From 9b28df097f8b74a2aa329ba32e86ceef4a90840f Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Mon, 20 Feb 2017 17:22:36 -0500 Subject: [PATCH 1/8] 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 2/8] 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 3/8] 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 4/8] 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 5/8] 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 6/8] 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 7/8] 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 8/8] 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