From 9bc0a6b927835bc845b8ca86bfb549404ab17191 Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Tue, 28 Feb 2017 14:26:15 -0500 Subject: [PATCH] update lecture 12 and recommended probs --- lecture_12/lecture_12.aux | 27 +- lecture_12/lecture_12.bbl | 0 lecture_12/lecture_12.blg | 48 + lecture_12/lecture_12.ipynb | 175 ++- lecture_12/lecture_12.log | 841 ++++++++++++++ lecture_12/lecture_12.md | 112 +- lecture_12/lecture_12.out | 7 + lecture_12/lecture_12.pdf | Bin 169270 -> 232410 bytes lecture_12/lecture_12.tex | 1015 +++++++++++++++++ .../lecture_12_files/lecture_12_21_0.png | Bin 0 -> 9047 bytes .../lecture_12_files/lecture_12_24_0.pdf | Bin 0 -> 9736 bytes .../lecture_12_files/lecture_12_24_0.png | Bin 0 -> 8571 bytes .../lecture_12_files/lecture_12_24_0.svg | 148 +++ linear_algebra/LU_suggested.html | 39 + linear_algebra/LU_suggested.md | 68 ++ 15 files changed, 2440 insertions(+), 40 deletions(-) create mode 100644 lecture_12/lecture_12.bbl create mode 100644 lecture_12/lecture_12.blg create mode 100644 lecture_12/lecture_12.log create mode 100644 lecture_12/lecture_12.out create mode 100644 lecture_12/lecture_12.tex create mode 100644 lecture_12/lecture_12_files/lecture_12_21_0.png create mode 100644 lecture_12/lecture_12_files/lecture_12_24_0.pdf create mode 100644 lecture_12/lecture_12_files/lecture_12_24_0.png create mode 100644 lecture_12/lecture_12_files/lecture_12_24_0.svg create mode 100644 linear_algebra/LU_suggested.html create mode 100644 linear_algebra/LU_suggested.md diff --git a/lecture_12/lecture_12.aux b/lecture_12/lecture_12.aux index c73dc14..4aa3a49 100644 --- a/lecture_12/lecture_12.aux +++ b/lecture_12/lecture_12.aux @@ -17,11 +17,22 @@ \providecommand\HyField@AuxAddToFields[1]{} \providecommand\HyField@AuxAddToCoFields[2]{} \providecommand \oddpage@label [2]{} -\@writefile{toc}{\contentsline {subsection}{\numberline {0.1}My question from last class}{1}{subsection.0.1}} -\newlabel{my-question-from-last-class}{{0.1}{1}{My question from last class}{subsection.0.1}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces q1\relax }}{1}{figure.caption.1}} -\@writefile{toc}{\contentsline {subsection}{\numberline {0.2}Your questions from last class}{1}{subsection.0.2}} -\newlabel{your-questions-from-last-class}{{0.2}{1}{Your questions from last class}{subsection.0.2}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces q2\relax }}{2}{figure.caption.2}} -\@writefile{toc}{\contentsline {section}{\numberline {1}Matrix Inverse and Condition}{2}{section.1}} -\newlabel{matrix-inverse-and-condition}{{1}{2}{Matrix Inverse and Condition}{section.1}{}} +\@writefile{toc}{\contentsline {subsection}{\numberline {0.1}My question from last class}{2}{subsection.0.1}} +\newlabel{my-question-from-last-class}{{0.1}{2}{My question from last class}{subsection.0.1}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces q1\relax }}{2}{figure.caption.1}} +\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces q2\relax }}{3}{figure.caption.2}} +\@writefile{toc}{\contentsline {subsection}{\numberline {0.2}Your questions from last class}{3}{subsection.0.2}} +\newlabel{your-questions-from-last-class}{{0.2}{3}{Your questions from last class}{subsection.0.2}{}} +\@writefile{toc}{\contentsline {section}{\numberline {1}Matrix Inverse and Condition}{3}{section.1}} +\newlabel{matrix-inverse-and-condition}{{1}{3}{Matrix Inverse and Condition}{section.1}{}} +\newlabel{note-on-solving-for-a-1-column-1}{{1}{5}{\texorpdfstring {Note on solving for \(A^{-1}\) column 1}{Note on solving for A\^{}\{-1\} column 1}}{section*.3}{}} +\@writefile{toc}{\contentsline {paragraph}{Note on solving for \(A^{-1}\) column 1}{5}{section*.3}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Condition of a matrix}{10}{subsection.1.1}} +\newlabel{condition-of-a-matrix}{{1.1}{10}{Condition of a matrix}{subsection.1.1}{}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.1}\emph {just checked in to see what condition my condition was in}}{10}{subsubsection.1.1.1}} +\newlabel{just-checked-in-to-see-what-condition-my-condition-was-in}{{1.1.1}{10}{\texorpdfstring {\emph {just checked in to see what condition my condition was in}}{just checked in to see what condition my condition was in}}{subsubsection.1.1.1}{}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.2}Matrix norms}{10}{subsubsection.1.1.2}} +\newlabel{matrix-norms}{{1.1.2}{10}{Matrix norms}{subsubsection.1.1.2}{}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.3}Condition of Matrix}{11}{subsubsection.1.1.3}} +\newlabel{condition-of-matrix}{{1.1.3}{11}{Condition of Matrix}{subsubsection.1.1.3}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Springs-masses\relax }}{13}{figure.caption.4}} diff --git a/lecture_12/lecture_12.bbl b/lecture_12/lecture_12.bbl new file mode 100644 index 0000000..e69de29 diff --git a/lecture_12/lecture_12.blg b/lecture_12/lecture_12.blg new file mode 100644 index 0000000..beafcd1 --- /dev/null +++ b/lecture_12/lecture_12.blg @@ -0,0 +1,48 @@ +This is BibTeX, Version 0.99d (TeX Live 2015/Debian) +Capacity: max_strings=35307, hash_size=35307, hash_prime=30011 +The top-level auxiliary file: lecture_12.aux +I found no \citation commands---while reading file lecture_12.aux +I found no \bibdata command---while reading file lecture_12.aux +I found no \bibstyle command---while reading file lecture_12.aux +You've used 0 entries, + 0 wiz_defined-function locations, + 83 strings with 494 characters, +and the built_in function-call counts, 0 in all, are: += -- 0 +> -- 0 +< -- 0 ++ -- 0 +- -- 0 +* -- 0 +:= -- 0 +add.period$ -- 0 +call.type$ -- 0 +change.case$ -- 0 +chr.to.int$ -- 0 +cite$ -- 0 +duplicate$ -- 0 +empty$ -- 0 +format.name$ -- 0 +if$ -- 0 +int.to.chr$ -- 0 +int.to.str$ -- 0 +missing$ -- 0 +newline$ -- 0 +num.names$ -- 0 +pop$ -- 0 +preamble$ -- 0 +purify$ -- 0 +quote$ -- 0 +skip$ -- 0 +stack$ -- 0 +substring$ -- 0 +swap$ -- 0 +text.length$ -- 0 +text.prefix$ -- 0 +top$ -- 0 +type$ -- 0 +warning$ -- 0 +while$ -- 0 +width$ -- 0 +write$ -- 0 +(There were 3 error messages) diff --git a/lecture_12/lecture_12.ipynb b/lecture_12/lecture_12.ipynb index dc44a21..41f1959 100644 --- a/lecture_12/lecture_12.ipynb +++ b/lecture_12/lecture_12.ipynb @@ -22,6 +22,97 @@ "setdefaults" ] }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A =\n", + "\n", + " 0.447394 0.357071 0.720915 0.499926\n", + " 0.648313 0.323276 0.521677 0.288345\n", + " 0.084982 0.581513 0.466420 0.142342\n", + " 0.576580 0.658089 0.916987 0.923165\n", + "\n", + "L =\n", + "\n", + " 1.00000 0.00000 0.00000 0.00000\n", + " 0.13108 1.00000 0.00000 0.00000\n", + " 0.69009 0.24851 1.00000 0.00000\n", + " 0.88935 0.68736 0.68488 1.00000\n", + "\n", + "U =\n", + "\n", + " 0.64831 0.32328 0.52168 0.28834\n", + " 0.00000 0.53914 0.39804 0.10455\n", + " 0.00000 0.00000 0.26199 0.27496\n", + " 0.00000 0.00000 0.00000 0.40655\n", + "\n", + "P =\n", + "\n", + "Permutation Matrix\n", + "\n", + " 0 1 0 0\n", + " 0 0 1 0\n", + " 1 0 0 0\n", + " 0 0 0 1\n", + "\n", + "ans = 1\n" + ] + } + ], + "source": [ + "A=rand(4,4)\n", + "\n", + "[L,U,P]=lu(A)\n", + "\n", + "det(L)" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 4 4\n", + "\n", + "ans = 23.586\n", + "ans = 35.826\n", + "ans = 14.869\n", + "C =\n", + "\n", + " 5.98549 4.28555 4.35707 4.31359\n", + " 0.00000 3.63950 1.35005 1.45342\n", + " 0.00000 0.00000 3.62851 1.50580\n", + " 0.00000 0.00000 0.00000 3.21911\n", + "\n" + ] + } + ], + "source": [ + "A=rand(4,100)';\n", + "A=A'*A;\n", + "size(A)\n", + "min(min(A))\n", + "max(max(A))\n", + "cond(A)\n", + "C=chol(A)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -90,7 +181,7 @@ "1\\end{array}\\right]$\n", "\n", "$A^{-1}=\\frac{1}{2*3-1*1}\\left[ \\begin{array}{cc}\n", - "3 & 1 \\\\\n", + "3 & -1 \\\\\n", "-1 & 2 \\end{array} \\right]=\n", "\\left[ \\begin{array}{cc}\n", "3/5 & -1/5 \\\\\n", @@ -99,7 +190,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 45, "metadata": { "collapsed": false }, @@ -203,7 +294,7 @@ "\n", "$A^{-1}=\\left[ \\begin{array}{cccc}\n", "| & | & & | \\\\\n", - "a_{1} & a_{2} & \\cdots & a_{3} \\\\\n", + "a_{1} & a_{2} & \\cdots & a_{n} \\\\\n", "| & | & & | \\end{array} \\right]$\n", "\n", "\n", @@ -236,9 +327,26 @@ "0 & -1 & 1 \\end{array} \\right]$\n" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Note on solving for $A^{-1}$ column 1\n", + "\n", + "$Aa_1=I(:,1)$\n", + "\n", + "$LUa_1=I(:,1)$\n", + "\n", + "$(LUa_1-I(:,1))=0$\n", + "\n", + "$L(Ua_1-d_1)=0$\n", + "\n", + "$I(:,1)=Ld_1$" + ] + }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 56, "metadata": { "collapsed": false }, @@ -278,7 +386,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 57, "metadata": { "collapsed": false }, @@ -317,13 +425,23 @@ "1 \\\\ \n", "0 \\\\ \n", "\\vdots \\\\\n", - "0 \\end{array} \\right]$\n", - "$;~Ua_{1}=d_{1}$" + "0 \\end{array} \\right]=\n", + "\\left[\\begin{array}{ccc} \n", + "1 & 0 & 0 \\\\ \n", + "-1/2 & 1 & 0 \\\\\n", + "0 & -2/3 & 1 \\end{array} \\right]\\left[\\begin{array}{c} \n", + "d1(1) \\\\ \n", + "d1(2) \\\\ \n", + "d1(3)\\end{array} \\right]=\\left[\\begin{array}{c} \n", + "1 \\\\ \n", + "0 \\\\ \n", + "0 \\end{array} \\right]\n", + ";~Ua_{1}=d_{1}$" ] }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 58, "metadata": { "collapsed": false }, @@ -350,7 +468,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 59, "metadata": { "collapsed": false }, @@ -377,7 +495,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 60, "metadata": { "collapsed": false }, @@ -404,7 +522,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 61, "metadata": { "collapsed": false }, @@ -431,7 +549,7 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 62, "metadata": { "collapsed": false }, @@ -458,7 +576,7 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 63, "metadata": { "collapsed": false }, @@ -492,7 +610,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 69, "metadata": { "collapsed": false }, @@ -507,18 +625,25 @@ " 1.00000 2.00000 2.00000\n", " 1.00000 2.00000 3.00000\n", "\n", - "ans =\n", + "I_app =\n", "\n", " 1.00000 0.00000 0.00000\n", " 0.00000 1.00000 -0.00000\n", " -0.00000 -0.00000 1.00000\n", - "\n" + "\n", + "ans = -4.4409e-16\n", + "ans = 2.2204e-16\n", + "ans = 0.0039062\n" ] } ], "source": [ "invA=[a1,a2,a3]\n", - "A*invA" + "I_app=A*invA\n", + "I_app(2,3)\n", + "eps\n", + "\n", + "2^-8" ] }, { @@ -530,7 +655,7 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 70, "metadata": { "collapsed": false }, @@ -577,7 +702,7 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 71, "metadata": { "collapsed": false }, @@ -703,7 +828,7 @@ "\t\n", "\n", "\n", - "\t\n", + "\t\n", "\t\n", "\tbackslash\n", "\n", @@ -712,7 +837,7 @@ "\t\n", "\n", "\n", - "\t\n", + "\t\n", "\t\n", "\tmultiplication\n", "\n", @@ -721,7 +846,7 @@ "\t\n", "\n", "\n", - "\t\n", + "\t\n", "\t\n", "\n", "\n", @@ -813,7 +938,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 72, "metadata": { "collapsed": false }, @@ -864,7 +989,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 75, "metadata": { "collapsed": false }, @@ -908,7 +1033,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 74, "metadata": { "collapsed": false }, diff --git a/lecture_12/lecture_12.log b/lecture_12/lecture_12.log new file mode 100644 index 0000000..c4a5ed3 --- /dev/null +++ b/lecture_12/lecture_12.log @@ -0,0 +1,841 @@ +This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian) (preloaded format=pdflatex 2017.1.11) 28 FEB 2017 14:24 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**lecture_12.tex +(./lecture_12.tex +LaTeX2e <2016/02/01> +Babel <3.9q> and hyphenation patterns for 81 language(s) loaded. +(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls +Document Class: article 2014/09/29 v1.4h Standard LaTeX document class +(/usr/share/texlive/texmf-dist/tex/latex/base/size11.clo +File: size11.clo 2014/09/29 v1.4h Standard LaTeX file (size option) +) +\c@part=\count79 +\c@section=\count80 +\c@subsection=\count81 +\c@subsubsection=\count82 +\c@paragraph=\count83 +\c@subparagraph=\count84 +\c@figure=\count85 +\c@table=\count86 +\abovecaptionskip=\skip41 +\belowcaptionskip=\skip42 +\bibindent=\dimen102 +) +(/usr/share/texlive/texmf-dist/tex/latex/base/fontenc.sty +Package: fontenc 2005/09/27 v1.99g Standard LaTeX package + +(/usr/share/texlive/texmf-dist/tex/latex/base/t1enc.def +File: t1enc.def 2005/09/27 v1.99g Standard LaTeX file +LaTeX Font Info: Redeclaring font encoding T1 on input line 48. +)) +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/mathpazo.sty +Package: mathpazo 2005/04/12 PSNFSS-v9.2a Palatino w/ Pazo Math (D.Puga, WaS) +\symupright=\mathgroup4 +) +(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty +Package: graphicx 2014/10/28 v1.0g Enhanced LaTeX Graphics (DPC,SPQR) + +(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty +Package: keyval 2014/10/28 v1.15 key=value parser (DPC) +\KV@toks@=\toks14 +) +(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty +Package: graphics 2016/01/03 v1.0q Standard LaTeX Graphics (DPC,SPQR) + +(/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty +Package: trig 2016/01/03 v1.10 sin cos tan (DPC) +) +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/graphics.cfg +File: graphics.cfg 2010/04/23 v1.9 graphics configuration of TeX Live +) +Package graphics Info: Driver file: pdftex.def on input line 95. + +(/usr/share/texlive/texmf-dist/tex/latex/pdftex-def/pdftex.def +File: pdftex.def 2011/05/27 v0.06d Graphics/color for pdfTeX + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/infwarerr.sty +Package: infwarerr 2010/04/08 v1.3 Providing info/warning/error messages (HO) +) +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ltxcmds.sty +Package: ltxcmds 2011/11/09 v1.22 LaTeX kernel commands for general use (HO) +) +\Gread@gobject=\count87 +)) +\Gin@req@height=\dimen103 +\Gin@req@width=\dimen104 +) +(/usr/share/texlive/texmf-dist/tex/latex/caption/caption.sty +Package: caption 2016/02/21 v3.3-144 Customizing captions (AR) + +(/usr/share/texlive/texmf-dist/tex/latex/caption/caption3.sty +Package: caption3 2016/02/04 v1.7-139 caption3 kernel (AR) +Package caption3 Info: TeX engine: e-TeX on input line 67. +\captionmargin=\dimen105 +\captionmargin@=\dimen106 +\captionwidth=\dimen107 +\caption@tempdima=\dimen108 +\caption@indent=\dimen109 +\caption@parindent=\dimen110 +\caption@hangindent=\dimen111 +) +\c@ContinuedFloat=\count88 +) +(/usr/share/texlive/texmf-dist/tex/latex/adjustbox/adjustbox.sty +Package: adjustbox 2012/05/21 v1.0 Adjusting TeX boxes (trim, clip, ...) + +(/usr/share/texlive/texmf-dist/tex/latex/xkeyval/xkeyval.sty +Package: xkeyval 2014/12/03 v2.7a package option processing (HA) + +(/usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkeyval.tex +(/usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkvutils.tex +\XKV@toks=\toks15 +\XKV@tempa@toks=\toks16 +) +\XKV@depth=\count89 +File: xkeyval.tex 2014/12/03 v2.7a key=value parser (HA) +)) +(/usr/share/texlive/texmf-dist/tex/latex/adjustbox/adjcalc.sty +Package: adjcalc 2012/05/16 v1.1 Provides advanced setlength with multiple back +-ends (calc, etex, pgfmath) +) +(/usr/share/texlive/texmf-dist/tex/latex/adjustbox/trimclip.sty +Package: trimclip 2012/05/16 v1.0 Trim and clip general TeX material + +(/usr/share/texlive/texmf-dist/tex/latex/collectbox/collectbox.sty +Package: collectbox 2012/05/17 v0.4b Collect macro arguments as boxes +\collectedbox=\box26 +) +\tc@llx=\dimen112 +\tc@lly=\dimen113 +\tc@urx=\dimen114 +\tc@ury=\dimen115 +Package trimclip Info: Using driver 'tc-pdftex.def'. + +(/usr/share/texlive/texmf-dist/tex/latex/adjustbox/tc-pdftex.def +File: tc-pdftex.def 2012/05/13 v1.0 Clipping driver for pdftex +)) +\adjbox@Width=\dimen116 +\adjbox@Height=\dimen117 +\adjbox@Depth=\dimen118 +\adjbox@Totalheight=\dimen119 + +(/usr/share/texlive/texmf-dist/tex/latex/ifoddpage/ifoddpage.sty +Package: ifoddpage 2011/09/13 v1.0 Conditionals for odd/even page detection +\c@checkoddpage=\count90 +) +(/usr/share/texlive/texmf-dist/tex/latex/varwidth/varwidth.sty +Package: varwidth 2009/03/30 ver 0.92; Variable-width minipages +\@vwid@box=\box27 +\sift@deathcycles=\count91 +\@vwid@loff=\dimen120 +\@vwid@roff=\dimen121 +)) +(/usr/share/texlive/texmf-dist/tex/latex/xcolor/xcolor.sty +Package: xcolor 2007/01/21 v2.11 LaTeX color extensions (UK) + +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/color.cfg +File: color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive +) +Package xcolor Info: Driver file: pdftex.def on input line 225. +Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1337. +Package xcolor Info: Model `hsb' substituted by `rgb' on input line 1341. +Package xcolor Info: Model `RGB' extended on input line 1353. +Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1355. +Package xcolor Info: Model `Hsb' substituted by `hsb' on input line 1356. +Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1357. +Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1358. +Package xcolor Info: Model `Gray' substituted by `gray' on input line 1359. +Package xcolor Info: Model `wave' substituted by `hsb' on input line 1360. +) +(/usr/share/texlive/texmf-dist/tex/latex/tools/enumerate.sty +Package: enumerate 2015/07/23 v3.00 enumerate extensions (DPC) +\@enLab=\toks17 +) +(/usr/share/texlive/texmf-dist/tex/latex/geometry/geometry.sty +Package: geometry 2010/09/12 v5.6 Page Geometry + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifpdf.sty +Package: ifpdf 2011/01/30 v2.3 Provides the ifpdf switch (HO) +Package ifpdf Info: pdfTeX in PDF mode is detected. +) +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifvtex.sty +Package: ifvtex 2010/03/01 v1.5 Detect VTeX and its facilities (HO) +Package ifvtex Info: VTeX not detected. +) +(/usr/share/texlive/texmf-dist/tex/generic/ifxetex/ifxetex.sty +Package: ifxetex 2010/09/12 v0.6 Provides ifxetex conditional +) +\Gm@cnth=\count92 +\Gm@cntv=\count93 +\c@Gm@tempcnt=\count94 +\Gm@bindingoffset=\dimen122 +\Gm@wd@mp=\dimen123 +\Gm@odd@mp=\dimen124 +\Gm@even@mp=\dimen125 +\Gm@layoutwidth=\dimen126 +\Gm@layoutheight=\dimen127 +\Gm@layouthoffset=\dimen128 +\Gm@layoutvoffset=\dimen129 +\Gm@dimlist=\toks18 +) +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty +Package: amsmath 2016/03/03 v2.15a AMS math features +\@mathmargin=\skip43 + +For additional information on amsmath, use the `?' option. +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty +Package: amstext 2000/06/29 v2.01 AMS text + +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty +File: amsgen.sty 1999/11/30 v2.0 generic functions +\@emptytoks=\toks19 +\ex@=\dimen130 +)) +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty +Package: amsbsy 1999/11/29 v1.2d Bold Symbols +\pmbraise@=\dimen131 +) +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty +Package: amsopn 1999/12/14 v2.01 operator names +) +\inf@bad=\count95 +LaTeX Info: Redefining \frac on input line 199. +\uproot@=\count96 +\leftroot@=\count97 +LaTeX Info: Redefining \overline on input line 297. +\classnum@=\count98 +\DOTSCASE@=\count99 +LaTeX Info: Redefining \ldots on input line 394. +LaTeX Info: Redefining \dots on input line 397. +LaTeX Info: Redefining \cdots on input line 518. +\Mathstrutbox@=\box28 +\strutbox@=\box29 +\big@size=\dimen132 +LaTeX Font Info: Redeclaring font encoding OML on input line 630. +LaTeX Font Info: Redeclaring font encoding OMS on input line 631. +\macc@depth=\count100 +\c@MaxMatrixCols=\count101 +\dotsspace@=\muskip10 +\c@parentequation=\count102 +\dspbrk@lvl=\count103 +\tag@help=\toks20 +\row@=\count104 +\column@=\count105 +\maxfields@=\count106 +\andhelp@=\toks21 +\eqnshift@=\dimen133 +\alignsep@=\dimen134 +\tagshift@=\dimen135 +\tagwidth@=\dimen136 +\totwidth@=\dimen137 +\lineht@=\dimen138 +\@envbody=\toks22 +\multlinegap=\skip44 +\multlinetaggap=\skip45 +\mathdisplay@stack=\toks23 +LaTeX Info: Redefining \[ on input line 2735. +LaTeX Info: Redefining \] on input line 2736. +) +(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +Package: amssymb 2013/01/14 v3.01 AMS font symbols + +(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty +Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support +\symAMSa=\mathgroup5 +\symAMSb=\mathgroup6 +LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' +(Font) U/euf/m/n --> U/euf/b/n on input line 106. +)) +(/usr/share/texlive/texmf-dist/tex/latex/base/textcomp.sty +Package: textcomp 2005/09/27 v1.99g Standard LaTeX package +Package textcomp Info: Sub-encoding information: +(textcomp) 5 = only ISO-Adobe without \textcurrency +(textcomp) 4 = 5 + \texteuro +(textcomp) 3 = 4 + \textohm +(textcomp) 2 = 3 + \textestimated + \textcurrency +(textcomp) 1 = TS1 - \textcircled - \t +(textcomp) 0 = TS1 (full) +(textcomp) Font families with sub-encoding setting implement +(textcomp) only a restricted character set as indicated. +(textcomp) Family '?' is the default used for unknown fonts. +(textcomp) See the documentation for details. +Package textcomp Info: Setting ? sub-encoding to TS1/1 on input line 79. + +(/usr/share/texlive/texmf-dist/tex/latex/base/ts1enc.def +File: ts1enc.def 2001/06/05 v3.0e (jk/car/fm) Standard LaTeX file +) +LaTeX Info: Redefining \oldstylenums on input line 334. +Package textcomp Info: Setting cmr sub-encoding to TS1/0 on input line 349. +Package textcomp Info: Setting cmss sub-encoding to TS1/0 on input line 350. +Package textcomp Info: Setting cmtt sub-encoding to TS1/0 on input line 351. +Package textcomp Info: Setting cmvtt sub-encoding to TS1/0 on input line 352. +Package textcomp Info: Setting cmbr sub-encoding to TS1/0 on input line 353. +Package textcomp Info: Setting cmtl sub-encoding to TS1/0 on input line 354. +Package textcomp Info: Setting ccr sub-encoding to TS1/0 on input line 355. +Package textcomp Info: Setting ptm sub-encoding to TS1/4 on input line 356. +Package textcomp Info: Setting pcr sub-encoding to TS1/4 on input line 357. +Package textcomp Info: Setting phv sub-encoding to TS1/4 on input line 358. +Package textcomp Info: Setting ppl sub-encoding to TS1/3 on input line 359. +Package textcomp Info: Setting pag sub-encoding to TS1/4 on input line 360. +Package textcomp Info: Setting pbk sub-encoding to TS1/4 on input line 361. +Package textcomp Info: Setting pnc sub-encoding to TS1/4 on input line 362. +Package textcomp Info: Setting pzc sub-encoding to TS1/4 on input line 363. +Package textcomp Info: Setting bch sub-encoding to TS1/4 on input line 364. +Package textcomp Info: Setting put sub-encoding to TS1/5 on input line 365. +Package textcomp Info: Setting uag sub-encoding to TS1/5 on input line 366. +Package textcomp Info: Setting ugq sub-encoding to TS1/5 on input line 367. +Package textcomp Info: Setting ul8 sub-encoding to TS1/4 on input line 368. +Package textcomp Info: Setting ul9 sub-encoding to TS1/4 on input line 369. +Package textcomp Info: Setting augie sub-encoding to TS1/5 on input line 370. +Package textcomp Info: Setting dayrom sub-encoding to TS1/3 on input line 371. +Package textcomp Info: Setting dayroms sub-encoding to TS1/3 on input line 372. + +Package textcomp Info: Setting pxr sub-encoding to TS1/0 on input line 373. +Package textcomp Info: Setting pxss sub-encoding to TS1/0 on input line 374. +Package textcomp Info: Setting pxtt sub-encoding to TS1/0 on input line 375. +Package textcomp Info: Setting txr sub-encoding to TS1/0 on input line 376. +Package textcomp Info: Setting txss sub-encoding to TS1/0 on input line 377. +Package textcomp Info: Setting txtt sub-encoding to TS1/0 on input line 378. +Package textcomp Info: Setting lmr sub-encoding to TS1/0 on input line 379. +Package textcomp Info: Setting lmdh sub-encoding to TS1/0 on input line 380. +Package textcomp Info: Setting lmss sub-encoding to TS1/0 on input line 381. +Package textcomp Info: Setting lmssq sub-encoding to TS1/0 on input line 382. +Package textcomp Info: Setting lmvtt sub-encoding to TS1/0 on input line 383. +Package textcomp Info: Setting lmtt sub-encoding to TS1/0 on input line 384. +Package textcomp Info: Setting qhv sub-encoding to TS1/0 on input line 385. +Package textcomp Info: Setting qag sub-encoding to TS1/0 on input line 386. +Package textcomp Info: Setting qbk sub-encoding to TS1/0 on input line 387. +Package textcomp Info: Setting qcr sub-encoding to TS1/0 on input line 388. +Package textcomp Info: Setting qcs sub-encoding to TS1/0 on input line 389. +Package textcomp Info: Setting qpl sub-encoding to TS1/0 on input line 390. +Package textcomp Info: Setting qtm sub-encoding to TS1/0 on input line 391. +Package textcomp Info: Setting qzc sub-encoding to TS1/0 on input line 392. +Package textcomp Info: Setting qhvc sub-encoding to TS1/0 on input line 393. +Package textcomp Info: Setting futs sub-encoding to TS1/4 on input line 394. +Package textcomp Info: Setting futx sub-encoding to TS1/4 on input line 395. +Package textcomp Info: Setting futj sub-encoding to TS1/4 on input line 396. +Package textcomp Info: Setting hlh sub-encoding to TS1/3 on input line 397. +Package textcomp Info: Setting hls sub-encoding to TS1/3 on input line 398. +Package textcomp Info: Setting hlst sub-encoding to TS1/3 on input line 399. +Package textcomp Info: Setting hlct sub-encoding to TS1/5 on input line 400. +Package textcomp Info: Setting hlx sub-encoding to TS1/5 on input line 401. +Package textcomp Info: Setting hlce sub-encoding to TS1/5 on input line 402. +Package textcomp Info: Setting hlcn sub-encoding to TS1/5 on input line 403. +Package textcomp Info: Setting hlcw sub-encoding to TS1/5 on input line 404. +Package textcomp Info: Setting hlcf sub-encoding to TS1/5 on input line 405. +Package textcomp Info: Setting pplx sub-encoding to TS1/3 on input line 406. +Package textcomp Info: Setting pplj sub-encoding to TS1/3 on input line 407. +Package textcomp Info: Setting ptmx sub-encoding to TS1/4 on input line 408. +Package textcomp Info: Setting ptmj sub-encoding to TS1/4 on input line 409. +) +(/usr/share/texlive/texmf-dist/tex/latex/upquote/upquote.sty +Package: upquote 2012/04/19 v1.3 upright-quote and grave-accent glyphs in verba +tim +) +(/usr/share/texlive/texmf-dist/tex/latex/eurosym/eurosym.sty +Package: eurosym 1998/08/06 v1.1 European currency symbol ``Euro'' +\@eurobox=\box30 +) +(/usr/share/texlive/texmf-dist/tex/latex/ucs/ucs.sty +Package: ucs 2013/05/11 v2.2 UCS: Unicode input support + +(/usr/share/texlive/texmf-dist/tex/latex/ucs/data/uni-global.def +File: uni-global.def 2013/05/13 UCS: Unicode global data +) +\uc@secondtry=\count107 +\uc@combtoks=\toks24 +\uc@combtoksb=\toks25 +\uc@temptokena=\toks26 +) +(/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty +Package: inputenc 2015/03/17 v1.2c Input encoding file +\inpenc@prehook=\toks27 +\inpenc@posthook=\toks28 + +(/usr/share/texlive/texmf-dist/tex/latex/ucs/utf8x.def +File: utf8x.def 2004/10/17 UCS: Input encoding UTF-8 +)) +(/usr/share/texlive/texmf-dist/tex/latex/fancyvrb/fancyvrb.sty +Package: fancyvrb 2008/02/07 + +Style option: `fancyvrb' v2.7a, with DG/SPQR fixes, and firstline=lastline fix +<2008/02/07> (tvz) +\FV@CodeLineNo=\count108 +\FV@InFile=\read1 +\FV@TabBox=\box31 +\c@FancyVerbLine=\count109 +\FV@StepNumber=\count110 +\FV@OutFile=\write3 +) +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grffile.sty +Package: grffile 2012/04/05 v1.16 Extended file name support for graphics (HO) + +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/kvoptions.sty +Package: kvoptions 2011/06/30 v3.11 Key value format for package options (HO) + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/kvsetkeys.sty +Package: kvsetkeys 2012/04/25 v1.16 Key value parser (HO) + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/etexcmds.sty +Package: etexcmds 2011/02/16 v1.5 Avoid name clashes with e-TeX commands (HO) + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifluatex.sty +Package: ifluatex 2010/03/01 v1.3 Provides the ifluatex switch (HO) +Package ifluatex Info: LuaTeX not detected. +) +Package etexcmds Info: Could not find \expanded. +(etexcmds) That can mean that you are not using pdfTeX 1.50 or +(etexcmds) that some package has redefined \expanded. +(etexcmds) In the latter case, load this package earlier. +))) +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/pdftexcmds.sty +Package: pdftexcmds 2011/11/29 v0.20 Utility functions of pdfTeX for LuaTeX (HO +) +Package pdftexcmds Info: LuaTeX not detected. +Package pdftexcmds Info: \pdf@primitive is available. +Package pdftexcmds Info: \pdf@ifprimitive is available. +Package pdftexcmds Info: \pdfdraftmode found. +) +Package grffile Info: Option `multidot' is set to `true'. +Package grffile Info: Option `extendedchars' is set to `false'. +Package grffile Info: Option `space' is set to `true'. +Package grffile Info: \Gin@ii of package `graphicx' fixed on input line 486. +) +(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty +Package: hyperref 2012/11/06 v6.83m Hypertext links for LaTeX + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty +Package: hobsub-hyperref 2012/05/28 v1.13 Bundle oberdiek, subset hyperref (HO) + + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty +Package: hobsub-generic 2012/05/28 v1.13 Bundle oberdiek, subset generic (HO) +Package: hobsub 2012/05/28 v1.13 Construct package bundles (HO) +Package hobsub Info: Skipping package `infwarerr' (already loaded). +Package hobsub Info: Skipping package `ltxcmds' (already loaded). +Package hobsub Info: Skipping package `ifluatex' (already loaded). +Package hobsub Info: Skipping package `ifvtex' (already loaded). +Package: intcalc 2007/09/27 v1.1 Expandable calculations with integers (HO) +Package hobsub Info: Skipping package `ifpdf' (already loaded). +Package hobsub Info: Skipping package `etexcmds' (already loaded). +Package hobsub Info: Skipping package `kvsetkeys' (already loaded). +Package: kvdefinekeys 2011/04/07 v1.3 Define keys (HO) +Package hobsub Info: Skipping package `pdftexcmds' (already loaded). +Package: pdfescape 2011/11/25 v1.13 Implements pdfTeX's escape features (HO) +Package: bigintcalc 2012/04/08 v1.3 Expandable calculations on big integers (HO +) +Package: bitset 2011/01/30 v1.1 Handle bit-vector datatype (HO) +Package: uniquecounter 2011/01/30 v1.2 Provide unlimited unique counter (HO) +) +Package hobsub Info: Skipping package `hobsub' (already loaded). +Package: letltxmacro 2010/09/02 v1.4 Let assignment for LaTeX macros (HO) +Package: hopatch 2012/05/28 v1.2 Wrapper for package hooks (HO) +Package: xcolor-patch 2011/01/30 xcolor patch +Package: atveryend 2011/06/30 v1.8 Hooks at the very end of document (HO) +Package atveryend Info: \enddocument detected (standard20110627). +Package: atbegshi 2011/10/05 v1.16 At begin shipout hook (HO) +Package: refcount 2011/10/16 v3.4 Data extraction from label references (HO) +Package: hycolor 2011/01/30 v1.7 Color options for hyperref/bookmark (HO) +) +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/auxhook.sty +Package: auxhook 2011/03/04 v1.3 Hooks for auxiliary files (HO) +) +\@linkdim=\dimen139 +\Hy@linkcounter=\count111 +\Hy@pagecounter=\count112 + +(/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def +File: pd1enc.def 2012/11/06 v6.83m Hyperref: PDFDocEncoding definition (HO) +) +\Hy@SavedSpaceFactor=\count113 + +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/hyperref.cfg +File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive +) +Package hyperref Info: Hyper figures OFF on input line 4443. +Package hyperref Info: Link nesting OFF on input line 4448. +Package hyperref Info: Hyper index ON on input line 4451. +Package hyperref Info: Plain pages OFF on input line 4458. +Package hyperref Info: Backreferencing OFF on input line 4463. +Package hyperref Info: Implicit mode ON; LaTeX internals redefined. +Package hyperref Info: Bookmarks ON on input line 4688. +\c@Hy@tempcnt=\count114 + +(/usr/share/texlive/texmf-dist/tex/latex/url/url.sty +\Urlmuskip=\muskip11 +Package: url 2013/09/16 ver 3.4 Verb mode for urls, etc. +) +LaTeX Info: Redefining \url on input line 5041. +\XeTeXLinkMargin=\dimen140 +\Fld@menulength=\count115 +\Field@Width=\dimen141 +\Fld@charsize=\dimen142 +Package hyperref Info: Hyper figures OFF on input line 6295. +Package hyperref Info: Link nesting OFF on input line 6300. +Package hyperref Info: Hyper index ON on input line 6303. +Package hyperref Info: backreferencing OFF on input line 6310. +Package hyperref Info: Link coloring OFF on input line 6315. +Package hyperref Info: Link coloring with OCG OFF on input line 6320. +Package hyperref Info: PDF/A mode OFF on input line 6325. +LaTeX Info: Redefining \ref on input line 6365. +LaTeX Info: Redefining \pageref on input line 6369. +\Hy@abspage=\count116 +\c@Item=\count117 +\c@Hfootnote=\count118 +) + +Package hyperref Message: Driver (autodetected): hpdftex. + +(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def +File: hpdftex.def 2012/11/06 v6.83m Hyperref driver for pdfTeX +\Fld@listcount=\count119 +\c@bookmark@seq@number=\count120 + +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty +Package: rerunfilecheck 2011/04/15 v1.7 Rerun checks for auxiliary files (HO) +Package uniquecounter Info: New unique counter `rerunfilecheck' on input line 2 +82. +) +\Hy@SectionHShift=\skip46 +) +(/usr/share/texlive/texmf-dist/tex/latex/tools/longtable.sty +Package: longtable 2014/10/28 v4.11 Multi-page Table package (DPC) +\LTleft=\skip47 +\LTright=\skip48 +\LTpre=\skip49 +\LTpost=\skip50 +\LTchunksize=\count121 +\LTcapwidth=\dimen143 +\LT@head=\box32 +\LT@firsthead=\box33 +\LT@foot=\box34 +\LT@lastfoot=\box35 +\LT@cols=\count122 +\LT@rows=\count123 +\c@LT@tables=\count124 +\c@LT@chunks=\count125 +\LT@p@ftn=\toks29 +) +(/usr/share/texlive/texmf-dist/tex/latex/booktabs/booktabs.sty +Package: booktabs 2005/04/14 v1.61803 publication quality tables +\heavyrulewidth=\dimen144 +\lightrulewidth=\dimen145 +\cmidrulewidth=\dimen146 +\belowrulesep=\dimen147 +\belowbottomsep=\dimen148 +\aboverulesep=\dimen149 +\abovetopsep=\dimen150 +\cmidrulesep=\dimen151 +\cmidrulekern=\dimen152 +\defaultaddspace=\dimen153 +\@cmidla=\count126 +\@cmidlb=\count127 +\@aboverulesep=\dimen154 +\@belowrulesep=\dimen155 +\@thisruleclass=\count128 +\@lastruleclass=\count129 +\@thisrulewidth=\dimen156 +) +(/usr/share/texlive/texmf-dist/tex/latex/enumitem/enumitem.sty +Package: enumitem 2011/09/28 v3.5.2 Customized lists +\labelindent=\skip51 +\enit@outerparindent=\dimen157 +\enit@toks=\toks30 +\enit@inbox=\box36 +\enitdp@description=\count130 +) +(/usr/share/texlive/texmf-dist/tex/generic/ulem/ulem.sty +\UL@box=\box37 +\UL@hyphenbox=\box38 +\UL@skip=\skip52 +\UL@hook=\toks31 +\UL@height=\dimen158 +\UL@pe=\count131 +\UL@pixel=\dimen159 +\ULC@box=\box39 +Package: ulem 2012/05/18 +\ULdepth=\dimen160 +) +Package hyperref Info: Option `breaklinks' set `true' on input line 264. +Package hyperref Info: Option `colorlinks' set `true' on input line 264. + (./lecture_12.aux) +\openout1 = `lecture_12.aux'. + +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 271. +LaTeX Font Info: Try loading font information for TS1+cmr on input line 271. + + +(/usr/share/texlive/texmf-dist/tex/latex/base/ts1cmr.fd +File: ts1cmr.fd 2014/09/29 v2.5h Standard LaTeX font definitions +) +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 271. +LaTeX Font Info: ... okay on input line 271. +LaTeX Font Info: Try loading font information for T1+ppl on input line 271. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/t1ppl.fd +File: t1ppl.fd 2001/06/04 font definitions for T1/ppl. +) +(/usr/share/texlive/texmf-dist/tex/context/base/supp-pdf.mkii +[Loading MPS to PDF converter (version 2006.09.02).] +\scratchcounter=\count132 +\scratchdimen=\dimen161 +\scratchbox=\box40 +\nofMPsegments=\count133 +\nofMParguments=\count134 +\everyMPshowfont=\toks32 +\MPscratchCnt=\count135 +\MPscratchDim=\dimen162 +\MPnumerator=\count136 +\makeMPintoPDFobject=\count137 +\everyMPtoPDFconversion=\toks33 +) (/usr/share/texlive/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty +Package: epstopdf-base 2010/02/09 v2.5 Base part for package epstopdf + +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grfext.sty +Package: grfext 2010/08/19 v1.1 Manage graphics extensions (HO) +) +Package grfext Info: Graphics extension search list: +(grfext) [.png,.pdf,.jpg,.mps,.jpeg,.jbig2,.jb2,.PNG,.PDF,.JPG,.JPE +G,.JBIG2,.JB2,.eps] +(grfext) \AppendGraphicsExtensions on input line 452. + +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg +File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv +e +)) +Package caption Info: Begin \AtBeginDocument code. +Package caption Info: hyperref package is loaded. +Package caption Info: longtable package is loaded. + +(/usr/share/texlive/texmf-dist/tex/latex/caption/ltcaption.sty +Package: ltcaption 2013/06/09 v1.4-94 longtable captions (AR) +) +Package caption Info: End \AtBeginDocument code. + +*geometry* driver: auto-detecting +*geometry* detected driver: pdftex +*geometry* verbose mode - [ preamble ] result: +* driver: pdftex +* paper: +* layout: +* layoutoffset:(h,v)=(0.0pt,0.0pt) +* modes: +* h-part:(L,W,R)=(72.26999pt, 469.75502pt, 72.26999pt) +* v-part:(T,H,B)=(72.26999pt, 650.43001pt, 72.26999pt) +* \paperwidth=614.295pt +* \paperheight=794.96999pt +* \textwidth=469.75502pt +* \textheight=650.43001pt +* \oddsidemargin=0.0pt +* \evensidemargin=0.0pt +* \topmargin=-37.0pt +* \headheight=12.0pt +* \headsep=25.0pt +* \topskip=11.0pt +* \footskip=30.0pt +* \marginparwidth=59.0pt +* \marginparsep=10.0pt +* \columnsep=10.0pt +* \skip\footins=10.0pt plus 4.0pt minus 2.0pt +* \hoffset=0.0pt +* \voffset=0.0pt +* \mag=1000 +* \@twocolumnfalse +* \@twosidefalse +* \@mparswitchfalse +* \@reversemarginfalse +* (1in=72.27pt=25.4mm, 1cm=28.453pt) + +(/usr/share/texlive/texmf-dist/tex/latex/ucs/ucsencs.def +File: ucsencs.def 2011/01/21 Fixes to fontencodings LGR, T3 +) +\AtBeginShipoutBox=\box41 +Package hyperref Info: Link coloring ON on input line 271. + +(/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty +Package: nameref 2012/10/27 v2.43 Cross-referencing by name of section + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/gettitlestring.sty +Package: gettitlestring 2010/12/03 v1.4 Cleanup title references (HO) +) +\c@section@level=\count138 +) +LaTeX Info: Redefining \ref on input line 271. +LaTeX Info: Redefining \pageref on input line 271. +LaTeX Info: Redefining \nameref on input line 271. + +(./lecture_12.out) (./lecture_12.out) +\@outlinefile=\write4 +\openout4 = `lecture_12.out'. + +LaTeX Font Info: Try loading font information for OT1+ppl on input line 275. + + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/ot1ppl.fd +File: ot1ppl.fd 2001/06/04 font definitions for OT1/ppl. +) +LaTeX Font Info: Try loading font information for OML+zplm on input line 275 +. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/omlzplm.fd +File: omlzplm.fd 2002/09/08 Fontinst v1.914 font definitions for OML/zplm. +) +LaTeX Font Info: Try loading font information for OMS+zplm on input line 275 +. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/omszplm.fd +File: omszplm.fd 2002/09/08 Fontinst v1.914 font definitions for OMS/zplm. +) +LaTeX Font Info: Try loading font information for OMX+zplm on input line 275 +. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/omxzplm.fd +File: omxzplm.fd 2002/09/08 Fontinst v1.914 font definitions for OMX/zplm. +) +LaTeX Font Info: Try loading font information for OT1+zplm on input line 275 +. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/ot1zplm.fd +File: ot1zplm.fd 2002/09/08 Fontinst v1.914 font definitions for OT1/zplm. +) +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 12.50409pt on input line 275. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 9.37807pt on input line 275. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 7.29405pt on input line 275. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 12.50409pt on input line 275. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 9.37807pt on input line 275. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 7.29405pt on input line 275. + + +LaTeX Warning: No \author given. + +LaTeX Font Info: Try loading font information for T1+cmtt on input line 279. + +(/usr/share/texlive/texmf-dist/tex/latex/base/t1cmtt.fd +File: t1cmtt.fd 2014/09/29 v2.5h Standard LaTeX font definitions +) [1 + +{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] +LaTeX Font Info: Try loading font information for TS1+cmtt on input line 331 +. + +(/usr/share/texlive/texmf-dist/tex/latex/base/ts1cmtt.fd +File: ts1cmtt.fd 2014/09/29 v2.5h Standard LaTeX font definitions +) +LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <12> not available +(Font) Font shape `T1/ppl/b/n' tried instead on input line 359. + + +File: det_L.png Graphic file (type png) + +Package pdftex.def Info: det_L.png used on input line 363. +(pdftex.def) Requested size: 375.80544pt x 183.64162pt. + + +File: chol_pre.png Graphic file (type png) + +Package pdftex.def Info: chol_pre.png used on input line 369. +(pdftex.def) Requested size: 375.80544pt x 183.9047pt. + [2 <./det_L.png>] +LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <14.4> not available +(Font) Font shape `T1/ppl/b/n' tried instead on input line 400. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 11.40997pt on input line 404. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 8.33606pt on input line 404. +LaTeX Font Info: Font shape `U/msa/m/n' will be +(Font) scaled to size 6.25204pt on input line 404. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 11.40997pt on input line 404. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 8.33606pt on input line 404. +LaTeX Font Info: Font shape `U/msb/m/n' will be +(Font) scaled to size 6.25204pt on input line 404. + [3 <./chol_pre.png>] [4] +LaTeX Font Info: Font shape `T1/ppl/bx/n' in size <10.95> not available +(Font) Font shape `T1/ppl/b/n' tried instead on input line 503. + [5] [6] [7] [8] +LaTeX Font Info: Font shape `T1/cmtt/bx/n' in size <10.95> not available +(Font) Font shape `T1/cmtt/m/n' tried instead on input line 746. + + +File: lecture_12_files/lecture_12_24_0.pdf Graphic file (type pdf) + + +Package pdftex.def Info: lecture_12_files/lecture_12_24_0.pdf used on input lin +e 765. +(pdftex.def) Requested size: 449.6789pt x 337.25917pt. + [9] +Underfull \hbox (badness 10000) in paragraph at lines 767--768 + + [] + +LaTeX Font Info: Font shape `T1/ppl/bx/it' in size <10.95> not available +(Font) Font shape `T1/ppl/b/it' tried instead on input line 773. +[10 <./lecture_12_files/lecture_12_24_0.pdf>] [11] [12] +<../lecture_09/mass_springs.png, id=118, 112.42pt x 190.7125pt> +File: ../lecture_09/mass_springs.png Graphic file (type png) + + +Package pdftex.def Info: ../lecture_09/mass_springs.png used on input line 923. + +(pdftex.def) Requested size: 89.93611pt x 152.576pt. + [13 <../lecture_09/mass_springs.png>] +Package atveryend Info: Empty hook `BeforeClearDocument' on input line 1015. + +[14] +Package atveryend Info: Empty hook `AfterLastShipout' on input line 1015. + (./lecture_12.aux) +Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 1015. +Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 1015. + +Package rerunfilecheck Info: File `lecture_12.out' has not changed. +(rerunfilecheck) Checksum: 2BDB89EC075D3A42B038A5DAC39843C7;535. +Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 1015. + ) +Here is how much of TeX's memory you used: + 10955 strings out of 493029 + 163811 string characters out of 6136234 + 270140 words of memory out of 5000000 + 14229 multiletter control sequences out of 15000+600000 + 37652 words of font info for 95 fonts, out of 8000000 for 9000 + 1141 hyphenation exceptions out of 8191 + 36i,9n,77p,512b,465s stack positions out of 5000i,500n,10000p,200000b,80000s +{/usr/share/texlive/texmf-dist/fonts/enc/dvips/base/8r.enc}{/usr/share/texmf/ +fonts/enc/dvips/cm-super/cm-super-ts1.enc}{/usr/share/texmf/fonts/enc/dvips/cm- +super/cm-super-t1.enc} +Output written on lecture_12.pdf (14 pages, 232410 bytes). +PDF statistics: + 177 PDF objects out of 1000 (max. 8388607) + 140 compressed objects within 2 object streams + 34 named destinations out of 1000 (max. 500000) + 77 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/lecture_12/lecture_12.md b/lecture_12/lecture_12.md index 9befcbc..82f9bea 100644 --- a/lecture_12/lecture_12.md +++ b/lecture_12/lecture_12.md @@ -9,6 +9,75 @@ setdefaults ``` + +```octave +A=rand(4,4) + +[L,U,P]=lu(A) + +det(L) +``` + + A = + + 0.447394 0.357071 0.720915 0.499926 + 0.648313 0.323276 0.521677 0.288345 + 0.084982 0.581513 0.466420 0.142342 + 0.576580 0.658089 0.916987 0.923165 + + L = + + 1.00000 0.00000 0.00000 0.00000 + 0.13108 1.00000 0.00000 0.00000 + 0.69009 0.24851 1.00000 0.00000 + 0.88935 0.68736 0.68488 1.00000 + + U = + + 0.64831 0.32328 0.52168 0.28834 + 0.00000 0.53914 0.39804 0.10455 + 0.00000 0.00000 0.26199 0.27496 + 0.00000 0.00000 0.00000 0.40655 + + P = + + Permutation Matrix + + 0 1 0 0 + 0 0 1 0 + 1 0 0 0 + 0 0 0 1 + + ans = 1 + + + +```octave +A=rand(4,100)'; +A=A'*A; +size(A) +min(min(A)) +max(max(A)) +cond(A) +C=chol(A) +``` + + ans = + + 4 4 + + ans = 23.586 + ans = 35.826 + ans = 14.869 + C = + + 5.98549 4.28555 4.35707 4.31359 + 0.00000 3.63950 1.35005 1.45342 + 0.00000 0.00000 3.62851 1.50580 + 0.00000 0.00000 0.00000 3.21911 + + + ## My question from last class ![q1](det_L.png) @@ -68,7 +137,7 @@ x_{2} \end{array}\right]= 1\end{array}\right]$ $A^{-1}=\frac{1}{2*3-1*1}\left[ \begin{array}{cc} -3 & 1 \\ +3 & -1 \\ -1 & 2 \end{array} \right]= \left[ \begin{array}{cc} 3/5 & -1/5 \\ @@ -156,7 +225,7 @@ Which we can solve for each $a_{n}$ with LU-decomposition, knowing the lower and $A^{-1}=\left[ \begin{array}{cccc} | & | & & | \\ -a_{1} & a_{2} & \cdots & a_{3} \\ +a_{1} & a_{2} & \cdots & a_{n} \\ | & | & & | \end{array} \right]$ @@ -189,6 +258,18 @@ $A=\left[ \begin{array}{ccc} 0 & -1 & 1 \end{array} \right]$ +#### Note on solving for $A^{-1}$ column 1 + +$Aa_1=I(:,1)$ + +$LUa_1=I(:,1)$ + +$(LUa_1-I(:,1))=0$ + +$L(Ua_1-d_1)=0$ + +$I(:,1)=Ld_1$ + ```octave A=[2,-1,0;-1,2,-1;0,-1,1] @@ -245,8 +326,18 @@ $Ld_{1}=\left[\begin{array}{c} 1 \\ 0 \\ \vdots \\ -0 \end{array} \right]$ -$;~Ua_{1}=d_{1}$ +0 \end{array} \right]= +\left[\begin{array}{ccc} +1 & 0 & 0 \\ +-1/2 & 1 & 0 \\ +0 & -2/3 & 1 \end{array} \right]\left[\begin{array}{c} +d1(1) \\ +d1(2) \\ +d1(3)\end{array} \right]=\left[\begin{array}{c} +1 \\ +0 \\ +0 \end{array} \right] +;~Ua_{1}=d_{1}$ ```octave @@ -349,7 +440,11 @@ Final solution for $A^{-1}$ is $[a_{1}~a_{2}~a_{3}]$ ```octave invA=[a1,a2,a3] -A*invA +I_app=A*invA +I_app(2,3) +eps + +2^-8 ``` invA = @@ -358,12 +453,15 @@ A*invA 1.00000 2.00000 2.00000 1.00000 2.00000 3.00000 - ans = + I_app = 1.00000 0.00000 0.00000 0.00000 1.00000 -0.00000 -0.00000 -0.00000 1.00000 + ans = -4.4409e-16 + ans = 2.2204e-16 + ans = 0.0039062 Now the solution of $x$ to $Ax=y$ is $x=A^{-1}y$ @@ -430,7 +528,7 @@ legend('inversion','backslash','multiplication','Location','NorthWest') ``` -![svg](lecture_12_files/lecture_12_21_0.svg) +![svg](lecture_12_files/lecture_12_24_0.svg) ## Condition of a matrix diff --git a/lecture_12/lecture_12.out b/lecture_12/lecture_12.out new file mode 100644 index 0000000..e7b5af8 --- /dev/null +++ b/lecture_12/lecture_12.out @@ -0,0 +1,7 @@ +\BOOKMARK [2][-]{subsection.0.1}{My question from last class}{}% 1 +\BOOKMARK [2][-]{subsection.0.2}{Your questions from last class}{}% 2 +\BOOKMARK [1][-]{section.1}{Matrix Inverse and Condition}{}% 3 +\BOOKMARK [2][-]{subsection.1.1}{Condition of a matrix}{section.1}% 4 +\BOOKMARK [3][-]{subsubsection.1.1.1}{just checked in to see what condition my condition was in}{subsection.1.1}% 5 +\BOOKMARK [3][-]{subsubsection.1.1.2}{Matrix norms}{subsection.1.1}% 6 +\BOOKMARK [3][-]{subsubsection.1.1.3}{Condition of Matrix}{subsection.1.1}% 7 diff --git a/lecture_12/lecture_12.pdf b/lecture_12/lecture_12.pdf index ed0f569e1339b5f53dbc1b946df146a0d62eb77b..e0b4e6c98e2ee90eaef7535fdeb037483f391c82 100644 GIT binary patch delta 173959 zcmZs?19TbH7JcVOUrQ83`SXtzme1VHjl1>@8d^3EA11 z3DbaWKqvtv>UuUCjHtdhb#qhw0h(PJ3rk~$2zb>dMM2C9W!2HPPBKJxVHeR?I|`Ae zT$9<&XULAl?@q4Q9V@W`Ta1PT^1Bf`9!*Ir7Sc?tx`b5hUFO2?ElRRB`^e!lskZtx znFL#%Ir%l24wU2?O$tnK9VEy^HSC+16V}R`mKcDh+02`(Vf72KcMIhofzqp1+CZ89 z`w=e;6w46&POnEIyQG*P9=nd9vCEDirY*wuEitzQHxz6I6~~bAKIx2MpBfH{0#ZZZ z;0(huPz-bld7H-){V|VB2`g23RblkXRTmdwf9w<7H8o18b9waZD~Cg9UafaGx8J|$}lt}mfE%B)HO}q*7KftDJ69m^jd5?nRXv^ z1-arXUdtMuvtTf-uN9NYyzG(_Au$Y^+0}e5_2l%Th>{KV&b2y^EkjN-f z2AUg@kATRF8M!SI1?@o6C&-OzR9WF6)VXMwF|~?=dkP9#U}j+&p;O|eqk|IWO^Jd+ zV%)eE3*1{xkAp?=GL}pxb8b@D-C%twJ}C&eF7sF6dX@Gmk!)dx(*i9acb)SUQ{MpS z2P%ZWO*Ah^;Xt%W!e*_jF6k!#DKdk){3W`XMaI##Ok(ckWUzCTJB{>-@M@#+vxAHe zP?3LTb_391V(ev9i?aFgiyx`xMBh`oR@LDrJ-aQ}yWHAN?Fkk@zaI*18~`^M9R&Vg zx48?JaBCS}yy)4zoJoC1COQIjIK9@L6X6`xhXkD2*r1+6OEzvRC_rZ8^EV9e}I zU0j{bjO_mT_D}q>vi*lZW@P>EK$daXV1(^`*EnUjNLN!vCb1HOU#mLx$74TCeL^h0 zLeH0qF9vP>d{aX3Zn!YDLI-6cOCS)4L^VU)0Sm7JxqqK2ZhtXM7L3Q|jhyIll=o5{ z3`{fpd8{rggQ+SB_8K#T3CWQZS2$?IT9KTxtH+#C;~o?_mrAk>UXui%=Q);0T!r|S z`fygOSGD>hL5^immw5GGnV#cjwRE%ftQtuI%mQEjEt zh!U0Q$uRTN#Yh}HK$igS&yHM(w~b~Qy1Y4hdHFt5l$nOr%ezKyx_ToqZ_JLsY%PoE zF{((++?6Zv{lmLw_r){TFHZm}7h#-v+C6p;Zr^vdiSukf->Vk|zI**R;SG=^t0H7V zR+o9L{DjJu2v`u3bjm%&f2d`KC@13l5&I*mr=sdnSt1|y)+7a37uo5ugFKipmGT-} ze+^_*<|3{%NzSBQHJ2+Y)n_m|c}+uO%QI1!(HkNJN?uXKUJ(DpF$I7DCq@{73Jbz} zxu0N)rxgpwHK4a6cm`1NCBXQWOHpfaHJ6IRZ?E-!Jlgb&fgT-?ZCyJx=$FiYy7$N~ z4B0-X7js2*sblH)=AmLT@R)|lYZKtIG^0G2HBhxPVcQf9=3=IG7jiNdpHD^yWZ#kwT+v8Zy43+QDm z@Fo%16C_2QkS94wQ&#O8273m?B&-WK`Kqq~Sw}!Z z@#vZul zb@p5H>z>l_r-txvNoV<|E~XN#Z|7-b(mkzj=9jE7FcaQ)JNm>7Zq|o%XWlM8R6C8z zPPViS@vE82$&K0S<$7DbQ>*sig5(l^S;UfQAmqayWZy_Ge?YbiKTQ>2^5?aCh!*N| zM~L1UkN48F6gv%si1${?#b$4fEeyveN=qfo35i40j0ZpOayOy8G76qAF?W6`Raawg zYeiK|Onx(%-DHjUJDy1=zp5VQFnV-|kb4K2dsSwSPTj*gZ7e7m$H<#0Cy}jzeP`iX zo&q!UexFL1^?`{V&D1GC&nQ5BnC^?PV6j9bU1T-cm_{Ukj@=8Wlk=zxNe3%Ddur1>iApUdZX~QnP_F+V7&iAa-y? z7k>d+&m_9$rmL%sQcKb?j(n=6XR}KiE4Uu(cDr8)w&B!?Z_EYUY6U>Rj~3_LV)NWK z94-)cP30ujz1O6~n0*`m*v_DLo^(JkdtR?BI+e#WdeBbUl42gyQ@YZF8Ef3oTJc;- zes+iJQQlUa>(=H!triw#3>%ShMm%YW0+hwV8`(Kw#CCR9lnt-1XQ;{+%&pn{lF%{^tIv7WC{m`i_P3?;(bpOFsN7EOWM6LK*kPl<p>$h6gu3A=x+MNjqO39)cJr<{=HpB%x>9q9hq+$Sos%*$*g}7vBk9 z6oQuOgQ80rj$0Q&p}cqX$Di4=rCUfFq=MjcVZ5)ML_UDZ7|qN$590zdTpy0EHRA&4!vi{IWs?2!ukFT6RiX? zgXV%5S6qaSqyOsUd52L4Dctm5G!FYec%1n!W?K9UMcFx0X zCuQd7H#XfJo_;*Cfq_2gLgPtu$rq>Z52!Qu{UD-ds>uKx3`8K$I-9_{rZB4>{1hKf zaif;zw1=bN&d0z)wd#P3K4yNw|9yINc3Ou7tj}mn3P%xQHt1{@uD2OII}6@599NgI ztF84%F>;$xj4aWRVAY|>fSQ9828R|$*d~4Yr;y9u#?=5gwFz%Edt-uXjQpU5$I376RZ5Mv zl_9F+eQYKg$pJL)0;7mRa-TE5ls#fFax#joKblWNsv^SYKFEn zgdd3q7W2mq6R$#2wJlpCd6hQ-G3g=fn=~Hz4l&|7?@p%{$Aw(Sf8~$KScI@ANU)^6l)Crf>U^(68Mjf$( zGXhR-Z^a-9pwV}C{8d)%Z(R~K+cIs~wfu1i=}09-Q?L=>6x=?&FRY$U?PfgmUhd<> zF5`s&hfo~>@8|=V^poDwn^SeK>_TM_!!$w0u3&)$#zenR(YcD{+X8Ygc-oWA~MB**(Zb9QpnQlyHx=^FN?GkG7|{5h|}gayG@=~3Q@Iv#mX%qk5?hdOZFw>p3dFQD1!B;2e`KVVQI~R$ zT*W!fOcTOJ^Kyf{Ed}jlXry3rx+GN9wlLoUXBkr!Lc0cMk{O}#g;JPDVg43CTu9J< zk1(2qKpHvpiFBCpn(Wwo@9vB}VGd}$Q;t+Mlg3bzNQjmv8Z3OD&_H=~s4YBLy^5{x zCT!P{-d!1|Az9x{_{94KRZdZXT53X`Vm)40+`dt-wn^{G*83#v(g`S266eN1HpvtR zVM{Rup$j36N$T{+ zd=<0Wrf~S+qv006m&{NDKLS@uF*c4N9Y$wi&5&jlX3EZ!<50!za@?l;o|9rgopZF3 zH2a;qvf_%?P}HWT(=hhbyyJxapi^50{v7W4t(jj$9FKi+a(>=+DLx0VgzUS{GTm{3V4$ zb{^I=sx0zN86p(pc6@^_fXYi?z!`ql^@rXmQBQus!)*&loB25%7eQW z4Mg79&qYr%W6pjGMZ@RppB9i)Jtf)%59i1H5Canom-H)cb^Sj zVN&dd!wfx7bln%Q-l$--Xm4u)tPZZx-BczJzPS(9RHq*2DMpL2CslG&H zH3#Dc=LGCe@q%XnJoi)R)XyQa?mg!1arxUjUD0GgX6G)6z6)%2(LS`d$s&e(2d1yM zuUq?|Dnb`F${2naoBB`eM+4aJ6B2GzxWiA209bzF))^imw#zlzBAfCUwc zctlC6S=ow~5+aSOc{!P?@ewr-!KXVv9K4AWv zGspj9|1mA-mpF$f%S3o;ysmT3Z_-dr5g8aU%Y>u+Kp3+5O_UbbX>8QGrjz`Q2`xXi z9^Fj=+FbKrO(P#kI`razS&X`-*BFhfS9VJ8wx2otZz~fYlix4*w~94<0<+`~o6uq0 z5c|oaQH0Xk41bP~?Ds9v@Wh1k_yMnCP?;3IhT-P*2{?o8kKM7L1v4S9~64fIm^p}2tXehhjB7feLBN=fM1=U+g8u|2kEQ{g$!Nt3UpDWI!wZz2;MWzTO#bQ`#es{KX z?*lDY4s;yANuy?$`D>*@ncRj-{Tw3gHbUN3lyXp1C6Dr_LN5d)4?@>doooBG=HX<@ zauy?F*xL9sJ8vG4K*@pEJlWkIKP;52Q)Gf}Ftg6jLwPr!kC zfoH|~J2ne5J@n+8TN{c!7kJ{wIfQ%glc9r@>e_^TqcNmJ1wYk)VgbFY?-XCX-2n{* z>xW!;ktL`Fegtp(xC7XHt2bP}oqO85s*XWFyaj|#zMqYx`6B7lLPqt5W4uji_2+jN z1GZYF+%_r^wxO7qJ1$$z6cDD6thBvZun97YP<^J-9zYFgG}TIVw#pG5&3~-<+KOe_ zDa%ReF?4679^D20QB}#|H9(G~Y;^{c5ks(J3n5VVSfQR3*Z`c@Dw&|oidiulLSh1R zcp*9IkH5}F&#{y3>*bGrxb;>oKE{-dYdWBUv8u)}-8(xyI};?!wQ9nMgrmwFId|+I zq6X{i>9l@*%~`3U)Kn67mczYf?gvfg4X(kzTZXII2 zr`Q*uoz!1hQ33pQjFvXsX1$lv@wa3mxCVvTt`j@h;s~PerX?z zPMMwROnV1WofLXe*`lqd3xuJ!Zl|!4wUwhKvy!-whY8EKDqZlu z$PUGLrffBqpTgf7X#jjaMRoBWH_*hhz;GULX4{?0_wFb6N3(I?7#+sSY<<6v7`<#6 z=vkbQEgm=-$`q5-ezkAiMOqB%@a}HHxu48m2V||v6I*#d&qHebq(C^ij8WxZpBN*+ zL(SR3I0DR9GTue16LI4Z5U_>qRKCOo@oJZ*zl#KQTaHX+eX-cdR8Oubri{o#LIANO=|F`pKdzW z#~&&#?puY-`467I`-hN!>X91R@u`&6XF{8;<|yE6St%{=anmfZO9rZqldDKL*4g7d zpHY3WzxqQKlc<#3>XJ&qpPtIj1&&%A8`X`WPh2b;x|Xj_bNM^<92wHNFY)c?GNJh6 zUV3DbV>ZOK+_>FU4aq`A(q>J*xtZ(FrxYDA9Y6l9cZ@Sjx~Tun57^c)oQ(fr#l*z? zZ`tWDKR6t)BlezX+*)EF4Q1?!$nMGnxX%-x7D&pk@nJf)@}WY<(`o1T^@{w}gQA>i zWuz|M{8vl4>Kr%;DhiMRP-OgiC9M0SQrme zIaD?8=|S~Gks|@CVVQ7FzmLyF@Ty7?Cd!(@@`toC%*!GEiLel-cfhx^-Z#DwIzr0A z#;?iW^ip`G9N&RH+{jCFv8f|Rm{yx9<`4Cq0>Bibl++v zW?Z2CD@|sR1)ca&Kj%e0F4LwXXwyW{K5ij^byv(l+0a&gV8A`p`H2*Aj6L`?N!Y?s zEeItYrEM_#hTGckoV>1~%Vx5BZ&pccHYGG$?VMHy@H@nclV?=%-J-6Agoz~$bWiycqrilGZ-D82N3)lh z>LScAww%ARqs!!>;Sb7yZo+u^EP49MLesMSc)L*Av8|zaS)pn32p5^@_HrJg z$9BR-l(69vJmH|uW;2#7OrwW&&3VgJwXL8as*C}aY>wNU=n}_v`%`unb1xG*T=KLE z!{yX$M$kV`rbd!|7Zg*4YXDHLL@@noTeKQ0LWX)*Kcv-`$JT)1*IEZL$Jh&M;2W2j ztuAqCc+{*w!zV$XdrF|SUzQ-9rNS{nUdq#*{V6fEHBG*)6&b-POI4Gg+UU7EgpgDz ziI_6X%2~35I+9h*&1!6XbGE(O84Qh>btwBE4!{1r; zR^-4trg84bQXJzC6)P2&>TsDS0|{Byb-zJ}ix84PXOgzeRfX22OEMB$61L~s+2uTC zv&=!O-jrn2l7077a33v^B@MG(_LS)Phdz0 zPIH5dZ)xMpUS{@5!B>qFQo^z%G2a#zlbrsJW$5h9*Nb-UfVeso&IXoM z*VY@|fZQL^f7NliHPVBgFRh7_cE>asb?TKKJu5N4&aM{%O`XEW{|!xlk%^TM?f+Ph zY#jgP*j#BVDFiVh`t8)6lCUg1d0hde^`y6p9V87f2^EL^74OS_3kI zHnF?$()HfKBQQBkVQkE;zkKJ;o>mV;F=RCaj=v50nf;SCU$)#p2bqgWRu4M2DcgRK z2gC&%h=Tr^^2diOm|`mKyPvqOAhnodv&`425@5L;A;mNeGew`jn!@@gd&X_WE^kVg zugpw@Us7~7*Lx4ZCFQBik8oc9ER|u=+)S65ldGaiv~x9)`qgK<2ax>8sUU0aqLL6j ztKdx*lBx=wil%!mDKhd{zxuAjd|p7y={x0CQ}w&=_k8~(Ho6*)*bcM3t=8SPHB85m z72rk=&SPLO@q)6QlBT|yj+TyAd)t{pM-%sa@SL*#Mx2l09-i~A9Bz0By*vTtml-iHyGmG$$J>Wp`$Z8gK6MiY8CpurC$n zw4Sv#<7(LOAw2D%@xi9?rSy-k#qoq=LqGw$h;hgWXF%^Lv}^5`H9Cdk7iU21lHsvs z-iTD*=Bijbm%p4C7mdqsg#@Nr0b1SsqBPwU&b%1st+snq&Qa9u;}HSQYvE-C=GB8( z<5{P%fu|tudFPi)C)7r1)NS2|_6&qtPq5Y1(+~FjP{-9e17n$8b7)dX8Mr-3IP07= z?7;+VW`O$8as?4?MZtrz2&b}$MR-yIwl%mt%C% z4a5#;3Ii1mK>2?NIIjOog&cns#ec*@YJl87{$S6u#%Ve%nuK&Czxv@EuuTJ=JEpTs z*TB#MonQj0TpQcBU!oaBDovSF7nr1Rl+TS)!E5j(g^0Un;LP*;>%_(nGE5>)*WqK1 zX(;nKU~0fqP)d@tyr+;kbC&)u0j7mrNk)3u{3fPAprI;#iBT!x0$p8Xg|x_a0P!=8 ze!w}kpkP5d1-ON4bgyP@N6Se+U^$kgI+@+u_Q)A(xbhdgU z`VNC6w zBw}--vm*l&X{P07h||atX_DyXvK{*{*8z34 zKy-F6{S8S)ooRagnm7TB0P30=ZM*f!LiJifD%U8%OAnF<3|AE}>w`8GDAg!^R~kkm zC^Mqr!eS9R=T@Xv4QmHn^khb)qlY&K)|N1XsO*&*2WOLYE(6$>(Yth#C|tSWA?`3? zkZeTnu|w%*O+Jc;&@i6PH6ZkfoD{o7p}Oe+;6Y6IA7}}f@6wr1|a+OvA=84|81*tvHpjLhLPppw)&Qaoy>gU_@$EG`SW1Ot(I7-{gu{zeysrzEEGS2uL~l;#(SSPUE&xpaDsUJ2bN$t zo}aVUy5gci0u$nVLD<{+Ey7s{IQb=}%M4vWL8gQ>KaMwMEP%M2Z7~FmX;|3g#{KZ0 zOEt$*I054nsDkIjmmClZN?c*t?aRt*ij_V#C=Rx+Uv;~1&goVI;K*(n_8?@qZYYw+ z@tT{6;9lbo;TDaSRKh~@do|EDP*{a-P(qP-D}~|8)4@d~Im4Y10{i*#QyKz(J(&}Z zt#OPNY?Ecx5YVx&V5u^(zZ@7cUpv(W^95I?ya1?7RvY@oP5jCx@!DVT;cgWRCzu`V zD`u0a1B93S_ak23R*8LYx#n?ncGb$s7@LANBy5j2#p6?ce}+3paqBQFoKO)DfhNj% zvx)&pD3kL) zliP|!ZLNLMHp!0tmIymr9m!_Ih^$FKlyHGIuYm!0bnP=+upwq(~5FF9d-WWL4{&H-@Dn{sHg*VG9hqtAz zzaYw6&`5erK$xCW^&cXh^Z!OX6AK5+zda@`8JE9CeeZ?FuBCz;Slvhw3xB)Zrj)tY zxM~|GqOByr16mSkjUylfVpEebR_q`|%$0lm zikVVy){LC~#u%rCL6U*Pz1aa1Fo3&i4(zlsguc@91AkekGo1n7d}=akz3FieE>LYf zyIU)+G|4I9*H96`&5bRV>bD#|Jpip}X`g6QA$5d-r{bc zmW4;()mre*Ch2AJlY!w#OAS;_>pOmx-%DN2H*}B=p?F%FQe3g9+A8MJ7H?s3(b0Ep z9>Gdv{}m<^zxh`!Bs=zZs-Zj zqv?ccMd(gqCF`q9?fwQu9KdHX4D&iot+&#(5n~q;R0WR!DIz6;!GwumJXH%NOnM$S zVtfa0>gS2EKJVcoHRPu1I>YsfXVv8dv(y1BSc-5Fv6HyY10xFcjHO7%Z%C{yC9%s2 zI4Foz&t_5k z>-S13ZIx=TuG$*i=74^)j7N;T$XC-ITM6=s*vKK2Z^m03;)N`ffPuvc{JlYBmYEQoW-{24F#X1> zyVL8a4INaK#|&x*oSZPdc1M}mzN$wiL8xjSUCs9~H%$aeM}hY>%HAmsN_U&g)Y(40 z_c_94+`)%{8ohHzLxH-L4ZxRN#dbEY3LJiNGSx>bd zPjs{kz7z}+RhQ?G$CV94lup^HXIvK8rSi1VWB-@tRReb=nxA4vMST`g2pM5BrNXnB z1ZL0UW^Fg8lwus_(73cdzjKaY4ojJJ__x#iU4o5+CMWqg>n>-j&+#N8JeXqW7Ct!6^z>e%&js zor4a1k^YcUVg9b0fQ4WeTPZRhgOhhUrHpU;4HM$<>~{=3h(mO{w>siV)&7~j1iu4& z=(P#W2SA{EYMFk0J{a6WMHbxp<|4%UH|RWR84bDW{RmdOcyLm15+(SxYvBehr^3Ue z*7tr4*1N0z-o#LQxO$tFw$qEfa|^$6ZD@_^)(1_?Rv4(cIDurq*z(&BI(p0i>I(i|Fo)}j%I{RFbs;SVw&{gR<>sHMs{X|l=KX?W+tv~ z&SnNo%m(IvyIuZg2Q#YyBfX=kIn}>^r)XqhChulvZ07vmLrK}2JBV7DxDqn`O?4Ov zm0=i!g&lqp>ii?7u>x2*30YX!^&Uj75nKb zq2g-fYWA-^BgTJiM1=mihKbSNmY@Ic=kHzEyZ${w$Y4&#NXPhhtbg(?<$oRf?|NKj zMs~)(_iJVA`u8s~h^KuJ1ET}7Q_|%e&^ZvtZoW{xgGE~X03GU;)I?8$SvdRg%J~J* zbit{0JDzP1heWohM2#kOCpQ^)AKkBqgP{U>I}QT6uUDTrG;Rt-4pgH($qgmwe~=g5 zktEi2&NfckHh4}rK3<3L^ln`Dt`7E-k&kqE?e+3rIczHKHf zN??M2&m*V zJB7P&_h?;f1-<~!e;&4;b_iBtQ5|U#{QcyWqja!^1yF^@Y@mPwn0tkOdJp{;(I~MS zMG7Ea-LMJL0h_>L;$}3|`Xk6N9TI|l>+4mBWt39N}Ph}U2Y4zFuR zgm}NoDFksLzM)3fhog&O*=#1R5z7SEwlhCzDR25c!DGn1$n1C_bb_{A;>0O;*m<`+ z&-^z5(az^fF|Dbe!=+S@ZL#Z01kD~OfMrWENe5;s(iDl3S-2va2j z!(RdzoUO{P2E!s-!8K$w{i+ofDda2FU1Ql6J;abxgj~EL|N+Cgm zss$-4k8E^AjP z8K23^))S$6#T5B_V9g*tlZ-l4b*6(z4KDQes1Zxyc@vOYTs3fuGaI$S(Js9#p3)G& zRyOBqGu>JfrJNojlp2%L*Pf+3mR4dXzjA9neZ2`aj!CVn2oVjZTm$)sa#w0TbIaM$ zXntjxcDnQy)OwgsdL}PH0JK_jI7KKmc5>tIk$J%vCkQpht%H+YA6Xykq?|`qR}{Xj zM6;n2R!RZ5o9SPkWa*E#og+^_B2l;iuU23ve%600k)L7-Z(U_7V{(fqt&{&Y(x|!a zEr>t4Dd?qc$W%_px_aA9a6p|{1C z)GydA^&>;>fnV9gq!|#v(3s?+%X|Dg9zTRj5k|tR35Vy(+=&xbchyA%^c3b8%NVgz zPmH|%H6+y(DExwd0Hzv;cH)8^g@R);K3C9`pICNwL8A~XkkKbVf z&BS3A^H`v&QQpp#pz;;eaL;2vHUy$O*51=nq;-lq9{sdxtff}1H=pq`+P_=dhmo_s zm|5jNq^9y%k_)3CtzKPXn?FY8Fyb<1BVf7C{w$Wbzn=+aN%goBAXQiv0c1H|M1jyD)oUk7vL=3&*9l>1` zIV6KFPBg2KX5e>K+T!CdrY*Dm+&wVa!pUY+RQTeCXM4goH!pfd)6cJJH+t;}svpj&4oafH6&aTSN z%4?5{?VD|ULmTC1U~PKw~Y$BLt*QB+m#g1;H-+=`r8DuIED=r z=AiQmRfCt?!dDmI*&0CE+YeR1OF~B+#^lkYu|HJC`Szd$25Rh*uSgscG>{LGq#|ME zA&CCpl5fIEht#?N=a@6k2vQMg8SgQ;{8o=3R;gDPM8o}#ZPGW$pi@_B5CuQoWB-=_p zz8QO!l3~{R3Pgf3y%IN_HoKyoR=bsSA>AH#IbAb|T(b3HDr!60oLMAVKEg=R3`z{K zORLuG8bgI7>OGRqOHd(B+pt}!2r*<+?I#GyGfBLZ>*(*(M=PS!9_vK5yu1L*_7wsK zi8EU>Ygbjl6DUAA8afqF743x^TdpGqOCe5l<-StaTJu}|rPWjHWtRm<;JUY~>umE| zyzLd%N0E!9g!L2|TxRIigG{BR62sbMMnyrxtmcLsEgxJqe0U5_a{6Au1elm7 zLy+uo(gpyd9lS!mYk#uIc2_Ay1VNT4nTmLH#mKa;a@B99mw&rI`)?~Q;+&nIDlN$M z@oEI#pQ?Vf!~$l{w<_s)lZqe8w#a_%H@VUrqJ1!Fcoxe;a4E+o>TULb;j5&IqjjXV zYlvtao|iAxE?x80kC{z{=n@Q!V?r0%8-G&I&LsmFc<>_Sfz^rdE_!od$$hW!x~8sq zK3^jLtQjzl4R?`@q^z&6o7oz8&UL_*O1W6)-#P>J5MLiwVWQH}K;7pXW5McTqW{yIuFR=x$H9`lmGHgh< zCvj;V*)V2NL_$Wv+Mmww@V-9ky?$6-&gqo^)7-wxzf3W`P!sBt^*`1CHB6Q|qTALNY?9^P?elUw#gkcl1P2{7+_rzO;4*Sl$B*&1bn=b2bx{OR zKR&dARO=?BdlwJV_Tq~aOsxd{GZg$1hwlQ#Kq`ij0@jHKWs?ZPn4mB}UQ?rTeQUv~ zq=W>DGRa-^3aT-|i;9Ki$qTV}&r}Hd%*rV9>}UES(byQ7X*4Dl_bmukTC@GoYz_|l zKw+ow!t$rU-q##N^z16iG5ZG~rj}Eb51sNjCe)EW1#(Wy+HY z=jKuTCRaJ&FwT641p}9T6k3`@6)%KqlP@ycg|3KeVC}ad>Yl}bAwn7bC{YLio|{Z| zuBsW>v^7n{FV%tdS|o+E^T-sRraGXHx3>LrJN+Bfb9RTDY+WOhBYX)b> z6+bz$1i3<%I)z=DEm2=*+#g~MS{^+_>7MYuf>buK=M8q;(8Mu1yD|?fX%#h_SYba2 ztTCN0AeO)^`3sG4Dj?!XivnY!FKtAy?) z@B?J0`f{%;#p_e)Q_HvRi~N3Z&J}c|@&zZZ$$PD5Y=lqGS>Jqfvlr8v1N2o4 zsIKCv0wETh*;~uzEA>H)xjSd!{I;R~jXM`vj|##fsrR_32cv&0Scl4wLf=@=l3y%I zqY@b6kcB&O*U`rZM!Yxxh8T}nkGq0SRNqLWawjBOSuuK%YvXkd3tL9S7-wy* zJV0XIIcuMqtFzRzpUXx8q{3|0_m{|iB z_J|<1j&&aTc)<)n#^<`)h)3G*8+xm4#AeQm71RvZ0UP;EKS@*CmG8fZ!QL@5BsCx+ zCo*FKXA)x~XEH<1@KY<0b(M3Km6UZPVILQneU*iid?E`qD_+x_mL(-)iq;)2fRsvn zB-p$;A5BDYL^4_!qw~m8#8`UarT9HjI#D`_ofJHgJBb)DUX1>nP&KN;BwIvA_Vrdw z9AeeXme?G2QF@c1qQrF5aYx5f_hmGD7xqJbTCc}%K>vFiBipW^J3=y^iHNF0(ZjjI?C)GS)TNs z-SO-`SLrkGk%vfr-gsBuk(y zGR$g}9#$Ncm6K=f114f4l&qgant^RlG+3XDB{BDv^-5~tYW<^ZhS_%sKrhi(@_csz zBWD|p+ni4OG1Yd9H>(*NB>aX$>CP+gTt)O;uRb~(uZM^0!C>n?G)+xRcZ`SvZ436; zR**@L>@e!wS;9zF424!}b-6O(Gxclvj^s36rD0O!GYjiFfv?-`u|GgRhyYs{EzQI# z!|QdKY%m=PsnKtYR7%qO6K`6|0j_<3UPi#tWWZaNQdP<;x)Lu2M>w&#(h51KI}gx%pE_Si9#HHu*qH>qc^~L0@1E#@Uk4%G zNi@DvkYu=#2Rl4|<7}3;l+iCvwGFR*vuxZD&M}{!@_(NHKepa6IJ0nB8;)&GY-eI? zV%xTDCr@nKb|#wGwkEc1J5Tb>TW6oD^HuGC>;AWDRrlS!`a)-hT^X3-MirN9%do#M zFNq~z4fW%H6A#-*z<^R{pRlD%_%!q{;a4hSz|CEx(q{{hPZ9{JqSV38ZEbDMyjTZd$?VT&-90269|IukC=Vkx7fU8Mc(IQQ(pw+BqxfRl{?; z+FwcK4~#m~Y5CTls5a$%+H(M)H6G#))S-p%9D0bc2QAHwJs~bXUCP&bu^Uu4#dMYj9UQ0d~xx9@p*eo+n2JV+J>PprHU z$l`>Bz+w|9tt@#DWT_~_P_$Ds)-~N{t`BY>bsiGGOM*kWr?|W2;Ss>ov-NkgV8FDY z*JAIV-d`#2tbo(+QRrfJ0dt*Ib#*z5f^R;d6W+^Q0FUxQIfp*fPYLCq9W;=40P}G# zU{w-Y8_5J|ImfV|+Pv3jD2-(3P;h5LJ)&T$|M6GP^LKWznIQOIPIhL8pSEV573zZ1 z(Ula$SK;jSDcW(3>goUz#Nrmczp&+J)6SN|+BmDKlI7|F$n6jsnjH8A+$=P#6N@w~ zV+%*%_XzDmJ=CrJ)a{b?$q$F5X>q)-^gYqils!M!_VgkGq1>^e3SfJOTy4`FQfnNs zHtMkiiq)FF5p)XCtP3(so$AFDh4ZyoD~`w=f`7U)6n%00nO^{q>!JIg&Gf-j%On?O z<&x;u-1759t|`O%;g!fhl7CBORmYAv1d_7MvrfSXOP6sZD|mLJeulZL~6D zZ0By3nKNp=C&LX;;EX@^*AWr5AxtnwDFU-B`y;CayP(+uMJK6T!->1@s&a&ZtH64y zj%FPomH~=9uflv83}iy6E=V$m+gB66yRkY{f5SJbHC2$=5y9JrlTsu$Ak|AQw*0Ol zn5WS#LpJ%NTs^%BoBi-^bb)25}h$6~(**eE~MnYwO1QzlU(KD{V#w``c-V#)t9=OC@$?eQgi zqjIitXOgFk9fJcU1eM~ff7yNjoV|g^c_A2jOq{s!cVai*^?wS!-l*XYi!Y3K(#%gx z?jb~-15pP!Jq6eD)^G#=Y3Yl`gyB88Qe-Z6$vQMtxFt%XqyIo^3Et>~1B+nT!2T=iV%<0ph;xE;NEJ#0SRq}_dtKMTb ztA6YVM6kd$lHg#W$w&{SGg@mW<|_Z#I)bWP-0_h!Ob7qo3J1syR;#^sWA>tZitQTs zzSdy&Ru0G$>HD9X`)lo%(tdWp@pjx+GkiAoF^=wHqu&gTHuglW9LScO~3ETT@^6j6Q?=kWZhG)%P=>H(oPSSN-ww zzPh9Hv0i{V(&kdVy5StFN$}Jp^Gt!Q$aRoBK?_ z;^BN{c2NTz;B2uxH4T#y@g{w{lne(82fF}5yM@8+pMQ<`RB4GmQ{#!Io?iBadOzui z2vJ_eF|V;-JNmo>dokJ=i3}QzxAckXCP%xQ-FsHTo85g=L;RcJUtl(WI;QvKy8lLf zoj{@kP#}6}-W~ZO{G|(|-DIfu&dy{(+B6@jVHCTsd3&A5O6|pn)KT@Fi(rJ=)HMU_ zWkafK-Fo3Z`eF*Sj!)#{#bp0}wZ*pIbj)zTXe(q%ci@V_lRlcT@aBEH^=^>acoA^fThRO zB>lVd@sLXQHVav+8>w(;;?$Ci{ox1*?K=V^YTajH6)+zv1xt4|Qo^>8fYcSA59`VQnZi;130Ybi45V{PlnmnVP^vAQ`KyZ%GsmCH`K&D}33O z;l34^1Cx<;RAjj}({RXOIL<4;5i=ae(Gr&u`R?w}7eC4LM8r44bhJNGK;YF}_HmCm zKN1;EC?6IbVgx=0zF%_y$40_IV8pdBoY?c8c|FK}zCfp-8orp)kX(%vQvA?_%ZgUl z@CPDXv}n0tc%NdRyLUgsUvW)4bVa>Lk~d3COXhH=XhGI)J0y{0!Qv=Gs6cOTIYz}3 zK?)+X^OSM09LXALYPbqr+%Q=&lrdb*udH&d`|nWjuU5#{a*0O($Uyft@V`u2nOXkJ zq?L{PKP0XtO&JwDiT_99nj#6O7>?^aX%Cix9(K}oN)$2XGNPrB8Q8{jf=NJO_-oW0@9)30u)yCZz+&j&tqA;fo%gwmc18%~bsUpt$iSQmIw&}`nwmj7 z96J(<0!iq~k{f*^&6h(~E+om+OZo0a#D4g^=m)%w>!6jb4+NBgwWCy}xZPVRJL{(6 z4+E(&vJBF{qqCkLK0z8yIrQVOV%LRJ+3nOUxnV|?Q*@IhLVGlzD;LLqw_)ukI}K+s zlefmC=BZI%M?gxKy%dm?2__SjQQ{6An&N{qOVYBYKhkNhl!=WtV%`~uR-WQ2*|fX1 zR0EdnRCQ!XHv?@!=x;vZaWn)$ohw$@O?88y|0o6oNnOic;R>SLP3DFQC+ul+Iy0G9 z?u*yEQcyecPUT=Ixd>uHJ#PJ$4IFoTtnA93Io3GZO8>n7)AhmDRq1S@`4#&BpD%)) zOqxo$AjbAkHd&1*{>R(hHctmdg|GOF{Dz*8+`C3GkkTh=J&Lj&37G zgp8`|>sL4Dv>G9yW1^A(_Fp`>J zB{4>=4}g+LEGhkSz?KR3C_bv5X;;cnip%!*YcpVnvR-%*!hq}?16y1y&E@7v>IQI= zH;VUz1scE9P@Fanqhn6(<`RE3qo>=fFO}_5M#$^vBA9L&Na3^c(M`V?C>9rFhrl}E zoV-?RbR})lR??NYiMs@$CniG;xs^$k-bt6hK3h^;E!-R)(J{5D{uCiN$x9Z6)kYHL z6S9b{y%lMh(6G!%rxc>f6?21N2Mxfe=)_l?BPdg`CQ!mv`;94~MX0*|X>5lmA7w0^ z9q{8wRi=(N+NlOAUVQS+@v$aJWgG~)$8RV5T^9WvwGU>bh9f`vqWcj(Co3Km))JpK zfqVwe6S}O#t&gc40g*)x-nRV38|9FZc^G8vE}feY1}70zrz2Wtkv@qThYfH8)^s-P zHR1K?NPA#@9Gx(=DRG8iZYI^(_(Mq1wJSS^5)6^!*sI5m6lo^=hk~xyekCro0=n+H zYhakr;?@~xMO_Eg^pF4)@$Bn|msnDw=EGMzv+-3oW;W9^aD~DC6lv;oI(mE_uVolP z1UTb+*PAb<-VN}{o|NtrwSZj4{E}Q60Rz$eirjNA(XY4tH_@v_J>J>qFJbUj<#ai5 zcBC8vqP)D9c!lqr`HToDf7UyluYzlSE$s&wIlQVW&d;LX*gowJH3V`aH0-v!f8M(w zKI6%)V`1%(r_ui=KlZv0s;teI4TjYoqjjvqblNFrqu>pMAzHVvnFG%5#5Hs`F=2E; zS1naHu)BWgY@{b3>ewn7$hSTn#nu0gITuW5K2R3ent)QKIKy=n*b%fr=Vv`&%Tv0C zwXevoo}Dh66VOl&qxD%?i`~4tq=b)0jIqz(daPV>sc(=eqr^~Kpj4^ij#3h(SLUs` zi)&Yyi*Qq*no5%w4F`l9;|K9HE?+t2TyCN+3Z@cq*=`gZL~vy7fOE zK;&614Vkl}K%()Z3@6ggqTC2Ki>Vf7Mb7Mj&EH;!8!8cKM3|p(*^3_Kt~=sWu%5ZW z6>nH5Z@IPJ9c6K=f{l4gsWjD|noi}Mo@JC?g(+f)8N&S;dFhXJ`Z~Kd*{Saiud>MY+r6(JmVYry5peTF4n!+BIHQ6 zUy>TsZ->o%NCzZ-S<&~fQrC~(8Q&DJRg&go(tZrPlF|0azpDAWz7{0BrLO;9+F_%P1HibrxI=SdRPSb-@8WwKY1SCJO1 z?EC^-`#*n$n>%8aiiNpd>wD%sNW(-boRz+bf$;<`AR>z@+=A@k7a*}ww>+qwsyLej zY$d4{EQLPzUVOXCWIS7fQZ$QXt3(W>h!}fah&udl1`}=)8(a&h=^2*bNP9D3sH4hO zsFE=f#l0rP&!Nkwb+rS~6;|)tGOm;n%}SR}%UB$b=&>yXAxEtlUCTdCtfH+>DS|7; zu^1rim2`q6_V|6O$$+S&K#36R7`Cwxk*74HZW`ts+9Iw)S+3OwG4|5)#CPCJW@md% z_1V6^lE!sIUgw49DX|-&aFT+eay%2XhmGlicLHpxHqiCF84e9H(Z;B$t+LZLMSyj< zqaM?-7Prs|8|jJa$O1fAJc1`rpdcyL%GcxL%((iEb@3k`7N8eMYCt~}KEXb6M2L^J z;QW1~;Q+kx2kQ?JQr}ERjn~NWAdSim#Jbou;A)-Gcv{hF_Po8)S*kWOtso$c))^a{ zts8{>#acYiHPB@<7lk-Ry9w0Zl2{I!cp8$rAxxtR`r(6M6_U*ujat*@$P~(01NSs1 z;}vdZ`*pSJ4lwT$tDa>!3)A8;vULQy04An%z+N&r$=wOqKD-U5)OuJi-a#QNGEV}q}=^UJ=XW+D>G<(^KN^qdghfj zUAW23<#^e*8+%7R%s9ezb|$ZCI~mI-!|&+acpn{{2cUOk21>Y43S_aSa{?5GJqATO zJWpOPNq_Q%HOXVMbDN3Zzy{y&cU>V67+_r9+fbz|p~qFNi{9YgYa$IM^db@UW98O_ zJ19*9Uu({PDKPnjyj+&ob^cWy_d~Y?b6DRR%Kz4IvD_?r<`zIK&mGifRxU%%65U85 z%MNr41`zVb_NATlV5S2lq}0UHOxQoVG%Hy&Uaq(~#8W);waaH3&@#DC+MP&qLA zgR#RJ0VEv{hU&0~U-i^CyL{A%hD}INMpolMg1hV!Buz77(8?0$=dIq1lz#uYGxbVR zwBLWS-N(I2rxG2FuHKNk=9#z3!mRZ=xITI!0UOn7aOd>x?fuHZOkS)8xbx=f{#>}( zWV~kZ>d=-`-*I6;U?{DfI`!_}V57J6` z!m>twYua74O-`OL1|`zxm8>-C8Ee2gJPBAGRS0V~gx!V(=@bdaRAP#(OJp=z9rP_& z(y>0V@Q^|bs_XtK2m1B?Q10QcIe z&jPLM=)`O0vx`@t--i512*$pn5Zq_x4LH{=u;*8wlAQ*)$rI~@`PazaR8WRW4`;XI zG~^diGddm=QJY{YQB5=O8PljLCD6kjiuMPu;-`0#GlZFkmkpBJys<>V#|97Uq&JPH zf9e+2mE*mIo7>6Ijp!&|%!)#s0noqk6Cy98$A;vXJVzrCONQdQ)uk5^2pQ4W(la6r z_P|zY(2+I2<1!+PB$h^fRQ--;*ziSRw~uG}&E|IbE>prJrUn>%f2ANAf(8dz(GMNr z;LJ>Tb?BSt>*2{`xBuce-F*WW524}WCMnd4?KpCQ0=H=SBcrZ|_IoT>08sp#2q(=e zBrD3Dfx`b|t|OD3nTOxm3I!!7Y5oX_E<^|-I~a+FWDMajC>I6XS2|km8TyMNjFcAF zqUWIV$N3uKM8Lj{1+0L3C@{gZ#oj7b0v8vxP()B~U)w;E%t=Sc98Ib6TE`JtFdb2( zbueauof z2IL05Gg6mKF4lX3v3o`b&=HSZ=qtjKa|NoNq9hDA!kLf{+xl;uFu>3Fl4oKGe3^=E zcg%?>JI#h~<i?Z*0N+V@sx{pM~4{oXSveS=hf28 z2Dgqc39O9I0JAaXFMaH5vyCG{IV`?E-(MS4{TDH(e^hy>PHOR-=yZXN#e;<9A-iEo zua!jdq0OONz0RJ04*=$qK_%gX0c$xfy-vxWNA$?_mmv{2LuLn+mpRWl5YIY$Gon@4 zc}wGg1Y|tZtrafY3N}=w+}uI)!H%W~XLfQ&PB{uUfpds(<$saI*MBkqiB0t^6JNj+ zJe*zEWy%A^EY)aSZ}iaSjGRn?e2KhygW%3gSW+@Dy5wv1lJ|QV_vPQ{6wtd4RM-2XJ1sR@ z-+2bd-Oj*`vcR*293&+W1V~KV3S{35Fzg%%B&Mh}WD$rWSv7;3SH{xcA;6&^MV*uW zjx!U>YE)|cO}TK@$T~SR`Q4T0^Tp2fdZa$_JQyL4svm5ZHSf3Yq=W)&q;N_fdD#Pb zML?~%`r~xoZ_w8|+ra-*Y5up+FmwGg7-T|XW@dq7lr*!lu>8mJ=T7c9VZ>FDGjg#Z zW@h<+o=X4d{Qq&oX6NSkPpf#9vzHXi1QYTCG~nTMS+FV&N;MY}8OzuAuF0ni?2EFi zv9a6;8^l}wI)kqNet8j)1zv&f`n(Q8iz5@ouo4pEbMkpQ4mDqLaqZ_^;U~AJN_a7c z_%w`R&3-fhzoz%4xF8M^u)`PI9Q6mmhWkYKi6o!e5i4R?OY9f2B#qAVG_Smmb;>>@Q0dt$?(J#4 zdBr!jUu6aX8R_ZTdwPWe)ukL^^Np15`K?>svGeIDTvhA9FM!6#Obcdn-d?d~;uA&c z2}^@DKO6_UC_SOPr!r^2%JN=pU5=%GWBduVLhB3k?P?VHvv2|QY|}4A4BqJM5_Lf++c12tN&@)Eo2gIpD64>3?Fv{g)7BVgK(T z$^pU5%E9>`A)+pG+#xl_6J{Hj#x5MbA=;nFpVOe?l6dx_O$4t^!jjIx`dtDXg81>j*lByx zIC_prS|mhl1KNfHTEg?QUOQeIypFYudlV2(hXQo)0FLA3>%+$%DA^W;y}Q$<0XgyNO)m>05uLdntuI!_0r~b*ah%8UCwC>?Y}PkUCNl_I zGFSZeQ$o(eY3O-26_7z<&5Ll_TRS(&VDn39ejC=ErUOi z<3=6tJbA>LezIg5u45Guh=ml(qi@bEVz||#V6qL0U3MR}fmR6a35d#aSrZ(Crx31i zN8=)ALqHe_kd5{4Iv)5X2ev?~wt0Rg-oac60Qe|gLLx4##eN{0+?h8Z{LQ?ZaqM1v z(#4~P;x(P%0QtdkfWu_|DoF3f-v+{1IEugN&JrxMPIL|?dGE&dpfzdKMSNp5%ja(nk*r3n&@y*05paED zPPTvaMLsBs!c&ogKiCc7gA&51uO-{=eoey&gR_vJn1j`z3jO#r5B3|h5kZ-cC1Jm! z)GU_~fbc|;G{Q0ZEJp8-O3M_=wQ+4*@dPwREyozlbI#q*p0n|!l13044k#JxO-0>GVqpr0kpqbfy*daL4vIQgx zg@fepW4>5NpAY$(hHWR6lU{cYfE~q|=-K>mjR_vs6Chb6g}G1`^HN#o?>wW`yZ+em zESMVYp!(nXCPOI35D?7EseDuCO7;wqYphD+{W06eZqRy}e|&hq#dJ@gz66_SdNp$x+J z{-p^gj22z+e_ukC&(tf;+tdroX>5_I$K6U0qb*|KosbiR{~Sxd@Q=k*A#H}^c;gI7 zbviXqw<#h|cL)MCIKwtLfGD21vZndFiqLGDVu8CdciUc&E69-W^J+J3a&LB-0cj&u zqZ~>@!~{9{#YA8Zh}A&7{q5{W|3 z^$R<+jo!YSwDf!%e#4L$lQ*x?7J>ZG!DIr{R@$n(fLd8cQ7*Ph;0q0_fXQ0s%ytMW z8xLr_E(MThx%|O+@Tkdc)2Bo}hDalTvkXZ?VGRIx7~rB3yVbo+ zcIFCVcT0}!rpaZ zI_DLdD$p590ZCS<8W+Mf4^zZMfzKjFIqHp8pR&7E5+8jlJ~c_Ex7(r+55CK0kvU{N zQ|wv3mHQ0Zh3GJ+mUmJ0w>k!mmuBR+q!oAr)czYIzy=j^(BczcJ8~R)Z9k%uCU4sM zLwA!qtNR0g98ydiatja{J=nXne_BS+#%E^a+WB#glGDphX#c&Kpg?;)HlfLui~a3X zIXzhWtI<*Jp;WHO0OwdWcCZbs-?pY>T zN7|=s+3JyO=79uUj`N|J()ys-_~yh3;=(EvF~g3aJI1G1<2x?&FSc9b{}MKAZ0Uv< zpcpjl++6?LQ?d|qurqV~@9Cey^nV}!(f(OE{-?gjHbJUloTGEdlfg)aqrpp_%+pJI zc#zRgg2`MC{Bf1?hzOBRcTJZJ4k#!oX$oPhD1q@kecIl6`uaZc-C1*Sf5|<`%=9?+ zGuQml{N!nBi?XaJ27x~ees}~8ddP+m6Zi?@?=Ph9?+@yWh2{5S0`|R?Ab%Jo$~Bl| zw*UZOK1@(#Iv=4#7T-c)M{x|O>O=>jh5?BR2q+@<_YVO1)%&_53V{ZZ0PWLf3xeAP zq6UF~9yUuF?sz9YaCxc3`L9mH8-_cA1nln@ZT4=0vdk!wBY=g0v-MH?R6NLu!>qy< zga`B$P~ZF#uK!gpQK&2E>zkLC*JWtIsSg2|mrn}D+l3Wb19vU7S1f^Egt~1s4WL}b zdGBP?_r(h6;h(x<6htz4=E zN8kbKp?@4hwDgdCcJTZtpe_an*-?G%6yStGI}UO_a0})J{!YBH$jIiP>$5vVnVC`K znn3(M0UjDjQXiJxZ2R^St)Rx;hJ1Ya{R!>2vjwCX9b6AsfP}Yqh^QR`T zHAtvy`1{8f-s?jMG6a~dAqqwxt~GST&-?1YALXsKos-nLXwNWOyS|RL9zbygfoi0lS5Xh`t365FQW)Q35D|27KoS zHucx9iMw)zKQTJ5nS%SrrQ#0dC$!e*ibkJLB1K6VBS|Q ztp)82uV=o+)D(BKoe}~!xBow7{0+!H z@WYdDWOr6Wl+kR&eRr}+1C&Q||1a4}kZ@vKf26E{dKi!x(V*@-hrG9Aa)evRZP^mU z#f$U=P~R>`i1QIhN0q!^eOQ4*-*07LpCAG@?lB19`h>?|*|ny2^`@}Bm>i8PmE^PFy9 zXGk|Td(rpG997LA7y%>-rpizqktZ6MtMR43Sajd7*;Wq3yZoybocCS^?<22Qz2U#6 zsLggH`{QKw7zqe}#`ipi?UYvM8zqpLvwDZq%EVQ7{z!BuT+2Mcqp0iHo^OBIQ@P;5 zQzNx*1*F714B-rAL1W6*A8K33E3@tuc%IrjB@udWWpW9;{hPb-J5Lw9hrsUuIOXgA zuDEIufBDW^6zUrE)g&Ja#L}=695bJNFsmD^O{=O^S?%l(41dCocrySK? z(ESX|)m`X@8fvm!*peL_@M9i*^{|5CC3y1hUCBU^z>j-|n`(1Fk&O z3jY!`WV#r{n~KF2cQy7kD#*#6fga^IB)9Mzc%}f(^CQ}dKsYXSyVsP2M93V~+1^y9?nJW_qpGEUWQ&&Sk@Cbpc`S~j@Bc22AN{Xp=}xlNNV~rK^7Y- zFW=#x8|7A|3+a1F zHvo`u3MRCME@D3Buq^S)5)2A3WFOP>uh+lnPLZU#fJL2{REe@fi&O*KI?Cnl3es^- zlF9=!dBuK7g0P#u0aQpUG)9`Iz9{r^%}zh^#^pzDcgeg>b>I1a)jA@5OI`JNpdNz# zreNoItgM|$Ad;D?rWJi|j?L!3h@w(Vg$LwGcJt78{MHImgnC^+dGYTFMG2GCafs(4 z`I?BnCV)q-fvIGKXD%xtQwq+SqWwsJHKu$bzxBOc|Ml}WxZ)UJf)V*Vqj*;-GYIaZ_>CN~kryBn zaMz;2``$8ae#J}hvi(MH`*u9FBaSvH2dnCy;T!Cmbn)|al;QGcd0ih@t6pyj&xr)BjgOfwEOi}9_(RDu@yGf7-SqTwjR zV8*$^uyx^mlgVWG$u&;tT}U7jj;zgN|0#+8g0a?4bC9lZcI6WXKIl^N;sk(w96q4p zI$TF-(E6yTflhO_3?0oOc3RQx3|*$HW_z<{mjzuq1vnBZo;~k0sYWd*%vLT>NF0M> zP99q5u|B}_GeeoL<#kxr&+n$|^6(Zl+u;(~4r%b^3AFvs=9!?s3Oo-mx=o7vANOTQ zh8Mo5}>A_P{Vxt*0YquEk($)3PRTtVY8N8YpW72#N zv2J^3c?!Rwm!e_oN#2H^Wx|-V^k)jZrLzbyf6(BE&h(gq*;BDM`uiIbp770Wd$Deo zg_v4>Qnh{iL#sNI77K9CI{Q8$y>^c#oR2`1Ge#$Ny4N+={_ATM5~zP>Y6)FC7JM;l zu>{%{E_<&-;GV1{cyA^>1c61AzS=rbfI04!Jk??t(>a2pn@U!^v4lx=V086wVG*%T z6^jX4Z0(y~(WasMd=UtSe1OJf_B5F!vqohq%i(wyG`9-W3N?W8AZ*K;k1`jXxfvq* z;MkFs#KrLvK3auCs?(n5% zgPq0vaN?|=!@@g{#8%?ts-h^jVoM07AOA*`CwMTl>rBMOk%Pl59paf`W8sK;gXJvs z@q~~yf1eYQ`yoEk(>)s^PU+-evwj#Zrq!i} zM27G>{32l&Yh}s)8MnjPbgwAFZy!&a__nRk1vEVQ@UNynY)mpa$baT~1V7>tD3|AA zIr@caN^BsuDD85NE9)|<5Gh*A-!@9W_|tWgc3Gz9<`#g+16INmnpOO=1cPY=B~}uu z(Nll>*_Gjz!$75yl{#>2nD}wKFDyrm_7P!kAXIi@Bs9%*nj5wZ(dLjd`PZ}0_NkQp z1uU1<^PfaMi^ob*ly91?W8JvEpp>0usBR+4-%&IwhXv~BPRxmQ*2Vk>P2U`+^eBqh zui@5_#wbALkrG+Vn#?@K6@exiIz3Xo=QN*ptN{P>^Cw=1hF}}xIw;w8r*D2BbeZL7 zgr|OrTkr3yi_UPK*hx^W;4QBu`h%m6ME_%mKTPcMa%qDB1UyA729r+e7i;u7hv4h% zm)@&x-$0{K)w9ISTadj=6aRU{JjlT2JF5RNNw^mr_u!Wmw9ZdRITZ})FqnAAfGF-oy{?sxH>A#Y{PKJ z2|fo;b}W)xes4zaj*2M3(%KlAgiuT_U^FybU~#z;RaSSlF=O`T234iHSR|F@$iiT% zqynD6UT6%P9P&3~uS-BnsS~q*6Y7Qad{wE2UpIzh9od*hl|i%V_$)+NOsUGERed`p z6z%bjl^v)dk~L|O(Rq5;S=Ud95XgK#%izwZAh{$pk4Ca>`&#Ne?6e^2m7|CYlqD#D z4t&LA&py!@aIRQ!>~1Mb(#Ga@*`40=IRPwI-!@QZaknQrb5bJOd~8(VP@m8nF!v*q zQ`mVvtM495zBYZmWXIXXAByFdYak%kN?JPDj5C9c*}@u>G2U^H(V)`wF3zn2yE|J6 z=usMt++DpK61YCd4ssyDLRf}#2u)Yky#bIj zpET z>B0@Z?t32WF#YL6CF6u=d9Wsb!?Fjlm%)x#gc`CeIiJ^d3yX<@VT%l^HH>L0CG7(D z4Ku{XX;!)Hc*Gl?(h0HPhiWt6Jiy@z2G_ zW7qyN*K`$X)V@tb7`&Dz(xnLsuhun9IyWa~VRU7vriz4uzDp?8(75v6_4QQzjK*Mm zDpSTyu7ZMZ#o4(%`Btsx-QNMxloVDne>j{X7f3_4`OI&Ws7rnZ{ss|)7Qh@z`OPOt z@8nvM9(;vEdF<$zW?YLt8p6+wB)_XrH)v^DM^ePa<`w5Y0r=uBOm}<#cU#G2ynU(1 zsc@F$3WvX-f(Uk&ueU;8+O!QG(M^Pm!^B7GAnlXOKB0!|yxBI4G@g?L;2&yv>I@rJn2$bTqY=71J`nDx8L!&gQ0D!{Yh!%^V@-!Xg?YP7)OTWLjaD&|z~5 znB$V~k>iiFr`)YsBt?v)0L- zZLD@)z#&->PP@DlL%>^-8X{)UpFVqZ6WMw~X9>pnyG^wxQWY~(gJ6Dt6&slwCk%e^ z_;;UP4ag^k@itM~%f!6rCo z{w%WK)Nd(Cd9Nt^mK8}$b*(vlQn`fiNbL+!XDMGBDX{JcQ7?TEip$iMGmB=Uiyk6J z@~4|FdWbl}GLy5z*O;#mMN{ik!Y{n*>#jNS-Ek>fo&Ay3+5^~Ss37#s+1q-*N5p%u z^hyzeHFDpVJ63uK(V$SNOQmZt$jKNmS}oAu3Zwh8S6SoZe9<|;2|B~m&ffCKZ!c}Y z7FHv{-Qp$(p}sAt?hU^x%0J|d$s)U8>_~M4ug>7=U~xRUV$Rm!Xf*?!ql{>S7c&YQ z+10tdhPD2DrwYhYDK;|^{PR*9?}NmVKxyj!(Y%Cv_tXK*e>IMfZ0)>_r;mj;4_nb* z_ei+5WszaHR%EI5@Tie>q|h4#6*q`Y)fTfwB30Osi%f>$?NLla6@q159w)7JfTSV< zyyX?{_@;5zdl=%NE??bJhgq1!Oe5%nyp;WAnTEEi(F4dy;tWxxLt#<0z`sjUllIe< z4rz*gMf#?NobgQ-->=z5Xp3vtuoJXo^y5D5p`TemP_TBzKkrQb)+k zJ!Q3~dFQytY#XK;Lamc$K_wmTetcx;SK37YZ2{`E2QP|HFaqtc%O|T$HJbY^?KcTv z^9Npl72d0X)itZiB=M7tB*p>mS59?S~5eA`o<;mh%vELB>I_WVJx;ZG4B<8Qgze=Gg<2LT0W z6K+D>kK!+Ui8B7r9HiXT<}lxK!&|TvP^adLJVfXLgme*abllrXY-Ab2!6cjS)xwD1 z=~1<=F;2SRm9#E>QO#2Q;VrolDya!zC;d$(`t$yDj9GQMtfu`6kh*e0nn=~`jID~| zxQlj6)}?5E#%g|yW-Kt9?pk_)3;>yKw81DIkKqM~reSJOoRE~|%iictT;2uoVM@miRksoqxHD z9NPfv3xBecktKom+;;1_-yAT)#ZQEYv{}q+P;g=Pn@vjQK`P(a+XJVl4RBb&``G2= z?3vrSADVgqCo{#0>0xt=-1e4wJqqJtjh7{6J3xYBtzT8?y>eKp|M?QFD?nyKC0$bk zQ6wGBuwxu9`Z zgNilh@*C~*jfSaJO^;N35iiMNZy)lwGj^-g6z|M~ipe?4gwPuT3Gm=+wvnVk-qPrQ zD*Es&9PJK1>+)BEbT4pyTjoIGwHQ=1UlUz6W%lje>TL2yT~XcpCZ>eDj7H~N?^Y!u zo5_#!qqZ6}PSWhYV3I*=f*ZPvbo08X@u~aW0XP(VFndS#)4+opy@6> zN}RvqE8@rFM6Ci8a<{j{S;KT6E@j+=Eb*lx)tkifTA`w}n04b}gxvmW{@L!~nbm8| z!m&HMVNcm#S^%s8omaLj5_M}}yzcrKe0ALJRYFPF@9B+fHwV5R4<^v8$K`Zx zF^tq)y(Gv1N=%@+7Try;x4+{8d+p4bjFnU?)PT|l#CDlbV>IJ9GxN^L9XmBrn;ZHrCUp@e%W1iG(5qxkiU9h#D%hX=p8Si~CYDs9(Om^Z z264({C&I!oby|hh7xs_#YH*N#7eTu(G&!?%O|1+3N!;)RKkZ@j3&ss1Y=@*$ee7Tu zK4u!&V%2GU>Ffh=^gWJsc_00#YpofimuHX*R~}h>oSZ)ln;`r#B#ZcgsFI_$A-v~G z84P4Cs{oQDn}df(wX*kZ?3DSQ=KAM&Sq1y;sTK(HPOO|i^{drNVt;K<1da>;QjF!w zF5jx+%2qe$t*_Z%Ak9<#bBMJJ*_m~beuy!0cd^)t!)Y)|&97{JEfiz#lzm_0zn|z$!&UbxOPgXRiAiVU69nx2b@bZtR-*;QU5gwuwPi3Q#|o z!mj8$RO=z#BU`Sp=^V%O^WsoYe4J_Un*(6pWIy&ywlzk|tpnwMt{Ee?RpyZSX&>m_ z@dC23w}Gl^YfC&B{Kv#?{97&QKewRsGj=tTe1|ei8!^j&B&}^8`K^UtG3i7r zhR#FN6*W=l^ae@hRWk}4eWAC~3vyAC4}kO@{h+>seB%=fC9&2-ZQNl`fo@lP_t}4@ zgZ_-O^k=dHZGVD%Q!5U5$rNnZy1R_G+(s}_?x~w#?L%DRJ^q+tb<)q4(6>3^q^rJ} zf$l58{xb|{|5CAZgT4xA1U?{u$hq$)Wg4y?2?(smh)!*NqIA^&4`WIv!<(DA-~eKO z9a0q<5Np6N5C@hDxxd;4ZUk;J996*G&!3Qc^eek%^RW$cSl4-t3t1|}rJ6PUC>)ta zPbVGLy3a3Ue`>n3MMl`3Udr{gXBpJ#@f-3yZRhf)p^(6})~X`TBe%=n1g5%7ao>GZ zkECf|t5w=Ri(wl;YSNnM>)&D!)dS#UUC_18G5JnOW5n|Hnc&+W_UcjNTY8pvQVNx- z-4xEj@q0@QojKD>n?kXAm4~isSN#XYvDcq)TWzKG*B`%Zl3A$Eb!xd;KHb*K^S5Sn zsI^%V)^ZEehEH}7BNqsuXdvc)FwR?4;OgbEaOHHast_X3tJ^nf^A}F>cLESchf+OB zL50yXa0@F95wsB}Q0aHG$7mgPHKFgI81+Z36&7+z`G-wy*~3@mEWr#t`@B#T-WnYXZ6zt{t$8Odlys+CFk9SneXYSA zb3R7d{$5e`V>u}-Nq-G-qzA}_T#urdxU@DRl%jU60^k1$Jzx~=n(RS(x zI+sYhsrF$SU*#1ObinsuJRYFKeJ(u;>VtSfhZ|0&~25)hym@p&OYTW+P3 z!lX%T+vvJ-YefdJqnwe7JqH^`Uce;{8r&i@PfvN5s#FV6e_ zgM3-J|Ff+z))i89acfyXGMyR`4LnJi)z!lz{15~@28opk0TC>TkpwJizJ>_~CWvjm zFu*mvX}-YK*QD!Z`{nD~#&0L9+23WR@!<00(t_y!W9yu{!wi@$9J8@)HH~fCwrv}4 zjK)qHHn!8)YHZuKeY)1cIv3v`nCqF@``H^&9o)oUj4A|N6aiG?CKw_>8N^JF3>g^& z0uCM|Pdw7q*Bg<0aHzbD$05w#UfLTXF z+kx~5A_h(G2Oavw4dUkk^WNMr=>W~&liLm&03rA#{Y3R@K}!9u!MHqwvU7+S_9nDL z4`M<64QyIt4n^=K{~5%vWllkYaU2Z@jD+?H{>@kmKD488U>NW#p9CbDgBgMke07+&`8_4t@p^- z3&J4lUzn|Iis;7?F9DxZ%3m0_UnaDH>BpoELYfe>qfKQ~x{c~A|070v>_ zWPWBbW1}N733>_x{InqcvNoS%VK{Wd;prv)Xk;S>lrZMbpI(LE*HL!vT?Rr#2mkT= zsOJ*VR?Oy9a4;Z7<}{|D3ZIm1St@p5Crjt!{Nx|XGhVm zR_`(JU+`ZWz1;}L=^#KvI99O|K!$Aw+h#(D@+^QF5%8J!^$n|c-!0tB>l5s=cVGrS z@<#k)7B}p0>&<`x8e$jTi982af>SzNp!AyquUCcVa5&&5=pJIS@J@jQ^q|*|oSjql zy5!tO55xZ@8$9Z?Yc@|)YXzuf8+4&;7u8Ti7pU;qv!L~tDF9rADt2TA#93EA`ejw$ zr4iAAzYh7en4TvnmYA=|C5Ugqm=dw!X#;Y>yrXEjh;CaR*~b}Oe{aH9Y1 zUgQ3CyG;*uM$wtMq@7KVSIV&N)iC|%-e0T-s!ledG(abK++fUOl%?%C;IgbudvJVG zvWTU#N2K7@p)p;AwaorT&PO1vr3YN%F9h$V2Db?a9R^6?6UFsv-5a)ts0-LrE<}p@ z)d?Fz>}F2Di{f&KUU=k*9*?hQU9*PZ)%Qy4T$GXQ%<9!wjZ0s!wBN22h2E^+=vtaJ zrOEP?&w=6mq(*Y?)~yMB>in{Q3$fB7p2^4ZRd1PTS5K@~nN`2ajIYRIN|om4XUyp| zVNq=a;s{wuOi@81DuvEz4NSvar*f`k(I%CF>_ETEmo+=wi2cpHf|^Ej=gq07S7r9! zoy$Lwi5wL=a$v2kk>@MUz*q%55r1Pb9JIzxGGJfwsF6|HLz5|$(&zr#OajLWe3Zie zJ27Sjc7{kNTG*aK$V}{@j;i%k9AZ{JF@k3aOp=m1+CQT-FVOlw#wv5eQdhtYixz9d zxUE5F^PS2#YenT3BM;&m`ysV1TheKd(pSAyhz858hJN19(EsgIS0JjM)eE9DB2HQF z0aBsz^3rKd^h@H?PQ7`#&UzDp;yxT1;eT0BC2j}23rHCes9I;3GPaM97%!G{4x+&} zSjJNg;eHD)2s;}T9<#>B8hHo!dsFqARACWrA+?sYmG!gsfC2rtL!%g%*ji87;})lX zOOTD0d302H2{Vb=R>Z8JCR-X?mO=S0z`k@bSRpi+sl9&y=BYxEGO7)(sZGs_Y2g#V z`KeL|x7+^PJoqA*F4JTW*Tf?c$pkV=U{f{I@y196%`bJk!2y4QP}85_Cu1^>CXuI* zFth2`ai=UL3ydbdWV$!q-1UN8bNQhwvq{&In*%?U@9%pX7$dibwdRxC&ilt(Abgi5 zla<`vkIPeiDievq7r|6i&_p)8zI2KTS95OPbk?}ctw~7Ij$vA3=Z;my><6zUu3QRK zd84x>`SIVlSg-ff1TvQJhoE8m2sgivUlCmq92IJ98+GP>n`;{$2UzoZHnDZzdLWAv z!S$+CHf&|KGrJ(JKBX(C+WlFwM3z zr4U(4B!c>hxzBUklsm(DJMH)C`#$JBMS-U_N@LLRzV9;p1{cC&buPmlU=U)9eEbM0n6XjRQG7<_Toa>9(M-VRt6gS2E!Q`KPSv+d zC{VXIOgDE2LdjO2@5oKiQhF1JWWn@x_;>C0huc>Y>4<}CJ)f==?YduD%rC5JZ;O9W zEbS|LKqi9_C--KoiT%9i^r;427N2dK&el3Ny7l-lsmuwS^oBVBz!{*zaC4cxQeubd zx=+bK4$u8%ITga@gk1`EAkCCXbBj%T0#iMbXXP$RGc&67^96o5gYl$3K!J{Y-Q$dk z?t0t$S;{t~PLrXoj{+>35=E+6hey`3RpWg8$)1y1AJPVz)K%)7dRRg~eM`T^Sk{*G zPG@GL1rwfTq^#Bs;D#!w*Mz~i7s_l6%Fwia`!Tf%|HiZ>r{_+-w2+Ohdes4NS%mIA z9=2_MxnyZG@}oe0^V9BIET+(a>dj_Vk!I8|{-({b=k=4vW}OAR=xA&MAsgtl5fxIA zQCXhP!`zAqwrBo}zHB+$O8|Gn*Xt){VZml-gz1<0=k2;3Fp}rWi0pkpx~k1mG5#yj zMgCM_6~<^?_S!2SIjGj-k~|zN3zhh2frMZHlXZq%qQKDxca-l{bHm^c;x*Md2lLB~@( zFe3jH;7I^lx*J5m2Lql>TOe(4fG7KKs=v{>Pe!=< zk2TMjYL>3zaPW_qW^Edc)7qX4GK9+i3s;?Nu1k`3(EG7&6P_M{?XZO{=jXQb)ELH@cOt(bwVqofW@C?dCfMrSh{kmv|*cp)8j1Idxn7W!I9v~h)6f7~qe%N+y5;cbim4$~YgFg!CmQbay$PiK01bMIa*zzsdodI z0*AHnd=4LFwhreSjk+F)j+lTuKhre^>`cVp--z$xhW<(vdSwiYU(b6HG< z(4EZomP*61HFekC*&RqlT8gWZ=<6($jAkP(HH@$&^g_k!^>1B}xd?V-}<=9X8*##fk)Fx^#Qww|0y+hhC*=R?BAu}5Vz|02 zp)Ftzvv-FKK-@M?$xa5FuqsPqT`k2VM|lorLirt^YdU=ChbWlAVHeYqp~VYig&ryiETU2Q4z zxiB0TouJ`w2q*1=$zs{oaT;i{VrC$$AG&aU;PX}q5WtLjA-1x#_#I=5m z%P|Dg$Clez)A5w=*+~hDQ*jdBdo)B4@P}s-0!~ zG%(Mb1CR7fZ|I=Ee8Xf`)c93d)hO4~FB8j*-saX8{X+MZ+hp@uuQSV${mWGc4TsbJ z)-Z-}xu?)S34!sWRvbQT;Jif&wV3q;dBCl4-s>HP)4IKrAv}Qqk&D zA5iaVhM5_48)L7kEk(upPS&?GEIWMwix9d}@_RD3pPpzD7uL4;tL6R>?!+A}Z~K%( z-(JP)I5X%)uXZ|;YHmM4`x9HkUt{&;v1#?uueB|$G~1iISLy-%c!7&cn$bRa-V;a)>4pY>z?alWLNIp^Q) zG~rhkxbYA>1(}VLhXlP)yG8NVjQI;f z_FC|hGmZX3{GetE(!hE>k^QC01TgAwXJk3J2F9{QGVx##On4m7Z$%SC=c#N z)POsWb1u{M$L5nTj@S)@@Ze>i0@?q{yl28W{r$uEtAF{3h{pK9dWqtX*7}QE7^lze zl#_eY#R15pni#&_BaIi23z0Y9%h5zO!C&!#mr#LSlOj zYcaLg{g00}%g`=|PBC4^7%UFQwL8&xJd+cm0*$?8!fk4$7*J|MT$o-Q|B;ZN);>yq zsAn~9XzcY?)6U{*#?4SI2Bm*hIaXrgcgVfUZ7+bJUf{;8vV?QA2k4dD6#5tVtNpv% zHFeIF7Gl?YLN0KZq&^St@A>cWz8q7GlflZanLl!Y!qR&w+FvJhqv0zly^qTDH^6xW$3f`e^)Oc`NIrOQo5M+e(7)v_Wx zgwR%7?M(`rAxK)$Z-vuH`1TG{j`R7AsIU+R{D-FoSEh_46Ne&e$9{I3i#r^nH$N`S zo7LAsdYBcQL{TQ1D;Hg$7YZG2PMk2El!T*9DrxV(>98TO0^)DoNcD|>GbQb4Wy>#S ztIzb3kg;_dCqZdVH?LV+=zqoSg|kO;E|rzdw@{A5$ab-`_L|s4a|}%3gFeBw?UO}z z)o4^m^OZ(_biSt#B$98!ASqvLv3oaCt#jJSz5Am!`MH_Bh|Ti{s$V4NwK>@MV#ivk z8~#WWQ+D%E1zOs`T2G$onB-7xQs=K9R>)f6%k){=@9;XEO=`%mtiXaT#mlQ!z$nXL zJwoM5KH49BI@RZyvz%Uw;Yj_lf1vyAEBWEl34K2IH8SpvhnLt+g)$$aH4T@}=g$SV zhq@g!%+FLq5N?o%;>6^@Fn@A~k{jFMyWNDC{h1Z)2YO5KY>pe$dOpB`sh)^op%(&f z6Sbjarch;)$z!JGp(VSYeeJM&K11Zf1oiikd+JwN)|5#Mjm(u6TQiJl%!JdN_HuKf zx>s+JhdC(g5#B z-In0z1P|6qk2Z$WEY`qjee))dN$5OIi+@BRm`QgrGbS|v(-aI zix->eVZ6;lcH-0Jt5)cwNOYd;zH4B~-a*h6l$=T*x#%CqFocDRg;7_f4qGd=w2Pt) zc#QP9aZj=~D&BOl{=~3dDlf2hxrm%aTLIUHcxa)#t;5z8cyJ3B_}MI8@FQ_edCq<& zMR5j3M*87f5}M>d$;Msm`!Rn>f5Ny#QKR)o-|KQf2^!(dRKd%DpMk=6@nDk4zNsf) zz8pO$hI-@h`J2>5u$L5qCvI1+nlvOi;3e>mE5#C5o;`-ugz69WSm<9X{ahy*h=EfH z6KQ)()rtKlxItWYzx9u)E4WfyC^c*_hM|3?+))N)qfS=KY z4S$?}*NKXZvFsaQ+^IFioIvj7e=wj`J7pMDTl2W1o=x3hM6wEmL&QQ1lymsD zt+Z$s{9}%0#n2Y(Qrlr)AwPP83T*DjA4bW87cpi+zr^!8v(=E%dEJ~AZ4AjZbrt<4 zkP?yTrXLz&R{PPReJY{3RgyKf>(s6Is)H4rRA?V$RxJ@qtWQsm?hq4GFO*c?kRi2R zZ~d*TUg5UCFpamx(^klNL*IDdw5sRq_g(Or2F_B4w1bV;+>&(zJ{;dX9iRjAl*d|1 zL117@CI^01&y-sHjJp&Vo1jw=`p}?&Go z=?Ah${Of@$A-=?!GpGsNuUfeSdhy8c9p#`S@exj>%uSXX)pZW~NcjP?zg~+!guD=t zlpUd@)0DYj#`h~uZD$w@qW}r#?FHodq9l0Q0-R?=boGI=A@?d)sY=0|>8$T`Njd4N%A>@q`PuhtEdNPYH^m8`K72`Ti|LWuOt+RR2 zht`II%ja=CgR9}Fu$K7*=XNw0)%6ym$)|WGf!~efq=y)BV681_lQ`{oBF!^+*U6;|cKd z?82RcTJk+0R(e6gV35&+Za*|&5NW8;N9BTYx7OA&rzSB*fbeU_*pqm1gkLzh~g*(-@y+NU*m7ZNKAvC8^IfV&1#^ z^5V2`5Y(mh%Lh!xDb>`^aV^kkt?YXfKD~PwM$A8A7iw*V^T<4p)cpV0TxbB~(`NR_ou2yWJx)oq${YQQaZA?dg zHNXaJA#}2VMR$q$4?=$Zd9UD)FA0ZUeb$LM-u=@5>e3=cCW47DbV3A8{N~}0vFWcx zt8g^&=Jn0Otcitk#+O(dVvzl7eM<^}=g@Im)$7I7^>bhqarn*aY)u~!d$#Soex#&e z|JS)qn;%ZZ%TRA8qS^3yO)8Eo1SLApEem-pLW_z=cGiNpu4$m&RDmhG{U`Dn#;Wg2 z(QzAEs})HXydz|CRuXg3-0z&xBezRqekKcJEwPw%0n!+%r`qv*R%MQymLXpNET&u0 zGOpm|u-zUfm+kguFLS*&@Z0Y_;fXHXnNvx)U+w<5vR(xvBCN?$t++J_*tT$_M?Vj& zBF9+=s}pR;n(YQtfpK)iKNJYCUhLeb)M4v0e(!%q8VE_4sj`>aePtaQ5=`!6a*y?0 zoTJec?4Y8+Y!I;be97->#bHu`t#GkHn4Yq$_iGg&C?#!oqw3I?E*iuqr}X%Tv=N`Q zKMD;=5D-{GE!(3&BinG2H20-HFoRiqrMV$7NfKM$Y;V_@`vsxHQnEJIRJWkXSRhr*`FgtA}s!B+WYl^Jsp zxll88CN)}^5bJ+a`@B;FTRSIl&kYlEL;b!iFRzyHnzGhQuG4K3QO(~7FoSRIGd7ZZ z{0PpiGWo4zwx;T0sm~=;DZpK9cgL94px0IiZjG z9i1&nmjgzuyGp*VH<^0P;>)Oi=`CCwcf@^?iP;eFbq~c89q+n3m5%lk>3a*y`e8t9sh}(F-?8{wpdx>?p9$HKVDkzMg?(U&=PQ5A5yG9kt zC4{t1)1l?QWJw5e% zOizS#$7aT%7Z!z})C?-W>ymLuZVAcsv(dVSm+WQCUk!8uzq}qy?lv<(S7H#Xhg6v> z&Mub5NffwZp)shdn~Ts{Jfd@tUjI3evrnK`Vg1x;f;Z&Pc)gB;)x^SeSYxEsSyC9z zs`Qg8ExaA-dA&pmm${ue#vzn)Z+a{K@h4h;n)x5POs(y+?~fC|DLij`TbUh^9gaH4 zS*^^gK)o#k`cOZu;0HBZU!~4Hj^bex;gR2Ep6}P+&do@Wno0z7)cXksgGy#MIVmQO&rr2Vd+_&eq>6wa+wG^ub@UB6%Y!)j4(f7 zVU2re=?)lsUN+NhvFx1d`2u`hwQP4VGnm$VQ@6k9F7HO_Fjhn~wflx_OyPArJ&}Oj z)n9BD>`606pN2g7XyXgz!Gj~OYUS~WB8LFjNJv#9t%A+BerzzWguNe1kXH3bq59WI zTHhGK;9YTShGb+LT&Mzz{>k7vWzXzJD$AsMX?5}r_&Jb8~ z%|B=(Tt`Ki5VJKCw!Z&~y9L3fyQ|>-myeB?TOqsY5RDY-wvu9@lWjjTd5dg(NwfwO zz!}nH$QR~I3Ahz>dfQ1mefzVu7)6B(R_Snd!E(~BxBWyutJmlmq2Kr0=y%F$au#JEmrZ&*SfS8f&TVeG$}E~PUn)}t;pqYq}WUJN7-mh-m^yy zrUR7?(&glxMlOruMLs5}y+IiuR8NNWfR6X4(-o0DLrn}ER^~AR(eduC5*HF~zYMK? zPq`JG-G+-@Th_e0dZ0X2t#?3}jo?`J>XpuCf9+i6OVRAnq6V2ThII}q+0k|5Or|1= zxA11qpxiVKm^F`F(lC2zoV`%%F_&y=r z@GfpGqW}%JsKrt3u4fo&guWY$zeH~uF&(vI?THweOqI-;>}u@U-VxU}>{&+HLldTv z3S#EZz2bpA3TCR=0&7)z&XN%7o{%*BoNddGj}LSFJr(rJ^^tAVA9r@ia+mv_!X#y= z^S-KJ7e;PYYIaB1!{!m7a}qfJGbKLrb4=*{qjb1R3OplWxd;ZT`s3S8i%?vo)&mtJ z%n|OM--HVs(NT~(zb|1{os7Lt;A*Re0qonni=ni3_$y{}s4)Gnd(WMSxyL<3_cE!w zSPXoas~nIo3MbtzO-cN;`oF>79OsuvMSa`4Q;b8ujZN5L_zFk>#Uqy0SP|;cIJQU2 z9v$2Q!jHp0hs#lhkV*J@R+jS&L%~0>2?I z8QYymX&2jle8(yNMA{v&GdviGoCI5PthY@;@8U=}Iwg#xlXm%<8^Jc8lnm=T`+o=< zSgO{>DLErzPLDGHu4R?JcxUfSrS-^hh=}(E)rx*2wccBNhi-k=g#j<9sn1 zbnxb4jiH^w)NTfbz!5xuWd<}8cq$FjPwc*ALh5dKId_)|rJeF0JQX^V_uTi>*`RU# zgWDcI{}wy&M1(snOkZS3Wx3gpervLjag3p}Vd6B5oh91#MPq{9a!Y59-EdlhhwW(jg&6<& z@8$5xKS!Gn;N>laH-wI3erbJguFc5trM; zd|~V?W-(CFhf1^k#c!Jvm?H)IaHcIFajQ!=8gEY zxucPNJ&uF8AC*(xY%(YCME$)<_H}vB>@Bjk^ItT-%IRD+aW1@CYVM2c&L9t(Zy+Sy zp2ub}&_!RM|La&4XG|J$VbP2#RC=r8(#bHt%PrTYu^F>lkwahjL!Zm%dnC-48A5m9lTooJ zWt#T0T}5}1sYip^Ga_=+b0(e;axFF&j4uyG+{(xcearD4kiY$yE-?b6SO zptx#Em8r-#>_co59o4&b0S-(@6L!0(Hc6sbE3`~~e`G_i@5YY;m)#){g`uY-J3}w5}uj_Sk^E5?`?8Qj)9S%z4Zok1^XU6tqY#FS)0^@ zohoLhB&ibLxdSAv)cm$I(bK&XJ2qJc=Kq;f^z#&(i>+HLqUc`N-&e^E01qPs#+n}r;a zG%sBm#GdVGk?M~boFc=c7}FKUZqv@Gpp5cv%!cN(++P)3tiD}+=hg*>LuaMIN)0v= zAibtx)~%`Ho4k2C6sb1h73%^d*|-Q~R>n8jrxqOe$UE&3*j=ax4ZS*&J_#}WDgKoJ zKbSHl%#AIljrrHxfs9Y#i~PH(&za~&k^Ux{{iemj0pySZ^Qr1&G{Zys8tX6_Su5>Y z$pjCHF?xNEbZnywFLin>y-tPD>hLZmXw3*f#E!+ zj{Q+q`Gc{fchkS~HDM57p9UccCr5wsn=Ys~tY;$-!U`8|M++$lOP_8ap3M$3saeRb zo+F+>D*kL;Wf>E$zk^j6Yl^Gtl1iVI+@!c`%f%M@6>0Z}GLoR$Q2 zPnkV;q?8)B$K!}C(faDKwQgZ(tk(2|reQggXK92KVWX~>uy+-p#xXegC0YG|>@&EQ z9aj~}tqAUVOXvp4_*gs^nAlj6q!TC4fO#8!(j?62(GPd8ygZ;tjXLh4pe7(CC$aNH zrJ{gCVc_G;?64%`Z@?@obM#wJ_;WtQ(spAm+ZNi^Rga5ew#j8*Na*0|%UTI%?q2Fl&yChe2pH43ngr*u5PuG+IPd$jmxYIH$|2nbpw`bm7UB7 z6NRF`>&e)_ZV%d@?X%DDUEd{_BD>7TMtwNqOX351d#ygBghWgB^yf0IsGM=~^&4~p zJu?;IKUgVk@ewALl{|>J%l(OtCn9OLN&iK$&62#Us zk3AO2Pz-pg%_mQsWR)WPFgf^ZOFfW*?`4Knxp_J{r1w=(GCQ$~e(6*l7wlta7!N|b z*|{$OdmCpw-kJx*6N^@xhOG#=*C5Tq%UhIy&5}saohg=gSeQq#4W0v2;w6{e`k$Y4 zbpoe--JAAnWsNH+$-mn0Wr+5NNH;`gp48{H<@XoG<}A_Ilg~ym>a3~C!s#8*eoNzG zbvX8sS`f|rxn8SLcp$LJELDsJ5%Z6AX)gr;Oje9ECrP9q00MD#$GHPHhOii$+NUj@ zV|B!j6L>>_#T&l zCM>d9Gd!71?%dpkwchXK#+vkQV(RzoeVuQ%lqSi6b+W(4gqe~G#usx-y13f5BEZk^ zlcBlDH`0q7#PJ31e7We$|9)r<&TPa#X!>qA7 z`7H6fbVlj4vKl|f9u$2d4bg~I&GjV#h34OLWgXrXvMIiye4iNOTDBF9%joAwRxuqS z1^-2ES0@Pt)9GKUzX=$an6@JQ>aXMe7HT-eTw#tq$1R{&HURq+!zb+ZGA`{I^pI4_ zOXq8M*~JXTQli>Xd$f5z6Vs?2u<-0_jP<~;kHzLwB)M8tI8quVGlzB%-@ii*9N8Tx z8Yi-?+O(qGdveGN9;~q!utj#nYhZj%|FVx=az*e<+NNU=2J61cjro<<9S4Rbu-ODS z=D3V84^MfJdZj|blPW&+nyHh6+Y)zMj4>gT9OY8ST-bb{b3^YWx#KG{pVPP;>zTsb zTe$M<{!%_xNx}zvDIt=2`Mw+lr1YmR`=V;c)gFu%Y!Vdj+yueb^1FK4pY!$|6ZF6L zW#PE?UV1U23XYK92^~Y%?$EdyyuqKXq?J8!S~Pfm7@Scy&Yw>DVUe>@pV<-Lcr`Rd zc?f6&AXoD`y-v(lRUfO@ZFCIbUR_|RCV=ZD)rxXj*(J}Lq!(ekg)0>>G*K`vmU-QT zAFIm{QuWrVs7+bvKn`W*c~g{|LSmZh616p9cbmRUB2EZfL|Tf13U=l4ykMdw3N79u%Wj9P z+sV{8!%`jPY2iIXM(YKvn62!rAs~}5Lt0%w{2Olre<@@Mm8BfoYS7BS!=s_Y`tZ!Q8}FALKGow+GHl^rT>p*g zk(k#|HJ*ERF{{}eGOt3_S|NGCb$xa~w^(D0RGODrvPLN<70d+$VS+n3^}|RI)|%J9 zcU&NETf|K&q~I1sTlY#Wla!=$FT}N(R)wx0IX9n=g|AUwdNjyb%CC912U12;&!VNL z@-M%W^J=YIC)9f7S_8^&=?3f9J?Lm z^QoHCED1N4Cf@*Fp0;o;7?sRxkYFgaj2h;fu$=jh#`DupeJX|}e)s3@AIo}+&H0^p zH6eejSvj2!L8nLoaf-yOIdXuwY^Tt`-+UpdpV< zpq1Lkrv<*ttL|4a#B4*#uh|UT>@%XD{Ix#yH)UGpUui#C7tMEQ6mj)kF%W->-XwMA ztygQudHV&BN0|#)!Zu!*RGR@ru7bgI!%u@(Br1=|A($G$V)JLB_K2wOA2!SaaD2t9 zH;kh-6l>pSl`PiQrRFg=m|}&qvr`Ih`x*?V$j`7qCc)& z8OIxG#1-f?bf%`3-XmI;bF0D_edAEF2)q>0ZXAIH{7v>MNr6D(`Sp4Dw3=qh%9JY3 zp6ig~-v9w(ZFJBUg6YPNpE>E{JPgl8RyoFY#TI3@(PIbW-;`07!|Uo#9^3|^EqjHg zi9Es_iOCF8es#*>DIDJ>F#@};q%MplQX{(>KY`#`U2PBNMQ(TP-FeN&XbWD!+)cw= zUn!tPY+qEZ|9Q9X_Ybu+1AV;8SGywixOR1gS~`A*@^w}xl;)JO?W8S*;UOm>9bCHv z!5~KB#U)!W6Xua=&ReQKv*q$0&5mm#-R&yr)DCUNqt{)s%mjmVk$K*6E@vy&N#?6j zC*+$^ZE2NNTJvy0roX`q9_%->pDqYTgz*7LuysSGWLEqva$ii7)gL}KA@6L-ub^~k zPDrvVqA!1=?@fzUtMJ%osn2Ac?nLm%9`*ioEB^RiT5r>|5>B?YKJxHFV-zYzx)-fddOw5t7bQ7f)Y)q_$00FMMf zn=7m+@<>I^gS2zWO9^z%U1jS4kD3QXl#>$B@Fg5hpwln14bFGUuvUGd`> zEg&XT>%Q{jUFN3aG6>JK$-I@;t$I~EESNO}$BAIeVt+G<jH^BUeogd-&KIa>gEss2rt5y#Ohy4@azm-C6wX_#n5C7+qsv4H@Mfb zs9Rle1iQa6?&|Ez0oRI-@2nt5GA`o{w%p^JA_?I=H}c1Plz39R)$m%+MwFt!N#R#} zgDBbsY++E@Hy^PUg~V$@pg|B%v)Uf4NFs6zq0f6lu=HWuS{>AX(S_zw{=T91Y1My# zaczyKbY72d&}Ts$c7iX&*u``Md#Vi{Dy-%G)j-kemgcECaW6jv`wKeXiEZ*f=;dsT z{~ArwOwK@2XqdQ|{#PYuCT3w|`&WYU-$~~GA4z8625mRI!yxA>n?GbAFZ zawHu`hD;`bIv*w96sLh}i^IG)gT)N)BnifBLSHyak<>KOc7;@|ehhP^fp(40cdc`) z^U1@%o9hl}KJvyZC zQ3rtRlJulVLY2Lr;%QQqk>du;zHi7I&V1eLkus+8JLLd~o)&Tf zNNp(uDR{toL_k>)ouPCgDh?-H)}A!zO%F{Abqef~TQKqKKdNjjje+d1DrV3SamAhy zHCzHjS<(qQ#6D;lF^C9d0C>79DPf2VGT*i6Ygj2XD0jjRA~VMtR0c>!V1Yfc2rEe8 zF3k@x03|H^f?Sg=U^1`Q-(wj(t#39xo-GG-mLy;Zq;`lB1h&vtbdMNBp@4aZJsl(l zLITy&GnEHr@@o!yNANpZKm_45R4gq@4tSD$Z=I2D3wk!Fy|N*b(DxUI`{3GgQ~Y2- z5@wDw`%lbM=EYF}-D zUgqVVDsN2fZ!~QgydEZOPIdubtL-FAM+``$48i+lO>_=H0-+)yM>s(XA^mGc>~}m5 zaXj!+JTw|)`~D6qAuAiuQ{of|Wub_VG>n)<(D{rX9#0cG9af(Tzcf7wi1FAz7*^Ol z9deX_T%*-*)8LMReNWCJ6%$8SSFv9}fg2gwFK9+L9Q}26~_kp~QZS+NgrUoN~8m%;TK?^rf2?V4i`#qKl_ zZo)VLY{^B1bl9orUrPlc(n0oH8pf6~L1sITDj9mx$(0slf`YdtFIS2Xa%7+cP(>Pk0P!98(bz&#hVo!B?)qC z|FU}2vb{`Hp}WQ#$1_TsOEv8b{tIhBl)o5Zk(Q%Qx&I>L>>(61Y*J4j^7h$ax-%1&6{NClhrD-<6{EF$$5Z@s z%@?zDGfmR;a!jn{tG2W(XG`i3WGs|425q^5%s8Z>YF&wo|xBsDtO znE^ARA1GCbw>Jli&J}n&^}Z}gjhL~&SfF42P8Ub!>)(-bjJ$QKv7&MZpR>ZPs+f{p zW+TSWCS(o5I?lZ}*d7YB1&M_x_Z3rzS~G!zru&mQDzoE*q_s*Bqp~K!$5n80u^HL3 z0`#zZF<&lzrm3}SHo6?joqzFq(p>n^t{&oa#uHg@`992=@oo){b~AWazuxdOKi9x+ ztt9RJz8!OhTEB>vsAXMpnHg3KJaUE;5T1f42w$SgLM}?bek$r$f~57pwTIyR;6AN) zYckH1-~>HUiNqaq(b-?rq?~4jo~5adG;qX)-I@F0Dz-G~8{2bdxPRwqO;=Pb)lQac zT|tUHMSe2h5LYf6E4jKTsgWdRX&}*mmOiMnP7Flc&6J{*e(t;!p28O}E43QoBP{OL zth=MU;dao2QX!IE&V_;%C-%n>=cTTQtle?RN*$A^sr;z75lfEv)C2E_qvZ6AyxEIV zSfuW9`M`zkgvbk9NvN^Tjt++|}Ucs*Oh;p7XhN>+~9{Eddlysae6 z*nnQvqRwzi7k^T&XVirhjDOSEGPKmu$S0Z7N75dC8Br4$dFcZl@DaJ^G<}QP>q);r z)|hAGxcz>5cjqDTGY*HE^{YR14XM5r<pn z;={Ms@956B+JEmN^|>`=E;sWN2a9gdt51U8nI(N-qV0%4UOe<}Ks!MXAVd ziI3w${Ffh0FV!zdEmlo*%y-3sF})S@BcpM&-TvD@ zMDuN*q0Popbg6}?ZvBWBWO%OCw*oHFHo*_g`JB^j<$ru!ABxXwIegkBa{8%bJ^Ez} z*Q7_u<@BxY`b+W&=2HBos~DU+y<70>S3IskX{(|+Sgi2qBS(_b!uwU}-)y!B=||-5 zS!`^yqV(|b_g~v|%Isw4R%nC$8oM5r6~EXr zdO&~9On)$jYbx1SKo!rcIUlRD|0FK?TJugDei`wrv{ga5?kmF49{ct4thNr1;ILg%dDXm}V;@#n_34gw+l+jdQY%p5L-#6^|Y<-O;;8v=5 z{Ps-roX`(}C*6jXb90f3uCJ6N%btmzkW#h6R-s}(@6i?}?(xx$`_ez;cQ%bJE>kyL z(D&77firS(skj!yXU{_&Sjq9we_k73osx=psWI#;p3$n7sWT~bE1<-GV4EES zKm3wMD(~FA9&Ovv{QLVyUi=anV)D6<^)_!F7h5lpPm29ohUsqIS^K1Do;FbXn#yMs@J2)939>P*+1R5aGOUekFbb##85 zTmDYGfV|kdoW8J;kXM(+MkguR(^rxU4mbk*B%y{Lc|=5M+8obPsQHg{_%ANlIe+ej zJMD2mWw2M>%V|^ReYk~jsnO-e?t~x>r!D6tZv?BXIpU1x1_HYUyX1LXmu(H~^-Ln` zj4+`-j7m>kGkLD0Eo(*MnjE}(3gdGcx(W$aom@*t@>3h2Zju5i6p zURgwuxH-kEecPvoBt=3CozIm-W`9X6tT6LRv)OGD;f0?*gZ63Ydp(r&(3fkN!9>Bqjp?-L$vi5k3jFwTtHah4_n(?s3UV_IglUa=zq~8Et#mnlwrx;}y2u z$2Get!1$}6w=u&YM_!FP$*Un~;(TBi-$_e{)LhT6a;%`m?pGRDkOC=5BY(MCeuJoy z9b-7}CfO9y1U*hbfjz$5_-dFT!&{5hJ+bm2C3p4uNKekk-E)FRpR@h%d^;y*I*~9( z9qMwxrr{ILO7ag0Jt*?bZq@ENd#h#3>8nS^CEupE=}rhMm_Ok*l+L6D4v3h?_w39o zmAm@XHqGL$n*(7DWxu;d9HQ7$;nAqdDpspe%68pHu8WFtsKp2_oZF`+eKYw)N@Y}VZc9E~? zV>QNju`OTG>xWXli*Iu%n(nbHo7K{(*>YQ`3M~9uvs)>g>-L^mTC}-G)sZk7{`I}E zAIL`S!<+*i>&az^+_I7!uA=7PxIV@F9oDVqf^?wd%%ohaUJD+wVZnv|?PhP}PjC)5ED(=^sFgfLZ z)&XM+SZKcw#4_+%KrbBR!MZGW&dh^`@5mu?Z!E5DGbwn%Qt?QFiU)R!Cjr8UO%CT7xa{^}qfmup&3 zszr12XNLkqasIsd{$yoTHR4Hgyq%S5P*pXD+Sa!H>gN*-G%le81b%s5#6jNst)aQv8ta53gv~>3R=PgnVryvu`n{*}m_pONrk=~&fK~5S z{YOQbQTqey?>|xEw$Kvw{w82Kvm#yktRjBIZ;e)0gVDzLceu{pY$-amyRXtYh1{bX zJNP`CnAI(j!mRlhwz#2i3T19&b98cLVQmU!Ze(v_Y6>wmGMB$T0U#bSFgQ0e3NK7$ zZfA68GaxVuFHB`_XLM*FGBGqWHJ6|30VjWKx?^yz&(bd(+jj2Qww`|R6HF_ndq448My(<;*u&%j9hF0 zMtT+)GBOb-Q$rU^dpl7>7gKJ4x~U03+0+5R#0+3&WMqON1Blo=csf~{Tetuyjj4bB zEd;397@AnxS~>yL>}~AbER8Jyyl!r8f^N>P^iHn)^#3?1o0wU==9YFa4FAGS($35t!2TbxiL1l^sQwAa z`Jeazl>cBz1u!u+`^VbV#zxN2))YV~VsGo<>SF2ykhM24b+QBe3ww7b%YT1KBwY;u zN%DU@3~eoKJpX@v{;$P<%!TaC|3Q(CiItv_^*?e;XK_mpQxgSCmw&K#adI{Nk67LG zKkFoGYGUbX`=2pP|H0><6*jTAv+?}D)Bcmzzb9o75|@?~k)io-LHt`SW@l_~Vrgd% zP-!%{_y1W5 z3)_2m({Zo>=vdep0Zc6H>;O&{M&JJxt+A_nrxg zJRw%;ZDEyuV#RY+;52hH2C6hGOu(zteYe`kmO~aM`bXC|4=OkX?r?wjvw=o@dsn-X z53R(8@uqMmlT$H75xOflucaha=6-eC?}~+QjS+e`U~1U5#&Te{k@qf{8|y&|)Kje4 zc^7q3j^%vF5==1$6)Hyi*AerUia5Q!V7}; z;BLvV^(~4j109aSwF-Y5uXM`o`O`3M8_$v4cnmI=E`LC+HBJre3#4fIkCxNb)@RR9 zp9YFZlu+5(#Kvnj1ED{q{j3goJf@U&?z>J^BL-~uiC&TW78ym&`I4aLHwx)2Hp zD!cWyI9xIXr?+fy%U(A60Qt&Jq>3*60s*>@&5ceWdTF1KaAuMt*{|KcaUn~!DP8@eDqF2L^l+|Xlqz_`~ z=ets?mu;w=U8;X3njc^(?~o>C#;hzaUZ?6qpDSS1MGM}6*C+jXyOOg!`P~)m4h*Cu z_?gYL%ImD-E>SxcqEtcfPLW-Qdy$T<*hFYHX&7yR@9nff>vI#%YNb>I=3aG0clg9( zTCrZ}|CiQO5=1;V6QkSY;k`2uqn9%3i>_KF&@;(whuMF(TSz;sybYs5*fEc0C1#>> zI9IR7el#4OK+Ye=!|KB~K*cTxg)(?nXkq99!dcXE9&~yrQcW(&^%Iw~XH(L)!Nq%5 z37xs*8)Tt4T!8MgH!?>1_2i1U zGJ}jQQzL&a4ce*o+}&Em;asV5L}=^`#CK~-le>|Azyqhaq0^OdgD~`RFPLcz1_mWH zD4JIVnS1GJR14cTTA~Lm6b^()J5Z~E(%HsdsEkbrSKLOejPKL#zS@D>H+n#-gl<&? zmcaT!r)SrSC>?sF+EXA8U@xXpnh&CY&`c^BK$LQU?;=lz6=Fbw~{!juls#JN`uOc)8n%6Zlv;jc(h*SigrQ z>jHl+iW&St!EaiZXnCi-tGhhXkrMHv@omN=Sg$(2l86>MzMAx zrI_maP-tAi9=6+MnUx~O3ZwFOG&u$K&m<33xuH_2@;O{+SwCgWg^&9f|5+L|So>u2 zGkBFr?NZ{lGBL-r9ZA_CYEU-KqqDo1-<^#wCBVe#eUk za%+(jl|Lw=9l~mSUl&v=1Z2`3+PWd0C-s#jBi6Ivco(%4A_b>J*e-0kF0*gH?MK(n zbHs*TK&iH7s;0b{IVI6eJPuvyKu2GgHNzE^$;itIQ}&>qT&dQCAF0{hWHipix7W?SIp*##F4XCQG-m$fEaK)<%1HAL($Vzq^l)Q>Ge88 zeh)OKIsd{D-%^y80Z|h~_IWYu6Dk6Av4a%`@j7|jj9vtqHFE_QHt7XtFhY8r4xPtS zzZ|7vL|4CSreQQ|>*LyO4-YDV6!HPx9>o@twusn%zg12YDj94&XTN{YVaJ54Q+a8a z<+?GzLw&WXIW{yR;%xCmyzcut?O2U4BE-LB4+k{!4V+@7ICAzr0cg&U-fcXmhIJ|C z$vlm&5y$_LHOFGxzBlt!^avZkhqqJ3vFX2`_L+NH+A(smoIuGt5u)GI63d=O&;vuk z0@nVTMDgIcCyN~0v73L#<1Eq!D9Mo#Q7ywbP_*sm3J~eU1_~htGGPzvp^OXl<%#JP zi74@$2E8qeyt7zDM?qGo3Hg93>+nnadacU%q8*xH^q!%`DMR~cwDY|U=xfjgse zy|ixD^sK3NO3D#S2*Kj|sR(1Y8uy2u!LRt#b=tjM)#!04Ov8p&8%=qUZiaU0}gSjXKQZvf_Ovhu(^z_wrm-w-d4hD56Y~p1&q@s$p~H z;sG+z;d=GdpnfM2t!M7Va2Y}9tIdWf*eH^k#92-uKWynVPxKo`1e z_^CHMh4y~{IpavnqF(ebAei$knh6pX4djY^0W7sJ6ZA$0O)9*}7FH|XvT|?D_{xt} z6x#G2)0@zuwVRQHA~8G`DR^eQCmx;CY+jfMNS;pRo+6iT%~c)INjZB2(v$}Kwt)&E zW{NK>4cYwm3~Dv^Q8bpE3<|bA-mK`vPH-;|KS+OzaCI*`T2;OlG2fKhBeL>`ef^hr zyI}^PE_OG#EY-OH2#I3dndP)2ah&#_b|^bCI^-p?2uVZ$c}a`;EYC3bV-EC+aieZO z7#2nb^fDNLTP*HXGVL|TGy?H)>6Il83k&9X{DZcwy3LhtoO+^Y5~>fKgMxsxj(AB!H(3nG6BIQZ5i6I)0%w?iz=!2}RXcwF%axGPa2 z7?)HBoR(ncR#S3jWRCYCddr5N-rS;*bIbf&cRk1Go`Q%3+Q{l#upd1_@;aj{EI<5u zj{in=Yy2q$8L`LLa+v&Xtg{(OO(vK3_c7Nuh#u!>u=UDEDqT1p>7R>sN4NJ+(A&(cg)pjuJl zw9l_Fetpk}?`)&(5{B38v(Z?^yYd6wVwUEi?r-!?)Cx}MjoqiD^_>1hh_@1|OVKwC z#kmkE3C?Yz#cn37K119E}uC?tPD)tFTj#BR4=mC=EnaREwjd_b8PjGWAkmLB$W zF8N3jshGy0pnYVkfwWgXml^zy>Uw=Ji_Et@Fob8*@fImVC~y{J1sGI!sWQ_ZPW*&l~}x&G&}cB}DKFyN5`D$i9Ad0lUG-)(G&#CY!=c zAyE=0GtEdRxs;iP@Y5q&2i1RTknZApXhv+4Uncp8;vVup;kr(-WApJ_2DC?Rk)58r6ypw9EYnM%6(G0krK{t zEVUb)WS4hCNa|Dh^OC8?o(z-nYcUa#$&$<&2DOrkN=nJ_99U1{+TDLfx+a%|&+&qe z7)pJIe?OErr)TR5f!Eq|yvPfaZ}V#JZ1wnJBAZLf3!q@+xH@2pdyj&dD|&=|kyT^$c%yUa)1X-OW>O2P`OiM{=Cq zAa(vVCNW?B8DvvcX{<$X4>^>d@mR(b^d=wAAyXrl56}Uud#3JEM?;CoznaGEIuOVW^igv>ksE%}dZ(iO|)&3nfS! zZSdPqkq55i83{Mo?Y)e3hlC6JrluT*;-PLSu}qwWZlgO9H)>~YzMy*|3O~iZnc>6eUlJw^XXs}7j*arm{ z~2}8>S?%DQbeoz@f4ifUSW!>mES&3_hA0nhH}5i%mUpttHNiiiYY2? zCDhjkjCLgGm75T1ta^W7;u*JMM_zo}lVMm54;ABF+@x1U8N}+I6Mi-g>TDj|BRQ(Eig$1$ zZ=W*=6mX?>j2R`;5*tQnaJTsGx}J9R=@=s|mY8F596P4hhuIKD>t7qU%2MC*tnT>S z7!V#8!oGhpayVN@$M5!Yf!^#4X>j^|f-IC@ot5@H0>h$+e9J}RV+&u_=xwz_N_o#t zMB&EBJff{dK9!ZM$N{{F_npD(!JI6yZr`V7bd88M_xb8~vD_;1w`^4vqidS)$a2vEqH;R6NF(&7YzJ z_D+B3GwH>dG|&*h+M+eg>OE&zraj6cy>}tIYw&?RJq;MPrKs_4D%Dm}V?Da@qE@+j z&NzSA6F|=8vFBj6Pj}8UEQ-g5tG_+NDX#1w=T_YBvtlf=No6+-kK zgIb=)r|B-7Gm^Vps5`CFvYdgd9h5L*L>u7B`Oub>At?3vLzwFL$D$&9thA zpJsg;*iI5+frMIA9d|^;d(X0eGPo$Mi ze7<8!CQ6mhlM2SHPB$F!_Nf+CT=#ATbSM~P^(43-g@*Hk>*(!a$Hee~_%X7B-EV-b z@JcMAYIh>NI?*3Z+u5Y9T#;5~@8Nj3kne&nIGb%fxhGtP-9>}CkF%1T=7+s$C}3u1ry?8!0m_k6IuHR$>wyJnowi&5D?CXUWl49n)1 zlbf{Hc-~CJ^4+(AiN=baME{LXqjyGguW5REdoChKgb@|RKfQ!GjEZ`OG&T=wJ3D@d zRtb0(+}m>h-EcvL5fe$xp9XFmsMZKEAZAU>@u{C?Z^=Cr?vMNtEVM?M9w=!b9cJ`Mj`b1Y2tfIuo66Qb;{Hmyjhs#%ObS!-ws?mcXjm1 zyg2IX(?pV=cqZG}BX(ztunT|EUgVqf)%K7DzvOf19S}k9dh6V9`#iW&0Rz|jiaJzJ zuBz>nFhdR)Pp0(!NlCv{;-z|tn`Ex)1mdVp_yV*P2*1WF<5b*TI<5F_twM>4OEyQ$ z4C1*N1iDWv8cUaa+YgARlTX6di!-qY$EL?QnyIa@S5A8rjcF~~kSl*Oiyu~zS<;G} z#L!O`7XxIm;$VJ@j3QmiA)G7KQTsZxt`- z!U7zEanipdq~Mx&V1p|NwUFv zVc&h}2-kli0G3``Tyx+YA@xG5MHuG@Y5$V|I_s{xFUUW|&dbGuKXh1bF@$$fNR5yF z43c*Mg@_g+Y@o}(K1$Zfp?b!o9%6>K&HD&<>zCV(b9psD^#y;wCCt+q3;qAuKvjFI#J`^dqH{zkFJ;C|;ZYty=bF(VM|MWbelhBR7pF z*tMHVagJEc;52_q#%FeB7l0o_(|*rX@MxtS;xqr#A zxNv}Og2IzMiPKO-@lpV;eojYO{0p6#+-hrOfXYo&y5j#q&VE9q4C%a%@+RX6I}GnM z>s{IHM-WZft(}n34wsaiecnMXZT6swQY4U-Ux4!((ENYK!eLLEJyE0m3PkB%`tWEh znTXvi$whI93`2hZ-FdsMaEY#~jw@Wsq`fttY9J%n#yNB$#*SX}FngyBVf`d#wCKfS+zKRa ztbUZh!g_yP9dSleo@owKlx5{FN=|>>M57}*D>_>h82EIAc~d`fECZQ!B|R3&%mQLu zvI`V+QZf0;1m2yta{9L-o>l;@h2G}WiezM(bl+AwCeJWYt;&PUMOlI&cAbN(#ZL)y z#0zT*E0Bl=_wP*Znz1@$RaRt;~A&c%NeNaJ*L5DTZbG5O)kc)xVeuF*t6 zF+!w!U`E(mb}wIDrLfNJ!q~w*yNUVRgf>1qRYAgX`JR|TAkgT|wffL};&7iaxlv&QBD)Z=yg7`p8`8T7fw5LB~BAT8ES5T)7@mO?dxr2{OyP*Qf--(Qd z4*n4l1 zox~|y5LwWl{^v8~3TWTUC_2CkTid6lQxjw754eIg}CmMT3A|375nkYQ5%jL16trA z?=-QS8xV6B0Z4kDLV&~Yg$~c2hR6(6#H7e+8(z+ew9bWP*LN(VBMRT_f+ly59A4&5J#v;*!XA3f;;HP~ z`QPE;XL(n=8&r`{%?1nBPDEDG54m^?S!-OCFR2LMH)@siUB%h|9ASUhNZ4S-vbZAW zh_JQ;;*9#2OUq;qb8~Ew7^z9nm}X*{y)n_~ZOJ59m98q7SW50iYv&E`?~XCwQHoDm z{%qY=WzMg%?a`NLZ&-Hq5kn@{(n8cH19a=se;1&R&iD+UW1WkgrQ^oeKo|Och`u7` ze-!TIUeBwYCt7E_Ve@~Cd(azopQ1421mq<0R7uS%a9 zKVu8NZs)SItTLDeP*#JK8wz9Dc*^GuN-k zaH*6#2E>xQF!Pev+z%Ly@S@P2&{4R$fSfUzS#1(5l=>VkzT(7ew?@Eq`A3gjR!y+j zaKz#1{%Oi0VCy%E+>H^GSKT87iYb7;&La6x7BE?xt^w8KP#N`qRiLt#6?m>9bg`Dl zE{^#QL)@?M@-BalzA7#sW=}>ww@blLJS68x8m$rFT=_FBg*4R+@^HU3a;e`g_e-+c zW+)BlO2Dm0#{>^PLM4L_HW~MN`nPvKZvIUe+@3n$Mz1rZOtTkS%<*!mbfxVcq1d6j z1vC)9EhV3X(Y6^W?(yF&LQevGWo&jlN3iv>wl3ZmTBCm!sOIa-c2jR{_zn95v3|8+ zRdcW0rM#9c`0-}oe6dcPABG3UJG?nmWbH#x=X>0TDTged-I|tS=2OQ5J7}INW9F9` zd~#N6=zk7DTU~5g7nhYt%3;(yb#CL_#aEByhURUE(Zm_P=VAcB%$431WpB{k?GBY9{6dg}3T)vSi_vO(GeV;~b0NL>qn~n345v ze*DwmN+rraEqDeJX@UsPaEN!lRz~wO59Db};t_vj6**(HcqHg4d?(G|Hj5&jv@P7mDo zwt{~p&tcZPt{QMAeFBK_7nX;;xf#t|18%(&R6fCy@W8KgZxZ{TQDgKTHp=cNo>FbI z+P}w~tRg6leDln%k@1hMvo)(8O2Z@}!R$<6NnQ*p=xmN$ZdXB>vrvkS&qFm$3Dk>2 zdI96GhCDx0Jhb9UgC2V_`j^{7@%7Q&$Ypnf+>@KlFSy53IisJmZKwR z(za`ks@n$)qzZgkduBjl}&m&|va4BbG5 zP2{J@mi6skeZ4eTSgvvLW|;G;e}s&Uway7p1p<@y)09f33uhAKgm{`h&i5MQl6!wJ zN4mMy=~ig~55j9j?Eaoc<~2e9_}nk_z`NtXphmvrGf`4xFF3x5bu8;yZu*#8oG0h^?q;g8EHkA%l``(<+5d;^&L{kpCLC;{iIlIv)oK|XhK?aDa{^7UPn&D2#6BXHB$#S>j;kqv&};++DsQ{I{H z@0ddcG8XvY7hj4oq=zVIzKMS!9aD$K6`bH_H0<(UB#IdOi*GQAj8-6dXYk-?Ug9KC z9(|2;jTIM7F5oSe(d-VDf%P_s_(NM7QhzsniTE;>X}Mn7pkvfBK#t%GS6=5fngcua z$@?c2AE>c?VbIaFr6zvrhQ-%SUwpnN8+g3D5z`z3C6NrepEMkv;`M(DbKR8g)H(aL z2%HPbDywHQ*v3R>(lweq44xh-iq>CL+74##n0EV5E_Gp91%x(!9D*0%836;5!=+Nh za9>6buDB5Mh|iVL++GWeh9P!x`#^J+zTSgl{|J#2KFW6}$k;{-jySK7AyGM1`bg81 zqJwHRw7q9-NLf|=it+(M=}>+My%V$g=XaCU-KJaFMRecIg|7nMTRR};KV^7ZQ^ zIGtE_7&SW&=f;jf-kOR=2ig-*(P0@9T~k3iIHH3+=bloB4VvsfzZYKQHed-<2FuAd z7E)8PhIm&>nlH6`rL2XdzKz z;?>t(RK8sQlJ|tk&`9fB5A!y0j-g-=T-Hd4dY~O|_r!^&n)=RiZPjA|^{{e- z?3-S~c&T;fPbsD0xz_?RrFO1K6&wNqbU=h+u4UVCtvdZeBK%BJUR8VRJFwlNOl^0^=f}&wdG4h+8Mcb`HH4f8B0~kUGqlD2D&UF zUO%Xf{zIJL_`EsSJ@>7e(UL0F>6zHN$uBTmXZ7pWSmTOn6;D4N^ad*rlHJoZBukYRvp)U8q#T>-+GrsEmjg!Wn{CFcvT$s<{ zwV|%!N(`vkPzT~c3}r76fze7=PZ^S@tD>!{T(N)pJAg#;y&AEm^i2DrY|Da{=J-y# zI_(X?yCzBqb8joTQb$(21xb&Q)Z9=f_B3Y@&b0I($b1aW>yOp>ZNok-GZw>$r^Jnn zHbV|dw)wOD#ur{y38!rK7{ZUG7c~E+mC8_n(TTbeBf?i_Vh*%QPa)D_C7LU}Oq!Uh zX5xQH2Uc>e+U8%FRf;I4_-x6Ho7m)N`}SiU7RQ6BVA!`$-7_*-x{idmlj$cHbPhw< z)W+BsZNU)sV0)~Nao_y1SIpkOrhG55^p1ayPR-+(4RwyEzx z5pi6h0Ix9=y!wLxsWcDvj>=~WwiLE!jKC)X_Tk((xT~r_4vXd*lK;ws8qkygF5`)| z44^-b8wC||&djpP?`IHxwVN^Wd(RaOU_S1Z%ju4qUDg=(A@(Uxn`jl}~yff7yTKenKB?yr0SLQsg z67WjP2^R410Jn|E%YVTEg{CMSd9<@vQ% zTTw-ceZOaQL$2)(q$=44#W{a;5#mtu#bb6pgu0w@ws`@a-}xTUvj9GJT=6)NA$KsD z--6B|-s$uQ(~d~I!@7`=yXk+sEd!a$+LY+q6)A&Mf{M&r_R4Xi2>BETpsrk*CM=-- zkR^3B1`&crwn@`Ut^~Z+n0}M3j~}k-_YXTFNzRHkj!u=%M#J1sT%LdL@+)UxPJ%g2 z2540lN(!s0v6hPm7A74W(A0vH<0$frhyNLMa*+xWYu*+yR>Lz_)5{H)LPMthOlMBIWr&CGmgp22}?{@xBepA_Gp} zUqie!{$2r5_9>!7L1{*DWxiDcFq$;i#qQ zv12!gQnOw7NZ;4NBL0OA3^Y`py-ymNYI1Aq3Bz04J3tb@)uZ*tCT}lnBcwCFusN2! zUfa!RE8yQ)mJS zDv(Wk_l)TaIBr`NOF99Yf4ZAHXHz&%o;5bB+ctma!%fur5A|FuB#0qEOU{xASn3I1$V!Y8!4+N@5vLw_V zl{vpCb33IO*;Iln&ZkA#Y`EGtt6IvW)*)=l)f00yyY^FCE{)aZRYynFVe1hu-3h&4 zNohjHX`|+B;6*JCzF@ zqdO3jUL5yT@kcaI3o%VS8bT=^G_gg{*(@&z&F}KLFtGGF{I2$4=Yhyh*HZ_NIE|$4 zsWh>6A&To}(vjT%pN9@!8$;a~-{&mlIqkK1{_Zljtrynw6A z;whgK2MbBKY6L%(qz*!#@ZT#NC_+FSGPUZ64cih|?*@VqXefd81IETn$ zYN^Uoi_E!_E7qeC)aByn(Z$TEFy!yzHB2>Cz{SRphVU!L+6NQxL==InyL!3JbSA}+ zLd>f1nV$ol_U2Gu^={lxD|dgfp@jWAI8n!Y?9^Q$l#fQM?0{WcLe2=zef-2_;+>=|NCQECRQc>Ukpf_~*z5=oEc|G#RY||-1dOC@8jx&F$B#~+yrJxv( z1nql8^r=u2RY1$XfDm?K9~mYGZes@UB(5+psv!|mvVElg$lS5{L5um(Pwy1nw^h9v zm=}8Dwa1%xV}BEp85d7qY1wgq$-yaKQJ^jB1%r`9_egg2DRT2?aOBq^uUrwM9#OIN zHUhb$Gyn1d`}vI5#>szx8@SJ_U05#@?RO3%wHp%2p;S|T%RMgb&-f7i%j~>k(~eC- zwZ|hY?_2%BWI7%vKeZpGm66U)mT-syMEolAtHFDG^H$9VCB=Z~_WM$-oV#rrcXv zEQAQI?^ol+5jkA5Q6>FWuyt#o!dFbTyg~a_O)vpIIr!Re^6u54MP6h@A{nZJQ_pGC zj^g6voxJE|Qiv}7gue_e6ID)sX(*2_$}|t&FNsv~#t4GQ5RaNV(8^-fnx6 zlLCmI=k-`D2)BQdDsxoP=Ul(f&<+P+&FrmsT2x^gd~MW{(5=Tpbg!WpY#R48g1O;+ zAa0}}`dM?phMMOPAjv4)jmuaxgUEw*OOkC+yL0mW8LNHE#? zC-0r1rlnC7P6Y}&Ym3Fn%@q)X(|96HQI9hQIHJFpUK58OsT1_Ra*;J#Pc ztuh!_+g$VPteqbHN;9o0&2*^k&YEENX-0meNX)-x8M~0nwZsVz%;~i3exsxJf}R;p zPO8i545GE-(q(A%nU6#@KnM89t4rR@(3Ee$Bp9qu)$3Ub9?gVY@HZLL*f;N0aS1! z{h^kGnugl25hA9`nh@B}5{Eq9fSa3_08=*&@3OEx;2mz8Frj|Cw#^h)sFMSiT!q`e z3QbG61XCTh-wJrA0|*yki}T#2GuW11Epb8e7X5#SMAQHGLsywQLfg)LLKLzm>pimQ z$w(AodA7y;14y|44O>A=@&p;hk`7{{+BHx&G0~bfH8JTY&sY*@Y3p!q^eoHO+Ot4W zh?a6B)!viQM%6mEg!H7m2 zliPpOFrW5|{w4n9+CQrMF-WJnOMu)S2)vu@wn}+AqL4{DIAmO(WK;t)kR&Z zQpqeoXG^<&G#d7C{_1eoAI-7^RvAm1zjYg=5C2?S2zWdNqBINh-h`$%CO-gl->&*V zN0bije3%g^owcY675c2y%ah|WHZHTTTcm$K+AW@x{tUN)9~t`Mtv$m>-j-Q;dl|Th z_A#D@k#@EDDsUgozhnFZF_S;W2fNOp#3Z!WV}n)kdezlT*MKGoWXj<~euoQlfNZIX zZ7q(85<0e7<^9>kJ;X^?+gY9qOeI9)#@-l!Dov;l#(+;jMX18qaECqap0P)|1KxkL zX7H_E5MiFi*i<=dhs7A#Y7Dkg@6gXJAQqST0e&>5YOLLhVXbJ}>>t-S{mnsiGmpPo z`^gX?<<1O~H>mGC61qM$~6mEZBg_2se5#qDpLbgyJ@yzm)$&{7bQL)=$(H6Y_$)bgik9Uj`+#FUTLm z3qw@^IV2Np*l!I98|K1Xm0koJa3`b-V=}YM6bK`)=zbuWdKe?Wog?G3Oln3Uzq zSXuRxx`T#JD!*u~0m1~SXl7MX|sTgDowkgciMR_&$AkO+-k zSr_zKr0L(=3O6O(L4f0{zD>KEO<+Opo%yxQ!N;V^BWoErY&yF#XUXgq>Ds#6O_A5n zCPdMXTgyl)R(VxK2B7t;BB8{&5AFvv3p4~a6d{LE11fe4H}B_z5$eF`B#WRIqjhsw z6VvZEq1;xnpH@koYNdBfry;Yd5NI+d;E>ZJN2QJ`VY7`1tzFx2yeR%6h~8sgyw@0l z^gUPlK=FyCwE(1H4Jo8m8@eoVvkAR%#bRw=28m4YPhW8@DZt6^JIwxYT~qX87Cm8! z$avf}EBB+4My#YHjxhZS#dnytsbMjIAkY3(GIf|DZxiE~Sj664 zHj2lC_>+X2=p40H~$a~kx?NpuxmPT~(! z62!AB3vF6&6F@J_VP5@INhGjWwFh1NO{PH%($(z`=CqusL`pP4=~O5=QHZE4FV^9w zjQ$2*irxpKw8hNCUJHE0hK86IVRF4Xn1~?7Td}}vs`+;guzT$l>mA;r!*`gMv2aN1 z0*oSA-^gPGdbOGuq|X$~u<;45B96)Eg8QG?LinT+Qvi6fN9Ib-DO4Oozrzn=v;1`V z1g@<1=6tV$^ipUTW7A&cbiQnx);LrTR7Q3v7Ls8~YZGMuKj6? z2XS5TZ@_>~C)gkErbObRP$TV_J=qC@?|WXB=P#{9?L66NFkb0<*MNIzHfz`wYv+#TGqkdBvo@4Rf)2a&}? zs_xrpDLIOsAm{XjpRX!JV~SRMA2xEKAuOcY3poMI`gdVVYgm6d>f5kSo;omRx9YDV zWB@a05Z1<20lPeTjE)caef`amw1HeE3yuxgy02Smnj!Q4XeTEAL5`QlqUn3$_t>E7 zy}J~X)u-Q3Z3t%g!);Z98m0J3&v5Q`FTzelf~kt?0)w)KEFRk1;zu$2n)YC+l8-wq zb^r)UMo3{hue7UKe^Dg}OWW$i1vv2^MnDpaL|f7$^Vs0n)ldVXNs&fPrSj%+P5yEK z$A6sIYQ{|)>?A}w!6i+*P9zRY3GVA1?<<4YQ3Oq$Q)VKo7t3&}S?;K~i~*SkH+sr` zE3m2gezEyPCnlW>Cw<~pQV|)&PVo+dsDaC|j{-KNf6dO)BqeqW$VWAD1B}O=0A+ni z4XSShh9E+Rg+Wbj>IFi(&lfpvY(~)nr|(7VU{|C|mw8=ZLq1MijL}NQLDQfezq zO?U6B?lj%!bg&PZCLS`9AC_|x)FgE%2F{;tpCpo7y?Oc5;_A+A+eXy&>E2;;zOGi| zfAj7X+waXVpGr$>%!-lu04h6Ox{1Q#MF-TJG?m5djG~o*GpzCeExZX&UUT->LKn87 znt{vN#4qV4?R-i1LM1)#-q+c>Z^I_W9-k`yJ#7M`k`>l4b|UV2?my~V3(Et_)W1O) zJA_?b*NFqHpx}nCOB^%m<#|obkwnRX)%h2S{J{&FQ?{rBCH2pK0C?yJ?jh{Sn#NLe zClHgS8EtBBJOQ(OA0mM>k>yOyQ+&?B`+3mBnZtxe)q0a>X<{xwdxRs2e> zKjdn>^=ZssVupzNU1Q(flsmv=oq>{SPINPsz`-M%8s~IE)F`_n+=@`Ip?U5Idr!9- zj+ZNUsiN&8sP%^-fSVMrmBl6e8n@l40d=Y-UM;}hd$+t>AhCV1QhZ2IA;w~yCabpL zQrTdm;C|zyopE6!STPV7%z(5_+i`Nh-Ec}GhhMK;d){34Dt7=S(=$g%rj%=u( zF!5S;(Y-dRKJykIZRTgNOIGuv#$}seaBP-*#hw@LRpu}9U%DWKNqhqa*7 z@`eCc&qWW1$0P6X>Si4jBc-Cqb78AM{yl@gsq!yLA^8(0^PJey$sOvVaQ$=)-cq$h zQbBUrYR_xkD-RIVXqW&eWtH)oARLVZ1;~^%i=(9rWoBEC{W6}+6avW@nqgjqFSPY z?zb&1whiGncFKFBrmBCe3Msm*MGj*NpvyL=eRmlepq3~f!Iv&8hfCZfRAvGuEcz$6 zTF<)OsWqH9Z~BIl*x94Xh%|%d^$`5(n>h$sK1F&9kyKve!8Rzq$rv%=+PEXSxA`GR z8vMNyq-r-Bv%0-E%yD{cc{V7q?rEI6!E>5N?8rm;yJ%mIh++=(rJpO7oLOSc+yFGl zchz_l5Vgpd+sQ)dUkoQdLtErj7zqsd3Je)_;8G6$IV$gqWkmxo>P|mzExE{ zt#V8`92TV);U)z{X|>uGG(`tPv`ab3Cpta@xMlEftdbIoJlDc)(??a}3Rqf^+ah)p z=rnjhs*{w*Rl-2T7yY%#+)%;5(BEShJMn&jfwQxjM=TdCFHRgam<3?GdoHB)l|h$q zea2j7i4bZ;x9Dh<{{Z(YQo*hj^aXMV=N^E)W)S&_ub@7=4~#zn6}@AS$|m$_{r33- z7_L+HuPsQ^P5w7-oLQ&;VZtU#ImRleWZ1R!mQ27hgn~^!@1*RJc6Ay|x44N(E)x#) z$XzYpRqE|vR0r971SZq=Wk{9Vw2;p=veqmLQi6#nuc4T43#A7PXY2BGX6pV28@J>X z>r^PorCb6IT!fe?Pa)>trm^G#9_>vPFk8je=>M?&C$u1Um33{tb|UC^pH1olj?pg> znO&%7+HsSeIF|&mUrzZr;SYs>s@@ngJU@%)|16ETKIa4JY>^61UFhrtmb*>L&*8ln zm;B2a+|EuE?5P|On>RpGCQTne7JRR++$LDg_Su(N5^tpwI12kJ_?rFiSRq zWrrJxG21i@eR`pOU|drmD?KBCNl2?H+ro%Of;Ig(Oj>n%^rWSa`OJ#(8JZ_z>BY`I zVrYG1B)k$~mTbUR-~%h^$3Vbh0YMy&eX3 zGMo2v@AkTcbH32ES)wo|rGfjGql2#`fp2Ac#-{l03b2i^&X<;Y^ajx!VSD3scY%3*S&~xTFYb<&XbQ|Y+{4m93-`Bs{9I%%H3W9vG1&;)b3mIkw@6F`vC3o>yT#rG-8THm8D!5e z5r@ukgU$W5*0>mn{sk8<0Mb6@U7dg{0t$oywcDyVXF%1?L$t5E2q2&{z{h)6VFy0{ z{l76Wqt$#9jV^DFZ&3TP-&JIEiD$ zG>WO;OHKcK_gj7nK3atx13jXi^JKU>J@RLURI&1O1XJvBAhUCJoOc)80HCYkouCw1 zky1?q{s(Vk)M+CK20#kb(X5CW3*8uUgP8X??x>L`mUI$ByvEUE|CPB6Uvj_~Alxmx zOUstsP~MJ;6A779qkJKJzmZhje(_A1b}f1QRQ zo2MVu9Yk>9X5TDnF)U(F$SDp#{1L9?1 z@pRx0&V3K~Hvl==alc&iuL5t){d$6O_Q*Blckz91T82+EtyX1el@ojNlx)GWa?%ib zml@H!>SBbC+4;GeER}ZoM497Z<`Jv;gGBDRLuMV*OJsz)gcnxE+Te%?Qshom1~8|E zb-_s<)@O6*=uIK|%W4b$0t(jNJ!kMK7%&(HMk=t4GC*-i#R_)EfoRW7WHd*$YML;2 z)onhC+!D$N3uX99oU>GQ%AQ6hW=35cIqLlQxzqu$tbV3{c_ljy+tBZQLLq;h6vJSt{6ou&9!@5cyHaNQ6}%aGOVi<9wx ztVrd9o@4oO0`H;4!>qH<&zuABB9l%oIK zvN_8n`*%G<=9_^+=3d{f3+mQ^_wA_L{C%ok2QZjoVE$!>LCX-H$C^93KfAkjMz^?S?l*(3~84+pOZ3Q1MW9R|)fQuQb%PMX~AS2uM zb3(JFl6FS);I;;&p?B>GsmoDWv%<{PeQ?Ethja# z4WRuP)I#^^BTsrnC}yI8i|4zQfB^5`R@KZcs4C@0L-3MEGgD?BD zv(fDlOIk`oPH|OQZtypmhI>K5!6mV$H*;1R)9PpuV zC~I`eUaiXJ0sOagV?}P+T7d&EJiQoICLbN23R*+}eW^#ty*UN<06FAS0q}VxaDSRhBZPf z#{&kY{xmX;PR!zkZHa>|NGjgGP*w1AYbHx1GL=zr9M#z zKGX=ylIKon)XsV`;061mI!Gm=*fJ+#puDgxR{V9bL?Q{=qsqB3pyj3eoCmJ$Yms#! z18u`5QtGd&zra;U0yzH`vUvAvLaIZ|mY~gK*@F(Nw3ui}d+9xH%8{&)ZQp*6-I(j)V53O~ zCgMH{KY4bf)tkFlQ>N|H>|wIi5XK|Ri-UrD73y?SXpl5qME|;oG+X~j_2&m-lt0Ey zVStP`S#l_QpWi+N29(dhQN%-5>L^nRGaLUoqEKL=Bb2+1vTbIuvkyF2hXk=`2ou;wUMhBHdL3X~(z-$C-G)4miExPw?8K0&sm1`wp0B{Ixyac-51!{d?g zyUCEtTKzI-{&%7=!j)4sJsJ+cmblGlil0SKLm(2!%03L+Jik+^rlmF-HqtERZ}r$3 zT3Id|ZtWyv87u8Z&n9T7h(H2ut*^!;PM}I94JDLdEZ*mzk*>Q}nAlJsZUf5vl}*w0 zN-$5K+2mL~4d}@t>lP(D6hdfWbBy-V^Aq1FQ%6!?hfcB3;hKGh1*KDx3Ab0h_25QL z0XI8aau=O5l-LmvMn*x*>C~1`eL-tt5Rs$D$uOB;Y4yi0f!Qzd#Po=T#4K7?r(V^rseDyP0_s?y)R|_9%25%6Rd%44@smdH z7${v3^@z(EIm8EmZ=820GH{~V{15xsX^<86wY>PS`1c0G{P59OM15+BD)px1h5o{( zMDq8@;kCP-*Y;i*A`!44zSf6#T}zVtmfk|Ymw+(OM!+BM*=Z~CDr*viKwG{sX?9p_|?YoIwTWq?xR? z^c-ju?i1Y{470|eR(Ye_);47p-~^fD`sRcUKz5`#j6%A?X)lwfzg=Dv*Bper?pz^k zqvLsSf0bgssX~=Y*mFP6xKoJ^Y*;JWm&I2u0V4kNMLFG9f$1Mw){N{`@b1MzGwHF` zNA7l_GBQhjOynR z0QiwrH$VY0vXXW3uKn6SK*64_8DMG&d09xtw#Fb5x*70u$399v<>eRb=Lb`xBC;2= zQ}XeUH6c@%j<9)Fa{_)S(v1EE|6VQYcB)8Apm&M$e-8>HUS&GnjYAV0d)n~zCg-Zs zzyxiA856Z=5hptYwz}PnoOBJim{LZW0kW{<@H@E2g0`=|A-23=X)eGz!v~5%wtR*D z!0XdJOvn^-iPEmp$rYLu272+g93Yb%9r3IU=hVy>8Ij znt((^$MO+8vDF&*fLLfUm>`B(Z){jVTo?Q8fj>ef4;V+{ zZ44wbzv+1^SY2GCbUkjvWS-k^?Sg9Ea4V5yyH7C=kvU6Wzu$k~xv)?49Q?(61h8>$ z)6Nzy|GRb#EcO{7ua?Q*@#&lsxRbW+Ij}Xf&e;msls*Q7KVfbMt zKyv!IoBo>Ap8(`ey(*MI9y$EfjYq?5?$+FJA^VGdM}N$TfY zNy>C~Cqa~eYr10IEYFp;;zbLoidp03+fa1rSa9lT=kJf{1Io$K$J$Xk3En*Um53eoz#fst>ns?vM_3U6cc8z6=eO`j8@bIHfI z8`L)+L+RZhNN8XtBej?+fIzsjo0U2X3w)Nz_+jFg&Mc>hwOXOTu5J zTbK>5J__f0j2_%E9RNkHM(Km+Phomxm$FF5UEEf-;u1JO$A>;<+jBhEvt1hVYc#J0 zbm3OoZ8In*KF~+f5=Gs`$JrF`=Ak)mrh+;-WXBacRl@mb>FZ`LP@qscFz46cyEb9F zV3AUR5(t-qm&~C`Jofk3CLTAEIF>^vlA&*NO8DQ5Mw2?>O~BJ^4To2M#_pRMgfr8_ zYG4tK(bpQ1PqZ{;pLhHM3IenwZi_shmN32p44lk5 zUI4*^MJLmyO&jbSbAG~sf9~M;7ByMtiL=Hk117+HmJRn25cf5>_1qZz{%s;i_4y4+ zce8P3%#T?i%~C9TV&&UHpRJGOb4ssKswt|5vjJ@s8!O`r5||5dK}!pRr) zI>v&p_%F!(W`Y<>pk~|~OdpOO!y1r0NgOEl1~6rhqrVXpB8SicMd~%(Z}*j)tW2Z7 z_FO!Yc)P8(K)LdI8zYf_wh~icP>HUa)JnZ%{G)oIS2_ddZ2xl6s;3#gk`MAHi~Ona zZwgdu2=>ZXLiP1k?sjpJXHx>I^bv}3G>S`25#YCvt-IM(ox=^ zCE!7q#KNkE_N^t?A&HLVrAt-5E?O2_IN8kk6vA3CBoG?5N42729oFf&CD}*xACrlF zB7b{&J0$c0dB{WMacwpGbJkPoAQp3h3`#DW@|O7%8i**U^jg0jo4qeZW@A5-d1@-& zPyQ-NV28O4o=ujqaM1X>6FC=Hmw-M=7Z8ToT72;o+gwmEvEUlEP=by^nbrCu4g zoj3x8_3&3*dQcPqb^i~Eo~t{?c<)^Y?Z7I#)CO|+P%N{P3quQSSDi~w0U!JnHNLzW zyp)4hcy?+lt*F*o8X0W+YJg^=r8+i#cD(=IbDD>@0_hYs2#Cb%_aDB}#1jL%2iz-9 zFAd*d386$^xRrxWvt>~HftETeS2 z)00X#3o<`9LkkPLTvITmU$3YN$MwK}3IsCN$G#HDChqWiBg*e4chvl!eNvWxfQW;! zH4Gmg3}d=nBnT2NGZPaGqlA^Siz^Wq6Wf0&B1A0zT3r80hg|*IaNdwW@jKC+D$-+c z`iDqsR@zcGG)Ll(sx-Lc2@0Xn^_NP41DV+L`YR#=p`=J9{_fV%NkxMVZhv%D%)dTs zM@oV=&up1uw$L_Jf#Q?1jt!R%A7#S6^DISM2UXQzCC`lVE$v> z3eKv}M4yRH1Yn&Cf`taLsmX8wHl4!dWJ&_B%5b8C8D)zeVL{b~3&S46Ob9Zkj6qmFk1Z-OjG1y>4QE>|h$==)0oga}0250+&O4l5SVNki`W@5)aIWGob9T1PLrQm z{dRTMK$^}4O~4Q5=Favv#O{=X)AZ0g-+KDtD(criEK+>KrlqLPYoM83JBfx{a@kH_ z0dx4I*OSbaTwp*01Rk|9s9^USU2KSkMHB#;^(~l=ad>wyMpLwmi8^%`t6uzt$%1C{_Of5+KpQ7h;m0=`2xyBHIMqhn%LasL$cHL z72E&R{WKV$&5;>9db5%kNJ+7ZGEOWp0+7lTm9w6TkbrOFrx4GUY=feXXZTd-#>YQl z_kmnOK)@Cp@BM2#V^=bh!OZE(@h-sgU~%N?9?H}tL-slSq^>-7Zm7FE2!08mZf-|84D_r@Hcw0P;$PQn;7EZ_KCIBYn zIXhoLaDZI(rASsx!>N^62<-BO6KiPOS%kKCfe0F|swK!hGDdd+_*Z8n9PF@C_O$6X zJoS(RNu&2^$hK7Jk&g1A9cL0WYm9Iu&gIk*2inHL~oP+k9YlABxW1k+0J5n zye45fIL4P_or&R7D@fG}FHN_e(&KU1Msy*fH*UUm_~I|ycj7x6CzyQ<1tZCveZL$N z>g`%k6L=ul1b6lIO*J0d)2m%Vdq~0X}+cE1(+PqeeDWY=Ji>ka zT5Y3=tz@9Hvc}W5xQ1~B0pOOfv4zOYlFl(fv*_PrX}{CC%%*RDmaIJVWS5a2b-6sb z%HLI31^d-K<%Xb6qllFLAm}X@dFteMu>eys$yPRs(j+@;r&Z;=5tB3f!A0~C>1M7( zO79Mx1g<5MP2~~{Tyot#)Az~ZfNkyo?faWhZj4=a!=5RIhb0Z61Avjcc1-PBaA}@0 z=;yv;POj!Shu8yKJK4sdvVI-EC?*Dhi!_b=jF+0lf$^iMv%pLy)-B~ygfBZyMv{a` zD1Qk(A6ut)9_9(A+c|Vu#lxgQJqUaI33YmyT8xXh2UxE6uaCebg_lP;RYM`j>2F|* zIRYypSo()#1wpXa8i2+FIm^0xSRt}MDR#@nj4cH!46bb_$Mxg#iz_9$ruc?`$d>tZ zaWrkSd71PJrvd6*u^J~S&X(mBTG3gOEiNqm;+CJcfmhh3eem|6otL=QcKZ!jRwsPc z8ams@&ZaN@AMSVBy+7WxUOG2d2xKamyohVA;vK0sbn_*ze1Mo$ML*Iu4Z>UdZ47!v zVNshMj7ai62G}xtknH7Q)jR?|QTkSF%EbIhtmej@rC3VUuy! z0@-xVA3;G{jJGq0qA^yao&LRhBQ7Oxj zYWs9Jhag~16A-@o2R_gOc72YHN(Vc@Z*hT_B zU<~QQ8_Kvyw62-3dhTA)dKL&yba2fULS_=(RN~+@Yep6+4^tfWNT^MNRT~CVP*TXD zzQ9r2DMR8G0bLO$KIo=LBOh!RJkZd_tM4SvC=9UT09@Lyu$fq;o_`22ULCAIii70e zNz0H{jVB9kP1z+={AuxPxoH7kOsW2Jbx3dRJrwP{gQ}54^-#GpMueA7)vOHt*C9U;p`2HDcY)uD8bBcPDv5H7``DuR@VGDO0o zLRkt;30PE$Ewi_}M}~z{T4RF>Webzg%9>zM!csCnc)SQ+=2@?48Z@9x$YSG0)vYqH z@R3rjTm(~g;oNvu<|ptgyHX5XhC7n1DoC@a$jtdZQrj9p9M45!aB7SV>UUj07+*F$N&G@GMPSX)suq_57ve-?Cns z3X6kmQcDwnaoosW;XsUS@{xNV7?@?JfG*_!hgcBtZ&~t$EVy3dR0M5v8kLphzW9@x z16m@*P4$WqQb)jz`^y47T8m0i4cKq%9QRd+59IuktJCAJ9hCLf z8-gysG}6a^K98pRH@+l47<ΜvRao@2$f=SZf5!+C0cw>y&fiqCT9qVm~ZefXC~| zT%=Zplx!R01ISPLjX_Ij2uyA16)414tISw|qbIH(rF@K&6WOB3Z+raeA;mfzfEON4czzI4bC zJzl+^-sq&K8(aH^&Lcl7#UeGE1`PcIe0a3y5H8s3{Ydli@(3R07_LeLpaOf3T51C) zxhP%k@It==ftnBBBO+YEW~3mDl2$f&uy%(QTF{K=pRR6;H&;XeaIOE`&EM_KN1~B= zrkd+F^2?7b$Ngiwwn}taIM6YFn5dhVSKY@~Wq%Rer}G7mONukoOw3;<<=-O{$`{hj z>eT-9&AtskEr|>4f&UB%7aBQ81Q)AfW?FHIX5()-!=j$-bpqU7U{JDcAq54j%zDBtaeD;!RCn3CB+b7XV!f z1V3q~hFI9Z6lo(2K%}ZJ|0Y!5fA;`H9P`Yvd(=eMlyZQz8Xls{767Uul+*^SeWa8EHl@zfMcerV}KCMA$ER( zY%b3aO|4Jv85e%ECx6a=Xed-w5mikxp3r?vt_`dHrp-AE&JVQ1IG(p-gQ}mSOYAP4 z<>}a&P7=eSeihl|_@L+Td2oHM36XAhSLp%9Kg^8>xm4Sd$15yeo z$>=$!z|}Z#ErOm~7js7^1mTi?uY9>B)OGFnIJTOuzGHwN1tLfq{d#*^(HL0If_VVM z=%Hk^uZOR$l57Bn6f!)+*z7Q|8Y=UdXx#r!UN@5U^!1g(K9k#lIyqet| z{WuGo)BDM2-j_>^*a_Y>sJXsN;9X63biYoQS6w9VNg|xcZ zbDabuD0VMx-Oc%>C@=|8TTEvxqwpUwOph=>8zKeCWx%CT?D%{TE#84}ESd=5}3@u-iHJ$2q zJjv~v^yyy|9tt)`Dq2-gQO^Jp2pxid85{q1+)e&A@O!Cwm;B2yMqS`9x_6`Pbqj98 zBFwJh3jfO~BFt(Rr*ET4=Zp z=6**rEEw8sd6r(VYO^RTbMb#qIU@#5gvRBB-C;3jDvjKD!Yl6HrSxd zfuV*e5aklrw2xYO!5a0e@xZPV1B6=gbpu0>%1ot{7ckWDaJq{~x z`O21%2^Y0168l>s2{F__l$&@0u|n~|=77!*x{ij~t2JXAq-aPS(dOcm|MDl(Z6%L0 zv2#-<>&n$H_uwn!`$|eFnu$_i3(~|&!pDN$v*$aVa<2n$i8w#aAys+ba$S}zKBIZ> zQm~-C<@Bqh8UOV%Pbe-7#{C==FCSdv3B2;vx8kq2Umja zmdw*dNv)I%=+15Rwqs8dzQDL!i#iprTf7-EAA$_RrY9xR&eE3APjX_O9dAHSg%)FT zQs{JgzPkf(h@gDJs`t={v$~z@>E*_iP4T-fOV$?D)^t?qHJ{RPaokLyQU7HVBK4DY zj@`4eX8`Nv57>pJKz3mknQ_Fw805g=o&MmXrGp&|NYhbil zRLcZToxDuQJjQbQjnW-0ehH46jj`~ZeaKQpnTrg_FYgQ~qP|_IMlFAOR%1L!LQh5; z+EdjLpKGnC53jcI0Ir~zr+ADd6k~)fjZd6!yIdEh+qIlwhsGiCo}~l+m;%o?tq>PHDk22ld|a=C4UA?0zE^I$#)TJ^>!GkiOe@fV=}8UEgm zwetojalU-gJVj99B-M^>`dd>;sw3#_<((Ds2fl@Jx5Ab@CY<`+aU}oI2ppaQsbPC3 z(ko9U3Uk$!xHd}z?qeLtm!d(6u=Ms{)WcT@!rrGzkYu)mz+l>MTbJ8A02MZMwXJsD z5O+aCD5#7|It^bz?S(j+15j>#aP;v~DeU}g4GHU4 z-~4IU@w)B#*BXT8?_<#}+x6-6&$^QKp~GG$Q+HmM*fddjeKJMHU0=5*VUz*gD+CgE z&a!jwaCZK$Xea5?Q=fV>jakV^C!x#QDe(^<_&*oc-&38?BcQRxGd$hlY(*RtPar^2>q)ul7XNM@+}=G zG}B8@cwT@Dx{9HG8GZX^1YlhK?O&XOS44d}bs;btk|AUsBH^`4ev{`9qd&2B6z&Vp^*sFG`4T{+TXLF5InmCL zDPtc$WuHiUWw3V1`2|@Z?{dW8o0T;CEV8W;JsuWj!LT73rofoU3dvI|q^{i!o;kor znj+YXNhSYUdBHq7nv>VUiK6qvHPCiTWmfZg!PBLsG35CS@m#>UbZ?T&~Lgw9}58$vPRw zls|#(9__7+YCS4APM*Mfre~We$G9noHU95J^2e%{K`@Kc@Y5K#6gy&<>`k%aM_RP? z(L!PWy|A5^Z6Zgrb+Le*Zl)txZ-vyL*V&_3ns|aH8DGvE!VsW|T~QOY822kIv>dCg zla>DDo(rUH%BK^IK^zhGz1u*qY=VDmH=cFYj8^!#49=XYb{1h^IotSDh#sYSc4W?%j5c43rG5`VNZuUv3!3B^2>l1B4C9Ag-Fb z#S&@KrOPgs7~${EQ0&R-GbpDex31TbhfFdAu>N^*p8?!VLdgw>?z1ptyx5RvklK`e z;}ebDZWxbl)TL?Og=jnEU3{)TSheswE)<60o%V32>@*%WzPZlCtXFl!g4JKEgRfsTODwxg8818V;x1J!uPe{09B`0sUHFjPAKwO}T zYr%n{xkD?J;dH_%vf(h!j@jgZIGX&rwkhY-PzY@#jKMGNyC#$C&U{~hIE!E~U|(KN zR;~Q5!wraX1Ww9Fu-ms~7NvOl%TldM;ltX7xykqBP-L1B1DzPx2fLsEVc{`0WVw8CJzt z#g(STa~C%VBmE=DQFx9FIa;5~nLL*?3MBt&X-Gi$cXtR_sUXk;!hvBB`cFdsH}|q-{KtfS`XQTp!jg-e)ZBUA=hYAAr!R*6H8yS;=jw@ zy8#S3m;4A2@Nx!|PPkOGYZAzEz6Huo*TOH|*%6lD?@?X1H~s}9`tQ*9^^0UI?*wS@HNyVQQJ%#|T4g>uAHH1qdPW{!L)XF+{^8{2pEz$ig}<4N(}O0Elf?C5~gAV7!ZAgfcS|30n<{pz&?`l9A#cMJ7J#638)@aZUOOKb`*UgR}tL zUdO~c7uWd3+rz0`W1t9`C#T}q1}e+YULjmRAoKfbI8{8U>U@sw8ID(!tg(fd^V>`d zd-7C0$s=ddY7gfEmV`TN4&ON^z+Xi(SWkHsH!b7xbMPEJgA(3~=5I}hKEK{Hg{|Qp z>_s8>)4F%%(6?J9yB)~Xq`$gHhF1Y3S;j*DB7`!OZZsWC(|n~L20k}Ern3AK|4cZr z#(-TWn0}4W%&xQ2hI;@}nk#UA3XBl{^_H{uhU~e+?8T5yruC9yJqQ~y(dz^pGzN)I z9Bm)oC=ivYY*JRQc4lQxh9@iEd?|B(>C?nAIS?CAqLq7D%j;T)#{N;f6cj+5I@OS7 zV2G!mCyphbuq7@^g?!vS6hADeF{_HsthbkLq!2lSQ>#3T`!}elfmOX*#*h3g zGXOu{<187&eb)AqgOW4YO~ePl*yILq3WVODPyU1?88bF_ISfC~Lu9nKzDJ=2&ZQu5 zlZWvFFC{F>=y?af4mf@=BOSObFQlDW8*-y%ey#olGuV`OAvt&dEyq)Ume>b~6?MyTc~_-o zvFp*R^)9M7AOVC7n}DliX0)*^?P|a;rN=e4S#=R$3rQ63R@kt~8YGjl-oE_&1yDz9TTb@Bt=Hk7(&V-~85Je?4N ziNLe8>E1AZ0Tv z$FhEV8FS%vMVmyhAZ&?~qV9(3e*x82Me;lF2IHt)pC#&7_hx*k%ZYpSk~=HsHY;IM z!j0~QHMeriu9Aa2g3-tW4fQA!xyTnr$4LcM=p{|7EB`%UI7*#}y<;APA38?;BN>U* zuXbWt_09dVtmT z5yk-7S*-%VTfE^rI(ADJxF87}l60bf&WY|vsG}L8D41kVL(1o?jrdOBw=SVm5N}of zQHaxi5=ahZjB{w=1#j|(psSVEnyoInN2vjfYuWug!`E<}duLz*!79WAGIFDB;N6tusAZUs_yXEN_pziSok__@(x=ZWOM%{hvQE&92MXs;LBZaynq#}t)FuaRBQ z#@-BIy_Wz95v5gMm|`3>-J7sNOw-SAxkHgd;S*au)zwcuvXRrTPX~ubcthWoOK$tM zVzJf0q~q%5)^Yv609!z$zwjcF(&%%O%PB0dO)ShcGTtH zMDiZ*vqCdGM#t%iJ+crX;g6r?Zv=|=JW1P7+LSQWS38~If&%lqLX%gPO>=n` zCDQETw7zSAd>`0TPr*7{~#-3KJ0#9;?3Z8*DN*}va3m^6_}m8-sLfZq4!V!l@4q+K!5UPI+6y5 z^JUaJAk zA#<8BxR+3?&(T&ErTuS#1f-C)v-Y!HOBjbQ$Q`xKg}Kx+Hk%c4{U)7 z>;92#$3q<4L)m~jYa|Y|lP0WY{N?c~$b@oBf@b+$yDajXB>44-2uV^OaT)LQD^u}Q zi+^845Oy$a=ZZ+n$SLb79U5xYpMm`qb&NFu{bU$yv<$GLt17$7oy<%cOwQOqy%28D zUsKq{wC`U62PZWFI;jzm!gX!0e#`B)=1g9nW8x$Ybl}MfLHi#(TF8CDgWZI$5G&{- zb**;>xKvd>;b?kuhEKu`aY3zH*8IL>N>NQ&q z{e2lLv2CYNA0RNddRwW(#G2vCPVj81Nj}}{WX6*dHZ;}>@j8i=I9DMY>x3(v?@LRc z`53c5AK1E#WhYa@IyKP?ihv(RNnviNf?~=_?soF_s}0Q1Fd$P6M|`{J(T1E6tbYm0 z&{q`A4|lCXelq*Q9GYUuVBKR6yrw*e=##p;H(lc2aWCg&8pmF$UP8h_ZN!!R*tJY1 zs|!%v^(GA+L_r6WbQQiTxf?MH*@EjDE zlzVkiP~;c6aoQ1si&y`#FFI1Fpt0!&m6UMq_{XmmtO95m`1R8B+PWGSt{oBLN@EFB+ z&~+3*>wK61gHmwdieJbAC4c&4-4L*acWc4-HjhXV7)iuc^LB-*g5juvZm}rcLQ&@3 z?N!H5d%jtR4X5iyB3l+5pmnvxSc1D9P$lY~L$su_**%b@aBp_cA0!W86ZmPKexAJS zBph`g4Qaq20eiZTRTl*CxM~V)pc(gE_?Yz_=ESw-vvVsS|oP9 zv+=UNXli^m&2G4v;PfQ;;`70z#ezl-)kZC)<~#5DcxnAvHH z?rN?_+pn@KLVxlb=OI#4bY<~bbK+9ARerH&P_f=v7Idgn2{KPY%SOS3f_2e4a6ErP zq%fBnV2UbmEa9!4;ny?=_kUZvC`0Nm{3~c}4WuBOx9>PK27Q~bBrVJsa^z?b_(ba$ zc7k<$p4$~rp))Tp{kZrZ4nI1|%Z_FHT;4+OkD6)NRe$`<<8;Ff1N9ua{IjrVlih@? zv#3l9MvigK2`>)$$A&$=o_1JhMI_3xs{^ z0V1$rsej3n^SZP$56SVXAVt%ev(?+rC3kMtjKg)M0z{VkcyLNgC*wbOn_hp(HM1g1 zzC)%%ox{e+WFO+^D^E=V4s;gy&35vUHL{Cqf0QFkJ9^~=J!f{2R9H||3U2Sk&vffW zOu?9^XQ2Z4Qk8z8_8zIE@T8P%5p^&~bq^P$K7aIC#l5uD@IUU27mqA@BBe{$)?4LV z6<%Lr&753vOJZAy9gH)JzG`YFsllXaWL&;ZV(FjFl=Jw4 zZhzi{KABJb*lw_aM3a1!BJPn4{uCb9O~~n9FK9we>Q~l2)g5ASlFv%Sa4ZoG-Gh{i zl@UmE{s?3=cV5i9FvT1I?6SfX^S7QWU`2T>;g6kYQV(wLCQ_bce+Tw@%_RWEGP6{1 ztSJ$OAGsW73)aK@j(Kf219^R((M0UEd4CJateN!&V_Q;*{^_wOQpS-z0o|z-4eBt0 z7V~C}YpwMl%pXX(^8o(V{iBwQu@TKMqW&_Vh*js6F5>RX;uU400;MddK@PHYbbHHX z&buW-kzX4cHm*q0OLHT=3`D}pj=Q&MWAhgtnavvcZ?_ST2D@Zwk4}UEh z+xjw81cn3|fH`zgy%Cw+;7=U1S|i!}a+IuVFh~kJU-vMji{Mw3T`xxqmN(AXQcDJzdMg< zB7)X)%mT0NotaYSZ`*oczmzF_jDLZO_|8dn`i4HCB9v)C?{Tv>-gD-DLQw~l;8y>H zWwaf-TNkmslcfgLg_!v>n1uRN9Q~#@KDUe+zY$B5{;MvT;=GH6hc1d-Yfb!l&u4?7 zZQSP?4mJX!SC#IFnOfY7i~O?FaMKODg24u1nn?iD#iI<~^%Z;i#S+SOAAe}{<}#W- zVyzu*E{QOcYRhXa=4LNBg!P?lWNa}n-g+^PchZvtC&ka?qLaoD;T{vTx1>tWh}Db- zR;X7{!*CYNiijwR$hC!_HUfWM*j_*t^!c(8wRUQd1!AeI-j5&0HjJ>gr3|(8x}<8( zO(deuRN6@6?&1evVXy$v``RUCumahROKA?2 z=$Ewd>Y+3+rfc5#6Y9jNSET>-be(r<%7%ukecmcPb=+Qzd_V$jSARqkkbvA$+#L;d zb(}i`%Z0iGq43eCxS9A>Nn?ij*A*QzoD6}t^q^g`wbmnt2IMTRT>@DX!yIQH4CAmu{=;%MJKD)3sBW_kZu;r-R}wvRnqVNUd|cf?~8hz}#cuaHBC$@8qYf-A@FQ)mO(nA+6f z)Srh*OR4BI#yu-ihBnrRhl{8@Zs+?6;evuOjtIru_0znh_!DueNGfsTeBf!}w!doL zThlz*z~ZlXwM zC9gD71BVNZUC#OnOdkvk(o78OnVI4aioTgkejUF`OnXPCJeDN<852m>PvUF79tH(y zectP$i$k8Q!S86lyxeP`>#XtlDjf;kLdALo^?Me?m4EAvdv&jCzjoDU>@qALBRi9t zhn#3PZYi0MPWJhj%P`iWe)ok5!%E<5PqWk& z`vptz=}Sz7eP2vSi1Oy0W^P)&y>vqrvJr-H%6*nIojoDDj|)I9p_mR0HxbBLzAFEB zD~WD4-96uO)Kn(>jBN%R+<IFbeZ&fCq$a?T#&zcXm}G0Yxfs=1}U|320wq)`c^^gPR(BD_!Np_0gwNEaqz-87!0-6 z$$vzwz2YvcJ!H>8kK1r7(^&3MKMS9S8F1h8ijVUBO%q{DVfuzpYcwcF5^2k zf2^OC`#f02w}=l6H|QAuP(x!uXB!OKS%gq?$$I}(17v*K9K>#EOxlCevn#`fg-Og8)6DYJ!;bD85cVLChuB26n}@h=D5da8I1Q`ij@ZD=Y%8I*X%}5?rnBP zM|@j>7wt6Q&^(`~euAWsk;;y)7B6F19WQN(d8cj`V7MC}3P6e<}wnV8*n@c>T_!5DQ9V+Y{DED6zn`+xl@ zCcITieBiwm-^SGcrh!JTbSX$^RwG);6Npc!_lPbRY#RluqTVez4SmH323-2NH2117 zWeM&BnrB>JR*vG~5`mQ9BbQ1!tuBy7=#vlEA`%uNf{BYhT&PcpqBd4d2snwJN?6BL zb@`p%c0BN?{MQP(E|`gO{>5`AJ%5R02-q>tdKDTYOeq)3nBakOx(emVG%_nct`1 zZ#2pmdO;{eeV|gL{XHx51?i|#(yA5Cd%j# zJsc9*{$5IA7E&QjlS-!{yp00+c+zAP^1DHRj&f=a$;w}>ik{FI4QHq>k~6!Q2nl)2-3aHQv{*Ba`UNlZI%#6MlLSIlhs|F#k!74AS8<# zG-mJxebnE4>;14B=xg~qIDZsK4#(7uxW36fib$G_s43!!ysdY;MWZ-S)9Fm28IoIG-ti#wL|JHc>>&muV#(!SRu;GU(%m8a| zBZT~R2@@CdTq{o!9NS1bp!50SaWsLdTDy6}+0Yh8;w*QYC!b(>WuVo!zo71jnPk&3 zz(G2bqW4v3v-``IkqNbr81Br~q6LA&BA+jry|wc1;Y21uv1G9uZ&R@^{*l%MpI9!< z7{-Dk!CTWkxpmd|n|}sgr47`U6tNB-sqL%SjROa*mcfD|J4Rwj?;L3#Sx&bsnHALu z;nzaSP$`m=XNT#5#CV5rTRozgGuJTzg>gK;0@?-yiYcqkTAmEkr?9QxHYeQV_qtsX z#07f{0pTY$$!c@)C*Bv1CHUaopA*t(PTDIWTA>Y&j8jK6HGdN!)$V6*?j^pyj?q?q zpir{btuj@Dzf!l0XbPP=rv&OYbXJAsOX(d;V-q;rrFV&$3Ulb2w43+nE$wE0MgZA&)hMCJ?Ilpq;8n{x?r@=#e}c z-{0`rF{QV4_zndUR|BhX!Ll3=V;CFnfUD~7NSe0rF1z!6OuFD?ZB00js0p5BI6Pk| zZZU(_6Mt4};1W7WvXPA)s4t@eAG|TKIq;a~7sdM(aIA|_5eQmovQh8%dD$Gz5k76m zU2vn_a>bV2=vwb=xJMWRhe70(!>V=@M&!a`!Pvu{v4Uc$3C?EtIJvW%(j>igx|K(};O)K2T-R#x) zD`)J8{Eo*fAe_4Vl#6OxM3!IBj{)n7RRZVE@`!z1~=SEkViBolBG@O|CDDF(C+!)+zE-Z&Q0t)yOcQ z;xTPDwl*~S_?5WX;Wox=9;4|^O(JNRok%tD2R3P*kTaZ0*#@X1u9ZWG{cTH3*)mWe zp_dWk#y?8IL(KNPepdY9Rq0Gk5sh@zStDQ4?=HbigZZe((-8aBdf_C6elr*CmYwE zYGqy>Yjxx!U_M|QWi;zuN0hB^mQA;%TK&^unngjlReek&5g8?HYG^-{9eJy#HGijy z3h@$M)*IEKn-lYKLA#=lu%@B~Tt9=@ji!2~LnD2Ao#*}9anYqxf39cTMKRuzt4GnX zU_mZX81?F?F0b~V9Xtbt#Aif2R@GJJ$$lZQu9yABneqD_mtO_DBy4EJD*T^!&Y-;E z+D`84!$6#M;*=(NQz%*$R0-@AW50*<- z^?cu688@gRe$_T54kMgTHLv8ni%Wa3L#@w-t}op1S|P$`de4k!{V zT^89kA{2$Bs>M1)NgCU5%YUnLKQ>eM^U+*qw#?sXS1jBMdX$@(QBdW)JCG5^hjL*p z*lk*DR(fTefcwW+=uR?(th3k;Ql_%M>ZM zi#?1C4HYuJ${E=q)MzmXPM-sS;R3A){{i(`^Y3YymHbV0^8AimD#O%Lh%&30c1}&Xx-<0RiMgUKpGfA2iaI!;L|F4hzVH-2)=gXU|e`>8nnE zus(|UWbn^pFrS|fy?^R<(xBQjTG@G7*!eIF#pW-s_Z0ttv0tD9o!(Ym8>Cm`hIRFo z-HDvzEe49w($xB+R|aZVoHpX2P#+L5R6C`1Kp2RFi3$4LX#yl2asa6(i)sa!R|+Ht zu=`9Hxs7~Re9j4b&b0agrrFd@vl%=bu?HE@ed}TEV5?X*8W^-z=C``L>zVu+7_5fWT(Nt>ph*%&JWGWOnXD>kPdlq0g= ztc5J!*cOWR>7?D4j#1?5^Z6^Y4sEm-eXika7ZJ Ks56is2t9$&I^opf@E>sLsT zaf+O(VaAxVg@0#7K$I1eU@~RU>@cLMJ2@6Z z&@OOhO!QN!~7kUDixAWd6|f~K1(AZ1WK)5?OJVOW5hjy3a1$7(u!Ts!p-nJHE{laGiu7?f zy0n@n?#0c_s-GD*3Ij3E7rR=M2g;;&7AMxXN7(AFY6zBD@N`qe&U(B3HYg`4I44>| ztf4 zg^LwV_Riki%&H%1PRp>Oz5CeDj6yBqD{NgtdkKz`f1?+2ZlZ>s%XtPTflNEvg8Ob} zgrPi>`WW;*kNlbb1V#8Qb8TPHvGq3<1~vPh^?&9$PKy^?hJYEjjdGrwIXY?dmU;4? zepOsd-+*y2)=?SSMUv}zr%Q9O%;$6RA!Z@IR3BJTL0IlS)h^Y37waZSkt!LJht~v& zQ$b2Z=n(JBfjT#yjC80gB|o^3+>NRn{cUcmpQOoOBsJ4{yQ$a61qCw%YfkYm92t-Zm2laUzZYUf{1^(A>zoGW#qqj#r45#0cAn zf~2r}px6y+TiRi{aYygRRpA3ssvJl{8t=!y$DJ!u4ifpd>+2*X!Z^Q#&s2d=mxnNv zZ8r@Xk@puPOVtmC|KevgqxbD0i9woOG^9$}KfdD}9(HU0@BZeu3x%+(gQ>xG66U)5t?dU|OV#e`m9#Y`rPCK$L?fjK{2x?U2)yQbp#F>tN6w7v>u=Dtq-N0_$39A0Y6K{SJIQ@caXfwN*QcsjFdoQc+8xe+yjVI=)D?J9zK2 zEFMUX+6DB<;pJLsU}GLYb-DC+cM9$(Z7+Qq+!GY1F&1~0?k+=hglE=V%705v)X>lF zpNg?wu8F{Sc@R#NyPtAyx8xKh12sg#U;gkG=H5Xc3ssxZTF;Xu^4P>mf5Nij)Coha zb!FGm<$nP453!4ZQS+YzmF`rha7c{(4fL$1J|aDm!msy5l93HZ6adn3r67N+p&0=R zf4{5j+u-9LuCbE1HP*PITz|#W|2_P47e$^PAwl-g@8qNF=g-dUN+L1GxU6bddzf0) z-0aXwU1G8@)QS}gFKw4Bw*m#^??QNVGFrqR$iRyO?T z52KW|RyMvJwPR@<$`XGRmL{cvJhkv0+qQxf5n;?P@ zqS3BVz02prW~jQTv9MfY#DAknTvX6^< z(>_F=n4EWPjc45nJB-kdf~XGii3@EVhXxrro#q@{3|w#plCI+y;|7#g_2++-Qzq9} zuhr9!c?Pv0H>;#J$A8YPjSHAmkg$Z$9PS82v%7x(E|^Y*)B)6Vy@7k}ZC|xc%r(&l z+ay1EH@d=ChonAp#aLI!KCuM@ZcU}|;x8$;*g9-|7c&qPuc!%=kz*_jiOIFy?Q~bs zG3B=)=${5I;*k_i8^OG={@TwjQ|5jmXTbOJC$$r~6%JnCSAS6x$3m+7_ixQdQbqAU zy>S{;{D~;`gJ4VcrDUBdW=jZ_Y8OIG3PuI`5eUl=YAUssFwnbTek9t`CN*k|)exAB zO5n`qDD;2Dq5Z(9i}b_p0G_$b3N^Z$E((1UJ9s1N!vN&W5WXk$E~2sJkg-cQ|kUw*f?qCOI+C$KQv&5o(S zL1dq{dDm}0e!^)U0GU@GqVVp%`p18L#XgG!CZqNrcW&090IlgSD5Y2uwvakfJD{Ba2O&RS=w{`oA*@;vd9v>&zk{!b^ z5M$HM_^8sI4osxy!)b+Q$m`ucj8@PJ-xnXV5m0L@=WF^PJ0tTKR*AAH0<5=Cgf4RE zPhKTM^a^r#MkAj}giAy>Cta+4X32v2hiNAhq3g&lxiR6bD2iV5;2PVx=Uf+g!d>q2RTE3>GF!z-7LeM7Bd} z?HV{o>BtVf$(0skLo0$2Bp=8dBR4vpbu(#U%lcVR>LUaOH-5DPIKnZv%mb9v2!GV< z9;PFFmlG{bhHg%w?Xq1?ERH$Z!Gx$9m}x4fa-fK(mjjUz_KwYYk)R^-0yx)myFkj% z*wJc534F=5j@|IWYlj3D_9gtG07p{m&U>%Wl{$SKbUxb9IyJGskIinVk4tAlb=fd& zkJrnqgh*Z(lF~^&F*V-InS{`-pMOqm#MN>86a1<8CfKRsN<|-Pp)gG-<=LWk6%GW> z5x?XvTSlyXb86V*vj0Lhi_c%P6E%2?&e#<_&uFE|hI};FYTTL~Mj0STR{{h<0v8a~ zqHQwLKj!sFlwxPCv#?glrj2qLf59h$ASLcM5YK=@CY*&g@AuomYZl}r!+)k~zJER% z*N}Zy+rl!w%V0m6lvXsaFkb82{T8(Y0@$hr&uUJ>VO*Q{*e?bNY79#2fX|)_ z?$FJ@@tl2QKNX@8pCu}{;UYNs3gOBL1S*T95`+ypviQcK5fK6(FFpm^3)pUn^E=I# z^YJ96rJIuXK^3nZ`^eA`n18M6$)^EN7ZT!g&?m%x_6-X=nBLC8>bx{>6&PNUjqw|{ z6MC#_5d6X67e#UXb8G<3wK+$96TI>T(lRvMoGj2!3VuQAN%2$LuxmEFX#xtDxBW!a)JHoR;i6eeuz0(AY_5XWj?vFw8Z~R$iL!v~*`pk(w2#DY5FdDnx(d&iTCOIe z+aB0osI{!XmqMGDeSc+iiC=%WOigpXQBS%@)HI~vnuZK^g(Jil`t+(8r{5*L z-~b!HMHH?2V}WO53+0I1tib(I_}SUkS#h*EfNq+fDf-WQX`}h6004Vxl+n{~6=f4b zkg%HtQO-xnsG|C!$uB{4l%7TtDh?eyMKoM}E${rhyn$@_$bVQ+k)d|JF412O^fEE2 zHKu}F4o1`%6&$lQ?4ps2>H33stn#`M@q8}i*u?OiDHZ0U5v*f$^)(?q>!jx89I2Xd z9h5Dd*3R>aAl*LM=}30}GuLZL6`Du1og?{!e7xR+8&4-q0@hGk({KWlEaRzL7vk`< z@nxn87(E@)_kU@Z*SXGLsIR^|ZEbO4;|}{W`2!7ho*X+b5#t~$F0;;m=kbF9UUj5% zV#Hd1_SeUEQu1dbvNgYp+4V4NFjE$k{||HAm1d7hCEV+^aY+5%Dosj2cR?^XX5b{l zM0U8naL~P3%f%K1Gy|XalBnI6OId}K!cx1p&0A$$LVwe7s*C6qUEPsC8^cKIp|LvT zh74TXHzi|VLi}tB(+5rYT7GtAj0wzNAg3Wy}i+3+&*qAGo~LbwK5qF{e6~q zGr!w^U)YqfFztH?O?P~)iJ1kyFmhLCXm7?EHxfel)O#wjiiR1A5tWgS!#=S6Ryi%ME?>htTFrW8I&SoxNA+mG7n z>g$3P3WRgzb7o|yZq_hMFvyq&AwG~tpI;&7Uw@KBlBrbF0)LB<@#ASUNydQa&Om2= z53D)){unmEYnBB5!Kp4P>RZi@luE>_NHySkw0RWN(e?;cf<-hiRebZd9Wov1{Z>6= z(o;}$Hs&lFzRo%dV5Lf2L7Q3|QhxzaG_p1kGF&(d3&?&>9>wZUQBxG|=keuOEj{?e zP=7L)l&uw@n;NhRAm**HrTmt;PljsL-$ENMwN@!B zl96Vk1%6g_@&BL4{Gbk5he-#-Iy0|;32EeKD$s{1)t30RWxrG4NH&KrRl*GwdNA(x z`=rqGHl)vG?CRnG7}pBWCS%u&!Lcs97k~cGL$1^LvQ7wW<>L!M^}lJ4F;bxDrE#wU z{^vuc^4Xw9u?VCbDd&CqID_lh1Q^Bv*Up{{!J=W$ z4eju+;@Eyrhe{CVve`JHhHAD~DKFl8`jN%tdhP(vH@~>xKNq_ClKeSavXx?qUfsGT|s?jvFa37k`x`>4oX?tl~ z$-K7%^remaxn_Dn=7p4Y7{`^}XA{^z5akb-l|&t zgQ#}=L`dx$>}$S<0$@WqmXz!b_+^49d#<|x$(TowcQEnT-@#=fO@I5fxPBek{M{f; zV#~vgJ~|u?*=!k8vgg%26W>klw10sNHqV{0>aHg@yD71lt;aqXEwH`SJ}s!8>kl&W z$T+y91xB{(9+zlRRj2{}j^w}DL13V^fO^Gfg#VUb*^##z9w<+$V|A`rA~M%Z>9Q25 zWGz6N8yU{iczf{Y<$r2UNwYIUvrGr%u2Rxz6C?d2hm(V?7w%UM9f6VL z8|P*HU(l<~-5tP{=^|ez*P+LC8UEHB6L}Eu_zvbX(kBIi*Dm!^Q~^0zv4xQ=?Bnxe z!q!*7%P1LdqFzMKf{tDz`YwbAbsz=iWOA*fKV{euyhZ@xT7T{P?>0E-sk^hbmw6Na zD5E6+z9fL_4YHQ)i3^{Z=ztir|2<)yz6gk3Za&BmB?lz-xAat(-?i$ovlvn98*Ibk;zGvYW5-aJICU?rJbD`loiUEnT32wS01MYmjvuz%yiZp!#^6N-m1d@Rm=#Ws;E zH-YuN^n)*oQG42)uKRY%2tCYlck023s9kiSi3b7Lu%&m-k5>#2T?O+ON$Z@0ZR`;7wsYSzC-ylR9DjToZoHLjAuIUx zVIXffnSTZ__!h;1fHhe$P76W+V9EakH?~v%#mK?3ZlSX}By@)Qp-4x(lNnF0gXY*u zUO_yq4t;mOUseE=2NlyzKpqnic)|D)LVd?VhB}xQV z&3_wl(?V)N&G=%dgACM2r2!$~;RVUskZAxnf-hce_FgWgsOn+=Ngxih3h4P|$wmI{xp~jlqthAp zJtxV~Rt8Lw52;J{%f`c)$fR9mDB+hm?29|{;@Ro_b1k2&n9kh1ni=oCAXA8!uTNwc zA9R~1$1x;9UBNF(E@YX$Td(e+(SI}_o#_-iTTwzVz(MUnxw@4}xFCESIPLjdwG*Eq zzN%ogH`>9(sLzHgRsB^;e>TT#%Hx*p&S&8$t_)9>HFwfU2AQ&idB1|2(LUf-wL-JJ z&5-T93W|e|RQggirMlR*!w3*;O=3$vW+3`!R{wLEh7rN1bw>@1?%G}iZGYjkFUg|L zB;n#J)~6)^86ss9Wx0q5FcCVi21n+$D~>Ca;Otw%ed9@69PKb{f1XkBdIi$)?l%D} zF{cUiTvI;6&FBtZvUVOYEH_bBm3&;&N?;jL*s>TOChuWGsn7bc3l90iQ*I|Hj7*2C zv=?g2V4#MYpu8Y@Ce#9mVSnJ{Dw825f+&}sFS8-eg}AqL7! z4Dr4@;%xMhUi^o(H~>Z$i4*Rt=|>LfMLk|M1cYlkwsHQOd9&E~(SH_q$?_r+CrV*x zoKpj0x54QIV>HHVU<&D8edk53l@q;u+5gdX%-(`;ybgq;JAMWAOmv}&)6)8T4T>eX zb#2OWE)i|@Zr@}?mT+A#JpNK((D`o7dDma1(-h`y_c>K`O}Dh^8Ed}q zfG@N)mY5hcGm{bU5`V7*KoO=+P!glmnX;~pgw9n~HoqkbhXmpwf{V1mjibZFo~Pk8Zu#NKIH)&Ov#5d^u< zHP_e3$bU|p-iMyCBVr}+bX}fc2g9|lvEys$=pvgyKL$Ti1jw<*Tpks4dg0DS?GyoC zN76WSfrq-v)jGBrj8)h7^9&Py584t~Znj^9MRqbKRN#w{5ocxFRuL~fwq8?F_(oze zPQcgwMEyumXgeW4%$NGu^1N#K)3=^WSW>Uf++lH<2vRtss+emR_@e4n8_{6!yYIoI9%xC=gAJtFh<|+9zkDNkKW$XSo@pZF2NqanBXZ)JFKztJ7x^SGaHN*^dduKV~LJWvVu)Xlu=-B2u+wZ(dIQ#AQHaq3Sihr)5 zWBwV|Si2C?&uoHF_~9miq2GNoq58H;0W>)V=JBhdbM(|-c#b6XoysCYeKAEu;YKdI z9Q1vNPMEwQLV5j;m0S^1_RayqO3MEOp-xT>NS)L(XDj={U;} zk{8ljEl9nixkRpN>H`>bEs`7FfPc^jv8}iMV>Xt!9;&A@x-wk(Q$wscCe8A-=zM@q z-?o4p9H!eBobG$OqN%H0xC*jQHSN_F_ep!hc8#*?FZB9-b`MAL_Ii?fyQcugN@W~= zic&j?Jt;Kn6@EI+d|AsDs;*&!{j@2%U;43zf@thI$0b_mlg8D%5-oS0cYk0t@4ZlX z#@qC6>SXkuEL}7{8zV2@kHnlfZK)-(UY8j{ zDhXPU0osUN*Tw)cc3x8ieSb81s54W8*%C%JF&O`%_1_fng^YbZ^Nun;>T?f0&!`$? zxyDK8;g}0oMJfRv@$_$U+ky)9+p}#Vw?dxkzv8RaoL+J@MyHRM9Ms0)npy|U&NZJT z#2WSb7t7XN4sE~gv21M~=L@Sd!>laKuZ%))*$vQL=;!-=gcLo1au3Y%Vg(N zNjB%u?Ch3K!?&!>BG+X)`S~y2vzSfUoX(#L0AaIK3(KISGoDm zN^h?oC8W-;AiD~x>c9BJ-EW5(ei@z8IrItco05JpOl%)(wudg&m`6gNAmA?6F;4+4 zOOi&0v;Ycs{(r=9Z)dryTDDKq+9MSaza=`wV7P(!9Z=B>+RSB_xRMtZWX(h$%TRvH4x5bWu(+$A_p; z@F(aRmwZ|AYx zC>WAxhYkGKlk5v%YcEY2{)oJnLU6oO0vF5-H0k&U(gkTH%JWgjpg^IsSv#;9^K1|Z zNiMDHLr5qZS`&4nTwx16=sVJ=6!B_$%itv1*Dhc$7||LImdIpFh%qEe$f4Bk3#+47 zo{Y$k=6@HM-ATZ4#NZiV9dM1p-k5#1k>b87qUaQMapj_|uar}Abm+BuOIz(p_y5}( z$P&wn^61+kV^_82|A7Ra5Ex`sS+&?K%dC@f7}<%cfD+461%qm;H2uT1UB7LYJXSr!wCCXHa7;+3_gPkTBj2N!)Ew~ z$-`t8<{QS1i0i97v}haC*|cf032-FaREk?(#Xk}?VgE_%F$cEN!q3okHk`!vw_G}? zkS=b@0mB$rXlm>(o7*|}m<9^HZM4Ts@JIp7d%jd3M;+phGY*gZy6VV8ubp_TPI}Ty zm4D=a{zQ6DjP9rTv3hwZ_AHjpabzs*22Jj=q+Iu2nq%3seqh<~s-unk4f#M%r&m1h zRJ=TDGCKT@BINNZDOs5|^{8*^oA9T1tTWpRl)~}GNX6+9smYvvxJbTVqwJb*FR;lK z7WepW6Are?nNY;EpMu7B*cT#85a~E341a?Y1U;2qZK$r6WrTFqZ6+EC9PESBv)v)F zxwkHx8Upz;ORn&184x5hsK7*-bhom1j>cIi@|q|*uuwleEjLjTQ&hh}d9r(~ii5+C z<%Y#a53TD8?A{GuC1}GymyRJ3X3_xP8K`vrIox2th-qT$U{)>BxV#r0O+Qd+KYv$Q z@12=1RgOx&4JZO%ifj5$Q+X|}eHhYhBV2dTXmrnIysvRvw)|57=D8lcurAiJ*=aMj zU26{NkN=tLg_nD9rX=8-(An?PGWx$|CW|f*qa>a`3=CtYJ1a>E4gp#L+yzdE?zFYvj(MHN|9#4Nj$XEKc1H z5Ue+`^Q)#VFjjti7!%UN`WBHm%xLZp@n@)V{dM6B>02?0uKiw>Q&2fmrm6I!kS%_+rs{=sRd{1l{|Bp2&J)@G0QV2ko{F<6M;qg z0~MyDEtyB5TAYAU)r}pV7)&?aB!~h=D`#^VY!|hSh#xFq7^ZcTQ@($GFvv_uXyS_; zUm-7KfU-;cL(OwTNg4?^Fn?VnqDPZ&SeFO{*9D0#b3e1m*mTX%Ok$48?xt-tppZ}^ zg+>RUsD)PK#+%j6`PtDUHJ{o={9>q1q3Vivc zeNdmxl%?EL7|?=iM*jH?ckFiT4aqUfMyNBhtv;Hh&*P@3pNZ+;8h>z3w5<=UkW-8! z47+$3^#efX0Og|-!{8jCo%QThY4CGGa?YIGE{(K!O!~_b^?D$X@sj7-%D&QNg?mmK zojsbvH_>u*HqM{ERe`~5fl#1z-NZ`CT0LmyLcq!|6`tUcJ`UtPi=f_ALRIbP$2-zc zjfi4$XINI*qZ+2y`hP9HND)oo;IrzJsILXG1|0Hjv$+Qxb6&*cH~~Kd?E~`fQGR9o z`YBN9$uErX4LEbo4whf1Gx#}Faz^k)2(m~!RB*cXEBlc@qVU@P1*`-RtuYJzCF z;1zco-}Wtpgj?Ch1~h*R=kdMUJ)h&&NzPbBYi_RnvBk1UlRHk(S{tO>k7iE**I@h9 z@`L%)>Tk+l{HVpG++*F5dPWDt3xrQ!d@ul+1%r>z+ldp^gNdic3w7Qd{7cpg>uG6! zm_8`xzJZrjXI1`_v>YMj#~}2J@~c!?H#9F-Wi_8COH~}?>oI@wJVk9AAw6?w<685; z#*FKimzBoiIX)2EmdbVVL-e+`(&--PDNhAf=JKg0Y5IEeUgh=%i8DfnXtcE#*0{gJ z#@gnfId>9_4|0#I_Zt1QW!icRG0;ZavHu2BEl6kN(>Wws>WR*w4&NsInbot)8)sMe z;|LY?Ou@D_q~(87;%5-#_BV~WUeR-XFgOI|Vw4{}^%wN<)pu29<^6)`*)wMe8^>v%Y`p2@<7)H2X*}ZaDQZ9YB z(#|jmUgo}s+}6mj?DiSOmTE~B%|hsd`vXSq0He3Sg-?I`WBnfq?Jf9y43$3++q`6S zER)HeF{dRmJ7Sz@H(8TBdY3hbSSdVOSB!~QF-Tk&T$Q)(xH(*_nuj^HVav6qZ6)(- zRxz}#?jXM|aY+YD0${Lyerfo76*%jPmo)~q8Y18n*cg;jCsjd#=!(s5WZ#MnH*O5u z4G%2@2i<@BeF$bepcGJ4`9ov@p@+WYjRTi@h|8fYL+U%2Y?yw{dIKMQnkISf$U*? zJE0utA5+H>`W|BX>7?REXweg`xdcdYAdpdR-2Hz_KR5|#qk0G7fEWHj&A&h^l0pm) zLf;t3aL1X6C#gr_WXG#rB4CqG%94Q`2g%wEj{C1~ywRDyia-!JirrNN)`gl~j;6t7ym9h7ULzA6b-1&nFeu~v; zv}1p44B*8b-uKzFc3_?ptz$U;%@h3hXw63I*B;S2Yw~g{=D*jf)tohX{Jyp7-;Yhi zRWn6cE+zP}gTF=ha5$Bt>N>Q?VdvW+b9)a_z*|(Gp1b|1-LSs3Y2AomgYnQ{sM95F zx=7pL4c9Gkxdcsi)wiRunJX4~vIy>qyWf9Z#d|*KOK0a^O+A+#1grNg343ka(dgB* zBICJkY>)PR)-S~?&8hOgFUaY?BHaIlES|<9yt^?iB+p%;9VVqevpm7@J6Kh=7dO1Y z!_;xuAm%g+fi%WA%$}?-Wa~LTD+x{`m*o_(hLAb|hbgDI_BzYQIaT8lE3Yiqp^$EN|Z)9b>euKj#qVJ5Hb z46FD+iucwEknx$eAP^sY@Ps)cp|#p9=11hU6-c51APH7(Y~aYd=T=o*^FPClUI^v&?9KlDg~>c=nkK0i*v;9yIsbh2XnYJC|wiG?oQ({nO>Ibrb5+} zkmJpnEVI86FmI(>scP`=Tr|XfhjCB0t>zF&K_9x>AQd#|u9212be)6W8?RF0x1$zAG)OeOxxx z14l6ghL`BrwmN$vOpl2j+nXQNX~hi7=Xv5pr|X9xlzF#Bw2hFN4Dx@!LgI!qP~XW5 zCUQa}VG4;}^Jp+J$7Xkq?#@0$eJtizmhu?u8Dh?O1txEJZ4MLNw~46Wjm2maJGNhC zr_Kz?XeVj2t-ZiZfF77vY3X}Mu0nLZmHE{271KW1Vi)yPW`f>H#HN~#2SzDJ+U!}@ zmDQIxw&^)yF74#eM4UPMV<_1Z8zcKug{tQ?ySLzz@_X^Ui%tR)ORc&nzLgs`Fb{v!Pu7q1M(XW@1&i zlT7XrKPRIYnzesq7YV_^!6Fadvz-pJGleW-@Mfv=x09o!gt~M2RvZb>P`{!LV=$Av+jQ|$L17Ap-Cnagmc~A#L;wa zEOn{CW*zIevYg4vKL#}EHO2rCh@txyR2hfR#98E2q{e*^kGTFWu-GnjMA zp?X;V@s^y8GsMk8$(7O2Otis2){up{cCf`@GUtP{Q{cXxY<XHwT*ibJm5i? z_C)K=qvL<-g^!{vuMgtbQ9uu{VCfeko28#PhrfTd)5WN#c+Jryjs9qG6?sCodePQ%U_n=cpoQU-Buq zE?3MOJ>6WbvppS*xW~9d}I^_q;MHoYVQMFV3P00}&^3sWZ(2mLSMF9m-%l=YLiPgZzw+R56_7FU*EjyDF(ea?I;Cc@-C z6ES1|cPZPKL;YQe>|nD%y)?>L3sAas|5Y&jd>MSeE4_B?+kZl{$wjR8Ivx6-4HQS(W$F!L)`OFQlkKru%8m?EP)QU#3%E%+3x;a&CuNM{7p(P@h%t6}Ok#hlfQ6eZgT(R&yPko|El z!bHG6)qK}Tp_ON0^rZw9WvXWpCCh{2`OtDJBa_ub>aZ?4g-2}B1_m0$M`$H*AH6>R zY!x1oAuP<-`(5Elz#!F1c^`i{#{hr3Kd9;hIFqGMbzx_pg#&eZ?-3b({gQn(ylYL5 zZD)hRy^zG^Y<$Li3CwKpQL=CoOU%QlG8yB=u4VLz37~4rv->=_iDY8T5$3=v*ZTQr zfxXV0gj7&o86Uv!Zd(E5aosUB{q%Jeo?hwLVBY3CStK(p{IZ8sv^eDHgSLMt?*+(O zgjQc4j_Pol4Wr1|u*}6jMzX>#2j|tZhO-1we_f8G1KW+EGy;n!`5Ocb@^jw3u!fbr zjqCsm)mx~`o5fpKm}7)~JXBT{WW-Bhhh2Vts^R-c;e|1S>rr1?QG0FgGOI&}Y><5MZH@?YBA67Xp-+l-XsyuW{N0PLj$#G&%{Xfah8)JgL2X{v8*QxNJV`ez8CICt6O&X!@Vv|T@1-@INui7_)`;B`Tgtw+*uYg>-~zrLXVy z6jr*2p9*SWcIdp5Di7o~AWyUiBnI-FI6?vyQU~lYV$^>`wudAafoGhk#2JY~jvwU22)i#g0N^uC&Lnad?x zOtB#ruWWxNH7DIyzHb01;P7!u>-CYS^l&?N{k`(UVI-WA^@N_9+Y`Z5i0$qQ*kxe* znJO>bEN>ohKJl$%2%2MFGtm)7n%(ltIXxn&b!N16bNYymvZM@;<5NvxLJve>2Y&kG zV5+zPsmC|$st=JU;!>G3>f}*!3t&|DHa+F|$-{pgl|XUiV!{4St=v9Bwjdf+M`%sg z7)8B>FY^kE?eMKa< zek6`opGr>JjCSIRHQ3iJk_vL5nW+VzU?*@Bk4!np))TP^H#lYm(oOfQAc5CXVq_g9 zZ6<#gW>{z3rGl04pX@J0l`5e{mP6;Bnf99|iA@?hIxpD5!t(?-T)iO@VbBWX&${&zY5CYrzB=Yw*Nz z!?8~2E0D-6)T?ALbXw4SLYQc`mRmc!b172 z-WVpsa_IDhSL51id!kjntRv*uPfFO>yNvkrUl#CaX(;W?xyXGyAdXWUmANj~x7~ld z10di^w-s&q#MH#S4L9MvYO-n^E_;ow7*5oaiS2YAQxFD&`SH9EpOnxim>R1o$*Iw5 z6LCxLaKjrAuw0=5?}TZ-N(E*f>#xkSJmvF5q2ime9T|wP<=;(~Uxv09dk(rZ`E1|( z9ae$894Hukmg<)p{V+Dt<}QU2#_)d_n(~$8Nz#n?bU8mhv2G}pZx^jPkN+!h)?Fe` z&%yl4se-p)O1j2vs+=Jaozuz5cP;!9qGdJs`!F@R;9iBUN8nd=@#9s;Mw46{oTCIB zrWxz;a{dSqSDpq%!9l&Nflyy@wZ*bsr54oEhKZ05I-L8M^TGjE3 z<3*LRXz2N+0(1e12NfCHLH@>)kjM;9Kxb1t=W~~)9`p2D9DHkpkShxpJTb2Eoe!6p z49@VC62*CRtbzplWh-Z6eHuRI=Bu3BbTc_cS66E$A$oduF%kAI=_f@tmvGwOEC5ok z@Ylu;-65lz%};j-Z09@xPfugE4tR;+Xm!TjC+`fkp-OJ}ag3jA42gU}KPTziIon zKESdLTiMCNTLeb-xBMKhmkN~VXbnnIyt`(75~ys}oAKLA2a*rbj9ULYWxI83ujCKV z9uCZ=vLdJWS@)}L9O#XV@Jz?5CU_vV-c&qj4?B*+^qG{a2V8&rG^Oz@oNa5U)i#bB zonioxR!n(oLo}f5A<+Svw??%e>G_yF4(A_(8x?QB9DtE-*fULK14zuo27zRypxD6u zIg>G4gmHP8jeM%i1bY9F5*+ihSjaTR zGqsJjXDQG$O~QXQXTO(Xw@Q?Qq80v9$-`0EtAnwN(#WLE8ICYAS7_zJy9m&jdl|j# zjNtNC-gO6@gWApYwp3)=_r~r zy`Tv}@J>OVRN^Cc_Z!G+65@R1tMDdf`DrprOdPft&s-h&V0PwzMwj z0G!XiD1v`+hc6}Q?lS&32llt~4$y5UbSzz>WhBcePVAz0b(+#c=1&-iQ0zVX*f$c2 z8bZBmWmOm{bpC797Z%VWlhqoQ%hXB$@wv^+wg#>S?Bp>?z@OJ)rHzBLM-p>Q8t}oc zY|b#m5A=9hQ*F@$KHZ@U-yPjJq(ReB$VZ###bbYuoizEFe)LZnK;pmYQ?`a{=xtu3 z@OP+QstT}tAu!w@7_fs_4J_l_+s(+&^SF~t_}PP>ZG8Ox0dr<-z*hPjrQ&-;H@+90 z5dZqjmjYABKL?6|lBg3yOzQcvFjM<{lGh8<%yz(_`4adU8efknA!@kad@Yjwg9d{} z`V4;#@t6p>1;N0hcLg||RVc%3#v?OFD)1#;C${+xkP1S2^qR;WIc{BvQO2eS@C9T2 z&VAXunS6}QC=tM5)-Q|3%qak>X5eXYzp#ZGv@DXxS9-Cp(uQ!?3n zHYEqsa?WoP)vxHGQYQhRGp8Sb;+e zpYeA>Xmd%Ki*$nQJ)bVoVj2(YO7WDf>>Y~$P6jxpLmyZk3b)N8S2ym!~Ky83WnVhGG-6rf7DE`EX zo`2pfNb{{fH3$-uCX}WJ5(!zGv?aiG+kb$oOLUg|GaBnndjU{Mzyi>$ zuyW+}aBmU!!Kv_1CRO;Wp$q(rrTSJ2-)W`w_imcK@b4*>!r%dyOS6CEY2(^s1>#x- zwm*(wkLF7NrLh?R8buIj|7uI!TEu8Rf?#LXG@8ax444;b`>5Hkb~HtszkcXo##uPl z0&A&=GjWZ%DP>EoKPI&O0a;yl%@N1@-Zat~R4DLw;Ab7ak>2zEH8OhsN$ej#emusq zk2?qFA_`ib)h$QPjidvq5<*v8K@KANi0gT z%rNJaDFW=w@K{nF;#13D2k+F%+4V(3tLZD?fjldy3y6eg&!{TrR)$GrJKLq=5GdEFRy=FVlrlTSE8RR;)+u+7isF zMll!cfQ&mh%MB6+Sta)=rjP}&nB?DZ(QOvC>`wBtb4^C+(U0Wtj3Xp#awI8xY*Ztf z*47|-$eF4E*}hJWP;e_Hx>7dT=9N@l=cCb4zhhrDHRFHJgERdAo$}`mp2u*s51$<= z;OEYDtMsY{t5~WI8~QKqs$bwJF#)c}zW6J~4sWdVD5(@l-AG49z#NEZFU8h}li+%u zfI-Rvv}41?i)goaWR$-k_fXuT&RT!fFv0!sIV%@p0FgtT$Ro0q1Z~I#1)ugScM@2y zE03tA!0&%%6S*wv8HTz%O0c$N?3FwvSOp)oJI_ThwN>7y2%|-cb}-J?xv1t!r}ze9rCrSw+)fuwp3e{`XZUQc^WNKVoJm1Vgdxp&XXlmFH*4lCVF zZW=}L+721amwE{*S6;m#XpciKWaNnO+1sJ2%CCRN_`$c9`>)}EHA^nncc6Ld#D|zD zn2#E**~>DAdw43sNWMoy7O60y+7^;zzi|O8HNCh+Gg1mwlmxOn9N~C%0s*bigFGv6 zu#gh)nG5MLm38y(9j2P(-|LwNt?ShE<|jHiRwQt0=s=YJHJnV2sAMXwlQY54f7$%t zZxMeWZ78UQ!MFMFtaO}dMu3=6e;DxQyEIXkfw+OU{3Xf!E2O)@E}kR_HW%-KdKo3l zEp4@p>(-!XB-J+x(7IfcP;V*h{AoGx7L@Ef#7U(QqI;C_=oDPFP$ySsKYa0Eo{M(x z3kKa#Rg!8Ee>XIz-2k`ydSSX3CxW+hj%emgJvu%H z<*uaf5K3M10BVil56}24u)&EHhd`KP5veJS%Xk#(VNY}7It`Qsh(<~Oi#VKI$4q}~ zT9Kkq8-=Uv+Fqut)K+aIUMM$9BeK5LI>T!m_e%wXU1pcV$W<(eK#(Q<*|6auEx2!q z8S&dpGIgt*Q*FL6)u3(+z03;zRFL=ZPHDB8O>#+`?_UE7U>4rNEE`Y$JS%nPAJE%0q~}jroG*w7I2;dWgWP|OfngZt z^OwlRbJ~HZtNs^YHBlIdX;3Xu?Lk@ByPJc%r%Vk=s5plmS$qSqA4VsdiAI*qqu0H! zTUuC|-xYG>Je*E;{Hn2~+{}6-8Dmns90ANLEJag?AL;9WSVx66i5QsL6XSp;NP(d7 zwS|r_V1xeHPS$`q2LKIYBx--%B=AXM8BnNgw8Gg;5bh)GJ2qB5k~qm!nn-b*!#wEx zj<=L$4vbvrRqsFGG^dL(P^yXrt(l_Utf@XJisXGlZToKJ`GwG|G-bcx5>)ROsl<~a zg4q=XJzf)``I(AdWZ8FGQ>vGqkdmp#!6?VM?$Y*`{@&^x=##%f6K{W}uDYWE8mVH8 z#NwwQQbkUh-#5@BfSSCECELSzSCHCcE79q&ry--6=l|`wY`B>CpRT4t=2drcbDSsrsx8jDl!u=vR zb9?0pC2vKjvvfDtHx_s(W49ZCOdJEv^<5b?q zX^xUk<@EN>ONmPNxjx_&!caHV2ax!9feD9XMP&+(|3K-UHJWEi8<4E+cKn3Kv6eLe zew;XZl0aX~NAo1zw!5hWgUL~~PNwz0PJ`8D<(Z_VQXsJOXDNXA{+c3P{QCqikK{{8y z-$<+s-C^)EPi<1ZIwc38612S8M`gj7pmzD=;dhHfjmnpm3+MBFIW%GImV=LN%?1NUNS$;pG4>{!N03vyip0qx$R(*E~OXMo`L_qNiG1~Jw|sLsRTuX}$Q%D-Im_!*SL>rqWc@mF61T!;2? z8@_VYo|}g;P0EGw_ooBhrjfllr|kXKw|um^j|Kq2!xy697iyc{YaaL$bfI@peH^2K zr)qF|lIC`z!Zc_Id7l|E|Fgbm2sVx=XNJR@yAoj5)D^p?Fu)64yy8u+I3S_X~Rm^Q*FtKYxi z@e+SCw*{)3$VtwK5-*&%-gWh-~9 z#Fcmnx<6C!=Ca9^#ib@82_r0KFfp0jx{^C>H-0^oT}e%z58BqPLpUiAU}|IOP7m33 z!V>epImfa^tzn(*mRA@EZyOpzu?JU!QqjxTgRiBBp-`4Tl?b?Ni;Ga0?oHC*k|$8t z$>^b=C8#JGLLI~0fbK<1CdH#s0I&rCQUr1lSeE2-zbvr` zo`++o$fxRBXII)K2Y>Jtf5I$9b=ypADyx@Vg8I&@up+ypuS;;7<>0qQU^F zQfJ=5Sc2?xl_}&M4rUIuG)~vf;TxFu`c~(~R%?GB9J&@!Xiyr3*-C%R-k3hddf(2Q zFA)WZ8qk4n{=WA35irNp7eepH)S3hSEJhFZ_Z)chc<`{@ccqW*ju|=yM2q8usq-YP zbp|xK!)C$ndS>S*8z?lO*p1!p=g2N5JRCdMJyqnC&TXeZ%kTt?tPHB{2Y-imn?=~B z5AqplH`;#C$5e%6XXM%TsVQ$G@*LutA`m>rM^`Z~NvzTjllc3Mkna(L zinRyB>jg8rC#q4Wf6Vi@;MWY$H%=11_mmzq-;8jH}b(A=Rki^M`C|#eI*;ngn!Mf z;L59uE6^vRa(zWQqTLc~S)Wj&ofNlGE(>oGOTvxO6)dJUjQwTG@5PY8&xvgK=CLBf zLBBE;)jtc?|KJE?ByEDH+J%}cxik7|h)c(oW=_)K&W3Ad>W5AXnM7_*RO_@fvqpi+ z>tFmmv$4UTB2$0JNj!ng-^yKsETmbH02O-~@&BfG+?v@9<~E-<){*}qbMQR{x#@!z zyWky7o}$-G!lw@sN%TWm)uYem!Q+J^mY-5(zb<{)PN-_gq9V^Ugd>Z{^Ft{(#703b z+-~F_>mt{(0A&>%R`k;ILS`8y1lQG&qm;@FC)BvTKRJJ=v_Hk@s7}Ouz#cNLu_YM^`NK?3XAwq%n$LNAh#6e7w;I+?3diK!4a6xym!RfR&#bWZ8VBRlxi4-*Qetw z{Z)PIb@e!Era)T*HpV#zIuJtzv&Q57Owk><+L3>AX%81|Xorar;s~ z`^?@h3#aVgKLRz|M7crg2oIc3Pvpzu6ODKj_a)v8t%S#mmjJAo_1fzXR`Xa-0zG%Q zHRSD?0G(#l7~fxWAgSLZ^vLBwdm|EVH*J~3!0&B^MxCTMi9Ts`uV-y5U6CaWK<~)` zxk-N%-SL`XPcfUNvTcqJw5g{itp{7o6sjEnVv1unQ$6ibflLov;Damd1BZh1AYwI) zBwDs(Ke+U1LsMm^BY_UZ9D`4c{REmJ=IT_!t^G}Rf>MtTWshblFoG)#p(~zuof_D+ zT1t+8zuA+-q`|>=jQRHYDf)mPt?du!N)&&n&2U(lY;?t1=QEiKUQz>PZFU-0h+HrO z!)!Q`f`M#)S{Vr~FJ=-MPDw7`Gu6je_J54xRWRxIURM&0fBahpJczFuq2fMFgsr$Q z?AYKEU3t~V%l9!*H*j123$YTC(78C6x2NB4?pi-9WvW8wFL%~%RzJ_t#F33O$V7i! zhHU=CO9R{nun06@3|ipv+~z0Qb$Zw2RllAYF^zuVi_n*Vi@|R! z-^RQG5;_#TmF4?C0e=R7`7;QsSZ{xIAdg801HtFPvQ?AzuH1#nR^3xfI$fD)95zFQ zs~PN+22@6f2dbS9Pgk>l;xE+<>Q(@%nP^06ZereLx1C?eQ_8~m92EPZ^3CRN3G}m| z#B1$So5P%ZbfeEB%>04SCgPs+edR`?X@Z@d|%+m3TpA z`(=PYloLgu?ExdcFk3o1UTS^kRlPWK?a16Ouj+olp`tsp=X7q@;>P2<9OqpCDjXsS z9vgg#*l+@0lb*`v7fqJO6<^6ndiza@-6*>N&){Ki6TloSaDVZ!6IU}Pj}`CjXBXG! zp*Q@#4vjIjXF0>C0oq;{8i0QY($MrZ(9H9dCf=Dl*%Eg4SookiJd2mUpLo_%mWOo-*HRJ%khj=OJT+yb9)KJ(LfCDB#oUGt_ z;=_Ny-hAnoUrX&`E!2N>r5o`{yK6%q6~{6Z4WbLpB@S?3MD~~v;>1BV2Z#luMFYW= zY$cgGTLe4_JT9tNV764u&EemQ6K9itx>nVSJB3H|pn8%0SbccS3 zrB{!8`3C5P1xqXhgCdpxrA=m{qbi#vic(; z^K1C95g>&kNu7VgLfyeH6H?%?sU^m$a84L3MvIpK5~Mj2sz-;xD^^(9Sz{@TnnJPVRX{DGb;HWs7Z>pTJSh z35?U?ed1oTO4aAnKQ|R=bV%`QOg=AV!@@Lq1$BG<0TF+)yXb%8eX}Jbb^L4;m}~%U zY&J$CQG}-tk{^^H!`5T!4*Yf+?&(e9->w9|;x!>l!d)i0Je&jZ&=d_y6GMLx1ig&+ zO!9?L26gc3v4UlOC&FrI;F#R>@$!zU;k7)t`D73_*#Ur`#5xlHWD_~_FA;TDlCQ-- z(5~lO@v?tVn5T;-qhRt|s7x(6oDm1H+=7y1B`t~#*gCw>?bOE-5i_s1DBJ(E{v2Er z2_>b*(`@Ds)M6c4%Fb`1YL2=z%^E??6b)ktm>u_%-x@t58UPl+08o4UB?J<4a=StBC4ltJd3&`5JC?(1>jNmTso zb=397+WEe79OvBvFSQ>8y6YmL9{F_XmHqF~H_dV% zRkVL5Zz?Q(iirKhv=`B2L_mYZ+HrTC-NwQLx9N?^ZX>0cefFw6)1hxad`^6Z!_lLV zusix*14z7gNkc>c!E?!h7i7m*-ce`q^O@7PYnCI{LchDtydj)z!%zB~HR6raT0UK5 z)F9-}HfbJUfIw^pD^H1Rk7pB$^ zgRoB~;i>FCKXyn{m=UZk!f+6heUJL67*t$|#bfugCiH4j2Eodqw*mavxu*Qb{CPo4 ztr{S0jK)2$R@6D9bXqC1s@L)@TwTD;Z0*+oA(JOZ?N(DeEDukvyf=8gdr=aYdNq`K zRbnbl&Tu*g@#4q2s6S{wcwnSye<~op_dacL_#%ybuEPptZe(+Ga%Ev{3T19&Z(?c+ zF*P@rVCw-Q9WymGGzu?FWo~D5Xfq%%3NK7$ZfA68ATcyEI5n4_>j5Z#cV$qV-Ig^3 zcMUF0aCe8`?h@RgaT)>ycXxMp4G`Q3PH=a3clVF?y>sVI-I-tW&5y2n&X%>;-fN#z z)#N0KD)d4ownjj4TaY6?GXoP3;G43#qM^05p^1g9EWNO;wF%(E%nnaZE@BTfbhNMq zi5fZrc>wA_6M!ht7{J1R0$}Fm=7uK+h}hb>+FO{JI|8UaFsNy1>HcN;D+FNV`cKbC zrh|nU2te`i;RLj{wX*?&96uob*NG}XAi&Wa2r#v<1_DGB6g8#fB>+?s^4|awKoHR0 z&>Eol!^qmg7$9q53JH>1b}~_*ZQQiw`%z*7PIN#Mb!7UoHLZ`+)iIIvQGl z8~~0$7stP9836%*CKe8M)`qShwLie@>@EJL@x#FaWcDuxbO3vxnW4RjHPFG~1Lgz! zuj%}&Pr!fa-q6m@+V$^j+rOj!lY@n$1JK%(0iK!Vqo%RrM{P3;5Io~wt0Dz5wFNLU z{ljkZ!|tCxC!qb`1ETtCXQ)3&7@F9EtX%;nKvQ@|d0WQ_kCFhY|DDPVm&ok_9e@8} zZ7pwT1N=J)@Xt2}APe~Gk@;`IhBg+~uK!c`zelPA|H1KpLXmPb{1}7~$m~N5CI+T| z7%d#cEnI*miWZK><^WSe>yIh@ZT|)`0oq$zfPf!r{yj(lJu?&2zxhO$}w*|9}3X{vD_Ip}eE2tKA2+|L8={*5p4Af1wBq+qwYU z>6zJC0Q9U(%pVu-gAX?=yXXH<@oymJf1TwF9qlb#0NNjIe`NmE{D1uZb<+Je7%`Bs zt;t`zqT*->GWl4q|1|vNHvVC6|Do#NH~ypPf1dwdbRf_LXbitNXKTzGV1JpCp6d7u zJG*~GRJ*&A8KOVXuDDjUAkU}L_P2LR$Od=0!An&jL){q9TeIuzk=^T#G|ldxPAqH6 z-$}r;Tmny0>aIMrRf<+l+Fd_Jy<())WAzC4^BLK7NG%Q~wcX7TC1t&$7ihw%9ztXvX!`hmGR#uv7a*zp zdQggA?A_qjMK-q0HL(ltKxO6js_@SIH7|_)DvW-5+ddds_)b!=4u7bcTWx&Yf2
f-4u36gN&gnJ~l@?GbK2I-v>6w~XlP13&#+Y)e)` z{6;?&<80lf*JACb-vB!ufEM3J74Rb5Mg7(m3b7OQUdrGQ+x5*6KCpiI6HK{J zPc<2}>_O2El8YQv^MAF$B-3rcy57rli+1w2I_<;BCKR2OvzkeWmVa>I6tMVZ@) zD?6G+(9yX~nxgx-FjZ&7vlqF+9SvH?59LiXghX@bl!(zP-YSS3VOqvtgmCcFIDZiYR-x0eo(%5SBj&tCOZOp9h{`iXJ*V=0rpbayP!cfAV3BC>U)6rr zla@)|@KW8S9Jr`RVC}fguw+|&14UOCAey`9oVt@IHuXq3{W_t~jOIiUVBA6_B zL}->Hm}iI)f=*!bi-U$C;Zm@0yHOaqqU_FDHVbDi4kw|&*D<`kMU zMc65(tbO>vWPb2<{BYl)Pe;yki=!Ww5J&aKA%A*kEQ_aAM76-ar^;{y-*c)jx zrGe@kY=uT1YKVbUGYz9iGP9MOw;`R)NB}``;6*&S20Ej57?{>C#cr5OjA29|^Z)RQ z?5K)8S77(GcL6N9W-p()N`$rDqSD$zSV~9IS!Fz5wc+xlm z$$v#4s&Af!#lH3hd3He3`_-GS?qm=Bi;rOB4+zM^hXaiGB}_F$ERoSC$G#sed01oH zJp?#o*%}hb+KU=UE$f$I2m(>lo@CSV!8X?Mz3)>s0@plD(lhjj z$>HxFd?EZBj0EQs?cXV2{5tOJ@v@fA&%G^Ub3a9i&l`mv<9F$@Cl4)>?0}XW`F7{q zinO*e6u_>Y0aru)+!e^<96cyb702kO(n2lkjA=^P1Z~?o4U1AYujv?do$9A*v4801 z%eM_9ylsBjMPq?bPL^@`NaIumt;`V$HNCqQxmE6|-uC9YWxu!Vqap&s2=(0wHSwdo zHBXrFEiDY+r#H3p;M463W@>Fdf7QnJkCgI^C>Iu@k2ITC=w*T)$eI~69>}5b=HF!H zx@BY}Ey2d{IH zj}-CV-{TFT9roO-?Wz z8S@zhy}3AL3CxnGe|}inZDlwi;W|{Stmp+N@)oMvgq3P@dJ-URJa zlRu2vF3Txdafr#5uYYl--?wpu2QzWI9CN!M`oO~V1~RfLaMF8gj#{-l;#>a5SJ zXZp4wW}p`bTRn*Y%3ODvNgz$8sB8&gw3Uj)klLgcDY~w(b8dT9WD`B+xzv!Z3acSD z5@)*`9k*E|D6S8DK!3-mC7=<4O^IQ4nN5At!`Bh1Y6HwQj563)gtZU8vfm?9?q|kA zak1S{i3S0M^~Qs|Imwd_L}uqkoH}#z_^-z2R1|M+9-}$}4`1(fie_cB)#5<~QDd*g z<>2HA;0+|2T$+~5hM^XuyE9eBWNM_C%ksXO%dY3<{r)wvU4NR)_s^F56)RYA24?}jE?|KU&!V-w(P=Crwv9-tcI-D&YXX&n=#946R1WgX#==JCF4sjjZ>~+}&g)g5Lkudgf ztH6A+iHj8y67eBDpTO6H+H%zp_n6>0X{}0O{AQfJJ35lACc7~5@{bof zv$c7+5$yt6T ziyQUAdX^2H-$&Zg^GY%zQZHn+Mwi#i4LGoZ_;eiy-(38T>#j=!xtkgjec3OkgtOvEMhL_z&H8V`(D}_u7zpaa=CD*Zfq25%b%tIhTVfyNwO3 z0rY82Kuqp+=uKd(hO8#k0$-9&xREIR{$tbMp*R<|J5Kk+3RVwU zx~J(oJwbsy%8QFx`gm7utrQ#?0W97n;G(!CObvJ>xbr)yo2q9 z)^{JWpY5aUhacWi+RCb1;)& zsQ!!L4apD8_|F`~fE-`6|1$b}-dlHAig%%m;PO`8YKx)5guWL&19!=O@=AY5IIt{3 zzD%S9%>yBGZr!iGw;wfxaaf?iuG}A>8sb&$JlABw64$6=BO#Ei*8jT6P`wq)>tvnR z()099r)BAC_^z#7n~(pE>Ziynj+Iq;@q4k8KM7r6hg38Fq;xO5yfDS>$@J0@_%H<| zN;kG~j)c=a!fJ*!?YHFp!bN}FcC|5Zvl{9k6<1L*WL_rrnY&KyMw6;pyATr&NEkNo79#LBHl% zF$0^+{RA<=VqD!FPI0uH_;o6-pp=Rj5+E0=2`+pV z=drs7=2ebG@M?ZLq%^s0 zC6-}LXeE>;JocB6B$LCTh7P4huhfgFI}*^1lUV7?GF!)64tG@=m9zBb5+mS36SV76 zQC}^@^5R2&KDpg&Xr%Zll!&}_bIncDV)shYS-IF$;7V&TabABR#Pa8qYLf`!E1q&< zt6DyvKH9PUSbDK+&`K>bS+S`9=(ti@C5L zYJi}}twJnE^|kZz>YPR98(H0FEcJxiAB9iO+$;65hB#fCKd>q@$tEV=RQyBhWL^+2 z<3+;o-(3PJnBIS9^u%C@vu0&BUV;|%mB-ka^q;?dS$|c0h`u6LLTG_K3h@wKrGY;< z8uj}OJEkFx$H?(U!S04p>e@(MP7aytau5H0mZ|H}P*vF)c08YYF=r$|b4m00f+$w2 z-Jl#NDWIa`O>ho|fF38O85Y-BPVfBLAMNm)F=2xw;?{pi#l|H|0?*mEhfn)DU}TFt zE9YpRTFxqUaDFWB(2?#MW@P8kTqAv|;qMWL!>4;ZCr{?Q@7TQZ#2$f6S~ zsu83|=@c$BWE7F&Z1Ec7O|mV>*FFPqyl3bL^N`>f6x#7;!|W^)`+K* z-#HoRp=E#Sp3Ma7lpzI{4lg3jcR+T%i0)2AdKu!Tq-k`TR;j3t;xLPrJDF6{T2;7J z$iUQsd$-fpy+;3m*e{*(Nx*QMqI7Y)=^$5}vvs=L-I(dh{Rb}O z<_04mCbhqx;%i8VYnu7F>n#PjlZXh!CS;rzw@ zBWLXvhCz=(!Z_;z(616An^~%fb?i(1`{=QnAwwHwYZYV+W2^4LQ^dg_yj5dH)F-?? zd~JWhgyRjfVZO;Jew`@naeR>izg~r12K6e*ImaP?DC}z`olg9KFH|&DmDm;dt)g2N zy;+NB(|2<38gKJGguR}0`SZJAO%BtJf0U4sb;s75N&30HINoO6eAeVtU~;wu@^mN2 zNOI;#2w4rtGw22UVs%+{4j3pE!yFx>Y~N*YiOw;jl>xONvcAU(~*Z0knCbmmSTz{gf6);!Mlkk0yERcC|m<5&2X z$m)B{J^Lo%>KQE8mU9dT=^tP$2YSGplhrk`@n>+5H~#S=BGYz39hZL^feP-9OF>?Zn?bMwCTj zbr5nHgfbQPS&YvrtZw|E?y3%ta=l#hY6H^6AZweV@X#adc+rr3|5$i`UYSh4`pLlX z^Xt7AtW2k`A915*{rLKWZ+5dDlM0}5t_YL&^MsVQ#w^(G6-jT=|H?Ip(!l&*+-p9ZDV1*yh}e9UI}z=W`jhwTjYRm3WlrPp2!p__vy%C-@*bvF?% znPD8kwGpLkEHWl80fR0v)}enhKB~PqeEo{qxiiDAsPR_Tmjbogi42m|o)2vlom#LB zEktPNfErT-on^S?^RnQl&4ka8Z#FzdbP8IZITfRU84SKMwqL?S?jDwR>%zh{K?Fos zr9^lO&?4#(%>d9q0ZTY?))=-i*sMZvn1@cV+IF7t3ESkI>HhF8g*botVLfAmMA&2m z3Q0Y`rVwSK=~{w4+XRgP`P8Nf`lsx5lft-D`B*YPNxt}0T&Kj){bJ&j#>2+*1Xb=t z^BZ^18MWh8OMll4eIV(=;u6hLb)kA%ynU5T{hkbR%8tJP`y^0hB@5BRqUNO}JX9dg zYQSo8mv%rkUYtq6=KykT_+R3FTuz_9&X3H;5}+e z7a;?5&uFd5QonER2`*o`_au;hr~kQ;3~1K8#FVQ~JZH4Dfz*KE&_QC-!DT7e%lCF| zb>^iU;b!a-JEOf?NkqvpgG|tdN{YroD7o1e!jqM&#Qu5uPw;=bX8rx|S-qHE&T1Xj zq`Ur*1@edN%dsS8ItbAC2BUjCTdK`Ubqtw+Z%*T;DJplgx;I0Z9c$UEstv zl@UlbIE?R4xuSpQ7Ke0)Rl7f=1_RAP+9?u$F>%zg)Hi0_Mk-PN3>RPO|5b0uq{=dj z1A93XircPSRN1Q2Wur2Bt?*NuA_T8lgHYPU(Di6fZJ zu=rB%a2i+G&$I&;3j(xE_3EiR^{^91xa>6N+@!tZvwkWPW|`F5Y@slWrO0M_o3mP^ zjt!$$#COK}98@&(N&zYx^(+R5Uz?aK5rDi-8uPzUO^IxmP5>sTNr*#NV**@9l%N@l z7hiE6
jT3Lmns5oo$e!7V4*m04tU^7Br%K76cZwEdOyKI@3LLC-L7!Ai|k+L#5 zb~EVykzyYnUP!+t@IYKK$<8P05u1{}>}K|6*4KQ*@W7x>L}!bte;wSWaJa{XQyXq` zw3g17?2W|5p?57ND7(A7OW;OathORd5Il>AQO$pjgek5*a_A5b>)hH~Wdu>|X&d<) zwlS(uy-F7UPl`?`DyAeXFpR=~oMyc@*DXW$_c}Nx z$Kot(`0G%xvvw1|ubzX&@i1S#13_9OJ~{-$TSzQc|Gg~_sgw~sYkLk3it4@esT>CM ztwK2Q&PruZOMzZdMh6qpjrsm#sstCSr(J)X2q&=F;WkX{N%WFzebc&}k?WGfNnZP1 z#iP8+gu%XKwgTD_64;hf;sn34N95yXcgyMlRLQ!=x|HUG6k{fK{1WyVm43@fQ4V;+ z%0nU}B@H2kPOrul8oFO3sx$;|i99d_98Hd&o&nj_I9XX%4Lf3Hnz_wNdlv+MdO?5J z=T65X$hFB-de1(~N8}Wn;FL0hh(6}8_&U~HwC7ZIJ*kMQ!!}Do(y_$5}kk3rCl_QDk(IJ`Rn5nwP6cnxlAijaWw|mdwSBdE*7e=2$7L?`V+I%c1!)MpkFSsIE!~&T@mBv7SW$rbXI>GVz zalcX?NJNvUb{KsPM0(UQO9Jg$}m zCdKgyq9lawR%L?bhkk? z%`q%uC2%L3c&vYc=LF^LrfPXng_|4&xxR<62qn;=Hm=r>0w(II)I1O06AdapW1qFG z7s0JQrwV!%(y?qDgUtlX+W@hg8xUeYA6#VoGz8*KDgOS$sT`G8NFPq&C+;U7UGI^m z+~eSEr>YT%vV4>TCN}dW#)Y;sr)SmmiRw8(PkNl+O$mS3u$00at|=v-@;QHVd2JBZ z#9Sq<8mOmIE_}QL`}F&*-oBSvjg-W`^}vNTK!$_ic8dGuS(Bfp$#==HZHY#MMQN^xd?-(CJB){seEx)@4-L1#B*Sigs0BGnB7 z%0rJSuP}cvO;1RENe8$u3Ipahi4W}?Pw*; z@$Hi;_)#VAt>mzGZ{S~+-it#qDEvog^3Z#z3NMXmiw7^!KtBu}9x{I;(oE`#U>l=d z%P&`1ISNDvb66okssx3SKrcdCc#5_ng2#++LbQM84%3b2JvHXT1JIVFg?J_={k#QF z*l{}`Q~!An!0~-cm}i9r!`@6CjMA&qc91}f1EUP7A|FoYhn^ghDBJp?H<)L-OgIsD zk4rr~1FYXUOyGL{bUkvy6bw3#Hq=YG_aZV)ntYv64i>5RtDD9Vq8s;G*}LO)kWPE% zb>n|=bWm-2Y1y_AwV_>u%e2}2;oxPOK>cj3sQtbq^YogT2FhgK#z; z|E_ZT9PyP8hBzM8nbC#*y0uCal(wNies+JSD{W&UKD`iZp;{G49i|>Glk4CGPTEgs zPL;>>@xD|f;Z@1i0VbMq&O$4(j+q~BY%SGT!`)GR)_`nLO{`*LQTNC(v}3pUC!(}e zgdxf40^n-=+#>ZcEvM)}eDsM+6ejH0a09iNI=l)+4#aCM6`f0m<%lZfx%8kRiN$|I z@QsMaCA{}KiCc|DO)*{^J*uV36RkXdg_`AXVgsmzcbPa2v7fN;vlcR8r* z^6X7MlWr>S>%-Ye1|BNd%?g>Xsc?T+fWr(9_oQCObv}A>?(J*I<36WN5Qit+{vE!W zcxp2C1olZhL*T{p@cD}G*c*|TGp%f6tnY>|D2$HqF_-;t@Cr|c1`c-l<@4E8n6WwB zq=f1Y!*3bFY_}4P)<()99J@ymS3j^td&F-KY}8D}O7T`nDVcA^iT))^;LJ z$FfK}1^<-<{YC=(*u;OdYc29le0|_}o#Hmq8J)U2zaUmjl|m6&2;R=!HYviu$P2nT z!(m2H6J6?$c-YdtgxO;S7vJhte;V#7nC-7LsBzrL2YLm@8WDpmX=EC66HuamLvyiC zVgN$9z?PQv*lc6tv)-qj^<8nb+0+~JFJD7ZVA3#Q+1xk_`YV5-ruh(!V-g0{qr>uK zuOI09el>CNjGysZaP36$ClVdtSGaQ9b7;lW@Ty}NGJksvNTU$*2r<3rHmSQs-eWKL zbD!T3WE($ZLM%Wx$P>KdC~P`LrkGfRNwWW~WB5>b_S&wOU?p)#QDU@OVDx}ux@=Q> z1R|ZlGFyfnGVFh}9s1R^<>;5rxVGKVi{WKU0zA>Bu2a4uJT?Qft(Z9&6tMb0CJx z`el2PL+3wj^ssX>>pf&pFj5NMsCD3jd1kova}M7?&sO!=_3@RT)_B7x@T|vnN70CG*(7zldf3b)rG`gw-KS^Yk7E2DfFh6rUpo;=B3rihtgv zJ}-a%BakG+lsqmGm{U{W7ki0%LUFSwNH%^#yDKK4eA`@`_!2wG)>7lcyOwb9?uq+Dmby_7tJttZRh z%S6Z?yrlysAho;I#p!iPk8D%oH|nj~&>4R`i7#STvv{cYmD``64?ev?(=6Wb{5f8g zV>_1YQ{>r8>ty#W!-Qf8EVRpACp;2#;ZcY1>;Q|n7`Z%SxMZtxfVzslerMAU1H+kn zCzIZ7)($;uz?pqP^n+zNOPEiKV#~4^r|^a6(8`P=S@fFU3W!q|e#pEqOLt=^un&Lo z1cy!zYxkIYt|Pv01*(*vSPh7=C+A)vt@em-_U=1Td`;Kn=2jghL0A*MBaHigBlT!0#^kiK8t|fmy4kj&jf>ESt#pW7_4?$`j50A?gPrx@8+lN>cbp9q4VXU&;ptqEA8fTxjKzd@vq0d8IbUyq$7m}mf3^|#L`pF0( z`)jUpVLw_S%_fbwM&u~{hhshkpZLPLBF_x=2b)@ zsw>D}K{b<4;L#YI6Rq67(c1nZ+eTX^YD`J{fL436BBq)XFh$LT&J2H7L1L|~Sc|1N z%(z49n2BF1=l6PGKnfL`$wR$`UF+JVT}CXKj$--`{6|?qMgw+a{x%`N^6QzU zcj95j#>bnQ0uLodCDwoJ3U#O9r%_KHVSL~Q(NmUE1v-w7-xESRyc=bcB2&BnBCS1nzvacDy!xHdaQ1>u4DK6UXxoQH z{5|tDTT;-YlvG~<4|A5pSdI*}8792NG~*nOoCm`# zK>&K}AH-?#vg?181~(sAXJZ7stokQag#{&K$x)*$5@j#r2k3}T_%uvBzkw3E?N_OK zqcItFk7{x$jq(I`4X~>U65t8eBa#y10Nm=7xJomDsRB`YczUX|^Uh)Bsf;SXx*&W+ zY9MANBw{3y{%=7c?kYm$@fw_C-;x2X)y66|CV{*8Hot$S{_>0AL*s{}Z~eS#g|-(w zolZH0>sO^UHf(ptZGs2LP9gZ!D`|0_MGqE}64pc+M}pN5S=H=d0Zl_u1TjqQbh8D{ zfS;e?Oe2%pY+SF#wXU7n*Hv#jsbp0%ZoW;b$tdqb51Av1s@(P8C(jI*j6&NY7UJY{ zv>@ay%}9R>(GHz>-3*ZkH5yh!rx+-Gu~C}VQz&tu1}P5jvl{36h$IVE7dYpzX30~{ zUm1lviw!WRiQfz3xi>q7y~b63rw^z8Qhcg>PIZ%Tv8UUnw`S2wh^)NNCt!T7o%gEJ zL^D&;-BZK9;HAs-5U+KE4dk@b7u_QQ!svvdT19{49V_#aK-7fR)Pg9MJ2){2Z%de- z;2mk7D%)eLnL(itIqs6dJi%ZJHhFvI*Xef3!;@QW8=qVygi%z4sGyV+*=*^?M7|C;N5{u&4_%eDuRp%aNP{lB|+TQ2?gn5&@xF_83$8K($-<969V0 zqg8mRL9&ph6Q|IV6)7EKaLmKoJiVp9P9A>^{5G*l&O@q30e6TEk7`y@*o`29ueeO@ zsx-)kcmN{&f;%<52V_p|A3_YNJ%5RK9+x%%*#Q-w6xL#SCG_1SGSm)1FpO8;LIQRV z$y^^G@X4ggcvI-@iYqweZGNd6^*T4d_#mRW#e!+6J4YE01}?UHnMHl|a??&uq!aAWU*cs|%PnrlMTwlh1U*$^Q6w$M z8Mvf#umS&N?k)Tz6e(dI=Gwls^qeeIOm;W?Xw2bc?WoA<(AhQqNmy&U`vFlyKj@xd zooy@iqSr$hhYX36Ixx`bYFmG$!zppueR~13hLYN23Mn$FX0J%6b9u@-b*FJ}c5x(j z+g@~XPe@3#c6+(FEsGf&{n^WVwKFIeUC&L@%3CLdl_RPZ))t@9;JOBa`Is7)-l z3;FSWO~@-P6r7UEV!&KhpNO?>xAH9WXb5MgP!*SdpZ*b%HH!3=bf1v}oc zVs=K{*{ZT)BQzdORFQu!&OWUc(Ljl_k=IbFq%w5r67<%i!|b%aGNtP?hlC7> zIR)ksYD3&K8s`vJhyXtIOG>J2v)tNWN6n5dt8#8^>&qZ-uxfw*;0Bg`<}93iX1Go@ z8rp#e1Pnr`i(@c`>M1GaF{HoQI}YQHyo@Y983hxVySl>tV|CNwF>k&{v-en1oD0J) z_Bm6@Ln%CN0_l6BovI#`XDp=uHXI}!|4QVBhGqszOjUCg)t z(0r+^223wEfyhZ)|u$WTA!eYsQVC-IWs%}hvBsC*&- zgZt1ay8E9_ieES>DZ3pPO>FJIC_jIBAAj%X51Gk<-(%vm^PUS&@!m^Tx?AtN6Qnk2@h(~ z8?rOAJunre`jujfNE`h_a;MdE3}Xiht?BG{l$ozzWh9X;G9cl5EDxG=LvG;hN(qH1 zV5zUMlGY05{=6KK4qoB2T4v5|iyisJ2^t@?DNQlYie6J3Y`Ca5+t}BbI4x_DhUdDt zixmE`a}R%X6Nuv{g8Yth2X74-S)VnFZN}4x4@{B=7kkq-O`>lf4j*-@EKHP(X4=(GJ{iVUkl0saqXF;D9g9iHcgK0V#zNg>$> z)OL3aM8dCQWIDG}VnJXaA@aSOc;$f9#W+wp&h3BUiJIK_=mR6R7l{-}3k~B+3Oa)Q z{&mG|YPlawdzU$vv1%u4ONkPCEX3wJ$?Gl;gxj&R5626#*X(GE>_R0%FHRR0enYZX z=Vw9ajm^-0`68Q?mB5H~?b=cCXJyRRDW{AfpypWh^8_~#$ZR+lzS0weGVLS1vy6_! z#`=Gosi(+gS5{j79YaMXz{*jcaQ5~r4V+KhA)*<+di@@X#DqEck1pRn3OW4H5v!?T_$vgIC9Sas3QbPCws z04CwkxM`U-o=2^qZ8M@XNjPfO(G8c+P#399`oYq$5(SZ1U`j&e=1cHAS z2i6@aa7TQA^C68ZLR_z)+*=FB5%C|UggY9-?!^HX&D^W^=#&@)PS%7!vPtgOJnouM zLNvzTGD{pJ^eWj5l_X#1I5KeO%E7O%x^sUps(CJ&;kiid-R}%KkP#+emkz&>gB~gz zw;V-UvMT9&I5e+8{ox#iCnyJk49I`eRj&^rW0&xyTdnognXeEek)SNncA{?rzr%|z zwZ`!G7`c=g6TTxF#p>WuDO6B|d>Z#Tv${|vf@mB)(7rLgd2gVIQ==2RP?xOE&GlRA zXw)6rHNG=|myqF@59we=W`E7qR;|2>F zX|9uwysQ3o1dN8-GcT%D15qUN`R876C~pf}CkM2N(-5S`E=-DTIA*7cq&RX58lxAh z77IM4uQI`#8cJZ$ppAq(-HH;YSuR}Rqru^d3Zau>s}v;u5&Zj4!hGcXD-Ol59obZ9al zIW;vj3NK7$ZfA68GaxVuFHB`_XLM*FF)%YXGnb$10V#iFRGe#;HBN8{ZlQ2@m*5F5 z!97%oxt@kikNNgIf%oFfndc!79PX=$bGK|n{a4OANF z2oeHlgG_$`(jXH67Z-q2P*4z+79eF~>t+u&w{Qe7yznqGGqe2D^2Y`6$?YG=OQZwX z915U&d2j|nY;3JTP{$XF|8<}`2n2An00GRv5D-90MO9Z$Sq8u$qpS�YO3bFGZ+2 zeS&~Z0E%D}5Yz$02r#p;2SENl08DJ4rrQIs#s@s!G5ATc@K1(D6@h2k;9FurYh_G_^5t`cu+h*bB`I>Ieiw9RQ9XSI0lO zK7oG#reFtK2+-{%_Y0Y=J@_vfP7YwG`9Bq~0PI2LKzmaN$id--=7sxDcm7!?;D1yP zw6%q}{S|HVm)C!506RK>AZBc+oLnzCO&nixn}eaK?0?op4r*ot;NRvMbv-zNCKyF#PYP%=Vuf@_%5&|B(UzN5=bq8}7f( z=zqM#|JV2VU#Z_aK_JRNYtUaofPdUG07bx`iw5xLrU9G$e=$I7FvRWOMg6O%Ht27u zf5`q7`4EWjpK&_C_x{Tl*7P5)K<%b@;J&MvPYrywuK{O@nqzkF3+w!l%t%@zds ze~Gk}Y)t?A@P|oK(#93w&dSNp0bu2Rk;BQs&kYdd=JotHS^py9{O4H-=x7gi1?Y3I zad2<~UcUeF`RB>-UufPzO>9j6?2UiABM@r(vTFZr_ye0b+1tNN_^-GBrSN~8|5|zw z$Q5LQIzMY;A{=0ul$z{VNtn?)EUn+w!3p0RXj@RNk(=#PZqx3a^kq%3#Q3oykgaA^ z=(*8tX5aQ{OP*=Fzk>im-~JVJoJHnI&DfcZvrN~_&%Eu&Zd8Dge4rifelmZpxQd|1 z$Dy^oKKwz=DE|?Oe6*R{{?*A1qYt%nwhtc7wJoNXNn%wLehYRD%k{p%W9Kn#CvCchw`durox$V&R(`;bL4(Rz_{nom&0Vt zkYmM{{zguQg;LOy@MOkn2_f)1U1z0R3KO96<87t^Fv&|CRUUq+KvoPTh=!=zB z8JxSRDT(TdN?7uh-)H2ZsS&u{b&l4RI7Oa0*L7IX>vK8$v}gAy{~q1RbT}C&wavUS zYlkaK@aed(E1L0F4B{ju5L>7{qUj{LA~GTU@`u zAt&M!Xp0cdDf<#_&$xfVDpJ)RGeeEDk$dH0Q~sHwK4!T{|G9jNs-S&#bRD%xy(rhr({=V%rFDnF4@`&svV+Sl@DgXC~wNfw+z#AvKT?fkWegPu1d zApN-Kj%e>OS`%TEmZCCx1lb*g;AU3T1?+=Wl+f~?H+~4DD1v{aG~amN=i4+z26&me zY@B8en&Zn11^Xvq)T|P0w0a4FC??qHFMwBewV1vVIn;>4y%;bheZhtWhSvfUnPAg< zDLKSbzzz|U`L0HL+O(paUj6*C*Ybuz&#P}Bl*&1)qX8PI9_BcTZb5_9)q26Xf(xa? zb)K=$YnYik3%xAI zK8cY>)MGQm0#D%)(eR558N4%jdc`{bD4Bab&jif@JUoAG#)7#xV=mS`=AMB3Wz%O& z=AaFf@4X1YG?!(4mwP+DhM%g;dINYal8^{s=OQT$51zBcbi+BH9}d4SMH&58%vsXw z=kBgV!47!E{w{T-56vgD8dom*gi;@$LJcoh(al-0OK%uAJN;LEgZz!YPoIT8!NrA; zZdZvziD-X`vGIjR;VQQ@G}wJK(afi)F~E-6qPwea=m%B8UIf>G^PP0~5dUMfso!eg zUb76X3EFAxuzGsCP1_lH=Q;8A1$m(a=`8FHa?tOcP1;Ht*uIR@%LpQ_T>%-UD3bUh zk}&=2N5`s9L~vDUS=LSC+3hL#B&Q?9=zHi%G53E|jSE0Qk!min_5O}|B4BE-rycXn zXqU%Y{ZRyGcDgs~mykNZ-W|Rf{qbeZsmJelA=_dHOtxta)-C@{7Mr*w43_4GZjqm5 zTsGLQ;wYhI2X%$zN_R9x+^;|?B*$p!d$F8YGsapaICR`g0S_)xwKt;a^N)vhSwAEq z#u|S5Q9^=VliCqQ~CSW>w|pD zRfDT~P9hbuF0p2PIQq=W$mIQ5tby=)ugA(!(AEPl=CO}U30}_fJv&b3&-CkpFv+|e zO0TtrpXqNOStZdeU(brJ{{ZUhuHuR7jh}xod#O}yz-wU>osPOF)HWKab~3#AeL;YJ zDG5XGY~cjsYfK)_Xpyrk)&V1R?)}E0&Xyn#QGrgN4q~wY{@&%gAv-;P>yy5m*eAT( zZP7ezKm>9&ibbWb##5k0%yW8WuF6GZ4hXXDQ zyh_7mXoMM8R7eJicA%dBERV9luo&)Yv~VjmkKKJOX~{j}S}6S*O&?T!R?L+sdk`C| zBVoxiajqi4Vh77o8e(kHClRJF)=7U~RKn2$aL9YOy9$7K#ca*SGL4{|A8RD;b`;1; zTDL^`sI0@PzxVE_82C{4ZWD93q*rsjV^M%2famQZA-S%9Hhjbw0XlOPddHq!uu*~; z%%W%Nz%Ei%rFzuYs*o85`JhKP&tZz>V{CJGr(ZXWJDbg_T4a1kPFha!+US4eZ-|w& z;GEyw3Acc4SF58rKSzh^8a z>Teu`B?>c$WUM2sOPpc_tiT~twoADPdWC5F=MDxULj&`-p>U?kANDutSi+ z8$*jR5~LFo)qCx{ui8!sZaJsyr%$Hd*>R zJ@aebIpeu1enBhb$}tn)5ZAAhjl!GhiN0jd(1s!zw=1VKyG4)l72Hqes4F_mV^Sm- zc-Zzf326x9%DuzAGu?k5RBg8oEGMX1t2`{?NYE8ARvB6F;EJNBm4Kxrq1&>FyN#!r zJKQi9mTdcMs&I3|?_ahHnW5x=pnkZF*b zmN4IfVG%5C*BTeoJf8O330m<}7S;d<(9r9#IiBp`7Pb56+7G^V45hNUEh%Jo0H2?% zTas9e9fuUo3lM+JS1A|sMq;b@(wk99#n(SPDi`Xn!B znASi;LRaN5Y=PC{9Xfa>_i}}apA@boD!0=1xEc;l?3yY}fta6J3`}lZ%l){x(*nXK zL9lNi=V9gx`_cTCR{Fzscc;gs%W|l7lWWjfg>H>g>(0Ct}`sMX-uEM2120Vdu50@EL8?`eo~u{x^>pWf;fq z>#3Zi93h3~@5R3snvg=zZ#84i)U}@;m)d{Or|r+_b{jQmio|3zHlmaV7YE#H#4Nl3 z@N-I4lX@a&w6avyI{Ix^8cGL!OdZzEl(M`i*&J2czC|p#r3qh;=k}CRO=*Jkbq8aInc99dE=f9BBJ}shq=o4R=ihCmWtVa!xA|6t zJgN6O?e9mvex%?*jSyop&`&jpRz-i;PWcD~K$YVu}*eXj>QvT3VaVy=saX6x6;ML4Qw zt?Ho{_GKf$ufLvd*{x%9&d7hfvYvO}V8Y8P%Kvhb;*-4bspEhxNpRE%Q2y}e2%XR<#=E#3So%1dQ&p9DLYOeRpYLT0}F8({FAvpig z#khf8_uxmacL!Mf7;$P9@0_Kv{I+RSKEO)C z!@ZG(e0*+GHx2XtmONF@zfO+Ug)0{6jWi7$b zUDrgX6E0o#OiE9d#FK-nmL+y`JWZQlBZJ_x$^bGg?qgSewgnn@(OSN>Z3bm+o(mg0 z|I|c$;5RDmW7K$_n*`>)yrFAi^0W74c!5x4@e*tyYkvjS_a-<}qN~X40TWHKIq(dt z95tT43)z1uIzRaF@jr*&yNEuExxz1?u-l9}Sj^@Le|fcpfF{`tzd?xx*N4p)bD`@l z%#clr`_YF&n)8R)Tq60%?iC{9NtNsRlzvAkC*NWu8wolU)PA>o zFH*EmWIwf;Ma<-JFma${v$bEsYL3Arh9aQ?o_=9QsnqSM?WC+Z3i>jFwVaMmQF!=`-$M})er~$wrmA~WluQBLO)L}{pjczN z=ivWDS=yDfAw2fw8nd3zD|zBdJLnRYSCT)3XVm;%0%|8}xO{M0wUbv2`ILVfqa+u4 zlm>!-e14V~VvfNF;vre#oP&{+s_pPb6Z>JZ7BHIBiV(|nhgT%wV?)i6b~Zn6nt0$o zNf0f6l_o}{aI!Bbc${|Mx`Rp%r(Q_`C-(&FICuP2U3$`BxsakT-BW~zCdr+ShqQz00Ii6^GR|-)QgpW|9k4;C#w|7FNlP5h}joOV8=@#fS>VgIun8eaQ&b z;+a}*rkj4Z$?{=t7d>^6WhY21x*MWSmNE@xJ3Qr(W@(01cNj5U?9)G%zV^kd*Aj=|lBqH$t> zTwbUCN}ey~p0x_M{L$nsSzR^k<4z`ch_P3k^3;eDi2swj#4j@42Tphy52O1Pt-$+d zIp!mDj{AW^vG`FYz`00h34-Tgm~Zp4PWUqRN->R9GDT)~0Pw~*2QIql^YZ%)+A3z| z9L7i4QWH!~R8msLA)KFSPOso$j9t@z&rGHiw^b87QuQl^M^k#743$^c3y4Mr(=^;< z=N-qxwK>KE@Sg+hqw6+MkWMNCTX8b$`G2M8U#mA<2>fKT!xinXk*?oal7+S7Du+z^ zB~tDmrO9DaMq*OXO7Q&${r?bFFG)+|}q7M$$MwSx>%D_>fxilcg<3t(2CMOrZ zRcNc@FM9mXH~5S#(Ma~N zMs%=F7};4~;j_Z=)xxc_s4~1lW9%b#DOsU;TiCEa>LMI$IiGg~Y}bC9G@u4l+c@iq z>FH4=Ugc_-eyj)z5Lk0M_*pKh!2(aY00X@<+2_DtUDRg_Z^x3?PuO&S`KmhCwIqi0 zYIVBnd&Kr7GYru!&)0p0x%;n$ zo)?oma$;2tPNp-_EZ#TbP+6mO>cV+DG{dSwy?^?k>vr-HmZgHDy=lF` z{H^rs;l7Kcn$#>I`7^I1ncCc}O?T(7oRkQJ_{!eJ76)5NwSHj*W~Rz;70`?W-e8=j zVA%2@Fk$VPEfGQRmnL!i5E_xob7EwRW&_DUl6Er3ho)fGWOp+yLO-so!>3C;=<(v*J_R9Zgj&_C(wK$m*Iu(n%@bFtP)6bxlm> zO@OYdT+c4H!??ev0Z^Lt^JeabBr_V50dkDd=o=wQk;e* zqoAHX!Qd~gmL+4iv&oYz8Zc968`%SD`j(MNqKw!OWfZ1=#rW@m;kpKa(^GCbqZ#yx zU#mm7m?BY!&ajO-rd|{(q0jh-S?z5;#psSg8`LQ8-nL#*Hz|7~RwohAs*IdfDDG*P zCWwmXdR~4+G;K+&U3WFF?bDU`&9Q9H&G2<^gg%8re;PPJTh75|v>*{lV~IF+ku}F} zWW^QagLk`shP2jgW=>dQ6qck~`oN`ShGOAlEaH-rjy^oBB*T`+6t=<8DHceV%JV@I z7hws?kkTRF^%*UYVs!mJUkUVM5LQ6HZ8__s?kyRhX%hM>5Y)^_60`0XX}&-zhDbb5 z0?0|TR4Ykt8wEs33SQ#MQrfAxgM$tPFgDKCVV>=OD3<_2A*SKcrh;V}kidNyHFf*e z4aTz;dY2FHBy8&z$L!31A~dAVOVy;bYeX8xcFy9HznM2)|IKZ;PI!8=f!pNv!AsAS zuNjOS%nHPgHPU(YhO05u2Fq3o(e3K-Rf| zmR-z$z6|tBzS${}k~*EDSABaFJb_w%gp>sf%QGpN9@=rwcy4`vbw+f=Jq?PVWyzvx zQAU#tb9CPNOrvze@8U{b`n<}Jhnbkk?0hq(CH5U#ID-*VJ^pvX#&?q$J0Lu?JVh3X zjFBdj->U*sn@(~m>}Bg;J2}oq?_J)2U>KW!2&=BXuy7KK4yv>jgsbL}>sMEoH1Db3 zW=Hs)h+}y^o(xBamCX?dGN5Od9>Z-fu)sK-uYi9B|0q@31RG5r9Jq1}AAbZ7dZKwb zi3hz+D4=d>3+u_1l^q(lvzZcS9|&W$N)jH3J#&jlZK9tA>m}51igJk1Ki|HqYcpbh z^%6Ulc5?xFIZ=<535*)oE->dMRNEja^n2)!VJ#nf&sihq_9rEoQNi>o3vR6V&&DAI zzV?h6MB;?zm@0P!&yvnvp-{_N#28p+l!%4#*p-b;PL9Mf5rcGf2i@vr6Z*rPwuVmN zv%gm%z_%7p>=FrR(DLb>h$QpA$5I-EzDsT51$8wnq?_X zw)Q-z0|OBq{FA|NaB~uA7UjM~8pg2pcrqmNQirfy^xN7nzv~!Z|ICqh`i`D|+_C!l ztdko79@Zh^caJYEExJL>oHl~u@QT^F zE0amK@CF<9+gWXeH~rd+Z$H?7|I#8(x?SvOD%c@UV{I|(iEEk=tlq#XxFy_ibA-jx z<+u4>UeEe!k8#}u)kSp$SBZf0Cu=j8Vl==VHq%Kk$dbI?KMt66Tk>!I^$((LU%=fI z4^m+zBK2P?KgYXzfKe_3&-b}vCXx%PnTBna)-WGh>lm&=|h}7?#WCu59^1?g&hntEJ;;>&*UM5kw#01=GpEenS zL)DUSBZ^9gRt4U^mLJc5c`Oth&S!Dr1*BOGQ zWn_c?G*LhT_Q!AUzJIAi00W3Q+JuW^5LWj+`9wzg8F;XN@ffdX*pNRlkf6&quT3G` zA7t)rCKoha&_b7gAGc4J20whd$tPjCPGU~Xu9l=qroG|a^Dt-8zVlHSKTFtE<0hag zM8QC3xBaToqo-@-sY0M~yOunAWkb60Hf8FI5zBc-e~=ZH-!Bo_O5Ux7x(z-$Hx{jmHdIgHcI|vx?K*;e-Jurg3dz9C0sYL5T1B)9)4Fqg9r1(&I ze{Nry!0xMm99Z`z;%P6eW4micVUyfU-Mc4Yuo`U$mDNFanZT}uyOWXpiC$$C<>fTF zoR5vQRggSU>|tQ}+wXO4(HUjmJ4nuI{%tF>xT2n+$?HtScQqAD1eC5a46k@RnpXW7 zV(7Q*u0%e{HRD@}#e5G-64G?#>Di9@g!egX5L8@$hT8m@4;I%slV`)Yrgv$yH!gH| z)$S=CQAqMVg2i>#@P?*RtCN8KkQchbVI%1dh8Rloqviv!CWc?SIh=}>3<>2`v4%IZ zNcJ(7OXKh74~I7L;=mDA7JlL(_WJJcVKFQCKIB^sbfx1Ps`ODJKiEjm(qT*;>l#QZ zg3b(oH4-b}E#@f{$u9&mc)M#|`pdPAkdiGvOL^)bVMpu80`)aS>i6FKPr= z%N^Ika5`+9k^)7ocrB3k6X&^FTM&zY%Sc;W*Q0*nnprO zzF0ngeMa{OkQFTQWTDNDp|<*t6yi-0Qv(WrCK^jVL)_pT4f%+_7t$D#OGWIfuG;KE zQx?aTma%3dTHtOtwn{7|&-UrvVMhmqDm=uVdP0|_7MW+U@vaw_lASm3bBj;m>=MI} zG}cATGa`-PMCO&e+YijKhwf@H`k;*!=)xV>=aCU-pJdlFyH3bVCNR}E#^$1k7Nu{zQ+ z6-f!)E!j4cIpD0v=%%^xEJRjB3o*~7Ct)p!Ro`Ior{@#)4aQ%z1{9roX1%(9wKEy9 z@!cD0v;y+Vjxl+sQwhq|VQD-vyC@`Pc07IS?g-v4JD$@ookjhTR_q3R?_%z}Q?@86 zY+jM$67ju+fB#Jeq%2lEq6gB0;(kgC)1sul%Uazmq+GZXS*`vH!#|oXIlyA6ZfbvM z4c_e8;%>~~n@;kQmA8)8H(?5YonX3I2;rdM@T&3Qn%_yYoN8AL<@ESd)ud|7l(_oG zENbY8-6e#!?9?KLzr`h>q z<~j=&i$nt;&qgsgQ!!Gm$uB@5C_Tfj#Ec_~IE*KP9WOzChJ(6&C4`P_Ib2C@VO;xw z5-7%gD|_4eX2iRCC&~AqL|C4T=EVO82f7!wbk48IGqv6r+p)%G>rh+rHJ!+yc83dFHm)>t$OCZH+My&WwT-R1KL9Cj;zW}!|6uvE9v8JV{A z5>u26o!3hvjoq_`C7E88Ho8NICA?r=5!!CJE0-vwXUHp8 zlbDHbjfXIXo0p}3{Hn+KRYy05VzPi7os*Fs@w7On4Php)UQ0mW2KdSFOOFaiu{7Dc znp728+-cmckyQ}x)@optHH&8X8I`$TFm9jZ_L0=AHWlA=KV=-^4eY%9Sd63tUZ}|w z&_J{sMtVC`7H8=Lvl^Q|f{?~^I`OZeRss?o_?1G-W5Sz%G1F$}I;EUpj_74}Wy)%- z`%g+UBZOrp7wTlKstNYLZZ>{-N*_Q5XDyM|AstghB8BlRRDRW{BuOx)pa8ZNV~|oFHb#JP{u2vMTfDzW@{EwzUdnZe(+Ga%Ev{3T19& zZ(?c+F*Y%mVCw-Em%JbX3m!5tFf}&{FHB`_XLM*YATSCqOl59obZ8(lF*rFjm!Ina zCx5KDV{~R+v?UzdcAnU_ZM$OQi7U39RIG|!u`9N1r()aISMPiK_U&=IfA!Zt&KPH} zwf0iOc%GxrD zQUGcxMGb(IxxKlQu`NK^)x;KP3Xlhyn%g^@(*P_SoB+1}u>hDl*qZ_WDb1PjFMpPZ zGr$<&>}YNZ{JYKE!_?gI9~V8q(cH-n=-!6)?BML;Z0ZDbbOHR$sw^(~A3R;Gj9vc8?F{_u1~^#!jWlyG zb^WKLe|>*p{(4=Ef%eV-7jqAne}8hBm;=m!&W^Umo_}-y1#@%){!7Ev8E9|$UkvC0 zPUe=zPG+{|&dz^f{$l^ro&Ty6@V``V?C5Cg`R{Irf1~~<2cV0yxvd2w91H8;oTe^+ zb6W!K;h6pz6&ZUA2LKE6f7s1j9skqkX72QFgQ)+R8JfQ&jLjVEZ9M^I=6@D&Oo|RJ ze^Uae|L;_0{C_9%{{xBtp9uW_MBe{@;{JDy{+C1i|MxuqcW6mhTU$kAJM(`x0sixj z0muXXxn%7Bw`gNKpsnZsDgM7lYMK8B$^RpajEnK#R*2YJ{*{B7k@-K2Kxavyhq;+D z(8bgWU}0?gw@?4tHSEpIoqueB_U3=}{I`_=1{P-K|K?M-0-D;`|I>Jm|8SYxoBen0 ze|a342oqvwx;V z&BfT>?C*g6Ps2ZMQ&%UazqfFvHem` zNs?VWjhyZqOg|xC-8kZ(O%j+ow8~n4dR_jgC$rr0u>ju=hkqN#-BeSn6^rd)Qx(iq zwC|-Nn#rS{``fb#riQK*QPjD7c-(?ndpYN-Iq-b+z>=%l(=AwcZfUk>33adQxo-*5 z=!IGdzEj(Wb9Z$Tj;{-AgU*&oT@a=oanfocv!ZoV`jm+Aw8|HPJR2E|kyGkADDE+x z1qO96-^tgBGk>PW)as{U!MgC9AyxV;N59p8xMpb5&m@wTQy9kYA~Ly?l%#xNT5qXm z1iu--RCR11$sP$84DE&}f7k8ix26@fxOJ=VqV=*v@}amWoYR*Tj>e!TgK{b&TeG%T zzd#Xm`}5E|qu>|ca24^pN=N3@0?-T-hH*)>c6`k81b?MS1i=nD#OXaM@<cHbxksd#kv#Au>5^#F+;qi(myHb|xo;q$@q$}wYqrkYIU$Vm(Jhb*Ci zhU%@Y#($Lx=UFqB62QCX_co`JN)DQMBVUTRJzT4izT&Zr^i-jD$va)^_VN_jR`y9i z4z=jtBYMh|7}P`?3_I_TvD@SEJ+Nit+MDpofn|lIB0&0!x_AE=`6pxxR&&H&{B-Iz zVnHrcithft+X4K~@Xk&GV9FKFJXKfyEsQm(gntov%0zQ0{=iH+w_HgrkZ{Cg?b7

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

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

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

Linear Algebra Review

+

(Gauss Elimination) Suggested problems

+

No due date

+
    +

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

    +
      +

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

      2. +

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

      3. +

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

      4. +

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

      5. +

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

      6. +

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

      7. +

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

      8. +
    2. +

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

    3. +

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

    +

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

    +

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

    +
      +

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

      2. +

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

      3. +

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

      4. +

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

      5. +
    4. +

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

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