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README.html
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<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="pandoc" />
<meta name="viewport" content="width=device-width, initial-scale=1">
<link rel="stylesheet" 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<body>
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<p><a href="https://lifecycle.r-lib.org/articles/stages.html#experimental"><img src="data:image/svg+xml;charset=utf-8;base64,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" alt="Lifecycle: experimental" /></a> <a href="https://codecov.io/gh/ianmoran11/ralget?branch=master"><img src="data:image/svg+xml;base64,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" alt="Codecov test coverage" /></a> <a href="https://github.com/ianmoran11/ralget/actions"><img src="data:text/plain; charset=utf-8;charset=utf-8,Not%20Found" alt="R-CMD-check" /></a></p>
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<p><em>DAG operations of ralget are now in the <a href="https://github.com/ianmoran11/raldag"><code>raldag</code></a> package.</em></p>
<h1 id="ralget">ralget</h1>
<p>Ralget creates and combines graphs with algebraic operations.</p>
<h3 id="combining-vertices">Combining Vertices</h3>
<p>Take the following vertices:</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a>p <span class="ot"><-</span> <span class="fu">v</span>(<span class="st">"p"</span>) </span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>q <span class="ot"><-</span> <span class="fu">v</span>(<span class="st">"q"</span>) </span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a>s <span class="ot"><-</span> <span class="fu">v</span>(<span class="st">"s"</span>) </span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a>r <span class="ot"><-</span> <span class="fu">v</span>(<span class="st">"r"</span>) </span></code></pre></div>
<p>The <code>+</code> operator places vertices in the same graph.<br />
The <code>*</code> operator joins one vertex to another.</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>g1 <span class="ot"><-</span> p <span class="sc">*</span> q <span class="sc">+</span> s</span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>g2 <span class="ot"><-</span> q <span class="sc">*</span> s <span class="sc">+</span> q<span class="sc">*</span> r</span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a>g3 <span class="ot"><-</span> s <span class="sc">*</span> r</span></code></pre></div>
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" width="100%" />
<h3 id="combining-graphs">Combining graphs</h3>
<h4 id="overlaying-graphs---">Overlaying graphs ( + )</h4>
<p>The <code>+</code> operator overlays graphs.</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>g1 <span class="sc">+</span> g2</span></code></pre></div>
<img 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" width="100%" />
<h4 id="connecting-graphs---">Connecting graphs ( * )</h4>
<p>The <code>*</code> operator creates a link from each vertex in the first graph to each vertex in the second graph.</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>g1 <span class="sc">*</span> g3</span></code></pre></div>
<img src="data:image/png;base64,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" width="100%" />
<h4 id="the-cartesian-product--x-">The Cartesian product ( %x% )</h4>
<p>The <code>%x%</code> operator creates the graph product.</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>x <span class="sc">%x%</span> y</span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a><span class="co">#> Joining, by = "name"</span></span></code></pre></div>
<img 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pEwP55S6Q7PoAUdFFwWx6kfrouzoW4cDyi4tkG44KY3poqiNLNBseIv7QywNyf47qyLP/QFmxVcZK/2KYK7aPg7z+TMV8CD8NxmNPo0oA4UXBZsC2ppg6XJnYIFCq5tEB9LYTfzyy8lBmpdZXBnrQvwzkqTmKt9iuBGq1biSoArT2e2+xZ/JSi4TNhBjf4VwcJQcO2DeMG9xxZcyHiODjsQX6B3VrbEMIFwCW6ESnDLLEg4dBtU+WFms7fxV4KCyyQ7ifHxJoe6ZXyg4NqGEAQgP8D48lvxeBfEO2sTfbXPJbgbl7bxSq7zv6hnWnQd8UP8jgsco/YHjEYr8MdWQcFlk06PUbcpV/hkm4OCaxtCILiMhH6SBLa7pcC6swLX8mP01T6X4B6T5XMTqrgF95N7R9b/Or5fuwblFcvfiAqN3xkwcdHGY+yZ3ZZ0lwrn6xbuBqLgGnCP9r3Y5J9Ln3hQcG1DKHKapSVQRdGamFv3g3Vn3Was9jkF1znVmrWmYwGlwKicY9LPJf0xfcgHzZ+KUrYXr/V699Ez/9qrG7S+RHepcL1y24mi4BqRrn/22fUvGd+i4NqIkGTtvbeBIoqWZGSQg3hnsVMDSZs8Za5Pe46QmZSDbxxcPTe215t1SivKW6DyS+8NnLpk2xlXkMj7dJcK9+tR3vah4BqSfdp3ZTLRzDIwF4GCaxtCIrgUUVwHW2UyIlh31hW24KozVO4aYfjT8SBla9yUzzs1rZRfkd6y9dr0HrOYEVXS9TqXt30ouCZkHvP+0Cec+tcMb2UUXBsRGsGV5Qs+T/4Jxy39+mce995Z8dbdWawFOf+8lbIv7Vn586hurWoW60B3qXC/juOtEAXXnHsTh+5K2rWvdem3Q90SECi4tiFUgitnnd+9xq1XU0+CQ42bci9l4IKkXQc7l65g3cLIQ4a1bGKAp9hPd6lwv37OWw0KLgcxbzj+pDk+bP7FyFwACq5tCJngOshsPe7UybNTi5Lfg9CxB2HKVOrThHxjXZ236IIb6GzIEbpLhfv1K95qUHA5qPiF488dx8dc71/hYuYGBdc2hFRwC0x2/B1FSBV/MoyZcJIogXBqEFLYQmei65QxbsL1QGs9SXepcL/O4K0GBdec+2GzHH9vKM8Ti0PdFgAouLYhlIJ7iqx0/B3q+PJPNy0LZqMzIJhjhEs+srDWNJ2pwiZ44AQtFxlRJV2v3PElUHDN2UM2O/5eVQT3ycAvnDBQcG1DKAV3NVHiD37u+PKXss5GwcMiZ3THpxyVhwcaEkdNlq8JROKZ7MDrfMhwqXC9cpsno+CaE0cUI+iLzinzb0PdGH5QcG1DKAV3Wj7FqL+v8uUfaXnHvolS/iqCS5pYIIpeMs9s98jt6JHWWEA0o7tUuF65T4GCa87o4srfc85Pu0juyG7PAwqubQil4PZ9SvnrjFYbZbkVer+nlb/VnbdWnMV1Z1yOWXgq9ZpDJ9dZUp9RVEn+4TkKrjmdGit/z7h+3z4NdWu4QcG1DaEU3Jg2yt8PnV/+j63uWNuWyl+X4Fo+XXeBLHf8bUXIU5YYnaXTfZ2d8Ke9QME1p65zQv+kO8iQX6k5QgEKrm0IpeA6TXTkzs4vf/heizv2fDflbzXXrTXW4sr3Os0433LUPNqS+k5aMMBFwTUnK8o5cXvMPYXzZqjbwwsKrm0IoeCmhTuDDrR3ffnfsLhjpZwhZKq6Krd6xmItUZJrKz8V+Y9YUV8mLbiEE6M8whpQcE05Q/5UXg57AmluMjsgl4CCaxtCKLj7yXrlpY37y7/O0n65/B48gkt6Wlq5/Jszo/BHSs3NLVmRS2M4sUHWdVBwTVlDnL+P+11fivDnrbRfCSYouLYhhIK7nJxTXlq5NbGZpf1y+T24BTffixb7sk3Or8jsp87K51tS41Wq3p6EVIGCa8q0fE4n8j2EhJWLWALOCh0yUHBtQwgF95tCzsHhK66H/pdnW9ovl9+DIrhPkcF3La3awfAKyt8vnC2PvmpWmotblDEuLGIlCq4pnzpNV+QHY5dd3Uk2hLgxAFBwbUMIBfejes6XV0iR1yJ7Wu3cu9D50C8vX3hBfspyCwi5+/PK35GuoblFnmwPtmvkdiMggaQCCq4pLdrl/JtR1Jr1TiGg4NqGEApuk/ecLyd2Z8ivvmZ1v74plPNvn4pWVy63eV35O84luGHrLar1mjr30IKz0MlhFFxTyg/1/v9m89C1AwoKrm0IoeBGe+NgxRbJsLhffWvk/LvcaVJgKS98qPyd7J59rmFZdMm7J7audojt35t+eybsB+jBKLhm3FFHc59c4N8TTAEF1zaETnBvkIU5/28guyzuV7tXc/69GfGTxZXLVZwWxD+6Bbe4hfHI5NtRC9NleRkhBQ4Cj0TBNWMn+cf7ZjdJDF1LgKDg2obQCW4S2ZHzf1r+yRb3q55qZrXhuxZXLkdNVP7OVdS2YN+1ls4/nyGS4+9mR83PAwfOKLhm/EpUoTQzi38ZupYAQcG1DaET3PmuZS0XL7ZjF/SL0qq43cNLWJy/6j6Zp7ysDqsf+3kBK5K7q9jrDCB4RNFy7tDjLlBwzfiylPpd2xdD1Q4wKLi2IXSCO7K06s2IktYG4H/gDDTtZp3VExYpZJXz9Y7iJbrU2rpd9mzXnYb5m0FHouCa8e5L6nff578fqoZAQcG1DaET3A5NVW9Wu8xmLeMEWe198yDKwjQ7CjtUCl6jq7V1/0kUN+TsfIriVgUZEKPgmlH7E/W7vSQhVA2BgoJrG0InuHW7q97cieDOJMPFBnJA9S6mpaWVyxI5m/P/4GhrDSzmE+ccRTnnclwvyJEouCZkFpikfptVcniIGgIGBdc2hExws6N8Iu7X72RptxaqJ4jlCQWttQCaQ7z1bbE4Asr0cKf97XMuA4iVgCNRcE04Sf7yef924xA1BAwKrm0ImeCmkj/UbweWszQtw/hC6nfJFlsAjS/i/T+z1CBL644t4Xxp6RLc0pf5j0TBNeEv4hubYno+ixc8gwYKrm0ImeAmEh8703hnfjPLUPk9OMiKHmZl5fLAqqo3H1a3tO4vKjtfOrttfN/mPxIF14RJ+X1nfw64Ahz9C0DBtQ0hE9wfw32SJVwPszR4TZsYn7cd6ltZufx+E9Wb5cSSkLgeursiTAxwC24Ffos2FFwTetTyfZ9dakhoGgIGBdc2hExwP6vs+762pav99Xwjyvwcfp1R0C9i1FbD9wpMsLLud1o4X5xxGiLa/wlwfkDBNaFZe82GdxuGohl+gIJrG0ImuK018Wr6VrKyW9G+oaBOWmstW8cnnnnrpqxy/tDiHefLLySsWcsSIF8zFFwTSmtzQ8+IuB2ShoBBwbUNIRPcav183y9RmVoFzIOwX3w3VOltXeWyXH6E+t1P4YCVLVPqu8bmV2eckZNJPORIFFxjbpAFmi2HNGYLuRYUXNsQKsF9lE8TDeuCKpZNwPj4PSj0qGZd5XJ2vmnqt+fCrEn64KLaZ97/a3WEHImCa8w/RJtRJ7ustRYmQQMF1zaESnCPkjWaLdUtzDvm6/cgK+Pn09bVfp0s9nn//DvW1S1Hx3r/H18QEoMcBdeYeUQ3gfDe86FoCBwUXNsQKsGVdAr4ydPW9epXolGqq9o5hkA4rEl4GVvIOr+K7HxTvW/OglqNgmvM0PK6TT+F36QUzH2g4NqGUAnupAJae6dfCSRFrTHfFNJuqfeeZZXLmzTj5z3uWDZWcMcnKWXzlwGHouAa89Yruk1HYbPkIQMF1zaESnC1NpGyfJpYl1r302e0WwaXsS4c2VLiu0qWXdG6JblU8qfq3aywM/yHouAaU6OPflv5z/TbciEouLYhVILbXD/vWbEfpZx/aPweHKwhey2r/cdwTbyavk9Y5pe8n2xUvbtZABDnDAXXkPTIqfqNneuJb4gfoODahlAJbnm9s+0HdSzrVb3u2i1pvpGiAiK2tGbDWusC7m4le9Rv2+seBNig4BqiX6Z1MCv8mviWwEHBtQ0hEty76nR+bmaF37CqV9H6FNgvW5cY+NNnNRseFhllVd0ric8kwgpf/TUEBdeQeJqhygnfEEq5FRRc2xAiwd1Ntuq2WbeCkabO9+BmXJRlqcfe1a2+dKhrVd2LiM+vzqOSA7kPRcE15NuCtLAUFaybxwoiKLi2IUSCu5hc0W3LLvuFRZ3S+T3ISs7KjZSSftFc54+w0DI3uR/CfGWhd3nu6DUouIZ8RJ2x6lJbdDv8AQXXNoRIcGOLUTZ2aGBRp3R+Dw4yilmWpLWGblR0Xes35zdjNR/MVv48MCi4hjTuRNs6J+yq4Hb4AwqubQiR4L7/AmXjD/lAObzY/Kr3KZLltxpZU7mvM5ibl3VmEX4ySBPDJ7sKdxQ1FFxDSurn9R2cIstEN8QPUHBtQ4gEt8EHlI17yVprOjW+MGWjZaGhMsJ+0m2bHAlxwjWgh/bBd1Qh3tyyKLhGXNH4Y3uo9G+YxEXBtQ0hEtyiYykbs0po4+f5SZ+alI1HfVwKAuAiWa7bdpwssabyDlrfshPkN85DUXCN2EKSqdu7aU1OciMouLYhNIJ7ka5PbV6yplNvtqJttWpBei/Zot/4zPvWVB7TVrul4euch6LgGvFL2D3q9nlh1nmUBw0UXNsQGsHdTDcv/a6ANVFg6n5M29pN5+/rH4nkqH7jsBLWZEtv8KF2y/R8nIqAgmvEoCfp28+QOLEN8QcUXNsQGsFlDDd2WGS6VVK/qiUrtlupltS+iFBCTG0jGyypvPoA7ZYr+SguqTRQcI14k7WsWZkSYiG3gYJrG0IjuIMrUDdnFB5jRZ/SyC+0zZcsChQ+NZISOSGzNL+HghGl9Gvpb3BmwETBNUKbYSSH7jUYO3IRKLi2ITSC264FfXuMJdZVx2le8w5qdbGidnk49dfiI2tySkRO0W2K40wLjIJrwMOIGYw9C8kFoS3xBxRc2xAawX22F337uELpFvRpPTlI3f5ZOUuCen1CjTC1ghyyoO57lBgTaUX4jDdQcA04SBIZe1K5zUBCBwqubQiJ4GYWmEzfsZkkWdAnXb4HNysZQgykDTUMzr2C31pQ9wWKyZncrRLXDwUKrgHLyDnWrmo9RDbEL1BwbUNIBPcUWUnf8bDgRAv69HUR+va7kdPoO2A0os9MvNnEgroPkfX6jYlkM8+xKLgGfF2I+aP1SXWRDfELFFzbEBLB/ZscZ+xp/qYFferDsmVv2saC2uXK9FSvM63Ilp5Edus3Zlbgyq+JgmtAV3a6yN/Yg9/cAgqubQiJ4E6LZE3VflWMOzgWG7rfg4PRRayYIi5Enzu4EKaffgWzipyibB1cgie0JAquAQ07M3ddJIsENsQvUHBtQ0gEty8zQW8iIOA2kzqfMHZsIdsCrz2NzKPvaPBW4JX/Rq5Ttu6jzezqQME1oKiBwWENXX6Q3AYKrm0IieDGMB/t71sxzUr3e3CQXpi1B8BpVo7esVGB+8nNCKM6rD2nzwCnBwWXzQWjDKW9qohriH+g4NqGkAhuRXak8UbtA+5SGpnN2vWmBcEadpKd9B17yV8BV/4NLc6ZLE8owJF9CAWXzXqyn70zjgByI4cEFFzbEArBTQufydw3pHTAtrIsvwcHU/LdCbR2bdYxFZW41rYMGUr3+E8N/9n8WBRcNj+FGzx9WOWCGDxQcG1DKAR3P832yc1f5HCgXWL5PTg4YMEgdC5h3bv9ymcFWnlvRpbeFk3Nj0XBZTPAcNbgWV3EoFwGCq5tCIXgLiPnmftu8ozljJlPmMPY7HKBRzxgPPXLyorfjkAr78SY85gbRkk5qwEFl81rhjEu+1Yy2psLQMG1DaEQ3PFsI3RZrsu23+GE5feg8P5zgdYuD2QOlh4VDThtWivGcuLtqHGmx6Lgsqn0udHepSRFUDv8BAXXNoRCcLtRgxG4GUAPJAaA9ViuYEG46S6Nmbs6BSznDC82R9XmMa1QcJmkGT83XbHChDqYoODahlAIbpNOBjuXU03/IbxBjXXgwoJIJa10ORly+I2YP/gb8wwriOBKlm2EFxRcJntMAi3X4s7UGRpQcG1DKAQ3epTBzssBLxkz/R4Ung7YyL0uO9bJzXyBWhGXYwUGSy+li0yuBQWXSRwxfrDpz0gHkVtAwbUNIRDc62Sh0e5nApVEpt+DQt+AZyyeGMHe16JlgJUX+I61p18Zsxw+KLhMYosZ7/+DnBDTED9BwbUNIRDcJOOn415VA+uRgd+DrIStPRZY9dmRBhlvvo+kZN8BwMhVoZBEVpscjILLpHMj4/3Xw38R0g5/QcG1DSEQ3AWMcLVufjMwGuPBwO/BwS1m5H9ObhjNAp8KMCPhRbKUtSu7ulleYBRcJvXMDG0Dt40JKii4tiEEgjuyjOHucwGK1jrj1Asv8IQlMOAIM3WAQs3AblyjymOj7hofjILLIrvQeJMSnz0hpCH+goJrG0IguO+aBDSoElga1XlsvweFkcUDCwC5hewz2Du8eEABIJPILua+k2ELjA9GwWVxlvxhUuJPZoTmXAEKrm0IgeDWMVkV61YzoB6NLWq4e32A7mBLDRe8/yHrAql8rdF938QkwyYKLosEU39xCxwcgwkKrm0QL7jZUSbJv+aGXQ2kR70M/B4cPIgye7w05qcwozFsVllT6y0j4ohB12dEGKeXRcFlMT3CNIB7vU4C2uE3KLi2Qbzgppo9350wfQA0xMjvQSHm1UBql2NLGe7+OKDYqjOJgTJci5xkeDAKLou+5lnLvihrSUbnIIGCaxvEC26iaT7xJz4LpEd1TJKwTiwQUJzwvsYTHvHkQACVfxtltLddXcODUXBZvGqey26lJVnugwUKrm0QL7g/hj8waVNndsI/Dgz9HmTFzXNtINV3eMVw9/2AZiyGGy6WLzUWcxRcFhUGmxa5FfGjgIb4CwqubRAvuJ+ZPnT/GHHb/w7dJ3OMC2SVHuJ/7bLcvIPx/jYmNvaG9DEcPj8oPtxoNwoug7thRq4wbhqYXNeQgoJrG8QLbmuTOVZZPsjKGsbDMdMBbCejYGWmMMPLuPklPIB4ZJ2bGO7+uIJRhHMUXAbJZIt5oSGlcvEkLlryu3kAACAASURBVAqubRAvuNX6m7Upu9TQjLu37/hn0ZpIjpiU+CWclhmXl2iTGYuLgXiJtn7DcPcGssFgLwoug0XkmnmhvwOafA8yKLi2QbjgPjL1rc26Muk3SWHtnotwJ4V5xMQhS04xyuBqRnrYTyYlGrHDN5ryorGjWlZFIxNmFFwGX0VzFLqbb3qw2+E/KLi2QbjgHjF55M8+kyB5STgJldyxJoGhHFQJINnjRbLcpMTXUff9rv3ZT433DytqYGGBgsugA0dCOMcPZYA+38EEBdc2CBfceOMg3bc3SL4kAr0gTPweFIb2/yfh71UJ2w7fgE/b7TWdD9xPJHCtHsobhH5UOGw0OEfBZVDbKEByDsOiA04BGjRQcG2DcMH9rqDRmPWCpCcF1KHWhukCHY/lpxJVA+jj0JsskRw1K1KZ6/6mEjXBpEBdg/kKFFw6WQWZQYbVrDUMkhFaUHBtg3DB7VHbYOdZit5KEiiC7XPGfg8X12kG0OcglSsLMKYRbweU9Xeo9IjMNCkxOZK9/oOCSyeF75HjfuT3wW6J36Dg2gbhgtu8PXvfDareShIkQG4JIyuC7CP6yg+A5hWmRpoWX0eSIDWquEyWmJS4YLDkiIJL52/OSGBN2gW5If6DgmsbhAtuueHMXQ8T9XLowszwwIuh30P2LlrlSZAB6XDzFD3pxU1mYpmcMIyd7iSGbamLgkvn+0g+A8NAA3cGERRc2yBacO8QdkbqAyy9lUwz1uZwlCSwdx6i176Xu3ZZ/oTDa6Kz+bodnZ3moSMXsIdrKLh0ej3LVy4xbPvFMympV00ji4kHBdc2iBbcXWQba9c9pt5K0g3e/iQahD49x6odkNy8jamfnCzHFdh7JDkpKfnoFeBkrrnThnw3ijllgoJL5+W3uYpdTZ7v/jpsOWEW7UM0KLi2QbTgLiZXWLteJoRE1uidI4PxnctGt1shSbMbFSn22kXO/sxl+z1kMGcsEvgHNY0+MC1ydVtOxWuTDdO3afndJJu3QufqrElkFFw6ZYdzFLq5zecbcSigxB2Wg4JrG0QLbmxx5q7Gz02aFNsh4g3Pl75LkWGjottK8VVrjh/6ZHPO/oxh+z1QFsw8HOSsXZYrDzIpcDvJt+pkQDDIWcR8aLWauSSHgkvlFplvWiZLN5uVwBwXhAIUXNsgWnDff4G153bDF5Vv+tCwH1xf+RUl+kjSsKglM8g8SRqYk+n31l9DmjJT28pyT6bVWSZbbyXpkdnn5KGQSbqKVF3Vify37sQC5mUyyrKi56DgUtlOtpsVSU+ifCVOiGgcJyi4tkG04NZnPpKfcQlufPm3XV/46WS2JC0h4+f0cLwZWVB56r+yfEDdcEKIgRUA2+8hhjFjsfyN8lF1TK0D3Nwj8wz3H6apOfcU8ZdlOQoNKMV43EXBpTKfmC0AZG6m/gifFNI8LlBwbYNowS06lrXniEtwpSZNXN/3McShhlLUYMefcd2j+11aOqB+GHFhYGr7HDNOQjP6jIX0QvSISQ1LcAYQO0P+Mtp9kj5+Ns5F5qVfDY5Cu8hK+g4UXCrDTX/FdtOvmnRZRPO4QMG1DYIF9yLbtH+/W3Bb13B93QdFKn+jezr+tK1UuD1RMfzmTdYcANvvoTF9xmIeGSdJS6O8KcjPLP+JbVywwyCPuSxfZty5EmdA9Q+Y8y1qnulI346CS+Uds+n/M6yrlsA90RRsUHBtg2DB3USYRq8H3IL7YhNpmENUZ4x2jXAHOjd+SfQUKVGiatXq9es3iYlp07Hjh716DR42LJZ0nDVr7tKl8YmJ/yQnH0tJuXbTPfmbyZixmF59ieNdCWdinDPLR7SKdtTMNon4i5xhdy4zgXbbKmzi82Z7k8PmTJbHFaTrNwoulWd7G+9nXzUp10TIRcG1DYIF95ewe6xdR92C+8Q70oq4uLj4qWSuY+gZNnbSEGVr4erhXqntvnTBrFmTJkwYPmxor17dO3ZsFxPTtH79p6tWLVWUIsyERJQoUboee8ZCkkaR3/9waa0TtmHBHIN98jHmncvpnNz0PZ5Sp8PoviMouDQy8k8xLmBw1ST/A21aCwqubRAsuIOfZO5KdSniiJxn/uL9HSPbAkv6FV4uSXERq68t7VrcLYg/MytJIEfkzJs3r6SkHEpO3pyY+OfSpbNmzZwwYeywUewZi/j+ka2rqPQ5P7v93xRh78swuHPXcQ1xa5kMxty81IK6GQWXxjHyt3EBr3V2Q82yKjBsUhBBwbUNggW3HV0rFO41fG7KlHGd87X2fNs7l5w4pXwbaVF088kTn6+qjCzT1w+qoSgiO1wCO99DOnPGYk7tqF5SGZXgRr710eex036Vthw4px2PD6zK7hvLDMLBW4tNY4wpVBjGU0qeGX7myon9u/ceOuMzAkPBpbGSnDLcf8srrw01y6qStElQI81AwbUNggX3mT7sfU0UwXq6l1ewOpaJbusQrJkNihVvnjN1emp6q6hEZh1j2H4VjegzFtKUQs1+laQx1VWTwy3rVy3htojIV+qphq069R42YeaShJ3Hr75vkJOXZQYhSd+SeaY+uwqFv+EpJZ8ascJzjo3HvDZiKLg0JhYwDkmjmlHQGIIrALxWggkKrm0QK7iZRhNqBp5g0h7O7rD9HuSm9BmLFaXauYYyh2KrugW3sbP87bN7N6yYN2VU/65tmtaqEOWZDn6ydrO2XQfETp0fv2nf2TvqEzSim0FIsQ0jyDyesVIGMcuX5myXr5V+wgmPoKDg0vj4OeP9qgBymmVVhVxiGYaCaxvECu4pIzPWBwaCyxuSwCAHewv6jEUsGTxu3Lj5qY4SWVv7l1dEleo78ejK8R1r4p5sMLRXx5gG1aMj3PobXa1BTMeeQ775OW4NwwxCmtz7XTJPPZF4l7GEdp0sNu9hiu6z2eQehqHg0mjawXi/yulBs6yqAAhrFExQcG2DWME1jgXNHuLyDnCN8j20ps9Y9HAp5zRXoayNn5YhBvFpyo/0/Hcndf/m+AVTYwd82K75cxULE1KFbQYxjcyTMpSDLm/4eUBMRRJJX/0+aba+I8vZ+yifToJrghgFl0apL433q3LoaZZVFXKJfy8Krm0QK7hTDWNBZ2jS3+SQyB0ur/gY9j6aw7wbdWLIzE1sU9vsyKmMPelXD7DNIBTBXTXpkxdLeFbl6J4Vu8k/Zv07SP98nGt7KLgUrpJFxgU26QT3RdUI13jBTRgouLZBrOB+auy7epuhh9zhX+4ahTpg1e6AnSjMlxsGD/132I4biuB6JoEVKtJrMIrl60IfGsfFBmX8jIJLYSvZbVxA9TPsNQTPAZLcKYig4NoGsYLbso1xay5S5YR/Iu0wYRswyPIelt4auev6cNSg/nSG44ZLcBepHTGqxO84n6Gv4Q9icn+nMX8x9ssouFRmkzvGBVSBGTWG4AqgcMbBAwXXNogV3Ipm0WSvUYKE84Z+kRW/B6Mk5pmb9JUrrOP2md9slEq7Ed0MwiW4G6bV8fV+Cy/foF2/cQsSDnktdA3d2BSYvxjOrG8ouBQGm+WgU/3Gaw3BJWktKMFo8EDBtQ1CBTctzCwNuHx/q0ZJNnEGfnFikO/BeX6q23wif4rK5QZhFuTmdDMIl+CekOXkXkXcYtv/XNKKH4Z3ffXZwsq7qKeadxk8bem2M99FGp/9Lltvpd0ouFTatDQpoAqT3FCzrApYrA0yKLi2Qajg7iMbzFt0aaPqG7/uHGiMYZBPwsl91Zp0jt4CFP2nMMpMgIdWDMcNp+A6H2zvL2jm9KeYkHPMvSPrF04Y0L7Jk/mco946b/aInbVqH8P68xWGK5vz9QEKLo2nPjUrsdPgZ8w845EYUHBtg1DBXWY2Seni9rHNfytf902HbwAf6Qz8Hlxk7NDeU0mQGHyxpQx2GoSd8vqInhhZgZCF+oOzLiavfKVk99a1nRF08ldq2uGz7xZtPOYzx9CE4crmfO2BgkvhUb7pZkUM1lI5g7wFHxRc2yBUcL8uxPsNzixTtqUf3/bXWpsWuaIeQEsbeJNTuuhrmHGbGVhVkq56S2X+3YcxK921ofL3waktcd8P7PxStYKK9BarGdNt5AznItsDRg4i12uhOyi4eg6TtaZlWPHHfa5aaEHBtQ1CBbdbPd5m/UNIAT9yVddm5nvwkn1lv3somrDvMlDU333FsGbKhIULVt5HX9rG+L6/fnD13DF92j5fTpmHCH+iEyuir+t1Iwqunj9IqmkZ+sy+g2QBDeQDBdc2CBXcJlzxXhVGOyTGj1BN7AQ+PmTfn9L0pZT78CF0c2M/UdbTaQJfDJRmjFQOcrqyyDbsS4Yrm+u1UBwKrp5votjZO3K4Qb9qm42j3ogEBdc2CBXckqN4m9WIGGYuY3CXIyO2ixcIkcDVy3INVsZcNxfot65ZFkM3ddh+yQpnGa5s7tcfUHD1fMj1THWedtE2+PGEFSxQcG2DSMG9ZuZmmcNNJTZMM3BnjP0e1C0JJ+QLcPWOXwwDz2EnVFcwXke5ioMNd59nuLK5XgstRMHV80JnrmI39LMK2w3sUYSDgmsbRAruP2QnZ6uWOJfqwQlOjP0eVCh+X89Da3c82oexc0240d+667nNfIuNM9x9leHK5n5NRMHVU5zzMemBZuUs4WRuMVBwgoJrG0QK7nzC6ynZ3ekfYL7ArGEOYWZM8+V9ZRWKKwmDDxfJctMyjw763rrHuGcCM8NmGO5/wMhB5HoteBcFV8clEsdb9NZ2ldweNoqxFAJQcG2DSMEdUYa3VRWdgsuXcEZFbAm+clnOhDrwSdy9ZCtHqfuH13vu3E3HHvLXfstsxqUJw5XN+fox2uHq2chOEq0n4/zeLbN+Wbn9CNT6O/ig4NoGkYLboSlnow64PGBfgHamh0l0fw87nNUPhFYvJxLOrIJ3Uyf37H/sPCxBS4pRdHaFVxiubM7Xhyi4emaGwaalNhBiPI8eIlBwbYNIwX3uY85GfedOpwCN1fS6ud+Dk1hn9dxGwTksItzTEJUJOQesfS/ZYlwAYylA+bwSrPxQQuoHpyWBgYJrGwQKblbUBPoOHS3dQV6gD/01e/GVa+iK13UdWL38fSTvw+YxR/2/AWvfQA6alMBoYUBebwUrX9fxreC04RMKCq5tECi4Z8kKvjalFXAL7mfAzhTj83tQjMIU4oHVy8PNYv3l8L2jeg6vNx/iTb2i2FnfMB4ulcoDQMUvKS59fwapLYGAgmsbBApuIjnE16Y7zetWjSZVq1Y1SUelhdfvwRMMHDyJ+wn3LESMo/qngbXPM44tqcDM+KCsqqPgakkL/xFUfr7yrYBptBhQcG2DQMGdEQHw3ZmSH96XQ2QdV7n33YILnsRtw84J7Mt95xgdEDld4ft85hMWB6h6iznN6Own60HlOytXzSzgXChAwbUNAgV3QBVAuyYVhPdlLacRQYxbcItAzX8aGeTz9SHeWT+3DaiL2GjzMtl7aXrrmnZEwdXyO+w3L6u0ctXCGNGIQwkKrm0QKLiv844PFSYUgvdlLq/fw82bu8mClBRw9L3KZhmCPPR2Cm4fWO2fVeMpdUqnt5vc1mcouFrGwn5SXdaCZEmwmuM/KLi2QaDgVoXMjn1bBN4XXr8HB0c4Zx98KcRrZlHJeec+A6v9Iz5n41vbfOQ24bgnHhYKrpYuDUDFx7gEt3eQWhMAKLi2QZzgPoww9lz1ZZxJshwavH4PsuJa4Ufwx3tGSdjVHHTducCH03de5Sx4xZsVZv1Rb8IKFFwt9buCir/oumxPBak1AYCCaxvECe5hkgBo15iS8L60eoO76B6yDV7/aTNXMA8T3ZPEv4Oqb/EOd9HMy8dGD51y8LSPWQMKrobswl9Dit/K575s5jHLRYOCaxvECW48OQ1oV2xpeF9qcfo9ONhFdsDr30528RV8xX3n9gVVX4/XEU/hdgQpr9mEgqshlSyDFF/hvmq0lHMhBgXXNogT3IkFIBH0vywH70tR4/CGav4hfmTA/ouc4StY2H3nwtxEK0Mi9C51VK/5AUPB1ZBo6rrnw+m+vXpVLtex43u5JTm6FxRc2yBOcHvUgrRrxBPgrtwmC7jLbiH7wPXLswlnNJpDiYnDyM+LZ/0Dqr64WXRzNUoAS42bBwquhhnh4KQN3JbWYkHBtQ3iBLdZe0i7hlYEd4XX70FhPTkMrl/+tjB/2aWEN8+Dh+wI04zeqsJPOAT3I99tKLga+lUFH/IG/zKASFBwbYM4wS03HNKuwZXBXeH1e1BIIMfB9csDuQxlXSwm0CAot8mv/IV3KzMWGkcSFFwNMXD1bNU2CO0IHBRc2yBMcG/z2lS5GAgfnXD7PTj4m6SA65e7NOIv+6t5YAQNqZBgOmMoy+kouBoqwiMex7wVhHYEDgqubRAmuLtghlifVQd3JRZgSSb5Y/sDuRvn8M735rAPYhrcyCm4vhkiUHB9uR82C3xMC9C8lzBQcG2DMMH9jYA8afvVAHflkzr8ZZeTS+D65bqAgIs/E4hNhsImwDqeO8Ckb3tQcH3ZQzaDj3m5YxAaEjgouLZBmOAC/G4V+tYEd6XVm/xll8Dk30X5kfxlfwiD1h5PznKXXegyO/MNAImC68ti8LqlLL/El1ZdNCi4tkGY4HaGZSjrze+m6+FZQLCYRdwJhL1kR07lLwwPL7mA3OYu29lt6OsTDAsF15fRfniHN3nf+nZYAAqubRAmuEC/9h51wV0pAnDkXABYYPNwnSzmLwyPdjYtPMu8kIvMkm7B9QkAiYLrS6cm8GMawb6lokDBtQ3CBLcIX/obDx/zhc5SAfF7kGcTsE28fJQk8heGB98Zy3/EAY8Tan/1VhRcX+p+ZF5GS8Nu1rfDAlBwbYMowb0AjOTSrSG0JxC/B/kn8JqWsqq1n79wbClo9V/wWx5n/bV09uslpkyY4OOEioLrQ1bUt/CDQPEsxIGCaxtECe5GshfUrq6wKV8Z5vfgx5qWLC8jF/kLw12TP4FNogzS5c9AwfXhDG/OUjUQQxSBoODaBhGCe6t3bNyXYfdB7XofPAHHHelA4ftIaPWyPCMsg7/wkErQ6tu/AireX5ejEgXXhzXkKPyg2sAsHYJAwbUNIgR3j3O+sdzLPQEBYzo3hfYE4vcgfxcFrZ4v51gOcMeNV98GFe+jiwWEguvDtMh0+EE1YRE1RYGCaxtECO5VzxrP9/zt6vgytCcfQ5LwfuNHBp9PIabB/YD5dWT5edgaj767KLg+9IG7zsjy0/3Ny4QAFFzbIEJws6Nceht1nb9d7VtAexLTBlB4LMwNw0kHyG9AL7AdcbXPQMU/1E1yo+D60KKdHwdV/9zydlgBCq5tELJo9pRLcPkTMsjyWzHQnkD8HuTRZaDVy3KzToDC3cFmbdGxoOL6ORcUXB/KD/XjoCq8eZnFgoJrG4QI7qsuwQVYVcltW0F7AvF7kEdq89Nw8Ew/QOEPAJHFXEQCJlxk2iMACq6a22SuH0dVHGJ5Q6wABdc2CBHcbk69BY1Z32wN7MgtiN+DP/HN5RKQjAzvvQSs/S4sfCXlFwkFV80OAsu34eLJ4Va3wxJQcG2DEMEd5RRczpS3LloDItE4OUjWA0p/AQ+3mx72E6A0eA46FWg2+rruA0LBVfMrOAK8whOA+EQCQcG1DUIE9xdFb6tzhwpQaAVd8lgDyuGgt2I15Tz5A1AaPCVygGwAlW+psyJDwVUzwo+0z7JcZpTV7bAEFFzbIERw1yiCC8jY5aDlO8COzCYQzwqQiZeLfWQLoHRraHqXLcA8wvolPBRcNe2b+XNUKdjKpShQcG2DEME95NDbIndA7XrlXUDhs29++NWbRfcDrM56woORwdKg6QegJqzUZj03oUkX7RYUXDU1/XLSLQELsSQKFFzbIERw7zoEF2jgCLLB+sftWFFoIe8RcKstYAhdcOqA34BzjvW7a7eg4KrILDDZn8OKjbe6IZaAgmsbxASvKULCTsHa1RQSev+6x5VN4j2iK9hqS/4+MhtQGhzJekYYLH7ZczqrZhRcFSdha7QeCk2wuiGWgIJrG4IuuHdOH9yTPLh9d4haOWise2I2Itqlt+W4vefhoRrk4RUgpRt+CKx+PNDZWG8VjIKr4i9ywp/Dor6zuiGWgIJrG4IruA8Or5PcrE0GPTLDQu83cQkuv00PyE3XxSeQWA1yvU+A1Q8GWgZX083RoOCqmJQfENrNS/4pVjfEElBwbUMwBTfjiOTDrrv87aoPCuXykVNvw05yH/B2S0j1TmCGXuA4fz0AOYcVKuo8V1Fw3ayr0rLvi5VT/Tk03zSrG2MJKLi2IYiCe2e9pOU8d7tgofe/dQruq/wHtHkdUr0T2CQHOOxUR6AZkz6FMAqumyXuJdQGB8CHhv0QhPYEDgqubQie4F7Rya2DI7ztqgOy6lmhT6lozOuQ0GIuqnwRvNIOYoCeHvpYNyi4brZ61lAB8ZddZJMZwWhQwKDg2oagCe4tmt5KEu9SBuyR/LBye5UE5IWMgZnJxtaJ6RL52tyVB7mPeHIY6ASy/MIHsPJFvtFuQcF1c8att7AUGgoZZGYQ2hM4KLi2IViC+yCRLrjSJb52PQsKvf8on+P+gsSTfaUDpHr5Y/ctHHab94iyX4FOIMtPAecgCk7SbkHBdZMeDjQSzOEh+cX65lgACq5tCJbg7mTorZTIt3r89ABQN6oBHyBBZr6yPNUtuPzuEiUhocUUSgO9+MN1yzsouB7KOi9WFXhi5jS/YjoGHxRc2xAkwb3O0ltJ4kvtBwy9/wYhIFeGxrAH+HVuwZ3KfURRqMtSfphnVBb5UbsJBddDfefF8mM69h6Zb31rLAAF1zYESXC3sQVXesjTLmDo/YEE9jCod4w15JpLbyM450Nk2hO/MffJHFD5h2S2dhMKroe3lItV/B78wNtkkfWtsQAUXNsQHMF9IEnzwvL/nqOx8Z3LRrdbIUmzGxUp1mwnT7sqDebtQeaVI7uTln7Z8wTE0r1uD0BhB+WcgguwJcvHPxh2cp4sB5W/q4+3joLroa9ysfzJ3XCDLLa8MVaAgmsbgiO4pyXp44Jhg3IEt0uRYaOi20rxVWuOH1qBayKUd5X/1u61OWdJ4h+A1vqUu6iTGKfg8t+N2fonfmOOkERQ+Rt6IzgUXA/jHdcqnz+OD1fJEssbYwUouLYhOIK7XZKqv/rMCx4lXFGijyQNi1oyg8yTpIFcYbH4Qu+nJfvOVmy9ydltqF/CIKclPf9D6iMyC1B7UsKOOJIEatAlsky7CQXXw6+Oi/WePwdeJkutbosloODahuAIbqI0k4z6KN9itw5OJ7MlaQkZP6eH483IAqq4tY9YQWC5Qu9f1duecQaVrTqQr5yHBYrgAuLRwJa7CznHzwXLAeY5Ukm8dhMKrof1jk9zuz8HXgBl9RAHCq5tCI7gSlKXwn/MJAPcKjiGrHD8jRrs+DOue3TXq8qJ05IXjXjn6XxkG71dPKH3T9OW5PZzhSXTRyIwZo+iiICHftjqSwO3EQTAODiF/K3dhILr4Rghjf068Bz50+KmWAMKrm0IiuBmS9KTr0pSxXpuERwUqfyN7un407ZS4c82zRn8RpUwt8gwEstwhN6/SDeC4DI7e2IE6FOSH+Yj5AmAXSdsMrCP+7P4nf+QY3r5R8GV5ewbh5PWrVn7w/A/AG6HXs76F0U36KDg2oYgjXCnkT6zZrWKWCgNUwwiR7tGuAOdgvgleZaoYCx0FfvarOW36XrLFyGnzGjg5+RoM7fdhAx9Np3t+iiiAFnZDpBN2k0ouBlHE7xfg838S6g5UJ4bcgUouLYhSHO47V0S0kdaERcXFz+VzJWkpWFjJw1R7oSi0Sq9DY/beiqN0q7C35q1fDNLcBM4wpCDHcE6wTzZUkF+pXtdn0UnwCF7yD/aTXlecE9rpvS3QnIiOTlB1gajYQGDgmsbgiO4SaVfUb7xFWq7vvkrivd3jGwLLOlXeLkkxUUMaOoVXOfMQvGaMR8On75s2xmvT0TURJOGn2fprSQdNu92EYAjWMb5vVvWLZs56eBV/kTvp8ga/hPIGVHOz0Jnd2DAdrJbuymPC25msv6bcAFYB2WiJlcQdMHNvn/1woWr94FpWQIh+57jjNf9mvjxk6w7Vy5cvM7ldmXVGW9dvnDphu/4LziCu5x8rXzfu4bNd33xO5ecOKV8G2lRdPPJE59/Mk0+MqysW3AbXdq7avaYPm0bPBGhvC1V+7VuX874M+lcQTNP1w1sweXwZeNPpXJ7h7fetQd4vyBHYXduY+iMgrxVP+DO24KbQX3igSRalpWocxuC07oACa7gZl/Z756KSdh3WYjmZl1MdpvPJx68JuKEcsa5XWtcZ9xwhDsCVUA8OrPd/SXcfFyVeSE4gtunVLxyprlhPVynjO9YJrrtCkma2aBY8Zecdgnpf7aLVFTmrZyWZF5IXjkztkebeuWdwZ6K1Hnj49E/STvP0x3IbjF82Za/UT6qzmrTT4PXEezBbs0dfIxvlHuAbOY7gYt+So9B8XTWE11o4TwtuNlJ9N9e/pD3CpSZ8VxBUAX38kb1B7bBj6lvINnn1qnPuOW6+SEBkpXiM9u0/U7Qz5h5zOdrmJwzbRqkWApb6V9/J57x5+XJtQiheXxlnN8RH/Z69zeecw6Dw8vXa9MzdtbKPRfVWneM7ssmvRA9YlLDEqaXMIwvssktvaHvVq5nEsoUqxHzlY6CTEAT9EkS87TgHmJ920DzuHvJ1mA1MCCCKLjp27WfWBJ3Klb/SNM9iyTD47qB0OeeORzkgfw1nXB4spaLjxamHpnt/HwLvcHu0PuPUpP+/GFkt9dqO9fZIp5o2K7PmDmr9l7KlrfQfdnmkXGStDTKLOZTBvmZ52O7TGv/Op4n/x36KVYjDih+bJAZBfkvcla7KS8LLtNkRQI9aQB/J4URPMG9T5maWx/UAeBNSqTsTUGdy6XlnknyK8coRsP8HQAAIABJREFUL2cpZ3T/qgQrHu4OyimdJHD1NJP85Lvhwelty6YP79qyZnFFeiOfXEL3ZZtefYnjXQmPTdm5v795r+lFffUP9LG2KDCSVmzg6MFWspfjBDlkFgLOKMh/EN2CUF4WXMaEggJk4WwX4YqsJJygCW5aAu0jS/Qj0Bov9Jtq3aPgnfES9YybgziqTqGecadzVJ1LMz4YxCJIO7k1buoQti+bJI0ia+WHe+Z//mpJ57ocJZXgPX2sLT0P1zG6wOE1upEcMi+koilwRkFeQnSLDXlYcBk/jU42Auqh2H7kCoIluJmb6J8Zz5jCP1i6sJXfAgjIXcb3InhX+irjjE6XrKDlNLtJPynnsrHZEDSD7csW3z+ydf/a+byWZ5QR7i0ez9v9jM+NZyUmkRwzP0FOZ26c//bVF2GrtYuIbnIyDwvuEfXV8VlMdQAYrm1jOT6GmGAJLsWSLshqxFzc4bDl9ItMfe5wN5xhV8A8ZI01pStyMLP2UidAeT/WNDLPcH8205dtTu2oXtLTKteKMMrcKI/n7T3Wx+Z4ADL9OV5FeC/nw9Oex+HEAwDNnUd03crDgutzU/kspjo4yV/PFniiXyEESXANHgx4Ivr5wQX2GUFLGPycZJ6QM9kXGPZAbUN2MAVXvqN/JD/H22hKfG1f1tJ92aQphZr9Kknl1c7DpMTTL7b7ZPiUhX/vPOu+qhc5wn3vYX83JNNYq/GEr6sa65FtvOEl5ZlEt5acdwX3gc+HqF5MVQDEDdtI+PMyiyRIgmsw8x0ca41s5nBTkpKDcsZ06iS1C75kX1AMBmqKbgRRcOX0w76n23HXsKVqTJ/5/6H7sq0o1c7xbu2DlR0jPXJb/scx/Tu3fO6J/K54BRXrvf7B54PJ8K1HrxmahmStpRv6Onhr8Q6z9i8jl3m6eUP39HGAcy5rRpiu9XlXcH1sYnwWUxXW8Ve0ngTryTYwgiO4HmnwyceywL0xKJYKVzVndFrNT3VvDIo12hna7evelhAU27AjmjOqzqyYzARTcGU57WCOoqxNhtg3UxIa+LKM7ssWSwaPGzdupuOX5Maspq6AZE09h9w5sX3lvImDurVpVKWwK45D2ZrN3/101A+LE/ef11nXXmUY+krSt2SeZLbEGccVZZ32gMVn5ytPya/blHcF1ydunM9iqgIgHk0iAbqmCSI4gut52vbJx+IewUjeNYjsvZO+t6gfBzQ3k9Nqvtgi10bvykhG0riFFp1xu+aMrtvXjfcefbj+K6vCFq3XnNF7ZgdpQRZcB7dTDuyO63scEIdAwXSSleHL1sM1qnWlED81poaPL5uX42TxvoTfpo3q0775s2Wcjm2kSLXGbT8aPHn+yu0nnQPxI3RDXym2YYTjil01af9CwjFCSKXorSRt4rJXmVBItynvCq5PXA2fxVSg4K4hgAlfgQRHcLf6frXd+Vjc4z+3/XLq3M5lCCllUT8Sfc/otpr/zLXVvVB3fMbbxQhpaM0JM+m3rxvX40z2vkmvRcFCRxlwT3PGnDM7ORN8wVVYrLdhMoGSQUaDQV7gRK9k7fqs/FeUgw+T9d432VePbPlj5rjPurxW78mCTvEtWKFOzI90Q19pcu93HVcsxXXozY3Tuj+fn5LcYQ4xN+W+wWj+Lp4nnbEldJvyruCq12dzFlNzAAQA41/rFEtwBPdv36+2Ox/LcvfHli3fTxxW3/WUaJHgPtTcTG6r+W6uretk+drSXpVdQ6aG1pzxpuaM7tvXTZJDaJb2qgCP1WfABW0fPWd2sk+M4CZAjKRczTY1S2WYnSmY3zT7maEO7p3ZsWrBlKEft/2Baeg7zXHFjmWfWj6qXSXXpZqur+ZnYroEmsm0Hkkxbb8sjy6j25R3BfeO6sPLWUzNAeBrtlLvv5crCIrgPtJ/tZV8LJ6PbXJM/pxlZ4sE95b+jIrV/ET35uH1w3PO2NCaM57Xn3GaV3BXen5QLBTcE5oz+vTVIfFCBDcZ7DF5Tp+yS8tOll6tN5+94HDh3MI09FWu2KDCKisISjLfH8JM23CU1X6ugL7DK+g25V3BzfJ+dvG+i6kK+/kr+pPAgt2IIiiCe1//1VbysXg+tkqqb3hEVUt4XX9GxWrec8YCqjMWsOaM79NvXzcL1bZMha05Y3/NGVVndrBFjOCeISuB37Cz5kc8YjmCcYQr2WnuwpnETFqhXLEO6ks1+Yhuhvp7/ZqWhoeM1itw2KsMrqzblHcFV96V89FN1CymOuCyF3HxB81LJhcQFMH1GNNp8rH84t5cQfUNjxpmCd/ozui0mvegclYi5aw542R9H1WCO199Fz9jzRl/1JzR59OVtooR3Lsmbgx6eHKdMAKW8PjO/2PuUbSPYejrumJ91F8O50PXMy+99fGwyfP/2n5CCbdJWdPScIpudeZ8XW0+izvgad2mPCy453I+xzc1i6mStBbgNP87uRK8RgZAUATXs6CkycfilgbpxKyOJS2eUrijOaPbat7N6pRZHYtZPKVwSXtGH8HdmDwhpqDFUwopmjOqzuxgpxjBlQtMAjb7JE+uE30MNElZB+RgEy3Agi8pdENf9xW7c91jdeZgTeLiH2L7dW5Rx23rG1m+dpXIT0dN/23tnlRa+iAn2+hWZ65Xc5uyPrV0m/Kw4GYw58MlyfRKq4gDr+6KITiLZgm+X213PpbRrq1KxpLMnV+/kt9CwfVM/fhazXtQQhE/2vRlowgLBfeu5oy+grvLUSJtzaA6YRYK7hVtH71nlhS7CDGC+8RwYLP5cp3c9wmdrJDIZ+y7Th++W8sGuqGv64o5G3d2Qg2X4KpE9W7KjlW/fj+yxzP5ni3tWgFQPC26DBj74/KNBy6p5mbT6VZn7tddpj34pJ5uUx4WXEZ8JieQnCq/EW5XP6EER3A9wfV98rGUX+YVI4X7q7+oE/akRf3Y4ntGl9X8uLmujZ5wT7f++PQp0syaE2Yn+J7RV3BT3KUuL/7oSfKhNWfMkDRn9J5ZUqIpiBHc53oAm+1jt8Um86Sv595Bzihva/Xhu7X0K0NPWuG8Yh4H0N0DyxNCmz0YWd5xsa8d3SbN+faLbm0aVyvqkuZiTzVu223Qt3Pjt+1lhJd0vf5o2oMPG+o25WXBzWL6jILsYxYSMelXoARHcD1L+D75WOa4N6pd0y+nWNSPE75ndFvNu+8w9VgplTsIgAn7NX30EVz14+cxq/JOJGnO6D2zc3pLjOC2eAfYau5cJ+knPb+a0oYj3PEveOwtDQZNKr/HzMSPP6YcPKSitp2XDmxc9tPYAV1eq1dRSRn5Ct3qzP1Ksx32pfOLuk15WXCZQfiSQO6b8/UhgXIFwRHcDMZn5iQojrZGcQaC42jLCpWoAIpNz80ZgzPuDrZrr4cO0CeEfYSRCoLCgwsnDg/77jwkaHI8MQ0/YzBoksyDi39ezWhvWuqev+lWZ+7XvqYnePcV3aY8LbiMMNPrYboxlzDn3ENKkILXHKZ+Zk6CFMRHmyJQRUpwzriFfcbgZG9j29dL0m1RgtunJrDVe8g2UPlmHUHFlxGOD5sdSs7ci6zfMyYFztKtztyvQ01P0C5GtylvCy41HCg0dcssEsTMAwEQJMFlh9JKCNLnwB7imoc89Y9rzDMGK30d3WNfQQmIJkZwvywLbPRuYhqQy4c3XwcVX0LMgiEoHGB8bhzG8b1rmxS4SLc6c79OMT3B62/qNuVxwZVv6x5J9kDTqHA4CIaEYAUgZ2pD0Dycme4+QbPHYwZZD9Z0fTYr6kCC8vgkRnC/jwRO0Owk5gv1aihTmkZQ8iVQYKTe5lmG6f68SYHbjPCSrlfz+ZSYt3Wb8rrgapdQ/Ui/PYMEOZurnwQtpxljTAFwzgOSzXAQNV3E9ptMXZJgF8HzKWS5ZDm/j2IE91fo6m8SMNdJr+dAxRcQrhnfzF2Uj+0Izz3ZtZFJgW0MqzPXq/kMc3P9HEqeF1xZzjjjCceXuJ/nGUbLD+GWN8kSgia4dP3bHrQEY457ijqpGsxEGw+oizHBjMN5hzqN6zK8ECO4q8gp3TZDgFlv5UGVQMVncwTzUsjWPQEl8Pl+vveSSYF+5ehWZ65Xc9vRF9/XbULBVci8deHMoJ5+pp39PtLaxlhF8NKkZ1MWzg4GdZifSXnGD25QzHTKk2pwY2ak6ZNzJroHAGIEdwc0/TSHK5gPsSVBxfnn6m5v9/nYDnCa0bdvYVbCyF6FY8GwwUe6TSi4HrrrvUL4mFzA0nZYRvAEV5YvaIZjiUGP35OiWavb4M/DCIRs30RWkrQ52ObWmQc1Z0zy2BuKEdyTHKERfNgATDM+BTY0+UGfoIbJzZysFZuPc1tpUowItDDzl0qm4c0d1Omp24SC62GIv55RE6MsbYdlBFNw5cyTKslNOBHE6QQPGUfWqgT+jIB58wfqzI4becKtBMo99UB+q/eOFiO4twgwZUYigWV4+4VzjsAN8NHx3uWzPUdfhfiItn7DtIhPIi4feLIePttPtwkF18PEgn4e+G1hS9thGUEVXMcI8OaRbQmrVq3ddviGoEXD7KsHt6xdtSox6RjP6rUVZF7et3mN9Hdi0kk/p5vAZJxP3rRaWr1+Z4rauFuM4GbnA2ZFSgAml+Kz88rhO/BIpmlnUPEYWmIfDXsZepvI842o9rluEwquh7l8a6J6vi5mbUOsIsiCi4hDjODKZb6ENWs1cJXtb1j5b4uAanfQkkNBVbzM4YiRxXCC4bJIrDhEtwkF18NKwhUzTs8Y2FKAMFBwbYMgwa3ZG9YsaHKprTAzMkpGMBPatAIVf5FnQPxQF+xMga/j5UbqNqHgekgCWnHnEFva2oZYBQqubRAkuM06wJolcQQ7ULOPmaSMCvzG6giLBtGQK9hbxg79fAKnx02pWN0mFFwPJ8hq/w78CuoRKQgUXNsgSHDfMTWT8mUFMLnUafIXpPjIJ0C1O+jWAFS8Hi2EmJ5sTXhJKYl38rHoeN0mFFwPN6FrtB5GgL8XYkDBtQ2CBLcHzBNMXg5MLnWNxEGKD9VGTzSltz7DghG1+nAWTD+sspDZxr/yF/WdbhMKrofsSOAarQf490IMKLi2QZDgDtMnmTUEmlzqEZkFKf5FVVDtDgbCjqjRn7to9rVDSeuWxG1KPguxO4uYptuEgptDWf0MNxeDYQ6LwkDBtQ2CBPc7oAsPOLkULGsaJQWjCSPKg4pX+QJW/avACO3ZZIZuGwpuDrV6+Xcc8GdVGCi4tkGQ4EItI8HJpUqNhpT+FBqfVx5bHFT8yWGw6lu1g5WnjehRcHN4ub1/x31W3dp2WAUKrm0QJLgSOQtqFji5VNWBkNI968Bql+VJsCF6OfMkOT68Ye6Z5sM9Ml+3DQU3h3eb+3dcvxrWtsMqUHBtgyDB3UaSQc0CJ5eq+wmkdPf6sNpl+UcC8jGnWG0Z0hZm5ivfJIt121Bwc+gNfoJx8emz1rbDKlBwbYMgwT1GEkDNAieXatYJUvqDxrDawQ2iWG0Z0v5VWPnLZKluGwpuDl/56cDQyyxRR4hAwbUNggT3GmVEZgQ4uRQsx07nprDalVU8UP4AitWWIR1fhpU/R/7UbUPBzWFahH8xr3rUtbghFoGCaxsECW5m+A+gZs2EJpeCSWgHfc5bE/6EeWLkmwqrHvoLcJoS7xIFN4ffYD+POXxslhkpRKDg2gZBgitHg6wIoFOm0Bw7b5mHq9WwlkCi0tOstgwxTcmj4ThligYFN4e1hCfxnB6gP6EwUHBtgyjBraGP32rED2HAfgyqDCkNTPLrYDMoBQXQDwO+ineQbNRtQ8HNIZlwJM2g8AHwd08UKLi2QZTgNoHFk50WAewHLMfOa22B1cu7QHnb75N5sOqhk4d7KIqCgptDKon36zhg8mdhoODaBlGC2xb2ED8lP7AfsBw7LYGOXcqQchOg9C2yCFZ9H+Dy+A5KAEIU3BzSyGy/jnsPFhNOGCi4tkGU4H4Ey+s3CZqSgTcPr4uXgdEiZfkUKOLfNbIEVn2/Z2DlaVmNUXC9RE3w67AOQGMRUaDg2gZRgjsIFocJnFxqCSjaDTBhjoPzZAWg9EWyHFY91KeUlmQTBddLxcF+HfYO0BxaFCi4tkGU4H4DG7KOLwrsx2qQFUGjrsDq5RsgQ+JUshJW/aAqsPIJ5IRuGwqul+f1WeR54Ei2HBJQcG2DKMH9BeapBc6BA8ux8zxffHAVaWQuoDRsAsLBMGBib1oKIhRcL63e9OuwNmDrFTGg4NoGUYL7BzkHaVZsNLAf+0GLWnXA4fuywyCWtUfJOlj1I2HRH6kZMVBwvbzvn30XNIaQKFBwbYMowd1MWeUxYHQZYD9gOXZq9gVWL8sFIQF3D4Dk38FooPM/LUA7Cq6Xz6r5dRjcXFAMKLi2QZTgHoKN+b4sB+zHdVCOnacHAKuX5ZJjAIX3kH9gtUPzcy8it3TbUHC9jCvm12Exb1ncDotAwbUNogT3Mvkd0qwRwJQ88iMyE1AampDBwRMjAIV3QvN0f1MEVn4eJXwlCq6XnwkkX1EOLfwMXB5sUHBtgyjBTQ/7CdIseDY/UI6dikOh1cvVPgcUppnJGjIRaHc8i6TrtqHgellGLvhz2MsdrW6INaDg2gZRgisXGwdpFiw0gkJpSHSc8l9Cq5dr9wYU3kgxkzUE6lk3g2TrtqHgetlI9vtz2Etg+2wxoODaBmGCW/UzSLM+By96VIWMQEHq7KLhh4DCCeQ4rHZo7IjvKZ7MKLheDpIN/hzW5H2rG2INKLi2QZjgvvABpFkDnoJ2pB4kx06JsdDq5eaQp82/KWayhtBGrEbQpiBQcL1cgi0ZeHgB7BAjBhRc2yBMcFuDbMqhsQUcgggJj1DkG2j18mttAIXjYVbHSsB1/ZysEeMoSYRRcL2kh/3oz2EN/HNQCzoouLZBmOB+0BDSrL7gLICgELcgo1oXb7cEFF5GLsFqnwPM4Uaz20XBVVEcYsWXA+gxSSAouLZBmOB+DooWAEvgoAAKZQrNgAOtP47cgNU+n9wDlR/xhH4bCq6K6v39OapOT6vbYQ0ouLZBmOCOA4WjgWfzA0k0yE/XRXdIfMlfyR1Y7b9RHBmMGFxJvw0FVwUw4L2b2n2sboc1oODaBmGC+zMoD293cDa/QRQJYpFBfoZWD5tVngOKzisrQ+JroPK0cI4ouCqAAe/dPAt3+RYCCq5tECa4S8lFQLO6NYR2BJJj54EfCQEggu74dcmE1Q6d9P2UMseNgqsC9ECSw9N+TUQEHxRc2yBMcDeQg4BmdWkM7cj3+fjL3iPzodXLoyDhdMA5MGnRv4ygTbmg4KoYAox36aI6xJhbICi4tkGY4MLiJ3ZuCu3IbMA6PzjlmIPxkGgHNL8EQ1aSs6DyHzbUb0PBVTGxoD9HVRlkdTusAQXXNggT3PPkD0Cz3nsJ2pHfyWXuslehKcccTAWMoOWJhYC1ryYpoPLvU2wmUHBVzAWafbioOMTyhlgCCq5tECa4D8gsQLPg2fxWk1PcZcEpx2RlWjaDvzDNL8GQRHIMVL4j5fNBwVUhkTN+HFVhuNXtsAYUXNsgTHDlQhDvrvYtoB2B5NhJJfHQ6mGWXrGlgLWvJ4dB5d+iLMKj4Kr4h+z24yg/ghoJAQXXNogT3EqQ+TGaoBizj2zmLnuarIJWT82xwASaMUfeAoxu1ZqSCwYFV8VxssaPo8rAgxoJAQXXNogT3Oe7AZrV9jVoRyA5dk6QtdDqYcta4HC+/4ByYNJTE6DgqrhJFvpxVHSs5Q2xBBRc2yBOcFtBor/QRnDGXAPk2DkCzfEoK7OsR/kLg6NL7gCmiHiZEqoHBVdFdr7v/TjKjyhyQkDBtQ3iBLczxLQWFJvLySPAotx+wPSDh22QMSg42Fky2Q4qTwvcioKrpqw/07HFxlveDktAwbUN4gS3PyTErR/Z/AA5dsA5HqHHgGPv7CNbQOVp4dBRcNXU6uXHQYUmWN4OS0DBtQ3iBDe2BKBZLd8B96QU/4LHTrITXD1oGgIcCgKaoaBuD/02FFw1r/iTDzIKHrZTCCi4tkGc4M4IAxiyvgIJJ+6i6kDuotAlKgWQZUPXRsDaj5JEUPman+q3oeCq6dDMj4PyT7G8HZaAgmsbxAluHLnK36xmncA9qfcxd9HN5AC4+ktkGX9hsGfySaAVU3VKhjgUXDV9nvXjoHzTLG+HJaDg2gZxggta5m8KD2cK0Giom4HCbUj8BbDfxhmAUZtCJYoPKgqumq8oOTFM8SNOshBQcG2DOMHdQ7bxN6sRKOWkkzf5TXfXkpPg6iFWEHI7qN/GOfInqPwTI/TbUHDVTIvIAh+TRfzKhBZ8UHBtgzjBPQvxpwUlJXcByIGzyh9H+4jp/GVbvwms/BIwukMpioU+Cq6a36BZjhykk5lBaIkFoODaBnGCe5/M5W9W/e7gnvTkN8X6E5pUV6Hwt/xlwVZt0Phlxb/Wb0PBVbMWGA5I4SH5xfqGWAEKrm0QJ7hywYn8zfIjfSogJQM4qa4CbVDJguYIZshNshhUPoryWaLgqkmGzGC5SYOMCUSCgmsbBApuhaH8zXoObrYOyLEDzSDmpCKg+eA1v7vkV1B5WtphFFw1oBksN/fIgiC0xAJQcG2DQMGtCxi11oKnT53CHyF8IbkNrh6U7wo8BQ0cW2UTynI6Cq6aNDIHfAzIEkUkKLi2QaDgvso9sfnwdtsv70EXmQE5duaR+8DKZdgsB3hGBGQDwSiOgutDFGDO3c0N4MSOMFBwbYNAwe3ElTYn6/K+BMlJ0mn+LGUOlvAHrP2FPITU7KJxF/6ytaEDdKBB0n1aFkwUXB8qwvOT+ZN6SQgouLZBoOB+yhFCK/tcoqRi/wP+nqzhN679CZrFXOFVQHgHeLrt8B8gpalZMFFwfQDFX3ZxGeJNKBIUXNsgUHC/Mk80fm+TpOE0d08AOXbAWcwV3mjNXxYQ18FNJCh86xXyu34jCq4PraC20LJ8gawIQkMsAAXXNggU3Kmmvj9XE7V6K0n7eOdyD/DnYQdnMVd49xX+shWHQWuP+g5S+jzNMQ0F14cu0ABC/uW6EwIKrm0QKLgLyU3jtlzWy62DHdl8PQGEI5gYxVtSxQeAG7gcOPp1EUiKTUdfKaHLUHB9GADNugGPaCEMFFzbIFBwV5tMst6l6q0kHeHryXX+JeZvivCWVNGzDn/ZkuDcWMXHQUofJwn6jSi4PowtBj4khfwdhIZYAAqubRAouDuN08hkrmcIrsTnFgZwhB/D7yPhZQAgY0VRcKoWiB+bLB+mxStHwfXhp7BH0ENO0H7HcgMouLZBoOCmGIfwPsnSW2kd3zRuQe5p0NHmy3d6hj3JXxY2I6sAm4TYS7bqN6Lg+rCUXIQeAg0DLwwUXNsgUHBvGzpOZiQwBVdK4epK6VG8nR7xBG9JFbHR/GVhNgcKFYZDSlNzBKHg+rARHmX+EDDRkTBQcG2DQME1TmByennHagXKvLbAI7LxnctGt1shSbMbFSnWgmusUo2SBYFC1q2Lkztcusu5FOdlAv9KG9Xz1pjKIDN9agphFFwfDpL10EMO+JHNWQgouLZBpOCWo0TNzmFz1bK9x/V78snf3YLbpciwUdFtpfiqNccPrcDlo8aTYyfz/O41rvrX7r0E09zp4dzl02GOugrVPoeU3kgO6jei4PpwiWarbAx1piY3gIJrG0QKrlHm6owupX9zyOCiqN4uPVxRoo8kDYtaMoPMk6SB5BZHV5qbxkTMPutj6LvxMketOcwm3G5vaWQepGaFGv0gpRPIcf1GFFwfMsLA6Rv2kH+C0ZLAQcG1DSIFt/m77HZcdSvtsK9cYjidzJakJWT8nB6ONyML8sQ+MM2xk6bzY9sBSCS8iEv1nfgRdaoWJQ0vm1WE4oGHgutLcbBt3i7a1HhuAAXXNogU3PYGvlpJZKqPFI4hKxx/owY7/ozrHt3TUyw18YdPWRYAZjl2blCW5dbfNT5GxR/kAm/RaySOu1o3dXtASlNTVqDg+vIUOKDFdrI7GA0JHBRc2yBScHvWZrfjN7LARwkHRSp/o3s6/rStVHionH50xTddGxQhDuoyquhlUL2Dm1QDiATueYK/SQpPseybx5M3jY3ffwYU6kx+HpRTaCktMhoKri+NwZmfqWuRuQEUXNsgUnCHl2e3Y5N7hLtopjTMIaozRrtGuAOdG78kFSNJDm8wqhhsmGPnASVOg8Im3sBhG8gh80JpB7yn2ZwCCOn7Aihk+W80L2kUXF/aQFMny1vIvmA0JHBQcG2DSMGdFMle508t0MupUs2ellbExcXFTyVzJWlp2NhJQ5SthYiKnowqxpQw6uhWut5K0n7OT4rjeTPjiGbCgnsSQm7yPndRB/NpEdRRcH3pXg96xEae39RQgIJrG0QK7nxyh9mOm+1LLnRI1NxCnVxataJ4f8fItsCSfoWXS1JcuGqAS4o0aNd33IKEw9o0Od8b5di5yNJbSWI3yod9ZItJifsbdXVzxzpr1omzYPb1Q1vW/rlkzZZD1zQ/Xyi4vgypCD1iHeGM2yEaFFzbIFJwV9LW1t1kSRWie33du2yZJW6p6lxy4pTybaRF0c0nT3y+yuVZTb1TCl1bPuuczI2q8fIHQ6ct/yfV5TQ/xyDHTvYGtuByrkwfN/P7vEGbtNjGaQfRwsCCQ0XmcdXK39pjPtMhKLi+TCwIPYJqbZcbQMG1DSIFN4nsYjdk99J2FfOXf22hR03iO5aJbrtCkmY2KFb8JeU+ODystEtwVyvF7x1Z9+s3/d9uVCGfY0tYuXpteo/pQzZdZ9V+jeHHtvyN8lF1dnB9UqlEMtx/jz5JvJ3PXSKmHU+p8xpDiwS1sQIKri9zyT3gEYCkIWJBwbUNIgX3OFnDbsh59hBUcj/LP/z9tXCHvPoubGRd2CXN+LJbTM1iihgXrNbs/S+mLtl2WmO4m0z3Y5NeiB4xqWE0U6fVmCQk6xTTAAAgAElEQVS8ymCNofmmBV/nyE+QfVBf+0GvnqPg+iKRM8AjqObNuQEUXNsgUnBvGPkDZDGjM6rjM6aOrZqf5X+wgfyy6LvP3n3RZdFQus6bPWJ/WbXPZT/Vje7HNo+Mk6SlhbxBddJ3bWM18B4tcaMXihi6MQm77qKtmdeG4xPaQas9KWeWGAXXl3/AVrUrydmgtCRgUHBtg0jBzYqYZtCSC0zF8nFwz77GqiAnx072pT0rfx7d/fXaJRXlLVC5aafBDD+26dWVKeOSE52HnV0y8MWChBmbPJP8ZND6NPbPBVPC1bxtbsO0n159zoAfBdeXE67JJwB/kvNBaUnAoODaBpGCaxJA8R+WYmnNERicJSu1m9JOblk85fP3mjZg+7FJ0iiy7d7Gb98q55ohLs2s3zDY2V624EpXORrf4WWzEmdY1ae4C6Dg+nKTLAQesRweQlcMKLi2Qajg1uhr1JRH6+iCQvFipXKd7VArsf3Y4vtHtq4b7jU6q8Ksv+jX7HNn/UVflHPw1mIea/rOZgHR0pnxghPcmQ1QcH3JzgeJSnz/1I4N0uLVWw9eBbiriAIF1zYIFdym7xm25Q51nf8ob1cesXPs7GX6sc2pHdVLilJZ+Zb8fOSEnxYsTUzal3Ld18zMKCnDecainCR9S+YlqAwVHuyh389dGpv07iBLbyXJHWgbBVdDWf4sGhdUcY3WHgTn5gk2KLi2Qajgtmtp3BiK54AEWGkuMIm15y7Dj02aUqjZr5JURiW4haqWKex9V+LJp+u/2ua9Xl+MmjCzVLvEHQdTblLvxn70RTkptmEEmeeZE7m1anjTAow8Q90aGvctg623kpTuLIKCq6FWb86Ct7ZonhlOgMPTBxcUXNsgVHBNnS0ztVOhG7gsttyUHs3ak83wY1tRqp3j3Ub5UOwzHoltpZS/deFE8sZVS3+ZNn5Y324dY5rUrVrKOwrOV6JyzYYxb7/fa2jspFlxUmLy0dQbheiLctLk3u86BPe8Ywi1pF8d18QFPRP3JyYfzXmGIbHz1WXMhIKr4WU+ZxKaRSIkbqcAUHBtg1DBNXe2zOo8SvW1TzwLGmlUZWdN2Ej3Y4slg8eNGzc71VHiQGxdpx62Z1WRXafjseR1K+NmTR4zrNcH78S8UKtKCa/H8VSf+1W1KDfNIbi/96rpHTTT/dV6P2fctyTGnIXz1RUWCwVXw7vNuYodpz00bOSJwCwMFFzbIFRwzdOCjSTk7TM7lLnc1ZuO3AQ+2Bnk2DlN92Pr4dJAt7Xaqe+ahJOPmHW8RJmBTr95+tDOxBUj2ItyiuB2Usfe+XjC97NmLV26KnFzcnJKyqWbrjA0/Z417tuH9DkL96szHAQKrobeNXlKMTxutuamtTMUXNsgVHCNoh04WRFGyBDln3TeoIlqmnVk7jIwk5USVLfWhZnsiKgxbzF3nWIHl1QEt51acIsWI1pKlKhQLH/9+jEx7Tp26dVr2LAxKk0+5dTkdJYhset1ndIIFFwNX5XhKHSb9bXITZEaUXBtg1DB/ZOkGjbmSFGH+szxuy9GOXb2sQX3FGf1bdm+CVmsRTmX4B79tWORHHVVwkHeuXkp5WRy8obEVUuXzJo1acKYYQ2K9urcsV1Mi/r1n6paoURRrSRHM+Ys3K9OHzgUXA3TIjhGqVu0X4ccuDwExYCCaxuECu4W44j6N6sr2sLlmEXFKMfOA+Z9tY732bFTM/a+nvRFObfg3nUMsf/uU9GlnXQzt6Ha6e27Dk0+kZy80aHJcbNm9WfMWbhfneYZKLgafiPmS65s/0Y+D0ExoODaBqGCe8QwwmFWa6cgQewSfOlltPB0inVfUZLV0OnWgL3vAn1RziW469yF9o57IZwwIqqMNMiGISuf3FRnvdo5C/frXKUMCq6GteSYaRldXlEV/n8TrQYF1zYIFdzLhgG3hrgenv3vyyDDHDt76HfVCe7q+9Ri78teSQ8u6RRcVbywy3OH0Q2ORhnPN7LmLNyvzt8xFFwNyeZPS+q5fY3hnSQdFNFILlBwbYNQwc0Im8FuyfIwp+CaubgaEFvSaG9mEk1veRPsOBhY1WDnYYOREk969dho4/1dGIbEzteCztzDKLgazpJ4syKq557lGsM7STIJOC8QFFzbIFRw5eJjmLv2ufOWfeJ/Xwxz7NDDyfIumCkYPvWzQx1IXEECvy5mvP8gY87C+drVWQQFV8N98wXYnd7L1MXX8E6BkjguNKDg2gaxglt9AGvP9cru9fjv/O+LqdXZeU2who3MUI80xhU32nuCKbhct+2EQsb77zESYjhfXevpKLhaoiaYlfBGjY/XGN4p8IR5EwIKrm0QK7iNmLlpN3gCdhnnsTHkd2K2AJbWe673dtqQCnOsmFzAaG/2dobe8gWDmGSWgIs6IeLCPVOJgqul4mCzEmtzPsQ5GsM7hVwTHRcF1zaIFVwDS9mUYcWdghtAGj/zlFT9Sdi3R5PWr16zYceJu9DqfySGBmTp9JQVB/gqnxZhUoBpoJ9jMIqCq+V5ttugm9U5H+LXGsM7BWOrcYGg4NoGsYL7YX2DpvxCyhKSP4CoIduMzXxl+a+wQPwq5pnMWKRRYp1JBzhH0TOIWcFklt565ohRcLW0amNWwjvzPstreJdDrglHjoJrG8QK7heVDZryQrOM35u0CKAv+z05dhikRjtG0Al+Vx9HTKZ8M/VJx7iTEv5MzH5pMhkmoxs8B6Lganm/kVmJbTkfY7zX8C4HzlQjwQcF9/+1d+b/URRpHK4QQggB5JAbMSAqCgriIiquggqIqKggsoKLqCsoK25ExXigICAorByKKBAXkaV1RQj3KYcc4UbuM5whB4Rk5i/Yme6ZpKe7qs9KZVKf7/MDmT6oVHcyT3qq3npfaRAr3NGp7J6sJgt8XsthRurDCNfuDQ9Z7Pbc/EJiW3vi+KIYF250Pmwxndimpyqg5mfPKp2Tg3CNDGtpd0Z22Y00ZPAMEzf5ayBcaRAr3KmkkHnsyRZeEtboOUfmWh1+Wx0jdj10W8oS+/Hl/Ju7fRJ9ty7Zdt5F49+SPNtz8iiV2JeXXQ+Ea+RDm1i7YDCn7E7OMwTehf5eiuijIyBcaRAr3PnkBOvQYcuSvo4oYtfYCbE8Mexby9Aua1YR21USAwh56NrpA7uz9xx2mVvye+Lg8+u1jUbf6hNlQ7hGvkqwK5YTWKwzbmzgXRzNmUG48iBWuCsIc9L+9Zr+R8yqWwTxntaq8trk+bZiE/nd5oyvQ99giLfGM4mj5+HvJ+p1uzImDA7CNfIj++97FIsVglnxU/UBwpUGscLdQVYwjuTWGu7/YizKsJd008J8e3hvfYfNnFwwO1yGZ7S3xu1jiMOsSEx4IDsys561Iyf2IRrCNbLC/jOJxQrBgwJ66BAIVxrECvcE+ZFxZGKi4wl9Ni1fZx76KLKuwmldQQp/kkWWx/NuDX8Dy2FkNj/ZP4wFg4evV/9iFJ47efKceTAcwjWSTZbZnsPMIrcsbqbMIFyJECtcZiXz4jSHBf8sYdfYOVo1ItyPvLd+3CaMYgDxkc5XscnNHiavLYkUxKAC4Ro5SebZn7SZIdy4iQkLQrgSIVa4wZof0/fP95F3vIwuT7OOXPs0TRPuLO+tn7d+ep2qfQOPy0F/JQftTgk8E25/JvM4hGukKGGK/UmM+OZT5d8950C40iBYuC0YI7X3Wi1Bc4xVjZ3AomrhMAX7z5hMCixXqe3Q6qhX8/hBdDGxTcz7rvoN2LFKEK4Ji+x0ZRTR0lTEzSIzFQhXGgQL964B1N1bSCaPi7GqsROcS1Z93ibRR6hPwCqbb94t2gOubag9g2W2KzK0fMEJ7DhiCNdEq6FOzirJNo3f5pZ3z9wB4UqDYOE+Qo8S6NekiMfFDLnd4uCDnUL/+Eq4ZxV11jcyRvyQx7ZXsgPmNLZq+YKNpc90QLgmOvVzdt7ij/W6zToYR/NlKhCuNAgWbn/q6vbjSZ9yuZgRFjV29id4T1sToS77A2qgVUS4zGk7G9bZJN45HSlB+Sj7FAjXhEWhZT37apPbti2N6Hbj0fiJv40C4UqDYOHSV7enp/Cp1/dBHfax9FTvi3ojNHmbfazop4fVj/xOBg1p/E4sC0Nc6RwR+j/Z50C4Jgbd6eSs3NvUoaCCnBPHTl3yu768XIBwpUGwcKlKLKj3Kp+LmciusXOtsY8I3Ait2GG+IfJTOzbwHgWxhWywOrw64lureTsI18RbzRycVNwzdF+fLPe++AHClQbBwp2cQPm8NiXBewqvGCxq7PxENvlu/nbLZbszEvZfyXzW66TcVpu4uLVPaCUx1rNPgXBNjLWroxHm9fB9fa/c++IHCFcaBAs3k7KCNXBLT04XM48woye73+G/+Y70EIsIHbr6aTubueg5yixSjZAEi3B8CNfENw5ysM1U/5BxiZIpNyBcaRAs3CxK9NP/CK961OwaO8cSLUK6nNLlGYuDm5mrlh2xmyy1OePRm09nXG8VdQbhmlCIbUW5NdVU4WaL6I5nIFxpECzcP8hq075ubd1lMmTDrrGTkXLRf/OPWj2JD27kK7LtAFlsfUJ2woxgsNAqrA3CNbHOeioyqKWnCFHVNv17hQLhSoNg4R4l/zXu2uE/Xqu0KVY+r5LmlqMBDnnCYtAgt8ZIX20fIr9anzCwITt3uwaEa2If+c36hMtttbnINmL64xUIVxoEC7eAzDDuGnS9nUkcc5j8TD/wG1nFofnn7mEfm1LFX7azozb14U9Ws027A+GaOE9mWx4v6RUJ/rAaLIoDIFxpECzcYMoYw44z1TO4XQwzvcxTN/MYtXjRIqrzDosVCU44QX6yPD7SPlQZwjURqPq55fGDiRHheg2fFgSEKw2ihdt8hGFHRjK/vExF5Cvq/tNJ43g0/9otzEPrzUMl7jhD/mN1OK/Oa7ZNQLhmGr5rffzAMC3n0Hwx3fEKhCsNooV756DY7SuNBtFP9AQj28GYak7KKdhisXL4haY+14Pa5H6cmMiKvygDwjVzm23FoxUkrNw9IjrjHQhXGkQLt9vjsdvfkG0cr6YBNX49cBMzT64rRjVgHbmQ8r7PtnPJ9xZHi9McDDJCuGYeeMrujBca5YxvViv+0ifEAOFKg2jh9r03dvsOX8sFjNBr7KwgS7i0/klN1pFJftI+quRbZBYPrxexXPirAeGa6dPF5oTj1T4OBoviK/utGQhXGkQL9x+x46BLyf94Xg29xk7/FnzS7TFTNQRufZxxxDFXyHSLo3fd56AJCNfMK3bxXiNSLwjpiD8gXGkQLdxR9WM2e97ENfXo/bRP3uerc5qDnkoYnzxX2gXR2lNM/s0+uMLRlByEa+Y95iiQxqVab4jpiD8gXGkQKtwtmZO7J/R/9K7Saub7q1hoxgM9acFZX/j+vB/hO8LI8NiPwyO0VTmJnq2dtA/hmplY1frOfZZ0RFBPfAHhSoNI4RZUiUQ99o3uebVOPterodbYafsYp9bnUTLvhMlJHu2/8aoTmYd2JTBqHccC4ZqZTc5bHb7apL+onvgCwpUGoU+490WEG63vcKFGOt+rGdLWvG8DWcip9V8YqVDGJXGYdElmhwq/2ICZdVIPhGtmMdlndXgm1xiZ8gPClQahwp0SEW40T8vYpGN8r+ZNSqTs3/1lldGRRQ/XDNzUh0PjqcYleKWcSna2Fg/CNbPFMs1w4LaHhfXEFxCuNAgV7tkkTbintc1rzR3W+HNMRl3TrryaNouNnMNIRpbFJb1k7Y9ZR95NcVb6EsI1c8Ty480vtjkx4wQIVxrERil0V33bJLKVSX7nfDWfmwO3piUc5NX6H/R6C0+34pGooT7rMdZxASII10y+VU2iYBdHJc/iAAhXGsQK93tVuNFS6X+5l3miRyg1du7mt7JiN1lG2XsqyaJ6unMajmIc+KLKfmctQLgUUizqQW+K8zoPZUC40iBWuPk1wsJ9R9tYyz9lyH9McQTbOL6pDlNXaYxOdvaJ34amjHy6xWlO6xtCuBRMyZJ09Lkxzlf0lgLhSoPghQ99w8Kdp73ucwP33/ffiPFp8LV6/HL5n472XE9JCz4D0c3/Rd8/j6xz2AKES6H9C8xDBxK/ENgRX0C40iBYuAvDwtWkeMQmV6kXTNNaBXU4riS6REsw8yuryoRLWg6n77/bIut5LBAuhYfZQdiv1OMbBF6OQLjSIFi4V+sSkqot/hle06ICrUe2G+03m+zi1/pVMs28s/etfCqytR5G3b3aJjG5DgiXQr9OrCNnUlij5vEHhCsNonMpDCZEmyq7XLscVrEfJr/E7uhCW3rmmcRJpl3HLFaIueLWf1B390ordtoChEthWCvWkVEpXJIkCwHClQbRwl1GiGaWiYl/8r+ac4Y03nsTvuXZfA3zlHdGiuXaUee0fZm2d6+LZBMQLoUPajMO5Nel3vD4BMKVBrHCLT6x9bOpC5avz84pcjz57oYiEpt1YERtR4tinVLflGb8WrO/cWqbnlnypbrOxxkhXAr/JlfpB75MdBhtFw9AuNIgUriXNiplvMxnrslASkxM7NUGr3Btvflbxj0LHccQ2NGRNp1+urqLShIQLoV5hJ7n4loLHuuxRQHhSoM44V7ZosSyl2sqXI3rYyZCfqSvxfVMa1Mlx+7teLV9z3OUnaOquxhnhHApLCc7qPsd1dCIGyBcaRAm3ItZipE1/EJko7SKqbHzSHu+rd/5d8OOQ1Wm8Gr7vr7mfQX1bWsg6oBwKWST5dT97e1q78QVEK40iBLuGZNuQyzN4305MSOhR/jpUKOT8Sl0ZGour7b/SvmIOzlht4sWIFwKp+jl57OM4SzxDYQrDYKEe4nmW0VZznutWRd9fd5RKRf5tv6gYaKvqNFgbm13e8K0q7hVbzctQLgUihKof3QfacMneloQEK40iBHu1aV04SobOP/e93yk7HVxM/ayTm/0MFTwmUe2cGv70Z6mXT+SNW5agHBpXEcraLctwapGcvwB4UqDGOFmM3yrKMf5XcqVzK/GtGk06JlukfS0v1gmn/bC0w/EbnfrwK9tSjm2ezq6agHCpdGKtoKvfxNGsFicAuFKgxDh5jN9qyzlF6qQFaknQSLrwXrblch2zfN3x2zuT5jOr+3e3Yx71pIfXbUA4dIwjbuHOJo0VnxH/ADhSoMQ4W5lC1fhVzW1ICUiXC1N+En+yXEMJdNG1OI46ffUg8Y9Tzpf1asC4dJ4zPSHLBh8oxb/NB7lCoQrDSKEG2gWsmBi45ejjl3Yr2G9xxcoyoy/1Kx9P8fZ4j6ab5O01WWfJJ/l17TGsJv0W1fqOyzF4Ihn7zfs2F/lS3ctQLg0BpqrOlxItUiSG5dAuNIgQrg5Tf86btzoPiQ9Itz+NdNH1eulLExrM/pfTW/nF6iQqQm3o7oRaEkJbPVJejP91lyuJV+fM6bZebmuy+dnCJfGiOamXaOrca5dWu5AuNIgQrh7mvYJe/bmrppvF9R5RVHSU36YTGYqynBTynDvXK6uCldbDraUS2nHWDLq6be6OM5U64S/dYzdzkl5z2ULEC6NMdWNewobDqyIjvgBwpUGEcLdrAn3lmc14X5BZijKD2T014NDG+8kU0uPe+MxVbjfqa/73cg/0nJsim5jF5nFs+0XDaviMpJPuWwBwqXxDTF+UJiekF0hPfEBhCsNIoS7vulDEyZ8+mz9qZpwPyALQv+mjAj989GgegM4CvdbVbhqg+eSR/NrN8qXVXQSH1aHayayl2KzMhRc73pNBYRLQyGHY3eUtO5BPzOOgXClQYRw1zRVRdhptibcN5PC/9Z7KfRPrxtSX+dYkuFitdC3qa0Gmk2seoJfu1FmkPwLZwu11wV1Xrc+2SWvxgaxTXW1qlcFwqWxjmyO3bGQrKiYnvgAwpUGEcLdoA4pzGjTVkkPCXHy+9oT7nDVvu+SpeFT8k4d2LL858zpp/1dzcOh9rUwoDauVsU6oKhzWj215nB3bXsWz+I9IYa21m+VtGbX4mIB4dLYT36L3dH5bvqJ8QyEKw0ihLtdG8P9oMrcBZmZmQsnkm8UZV7Ch+PeCu+t1fmW5nWiSxbIZH9XMy3UxLvhF2upFc39EGgU6WLko/49nNNNDW+p3/qvh8cwCJfGBUPlzzW00svxDoQrDSKEe0gTbjqZq0UpXDc09GSb/MNrqfMVJTOxEdHhczHu2aqEKOEXA5u6WzTggJciXdSmyrYZivn4ZsQN+q3Od7lvAcKlEQivfykq2+7dkvtvRvkD4UqDCOEWhifNJgxp0D4Sh9uv7tgJjR9TZtfrMn5s+8ZNdL5N8jsP9QBRM/zn1nAbU2XPz5E+HlC3Xq3POZnv2/oY3430pILWQLgm9nwwtF+1hs2qJ5ZmId/jokhc/ADhSoOQpb03hEVVq8vs6EqzZxrU67VAUabeVfu6+xZfnda0VLjXfbr8svdrCZzb/Z8JU1du2JUzNYF/hcoCdQSXNFA38mrxXKx0ukuHDo0T09LSoouRn2rhYTkIhGsiI/qLVbqAfPD1XGNLBAHhSoMQ4R6yyKVwKRi8Oq1x5H3RKIUk3v7i1K1eVp8VZi8ubXTuJ+XwtnpC7aKWEnd6As8ShCcTItcfSSV4IPELD61AuCa2Rv+QR8P5TiVnVGiHPALhSoMQ4QaWM32rJZTNn9RQfWN8W7RlygttqpCU+9784bCpr1YU7zE0vIv7UN03ahfHq687UFKi+KBdRAyrtc3X6njJigPhmrlNu69/jW6/nXKuIrvjFQhXGsTkwz3JFG70SfTyh+FQhZ3q69ylo3uHnnkb9PpoidOSDYWrTS2v5P2QeyYx/N79Pfxyk8vMiXaka15I0caFz6WM9NIIhGvmY+3GRkOmL9cxlQGtFEC40iCoxE42w7e6/OMX3691nS457tH5b3WpQRJuHjB5U5G5PQO55gqVirKEdw6+e8NOVDNXD25k3yc3rNC8EHls/jCZXtrbBgjXzBFtsCZa32F8Iv+xfRFAuNIgSLiB9VTfxq6mOm9cXFW8/evB7RJJcqdhcyyHTBkVfLIK/d6dWMaE3rpq9G1u6jt8Wy6qrXrhY3XjSqMXbU6nA+FS6Kze2D+0jaLm/DPICQHClQZRVXuLN9F86yS/TN6qz55uTkjd7u//L4d+RslaxvPzKr7juLtDb131w/6UKu4GmO15QheFPDVhp6c2IFwKk8P3tWrkL+9s4zLfygKEKw2ihBsMGGe1FMVFtoOTC9/pGnoKTOs3cZ15aPYgw7eKcsDzfaFyE9Gqa7frzrddbYlcZLii5BaPyVUgXAo5SaEbGynUEWj3UMV2xjMQrjQIE24weGlDjAy3u105ULJ71qvtk0hS+1dn7dZXQiumDeBqLOE61Bp4r3Xbo1fC+VAW8mw2zLGwcB9WX/5MlnlrA8Kl0SN0Y5/XXv5mTKtQaYBwpUGgcIPB89lRN67cm++tv4XrJvZLI6RW13cWRmeWDjB9qyh7vX0X2jc+FBmGXrLtXzfyq1IRpU3IC5+or+6/w2MTEC6NOaEbO0572bUd/xTJYoBwpUGocIPhtGCHDx3J8TmblfNrRve6hDTv89mqPG0dG6Vi2vwejVPaTff3jUq5skOv8R+Pcn/nvhm6iA3hFxs9J2mAcGnkp5JI7Y8tZHYF98UzEK40iBYuP/bPGdYpmSS2G0qvmKbcXW/kuI61j3L5XoeNT84rOdbrVckiJFUd/3jmBq+PzxAuleeSap1UR6D6NucbyycQCFcaKq9wwxRtmjygP71i2kzykaLMSxnH4buU7DD6VlGyGBETXrlSt7Y6E3cw0XNxdwjXTNHxzdqPa8vxA1UnVHRvPAPhSkPlFm6Y3fSKaV+0+iG0VWd49LT8Td+8ucjTNwjQItoUxW3JMQsu71+zKNTiryt3nR96nefsPRCukcJt+h/YsEq5qlcFwpWGyi/cbcyKaYoyinwbDF7dkTmyd1oVQoi3aq3meDYNXgvZclbqGp0x3vPwMIQbS2Cv4Qe2hHOUoDggXGmo/ML9g1kxbeHQpO7fPXtbUmn2x3Qv7Z9m+FZZxmVZRYFxDd4Kp/kjjEC4MRRvNP/ItlTC5ONhIFxpqPzC3cGqmPb17SlDlDd06c2Jl+FRi0xnPDI0XqAEEXssfwnh6rm20nxjFWV1if3/jEMgXGmo/MLdT6+Ypkyocf93ijJIL9xmD/YfPnbWom0nXQQCmAIUysjyP+udQ23YW4YVCFdH4Hf6z2xTRXfMExCuNFR+4Z6hV0xbUP/x8OaxrAEppcJ9vPc9N6pbCQ3bdnv+n+O+X7z9lN0jT3N6lG+I3nMP+u17HmORnKfixRCuDtbAO5ePJcKBcKWh8gu3hF4xLYOM+CjEoWDw0nfdIhUV1GxkefvWzJ/8/kuPd7qhenhfYqN2jwwY8fnsrOwztOmqfEaUr6J8Smau89n1YtZwRZaXdXgQbhkFLN8qCucUckKAcKWh8gs32CLsTVPFtMGaYyepp+wfpZ5kjAu6tGf1vC/f+/tjdzdLVpNKNb6zxwvpE+cs31kWZPsnPcpXyeiYSGYqujGFS2vcDzDsY1rByydfCLeMLWzhbq/ovnkAwpUGCYTLDCNQdAnOAysH1Uy1iLi6sHtV5qR3Bvbs0LRa2L1JTTv0HDhyUubK5fQoX2X8y31CwtXEXLxj+ottqpD5bjt+dQm74+fd3wcItxSLB1xFqYTrzSBcaZBAuMF1zPfWSr1iCxwu8z27c/nciekv9LizSVVCPmNG+U4KCfdI8Owv73atqT1MK277zX7A9fSIC+GWoqta2jR2DD7EsYrunXsgXGmQQbgXmNryuf42cCb7Z2aUb1i4o1rqYiCWum2ekXVH/fqr+/glCLcUXWyzYQze29+yigbClQYZhMt8VNzjv+kVrChfVbi99UFnfxvz5Yx5i5Zv2Xf0gqP4+kLGfJz21f3KYQi3lEU64caMwYdZXNG9cw+EKw1SCJPgsI8AAASSSURBVDe4merbjRySKK5hRPlqwn1SL9z6tcpeV6vT4tYOXR97dsjrI8dM/nreohVb9h0zavg4fT4u8nWj665CuFEKdb8EsWPwKvyzGZc3EK40yCHckj8ovt3MY1XRVnqUb0S453eOuTchKtkjwWB+zsHtG7J+mjPtsw/SXx7wTLfOd6Y1rFmm4eQ6Ldp06Nar75A3whr+iZF1R/s61XVXIdwol/XCjRmDVzEXaYp3IFxpkEO4weCfJt/yKfZwhB7lGxFuWOl/jutcRdXpWVYbeWcObtuQNX/OtLEZ6UOef7rbPZqGB9Ln4yJfP3TdVQg3Sq5euDFj8BBuJftRSocswg1ejs1VsoFTLq8rTalRvppwox/7T371cBIhLiPq8zbR5+MiX4fbt2AAwo2ijworHYMvo/LFhUG40iCNcIPBC6UV05bs8BDGyoBVgj2MLsDo4pzxblveS5+Pi3zNcN1TCDdKwCjc8Bh86Z5KWEkSwpUGiYQbIvfEwf0Hj/NKVKtisaxiqb9B4uP0+bjI1xmu24NwS1ljFG50DD7M+orunXsgXGmQS7jlAfsR12cEfR4j64721f0QNIRbiq6Qs2EMPsThiu6deyBcaYBw7bjI8u1av1FnzenzcdpX97FLEG4peTrhxo7BK5Uyew2EKw0Qri3HGQMKV/w2nEafj1O/rnHfHIRbxgbmxxJlc0X3zQMQrjRAuPYYa2OpZPkfKbZKsXLGfXMQbhm57DvLu8C9CCBcaYBwHXDE/LZdzuN9u5NphbUeWoNwdWxn3dmdFd0zL0C40gDhOuGcMVP4H1yWhxYxCj54qwgM4eooXk2/sWsqZVEzCFcaIFxHBI7o3bjea2FdI6w8Z54m0iFcPYVLaTd22dWK7pcnIFxpgHAdEriwa2U4CdWSDYc4Lg09xvFjL4QbQ+Eq841dWzl9C+HKA4TrhpIiDgnIYjhJ8a3HOocQbizF24w3dkelHE8IQrgSAeFWMJdWGKyQ5alkbxDCNXNxvf7G/p5b0f3xDIQrDRBuRRM7PKzsdZS8nAaEayZ3X2RgYfX+yxXdFx9AuNIA4VY8JWe2a+Ukf9t8wkf0A4RLpSTv4sX8yjqWEAHClQYINz4ounTxos+laxCutEC40gDhSgOEKy0QrjRAuNIA4UoLhCsNEK40QLjSAuFKA4QrDSKECwAAwAMQLgAACALCBQAAQUC4AAAgCAgXAAAEAeECAIAgIFwAABAEhAsAAIKAcAEAQBAQLgAACALCBQAAQUC4AAAgCAgXAAAEAeECAIAgIFwAABAEhAsAAIKAcAEAQBAQLgAACALCBQAAQUC4AAAgCAgXAAAEAeECAIAgIFwAABAEhAsAAIKAcAEAQBAQLgAACALCBQAAQUC4AAAgCAgXAAAEAeECAIAgIFwAABAEhAsAAIKAcAEAQBAQLgAACALCBQAAQUC4AAAgCAgXAAAEAeECAIAgIFwAABAEhAsAAIKAcAEAQBAQLgAACALCBQAAQUC4AAAgCAgXAAAEAeECAIAgIFwAABAEhAsAAIKAcAEAQBAQLgAACALCBQAAQfwf0u1BrTvYjY0AAAAASUVORK5CYII=" width="100%" />
<h3 id="some-more-on-vertices">Some more on vertices</h3>
<p>Vertices are created with the <code>v()</code> function, which takes a name and list of attributes associated with the vertex. This creates a ralget/tidygraph object:</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="fu">v</span>(<span class="st">"x"</span>, <span class="at">Latitude=</span> <span class="fl">78.26077</span>, <span class="at">Longitude=</span> <span class="sc">-</span><span class="fl">94.11077</span>)</span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a><span class="co">#> # A tbl_graph: 1 nodes and 0 edges</span></span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a><span class="co">#> #</span></span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a><span class="co">#> # A rooted tree</span></span>
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a><span class="co">#> #</span></span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a><span class="co">#> # Node Data: 1 x 2 (active)</span></span>
<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a><span class="co">#> name .attrs </span></span>
<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a><span class="co">#> <chr> <list> </span></span>
<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a><span class="co">#> 1 x <named list [2]></span></span>
<span id="cb6-10"><a href="#cb6-10" aria-hidden="true" tabindex="-1"></a><span class="co">#> #</span></span>
<span id="cb6-11"><a href="#cb6-11" aria-hidden="true" tabindex="-1"></a><span class="co">#> # Edge Data: 0 x 2</span></span>
<span id="cb6-12"><a href="#cb6-12" aria-hidden="true" tabindex="-1"></a><span class="co">#> # … with 2 variables: from <int>, to <int></span></span></code></pre></div>
<h3 id="edges">Edges</h3>
<p>Edge attributes are added by interleaving e() between graph multiplication.</p>
<p>Here’s a simple example:</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="fu">v</span>(<span class="st">"X1"</span>) <span class="sc">*</span> <span class="fu">e</span>(<span class="st">"E:X1.X2"</span>) <span class="sc">*</span> <span class="fu">v</span>(<span class="st">"X2"</span>)</span></code></pre></div>
<img src="data:image/png;base64,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" width="100%" />
<h3 id="installation">Installation</h3>
<p>You can install the development version from <a href="https://github.com/">GitHub</a> with:</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="co"># install.packages("devtools")</span></span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>devtools<span class="sc">::</span><span class="fu">install_github</span>(<span class="st">"ianmoran11/ralget"</span>)</span></code></pre></div>
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