv}2*uwQ5dTgZg+!QEF{r zyiPc&-%+NiufKI!%GHhi%m~)NKVE!SdM{ktNUi!N)!tzj@|kLZLKWlaXIZl2S)ZY$ z#oghl>46VFXO}xx6O))F*c`RL=Q14q`6fawk{drKxIa*qI8#;-Qea|c(8G6Bta7;X zC-y;+_^`Ds^44a6N$2#-7b9;++1q3Yel}NLNYCebe-mRc`hmv@hT2Y7>DEw)-9sO0 z7kXrfmF6H8&B`inacJ#8%@9Ad%l4;I(A3%U5>{&UA?{2FrNI|CQ|X6PdcXBbD4NtD zjX{7#-`15pBD6+&Z+$%0-`=`dW7m+yR(7U0YoHpzQE)nwj(ojcCHtq=O94~FUZl6X z&NSrvT&nHmV~NePKv;uE;cF9{HQA@bvj$`;(XjlZc(0B>UomUj?LMRM-1lY}+)~5LDGAtgyK@XQe;f}0g1?$a3MNrviag;;n+m@+YpQ+=!^H1kqs1p8#wb+ed z_~&GO_FbfXc2ViodjaJ3{y$dp@;3Ro_I~UX4Gj&q9aiXZjjQc0E{Rm^NTpeHOkRy} zlF9kGppvN6r3}5msS5l!?lIl{T~=bQsB^V3pe<1$+TU(68~vtXh?0#AE>(vF^_jozn?L+Zcw5|P*0JzE458Ezt>Df6Q187NQp>d8BV^M!) z{}gl6vwBWGey40n>&Ir&4t26n!qS-TK6yOeUQFJDpBF0!rrjh)?Ko1MLJjP7+3)RVH3M-_D* z^>jGR$90}VzRaAUwpd=9X;OGCK15!yf4i&IFDJ!3q-;XfILMIiWb!+UV8#2giF~W% z2s2B%oac+3)mozzKLqd%xiQQZ`EPA@Vk^F=$uwchbxqTgG7}wfweBs)CZ1LaYJV6V z4VKK>i=Bs)cD*&*jC1G8RZZB=<0M7Yb@UUIOqrZx-J1o&n_Lf9-rU4Jupc-eLt9s< ztvW=R#3rNV%9g8AB(dJ%TI?BzR0a;dix$vN&KyP!!36Y>QAU-JTo9I?)htOB+DEXC_g|~Kh)-x|rvYM}Q z99`ECnsU{ybahq(iFmjiQp=%*w{>Sn~$I z=e2&?UgMMhF_QN7u+l(MjF+aYfh>DcQ!=VsY37WaH1Q zpB+src`wJiPlMJ-rKM!|OV6S{m9HfkAF+Lkj|<#x|;CTKp%;K_Fj1a^QQlbvtx zkI^+Plj@M3S@yAel$4n?xy0M1x8z3^n`)SO*+EC>cN8aPh(9RX{zoZwJMUl^~5Y$y9WivUBksB&C-7jo}b`0*~`K(4Z}=|d@Q9K8b|C2lpo_bhlWPl;A^^v z%K+SQugw*u$zFfJrEAJT_Xby44JWT{MhiF1Mq7t#>DEi;&0uVId{`-B>Y&TyQa0i2 zm^UVvz-%4n`(KO`v4RFAb3?EH8G3d0Ecq_=rO%ZvB2gS1jro-6a=wIGEHa$cV-}{N z)2?EYH!85BA1%3f5`aTnN2<~158ApohO6luozQ37rHykP$cLv+o6<2Ytc3G1$um7P zR0ewGOXI<(zN@_#QlNVs*Zc-zMbpgi1D9P?CMFv#WpPSOB6gN>sS&fI+W1K_gU*!(dmEeR_NR@N-p5=KBcy&?qy=SvawXV)nv_M_r@c{LCf2+ArecN(7jXm zv>G*Wo<+o*@Ay3wB1BN!z5L64r5oFtc13Hof@Y;fY9VTxhS9c;Hoq@q_gv@AH)0vS z8N;>67hXH32*;2|bZHNqegEE`DxtYUE9v`cLr~LHK$UcNaEUsp<(6QtO~Qn8)%eOk z0afnnXY{TKCcHMlffaR!#u0vo~_PIvmWLQd2BsJ$yzS z(iP?h4IeD{|6IBBkgD4)SH5PRj&=I=Nx_K8SD~bGhv;?HJ(!B;jfjn;WS@A+FqFls z9caZXLyOil!E9Lj(82!BJrw=7OvqToRf7zMU$=iLNbhgdd*{wbVhtOLQ*!>D@;<9@ zUo5va{n$8h!nHVf%SN`{n%!YW>bRLq@Tw-)J(PK)=b3G83PZQLIY3wDj}zO@SSi!B zE5kZT4bL*&HaqlT%7tR&m5WQH?TM*Etp`>2l1nKwQi*-a{k;t_84{U?-?qzac4cW* zP{$(zg@$roKOERi-xfx);aHwW_cR%p>ELPuJ;shj?NWSL><+U#AkWGdUbQiA|GLCF zj?@4R1HTY2+*&tF@G2vr4m~Zg$-k~@X|?P)I(W~f(QEhhoBNGLSEIg3e3jQg zqoJ#^a&$cw7N+JH@!;;f^-!_)eA)!yRt z_2c}NIIGmb9bLwON$+WxCxum=rC~Dq9>r>Q5h;Big>G`pJHA%{jYHt|@e7bVdQ1Oh=C6PeB6 zsb?C0N`K@MeO^IM-^%?Jh(Mak;L77oW2#FK$QXC?3Iy`(T{Rc#leC~lWMfTwDJ29l zlg*2T)TVs!wdMET?ecN*D4~oTzRpU)%6qrj8VSBu&6S!MrUa5ixlNI`&#%#MtHilg z#qin9tD@&K0?AAd6G$P=@!P62-w(F+-`8MT>IH3BV^(?xWWs8K&mMzK^5kZ z_x;RFBIvWXac3Ckd3En@S>II%q*($q8!Ok=#l>wjZ+TuEhd4?bo||T z{+NaJ!pJRe>yQ_#WifTx8hCjj2^ku&t_e}PC_)^K{0y`;-ey`@pfl+_lH$#*k>G7% zNcn{zh5(CDUn|_2CZk;AZa|+-Z`<6u0h$8>32^+|_sMv_1LUII=g!!1Q{iFa=FR>R zvEaU!y=~7qgp{FRjgb#v2i*XniIq$CfxRz3Gn}9uOe(gsBpG5@SSi2-8xJkXX1st~ z2CcfUZO9{)Lk*a~E99!MD{yp&6Y|P`{pZ2r0nXd2)?oNL^F5@D&9ruUh4(JA9|QQp zSR$u?E;`A{qN> zaJ=Hqe!`!9gBxH+Jj+1W3JCKIvyRal1F_a!Q5llLTfE$l{-`&%S0 z+yASSV<-(T&y{-3C1f{DmK4~`ho95dJE;!Ykd72lOR zTJj&pDMrUU_}7*QjF}7c1{u_yC6|FgWOsfi=Fjv=;VXu|^FJ`LLf-WLc)xClXizih z-*E&B3&T$tgQ9EnpEEu{OUr9Ao=UT5F|$&bbBd->$3q}n6kxSjjW=&7Yb>!K6E!wd za58SCupNIxYb3pQ;w-6Rcm#061EL$=)OewQW!QstO~j?*mC>qDv1X}m2!z2=_3pG9WXyAfOQ-f3s(wXqCwL;@)wmhA|yQVJmUkgCzZR#?UTAW9_evJ8+oOpSl?cNY%vi}JP}U4CK-Zu3Zp+gVrEFq z8^|1jhDVTy#3uYB7(c#34~|R+j?9uk5@^jD_W~IvjOkhH(RV3b+0Lc_wsjm$eQ+g9 z2!mY!r+EWT6P3OBjO^We7FKk}$Fwq|rGpFYua`eX#7c)nkcxPkP5=IjMK(oCvavTF z*i-@Jgf-c@eUgFGgM3Z0Mdj8vOzLc3kKho<$z{Mk9A4mSqLs@cD#|W?=gezO;gWfs z3HuK$&4r~!V+a@svvPZfb`8ik1MrqOFnOQw&eBBZUM^gR$R+ zHKiElcpvowd8O&<|BFp|+s-XlGPg7U5dYw>lurW#X8!TevN0*<`PXK76;NE)u~}4~ z&WzPHI>o^OMr&fa_g>(|HcPllNf!97Jw{s{)Dtnf&RAeKE&P0vf9yrSrrh@z&p@m| zrKl#)X?{5Bd=B-bY9!xFOf2P&=oP?3lsYqPxU~xDJeRx+4g^TU+FGUDVB zNcw|3*(N3jV&e9`;l&0}7#-0@d2C$**Tu+V6!aR}GCO0jrcaLl9mO$=X4LhGLLd(* z01dFsIKR+7kP`>t6VF^0jFa{c5Sy0%w-#PLKKN26rGXL>kPbq__Kfn1?*8U^LRY-W zZGh0AlmCrS+Pe8T-fnXc>K+}V3$&Ln(deugbz3(?XCz!CB$O?z*A6`gd>33YdJO_G zBTe56pa{xUc#gbS#JK;%MB-us;h>*X8TuyDs*DQ)sU@crn0W-C2|g5p5pCt2ov>{9 z6EHZDIIV1GhzoJimi%X}i$M%q#c8ziR$whU8Ryd4$n;Exn%0=6s&+t!FU3(ebAKpH znvy^=1VANX8+Nj$L}R;%sbjY!w(-jX$AFIjj4m(y>Vu|gpd!QdpSJ3t;F8fBG=Bq3 z5LPNlSN6JLZIWBA64?Z>KylrS43gmppv7hjJW>_KC)T+gTvxC;$Zi?o0(j#+pqPS^C3fIUieU4yu}%3?;Z_ z52f*pxSud6X~>u|G}g?ibp~hwZL2D6xyl6y-eC4BmS{SjxBzxJOask*SGKOYgU&{jTnrKQ}UmKs_ymiS`B}3llu#U3i zPZ=PyTK+~Vh|HsBv~^!M6D^TpG<4|=ss!#(F+)ZjgIQ6niPT%-c!LX&m3~0Bc9$;c zM><3vEQ(4It9jCWMR0DAZx6UdZ$EaB8nvMTr-Jmxg4zgsUTS1>zHA8atn+1_TVMe? zP>z^ab>iohlA$@d)cOk;3~~;c769>RdiAz8cgh)gEfVN3?MP{LedK?+)SuJusYpZ# z;P7a$e{QJ1a}9~&xA2IUU2{`L7-EUH@M&J*-QoZx-1dyKdj%BTW_1un7~`{zoR#Ic z8?5t5k9&*--A^E=YpHiw1>Aw^@?Qu#K5BbzYYlY4J%FLquGU=g;D}^F(=jbj?5~3; z=`81xP-q)nfIOt@wj{eUSAgrAO~10AUuGN#)Y(3Jx?@k2%w&^m5r_g5=$+HEnlF?~ zoxr2LSEg@3$hW`ew}^I(V5Xeu9^*H?v|Np#~z|yMOY1R_uzVVH@ILA1vpMi3l0P#KRNsy>?U3q>R@eSdaYXgP59} zEVn%q#^ElHU_=N5gKsB~CTp5U)OtkLFAe0 z^_2>|@qFpdt|mMXa4666F3SxT{VD&`!8w%HcO(|dedTa(`BRD2 z(dw6sYjWw!sZiR}y|&w>CI{Dn7K(56q70C_Uzb+VdaA{enicfFS^*DCyq-ZpSa217 zIbG`Bu~Pitt^6q=Xkbi|8B`&$v^jl}?pj4ho^k7~A zWgDYa+>_|9J}ZfB2DtOdmkg3mPmIuVFTLuIT0N~M`9TwK2XOWipD6`Xpt3||-gD-+ z?(zWswv{`t`vxSVJAvgESt32NZQs_QzYn)+`+3&mU@p}QrHR>Vl!gL1=auxyV_LL9 zslz+$`uGA&aM!Z`)x3o|x_g;h#f%I-)3nS$b@UFtY~Td~XQsgD8>M$*0(dX(WFQ%i zI{9FE<1I9Y_vDS;e_IH_V3*7NsZBTYr7uV87in&8^rh6h69zf!j7w=l2mTCR;)0T^ z5NI||cB}mxYS;g8WLSE3)s-dxLHRy3MP&b?GA}H^#)}IY?cK`9wqSp`<|EV_1{Dl? zs4)YX%ltO1qfnQrNu`gs!}(9v^U^x=KSgyI)6pr$cvzrF=>W-Ce7z(vW23={d2Vis z3+Q$ICib|gQ5gywcIaC}zqi?vqaI5+l{!5M4>T#Sfwc|1M;y`yCg&_Ck!Ja{T@&^@ zYLVAOy(&sGG88!ezkneWwbuYcodZ!*AZ5I}KJIH=HKuIy-A>=&wen$IQ(vylw~D21`C5+- zb1;z{L`N=H)gNeAP~w9fCgntvo{0<;P`#H^g6<88DBpu`Oy08lb^|vq)bL74%Gfi-VP|l`(T3{s;CNXu zul!iM{xiUC2vCw)5;aP9*)vyOb$B4AdSo}8HvTr2Eww|Hm+*xpA0P4a=k?Col74BW z9cusbo0-kF|4410%SA|_FiJ_1Kqanf(^Vwupn^zvu>|RQ#b@kpGBKn%s?Gu5Jx;B~ zYr$eS?q`Ov+T}(D6M9*COe@ZCr~EHI2`=3-#tjlw>Fr?l1WK+jayQ4=0Qnds=?+a9rNpvsZK7QJ~VE`1Qs|yu!fUTzI&jTD?ka z_ZMGY8>!L*E%bViuuk7c(72mTSZ>ZorUb+6zxS!gZO=TDqx(}a%YBI8x2SD2i~wJ z(PNs<>(WvWfa+*Y2UU;#pO^bR@FtgBeg%`E+dYw>y-(o=we|=e{9w9Cx*X9ry-+P{ zPCF@Qq}Lg}#@aspGz)5wJ{eV2Y0{L|WC35@PC5&{?ejPqu~xo{+H>ryZ7(Am;B?gZ z@czoBPdMDww^%zVlQG=H5?58FVv~Q7Vo~==;TghNzt8T8j~jG3ycotzmml0eC$n)1 zCJE=FHIu*9MG8q~Jk-oz|C-O1@acX&+V5Y$GcA(=+A}sk$=X6yD-g^EzrV%c_085X zh&<=oC>JHDv{pS-tWw4;3Q0LYl=5P>uD64%+oA_q$G-3}YM3aG&rX-e{HkI5A`|#8 z)+=j7dTag+igo1C(uN`OXoGB{QQ@qqQP(QLj1E=vc?Sr&7*OqJ95gPIzt)dDPB+*s zQy=qiS?}0vXJ){)#1P*)HeBkMOU^2QL|@F6^^~uWs5eG;0%Gw4x2NT`QrJF%dgS zU$s6T+KmVY()lfP8VgQ<*|HCRba|E*h~nKnJtcZ}r`V5$AQNSXg;)W8c5K6MdV&Q7 zA#bGr>FIvuz~8Bn;K5xy%%;^iIi{E%)$nXEO4n za(j;wkoFEhO?@I_Vt4RjVxR`4wL55Po)IS%LG++Ao>vDW8be#E%lgB9ryd<2T+wI% zG~oy!N^ge?SKTBy1Hq^?rmyV`#w=g{efN)$zxSv0SzFOOU{n~$?%KSRa2~?=#C%w# zqV7Q6TA)LT8v97c-(lP`kif$2i*6Wf=_B`P>8z6mIOs**5Nqdv-tkX1#w^Ht_ytG+ z6HuSMId9z>Dr=2e+ixmEAMu2gnM(K~NF0eTj{rTbjqVV#YcM_kW6}CcwK_CGrZ65T zU6_HmEQAyS*?eM2*88<(zQV_5NGIp=asI+>NjVR#x8wvGNuu|f;XtiD?LR-6b~x<_ zZcX4`=K*T9!PP>6i<(jnB`E^VTm>4-YR-65%Dbup!>l6(3aQpomh236RckHfMw-l4 zxp^R5=>T=EPlV%5J%D45k3Q2IviF}PBq_%ydlZ0ec)&L0Ass@}c(bD_E#AT@!ER^x zn5O3`Qc*-wAN;+1piGa1ftSs?aW8G$xvjD% ztqqT=?YX$${nXivj?Dz;IJp$W&@3Ts_>^kT5I;%HQ&E#Kv7+L?IZ-~nJD$nFd^7Ke zysGn&#wkdqGtlfcqhW>;_KT?W-ley0%4Txd!}4j9VD%OQWj)|m6gctL{VG$j#H>_` z9(zsmkCL0bb~s1bQAH97PwRI?2RHZ_CG1gw4hg);9RS;oPh~i=I+Ft9DqAFdQGCKb znG27Te}qS9_h)FM=fMfCzXvDK8(I63qm?pijonNeMx_6qYf-WLd zUaN#U0xN8&4m~v;n#?DyX{9VuT2`Zn6h%QWx9$Ai{OsXl={E>wK>_J06OknD*7 literal 0 HcmV?d00001 diff --git a/lecture_12/det_L.png b/lecture_12/det_L.png new file mode 100644 index 0000000000000000000000000000000000000000..aaac5a216b9481a0bad07f7450d9afd6c3bc1402 GIT binary patch literal 40288 zcmeFZRaD#2^XMC_MT->)?oyl?3vkn&&+4O`SMX&76+3I6953<$jeEq0RSjq005~E{Tbq& z7G7n2#2-{wDR~Wa#PCBmk3zf#y1mzSQ+NFA=4s+$0kCv%w71}JHFL4BaB#J9bUQ=o z6bArk0P@n38eSR4tG-Tb3;xWvTqm}}JF3OfJ=eWYY7Y_F5Bb8XHZ zA}w_0V%p^Lu=CFz7+N0hd=~0^ihBdt& zLG~=ia1y%))Dhvw?9y7TMt!(buzWfgNCKe0`2~;*kod%IkoflIaAyDNXi$hy3LS~= zKLe%BdKQD`-#iBdl4QpJH-HiUKh5?`QNefb7nzv2d1z@9)MUV9IiOPA1*Q#^nu;l) zwqc8a13c}k)LXSlusu&aj~u>%8@p?}8M)$q)Ne^k9?Wl=v=p}e*I8`+C0Q4YBlZ#n zdB_QMaYBMGC|}3oGR70dhkd~SK3X|5$PaNXbMx>7f5CVzOmtHb)BPI{hjLWRfQkJ~ z+D)F6+D%vV{6oo8TjEfTfuN4^ppya2Q#jS$HC$1W=X*Z}pesB`k<3ol+ASKRj9ms# zCx&kB@y9#Md&j2%xejOD&onT#&%U|+$k1Pozv%26B&d4 zNj#iVo$saJFbq5ge?LiJ!gG`R!;v>FIj#T^f z`Se6a@BjO4>{>DF;iy_&NTTkPf(rBo$f6Ae@hskbGtBi*5^{7psQPg;S&CKy@nclf zhD7#FXGqbh$e&zMsvK35=EBjiU2qg<WsbdW7zvMI$d3Lq`amjG~$r_$JDr>#U++Fwu+gyPqfIv^tyUf+ig=xQeD z{YnXVfoEiUQzZD;|E6}iGnQ=a175IU5pIae9(<-#Vn4HqWy0|ZDwLpFgRlM9=S+G{4JCyr-!Gm80F1Up7d4ukWIiSdj9Cp zVDI@--NjCH@mY6W`d!7#$j-0CgP6*l*2Oe>V1QhR#2U<1ZFiRJD>Gn2nqfnd+wM7l zqJJS_UJte9`*3B(dr^X*(yt_hgbD1Nx4ly>u1lqRu3X()n8rMrvdti~!(ytrj&QY- zW~C8>lp7cRxc;{WtLX_Q7pQn&>H{KI&Rafml)fkFB?LQ%pgz zDO=}O5cCEc!IU>r%K_|(GbERnSDTdg$(j*!j(mIiXWPNSF{%o3vhNC^9t@e0YTq1; zR?CVN_{-`md8O=yJJn|M?I%OMCeM1VlSsrekAhEIvo5$7`5P)-XH}l~vpbwwt}q&N!`@7^V5CYdk24oRmV~4BquIQ>31$Aus5K?Phzm+WCIb?Zflz);;X^t zDo9%9YYNM~{=8JfvlzX!WqXJyeFG-28fxDenB?1jNC8#4ah4g=g9Og+=o2@q-`NvP zSX*veg2_#d&}rj5`|9N3V0YSu1PK`V8kEOZ;D@rDNxjdblA*nxn9$2~Lk;(p*DeHh+gvpbK4LsnprI{Wc;)7f^&Vj6Gb>Ruj1XMC{uM4c7dPK7}m zwnzeTy^h-*5bxwrrXH>yD)SLJ#_icLBp%l>_A)54C2xB@aSh4Jz}K^1rWYGzl$NlN z+HXE8ZL6CqUOBS%^tHCUAA6b^%&Cke*Oe%^5j_|$?ESDg|G4Mij2Ee=USIQifv((r zKhUG`u@Zjy*NmxmylnxB<1fM6!2yFTgF@A7KTpy#GN&4FH_J;QgWsENV9Q={HrESm z-kZefSG&FEZ3n;g((HeKT{`)cT0EH*;?Q<-{clyY8T+IgaY|;V)ySsoLOb&8N?qt3q=u z6b|DWSk+4+T>PG{IaNk@&0rj!{faldpLtqc1*`lU8oBsOaNv1qx@!dA;qRRNnz%4U z$W7ZSl;;2 zH>-IORodxBeWqlKlkkasM;U(S7SQ{ut@gsy+gpd-(JEGH@I@)jJR6Dl*h~)b^Hb1x zu|mtLY5Ont)OpH#8GD*fI96DutHmdit#fq7P^rRgp^2#Qk*>j=m#*X@bXtofu<)2g z!*ZNw#+mr5gKdL!uZ`FmnfA-HSC@&t>&qNFl!Jsk%?1}%x(`cax3qUOZ7I9+JSFW; zcce`MjdnZ)`lSq--2}iH@bO~ZLW?Z?QV39Wah)W5tU)`g{OH#YcoML%Xw-I$cF`M_i57)llj0)799oS> zc0@>XXo7pqr)M7XxOE@aGzY(z;%L{m3A)S8VWE~IKRr&bs_(C!zFO4Ll6M`QD~(Cg zC413m8=K}@KhAQA9ezLH-FbDE4zkk{rcgQYYiI$`^li?&oj@%?osAlvaU1$X&Fa7= zF8)GWu++Qfg^g4vj+l=1WA+VAQ0*f3>pdY=d*K(2{YtxWnf^cD!-a{z?`448NPBWJ#E)$t+>h^lZh6WGmid|1k(|Wb)mDP30QtAZdvpNTJ7pxREnD_r$x*hA{=-Q{fk&$SmY zfQBScs(tH5f7PNCoC`bqgy{w6Lw3UZN$}&JY1MC%g_#~VW&hk8R(0>V{cP>8dqXaM z8No}jy~vOJu5RXqsy7^{*!~{g{TX*|zBcC60mQwq@__p}@e%cMhelilvIdEm?3s>#js#u9J?hVC`caV0Gw_ zwQiZTp&M zBi$0R6A~cq+)FS-y5n%%cR2i9_vO?98Jz)#RVhu@P|4F97(SHs_2oQ0+ENq$ZUi47 zFr6=fVFB~22xM{X3%zmZb^GO#bqWPK+ML*y&%@X-2HEtoiorp|IIevKD}@EyiAmsK zex=fZgy;R}C=GVg>YTWvTQhWm<-XeRQb(Cm@^%d1lZ0A_*O1l`|aM9 zgsNk0GNLtCIYW&dqx%oon;!+5B@=PwqC5C7Ag1f{1cuDul5$<>Mb@oEhI7+e*Rj&(; z5I~Wi$ceP;MzH`eo{rBhf6RS>D#iq0mg~Rxm@N8=#IFo#0Z>_a<-_Rr>xNj5t&n81 zdL@1`VAEOD)gM=u+hp1%eAOXx)#20g6tjc2JiR~f@v1c+C!^*1avifv%<*GOJ)xV} zU1}rrS&k2^5WkOH%O|vCwgQwLR0MXL4AHIRX&1UC$WAq$I4WY-Xnv=JH`^5uyK~tI z-L(SM`qU$}bG6rtUMeWe^J zjLr=US?(_^sB;6~Us&A2OV&J=ymBebVocZfn`6aR|9T_HXp#%W*1Pik7_%$b(uq=GZ4wt2Di>_-9A0em!+9}*ic+i+XQK)!xWi{^IzV ztA2YbM!UVS#IA)Xc-@6>C7|rduf|KNYMab~A}`?;YgL|U6H?a>mi6xRv%tj{evi+l zr{0VNU~L@|0+_s{;vzgukMGYV$>ckA0|R_+Qd;9teP2 zU}Zqf^Au(~Q1P3sV)`O*)RD%|WHH*S-#^+>)s~X4#WS#w25GRqVyAzAS+Zii|4KUw z4q)i5yifV6=(UFm$k0|9z_YPh99U?U_Y?|tx&>wcxR*|#tJ#)PQ4GHR#JMq-x)ieQ ze!Dbr^<|O;QM>7qr>!dekcWiP477jYGIJe4%}NxLueV3`FmRv!tK^fId23TdsJ3|1C{yfl-RF zv(?Rsf;DBO%`A3}4(Tqb*&7&@GP&*8XT5*h({$lt)VxWuaOdq?-*0AIM4`fw35CUk zQ;UA*dPp=NZT3<_j{4^tWCyRG@lqh!7kmpv&5=PvHBkRprc`F^(LLwFotxqA?2S61 z*fJ^?@y-j19yAQn<_%v=#^}P&#FqJ`zM`XS##qcBQ}CUVqV%<7 z(wjdP487uBqExp%!^B*Nqvz7|+@-PPe~L{>V96WkMe%K$G{IgSR|3hYTKZS>^cWS{ z*Aokd$it@T@w*EfwK~StcU7qi(`04&eDh4@Z>g%AJQN{73Ma@^p&BNSJ@TvC!F+@I zll`X4R1EmOa-cU*YrkF}rFcd4Bt@z%Z9|OFCaiA{n6p(oJvfqFBB? ziaG0l*9k~}lIz>%Gw>C7?#gnOBmgXVtLw4MkNS`VP2)^Go~yz>b_{lnhy7S#~Y zg+ztLp=mj4|52HC%b7;-m**edL>jHNWeEk^sjX>E9;)uG*yX2q**S9QmeR?@Y`c$c zy2|hIeALGA%iJU}x5%Oe7A^Ch%R2-Ub)nMTLn<;CEPTtu)H&>>=I=00tI0IHkisKI)>_zlZmLRSw( z(O|*SrgfZ5#GnlB+N7g%HndbHvs67)E?jyT?5@l1Xd%6M{*mI8r0;YuB(0=uS5T)> z(BBAVcP6ObnNX!Q=4c06T{Wn#t>@e;EUR}zM!u$+k2*57?^$k9Ql9b|zc8y-*J)a4 zp@Du=fQqalGWW`|@i*<99xg(O!!LdG){AGzj0Ril`Gm?Z+-+T`Kx2N4{+c}N4jg3z z83g1h{Tbu#7CE8Y;1RNDyfp_B`x7_O@HwciCb!C$@NomxMTwV@kubW(TH3vgf@L1} zc7QcpxB!poCPRCDB1)f=*`slxKVxCViHdvybw($?uX>1M;aW(joxOn<&DqO~<@zBm^dxjxhd-V%s~t- zFP|zc|Fl@c@wx(6A_+KI%W*; zjwTAuW&6X)c zwxeysPb3Mr8Nul;=Zuz!U^S1uL+iNwS+ZuFuDg>kG|`8_)OTX-w_paA$d+4C06TB# zS{&@P5Q+4~A=T$!LWd0=Lm-{%xz7-vIK`-dk+3z_1r=}W-l6P^G7p&#L8lLAWl#JL z8*puA%Q^}8zWQo^s|QvG_1WwI)*f&wV9ZL1I)I-Z#zA`z)q-)T45C%@%>8s|1YOWCGOdImmb=i)6AZmH zIJ(CVQn_oIJh1_s(#bAQOY>XJX%-89Zi$nKdWTcn+Evi^U5=e-jIf9r;}q0M1+wrH zi?OEiWw(nU>*+6t;T$`E5asLfo)eGWlaC)M((9w{KQ!WO?(h>A*sSx3P@sHg(jTs* zEfU+e_z`Vde&_A56q$06+_K&-i>H6|U?sy-{p`eqE3BuSiqcxrg_dCU^HfViNFQMS zx)#-Rh{U5xSO9H5ulV|TEz#+rx1G6y9GA!Uj#uPTU+6p*_BYBkQ3;vA>S^mkG+9wy zQ`fCNM~P^UR>Uxo(ll_5S&gRGMn>k~fCK&#krAkdrkhCqXYx{?RPUownwzp&fEh{t zu|oRbO=LG>ZJOnTYb~r-;~q-m_B2WHw7>rNBf$srJCzQ^JmJaTR1XTkJSFMB$(1+#=$!fxA|uF8w%dVYV+IqK_4#*@DI*Rt zGbwah88A9s4i9f_24RueoE~X5D_?wc&DXwi?Raq|DUU{D zEvb6mhWh@bD&rSR)e4Rw4`%04t=I9gWN#&-j_?u4KknPh9YQvAAG?J5Ygeh7u3cRE zAL8psXXhakrpRm{d}-obxx?{VHG*neW<?&?IAxc-M)ZVzgvf67S9g)}5 zC%$hjsLP1kY`H#jV~6Zjl!ch`f(QXYSV#*xC@r)Hg;}KUg@DqX9zgvazm}+z8M(=C zA+uX_6`6n_pn9nY3k6ox_B#f+OoJ+8Unu_y?2v0?*w$CDTb*^F>T)R8>oSpu;cEVw9so4sp`e5{JIP)Kn<$h3_MJg!-l#*2EbQr`gaqiZ-OSpi`R7cgeUkI$1_Cj8L4}=?Wm-_Z>^@Md{)sA7v3Uwikgh>*q9~O3HdOlb z#@CO;xN6KrD!0o;K-=PFeQT-aHWVFy86I_Zrj>=XV=7a!xBxEZ0sb zwo{^XY~!(qw<1PoZUhKYHKZdNpp67TBzp~B*X5+Le*gfc%}mrFvA!7&2d$S$LpIgL zY#ZE{oXGf7i)soiJ=nG01Z#45<2e)c`08@zP@dYDmI(0p> zol0Y9zXpLXz!-<7EH=5~e}RSpA*c8D(h^hh0`Oj%27KsK)8DIjtAD@l+aOWh&l(DcfoQv-zSZlC){zx@=|Ks3VLebDA^aM9jtU zibA{RWbFerU^vpNI>x0rOk;6=>x_WiJ@~+zOy9M;>c4scax^gLDJ}cjh>)$|W-go{ z{oUGTG!ryb?Hz*8v&d36qusEIn2770_w>9(@?OR!lFd0URFz;iI$$ zY~-$obb8C!5%HSVzw7wEa+LGShPj;zQZ@SXKMd-ycG3~ltG+Hm+mamUX%O^pG^rel6u*Sl{$Z>VT<_^57_FI#>RUR6n~n}?u;Dz;Z+Z#WuY_5^)D7u_0d32g#jPo74@!N4oh z53fxNe;fBr#H1Ds3ndmm=^1?Y;5sN;m$@bcXG}?8m$lC?RUVEguDVyN-@~i}edSap z_dgB(cdOr@uthG(;+9a^?DN(_PnK%#eWaj1 z1@$11RQXGQQuN)J^S*!jim8XY;_+t}y4qGoP0O;m&hM6p&zA4Te2@OTQ|$bU&OCS# z^ebxh#GOaWenrU?I@{GAZ${Y55;;iMsC(qb)Q)B9%FK)jLnJ1xti;f`^>#z6+r739qSdy+<|5-goim z-(}FixuuQYsh}r!7{Ve8ke{j5dvBI3`=Il2KL#Nm>?J{x$rW|is!tPk$4c+ZqLDviC z)v8*O`w2&CS-TaLJ}hC2>lr0zH`l=G7BGG|++TIb4s^BDg7wn?^>;guX`361$39d2 zLk%c(foL-LH?}au;O=oo!82$gG{f{K=51t z;iIjQo$>-%(oa-y=m@C6lV-WpQTxMMEHROg){z?$f~xVzmA=r{#gV=j>TkzriU>nP zCaQ}XOX)mi+QqaaEg>!kttylUTWgn%ml+CRo#RV&;{z9nVl*S^Dhau+K^^CU#p&kf z6HaH>fh+aS*i&ZV&k8UXQw`r$_0D-)Lnucf_;Tj)Ix(~MsAp`mTD2U29;0Y16)=Uqn-KACb5FmfDBbzfX5JjM@`-^9&C9Z#0R}0>?wMMm5vnjzsDw)N-GJrkb2q!y zU#<`NJD3&7fMe}14TAiOc={MU*Z^7iylAN7=rChnJfJH&zy2f0&(*|vxbzX`Q+B-; zsU{?YK|FfMDro*hFu%9YEg*pVB&duf^v6f!OS2VeoO4kl%5=p_Tt&=x?)GV>_=Wim zQ~(7netA1vu0XlZkx?i6BlqmA{=2%v{5F?YCHcd#P6p2o#i{M(oxLo+L z{PR1nWiNd={yb=&F_8kP2>_6l(^_{gg?tmq;|MklRw)Jf{&u^fG-J&AwKiGPb7sB% z_DZ)ia!KXV9DDi5@WSPMx32SgA?gy_1!5Ubj!j1HZmr>7ybr%F&d~2pk_B*oXq!Pw<%ART`SlZD%lQv{MJXid)@O0#Il~rmqGT5EfRSkDKVnPPnCg6NuRV(z_f=cl zNN0FIU(oAQR%tM~|4P?vzj6eaOVBNAU+VVu99!h&F6*Y8IvM=9%!-erpw$>CU&tM9 zaeIlcVrAQT*Bh#brS3tS4eliWGIGcEzu|gBKTThiqxEDqc>nT+58%PRti^P+&rfN- zXv?^sc_h<W;PH4I-Uj!lFjev~-rZJEs5BuGXQEQ2l zO4X}@1N$3?#ntH|=vSUW9hr{N>gI7RouitlhsE*BtU=ua)%vy%6Q<0~MWtX0W|CJ2 z?Eh!VM1CKvmaQR-Ax~8bS?!$!Z35TLX7s3hI(xKWO{jW;U$#!4?X_v90Wyvade!6o zk+NWY@TMbv@`uFQ)GT1RYQ`i~Tk>lpoT4Wx#u1qG>f3NiO@m6iHKn~TJFMrtSe1ER zZCMOrhdoRPIH%hx?Yvr^ygL}fFA+`kD!-4i=K=QO7-z@NmoO|MbMh^U|824xIc&N= z*vX^DQQ4ONpYWML8v>to9c_AD6YiI{^A}`59Rp)a1qK{oe&mxav+}FW$&&|I4D$A! z+1Yt9OF#}L{MMh3GtG6V>u989`We}^$!~w%pjUtaRg

p45X@ ze~Fa)mSqbYlcCTLgJ^+AW=S-M?6`9>Q_XQJo3t-P9x3P#9qnW+RM4k1@JCFLTJ?^! zGt(nxumQeads8ag?U_X8g9SnJz^S{kIXw$MXnFTQeGF^Ll%zp+5m)*B(fZpVap?!> zIV0tVpV(+iR%-tGljJh*#=bmG%Id|vy-KvWQe7udQ+40r{UvM5SHlLlGVI1-sOg8A z*?%^wI#jN~R*~~>x}^CoU7aR#j}90+zq1SdFspq-xL?}NpYv~fX*y!BT{rXXxfk;l z|BP|ZVX?61_=rJl-8NCEHeypLr_?jE3BI}5=|KhO?+|1PApw}@lX${JQ)%@NQxPy_ z!As$=gDMti{>1yEjWq7JI6shIaaXn5ZWX3s;5Qioy?H4g!R~pVxJ+I9KhYqEtDCONJTMCN)|BmT{I{^g$)ny+7cvAcARw*|7%W>tz39Q}HR`JX)$ zjjgg+xz?`mK9SP`|3gXqk$3N7fxP51FL7mO8f}np;z$8r`wQ&HDc#s($z2SH>8sek zAO<5d;Yj0$g^C+^p?VX&Z6TG+0ird-{yl$=gEE)tS3ZtzFj8gW*ug_0}92^?RTH!6|u%H3qCo* z$tjjdf{kK@s~Z}g@$FsGZ8?g!`ovd@G`uCXS@b4SRAhs0SD*yeY0?Yfofo0BwQFEQ zDWs^vbWcY2Lf0_?I(?=(S1&@v01I!E_$uIi-gcF-EQRp8PMLXfv!k86Hx=%O>;x3u zxo@@#m2KXe+SyG6w8e!8Ud(Ym;jBH^(?@(&FGH;Q2Q>v+-P%=Kcq zQBUVfDl;v+dRaS1(fo-&CVjc}B`rv62rSky0kpe#OvFKYVhAGC_mw#zV)pMKR)k!B z%lv)J9D~sE(L&5WMZ@z8UB!XA%#-=5@yu7>Y(aq-GfV)%uH2vX#AdG9q&S=S_D-h; z*cpZc5zid0*g}Xk!`o|ujxSplhj*o!)QdQrbPc5E5xs-U?7qv+Q@i)?t=dfk%=C^= zPou%*?mQ9}<(y4eZ@bp&f}BZU;wx@iB&!bkz4zMY#5NFt=Ka2V51Aboq3YIl&b_w1 z2!CI4;_nhK_0~q#$9h_;SUp_PREJKYPh!1!_;kK~ZtDLGSLmW211UpEIvsA{aCb{S zuJncN@|{Cviz%<8kRqeh#!557o^uzLzib9lYMqv0NUZlgL{L=pCG5L>wXnKkZmY@9 zU9&_z_xWiDF!87!P*qU$Wh4x(y0!Tu8*Y+2XqiMay!HpRx~Yk)*2`<${>{yfp%c3( zp~BSos_46xxy1O!_8fO_heC&Hv!js3VIt|DzYYsq!^dUy9Buax%X}bJf_FNIb~HPK z)%rrJA3&IY^RMgNdbIWW2kUPY;?TxTxHL0(B7UvKEfwj~7QC$B?_O=j zbT#!iIe0x;ibxI;J7wZyg;QHq=khy7zz3C7n25xrZLVQpCxh@vB<0ak)^4oT_N30Y zo`)-3FeR%U_&2-O8*47_fo9;Rhf^hS7etV_MTcm6=2Qp$u=Fjdv&6afB*}<{R6bQJ zgLHgBaF6D*IHK()8vcSY`x~)C4^6C&M(^_2FYaPRr~XVc9bWZ3lhl5%pPS zgi@qNFT(LmjqE0uAcgo$oBCFKO(HKvuufZ$bU<0d*43(3E8CCrcD+HBbB`+@fQ)14e)MwCd78z^?j3EePx#t`wJ zn{rDz<+T7?gDzEWM;){>(6SE4;F<51m)6*idPD(78j_}d#^aG5*W<&{#q$Bwz_b4- zV?gs}#^RULeVXN~!I>Kd75UvUsvd4bk1 zSy9RG-`EINWj(KV9Y)dw>)2mLGRKrCc-0j{AEM!bg*BtBq)BKWu_^+ZJ3&@s;}pXn zGcY8rST}p!LV+Cg-yzQectKvUaKE}*Puin@!8D84kIg!nmpm=YBUd*Wkal7?#_mX~ zr9?AZcaY48_pYNVbgr3Iuv7%axS>Z(EIw8V7pbt1d_Cn{vj2o}j0K>I*h^p2Xna4JhQ2-!EBSrGd|#?~Lb_TBR8>Y)oURHA z)BSj>lrt4`PjX>w3k3R!FBQIjV1JXLhyY?UY3qycSzCD<6ce>YX}!h)N)BNUX8fax z%7{mIc%ahyZVLR^5P1A1;6F6UAax*mASuMIF9Jp_24LDxWUTlDPlil%uvJzQ-QMLGPtj3a;&JqVy)K>jTSVO)cs5c*==8Yzk5r*- z%ruC8UeLt*?Q5Jg%2Gh6jS)ztLWKYoGq(5Z`1E8imk4FN6oTtsqGdIaONdJ3#fO;k zgVc(nq~CEj`)@xQ?nNFV?3p!(x(7dL?JzatP9{ctO>w42U3cw$p+ z8eNB~Yg@M7Xo-Y(sG@3}mM&*%d%GTmMo3ETCDx)&)?i(0fXBeHog3@33~6a|QVimB z{=w}$^4cR{9?*#Ze=2PQ{139x(eYycBLE2Mm1sixmj(PEX9I!aPED_A<2wk{n??mJ^ut! z4Q0z!ep{=?8BKr3ou~||?x2oT~l*I$lk}OBYV~$|b zwECTUk($4VJ$~1fD#e}{A+dGj6!32?2Q|P_1VSoE&|*h#BI`|c;s4TR`i^FibptiK z$WwSX^R%Hj{-S_^+Ao!TdWn}|osJmp!uR2eH0IJ*WI0~D3P1>wtbs71iE~TN90cu? z{ffqE1VA#{RW5IV*BwWyOwfTjeqz6^Y1+VjHs$tC6JkVmrv}7i(59feMF|ir5t*H4 zi^TIVPn5Ix$uy2+#Dbpn9?ENQ1v}cm1-uOzw?r|u&KniK1-k#UV&dMoB4Xq!OZS5& z#bfu0oOaw?b`x zH=(y|lP<05rFPmQZgRj{clw0d67@)0mp*ufyFncGYi z(#$z+(e>MTP4}-p=xq39Bny2Cu|I}Z-pkvV1B2A0faCFN{A$tOFHM5Y@J4gx2p9l0 zTrt^4Zi4x1I;e<`H^MWa2IR+>@`p>)1zX7vm^RI{q(GHgi|k|}S!xcVK5r$P%j()t zR+fN=yc@T(f}c#!|MfRWe=@uDDo0Jn&epeU$z|@{ObAvZTXI>g9QEEA4YDg;-DS7j zj_M~ET5x>JN~ed+0LnG%@`*kU`hYz09<8PyS#dRu{md}QX9m;(K=rSN_U z!a>lH;`8G0;e%XFm>w6RyOa6c@6JQ?_6WDz*|!vKQ`@b;c`NQ`xms=n^c>})gRj(j zJ@)H08FV1$Ye?TOk(z#SEUukc3lMP-e`24W+;zV208W>uv+QQ|&m0mstll{LJ#>gT z=L?HCP;s^Sp?R*oSYa=~e;RRRF>u~^-K}u%7&-ojcX~2E!T&e$X>#SpXI4<2M@AOL zopJLtZTs&2@8b&r=f=V3gW%OX+mC~V-giQx=>b6gPU;(;Q-*(bA14(v#2Vrx*)bP5(k+MXA{y)_8u5~0h#yy~8$fY2>4GSu)4k-(d^BvwF7UjKrOWELIBoqm-{htZ!$X|N zu_1PD7|y8GFFgzrJW&+oD#~aXBdcbAQ%+u#h4oF7{mDcphR6J;0j213%-SI;0MUI) zoob5wg^pxRkZa^naN3EsXy1eP-}Pu+Er z9)A7RNNMHvS;rk_$K4iB$K9&d?{41!RL_;`&t3++YgciNal+n+i2OUARFo=nNR(Cf zS`%7Z@!^l0`W$UcQ=t#Ue5#ewNAS!CI0Nu7RE%$ zQ6s$GE#S*S@Rt_Jg(-pHPy@cA6%{0Aiw)S){JQ@)TraEV67ZC)UQeUDil4(}sKvNz zR~NV8o??LXrRY}2z(yZ*ytJ;cpD^Z}i_H`*qrt$=NBf6W0VAP{+Q#+k&!X2N9*bwq z<)h_+xLSc{CShhmEAal(+vQ%*n{V25IaKGrb?Jm9UP=XuVjU!3C_ zp%^M0zThTrONIuL`}>?yKN3&Ed)H0jPo-$>S$=2C=SHjB{aiW{hVA4E(j-Q&^af^H z*Ut_`5IP;CejN6!ep%!GumVzf((^k3cY-<>Z!sS9CLK5W#i!+^^PVGm`p8tCyl`$E z2w0e&5t?Tb2I?#h7!fxh6`g$%zdg+wEL?+4Znnbc6Ds8Bl_~LoyQ6`>zgC=ywZr@$ z<_p*6oLzo;iq{2KiajW&DOW&0P~oc@Arh9U+uI2vq;Lr|ObqwwEZW=fRx0j?-@5G` z7bBj(r61)*69WkV=RZZx-W@OpQU>4nV@fc=7o*f=r9=Nr-x&1@7>Ulq;TjDwM)1Y> zMtJKX_-wY_o-Rky_?NtN?$y>pkfQ|8?Aux?3V*D<#t!=;*zur%VE|I+#nt&`w1K={MMj)59`#*E)tk`*@muemRT!GQCnc(~x{ZK8nZZ68L*%?;2G_8g$>a!VCN z{oqf0cnJcmMck}DC3zLfTjqR;YI*bTc16Vpn{BxpZ;eC2biVb_TR9UhTIl0|Rf@+s*==uM!_10lgeNo%6fOLtplr%_pgCM1pG)PNHcMc)l zAcAyBN=tWlBO%?LLo>iI^BsOZ?|VJh_kI8BoU_+nweNMWwGToO;r&QJC`=Vy33Of> zJvaOiBTRqaHi9Zz>%tr~{x7h#PvPiPS)g%ZR7YCeIkc)h-nN|bZWw?)kI>ZLN$2BQet(@?6EQanx9~H{jJYY8VN&N2WIT*+zJ)j1 z^rDltFs27nY$&ZC#38oet=C=rQa2OqlCu>N20Xu#o~pl+(H{wZ)#Kky zwi%P72sn<8rg66Ye(Am&)`D6JG*aq{_IVFX(-OCUKuc)%RzODn=LxEos+r zAa^z&_a1cuxq4*+X-LH|vLzk6mu-IZuWHffvQ#AtTfa@G)@Jw{*j2kk-|3zQ!n4Yb zeo}j2rF~l=D9*){BjvwO8>U&P4aK$Sj{HiO6O~R^7-^8T9C#Y0*)BTmwJ$ zFAAJp$z}H+4Ie=^#;9Ti-2ef2Pl3=huz;V(eU*5a+%Xj1{z0?)e6`AEF9H1cT>Q>Z z0=BmHD6+iVqWk!$P@H@ge2orWUy|rN!nlkZWcsk{P$JQA)4_AN{Q~d6`Du1Kmm0Jc z)|tMFsP9YCh)3pT-5BXYOpTLL!V~w+Gcy zB79E8a3EdDfl~5A1bdR+!&;aB-CBFFHq82RW^MI8;Ni>^ehuD~leied%YQm(R}bi# z6%GBdJs+P#E+0r8|9V9ooa8BY>v$iV!f_n%9Qus>?<+<8*a<&u9QJ6R_v5au8>r-p zw_PNw7=x3+4y2BVoi^|TzgB^EVbK{JqA2>qCIj8O!2OjJ@lJYZq(k74j)7~ zAk8}#5&!o?a?NCls3gr)n(PT+hI&wsLZJH!Rk^Wabca+9#K zhI;3B^8l&IhVdMWwF#sIzc8Qy{ASv%Q}b3~YUqHSgnq?mB=tG) zfWIu9fKgKV8JUh;ZO-KmwqFyUgF0@b8n+}Ipzz}rfBi)BcKA6l&N$nfb==qfIjQ*! zRso;XNPjnddQAJ{exKmU>*aKM;ayf_xSS&x#zSFi?b|C{?MgVLL>Y>Qi4hrt zk@VIpqJ9_UnO+U~7mH}w3>9Z4yR{lH8!S3MSDraKgMl&9B@%J!_?h(aV1-J61DpOq z*X}Pi2b%y_g;kiDbO<;6)*tHD^Ha3i#V=!P>2+vEx3O#uu>8Tu9M7EWQ=Zq`wcC`w zaGp+4!7Q7f{>9Fd)z{MPa>N#MIwCGr@#DuAlBPWo@8$RQk%KN4GG2_-e#=>OqE;2n zNO7|us{Xe9%lP!Y+xlQ**m}-T@7{b>LC0WoZhUWF2tS0AHG8Ia#ZyJ^t+WoSs-N6@ z#qpmewY*YW;bgkK&BT05%u}<>u92>82URP#f{95?BS`Dj;>iZC^S@dAhsxAD_IB$O z=BMVLjXWnZ5{RF2Fl`bzqHPy!in(4gy&Ez~A-pjS<#Ug@mL)R$6V+oR)-_D~Afy&Q zQSsQZDS@lyyzoQ9q7~T(y32h(1F~gCA{Wsy;*a)v2c4MXv!GYe0i17QVQm=x?3yj} ziX`toZu4?}V#zg|LIwOPY6}h5FO>2#V1>)P&`G&L@F8Pp>2K6pQMAeDe;2bbKeVQn5PP! zRHUg%`1=lr56gNyb#fsi;lZ@gZ_8+Y=ga3OAobgW8Q!p$E}Xr)G+(_(wl5LJY#3vp z@t*#puBI+n6ZC_k zI9t9e({_%)bHPh27#upUw30W(VmC6jORMkmj_V&2Uv}oN#vC8J`iu=bsBn9CbEM8y z-uPw*NNmn&L#l6=I(}DHz4o%NEW#C7xzei;xp}TaY4bo3P`NQus%})6o1eR2UzeO~ ze^%!HtEOBY+!%hZU~?iwS4hCcD;(;wB#M+5PN6INL2Va#p zSJ!|{aIHg^!kVM+0Gvv|`BSNZlU4j{=2QuagGRDi1a5nbJAU=Kj4Ur)oGoN-ckg^L zRU6lzY^3(&p$e&>2&3w@J?$B0M%j&}rvuZ9%S%McosLlO-cVikADiBqR?swgKN-LK zDV*@u!l!pgq0IjvU#_WoO`c!Iwz-!jy@AmR_ZeOUo`y(Cm5y6dQ8bt?klz7&MFJxE}K{S z-?OC)*#ZxMiwSeEF8hX_zNLx?dB(y?<|$1k$NIDy*X;KyHyefN-|s4^*UpM?{Rb9b ziXiv_){&6kMjBx4?tr{{h=A{clh$7HoO$`FizN$!AL+8tj5mM}&|QJ2b&PzG{9AVT zas0h`YT^urzw_7&IP|m28eQt`dLhKdLGFsOxvct= zw`ImmEc-u;lU}d_DM@Wf^w*kxf6b3sIgBcic8e2}#?xVoSgYc#9B5AJCv`@8^LTHhSb((%7RJeDr8F)`FMyeaGJmqtJF{`7`+-t=M} zR^-@}|S^!1Ipp3o3yq32v2sQt0BKbh7?)!pQf z*IUI{ka1yQy=|(RR)ahG-0~(MYZMfC;Go~PE>L(r-J^Z+@Y|#eeq6A)E14yJRU$sL zpe6kShb+`7UN;WK5Z3hpu@$=D_-^1BUQQ+|v)zgy;hU>D=QYttHW4+Jh$4%}L*zcd zLCwXJyu7UVmrYMuc7+SJAu2u*w{q^(>o88;!I`~0YDO6s`I?45)#q9C;#q3K2XAGZ zyPLP&LFI`j+L^$wUU`v(Hjq3@X#{!J(xg3oXnwDEO=Uwk6@Ngg^$$ z%tW+YA~c^Knfd}+NMd=2jw$lyG9L{Vu8D>zwt15iw2iHi9eLYGNHHTsTa#!!VCNAt zF6@0F(IB&;)G*JRdil1Jht^vc`}ih_tvu7M56i;9iA)6FUCr-TtNB_H=C9K7!I1ml ziEdE;O0ug`ocJn)4d%;}hZted7I`NrRMu!IJe@~WHNI!^G8fuuU*zsqhHJv|_xwXN zE~$bAJ|0om)x0J-nr?qf1lNqLyni=UR^Mc99cu=~JE>U7eJE!c>i3D@!NnROQnGh> zsrYBOan!*pbcGowv6(7|%}6>uyZDP26T{N^_!o}CnaVX$FXFX?mkP83YU~)q$8NRZ zft|fhN?4p|B!U5|D8{LSRJnfdI~$y!W)tr_``hu?9IIa;_Lpr@HRz8ejrNs^ei}Yg z?br#iLDYe-jzOV{^5lHtsdKUv8xm`vz{-+Jy3;lBJ>1pobF;(Bc^!?2$~AqM;}S=z zD{HKcK)ZG&^*6jTvi9g#13Wf)x_VB#GDmjMiM9!6NM5>E?Y^~PR<`2X`?|5ygDXCt z1-CVAjnfjd$6!poFxOx%%>EbgBqqZ(GRvw;y37OFjmg8u&`$T>~Z%p0KfAb51#5o z=CFE$8>?q~yws5b`ZOv1Wo#yyQxt2pW9yL!I%h@YmW~;Lc6D}RzVGkb=>Z4pepvGh zNdu3(qSzDLvWF7EvnW^FDfCT{WSJCRTEt&;I)67+4{ysiz-Xf5c;794LYTzl80qSj zc0h1YHf3s}@_j+m6?==g2irdv&Jr|Mk^hdhbyw2Qf7)UGW{}^#!uH;$BQ}>*B_4A& z@rPP`9rDAff#A(auduZ!kpmUrxXlpCaU4rp7hQs?r963MU8#|ayv(v-rq5~&2`SZq zoNVQU2NwjwGQxRwah>BoEVTc)VMPT0nrN2UCqEU7F8A=2J@~7pMx#E;zLznWFJBSe z^qo>{*7~iqbbjd{2aoviUR~^mxi^jI6Qt&?(6|Sdw1rTd(WEz!O{%j9(CaL zQL6g{2dpJ;Y(!=wj|kl!EflvN`_Fsb;+(g)Xt&!lm!QZDOd~8?TT2puNwWY>z##f* zm2((@V`7Sd%-jq%tfiuTN9N6kH;}V>+%fi@+}HvN(Z`UPL+(nt z{0$jb*kpN!xZREvNnJb$HKWe-bPaoMB7i|#^1eHR$CS)(#rft77Lsgb$Q`N)%)Zh6 zBBTKwf-ibTdgb<~!HcV?V-Ew2M{$-D%V)kH(`#_abFns2WULUduv0s~&@Z*P#td9{ zzVk{m_!`dJrHfs!KYsx}c_6RUGwDY;vw!mq(mi8~HX1ypE$Kv$rHi31@Rbj%-qv9| z&9E-us`oRbx(n;1n8*L7nasWs2GhSuQn&i-8y{&a(JdZ$D|$Z`8bv`ozR?#-x<%vd|TfK4gr4Ebs6E$4go6lkkBm`w_+44=EsuxGA;1g+ANI zxN?hRYQV&H`Kiiy9@jewACrJWYN!p{J@eT}xf0f|vPX&8AJ;||C9P+5HLR8v!W2ra zxRan48kv~}YylWKYp>Uzd#)hQ#eE%XkVLJhAO{OnY*GFlw=m!eYP9i_z2R9%q&oas zyy;#IfG;E|6vyj{%EGWBamF9^W?-^!4L|E!+`SA>Y=US_di6Hj!5 z;(2V9g(fVC7*p+$5;C&G+G+7`2;L6ztlP}A^E)C$@1ugW`SCC&g2&Z~(KE3#)48rg z$h5l81qBVgt621pbUqD;m1f?(YA?&Wr>TGBZ}+)Ss2Q=Uv5RU@y|6>))3j!#TY2lm z?{kJEulJEmcmhTF>z37TJ1#mS1km@e= zE#CeqrS@R=S(urcZdy|HW)1CM*5jLWZJSnn0nvE*ykkj}KF)P$$t$UBE zYp1dk>fiNKonLw+r7!_f-G0Q6L@M`j^SYQjz$tjAnGMz!I=w_sHn+&> zzfpqFyQXEeK9j3bOFlyt_e{T1c?A3uFX5ENQX)*S9qg50#8WTDG=Zsy^4>kiC`q)WLoRbai{+4SF8@)LI zDiPVt5q?Rt*ZsHD_ymz8{(164{gKC^xhrhPnoE17uRIz4tupy|e`ds*?9Dj4#a>Bf z+DT%?h$N7WZG1(_5-biP?CtY*#^}uhC}-ULuoFyT9S0tmzwg~oyc%~jFSTb zC*pByCTPhPAaSAt`SZB1aqreAQ+Fx~;=al}quXe#X{M^&RW$`ZL=p6!b}rb``EQ zSXOy!@~>X5n!D*Up}hUV`FABj7oyL7H@$^sYd%Cn!&dMVB^&M|))V^_C39Z88PiWJI`@F6{i( z<++~FDPhe#^-N51P86KKKhr{1K1jQ1{nLCjd^rxawUhFDLn^ZxEQjg>E2_ga`P1e2 zI^-k-xRVh+SnzQl(4u`q*$tK)B`4bbO$pq)1Me-uJlO)__QQ)&9Z>uEq%MLbqOER^ z%_{(o86YM}?uF@q0@^a;;t)c;aBXfaYr{h3MCIq#hkWoJWRgE=ElpA^W=j=?i~JHanX3MT zgd*Fyjz&VR_Au4?o5#PszJ5sM+?olIW-YLjYu!!gxj2GAaA&-w^~Az+l3VIguY#Mj zNC)b5`;d|AUYbrwKk>Z!pw`p6shU+8MG93Dyy6(^~zJKlayO z@jQ!66=cz?B6yN&8`qO9x5Q)2FbUejY0mW3Xy{e{i^ z8V+j1G+tV=WarK?LeqD*;Gc=dIojprfxoaxHC3sZk24F!baTE4x3|ke2RU z0eFs-;zEo_cYRkYjR)c9U{79&(JBgY?6$#YBDSPhdWWqVFiIbYVS;vsdK>EMxiz$H zd47?@Y6>{txk}(n;?eVF?#vX{1JfcT_#!A#)45_(`%1HZE~Lz27a`yL-MQGrg`WGB%w{kA|@I}dFB z<>XQ}9Q)3wMuBSkK!WMCZef?#>McO23S1(&?w68C@Q>j2g>W`sjh)$CE z1DAtt;`ly6JkHNa=Fg#NZy*CMb(SiT55FpU2OQyXk40E*@xZCoUlD9za1R8h;F89# z!jk@DHR;9vMO^!pXIg7XM)>h)?`YB~cB$IZw#_#PDhvn3JXU+E34-=Dk96>MVG>~J ze4DfXDJl-!mHlxYP~NyUryr0pQ9zMoTgCg2KcsEjK&p@0EB94rf;zD8(ie6bk!>Vc zFky9_$K2BTd91ioM4jhXg#$Vh8FtHy^i4E06pB2VG!$dHNN{K#Vo_evm!khO3m|g% z{K3WuC?Q)}4Q(5{%3=pj2UIr!OMvPc)SFSjc$^~T?nIXtLf6U5II&;JV9&X{FfwSS ziuVTz;$yY!!ZOE>yYQw-W{XDIf4;A&Na-qLv46sI&5zZKq3)t>L4R)J_*<~>=16Pa zcBx4>V~qj)Tt1*axj+k{m6Sg=IScf>!*gfmV>1%!iJHCRKSajZ2Tl@qe#GAzW?6{H zNJ}q25x{bX8|a{f(F&xyc-LXYu z6;hvG+n!xpBs-2ff=yUkVCb<0RJ6Az`ZXg?pcbvuTuY3KYPO0KOSYPnLj50VtfK6+;E@I;g7Mu%b)#lQsCoc zOC}Q4VPg4*9Uwh><_>#C0Sh7eL@z=B_d9~YC&_bz)_2<7W_h;^27#maX6D)MK~`Hw`xAJ_tAYVU^ZsCi``mFnb)k0zZtYm$_%I3741tSiG_P`;j$?~f_IY~L7Z z%&(eH_B);G^!f|9HlbjFI&)nz_e0y4th)!QBjoYW@3*aEb^a|`nKCV(?&w5xal>8^ zWW8PTh+Z1hCmNr(LN{Bue4jxi{c%PZgN!UK{jKN67hDH7i?3c5a`F3+rpEY|-Y8Py zkOCiaAp0oqEyX%56^Mp`LBnMBstP@Q$id}=W=i#HNhe<{Q@Em_E;FVr7@-X%$gFExoIahQ|UcTs&SHebff$|JDi%R#0Q~bXEO3dTzyRLT!?oAEyAkV`n zqne%hzeF)?Zu2RRhP(wgH+K)yDc##lQlELM=Dfy|+M^rm#92SJg-;fW&sir*?&r?3 zUg#<;SG&I2RR-C=SsDop#|RlUR~7xu5Z0NZ*$Ue|DvLy?vl)~6{L=YwmWJk30jL`@ z1xrgEU%?#b#7R2lkDc=iB5Mx*1U89jrvoI?=Zfa2Omq=u35``Ka&pdQIj)ywKYOG? z8i}#zR12|2a_!~=pw3$@w4_<9sD znYQD&PtkNIq3tI+6ol{N65;q@N^FTULfEls6o zzqgBO#rD!EOLF%O4QCO3xZTrpTUitXJ2oB<_Ms9M;#2W7xmz91JAQsSCFI?e`Sd85)4b<3Z5E@RJqE9S^-hEUV%d7YL`b_2F8P7<5I`zh|eqM=k zvlPKx$Z~$xapnm1rP2A(p1Mun<(6f#zGeA!r7#uPs?^g~H3&0vJa^Q|BbwrS{`^d| z_Y8Wo_d4aCXdLy8$!-|um&gV4547Ib_KiYSz5v7VGBnI&^PGvu`xdcsiQ%Q&83LuN z_+Sv>W$NYd7Zk%|qwmQv3>T?>FwAF~{1N#1hXuv?^act=?@QroMwytGkGd&~+eoSkzJg>1;Ijxh?I zB7Aq2itu;gIVdg-uPUb&uRC@2BukBxt8r9fryf}|ce%G%)#v_x!g5N-FGO|5D13)R z`3ghPFXXCBBkB3l(5LhWQ#0OaL_GuH7yqY?<;L%}SS>$vZgElj8Vd`G6ogjxP&1gN zaCpOA_H+8n*z?kGS5bgkc3&4g$$?H^f`nA4Boxnwiv)Qs$?tCE)SAU3(hvlCPO`V4 zRoI1<+RxmG2d0IuoG>fBzUgtmsg1;7KSq*g>vcFVH3H3Fkn7%4lXZ))ZxuxyP!JDg z#K{WaJ#Rz%kS6tZmw#%t^oy&sn*|OdD8|?|oN%O0GMY-Ydv$abD5A1p8Oy_6(hM;< zw&xRn5>Pk^2Kx@`4kQyf;%sW8)h9c{8i7)6^I0??*$cMz$i*F=;qC z6MyZTOW)0qs;6|h97U1bf25g^342LEBCRv(QkJ%(bW<|BJ>PY9-nI6ubR(!E4mVUR zJDMDI)s%5-t?;l*!i;q_mYn;-W{>Seh}jHJQNz(RVoFx4o8~V$#YnC>9)y=$N_sgC z01qN(`&K&|vRjs{i?=8FPp$>saKuPjmAfkb(I{&qSJ-mzXgl8Lk4Qt!R0~Lq!s7M?v)Qf=VutuCIiP z)bl9>SyWWduahhWe6y<}z&!j;&V3UH_~Q6rU9PL9yCTO~6&sPYQ>8$TY-@Pn4kFNM z@40^j*B$ZvRea=0dV_hySmrRdSF0uCj;D$BbL}-Id5K3e1JV{Em$#R*%WBZFKDfkh zw4D6iP-@Lvmer+h5IFO$1<0E`?bi$*r(pz3T~i~SYP#gNF$mRxM8RQbcOZ`266!VejDnH%=Lm64<6(ZYi4ki(aA96@f0f`cHAI1`@G;^J?O1}?fp=u7UC%kOkT4n&oIB%&HUh3!Rs2QMWQqesVfHjm#L5AY z;px*CpYVt;f9pWRO-)NHE15a^>YdmIs9Ms2eCu<2FU{CLIf@8F`#`=MeHhQQauf*-eymYQyklRE-7sN`3M6bG7`K2XWtzctY^ z$y`vN3d|djQpJeS#h%;VO}O}sf&;da7ML%!;u!t;LPGXFh|PwgX*D6D1mEv6!8Ae- z-1BZ|2q=Cs6Q5GbFUUP+^77u*c~4?%+r2*Ovj5|4$vuVRo^Lsd^a)*O>0^?8`9G># zK0?u|!7^h{W>T*vHIqMmfl8?#cfZZp`Xqb0klXvkNACN~se=r-62k-7~) z!Y(1A67B;7cpXAv&~6`Ro&+z^H-X{vW)}#Y);*TWZw`cnwwI95aqHFUMbf*QnB3S8mvsfBN-2N9c`oO~p1e4v ziAFb+bm(&df_?|F1KS~YtnXFm z>rbt9K-pJ@Scy}q4M;%rMFT_;O*$$)m@jZx94@2 z?l}cz*x#NxmK^BEu-QL91ozC(Lmm@H-t8s+6u9U*IT~F0X1SS~u`&ng+d_XZC7~o@ zt0BCdomv<2AB}_bD0Q?!SS>*{mQ}1!WwoL>tdEAb}vlpNFz6Q<_%g z@!^)a05iB-G;YW ztq0pET)UWds%quApcuyGJ3f9xu_L(`WRd*Z`F%b4lJ}`U?k#0MaC|dpO_PwNj^u`~ zP|7$Dzx|dF= zlLEbvmB^&I$j0!?+935*d&k|+NPIg5KrRJmc5m!|j5NB}Ji%jCUjxv)l-zILLRMUr zJ*(v9C-&ncT0qbZnuu6L1~A;;4u@|96M>3dIt`!#Hfbou%7F$VZ%cGk3Fx^3>@og7 zNQ^RvGD)>$eD6)sHt)eE(|4AzO224zW^H5rk0_Wb|If=x$M=rW zZhS?U4etoT>^st+546m1S6aSgrLZN5fu@{R{;xM}%g5Yf8%#fo{&b8rr2bF)-H2o1 zr*DRRu3*dj@k>CiW{M|1K7RTRRS25*-Xi&rg>Sdz6r&H3uR{|>oMD?&5=GzEe%Q(p zS`u~qi)+$HBhuwVJuJXDe_O=!K5HWbNW#OwZpy-%0l2I*RR#1dHfesqm+jrr+0T9Z z8I&s^LS7AVd1oFS>l!x_6I5N!bK;G#TZ`m*<}#qC$*M_25w{u2d&K(mG{D5@|14ZQ zxpgrtNxM+9C7V+_>un>?5dYr2_82()uJ6SK-FS9J1$NF>xT1LYEn@?`hEGkeCVHs!d|NJZUTX?v<9MCRxiZ9s;8)N_ZZU%TzP`I`p zslw%>9qKYr%iLIIb|6*c<HIyS0u<-PnOUP|F5iS*2 zAeONLl$ZzJbMaKaeR!73^T#&6u}17YNC(unD2v26SWdI|FRtd z2=o7!?KtXa7jkEnl$4aFCpLsYgRP>mjbsbUt1h^`1kG5h((T?-AD~w$VxrS9F@@)R zv+8BAW#|}li;|ZEm_Mh0!zu76dsle|pzZY}6F}rjKh$MVoLeMLSh{_G6 zf2n#nqS$bgL$K?rMYswi<$2KzYSU!IZ6frNlzWz~CX~!Ux-V3JersZlME$${f}|#L zZp|lClPkciTvuLEO1Vu~y0;DB?i)LcM^ykp?EolVY>2w7zR+SVvM#>vctoosTGH-t zK3|YPxijoX`#v*sF_tibh0t%-aaX2S-`vZb4JX5L$8OLRVD1--b3>1}Ew=ySdf%|V zOtS4wp;EE^rt0A8cW7N*J{=yH9eNuet@cW}_?2XD|HQz2V{q`jdOm^uM9vp8f`k}F zLw&v8N#uw!!eur2EHR@{og62k3H zk&VcDs3^KbvGWK{;}d8Xu^65ti)h)kJpM2*(?v9vMsmd1YZ-s=kQ4lS7o;KO0S}z=6T* zy<_GB83aOV++YRFr{F(DVnBtD{s+*Pd4$`R{JkTO&dl4oI|@fVN88~A^SYwg>?h*n z_-k(Ok7z&H%OGjt!Bv4*Yds6(auGoQXUxt`lfB)DDnE=)4;vfHFRGyFuMdUHG=tLZ z%)}|jy7`)dS^bm84${3`hUDuj8x!WYeLA!Ew}A_3Oq_RwQ#ES3FKroZ>=|0rVG zo((RWy~Oq8VdE$0L1SPTj>}Cnb7q&12vCe7ji7a5)3sDDVv9;7cVJM#?C$K8;0*6< z_SZaV%D3m}c_ke4`jL?6pM7##$djiim8m2~I}AZd?_B!h{r%|*juL)-cCQh$;KA2-OtJG)f~PY9%Gl>&WH-@-!-VEb@6)>vB2r>CCX(Y z`5YzmWu0giQ?{@v29Kw`FWx(<58F-q9|IAC(4xFzHEUXj4C~U!MM%WOA!NpUK4-V* zUBCAd;{(S82S4carsbLH*0LgI%gTm_gZ_)=Q%}HRf`HFWo@l!q6T2||JFY6Rb8ZPe zJW-bo#U6O?R?Ao{IFBNiAQyi)m?iR`O)vZkDtD!qS&&g`x13m07WWH|F30~9{kl8o zD0V@SeO0kSz})HuIU$zJf|O=%e`^W&*VBv%1!LX2W`+>$OZI|Fc!&SK`ys;p%vf<^`T)~O)ucwLGXKcS;fHew>;*ZL3Ua|bCtk~1In=P4c8;Qj%K~0G&$7v8 zrdj!Ziw5R5a5%BF`+t|L(>{a$t7LusU&&hfRI-Nl)!3Rb6l{^)y{KfA-Z0wZ2AQCY zPM~Hh+YFh@esB?|v9D;tqqEJ%sKukxz;i4p7&~iJJI=qrye>0EcrH@poN{CAs|{-H z{XL$G9PeEg9*NXz88dK2&F|SPg%8RrTzJn_`vYj;i{o{c9Z+m6_}fEe3*qtW=xdXF zTmlQiEHDjd*LJ+Bic2~e1)tmp#==XJHveKiD@AezDe5>xh+uO--v76GIqe*XTh%Sl z!Oxl1>B!fUNk}&U$UcCkt@6?$ld|`iD%8~tKLHNC%1j=MQvfM2nx*XGzGln7e53FF ze5BikO7ylP41~LtJjb!2bI-+Ada}*F=qc0tJRvJMgAsLd2C zWqkO92e=oqWGpN!GAqe3t{39vi-3+6O{U=rt3;?@D?X&kdjRRBco>o9l zZ@Q-B>Fxx3v7YpH8K8U4d)S|3*O=M4;TRSNTMLcXRi)Zo5=>!)w~ChDGcAU!oCpK6mrYE0z^xzIAH zLa*Omq`uGv@iUs5e&KaNgl%vI|4#2sT;{3VPG~-T_V@Q)@T;bLTMk+#;VXUZPar=O zT^vU<*1Z7G=|+~fQItHJEmVkR(@!)*xoG;BMp~HXq1|A6jmiZ0J^~s5vV6dic@wx6 z(>SUuJ$t^BcIRYOX`{Tu0xO`uqm`G&`L;S&RHtzhTkN3#>5^WX_( zlf@R&GBizrPw^E`-CH}2`0J1bdU^cg2X|+Hwi6O`6GT=3=Rx7(okIIs;X^$_5*;#f zzn6I-DF1Ugf!^U=7NRBb=5L`iD!QqFvPbKn?Or35-oqtVmmHui%fP_Vzubv#99&Ij zLUdC%^1gkWD(2tNBU=_dKy(;nSqRH4?zhangv{AYq#1L>u^c*!W5=}%Sg|CwKw%UE>|QX*J$m!_b7XbY z8RmJ<;>2)x6Yb*i$=^C#GxjJNcM!o4v%(i$zuJT!FJu&l&0eZ&y(ome1!Mro7BXg6 zcSB30U$@5(`)*@q8MB(6iF=acBfnkf$3%@o&D zK6cduz-yJAzQROT&wo^>kVLed&(E4aggo{ZUTa>}U&v9+`cxVQj71scvo02o^w>`@q#Z^oFA z?AgDiI?uOdVYo}cw@9Wv86BCddq$?@Vsik>q ztoBM%tPFZlCwj7V%z$z~kMV5k*)#I)_tKIYSG+CHfj8I#?I!8wwgAjz(`d?x8k@K; zRF(qVliI+){$nd@zD&VP|r>hkkh7{09ZhQ z;B4lNH%hG8-4UvgmaRYw`GIlJV;NBH1MAoU>&Q1udmK`Djx~nWWoNtw?rR-81Ld1^ zGw&1KyD#LK0t5`E7tSkLc#+{|deGV>ROAj2lOa{GnPZkuxn|`5>b0a0Wh7_ALYtb6 z_i8q-`0!6c9|u^Vg@7xay9f|E3>ciUDy6))nbF1a+pYAxH|Pf>S932}Ja+Dteuwf( zhn4bQq0P2$G(y8Z`Ou68Y{23w(;Ky|$MV8@n9Kc`nWu%EYhfqIJJlc%cxMBUJ2w%< z!VFE^(Vg+KfSSKuiiixY|Fm0g_QL^?TAp zEy21t^>NburRjeK`BTYC%q1J=aZZ7B_6dU1BhJq7#fD3g%E9!kJJs_q*;deb9-QIq zI0aX{-+z~B9IU~!FLcTAykg`tq}dLu-Gc_(qsmMFQ6$v=hH^DXU%x$_gs%B zLjpV}u8d&3N#gL&NLv5u0)r4P>kLfr{=3S7X%go(!4iIGqNxO2K-pF>&}q$xwAyjG zX?L6-%6Np*k1OEYapnRKGdLuUs0dNACJ$arVc@s{uQdh8U%Ofx ziV$!$@=WUmi8(Sm>zdM4iw(6QzWrv1$Hf9@J8@wrJe`DllJlRh_SM``(@c@$MlmLJ zv5WE-fC*5Rok)w;VsqAi7}PO}nEA?F|60LH70S-4e0+(De{h@dUc(_nxogdRCiZSu z+*Pb^0Ke=J5@Mb>_E`Var^2rmA%4_tSuVV zv(Y@Y(l@!Sh?D(m`#|7glwD?dv@zZnfb2jl>ix$q7;39HZ>$_^5Fh82*pt-8=1x2} zvTk4KwLBIrl&1%KTLC4e@Svj<6FGC&7eE!MjB6=7v>%A&8c>f6Yt_tx1ek z%YaPfam)~8_X;_R60y8}CWb0C)}G*ajsHCOBu{VyU(_B(`)-b6Ju@R z`0DZ$+6eKi2Z9$Y%sXM*<*91O;WupibhymamYr%o81 zlKf?K8Av3^-MXsYWXg1A|BcuFICKdn=V~EvQqK$XQr)uk%K-9VV=OTA7UikKdevqg z3&c>+9EZei^%*Sz{8%fpKD+F;q6UIlLK-`_eh(4=>5JoF%KZ|pnX9?K91s)+(V<$( zIdi)Z_+f^rwtv>NyL?@WOBtK6_X1;X@yMHA(^1(pOUk=05notZ$t{QqBM9yM=cVT+q*KfEw z@IN$RCP3_cev00!{vNxQ_iK7*dc5e|R0Z9_5r#kA)>wD01X_N%ALnlWV1uweums^e z2Kt--n7Rz>=y6y^x0Ntb(G1e_&ak88^`B0q)#&v4f{z0WznvAIzl|AS93=*IiwjR5 z_Oz>mJ8k;K${x3$TP@H7Dc;_8ljLNN01uBV2+%X8P-*Etp)m4Nf1O=(+`xJ<3Ca~3 zD2v(zdu>Hwqm}G8;oIxN2f@F$UQquF?NFG=41vGQLZyA%841DBFP^cWZl;Hd@uQt| zCLeo-psa;4!oO5OrXTT}~JsI5F_>E}w|ulrT$`RtA~L zJcm6|@YD+Sr<&9$48|y zbDTN4Z_-A(eq!~Hgim|w&mCR{2>~VI0Ww2@>Pjic|75rCW9=r-KIyUmx@3Ra%*;c- z)u+!(C`iQY10-TumUEPU#FednG^s=X3?kU2dd^~XrHAW3i~m3E zUHLy${o6n7g~Bb77z#}ha@!eHl%2%bWhqORv6BWPN|qvHXN-inJqm0Fdz+&sX2=IViG3ndNZYC9Gk_-pg zFYkW+^!TI(T@vh*WM^mW_89|!{ZTF24J2QM5=SP5F>7N z{os{;xo=SK>&Wi}zzW_vJ$?(|Zuxd&5<{dpVV_k@s+OfvcB*;9cw?^pKNQW|MF0%B ziTeyik%V!9y31gTBTJ?9oE)hSm={-v>wIrt%g`t5^|F%ZBmhCxdEoV#eu)__$CQ8k z8E{phX8#vly_r4uZ~2k`mE~Z_=1v+dtO4^5b(*fl?M>HhH+eDqKmq1)t7I{zIs0Ez z)j@~^2l|~oocO{A-Db+E;s3I=`NPtk3~%uaBk#q*9vj3By1}n+rZw7cp7=qXrT@#= zz#B8y0IQ4K0Yx(JoW7JhZp}Q;r;@<+wcTkY-Uzf0>rh7pMq*O{k~F^0lw|^XMp;pv zpp}*-{yX-459Per82qi~0%M=?Q!q)M9&8oS98&E8Hk&J`*D!l;XnC4k@28gS(x*Wy z@_GQ!d-=y-W^+E&byNUq_I1ivLXD}-xyHo8VBEwX!@q6c2e#`<3!tiL!oI0sP)>qs z$6KS-cjTKLLM|wM{0*mE2AjXUAcMMBnYy&jpyBBM8gjnul137frTZqo32wY2<7Za) zXY7*klf5djpIN19U;6uP5i}Hx7pDlA(HsZz#2;Vl#oU5sc%EGN&+hX1N^)d-QA%9) zxV0B(SE$1Yeez3o4uSUg!-T5OIjTH&43;K=PxEJixuYLKtER12PbLAV+JSq9)ge}Z z>fHnSva0;TcK76_D<(m>R_n`an}-)~>Mlk-mntT#A1{*s;v&zw?itn{dBx0vJbi<` z=om3V_T*n=VUkjb?~bS^M(dMcYe_EK?aP z%QIW4c6YF2U6y;{fva0Tm*fINDw#+>+wI_rhoHz~>TtGW*Uk{`@r%f!Uxp;f2d0mz z)>&taKe|i9Pddhh%YPKS2SJfyK<;#rN%g@u#nYLOb7%?c%;*T4t2%@EGtMufbrwFu zPIx_>nev6jABJwcyr}r}3bw*GvnWc-G0uxpibtzio4lAIDcjPoL<*X#q|A)r9O&E- z^d>G+Um)7dT1|RULsbs_G6q{QWv)=F@tsRzFkgjD8qNE6yiIp^Jhh1l4nglD=8k4Z z4G?qZ%O22anNbOZcB98H20e;rdEwgw1@2^%Z18uBW@^5N4V^bX_53|5YYB|}1lud7 zn^ZdQB@6!cr@{h)>@QGGsb6f3w8|3?>R6QA7J6V^aEm=Aq@rSY(U8sQiwQGy!%a}} zsq@44ZBo-FfgU1%qOl%AYwe~}JotB8uB`dh#UqPeY#P5M7t1n~q0lm&;J?h8h`~%D zR(A9&PDw!{h-&!Pe5A0S2+2(rjhlO5aQEAipv>3A3AxO#2I=_)m6)@_1{=h+N}c;<6f6wojbXQq%X028 zSCZ-5*PKul_bvY!+|EM|^UP&o#`cY0uTUDh+hox!5ab!ph_5+LJWus!_JX4g$x|nX zHi>J&e=}X(i<|G^d^NnTA5NQ8zgWw}U!~i5r}7cCB@X#Sx~Qm*MGUWUM}nr>r|Ry4 zBwW+>)l@Vq+!=TK&iTBlg}!!zaE(VvOv5Nah`g~`8jzaY#hpFGKTePv#;&hN^KvfH zNGS&U9;LO$(ymqM(jcoU#!Fd@lW!RtS z#JMS*L9v{?)zc@+T}%_`d@hFb6>1ix5=H$#uXeoG!Rq0U7Hl~eb`)AX*&816+%N9v zUc6SEDwMRey!SX=9TV-H9$SDAD5yu~9U{D&!fgC{na1HQJ+z;eyb{^nI*e$%ZX*uI zs2_sZST{NNBK=KVjqxj=E!H#?>h3H5Rg><6bK=;v3K;vt6yNtJF_F!BIyYiXX!k}s@(G%Vktuxo$__Wu(>E1Ic+@43mkSzk23K{JgFf_ z9cfL#6w%IoZZkp6uyuPKhS=aBDR*+kgDgsPNY~LUTK77Nj%in|qAm7U?T`Z%nFps| zFP;;AlF6easS(qvGd-e0wbQ~PVK4goxc84+K0BHqgg$v^5kJ>+LmQfcRtj`-BfnV{R;-JoGatDyH%jQMJ zwTFjG*Lw=u+!F8UtBGnC(IjiXeIw!zqjX?D z&`dAYtB7T&s89Fs_m=oyU2`2rp_mG&83I|>Ouh<i zdNd93wU)?QSF)#3&S%8ewAp~~?`hSS^&tp)`9T}bro*f6P$UvBBiUZg-iHsg&XV@c zugV=PKW}f4QsJ?w`Aa3>Zu5wevFFbCqp{PcY*2oFW_hotbg}*oTkjo}%?plM4o_z! z=A^)WvP}^5ofcKmN9S&ZdpA^j`_xGaIkdnC_?z^T7pw<0EPX`VTBV>i-5~#%i1)i{`)O`A*I+zv|sm zd3<5`Y@&w3{g|_JTRbtV@F&w=X5@#rpC+$A8Deuc%OIwkiu!)fQsn%y6SX{ywim6C zyWJxeP_QmHKwQA$&eU4H{ioo=qT5O`)wNrD_Cc9XQi6)QNf_wKRqDQn-?zCWICT_b zr3JpFfiZ)S!VtSwq&;KHSaA);Vi{7p$R5-6nkHE(xtrq8jR(%g_Zg9WBQ%i0GQ*>6 z^FPzydSA_r{xFmyogJN`+ADTSxzQ0hn5$F%#J)BeVNL+2hC~``5Y7wjo#D5vnH2R$ z9Yx#IY>`eoA4vCALjp=JTP+JSD&hg7B2s}V+6_w@5&JA)Ml@*r?;vB@GynN+t=F)a zL?+sH=UE^qg<+%WdNtyvg@oF(qoyQlJ#4ySF6C3XZIknug1F%W9}b!M2%U0NjZRms zD$<;qk|ncHBRO2yL?pj=)34Kz9Thc|K)z&y?=;yN5R$Z!Gyhe2K}#PeE21SY_SVfL4-#ch7>sN77ie!EXzW0 zq#facVl@X3)56C()F{pJwxn++`_6@kV7{hhMX$i#5O?>5pBwZ$#iL*H3A4eL7%$&K z$ADMomielZx(hh&$y8o<{SX3!pzCqMe?;N7Zm@@@uF^PuZJ-~&6ALuKe^e^}A$P*K zV)k)ki0p9^xPrXiZRi+x2!f8E9C3XrFS#2pv-;Jz-yJM>HN#RV+STQg9N+31VQGwaiDRY3I6$!AanUOa;X; z(NY4DN?Mdoxwd{8g5;krkv|Cd?hcHL{8$v!293XO2sL1NfY$Al?N3!cXV1-b{1Bio zfVABtZb;;LbLtu|aj|!W5V7v$Dgjufp6b>tdyQY8XPE{FjbR6h4ndzKeLrqsn~CE| zFkt3QU}kY0+;m?$g_Z+Bp;ub8;nySm0yG|$nHyW(BY-+jRX$_i)_6Ds}{ zb2tQjP+-f1gtX8^OKFT)<`-NABk|G;OZI$!gV7lI3Yus39#3j zjPuWcn)I6WH7?eIx>DMrmupCcRMB0AMHI3}@NL_0B?Gf)q#Y5|~krfz~gt6&K9+8iq_L)y9^N|kG zohWds1SwwU%I3I{^;{4;aH)9QTRr2T|ASbiq)6v%AMT^BUgkf7vLIP@k@^tVHQv~K z!Lt-hqAXjMWbUlsT@a{lcc4NI*ePxyf5|W6BgjBl2mX%0d3qk2!u8$TQ1aV&n z@d!~1x-H0GEfKq?~#)o{3m%f37yexGpV$nm8LE%FWby z8+?Hj;s9A=@%dBbmvQA>(t%4aUAeUjc6B*(^p?`vwzTl&FJ~8`+w7b!h=D%AN;zfw zf!B4pPsf9A00^4zEjlSz_Ewzur0w~hcnX5Dj{u1qw=ZFvFClr|2EHq)Q0eup3Oj*M z0T?d7(iyDFC`-goJY)viBDK}w5OuFQ+wj18|9QnSQ>wCdf9F~)^7SlbN;E+xL^qo@ z3HSt#i*ic9#n(4tBg8MJq8_b_DR!}AUOtu30xuMhFdW(oj{Y-3VPJqSeyl}74}#b( zfN&a$_Hy@C{E988Bi;t`FzFFb15`%6e^6;j&1b=1Y#GC0W8SrHj&a8!sMiSuFn^FQ zw#{+R8%dh5E%aaVxaVMo+HH}6vfF{hYPGDndkJZ z;@Brptkhb5*;d`i`)RX=$vp)KOxWrkD%iFEZneRvGZ{|4N-Xnd4u3aF>V!3fLZA0 zOQ4~$d;Mg5g{_&4#>fDSMF-m-Rx zo6_;dsi--biNn1>l8#G&8>{t!HMO2Ru`k8Tuz>R$FB!xQcb)>yf;6+B8yH6@0>JzK ekN*ebu!T{=`?X(L6RTsSN9(q}ddV%@u>S#OwDwZ~ literal 0 HcmV?d00001 diff --git a/lecture_12/lecture_12.aux b/lecture_12/lecture_12.aux new file mode 100644 index 0000000..c73dc14 --- /dev/null +++ b/lecture_12/lecture_12.aux @@ -0,0 +1,27 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} +\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined +\global\let\oldcontentsline\contentsline +\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} +\global\let\oldnewlabel\newlabel +\gdef\newlabel#1#2{\newlabelxx{#1}#2} +\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} +\AtEndDocument{\ifx\hyper@anchor\@undefined +\let\contentsline\oldcontentsline +\let\newlabel\oldnewlabel +\fi} +\fi} +\global\let\hyper@last\relax +\gdef\HyperFirstAtBeginDocument#1{#1} +\providecommand\HyField@AuxAddToFields[1]{} +\providecommand\HyField@AuxAddToCoFields[2]{} +\providecommand \oddpage@label [2]{} +\@writefile{toc}{\contentsline {subsection}{\numberline {0.1}My question from last class}{1}{subsection.0.1}} +\newlabel{my-question-from-last-class}{{0.1}{1}{My question from last class}{subsection.0.1}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces q1\relax }}{1}{figure.caption.1}} +\@writefile{toc}{\contentsline {subsection}{\numberline {0.2}Your questions from last class}{1}{subsection.0.2}} +\newlabel{your-questions-from-last-class}{{0.2}{1}{Your questions from last class}{subsection.0.2}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces q2\relax }}{2}{figure.caption.2}} +\@writefile{toc}{\contentsline {section}{\numberline {1}Matrix Inverse and Condition}{2}{section.1}} +\newlabel{matrix-inverse-and-condition}{{1}{2}{Matrix Inverse and Condition}{section.1}{}} diff --git a/lecture_12/lecture_12.ipynb b/lecture_12/lecture_12.ipynb new file mode 100644 index 0000000..dc44a21 --- /dev/null +++ b/lecture_12/lecture_12.ipynb @@ -0,0 +1,1123 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%plot --format svg" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "setdefaults" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## My question from last class \n", + "\n", + "![q1](det_L.png)\n", + "\n", + "![q2](chol_pre.png)\n", + "\n", + "\n", + "## Your questions from last class\n", + "\n", + "1. Will the exam be more theoretical or problem based?\n", + "\n", + "2. Writing code is difficult \n", + "\n", + "3. What format can we expect for the midterm? \n", + "\n", + "2. Could we go over some example questions for the exam?\n", + "\n", + "3. Will the use of GitHub be tested on the Midterm exam? Or is it more focused on linear algebra techniques/what was covered in the lectures?\n", + "\n", + "4. This is not my strong suit, getting a bit overwhelmed with matrix multiplication.\n", + "\n", + "5. I forgot how much I learned in linear algebra.\n", + "\n", + "6. What's the most exciting project you've ever worked on with Matlab/Octave?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Matrix Inverse and Condition\n", + "\n", + "\n", + "Considering the same solution set:\n", + "\n", + "$y=Ax$\n", + "\n", + "If we know that $A^{-1}A=I$, then \n", + "\n", + "$A^{-1}y=A^{-1}Ax=x$\n", + "\n", + "so \n", + "\n", + "$x=A^{-1}y$\n", + "\n", + "Where, $A^{-1}$ is the inverse of matrix $A$.\n", + "\n", + "$2x_{1}+x_{2}=1$\n", + "\n", + "$x_{1}+3x_{2}=1$\n", + "\n", + "$Ax=y$\n", + "\n", + "$\\left[ \\begin{array}{cc}\n", + "2 & 1 \\\\\n", + "1 & 3 \\end{array} \\right]\n", + "\\left[\\begin{array}{c} \n", + "x_{1} \\\\ \n", + "x_{2} \\end{array}\\right]=\n", + "\\left[\\begin{array}{c} \n", + "1 \\\\\n", + "1\\end{array}\\right]$\n", + "\n", + "$A^{-1}=\\frac{1}{2*3-1*1}\\left[ \\begin{array}{cc}\n", + "3 & 1 \\\\\n", + "-1 & 2 \\end{array} \\right]=\n", + "\\left[ \\begin{array}{cc}\n", + "3/5 & -1/5 \\\\\n", + "-1/5 & 2/5 \\end{array} \\right]$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A =\n", + "\n", + " 2 1\n", + " 1 3\n", + "\n", + "invA =\n", + "\n", + " 0.60000 -0.20000\n", + " -0.20000 0.40000\n", + "\n", + "ans =\n", + "\n", + " 1.00000 0.00000\n", + " 0.00000 1.00000\n", + "\n", + "ans =\n", + "\n", + " 1.00000 0.00000\n", + " 0.00000 1.00000\n", + "\n" + ] + } + ], + "source": [ + "A=[2,1;1,3]\n", + "invA=1/5*[3,-1;-1,2]\n", + "\n", + "A*invA\n", + "invA*A" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "How did we know the inverse of A? \n", + "\n", + "for 2$\\times$2 matrices, it is always:\n", + "\n", + "$A=\\left[ \\begin{array}{cc}\n", + "A_{11} & A_{12} \\\\\n", + "A_{21} & A_{22} \\end{array} \\right]$\n", + "\n", + "$A^{-1}=\\frac{1}{det(A)}\\left[ \\begin{array}{cc}\n", + "A_{22} & -A_{12} \\\\\n", + "-A_{21} & A_{11} \\end{array} \\right]$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$AA^{-1}=\\frac{1}{A_{11}A_{22}-A_{21}A_{12}}\\left[ \\begin{array}{cc}\n", + "A_{11}A_{22}-A_{21}A_{12} & -A_{11}A_{12}+A_{12}A_{11} \\\\\n", + "A_{21}A_{22}-A_{22}A_{21} & -A_{21}A_{12}+A_{22}A_{11} \\end{array} \\right]\n", + "=\\left[ \\begin{array}{cc}\n", + "1 & 0 \\\\\n", + "0 & 1 \\end{array} \\right]$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What about bigger matrices?\n", + "\n", + "We can use the LU-decomposition\n", + "\n", + "$A=LU$\n", + "\n", + "$A^{-1}=(LU)^{-1}=U^{-1}L^{-1}$\n", + "\n", + "if we divide $A^{-1}$ into n-column vectors, $a_{n}$, then\n", + "\n", + "$Aa_{1}=\\left[\\begin{array}{c} \n", + "1 \\\\ \n", + "0 \\\\ \n", + "\\vdots \\\\\n", + "0 \\end{array} \\right]$\n", + "$Aa_{2}=\\left[\\begin{array}{c} \n", + "0 \\\\ \n", + "1 \\\\ \n", + "\\vdots \\\\\n", + "0 \\end{array} \\right]$\n", + "$Aa_{n}=\\left[\\begin{array}{c} \n", + "0 \\\\ \n", + "0 \\\\ \n", + "\\vdots \\\\\n", + "1 \\end{array} \\right]$\n", + "\n", + "\n", + "Which we can solve for each $a_{n}$ with LU-decomposition, knowing the lower and upper triangular decompositions, then \n", + "\n", + "$A^{-1}=\\left[ \\begin{array}{cccc}\n", + "| & | & & | \\\\\n", + "a_{1} & a_{2} & \\cdots & a_{3} \\\\\n", + "| & | & & | \\end{array} \\right]$\n", + "\n", + "\n", + "$Ld_{1}=\\left[\\begin{array}{c} \n", + "1 \\\\ \n", + "0 \\\\ \n", + "\\vdots \\\\\n", + "0 \\end{array} \\right]$\n", + "$;~Ua_{1}=d_{1}$\n", + "\n", + "$Ld_{2}=\\left[\\begin{array}{c} \n", + "0 \\\\ \n", + "1 \\\\ \n", + "\\vdots \\\\\n", + "0 \\end{array} \\right]$\n", + "$;~Ua_{2}=d_{2}$\n", + "\n", + "$Ld_{n}=\\left[\\begin{array}{c} \n", + "0 \\\\ \n", + "1 \\\\ \n", + "\\vdots \\\\\n", + "n \\end{array} \\right]$\n", + "$;~Ua_{n}=d_{n}$\n", + "\n", + "Consider the following matrix:\n", + "\n", + "$A=\\left[ \\begin{array}{ccc}\n", + "2 & -1 & 0\\\\\n", + "-1 & 2 & -1\\\\\n", + "0 & -1 & 1 \\end{array} \\right]$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A =\n", + "\n", + " 2 -1 0\n", + " -1 2 -1\n", + " 0 -1 1\n", + "\n", + "U =\n", + "\n", + " 2.00000 -1.00000 0.00000\n", + " 0.00000 1.50000 -1.00000\n", + " 0.00000 -1.00000 1.00000\n", + "\n", + "L =\n", + "\n", + " 1.00000 0.00000 0.00000\n", + " -0.50000 1.00000 0.00000\n", + " 0.00000 0.00000 1.00000\n", + "\n" + ] + } + ], + "source": [ + "A=[2,-1,0;-1,2,-1;0,-1,1]\n", + "U=A;\n", + "L=eye(3,3);\n", + "U(2,:)=U(2,:)-U(2,1)/U(1,1)*U(1,:)\n", + "L(2,1)=A(2,1)/A(1,1)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "L =\n", + "\n", + " 1.00000 0.00000 0.00000\n", + " -0.50000 1.00000 0.00000\n", + " 0.00000 -0.66667 1.00000\n", + "\n", + "U =\n", + "\n", + " 2.00000 -1.00000 0.00000\n", + " 0.00000 1.50000 -1.00000\n", + " 0.00000 0.00000 0.33333\n", + "\n" + ] + } + ], + "source": [ + "L(3,2)=U(3,2)/U(2,2)\n", + "U(3,:)=U(3,:)-U(3,2)/U(2,2)*U(2,:)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now solve for $d_1$ then $a_1$, $d_2$ then $a_2$, and $d_3$ then $a_{3}$\n", + "\n", + "$Ld_{1}=\\left[\\begin{array}{c} \n", + "1 \\\\ \n", + "0 \\\\ \n", + "\\vdots \\\\\n", + "0 \\end{array} \\right]$\n", + "$;~Ua_{1}=d_{1}$" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "d1 =\n", + "\n", + " 1.00000\n", + " 0.50000\n", + " 0.33333\n", + "\n" + ] + } + ], + "source": [ + "d1=zeros(3,1);\n", + "d1(1)=1;\n", + "d1(2)=0-L(2,1)*d1(1);\n", + "d1(3)=0-L(3,1)*d1(1)-L(3,2)*d1(2)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a1 =\n", + "\n", + " 1.00000\n", + " 1.00000\n", + " 1.00000\n", + "\n" + ] + } + ], + "source": [ + "a1=zeros(3,1);\n", + "a1(3)=d1(3)/U(3,3);\n", + "a1(2)=1/U(2,2)*(d1(2)-U(2,3)*a1(3));\n", + "a1(1)=1/U(1,1)*(d1(1)-U(1,2)*a1(2)-U(1,3)*a1(3))" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "d2 =\n", + "\n", + " 0.00000\n", + " 1.00000\n", + " 0.66667\n", + "\n" + ] + } + ], + "source": [ + "d2=zeros(3,1);\n", + "d2(1)=0;\n", + "d2(2)=1-L(2,1)*d2(1);\n", + "d2(3)=0-L(3,1)*d2(1)-L(3,2)*d2(2)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a2 =\n", + "\n", + " 1.0000\n", + " 2.0000\n", + " 2.0000\n", + "\n" + ] + } + ], + "source": [ + "a2=zeros(3,1);\n", + "a2(3)=d2(3)/U(3,3);\n", + "a2(2)=1/U(2,2)*(d2(2)-U(2,3)*a2(3));\n", + "a2(1)=1/U(1,1)*(d2(1)-U(1,2)*a2(2)-U(1,3)*a2(3))" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "d3 =\n", + "\n", + " 0\n", + " 0\n", + " 1\n", + "\n" + ] + } + ], + "source": [ + "d3=zeros(3,1);\n", + "d3(1)=0;\n", + "d3(2)=0-L(2,1)*d3(1);\n", + "d3(3)=1-L(3,1)*d3(1)-L(3,2)*d3(2)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a3 =\n", + "\n", + " 1.00000\n", + " 2.00000\n", + " 3.00000\n", + "\n" + ] + } + ], + "source": [ + "a3=zeros(3,1);\n", + "a3(3)=d3(3)/U(3,3);\n", + "a3(2)=1/U(2,2)*(d3(2)-U(2,3)*a3(3));\n", + "a3(1)=1/U(1,1)*(d3(1)-U(1,2)*a3(2)-U(1,3)*a3(3))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Final solution for $A^{-1}$ is $[a_{1}~a_{2}~a_{3}]$" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "invA =\n", + "\n", + " 1.00000 1.00000 1.00000\n", + " 1.00000 2.00000 2.00000\n", + " 1.00000 2.00000 3.00000\n", + "\n", + "ans =\n", + "\n", + " 1.00000 0.00000 0.00000\n", + " 0.00000 1.00000 -0.00000\n", + " -0.00000 -0.00000 1.00000\n", + "\n" + ] + } + ], + "source": [ + "invA=[a1,a2,a3]\n", + "A*invA" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now the solution of $x$ to $Ax=y$ is $x=A^{-1}y$" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "y =\n", + "\n", + " 1\n", + " 2\n", + " 3\n", + "\n", + "x =\n", + "\n", + " 6.0000\n", + " 11.0000\n", + " 14.0000\n", + "\n", + "xbs =\n", + "\n", + " 6.0000\n", + " 11.0000\n", + " 14.0000\n", + "\n", + "ans =\n", + "\n", + " -3.5527e-15\n", + " -8.8818e-15\n", + " -1.0658e-14\n", + "\n", + "ans = 2.2204e-16\n" + ] + } + ], + "source": [ + "y=[1;2;3]\n", + "x=invA*y\n", + "xbs=A\\y\n", + "x-xbs\n", + "eps" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "Gnuplot\n", + "Produced by GNUPLOT 5.0 patchlevel 3 \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\t\n", + "\t\t0\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.0005\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.001\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.0015\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0.002\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t0\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t20\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t40\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t60\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t80\n", + "\t\n", + "\n", + "\n", + "\t\t\n", + "\t\t100\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\tinversion\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\tinversion\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\tbackslash\n", + "\n", + "\t\n", + "\t\tbackslash\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\tmultiplication\n", + "\n", + "\t\n", + "\t\tmultiplication\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "N=100;\n", + "n=[1:N];\n", + "t_inv=zeros(N,1);\n", + "t_bs=zeros(N,1);\n", + "t_mult=zeros(N,1);\n", + "for i=1:N\n", + " A=rand(i,i);\n", + " tic\n", + " invA=inv(A);\n", + " t_inv(i)=toc;\n", + " b=rand(i,1);\n", + " tic;\n", + " x=A\\b;\n", + " t_bs(i)=toc;\n", + " tic;\n", + " x=invA*b;\n", + " t_mult(i)=toc;\n", + "end\n", + "plot(n,t_inv,n,t_bs,n,t_mult)\n", + "axis([0 100 0 0.002])\n", + "legend('inversion','backslash','multiplication','Location','NorthWest')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Condition of a matrix \n", + "### *just checked in to see what condition my condition was in*\n", + "### Matrix norms\n", + "\n", + "The Euclidean norm of a vector is measure of the magnitude (in 3D this would be: $|x|=\\sqrt{x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}$) in general the equation is:\n", + "\n", + "$||x||_{e}=\\sqrt{\\sum_{i=1}^{n}x_{i}^{2}}$\n", + "\n", + "For a matrix, A, the same norm is called the Frobenius norm:\n", + "\n", + "$||A||_{f}=\\sqrt{\\sum_{i=1}^{n}\\sum_{i=1}^{m}A_{i,j}^{2}}$\n", + "\n", + "In general we can calculate any $p$-norm where\n", + "\n", + "$||A||_{p}=\\sqrt{\\sum_{i=1}^{n}\\sum_{i=1}^{m}A_{i,j}^{p}}$\n", + "\n", + "so the p=1, 1-norm is \n", + "\n", + "$||A||_{1}=\\sqrt{\\sum_{i=1}^{n}\\sum_{i=1}^{m}A_{i,j}^{1}}=\\sum_{i=1}^{n}\\sum_{i=1}^{m}|A_{i,j}|$\n", + "\n", + "$||A||_{\\infty}=\\sqrt{\\sum_{i=1}^{n}\\sum_{i=1}^{m}A_{i,j}^{\\infty}}=\\max_{1\\le i \\le n}\\sum_{j=1}^{m}|A_{i,j}|$\n", + "\n", + "### Condition of Matrix\n", + "\n", + "The matrix condition is the product of \n", + "\n", + "$Cond(A) = ||A||\\cdot||A^{-1}||$ \n", + "\n", + "So each norm will have a different condition number, but the limit is $Cond(A)\\ge 1$\n", + "\n", + "An estimate of the rounding error is based on the condition of A:\n", + "\n", + "$\\frac{||\\Delta x||}{x} \\le Cond(A) \\frac{||\\Delta A||}{||A||}$\n", + "\n", + "So if the coefficients of A have accuracy to $10^{-t}\n", + "\n", + "and the condition of A, $Cond(A)=10^{c}$\n", + "\n", + "then the solution for x can have rounding errors up to $10^{c-t}$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A =\n", + "\n", + " 1.00000 0.50000 0.33333\n", + " 0.50000 0.33333 0.25000\n", + " 0.33333 0.25000 0.20000\n", + "\n", + "L =\n", + "\n", + " 1.00000 0.00000 0.00000\n", + " 0.50000 1.00000 0.00000\n", + " 0.33333 1.00000 1.00000\n", + "\n", + "U =\n", + "\n", + " 1.00000 0.50000 0.33333\n", + " 0.00000 0.08333 0.08333\n", + " 0.00000 -0.00000 0.00556\n", + "\n" + ] + } + ], + "source": [ + "A=[1,1/2,1/3;1/2,1/3,1/4;1/3,1/4,1/5]\n", + "[L,U]=LU_naive(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Then, $A^{-1}=(LU)^{-1}=U^{-1}L^{-1}$\n", + "\n", + "$Ld_{1}=\\left[\\begin{array}{c}\n", + "1 \\\\\n", + "0 \\\\\n", + "0 \\end{array}\\right]$, $Ux_{1}=d_{1}$ ..." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "invA =\n", + "\n", + " 9.0000 -36.0000 30.0000\n", + " -36.0000 192.0000 -180.0000\n", + " 30.0000 -180.0000 180.0000\n", + "\n", + "ans =\n", + "\n", + " 1.0000e+00 3.5527e-15 2.9976e-15\n", + " -1.3249e-14 1.0000e+00 -9.1038e-15\n", + " 8.5117e-15 7.1054e-15 1.0000e+00\n", + "\n" + ] + } + ], + "source": [ + "invA=zeros(3,3);\n", + "d1=L\\[1;0;0];\n", + "d2=L\\[0;1;0];\n", + "d3=L\\[0;0;1];\n", + "invA(:,1)=U\\d1;\n", + "invA(:,2)=U\\d2;\n", + "invA(:,3)=U\\d3\n", + "invA*A" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Find the condition of A, $cond(A)$" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "normf_A = 1.4136\n", + "normf_invA = 372.21\n", + "cond_f_A = 526.16\n", + "ans = 1.4136\n", + "norm1_A = 1.8333\n", + "norm1_invA = 30.000\n", + "ans = 1.8333\n", + "cond_1_A = 55.000\n", + "norminf_A = 1.8333\n", + "norminf_invA = 30.000\n", + "ans = 1.8333\n", + "cond_inf_A = 55.000\n" + ] + } + ], + "source": [ + "% Frobenius norm\n", + "normf_A = sqrt(sum(sum(A.^2)))\n", + "normf_invA = sqrt(sum(sum(invA.^2)))\n", + "\n", + "cond_f_A = normf_A*normf_invA\n", + "\n", + "norm(A,'fro')\n", + "\n", + "% p=1, column sum norm\n", + "norm1_A = max(sum(A,2))\n", + "norm1_invA = max(sum(invA,2))\n", + "norm(A,1)\n", + "\n", + "cond_1_A=norm1_A*norm1_invA\n", + "\n", + "% p=inf, row sum norm\n", + "norminf_A = max(sum(A,1))\n", + "norminf_invA = max(sum(invA,1))\n", + "norm(A,inf)\n", + "\n", + "cond_inf_A=norminf_A*norminf_invA\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Consider the problem again from the intro to Linear Algebra, 4 masses are connected in series to 4 springs with spring constants $K_{i}$. What does a high condition number mean for this problem? \n", + "\n", + "![Springs-masses](../lecture_09/mass_springs.png)\n", + "\n", + "The masses haves the following amounts, 1, 2, 3, and 4 kg for masses 1-4. Using a FBD for each mass:\n", + "\n", + "$m_{1}g+k_{2}(x_{2}-x_{1})-k_{1}x_{1}=0$\n", + "\n", + "$m_{2}g+k_{3}(x_{3}-x_{2})-k_{2}(x_{2}-x_{1})=0$\n", + "\n", + "$m_{3}g+k_{4}(x_{4}-x_{3})-k_{3}(x_{3}-x_{2})=0$\n", + "\n", + "$m_{4}g-k_{4}(x_{4}-x_{3})=0$\n", + "\n", + "in matrix form:\n", + "\n", + "$\\left[ \\begin{array}{cccc}\n", + "k_{1}+k_{2} & -k_{2} & 0 & 0 \\\\\n", + "-k_{2} & k_{2}+k_{3} & -k_{3} & 0 \\\\\n", + "0 & -k_{3} & k_{3}+k_{4} & -k_{4} \\\\\n", + "0 & 0 & -k_{4} & k_{4} \\end{array} \\right]\n", + "\\left[ \\begin{array}{c}\n", + "x_{1} \\\\\n", + "x_{2} \\\\\n", + "x_{3} \\\\\n", + "x_{4} \\end{array} \\right]=\n", + "\\left[ \\begin{array}{c}\n", + "m_{1}g \\\\\n", + "m_{2}g \\\\\n", + "m_{3}g \\\\\n", + "m_{4}g \\end{array} \\right]$" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "K =\n", + "\n", + " 100010 -100000 0 0\n", + " -100000 100010 -10 0\n", + " 0 -10 11 -1\n", + " 0 0 -1 1\n", + "\n", + "y =\n", + "\n", + " 9.8100\n", + " 19.6200\n", + " 29.4300\n", + " 39.2400\n", + "\n" + ] + } + ], + "source": [ + "k1=10; % N/m\n", + "k2=100000;\n", + "k3=10;\n", + "k4=1;\n", + "m1=1; % kg\n", + "m2=2;\n", + "m3=3;\n", + "m4=4;\n", + "g=9.81; % m/s^2\n", + "K=[k1+k2 -k2 0 0; -k2 k2+k3 -k3 0; 0 -k3 k3+k4 -k4; 0 0 -k4 k4]\n", + "y=[m1*g;m2*g;m3*g;m4*g]" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans = 3.2004e+05\n", + "ans = 3.2004e+05\n", + "ans = 2.5925e+05\n", + "ans = 2.5293e+05\n" + ] + } + ], + "source": [ + "cond(K,inf)\n", + "cond(K,1)\n", + "cond(K,'fro')\n", + "cond(K,2)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "e =\n", + "\n", + " 7.9078e-01\n", + " 3.5881e+00\n", + " 1.7621e+01\n", + " 2.0001e+05\n", + "\n", + "ans = 2.5293e+05\n" + ] + } + ], + "source": [ + "e=eig(K)\n", + "max(e)/min(e)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Octave", + "language": "octave", + "name": "octave" + }, + "language_info": { + "file_extension": ".m", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "octave", + "version": "0.19.14" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/lecture_12/lecture_12.md b/lecture_12/lecture_12.md new file mode 100644 index 0000000..9befcbc --- /dev/null +++ b/lecture_12/lecture_12.md @@ -0,0 +1,674 @@ + + +```octave +%plot --format svg +``` + + +```octave +setdefaults +``` + +## My question from last class + +![q1](det_L.png) + +![q2](chol_pre.png) + + +## Your questions from last class + +1. Will the exam be more theoretical or problem based? + +2. Writing code is difficult + +3. What format can we expect for the midterm? + +2. Could we go over some example questions for the exam? + +3. Will the use of GitHub be tested on the Midterm exam? Or is it more focused on linear algebra techniques/what was covered in the lectures? + +4. This is not my strong suit, getting a bit overwhelmed with matrix multiplication. + +5. I forgot how much I learned in linear algebra. + +6. What's the most exciting project you've ever worked on with Matlab/Octave? + +# Matrix Inverse and Condition + + +Considering the same solution set: + +$y=Ax$ + +If we know that $A^{-1}A=I$, then + +$A^{-1}y=A^{-1}Ax=x$ + +so + +$x=A^{-1}y$ + +Where, $A^{-1}$ is the inverse of matrix $A$. + +$2x_{1}+x_{2}=1$ + +$x_{1}+3x_{2}=1$ + +$Ax=y$ + +$\left[ \begin{array}{cc} +2 & 1 \\ +1 & 3 \end{array} \right] +\left[\begin{array}{c} +x_{1} \\ +x_{2} \end{array}\right]= +\left[\begin{array}{c} +1 \\ +1\end{array}\right]$ + +$A^{-1}=\frac{1}{2*3-1*1}\left[ \begin{array}{cc} +3 & 1 \\ +-1 & 2 \end{array} \right]= +\left[ \begin{array}{cc} +3/5 & -1/5 \\ +-1/5 & 2/5 \end{array} \right]$ + + + +```octave +A=[2,1;1,3] +invA=1/5*[3,-1;-1,2] + +A*invA +invA*A +``` + + A = + + 2 1 + 1 3 + + invA = + + 0.60000 -0.20000 + -0.20000 0.40000 + + ans = + + 1.00000 0.00000 + 0.00000 1.00000 + + ans = + + 1.00000 0.00000 + 0.00000 1.00000 + + + +How did we know the inverse of A? + +for 2$\times$2 matrices, it is always: + +$A=\left[ \begin{array}{cc} +A_{11} & A_{12} \\ +A_{21} & A_{22} \end{array} \right]$ + +$A^{-1}=\frac{1}{det(A)}\left[ \begin{array}{cc} +A_{22} & -A_{12} \\ +-A_{21} & A_{11} \end{array} \right]$ + +$AA^{-1}=\frac{1}{A_{11}A_{22}-A_{21}A_{12}}\left[ \begin{array}{cc} +A_{11}A_{22}-A_{21}A_{12} & -A_{11}A_{12}+A_{12}A_{11} \\ +A_{21}A_{22}-A_{22}A_{21} & -A_{21}A_{12}+A_{22}A_{11} \end{array} \right] +=\left[ \begin{array}{cc} +1 & 0 \\ +0 & 1 \end{array} \right]$ + +What about bigger matrices? + +We can use the LU-decomposition + +$A=LU$ + +$A^{-1}=(LU)^{-1}=U^{-1}L^{-1}$ + +if we divide $A^{-1}$ into n-column vectors, $a_{n}$, then + +$Aa_{1}=\left[\begin{array}{c} +1 \\ +0 \\ +\vdots \\ +0 \end{array} \right]$ +$Aa_{2}=\left[\begin{array}{c} +0 \\ +1 \\ +\vdots \\ +0 \end{array} \right]$ +$Aa_{n}=\left[\begin{array}{c} +0 \\ +0 \\ +\vdots \\ +1 \end{array} \right]$ + + +Which we can solve for each $a_{n}$ with LU-decomposition, knowing the lower and upper triangular decompositions, then + +$A^{-1}=\left[ \begin{array}{cccc} +| & | & & | \\ +a_{1} & a_{2} & \cdots & a_{3} \\ +| & | & & | \end{array} \right]$ + + +$Ld_{1}=\left[\begin{array}{c} +1 \\ +0 \\ +\vdots \\ +0 \end{array} \right]$ +$;~Ua_{1}=d_{1}$ + +$Ld_{2}=\left[\begin{array}{c} +0 \\ +1 \\ +\vdots \\ +0 \end{array} \right]$ +$;~Ua_{2}=d_{2}$ + +$Ld_{n}=\left[\begin{array}{c} +0 \\ +1 \\ +\vdots \\ +n \end{array} \right]$ +$;~Ua_{n}=d_{n}$ + +Consider the following matrix: + +$A=\left[ \begin{array}{ccc} +2 & -1 & 0\\ +-1 & 2 & -1\\ +0 & -1 & 1 \end{array} \right]$ + + + +```octave +A=[2,-1,0;-1,2,-1;0,-1,1] +U=A; +L=eye(3,3); +U(2,:)=U(2,:)-U(2,1)/U(1,1)*U(1,:) +L(2,1)=A(2,1)/A(1,1) +``` + + A = + + 2 -1 0 + -1 2 -1 + 0 -1 1 + + U = + + 2.00000 -1.00000 0.00000 + 0.00000 1.50000 -1.00000 + 0.00000 -1.00000 1.00000 + + L = + + 1.00000 0.00000 0.00000 + -0.50000 1.00000 0.00000 + 0.00000 0.00000 1.00000 + + + + +```octave +L(3,2)=U(3,2)/U(2,2) +U(3,:)=U(3,:)-U(3,2)/U(2,2)*U(2,:) + +``` + + L = + + 1.00000 0.00000 0.00000 + -0.50000 1.00000 0.00000 + 0.00000 -0.66667 1.00000 + + U = + + 2.00000 -1.00000 0.00000 + 0.00000 1.50000 -1.00000 + 0.00000 0.00000 0.33333 + + + +Now solve for $d_1$ then $a_1$, $d_2$ then $a_2$, and $d_3$ then $a_{3}$ + +$Ld_{1}=\left[\begin{array}{c} +1 \\ +0 \\ +\vdots \\ +0 \end{array} \right]$ +$;~Ua_{1}=d_{1}$ + + +```octave +d1=zeros(3,1); +d1(1)=1; +d1(2)=0-L(2,1)*d1(1); +d1(3)=0-L(3,1)*d1(1)-L(3,2)*d1(2) +``` + + d1 = + + 1.00000 + 0.50000 + 0.33333 + + + + +```octave +a1=zeros(3,1); +a1(3)=d1(3)/U(3,3); +a1(2)=1/U(2,2)*(d1(2)-U(2,3)*a1(3)); +a1(1)=1/U(1,1)*(d1(1)-U(1,2)*a1(2)-U(1,3)*a1(3)) +``` + + a1 = + + 1.00000 + 1.00000 + 1.00000 + + + + +```octave +d2=zeros(3,1); +d2(1)=0; +d2(2)=1-L(2,1)*d2(1); +d2(3)=0-L(3,1)*d2(1)-L(3,2)*d2(2) +``` + + d2 = + + 0.00000 + 1.00000 + 0.66667 + + + + +```octave +a2=zeros(3,1); +a2(3)=d2(3)/U(3,3); +a2(2)=1/U(2,2)*(d2(2)-U(2,3)*a2(3)); +a2(1)=1/U(1,1)*(d2(1)-U(1,2)*a2(2)-U(1,3)*a2(3)) +``` + + a2 = + + 1.0000 + 2.0000 + 2.0000 + + + + +```octave +d3=zeros(3,1); +d3(1)=0; +d3(2)=0-L(2,1)*d3(1); +d3(3)=1-L(3,1)*d3(1)-L(3,2)*d3(2) +``` + + d3 = + + 0 + 0 + 1 + + + + +```octave +a3=zeros(3,1); +a3(3)=d3(3)/U(3,3); +a3(2)=1/U(2,2)*(d3(2)-U(2,3)*a3(3)); +a3(1)=1/U(1,1)*(d3(1)-U(1,2)*a3(2)-U(1,3)*a3(3)) +``` + + a3 = + + 1.00000 + 2.00000 + 3.00000 + + + +Final solution for $A^{-1}$ is $[a_{1}~a_{2}~a_{3}]$ + + +```octave +invA=[a1,a2,a3] +A*invA +``` + + invA = + + 1.00000 1.00000 1.00000 + 1.00000 2.00000 2.00000 + 1.00000 2.00000 3.00000 + + ans = + + 1.00000 0.00000 0.00000 + 0.00000 1.00000 -0.00000 + -0.00000 -0.00000 1.00000 + + + +Now the solution of $x$ to $Ax=y$ is $x=A^{-1}y$ + + +```octave +y=[1;2;3] +x=invA*y +xbs=A\y +x-xbs +eps +``` + + y = + + 1 + 2 + 3 + + x = + + 6.0000 + 11.0000 + 14.0000 + + xbs = + + 6.0000 + 11.0000 + 14.0000 + + ans = + + -3.5527e-15 + -8.8818e-15 + -1.0658e-14 + + ans = 2.2204e-16 + + + +```octave +N=100; +n=[1:N]; +t_inv=zeros(N,1); +t_bs=zeros(N,1); +t_mult=zeros(N,1); +for i=1:N + A=rand(i,i); + tic + invA=inv(A); + t_inv(i)=toc; + b=rand(i,1); + tic; + x=A\b; + t_bs(i)=toc; + tic; + x=invA*b; + t_mult(i)=toc; +end +plot(n,t_inv,n,t_bs,n,t_mult) +axis([0 100 0 0.002]) +legend('inversion','backslash','multiplication','Location','NorthWest') +``` + + +![svg](lecture_12_files/lecture_12_21_0.svg) + + +## Condition of a matrix +### *just checked in to see what condition my condition was in* +### Matrix norms + +The Euclidean norm of a vector is measure of the magnitude (in 3D this would be: $|x|=\sqrt{x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}$) in general the equation is: + +$||x||_{e}=\sqrt{\sum_{i=1}^{n}x_{i}^{2}}$ + +For a matrix, A, the same norm is called the Frobenius norm: + +$||A||_{f}=\sqrt{\sum_{i=1}^{n}\sum_{i=1}^{m}A_{i,j}^{2}}$ + +In general we can calculate any $p$-norm where + +$||A||_{p}=\sqrt{\sum_{i=1}^{n}\sum_{i=1}^{m}A_{i,j}^{p}}$ + +so the p=1, 1-norm is + +$||A||_{1}=\sqrt{\sum_{i=1}^{n}\sum_{i=1}^{m}A_{i,j}^{1}}=\sum_{i=1}^{n}\sum_{i=1}^{m}|A_{i,j}|$ + +$||A||_{\infty}=\sqrt{\sum_{i=1}^{n}\sum_{i=1}^{m}A_{i,j}^{\infty}}=\max_{1\le i \le n}\sum_{j=1}^{m}|A_{i,j}|$ + +### Condition of Matrix + +The matrix condition is the product of + +$Cond(A) = ||A||\cdot||A^{-1}||$ + +So each norm will have a different condition number, but the limit is $Cond(A)\ge 1$ + +An estimate of the rounding error is based on the condition of A: + +$\frac{||\Delta x||}{x} \le Cond(A) \frac{||\Delta A||}{||A||}$ + +So if the coefficients of A have accuracy to $10^{-t} + +and the condition of A, $Cond(A)=10^{c}$ + +then the solution for x can have rounding errors up to $10^{c-t}$ + + + +```octave +A=[1,1/2,1/3;1/2,1/3,1/4;1/3,1/4,1/5] +[L,U]=LU_naive(A) +``` + + A = + + 1.00000 0.50000 0.33333 + 0.50000 0.33333 0.25000 + 0.33333 0.25000 0.20000 + + L = + + 1.00000 0.00000 0.00000 + 0.50000 1.00000 0.00000 + 0.33333 1.00000 1.00000 + + U = + + 1.00000 0.50000 0.33333 + 0.00000 0.08333 0.08333 + 0.00000 -0.00000 0.00556 + + + +Then, $A^{-1}=(LU)^{-1}=U^{-1}L^{-1}$ + +$Ld_{1}=\left[\begin{array}{c} +1 \\ +0 \\ +0 \end{array}\right]$, $Ux_{1}=d_{1}$ ... + + +```octave +invA=zeros(3,3); +d1=L\[1;0;0]; +d2=L\[0;1;0]; +d3=L\[0;0;1]; +invA(:,1)=U\d1; +invA(:,2)=U\d2; +invA(:,3)=U\d3 +invA*A +``` + + invA = + + 9.0000 -36.0000 30.0000 + -36.0000 192.0000 -180.0000 + 30.0000 -180.0000 180.0000 + + ans = + + 1.0000e+00 3.5527e-15 2.9976e-15 + -1.3249e-14 1.0000e+00 -9.1038e-15 + 8.5117e-15 7.1054e-15 1.0000e+00 + + + +Find the condition of A, $cond(A)$ + + +```octave +% Frobenius norm +normf_A = sqrt(sum(sum(A.^2))) +normf_invA = sqrt(sum(sum(invA.^2))) + +cond_f_A = normf_A*normf_invA + +norm(A,'fro') + +% p=1, column sum norm +norm1_A = max(sum(A,2)) +norm1_invA = max(sum(invA,2)) +norm(A,1) + +cond_1_A=norm1_A*norm1_invA + +% p=inf, row sum norm +norminf_A = max(sum(A,1)) +norminf_invA = max(sum(invA,1)) +norm(A,inf) + +cond_inf_A=norminf_A*norminf_invA + +``` + + normf_A = 1.4136 + normf_invA = 372.21 + cond_f_A = 526.16 + ans = 1.4136 + norm1_A = 1.8333 + norm1_invA = 30.000 + ans = 1.8333 + cond_1_A = 55.000 + norminf_A = 1.8333 + norminf_invA = 30.000 + ans = 1.8333 + cond_inf_A = 55.000 + + +Consider the problem again from the intro to Linear Algebra, 4 masses are connected in series to 4 springs with spring constants $K_{i}$. What does a high condition number mean for this problem? + +![Springs-masses](../lecture_09/mass_springs.png) + +The masses haves the following amounts, 1, 2, 3, and 4 kg for masses 1-4. Using a FBD for each mass: + +$m_{1}g+k_{2}(x_{2}-x_{1})-k_{1}x_{1}=0$ + +$m_{2}g+k_{3}(x_{3}-x_{2})-k_{2}(x_{2}-x_{1})=0$ + +$m_{3}g+k_{4}(x_{4}-x_{3})-k_{3}(x_{3}-x_{2})=0$ + +$m_{4}g-k_{4}(x_{4}-x_{3})=0$ + +in matrix form: + +$\left[ \begin{array}{cccc} +k_{1}+k_{2} & -k_{2} & 0 & 0 \\ +-k_{2} & k_{2}+k_{3} & -k_{3} & 0 \\ +0 & -k_{3} & k_{3}+k_{4} & -k_{4} \\ +0 & 0 & -k_{4} & k_{4} \end{array} \right] +\left[ \begin{array}{c} +x_{1} \\ +x_{2} \\ +x_{3} \\ +x_{4} \end{array} \right]= +\left[ \begin{array}{c} +m_{1}g \\ +m_{2}g \\ +m_{3}g \\ +m_{4}g \end{array} \right]$ + + +```octave +k1=10; % N/m +k2=100000; +k3=10; +k4=1; +m1=1; % kg +m2=2; +m3=3; +m4=4; +g=9.81; % m/s^2 +K=[k1+k2 -k2 0 0; -k2 k2+k3 -k3 0; 0 -k3 k3+k4 -k4; 0 0 -k4 k4] +y=[m1*g;m2*g;m3*g;m4*g] +``` + + K = + + 100010 -100000 0 0 + -100000 100010 -10 0 + 0 -10 11 -1 + 0 0 -1 1 + + y = + + 9.8100 + 19.6200 + 29.4300 + 39.2400 + + + + +```octave +cond(K,inf) +cond(K,1) +cond(K,'fro') +cond(K,2) +``` + + ans = 3.2004e+05 + ans = 3.2004e+05 + ans = 2.5925e+05 + ans = 2.5293e+05 + + + +```octave +e=eig(K) +max(e)/min(e) +``` + + e = + + 7.9078e-01 + 3.5881e+00 + 1.7621e+01 + 2.0001e+05 + + ans = 2.5293e+05 + + + +```octave + +``` diff --git a/lecture_12/lecture_12.pdf b/lecture_12/lecture_12.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ed0f569e1339b5f53dbc1b946df146a0d62eb77b GIT binary patch literal 169270 zcmeFYWmH>V^fpKZXz}7w3KWOp?#10T!HNV6QoJqhR@~j)1Hq+GDDDs-SfRKUcX&g8 z|9RJZn^|ktn)x!9FC_QeeeOPI@8{WaLaQbv!@|MJgGM_(-8+ZI$xg{m>0oMuCM=A` zrUbILbg`o3=i{LK??Pjfv9@&qIZ?97*qXS2q(Ej4<{>Q8Z^4Cy?%%=^3@r@#u)OKy=dDW?bsyF0+12ppb82xVH{7Qa&KfxbK3I)Lk83#F|@VX~#{SNbhiA4^@+|ko~ zgGHBhK6kv~=%c9%gyTR`jfWPCC}HmCm5AF(_Pz7GaN$ zL#ndEo$DzS^m;UIkz40B`rtpMy~i4jk%85Rj;?6ukN&7f9Qpi1J42>p#`r=lr^1PV zlEQuPlz3UhA1yq^!XLvwV4aZP1DH4W zg@8@2(}(cqwA?>4EJ|$Yu<N^qjwBkYq| z3wIYF4pX~ZZ|xc518qCu-B7}5Ng4QPz9NxtI{xLHz;|wVk3d?e4H{KX)P`62^iDjWRv!77jmo&{iLb&~Oy z=9%Qgt+8q8_dhbZZtU5u3X;8lw{ZGgIy;P+#MWj^cP~^Os|qiE%WWeXV;$YU>Vu87 zwqZH^Nq)OK8p-Nv&G_AOc1C6ZCcTPoJlCMYu9~Y1YKOQ-zckTmUe;1+C|?pi5}FS> zaq<`9my?5%?0j{(cBMA_gXEoYvR~0s=gP41ciHOqGfw~_tK*o@8{k%irlr3T^3-`7ky)j#(Kk_-Ep*V9dc+a792d^xTw+gZKaB zwpw35gDBbbR84I_W-e%Kny#iU|Gts8GqD7rvFTcyBb-`*lLw7W4rFa<Ww zVeR6q26B>gu>0&_53+Zm!{q_b3ke3_qy`7>1LYepC4SsbaY%6zngQh$5K>? z>oQHWZ-bR4Uy~N2d68zam*FZVPAP(`oL8r~c*+t84Vv-S6Bs|Jb4uxB;SAxs*rnDm zPT{ZsnP0ybk4+F)dr8zoak$j`(Di%{`QjNN<%6e~*RRMQy@z#U*(=`13oEA{#3)Gr zFI?Q1ez6TAA6UHJkw!kVvG{nn<7oCVFFNf9(_~f$;i0J=^|S9+zjEbU2sTN#kwJWg zeHyKi8du={uE&`*wDPfrq-V>fk}y~xCdT))d3)=FT1^68u|Y`-_dOJ$`IIpTQ}o+@ zpq@lOupg*at@%sLR!zIgB$@V}PdZ;I;^+82hVGIt-%vEx>~{a(zoAQbum=Ktp%qIy z*^;~$!8~>O&$<^%KQDcvCp!le4fQjc@Fw~=^}}VLfiY0_*&Lm%@9EiGl>wqakYFuw z#lvD}c-G>Ddf5$1oBR!(+1RUhNKqYb0bShN72nIw0n*w-Fz}ozY$maiY~TEk=#UGs z0PRQ-L=_9LkduT1A>1UL{tzcT;#I74yMabG%SAs5{r)z%qVlzw(JCoseUV3drS!%u z);>+ih^T)>5N%*Z5F?WEx%mL5B#tOw3Z{aC(@7^XVBzmC;SWt0%5Gy;t>MuWZnz&| z5{SP%eUqxL!;!RSh3qd)H~{H0T|#zs+7A8Jn_g|HUp!Nv6*FFL`!-i5Vh{7A+{i2? zoalj~>m6kqUddkQ9f(Tb+Y(>kW$38KU%#cEES#%u)JL()ib*<(I4;OAe0{qQ%W@0& zf_wU-gq|jA#U5JUh&Iu0SJd$)S>YgjhGs~WRg!a8BE3e05R1Q(aM^Y6@o#^lAC;wQ z1P&{1e=|#0O#PXahbocVd8lq)P(P1j`={m$fqi$Z%T#z^4v{zImsdvb2FbF?NT^3Y z&Q;scM??!A|A>)YUaCa?h2eop?X~uMaSCp6Nal9+lYmsN8_B9s-4@d>AXUiWXrPlx z9#e4}Ya~)0Cfh3;B{QVv!kaiQ+M}uMP%c;H6TWOXH!^0=SoWb0)`+!!7g*>OP-%*q zU^Hcrd|T(Z_A;7r+ghOCoVYg z%tN)@f5e6(`sVbVQKc7eWU+Re^jK)A^nmCgMc+?C-82?T6#3E@;8l8+7poZ_Me~QcZ7(hgPK3toD8u5r zIdiyEFkV!(H5b(e2QK9{a}3;s%E1WhFr+QmQQcaSiK&|LN17YcX60VSDowd@k?E4bp>t58%#{2NFAmj`~(^> zbY9*mzwFcs^`_-f_Ou%(aCT(J-O}H1D6Zy?55gUJh3j`TC!RjEg?;74n$BK4@0YSM zhu(U{uIxsPDdhExNeWpQtNd@hWi)288?e`SJgIw{(-$QCC*=uw?8NA@}!&Ig!GL)^lmli2c=F-#viQHmC4ugrTcGnbMgxhuF3fT z=20}<9>Qke^lmBZKY73-K6p+kpfcWgG8K;7^ou_GUzWBILE(M=SL)vGMeeAJ()XaX z`08GoNUYYGj9NY?p;FiBS~^9wdk>7HH7cES(WZ%orX8uI zOt5&JjN;7VZ_U%2s0Z(psD;aqaTsrKSJNrVnfeXfL|qV&t+x!qH5{Zg19WQ=2f2}H z2Y_~NapNUA_Vq8k5G&m%pPKvLyIYY^eB3-KGOTm2&f8gTX*TV&Rc2bt$?$_wPGO(; zMjP?gR+Ri(38`Y161cK}D!qC!6d1v8OUpB9I#6n7(GTH^JNSc>g)%>wT|w6y`Sn3n z4w`-8ryf5JT%_%`H&IBl1qRG83|Iv^iA~%LX_nfXE^Kc5z^q=WPGxnM0c-^iRkm$Q zCuh^Z^w8**nBS?R&b(^=UCAv9HiH+j85Fb+>J#LwS(2T8H1F(3JHZoG3X-J>q&C}F z{=aB;@^Q^8d53ZY)8*jBE=z^g+SAJlH170s#rsT{^-Qd93C##U90hMwmckjlCUOa~Lmy>m( zK1(5bLXuhBqjpocHX73@TaEI$M6unTV2X2(m#&Go1O5^?0+`Bdcg-<}VJi3)sAmZIzyH(a9QRR1C~MhaaFDac1b zM#=Lnx(}fw4kQ`9G&)?Z%30U*3scAA*z5WC{49)lUpRymlb~^sq4F0KYla(X36Qpy zA2-i;SODl>;q$|b7>ru_e}c`zUGeVoJd|{FeO=bJic^_CAvRqQ_*aUtsy$ayG2pnr%cZ{Z_TeMc6gamdFuW=74~9fzAvo+6PF3!Kchugnso0r#q0Hm^S?VY=F~ZSQkBN0 z5Tfj758<6vi6fZ_k8;bwn-7r25bU4B>5}e62TXV+?LPJCA{?96)rOm0kEY>*?!i=0442r7OC!2_DZjHemK8?8#_Ce%vPUI%m61 zA6|eJ)VoMk;#;^_W>st`T+vW8Dxa6xBy{q*N4I&okjVup6@F>^OWSnvh`0o#0J5`-hJsfN$qP9rE6D!=;R~QZ432+W)qX4 zpp{T8Ri(H$Mjedfs<6#DdCq*`#01uv#Nc7KieeD0>Do&3nA3815@%bX7bd#Ngeol9 ziyD%+#S+}m;D+Vct)mXZohf)OiZ;=Wd*I1z$6^6-1ZS*&3G7Ev&U$&?66A%&aV}36 zQ*Ak?{lQ0H{66)`Zv}TYq$lvhr>#7wERCXgDxxYzq7vxKb2ksims6y?w7dZN3b$G^ zusA*G%1S9u_dFwIGM^3^2@AF^lSI+@zaoH9HZP@b1m-M$$gHdMVQY0IoDiL4vWe9& z`ALP1^ylOtyTkDJxc`)Kp{A(>7he&nSI$$RbmM?#)P59Ygk|^mDze^x)Wb|;-B~Sk z0kd*A?&bU>%0uteC@ra=tq41W@Yc}@wlm0`DpYsD@|^XCg3Y8?ih>xkheT}-xa4QK z2u5wR*s*9;VK(nv*O!5b)IaSNE5CrD|J(cyvKku#FDCS1xO&nW4wVQ}hvw=zMrb<%_bq1W*|FTvInu8=ukWMhHTD6T0u^QIT3vCcES zNd7WXeo}TO8QM}G%?e5CVY0C+#648G8s0xEW@Z=)>v{}IZ1!HRqiWQ-NjXy(0&=1& zjl0M3IsA~t)fZALtC-o7art5zSFdqh-F^KfJ@K7Rjjm!mko;GTRX#lvEw#@|Yl@eniq^JF6r;i$euFoMX?JCCM zsBQ(G!0f}{C3Mqgv8bCj9VwUdhBZqZ0)yOpG(OgtKaqk2c=b82VtUuO#j0jLLCMEo z8sPrGob-wj#coLrN&iDiE2TKmvX%a<^4pt7pnSDxh2?)Bx z?ZhkpCW%Q*Gc=2nDnxp*mXXg-bB@c_p5pV%Gc*aDE%B=H`~sz~o9_XP=Ni-nJnHbF zN+|%@1xEO4E&ii~dPb5oUAk2jdWj-qosIFE*b3Wh{Y1^>2%Ba(wfuS~vCEel5b@N^ zY0=%DsfLSwFKK^LyNxJ_F5w82PL`A#B0pREl|VmW_<8(!CU?I!7sSH6 zvT0ZFG6nFQ5H~`n8D)JjhbYvgY(*SXJv*sNdeR&}+;Q8Hl!PH7L<~44S(+ z!lz(-yC<5fpZTS(GpI!bs7q`C%m?WS%k2XPr`N))x1XbJ_o6RMtB5nFUpXrG^q;{* zTj_EB-ZHk(n2i=*aIUYP#kqM{ld*1N&OksxDTJZFl`B0DV%f2P9x@rCOg)h=>{|&< z@Cxz({RN(F9>6BA);qtCz6%*cc};eao9cb<1egv>smU1@?3uyI9FB@vgzN0^i#jYZnnxH= z>JZqf&@W)MN&Gpuj2b)u#&wE5dxhGV);k+Y^UJ_VX!GDjy8QQX(Xu-y&9hj1LqXd1 z%nwbgDK~K(X(w|PB6I;(G{A*nub)_*7fU4Fq8CJ+?BC~P4puupu%3=K#`nr*>Q%?| z@y<=zBh0VnXR&99NvAW7v&!oD=O7df3#7p2Rhnf14|)-u8H*{6pSUfO&Sr54H!^>6 zBL|8^J~DGn=!bGS{!TeWjD3aXW)y0z_RX+3;K`5BLp>`An-V(AP_IA1DBW))nIdwx zeZd8)8RjguLYVMHt$w?Sj7FW1C(;6#GAG)gh5pM3t+bfA;Lnh9N_|UT=BVKKoSHSj z8Zrabk&%%4fk?g#pClDTMI3`V*8B;O0O&|a?6WmLkfsR}eoopD_ecInNSYv0^~awc2b~L`?FWvAQb+6y? z$-MurIubRuxe#0`WB>Ldmqbb8hc%Do#V1~&T4_UVeV^%J;5zJ`P!K)(x8`3twg=Yv zVIir8HiT^KgA^uCf$YKHuj{&9S88sWex*20e|?|~k+ijLEHBzJ%E`%3b5qxuE4OWdb-$B7{g zFK;_Nl3Hc#bU_O-7Z`ub>Y#m_xmK+Bey}YPA}1{33x;uM>M=i*X>zvb^#oR76K97mIlk``J+v%(o`Pl?hvL%P!eX|dNNb^Cy*2WBZu4|dx zQ3))U%G^%=!iPx7okh%%X(4!$ZTwv_%8b(A@A>-{tFz_Sub?SjQnf058LZiuips-Jz7@zbF;FSX*@y3V zeag2bcg4)idDqcot{?v^5lO(-1ZGlx$-ZT8MpP`eP`rZ_4nGY%5+YunWmtM?00`$A zhr!`CHS2-Qmfi8B%sN7Qvn?2vO??BDpuFR%pg zsv1GiCQ7hwt<#(=^HTLOiaON!3g;%Nvc1M9vjpttNOF49uTQ;^F&I?VsEUL;1 zJ6=gLHY%6p;Z#&j3nM(fX>1zyKHBCoA#eCB4w^_daPqJbMdpao{jih-C6$3>88R9~ z9niRam^a63ZMU3T)om82Bw!F0jZg`1i=}Y-%XXrK1_tzi00KVDMl*}$ax)slO(we0 zI4FBq@uIA#35fI=*a#rMlYXkC4XikLY-XA7Mt#aiw$7CE!AkffSr3%UBbyafOFcP| z%mrK9udWg3G-9`iOyheraK9+e-(j^&7z|#Q%dXcehmI^Jn=MbPRO65oY;mc0D(Nj^ zLYvgi$pay$AXYm=eSI5)OYhliehaO8AoG9(`O3Q!m<{BlM2SPD#RS! zboe!h5X3-x`0}O|g3Rs8K|d-!`@xML4+f zObqf3{aJwjYjb7ixiCdj9J*N*RQbt`@tus<1Q&s;##qx_zO>Oata2 z(_2z@x6V&^EE>tVWZm9DtqqKV6N_S#gdKvh-y%7 zNCnHej1#alrb1bF!WP=<<@fQ&kt2rU&usTfyczmZ&lOc8&@?PbMp?Q8ZYvCULu&qb~LBqmn7F6Uj)Olb{7E>B!!EPguz$ zL3o_VZHx-s{$tNCQ_|nfPeb#%IQx z4Q1V1X$wq8Og1e#1~i7@Wr^1yPDz=VfgPefe`2lJ};q7$SJJe`5W$p`| zN7q|w8`{RdT^fb!o0K*bL30HM;WppR^*@4Wjyfu|iC+_JE9^LJ-WB0clxlE+tB|^` zXyT!hVIzPM($QNj4{d^~_o*Qjx%8P38f|7Tk*TaT`nGWb6p+Qdo}PR+UZit-MZ5(- zzXOxeo(j6ybg`^^Eu#F1LawS%bebny>OUL%0CuJLB4tTOUTD(z7o6)wv&EO;Gfh*U zv?!&m3bR=DYy@~IC;wIi^2Bt`1g-r=zg=P_RHdw#L_VRfy%{)-P6{^f&=|>(m3=Co z;3q)Q&~bXWNKSsGrF_y54Gv=}HD)Vktr#ViTRkRrJMPq8I5D1Cw|WNW8!wv!)vt)! zLV+Q69lL|@@M!Y@Z7-UmmWq+i*l-t+Un0M0eVGg40l~Pas65DSQvnhZ%g@DCrsJWF zF4hC$z$8gmHzhWxy2nvv(2*i8S@V4(#L)_n`_*g@lW(nHSqM(}M0M&AoO6j@3RJ%E z+XmXW%YMc^cN;&*)%h&5E%rBbREb}q7pA$ZAjmaPio5l3XN;fmS0U|e_P7>AheMZd zg4F0(oq7dL<$nFE!+Fm~w%)>$)E|~h$=?$_s0$!E6-FIzsYs6%5~nMZt=*%)c}!4c z_Z?hZP5R(wbD#C$t+@ z9n|Z7yuG4HhE4|X|1p1!o*aK`18qz^(Jqk9a#1NQR4`hk8hu5DA%0cNEhd#ua|gf> zC+^=R@pr7scAfkH9%`hb)$6}|tulU#T$VE+8e^!qaVV#fw~U2=TeJZ<8isH;SN!)$ zf5Xz0tO6zoFWyKg<0u(~_tbenKyc2?Ml&=4#+!Gt?90gdwWO_r0fcjjMjAz z6h!yIR0i#Rs+B^6MQ-89q9r-B^*$GOD^mrc^BDWqDQ((V3RYE7`A?skJyonr-Xh$8gr*kTd{(1bC@wyM9-N7Q_6@9ms%W?hu(gCZol5IU!ce|w zLi*UZt+ykc&l900E1|Zu<`KD-m6?)n4GY7c$@;y~AOVyQMQQ+bX-Kk?8#?tcLApC+B~wRaJiCjDSdeKbf_#JTn1*^ z7eF9MC2_64D@WR7u>xmu2+}?%T^n4egR|vt3hmx|8ESZ+#G^&7`?HPM=)rUfm|wR+ z;mm3P2Rpg|q(&rpPrr2N-++Qjt?KuJ+Wc%a?CXP?(A41CCI-=R39wtJAG;2Kh3vPb zYSul?B+@qky#zo%3Ufjlmc*}_g1i4>9y)E#(j~tu0n-_DN#3p0=8!UJEWB9;9;1T0 z0-Iu>gArjTK4=L7c{H;lzR@%dZaG>2L|Uz-1&h;$;MPKW?XL>RqIxtrYj2yS_wfP8FT!Thu z__~YR%{7NsRoRI7Foj#uff?+%OUHn+Cya^;TRJN}OzOq9MW#YLly)9R1QB&|1@-^$ zmB)rOm_Dt%g4l2(nVY*QxbWO1vf9QKPgqo&t@J8}$yJH~sFjlZS{%1UHEgSev1_eXmL=}N$hSH?n zUM*KPAR?~wdPcT~&D;Fm#i^o2Z>gwP2ndI{O?3rtQ-S5bb;h*n#CuV;B*B;7WE5bT z+aW9S?J%&6C!V;_YlS)Ii1LM2msOCfJs65Je324J1s5c*N!kSM@T42d zz`~i|IdOds5m|fZD%}SCwj?Lr4mD4lu1+rOusRr$HzIb!MzeQ{ZYt_}Z=W2OZa}|J z!rO?=A1ERzotxAcokl!pMSP*F4%4xu+1k{`kB1U2or=WMKoETru}^^+p|m}!1kHRj@}p+ zCWiCsvrwWQFmdg#wBZoUEO3D*2<>w^(K&Gfp`;FC*O|ZrPsHUce<{<;qJJY}=*{#N zE5!Wvx_{r%qO(}UZZbDvOkgseTA$HGj`uLQ^aZR1pA4TWO*nN(g-OhLCv{#s>2 z2E;0DR_z{rAufit-H&KCoJAq zVWewVBNzoD7GG`LM+hj1vv=e3euM2(tL)SjPO6*BkgMOfOiXLBbRKpVdg+~}Ssce! z6L!7Vk!6(f`<$_7ky-E248<0{&k6{~GdTUIT_*xRcrgIg($_nc-xY`HOuFDjY0L*( zvd}T#2H}Xk59uZUGu+@?)QEf|@<+nHyt#6O`?oC`b-7*qd+6l8b&+i_F_Xl2{mp!e^EXSb%3Idyog6?_PcO&D}5zu0qpr2%btoh zvBq50Loh}&%0fc&s>Ok#3LO|-Z5`E}R+dvz;3h!^QrMTH4s)vODuo&CjO;nzvx0_z z_pO}qB})}9O(yIPW1^J=lqA_q@p+%mimr_G0W&t$Hml`w+L~HW4GX$n0#v2|V8S1! zEX4te9DbEoGnokZrTHSc_hafvpoFsvimkO_6ElZ;Fv~RF4Oh{iNX20Sx4f2NTw&)` zjNnz&%B!IL`b+)@tThYbCZ@WSi;f{GocVAwtoTNld*dBBJ9@DV2jWzK!TuYnt(;Ud zO0EV)IhnpduM6>rn34by_pzEO3JrjjB&q?m7hQl_G@|m8Gol={NI3Ep?AjEIHUx}Q z*j*f2T#0glbRV@UT9+UhbMW0yJ-M5NF?s|}eL>=3ke(`1EN029 zR2Lj{xG@B0`fd(}$ypp}8oXWj17pyX5bgWxTiCAcR7)~vQZ)@BT~Pih2diZUC8Ikl zv+$yNOuhpj))qWjPI!D?e;y6T2v{|D&Ua0l#fe~*qzu>Zr+n|ZuOK@51B9lz& z)L?=S>P^2(s$wb#Y-JSlk9yP|L%(9zmno>Nw2!2#cI)Za>$5bFtsZq*@YuEV%pmG8 zB?8P88W(_izC``@0gAIWTpKdKvdTxdfC`pHYkyhdGD0LIQk+2(YaWdC;01ZGWxc?m zxFMcX(Jc3tMHABbynPH*8e=)@P8knTz~O$W!AUulvy^F6EFIkrEp*|`}oo{a&oj;v$5xZaX@}D&AL{rgJeDqsH6W1*}ZHj|D;1k;e zB-4GjWl4oKMm(;Id&3dl)E^uxneV3i(RB+7^Wayz zjinfV0(m)qos@A@1!!#j^X>CzOquk)ST#gs0*Fs9w0>-@k5aeQ6*t>_|1RkDEc`xV z$c+K7dMJAY47zhADOg_|O zw+>v{pCc+>$~yM*Fu6aQdX}7-IOMXa&smt_x^_miF}it%`Fc{DpF3Y@D$8Oy9e5UA za6Wvez`x$}T<~coU#6dX+)R7%Z;8x-3}u^wazgHj{I4z8;+Wy~r=cGX{V&W=BZfN#dX=Vby zOsc5^(nTFbc~@iDHyp#o%k$lm@vmaoz+abAFW9$qlM<^I{rTv%rC?>owLRa;W)S{_ zxU~Fg{H^LYs;J^ABsC2RY#AX*mlZ9gYP`*@&J!ksTWil>??YmI-#Q%R+B#HvrH5Du_2*W6aW&EcWX~D|&mKDF~8{ee^?3d58 zGKODd)W@?h45^~zu!2)-R$>Q$IDcE`HPJ0qT0>>8;+=-3ZBso_Ol6RZ>0?G+V@54< zVqR0-E9W+NLy>~NW3YUFvO9TuDkKETJZY>u>-5#cxxI4LS3i_uM0sJ5aUe!jVM#D8 zy#*Rmv7x$O^BQ10&vjeauXQay<@0)I%*@%Nr*m_wGBJB$OU{B2;)w?|fipF)%dT`O83H_&(VrOL%E4 zscOa5XCv`ZBj<03{KmW(M(0(R;)SZWhwHg!Lr&_m@mJ+$EI%I}Z}OQ1Hev!yH(23M zY=koxD?&KCg?ue|P0V%7?rf`SZz5)y5@O_2P?Ixb^rd%ba4EvQDB$ww6_4p7Hd2h+ z>g{$!Du~7{5b{>*nKCouf`q8P(PUc7zs3qTmZz1tX+*PYRP$Me z4tcsU(+9Bg;MCz!=gkf{j+)4Kv+EBw(M-Jtw?ACozt5vJIBKl&OUQrEqPVj;8_mZR z?jH^SOFi$;WwY*o)}*K9;c?&Kali109=1+^+N$e|6Y2xP93QbE2x$74>Ad&$54q`E z;|cMRLGy!ovcugW;MbiS!^`sQ4!7uzkasANXv~^WFtFjfag+YG%fH6WZo=<{n{q(y zeuZ)87t3$%ph{t>)w6EEm4o=7<5ei;d%!K5B_Y*QtBCu#P^m)syi&7Avzs}hV|oAc zFNM9wJg?lb^0SZe1MtqHa=J>Fdph@?E$^-#Ws@o z{MU=U!K1ToEyxD{s}(fAr-n*Eqdfg9=%3%%aHcNbCh9$IRqdU{ba#7sK6R;mxJQ7 zk0PHfzE!sMns)tJ`X$_Q@E86RZ;7^{w7OQ&y<{;i>d=pd=-@UcCqIZ`FpskjUc>}2 z;d(!L+w`m4OLvxFoywZ?Qhfk(@1l3p-5V655+cIchSNW`k0<>Gu^>~#z>h333ZDU3 zHp=6O&GK>gDy~Xo$!0OJc7AP!IsJyhXyJDRT&MYIAZAy{gpq(jgntqn9(EmpF#Ek{ z`w+0B4dE3NJvvUP)sFu_(uMZS8#8F4ED=3D0Ruqqqa|m)MdI)O?)DTkq+Z>V8j=v=2$N}E6&g;8)+j_Q0+fW_1AQ$&fT#gh|*JA5n;Xs+D@=((CEX*u6 zI00(u&}4ReaNOXi1A~B0Y6lMb-R`{K{`|+nl*#kSdwSz18-uHnbIF(_+Cvv(g ztA%!zbs^^?TzJ7_fVhWc4q5Mw$7N9V2hTsM>l+uB9nIH$byjZ?5@zU9N581e`k~H4 zlG=+=;-MXdLkkOzjCYisUqafBZylTL#1rTFg|euvHi8mcOCw!J=p#nD^fzKE(e&wR9Umz@m*B{gTXJ=*8TL>bD_!iz-lilIw4cY ziq-!9F1s5AwuPZd*D{#<;8bGnIRef&AAyqAKxN29uGr%`)5!8ouh`JTUDsiR!^p|l zukFNRcM2W`@B6uYu?LqM!p;@l{Zn^Q(r??ukHrnL%dR6b_AB9@4^c<2uiY{6`s`_o zeD1!5t)fnRahYh<)0`If)cy$=0vT1NvGc zi@Z9B*-YjGQWiViFqFGY5dC&cX|oSFLu~XEpBxTI11h|j}_7HNNFa4UX_f$`YqV!2-d=^Qf2dh3zu~>MmjqvWo zSGRiwnN&T@#ZrTvJLX{b*MfNWd^%9kt3&N?=f&7XVt1$dXO*fQiEgXFm9QmppVKZ} zZoAo|mU*&V1N_pWAP91z#a@1d6hub=%Wo?A*YayeZCzj>8ibepEpvoy==DXao?n_< z+X;l5JTT@V+&bH!@z>@$D;!yf-q8!t!b`pvv(jiMN4aAw z?&12)9e|%?eMuz1!_JWpB(1Tp@!JT9zp3H>+EW*u`#tv1mwdM0itWhUYdR(7Rxfe| z>-53_6q_}QU1{+*S=IWSEJ!gq-b_qw^aC06)uTk8F1L z9Fo7BDiB6e-JVQP8xMKe@b~Gg3AY`2A}w2K1y9>GDo_!pd%$>%Ygjs!+w1RAIfir4 z?9U8c-WCu1woH4V(V!_ugV2k3wP(U*e4M zi*5SG9ep2w9xSVURi!8nnHT>j8mAh%?Za_}jIsv;c9^zay+cGK%94Fv=;-JjVfXEs zMf*yx$nRx~HvO3mm;&z&O_^Tm6hT&Yh532-h`#?##d+z@l3c}WJcHK4dn&+5g+Na7 zDGYFr)8PKlUhS*Y3XzLS-KLkus$prTxfE<%!@G~e@_!Sfls>Kdy~O?oI8Rs6WyaQu zsl*?;fGxA^S9-zky<|H7zCc)xdVN7v`^1ut)#D;%GK`u00p5JspP-x7LrIt+_poiEIj9FtY2U==R!ciH&`3B{425`GAvH7;N1}spe!_LVC%xwk{Q5+h!C(kK-YC#M^%5md4 zNY3Vg77>6B{C2kXB&IqL@ujUD8-_s%q(bES$H0}$+X36BNK-AphmWLBH_Z?RVNpYL z;P%{?Y_%P-I}Jg~L&*bubR1?+0@d=lO$6C`5iL45`-8g5zpyGRV28oCLtMJ2U<}D7 z%EE~5i9=rg0vk-h#jfq%C-UEK?-(Kyo80As8c&R;QBeQUp&pFkifo|+7k${4*}-r| z$Z9f4@AL1S(Ii8U_RMt|y6t;OXW2mF==k}Zlt?7!`HXXx9idKD$|DIBel9V8}*2X(;Z>c2&!M zICiVX&XSjSGYzmhytSzGMJl0#`!q}Z>Q02B&P3DcE=fJ94f+9mkbTFSs-W{tl4F13 zNvf})oOn#L5A4l)N!_)4mj>moHseLK)$*BkI zq)$KMd?qBndAJe&p?NSF+6PPpQ_=03t3W?LX4E)|H$1fU`*CpL#S6J=n;*Pq1M8>m zQ3dZ#bw21~%@#c^%f0uV_xiU27VR}$ukJ-0Y2n<64PVn93gjOh{ zc4=@Tel|!eAZW3=ewc^Y(`GYVd@eqQFD_%vsSFgh&^ z=D1g>vH{4JfTiL9kB3d6+ABBZAd2;u^QJn_o-6Bf7j%X~B8T5LUZj10n|XgrPiShT zjf7+cWJ;b;oX{7Nb!0kgOBDc_vd-~e3#JoE?rpEOK~3nLySke`41 zs&p(&1Ld!pZ?dbY5t zG%dag*;W^leTvHJBrh0OzB`<3FJqa7xH9<{AtR_a-)R-q268d|>N3p0`P&`FA2Stv z!vMlhDZVjndu^F`RqA4YI0|*cBb`R|lLNv8ri>N|H-RaLQyIAr%Tx^zom%OK^DCYs}>9;63Oz@C- z`&PX2{qBf+Teqpp|Fe67HQzd$4bL4Xb)S#agI;I62|)qoTHhpVJpn={e?((Fz$<1H z+7F8&_$q+Zg*6Cghe1)(PZe{Ac}io(q>W0Eu$Z#L{U1nSEIh*{JH~<4X zK737%86Yg_9@K*5X@OrlK!yI+Nv~-RUJ@a|7E#&09N$_@ z+^C_H^d|Xo(Ww?%FIo$=eya3b1IOzPJNKe~{ew(P*6G92E*``X5&g!~zmMU`c zszb!cnZK}_AD;;34!v-jPb%_sP%6~tNS9N%THw!Tm}3sH)e zoLtNiAZTQ?_H$QPj}_gUwZM9#OAW4nD0xtMAUIi{3N>3mO!lu5q!p}{2Vw3dEu9Xo z@H!4iUMua{kyV||tZ?=0ttFrT1?R}|WfgxVY9B=GkApz*($p`+aoYJ6A|5~6_f}DD zc^HVa-O~uceIMWaS{O9qv^e5)(*t$PCx#j2*ZSZxb|9W1k)v%=X3Ev&NwV5Tz~$1C zn(gt!q|TRe6`sm^w-53^P0&xqvwrW1DGgf6^}S8GP;7An`9~-a%lfk++z1VKV$I_w zM{eVAV<{1esMDp((eA#_CxS&iGi^E`h7T@AnSe|kLMD0~`q&){8h_3;ub>(~+26C$ zm(CmPJxt<&6K}{j*GBGx_~P4nmDA{(J>Zn-3WwS&`_o0!uZrOgS*_74!j1WLkH5`v zOb{eGj^D$#T1Lw}oxWGwZy!Xl7`+nBDoyrr>IB@!{^-j|hM)XG&G9)T{E}1#3jveD zZW^CwaFdxs+!g;P7(0LGP04mzJwo06WL~qUUa2WBb+$+0O$<-8K$+b`XaJ?{2MUsw zbrd~?NWlxphZ;YvfDIX*ziBL_Sshw92+!1NyIDp3&;Mj5>pcUykC}EMb$|4w8h1H^CY7%05J`MG|N7KvD+SnJ$ezzKB+2# zz7PIDukQKjXrBftysUzA{#PUtOnahv+(=oX_K3(b>)IXSe*-M(U+dcKfYwYJUSlhX z8IuG4OLN^`Abe=C(@Ts*G7z!gh!$L`C&qK=nFb5sb`6z{1C!jFGEs5N(7)p8eUUiQ z-6@s9#xS@0s`Pf8jXYALsS|y!9zGl+L{x`_gsbs-bJ97c2s8*s)KQsPz%MR08@u&K za;&eNHvSTr-#o<{NF;h6bd2T!okrFG@Z)-8nAX}^esQ`i%oL0g^YfeS{UYXN1VzVL zy+`Ohn-HVD-J(n#;wcgP1!Nk%NY0#a%Xu6rOPGI6=~&i%RC3aAUCzN!=WDqFN8AOhi~x8F3DyA@A# z66R27ixo^|5kQb7ymvolZ8?*n-HGK~dEM>m5pX7vQI*O@h^o}Y_av`J{Q${g_)W#^ zlrm6hRjdtE!hlg^qHn}KV-03nr zi1(J}z;>eq-NHLM*yE)IeTZsef7exdh5lokB)cQcSAPS=j%qN=oouE z8rM15r!44g6B`4=B|nT017;Q1IMFXz9GI(Z7fM-t6%Jh1IB}xEd1-UEpAKD|oI0#d z97;3kjpB54fo9^1&b{K#aE89Nmco@Y<8~aV^={-PkuJRB4?UdUTsHF6yQ zyh0(2a12T7&KlraT&?&}Kw`cHZ%pwPcDeYJhoLSjW&Z-QZ_&rL9sY$V*O9cjzfuPE z)*RR^hBmuMIvg(xZnjvkeaQ(`EGrYNDjtu=QVwx7bQv`{e9<)(7>dD;xTzv9a=yjG zcaVf0C5yPB;ztG!ho43I1e^JAdPfMyUY$AOHI`?Cl*V3>C5vR0G#%OTVhUGD!U`XD9zjA<>_Ky|PFA5K<*FesZZ%WQs1YAoc_SqipJ*CFm9c}lIK7b_Y`H7^-BwaUWnzP zJt2I>AbqMu`^LeA3zpR&lJzY=Jixy(vYZqjvU86TwFdWDQLc53C4~BvF2L^Cbi%K? zYN&stJbI-33xOHklO|Fb=X*!V7g!pXPkJQx+wld;1ViZ;k3sYsh>`8JDmn(_FUd6X{{bP1k#c=^-fb4z6e<1$pu|^0lGb5S70nq@qFYYb2OaXp zew-gxv{RnEtES{J5qs4CfZ+%LO%qfGimk;KoK74=-`>yCAf(zPji%ydG0)*~;7X;# zaN2aFMRFw!F6fo)SOu~e4u{iCZqc@|FLQO2eZkro!ERY`(k;FkQvWsGW$@vfw3Y1Q z!D3>S#Gf94N(jOnyhm=)LS{8T5TW`9l_vUmtJpq5YqQ4CG^oilux4V3!Ldsv@rQ4o zg^DUE@J@)GuoHtl*V{p}e}+CEtM5f>0LYbFbsKZC`A4HZ+XyqCq{&DMg6g4DT=+&e5*59cBmq-mQa<{*ywdw{+Z2iJp?HGSZV zoCnYt&q48edfR5>r&pJBdelOc+f$9?5)}Z)oLCZBqdK6~!j$NVL@lToTlfgIg3mJu zGBBDsc(GqHJGm7NFTOHhGh-T5B{nufz!u#ROyrnLx{3RBB3w2;*WhXT!5t0^%)r@f zFFzSHJYJV_(n91$(%60bV)aXzN#((}uEeDuP*nylAv4at;Bb|WL$;h9{5wN>=f5?L zmOl32$GVcwi&oIV5x(TsPm&+*?Og@C(=q3@ z6BQ!xNuoLnPw$X7r@vwujxb7uvmS`mH4i|JiOX>-=xkG*i&?6H( zE6S*PP_DBXj-k_lDl0gYVMB@Du}#>QgoKNiC=15pB-7* zjck595sAfOs13#gq9AIa*HmG+*?00Rzp-?;F!z#`+Q?i&Wl&L*8Xwm;W7wcU*pZpZ zI2i@G2jxkBuwz`JYvutZ#yo&>5v5AN3=~&W4=5 zk3-1p-DK>3pW9L*ZTMFg^SavWxy$mD>GX!n@){ z7kk|S4kk9s)zw9vP3$&`d9-Z?e0>_Uke?+uhkYBG8L15@ztq9NNP~7S7q^TT9ydP* zO(RZj_9LTj14b=9(<@&dD@-KG?V`GK>Kj0MQ@YYMWFgrLo+qkCNj#aLu3BclvM|yj z1ZrO5`lt)dL&@sEKcu!eK2Jkjx@CVf)mm!Lyy)JV+FbL9hDMxAgDIi$^bql&c)rD$ z&_LnZfR5*rB6P#bJOtL6agy-04rTMvB!|WKgRyT> zvy^aK8R>FU8)%MxoFOezwVtOQ#*F9rzaUw@Q>EQIDl-RwM$7-!>R+qjCk%FFY@ZdiXRD9+==y0 z&OU?%(qNx3B^S@>13i*UZZTS15KAeaQwt>kU$O9y&2GOaUCaY(NUc4g(srBOs9@RS zS8}4Q6bOpbtVqgP#?gRsM|{CE>YrF(m42*b(k3KCj*kPKXuZW2*f=7i#chZngM?I@6*ow20)*A$r6!IrA%Gl zGlS?~n~^tu=943lvUU?_Dn7c`aAL&OxTNLfqcPE&t`hJyj>N5l1g&$^s6UrbL0nCw2nLJrC zUD~X_1AUucyEz~9kK^d~@R5bl^yAj6M24gwD|WjCe7{p8m!pOW0}NsbVG9tCaq8yB zvthuv4++34M=`|fM$8uu0IRkewkc_k)ZRLFRCeulFgMKTpL4MHu1CE~*%1T^V$Z5$-1P?kK?%-;_2m8 z=Q=tni`S;Ee^(wAf5J|DQQLjr!bs(8AFK$d;uSMYAQZ;DZqPPkruC~oJP{xlIGWf) zm;0)Io0$JsLo~0#N!Ne6H|;PXAY9VLeWgE#uekY$ogIyj1(+9pQ;mh?bTkQn-s*O0 zUC{0EHz>7p)PJ9O01YrFs)wlT=@L=`;Y|4sY&-ds?EkAh83x#sQ3s=cf0k8rvG?>Z zQ$O&IFxes?;GQr$F8W3lv=oPP670?Wa?0u@tim(YK@N`v$y(043IpZ1Q`JllGU1T8JMjD#Lh69 zr2M{iB4p4|OEIR#qO6w2A|P8#=9jF7KGnAE#gF(IW#|9DLBo~21&dMH8rZ{CXU^ns znm=co!HtU0{D1Z7NW3r9JC_vn_t5}fOL3pEDS^5l8L3G9hoQlnSTC!}yhZq93cfLa znaq7PZ3c(W#g_Qu7ggQ@fa>x^zrRJ;2mdSn_cz|5;yu&R&n*KJ)gVxt?gGhdNd;R& zh-1fy$ddVVa<~IxxG)XcVhV{SA%jqTp+V09AW36_$fl~!Dv$k6%p+`aYI~d7YB!fs z>DF7;=H7C9p12lns0_Y{=$9dLaMXpPq1vKbUffjel^x)t5E>6V)rry!;T3U zx@Lpo@WhOw_986q2ROQ;33wjm07ajs;*afL{Gn;RB+U87&{>~t)&xlWVe?Kwpi$bY zoM~d=2vO=bJNomYDM`y?-JBAl`|I?59fz5Wigk2|(=OMpKR_M6=F^I&)7~k!7GF_m zgp;g8a|73Mi849id?Jaun2S2pu%hg#+ceEqr;~Kuxd2lkp zvmm_a+#?+6@i}uWS2xG@%-E_b;;N<8B=LSj|I%&9{*48PFA__Q!i~ZR?F03!cLg`H z$=9A4LD2O;Ldb`{2R4b&B_MN48nR-vjJLy73cj{V0+|F#Y;Xa5a`fVj>G&t0!TU=$ zhfbP)p>FfylZ*Vw=kGvLLvld)11c)28}frIhs1mmBKv)W`0xj%df+a3Q@1>{30_gf z#owtVb=poNUc{vu^~MD^1&ZB;p&eafzr!uvy;J}2ESoZ^ktG;@Y5+QCW>n81l3rJG z1%OuwV0R3%i5yCDre*$T(J&o#oxa8DQWQO7Hmczdi-t648Au|fd&5R%M%HACE4R4x+JeeK8W&{>b6(_!^oqOIJ@U1H z+OQ{h>}~r2ick8k6BurL@3;|edJYl5=GwJ<)npm4xkUzJG9PZPC&+@O1h1j9Rit~! zgU?;!!Cx<7>l#60%;vcEvus?yhZvx8q{)uMaQxY)iC#6F)kllujPLlEjX#apt*tyL znm?SWG*oVCbcR|=)=@o}MNQZ3Jd9Mmq}2?QmwhfuEWg4z+$U|FqhPkHZpt~xM92m( z@2lB?(CS2nIsmc#5P4QKoP7W<7KgCMPZ=ee>T$`~P4b$f_4Ym{XWrK8kN&8}ita5wSiNx7rgaJf$PEBTamfKv1i#|!Mg-^1OBr{gkL>vQ_#>nt zfN(&R(Y*BrHP&crU`FVqDy;d&e>9WrEl&+hT4opcl0Y}b{Nfh3NQ<@A=FfhAizV-F z@7;%tftHyj9gd$+$XPPziR3t95@s@)ixju5gy?dB4FZPo#a+w?WJPI#{~Pty2L}U- zthrLty{Ni$gu$;-pf)?OdFutN5>=oKiAzTh>-yA;C5xd*oi+{Vz{`-h!4ZvDzOV9@ zMe17&bOCUZfIix(!Key1=qn&3XqM)EI{p43-1IGQPMQ%Pbt&TSuf2<;6Q^m+tMsT} z=Pog_F4YPypz1N7=$2+Nl+jWN=HEcECDfMGr~Vp@`D%tQI!HO#_NYV9V0Ye0ze)7Z z0y~DpX}v%+Ru4rk98ukG9Nc74IaOe%sEdOf{~6vkQCuU7it5g01Lf#LgV^v)w=Q-u?&UGAy-`Xu3YXK zL&;CI{?qvpWo2~zRnZLB-bB|@EH7)@EYF+0c4*PSuZjzkP2Z*Z!W}7p(X-aXK3iG@ zP7%v-XnLaSRyq#!!w&w-xXj{yDwj{XQP?ND7!E~zGCe(Hud<>4<3X<-!f=2!>Y>1X z+grw^pE%#t;>p`Wo09AqFN!xhpv{AF^Gw@Vf$erH55|=XW z@m3xU-M`&Nmu`DA+|HIh1SDy>i{i4l()UxAd7c!hR9+Km&Tv`p9BpmlHPFmdg2IMJ zCl<;4re;*B)Q1NA9mRGJB7(nVr!&WGc1M69nb5!aV~ zq4#F5{~%yI7f(vQ9w|@>PzirjhXx{sW@xyc#Emu-kFyAFXDyy{;lriyZZTS9*F77a zpO=+aZk_wkB0OE)EjaHlFkyt1A5%!8`_uZx%p#*|6g{p7-v8ShiSD0J3bW~{e!Qmd z8Y<(Sjrv?MswrFmfnWZTaxqX^k~d?>qItVb1^D4dwf-DmE6!Z0sabGxQrtKwZe~jZ zr>K{Bge|Dz^Y~E_MKh{bXb%oQFuBZ57k#32TDMi=z!YPQNhhD`x z2W#-)kS@ZLqf&5|*Zk<5#xqg)IJLR_)77u1H)ls0?eH5i)=uj0LYfvB%8a|Xyx+ri zo}*UjDXI_FPf8%llcMsxM6$t~hoYDYICd1Z@U*A3Vaz#a9oG=p0)H2N?KcIm|BJrU z46CZ!SBqaygc6zWU$4S*R?adD2R)x*FMj2|AO8NE@cnDXF_^SdERyEpFN3=TZhf_l zxlIClLi*RdARzT&PNbV<)fG1RdRq>3>$v_3by#N2uW(iU3bc9+ zk1L~nh8Eepetq_XCz%0$ZCj35k=Xf3hqSkm^oAKJvGBDOskmJ)em7whmY5oJK}kp@ zpo(av-i99wkP#Af;^rRlE0XxXYc*fx8~Vp<8!yyka(H~V&fb-C08@CW383BvfEl_S z#P^>^cP#iyb`I}rV%BSuG2x4D{BOoCYw*0L2L(eO6+sv<*NiKlFG7{_lIm8x#h;S> z0FooGgYjs45&6*lX_w_fI_OGaj=Ib3bre7P8I?h0TUyVNEd_wgNC!D6J(PaAp}7yy`7ZgaCuWb(`-6@VEZf?xb-@I-K!<$_SW$y)6LN zGABaJvYJsiOIZ{3XZe(w*L1D$_27X0E$G9p1&)T4RUQDG`ETn4_VIo{@GAEWt!fb3 z9FgzKB?r$F789LbTjWDHY?f=h;!VLT-XI1#sJ`k81|aeX28N>hu)T9dV1~@tVr>MA zU*n)U7ar0pn`raa65EXC#U1CcnU=c=g-_T5Cjn@G2B8@ICd596-Mg4l*EN86tBt;z z05-pVzbQMg!r!vvgC{e^AdTlOgqZ%c7_@kN_^7G3FkL1oKu?<5?f4&2QU69AK%{t+ zU$E-Ph2WK+k5XoqJN|#s{F@eZx41h!!7VnXSYFr{xBIima7cqU8yOmBAaved9(&dVRu*|mdo(kH35 zXur#8Png`&v_ePAYCwYt?R_%@Lh(R~lfQi7Jx}eKu)YK5iWhzjl;udToRY^w#cj}w zRT(JpYO5ucy5(M~XsFlzFV=$ORTyEG0P*(SSK@xv!57t4=noH*Fn8@oQ#GDwrRSS% zs}UvV3HhcC9zf@uFOF@x@mN68eZ8P?( zj=UQzb}2jJ6cDStZez=?Se)|QkaA_J`IBM#f;KsRo0L%a1irTEZ(#g()Th33&^5C2 z)ZTXl`WfF^E@01#XnW~zIa$giD=y2%wLjtGspzow}7O*Nu-t|1WulgXdk%c z^^ce|XYM^OdEB}@mt~im9)K%9iEo@&zJ`IA)iMB6*~yM)R_VeZM`D^1rp6d%9KpfQ zH;)er9h?t`HG8a8Hb*OQ)Aqr$Kh0;v$b{ez^GdssCtn_I-hx*w&$IUdh@-R*5m{4A zeSJU@&~ER`>dMn2voo$W*h`G#E?M3RtN3O4k}U>QwQ(W20E~L2x2$*Jp>}mCl6aw~-j2#S4cK5%Rs-`VSLThvkQ0$NUkdiAEVpL$|d3qK#jWzaVIfH%Vxf3@OJ(_d5 z*X=<~zMiVWOMiB-YNoc1YTL(J`tv_?&pjS49cER`uMN&Wgb99cy5%OjycTY(y?8mQ zxNgZB(*F_>LG&O=NfV#beU>yMTG6^qn9#=V-ehHbEla(*rZ1EbM8!#3fCmQV%C#`V zkzl^jAWv6%C764?x7&uzg6SWXLt~B^iy0=nKCjWR!kspp0Gkn7y}YvrsUABXFM~eW9WnhB@q*Xr4qsy>lZ&LgO+UvLsd1-C?iGOv7%&9?!n!YZ= zrsJYb5I%Xs{>97+WXqI<3bsq$lwz(Ffm5n@pe0^>{LnDpT5;u;oHTWL$f_P$Kc#ryy3w zvt^y6W`3;b1@{-%9EV6rMzj!tgl7*cYjeljPM|7E%8F($6Qe7UDWmQDs3iCCOlhDN zUTf2AFz5-*whGoPkjqU*Cac8n^isTHTeKpr>koa5%$+PjgFCrO3G(tnmD0&W5ExkF zY^k}Snx^Kj^?fM9J>+^X*}7@;4s7>KKc(%y?)0nB$k5Fc zeZ>=_zAD&{N)1lOdfAeU78fnnSd({Pjg0fm6g67|N8&the_w~=0eX9OG1u{kTSooJ zKL)rZ3+8nk{nCe4mS~dW`NXi~c{-KqMhaYrv^RO}jdkf_s>k3?8sLuRn)2{)@_cJF-Wr72TnIXwC(UrEL7R-aB$H08JqZKXmlXC00XHYT?} zZAwK>`EviXLvLYopJIK`-p?Vc>lAhx4;;;D0adU}s2Gb}=TOCmUM*mETC-#q(~@e@ zXA8GY-g&LWx18=onw-2`C*Y%LJUQ}-R{!_}mMO-0zkMKDaQP%ElUv&~P_4D1e6jZd z>}R1S?2FsuU3BrBhJh+sp01QA1+LTJ~9pVka<7i1s6 zZdImLIfKoBwH%CeE&o{_PnD7b^hC9RTm-VX8Tn@Mlf#Yp9oWi`5=E`Scqpl1k+>5_ zY&M3~)Za{EuwbVz4e3K3w9%+EtIyC08ZoF~+I8|~SGwv|BAsfuYd%6F@Zey(UjA{} zlAUVkYXn9fr1#D5!0e}L)Kb_#rkUYpc}% z`yzbZ;^HDqT~obt0w(Y`2W;Jypov($`vt~=^D?o6L9NDm zu{`r|r+4?Rr@>Qbjko8un{%2;(!pj(tO|+jeX3p8-L*+$AO0kGeuDDRB@gZdkh3VZpY=&x$povgi8gF%}>x)yWcMi+^~u!N_5KF1fyL zdms#$K-YB>ibsn{f%vP(DIT4tNq1*K(@-hH4fDYlz^zD^QNdE|_d37)HI!tGr$3dF zRLK-HAW{Ywtw?}*Y1Z1I^O&xU&r?v~uOH8=EFl_r#w5b7Zgz@RTydtPd;t4P^qD2t ztY3UBEpG`?S7?+bT&h@dcq@lQ4TBZ=6PVZRL~D;3(8HBJGsJRt&sHQel;p}@w@+DQ zc9)zViK&Hdc}ztMz$zbR?=TO-c-tB7jZdj_g(37kZ`qUa7kbA3j|y>g^mO$9s}&Ru7nrhX zDxs*cDJ6+#DI^}0JS&Ay`x;rZb+kW%Y}N7L_;PT}3A3-(sTRDZ)2;)=%dkG}JrCyl zQ1)#v@s-aV=v&%B@A>?t_323__X+Vvh`Dhv!i{j=iTF<~Wt6bhtyxn+FbOgT>L`Qj z72n@^v}t%?&Zt-HTRx5IHmNb<9nW5DuPqL{v@X%Gn3YkngyJ`6zZdrnu58+JtI#OL zOYVBOp;|ijnC7(Ldc^sgEEV#!2sxLJj*ep>_?5?p{E{T|Wf3O(!w>)7S<+vRWWJ6N zK{lU*m+R7$^;=YC3gukYLlL<6=H|6+$&3@&T6~F!!s3aOkgVjh%R|SSSfRS3MeyXX*)`HV@FXdag z7~77ndnPDNBycYbt}*Azz(Ll-T+ zsW^yw1G2>gYqD_fFVXe5Sc!w7YvH6UWOhuZ=KKDNIVhf7$}?LeEWPlUF z{)~Q5S;voBv}FW zE!stn@e`??yGT%8_PMBdLBi)ADWsm_fxeEoBX}321=+q!k${Gr8BDPOVjT3j`Z6wpWP+Z z!~-!1Zr>uAWXl?#qw_2A|M;Q134RAxMzBn^ky+kX8SN8oqW8<$ zzqpwIMh}-*w}BdWk4JR>dUac(FsCcua)b@;Zm+D2-96qiDkI&W%p0RqUD2(cXEmIr z?$AF_FacXO0sEfZ$=wCTW@k*3PeDuf+#%_lo!qLFJXEF5&)OFQ^`+UyX3kBsw@4zj zOz9mFA+pY7Mo0`T<4&8F;5EaF&7-|JlClh89~EDTRxs8XsSrz6b7 zNQGhR3#*j+Regt*HP?4#*yJb96u2+XNsON1zRMq0pZwbe%_KY_lnP(Kb|w1%{C6y* zWBnf+K#a8iS$2;Z`2Bxec8~G@Rd$b!iG}umz3iSj;lIl6eYN^|u|0ur9dWzu_+DMU z`(0sqy%MbE4~Z%0clHkZW_zg+f%$N8f~ANnhEbM95ZeB7UXbvZAkI?ddTHZ2)1OH5 zI>z-x$cst89eYw7lwBgWaLV>HN*l}~$jTh+DNJ@oJb@oRcp}+*4_eyh^&y7Qm%9-w zkI|Dg=l>0=F7JI`Ejp+ti=f@FgB~uqRDKt-E1Mn+Bmvg`$M|=b+vDRT9FQC2W=0e7d^NBQ~am?P0Oe4QytevlObNwA3UmuB! zT!ZfZwh-D$~+eW zB>5_4Ed?)lM4vso3PQ-*1p?f6X(|T)xN^B#(vWE=%*1?QF`hle4*uFs>-D^r@s(&Y z!-)cUb|s9cX@2*=pRN+oD=G7m0{aUq-t{KPU00`L{mKgoi=T2x63mSp-o!FuX<~Qy zX#Dqr$X*yEVf+{N%65}hD=i|h=X49FE-BKCP7qVTz+A2&c`pyum07?T1&L?6y()49 zg@VajlrBS4+QEiZq-w0)H!eRux^0^%IPZc;O36P5Gv>~JPx_ZCS@lRMWnRMT2)ug} z+^<<(1kzF0d+6>VkLHLny+`99h?AMKylLX0YctA5`nz;@&%>X@|4c{Y-_UU6sY4Lw zB^L6Dq0(@dW_d)ww8f)LF&T(-L-~smy zxi0sDyr$qNtRP7(wXvKOvo1)$G1fNLj@?=^`>Q*YQrYmdgN=-r;{X}X+9L?6am5ZC8&tbJ>GfWi|vy&h_iu7F?eqI&7B{Q83 z&nR|O1^G6K2iy6^{jb8e2fGNIS=Z& zY8eWthNi|8RGBLZht{ExmUxO!BhrQU%Iu{CwZ8@ zg4aY+Cs%>K@b6~x-ux-eH-e2zE=OJTkVxH&Sop2YtC=vWfD|5q$t{%MxAxm$gE3Dc zo81XRl%I2E@Eh&^HhSh7bRVeB#LkVe+`}(egG$4=oJk1ou%Yd9b!7rjq^xQfY}wUo z&;Ae()m$WCMAhIxP>l63ATr7?UyY}g{1-VyFm6PoyojwyP zNTMn=_Z8x$<{~5cIS{C2H5!JjB`sp*af~R|14X%Os=1rhEv@1rD%SN{UK5@J*Gq_| z$a1iasJQCja%?4HKgocFW4%G{d=H6MiThBlf$Vx{Zi&f?t`$5lFJxWt2U_6c97^{s zR~G8GR(+)sVki>V@kY$^G?#hR{o${u za6^hy=>mJrys7-)*7%@;a?zdoIlBhlOCk-?g!FZe`j?gQO&-wx$b8V>m z5_+vF=KeL$?EZ)&HYPt@7E{I5^h%DDiCD>HdFeO)T;jADNQ%q^uET4%9zG+x>2~k> z0;L-eZB|#EIXBlg`(;TE&UmI;p`!9kE}bLxzzocvUkL5B;lAJh$GTi`eGJWH3$S3# zj+XR;RLm+zRh$iPunKz8Yh6hgDT^H}3LNA$d!Ax}FwNbO?boM|%ROSG)jRVprzk$QYh~7a5Yz5UAD9sp@D|PSL@_OeWFG!4S=usS z(~K{}$I4Q{0#`gT2OooOzWk&v0_h*L^1}cOh$)cUg&e z_A1z6khuNOIP%~boz)_WJ0lo``xPrB-ZG4Rk#IuH%p^SEMM!g{{P9dSD{6k3aUzA6 z;)Yn2*zhcA;SXKBGVU#f^3O<;AUzP?uKrj)3*>Y=_>QAFW4Q#2oLj!@hTIV=K8F!m zj8f1G=A0aST!8H#{~2`wp(<_>jOhep8?6Y)gS8&PN2x6_0 z!V#aAG@b_8PJ=A%kkVLDl*aKsc=0(zYP&QjxZrhrj)X2@_h}k{5W8kZ zTB9tjpdrjT*AT>NdYQQN9&^6A-7bl|jpuUdG!lgb?OYx|+>SqFm!OcL>OBXOA8_CK zE&G(gtF{R)HA1FHcth^@QE~sEb;`lx2qluAe8NE2Z;8{X)v>p{^0qd|PwI~|Wj-*O zE}%w~b+=s)FI`{gE{OGxaxEbFxMW0cWad94>H`Cnrnq)+K&z+?h4#@8j?NEq8*`xV zTU7*}N`Xio(<;m#mo(DvPPIHt);e=}(Jrmmr#L~7xWmv_Qs56<7SYoU8~uO|dH6<~ zy^Rh6bjUWkiFONNiQ;W8%q+R|2p7ZaaTS18P0AM?)vd+1xXc1gR(L9t;=-FE*|Nl> zBE_y`c|b=ZPqk6s<$2HB<$Kp?TrOF!7;3l{idl-g)axE_EB|?=@q3 z=kHj>2xD|L=gXz#eTdobw`Eb#bZQaNPUug~oor-k^p1+%?{7vrkbeOh?k zE+oeC6lEqe?Gq~Au>pPs7t|^^=NtsOH=IYQ>t8We^vNdk;T;IEHR7vhG}fN&SAV!4 z(@y)#ijWl4&^>4zXS*)CZ61Zu34eI1YqknM==?^k4hS0j!c$G_vDV=|_H@$)1yj@r{*if=@;FNb-SfQiK5d3tKkmJOf+ zs$JmEQTs~aB_;4bmiw9F=2Jx-88GdRR;nRxzZ z7IDH@5rkvxZ|6KKlhWsQ-_^)+e8`D*bCHjfX5poD!vCBz)+K(O+4&K1@EhFLPu%Qq z-;+PH^TK_%4+z?CF5@oGdleqm;qB9(#A|cdX^_Vscx_o_)JpJZuFga>U|35EDvg27 zS#OE!2WDi5buNgf%bw;J=pQXAK91N3jebt!1Iq8mnLi_ghBK$~*&j3G_`)gSgu=xC z%U7)2A&o%=ej3fN?h5R9)OgfDU#$NpC29x>)nvlf!*3!k>(L;Gg_+-3!0q+h~~9(w%0n*DmmXkC==H;aflpmXp&TNYW;tQBQ! zk)LN`enb>pjc_E4n7Uh7a2J~CbZnAXChbNmd%d8~B?Cfm47-aNd;WEPifGFmJ*{>t zUxG6ERSA;C8g8DqTjGM=U@#gRo+B;%rmOSo)BCfyL^5;ViSHeL%>^H}&?&Gm=RnXU zZtBaty_DbQM9G<3Vo&O5Gi3N|)#MOwe#y0JVC`p+1|}EGBN6@x!5t&vDxak{MNT!K zipNX=&2Cs+2TfKYOU@6;LuOE)Ak7uznK~NBL{6<&V=T!{F;$@=fKQ)esux@{8QaWo(J5DN`o$HiT&{zvRb+3Ce zl{sjC$$<3pmGVi9*UK=Seb?tWdwWb}G*Xr*qvCZ1CcpZ?KxW3kT+wRbhQ`2t&ahF?Jjv7o|y3s~akBNuG zS>;+fBhNJ0%^k)qP1mLs9Z({(J#P@!kxNTut6895ysjPn_L-B^V0@FINtH{Rm85x#4lt~ma4TQsQmEBZN=qSEHM5n zJw#2D6{lOYdV8){rvD<8KSdwL6q_z#-Xo?Hk$o_j~)y~_=UpP zco664vA9PEajPC_I`sT^_2wIvlaj-lx5=7c>VPKCJeAQO1&S%&O@npbOErSW-w>E; z@8zj-)gVq1ltSihh$ZRzcF%_aU#7bG9%X_V5kV#hWlbRViYn0Go+glYAGV;`pw=d= zX{#a>TdtoNITrPn1wH&@9erFE4|oVeoGx*>AoK3gy#ylRiUmDd;rFU9a=abCn4(cb zCdrGt`QwXYWQ(FTM8pH%-;-CvwMmPT#OnLfUDV-9!SNJ&^WielIu}?BPUK~LQut9h zs;0@lNOlKarQ6dxZ3~r$EMg}pSm6DHn`J45)I@EQ{00`|?dh(Rd*5h%w$W>WG$H#~ zOyy%fd#;)<8Ss$RearT4{-;r7D8ELCrmxZPl5`#Nbv_j1gE((kvK5cDa*Y@kBb`pX z^Cp9SDqp%34jUo&uyvs$>1LjXw?IP11n*Bse)E2ZPKEmo^+y`GS2_Y1y88P;T#m?g zFe#!bwtei(9dIyen9%0R+5Hl5uyoOUJFu~fcVIiP;RWON1(AyJpB7FKKK+*m!tZZ* z<9`+TPB4YKdF3JPV>`gVHP8T`ov?N5lr|?)@+G8gm;0DG^3H{e{4KHTe@YQ~y`R;E zj943?|Mdb7#wwr;;+c$tSx!9c57blpG|BtN8VroJ$Rv@B(m$^=sn;t(3DxHvxq>%5 zBv^g+;TMKDQaH*7R#0MaAm|dJ^Gv^jNkw1-(_g<>DO6dfb4O~8?(0zynj{N#V>b72 z;g1?uoW!{_7}hazN|BTWxukbcpM~;3JrE!{MtxdH%6*tnY4E!9p!Qg}NjAgi;NH#k zUfpgn)GL}f9 zi@owDIW^d|+YCZr*Nbt5zhHAP#3aS{?X!MDEsd9L8!`y7*$OEc{<>M6 zO|i-=#I8+Zug_+Hg?Z~^q8+aJk-be)QhdC6k3i--cSL>EM{bSIv3A0S*?d!U%-i+L zyN|gFk=-iR0;?>L$8{xcL&?cJ{rY)n;<!Y1e=le?dOz#SS6UQ^P4EtNu9a? z^Mo|}=y&3_%Gd#sjECF!P1?-cqly|`<~ZsKBL?LutEdj^cAgZZHmOaVX8ihOO^cL_ zWmBya6Qft+$XJ^MPCfK)yA1;F)4zV)Y>3JU!1X{YEc|T>3Jzs!^4uysn=-HzuA^X!R>L`%lT5ij0M+16UCx1vSlxRNywe(!!69XbzB*gW%J1W^AC?=}IJM znIQde%lRF)gu~@9Rbezt^I;j%Mq-K~#afCreFTEi=yH2RhoxN8)JR)Fag{+~fZm#2 z`W0;W!du*Ri8L|;v-g3it24yKykkL{nkqLXkc}<}Afpy6bj6Z@O2~c%Ka@%N#^otY zEiDZD;^`|6vQ_GXD!g6FHCDN*4qrBnt0z0J1{rj{f)Aq87Pd0v zCHT0E;GZ;UoWB-0JM1PBok~9`TJV(g_^BI3eELsPrNHurreQs0OOt?B>LOIs3w{q_-nLj|}kOb(8;)e28SXFk)4VO|tY_4r) zd;7x9e>1Sla#-#JmarDd&%#&rvbmyOmD!R*3+9ftd)da4OaUC03b)GS?5}LpXG^5= zCV%|;0B&9LzbgmQD(^&J=!Wea*e1w{^70O`a=YOb5rs7N_cZgAj#fu52qUSQV1;>JEs#sD5w_DurdCbblG?=!CSVmZO8UNSYm) zTJaPnQ)8@@$z+7)-7fH@7JW*x7~ajc2(|eE48QVV?0rq>!bG_Wc8mXt`q$K|d#U!L znw*9AsMF6Bxwc4OrWVK0_=P|!CMyl{JBr*@nY=Eg;5{cuK{`()D_4{WG_7lzyA;e0 z-BJ^4*>WOJ8$T4cE0`lww5$3(GnSF&@YfjqZYJ z&D$JczryK+*Xc=+g-xk>Qek|EYN#8MLfhRVJm`N;9o-rmjMM0gaG&31US?>X#Em0RC*#l%{9@3`kW^eZq-#IfLq34e$+act^2%jh*T~ko;%xT zPSJnIHO-@jV}`bW4m%f8ag-r^J~#7-7i-#qKvP?Y9p#o@0siq1gJ&C|iA^+&3`vX^ zSpb}xJT7h!0mmQT0R2;>%?{UL*yZj5vVem+VkvBg{Wvic$w|0|Xg=Z&n_$euaZptJ z9SvV{;&kN=rs`8jad6!699C)J)|_+{Kln^pgXPaFhgxKxwwT4AY`jyiq*B*+`d9>X zYQ5fljSWV0N-=s@1jG=iC<$@MjRceuUq5q*aD%nP8-1wB_8A{#3QK+g!lSYMmP4f3 z&7!T(=2V&2f68m?U81f~O(BFdrtiP@2As4|TYci6Hh76XL7&k`qne`Tkw zEOYF`B*sV~oNhNwyEK)$6Jt#ZPx8o&8JKvS5zc$B1sd?ibKXuts$muJ&o9G_U->g_ zTcA&$G%#@phJcyfalnZH!BmDiZPX_TDNiuAtijBx!*m*5Tw1a}BDPUFGdY24i#XAb%Ay>q|$=3(Y-9_Bnk z_vxx#yK1k!wp7wE58;R?$U;e{Wl})?fpG|&4d=n~Zr`nvu8X%FVx7*W&s7XOR3mEi zn^Atz)-2aLmtmf4Y8j;rf+rr+4_oC%qiYzfuPmgsts5OSeD|VK@?}=qfJXBj^+OLd z(|-!NEiva67*@93od2XCY0^FW{N;=($8yH2c$S0xQ*WYT{DV^U&(nO;g?{lP>;)xR zMw?57w`{(Qgu>VPiA6V-iojLk6cPO=AvgH~4jE*-76b1Be!YWK{y`%AK#xjC;)oW> zvOMuywN#Zcil#X7FpTO^^F`k*q6tCRV%&u+NQ=KUqQLYw>6}JZ5nbQ$tP2;WHkT|W zpUjaH$wR=T5oh!U-=1yN|7Cirpkjbs%1UI8Z#ko#Rc@X5o1-N#9BoKm!=3!d3;U30Cv@tR(O|GluYd72_=2GSdaQ3>8ZP0@Kd8)J73A1J`UMPhqgcc{hv zgN7?+GkEx&d2}d;PB)W>${ivG4xM0iJV>l@Om!ZEiK1nMqWG7vZ|d7@v4zm2!m(-b zOgI6}G!a9Fn*XN@j|x0m12$1VI*13&(wd;mlQnFB)%wOy1e3UqsLp(vkM->l2QKg z5dy+fZHz;D2TseGf|@)3KCV_|{loI|be)N5OL=#QXv6HE0_J*0^JNo|L5K4021dHH z-_?(VJ4+ii&CHV?Kmn)#;lr7@E4&ekkOSeBg(|@-9gO}mu4!uiKoxV=M+1K%jo*Da zR~u8al;L0Cee-epn)M)hGJs`$okJCu>*)LfX5y`%H{84XVeSF+oA6}Vf4l^4D4y>t zuFN)uRr=}Oe)USZ080##E?7C@dc^(q2IOACbjw_(n=f4DS9c3?pMvJA9>`g+g?8ul zkB^L!=XE)UxQEIVv6+>8i4(JhlEi!->14kyG-p_p$OBFisiimH4H@|>kfzdlK1lhb zFVca5H97X5=D?<6UqTP-zh1DJtcn!{6Yu94f|E-b5O30+2Rouo)|yJavecFMZslvp zkRO0vIe{nncy3m9W-v#VkNS0{*DB(RfX>Xhl+$m_9ACiaPnTCsx(vDrs#Yw`<;eQQ zZbN0Yd6K#Rm+iP9Ow4lDQLYKDzWrFcnuaumfju>|!;vv8cLhu_BUnJgsb1F3dG9lL z)|Cq%t*09E)DNdSkY#ZXqXpDTY>fc0S)oU{6GuPYV9&eZw(*{j;UpREWsUo|tB0>({Jg z@M!yJHyWc2nZ|SUypOZ7RoAIya@t#!bq$3H-%Z}s#)io=Fox7f>r&`8`zN zt^!)!mp^3S-434;^0E`(+r_=}VpwI6WOv@4gBFH_*+HHZx%#jIEhcXsar4^?tuU+& z-RoF}Sp6<<2MgQ^^S_0@VMFv!qI$9zhcRCb&Pj@vim+*qq^-n1 zs9S!>8~QwCtjj2K*UqBVUC7KO_l6=>sj8#+dG9|=tLqs#9>B5>sBh46DglT)voFas zwG7{(Fu+i#(!BOKNHGFk5XqNvPdlw299_ApI{wZC!f!_Ja6=bsxeuxm^+J{lk5 zm^J<&Sb1U8(b6)+JJ*83+L)0qOy7MUw6G>$_3EBZQkVz5J4x+btNxlNSs2Ye2~yKL z-Vd034cRef`gSu$Yqhf|Uv|PcnZ+O3Dy~u%YZdbnUeS7j@G)TS7fZI5O_O|TNoP5~ z;?pmGAV><5tR;MJn%+@sl*V)?BgD$cpe+f=;KK%0vJGM#lR)S&4pyx0qj&*e3Mq{J zJ>1wyezCY3@M?^XhyAB#fR;QqxV>$U9a}^muWS1?gnb5U&SsJkQ^`L>MGrZ=1MUis zFk_BO4OBueG^+mG#`@9;TRgbY%;vf_b1R@>sI}gj>w;Yuul<VYLEjD0n{u~%T zM5Ej*RonST%5K=#Jb16U$W?|W9^a4ktVaoOC+FUjN;y-rlA>+nnPT!|z%EOVUCWiq zFZtQ`?X zEX9%Xr7`EnFCg?~}*+!_Lc@yh(BG%7IQZU1SUHkLM0$#9b9Uaj0$B84kMSi<(b0>Re0MV3nim zTH%tLlXS2>gdOM;`*d|5pQ%_-m6Rz_btzWuZ=_D6QBnlx#8Y)CcB-AIPT{WqhAQiG z0y`e(@L?vG}&n(TEUaWPyJi|4c#9v~QYT_M>nm4n-(4 z`rUQ8Le)h6Kkq~JH8@45xPAXZS6|vMBvUR?|M^p)Dgpvtog@t4xvl0_k7tR1T^(QXsyf+klDaCMLD|Dna@D!sbABZkp^oJSA3c@Y`M8M2XC#v4 zD7S2^ZOE|3$>omK_i6Aa*7wDhynJG+RyxZc^M75Y_sRYC4Yo`=DU4Hq2PmlEOKQk{ z#C}`au4vj9q|Z0)WAju@x_nZfsh5luSdbvp-_u{;=Vxevkxy*$-q(UwgO(~Rzp#_E zUv3kf)vz%_IwPWmCL%BUZ=b!}cO09w8+B%;) zFt8oZ8n)A5ddTe>GPt$Z(}j;k=H-24A3CNJ< z@0JV(+XZG1pY9+M3(6MGtHzivGE@UnbBttr9p5ID&+^(LshQR)NOX5REAA)jiLY86 zi}$fMlInjH!Pj&g`e9`E8bd3BIN_C=bWl8RDp^n|iBS~dPxrF4VPlKHiRZ7dwv%AW zno(6g@ zT&bELw5;h`U73m*6^{I+?BO$AtMs#BN>^-O5jXxP7ilY##gcwTS(#p5w*G_FMD)EB z48p(^DXI$nQndNYhD*jOr6Sw6lI^KyaWxWFcT#~*B)K|WttEyFkc*KrH!c8BDkyV& zU=ZuQnv@=HjC{nrA-6=AALR&CZWgyHbBb92VyeFpUQ)=SoHr_90yZOzW zCpUL^vdV7$PoNCZ*x|Ux{m~qKW2!Pk#-CAB-+;Ch$G^_6f6C2B%~{L*mDCbZFOE;I zolc^a^#8tx%KxXG9Gu)|rgD%w;n}}h;46tvr2W@zo4EE5n%$KUupryzz8m=$inZ#6 z?BXtQnya-lxi3EwOzl>#qi(1d}f=Pn3PFSs3#adW)r%{OIS#?DTL~xHZ{D zUlbU&yv>j#{D7`G*J7?;mS?EhtPx(AP$k_r=qH`qf;)FzTsi&Leb_%|-(f(c_y>xq z=TGIh@uAX!Z+{)g$Qw)f3qM;@YyIvTQrk~36WyW$R1(LeEJ1CtLMT+Ga_UhTixs-Y;`=KZv1B!Qj}5TyEN6Wf(c(!9Vg^CW`n6^8{Ver;eGEmy^@rt&wJP1 zBci#hXxkTWRU3OFSVU_@yHNPhUAKY34DCPs%9Cm{p`__%-`ua7{-#KMSvU6(=#6`TNbu!_d3eqcG z-VOdqAEGJ#RYx*JO18)s8Ayd``D&(ofTzGE+3^}E&G#urs?|#BeE+;MpL7ygX`w2H zKr5b+ZzW=Ks1PL}`LuZn$Q;^=6pV%SC%d zhO0nU*+!kZr}vi3gF;z&2|s~>Lp?gR&mZYsA?ML|@^N=fqq3RQ0XEib39M6nEKp~l z>8o$X0&9T0xE$mP{2Cg%RR0ri|=`NSCEP z9G)F4*~)50XE#sfOVCCnRWhwqAqT$tqio`x4#&_l+89;eDy<=Y9?SuU2qU5YtTE{cQP zZebtUS^XTXI zB$)&X317?m3nI4}u}YQXk4s-IuvcuFypfm*Qy9*DHwgveWpIg44g89{vS@`Q4An|CKf|V5r>fxsw=vN>T8%0C9Sr1Id=O{N2vWFDFCm z3}sNivNXr$UpN~TtND~WFRy5|m1c8kYOsQ}D|ALAzL*0Vuk}oat>R|vuvYh}CBpGf zUw5>~9fuFa9=+$M$0rmo2O%ty>)1`};Yd^S10TZlj7kU>lO_I3%)QJ9vOWCRCac(d zAxM|ia%_Vp?C%?HK-jv(4>f+_ZB2i075QH5`*+9u(=*l2oV*padDyss`a@a3Ghm$F zYeV)Rkpgdqw*t5d)y9y-fz%f83GLVKr^R$jI-u%YLq3A=uDHZK#>Kb4?I`#NQ>d_i zyOl3%r!UqGZeQjK?1}Z@2QT-*UqD$mo^|2OUq!IS;?5;6*=!tRN()lI?PI=d9zww$L(?4J7=~ z1*WtX?HUPmY^TcgloTNZN%nD2W~%L3Q5wnUy=s$s`8tonIxzqDP8Xq{LiH<|5Karp zc}ta3Nu%K63hUvo$n@zAnlyDkirK(5skQq3fHm6kRR-KILKNp z#O7L7zFhI75L2a@Lvma_^t{HE9S3kj!id$7afoDl;R#BfkS6giN6AN1$DYh(CHff^ z{5U0~&s?IA^o$`?=>u(oe9zUp_dnB+tP^4@ZIdVDzC;^4(V zIklLRzOTPT6wqwbRM2L8b%^IK!pLt{NZPl`h34`8C&1Rj7y-b8(*`U8AD}229UpQB z6tyw^@YCg}&e*4R48`r*rcMh3lL<80xJdQ-@G-H4^l%mAe>>2dCxR$g`yGpov-qdq z=MfhC_!f*CtKFNJoLB{hji+)&6&l8&vZGRHt;`7ZX^S&SLo{<8g-};sMWhHIyE9bf z^I>HBZt&rcHS-|~#sB!z<>ZKix&OsEYpOG{M2^c&q%+^jXn_GNw(#F6b<@Vw5mvvR39ss?;vJ2Fj-}Wmx4P% zrq!EQj(<$>bnYXtaHCyG36}eC=Ow?)wJHP9OEQ58_oocTF&;3Zgn-}+t=<0&HiAZ* z(wjP?v?8xnyLVds7CpH=!7;Bhd(*P$LlTE7_0!7`i1c7$dyd4?CgVFK2ZlrO+7$Np zt=IjVtBQr>H%g|dDF$?bCENNjEwR0?h;QaO!m9QHkCke_j1CmWCh(}eWa=*v7!w;t zrojhpT9hqVFdNA8a_X>bzj2JEJcsEA09o4f zpU4cjGw5d(BfriPQ0h%-HPhtNF64Hz04dN(xGLT%r?%8u_@^TUKw{m&Mtj48U4_Tx zB3TvN0>!`icE8s6GszY1oZv{ABLQ_RGkI^FP?e1qfBv=f?R_fk2P`mGjtj;Q#*XIJ zkmA4ic#g%%qr^$|VyrZ#7G*98a;jk5M5c+f%G~F)JZjuEG>X*3wU+q@?&4z}m%6lN z_!UC`8mZ`~$B2>|T!r`6(H2Ve{Kbx)of+a3IuYK!&nP9zr5={#91iDH+b_;$pKfXz zijC3@sWSFu*j-3Z)akF0k$d%b$c2O@D-kHu2OgiwNvPUBTg3{qWv}csEq_I63s_xh zMoN`C(1`BEk6i0Eh*MgEx#%dBrX(E*e_hm>ot3v1t_=h<0d zzgDJT&%d2OWMKLBwfe%>osvU*h4mfI__(QPo!*c4o)m_98aa{iN|wcrOmU+$MdL+b z0u@X%!U{n^GAk6Y{r-!sXo;LwhclKSWo;qn zh5u=A*S@Fiv~b6v3;RErA`z7+1ZzjB2X&S?zpt87JJ!Ogszog*>_2Ye)LVnq<+!p` zviHzvr`c>YJ+sG{OZYP^3$q{0Be6^5KWbHkVp|@eued(Fa+2CP?B6Siynla2tDmbw zgP>{}z2h&_D3e`nH{RKl^K-C?G5a zP+D}rqX!=SY(v`|m4lK zc(*{9@8HPg9%98gQpkV1+zy_c9x7+k0t$` z_Iqt6lIe#;o91qTrfF%iF))G};wZ8F{M6C*9q1D6=BCA%@;&J+7vz+?xmgj9l`1YzdC%*_bq? z!cAGS=FJ?-oz9M#9lSqN2_(HawRE(0D0fGL?;ctWiJCBvlb&k>=e-N;cDb7unfcWr z|5@oK-pRf9qsGePHS)fxQ~51LfwiEQo@dbGHY0VpIDAxhx!s<6xDG{M76}ePg18V; z#-z-e8d?|cc;GfyH){!~Jug$z$$5KLe}6~|D{st7i~eGvQlJm~4khgN%gGx)k9#A* z^F@!{e!p#YQnF8t*9GpbiC}f_b%7l9P_1%WBQ9SMRo!Q0b4$HvCETKQG?NRN(IRn1 z3OGZXm&`Jl&Tyt-5o4w!r{U{Qz{cV_1qQ#5z66z!)6U3wi#xHfYdqN<+J2Jm z>}2p=?B;CXwA)&x(IQC>EHgUR%C2H9#gu=8?+6z$I8^0^yuYifqg?#0F(sF~IbC~c zc~BPn80^ML8&l8d20vYuQSO^v-KffyInY^&)hG@6jTT;ZSS$Nsnw_??HmBGq+3y*` za*69iv-j0a|G^Qzlfeo4;g}k4z{f6n?~`*bbNzdBUO^1+o0jCs9AP##t|XMysYV2X zr~@^AM;Qxm2M(dq@Wftg&yHD%!fEIMY(v7(+0(_Qb#@`&Wy(b5#B3xSYl{s+_`)o8 zAuo{Z(wTWUTu4D~8mPrl8!SOpI|%PBMO}5!AjpC>JJI20WN0lij9=ViE&ZA{>Eu1y z4>hqyHvyRcQl>WJ9W8yCk#sKWLcnszLPc3hK9^1Ki;ekUX7YPt-q%QpzNRj7zA&|`JgkE|_U(l9n6=YnI1+&;g}p_; zL-j{x<Sg9&bq>Q~G^N|5_?Xiw+0JmLQch5R=yug4tkE(*-RMXDmCbv zSlkPD!x}V9z~9Q*xLSKsW-`Sa^PV>8KykQ0CJSZ>{B;Y^&qliKB@a^F7w}9k)FU!&1#F|^9gI!<0X#=q2hp58^Yi~HM-tThfC*gcs z|ARUSP1U#>6i^vxN04C<0oN%SkajIB7(11hRjLgRqN5F(uQ-NaFU*!(m!qc+F;4kD zkc5-gjpKC@U@|o9OMz!h_f+^^@3U7pZfe%I*!-Mjy%icMzHxtPsxKL(6dtZ@=xk8V z8-f%>3K&B%pY==V{pMhc;2R{~_z|4>mEOd*Qw1HB)uJ{AjCVN9ZN9ewD2du8TZ4OD zbG+dk(hC@ubMJJR_V$Zn51bZV1J}5Xz4d$DRVAm_Y3bc)=)p7FO7znDT9_pSQb{Rt z)n*1$wI|4z*}jeL#IgO3;$e)I`F^+5FT9^lslc00uHSo@A;|M-Cszn06_HXxqn6NF))JinSa) zTXkW&X=$Tu6&@ynYGJW8)sPw&?_gY#-M)o1o*a!mj*1NQfEcJF9`wIb*Iw$q$CUzpdE_CWIozo z6h8yn>Nk7Jmq)4%I{kiw1>>obwx;+i}W}gVeJ_Np6WpYYw(?W`sJ4qt&je)rXd|#IM8O< zjW>%OLfp3RP{QCHN6GNP?~kF(i?_4kPtCay3>baL_+4$+G619?`4TE+igJjs3vt=^ z@O@kd8?ta2Vd*Y7zs~pL;OD;T6#kHLYR-lmI$#4KmERe&7_FWkzjCZYF+xP}Iayi1 zYHNJtP+jqU3I1ja*WZ7S+%1OCFHV2&`WP_R7#{O?z>@6)WYUp8ba8gE)MZGpxdyUT zsM6qG)(=P;?-<|xyU8k|Ei+puz4VWk&9%9uY&CzSDjX-jll z1c7G+E~#RAA=cGRm3;I(p(5E1#oP^%x`5KPj657F#nJl&t^rDq1AhL2DE*a4&ZL#+ z!o#LzfaVfjyaA+zB4oMW9p(kDW89sZy?`~}8#`nzYGl27@mrFDCw+WT17E~;cta=_ zdNwaBxKM`9<7oU~UqidlT3=1_3ieTzdS|Y5YZHHG|AehYxO_MSzV!02Rov{ zLU#I)#OyjF?;Wp^U?WYeCm9E8a!axXbh}9(-1?!FS9CLDFFw4+ZTu(Ol|?-|~D} zN1&xP55E401foBG-r!@-CY*n*nzMs|`o&bu?LI-2*u(V(p?i)|RN|8Xh^Qnwj4l)D z@99(?M9K1nh6rI7uBq#+qjBBcc!S_NmrUKQqtczDr(ODdrfG43u=GmXueIYur&|nU zLvu};X)<;fZQwyolX>jC5G&+Uj{Y`fMNj^?3-J+)^1+*xJh!Rc#UguTkog#f^w{Lq zTRqO#e^M@=B{uLUI7~3#T6Omk<^dOKAn8k3jlJj6=W2s3^snW~Nq#BRDn!d%>jYv3bLq zY{%8Cqs?u*q+bbAxHC;&b(DKd5Iq#Ums*gDY^~1zy94KbpreLahaS~lks-@FA!7<6 zkqJQ65xhcX7iwHR&P!XR=`;zZW}{jo?3hlnjDU1CX@DM^y3g1jxO0$NXf2k>ALYVL2!`}2xdo9x%Xo0F%j_Pz zo0aakTG|ky2|C}&N&U^%z4KrAtiGCqDtm**4z0S2+W20qUCMh7QTXg{v$4hZ%aIac zF*)JH8vyh}3i`3C_}3_QYIIPWX*w_~oxMWa@9$lA89w1RQacJ@QIpT;d=f@*uxDPH zFK>Mu^ABCIkiL_Pc>FF{#iw=WD_S^kCV)-M_x>tq8|h9lR3P5-O?x)TmYRwwa8LDW z>-n9$!`(Cbce;99pI%2uyo3rg1)#L>6FQ?{F{B7@9WbO-p-xa;Mch=hG`Dc!sTe#m z+3a&L%7G5I{sw8nY90A4^tl_#cOywMG?YPz;c%w#n4tif())e2A+Y+@*29odF5;-h zEzw^C#YK%MF{`F1z+$HpzVoDv7)QtaTI>r^TGi7*|GMrHa@Q*y@dUsS(kXKWP5_Lghxm+vWWi>Uh=)zYXDRed zAnJ@cms+%$>fte(wku34UdJ!agSER=7yt3Gh|XG%`2^xHW)>@83+a4h>n0?;f@_R& zUe(i{mD#Q;at*dO{hSF9_0~T;zw^E55x1c*{YQljAxB3=ld(*f>D}DD7=;2{MGzL| z%S{anQ4Y68qSp8oY%0Aa%Aj)U2=@*Z{6YqaS$OW186OSW+Eyf1M_-w3H&;jb`ZW{H zL2HvE(sT8JGn1?6M@(StfoIDnhZn*eg>Wgr))~lyhpc z2yZ40%A;QTu(sURA%E8T9V_QwIt|`nJvJii=?D(t`j7S;SiQ@h_kH8i!vOptpRDP= zUAQFr>1>B0o^D@lua@{%qhhw<|FUd;W3v^A=6>Nn{o;b2Y^62jVR<|aJBm!7f;57gc!*sD`HpyQmloc%@bNyG||fron%qitZuKPfY5Lp4s5PZ zkIv?!3+HJcn7l7uv;Morp5?8a98(D~i;ytJKEl4^-PF?kWj?k*AO;eZ%`&^f3D5PS zgy&Q2;y6QG=dgQ~kf{!-#cSv6n+`b}VkoF$`~*4oG34tD6vT>=9=;~OiyS50NU^su z*9Wz0v^s8#;1t+`fIy9lDm9NcJ1Rn5a`eyegBQO@0j`UJEua*1JUZ%0gRGywmb*ut z>?i2`rsC5UaG|YnuDs#_tV_bsm;;cv+c0F+0M;54t9t8Tw(Z8;+-yqSzzx*dJnO}OnZ zPFdlxP+C7=sO9j|Jo4~A)D*|A4t8JZ|Du&@tnxnrq2-;Ws?J33z68kBI#qUcf10DX zOTvM?qH6z~RpE6_>8FjP!%Xs}El6Lz=nAAOLsxgsuR$$kw&1?cR&%^SR93Wa^rmyG zb{p0o{!xMUS69E$0l~p;ch&jU_P%+Ulm+{?rpFPyh920T>9jOG0JVm?Q;dyCp^83X z^YGDQPvv2K#Ub**_eBK(9cG^Xa>!4!P`AxAHIlfwrS!-zd+yoR#WpCoho`!bEF|kA zCh@n`dyVe5gPZ)#)%+HeV>h9n1=-3D4#Qon4$;0bH#E&VKZYKS?0sCdatW9}9G|yn z7a)M7RcUJz%BB5>Px5Sb5QZobh7oEoaq?!A?XdY1SXqZ3l3UE5w9pk*&Af3fS{JSljVwj+nXQeFrzX z%`oZ-Xu}KFY-*mW_fi5$SycH(8R)*Ybky&id$;L&mEBE@S)X+gwmYT@hCA~Px-}Oj z{7S(qliDrYHS?$^A2U+i+^o^#QCT4r!dy6Nv3>)%PqqZZS@|s(u<#KaFKz^0Qt!LD zEd3JSQFDDsQ&cyZmq2C6_90dak17;)dY5 zVNX&tpj)j;TW@b$KQB)6%m$-8f$yRhpqV=TnMqCEo3&ZdrX-&DAG~o=!0*Syx?g? z#u5j2daVn=!79#nf>s<;l2eeLWd2ZE*$)pwM_f5ac8)919^z`tA8RYf+D%-n7EFg{ zFb`KYI~pmfMD^BmIWyWuKJ0Q5YM(;jVs-C(i~pYi6_HkN{p@S2S>3GFxFw*s^iWhBUZ=3I zX@~+Z!u*?Z*j-m|4jzV}zSsgiH`lgqul*PQgS-q&{Pp>CGYE!1vq*kRbD2p0tBxQ> z0H2jAmNvFFa}cUz-&w~OCz)Wpwasaw{QXivXwUq_m()8JV`Kw!5|x{$y5I$hb3*vR z>0C+tU`^J2p8{y_gY;mj)iiIr$~PoLvn9JxXuA>b-kCksTKzf!W4CN|o~f3{>g{s` z=&a=OZ7|F8MzU}08Mh-il+FmXpNt>9us}F74$xzPDBknQpVbKbO4=M!X?33_8ZzYM ze@h*L!y9LYo+H=}nF2gzfi`^YDhGS`yJ?7$9q@Ip<4bgw7a(!O(%bRCOpAb@Vdci6 zCZVj8ky~OQPRM3g0T%DM7l4{!ng>?ffW6&%AqW#(bwk6nbKTSCMev^c#6wa8syH~& z@`le71uduBX6{38GNMcz=YhL8q1Vgn>xUng{5mi2!G644S!GBWRPa{ zTS9Y{V;PB$K$(D>qsI*v6qv%($1K~rZ4G}>n5Q_r_33Z*4#I*Sqdfr+sK&|m)z$I_ z>3glC9)IGa^tcfmgJlFu_q)@na{d2&q@ezKA_)K+WN@#CxKM0NRt_v^ZBN`|dV2wY z1reYUD_&>s3>obJ#~6#mN4(*~;dpS?H_NBt={xG{VT|P@cxjh#aUn#zwqis)WgR0# zpah6Cs{f+so_t26MdRP%F?PS6yO%5Ay~h0T^AFt}Cw#B9#qOB@=@J?!`SUAah`G<% z4t#!5EP4@OK`B2iHr%GIiT4oYfBuZqykhd05xI9Iko#Xjug_BS_gshv*T7IOv7qX& zk<)Rg4v+5PqMS!3CXcX5UYqX{h5rjnbR2$LfNAB#@AcRUuZPa(yaveQ?h|n`p+T%S z;MHg7$jb`l5gp_&0`=Cww_jWa5p%GKz-^x+9y5z5 z?OwAmA(t|3MK}|F!l{f)o!eaRZ^z@ED z!R>f<1+#5YY4V;LC2g!O2wuF*g&|{9MS9m)&18(<(sd1u^{xb(-~`ju_JgJMC^cd( zjqXV%Z$A=Wlp!a~lv$SzDZE4l>|eF{mdI$CHN$X-$rC->-ze9DllRBou_swbS?Vjh zTJFX5-rSlsDsw*Dg_&7OP0W~pIceS_%UuuzLh$JXZGwOALwh2- zm_rh-!t;BS5gwOWA99ML-;h3@?0J8vf3D7N4QmV>bz^S~el$7hk7EKzvEj!J zW*pMhZ>PJ1)1eJgn|cr7!cwq?#kz(pybBf>;E<28$IH<}_S`R=r_FVu1}ys2$EKaZ zb@OIZd$I?s#@2E_N))kVXdR0rWkn$_o0M)_M%)*Z_TrP!Pm+tdadU&|M=zeZ?b87i z@sJfP09-~Gn4(NRb6r)1QhZ?{QUpB)XO(bC=qs?I&B>1j>L|DrsVbT9+6L)82%iSggbTBEv!~zp3OmIW_rw8D?QPjWqQbtgg{T z18x)iZwV2iLvXxE0LQ1Bo~^Uq7C7h*KQ#rjqGR$^kgC^~riMx(sSsi^gh{&HR_$s? z50)S8r^VYs8c0|}q?$=JlH%6`NK$m>^Y#X7p}N+plTbx8?neBH&c^N~DisEcC-c7V z@lW2ajvfJ}tU~}_=CF=n`AN4y*N?ZeE1)2&$@QM57FQhuoe!b`E4J8IaX9m1S+IhS z{)ez}8YP}y7qhGcxwvJkGY5-y6;*Hd$ziTLFYE3OfoC>!N1(u!kExt3xA-C@0>3C~ zJ8Ti&T%7cj-=lW#cdcVT?nLuB$39-qK6deoRNxc1dd=hG)-_j~LONxcwbLByn{4bw zk~wuKc;Au48+A7du(89fdN%{g8l@GP4!% zOmHf(C=T=w5XHgG{fRMQUPgyxG*h0$Ntjc`T*i7``klI{qlJj~ zn^(6Ss6QoHgZT(De>=Ibd$&86zCF`O#6~%b_+_SXHy8TN<$+B!2x8 znsIa4fa|3eAza&3IsZrF^)xK10w)B&SQ&Lk8><8SIe=3u=psl(X60b_)b$ zmcFleyQm{`N}g42%d$4s3LgQ7{$#025ybP!FlG5VU+mT04nW?JlC?d%!jD?IX~6iT7Pv=I(BitRFY%d-%N1g;mPE zHi+Skcca4(`%`gA)?Oxi&xXlbuX0@mX*~}8$rcHwYYYSNTimubh}$2l^&Zo&#_!@5 z+9qqs9hpCQ9WBqnsAZjc4qJMhs#ybqmWzvpI-Y0;A#Mb%Xo2_l;t~I@mdAkh-n;w1 zZ!Y)n-?N9elBztO&d8>&9c?Z~ORrvb$zQ=A_JiC$oSny!@sobESeDjn96rO&8h?1x z=pMfHcyY4#_)tBa<+Y(+&*ydvo`xwOo-S?@(?Hg>wD$qFW9FIb<4LveXzKh zVrF&yw_Ys#j3KuRgIRWWr6upR*OGXU@BA4yym}kuElE$Z91T0ln|kLQIIj-F$vOr4 zJ+^jxYiM3`Yoxkg-4Tjr@IBUa_|Iq1kfnu;;Cvfwe>S5wddpnOStED5LzA^Q+t`7h zqQ`e1t~IGe)CH&q0(pBdjCD1ukzbyj^YMgY7`F7=P(FxhnAGdG*u~rVK)p^J-hEHz zb?_v`Ei?zZH0d7zf4dtF@EI!30JRqr-HYQXRW(|kgn5q1{pwpoeh zFSI}k-Pjq7$WHHi+af!*S}xo0lB~l{lLg#Pq>ZoXq>Ne`XSI;0Jx=g4Tb<$bS)TA6 zwWwDRw4(br)Aw@9+GsAvyTNB!1}*hnup1GH^xKuSfj|J9dXf5+X2ZAF|B9ZcMsYr# z55@)4{G&t>$iMw1T}`H8@;pADKD;}gG{{_gP;}IEg@-Q0)S<|QZyndevl`pZ$`>09 zr-mV2Ku?;5>l=fkZZh{rUIAC~pyWDdaZNNAS6lyA4-cJLpSE?ItItKh(=Ie7wYa(3 z-Y%z&x-fh0#5HD-csY37zl{>O`O&Ho2&%Y1c^v#h?)K57l3R$TS=N>~`7s z!kAI%cJ%1(uMRL+*b=PkearGf(PC^gXcM6Z&=V-7S78gWH!TW`(|Xw3`H|lH&S$HB z(Y}7T<#s)s<_>5sH=I(Q`bg&<8CPv*e}GJ8-9nK^E@?En=njvIYgEH-IqM=`Rjk{; zwHx(Z-Cib3v+FYTxI4{t=}`eKExAV?HGz=z?SXZx`>6i~MWIEv;o_j@Lc!Zz2tKBU{kPI#!p=&yf4YIs9)YrI-cjD(?A zqm_iW0~3#X%Db84IvrRtA#Uotd3GsqF5?4Ha|f14no`s89rxLw;2_;tVg|~8=I75Q=t@x+!SGb)7!l>4gy!GZG(&3lYsvSAvuIDlSK+_th#V|J6-y+ALvoz@xYBO9*FGx#QAYtYZma!jJo4Ho9()d(lg| z0xON>A!Yb^IxC&Iwwe+vJ=oaR-lyvZw@ED%_5G360>>4AJ2L-F9k2PkRL?vczPR#r zD`RLUM0ecx*p$#>>KhiHa|CC3(+U<|$V*Sbf)Zt5 z3U?-_QEy%XeBY^z2suw9X;6ARdkD9r5MNLd%`B3yDMl;0s--^O563tgHt` z3)maz_jFdM7Vj(^Yb-flxTKw58qqRWOG<)V=B-ZJnf|TTkCo>+E62QSokN6I?ws;b zbst?2YF{;Hd7bVg17f6DM>e=#{XD@*GS$NlB$RokE#$$|2AiK~$kC7@U*7YEpW-Id zE|-^Sx969s$I)F@lBv$SY1J`*?dxZE9Ixe6;-TFBLNG$F{3%gs8%PUK*q$I-v57ru zHO@<1T%A3ptG!gjAxrS>3GNe7b7tLq=-fpS7A9GI>ww_pdi3-5B!vsXLeTAEzVbWv zn0qa9dydXe+G6{-ePZ8I-hlUFlxMuVRqT?LbYOM+?a6vk#~pU5FV(SffJ<=I_~a5;jnu^U2Re!c4^eL+!bmgp`V;mp<$wlc0NjuQA`E>0`ElnawB=%r zU))}vTcwq-C`>SsOg7TPPP@F-1a(G4Q9~^aC-n+_ukvhS@dzz*@z*!!;AD<8Ag5?A zRv>Vfks%|Ujmghq6Y-!~^FYd;yP-+tr~&`gKQ|LKes?xF=&yH>O*4-f zuM$f3bP{><2vpy19}3&8YMY`5yXS-<5d`MH(wN_6w{@B&LMT;|6)T-iS@2GqcgX%I zitG%C%m<0TNBk_bPQ9y~AtMxYT;P&N1OXXb`z?QZAK;-qsC%K0d}x}jUbU(Cf3WwB z;h8;6pLc9$Vos8YCbl(6Cbn(cwmGqF+qNdQZQI%V|GfJwuJ_CCUi)D`?D^K!eNLb5 z>Z)INS9g`g!E2YFaj}I7)Fq6fThM<$!xiq*Y}E)xy<$4ImQ3cejr|N$lmP@)fc9Oh1$+bsK5-#UBdDsyzI;Z{9&9<=Imf9hb_$N2O4c+Km;$UY0?_DNk zj$dzT4?1>CXI`DW-S7NX7Q!&ua*g}X&wn@YaIWQOtxP@$H5*|V64)htvs4WP76yVl;5tpw2i+R+@#n>%hb0Ng>m~|Z2 z+;bav1`3Brb-v-CQH|348mBS_>1Rml^VeE?_g2Xy6VkSi#8a7z;^{ZcZ=Js#{sdQT zPs)FzU49S|YfuC!y%hw9javTQBuEm3Ag3scN}(K&+aVV>hWe|wLF!@^pH9~Rx1C`K za_zx&B9(*5VRC|CZNM&62y&S3aQG-+l%lVHB7^BpT&LS@^NFWTMd1CMrU407gJ0*<{=LZBTK4CAdSAtx zs!!Z08d~5vNpOyGKnw)h`?+-j6AAH*;-GYoj{a;5Ma11Qj!`U63?~1$V;1P zE%ksvgEa%-C$snYs;_Aiv+9x4JZ<45NwZc%@J9JpP6k@Dn9{_7^~R_w0rEDZ}VfhIaiP?Ku`r% zU6#4s=6ALo-nxE$QNd0HluJh2e7q0_-Z+H44VsVL<3$zwwJ0M%j{V-$IjT;#j}hml zl=We+LjUe@lcK{~PAxn@(R%kq=XcFkeNpr|ok-zbrb1l_JUn2e2VoX6W9slV7z2F9 zs$vcwO-_?B1H>2hZ`Vf|-dksMe@Yf?--sR7TDBj_Kb<|V`Ic^f-bVd=-@i}5+KeEc zyQYD!ViNgJ?X6#L zVz196alW?RK!gDR4E7;s=+Q824i>#Td$7qdTJL`9d6eJ>58$p^-}?HwuH1%eOY3qb zt&CeEMGWv&H?atXrT(w|Z(eSRg*yo7;e0o^iutuJy0p$!O~!V*yuy%LUv^sDeahku z;`>nh^K#~2Y*74%vkuA{_}na(@1TG)+3@gGBpt^ ztT6qtxJN%ETBq01UZ}HO(bvXnEPw~7@ox5h1hacePdssDYvq8FL6At74g~|8PVHCw zP~Pw=Du_N}=Fh%NQp(N2*a7%ID8JnT?X$3*NcbUtrf8c$BGS_QKz!X3yIF{yc;_MU z0{=MK{zG{+PTo$0<^7;R((uWkS#XWMri4vaN30TM4Ew0zKg zhab-=_9MK6-~^2mRfZR^4KM)9$j-mvt~N5IF&jWse2n^+eIWp>zXFUI z7GPC{;!*2tf*`(9jGq%#uR2g{KoJ2}Ab(+f!o~_D%ZG=d9xk7Z=NkqpA!B1E^MNPe~E1)stjvS%P6u{zG#8-B}e$9T@|z z*8t>gSpyCtU_1Rs)|YT5#P*wyCtqvTVUxh0x+bcZkw{U1uEqZAr=p2f&!})FP#`ER zs@y{`@T?*y1<+mFc>8>4mPX@UsRXNx{Xs6UCtDgS7;01Z=^V=Q|gjY zFWTGK_afkC`6;%FgaFVr7`XYM&Q`PnWc`Z`M_k3EVsE*?aZxd<^Hs+g(?4Q@x#m0g zTVe+QVAae(D6_TG)bk{T&Ic;NIKwFA+Z7|4ATU4~8@P&=Xdvr0=ZSx)lK=pqRO!z7 z9jNzYHm6RaVHo5w!2vx*WpUA=wLDy~FZx^4{#d1Opa9)FAzLNKUx81Tkb3*<@LI?K zfQGRLk}M)nwA_$@qNQIz3k~q4Q5Z8C&R%Jx0dYM9y8c8Ug(=(A-*H%qcBYX;Pr9^; zJv+s7e{DS=d}xZ~_WbIff^z2FEk%Ualq8p7?7Zq_xo646!Er($L2L&83UvOaxPdhOsQw-;{47tvjL^ZHs^WgQu)=76id~mNg zryqLZqqbn3@)8m>-rn?zgnyz~w zX>t0Zf)%K9ihw|Jngp?JIhDBoEj?Pt#@Bfz3)6k?_I`h}kRZ(A&K*vG)xbGA3w$Q6H^1(*8~{0 zzGD%H2Tobu*=H+G6pdG%D`EEQAKK<8HrAT(WBG)N^R?IaK|%B>UOW7^gj;cbP)SU- zHg`usl2_AJm7Q$?#lcaSfE?a|m2E-~pN3N4mi|g{Udz0lQ_*IzPqMlX<~Q2Tr7zvx zr&hlzK@KMRHJ;9fL~CM6Eds4}zny7Qmt5f7Zc85PlM3wW-HP)rr}F#5m?5`qk&PXt zW-Nz$$0hHpR+nZ8tKUCP;otYbgtP=) zFMnN4CJ&3k37knRB_;P=XnG#@4cpvbaMNFVbHYq@rnezlTQU{{2YE>~p5_>m&RWGD zJ*2`4y>%q(cD4BxlwNDcw7u!y;1JE$42zG~VB_}9lyP(nZ8Noplzh;y56t8~DOR4P&bxtoNBZ{rlq@f;!HJ_p+I9_5070t(J{~|eW|!h_l#rDhFx7dd z-ios7i?rc-Q<>XY&WY#TG#PZz*P86Hxcrjq#QHMxMy~u-Qrzlu!5T0FS6baYts=1# zm;78Onpa%P1pj7ZEf4wmGcg)M7r+l+RRI*^m^>gzmbPU-Y`E!jDrk4It=@9m+TP1P z#pvL)FY~Rv%1`0&seizSygqd`$S-LhOX}Zhj*oxH5UPIERMP~#y>i>?#UJ|dy^dD^ z-~scUt&ePMr|gmcQekUYe~~^aBg%LDpSIdpJoUE+;p!u#x<4e&=7Ay%KX!1xerCgc z43$Nj%#^*QIa%vLR{$k)dEsGQ=^dujiL8?e+uVX~eZbzDTa|O|ZE-c*YJUUtNS%F| zLjN7OPP4mWo3iP#!`dSezyhL@O#;C-7@PKqdWtqLbt|&74uO_g)ba|WV-;VrT34&U z<*X?6FvSzImh`8Jpg^%gMTI$ zZgId-jcbmt$&(0dUubX48l+~Vcrn)xQZW!LKn{xjwLY$G?lM~gkr*s+Eyi-1ZS(cC zcLC{nWsNKnWs4UKd`oti@ynyD4}j-TrZwj6|(Lm(&u@h<}$3UF;D9^{Gl zGm@|VEEkY*(Hi&O0Gwp}2W}4ia3FiZ1Z>YRuu~1K=sskbF_9xB15w-yt~a!VAQrl?f;Zx74tSM0b2uwl#eokDP&-^*IRcIp*Zo6&(_By2|sy$9?_ zh)Jq*pB6S1`ZqX0joYM?bSiRH*2&iX-gPE8VA;}6vyDx~)EXCEpt%__3r9QSljRFo zFo^bH63E|V;pVQmwW>EvfUd?bJ4)Q4rpV=8ackG@dp002v)YrFv*^Q7wT=ok*LT?f z01JEh-4o_f%N>Uyo4G-^$!jcN09mr6ucP;q2$yr5+S-#R{iVozIDqVen5!ACo|r4x z6VKc$FpVqLqBwa#w(~Ic@uPXN54g4vYY|ZHq;cWhhpW9p0`N&B*isUmibV8A zA!VaV0Gd}$sbQWFX*yiZRd>BgF7$|T$=Hfz=U;%{4VsOa1{WW1AhUrwz+)u%2e2@X zpqbei6N~-Vaq3L)DTXvHYwJF6k}$qX007{unUp%l!Jo0evf_7duJU$yP67`ARE!+# zl`kE}(`&L>q0(jH@Gfz%aI~|ZX*iAmb7Pp}X-Q8QMq^o)C~Ma*Y)f5eM`)@X;rd33 zVF3I=%F>~~qt^MnZlvQv%ALL0M?1eZIa4}D|8T7wJXtPc0(_&!`US9n|8MC*Dvf$I z!<2u-S=mKgEidhAv%@jN`=X&Q3YqjhVy7#v3y%Rj9&R#=l5QQyq79l1C&u z0D$?p*=9B>aJ>W=f&^S(Oa5;?J#8O+LuRTR|2cr@zk+%G??q7mKMNrGKSxk!Wgz;G z2bNC6%+k@wo`_DwQqR%omyv;up%E-EFRX*3y^)?3tn2DUFUUXU9}uE18Kz$g{~RIt z|Ih!^Jy8AsdG!A@fByNob)0PS6`%jC4p{!jc*2rK)+Uao3`7jf3@os8|B+%OV&P!s z_;-ql2pB;4KQf3|IT)D#S7kcN2}&`3ZIMPP+}BZn5~N^h+T*J82}96V78N=-c#|uX zS(uYzwtY6;H;0Hw2}B_LKF^ovB8Fh9^{e$N>Sl8UYqWVO!{VaxG3ySFI=%~~+Mi?{ zBo8)(*v-!qG!8(9|IHx>z|YSgD#Ono8=JU*748`Fj!$mL5=7LIYn!tFrB6XjL`2G2 z1TUBu#%YViKR1jIKnDc~llke#fr0`AKtRH}!)yad`LXxmoWPH-L6~>wL)nPSQP-IO zAWqH#c~38IC_NyD-~ckx0ax#0Fm!GrXbLQFuw&m?T4bdAXx&(@9%#g1!B~(ls$Sv? z|6lInw|8$ZFE@VN9WUF^CTh|IzJ%x}p!9*RLdadnqCM4rK-!3qMzUv~q18Z!Xl1Xu z0VFMGvq*uyfN2mH3M|k&k>ckbJYr~oyNmCiU{?MqG|;z*iVsXbsOux(+Lw2m@8Hw$ ziwZpGLmJYr*A__z`6mF@0g_!{gBZZ0WW`&+7Y7CK=lJ~YzuviX>={c3eTrz$kLKNs z2wFmg1>ir1`I&SjX*Om|K^ePbz{qXqS0$!9*#v2W5ejF+<_dO&45#^Ko5MBWE7dR>S;4fhiWIDhA z;d$Se1=t=yX2b^hnL09y80!G$37kE5*cV(VljxXGFoA6Z6O{kECsA+77s9)TFf=$Q zUal@_56CWj5XxsUCnvn!t3_0o5BNNxE}3rbfQ^6#8yElw>HVTDK=S`I+xH=}=*idygmu3P z6V7k(ynUj83=@Xff_`dAU`8j=g7@4I7HYtSLi^6>^nBTLeo4P{kG`uUeihGtwUa0j zx;$;M596;0qz~TzG!#? z&u7vQ5P)|?Xyj!Ce{VQWV*H%R$!=&Ly&j*Mt*2+C=W4_rUTE;u@NOl4>#M5=n=K)t zPh|R?cX+&?-wsxh7wnXaZMR}vyd)37&f3%v$?41qW=`(n!Rg}bAI%0#21*4FZ3$2M z%3z1X-bII~=cO&sv@O?20v;oBB-%rQ(atUc9roq}t|VO0aiET2j$NY;*!-(H{3ZK0 zYBU(yS=8V*eL&@KK5Z89U= z(U8*d@M6B?er1-%&mrwYT-ji;5Za?bUj2Ye%>9`Rp)gqthFKm7(dl7IIITWAZIB(? zovtfHX>Dw_nJJu@Op_?dP{{7KSu(1Yi4#Jy;h9wzA$x{$0_M9VQu%C-9`cRJ<=YM@ zcK*PX{<);p~8Wws*a3A_2ujNWjKng&+Bs%Lp9PcR66v*NFT)p!u~Oj9=(c^%_aI`TylzsnH`knx{%w{1uw{+QpO80K^;S3)E9{xL$ltZ%zxHUUv!kh-!cYdma_x%>KG=cJFV_TUg zC5`A#Fv>Eq?$B>$_0&9f5c2-^=2P?$IyDxuQs+kR=RfEW zU9q+KdRh&y^5q1JVmbVd;J1thx%`YOi|cB%XKl^TmKLGqhdb?Et(zqb;t`k*QeR&J z{Augv7Re(K?w{o`S`a{SvInd_Nt#;@V{Y> zkqvUaG<1K*#isDE$-j#pK-vf^?&=`yeo6Z2ppAo@OyMxoY+(w8+2A^};6?ehzs*Pe zwwJIOLfXPq8EhqCZz(#oVVtJ-bOWw=doW(Kd?BAG8n!SkGxby<|IM;~QzsL37(vbG zZc9yt0WZD_7?{FIz!EzTn_C@fm)7@EpNY2D>KIKyK$5?KrWKZ<>p8G%8 zx$Xl}F3BfBwD)05O05dRAww<%+oBgTr+h~zRk((v50tgIHlDU1X{~c%F|A2{CmMrW zw9#}0bW{}+04Re#d;Unaf-c%RBgYVfwHxhs((3;=*M=GJ4?-%wbsya_qRIr zrlD$crQ^*VsSpr?9*7yV`XzpvAdhW z0jf{s4Hl=~jV#P35f$fUkNrJUzW_yQ!M_x7Lim+~4fO4EaP2Qk<~hQ9))1CZ6Mq8b zK*sHb=he+nYWF7Gk7xw`&Q+wbtibuE>_ELgGgMO57JSRdSea*j4{L4j94e5vIc0Sz zZ>KRZ^MDEY9rlft3hY-+{@?wYNbiRFzpzG0GC%Rv%&M<4Rk8?H>+<7h zA2_78Sc1?gZ}&kVep($z(Zv-ff>RR9Gu{#oB52*U)J!bullW4J1g^ueY3h}gz7 z)GvBBlgN=0SfK4~ci=mqT*wrXy|VAkmRE0WpT_oi$=zBb^w#TnRCkv8f|>TZaCOGf z;?>fO(Q&FvZhUvb+gxLoo+Y6IeZDyLmPq2No0OW;i7DHn%4Y>Ip8gQ0uapSeO8R%qau?(y6* zM8$1ow-G!t(zIst)EDqf8&zQu!H3djL#A|dp3kFcSz-}sh^iC4@`E{@hDoFqsbK0f znoorL8@1nq|GJ6_-Kto+CN90ybsca+kgS~7B|sAFS09=!Q%oJeD=XJv7K`xUaj`2Y zN3gU#tZw%jrjQ?ggrAgHbIYBiSDQEyyM|1RX>3f+z3`72nLnc=@-;s{rConpfr#js zgs$*7lxeltjImi#%9a*!8FYCN=iI1dCZ9XeS|+0m-zM@Q@bCDxn|<$ohow2GrB{vU z-Et@~`kvr{mu}YY#sZPPnVBFGzF_50k(fgE{Uq#)mPufMdQpax?$s83R@g+}Q7(7J zMsFYpEp=;**HM=unWl#JLfht|l4VWU&wTEEI9CWB2DH;| zB4mLjYZb2>9c@2?;-b-+=;gWDhmff4mZ(3N-eQe;j zuE-5z;v95b3@=78bL@(xZx)LQxDKO2#3Ex#t^wT1xuZX2#v)DE)9$@6c6jwX-$;E9 zdi$4BY{e3>_sJm>q!TD23@x1{|Dxe`S4+H*w~E7ldr3X7Vijh@#8mIIYZ<;NztgOQVLr*vLtRONabhJYyui2nBhdH=PjYoY zQHu7bOSCL~(A&WPT41u*&V9%=82giDQ^}HN%N^w$q)z+AcN#Mc1r?CanskFZu@c61 zw8iitq%VsFB?)dL0UAG?Z^Sh%>!BLtFWocM*rYtX48UMbj4VDVSDEDf#J zVt*{Ydz^T}25EY~XBV1anl*yox0`L=kx}}Knd!4^1VR`z>u(1x5&&qMditUca~_e% z_VkNDIhTf1nCV?@v7iO5eYUYu^0Q5^Fm-~}wI1hI9r}_#ojtpVR-DW5rk;*21Yf-f z{=4;#XmPA;Am-69r*!KcGHwzz{I6vU)cB0|Ct|;rO+Cwo)bGJ>A`aBb3JRRkHSP(` zPTk#Vl)ArSD-`I`B(m+AiIo4!v%zi@`_Fc|xzgo^C^ITV&FViqQIeS1@&aKX8as`-h)=UlMx%fRC$n$RnB}5UFlr?qpo9xx3@NBI?B{uIl9<4 zYYO(v(1g)tlkWbv=PxKtua4j^|5R2&T!rRF)>Brr?eYSZ0?94b2hWTqro)?$6qhL7 z11mja%iE8}cB)z_1+fKGv$^>PNYHXh`2Ak)_rVG52V=OsOGNx%g%JDF!411^B)bho zV)lwdoQv{5oIB4}S8~DHo3*UA?`9_N2dhzR`7_Y1v&|VVuIc~Y{7r#_52TnTZ2yy)ii;BOw#))AyHOnd7$q}Va0PWGF!UnDfG*;me*WNJ7lfDcv}JbLNHeJG3DfAoxPk6ib+4d7+s1{=CN1OMY=_G+I@aW zXI=RS*1lG{zLwd3?#6;q6g+7E<>`DX%{Uh*ATe5%rg3dPZd zbty~kMyWLj(TuxH4HAw^V#=~{OY5zmWy9IJ)nFs4@b{oBHq9>TpAgfqR-tlvc`V@r zQwfG`m6>E;79=b06A+4|J}wl}JiR2``3dN4V?XiFwN4VySzkK=A**wUDk zy;O3)ou53a3=;mB9-~*f)oI#FqCS~-J=O@f9(t?++_qmve!!6EhV(-i&DvhsYR9*Og_H$7m*A{SO+9$@IeCH& zAd{eaMnb0BpS%V;ibJ{0x9`Y9h)DA0v+wGWuaLS|`k})k z4q^_YEY()@nFU2R7m(=7$L$5{3z^u}836f?JJ>V6Wqwsz_A9pelLBUJM6VqgQsS*k zGVUfO!Yo`3i>p@9P`QvfSnJsUjZE@g& z?~a+@A0hd^@9iHSDeNuQ@9uPhwJ#s@s;vFmjDm5dR;B#uD?U~COWx+fU3`+1EdTqx zn|iWrP68EZgS~Q zi!q<9iS;+~>?{kN)wN-WSI$)dkLvdDVEVA3d}`ha8Pb<7J}I+K=D6O7=?J7`dhX*f zEzDx>!7Lw^Iw=l4!dFIZh*{BlXL7TPQTNkl*m?Ll*J5bhFT(E%{NHED?D(y5&l$6`2k)7}Q6ztx`Q5Ql zs?&uv+|9|@Qof7|)+}YxqOAL$|2#{|R>QLbnUkC^RhhEvp19I=Fy*spMLEDM;UpTXs*Ci?8|PrDGY~cl&E}_a5WW-QGa;jH`3=09K5kDEUO?N5YIaQVVaJ zYH83@tv)Qd&FLVXORa4(B=;Dq5kWEw^FCR;AvWuh@kP@}F_ko~a_o0FQ7 z0$RDcWrvn34#Cm;A|4)t_SOcanmAlCR`}lrkqc2J!cE7Pnpg3R8j{i*3@I#h%JH-@ zcu2;T?>=Rlu85L}UTM21Y!aGVqt+Z7a#mi|>d0AlB_T^Wia@=ssa8mAD>%TF9W?cv z#27m-OJvTFTc&-x+pACSLh5f(zWS4dnePdm&9Zc8Aos1bF-p9(noV1_JEIA=BbQmY zy2$YqhqE9JFMB(iV~m)95L%O?*go?7i}Er=v?tl+YMMCm#SFh3ql-q7v`r^Zh4MHA zq4RKwrJ}u0IP3S4U*KnmI5vlkK2sl>D2$HER=T`Fpyg2Y9TOOqZJ%0~9I9uM38>r& z{SdpSLMbMD+2!BCv;n3+<&BUP?5YXg$LnDqxhQI<3~^q4qP&JzGH+2H(cgFfXp=W^w+xfi0m1f03AxX3d-inMj)N}xN-e;Oz`pY{R5y7CG701dkKHHR{nco z$~rhdMx$tW(XA|dxxKRH$D!#nyDzQY;!-f7ftM+sS+Z@IDA^x4d%81cnk?+X_YR6( zHYS(i#WiuV(%KW@#P%YT$9XOzlcAMC4@jd5n{n0C14KJKTNTZfs}eNirZD6XZa2GWn=!_}JbV$qrmq)f}f_1+Msx z6$xcx!_kD_bRHRbAKW+fD?dYjJ+vxH1?trH%;L1P+r?`Wm(v;$>$^A#q{HKFR)NN; zSCYhuOkl6<#&Qq23AE6I?bg~z_J{jOC83eXnRl+ustDBn@vwm{uVIlJVsngq!hK7s zqbjWrh~&CRhvR8O0PX(6U#e(U*=cgv6u3uBs10dS~2*1 zx|Dve@yOW2+0m#z!Eo`Nz>hH)iJ1OusbGGg4(gbvbcek`0oL+IVmh)70=&b)Ca3}@ zTM~mxk`jS7qGfbyKgBNj*n#`tw#KHoE0w6f=*=k~zj?o^Ho#jD{(_-usrt=EiXykO zzNuJASO0R3bUL4`mKfHpdk^yX4ta6cg5_eCrX}|cgzBB^=Pep>1cagOZ3-NX`OnZk zuWkDsm$b#x5%Za#!d@79Zm_)WI{SteuHLA*(UsEBUNF*nP84fs%A{}L$iYyQ_I-8<+ZRhLjv6|wzz|` zcecPJxolOP=%q4GI-B6M&3p9C7DR7~YAdg-TpiTWoHLt;{rkt>XSiiMiqy|@Q6ioQ z?9CP%wJQH-`DW8U2HW{6ZmS-mzZ<=vP(H@F`3Sl?CKWM`9yJnY#FqBT;_i6fmP7hf z;&{=+i}>~h9No`S{f+!&bR|2RFL>56qdxfM%;EHxup<};5HS&3>gcONX#Myd)y4%VJ#vKv&-q`@7<$C9Q>v1 zvYJO@^;%xWqRGdUqhAx zsbyXw-~^E^ReB(hpkQZIZ)Il%-KXNi1?q|Lx?xQmvrD7+nz_VMhn}lzGLVJK=Rbb@ z!qXA=(0U4_uQB@p!K4%uMFD>JS#e>%+~ZzoD3@(6d*Y`Dy_t>*;S)=H(rnIf0C}=X z5OxuC!)Vt=s6Tv2qGWB~KC@fBjSm0)B1T;73hz0Dd1c>BEy}rZ8P+(2$)f8zoC!57 z4fnSiwQK|HFgo|5izL0mS5SDgiEg>Nb@M+WQ@ zjA?ee5pRK<>>!7IcE;&Od81e^NMAQAUjVKqRiXcEcw?m}q9^*d9sa)=-k8{#|7~Am zBx0p!VET9Je>S|aaQrVD-W(wm6)#p@2TtZ1Eu&;*Q35=h|v z1@$3%1;5w%mSr)hf+M4#prN9mK-k%(_SHf!6JiY*Aqp96Qxu&0u$ScN$^Ilz2++Ur zcBdfCxd;OE=mS*cF@BO!e+LZ>4;^{G2o)R$HJ7z%Vag!~H_eZwhYywbcCZr?+}@^l zv-JJ}d(C+RqKl19>8G>fTgL^D;Nt%sgok1g;V`;;1|}RJDJyM@wRlBH>3XnHql%=a zr$nF zWrptogKj~C59<|mCC=0{1^962<`u$Wx%R|%XFByzQmu%UroNV->T5h zkHQ>Wf(XC%{;BeX!vg_>Cu$Q^)u{jgggL()1HaQ#cyiC^KT{$3jGPMUsm3<&g9r5a`OXvq^7W*jYu{kLHqW(4$DpvU zkG4TYIosbY`&PzNZ?)}Y5KkRyia(oP`=zkIsfB*iSj0CcW8ziMVKK**?zQ~)P zMn~jY25U<|))#6F%(j;e1kS&`=h`O+06&ilsXL=xljHlv{C)=x8USL_f`(xm*xL6e z$H!#2pFVlZ(-JJro+<%^JM9zXi} zZO@my5)*?Cz=N(0Ir8P)==*_DNiczZdGNWVO!E_+4&11KdRNCF(16HRC#9Yk?`;1u zou=EaKATFY=MTLQI^^eFJt*|9%AF2tM?=QtE+0M?HX{_G0Ek4L8a*+QE`f(d{s= zxSJk%9@C2Ku04azwA(Xh3`S!Cg~Ed#g(?2Kn)ZRlz^jJVI-bsgYAoJjj(fAYYp;#y z^z$$rHAZ#X_<3T!UN6*0wssq|NBdCfVFrhkKLOy>BZBVn?rX{RrZzsYuPeh2tQVx- zveWJzs@^>p95Ya&{hxD#MR_Sden=OsMgAP{nCAgo2car2U4_pFfp}5CH|T1-eX*RP z04I=v(f+3XO^Pl6cbK?bW4zO2Xv-h7o)83udx^^wLtzZA-0Wfo57N=-;n9wH*}k@& zK53zumTC^+?eH(H3jveNh^M<3BD|bxYh}C3gNYs6WiHxso08R(lDmovUc7NxD<>FB|n%e(OGiL+&{MrVWI0u zUCZLj{T-Bl@SiUPWW^SmKG#}_%j5!)8m*q)S_(c}_u7Zo*4!km^-mG8)#8}3!xM*i?(NW3Q=D+zf@~zU|gvp(FU#}=qeLt#h9?G3c zqlYxZ8MFIEhlmlZF^XqnnNsFj->yO~tDdsSseNqaZnsO~J14)lJ4(1@vGnqt5TD(e zt0-w}?4C+7?6bP_RCXp@BtS^pe;iw-n9$bfrwr;=jSX;P_RHB>>Yy#`Wakd|(*e9P zKieI1nGgP_EhLe+rFMAp0>B>iX)Y8+Z2deRE?36I#O7u*hQ}eSGL_*@t|~*9R)+A@ z_ivTUgQje&U8$U8pmMH_7TO5){%Fd~-=kt4Lb1^{rmO5y$B87M`(kth1qPvZazZu7 z@uJc2SO;Y(hM{w6wXfT-{d|*bPZs;g*i7N2>>);)zVQ|j0^`~kL|;c?7_70%`Yd@b zoe`uRgYGL-Gq;#|vqY-s1YH5|l#r(K@5B%33{kl$?uZ_NIhGvXkQUa}x^KT(jWOm% z>{)#)TlE58RmB5wvG7F~%QNIS7D;jQvGAE&y$(IRen{A0-|2f&Au6F{$$xh6NLwn>;w{Zn05PCX6zgaBR1lG8COi@`NF) zEOURL(yC1#6|hsGa*E1Y?;?N8d&qBYpY001-QCtp+R#{z2}uJ-OF*}eGiziKFvX|4 z#;hfj`Kt&++m}77Vy-Vi1qm7O_<^M+I_aOO+G=Uc(=2FpdYUwdFwnVDId_57aGKS< z>aOK1xKw+N?jmKFRA?$H^Y;5HHSxEdjK7QT{?EOBl=OaOU+9mC`ZvlDthq|C-H_Cx z>{Y-{}j8vD)$> z5|do=#8F7XWv|bCuu`;`y?gxu|0v2!b)XUYT30FVQFq4aL#5Rctq!LRo({KlCEr@8 z`1#=)pheocLIri;Gtg=`?=y`(wxE1#os&L!bT?rlr-5GOghA2Br!;T>#(&b7mcQEt zL#!8D393VkFX8lq=KMCEyJd-)0j!3f0`@zW(;w6yT)gW+{uTk%V|C2$NN|Q-jGL#s zV%qx`99Gkuc5{4HcrdEWIgnM{AZTaqTnO!RT7fE^rn{HB(;8o=n?;IN40uX?DJr|X z2P0&RpZmLi4MK`7l2`5JjTHj59@UvpqBMg~^Em1%4#zxyP_^}q-?G0-!Qf<=C)r<~ z3;YnQV%`=)5jIR=7 zkLRCMUY;1IF))9{d3_&p|LsZ6P&GrZVA?46)W=_PwG)IH`MBtnbjY9xpV__@RX0u{ zi7@rl(O)0KU-JYyN??Mv)Hg$HO*za$seQkNN^;3{O#)i=hoC1CQ3UlOQ4@=Fu*z%_ zN3av>J$1tUW#}O`C=n}craCQsJnDe? zeh6MWH;0x5nQ$1ZGrCa5d1mK^t$ok%NVF7#O2V1sDhOU%U4k(vwQJWiW8M zzQzU)hrSyHv3F*Vzf{)jPR{{z%Ls`FD@b5^4`t?YAG&`q zp%R~nVpU2d0T@bF|11$}s571aWpd4_n0Vggq9QXqMBC+f5?{z&m^CGvawYT|{PiWz z?lR}_haP`BGVHRHJ_DZjb2MUt;Y>Y(>UUfHUmZ0jpXXF8;t?6sVa~N?XKx%h! ze=U5^i^%3BJc^YSj!ROrS7a87%oXuHH$PFw#>+gh<)oNuV4PFp9#K~xcDFRKj@UPq zV%IRBZ?3BFwn1}G$BpZ~!rFgj>0Zi3IWov;_!4&!vV|xUPJvdLT#DT&bsc(pD4{8W zrQ$WQy$4_ucHdubniY*0hKY->5n9k83zm<(4~m6U)XLMyK@c|U*-eVGA;K2Gyk4D( zA`PB&e4ijl7`J-mOz?*ez`Ki!joDb*it-YmV0+@&dZ}nR7>3ldA6-7#`;LIrq4Z1Q2UFeO!S-HOB&qEP2EBJJEc{uxc$dY%MrO4m$$_OWd?pTo&@`_j9 zaQsxc+;uY-iFX3YR>XZ;i??j%H9S19FQQZC7K)!vVk@fLa{W0&EL3mS_uFHiMBi!y z&)r^rQ;|$|Q2a6Evlw{u&?^am|9jzlziDH`aX1xYe@XWh0cxX8Q)5=lG)oOp&&s1m z48HN{J?ZjXapTtECgEzEJcF3o)aBq#YJy}nDS88c|3Ymy-Rz+m7HQMqu}SWvAzBrj|B>o@n$4kLSAFNY+9*k3K39tUE*`<>!m2LdV$CWO@!R~vn`}&fryzosSgaXoEIxe`6 zBKaCLFuASgvy%O8mpSvJrXniYc8?N7vqGh0(5Z=W*M|Ku;6s*dz~Bo~{+u)!^uH3J{i7T*B2oS>;7RGC1!7=v+5TU{E~${$|a&I)T*{`(+EQOu^H*LH}=*!ojmz_ z8&_`~I=eX-G29+7nOU)90rK~;!w z*XF~wRbG#IDupIN!7HPcpp}EaVyl(Q63j@a5)|cCA?WYOUGbP4OT1bA1k8KawhmHJ zYyKP!aLw%chHB$tc^q%{L3L2&i7K=F7_%%tnXL!krOe>PR05?t&A+_xIle6lir*}5 z8-kQq_{hm7gQnsVk83gN?Y3H~w3D}ocIIe#i=I$d+RU8U zI%%UsJ=uFXImU}*{X&A}BHUy-DBYNBqe>>rK6b2nAJ3BAv7SWq4*~rbfd{=L_A`7L^XQ>GsE_#KkKJ(gx!mz*~r7x#*b= zO!RUHbmQ-kiX>RbY=#rtO3s7wW&DbK`}SD_EA+y% z;CfWeHcU%@-n#&CfP1hqPEh}ceFY=tZmJa>IwHL)%Ji@>l~~{pnJL6;Z7_UeQp#A9 zreGD9ahTxXC%Y5yJgI1|#`EC!v4J@iu9{!G z$$rA2K5aryCXKsy5H#eVWN1>CiZ6E&2&3tkx|_d2&C+TlM|h0WA@1xmRNrVDex+_q zRqF{nt`YHBC82p#T|ExYdqfjHOp1KI{yaw|Wlc}(dfX8{0u2$-qf#1$jfo&I-kwEH zFAQ2Sn;!L6a*9&YQ0l;UJD#Rk%G{K8{@bi!2bp$Mu+fRMd>*qoFj^_1a(@v>`qyH~ z^+>Z6x<0cFWEZbHFh65o&Pf42{&#!~y&ktw>DKdg*-N^-IE=xM6$Mi}qY@&kH2Y8m z%Xv)jG5;F*7#DIsa4Ff3+o6JfQ@&ZM?a6`wRU-e9^uqbvXi>O7UO0>@lU<5#arJDb z%eUS<+dB@Z4|U`k&9B@!<<9$h2G$mkE@AkL))2YTuGrF8S$ zos;LPP&}$vvBNEDm6Gcuv6r~fJ-^AgD z=WZ>B4qmZVPB!r<|rV)qp%^p>l)QvaO z;sFz*aXL$53__oF?8&&YWLtYMmu4=ak}C>K<1D+Ra$2RkrsU#c{KtR{d%ZT}BzYF3 zd_t{a@)EdR7-)m%os+DlwoB&PyD0WqZnE}K!4K+4M$S=56h*5d&LCNdNnygJ%LF#a zoyEIfU3N=6T>TCow5B&jS#0aARJm`c#S8n2-_VbTRtHk|t660X9&5?|3uE`xD-6>` z3wGPKZQHhO+qU&=+qP}nwr$%+zv-k;`r=Eve?eVUDygyNnhRySRJnZ*&F`%?d#h4g zW8JSX_gy(uBI6v@7hdEA|JDkS7FznDN3LvKh?N$w=z#q0B#Eza0YX&J_C2 z3&UIJuA+J_?=NiQywvQX=2}jpt`t_U(wx834!Aq#A;2#4x$pFAT&RD>V|1ac;2%nK zb{jpMACxwcn6RGqBOo46Qv#?>Ax5@Be!Cpwc9q8{m#Zc0>plOQc6V?;`6bw0bW{Mq zp@MGL!coezm+QM4-AB3V=3jPS-^l)UWzMiWUOxXh1M(G5llYwoZDU5%q=0LDe@HVk zf&B&Us@2!^E{K9h>Y*as0JeOrVM!hHTVicL^ea5df)&xN{W?30Of77sjW`6&l=sdn zi@W7%vA%s<4k@5w%1yVu2Gi#omzTRuQ_?uQ8sCy#5+O4~TtQ8ykaqNeRET0qMMoRS zy=-y!;~%8yf%tJ$7n^$YZj`n&90hpz{uo=r|7JO&r&(FkFV(w2`uxo3spv~NDt#@E zSWYR0q+VrGI$ep#m|d+>)F;(lp%i~Z|d`#_d)?ObYNSX$3@)NFBqFgwaz}7*??R_@ltEmJKrUD z>DrUi^l@>?YFXzOszIo7(Yyu_`(gRnsN79Y9K_}Ggk}#D?Fq#Qd0IHzIUC3`bjCil z+8hduySk*I{0F92S!mpa!6nm`+@&_5iyli$gwwVAec25+`{m&*;`3!sj#25=e4S1iXA!5LzF7e z(___>xCEcjMU_9N+b;}EAKgN^#%{H`xqx%|vpct1Y(dpkzyh{mq_MzH-e+R8!9%M= zr$4QJ$7aqbgtSU=s|2lB&kH@4W%o zf$G`)AgYn#KQ;f`sxd^4J)gyRJ-U&xVh$Mw0wz)K+iCCY!_lCrW`GlC>ZEG!5*&(D zvN5hIN$Z5&+8mxz;TwXyVdwmXFR}wQL~mke6#=pUueRX;61|XM7m*?R?(TE-sugU~ zj_?+JCVGoGi`IRnEFYav+U;(Xn&)^uq~3WWh5Qvb>n!0m`!O5yz1c|FiP0vVn{)hu z35$UeVo;;RBoU?|Ol25YL^5B_pJ{>V-VL(7`!EI~whKLJyM$ZIQV=nd2J1Qi+r{2( zqlmU8g|Wd#h;G|8lFVZCv)SQAb0We$WOm8QYYq7X*R%8qVthV0H;krxFKhHJSKk191($;PfmUzhM2Od%=~CJliE0qek&_O z#r1IKJd=`Sd%h-LkuEVVf*Z=-M;1M1>ew9HY})On%lfm(&|`6?VX+`5#WbPqn1tMZ zC#>YtJ}Hjw&2LJ$7^{|ttGj4*l1HD1KQa^GM^koPUE;MP$U#N}LE-^Uko?^C5wKox z%^5Q@kJ#td#4aNqZ|Sm0v}ZEGP}`=0SvG*YE4IhxI(^^yryTd0dalt|TA;!#jCmEh zQYhMH09sr&T+63bBDiQi+w=1QXd274r~O%!VvmJ{=vqaBQj&K&$DxnRL3Zca?4Xw4 zp^Sd`{XEaV_q`-GOr#}OOCfd!8&NE<{&PMKD*o`WON*8X&will1Rb!rCq1ru~Cfy}B|tqivg3p3o8f>LwoGB_SyGP{!aleU8zt zeshVS<7;gU9$mU)sf=80lf^*gNsmS?1vTyE--~vS$^P~VP>bkWx?5avR#CmMQbCB> zYBcUO>iwGgfGQCf7C zFSF(K`mDFEi+9fTCZmOO111_Yg+KzloC_%s4FwTM3RuM@hE_BHfIvY80s@8f@R%jA z;9$P*MkL!z0UiY=BK{XXI1(HscywJw&;mvQJpy3+Ef`p27=Q?AktlIdfIt8RBKZ?L z{5c-1JgD0MA)ppvpAQL86w$GgV8@r&KyKDTCa2FHkjFqTAUrv_xc|-}AQ5{R7z~UM zpp&4Pc^Ot25he&YI>7(~<>o66g{N`WqPeTNzP_!k4PhLXH2B#e@eCEfV`zRBfS3a6 z@&Gghz%K@79=JpBFPcnb7?Qy;wBXkXgBW*VmjIpuz&K#2UjYOP`7k0tfEOVB^1miQ z+<;zglm~Q;Gx`94{kc;BkzkSElw0}dIuVB9I|BraXcuR2LLWm2@&IBOIMDN|D~JN$ zc_07;phswkprZJ6k9c$lFmO%-fIe+-z~vMeK!WLD|5M>WUV~eUWCSR%Kh~oAI+k=> zHDLjjcsn}<5G>K>Dt^^;aFpl`cl`tYu&YP`FXHb%JM+7*2oqbohR(@Pa%D zfcLAXI&N&3Ap!}I?YF)AJ#m`q0#nQKs-ZvgV}H(+lmtEie?djcfc#_-1cLwA5HLO& z1svp;ISvrwwJh#0d_{{t$;1}Bp z?nk<_QvqUn>87to%K||RRtka~rU+E@77Fn0*EFnP*^o~m91sT9?Kg_me?!*)0v1kK z05+aty^b7)3<~0#9$(DFKz&*nB&6Wf9v!8qz<*U$I3OWj-v}8s4IqGrN1#_Ey=k<1 z81R<}LsclBuWted0ZoWtAsqq0Y*ZkCc=6x)+CU^=upq_sG($4=DNeROr~g(UfFV1^ zAo9!BeO#o0JUo2#x1Tcb((K;Vo>rKUZ@xichb4&y+2Dz)$d+deQc>IfC&TWdlekQw zseLm?ruAt?UlW{P>gcerska2`&b;!!jmGhZ3jnd+o+rdSaC>JV^d;7(1r4j7s!8x5 zP~g3|JuX2_0tv7(#fdV;DwHqD&}oy`)%MkG%G0H^IFhbmHa$O2$Cbd%`ovAZcECva ziH$|f1^MJhF1LDo?M6qMB5+##_%UTK4Reo7i;P%3L;lc_Jj%9_1^+kQme@I*@8=6$ zIsH53h9aSxTdRml398R6zqgIY(8RBciX^AoJ~2Z_%BZ}`OY|ojhec(`o)Y}$-i0PONI!DcqsIyA0{z(yFU_YNs(nTSvbGCzb9u? zNMMerulS;m?-CoVfXKk4Ndai_xEa$8=kwTr`L?s3dMM~sl;H`prLNY2+Hzo$F+AoM z5sN}m?^U@uw?%8(hb4FvGaoCYbFCXplQLX;A-zG9dPP6HT0!fu(CC!HbTP`rYYXX280Nhc+$wH~I^w5JrLyS#}I)`^lGXh1O9XxwcD*6&OKy)Lh* z`l~P5EfMfIU_(V9?VE2nYV$87-rKM9u88{4oZ%^1)2WDg;E9V7pA+jP1MbSjeDIH0 zdB0)*Ee^}|xi*E$sMesdVmCREx=mjHxox`@^tt2*vukU2Zuia5IJ2P<%3Hvcq5M!6 zes2-P?m|YvZqXBEeAnm-SA2=Go8pN6qN^U`qX~B-#4F~EF6)BZ)+|`BuUq~}e5xuS ziivh}e94F!wTn;($&Vu>@hs4)M4v8kNgyn12;>|w2t!V8Hl&&X)aElwDEDekJoXW# zWnGJQ{A@R7-$JVjQ>5O#J8-@sN+{*Nx1lM4>mzeRXx|9;Ua9ff&7S-mSnQ{;=t{%R z8IOfj_cW+;g3X+RX^Iy-F)OVXM*)u z(ZuXLz4WUFCT!D+5J75Yrt@A^|aDzvuY@yI6?%2hX^V{pjRnXi4)bxIzsD*29)z$&A6n&e?9ip{y z{(dQ<=BXEOvcrvLyOEwupBLkQw^@iIEx2BbI%G{xKZas`Wkhp1PAq$0NR<=XrE^Z- zz-oQI%rGDkHC1VYj*DEecOUy|Oox5x0_4`2)G2PNHRH<-Gg-8;x=H2DFuQQSRF+Mm?VO>Nvm(#M zNs(?qonE-myUv;_BM3Esvi$0J_Zb@Pb8#Z6>w)ui zqyI|5v|M97qP5Uj{?bh?7Y~-{6}BgqVd7*8l66`3 zWBdMmEC|=BEv53~igI^0nnlzPitWS=IY)Brxr7#@Tte0C1_VG*+bacA3*Uw4HMd^{ zXlO@GdTw)#rAYz?*6KN^x;69I3v-K+C^$b%gOZ*R4THfRqM}TQ`_5Fx#$vU96^&a_ zDrfQKP1c}(n3>g+mqJ_1fa!OiXHE)4a643EebLpeu0QqVdR3YMo3^DZL>VObj^WDw zoP@bQA8V_6ac*v1Lk^oM2|AvMb@r10m2Mu0ZqU`Q;WK=S6G7k|tIsy>dvkTW@iKO@ zeFAJ?n{p03W>DMwd`yHL;d4{#U$IuEQ4t^1I2=t!QrV+sOnS&cM4X~~bUN7C)!Jl` zH|?hN2$JeE+%7DmOmT#ZN&J#23uwd}6wX65##uB;%O_>ZaczzLS^U(*Oo^k}X)tik z@p*UI^V9h=X8+PDp~bw8Dq&!-9K~U1s#oRxav$l*7pS3!Hr-D}eChYN#(@o3=V-2a z@*%ag>sYe%u`l57KvGOMvTdkjAQ6o3@Hq3K_bD-FkC7z#Uy6GEt0ljWZrxpzB*g-@ zafET(fZ3UY*dt@gW%ZWGZs|#(tZb6nyS~u?U{WzLsh@Z_acz2@dxh@?zIm{6 zH)D??*iPBG%83q|i5b2VX$Z#j2Fwn72vl^=iFRzlw~W{c#Z%SRWqL-rjNirfb!K`4 z;c?k!i0tMK)5XlHDbjo{5dAuua5ToVA7%dz^ZaIpHjv(H-aS|?{JzE(QE}_MJF2|~ zMZLNYOg8gSkKQKdENU?>GqpHc3`93U2$63=TW(k3IY>Q-`>&1UWg44i@49ks(vAvz zwZy(-mDc5m9`ojLT0Ukoa@HvkxFLnEuD4UP*=Qst-gW?ZdoUsCt~Yh3gk8tJpf-}? zex?LULNfi$sAT&LUdkt7ZZWBH6(IKS-U^Ofv(4UIto<@M!wj7F3*t-(ITMxBJYT8r zq@=BFpq3C(Lgzch1fHLNu2isCAcE~dR)@;JUkr9mt7&8TK&e{Hl2nIDW-DRgyLGQn zymzN|8y?op|Msy6jCH^6nA~M?pe{f#w@F-2Pvc!vca|dXy@AyN5FK`TEPqIju}+FoYW*n-%*UW zZx3LO=wo~yT`!rYyigbR^!8^Tk8Y{I#^bJ}X*}Nrho%3ktn?}@WnWg!71;t+)W9I` zd46i~ZuEE-sf1bYPMMOUFJ6(dRvdIZ-AZZKW|;~f9Vo3(Fp$U4**6>!>rx$DL|04W zK_%B$s2Yb+fq4vA5X7dU4lZrRVA)sIXxghSn7N`qG0Ag!`kMOr7gw4*K*#rTa2p zFlkqpdexI^vR{?%^!?`Bd|q%g0SRK8o`TFihg8UuDzjfp{O@W5;oe><=?r^!`OtMZ z?{{#gHdO|6@-@-W+_n4;R5Z~sZkD=~+hy&-=@wke{OzC~gY|!dXH8swb;CS!(&6je zxIL=uri-ak3pp9>`OJ+XUjF8P7E@}dYF?(gJ_Ip|Ge7Gjn-U}?3LKXAM5 zj!ogXV~$JfH(_7}f#zw*fKL2JjSPS0ox?A{Fr5!o81BGcb;w^D>a ztU&fBKsr<+Ba|v&gCtFTvWVn&W$NraIi^JLXq!lC^rj{_7I;8trA0ALsoF*jA?q34 z1;ev2&pE|lgmd}UOLn*7-fufWI-cRYA_XTTq&BX!X?dv^&f#F8_2eEN8Ia04B|fbW(?62iX$GP+ji{Z{wQInDjnc$D^trjN_0i1N zs|vr{xzuO!ph;>WER$#;A5LAqq7!DBb|F$7O&hKTX&9|D{@O=$t5d7xd-}Z@gz}L) z+FakGBc-`Wjx=V3{(b%OhH|d#B64@%3o&lsAdpYUe__pVsXUL@&TsE*`0g+;U8$du zImGHla}9hzLb1jy>Rl2@Dn06%bGCZH2yM({N_PUeA62Bv@My05uW&g<`m@Cdhxu&U zyAEaoXW5?}PVJpe>)SgOrK7w6+-#^iDoJgX`dMGrrD9syhvmU6v(bcXEWGXt~{2tyRzDPlss=e zLrq$?bDVejvl4oPt7hYg#4yJ~v>z;a9Cj4y_v&(~vyKA~ zQnzeFXZ0C4A-3U#80l%-V%6D%IWFFjmQYbi^6Uyp6kuZ{+UxrUm1C6#BiyVbJ-&U%m0yJsc27G%ybCu8v6}wS2hAIjmcZD z^kw8?*SA^4iHJR_H_K|c36NHx1fcR*mVq!p5F4k;^+YF8_bzKo;YrgD40E*qOxb%g zy(%wb>nD#wu#{Zs^J%v(o46rJT54FXT)){r!rieqw&2ValA{uMjTY#A66z|u-i}8L z4*Wpuxqn+e+5QuibM08Iul?maq3B-fSOS8*(F8v0Bhi&B#KW zteyyFBt=t!6at&lVuJdxA)_w@6l&8evgkd`{_k4%z{sa!w}togx~9lwrkl17Ln z8RmIey-!$h@8s~~`4193Z6>ApR>_?n7CCBprKx|-51g>4*LHKTB_QBN-I<-@KT{v*gpT;IxrqbB|EB|fU} zOd{M1YYbH(X?`A48X@^rvdG8wRd096HZjPGN4M^U6c1g?Me_X;Dd5*9J+r8M{JZ`{}(BScv!vZnFWVIJbH#haO~Y+Yp=AmPl2lso35GNOJ-X zk9Qt+7F7O8VonIz3RMnYv{p&ebk}qt)-7_7_G-sxLA6y-tOO&?SSbT4{SYjt(fQR9 zd>z{g+>g$u&Fi=VD7|UZC)oI09Uh3Scv)FYga6lS!8ozpVqE3K^Ko4gIG>xml zf-N3jm?Htkx0tSw%5GIOkNTPPL|Au*UMC7_YO^7Xrm|y5 z|ArBL={R1|eIhfpJ99z1z3g9bJ59cs#K?HjaRl=n0~1bZTu}$@BEhoKw^d>bxR9(b@e|lT~1V%Ia9!)0rXcQEpwiMgS&9&O#uoKGZzFYkDyoyT>|3bd2 zp0HwNZ5oCI$q!c4uG~U)TFbBBKODU9`RP8?S(Md1V_q!eY*~JOg07f+N6@o7CAAEr zv`NknLpABU@5d{^VP*#5s*ZNVJIyYa{|P+g5r5ZeT@{`xJ;q)Hn$`gx8=vvUkQ<$s zk4EOvg3_HNjO+kjlfLN7y&{!GJbr;!SCG3Jl{Ci+c z!Z(0a`HTk1&aYJD>k`fMY`ok=sj^mVVh?lAk+x&imW*ED9dtt0z;S0oV`(dtAsE5z zkRSW$Jhf4%b-5{O+x4=;h0vqJ9dfLt?=`7MJJ_*hM=Ju0HeJ#~iNeG-YSYF4yM4ab zg3`DuUmYVpnx%8+J%`9eoOD|exRI-Xxe2ZvMY{Co-)<U9 zz>kHoNNyM-y&`@69Ppgw(ziA0fzBOm+JOIOG}dU%!)of_*{BkTet_*A@cNjM_!^8s zw&0=lvAN@C3S=lx>3`eb_n^kVXojYD^OT`I_+_Cwc$fm^Syssw#mD!vMKNZBM=olQ zJ!aH2T|jqrv!9>Cf%tN#P19;3Wu%u9{6qb@p@+O86I00E9Uk#bw7MjsmBoM*?q z%{kL+m~(T+oyjv22#s2yC9%M-cw1W6;d3VVocS%P^b%Tkn6{fY zQ#yqX(x*@9Vm$lkng$-5kd&c0ezEqtrg$E71r3_ za1Mg+=ye+#Cf_VcAK?qI+FxjE=XKld(v%AKPNg*e&-y3$6zk^#TG6R!vDS+z&pnG9 zq$rvW!cRkX#y?LhLc3f_NWojBux^%wTIk+WK@13-5#F80Sl4+X$Uca{n+5(a| zjO8uGcv)oGMGhZ)Y|a_OV8KY0Ye!oiri)787->@9oZICD=7UTF_ZhxRwvhcw7cNH` z;vWg<$4R;Ho#ruPngXtj>|btax|VCD=nM6CgvcvSp}c>q*&RSg=tRg$4~Z2C)bLlj zAxgDsZ9UYYHy@CLYg^=5e)QdKvfWK*k`KlEVU8TAaxwO|uA`t29gHWkUR8J66VR52 zrY_ZYH&M*Xi)#*9jdPM|{a`_^MKSDgs?#slbkJn=Il3g*YYj|~yRE%kp7(C#c^b{{ zNfl*Ag~;|a9{hxD=DlbpD~ISPBKn%xY&Xjk37Bvbg;HaCK7k+&ds^x&=RI1|hr4~Coh>WULgGY{>? zE!(jO&PwN7wcm}G`(R(Yuuu*Gwr0E~mqvy<07mr(zUa}a`9DCA<$r)6J2Tt=BY;f* zEze|U{XabT|Bmf3vNAKV|KB3`|Gfj(w%ysKWNwiS$NDgWe7zwi;wIw8gnYx%&1UNq z1X;#rtJQWZDdORGmh;Ye_r>Q*`$v97Rdq*IeeJUAtCS?A8JN4ubN!zNre=nQ2Vi9) zlT|ehPc{G=nH!0e6r(u8{Kg_24V(+u0}zW~DS&D`Z$Juc|LEXgqzEKJQ`4J6GfSHT z*nIl@FE)t9I)E&#EiEn}mK&Q}Z7LZWfSrIT>lIH`tr!Hzsw)W z@w2=iK&C%OF=%?w^zVaPLxUo~W)J|2kz4C4-7JB4Kz9!1I3mnD`kP&B>YtEFcHke% z2S1{KwlsF!-(LFP)dRjeV*Lj{4O62NLxaONc$-UNvkQ0zl_uBUP)}14^f`Y$**X6g z2|QDaOT*6`PQL&9hk2OnO+OpnpZkXY>u>^Ry9cTw>&$b#_yiX->T+c9v!@k+kc0gH!}QG>1zD4{)#XDS8-QZ=yt0Y zy|)1veXT+ouZ!b`+WR*}=4lx!2=X z=zYN^T~KD51lPg^jj?v9{8@kVFBHiU4(;nBJZ>BHQ95xV`pRh&`KuwuX~%*k8ZBjR zPIY;Py&>hDLWyt8o@NgJ45M(5%3yU=QXgRLob^AS0t3(GEwmFb$O5A8)QQgNyW%r4 zRZgU8C82Mj9L<*-8d&{~*kKzS3{%15llIYlU(`{<5+%SRHMfCw|2c3f&6%gKDS*Vl z#OdFNB|ERTMXZ1&N#u`Njasz*1dG;@(Y_08JWunXbC_hTCY8QsB{2@CIm=KKt z_=%m%l`(zT><~$07Fs5D2kw&We%-2BZ8c-?qOJHS=5)NHSF4`ML5FcX&mR!@);i+J$@jLuK|lq)1~lcp z3+Vwv7H7U@Dd{rvpzL7CH5a5+?WhhbyOVEMQF%kL-FGESy5|>-v&9T~-tyOf!;@o5 zS7+JAF?P|r4A+#g?_7>4=aM$SN#!ZCxXH*I{mmMgm_#X0Vc9>FVwkieo`G2}=v`Ht zhH?Fmsnq!nSL+F`Uu4Ygt-%^sQOg?J(02OZdqc-236pCjyev_l$Km}FEk-z*BZHWI zIP_tQ^I=6DNh>Vvk>D=IhnyKcb@cbX`S>noa3qepBX%Sl&dba1IX4QYb&|%AP6_r3 zWxq|Q^2skX1D<_~iRg~Q+mU3!Ekn=A37E?c)+;}{hFGLxYAmKp3*m`+6S$JSzQ$+y z$a=a2M|(n6`kIxV31V=RxxZcPUnY};Dd&zMz%4RdaNPIP^j|^7`prvAF0=3hWNG?N`(Dp%sWu)Nu zOnM}8K4yA5{liU&(tu+XNPOqK>{HUEV$#%j?jL-rbG@B1mu}E#%k&tOP!0v6mA3NK zDE?k7Zlw>IpP2fvrPRs9<>f~bn@TP)cpQ=djWx_3fy<Gclm9RBok(Ub|p50^~KTbaeE}|9+_Uv<)%sgh0*we8JJO`Lw5hN2n&* zYQ?WoVCH^S@yK<2=Wn2AJpo%-D8iM=erd#NLptP^6*`s2a|7}n#q6brNJhVyVvlPm zLdiY`GE*XKjv8P#c4v&DI#LWW?r7Gps}_rlFfYJM9nQA~VM7J=H#3~r5nuSDuxdO) z%t>I~EQXEl^sH?SEa9RhrJL0H1KxZ|!7BfPj>k&;A9oOY?(W?z5CxT9Ze&<9 z{cQRATWH4!8HOC=caz+rjuvJzVLlJA<^J8uz~R9^G@HW& zN?|}~_YPw9*}VToj%nA9pB!C7wlbFNs>Kd-4L530VNDf5`Sqc)=C;GvqW$_ zCwPo%>zjp9;P4VluzG%ML-w=hjxB=kzim_Mu2s8hH_sSsYwmhIvo++oL4S^pw92J8 zUGCA>-%zbIfgF+_eFxDK;qQJ@UAzZTE}y6)tJXFpd>nKxW9~ z{c0hbhj;&`$x;1EFkK9?_I|2Iidn*a&Vo$pxbvJm_!)pw&mD?s!8_yHsGoX$U6WHn& zVdDBT-mgr!!_)-I3i0YZcz1QR$uF0UH%yq?h@9{zx)t%H?ECb$!1gYbL(&GL{SSQ9 z#@4;Uucva%?|bwCGAvz`!ikr4~qkNY^b_u_W-=AyjmkX!*f1R&5YHV^KcCa4|sSnx&s?01d*)kEM-J*%4K*3L@v!}3*N#xMER||_$)~;2rhxmBQsKlPjhnS>Wh0S_a5Q*Spu6*f{b%D-I`s=Sn}8SmJXaF23p8Nvu^ zAXi3GW49^t5?2na;!_96qy^=eUulL);qf-DeG73ytLf#z{mn^a-#l0LuJxeW`8uEle z8p`$@vntficvsdvi$>*ldU&4#nbQiFZ-&J+Q-b_FI9Dn<`0@|FhRuQgR&~t1Mx(e4 zuS#MlxCogAN>!D*oK%x@O1W$!*q~_wG~qu%1GVOuOdyqcfq*w4{0A<($c6LPgWP&; ziI_Yj&<~KNZ-hK`{#5nMO`rofsP$3~to(`=uh$dxTBq~+tzKfqa3vZyIA68!Mk(AN z#^HuFPd0_V*8Q&he+lA`5ar#u(NbYhdu_Jygz!vSr8(K^Nq@;Z zH8&MLm7Z==>Hy3l=O=>0Ey2?wlL>7LO5<<(tMi4qfuVv&aHg^lM!U_DwXVJEfKO2} zzOzuuhmN}V`rj<0{>$T{c{`W&Wy$EpB8d;(Dqx+3>^AkG!YG*!&|FG}SgZ76&cvLW~*x;CaE4zww>NA^N$Nd)m4(D>9UKfEZZ|FiJ2un-< z*xrfn1|qO=g^62o@hv}rM)i{h6{TM`Tk5?{#mlv~yvr!Zt7^v8Ng3a+DZkC+qn-{T z7pnIv=X|HE@ta+2XzLa>+DG$BJtndeo)&h)+qM$uS<*iBJ>x=p- zM&|vnGSsfh%4#7Iu&?wlNy(YUO)L{;nmNDl-oW>-H}EZM)_Gr;8u&f=6+I~t&y>^D zpQKdX_!PR`WC!Udzr^0mL3A$pu$(Lxp=XnfHl8o=07A29@NR_ep5;%mU)R}mm6<6; z5|DbgI>F@mj+;m~aaG?HIOp1FDY5bYu&=^@0a%YOK2s?d${AF)0Pz}zq4q&&gchjlr_JwrP`|m`HsJ)YPu@HIMoVc3~~ z+i#CecG9Zp}(>#kE=LJnX`}* z3w>fV@$5SdoT$k%6{Z`Gu2yD%?}bMkbLuz@)20&8yI#nXi-{Na)X0QiL`j;Ce%jF| zv7cNUC5B_2&1QhcZ0I(RmmnM0Uj-FV`q(#e)6ppFO-Ms-rrL#auGT`mIQ03h?j@XX zwZZQ4Il;O6jb{BD@$}Hk`VcUuFKIk@%Bu?BZT7y9T&n^59gwkDsJ~2H%aBk_0)vhb zVpWNc`G$!b7SQEb*k*#mVQbV;rge0#y_u~{rCt#$aIM9D8i&@5lY@6(kb6UVd%;KAt?CDw-jR%ek_F9OjLSiaP^b>hRW zmr2yqI7uB-n)=Voz}@~}0?dPt>55|ItA^N5Dq>eFXD*_kLFut%M5tghtGndqgg-{` zT_EJaOoJh-beV4?T#Xj5xynll=rY0@96SGy>G0=JG`dO(!=FP4)LLb%53HEF!xk`j zMvDAqD?8sd2ffShV^rWxTHlEBr*fkkE^vIRiNeN>Fkjb)3jw^<=fZCMM)<%&JoX!A zHz+=A*xR2%gr+NL?ZYy7ea~shIM+B>!W>Fa7$LxI`96oZp2ZubB@}2D!v1*#hnDd2 zK8L$s^H-|-hX7F6(08MwV;?c8WJ)ipR9~g1fnW18@ zKIyyn>^C|U=SX|p_JoYTMMXk3tbJ3-GZ!*ty$-YI%PQk5q=m5%4i#azo&y4)+S&3u zI&%;X3S!r_xPXsbMgi4m6Q+@pon=BnazgL0V4Lo^H9<#%i#-hN5Yvp5S=|dInv$_k z9hW9Rm}1P=MtnfY=AgB4f6cEE+C!vFJOrDjr3>UWi!yo=QP-yVyHnpd3#i(H=RZp% z!^>pg#g;jJ0vP5fvv9k$J#Ftt#@&P9PvdCt))*lesAC%_mt!jenRE;(D7`^(2gEA7 z+aTp)`pL=N^>cE=A({~bQ+0>n9W4KJavN#;8vzq+Rt|&Bt0^-y7lc=F_X=-C0HpA{ z^skL$E5!U@-%)PnX%QWM(h5PEetyA2Ig^PU%;^WH6?Nj`H0R=*p!BprzS; zK29ZbXx+LPcZ9E=o@4E}z38@|H#eo$1u&DDC1yDVu^%YTMd?F^MHsBHefUJ1az;dK4C4@J1NKaA}f zGpSw;pCpE#m??J*c?l>-kJiTUwt)BqiqbA}h*al60^}M`)#!`fdZvlF==p?41x=wJ zP^l0{tCW<2@ER%~SAl4^-Q z3mI)ciB%4QdIjVxvJDxGqYsRsYD+Kzn`s;#$Rdr8#mE`DCOqnCh_x;9h~(Ewldq$t zy%hF(BFi5%`%^`#Jb^xdkm}Z1zif)FNx=NIMfV$@whT6kS`X`;KMsuV>yL~@a@a2M z-+!9MIekP?fwQRkOnWS1i&B#lWdk-LXPS0z4q2k{UnM*3-|0M z%xT<7UOwc1Ehlb4+gx*|n`1BBg?6=j#A&APU%~sx|060APUfb!?kn@Vm1C;VZmMDj z{|Vax>;6&oB+ z6@B*=P|I<}ZR}qL!cAHBSR8r4%`KNC&3$B#OaA6wx~iOe?c8t*XSyX%J6ILmC!0rX z8M!j&juheo+qpVa-=%@K+Imda?PPuSKgJwe^%+dOom5`Jd*I@2IEe-cUU4XBG1TH4 zP7O}e-XQ1d`b;+~b{=LlWZOmBJNXQFkrJ9Pkt0xECqsv_m8m-QX-54Tn|E^xSQ}vT?V4vUvu&eppchc$BWFgO@|qp+cT&7S})k;%tSo_z_f@6-4p z6F>ySt3lohEzd@CgyJ!7O-Ktnt1mhQZPmrwd=VyIj+&@eW2)wRRgJ7A!IUfeh^B2z z%og?OLV-v`!D;UkSHbt{ihcIuFnH#ErC7H1;*(OX=^PWA-^x;#zBQARGF&UrQ*Q=; zkpb~DV-)JAe}?^2oNe83b&8{=aG)^c(8W7u5Ih#Zl%DPxH)J)6Iq-oOedIVxw-4hDW(J8QBw{GdEOFHBK?4OL-%5Xd3q} zCVD`YttG_v4cK*KRb01;aIR)iU+k<<`c-L2xRUBDe*lFDO3)o5BMlC-E;!Wx{Tygm z!av!-n~xRE6_1;G(J~S(KbH&&n{F!VH}dZv-_jCSmY)aC=>RBsbsb9_iWKPbJ|Y`6{M+WIDc* zg|3DCe2;$@APAW)S%(gDJlsI-{u?#%F&f#((i!;MI{9d$D!)fa{U)d8-PlNs_$^Wo zG*iWTj_x}?gtjZtUU&qo?ELSEBKYNMR;h`uy!H^Zn+V2{(;?_mF~u^Kl6{MATCo<$ zkvA(xBD+@!(9;A^yWEjg#XNXPN#h6Z-^@=cJsBV+$phnd zDrlFN399H?doDqaW^&!AD-;E3|Jn)HeO~*fIVZ!-cCRti4iSJ#lh~>O<*Z#?pQk-m z{t_P>B77`3+H%eL7z;Qu0Srxw1MY8GqzZkoRMq!qKJEO<8ZQHhO+qP}nwr%4*wr$(Ca=%HEK?a%h zf2gin&z7n?fQO=?9~7y%+7v*33juLwgupdn#rz=)lZaTNx7k%wqgE&TB|VDvATLmIog+DUoOh`^loK_F0a%ZfeiLu1p7tG z{FyZc8+{Wt?THnfQC_i4&{<& zD=($&8ClFu|E>aHBy*EHWOqlnQILZjneTio1no?&-TJrRxuW0BQ>*AK-ECbF{E4v2 zVY-=n4VM!15ji(9hGl&pOeA-0-u{YNKjoC$!hucA;*@ZAqj2zw0h*+jR#&fK@jH4v z9uGi570bC_jM#Hb3@L6(Rw$M2yAtbfbjpy!Ggo@9=uBhwZh95go;Vi*Yk&WpGxaTP zWQ~v=C2lunbp2AJf0Xj|_v?`c{V-8cv&UpCZpm4(LEveKJb@5IBuRf4Onzc(pIy4g zFGc*1y9ue*ro1y2e=FV>h%&c#;|D4Au%AI8_ktz&>$KUVBWLDBWhogg5iW!2JNj!f zvvXKE-`!$sTlJ)Sl!K2Zf@bGaD-98NRZykot)B_wt%$x^>3D5x4OdN#lm09g7+W8k z&kDW@$jR4=V*DyXe|})8wgRq&Q4QToYg3n`asuR`M^gcYij2is`lS55Q}5?Sk`ZKTxa5or}?}j4yf;UsgUlPQ=O_FMFOUs$$ZKiJxdFfEsC{BX43Cn=C+F=BA$z- zVF!I`t#M;sAV$A&ty5khZW(Sz4~EuY_%mAkL9&%Tt+057iwzaHDzLAYCDBzu_+d7GQD|$TG>I3iRG6M z2%yg)8q9%{B}`HjVi#ZtwwwG!pq*HJZk8Ep@c}|R`q8h)2wx%*b!9b1vMkWr6c{+B zL5b_gA^>liq`d1oyqbU%gY7_~cWU!{S^KDU9Q-2C1#UEiLcJv$U%*%*tIJO?cC=}Q zQ$cV<4f^`m9)((SVnfHj8(a3t<%2O6q_&iN}FpA~kr$ngVzvKP`2&1{OeB|3jW z5x8aEiOAzg$FiTA&lO=71YzzrFoK-GKLGMbA-TD*D9ddJ)i@Uc1=E2Szz6f&y35j( z<_yDrc+x8O(5^m+A=-Zv(^aiwzK>wR zgiH8kf~ty6tjs`E^-zebq>@e>0d+jv5F3GYx>i_53?p3Tp4&8l{&w#kx6(aSdT#)d zZlfKX|NZDy&Om$->md-J<;u@;f|2lniMou6%|KnZYWX74eRvZ;2b_f*mDTJFlmiM8 z9&c)*t+E5ml1SPe)=vT0Y0X9ys^3dEEAsJiGvx7kJ=o`%v?PQ9g96*C{a!+vZ zO1lnhE?QpD?|d$}KaF*4ePBHUbPW+=0ZDi?&lAvZlo$;`uJs2>UJ z!ld5=*4*lK+1Nfd*J|Y}p{RekyvE4GW6yM_N}9cjEGG6-e_JWhsdPrBb=Otqee1t& zU~gRy1~WF@da15HJ?h;<-QP^8L!2$52+6fg#nqv(|MuE=yFol%<%LA|!ILrHMsb*; zjw>7=bi%_kqy4nv80W@B+snmuj+|3FHGnSbF;+PA(6*-ho;BM7cHj}yzQRl%E2~Hl1 z5%8(sw^PR>80Cvl@pVpd32w0vXVgqCXTBWhB>kI8YZSvL=Z|@AOHujf>%*41PrV#Q zz`4Xt^lZ{@0`uSL-(ool$K3leU16(jFlxMez@3njg7wx^(Xvq@-n7l#`DuIG`nK;K z+@)oH+bL@&-)f9rFnsQecQo~RG#0&@eB@Eqnl!34gP9K1ZHF3>`ps@un`e+iFI7G7 z?Jec^+NYV8NngvqkyI>a>?w3Net}i*#TjB1V)H15(Ju651z;X)+04I&hLZFujcX+{ExT1m;!W) zUeA9pZ^hr0ipYR#G!2o{o&B{M0nk2F5%9o*RLLOV&=IKg3`EKOgeSDirfm<#{PklE z!jZ6=tOaWiuAk&8AsoNpZYy+w%65V}t2)Bkpg2R!pvQefowja%3I>BeE&LLHYu)Ik zmATr#+~tr|a*eW}3xO#MZ@I=S>+t?+Tm0df-d-Uyahy#|YqsZpm+%zefJpyY61;5m znfK9j(gTdBOBvi$1=c-OZ^o4!7dMd49m4UQ`|CN*3OnZm9cj=3Vja}$fp4yw2tv}? zsGw)VMRow$Vhn#V%2RNLZ8^+sIk=#g5TG!gPy3|Wwq z+L%YYbCcm9@S+GuJSMzhz>Qs~x+rHh;a=Ys?dkZGjzriBgPT9zNy~OA zmK@Q3+P-ID5_M0Kl1B*jR559q@{J85+L8Fkp!NQAxnEA=A-1V@Tyt(M1)kJ}P$D9z zwhzR;V0-G5q2rlmByVJ%k}|2~geX62dGxpp?{yOJH}&ej(4ns7SU1XVq7@_bOwZJX zK%9=%TgGy>-eJ4gmzC0!0b_G=`>cAdU|xxe;3!P?B`-##kBEfMn{)89Eg*+$BKVu; z2bu;K)@03iPJx6-(1QG*I@3y?&1q?7NR;4`GP2Ed#H0pAwl(IJ z$G<(K$yZIC=w6;U9R`%IVF*o~Fw1gc4u_HW#nJAARU8M{7hcf6x`NX&RAG7bmX@rh zuXTx$U3Hrz#G-@U2fiZy$%xzd0iVG8GBQG*gwnYgdV07-k7cG~&o9riXlNxzsqwD){*@3dY{Od{k9s{Bf#tA71YCiIKkF9t7MAND6j$olG z-@R~-K#=0uT!o+_7K;^Ih&r)NhutS@pvhs9eA-rgr?atQcPam3g5Du)@uUPXD`Hd2 zogOUO0-ST_5isR=|AI=Ec&?(~tirW$is-J6lUb+96XNE7eTv-41cDfX^Bc%5N20s# zFV*}%|A0FGWFDu^c?|js7-g(^##j7h4NuT6jW8nBqXlqB!rJ=siD$K(2<~$rh(@C|3(od6cHNc}8dwyJPG$gwr}^;Q`OEIJW(tSNI=NB%4+VPlz-nwk@+L!*xu z^REa-S9m7bW86JnTZERb+k_XPy&6!eUO-MNOJ^pZ!s$i&v%)=leI!>0oMB*dye){J zCJFoYk+(JS^EKfGRVv;8OwpWBJq3zLA!dJy&nu+*XPHd}7zzWlp+0do6vd}AZbTF} z_=KJMDUu;@Zt&;Ci-b!V`OOvt_pz?UeMLvPJC2CPP3L%eZT~9PkvDZd3leCzk!p)!jHc|eNU-{+) z>}Jzf2=eng6SjRvrj6|5B5>>-B4Kfsp=m+eKGln#Zn92qR`>>>{H&!;#s)_Jfha-P zxmtHtxK%rm`@*E6!5$#jL!zawL&~r){zNjfGuTwvoK`X?yr|F?WJC(eCjzVu}NX;{&u|iigN%uKYp}(A|>&= z!Fv{46%6a{A)oQ-Q*GK=Zz$zTc7V9H-Fc8zbQGM2Zzd@G;7zkU&27G`x~qKCu9$3i z&^2Ab1T@kth@8Eg$?3%zT?Ml0zBY>fccZYRp3d-@TzJ842LbfU5Cx|qwbD+OYD4VA zI|#b{Y=~T|Il^bmNJB>KQtps`fUip|ku}K8D3+}h3e@S;Xxt7{2uEJ0VCkS*o(JFx z<$sq15;#ZK93-rRQpoST2?A9%YrD+T@3TVGh^o~@)Fvh|^j{WV0Z@Qd@;sxtO=#O5 zZd|3;MA_TWTOQ;}hcBeUk-}(GK98S4(~@iNQ6h$%{mJ2rNtzV6I~D`GEe4nFCDGXcNWI=_oonTHR zqQ&ut|HzYQOtUPs?`9EozX^FN+b2v{Q`0E;8TiBxbdcX<{`;VH8j~EW_wwhzg;4Md zH>F&c2X0WRckN9Si*i98L}-m`9rS*SlQ?0eu!@Rv*@Nf#<4v^A3MCvg34}%<-=`*9dEX(U^KD{%Vt2=o_d)4G8>J+gh z3pB?8u0|72Cb)Z@;N1@4+1iu4jSp%eRLVR0HNQ5csaHw4HdkPcPTVxq)))Cy*Ve2^ zUq|6Cnp^*h7;Yo>^^Fr?Rz1~M;HYjJFO9xG@UEZd4KIK#LOp-Zv2DC{;dskAToJmjD= zvwJ}x+^XbslgLt-=l^#am3o8!?z~7!hj=~dE6$rbM|Mx*{)$rVdhZ)oxh%|K>0aB=>;O zZf>SCU41oE^s&P)C;O%#E<2>e%V4}U*2?S;p!$Q61%7*dNQcQ29!K}hgG0Hg=Bx&} z=ko?3&7ZOGzQI9{$f%XxZCrjo_w*W_pqo%T1D-DlfT4rpN1pMa=#*I)7sc*jJ)>&ew?7H}9t@&QrOS%ku>G zdf#@>qrn*nDmC7+gsBZ++PJT8yMhYcQ%2PW$JqL&oDwoMe5v6sS-v8kjzTBJ404mJ|?EAEwYynPz5j{ExA%t*CXtetAnld zcsXC6q%nkuQw=%CsFEMW@`g*+V{My?Mz9}f0S~YRMld=boS2jATs3S9MI6$}ClfQTFDpuElc;K_4eDh|~~?$&bO zbunF+sdvu`sWimOiZWuzXDSwyZ)$0WSi8<1U!BA39}qZPa)O&sU}F>8v2ZwT_s|G( z$^q@-cCua^BW5^qgUFAfh(F;uk$Bo6^5F{(_A(=99^#!=!=4gJua^REe7m5;@(KXR zv^a7Z5%vkrQ-SDHw^)16e^bo#4UvSt|2V()Iba}4He^{j2WbTdEG4QJ^N*#pVNSog zjJ3+o^@dei@F2%o%K3eg(3LO?05=+^B(yP3CH$(q+?$Kp$nVI#p}1-Lw&lpKi2o5a zFDfhHbWP-*+FV;2#GeSz9^~-8Kc%^?t?PUwS#Fw{ksxo>Nj}0GM}66A7Y)4kehP@U zwIQUw^5EVv6Vb&?zS^wUuCsht%*0x7&|b=%-#+%YjQ9{jWZ#hXBoRbACa!xbWe9l_ zc2AhS%o}hrxh{t={|1 z4p$K0imn!l*aH8X7R+=^7yJ|G`ta1}P&=*}B;3zqa>CQH&ZTdtfWcyq{H>e_SQ{ua)eTUA_%*wi(l^NVFSs>K5L|E#*TmYIr8jIJ0y?k;N@ zEuL$e=GO9Hb^c{GaFR~g-%|2~CzdfJz!3zm-qxIW-{_GC-dSg_!;YZ1>gkgR|TI zT5zC&OYYAW(Xp_B4agF`{G3$j(*m3lOpw|2k^8LF!PZ=Oxh~=3ezQDB2OeT2*}AI; z#gVrIt1@fytjk~1xnMMzG|=Z?%GPR=1bU`O)OXb* zxTmh|&v|pX?=l8~tHAwJc5OFddjWuso0#tm-iH%!%Ti*%UsAC7Ct?!ZIPjXcXVT+- zR|2C`C^0#@_}6056AO9I zZvWojA9R_R78Gs1fSFhJ-lbz-HfKuO8{2*&S`p8DsK4f)eI(CH6G&2an~Bddw5W!1 zx;~V{h`@WU3uBZ_xe7fcv9Mt~b9~T*OR)z;PS0*v8_wcCO-%c)K>rcbk#88&vebMmx)2GWHMEc3sCBs4m()awzh z;auyf`I7H*iB(0vgc{Yb2}5W|g}g7Qe|t4dZ@t;4A+QmrD-9{CIl;14iiy0Sm$9Q> z57Kh}8N0PpIpt#tTsqiF{Kc~q0* z&pFR~nmja5Pw`kC;H8!O7dOYF^-x26yvW!2T21#(*E>>&%oXA&WaS?p$>IU($HP?n zB4%zPWc@a^SxGk=2~r7>vtNpiM_AzpU#QlyBz~Z(ns_kEYa0d6P)N!BA)$(`9AHjiwGc9%&KI}gbW#qio$Gd3Y-BVYEw~V+j!|w^ zvQo^w76SQsx8k|b_xcNFhK4=r2jP`+xF)a)2CjI)He6fH>gCK5qD-Sh{UPJiwRX8J zbBA=Us^|u0SFb*t{gyVl1x=hJQ)1<>urA_I{dO*I;}ekh8NDtRLBrDmI@Vk?0C-@V zW$1$!yVjWA->20lEds$Ucrw8Boz2? zKTO%ouaTZ(lcP5WvtMTNJdkdHA8h|#MjKCQcLE(c);FRtrJ#&t7l*nS%72~wVacyp z8VCwfJ_qN_S4;86X7r`~AG%Je@psx2PQidgs&38lUrHlq$2@Zb)mgvqfKl8+A|$HawN%(cp~d$vH%vWcd_+(;85>(H$_lr(5BOG&yK-cj zl6Jj;Tt&nHO<_(UrLSoQbaho3$mh!-^et0wtmDNTU{~YT6;df?qGNYq zNaAIc?kT)ml!_|@BAlHkYpG*DrV>kv2x(pS`M|lb z5YnZLjRC|7x>6@>&`RW)dGqGQN?u8UG6`I8llFn=)}R$mb3uT*jpT?A;}pvKa)3QS zPn233iYGuod#Zmw_P>%D6kvM#rt`r&4VO&6by<tU?H@&Ep|1R8QBKpAP2^G3xU=8H;y@FIQy9^_RzK7z`@Zw}3yQFFq@^f@ zjUQG(BZCLx`krEZ)|iPDsu=&Fo*^vj;PS4B+wp~$eu|n6f%nplOb#HTdsj$Fz2h895)hd|0RW7iy%P>Huc+vlCRzK485+7!}UF8(4oJ;9-v! z2-d0aQQ`WF98JwdqDW;rT3le}QAk$>_ve9XHxe99ulJrakErQzvfg0M)*OWo)W(^_ z!#}{e)mi%ghbm_Kf2m?7*8ii5nK&33{x>rIzg0042OAT||EDUp@iKNP+i9}3$))TS^|iIB-MW{(7;y#b7Sp*r0mGrR7!!_Nfe7apc1eQZVq6Zzasz{ z-0PW|-;s&XgFTSzoxs_;KLloXw+7(x=xRu53aSdgVNuK#5x~(`GXTy?|H&I&U60=h zu&l1G-)e5IfU7@^w$VT1%1hCFYGw5R$oauZytoJbF3GKIZUBy7 z;OtJ$U-oBs!gT+4z>4361S|tEmOt{XnN_ucbvTFuB-aLK7iUl|;A7nBfZ5jof6KcA zn-}=UJr!eaYVGtncP(Gq~3_y+8L6f31%AyeI$OsOP z&-rGCM!<7T&J4imn(Ju*IyJJsKhd@2nGH;fyHERtzl)Q;-@b52h-Z+j!Po7-^=b5(N?TR7G|EVQE!DI>SqChZ(NhXKKEAYpLr>x z8~_oH%)Cg_xMlqTZ))P&w)^_MUj;g^KTJyp;KD#_^C|#GY}dQ2)<(P<5$2(^WPe5a zBb9-8stFuxl?_&i$fo3uws#YH$y)iywA!aw0G@(c;ml?j>VJ%gK3n?W(G)Nn!X2bz ztSvNkP)SwzO5%wJdYn#G$$c-VxE%ZMbrcM|wY~{7tAd-wrcf@Tr|Aggs6r zZ#v@~Z2+jcFrHK89j(X|6!H}wW5BuH&*E)i^1NJzUzz!}U0d{*7I*Dm)qgc*Wq75^ zE(KRKrN430K^%}e4B-ghiE|x0eDc3x*G<(qOJxajC~v37S!7tShN&wPI!Om;Xp*ur z;x3beu}_{4;m~w_H*}p5Qe-JtWtoGd;*1@-j*Tb6P;WA7@s8`_Q z$cRVxA)*a{$UVM6r3OfghqMl>M+C3n?(WslUxHYr#~~G{)^5_@4e<=!1rC!`V*{aC zp2#4aN2T~bSXIlVL`1f#UMXjuFAEws%2WaKywb$R%`#Ka=|x5j4PGRn>K?MO=XC`i z0rJf)IBbpdt{TW*pD+(1>-~?x+;vySzuj-HVi;-&Mh2$0N*mK*6I|>r*SjhwBBfBR zT_7>$a6#BtI{0e`FRMdcgwZ2|-GO6<$?Sc-W|T#`FtYB5(ZvaFhh>5eIV2cm$>$EgIaW(e%$>!@csN(`Fc?nSPOlqT&g1^Vp=ivF|qQe`s7 zpH7)l)%N}68jG5$q-93zHdA&f=g{01QMR-G)5Mq2CLgJ6>^bPXhPBDX6FEc$+$&gb z9zE(sf_wkK60xE2X3~0A6k5BJWbt_U1!p=f_AbO}Ig4}WZ_S}j05#KS4~fekf?~-d zbBk-ioL&_>b|J$GoZQBuq@|_f3Dk7R*x_ku3COhs9W z$Re;WHC*kzYhWlzp&<3bmt3LS^w zPq!V?S!^fN{v=55Xt5#i53;#QF8L5$ zW<#WeHd^Hnp5)_J=|k^0#n^0V>rCRr?B?#|v;7;3=1pUi!hZO%oS&(W=D22_R33fe zMtMw4Upz8fbtDKpJ=G@TMMWDj2K!LH0)Jk#Dj-WEr%0ZUp67%h*0J|_7qbn&5EYe` zNt~=q>{>BjbQOOjnN@>VUHrNTHCtoeWDacsvbD2mf-G8$_?{QRuzwPC&nrGbjLI%g z6S*lqGvp7hOCKkuZ){x8*Thl9H0wntv*ZE`IY7Z9;=TP{$V}6)YYGu(QB0qJ4)G3q zEp71fBNf(t(cRe;ML&r2 zL{GCwOe5slkY2Q=p@)V>9KInW;fJW~h-Q>3n;Lg9_R-EU6#5QhZHF8Y**Q!(CB?C znLrjEsA63vJQxj9Tb@05{|)3KUI)teaB5E{Yl@s+^YyLJXHx z`xgyU1v9$hOe9<%B+0IA!pJ`$S9d2Y_=RfyPES96i3#*(>ugVb_1Qq_*`8$#mY|Gl zz@200HA5u+%!=YY6LeOkP=?@pK@BwWYQ?R!{fj){9IIuB%JE&A#E{%zby?EKEB0oN zX+=};pO^OUfas#GaZ066%=rA+H_+!&&wkM<*j}Vupd=&XxNWGde)h4P#H=GG{EqB8 zAb8z!8uR>2PGTXX$XlP}jap6bqHNT-ALHx~(ncvsrTDvv4R$Pe^L%4Q5PP_! z&DP@I=zmV{`S)&r<5g1)V0nkevWvGjHEM>FHyDffUs;_9jDx>r8=?32`hjq*vES(l zsrWdp?h27LLYB;x>g-LnwEk2^aMB>v+)w~Bk%ay)yq-y`nQ5%Cr5q8;=uvqnC;e7B%`YSFjlhALK(XBj)S<;^)d z+H-%m@HX;_g3q*Z@nfUQAW=@Gt6dc(ol{+R_h%r-N|;>5sUl*_vu+CYUhIYxBBo5h zAA@Xl!3|waDALoiM7y}4%e9IB_KN1S7{GUM^tIW}CiS}?;-8YMefNSf(9a3cgF(R- zqy+t$6N4Uay|ExVmy1A9-L@2|Vn9>$Rd1xTeF#=o^(%2Yybpyr^E+-dd5QgjnwW?_%(5He?!+~O@@{9l`5PbxV zm2vh3vqmiNf~MQub81!|4|jG&lSY0Cr77h52Crh6Z7p#;b7z16ZK#zV7RD`4jwQX$OZU^EsNh|ue%gRQ zYBhPQ05!-=yAGXUd|w3D$nc5Z1pGntFvT7+&BbOWgnfGQ6-!GVy`FJe!pH|o4UL>t&qfO_ufj;C4a*_l(Yhsr`T zI6}Udanq|p@F6(iUnO}a^U`9xQFzO%d@B;y1NtVyP`CLntQ;Pmy1+Sf_C94mA5FeFbI+=gh5bK7)~lRu#0Tr zXf%0<&$Q2TW%b>Q3yLeDeh&B2(+ycLByQ-{Xq^a%3bo`FlqvJp)~SK++m-eOL!gdp zA4-Qf^pbI{Wgzzf&2D|h-16TCrV^{D2`^~1_#v3eLT?*7hSL6V-*blJ@+K$3`qO8u(+>sz*Sp@D#2=E$TPKY$ya3MLH#*M3HNI;wEk9ia;0<>B^;?IX<937~vM5=hmXW!HR7Oih^ zVj2{EI_U9^KsQtC3t2>4J=18Em3}Q+Ehi8!&iCsm*&uq8Iwe|CXHd-oJTq!!4(9Wx z-@@U64~q@3SACaVX2m)BFQnaY?g795#Ya2*ECgJ-8}jCFNTvtwkFxm4>!{mY3|_k~ zIC>49BQ5RDZphyrgJVhG87dx)ZFVDZz9-^Ew#j1|awNQ-^1DeH=uCDM5@khOXJu+= zmGk5zl9+-Iqn^**e5iHi$g6>4&F2ZpBiPM?y)n3`i=V(n>Xz2yAXD>bvO|P3lw?E+fjv1W}FEFPN&OVILRn1JmCv1+l$~T!3;n zbNGyOhI>$WrUb|3Q^31e?B1Vyvhp3qlM4mNT3h)22ug@$3<)1n?3Cwie%#Zj$T?P9a zc*&70|3M`z%oPt7>!01@E9Oae6Q-8J$#$DAK~PWfvh9kc%)I8~~ zWq%IneSGW{kXIy;#*}w`$|D;>KCE@;THX22L3U7R)9B$cuw<0`{c-7gTfpV5eT$bOpHC*q zI%dj$2xIf6Y|=u3^jjmW>&pH-d0sxpxP_l0!6zAapHtL*y3CTlIT>ihC?jRsD7Zo7;NruUHvR0e!e4kR@y+_P>(=~ZY<&Av6;%`hbJ z_Ow?~G6F7?GKaM~b@kB7AH8@`49Lvw`V6uo$`z0b>Uem0YTWN9h$nF)A5PMv>wuoE zT%{{}d_7*%u!(D_#O3WcN_R}Wa|$~(s$Lj&#P#lHwZPwQ!jZ!hgxp=eM_U{>N`aCR z`d?=m%qxUHahM9PU(U3#;kr0216e8JIND4a#xLdV+~~0PG8C+|AOAb-OXr1Zy@3s9 zonN|S92IJLj^nQCV6DnRAq4&kdGd;f)}030L)nkv&UnPchn$~FZ-|j)efPpQc#yQD z;OBSPpw0~I>aJj3s?U{PHzh#m_7m()#-ux!acwsas2-c5QBKYu$cIHYsq5+~I(mVIk8hO^VCMU!~X3U;k-iwg^B-IRs zelf-RIo5P6&RT5$MEyZLF%!|lrsoPQk|t{N-JQde_o4Y9+7%5DR3H&A#gY`N6FaqSKY!Haq9Y1nXi7ZTlrPRPzz7Lm$dvrO(ih_T`7oujDBYv!CKaZQ< zQu9gWk3Zoc`FDp_FBl%#0IiIDA6T?l6HN(oWjPp(&?oel(~@=V|o5X?^jr421%=fKp zAZyHjdVIl!+H*ZDxuGN&pw0I$pWbG6BvSt^wX`ej6FwR1Z#0FAp&(kFNodz_H2QN( zT(WusmIyAfx^nBSLk&O!cD?{hm~XWm>QkzyvKoT^v_VIV3#6RnhhUU-`$%0XLmS{p z0`4Sem&6H^B69xAUUeXLmg$%8Bt&no#I{y2Kd=zU!H`R$wp&z+SKecVPi>!yLrN;2 zh`6}}k(<}xn5Uvaoxf?f3bf_%xfWP(_sD^LceWjhywsXl*sPJRHir@z*n?3;Y`){h z>VRbUfUAh{FjjV`iAtk`8l-QJEA4S23pr*9raM9;N*){1^5@PI6dN=wU3Txq;r4cL z3Hu$GSSWLSRq=&GhMW!F`{7MrcrF{^v0C`^YlCO?Zkl`NkO~300;c}4@ppI8v}rX- zTqe>=2QOnXeu%!}=*bJ*U;D8S*OnKU=?B{QKnDVYlHR2wU0(x#veXal{Hyq49R(Rn zo2DWDcfVFYNaqWp#W}p1DPy*!0^isXr*(<{Qc!9`$co+==uPO%YuMCfWe?gabMQN8NhKwq4}IPnYC&s5!R-Z{zk6fr(lBq)m<;tN0NNv%YD52_x~IT_ z|D_M(rYdFgP#+88tnELMT8wflr)GtGlmx^wtzO|(-w)NJ&=9?Bn8f02Nt;AcI zwA)Af-}~h~S6BR~7-IC2F>-T*78)df+*!CcnMRqZkitEP5&T2|m`0;kuPTQ@InniC zuFESq>J0^urw{S|p*|Tx$-%s*j=U0PC5qc(t}R|}nLE6Ojwm3+2wyfv;=`u-L@I^u z;&@hPjE+aXS+$`V_Iw>!-qwvBlbW&=*{YL|OD$mo7%3#99Y#n)ZHwDh^h)RVMM^DL zc)_<{n{6v{f_NWKLBksehzQkp`;auVXX!naG_&w=i_q>J_oESVIRvx7f;Bja9=qA5 zeF%z*G+j>mLoO3vbJ=WYSYn}*VBk%$St##7;uI)T%3I*E(NX!c{5*CE{|-fARcm1o z(UiMm#-~YI5+b3f3vHSEt2^#5c+#3FD7l%~&YjAP)3%%2+BlC_<|x$_<&**eNCE$p zyW3l1{nh#mwgvT4!|Nimg-3_C3RTM&CnwI_I6#$ujeSID`1tlOlnpGoWCs48eu&foq9sVLyH3aMFE}mE4e1{QL8&>z2#fvu-C^#w2ISZw)o;pE zgP7Z}{K*zwT;t+Gw^;EW<{N~&DMLVaF15g1DemYOcg-SAi~8Cz35cj7>ph_2Z2_~D zP7ay&7;hSo)tvl0wHAlbb7!XufhRLOfK!T9(!``yIP2TL#k$3GXfd#*7rL`RikT`U z90!Z}A8K7@Znzx$k@Ow3#x5^^bsPtn2YT-Ur+KEJx_52(Z2Ol9|NO`^SSv->0EV+M zx#%e_e~iLzWO8+HwcVHBs^l+qd(VoMF;>JgDB`dt)89IHgBc%JSW(s}W| z*LDOBOv=Tb!Vqr;7{%Th3T!q)+BZMseW)r+dh%{js>{=&w^e8!BEcXRndt4Z5`5Q| z=1@RcIlHaGaCx}Lkim=pTFS;Mn4t`YgVx2xF*4)<^KyFNWWx9q{eh=o~$FWa}w8a|xN`21Oss4y0{%GnrdS;Na>obUPr6gm2sd2*`1Y@v|q*=do{7Xqf z0^4CsR{>t!mh+GA&7#-?PcIGb<+8X8Z|+xk)voshJ)P*n z#4C;DzSkt98Z^r+yJ5-Wm^XSM6N-S0njAW~^Jx>JHZ&n z{szoCF&Hz-`b3d&QH>6So)Mt4^0Sb7+F%zSTE8SsL&u!w>kg`pcZK#bRm84@bIE%` zSX~>(vzrU$9~cyk6GLK&)h$Kw3vEGL`%^T0OHFJn9;o+=z9M0bP4Iu5-zBHu<;r6# zav0k;arOII)pAHp)Db+gF{GO>(bJLj6oEG;t}b(D$X9UVhfEh_uV|j7!1A>^10t(5 z@e}p9hYN}<2cuuf+KgdL)SX)OmKrWpI#Z_pK~*xSc09#!7j^mfM{5sMh;f5FbxTN> zB>}qw36}WgZ7VXT8BlV#W}PH0K65B4_QmVbel60kFy5tIwAU@xPp%84`o~8uUU6!r zMap#<6gOq_hT)1-sUAhM?!JyO%Z0@guSZ78Hq59T&*sF8a)qB|c||(7qB~+yaZ`R6 z!xGHn$j4XE9;w!gdHJUqOI3-6cmnRJRSd!);ckfr4UTrb!ZC+-@$_i4Uc^knQE#Na zE+O_Z1U|>UD>=nM8-3AAnEJQ3^(UWRI_!cR7jYXtaLCmc0ggxU_`YuF2LIv`ItC*S z;st9e^_%8CzC9#JLpSN?xzy0Bqd{4#p-jn03~UiE#g6IZSs^MVQ^{g~T~)rhdsQ^h zA5VT|0AdSX-*Okcbi+L#)0vkDETwmbLtAJF`2Gvl7-uuzB>G+YoB;ByMUOW*j3zKH zEhYNCy{TP>Fj1_y7&5|s#DDyLNvbWmiC$_e?%4L~*RIj;VI}}9*Zefl=rcSP%_7o= zNp~v`%`&v0FY>Ej+{<;Q4D=H3YIjeL>-#QY?pv~nrpC696irO|F_CDIJ3fZi@ogML zjdlm8$ZIKPBjr5C&260q50*%Cn~@dVgD8!7ZvrK?WI3bunH|ZLK93VCeY09?#=!9M zf#5%RU~1E-ovc?c0?OJ+D02J4dJgzgfQdq`gIYb6C4pGsJkicFqjaOcToHFk#%)(N z*<=YvxMM%ddly2fa`%~S*Dgl%>22of|yLTHKbE_uN zvrWj_36pU<#&H?2?Sl2#JC~1+1`%aGo)PoaZh2Lt(AQDXcp~nI*dI%?O+rk?``^wf zHI?N%b}XcYG(PHH6KYlGsmF7?Tf`%3yl9G@EV~rcc@T*k-o%D#j8#*R<>}A5bq%+(cJpT|Rb&xtb0HOe{;?X~VxUI!BfsLujo^?TpiNpUR#p zSRzQ)9HR*@cl;Nql`+$S?Up@M=Ev)MTqB+?CF>%_EDmxC$8x0whIHq|4&C`sRzL2#R)T-?s(K zt(+PHTfp0F!|bpb((ReJ&+^Z*Gu1k=io#KF z?X{l(Xfos12qQ2vFCO0u6adCDbr8w$vuFHG1LHY;`*Hp+b=egq9%eV4=oWK}koLa- zH9*S0L!EJuW9jqvp;%kfPMZ|Dg=+Sc1deRb7OB5k>h=nK%XW?WigIAbnMSjBMw*7K zst0XSrFVtsA$<0HQ1^kM#HoPW{49uTn)@a$u=l||{+X(@U>`use2hh!DSfdlZr@ax zmUYbC@OYu!qhU2^D@;Gv)9Of8sqqG_oJaAsQy8k+jHrW+LtAR<$#nh%_SQx< z2Na<$Nw}RR+PvG$dqosjT*lMu^0geiI|cK^*w|EHs;36ew=CrfiPH#F4=*N-dF&X7 zJOti5`=c*b-moR$ujl|{U8?~vO-%L+m)NK+TJ2py2crq>55Po>8?&h#Z29gW5sZ*T@E_| zjLUf(^CJ{zR){a1VzaPX=Mi75N_P;RGsMmQxBQDVAN{@GRBlpl>wKA}kOTgyL$fQrt^L z6*E(dFCLr!_#`W4U55RYvMcB{qAEaAL{Iu^&*~7F_XGs?z)}jw>Ue$Fv^gCQ)OsOj z#sweALF%3DBMFQm-|9)XDsNm9LX>2PeWJ}$!L}mI{xyaHypSRX{)Oz%PC(x^o_<#D zgI9m5@^pJNM#vg|{_y&osHf6MC1AqC?}P-b0XMOYl~%ZpEuN4`w&Paz%%`dvMT@jC zY~L%1El|Q12`t3w%Oy7L#iP3)HY2}`slT%nkcN+{7w({mtr#!8D3O|#yIW3cT zUonGM@-BgA)WIzQ%?ywl-u(L`C2wJRJV>MynOT(;D?GCZnJnr3;aBm!1wpB~E>)Xw z`HcA2AVdh-Jw+FLSJOU#Hy_B=3`eJatgg%?$1x9Lpda$0*?jf21naiZb3 zzHDV2cC!-{@2JW8jN*Z00IZY>=ByD8Qbh*Bo&=XD!MLn?5~lbarFWy2Z3nbdHuTB6J9JmwVxg9OQ; zmaSh)0u##Gu{CQP0mO#!eEhUce@KaF(F{KbLhxLhLV^TytrFvB@*`E)lSeVdF=E$- zRj5{c{v?w*Ugaw)gZ^XB-jn(`m={LOJ}7Svxz^jVKKClJO*fM9Y;@1h%g5xmsk%Df zNwXxwFG}ONNdpUzxn>kiEhO6ZKO7jr!Jp~-4qRfc3?Wl*VU~>qU#`nVhxaL|6q}wb z{{k_%%y>%vVki@MYRPIF4Vh3lU9{d5N5Wg!pU8{}EVHJWRUuSZNXoi&;n$7<)M#Jk z2|M$VRp8HW-@TG+nGMm9Smql&DuDUcD(YYz%D~)I$!wW=OiARbsbU_tPsIO$)%j@< z8JvZ%O3ROkb-r>(LR{75>YS|iQk@{>4l=Dj1Jyb`Opdx@`KFy56-6O<3bAKTr@hTL zw@Tbuj8?t#_PEzRrPV)$OIjA(JJ{>HXKgkHz3y{OVEA{sW9(Z<7~qgV%g)nJ8jBz< zz1vu;oOfswkfq{kTKV$T-Qc$b4*iO`=_Ew<$qjLr$VCAOTI1|vwydN1SnOBd`RyG9#AZz>325!CSGVHGU%O1TfU7DpSv)zpTKvCKzBU#p zJr21`{H%;Y}+TmwL z-gsT-^S)|aRiDgF!>$rWu)0Mw@-k>*3WmO0b9Yvi7?QqRKuTv56@+=4KF{}l#;5dP zj~h9!Cvvmco_$u5ie6@RHZdzYuGc3Dn4@cu5Pu}X=~9 z^u8hq{n~~>T`xGLh^=B)2_8K$u>s7P{}iAZl~QaxUyQ;|_$!V=mn)-R+a^>yd6cPd>fhG=roB&h5Fg%Q%{V^4yy?ZM z7Y=ILQlb(0(Q~gy6G8ut4wqLf(j_`Nl>tKJ%Zx=_Q(c7`3hKOnGVA7r;!IrV&*!%? zgla)Z@_sffWJI%9?ak;@sE1$Z-tQ@EK{mdi?_%(`t%$19y^~Tis?QfN6(e9~O&G*+ zSN!hiE{dWhNH6|}GypA#Hc#x-ZSGgg5O^DNw?V!wA)%81fGk_GEjJe~NrjfgkK8#> zStK>tz^W+_Tm0f&C*KmS!{{HOew8MD&(|~byUPf3k}}K0zeplzz*aZUMuB4xDtBau zKLXp6?qn=6I_y16L#JGjEY6K=8XrlKc;%MbBt8F_!J70&T;vo!VA$KzAFTWdY|Av= zBv8d^O}v{X0pUaF#3eq#n0Xh|l?$|pCMyONcjDpwOIr_u4;^KQ98eHzRKR4D3}@o9 zD>Q}Mo&YJ@%p1nzY2xp{e1SCkA^!e|aK(gf`K{1!KMNj`%Z3=EgusTAlWS>aXqQ^K z`nW%8S4E;9chX_619dlnvQUGP6Zz^X1MlfY<_wnjdgykr*io7pYxIC7MAK%-I)=Q7 zMm1UuF<^&6{0me+BOeKrphRCKyMN|K{;!Is5d&Yeqm)v2WkPyUf>B;mk%H$1~2V2jCg~aD;uk0y6 z75xuj51BF zKjQl|O4okUhe0||)nc64%b0Yrc<(k!}rJ^0-90Ku@yEo;vo($FWHR{4N4(YtV zHu)WIJUExPBn|z;OJa>E&2$j#-FITqq$V$^qUP7V)yc*1mT0O9Oqv=KZ{h*Dkf3^yRfQdSXa zfmziJ8x%bC5BPb~*~_xwv-WMkKK%B*LaCzq5;$DFXVcHZAuZlRYbuqfi0jONv5TTK97M9h9oe zHBHyiDLla@&+hEjk?wimlG16~$#m|PrxjsRxHW+)s{B%rrpAcI@c7fpwDYy!;9N+6E`Y`~)Ttgme~5 zGtuO?Hnn0r@50vxCIPIZ6WPdXgaZgT@F|tzZR=EN$XYKQjitdKam-)2-dZR^f8cvr z(*2p*rTOdCFKmeu9vg$Q%Z8je4Nr?TB3c}6JL}YlE?vVNnZDFwj72v#EjN2UlC?~G z!Qn{_7PFBHHB{^}KOwn{!Mef1#~viI)zjV|*AV~W<{TM(!UGs%}?lBU_K5Ix|13J(HHUgXtLsms5z)O#;T8X9xDyd z?LZ8S@__E|rc-={93A;E?YjamA)d5hS-XW*+843N?>LI*%nYWOU%iMDkqwWrTp(n3 zRM77E3!Y)u>jujdUZX9CGT1g8T}PsHJ)DKu+jWiUM-JWOxK0J5Ctk}B*@f{#F{7)N z;CKO+c~23|(r0GJF=24SP#Fe_B`BQmbeHlm(ytV4`(`wnfJ~4hfjT*|G7=lPS2Ppd z-G0`po)Y>8Y&LY;1pQ&ypu@Uj*a}j{OhD=qMm>Khu5|`Qk~i++X09soezyhWyE(Se zl#V>r&<$1W7fScZIQfRN)~;yl99TE6q1#z(^WLddXVgt>2-_=EapCvFJE?G$ROQths4Pt*M;$4`;Si zX{9+K7YroKbQ~Ai`I=cD|GM$uyaU@^Io=cBGdD&%dN2}X4#~08lV8Nsqy$dE;OFBZ zQ2Cd*KNV~sMu49OKZ0BH#noI9i?i1<#$D2_OG~49m(ve!OdRFDm(ypEWv@GxS&AYj za&HVt+$WGkZ$|u|UhA%aNqZH(FkZ3X;k9W@9q=*({Qw$&Cy#dC1+CU^J}6&|4{7}J zCJ)bCK9)`c3f45D9tQn=<-cZ5orhU&XAg;@soKnY94Lx=KDZ|-z5)RUEJGt#(A37 z@rJ%R8ddDd!lS|8FYRABM`ryuSpqoEFFFh}-J^p#xsIZNu zVcx7!Vyo(zf55HtP&CuZkj3%L%>^GZQ>UxzDa;NXci2`- z9&Z?kj9vH$qKB-tLoR_AL_?~qyjz-12*N{6k%)oM!C#g8x1E@p^ff5-!P{?^TP*LX z-0+uV^-JKto>)GzJt)cg#&1#>v(!C)tiz%XxSn~O`IzZt_?*u5i-1B&A&n};PuiFM z7Jcj|V^;gxK-C~SyH@%g=k~j<{OiZ8ioKHCO-x-#6XmZv6U{hwIiFM#3QX|{%iE=7 z$I#@|x4>`r&{Na;;lDVi0)9|`>|)VhS!Xjd>;ItL;hD7962jajQxC|?*^^Mi68{L2 z)u*USr3^I}T?ysuISe%QiV~W|8+BfW^T$~tDWktNIsZkvdy;yrM?dUTUwRt&kruIA zmP(EhGDZ8RZ$k;vmtOrbIHgUxkG?f4uSzT0hh=++7l5gn<-8#W!8Pxpzn*ed znJ{s5*#bIfo-JECYZl+-AfRUzIuI5<$QaHqyYme{_~&L7Xo)0gNmeJGYphpH`c1Po z1lDu*PryJayTt?*^>xV(g3(~V-8y%bqB8$X8J{wj(G^LLIEH)EjVd|KYoH-hX~5~s zVu$t_a30xE2it}=;nN?p*p^gZS3Xa6vnNZiny3FU>DS~>gcIutozhbxG>1J`Ln+}( zm(qfvNN^4EoBCl)_{q4-k&(-lN6>0?G((dgvSI_s zBrzroOqknLt|iKOAf$;wU%zt_?a$zq8Ojt1=pb&fmppt~%Xj3naVvPOaQeV*3(dZP z7rFh5bbCjbW7#KyJEPBSle+223hPPu9Y91@DM`$X#9I zsQp1@{d?rcxHK2GO>o#;woQxrISN+oq^mFQ$?!9-KfTpCAP0WH1?h|wVn5)9C<-E< zSM`;qfbbaF5{j*siowq6UnV?yE}V?Mk8(=9v^9{dOdIDdYjrHVG4SX7b*-))PjSz$ zQ|u+Pbz5 z$zEGs`c|!cW`*;TzfKrJJ1Oi!Fn5g|Eg&TQVyBEN8gT=!)t3i&;eM0Z2GgQMIWx+6M42`#XApM%_d*oO7 zE99fZJYMCVnHBG=Fm^DsQI-Tr(t%Kx_#T|8N4;N3%MFrrIEN@xv4Js41`p`@fe>BG zAVDXcQhY_BcDGB-k{(5cFf4fXa}zbCD1mK?ve0#tj+(z4HwPucB{ZQEYjtd~gxE1I`s>Z4 z1*-B`9B)++R0curi*5ypq!D6!l9D~ZXA7bJ>|L$b_nOB@>W0_8g?%bdIlH^!IW?2G zO@d_DVD<0RP8$q-o$r1)X*X~@s0i1J^q}ZsETAkWrfbKGdI{ocZh0&^SoM1bdceny z$?z;?4isVmqjFH~(BfycJhxTd_GakKU{nI#*S6Gi>Rmwh|2{0`5nygO;A^0zp&C^7 z=4h=}bb7reS;&T3rP@Gcyw|NXAlQsxs*e~LsgWJTQtT(aq!W(aLFf=4FUk-J4PGK| z?S-*6;wtrPaANZ}v^W2GgzDoDnlkK0NI7SVrI z!NiLQxO(Dri#!d;U-~;CguW#`br^#OU89@#vtJBNd@%hi6~~?TU^nI1Un+12A6{oV zNbrEOD#KuPAAc2MWp9K~Xu;=C`BA1v9(H@gM?au53PlVn5t+;^O|f#mj?dXuo&pCX zKnk#+i{<9Nk&Y)vrd(}WE2GXnyLV5u--lEQ+0h5F?levXfto;{uFQJb&E=&@_$yf! zq{Q%hWgoGF466ty94KmdWsNGU-wp2-3dwG9$mh@5wCUyog?Z^hT*wT5;ctU05RWB2mX&oP3D%o}FrI9t=ElxwxSSW3#dxvi=eOQ4Tzkti5`}oHtYl8RX_bi? zKApcDcDvh{xzUB^BhZY1qC&{EXkn`(Ovmakhx>~{SUKllPfPZ)%)CtM{`tmjF>u0u zOcpP%UkkX0&f#=kG5zQ;@&{kyt8g}e?`p?ERh7u{5WPr*S|`^$hDNEmfWyg|7VwVO z>C#=fV7Cc=+clwfmqS3-pqxPo`?w6zqqgo(%d*zW{|Rf!P!MlWbzTMIrU^dujP>;< z>z4bamtDJJOgx2x0J^5e9;{0r;PIZ^>ZNFHK_)yZ&vVHO!5%a24JMQ#`D?|p4P^#T zF{V)W=>`+B=yS!_SZVfsJFZOkM}&6!hLq`wiHht=OHk#CiKdv^53t?Wyp!3W>F~v9 z2_M;#zp^86#8a)l2G1!t_v*h@9ZSmfqj})x!H18rA)`WRmCUK^)!yJ9wB&!mD~HQ7TR85cfbWpCAv31W!MzqJd}3OCCxnFkeh#Y7k(<}xY^^T zEjDQyBpT(ls;D&XTn6nfINm6(aofhr{()!5YZQf9>&a^X_{8tp;azawBydy}5M!l_ zWEUnlMnyw1iF=143JMEg08s?Z=0Uc7&1W6(#eFJs<@;Y(7E54!!Ytcwo`x<^m^qDO z7$9!iu|$WzqKhQ)md5n+;QTW~&$u72W}NWv>?xqUTqrZ*SeLIb(C~Pk^fq0gVSjU< zcgqU3vtfIjYR8=6h1#pC`6(aO^?gtc{n@>C$X!&hr@v)v;LOC)bQd=FT|&A0j85jQx^7{UqASX5u`MsTAB7PkY4ngY z$|X)4+x?mAI&8gBP%ASJ4N=$h+mxvgA|$0Zu*aG0p|Dx*kZ`hTRxBg7dAldDEs<@~ z5)<9?XB#|k7v~A7I;+g#RCDhx8V8+0P`~Gfo2x%=fX@PYyNfo&eY%N1*$*#Vr2Un@ z{%no{Y2|YbRzOaPNvYk%@ifOpzXiopacNuJ@|FdEWlLf4l651Frav=t{W&V#IF0dV zNBfn)%%5UC4m0c<1|shi*c+}7vtSJxkI=}YabBK|nB79Y!lbuye04(?aXFA$rO+m2 z95`T*FCjXWLM$yN8&1F5&TO4)t09)ZC3z2+{W}yC5cPJXBQ_|4>T%EMSt)|~N4q-? zB8i>2==_zW)XK&%X4<$MljV7r#woVL6oS4w0dzC1i7xi`3P7Z@=& z>59RX-Z5B1&#C5WM$iZCI`FisBdTDPgp2PE{i#}rwh(DZ0)w1vW4x#7r;@egk9WG( zM1X<&KV6(tlP!RftlPV>+O}=mwr$%sciXmY+qT`iZQGhNaU*WTnIBLu^^%!U`IWZ% z#j@kKDqPVEN9$H(%5{PYwxl58DQYShG)PSvSoiCBUeeu$wycvR9K9p|7H)WQq%k%FkM8Ue9ZH4iY&mY?_<4SSB)09LiPvP(iD+^s`#e zzQa=Q39POx?4BPP`Wk}~62BbGYGr)2MkuAeyC4xW3SJKsE>(j*VD}vj(;BqVS43I({l3)}!_i*oBoGlL@^pwgpq& zBTQ6&c+q~bY=3(BtBB+=g=c#0FXHQfEzypzYI-cOL6GwJTYa&^Y>%1zhABOw3SAV; z5!nj2+{-I_HHvMU2(FEL&Lgu!hqOoyxu~{jB{g}Gk#phs?iy24qtmP&$z!WGkaW?% zbAk4vGps=~MAJ>2ZUT`S)zvWA8SgX`BOW_otA%t(%$M+XWyy5wT`Rg2*hr8u2}LTKZc7jPYo9Y>uP>u2lAZtP zaJ?mTg*2BD*=fBh-sb@GMQ?PBD5roY(b(pN)3)?gs@Wz(BH$-1_Y9GX=wGUsfGY8) zHHY2k5Z}F`puF(*Lt)<^hWzgA5K85Mf0s+R>J9%7IX76lEUU^kd@pe>~s{K*+=>;Sf&{ADdCRC1@?nxtBVhlQ$Pf(0g-KSeN+&a{BnND zuxL)=$sui{#zSL&7A`cdFU)={Zsy^qzNZ4#s|v-80yYx&GM(Ou`@{Lk2(snHpof^n z@NU!b42x(wvY}2z&?$#9M%2iRY@ZRqz!KO(d3bFiS3Of-sHVFkQAGDs@3FlWoKow= zS4E4RM~|NG@vJ|xBHYXXo|XU+sQhPSUi^-Yd2mM~)yK4+#iGG|5YUEjFhy-Od2T&8 zA<)aCt{H-)73cy2+WiN&k~k5%IlM9C&>f+oph_swz0KLAJ=)i~IB8QaN!S?fW2)$i zKI*@(h+#Jl$Z3f#wlVvL(a2%PzDxq<;GZ-#nXP0fdb>T$S@v?MKK zKDx;Ad?hd`8*&=I{p6f_lP_dpL0|y(5>vx`k!lQahS-MkyQybSvQ&v_AE5>(tea&} z$3`DNq1fE1l-f5$N5tVMHWbOF!oy{I3%~qQTqvIlxy|Bfz;l`*+v?lzjf8u`3+17D z8nSRL;Xn-U!B9|C!1}`5NQc2Wa>T}5k7=?B22+CS5_{O$WG6Pvx4uNPA{2(s*pNkl zuWBddxyCDtNF)hR5{?m{vdJepFbk0$IfUUVcBAs~8W%C?drmI#z#0Ucw*U_)>x9-` zL85S7wvr7nQJNoWuqC%!MCy_LIhG2K0RV)K&tmdIvSR^h$KbrgCF1jJ>`fImd3r}_ zU3ibt%s5wI=qL{e@lMm;H>LzyVTHLK0eU{P@?b3p(_bQ?AP7+&OW0#4nzV!4`^nU2 z@pJP7E;LKOhNda%dGZNc%loyqeTMSmf5fCo*YB{=a%^S|tAkCCFlh}^Th+uE`5?(b zw)29`@h)f4hlSejKgeqB%1+kY4$>hBngMf@ppQE+BfMo=?Z*YK9PTE^zOLy-qCbRf+NM9PGVpx4)d5Ga%Mz^$HWg z45nIr=eD%Mb+^yLvbvA8+N)Zy;t+Y5W4$G`7Yh-&@uB%RE_jX1-y%$T>F%UJt{{ssejC&!|{i0PSKuBP=jw`&>(s zu6~LHVo?h|a1b$ZjUgm-nRE}l+Ub0*rN*Te4}XQJb!%LyE+v<1i$O%c9($qo!S?0O zP4bq%JR^6o;BzFWdzPTML*x};n7BdP;P z7W0RUjf)!OV7S_i#$5JYk%Pi8-0B@|PrCIGSO}z})|O3aH|yt{jJ;+W)5#|0<_|U< z(fo@zQzf5;Q&S>r)B=wTm2r7irXJQ70{e8?Thk8e(I`!M8sSqlGHY|<`8dQ9a@1M~ zGTR3twxvPR{S+cS2X%0zCf~g&<8f$Q_Q93?YDo8&VdvcqS+{*uL z9A}dK7%CHb#eGU8;0yzfX1IRGj4AJ=jjo|AvyA2_XwzMBe3>GJHlGScK1y4 zuoC|AkOh-H9A}YhMn_-prIN~3wg#@_Ux>;PwSY!Yo9kL_>VQ*-)Z_d=?53##uOJ}q zGnaRNhj><6%Peh!v^WbC^n@2N3)lutz!PvHU{3SQq~z@vH%zSKx9%Q{=oT`!M63!ckl`$S1L`w+L}I$*}hD#>6HMO@?< zdXd&D>NQ>@9y*XQc^gl2lc4TR~xCdw1=b`TLaV9eWB(xCJ20S!$hWz5ZNzx5C1?sigiz%;RQU5p?3< zch4)OAjr)XaMVgc9Oi3vNtu#sDIm}SLSN=Q=xP|Sha%)T0X$O%6fY;3>vOBT2zJMO zmOM%b?i@$fr~U-$MnlvdQB6hV19MqFfnh-^BU>jxH$7+-K*U>XPc3J7h}jlutFfrf zqpWzT?{7G*`kVF`MMt1abRMT5TWV_V7PnNy=mhcKkrg!cd-10Ro2hur!}rQP%pagGUT;VY z@-U&wdzJk7zT39gY_=Dld_Z6ip5)~!#A1w>b$8JJiW5h}R_2o|Bm)T3KtSB+zH}f| zmsh_W{79Z>5jt{l=0VPvta2n6TSnwVr4hoUg3 z$Vz;3u%g(E_**2Ycc)0dcN)8w((G+Zto5C5y{GsBARnl?~Trd0tmxf zjt{Omajp8HCRy$}tHBxd@gOE%nIHC6*w#~18KAo2({j*|*xuKrqcksS`YVn?`te1i zdFJ)ejYMSB)cYOh+28yW;PeB@U>8`5DH4 zvLEQ@@~sh0S)bQSUxW0JDW9V2(fiY#Pw|6w(K9TAI3PI!ycPL=^J8z7cq&x-U94mVDgvr zbgXY5WU!$Q=xXWd?*?YJHB(AYuvtssYI9FB9O-9)n(Ote!eD(n%I3n!n!9f2iVEsN z5xtmm&z?NeiI5w&DqLKljI0}{jMba752jD`7>hhlq5ZbqXd%qm_XrqD&K9ptB=nRF1F_iUaTba^B!x?v=wXRVIjWZ`Hw##ZCQK8#6hk_d!R4nqblS(apBHMiuIs({SRZf;F|FRF=~Uvs3c`zh*_Mo? zV+9oY8@=GK`)00h@dfvCI098gU{$<8mb!sJFfjDUj&*2`&*>WPhAW&3Fbsg1FZ4J zzaQ}{K6yNAO8S7F!(f0;3ao+wb1s4bcq_F_N=- zY5&_-U^J2WueJ#6~*?|^#70;O^>nG%Ed9#N(x9R~3$?k5e7s z{N;*k=usYe_#<0qWUfI&Of9;bFVR^$pH|LX_}woz-Qq+s{amQNXnJF4`mK5P3}`kG((Q%&?_!h{u1a!kiCCxB;OkfA8=L{*AzBRE zcuLl95{bO)4Tlw!S9R7}U(huicM1HRPf}+ebIIKUEcV+6A)XpJ;xYqa;AoIdnzSqs z8YGp}S;TDsR$rh%o6dvqP3zye*?n1+<&cC6Ao3d*7%7B+sVJZj{;W;k=(*thRCPTX;ekdyg~=MEK>*(2G!2^o#|JMK%R>l}I+{XMFQ0 zDhdq6I8Nu~hJN z{RJ(|)lX#vI88iKHQ8dLcC-IK$#LlemLdIGR1?E!jiPuM@uwvQ1;5W5EpJ~Q&2@)l z2<$KNPvjHi-A59EO+4a?QdPCej{tebnE>&7?7!gG26J;mC~!5pL^CY`e;>BUIYDEZ zwtG4g@C}E{6Sonq(BVF*);?T^#%1}e-8!3p7rgiwyz=T8CULy(g=CorFkj%cz|)2X z$gvAoa&FZA28?KJ*?%b9AH^wknTb1$8gmt`O1vMW17Z<9;N2TE^QKuMN9bicb5t;3 z^&>!_id8VqGCRxEd68(VnaG40HG4EkQj~r(!>doNPOL(Ns*Q!)kk+lvSxe&vVOl=Y zcZ%aPWIeipS3^JyU(2iWN?O7f*X1H}_{6jNRM7n~OLi!Vd2h)K)^7!2$sC?qeVQg}>f z-ElbqhMI)@`ejBf!|sq=!)^lMwke8_r1J*ooFUpCdzjBm!Mwp=&6h;~K)p^e*HSBE zB|mcji92QzaWkQ(Le?h_@MtkIRZ1{)iRn-9;~Nk|aYE`XK*BUs4`;SGCgCml7L~6CVs@o@WD&?f(gYf=xro@j*<$R){fZU zWSE^mVQ>M+FP#qxvAg0*&C2V>Lv0zCA6a)lh`1VH20a<5i|3kYgY*LkkS3c=yLBK& zSihN*dod>}Eg&0aj;AqeS8Y3S(DF;Xi5^d;*ET`SrA@%ifG7kwF2v@q8X2~IvuXW= z-`P$GVz*Xl;8nCKN*PtTP(C$R54t7t-y<^p2_G1DGdNbr6!JV-iM^FU)p->I)~J`* z9IJT}bu}85V0F5CZ9Pr6LmZ1|&oRSB54J8na{cl2z7my`P5g>aj4zk2rdTnuXH=h-P;sOnLO6C@+kzZO&k0e92j4LaXjjeNmpA`dbNxuV zlf&B3J3I|GgF0fUUtAVP%AHr0`^?&hkZeb+o*|Ursv3ZZrRM8NUgX1#n?@B44|WsE zCc?q53X0xA^m(5*UD6fAYNBPQYrK$Va3!`H6GLJiAlesNHQ7k|(U?FOkaaSq?%TQ@ zv)TM8BA;bc!s9h*neNDJ>;ou~-HtA|r>>^7g|t9Q?`v zO-3^*_7y02WgcrG0!Hbi70BRw?NPg8I69+WFTYFPo_|<6PLmFP;Dj}sv6 z`@R8~reX&-$e0pfoB;!2mj}~?*P2G<46mGs(C7_An^CI)xWXIEHZpG*X9n-d$*RKf zMXTa<5GPq<`4JZVpuGf975idL(Lre6snV4Bu$j-;cMkhBB1`n48V?J;LV(`GcqI7^ zhSWv#3GMdcN?A><&oA-Qk1j`kilNAXmh`2rE3?aU$0nJw$`Uc5SX<#*;cAq9puh@ zWOmKmSe*`mDVaU+&QOkIHCm8ah5IS#g^Du_482@NPIPS1IpIrH;Pf*B9PiBhhhx~X zwSi|%)Ph?1@&|j)8O;RdHOq;^0IfCR6RXbAunFxaO8Yi%?SYqOFXCf*i`%e0{ zK`j2I-6LUMMq)Rk+jUbXP?Iq?(QIG^7~nCYJd4v2eM_&S{7dH|i>HST#WJQ=+C*S6 zwt#_|ixH$0;vYfZ0YSOgX>HV-?sC+OPd7Rb^vb90e#q7o$=Q4t%C`8mdn#6S{aMLU z4iXTC^egwHd~}RR-_2E3PReOs!Q=st$fy#TvS}&wXIU_AjlkX-m^U}G&PnVG9h-7K zzBzX0GRhKko}XuJp)F`qjtgIcV|2oq=(uu+*;n$!v^evuahzR4lVnA*Sx-66vPNg?I-BKqNhi~~i2ZGpv zIh4Mm%*-%ah=-!rT4}R>fMLF!LOHPwPL{^&pA6$Adb`R!AvKV#X%dp&*7V3C65k%* zVr{JaI(D2BLz_hDth!(N;!rFB4}>OjalF!j2T^|?fGezm2sLGG89q_kG*z8T=*@h& zIl!Wqf64YbUAiRvC#7f*Q%MCLQy3sD$%CDdsB;sDF(RD3;r~EJ;jZu4SX_*E-ubg> zSDFZ_WbZ1du>*z&RJb9xPo2paxR1?3S(+lD|owg+>p#G0W$XY&b(119*&{z_#weIYnU@AAP5x(B5~gCu{?l+}azgr_zsZ7CH-AHbdH@w4?`5PEiZR}cMvQtx?m<}}=T735dm z#7_HU>Q5PCk$ye~7pyVakiX1D5_d#C_+GNv`M;oi?$?!F+sNS#yC4cr2s&?har&a zkoL3~jElG4myyQc$04r>Q|AivC7X_5*k}=Y+AKZzlfTS^VtE7sm)pKPgzk*9G3SJS z@^Q62m>Ohte`Qp*YX%-K;^kY~A>NeVJWtfS3B&%(xM%o)q5(sn0Amn#mP1N9l^3ZM z>yt~MO@=k+4Mq98WGt;!;c;O*wi`C^GUhL+^Eb;<_5^Ce#6(JcXAXHHe{AzV)v&3@hc>8d!*PYNQg(VHxh1B9&T`++L^{0abhd(LPjC=H% zM-b=flgsg5Hc9qkBCH7ic+(g`7!}xc{FyBPEnAePo~BS@te3VkTF8a@oXp8_$cZWy zIi|inCNE_h-`%C^gi|^Xi>zmY}xc&egMSG_$Ji1KfN!+*lH-vc~*C>__@LUse79O zc;Y@)*tRY%pM>BKnAd(0^I82hymqWbEr$*Gd+#4K3YG z4=BuTQLg>kdHcR!%6b8ji?-z`_vNwUmsy;KaMU-aEunY6vD3nlWV;rv zq$N2_J=BO3nP9@hcC>OCbEoYnnHiRYCmUInbe{2qT_sBbi*>MQDndZ12|%u!_I%zR zUmtKqX(b4lQ-Vy8fQgdDdA3z6F)3NCaPhsI`a&Nt)}j&<#YDhp_4=k8?1diNq^t%h=+YU9RT>y|U>d<%d$=ZFwX=MJA*g?Dj z?Od&0ug{)cUpN$tbl%DYO}4KwIR>IpPaxPy6e-TZfaCbT%MyiPo$oM5I~NLW=DJ7} z-Xo@F{l@~|SZNoj%&XkjMKi9QC%W0E9)dDLtP;>1{@U+jb}(DwFT!)iV{Do`N7zwN zcD5Qfq?|AnZN3Pn5m@4~n41TAtqP_n4o1tmrQK>@9BsX)bl~>rx^;0a2?2+JN@|8i zMv)Sih!T%~PK@0{kT6ZSCE&Jg+qP}nwr$(CZJS@)wr$()zW-)oW^os@tg2l`WGyn! zd!E;fbd-u*sdvWrg+$Xd=j<&{3g5nd2y${YVaJ{7o?31ToEiR7?&1IZN^+A3?M1X& z5SR5Nned`3@g@E<%pwUrs^PG$2j6%)l`x5ccr?{I(X*q=_Q-IEIHpdPgtv7PL&bFd z)mL`!m{v!5v#`5YJZ3Y za)<`N-jW~+drA1^ZfiHT%EkWll9J7
ut129K=NF=cQ+7+*&o6IN~PdXW%pL!go zRlc@747vQ+Rao6$N5$qoNitMC=}el5 z8{eO@JbuxTdKBHE`})II@^(k?6uk139z*@-Z|%p~Kj4vq_D(~DlsSH8P(UHFe`P=K z-`G*Om|EmV2vKZ_KYY6U%r z0b|krfIjh=Y8cz&R1$0U849!tdvR_~dTV)Tc_`$bLP#C+W>WNkX)Pv2+d3qY>{U#< zm4|an;HbM=FMy@C$IVo7aIxBdAlLkH5v0aJ9%T?hhmel*^G#4j(l!j+ae55d?W1G9 zW-~4(>nc?g?e;XaoO|60sJ`(26yhF;qw;KvZHI`n_sXuL9?A<8#l1y0B0cYqk@RG% zV!0D5krKitj*$@f6i~3#*{5e)dhL-t+cOw^ZE%xEMbh&tY>YYP#XV1lS1AwvTPZ0I!vxHKuQ6f>JB8)D@pIRM8Yew+o(;SGTH_A*owBH-AUwF91)U6 zNpw;0a4R}^%AWI5eHh!d8NS01qDW~v&Mz1X;l^Lp$(?ejr=5^X4+mko`84O~+xVOQqhS-lHLG@ej4BV{y?m2H1_DU!StDt@jMR zO1#)H+zcBC2542&4)riNHROskee>8^d3{ZaCRe}h4VFHkYMQ}ULX7sv4Jg@rQbDef z{hYM{0vVH3hzfX(0a76JYwBr^1s=0sU52PX#1LFGVplzM;M+% zowr~ms=EUNzYt24=e}c|p7F|p2+`??UtqOyWSP1RGcOHU3n+r~11BLq>!?q_(CBJk zPdt3aV1S8?;~{y#_#J&gRj`o>yJ&{Jq5yN;JcEWsh(3!oDWsy`4E8*yEJZpf5VI4d zUgq5-Y*gudPk1w_FqJcWocD+7->%j{yi4~d*%Y?{%-tX%v0VTEX6^MUsm8^d+iOIE zt1FwDySd0JxGNpwCl%4-S`wu;;XDWvaivEmvjV-KJO6;F)?i?fE6}lN?BKc`;~21H zPJjlGGMD1}S*Fc3!kGLGYJCR!TDWrCqk>VdFS$f!x%GY4b!`+=fMf8pT3Rx&cE=n4 zLPA89D52VkUWyda>+B_t=?v;PiGgSvu$K27LLQvV<9KmI{jXnMy5M2q5gzmekE1`J-J!?uT}){fp>`(D<9km+~y zem})c0GBF*Pq@MH6)E^N3+v7~_8KJ(0FHXNbw=K9&~1vG^*oZ@+Dw$bATm)+$X}MK z?*~j^aaDxEXHXkByBi#diB~%@Dev-Qq8d=#fl4pS2(a{aEzn`RAfK1h+V<_;HKFc- zBliu$N1U_6T^7g_xj`+6dkP{r*YGTr3f4%60Qf&@aAZufk&In^_8-iwyo_Fd-N7OJTLN?fZY;s)pCEB z#jw1;FKQIWWoxIk8;t*RqtM@|hPk)DM9V1k$P^@o#%;X^H)VX*dluvVk_pvKjMzBJ zU-Lobr_`5#Z^FV~z7rg50)RNCq33q7p&NtAb98l+xQTgfpD0+g97FXP4U?e(nP`Z8ji|%@5!p_B+NM-G~WJ8v~N(7Rs zz3^M{h)9=hHLSu#)n8)8AojWBU{r8O0o|`Pm<()Z{>6fPtYdF%9&ix2Bk+gC3O}VH zqZCWX&pg|+TVL1G7a#eSdjPkCpA(o)PDJJag(iDb3bBhitsY+5bLwkGpDZv(YuGeI zuyQgls%NZBCCx9OQfP^9@*Y_e+_RLP2)Hje`>3pihRkQPos?$Ifi9QD=sX~GZ%WzY z%Eu4z`+!5mCXj=2tlZFi=HlBoo#Nf3|5G$lXcT`Sim6bi4HMhR7fG{F$-pVu;^0Ke zy%J1z=e}Gjiz6yd!duy%Pfd(w+3T||%-F`ucO>_*NqhPEp*i)>1mY-{wuf-V?0*{e z$?jPQ8XBqTpAB;D=#@fJ5O=_R_Y{1Op^SQafHV{8-UX;vn_Bt&F-N_9S?@+Zu2;egaoJsW=DF6bEXBA)oYrgBLELZTw#P?)u_3s zCHcHpj^yigzG&r<2X1c^qT2E?JKsu9fimv)`Ks(u4=TM4EBpESqRL*8bC3jGq+{v) zn*h2|jw&o@kMIYbI4S-oquCBg2Q$fN4O+sP;y3Gj2%!qOMYWS?DV#LR0Jf@!D$y!+ z6NXvo+7RuIVH(%%-{&coXx(nflE4zWa&i*NtJEl&w8fqlvu$*pmG+$4J89f*1(8V# z3A*SU??BEcQtGsVwX^7&$M(RjMSGj0-=PXGS(Mb!b+$UmZ;4gj+plHZ=0w3I8^Pt^ z$%%7e0T6!`eo@+y#9Z$J6FinWqxnFbugz}xvgjNsJ{}DDVezdcaU}=&E(12gM3gTqu}kbF=Qer|;-sMMx9eM0#06#I;eMcvif6 zkFd)A=M}9f_O8W9FfC8^3WsF+5y{P9evGNQf4zO@uDo&P;?2}F3lSH!{q_M~FrJe-_?5WXHZByKsYGQ${Ix4M8Ubg)bN z*vgsqmB7ER3WSPJ>QsY&)Bj;lV>Xhz!%d!TGnSQZG?MNTY};m*d(8rY9=;%;Y`_7B zT{;X>6PF`B(M^nRUOeg4U|F-bYj)rOs&@mVx{Nesl~`rK_>aita{b3h$%3>ZQ(Qf5 zJU6Upk6;?3N6BA{Z(6oAE#wMCY$|---NMOyh>_k0S+~=>P%n$GT1M zv6t7t)VVBt0gyNnyS=~v*QkiZ2#?vLt7V=^wjqOVbfnlCp|{-~JOOgXofT2>OEYAr z4THQr#Qp8p_E;6`0d)tAn~Sqe#NhSRd}HAmLjzp-$Uw~ymQ>O@$4<6q)IQa6wen4W zsg<4+nX@5>+VJcmn+xJbWF8E63&O+M3vbgPB-UA-4d)FMwrGZx{$$|`JcW&=<+< zD_^Bj5&|{V5=7=EF38BOMW!Xj1x6Q8mDC-W-`t!Z9+V4H8=u_-xwkY6B_u_41Hj_a zT;GVo-~#LfxD-GRfSAYV9|kcvK0Xd11clhz=;GGM$m9m3;A5nythD?!{h0KY1EK@c_d91w0FzhfFXR zX0Xk_lOn)%U|bs-99;fBU>Y1iGq|uexqN1aCSZ+qEN$-WZ_)iFJF7Q#LT~V{If!ie zJ@Sm8+~VZo#^BH%H{g~KJ-2Iij_mPTf`-|Esn-+YFAJ#t}a zZSer)`I(D)Eir+B$k5`R*1|9I8+itA@aR5E4sNaWte@Dr>Zhzccw|5nP#|8(-5G`z_!G@DRU}64Gl^NO?+8e*DZma$s0c~V|azDxieUVGn6j78El8S$C=r4C1q4FoW zD%&^wl|SO-O>Sg=p6}42663S5`;t@RlOP4AW(MEg4*5PDnVLPn;Zgp;jK5bj*607N z5ZL^$%@^}i{psJ)Q+@Jn-$2AB)>h_sEA^yYSQ}aX)k}U@-}dM%99(|YukR6m_V3xp zohUfaPQWOG^po4@c3>K1pHglWLlc;oXp8qhi~+Eq>u4+0M`vH^Yc5|UA$Cq_SUu|C z^UKlB-R%Fs&6_>9(u&uxfAh5y+{poFoE>_@DLb7K)+V*r%ih1wUZM__*n z`&u?IR^HmhQBq!^_4*H^+L^coba)iLk-AR4ijucC2R*UL)<*N22v@xX>L<%5ZtbXAhZicb6foVgoLq`~;dg@8= z+tBHpKvP`H&o98N(<)~tu;x8*<+&S< z5P|6b(h(|vtBzH$^I>wv!RK}z3$Z>_rGehillvTyNjYp;>Jf}4er2Mv3-Y8e%pyJz z4;a`gAxD}YXXen&%9LHS#dNOK_)$-MhHB@GdZzsoQo#gbkE($@P%q1T?4g0TVt*+L zonc;Sag#69T!SF1^Z`R@UT$j13R5^~wnLqhLoIq4GmJW*x97ccEf?g}YM1!3tc2z@ zdFv%XDHx7>=|}y!1*72@RqQ$IXZTP3R%)>WbSJPxDZ%QJQ5!#C5_`P4g(4W>DNo9t z!f->VNg=g;vEvN7)`gCf&7)LL`D9-Wj7$UKeTK-ZY6_pDS@?9`m z%H!Bqsxt?VLN1YF+1k;SotUCa3Li3TAsX&^q1atQr<4d`9~RT{zUu7;rved!E=i?URoPVkPrU+)jU0h zSQvi$?8MeP637saR3hAU!euFH*dsDV$@Wk7^r(DVt)F1!7D0>#39WtONwLm+csRV+ z0fNrT9XL~12ab{^fyOb$JdHNNIsz#w##(tqLTc-lwt$6RfOxTss%)V?AlqIh^xMf_ z{eTt@xYHD>eLZ()QwrLcl;~<31v(B(u_7?luX{qoHrc5vgYrvk*9RrUm)$R%3Qyfq zGPED5wLe%qhMEK!9Zx4X)>4-o9qcN+0$R6ykvJBkd?&Y*9PY<>Oh+u1n2a}H7E7Mn zz*U8lJ>rhFZQtXRs8-qt6mmfI3ugFXhGG0sIDbmMKrO*SEChmAI=Ya@V~xdu)2{EO zfM~3A#&Ar2#!9c3Q#d2lW^*(BEV_kRKD_yi?uPzdC!S*y(UDOEU*>ykbnjsqDgtdi zr-?5hhGv7Qr|zF>m9U3@eZ4~H%)J8f9{OA&&nEW4$B4T7?9*wjXOeR7Ajuv~NpGc> zXS*nCpy9QJRR2}aI)j~e5DjNb4i!1{KUMVqv#){>3TJ-t3JY${=G3%?IHjAY2KG^}xHw*l`Pk#@TjW?oPTo3?K5ZKdS> zqL~nPO|qsdfZ0EuRyQY(EHD1(uz<6$thFZKIdACX8SbDNJE}4FD`2f*h*$lh@*S*A zIU=<7y#M=zV}z0L7XCNzsf>1?kYWM#&Y0*L;%PEZZ^$M%w)U8_qKAPrJ8_vXhDpE zIT6S}N>kYGTu>K-G$sJQ**`kqFV#IkdAsW~4%g0VbJgrhI#uu}PrVcqwE9g7wPv8r zl@lzbb=YG!JhU#Y#N8m5P_6TatyzdYeel01ISqm4yTK}I@7o8H9v$#~JWwpqJKX@bRB;2oPg?LiZjZT7d^dn`Iv zvY)fgs3%EiNOGLZ#@oFkt_-*bA6|G>#wE)5-9F{4%lhf*vvAoo)(9&CAj<6-c_>Ux z&Zb3GZ;H)$?bCP|8>s7=l%>1E(9yf{<&HXGqZfr(j~!xf)krceFz;N_9JiV(5p(lZxEVkspC*^Ktm%1I5Z99~BOZAbu8}jnWHl3! z{Pu!*7cEB;p!qmjz?nAo&J{yNt;Z#dU|fX2Z6#!QfT{&LHmruW0TvgVEu&Rhoca`C zIlaJ9Hu6G5`q0dbqyx()=^6%%(q^@t%ODSUm#uE$AE6iYQmC|{Cq`0^T)uqL5V|x7 zy+dfvEVg_i3p=y>rPr*+{qPlCN^ze-uF6j+UU%QTG4$J!FDvgN=Yv!GJrl%?{mCR_ zGq0bHC$R)(aznVho3&r`!X8tlWIu_h5!xUn9{1V}U{464#=y?hBL?@7aaT>RjaR)E zc94q~Z}OvvC{oU$^PF#Ud`qv4UZ&j7C?C<;TfumviJ?%aR1|jAouzu=DJp^8T(M|f zSUwnKXOwfCMC&1(q6cks`!Y_l>Ad?eKKBGIp3SLw?2r~`b}_Q~(Oo^ymSV$t*ulKFv_66+TIR*S3n==V zTtF#LxxT}I_?3I^QsG<#+DCj8y#0bk`y4D4ssVNXFKo4_4@wjCOM=Hl+&C5c@qroR z%ITUp{T44MX(v$E_<_}bR-WIN&xx5MfdKK12X8MZ4Bei`mfb1ro>JYi3Qo~NDD5xZ zDA7{P5)bg{Cn>1wegs*+^JQUb%A?!`L@E@4Qm86^o5zN{y)a)kb;22%r<6Lol*J21 zN(a~BR8lK~NIFIAY5{XBp0$gHcn+B#`5EL!it@(UpAy0@R1d&eerk1S0Br8pdfTzRG1uCh zJ1jeA>sPzJNSD^Kc*Q~!7@It6&_9N#8aaduHq>+`Ntuc07GkT@j4&2}4L*h0b2JlR zi(jUI*haWEVtLz6<+}zN&4;NSbZ}`sggkf>-J#hMJg$*?meqrA#VI885vfq4YIx+O zns~ma^QfM9aGLdj=G(+=zgN<~hXttQyQf%NY0!-x3!WCjGGt)leF0W;?7Gl9wV3s! z=}yEykY%;(jm(XTPXY<_2~TLL{211s(Uw{id+YCptzW6yLNGD3?R-k3Psr0f;X-uH zG4U$i0Q9-|timL6jK2Rpa=AY*Wgmg0EKh}7)?!1S;*AXis@Kc4v@Z}azR7;2&Jp7v zw3Jt{skBYZG!?E*BDR>>V8;*wfCmcqGNB|IQJzFMj21GwAD!%xo$zvF@0bk}sEN16 z0w8iC_XP2k%j59gPqj%-F8h9H3`NtTlR~Ie$fc!2ha96Vsk{6JI3`3-MEdxso2=*mM(zEV@xy^`p6)%;r~gP!HC5RuCl2nFwX~gnW)Vo} z9=+Kh8A_@7r@NDF{3Cwto{O23*$AF~v~@LuFU+)<)~4GNF~;)H|A^{_Xdf6H?LAR^e_DjU_#~vAlExm0d4BPGg9WvAG1F)Ex{uJ zuz4!Z;8L=qQkf(y5Z{A|KjTzf#;@;{5hdl1Kv`+zzMmNjs*)&gV-@Ky06owMh(xZX z{t8iYdTVSkktbsGNA%y1czeM|s4MTcwwq1(7jQi&#_D9+R+F1j>2vH_=HDsDw#g%K z|KpnZlz-nXOVwd#yTbh2`?;3K=HraLmD6nIgZ4!mte5PT>9de4+Y7{9m z?LKoi4IH;H<~duANR{@zg}k|bjH(E8>g48bZMzM%k`sCf3HYyB3&7&k$c|Ztmf=6(Ad%>vOHEJxo_2VY?LRgTAW;3r*jQUtC&E&QN2D zlVz)GQNdx99V)eq?y~2hU%s7*3VzIDsGhZc;MDgsr4u$!D`1h-5NYF8CtG^{{aNwI+luk9u_sJPI<{h zy{QA+uB%+U%1=SH*>L8RTXcGyJU&JW|kAS&<6o8%i;ob();c3l5P1 zWS?7WvZkex8+rvq*key~t*6#p%&1kOd)FEXdGnnRmJd z5Xs}{g$Oxbhal%nUWnDC#2**eM4D1 zX8JcbusNg~D~?Ddb_ z#SrHOBADuqnctVt8JKbdvUcKrI#bsRjr$6;3z<~@M{rMEa2jdYNr=a7sOv%J~}_9!xp^4hTbGT=|N zA=N!~;h<-q9Q?n3>=|xM(2RW!;W*A}C=~DO$;;SB_g)f)x+-A+BTowoy!!L1dOxH+ z^6-7WK6USvV_5n4#NuM%#>q21QRBw6QLP?l)q;X&r4Dg8d{sfuQOs zxgYA{qeTp0P6yyrU8=)sMvP!%51uU0?!`r4F0m&Bq>QJ>lwkdv3negYwwnNsIZ}HX zNTz`^bZO|njZQKR95l(=)+Idc^Ml#2dUzHg;_{0RI%<+2vN7r+?lrSh?><1SXX{w4C^@rqQi=a_J#S37MLPo7zZ` z(fi*@@ zh3VZ}g&apiPIfgrrzF9rsR_RiS<+ZuWI1~hYl@T4g2W$Ig~~r%L~{9IsD>l8n_SxL zJ^XZ&(^Pui5V1atH>}lKxLXD=EguoQr(FsNC@vBVght>h#Y+&jVANxduHE06 zpDvcml)AUE63o*FRvT%dLg19*R5~AD-tCUSYon=`8hxs7+AET%714^-!$ykDZ5J(m zSHd$pZS}Xpe;QhqJ{QTiQoewJ>^E8vv1Tg2QC^#={vAg4>4c2i3mD%d!koOmqdak5 zgg?}%I)pBN1_6T*fMK`68x<-QY1$HN!CsUJ!ej+NlV$gtCs0$q^OABSW>Y1K_+rYK zu_;O%T#Z~8WA=S)zj2(o?jP0LWFQ*ps z@L9616|&S<TV=j`a%N|__)IyCq2o(^G-=VIfo^$B)Wg)V=|?0e zU_P%{|6PBqZ`f?Mi4pYLidDtQMwZjzwJJlpjaMbRIU)gzv`Vrlb^EPGYB;%(>b?a5 z!|T|h^gq4nvvf~3Fl;(O>`r_#q^ZqUAT6_S>YLeic)U5+T(lapgTHH1HqILVCmBmz z&}sM?m&oohy=U=rUwdI2#fLh-(-dj^LM*~8AQ460?bMAu)2UciqDv75Oy8fU)#bl@ z<@QmM)w>ukoh&dt322$%=NVPY^oz$&J_sf=Ei|&M93!$uu;b55H?YrtZt?qw`wJte z2aAo94?|3v6}1(R;k^p+`RdlnGU2LZ9CJ5Wb$UJ0V2UfU+om?sN69B;Wg58u2$AK+ za(rQc%B>uusIoYR0SVTWD=jwYtCCH7Te5JsDZxpy;Gv9?Zn~~pmosMbQaBH@e~{KO zRgf#ws|hm|S=)Jr%?JM&EuK6&TpW?qA3&rgxIr8sd?wp`s126TR>ofSZYxj9vMmnr zTS*}X4tOy)2AY54ZXOOeDjZ7UxA$#>@0$bla$W7sUVj}O3u0+5*JK5dKVS%OrosJ- z(9*1ded1&rBIVO&v{>!6 zUW={CaCM-P_r6yxg9qm`|8VYpx(cb|v?SWgzCNqn4^D<)2WYg8iFugxKR8uRj|^xF zz@YM$SgO<#u3)r>U6^a~tOfJuPgQVVv1M!$1Js!}Q(R}2*7QBXQT0YK2&67z39|;g zj)w4hrOV1#6nsioIu!rNL2lSUV=3BFM(maUY76*zWOEXJXcsT60rc_=9jbEZ^7oF4 z)cq@F#Z>4fy!Y1cvjxvG(31ltekRyaqhy5*_4WWcl5K5V@)~9f`-Kn-BI2)CujiH;jV1;i8cN zQtkCANMmG)T^9RGj8uFzDPaPQmy3JLq?nIr?kbj3 zFJdoS3d5VIG}YK0Cm57=d$xH+ ztFNxc7$RoA!Uk+x8)$}}H_PzosLFbq9WnvbDPmz3+cXV^ty*qPec_{*&uUEHCXP$diZL%NXQu^PizImWk0; zF@GZCBDyhufN0%WXfc+vsnRN~**h}w2T=G@BvX7qwO&*Xl4{*@@HW4*Fl40qnt(A= zEVkPC*YYtVocWo{+M+i(FwN?}Jq`7_&Qzd^@f;|u2neWgaY5MQRSB?U60SKgtmqVt zKuR0H+V|cXh^IR_!$5{VN01JwUeDb{aRDK3yJdf4m|OyJCZ*0iu#@M9tg#BM_2{g& z+5iI|{tm^CrM$7lVXUKf|BPgK=mCG>9m(wf-LwhB$>%JH6~+s?umiuVAjUORzyzbn zqKC6(_AqKPcqPjvX-gKnqgHnk`C#M2ji&H>Hw?4F6<)4NNMq8O8f=~nS9M(~%===~ z43{@mIEkO&FN5tMz~F0)$uf19yF$cmx*#r=X@uXER3H+m-dh50`K{AC-G9xSSq|_M zSgn}x2pIPVZ7#QhXMKGJ;Isb(kw2RCYfHDgB7};{({3fQK-*-g-)^KcF6pPjp_smL zce)MJqNZ$GxD;?BINj0xYI4ngQiLh`j~*m;W@)c%bArzJ!L@0cSXVqH4O!%tFhwc` z*2~X=tL~J_i2#*KPl|^v`_h7?Q?5C3bf?roEe=EzMm-y#yMY=tVe7*1eabPI+X!oJ z{exs02Sk=lZTdh9@g+Y>ZLyp(kB}AK=_~tH>9cKFSR~K8d)l>U$h`FBkqfk~I4wQNf)WfBrRsNG97kPhjO zYdcj7{}4_#qssuNzf!V8Q#k9D!_d6<1!Q9o>>bAhri106n0M&S^1gf=!wqF^B||u~ zb~YoRE2g{WP=8Dz`y{-n?^6YxmmYNv)b^aRLBTJODpgxEwQdPLw!)=RSp8MA;fNx^YnMv@;-`)lF{ zUG&fPy{EDQoLf&ThCwN)8S3u(6MR`=|NK^E4|oxaROadg_Jf}>ZtUoBW@m_W(&`j| zZ14AlV)4q7yEUJZ;Q%KjzhT#AYHx1uFbLVm6D^D=zx|S@IOyPmL^stYqSC9hoI&Uc zuCF#zSIK6M{!&_3Ct2Sqa^b*OkP0lCp>~gmvJ83V{j%woO2e!E_8w4KzcKM!&Td?i+ z+=E+mUFf&?v%_aulwvfsB}~5}aFo{$^WbR%fx_Np`*@2M@}Om;A206#kx)<2qGdH1qKTU$Qoy{h_hesy8}EqKB0X}@vn!_^za z)X0c2lXy7Vzf~sD8_5D4ME;C##{a4o0Q-`%8eocP z@8aO6mX)ch&76&*Ru!Gbc-KNkV$y{z~F@~!b_{s9%zhzdi>0NIUJ zh7&vrTy$OUhVcUp943=3Gaw@zs^0xeY@RSQ%-l8|}2KWAC;gFJpjI)5V&;Z4qfsk<9nRaRT8 z;m{5hgNn3Rq3?%nYr?peD=xA)pgpuvpZn;wQyF-^Ulh3h0AkelCvBEIR5$BO+HPz} zV?&@HVN$SD%M1+bV2Hk36QsymM#)&JGl%f_7a6uHz5UQkm6bY(!&LSWhA?$%m-7Q1 zXe9nS5MH`z`!nJj6AdjZz1#Hx6)ciE+3Zs8T<`EOn9$JU$m`hOjx4@u^;FBANH}gwf}Wn;^+BJ0XuD?B5$Z?HMkTd_5VBj>e%=1{U{N7$fKD3!xpDQ9f3^UCOJ)y5nlFCGXSlVYA0&>_8o zm2^^K=FM=dCZPOL^L2&W?ze%bzFfi(Emcz1>B_cB`>M0@uXtDJEv~^XdOX+s@_@Bcf#GdE5y>mYvT{K!xBSnvq&H#g1WbjVO4m$~G34Vu< zFE5&-5Io2N=WIQ!)r&z$K`@e*mS*K~7X!tLwLu^KaD7hn&3 zbqExmuatjJ=)0&EA2XR^xanQiyvX{P&HWWE$Cm1yTb<~ZG`S1k8g_VD1eSZMy8O_$%_zt{G*3#jw3?&f9%aH9xxXg39LnKAXFPiKT7g9TPWT z&7G{C5RqSsmjEg-=cI*`d})2GU*y}WW`$5Y5~phu)$jVVE&T^H$0##FnmCDwZ>!%`0YFmuJ=Cj~6{;yJ>m9`36q&{9|7qNGDa%1X#ZrnlukQy4Zh+`F)MRcwswx|W zaxKnx`XOl9B^RBZ(n>o(7Cu(jR(nJjQl?2zu2lw2MYERyQz&`I? zZjhq*0AIMu;25-Hb+hv9B%~DbG7mC%IkxnD3FGEeu%7L2$yNWsR#s~O&8?~K9lIUQ8?m=B-@RS8u zedmVn#yW1%3|VoD(3t6}nlq%)Ju`aV0Bi_Qct{|(9 zcOX3B|nK>ubow=E* z{uVtK(yvxnG&$2B-$Ng|@Z!eapNoVWg@9+^9~$8MMNH@THdu^U6#?5EwI%;Ed;oQA43-NPGItmEoL!_vhv_4LiX z*vS!q(@@|x5v>WWWlmEms%P9}o(O@_ZHz(n%=|EToV6EbMqzv$Ti*v?S1*3qTI4j6 z+Ji=={X>)rBAqdd)$EyA?_TGwAaH)a26g+04*>TEeuL)|WdH`a@bQ9K!Wlq7mK>EY zS<#hbAcLG2z0=3E)tB~fo*1}2i1CLEr~D{eUc3z}xwfE@b`&W*%PW1+3IB-Vw>B?$ z|N2RGFr_<0n9saEU_I!=RPI?&t?QbGEEsxzjA){!ko&kFq(SEUL&HO=px>G<_*&~< zI=Zky9KV|>Fz0AFFI9Vzbdq1lhjzS;WTJ!Ur#-i+d7qN|S)&RKv>1zU^Fpcagvy{= zh8rsO%$f%=L1jwLAgSAPiz%7%H2X{ICSUe^*++;_mLzT-O#Ui{njAHurcwy!X~EGb zHSNvZ9&qMN*Rg}9SP8x_XR;%=;mo!PrP`#Pv(Uc^cBrJ*OtE~O91626~i#-w# z?hs)1(t~Tc@H}eC7^9+3%hj4xt(0vL-*_~haItR$7q@x8w#%J0oF0#5xs>zlUI%r* zBbhKc++;!CdJQme`jH3wPBiG&9;$NI$e4jgndA#{FP78y+ZN>=0}7-;k;7WdUIY~F ze4zz)!FnlXAmLkOB)QcLdEySnyX=NAee)f&@#nN(>L!`@LlNE#;;-0BYBI?-XN7?yrWZ$*oUr?=UBtW^d+B!cjkF(A{RQtW5(cllKzv6oON{jWKD^ zeKaeU-@rQ^BHCdNrn@BiD!rj7s0DRyU?ZD|o-=7&M6w@3`kL62lKG~ap1&_|B~4iM zgQVj%v?RYwdqEsjd6?Tl(iIlL6wrEWhpjQZh!-Ebtrg9+EcR??2*~UqRLGqJ(P;VC zt-GHV8kt=)xQ9th6juWG{fWAR&QP=!$VH%0{&-25uhdd$hS72st!PX|aEqS96j98Y zhliRoYchqYh3T$3rbnpaj$r?_?0nE7I4aTS*fz4F2g`R$r-j#wBPtmzgXzz!!%IdJ zJ&d^ZFp}tIB&@J~znt8)=Bghzy!QLo&@_cQ$t#GM&yQB=2utA-wJios(UFC5I2{!= z#?0<@`mmeuqg1xU2eMQ?W4~^u{RzRCQxQ(Qs=fejjap^wx32L~Z&O&=xBV)u0x(TB zsGnh?7P1;DIrD{YJP=X(*e1wyI%U0gU^WDJxmAnb88kvno}(2=T+C0rD~P+x>~xs6 z6M~y9&+Z^AMZ@k{G{bp_t6SIONm=oGIN*AMF|-SAb0K%oSS)P=DMKTT1WUk8xQ_y* z9Pxy)7=Y(RZ$HSJ)IN55)3gn}jNtDczAnn#jBWs z_ciDvucf>mY1TCBm^%?k1&u&F<0^|m0Pj5pt2t6Un+ME$dy@>|)qtCGH{UbbdV$Xn zOq;gw=%LeUoGzWK(0L}EmQaf*SQTqxkRIZzXa(06T05wSh?%(6=^bDj9pGFC9=I&> zd(;g6XZXe}#0?IF*_#*&gMkpFPnKIQG~s{G zp%(TUCyyKv>QPTT2dKobb0Vzg_A+X(C@22u4)z#r9dSD-)}v9P7KrwIX_bDFtKn9* z_NUt##^<}7ma@p$^CFOA=f3fJ81ron-w%uR78Yg_Iw)c&vz#rHgofZV;v7LFuF`L! zZbnbiZWnZN7rqZ`t+}I#>7%j{AsA4ilnzb^~-kT{X-;4pLxkf(3`D&Jp=Um9uS|r#!aY0F1 zsxoUIV}MAj&`#j|2UF^ShHM?L8oEWtZ<&Bu>N`Tz73#1kq3X@)kWT}bn3?q${mYw= z1xV24_~@HQ3?c_d__66yA^s^kB?n`RMVw^0N(jT1IoeOmY`8GZCgf4OP8;jP`-k4r z*ezgrW3IEND<7ZGq^Zy;$XoD}xHEq4(Oxn}MjXDl)|BZL2<7>4KnG$23&0?7!yllAC_aZih<<{Bb=|4GRMO63R8{j0io9eLT%aDZd{Np*JTppJ zBsG|wXSm@=2Zb%>;ha5u_bUFPms2#Tj{XotI=jjK^`sT*6@Bd-yOg2wP(F_=a33m} z9=1Hp#6>M?CA=vaGpeoMYc%(<&Agw38@Qb+LPumJsm^Lh)?!uh4mm|Bwq9~+xueY5 z=E<5*d$ss8n#eMMT{!|}y~ZD;`q{Hr;UdQc2G6yGm!omT2JZfR^6eD}+}DIU-B$2l zDagSDS6ssc{V@pZHy_*#-hQ07Z<2U(O^C09iKOtAIU)maAsYd9y^-WZWht$u$8y3M zQLr?vYCLttgcgn6$Z*v=wr1n*e^syZqnU^tGdOzSG`Cl_%X2*7mnL8(#IXS!sBNN8 z7USMi-3ztrJn-2ADA2Gkn7m+WfN+pGR9o*;;_16c#jOl6Kk|nzg5Y^zX5t0Q=NiZo zveCp6-*VAfH>-Dsb1T~mK^V}-D`m7(t;E4Zw{^_(TuU!cQ@!l%@)v4BB#R{9AQy&jMVu>AW%M2v#gmOkXOleE@RZGM?Z z8zk^4z}#F-plU#>m0(JFK`K)QcQb8iSYZW-v2qDdj|Xb1fr^6wP95sT}uk1S177OF4BWqS8NRtz$fp57kCLneDb?@8P628ig zsde!3UA_Ddi8xQik|2lz;7e1z@s}n9KlzVjx*HamOR`bDd86FsfW=3a(6sXLOZ&@G zGyPe;@sexsP~$IsOvjHc}l_5A6Ns6PC39Gel%fR*zNDF278 za|+IdiJx>%Y}+}pZQHhO+qP}nPTrU&wr$(yetYq++O6HWoBOHXR8P;-4Qe##;FX|A z-*DM;nqhM?S%xv2u`GzAVJ_vIqG}TIm(S*oG?je%Iut!tm;KjZj1C2%SVlom@sGHH zH{N)^W`wLcOXkAA=|Pu@jK8!;Tr8P$nkdYWit02VDf?^lwhF1cdYcy~ELhWQPCcVQtjG#7n88Y(P68In(fc#U_L{8HT4nevxLL!O!D%7 zIyZ_qg7+}iZsJOAksHNC#EkDgbwDZ)bKz#UaCBSP7&j3@L3!(8_E0*uZh$mDS#%1B zC0xO8%*bDA{=MoTBUEo9&4t6c!Y9*`xYWSG64^*gGSScsaKA;eS3hZF?Ih_EX-SN@ ze0FibvA^J8ZV#UR>`9BE!i@ntVzwpu5bl4XN8 zKoeXS2~Crt4_oM&ZR$*#hvs1w)&M*|5q>dArWTJ!(*`+LUxh>!hN_3nfrmBlz^M2d zV`N3sB($qBx~9ZbaB3o)Ryd>u6%8X$_W^eXoW4d$4+DRX!YZY|Bbok75C}7X@&8g( z>_W#-bUlbJw2P+HV|6b7aVwN^8rcQ+PVm5{@rXr@s_9mv# ze05O~w$L6MHEpIUxv~wUF~ zTwEW&Ol;v%9%+X(xn0$GZgT1+lq3w1`Jv7ze*z#n6b54getFDH_`VAVn}y zT1!t!pw^OZYyo6QU@q)+AXMELTN+uQrZh5v1e64D1G7`ehWB`|{vmi1t9N-zxfuV( zkX#@!Aad`5$m3mG0e6&wZ+<$j0N%Ozm4)&1TmJq9D1#ddP^X_w5OeMT(y^hD;U@xM z|7$b1U*snDmQNhR&(&89nfaOV_3@$kg&nLr_UfXHA^$rU0E5#Hd0XKN zZsa6C>G$O)%;V~%jR}+!FbBwX?(euMENF%n*ZL-==hyT%#?;RIgFZH$TpHoyuaN+P z185cwXVwN#ZqCo(*YHm{_pd7Xo`2=e*v`(#;qJEEuh_RdeA#Q5x4-<3zyIM>lZd~+xu?JIwEITJ#P%jIU+yS-{I{3^ zG<*5d;7@&`IO|#)9$)zfzuqO_cl;7R1coKKu|EJIOp_mVcr&q+Uj{8MNsUerSv1;Q zSsEZSF*g6tr+QsD6KI!~M$kXM7w`7ee_&~*rhcc(tqd)V;6BRlaew!LgJgcWU;B{1 zCvznKQ|lUnc{l!j%D=J7U)4R$RpHrloZO4Q9d8h#B11EHd&B(?*Ej)zsnOTB zV~tHf?d$74KL}XAU`FrttvQL!#iiT=r}pbpG{5M-{JpL8vQSDVV3oo6G-=Wi9`95tlN0e zAA|S<>m((N;O)Q_pfE*c2Pdgaho?7zXKxb=hk{S+PWSi#I&Sd1pjF6K_VW;u`SpKu z_jNl*ARoi2#4qCegAOqAGZq?`3URM`{#qP6*F>f<>u$)5!=ImRa{A>|=e<}MYB#FeV@VC?Nkn8W6)EQ>jRu4n#Nw{|Mf zE0)8@S*64dhA=NW2V1*j&R3)fcal^m$B!qkC1!}&6+Cq$rj+v(Y1>+vh5uyrq_f@_ z_}7^tg}?n#cwVqPdp1gK=xU_3E_!7VeK`A|+dxfTi~>124|b$6!Dbn{#4C<$uhVar zhxQal+aGI1qmtIw2;3qJW}x$})5~S(0h0I^Eeg-;E_*fN4#bjT3NhtZ*JWRpM!!#V z1qNDuYTIdqN!Cvn!t25X+G|&^mAg(hdR`MPxZSxQB#FxMihT6hs+cdD{P)abk~g8z zY?cA4)WYO+&7qsslOPno+O2$)OraC*{BY-IfzQ{zGfL)sP7#DxDojFO_I*U`TIqb# zk~t2zzq;J*zKjk6{>s zZ617JcD?lWshu0N#YV>yNq3`>ra9$P+E?lI2CuM8ux*be{CY%=)Sl?{w4dbs>bm2G zxGdDo4Oxp!_h4Glb$PpAGcgJ$i9D7a0_7`D?)XDb$5@iZrrXQV^`iB3brv>d`$oCh zF;TH3e76->n-OQLNQ=683~PUCTA-%>?=PTv8EL>6y>5QIE$jg@#!oVtZX|=v-^8b`)B>tql$~-S1Q@ z!S(@HYoJG+$vhQ&t<|>W@44w|(<`^`(@wN|>?M5T> z2`wE@!WkGrSZD3ffM#UNlzb?)1Vp|SL547*5ap|Jqfu~5+Ou@-!3=3-L*{AbqGU;A zD1Er}q4`4VH%JM}D>qQxzo|Fu!fFJczWZlE(ywLKhIvGqEiws(Yjj@%L(kXdE4q-~ z$f@~s&_d)pRt+mjP}@96f(CviOLaY#j)RBx3siN>xruA;%XM=SNKLVrR5N~<%?0Ms zgr1PwqWi?UVA`Y+!)uH~+hM4ZZsb1fH@>>fJtv0Gs?&sMob`ym=bV@u)y4F9R;ifK zRMG>Ri=PbhFzzxWL}K&BMIO=oVWteRrKptw@Zz>;BO?T&TcK7fnI*5}XIjXKw!AB7 zuwj2hAnxHQ^W2LZ4xK0sdAp1+%7Vw{Cz#f50i=QleKqG*pVkFJB%fy5Q_Fw9riO@ceHSH8}d#G*KbylP1xh5PP@dFcsg6i1d zUk3Q(fynx~sJzC+oW@0sP@a%LeAJ$`vx%0c6=T}QV2D_?S0L4v%X7@!LOc&9je;}m zN9Zik=7crjJmKh!mt_%_~dWDdqag~d`(L&oCZPEax%Qlbg%O{z1Cko0Ij}=F@VveF>iY5 zP0j>KW5fh#Ka@-OyqPpHftG}&VS0TEXpGyAm)P9H%dbqeXu7g_f!`i6v?Nx&o*O34GZ7Y4U@ z0ztJ&9`p-il$T>^tgbiJchgir0?T>)9L8H6-o?{{j$a(qBL@Sy{AqD+t;4N`S<-!1 zMVc>H)yA)8M19nK>jkfKvfTZpB{qgc8URcd6USMd{uXbQM+59{)53N~PgZ z>@gY*uGbsP(ID19H&u;;z6X<0>_J-@d9RELYqwhV0^_Mh>=Ok8V&N9usDUy41x40)Qv;AZnIn${|Vmr~ zP&*z8#vw7k8vQA!{Aees-?Az5kgnYgIY61N`bxEt_EtmL60s;9d5~E(Zz*KJNVlAP z8(_v8MRk;oeg#O{%fFd$GN@i_im^BPE+~$YrL4Ey2wSS&NyK25S~>LDg|t*+L8X9) zMbDNfsuBsMx5}%(47hUJdRJj9#ZDSBk{rpWY=Uno%FRh*h4x0+7-c=R6CfCNyNWoF zmjbKg3yVvinc7)XUv zVd1U<%rS?z)*uJlka(fn@>f5F*FyQlHB8V2MwJ3>K!rz@H6MM~_|2@Am{GXj3JGnG zQNfX)G#gCjsIG`IW`?v-sO%qt)VA$OnU=Qrm>tK`SStZz6BdQ$aeJmPY+pXXgaMGQ zsaF``@FpX-RiNxUxT!n`l$o*!?-cli;tnCBWhq8E)U*2FzF7^m-#s^GCH;E9s@^h! z4=2jjpz95ChQZ=0L!Sn#we^vE`Qsr>0sGY&#afCa0Xf~_t$5(ePY>lF*;0e|#JaB; z&5cmTvK5%YEp(g%%Nc~THgvJUxVV&{H2h=g?n5cG9G7(1|@1a4B=@28kEG~Ny9ZE1wG_~SS4bTSj6GOGL#y%&**NV zmc)Dg5T1&!YE!HOxgw=}yOT55Vrh9Sc7Q*hm`({)u&2mF>e)zJpD^uC+NZz=m06Mx z!mT%~Ok|C84UNdRvD>+M&OuUc7ObE6n<-}mQt18J<_2)JcN^sB_tPp{kO{yGzm&Ts zPP3f$^8)SYbyF#(B8%i}abp~@Shf`D!1;Ji@WqWHNl?RL{Z;EYY^eTP!abUziwt_1 zZ)GB@DCc2Gk@%~FU_w{4R4hhW(qz!v@<&3R%b`oNrp$0xSq_e*8|7j53)uOR_AIhH z!HHh2LAIVsC0(I-S4Imhhib#roOi3g#ScHmDIEg#Au+QX-`L|pLP=OqMC8TBeSjC1jgNH3M2E?R0WrnSW_&AK zQ9?gkP;uwu-K&(RnQTy?4)&*$f@rLXA$>%9zo%!ST!S9+?OMwx2km}Fh*mjyZ)s)mdVmzjm-B$Dy;WaE zKMW)`2s3NfkTw6$AHR7H?eF`&^&ZgnCU-@_n*+z5#WEvDt|95F6xp@C#k#7#>)mn! zjBn<@krxdmhQeMUIc94~5G^@e&<8H6RKzZEB*}WDoyqGUs#LT3_2oJ?h6e+EnNafP z@rNnlWLxo$7gqXcBcU|O5O1a=6$e5DoKbX^H)D3xm>$b)s6^F<7ldZBwM*@F$QDPX zne#Aic7C7Zt4c?rkhwDn7j}s|T)C5)A{zHsl&WD24NGJ9Y0u5OJ8B7sIBZIyOlj$ z?_Bpr?FuRykaVC~|Dw^Vu=hCDz{Y5399b(OGe4HsOTNw&A-wo6@yA|`(3IE+LJYLc zM}Sz^%g0e%+vc-v4&!V?)D%xGd!t;WL3f1=yzrlIj2S9P5&>;T90ls;);^I^aTEqE zAY%PWI%>;1gSPunNK*rq#pGCMRWWiApqNthXju7!Sp!TF$P3Lkl&A)7apZlNYvbi= zjnd}4aK_zIiuk75>2kP|>_&dW=5F&zV!D4I4wxfWp99Zr6YPXfw^hd#=VDq;p6gvl z3uv2nTprH9EEhoPB66y4v@)5&8`7dr-(U#yU+d!*QkgSIy5Qp8N~o~t9g4q+sKVHM zlH90LU5;3ljGvLR?;^vU?Uu|A&{YnC_3s8;DYM7&v51+AXW$LjK_xabd<_Xwale!1 z$XT~kvR8V*o8B1lTu^FU1ID%>#`LY-Ss(nTj<>jR^N`XUc!8CzMx;c57o!IgC+aEk z>?!qAnaM}eQ;D!A3RU-WPq`c4X&5xayeL5p)cU3%kt*!+wbf5l4@uH)jrw#;+&z)( z(}s=q+<4LSmnL7YRSsaHGMp)0oUSkb%Y{WeJwu4_9=fI-S(NMF)u|}MeNK^xTyx7T zA}y2gbq*gre}>DneYX0Ydm9X|sl~GH306f~iDe~Q316WN6Frl7Y{lDTdG9VlnhYc! zQo>*}r9da$xM)jdZARmGsnmpPk686pPcfLO2jm~Nz{kZyO4b?2%jt7~9%{fIBfcMS zLhs3h7)3c5tt~rCb@`@_82f6n7a!jy_YZf=uEafo;eO_hq%9#;&NO3Nk`7=!jlBv} z`ZjdeceS_eHvno09D3RUC0ga2Bqx$%DBmI)?Mw<0Hsl0Ar35Tpw5bapS=ZCkz>Q#NhT^zdL z1O5qzeL>!VyE=w!`aO(hy8hiv#`S`97R19s5Ca4xiY;&Lgu$7GW{Sp&ogKJMvpJVEHJ1YL z1CMC5N{62jI;gtyc@L6wV+~f}D~^lZ19MzpkSk`U9Nk~VXI6Wc)ncRwrNhY4KY7Ml zM~h4)@N8yxU6ONkphw9(3nM>BbtrZ(t2!hiM)a0<3se77WlRbeRtV91GP{zKfsD^; zMSDxu_u^^c{K$NC$2pB@sXLc=f(K)#kUKKmFmcPnP- zywaI5Q`ZN%hkWiFiNE>NDnG`(A(6e5v4E_d4D>~g9E_Q1YRT&F@hut?$l;-#if z9x6XHsqOtG)N%r_!_Q#MWScW|ir#h^VBqYArNt5k8XmvnHN_T?Ty%KTRs&5|y6f`g zwX~w`Q$Pl(c=dR9S0Q|`z8(Bs4{OSd6NgS}bSFT%O(4eN(p;q5=fzq%PN#<<2k1y3 zJmZ+|OB(9m3B(ST$t$zX6$KGv8UWJ%YeB8RSYghmwA*kHdLOZ2pnQuZ^;D|76lL>e z=?>;Y|6A>VcdGcvKpg=mBUN8{$GMkatAykIzIr36-!4T72*vW*M;1v(RD(ZoyOFtn z)g?CnCmqRA4xYHGO6uY-0*f62J?t(~jPS>7WJ9IrBH)??nk{8(`24+0AsR!HI&D6` zw2Z_TAaprVLjQenOV*a{bqp}Qxu-%S(*NcXrGa``jsY&aRUk6VtlV% zw+bSyD1Vwy6IJBwY~qur`z?BLkt{= z!cVc?5ufI%>)I;#*70*E#>Y`^%r4bYK}iV^1Q*l)Y^o!3YgxFB-{Lhw!=ES2>0RJRfe(b zZ(G2@b`BbjW{xFX;XDJfmVaKKBwxsq!7z7$}(Twl$YJIDBmavwqs z_k}=n(|_V~Bc37hBl?zSCK^xan1cS=kR6lOykczy^804J(3BU}DvvL|-eJ$~z?45Q z-xiP}Ri}b?jsuXX!cHQHMA|;kepI{IOYDKy{W!@95?m9ec$)cBW43&6klZAqbH}>; zcIvpZAdDRGq+cv0EHEJ^tCsN8DY9_BUh6|TM9k}45)-*jve|)cbd`H~?Of$CI$Hgm zq-k^KPs8|Klc(`tp8Vl1aVnq0lQ3tJP=km|YrE=3aL`Y|^vOsh&Zn55nO&Uq@Q)Pj zzJ}NF__|XUXU6G=-`oK0Ekgr(!>EK^l62X7R~(Uiyr~q8!L~)y);g;{jOr;!YGV&u zsLF*^J+BcvqYy{=k55R55L{`Q9|I4(qwmH;`#U-NJvRm*{CXnGh*$^Dli z_7$%vHC}t=^yga1yut%)toUOYxLCCx+sh`Bx5XE?gSlYO;EB{YIANLixL@JLls3Bp zM}jatKu<*$`1hqK6dNV+@jnXMR%^6#^4`yFm%dF+E@0w`DeZ8rC+l$&%nPO}1%8xS zAbR+hddM)Or)gVX6!efWVW$!g%jmKGytV}oV3E_%?JyH{QTyHc;ik2DoM~{~Zd}o7 zZs+`)a%w-J)n_Bj_(e;_6L{x4Fm&d{yzZ*u?8`!x!A#TCGlh5F_XiM?LpJT?W*bfl zNz2crH#We4Js#@f6NK7xH0S5DNXtII{dv{+JwO7nFMqkSVp|*iwNALhe?~CgmzqhQ zIS`EDO_Dynl)-OB*EHq@c%W20UvRy1TrMQYfgmY&oxj~n@VEc{9`u7Yx_P4H7omJt zEhCekDW;0BiHWn;`4^If*#TRX*2G3Gp5A2bpMjC)DX5fsXmM6eRisVHdgbu4f-A-8(l|i}4-@=KbW0;5=)uN);6lB0vE(m*R2KJR355k&f*(Qvf3Gr*8ljt^X zN9JP|;FJSt;7Ziwee)V-z$!0ivSvkB#)9v9&&D(|UXqhw^2A2&AGdKQ{F8%gKts%I z`?GziOwmM262$o?J@VKF;=mnt;gacE(m2jU)b2N!T2IJvgxRTEtl(7{`(G=E8gRn% z3EuQAfEYQ9X~%&w_3^I9B;`uLEKpcnDht}|n62CrS%-Jf2PHX(zr+z*4*32_3Ky0$ z3Fks>n}g*kJO6vp&u2X{{7fBpNt2{Qpk;>T$0*T?U6)C{hhEF~Vv!(~*``-s&aw$f zD+J1Q_o#w{>73V}V`#RUH}?CCX*odHetV6qbfoR|miy{jJw*Y}VU`oVs2acAu)<_a z)l^;vBJR{9eTId}m!15&WFJ6Wl_IUcp}D|x{2j<4A;FAqjidvgi#aYk*-1%!P0Y&U zVr=*zmeSfyi9ut6{5x7m2sCzay?HNvkX_~Suvy3y@4?cdc_Dkg{nQ+Y=DzmSf(AtAOM`FK34Pgu*Mxku7dD zus^$^j&sGq!al78ZL!O?Wi}I~c>)xDNg#5wI1}-38Uq@o2+lZdIe|1`{ zb$*BzDLfmE2u~H_Mbbp+KxbT8^5F)_oZX zyw1RKH#?4y2(6!X46IGa(n^=2G=C&t8RT5P4*%(Xo(miC+IH@0ZVSY3-@y=c3PqkU zzdyDjK^pfkCEYVS2Dz-E@FnuVvu8SQz8;@cTggym-M^Ok3I3Jp|FJ~h#=rR4XiGti zPEWYA+EaN+c3`&5UExDQlXg|tlYmwAKJHvbgR_$|Zc*B~8~MS3kyQ&K?~-&{l|)RZ zRX0t$5qH`c;iy(hj0`Hb{6aMY^(^Y?4t5fiDLVCdP3KoN)B#fDFq`&XaS^gpl8FIu z$+i|naZUAXl-tB(yu?$otHVMAkkZGgV0;Don(($Zt#a2n53YOt!T+?x#+LJ-Kq>GE zsWgC0fV-n7+mCv8zV2I^fjw6f*l)(XXIhOHLFm+WTTs38?r z?6sK5n+~Z-B_;K`UJ%ihalk_u&iQbUC;@1t1lFm@lq{nbQRRB(8=%X;F-CZY_Lbqu zL>!25#3(KLTKAvnJQ4Z{u)xK32Azb^?)}8I$5=sH#EGm?;$D2?TIVnkl%Njq8g0yq z1;mCbj_06?B?LsPdM@(H-sj992pYzE;oqNJeKq=9C=&cu;ZO&Hida!uov56L$L$c^2Hx5`j_25PPp6`!{`wI=Hxyf59B=SP8wza3z2Z%~gQlr%&QZo8i{hC+Qp zb_NBE@5lLWh8U;+{glyn*B{Z0H3zPS%RZhKSP+1n>0Hk@z(;#k-Ja{y*xrBs z*EXkNW<@$~aLY`OzNdTDY|H_oNPduWYmM6!&YM;CbNMh_wStGk6;}&-@jr1HJ*j>myQwFkk2O z3C0uZBvXGZV#Iw#1{jtf$VtvkDH30-0C<;&7(OqlKqx~uW%DIkH|?^XQkwe#W{ofs zRo9pJ{baz5Abbn_n;K&E`2r2D{iH&h6u|H0v0YoC+e4GI9&jPOR3p=fd@ZEjct6iP zdg1UKBDa^9jMe=kfZX7~-;#gs`wb&n^MjMAZ%PoOb~riG@%a@H40>LewoxANX%E)} zgsN|0!4NhVS=_4dfW_J2(-et?i1>+2Ho#Gay6NOSq?b6|M82jHSMgp-*mW;?`evaC zmdp&A?XjUX6?vu3qSB9@%O4)y6>)^qq~P}(GGf?-N~)3BtISw0wg?`}y^Xe6x<4|H4yzLnI$>A z*?7=+wi?gx?5Cr0u#!#NNq~sm;rC=Rf)MY!T+o!tw4cxMJo&fMJU0cNW~XV9=BzgA zHMO9iziVMIcDZyaqO;P>xT;V`lgRJn7c5&?nvH-9>n5mu7YgTAL`LmHH>d z@IzMg*{~#0vR>5or1nKtFdf#*Vwv)0UJ&{#2WQe`>Rp)tK3Q9wwd#l`{dGSRMEIzf zCNVyeppp_^aO}Q~nYQmL*%Yz&>Uce2Bb=`q=ajzB4T{iF*x@v&IxFsK0i7UqBpBsk zdn~^&qtTey7{76*AeY$?mKa;Ma--lmAHud^vc&Jl@kk8@d1#}N;AUEhYxG~5n_h}b z-mVKfbB#v2=*~I}1z+*%GB-(*lor&xSd^lv)`yS1knFNP?0<(JguuhWK8Fn##?IO2 zklbZ?$quBO;2sl_a+f5)6Z(eE27Xl&H{Pn4i(3xOx;{amA}HwZD#v(vkIkmUS>NrD z#V53zJW50g4+Cm44R;7}H?4XHEd_{^`Gd;88^{``1TER#fZfdlnjMf1n^vDg3#Tx+poLX!<6X2#>^cV(3PolW0O!_49ORjrS#3zwxHN! z9P$tJ`h972ca#kI{ocbz<(;ne48FF*JcA1J@rJBu&)};4T zlE1GicCn2_{H*V1^LA}UPdqhYwV;v>VhdJo9v$kyq@%K1-VX*jU2@4Vs5lIvO6?N{e)J1!0U*4SGwiv5ou3k}#|)hF#gHdqfOMo{eRo~+D4 zIPnmenn|h(ORf%O2kP7{AF@LdCN2rQi7G?_Gy28gP3B>1 ziFEj8j^8R|SO*7Dn@%<->*677Qs&=WaWZAC+^T8merJ0Pz?X*6++i-0;qmq5%LjJ+ z>WVgp8G0x&DRJnz1_AVq>rM19qVPpQ4|xDXdKK(ukTqg{?tsB z;RrV&>LlIK_`iUEjaTA5CEJAX zMFSpmusrR@J6vlJhe$JeJCwIARgu%k9ZEk`wAA67xOm;r=M269;#dL^Nb2a%$jjPN z-AGvtS+_0Nz5myLWv~feti|DzTmqm@m8tvEaETOevVuU{jHN2z=Th~J; z?mSR+XfJ6dCPEgP^U|P~h*Wr0=uBH!;KvZ8uwR(m>cP%Q(S~GdnP|;7@)P!j!fO`1H7f|+o;IMFnqDX0Thz5u zRFI9X6p;PPAWSYx;0I?g;c+mGSVBvDNUSa~!#{QP>l3&J-`QYT7R~xu1K_*z{AKJ% zWiIiqLDPfbC0gVCSi|ad0*+p(XlxDUD?P>oKp13#J6Cp@tL-)txB5=8^V z5%*o5ufqW9+#J>EOODbQ)Hpp5u6NMSf{>BA9y+Mp)&+?@TP~Qi_dOky4*s6yvTdeX zyL##Div$YMtV}2oGubwdFaT>s%=zNQXX}}g5Cf!r!*e(QuOnvbXzJCdlfr1DYAlI? zl~q7M+pGkIriJ@A@Jw3UlaW6vZlgyw@2sgCW2Ktx--(mHw^i}PNqH2YzAo1x6Co{m znl{w5*t5CcUK$>)^hhxa134kQFOyB2aI@f}V7P&1i*ox5Le5C)K-KWf`5&ly3k`7S zdJb6xiSo5fFCs~j6_|oRN~iK*W%BK;82faqM}(2tK}e zW{Z%7PiU719Rr(No=hgzXXb5fZOM>-z2-&&+foRgDkqLeg&!~x5;-{#P+!m2$H0^c zWwlS6vaDb8Pw;hJ8;{l!$co2ScqF`?E((2m@;vc3=jGDdN9v@|wI1zzbcthMf=q{2 z7%`gtQ-1HGk1+i0g~3+?eJym{!{PTU^*qYgVa7^V@?QlKDmmx;dX1~HY%C!Fm^rAr zPn7XCZP&K;5m7siN3?~SA$0hqDe3BipzE!j)GY|G# zvD9b!hr7EllB!@)b;wNmJK|thc`dRoy|=;7*Gbvm7QC<=VnJE@<}cp+1zVybzB_;~ zwwlQ(80{MnG~QxogUst09X8^~(kn80VX3l)Tm+!ljHm#uMO>zEGN=PW%)>?odTYvj z9?yqLOq`L(exRSCCcaOi9-O*W$TD8DxT4nTbI=0VY^@Y%QgA~qhE{fkc6xo#=jptr zW8Z*}cB}n|FL69A^IUvW+-0ED=5WJ>wem4jq0Ju)gxa57Okss|b4ZAsxKH4Fx^BrA%f^#RI=uFiG7&Wz(`h+9bwQ<~5M1 zZ03t)^}e%aN0ud`bTa53KIIZ)``B`lGEMZDl~b2wF57a=nRQFi7fbnp$?H42r;A^^ z=Ien{!-8xIQ+?pt70*P#s4}wz8?qmfLI+RL%CJYY!0oFy-Mpv9Sf_(-1ukO=xQ+{A z`dk`5_(+Iuii{wppNsfhCZ9Tr`IJi6_8i146KiJSWkf;1l<(t3vful9RvOGJH91oc z&l%A4g8y9-U=4xs&wqK^Sq4-TW12U-o1>+}M0xc4h+Pmx(ftIUf7wWSF z^UmvwgT4cD zF7FD0ecWF&bSrmXgo0V+!hPsp>3yfr%i`hUa=T_kKI=dq{RU$>#cvJbyuN`P&#pEI zSBbDo8)*#PMb`^GWT5p+VLN^VvN-Ct5PwH$_~yVG)i{+0;&_d{v^Uu4%hJN8f8OE1 z+KuEt?^cva3O@Lgd%MxG%Y2Jm!VUvJ9>xnWnfum2=2?O3`<9>@HT*eSY)RmeFJXIO zFt_)0>{{((AB^%fdhH?C@d$-rHGdPh3l~R_IFePy7w?DZF4QYua+Hg<_|AZPleHJ% zgx6GT1JYNV)Dg4r-A!~I6Sn6J$@lcg#?Wpz5&-WthNoee(o}eGNMB>!$Mvx<6ay9Iwt-q{dajygmC1+c2t@hl@exD=cNd;60tiCZkyC}VAlESaf_mXhnmzxuk7l$pI3or` zQG;VE??aK7(ueOsrO8N_&E6B-1aymGI#ZG#)HYS`I~5^u#hoVDO@9lc1I;+~!%myf z6q2xz!3A2PMaiFtml{)HW7Oz>ZhN&d*Iawcmh;e$PE}B;PmN1)=x7Hz-zl!;>b>}W z$A@pldv|^;cVZGZT~LN=0;%H?p}1Ou8N^9~rLB}D!>hSN?{5?=**)REkXwCCg3`h5 zjAm!r4?V>HxyyYv@M?x*=V_y8XjtE_qUhYy_^Ql0JmR_@H`qu7hiXvQ`-rdn7m8=}J)1~}5FDT5Ax5Cv!q ztDae0g$R5+IY+gNVEt%OG*arDTyG@}y=Q9mk0v%TNrvZ3P4QTXLwHe(0HA$NlFjtq zkj};tY1f5dk5nkFznV0q9k$&>2oZ9DLX$;PC3PvP5`SVB)MyI{Y3cNb=m=g1lJ>YS zEW9uQWyeg|3Zh*$*ePo_NFM2Tp?fXMCf(;ta8|xHCmk=3&SaTH)`k)o+lbwPo=HPS zgPoV(^~XT}6g*&Oo-6w(F~k_Vnb-pRS*_4jloRPE5orT z-^^sBk!uD+5PkCcHrH4al9!=KV(#%OC{_dVx!LplnlWS8kU4{_mPq`fYi27f2Rnmj z4B8+F)E{W*5G|Y+aoffJDC`kg1G6@O(3BbJPw*AxM{`GxO}m#y#f99`D+~`6EqwOP zmYpu_PeVU9M2I&f_ViriuGBPvi!_8?M%p(*HwyU4=c9HY@ zI|W2{5B1e)1|zNtVj1TMkorO7*JQa+ePHlhj=>6A*_irE{O3059D3MYE3TXY{s~hW zC-;%neq}Goy|01gUXz6Vs+h;eKvPHv?Q2`>=rHXh$|B9)H^NFzK&%=~tHasO`UXPu zPN``Lk*Q{5#q1s-z>90zncos}Gl)qtue;+$)mXMvTn4iB(vaKn&zPOm13~W}CTbk2 zB9R4;yIoFo3aM*)jM6wRiN5%$dEb^+bCe|y?r+Ymkxrh{U;`e#4{mAvz(0yRJQx3= zh{x9_s$RNhvX3|ovIs;NNeY98J5nTvBoJIqwV?HJ^iW9qyiun#+>qx~WPNKNM@~3F zc+p3l{)RB1s_L!0R5~DWy&4c0$`fW3sOCH)Q)xQbppA2$E^_} zlU;Q)8$2yQ27(>HnwtzRYM58OpR(^=0*A-Yzzef+CEZ9Ktn|7L=76hG2}z3mE6P?d zi*7nwIW>N`oNpM*+FAgs^kveD|5?rO&nJV?hQ8R)HpVvh0@=bKDvWx&pw&Y6+e@?S zIo~q5o@Q!h>vqGL7DF*Gi?6E~)epP~^W(11T-ZpmyQMJ1380aO}Dwf5?KJX{l*g2ULr9G4p9GMd{tgBoFX62#veP z`sl-|l~b0nD%oTEOKoMVUKMe8al!(3h&-VrWj{#HXJca`3LV{Qm-X*fIh};OJw&`% zaw|ydH4A9}%1^Y|ZH=>uG3KHf`iDdIh!fpCj^SHJ9%5(?VR_B>7NbG}8xT^&QU?X| z+PuAXNu!XBE`}RJ(}vGM4E^Qac^Z*;sx&D*IvWIQ-Bsl_=SOgUHB=HE$E%(cG0?8J zTGk-PD+ERsPDbpQcC0K{s0_3VaIR*Gnx|4mtr|s^N0H(XL){zbxo<0*QrDZMW^E!+ zI9s14$0A9~)9?T_N5gf&soK5_RNpam^~!$tvrT~~HI*NQcXO0jw;Fq3-V`_LrW*(^B)xOx|=WX1K z8Sed;d=2=~DI+^L2eNN5HHLaGhlf<-{&O-Wa*iB}!ms}b!d4fCU3UvR3_ZN9&`C;~ zpJAg!PG^w+22m{7t_Npv;xnHO_rN4_p6C zJ!;JhWif?OruR%?!L4)J4oZ~ddBStx69W(AFTQF~ae4Q#!r{OA~b=TdofO|=RZpZii_Q4l6Es=Qpb#UFZ>a%0#fw(x!faiI4aP*jkARd`@4nn){~ zL#EWqz2|E0#3E$$fTsgRl|H@_hkA*#>(0+;?Tt_gMDG)Du>|1OXf`lb%~LE0JLyn+ z7m`v33Af7s4AJb-?{CXyk#vVXxqkNaI?NoG!u^%gfQZr z&s1i*FSa{E+@(?A7&ET|-3P-yEkqgf?x6pMkgQ62c7GH_qY_;H6i&!RTb?!hpV|&Y z^qF&+;m~aS4Q{rW8jU+kXUrLLs5FRyQ^;@xar6mb4fvuV~XlNataOJgo zBZwvSD^TW)Q+mbC6HUsSF&0P70$&Hgl|R}8`cgeBS3X6PBX|_w92tx&4cm#b%6P29 zjS0K^Z~4D+VUV%)!3PNU1Cthbp!>9^h`grI^T$4CQ~X@k*X2g|TxYeG8zPy0oG`_z zZa*q*WVAY-ECnMZ_q0|FS<6%Lq43VKCRSK?Py77a{7^%MEOm3Br8{m9IF|m;H=W8= zx`G~&DWz9|HYGJHV!EK5=ye(x#o06`|EsZgfDt8#wnfLbZQHhI&e*nX+nzaN`;2Yd zwr$&dbKm>#=O*_i?Z(p#Y!NyGi2pn%2Ik#pCfOC#>*Z{5G)Pu z5I(tJ4%qM9<}l7(XYx#1LI-laZzn=djTi<2-=GH;fe6)V)E%l?MPz41idn^)vf#BJ zvy_`8rw-M{LdU=sKl`CYsT0uZ6fI3cn`9 zTUApFxOW{eCVF@4B`ac+qOH>X0N7;__d5e6MFmLC)LkY+qT5Q1j@UNb-Zh7@aFP4A z3ar^|Ry>#J#uIaZGuzk1+2$w&9+;Uu$3wflavH_V z;~0vAo=?Kf8v0rq6m>e!>GL*%wGg$%FOO-5-7MA@=|+Hd1j1>wOscaf`7yK3`6p26 zzPDN}P~tA6-RLk`yFll2hUa=RV>qDE%fR@5OL+CWuLbot)%HfXj_@#V(cBh+4rByq zcjbMC1grvpycD@2Z>MaalYn;Bc&sV52pW6|&;i9g0eFU`p=zDier%(DDwrp9hP=_H z9y&2AJS>4yl5ds6aHc@DpaP!&sa+6=c$5^SlUe}QIZBPone7m97asnwpSK~L4 z^8q7vE|_M!!;zcU6P*X#qX}04Aq~y6I}sSF8t?_GqWnG4YC(%Fq?vT% zYq)Wrngjqj5Zg3Wdci-^`K#h299&|EUr18?fP%XT-k3Z6F3YMNZ>AN%#gX6Z`kp>1 zdQ3CLq<|?Br8y&6){rK@9*pnf`rVo?e@DX*6re>7dSwj}ZRJ#3XG1mM7%3Mq10u0= zE1LsMAS3+!VB-xr*(KCTvZw1&vS~u$t@hKd3GBgtfz<#@3~f_iOz^cn);i=P!*My6 z`9p1f5ZFde)!3h29^z8axtoQW+kXwy7H9Tn0+g8->*x@xZB{J2OPQ;()K6DOlS<-d zfL+jir$)HpZ=<#T^$&D5gyD-fEbW8;lO%}O!Yd{0dY6#`6xdk$U{3m>nJUD-y(ao~ zaJe6F>mMUdl;yMpPp<)$e_@fUYnVSuVcB7oSzx{nF-8tSB?8xREhQqOpb$^asGpGY ziuDrqo)^-H2ar9g6tCYm1=TdRld0C)`+9*zp3WR>1pMGUdr4=H~$ zICe3GQAl@9cYap)yQ@_jy?H%{siE6xnPFf%chVdc#^tOw#*>5zDg*G!j)4{55Q|Yb zjWtzfrbisPERM3Cie)D(xIyU)ii|Ef-Y*D@y58-b%2#=md$%CXQ9Yx~6yq@^7r0nD zajWs*E;DP@MbC94Z4Sd$%Y_Uj_zMOLJqEzSM(N+_RW>=9;87TJxKqv&(wHqH^*+=! z&3NU9+%5bl$#So14uZlnYV1E)SPLxMx}^_@^+z}bPUx@t1Z^PgvybtRN3su&A6h@3 zO~O-VE(9)n%9QB%vv=2OwS6xP7+>m5iQ-hBaGAAmTuSlzfqoH+DX_7HwD#htf0CD% zb5RE^l>{G#G!-0bK+^WyAGlZV{LriSa~(rbXy#CC*sv}5LW7%wUrn-`1uztLJ)A-!w}-m#K+D}pug^&w8PbcGUynu@ z?4V@|CAsY;7$7ZG+}M*!MG)z56yMf-5jC`Y7Z+Gwy<0$t?=kX;><|N6TO!gb(q!+ z0>ru5n#i<$@nMf~J!B^AyC}Yiotvp+(xfQTrD0p)sMyenvP-&Fg$qsMlj|G!FR<~u zVk<7vbfJsaXJ5WN%T%c18K+$UiPVavQ1j^P-?r3a_^a9n3-YVh5@C&I1p~z70qoAz zLH9ouOsftqA zcx@P7eE>3TlKb40D!nJq3HQ*YgY}hnN?@*iq%uT>zm!~$Q|###zkaS|Hul!PyQC+A z$BJ+{7kKz`$CNGR+^{`|$?hPXLg zMP9`6RZc{C-MfBMKweIY-6qR|!rZ=^hw(CxZWo03h`h}EM$9K*D6OKOjlNvXJ9X#l zFrs2B7ZiAt2q!zaepSx0W%v)R%LrAn-5i0Ti+LDf81YK+67KAr#5JgHRCU_a$5RS< z0}gE%K`uCTEf)S>&VDkbqz$wQE*YzIC}n(GgED)W?VcS+?TuhXG}T_#nmRo_57f!v zM~TlNrzLmxNGr*XM_tQrLeewzjb8c;uSO(CYS0XVhDrn0N$Uz|=7gk%7~M=~+$;X8 zu0A9PwXQCG8dQ!*!sk@R{jqWVCg&`$FeP8B;Fwt)FE2=q;?av-J=S^Nf-~YxY;0mA zEA0jcrzI8ysgbaAFrc{<+GSEmW|EqUF1!M@^kV#NE3Aw@xt57ceGnlG>;;!Ai?Z=j zP8`0SY@)_Cds9QbNmcs~^yg%_rm7BP<&9c4XW;xj7}t_~O$b4y{Z?NwuR#f)V_6;D z&W)QG{Yz<_J7>>j#ZR0P!5@8Nzobi3p0CfAu6-C=cMW_*&j2;~g#u2kKi- zk_1RE>QC}Cmq2JsA`F72*k_Fp0v;08ay=2rdA2A!2S;xuf%)id^7eNWio6fX^(zsQE8Sy3td4^_pQ!`Ib53waI8%TE! zo5cBszDvaZQ?hn>j}DE3Gfs1TCyMgy#fG>>dG21?LYQD4dF>Kn=!)isT0(@L2eKYF z8Ld}>P-YI88rtyt5XRA1-0i6P<3&~uGcR<#Aq(kD{aPOJ^g2xF~Dna4Y3 zlh{{^>U43jx?O=Yqr&8QPsXR#(mjW>P81w_-(q`fy3;-al3)K=Q}Hf`&!r2w4F=07 zN9-ph;Ar~d?mIC@OEF7(vwE3CfE`OaNBlovH5Ac zQL__O{3q_UrG{AtW+6)APY-5Un0R>XK55Hs zUC~@Q)(6Fcpb%0}Wne`?A|@cBpn+wWX9o;KgkV64okyDO^+)u_ZU7+!4`adt8}3z* zKxF_UgJlR11f*hs5Ku-TxWC;K7J~C<8lQuOZK)dqXtm>Te|>%Zv3a`!s&)JzcSJq| zX%PhCu;bI#he#>}hKXp)f8__q>eUB`riIam74HQYZx>*O#dQH_X^%w|zzq$~x61(F z(jweN@JGV|66Wf22Uw(32nJ*!W0{M#NV0I|UYS@}KCt#w+3-zbOSVq5MUoBHg=0!hfjkb$Ax zh5+mu0aTWLOA&RTM!qMmfjhkbNl!84D4-7CTl4srp~qlD{(BPS0AR79*1hHwK*xv9!cGHUUR*!d$hSM~;M`n9o8KaZ z-|k-(U>w7cp|xlvD2QESkbRqn%>l%aA-;B~utls;1Vo>yxaXIza+9E;-^>KpJ6@qD z#lM{pBGL+&$6zHyh>LPeM(Y3ZQ(V96CwutgKlp5v%{fXX1G=D6H z7!VeS`2BZK1RL~gWuHAN0cjj{ zmyUpl6b1nSIi;1;l^y&hzcu{iC*cnM?`Y4;x;_lnHB>DE8VVX3;AZE~+ozYw8#|T? z2?*#{mk|tuKFOnL;@8A2b|^>T9Q*n==L@^ckJFb~$AEq{1H|4V2^0~seri%ibXnfi zC9ZPasWp1v8LTr+Dcj`KGo^5o2YCn$9}SpJ3OLj<%pX10b{T8VZ%v>6j^!QMpk2#9 z{#V^5kH!aQqhz@U)(OAiGsvE*0$H6lNPFK#+E#nbZAG+^Xz-wmICc#8MPe)WIi zkn!-@Qmyf+o{hwj=p_tQSX`JjV9`WHrw)9WdAt-fOWOL%gnuo($7YJCpgw*bbRGMVuz~QL}ft`vR?lsCFDu+qZKxeTDw0 z4?JTd8(mG@#2_$(ZDYzH5xS3UB*)pO|3*MYSk_1~zmPw-4G5>nQAkC}l5)m`S;SBP zn<+4IvmqE6NOe%5YPv1`Z0?w6tAPqUE(B9>th1^Ozg<@i@r9X~WE7^7iCJ~Q2sL0Esy}~-?uaN{Ltftq zKR;V|(>yKj3m6N|poj%`O|fGijf%KBQr*rk2!hb}bs@iqxpUZQ=uWxnO>%3s(j_?! zkDi>zdzmE zq+)}3HpZd=@c;(cgTh1?lw|4XUroM*LZJiqhe*Mn5^gw_VAt9QNRY5j(xj~h*Rqo zYzYS?FzX@hZm3b0DsrPpF^o%kxARrbv02JLh;nOf-ivgzBQ`Ss3X)*dSUD%{@J966p(kv_~=)P@|xrVe}!ZNGzIU$&fNzf}Z-`=eK8 z%pX{~ct*o|4P-g;yuB|R-e9A2*XAteR%+NJ(#%bzS5&%9X4w0WFpIL>7EnZM;X5cO zOy8De$wKgqqJ5oJDk>{-D22z14PaVtx74>*ZOcVN&ud}#sMR7!CaL*MBww}5u)(l4 z5jn@%43|TS3%?HxSFVg6e zGLe(wRn&NrF%2IU1x+T#VQ{NZMH|i(YQb)E#rx$x1Mx{FAr*_jGqiWzyQKC!95GgC zK3`T(U81OM=ESNYk;FHLyB8I%?>D`yv}(`HLQ|5?ntp)D^Ev(Fm*P(CdzSW#N4|kI zg5l1^55UkuIsg-d{uc{8nmfTPt>z}Sv8zJbcc(_vc{tQ3iLEBNh0J%aqrVC*)4`YZ z=t5Ta#x2%yAs(Dexz8E$%=2_&3~VlS(upViK!HTx#Er^*k1dQyjyOA_r%qKgY5ru@ zU6cywz-wt5JP-en*KW>nb)T=jVzw->APu4Ayd-W~^`6rTYglDg&M}X?f#61PVuS><@e)X$FRe9HmGE##hT4K#ll6! z!6uvz%h!=RO*`1qcu2?-ku3fsF)@ws9RgCXE=WpJW$2(Y0WkFZ^a{L%7l*Ym`Fvr& zOPQf0o_khiFv7QG)nh`3j3hi2t9}b5H{H&@5%=j4Q-XH}Y5(lwN%(a_jSL8QM0hSMuyyUare=UCc;UJRIZ%rm0%q?m{-Rp?P~~P~LkL zoFR9y9((7iJZKp3uU&G2H|LrYxP_{aM@lH)tF^COtOt}gY>OE6c=K@kE09IwQ&t~A zUc$$^c<|vfG8wBDCogpMEBN%*t?UTlsG@8mYoAj5+=U1m!u?|hNa}fjgSx*O4K{x) zmUEldGeg@GpoUtSDW_2*gA0iK(#AliB|(}Z^VcSMUQ1lI)XTjAZS9G9q}kenfVuUh zJQ&kHb<=p2>AsDQkyv6|65syfgTMJO%y2(Ad9;#DJi1$NgQO4%|8rYpb5FlQR@%2r%GN255W(V zIWq#-vF762*JG_rr66fL%<}Z^&KDVUQbJ+SH3tSBeGU~fYqu17)~UO39ZfTi!^9i3 zh8N(KnfoGq(9eh9QtIzKdv+)gYfkDN@lda;_*xi9-t{z1r3fAH0O+Ch$dL2Ig8?$k zXRC9n#@Mh>F(Dl-0To-8L#+~_0XHqMPYKtug9+}UBEvSOljKuB(g#0TegNnY9M?K5 za9S2^X-`o#`kjSEwsp~_B8hvvR*`vDLq3gG(#P|mG zbfU)uGNKGS{;hd?R!!lt=8bf+AK4KdAGnv3}bC>`9{jB zYgL-5#(fTYOIpvBNo|c|!_>FW)gcXy!b)sHSpOQvgcX#A=>!39K4RCMp%-|Uiy_~M zB58hFxjKe8q~g9_c<55CaL~cCM+;FuCmV&x9a6j9(j%fK^g4q7dGvC3FYgv&kw%#MnJbZS*1$R@W}@ZQC#mwQ+p+U_TJFCQ zbNb2LKi63q787RfE&>5juQ6*ko(s6B`8v;-XOY+Lm)0HGWd#uLG+I~1h{+X>wUd#R z{h?)A71KG=y{%$L=yW_J$VI(R=+j?Xz5YuT zatLxQ6Xq>+=e_gt2t{&?+D=757dmzJ%)OL1`_}ZTgb`VUe+B7d9Qy$vd- z+OAi8HdDfifc^m1rZml&3>CUgu<=~dvPrg6i`>fkRbj)_g4%=m_?Xb8C zKaoaEG=rYk%O`n|p*E8q@k+$+KE#eimn}9~>BD@~9Sg7bD)V(sn|%dpUb)2sZ#I^# zK4`ms_`a_TYX3&d7bTq;uNs}qG9e+SaA&?n6^>}DjZfrh?&PwF*BemSz3*k=iGk3y zI?K|v2chyj9i-pV=eqe?Oy{kXAoEizzT&@>a}TX@Pwae0*5tKn`3M3eql$yXhD^h; zRlzN7vl}S;vMySGf;MluN%wKi1EYmW>zDPz!&Mogh-WE~YBL9Q8=<1gWArn_lv+_zk^0be5R8C5XMIAo_IZ``562>0445s|M#dez8o1Y#uR6 z&5}JsqA00{$%bIpW30IpqfZm3=O=G_1znS1Rk}MD)+=@qhMi>Ja(3UD!rWpGCtaN-)xsKA#g8Ikmn!r9DnrOg?6h5FdY7m!o|3L6=a_}$r zQ5rbsp-|J!#Oat2N7!!Og);ARg9#z#0@pRvY$X%4M7${?YXP(JHEM+wzfQcf{IuI+ zCW|Z)(Y#5P--rzAY-%qV43V5H>)jqxoN-^=>7Vu<106Di8Q@j%hxY<6RFy<7Qgv%KRZz3yM0VFlAZk%tYUWjN zae1N7POSNu<+GDn$#NzGge)o3)na@4OOV{Qlw;vLicGRPRv_z8+LYe%+O_spqy)1> z+Z36K)ude}2#9p_cI@TLB#d3+F`T;#Y6=fU!rbP^Fka>{3aVnQg^cKE~GJ6 zTPTe(j5jnS6F;H+s!(}Fn$zIwyl;W^hALbxisy#ak@-EeCAk@OG0h5-=%B_|Z>I6H zm97XPG%gH5&$ALwO%OEA3}nppx!S>ko7T3QALF4OpBDns?4$ZY+mt%S&ueDF$j7bH zft9ams1k}`E5C4RSef?Gh>_ME>uPl-YA3tvc}x>nuS@HxlDll=R@nq>C7P;=@drlN zM>=Otln4+Hu4mn}n`s1IOhtMH#*+YB#=j)jE_TUTX5QlIQAfNDznT_&G>Ynku$H-r z+`G{i_!W6Qu<~ZKW(xoKvfvHt@pE98S3_CY8)fQab3T#4z^8dxh%gO({pX5>vU@>jO>CFZPvyjmt8`cyMf+!|3>V`g&PL{7#b)n zGe$*22Zr7YR|V^=D}#{7Fzwm+yo)0xyuR6LioK)rZiTFv3_dSzAGn{q1lds94t2k~ zM|G51ti^{3G|3$?yLyFf3}3?FeM%#73QX;yjf|Na#veiZ*b2+4baWbQPLZdzl@hXW zI4%~M^ltiLD1ARFxN4z=l^aecbBP|2mn_mkZ{}rhv$o6?xqdZ2W6d`MqT68})22#& zai5YJlTU43T`$-LhZY)-qy60tNl|6ibu`K~TwPa5PP(?3lQ#`TiqWKAa&#(qgFw-9 zE7Vv4GNyRcEq?t1$Gq(T2Uh{qsd`C7)BNb~_$5ld?^*}>sP;QM?Dn*&(|Jr?+ zuhJZ5BrDv&9tKzq$LD}z8=(m(qh6GSmmKmWsZyf>sZqZ9UJqe1Er-*+P%yEQ-?4>c z@9E)p5^omS)i|@vzm~se>q{6t6rNyPYJpl-dY&pLhoQ817@sA41=${61&8V)xrhz} zT1=7_G;2_jRKwI_rT$8;qH?kW&V|x;cY+V!^N@=7aB!aM)P^xClUQsihIyH7__y<* z-?xp5iv{;fJDNZog&ak*?Funk&q^8Y%ADqc zoB>v&y#KD%G zFF(G|x@~NNwe3Lj!VABg->9!-AlES*m)_8qeFcVhCu_t_M>$zs=kE~;ZV5RE6?9%+ zsA-hV4JLxzMIZJ{@6{2`MTViN2Z9g)MjC4aKZ$YahBS=gSx|qBOu?IV6d+~lPibZZ zkgXQQQ^;#G9OtjoOmOp(fP1A4wL)P~4Nh=xK?gRXCq~1Z@|=)vNKFE&93z%XxnoOH z$=Dd%{W_|1GL^8w()DC&V%z&Dt;KdN%%7c`pI~b#&;XG#BQGG3Pnr7ctJ`dz9Ps!R ztbGlk1-{lIE~22R1appS#W_~ zp4TT;GGw-Nmj+pZWYz?V(rdMwC>MwgSM7yG64%7~l(0 zF|ec34XEw%^vn;mSU;O*u61_XD&A?n-L}qNrvf8B^Zh#NDDzU9a0dGZECcZrX0pxW?@RZC|>89b7bBnKwt>V_g{71_Pt@M%Y(X(F3NM_HkKkIZs$$ zA5qXEy?S_HjSRej+2Y6oGiLmW)6qA0D4<+aGsplu^r;eMk*yl4znPa{Oelbhl(6jAG+!jp@vf75ZC9jZT`fVpLpj@^tj%eT9W zqVdE;=(!Fj+$mkVjsACq5h}=fP@YlXy$^=#EI(C1l-Nk{f1o>;(+^ipSx(kp>U;Dj z{vF&15|xK|BNvO}rw(-nx;=Ck++cmmHyO;PF5&Wc2I4E*{9L&|{CmT;>ua(l)L^vi zP8YHJCcQZB#PH5`J+z6IiC>!G{ihlO_UM93xfHmqy7Y1|eZEk~)turEPmAAGk#NLR z&AAqk;eJ;c_Q{B;8Rfb+XUT)n`vldb!-ZE@->2}Y)hn(2&+#?U<}s^iX7-3mHO-70 zX+v}?DAMelGfV%wQH!3Qd_8vf_3Pqq1-nI!Tcu*)#?bvVZ$Ko$#L3>2IM23Hix*b# zQ^wMDUTtd0jfq!k$>Pak41&YO0mbgpN`2%8{E7Kw_h>i8?A;#My01~CMEJAf&Wg(n z13|iK-`6p}Ryp!F#=Y(mQGwA%-A%{Me9jE%ew=zshH%P&K|dWZ*iH8+pWWb@^s0Fp zNK`|ud*w)(ml4y~XT4}dQZAE;V^wo9L;s&)k8)WdZZy$^C zAL+ljUf`>_zBq%_P$)IkmNi^NX>v4SYM|PS83hvXs=^k;r--6&A@9fnwZOp@v(O9u zY=F*#toQ?+X~VtqOm&n+Ox#4*x`SM%zMj-9d?4}BlgE=a z*st1Y|LLx;x2?y1&=9~}zoQ$Ldo-oMbwy}Hga+ee;MTS`$$J^4sUFqyR-@fzwXgB}R*?=GIY3>q zV*i2v(S9bwIRV!txjJWaStqc{sn}RloTGl=DGQ??P!YLy@N%%8Crt#8qyFXn)}?EE z_TsR6B>I((EVJ-7T2`-2wl7sp;LRC}8zE=I>&W8BIy=ygN{Y)mZsfA!O?GI!H}Q;| zv#Taxg#PC>L`@hqvGqMCyEl%8cvP0FMEQm zGfRSIt3gEb?92Fh;MTIRRq%uF)!#RrR=_5SX2*5;=C`^zigyF3|5S*4^a-zvIQaCj8@4dSESS?7N@#$Xv^@&B)1h} z5YtQ~lr%y5l$G8s_D&_9><+R;jl@_Iw6;>Z^F1IBfN$(2aZId71|hljY57`dzU3-> zRSVKG9SL6&x}l<==Qj`Qz5 zX#-^wbpkgFXLAB`4|@|wM-x*5djlgY12Yp!dU;1XV;3V6M+$pm(_b@MMmiP-Iz~21 z`adQfZg!5wP85_-|L08>cD5qF@;d|+B3w+rnmr6mOdJfH%nXbyv<$4|3=HJIb~1Lx z|1T3|M+19%6XRbk9|LPA6DWFlWl?oHF&ArVLjzmeUyUCMWpfKBg5Tr+)Q5&Z)x^>1 zw`c-pIz|>oR!$~1R$3-Hw*OntU;E#0leTa*A^5EnE4_$`p@o4hC4rT_fwQ@ji2;G@ z|Mxf>9TOcR<$tIKnb;cJ8CpX9XYg71w^<12<=dmtw*l0i83wMwDt5ima~ zOr(6fE{yW9%_N!u(buRiBv734iWOes2@{%^q%S~>(zuYf@)sYYw7PG@e_KEY_zQO! z(;Q!8N&n79;Rh_@1t$7}c%^Pr~wA^HyeQnKz< zk>r4B%5=b-;(3+62PP-W+suzPArNcLB}Zn>SUJf$+O5uwA6SF2brj8GqQD&_E<=#m zPx<(a-Ib@~&pnYr;TkIUq^TO^TqW#xbXw#p<$?IG^wK~sFZS)j%|r0rOJSyQFJq&$ zsR>{W@}7S#8R#Q6IjE?*Ij3ax{M^GO_J=e{N__0m5de&1G>IHYy_!dJn$oHgtprry zxvTH+%)?w|+Ctu)+c5mhYt$hfE_q2!4zus%xcA@1cbCO)=R5F_1ZLaQD&vMBV@J+a zA+Rp}L0}TGGK1(m&v2T0;WB)Z#AP@}eEfoWUvmaTJfcL~(!l|ye9c2V6sk@<&!XtC z(Mqh0S3%>DM`3(kX|%R{k69r2Sp;orW$|!fu|BV0$(S)+&?>UqjQWB@`BWn*80BI6 z@3XB`en#>B+XG6Zo%#!(oS2z}1Rt@^9uC7#o;Ot_M8lu>rhax=h%Pq5cn)7{ArJ=T z&(c|4!ot~R;g-G&UMAd&{J(L5%^~sl0X4Ske~DaxIgif39O-|TySM7$_(iwjZvEK8 zJ!zmHyK%f-V=b9FE9xT(bUXS{R9!H;;(U$6#KnOeMu5!fEY&Lw;lz~IFfO&OUI2lk4!jSqxetkEyb(>tE?}!r<|IEvXq1qPdOr5c$LA4tEo$nEU^Dtf z4z#l?GCzemLrD;PFtp4Tb5lYrx*{kR&X3wnDCg$;>c(?rRXORGlXe7dBI2sMQ&jbY zOX^&=)+r&ead0z9q|K^b0q>doY3m^WaV2-Dls$<#c|M5IIYWv9I>2pv(-Y+TasC z*L}{lt<2uba5o1TN^`Tt5QY`LU66FO(PC1O1am#x1g|@AW)vL+txb{SPd6~7f5R!& zJ(P)?llJbqCN1cmK>j4e4eKR3CTOSX&1Ys7=OELvUaENF{@XS4cJq3TPcIR-`+j}m zoaEUuB_*=Y?FXeRIh1^2yga5!H(67vvdR*uQXA-oCfsy1*oNW4u1P z*zxUoeSEw;ebpAJTeHT43;l?kR7x>5TQL%qUD#Wzc|4t;Uv+E?S*3(&ybTlwVb`t!;f8vyG_S(|xhor2(M;R?DNX`G>| z9eD^xBKjVKo~YmeEitjdBkBI;_B-yy{v;l*K@Gd2NArKVK7K#0l;F$qcjL>D6;`l# zHT>{oYTJNm?XtAi6nKK;Ra{?2d_t|ty7o1@Laz#y!>!wz+~WXUA^QRjjsOl_04yfu zod-Ut;ab2F?7Y6X$h%5KpWM*HZFlK_9*Ff zE4b^%(4MSL=)^Gd0DAn{4)58ZjKR$#rhWlxe;C36g zBqblII~|1$&avYF&}P93+S`wMz*cmZ+Th@tJZ(!r-_qz$*o=cj-#i z(zkH+2v2|<+9w$77~*zocx!emdMows-<=8sLxm3TS-RZF%NkcLU-en2P%4%Hw9_6-g1OOYNXGGtTr#o>Dn%=nlKe54$2Zg`E zxwFe`>C_DYwi5j_zTy_TNhm%XWH7Ip3QB+#ac3$XTC+Nn!(}eHm)p~JDlE(MIp$Sd z1y_oV5w7T4I|Wb172TKBOO_VSogIfyUrKV#XA`Q`#M%%&ES+RFL|JqNuFGaVUJDB& zRd0f}3nSkkKG$ndk0@GEGBzENE`bZB-G+v4L)X8-)2L2Xf2mu}j(h`kUucwgyOs;q zGi)Nq#3{twph0!$X!5|MKjl1C8efQ(>|VQ!A8i$6=P_ZSxN50*0->DOFsV?vm*AxT zVw|yYIpfVfIa4gXAXS^*@yT7UT0%hqADCus@m13G{M)$;(LOQIT*LMVcAze>_y8cu z=^P#YFgv24e@TP!UQ0BhxpY3G^eLfxIW70rQ1fy&>#n@uZRgQjp2FKI0C#`Obk0cO zHGo|*(aWE;eMwWqwS{xpD*NDVkA;7_cr^V>K5%Egt-UPOQU{K9y57%OKqMd89UAi( zYAn+=D_d!4#GN`=U~#UaTLC+@yZc^`z3elt8b;-=W71kd7n0Qhe`u4%a3FBORv8vX zEIn~)DnFI=EL)Y1IuQ=#-r5S;l6gqdA@v$Yq#>K<_F(LaP_*zfS1S62E|s47_rGzo z|Eq_nu4rNkMK5VhzSa@F)=an5&XYR zeoK)yu{Hbk>6sWg{*PDsKiCV2JI5&tB##oZ=Y$6(3laGczU$w>0ql7v#G^G32BsHCyPv?A(9Fcw za3cO`H9DhCIUFk#kt4*YbO18Cj{_wS0+|7lG%e7AqlGI*y&a-qS(ta2GcAmnBbb<@ zwteQ#7&65G^jRNuycXU{KA?QbE6VP|l@7bfK#i}E?P^(VG384+vV5(pqtvG4UVJfD z>4e)7oo*KlYc?2dQ)uJtsKqbt#p?^W`7g%Uf9*XdX9GuP_ur`w6eAnQuf`}8DXFNO H7}Wm)rnA== literal 0 HcmV?d00001 diff --git a/lecture_12/lecture_12_files/lecture_12_21_0.pdf b/lecture_12/lecture_12_files/lecture_12_21_0.pdf new file mode 100644 index 0000000000000000000000000000000000000000..6480131f2b6a7bad8b415ea85456f6299fa6ab36 GIT binary patch literal 9752 zcmbt)1yoy07j8=_PH`^~iWDf81PfZ+DGo)728STQT}q1;cZy4aV#SJ=qQ#}STX8RL zFSPgG|K9)pZ>_i1J4sH?e6wfv%-%C+?X|z5R}z%0*Dt z;JrS*B5I5!9{G`dK83=8MB4TB+cp+E;iQ8}M5>mqBdqp%Z!lps{ZVs@G;$Y^#VPUTfB3(t_|o13&K9PTX+Lo zX8}~rna#p)_L`oG33#K8AJi=KXva&<9th`FE+6yj3!H%a+#2|&j9XjnSFexbPF!wz zn_inmUnX2e9zs@>Zya+ga%uHDuj}_mQ|eu%PL^*JT=DehZXY)_>1PRNvye56-BaPFP4W~LkO0#XTI%UY@N~c$aq*3RdSI0!l3V0-^Jg;DRZE7DZw9;YV zaJn&I*~=5$Tb@?F{iN@ccyhbMMI?oUV&TmB$F42zD6f!g1v-`#X{~r^3Wt;~`D^}s zGl}XH@p$e2>I7OWxhGg9gD5i$WxB^7S6})qGx)uD8|7jVf#cZp@_XFoAEpy#}o+ZEi_`GM3?y}c0+Q)Xcc!bOUkd6Yw zWTEb{49nxEAf-332&@NQ3~2>JM_uayF+E#;Em7KoYh6z|)YAF(7BjT0dQowuomzxm zLgSb-bVF225|bQpM^^jf6BO(PEWQN$%SVHFd`p4~ONu&ZBcXMU?K)Xg1bZtLdX^jJ zGB2}E%bbSW+)XkaT0BHI@<87`R#59s%GL~%q~U382c!(U$=iufxavyWb3!h%ME2#6 znbV}IfUzT?S1O4#HF`@f(!2B;3M7HCB`t7+yfpg#P^3mnv@TZs=d<#}#xZ$<%4rJd zR-S{0X7myS1Ebh9+Pc9YRz7p_QI;njRsj&pD_%4k>z#CLl)(D~?)2y;S@NMoO|H#Hm9z8(A7af#vLO)r#D4MITc^6GBl(5@~1?29(W3YwFw;r_sM*|YMQ<%{G{s{ zRC?=qe35{|zSkZ4Mw9xc3V8AnXiqBSW|h&sIXp{Zd_0M#GgysPPH)U} zjK%7(TK+J-dKn8u z>J1lj=LaX-OvYvntq0k&dsH1mwv0&9?f%GQQbV6wQB-OLA>#Eumy(SXO9>(zaPZrj zGF#0@!?rG_s0DhPUzBUVZcK87odl5+g`G@$kI2DWgRhd3*$NXQfET;XIL*!11Fh5J zrQY*R>LY7H_542cR+Mak$*XwckTcAzv6HYY^?(Xrv#Rwkt*l*cYjC?c)}Gu1XUF=Z zepIr(`1=i3V-=JxS5K@zPc!(rq_q2#IL-qWs%0*zX7cXqTLX1v%qFqNY1>=wcQAN{ z`|DG&EsqPC)WL{Iu?(gG4<}5Od~NEHTB=={T9A;c(W=8=HWRS**v7er{EyjCsmN6~4+_l_j^z_Ww zr-54R(W?hMC!A>|URC)AMwPA@*H1^P4WSgF5#R<*@6VOC8#PFV?jLiBsJ6(qwTe&! zI;)Wu%1!T6rWm?{1}}~mK6YMom6jWUInVZ)4B9O<4ce1qPQ5_PP1v`nswR~{45+Qi zA7KLG=`O&yiz@E^5pe~GgNOT0;I0VzEB^QuaY(qrrBvaFXagW1a0ehRc0&$C0l+RM z0ssQojSUfZL=1wc_2qC_IDC7Q18Gv2Q%?=7+S28q% z{!*-D=m16Z1N^fcy8_h2!cY|E3eZ778~{#EUH}-(4bb}~Er!sE5O)OJg-^d@B`F7( zlilCO@w@+D=${i&MQC*}v~{$*(`D@TCoBViJ2?Fs#ocVh5K`h$XA5Jfij?S`$RE>G zfjYvR9E_okfIE|^{B2e|i1L4haJ+vF>wkrCcWQpedO!dV7dPiWV!Bx^Y&fArb<=1~ z(VEXNIO*HGJVQ)6P2jy?^!rGRv>1ok)`4C4oa6xUD;@v)cu!J%OYb_C&lZ}oPEJ$DcqyvlR`WDC^m1-D&844z?fq$8eqDWGUE!|F z*4*A4mBBrOK$YkF{XQnPi&9%fcwd|`o+pEE%jsXa0{95N07-p={l8vPzZ6(1N4@{` z!y}J9A6GY#i)t?n!SNx|y{``)kB)H!J(4b_3v5YZ{a0{jrla=%6#LlR8sdUK+nliF!($cZ^!$V?=@LIoFkO`K+H_<*uk=~G|jN1*nUH@r8v)*VK&6S?+Xa0Gdnq6wc z8fpnwd%lMDfryytUJ=Wd6IYrY4>*e=tZ+%WezNkSY}?}a-FCehkN=bh9Nu4f5ox_c zc9rcYEoIq5kDVN}b0k-2uFO8Uom7xn-mf*Sz#@p9`si&qMQq|?W_MQ@Uck~a;p|h= zNdi(n4|5VZ+?}Pv#!ixc$i<-5UgPQ1dv>!UaMjXeB(D9&!2H|2hPg2c6&%}HcMd~b zbKZgbU5?V;v}f1-=%kUk_w;iEd_}0UKjRrC%Gm5BL|7a;RsLk6*$Jr*A2IFk4>m>> zABMN;O`Rs5btyrr67s z%@3m`qq~A-ozR}wy3{RQr0ChUM%T>!gR$)Vlp%`uHE1Zen%-kEcT`6q)zh}eO-)Tft(Oy}xL>@~;987V<;n3n*z#~DmJBULYeqf~Y!3R#>i1CNJUi(j ztFL*|J@es*yshderriEILp`QN7YCK@1dG+kG$~wNJImU9!`9?Wm^;gS!(D9tk*hA~ zC-vkLGz_FjF*K-DzR-Qb^{-kWETeC{(F$h5z}q%ZC{bCi^}`ZFVk8TL@hb&N2v_Pi&E)$Ae z1|@H&*I(^{JIQ9E(v)~QIzD@@fGXKZ{7c+3Fa6zR__-WU__Z_Rs$^^?7-|kRUN@LD zOLaqQSrqO0zFx4TK;BfG@uH*l3e6SOI$3Kcs#Q2&o>ZwNE}kUV`mDjbCa!Vb8|%Wo zncdsyngfkfoEtpP_Ivn~b5^m@1KMhq4qrI7ua*jt_&nmf5U3szE9+_<$18CX z(LIPnsyXw*3uIPCcMW>DO(D2Npf3~7@f6FRpJ0Xt#fUm9BT`GVaB6ngJ~x*ZjWNbq zdxnvHl z(MRAJcZvH6k^S+ex_y=DVaHQV*i_}kxA5UlI`Y$muH zr}=EDwVS|tH+r-vK?!|#6zEXB8baIE`pvt@LEM`%nZExgNPf6z)`UM9+sP&8LZPq) z)&*K2!@y2m4a$pQiWGTll_Az&PptG<-_mGmt@Iare(HBOY4*U-tQ0G`sexRr!uCy>4Xm zMb;9#SW^37MPrui4y_Deyd)X9kGT-C$Q0V1aab?)y6EUB$xYP{u>tvbs@RZR`~rFA zIBr?4=vO*jz9^IEio~y#4*`b-bn?-S7g${e#&%(;h3UvK6NITxUM$5BHG32H8bK0i z%{DMIdDksVa?Xnm)pyaBo8jy3K-N>QEg1VkksHvKQhqO{_a8bV%R;{Zb-P_DE?z!5|FA< zWSGpXqs^6pR3VLY>Kdd$!{41sgcr_TJ2Y;fBRpZu+5Q>M(VAPc`Sac9-~g`LDSo!d z=SfM|Q|j$53E%hFEaq@4dAG(1li)2@iZkBQCM@H(h!+KSZC|TQiT+2OOC%V^nX*%)rRhtYg7Pr7o5Pos)DRDtr@^z=6uIZs|&RB}aEzS+v# zOHx$^?$sW!@|WHi_8+{#RP5Dj^lo`|J4bT!GsXYG;h9$es+rkkew+522CedA1JA3d zu&`AAeCW9-ewx0X9?8mt5QU!X#i&DFLF@?EROZl3#wz?Il7DD7^~?qGUfA2y1W5Rd zz7F3jII~U5h?zS@dVY|?Xb#gUhON!<7e(AwtGh@o15HDp!(0>&%;0W zTDzVs)$hH!T6!O&Z%efI_R#?snF+(>`+)FA-4o)VF$X#4oNA5jA@lb{NUqER(+u>E10;(bc`$@jei`atHel*r5hV(S(pn*d6&N9 zeKI+#z2RosyVahbQFE$xuw_h6ksCV}N}^LB4L)28F+I@aOIiD|M`J<9$WR*;wHvk& zVA`E*B)^FAtbx3QQ`=_lQzCZ#%iuCn}6OSvPcd76gbpp}*)o&r+4o%xl+oANt3?;#A zr?H)}9zDk6Z8p+abj}R!C_#^~$VnsDzJ-1}`q578j$w?^__{ndZ8%W{W?|iSTz)Od z-A$Y>5{Snm4gNH-rTUR$qieEGJ@l2ewK?g0Lv=~j8hMN}te-!zaiJ@<87{l=u>B}R zNFWmKF;F<=U)$;2;P(C1C)>0AskS!TzKC!A`%gBQ@jEW{R!Xg)R!Pue<)d*s6_wb2 zTfcAbf|V^#Usv9@BGBYK&54;wVq@+o}41&_-r| zT1^MQ(cvnkVO{F-VX@|-PhQFR`c~$jSC4Z$=M0;n3d1F7wbM1! z1yLcT4>vJ>xGYgAL}W`x!rZvNJ!i38y}$HLqikhn-jy)2BqpVKf*VKM&5* z1wcK=*JZTVgg3O7>{-@Js3-}NIQtiAX)BB!YZZWKaYR!!Uy=H*=Ir;Rr`_gqp?(jj3U!! z!?t*uww34e-5PH*dRu-9H=W$31VEoZ806ss!dR`L^&d2z_k|YF19skUmBnhmtI*J( z!OpJM8${3F=yNb{*Cv}#lg`)h#i>Qs)Z%`e0Rb_AyT3Dmx<*zX9AedqG%?n+FxE=j z#vH9YiGRm`#?llj%h1F+xv2Nn55<`{Bm=#<4Q?F|iz~Jxo-QL6%2uzu#nQ>dx6DX1 zu`iQQ5>0;z{;*013t)w_W!-Rp8Xlq3Bk;iQ|ANUV7n7O%o<_HLUr-=;QU%?MB1i5a z-K|V=QFsT;?+Iua+>0hEo5vlUHkM4%Ai2!p&EV=Boj@eU{hg7}5`It_l2@*`&AX+< zEpktBS@1Kdu#we@t6PKs8S^ElubYyLBW$RH@u4-uaJ=8h#@Qk%wbOD@4)TI0;)l16 zn79>Hq$zF|l6l@Id1dqwt!k8K(kjI~Y# zXj6)FXZOMDCRI^lmPlq^kTBjZwo1hnRN4T3`jTCx9I0%uiS6n zS2XUev^}D@a8WNUJQ@?zXoS|*WY+LlRc|jrj%V~DguEKJLxoQx_y({k_*ku~YnsfK zimxjad+Xz-O#AbsiY5EL3muFZq*t2@o({oeUp2bii0-Lwsva1psgQ(`p@^WwI=tGh zUA`XJ!z4SUZ2KA2z2|MuWwhXZ9I!iG3<-+JjIh^AkBVuc!W+7$VSgM@!e0!z-tpnj z>Jr6t<&BlwTA;1dRE0?8hR6!V$ue){$n$pW4ASwmhC86LbQJtd#R^>+FaWv?9!W69 zV;Yn`I=hNe@O|Dx!64zm?d%&Lh1MeVvqqw30#}Izeb2LEqUM6Hiqx;XH%+}?F61&_ z)nV}0?H93KReWLZTp%IX&-yYjvR{D-J~vZ$^?TL8K``Kx{B^)(F`vm*aUmT!O`%no zZ$F0lN^3#N`Kl)FY|-#4;0wB4=rqBrUI6Pqok!~1%EPsb+C(0Q6DgIJLwFt4h<7$Zesc*-r{`N1%(iCwh}Vz4QC zJR6h^S~FW4L>4jwYOe+j1=N_Sui_%8dyh|-M4GRjQB&cbNfPanoYj4C_iHBn%ucOe zVKn=Sy0oXWvC6q={7sd!XI!9n73L}0469wjm-o&e@y@y*J@cW*cF{Um^~4%{=Epq4 zR_30P1bQ@M+EL6daaeqQHcTAXOc<=A<~j719c@Mzx|s4%$$t%R?xC4@=-xbxlwVj zCa+yFdQU;70CkVFDpW|;`K4176 z=PIm@fy{=R$Zps4#SLlgT}uO7!+2ON(jGCdltI5W?ZC#@Ny#eaqJ3rWm>CY>$8LPBSz@;?^=>A^S{BI)P^$Q_trm@Qgg$*iPc zLLKnTHvrc|;FQ1ZaE4As5oR`n0iF7jhmtGCycW#52Bg>+q2l?^-+WQ>b9QfG8W`+nmP7{%L*2wkJe&d7GsW<5Ps| z=Z}T~voT2?p1AiS8y^N3!XIomv9ZFcH1~Y$L~BIZHp#K3NOyCON@oKj>DRoBm(D-i zUap_ypUnt}CXGEz$T15D-Qx`E$7U=PD9!v-O}yUQTyfaO);Kz^hdb(*<3<(!L00~; z!i@02P4H&}wzqOWqR+ZK>Ee5%&w4%Iu}~985hN|kg_LTQO0z=}a&$wMpM{h@>O~#a z8q+cwlOC2XQBbjoJ_c=g{7BORTN#xon~IN+QO?arr3<>{?vZSypWa=kra6*4z)DYa8gBN>;I~kG_b^|c}t^(ZE zG5xNzHZ(&}0ieGmMSt@KtUwMB2Y{868w3FIK)?VX2n_mzK#+kOT3Z;4*qT{G0UW>D zi8vbH5fBg%@2}$B`0mQAATZZ2K+Moi8fsx?j^HQ|-TZ=7;ZPe50PpYicLnJ`3wP5& zWd5Nbz#Td8ce3D)82Ps~es||&1ph^fs3GWxJ4^jSMGYOHzbKafn`JB<9N}W-h7Nxk zK;H0=G7$KCD*rS$;Fm*w?->bO#E}vUTQdN=riHDDt)s=Cz%R|37AA0W$3OU&yN&k0 zK49S847m}^%%8viRr+5o|9>!UAPAw46TroJ_fp^n-dXidFBkygxf>4`59HSqgopDN z%8i)xojig^LOgLHRs|Sx*8>>91p)qE5(sVxrfzF-cg6;A*XiG#_U|Qp$6NhgnQ|5; zcQ(4Cwp9LNr=0GntiMr2h~fUn?P7@2JBW1;U^F(gaDV}TY(P#nZUCb>9B#+Qjv&|& zpqYcAowHsyx-~a$QF*yFZ0Nh+$U@m|u;13J} + +Gnuplot +Produced by GNUPLOT 5.0 patchlevel 3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 0 + + + + + 0.0005 + + + + + 0.001 + + + + + 0.0015 + + + + + 0.002 + + + + + 0 + + + + + 20 + + + + + 40 + + + + + 60 + + + + + 80 + + + + + 100 + + + + + + + + + + + + + inversion + + + + + inversion + + + + + + backslash + + + backslash + + + + + + multiplication + + + multiplication + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/lecture_12/nohup.out b/lecture_12/nohup.out new file mode 100644 index 0000000..f0d30e1 --- /dev/null +++ b/lecture_12/nohup.out @@ -0,0 +1,2 @@ + +(evince:8926): Gtk-WARNING **: gtk_widget_size_allocate(): attempt to allocate widget with width -71 and height 20 diff --git a/lecture_12/octave-workspace b/lecture_12/octave-workspace new file mode 100644 index 0000000000000000000000000000000000000000..41ef164d111fcfa9cc9ec079bd8194241d90356e GIT binary patch literal 11 ScmeZIE=ep))iu=hVE_OY#sfM4 literal 0 HcmV?d00001 diff --git a/lecture_13/.ipynb_checkpoints/lecture_13-checkpoint.ipynb b/lecture_13/.ipynb_checkpoints/lecture_12-checkpoint.ipynb similarity index 100% rename from lecture_13/.ipynb_checkpoints/lecture_13-checkpoint.ipynb rename to lecture_13/.ipynb_checkpoints/lecture_12-checkpoint.ipynb diff --git a/lecture_13/octave-workspace b/lecture_13/octave-workspace deleted file mode 100644 index e69de29..0000000 From 9bc0a6b927835bc845b8ca86bfb549404ab17191 Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Tue, 28 Feb 2017 14:26:15 -0500 Subject: [PATCH 16/16] update lecture 12 and recommended probs --- lecture_12/lecture_12.aux | 27 +- lecture_12/lecture_12.bbl | 0 lecture_12/lecture_12.blg | 48 + lecture_12/lecture_12.ipynb | 175 ++- lecture_12/lecture_12.log | 841 ++++++++++++++ lecture_12/lecture_12.md | 112 +- lecture_12/lecture_12.out | 7 + lecture_12/lecture_12.pdf | Bin 169270 -> 232410 bytes lecture_12/lecture_12.tex | 1015 +++++++++++++++++ .../lecture_12_files/lecture_12_21_0.png | Bin 0 -> 9047 bytes .../lecture_12_files/lecture_12_24_0.pdf | Bin 0 -> 9736 bytes .../lecture_12_files/lecture_12_24_0.png | Bin 0 -> 8571 bytes .../lecture_12_files/lecture_12_24_0.svg | 148 +++ linear_algebra/LU_suggested.html | 39 + linear_algebra/LU_suggested.md | 68 ++ 15 files changed, 2440 insertions(+), 40 deletions(-) create mode 100644 lecture_12/lecture_12.bbl create mode 100644 lecture_12/lecture_12.blg create mode 100644 lecture_12/lecture_12.log create mode 100644 lecture_12/lecture_12.out create mode 100644 lecture_12/lecture_12.tex create mode 100644 lecture_12/lecture_12_files/lecture_12_21_0.png create mode 100644 lecture_12/lecture_12_files/lecture_12_24_0.pdf create mode 100644 lecture_12/lecture_12_files/lecture_12_24_0.png create mode 100644 lecture_12/lecture_12_files/lecture_12_24_0.svg create mode 100644 linear_algebra/LU_suggested.html create mode 100644 linear_algebra/LU_suggested.md diff --git a/lecture_12/lecture_12.aux b/lecture_12/lecture_12.aux index c73dc14..4aa3a49 100644 --- a/lecture_12/lecture_12.aux +++ b/lecture_12/lecture_12.aux @@ -17,11 +17,22 @@ \providecommand\HyField@AuxAddToFields[1]{} \providecommand\HyField@AuxAddToCoFields[2]{} \providecommand \oddpage@label [2]{} -\@writefile{toc}{\contentsline {subsection}{\numberline {0.1}My question from last class}{1}{subsection.0.1}} -\newlabel{my-question-from-last-class}{{0.1}{1}{My question from last class}{subsection.0.1}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces q1\relax }}{1}{figure.caption.1}} -\@writefile{toc}{\contentsline {subsection}{\numberline {0.2}Your questions from last class}{1}{subsection.0.2}} -\newlabel{your-questions-from-last-class}{{0.2}{1}{Your questions from last class}{subsection.0.2}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces q2\relax }}{2}{figure.caption.2}} -\@writefile{toc}{\contentsline {section}{\numberline {1}Matrix Inverse and Condition}{2}{section.1}} -\newlabel{matrix-inverse-and-condition}{{1}{2}{Matrix Inverse and Condition}{section.1}{}} +\@writefile{toc}{\contentsline {subsection}{\numberline {0.1}My question from last class}{2}{subsection.0.1}} +\newlabel{my-question-from-last-class}{{0.1}{2}{My question from last class}{subsection.0.1}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces q1\relax }}{2}{figure.caption.1}} +\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces q2\relax }}{3}{figure.caption.2}} +\@writefile{toc}{\contentsline {subsection}{\numberline {0.2}Your questions from last class}{3}{subsection.0.2}} +\newlabel{your-questions-from-last-class}{{0.2}{3}{Your questions from last class}{subsection.0.2}{}} +\@writefile{toc}{\contentsline {section}{\numberline {1}Matrix Inverse and Condition}{3}{section.1}} +\newlabel{matrix-inverse-and-condition}{{1}{3}{Matrix Inverse and Condition}{section.1}{}} +\newlabel{note-on-solving-for-a-1-column-1}{{1}{5}{\texorpdfstring {Note on solving for \(A^{-1}\) column 1}{Note on solving for A\^{}\{-1\} column 1}}{section*.3}{}} +\@writefile{toc}{\contentsline {paragraph}{Note on solving for \(A^{-1}\) column 1}{5}{section*.3}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Condition of a matrix}{10}{subsection.1.1}} +\newlabel{condition-of-a-matrix}{{1.1}{10}{Condition of a matrix}{subsection.1.1}{}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.1}\emph {just checked in to see what condition my condition was in}}{10}{subsubsection.1.1.1}} +\newlabel{just-checked-in-to-see-what-condition-my-condition-was-in}{{1.1.1}{10}{\texorpdfstring {\emph {just checked in to see what condition my condition was in}}{just checked in to see what condition my condition was in}}{subsubsection.1.1.1}{}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.2}Matrix norms}{10}{subsubsection.1.1.2}} +\newlabel{matrix-norms}{{1.1.2}{10}{Matrix norms}{subsubsection.1.1.2}{}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.3}Condition of Matrix}{11}{subsubsection.1.1.3}} +\newlabel{condition-of-matrix}{{1.1.3}{11}{Condition of Matrix}{subsubsection.1.1.3}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Springs-masses\relax }}{13}{figure.caption.4}} diff --git a/lecture_12/lecture_12.bbl b/lecture_12/lecture_12.bbl new file mode 100644 index 0000000..e69de29 diff --git a/lecture_12/lecture_12.blg b/lecture_12/lecture_12.blg new file mode 100644 index 0000000..beafcd1 --- /dev/null +++ b/lecture_12/lecture_12.blg @@ -0,0 +1,48 @@ +This is BibTeX, Version 0.99d (TeX Live 2015/Debian) +Capacity: max_strings=35307, hash_size=35307, hash_prime=30011 +The top-level auxiliary file: lecture_12.aux +I found no \citation commands---while reading file lecture_12.aux +I found no \bibdata command---while reading file lecture_12.aux +I found no \bibstyle command---while reading file lecture_12.aux +You've used 0 entries, + 0 wiz_defined-function locations, + 83 strings with 494 characters, +and the built_in function-call counts, 0 in all, are: += -- 0 +> -- 0 +< -- 0 ++ -- 0 +- -- 0 +* -- 0 +:= -- 0 +add.period$ -- 0 +call.type$ -- 0 +change.case$ -- 0 +chr.to.int$ -- 0 +cite$ -- 0 +duplicate$ -- 0 +empty$ -- 0 +format.name$ -- 0 +if$ -- 0 +int.to.chr$ -- 0 +int.to.str$ -- 0 +missing$ -- 0 +newline$ -- 0 +num.names$ -- 0 +pop$ -- 0 +preamble$ -- 0 +purify$ -- 0 +quote$ -- 0 +skip$ -- 0 +stack$ -- 0 +substring$ -- 0 +swap$ -- 0 +text.length$ -- 0 +text.prefix$ -- 0 +top$ -- 0 +type$ -- 0 +warning$ -- 0 +while$ -- 0 +width$ -- 0 +write$ -- 0 +(There were 3 error messages) diff --git a/lecture_12/lecture_12.ipynb b/lecture_12/lecture_12.ipynb index dc44a21..41f1959 100644 --- a/lecture_12/lecture_12.ipynb +++ b/lecture_12/lecture_12.ipynb @@ -22,6 +22,97 @@ "setdefaults" ] }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A =\n", + "\n", + " 0.447394 0.357071 0.720915 0.499926\n", + " 0.648313 0.323276 0.521677 0.288345\n", + " 0.084982 0.581513 0.466420 0.142342\n", + " 0.576580 0.658089 0.916987 0.923165\n", + "\n", + "L =\n", + "\n", + " 1.00000 0.00000 0.00000 0.00000\n", + " 0.13108 1.00000 0.00000 0.00000\n", + " 0.69009 0.24851 1.00000 0.00000\n", + " 0.88935 0.68736 0.68488 1.00000\n", + "\n", + "U =\n", + "\n", + " 0.64831 0.32328 0.52168 0.28834\n", + " 0.00000 0.53914 0.39804 0.10455\n", + " 0.00000 0.00000 0.26199 0.27496\n", + " 0.00000 0.00000 0.00000 0.40655\n", + "\n", + "P =\n", + "\n", + "Permutation Matrix\n", + "\n", + " 0 1 0 0\n", + " 0 0 1 0\n", + " 1 0 0 0\n", + " 0 0 0 1\n", + "\n", + "ans = 1\n" + ] + } + ], + "source": [ + "A=rand(4,4)\n", + "\n", + "[L,U,P]=lu(A)\n", + "\n", + "det(L)" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 4 4\n", + "\n", + "ans = 23.586\n", + "ans = 35.826\n", + "ans = 14.869\n", + "C =\n", + "\n", + " 5.98549 4.28555 4.35707 4.31359\n", + " 0.00000 3.63950 1.35005 1.45342\n", + " 0.00000 0.00000 3.62851 1.50580\n", + " 0.00000 0.00000 0.00000 3.21911\n", + "\n" + ] + } + ], + "source": [ + "A=rand(4,100)';\n", + "A=A'*A;\n", + "size(A)\n", + "min(min(A))\n", + "max(max(A))\n", + "cond(A)\n", + "C=chol(A)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -90,7 +181,7 @@ "1\\end{array}\\right]$\n", "\n", "$A^{-1}=\\frac{1}{2*3-1*1}\\left[ \\begin{array}{cc}\n", - "3 & 1 \\\\\n", + "3 & -1 \\\\\n", "-1 & 2 \\end{array} \\right]=\n", "\\left[ \\begin{array}{cc}\n", "3/5 & -1/5 \\\\\n", @@ -99,7 +190,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 45, "metadata": { "collapsed": false }, @@ -203,7 +294,7 @@ "\n", "$A^{-1}=\\left[ \\begin{array}{cccc}\n", "| & | & & | \\\\\n", - "a_{1} & a_{2} & \\cdots & a_{3} \\\\\n", + "a_{1} & a_{2} & \\cdots & a_{n} \\\\\n", "| & | & & | \\end{array} \\right]$\n", "\n", "\n", @@ -236,9 +327,26 @@ "0 & -1 & 1 \\end{array} \\right]$\n" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Note on solving for $A^{-1}$ column 1\n", + "\n", + "$Aa_1=I(:,1)$\n", + "\n", + "$LUa_1=I(:,1)$\n", + "\n", + "$(LUa_1-I(:,1))=0$\n", + "\n", + "$L(Ua_1-d_1)=0$\n", + "\n", + "$I(:,1)=Ld_1$" + ] + }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 56, "metadata": { "collapsed": false }, @@ -278,7 +386,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 57, "metadata": { "collapsed": false }, @@ -317,13 +425,23 @@ "1 \\\\ \n", "0 \\\\ \n", "\\vdots \\\\\n", - "0 \\end{array} \\right]$\n", - "$;~Ua_{1}=d_{1}$" + "0 \\end{array} \\right]=\n", + "\\left[\\begin{array}{ccc} \n", + "1 & 0 & 0 \\\\ \n", + "-1/2 & 1 & 0 \\\\\n", + "0 & -2/3 & 1 \\end{array} \\right]\\left[\\begin{array}{c} \n", + "d1(1) \\\\ \n", + "d1(2) \\\\ \n", + "d1(3)\\end{array} \\right]=\\left[\\begin{array}{c} \n", + "1 \\\\ \n", + "0 \\\\ \n", + "0 \\end{array} \\right]\n", + ";~Ua_{1}=d_{1}$" ] }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 58, "metadata": { "collapsed": false }, @@ -350,7 +468,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 59, "metadata": { "collapsed": false }, @@ -377,7 +495,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 60, "metadata": { "collapsed": false }, @@ -404,7 +522,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 61, "metadata": { "collapsed": false }, @@ -431,7 +549,7 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 62, "metadata": { "collapsed": false }, @@ -458,7 +576,7 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 63, "metadata": { "collapsed": false }, @@ -492,7 +610,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 69, "metadata": { "collapsed": false }, @@ -507,18 +625,25 @@ " 1.00000 2.00000 2.00000\n", " 1.00000 2.00000 3.00000\n", "\n", - "ans =\n", + "I_app =\n", "\n", " 1.00000 0.00000 0.00000\n", " 0.00000 1.00000 -0.00000\n", " -0.00000 -0.00000 1.00000\n", - "\n" + "\n", + "ans = -4.4409e-16\n", + "ans = 2.2204e-16\n", + "ans = 0.0039062\n" ] } ], "source": [ "invA=[a1,a2,a3]\n", - "A*invA" + "I_app=A*invA\n", + "I_app(2,3)\n", + "eps\n", + "\n", + "2^-8" ] }, { @@ -530,7 +655,7 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 70, "metadata": { "collapsed": false }, @@ -577,7 +702,7 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 71, "metadata": { "collapsed": false }, @@ -703,7 +828,7 @@ "\t\n", "\n", "\n", - "\t\n", + "\t\n", "\t\n", "\tbackslash\n", "\n", @@ -712,7 +837,7 @@ "\t\n", "\n", "\n", - "\t\n", + "\t\n", "\t\n", "\tmultiplication\n", "\n", @@ -721,7 +846,7 @@ "\t\n", "\n", "\n", - "\t\n", + "\t\n", "\t\n", "\n", "\n", @@ -813,7 +938,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 72, "metadata": { "collapsed": false }, @@ -864,7 +989,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 75, "metadata": { "collapsed": false }, @@ -908,7 +1033,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 74, "metadata": { "collapsed": false }, diff --git a/lecture_12/lecture_12.log b/lecture_12/lecture_12.log new file mode 100644 index 0000000..c4a5ed3 --- /dev/null +++ b/lecture_12/lecture_12.log @@ -0,0 +1,841 @@ +This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian) (preloaded format=pdflatex 2017.1.11) 28 FEB 2017 14:24 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**lecture_12.tex +(./lecture_12.tex +LaTeX2e <2016/02/01> +Babel <3.9q> and hyphenation patterns for 81 language(s) loaded. +(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls +Document Class: article 2014/09/29 v1.4h Standard LaTeX document class +(/usr/share/texlive/texmf-dist/tex/latex/base/size11.clo +File: size11.clo 2014/09/29 v1.4h Standard LaTeX file (size option) +) +\c@part=\count79 +\c@section=\count80 +\c@subsection=\count81 +\c@subsubsection=\count82 +\c@paragraph=\count83 +\c@subparagraph=\count84 +\c@figure=\count85 +\c@table=\count86 +\abovecaptionskip=\skip41 +\belowcaptionskip=\skip42 +\bibindent=\dimen102 +) +(/usr/share/texlive/texmf-dist/tex/latex/base/fontenc.sty +Package: fontenc 2005/09/27 v1.99g Standard LaTeX package + +(/usr/share/texlive/texmf-dist/tex/latex/base/t1enc.def +File: t1enc.def 2005/09/27 v1.99g Standard LaTeX file +LaTeX Font Info: Redeclaring font encoding T1 on input line 48. +)) +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/mathpazo.sty +Package: mathpazo 2005/04/12 PSNFSS-v9.2a Palatino w/ Pazo Math (D.Puga, WaS) +\symupright=\mathgroup4 +) +(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty +Package: graphicx 2014/10/28 v1.0g Enhanced LaTeX Graphics (DPC,SPQR) + +(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty +Package: keyval 2014/10/28 v1.15 key=value parser (DPC) +\KV@toks@=\toks14 +) +(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty +Package: graphics 2016/01/03 v1.0q Standard LaTeX Graphics (DPC,SPQR) + +(/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty +Package: trig 2016/01/03 v1.10 sin cos tan (DPC) +) +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/graphics.cfg +File: graphics.cfg 2010/04/23 v1.9 graphics configuration of TeX Live +) +Package graphics Info: Driver file: pdftex.def on input line 95. + +(/usr/share/texlive/texmf-dist/tex/latex/pdftex-def/pdftex.def +File: pdftex.def 2011/05/27 v0.06d Graphics/color for pdfTeX + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/infwarerr.sty +Package: infwarerr 2010/04/08 v1.3 Providing info/warning/error messages (HO) +) +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ltxcmds.sty +Package: ltxcmds 2011/11/09 v1.22 LaTeX kernel commands for general use (HO) +) +\Gread@gobject=\count87 +)) +\Gin@req@height=\dimen103 +\Gin@req@width=\dimen104 +) +(/usr/share/texlive/texmf-dist/tex/latex/caption/caption.sty +Package: caption 2016/02/21 v3.3-144 Customizing captions (AR) + +(/usr/share/texlive/texmf-dist/tex/latex/caption/caption3.sty +Package: caption3 2016/02/04 v1.7-139 caption3 kernel (AR) +Package caption3 Info: TeX engine: e-TeX on input line 67. +\captionmargin=\dimen105 +\captionmargin@=\dimen106 +\captionwidth=\dimen107 +\caption@tempdima=\dimen108 +\caption@indent=\dimen109 +\caption@parindent=\dimen110 +\caption@hangindent=\dimen111 +) +\c@ContinuedFloat=\count88 +) +(/usr/share/texlive/texmf-dist/tex/latex/adjustbox/adjustbox.sty +Package: adjustbox 2012/05/21 v1.0 Adjusting TeX boxes (trim, clip, ...) + +(/usr/share/texlive/texmf-dist/tex/latex/xkeyval/xkeyval.sty +Package: xkeyval 2014/12/03 v2.7a package option processing (HA) + +(/usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkeyval.tex +(/usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkvutils.tex +\XKV@toks=\toks15 +\XKV@tempa@toks=\toks16 +) +\XKV@depth=\count89 +File: xkeyval.tex 2014/12/03 v2.7a key=value parser (HA) +)) +(/usr/share/texlive/texmf-dist/tex/latex/adjustbox/adjcalc.sty +Package: adjcalc 2012/05/16 v1.1 Provides advanced setlength with multiple back +-ends (calc, etex, pgfmath) +) +(/usr/share/texlive/texmf-dist/tex/latex/adjustbox/trimclip.sty +Package: trimclip 2012/05/16 v1.0 Trim and clip general TeX material + +(/usr/share/texlive/texmf-dist/tex/latex/collectbox/collectbox.sty +Package: collectbox 2012/05/17 v0.4b Collect macro arguments as boxes +\collectedbox=\box26 +) +\tc@llx=\dimen112 +\tc@lly=\dimen113 +\tc@urx=\dimen114 +\tc@ury=\dimen115 +Package trimclip Info: Using driver 'tc-pdftex.def'. + +(/usr/share/texlive/texmf-dist/tex/latex/adjustbox/tc-pdftex.def +File: tc-pdftex.def 2012/05/13 v1.0 Clipping driver for pdftex +)) +\adjbox@Width=\dimen116 +\adjbox@Height=\dimen117 +\adjbox@Depth=\dimen118 +\adjbox@Totalheight=\dimen119 + +(/usr/share/texlive/texmf-dist/tex/latex/ifoddpage/ifoddpage.sty +Package: ifoddpage 2011/09/13 v1.0 Conditionals for odd/even page detection +\c@checkoddpage=\count90 +) +(/usr/share/texlive/texmf-dist/tex/latex/varwidth/varwidth.sty +Package: varwidth 2009/03/30 ver 0.92; Variable-width minipages +\@vwid@box=\box27 +\sift@deathcycles=\count91 +\@vwid@loff=\dimen120 +\@vwid@roff=\dimen121 +)) +(/usr/share/texlive/texmf-dist/tex/latex/xcolor/xcolor.sty +Package: xcolor 2007/01/21 v2.11 LaTeX color extensions (UK) + +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/color.cfg +File: color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive +) +Package xcolor Info: Driver file: pdftex.def on input line 225. +Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1337. +Package xcolor Info: Model `hsb' substituted by `rgb' on input line 1341. +Package xcolor Info: Model `RGB' extended on input line 1353. +Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1355. +Package xcolor Info: Model `Hsb' substituted by `hsb' on input line 1356. +Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1357. +Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1358. +Package xcolor Info: Model `Gray' substituted by `gray' on input line 1359. +Package xcolor Info: Model `wave' substituted by `hsb' on input line 1360. +) +(/usr/share/texlive/texmf-dist/tex/latex/tools/enumerate.sty +Package: enumerate 2015/07/23 v3.00 enumerate extensions (DPC) +\@enLab=\toks17 +) +(/usr/share/texlive/texmf-dist/tex/latex/geometry/geometry.sty +Package: geometry 2010/09/12 v5.6 Page Geometry + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifpdf.sty +Package: ifpdf 2011/01/30 v2.3 Provides the ifpdf switch (HO) +Package ifpdf Info: pdfTeX in PDF mode is detected. +) +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifvtex.sty +Package: ifvtex 2010/03/01 v1.5 Detect VTeX and its facilities (HO) +Package ifvtex Info: VTeX not detected. +) +(/usr/share/texlive/texmf-dist/tex/generic/ifxetex/ifxetex.sty +Package: ifxetex 2010/09/12 v0.6 Provides ifxetex conditional +) +\Gm@cnth=\count92 +\Gm@cntv=\count93 +\c@Gm@tempcnt=\count94 +\Gm@bindingoffset=\dimen122 +\Gm@wd@mp=\dimen123 +\Gm@odd@mp=\dimen124 +\Gm@even@mp=\dimen125 +\Gm@layoutwidth=\dimen126 +\Gm@layoutheight=\dimen127 +\Gm@layouthoffset=\dimen128 +\Gm@layoutvoffset=\dimen129 +\Gm@dimlist=\toks18 +) +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty +Package: amsmath 2016/03/03 v2.15a AMS math features +\@mathmargin=\skip43 + +For additional information on amsmath, use the `?' option. +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty +Package: amstext 2000/06/29 v2.01 AMS text + +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty +File: amsgen.sty 1999/11/30 v2.0 generic functions +\@emptytoks=\toks19 +\ex@=\dimen130 +)) +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty +Package: amsbsy 1999/11/29 v1.2d Bold Symbols +\pmbraise@=\dimen131 +) +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty +Package: amsopn 1999/12/14 v2.01 operator names +) +\inf@bad=\count95 +LaTeX Info: Redefining \frac on input line 199. +\uproot@=\count96 +\leftroot@=\count97 +LaTeX Info: Redefining \overline on input line 297. +\classnum@=\count98 +\DOTSCASE@=\count99 +LaTeX Info: Redefining \ldots on input line 394. +LaTeX Info: Redefining \dots on input line 397. +LaTeX Info: Redefining \cdots on input line 518. +\Mathstrutbox@=\box28 +\strutbox@=\box29 +\big@size=\dimen132 +LaTeX Font Info: Redeclaring font encoding OML on input line 630. +LaTeX Font Info: Redeclaring font encoding OMS on input line 631. +\macc@depth=\count100 +\c@MaxMatrixCols=\count101 +\dotsspace@=\muskip10 +\c@parentequation=\count102 +\dspbrk@lvl=\count103 +\tag@help=\toks20 +\row@=\count104 +\column@=\count105 +\maxfields@=\count106 +\andhelp@=\toks21 +\eqnshift@=\dimen133 +\alignsep@=\dimen134 +\tagshift@=\dimen135 +\tagwidth@=\dimen136 +\totwidth@=\dimen137 +\lineht@=\dimen138 +\@envbody=\toks22 +\multlinegap=\skip44 +\multlinetaggap=\skip45 +\mathdisplay@stack=\toks23 +LaTeX Info: Redefining \[ on input line 2735. +LaTeX Info: Redefining \] on input line 2736. +) +(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +Package: amssymb 2013/01/14 v3.01 AMS font symbols + +(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty +Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support +\symAMSa=\mathgroup5 +\symAMSb=\mathgroup6 +LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' +(Font) U/euf/m/n --> U/euf/b/n on input line 106. +)) +(/usr/share/texlive/texmf-dist/tex/latex/base/textcomp.sty +Package: textcomp 2005/09/27 v1.99g Standard LaTeX package +Package textcomp Info: Sub-encoding information: +(textcomp) 5 = only ISO-Adobe without \textcurrency +(textcomp) 4 = 5 + \texteuro +(textcomp) 3 = 4 + \textohm +(textcomp) 2 = 3 + \textestimated + \textcurrency +(textcomp) 1 = TS1 - \textcircled - \t +(textcomp) 0 = TS1 (full) +(textcomp) Font families with sub-encoding setting implement +(textcomp) only a restricted character set as indicated. +(textcomp) Family '?' is the default used for unknown fonts. +(textcomp) See the documentation for details. +Package textcomp Info: Setting ? sub-encoding to TS1/1 on input line 79. + +(/usr/share/texlive/texmf-dist/tex/latex/base/ts1enc.def +File: ts1enc.def 2001/06/05 v3.0e (jk/car/fm) Standard LaTeX file +) +LaTeX Info: Redefining \oldstylenums on input line 334. +Package textcomp Info: Setting cmr sub-encoding to TS1/0 on input line 349. +Package textcomp Info: Setting cmss sub-encoding to TS1/0 on input line 350. +Package textcomp Info: Setting cmtt sub-encoding to TS1/0 on input line 351. +Package textcomp Info: Setting cmvtt sub-encoding to TS1/0 on input line 352. +Package textcomp Info: Setting cmbr sub-encoding to TS1/0 on input line 353. +Package textcomp Info: Setting cmtl sub-encoding to TS1/0 on input line 354. +Package textcomp Info: Setting ccr sub-encoding to TS1/0 on input line 355. +Package textcomp Info: Setting ptm sub-encoding to TS1/4 on input line 356. +Package textcomp Info: Setting pcr sub-encoding to TS1/4 on input line 357. +Package textcomp Info: Setting phv sub-encoding to TS1/4 on input line 358. +Package textcomp Info: Setting ppl sub-encoding to TS1/3 on input line 359. +Package textcomp Info: Setting pag sub-encoding to TS1/4 on input line 360. +Package textcomp Info: Setting pbk sub-encoding to TS1/4 on input line 361. +Package textcomp Info: Setting pnc sub-encoding to TS1/4 on input line 362. +Package textcomp Info: Setting pzc sub-encoding to TS1/4 on input line 363. +Package textcomp Info: Setting bch sub-encoding to TS1/4 on input line 364. +Package textcomp Info: Setting put sub-encoding to TS1/5 on input line 365. +Package textcomp Info: Setting uag sub-encoding to TS1/5 on input line 366. +Package textcomp Info: Setting ugq sub-encoding to TS1/5 on input line 367. +Package textcomp Info: Setting ul8 sub-encoding to TS1/4 on input line 368. +Package textcomp Info: Setting ul9 sub-encoding to TS1/4 on input line 369. +Package textcomp Info: Setting augie sub-encoding to TS1/5 on input line 370. +Package textcomp Info: Setting dayrom sub-encoding to TS1/3 on input line 371. +Package textcomp Info: Setting dayroms sub-encoding to TS1/3 on input line 372. + +Package textcomp Info: Setting pxr sub-encoding to TS1/0 on input line 373. +Package textcomp Info: Setting pxss sub-encoding to TS1/0 on input line 374. +Package textcomp Info: Setting pxtt sub-encoding to TS1/0 on input line 375. +Package textcomp Info: Setting txr sub-encoding to TS1/0 on input line 376. +Package textcomp Info: Setting txss sub-encoding to TS1/0 on input line 377. +Package textcomp Info: Setting txtt sub-encoding to TS1/0 on input line 378. +Package textcomp Info: Setting lmr sub-encoding to TS1/0 on input line 379. +Package textcomp Info: Setting lmdh sub-encoding to TS1/0 on input line 380. +Package textcomp Info: Setting lmss sub-encoding to TS1/0 on input line 381. +Package textcomp Info: Setting lmssq sub-encoding to TS1/0 on input line 382. +Package textcomp Info: Setting lmvtt sub-encoding to TS1/0 on input line 383. +Package textcomp Info: Setting lmtt sub-encoding to TS1/0 on input line 384. +Package textcomp Info: Setting qhv sub-encoding to TS1/0 on input line 385. +Package textcomp Info: Setting qag sub-encoding to TS1/0 on input line 386. +Package textcomp Info: Setting qbk sub-encoding to TS1/0 on input line 387. +Package textcomp Info: Setting qcr sub-encoding to TS1/0 on input line 388. +Package textcomp Info: Setting qcs sub-encoding to TS1/0 on input line 389. +Package textcomp Info: Setting qpl sub-encoding to TS1/0 on input line 390. +Package textcomp Info: Setting qtm sub-encoding to TS1/0 on input line 391. +Package textcomp Info: Setting qzc sub-encoding to TS1/0 on input line 392. +Package textcomp Info: Setting qhvc sub-encoding to TS1/0 on input line 393. +Package textcomp Info: Setting futs sub-encoding to TS1/4 on input line 394. +Package textcomp Info: Setting futx sub-encoding to TS1/4 on input line 395. +Package textcomp Info: Setting futj sub-encoding to TS1/4 on input line 396. +Package textcomp Info: Setting hlh sub-encoding to TS1/3 on input line 397. +Package textcomp Info: Setting hls sub-encoding to TS1/3 on input line 398. +Package textcomp Info: Setting hlst sub-encoding to TS1/3 on input line 399. +Package textcomp Info: Setting hlct sub-encoding to TS1/5 on input line 400. +Package textcomp Info: Setting hlx sub-encoding to TS1/5 on input line 401. +Package textcomp Info: Setting hlce sub-encoding to TS1/5 on input line 402. +Package textcomp Info: Setting hlcn sub-encoding to TS1/5 on input line 403. +Package textcomp Info: Setting hlcw sub-encoding to TS1/5 on input line 404. +Package textcomp Info: Setting hlcf sub-encoding to TS1/5 on input line 405. +Package textcomp Info: Setting pplx sub-encoding to TS1/3 on input line 406. +Package textcomp Info: Setting pplj sub-encoding to TS1/3 on input line 407. +Package textcomp Info: Setting ptmx sub-encoding to TS1/4 on input line 408. +Package textcomp Info: Setting ptmj sub-encoding to TS1/4 on input line 409. +) +(/usr/share/texlive/texmf-dist/tex/latex/upquote/upquote.sty +Package: upquote 2012/04/19 v1.3 upright-quote and grave-accent glyphs in verba +tim +) +(/usr/share/texlive/texmf-dist/tex/latex/eurosym/eurosym.sty +Package: eurosym 1998/08/06 v1.1 European currency symbol ``Euro'' +\@eurobox=\box30 +) +(/usr/share/texlive/texmf-dist/tex/latex/ucs/ucs.sty +Package: ucs 2013/05/11 v2.2 UCS: Unicode input support + +(/usr/share/texlive/texmf-dist/tex/latex/ucs/data/uni-global.def +File: uni-global.def 2013/05/13 UCS: Unicode global data +) +\uc@secondtry=\count107 +\uc@combtoks=\toks24 +\uc@combtoksb=\toks25 +\uc@temptokena=\toks26 +) +(/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty +Package: inputenc 2015/03/17 v1.2c Input encoding file +\inpenc@prehook=\toks27 +\inpenc@posthook=\toks28 + +(/usr/share/texlive/texmf-dist/tex/latex/ucs/utf8x.def +File: utf8x.def 2004/10/17 UCS: Input encoding UTF-8 +)) +(/usr/share/texlive/texmf-dist/tex/latex/fancyvrb/fancyvrb.sty +Package: fancyvrb 2008/02/07 + +Style option: `fancyvrb' v2.7a, with DG/SPQR fixes, and firstline=lastline fix +<2008/02/07> (tvz) +\FV@CodeLineNo=\count108 +\FV@InFile=\read1 +\FV@TabBox=\box31 +\c@FancyVerbLine=\count109 +\FV@StepNumber=\count110 +\FV@OutFile=\write3 +) +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grffile.sty +Package: grffile 2012/04/05 v1.16 Extended file name support for graphics (HO) + +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/kvoptions.sty +Package: kvoptions 2011/06/30 v3.11 Key value format for package options (HO) + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/kvsetkeys.sty +Package: kvsetkeys 2012/04/25 v1.16 Key value parser (HO) + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/etexcmds.sty +Package: etexcmds 2011/02/16 v1.5 Avoid name clashes with e-TeX commands (HO) + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifluatex.sty +Package: ifluatex 2010/03/01 v1.3 Provides the ifluatex switch (HO) +Package ifluatex Info: LuaTeX not detected. +) +Package etexcmds Info: Could not find \expanded. +(etexcmds) That can mean that you are not using pdfTeX 1.50 or +(etexcmds) that some package has redefined \expanded. +(etexcmds) In the latter case, load this package earlier. +))) +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/pdftexcmds.sty +Package: pdftexcmds 2011/11/29 v0.20 Utility functions of pdfTeX for LuaTeX (HO +) +Package pdftexcmds Info: LuaTeX not detected. +Package pdftexcmds Info: \pdf@primitive is available. +Package pdftexcmds Info: \pdf@ifprimitive is available. +Package pdftexcmds Info: \pdfdraftmode found. +) +Package grffile Info: Option `multidot' is set to `true'. +Package grffile Info: Option `extendedchars' is set to `false'. +Package grffile Info: Option `space' is set to `true'. +Package grffile Info: \Gin@ii of package `graphicx' fixed on input line 486. +) +(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty +Package: hyperref 2012/11/06 v6.83m Hypertext links for LaTeX + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty +Package: hobsub-hyperref 2012/05/28 v1.13 Bundle oberdiek, subset hyperref (HO) + + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty +Package: hobsub-generic 2012/05/28 v1.13 Bundle oberdiek, subset generic (HO) +Package: hobsub 2012/05/28 v1.13 Construct package bundles (HO) +Package hobsub Info: Skipping package `infwarerr' (already loaded). +Package hobsub Info: Skipping package `ltxcmds' (already loaded). +Package hobsub Info: Skipping package `ifluatex' (already loaded). +Package hobsub Info: Skipping package `ifvtex' (already loaded). +Package: intcalc 2007/09/27 v1.1 Expandable calculations with integers (HO) +Package hobsub Info: Skipping package `ifpdf' (already loaded). +Package hobsub Info: Skipping package `etexcmds' (already loaded). +Package hobsub Info: Skipping package `kvsetkeys' (already loaded). +Package: kvdefinekeys 2011/04/07 v1.3 Define keys (HO) +Package hobsub Info: Skipping package `pdftexcmds' (already loaded). +Package: pdfescape 2011/11/25 v1.13 Implements pdfTeX's escape features (HO) +Package: bigintcalc 2012/04/08 v1.3 Expandable calculations on big integers (HO +) +Package: bitset 2011/01/30 v1.1 Handle bit-vector datatype (HO) +Package: uniquecounter 2011/01/30 v1.2 Provide unlimited unique counter (HO) +) +Package hobsub Info: Skipping package `hobsub' (already loaded). +Package: letltxmacro 2010/09/02 v1.4 Let assignment for LaTeX macros (HO) +Package: hopatch 2012/05/28 v1.2 Wrapper for package hooks (HO) +Package: xcolor-patch 2011/01/30 xcolor patch +Package: atveryend 2011/06/30 v1.8 Hooks at the very end of document (HO) +Package atveryend Info: \enddocument detected (standard20110627). +Package: atbegshi 2011/10/05 v1.16 At begin shipout hook (HO) +Package: refcount 2011/10/16 v3.4 Data extraction from label references (HO) +Package: hycolor 2011/01/30 v1.7 Color options for hyperref/bookmark (HO) +) +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/auxhook.sty +Package: auxhook 2011/03/04 v1.3 Hooks for auxiliary files (HO) +) +\@linkdim=\dimen139 +\Hy@linkcounter=\count111 +\Hy@pagecounter=\count112 + +(/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def +File: pd1enc.def 2012/11/06 v6.83m Hyperref: PDFDocEncoding definition (HO) +) +\Hy@SavedSpaceFactor=\count113 + +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/hyperref.cfg +File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive +) +Package hyperref Info: Hyper figures OFF on input line 4443. +Package hyperref Info: Link nesting OFF on input line 4448. +Package hyperref Info: Hyper index ON on input line 4451. +Package hyperref Info: Plain pages OFF on input line 4458. +Package hyperref Info: Backreferencing OFF on input line 4463. +Package hyperref Info: Implicit mode ON; LaTeX internals redefined. +Package hyperref Info: Bookmarks ON on input line 4688. +\c@Hy@tempcnt=\count114 + +(/usr/share/texlive/texmf-dist/tex/latex/url/url.sty +\Urlmuskip=\muskip11 +Package: url 2013/09/16 ver 3.4 Verb mode for urls, etc. +) +LaTeX Info: Redefining \url on input line 5041. +\XeTeXLinkMargin=\dimen140 +\Fld@menulength=\count115 +\Field@Width=\dimen141 +\Fld@charsize=\dimen142 +Package hyperref Info: Hyper figures OFF on input line 6295. +Package hyperref Info: Link nesting OFF on input line 6300. +Package hyperref Info: Hyper index ON on input line 6303. +Package hyperref Info: backreferencing OFF on input line 6310. +Package hyperref Info: Link coloring OFF on input line 6315. +Package hyperref Info: Link coloring with OCG OFF on input line 6320. +Package hyperref Info: PDF/A mode OFF on input line 6325. +LaTeX Info: Redefining \ref on input line 6365. +LaTeX Info: Redefining \pageref on input line 6369. +\Hy@abspage=\count116 +\c@Item=\count117 +\c@Hfootnote=\count118 +) + +Package hyperref Message: Driver (autodetected): hpdftex. + +(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def +File: hpdftex.def 2012/11/06 v6.83m Hyperref driver for pdfTeX +\Fld@listcount=\count119 +\c@bookmark@seq@number=\count120 + +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty +Package: rerunfilecheck 2011/04/15 v1.7 Rerun checks for auxiliary files (HO) +Package uniquecounter Info: New unique counter `rerunfilecheck' on input line 2 +82. +) +\Hy@SectionHShift=\skip46 +) +(/usr/share/texlive/texmf-dist/tex/latex/tools/longtable.sty +Package: longtable 2014/10/28 v4.11 Multi-page Table package (DPC) +\LTleft=\skip47 +\LTright=\skip48 +\LTpre=\skip49 +\LTpost=\skip50 +\LTchunksize=\count121 +\LTcapwidth=\dimen143 +\LT@head=\box32 +\LT@firsthead=\box33 +\LT@foot=\box34 +\LT@lastfoot=\box35 +\LT@cols=\count122 +\LT@rows=\count123 +\c@LT@tables=\count124 +\c@LT@chunks=\count125 +\LT@p@ftn=\toks29 +) +(/usr/share/texlive/texmf-dist/tex/latex/booktabs/booktabs.sty +Package: booktabs 2005/04/14 v1.61803 publication quality tables +\heavyrulewidth=\dimen144 +\lightrulewidth=\dimen145 +\cmidrulewidth=\dimen146 +\belowrulesep=\dimen147 +\belowbottomsep=\dimen148 +\aboverulesep=\dimen149 +\abovetopsep=\dimen150 +\cmidrulesep=\dimen151 +\cmidrulekern=\dimen152 +\defaultaddspace=\dimen153 +\@cmidla=\count126 +\@cmidlb=\count127 +\@aboverulesep=\dimen154 +\@belowrulesep=\dimen155 +\@thisruleclass=\count128 +\@lastruleclass=\count129 +\@thisrulewidth=\dimen156 +) +(/usr/share/texlive/texmf-dist/tex/latex/enumitem/enumitem.sty +Package: enumitem 2011/09/28 v3.5.2 Customized lists +\labelindent=\skip51 +\enit@outerparindent=\dimen157 +\enit@toks=\toks30 +\enit@inbox=\box36 +\enitdp@description=\count130 +) +(/usr/share/texlive/texmf-dist/tex/generic/ulem/ulem.sty +\UL@box=\box37 +\UL@hyphenbox=\box38 +\UL@skip=\skip52 +\UL@hook=\toks31 +\UL@height=\dimen158 +\UL@pe=\count131 +\UL@pixel=\dimen159 +\ULC@box=\box39 +Package: ulem 2012/05/18 +\ULdepth=\dimen160 +) +Package hyperref Info: Option `breaklinks' set `true' on input line 264. +Package hyperref Info: Option `colorlinks' set `true' on input line 264. + (./lecture_12.aux) +\openout1 = `lecture_12.aux'. + +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 271. +LaTeX Font Info: Try loading font information for TS1+cmr on input line 271. + + +(/usr/share/texlive/texmf-dist/tex/latex/base/ts1cmr.fd +File: ts1cmr.fd 2014/09/29 v2.5h Standard LaTeX font definitions +) +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Try loading font information for T1+ppl on input line 271. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/t1ppl.fd +File: t1ppl.fd 2001/06/04 font definitions for T1/ppl. +) +(/usr/share/texlive/texmf-dist/tex/context/base/supp-pdf.mkii +[Loading MPS to PDF converter (version 2006.09.02).] +\scratchcounter=\count132 +\scratchdimen=\dimen161 +\scratchbox=\box40 +\nofMPsegments=\count133 +\nofMParguments=\count134 +\everyMPshowfont=\toks32 +\MPscratchCnt=\count135 +\MPscratchDim=\dimen162 +\MPnumerator=\count136 +\makeMPintoPDFobject=\count137 +\everyMPtoPDFconversion=\toks33 +) (/usr/share/texlive/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty +Package: epstopdf-base 2010/02/09 v2.5 Base part for package epstopdf + +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grfext.sty +Package: grfext 2010/08/19 v1.1 Manage graphics extensions (HO) +) +Package grfext Info: Graphics extension search list: +(grfext) [.png,.pdf,.jpg,.mps,.jpeg,.jbig2,.jb2,.PNG,.PDF,.JPG,.JPE +G,.JBIG2,.JB2,.eps] +(grfext) \AppendGraphicsExtensions on input line 452. + +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg +File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv +e +)) +Package caption Info: Begin \AtBeginDocument code. +Package caption Info: hyperref package is loaded. +Package caption Info: longtable package is loaded. + +(/usr/share/texlive/texmf-dist/tex/latex/caption/ltcaption.sty +Package: ltcaption 2013/06/09 v1.4-94 longtable captions (AR) +) +Package caption Info: End \AtBeginDocument code. + +*geometry* driver: auto-detecting +*geometry* detected driver: pdftex +*geometry* verbose mode - [ preamble ] result: +* driver: pdftex +* paper: +* layout: +* layoutoffset:(h,v)=(0.0pt,0.0pt) +* modes: +* h-part:(L,W,R)=(72.26999pt, 469.75502pt, 72.26999pt) +* v-part:(T,H,B)=(72.26999pt, 650.43001pt, 72.26999pt) +* \paperwidth=614.295pt +* \paperheight=794.96999pt +* \textwidth=469.75502pt +* \textheight=650.43001pt +* \oddsidemargin=0.0pt +* \evensidemargin=0.0pt +* \topmargin=-37.0pt +* \headheight=12.0pt +* \headsep=25.0pt +* \topskip=11.0pt +* \footskip=30.0pt +* \marginparwidth=59.0pt +* \marginparsep=10.0pt +* \columnsep=10.0pt +* \skip\footins=10.0pt plus 4.0pt minus 2.0pt +* \hoffset=0.0pt +* \voffset=0.0pt +* \mag=1000 +* \@twocolumnfalse +* \@twosidefalse +* \@mparswitchfalse +* \@reversemarginfalse +* (1in=72.27pt=25.4mm, 1cm=28.453pt) + +(/usr/share/texlive/texmf-dist/tex/latex/ucs/ucsencs.def +File: ucsencs.def 2011/01/21 Fixes to fontencodings LGR, T3 +) +\AtBeginShipoutBox=\box41 +Package hyperref Info: Link coloring ON on input line 271. + +(/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty +Package: nameref 2012/10/27 v2.43 Cross-referencing by name of section + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/gettitlestring.sty +Package: gettitlestring 2010/12/03 v1.4 Cleanup title references (HO) +) +\c@section@level=\count138 +) +LaTeX Info: Redefining \ref on input line 271. +LaTeX Info: Redefining \pageref on input line 271. +LaTeX Info: Redefining \nameref on input line 271. + +(./lecture_12.out) (./lecture_12.out) +\@outlinefile=\write4 +\openout4 = `lecture_12.out'. + +LaTeX Font Info: Try loading font information for OT1+ppl on input line 275. + + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/ot1ppl.fd +File: ot1ppl.fd 2001/06/04 font definitions for OT1/ppl. +) +LaTeX Font Info: Try loading font information for OML+zplm on input line 275 +. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/omlzplm.fd +File: omlzplm.fd 2002/09/08 Fontinst v1.914 font definitions for OML/zplm. +) +LaTeX Font Info: Try loading font information for OMS+zplm on input line 275 +. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/omszplm.fd +File: omszplm.fd 2002/09/08 Fontinst v1.914 font definitions for OMS/zplm. +) +LaTeX Font Info: Try loading font information for OMX+zplm on input line 275 +. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/omxzplm.fd +File: omxzplm.fd 2002/09/08 Fontinst v1.914 font definitions for OMX/zplm. +) +LaTeX Font Info: Try loading font information for OT1+zplm on input line 275 +. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/ot1zplm.fd +File: ot1zplm.fd 2002/09/08 Fontinst v1.914 font definitions for OT1/zplm. +) +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 12.50409pt on input line 275. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 9.37807pt on input line 275. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 7.29405pt on input line 275. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 12.50409pt on input line 275. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 9.37807pt on input line 275. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 7.29405pt on input line 275. + + +LaTeX Warning: No \author given. + +LaTeX Font Info: Try loading font information for T1+cmtt on input line 279. + +(/usr/share/texlive/texmf-dist/tex/latex/base/t1cmtt.fd +File: t1cmtt.fd 2014/09/29 v2.5h Standard LaTeX font definitions +) [1 + +{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] +LaTeX Font Info: Try loading font information for TS1+cmtt on input line 331 +. + +(/usr/share/texlive/texmf-dist/tex/latex/base/ts1cmtt.fd +File: ts1cmtt.fd 2014/09/29 v2.5h Standard LaTeX font definitions +) +LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <12> not available +(Font) Font shape `T1/ppl/b/n' tried instead on input line 359. + + +File: det_L.png Graphic file (type png) + +Package pdftex.def Info: det_L.png used on input line 363. +(pdftex.def) Requested size: 375.80544pt x 183.64162pt. + + +File: chol_pre.png Graphic file (type png) + +Package pdftex.def Info: chol_pre.png used on input line 369. +(pdftex.def) Requested size: 375.80544pt x 183.9047pt. + [2 <./det_L.png>] +LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <14.4> not available +(Font) Font shape `T1/ppl/b/n' tried instead on input line 400. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 11.40997pt on input line 404. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 8.33606pt on input line 404. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 6.25204pt on input line 404. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 11.40997pt on input line 404. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 8.33606pt on input line 404. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 6.25204pt on input line 404. + [3 <./chol_pre.png>] [4] +LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <10.95> not available +(Font) Font shape `T1/ppl/b/n' tried instead on input line 503. + [5] [6] [7] [8] +LaTeX Font Info: Font shape `T1/cmtt/bx/n' in size <10.95> not available +(Font) Font shape `T1/cmtt/m/n' tried instead on input line 746. + + +File: lecture_12_files/lecture_12_24_0.pdf Graphic file (type pdf) + + +Package pdftex.def Info: lecture_12_files/lecture_12_24_0.pdf used on input lin +e 765. +(pdftex.def) Requested size: 449.6789pt x 337.25917pt. + [9] +Underfull \hbox (badness 10000) in paragraph at lines 767--768 + + [] + +LaTeX Font Info: Font shape `T1/ppl/bx/it' in size <10.95> not available +(Font) Font shape `T1/ppl/b/it' tried instead on input line 773. +[10 <./lecture_12_files/lecture_12_24_0.pdf>] [11] [12] +<../lecture_09/mass_springs.png, id=118, 112.42pt x 190.7125pt> +File: ../lecture_09/mass_springs.png Graphic file (type png) + + +Package pdftex.def Info: ../lecture_09/mass_springs.png used on input line 923. + +(pdftex.def) Requested size: 89.93611pt x 152.576pt. + [13 <../lecture_09/mass_springs.png>] +Package atveryend Info: Empty hook `BeforeClearDocument' on input line 1015. + +[14] +Package atveryend Info: Empty hook `AfterLastShipout' on input line 1015. + (./lecture_12.aux) +Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 1015. +Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 1015. + +Package rerunfilecheck Info: File `lecture_12.out' has not changed. +(rerunfilecheck) Checksum: 2BDB89EC075D3A42B038A5DAC39843C7;535. +Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 1015. + ) +Here is how much of TeX's memory you used: + 10955 strings out of 493029 + 163811 string characters out of 6136234 + 270140 words of memory out of 5000000 + 14229 multiletter control sequences out of 15000+600000 + 37652 words of font info for 95 fonts, out of 8000000 for 9000 + 1141 hyphenation exceptions out of 8191 + 36i,9n,77p,512b,465s stack positions out of 5000i,500n,10000p,200000b,80000s +{/usr/share/texlive/texmf-dist/fonts/enc/dvips/base/8r.enc}{/usr/share/texmf/ +fonts/enc/dvips/cm-super/cm-super-ts1.enc}{/usr/share/texmf/fonts/enc/dvips/cm- +super/cm-super-t1.enc} +Output written on lecture_12.pdf (14 pages, 232410 bytes). +PDF statistics: + 177 PDF objects out of 1000 (max. 8388607) + 140 compressed objects within 2 object streams + 34 named destinations out of 1000 (max. 500000) + 77 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/lecture_12/lecture_12.md b/lecture_12/lecture_12.md index 9befcbc..82f9bea 100644 --- a/lecture_12/lecture_12.md +++ b/lecture_12/lecture_12.md @@ -9,6 +9,75 @@ setdefaults ``` + +```octave +A=rand(4,4) + +[L,U,P]=lu(A) + +det(L) +``` + + A = + + 0.447394 0.357071 0.720915 0.499926 + 0.648313 0.323276 0.521677 0.288345 + 0.084982 0.581513 0.466420 0.142342 + 0.576580 0.658089 0.916987 0.923165 + + L = + + 1.00000 0.00000 0.00000 0.00000 + 0.13108 1.00000 0.00000 0.00000 + 0.69009 0.24851 1.00000 0.00000 + 0.88935 0.68736 0.68488 1.00000 + + U = + + 0.64831 0.32328 0.52168 0.28834 + 0.00000 0.53914 0.39804 0.10455 + 0.00000 0.00000 0.26199 0.27496 + 0.00000 0.00000 0.00000 0.40655 + + P = + + Permutation Matrix + + 0 1 0 0 + 0 0 1 0 + 1 0 0 0 + 0 0 0 1 + + ans = 1 + + + +```octave +A=rand(4,100)'; +A=A'*A; +size(A) +min(min(A)) +max(max(A)) +cond(A) +C=chol(A) +``` + + ans = + + 4 4 + + ans = 23.586 + ans = 35.826 + ans = 14.869 + C = + + 5.98549 4.28555 4.35707 4.31359 + 0.00000 3.63950 1.35005 1.45342 + 0.00000 0.00000 3.62851 1.50580 + 0.00000 0.00000 0.00000 3.21911 + + + ## My question from last class ![q1](det_L.png) @@ -68,7 +137,7 @@ x_{2} \end{array}\right]= 1\end{array}\right]$ $A^{-1}=\frac{1}{2*3-1*1}\left[ \begin{array}{cc} -3 & 1 \\ +3 & -1 \\ -1 & 2 \end{array} \right]= \left[ \begin{array}{cc} 3/5 & -1/5 \\ @@ -156,7 +225,7 @@ Which we can solve for each $a_{n}$ with LU-decomposition, knowing the lower and $A^{-1}=\left[ \begin{array}{cccc} | & | & & | \\ -a_{1} & a_{2} & \cdots & a_{3} \\ +a_{1} & a_{2} & \cdots & a_{n} \\ | & | & & | \end{array} \right]$ @@ -189,6 +258,18 @@ $A=\left[ \begin{array}{ccc} 0 & -1 & 1 \end{array} \right]$ +#### Note on solving for $A^{-1}$ column 1 + +$Aa_1=I(:,1)$ + +$LUa_1=I(:,1)$ + +$(LUa_1-I(:,1))=0$ + +$L(Ua_1-d_1)=0$ + +$I(:,1)=Ld_1$ + ```octave A=[2,-1,0;-1,2,-1;0,-1,1] @@ -245,8 +326,18 @@ $Ld_{1}=\left[\begin{array}{c} 1 \\ 0 \\ \vdots \\ -0 \end{array} \right]$ -$;~Ua_{1}=d_{1}$ +0 \end{array} \right]= +\left[\begin{array}{ccc} +1 & 0 & 0 \\ +-1/2 & 1 & 0 \\ +0 & -2/3 & 1 \end{array} \right]\left[\begin{array}{c} +d1(1) \\ +d1(2) \\ +d1(3)\end{array} \right]=\left[\begin{array}{c} +1 \\ +0 \\ +0 \end{array} \right] +;~Ua_{1}=d_{1}$ ```octave @@ -349,7 +440,11 @@ Final solution for $A^{-1}$ is $[a_{1}~a_{2}~a_{3}]$ ```octave invA=[a1,a2,a3] -A*invA +I_app=A*invA +I_app(2,3) +eps + +2^-8 ``` invA = @@ -358,12 +453,15 @@ A*invA 1.00000 2.00000 2.00000 1.00000 2.00000 3.00000 - ans = + I_app = 1.00000 0.00000 0.00000 0.00000 1.00000 -0.00000 -0.00000 -0.00000 1.00000 + ans = -4.4409e-16 + ans = 2.2204e-16 + ans = 0.0039062 Now the solution of $x$ to $Ax=y$ is $x=A^{-1}y$ @@ -430,7 +528,7 @@ legend('inversion','backslash','multiplication','Location','NorthWest') ``` -![svg](lecture_12_files/lecture_12_21_0.svg) +![svg](lecture_12_files/lecture_12_24_0.svg) ## Condition of a matrix diff --git a/lecture_12/lecture_12.out b/lecture_12/lecture_12.out new file mode 100644 index 0000000..e7b5af8 --- /dev/null +++ b/lecture_12/lecture_12.out @@ -0,0 +1,7 @@ +\BOOKMARK [2][-]{subsection.0.1}{My question from last class}{}% 1 +\BOOKMARK [2][-]{subsection.0.2}{Your questions from last class}{}% 2 +\BOOKMARK [1][-]{section.1}{Matrix Inverse and Condition}{}% 3 +\BOOKMARK [2][-]{subsection.1.1}{Condition of a matrix}{section.1}% 4 +\BOOKMARK [3][-]{subsubsection.1.1.1}{just checked in to see what condition my condition was in}{subsection.1.1}% 5 +\BOOKMARK [3][-]{subsubsection.1.1.2}{Matrix norms}{subsection.1.1}% 6 +\BOOKMARK [3][-]{subsubsection.1.1.3}{Condition of Matrix}{subsection.1.1}% 7 diff --git a/lecture_12/lecture_12.pdf b/lecture_12/lecture_12.pdf index ed0f569e1339b5f53dbc1b946df146a0d62eb77b..e0b4e6c98e2ee90eaef7535fdeb037483f391c82 100644 GIT binary patch delta 173959 zcmZs?19TbH7JcVOUrQ83`SXtzme1VHjl1>@8d^3EA11 z3DbaWKqvtv>UuUCjHtdhb#qhw0h(PJ3rk~$2zb>dMM2C9W!2HPPBKJxVHeR?I|`Ae zT$9<&XULAl?@q4Q9V@W`Ta1PT^1Bf`9!*Ir7Sc?tx`b5hUFO2?ElRRB`^e!lskZtx znFL#%Ir%l24wU2?O$tnK9VEy^HSC+16V}R`mKcDh+02`(Vf72KcMIhofzqp1+CZ89 z`w=e;6w46&POnEIyQG*P9=nd9vCEDirY*wuEitzQHxz6I6~~bAKIx2MpBfH{0#ZZZ z;0(huPz-bld7H-){V|VB2`g23RblkXRTmdwf9w<7H8o18b9waZD~Cg9UafaGx8J|$}lt}mfE%B)HO}q*7KftDJ69m^jd5?nRXv^ z1-arXUdtMuvtTf-uN9NYyzG(_Au$Y^+0}e5_2l%Th>{KV&b2y^EkjN-f z2AUg@kATRF8M!SI1?@o6C&-OzR9WF6)VXMwF|~?=dkP9#U}j+&p;O|eqk|IWO^Jd+ zV%)eE3*1{xkAp?=GL}pxb8b@D-C%twJ}C&eF7sF6dX@Gmk!)dx(*i9acb)SUQ{MpS z2P%ZWO*Ah^;Xt%W!e*_jF6k!#DKdk){3W`XMaI##Ok(ckWUzCTJB{>-@M@#+vxAHe zP?3LTb_391V(ev9i?aFgiyx`xMBh`oR@LDrJ-aQ}yWHAN?Fkk@zaI*18~`^M9R&Vg zx48?JaBCS}yy)4zoJoC1COQIjIK9@L6X6`xhXkD2*r1+6OEzvRC_rZ8^EV9e}I zU0j{bjO_mT_D}q>vi*lZW@P>EK$daXV1(^`*EnUjNLN!vCb1HOU#mLx$74TCeL^h0 zLeH0qF9vP>d{aX3Zn!YDLI-6cOCS)4L^VU)0Sm7JxqqK2ZhtXM7L3Q|jhyIll=o5{ z3`{fpd8{rggQ+SB_8K#T3CWQZS2$?IT9KTxtH+#C;~o?_mrAk>UXui%=Q);0T!r|S z`fygOSGD>hL5^immw5GGnV#cjwRE%ftQtuI%mQEjEt zh!U0Q$uRTN#Yh}HK$igS&yHM(w~b~Qy1Y4hdHFt5l$nOr%ezKyx_ToqZ_JLsY%PoE zF{((++?6Zv{lmLw_r){TFHZm}7h#-v+C6p;Zr^vdiSukf->Vk|zI**R;SG=^t0H7V zR+o9L{DjJu2v`u3bjm%&f2d`KC@13l5&I*mr=sdnSt1|y)+7a37uo5ugFKipmGT-} ze+^_*<|3{%NzSBQHJ2+Y)n_m|c}+uO%QI1!(HkNJN?uXKUJ(DpF$I7DCq@{73Jbz} zxu0N)rxgpwHK4a6cm`1NCBXQWOHpfaHJ6IRZ?E-!Jlgb&fgT-?ZCyJx=$FiYy7$N~ z4B0-X7js2*sblH)=AmLT@R)|lYZKtIG^0G2HBhxPVcQf9=3=IG7jiNdpHD^yWZ#kwT+v8Zy43+QDm z@Fo%16C_2QkS94wQ&#O8273m?B&-WK`Kqq~Sw}!Z z@#vZul zb@p5H>z>l_r-txvNoV<|E~XN#Z|7-b(mkzj=9jE7FcaQ)JNm>7Zq|o%XWlM8R6C8z zPPViS@vE82$&K0S<$7DbQ>*sig5(l^S;UfQAmqayWZy_Ge?YbiKTQ>2^5?aCh!*N| zM~L1UkN48F6gv%si1${?#b$4fEeyveN=qfo35i40j0ZpOayOy8G76qAF?W6`Raawg zYeiK|Onx(%-DHjUJDy1=zp5VQFnV-|kb4K2dsSwSPTj*gZ7e7m$H<#0Cy}jzeP`iX zo&q!UexFL1^?`{V&D1GC&nQ5BnC^?PV6j9bU1T-cm_{Ukj@=8Wlk=zxNe3%Ddur1>iApUdZX~QnP_F+V7&iAa-y? z7k>d+&m_9$rmL%sQcKb?j(n=6XR}KiE4Uu(cDr8)w&B!?Z_EYUY6U>Rj~3_LV)NWK z94-)cP30ujz1O6~n0*`m*v_DLo^(JkdtR?BI+e#WdeBbUl42gyQ@YZF8Ef3oTJc;- zes+iJQQlUa>(=H!triw#3>%ShMm%YW0+hwV8`(Kw#CCR9lnt-1XQ;{+%&pn{lF%{^tIv7WC{m`i_P3?;(bpOFsN7EOWM6LK*kPl<p>$h6gu3A=x+MNjqO39)cJr<{=HpB%x>9q9hq+$Sos%*$*g}7vBk9 z6oQuOgQ80rj$0Q&p}cqX$Di4=rCUfFq=MjcVZ5)ML_UDZ7|qN$590zdTpy0EHRA&4!vi{IWs?2!ukFT6RiX? zgXV%5S6qaSqyOsUd52L4Dctm5G!FYec%1n!W?K9UMcFx0X zCuQd7H#XfJo_;*Cfq_2gLgPtu$rq>Z52!Qu{UD-ds>uKx3`8K$I-9_{rZB4>{1hKf zaif;zw1=bN&d0z)wd#P3K4yNw|9yINc3Ou7tj}mn3P%xQHt1{@uD2OII}6@599NgI ztF84%F>;$xj4aWRVAY|>fSQ9828R|$*d~4Yr;y9u#?=5gwFz%Edt-uXjQpU5$I376RZ5Mv zl_9F+eQYKg$pJL)0;7mRa-TE5ls#fFax#joKblWNsv^SYKFEn zgdd3q7W2mq6R$#2wJlpCd6hQ-G3g=fn=~Hz4l&|7?@p%{$Aw(Sf8~$KScI@ANU)^6l)Crf>U^(68Mjf$( zGXhR-Z^a-9pwV}C{8d)%Z(R~K+cIs~wfu1i=}09-Q?L=>6x=?&FRY$U?PfgmUhd<> zF5`s&hfo~>@8|=V^poDwn^SeK>_TM_!!$w0u3&)$#zenR(YcD{+X8Ygc-oWA~MB**(Zb9QpnQlyHx=^FN?GkG7|{5h|}gayG@=~3Q@Iv#mX%qk5?hdOZFw>p3dFQD1!B;2e`KVVQI~R$ zT*W!fOcTOJ^Kyf{Ed}jlXry3rx+GN9wlLoUXBkr!Lc0cMk{O}#g;JPDVg43CTu9J< zk1(2qKpHvpiFBCpn(Wwo@9vB}VGd}$Q;t+Mlg3bzNQjmv8Z3OD&_H=~s4YBLy^5{x zCT!P{-d!1|Az9x{_{94KRZdZXT53X`Vm)40+`dt-wn^{G*83#v(g`S266eN1HpvtR zVM{Rup$j36N$T{+ zd=<0Wrf~S+qv006m&{NDKLS@uF*c4N9Y$wi&5&jlX3EZ!<50!za@?l;o|9rgopZF3 zH2a;qvf_%?P}HWT(=hhbyyJxapi^50{v7W4t(jj$9FKi+a(>=+DLx0VgzUS{GTm{3V4$ zb{^I=sx0zN86p(pc6@^_fXYi?z!`ql^@rXmQBQus!)*&loB25%7eQW z4Mg79&qYr%W6pjGMZ@RppB9i)Jtf)%59i1H5Canom-H)cb^Sj zVN&dd!wfx7bln%Q-l$--Xm4u)tPZZx-BczJzPS(9RHq*2DMpL2CslG&H zH3#Dc=LGCe@q%XnJoi)R)XyQa?mg!1arxUjUD0GgX6G)6z6)%2(LS`d$s&e(2d1yM zuUq?|Dnb`F${2naoBB`eM+4aJ6B2GzxWiA209bzF))^imw#zlzBAfCUwc zctlC6S=ow~5+aSOc{!P?@ewr-!KXVv9K4AWv zGspj9|1mA-mpF$f%S3o;ysmT3Z_-dr5g8aU%Y>u+Kp3+5O_UbbX>8QGrjz`Q2`xXi z9^Fj=+FbKrO(P#kI`razS&X`-*BFhfS9VJ8wx2otZz~fYlix4*w~94<0<+`~o6uq0 z5c|oaQH0Xk41bP~?Ds9v@Wh1k_yMnCP?;3IhT-P*2{?o8kKM7L1v4S9~64fIm^p}2tXehhjB7feLBN=fM1=U+g8u|2kEQ{g$!Nt3UpDWI!wZz2;MWzTO#bQ`#es{KX z?*lDY4s;yANuy?$`D>*@ncRj-{Tw3gHbUN3lyXp1C6Dr_LN5d)4?@>doooBG=HX<@ zauy?F*xL9sJ8vG4K*@pEJlWkIKP;52Q)Gf}Ftg6jLwPr!kC zfoH|~J2ne5J@n+8TN{c!7kJ{wIfQ%glc9r@>e_^TqcNmJ1wYk)VgbFY?-XCX-2n{* z>xW!;ktL`Fegtp(xC7XHt2bP}oqO85s*XWFyaj|#zMqYx`6B7lLPqt5W4uji_2+jN z1GZYF+%_r^wxO7qJ1$$z6cDD6thBvZun97YP<^J-9zYFgG}TIVw#pG5&3~-<+KOe_ zDa%ReF?4679^D20QB}#|H9(G~Y;^{c5ks(J3n5VVSfQR3*Z`c@Dw&|oidiulLSh1R zcp*9IkH5}F&#{y3>*bGrxb;>oKE{-dYdWBUv8u)}-8(xyI};?!wQ9nMgrmwFId|+I zq6X{i>9l@*%~`3U)Kn67mczYf?gvfg4X(kzTZXII2 zr`Q*uoz!1hQ33pQjFvXsX1$lv@wa3mxCVvTt`j@h;s~PerX?z zPMMwROnV1WofLXe*`lqd3xuJ!Zl|!4wUwhKvy!-whY8EKDqZlu z$PUGLrffBqpTgf7X#jjaMRoBWH_*hhz;GULX4{?0_wFb6N3(I?7#+sSY<<6v7`<#6 z=vkbQEgm=-$`q5-ezkAiMOqB%@a}HHxu48m2V||v6I*#d&qHebq(C^ij8WxZpBN*+ zL(SR3I0DR9GTue16LI4Z5U_>qRKCOo@oJZ*zl#KQTaHX+eX-cdR8Oubri{o#LIANO=|F`pKdzW z#~&&#?puY-`467I`-hN!>X91R@u`&6XF{8;<|yE6St%{=anmfZO9rZqldDKL*4g7d zpHY3WzxqQKlc<#3>XJ&qpPtIj1&&%A8`X`WPh2b;x|Xj_bNM^<92wHNFY)c?GNJh6 zUV3DbV>ZOK+_>FU4aq`A(q>J*xtZ(FrxYDA9Y6l9cZ@Sjx~Tun57^c)oQ(fr#l*z? zZ`tWDKR6t)BlezX+*)EF4Q1?!$nMGnxX%-x7D&pk@nJf)@}WY<(`o1T^@{w}gQA>i zWuz|M{8vl4>Kr%;DhiMRP-OgiC9M0SQrme zIaD?8=|S~Gks|@CVVQ7FzmLyF@Ty7?Cd!(@@`toC%*!GEiLel-cfhx^-Z#DwIzr0A z#;?iW^ip`G9N&RH+{jCFv8f|Rm{yx9<`4Cq0>Bibl++v zW?Z2CD@|sR1)ca&Kj%e0F4LwXXwyW{K5ij^byv(l+0a&gV8A`p`H2*Aj6L`?N!Y?s zEeItYrEM_#hTGckoV>1~%Vx5BZ&pccHYGG$?VMHy@H@nclV?=%-J-6Agoz~$bWiycqrilGZ-D82N3)lh z>LScAww%ARqs!!>;Sb7yZo+u^EP49MLesMSc)L*Av8|zaS)pn32p5^@_HrJg z$9BR-l(69vJmH|uW;2#7OrwW&&3VgJwXL8as*C}aY>wNU=n}_v`%`unb1xG*T=KLE z!{yX$M$kV`rbd!|7Zg*4YXDHLL@@noTeKQ0LWX)*Kcv-`$JT)1*IEZL$Jh&M;2W2j ztuAqCc+{*w!zV$XdrF|SUzQ-9rNS{nUdq#*{V6fEHBG*)6&b-POI4Gg+UU7EgpgDz ziI_6X%2~35I+9h*&1!6XbGE(O84Qh>btwBE4!{1r; zR^-4trg84bQXJzC6)P2&>TsDS0|{Byb-zJ}ix84PXOgzeRfX22OEMB$61L~s+2uTC zv&=!O-jrn2l7077a33v^B@MG(_LS)Phdz0 zPIH5dZ)xMpUS{@5!B>qFQo^z%G2a#zlbrsJW$5h9*Nb-UfVeso&IXoM z*VY@|fZQL^f7NliHPVBgFRh7_cE>asb?TKKJu5N4&aM{%O`XEW{|!xlk%^TM?f+Ph zY#jgP*j#BVDFiVh`t8)6lCUg1d0hde^`y6p9V87f2^EL^74OS_3kI zHnF?$()HfKBQQBkVQkE;zkKJ;o>mV;F=RCaj=v50nf;SCU$)#p2bqgWRu4M2DcgRK z2gC&%h=Tr^^2diOm|`mKyPvqOAhnodv&`425@5L;A;mNeGew`jn!@@gd&X_WE^kVg zugpw@Us7~7*Lx4ZCFQBik8oc9ER|u=+)S65ldGaiv~x9)`qgK<2ax>8sUU0aqLL6j ztKdx*lBx=wil%!mDKhd{zxuAjd|p7y={x0CQ}w&=_k8~(Ho6*)*bcM3t=8SPHB85m z72rk=&SPLO@q)6QlBT|yj+TyAd)t{pM-%sa@SL*#Mx2l09-i~A9Bz0By*vTtml-iHyGmG$$J>Wp`$Z8gK6MiY8CpurC$n zw4Sv#<7(LOAw2D%@xi9?rSy-k#qoq=LqGw$h;hgWXF%^Lv}^5`H9Cdk7iU21lHsvs z-iTD*=Bijbm%p4C7mdqsg#@Nr0b1SsqBPwU&b%1st+snq&Qa9u;}HSQYvE-C=GB8( z<5{P%fu|tudFPi)C)7r1)NS2|_6&qtPq5Y1(+~FjP{-9e17n$8b7)dX8Mr-3IP07= z?7;+VW`O$8as?4?MZtrz2&b}$MR-yIwl%mt%C% z4a5#;3Ii1mK>2?NIIjOog&cns#ec*@YJl87{$S6u#%Ve%nuK&Czxv@EuuTJ=JEpTs z*TB#MonQj0TpQcBU!oaBDovSF7nr1Rl+TS)!E5j(g^0Un;LP*;>%_(nGE5>)*WqK1 zX(;nKU~0fqP)d@tyr+;kbC&)u0j7mrNk)3u{3fPAprI;#iBT!x0$p8Xg|x_a0P!=8 ze!w}kpkP5d1-ON4bgyP@N6Se+U^$kgI+@+u_Q)A(xbhdgU z`VNC6w zBw}--vm*l&X{P07h||atX_DyXvK{*{*8z34 zKy-F6{S8S)ooRagnm7TB0P30=ZM*f!LiJifD%U8%OAnF<3|AE}>w`8GDAg!^R~kkm zC^Mqr!eS9R=T@Xv4QmHn^khb)qlY&K)|N1XsO*&*2WOLYE(6$>(Yth#C|tSWA?`3? zkZeTnu|w%*O+Jc;&@i6PH6ZkfoD{o7p}Oe+;6Y6IA7}}f@6wr1|a+OvA=84|81*tvHpjLhLPppw)&Qaoy>gU_@$EG`SW1Ot(I7-{gu{zeysrzEEGS2uL~l;#(SSPUE&xpaDsUJ2bN$t zo}aVUy5gci0u$nVLD<{+Ey7s{IQb=}%M4vWL8gQ>KaMwMEP%M2Z7~FmX;|3g#{KZ0 zOEt$*I054nsDkIjmmClZN?c*t?aRt*ij_V#C=Rx+Uv;~1&goVI;K*(n_8?@qZYYw+ z@tT{6;9lbo;TDaSRKh~@do|EDP*{a-P(qP-D}~|8)4@d~Im4Y10{i*#QyKz(J(&}Z zt#OPNY?Ecx5YVx&V5u^(zZ@7cUpv(W^95I?ya1?7RvY@oP5jCx@!DVT;cgWRCzu`V zD`u0a1B93S_ak23R*8LYx#n?ncGb$s7@LANBy5j2#p6?ce}+3paqBQFoKO)DfhNj% zvx)&pD3kL) zliP|!ZLNLMHp!0tmIymr9m!_Ih^$FKlyHGIuYm!0bnP=+upwq(~5FF9d-WWL4{&H-@Dn{sHg*VG9hqtAz zzaYw6&`5erK$xCW^&cXh^Z!OX6AK5+zda@`8JE9CeeZ?FuBCz;Slvhw3xB)Zrj)tY zxM~|GqOByr16mSkjUylfVpEebR_q`|%$0lm zikVVy){LC~#u%rCL6U*Pz1aa1Fo3&i4(zlsguc@91AkekGo1n7d}=akz3FieE>LYf zyIU)+G|4I9*H96`&5bRV>bD#|Jpip}X`g6QA$5d-r{bc zmW4;()mre*Ch2AJlY!w#OAS;_>pOmx-%DN2H*}B=p?F%FQe3g9+A8MJ7H?s3(b0Ep z9>Gdv{}m<^zxh`!Bs=zZs-Zj zqv?ccMd(gqCF`q9?fwQu9KdHX4D&iot+&#(5n~q;R0WR!DIz6;!GwumJXH%NOnM$S zVtfa0>gS2EKJVcoHRPu1I>YsfXVv8dv(y1BSc-5Fv6HyY10xFcjHO7%Z%C{yC9%s2 zI4Foz&t_5k z>-S13ZIx=TuG$*i=74^)j7N;T$XC-ITM6=s*vKK2Z^m03;)N`ffPuvc{JlYBmYEQoW-{24F#X1> zyVL8a4INaK#|&x*oSZPdc1M}mzN$wiL8xjSUCs9~H%$aeM}hY>%HAmsN_U&g)Y(40 z_c_94+`)%{8ohHzLxH-L4ZxRN#dbEY3LJiNGSx>bd zPjs{kz7z}+RhQ?G$CV94lup^HXIvK8rSi1VWB-@tRReb=nxA4vMST`g2pM5BrNXnB z1ZL0UW^Fg8lwus_(73cdzjKaY4ojJJ__x#iU4o5+CMWqg>n>-j&+#N8JeXqW7Ct!6^z>e%&js zor4a1k^YcUVg9b0fQ4WeTPZRhgOhhUrHpU;4HM$<>~{=3h(mO{w>siV)&7~j1iu4& z=(P#W2SA{EYMFk0J{a6WMHbxp<|4%UH|RWR84bDW{RmdOcyLm15+(SxYvBehr^3Ue z*7tr4*1N0z-o#LQxO$tFw$qEfa|^$6ZD@_^)(1_?Rv4(cIDurq*z(&BI(p0i>I(i|Fo)}j%I{RFbs;SVw&{gR<>sHMs{X|l=KX?W+tv~ z&SnNo%m(IvyIuZg2Q#YyBfX=kIn}>^r)XqhChulvZ07vmLrK}2JBV7DxDqn`O?4Ov zm0=i!g&lqp>ii?7u>x2*30YX!^&Uj75nKb zq2g-fYWA-^BgTJiM1=mihKbSNmY@Ic=kHzEyZ${w$Y4&#NXPhhtbg(?<$oRf?|NKj zMs~)(_iJVA`u8s~h^KuJ1ET}7Q_|%e&^ZvtZoW{xgGE~X03GU;)I?8$SvdRg%J~J* zbit{0JDzP1heWohM2#kOCpQ^)AKkBqgP{U>I}QT6uUDTrG;Rt-4pgH($qgmwe~=g5 zktEi2&NfckHh4}rK3<3L^ln`Dt`7E-k&kqE?e+3rIczHKHf zN??M2&m*V zJB7P&_h?;f1-<~!e;&4;b_iBtQ5|U#{QcyWqja!^1yF^@Y@mPwn0tkOdJp{;(I~MS zMG7Ea-LMJL0h_>L;$}3|`Xk6N9TI|l>+4mBWt39N}Ph}U2Y4zFuR zgm}NoDFksLzM)3fhog&O*=#1R5z7SEwlhCzDR25c!DGn1$n1C_bb_{A;>0O;*m<`+ z&-^z5(az^fF|Dbe!=+S@ZL#Z01kD~OfMrWENe5;s(iDl3S-2va2j z!(RdzoUO{P2E!s-!8K$w{i+ofDda2FU1Ql6J;abxgj~EL|N+Cgm zss$-4k8E^AjP z8K23^))S$6#T5B_V9g*tlZ-l4b*6(z4KDQes1Zxyc@vOYTs3fuGaI$S(Js9#p3)G& zRyOBqGu>JfrJNojlp2%L*Pf+3mR4dXzjA9neZ2`aj!CVn2oVjZTm$)sa#w0TbIaM$ zXntjxcDnQy)OwgsdL}PH0JK_jI7KKmc5>tIk$J%vCkQpht%H+YA6Xykq?|`qR}{Xj zM6;n2R!RZ5o9SPkWa*E#og+^_B2l;iuU23ve%600k)L7-Z(U_7V{(fqt&{&Y(x|!a zEr>t4Dd?qc$W%_px_aA9a6p|{1C z)GydA^&>;>fnV9gq!|#v(3s?+%X|Dg9zTRj5k|tR35Vy(+=&xbchyA%^c3b8%NVgz zPmH|%H6+y(DExwd0Hzv;cH)8^g@R);K3C9`pICNwL8A~XkkKbVf z&BS3A^H`v&QQpp#pz;;eaL;2vHUy$O*51=nq;-lq9{sdxtff}1H=pq`+P_=dhmo_s zm|5jNq^9y%k_)3CtzKPXn?FY8Fyb<1BVf7C{w$Wbzn=+aN%goBAXQiv0c1H|M1jyD)oUk7vL=3&*9l>1` zIV6KFPBg2KX5e>K+T!CdrY*Dm+&wVa!pUY+RQTeCXM4goH!pfd)6cJJH+t;}svpj&4oafH6&aTSN z%4?5{?VD|ULmTC1U~PKw~Y$BLt*QB+m#g1;H-+=`r8DuIED=r z=AiQmRfCt?!dDmI*&0CE+YeR1OF~B+#^lkYu|HJC`Szd$25Rh*uSgscG>{LGq#|ME zA&CCpl5fIEht#?N=a@6k2vQMg8SgQ;{8o=3R;gDPM8o}#ZPGW$pi@_B5CuQoWB-=_p zz8QO!l3~{R3Pgf3y%IN_HoKyoR=bsSA>AH#IbAb|T(b3HDr!60oLMAVKEg=R3`z{K zORLuG8bgI7>OGRqOHd(B+pt}!2r*<+?I#GyGfBLZ>*(*(M=PS!9_vK5yu1L*_7wsK zi8EU>Ygbjl6DUAA8afqF743x^TdpGqOCe5l<-StaTJu}|rPWjHWtRm<;JUY~>umE| zyzLd%N0E!9g!L2|TxRIigG{BR62sbMMnyrxtmcLsEgxJqe0U5_a{6Au1elm7 zLy+uo(gpyd9lS!mYk#uIc2_Ay1VNT4nTmLH#mKa;a@B99mw&rI`)?~Q;+&nIDlN$M z@oEI#pQ?Vf!~$l{w<_s)lZqe8w#a_%H@VUrqJ1!Fcoxe;a4E+o>TULb;j5&IqjjXV zYlvtao|iAxE?x80kC{z{=n@Q!V?r0%8-G&I&LsmFc<>_Sfz^rdE_!od$$hW!x~8sq zK3^jLtQjzl4R?`@q^z&6o7oz8&UL_*O1W6)-#P>J5MLiwVWQH}K;7pXW5McTqW{yIuFR=x$H9`lmGHgh< zCvj;V*)V2NL_$Wv+Mmww@V-9ky?$6-&gqo^)7-wxzf3W`P!sBt^*`1CHB6Q|qTALNY?9^P?elUw#gkcl1P2{7+_rzO;4*Sl$B*&1bn=b2bx{OR zKR&dARO=?BdlwJV_Tq~aOsxd{GZg$1hwlQ#Kq`ij0@jHKWs?ZPn4mB}UQ?rTeQUv~ zq=W>DGRa-^3aT-|i;9Ki$qTV}&r}Hd%*rV9>}UES(byQ7X*4Dl_bmukTC@GoYz_|l zKw+ow!t$rU-q##N^z16iG5ZG~rj}Eb51sNjCe)EW1#(Wy+HY z=jKuTCRaJ&FwT641p}9T6k3`@6)%KqlP@ycg|3KeVC}ad>Yl}bAwn7bC{YLio|{Z| zuBsW>v^7n{FV%tdS|o+E^T-sRraGXHx3>LrJN+Bfb9RTDY+WOhBYX)b> z6+bz$1i3<%I)z=DEm2=*+#g~MS{^+_>7MYuf>buK=M8q;(8Mu1yD|?fX%#h_SYba2 ztTCN0AeO)^`3sG4Dj?!XivnY!FKtAy?) z@B?J0`f{%;#p_e)Q_HvRi~N3Z&J}c|@&zZZ$$PD5Y=lqGS>Jqfvlr8v1N2o4 zsIKCv0wETh*;~uzEA>H)xjSd!{I;R~jXM`vj|##fsrR_32cv&0Scl4wLf=@=l3y%I zqY@b6kcB&O*U`rZM!Yxxh8T}nkGq0SRNqLWawjBOSuuK%YvXkd3tL9S7-wy* zJV0XIIcuMqtFzRzpUXx8q{3|0_m{|iB z_J|<1j&&aTc)<)n#^<`)h)3G*8+xm4#AeQm71RvZ0UP;EKS@*CmG8fZ!QL@5BsCx+ zCo*FKXA)x~XEH<1@KY<0b(M3Km6UZPVILQneU*iid?E`qD_+x_mL(-)iq;)2fRsvn zB-p$;A5BDYL^4_!qw~m8#8`UarT9HjI#D`_ofJHgJBb)DUX1>nP&KN;BwIvA_Vrdw z9AeeXme?G2QF@c1qQrF5aYx5f_hmGD7xqJbTCc}%K>vFiBipW^J3=y^iHNF0(ZjjI?C)GS)TNs z-SO-`SLrkGk%vfr-gsBuk(y zGR$g}9#$Ncm6K=f114f4l&qgant^RlG+3XDB{BDv^-5~tYW<^ZhS_%sKrhi(@_csz zBWD|p+ni4OG1Yd9H>(*NB>aX$>CP+gTt)O;uRb~(uZM^0!C>n?G)+xRcZ`SvZ436; zR**@L>@e!wS;9zF424!}b-6O(Gxclvj^s36rD0O!GYjiFfv?-`u|GgRhyYs{EzQI# z!|QdKY%m=PsnKtYR7%qO6K`6|0j_<3UPi#tWWZaNQdP<;x)Lu2M>w&#(h51KI}gx%pE_Si9#HHu*qH>qc^~L0@1E#@Uk4%G zNi@DvkYu=#2Rl4|<7}3;l+iCvwGFR*vuxZD&M}{!@_(NHKepa6IJ0nB8;)&GY-eI? zV%xTDCr@nKb|#wGwkEc1J5Tb>TW6oD^HuGC>;AWDRrlS!`a)-hT^X3-MirN9%do#M zFNq~z4fW%H6A#-*z<^R{pRlD%_%!q{;a4hSz|CEx(q{{hPZ9{JqSV38ZEbDMyjTZd$?VT&-90269|IukC=Vkx7fU8Mc(IQQ(pw+BqxfRl{?; z+FwcK4~#m~Y5CTls5a$%+H(M)H6G#))S-p%9D0bc2QAHwJs~bXUCP&bu^Uu4#dMYj9UQ0d~xx9@p*eo+n2JV+J>PprHU z$l`>Bz+w|9tt@#DWT_~_P_$Ds)-~N{t`BY>bsiGGOM*kWr?|W2;Ss>ov-NkgV8FDY z*JAIV-d`#2tbo(+QRrfJ0dt*Ib#*z5f^R;d6W+^Q0FUxQIfp*fPYLCq9W;=40P}G# zU{w-Y8_5J|ImfV|+Pv3jD2-(3P;h5LJ)&T$|M6GP^LKWznIQOIPIhL8pSEV573zZ1 z(Ula$SK;jSDcW(3>goUz#Nrmczp&+J)6SN|+BmDKlI7|F$n6jsnjH8A+$=P#6N@w~ zV+%*%_XzDmJ=CrJ)a{b?$q$F5X>q)-^gYqils!M!_VgkGq1>^e3SfJOTy4`FQfnNs zHtMkiiq)FF5p)XCtP3(so$AFDh4ZyoD~`w=f`7U)6n%00nO^{q>!JIg&Gf-j%On?O z<&x;u-1759t|`O%;g!fhl7CBORmYAv1d_7MvrfSXOP6sZD|mLJeulZL~6D zZ0By3nKNp=C&LX;;EX@^*AWr5AxtnwDFU-B`y;CayP(+uMJK6T!->1@s&a&ZtH64y zj%FPomH~=9uflv83}iy6E=V$m+gB66yRkY{f5SJbHC2$=5y9JrlTsu$Ak|AQw*0Ol zn5WS#LpJ%NTs^%BoBi-^bb)25}h$6~(**eE~MnYwO1QzlU(KD{V#w``c-V#)t9=OC@$?eQgi zqjIitXOgFk9fJcU1eM~ff7yNjoV|g^c_A2jOq{s!cVai*^?wS!-l*XYi!Y3K(#%gx z?jb~-15pP!Jq6eD)^G#=Y3Yl`gyB88Qe-Z6$vQMtxFt%XqyIo^3Et>~1B+nT!2T=iV%<0ph;xE;NEJ#0SRq}_dtKMTb ztA6YVM6kd$lHg#W$w&{SGg@mW<|_Z#I)bWP-0_h!Ob7qo3J1syR;#^sWA>tZitQTs zzSdy&Ru0G$>HD9X`)lo%(tdWp@pjx+GkiAoF^=wHqu&gTHuglW9LScO~3ETT@^6j6Q?=kWZhG)%P=>H(oPSSN-ww zzPh9Hv0i{V(&kdVy5StFN$}Jp^Gt!Q$aRoBK?_ z;^BN{c2NTz;B2uxH4T#y@g{w{lne(82fF}5yM@8+pMQ<`RB4GmQ{#!Io?iBadOzui z2vJ_eF|V;-JNmo>dokJ=i3}QzxAckXCP%xQ-FsHTo85g=L;RcJUtl(WI;QvKy8lLf zoj{@kP#}6}-W~ZO{G|(|-DIfu&dy{(+B6@jVHCTsd3&A5O6|pn)KT@Fi(rJ=)HMU_ zWkafK-Fo3Z`eF*Sj!)#{#bp0}wZ*pIbj)zTXe(q%ci@V_lRlcT@aBEH^=^>acoA^fThRO zB>lVd@sLXQHVav+8>w(;;?$Ci{ox1*?K=V^YTajH6)+zv1xt4|Qo^>8fYcSA59`VQnZi;130Ybi45V{PlnmnVP^vAQ`KyZ%GsmCH`K&D}33O z;l34^1Cx<;RAjj}({RXOIL<4;5i=ae(Gr&u`R?w}7eC4LM8r44bhJNGK;YF}_HmCm zKN1;EC?6IbVgx=0zF%_y$40_IV8pdBoY?c8c|FK}zCfp-8orp)kX(%vQvA?_%ZgUl z@CPDXv}n0tc%NdRyLUgsUvW)4bVa>Lk~d3COXhH=XhGI)J0y{0!Qv=Gs6cOTIYz}3 zK?)+X^OSM09LXALYPbqr+%Q=&lrdb*udH&d`|nWjuU5#{a*0O($Uyft@V`u2nOXkJ zq?L{PKP0XtO&JwDiT_99nj#6O7>?^aX%Cix9(K}oN)$2XGNPrB8Q8{jf=NJO_-oW0@9)30u)yCZz+&j&tqA;fo%gwmc18%~bsUpt$iSQmIw&}`nwmj7 z96J(<0!iq~k{f*^&6h(~E+om+OZo0a#D4g^=m)%w>!6jb4+NBgwWCy}xZPVRJL{(6 z4+E(&vJBF{qqCkLK0z8yIrQVOV%LRJ+3nOUxnV|?Q*@IhLVGlzD;LLqw_)ukI}K+s zlefmC=BZI%M?gxKy%dm?2__SjQQ{6An&N{qOVYBYKhkNhl!=WtV%`~uR-WQ2*|fX1 zR0EdnRCQ!XHv?@!=x;vZaWn)$ohw$@O?88y|0o6oNnOic;R>SLP3DFQC+ul+Iy0G9 z?u*yEQcyecPUT=Ixd>uHJ#PJ$4IFoTtnA93Io3GZO8>n7)AhmDRq1S@`4#&BpD%)) zOqxo$AjbAkHd&1*{>R(hHctmdg|GOF{Dz*8+`C3GkkTh=J&Lj&37G zgp8`|>sL4Dv>G9yW1^A(_Fp`>J zB{4>=4}g+LEGhkSz?KR3C_bv5X;;cnip%!*YcpVnvR-%*!hq}?16y1y&E@7v>IQI= zH;VUz1scE9P@Fanqhn6(<`RE3qo>=fFO}_5M#$^vBA9L&Na3^c(M`V?C>9rFhrl}E zoV-?RbR})lR??NYiMs@$CniG;xs^$k-bt6hK3h^;E!-R)(J{5D{uCiN$x9Z6)kYHL z6S9b{y%lMh(6G!%rxc>f6?21N2Mxfe=)_l?BPdg`CQ!mv`;94~MX0*|X>5lmA7w0^ z9q{8wRi=(N+NlOAUVQS+@v$aJWgG~)$8RV5T^9WvwGU>bh9f`vqWcj(Co3Km))JpK zfqVwe6S}O#t&gc40g*)x-nRV38|9FZc^G8vE}feY1}70zrz2Wtkv@qThYfH8)^s-P zHR1K?NPA#@9Gx(=DRG8iZYI^(_(Mq1wJSS^5)6^!*sI5m6lo^=hk~xyekCro0=n+H zYhakr;?@~xMO_Eg^pF4)@$Bn|msnDw=EGMzv+-3oW;W9^aD~DC6lv;oI(mE_uVolP z1UTb+*PAb<-VN}{o|NtrwSZj4{E}Q60Rz$eirjNA(XY4tH_@v_J>J>qFJbUj<#ai5 zcBC8vqP)D9c!lqr`HToDf7UyluYzlSE$s&wIlQVW&d;LX*gowJH3V`aH0-v!f8M(w zKI6%)V`1%(r_ui=KlZv0s;teI4TjYoqjjvqblNFrqu>pMAzHVvnFG%5#5Hs`F=2E; zS1naHu)BWgY@{b3>ewn7$hSTn#nu0gITuW5K2R3ent)QKIKy=n*b%fr=Vv`&%Tv0C zwXevoo}Dh66VOl&qxD%?i`~4tq=b)0jIqz(daPV>sc(=eqr^~Kpj4^ij#3h(SLUs` zi)&Yyi*Qq*no5%w4F`l9;|K9HE?+t2TyCN+3Z@cq*=`gZL~vy7fOE zK;&614Vkl}K%()Z3@6ggqTC2Ki>Vf7Mb7Mj&EH;!8!8cKM3|p(*^3_Kt~=sWu%5ZW z6>nH5Z@IPJ9c6K=f{l4gsWjD|noi}Mo@JC?g(+f)8N&S;dFhXJ`Z~Kd*{Saiud>MY+r6(JmVYry5peTF4n!+BIHQ6 zUy>TsZ->o%NCzZ-S<&~fQrC~(8Q&DJRg&go(tZrPlF|0azpDAWz7{0BrLO;9+F_%P1HibrxI=SdRPSb-@8WwKY1SCJO1 z?EC^-`#*n$n>%8aiiNpd>wD%sNW(-boRz+bf$;<`AR>z@+=A@k7a*}ww>+qwsyLej zY$d4{EQLPzUVOXCWIS7fQZ$QXt3(W>h!}fah&udl1`}=)8(a&h=^2*bNP9D3sH4hO zsFE=f#l0rP&!Nkwb+rS~6;|)tGOm;n%}SR}%UB$b=&>yXAxEtlUCTdCtfH+>DS|7; zu^1rim2`q6_V|6O$$+S&K#36R7`Cwxk*74HZW`ts+9Iw)S+3OwG4|5)#CPCJW@md% z_1V6^lE!sIUgw49DX|-&aFT+eay%2XhmGlicLHpxHqiCF84e9H(Z;B$t+LZLMSyj< zqaM?-7Prs|8|jJa$O1fAJc1`rpdcyL%GcxL%((iEb@3k`7N8eMYCt~}KEXb6M2L^J z;QW1~;Q+kx2kQ?JQr}ERjn~NWAdSim#Jbou;A)-Gcv{hF_Po8)S*kWOtso$c))^a{ zts8{>#acYiHPB@<7lk-Ry9w0Zl2{I!cp8$rAxxtR`r(6M6_U*ujat*@$P~(01NSs1 z;}vdZ`*pSJ4lwT$tDa>!3)A8;vULQy04An%z+N&r$=wOqKD-U5)OuJi-a#QNGEV}q}=^UJ=XW+D>G<(^KN^qdghfj zUAW23<#^e*8+%7R%s9ezb|$ZCI~mI-!|&+acpn{{2cUOk21>Y43S_aSa{?5GJqATO zJWpOPNq_Q%HOXVMbDN3Zzy{y&cU>V67+_r9+fbz|p~qFNi{9YgYa$IM^db@UW98O_ zJ19*9Uu({PDKPnjyj+&ob^cWy_d~Y?b6DRR%Kz4IvD_?r<`zIK&mGifRxU%%65U85 z%MNr41`zVb_NATlV5S2lq}0UHOxQoVG%Hy&Uaq(~#8W);waaH3&@#DC+MP&qLA zgR#RJ0VEv{hU&0~U-i^CyL{A%hD}INMpolMg1hV!Buz77(8?0$=dIq1lz#uYGxbVR zwBLWS-N(I2rxG2FuHKNk=9#z3!mRZ=xITI!0UOn7aOd>x?fuHZOkS)8xbx=f{#>}( zWV~kZ>d=-`-*I6;U?{DfI`!_}V57J6` z!m>twYua74O-`OL1|`zxm8>-C8Ee2gJPBAGRS0V~gx!V(=@bdaRAP#(OJp=z9rP_& z(y>0V@Q^|bs_XtK2m1B?Q10QcIe z&jPLM=)`O0vx`@t--i512*$pn5Zq_x4LH{=u;*8wlAQ*)$rI~@`PazaR8WRW4`;XI zG~^diGddm=QJY{YQB5=O8PljLCD6kjiuMPu;-`0#GlZFkmkpBJys<>V#|97Uq&JPH zf9e+2mE*mIo7>6Ijp!&|%!)#s0noqk6Cy98$A;vXJVzrCONQdQ)uk5^2pQ4W(la6r z_P|zY(2+I2<1!+PB$h^fRQ--;*ziSRw~uG}&E|IbE>prJrUn>%f2ANAf(8dz(GMNr z;LJ>Tb?BSt>*2{`xBuce-F*WW524}WCMnd4?KpCQ0=H=SBcrZ|_IoT>08sp#2q(=e zBrD3Dfx`b|t|OD3nTOxm3I!!7Y5oX_E<^|-I~a+FWDMajC>I6XS2|km8TyMNjFcAF zqUWIV$N3uKM8Lj{1+0L3C@{gZ#oj7b0v8vxP()B~U)w;E%t=Sc98Ib6TE`JtFdb2( zbueauof z2IL05Gg6mKF4lX3v3o`b&=HSZ=qtjKa|NoNq9hDA!kLf{+xl;uFu>3Fl4oKGe3^=E zcg%?>JI#h~<i?Z*0N+V@sx{pM~4{oXSveS=hf28 z2Dgqc39O9I0JAaXFMaH5vyCG{IV`?E-(MS4{TDH(e^hy>PHOR-=yZXN#e;<9A-iEo zua!jdq0OONz0RJ04*=$qK_%gX0c$xfy-vxWNA$?_mmv{2LuLn+mpRWl5YIY$Gon@4 zc}wGg1Y|tZtrafY3N}=w+}uI)!H%W~XLfQ&PB{uUfpds(<$saI*MBkqiB0t^6JNj+ zJe*zEWy%A^EY)aSZ}iaSjGRn?e2KhygW%3gSW+@Dy5wv1lJ|QV_vPQ{6wtd4RM-2XJ1sR@ z-+2bd-Oj*`vcR*293&+W1V~KV3S{35Fzg%%B&Mh}WD$rWSv7;3SH{xcA;6&^MV*uW zjx!U>YE)|cO}TK@$T~SR`Q4T0^Tp2fdZa$_JQyL4svm5ZHSf3Yq=W)&q;N_fdD#Pb zML?~%`r~xoZ_w8|+ra-*Y5up+FmwGg7-T|XW@dq7lr*!lu>8mJ=T7c9VZ>FDGjg#Z zW@h<+o=X4d{Qq&oX6NSkPpf#9vzHXi1QYTCG~nTMS+FV&N;MY}8OzuAuF0ni?2EFi zv9a6;8^l}wI)kqNet8j)1zv&f`n(Q8iz5@ouo4pEbMkpQ4mDqLaqZ_^;U~AJN_a7c z_%w`R&3-fhzoz%4xF8M^u)`PI9Q6mmhWkYKi6o!e5i4R?OY9f2B#qAVG_Smmb;>>@Q0dt$?(J#4 zdBr!jUu6aX8R_ZTdwPWe)ukL^^Np15`K?>svGeIDTvhA9FM!6#Obcdn-d?d~;uA&c z2}^@DKO6_UC_SOPr!r^2%JN=pU5=%GWBduVLhB3k?P?VHvv2|QY|}4A4BqJM5_Lf++c12tN&@)Eo2gIpD64>3?Fv{g)7BVgK(T z$^pU5%E9>`A)+pG+#xl_6J{Hj#x5MbA=;nFpVOe?l6dx_O$4t^!jjIx`dtDXg81>j*lByx zIC_prS|mhl1KNfHTEg?QUOQeIypFYudlV2(hXQo)0FLA3>%+$%DA^W;y}Q$<0XgyNO)m>05uLdntuI!_0r~b*ah%8UCwC>?Y}PkUCNl_I zGFSZeQ$o(eY3O-26_7z<&5Ll_TRS(&VDn39ejC=ErUOi z<3=6tJbA>LezIg5u45Guh=ml(qi@bEVz||#V6qL0U3MR}fmR6a35d#aSrZ(Crx31i zN8=)ALqHe_kd5{4Iv)5X2ev?~wt0Rg-oac60Qe|gLLx4##eN{0+?h8Z{LQ?ZaqM1v z(#4~P;x(P%0QtdkfWu_|DoF3f-v+{1IEugN&JrxMPIL|?dGE&dpfzdKMSNp5%ja(nk*r3n&@y*05paED zPPTvaMLsBs!c&ogKiCc7gA&51uO-{=eoey&gR_vJn1j`z3jO#r5B3|h5kZ-cC1Jm! z)GU_~fbc|;G{Q0ZEJp8-O3M_=wQ+4*@dPwREyozlbI#q*p0n|!l13044k#JxO-0>GVqpr0kpqbfy*daL4vIQgx zg@fepW4>5NpAY$(hHWR6lU{cYfE~q|=-K>mjR_vs6Chb6g}G1`^HN#o?>wW`yZ+em zESMVYp!(nXCPOI35D?7EseDuCO7;wqYphD+{W06eZqRy}e|&hq#dJ@gz66_SdNp$x+J z{-p^gj22z+e_ukC&(tf;+tdroX>5_I$K6U0qb*|KosbiR{~Sxd@Q=k*A#H}^c;gI7 zbviXqw<#h|cL)MCIKwtLfGD21vZndFiqLGDVu8CdciUc&E69-W^J+J3a&LB-0cj&u zqZ~>@!~{9{#YA8Zh}A&7{q5{W|3 z^$R<+jo!YSwDf!%e#4L$lQ*x?7J>ZG!DIr{R@$n(fLd8cQ7*Ph;0q0_fXQ0s%ytMW z8xLr_E(MThx%|O+@Tkdc)2Bo}hDalTvkXZ?VGRIx7~rB3yVbo+ zcIFCVcT0}!rpaZ zI_DLdD$p590ZCS<8W+Mf4^zZMfzKjFIqHp8pR&7E5+8jlJ~c_Ex7(r+55CK0kvU{N zQ|wv3mHQ0Zh3GJ+mUmJ0w>k!mmuBR+q!oAr)czYIzy=j^(BczcJ8~R)Z9k%uCU4sM zLwA!qtNR0g98ydiatja{J=nXne_BS+#%E^a+WB#glGDphX#c&Kpg?;)HlfLui~a3X zIXzhWtI<*Jp;WHO0OwdWcCZbs-?pY>T zN7|=s+3JyO=79uUj`N|J()ys-_~yh3;=(EvF~g3aJI1G1<2x?&FSc9b{}MKAZ0Uv< zpcpjl++6?LQ?d|qurqV~@9Cey^nV}!(f(OE{-?gjHbJUloTGEdlfg)aqrpp_%+pJI zc#zRgg2`MC{Bf1?hzOBRcTJZJ4k#!oX$oPhD1q@kecIl6`uaZc-C1*Sf5|<`%=9?+ zGuQml{N!nBi?XaJ27x~ees}~8ddP+m6Zi?@?=Ph9?+@yWh2{5S0`|R?Ab%Jo$~Bl| zw*UZOK1@(#Iv=4#7T-c)M{x|O>O=>jh5?BR2q+@<_YVO1)%&_53V{ZZ0PWLf3xeAP zq6UF~9yUuF?sz9YaCxc3`L9mH8-_cA1nln@ZT4=0vdk!wBY=g0v-MH?R6NLu!>qy< zga`B$P~ZF#uK!gpQK&2E>zkLC*JWtIsSg2|mrn}D+l3Wb19vU7S1f^Egt~1s4WL}b zdGBP?_r(h6;h(x<6htz4=E zN8kbKp?@4hwDgdCcJTZtpe_an*-?G%6yStGI}UO_a0})J{!YBH$jIiP>$5vVnVC`K znn3(M0UjDjQXiJxZ2R^St)Rx;hJ1Ya{R!>2vjwCX9b6AsfP}Yqh^QR`T zHAtvy`1{8f-s?jMG6a~dAqqwxt~GST&-?1YALXsKos-nLXwNWOyS|RL9zbygfoi0lS5Xh`t365FQW)Q35D|27KoS zHucx9iMw)zKQTJ5nS%SrrQ#0dC$!e*ibkJLB1K6VBS|Q ztp)82uV=o+)D(BKoe}~!xBow7{0+!H z@WYdDWOr6Wl+kR&eRr}+1C&Q||1a4}kZ@vKf26E{dKi!x(V*@-hrG9Aa)evRZP^mU z#f$U=P~R>`i1QIhN0q!^eOQ4*-*07LpCAG@?lB19`h>?|*|ny2^`@}Bm>i8PmE^PFy9 zXGk|Td(rpG997LA7y%>-rpizqktZ6MtMR43Sajd7*;Wq3yZoybocCS^?<22Qz2U#6 zsLggH`{QKw7zqe}#`ipi?UYvM8zqpLvwDZq%EVQ7{z!BuT+2Mcqp0iHo^OBIQ@P;5 zQzNx*1*F714B-rAL1W6*A8K33E3@tuc%IrjB@udWWpW9;{hPb-J5Lw9hrsUuIOXgA zuDEIufBDW^6zUrE)g&Ja#L}=695bJNFsmD^O{=O^S?%l(41dCocrySK? z(ESX|)m`X@8fvm!*peL_@M9i*^{|5CC3y1hUCBU^z>j-|n`(1Fk&O z3jY!`WV#r{n~KF2cQy7kD#*#6fga^IB)9Mzc%}f(^CQ}dKsYXSyVsP2M93V~+1^y9?nJW_qpGEUWQ&&Sk@Cbpc`S~j@Bc22AN{Xp=}xlNNV~rK^7Y- zFW=#x8|7A|3+a1F zHvo`u3MRCME@D3Buq^S)5)2A3WFOP>uh+lnPLZU#fJL2{REe@fi&O*KI?Cnl3es^- zlF9=!dBuK7g0P#u0aQpUG)9`Iz9{r^%}zh^#^pzDcgeg>b>I1a)jA@5OI`JNpdNz# zreNoItgM|$Ad;D?rWJi|j?L!3h@w(Vg$LwGcJt78{MHImgnC^+dGYTFMG2GCafs(4 z`I?BnCV)q-fvIGKXD%xtQwq+SqWwsJHKu$bzxBOc|Ml}WxZ)UJf)V*Vqj*;-GYIaZ_>CN~kryBn zaMz;2``$8ae#J}hvi(MH`*u9FBaSvH2dnCy;T!Cmbn)|al;QGcd0ih@t6pyj&xr)BjgOfwEOi}9_(RDu@yGf7-SqTwjR zV8*$^uyx^mlgVWG$u&;tT}U7jj;zgN|0#+8g0a?4bC9lZcI6WXKIl^N;sk(w96q4p zI$TF-(E6yTflhO_3?0oOc3RQx3|*$HW_z<{mjzuq1vnBZo;~k0sYWd*%vLT>NF0M> zP99q5u|B}_GeeoL<#kxr&+n$|^6(Zl+u;(~4r%b^3AFvs=9!?s3Oo-mx=o7vANOTQ zh8Mo5}>A_P{Vxt*0YquEk($)3PRTtVY8N8YpW72#N zv2J^3c?!Rwm!e_oN#2H^Wx|-V^k)jZrLzbyf6(BE&h(gq*;BDM`uiIbp770Wd$Deo zg_v4>Qnh{iL#sNI77K9CI{Q8$y>^c#oR2`1Ge#$Ny4N+={_ATM5~zP>Y6)FC7JM;l zu>{%{E_<&-;GV1{cyA^>1c61AzS=rbfI04!Jk??t(>a2pn@U!^v4lx=V086wVG*%T z6^jX4Z0(y~(WasMd=UtSe1OJf_B5F!vqohq%i(wyG`9-W3N?W8AZ*K;k1`jXxfvq* z;MkFs#KrLvK3auCs?(n5% zgPq0vaN?|=!@@g{#8%?ts-h^jVoM07AOA*`CwMTl>rBMOk%Pl59paf`W8sK;gXJvs z@q~~yf1eYQ`yoEk(>)s^PU+-evwj#Zrq!i} zM27G>{32l&Yh}s)8MnjPbgwAFZy!&a__nRk1vEVQ@UNynY)mpa$baT~1V7>tD3|AA zIr@caN^BsuDD85NE9)|<5Gh*A-!@9W_|tWgc3Gz9<`#g+16INmnpOO=1cPY=B~}uu z(Nll>*_Gjz!$75yl{#>2nD}wKFDyrm_7P!kAXIi@Bs9%*nj5wZ(dLjd`PZ}0_NkQp z1uU1<^PfaMi^ob*ly91?W8JvEpp>0usBR+4-%&IwhXv~BPRxmQ*2Vk>P2U`+^eBqh zui@5_#wbALkrG+Vn#?@K6@exiIz3Xo=QN*ptN{P>^Cw=1hF}}xIw;w8r*D2BbeZL7 zgr|OrTkr3yi_UPK*hx^W;4QBu`h%m6ME_%mKTPcMa%qDB1UyA729r+e7i;u7hv4h% zm)@&x-$0{K)w9ISTadj=6aRU{JjlT2JF5RNNw^mr_u!Wmw9ZdRITZ})FqnAAfGF-oy{?sxH>A#Y{PKJ z2|fo;b}W)xes4zaj*2M3(%KlAgiuT_U^FybU~#z;RaSSlF=O`T234iHSR|F@$iiT% zqynD6UT6%P9P&3~uS-BnsS~q*6Y7Qad{wE2UpIzh9od*hl|i%V_$)+NOsUGERed`p z6z%bjl^v)dk~L|O(Rq5;S=Ud95XgK#%izwZAh{$pk4Ca>`&#Ne?6e^2m7|CYlqD#D z4t&LA&py!@aIRQ!>~1Mb(#Ga@*`40=IRPwI-!@QZaknQrb5bJOd~8(VP@m8nF!v*q zQ`mVvtM495zBYZmWXIXXAByFdYak%kN?JPDj5C9c*}@u>G2U^H(V)`wF3zn2yE|J6 z=usMt++DpK61YCd4ssyDLRf}#2u)Yky#bIj zpET z>B0@Z?t32WF#YL6CF6u=d9Wsb!?Fjlm%)x#gc`CeIiJ^d3yX<@VT%l^HH>L0CG7(D z4Ku{XX;!)Hc*Gl?(h0HPhiWt6Jiy@z2G_ zW7qyN*K`$X)V@tb7`&Dz(xnLsuhun9IyWa~VRU7vriz4uzDp?8(75v6_4QQzjK*Mm zDpSTyu7ZMZ#o4(%`Btsx-QNMxloVDne>j{X7f3_4`OI&Ws7rnZ{ss|)7Qh@z`OPOt z@8nvM9(;vEdF<$zW?YLt8p6+wB)_XrH)v^DM^ePa<`w5Y0r=uBOm}<#cU#G2ynU(1 zsc@F$3WvX-f(Uk&ueU;8+O!QG(M^Pm!^B7GAnlXOKB0!|yxBI4G@g?L;2&yv>I@rJn2$bTqY=71J`nDx8L!&gQ0D!{Yh!%^V@-!Xg?YP7)OTWLjaD&|z~5 znB$V~k>iiFr`)YsBt?v)0L- zZLD@)z#&->PP@DlL%>^-8X{)UpFVqZ6WMw~X9>pnyG^wxQWY~(gJ6Dt6&slwCk%e^ z_;;UP4ag^k@itM~%f!6rCo z{w%WK)Nd(Cd9Nt^mK8}$b*(vlQn`fiNbL+!XDMGBDX{JcQ7?TEip$iMGmB=Uiyk6J z@~4|FdWbl}GLy5z*O;#mMN{ik!Y{n*>#jNS-Ek>fo&Ay3+5^~Ss37#s+1q-*N5p%u z^hyzeHFDpVJ63uK(V$SNOQmZt$jKNmS}oAu3Zwh8S6SoZe9<|;2|B~m&ffCKZ!c}Y z7FHv{-Qp$(p}sAt?hU^x%0J|d$s)U8>_~M4ug>7=U~xRUV$Rm!Xf*?!ql{>S7c&YQ z+10tdhPD2DrwYhYDK;|^{PR*9?}NmVKxyj!(Y%Cv_tXK*e>IMfZ0)>_r;mj;4_nb* z_ei+5WszaHR%EI5@Tie>q|h4#6*q`Y)fTfwB30Osi%f>$?NLla6@q159w)7JfTSV< zyyX?{_@;5zdl=%NE??bJhgq1!Oe5%nyp;WAnTEEi(F4dy;tWxxLt#<0z`sjUllIe< z4rz*gMf#?NobgQ-->=z5Xp3vtuoJXo^y5D5p`TemP_TBzKkrQb)+k zJ!Q3~dFQytY#XK;Lamc$K_wmTetcx;SK37YZ2{`E2QP|HFaqtc%O|T$HJbY^?KcTv z^9Npl72d0X)itZiB=M7tB*p>mS59?S~5eA`o<;mh%vELB>I_WVJx;ZG4B<8Qgze=Gg<2LT0W z6K+D>kK!+Ui8B7r9HiXT<}lxK!&|TvP^adLJVfXLgme*abllrXY-Ab2!6cjS)xwD1 z=~1<=F;2SRm9#E>QO#2Q;VrolDya!zC;d$(`t$yDj9GQMtfu`6kh*e0nn=~`jID~| zxQlj6)}?5E#%g|yW-Kt9?pk_)3;>yKw81DIkKqM~reSJOoRE~|%iictT;2uoVM@miRksoqxHD z9NPfv3xBecktKom+;;1_-yAT)#ZQEYv{}q+P;g=Pn@vjQK`P(a+XJVl4RBb&``G2= z?3vrSADVgqCo{#0>0xt=-1e4wJqqJtjh7{6J3xYBtzT8?y>eKp|M?QFD?nyKC0$bk zQ6wGBuwxu9`Z zgNilh@*C~*jfSaJO^;N35iiMNZy)lwGj^-g6z|M~ipe?4gwPuT3Gm=+wvnVk-qPrQ zD*Es&9PJK1>+)BEbT4pyTjoIGwHQ=1UlUz6W%lje>TL2yT~XcpCZ>eDj7H~N?^Y!u zo5_#!qqZ6}PSWhYV3I*=f*ZPvbo08X@u~aW0XP(VFndS#)4+opy@6> zN}RvqE8@rFM6Ci8a<{j{S;KT6E@j+=Eb*lx)tkifTA`w}n04b}gxvmW{@L!~nbm8| z!m&HMVNcm#S^%s8omaLj5_M}}yzcrKe0ALJRYFPF@9B+fHwV5R4<^v8$K`Zx zF^tq)y(Gv1N=%@+7Try;x4+{8d+p4bjFnU?)PT|l#CDlbV>IJ9GxN^L9XmBrn;ZHrCUp@e%W1iG(5qxkiU9h#D%hX=p8Si~CYDs9(Om^Z z264({C&I!oby|hh7xs_#YH*N#7eTu(G&!?%O|1+3N!;)RKkZ@j3&ss1Y=@*$ee7Tu zK4u!&V%2GU>Ffh=^gWJsc_00#YpofimuHX*R~}h>oSZ)ln;`r#B#ZcgsFI_$A-v~G z84P4Cs{oQDn}df(wX*kZ?3DSQ=KAM&Sq1y;sTK(HPOO|i^{drNVt;K<1da>;QjF!w zF5jx+%2qe$t*_Z%Ak9<#bBMJJ*_m~beuy!0cd^)t!)Y)|&97{JEfiz#lzm_0zn|z$!&UbxOPgXRiAiVU69nx2b@bZtR-*;QU5gwuwPi3Q#|o z!mj8$RO=z#BU`Sp=^V%O^WsoYe4J_Un*(6pWIy&ywlzk|tpnwMt{Ee?RpyZSX&>m_ z@dC23w}Gl^YfC&B{Kv#?{97&QKewRsGj=tTe1|ei8!^j&B&}^8`K^UtG3i7r zhR#FN6*W=l^ae@hRWk}4eWAC~3vyAC4}kO@{h+>seB%=fC9&2-ZQNl`fo@lP_t}4@ zgZ_-O^k=dHZGVD%Q!5U5$rNnZy1R_G+(s}_?x~w#?L%DRJ^q+tb<)q4(6>3^q^rJ} zf$l58{xb|{|5CAZgT4xA1U?{u$hq$)Wg4y?2?(smh)!*NqIA^&4`WIv!<(DA-~eKO z9a0q<5Np6N5C@hDxxd;4ZUk;J996*G&!3Qc^eek%^RW$cSl4-t3t1|}rJ6PUC>)ta zPbVGLy3a3Ue`>n3MMl`3Udr{gXBpJ#@f-3yZRhf)p^(6})~X`TBe%=n1g5%7ao>GZ zkECf|t5w=Ri(wl;YSNnM>)&D!)dS#UUC_18G5JnOW5n|Hnc&+W_UcjNTY8pvQVNx- z-4xEj@q0@QojKD>n?kXAm4~isSN#XYvDcq)TWzKG*B`%Zl3A$Eb!xd;KHb*K^S5Sn zsI^%V)^ZEehEH}7BNqsuXdvc)FwR?4;OgbEaOHHast_X3tJ^nf^A}F>cLESchf+OB zL50yXa0@F95wsB}Q0aHG$7mgPHKFgI81+Z36&7+z`G-wy*~3@mEWr#t`@B#T-WnYXZ6zt{t$8Odlys+CFk9SneXYSA zb3R7d{$5e`V>u}-Nq-G-qzA}_T#urdxU@DRl%jU60^k1$Jzx~=n(RS(x zI+sYhsrF$SU*#1ObinsuJRYFKeJ(u;>VtSfhZ|0&~25)hym@p&OYTW+P3 z!lX%T+vvJ-YefdJqnwe7JqH^`Uce;{8r&i@PfvN5s#FV6e_ zgM3-J|Ff+z))i89acfyXGMyR`4LnJi)z!lz{15~@28opk0TC>TkpwJizJ>_~CWvjm zFu*mvX}-YK*QD!Z`{nD~#&0L9+23WR@!<00(t_y!W9yu{!wi@$9J8@)HH~fCwrv}4 zjK)qHHn!8)YHZuKeY)1cIv3v`nCqF@``H^&9o)oUj4A|N6aiG?CKw_>8N^JF3>g^& z0uCM|Pdw7q*Bg<0aHzbD$05w#UfLTXF z+kx~5A_h(G2Oavw4dUkk^WNMr=>W~&liLm&03rA#{Y3R@K}!9u!MHqwvU7+S_9nDL z4`M<64QyIt4n^=K{~5%vWllkYaU2Z@jD+?H{>@kmKD488U>NW#p9CbDgBgMke07+&`8_4t@p^- z3&J4lUzn|Iis;7?F9DxZ%3m0_UnaDH>BpoELYfe>qfKQ~x{c~A|070v>_ zWPWBbW1}N733>_x{InqcvNoS%VK{Wd;prv)Xk;S>lrZMbpI(LE*HL!vT?Rr#2mkT= zsOJ*VR?Oy9a4;Z7<}{|D3ZIm1St@p5Crjt!{Nx|XGhVm zR_`(JU+`ZWz1;}L=^#KvI99O|K!$Aw+h#(D@+^QF5%8J!^$n|c-!0tB>l5s=cVGrS z@<#k)7B}p0>&<`x8e$jTi982af>SzNp!AyquUCcVa5&&5=pJIS@J@jQ^q|*|oSjql zy5!tO55xZ@8$9Z?Yc@|)YXzuf8+4&;7u8Ti7pU;qv!L~tDF9rADt2TA#93EA`ejw$ zr4iAAzYh7en4TvnmYA=|C5Ugqm=dw!X#;Y>yrXEjh;CaR*~b}Oe{aH9Y1 zUgQ3CyG;*uM$wtMq@7KVSIV&N)iC|%-e0T-s!ledG(abK++fUOl%?%C;IgbudvJVG zvWTU#N2K7@p)p;AwaorT&PO1vr3YN%F9h$V2Db?a9R^6?6UFsv-5a)ts0-LrE<}p@ z)d?Fz>}F2Di{f&KUU=k*9*?hQU9*PZ)%Qy4T$GXQ%<9!wjZ0s!wBN22h2E^+=vtaJ zrOEP?&w=6mq(*Y?)~yMB>in{Q3$fB7p2^4ZRd1PTS5K@~nN`2ajIYRIN|om4XUyp| zVNq=a;s{wuOi@81DuvEz4NSvar*f`k(I%CF>_ETEmo+=wi2cpHf|^Ej=gq07S7r9! zoy$Lwi5wL=a$v2kk>@MUz*q%55r1Pb9JIzxGGJfwsF6|HLz5|$(&zr#OajLWe3Zie zJ27Sjc7{kNTG*aK$V}{@j;i%k9AZ{JF@k3aOp=m1+CQT-FVOlw#wv5eQdhtYixz9d zxUE5F^PS2#YenT3BM;&m`ysV1TheKd(pSAyhz858hJN19(EsgIS0JjM)eE9DB2HQF z0aBsz^3rKd^h@H?PQ7`#&UzDp;yxT1;eT0BC2j}23rHCes9I;3GPaM97%!G{4x+&} zSjJNg;eHD)2s;}T9<#>B8hHo!dsFqARACWrA+?sYmG!gsfC2rtL!%g%*ji87;})lX zOOTD0d302H2{Vb=R>Z8JCR-X?mO=S0z`k@bSRpi+sl9&y=BYxEGO7)(sZGs_Y2g#V z`KeL|x7+^PJoqA*F4JTW*Tf?c$pkV=U{f{I@y196%`bJk!2y4QP}85_Cu1^>CXuI* zFth2`ai=UL3ydbdWV$!q-1UN8bNQhwvq{&In*%?U@9%pX7$dibwdRxC&ilt(Abgi5 zla<`vkIPeiDievq7r|6i&_p)8zI2KTS95OPbk?}ctw~7Ij$vA3=Z;my><6zUu3QRK zd84x>`SIVlSg-ff1TvQJhoE8m2sgivUlCmq92IJ98+GP>n`;{$2UzoZHnDZzdLWAv z!S$+CHf&|KGrJ(JKBX(C+WlFwM3z zr4U(4B!c>hxzBUklsm(DJMH)C`#$JBMS-U_N@LLRzV9;p1{cC&buPmlU=U)9eEbM0n6XjRQG7<_Toa>9(M-VRt6gS2E!Q`KPSv+d zC{VXIOgDE2LdjO2@5oKiQhF1JWWn@x_;>C0huc>Y>4<}CJ)f==?YduD%rC5JZ;O9W zEbS|LKqi9_C--KoiT%9i^r;427N2dK&el3Ny7l-lsmuwS^oBVBz!{*zaC4cxQeubd zx=+bK4$u8%ITga@gk1`EAkCCXbBj%T0#iMbXXP$RGc&67^96o5gYl$3K!J{Y-Q$dk z?t0t$S;{t~PLrXoj{+>35=E+6hey`3RpWg8$)1y1AJPVz)K%)7dRRg~eM`T^Sk{*G zPG@GL1rwfTq^#Bs;D#!w*Mz~i7s_l6%Fwia`!Tf%|HiZ>r{_+-w2+Ohdes4NS%mIA z9=2_MxnyZG@}oe0^V9BIET+(a>dj_Vk!I8|{-({b=k=4vW}OAR=xA&MAsgtl5fxIA zQCXhP!`zAqwrBo}zHB+$O8|Gn*Xt){VZml-gz1<0=k2;3Fp}rWi0pkpx~k1mG5#yj zMgCM_6~<^?_S!2SIjGj-k~|zN3zhh2frMZHlXZq%qQKDxca-l{bHm^c;x*Md2lLB~@( zFe3jH;7I^lx*J5m2Lql>TOe(4fG7KKs=v{>Pe!=< zk2TMjYL>3zaPW_qW^Edc)7qX4GK9+i3s;?Nu1k`3(EG7&6P_M{?XZO{=jXQb)ELH@cOt(bwVqofW@C?dCfMrSh{kmv|*cp)8j1Idxn7W!I9v~h)6f7~qe%N+y5;cbim4$~YgFg!CmQbay$PiK01bMIa*zzsdodI z0*AHnd=4LFwhreSjk+F)j+lTuKhre^>`cVp--z$xhW<(vdSwiYU(b6HG< z(4EZomP*61HFekC*&RqlT8gWZ=<6($jAkP(HH@$&^g_k!^>1B}xd?V-}<=9X8*##fk)Fx^#Qww|0y+hhC*=R?BAu}5Vz|02 zp)Ftzvv-FKK-@M?$xa5FuqsPqT`k2VM|lorLirt^YdU=ChbWlAVHeYqp~VYig&ryiETU2Q4z zxiB0TouJ`w2q*1=$zs{oaT;i{VrC$$AG&aU;PX}q5WtLjA-1x#_#I=5m z%P|Dg$Clez)A5w=*+~hDQ*jdBdo)B4@P}s-0!~ zG%(Mb1CR7fZ|I=Ee8Xf`)c93d)hO4~FB8j*-saX8{X+MZ+hp@uuQSV${mWGc4TsbJ z)-Z-}xu?)S34!sWRvbQT;Jif&wV3q;dBCl4-s>HP)4IKrAv}Qqk&D zA5iaVhM5_48)L7kEk(upPS&?GEIWMwix9d}@_RD3pPpzD7uL4;tL6R>?!+A}Z~K%( z-(JP)I5X%)uXZ|;YHmM4`x9HkUt{&;v1#?uueB|$G~1iISLy-%c!7&cn$bRa-V;a)>4pY>z?alWLNIp^Q) zG~rhkxbYA>1(}VLhXlP)yG8NVjQI;f z_FC|hGmZX3{GetE(!hE>k^QC01TgAwXJk3J2F9{QGVx##On4m7Z$%SC=c#N z)POsWb1u{M$L5nTj@S)@@Ze>i0@?q{yl28W{r$uEtAF{3h{pK9dWqtX*7}QE7^lze zl#_eY#R15pni#&_BaIi23z0Y9%h5zO!C&!#mr#LSlOj zYcaLg{g00}%g`=|PBC4^7%UFQwL8&xJd+cm0*$?8!fk4$7*J|MT$o-Q|B;ZN);>yq zsAn~9XzcY?)6U{*#?4SI2Bm*hIaXrgcgVfUZ7+bJUf{;8vV?QA2k4dD6#5tVtNpv% zHFeIF7Gl?YLN0KZq&^St@A>cWz8q7GlflZanLl!Y!qR&w+FvJhqv0zly^qTDH^6xW$3f`e^)Oc`NIrOQo5M+e(7)v_Wx zgwR%7?M(`rAxK)$Z-vuH`1TG{j`R7AsIU+R{D-FoSEh_46Ne&e$9{I3i#r^nH$N`S zo7LAsdYBcQL{TQ1D;Hg$7YZG2PMk2El!T*9DrxV(>98TO0^)DoNcD|>GbQb4Wy>#S ztIzb3kg;_dCqZdVH?LV+=zqoSg|kO;E|rzdw@{A5$ab-`_L|s4a|}%3gFeBw?UO}z z)o4^m^OZ(_biSt#B$98!ASqvLv3oaCt#jJSz5Am!`MH_Bh|Ti{s$V4NwK>@MV#ivk z8~#WWQ+D%E1zOs`T2G$onB-7xQs=K9R>)f6%k){=@9;XEO=`%mtiXaT#mlQ!z$nXL zJwoM5KH49BI@RZyvz%Uw;Yj_lf1vyAEBWEl34K2IH8SpvhnLt+g)$$aH4T@}=g$SV zhq@g!%+FLq5N?o%;>6^@Fn@A~k{jFMyWNDC{h1Z)2YO5KY>pe$dOpB`sh)^op%(&f z6Sbjarch;)$z!JGp(VSYeeJM&K11Zf1oiikd+JwN)|5#Mjm(u6TQiJl%!JdN_HuKf zx>s+JhdC(g5#B z-In0z1P|6qk2Z$WEY`qjee))dN$5OIi+@BRm`QgrGbS|v(-aI zix->eVZ6;lcH-0Jt5)cwNOYd;zH4B~-a*h6l$=T*x#%CqFocDRg;7_f4qGd=w2Pt) zc#QP9aZj=~D&BOl{=~3dDlf2hxrm%aTLIUHcxa)#t;5z8cyJ3B_}MI8@FQ_edCq<& zMR5j3M*87f5}M>d$;Msm`!Rn>f5Ny#QKR)o-|KQf2^!(dRKd%DpMk=6@nDk4zNsf) zz8pO$hI-@h`J2>5u$L5qCvI1+nlvOi;3e>mE5#C5o;`-ugz69WSm<9X{ahy*h=EfH z6KQ)()rtKlxItWYzx9u)E4WfyC^c*_hM|3?+))N)qfS=KY z4S$?}*NKXZvFsaQ+^IFioIvj7e=wj`J7pMDTl2W1o=x3hM6wEmL&QQ1lymsD zt+Z$s{9}%0#n2Y(Qrlr)AwPP83T*DjA4bW87cpi+zr^!8v(=E%dEJ~AZ4AjZbrt<4 zkP?yTrXLz&R{PPReJY{3RgyKf>(s6Is)H4rRA?V$RxJ@qtWQsm?hq4GFO*c?kRi2R zZ~d*TUg5UCFpamx(^klNL*IDdw5sRq_g(Or2F_B4w1bV;+>&(zJ{;dX9iRjAl*d|1 zL117@CI^01&y-sHjJp&Vo1jw=`p}?&Go z=?Ah${Of@$A-=?!GpGsNuUfeSdhy8c9p#`S@exj>%uSXX)pZW~NcjP?zg~+!guD=t zlpUd@)0DYj#`h~uZD$w@qW}r#?FHodq9l0Q0-R?=boGI=A@?d)sY=0|>8$T`Njd4N%A>@q`PuhtEdNPYH^m8`K72`Ti|LWuOt+RR2 zht`II%ja=CgR9}Fu$K7*=XNw0)%6ym$)|WGf!~efq=y)BV681_lQ`{oBF!^+*U6;|cKd z?82RcTJk+0R(e6gV35&+Za*|&5NW8;N9BTYx7OA&rzSB*fbeU_*pqm1gkLzh~g*(-@y+NU*m7ZNKAvC8^IfV&1#^ z^5V2`5Y(mh%Lh!xDb>`^aV^kkt?YXfKD~PwM$A8A7iw*V^T<4p)cpV0TxbB~(`NR_ou2yWJx)oq${YQQaZA?dg zHNXaJA#}2VMR$q$4?=$Zd9UD)FA0ZUeb$LM-u=@5>e3=cCW47DbV3A8{N~}0vFWcx zt8g^&=Jn0Otcitk#+O(dVvzl7eM<^}=g@Im)$7I7^>bhqarn*aY)u~!d$#Soex#&e z|JS)qn;%ZZ%TRA8qS^3yO)8Eo1SLApEem-pLW_z=cGiNpu4$m&RDmhG{U`Dn#;Wg2 z(QzAEs})HXydz|CRuXg3-0z&xBezRqekKcJEwPw%0n!+%r`qv*R%MQymLXpNET&u0 zGOpm|u-zUfm+kguFLS*&@Z0Y_;fXHXnNvx)U+w<5vR(xvBCN?$t++J_*tT$_M?Vj& zBF9+=s}pR;n(YQtfpK)iKNJYCUhLeb)M4v0e(!%q8VE_4sj`>aePtaQ5=`!6a*y?0 zoTJec?4Y8+Y!I;be97->#bHu`t#GkHn4Yq$_iGg&C?#!oqw3I?E*iuqr}X%Tv=N`Q zKMD;=5D-{GE!(3&BinG2H20-HFoRiqrMV$7NfKM$Y;V_@`vsxHQnEJIRJWkXSRhr*`FgtA}s!B+WYl^Jsp zxll88CN)}^5bJ+a`@B;FTRSIl&kYlEL;b!iFRzyHnzGhQuG4K3QO(~7FoSRIGd7ZZ z{0PpiGWo4zwx;T0sm~=;DZpK9cgL94px0IiZjG z9i1&nmjgzuyGp*VH<^0P;>)Oi=`CCwcf@^?iP;eFbq~c89q+n3m5%lk>3a*y`e8t9sh}(F-?8{wpdx>?p9$HKVDkzMg?(U&=PQ5A5yG9kt zC4{t1)1l?QWJw5e% zOizS#$7aT%7Z!z})C?-W>ymLuZVAcsv(dVSm+WQCUk!8uzq}qy?lv<(S7H#Xhg6v> z&Mub5NffwZp)shdn~Ts{Jfd@tUjI3evrnK`Vg1x;f;Z&Pc)gB;)x^SeSYxEsSyC9z zs`Qg8ExaA-dA&pmm${ue#vzn)Z+a{K@h4h;n)x5POs(y+?~fC|DLij`TbUh^9gaH4 zS*^^gK)o#k`cOZu;0HBZU!~4Hj^bex;gR2Ep6}P+&do@Wno0z7)cXksgGy#MIVmQO&rr2Vd+_&eq>6wa+wG^ub@UB6%Y!)j4(f7 zVU2re=?)lsUN+NhvFx1d`2u`hwQP4VGnm$VQ@6k9F7HO_Fjhn~wflx_OyPArJ&}Oj z)n9BD>`606pN2g7XyXgz!Gj~OYUS~WB8LFjNJv#9t%A+BerzzWguNe1kXH3bq59WI zTHhGK;9YTShGb+LT&Mzz{>k7vWzXzJD$AsMX?5}r_&Jb8~ z%|B=(Tt`Ki5VJKCw!Z&~y9L3fyQ|>-myeB?TOqsY5RDY-wvu9@lWjjTd5dg(NwfwO zz!}nH$QR~I3Ahz>dfQ1mefzVu7)6B(R_Snd!E(~BxBWyutJmlmq2Kr0=y%F$au#JEmrZ&*SfS8f&TVeG$}E~PUn)}t;pqYq}WUJN7-mh-m^yy zrUR7?(&glxMlOruMLs5}y+IiuR8NNWfR6X4(-o0DLrn}ER^~AR(eduC5*HF~zYMK? zPq`JG-G+-@Th_e0dZ0X2t#?3}jo?`J>XpuCf9+i6OVRAnq6V2ThII}q+0k|5Or|1= zxA11qpxiVKm^F`F(lC2zoV`%%F_&y=r z@GfpGqW}%JsKrt3u4fo&guWY$zeH~uF&(vI?THweOqI-;>}u@U-VxU}>{&+HLldTv z3S#EZz2bpA3TCR=0&7)z&XN%7o{%*BoNddGj}LSFJr(rJ^^tAVA9r@ia+mv_!X#y= z^S-KJ7e;PYYIaB1!{!m7a}qfJGbKLrb4=*{qjb1R3OplWxd;ZT`s3S8i%?vo)&mtJ z%n|OM--HVs(NT~(zb|1{os7Lt;A*Re0qonni=ni3_$y{}s4)Gnd(WMSxyL<3_cE!w zSPXoas~nIo3MbtzO-cN;`oF>79OsuvMSa`4Q;b8ujZN5L_zFk>#Uqy0SP|;cIJQU2 z9v$2Q!jHp0hs#lhkV*J@R+jS&L%~0>2?I z8QYymX&2jle8(yNMA{v&GdviGoCI5PthY@;@8U=}Iwg#xlXm%<8^Jc8lnm=T`+o=< zSgO{>DLErzPLDGHu4R?JcxUfSrS-^hh=}(E)rx*2wccBNhi-k=g#j<9sn1 zbnxb4jiH^w)NTfbz!5xuWd<}8cq$FjPwc*ALh5dKId_)|rJeF0JQX^V_uTi>*`RU# zgWDcI{}wy&M1(snOkZS3Wx3gpervLjag3p}Vd6B5oh91#MPq{9a!Y59-EdlhhwW(jg&6<& z@8$5xKS!Gn;N>laH-wI3erbJguFc5trM; zd|~V?W-(CFhf1^k#c!Jvm?H)IaHcIFajQ!=8gEY zxucPNJ&uF8AC*(xY%(YCME$)<_H}vB>@Bjk^ItT-%IRD+aW1@CYVM2c&L9t(Zy+Sy zp2ub}&_!RM|La&4XG|J$VbP2#RC=r8(#bHt%PrTYu^F>lkwahjL!Zm%dnC-48A5m9lTooJ zWt#T0T}5}1sYip^Ga_=+b0(e;axFF&j4uyG+{(xcearD4kiY$yE-?b6SO zptx#Em8r-#>_co59o4&b0S-(@6L!0(Hc6sbE3`~~e`G_i@5YY;m)#){g`uY-J3}w5}uj_Sk^E5?`?8Qj)9S%z4Zok1^XU6tqY#FS)0^@ zohoLhB&ibLxdSAv)cm$I(bK&XJ2qJc=Kq;f^z#&(i>+HLqUc`N-&e^E01qPs#+n}r;a zG%sBm#GdVGk?M~boFc=c7}FKUZqv@Gpp5cv%!cN(++P)3tiD}+=hg*>LuaMIN)0v= zAibtx)~%`Ho4k2C6sb1h73%^d*|-Q~R>n8jrxqOe$UE&3*j=ax4ZS*&J_#}WDgKoJ zKbSHl%#AIljrrHxfs9Y#i~PH(&za~&k^Ux{{iemj0pySZ^Qr1&G{Zys8tX6_Su5>Y z$pjCHF?xNEbZnywFLin>y-tPD>hLZmXw3*f#E!+ zj{Q+q`Gc{fchkS~HDM57p9UccCr5wsn=Ys~tY;$-!U`8|M++$lOP_8ap3M$3saeRb zo+F+>D*kL;Wf>E$zk^j6Yl^Gtl1iVI+@!c`%f%M@6>0Z}GLoR$Q2 zPnkV;q?8)B$K!}C(faDKwQgZ(tk(2|reQggXK92KVWX~>uy+-p#xXegC0YG|>@&EQ z9aj~}tqAUVOXvp4_*gs^nAlj6q!TC4fO#8!(j?62(GPd8ygZ;tjXLh4pe7(CC$aNH zrJ{gCVc_G;?64%`Z@?@obM#wJ_;WtQ(spAm+ZNi^Rga5ew#j8*Na*0|%UTI%?q2Fl&yChe2pH43ngr*u5PuG+IPd$jmxYIH$|2nbpw`bm7UB7 z6NRF`>&e)_ZV%d@?X%DDUEd{_BD>7TMtwNqOX351d#ygBghWgB^yf0IsGM=~^&4~p zJu?;IKUgVk@ewALl{|>J%l(OtCn9OLN&iK$&62#Us zk3AO2Pz-pg%_mQsWR)WPFgf^ZOFfW*?`4Knxp_J{r1w=(GCQ$~e(6*l7wlta7!N|b z*|{$OdmCpw-kJx*6N^@xhOG#=*C5Tq%UhIy&5}saohg=gSeQq#4W0v2;w6{e`k$Y4 zbpoe--JAAnWsNH+$-mn0Wr+5NNH;`gp48{H<@XoG<}A_Ilg~ym>a3~C!s#8*eoNzG zbvX8sS`f|rxn8SLcp$LJELDsJ5%Z6AX)gr;Oje9ECrP9q00MD#$GHPHhOii$+NUj@ zV|B!j6L>>_#T&l zCM>d9Gd!71?%dpkwchXK#+vkQV(RzoeVuQ%lqSi6b+W(4gqe~G#usx-y13f5BEZk^ zlcBlDH`0q7#PJ31e7We$|9)r<&TPa#X!>qA7 z`7H6fbVlj4vKl|f9u$2d4bg~I&GjV#h34OLWgXrXvMIiye4iNOTDBF9%joAwRxuqS z1^-2ES0@Pt)9GKUzX=$an6@JQ>aXMe7HT-eTw#tq$1R{&HURq+!zb+ZGA`{I^pI4_ zOXq8M*~JXTQli>Xd$f5z6Vs?2u<-0_jP<~;kHzLwB)M8tI8quVGlzB%-@ii*9N8Tx z8Yi-?+O(qGdveGN9;~q!utj#nYhZj%|FVx=az*e<+NNU=2J61cjro<<9S4Rbu-ODS z=D3V84^MfJdZj|blPW&+nyHh6+Y)zMj4>gT9OY8ST-bb{b3^YWx#KG{pVPP;>zTsb zTe$M<{!%_xNx}zvDIt=2`Mw+lr1YmR`=V;c)gFu%Y!Vdj+yueb^1FK4pY!$|6ZF6L zW#PE?UV1U23XYK92^~Y%?$EdyyuqKXq?J8!S~Pfm7@Scy&Yw>DVUe>@pV<-Lcr`Rd zc?f6&AXoD`y-v(lRUfO@ZFCIbUR_|RCV=ZD)rxXj*(J}Lq!(ekg)0>>G*K`vmU-QT zAFIm{QuWrVs7+bvKn`W*c~g{|LSmZh616p9cbmRUB2EZfL|Tf13U=l4ykMdw3N79u%Wj9P z+sV{8!%`jPY2iIXM(YKvn62!rAs~}5Lt0%w{2Olre<@@Mm8BfoYS7BS!=s_Y`tZ!Q8}FALKGow+GHl^rT>p*g zk(k#|HJ*ERF{{}eGOt3_S|NGCb$xa~w^(D0RGODrvPLN<70d+$VS+n3^}|RI)|%J9 zcU&NETf|K&q~I1sTlY#Wla!=$FT}N(R)wx0IX9n=g|AUwdNjyb%CC912U12;&!VNL z@-M%W^J=YIC)9f7S_8^&=?3f9J?Lm z^QoHCED1N4Cf@*Fp0;o;7?sRxkYFgaj2h;fu$=jh#`DupeJX|}e)s3@AIo}+&H0^p zH6eejSvj2!L8nLoaf-yOIdXuwY^Tt`-+UpdpV< zpq1Lkrv<*ttL|4a#B4*#uh|UT>@%XD{Ix#yH)UGpUui#C7tMEQ6mj)kF%W->-XwMA ztygQudHV&BN0|#)!Zu!*RGR@ru7bgI!%u@(Br1=|A($G$V)JLB_K2wOA2!SaaD2t9 zH;kh-6l>pSl`PiQrRFg=m|}&qvr`Ih`x*?V$j`7qCc)& z8OIxG#1-f?bf%`3-XmI;bF0D_edAEF2)q>0ZXAIH{7v>MNr6D(`Sp4Dw3=qh%9JY3 zp6ig~-v9w(ZFJBUg6YPNpE>E{JPgl8RyoFY#TI3@(PIbW-;`07!|Uo#9^3|^EqjHg zi9Es_iOCF8es#*>DIDJ>F#@};q%MplQX{(>KY`#`U2PBNMQ(TP-FeN&XbWD!+)cw= zUn!tPY+qEZ|9Q9X_Ybu+1AV;8SGywixOR1gS~`A*@^w}xl;)JO?W8S*;UOm>9bCHv z!5~KB#U)!W6Xua=&ReQKv*q$0&5mm#-R&yr)DCUNqt{)s%mjmVk$K*6E@vy&N#?6j zC*+$^ZE2NNTJvy0roX`q9_%->pDqYTgz*7LuysSGWLEqva$ii7)gL}KA@6L-ub^~k zPDrvVqA!1=?@fzUtMJ%osn2Ac?nLm%9`*ioEB^RiT5r>|5>B?YKJxHFV-zYzx)-fddOw5t7bQ7f)Y)q_$00FMMf zn=7m+@<>I^gS2zWO9^z%U1jS4kD3QXl#>$B@Fg5hpwln14bFGUuvUGd`> zEg&XT>%Q{jUFN3aG6>JK$-I@;t$I~EESNO}$BAIeVt+G<jH^BUeogd-&KIa>gEss2rt5y#Ohy4@azm-C6wX_#n5C7+qsv4H@Mfb zs9Rle1iQa6?&|Ez0oRI-@2nt5GA`o{w%p^JA_?I=H}c1Plz39R)$m%+MwFt!N#R#} zgDBbsY++E@Hy^PUg~V$@pg|B%v)Uf4NFs6zq0f6lu=HWuS{>AX(S_zw{=T91Y1My# zaczyKbY72d&}Ts$c7iX&*u``Md#Vi{Dy-%G)j-kemgcECaW6jv`wKeXiEZ*f=;dsT z{~ArwOwK@2XqdQ|{#PYuCT3w|`&WYU-$~~GA4z8625mRI!yxA>n?GbAFZ zawHu`hD;`bIv*w96sLh}i^IG)gT)N)BnifBLSHyak<>KOc7;@|ehhP^fp(40cdc`) z^U1@%o9hl}KJvyZC zQ3rtRlJulVLY2Lr;%QQqk>du;zHi7I&V1eLkus+8JLLd~o)&Tf zNNp(uDR{toL_k>)ouPCgDh?-H)}A!zO%F{Abqef~TQKqKKdNjjje+d1DrV3SamAhy zHCzHjS<(qQ#6D;lF^C9d0C>79DPf2VGT*i6Ygj2XD0jjRA~VMtR0c>!V1Yfc2rEe8 zF3k@x03|H^f?Sg=U^1`Q-(wj(t#39xo-GG-mLy;Zq;`lB1h&vtbdMNBp@4aZJsl(l zLITy&GnEHr@@o!yNANpZKm_45R4gq@4tSD$Z=I2D3wk!Fy|N*b(DxUI`{3GgQ~Y2- z5@wDw`%lbM=EYF}-D zUgqVVDsN2fZ!~QgydEZOPIdubtL-FAM+``$48i+lO>_=H0-+)yM>s(XA^mGc>~}m5 zaXj!+JTw|)`~D6qAuAiuQ{of|Wub_VG>n)<(D{rX9#0cG9af(Tzcf7wi1FAz7*^Ol z9deX_T%*-*)8LMReNWCJ6%$8SSFv9}fg2gwFK9+L9Q}26~_kp~QZS+NgrUoN~8m%;TK?^rf2?V4i`#qKl_ zZo)VLY{^B1bl9orUrPlc(n0oH8pf6~L1sITDj9mx$(0slf`YdtFIS2Xa%7+cP(>Pk0P!98(bz&#hVo!B?)qC z|FU}2vb{`Hp}WQ#$1_TsOEv8b{tIhBl)o5Zk(Q%Qx&I>L>>(61Y*J4j^7h$ax-%1&6{NClhrD-<6{EF$$5Z@s z%@?zDGfmR;a!jn{tG2W(XG`i3WGs|425q^5%s8Z>YF&wo|xBsDtO znE^ARA1GCbw>Jli&J}n&^}Z}gjhL~&SfF42P8Ub!>)(-bjJ$QKv7&MZpR>ZPs+f{p zW+TSWCS(o5I?lZ}*d7YB1&M_x_Z3rzS~G!zru&mQDzoE*q_s*Bqp~K!$5n80u^HL3 z0`#zZF<&lzrm3}SHo6?joqzFq(p>n^t{&oa#uHg@`992=@oo){b~AWazuxdOKi9x+ ztt9RJz8!OhTEB>vsAXMpnHg3KJaUE;5T1f42w$SgLM}?bek$r$f~57pwTIyR;6AN) zYckH1-~>HUiNqaq(b-?rq?~4jo~5adG;qX)-I@F0Dz-G~8{2bdxPRwqO;=Pb)lQac zT|tUHMSe2h5LYf6E4jKTsgWdRX&}*mmOiMnP7Flc&6J{*e(t;!p28O}E43QoBP{OL zth=MU;dao2QX!IE&V_;%C-%n>=cTTQtle?RN*$A^sr;z75lfEv)C2E_qvZ6AyxEIV zSfuW9`M`zkgvbk9NvN^Tjt++|}Ucs*Oh;p7XhN>+~9{Eddlysae6 z*nnQvqRwzi7k^T&XVirhjDOSEGPKmu$S0Z7N75dC8Br4$dFcZl@DaJ^G<}QP>q);r z)|hAGxcz>5cjqDTGY*HE^{YR14XM5r<pn z;={Ms@956B+JEmN^|>`=E;sWN2a9gdt51U8nI(N-qV0%4UOe<}Ks!MXAVd ziI3w${Ffh0FV!zdEmlo*%y-3sF})S@BcpM&-TvD@ zMDuN*q0Popbg6}?ZvBWBWO%OCw*oHFHo*_g`JB^j<$ru!ABxXwIegkBa{8%bJ^Ez} z*Q7_u<@BxY`b+W&=2HBos~DU+y<70>S3IskX{(|+Sgi2qBS(_b!uwU}-)y!B=||-5 zS!`^yqV(|b_g~v|%Isw4R%nC$8oM5r6~EXr zdO&~9On)$jYbx1SKo!rcIUlRD|0FK?TJugDei`wrv{ga5?kmF49{ct4thNr1;ILg%dDXm}V;@#n_34gw+l+jdQY%p5L-#6^|Y<-O;;8v=5 z{Ps-roX`(}C*6jXb90f3uCJ6N%btmzkW#h6R-s}(@6i?}?(xx$`_ez;cQ%bJE>kyL z(D&77firS(skj!yXU{_&Sjq9we_k73osx=psWI#;p3$n7sWT~bE1<-GV4EES zKm3wMD(~FA9&Ovv{QLVyUi=anV)D6<^)_!F7h5lpPm29ohUsqIS^K1Do;FbXn#yMs@J2)939>P*+1R5aGOUekFbb##85 zTmDYGfV|kdoW8J;kXM(+MkguR(^rxU4mbk*B%y{Lc|=5M+8obPsQHg{_%ANlIe+ej zJMD2mWw2M>%V|^ReYk~jsnO-e?t~x>r!D6tZv?BXIpU1x1_HYUyX1LXmu(H~^-Ln` zj4+`-j7m>kGkLD0Eo(*MnjE}(3gdGcx(W$aom@*t@>3h2Zju5i6p zURgwuxH-kEecPvoBt=3CozIm-W`9X6tT6LRv)OGD;f0?*gZ63Ydp(r&(3fkN!9>Bqjp?-L$vi5k3jFwTtHah4_n(?s3UV_IglUa=zq~8Et#mnlwrx;}y2u z$2Get!1$}6w=u&YM_!FP$*Un~;(TBi-$_e{)LhT6a;%`m?pGRDkOC=5BY(MCeuJoy z9b-7}CfO9y1U*hbfjz$5_-dFT!&{5hJ+bm2C3p4uNKekk-E)FRpR@h%d^;y*I*~9( z9qMwxrr{ILO7ag0Jt*?bZq@ENd#h#3>8nS^CEupE=}rhMm_Ok*l+L6D4v3h?_w39o zmAm@XHqGL$n*(7DWxu;d9HQ7$;nAqdDpspe%68pHu8WFtsKp2_oZF`+eKYw)N@Y}VZc9E~? zV>QNju`OTG>xWXli*Iu%n(nbHo7K{(*>YQ`3M~9uvs)>g>-L^mTC}-G)sZk7{`I}E zAIL`S!<+*i>&az^+_I7!uA=7PxIV@F9oDVqf^?wd%%ohaUJD+wVZnv|?PhP}PjC)5ED(=^sFgfLZ z)&XM+SZKcw#4_+%KrbBR!MZGW&dh^`@5mu?Z!E5DGbwn%Qt?QFiU)R!Cjr8UO%CT7xa{^}qfmup&3 zszr12XNLkqasIsd{$yoTHR4Hgyq%S5P*pXD+Sa!H>gN*-G%le81b%s5#6jNst)aQv8ta53gv~>3R=PgnVryvu`n{*}m_pONrk=~&fK~5S z{YOQbQTqey?>|xEw$Kvw{w82Kvm#yktRjBIZ;e)0gVDzLceu{pY$-amyRXtYh1{bX zJNP`CnAI(j!mRlhwz#2i3T19&b98cLVQmU!Ze(v_Y6>wmGMB$T0U#bSFgQ0e3NK7$ zZfA68GaxVuFHB`_XLM*FGBGqWHJ6|30VjWKx?^yz&(bd(+jj2Qww`|R6HF_ndq448My(<;*u&%j9hF0 zMtT+)GBOb-Q$rU^dpl7>7gKJ4x~U03+0+5R#0+3&WMqON1Blo=csf~{Tetuyjj4bB zEd;397@AnxS~>yL>}~AbER8Jyyl!r8f^N>P^iHn)^#3?1o0wU==9YFa4FAGS($35t!2TbxiL1l^sQwAa z`Jeazl>cBz1u!u+`^VbV#zxN2))YV~VsGo<>SF2ykhM24b+QBe3ww7b%YT1KBwY;u zN%DU@3~eoKJpX@v{;$P<%!TaC|3Q(CiItv_^*?e;XK_mpQxgSCmw&K#adI{Nk67LG zKkFoGYGUbX`=2pP|H0><6*jTAv+?}D)Bcmzzb9o75|@?~k)io-LHt`SW@l_~Vrgd% zP-!%{_y1W5 z3)_2m({Zo>=vdep0Zc6H>;O&{M&JJxt+A_nrxg zJRw%;ZDEyuV#RY+;52hH2C6hGOu(zteYe`kmO~aM`bXC|4=OkX?r?wjvw=o@dsn-X z53R(8@uqMmlT$H75xOflucaha=6-eC?}~+QjS+e`U~1U5#&Te{k@qf{8|y&|)Kje4 zc^7q3j^%vF5==1$6)Hyi*AerUia5Q!V7}; z;BLvV^(~4j109aSwF-Y5uXM`o`O`3M8_$v4cnmI=E`LC+HBJre3#4fIkCxNb)@RR9 zp9YFZlu+5(#Kvnj1ED{q{j3goJf@U&?z>J^BL-~uiC&TW78ym&`I4aLHwx)2Hp zD!cWyI9xIXr?+fy%U(A60Qt&Jq>3*60s*>@&5ceWdTF1KaAuMt*{|KcaUn~!DP8@eDqF2L^l+|Xlqz_`~ z=ets?mu;w=U8;X3njc^(?~o>C#;hzaUZ?6qpDSS1MGM}6*C+jXyOOg!`P~)m4h*Cu z_?gYL%ImD-E>SxcqEtcfPLW-Qdy$T<*hFYHX&7yR@9nff>vI#%YNb>I=3aG0clg9( zTCrZ}|CiQO5=1;V6QkSY;k`2uqn9%3i>_KF&@;(whuMF(TSz;sybYs5*fEc0C1#>> zI9IR7el#4OK+Ye=!|KB~K*cTxg)(?nXkq99!dcXE9&~yrQcW(&^%Iw~XH(L)!Nq%5 z37xs*8)Tt4T!8MgH!?>1_2i1U zGJ}jQQzL&a4ce*o+}&Em;asV5L}=^`#CK~-le>|Azyqhaq0^OdgD~`RFPLcz1_mWH zD4JIVnS1GJR14cTTA~Lm6b^()J5Z~E(%HsdsEkbrSKLOejPKL#zS@D>H+n#-gl<&? zmcaT!r)SrSC>?sF+EXA8U@xXpnh&CY&`c^BK$LQU?;=lz6=Fbw~{!juls#JN`uOc)8n%6Zlv;jc(h*SigrQ z>jHl+iW&St!EaiZXnCi-tGhhXkrMHv@omN=Sg$(2l86>MzMAx zrI_maP-tAi9=6+MnUx~O3ZwFOG&u$K&m<33xuH_2@;O{+SwCgWg^&9f|5+L|So>u2 zGkBFr?NZ{lGBL-r9ZA_CYEU-KqqDo1-<^#wCBVe#eUk za%+(jl|Lw=9l~mSUl&v=1Z2`3+PWd0C-s#jBi6Ivco(%4A_b>J*e-0kF0*gH?MK(n zbHs*TK&iH7s;0b{IVI6eJPuvyKu2GgHNzE^$;itIQ}&>qT&dQCAF0{hWHipix7W?SIp*##F4XCQG-m$fEaK)<%1HAL($Vzq^l)Q>Ge88 zeh)OKIsd{D-%^y80Z|h~_IWYu6Dk6Av4a%`@j7|jj9vtqHFE_QHt7XtFhY8r4xPtS zzZ|7vL|4CSreQQ|>*LyO4-YDV6!HPx9>o@twusn%zg12YDj94&XTN{YVaJ54Q+a8a z<+?GzLw&WXIW{yR;%xCmyzcut?O2U4BE-LB4+k{!4V+@7ICAzr0cg&U-fcXmhIJ|C z$vlm&5y$_LHOFGxzBlt!^avZkhqqJ3vFX2`_L+NH+A(smoIuGt5u)GI63d=O&;vuk z0@nVTMDgIcCyN~0v73L#<1Eq!D9Mo#Q7ywbP_*sm3J~eU1_~htGGPzvp^OXl<%#JP zi74@$2E8qeyt7zDM?qGo3Hg93>+nnadacU%q8*xH^q!%`DMR~cwDY|U=xfjgse zy|ixD^sK3NO3D#S2*Kj|sR(1Y8uy2u!LRt#b=tjM)#!04Ov8p&8%=qUZiaU0}gSjXKQZvf_Ovhu(^z_wrm-w-d4hD56Y~p1&q@s$p~H z;sG+z;d=GdpnfM2t!M7Va2Y}9tIdWf*eH^k#92-uKWynVPxKo`1e z_^CHMh4y~{IpavnqF(ebAei$knh6pX4djY^0W7sJ6ZA$0O)9*}7FH|XvT|?D_{xt} z6x#G2)0@zuwVRQHA~8G`DR^eQCmx;CY+jfMNS;pRo+6iT%~c)INjZB2(v$}Kwt)&E zW{NK>4cYwm3~Dv^Q8bpE3<|bA-mK`vPH-;|KS+OzaCI*`T2;OlG2fKhBeL>`ef^hr zyI}^PE_OG#EY-OH2#I3dndP)2ah&#_b|^bCI^-p?2uVZ$c}a`;EYC3bV-EC+aieZO z7#2nb^fDNLTP*HXGVL|TGy?H)>6Il83k&9X{DZcwy3LhtoO+^Y5~>fKgMxsxj(AB!H(3nG6BIQZ5i6I)0%w?iz=!2}RXcwF%axGPa2 z7?)HBoR(ncR#S3jWRCYCddr5N-rS;*bIbf&cRk1Go`Q%3+Q{l#upd1_@;aj{EI<5u zj{in=Yy2q$8L`LLa+v&Xtg{(OO(vK3_c7Nuh#u!>u=UDEDqT1p>7R>sN4NJ+(A&(cg)pjuJl zw9l_Fetpk}?`)&(5{B38v(Z?^yYd6wVwUEi?r-!?)Cx}MjoqiD^_>1hh_@1|OVKwC z#kmkE3C?Yz#cn37K119E}uC?tPD)tFTj#BR4=mC=EnaREwjd_b8PjGWAkmLB$W zF8N3jshGy0pnYVkfwWgXml^zy>Uw=Ji_Et@Fob8*@fImVC~y{J1sGI!sWQ_ZPW*&l~}x&G&}cB}DKFyN5`D$i9Ad0lUG-)(G&#CY!=c zAyE=0GtEdRxs;iP@Y5q&2i1RTknZApXhv+4Uncp8;vVup;kr(-WApJ_2DC?Rk)58r6ypw9EYnM%6(G0krK{t zEVUb)WS4hCNa|Dh^OC8?o(z-nYcUa#$&$<&2DOrkN=nJ_99U1{+TDLfx+a%|&+&qe z7)pJIe?OErr)TR5f!Eq|yvPfaZ}V#JZ1wnJBAZLf3!q@+xH@2pdyj&dD|&=|kyT^$c%yUa)1X-OW>O2P`OiM{=Cq zAa(vVCNW?B8DvvcX{<$X4>^>d@mR(b^d=wAAyXrl56}Uud#3JEM?;CoznaGEIuOVW^igv>ksE%}dZ(iO|)&3nfS! zZSdPqkq55i83{Mo?Y)e3hlC6JrluT*;-PLSu}qwWZlgO9H)>~YzMy*|3O~iZnc>6eUlJw^XXs}7j*arm{ z~2}8>S?%DQbeoz@f4ifUSW!>mES&3_hA0nhH}5i%mUpttHNiiiYY2? zCDhjkjCLgGm75T1ta^W7;u*JMM_zo}lVMm54;ABF+@x1U8N}+I6Mi-g>TDj|BRQ(Eig$1$ zZ=W*=6mX?>j2R`;5*tQnaJTsGx}J9R=@=s|mY8F596P4hhuIKD>t7qU%2MC*tnT>S z7!V#8!oGhpayVN@$M5!Yf!^#4X>j^|f-IC@ot5@H0>h$+e9J}RV+&u_=xwz_N_o#t zMB&EBJff{dK9!ZM$N{{F_npD(!JI6yZr`V7bd88M_xb8~vD_;1w`^4vqidS)$a2vEqH;R6NF(&7YzJ z_D+B3GwH>dG|&*h+M+eg>OE&zraj6cy>}tIYw&?RJq;MPrKs_4D%Dm}V?Da@qE@+j z&NzSA6F|=8vFBj6Pj}8UEQ-g5tG_+NDX#1w=T_YBvtlf=No6+-kK zgIb=)r|B-7Gm^Vps5`CFvYdgd9h5L*L>u7B`Oub>At?3vLzwFL$D$&9thA zpJsg;*iI5+frMIA9d|^;d(X0eGPo$Mi ze7<8!CQ6mhlM2SHPB$F!_Nf+CT=#ATbSM~P^(43-g@*Hk>*(!a$Hee~_%X7B-EV-b z@JcMAYIh>NI?*3Z+u5Y9T#;5~@8Nj3kne&nIGb%fxhGtP-9>}CkF%1T=7+s$C}3u1ry?8!0m_k6IuHR$>wyJnowi&5D?CXUWl49n)1 zlbf{Hc-~CJ^4+(AiN=baME{LXqjyGguW5REdoChKgb@|RKfQ!GjEZ`OG&T=wJ3D@d zRtb0(+}m>h-EcvL5fe$xp9XFmsMZKEAZAU>@u{C?Z^=Cr?vMNtEVM?M9w=!b9cJ`Mj`b1Y2tfIuo66Qb;{Hmyjhs#%ObS!-ws?mcXjm1 zyg2IX(?pV=cqZG}BX(ztunT|EUgVqf)%K7DzvOf19S}k9dh6V9`#iW&0Rz|jiaJzJ zuBz>nFhdR)Pp0(!NlCv{;-z|tn`Ex)1mdVp_yV*P2*1WF<5b*TI<5F_twM>4OEyQ$ z4C1*N1iDWv8cUaa+YgARlTX6di!-qY$EL?QnyIa@S5A8rjcF~~kSl*Oiyu~zS<;G} z#L!O`7XxIm;$VJ@j3QmiA)G7KQTsZxt`- z!U7zEanipdq~Mx&V1p|NwUFv zVc&h}2-kli0G3``Tyx+YA@xG5MHuG@Y5$V|I_s{xFUUW|&dbGuKXh1bF@$$fNR5yF z43c*Mg@_g+Y@o}(K1$Zfp?b!o9%6>K&HD&<>zCV(b9psD^#y;wCCt+q3;qAuKvjFI#J`^dqH{zkFJ;C|;ZYty=bF(VM|MWbelhBR7pF z*tMHVagJEc;52_q#%FeB7l0o_(|*rX@MxtS;xqr#A zxNv}Og2IzMiPKO-@lpV;eojYO{0p6#+-hrOfXYo&y5j#q&VE9q4C%a%@+RX6I}GnM z>s{IHM-WZft(}n34wsaiecnMXZT6swQY4U-Ux4!((ENYK!eLLEJyE0m3PkB%`tWEh znTXvi$whI93`2hZ-FdsMaEY#~jw@Wsq`fttY9J%n#yNB$#*SX}FngyBVf`d#wCKfS+zKRa ztbUZh!g_yP9dSleo@owKlx5{FN=|>>M57}*D>_>h82EIAc~d`fECZQ!B|R3&%mQLu zvI`V+QZf0;1m2yta{9L-o>l;@h2G}WiezM(bl+AwCeJWYt;&PUMOlI&cAbN(#ZL)y z#0zT*E0Bl=_wP*Znz1@$RaRt;~A&c%NeNaJ*L5DTZbG5O)kc)xVeuF*t6 zF+!w!U`E(mb}wIDrLfNJ!q~w*yNUVRgf>1qRYAgX`JR|TAkgT|wffL};&7iaxlv&QBD)Z=yg7`p8`8T7fw5LB~BAT8ES5T)7@mO?dxr2{OyP*Qf--(Qd z4*n4l1 zox~|y5LwWl{^v8~3TWTUC_2CkTid6lQxjw754eIg}CmMT3A|375nkYQ5%jL16trA z?=-QS8xV6B0Z4kDLV&~Yg$~c2hR6(6#H7e+8(z+ew9bWP*LN(VBMRT_f+ly59A4&5J#v;*!XA3f;;HP~ z`QPE;XL(n=8&r`{%?1nBPDEDG54m^?S!-OCFR2LMH)@siUB%h|9ASUhNZ4S-vbZAW zh_JQ;;*9#2OUq;qb8~Ew7^z9nm}X*{y)n_~ZOJ59m98q7SW50iYv&E`?~XCwQHoDm z{%qY=WzMg%?a`NLZ&-Hq5kn@{(n8cH19a=se;1&R&iD+UW1WkgrQ^oeKo|Och`u7` ze-!TIUeBwYCt7E_Ve@~Cd(azopQ1421mq<0R7uS%a9 zKVu8NZs)SItTLDeP*#JK8wz9Dc*^GuN-k zaH*6#2E>xQF!Pev+z%Ly@S@P2&{4R$fSfUzS#1(5l=>VkzT(7ew?@Eq`A3gjR!y+j zaKz#1{%Oi0VCy%E+>H^GSKT87iYb7;&La6x7BE?xt^w8KP#N`qRiLt#6?m>9bg`Dl zE{^#QL)@?M@-BalzA7#sW=}>ww@blLJS68x8m$rFT=_FBg*4R+@^HU3a;e`g_e-+c zW+)BlO2Dm0#{>^PLM4L_HW~MN`nPvKZvIUe+@3n$Mz1rZOtTkS%<*!mbfxVcq1d6j z1vC)9EhV3X(Y6^W?(yF&LQevGWo&jlN3iv>wl3ZmTBCm!sOIa-c2jR{_zn95v3|8+ zRdcW0rM#9c`0-}oe6dcPABG3UJG?nmWbH#x=X>0TDTged-I|tS=2OQ5J7}INW9F9` zd~#N6=zk7DTU~5g7nhYt%3;(yb#CL_#aEByhURUE(Zm_P=VAcB%$431WpB{k?GBY9{6dg}3T)vSi_vO(GeV;~b0NL>qn~n345v ze*DwmN+rraEqDeJX@UsPaEN!lRz~wO59Db};t_vj6**(HcqHg4d?(G|Hj5&jv@P7mDo zwt{~p&tcZPt{QMAeFBK_7nX;;xf#t|18%(&R6fCy@W8KgZxZ{TQDgKTHp=cNo>FbI z+P}w~tRg6leDln%k@1hMvo)(8O2Z@}!R$<6NnQ*p=xmN$ZdXB>vrvkS&qFm$3Dk>2 zdI96GhCDx0Jhb9UgC2V_`j^{7@%7Q&$Ypnf+>@KlFSy53IisJmZKwR z(za`ks@n$)qzZgkduBjl}&m&|va4BbG5 zP2{J@mi6skeZ4eTSgvvLW|;G;e}s&Uway7p1p<@y)09f33uhAKgm{`h&i5MQl6!wJ zN4mMy=~ig~55j9j?Eaoc<~2e9_}nk_z`NtXphmvrGf`4xFF3x5bu8;yZu*#8oG0h^?q;g8EHkA%l``(<+5d;^&L{kpCLC;{iIlIv)oK|XhK?aDa{^7UPn&D2#6BXHB$#S>j;kqv&};++DsQ{I{H z@0ddcG8XvY7hj4oq=zVIzKMS!9aD$K6`bH_H0<(UB#IdOi*GQAj8-6dXYk-?Ug9KC z9(|2;jTIM7F5oSe(d-VDf%P_s_(NM7QhzsniTE;>X}Mn7pkvfBK#t%GS6=5fngcua z$@?c2AE>c?VbIaFr6zvrhQ-%SUwpnN8+g3D5z`z3C6NrepEMkv;`M(DbKR8g)H(aL z2%HPbDywHQ*v3R>(lweq44xh-iq>CL+74##n0EV5E_Gp91%x(!9D*0%836;5!=+Nh za9>6buDB5Mh|iVL++GWeh9P!x`#^J+zTSgl{|J#2KFW6}$k;{-jySK7AyGM1`bg81 zqJwHRw7q9-NLf|=it+(M=}>+My%V$g=XaCU-KJaFMRecIg|7nMTRR};KV^7ZQ^ zIGtE_7&SW&=f;jf-kOR=2ig-*(P0@9T~k3iIHH3+=bloB4VvsfzZYKQHed-<2FuAd z7E)8PhIm&>nlH6`rL2XdzKz z;?>t(RK8sQlJ|tk&`9fB5A!y0j-g-=T-Hd4dY~O|_r!^&n)=RiZPjA|^{{e- z?3-S~c&T;fPbsD0xz_?RrFO1K6&wNqbU=h+u4UVCtvdZeBK%BJUR8VRJFwlNOl^0^=f}&wdG4h+8Mcb`HH4f8B0~kUGqlD2D&UF zUO%Xf{zIJL_`EsSJ@>7e(UL0F>6zHN$uBTmXZ7pWSmTOn6;D4N^ad*rlHJoZBukYRvp)U8q#T>-+GrsEmjg!Wn{CFcvT$s<{ zwV|%!N(`vkPzT~c3}r76fze7=PZ^S@tD>!{T(N)pJAg#;y&AEm^i2DrY|Da{=J-y# zI_(X?yCzBqb8joTQb$(21xb&Q)Z9=f_B3Y@&b0I($b1aW>yOp>ZNok-GZw>$r^Jnn zHbV|dw)wOD#ur{y38!rK7{ZUG7c~E+mC8_n(TTbeBf?i_Vh*%QPa)D_C7LU}Oq!Uh zX5xQH2Uc>e+U8%FRf;I4_-x6Ho7m)N`}SiU7RQ6BVA!`$-7_*-x{idmlj$cHbPhw< z)W+BsZNU)sV0)~Nao_y1SIpkOrhG55^p1ayPR-+(4RwyEzx z5pi6h0Ix9=y!wLxsWcDvj>=~WwiLE!jKC)X_Tk((xT~r_4vXd*lK;ws8qkygF5`)| z44^-b8wC||&djpP?`IHxwVN^Wd(RaOU_S1Z%ju4qUDg=(A@(Uxn`jl}~yff7yTKenKB?yr0SLQsg z67WjP2^R410Jn|E%YVTEg{CMSd9<@vQ% zTTw-ceZOaQL$2)(q$=44#W{a;5#mtu#bb6pgu0w@ws`@a-}xTUvj9GJT=6)NA$KsD z--6B|-s$uQ(~d~I!@7`=yXk+sEd!a$+LY+q6)A&Mf{M&r_R4Xi2>BETpsrk*CM=-- zkR^3B1`&crwn@`Ut^~Z+n0}M3j~}k-_YXTFNzRHkj!u=%M#J1sT%LdL@+)UxPJ%g2 z2540lN(!s0v6hPm7A74W(A0vH<0$frhyNLMa*+xWYu*+yR>Lz_)5{H)LPMthOlMBIWr&CGmgp22}?{@xBepA_Gp} zUqie!{$2r5_9>!7L1{*DWxiDcFq$;i#qQ zv12!gQnOw7NZ;4NBL0OA3^Y`py-ymNYI1Aq3Bz04J3tb@)uZ*tCT}lnBcwCFusN2! zUfa!RE8yQ)mJS zDv(Wk_l)TaIBr`NOF99Yf4ZAHXHz&%o;5bB+ctma!%fur5A|FuB#0qEOU{xASn3I1$V!Y8!4+N@5vLw_V zl{vpCb33IO*;Iln&ZkA#Y`EGtt6IvW)*)=l)f00yyY^FCE{)aZRYynFVe1hu-3h&4 zNohjHX`|+B;6*JCzF@ zqdO3jUL5yT@kcaI3o%VS8bT=^G_gg{*(@&z&F}KLFtGGF{I2$4=Yhyh*HZ_NIE|$4 zsWh>6A&To}(vjT%pN9@!8$;a~-{&mlIqkK1{_Zljtrynw6A z;whgK2MbBKY6L%(qz*!#@ZT#NC_+FSGPUZ64cih|?*@VqXefd81IETn$ zYN^Uoi_E!_E7qeC)aByn(Z$TEFy!yzHB2>Cz{SRphVU!L+6NQxL==InyL!3JbSA}+ zLd>f1nV$ol_U2Gu^={lxD|dgfp@jWAI8n!Y?9^Q$l#fQM?0{WcLe2=zef-2_;+>=|NCQECRQc>Ukpf_~*z5=oEc|G#RY||-1dOC@8jx&F$B#~+yrJxv( z1nql8^r=u2RY1$XfDm?K9~mYGZes@UB(5+psv!|mvVElg$lS5{L5um(Pwy1nw^h9v zm=}8Dwa1%xV}BEp85d7qY1wgq$-yaKQJ^jB1%r`9_egg2DRT2?aOBq^uUrwM9#OIN zHUhb$Gyn1d`}vI5#>szx8@SJ_U05#@?RO3%wHp%2p;S|T%RMgb&-f7i%j~>k(~eC- zwZ|hY?_2%BWI7%vKeZpGm66U)mT-syMEolAtHFDG^H$9VCB=Z~_WM$-oV#rrcXv zEQAQI?^ol+5jkA5Q6>FWuyt#o!dFbTyg~a_O)vpIIr!Re^6u54MP6h@A{nZJQ_pGC zj^g6voxJE|Qiv}7gue_e6ID)sX(*2_$}|t&FNsv~#t4GQ5RaNV(8^-fnx6 zlLCmI=k-`D2)BQdDsxoP=Ul(f&<+P+&FrmsT2x^gd~MW{(5=Tpbg!WpY#R48g1O;+ zAa0}}`dM?phMMOPAjv4)jmuaxgUEw*OOkC+yL0mW8LNHE#? zC-0r1rlnC7P6Y}&Ym3Fn%@q)X(|96HQI9hQIHJFpUK58OsT1_Ra*;J#Pc ztuh!_+g$VPteqbHN;9o0&2*^k&YEENX-0meNX)-x8M~0nwZsVz%;~i3exsxJf}R;p zPO8i545GE-(q(A%nU6#@KnM89t4rR@(3Ee$Bp9qu)$3Ub9?gVY@HZLL*f;N0aS1! z{h^kGnugl25hA9`nh@B}5{Eq9fSa3_08=*&@3OEx;2mz8Frj|Cw#^h)sFMSiT!q`e z3QbG61XCTh-wJrA0|*yki}T#2GuW11Epb8e7X5#SMAQHGLsywQLfg)LLKLzm>pimQ z$w(AodA7y;14y|44O>A=@&p;hk`7{{+BHx&G0~bfH8JTY&sY*@Y3p!q^eoHO+Ot4W zh?a6B)!viQM%6mEg!H7m2 zliPpOFrW5|{w4n9+CQrMF-WJnOMu)S2)vu@wn}+AqL4{DIAmO(WK;t)kR&Z zQpqeoXG^<&G#d7C{_1eoAI-7^RvAm1zjYg=5C2?S2zWdNqBINh-h`$%CO-gl->&*V zN0bije3%g^owcY675c2y%ah|WHZHTTTcm$K+AW@x{tUN)9~t`Mtv$m>-j-Q;dl|Th z_A#D@k#@EDDsUgozhnFZF_S;W2fNOp#3Z!WV}n)kdezlT*MKGoWXj<~euoQlfNZIX zZ7q(85<0e7<^9>kJ;X^?+gY9qOeI9)#@-l!Dov;l#(+;jMX18qaECqap0P)|1KxkL zX7H_E5MiFi*i<=dhs7A#Y7Dkg@6gXJAQqST0e&>5YOLLhVXbJ}>>t-S{mnsiGmpPo z`^gX?<<1O~H>mGC61qM$~6mEZBg_2se5#qDpLbgyJ@yzm)$&{7bQL)=$(H6Y_$)bgik9Uj`+#FUTLm z3qw@^IV2Np*l!I98|K1Xm0koJa3`b-V=}YM6bK`)=zbuWdKe?Wog?G3Oln3Uzq zSXuRxx`T#JD!*u~0m1~SXl7MX|sTgDowkgciMR_&$AkO+-k zSr_zKr0L(=3O6O(L4f0{zD>KEO<+Opo%yxQ!N;V^BWoErY&yF#XUXgq>Ds#6O_A5n zCPdMXTgyl)R(VxK2B7t;BB8{&5AFvv3p4~a6d{LE11fe4H}B_z5$eF`B#WRIqjhsw z6VvZEq1;xnpH@koYNdBfry;Yd5NI+d;E>ZJN2QJ`VY7`1tzFx2yeR%6h~8sgyw@0l z^gUPlK=FyCwE(1H4Jo8m8@eoVvkAR%#bRw=28m4YPhW8@DZt6^JIwxYT~qX87Cm8! z$avf}EBB+4My#YHjxhZS#dnytsbMjIAkY3(GIf|DZxiE~Sj664 zHj2lC_>+X2=p40H~$a~kx?NpuxmPT~(! z62!AB3vF6&6F@J_VP5@INhGjWwFh1NO{PH%($(z`=CqusL`pP4=~O5=QHZE4FV^9w zjQ$2*irxpKw8hNCUJHE0hK86IVRF4Xn1~?7Td}}vs`+;guzT$l>mA;r!*`gMv2aN1 z0*oSA-^gPGdbOGuq|X$~u<;45B96)Eg8QG?LinT+Qvi6fN9Ib-DO4Oozrzn=v;1`V z1g@<1=6tV$^ipUTW7A&cbiQnx);LrTR7Q3v7Ls8~YZGMuKj6? z2XS5TZ@_>~C)gkErbObRP$TV_J=qC@?|WXB=P#{9?L66NFkb0<*MNIzHfz`wYv+#TGqkdBvo@4Rf)2a&}? zs_xrpDLIOsAm{XjpRX!JV~SRMA2xEKAuOcY3poMI`gdVVYgm6d>f5kSo;omRx9YDV zWB@a05Z1<20lPeTjE)caef`amw1HeE3yuxgy02Smnj!Q4XeTEAL5`QlqUn3$_t>E7 zy}J~X)u-Q3Z3t%g!);Z98m0J3&v5Q`FTzelf~kt?0)w)KEFRk1;zu$2n)YC+l8-wq zb^r)UMo3{hue7UKe^Dg}OWW$i1vv2^MnDpaL|f7$^Vs0n)ldVXNs&fPrSj%+P5yEK z$A6sIYQ{|)>?A}w!6i+*P9zRY3GVA1?<<4YQ3Oq$Q)VKo7t3&}S?;K~i~*SkH+sr` zE3m2gezEyPCnlW>Cw<~pQV|)&PVo+dsDaC|j{-KNf6dO)BqeqW$VWAD1B}O=0A+ni z4XSShh9E+Rg+Wbj>IFi(&lfpvY(~)nr|(7VU{|C|mw8=ZLq1MijL}NQLDQfezq zO?U6B?lj%!bg&PZCLS`9AC_|x)FgE%2F{;tpCpo7y?Oc5;_A+A+eXy&>E2;;zOGi| zfAj7X+waXVpGr$>%!-lu04h6Ox{1Q#MF-TJG?m5djG~o*GpzCeExZX&UUT->LKn87 znt{vN#4qV4?R-i1LM1)#-q+c>Z^I_W9-k`yJ#7M`k`>l4b|UV2?my~V3(Et_)W1O) zJA_?b*NFqHpx}nCOB^%m<#|obkwnRX)%h2S{J{&FQ?{rBCH2pK0C?yJ?jh{Sn#NLe zClHgS8EtBBJOQ(OA0mM>k>yOyQ+&?B`+3mBnZtxe)q0a>X<{xwdxRs2e> zKjdn>^=ZssVupzNU1Q(flsmv=oq>{SPINPsz`-M%8s~IE)F`_n+=@`Ip?U5Idr!9- zj+ZNUsiN&8sP%^-fSVMrmBl6e8n@l40d=Y-UM;}hd$+t>AhCV1QhZ2IA;w~yCabpL zQrTdm;C|zyopE6!STPV7%z(5_+i`Nh-Ec}GhhMK;d){34Dt7=S(=$g%rj%=u( zF!5S;(Y-dRKJykIZRTgNOIGuv#$}seaBP-*#hw@LRpu}9U%DWKNqhqa*7 z@`eCc&qWW1$0P6X>Si4jBc-Cqb78AM{yl@gsq!yLA^8(0^PJey$sOvVaQ$=)-cq$h zQbBUrYR_xkD-RIVXqW&eWtH)oARLVZ1;~^%i=(9rWoBEC{W6}+6avW@nqgjqFSPY z?zb&1whiGncFKFBrmBCe3Msm*MGj*NpvyL=eRmlepq3~f!Iv&8hfCZfRAvGuEcz$6 zTF<)OsWqH9Z~BIl*x94Xh%|%d^$`5(n>h$sK1F&9kyKve!8Rzq$rv%=+PEXSxA`GR z8vMNyq-r-Bv%0-E%yD{cc{V7q?rEI6!E>5N?8rm;yJ%mIh++=(rJpO7oLOSc+yFGl zchz_l5Vgpd+sQ)dUkoQdLtErj7zqsd3Je)_;8G6$IV$gqWkmxo>P|mzExE{ zt#V8`92TV);U)z{X|>uGG(`tPv`ab3Cpta@xMlEftdbIoJlDc)(??a}3Rqf^+ah)p z=rnjhs*{w*Rl-2T7yY%#+)%;5(BEShJMn&jfwQxjM=TdCFHRgam<3?GdoHB)l|h$q zea2j7i4bZ;x9Dh<{{Z(YQo*hj^aXMV=N^E)W)S&_ub@7=4~#zn6}@AS$|m$_{r33- z7_L+HuPsQ^P5w7-oLQ&;VZtU#ImRleWZ1R!mQ27hgn~^!@1*RJc6Ay|x44N(E)x#) z$XzYpRqE|vR0r971SZq=Wk{9Vw2;p=veqmLQi6#nuc4T43#A7PXY2BGX6pV28@J>X z>r^PorCb6IT!fe?Pa)>trm^G#9_>vPFk8je=>M?&C$u1Um33{tb|UC^pH1olj?pg> znO&%7+HsSeIF|&mUrzZr;SYs>s@@ngJU@%)|16ETKIa4JY>^61UFhrtmb*>L&*8ln zm;B2a+|EuE?5P|On>RpGCQTne7JRR++$LDg_Su(N5^tpwI12kJ_?rFiSRq zWrrJxG21i@eR`pOU|drmD?KBCNl2?H+ro%Of;Ig(Oj>n%^rWSa`OJ#(8JZ_z>BY`I zVrYG1B)k$~mTbUR-~%h^$3Vbh0YMy&eX3 zGMo2v@AkTcbH32ES)wo|rGfjGql2#`fp2Ac#-{l03b2i^&X<;Y^ajx!VSD3scY%3*S&~xTFYb<&XbQ|Y+{4m93-`Bs{9I%%H3W9vG1&;)b3mIkw@6F`vC3o>yT#rG-8THm8D!5e z5r@ukgU$W5*0>mn{sk8<0Mb6@U7dg{0t$oywcDyVXF%1?L$t5E2q2&{z{h)6VFy0{ z{l76Wqt$#9jV^DFZ&3TP-&JIEiD$ zG>WO;OHKcK_gj7nK3atx13jXi^JKU>J@RLURI&1O1XJvBAhUCJoOc)80HCYkouCw1 zky1?q{s(Vk)M+CK20#kb(X5CW3*8uUgP8X??x>L`mUI$ByvEUE|CPB6Uvj_~Alxmx zOUstsP~MJ;6A779qkJKJzmZhje(_A1b}f1QRQ zo2MVu9Yk>9X5TDnF)U(F$SDp#{1L9?1 z@pRx0&V3K~Hvl==alc&iuL5t){d$6O_Q*Blckz91T82+EtyX1el@ojNlx)GWa?%ib zml@H!>SBbC+4;GeER}ZoM497Z<`Jv;gGBDRLuMV*OJsz)gcnxE+Te%?Qshom1~8|E zb-_s<)@O6*=uIK|%W4b$0t(jNJ!kMK7%&(HMk=t4GC*-i#R_)EfoRW7WHd*$YML;2 z)onhC+!D$N3uX99oU>GQ%AQ6hW=35cIqLlQxzqu$tbV3{c_ljy+tBZQLLq;h6vJSt{6ou&9!@5cyHaNQ6}%aGOVi<9wx ztVrd9o@4oO0`H;4!>qH<&zuABB9l%oIK zvN_8n`*%G<=9_^+=3d{f3+mQ^_wA_L{C%ok2QZjoVE$!>LCX-H$C^93KfAkjMz^?S?l*(3~84+pOZ3Q1MW9R|)fQuQb%PMX~AS2uM zb3(JFl6FS);I;;&p?B>GsmoDWv%<{PeQ?Ethja# z4WRuP)I#^^BTsrnC}yI8i|4zQfB^5`R@KZcs4C@0L-3MEGgD?BD zv(fDlOIk`oPH|OQZtypmhI>K5!6mV$H*;1R)9PpuV zC~I`eUaiXJ0sOagV?}P+T7d&EJiQoICLbN23R*+}eW^#ty*UN<06FAS0q}VxaDSRhBZPf z#{&kY{xmX;PR!zkZHa>|NGjgGP*w1AYbHx1GL=zr9M#z zKGX=ylIKon)XsV`;061mI!Gm=*fJ+#puDgxR{V9bL?Q{=qsqB3pyj3eoCmJ$Yms#! z18u`5QtGd&zra;U0yzH`vUvAvLaIZ|mY~gK*@F(Nw3ui}d+9xH%8{&)ZQp*6-I(j)V53O~ zCgMH{KY4bf)tkFlQ>N|H>|wIi5XK|Ri-UrD73y?SXpl5qME|;oG+X~j_2&m-lt0Ey zVStP`S#l_QpWi+N29(dhQN%-5>L^nRGaLUoqEKL=Bb2+1vTbIuvkyF2hXk=`2ou;wUMhBHdL3X~(z-$C-G)4miExPw?8K0&sm1`wp0B{Ixyac-51!{d?g zyUCEtTKzI-{&%7=!j)4sJsJ+cmblGlil0SKLm(2!%03L+Jik+^rlmF-HqtERZ}r$3 zT3Id|ZtWyv87u8Z&n9T7h(H2ut*^!;PM}I94JDLdEZ*mzk*>Q}nAlJsZUf5vl}*w0 zN-$5K+2mL~4d}@t>lP(D6hdfWbBy-V^Aq1FQ%6!?hfcB3;hKGh1*KDx3Ab0h_25QL z0XI8aau=O5l-LmvMn*x*>C~1`eL-tt5Rs$D$uOB;Y4yi0f!Qzd#Po=T#4K7?r(V^rseDyP0_s?y)R|_9%25%6Rd%44@smdH z7${v3^@z(EIm8EmZ=820GH{~V{15xsX^<86wY>PS`1c0G{P59OM15+BD)px1h5o{( zMDq8@;kCP-*Y;i*A`!44zSf6#T}zVtmfk|Ymw+(OM!+BM*=Z~CDr*viKwG{sX?9p_|?YoIwTWq?xR? z^c-ju?i1Y{470|eR(Ye_);47p-~^fD`sRcUKz5`#j6%A?X)lwfzg=Dv*Bper?pz^k zqvLsSf0bgssX~=Y*mFP6xKoJ^Y*;JWm&I2u0V4kNMLFG9f$1Mw){N{`@b1MzGwHF` zNA7l_GBQhjOynR z0QiwrH$VY0vXXW3uKn6SK*64_8DMG&d09xtw#Fb5x*70u$399v<>eRb=Lb`xBC;2= zQ}XeUH6c@%j<9)Fa{_)S(v1EE|6VQYcB)8Apm&M$e-8>HUS&GnjYAV0d)n~zCg-Zs zzyxiA856Z=5hptYwz}PnoOBJim{LZW0kW{<@H@E2g0`=|A-23=X)eGz!v~5%wtR*D z!0XdJOvn^-iPEmp$rYLu272+g93Yb%9r3IU=hVy>8Ij znt((^$MO+8vDF&*fLLfUm>`B(Z){jVTo?Q8fj>ef4;V+{ zZ44wbzv+1^SY2GCbUkjvWS-k^?Sg9Ea4V5yyH7C=kvU6Wzu$k~xv)?49Q?(61h8>$ z)6Nzy|GRb#EcO{7ua?Q*@#&lsxRbW+Ij}Xf&e;msls*Q7KVfbMt zKyv!IoBo>Ap8(`ey(*MI9y$EfjYq?5?$+FJA^VGdM}N$TfY zNy>C~Cqa~eYr10IEYFp;;zbLoidp03+fa1rSa9lT=kJf{1Io$K$J$Xk3En*Um53eoz#fst>ns?vM_3U6cc8z6=eO`j8@bIHfI z8`L)+L+RZhNN8XtBej?+fIzsjo0U2X3w)Nz_+jFg&Mc>hwOXOTu5J zTbK>5J__f0j2_%E9RNkHM(Km+Phomxm$FF5UEEf-;u1JO$A>;<+jBhEvt1hVYc#J0 zbm3OoZ8In*KF~+f5=Gs`$JrF`=Ak)mrh+;-WXBacRl@mb>FZ`LP@qscFz46cyEb9F zV3AUR5(t-qm&~C`Jofk3CLTAEIF>^vlA&*NO8DQ5Mw2?>O~BJ^4To2M#_pRMgfr8_ zYG4tK(bpQ1PqZ{;pLhHM3IenwZi_shmN32p44lk5 zUI4*^MJLmyO&jbSbAG~sf9~M;7ByMtiL=Hk117+HmJRn25cf5>_1qZz{%s;i_4y4+ zce8P3%#T?i%~C9TV&&UHpRJGOb4ssKswt|5vjJ@s8!O`r5||5dK}!pRr) zI>v&p_%F!(W`Y<>pk~|~OdpOO!y1r0NgOEl1~6rhqrVXpB8SicMd~%(Z}*j)tW2Z7 z_FO!Yc)P8(K)LdI8zYf_wh~icP>HUa)JnZ%{G)oIS2_ddZ2xl6s;3#gk`MAHi~Ona zZwgdu2=>ZXLiP1k?sjpJXHx>I^bv}3G>S`25#YCvt-IM(ox=^ zCE!7q#KNkE_N^t?A&HLVrAt-5E?O2_IN8kk6vA3CBoG?5N42729oFf&CD}*xACrlF zB7b{&J0$c0dB{WMacwpGbJkPoAQp3h3`#DW@|O7%8i**U^jg0jo4qeZW@A5-d1@-& zPyQ-NV28O4o=ujqaM1X>6FC=Hmw-M=7Z8ToT72;o+gwmEvEUlEP=by^nbrCu4g zoj3x8_3&3*dQcPqb^i~Eo~t{?c<)^Y?Z7I#)CO|+P%N{P3quQSSDi~w0U!JnHNLzW zyp)4hcy?+lt*F*o8X0W+YJg^=r8+i#cD(=IbDD>@0_hYs2#Cb%_aDB}#1jL%2iz-9 zFAd*d386$^xRrxWvt>~HftETeS2 z)00X#3o<`9LkkPLTvITmU$3YN$MwK}3IsCN$G#HDChqWiBg*e4chvl!eNvWxfQW;! zH4Gmg3}d=nBnT2NGZPaGqlA^Siz^Wq6Wf0&B1A0zT3r80hg|*IaNdwW@jKC+D$-+c z`iDqsR@zcGG)Ll(sx-Lc2@0Xn^_NP41DV+L`YR#=p`=J9{_fV%NkxMVZhv%D%)dTs zM@oV=&up1uw$L_Jf#Q?1jt!R%A7#S6^DISM2UXQzCC`lVE$v> z3eKv}M4yRH1Yn&Cf`taLsmX8wHl4!dWJ&_B%5b8C8D)zeVL{b~3&S46Ob9Zkj6qmFk1Z-OjG1y>4QE>|h$==)0oga}0250+&O4l5SVNki`W@5)aIWGob9T1PLrQm z{dRTMK$^}4O~4Q5=Favv#O{=X)AZ0g-+KDtD(criEK+>KrlqLPYoM83JBfx{a@kH_ z0dx4I*OSbaTwp*01Rk|9s9^USU2KSkMHB#;^(~l=ad>wyMpLwmi8^%`t6uzt$%1C{_Of5+KpQ7h;m0=`2xyBHIMqhn%LasL$cHL z72E&R{WKV$&5;>9db5%kNJ+7ZGEOWp0+7lTm9w6TkbrOFrx4GUY=feXXZTd-#>YQl z_kmnOK)@Cp@BM2#V^=bh!OZE(@h-sgU~%N?9?H}tL-slSq^>-7Zm7FE2!08mZf-|84D_r@Hcw0P;$PQn;7EZ_KCIBYn zIXhoLaDZI(rASsx!>N^62<-BO6KiPOS%kKCfe0F|swK!hGDdd+_*Z8n9PF@C_O$6X zJoS(RNu&2^$hK7Jk&g1A9cL0WYm9Iu&gIk*2inHL~oP+k9YlABxW1k+0J5n zye45fIL4P_or&R7D@fG}FHN_e(&KU1Msy*fH*UUm_~I|ycj7x6CzyQ<1tZCveZL$N z>g`%k6L=ul1b6lIO*J0d)2m%Vdq~0X}+cE1(+PqeeDWY=Ji>ka zT5Y3=tz@9Hvc}W5xQ1~B0pOOfv4zOYlFl(fv*_PrX}{CC%%*RDmaIJVWS5a2b-6sb z%HLI31^d-K<%Xb6qllFLAm}X@dFteMu>eys$yPRs(j+@;r&Z;=5tB3f!A0~C>1M7( zO79Mx1g<5MP2~~{Tyot#)Az~ZfNkyo?faWhZj4=a!=5RIhb0Z61Avjcc1-PBaA}@0 z=;yv;POj!Shu8yKJK4sdvVI-EC?*Dhi!_b=jF+0lf$^iMv%pLy)-B~ygfBZyMv{a` zD1Qk(A6ut)9_9(A+c|Vu#lxgQJqUaI33YmyT8xXh2UxE6uaCebg_lP;RYM`j>2F|* zIRYypSo()#1wpXa8i2+FIm^0xSRt}MDR#@nj4cH!46bb_$Mxg#iz_9$ruc?`$d>tZ zaWrkSd71PJrvd6*u^J~S&X(mBTG3gOEiNqm;+CJcfmhh3eem|6otL=QcKZ!jRwsPc z8ams@&ZaN@AMSVBy+7WxUOG2d2xKamyohVA;vK0sbn_*ze1Mo$ML*Iu4Z>UdZ47!v zVNshMj7ai62G}xtknH7Q)jR?|QTkSF%EbIhtmej@rC3VUuy! z0@-xVA3;G{jJGq0qA^yao&LRhBQ7Oxj zYWs9Jhag~16A-@o2R_gOc72YHN(Vc@Z*hT_B zU<~QQ8_Kvyw62-3dhTA)dKL&yba2fULS_=(RN~+@Yep6+4^tfWNT^MNRT~CVP*TXD zzQ9r2DMR8G0bLO$KIo=LBOh!RJkZd_tM4SvC=9UT09@Lyu$fq;o_`22ULCAIii70e zNz0H{jVB9kP1z+={AuxPxoH7kOsW2Jbx3dRJrwP{gQ}54^-#GpMueA7)vOHt*C9U;p`2HDcY)uD8bBcPDv5H7``DuR@VGDO0o zLRkt;30PE$Ewi_}M}~z{T4RF>Webzg%9>zM!csCnc)SQ+=2@?48Z@9x$YSG0)vYqH z@R3rjTm(~g;oNvu<|ptgyHX5XhC7n1DoC@a$jtdZQrj9p9M45!aB7SV>UUj07+*F$N&G@GMPSX)suq_57ve-?Cns z3X6kmQcDwnaoosW;XsUS@{xNV7?@?JfG*_!hgcBtZ&~t$EVy3dR0M5v8kLphzW9@x z16m@*P4$WqQb)jz`^y47T8m0i4cKq%9QRd+59IuktJCAJ9hCLf z8-gysG}6a^K98pRH@+l47<ΜvRao@2$f=SZf5!+C0cw>y&fiqCT9qVm~ZefXC~| zT%=Zplx!R01ISPLjX_Ij2uyA16)414tISw|qbIH(rF@K&6WOB3Z+raeA;mfzfEON4czzI4bC zJzl+^-sq&K8(aH^&Lcl7#UeGE1`PcIe0a3y5H8s3{Ydli@(3R07_LeLpaOf3T51C) zxhP%k@It==ftnBBBO+YEW~3mDl2$f&uy%(QTF{K=pRR6;H&;XeaIOE`&EM_KN1~B= zrkd+F^2?7b$Ngiwwn}taIM6YFn5dhVSKY@~Wq%Rer}G7mONukoOw3;<<=-O{$`{hj z>eT-9&AtskEr|>4f&UB%7aBQ81Q)AfW?FHIX5()-!=j$-bpqU7U{JDcAq54j%zDBtaeD;!RCn3CB+b7XV!f z1V3q~hFI9Z6lo(2K%}ZJ|0Y!5fA;`H9P`Yvd(=eMlyZQz8Xls{767Uul+*^SeWa8EHl@zfMcerV}KCMA$ER( zY%b3aO|4Jv85e%ECx6a=Xed-w5mikxp3r?vt_`dHrp-AE&JVQ1IG(p-gQ}mSOYAP4 z<>}a&P7=eSeihl|_@L+Td2oHM36XAhSLp%9Kg^8>xm4Sd$15yeo z$>=$!z|}Z#ErOm~7js7^1mTi?uY9>B)OGFnIJTOuzGHwN1tLfq{d#*^(HL0If_VVM z=%Hk^uZOR$l57Bn6f!)+*z7Q|8Y=UdXx#r!UN@5U^!1g(K9k#lIyqet| z{WuGo)BDM2-j_>^*a_Y>sJXsN;9X63biYoQS6w9VNg|xcZ zbDabuD0VMx-Oc%>C@=|8TTEvxqwpUwOph=>8zKeCWx%CT?D%{TE#84}ESd=5}3@u-iHJ$2q zJjv~v^yyy|9tt)`Dq2-gQO^Jp2pxid85{q1+)e&A@O!Cwm;B2yMqS`9x_6`Pbqj98 zBFwJh3jfO~BFt(Rr*ET4=Zp z=6**rEEw8sd6r(VYO^RTbMb#qIU@#5gvRBB-C;3jDvjKD!Yl6HrSxd zfuV*e5aklrw2xYO!5a0e@xZPV1B6=gbpu0>%1ot{7ckWDaJq{~x z`O21%2^Y0168l>s2{F__l$&@0u|n~|=77!*x{ij~t2JXAq-aPS(dOcm|MDl(Z6%L0 zv2#-<>&n$H_uwn!`$|eFnu$_i3(~|&!pDN$v*$aVa<2n$i8w#aAys+ba$S}zKBIZ> zQm~-C<@Bqh8UOV%Pbe-7#{C==FCSdv3B2;vx8kq2Umja zmdw*dNv)I%=+15Rwqs8dzQDL!i#iprTf7-EAA$_RrY9xR&eE3APjX_O9dAHSg%)FT zQs{JgzPkf(h@gDJs`t={v$~z@>E*_iP4T-fOV$?D)^t?qHJ{RPaokLyQU7HVBK4DY zj@`4eX8`Nv57>pJKz3mknQ_Fw805g=o&MmXrGp&|NYhbil zRLcZToxDuQJjQbQjnW-0ehH46jj`~ZeaKQpnTrg_FYgQ~qP|_IMlFAOR%1L!LQh5; z+EdjLpKGnC53jcI0Ir~zr+ADd6k~)fjZd6!yIdEh+qIlwhsGiCo}~l+m;%o?tq>PHDk22ld|a=C4UA?0zE^I$#)TJ^>!GkiOe@fV=}8UEgm zwetojalU-gJVj99B-M^>`dd>;sw3#_<((Ds2fl@Jx5Ab@CY<`+aU}oI2ppaQsbPC3 z(ko9U3Uk$!xHd}z?qeLtm!d(6u=Ms{)WcT@!rrGzkYu)mz+l>MTbJ8A02MZMwXJsD z5O+aCD5#7|It^bz?S(j+15j>#aP;v~DeU}g4GHU4 z-~4IU@w)B#*BXT8?_<#}+x6-6&$^QKp~GG$Q+HmM*fddjeKJMHU0=5*VUz*gD+CgE z&a!jwaCZK$Xea5?Q=fV>jakV^C!x#QDe(^<_&*oc-&38?BcQRxGd$hlY(*RtPar^2>q)ul7XNM@+}=G zG}B8@cwT@Dx{9HG8GZX^1YlhK?O&XOS44d}bs;btk|AUsBH^`4ev{`9qd&2B6z&Vp^*sFG`4T{+TXLF5InmCL zDPtc$WuHiUWw3V1`2|@Z?{dW8o0T;CEV8W;JsuWj!LT73rofoU3dvI|q^{i!o;kor znj+YXNhSYUdBHq7nv>VUiK6qvHPCiTWmfZg!PBLsG35CS@m#>UbZ?T&~Lgw9}58$vPRw zls|#(9__7+YCS4APM*Mfre~We$G9noHU95J^2e%{K`@Kc@Y5K#6gy&<>`k%aM_RP? z(L!PWy|A5^Z6Zgrb+Le*Zl)txZ-vyL*V&_3ns|aH8DGvE!VsW|T~QOY822kIv>dCg zla>DDo(rUH%BK^IK^zhGz1u*qY=VDmH=cFYj8^!#49=XYb{1h^IotSDh#sYSc4W?%j5c43rG5`VNZuUv3!3B^2>l1B4C9Ag-Fb z#S&@KrOPgs7~${EQ0&R-GbpDex31TbhfFdAu>N^*p8?!VLdgw>?z1ptyx5RvklK`e z;}ebDZWxbl)TL?Og=jnEU3{)TSheswE)<60o%V32>@*%WzPZlCtXFl!g4JKEgRfsTODwxg8818V;x1J!uPe{09B`0sUHFjPAKwO}T zYr%n{xkD?J;dH_%vf(h!j@jgZIGX&rwkhY-PzY@#jKMGNyC#$C&U{~hIE!E~U|(KN zR;~Q5!wraX1Ww9Fu-ms~7NvOl%TldM;ltX7xykqBP-L1B1DzPx2fLsEVc{`0WVw8CJzt z#g(STa~C%VBmE=DQFx9FIa;5~nLL*?3MBt&X-Gi$cXtR_sUXk;!hvBB`cFdsH}|q-{KtfS`XQTp!jg-e)ZBUA=hYAAr!R*6H8yS;=jw@ zy8#S3m;4A2@Nx!|PPkOGYZAzEz6Huo*TOH|*%6lD?@?X1H~s}9`tQ*9^^0UI?*wS@HNyVQQJ%#|T4g>uAHH1qdPW{!L)XF+{^8{2pEz$ig}<4N(}O0Elf?C5~gAV7!ZAgfcS|30n<{pz&?`l9A#cMJ7J#638)@aZUOOKb`*UgR}tL zUdO~c7uWd3+rz0`W1t9`C#T}q1}e+YULjmRAoKfbI8{8U>U@sw8ID(!tg(fd^V>`d zd-7C0$s=ddY7gfEmV`TN4&ON^z+Xi(SWkHsH!b7xbMPEJgA(3~=5I}hKEK{Hg{|Qp z>_s8>)4F%%(6?J9yB)~Xq`$gHhF1Y3S;j*DB7`!OZZsWC(|n~L20k}Ern3AK|4cZr z#(-TWn0}4W%&xQ2hI;@}nk#UA3XBl{^_H{uhU~e+?8T5yruC9yJqQ~y(dz^pGzN)I z9Bm)oC=ivYY*JRQc4lQxh9@iEd?|B(>C?nAIS?CAqLq7D%j;T)#{N;f6cj+5I@OS7 zV2G!mCyphbuq7@^g?!vS6hADeF{_HsthbkLq!2lSQ>#3T`!}elfmOX*#*h3g zGXOu{<187&eb)AqgOW4YO~ePl*yILq3WVODPyU1?88bF_ISfC~Lu9nKzDJ=2&ZQu5 zlZWvFFC{F>=y?af4mf@=BOSObFQlDW8*-y%ey#olGuV`OAvt&dEyq)Ume>b~6?MyTc~_-o zvFp*R^)9M7AOVC7n}DliX0)*^?P|a;rN=e4S#=R$3rQ63R@kt~8YGjl-oE_&1yDz9TTb@Bt=Hk7(&V-~85Je?4N ziNLe8>E1AZ0Tv z$FhEV8FS%vMVmyhAZ&?~qV9(3e*x82Me;lF2IHt)pC#&7_hx*k%ZYpSk~=HsHY;IM z!j0~QHMeriu9Aa2g3-tW4fQA!xyTnr$4LcM=p{|7EB`%UI7*#}y<;APA38?;BN>U* zuXbWt_09dVtmT z5yk-7S*-%VTfE^rI(ADJxF87}l60bf&WY|vsG}L8D41kVL(1o?jrdOBw=SVm5N}of zQHaxi5=ahZjB{w=1#j|(psSVEnyoInN2vjfYuWug!`E<}duLz*!79WAGIFDB;N6tusAZUs_yXEN_pziSok__@(x=ZWOM%{hvQE&92MXs;LBZaynq#}t)FuaRBQ z#@-BIy_Wz95v5gMm|`3>-J7sNOw-SAxkHgd;S*au)zwcuvXRrTPX~ubcthWoOK$tM zVzJf0q~q%5)^Yv609!z$zwjcF(&%%O%PB0dO)ShcGTtH zMDiZ*vqCdGM#t%iJ+crX;g6r?Zv=|=JW1P7+LSQWS38~If&%lqLX%gPO>=n` zCDQETw7zSAd>`0TPr*7{~#-3KJ0#9;?3Z8*DN*}va3m^6_}m8-sLfZq4!V!l@4q+K!5UPI+6y5 z^JUaJAk zA#<8BxR+3?&(T&ErTuS#1f-C)v-Y!HOBjbQ$Q`xKg}Kx+Hk%c4{U)7 z>;92#$3q<4L)m~jYa|Y|lP0WY{N?c~$b@oBf@b+$yDajXB>44-2uV^OaT)LQD^u}Q zi+^845Oy$a=ZZ+n$SLb79U5xYpMm`qb&NFu{bU$yv<$GLt17$7oy<%cOwQOqy%28D zUsKq{wC`U62PZWFI;jzm!gX!0e#`B)=1g9nW8x$Ybl}MfLHi#(TF8CDgWZI$5G&{- zb**;>xKvd>;b?kuhEKu`aY3zH*8IL>N>NQ&q z{e2lLv2CYNA0RNddRwW(#G2vCPVj81Nj}}{WX6*dHZ;}>@j8i=I9DMY>x3(v?@LRc z`53c5AK1E#WhYa@IyKP?ihv(RNnviNf?~=_?soF_s}0Q1Fd$P6M|`{J(T1E6tbYm0 z&{q`A4|lCXelq*Q9GYUuVBKR6yrw*e=##p;H(lc2aWCg&8pmF$UP8h_ZN!!R*tJY1 zs|!%v^(GA+L_r6WbQQiTxf?MH*@EjDE zlzVkiP~;c6aoQ1si&y`#FFI1Fpt0!&m6UMq_{XmmtO95m`1R8B+PWGSt{oBLN@EFB+ z&~+3*>wK61gHmwdieJbAC4c&4-4L*acWc4-HjhXV7)iuc^LB-*g5juvZm}rcLQ&@3 z?N!H5d%jtR4X5iyB3l+5pmnvxSc1D9P$lY~L$su_**%b@aBp_cA0!W86ZmPKexAJS zBph`g4Qaq20eiZTRTl*CxM~V)pc(gE_?Yz_=ESw-vvVsS|oP9 zv+=UNXli^m&2G4v;PfQ;;`70z#ezl-)kZC)<~#5DcxnAvHH z?rN?_+pn@KLVxlb=OI#4bY<~bbK+9ARerH&P_f=v7Idgn2{KPY%SOS3f_2e4a6ErP zq%fBnV2UbmEa9!4;ny?=_kUZvC`0Nm{3~c}4WuBOx9>PK27Q~bBrVJsa^z?b_(ba$ zc7k<$p4$~rp))Tp{kZrZ4nI1|%Z_FHT;4+OkD6)NRe$`<<8;Ff1N9ua{IjrVlih@? zv#3l9MvigK2`>)$$A&$=o_1JhMI_3xs{^ z0V1$rsej3n^SZP$56SVXAVt%ev(?+rC3kMtjKg)M0z{VkcyLNgC*wbOn_hp(HM1g1 zzC)%%ox{e+WFO+^D^E=V4s;gy&35vUHL{Cqf0QFkJ9^~=J!f{2R9H||3U2Sk&vffW zOu?9^XQ2Z4Qk8z8_8zIE@T8P%5p^&~bq^P$K7aIC#l5uD@IUU27mqA@BBe{$)?4LV z6<%Lr&753vOJZAy9gH)JzG`YFsllXaWL&;ZV(FjFl=Jw4 zZhzi{KABJb*lw_aM3a1!BJPn4{uCb9O~~n9FK9we>Q~l2)g5ASlFv%Sa4ZoG-Gh{i zl@UmE{s?3=cV5i9FvT1I?6SfX^S7QWU`2T>;g6kYQV(wLCQ_bce+Tw@%_RWEGP6{1 ztSJ$OAGsW73)aK@j(Kf219^R((M0UEd4CJateN!&V_Q;*{^_wOQpS-z0o|z-4eBt0 z7V~C}YpwMl%pXX(^8o(V{iBwQu@TKMqW&_Vh*js6F5>RX;uU400;MddK@PHYbbHHX z&buW-kzX4cHm*q0OLHT=3`D}pj=Q&MWAhgtnavvcZ?_ST2D@Zwk4}UEh z+xjw81cn3|fH`zgy%Cw+;7=U1S|i!}a+IuVFh~kJU-vMji{Mw3T`xxqmN(AXQcDJzdMg< zB7)X)%mT0NotaYSZ`*oczmzF_jDLZO_|8dn`i4HCB9v)C?{Tv>-gD-DLQw~l;8y>H zWwaf-TNkmslcfgLg_!v>n1uRN9Q~#@KDUe+zY$B5{;MvT;=GH6hc1d-Yfb!l&u4?7 zZQSP?4mJX!SC#IFnOfY7i~O?FaMKODg24u1nn?iD#iI<~^%Z;i#S+SOAAe}{<}#W- zVyzu*E{QOcYRhXa=4LNBg!P?lWNa}n-g+^PchZvtC&ka?qLaoD;T{vTx1>tWh}Db- zR;X7{!*CYNiijwR$hC!_HUfWM*j_*t^!c(8wRUQd1!AeI-j5&0HjJ>gr3|(8x}<8( zO(deuRN6@6?&1evVXy$v``RUCumahROKA?2 z=$Ewd>Y+3+rfc5#6Y9jNSET>-be(r<%7%ukecmcPb=+Qzd_V$jSARqkkbvA$+#L;d zb(}i`%Z0iGq43eCxS9A>Nn?ij*A*QzoD6}t^q^g`wbmnt2IMTRT>@DX!yIQH4CAmu{=;%MJKD)3sBW_kZu;r-R}wvRnqVNUd|cf?~8hz}#cuaHBC$@8qYf-A@FQ)mO(nA+6f z)Srh*OR4BI#yu-ihBnrRhl{8@Zs+?6;evuOjtIru_0znh_!DueNGfsTeBf!}w!doL zThlz*z~ZlXwM zC9gD71BVNZUC#OnOdkvk(o78OnVI4aioTgkejUF`OnXPCJeDN<852m>PvUF79tH(y zectP$i$k8Q!S86lyxeP`>#XtlDjf;kLdALo^?Me?m4EAvdv&jCzjoDU>@qALBRi9t zhn#3PZYi0MPWJhj%P`iWe)ok5!%E<5PqWk& z`vptz=}Sz7eP2vSi1Oy0W^P)&y>vqrvJr-H%6*nIojoDDj|)I9p_mR0HxbBLzAFEB zD~WD4-96uO)Kn(>jBN%R+<IFbeZ&fCq$a?T#&zcXm}G0Yxfs=1}U|320wq)`c^^gPR(BD_!Np_0gwNEaqz-87!0-6 z$$vzwz2YvcJ!H>8kK1r7(^&3MKMS9S8F1h8ijVUBO%q{DVfuzpYcwcF5^2k zf2^OC`#f02w}=l6H|QAuP(x!uXB!OKS%gq?$$I}(17v*K9K>#EOxlCevn#`fg-Og8)6DYJ!;bD85cVLChuB26n}@h=D5da8I1Q`ij@ZD=Y%8I*X%}5?rnBP zM|@j>7wt6Q&^(`~euAWsk;;y)7B6F19WQN(d8cj`V7MC}3P6e<}wnV8*n@c>T_!5DQ9V+Y{DED6zn`+xl@ zCcITieBiwm-^SGcrh!JTbSX$^RwG);6Npc!_lPbRY#RluqTVez4SmH323-2NH2117 zWeM&BnrB>JR*vG~5`mQ9BbQ1!tuBy7=#vlEA`%uNf{BYhT&PcpqBd4d2snwJN?6BL zb@`p%c0BN?{MQP(E|`gO{>5`AJ%5R02-q>tdKDTYOeq)3nBakOx(emVG%_nct`1 zZ#2pmdO;{eeV|gL{XHx51?i|#(yA5Cd%j# zJsc9*{$5IA7E&QjlS-!{yp00+c+zAP^1DHRj&f=a$;w}>ik{FI4QHq>k~6!Q2nl)2-3aHQv{*Ba`UNlZI%#6MlLSIlhs|F#k!74AS8<# zG-mJxebnE4>;14B=xg~qIDZsK4#(7uxW36fib$G_s43!!ysdY;MWZ-S)9Fm28IoIG-ti#wL|JHc>>&muV#(!SRu;GU(%m8a| zBZT~R2@@CdTq{o!9NS1bp!50SaWsLdTDy6}+0Yh8;w*QYC!b(>WuVo!zo71jnPk&3 zz(G2bqW4v3v-``IkqNbr81Br~q6LA&BA+jry|wc1;Y21uv1G9uZ&R@^{*l%MpI9!< z7{-Dk!CTWkxpmd|n|}sgr47`U6tNB-sqL%SjROa*mcfD|J4Rwj?;L3#Sx&bsnHALu z;nzaSP$`m=XNT#5#CV5rTRozgGuJTzg>gK;0@?-yiYcqkTAmEkr?9QxHYeQV_qtsX z#07f{0pTY$$!c@)C*Bv1CHUaopA*t(PTDIWTA>Y&j8jK6HGdN!)$V6*?j^pyj?q?q zpir{btuj@Dzf!l0XbPP=rv&OYbXJAsOX(d;V-q;rrFV&$3Ulb2w43+nE$wE0MgZA&)hMCJ?Ilpq;8n{x?r@=#e}c z-{0`rF{QV4_zndUR|BhX!Ll3=V;CFnfUD~7NSe0rF1z!6OuFD?ZB00js0p5BI6Pk| zZZU(_6Mt4};1W7WvXPA)s4t@eAG|TKIq;a~7sdM(aIA|_5eQmovQh8%dD$Gz5k76m zU2vn_a>bV2=vwb=xJMWRhe70(!>V=@M&!a`!Pvu{v4Uc$3C?EtIJvW%(j>igx|K(};O)K2T-R#x) zD`)J8{Eo*fAe_4Vl#6OxM3!IBj{)n7RRZVE@`!z1~=SEkViBolBG@O|CDDF(C+!)+zE-Z&Q0t)yOcQ z;xTPDwl*~S_?5WX;Wox=9;4|^O(JNRok%tD2R3P*kTaZ0*#@X1u9ZWG{cTH3*)mWe zp_dWk#y?8IL(KNPepdY9Rq0Gk5sh@zStDQ4?=HbigZZe((-8aBdf_C6elr*CmYwE zYGqy>Yjxx!U_M|QWi;zuN0hB^mQA;%TK&^unngjlReek&5g8?HYG^-{9eJy#HGijy z3h@$M)*IEKn-lYKLA#=lu%@B~Tt9=@ji!2~LnD2Ao#*}9anYqxf39cTMKRuzt4GnX zU_mZX81?F?F0b~V9Xtbt#Aif2R@GJJ$$lZQu9yABneqD_mtO_DBy4EJD*T^!&Y-;E z+D`84!$6#M;*=(NQz%*$R0-@AW50*<- z^?cu688@gRe$_T54kMgTHLv8ni%Wa3L#@w-t}op1S|P$`de4k!{V zT^89kA{2$Bs>M1)NgCU5%YUnLKQ>eM^U+*qw#?sXS1jBMdX$@(QBdW)JCG5^hjL*p z*lk*DR(fTefcwW+=uR?(th3k;Ql_%M>ZM zi#?1C4HYuJ${E=q)MzmXPM-sS;R3A){{i(`^Y3YymHbV0^8AimD#O%Lh%&30c1}&Xx-<0RiMgUKpGfA2iaI!;L|F4hzVH-2)=gXU|e`>8nnE zus(|UWbn^pFrS|fy?^R<(xBQjTG@G7*!eIF#pW-s_Z0ttv0tD9o!(Ym8>Cm`hIRFo z-HDvzEe49w($xB+R|aZVoHpX2P#+L5R6C`1Kp2RFi3$4LX#yl2asa6(i)sa!R|+Ht zu=`9Hxs7~Re9j4b&b0agrrFd@vl%=bu?HE@ed}TEV5?X*8W^-z=C``L>zVu+7_5fWT(Nt>ph*%&JWGWOnXD>kPdlq0g= ztc5J!*cOWR>7?D4j#1?5^Z6^Y4sEm-eXika7ZJ Ks56is2t9$&I^opf@E>sLsT zaf+O(VaAxVg@0#7K$I1eU@~RU>@cLMJ2@6Z z&@OOhO!QN!~7kUDixAWd6|f~K1(AZ1WK)5?OJVOW5hjy3a1$7(u!Ts!p-nJHE{laGiu7?f zy0n@n?#0c_s-GD*3Ij3E7rR=M2g;;&7AMxXN7(AFY6zBD@N`qe&U(B3HYg`4I44>| ztf4 zg^LwV_Riki%&H%1PRp>Oz5CeDj6yBqD{NgtdkKz`f1?+2ZlZ>s%XtPTflNEvg8Ob} zgrPi>`WW;*kNlbb1V#8Qb8TPHvGq3<1~vPh^?&9$PKy^?hJYEjjdGrwIXY?dmU;4? zepOsd-+*y2)=?SSMUv}zr%Q9O%;$6RA!Z@IR3BJTL0IlS)h^Y37waZSkt!LJht~v& zQ$b2Z=n(JBfjT#yjC80gB|o^3+>NRn{cUcmpQOoOBsJ4{yQ$a61qCw%YfkYm92t-Zm2laUzZYUf{1^(A>zoGW#qqj#r45#0cAn zf~2r}px6y+TiRi{aYygRRpA3ssvJl{8t=!y$DJ!u4ifpd>+2*X!Z^Q#&s2d=mxnNv zZ8r@Xk@puPOVtmC|KevgqxbD0i9woOG^9$}KfdD}9(HU0@BZeu3x%+(gQ>xG66U)5t?dU|OV#e`m9#Y`rPCK$L?fjK{2x?U2)yQbp#F>tN6w7v>u=Dtq-N0_$39A0Y6K{SJIQ@caXfwN*QcsjFdoQc+8xe+yjVI=)D?J9zK2 zEFMUX+6DB<;pJLsU}GLYb-DC+cM9$(Z7+Qq+!GY1F&1~0?k+=hglE=V%705v)X>lF zpNg?wu8F{Sc@R#NyPtAyx8xKh12sg#U;gkG=H5Xc3ssxZTF;Xu^4P>mf5Nij)Coha zb!FGm<$nP453!4ZQS+YzmF`rha7c{(4fL$1J|aDm!msy5l93HZ6adn3r67N+p&0=R zf4{5j+u-9LuCbE1HP*PITz|#W|2_P47e$^PAwl-g@8qNF=g-dUN+L1GxU6bddzf0) z-0aXwU1G8@)QS}gFKw4Bw*m#^??QNVGFrqR$iRyO?T z52KW|RyMvJwPR@<$`XGRmL{cvJhkv0+qQxf5n;?P@ zqS3BVz02prW~jQTv9MfY#DAknTvX6^< z(>_F=n4EWPjc45nJB-kdf~XGii3@EVhXxrro#q@{3|w#plCI+y;|7#g_2++-Qzq9} zuhr9!c?Pv0H>;#J$A8YPjSHAmkg$Z$9PS82v%7x(E|^Y*)B)6Vy@7k}ZC|xc%r(&l z+ay1EH@d=ChonAp#aLI!KCuM@ZcU}|;x8$;*g9-|7c&qPuc!%=kz*_jiOIFy?Q~bs zG3B=)=${5I;*k_i8^OG={@TwjQ|5jmXTbOJC$$r~6%JnCSAS6x$3m+7_ixQdQbqAU zy>S{;{D~;`gJ4VcrDUBdW=jZ_Y8OIG3PuI`5eUl=YAUssFwnbTek9t`CN*k|)exAB zO5n`qDD;2Dq5Z(9i}b_p0G_$b3N^Z$E((1UJ9s1N!vN&W5WXk$E~2sJkg-cQ|kUw*f?qCOI+C$KQv&5o(S zL1dq{dDm}0e!^)U0GU@GqVVp%`p18L#XgG!CZqNrcW&090IlgSD5Y2uwvakfJD{Ba2O&RS=w{`oA*@;vd9v>&zk{!b^ z5M$HM_^8sI4osxy!)b+Q$m`ucj8@PJ-xnXV5m0L@=WF^PJ0tTKR*AAH0<5=Cgf4RE zPhKTM^a^r#MkAj}giAy>Cta+4X32v2hiNAhq3g&lxiR6bD2iV5;2PVx=Uf+g!d>q2RTE3>GF!z-7LeM7Bd} z?HV{o>BtVf$(0skLo0$2Bp=8dBR4vpbu(#U%lcVR>LUaOH-5DPIKnZv%mb9v2!GV< z9;PFFmlG{bhHg%w?Xq1?ERH$Z!Gx$9m}x4fa-fK(mjjUz_KwYYk)R^-0yx)myFkj% z*wJc534F=5j@|IWYlj3D_9gtG07p{m&U>%Wl{$SKbUxb9IyJGskIinVk4tAlb=fd& zkJrnqgh*Z(lF~^&F*V-InS{`-pMOqm#MN>86a1<8CfKRsN<|-Pp)gG-<=LWk6%GW> z5x?XvTSlyXb86V*vj0Lhi_c%P6E%2?&e#<_&uFE|hI};FYTTL~Mj0STR{{h<0v8a~ zqHQwLKj!sFlwxPCv#?glrj2qLf59h$ASLcM5YK=@CY*&g@AuomYZl}r!+)k~zJER% z*N}Zy+rl!w%V0m6lvXsaFkb82{T8(Y0@$hr&uUJ>VO*Q{*e?bNY79#2fX|)_ z?$FJ@@tl2QKNX@8pCu}{;UYNs3gOBL1S*T95`+ypviQcK5fK6(FFpm^3)pUn^E=I# z^YJ96rJIuXK^3nZ`^eA`n18M6$)^EN7ZT!g&?m%x_6-X=nBLC8>bx{>6&PNUjqw|{ z6MC#_5d6X67e#UXb8G<3wK+$96TI>T(lRvMoGj2!3VuQAN%2$LuxmEFX#xtDxBW!a)JHoR;i6eeuz0(AY_5XWj?vFw8Z~R$iL!v~*`pk(w2#DY5FdDnx(d&iTCOIe z+aB0osI{!XmqMGDeSc+iiC=%WOigpXQBS%@)HI~vnuZK^g(Jil`t+(8r{5*L z-~b!HMHH?2V}WO53+0I1tib(I_}SUkS#h*EfNq+fDf-WQX`}h6004Vxl+n{~6=f4b zkg%HtQO-xnsG|C!$uB{4l%7TtDh?eyMKoM}E${rhyn$@_$bVQ+k)d|JF412O^fEE2 zHKu}F4o1`%6&$lQ?4ps2>H33stn#`M@q8}i*u?OiDHZ0U5v*f$^)(?q>!jx89I2Xd z9h5Dd*3R>aAl*LM=}30}GuLZL6`Du1og?{!e7xR+8&4-q0@hGk({KWlEaRzL7vk`< z@nxn87(E@)_kU@Z*SXGLsIR^|ZEbO4;|}{W`2!7ho*X+b5#t~$F0;;m=kbF9UUj5% zV#Hd1_SeUEQu1dbvNgYp+4V4NFjE$k{||HAm1d7hCEV+^aY+5%Dosj2cR?^XX5b{l zM0U8naL~P3%f%K1Gy|XalBnI6OId}K!cx1p&0A$$LVwe7s*C6qUEPsC8^cKIp|LvT zh74TXHzi|VLi}tB(+5rYT7GtAj0wzNAg3Wy}i+3+&*qAGo~LbwK5qF{e6~q zGr!w^U)YqfFztH?O?P~)iJ1kyFmhLCXm7?EHxfel)O#wjiiR1A5tWgS!#=S6Ryi%ME?>htTFrW8I&SoxNA+mG7n z>g$3P3WRgzb7o|yZq_hMFvyq&AwG~tpI;&7Uw@KBlBrbF0)LB<@#ASUNydQa&Om2= z53D)){unmEYnBB5!Kp4P>RZi@luE>_NHySkw0RWN(e?;cf<-hiRebZd9Wov1{Z>6= z(o;}$Hs&lFzRo%dV5Lf2L7Q3|QhxzaG_p1kGF&(d3&?&>9>wZUQBxG|=keuOEj{?e zP=7L)l&uw@n;NhRAm**HrTmt;PljsL-$ENMwN@!B zl96Vk1%6g_@&BL4{Gbk5he-#-Iy0|;32EeKD$s{1)t30RWxrG4NH&KrRl*GwdNA(x z`=rqGHl)vG?CRnG7}pBWCS%u&!Lcs97k~cGL$1^LvQ7wW<>L!M^}lJ4F;bxDrE#wU z{^vuc^4Xw9u?VCbDd&CqID_lh1Q^Bv*Up{{!J=W$ z4eju+;@Eyrhe{CVve`JHhHAD~DKFl8`jN%tdhP(vH@~>xKNq_ClKeSavXx?qUfsGT|s?jvFa37k`x`>4oX?tl~ z$-K7%^remaxn_Dn=7p4Y7{`^}XA{^z5akb-l|&t zgQ#}=L`dx$>}$S<0$@WqmXz!b_+^49d#<|x$(TowcQEnT-@#=fO@I5fxPBek{M{f; zV#~vgJ~|u?*=!k8vgg%26W>klw10sNHqV{0>aHg@yD71lt;aqXEwH`SJ}s!8>kl&W z$T+y91xB{(9+zlRRj2{}j^w}DL13V^fO^Gfg#VUb*^##z9w<+$V|A`rA~M%Z>9Q25 zWGz6N8yU{iczf{Y<$r2UNwYIUvrGr%u2Rxz6C?d2hm(V?7w%UM9f6VL z8|P*HU(l<~-5tP{=^|ez*P+LC8UEHB6L}Eu_zvbX(kBIi*Dm!^Q~^0zv4xQ=?Bnxe z!q!*7%P1LdqFzMKf{tDz`YwbAbsz=iWOA*fKV{euyhZ@xT7T{P?>0E-sk^hbmw6Na zD5E6+z9fL_4YHQ)i3^{Z=ztir|2<)yz6gk3Za&BmB?lz-xAat(-?i$ovlvn98*Ibk;zGvYW5-aJICU?rJbD`loiUEnT32wS01MYmjvuz%yiZp!#^6N-m1d@Rm=#Ws;E zH-YuN^n)*oQG42)uKRY%2tCYlck023s9kiSi3b7Lu%&m-k5>#2T?O+ON$Z@0ZR`;7wsYSzC-ylR9DjToZoHLjAuIUx zVIXffnSTZ__!h;1fHhe$P76W+V9EakH?~v%#mK?3ZlSX}By@)Qp-4x(lNnF0gXY*u zUO_yq4t;mOUseE=2NlyzKpqnic)|D)LVd?VhB}xQV z&3_wl(?V)N&G=%dgACM2r2!$~;RVUskZAxnf-hce_FgWgsOn+=Ngxih3h4P|$wmI{xp~jlqthAp zJtxV~Rt8Lw52;J{%f`c)$fR9mDB+hm?29|{;@Ro_b1k2&n9kh1ni=oCAXA8!uTNwc zA9R~1$1x;9UBNF(E@YX$Td(e+(SI}_o#_-iTTwzVz(MUnxw@4}xFCESIPLjdwG*Eq zzN%ogH`>9(sLzHgRsB^;e>TT#%Hx*p&S&8$t_)9>HFwfU2AQ&idB1|2(LUf-wL-JJ z&5-T93W|e|RQggirMlR*!w3*;O=3$vW+3`!R{wLEh7rN1bw>@1?%G}iZGYjkFUg|L zB;n#J)~6)^86ss9Wx0q5FcCVi21n+$D~>Ca;Otw%ed9@69PKb{f1XkBdIi$)?l%D} zF{cUiTvI;6&FBtZvUVOYEH_bBm3&;&N?;jL*s>TOChuWGsn7bc3l90iQ*I|Hj7*2C zv=?g2V4#MYpu8Y@Ce#9mVSnJ{Dw825f+&}sFS8-eg}AqL7! z4Dr4@;%xMhUi^o(H~>Z$i4*Rt=|>LfMLk|M1cYlkwsHQOd9&E~(SH_q$?_r+CrV*x zoKpj0x54QIV>HHVU<&D8edk53l@q;u+5gdX%-(`;ybgq;JAMWAOmv}&)6)8T4T>eX zb#2OWE)i|@Zr@}?mT+A#JpNK((D`o7dDma1(-h`y_c>K`O}Dh^8Ed}q zfG@N)mY5hcGm{bU5`V7*KoO=+P!glmnX;~pgw9n~HoqkbhXmpwf{V1mjibZFo~Pk8Zu#NKIH)&Ov#5d^u< zHP_e3$bU|p-iMyCBVr}+bX}fc2g9|lvEys$=pvgyKL$Ti1jw<*Tpks4dg0DS?GyoC zN76WSfrq-v)jGBrj8)h7^9&Py584t~Znj^9MRqbKRN#w{5ocxFRuL~fwq8?F_(oze zPQcgwMEyumXgeW4%$NGu^1N#K)3=^WSW>Uf++lH<2vRtss+emR_@e4n8_{6!yYIoI9%xC=gAJtFh<|+9zkDNkKW$XSo@pZF2NqanBXZ)JFKztJ7x^SGaHN*^dduKV~LJWvVu)Xlu=-B2u+wZ(dIQ#AQHaq3Sihr)5 zWBwV|Si2C?&uoHF_~9miq2GNoq58H;0W>)V=JBhdbM(|-c#b6XoysCYeKAEu;YKdI z9Q1vNPMEwQLV5j;m0S^1_RayqO3MEOp-xT>NS)L(XDj={U;} zk{8ljEl9nixkRpN>H`>bEs`7FfPc^jv8}iMV>Xt!9;&A@x-wk(Q$wscCe8A-=zM@q z-?o4p9H!eBobG$OqN%H0xC*jQHSN_F_ep!hc8#*?FZB9-b`MAL_Ii?fyQcugN@W~= zic&j?Jt;Kn6@EI+d|AsDs;*&!{j@2%U;43zf@thI$0b_mlg8D%5-oS0cYk0t@4ZlX z#@qC6>SXkuEL}7{8zV2@kHnlfZK)-(UY8j{ zDhXPU0osUN*Tw)cc3x8ieSb81s54W8*%C%JF&O`%_1_fng^YbZ^Nun;>T?f0&!`$? zxyDK8;g}0oMJfRv@$_$U+ky)9+p}#Vw?dxkzv8RaoL+J@MyHRM9Ms0)npy|U&NZJT z#2WSb7t7XN4sE~gv21M~=L@Sd!>laKuZ%))*$vQL=;!-=gcLo1au3Y%Vg(N zNjB%u?Ch3K!?&!>BG+X)`S~y2vzSfUoX(#L0AaIK3(KISGoDm zN^h?oC8W-;AiD~x>c9BJ-EW5(ei@z8IrItco05JpOl%)(wudg&m`6gNAmA?6F;4+4 zOOi&0v;Ycs{(r=9Z)dryTDDKq+9MSaza=`wV7P(!9Z=B>+RSB_xRMtZWX(h$%TRvH4x5bWu(+$A_p; z@F(aRmwZ|AYx zC>WAxhYkGKlk5v%YcEY2{)oJnLU6oO0vF5-H0k&U(gkTH%JWgjpg^IsSv#;9^K1|Z zNiMDHLr5qZS`&4nTwx16=sVJ=6!B_$%itv1*Dhc$7||LImdIpFh%qEe$f4Bk3#+47 zo{Y$k=6@HM-ATZ4#NZiV9dM1p-k5#1k>b87qUaQMapj_|uar}Abm+BuOIz(p_y5}( z$P&wn^61+kV^_82|A7Ra5Ex`sS+&?K%dC@f7}<%cfD+461%qm;H2uT1UB7LYJXSr!wCCXHa7;+3_gPkTBj2N!)Ew~ z$-`t8<{QS1i0i97v}haC*|cf032-FaREk?(#Xk}?VgE_%F$cEN!q3okHk`!vw_G}? zkS=b@0mB$rXlm>(o7*|}m<9^HZM4Ts@JIp7d%jd3M;+phGY*gZy6VV8ubp_TPI}Ty zm4D=a{zQ6DjP9rTv3hwZ_AHjpabzs*22Jj=q+Iu2nq%3seqh<~s-unk4f#M%r&m1h zRJ=TDGCKT@BINNZDOs5|^{8*^oA9T1tTWpRl)~}GNX6+9smYvvxJbTVqwJb*FR;lK z7WepW6Are?nNY;EpMu7B*cT#85a~E341a?Y1U;2qZK$r6WrTFqZ6+EC9PESBv)v)F zxwkHx8Upz;ORn&184x5hsK7*-bhom1j>cIi@|q|*uuwleEjLjTQ&hh}d9r(~ii5+C z<%Y#a53TD8?A{GuC1}GymyRJ3X3_xP8K`vrIox2th-qT$U{)>BxV#r0O+Qd+KYv$Q z@12=1RgOx&4JZO%ifj5$Q+X|}eHhYhBV2dTXmrnIysvRvw)|57=D8lcurAiJ*=aMj zU26{NkN=tLg_nD9rX=8-(An?PGWx$|CW|f*qa>a`3=CtYJ1a>E4gp#L+yzdE?zFYvj(MHN|9#4Nj$XEKc1H z5Ue+`^Q)#VFjjti7!%UN`WBHm%xLZp@n@)V{dM6B>02?0uKiw>Q&2fmrm6I!kS%_+rs{=sRd{1l{|Bp2&J)@G0QV2ko{F<6M;qg z0~MyDEtyB5TAYAU)r}pV7)&?aB!~h=D`#^VY!|hSh#xFq7^ZcTQ@($GFvv_uXyS_; zUm-7KfU-;cL(OwTNg4?^Fn?VnqDPZ&SeFO{*9D0#b3e1m*mTX%Ok$48?xt-tppZ}^ zg+>RUsD)PK#+%j6`PtDUHJ{o={9>q1q3Vivc zeNdmxl%?EL7|?=iM*jH?ckFiT4aqUfMyNBhtv;Hh&*P@3pNZ+;8h>z3w5<=UkW-8! z47+$3^#efX0Og|-!{8jCo%QThY4CGGa?YIGE{(K!O!~_b^?D$X@sj7-%D&QNg?mmK zojsbvH_>u*HqM{ERe`~5fl#1z-NZ`CT0LmyLcq!|6`tUcJ`UtPi=f_ALRIbP$2-zc zjfi4$XINI*qZ+2y`hP9HND)oo;IrzJsILXG1|0Hjv$+Qxb6&*cH~~Kd?E~`fQGR9o z`YBN9$uErX4LEbo4whf1Gx#}Faz^k)2(m~!RB*cXEBlc@qVU@P1*`-RtuYJzCF z;1zco-}Wtpgj?Ch1~h*R=kdMUJ)h&&NzPbBYi_RnvBk1UlRHk(S{tO>k7iE**I@h9 z@`L%)>Tk+l{HVpG++*F5dPWDt3xrQ!d@ul+1%r>z+ldp^gNdic3w7Qd{7cpg>uG6! zm_8`xzJZrjXI1`_v>YMj#~}2J@~c!?H#9F-Wi_8COH~}?>oI@wJVk9AAw6?w<685; z#*FKimzBoiIX)2EmdbVVL-e+`(&--PDNhAf=JKg0Y5IEeUgh=%i8DfnXtcE#*0{gJ z#@gnfId>9_4|0#I_Zt1QW!icRG0;ZavHu2BEl6kN(>Wws>WR*w4&NsInbot)8)sMe z;|LY?Ou@D_q~(87;%5-#_BV~WUeR-XFgOI|Vw4{}^%wN<)pu29<^6)`*)wMe8^>v%Y`p2@<7)H2X*}ZaDQZ9YB z(#|jmUgo}s+}6mj?DiSOmTE~B%|hsd`vXSq0He3Sg-?I`WBnfq?Jf9y43$3++q`6S zER)HeF{dRmJ7Sz@H(8TBdY3hbSSdVOSB!~QF-Tk&T$Q)(xH(*_nuj^HVav6qZ6)(- zRxz}#?jXM|aY+YD0${Lyerfo76*%jPmo)~q8Y18n*cg;jCsjd#=!(s5WZ#MnH*O5u z4G%2@2i<@BeF$bepcGJ4`9ov@p@+WYjRTi@h|8fYL+U%2Y?yw{dIKMQnkISf$U*? zJE0utA5+H>`W|BX>7?REXweg`xdcdYAdpdR-2Hz_KR5|#qk0G7fEWHj&A&h^l0pm) zLf;t3aL1X6C#gr_WXG#rB4CqG%94Q`2g%wEj{C1~ywRDyia-!JirrNN)`gl~j;6t7ym9h7ULzA6b-1&nFeu~v; zv}1p44B*8b-uKzFc3_?ptz$U;%@h3hXw63I*B;S2Yw~g{=D*jf)tohX{Jyp7-;Yhi zRWn6cE+zP}gTF=ha5$Bt>N>Q?VdvW+b9)a_z*|(Gp1b|1-LSs3Y2AomgYnQ{sM95F zx=7pL4c9Gkxdcsi)wiRunJX4~vIy>qyWf9Z#d|*KOK0a^O+A+#1grNg343ka(dgB* zBICJkY>)PR)-S~?&8hOgFUaY?BHaIlES|<9yt^?iB+p%;9VVqevpm7@J6Kh=7dO1Y z!_;xuAm%g+fi%WA%$}?-Wa~LTD+x{`m*o_(hLAb|hbgDI_BzYQIaT8lE3Yiqp^$EN|Z)9b>euKj#qVJ5Hb z46FD+iucwEknx$eAP^sY@Ps)cp|#p9=11hU6-c51APH7(Y~aYd=T=o*^FPClUI^v&?9KlDg~>c=nkK0i*v;9yIsbh2XnYJC|wiG?oQ({nO>Ibrb5+} zkmJpnEVI86FmI(>scP`=Tr|XfhjCB0t>zF&K_9x>AQd#|u9212be)6W8?RF0x1$zAG)OeOxxx z14l6ghL`BrwmN$vOpl2j+nXQNX~hi7=Xv5pr|X9xlzF#Bw2hFN4Dx@!LgI!qP~XW5 zCUQa}VG4;}^Jp+J$7Xkq?#@0$eJtizmhu?u8Dh?O1txEJZ4MLNw~46Wjm2maJGNhC zr_Kz?XeVj2t-ZiZfF77vY3X}Mu0nLZmHE{271KW1Vi)yPW`f>H#HN~#2SzDJ+U!}@ zmDQIxw&^)yF74#eM4UPMV<_1Z8zcKug{tQ?ySLzz@_X^Ui%tR)ORc&nzLgs`Fb{v!Pu7q1M(XW@1&i zlT7XrKPRIYnzesq7YV_^!6Fadvz-pJGleW-@Mfv=x09o!gt~M2RvZb>P`{!LV=$Av+jQ|$L17Ap-Cnagmc~A#L;wa zEOn{CW*zIevYg4vKL#}EHO2rCh@txyR2hfR#98E2q{e*^kGTFWu-GnjMA zp?X;V@s^y8GsMk8$(7O2Otis2){up{cCf`@GUtP{Q{cXxY<XHwT*ibJm5i? z_C)K=qvL<-g^!{vuMgtbQ9uu{VCfeko28#PhrfTd)5WN#c+Jryjs9qG6?sCodePQ%U_n=cpoQU-Buq zE?3MOJ>6WbvppS*xW~9d}I^_q;MHoYVQMFV3P00}&^3sWZ(2mLSMF9m-%l=YLiPgZzw+R56_7FU*EjyDF(ea?I;Cc@-C z6ES1|cPZPKL;YQe>|nD%y)?>L3sAas|5Y&jd>MSeE4_B?+kZl{$wjR8Ivx6-4HQS(W$F!L)`OFQlkKru%8m?EP)QU#3%E%+3x;a&CuNM{7p(P@h%t6}Ok#hlfQ6eZgT(R&yPko|El z!bHG6)qK}Tp_ON0^rZw9WvXWpCCh{2`OtDJBa_ub>aZ?4g-2}B1_m0$M`$H*AH6>R zY!x1oAuP<-`(5Elz#!F1c^`i{#{hr3Kd9;hIFqGMbzx_pg#&eZ?-3b({gQn(ylYL5 zZD)hRy^zG^Y<$Li3CwKpQL=CoOU%QlG8yB=u4VLz37~4rv->=_iDY8T5$3=v*ZTQr zfxXV0gj7&o86Uv!Zd(E5aosUB{q%Jeo?hwLVBY3CStK(p{IZ8sv^eDHgSLMt?*+(O zgjQc4j_Pol4Wr1|u*}6jMzX>#2j|tZhO-1we_f8G1KW+EGy;n!`5Ocb@^jw3u!fbr zjqCsm)mx~`o5fpKm}7)~JXBT{WW-Bhhh2Vts^R-c;e|1S>rr1?QG0FgGOI&}Y><5MZH@?YBA67Xp-+l-XsyuW{N0PLj$#G&%{Xfah8)JgL2X{v8*QxNJV`ez8CICt6O&X!@Vv|T@1-@INui7_)`;B`Tgtw+*uYg>-~zrLXVy z6jr*2p9*SWcIdp5Di7o~AWyUiBnI-FI6?vyQU~lYV$^>`wudAafoGhk#2JY~jvwU22)i#g0N^uC&Lnad?x zOtB#ruWWxNH7DIyzHb01;P7!u>-CYS^l&?N{k`(UVI-WA^@N_9+Y`Z5i0$qQ*kxe* znJO>bEN>ohKJl$%2%2MFGtm)7n%(ltIXxn&b!N16bNYymvZM@;<5NvxLJve>2Y&kG zV5+zPsmC|$st=JU;!>G3>f}*!3t&|DHa+F|$-{pgl|XUiV!{4St=v9Bwjdf+M`%sg z7)8B>FY^kE?eMKa< zek6`opGr>JjCSIRHQ3iJk_vL5nW+VzU?*@Bk4!np))TP^H#lYm(oOfQAc5CXVq_g9 zZ6<#gW>{z3rGl04pX@J0l`5e{mP6;Bnf99|iA@?hIxpD5!t(?-T)iO@VbBWX&${&zY5CYrzB=Yw*Nz z!?8~2E0D-6)T?ALbXw4SLYQc`mRmc!b172 z-WVpsa_IDhSL51id!kjntRv*uPfFO>yNvkrUl#CaX(;W?xyXGyAdXWUmANj~x7~ld z10di^w-s&q#MH#S4L9MvYO-n^E_;ow7*5oaiS2YAQxFD&`SH9EpOnxim>R1o$*Iw5 z6LCxLaKjrAuw0=5?}TZ-N(E*f>#xkSJmvF5q2ime9T|wP<=;(~Uxv09dk(rZ`E1|( z9ae$894Hukmg<)p{V+Dt<}QU2#_)d_n(~$8Nz#n?bU8mhv2G}pZx^jPkN+!h)?Fe` z&%yl4se-p)O1j2vs+=Jaozuz5cP;!9qGdJs`!F@R;9iBUN8nd=@#9s;Mw46{oTCIB zrWxz;a{dSqSDpq%!9l&Nflyy@wZ*bsr54oEhKZ05I-L8M^TGjE3 z<3*LRXz2N+0(1e12NfCHLH@>)kjM;9Kxb1t=W~~)9`p2D9DHkpkShxpJTb2Eoe!6p z49@VC62*CRtbzplWh-Z6eHuRI=Bu3BbTc_cS66E$A$oduF%kAI=_f@tmvGwOEC5ok z@Ylu;-65lz%};j-Z09@xPfugE4tR;+Xm!TjC+`fkp-OJ}ag3jA42gU}KPTziIon zKESdLTiMCNTLeb-xBMKhmkN~VXbnnIyt`(75~ys}oAKLA2a*rbj9ULYWxI83ujCKV z9uCZ=vLdJWS@)}L9O#XV@Jz?5CU_vV-c&qj4?B*+^qG{a2V8&rG^Oz@oNa5U)i#bB zonioxR!n(oLo}f5A<+Svw??%e>G_yF4(A_(8x?QB9DtE-*fULK14zuo27zRypxD6u zIg>G4gmHP8jeM%i1bY9F5*+ihSjaTR zGqsJjXDQG$O~QXQXTO(Xw@Q?Qq80v9$-`0EtAnwN(#WLE8ICYAS7_zJy9m&jdl|j# zjNtNC-gO6@gWApYwp3)=_r~r zy`Tv}@J>OVRN^Cc_Z!G+65@R1tMDdf`DrprOdPft&s-h&V0PwzMwj z0G!XiD1v`+hc6}Q?lS&32llt~4$y5UbSzz>WhBcePVAz0b(+#c=1&-iQ0zVX*f$c2 z8bZBmWmOm{bpC797Z%VWlhqoQ%hXB$@wv^+wg#>S?Bp>?z@OJ)rHzBLM-p>Q8t}oc zY|b#m5A=9hQ*F@$KHZ@U-yPjJq(ReB$VZ###bbYuoizEFe)LZnK;pmYQ?`a{=xtu3 z@OP+QstT}tAu!w@7_fs_4J_l_+s(+&^SF~t_}PP>ZG8Ox0dr<-z*hPjrQ&-;H@+90 z5dZqjmjYABKL?6|lBg3yOzQcvFjM<{lGh8<%yz(_`4adU8efknA!@kad@Yjwg9d{} z`V4;#@t6p>1;N0hcLg||RVc%3#v?OFD)1#;C${+xkP1S2^qR;WIc{BvQO2eS@C9T2 z&VAXunS6}QC=tM5)-Q|3%qak>X5eXYzp#ZGv@DXxS9-Cp(uQ!?3n zHYEqsa?WoP)vxHGQYQhRGp8Sb;+e zpYeA>Xmd%Ki*$nQJ)bVoVj2(YO7WDf>>Y~$P6jxpLmyZk3b)N8S2ym!~Ky83WnVhGG-6rf7DE`EX zo`2pfNb{{fH3$-uCX}WJ5(!zGv?aiG+kb$oOLUg|GaBnndjU{Mzyi>$ zuyW+}aBmU!!Kv_1CRO;Wp$q(rrTSJ2-)W`w_imcK@b4*>!r%dyOS6CEY2(^s1>#x- zwm*(wkLF7NrLh?R8buIj|7uI!TEu8Rf?#LXG@8ax444;b`>5Hkb~HtszkcXo##uPl z0&A&=GjWZ%DP>EoKPI&O0a;yl%@N1@-Zat~R4DLw;Ab7ak>2zEH8OhsN$ej#emusq zk2?qFA_`ib)h$QPjidvq5<*v8K@KANi0gT z%rNJaDFW=w@K{nF;#13D2k+F%+4V(3tLZD?fjldy3y6eg&!{TrR)$GrJKLq=5GdEFRy=FVlrlTSE8RR;)+u+7isF zMll!cfQ&mh%MB6+Sta)=rjP}&nB?DZ(QOvC>`wBtb4^C+(U0Wtj3Xp#awI8xY*Ztf z*47|-$eF4E*}hJWP;e_Hx>7dT=9N@l=cCb4zhhrDHRFHJgERdAo$}`mp2u*s51$<= z;OEYDtMsY{t5~WI8~QKqs$bwJF#)c}zW6J~4sWdVD5(@l-AG49z#NEZFU8h}li+%u zfI-Rvv}41?i)goaWR$-k_fXuT&RT!fFv0!sIV%@p0FgtT$Ro0q1Z~I#1)ugScM@2y zE03tA!0&%%6S*wv8HTz%O0c$N?3FwvSOp)oJI_ThwN>7y2%|-cb}-J?xv1t!r}ze9rCrSw+)fuwp3e{`XZUQc^WNKVoJm1Vgdxp&XXlmFH*4lCVF zZW=}L+721amwE{*S6;m#XpciKWaNnO+1sJ2%CCRN_`$c9`>)}EHA^nncc6Ld#D|zD zn2#E**~>DAdw43sNWMoy7O60y+7^;zzi|O8HNCh+Gg1mwlmxOn9N~C%0s*bigFGv6 zu#gh)nG5MLm38y(9j2P(-|LwNt?ShE<|jHiRwQt0=s=YJHJnV2sAMXwlQY54f7$%t zZxMeWZ78UQ!MFMFtaO}dMu3=6e;DxQyEIXkfw+OU{3Xf!E2O)@E}kR_HW%-KdKo3l zEp4@p>(-!XB-J+x(7IfcP;V*h{AoGx7L@Ef#7U(QqI;C_=oDPFP$ySsKYa0Eo{M(x z3kKa#Rg!8Ee>XIz-2k`ydSSX3CxW+hj%emgJvu%H z<*uaf5K3M10BVil56}24u)&EHhd`KP5veJS%Xk#(VNY}7It`Qsh(<~Oi#VKI$4q}~ zT9Kkq8-=Uv+Fqut)K+aIUMM$9BeK5LI>T!m_e%wXU1pcV$W<(eK#(Q<*|6auEx2!q z8S&dpGIgt*Q*FL6)u3(+z03;zRFL=ZPHDB8O>#+`?_UE7U>4rNEE`Y$JS%nPAJE%0q~}jroG*w7I2;dWgWP|OfngZt z^OwlRbJ~HZtNs^YHBlIdX;3Xu?Lk@ByPJc%r%Vk=s5plmS$qSqA4VsdiAI*qqu0H! zTUuC|-xYG>Je*E;{Hn2~+{}6-8Dmns90ANLEJag?AL;9WSVx66i5QsL6XSp;NP(d7 zwS|r_V1xeHPS$`q2LKIYBx--%B=AXM8BnNgw8Gg;5bh)GJ2qB5k~qm!nn-b*!#wEx zj<=L$4vbvrRqsFGG^dL(P^yXrt(l_Utf@XJisXGlZToKJ`GwG|G-bcx5>)ROsl<~a zg4q=XJzf)``I(AdWZ8FGQ>vGqkdmp#!6?VM?$Y*`{@&^x=##%f6K{W}uDYWE8mVH8 z#NwwQQbkUh-#5@BfSSCECELSzSCHCcE79q&ry--6=l|`wY`B>CpRT4t=2drcbDSsrsx8jDl!u=vR zb9?0pC2vKjvvfDtHx_s(W49ZCOdJEv^<5b?q zX^xUk<@EN>ONmPNxjx_&!caHV2ax!9feD9XMP&+(|3K-UHJWEi8<4E+cKn3Kv6eLe zew;XZl0aX~NAo1zw!5hWgUL~~PNwz0PJ`8D<(Z_VQXsJOXDNXA{+c3P{QCqikK{{8y z-$<+s-C^)EPi<1ZIwc38612S8M`gj7pmzD=;dhHfjmnpm3+MBFIW%GImV=LN%?1NUNS$;pG4>{!N03vyip0qx$R(*E~OXMo`L_qNiG1~Jw|sLsRTuX}$Q%D-Im_!*SL>rqWc@mF61T!;2? z8@_VYo|}g;P0EGw_ooBhrjfllr|kXKw|um^j|Kq2!xy697iyc{YaaL$bfI@peH^2K zr)qF|lIC`z!Zc_Id7l|E|Fgbm2sVx=XNJR@yAoj5)D^p?Fu)64yy8u+I3S_X~Rm^Q*FtKYxi z@e+SCw*{)3$VtwK5-*&%-gWh-~9 z#Fcmnx<6C!=Ca9^#ib@82_r0KFfp0jx{^C>H-0^oT}e%z58BqPLpUiAU}|IOP7m33 z!V>epImfa^tzn(*mRA@EZyOpzu?JU!QqjxTgRiBBp-`4Tl?b?Ni;Ga0?oHC*k|$8t z$>^b=C8#JGLLI~0fbK<1CdH#s0I&rCQUr1lSeE2-zbvr` zo`++o$fxRBXII)K2Y>Jtf5I$9b=ypADyx@Vg8I&@up+ypuS;;7<>0qQU^F zQfJ=5Sc2?xl_}&M4rUIuG)~vf;TxFu`c~(~R%?GB9J&@!Xiyr3*-C%R-k3hddf(2Q zFA)WZ8qk4n{=WA35irNp7eepH)S3hSEJhFZ_Z)chc<`{@ccqW*ju|=yM2q8usq-YP zbp|xK!)C$ndS>S*8z?lO*p1!p=g2N5JRCdMJyqnC&TXeZ%kTt?tPHB{2Y-imn?=~B z5AqplH`;#C$5e%6XXM%TsVQ$G@*LutA`m>rM^`Z~NvzTjllc3Mkna(L zinRyB>jg8rC#q4Wf6Vi@;MWY$H%=11_mmzq-;8jH}b(A=Rki^M`C|#eI*;ngn!Mf z;L59uE6^vRa(zWQqTLc~S)Wj&ofNlGE(>oGOTvxO6)dJUjQwTG@5PY8&xvgK=CLBf zLBBE;)jtc?|KJE?ByEDH+J%}cxik7|h)c(oW=_)K&W3Ad>W5AXnM7_*RO_@fvqpi+ z>tFmmv$4UTB2$0JNj!ng-^yKsETmbH02O-~@&BfG+?v@9<~E-<){*}qbMQR{x#@!z zyWky7o}$-G!lw@sN%TWm)uYem!Q+J^mY-5(zb<{)PN-_gq9V^Ugd>Z{^Ft{(#703b z+-~F_>mt{(0A&>%R`k;ILS`8y1lQG&qm;@FC)BvTKRJJ=v_Hk@s7}Ouz#cNLu_YM^`NK?3XAwq%n$LNAh#6e7w;I+?3diK!4a6xym!RfR&#bWZ8VBRlxi4-*Qetw z{Z)PIb@e!Era)T*HpV#zIuJtzv&Q57Owk><+L3>AX%81|Xorar;s~ z`^?@h3#aVgKLRz|M7crg2oIc3Pvpzu6ODKj_a)v8t%S#mmjJAo_1fzXR`Xa-0zG%Q zHRSD?0G(#l7~fxWAgSLZ^vLBwdm|EVH*J~3!0&B^MxCTMi9Ts`uV-y5U6CaWK<~)` zxk-N%-SL`XPcfUNvTcqJw5g{itp{7o6sjEnVv1unQ$6ibflLov;Damd1BZh1AYwI) zBwDs(Ke+U1LsMm^BY_UZ9D`4c{REmJ=IT_!t^G}Rf>MtTWshblFoG)#p(~zuof_D+ zT1t+8zuA+-q`|>=jQRHYDf)mPt?du!N)&&n&2U(lY;?t1=QEiKUQz>PZFU-0h+HrO z!)!Q`f`M#)S{Vr~FJ=-MPDw7`Gu6je_J54xRWRxIURM&0fBahpJczFuq2fMFgsr$Q z?AYKEU3t~V%l9!*H*j123$YTC(78C6x2NB4?pi-9WvW8wFL%~%RzJ_t#F33O$V7i! zhHU=CO9R{nun06@3|ipv+~z0Qb$Zw2RllAYF^zuVi_n*Vi@|R! z-^RQG5;_#TmF4?C0e=R7`7;QsSZ{xIAdg801HtFPvQ?AzuH1#nR^3xfI$fD)95zFQ zs~PN+22@6f2dbS9Pgk>l;xE+<>Q(@%nP^06ZereLx1C?eQ_8~m92EPZ^3CRN3G}m| z#B1$So5P%ZbfeEB%>04SCgPs+edR`?X@Z@d|%+m3TpA z`(=PYloLgu?ExdcFk3o1UTS^kRlPWK?a16Ouj+olp`tsp=X7q@;>P2<9OqpCDjXsS z9vgg#*l+@0lb*`v7fqJO6<^6ndiza@-6*>N&){Ki6TloSaDVZ!6IU}Pj}`CjXBXG! zp*Q@#4vjIjXF0>C0oq;{8i0QY($MrZ(9H9dCf=Dl*%Eg4SookiJd2mUpLo_%mWOo-*HRJ%khj=OJT+yb9)KJ(LfCDB#oUGt_ z;=_Ny-hAnoUrX&`E!2N>r5o`{yK6%q6~{6Z4WbLpB@S?3MD~~v;>1BV2Z#luMFYW= zY$cgGTLe4_JT9tNV764u&EemQ6K9itx>nVSJB3H|pn8%0SbccS3 zrB{!8`3C5P1xqXhgCdpxrA=m{qbi#vic(; z^K1C95g>&kNu7VgLfyeH6H?%?sU^m$a84L3MvIpK5~Mj2sz-;xD^^(9Sz{@TnnJPVRX{DGb;HWs7Z>pTJSh z35?U?ed1oTO4aAnKQ|R=bV%`QOg=AV!@@Lq1$BG<0TF+)yXb%8eX}Jbb^L4;m}~%U zY&J$CQG}-tk{^^H!`5T!4*Yf+?&(e9->w9|;x!>l!d)i0Je&jZ&=d_y6GMLx1ig&+ zO!9?L26gc3v4UlOC&FrI;F#R>@$!zU;k7)t`D73_*#Ur`#5xlHWD_~_FA;TDlCQ-- z(5~lO@v?tVn5T;-qhRt|s7x(6oDm1H+=7y1B`t~#*gCw>?bOE-5i_s1DBJ(E{v2Er z2_>b*(`@Ds)M6c4%Fb`1YL2=z%^E??6b)ktm>u_%-x@t58UPl+08o4UB?J<4a=StBC4ltJd3&`5JC?(1>jNmTso zb=397+WEe79OvBvFSQ>8y6YmL9{F_XmHqF~H_dV% zRkVL5Zz?Q(iirKhv=`B2L_mYZ+HrTC-NwQLx9N?^ZX>0cefFw6)1hxad`^6Z!_lLV zusix*14z7gNkc>c!E?!h7i7m*-ce`q^O@7PYnCI{LchDtydj)z!%zB~HR6raT0UK5 z)F9-}HfbJUfIw^pD^H1Rk7pB$^ zgRoB~;i>FCKXyn{m=UZk!f+6heUJL67*t$|#bfugCiH4j2Eodqw*mavxu*Qb{CPo4 ztr{S0jK)2$R@6D9bXqC1s@L)@TwTD;Z0*+oA(JOZ?N(DeEDukvyf=8gdr=aYdNq`K zRbnbl&Tu*g@#4q2s6S{wcwnSye<~op_dacL_#%ybuEPptZe(+Ga%Ev{3T19&Z(?c+ zF*P@rVCw-Q9WymGGzu?FWo~D5Xfq%%3NK7$ZfA68ATcyEI5n4_>j5Z#cV$qV-Ig^3 zcMUF0aCe8`?h@RgaT)>ycXxMp4G`Q3PH=a3clVF?y>sVI-I-tW&5y2n&X%>;-fN#z z)#N0KD)d4ownjj4TaY6?GXoP3;G43#qM^05p^1g9EWNO;wF%(E%nnaZE@BTfbhNMq zi5fZrc>wA_6M!ht7{J1R0$}Fm=7uK+h}hb>+FO{JI|8UaFsNy1>HcN;D+FNV`cKbC zrh|nU2te`i;RLj{wX*?&96uob*NG}XAi&Wa2r#v<1_DGB6g8#fB>+?s^4|awKoHR0 z&>Eol!^qmg7$9q53JH>1b}~_*ZQQiw`%z*7PIN#Mb!7UoHLZ`+)iIIvQGl z8~~0$7stP9836%*CKe8M)`qShwLie@>@EJL@x#FaWcDuxbO3vxnW4RjHPFG~1Lgz! zuj%}&Pr!fa-q6m@+V$^j+rOj!lY@n$1JK%(0iK!Vqo%RrM{P3;5Io~wt0Dz5wFNLU z{ljkZ!|tCxC!qb`1ETtCXQ)3&7@F9EtX%;nKvQ@|d0WQ_kCFhY|DDPVm&ok_9e@8} zZ7pwT1N=J)@Xt2}APe~Gk@;`IhBg+~uK!c`zelPA|H1KpLXmPb{1}7~$m~N5CI+T| z7%d#cEnI*miWZK><^WSe>yIh@ZT|)`0oq$zfPf!r{yj(lJu?&2zxhO$}w*|9}3X{vD_Ip}eE2tKA2+|L8={*5p4Af1wBq+qwYU z>6zJC0Q9U(%pVu-gAX?=yXXH<@oymJf1TwF9qlb#0NNjIe`NmE{D1uZb<+Je7%`Bs zt;t`zqT*->GWl4q|1|vNHvVC6|Do#NH~ypPf1dwdbRf_LXbitNXKTzGV1JpCp6d7u zJG*~GRJ*&A8KOVXuDDjUAkU}L_P2LR$Od=0!An&jL){q9TeIuzk=^T#G|ldxPAqH6 z-$}r;Tmny0>aIMrRf<+l+Fd_Jy<())WAzC4^BLK7NG%Q~wcX7TC1t&$7ihw%9ztXvX!`hmGR#uv7a*zp zdQggA?A_qjMK-q0HL(ltKxO6js_@SIH7|_)DvW-5+ddds_)b!=4u7bcTWx&Yf2

f-4u36gN&gnJ~l@?GbK2I-v>6w~XlP13&#+Y)e)` z{6;?&<80lf*JACb-vB!ufEM3J74Rb5Mg7(m3b7OQUdrGQ+x5*6KCpiI6HK{J zPc<2}>_O2El8YQv^MAF$B-3rcy57rli+1w2I_<;BCKR2OvzkeWmVa>I6tMVZ@) zD?6G+(9yX~nxgx-FjZ&7vlqF+9SvH?59LiXghX@bl!(zP-YSS3VOqvtgmCcFIDZiYR-x0eo(%5SBj&tCOZOp9h{`iXJ*V=0rpbayP!cfAV3BC>U)6rr zla@)|@KW8S9Jr`RVC}fguw+|&14UOCAey`9oVt@IHuXq3{W_t~jOIiUVBA6_B zL}->Hm}iI)f=*!bi-U$C;Zm@0yHOaqqU_FDHVbDi4kw|&*D<`kMU zMc65(tbO>vWPb2<{BYl)Pe;yki=!Ww5J&aKA%A*kEQ_aAM76-ar^;{y-*c)jx zrGe@kY=uT1YKVbUGYz9iGP9MOw;`R)NB}``;6*&S20Ej57?{>C#cr5OjA29|^Z)RQ z?5K)8S77(GcL6N9W-p()N`$rDqSD$zSV~9IS!Fz5wc+xlm z$$v#4s&Af!#lH3hd3He3`_-GS?qm=Bi;rOB4+zM^hXaiGB}_F$ERoSC$G#sed01oH zJp?#o*%}hb+KU=UE$f$I2m(>lo@CSV!8X?Mz3)>s0@plD(lhjj z$>HxFd?EZBj0EQs?cXV2{5tOJ@v@fA&%G^Ub3a9i&l`mv<9F$@Cl4)>?0}XW`F7{q zinO*e6u_>Y0aru)+!e^<96cyb702kO(n2lkjA=^P1Z~?o4U1AYujv?do$9A*v4801 z%eM_9ylsBjMPq?bPL^@`NaIumt;`V$HNCqQxmE6|-uC9YWxu!Vqap&s2=(0wHSwdo zHBXrFEiDY+r#H3p;M463W@>Fdf7QnJkCgI^C>Iu@k2ITC=w*T)$eI~69>}5b=HF!H zx@BY}Ey2d{IH zj}-CV-{TFT9roO-?Wz z8S@zhy}3AL3CxnGe|}inZDlwi;W|{Stmp+N@)oMvgq3P@dJ-URJa zlRu2vF3Txdafr#5uYYl--?wpu2QzWI9CN!M`oO~V1~RfLaMF8gj#{-l;#>a5SJ zXZp4wW}p`bTRn*Y%3ODvNgz$8sB8&gw3Uj)klLgcDY~w(b8dT9WD`B+xzv!Z3acSD z5@)*`9k*E|D6S8DK!3-mC7=<4O^IQ4nN5At!`Bh1Y6HwQj563)gtZU8vfm?9?q|kA zak1S{i3S0M^~Qs|Imwd_L}uqkoH}#z_^-z2R1|M+9-}$}4`1(fie_cB)#5<~QDd*g z<>2HA;0+|2T$+~5hM^XuyE9eBWNM_C%ksXO%dY3<{r)wvU4NR)_s^F56)RYA24?}jE?|KU&!V-w(P=Crwv9-tcI-D&YXX&n=#946R1WgX#==JCF4sjjZ>~+}&g)g5Lkudgf ztH6A+iHj8y67eBDpTO6H+H%zp_n6>0X{}0O{AQfJJ35lACc7~5@{bof zv$c7+5$yt6T ziyQUAdX^2H-$&Zg^GY%zQZHn+Mwi#i4LGoZ_;eiy-(38T>#j=!xtkgjec3OkgtOvEMhL_z&H8V`(D}_u7zpaa=CD*Zfq25%b%tIhTVfyNwO3 z0rY82Kuqp+=uKd(hO8#k0$-9&xREIR{$tbMp*R<|J5Kk+3RVwU zx~J(oJwbsy%8QFx`gm7utrQ#?0W97n;G(!CObvJ>xbr)yo2q9 z)^{JWpY5aUhacWi+RCb1;)& zsQ!!L4apD8_|F`~fE-`6|1$b}-dlHAig%%m;PO`8YKx)5guWL&19!=O@=AY5IIt{3 zzD%S9%>yBGZr!iGw;wfxaaf?iuG}A>8sb&$JlABw64$6=BO#Ei*8jT6P`wq)>tvnR z()099r)BAC_^z#7n~(pE>Ziynj+Iq;@q4k8KM7r6hg38Fq;xO5yfDS>$@J0@_%H<| zN;kG~j)c=a!fJ*!?YHFp!bN}FcC|5Zvl{9k6<1L*WL_rrnY&KyMw6;pyATr&NEkNo79#LBHl% zF$0^+{RA<=VqD!FPI0uH_;o6-pp=Rj5+E0=2`+pV z=drs7=2ebG@M?ZLq%^s0 zC6-}LXeE>;JocB6B$LCTh7P4huhfgFI}*^1lUV7?GF!)64tG@=m9zBb5+mS36SV76 zQC}^@^5R2&KDpg&Xr%Zll!&}_bIncDV)shYS-IF$;7V&TabABR#Pa8qYLf`!E1q&< zt6DyvKH9PUSbDK+&`K>bS+S`9=(ti@C5L zYJi}}twJnE^|kZz>YPR98(H0FEcJxiAB9iO+$;65hB#fCKd>q@$tEV=RQyBhWL^+2 z<3+;o-(3PJnBIS9^u%C@vu0&BUV;|%mB-ka^q;?dS$|c0h`u6LLTG_K3h@wKrGY;< z8uj}OJEkFx$H?(U!S04p>e@(MP7aytau5H0mZ|H}P*vF)c08YYF=r$|b4m00f+$w2 z-Jl#NDWIa`O>ho|fF38O85Y-BPVfBLAMNm)F=2xw;?{pi#l|H|0?*mEhfn)DU}TFt zE9YpRTFxqUaDFWB(2?#MW@P8kTqAv|;qMWL!>4;ZCr{?Q@7TQZ#2$f6S~ zsu83|=@c$BWE7F&Z1Ec7O|mV>*FFPqyl3bL^N`>f6x#7;!|W^)`+K* z-#HoRp=E#Sp3Ma7lpzI{4lg3jcR+T%i0)2AdKu!Tq-k`TR;j3t;xLPrJDF6{T2;7J z$iUQsd$-fpy+;3m*e{*(Nx*QMqI7Y)=^$5}vvs=L-I(dh{Rb}O z<_04mCbhqx;%i8VYnu7F>n#PjlZXh!CS;rzw@ zBWLXvhCz=(!Z_;z(616An^~%fb?i(1`{=QnAwwHwYZYV+W2^4LQ^dg_yj5dH)F-?? zd~JWhgyRjfVZO;Jew`@naeR>izg~r12K6e*ImaP?DC}z`olg9KFH|&DmDm;dt)g2N zy;+NB(|2<38gKJGguR}0`SZJAO%BtJf0U4sb;s75N&30HINoO6eAeVtU~;wu@^mN2 zNOI;#2w4rtGw22UVs%+{4j3pE!yFx>Y~N*YiOw;jl>xONvcAU(~*Z0knCbmmSTz{gf6);!Mlkk0yERcC|m<5&2X z$m)B{J^Lo%>KQE8mU9dT=^tP$2YSGplhrk`@n>+5H~#S=BGYz39hZL^feP-9OF>?Zn?bMwCTj zbr5nHgfbQPS&YvrtZw|E?y3%ta=l#hY6H^6AZweV@X#adc+rr3|5$i`UYSh4`pLlX z^Xt7AtW2k`A915*{rLKWZ+5dDlM0}5t_YL&^MsVQ#w^(G6-jT=|H?Ip(!l&*+-p9ZDV1*yh}e9UI}z=W`jhwTjYRm3WlrPp2!p__vy%C-@*bvF?% znPD8kwGpLkEHWl80fR0v)}enhKB~PqeEo{qxiiDAsPR_Tmjbogi42m|o)2vlom#LB zEktPNfErT-on^S?^RnQl&4ka8Z#FzdbP8IZITfRU84SKMwqL?S?jDwR>%zh{K?Fos zr9^lO&?4#(%>d9q0ZTY?))=-i*sMZvn1@cV+IF7t3ESkI>HhF8g*botVLfAmMA&2m z3Q0Y`rVwSK=~{w4+XRgP`P8Nf`lsx5lft-D`B*YPNxt}0T&Kj){bJ&j#>2+*1Xb=t z^BZ^18MWh8OMll4eIV(=;u6hLb)kA%ynU5T{hkbR%8tJP`y^0hB@5BRqUNO}JX9dg zYQSo8mv%rkUYtq6=KykT_+R3FTuz_9&X3H;5}+e z7a;?5&uFd5QonER2`*o`_au;hr~kQ;3~1K8#FVQ~JZH4Dfz*KE&_QC-!DT7e%lCF| zb>^iU;b!a-JEOf?NkqvpgG|tdN{YroD7o1e!jqM&#Qu5uPw;=bX8rx|S-qHE&T1Xj zq`Ur*1@edN%dsS8ItbAC2BUjCTdK`Ubqtw+Z%*T;DJplgx;I0Z9c$UEstv zl@UlbIE?R4xuSpQ7Ke0)Rl7f=1_RAP+9?u$F>%zg)Hi0_Mk-PN3>RPO|5b0uq{=dj z1A93XircPSRN1Q2Wur2Bt?*NuA_T8lgHYPU(Di6fZJ zu=rB%a2i+G&$I&;3j(xE_3EiR^{^91xa>6N+@!tZvwkWPW|`F5Y@slWrO0M_o3mP^ zjt!$$#COK}98@&(N&zYx^(+R5Uz?aK5rDi-8uPzUO^IxmP5>sTNr*#NV**@9l%N@l z7hiE6
jT3Lmns5oo$e!7V4*m04tU^7Br%K76cZwEdOyKI@3LLC-L7!Ai|k+L#5 zb~EVykzyYnUP!+t@IYKK$<8P05u1{}>}K|6*4KQ*@W7x>L}!bte;wSWaJa{XQyXq` zw3g17?2W|5p?57ND7(A7OW;OathORd5Il>AQO$pjgek5*a_A5b>)hH~Wdu>|X&d<) zwlS(uy-F7UPl`?`DyAeXFpR=~oMyc@*DXW$_c}Nx z$Kot(`0G%xvvw1|ubzX&@i1S#13_9OJ~{-$TSzQc|Gg~_sgw~sYkLk3it4@esT>CM ztwK2Q&PruZOMzZdMh6qpjrsm#sstCSr(J)X2q&=F;WkX{N%WFzebc&}k?WGfNnZP1 z#iP8+gu%XKwgTD_64;hf;sn34N95yXcgyMlRLQ!=x|HUG6k{fK{1WyVm43@fQ4V;+ z%0nU}B@H2kPOrul8oFO3sx$;|i99d_98Hd&o&nj_I9XX%4Lf3Hnz_wNdlv+MdO?5J z=T65X$hFB-de1(~N8}Wn;FL0hh(6}8_&U~HwC7ZIJ*kMQ!!}Do(y_$5}kk3rCl_QDk(IJ`Rn5nwP6cnxlAijaWw|mdwSBdE*7e=2$7L?`V+I%c1!)MpkFSsIE!~&T@mBv7SW$rbXI>GVz zalcX?NJNvUb{KsPM0(UQO9Jg$}m zCdKgyq9lawR%L?bhkk? z%`q%uC2%L3c&vYc=LF^LrfPXng_|4&xxR<62qn;=Hm=r>0w(II)I1O06AdapW1qFG z7s0JQrwV!%(y?qDgUtlX+W@hg8xUeYA6#VoGz8*KDgOS$sT`G8NFPq&C+;U7UGI^m z+~eSEr>YT%vV4>TCN}dW#)Y;sr)SmmiRw8(PkNl+O$mS3u$00at|=v-@;QHVd2JBZ z#9Sq<8mOmIE_}QL`}F&*-oBSvjg-W`^}vNTK!$_ic8dGuS(Bfp$#==HZHY#MMQN^xd?-(CJB){seEx)@4-L1#B*Sigs0BGnB7 z%0rJSuP}cvO;1RENe8$u3Ipahi4W}?Pw*; z@$Hi;_)#VAt>mzGZ{S~+-it#qDEvog^3Z#z3NMXmiw7^!KtBu}9x{I;(oE`#U>l=d z%P&`1ISNDvb66okssx3SKrcdCc#5_ng2#++LbQM84%3b2JvHXT1JIVFg?J_={k#QF z*l{}`Q~!An!0~-cm}i9r!`@6CjMA&qc91}f1EUP7A|FoYhn^ghDBJp?H<)L-OgIsD zk4rr~1FYXUOyGL{bUkvy6bw3#Hq=YG_aZV)ntYv64i>5RtDD9Vq8s;G*}LO)kWPE% zb>n|=bWm-2Y1y_AwV_>u%e2}2;oxPOK>cj3sQtbq^YogT2FhgK#z; z|E_ZT9PyP8hBzM8nbC#*y0uCal(wNies+JSD{W&UKD`iZp;{G49i|>Glk4CGPTEgs zPL;>>@xD|f;Z@1i0VbMq&O$4(j+q~BY%SGT!`)GR)_`nLO{`*LQTNC(v}3pUC!(}e zgdxf40^n-=+#>ZcEvM)}eDsM+6ejH0a09iNI=l)+4#aCM6`f0m<%lZfx%8kRiN$|I z@QsMaCA{}KiCc|DO)*{^J*uV36RkXdg_`AXVgsmzcbPa2v7fN;vlcR8r* z^6X7MlWr>S>%-Ye1|BNd%?g>Xsc?T+fWr(9_oQCObv}A>?(J*I<36WN5Qit+{vE!W zcxp2C1olZhL*T{p@cD}G*c*|TGp%f6tnY>|D2$HqF_-;t@Cr|c1`c-l<@4E8n6WwB zq=f1Y!*3bFY_}4P)<()99J@ymS3j^td&F-KY}8D}O7T`nDVcA^iT))^;LJ z$FfK}1^<-<{YC=(*u;OdYc29le0|_}o#Hmq8J)U2zaUmjl|m6&2;R=!HYviu$P2nT z!(m2H6J6?$c-YdtgxO;S7vJhte;V#7nC-7LsBzrL2YLm@8WDpmX=EC66HuamLvyiC zVgN$9z?PQv*lc6tv)-qj^<8nb+0+~JFJD7ZVA3#Q+1xk_`YV5-ruh(!V-g0{qr>uK zuOI09el>CNjGysZaP36$ClVdtSGaQ9b7;lW@Ty}NGJksvNTU$*2r<3rHmSQs-eWKL zbD!T3WE($ZLM%Wx$P>KdC~P`LrkGfRNwWW~WB5>b_S&wOU?p)#QDU@OVDx}ux@=Q> z1R|ZlGFyfnGVFh}9s1R^<>;5rxVGKVi{WKU0zA>Bu2a4uJT?Qft(Z9&6tMb0CJx z`el2PL+3wj^ssX>>pf&pFj5NMsCD3jd1kova}M7?&sO!=_3@RT)_B7x@T|vnN70CG*(7zldf3b)rG`gw-KS^Yk7E2DfFh6rUpo;=B3rihtgv zJ}-a%BakG+lsqmGm{U{W7ki0%LUFSwNH%^#yDKK4eA`@`_!2wG)>7lcyOwb9?uq+Dmby_7tJttZRh z%S6Z?yrlysAho;I#p!iPk8D%oH|nj~&>4R`i7#STvv{cYmD``64?ev?(=6Wb{5f8g zV>_1YQ{>r8>ty#W!-Qf8EVRpACp;2#;ZcY1>;Q|n7`Z%SxMZtxfVzslerMAU1H+kn zCzIZ7)($;uz?pqP^n+zNOPEiKV#~4^r|^a6(8`P=S@fFU3W!q|e#pEqOLt=^un&Lo z1cy!zYxkIYt|Pv01*(*vSPh7=C+A)vt@em-_U=1Td`;Kn=2jghL0A*MBaHigBlT!0#^kiK8t|fmy4kj&jf>ESt#pW7_4?$`j50A?gPrx@8+lN>cbp9q4VXU&;ptqEA8fTxjKzd@vq0d8IbUyq$7m}mf3^|#L`pF0( z`)jUpVLw_S%_fbwM&u~{hhshkpZLPLBF_x=2b)@ zsw>D}K{b<4;L#YI6Rq67(c1nZ+eTX^YD`J{fL436BBq)XFh$LT&J2H7L1L|~Sc|1N z%(z49n2BF1=l6PGKnfL`$wR$`UF+JVT}CXKj$--`{6|?qMgw+a{x%`N^6QzU zcj95j#>bnQ0uLodCDwoJ3U#O9r%_KHVSL~Q(NmUE1v-w7-xESRyc=bcB2&BnBCS1nzvacDy!xHdaQ1>u4DK6UXxoQH z{5|tDTT;-YlvG~<4|A5pSdI*}8792NG~*nOoCm`# zK>&K}AH-?#vg?181~(sAXJZ7stokQag#{&K$x)*$5@j#r2k3}T_%uvBzkw3E?N_OK zqcItFk7{x$jq(I`4X~>U65t8eBa#y10Nm=7xJomDsRB`YczUX|^Uh)Bsf;SXx*&W+ zY9MANBw{3y{%=7c?kYm$@fw_C-;x2X)y66|CV{*8Hot$S{_>0AL*s{}Z~eS#g|-(w zolZH0>sO^UHf(ptZGs2LP9gZ!D`|0_MGqE}64pc+M}pN5S=H=d0Zl_u1TjqQbh8D{ zfS;e?Oe2%pY+SF#wXU7n*Hv#jsbp0%ZoW;b$tdqb51Av1s@(P8C(jI*j6&NY7UJY{ zv>@ay%}9R>(GHz>-3*ZkH5yh!rx+-Gu~C}VQz&tu1}P5jvl{36h$IVE7dYpzX30~{ zUm1lviw!WRiQfz3xi>q7y~b63rw^z8Qhcg>PIZ%Tv8UUnw`S2wh^)NNCt!T7o%gEJ zL^D&;-BZK9;HAs-5U+KE4dk@b7u_QQ!svvdT19{49V_#aK-7fR)Pg9MJ2){2Z%de- z;2mk7D%)eLnL(itIqs6dJi%ZJHhFvI*Xef3!;@QW8=qVygi%z4sGyV+*=*^?M7|C;N5{u&4_%eDuRp%aNP{lB|+TQ2?gn5&@xF_83$8K($-<969V0 zqg8mRL9&ph6Q|IV6)7EKaLmKoJiVp9P9A>^{5G*l&O@q30e6TEk7`y@*o`29ueeO@ zsx-)kcmN{&f;%<52V_p|A3_YNJ%5RK9+x%%*#Q-w6xL#SCG_1SGSm)1FpO8;LIQRV z$y^^G@X4ggcvI-@iYqweZGNd6^*T4d_#mRW#e!+6J4YE01}?UHnMHl|a??&uq!aAWU*cs|%PnrlMTwlh1U*$^Q6w$M z8Mvf#umS&N?k)Tz6e(dI=Gwls^qeeIOm;W?Xw2bc?WoA<(AhQqNmy&U`vFlyKj@xd zooy@iqSr$hhYX36Ixx`bYFmG$!zppueR~13hLYN23Mn$FX0J%6b9u@-b*FJ}c5x(j z+g@~XPe@3#c6+(FEsGf&{n^WVwKFIeUC&L@%3CLdl_RPZ))t@9;JOBa`Is7)-l z3;FSWO~@-P6r7UEV!&KhpNO?>xAH9WXb5MgP!*SdpZ*b%HH!3=bf1v}oc zVs=K{*{ZT)BQzdORFQu!&OWUc(Ljl_k=IbFq%w5r67<%i!|b%aGNtP?hlC7> zIR)ksYD3&K8s`vJhyXtIOG>J2v)tNWN6n5dt8#8^>&qZ-uxfw*;0Bg`<}93iX1Go@ z8rp#e1Pnr`i(@c`>M1GaF{HoQI}YQHyo@Y983hxVySl>tV|CNwF>k&{v-en1oD0J) z_Bm6@Ln%CN0_l6BovI#`XDp=uHXI}!|4QVBhGqszOjUCg)t z(0r+^223wEfyhZ)|u$WTA!eYsQVC-IWs%}hvBsC*&- zgZt1ay8E9_ieES>DZ3pPO>FJIC_jIBAAj%X51Gk<-(%vm^PUS&@!m^Tx?AtN6Qnk2@h(~ z8?rOAJunre`jujfNE`h_a;MdE3}Xiht?BG{l$ozzWh9X;G9cl5EDxG=LvG;hN(qH1 zV5zUMlGY05{=6KK4qoB2T4v5|iyisJ2^t@?DNQlYie6J3Y`Ca5+t}BbI4x_DhUdDt zixmE`a}R%X6Nuv{g8Yth2X74-S)VnFZN}4x4@{B=7kkq-O`>lf4j*-@EKHP(X4=(GJ{iVUkl0saqXF;D9g9iHcgK0V#zNg>$> z)OL3aM8dCQWIDG}VnJXaA@aSOc;$f9#W+wp&h3BUiJIK_=mR6R7l{-}3k~B+3Oa)Q z{&mG|YPlawdzU$vv1%u4ONkPCEX3wJ$?Gl;gxj&R5626#*X(GE>_R0%FHRR0enYZX z=Vw9ajm^-0`68Q?mB5H~?b=cCXJyRRDW{AfpypWh^8_~#$ZR+lzS0weGVLS1vy6_! z#`=Gosi(+gS5{j79YaMXz{*jcaQ5~r4V+KhA)*<+di@@X#DqEck1pRn3OW4H5v!?T_$vgIC9Sas3QbPCws z04CwkxM`U-o=2^qZ8M@XNjPfO(G8c+P#399`oYq$5(SZ1U`j&e=1cHAS z2i6@aa7TQA^C68ZLR_z)+*=FB5%C|UggY9-?!^HX&D^W^=#&@)PS%7!vPtgOJnouM zLNvzTGD{pJ^eWj5l_X#1I5KeO%E7O%x^sUps(CJ&;kiid-R}%KkP#+emkz&>gB~gz zw;V-UvMT9&I5e+8{ox#iCnyJk49I`eRj&^rW0&xyTdnognXeEek)SNncA{?rzr%|z zwZ`!G7`c=g6TTxF#p>WuDO6B|d>Z#Tv${|vf@mB)(7rLgd2gVIQ==2RP?xOE&GlRA zXw)6rHNG=|myqF@59we=W`E7qR;|2>F zX|9uwysQ3o1dN8-GcT%D15qUN`R876C~pf}CkM2N(-5S`E=-DTIA*7cq&RX58lxAh z77IM4uQI`#8cJZ$ppAq(-HH;YSuR}Rqru^d3Zau>s}v;u5&Zj4!hGcXD-Ol59obZ9al zIW;vj3NK7$ZfA68GaxVuFHB`_XLM*FF)%YXGnb$10V#iFRGe#;HBN8{ZlQ2@m*5F5 z!97%oxt@kikNNgIf%oFfndc!79PX=$bGK|n{a4OANF z2oeHlgG_$`(jXH67Z-q2P*4z+79eF~>t+u&w{Qe7yznqGGqe2D^2Y`6$?YG=OQZwX z915U&d2j|nY;3JTP{$XF|8<}`2n2An00GRv5D-90MO9Z$Sq8u$qpS�YO3bFGZ+2 zeS&~Z0E%D}5Yz$02r#p;2SENl08DJ4rrQIs#s@s!G5ATc@K1(D6@h2k;9FurYh_G_^5t`cu+h*bB`I>Ieiw9RQ9XSI0lO zK7oG#reFtK2+-{%_Y0Y=J@_vfP7YwG`9Bq~0PI2LKzmaN$id--=7sxDcm7!?;D1yP zw6%q}{S|HVm)C!506RK>AZBc+oLnzCO&nixn}eaK?0?op4r*ot;NRvMbv-zNCKyF#PYP%=Vuf@_%5&|B(UzN5=bq8}7f( z=zqM#|JV2VU#Z_aK_JRNYtUaofPdUG07bx`iw5xLrU9G$e=$I7FvRWOMg6O%Ht27u zf5`q7`4EWjpK&_C_x{Tl*7P5)K<%b@;J&MvPYrywuK{O@nqzkF3+w!l%t%@zds ze~Gk}Y)t?A@P|oK(#93w&dSNp0bu2Rk;BQs&kYdd=JotHS^py9{O4H-=x7gi1?Y3I zad2<~UcUeF`RB>-UufPzO>9j6?2UiABM@r(vTFZr_ye0b+1tNN_^-GBrSN~8|5|zw z$Q5LQIzMY;A{=0ul$z{VNtn?)EUn+w!3p0RXj@RNk(=#PZqx3a^kq%3#Q3oykgaA^ z=(*8tX5aQ{OP*=Fzk>im-~JVJoJHnI&DfcZvrN~_&%Eu&Zd8Dge4rifelmZpxQd|1 z$Dy^oKKwz=DE|?Oe6*R{{?*A1qYt%nwhtc7wJoNXNn%wLehYRD%k{p%W9Kn#CvCchw`durox$V&R(`;bL4(Rz_{nom&0Vt zkYmM{{zguQg;LOy@MOkn2_f)1U1z0R3KO96<87t^Fv&|CRUUq+KvoPTh=!=zB z8JxSRDT(TdN?7uh-)H2ZsS&u{b&l4RI7Oa0*L7IX>vK8$v}gAy{~q1RbT}C&wavUS zYlkaK@aed(E1L0F4B{ju5L>7{qUj{LA~GTU@`u zAt&M!Xp0cdDf<#_&$xfVDpJ)RGeeEDk$dH0Q~sHwK4!T{|G9jNs-S&#bRD%xy(rhr({=V%rFDnF4@`&svV+Sl@DgXC~wNfw+z#AvKT?fkWegPu1d zApN-Kj%e>OS`%TEmZCCx1lb*g;AU3T1?+=Wl+f~?H+~4DD1v{aG~amN=i4+z26&me zY@B8en&Zn11^Xvq)T|P0w0a4FC??qHFMwBewV1vVIn;>4y%;bheZhtWhSvfUnPAg< zDLKSbzzz|U`L0HL+O(paUj6*C*Ybuz&#P}Bl*&1)qX8PI9_BcTZb5_9)q26Xf(xa? zb)K=$YnYik3%xAI zK8cY>)MGQm0#D%)(eR558N4%jdc`{bD4Bab&jif@JUoAG#)7#xV=mS`=AMB3Wz%O& z=AaFf@4X1YG?!(4mwP+DhM%g;dINYal8^{s=OQT$51zBcbi+BH9}d4SMH&58%vsXw z=kBgV!47!E{w{T-56vgD8dom*gi;@$LJcoh(al-0OK%uAJN;LEgZz!YPoIT8!NrA; zZdZvziD-X`vGIjR;VQQ@G}wJK(afi)F~E-6qPwea=m%B8UIf>G^PP0~5dUMfso!eg zUb76X3EFAxuzGsCP1_lH=Q;8A1$m(a=`8FHa?tOcP1;Ht*uIR@%LpQ_T>%-UD3bUh zk}&=2N5`s9L~vDUS=LSC+3hL#B&Q?9=zHi%G53E|jSE0Qk!min_5O}|B4BE-rycXn zXqU%Y{ZRyGcDgs~mykNZ-W|Rf{qbeZsmJelA=_dHOtxta)-C@{7Mr*w43_4GZjqm5 zTsGLQ;wYhI2X%$zN_R9x+^;|?B*$p!d$F8YGsapaICR`g0S_)xwKt;a^N)vhSwAEq z#u|S5Q9^=VliCqQ~CSW>w|pD zRfDT~P9hbuF0p2PIQq=W$mIQ5tby=)ugA(!(AEPl=CO}U30}_fJv&b3&-CkpFv+|e zO0TtrpXqNOStZdeU(brJ{{ZUhuHuR7jh}xod#O}yz-wU>osPOF)HWKab~3#AeL;YJ zDG5XGY~cjsYfK)_Xpyrk)&V1R?)}E0&Xyn#QGrgN4q~wY{@&%gAv-;P>yy5m*eAT( zZP7ezKm>9&ibbWb##5k0%yW8WuF6GZ4hXXDQ zyh_7mXoMM8R7eJicA%dBERV9luo&)Yv~VjmkKKJOX~{j}S}6S*O&?T!R?L+sdk`C| zBVoxiajqi4Vh77o8e(kHClRJF)=7U~RKn2$aL9YOy9$7K#ca*SGL4{|A8RD;b`;1; zTDL^`sI0@PzxVE_82C{4ZWD93q*rsjV^M%2famQZA-S%9Hhjbw0XlOPddHq!uu*~; z%%W%Nz%Ei%rFzuYs*o85`JhKP&tZz>V{CJGr(ZXWJDbg_T4a1kPFha!+US4eZ-|w& z;GEyw3Acc4SF58rKSzh^8a z>Teu`B?>c$WUM2sOPpc_tiT~twoADPdWC5F=MDxULj&`-p>U?kANDutSi+ z8$*jR5~LFo)qCx{ui8!sZaJsyr%$Hd*>R zJ@aebIpeu1enBhb$}tn)5ZAAhjl!GhiN0jd(1s!zw=1VKyG4)l72Hqes4F_mV^Sm- zc-Zzf326x9%DuzAGu?k5RBg8oEGMX1t2`{?NYE8ARvB6F;EJNBm4Kxrq1&>FyN#!r zJKQi9mTdcMs&I3|?_ahHnW5x=pnkZF*b zmN4IfVG%5C*BTeoJf8O330m<}7S;d<(9r9#IiBp`7Pb56+7G^V45hNUEh%Jo0H2?% zTas9e9fuUo3lM+JS1A|sMq;b@(wk99#n(SPDi`Xn!B znASi;LRaN5Y=PC{9Xfa>_i}}apA@boD!0=1xEc;l?3yY}fta6J3`}lZ%l){x(*nXK zL9lNi=V9gx`_cTCR{Fzscc;gs%W|l7lWWjfg>H>g>(0Ct}`sMX-uEM2120Vdu50@EL8?`eo~u{x^>pWf;fq z>#3Zi93h3~@5R3snvg=zZ#84i)U}@;m)d{Or|r+_b{jQmio|3zHlmaV7YE#H#4Nl3 z@N-I4lX@a&w6avyI{Ix^8cGL!OdZzEl(M`i*&J2czC|p#r3qh;=k}CRO=*Jkbq8aInc99dE=f9BBJ}shq=o4R=ihCmWtVa!xA|6t zJgN6O?e9mvex%?*jSyop&`&jpRz-i;PWcD~K$YVu}*eXj>QvT3VaVy=saX6x6;ML4Qw zt?Ho{_GKf$ufLvd*{x%9&d7hfvYvO}V8Y8P%Kvhb;*-4bspEhxNpRE%Q2y}e2%XR<#=E#3So%1dQ&p9DLYOeRpYLT0}F8({FAvpig z#khf8_uxmacL!Mf7;$P9@0_Kv{I+RSKEO)C z!@ZG(e0*+GHx2XtmONF@zfO+Ug)0{6jWi7$b zUDrgX6E0o#OiE9d#FK-nmL+y`JWZQlBZJ_x$^bGg?qgSewgnn@(OSN>Z3bm+o(mg0 z|I|c$;5RDmW7K$_n*`>)yrFAi^0W74c!5x4@e*tyYkvjS_a-<}qN~X40TWHKIq(dt z95tT43)z1uIzRaF@jr*&yNEuExxz1?u-l9}Sj^@Le|fcpfF{`tzd?xx*N4p)bD`@l z%#clr`_YF&n)8R)Tq60%?iC{9NtNsRlzvAkC*NWu8wolU)PA>o zFH*EmWIwf;Ma<-JFma${v$bEsYL3Arh9aQ?o_=9QsnqSM?WC+Z3i>jFwVaMmQF!=`-$M})er~$wrmA~WluQBLO)L}{pjczN z=ivWDS=yDfAw2fw8nd3zD|zBdJLnRYSCT)3XVm;%0%|8}xO{M0wUbv2`ILVfqa+u4 zlm>!-e14V~VvfNF;vre#oP&{+s_pPb6Z>JZ7BHIBiV(|nhgT%wV?)i6b~Zn6nt0$o zNf0f6l_o}{aI!Bbc${|Mx`Rp%r(Q_`C-(&FICuP2U3$`BxsakT-BW~zCdr+ShqQz00Ii6^GR|-)QgpW|9k4;C#w|7FNlP5h}joOV8=@#fS>VgIun8eaQ&b z;+a}*rkj4Z$?{=t7d>^6WhY21x*MWSmNE@xJ3Qr(W@(01cNj5U?9)G%zV^kd*Aj=|lBqH$t> zTwbUCN}ey~p0x_M{L$nsSzR^k<4z`ch_P3k^3;eDi2swj#4j@42Tphy52O1Pt-$+d zIp!mDj{AW^vG`FYz`00h34-Tgm~Zp4PWUqRN->R9GDT)~0Pw~*2QIql^YZ%)+A3z| z9L7i4QWH!~R8msLA)KFSPOso$j9t@z&rGHiw^b87QuQl^M^k#743$^c3y4Mr(=^;< z=N-qxwK>KE@Sg+hqw6+MkWMNCTX8b$`G2M8U#mA<2>fKT!xinXk*?oal7+S7Du+z^ zB~tDmrO9DaMq*OXO7Q&${r?bFFG)+|}q7M$$MwSx>%D_>fxilcg<3t(2CMOrZ zRcNc@FM9mXH~5S#(Ma~N zMs%=F7};4~;j_Z=)xxc_s4~1lW9%b#DOsU;TiCEa>LMI$IiGg~Y}bC9G@u4l+c@iq z>FH4=Ugc_-eyj)z5Lk0M_*pKh!2(aY00X@<+2_DtUDRg_Z^x3?PuO&S`KmhCwIqi0 zYIVBnd&Kr7GYru!&)0p0x%;n$ zo)?oma$;2tPNp-_EZ#TbP+6mO>cV+DG{dSwy?^?k>vr-HmZgHDy=lF` z{H^rs;l7Kcn$#>I`7^I1ncCc}O?T(7oRkQJ_{!eJ76)5NwSHj*W~Rz;70`?W-e8=j zVA%2@Fk$VPEfGQRmnL!i5E_xob7EwRW&_DUl6Er3ho)fGWOp+yLO-so!>3C;=<(v*J_R9Zgj&_C(wK$m*Iu(n%@bFtP)6bxlm> zO@OYdT+c4H!??ev0Z^Lt^JeabBr_V50dkDd=o=wQk;e* zqoAHX!Qd~gmL+4iv&oYz8Zc968`%SD`j(MNqKw!OWfZ1=#rW@m;kpKa(^GCbqZ#yx zU#mm7m?BY!&ajO-rd|{(q0jh-S?z5;#psSg8`LQ8-nL#*Hz|7~RwohAs*IdfDDG*P zCWwmXdR~4+G;K+&U3WFF?bDU`&9Q9H&G2<^gg%8re;PPJTh75|v>*{lV~IF+ku}F} zWW^QagLk`shP2jgW=>dQ6qck~`oN`ShGOAlEaH-rjy^oBB*T`+6t=<8DHceV%JV@I z7hws?kkTRF^%*UYVs!mJUkUVM5LQ6HZ8__s?kyRhX%hM>5Y)^_60`0XX}&-zhDbb5 z0?0|TR4Ykt8wEs33SQ#MQrfAxgM$tPFgDKCVV>=OD3<_2A*SKcrh;V}kidNyHFf*e z4aTz;dY2FHBy8&z$L!31A~dAVOVy;bYeX8xcFy9HznM2)|IKZ;PI!8=f!pNv!AsAS zuNjOS%nHPgHPU(YhO05u2Fq3o(e3K-Rf| zmR-z$z6|tBzS${}k~*EDSABaFJb_w%gp>sf%QGpN9@=rwcy4`vbw+f=Jq?PVWyzvx zQAU#tb9CPNOrvze@8U{b`n<}Jhnbkk?0hq(CH5U#ID-*VJ^pvX#&?q$J0Lu?JVh3X zjFBdj->U*sn@(~m>}Bg;J2}oq?_J)2U>KW!2&=BXuy7KK4yv>jgsbL}>sMEoH1Db3 zW=Hs)h+}y^o(xBamCX?dGN5Od9>Z-fu)sK-uYi9B|0q@31RG5r9Jq1}AAbZ7dZKwb zi3hz+D4=d>3+u_1l^q(lvzZcS9|&W$N)jH3J#&jlZK9tA>m}51igJk1Ki|HqYcpbh z^%6Ulc5?xFIZ=<535*)oE->dMRNEja^n2)!VJ#nf&sihq_9rEoQNi>o3vR6V&&DAI zzV?h6MB;?zm@0P!&yvnvp-{_N#28p+l!%4#*p-b;PL9Mf5rcGf2i@vr6Z*rPwuVmN zv%gm%z_%7p>=FrR(DLb>h$QpA$5I-EzDsT51$8wnq?_X zw)Q-z0|OBq{FA|NaB~uA7UjM~8pg2pcrqmNQirfy^xN7nzv~!Z|ICqh`i`D|+_C!l ztdko79@Zh^caJYEExJL>oHl~u@QT^F zE0amK@CF<9+gWXeH~rd+Z$H?7|I#8(x?SvOD%c@UV{I|(iEEk=tlq#XxFy_ibA-jx z<+u4>UeEe!k8#}u)kSp$SBZf0Cu=j8Vl==VHq%Kk$dbI?KMt66Tk>!I^$((LU%=fI z4^m+zBK2P?KgYXzfKe_3&-b}vCXx%PnTBna)-WGh>lm&=|h}7?#WCu59^1?g&hntEJ;;>&*UM5kw#01=GpEenS zL)DUSBZ^9gRt4U^mLJc5c`Oth&S!Dr1*BOGQ zWn_c?G*LhT_Q!AUzJIAi00W3Q+JuW^5LWj+`9wzg8F;XN@ffdX*pNRlkf6&quT3G` zA7t)rCKoha&_b7gAGc4J20whd$tPjCPGU~Xu9l=qroG|a^Dt-8zVlHSKTFtE<0hag zM8QC3xBaToqo-@-sY0M~yOunAWkb60Hf8FI5zBc-e~=ZH-!Bo_O5Ux7x(z-$Hx{jmHdIgHcI|vx?K*;e-Jurg3dz9C0sYL5T1B)9)4Fqg9r1(&I ze{Nry!0xMm99Z`z;%P6eW4micVUyfU-Mc4Yuo`U$mDNFanZT}uyOWXpiC$$C<>fTF zoR5vQRggSU>|tQ}+wXO4(HUjmJ4nuI{%tF>xT2n+$?HtScQqAD1eC5a46k@RnpXW7 zV(7Q*u0%e{HRD@}#e5G-64G?#>Di9@g!egX5L8@$hT8m@4;I%slV`)Yrgv$yH!gH| z)$S=CQAqMVg2i>#@P?*RtCN8KkQchbVI%1dh8Rloqviv!CWc?SIh=}>3<>2`v4%IZ zNcJ(7OXKh74~I7L;=mDA7JlL(_WJJcVKFQCKIB^sbfx1Ps`ODJKiEjm(qT*;>l#QZ zg3b(oH4-b}E#@f{$u9&mc)M#|`pdPAkdiGvOL^)bVMpu80`)aS>i6FKPr= z%N^Ika5`+9k^)7ocrB3k6X&^FTM&zY%Sc;W*Q0*nnprO zzF0ngeMa{OkQFTQWTDNDp|<*t6yi-0Qv(WrCK^jVL)_pT4f%+_7t$D#OGWIfuG;KE zQx?aTma%3dTHtOtwn{7|&-UrvVMhmqDm=uVdP0|_7MW+U@vaw_lASm3bBj;m>=MI} zG}cATGa`-PMCO&e+YijKhwf@H`k;*!=)xV>=aCU-pJdlFyH3bVCNR}E#^$1k7Nu{zQ+ z6-f!)E!j4cIpD0v=%%^xEJRjB3o*~7Ct)p!Ro`Ior{@#)4aQ%z1{9roX1%(9wKEy9 z@!cD0v;y+Vjxl+sQwhq|VQD-vyC@`Pc07IS?g-v4JD$@ookjhTR_q3R?_%z}Q?@86 zY+jM$67ju+fB#Jeq%2lEq6gB0;(kgC)1sul%Uazmq+GZXS*`vH!#|oXIlyA6ZfbvM z4c_e8;%>~~n@;kQmA8)8H(?5YonX3I2;rdM@T&3Qn%_yYoN8AL<@ESd)ud|7l(_oG zENbY8-6e#!?9?KLzr`h>q z<~j=&i$nt;&qgsgQ!!Gm$uB@5C_Tfj#Ec_~IE*KP9WOzChJ(6&C4`P_Ib2C@VO;xw z5-7%gD|_4eX2iRCC&~AqL|C4T=EVO82f7!wbk48IGqv6r+p)%G>rh+rHJ!+yc83dFHm)>t$OCZH+My&WwT-R1KL9Cj;zW}!|6uvE9v8JV{A z5>u26o!3hvjoq_`C7E88Ho8NICA?r=5!!CJE0-vwXUHp8 zlbDHbjfXIXo0p}3{Hn+KRYy05VzPi7os*Fs@w7On4Php)UQ0mW2KdSFOOFaiu{7Dc znp728+-cmckyQ}x)@optHH&8X8I`$TFm9jZ_L0=AHWlA=KV=-^4eY%9Sd63tUZ}|w z&_J{sMtVC`7H8=Lvl^Q|f{?~^I`OZeRss?o_?1G-W5Sz%G1F$}I;EUpj_74}Wy)%- z`%g+UBZOrp7wTlKstNYLZZ>{-N*_Q5XDyM|AstghB8BlRRDRW{BuOx)pa8ZNV~|oFHb#JP{u2vMTfDzW@{EwzUdnZe(+Ga%Ev{3T19& zZ(?c+F*Y%mVCw-Em%JbX3m!5tFf}&{FHB`_XLM*YATSCqOl59obZ8(lF*rFjm!Ina zCx5KDV{~R+v?UzdcAnU_ZM$OQi7U39RIG|!u`9N1r()aISMPiK_U&=IfA!Zt&KPH} zwf0iOc%GxrD zQUGcxMGb(IxxKlQu`NK^)x;KP3Xlhyn%g^@(*P_SoB+1}u>hDl*qZ_WDb1PjFMpPZ zGr$<&>}YNZ{JYKE!_?gI9~V8q(cH-n=-!6)?BML;Z0ZDbbOHR$sw^(~A3R;Gj9vc8?F{_u1~^#!jWlyG zb^WKLe|>*p{(4=Ef%eV-7jqAne}8hBm;=m!&W^Umo_}-y1#@%){!7Ev8E9|$UkvC0 zPUe=zPG+{|&dz^f{$l^ro&Ty6@V``V?C5Cg`R{Irf1~~<2cV0yxvd2w91H8;oTe^+ zb6W!K;h6pz6&ZUA2LKE6f7s1j9skqkX72QFgQ)+R8JfQ&jLjVEZ9M^I=6@D&Oo|RJ ze^Uae|L;_0{C_9%{{xBtp9uW_MBe{@;{JDy{+C1i|MxuqcW6mhTU$kAJM(`x0sixj z0muXXxn%7Bw`gNKpsnZsDgM7lYMK8B$^RpajEnK#R*2YJ{*{B7k@-K2Kxavyhq;+D z(8bgWU}0?gw@?4tHSEpIoqueB_U3=}{I`_=1{P-K|K?M-0-D;`|I>Jm|8SYxoBen0 ze|a342oqvwx;V z&BfT>?C*g6Ps2ZMQ&%UazqfFvHem` zNs?VWjhyZqOg|xC-8kZ(O%j+ow8~n4dR_jgC$rr0u>ju=hkqN#-BeSn6^rd)Qx(iq zwC|-Nn#rS{``fb#riQK*QPjD7c-(?ndpYN-Iq-b+z>=%l(=AwcZfUk>33adQxo-*5 z=!IGdzEj(Wb9Z$Tj;{-AgU*&oT@a=oanfocv!ZoV`jm+Aw8|HPJR2E|kyGkADDE+x z1qO96-^tgBGk>PW)as{U!MgC9AyxV;N59p8xMpb5&m@wTQy9kYA~Ly?l%#xNT5qXm z1iu--RCR11$sP$84DE&}f7k8ix26@fxOJ=VqV=*v@}amWoYR*Tj>e!TgK{b&TeG%T zzd#Xm`}5E|qu>|ca24^pN=N3@0?-T-hH*)>c6`k81b?MS1i=nD#OXaM@<cHbxksd#kv#Au>5^#F+;qi(myHb|xo;q$@q$}wYqrkYIU$Vm(Jhb*Ci zhU%@Y#($Lx=UFqB62QCX_co`JN)DQMBVUTRJzT4izT&Zr^i-jD$va)^_VN_jR`y9i z4z=jtBYMh|7}P`?3_I_TvD@SEJ+Nit+MDpofn|lIB0&0!x_AE=`6pxxR&&H&{B-Iz zVnHrcithft+X4K~@Xk&GV9FKFJXKfyEsQm(gntov%0zQ0{=iH+w_HgrkZ{Cg?b7

-PRF|sqbzA<(IxZ-*CP{S7hcaMu^uT&h2z+`irtfd-`? zx=m#i@FEXUy!htZIjt>NzQAV%@pKdWUU{e|nnFkEo zjg>HI{XITYLqxSG(&)B5h<>5{-Q2gMZhwUU#6C7nd2>Mo3!Yc79lE+7Gk)!r15qG1glIe5<4B36`4@F~(uH9R1MfpZ#v466` zM&f(0gHbnkU)lFzuqsskdPqnI3;29%*5a5j1Am~tIY&j>KkrgIO-C5)Yf-0lrAF(L z5q7K|CDHK`<*-mXY?4nnlTCgSy_85%=>p!VkEC-8+CHr|n(!Iq(zW7O?ngof-oJQF zsTu*?ldognJKfcwo)}bbTaQ!Kvws5SvD_s4Q1)fN|9s8W8Y6*8S~zv|TKXdoiW3eL z4-gM4!X->D!w+q0)2AwRr!<*od0Z-x3&u%C(y;>dWuY7z5}& zuOYK?i!G)X=$B{?ZAk$$z2=aZRo!r7fU@M;=}G&ZLE8N=PmpDc{NRu&aFfc#(XxiV zCmg24fP)|Wr}`G-;SEHw%6~fa(n?YJrx$F;Gj3JUJ9)_*B0~8TY_z-o}Bw5u+{-gm7H;?>rlZf|6(* zhn}Bg8PZ5`sgjmhZ+|o7+9)rWavA4_)tI^mISew+=0B(^iFK5Ku6=JVV|gY}Y1nJD z1jxC=t?KaLAj+Mw-7oF^`iQiAq0!py17NO;fS@&&n->^+kxK`weoNON za*-&f7d&;uoLjO*r&|Cs>qZU)spVJ>qeIF0awHrqepj%?IDf@vs~D4^gIE|es@iV5W)4B`N_}S$|UIiTW>dkep05zi3cC7QX=ydsKA9-dhH2!l?Vn_ zE;>w@L&aRC9qwsK0^u4vAe#Y9trt{vI`BQqATt~(CFPR9_Z*}{!K2Psf=W|H?nw#| zy8m&i6ym>=wSVf6tmcP%N2HTX8aAGQV+bjB5K5hv*`;c8NE71YoN0f$Ok~4J`3*dI z7OyXOms0&AsE3TzaOi@^ywa#K|GO-l!+LE!4_^@{JL6l>?6B&vOcou}(m2?Zp+^me zGR96^f$T*FkL8)RX<<(cr#)w7^{NNB{lzAM8josKu75W^Q$%m%3ZFEm_TD#U-vcQ; z(Sw}|D3|UAN$6Ft&A{cIxxk<}O_EsL>90EvD0rH*KcwU^QAISsYRN?zapboudrkfF zSO0VJgl=*bg<1=Q@*Ve@O<$627vqKkrSRN+W`E0tHA=;KdaUR-qx7xw@)~b}Y5fXr zM`WsfCx4{z^RhQ64A88!v4P;hDpY(TpHVG#62$Cdpx$MT<6b?&Q7^$~vCb@n-+@=$ z3%EgHZA9f5k8675Ue^*uyU%`Cg0p4tTfwgdOfzDd^uYRBx#VMDtcE`KrPZzED`;W4-`&R%hd(!>ZhV4KSC ze?Si%(J&u{T)|x%dcp-}s+L#5O8c2|JMx6GJ zT3@z&Q?MS1_)t88c~kV3+~xeOq`c$c#zq56dR!u_yUsLbW*`u?2BD=9TBXpp zCZV^wWs3HQO3Z}d^^LH30-$!%x-(dMVYdL4Emgt=39e)z>&>yMNKx zR(95BQ9WjXOT#>cu7&3RX+#t|Q}55XnbO z@I!{ja~YaK?=*O>2hBpd-3h*bUI?j zo)v=~uTDuEOYL1jeqJ}F_1Z8*N0RaVyreomhQ0Lc9Vq=wbZCzNd;F!6gMag^Ih#p8 z59+9vBwuSwjTy!WM%KIpKtm|}RfjE33Gl=C=O}E+m?E8rhWFv7lN_HF0luSM!}Wu% z3icg0Jq_d-tjZ~>RfIl=J?s230<>23oW@`k4AQ8qb}wbHw7$AdF6#zYGJb1o!!>EC zj9pU(Q|j{xzoe|Ei$0Q_5q~!1LyLv&GtU`*J~D@{9xtA2qdLY!O@PAvgwg8sXD?a; zVtr?z1QYS>O|1*V>WL1iz=q#J0c7^)A6KaatnrH!D0G_@nKCv18=!UIoKC8ruU}1gWfI4eH1b?HyXVHN(@@*ui z_+jW1)jVR$kWy_3=CXf9qK=8jb@22pk;zlPiS+`3p16UK_cl-3h;>NUY2xdGf(b^! zrdhsHlJ}JQbqAFo7U6`wwDow^W%2N+erZ>BLnxvqv~);8z2;snDGo^PC zvPZ6!G==FCY(=uo-#sE&aeH~@@18M*|5HW*oUS3(>XoQMnq3^Y_ev6SF$nvUu37p} zPEqSND1Q?mQ)gO49R<9w-=yI3rAcK}(-T2?$^jn<-F)PzhQ|NXPidhr)t0!F_|Yn< zOF>oe1%0*|wSR*Na)~1wO;q4>YuF2QzA&^(?uLt+pu3UsTd90dCU_0~;`|Q|@vZ!_ z8_TDUsxqF_w=KF-R*M)@m*ZHMF8!RKjhZ~T&f>6*6Woth)z09>oI~D^H$3Ik)a@qO za&a)2rgDNUlLi}iFd~6-c#)NRCsz&GqUHnhT)4&ivVS0olOE23I=QUd{ill;@wwEJ z75zqk6{GbqKZZ9N+gjYX-mY^qw5V)7%Djgn-KBGd{YZw19G4X8VO>f79^{C@E`C>U ziyQRpv>$R@!<+!W5}~Kk%mf16Ey~tGOXf2zgF8&FrlN5zi6Qr{`w~|VsJj~XA)XpA zAiq@2LVvd)gvNum00w!1H_SdX=!xJtI6kO3nmr4O?FBeVIV$+|tqZN}N5-o7jAYj* z1itOjGu{uk$&MJ@d&JCQeV^UToS$DI{^gTu1P~PnEH*M{U&N_$*v_9*31(MX$c*A$ z&j#$K}l_86I&7DcoL;s zE-n$#I!5BH9D(;lLq=Qn9cGN1MfpNzrV@ii+!Pgf#tt$$6016OrhpzBB@;s}ku|Q} zjDG~V&lMPVUx2WQ*LzT;w}!$2%3O6}l++U2pI&{#dFegz5+jV~mljIbfX5?QCb6qX zC-N{a{f;eHV7XQ@fU@CDOR5Sb``!+0cU~Bwh-NO!vzvRERtTfh#czp!QxjI05W{5) z0lz>AJ!7@O&T<6paLPr+L6o&dyQ?r03V+Y}P4lhO7{Yer%blA+h7EsgG%UF`p9G|Z z`P>jTt^X;wMa&3~w; zdkj_`k^PkMiFZ*gU>&)8Eip1M1p;^cMsJa2?_%RZry)*8(f|)R{v-4v944(-JPce* zDEDK5A!j{lw^s|R|Bq1TqN6h3+ug&(A8tufgTjlz2Pigg%;G(sFML%`hLQKQHO=(J z#@Zyz}HPI1c5`xm5cU`nG^6W@Dq6tmxd6fRqz)}D{@4l=`C~5Jfo%xA_zrMciXGX${;Kf`< z(aZh3lvh5OPfEkIEuqJyf}+IFd$G6>PUwsY6BoVkT&?SGnKZP}F_nh$Hh&>sPrI8d zfQpCp)>wu_n|Lb6?o4jdb-WW9_CJR9q_)~l<4Bi){W+L&KkXG>b`uPAn#8$nz0C7> zt83xG>s=yCu)KVW5pp|saVW!7DnsdtD%PKC>H<*C^eBG4io)JD+d3SyKdlyB@WLJORkPIu5Vn7?YHh&Gk^2#L`Si}}DQsJT~**F;ySQx34ccb~8j+6TYb1P6Li$m1`sk z+&JZDv6y?Us*O7O__@0jwq!ys%uw#r&_u=TO9%vk>jQ$xui-W-o1Qgw)%A~h=0P0~2QCYX_8N~R#9 zyv{ojuEOCQUw>+@gnvWXhByxxA?fj`;rkwUMeWlZe)W(O*7%DSH`(2v+n-RL2Cd=K zliy|lA?WVc*{VLUgxSu=M@W^A_I#;F2QJuR;cUdHK?3VUgQZ@%|4y|jnpb?V=<1C- zg;K+r=krSo>lxe3CpSTI)2MrTqnls%e8x`du~x^xOG?$$V}BuHlQ|W3Hm{J1z|Jud zcIANYd|XF?T0fN-q`B%dBf#n z&MKvP6@Pl|7L6ub>#ELk-VNYr8nMGwO;Y%Lr!VMnCNH=c0`LalzsRNs3z7|b-hPV6 zmMV~_N06RAUEH$!zSlZVzt&d!^2=`!Z$xL{ zfXGu&HX|0h?mIhxA>|>22gxVFVnIB-Cvo7hG=IQtlF$mpT(VLgF{*Ut7D2`KQ3u;b zq=+2c4bHkdz<}Ej&rmwhQL5)Fap^z$vN6ZXo~q#?M?XRE=`qVOt~;1fQJ&yY2+!xl zPOb<-a+?ojNujtssIv-tso%XIe9O}FbP|^;K+;HW|j~%_QXR!DKF3=h`PI!A9`sWs9K1c z`w$m9tM(4e>>RkAqiQY_4js~(9on|ZOxbXhGE0z1YR8akM~2%D&)N^;8YYUY=Rmsj z=#x7LVLs-Wam6dDK$G%QR&FxO_t!J2%6}>&!y?EwtjY`MJi|nN$Z|BJsh~47n@G`u z_ah?fmB`@={&|5{A$}pJB;ofVmkHlBFDwFZh+~57OSA#SdUlBTbz%WmN+F;r%Xwl1 zs9SCWSC2Vgouw}U&RQc-lx^V8kq5_(E)@FrX25^ZAg~UJjsSU@bsrWs;`G7Z7N&FlFc$DOs!=krU zBr%3UCdnsIkc8e-F(*(YXLS&^9Vjh82*Y#edj2NKXdOTqhd3x>xn6OL6mx1(0H1By z;BEHRj>mL-1bMw@r$`TqevZBW0)O7yL{>{;LzY~KJ-HUMIEItjFm3s!WhcnycwM-y zWbz9U zk*6>HmUwQ8*2Ibui4pnPL=f+3pIbpCcXXQ*EOv`ilL#TDxP$n3Y!bg*$$#G#F&>f0 z=hcr3aj9cH`$WH@gKCUGB*6_$LH1S7p^VNYXN6A7tYxRr331vdKDPAIRVYDFugJVZ zd%h4BajP|LLiCwPPo#1vgf9Bb^vf)gUpc^A6dJjli=8K6kzj*^+&M7}#4;*jOWj;y z$%byLicPlDdU227R{+{ZM@pM>ob9|-Q%Lu)M0hoN|%K`JmDoN#a z%`$B#&_~^T|J5nvI#*n_Cat67voU+-DywGK=;h#{2#yt&x&q9q*0mmIE&cWr_DnG( z94!90E{|FLlcc0gRUuwN4=(S9Yc>e zS}6G<@bQ|z&Yy}`vw!?4x7s$0uc809l#5y+t=hM}b=P6@^v|GtRon-A+tR2Yk?pwUxPz5!Y{O5l6HIQiI!a==U>^cbiOvRO5)o$H*>8Q zTW02ndC?C~zqsA(J%;kz^kPjYGvIK@TWBW1i3tc>H;nEw?0?@>T8JOLOT#fTm(Rrf{as8BCr4ut8LI3E*_aYG@3;emt z7=Mt+V+Lv~NJG0puPPldtj>^aPe?-^{9!C8BP zoFI9n;@A>I;eQ#>1hDzN?Y;~?pH}uKSZ!3Nn#jX75i6t}x$w+<_7#RUE;}@VYh--L z@*0wnc&Ou`#+yER0kJ;Wyx(dv3-ghcHZHu|3pFZ>Dw_QO@D&YLub(1dpf>EO*R(7Q zG4@k6=fQWvBb^{?Bp(oC4cmA_N@DlIt<^4_EKZ|pcz^5#4)zU-{WFo)x<1rM^~g%~ zw+)MbrT#55Wl6`_borEx{C8Q@js<=08T}Vu@i?I&FwA_Imb-l_M|dPQ@LkureycgW z(iss-BBog-p=Kk_h^*zcPp^XV=Y~!#NcF`vsrda6y*1Z{+~Dp9(mdR8+&39Mo!S|I zvfso!?SD9fGgB}R#H|l~q<2ZekI1!9N^ptp)sQaj9+|BPnSh^hlFkXc)gbN=%xL9n z#~GXE@Vztl{?cXSe~?Vx3o($7gAJLeJV0zv==?(X*Sa;perH8Gd``nGN4N8vhhGyU zszrByJ`_LdP(6MP6+jA^W4L$D4)YfC2f~QVI)8*JM0^`l0nB9t4MxP_t0{v+GP)X1 z$;(_O!hevjis0l3*0PoEJl4sE<`fEV)@cI9!*N8<;Ds7O`H~4t?=BTk0&1RDM1l(N zy93UXp58x$?$`bpK}$Xnvq0o4^uEd9P0r^{!EOoA=Hb0(Z}q?*kq8w_ju2QOuHib@ zVSko~x@V;_I$*hQ-a?PZLD=?GalC)5KQ%V>bpf&dh@#0Q3q&sQSiGmNjPFQbah&xE(B(gIP^dT`IS_TxWy^9*n!{nClY5&Lo?b2D`}Zr2 z%O873amTz99nJ%R3(aCVky7`~*3I1_leHwB(fumtY1U06Bz3>lhHm6C75J1%V}I^) zQzmBAm!`o{a#kLvwlfml?_l?XOC#E2#;`qvsBDB5Ezn(QUylFWYwo9w3a_!sG~$Yx zD3)3=YMAyH-{l7`jz94zz;Uo`1$c!Q}&zo!aw9z9g#Aa?=DYnm4!5Vr6N&5Hs4=-IRqG@!~aHWx& zxNHURQh~W@mnSmUh&9<{PGH>XtUBaR)=jr<>Dr5s;TqM^cp4>KU`jgh;eR~&mBkv0 z8e6Y9W+U%aSt%AIdWhA#nQIMVkYEjlh>XXyUyb7eUFbDd{fTaR+6wp(0|*FEJdpjL z&F1qJP##f_@#<&HEF+wYoZy$yxWd}HqRVW}Zm`B`87d>`8M#_TqS&WqAThxj@8OjU ze!+%+zBDcL>Eq4xDMCIUaDPy!Yj`%OMfNz|yC9yJV}YPPEIzaC%!DY@od+sI_FyZf zrl_z;^|^6AFDHLg#8f5agrVM;9 zf6YOB=_x*}skOl}a@u#-M5!QX?{G_4q1Z^_Ejv&QRR|`CwSDpK9e-+4@f?Gp3SON^ z-0iZ=wnGwm`*w}1J2F7u5~n2Mo0ykQvuTZ{7E7}W%(_6Qnmx+bW|=|LTa@wo-g$8H zEn|F_9^mHR`xPCAOHIsqTD_j~=!Y9NUS9h6#FW^CmtZJo^TR^lYhmR_QqM>QYNk52 z1A1W8GI+u()N)!#Wq;vwD`dpH)24pvmgrP?PWSG?A0F5j)+3Ne>mYs(8b~;r5?PVz zweiK)5DBoe5@Ac*R<{NiO}Eqa`1eQ86_gyU65=lv5W)zN&%pU4?X4<Hkl!-4zeFd@z^HC+<)GMgMKhhiVq^;Vu*e( zrn!^Ch3$G{CMdrP;A$ut;zLH_IEVUPz>&Sdmc}-X^97vVrrK8d)^md^!qCNSJ)or^w>tFljuhyIKiD zqWhFR7&48A5wCWzcOe93gTWOo@t44f6bq=rVbl4eY&2T`+5BiCmB=HKp28{nq1~th zC>B8^fPVzA`p2&FC^{+5o&wg*>mx=b>gi`An>$*kyrEZ@n~B4QgGvcv>v{~t7RMhM zckji`LMXJ5!y3?)*4Il*5z@9qJBC(~+DV){wP^|5Zlm~2>$G_P4v*oP^McnHDHmjJ zHvXM>9G`PTtedHePq4cCWTvSU8*sQsQjmm#1%IVG!U7fw<}s@38xZr8NrQ*s!(n{l z)^S0ZloKZnV^bOwT`ZbQDSBN5>1x^kM`LCv0{yOUu3=+qCwT#?ice>?)F&9xz z#&i8j_tD>F>yx0KePe|O!s}NXQQcX@TgZ9?dkkTK%&9yb^o+i~A!)ms)$rt?V#;=C ztQ_^st4bHqo^bd4dU zcE}65_lqq=t@=sz$iFDQR^PjXjejIW3lClu9W>?3+&AMa_1`ZpzXB_!gs%VP; zLZVdWSg_ujVI6pI5Jbl~LVcY7Zj?w-7cC@^^5BCRBAzVAlst<<~cz+=4 zXEti4k*@M${WV3sD#TA150jYAUO^yApCsjV=xRp{mgEH-FtdI{?OE;(CVvqZB~o6=){at=C5Hz{_P4C-li?-(9>g6Fj2@_m z(_8U%#(Ob;Xaka3Q`N<1HO{{>W1QvH*hN_-SOs4Wn5R%QF@r5@KAtL|vbr5k$I%11 zYJYk&O$=s)Y#c0p{nS6xfX`D~BKP&eGr_d?il(f+C-iVZMXs%ppD0m2b$|PAB99v? zTALJ)40+42q!zKQfUnC`sD`ZDgNnUxC{t5Ef5Q1&deWoZ+F=?=nM7VamLC*NlL9=L zwhlVqbDa6^ZEE@}fy*0|IzEuVgP+wG@uvZ;q7 z-s<3!5bg}V#w?aC?@;jFQ16j>jnPq}_^8h%3G}`?duL6{WDK_$snNyan5j)WsH!V-;j{A@5Cx0tZIK-TMl@#=_ zl*`3r(UEl(A}1TJxMPcib~HHwB=niLmnYh=k6SU_Vjb87a5o1-)R<=#q$iG|^!cG2 zThK08z!zel7MDiQ889X+-KxHasRGIzzra$zHj8j+^)b6M*ABrf`{fA7%b?oEo&YP_ z4dwj##=OF>tf(<`b$<ho#_oo$N>o zV@k?q-}@sDjCIQAE;lH}jPC4tRToh$#{fN)H|+40QbQf*ryUNeO1GYj5aJ7j1a`2V z4o=fWWl`?2Xe+w-geJYz?Z&7nlOS5^|M>Y-kpk*)XXbwa_kTsq_J$tDCNfJkRf>n; z?b96Mv?UTx`q;Q!w~NBfP|HdPGrBT15G4|3iulW-I!bFvxqx!p>c&{iGg-mh$#)jhp$Ot3_`g>1>=E;K9K0V z=JD(a{avVbt1@ONyCM9oX#1C2FbRF^bAe(^u|CRcsltEP3EZ!6C#043LmrjdF`%TS zv)dt3UlQuAWw}zHava84O4dOIa3H6t3V#xG(o4D zW;{D*thK54__+WUQTNRWL$P=aN&O>-rdgCx#W3evv-|P*BJPc-f z%C1#l6eZ}PRhUhF6u5pUDN37cVl5xuGknYE28%oX>dWmyPU1mkuike+o4}$_QY~=U z_uqfVgqS~8$+Iwsb&*1Qcp}r0@#@E_1K}QmY1~+bZ!aDguB#&IP6tUnmwgu5#}Y%1 z76+fL4tT8LO(0phlAE3gIRE|>3Da3X5^o$oVLWwDUaV+>;!C?mfGez<)!26ds?$9E zjux>M*~P2zt7O=5;py1y{S@JjLS+@XvzdS25D!zMx(q$}!isL*BeiJWaw!O-LAp(4 zD;zI)YHB0@ZX+soc-Xj;!x##Cs90ZTK6x&Gv%(Mx&d+6-sU?Y7U%qaYb7q4LUpCxH zW3E1Q-|gkIZZfiAT|3KZ8MaVsOsi{D~LikX)-pGU(pFx&C4h{4Q6s>DAeq z`VBW~yl6Sr3XzF$kcDH0rzZ+%6Fpgh*- zO@uS^2Sa_qxZVn{5(_Bw$dChG!MlI!VDND`=)xd7T#=05+MIS04Zo55^C=Jx0Vvm? z^W0#5G4*ULZqTwXakUu>894XThF`;<@dbx6k;2d`eJV4lL}F1sYPq<+w0q1{EX|4E z$bgqHb>N9|~4KtXllx$Xu}ttd?$xJG|?=dSz^ zJ>RT)O}y%4e;$6wDkanf*>T_vkMhA2(_?Anq-D=r@E|F)P~Gw)NpMjjjpS%#2(e#K zHdsDVHuC4VRq`$ZHA!Hkc-wKqhcIm0(9)&MB43-UA-&iVDB^{DtS9sj&>gRD71O%N z-x~XrZ$UtZ#I$k1b)J4rRHT2G1V4qq4P{o0c_Q`>r~w0XheHE?U3p^Xc9jewRaJ@- zN;>2_{-`n!I>%I#84E6n;DUOKzp85sGhfBq6GKqPcU@&l$Mf`Xn6SyFj!zTcphXIu z0+ByGX`yc766-h;#=+-|$qN>KC3r$v$7OnZA^h3Wm6_NLPg=S8`$2zevwC21L*9Yu z2rRosKM_S*D9iwU%`cbiSRL;Iq@W$Oz8Skj8d^wm9piv>(#7Y)_-aLwI=5WJU{a%t z40H#xn_CqtKWn=o3Z15WFt6J4ljU$m7|)#nAsv%oJbR{w!3FkR88;9?7G+mtzuc55 zuNwnu0|T3l73%f+BSwG7xsAe|lT=jAXaoi&5F8m{VKR5ix#gzpcDE_g3QSn%(N|DF zb^V(ucf)t$2iQ!&v?kvGn1q0kl__(T(J61zf|=hs|D&uxApbP_;)=(z7I`_VIQV== zJ`T3*=EkjJ=9N<85HJ(|M-8FwF(8qz^vX6ZF}Q(j>b_@7kt~1D-xdkoMMc-YA`#4S zoX0Am7BDeMxW>^O1}c(bSNnhNyxM19UfVR%8?jR(+o|)ESd;b^ZG@! z{Nn~D3RuuA{O!^7)xYtU^eXeyDoJ>F3YLF{h9!w^N2%2C5g3NqF>^Tm3H>Njz?6$% zgvl5kKaFv1n#q4q-Um3|;^SNwUz6m1-094Djn=c9&n+sW|Fh!XL1gCmwvFu1*^``l zRP1nm70Fp2k+R&6_Y9C4^5gsj%F~k>tFOq62(mhv&l}ar=RcvBo?0(-kOhPs3>?4@ zD~ekY@nq#=W&ZI;QM!Vqr5}O*`Woiumwf8w#{T5;cAbALO*izg^-R^Qc-frknC$B? z09n*(*Z}JbKe*u?Kx9+N{=NN&Tmn6H*K$qiD)=EVhF6;tLdPCi;{6_0T} zvA)fZ;xmbU!a?I1cchA4i*+3q7=f6RN1|T(V48ozJI9;kes(nku;Ze1ofae0BK?iv z5hG)fg`c;V7cfpFZaNR}XQ>On4H;K0Jo#U~E&e!nD+Sm`C z%fvGLBB$B9`?sZ&X1m<>(j2so;4M80LZ;Ac8>a;8NJ}LZj;|IvCkCqwRcp4*jm3SyOb)Em6v}xgPZ+s`7Mt{wZyMSu(pbWRVt^0WZYQh zQ0>CAtk9R!RkbU_sy<1HZ?KI}%_ZM5o2o)%RsTDKKcJV@{ODJN*fYX1?tmm)7##{_ z{8)}f0fQsaL+ z@{q&0`5q2^t$BSH2)mkjoCWt5hN@a;kk`7{tX6*KdjlC?QrfAYe+^u2s(mXZs^bO3 zlNfJexaNE2?l0z#3<2H~zgG|SVTcuEZ)7R(>%e!@_G2qU7Mv7=Hh!Z`g{VrikU1Dn zv!;hIm9~@NzVn~;4G-zagiP#e^S>bd~;ZNYiws&`TM za-@1pysc(CNm^K2cA)EeYfwhQH_ottVt^1p~M5SD*YSoC6k z(iN)3!6K&-4=5qu^evv)q55Z7zS88Ge1p%;Cz_;!`@KE$*jmsZO?oriwV$m2BVaRs zGi)C0(S)ztG905bekA;GEUIXPDn2bCgH)YmI?CS%#RP)}gMO|wvlEtqAcxpm>PAs( zy2OV8`rI$qK1d^QFGa^-ZnS@uYoYI@2d969N}%kj#nJP?Q?={&jH}Eu9`2Vb5fo+H zg>Qmi=q_>2t@1mqO`vDAn(gAdPR>BgBClUz#hv|&qum0}_#*Q`r(7+`?m_tkLIG-| z8ATPS-U)X8%`YRXsY5$Fe0e&@6d+p@+pfmitRV~qOGS)`M7r824w zM4yhLZY(^kQ)S4v)~%2(m}zG-jdj=lZQ0YkTbJNwgkrMKbLrg`w*38p$~O0;x>s@z ztNtzQ{aei{Eln|GO>4Vp>Jm#GqCDFj8ojcZroCNyY~|cMZNi< z5keScJ69*&-CQC$f?3DOHPpA>&iUA4P9Lq|z>zFPR0JxFbH3R<#5-8N}A11!O>dd zWCQTI*0hf(tL=raTB^fN4AfwHn0HH?61Aldc=xnpYiVmmrsYZbzHm1$mAVYDi=j+r zEyTZGiCx(-gTsFm!&mhZAKSc*U%9Wc1~$8k&A`3LXedKj#5O40^x#Sp>*k}J_~(pJ zipPm|2f=-z5t$~eo+P%qq0r!GDcbgj(&HXgeIRWS;mIxDJzFQwtHAQ7pWA&Mwx4ZB zP`JK?0m?CbDS*=nJUyZvLXynyg`VSQQ#S-Ry^u^SG>3l&?}bBEL2%?qn62=`t)_EW zMfj+rHM=h%3(~GZp>11iM4Hh7&0zV2!i?&cu6P)tQ*b4LqN~kIsWP2WA@(-&p1)^6 zVd5p}B%z+B_ONE|Z*tE9v)flu5cMfke)41W&D~x;khM4cqDKH@rRB+epLlSS`_VSmSztkJw<%yL%!cHjRD-~jdu4dnitxm6wU5o@(aW-;%@=&M@mvEsrw)P2H#=72QU6`f`HSk=U)KIRe zIc}2mp?KL#IZ)SNNn*RKGMz#K5njcBB4XP6)3WoM0r~q_m3WB!b_6g2p{|`zIUqgx$o6pu6yqcnn zXMqv0^ZIJ(8;DKB4(Te|5ymnw%BVSo&9yG^wRn=OsH-+wTfhZ{Uqs^m;npVeYyuBM zZ*k&7-+5HlA2;4Tc`e+m=lMqg-=sI+%`1PGnk0{}oAEl;86%J4qG^?%Vj~72P4qZ* zHtjj*F>Vzjx+x^MQU{u@nh;C+-YmsD@Ip{q29? zxE85sd_jZp$F5Vuj2?#loi15+wD{MX&#Xnf{!`@^kmRI97yx6nV4Zvy>-F%JV~nL~ zeHI78X5-T@gE2PFUklx4h^jbmPZ#uDQvm51gjKLh9BTZK%BIu_4^2s&3Muf`ngnCZYzKQ%m_z|`*L1lj-L+F!5E10t~a^+@neo_$_+C@IMS9d)%Napy# zZd_EW&*lY99P@de5LY{qVc!YD!6DF>Hxlj!QKv^SA5tG08>L8h%B!--ZUyihl_S#@ zS<{11{oWAvZc?w(n3Toh`4d}(P1yM9ZHH=$w0b~@sZ*<7O@gvuio}w86a;B?iN6qJ#}1^|!%}{HT?J96 z#q-Fv#iJe*rS7`!E1}XDt;9rEMLQouPg3*P&s&DXWVOW-9L#@i&ZhaHlL}?O z2n(K$p!NM!dmReMALS>hcM3HLq(ov@Tn0uDX58pluOEzFe{wWg zcsO#`I1X?nkrho?jgkySNwe83E!Uxduz7Y5>Zwei5Ag-6QEz;P4H%=JP5ux==7XrD zeZly#pVfoGao#(1d4+#{$^{>NSod>>YsJI3r^~&X^tjJe#?3#IdG%%uDk9>kPC{Tv zC8wMYuXP+$Rh5#|({kxkY<%TaFEj(^H&ip<5C2T;b)Nk>Fv1)!4*nns)^p(+H!(S- z0J-A9Zo2D!ienA$xFP}mEbGy7nTqG*CzT-(%& zDRE!TCqOS(>T7{OZV;#hKPV?5(V>%`sHGveKOV?1TA-G%LaKs;MoW4WpZUe<6|!+y z2D2f?ek&q5Y@~ns!FW_3r#kj#Y+BjnF7bU?YFuRw=hz){`zsm36hAFlgmwL74^cj1 z<*S#9MKU-i_l8X`XC62eC125;@g+eg~J z6$Hh!(6}ic=zC2^k7Az0g0^PL45F?z^m2l{u`dJk8C>Nu*c9CY3`^T3J!g|-*>$Tt|6(k@omq~osfGb1KzF^xVgV`!gNa3P4t|THWkg{ z=_7xbMYV!P_gM|&Y>Nv1Zghya&o|J#Js2SB(~K|>u;HNrf-2mb}klbdWKbfTI0oJ zs`94F8)$g1Q{z1=%gJxE(KbdnPY6|Rf3lG?dMo5x>FMBI;JUj?0j~;R=t`3=5Fx=$ zFu(`+$0-{H{{mM4&t_708|6z0;@0a{>qgz$6_()m9x0Wys{=_oFU}xC>`>O`^$CBG zh{<5(mv_V2~Q67nTPrl$SVKpY){mc$Gfis&9)2W}sNbmVMWCp_zB2vf?EB_o(1PtV2!_RZn#SaO%GF&%;K9m_yBl-8+p)IXomc&UHt`iW`K zBG~Cu2-*mox*6A>Pqg6Dp_>avs|%yrx3fL5U6MK>btVdI@>oXz>JJhBSi(o3Q%6W+&MGNH`)Id?{rcl3%p1Nq$dkDH1f8kXgWE(^_UaWJEK&sKc5S_ zxm~Sc#77GsD|0kxn&b@jqg9B_u5oodZn0@-8#UEBVdehIX|=Wz)R=!4qog?h*gFf7hfv+*8x{b)D@Nm{<1;nuRy%9Q=*;q%4c5)L zsq4fpB59*8JCzdb98^1ysjQ-3ToU=G2sD(ynV4RvlD!ZjqyGjAzC)6g<^Mk7?V_*~ z^VPiEVtBbqmu3W$@t%Kix%Z5hbgOEG&-{bHL69I2i$1UVrs-5ZrV8whu2}UhAkIWw zvFVUT*;tGc$Tey+Bp7$2;fPZ_|OV@WCFm_(P0Y=};Yy znK<7P$Slu37G_bt-{^d|5vdREwr&E6(G!`tP-@R5P>Mh=B=}iH1_RV-){r-MsT}m$hX_2PXJqSQd#K7i9p!XWUnYmGmX7kx505x3 zC}x?I;9;!Lo|4=FQZf-ENvyKeIg8{-GWEVg56UQ-N5X&Uxw+~TM0+B*rhmcq zy?4Z#I+=eEr3{$M=f$?Qc#Y#|6c(9C!bUn_h~EQ18S3^2G;y%*;wxw{g7w6Q)rQNw zvWIu^4RZ?RURgUxdt(u<^c*fM>Ro?1{S|`VM|B+`uvWfWvj0zM0?Rc< zS5}dEWQfMzP*PohWR`pNeMHL|j2nvoj6*yJP_w0z zbFP0?+yE0;(});Nk>Am%Q@(FKT^74=_=gAot-U>J5rRp)-k4>ke^O0zq^hDVEp;q1 z3nG&1e>LJvA%u5E8Z3^a)G5IN;0d?4)|aNtHODU;@y3?R#c9Yn09eSPNt7oS$$|(G zWxgY}VI&|mHp{L1RUl|LoPpEe?hzUZcTs;q7(4eJylGV-6iO~rm(6e^EY+<>zWvVN zczLy>*rFybdn%UJ+jt$k?lK&mSO#FZ#4QvbnL?2TTjxo(Y0*Nzn>H`*yCk?udqO9= zqT)hE(btYnjr~_(;keH4wnklARJ&5Ux?_St*!9p?WCj^8&C}Fc%>vq)_Pse&r+j}1 zP1Y(ZTVPE4i&fZxGyvH1p&Z!yawU8e^xg@l%Eay7!jc&Qsme`?O!vU8#Frgv^q_do zIcIka%?6i`t1SL#cf4<5vG2tiV%`qnpRYe{$1JceRno+wt0*Jp>nFX9Z!;gK4xK)* zE&Nlcl#u_2JCuD&%mFg=gdB`4AohR2uZ$-=e&tbJX6^W(2gt=$SkEckvf}HQ!^dcM z@(&UPMAY&KY6f;@aRm5jKdV_g7%4@Dhpy5lNcv%}QUP~kJEE{O;p8NIFJXc$qflQs zMF(s!a`xv^ps*n4Hg!Pb%O8tJNJ$1IglAAOX^OGSyH zJ5ZHShl}nqgH0&5`v5u#noLTEbFE6Q^jhX-E{Q3Go zMydJ*UxVnX5(qNu#9SD*czb_Dk2d*{@zIg6Hzo%TSn2cfbpr9Z>;-B7FJ`z1O}L-B$`y6WKbkdLr$(qC#Zgt~tpW~aHg!MfbnQE{lO zo4l$=#_gh_-qvgN23(ZC48dYWpE3ykUZO`T0g$X^KTJvDF- z)d^k67B!qdI`W-7_0%4+!s$fJqUj-u4Vv6KZ82ZVO}h4Ncn)MXj!_2HkbFv)J|6Xx zoI(xC9DOMG?Mi=ll}i&=g{TzRSVeyU%zUOe??qop5Av{a1dz9q*Irm}l|4G*PYUXl z=@#&{Ta_X0eSrsExeQd-IVhbtGr`Z|C|CQLAvL)wuOpez`Is>o>iT+&duMS@OYp;| z9;~p=nv5Puo=zX5c(~z=<2ZN-JEmR5&WAeW_>oJPDr0|yTf-3T&-pEUH`$*W>$E1; zzs?6w0S736gyIC@v9Q%`8#v^3?CVr4i}ZP@oPBb}wB`g{i7wdZ8O#|v4&433jx6-L zp&2;j2t9FwhoJqkBZG23R<8iORXH}>=mbZ(ZNkC?g7|mIb)TAz4f(vm@{Rj+`{t4j zwP?w7za4+@I8p&=>tY%I7$5{2DVi}1HD{xeVE;c?V0+H&p+j)gi@vP4Y~H74QR99qE;0~zziuxa zAR%jUUK=_xuHL1U03DE6iY<6FAzv4pOpz(;w*!XwG z-Racs>7Xj^!AB{Nkx|eA-HY`sR>yz-bSEnjt8vcqJbCd0xgNw8PaD@y>Wv>!*$X@m zj>Pm9a=BOL=~)zo8Y5c|!U5E6%3DVv6)X$TM~I}`-bKEpW~RQWP+7(7x%|-~RiKT7 zmT($39$CQpkul6|ZZv#K0@{%J*$N51p^ooaIM--Tm z4ECdcomZBKMZzO`bXjE_$lYgDq+cEpX>#glpzsQ3oFF6R@F$1RRkD9ZQj}e{`vpQ> zxo^%71H&k)02>P#DdtX$V`>XmZJaxN6vD1;YTfzC$C7+{9t7(LxkzI^jS<6UM1Z zdc+&2Hn$X6HJt!g`nWM!F}L>g`&YsZ60&ZWf7Dz|g%j3()|7vC5Fu{9iKJ@#M%6>D zZ2B#(bBcFcZ|y_$O`|u{UhTOhMRc$BuTU%RltS>ruLS8?v8**U5mErg*3xj;L`vZJ zLR^%e#b)m`2hN{xA9LGXzzT+9U|PQbOG)w61BNJUThd%In3ic%E2eXtku!>#hFX}+ zE4FJL3>$e4&tQMB0aaEei2rpIf(6BLR#(tPPR{cEl;;P)lf2s+cE4)FQw_iHuhYqu!^p2%Lz+#>vkhWx{fuUMI=kpxpWU^d>zfDl<#ibD}N! zEBqr#Mx3^)i`0e?M<&UovmCA*D#|XDQ=ky8-mKsrg<^kX7%VCO5?7~g#@|nlzTzv- z_;A}ZIp^eLzLVlZK)7`y9^dDVXZdb>B9e3+AVzhL(-PhwRI91U--OD} zPCTuUR`a>fS8(gp_%ncgl=8klQURWi4H@&orApe+qktgV0rub>9-b&hPElOfU2B~d z-|3JQAkcqDpwO!UHCN3jzoKs*xba`L!CZC`)iNM31u~C$cA4g$T6}l=ys-NH3HO$U{Cdn1c@p#hThtG{gkL7WaMvv(-e*idL za3z1HaBIe&w?Ns(RrK<7PYe(pH)Oazb%dHR1fqV)sif2zw?)D12yv17CAk>CgupN* z*&sEL8pPqHM2DzKAK-$K&;_BGO)bZ5nSqyrq9UE==%0*SiR!3C*UQxO;|PD^1+agd z1B1dm#DK%1&K}(}OBGb4qJf&|;{w2|H1|d;#3{JnM?p!RTP%z8bLd_6E=czxcAmwZ zE3vi0G>NzsrG=dm>#_2uFEBvsiuf{@3T19&b98cLVQmU!Ze(v_Y6>wnGnZiN0Tq|o zY61)%F)%SVI0`RJWo~D5Xfq%%3NK7$ZfA68ATcp8F*KK->j5Z#c4b&x+mBgpg;$}t62bzfkDO<1cZW} zAhJLx=nX&*WCf6a1z7@kc>z2kA|hxE02wD|Z&$F5Efm1~%E7|M#{MtMUoHR(?|&k% zk#1lc2!QeR!2{&ruG#st!ON1Od6e zHlglr;Q+P-D1$9Q5H}DDz}m?b;P8(Hz|sj~1^%lwH_lgoE-5zv5a8wvvIM_|fxIk1 z&VNDd0B4Y^BiPOD^%($m1K79%A<)+uK%D?!h^2$O)n5g?+O3`bF38!{>D9yW6?-L9 zcXETeS-OIqp@7${>aueGs1s@ng#MM=4g3lNoUC6xt(+{~|7z)P?3Lyfg#y74Hvkmm z1^p|R1qfh&1$J|G0D8aXekF5u1^-=!yBio{^REin0j?k$psSSw$j$AQ=9T-e>HMot zz<=r<=l;r^Iv<0<+TW)l@r9l8(;;pM&nX-g1)AI1Tg>4RObA@6Z!u@;{OwY|4-!o z---M08vUn3{J%ZV|4uFE?%<#bbOik!1o-D215gJ1b;*D&|BE}&5$xdo-v#`;ryl4Z zRceB4+#P_f{|^6yUJ7FKstAV&r@%j~U^h9i7syH-47IccSOXniXZ5#T2Vw$L}VcND}OMA#)!x#7m1cF%od-<<2{arlQJ9%jt4SBZzdawTNr~axx zRNLDb1o;0+^i-Uz{$ueMi?pW;M~EB1!N)D|dhA{go(MmW|9_M5Zz7(5tyO?f zSFjhrh?|p}n+Ndv|IgpQRwn;O^A2L^WcAm7j?sbwAy%)O>^}^D!Iti>uCLnueePeI z{^$Dd?G6HYfh^H}&O2F(hS`0}%7E4q=M9a^8uj(?zz=JI!Au`W_! z{#5gUvvKmxbDQ_vf%Bg&Mb_<+9wG;(?ljOzK7~IWOK$=0FUEEuw(Sru(^AZgL%kS( z-_u#;H3UOJZr$zQ;~JW#B~M6{lkI%2D5tk9L3ADkK?L+S&R7AK>Gko19XO3Jc(sKG zhm6U4w>L}!qr*dk-RFqCTjXrH@u&=F=a=_lKW zr|3$h10x@jkaMjy@z!^2H~sP&XL2QfX`NB6he>+6Do;mkmIh?3OG;Q=;L7~XZ(z|3 zXnN(lA-xXf@ASW}u0TPNPRb;*8QCn9+vvIQ>rw^DAD~A1#9Km<&Cerdp*lOPvHJ!_jsLr(|o^1oShQ|nP_aMnB#<-zMbL@G~92Kz~MPA ztVPPnF-P?T4$YBIu`t4!JTDJCuDTm}t<^9lN*1Z&27G3e)Rm2e-D(O_Z()XMXy?TD z<{$>1Xtg>J>V})_G8(CEG9&K0$V=r7iq0~lXm!apla1ZZX`a2 z3v0#HGU%zJ>PC!Jcd{rNk^|m0@5G(Uh;Wj+;I7oc^y|h!WKlO6G^4fp)u(FCZqpZ- zAJKS^rt?;^>PKLI;QqrpecP?8@I!zys|Sv5#tlof4pSUVy_1I!6gyadal#m-=eO@Y zF?trgKgJ>N%;FZ6(r*})8|K!su#~2v6=WNU%-tFzE(-jJeQ?ik6|Y9iuVmD5dOX-; zV(H;=o#q9}v_pNx7I{kMKngORk4Pi<yJ7gH~wtY z5bpmr{E-b>>)7?UI$s}uYH78B&41`C*+RPjxX>uQnU!nSplCgtWRzej(fo<~we{@+ z&0Wjww#6aVZ<1ezvOB%YdJMqXJRSw4I6U1hF(v~1B{tc+IS%0h-b;7c^2)NMGKV*= zU^1JpUDV!NwCO3~8r!qvrE9V1#SL&?bT8fFQBI4ST;z017VYqV3U5YtmjiC^84s3I zC4M9owTWN7X|hYsK0x8R)y~~nwW*(DzgF>@A5e18sdkfQu~^a26V=7V9;ccYqv(^Z z)k%Jc@6yV5#69{MpstuM#EtJdM&a!f>??`9@SaAlVEM#md66mQOf}$>>gP;Bf5G}D7R2Vwa(T`iC}<#7G{gn(iDCORJfshGW$tH zqW=fY2mL%ty7>BURLU)bDZ7};rtjc&pNKn=kkc)7j$j%1$R$&{X>tW(^6(ow@QUR6 z0+b1yDi6j*$=WcFV68dql{hl4QwQ!$j;Y8Q!&B(MU*JsKQa5l_J;a==G+2|X3c;bn zKLpVq7l6xua=VK5x1@&mP#=& ztSilPM%zz~31qD)^zNoXetdmF!sOIk+_wLdN~9Hu`v^&H9c(S737m+=1rm(!SeM4V+rp^9haQmPbjO z@&zVE$vwFxo2!3h>KmCKxBZ3Y#R5AG<4OykqNSsN{e`0MWp=Z-Lb~ z+CpC-#8@iZS{gpevhTql0(nHnnfzV=2=7lKxeiK)so2oIly z*3-H8o)`+Uc$e*g=Y5A*mAk+*ZQdq-BIDTA3$p?vQHiv*kUiig(H8>YCYw2du^`f1 zbjLU0j|fB(GggTgDt_XYN(_Ayi-+%)vL5_y3Ks`<^pRh%Bem(O+tmd=`=mQ{vUp6dL$!Ku1I2=AQKeFFknPYzWJ@DQba-kvXC|qcoBSCWY+11$zrTX%J^pR&Q z*POe}*$kXOqe*GthI>uqxF=uSZd}fC#hKqb5$05eo{)IZp=N4>jF*4)mewkkgz{LD z_Y?lNM1HbqRKZhHCfVoi+F%^~$<=SVR9*tO?w6ZUU*8&uO7$I>>=&=TTbPz>klC=G zJGj(;YAzKGRsodO2>sI%NwFapqxjAO_r6w~z33*y0%q3cT z!skc~sXEI67Nu%F=kD60!Qo+*>@Q;Mt&r<&uOn_&W6Nv#4mr|o1d0R+4UMMy9Q5z5 z=^$}_@}&}P$(nP#BS33N1%V?A@>$^uOfNQaklQ|XM_PCXx%(4;g}UJ3JLULYDfC9A z%}y>E_;6Yh9Bn5U)cX%S0%DnQ-Mh=#nfT%;C-FO斞k8;+F*N;<^#a9c56)7j zy1rq)a8V;#i%Tb=w(B@f+rXPzj_+MHs(&+~LG^b{@O0CjmODVsm2SE5I9xO}qj^9z zCjZ54rW5c|9q4R-_x7w~zCXbP`Q)i`LB_VTD%hEa!|eTFs!*Li*AtI&wK@ZF6O7$Q zjbRQ1lsgXPMEm335w>=sW|g28OiI(bE=FnEbduN>U3=-G+HY2k=ck*MZnJjID)!7S zcrU!ApA_IqM5tulP&B$YMBvG%KA*44U+4b134>{ikbvKRwY!4eN|bCfmT6b^A+5k% zH=(jRISLoZ{fyOU`dYD43MYCde(tZjzLW8>WDfi`{5${LBqZMM(Xp5x;BYY}R;xpBvZC-o&Fq~g_ zrA_`n(~R)YOHyvXAz<&MRJ^}8G%Xku)AbqmeH0rE~8wFjSuVcdpzJ8HSbu z-tV=4R0)#35djnH298@%`=W`(cteXcdmsDa9kq%bL!oUp+w?uMRrX`}Ks_jFZEeX7~Fm^dpc4YbQ2ls6;2eE8^8gXFgbr9!K z`x+im-ACNh;zJkJvob#XOj;h2$r5DbN6*WDp*@GZB~cVi@3-Ar&%^>0Nt)DRq;i~4 zJM4URr^h`43dqQp6q@ED%5GIhh#a3D3Dm!QZ~DFr$kJw9X<)5-3N1 z4!j7Q2J0)1{WPw4FO~&uQbb$ri#)m=C6nV<1!jin1tjb;UbyF8y9UXkwo29Vf1?YD zBCSp)afL<4Oz!J4Pkh1dg*LfjOG(_wU&&eZphFhK-5{bD&FV|-SV&jfH+0V5{YAKb zt+GzC0$y~URYu&A$Fxb2;z`7{{eq{*Ms6zFtxh?M#Qmt52BlhH3W@nl?nb5a z^`CjC82ME&-s5o+Q~+Lsz2ZG zbY3or=sJNlN}?COR!s73*zqjFIYM7@?0pbi7+AeNQy241I5Oo-NsE^Gi9lxFE>G2> z;_A^#YoM@~Ndi`-lYMbj=2xSTWeI@|6UZL0!!3Ah7DZHx3H^2~dhgq!0q4+`6^nB> zkCor{GWL^}N<$r9+zT z3|@--VQycgQNlCDmV{PaY5gc@^Q;ho@d(WtXq{wx;W{i1-Z{Q&b0*Lyr*uTx6TYQ4 z!k15?j7t){Lm%)ZJ(JDow{864xVzsf5eg!IzUA8Wlx?}$ zXK4eReKok#@(a@Wndb0&>bC(M8JuGsOw`bK**~K_K71`KYPi?4QS|ho-QN83mn}*8 z48BC{Pc|y?WgQ6Gcpj%Y#(GzEa)Vc5bTo+8o(t67iNb|}(kJByCOM2fWEpr_ zDseq0RtHO%LL#>Yqu=O%wopggLew}f1VRsBuP|^tZ-{jXmC$RZ9p#&9NrrmNN$y41 zg@gppn{{bFB;{!_*d8wCi1Q1O99z!k(CsbN*L!u^^iO~QAKa0!Cc(pn=iOxR`-P)i zHiXCSm7N%)?W*tm`*;Jt{%sIF<_omoR{MGSXVtMe3POvQ15I95|3MXq)6vvj zDRWgWj7oDYq5o`uPQyev>2|nBlG056ebZX+-NMKFWW-&}Jo0gaiWTmubcSJ@beeQ0 zOn7;mQ0_ziP-8zVuC6)|#Btpv*5W#vNiYDDO_PCWLJ*DSN(D}I!Jyv*Gecc4IGJ^dL3_9#~g z+InQS8qQYr^}NLzKEWYS9}88e=gl_sMh~#e^ZM#rUVITaeIkcaOh0g5BITwFOGE^2 z{&*Pg(UqHzV?noll?eeoS8o4BbR8Pi$>x`o61VUkm}sV0sMPFN ziO9*#?=wH)dJs!Nr{@1OXi3b~I$?mpf^*OQMLqTZA z1{1gNqNtJ4BuS@S5=p9%Qj+k3_4Ww$RAy?c$2e$zASn&wmX^l_P%Yvjaa8yn&MKH0 zP;giF9f@r6EiPjDeO%$gu|`Ay17}Q;C4a2JYS(`Ywj%P?Bt;0lHoF!QN}LUtz>eB4z%p{G#mC!fYX?u1HBP^ zq7V#@h2Bb}LOLPb?MIZQdsC7Dz7wq{*tWWV^;$FI$@h~VWkU4nuEtzQQ-MAS=;ec} z?L0$XjX4p5roLW&z6%^3oJy_*i>bv-;TnX6T~$ooag!}j+@-ivyy(TbI9%M_p=b-m z-TpWfcXxL$?pEBrSaGKmyFh{E%Vv{(*ks>kCO>(Z=td<=JJ$UI z`8p`?;pcq9W({yFlf@!$#W~L!-z#Ihw_WTX9PU6J@dSz|g+7&=U`QYg&nAOIYpo~Y zv<4!J>3&=cZzV^0fY=^-zJXg~PpPNJN_|iR zD{D86!U|5)v|zf(P{jBK8vz_%fl)yUe5Y+Dl6+n-bq#|__E#I#^hUlBH%L+R2DYci2$sNYX zFb@QH!(D@Ki+num(gI2uxvJY+mY>Uf$6KZ;>Ao!DKU-ds8X}#wy(75AmhmJ@n8g*d7p0)do`@>E_vt#d&0HUd`1P~3eNb*8QX8`3K+_oiZU433-`mvuy zB&)testu1hE#)9M^2V9kp_ZqckGW--*%mz9uQg(gOF8V9GJ#jt<#4Vv#fT1DKf!X6 zOu7cdmo&pNG`h1C2nL{UO$?2{SXrecsjRWq?Vp0^NR6Wk%-n8Ej3YSXBvQ;eL1%ew zz@9Qe1zPO0RQlP?#rhY%1lb>0%1Qs+y~%<;QbBEZ{CO?jLw%AVqtOnj;a~`f-7nCX zu%wnH@by#)^5s)ql^Kk&SCYBfEqpZV>YkMZ)$Zlb%5wdbUsR|uWYG*@QbaZW1-J4S zZqy5+AS9Yw7TRJ4Odfn=&kHiaXB(|TV7Ony5|7`z7BNgH*L-#IF|LJ-O&CRRsrWFb z$%_{2cf^1IB;uJL<52=%B0^!_OG%Poq41lu;=In8*rw z40UlxW(!?}B4yhw%Qop<(rG#VGr%D$B#0Kq)#O-3%6=_K_TelaZO}^NI9ZtN@7W`X zZwTOIVE4jqy8h^?H8@)wVPAC>B4(sDyp6B*VV1_b0NA<5LWO1}cBHYY^Nc%!9y%JH zg`DX4WvivZ+FhkNjhrpe1`A2RsMQqst%PDNc%XGw(gHnO9YS4qTDMJhMpmVu^Z4vb zBAe?lI&#Nd8=7!D8Lyo;2uV&c0*%oOw41Sn7|Ci5s@4$L;*qsajWseKt6SS+@3V!V zZ6kqwG)~H!`c33WgW8!Yv;*J8JIu$L927SwvAaMV7G=)&$I4uC{K;9CMtDyHg*LqOHZF4accnF@wz+R2M~!R@r^1nRKA)6fXL59}{l zt(;97TZtH&9xJ3sY54#PrW3CVM3)?dvC?vtj)RbFIfKVtJz1UXrQC5<=9eO8;VzN= zgN7eZR%UbS60+aFb#>>r@+Yvcou}Jxq&ISJ{GOxrG=PHB-HcX3+-j*i0&jKgTQ8xZ8IyzEFJ=_jw70#zDqT;{+y4(=u}e_ zm7kuv@UN*|v?ia(50C^QXLJYMM@vn;?nQD7jo!r#Hy*u>E$#LfEiwKyGk@tlZ8I@B zVBV}L-It87zIX*zR$u3xN^xUlX3WT92fP8$tyk5L**SUh$jlU9>nsVQHE3wo&wixE zrYg1{_iHYR5$+x#=5zt1f|q5~aV4KgcfE-@4D<5;mZ7OHQO`z@p(R8#mS$czz*~)8 zI~f@ygEmR_B?_7PMUkrTB4ExF+RV=5Fg+*z&lcDJX0!vjhq*8VL0&pk>*H2p=LlD` z`oZ(&=*wmG5y_Y=9cU@LkH32r4u+pXoT?=UrU&dzU(F@aE}XblxG<9ZuEcvNqCc^e zp1l@)N1aVm@}G6i>Lux8`>di$^$lB)-^DXYX{O2=vP(}^d~#hCIYc_`-ASf841d#F z=6bD$gL?$T^RQK5wl^hRQX6~dl|jEfX6t!|fbx%#6Mn0+5M7?vx7=qhg(DP5boq@w zWzpRv8B+<7A&Xa(H1q2?vnQ!{^TWX?E^Fac?hQj?X)Bp2Rg$x@1`=TMPchyEUJ*Jtyxw$eyZChSs8a8HL3vais z3JV)@oLO=)C;g-4BJT1LSyMI0Qz8hP=0LJMfsAEIB5oeu_D5rA z5%auD-l~nI$H_+wAJ$te1?Zkv>Too*W)Sc^d~lCZaWo}Iqj0!k;;RJVLn7mUdhuS< z?H*GIkS>7B6uj_N@$IM$K$olhpl|pTfki4~C(S%F@8|C{!-h;aTp@J{7r&~x%=`x_ zOs|CPxt?DPv`sfCY13q3rsHG#vrpZ7?XO_JKCeb6CHvFAqSHG*-{u@Nzh~jDy@vu93RAxR3W`+KJ^cY&K;?)d5@rV zmB{(%>A#?>U(WK#Q-Fi!@aY=`FgQ5bAaJrKh4z5REzTx(bl*8z_Q ziU8?nT%TdO-%s?)P$u=iRvq0PZJ2;vt3?_8;IHI?7!T#iyRj!E83qI+cSL&Qk67)? z5Cd$-`;EmxTH8!~(VKWol5v~Mnv)?K40u7lzVudUa}q}#CEI>+$v;aP(H+pt51Dfo zNrS3JIl`SUEy@($Ei|>VJcJ0bYaKlgnF+P)HB?oj(j&NT+u2w9)6cypFTFrlWNJ`~ z3T^zWpe=Rq`1DQecIh8-8$MGpipQV}blUQ9=>XK_KB12p)k(3bNGA?;Lo%{T>iMtA+O&Ql)NLR1+<=0M5W()txAjtVT ztM7H}QGjDb?q{}e{=DSXHBb^WNg_xwR2M(=_beJNjUQ~eweYY4*sxEaNnc%o7=nKLQWOqFTze0w)=>=tLcISb#MTzwlzcMq0Jp z9NNw~gxFi#N5?Qxwp^`a81zi|db?rfn0-fcgxSzwyx?zFA6%X5if;eGYyrJWEQ2}0 zlG?X=zF)u`4?zYGY6JvNR`(J`WyciGb30Y;kz2Yg=6XWra(mF>>W=#HbOA!QK|8m` z21{vOh%o8^KIBi@8Ia|ofuM*;IJ1~M<$aLfG-rCZxWJI;rGs)&Cve2=t$B>okcTKk zZB1+XSHUrcAM6ZWch@%_%T*C*{sM;{1q!~E{Zcg~rK}YE>3+-9?E>rjI3cqy9u**h zn@dqY)G5z3EK>fAQS(`2{)&lswSbYmf>Q>jXk<%pj~Zq2hcQ07B&1Z}G{}oEcF~**TS)H=YkX zCXfYd3Q;H=<9vdTRhYgVDhY=g?4iZJe1`nm-!qfYa?L9G#B~=ZX9JZY;L2H&v_5l8JZSbmpYE^pZu#U7-Sg=zRP<2T z6wATIfZivT$y9>VqOh;~x3WTpWPU-uhrz2Da=p>m&C+NaNq=u7KjvoKYr=1VQ)fh~ z2=8XRFs0keaQos{x#pQ1GFCpJ6?0=~?w_GF4ouaov_!pk#Ljeu=)P~k|GgtTq*p$k zA3aRF!$+dvrPyfIwS(JZQl$aXX!+U*>OyZsQ%EF`3~~4fcU+M4$fs;{-rN0Hs_{Y* zkAWK+7?HMt%$sTPGOw=nCtpYoZPg&+Z6`);ZcX8lb8YS*gLCEMdXmr^vu(Zct}+!l z0bXh|Gp!!G_vOU8`oC)b0dUVz-)`pb|nS}F&zOUkCDEw_GcZGLp$&mWkut*WX|H{uD}@BR?A zSGvkNzc_GF@8w^%W3iL=g&J@BDs6v$WHtQ?7$#$YWS`oCwOXFzx7Jc8AOUhCw6Arr zQkv;ZyN8;;k2wB)saf*=7ws-nxC|gZvRot!2#C2V2LvRzb7K)9-gFv^hWA^n;62+n z-AaEIEP7(hjF0u)J38@TxD&7P=x~v~`0itBjvXV`52;BN*0$XZuAVb2tG)~qD$wv(Lb#{4aSPo}n!-!q}0&i^dSIbUle;)vDUqqKi z-oYPZt&k-PHJiyuV%RAoB>BQ|Jg9|pjocPx8~<{JvxS#xZ=PO*2?0Sdf@$t5P*`LI zNLy^Hv@5nLHaAyn>%QI8SC@-4q(%ovia1JxL+WBkl#MBEcRv};Z(^jkm@UC#Uq~() zYHnsMhDpE&SrDwFIEdy_@U1BNxTwB% z;Bp@NPNp$00RzfQxlh6%lz z``9!6fpUT;uX+n(>s%>|pOQI=_-chGxS}Cr*@G`GovSV`_hE=I8aK!C!w0ZbaEO+` zs~MIXVa}-*2O|Z03E&YcJ#pmGZuLX* z#B*^Cqvp$*7e%=sZucol6XN#F@H6_z@tr8COU{!Sj>tQv>`OG;@A!W)+{tEGa+7sd zqG$pPoB!D_mR#pfHS|PnzV}i46*pX+u7!RQ^n2lFq=>C{RN+qneKUP*>?LY}r#8xa z);`%DX;zUz7B1kYN}Ec?WvA4nhpy3f$r=H^x6@FR+E5qXsR}wvA%w0BqD-#Du&8!H z3Fw?eXx_wzT%)2P~61p%EQXI?M6W7)JjTtA0F!iNny#nIf zX+P2mLfnsj$aIcvMObG=ZSR9kLkA*SYJ~UM_k{!J8g^;Z8ymfOzmF*LAlg0z{+QqV ze3WX~o(arSRY-pSIkF!ax>A^*o;z^&`?K8CnDVuU@N}e#rhL1!D1qWW$prh;$>ekn zR+f%!*B>w+RK9jdE!s&HUl2QEwJdy=SgQUL2EmlhKj-n|%pw{)pYYGW8;dUPK-9b) z2SjVn&5vHw*UAt2qpj|wK{$hjGv8f>(+_(Z0WD?TWCazS9Vy_2As3X&&{_*aLVTy_T6DJT0$DvIDsPBeTexd0q6t9 zo!wmVJ$hX2)m;C8G~W@E|AU;%%R|XdY5(~v3K)#SCg$p5ZSRzd9uDh{z`@1I#l@c* z5e`fCKX!FEY$6;7H&3eAcUTf)E_M_)$QLJP7fKL_`+pd{lpOq=pi~$eSO%a=N8fpk z56|yV`>1{uLny^ucWGj3>SIyUYEfIfZNm9p9}M<7Y)SK%`Ikqbgy{HaD#g-9ww3nm z>+H*Q^D?YK8javVOmT6zSQ+f?MC=n!9Ah7G-w;q14pRt`XRvB04LQz%JOoxY%|saa zy=g#RHYKIPn17nQA54yAc7+ zK@p@Qpd{G&uiUNUx-2=WVa04Mw*ofQV|}y70q)BRa1qxL-m~LGaQq6 zA5K;c`Xx?XX7!$lnvkhzjt16s8Ckz zp2TsF=&%2&SPgI)?a8jy@6KC?GGD%W0&dP%UNb%I1vxmaT+!s99RhC*j0F0>_2b}N zmo~9s_=1B?U&On{{G7wVQ&Bd(&gHA!L5!#rrx%9Uk}C(`g>TW4Z{+rjg8I*S^ZJFe zvlmV=Ty~;%9i|XpAYjH9fa!p8=z#vF?wEwW>p@sLu#dLooISj1<>4P@4du^-tiC5# z^I3e*h`nC){yI2-6*|h5zI$nl--pDd^CPe4Qz2uNDJihXu9U(E?tf3WMSv?5MkqXh zXUQJs30{s94eUYHku1;A|8Q5WQYXqjiiAIJfndBn&N=Fe50E%hg`jZ?MWVh-e~CzF zgd(F1^6w>T*o^eh)&=kT6wTYF6%lv$qJ<{E3@_VRdI>a%wG z>h13R@c8)m0Gy#zsG61Kf|+n!w$X-X)-kT=;*}$fM__X($L6v@BGc^VkP6?2PoX|c zMlXLNu-dxP3fyBD3N|Sb(L6hjddj-@of62KWmhHSqx&hP+{i`e6G%U3TqW-;W7e zg0ANi+mBO6KdpV{!Ea(kZ7WYnV#pP=R96KF-WW7W0L`>q{pXO&0T{?ns?HGM&Y*ij zdMPTtAQ*$>q3u4))*2^6?Q}cTL63@DVp$QnnTaOa`>m z?rnYVD6G4V6n$oG2E1d9vSGEivjuNM7EM}HV`zvF68<)>&+MljF zgL1EyZ>g`Ci!y9HEJvm^LBjE!!>q_ceDwJ`@s-xkOtYOPRTDbK(m9SnU+_D~U_|^9 zjP^HKFL-U<(QW*tYLNham-WQ5SgSH=>F5^fJng#h_3)POQYtjxM%P;@3iQjeY#UVt zI;-8bKQbXEeeT{GEc8h*HUD#m(Uk3mNi!O zVY^1NZ*!F?qi45wtPM^850?BsFccfqTc@fMzZ-wE`e;|RO zYo5dZhhf_j7iz#C*GlsDE1YWU_am^^0+CUF0_}-(&9tJ`)Hy(KcjE}=j2>PC0^O;e zu$C-Vz>(4%jMeQ=#_{BOJqa`Y18YWL+Z>bX!hLlxeeSnJW!-=z&W9|t>nqKSDijql z&jovaujYwTkNFWfAdb^0N^k<;cT*YJU+g2S#STvHUZt;!%0%(xSGd*gKj|vwW2{KD z{W;3{TlrSq?!|QtPeS{%^$HVE!nX?RKXy`NEOJce6w>RYO3l!A#50oDnQ+8i*UHnz z-5jW^LbfnC-wus9F$r_ns&D5iqAU8G-Hcj~XajyzSw$<<4jZi#94X}5q8U;Q=@jV4 z%;$B94euoak;+?5IFbsOQT!YuiWE{ya{c#F@Vk}crb_dg>(+boLpU&?NcIKi=fvBd zHP*j>7Ww=PN**WK_0sHdgMMjOGY`Ygwg;|U%@-iM!J9kZBOJgVl+C`8Ic50o?!whB z-e2S;b$})&WZXkZK22oTA8Fuj$XWa-C&Od<11Fu~n2CxLBCk!-uGs!G`w}N$<|4_U zS6|olRbCM9CjBp|D$37dK!j6>YvILoTUIyI+f0_ZGzGI#cY1DvGn(C;Sy?gh(ny8mmR_-O!@yGdHYDg!p_RYnv#o$pYp#e3)*>E=O|UY;j8P;>SHYA?3kqk z{^7JhB!R&s$#ANJba+%$R4x3m{{DVmK25m~g2i%I$Y)7EFilNEm@KFsUvCbyr@b%E z=kI+_*Tch)sSA)kB;Ska%}}StzlZ;n-<+foNK}_Xj4DNB*^l&Ns7O~OU|<11UciKh zG=GV55(rQtEN+hDB52Pesfakbn?30BxrPmg4grBGTzP9 z>TGzGcM;+`qXIs=DO5hu{`2%G@hR*>9gbGtR~-ovig0)NO%~>eOSX-#a5s#8MHI^e z_$y`5+tnY6bwtf#Jv)~aY_=iUb%q?zQ$NU>YJqsS0e=lNPt()|?t>KTNgg0bS4JG(4#fv@`w3juB;>k ziiayag}?S)b24EzhucwHYr8)i*@y6z=RI5B5&Xt62xYdtaxkRzJgMn(ZKaCda_-5T zd)AUI)t|d=QEDmXHO{(_$<5*0&{TaA9aA~h{o#r}m)Ush*wZG~e96#KFVIjY3N+ Ir3^v&F91=L-T(jq delta 111072 zcmZs?V{GF@!7f>_Q_x~gNhV3=JKxjh*e=vX-LQFA%;fa5yZxbF2@otd=8?Zn zlL`{N{YM!D6q=;&v8T`0IyQ%uBlpVfu_5(0PHr&Izd?|fU>UNp+5$Dl>~7HSK1ez#kj- zLQpR2LTB125Hi-`9PBZ*wHX!Lw9QgnQnJzZ9m-t`puS15=%n#dPUMp-pz_C#&>mDe0)W0AJ$;4O`cJqP|mEk$s-=jNVRiERlcoyoBx() zJ@mmjh=)^BvK8yx%k|xjMDGyDKj-19rmNYFa`$e>a&KXva~*3}tni_`kJ-_vE``e# z>@QpWRH3Q6jT#40h@RQXo_1E7H^}CTbZf2MW7oqV291qqPVD}PqI23Q^_{_`o**Ug zE4d`a=Cr2fSni(@3K)Z{!moC|uP&U|5(J7eZ|ZmiB+mT4+s*gz8v}u`u=VyW`SxG% zuKgeG2rn8rx>F4T84`l!3gnD$*khW)0k6E_cb>ije~_b7<0;retYb z_GB0cSP&MDVhjlL|D6B&ZI-qj0tI1ZOc%leMge7JVopx9r38#<%ES|MAoe}d_}Vrt z{yT2xIAHX$CO%F8qk#M#4*G(k;jKHmNN_586{bQ>@1zh{lRbyx{*Rv%CHH>bV(wiq~U>ghOQh2F`Rw?=@bn9g5AL)osgnb?9?cnd1}b&`BQT$xfIQGtDbK3OwLSfehe0wREDsmIV*xQBk);Jh$9u1@(btH!tsPYRFs#Ds zvq!?#c;Z;b7-`)#k@SZUy;eAjRp)zTFY_|BZUA$iszqgpqT~X7knzSfNTE{NduL=E zlepxYy_TX0udd2aR(C1l{j=mF!pE{JxYPoJ5*Z#zJNXo>s_y_^$yk{l!xLumyy*^Y zDQYwEMQCLCMj+B8ZxvQJN*6z=$nv5GY1ztjq!9(=k(!Co!PIL6Z{!W-(I=^}&f*no zT7cJAlt=2g**s)eE}R(MLlL*IHDuBKr~{W0L&!-grPYWTR6EyAtxB(aXm?t$q|Zro zam=RZru(^>=M9G<$7$q%GTpWX{xg{)U3eZQj zu;pLa?K$|D{+1+KppqzX}Z(PsdeG$Nix8@bgAxnc^h-@ zg@XkUhODET^0>y%NKl)0e00d}*fn+A+4lji$ECjYqQU?D$z%n@1#g4zeuoZ-+sFaH zG^&1q&g90&{+oQsap#u*%{*3)<{`I97m)wl_;YwL3O3IFE1fVAGO;qT{ZCe5CS>Dc zNiuF$DP1-J@P0hg@K`P}xtq6-HoB1091?eIjfig8me zbT4EF6c7@s0SiSv6$KDp$K%g-{&wER-tUZIj<>Jo*j%^1RqQpq_&;hIon~_903P)F%RW5&jv=pMQhW0{%y@c-s#| z(t)z@CnNx94%mYd6Xa36{A~c22nxvCBOo!1U2ql!H@)85XHY8 z0i=Q&6G-q3`giISUR;nbamRN@@zsFk;g>p?-yAKY7x{HD=Hvh{uF=U z_tbgY&`|*M;x-ip_2lfy22O%N!5;;4X%e!i@GCqR0qKY01WpJ<6pR#XL{tnIkpbv0 z!PU^O4JhCcNMXzY@r@=Xj|lS^`W1|`a5Ml+B$x1vKsbeC3$TbO87OE)?mfoSPfY>BA8C}IxKP!drC0l`E=fdc;i1p^-Zr7!st^ka1dAhQ|B*#nB~ z{}3Zs+U5KFK>{8n2zLbe(UZZ5OQQ!HxF;ypfsKF)m^T>sb?E(-fA1gv(n$R+U-<1N zQ6unp-Q^rL2>Att^b*_#{b8J2cor(MD*%IVF}Bq%zlRS5i5B8UR({wmGrKOpb#IY9^&dfMNaGjPBFVo(&^>t}2k9I!v*h~Usp z>nDQR5cu6u28Rga`C-l~h@b=t5exu>~C+M z9d<zu<6b(T+C|mz~th9e3kB{A5o+FT1o5C>X5q=g%LL!5EU8U#$LG{H+u| zaU?h&s)8Af{F3-bvm|eWqHnuN68sWfAk!TlhH`lw;&QkYd@JLDiVb-NedZZ^%mE0h z>j{z_-fqxg>Soh|?e+aD^%PAt^QB+?&Viun>y5$EY~P?nQ|0#AWSqpYPCCy0^^R(j zD6+!}|42v5z{ijAUih0^nY{St2>jLola0U`1>%+*Hnos89b9Fm92BEE2E5nDl3-4I zVa_B!p+DPDgv#FBYA07LHJvV1mI+YG>9tcau9b@&PO|Nr*A%UIiF6Jcuq$5sW{nz- z#^Qmt4}w+v_f~fQE!js} zleIGYm`-ifDs+@Mo=$Iauw8{CE!zqHkJUwvLkSHL99t)uz~97V5E8WpJej^D?gN`1wyxK&Cl^x~RxEV2pq3z=6FO8cw*yfSsK6FWd~G0$)Tf^Ui;Ah?Ijww-@^ zSpVvQhlVjhHp27X(hnfU!J_nWD1MCl`)50{ysw9#|2>V?MIRd{ozi8#-Nq6Uqs4Q6 z*^lb?XitFV^Dt#6oV0_bHq1`O*;eA;wt1G(>pht6!|`O<+O=}3MC9_E!t85}GMa7k zjzKQ+D7=>0tOMGYXO8P;NzH4(ewIY1D^ z{4U6;QG#3e=jNZ0EIuT7@sq?<$I;fO&=yn9;NnNHg9#P*y8aRmv#FO?0E0ktjdel? zYm4nmeRZBNE4}Ao47StR<7s3Orjd=oE_mU@K#Y?-aNqb42pfhU4||_?qq9VGWZKc~ zp@gdz>x<1AQ!RiD{VR;&qxjjTflsC1;IM7o!9%#(!-;bRZ1>_|!5D%&6%9}=r+kL# zWl8qR_~d&;&dKu>oN+@j1FU}pZBc1g8U+!4E!-8ioI4vZKBK|&PySe4k7xUJ7lPit z5C+4ZL^9PJ%%+R3FSwr)J_TVv4PKQ=)g+gv)?l0O)eit$&A#KouI`%G?q(gmP)y5K z-GwK&K~~aw_SK4X;nKnN3PtSm`=r~>#%;&`7}Ilsb@->=c`pZPcQe!YW(gsXS?(phXt+X|`iaLW6XPH1|uCW~zyHXvgk^6QPMmb$S7EhlGviS;Y8 zv%B|SiL%25yGM0rZO9^Ozl+hFnfsv+bhuIzH zr|Q@cY&JmLF}|gF#lM|Ii4@-k<#4YD&jsmPp_J@{^KhZMes}L8VaQME!5)6F*~q89 zw-OKlYB}h^)0;$(+ekOTz^yI2P3(rdv&kyIKtc`jc75S5lg86DBR6XhU$skJ%nrnS zK`zZ$D-*e!_WSnUXu9@E-DbC=if}9m9GD({94>D!{p6XVz7PH%nE$j$MPD)hF!h=j zUhL{`g@qw{C-W*0mUmS>MDr=g(_1akTm#@(w(BCJ!%pO_{#i0C`o4{4J~WP)nb>An&iZ8s8!O?yg+JZRW@rmns>^&RtqldNAgr9j{x)t^|cQO+L2 zsjD|&l#BD>@^GrDN3(T3Z|n`4W>B1bN1a#L^D3QZ*IT#|d4^9-=xom{z6(y6Sp(is z5d_-bUbF7d*1@BDW}s?(P82$AcH$jY)$--VJw`m9rMb6jSt%CJ_14I!qV@;@_(45r z2l-FlkC?hMdPemK{v9VW<6kL0xY<_2UTommJGm+1QOkBNHK`e7#OIN>^ejSuX;u`t z89p3Q7sM=#U6l&w9W*zY?UJlg7y#H;rR=6`?%dcM(h#e;IvIKBR9HeBrynkR@`oZb z9w=K@zNGuYp}<;CgqmkCZ+hW4t-?f% z604fo4NGa1d!z5_EaVqoV-|2<$1 zBN7Q2D4RX)9%pJjlH+uj>088D5ff4t%s~buyp)bfevismGMq@P9MI+y4na3b^iJY8 z;#QNa7Um?hA{wPgN3XXsoPg(@B%QKNnmz2>ha#M14*|633mAkCI%sx9Nn+;!wvL0oVA%3e@RDf|{HS80!DD_pml9pG^sV}* z{RDO&eXLbgQsS1a^F&~E;qBF+*8iJOqr#9Slke0{s6MUC0kd5mw9xD2$xs-s&a4u< zVEp_>U3HzUO=7->FU~tLg**&p+4|BII*`+uLp$+y2&ML@0FWBJ(Rh|kP|y8}Snu6P z)HblgJ=~nN9B1jS9bXw*umpW$YD4dH$o8Hdm32?4mu*lVMQ2`sNF?sPbO8Qop zcK#li*c-bW?)rQca6csUEqJJ#usf8S9dsi($43sW{gDU z7A3TvzNrPNGK}Pp2gA?rV5;;Fbb{U3j)P}7JdUQjLgIA!ExD!IT(Zg`kvk8SDReG= z9~V_j0MJqEb%X4qy%EuWb;Dp^`vTg%S-G{D+kNH5hF%sn;{5CDej(!LU;z8>{)~c! z1Iy%GS5CzeAsK7~l$<#@6i)efKx(9t<)o=N4oqYga*eOf{To711w#*JW$_p+d{$T~ zRVT{shtq?wM6~=tPy~ZdW2@QH`s>W)l7Oo?3IJ>Fg z8c;BZvT8BVvV+a@GU+veC67ThNUbF4{_0a_l9Fh7hFa^@r0Xb){A%6z(jeA(;l!7hvHKNO6e< z%J^wsw?cH`iTGMPnZ%mg@fp#T1Sb6DnoIlwAwYb1batw8xYB&E-wWEkcE+!t zZa$F5sa((JPMt6EWE>Yi4)_cB(iy{xD6Ec&oYKr}S{3hIX`Vf|edkBk!Qd>`?=+cM zNXiGEZjCgh*+9tk6~>d`C{)^Owb5OP|6xyUzE|dCTkfrIj6}F~uM2+Bc7_8rhKUf+ z@=wW;zwrQMEVx}iUfHbj2mYTY@mn* ziRa0j1nqIInDg^To>-!gWF@TvAK9q186sOA7Zn_--p7R-R&(i*wt}u`FVph1aP5E> zWtS>7W^MbYZVg>50Rj%4@Tf>x9?!AxyzWvNCD}VkYu=ek$qk8q2DV{C52E7-Pv|G! z&L*0dJiR-|FjDws>E{~cDf7~QI{3RZD??u!jbSJpE=F)Y8XeOicqfp}@YC5?kI0fu zvDjD5uiM7TspWCh<2-6=P8zkl+_cnGP^z_Ud-OE1@lU^20JykJ`n%gyTGFuTm{HR$ z;@1*t1Us%B4Ik1u4J4KK=yI5-RFhc~a1hMv#DJ{ zaEXC*kJ~w-n0G6@YVO>Y%GV}0U?4-yN~OG)D{t-qV;N-`1TEOOODmkKmS-sRWx)#foNL9$LM(R4uP+ZKB3`x%=%@MU|=-_3NtIIlq?GWHT4C)A;_)W zU!b*J0hXL8Q!KSJ{tX5f#Mdl=dLwoHn3mWCDeU$Q${M-`>D~Fn4E&n{`Im7Un$MFD zPdfj7?iFX__sdd z17TL%~2YNON))^b1k#Q?~H$38lfxo7(!d(vWGr zgLyO~Q%yjCOgVNAE@5z9wg*R3v%oD(g(taZT}GYAbUa0p!6&EaoAgx z1YpoOuz=ms?UbxfR84O}WbEN8lnsZwQwNfyT}zTAK83Y@kih%TOQ?ep^q|o}b~p+k zmxe;3WZk>Dpdr+l=;HuW-N2^wkHa1SZfW*C{0x&ivks*W(oc2w7NB19V&vbyh-f{+$vxnuL-O8hOwEu6k}U!w zJ>MPf0PA5iPTSW1r!=n}l@L>SgQ@qo=fm$7WOu65LR(`J{^Z=}N231I8SK2!y+^Q= zq;zN7UoBO1w{WlVL`d;$xa2#%Xt?aiWV0M>DO=8X(0pv-`SNt!7=N_7re0>$u<0w*hZy4e zu>;e?DoalZ4Ve0ihxP%5C>q?<5%7=!OJ_|RG32-Byzh~5yHc|aw5sZdU-yzEBD*IUN}*894S!5QS%&-*god=goqDnNGUIZFPZ zSzJ7DrZaJkjAF|8?^fLGcyXHih`Ew;f$QO;Z)8U|17xbpwZkcGZSFGW+;Ugj0 z>IaGRJ;^J8-`6vvihlZ{lR7W8dRUe8$oIJxKBSSvj~Z1ba3tjF4Y`=_p#*iFzPbcYm{3^c3gL7S2EL;pi(7+VA_B zdN>P@iENfd53YYSsZ($Sb095Tka+egY_-C_5Bh>!YUSR*V~3Kh*80GcAYtXy@BYWB zJ!Rs-h8T(SdtpwUamphFSa~GSL|kd>GLc0o7r%Uq;u=W%0Q6o%7#pm}!CBPeV=2K- zerm3r*9N>xO_lPk70&~Wpmws6!2t>M=k3-^#}MZm_>tG4_smXR1jeH$Bx?4~-SY?a zd#G^4*YVO)x43WNtm{WsTCwh}YcS^FEH-_2Q7p)jSvZnfG>R?kqo}+q9sfN@+xQ=9;YUpQ_NXT2hpD)+?>ECLr&(|W<}$e z9)EuC*MEU{+B8LA%4>H+DuQmjAJDY+V1_ zzPW;{s$Orf7eWO`uu?V(DLbDfnV;E@14CfqnH!p)rTGe#po$42Dq>0_mZTzpgPn_O zO9?3-;2iRu_MHB%e)O@~T(8f%jk=7w+0na;pa_{+q>#V`2^)hC3KKU4ROK;gf*~Ry zp&%n6fjc>64mCop5n%o`Ll809qb#`s05~g(j1+0{Rf3K0{k!Qz$}Xs7~vvh(2n=R!@9eS?pMFQVeYu^feo>+r~(c4 z1Dbf?;5~wff%zy`;7{WE=b@v3WEJHdF;{L0s63Ci8#MoD85t1}5D-=Hh(m<}+|~9_ zfPD8fIR-Gp0t&vzu%ml^*E?B-Y*O9*6{Y_m}O^`lQGj z9Q5l`kX7Zk)1XKJz@(0mmXL^;n3#+NVt^MoqdqzNZuY6nAHTss{7wOYxhtd?0678b zILHAE8`M2;2Pgo7Tf%`boY!wC2>50FdISRr2Da!xL3a%497-$zSd0!crteyOJ6mp1k3B0xI=2YaADnKA^S7IbiX-yGw1 zqNJiZcYp4FGcWpue*kd5na2QK1Dyeg4^x%&dgwz`!KLgwW9-qnQZz@(A#fP1o<#oKGz>kjN;4 z3i0#U3<7na@o2!_(~@&@Ab^L-O9sd^^gRB0ly)mYnRqY%D@sNROo=zfU#W$`-q&5xB7LjWv z$$GeSM`tz{QYk$iP?;5cZ0P>m8gkpx*~HgdQjf`B&INd~TDr3AxQfYwLTMw4R* z#u+85)&WfR`uy7s!e}M{M&e!Nu|!vyfUUN=p2vl7HG6(>VqJ4?>}E_`Zl|YSg#SF5 zruV>SQ5f^}_CtVE((J4aU15d%s(8w|@!uu#M11bJY3Tm=7IsM(kr{CpGuI%vlXK&^ zT&t8?cTF3`a9YzZB8SaDzg7!`zLi*@z$i?700zAFRpJ_e&Yng_Y^C+BNv{p}P$lBM zT?;8nEw}w_b`n)7h5Tu?d-Lij`RP3D9^KsZlC?L!K)_P!;X1#V1{_b3-eHcb4OE2< zISp;PkUa@ohx*%gjXxrr>~eEGjckCE|sCWyAPwU(N70zZcLReu>IEgYK zpoi&<<2u-8RCzXcYfva^XY6q6pV@gk9gqYpDjyz<6Rg^-z7rGRaoY2grR`2UQL9G& z)c0N}&PRy{i|7YUVri5UIGWKaAn!IfTmkCXf8E{Xj=Lhy_aAY7T)=9J^Sv?F1mI{L zAqb^y^`qLCft-T(R}6$mZ@rt3VObrn0E zDwSkI)C(Q-P{wGE#xv%pPs{lTq{h2gZu2W$r_vN%s!>f;m_)iM2((-$%f_P;Tmb5F zO#iNEw0<8VkBTkwec7C25^}{>^Zzl^4NZ24k(8I1keH|f7c zw(^Q!vPz|nOEDDk&j@d;CMJ5$W{NG$@J8?nDX`^2`?I{I)&GEIH^E#OeQ1YPwc!W0 zp@|FZVH1EVRbtG?f@8#1Part z(DXz33mVqOGSm^>29VxeKp0 zUZHx(nWmLmN+^6v-e#ssIw=Hs1RT*G4kKj`s|P@RPc?s1g<~$(f*yotmgU#DhLpKt z_Pal_!7^I*tU?F;tJqPW9|Kr}H8#D;J?KX+??+mru_0oy0(7Y>&Bn$f-|mk)I>Z@6 zjb^$co$R1iHt{^xykb+N$}LiKQYN1ZO)>#bf$o1)vH~!uHS0B7V&?(>Xt?Njyd@t_ z7C*8XC^vK{qabF?cAn9usN0S&cuPDEOup{!_nN2ME?I1$+l}{!f&uY%y8uEd*;QX` zl{6gA=G!k3)7YiRO;6YwDijh$ni=6rJ{L@r#% zx+j9dbsO8oG#M=kCB+PBg*%861a%H{$fU}w=8{bXdRx>x!k$?CpcNrcC>_6*XKs4e z2)=xU<)Tayx?8k!(P?U_~;`1gx75^;05rk5jw`18a z{&~GM*>op2*4kRK@dm2PSwRE9jUXL!4~d? z{K}m2KEE>HyDYu#&;v8?jnuh{DW{j2JG^y$f{IOo&G`465Soe^IbWZZJsEq<`t%P@ zzp#Lw4Uu^)D;SnlQU)WoA*{Y#T&#<~+swsAJ`$AKqXv|Vb=v9cp7gxdYYh~PVW_o* z%Vp?Z1t9gs>N8Dk&*}CSJbk)IQqh5wv9G4Us7T6kYn5m4*hE1f`EPA|+cVC|KOwH? zAb&~LyOPv{Ou;=wi(@i>`~`TK9YGF1`xh7ErndftU0y*%I!r|d!~b7y5$}ojHw!Y+ zxddjdTpAEl#YW;Pk&ZUY)ijG|LCw_L4i7b%Dc}U*QDx2KyQqtHA!GJz~FXOd#^!~=Iq%&<3 z0Jth6Taxi9S64Z!$jo0?ST3_x#q-_yL7teb^2Jh;V`+eP&q#Vf-grLP)x|vJ+)+!| zM2EV+t;5{|DZH38Z}yAq7R@ufQHphCQql<^>LcI?S0|VSsk69|x>xHv@%K?fQ3cJ! zZR7X~#vGXnlvjU+QHH_RfSa+e(wt@29g|Y0{RFbc&7m zRlp+s98Knk6rt;|qVX>#;$1>8$DMY{;6gCu&G+24TJ}O0w&kMx@9%|oJE+Q|FMiMc zJ5!o;8-+=jQt_n6<9T zHya&8!&*}knDpfkcrcoy*?E59EkP2ossQ@>eB1#(iWEIo8Oo3R3Sy}s`*tLy{L;1e zT(lZD2VU0V$!@^;syMHk$+qqMrYFbFWen=PBFS@U9A&k;p0x8sBF$Dq07;)C5@Wk< zTyJOP9aS>L5$TukpYnnvYQHofJjvy&qqgmB*U?P$qgBHXc*yN0U7ZCf%RDUvBRih~ zDY(|xue6&h)$IqD`;^-~iX0+VOONA6xhay3w76}&qid~$Y^&#Xm_IuvFKtTaEpgJo zQvM`IC0A8dwobrs@+HFP0HXHY8iz*uXhy>EQ(Qh`J*F^)94>H3+n33Yu!T;yW4;}| zg1SP{IbDPrc=`GieLnOHdl|ps+lAHhTa7)unV0oG;gS9)zo+Jk+oGr)5%>~PQ3DU0 z7x7{pI_SdAs|DF%ubYCUaZ7QHe5V%~!Ud5^GN{bdr2I&`yY?{)fT$Ij1XRkzSo#4f zbK8=vgL`7}@`dKuuupoqMLY-WvPIzv)2l85yx)ij8%gsyNWXp)XJtzEk|ADUueI1P zQQ3o@vG1$t`(1Mx{HS3f+c*(tD}&vzl<==2#AzWRb*WyxbC*si68TPy-{Hh(?_Bzf zi9-Z<*{=Eu3*Y`2I|zI|GAByL0# zJj%2E7h+#B2G=To-Y`Dv;hm$4 zTf*|?=8!fB-$d{ZI08UCHM84Ph*AI^iZADo6 zer3-TxVi?Qq?itpiT$d1U-S*vo9lN}LSyHw=7{bm5v1D#dRhGw3xbz=mT4!YxtV=J z)z(ykoiH@4_LqkwzNErNY*qx~J*#NP6kqN57HV`-kJ;#;(^jLKqC29uK+j*|oTk=c z{?gG+A1U?~;Oyt-nk=3t`Ui%GV2ACva(kwWI-M;4%nOgJ?F=nU?5rwCg?1Ata>piK zC{L=`E-(LK7!~92<9o1*{7Y`CGi-0gP+gNFG18KuQ!~-MYUl4~gap)%L$F#-NsU{B zeKDDl#~(jvJSyR66-`@0gUh2eI97F*R?{2zYs1VAfJTqjT=z>`>dGxRX^Z&)&}X=6 zwZx?Xblh4vRI6loO&SbDKGV5lE%$MC`f^S4k7R!-^G>mu58qM(%h&RwNwbX!Ysm_J}90! zDOG|6pe;^nG;{=g)TC&~yXYDF}=kIu}xW?0U z2GVT(V?xJfjh>S>^8AUDbQGvNW^_`MQdwlUW5J zz%I)pw@s1g_6iOdiq2sY|{G1w4W`)Hv5RKH5@C% z&nPgXpYQRCqELhKMLX99Who){{i}9bfR~0@@39SDBWOMBRTBl6My&rg2=8zUGSyR{ zPSJ1iJ&VJ*9aDyG^#m1X%c?c`&p9~c2r+`@9&B-zv`VBAJ;AWT?FuGrZRu?;!22=8 zy$e?9@hOY8rDFLthU80r4YO4FEZ?AQ14qeEZ{g;rbmB%XGb}x%SNx-NxXS4+njl4U z|5N11!sVXtakGHyzJFqnYz*_0z#2vfpY&^zo>K#hLq6>=$X!^cl&+T~oT*!(6`T9h z8Ci_fi$B-q83Vm_E>C9y+?aj>@M>OLv8O*$NVgbW%M%N#bD3XJJEzg#P;q@dN&Z)X zvss^ch9VC_Ii*oGeHF|p5~RiV(M?fT-y?VPO9Jb%FkSz&gq$XZnR{FoN!6~5J5*6- zMvP$fCWQlHf8|lM&uNv9XV~SN-txXIk7KKoy6_XZeECQf4fX8b#^1~%Ks~#H$x9>I zeEAM_UjKc|Tbu3fiuC4a&kNjLcP_Q)7-!A7H$`FaY9aD`>j3P?rL8N83R88e0?!pW zX}trC#XJ0$V}SjsV*goDL@WJebnnI8xm~=sx_$I)>q+#b;>u;Z%UAk7PuCn2#6K;(2QjMfT zgV%qW@s1wHKZH9APKrRd)UX}exXSqs^8J_p_E0Z-1eQG3)^onxSTgO8md?IULHs1r zC4a`l+F6jaC=r_8?$gap;eSB8>kRaK3ZwrZ_fiwBgIYb*vZjst0~Xmj4*ZJ_v*AVc z>OM~oqSA`m=pqlmvlM*t%j0i&TWxM$mqH7vne#I2t{@Ef#}wpm(v>w&FUL0J7DdU; zk(SX?C}o^{p%tT<(=gCS@-A9E`~`++d!fFaG{h$#e41qJjs5}Mf4z?`5`3{9GSDus z8kFf@BY%8k_Ez?%0uIYwN+Oq1%b;min3YeKqjfyUsWdwTVrlBF4Ne%eG?l z9N}WUVVI$h^QYUVgZV}-I49N{!-4Ua7qnEt5c*X`Cf%6avfU}&>f?Ht3Xyq7b`C#PgiN;-u zUlxBTcr(R~0eW%HeH_;K4UyMPnNMQ}H=N3Lvd+tft;zJzG(EFSoV!zoLfNw+t&Hy* zeN|*uihJ3+-YdFhI8kG~#A$-Pz1F=+i+>WksS9TH21Gy^Vp^$IIjmPU=5a5+cV<^g zEUCK-Ss~VqHRlB=`b~}3dFhnt4W=}1*)5oakyj{h0LrjR)$TGGsMtPs(tj;1oSg&{ z*pSarT&V@|U3B`zbL$LJ?|jyQJJGy)?!`1y0h4n-ZJNUrICI%dSO3;Cmo1>f!5}0X z{JI=md^sDn)D3at&79RNTtmW;OV`KLr0AS++FBw~EB!)I*6m$B2}HMHh8axlts}wa z|ERA!0>EPC6YV22<=#AeFJH7nOgj)?V@}0xux8MEPE{0Q63co#jMMU+u7)+buBA~v z17}<$-DlosV!t+;sJbxQW%6>5-m%~@Q9})Dm6;{OHASe60*guKDg?4Du{?Ufws!7E z!Nhl9C+rsS>R1aSr_EMx0qjH=cHJW>tj6CPo!+#^qCCUq7i@es z(2oeciyvSnXX8j_gyWD`n>>4gajwT`Pg=BkR*Qn?SSs;t9?<~^I)p^)@@7Y)5+^K? zkyr&36zAedsVgch59ZTpO;Z>*a%$tRr^_PgYSfkW6IN?OPul@YTapVBegWz2EIB+q!p8NQUTL2umJ+^FHhI`)Sz73Nn6pO@O>~mo+8!&MEJ-pyP;Y_TDmK3!@b{NVe_-5QPY|4t zkvmS#Bs+(bDQeQ{8Mo1OS!#jq*!a79;@nKJqwE?NZ3j9vhG#6`-R2=kf9Z0sKO8kx zd7157bP7aH7?;-xK+lOmaR;)7fS-(6Ci{ksMZ(U{)zLo~GM$U%6zUtShN_SHwCbs7 z>CeH>I=!ZQTgxD=Vy_wQ@g>>C4I;{gq2?U`3iqwvoDz&SJ!B96HDE063w0A<>on z>zND=xfGMjucHbu^=+B$m%7-04wEa98G~O4pY+_H`i~B{YZ@7Ks`z9$1o#Y+CIl@| z9R~Q+C3EA_8>rdj$~Vdg@NfjL&1g3fM+Yu*6@|JV{+8bYb%2oU|A(q${-2>7?*F&r z|F5MSBg_Bc>X;bQ?@EBtz&IG$+5fky^Mqv8z20ae)OMZUMC?TfI_nj?rJKmWf-@1H zI_njUJ`=@2&Lxy~jl>p>&qJisb`=79C--{HbJ=Fqb`;Qbnvd(CM0Anp3fWA8v@fTR< zFMt5x&*lI`ghc+8?oafuL@>nfU=SFLbaMwGd|?PDfFleJ1?a2m2%&w@0ss&K@_!2m zf}@a_c#sze1_wD{0KZ!Y0o0WY0U*qTf96AhJz(x=ln@FA|23oVuQZr#RzpBkkZx{J z1R6#3t3Oqk2NaCicVFQ@hwF+!dL#V*UOB=L5XWC*Ks?=rO%bq%o=`2-KNyUO=-)Oc zC>kIRl#-AT7Xd&Y0-!!%XW?H3On-dcp}(EK&6pVi{oRr707uLi&_I|Y6!S&oj{_(5(kxbGhXhPj?-j0$v-7%d?F8)^>yOS-yH z2+Y&%zr9*$5JnA32qz4q1%E~E3IXr_Wrv~EVLniZ0Spax{);t#*-d}x4Gu#<4Uj0< zuO|#93JCl!A4X(gSIkocg`wte7ZjtRf7Vq)fRT`2ViOgY0DwF^K)ytnv&O8%0sbNw zRYIUXzsU>`7D6D=m=FMF#z250(u3&N!HNNdK`6}3FqA9i9GrhSe}CJ70AV*6!V~q| z@Q;dMPY(}_{C-md)6U=P-&%)4eV|~XxoIR=Cc@=aMB90d5~H`^`Y_(oaz{*}WpA`N znrr5nzq1a0md3SH)z4H;D2XAvi7t=NK(O7D|tI7w01q0uY z-#S5AAV>zMQOTz8X=)?!QK1aVd+Rs+6TAvVYSTxkYj<;@C?r{+KN6 zYfb7G^K5X^QwhDLAN0P_vkoafEtl7|c*JD4mTmG~n1rq=ImTI_<|&6VXEg-tbTDJT zS`41wjZ4D==83nHX7t z3B`J?{JHyNR&Ioy5ycWy^`s1Ig*deC2D?U^}YPpa=Pm zPkzLI+c;_1&$m#ji?)Ktq;^gOui8C-&)ja+7tfUOX6$QsJ9pZKk7mQgDeeK4!=Q$A zKYK(GynmuGLA*ufQy+DVsdXPnr|qPPz@zKEW8=wpViD^znY(MD?zWo^di(A_${#AL z0w~G2XCFz4tybxVa7p>&5=WZ_tCD=XM@a%2YX}paMhIa!J2n!n!4#;H$WvQhe74K#?Cro0W{NPGm&49D2|D<^ktV4lqIww!ub~Uu??V zBG<@2z)B*t%k>8);@Pxr#l4z*^<#tXn-Rse9eUDSCbRSXVMf2FBF~+2G~fFYs>xfX z&vN_&R=<5S3O3#rMXvEZT9S-J4!UDrvJtxH*QZ z&P4R2lZti%dHpm)Ib`jwlr&Eq9N`;ETIU9~*yVMZ-g8-0#SpClO+Qy2@R?Y+&wr0Z zme_&Nuf~I>23mEF{@NpD!zhMF#CyY*)olg4!e71KCX8AaH2;`oY0}};FHqdc)C`YI zp_E-T;Euold}txqD``rgkE5R5*|bDg;iPUyVL8Q}Z#qKKi*$xoZoxnV6}YNFmZJDV zFIn97KrAiBWWDa5V@o7}!Pl@jDu29LpEshOq!K7O`DKEW^bui%2JwrFWFx=lRL94T zTmDgFwiK$)A5Uc03jH%PSCrF+wxdfw@ee-Zp>aFldzd~>1m5)97Cieev~PpEJv|W=!ICwG+8C6%1o#oZDW5lepW_h zBaAmJ7#!#yJ>EB3;3*l-`L&A zw%*rCB^m>4aSV3Z4BgKN-zGAiHG4>$wY`-os=mj7c9DMc7n+%69P6P*Gs#3=4pMD)MIAtW6)5crsLEWU$Hc<#n_4 z&-M?z1MTr@cV;(>Al#MR>z#~(&5gwGM6rY!djXt>@qtluos4m_A8Co*h8|U0T{83( z>X6Pj9&g4s{D*n`GYeo#-?ZN0)}s9E z8$?ugy6@wz>;)C;@PU+OcvpXeyg2R-`; z=TZ}z6**_1QorS;x3|HrArVMi{FP)6KR?f=L8L&5Ht|hdDu2L64bNJ$+0@}utVU@i zTry1CklJF1{vNPeQvJ%-s6FJYA-LSn}RUWspAUIB9?OO-t4d zDZiVo>n71Ei^0M@=%ALQ-i*kbB}itz-KSDM$QG>0n=Y{*1oeJ|?hY3XS0Rt?CG={0 z8#;Y@;-14NVoOCDCNv!zojcOCQ%kI4787*x?tkayxf{uCIB0~#hV%AUA@*YX#MUyq zmxixlOu-Cm?r%pr@lnax;=V!_;R!fQ6T>fg55F)KniT9}6`w*xwDSvHD=OZ{ zx_k<*C?sG+0R3poHC{3=vp$S@ov;HcGdJAg^oy9JyZ@?r*5U<2VV4+M%NN+w@mvUZ z@_$ZDuXW0u7tGP)y)BN`>=PGk&#@ z{?@S}-`|!c%{RQL!|aGX{Dit&DwzwE>>|U@>`&baj3VS6n^#J9>aNk|+YYtR?!sO$ zYvlHuvpRmS#5~VSh}b(Fy;V15(w0imoqw6Qpfj>WdVgpCXv&W1w>p(s%ua$h4y4oyTWAtpIC;%!pbN#(S9&*4@oj&fHwf z{;E`3LAl)i@YU$S5E<*zo5k_F4S)EtEKx5K$M!^C8aUE@AgnwVm^SXsmpEB%yUFy- z<3)*e(xr&c}qaEtQnW^BK z+N`87Il8L1j%>6ySowz9%Z2cSH@xwBVvO#!@F>pBJ5vOC!B6o}P8EjDIui)=>W3o-5~11(Q~VG|CnP`Et8`MagEGZiPy@v)OfE zml(Fqe_P`&*2~tY-(S9&Ay10kTRQy4#ipJTaV%ybf4{&_VNP{7L{9Jg(T#Qo1PSvK z|A({=mOS$8bNBc*A9oB4yO#Qjog-Ib&#^uNLXKlJSG!0ORJ~W4&wp)Rgb=qgCQ|P} zp82aKQx6t(KlTotqhHRX5aOUVTi$SHK`e^V)!L92G?P^lv>#R_(sF=GbWRihaKwU_i*j5r<5p?I}tln zh9B^M7P@K2`*Zop$bU|C=HZ399j#i!B;SwH)bHdxKjh}4xq4_3VsZm1#7RF?`N(!SPD&HpAzznH+^}h@u#nmw((wtehd8bbE?v3X79Z zH&BzQn;~x>6f-()SA+X(Mdd+yi#soF z74IqDb&eft7DXX%?G#V*MRrlcEnVFfqK3K%l81d>T#eO(XDUnUVtQDOI##GUZxaJg z|0EhzTgzz8xqm_4V}8NhsGdZGVGBPIbA~u&(|-n2>SLA&kf5EX(06B@t82}i;WLfOgm)VRyg8}@fGzshPN)AzaCu9iP> z*asRB;*o{n&j&v!4WU@k6Lobg1RWzi?@Nm129s~sA9*crcb)`mFPQu1=uR$*Da<51 zDbqc&`F}2LPA_wt!izQW5qZW8tR~e(-CA#(vI$BRPv}TfO9vV z_ZFvJ9^ZIyayFYkz@!t3y%SzwkisR2Mw4NmdVgy8$!I&>oj)Fb!Xoq9lb3y~PUhmH zaawwpSNqVxr;jO~S>g*DxLN!474Ls}<{*T&*lMz6A_QA=Dak-t)L)6yd zZnzKfzRmJXIoo^hO9}l?LV=I-LeM)y!QvDLg=Q;5Wp(_O6h*HqtKM8POUBljqQbIX zPJfs6`EINa_N3sOwqkL`lUf$Df zl7ebHU9a^e9v514N%-m#faGwr5OKJhZ8KuiYl!{cobHkSY!XAX8>vv-^Z2R*LL=)A z+OZ6zo~+BAF9g@zVH-VdB2`qgq;F&bS%1k69zD`;c zPfF-&x}AYL5J1(!OpXf}`^LpYrfYN>BXD|De#XA|*^O@H-A zzIz7@(H<8AGO3lLD)#KRPAST< zxp5=Ca|V0yCo;;mh6(y*DPrF{`IK*o)rET^T5&jDFKP9WZvV`;)5n8e+kYTp&ER;m zWFHnNC`D~3+*7o!TL%rvQ<#0*Kd?Pf({O`@{HyaCj!kT_!$BwE)mH0vg@4_)sOoR@C7o56DT49S@B~K=Gd={H|K-qUKWaj_HAAuL0y^=RJ)lV(6&Gik~e7F6EKM-2v<+^9CtPrG`FHmAjKKEPsjbb=4?=|bnT zEaNIVCxypJO*B3k-h`h!ikTm&H!Wu0Xq2(XCF>>j`oVe5I$v#K zy$hbkv)K=WV#l&;JbyK1aCx#+ffwN$dw}-xnUeN|7$(tpTKU@Deq{n-Pbq)yz`yZU zKhkCvUhVUlTf+NjRl?$x3VElhHj6$!{o5$VY#t{?ZyU#Av&^9`>+Rs6oj4Ko?^`Uk zWJ+RQm4y8(`q^F+)l7||H@t|6{4Ul_niemHfODU2JKQI;D_%;k43&1vJ%88M5XQbK<{=zY{bUp>KTpNHom|r)J$}O zLQa*95JZ1q#m0loTG60J~nfi z#0G>Cs@LP&cxBR32N;)1{5jmHAZNld!SI=V(`^aBQt5Q#nMe7N7vz(k54vZK$5}vi zF*o~mmtASsrWet$?;#V_a)v$s)||Nl5*H#9Qh)K1sgWxW>s^IXu2#3bD@E=33BuRg zC!2mRythrfv*$_iq~M2fI2BHfZ|-%*1@XBtb;ujP|Us)SA?bIld8Lt|)UEF>DmUe%OXWL#mfx4h9RQ&Vv2=?*Zl;YX~t1mK# zRzgil#IP}yvV*X^yirtF#k*4)(Z-gMbKiGMDzDLI=GE(S~KA4@qc zQl%9yl5A~`#Z^J<^bqT2K=Uvl@*Ry^a1Y)Rs?67rdXL=irDDZrO3AzJ8)H!& z=n-n2wZk7p&U))khtI_mXrIwe~2G?WTPM0PX!3HY-2hw=9Sqf!tWOHc2ufU^Y%U}k9p0*EOp zY0D@`0cfNY)B#c;Fvt;T15k1?wy`t;$XS|zz)m1qfSH{mz~(;+z{C!0YWc66oS6Qd z0N54e==@J&W{!5Y0C@?2H4#Zg1vP+#7_*uf00=e($VvYb4t93p{l^<*V(I*^>KFjd z|CMZj|CNmYEB)8%=>8vx35k^zU}|aN3@`?nTY{08|HYdO*vt;V^&i;O#r}Ux|0Lw} zPksQJe>kKCn1amy@piGXQ2^S405oEDw)QU0AV+|_ohir>4EPs+_im1s|3YM(f&Ucw zKM_D%OB;{>-GlMvHi~+pnv%JXNOJgz&0NLciDf+`uC#D64J^V+FJDgZHRxHCBPT{=&~^Vt6fi_ibc*2Klp5d?PrH~;^X@;~~&`w9ed2bmzPF4>vz1zV*x zg_inC{GKU;rJtEHQm0>HgOwtp+O5O>kuXI;)a( zC>FqwVvRN`Y3qeW--=(EzXwav>QiH8=zJi9_UJ3oXDmYUuZ)GBc2}Xoa)Wk|uPN~j zE%HkP><_|!bnm%V?q~nPQezn9^hS2Ii6gIfHU&G?Orb=)gKXc+M-E2d`_|h9Va_racheUo$YLydM zw=x2;0WsxkQ&?V9TsuY^z*8OWVN;*qDHIXT16}lgkzMa`_JaB~1P_6rw3iS!6im3z!k5X< z_T;t;;6bxp1v6}sb)wN&$G8fh&VOh76iLN6TkPW=J8W0RE=M9Ss?20h>%%e3aiP;J zT2niJIag0G-@{YgqDcH1y|g%gnPP}|s)Sb+C42*0o!I|;pp385nVmdU!z z@1*A@RXGx@QbPPfomutmEDc||j>K#n7-d1^<+#S+eHF%GrBVUoR(8R-f6oUhSea_z4V;BZ6ErO{H*g2%ByKqiJvk7ep^)hE_Kmw^UBiJ=h`>m- zVjP;q!Wq9DFNf05hoiZZ)ik(@2XtfNIhlN~FYtY!A9Q98BynBEZX`H!)YSN$?NH{g zNn;6ek#A6^{ z$sI|)ePidK6JA{)-#DKCMbfbVE3 zo$my#LFmb!?v;Y<{$0V*}qo`^cch@L05A#t(>3$V5%k7@B?F!K*PQ z@AU-HC)oE?O)_32PJCuw-N3}N5laEbsS-ZuJvYlsrbbIE9(VaZRnNYEx=iYJ3l`Kb z7%2*Hp+%}~Pb(CEdNin$6*cZ`H_GAu>RqeA*-SwdQ8(K(oaM{6TPEj-=hr-bQhC3$@CB7~GRF~dq{QOCKBTLhLf>fbtXSkoAT!e@PtTTX8l>DpP`P9HEimdy=ug%%ZDrMh7GgaR2*J5jMd(s`T1^ise z4XS4^Ug2)>>|{rI^`ug!J(fz__V3QAPs6Nn?&Sg&`=p@Y+dI>Lg3EnO97Q@A$PB7~ zIg!oR3B2X@dcPUz2G%Xe4p#1O&i-_CRPIYc_PY&OfKOSgTwGqL|NSc8TVWY)LIq}i zeFqktK3mNG#VX1+u1D*Y4A1@69w%IV(CrJ(c>%RFD2P)g{wzkWg}F}DP`Xpdo`9fn zMsG{QB*yzPj^wR>D268a!J3tcY~!&E+1|}!i@B9xneQyv?5onFVj1ZNrf}%n!VQK& zU)q^+HxczeiyEzXg=ZuUc4)+6?_O(dU}+AFNz2rx?Xcl^8G!eFB?hYhg5<}gfAZZC zz3=dLXc0kD_3cbGntp9Qz_l&MAuz*nklvGai{sJFnNBi){K;nUBb7*imk*NVf@$fL zsCa#AHm5Kfridd17FQ|!QA#|!W9dpG%L0Nss~dB;$r`4?7(IQvu#S@4{Cf4#VeZA` zsW;Z*sG|#K2SVBw5n*n%P`Iu?BJSuAHwFwfF!S8rDfeC1kP)usG9*UqM&4cISBl|} zGYb8`al}7=vX$T$0;@FAbVTn4DDUPQ8UH{s_H0|F)XeS`qbZlUOPb(o&6gB1D{}|GB&ox{# z=zwiI{@a-xJRjm_&lv)hFc7$Vf;D{F@ca{vxLc5a%Es3dYGX;et{aDSh+?%=HI_sa zgZuJM#mzz{wk3v4(;(!}LF5%}eVZ7eaP^KL*68GHCjH-c8$=&}+-#Nq}n+0nk#WO42%cmW4$RZEnen=+G~KUnw1kjQ&Q-)w;(Cq?jc)H%@fIo zi5A`S{dxRG!;yZDkflJeKmHN4Q7XrG(@4F42`e2T&MxMPbPC;;i)=#!tvlqu7EAgD zM<{l9F%}a2-FIv6H7>pi6)9Gah=x!MA|B5hI{hNYtPSStwV{$SC7V(k=Psti(<8p1 zIBeR5&}q8kVmE(VQ|PvSp@EO+zf4nL8Z%oZt8Wv!sJ_Vs^ZxEh4s>rV-AeDm_H)AT>+9M-PMjXZA(pZek^e>8 ziStu^^Z(H{_(Gi|w+vf@2gYn|cd358s>go(#_BvV z(odOT(tt$lG{7d=>u+!u3zqT9376St(cB~N7lZC0bVTW@0DpDy-RS3+o{o+5hB<=Qn{H6I}!{;b0X4E1vZqj5)K%xDbb9qBt zWQxP+dbKoCo8D@%;)wY*4b9PiY7{eeMfa4FO6Wau?edLoWPTS;W65jrS;zDTL;3Dj z!LB)z(5e5QgVYGHHfQDp7wzch+4!ihVMu4@u1?khvHw?{kxY^GX+U^lA7y)XK2$a( zCMo~kWGbJPo6UQUm56w#YfK@DD*|;fC1ZBWC#7{b8l>iM36s%Njs8o2Fsehyw_4z6 zM3GS3YIS)^8 z_m#KlrAC{;(XU;(DPldo97D}Aw^7FnXNA-f51c3?MFW1_s}#yBX%Q7_7e*hCvTqSD z!YECeLCl=^@D<%Hc}HGQcRaCE?mSpHDPMl&5g3KTmL;pcw zRt3A$2^RFU3s?&O^+O)ewXkHt!v8m6t2mEOF$Ma+U}=c5qCg?+#W(6WVTB=Hn1iBC%ReMQ2J8y?Uk+6sW`FyFS48X^W_tpB8&_r@xy_UXBt+ z!|qTT=Y`&Xv%eJ#QfI*|>PdxbRKJ$eBNmwde8{{x9^5tGsEiaHWKrdKsW8=S9Ax}c zbw@d0GiL0M{-XZGo;VfkqXg91T?-IHOH2K2??>K&5H>o8M`=1f)bj<4z$JpCnCi4? zUiZt8PPn!BOjD3mS&y$uWA4{e_syUc=E4)ASH4q!o&1&8KW6FKTV0~EZ;U-k@{%-shmpH|(!$yQgMSiXbI>wsH)geaK`>vpTHrp>v*YT2eMY z{WsPRdUCW3+H!Wu-Ds{Gn=qcBfbvHnq637!<~<23pP6tEy(kZ2XojL4$`DBMWeLa3 z6m9*vne;u>{&FNA(T{Ig>GFje^(VwEdsY(6Gp|fMS9x52 z=*&*E#(hD%8q(kFE=Zc8PH`1(jlgyrSCxyOSU*h$2w#i5)O@q2B7K_u7jB7|L)bzN zMh>Q|z3d5?tA!o(2p7z-w2KVNbY9dXkn4GB5pxua&wu=-dx%M1?0)h9ZukKf3OB9G!DvYLT9zSx~v4GEgbA!k5wVpxkcnD?i^vFZ6E{C0561-X@Gx;6=|1;< z4^Zu`hAcRqcYA1Vm%39zm}k50Kq5JrjI&4{z(lrI5GFncIOxDht*iWGJi^_Q?k*_> zj8U~=;5CF2{)FgB?CIz;yX%#I8!Iv~qQ1n`i*qmRPA=pq4x4%M{DUIzsw~W?Uuoq# ziN3;vnot!nhWN-ml$8w-cKD-#wnfAm5vMLV#)M<%mb2HG|Puwh!<9; zU>|xOBaP;9#01@`zewPeu8T$-Yn(QJU=}lBcF-P? zO^?8<3V^2azs2pjvQ2v-EGK4FyAdz z26#R)>nPRxts{O)iQZbB&xxV2Qu3w6LZRB5yruo+KaD~7K!x#tW>_$rrqn*gh*m8g zw5xhb0_urt2OFUOGUEN>MU1OT7=JiI1#48tzXqf$xorW2%}OWj+nk_nofo@)`Nlx^ zOJ8Cs{i@l#4uQzavnXtKA)sA+IuHl8eCck;?L*;cM~?gq-hz;a#Cv}zL@c|L*ZFCL z*xz!~W1eG#NM{OvK|>ILcGU2lBd|1k6t#u|&IoVx#T+dm>hPUAz*+uEy!{{nLt%Z{ zxw+sMlvJO~A=)VzZKM>s|>EbvU11jIuvF>0v!(Pp6DhDXZZ0wa;H53^R*n zh;G;4TYK^`-r5b5UcyIk5vy+Qf>Wd~%F5o@=qF*r zEX81DS8#;g8h@B4Y)fzLKx7*=IAGfA%VrjI5cWrZcd2_(01}ArnETn}Y7wA>ea1U8 z%tTy2C8761~&;)=^vgTGVqxZecBRVfWL&ia63-J{y5yq@C5l4W3 z{O_dEFtXcI=sZ+M`s$!ZxFo3Z(@gJVUpe}DZ&O&!c|OP0Y)p@nt|I!PF>U%IRN;cY zKu&0!VK8Hi;bRJ}r5J&27g;c;Ii|7+hEzFw&JjJ`Qc;mu;XJyoi^$p`2DlUIebMG z1Dh(pWxZ&Qqn4DCO@P`7&9mO^;xvpO^{H0%p@CMb<0(})1vUUzqTg=GXDoLl_4!Z! zY02&dw{@M&w2tX_Lf%`wM=Z<24*Lj{ZZJvIoYC2UUjOe{cIvwqf<0>7Jhk}O$7YOqpk^1 zd^fdHD4;0S(#b3EUC)DmEB4f7aMvdXhYk!MVu!<^S^a<-M9T8IJm5$={N|9uWC0Kn z>%u*$T6wZ(5TwUDSqW%vYWprwTUFBTphPk~IIWAeV=A=pRal$TL6z%oiL=~k8MRl; zqCkofLCkyQbwT*7so*!{hYvHrQjRvbq~)es%$;Ox{;H;Qzt?1c<)})~`8n@m?ncIT@?qniY?++N1 zl%p+-W$Bh|aPrQ^{=A>3>!oye$`mfKFM8R7MnmpFk((IY=>f~mXL^raJwGIiOnqD2I_``w6L^w<0>=q4S1oOi8ZTZKRhmq^>K1v#$L*w8KH zQ~O89!y)pa98e7+ai<8Kq28QRoNrL&xQX4g}y z#@>M088GHb&p$k5S|nQABk%DwenmLbQ?REku+ZTvTA__`tE{;3;YNxPvR!)AHIQ+L7n$~B=({y#r zz2Pn=4bi+poq%6=(CEsOhRkGWk6o@O01+mYVM~A12;zu89*xc_DJ&BFuF<;s&pU2^ zM(1tKn4lIIr|1fFmTgZ;Q+bJ_H!t{90Aft-ox^VLA=#ju8;PHD+&;b4$BxsDt_t);ML_o$L;jg87Nh#m5?J@Pi^w>}R+38L!K7owPU`D>QPD@9j|G z_80|{UY4$}SZMynxQ?H&x8$c@cf+1{7YhM5SxleZpUKm^{ijxl>7hwc$N$C$*8Q~GGj++IjGqnd0`XD z5P~8}FYkjVFi@T8G@bi@=CfqD zoXzD_(~}mF4wy3hi~Gu%xx`bScWB$(RpqH~eZ;iAbLk0=@D%B{?6-SF{L)XY>$LK`p$zx8<*s zPApvJ8-pr2m;^)M^w6G5p

HCtS(tonu-zBS*Rk2qK#X6p*SSwnj?@m_UJNZ@#QKYWNAXFuFP5RB z)jBp61FC_)y)=<^P+0Y0x@PTO?39;EK{n%kaVK#h2wL5C3IdFWv?19@_KsWoN)#da2EpItC)jDPKj*S zAUpI|R01q7U$=c#Y7R+%j>c8j5G@?_JF3?N+$>)__{yN|4s{22Bv52lUdG-Q!-|J1 z9Z~+#&$12r+Zg^_q>=_vmD^Ehk@KR+VrG_|RK8ZlMoiTUnF2lN<(W<_P&J473Ri2X9JT+WRy^i(F`EmvVKGhax{GH)G)0d0EM`~ z7wpF&^@$N(O<2X6Xco3mFgVNwBd#Wh0qwF%d#<>8vI0?qZUl?nt)IO$zbjmDeux)9 z?N~yEdr7hN1~iF(tEc4{-CHd~l>{6`V86iE@>&tZoBJeH~77VG&V2)F)!k(X6!ok)7=XlO2p1$}d^ z&{^M~4wFZDETo9pwh^%dT)NdX z#bJna&-Auf0{`Cc^4phqRK4v0lJ1LebH4pvsm%!cBVG_77M)MdIR+#?21RtnM$HQB zwOV}K07d; zK6>$Po^!C)h0ooYMHJx+201&)I6X^s!P?Sk=`Y>-(RcI5xZC*}^Z>fUAsPZmc(c$T zFWIDG!wJ{Gfk+yGZS7Q6ELckoOZiCkUDh=Hp&D&})lHF#Dol|JybUBejSoGTi>S|R zs0>Ypezsu%({uezNMMxQH{DImU*{nVm+%3s?q0fVZSu3NTAxxBSNnAKj86|6&AXLJ zX7)tVk-#hbYEmv#xrvs$uBo2+w8)FF|zJ@Ro3(JUhoR=?a5aN=h75HPPWUA zt`s+a{=IB_b_nz9o`j3P4<pHPomK^qUSQv6SyPtXr5x|+^>@QH%rh1e?d^oM?u|~jK3g~ry@JK=OWx2 z8IukHw+pZA&!~PvC3^2#Pts(LeX@cnyf3!JC|=ck7mLO4Cu>3Clb5^`_0!44-D$W& z@@Nq#|8)MQ@F`2T@6y69TiSBCI+6)Mvi8qK`ZLLxB|`2O0_*b@p(-g)B^`Y_K4#y*HteRGs_gS2Qz zFF$Mc2W zkI^+=^>YZ;2-M}u*oI=X3nnn8hN(Y+bwd}Id?bq zs}KQig;4?FXeCl$fZ}lirRM}vcjY{Vx@@-J3}^QF*9dVTt0uG>-wwbe>yU>Zpzqs- z(JF1pE1Ii_Yha_8Mqs>m*;g&D(8~-MKbD8;AKTbs?X@$jf2VZfB}vyQpt=w;f0`cD ztY(_x@ax=1@$@fmP??d)Hbz>`yzt&3<^bU$U-U@_rpEL=@@2|+1|qss2W3LCrqK zFXuqwQ{LHd3dPcx%$riuuY-hde(%tIeo-EHH6zECFknmq^7W3rhE+j*07$BgD{iXg=d7kvw;*1T9y!sV{5n)V?!s6ApH^DJ@ ztShkA@yfJH3qpZ9G>^;Rf7xpyvz=E4E{0blLWu!KIWk&p(~Tz)Z_IDJ(aIIyNhv%+ z73NWr%qjOa2#awe<6yP$=G4GWNb!xbt;ku=*OU(>bRkHHf~~&ZSDitgq*Ou144djb7>RsDNL=@GgY<0yICYT+_gVQCSUMWYtjL_8NJN6s zPybgk)t+qTrJ00^d&`k-lhHPUPdPmVF|-pCY|MztSSXuo8S8ky-xA99SzL>~JdRv2 z6#K*oSzLx`rz1FUf5nf|#=GIx9B>WwJq7=+pytOFLr+({+glJhbW7>xaH1r%H<=ozQ0jBlORDDLD1O~wBtqIclE13{k{UZ|4j1B z=saM+pfOBqJjm65O=0EtR{j!WAk1d^B;t{8G{?m4f2;4I2w|*9f27z|g^`R7K4dMe z#%D_kv$dY^rPk+s&=xuOk6{aY*2$4o3OuN0hMv!OaRrwpTSAwWHG<0vH=ZxD5JW+s zrV+P|RqtH~0)ZDyMorluCvjTOfouY;oz5rn#fML96~>|Hn#@xA&$KaAmR(PgRHUyb zp}!@5e`)pGsvP+z8(2SH)-WJwxe(oJDV)~D|7j@=jWd$6vydx=i{#Ru>mbI}JjyqW zcX;-+LeuQFL(&U+uoSBG1m&rv&C2tKFGRqahk3nxN!G!03=N!nXd(*AA-~`g+*qHV zSr0)}sdxWn7IGDNK%ylG&i$k4s7k=jGi5+9f1!X|3i=$`QAf;}?L<-8K0|WAD3b^r z?H|uaqC=%IKW5QE;2P{leMQDQxZ@(oWzRgkPGkO|F&(IIe>xqZo4Jz#zi5$I_FF>{ z&l%Zws#n2~JdNASi9`gQLKy)ZwVLEHK|c?RHoB{Y-oYSZ$hM9S)9a7bCr#=<;DyOwDLzdA948ch()L)gYgr zxscp_#mr)Fj))v@aET2Z)C(;Iw)$72fAj5{=Izx!!3utBO6AAF#=Znn2yS(2xu|xl zawmNZl@<-*6R!ytmDmYPG%@{&GdD17sBGq|@e2xP$rar?!DTIecz<#XoVD@paevGr zCc-X!M==^os8D=sHI3ldrPJS)>XiCka#A)*8(sdm_kBk=0dw;Cw|NqhKXwm!f1_%k z#9iML=RRL5+HPyvQk_Y-1a-FWcqXX0py-F%kWl>|%rx`Q+W1v>RQxT~WZ8Hwvg-_h zu`JO<=k@1KUXEhxfi+$Bu|>z~I@4E|F#40B={s%+0{$?H4pd6jwE#u z6RlarK4UQ~CL?sGaF^j9T_Z@Ef5JO4Mw?QF0=aUrW48>U4kxZqX>e7io&a?UfA5k6 zfzK|pf! z$DbMQ_}nB>^M%G20(|V=(ApOB2`6iK>cs}p4>2|NJ9w4sG$F-YB+*ncw;<0%h_rG2 zKjV2K$62O@zwOc$;Ib3Tn|y{{Sy^I(^aJI71;RgM(EQ=G%o!&dz3Tl6mnsM8c2b>m z@jC@7_*>c(Xs1Cu5er!Ce_R*9Xq3#SvUA0z0<&yP=>Dd6G(CeFaEt11xy)9oN({q6 zt^@%(#1tjFG16+$i@#`9(tz9AB&c~tanj%KWYNBC&kWAxBvu5H#u-@VcjW{;f90l~ zcG<>2@5DX5Iu8y|yKo6hJR(;NAMwIC8JEq*-Za$MR(!q9S=Qa2e4({P`a2^w42glGgqM&!aslb=K^xct|^TD0R|D zYx{@v3H!GMzAy|3e-gjAq;|eI?rw?w$*C-p;7URJ%3e^cs;}^DlxXRpyJTdkZ>0L-I4)*x z^$;Q3sX2B?no!U`zUGRR?H~Aa(j_ht?8<#dJ(bTU@FaKke-x{A@O_S{)I&IFbZGoF zO(&T+gN}e}mMfU_H3X*4gWVklhX_Z-kH>kc#-^T1VTcTMXG>c3ne=P)Ue%kuRmG8* zoA9CVEY9Vl*BAn-cF-7ytGRNGj+9%f0kv{5_S0w64n^c3k?Kaf3pr?1KPLiORmnTjRwK3P{{KMXf{!=%F#eV*{0f!ENlD^4#VjSJ+^TyEaX#u~aQRqIg9>36jSw}pn+nqe~ z2KMl_@H|*Kfdxv)w9^?|0A;b@Uv1SD3%sT(whleGuY+VdY#ioH>axpOGuDWG=Q(SU zap`0Je=K|Km}TE#h*VTc=x$P}3`_wgYD2r2Od{0g#rHsaaikhW0wR zHl^g$pI;=ggd#as6P#kHKNM;0I!$=j+$tHDipWW`^y?-_rN6;)wMf9@k;GiMx+W8MquG`YerHf65Xz~V(~ zyf1vuFt$l0!Z{9L+sJcchK73HSws70{2hphF}h2XODSyY@>{CGr?zY1^LgM(jumW9 z?rGq4(wAK_z29mQrG#o~DTu>-%Z&v-%hTN>Tdr>(S2$+A0tXJ0kaj|Wv9dPgLx(N9 zf5XKSl;JJX+>>6q9(gO9Jx4&bpk_G^am&k{41LpaI#j%Sc-o=16|3dUvym$A*v(i&i9JBnO8o6#V|j z2Zq-0e$K?GBko1kp+s#1zRW?He{q*V|3JF=d0#kIozW}~J+n+6Y%gIWF!7r5x5tsV| zZu`9b9NxF~py5~@Cx14Gf4I@v8v!(n)bx_6e6$0UgCLo@`JMDqxHhw)>extpckR^A zE(e5aNwwZl3OJtK4OGr#^j$x!xzS?ElE>wdXtwC-k}+eKcV~gRaO0L;6JC7NuU|#J zGl$p-Mcn=23R{ZyW^YvFG^ry}YGzjEg#N9(S8#olA|#k`AG}?mf9ibto8u4asT4I6 z7(2mufpWj=yg}brTYow2>fm(82pv#6{if`0$!+NX7aftGa|gd1k8L!hU_Ydw+W$mk zgR#N(p5J7=ckiSOT%kzH$I{-!di+c<#mWHJb8zz5Hi}Ce2#j64?8L4lx@D{F+Uf68 zRKowXXuORH@HcPxf55XDX$i)Yapo~HP^TyLh&WhK3hx8+5sk2B(5*MFPiPc3(H8+*=^0_;j$el-vTEuH*T$hmzzxa-n|-0 z@LKtzQtv$k)mcqECUZ5&Kh8k#;i=_+Be*Me(Q`EBT$34mf3s?48ymZGlgwY366tIW zGrqx+7A^*r?8Q37ooma`r2Obe)=_?ttW}1|VG9XRp8E>E->fqCy_@EQ4T$E|u#{Dt zgH38tkv#?KjmCQMOHO~7-mS}=r^iq_TpJR4&s7)6B|EwXWK25LdqhvW1)n(uJZIdlYBN&0`fmTMa5|JlE? z01_2#x>nYuHbZH=CNp){t%4y&#O9t&e&K)rycBO)e{9v(&*WYR`BS3-0|;C||I3Ll zJhs8>gR@!R3p`bmkLWq*ys~&%=H?zXa1TpUz|z{ti(VCke0nF?KDA}v=GeHE!)H*A zC{0iD@+OY}ugHc~zlhE4h)sUlTQw!xu^^Qp6Pxv-5dhC-Rka-kP<&J zdg;;yhn9f2*K}9_JPor<9_{^N=R|SYv^jB#Wevk!rnbdDu680yR_Dx_+ctfNaCVId z`zC;shHjMh2jqZAP(B^`Wj1H*67-Fei`v4Q_067m672)=ZU6PgvF0t^fpECk*^3!U ze+ptv(!;tir~Yz(4JYd~uppq6`ohm=)}ps_tf=^`(i< z$9bKBS2g_a0~B{f%6})Bftl=xOMQAa@FwNl7l|}vLPcA;)1ka5T0Xv=hF6rx#X((@ z8yiN7Y8|b=1MW^csm07GE!eOpR77AFe^Ad*l)tjg1=iM60(|>mh4-0W$GG)p0Nz;c zbqP|8$+*QMk+wFP;o(Ct?qR7qJ>kUpA_oAtDN^m{rgZITi>d+3<3D*})s04Q7Pin- z`ZSpD5uv&#E1guYKY2c3<4EK;k{D!g3=*Zu5t`MJhU&e+Y*+ zJet$E;EbsnN+J^2UG(8|p`i(MrZzAHato_ymAT2bmqOnz9)bP}aCL(!Zee~uY*@eW)4Q8PlipVUP;WwhE8#ubj|{*j}BWH9Co zMV_^O6^d`a=+NmXhUgO0ics18H34E^@guLiqaQVl$&@OLf5W`P8f$~6x`^(`(e=P6 ztl2>LrP-M{0wSL%WvEVoUjS*`Tr_^v)A|EKZXcFD4fHN28 z3^W6heYoI^h?wQ{f*Gj;{?05pMS09BwPfSCor!o z?A?LRuKy4-cXqG?$cw89ODHO+e*wfr8P!Aq#`b0aIjMij?Ok1X{>cWKy1M?WJ34^t z|5&!h|6`f_kM%!MXV3pw3~@|R>9Z~2%r*muyb^C1v&%d9n65v_JDtB@8N9qe-HBCRAW0U zTd)6b^8d|{b~XM-3}JhVf8=BO4`k&cVdV)lQ?hdXM{ieWH{gF@P2hj_MjmKpt5= zIhX;=tnADHE>nx@I zj?98M30yFT5d4wPxZOTa{)X(btDMuOkk1tN=H!|t8VzBUf7QuclHnE>Nli>gbjrew z^Lg=y3ogIyF1d(GCY0-@nZhMUF}OX%rddId{V9T+=vg@I#92p&Ofo_h>j%ga5##WL zMX&)AynTYDU=q^eEpXQ3Aod4$cdHBgK^mpxgs2s3c1!%Qk1)HSaLOvj!G)T669hTq zr62tos??<-eA&bSryMf1HlQ+M;W+|dw3{7_te~Y7#6mA_%(h_y7^kqPP zi~?WCFqd(Zzu`pz)Z~>Qb!HGZC)gF|Tv9Mu{CA>tQ7L4%G@xI%;Zc9iZ%U?2?cr&!WiRVAikH*Cvpl;{gPXo_vlf6OE5i)8tgHaDCXJz=erqsg2ipgYwX_jtTl zqCwxje+H2o3m(muywy;(yOK>FJwHLsxoF?%M=d#{ozU)Q3grP=mM!8Vr}2V~CyAY- ztp;-TQMld-hM;nG$BIi!OOGH{qD$gVvh-;Eub&gkoV?sa2yoEquP&)0YPL9M5S2~W zrAR0tK~+@pe?=rMIB zo7j-v-5RebKW&>t@*u)*NKQ{YsLNEMyj@KcaXra&w%~i$lDcs(^do)Wg6TSCMKq!& zh#Tryb#HsD3@IfF30{UXpd}srj^k1dwAI+m>L&MkNE5W}qO$uF?N{x3T3|RAoquTD ze>h4r@FfVFmutKFjZ30mbM|wpT0>WCQ8@)cc7ovLBgOeF9Di1}zpw2~YvicBp>e|x zj(7GYM>^TCn%H9i_kd;BV2EM_(pAq=|x3N zOp(f|k-F7q(sf7jB+gb3Rnq(Eg=W_?+B1c;0&Q+=vI(Nni2Tq*7;p1Icb=o=e-VnC zrP(RT*Zz7ba;s287`h9wI&N{?VD1SZ=a}M>J8F$qR&g zhW4d*6IeT#fn0z__yg+nlDJGw68!DF^;^5C97eC0?^aYllD%O!E;Atr+<4^=(xus@ zv?V!Li~L+Wak(I5GndR87hhi=e-jkpJD93f8M>KMpSrp%0#)9TvjIjWLtXV<-P%PL z;fZ+{mS~ZdAv)Ph(rYX)3kwm%?I9#T2&uS>F-oS($aG-;@^4uEL3m&cA;T|_rsFbh z4y$pZ&TW?30>x_6K0~D$Xt~V6sA0BIkJs2;91?H1_{^}*5Yo%szAR=!f8yS9u9l!n z^KOv#+f#$=OLlBBFvmZ-YQlak&3)uOy9+4w$+qF|f?x)@a0ATDrj^%@5`jl^ZmF

YO`8n^b_G$A>ew9Y~SM!|HPppV$uj zcv+H47@vtIg*3MI71)3_@YL6UG-6`xZ?73YSmB(bC zi}%?qjcOcLHdvMMN7)j+Bngz`N=k3@Yye>?;Z$m|P*lsyyZ-8ED%=Q9u_BsLE2xkO z*VSgafB+aWvr}`8`!0r)Xdq2(j7)c~bQO$`CzX>GXZIH#j0(EzC8V}K{U%7dHKS;?Jvum4qUsuk7OU}I1 z7&L;I>;c{63)f*1Kbfeb-((jxQiU*s@IhD>C#zB0*Wl@%1DtBq2&u^4ERlqrgI7%@ z^6NLVILuLH2mST8fBb-pqPoZ_Qu-N>pN;ng^rd;gMavDn5}g8)Vq=cn3fsUp$DEOx z<1!z(o2~*6U8fU-aFQ%%pP4x$LK2DYe3RL&S$m?J6^{L5oB1WNN=Z_W@5$LW8V_fm zV=)A84wBlnqyCG&a`>O{cK^t#%diHX;$uzH?(M8rVan|of6^cOnz;}$!v3b&h4AoS zfey8e{FjiG9~`xJP>HNUX)~!;H?nOle=1@QO9ZPs3INTCA%FEfd6L$dmNkvYXBN-` zLw+GjqSIxrPYmrNm$^J_#aduCuBTZQD_gyjLA?BwNK`qmp?ZcR`EnC9eFGL~ zsQ^bmyseQnfBPNalrOi0ZO$;}M^Eu6%;M(n^ItTaMYu0?&SHFBKJEqIR*UYZVN_~~ z=a}8Cr?Z?~ThIUQ4{T3SLG&$-kH^N;1d4K{*1D*qxy!om@aF{NQW-jt z7#HXv7lQ=`(MmyoGm(Pw?t2;txzwTr6?WTEDvSk`Usdf(n|vVE)?cX{xO?J5IiI;( zbxkb7R7Mdv#u7U_{;P;I4qxnqAM^b^m`aL6m0n^zD^l^%$Z6%|NqXp| z;Fk(24|L1@wgLpLSv{%&SSDq<;&Tjr^+DGrA0zibe*|6`M)8?vM$O4Xe7v7grKIwD z^c=K?C&8sp>K});i#pYck>RRgT}5264vjjL0bP8#NF@K6XybX=tYo%Dus0L}yznmM zf6O&6H#3wQ!={CpIE4E%9ha(v9|$=Q_DMX-o|cSz6g{V^eW;L6voDn^!4{`X=4fv( zj-oc35||)uQtV~0IxH-YMmx+s6nBQ}yStFDx{6qWv%Ck?)S^}8g5D1)Q`;z-7$B0U zLj)C+Fy*OO8=`FvELl7w=UeEVO<#ATf1snO3jN~WmzQBQ7)b3eRxNTMBB5GOP*W+M z*Vrop@V8RnL4*qAt?{M9I9`(-YfK5?0cP%e$9A9i!OM}VDVh^k;#1|N@m(J(JW77<3?ktSGu}Y4flB^XzQ5FNe{?C) zEOMNps1?aS?sj*YWSVA^W9+ROROebUTHK1Y8Z1)k_MQd#{DU$~S1G|nIVuqE2|WN3 ztbfhz1$o;X>w5sd8*Jw)f5it#|8eY)Z>fpG^7Mo>dkJH6#&dLnRzcuyXe=wk*=m+pG zz@p2d0Et{h^;W61nmsCw5ASnrR&X@s(H`;b>W5X?@@sgsM%@fWc?mJcZ~Hd9ivdVA zKx5q3e%@0k_L@Qs-rfjicNrLxxX+}h#XCpIz`Xz3!YFt3I98Xnno+~%B)S?}+8hi8 z_gX&}<&r|cH{W0UMX#`Oe=@>F^WnUEh!VFWVeE4~C6^Z&mnB)HNLANM^pU=y(s{`#vqi^g;ur-h}sm zVJ2P&e-zU4J#k&LqX(_nLB{L{oJ&i0H(@`wj2vk%xrIlI8)ofDf9T&tdM4UDX@uiL z*p&X-DS>k)>x7DGEv{;1VQQT7azv4o9}HKYJG0_i=W#t)9BV##2|Pi&G#lB%(p?#o z6MK@n9D#+O*|BlJ=G9Kc4=ucp2I)`11NrdD9))PHIh(KR$j9JO*>HQeP2!&WkD?o`JcQXTjz)~(ZkGGu1 zE&|JP65CF{g~Y<1Q-0N#!t8LkdO`Gq9$jSFl4SC9_vr0je<^DkyMz|!Xt98oHXaA( zbxSO%9CzN3KeUk@&ogW%&x}V}mDi9Ah#lT1YGa0_7IE@PtRTva^<_*7h-n-iC-r$o`mCWJ{%}XZZaXv_?~pvxk499{lr)e z{)8xy%*a|9e*-e?vp*5>E2<6tf$BJuPx&fCLpqNJjencGeMWgM?S@vAIX3Q>NFc8y z_1twDQ#3K_@PUiA9!y<8uZ85Ey+~@c3=(35)}V&`W6S3#uCgtM)@MtIwrBWdG%bd< zlTNcS`V0#nqL^_5|4;64pTt8C%L58i}4Z3 zu<729boVQi6U6bd#{Pwgh;RK|2~>ez_gM= z8x%5?rDMN;mRTxX;Oy>$JNGV88e+n0x|sR=bu?z>dDXzmcArV$ovU&`SkNEdk{D1x z>OLja39AuDF~f!i$L;KZmtFaGTRw@!U!^n=f8jvGUS%(XubN9G&HUciuIT;Yn}UV1 z#^TfiNs4#ymVw0coKe3>NJ8I;2z^4jgD%4kp}{8)y%>u>0j&`+FWv_B}2 ze3KpEIYoEOrfEO3lLFOZjDR)iKRL-}{&j0F!^6<@8EWgbSMJ3dJAX7FV*~X}z49^z ze@q9`P6U;Thk35WQuac}R&TYNc435p?&iHwNr(=GDV#N{mDb{Fe;1>|MgnGb?B@x% zigf`h3gpDp%gBEHf;^GgpAJcQy5TQ2r&PL|$k>lrVX`{Yq;&V>ie1M?xyu`simyWr z#dYuf)}ViG$#FP&1SfY-yjw>dicl#je+$03rVRE7ePZ$?r8lpLLL)dI;z71zrMXzk8C#VT!2&hGVXs6Q{aTR+#N}I=)u$0) z5n&SeJJZ)En#@@_2+^60-%g(OLT}0{%_v`^DA?#4%#9q^jljvT;g2ISBJtXJ)eRC^ z6|?W}aPxcOXTlciECLFFB0VV6e@Yc6IcLDUa(sH;#y^?Nh}(6R2;US_g`5DEHCf&^yoKNFIqO$?A} zO2PY|d^%`%i>CIsjCf;HaIA`!E(*dgw~nQ} zawdf2G=nbV5h9bvf5TdTJDx#C!eOPfzT&-ge>gaqpYEB$PLcXU~7wPcahB3hRRrZQvki|aVNo`K-k{cnd` zPe9GU0@?W&0tO08-YzBB*9Y@yUxm51jm-lEF-?~f7h?VE`0=AImFhPOlI3u z53#t8TIwJ5prvdfH5ajgdm(c@XT0K@j{FkWUyBu2PkGtsB$HbKt%Eu5n%GWTvF??x zYwWP2Yl%w}M6we5bU8Tnm}e$5Aej_Xj7E)ECeW|htCp_p|5g`SC$rwD|Llfd1 zYJ2rEFHmsqe-c~_?`1z~wji(oVpwv@)?{7F87K{m`J{|#E5Z)73+p!UCxfEnT4SjU z39AeA-hw|CNp~Ki3pQVHiU=+k_Rg)r47j))n(^QmzzZcMZ z3ej5GPS3PJVod2*n?f01UBWwR);>!cIllgF5Q#PAl0^1oQbvz{9^xAxXlX z^SGX*e=|}j?xQ-}Jv&VA9W`UsBe-22zZqBmc2q>tQT{$n}I%IukO`8i1 zBSPha1KLK;3VVSglnP}j?gPih#!u&;o;OH;xKTq@YeNJ@l<(v*^U5tGB0`GkTTJll z?>qYsC9KN|PR)(E-Km)7w(ah%j(GMnidEH9l%PNfK!23)?(Sn>)~}d0(O0Em?4oAT zfAVnms8wn8a&kGHjsaA@vA-e~A0Kb^DX=u1CSZU3?Y6G@3i|mneB8BLlMHqHei18x zMWhn;-g4x3^>wu$TEDf|Z=a5YoWlyM}jdU?&@dtM^mO!WrBRKa*&>I><*t?i!DH zXW1d%l*0n=bgctAly?{D@3Ta*(qCJQe~=LsMA*CqN49{@sd8|cZy5Jj39C6j-K}Wi zi_hog(Sha7JORs5s!Jm!svOwd{-a%^E*6XprRiPH0#TV%q&VTypZQk0W_BGoKZ!56 zEn{@`|E@UU8R1^|K<1uh1zqp9A2#6XkiLE=m^GiuGd?M$6rf9_j% z)c2}S>Rr9(qf;2wN13QdRfor}VLt-Yso7jft6<+I@)*bL+VTQz>E5c%LItUSB;WDB zuC6W|O`1u%R#d7?8fit?2KOi$)?3#=9r`O~s4%~i*EU|HPP9_@!`ZMOR*MaC*Zq;o z)7+JvmnYcoE@!z|e!GYz0q>Xle@-sIbWp`{szoY1^Y5^iJs$km-9X`Fr$=&z5$(Y- zM))wGY}tgj+WAj>DygKrp6(Q@r{^6a_UoyK06VJUhn| z2c!SArpKr=3Sh*7*hfbgxomMJ zzomTV*ed@bNdGLZIK0ggo3EH79ZE@!{wp1Za6yb4<4ZOBTz{n`gn_pVWlr$ve0bTb zSIlOe7^AKbN7exKcGREb@MelPf#&L9@J^aKVeRnMJyz`BL3wg6e}+e?VovSaPf;AkHeac^a`N|zlqcra8+^dp>K?;BXuFqlixxby4mE;+R>-^ z7$~vH!$y&-w4#sEwu0N>%Pcki1`GU+Dv7I~!ue^0Gk!9><9kIAnc;?Yqw z;l}%uTQP<*E4f;)X;^eBT+3yDf~rgvZakw7>8_vfE7{o|3$P?u2 z3wV`l(w?8@nA56}VIDwtm8vj91c!E!V6bs+y+e%RZjUb(EqWs|gNpYheRPCxOdx#Z zebt40(Le~%x1b{Am2j*z&*h~bYxtf^nJ z&-wg#NF{~ZFVH$x7psc}HLD6`CL~~O5$ZATGsY#V4jsA61{5!o=SQql;{!9Rk zp!WBj(Ry8ndGePt(;#U}-Nc2oEFeBOZDM1aGwqRn>U`w^JlBiJvT(+bG1JqLefRfP z>Vz^Vf7NthF%9{T`TqM!R?~Jx>RVCWZM|Qu*Dv20kO0)I{je-wF!G|#5if>IyHmr? zFtiuaKUeASPPvr9y(8XRyUNI4ebX7>X*NZbjkm?3$;*B+Bw8nN@`bKG+2M-DyMvTZ zT2Y%4obry(+vbD9q)R(yCZO;HQpJ1P0+O_ve{&VTX5&ny^vEMp{55M?j0`m#~Jj@+rTY??!e zcNqxzZYUtxL-eXD!`?xnFE+_d zZbK$JagI7*Hr@ujZ*!-{#)2Z5^5-Kyt=oF2lrOF-EO`;#L~rCvHp&RgkALpZQnIF> zak$Zzgt78n>>*mKo>z}J_-Kz2SoK*(f92G4pssi#M`7)aXYz!SW)6G<&kyeWDA>|3 zSN6>Wp`n@94i1nJNfHbi>DBq>DpO|OZQfB(p{&QNC?=j?&UU)Qw>7%JZhj6iQO!#h zs^QtnOA)J;jON|`5zWjou*GZId23bNQ^+|zsg>@kS=edaT&cw~d^h6x+2c*re-o7& z$!DFHDVa6TiEWkQ1r#~vNtYJt^16m~Wx;^S)JpGL5BD*1iKXNSTGmS4$S*tQP3BN( z5J{}$7DLpy#qd~6W?T)sP2y8O9>4O}Bg~~Hx+58*f^vaBE&qc)a%q)b*r7DVOV#DV z@}!2OnP1bwq4Zz|2Dy{V|DjDAfAse23OyB%XizmZ1=LBv-*2CPYePrn1TD$`={5TC z`?LH}=KBzeB`BY<4sKL&+pFp@S4nTuTLGDso&-(`0VNPoE}A&&{63E;f{S#w;B5h& zsmsF#(H`2i8Mti6T&0qiG3`Or*A!^N|58olYNLo-68jyFykF@Tntz&Ze`Q+bYKk0C zb-i!N0J3I3ScV{GXQRm9fj|QqWpG58es3}UmIgfL_x*Dvt8coBM}}_9k#>yk5SBxo zagbx_^Y@`xThmUP6uE_J_LKyUY|s{|zgg<`3Vq9VjrxjmV8@w8vv)?ChODXwZBnIo zh3FxC_IyzHfuY2yfZO~me~4?E`z9{1_rX2>nX0s4A3)1|j76F$eX%TV-&B~EbPS|p@dmA&NAa~&AJEXpc1#z2xBT<)&9?E~PuVVkWa71kc(Q-n zu&vzh?a|S(B8E^E8md{9f67i{sU#AKxRq(Rh`&I)d|OlCEfH2*f2|H+2AFR)ZO32O z@9qyq4~Jp&533jU=10C`e3rx8@*^r9gX^ck8yPy<1Uh9y{;CT&{4u8(MTh9{`)EKf za1gPyf?%PvQ4Hb`=c|zQa9d(6ZOeXMRd7ynW|=^ROt{*5({%ih<-Ji~aiAsB+EX;t zhLS*QtChn4QR6RXe^sg_z%9ChpdX8B3`y>nkgecC%8aOkjYC^%>dAEe1oqZOH3t-- zE=jnZCfdB)%zH%?SX{=_>+-c6ygLQ+#MszWV5+AE&$le)3W?JQR1YsEjd|=Ch&%+| zJNu(AR^G5B;IHTaV_mBOFHKDL3zyiaFu$s~o7`8MdO>|Fr0l0#ok z$|}A}w;K3Jh{?s=(wv>q7L)lqCz;ybB3HV`8JX#dP#Ed1PDI5_-H&6%aI0MoI{}Q# zc^vg%%=;n=-yUZtY|pO(K&10_Qa`-69;n1xehnf5Wx_q&h(?&X*rSE?I+%_s&M{$P zoPo`yo_c4Xe}O!G56DBS#bS4L(>9Q?Y>BB?QG z8%78{b&3o0Ui_wsiOB}vQeU3U-)zYRT$t6X@*}5VpJ#v7-g2ewMzT!elk!21JCDY- zTD2(17YI@eF&o2m1~~cJ5GOt&FCJ{zR){a1VzaPS8KUyhu7umg)EP}-RoQ+THb93oaP=aDhX1zX7DEo1%N)gQ8=Q8p> z+l(+|4Mk(6kFL%Q3ZqHTKDQa?PD^e$rEGKw-CP}wx~$Uk7s)>_7#0ejTotWib7#Jw zEDxfbEesM{Df0QE66%;tTow5q>)`|{Tb5G_e-!-0o ze^%~;SAVMVbbB;L$QpkB@cNvnr_x9zV8X-igaoVsH?fVCR=AEWo{&kl<5u>}r>Yu7 zi?lIp-z$kNP{I}oEX3-|B{uEFqq`(tQ;aBS<({3BQ&>cI8w?Y+^5#*eJgs{QKa;dM zEt7a(F@sm~E`ev%!7TyJ43HY${QDy%e{W%WJV>MynOT(;D?GCZnJnr3;aBm!1wpB~ zE>)Xw`HcA2AVdh-Jw+FLSJOU#Hy_B=3`eJatgg%?$1x9Lpda$0*?jf21n zaiZb3zHDV2cC!-{@2JW8jN*Z00IZ*sYFNJA=c%afZPY-Ph4z?sx=u3DnY>OAHZ z1A_#~p_Z**O9B(h+Oaij90A0JfAM_$v`v3ViD=ObKL|qbT$@6I1aqwt<7e_CRoIh9 zF~u=r*M?Q7R($>>lQ~}HD=LHjW6$1``Z$;uM$A4aZw|TE+p<3QDzZ&ClJRVG&(F)p zH7{`Vy+A!Q*U9Ge~koRuFFM- z_bI6qo1QHH0x`JEcuM{NKS030Vki@MYRPIF4Vh3lU9{d5N5Wg!pU8{}EVHJWRUuSZ zNXoi&;n$7<)M#Jk2|M$VRp8HW-@TG+nGMm9Smql&DuDUcD(YYz%D~)I$!wW=OiARb zsbU_tPsIO$)%j@<8JvZ%O3ROkb$`BcM?zfH?> z92G?&cnYy+Pp7@jH@8aMS&UY_^Y*ycKBd(^g-co%+&kFoyJu}S2EFccO|?gDY^r7HRB0B2=#Pf@X!H?u#Z#~m4Yj9c z`aP_0SC;W2f5jYCPF(}(jZB9(#J53QpoDkM|9tKo7WT(G@KSn#5&jhSEht_C!Ox6} zAzMk1$m>rw(-^W8*(lz@j}ofT>t7RUZBRHIMW#>JD6u_xwg4^ zUJqvcin&@@z{fGp@t$+mYjWv8s-MmEetF#vXe%_6t+=^*I-x}m&*BQ`svAu_F(87J zK*~TPc!frSr97M`X!fh`#zeOnWNPc&k8CJd>{s9U?HvTfW=$vwXn*ajSGVHGU%O1T zfU7DpSv)zpTKvCKzBU#pJ zr21`{H%;Y}+JE6^M&5W`=kva5TveaUO~bAdMzFd?H1aZNVhV=7TXT0-l^Bw~ zTtG@^6BUGcn?BF?e#WQtV2>L)uP1V|*q(h>l8Rntb~Z69IRtF+H4Sv4HU;0~SjeSg=5wU%}zIjaS>L&-xH zYvl(Uv9h=HE4CKF(dzW{Z3pzeA_@K4hCy8~IHicKVpa(rJu$HX%$ffbpc$1?Y&>6# z!cO=rjzLGIF37x7c-ms|(E{4M0}@(wHtPye&~5{8&3N)KzaE7TWyysJ_{*AbrQO_{ zoa?gtJD|q*fPV-EW8@>N{#~anB?+Xr*ab9pE%a?5TW@6~?*JKMy8$16FxPv{%o}}o z|1(Ub)~dUO�=)TEBJ<;z_PrnSW&rD4jbBXrR4rtKJ%Zx=_ zQ(c7`3hKOnGVA7r;!IrV&*!%?gla)Z@_sffWJI%9?ak;@sE1$Z-tQ@EK{mdi?_%(` zt%$19y^~Tis?QfN6(e9~O&G*+SN!hiE{dWhNH6|}GypA#Hc#x-ZSGgg5O^DNw?V!w zA)%81fPXAovMo0kE=h%!#E;xLP+253*}$qP5L^7>TqoZWt;6Uap?;Mneb3i3^t;Ol zbCNR4#J@-)XuwuC&qje`5Gr?Mhd%<_lkQ|JF*@u$Ohcz!kSxxPY#JX)k$B~n+9W;y zn8BL#MqK0+K493}(jTn+32e(W-6T-OX-&MFCVv6pL+HdMKEarI7t@ssw1_4v1{HVW z;r&Zn4}uRJWr!S55NlMxWRnbM;<76=h1;G0DcZ~%#^Y(?@4tM3H2Wd`{)lkJgl_q* z&~QHs9+Jz37^8&1hLe+PX=Z4bTDkhTKWbM+q91qCVXp&qH-WNHgOU^Z>L~;7=|$!Y zmVfwq=ytH!QJNWR^nfNr(`LvzhP;VJHChcZV248d3sgTN9|@G8L|-Mlf96O2uZpJ; z17EbGlu~zPLVA2RbAq4rz~#)eh;#um<>80Vp1?B^1UgINjj%RnNwKxsXCW2hMNrJ% z-Uf>B;mk%H$ z1~2V2jCg~aD;uk0y6=_(WE9X zsiNlBz17LZ@Rn$*3QU?A+U?#T!+-CYiG+|3{RDK#X8sp33ac{}IY*(?NXsH8X-{YP zqX7~j0X(?YF`B%mrlhnBQP0^_dW>Vr_IZ~*_1}q(Hmx4taxV{Y!|b1!`}gO4EZDeV zVCF1z8eQk#Van_hkim#jUGNMyAjMKv5o&>1)eRdIJoOLwdD7X-vf;D#ZGXT%{Pw*< zsiOK4I9$DF)6c>oE#5&$?(2`;e`&IXFC_u;mm+|CkzMVBte!%yic28P(6 zh7De6=^)9o@|?!;71e(^wVP0qM9*=svbsJ6pOF$yq%W##+GG<>aeb_LOa#SV8T#Q| zWaTf%KM1MVr&BVM{b4=I_ICx!72H^*AGky@G-cliiQlPK4xgBr~l<>=+2K|rMcMawWIs?NnP<4l9yAm3LU zdYlU(wl&Jj>3s~gmdd3RzqeM(q71;c5km*i<=BS0GaFyk!YiNCX45OOaNszv-I50- z%0}jY-;_WdlM?z>oPX7jGlWDz#8AD_xN+>dXmc%lGiuqTwT#*ZC&c^&CJ=;l7E9x} zARrIBlB+6`!yO9ONsO4*{}Ky&eEoarP{xu-WCEgd<1AyW)3eMTRYR!o!}c0PF=4l? zp+MA6vS38Lg7N;_`SY<-Zo$H;SVTL_dQH+S4n8x{r`pTS}z@qrNJL@%wM_QS|~z);Corp{h8XO`Rmm$Y>5*d8-udThMYMK zPm47oS{!XV>(q!YUBexjzSLrjMK?ArH+w#kwM=`#;Yke^vylrmRO~W8A-Rmfy1~N7 z9wf5W)7~G~5P$#T<{TM(!UGs%}?lBU_K5Ix|13J(HHUgXtLsms5z)O#;T8X9xDyd?LZ8S@__E|rc-={93A;E?Yjam zA)d5hS-XW*+843N?>LI*%nYWOU%iMDkqwWrTp(n3RDaO!`3s(5*Xst$6kek(hcehU z99>7EbUmDf*xPlD=|>LTJmmhe<-eX21SxL?&4;yD)N4}1?0Oqw$YT1Jk`(*RqPi^_sKZ79;D^zje_rp7>aFtZ$+crB+@a|eBc44Yvph}=Ir2e#w zk>HtjQBO*o9=mh-yVfw&R}%+V(`TEgm`l4iwtqImBLzu7oj>G^tr{ZCQdT$ZxoJtQshsu?XSP&nr8yxN3?$5S92eR7npq$J zx_|NDyaU@^Io=cBGdD&%dN2}X4#~08lV8Nsqy$dE;OFBZQ2Cd*KNV~sMu49OKZ0BH z#noI9i?i1<#$D2_OG~49m(ve!OdRFDm(ypEWv@GxS&AYja&HVt+$WGkZ$|u|UhA%a zNqZH(FkZ3X;k9W@9q=*({Qw$&Cy#dC1%Iv9Z$2nrj1Ou2@+J?@Tt1dg0}9qOq8Y0DQt@BVc z)5?&=@yyKyA2Cy>tLrJu4jp&cQ|hn)yElNJGwkkk`kXibRSzC-7>JBr_z0qhthGZf zffqzWs;sRH7NAK+i#XzEbpn@@RwxuOW?nrSU$2n zD9QT9Z&Dbu)IENz!=etjo_U=4nCWHsoX+)&fI>+jjVi=X+L!(oee5S=R{PpO)gU{& zR{9<1_Peh9>&L8$y^`BaOkGG5<*z#v%{X>BpHvbGOz{cJ+ofd3(B#y&z<+P|&{Na; z;lDVi0)9|`>|)VhS!Xjd>;ItL;hD7962jajQxC|?*^^Mi68{L2)u*USr3^I}T?ysu zISe%QiV~W|8+BfW^T$~tDWktNIsZkvdy;yrM?dUTUwRt&kruIAmP(EhGDZ8RZ$k;v zmtOrbIHgUxkG?VMmpXujKRc<9y&5D^`z#2YppnNRujN}h11jj@c>*zzWi z9MaZr(ptT}zsM{&h|U7dBKvbphj;br6=F)tR}cyRjP11>AHSY*R+%tyblCzrXr3)w zI%^i+?WKFAo(FT3*%KltZn6=;bhX-QTmo@=aEO!`f;Hh%=xbM{ZbKqC9q>_8D*<*-!`D zhBo2TAG6q&R9{yOR$=!|1s&;j|CGQzA5nJy%01;Y#DU-C*AfhNQjf zZ6)&K&3iQniG-KZf`6e%a1HXC`e97?$+*jrk;|1w&}wuvLz5q}Vgtw|F(wR5nA=pY zCCYgqq=`XazjG4p&)}6A$`lFcAa1djJbYQpcjU8iD|oGN`oL}r&Ax#bx&6-~VC^(c zKe=Fo#;woQxrISN+oq^mFQ$?!9-KfTpCAP0WH1?h|wVn5)9C<-EDZ9wYxN5i?$_I=(cIS^RLfgoDToZ7m!4#{3yUHVq7 zd}f97lD|$ELOUt-#{Q=JUDBM&VJ(^xhaG~d$`Ag+)O7BtcL>qBaSSu42W3Au@QbR9 zOqi(sB!wG!TDup(bc4miH>*L8%zZ-dr!!Q;9A&{UX@3ljw|XG`n(KSySNSXCqr^O3 z<(`=p@2fC&FtkyY1WD3?P?q=}oT*2>UrEail5{wSC{wY4F-isx==p&VUCSUrC!JD! zMWJ@LOU;rVMTIadc=mG>HKpU-*r4gu-XZRh@OZ4wPW6&*P*Yw07-gZp!Hm{l=Lv^c z2?L5i$bWz++-!UHf4{>B#8VI#5iF1(?{8x0i_k-g<9Awuh`HWzptP(1TQyBeFG6dn z%1}#8QCk**@rJz~a;BJ{#*@6FUKh>l@=Mt_2PMKKG@%n~b!@SO*fB2p>&>JEs`6MI zZ&eUf20`wNZUu>?5n_9il0Cp@3!(n(U9H#mnt#Vg>W0_8g?%bdIlH^!IW?2GO@d_D zVD<0RP8$q-o$r1)X*X~@s0i1J^q}ZsETAkWrfbKGdI{ocZh0&^SoM1bdceny$?z;? z4isVmqjFH~(BfycJhxTd_GakKU{nI#*S6Gi>Rmwh|2{0`5nygO;A^0zp&C^7=4h=} zbboriCRxaaTBX`RWxUs|G$7cFV5*N87^#sR#8T`hy`&S4-9hLOA1}%f2@PH%Z|#M# zHsUJvYj9%!tHC4yx^MPP!3NW<+MYlT@_C^(>_l;U!Nzve4rWl~=#Se<2NuzPRl&rI z2)KIUbc;L<$Y1(9A%wmqJ#`p^2VJ9^_kXir3{8A6{VWy7o%dij<=9^;a0nk>XF5pm zfU_#YV09mV6=G#?givU~=TG@jrbixjd&EaSpfd_Z3@Z_t%q&f@a=wnw*;Sqb2P8lW zu%L_O=Dv}RCr74SZCWd%&OW<$Pqp8NR0-M92eIxnP6dIQK%cJ6dfCn8rAhcJS$`I! z#PEA%AF+cBs|Y6?C~A0RjVi0(4eu2S$!>AT=g--+>E;53dFeu2$P9kswxkTM1rJA6 zX{vNIM(tL}t-HnL@ZA(Zl`oJ+4K8H#YX9(E>Q+C(Gz0;9ZTN#zdU~b48}TzRjOvX( z%OLW@w{{9vR{IJIkRK;qSR(QwQGdr=oP3D%o}FrI9t=ElxwxSSW3#dxvi=eOQ4Tzkti5`}oHtYl8RX_bi? zKApcDcDvh{xzUB^BhZY1qC&{EXkn`(Ovmakhx>~{SUKllPfPZ)%)CtM{(t$#Z831d zeoPiGuU`wehtA=2UNQaXF!Bdq;;V2rfbVL@K~me%m#nc9%my)}Wk03H!JV(WAERPs_5_%Kr&#$xsk)P<37f57Sp>`6;d<%)@>nA#7p-PgR6*`Vq0 z#b^m1*^)$xA$W$B+xx5*+FoFHzy(Vsx;H;%*c9PBly=Z1%{?xqUTqrZ*SeLIb(C~Pk^fq0g zVSjUOCPfu{z@RjcBsPjt zaK~{^WzkCDz{7_Y3y5Rc`gH4UImG42XcnH65mIrKYbI+1aprq(dmY2WZ7`JhWLLfk`(G}4nK&;vS}nXrRa(&*K{}<`}NNcQXukBRcmwcamlR!_iWE3XA}91^l|`S zJHoks?$z^Zl7H(ip-{+ORIsPNWo+Qg#L;vYHuqgZx%-Sx=B>JJVUwaO%51SMFS#Fu z5hH2zkTc39P8-|(nd>@iy-`prGY<_>*Yw+zsSqM0r8lt0neCylS?-WonH<#P>IKu(ECsoll#G{;511;tZwXbwd|% zIgnbV(0?Xn95`T*FCjXWLM$yN8&1F5&TO4)t09)ZC3z2+{W}yC5cPJXBQ_|4>T%EM zSt)|~N4q-?B8i>2==_zW)XK&%X4<$MljV7r#woVL6oS4w0dzC1i7 zxi`3P7Z@=&>59RX-Z5B1&#C5WM$iZCI`FisBY&!3m4u7$4*jWGh_(=ENCJbLY-7Bq z>8Fylg&o2#hw{Xpj|t3&Xp6dv(Gsw~5y(3-ghJsID3Tv3xR1stB(-p(KNf9IR6C*w|dpUe=b?`)dzm z5gUFOr`%V`)7dCoHk^q&?YJ1GGa&6*?0>Tcb&@3^mvtGul~WcD5;-hvnwz#*CNfVP z%2oVOL94U$vs%x-!&2`FtgbBVo*x%1zhABOw3SAV;5!nj2+{-I_HHvMU2(FEL&Lgu!hqOoyxu~{jB{g}Gk#phs?iy24 zqtmP&$z!WGkaW?%bAk4vGps=~M1RvwoNfY<8r9V>*c+D-*f>IdwC@lj`k?hM;m^_S zcNUC2%KhOWs(j$MxYMXz$euK;{RuLF_O}wTLGs$*cfLO=+D+SIk^%-j@x%(9uajL$ zN}{?#w@s|dI0uyowkcKeI4&0ErHWcXpFx4|1r4}0LRWlc`?*1~jkL&|&3|1tWEe77 zu4Ml=f~#D#nzjeHVk@=+pUCQE?q(w%J7BAYbV$sX@OEX%bn9I!x)j(*kTD5GDw}Rg z5Bh7LGh(kVqbib}|LAbNC3J-}ml4@%y(-@40P{s}bc`scfG5$|=7rO?^i`_aCPO0N zCoK02k&EbGs+fQ(@uxM1-GAs1-@T%syzurzVc#Ey{O;@!O67ommrJbQGT1NBS&SrWo=m;f}`z_Jd}tiw~1i zKm@A+k!^8(R1lZ^a(>CMXinnEA#J0^Lt}pyE;Oz$%zi9x=HaKlr+)(0s|v-80yYx& zGM(Ou`@{Lk2(snHpof^n@NU!b42x(wvY}2z&?$#9M%2iRY@ZRqz!KO(d3bFiS3Of- zsHVFkQAGDs@3FlWoKow=S4E4RM~|NG@vJ|xBHYXXo|XU+sQhPSUi^-Yd2mM~)yK4+ z#iGG|5YUEjFhy-Od4Fy_I3du>qplf(q!s7_0^0otw~{y!x;eZt}1)$&A*jh%oG&1veHI4Ock<+%W;Q$LQ#pMN~-8aYw4kWg=K4q?WF zX@(t+thF|*@I~^iBNV&EjSuzx4CjSGldPnG<=b!7VcfMVV=7(o>yMEfgZ~T*Jqe>7 z*tPktZw|43mQbmPFjW6BxN};?9q0rYSy4Y-7Q{7={9u$zZti354Hp_)io{hXEa4aZ zcpw0mUkWrNzrzJWK_1kRESWG!a9Uq)ruC>+_qG%kp2YF-xw{lBrRh;y2$c;B`_%)avHz=T}5k7=?B22+CS z5_{O$WG6Pvx4uNPA{2(s*pNkluWBddxyCDtNF)hR5{?m{vdJepFbk0$IfUUVcBAs~ z8W%C?dw)(Y@xU4coVNfEDC>mQUO}R8UAB@9Fj1NxYOp1@TSV%S{yCNkj{yLLj?ZH9 zLb784X~*Ea#3kbMZ0t=HHhFqSXa6zki0NDe8Ih30uqiwYGhR^5cKRq)FHB zu+egCW(})@O^+~X4N_ax#2EP?$w9XBg3a+RXVHg++V4NeYVFES*4z%#AqkoRbCaNt zJ1`@>Wm@gW1+E^kr*p;NY-jxa4?kW(iFH6D6r1C{GKE3P1xGrg^h1gZC~H&NL*>YuIWXhKZI@CtKv&M9PGVpx4)d5Ga%Mz^$HWg45nIr=eD%Mb+^yLvbvA8+N)Zy;t+Y5W4$G` z7Yh-&@uB%RE_jX1FEU$mB=|a2wo4v%Bli;InSt7!sAZL-#Z5V zueY05ZN3r`17*l9>qL?zXrVtWWCG> zUbgZ_g0`mZj7d_HufXfWTC0T*ne3Nu_fp9q1y4 zr3IpoCY2Hcz3jHH%yUeqC$Wa=X$UEQo&T$ah#V(zvKcj6M2}m+T_jMEQ$*Kqp)^BQ z+KoNCWi6rj{)<4oGQq0fXCmrNT&4S5OOmdBiUeX&3qEiVF>#F{By^c{4}ZMc>3puG z#-$bye}$=aYh0-=C6{Z9K}5eEd!hEh_T|n^@|M3mBX_Xib0p9#p)(G96vr~K89!nuj@w!3w@aLc!7bQ#5^AZ3@Aad8)V&u zH{8;#A&&kqB%ww}L+5o)+kYxXx};n7BdP;P7W0RUjf)!OV7S_i#$5JYk%Pi8-0B@| zPrCIGSO}z})|O3aH|yt{jJ;+W)5#|0<_|U<(fo@zQzf5;Q&S>r)B=wTm2r7irXJQ7 z0{e8?Thk8e(I`!M8sSqlGHY|<`8dQ9a@1M~GTR3twxvPR{S+cS2Y+^4^sc{N7F?i& zQT~j7%?4<4kV6Ges5!$^TTu;XeEg(XaxHhhRp6CaCXEd+!T!O9?zdm*Y`srerT$Pw zoa?*}Rf4Gu2DKZSSmZkjEVGQ}C}`7NaesW7B84`e3P$A_|2paxdWf(R{_>ColRX?~k!warU+|@p%2l=o zuH#>b$`Q4IMo^pUT5alpQ;5{#{6FlbsRFMcAnr4lcYlX?R$9v}ZG*Hp3l#K(7cmRi z22H>da3Ww%^US2=?H4yptmC)t9*pP~GPg%0=nNqBuw6_~Wq*WgN&=xLxMM9eX6-4c zIe7^h+}y8^As{Trc-CT#w9RsWjgT#io3Bhs?f21;b)IAloy3gpoFv#4U)(rwFS!!= zQ}n2_h${hX_gAH(b=dRG5gWcg8Ho#GUevA3I3)c`K>|L&;&EH;t-2oH20=>g3F{0; z?EBOuwFG<%o`1_^`$S1L`w+L}I$*}hD#>6HMO@?NQ>@9y*XQc^gl2lc4TR~xCdw1=b`TLaV z9eWB(xCJ20S!$hWz5ZNzx5C1?sigiz%;RQU5p?3!u_K^*35bxE0$ zYbhYm0zzNrJm_i|u!kb#IRQLV1{5zRnCo+^ya;y3e3m>)2<{w5)~Egi>PAD<9#Kt2 zw%oH2n8$OM@ zOXagO?)EW?|rc+A81%00{n31*1VPvta2!90U(wdlL7l)!SsK`oubFiY=jQCq5sd(&X z{u~0i2ja+RL3+OJ;I{ElqHgaE^%2R+kRqCMRPT+>g#rk}TaFK|IdQG}p(a`GI;+7M z_3Abh4rmv4MW^-5(IH%?2=DK+8n0J`38ih*qS-e zE{_{KHjigjIbx*M@LX;%51%o*F@NexvJ1h^#GOdu4oA@hZYe{rUG2Bnm1^})Gfbr7 z9ce;~Ek|NwSXu+sByS59yIyCknyLg$M;foY;_sOy4yb|o8ODFIAL!@utr1RHpVv!Y zgY=LopQ7v0`_r9JdHvmp_39R`ermkpg^m5iHW`J-$`QQNxv_M-=2?yxw|~(^+$MS6 zM$Yo@a*6P!K>w|6w(K9TAI3PI!ycPL=^J8z7cq&x-U94mVDgvrbgXY5WU!$Q=xXWd z?*?YJHB(AYuvtssYI9FB9O-9)n(Ote!eD(n%I3n!n!9f2iVEsN5xtmm&z?NeiI5w& zDqLKljI0}{jMba752jD`7=MdAPoe#`-Dn}q+4l$-O3({Se%?V!Kx7_9dh3B`q9#le zxfDY>mBHnwI&|8{x1SekwXW;E_*frs3o)(Urs-7TzY4;Oec6_bq<>=t6#5&z;II2; zu5a-L_i{J_RYhP`yg-(^fj}@Y^vI5NXpYbfHvK6Nib#C^{Z!hTlY7N^uH@!9@oK}1 z=fOekqOg2>fH}-J-`!qOM<7tRE}qcw4u3Mz(vB3^>@XCiM>)i1{hBG@UI=b4%93a4 zNXT5hT<-PU=E&x#On)HQp1x|?aw5DSP*h5FAxBZTfN0wx$joyCtntRbAMqpFw)OD!@a>hZ2I-@fO^IPrE)Qu5`*_1QKlv1kd%0LgntPnF-CJTxvl%9R~3$?k5e7s{N;*k=usYe z_#<0qWUfI&Of9;bFVR^$pH|LX_}woz-Qq+s z{amQNXnJF4`hTr?_6%q?5Yp|1`|o0u6|PEhZHZW?*5K<`kWq$lvj1uT3^sL9Cr!)oljC{A9Kmw11$F22O*vsIpQ({Vc=+xO`5bU5E>+v)LF!B z09Ie1K%35k@J;LAx!HYLmF19x3n20v7Z@pofT<{;5P$xxP2cG4^|gmznAvmicFxfV zX_O}xmm5j4Gd2nI3MNK@=?u!S<_^Ga08{f!#5htjt$ypUP8b8e$*Nn;); z5K${NjGN}pY6u{C?U2zViO=1b+E!Ifj4?D%)4$HF6d!oC6h z8%<2z0)Jj+bKQ-swsG!TctRL^k2DKJ_~p#di%?bcj0KEEHU)K+NH*tZeDf$O3Jk?K zPVHem+O4h3FnbXSwRYdo?H&7?7!gG26J;mC~!5pL^CY`e;>BUIYDEZwtG4g z@C}E{6Sonq(BVF*);?T^#%1}e-8!3p7rgiwyz=T8CULy(g=CorFkj%cz|)2X$gvAo za(`~r{sxR_ZP|Y)+#kg$b(x7fj2d$ltxCKfqyu6RJ>cCNH1noeB1hOgkB^zJ4Q7a*C`S+({S0ztWa*V2yRRzHuO3O)7a94D2N+Brl^CgCml7L~6CVs@o@WD&?f(gYf=xro@j*<$R){fZU zWSE^mVQ>M+FP#qxvAg0*&C2V>Lv0zCA6a)lh`1VH20a<5i|3kYgY*LkkbfqdO}lj< zMp(a@lY22IDlH%zW{#&ZYgcVManSNhyonx9rq?z>%%x4h&44HbI4;EIuNoP)eY0u( zgx}dt2x7NZY2a0~DM}etxlleeR}Z=+^4}ve{Rtl!cQZIv$Q1HCS&6-sLDhK`1J7Xo^d;-M_$|G^GM)cCdhE;X`^zq8`?$e-II9AzYwyuI%;^g{BBl#(j z-Isfhjl)ouxS{P$VLwj(y;k?xu&*Ha<+7&uHMHGiIzEVT2i5b ze@~63_EEM?{EAPEFPE;SSTV9^RG*emaikzZICfmyf*eTC2~mj$-!TkmSIyp+H~(03 z{Ybi#!`je0JPkI3I)7rQUtAVP%AHr0`^?&hkZeb+o*|Ursv3ZZrRM8NUgX1#n?@B4 z4|WsECc?q53X0xA^m(5*UD6fAYNBPQYrK$Va3!`H6GLJiAlesNHQ7k|(U?FOkaaSq z?%TQ@v)TM8BA;bc!s9h*neNDJ>;Po3WYH z>wy6ZT98?V`zh&#iZcuhyFxaO8Yi%?SYqOF zXCf*i`%e0{K`j2I-6LUMMq)Rk+jUbXP?Iq?(QIG^7~nCYJd4v2eM_&S{7dH|i>HST z#WJQ=+C*S6wt#_|ixH$0;vYfZ0YSOgX>HV-?tgOBj88W@5A@2X?S9DC6v^3q7s|Hy zwRRZhxjUcux6kI1MJnX+jq^k-QxZjHd+8kjdX zv(8EE3muzsKE642<}%6>be^AQZJ{k_QjQB>f@5^TndrE3huK&1#I!t&IJdh8$~03; z+<%vU6h8pgsthqfL|*@Cwl<^eTURH69tDHQU=+4U!b2~{4Z=aL+4C4?#A*5Sty?{Y z?@%!<3YdefzqyH&xEj8fg)nT#2 zQckF{gQwaPAq%y7unO?DWds~1W+{Rf4qeyDbiefax3w5&5ULfOgAdy+Quz#yq z-sR~BTIU#9%PIX~?Cp0M)Z6gSTRK$_fIoWcMXoLgAJ7hGP->4lVnA*Sx-66vPNg?I z-BKqNhi~~i2ZGpvIh4Mm%*-%ah=-!rT4}R>fMLF!LOHPwPL{^&pA6$Adb`R!AvKV# zX%dp&*7V3C65k%*Vr{JaI(D2BLw}n@>8!e6`r=S50S|;Gb8)=Vfd^54AAl>Yf(SKb zZ5cjM+B8+2OX$sfxjDe1mw(CjI$gRX{3oSo5K~D79#a?~EXjkNk*ISMh%q9Zz2W~r zM&YjS*jQYQci#E4X;+#Es$}mfsIdcv2UNHrw@;nWV7_V)++;F#_b0Q70DtYPsXF!T zU-!UD5$aY=^d8X~ztlDvyNl~Q)W`+p5l7pGKsvSubF9Rgp+9Hy35f$H_{#oDWj1{w zI7jdD(JtBS^ z$_+4R&=Md))+D_(j!d?FynpA04JD4YAIS>un5St96oNtz{dTZtg&-({G9E-c+KS(o znMRpY6YkGTy&FZ8d|}8Ks1hLU(Ibw~4ngP4_*0Z0&_Q>r^qZKb!J6FikLo@f*JX{T zkC$X-EJt&>V6s7{8+FZRL&21*R(a=Ys_EClowpMmy&q~uTmgZh<$wOux(B5~gCu{?l+}azgr_zsZ7CH-AHbdH@w4?`5PEiZ zR}cMvQtx?m<}}=T735dm#7_HU>Q5PCk$ye~7pyVakiX1D5_d#C_+GNv`M;oi?$?!F z+sNS#yC4cr2s&?tXz-j|Wa;Kw1a2vg?@^M56qj$qhm5qjDzJ@}Kq z%!6Wi1Ob=ZzC48PjI%N4gnsgIwLO>`WOaXKRJLmd9xvkMTiPMsl;1p0)Vm48{>->% z_<*7TL!SU+5O$VBN;;JnsTJ#!OQ21LHRlaQ`MYE+tyST1VLP@PHt;g$FR1f3%To3P zYQn@sN_}Szd4D2*Z1X?k__$u=nH)ex=S|LLh}D!I#`3_k#B%C*`*5z;ozN+TB@Nhx z)Z$uQFo6d3r-KBCKPl6Ud-Rz{5a;QW%kf?|N%mqQtO);j(-=V*71(wBnJoY1r zrch$6m$oxn$c6cw%*k=ci7FL2roKHUFJ&9w-KFZ}{C@?u;@V*=#HGXX)-|RJ&$W$W zuCgpe{zt-~`jT<_h0IN0Wk@q6($|d)o2eEunW28T>gi|^Xi>zmY}xc&egMSG_$Ji1 zKfN!+*lH-vc~*C>__@LUse79Oc;Y@)*tRY%pM>BKnAd(0^I82hymqWbEr$*Gd+#N8kz~6Ty?_)?n@Q#LRylryJ$YW0rGLrYD{?~Og%Y%r5Ap8{z4{_j%lspm zVxmtn^E<2NOS<$@lm^4QIVvhr^T?znIZQp&h!dG$!ozm7av5`{?I@WUmV+l7S(S92 z@q}F^O9G2^uxKhmK&c5puABCJ-X32ca7Ae)2$)lXOpt(ylErzpRVy(mS*>vKy`1_& zAAc~`q7oCuM8IhE`hFsk&a=cZ42MrFo^$xZszu~BY&o5{l@~|SZNoj%&XkjMKi9QC%W0E9)dDL ztP;>1{@U+jb}(DwFT!)iV{Do`N7zwNcD5Qfq?|AnZN3Pn5m@4~n41TAtqP_n4o1tm zrQK>@9BsX)bl~>rx^;0a2?2+JN@|8iMv)Sih!T%~PWG6W6sVm__%Zm=k!6;1n}6GR zD1E=c2q!02Lvh`!y{$WF9L+zaJH+Lwr6**FThbP-1a#PvOoyWDN7Fy&8KOvDD#V7{ z@qLdjRE9{wj}}#~Md#z{w~2=cjxxD4koVXmVNsVq*7i4hjJ0u3W`^&;9t8dM=2kv= zzxAH2mqx7V6U3IaasVeivIECZAb-mBr5Vw}Pif)|s?}GV4H3)LkyY(WIJ02YGu+lN z7&MV95WLa!+;;hgP^~2JSJwY)*0%jK4-@Vk9c9cmDOK5a`}gDD!>x=5-isN25JAkb z9oWz^ihmx{jbg{g3p?3E^(dc&|J63{DT7^K8m;{!K%64M2KSN(p}r(PPJiyL+1sZ^ z|6Y=lXR2ICBGP~v#l0j*8h*D?>x;5xDKX`_F!b}iaLiQu+jwC*em7J#clO1|w=w{N^X+H?euT&^?#exwv?*2PEV`~t8hlo{r&jlq|nC{VD??`fexUhwJNh8 z6Q}R{VSs*e9-`9i2xF|0_K4A}zz(@R0Sm1pm{fT#WV0i&`16{0{uUCwQFjZ!z=zeI z-o+kJdY)49g@4fQZ^$?K4-$gk=7d61IQ`8O1qhq|P5SWnHxxQDw0}>HTUxfPrynWw+T|G+P@icmlOx;F@fPADAY)jtvVT@?F zz8p!Y!Bz)fEF)&MC4c!=Kx&{Uv(I)h0z5)0hv$hv%e4jJj0QAY`3vQI%dp4aIZ{Tm ze8YiihV^r^lJ~UnwDF-k%Mg{vdoodY47H;r7Te+?Nxo5%?oSSOkT|aE*q{w7ZylLZ zaCBG9#X zXYhPB*UY%ye?+z^I1r?5YR@vM7GhLD z(;C#U%LptS#(z)-({IVC_y;XY<&z1JHn#myb1b|}_Qwmg<*{ZE9C*-8y|r#`aCQ^D z5j%p89Ud6WL;Ew8L`ZldND8lm*MVMv2F0x5dL-I4obeK~&S} zX8O|l-gqkavtEokRIhNac(8`j{}r;h($Zy&19l+5Un!xszUL3BN276vW*Y(w0@hh> z72<=Hgn#QLm)hiWQ`px^ES+Dr_YE(Qs?0EbNJcH=b^?=o%1}y~wGch(*kZ{sUIX6HKnzW_nmnXbK?c;eT>MK5L5l0fmdJeR&=qF@pffnB>Dx z0gv5ZK~)CD$!?1<-=ctL9iCvY(g?q3*Gdwi{+KtOa+*;t3It~5Qob|Zk{cCEpLq{v zN`_SD9~}7ctNy#S!XD~(^G%d?!5Q9yLPni`AyaQ(DJsZEv$w27gR7~sv%EScs5_}~ zkAKQh7ml=%O4<&1A(0(R#>$$3dJDP#0xH)G4HKvr8!T=Pym5{&8cgK^!4jF%kH9p{ zXIO?Ze_*YA!N0URowtgE73}IdM9w>3eAr!VQIrFWADXlPSwN=0w3r&+$g%%~ghf&* z3b!KlqEQ#FZ%E`WV6HhM0xhr_)ZlQ0@p9l9{@#D*9mkTn)7(Kqq^d8kGyhzAf zHtyakBx1wWDYk6r!2!J|jS0#&xqkJs#%g<;s_m19+1)&MO&R2>;bfuxxPq!r5W(JC zq-R-@DDGP=@HZ+ro$@-LGP15$))k|{ndj8Zyn_Bds3M5z%4hy{q)z|wo(ezqj&*-q z@>hSF7j5O}9R@vGL$p(5Q(|N!I7On5-ux1eHo;)^i-z38%h%)gb-(r3f)g*@UjF(= zWC7EugXKF1A5kbjS)s1zINz~JU;yL2J6y&0?H6pKb6$9pcD7_v`v{p8WGD60tMI{O z4INZMhs_nRIlQoOBO}(i87c3djEb-ncLIN<>ZTwXUfyUI4Z8{S)Rwm3Z+BS=@B@k9 zV28zXn}>AKCy_e^Xd}I#h&k6DX;PrqCBp%~MoIuAykp^=F@1*3MxY$1)2VMTeh|KZ zjfcX4NKpE_w%AF2bViFpm2e)!6~Ze%T^qVK*;hUiB!B~5NRO@z}1q(G9Z zdLOkOA|=#qSZaqwSM`lX2;e$S3{)H?0e9?JGGJ}Zx{U<+*c;i};W!|75I=^EL-Umr z6r)H_&Gc_KYwWErqvL(2cmuZw=pbdv$%&i-g_C&yxK}{ z9Z!$JKYRxYjgTh=IMwYe`kfzdvgRJ`m%346P_akxB8;e4Erv$jpG1~uRG1v3+c-HA zo$Eo9cRT9Srj8<`k{;FE(3O9Yi!|TAYoVCj9-nb1d~BBW{rxQFf0+U}r%P`Lbs50( z#C)5*(SpOptiaBKb-2Dt5>Q8Q9r$@c_>3uv_wfkiEkoDvDG=^4-eRFN*9^*4#kkZ9 z{bee6*b5iFnfaGs11St6&HWVID<+`=mHsV*l*7CalMB*GoO62SqXmE6oq|WWRca81 zzl}AyT%xddBmV^`aV_a#M+`ch&D=Qt&h+XD0IdTz67i06Ed@je+7TZ<)gYxS+@x;49YQU1*AEYe$I2^2vrH&D&3K3Lz2!g2G(8` zNVQ7sh8d}Ku#0yXWsbamzj;QHYqx1MkTiwW<>iGvQn5*r+c%bs++ysSmh_dr%44@` z2$>}b1=4ema3?-QrE=98-O_cQHt{=JE$*COxK$5HqLQ$?=hlD9KWQ4LzQ9^zwsI&s zO^7;hc{v>EXaJAvhv}ubk~6P#41>p&%~|mypIbj}4I3^HgUhEFI#zb8fDONxN_Dq> zhq5C#5a2s*KmbA`CkI-1o)0p=)x)PmE8kU$1138!NJhI#oUnxS!g@HBpgxHKw13G@ z&`=0MzI7gjDII@TKna@kG7imcV|Sk!awq8XFq?siVNq3VC&xm+*NnE$)Sv_it4DawtG z9`hwE<#DZu+!NnZBT7FZGOY|&;biDW6)rCUiEO|qeq$ST-oKU>#;DF@KeTx5HUK;S zG!e}GI8rj{7;mWeWo4QX9Tm6s{Aj}xOQh!=B;hVEGWRKCQ@#}wQGS=MCo^EVp+4L>+C;MsLcS8EL zVsmLqldXGKQq~Fw0OYB>%fK*`FR`aJ{)FJQ{{@A3TQT8X1YG~E;BqJIMp*4O|2UKf zGT{&b{cE;C^1eM_Wpk#7(E%fg8@Ir~{$ipeVjeSiyR^_UO|Y0Q#>Jy+5Wcr}2apNP zcQtZOITJasoGW4H>6@;|8{XW{%SPZO$r5AZoNOGSJpFtKcE%roCd#5aquag0EvUX*?gnV>gVRk z=_i3maFRYaEJwYV+2UKv&?Qek{}0=tzonCV=^vL`{sIe^zMKLK12Q);m++(k6$LRf zH8D7o5&I{9t$1T}B;1yEM;&!+S8Ut1ZKq;&jE?P&(XrF9ZFX$iw)y3K@7%ew?#!?G z=0~knXXDw=-p@X#)+$m$1!Y=66FVcIn4PT?Eh8NR7eG}>UBS@W+R((pPKH*<&e{a< zX=a5XB^7o68ai3n*@_rC0l5I`Kofun&=|nP1YqQUOyE|BznL7a}J~1e% zscHUY`6~oqFnb4!ziBu-TG*QXivbP5 z0cd9EU}6n)bo_+*#QtkK|LPO)U%EH6x3_lxJKOH>sQ=_(;p7OkHl>4MWcsXW?DSdN z%)%Ci{;yS$v^BK@Ff#nZZsKhJPoE3W;qL)a{IxTbpCk-T>};*w0VY6G7b^RJWczrl#w8rzxtwJXX_hPEbupX>FX zhQHj#&JGTrs{VcBKb!vN`R_#s0^NYdFiZ1x#@vCHDZf&ksxYz!Mn$xHx){L*g6xZG zRq}IvE9^RbQbIR5OATHtgXrqUx!#-I=Z@{)cBQEHhPu$L$vcyP=Q+4u#FX8+NNZ%R z?9_Yy^m;{bsVC}@o)@z+8{k@hYz%69Tce6fdWElF@y1)39iT2AD1C`ta(z)r?(N~d zjgxC)(Ap5|z93iS9iNcJA3ofZ_x%|h=s7^PlUk`LSqmpKBKKTZW{e3j^DKjs7U1a}4$^9h2!+b%F`1Ujclbg;AO?UIfygbNIBqv)_o#E?y zAQWEOpX}J+AP1;_?G^;_*MXRgL3{$`(>(QZ-kg`mlm@HzLSx&gv2`2<@M3mY{WP0#+;UUgryRN|i)ZsK z|2T8_Dfv9^7RaTojUb-~^!u~S#}T22?(}jtzQutshZ3ZJL%ZcVX+>eZM8_#Mx=rTe zr_5HsAl2>=Ml2E*x7qViu4lx=hof)^E^2oJnL}I-DJ+mIag1k{Es$%75{is#Q^iP1 z+wLu(G%r9S(z`0A(XW7;Z%l>!a(`FhEe->@WeT_0o!#0>3u7fB>)aFzjv7&@ft7x| z$wY0Fa;lhrDf>p=d=!LzH-3jI9#?5eg}@TEz=KDOD^x@`o* z8&Q^jNw@SrlgECLa(`Em$umRtyno77c+eRP<1||(vaM-0A$OOro`%bi*V`Yz9fl;s zex-)7)84Qi{1GkOr3}zPLK`iv&-c}&`02AD9oI>$yMQx)k1buCjwYUup{BL0 zfb^cj<@65Wvm1)Bo%?{-u){r9>8bbzwo{0Ig{|no{N*^sF(K{`{(dfFHAei-7-?caT$m z+`IaY9d2sc)@JKVl|kd4SEU&RtM^J3tiiT*IR=!q#CYC^g|3#QcVL|%R=NE)vqCqQ z!u=E?6L&P3C+d?P@6v>;$u7>uCeQc%;ASgXsqvx5zSp)*c^=?#Y-pmOn3pKFUdia? z$fDd^X17G8kZ9+D?>2WW;j$`ioBU3H_>C7jlYVnt#(5-#gp-bR+4t~q9ZUy!J|2gv znCcYB@8BuUblB$R^h2i18pSmb0Tk}%Cxr~GoZ3#gM-6!*zKCRoo$lFJJw7T+lQ3uX z)4Ny9sx21_DSQ$B4PDTorYF0lK5oMK)>y9tESu4?rO1ruJ0+bOnIx21MQogZ`X%at z-VaAIr`$Fn>7Zn0mT>DnL79B7^up@;b~DEx3k2KUe1elQpePgH{`|~Mj?X(*RU$L9 z>xX6li9T66TTNx?yMj9NT`?XfsvTl;FG;I1B2V1WXS*#pk^yJP7J%nl8{O+LsI7SF z3_*^FK<=pthk#XR7aI*&TVNW0IyP-FYL<>y%K@h^K;xSe(TJDB&CN-0G}n@a| zzhIqI{e>R9ztCd~_v3vvJ<>Vxa<}j@2+eQh$}zJ&eq4DYNEwr`hfj8YYkrH--!iF5 zz$8Ut7Q!hWJJ;<2y@VlH!QIR97(2sbyR5!!daqg=f^>R4lk!AG5}e|5&waCxw7yJU znNI!2J|gG$pvbXgVM2vUiW{o$X;-1<6(DZUqeZTUp9U$pigS)gwc-v@crA;!)Etv# z(09ZiJIO5`Z02W;!&*6io1+tF2SJHuuGi z#UvgI%KXk!3-$owXnBX0hexd{2trTCRs*$fB9Ld%I~qE2b3O>f%1R9tN- zmTckkS0ZS_b1y0-cyzwS*9GLIx6y$kN&97Uyn^rojSh&+iSGSZf|UA>BW2*(87(?16CbN0RFz2|-!pk;O58ukY!F-P`) zC_Me%)i7ExuBg(KZ|4APKg3DB52C>BQAxthDdakmVqht^f%EjeMENbw(!&H4L4D_G zF2Ms@ms=c9oHDSLgSJAx$$M8{562v%O%`(zfq2{O5`j9nz$J7~ZbXnY$J2Th<74}1 zb>0n_?fdBpX&Tiy>Z(#7Ca4rpu|>?SF0+B zQ*)!|&-V!z@6c4P!@8II0Le`C0G)e@P!`MMYalb3{bv6rT0!GL2GA-wgQX_prA(3< z1byMj|6`RMG5h@0#ZpuGflW&jzx~Z+F)_p7|=Pi z<0VqydqR6U{bH&ioUTsK?rpq(VOo=rz9Aq#>@}bUj#eh*G{Z6>!*o7Ek*{VN^l`7J#_Cdbdeb*`=AmsBJ+>O{W_@2v)fm)eig)7F!iRx*xFHmiEiS$+qkI*$JIigR*SE6js)pGJ`fiw_Qg80NxbOJIiAkEDFoq@B2 zyc&)oRF%?jKx#lL<;!IqV;it#MSUi#RWNvbt?eXTnU+QUsRIiCELxqV2gPBRL|^(W zXtGxpBWAa5=}^ykfp=^sZ|+Q)-4oJX{h0Go40e)CIW;$bxRhg!)As9f%rHhtMiv=# z-s`B#-I)w{%svZ4+xd@1mUJVR!PmB}JOTq4LIjQsO`RqiG_^L27EqzcbX?V89Q6o; zD(^EteIauLDcK3F$?(jXU3wNf>jk?LF<4n^u*M!KfnnrFOG(=wt{7b3mSIQ5%z22D zzl@1=qL~$c!qCgGQw5P@+Wzh``Hij3O;TEU1U9&jA zEk8~hoFwga16NH9Q*v!)?#npUzN4KMCBi7Z;wCv6r>kNO|wm>fd56Xm3NiV z;l1D|2ZZDn=N*iK&2O9`$Q;&%3O)Aa^~d?V-;x-AS5+Z^F+8*s4_EZoSHKBx6U6YJ zUn{=rafYYJ$h-s$PTog;Y&2~2r-%R#UAbSVQ3n|44PXA-xT1esuS z3#EmBy4krVZe|Ykym_0`y*TdSF17eDk+xE1zTV(HXK@&j8LX5#{rnk1FwJPJ);saF z1XomiCx%zRL7gs98P|C0z%oy6v&?}l{saz^S}Tns=jP`@$}bW8fHCLflug!qABIQr z-q-e566#!9RP`?uhb^e1`7aMNLL;Z?`7SGeB!Uyu6pE%+v9PDMqT2<|Gt0^`Klu=6 zH3mTt5v$*@VaO!4Cm?d;a?Q}{Feg>RT4N5l1n^-~*&ihW@8@ynZeKSmUGl@2kBG7^ zTO5e%D%~0YuLBO3ymkS9;5_rXd-WQf_~RgCsXQ$?AGKwRwVqCwgp!b%Sz+2+5{ajO zs+rju8DzMmrno*R!1Lx&Iw-QOfi|Bl&8fQ~f$3PM?MqVa2W5I$Jlr zKQ7A5DqedCjeIffHLF@3+h7c|`G`G#=DSc36m&>1Az}wqqtgg&1}n#Lb-esLJqER> z`gCd3DP8W3NHfggYT1^BLI){FDqQ*dd$(}|*T$9VSie>GTh&PwsEbjn#9~piw&}Ef z>qE`mwy*9(|5#e7eCdE-ihA0Wf4E|Ammx9S(HQ(BLpeQvea1YF zdLjKQ6Bn!sHvWz|op+?oBrK+1mWra82l-#lxSsPVW0su2-PTk$@!?-~gBF@S zRmEztHCj!~&dkY7XL*<|Vzg6#`@%Czu1x+|pb@~KyVU}UHCZzsQ?ds_vsL8A-!X11 zs@}k_UkO2_`eD-R6S~xBGy52_^RH9~NIzJRZM;l}*DAaQIHIL=qw#Hv$&p|XKd#Oqc^YMJ1PZuMDm> zUx<)U8T8d_|LpnL*=*XjMj*azMyifYiKi|ewNnXp$f}ceaS{VWwMjHmynfb+SaNnH zUH5_m4_s{&!1MQCG`z~NFxqkm-pTqfmR8WH64W#~UuJE%c=vOEtm(C3HwXAxDY4FD zN(kIY=`L7)W28;rGWeQ5JM4NJVvmJ$_$;DW{s__x(Gntw@7=D)^e$9ssTWEifXwjd zmad=m`<=fjCa-j3)8)}J^FUf;AD&{XOu$Ev%JD&yGSRU#)#MR1h&Lb5ORzW4`rAKz zM}I>QSA#~#C&UPU%4VXrpe7#nLOy+6txYl=RG8#DvTC_{@+=ugQ8#Usu`h~GlA4)d zcl|;posBsA7zIw%{FV z#5egRt}>`6Q!iFSGNNm4d4|w~{bJJP@^I)+1o`{U$68d=n=nt&(q z7(h9e4!Ve1S*#87IX1&3K3g?7LXgGjL1I+;!d=o}GXJpDI4%U|7wv_xFI|&Js+72N zet?N+*1l_h*Nv>0b#N+Ad+=4J4+lPH`E$JU>x8a3X(Hd7?B}iEgOdn10I_R~jPc5U z;pS79iGa3%7%F>6)2UiRs4;I1(a*AZtp|6wuxtyL?g4@g|Tc#qxTC)9Orh1b3wRbRd-`mWgck{oj{mI z7SdsVibV&bk!>uQ)#l8yNM&V4k#yEcp*)I*G!jL^JTWx>+XzJKt!2fJ9WKy=et}$t zzHecQ3hg>9OafKDe4v&wG>Ox_z)1Vn^Ta`=*&t@5pMl;aKGM8qT*8S__GF|o1&>aS z_n9crh_kz+PFJEgrqVllMiq2^h?hjK@a0c`lN^%G;~?q^V1B>aQFoF7!+(l~9?7X? zSl-AW!b^7aZ1xtftE(8pBQxt80k+q{vkTB>n0UCVn)lAbWC2+?(0dm|2$WE=i`J_R zo+Tq(FuKzDg^@7{zqYJ@Wk4l>?cH*-&hi)Os(h((L+-cOjbzbiNHS^9Um2>#pO>2lUas6OXPxV-WZ;N&rMmR3iQrMq ziKjDRx!AYTbcWL8@Yf5F!QBIHIXpG+ci{DsF?w_%@`>-mr9-LIx4Vb<_-i?BOL>_U z4rpk6j4-tve<){yoI~hJa8LzN(7SJcUFN~^ryL3s#CKVSc=nrb6yh}GOlshnYft$D z5`U$FitAY)4KgupQJ=|}>5H+S!6MjmLeh;nvZ-p8vwMk&{Q*PjM43myRj)-(2`boW z!tS5Bp@hY&>>x3jMvbdu{%P`yC~@hPi@<8?O~Io23fMYfBdrA0y#c&K^lfV z1<~CP-cUw5!=N$@Q8Zp0+h*~9#$>|lO*%= zWVw}tXOj-9?4?6J^=z{ap39-iACP}c8*o4{ePbCk%kQ1lB0FW#M@E@qAG?yEM2T0v zqz7sIT)xb}>^+&M0R4fhQJC@pj{gg1PSqZ3?B@V{;PVKd#+v?ZF5cCDLKPJ}w`xSu zEwX7}w_;q#Nq$r~QJ2~8=G+XlR#Ro6(}3+k%(%SvWb8lXq8UZHF9eOv)8D4r$u48@ zb+XJOT}PCb6GZMIluC>ZdVXj+uI4IoAQdWJN<223>S#2%PP2)|-KB6=js#f@SDOI5 zuqzdi+v#EW%W;D{Vj9nX*!d*P90W}^R?OjA5%r&nR??>_o*^|4a{HV1Qu?;kLqwi? zyv%jI)#4SzJF=QaBC2pP!H?EB0S9)ebCO7%s-Ej57zRrjBoi2!yo=KJxU)`BPr#DjfC%HK{GnV`bOz~y~_s^e6N8m8dIhOr!hu>CFhHM zW-Bo08wYKERa%>WhH{fH6~P9opk#Y4^*B?8yq7rJm&L>B3m_K0@IXjL$*~uRf#sU@ zvqUB{Kw~7J=c_m!?yZ3zYm}_ir%H8h0NbU<=liN61hEizmu~8Y1Kb--I36AX zSd@~;F6K;sR0&cStHCumekVUJtKafJu1D32WnPNDtDU}H)?IKDJ%|k{=Hv2@@<}ty z44#0U`VSCDyJNp02&M6TUF8FKi5FcjgeeridoT;aM1gLfIL;o-Ic8gi`r3&ZR+Vu4 zFk$b=XPpp6yiK_>X3j>Ip^1?~H2EdpSjBGt(_aLCmmmj%U|K_2Kk8QRaYK85Eow$< z=eVmQv+*|1+iVa#f45J)i0%g5x1Hhc7hMbYkLTj_O%$URR?``Nq6ZZAxMzdRU_hb1 z)NhYyv?qep68#2HSZI6y16Jrpgl{Gm(vF??XEyCXJ}(IE&^XanQ$w>X?U$eVmhcK7JFKqB1r8BnEyJu!f=3L_hS?)T8{L;#SdVM{S^J*wO`_Y| zeCWPaUrv6mhQPEQgSVFcj@ZPj*&{0x%G_&zI<(@CD^M0-=%{AfUZ2F#Xfl_|9voZ# zs$`4VlR&s4e=+xCx~kCuzml4;45KaYjt|S!Q!1-wb7G3tQF6yU*Oaa<&l~B?YwXLf z+Jo?VYCiy)^RWTvVR{dYuhr3ETSXHQ?QihmLIn8?mUGBiKN+uD1u$i_TObn^PWUFI<;d|>i3l|QNVhyVz9Uf?? zhboVt`B@S91l()0G_?IKp>fW8`fFQ8!fCS##W7eA_3GK%?CA8gN z@aQztehK9A66p6JL_L$346g6T)>Bs3tTO-tUp`3i$XmCCbp zr*p4x@xqX>y>UHxfyxzbBs@xgvzv7O`T2~{zP{LEoW>&|tXc@*j&mtI!Qb29`|hNE zdH5&|%w$wgV$paJGtBEFM~c@-;5fF&hBqTD^kabObtGR~!D=M)mDF!eAuSyb6EXkx zaa;m*sD!pKFLl1TI;n-#T{DDFe4>b8jE-VTnwYO(+QYu6+s_lbhbz zm`dZ9fyoha_eS_8(5(sG0(yw-iDzPVUW;{%SHL?H;!?Y*9geCRi(Pj2qXt(4<>CZ= zs5WNmT+=oMQ9vmHhPY>ceuC@6bZdrY(ZRGB4t{~#)-Kj1@wpTMyskb%INB~bFhn|k7xYd2-7`R zQD$vgkAty0od{Ws3qKPdvuB9@`0dne8aEQm=K}JoMWajL%xkKDxpbx6o5=rg(g@#q z=x=kt9xjU(y|F00VqC#6W{HE{q}?|p1*9Lie0@C@aZ(Q=yZ(8%&5qRhMtsR}UVVDL z&1DlMm)e(Jio+p<7Z0WbNx^0~HTKdgqY;?|Cmchp@Kd9vu&D`4nfQXhL^nGnQuPh)mn@q;i;~o-+I&HRS_5kNsy7L#_6=?a*nMNI#yK6lY zUm3H&sI=s1SGn7{7ilb=(fn9$VP>}S1p#`bFMeR*iPQ&w2KS-{cd)3oT{pEK)lUm` zn5F@v4ZgN>+`o#f{aueiQ)fSX+TOyErM5@7$?XQSxixtRiThFN08|XJ00?RyB#lA!(@+^W7O(4thbP{DQza948kJ~-8s-_lauW(2A zQ8Pxbx>)VIQ%(p9jVVX7*x-Oc*#uv(teM;LRa0VxI?~X&eh^x2lcMJ3o*ig+X&^Y) zwl5CMW^v7Tky+efEQrFtq=T)GgT3&^TgvYQ4fNlC>e(d}d;{rqOdJxEXwkm^`L{YW$st-i>kFEW>I$L@Z`qRcA1k zF7z{hgpke=7aso!<_aDUzXJ(pV2ULkRLBwT4Yk!1Rmiv!^x_nyt~rW~+2kuXyd?V* zu7D3_?s{kBawT_%#`YZo5Fg9j$lCI}=W>x;8^r0`-sA#ftFXZqG;&eS7 zjqvD1hhl^Wm>=R`AAX3;oPDrp#cHAhY~!|nle&npyINJFyT`6oQA>b0NYL68?(cPK z77fDmL^+ZS4EuOMk7ILJ>@d)PFpr9dmJ{>HdQjce1QonA$3NWkMf)xZdTMdZ z3aw?|9>!6wJbB>X+TSVM)YH=L9@-JzdhLCMN-GfdoASYG4Ae%?t`j;Hgv!S*t19V# zSq~aPDcfYI)%d@6o=J$7_a&Z7TVLLpulS`gX~(mmls1|jz4x~13AWjr#&jS zl1q|)g!x;KY)O%DMfz_$WoN%qcjvKGEDJ_7L$lGPUCC6!R+x4b8_m~vBOs}ioWdn` z^t5FrQ_MH@wc0+L(5Cr>LYhe(o(!MX7*o|qT5he}~ z;9d7@7QJDj%*|`I30DPP&9laol5CP1NQ>*5;HKdfPvL0aBzQZ712?6A;p|R_o-0X= zVxszK)~uCUl-vY;j}|fP5Iy?E44l<1qja94igOomP!lR-VNSOy0# z#qn>s77Mk#DyKDxjKT6ulj$dVH0Jp3v{T(+C=$X%;;k9J5ENUVLeV!tuSzolL+(=& zPS%)DBe*f|o3MsoXWeFh$n=)}E3!=Z;zT`|BZk#s0A+Nbac9V3TJ#SS04sH`dz51- zJNvMT%G>%odxml>vwJhSA;x|)1>UoIn%ZDWWcZ{9lpy9F*~d!-;1+5${(=htnu-z=W8ZV%hAlc zt}^lpqqu{A*PEYz1)>frMf8ofCZh3a_-S&{_Ne13Od4R!`s?EAF=SpCj@X7Ii?b3M zhTwjjo!7If{dOL=@b-n4P_9Yq2#osqwM&R;L!?&QFj+;#(Z~*5R8}#Wyx1>>?T6!) zHj(irl|EyByfWa)L5$`^IUcINfIC>NQycfY$i{nR4Ndod;Hp}n23a-={lp@)Cafw> zXVLr~1Vt~6vI&` zVZ6>3VbBQc?seqKO-Jw!1Fs;*7U?@@LU#p?8e3pWVPaU2X#v^}`JhsqN07&i0QAy( zehKZBzc+7xWtQ1qlcPgHdz)qjD*CjU7yL{@x_a7g*uhlL9vWe^Y%OkLGA)DG5P{M%-CG%<9bS#Je^o3||Smp9K zh*ye#^E}}dBMr|)HRx|lR`wL-f0uA?7`C{M-4tuaibZGtHYHe@k+*o7i z-Z^Pa6C2P(3CHMtk6swiwy^y1(ywS}W=LEVMikCDw8|l22hB$~f+TfI_eFMM^GkN= zE>7uv@z=;7rFsXW2l%A^YwdF3A|N#3Lm0__?w0({jTzgAJ=ttu=HvG>cMO6s4%;r0 zqvs2+pCSzeAdAG2bRdr4JEuX-&J#rXR2>=-j~W@PHlG22oSjB2iU1AS9M^^7Z^amo ztp?aR5HY#U`-m^8GNao0)ErdB>H>s9RBBuX7jV|uYx%F2FP^(ncy12_dTg}9jnuV& zSGRm@?Q9abV$@80RT(phX0yU;WOyl5@nXu_)n;|?_?3TyB9=aE_vAjTO z?PpxqT~CjYvRP2MK|P@Tk=@AXc(Q0)aj+aBhAKtDWXck zo1S6WaV`oQMtF0Z#P9Y;^S^6mHMV&* zpDpXs{l<|r!5gW?3TxLtf>ru|z2B&GPC5n;I@2DUSnDpz{fd z;mJCVu*omv1U39V4$U6mj(dHQN3*PieQ;z+L+fV|Fax1BARDh@Ny(|DEm?Tfkmn+U zOD$E8E2zm@EN;cbs`wjOvEEEiWzfc%5jf2pUI#4h>uuD}JO}Dz2Baf@jes~6wng)3 z$a~AY(XH4#51YXh3k~%dJqA_*4hftp+xW{zm);ViwJ?nRPvUez2c8CIN1)W`SQAK1 ziz7(V7muaPd3!3x^_qhs#&&8UqB~)xaT9dhrq<8h^ipL}G&1)A>)El3LgmZ2mGO zut*;$26lC13akXHQVgX%1gVt5-kEJIH4Q)`8l55Lu$JK(xHzliLBO$C6kcM1MWJ1>B$LQz+LdS*O2?B zS3NM&V87*RG_N2cdSc9O;$D9*<0|=nTye7zW&=~7U?~J* z!f<+!Q7^FTz2}&JZ05_R7tfg0K^s_SN^_J|WP~CgK1a zs5lwFLGr>d;33Dpi~+!3l_*|~=AgxMGJrwsDjwpAv+Aru|`BjWAOW21F7Sk4bR*gU9>ha+Yf~VJ+BMk6S>^( z09pGqT%aR=NOcD8W+(Qn!}nYg53Ab|(1#6m4wEe;bgT^wA#6)YGAt~?JNSt=tMpi! z-jZD*T1dup`@1*|H})GC-NNVo;K8@I23f^`4R+m7#k0Q1FY2usFu*9{!PNT>s;%0K z2=hzItE!SXRt_l#m{EV4r1SjX5>GN9*VLzbb$S_z8_K(6`?=mMA6DK85S@e?&lU*1WV z{~v)1!50c;Ze(+Ga%Ev{3T19&Z(?c+H!zn^{sJKdF*qjBPAU0J4@QK#&uV24H6A2(bB&1;E4(WNP_OX-g@N~8?a{ec`ljUDGz|QP%q^X^W z%ReRk>-!7y*XwL#3338B1Kpkff5~MG1ejVn+1nU-{LTFr%-+%RUm7k>mLT*0Vn7dY z1ezN;n%V%Joc_Z6#r~%||5Yd8f2rQc-rmOJ-`#fqM*U9?md;K<8#6`(7S_KxO`QMc zHn#*JF#U5>q(NqO02b!|u$#Kr|EJFt==g7gsQ)=LG=E7Lnc9JDJOHLZe=`Ioc{}I7 zDFM{~cPcafzZ3cYfyDn$1pa>_@Bcq>|GP&2%Mkzno#+1!E#YEgBX492{C5-JKkpcT zEa0C@2K2v08`)agc>JH@|9hkc@IOfYA7P}OjsCVm7-are4rWH?|1erQNm#lAO%*Mj zO)LOrMmB%@^sikFWD0b&f3XAs|LXZ~D*+5F%*_AIr)ptoVh#GI@f`o*0)kBcJNLg5 z{mYz5RZ&Y=L7wh^zf=E>Q~ayFv#N*vUuyrO6gfN7|GD@FMMT8T9pJ^l^6eXdft8Ex z@5r&T0Jz!NeEts^{{>?CueF?!v!kUuK<97S%m6b$%)c!E7XLrK|61w&H-8v$kcpk? zKc_{-*$8C%_kjIR!#{2l7e~jxy8b)!e~bRl^}k0Q2y_RUAgnCfnehIwO3g@fuEEV2 z92e8+>tTT$47M++S1ruH4nzdf#`tY7>FLp0gW<_LHB zNaIiDn(vQA{$P*dYm!nIgWZAF0ESUhaB@nSaP;^<^?PJ!aG?7dx_6I&E;|OEg4YPw zH|c~V(b>b$@vh$F1Nz04BlgKSj;TZAS8JN*MN}P``KGrSeTVtW!-^}L$Z zjFZAF(1`Py+&Y-OtrfR_nO_}nGEeA&GI5WQQW2gJsh!lLM2@9ZJQv{JNM{V6RMkdv z``MYVUkm3zzDArrIe)5BHw6#TMbHeb)Mq}TSq1;R>bVawXTcS(-y^>;=Ev1Pev#bi=GU|v5;)l z3Z#0DCg8e$-#jhn8(V)F)>x@6ePRY^h6};E__}&@#PSFu|9=&V9eVJa*NE@~X(-GP zl>c3H;Y}=GzeUyy3RleCa>g=Eeq9H8>U0Wv-$AuIu1$;4Srvo0bHD?VDrxK|$MtHX zK8q*+=y=OLkg;aZFbSn-Warp$yft|rg&wPRr^hBxx((^$-u}`)eQ&yoOzF^313gNH zNMB9)#zyT@>3`d4GmZkltEX}6n}Sj{hFAk{k{Ae~)lg6VNLp&Lz^nL;u61i^l58{U z*gu}TY)!o2Zk%}9VCx4AM2NV3BPUZSuTw_TzY`l75 zb?UX}*Ut=;-R@JfagkA^hu^gvTQM8lqFO7n$Qj|x%|NWLBLB9t)e*sC7Ov6Bw}$c! znSp}FUUzHi@Cf)}ML2r7VU)6|OPc!{^T|z;X&yd=EF>8wYx~mY#M}vOAR`X)j-w=3 z=?%_let(%38rFrhJ%TCweCJyZh3Ivu(thXf)XTH|;%}vioN%z?W7%A)H?G*e))IyR zqZhnIW$6Db3sto6>eD%;B~UicYXS9m9er;KzFR$vYK};N?pK8tNfHTP4VT2xp=f4rfXrIAz8Fc zkbj}rF8n~m_3dZYT?o7qm7gvOLMPs8u-1|Z-8>ONV1A_3uDxk-!sBn!Dz4R?k=S?D zuFyykvW*xj&VCrPpl6F9c?jJ_;UirITP29a*fGT2h7?J5Cww>VeOO8- z+=Xh^nWXn8=voqyZ9Uc%42A(j2k{Omo_C^f<8mosJ-cJ-rh~}Q$}-sRwk1L0zpUx1 z`)i;=BsVCx`E52DGG%Pg_iy1<98&J^4;&e;zTOT;wh>Rg^u$h%$8a}^dawv$F@Lq3 zk^Sh;bN2v+ZmRZTECmQUIuuEYag~g7!E#*Dj4rWX_O!~%Xc{6by~>5Zc-UK%M{fz; zb=fsyv(T~|Tu0($V4$mwga0rNlfj9v(2Ab1k({y9ScN=Cj%a|30=YUqoZJF=Vlx&D8i#WD!`#WB}oXIz#ERC6S0QN)nTdjzSQ?(&;>&-`ZVEcG>isqDeME8uJ^KY>1ju|KhJpCi8$FAv(V^H|x{j$t}kTmI!&=>fw9qRP* zTz-xT^EfakPv@hZt#I#HW|Hx{sFr;?s@nfqh_8zAwdy@{lTPvZOMg$;)tmWrK4jm( z(}~As{zPA8e6_g%EARdyKRivWV1t2rE#c7DV1FqG7CAkzjI*CwN+R^^@m+CY=7k?l zBfD2_PKsUeAG@NcE#>~Pfl8JgDBv+-!r8B2&@2$F3bLxn1o?v|DBuceVtdxdLtC|J zzP6iN^x%rcCGDL9tbb-Cfz_U4TUSrqsF{6RuTz%E>lb|83u_D#*<%}W=zST+MmXuga;=S zPNMPlF<#hlwxhBS^nkwjBFx>^ObzTLs~Kc59-U|>5HyDD2Y&>>=spX|?OO(kTn5?e zM)UT>d1nh8n>^EHty2c2D;)COcg#>LapXac5i|E<0jDYYxFoOKY^Hcit>1*=6V0mp zm269URukMrXr;#TOxI_$p)ePhY0LP*GabhiaZQW&wn=YK_+&XSRqa_uH?e)vQO72f z*|hFMX;tt@jDHxVYH+`9gtVy{36utgi_fG{RUtx`wNF>}!F4-rd#V~zjmu#%B;-$& z+XmcGPS8skg}#VvVw&{09}i)?bwqF{8!x(-Xq6hcwbE4Awm`b;AIlu@rr48t>{%$n zG2K=e&mW8S5+9J+o%p%zjpXyJFeO8k3=QmnXBfrY*nbGZw-G%Gx1ZPhL)e8sM_6PQ zK*v&nYy?BcQ(5zU*gs}!)H4%1_@N+ezycB{J09 zJ~MI1mNlui$jWG;XO7@y3pV_GgCKwib(QQFhYn=M@2Uhh-W-)Y;whO;5BVq_AV+Y7 z$EK8GoPR6NUj}`eu&w>Q?q;OGUIJBnOhNMIQ)>j-uufrvM^wc7VArj$iQu2fgff8P zt5~C2Q6zwzyoa?N2G#WPrvsZx!to31dyD7=yGfIl-Awt$wfI)A2N&5G&S2U)?UFRt|@+C)c6I;C!+ zT>)I{Hx(%am@gwL$S6k&IK8S(aGxf~#*!e89{k2Xr3ize;5v9rc<9q$q*k0ThnBW1 z6On_qmFUK|ze6qFmis{ZDrS;=5AS;nOo^;ZtSm(RV|M9hoZ^z5nhbtN z_+>eW5ry&S+u8!Fd$$P3{q)y1f@HRO9;G|1j#;NI`|1_s_uEp8sG21F)7r@pqfMm| z;&bKDLH2eil0jH#+4oxIhQzP!NOy}UyMHDM)jrnBnxdTY)KMe+xgW}1MWsfJQ%PjP zdujeiPdaeBS*)gE-&0NvB)k*y-~0k|>n-SsypVD)RucL0nXsX$c;bHn20dc>S;}_y{%?uPF582C37?%71MB zzEc+=B$?FcZ<^V`Jq$KJCC+4AGITHylx}Rv+?!EIUz9a^+5G zeYO1+?OJ@C74gnOEmM==)YjAO!6g8FIpR9FwO>qMh69a)7@FTbw=lug*+)2^z&?cb*#7yUCLiR!SVVMBU^oMzaP2eh0z z3gUECDkF4`B$Hkxx|7)hRVvS4ucusWVdBBRnF&v4kK>ewCftv4>S|vV#)T}C2l!?u`-FtF6f@s{X(E`k)_E#l$v3{Nj z4Au%n9*^|aVRhdi`8WS8-$ zVt&PEcF~eXT>%H;Gl! zIQFSo4Y-KceOHuV&abwgI0WNZ4CN5{;yDW7OoU>Ja$?xkb4t5? zmBwRzS${X9&*1qZ*u1~@8?4^fX@4TlL|>`9(C zTYvK##t4P8qeA|avG{Wd}Es7cC`j4Aktv2J9c586&a{usA3DuH`4_;_mcYYe)l z$L48?1lwnU9mMNAEZoCh=LTA!@I!>xD1RZ|YLB0Xv!P4Lu?BIl_9=bOT0 zOk(`ek3H6VHhLpt!Ez|Zj-J)~Ls8)t-Ytp?tlRe(x9KWowZVsokme2;hmekS1b_8Y zCc169R@a6pjtf^L3W4-_L~8H12a#6sQZ2DuDy(=NW3$rfaPJzkAIOH+YC~G(!R#nU z7H(N~XEO2xRM=(;sn@$mVlk9#X%@w76hrIN{rnA$77K%*uLlW{zxlz2;RdA6Ih`y)1Lo35oF_MQvP=sFeX6#N(2#=bz75I~1dOWl_ z`kC{07~%zG_I6nAZ*d@i>C0-Pt#yLQ&BQ}06&GcI675c7==#WKcB3%5?0;O(bY{1u z-?11uwKJj3JD^j|>t*oLDMBPk<)?DqIlFSH0(ctnk=ZH{;%JmR{5>l#lf6(ThL(*WfnnwO9kPv}B_sdrsIp0u?U;V1}# zRC>L8ys8iSHTdEp*@m*2j(Md->PyNnf~1DYk_feBlyAmk?GC;(vDTO!4&m1r{p#-~x0`z9wq@?|DitAL{W?V~3HH^D0;ca!Az_(6*IOzKd>0liwWNH=4OUaq zzQn?(%axOjGD{KBl7E}=6#ugA)Yx)Ba>DCXw)D0pyfPHWDDom2^mLHH(ckeQ?A*5o z3n!;2Efv9EazNT`X@ev9uDjMbKOW4a0`TJQ_13}dp>jl#cprjSwI!m66{O+4-Cft* z87}bl#AVFaI>p|gB3Ab)q1vPcn{j4Iip4(g!X z@|D^ZoCVZuhBdwb*|z0cB5RnG*%OWqoyy6{6Ygf)U2$B(uy}^oH@+7v$hjqeq1~A0&5Q24kzpDe9-mSR zA7Mx2rG@@WpE!Mw$o7wpK56Zk&g=G{gg2Q6$hnpGOMm1d4UMjGUR3l^fbn*j^iWg_ z)EcOb5h}J!soo-$ejXKv6}5?3$@23&_zm{0Y=pHyW$?z6Y{Lp}8RP1Qd_Lb(3u(Z& z(i<9cg2jt7jUdxK_`4W8r8j8m)O_{sd*#R1^fPsd+|zZMfjd(MUN?Qlot1}n~avT)@y15|M+XtvYv*uPaa3vxoH05#8cj^H%EMk-ZLG`hVt}f$T<|s3 z_~&un(nAu6^k1V&LqN(#O;(WfxPE#B-^m5vQVOplKLLx0nh zw{DuHYp?J!zeAaYZd7yzWd#DzuQ?l0wc=ITZdZoYsq97>N2WO zKNHUYFAnyv2!;{#&24=X7KF${a-?`^i^#y9x6*h5MCXOwhGbVoZ{M%Qve?lZ%?4e( z97U@;bD!>~D}F-P^*0djHd z_GV&u`l|KcYon;LTqp_&-@1y9BBG$pewLe1ak=if9P2%E76e2BQV_G`(|>j7{KH}k zd+S+}d7K9^hq6h0zA1zFqU|hapdAD%z5ETn&^mM^5`hDh@VfuJ)DG_}Az6M3V(#=Q zKSU|{Ri-9S&Z8=bY>bX;T*HK#7`Y6pma;Y{N1A(~m>O~Pt!nz^G#OdzL+k%kaFjHz z1eP2myX3fm2!4S%FCLn!v44;*o$u#lVclXv5?ZN92~MJ<$mT>r#hKbK0Io~Q$gBB2 z=_v&U1BR~22HAZ(FwQmHq_ z28=m-;aWd$vZCtHJ)j=LlT(> z|7cv1cFArgd}e@hoCsibA+me!_l96KPfldmYA&WU9(D0HGRDcIoRDPnHYb0M+VDgE zoE%^*BQtIO-Rn~*vVSEcf;sq0#`CuWa65+TbeVOevB@$axPHQwuOK+&7`k1fPeC;U zGi<(3PHD0cT7(I8-{hz`GU+{kIKp@6SCmj4aL+jo zqN^UKVW?!tRb@|12ae}>m(DaYeK#lVq~W$Bs+3DmI9bv%<^6#;NJujtYY|)yofyeY z%epBe?ISfjbbn)E@h0QZcqgUTfs1*EEEr{!)lAhJ%fJqf zu@)qFhv`bn4*pG~*2Y1yCbRa)mSE?xvho%vf8~d$`YrI8(NQBqyu3{ve6nfUqboe^ z(6lM?Yq2CaCDpr>89=&PE54n!*T=9UE+hL8pfPr?LXSWEjiNL(hRe%!=6%4MBF0wknaOYXnorO-k=4`9F6vixSuYUKmG$ zZJxFXS>NlRmgIue$vvP?_x7FfzYw5n6~)SPV}A)=Opc)}PwT9SUw6*xY`ojqr)HT* z<|q)X5!H&&i(U4{f$f+XcV^{?NQJM>ae=Lnnp&4iDQEL1*1|c}?T7xn_0WdKdfjuo zv$ugBxZW2*a)lDgXYu7~BoWDYWhLNdtR@RtRHR0_{{)7KY zz<>T}7Tq4|{@S;c5Q~?P@M_>x_LFckX`R+S5fw{yS6)aAReR;S)fEkHN@KKA-tfl$ z8w*WVf+xF4a@R=^mn~OimhMM#+QvAmQjv**r)m5YW(0Yny}W~RMNFdSc=wk-RbgBJ zQ8;GJd)9P9Zc5h7k+gyJHax2`*q+$wQ_Uh1&5Hh-QR ztwN7khS#8vq~DnCRuQ47;Iw8>WyDrWl9Il4>LD(sI1UG4(0n__QnoEhK-nrLQfZ3Q z6i&U-unMLI7sfrr;ZqJKL~tV;Mk#2&wc+(Hc@MxJ83sn)!g4|t@qR~J$Tb7BM)Hhet9-wb3R6Aku|UHtTwgfxqFP_V z#H&2oFX>apCi7dU5AJPilTIX8(Ui8&@NCGJk;{KCeG|qPX)m3E!}cRt%( zQ{8guUVVUkTh~`_I{Ra9f6@PKoUqQ;OOC?aW?nD7sx8}nWsk}LDme|!IL6Qeq(~WT zy}`#6sVX9!n-E8RKL4!ZtuRQ+siwa>Jxybls#4HAjiTt}5QkPox_>q$s*hahHrGe5 zaj_NQkH!{UT^45HL*3Q*l2=paKhfYtMy^m5hf8z)%Ulk=O|wJHJNKSJ>4DhBYj8BP z2Ddvr(d-0p9$-Ip^AWH^KDzDZ7xWa%GQf=xi1DbH1sQ$==A7=O5k8GT2D^Ah9z7*M zg)qD+v+EVSE!AF9mVbBR7_37PD!cqg@ymeDK@PMI_*M|B>C!A5Z_7}(O16IX^SE13 zym(n9ueRz-)T~Ug6751)vGLI}$LetPgihd|lNr4JKoYQUKeV6eefQpg9PcJmfEL)`)>`s02E(nXfTG*iKDep@)8l69fi@S*A8?sP-|AfY2 zvJ@p)nZ8pouSU}bjXT{H+oF8R9~W-6vY=bP`FWuUwd!?#1lFmZlp2Gq*zxa1GKcpu zyf3#KdV-}?XMga&i<~uJMZ-y&NyXc-;<4!0k3VyMTvX!Ln=QH@5E{9D^kl{lkA2mk zvXwI7pE&i)BB^JclnyN3vePW+t%~=RprF9J(!!0^rOb%Bsb*uUpJzn6YCcV;-^2pq(>e3?mv%soJ3Rp9gKA z%cOq(apYDD62#iEAMVXkI>*D7c3zZpp5JsgGptybMc&y9C_bat)jK4TN?Hl|Mv75o zTKar%LQU0Q3`okU10Q&BZ=5z93vP3K<0o|0)PHURydUux2r1trfO!h;E^H3hSsagQ zqdGfI6>G1MK&XO(BG)*{r@d_3Na(-s#Ay2pc25(ClsqsLlPo)gBfKqFxh*IIa%b{X z!|n*Ia*$e0i_+|SzJ^$&nlB35LDw9pZh$T?`kv(vd?THG!cy>^07aFJgMoTorIN;T zB7c;jw@_u|cRs!m+d)f|MD3#xqsl2Tp&1_zI%Yu%ye-}L-ZzqKvny=`8pt?L@-JV%magzAFrUDC^(fvz8P3C_1D*PL zC&dai2ktL%AbN;cgT{D7LRt4%HbqI}vwuQZe|KWqgyUq1J4A%Fb$ZQo{M7n`pbP$i zVjwVd0Rjpw9|s(>{8_SklP7Jqz@ zoBC6|1Q(pukA>_UW#UF1iu5+y@xiX#y((9uH)2W?(E4WVOOT)~TgAgxi7< z-L`)BZ=Tn zQhq^KX*Zh0ST99iwpxg+t_!j_^4Bhv0n{GN- z9<`0{dMM%gf@oL_#Z~lM0c;uaq+$s-H+eNPf*X$q7+I24P}FsBrs7vSwE9iNNMv-7 zJ&{x)K+a#I2C}%;68MD|Uvz(^&o2-^yG%r^?fF?XS_@||e6B>Z5ZtaIGk*m@4iL89 zL&0{isj{-V#;*!OO>;?`+(AEl6J$|nHjM%}c;@Z&+h3Qxy3hs68i^UK_ z>Y%CTwF2Qb(?ZQv6+oeD>A8vP)!PuvSbwkuj( zsunWb83yGCB@8B638lK>1u9o^zG^LLC5^J7H&9_s2$O^aMuX|2{5o!HUI5Mo;#Y%n zl8a#`R+$yE?oY~Zp+necJ*?Ibym@Q{nOS<~{oE_9N-7Akb$=)bz|{jXbkqjo=nIFA z3o#i&)IJe4bd1IRuCLk39AN#M1sQ0wUz))N-%mfLH{_;tk9C60!iS_<$-o)KSFS*D zdX*J6uxHjp?N@Cps3p;jJp6W!7F26=+hSQ2d$^O6`O9tBq9^j?oREBHKvrIcu7HX$ ztoY|I-&x~s2!FG%L4MS3Ghwj8Y6jn5mAj^Y+X|}?E4Y(YsWzxb-xBT!x}~PeE(R;> z9%S7#+{}(q_>eW#iH9*2PTNQOv+LBclV!1!Y~ijNv+JxKw`^xx^vbC1xeXSsGwil; zq+Q+qyf2~nP>0YX9)i@YFggzn<>PcLIGa)0=O9+Zoqvg)d+Dntu5(R4{$As*&{4^x z%N8sM1VT%C7VWZ9E}vWU1X#L8;(kn(^c_ZkeVcL`q)}iH#&_R5{NsQtot#z8>o}#1 z6pmg4I{5_qpoGS*y)FrzwbDr7Z8{5<`QTg=xj((trrk2FZm&z5>X0Z!nwbeiW=*#^ zhPE}RjDP9V>if0mQbI5YZ?N@;wjH^Q+~mynV!9||+N#KsFf}zmKwD;{6D+hl|AFXB zTX``*ijLa7O`hnoycgE1Cd1}(Uwdk!%I2qvwy&<8aG4L5lg%xKWutksz;8%6Wty9!Ht9LP>yLc`zHg=v& znHl?;@2#z*#DA|@+K@KXgdJ5m8$_sn0wED6CjbDyz5M#Y%w#F6e793gezX3A?XI^x zT7T37)_B~9i4JaE6EByO(Ifpi>(u!AmCHiyUM=~Hq;bEHOu1TyBNcD-pT6^aLk{oi zVEnKztqP9vzoQFMDAA{N|=2v>k?=BSB3sv-~~r(rqE4KJd1E8dhY-1uggh3LVqB zuuS*pE*cQV)b|n=p`}w;PKdUnW+9*zv`0*#%YwNFMtE#Y3f#n3#FPP3V=)QjrWpMjIv-rwib{NHEUfl9?eHc-sJ z23x50Ap#Uk&mY=N`iVl~^ovsrDB0RV>!BkLB5rmh=Az$r)m@31A9+PPR(;ua8bl{={r&gPxUo?X~(O*QL1&J?~ z(XvAO8-~&_`?LfrIrQ*x<$ou|c;{G!S2gG;!Bu?-U!9cJpUs_SpKPm9`QPZ|(0WUx zom2D(7Y>nO?gZp8xE`iX)!2yyCsHl1G(;5ht8JD=OFro^#Co{(!`VYFp6mxV$$wde z+@0Y>C^J;*cf`Y`@w!6x)8o_CxLJswHNn3x+A*gn|Ev(vUtmr=-+x;JI;2B%wbv$Y2!U(%p|~E15=Ru>LO;2shugu}D#OM3<9_SDkbf1cyP*zQTgd$kkG zC_WD6@ovY+>z`5zKFI&WQ$%s&cR)2qF4eE4p1CAuuG4^}%&ASxreJ2y@w~xAj@nqQc0+9EW8ek>& z8CJmW_OyL*&^4)`J zI=iV7rC)$=vwrr9zy( z)7Ces(%n~d#D5N16VxjSGpOUa+;QKgb*VVkqflz(#B3GKO9qE9b?2$0Sx;L&)gQEx zXzSzh{)0pcd0D$IGC!(c`A=C7hZ4fL6fEvj>b4u$m&>#BDIVo3O1eZS`JRecs8yu* zGVN*LR}vzX;`XZN*_0euz%#A_Ap-|7BzW^wx2p`xBY$gMTl?1cI3(OYbsJ2!-6N0e zPpyD)T*J|{Rlfcn>6IGZeUe+2%(3k^QEDU@4FvqMRzHWPOJbqw6hy{xW39TdFR5?m z`U=^5mX2`8$mO*Q$;J?1cXT|v9|s^c#^+F$f^~*(psz!jEZ~3G`m+`24Pr15MPTJ> zd*ej*rGN7M!cxnLblbk>9FP`h#V%ze{uH-Wd+=03M^WCg4BLNbV&YkjSL3>Dg_ID-A=63zi1w^yLt_++!*<}UOzk@0)oIZR^Kz;QmGrUHjusW-T>X@Fr&qone&yr% zqu}sC^a1vjS5e*O+R~FQ*jIK+$~0=iBM4$V{GnaS{XFjMa36j8%q?F!f>{PPzo1n zz0Vv_h#nnIaaQVsUyDT*B`fZods0|l^($BUvNlFZF!k$MM~z714n=5y0O2_#+n2tC zy0OMfb<%@)l?hrRSuCZwZM-25h)#h*%YUNGq^^`zNCAz~RxP0*EiPZgE+6;7lHfb) zXnGj7rsXmkP({0J8kE@X5qOvIh2XT+WW4Fr4QhRC=DGIsb0(P~Yhg$i-4MKid6L9p z!n*7IujK$;RcEwuQ}I5vLvwEVySq8VA4r8wQP8!Qo6}6|%3Jz}?+hFmaCuV90Dr=? z854+`iXHT*>>YWR)8U=U^U5xs4RB0C?~u&`7Z_%!r|m!J+%h-jiyMTK5GeVzbx@F< zWiukw>QX&lP>>rQ+?|pS#ksbb(lgp~(L(bSWptXn$vaCJ#_^>kSx7#J+o5+2$=0?_ zcRSL0`dM?~mjD=|y>Dz-6K6S&shf^0QHe(shJSw6S?)>JaX5OJLP-8BWt-;UX@6D-M_3Sb zd^Nu4t9z0a_{{-yGOAB5NY^G#J(v?{FPdsbmCMw>8aa=FHGKE3ualGiF?h}mU6~KV zUX^3$!_j@EBX=?Sj*f#BqVI%IUszxLXX5AlV&Be$Lg(bp4S$iag}v;888a+k&XV^q z<#|5N%ZXxjm@tAbliA%m$bYgCdSOJ7o#odA8L$%RX7$n7V=;!rXE04#M32*TnY9c! zH!yjO6~Y4v0SXF)S{wF9ZPP+jYQ{}qX1BIN%w{G2gX}5#v$>pXxO!Nq>Q2=63p^?< z4x8@WZe0xiu)sS9gnKC(&Cs#mO3fd1O9yV4mi-UB5od@;X*8jJdVk2y-nz8Sn{|Fu z-J)~(`6vgxy({eJm@ynw5T-fC09WFP{L808uYrTmoM6@!rpQ*G72y!Lo#eE%&#z$Hgtn6Voi<{SVfhfQ?oxwQ%U( z+1d|_-lb)vA!S*ysDIDkAhvos&2v9#2-|`(NuIp9?p0$=rAJH%wd-L!aRJC~O7b7R z0WvEaDxyTvc<|pjS13yDFBhebI!M2d%+Yji_}z4At)|nys4BwSr4#8y%#eZ&eM@{t)lP6qqLy zZ#}8k+JT}p*MG8<$3+rdQ1gk;bB_1KkTSq2CkTru8nQPG#P|Qc!&o<2?S6?Tq*F&+ zfjhp*YY&N&bzPaTd1wQ{gK!12vS8}0GuM0coAGpk#mE%~p_?2@b|ms@Uc2JZ0;-iD zB%^<*rq&pu?z*)(SpGV5?lGpfw6@nTrb|(!2r3Ts=6}MAVSO43Y-4QkK$}AYR54!P z1gk>v-PF(7oc&Cld1h8-*>1&|XvB;Q)A!dGtMWY$uZDy}_+ow73xBG&tux-*Ii-?1 zG+u=6yfg`Hvu?Yl`H^0q!IZR<1a61r-sbbj4L4mx0VacUEh{WF!BwN*7@sU@MK5>A zN#Y*bAb(@L$iFX!t5cNK8L2moz@=?Xs`pVFJsXCB-XVDjNlp4B>CcUfh@o+It<_)f z*Ew=Rdw4{8G@Ym=uUViiB2UV+ZrsT>MlqcgVSk4Ry+>rR3z5<`;^xy^B@r%FFKI7SrU!M*Xf zrp#Af&nq>uA5iGo%_kWomY!I61ZNc-bQ`MO>w#C^Wp#R=_JoQZOnL68Kp{Wty$69= z{D1u!KsxBRF+Ltdd2S8JO9t*UQ)Jja8Ul1yL6zMowr7!XMEi4@#viaArRawkSa^w< z;#Tmj_H3V?+V03<;N~QQw*FkECgSM;Z?t7&3HhfE2v$1*=Ey|p5{(l-U-JVtu7(<} z?+nEX#obW4B_*GjY*HsKV4wI0qd~Y{4S#6ncHDn7&-9455uP&l&s%SFft|yzPgSuX z8vYIxj(5Rc8eiyFir9J+)08nxzUWZWcDl`O2}LCJ%6Y;27aap49#x{Fr@ZA**!j0Bsnhl$i21`ta!bLVUVYHr&Ysm;QVMOc z#Rg`-`xRt()(?gw-usm^F8ns|ARN@k0*q#Qpk4A|zgiGXXS{+JrH)Nhmz%(fD6vuv zpUfMC>bIV2Hvz4=5EjnqOvQzp9@;xLjI3DjX>%CPCkd7Z!IQ=)Cf=%9{C`*PMz~Vc zNCiOLtk?<)Ts((U*zsZq)K}~TGnnTuQQPKODelNLaao{!a6#4qTftvSz1Hk}qRYk| zDE&B?G1jo%kxf$_HN~-z-{JV5|4xPojjw~^5AngvXdMLME$0wDWeU;deCW(SI&1Bx zVjeo^t!dgsnSMD7qg8hPRDZW7EnImtpvENeEov~D)y$8D4s%UpY8mkK;XmC!3B;i^ zuFwRf-gfdEX@B+Zx>KrML3oLjrR;%hq^#CPT?9E6u2>hNn=IyzND;a)oS*DYDS9jF z6WfN6PUc7;)x_T+^>rD;aNqErG12auJj`kff;#%%lL^hoVuJ(k7k`4J1VXS`vE){3 ziJhE^Mr)2{G#)aflF@R&0!6ox4mZzL_nJtzyF0aF!nR zC{FBRLSmU!0e>U*Yk#gQKzP05F_V10UzJiDB^KB&{{U~CBf@k7l#78$&#~;42^Vfk z$j5H8@bR{XG&(1KxIo!$+^hDdUXUX=2QzT5k8Yk(g5zgr^PcSc_)kK`$c7?_foQIb z#d8ELT#yTQ_&H;Z(i~z(1?tQW&|-dSVWhlt(O^Ba2Dc))kbl<6T!-(}vZP*#1-pU{ zS+~qsHdB8yHPL{QDqi}yYttzm)0ppFGHi7Vp*e`3dNUYt7B5Wb`#!~+ZQASy{~!MQnx{2{Xi}PkM#h0hnN*x z>ahFX75q_Xl7GB~`7M{^b2Cx%)deXhJ1Hwp1GFfe>R0};H_W}SErCx2+NBI<$i7DKB762;HDb0A_? zVLpOZ6p`m!w-%10EX;R4v+sD#%m4)AM%-po_aEh5kyUd;gr{O3qa>#D6dl|Lw4cuU zPBmPRXIp_fIHACH`kBl{<}A%JQ5i&wTF*(TvzSoYgdcr&{l(8S zBMWV^rXc;=$+*RRO*rh)oBu0lA->*Znk+f`J?tlLaod{z0d<`x0fb~fPd(-$S4cfh9 zQ3?jhnZ%x%^MM@BITr0K1)FjhJh*@ zNPj?;lCt?P-A{DJ+toA2QA%&Utz9XRVL!uUa@4h-NzY@?`Ln+*Jss3DL$^N@sI=WI z$fV=Y=UryuLQ1N|d)V#lIUGDr^!sMHnb>TcSGcv|OJEo2~pQ&U7jY*ta@D_LwA zIitFviXY@Xw2lm!;&1goKEN-Muvf_M`05O=F5kD$FgEIQT7Sqx z9XYOK9!U&?sQ`POjSWZJMvYPEj%HLdFA>M=ri*ONjyEBq?}eRXY$iaM$7|cRZQJcu zTifQ=?pt^3Zf)<@wr%UJZQHtDa+h3km)y6R$&*YnGnvdh`28_@gCnDh4|fZKqAs_4 zCiB(rm0qnWb2Lt9Go=J9s71~ek36cq_)9HY46t*ZDVxIaHFIIZNd7<}!jFP*aM1>I z_>@jeBzP6Z>~EEEgf?U=$h{7BPO$oc)3H?3*99@(~9>I*)kX z&$LVp+O&Ti?b6X!zEer%pU+@CVgU=T(is$4*hOlIcsZzz203fxegH4@{ZkE!?#|>6 z)v|Z#?9G->`&0X+⋘g?CLU?KWwJT44Ru8Ghp6UsJLgh6Q2_?-x={1<*es|yFleB zwdqmXDygGDlO9sr^tQ3ymDU`vxrcQ08bZi7+ddeDWd+BDkJwBsHn2YM(WtmyfI#Ee z%_}Bxy>IXe2JA|DeoW%YkYB+4xHrY&hAjPAoZDuO1JPW`k3XSW1e1tCm;a#du7tcE721=&+PYyGW zx$b2{D@M4oZJ;2(awQSbbVf8#N*ToQR8vwU6$^Fm@2p4TSqD18Jex!0;!^qaA#^YX z_JM=kw%Q%puG`~s-5bHW!98FOt(s~dY!E-&?4!1ECST4;U}DH5yU(algplE&U=&E(<@lx>~b@2W)gHF;LNn<*Wtx2!`3 zcjYaWCF=K6@#PrJj^V%O_m#|sp1N1J^hD@b2|g#|jvtugrLhp%iFv4?Yo}412>wJf z`hS#odoAm@)K}gnq~adbj~~LVsOv+O)I}U0Wn{FMJ*!s*)Mb?Tt%@8N>}|_= zI8Srfj=`w+=s>|2av>2Dd3B>~Y+#k(N-XlN(yxh>;#SB;q-4C3 z!IZI0ZQ5)g*DW`J<_pP^Wa=+PJNoqWJV+PgFI6F@oaWq_1KlJ?0WDp?xU6^B3$y$Q zQME*l+<+wv1D!Uai|z&3^btihIku(#m{0siZCz+EW^HZy6r>WFjNh?>=Y7NKRnAFJ zVM@Mk!67?9nkX+=ljh!sS}WFd&YCykMQU_>I4kXnfS@@R0w@`eG%GIGH6~8um{|Oow3ptn8GHqP}JfxVPO5!|uyU)wN;#5g~7?}Z* z&MgE!-kUpj5g5&TcxAIwU)CHO5?G=ex>WsqPMtt+ooLx^*E2^9wf9vS2si=r0r=7tN%n^;Il8_^Xy;5K@3>+8LN{pEnVszpesylT&_c~9ZR z>N51;5TaDW%*5y|x|66q`Q6B>@zGbN%ar|`zDpzy1~{)_GG@4+ls(6c^F(y!A6MnG z-~_dGS4L8K!b;JMcyr@C6U&>)>4%5A*kTUA8rqH1I(fc{{~~$7q@rWqy;Fnew99Po zk%}_+KNCXJJWn4zFmpjFt;gI7=s7Z9U{&7_(?R{x(db zGJ2HH4+m%#_}K3q3H%EcEvC3wgU+Do5pn9g2eV^< zoqYHHj0+9V&ZpGQioukhi0sE-&QzlFp;P%ne&c~s+TmXlGDr-)akm|~BPF;c-MR(x z@Kv`z%4Nc~yA(-gh%6Qzph8~j31!3QMgka#@PsA`j^{%J?stUT{N~91j4eMB5;YWzJ;bRp2C<iAivUcVuh$a2Ivc=ZL@lJL|B-vpRu4$hLku+r zq|@id9PxSBA=F^Njtn&j)M4aH_Bb3AAfPXs0M)2DbDi5P*6KNzEh~FlCKI69gDlc- z*JDKkcDU~G@F(#WMsOR)a->f!a9=+q=Hs6i5ym z>hFk&Si}iOLiV0YczXV)o$R07%<<~9=v86^S=3VKQluRAyNResCwqpyS; zJ$)=ADyNMEJhUf7KtB#@oW4rp2At~ z)lc3hZiO$G56kv`qbe4doqGy6GIXQVq>Sj&yvcJywc2Al?A{YZSB4U&5wYKF7tb{y^|5D+&#O5@4^~%Zw-;G z4tunnPg6bHou<~JnwwR?Twcy+{reAre>+s)x6eYOq>m+@W9?5(ceAiH3?EvMAB%^V$nu^(FfkND`O7vooe7!-D>Oc_R)Y_4mm+*FE&pVP(f)~rF1P15umPrhhV;6mVRBy)|kA1Z^D7Juy@s#qGu zJp$SRI@XW4TVv|N=NjE>t#zNpsKap2?zq&^-=$Zp5;rnn3fZVBiOQ?Jsn~}0i-IQ- z<8b)Z>7q@h3w04U`Qib&k6=QwNofBhkXhO~Z{1S6?+#eYbso>FCeJZ6*K=Yu(J11Z zetQ-buI@HIEw$)P&%o1C&RD!bC=0p#6_(=%r1n0_1LD!I5KR&IbBP0SbkX*pMB)F& zf{)~mv&(CGNUd$FQ}*6yGIZ<@_R8XG%5IJ3>#|E6-`(@*mf1Af;tJ>ScJ?W-{rLd ztavVN^YxZ2fgC?!RuiIe^~$l&9{Gx!Ek9NyZ*=t{VWAD% zZgVDdH1Ww;t!p@?sW$GlxOcCZVxkk+Uypw7G^DmCC)o?BO+zX!vR&StY7m70I)9G7 zp#+Lmuk8R}NUCWVQJWr%tsm{;p3Ot=AhUCdut;5#zU*qgGT)JZTeRFc9Muojm^M{i z*^T!XAiP6XkL<~%vQnq>s+6gs^lykGgvKgm$1}yu`lijn0cGE1XqMcCI{dARvfv@m zKaR->zPu|g(AFAaUMXQh&vyO*rC2XGU&Ll9`mv^=wr4QwhKHs%Pk_jcdhW(h(KK2F_m9_}McFE|lB*c8Ju|KqsvLO$L17SUlHO-A9(z2T*Oz zGz(tS1{OC6<;AuB4jYm*750yH>b&N-Y`LdfW5${zt4Pb0c@ZnSb7d$1+b(_MSf$0T zy}qebVr!Dn?!sMw)eyo^A2fBeszN-rM^C-17=`d-Yh(rRQRRz`)e z`+-#3>08D)#E0PPWW?4JNzC8%FxG&DEnV@5~lV2Eg} zFFK*Id@}mQfxP@d_a)*a@xxerc3XM;hjk>smV^3e)aqT$v8vDBUC146&a?=Atd;cU zsbbqoLD$~^`5a;uT%N-$~BFlUFvpRd*ih85cwLT$r*G-=B|Vg z{Np~foYt$rjw1#DX2nITJs$3PnOGMG&9{!Bu>_?Z83a454jp!md>~MP{bYGo!wer0 zE+(|SIk0@gX0SyjEbyus@gd<-aUj7{Qew#7VuE_|OMdSw3jl%*!*i+6fuw8Qn)VP? zZPZa%UcJSxy28&30{_9jl0`CnweYnM z^2o(~JP81pQf&#ap|eK{G2bT|#HgK8yFAh(qQ(u|L;ia8@OJ^X3vqIakegB_ld`iI ztPs`yYW;GU<0*SgWdBQj-0aKNVgTkk%#`&pCo;|8U3bg_Ajm~cJYyrjZT`;r&lq*2 zf}0;GbT^+RC}%;4U#!R)XNsZQ)4(uJEWEHI^;`p>g2d2OG@8`M%^c+Yu6K|5{MS#w zQx{g`I{mQy7jKZC&36(DOs(EjJ6!9;olHEde-#%u(dOcvQtjE}&~+>=_wTS3^F;2C z%d8CRaZ67(k-(_un3XHq*96Ok2tVWqm| zQ#ta0F?U-xMsd-C3;0FQL5BQ1WuS9EG^CJZPm9z6Hj@AadQr~<_SA=NPrzci5{gpu zxK%ULY0sQ8N|6$)o=Z{inSSjr_8!`+T{~tC(uge5KcdVr&V50#3H!rxsiyanyRwf(=X?*LFGsOsAKpN=QIJ+tKISYp-1!gudnW=zg0*l_MTs;XB%} zxlZuoYT1MUI^25FJyEgr&70JrB+z=DlR4Z^%enA!ry}3LqRC&R`k7xk=xPmU`^MP$ zCG>e&Q1d5RxhUzxY}xc^h7Aopg+KEps&H6Ob8I|MXDgROy3Ux!@pUJQND6|f#Z?i& z)E0~>@UWMD&7AAuZ#|W_RE#c6ukuX%RK`EJ%s;;M8CjjzqU$FLl8h-05gR&%#8rv3 zxXEp-=Fhoc_YT>#?jhgHI|q&xE^k!Yhm2Hdf+3ytlTwd8xXTn1Qz2LMa2&{=0HYIc7n2eY%w6?%-butc%FUR?fiwd2C}be{ z4SQIRRcikF5O@a(kuFp;3L|mCG?yyFLFz{8=q?_5!w3II?4 zF$`2NTgaO3d`;h^8GL`QaDGz1jMB@3`^)K`z&#e0Xv~WCyI*z0I4-86|H0!Rk%U``67AABU4?cTb#w&1cZCWT@-$_yM zecVa|70ND4cp*V!6T!>kPiDgy4LzlM532|dQ87U+xOAx%#bi!yLwNw;X;C@KO8A)T zEAJ$Slq%siCZ*fY^4w%;)q=X4AoU{{rrmd55Ux@t7p5#-&U;EsLi8`Wic?51xAsQ?P8%V{V7;!Q_i{Y6+h6|Zad+a2>~G=y%`HQf0{sWOgu#Lbi+&$ph=ire;XpoJjB3Msj*hj8X>iPmvBah zC~I~<@AQ&6HQ4XM`m8r*QO-0ke&?2s0^u$P`JKdS+*WnmH%+}QHf z6mhod1xbYVnF-`+R^qWaijJkRf|U_p8&pW+%4XAjJly@`d|=wIs6NP6)%LN|>gjOm zG23)-wMz!Ngd#*h#Row(C)+L-IohgoZH@kT%|ut7fJFl5Wl0@fa;Lr0GM9*hOk?Fg z;{K7<;g0DeRT9*_%NY;7CI*ow3yB_)u_Vyuu@Bjmvu$dQ>6dtB%wb=XkH&dF?V?&S zJRm=rXBYOou!^7;Uf#6sbm0$w4x%ALVIKUlDmd$3rkO?neBK8Ngq+KXDn}#t%@;~- z>g+&%w`DO}G|{`6F{5KsC^z8CAv51bx_+0=&*5!ovh|u+^wM)UD-X!quJ0oMxZfrr zUna&sfvi!{@Ihg>;*}x#t7;I`F>E{bey`GK3C}MMI#RFLf*YYr<^zuln|q!|Pr>%I z4uf5A?966=-taFIr(19o?x@U@|H1fq9&G+vR(ZLHx@E0g#Gcs~bmMfLU$u->`l(**&_FkrboQFCQxig z+(X7xxexwhN;B%ojf=~9$B?i>voWkc+o35M>;}#N(_E9~RrTbgOY2!>i!ihp9r{IQ zmx31<3`37X?IkcXntOwP&mYjZ*X_{I>Y)0SPl;GMZ+-3GIOf~VRfxALz{#-yCoor@!QE}WjH3-a$BFS&RxC)e2yJp|KInT6(m z2v0Nhf4A<8dN(l%@sPferU~Rx=ur%t?l2>Of(GP?d1eYdZB28EhRw2ZS=2ib>#_VJ z4qa5~o4eJGXzzkp%|c3Dth7_4#?7gxADb+yD)r?DAZIeGt1mu(4kHVC=f^ATxtivG z#`vE$`_|yWIu9aS+xqq)r6=UaH<&&qO=%uQtFd z4B7^E0515ntWd`^n;%L7y^}fon-m6U|IJ5*qhknx5(q^ZYmYpEbMApQgyCIKcZg0S zm~{{+XAwYaX$q3986{9CXg?Gepx;Dt^^`z(p$E4_V_XGIa%;^5HEbxwz@GA$kZwXx z0jU-vl}o$jz)->35Zm=UqJK1*u*T8(U}5gib1$#Ubtx{KotvNFU?WlwlQIoZ77@v( zO?~t?XtGKUy#EN%yM)n&UTKz=_^G3ca7t*)J6ioprj@vx#353eTebdeD5uJ7t{iVG z8Cr=3h4WHietLS*NCXR~0|Av}f^Ver7lESU6qARAKVV~p6*%RkV7c^c7w8G;@F!1} zx+;J8GGZ2epcI_o8BHlBb{ybDP9T8;ugWco{4z~)#l?JQ%}Ge6z7XEor>^$c=*#pr zrC@R^b9fTK^P+fe=<`mO44WCK1`dsB9$p>N2S94~a#5cY=DJ_?zzCqd5 z)smd8k->%1y_go>={+&P@D$kz~)dq~olWhs2tkvD~ z%U-^(qQu!Lrsqn(z_yEiKIxziFny+b<&w)AI)WBZMSyxxD=QQS?$)+M_H9H z{AT%8k7q0$B_^;Ls|ld5l4I--x4wL*Lq=-Y+|%=C3fv;ZGEjJNHaIjuK&&@5U2Q;o z){xv|t8N=p#8>i0^!Jm5EHbP^2G`CY>Yw=+SzyUdJbpa#f(!?ii)jfPNMtsUy^2Y= z;8>-snUU3XG^oxjqsEeE9sS@fWGmihIzSYSqv36e%6fG5ZxnzbY4=rlbe8pZDvq~Z zvY7Q(z)Fba8nqej&2C&9R=NUXR^xiRS8CmkB0mM zz5|%PzjVxTwE9%nZ8ZLO?@E-cEYuhMpCobWU`LS0U01;s-n(+6@l5I>p@4S~v6}tY zh3DPh7ktOwMh5_?Hmglnx`g8=<=J5ej&HX6zJ0Vp{Nl9WUyT^3dpAPb#h^`%#izZg z)A?GyrW8+PM&i!$gafuJ-j%=%&zp+ycUD}TDEFON8v&f22e?LkKBC&X-kU#*cO;r3E%sn|<&?9x@g$^J-FyugrZ?ix-X-Vo;pU_Gq>jm+B(dkdLe;x<vyh}~^nM%)>z1K^;@lc6k`!n(09~~PYW`#81lX#xsS5gj`I>DWD;{QPY(tD&LID$5yxH#oG6g|-nBZPaR zq7CT(EdGT_Y=oUCNy=z4Iot;HhFWEph0NB3i5A#Z0C*ABaB!6iL+{kxHXfHFCP`+; z2(&ElV`tqoaqMY-)ZNkOjk_yx-LS!6>G2cP=x(=B&UiHXi~uZM*KLN#?-~I;PZpA# zW4MEo{T7l3zVH8lWr1NmQe%~rh#SLI2Z9fkTEg=io+s6$NTQSG7;p^)uk&?JYpHhw z%L1%Il!t49_;EWq4z z1*2V!R4OHxr_?0=OLgbbQxFEkB)1mgkTZ-Y6gR^9m6qHr^h_omZ4Yoo4aeA!w6xHA z3f-aiL$B>5@riXO2yyX7;s1jvlI}kr7C!m1xZc({8K(?UcDL&5k^YV3* zZE-6DDV_3NDqPAj1IME+=##P@d@Gb)i>sB6gZhFGja&EpuOKPn{}AKhVNIO^fd7VK z;bmuG1sv7#=*n>9ZsbM z=;*r4kD&QKRi{a-s0n1el|-(Vp}?3SgL1*bYttbQ{X}DII!NAUIIk8qjAKeM=Z}ET znOY%BIGmeLt@iP@5P-pA?N2gJ(e5{)Du6*om)kM!+ntpk@I*+QW7|nnNs#SLY6hoG zPr;dLh)HvmA7*u#pqVbR9MYyTwO~~NNN!i9qfHD&8h7-AqfSKx&P|Ausa>y%W87`B zNoK(GHW-PC{7ZSp`(5mf5SEu@BtnkSFrT;dhZv`%s&_45Q$!#9gK!AfidcJ6IcX@~ zVFq?JGmZ9wAjxb@GN;!76JANniiJq)w+7MbuspwcI{JhJ$PjH!tTEjw);-G6PMyEwC)9y)ss}uF-3gTbiUEPJ;JQZe|^{_U`TbP4ZqwfUd zQbFG1Q$tE>S@FtN&CTAO`>C&qmLEWElce7fF1hbFK)99Npv51KjiE{j2R8V!I` zNR=8#=Xw8Ts1q+Grbq-Lu@Vy(%=uffpc0WKI+P6bv*qjT6JgMG5P26xhmTa?Wju?T zh2D!33(8})=6lV6A{Fj2b{zQe9`%73?dgn#v)l4gLB&*+>;; zmF~OVqea`QJM+tlnNCRXlj`W^F?knw(Lh5r`HFAs<5q;}(l2Tp4(J?kF5jXKH$z3%i zk+?v#e+K#~WDh~{?ZyasgT;+BZOPFGAn?Uts!KC9(CS=gU0Ge~@@bD#YO59dXPS}u z1p{k(&x9t9e+0`Gl5`GL-iV&nx1IZ~+u(+%@UL2RoNA+>uwbR(23ik)`h5|1d_6pV zWeMAd%tIj22i^Xzz736Ly^>7EFW@RyHhdOQRG@`(k+-HRG~Be+bz-QarJ z<(co|ykQh5emJ_83%Mzw)}0YF^QQ-G=CreOy|rVxiWZbhpGNUjbJSuZTn2Hq% z*UsTm{OQ;LS=Om}uk?e(slyAa$egIVC{1eOT%w$gcM39Bc`5GYUUiJ=ehqtKvd7x@ z+190*TLu26U=w+Mt{Bqr!k06O&Q?ZTI*Jg!NBfXfC*F*rz2KEeiu|d1w)9UV)!MsK zX)DT}ZTF;kgCp3lgt#HYMCSy(RKvN<%zruPjGX5Hb#KDI+m^l_KF{&##nO(S&kwv4 z0vi^TWWRFzAeoBx92+>$hL5U}f#tE;L44e+)_axiQ~*XPbfH{^$SO&$)xiSIVeIbg zjzCFEY+XX^`j2hyz~4PYp4MpRYrRE&`MO7vx-osC0;BW0XRd0Sx7K`TxYQo3mj`EC z{@u@j`}_0bXFZA96+0rNu(!ww)f5ZMB~!7AH0ed40PTUs-9)6|nzV0Rhh!D5%^m(;A7xz`6}TaH>}cT+_xsQLrD9@5;VxnYs={&( zpZYI>Og(!j-EEGR>H=?QqVmi0hCMgC?OhBFWbClbf=;T=dZuGty?KKI8#MW^7Xc*uWDdkPKB;2U8sy!&pOA&Vw`F zUl+oAqc=pw0y~lXGqM|Lq+{>soqXm6%$G}=U{Hs8okbmVC-?n~F8T*a<`(MD5t^Y0 zX`+IgE*!mys)P<4OE0kdug%}xYqT){;#@!9x08OlPlyGq_g(@~>*Hcuh`(5b@74(( z*Kvz-%8>?BQTWh2TTURY)|`+%eVBV(MK`JSPVUK54kXN-U5dw+V?{=}lpTSBa?pn7 z?sUz)^B4EXBoBv~K7(422}67;tQ$=N_NXTY z-wFGobJ?$+r4LR0drjtVD5CTUwHGIJk+Z${Z?Iz4n2AFJohQ)(vvo4%bqO+xp7*pE z5^045xocAp5!@LhGWWqr3TjS ze*Ou`odI&C)7J+&$n;J7OIsTNk}&*us1Tkrf2x9($DOEq>CWg+43)a&o^MV$s&fG6 za;z%(3NBO{BHXbzwhA81%Dc|17HzCuJKFajK2(*OPR2E=$n{{lIXbB9$+DOV+<}&U zKJ)X#l`o#X2=g*ed{ zSigZ#O&QKzPiXy$nVycze6=-wTrImQ&IH>841tqG8wJpw zFPW|xDT2m`i{^&;GY(H_DufP5ZX2a6w52clsO;TPjQhI0=A=Jy2Xwdx$qJoSi3xoTsL3`o;`4 z#TfF@2y?6k*;YBQY|$sm@ywkGztLDzsF3RdsJW2xp%z)T(%D{OUwkXQ5UYB`Z-dRW t4TU!og0(KTc5=`Rh\linewidth\linewidth + \else\Gin@nat@width\fi} + \makeatother + \let\Oldincludegraphics\includegraphics + % Set max figure width to be 80% of text width, for now hardcoded. + \renewcommand{\includegraphics}[1]{\Oldincludegraphics[width=.8\maxwidth]{#1}} + % Ensure that by default, figures have no caption (until we provide a + % proper Figure object with a Caption API and a way to capture that + % in the conversion process - todo). + \usepackage{caption} + \DeclareCaptionLabelFormat{nolabel}{} + \captionsetup{labelformat=nolabel} + + \usepackage{adjustbox} % Used to constrain images to a maximum size + \usepackage{xcolor} % Allow colors to be defined + \usepackage{enumerate} % Needed for markdown enumerations to work + \usepackage{geometry} % Used to adjust the document margins + \usepackage{amsmath} % Equations + \usepackage{amssymb} % Equations + \usepackage{textcomp} % defines textquotesingle + % Hack from http://tex.stackexchange.com/a/47451/13684: + \AtBeginDocument{% + \def\PYZsq{\textquotesingle}% Upright quotes in Pygmentized code + } + \usepackage{upquote} % Upright quotes for verbatim code + \usepackage{eurosym} % defines \euro + \usepackage[mathletters]{ucs} % Extended unicode (utf-8) support + \usepackage[utf8x]{inputenc} % Allow utf-8 characters in the tex document + \usepackage{fancyvrb} % verbatim replacement that allows latex + \usepackage{grffile} % extends the file name processing of package graphics + % to support a larger range + % The hyperref package gives us a pdf with properly built + % internal navigation ('pdf bookmarks' for the table of contents, + % internal cross-reference links, web links for URLs, etc.) + \usepackage{hyperref} + \usepackage{longtable} % longtable support required by pandoc >1.10 + \usepackage{booktabs} % table support for pandoc > 1.12.2 + \usepackage[inline]{enumitem} % IRkernel/repr support (it uses the enumerate* environment) + \usepackage[normalem]{ulem} % ulem is needed to support strikethroughs (\sout) + % normalem makes italics be italics, not underlines + + + + + % Colors for the hyperref package + \definecolor{urlcolor}{rgb}{0,.145,.698} + \definecolor{linkcolor}{rgb}{.71,0.21,0.01} + \definecolor{citecolor}{rgb}{.12,.54,.11} + + % ANSI colors + \definecolor{ansi-black}{HTML}{3E424D} + \definecolor{ansi-black-intense}{HTML}{282C36} + \definecolor{ansi-red}{HTML}{E75C58} + \definecolor{ansi-red-intense}{HTML}{B22B31} + \definecolor{ansi-green}{HTML}{00A250} + \definecolor{ansi-green-intense}{HTML}{007427} + \definecolor{ansi-yellow}{HTML}{DDB62B} + \definecolor{ansi-yellow-intense}{HTML}{B27D12} + \definecolor{ansi-blue}{HTML}{208FFB} + \definecolor{ansi-blue-intense}{HTML}{0065CA} + \definecolor{ansi-magenta}{HTML}{D160C4} + \definecolor{ansi-magenta-intense}{HTML}{A03196} + \definecolor{ansi-cyan}{HTML}{60C6C8} + \definecolor{ansi-cyan-intense}{HTML}{258F8F} + \definecolor{ansi-white}{HTML}{C5C1B4} + \definecolor{ansi-white-intense}{HTML}{A1A6B2} + + % commands and environments needed by pandoc snippets + % extracted from the output of `pandoc -s` + \providecommand{\tightlist}{% + \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} + \DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}} + % Add ',fontsize=\small' for more characters per line + \newenvironment{Shaded}{}{} + \newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}} + \newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.56,0.13,0.00}{{#1}}} + \newcommand{\DecValTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} + \newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} + \newcommand{\FloatTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} + \newcommand{\CharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} + \newcommand{\StringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} + \newcommand{\CommentTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textit{{#1}}}} + \newcommand{\OtherTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{{#1}}} + \newcommand{\AlertTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}} + \newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.02,0.16,0.49}{{#1}}} + \newcommand{\RegionMarkerTok}[1]{{#1}} + \newcommand{\ErrorTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}} + \newcommand{\NormalTok}[1]{{#1}} + + % Additional commands for more recent versions of Pandoc + \newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.53,0.00,0.00}{{#1}}} + \newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} + \newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} + \newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.73,0.40,0.53}{{#1}}} + \newcommand{\ImportTok}[1]{{#1}} + \newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.73,0.13,0.13}{\textit{{#1}}}} + \newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} + \newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} + \newcommand{\VariableTok}[1]{\textcolor[rgb]{0.10,0.09,0.49}{{#1}}} + \newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}} + \newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.40,0.40,0.40}{{#1}}} + \newcommand{\BuiltInTok}[1]{{#1}} + \newcommand{\ExtensionTok}[1]{{#1}} + \newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.74,0.48,0.00}{{#1}}} + \newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.49,0.56,0.16}{{#1}}} + \newcommand{\InformationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} + \newcommand{\WarningTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} + + + % Define a nice break command that doesn't care if a line doesn't already + % exist. + \def\br{\hspace*{\fill} \\* } + % Math Jax compatability definitions + \def\gt{>} + \def\lt{<} + % Document parameters + \title{lecture\_12} + + + + + % Pygments definitions + +\makeatletter +\def\PY@reset{\let\PY@it=\relax \let\PY@bf=\relax% + \let\PY@ul=\relax \let\PY@tc=\relax% + \let\PY@bc=\relax \let\PY@ff=\relax} +\def\PY@tok#1{\csname PY@tok@#1\endcsname} +\def\PY@toks#1+{\ifx\relax#1\empty\else% + \PY@tok{#1}\expandafter\PY@toks\fi} +\def\PY@do#1{\PY@bc{\PY@tc{\PY@ul{% + \PY@it{\PY@bf{\PY@ff{#1}}}}}}} +\def\PY#1#2{\PY@reset\PY@toks#1+\relax+\PY@do{#2}} + +\expandafter\def\csname PY@tok@gd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.63,0.00,0.00}{##1}}} +\expandafter\def\csname PY@tok@gu\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.50,0.00,0.50}{##1}}} +\expandafter\def\csname PY@tok@gt\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.27,0.87}{##1}}} +\expandafter\def\csname PY@tok@gs\endcsname{\let\PY@bf=\textbf} +\expandafter\def\csname PY@tok@gr\endcsname{\def\PY@tc##1{\textcolor[rgb]{1.00,0.00,0.00}{##1}}} +\expandafter\def\csname PY@tok@cm\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@vg\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} +\expandafter\def\csname PY@tok@vi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} +\expandafter\def\csname PY@tok@mh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@cs\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@ge\endcsname{\let\PY@it=\textit} +\expandafter\def\csname PY@tok@vc\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} +\expandafter\def\csname PY@tok@il\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@go\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.53,0.53}{##1}}} +\expandafter\def\csname PY@tok@cp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.74,0.48,0.00}{##1}}} +\expandafter\def\csname PY@tok@gi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.63,0.00}{##1}}} +\expandafter\def\csname PY@tok@gh\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}} +\expandafter\def\csname PY@tok@ni\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.60,0.60,0.60}{##1}}} +\expandafter\def\csname PY@tok@nl\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.63,0.63,0.00}{##1}}} +\expandafter\def\csname PY@tok@nn\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}} +\expandafter\def\csname PY@tok@no\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.00,0.00}{##1}}} +\expandafter\def\csname PY@tok@na\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.49,0.56,0.16}{##1}}} +\expandafter\def\csname PY@tok@nb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@nc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}} +\expandafter\def\csname PY@tok@nd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##1}}} +\expandafter\def\csname PY@tok@ne\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.82,0.25,0.23}{##1}}} +\expandafter\def\csname PY@tok@nf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}} +\expandafter\def\csname PY@tok@si\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.53}{##1}}} +\expandafter\def\csname PY@tok@s2\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@nt\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@nv\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} +\expandafter\def\csname PY@tok@s1\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@ch\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@m\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@gp\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}} +\expandafter\def\csname PY@tok@sh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@ow\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##1}}} +\expandafter\def\csname PY@tok@sx\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@bp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@c1\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@o\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@kc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@c\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@mf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@err\endcsname{\def\PY@bc##1{\setlength{\fboxsep}{0pt}\fcolorbox[rgb]{1.00,0.00,0.00}{1,1,1}{\strut ##1}}} +\expandafter\def\csname PY@tok@mb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@ss\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}} +\expandafter\def\csname PY@tok@sr\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.53}{##1}}} +\expandafter\def\csname PY@tok@mo\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@kd\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@mi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@kn\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@cpf\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@kr\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@s\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@kp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@w\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.73,0.73}{##1}}} +\expandafter\def\csname PY@tok@kt\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.69,0.00,0.25}{##1}}} +\expandafter\def\csname PY@tok@sc\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@sb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@k\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@se\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.13}{##1}}} +\expandafter\def\csname PY@tok@sd\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} + +\def\PYZbs{\char`\\} +\def\PYZus{\char`\_} +\def\PYZob{\char`\{} +\def\PYZcb{\char`\}} +\def\PYZca{\char`\^} +\def\PYZam{\char`\&} +\def\PYZlt{\char`\<} +\def\PYZgt{\char`\>} +\def\PYZsh{\char`\#} +\def\PYZpc{\char`\%} +\def\PYZdl{\char`\$} +\def\PYZhy{\char`\-} +\def\PYZsq{\char`\'} +\def\PYZdq{\char`\"} +\def\PYZti{\char`\~} +% for compatibility with earlier versions +\def\PYZat{@} +\def\PYZlb{[} +\def\PYZrb{]} +\makeatother + + + % Exact colors from NB + \definecolor{incolor}{rgb}{0.0, 0.0, 0.5} + \definecolor{outcolor}{rgb}{0.545, 0.0, 0.0} + + + + + % Prevent overflowing lines due to hard-to-break entities + \sloppy + % Setup hyperref package + \hypersetup{ + breaklinks=true, % so long urls are correctly broken across lines + colorlinks=true, + urlcolor=urlcolor, + linkcolor=linkcolor, + citecolor=citecolor, + } + % Slightly bigger margins than the latex defaults + + \geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in} + + + + \begin{document} + + + \maketitle + + + + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}27}]:} \PY{c}{\PYZpc{}plot \PYZhy{}\PYZhy{}format svg} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}28}]:} \PY{n}{setdefaults} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}29}]:} \PY{n}{A}\PY{p}{=}\PY{n+nb}{rand}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{,}\PY{l+m+mi}{4}\PY{p}{)} + + \PY{p}{[}\PY{n}{L}\PY{p}{,}\PY{n}{U}\PY{p}{,}\PY{n}{P}\PY{p}{]}\PY{p}{=}\PY{n+nb}{lu}\PY{p}{(}\PY{n}{A}\PY{p}{)} + + \PY{n+nb}{det}\PY{p}{(}\PY{n}{L}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +A = + + 0.447394 0.357071 0.720915 0.499926 + 0.648313 0.323276 0.521677 0.288345 + 0.084982 0.581513 0.466420 0.142342 + 0.576580 0.658089 0.916987 0.923165 + +L = + + 1.00000 0.00000 0.00000 0.00000 + 0.13108 1.00000 0.00000 0.00000 + 0.69009 0.24851 1.00000 0.00000 + 0.88935 0.68736 0.68488 1.00000 + +U = + + 0.64831 0.32328 0.52168 0.28834 + 0.00000 0.53914 0.39804 0.10455 + 0.00000 0.00000 0.26199 0.27496 + 0.00000 0.00000 0.00000 0.40655 + +P = + +Permutation Matrix + + 0 1 0 0 + 0 0 1 0 + 1 0 0 0 + 0 0 0 1 + +ans = 1 + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}44}]:} \PY{n}{A}\PY{p}{=}\PY{n+nb}{rand}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{,}\PY{l+m+mi}{100}\PY{p}{)}\PY{o}{\PYZsq{}}\PY{p}{;} + \PY{n}{A}\PY{p}{=}\PY{n}{A}\PY{o}{\PYZsq{}}\PY{o}{*}\PY{n}{A}\PY{p}{;} + \PY{n+nb}{size}\PY{p}{(}\PY{n}{A}\PY{p}{)} + \PY{n+nb}{min}\PY{p}{(}\PY{n+nb}{min}\PY{p}{(}\PY{n}{A}\PY{p}{)}\PY{p}{)} + \PY{n+nb}{max}\PY{p}{(}\PY{n+nb}{max}\PY{p}{(}\PY{n}{A}\PY{p}{)}\PY{p}{)} + \PY{n+nb}{cond}\PY{p}{(}\PY{n}{A}\PY{p}{)} + \PY{n}{C}\PY{p}{=}\PY{n+nb}{chol}\PY{p}{(}\PY{n}{A}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +ans = + + 4 4 + +ans = 23.586 +ans = 35.826 +ans = 14.869 +C = + + 5.98549 4.28555 4.35707 4.31359 + 0.00000 3.63950 1.35005 1.45342 + 0.00000 0.00000 3.62851 1.50580 + 0.00000 0.00000 0.00000 3.21911 + + + \end{Verbatim} + + \subsection{My question from last +class}\label{my-question-from-last-class} + +\begin{figure}[htbp] +\centering +\includegraphics{det_L.png} +\caption{q1} +\end{figure} + +\begin{figure}[htbp] +\centering +\includegraphics{chol_pre.png} +\caption{q2} +\end{figure} + +\subsection{Your questions from last +class}\label{your-questions-from-last-class} + +\begin{enumerate} +\def\labelenumi{\arabic{enumi}.} +\item + Will the exam be more theoretical or problem based? +\item + Writing code is difficult +\item + What format can we expect for the midterm? +\item + Could we go over some example questions for the exam? +\item + Will the use of GitHub be tested on the Midterm exam? Or is it more + focused on linear algebra techniques/what was covered in the lectures? +\item + This is not my strong suit, getting a bit overwhelmed with matrix + multiplication. +\item + I forgot how much I learned in linear algebra. +\item + What's the most exciting project you've ever worked on with + Matlab/Octave? +\end{enumerate} + + \section{Matrix Inverse and +Condition}\label{matrix-inverse-and-condition} + +Considering the same solution set: + +\(y=Ax\) + +If we know that \(A^{-1}A=I\), then + +\(A^{-1}y=A^{-1}Ax=x\) + +so + +\(x=A^{-1}y\) + +Where, \(A^{-1}\) is the inverse of matrix \(A\). + +\(2x_{1}+x_{2}=1\) + +\(x_{1}+3x_{2}=1\) + +\(Ax=y\) + +\(\left[ \begin{array}{cc} 2 & 1 \\ 1 & 3 \end{array} \right] \left[\begin{array}{c} x_{1} \\ x_{2} \end{array}\right]= \left[\begin{array}{c} 1 \\ 1\end{array}\right]\) + +\(A^{-1}=\frac{1}{2*3-1*1}\left[ \begin{array}{cc} 3 & -1 \\ -1 & 2 \end{array} \right]= \left[ \begin{array}{cc} 3/5 & -1/5 \\ -1/5 & 2/5 \end{array} \right]\) + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}45}]:} \PY{n}{A}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{]} + \PY{n}{invA}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{/}\PY{l+m+mi}{5}\PY{o}{*}\PY{p}{[}\PY{l+m+mi}{3}\PY{p}{,}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{;}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{]} + + \PY{n}{A}\PY{o}{*}\PY{n}{invA} + \PY{n}{invA}\PY{o}{*}\PY{n}{A} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +A = + + 2 1 + 1 3 + +invA = + + 0.60000 -0.20000 + -0.20000 0.40000 + +ans = + + 1.00000 0.00000 + 0.00000 1.00000 + +ans = + + 1.00000 0.00000 + 0.00000 1.00000 + + + \end{Verbatim} + + How did we know the inverse of A? + +for 2$\times$2 matrices, it is always: + +$A=\left[ \begin{array}{cc} A_{11} & A_{12} \\ A_{21} & A_{22} \end{array} \right]$ + +$A^{-1}=\frac{1}{det(A)}\left[ \begin{array}{cc} A_{22} & -A_{12} \\ -A_{21} & A_{11} \end{array} \right]$ + + $AA^{-1}=\frac{1}{A_{11}A_{22}-A_{21}A_{12}}\left[ \begin{array}{cc} A_{11}A_{22}-A_{21}A_{12} & -A_{11}A_{12}+A_{12}A_{11} \\ A_{21}A_{22}-A_{22}A_{21} & -A_{21}A_{12}+A_{22}A_{11} \end{array} \right] =\left[ \begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array} \right]$ + + What about bigger matrices? + +We can use the LU-decomposition + +\(A=LU\) + +\(A^{-1}=(LU)^{-1}=U^{-1}L^{-1}\) + +if we divide \(A^{-1}\) into n-column vectors, \(a_{n}\), then + +\(Aa_{1}=\left[\begin{array}{c} 1 \\ 0 \\ \vdots \\ 0 \end{array} \right]\) +\(Aa_{2}=\left[\begin{array}{c} 0 \\ 1 \\ \vdots \\ 0 \end{array} \right]\) +\(Aa_{n}=\left[\begin{array}{c} 0 \\ 0 \\ \vdots \\ 1 \end{array} \right]\) + +Which we can solve for each \(a_{n}\) with LU-decomposition, knowing the +lower and upper triangular decompositions, then + +\(A^{-1}=\left[ \begin{array}{cccc} | & | & & | \\ a_{1} & a_{2} & \cdots & a_{n} \\ | & | & & | \end{array} \right]\) + +\(Ld_{1}=\left[\begin{array}{c} 1 \\ 0 \\ \vdots \\ 0 \end{array} \right]\) +\(;~Ua_{1}=d_{1}\) + +\(Ld_{2}=\left[\begin{array}{c} 0 \\ 1 \\ \vdots \\ 0 \end{array} \right]\) +\(;~Ua_{2}=d_{2}\) + +\(Ld_{n}=\left[\begin{array}{c} 0 \\ 1 \\ \vdots \\ n \end{array} \right]\) +\(;~Ua_{n}=d_{n}\) + +Consider the following matrix: + +\(A=\left[ \begin{array}{ccc} 2 & -1 & 0\\ -1 & 2 & -1\\ 0 & -1 & 1 \end{array} \right]\) + + \paragraph{\texorpdfstring{Note on solving for \(A^{-1}\) column +1}{Note on solving for A\^{}\{-1\} column 1}}\label{note-on-solving-for-a-1-column-1} + +\(Aa_1=I(:,1)\) + +\(LUa_1=I(:,1)\) + +\((LUa_1-I(:,1))=0\) + +\(L(Ua_1-d_1)=0\) + +\(I(:,1)=Ld_1\) + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}56}]:} \PY{n}{A}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{,}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{;}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{0}\PY{p}{,}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{]} + \PY{n}{U}\PY{p}{=}\PY{n}{A}\PY{p}{;} + \PY{n}{L}\PY{p}{=}\PY{n+nb}{eye}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{;} + \PY{n}{U}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{p}{=}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{/}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{*}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{p}{:}\PY{p}{)} + \PY{n}{L}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{=}\PY{n}{A}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{/}\PY{n}{A}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +A = + + 2 -1 0 + -1 2 -1 + 0 -1 1 + +U = + + 2.00000 -1.00000 0.00000 + 0.00000 1.50000 -1.00000 + 0.00000 -1.00000 1.00000 + +L = + + 1.00000 0.00000 0.00000 + -0.50000 1.00000 0.00000 + 0.00000 0.00000 1.00000 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}57}]:} \PY{n}{L}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{=}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{/}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)} + \PY{n}{U}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{p}{=}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{p}{:}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{/}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{*}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{p}{:}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +L = + + 1.00000 0.00000 0.00000 + -0.50000 1.00000 0.00000 + 0.00000 -0.66667 1.00000 + +U = + + 2.00000 -1.00000 0.00000 + 0.00000 1.50000 -1.00000 + 0.00000 0.00000 0.33333 + + + \end{Verbatim} + + Now solve for \(d_1\) then \(a_1\), \(d_2\) then \(a_2\), and \(d_3\) +then \(a_{3}\) + +\(Ld_{1}=\left[\begin{array}{c} 1 \\ 0 \\ \vdots \\ 0 \end{array} \right]= \left[\begin{array}{ccc} 1 & 0 & 0 \\ -1/2 & 1 & 0 \\ 0 & -2/3 & 1 \end{array} \right]\left[\begin{array}{c} d1(1) \\ d1(2) \\ d1(3)\end{array} \right]=\left[\begin{array}{c} 1 \\ 0 \\ 0 \end{array} \right] ;~Ua_{1}=d_{1}\) + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}58}]:} \PY{n}{d1}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n}{d1}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{;} + \PY{n}{d1}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{=}\PY{l+m+mi}{0}\PY{o}{\PYZhy{}}\PY{n}{L}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{*}\PY{n}{d1}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n}{d1}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{=}\PY{l+m+mi}{0}\PY{o}{\PYZhy{}}\PY{n}{L}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{*}\PY{n}{d1}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{L}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{*}\PY{n}{d1}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +d1 = + + 1.00000 + 0.50000 + 0.33333 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}59}]:} \PY{n}{a1}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n}{a1}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{=}\PY{n}{d1}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{/}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{;} + \PY{n}{a1}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{/}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{*}\PY{p}{(}\PY{n}{d1}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{*}\PY{n}{a1}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{)}\PY{p}{;} + \PY{n}{a1}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{/}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{*}\PY{p}{(}\PY{n}{d1}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{*}\PY{n}{a1}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{*}\PY{n}{a1}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +a1 = + + 1.00000 + 1.00000 + 1.00000 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}60}]:} \PY{n}{d2}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n}{d2}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{=}\PY{l+m+mi}{0}\PY{p}{;} + \PY{n}{d2}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{n}{L}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{*}\PY{n}{d2}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n}{d2}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{=}\PY{l+m+mi}{0}\PY{o}{\PYZhy{}}\PY{n}{L}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{*}\PY{n}{d2}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{L}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{*}\PY{n}{d2}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +d2 = + + 0.00000 + 1.00000 + 0.66667 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}61}]:} \PY{n}{a2}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n}{a2}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{=}\PY{n}{d2}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{/}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{;} + \PY{n}{a2}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{/}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{*}\PY{p}{(}\PY{n}{d2}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{*}\PY{n}{a2}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{)}\PY{p}{;} + \PY{n}{a2}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{/}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{*}\PY{p}{(}\PY{n}{d2}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{*}\PY{n}{a2}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{*}\PY{n}{a2}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +a2 = + + 1.0000 + 2.0000 + 2.0000 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}62}]:} \PY{n}{d3}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n}{d3}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{=}\PY{l+m+mi}{0}\PY{p}{;} + \PY{n}{d3}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{=}\PY{l+m+mi}{0}\PY{o}{\PYZhy{}}\PY{n}{L}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{*}\PY{n}{d3}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n}{d3}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{n}{L}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{*}\PY{n}{d3}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{L}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{*}\PY{n}{d3}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +d3 = + + 0 + 0 + 1 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}63}]:} \PY{n}{a3}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n}{a3}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{=}\PY{n}{d3}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{/}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{;} + \PY{n}{a3}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{/}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{*}\PY{p}{(}\PY{n}{d3}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{*}\PY{n}{a3}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{)}\PY{p}{;} + \PY{n}{a3}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{=}\PY{l+m+mi}{1}\PY{o}{/}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{*}\PY{p}{(}\PY{n}{d3}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{*}\PY{n}{a3}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{n}{U}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{*}\PY{n}{a3}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +a3 = + + 1.00000 + 2.00000 + 3.00000 + + + \end{Verbatim} + + Final solution for \(A^{-1}\) is \([a_{1}~a_{2}~a_{3}]\) + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}69}]:} \PY{n}{invA}\PY{p}{=}\PY{p}{[}\PY{n}{a1}\PY{p}{,}\PY{n}{a2}\PY{p}{,}\PY{n}{a3}\PY{p}{]} + \PY{n}{I\PYZus{}app}\PY{p}{=}\PY{n}{A}\PY{o}{*}\PY{n}{invA} + \PY{n}{I\PYZus{}app}\PY{p}{(}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)} + \PY{n+nb}{eps} + + \PY{l+m+mi}{2}\PYZca{}\PY{o}{\PYZhy{}}\PY{l+m+mi}{8} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +invA = + + 1.00000 1.00000 1.00000 + 1.00000 2.00000 2.00000 + 1.00000 2.00000 3.00000 + +I\_app = + + 1.00000 0.00000 0.00000 + 0.00000 1.00000 -0.00000 + -0.00000 -0.00000 1.00000 + +ans = -4.4409e-16 +ans = 2.2204e-16 +ans = 0.0039062 + + \end{Verbatim} + + Now the solution of \(x\) to \(Ax=y\) is \(x=A^{-1}y\) + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}70}]:} \PY{n}{y}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{2}\PY{p}{;}\PY{l+m+mi}{3}\PY{p}{]} + \PY{n}{x}\PY{p}{=}\PY{n}{invA}\PY{o}{*}\PY{n}{y} + \PY{n}{xbs}\PY{p}{=}\PY{n}{A}\PY{o}{\PYZbs{}}\PY{n}{y} + \PY{n}{x}\PY{o}{\PYZhy{}}\PY{n}{xbs} + \PY{n+nb}{eps} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +y = + + 1 + 2 + 3 + +x = + + 6.0000 + 11.0000 + 14.0000 + +xbs = + + 6.0000 + 11.0000 + 14.0000 + +ans = + + -3.5527e-15 + -8.8818e-15 + -1.0658e-14 + +ans = 2.2204e-16 + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}71}]:} \PY{n}{N}\PY{p}{=}\PY{l+m+mi}{100}\PY{p}{;} + \PY{n}{n}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{:}\PY{n}{N}\PY{p}{]}\PY{p}{;} + \PY{n}{t\PYZus{}inv}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{n}{N}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n}{t\PYZus{}bs}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{n}{N}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n}{t\PYZus{}mult}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{n}{N}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{k}{for} \PY{n}{i}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{:}\PY{n}{N} + \PY{n}{A}\PY{p}{=}\PY{n+nb}{rand}\PY{p}{(}\PY{n}{i}\PY{p}{,}\PY{n}{i}\PY{p}{)}\PY{p}{;} + \PY{n+nb}{tic} + \PY{n}{invA}\PY{p}{=}\PY{n+nb}{inv}\PY{p}{(}\PY{n}{A}\PY{p}{)}\PY{p}{;} + \PY{n}{t\PYZus{}inv}\PY{p}{(}\PY{n}{i}\PY{p}{)}\PY{p}{=}\PY{n+nb}{toc}\PY{p}{;} + \PY{n}{b}\PY{p}{=}\PY{n+nb}{rand}\PY{p}{(}\PY{n}{i}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{;} + \PY{n+nb}{tic}\PY{p}{;} + \PY{n}{x}\PY{p}{=}\PY{n}{A}\PY{o}{\PYZbs{}}\PY{n}{b}\PY{p}{;} + \PY{n}{t\PYZus{}bs}\PY{p}{(}\PY{n}{i}\PY{p}{)}\PY{p}{=}\PY{n+nb}{toc}\PY{p}{;} + \PY{n+nb}{tic}\PY{p}{;} + \PY{n}{x}\PY{p}{=}\PY{n}{invA}\PY{o}{*}\PY{n}{b}\PY{p}{;} + \PY{n}{t\PYZus{}mult}\PY{p}{(}\PY{n}{i}\PY{p}{)}\PY{p}{=}\PY{n+nb}{toc}\PY{p}{;} + \PY{k}{end} + \PY{n+nb}{plot}\PY{p}{(}\PY{n}{n}\PY{p}{,}\PY{n}{t\PYZus{}inv}\PY{p}{,}\PY{n}{n}\PY{p}{,}\PY{n}{t\PYZus{}bs}\PY{p}{,}\PY{n}{n}\PY{p}{,}\PY{n}{t\PYZus{}mult}\PY{p}{)} + \PY{n+nb}{axis}\PY{p}{(}\PY{p}{[}\PY{l+m+mi}{0} \PY{l+m+mi}{100} \PY{l+m+mi}{0} \PY{l+m+mf}{0.002}\PY{p}{]}\PY{p}{)} + \PY{n+nb}{legend}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{inversion\PYZsq{}}\PY{p}{,}\PY{l+s}{\PYZsq{}}\PY{l+s}{backslash\PYZsq{}}\PY{p}{,}\PY{l+s}{\PYZsq{}}\PY{l+s}{multiplication\PYZsq{}}\PY{p}{,}\PY{l+s}{\PYZsq{}}\PY{l+s}{Location\PYZsq{}}\PY{p}{,}\PY{l+s}{\PYZsq{}}\PY{l+s}{NorthWest\PYZsq{}}\PY{p}{)} +\end{Verbatim} + + \begin{center} + \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{lecture_12_files/lecture_12_24_0.pdf} + \end{center} + { \hspace*{\fill} \\} + + \subsection{Condition of a matrix}\label{condition-of-a-matrix} + +\subsubsection{\texorpdfstring{\emph{just checked in to see what +condition my condition was +in}}{just checked in to see what condition my condition was in}}\label{just-checked-in-to-see-what-condition-my-condition-was-in} + +\subsubsection{Matrix norms}\label{matrix-norms} + +The Euclidean norm of a vector is measure of the magnitude (in 3D this +would be: \(|x|=\sqrt{x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}\)) in general the +equation is: + +\(||x||_{e}=\sqrt{\sum_{i=1}^{n}x_{i}^{2}}\) + +For a matrix, A, the same norm is called the Frobenius norm: + +\(||A||_{f}=\sqrt{\sum_{i=1}^{n}\sum_{i=1}^{m}A_{i,j}^{2}}\) + +In general we can calculate any \(p\)-norm where + +\(||A||_{p}=\sqrt{\sum_{i=1}^{n}\sum_{i=1}^{m}A_{i,j}^{p}}\) + +so the p=1, 1-norm is + +\(||A||_{1}=\sqrt{\sum_{i=1}^{n}\sum_{i=1}^{m}A_{i,j}^{1}}=\sum_{i=1}^{n}\sum_{i=1}^{m}|A_{i,j}|\) + +\(||A||_{\infty}=\sqrt{\sum_{i=1}^{n}\sum_{i=1}^{m}A_{i,j}^{\infty}}=\max_{1\le i \le n}\sum_{j=1}^{m}|A_{i,j}|\) + +\subsubsection{Condition of Matrix}\label{condition-of-matrix} + +The matrix condition is the product of + +\(Cond(A) = ||A||\cdot||A^{-1}||\) + +So each norm will have a different condition number, but the limit is +\(Cond(A)\ge 1\) + +An estimate of the rounding error is based on the condition of A: + +\(\frac{||\Delta x||}{x} \le Cond(A) \frac{||\Delta A||}{||A||}\) + +So if the coefficients of A have accuracy to \$10\^{}\{-t\} + +and the condition of A, \(Cond(A)=10^{c}\) + +then the solution for x can have rounding errors up to \(10^{c-t}\) + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}72}]:} \PY{n}{A}\PY{p}{=}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{1}\PY{o}{/}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{1}\PY{o}{/}\PY{l+m+mi}{3}\PY{p}{;}\PY{l+m+mi}{1}\PY{o}{/}\PY{l+m+mi}{2}\PY{p}{,}\PY{l+m+mi}{1}\PY{o}{/}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{1}\PY{o}{/}\PY{l+m+mi}{4}\PY{p}{;}\PY{l+m+mi}{1}\PY{o}{/}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{1}\PY{o}{/}\PY{l+m+mi}{4}\PY{p}{,}\PY{l+m+mi}{1}\PY{o}{/}\PY{l+m+mi}{5}\PY{p}{]} + \PY{p}{[}\PY{n}{L}\PY{p}{,}\PY{n}{U}\PY{p}{]}\PY{p}{=}\PY{n}{LU\PYZus{}naive}\PY{p}{(}\PY{n}{A}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +A = + + 1.00000 0.50000 0.33333 + 0.50000 0.33333 0.25000 + 0.33333 0.25000 0.20000 + +L = + + 1.00000 0.00000 0.00000 + 0.50000 1.00000 0.00000 + 0.33333 1.00000 1.00000 + +U = + + 1.00000 0.50000 0.33333 + 0.00000 0.08333 0.08333 + 0.00000 -0.00000 0.00556 + + + \end{Verbatim} + + Then, \(A^{-1}=(LU)^{-1}=U^{-1}L^{-1}\) + +\(Ld_{1}=\left[\begin{array}{c} 1 \\ 0 \\ 0 \end{array}\right]\), +\(Ux_{1}=d_{1}\) ... + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}75}]:} \PY{n}{invA}\PY{p}{=}\PY{n+nb}{zeros}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{;} + \PY{n}{d1}\PY{p}{=}\PY{n}{L}\PY{o}{\PYZbs{}}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{0}\PY{p}{;}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{;} + \PY{n}{d2}\PY{p}{=}\PY{n}{L}\PY{o}{\PYZbs{}}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{;}\PY{l+m+mi}{1}\PY{p}{;}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{;} + \PY{n}{d3}\PY{p}{=}\PY{n}{L}\PY{o}{\PYZbs{}}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{;}\PY{l+m+mi}{0}\PY{p}{;}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{;} + \PY{n}{invA}\PY{p}{(}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{=}\PY{n}{U}\PY{o}{\PYZbs{}}\PY{n}{d1}\PY{p}{;} + \PY{n}{invA}\PY{p}{(}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{=}\PY{n}{U}\PY{o}{\PYZbs{}}\PY{n}{d2}\PY{p}{;} + \PY{n}{invA}\PY{p}{(}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{)}\PY{p}{=}\PY{n}{U}\PY{o}{\PYZbs{}}\PY{n}{d3} + \PY{n}{invA}\PY{o}{*}\PY{n}{A} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +invA = + + 9.0000 -36.0000 30.0000 + -36.0000 192.0000 -180.0000 + 30.0000 -180.0000 180.0000 + +ans = + + 1.0000e+00 3.5527e-15 2.9976e-15 + -1.3249e-14 1.0000e+00 -9.1038e-15 + 8.5117e-15 7.1054e-15 1.0000e+00 + + + \end{Verbatim} + + Find the condition of A, \(cond(A)\) + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}74}]:} \PY{c}{\PYZpc{} Frobenius norm} + \PY{n}{normf\PYZus{}A} \PY{p}{=} \PY{n+nb}{sqrt}\PY{p}{(}\PY{n+nb}{sum}\PY{p}{(}\PY{n+nb}{sum}\PY{p}{(}\PY{n}{A}\PY{o}{.\PYZca{}}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)}\PY{p}{)} + \PY{n}{normf\PYZus{}invA} \PY{p}{=} \PY{n+nb}{sqrt}\PY{p}{(}\PY{n+nb}{sum}\PY{p}{(}\PY{n+nb}{sum}\PY{p}{(}\PY{n}{invA}\PY{o}{.\PYZca{}}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)}\PY{p}{)} + + \PY{n}{cond\PYZus{}f\PYZus{}A} \PY{p}{=} \PY{n}{normf\PYZus{}A}\PY{o}{*}\PY{n}{normf\PYZus{}invA} + + \PY{n+nb}{norm}\PY{p}{(}\PY{n}{A}\PY{p}{,}\PY{l+s}{\PYZsq{}}\PY{l+s}{fro\PYZsq{}}\PY{p}{)} + + \PY{c}{\PYZpc{} p=1, column sum norm} + \PY{n}{norm1\PYZus{}A} \PY{p}{=} \PY{n+nb}{max}\PY{p}{(}\PY{n+nb}{sum}\PY{p}{(}\PY{n}{A}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} + \PY{n}{norm1\PYZus{}invA} \PY{p}{=} \PY{n+nb}{max}\PY{p}{(}\PY{n+nb}{sum}\PY{p}{(}\PY{n}{invA}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} + \PY{n+nb}{norm}\PY{p}{(}\PY{n}{A}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)} + + \PY{n}{cond\PYZus{}1\PYZus{}A}\PY{p}{=}\PY{n}{norm1\PYZus{}A}\PY{o}{*}\PY{n}{norm1\PYZus{}invA} + + \PY{c}{\PYZpc{} p=inf, row sum norm} + \PY{n}{norminf\PYZus{}A} \PY{p}{=} \PY{n+nb}{max}\PY{p}{(}\PY{n+nb}{sum}\PY{p}{(}\PY{n}{A}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{)} + \PY{n}{norminf\PYZus{}invA} \PY{p}{=} \PY{n+nb}{max}\PY{p}{(}\PY{n+nb}{sum}\PY{p}{(}\PY{n}{invA}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{)} + \PY{n+nb}{norm}\PY{p}{(}\PY{n}{A}\PY{p}{,}\PY{n+nb}{inf}\PY{p}{)} + + \PY{n}{cond\PYZus{}inf\PYZus{}A}\PY{p}{=}\PY{n}{norminf\PYZus{}A}\PY{o}{*}\PY{n}{norminf\PYZus{}invA} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +normf\_A = 1.4136 +normf\_invA = 372.21 +cond\_f\_A = 526.16 +ans = 1.4136 +norm1\_A = 1.8333 +norm1\_invA = 30.000 +ans = 1.8333 +cond\_1\_A = 55.000 +norminf\_A = 1.8333 +norminf\_invA = 30.000 +ans = 1.8333 +cond\_inf\_A = 55.000 + + \end{Verbatim} + + Consider the problem again from the intro to Linear Algebra, 4 masses +are connected in series to 4 springs with spring constants \(K_{i}\). +What does a high condition number mean for this problem? + +\begin{figure}[htbp] +\centering +\includegraphics{../lecture_09/mass_springs.png} +\caption{Springs-masses} +\end{figure} + +The masses haves the following amounts, 1, 2, 3, and 4 kg for masses +1-4. Using a FBD for each mass: + +\(m_{1}g+k_{2}(x_{2}-x_{1})-k_{1}x_{1}=0\) + +\(m_{2}g+k_{3}(x_{3}-x_{2})-k_{2}(x_{2}-x_{1})=0\) + +\(m_{3}g+k_{4}(x_{4}-x_{3})-k_{3}(x_{3}-x_{2})=0\) + +\(m_{4}g-k_{4}(x_{4}-x_{3})=0\) + +in matrix form: + +\(\left[ \begin{array}{cccc} k_{1}+k_{2} & -k_{2} & 0 & 0 \\ -k_{2} & k_{2}+k_{3} & -k_{3} & 0 \\ 0 & -k_{3} & k_{3}+k_{4} & -k_{4} \\ 0 & 0 & -k_{4} & k_{4} \end{array} \right] \left[ \begin{array}{c} x_{1} \\ x_{2} \\ x_{3} \\ x_{4} \end{array} \right]= \left[ \begin{array}{c} m_{1}g \\ m_{2}g \\ m_{3}g \\ m_{4}g \end{array} \right]\) + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}21}]:} \PY{n}{k1}\PY{p}{=}\PY{l+m+mi}{10}\PY{p}{;} \PY{c}{\PYZpc{} N/m} + \PY{n}{k2}\PY{p}{=}\PY{l+m+mi}{100000}\PY{p}{;} + \PY{n}{k3}\PY{p}{=}\PY{l+m+mi}{10}\PY{p}{;} + \PY{n}{k4}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{;} + \PY{n}{m1}\PY{p}{=}\PY{l+m+mi}{1}\PY{p}{;} \PY{c}{\PYZpc{} kg} + \PY{n}{m2}\PY{p}{=}\PY{l+m+mi}{2}\PY{p}{;} + \PY{n}{m3}\PY{p}{=}\PY{l+m+mi}{3}\PY{p}{;} + \PY{n}{m4}\PY{p}{=}\PY{l+m+mi}{4}\PY{p}{;} + \PY{n}{g}\PY{p}{=}\PY{l+m+mf}{9.81}\PY{p}{;} \PY{c}{\PYZpc{} m/s\PYZca{}2} + \PY{n}{K}\PY{p}{=}\PY{p}{[}\PY{n}{k1}\PY{o}{+}\PY{n}{k2} \PY{o}{\PYZhy{}}\PY{n}{k2} \PY{l+m+mi}{0} \PY{l+m+mi}{0}\PY{p}{;} \PY{o}{\PYZhy{}}\PY{n}{k2} \PY{n}{k2}\PY{o}{+}\PY{n}{k3} \PY{o}{\PYZhy{}}\PY{n}{k3} \PY{l+m+mi}{0}\PY{p}{;} \PY{l+m+mi}{0} \PY{o}{\PYZhy{}}\PY{n}{k3} \PY{n}{k3}\PY{o}{+}\PY{n}{k4} \PY{o}{\PYZhy{}}\PY{n}{k4}\PY{p}{;} \PY{l+m+mi}{0} \PY{l+m+mi}{0} \PY{o}{\PYZhy{}}\PY{n}{k4} \PY{n}{k4}\PY{p}{]} + \PY{n}{y}\PY{p}{=}\PY{p}{[}\PY{n}{m1}\PY{o}{*}\PY{n}{g}\PY{p}{;}\PY{n}{m2}\PY{o}{*}\PY{n}{g}\PY{p}{;}\PY{n}{m3}\PY{o}{*}\PY{n}{g}\PY{p}{;}\PY{n}{m4}\PY{o}{*}\PY{n}{g}\PY{p}{]} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +K = + + 100010 -100000 0 0 + -100000 100010 -10 0 + 0 -10 11 -1 + 0 0 -1 1 + +y = + + 9.8100 + 19.6200 + 29.4300 + 39.2400 + + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}25}]:} \PY{n+nb}{cond}\PY{p}{(}\PY{n}{K}\PY{p}{,}\PY{n+nb}{inf}\PY{p}{)} + \PY{n+nb}{cond}\PY{p}{(}\PY{n}{K}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)} + \PY{n+nb}{cond}\PY{p}{(}\PY{n}{K}\PY{p}{,}\PY{l+s}{\PYZsq{}}\PY{l+s}{fro\PYZsq{}}\PY{p}{)} + \PY{n+nb}{cond}\PY{p}{(}\PY{n}{K}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +ans = 3.2004e+05 +ans = 3.2004e+05 +ans = 2.5925e+05 +ans = 2.5293e+05 + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}26}]:} \PY{n+nb}{e}\PY{p}{=}\PY{n+nb}{eig}\PY{p}{(}\PY{n}{K}\PY{p}{)} + \PY{n+nb}{max}\PY{p}{(}\PY{n+nb}{e}\PY{p}{)}\PY{o}{/}\PY{n+nb}{min}\PY{p}{(}\PY{n+nb}{e}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +e = + + 7.9078e-01 + 3.5881e+00 + 1.7621e+01 + 2.0001e+05 + +ans = 2.5293e+05 + + \end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor} }]:} +\end{Verbatim} + + + % Add a bibliography block to the postdoc + + + + \end{document} diff --git a/lecture_12/lecture_12_files/lecture_12_21_0.png b/lecture_12/lecture_12_files/lecture_12_21_0.png new file mode 100644 index 0000000000000000000000000000000000000000..2633731df9d9cdb4e52b0554900637c7cfbff738 GIT binary patch literal 9047 zcma)g1yEa2v~92!clY8>Ah^2~_uv|eOM&203I&Q3XiI{&P+Uq0THGyAXz@ZRw79#I zpT76z&wumh&--U4xqI)s*E##Fv-X`kH_1?6lL((49{>OlX=|w&0{|EZ^iL5N3mv&t zUZw^B@HpI6RSn&podJN5#dq)A470#ALx-nw+wn@|Dz6MxGx#`T-jZ7Je6K23+R8Un z_eyNRM`T3H&^>o$HU{KEIG{fp_;*hjOs1TS^iY$$^yx4Ve94HhN9bn z{AC^q4d8{8C3$-TH&+Qkd;T6QR=G#_D6aR)otM$TK=LR(Op)-zdWbL1)g_ynTIq52 zTJQJK^)lS=7%}zPmLPt4S2&5Vh`ihbf1xd;$2j(BgfqOj>v(G}&sX3k=g;oAZ5S0k zfRXp+F)=C@6@FN6D)r)QzI@oL)F8k#%pAs=32$1$W6mBsqvX&W;8J@qJnGVUcwC|h zDHGQ82^f8(>=mdhbBZDs7X^x8uecr0?s}#_(LkXl+`uaxf5QOt2mot%XZY$nK;QvD z>E;+};9c?gZ3IB(;0S~bUy++WNqB^5$V!S{KmPgeh!9Eia(&#tiLdY@7?=~{ zkN88VF>uKoSw|CvdNo=SACsr3J;8JV87IDFKiA^_o_hA=lJtpaT!fmVp%^7a$?JMG z>Eb)X2va@}P$jKdyiD4T(s|Lr$3a83X&Ny)!Sq>W>kpw@N`YcB1hz3knvz97r{*U6 zw(!ov2_N-!*8w54Zn~sg#0WBz6zN3wKAS;8r$G^frGWXPs<_79Fo(Xn?RiWu&I{}d z@?c!q*!vjvwYPp6QkphEA-wEY{6pe@gw_)LvRXphrRPbH{Xt z9aX@p>_AqH+xb$eS3(8n<2%1ppianB4sx@^4K-mW0e}84FG7+-;-ob0w2Cqtv~7%W zdE**#15*OwXNhO;b-6s>c#rh_4LtD)pt$C{rn`=#)zdXd;ii7lq+V@Rt?H$Gekszh-F=*sA_ z=6W$2I4bu}eZ*rdYy>jGoY}!8%dVM?c>8CJYBc|SxB$tR=UDid?^{K-6=B7y59Pl< zy(u!R@H2DN$oTlIinh$MG{nf?Dyh_^hO)}EG*Ek+((I@pZ?8uLBn0H2 z#GJI_KOHdOG$_$qui#UDS3_T7Rk~QrXKZ5p++xhk(;5|9%R8VD>0QeRXf{RjI|5f>EB_T zrn8B)bL?buSHDjtv&}^7$)s5ws+<0CvoyPGuHw?lUQf|7`g2s_0}U2M9CqBJIPL^f zRhmAzKA*m>)P~e6jTwzgi%bid+NJt>&vgc8raxMLR0m1)o^c&;$?ApaD&*$C@pY~B z%EqUWD&rnVjrqVP?lxFtAEURATj#)C`?V&4$?L$^Kd7U@J640%64v@PPBqCkGj$$I zIs<&j$_brk;|;`(3SNQ@MooB#isn$CDh~$7pU-4Rrq=rX_5JLA(#_-TE$(l$P%r5% zja?*mWJP|wkHMPh`Sx*i6<(a|+~EAWczC4Wz4(W#TLYr%)NYfk05koY=US2t(ng~7 z>}#e?q)nAgVVip!-qP1)M<~r@n-^~$dxAX?bH8l3+k_mKK6!YL)2P;{l%Z@y=`ao=Z4 zgGzp6D-1jkj;AouIm2h+GjNvrJH&*`Qx|U6OW(;~b)J1LY0eW^X zB>W|2yb~l|`5r73edUZE>o+f}8EPhL8t}ap{KooO>~Q%aW`Fq_|JwR=2r9MzjF*(3 zlrm+nVF`Rou~Rl*_$at$$*gtvsiWFz4O?8%Nm0C0)NxHAQFQH9s6TZ2AeQ_`rfN7a zJo7?s-V<>dQlaLqzkQ`}8Oh{|tnaOd-p(C%fqiW3!ejhc|HRbw))ZA4*8~`>tC;D| z_%+%FS*J#f*XFdwkv)Dzyuj>HV^%I$c^@csanvVM_BAam_2z^f#tzrC6T6Z;V{&Ej z_IT?p;BglrunjwExjg>Gg(xkBTyJDjw{RA_-lz>HwQ=to1UK$9%{GcGChNzV(3ROe zkl&2O{irPqpQ!uRP++EL{X^eVcrQjqA}~?LStj0A**0#|X5u{1I=C5CdAa-Lbab;y zSjRjUOS?SE`MQL-?`o9$MsW>0qrUOD~i@q6aB!>$8s&gS!S%R$J!2TR%EccLnW zO<$`eIq2)is?(^6C{Gq3(^iXfaM^C{_3}ZFSscwPuY}qqL>Kg4;qYO9 zb*3+lasP`vAT_wCZZc(~GAW+#9+n zyp@X6>O4*lB1>a1m~2LOa|0RS;C0e~BHC}s-)2m%5CI}QMV z3=9CE@yq*aBnJRsvKi`{s-sXSbk6@csHmv;`S~?9HCq@|_x^+93=IDC^rci( z>iqmxL`0G#B%EYqmIMUi904NCw82|uBsj1=Oq74WDaPS`lwXw4P6cyd4qq~5^QI(bG z6;T!zD};nM@86FgH;`&YYHiDH2bTvB1SGLP(X7%81P3i2ER!XY!I5x_JPWoAw#u1G zi_kXBaJW6?G@31`stv%_29QexfZzZ%=&#KKfG-=4lN!KI4JU#OU}i@8ij39< z%IX3w9I5P{S_aS~0T57FEqX$zj`cDC@4(W18In=yRs|J&tp*H)3R+f*nzr$HLI2eU zhl>Q0_?6kC&;+6P+|~xG3~plsERz9_1vvL*MK2U(|8Z(&_LG$rz5nr~q<8Yj~AQ6X23+>?fX@Q@kum5ZSsI8~|comb8f`*7PL#`J9p!U#KQ#K7*+|N&nJ{<-R?e|OP!Mw9e4DEa_Y`?Bs z3XNnM=gul0GYln>RLpPSo|XKjO-yGb#?vHuZ+sB2a@*Usiu`^Ma376)GLp$Iohe=~ zc6@rk?3517UwR?v%3a*9GXe>3!tHF**0Ms=`$N!_VoRCVwTNgQwWi z@7P-ig}9c%i(p z!X9L9^?WxBUGBt?1w8`r4pqjxlLz7~7qB^mr5=IUdTq4@S2#AZQ0;x2g6yE1?9ygHNyuj z1%>|47sTqTbfF~3qB#KwoA+I1_|*z=D+xsh_ZKI}E}KXV1uoyIFD?W~>L=%p5X~8t zR;PKmRMH{zC1#YKfX`<_B>6x!+a7y%!relxWhev~4iQ1z(E+XBMgS=;N4||JgLw`a z+LAGe$@l%)f!6a>ZJ=CxG)ImQ@q|q*$kfyPuH4^zXij42(Bw@Kz|iFVe>*$fDYB3! zK5ju&Xdb%>VHk)lb(r{kJ_$@+xL4N+s_=hIbv#@xJy31wCqLQRW_WhRh)w~Um%;E3 zehkV$R|->l|0CpZ!2??-!C9J=ulgQ}fArk#)!*Z8o%5Kz8fqY7nJv`yfGn*N=!=oD zVUL8FLHQq>{jCpH7wJkDDErEPU`~oq5jWr#P&x#H`aR3M_G3c{)?Aui(cm z)fC>gk?kc54OoQL0Yr)m4=qh-yW4RR0#P}K$?|t}H%9WT8!ll&A9ej`DX2emTwQyJ z(!`6$V*ssF+V@j*!43$78!cO_%tr@(A)^l&ua2eU{@uD?SdF#hA&`jXVm8fKH`9e| zoi6h&dhUUVA+0ttNyy}IF&_a&{F#m-t&P?qfA)m;!dYPaIz?GEe>R!P`BO_+Yc0yh zCqCs1A^-Q_7qEDWOXSjQv}AKdwR4h(19f&OEVKsY-4b+tEXeg?~K73PE@-yMR4tIuf@W3<_ouO z0Z3?n>c#m=P0N(S`_x8nY>3@GXz1q997X6!CH&a;wX&1L?E7`%Hj0360xeDsrE)EP zKBO3kVH_k{B(Lof!H;47L%Nud?iA2JwY2`v(m5W|#elSf5T)#Oio&)6EpiHaL8t{! zG`185-VHfetOdj_bVMs-TSP&_B!RDO?2vl_g~Q#>VOS2-CBx4liq|H+2B?(k9M8W+ z-UV{%sfEJ)2k+wJl3Q2ux>%#NN$WndDTq%?b_O3A?I;Ex!JFt(1XJ{@cvcK;A77qN$Nzl%4 zJHAkrpKUN%Axg2@q*4E1$V87*ktrd9lugUh1Z$7@gM0P&U z7)+Jzoibh0+7MRi;eby7yqW&>>NHOA1H62+(i8mh19u-LB!d7Z&j*Qbtz?0z*U}+3 zD9}9pXVd-H!TdLe58cjVW7RPGHwye?TPU}Md_Q-%Suk~p{TtUa6wN|@9clfeR@Ww} zih!(!^rr&E@Cr2kn9E_Xu*Ibm0CE`2j-iXjgxul5j=9mn|F^T@1hKb{m_qJ!Bjez^ zi))^{y*E~)R@QRN5K-W%!$wonl?GS#sH;SE<3KD}_rzhNu_?qOC^v!->GW0>bSR$A zRMt8f;60$xGp9Ose zQon$9F+nt~wSqq9-?kRljzzL!z&sd;c!K|_;{V)Bk|adXVUP)ghkoV}5AY+hTKI)D z{D-UA>uo>e$odcehr%T>Ko9+#h)2LbX>eS${_X#N7$NW0HNsq4!a$Pu2#^ABV4QK_ zpQxU0fhS1J>T-N!X18w6YcTIY@@peT(On#|aZPSwc+x-iOVxl?*NQo!RTzjCI1a4h zy{JhnxEiS+16CUNhHfDY9OM-R@Q=ZW!z@8S11@?dB+7vhebRD#Q4mfCYQtj?8lZ%( z`7I&Dc105l@d68JRMy)Zxkee74lCRjC^#+yA^dDWM(f?5hH6sRJeDP1yPEN z3~??^?nWwi2i;#*1U-5l0`KuQN78o-l$XLW8^>60^{OrJmrZ5EbAAjTTrfR^`P0n-(-3y(c-#+^0y;a_jB}1{Tj;cn2!B$<=C+(9QhQ9%y}*vK25NhGtQ z1sXl-LthcLa_aRC#uutSx%CumKv}F^xY4S_ShupsA~dojqWi&OBTcdHGy3$LSl~PV zKQ>6_A(bPdoO|~fN^<)^S@}$AKJicbN!><dT)Uh)jSsmReu`)Vt1)rZ}^?u{{ zGf6r?W6Stt)=X2vUQ}nHx_QqY8?wsznAWYZeC`toDhtVWZqBh$S2&7WW+Oqg~a$n&Nnw4vrwz21d=aH z9=YRqw*27Cu!HG6SIg6O+@Mj;gyp}PN!l5P&n(OG6VVTijcY(Xv^d|cK{Wh=u3a=B z7VP;{mu|GO;@?Rn+;g|s6E7>Ufx9@$Z&)FMYq>JD(SbD->OERB@8K$EibOx-bN~n? zT=M>ujh~(^0Qpy{p1eWq5_^`K^)|NzuyKCMKUEy-X%u@ZUA}G%;KMuUvu)-qn;YG@d=U48(-8(`2L;O~8<7?U#gIph2(h^7*$rM41emIV^ z9~stle*``<`>QGFV&gqpte>FIQ60`T_8$k^Va!t|pmW>%J+lv!yJqlcn2E ze$6*lZn=0BxbXzd^K-C21ERCkR?Wn_gF?M#Ms_-l-i5SP@5c$Zc;9RF(%1y?&Vbv! zfDgO(QPF2rEAO!(L0ytBX_0=z(W#@<+KuPPaF9;&ch2gZEvSS{pkyE8^idQ;i1cg& zhD0MlzSM3{YVEE?9L8c=t+>ewvoPYTNV7c<(jqcI6TNe2?c)(hW#%n$XicO|GHbe9 zN+0k;{8|Z5EO#;PYwIlI>YyKRQaCZI^SfNovgVeP55syW{GMK@=Uta?D*!}JE%Xa- z#WAtCzjlW;A>N4$Vw*Dd{5$SWUu;wweLDdK{_zx6t`T@=S8^Ko=fbUFcEjOfw}mzq zOA{};P4n=%%Al#_0n7tdDB-6tC#pcns2~5L=kRlYhZenTff z@LL1H%4EXLRj0T+&HV$>{j}E+CJ!BQG0GPg4!mXbSkeAHFPI^pxtV7twa7YR?V_7c z9Jbsf&FNvo>Gk3~xU7n2|5XOjP*d${cj_-vaWBahFi2pVu{oh1cDHDJ0>5rcDw}H* zQJo-+wd92>>&AU@ILE~z;3#pg*-&&xygP%yssWWTx5Y3s~ZM(BF#s=VGs zC<$)&CBxx=UxTyHijCHxf)M-32GBI>uBaIN+)(5Pjo6}LJ7#BAcM{R`tFO!q$0SLk z=N}Vabn&Y|{7NpFYJS5aUkFA)mS4fN|0ZQ{F;z>#@2PjfCB*iS`A7$ z^LgH*JfLomsA5m)*{6r3)F(Bt5bWZm!9fb5>=(QI$K>jXn>34|4!#3eppjfKL75YG z9E;xRs#E`-x8CjkMs~x>leb|yxpDz1g*Ik7=Fpa3?>I{O!n&_A|04Cp+0DCTI$+7d zwYR6i457{vwv9FVKkF%R)X7?kt?PY!v%9MAeQY1(_b>PD{U5~yC4jlAKk6@&?+`eX z1pjCzkNX-N6)fGZ!eWy$@hBxf`*mhdwKGHCo;FVyq9o0$xmPTQ8X@d%|9)L@QcRP` zD9hALJ)?Ii-CtVCZrh{MNS1+OE-=YTqu3&(!alw4aqM&S30M2O4Q1i(r-{8wdItA) zHu>>j=#3(~&uX6D(&>Cv_o$d)w@q~jj4VG4dx_X8XOD=C(x}1T?^Wd1)cjo?!2^MC zQzMA+85Z9kRz9%$;Nx{;T2*w+S5vI)mziV$ zw*8`7MIb;%OUs42;3PFY9Po{oC#W< z`SRO$5xLQOK~Fc!@w=^wrDXfEII(AeNZt`MQN(FuQzJ3clldF&Nw{q@gMj`>OLcMV z_kmw5mqtvNjUoz8E?6oEqHHWClXjJrhBr26;}YId-O}gJ?~|K+-JG4}u-lp+v=sYV z&q5-mi{QKgr#)%z+fgTtGuvMSk+l;>`M>fOD)TNvkA|`7)I-sXOL562`@2;MV;v(vvW5uap^2`^k3K)E20<>s|+dJ-i$;F z34`yMAc-EA-XrT98@8}LB#+eEG%@e-xmT#8KdNbKmwiW7G1Vv*@v_ZH|)#Rf*~;<-8I~ z?T3#g4L6M z#aWY}&OF9*jM`KZpR#lNz|)npERtWX`A?xxVI)ZU%xoxVnLhiv_wFikcXXwh=5O>1 z5aRQI&dpTrOTr= zW&LRM-$V;pe>~$oh!htaGggU})L3F~nOxgUC>s(`Fq2Y8exu8f`=So6_XSU@S+u3O z(2lIv&XU-6hA)dPX8_+q?ulw9o%z&;;M%`Wm>uMmN?Hp7wQ#ZAw3Q1!NK-vr-#6iF zUA6y{)z>YY)g`kpYw8BZzGJ^NYY2UvXu_6KZ@KltlEYG>Y2+NY+(Saec0S9@T>TSG z|A&yba49J7^|+%dX%e7CYh1%Ejs*TQJ?kih7cPF zVhtDP8rhtgp=5`saOGN!0D0FEl;pm#JHKDHdHTiSy|n?zIl-!4Oh)yJ%?D30M@Ml% zA0MRgAdm|NeWRWztie~S`XsP=x6ss+lA)-oXn74Pes)ToVYH-`Awmxv{*uHn=l8Q^ zq9}2jun{pi;7lP|zg=jwJN)ma$WGzMB5yZ1CE2B7p^NI}w`T<8U!xx-+oDJuG>hI! z-$_ByAEG$})hz>E90OftoC93Z7l0^GL{bnaDkv&tDk3H$3X%~42?E7sfItO`t*ieA z@b-0ahlKvW0S5YpYG?q|6Gnj=PKvT6-ashwbYA^3PwL%7}qZg?Z%TY?1S(wZL38f3JHHWKImV{L0My2b!$@`a$XRB?2 zf*A`of;wkAS80rn@;Ns2T}^RidBn%~V@`PDGuj)o>ov2y>ztQoN9&(=T`vHUtcwfi zC!0{x%i}lwv#hhvHHb}h7rp7ncRm+0|CoK!HDz7nwqRSaR{L=MW5iW;6X6i>q+6O~ zd440>tJk2^Ak?*?(NVCmVUI+Afn}l2^!jWK{bX#7@G7W0Nk0)P2e;6NJCMeIF59J> z6=#?=bN2%N7>8gaovfX0^^=H012<2S&cD1zo8Wq*xbnzd$4H`K7yjV$Zce&7S^CrR z$)*bsv=1U(DWqcdOx%yuVZH^gW3LkUjz2yRWldA~y+5JQV{XDvgfsIkSs($?MLtxm z6xdMf2Jr_c986|AdAvS5@2GD^&uOSzYCy!k7Ri8dLwu{gR(-=0b5m#+>}d{bgM5)h zl}xk+IGSTEv*&I+?_kJ4w@9^61aY*Xrbq}pOWf`EHJd$4TKqli4qCn@P=HR^>M9xX8;N(8S@jt}RK7APkp2yGdoeZ1t9 zLbb_-1qp?_Ut!$wWos64ac}0KCbdfQSsbJwg z^vRM|9)Y^W36Q=v!;M#%vmo7uM%AWbPb_CTklIAGu2!vBN>DeT%I`HlQ#Q%}$lecV z4pqk)9KLfmQ19ufUvX4clsYINsI(Rr?P4b_8^z)2E(7sPZ02yt*UG2GqAB;atW4Ic z-dB9-<<;jIW3$~7S|^&wv*VIot>2#*VH>WB)ym|LH!l7-{D@91qROfv=HA=ZEG%fO zQPN#-j)st&B4G*_o7#$~o`q<+POcmZg4OA>uamxCWBFlb^e6jW6@cO5Vvg@o8|yaD z_j(|qM`4m0|z;<)J0KMAgrv$2}Z$yFMlBF@ZIkJ2{OLJ)|GE zau_WaiV#dX1Z*#VM#l-q2-uEsE~IlAY)qbtB?nMuPC?N5O^T}qh;XIxCnYz*#Pn59 z>dc-}Cq7=8OXt9xrs*bb?9&#Sv3*P>;WC?^4mfh*;_)a)m5%U={)nKj5EEWYN0+a^ zX@yQy)|SytnJeqUEU-4yoDx0sTNGKsG3}*htu#&dxI5^#yYp~6s}iLBa*5rfUp*6L zZC*3Zql2oUcMFJaTSZ`bL@31oieLbNytcujw;xc+XeJ-&gN(0BgkjnI?{uai^CBB* z%S%FRC7`O4P!+Xtl|1s{{G7^z2<7-bhM8EUHIdI~aVcNaHgqI0M+rk8?*=6A8ZRY8 z0n=)CHGYOZHCS4<4h<3At`tJ!(Pt5onl6=%ZevhnKyM9f*I}P_Fko&cw4Qp>5!_(@ zQ1Vi2S|-q=+=zQxvnROQKQ{gu5k?70mfg8fBK%}wi9VZ_aCBp6@8?Mor}rFxi^Pz1 z$&YKDqB88K4??0$__Z>OY5{=R0<74pvvbuDpl;jFI@(Z z?9GZhs*xY=R@p-tUrhdkE>m@bnxyi#X&>iZI=&3fG0F5Pgk)%)#s!JHyD}`8d^>-iYKRpr+h`Pk&uu zk(BSvNZfP*rzYo8@8ld&`ZH3wx}j-ZN3ZjOPO=y7>g#|JDn6A!C)r}~mmiI73gRRQ z<-(QHN?}l5oW(^93KE_rR0GfZ*$e0C?sWM_iRCQ_yQx3|}s)gSRy zN+Br2Yf2)hJ2TdVSx$A}K&K`<0IY!V%YZhr`?^yK;f8tKxXfX-*9}3#Yvy~ev&bBX zvY7il$8cv-;zGcc8(w+oj|c09hTky(13CB;`V<<>F<~3__g*!`XE|WQ&0Z;8qK&A@ z0cTEKcumY=h0h+smb#YrQ`wD!_F;kZ*Y1aF=NYM6oa%ZBIAeQLoKEfXh9w=n@>NWz za3F*5>-SO$9v?jK(vi~*w#lc1_RUv>+t0q9N;A3^$mC_Yst{*WpRo}VXN%%8WD6Jm@cPUx*B_6$*$*?!ZJ%{qSN~5v}bJ zF|Y@e!Kp3%0+dIG`RxMB4=x56%Ya~fAUNMt#K@FaeY6>lGAkHXH+_*9FQuJR_tQ(W z*g|s3;_J!dq-8^1XwC+6$N$y>cp^eR;3b+%Dc^8H5 z8Q>ttGN1>aog64~sqJ?c?`f)!v@j}m5Sl2)vp`Ci@w4)%fS`{e3NWWR8kdQDme9=a zPOFsV|pP>&%^5%S-I0<3IxF;+U5A%)(m4pJYa24exY;+UYXOmFsYahPh8cYq7l6LRL z&a8H>bj}T&F|=yd(6;o&niKuLc`c)|@xlA*Sdk|98{IBHtNMW)NQkTB0v7M{80A~| z@ev-Ha}fHRoO-~_oSkUuR$KhTBPE8=Sj$3w{?FFRc^&K@3vem(b@LpxYpik>s;wrI zgmjvmWOd+Z=`=GP^bA%^X@hu7{J;>AWI7VjZS(54#rpEG3`@`Ix9L*V z);dCy*pPS}|0C??`%iPK?@bml(2NXUv)V~YR`Cr>xCKJx#X81&B4YYGMNC_c&~#f) zNH#@S;j&`GbmjTSZS$ju?FLg$zZrJ~VzBZ&%5sP7GRHwe+@hZbJ0)=EP`c1ek#%}I zxge`-P-9k>i68sz!=P}AxTK}5zMe2V|K%0Jx#y(Q1f)FfW+c+MJIe=6-6VtD=fkgd zn@(oZSWOQhRm;;+xON*u3qiY$^Ai+GIM#D+AOl=8uA#d<4ia9^POk`u`}5{pAv0fW?qU8M&CqfM zf^n7T60Gi;D~HCd6cMBQwF&i!a)KC9T|%uoOmlVf{dmdv5B`tc@c!32l&w9am^s#l zR}6#0ajd+LL*(wNQ9a&jPQ#-0{PDP<{|E2YX~^-k9;myc;aO+=%*+hjawSQeLtax2 zx|E>Ind`Z~rMNOpGrvDWyoBY^&{^OPJ^za(h(`^#NOH`&+dbOp|?u3C>( zwn|nKzY@2s3qLnWUZ}${uU1xkm88`aZOwt&>qg@i@jiGRlbjt-+c{Gz_nV4SE==?R zf%&33M@y|Fl?tbe<0_S;rQ<|v?{!4a)D=#ekq*L(!L5TPp;M=(CBP`vsnO$fub($1 zcMTiUzoTaPK;EHqtyF--`ytOcU-cO5V^8}eUWucS&VCe1&8a6|0D~f?OW^%&3jQqu zJ;`v;b1XYvg0EC)hLqWvQ5x!nGjpSMd3nz;=wh8jb}-7L-RL2ZBRAaUC1WAX4ReE( z4VR=bs_t$Y<1kV(o;?(@#7gV-!88hv?HPKfl6j0KZ$3tj61QU_yQ582yDF1|uIK7D zGnMDP;iI$Kef>3!Dr(K}1ZVFJirtnQu?;VqufcsdEvL)veFT<2V#bRS6)=B{gYB!= zLZ0=s_j(oCi+DXwp&9(iCNo+zXUv;|?dY6)E?d}Y)5Eq(2Ecy17WgifK1%4(t4!En z1F^y*Jqxc{5vNpE5*S_BPx0)#!+mk~Ma8XOEsbNIywk>V8>2?Ia!wH&pkHB$vamef z8~Ae1b#Q@)W=1`QGiaPl=f&(Oh`VJe_<4HiE6cZgU86?Nb5qjYb2oR!#Vy?W)*3w@ z9I%enbB@;2*gv7O{hSfRk=!2>E~(RymFv@Hd8ZE*bBVdcHjdOTSk8zkr%NLfoFGO< z?rkQ3Dl~(!YZNv>`CWMYgyg#F8*E4>;YnOb9)5ugLp+BRH0Gstj}O{3rX2BW#RK3$ z0kup_(>Yd;zL9O%+rkXg*eSxdPvw_miCVmf2MoEBo|$eu$n@d&!Ra|Ud@YskMbBi= zslmj$#ux|v7^tfMTBo%?j^VvwY98~c-zCbzhwY_?c(*IXD^1VRYubacVZ^=8!c&UK z3is)z?oNJP`nuID>quQR|c+WP3)q<_$q&yTnPv(6bjJe}sKoG2o+M4R?-k-p{Hh^b9e0 zZ->WZ7@8|OD9Qr+VK}31Y6-#(x7X6l@Qx|nWN%SL*h`*xIm~9E%MYgBT*H<_xO!vi z1>yB*=Ib-e;c6T6+~RT(q-8ce3LGh9nsg1K9;4-FpPDzl+}jHRdeKCPLL|{S2okg@ zus-wTWTRhEH+=IFqM&`Wlh59YWBl40XPk+-_SDgYI6~Rz9oAfZLz$h-SjzB{HJ^S> z)su~Bc`-Fm#-YBB)))6D@}q9Swj+Xrh6x|uC4-+d35}AOc6GSWlFFu&&RnsnQStV@ zCBh5ms2iEo*A|>IV(+X)fZFqFHh)Ic2Kz(nW_VemUL+@9&8T)dCw|#wF`vh+vIYO(jf?(lB9y#3%PNIbr)!(~ETmm{evG!4x_r!h}ic*UVssQlqE27co*XQn4J= z_hWcspZ4SupF|gRDT8HlXlSm_bDzF8uY|@_zS(-Wo2;w|-mTkb<}JN87~FsJKyE;{ z$*c9{%{i2QHKab!P|;Wf z7f(G2+77F{;?laLJ7RPzvEDsQ-Q47GWNWDXau!}YVCiza+_3xdayczl&zfjA=;1z; z%$RmM%|HBM-;@a31g>cc9WR+I)1=u$FuNGnRVtiV}`DsyT&+Pc8#A7P9BCVeS}GD~QTjpQZlT2}MrNwm&J ze92Gq_LfMq_HD5?9}}QQ$K}sR4(r=Wnb+CoU4+mU5*J%0r)1nPL3zew$zwNV!)3!M zGQLM1yI+F6N(Cn<6N%E+dP8~-Ogc?E;WWgwCBZBwaout5{YH}=RuWj$PPA@lfe*3B zNu$<#LwgUubrQP)i~voq%kt7klay@CEjy0NuEaR{h%q2+6^cDP7GQ3#vaMD&uDQ?i(w>KhK(cg*@E5~RyY zx_KqoB|f3AIye?7?`;!LW_T`kZp@a?bJ;D2f3OAz?wBb}fdcB}6T;3x^oml;z2}-rzKE7)39T-5X`)NA zE82n(n~9dE)7W1#C1}|<(TuYBlAbg6^0c^8eM@Gv#TL!ZkC&Pw{`#S)bM7+pht(W< zebH2~`kEX!gL4^ikY$*mBA@8tJF(sq)ggh6tikly@Q|E~yH3sPQu1kp3x}9XSK8Nj z&KMlh+Ff*?q#jxj|!9s0V7-SOsN9Y z{f~uIa7!^q=H})`PKekdM$`5EN-$S&WMzA#=wzm%a5E2!11d0^FwtUI=pql@$ZnLi z;@J1UZ|XfU_duAhm2`Nb&d2oI~4mtn1^;lkxn%AsgD&H!u5&j5&{%Z15{q$=gct-z=;;i$eXzM|zI1 zCyusdEhDO@Wour?qK-N;$z{w4k=sxKKtK0SGx*s0kFGvGyCS@PX2F_mxr~mMD2B6l zo}TU*Qg+Pq&{XdT!i$O{_9W{n#|TX`Ma~&VGDQD1{&zTJTIZPSg4Hnn^b@J zi+jVIP_PZNCA{Ii+KbPj1vJ2&H_(r9S`ig$YE;-c)w;u&`5T|@%{sNnrc@;I)qHU3 zP}Ma!9%XW~(L?&a(6jZ7t=&7osuOCat7)aHldz6GTz#4l!F$To94bZI%sjoM8{~`T zL>!Wd+0ucqOt6VBwk4kZNGy<}T6u$|orQ0anPhDDQB*-VLlg3TjoQYa8Nrf$%~3u& zMy*TWjz9S60iASgR!SO`PVpW;U+}aNrYA+N^nL0Z$&{k-E*sycY@?6?3}LBv95Lw= zDI|?zDstJ8~=hwWNZEuU1`LBl*Y}F4%os z6(k*OM!M+kTXGvr4jNiHnJ2&PwpfzpmgkK8=A{i2dG#d91UDPS>|MExBIcMzH5#LY zQZXm_3_^L0kX#<}T@ByDM>Od!&ZshY+y4rLRg@WH0$5fR+ut=`RXclRP+}}Ey#S+_ z2S_Ra^`7d+=9t|SJ|3mld55DBHaTAl?<#L9?;E8nk%W<<38BT=zuc}{xfLZPNtMdQf_YybZ!l;;LC!$tbXFXo4GgM zvh78xr%gmH1TLbBdLF06L@fnva+EKjAv=dqpgl6`xqU7fA^AvOf)t z?NvO0oSCY+_`Yle5e#{!v<*2g<0xW|byTezoE^d`A-ibftudF42rPS52uzS)?aOtYzS+!*b;5H!YHKH z`b<3<*+>|#4j=*^T8rn7?PqSjTY)ResD}lqWroGU>Rh(PnEeG=e3bnX%5VW4qjo(E z5BsWcL3-ONY;{Z~B8{iR3m1p+jAujlOLT(eSB>ndV@WP-Uw>Ldp{!YEg9w;(MKZaYRe=*y(ct_dc7#)@nW$p-bGLqfXafK#A@68$rWWiqP3Bw zaWbq9WtW&sTz}B=+0aJYwAiJ&2K9|O`5?XvNwLQy>VVU-%)5hRJg#P0J*=c-E`42`Ob%%dPLX%acE zFiv?`%cp%5oBEMK8~erZ72(rxr$?Lcq`lQ%^P?7u>Z$2sbI=Qv742x-45h&;eQ=OR+nStNfg}#6^Sv`cs zzQ_qd^L2BRWmQ;zK|=}OjO#^tD^W~G2Y9bT9w;M<+e5B#oszG4aP#`!b<+H;|7g6~MXp30=V-DnQ;u$%+ zaAf;;5k)_;BRB25mUJH0^6y`*`$LphwwVe6<&iG69}N8GVw2rHaPLGl-S;;@+}mzu zVYaDK-}SZ?t`TP0B*&T|{gHQAIu{T{v+ilMd{%3H@%=de^edlm^2GhbTvPwhUG~61 zY`Q|e(ya1o;_m}36$c$GP2&r?xZ}RLu1~_>OUXQv{VKSB9bBu=5+waC=CsFyI$@9Zp-`Fb&{yt9S%yi%$T#XRvC6Ol2p$MXx(8T_t! zyChpI?^plrwO_vY!)*`<=bv5!-=_5cOppIg%HJ{uB5(&IdvjZajs35L{w*YDV1;A^ z^bv{a^KB23F>lu0XoqRlwUi`rnn72Bt_VfbB0y;orOgGZ@4M z0y496umQoG+z=p`4Z`*Zfgp)6urxOkvNpAZ13|yq2{{2XIfVbqp-^qeoV&vb}_}!hO zA>tP)qJpF&ZY}i-6*h2y|Dss_UzRbqcR;|*4DA0jfQ-Q(Wia^nRQ_ph;4g>#-ZP@s z$Ri}?)}}yKb#rSWYX|c`fnS={&5aRe4u9}3w;S!heIVf58FC<*nLq#jTj{^G{Qto? zz-&l;>_8~{?Ms0Jd~4NPy$~Q9=k0i)oZP>jxH;K>p&ZCb-^wF-B;*qmxhf#sw>?0B zP;T(=C4uCIY*ekyZ_m^KZ#(_F)Be4LZ+WZVD^uFs_|`_Z)Rxj;?3CjzmGw7@2szyU zxE+Q(t%F?mKsqA>b9);gm<7zv!U3c+Lm+HLl*$QA5u zj2(@Tr+@zM&Hh8Yf&YH2==Uas86dZSjp;8>|C-Go+}nQ|x!A)^03aZk9RT|40&+m1 z5Gc?D_y@)fWk^cB61_Iss=${xH7>YE@KQS&2E~NkdiLtS9{aXh+ zH}b#4Kjk>Nq5sms$<6sMIW7qDUGTr!aXhOjq4ZgTry yhqaW=-Qc&jx+V9NY;2JJ{|`4QX>Ee^^IyE71H!-_@yoj05Ka()hDKCg4DdhY#voS! literal 0 HcmV?d00001 diff --git a/lecture_12/lecture_12_files/lecture_12_24_0.png b/lecture_12/lecture_12_files/lecture_12_24_0.png new file mode 100644 index 0000000000000000000000000000000000000000..c8959a778ef58c458d330d44e24be5362a426045 GIT binary patch literal 8571 zcmch5bx>Si)8-@u2@(Q9f)iW=VbH;X6Fj&RbkN`oE+M!DXK)ERSQsR@I}8w#*19%6_Y5W3!MF8e+(=q|zfIO(8$anetg(B)rXQ zzP#I#1S7>SvkA!opM>>^+v-_ait*ZV_A^4Hx>b%sd#>!*snykmjuLz&@$)ymoiVR2 z8DwQkj?>qAevE9E;{13NT$ip7A9)p+Zo8hjrS*pUxJ_h8#=O-L!pmGw73`jmuAI(?`!pm=yY1WFIt+ zI+Y%U-QO^YUc=?~Kf{*9+91>p1qfiL2!D{=4FJJ)&e?k9`qO_AsmxWTDovD9w~poqYlP9 z0(8*hRATr)#~=;?ScMqZ5|9Kl)MD>r>*SO12eVA#s)ee#&>BCQ?{;z_#}8$Fi^I~z zN&on;TkMIHekA@BJ%!>^%?J;A#z+DKnP*?9HV81K3N-jro>;$ap7bii;Rvh92bDd& z!31HOgnX0^on*Ad&kTPEm*~b(`SiE;apj}EUdIfK)}D?dLt#p_F!$g7-a_c*dRc!z zyTbLSq74r_;`AnaghOObKN9)6NB(;xHgT-%tH)MA&BzqSb4AV{ac8eCpTFV@^_Ml* z;3s)e98)JNQgo-`ugzf(tazyt28!Q(dtQhv7|>vtA?K&yPMDK2%J%kAgGYNjJ zAXNBsYJReJ=joXrK2~p6Ew9Z>u*!3mXK*5|SdmD(UgH6Li-9+AeJ))rSZG6!?}y&n zzYC8YnJ=DP5PRW>hTI1;uBEuh3o97&zJ8h>!8s_f{(3FkCHcEgo3JU3bI4_v!f&D9 z%0~oOAMa@Ho&@I7OMM`!#Oe4f+#@KBS&-@y$E)P6%tWjcxh2bE!R5;N?UQ%3cc`%Z zonm29{X1h#9QM%qERR?Z=vm}hnhJ}<7pLLw4UdzLZZEDmt|_iVU#hC8$Fh>WYLu%q ztdwz7+!w%9e_!gtw#O!t;xX>}uz~=1bik8JHyTmi(P2 za~$(MGn^U5%%g})fg=;zZOO!|^sQu~Fj92{g zYecc+Ft0VW)tdFih{uRns@$;ssPC}NFl|yhizuT)Iy_~4lyoE~&5w(4)M3z6`}au*$Q`NRTS*vnG=67Tn}hEXL}RU|O&5|4L(nYEIJ%~^OkGul-W z>)PtzZsBe@C&4FexXS(N%<9Feo8=r*sa2H4h9yfy9GY61?s}s-4)6Uc!7@6H zL#@2&4|Y#%_h)uyGA!P~y(_78@f@_1EA5J)6$UjvW_U&YbJ6plGEY6KIl-y;sp`3o zB8_6X zggyzy3S|w~mLcyI>;2f<8CM^7B|j^Fsh6Y&s$QYDBrpbZ~b`1xN1dY_H zEUKc7XKU@3mHIixDiBJx|Fjhyo?7d3RdX@@NwM&B zf9YWBJK3`8^5{imdvZX*eK5vs_e8<8UD32PxE>BWHQgr4eVj1i zuoh)JW-Qoz){BUgaBG~af96Q+)iKf zHnH}Kc2jRE-)-N^>q-B)TmIX&%Z5|#SK zqhX>Vp_(C$CAc8`h@We+UTcHOjC!8@<fA?NDm4|ar6ila#?_WaMba;@r`g)@Y{1Narl~@dBm!!_>8G= z2{m$DsAjtxJ1rZxDcpU#>i-=4xlz{G!gj5h$zIc6)49&V&Fkbtw3?DsH18~fXHbRW zZw_0P&>wRpp2gGY68#VO(FZzZ;6R-=qfnt6fPLyj9e^iVGbJY(=DwUY$9sxcfRGGps(RST)7B7Sh>c%HaZ=I z2p`z8Kj(Z-61!i&Y;gNxw{#&7%d2Wxr+H7=T=q{DLulbiVVFhWaaA5cQ1z9MD`W;4 zLOh)$d}_-JhE7wkg69$ec~RS46p za#P=w)=`;tX)y6Lit`_@&TI}P!j5>hNNZoEQ^s9!?;(6~)C($YiT91WIbqCTgesWw zUkRPjSkpP#r#Nxh-}!U>%{cmgdHjn7UQ%Lny_H1vow>;RMs_HwmGwZ~t6{fsuHns6 zv|5N3MXBin@y%%Hbakm8qIRM_S4YxlTFrrHKNuwF5ec#cg_%g1gl-!n&OMC0not#& zd*4n+wqZPqrfkiM-!p<-k2Mj+i=*u6;A&YjibI3d(+&IIv$yT0?HKdMH7nnd-uL!& zrH4NVU{u@AhRb4*m;l&mScH* zNa@bt z)bR9tvC|Q?OO6@M@(bq|*MrHO?$*IK$iShmjW{^3UEN<&QtwJ?tM@ozKOrFRv4koD z%>99!L&6~d`LK3l?eWId^;q(C;g>cy_L)@lv5DSNQBxHF@MQr2fWo0EIBBG|IMngmM zU%dnYfF^(v0Kfx4gNccW>FDTqd3jk`S?w7a>xqfKJ%3(8O6p5T7fnS4efiRrl2VS7 zQ=gTUnTW`cfIuG)?|;sQ{v-$l(%RY@6%{o$HYO`8OHWVF$H%v_vQk)B2!WuWP$&@* zQAI_Cj*boziL|k?0Rn*x3=9AODl#$>5Db8{LiF_XgoTAsva)D;V`He56%-K>3W@y3 zU}J-7ZABwd6%{BT5ar@B$H0J|6NQg|qoadLOB>dy(2*^ab@oO=$DjZp6nTkkU1Rgco_&(%F|I#fdEWpxnpD_`y#)Mj6DxxpopZv zQGw7~K_pTn6#SrteXUWj)_}a$j)gH{e+WR;#x=WwK2TOU!-nsREWif%Jc7uq(gwg; zL1JzLU}$|7Mg$Ox1js@FPmxr%HUP>oObgk_!ZErqpkB7#KOE3ZAdoCQy?>aX`JiKE z3K%q!M4|bh*`hh438RVW=!_RebqNdi6&99RS)n<@o~`bp!_DiVsip-Wf<_{3R&>UI z46U*UN877=n`d^O#uXazp2i)s9i?^OXBQ?r`bGvS>*jy2@j|o(x@gh9k1UiGWC4+w zG>Yhlr!I;H?&$F!T@fHZ>>z&Bh63V)f*G%41eV5gZK3IHmm<1 zydS#E&PDz;!%I`E_u|UJG0p}f49;bBib_V)NF?sZls18Y^B5o=<>~rjZa-^rY<5^J z3nAEM`Fpzr9}aX{N;b!;opVuVs?D5xXDE`DW3>8dIfGe75SFVK=JWth+tae;+Tqk|CxWpUfpv zMSYkI)EOU7nDJ-ZM-})MTFq`0RM@173j}275K2Y4Jt4KgvMT-#XW~NIB#DVYhm+tg zIo8c7Bx1Q=uQ9|{wMg0gI5>kjg03^T59nYcS`XRTVQGZ@ku(OIkot*-gOgLMpwW6XTO4fDqB3i7+_ti-jqiuZ$;Gsn&kx>rph}sN^Wi7Zm z0a%?Itm`L_kVZtTKz+MVHiST>tu93+PAS`8P*7rdU#r>h}V=AZ2lJU9HdOkSy|}k%Y@YGsumU9O2@WIc;>VFK3e3b@+mV= zPDG^emdxesI&o{?mdDTgiRxT#1q)&R2K7O?pMgsnNGY0%tP8k>?|)!ZNz&phm4UeE z4oT9~!rsq>=#yM7y;tLFq#_Fj9^X`Z;$gHnhe!nmT5WcJAJP>EZS)U2HmBgvn=jV_ zG#Afj?@USNxbe~1&)AGzt?SZ7;pxJRW#ip7rp8AiW4SUfJs9ARs`P!SjV zl$0)z)4k`X@WuYCzhE{q@sy57+Anff%UykuC3V=HgdW33s~<@ef$5Lua%p6;ah&-z zX`|uL)6T2}rLl}~(glN8;D@(|j&pa1Tb4}7jKa+9u&`0+{M}(Vt6L+kaE{M}GWURi1M@)=&=es9?fiV#H2&+GHALah$$jxcH!@1)6d)~3Um0EE%LfK)$P4s- zi&a>*%|oq3QxSk&E2w(=i-NW?P%FE6Z{`*~jv8Nn&c;N@ylg%BH{0RAO)MVep4XF$ zz2fO|igb0nlA3lFaENoKNWylm6W-ggUuRgZCd1+oJ`p_sTT;&!mGO?mkii3jp~Zln z8sI1ksh4=Yh{9_zmTR4v{hPY8KzWg|%)eXrcu9kIURZYCdP@?{AAKcNFS&nX&2pe0N!JEaBDosH5_zesCg8fD$_|1;^-3viKfo@)? zg&ZlV;r*YUh+)9f0=Y8;E1|b+jrN?p|&|hkE9VtQva9oEd_YHyoN3dvF!0|Bmecp6I(`$ zac(t)bWiVMWpn@k_$%1`rv*B{yq0)Q^MKA;;v%ALTg{kNs}{|OK= zx;S>dYI2ItvcMlIy1~V7jIbF;A#*3RRC1IN(!HBw4iAvqw&o2kt88?ziW|q($9D$? zT~8VLOT9I`$Jiy(;X8u-ehFpSVFSdQv4b3Q__P0FhtdcQlz+r0Pk4Y@K0x$P__U61 za76H^DY3i%mk1hp;%c#PIQFxrjUbua8rQVlbZ(~&+Z7SI+48T`;j{6SVonb|mx*wl zEfOZ3G1h*Y_|y9hM@%*c_;i7Bs#|lKw`N4YCd}|gu7XN0qyj$6$DZz1EX@uX>G?v* zY30;-ri_M{g~ad1o^fzmYRuJ3`f`nx`GRSnS-(O_t8+gQRLHTl)BYTi-Y!HrBp19PrG zy8dg9J!XUcbiJYL#qF@ccM?NNHc{)CejiC0g!I?<+^U9E*RQ~@07T~fw6@yhw^z8r z4zF9rhuC#l8#B+BmURl{t`NBLo(~iS^s%WNI;t=pWDHRUP!OwjxpBRS{>C&lyaqqw zure2pB}FG3hRb7-+RqSg*8?fx{)JOiG+R+_J-+XE&Fl|8$gYy|dz)%i&|}fdu~DY~ zMkc;7$b6SWc%6dJxFORzh|`FMa;r96S14WWUN;)+kLbDxA7%aY@Ee1TqhtUFY0+mL zd(W!EYcm+VKln(QpQ=7>u|73%KCz+kTGa9Fy?({0iQf()`gf%Tzip{}qC;xtuE91} zY&&;|bPUZiPAI84jN=yjWead8cb0!DpCTgBJ1xjy{`@!OQjA~B{l||A8|w_1VwB*^ zmGYFyoRBg@Rc$7Xv1o3_iO$Ce-^+%d_ZnjYr5+>>hCd|&^?z)TR(1S>u!bS=M_xKi zS1g;(?o`jZb>bp!B=iD!Y71DMh*!w+9Ty!1IGt2s!}x*NzJoa=EpQI^0jm0vvR6MH zv)|q}kb3IYD;$Ik+X0HB=aNW9M29982n$4EwMVAzbjiXIsc zsKAlZQzt@!-gx9P3xvo|WG%p7%&@3sbvFsa_h30M7HtFgt~7R z`pF!rJwVX)wR~gZ8t47I=e-cpd6h?6)t0?+q%GqcWo=oiciAgW;Wp}Bnb!w}+lmpp zCDTH9hCD$6yLIyzo^zSi($PIoQNosoti!!d&(7CdE4E*z$yjT3sFIVnjb_7ZW_mvIPta|^J>*lOo2cjf zUx&-*wrAZ~4)`GBXbI4vnX!k0Udxn3?WZ)lT2_X4s1-UK1Vu`DIoo#ucOLvR&htxY zq;|TIQ&oQghl5ku(=0=nMW?*nWAcCx*@s7bbDJPgI9W31g+%XWKI{U~JVJ+$fC?7T z&ScZd^}BQjnyungX;pobNb^zBuI{6(dR#Nxo!@5R^$S{NZb_rD1k%9v8sCtTSUots zp8}tp*wDK{QTKp7c|qe{we=NX4AJTht@e}cUAmncIxMG{_m#rCJxPp+qn}0{`&*)I znN(`HGdc?R>L!%ji*hKjJjmzhqHl~9__g8=3(s2gwcW;tli$F`{Ztm;>Yx+OQ!a=MG?`2l&?P=3t;Y4j#LM^=UG@wTCh}{J<^)fnw6Y7 zmrSkdk1#KjC05a$dD^SJOFhr5C2x5z_i}7g!XdcjBHBfG z_q9o_@ssUJC}*m{{mugGr1-5n`08ssf%UH0&Y`j>&Ss&8=T*fFIX*TRpFihR!kIOX zF3Ou`gk&@k2Sd~cy1o)3!g=!QcjjK3Fq?l+`QD_$qmylf`d#Y7Jl}*LS5rmi+^3sb zE-VOVEnD~)*)!nDO{ynTl4spOQHaC~+TH|fx;&gQD2tMQKLtp7ceR$@l`IIh_e0I^ zjXaK%+^B*=4B-be&(`ZZ=*p}?)9C0D0QYAGp|M9gD*oq}Kb69R>~aK*R#uExTdgrw zUhJ2u6O~dc40baG`2sls)w>L-AJYlPE>7g}7ebdl3VV>2b=z_o!bWqizr`G1KQ^nw z;mZ~{qz>bRpMH@Q8+Z+_tg|oY4!jE57FmAO-q3lO+~6kT@RK1XO6BBBwqYmFa0DmGs$XFWE7H4^-Ojx_I@qPu*&ov zd~e3W%3#;XNx{SV{@8_B-6Yl-FB1Evb4v+$(Jo9LcNt?Opfzs?(|53gkW`I!2wMqc zvhPMerS|I5;c?`a64vU6D&+q*LSa=FtRegQjJytT>nZWn6(DQcB-efNDeU7+^!5Jl<4Ym!H41$m@Q@lo*A2OOWV&r+_-cm@4xts z5p>^rc9k;WLRa=T&mY5A(!gQsBP-Q1ROTqPU&l~d8`YK<`6UMqYG$NHF|(ps+Rkvf zZ}tgxnE}Y(#!Ts`o%X7~Fte0Dl@NjQ9r@Qr+o#BHchG@IK>Y^+E9N?+vdfouBV)b~jHTFF!U8;)?!$t<^CNF19D^iRB+x z{mMZ1&q*ESCNa$(cBSj_0BLUF#m<&3z638#r{beE;aZ2 zZg`eM&HR&9^B~jZE@PFM-#caAY z-%1uXdNOyCmACD-ds*rXt^IYdB;wegAJ~>?Y+pRL_1~I3=k_0Ly!$jO?)c}$aTl#Q zPew!1ed-?Jn7D0++kIz@D14%yBfI@>W45jJ^ya1*KId;v$}&%Qd=3x8+mhLwrrJ&j za0Oq8B#cWm;FoYDWYu2I+8+gJnEBs@i1*jP>3l~wB7*wpBtfYs#ZBq!qh^7(!=i_3 zrIJ3_-WFm$mo%b>i@z?a&vTnrZ%1AnOLYjIj;r^TzB*_hrp(n}<;|)Q&U?u4zDhbi z8;rvqYS>GKjI|%n8A%=|XXoA6k$`jvS0BcYa(tCiX(jEg@-*uct4?yUZQ`eNX5 zz3^b~>;q_7cKj-$<#Et_W8oCH85Nn3U|$efQ)=8$c-?`JpX(cdwYAeCSKTY3cSZWO zQhZqYf{?2Vwps_l0H=j@PXhxIDyCO{Jy2+aHGF8kaLD#8u?B((-%8%{rz55XbB7>T z<3*(20&(4U%uPq-9^on{OeKrITuScf=Gqs&tF{i>#0{0Geny8k>;}u)-lL~o+5Js| z41C$lv~tBFp_yE`4o7+YPMctcsX zZeBiaK4I-Q{2)Fc=nasYR{+GzEAe9I>c2QRIa}G;`22eZbu|rHv;*BgE4a9W6zw#v z-KCv9KU&#+1WP-61Neag-oQ5^oC2I8N$E#bXejl6LRGB2tQ`STR?ZgI+`!ko^l} + +Gnuplot +Produced by GNUPLOT 5.0 patchlevel 3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 0 + + + + + 0.0005 + + + + + 0.001 + + + + + 0.0015 + + + + + 0.002 + + + + + 0 + + + + + 20 + + + + + 40 + + + + + 60 + + + + + 80 + + + + + 100 + + + + + + + + + + + + + inversion + + + + + inversion + + + + + + backslash + + + backslash + + + + + + multiplication + + + multiplication + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/linear_algebra/LU_suggested.html b/linear_algebra/LU_suggested.html new file mode 100644 index 0000000..f1998e1 --- /dev/null +++ b/linear_algebra/LU_suggested.html @@ -0,0 +1,39 @@ + + + + + + + + + + + +

Linear Algebra Review

+

(Gauss Elimination) Suggested problems

+

No due date

+
    +

  1. Determine the lower (L) and upper (U) triangular matrices with LU-decomposition for the following matrices:

    +
      +

    1. \(A=\left[ \begin{array}{cc} 1 & 3 \\ 2 & 1 \end{array} \right]\)

      2. +

    2. \(A=\left[ \begin{array}{cc} 1 & 1 \\ 2 & 3 \end{array} \right]\)

      3. +

    3. \(A=\left[ \begin{array}{cc} 1 & 1 \\ 2 & -2 \end{array} \right]\)

      4. +

    4. \(A=\left[ \begin{array}{ccc} 1 & 3 & 1 \\ -4 & -9 & 2 \\ 0 & 3 & 6\end{array} \right]\)

      5. +

    5. \(A=\left[ \begin{array}{ccc} 1 & 3 & 1 \\ -4 & -9 & 2 \\ 0 & 3 & 6\end{array} \right]\)

      6. +

    6. \(A=\left[ \begin{array}{ccc} 1 & 3 & -5 \\ 1 & 4 & -8 \\ -3 & -7 & 9\end{array} \right]\)

      7. +

    7. \(A=\left[ \begin{array}{ccc} 1 & 2 & -1 \\ 2 & 2 & 2 \\ 1 & -1 & 2\end{array} \right]\)

      8. +
    2. +

  2. Calculate the determinant of A from 1a-g.

    3. +

  3. Determine the Cholesky factorization, C, of the following matrices, where

    +

    \(C_{ii}=\sqrt{a_{ii}-\sum_{k=1}^{i-1}C_{ki}^{2}}\)

    +

    \(C_{ij}=\frac{a_{ij}-\sum_{k=1}^{i-1}C_{ki}C_{kj}}{C_{ii}}\).

    +
      +

    1. A=\(\left[ \begin{array}{cc} 3 & 2 \\ 2 & 1 \end{array} \right]\)

      2. +

    2. A=\(\left[ \begin{array}{cc} 10 & 5 \\ 5 & 20 \end{array} \right]\)

      3. +

    3. A=\(\left[ \begin{array}{ccc} 10 & -10 & 20 \\ -10 & 20 & 10 \\ 20 & 10 & 30 \end{array} \right]\)

      4. +

    4. A=\(\left[ \begin{array}{cccc} 21 & -1 & 0 & 0 \\ -1 & 21 & -1 & 0 \\ 0 & -1 & 21 & -1 \\ 0 & 0 & -1 & 1 \end{array} \right]\)

      5. +
    4. +

  4. Verify that \(C^{T}C=A\) for 3a-d

    5. +
+ + diff --git a/linear_algebra/LU_suggested.md b/linear_algebra/LU_suggested.md new file mode 100644 index 0000000..f809813 --- /dev/null +++ b/linear_algebra/LU_suggested.md @@ -0,0 +1,68 @@ +# Linear Algebra Review +## (Gauss Elimination) Suggested problems +### No due date + +1. Determine the lower (L) and upper (U) triangular matrices with LU-decomposition for the +following matrices: + + a. $A=\left[ \begin{array}{cc} + 1 & 3 \\ + 2 & 1 \end{array} \right]$ + + a. $A=\left[ \begin{array}{cc} + 1 & 1 \\ + 2 & 3 \end{array} \right]$ + + a. $A=\left[ \begin{array}{cc} + 1 & 1 \\ + 2 & -2 \end{array} \right]$ + + b. $A=\left[ \begin{array}{ccc} + 1 & 3 & 1 \\ + -4 & -9 & 2 \\ + 0 & 3 & 6\end{array} \right]$ + + c. $A=\left[ \begin{array}{ccc} + 1 & 3 & 1 \\ + -4 & -9 & 2 \\ + 0 & 3 & 6\end{array} \right]$ + + d. $A=\left[ \begin{array}{ccc} + 1 & 3 & -5 \\ + 1 & 4 & -8 \\ + -3 & -7 & 9\end{array} \right]$ + + d. $A=\left[ \begin{array}{ccc} + 1 & 2 & -1 \\ + 2 & 2 & 2 \\ + 1 & -1 & 2\end{array} \right]$ + +2. Calculate the determinant of A from 1a-g. + +3. Determine the Cholesky factorization, C, of the following matrices, where + + $C_{ii}=\sqrt{a_{ii}-\sum_{k=1}^{i-1}C_{ki}^{2}}$ + + $C_{ij}=\frac{a_{ij}-\sum_{k=1}^{i-1}C_{ki}C_{kj}}{C_{ii}}$. + + a. A=$\left[ \begin{array}{cc} + 3 & 2 \\ + 2 & 1 \end{array} \right]$ + + a. A=$\left[ \begin{array}{cc} + 10 & 5 \\ + 5 & 20 \end{array} \right]$ + + a. A=$\left[ \begin{array}{ccc} + 10 & -10 & 20 \\ + -10 & 20 & 10 \\ + 20 & 10 & 30 \end{array} \right]$ + + a. A=$\left[ \begin{array}{cccc} + 21 & -1 & 0 & 0 \\ + -1 & 21 & -1 & 0 \\ + 0 & -1 & 21 & -1 \\ + 0 & 0 & -1 & 1 \end{array} \right]$ + +4. Verify that $C^{T}C=A$ for 3a-d +