EVOLUTION-MANAGER
Edit File: tf_idf.html
<!DOCTYPE html> <html> <head> <meta charset="utf-8" /> <meta name="generator" content="pandoc" /> <meta http-equiv="X-UA-Compatible" content="IE=EDGE" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="author" content="Julia Silge and David Robinson" /> <meta name="date" content="2022-08-19" /> <title>Term Frequency and Inverse Document Frequency (tf-idf) Using Tidy Data Principles</title> <script>// Pandoc 2.9 adds attributes on both header and div. We remove the former (to // be compatible with the behavior of Pandoc < 2.8). document.addEventListener('DOMContentLoaded', function(e) { var hs = document.querySelectorAll("div.section[class*='level'] > :first-child"); var i, h, a; for (i = 0; i < hs.length; i++) { h = hs[i]; if (!/^h[1-6]$/i.test(h.tagName)) continue; // it should be a header h1-h6 a = h.attributes; while (a.length > 0) h.removeAttribute(a[0].name); } }); </script> <style type="text/css"> code{white-space: pre-wrap;} span.smallcaps{font-variant: small-caps;} span.underline{text-decoration: underline;} div.column{display: inline-block; vertical-align: top; width: 50%;} div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;} ul.task-list{list-style: none;} </style> <style type="text/css"> code { white-space: pre; } .sourceCode { overflow: visible; } </style> <style type="text/css" data-origin="pandoc"> pre > code.sourceCode { white-space: pre; position: relative; } pre > code.sourceCode > span { display: inline-block; line-height: 1.25; } pre > code.sourceCode > span:empty { height: 1.2em; } .sourceCode { overflow: visible; } code.sourceCode > span { color: inherit; text-decoration: inherit; } div.sourceCode { margin: 1em 0; } pre.sourceCode { margin: 0; } @media screen { div.sourceCode { overflow: auto; } } @media print { pre > code.sourceCode { white-space: pre-wrap; } pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; } } pre.numberSource code { counter-reset: source-line 0; } pre.numberSource code > span { position: relative; left: -4em; counter-increment: source-line; } pre.numberSource code > span > a:first-child::before { content: counter(source-line); position: relative; left: -1em; text-align: right; vertical-align: baseline; border: none; display: inline-block; -webkit-touch-callout: none; -webkit-user-select: none; -khtml-user-select: none; -moz-user-select: none; -ms-user-select: none; user-select: none; padding: 0 4px; width: 4em; color: #aaaaaa; } pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa; padding-left: 4px; } div.sourceCode { } @media screen { pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; } } code span.al { color: #ff0000; font-weight: bold; } /* Alert */ code span.an { color: #60a0b0; font-weight: bold; font-style: italic; } /* Annotation */ code span.at { color: #7d9029; } /* Attribute */ code span.bn { color: #40a070; } /* BaseN */ code span.bu { } /* BuiltIn */ code span.cf { color: #007020; font-weight: bold; } /* ControlFlow */ code span.ch { color: #4070a0; } /* Char */ code span.cn { color: #880000; } /* Constant */ code span.co { color: #60a0b0; font-style: italic; } /* Comment */ code span.cv { color: #60a0b0; font-weight: bold; font-style: italic; } /* CommentVar */ code span.do { color: #ba2121; font-style: italic; } /* Documentation */ code span.dt { color: #902000; } /* DataType */ code span.dv { color: #40a070; } /* DecVal */ code span.er { color: #ff0000; font-weight: bold; } /* Error */ code span.ex { } /* Extension */ code span.fl { color: #40a070; } /* Float */ code span.fu { color: #06287e; } /* Function */ code span.im { } /* Import */ code span.in { color: #60a0b0; font-weight: bold; font-style: italic; } /* Information */ code span.kw { color: #007020; font-weight: bold; } /* Keyword */ code span.op { color: #666666; } /* Operator */ code span.ot { color: #007020; } /* Other */ code span.pp { color: #bc7a00; } /* Preprocessor */ code span.sc { color: #4070a0; } /* SpecialChar */ code span.ss { color: #bb6688; } /* SpecialString */ code span.st { color: #4070a0; } /* String */ code span.va { color: #19177c; } /* Variable */ code span.vs { color: #4070a0; } /* VerbatimString */ code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */ </style> <script> // apply pandoc div.sourceCode style to pre.sourceCode instead (function() { var sheets = document.styleSheets; for (var i = 0; i < sheets.length; i++) { if (sheets[i].ownerNode.dataset["origin"] !== "pandoc") continue; try { var rules = sheets[i].cssRules; } catch (e) { continue; } var j = 0; while (j < rules.length) { var rule = rules[j]; // check if there is a div.sourceCode rule if (rule.type !== rule.STYLE_RULE || rule.selectorText !== "div.sourceCode") { j++; continue; } var style = rule.style.cssText; // check if color or background-color is set if (rule.style.color === '' && rule.style.backgroundColor === '') { j++; continue; } // replace div.sourceCode by a pre.sourceCode rule sheets[i].deleteRule(j); sheets[i].insertRule('pre.sourceCode{' + style + '}', j); } } })(); </script> <style type="text/css">body { background-color: #fff; margin: 1em auto; max-width: 700px; overflow: visible; padding-left: 2em; padding-right: 2em; font-family: "Open Sans", "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.35; } #TOC { clear: both; margin: 0 0 10px 10px; padding: 4px; width: 400px; border: 1px solid #CCCCCC; border-radius: 5px; background-color: #f6f6f6; font-size: 13px; line-height: 1.3; } #TOC .toctitle { font-weight: bold; font-size: 15px; margin-left: 5px; } #TOC ul { padding-left: 40px; margin-left: -1.5em; margin-top: 5px; margin-bottom: 5px; } #TOC ul ul { margin-left: -2em; } #TOC li { line-height: 16px; } table { margin: 1em auto; border-width: 1px; border-color: #DDDDDD; border-style: outset; border-collapse: collapse; } table th { border-width: 2px; padding: 5px; border-style: inset; } table td { border-width: 1px; border-style: inset; line-height: 18px; padding: 5px 5px; } table, table th, table td { border-left-style: none; border-right-style: none; } table thead, table tr.even { background-color: #f7f7f7; } p { margin: 0.5em 0; } blockquote { background-color: #f6f6f6; padding: 0.25em 0.75em; } hr { border-style: solid; border: none; border-top: 1px solid #777; margin: 28px 0; } dl { margin-left: 0; } dl dd { margin-bottom: 13px; margin-left: 13px; } dl dt { font-weight: bold; } ul { margin-top: 0; } ul li { list-style: circle outside; } ul ul { margin-bottom: 0; } pre, code { background-color: #f7f7f7; border-radius: 3px; color: #333; white-space: pre-wrap; } pre { border-radius: 3px; margin: 5px 0px 10px 0px; padding: 10px; } pre:not([class]) { background-color: #f7f7f7; } code { font-family: Consolas, Monaco, 'Courier New', monospace; font-size: 85%; } p > code, li > code { padding: 2px 0px; } div.figure { text-align: center; } img { background-color: #FFFFFF; padding: 2px; border: 1px solid #DDDDDD; border-radius: 3px; border: 1px solid #CCCCCC; margin: 0 5px; } h1 { margin-top: 0; font-size: 35px; line-height: 40px; } h2 { border-bottom: 4px solid #f7f7f7; padding-top: 10px; padding-bottom: 2px; font-size: 145%; } h3 { border-bottom: 2px solid #f7f7f7; padding-top: 10px; font-size: 120%; } h4 { border-bottom: 1px solid #f7f7f7; margin-left: 8px; font-size: 105%; } h5, h6 { border-bottom: 1px solid #ccc; font-size: 105%; } a { color: #0033dd; text-decoration: none; } a:hover { color: #6666ff; } a:visited { color: #800080; } a:visited:hover { color: #BB00BB; } a[href^="http:"] { text-decoration: underline; } a[href^="https:"] { text-decoration: underline; } code > span.kw { color: #555; font-weight: bold; } code > span.dt { color: #902000; } code > span.dv { color: #40a070; } code > span.bn { color: #d14; } code > span.fl { color: #d14; } code > span.ch { color: #d14; } code > span.st { color: #d14; } code > span.co { color: #888888; font-style: italic; } code > span.ot { color: #007020; } code > span.al { color: #ff0000; font-weight: bold; } code > span.fu { color: #900; font-weight: bold; } code > span.er { color: #a61717; background-color: #e3d2d2; } </style> </head> <body> <h1 class="title toc-ignore">Term Frequency and Inverse Document Frequency (tf-idf) Using Tidy Data Principles</h1> <h4 class="author">Julia Silge and David Robinson</h4> <h4 class="date">2022-08-19</h4> <p>A central question in text mining and natural language processing is how to quantify what a document is about. Can we do this by looking at the words that make up the document? One measure of how important a word may be is its <em>term frequency</em> (tf), how frequently a word occurs in a document. There are words in a document, however, that occur many times but may not be important; in English, these are probably words like “the”, “is”, “of”, and so forth. We might take the approach of adding words like these to a list of stop words and removing them before analysis, but it is possible that some of these words might be more important in some documents than others. A list of stop words is not a sophisticated approach to adjusting term frequency for commonly used words.</p> <p>Another approach is to look at a term’s <em>inverse document frequency</em> (idf), which decreases the weight for commonly used words and increases the weight for words that are not used very much in a collection of documents. This can be combined with term frequency to calculate a term’s <em>tf-idf</em>, the frequency of a term adjusted for how rarely it is used. It is intended to measure how important a word is to a document in a collection (or corpus) of documents. It is a rule-of-thumb or heuristic quantity; while it has proved useful in text mining, search engines, etc., its theoretical foundations are considered less than firm by information theory experts. The inverse document frequency for any given term is defined as</p> <p><span class="math display">\[idf(\text{term}) = \ln{\left(\frac{n_{\text{documents}}}{n_{\text{documents containing term}}}\right)}\]</span></p> <p>We can use tidy data principles, as described in <a href="tidytext.html">the main vignette</a>, to approach tf-idf analysis and use consistent, effective tools to quantify how important various terms are in a document that is part of a collection.</p> <p>Let’s look at the published novels of Jane Austen and examine first term frequency, then tf-idf. We can start just by using dplyr verbs such as <code>group_by</code> and <code>join</code>. What are the most commonly used words in Jane Austen’s novels? (Let’s also calculate the total words in each novel here, for later use.)</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><span class="fu">library</span>(dplyr)</span> <span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(janeaustenr)</span> <span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(tidytext)</span> <span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a>book_words <span class="ot"><-</span> <span class="fu">austen_books</span>() <span class="sc">%>%</span></span> <span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">unnest_tokens</span>(word, text) <span class="sc">%>%</span></span> <span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">count</span>(book, word, <span class="at">sort =</span> <span class="cn">TRUE</span>)</span> <span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a></span> <span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a>total_words <span class="ot"><-</span> book_words <span class="sc">%>%</span> <span class="fu">group_by</span>(book) <span class="sc">%>%</span> <span class="fu">summarize</span>(<span class="at">total =</span> <span class="fu">sum</span>(n))</span> <span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a>book_words <span class="ot"><-</span> <span class="fu">left_join</span>(book_words, total_words)</span> <span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a>book_words</span></code></pre></div> <pre><code>## # A tibble: 40,379 × 4 ## book word n total ## <fct> <chr> <int> <int> ## 1 Mansfield Park the 6206 160460 ## 2 Mansfield Park to 5475 160460 ## 3 Mansfield Park and 5438 160460 ## 4 Emma to 5239 160996 ## 5 Emma the 5201 160996 ## 6 Emma and 4896 160996 ## 7 Mansfield Park of 4778 160460 ## 8 Pride & Prejudice the 4331 122204 ## 9 Emma of 4291 160996 ## 10 Pride & Prejudice to 4162 122204 ## # … with 40,369 more rows</code></pre> <p>The usual suspects are here, “the”, “and”, “to”, and so forth. Let’s look at the distribution of <code>n/total</code> for each novel, the number of times a word appears in a novel divided by the total number of terms (words) in that novel. This is exactly what term frequency is.</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><span class="fu">library</span>(ggplot2)</span> <span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(book_words, <span class="fu">aes</span>(n<span class="sc">/</span>total, <span class="at">fill =</span> book)) <span class="sc">+</span></span> <span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_histogram</span>(<span class="at">show.legend =</span> <span class="cn">FALSE</span>) <span class="sc">+</span></span> <span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">xlim</span>(<span class="cn">NA</span>, <span class="fl">0.0009</span>) <span class="sc">+</span></span> <span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">facet_wrap</span>(<span class="sc">~</span>book, <span class="at">ncol =</span> <span class="dv">2</span>, <span class="at">scales =</span> <span class="st">"free_y"</span>)</span></code></pre></div> <p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAqAAAAKgCAYAAABEPM/FAAAEDmlDQ1BrQ0dDb2xvclNwYWNlR2VuZXJpY1JHQgAAOI2NVV1oHFUUPpu5syskzoPUpqaSDv41lLRsUtGE2uj+ZbNt3CyTbLRBkMns3Z1pJjPj/KRpKT4UQRDBqOCT4P9bwSchaqvtiy2itFCiBIMo+ND6R6HSFwnruTOzu5O4a73L3PnmnO9+595z7t4LkLgsW5beJQIsGq4t5dPis8fmxMQ6dMF90A190C0rjpUqlSYBG+PCv9rt7yDG3tf2t/f/Z+uuUEcBiN2F2Kw4yiLiZQD+FcWyXYAEQfvICddi+AnEO2ycIOISw7UAVxieD/Cyz5mRMohfRSwoqoz+xNuIB+cj9loEB3Pw2448NaitKSLLRck2q5pOI9O9g/t/tkXda8Tbg0+PszB9FN8DuPaXKnKW4YcQn1Xk3HSIry5ps8UQ/2W5aQnxIwBdu7yFcgrxPsRjVXu8HOh0qao30cArp9SZZxDfg3h1wTzKxu5E/LUxX5wKdX5SnAzmDx4A4OIqLbB69yMesE1pKojLjVdoNsfyiPi45hZmAn3uLWdpOtfQOaVmikEs7ovj8hFWpz7EV6mel0L9Xy23FMYlPYZenAx0yDB1/PX6dledmQjikjkXCxqMJS9WtfFCyH9XtSekEF+2dH+P4tzITduTygGfv58a5VCTH5PtXD7EFZiNyUDBhHnsFTBgE0SQIA9pfFtgo6cKGuhooeilaKH41eDs38Ip+f4At1Rq/sjr6NEwQqb/I/DQqsLvaFUjvAx+eWirddAJZnAj1DFJL0mSg/gcIpPkMBkhoyCSJ8lTZIxk0TpKDjXHliJzZPO50dR5ASNSnzeLvIvod0HG/mdkmOC0z8VKnzcQ2M/Yz2vKldduXjp9bleLu0ZWn7vWc+l0JGcaai10yNrUnXLP/8Jf59ewX+c3Wgz+B34Df+vbVrc16zTMVgp9um9bxEfzPU5kPqUtVWxhs6OiWTVW+gIfywB9uXi7CGcGW/zk98k/kmvJ95IfJn/j3uQ+4c5zn3Kfcd+AyF3gLnJfcl9xH3OfR2rUee80a+6vo7EK5mmXUdyfQlrYLTwoZIU9wsPCZEtP6BWGhAlhL3p2N6sTjRdduwbHsG9kq32sgBepc+xurLPW4T9URpYGJ3ym4+8zA05u44QjST8ZIoVtu3qE7fWmdn5LPdqvgcZz8Ww8BWJ8X3w0PhQ/wnCDGd+LvlHs8dRy6bLLDuKMaZ20tZrqisPJ5ONiCq8yKhYM5cCgKOu66Lsc0aYOtZdo5QCwezI4wm9J/v0X23mlZXOfBjj8Jzv3WrY5D+CsA9D7aMs2gGfjve8ArD6mePZSeCfEYt8CONWDw8FXTxrPqx/r9Vt4biXeANh8vV7/+/16ffMD1N8AuKD/A/8leAvFY9bLAAAAOGVYSWZNTQAqAAAACAABh2kABAAAAAEAAAAaAAAAAAACoAIABAAAAAEAAAKgoAMABAAAAAEAAAKgAAAAAMw48TsAAEAASURBVHgB7L0JlFXVmb/9MlkFBRSjDFGGVuIYCETAtPGvSQiYQAZNayN2lhJp7KbTCYkdDNqLRCG99CNLQGPaZRITVyQBpRsBCdEYURAUhxAJoCgyT8ogUxVQTB+/3TnXc2/dserce3fVffZat845e3z3s3ft8549Njl9xhgGAhCAAAQgAAEIQAACBSLQtEDpkAwEIAABCEAAAhCAAAQcARRQKgIEIAABCEAAAhCAQEEJoIAWFDeJQQACEIAABCAAAQiggFIHIAABCEAAAhCAAAQKSgAFtKC4SQwCEIAABCAAAQhAAAWUOgABCEAAAhCAAAQgUFACzQuaWpESW7lypR04cKBIqZMsBCBQKgSaNWtmV155pdfZfeGFF7yWD+EgAIHGQaBTp0526aWXpsxMSSigH3zwge3ZsyclBBwgAAEIREFACqjvZvv27b6LiHwQgEAJEGAIvgQKmSxCAAIQgAAEIAABnwiggPpUGsgCAQhAAAIQgAAESoAACmgJFDJZhAAEIAABCEAAAj4RQAH1qTSQBQIQgAAEIAABCJQAARTQEihksggBCEAAAhCAAAR8IlASq+B9Al4qsrRo0cI+9rGPWevWre3w4cOmlbfHjx8vava1QrlHjx526tQp27p1q7umEqht27bWtWtXa968uX344Ye2c+fOVF7rbF9WVmZnn322k0XbVZw4ccL2799fK75evXrZtm3brH379o6h/AR2CqN8nTx5slY4LCAAAT8JqG1s2bKlE+706dN27Ngx27Vrl2sDEiUOtxOJbmqj1L7ql4upqKiwc845x+0Os3fv3qRB1a707t075qY2pqqqyrSrTK4m3F5lG/b888+39evXW7r8ZxsX/vwkQA+on+XSoKVSg3HNNddYz549rUmTJqbG54tf/KK1atWqqPm66qqrTIqlGv+BAwemlEXun//8553Cd9ZZZ9mnPvUp+/u///uU/uvqUF5ebueee64LLlbdu3dPGpXcpNCLo144MoGd+A4fPjxpOCwhAAE/CVx88cXuf1gflR07drSPf/zj9rWvfc19sCdKHG4nEt0UTuFzMYpv6NCh7gP805/+dKxNSYxDbc7gwYOtQ4cOri3s0qWLe/7sZz+b6DXjsxRZxZetUbumtGXS5T/b+PDnJwF6QP0slwYtlb6s9aX84osvxvIh5U+N0Jo1a2J26h1Vb2R1dbWzU6OjHkf16rVp08bZ6z4wUgalxOprP2zftGlT519phu2DcLrqa14N6EsvveT8Bo1b2E9wr0b9r3/9q/v6lt1bb70VezkEPQ1SsvU7dOiQqQdDRrIrP5JHcobd5K5eB7kpDoU5ePCgvf7663KKGcWphjpIRw4vv/xyrd7jwE7+xVFX5V0Mwwxkr94VDAQg4BcB9e5t3rw5JpQOMFCv35tvvunaK7UV+n9O1k4E7WMs8N9usmkL9RGrg1neffdd1xZKgVXvayrz2muvxbVxX//6151CqpEYtauBnEE7k9iuK95ly5ZZTU2Ny4/ayWA0TGH1C9os3audDLd/yfKv9lVxBPEoDYUVl3TvAfnD+EMABdSfsmg0kqgB0Je9evTUsEkpW7JkSawRkyKpr2g1GLrXELfc1RCqZ1KNrhqrdu3aOYVRcfQ60/vXr18/51f+dLrVpk2bnFJ5xRVXuAZVX+pvvPGGbdiwoRZLDR+psf/MZz7jhr5WrVpVy09gIfk1VL97924XrxrWJ554Iib/Jz/5Sfu7v/s7p2CqIXz++efdveRT4ym5Jb8a2j/84Q+ucVW6aphlLz8Koy/7QYMG2aJFi1zSSlMvICmnR44cscWLF7uhdfVw/vGPfwzEc9fA7sILL3S81EO7du1ax+/pp592ftQYf+5zn7N58+bFheUBAhDwk4DaB03Hueyyy9xHpdpOKW9BO6E24wtf+IJrR3Qv98DoAzubtnDHjh3Wv39/18OotlTtTC5G7ZMUv0Q51dYla9cV94gRI+yZZ55xbZ/S1r2MRoA0mqP2Xx0Xl19+uWtz9Q4IjNr1IP9qUzU6JcVXcmg6gNr8bPMexMnVDwIooH6UQ6OSQgqjvuLViGqekxQ5fe1v2bLF5VOKlpTOV1991SlP6h1VYyajxkYKlL7QNUwlhUzxnXfeefbnP//ZzZeUn8C/jvlSA/3+++87hU6NczIFVMqulFA1VO+9956LxyWY5I8aNA27a5hKX+ZKXz23+hJXj6KU4aeeeso1/pJLPaYKIyOlb/78+e5e0xC6devmZNOw/pw5c5wMCiMuakDDRo3uggULnP2QIUNc3tetWxf2UuteinifPn1iLxE1zOKzb98+1+O8cePGWmGwgAAEik9AbYNGO/Q/27lzZ/fBrhERfahWVla6D0d9iEpJDIyUN80H1/+9Pt6vu+66wMkdeZhNW6hw+qjWR7Q+hJVGOhN8FEvhVTumtkU9lGrDwnLKX7J2PZtTCNX26SP6ueeec/FLNjFJNPr417vhlVdece+Oq6++2smR7XsgMT6ei0sABbS4/Btt6lI49dOcS/WEShlVz5+Gs/XFK6P5RzJq2KSUSkFVw6YGRkYKnxRGGSmNaqCkzGoBkRQrKYNqpNRY6SejxlXKaWKjp+EtDfWrt1FKqhZF9e3b15YuXRo33KM4pKhKOdbLQHFJ3mHDhtmzzz7r0lOvQzCEry9yvSACBVS9C4HRELxeMOrVkL3meCldyS/5wi8WhdGLJVBK5V9pZ1JAg7SCq5RvTXUIFNA//elPgRNXCEDAIwIaPdFIkdoT/b/+5S9/ccqgFFC1g8kUQ7UJK1ascLlQu6L2UCbbtlD+1JZJgVM66nFU2yXl8YUXXnBxJf7RiI6MPsbVDoc/asNypmrXE9vixPj1LEVW7a44yKidDNpCZ/G3P2ozg2lcclfvbbZ5D8fDvR8EUED9KIdGJYWGotUwSomSEhn8pPBJAZWRW3g1pRpTNSS6JjObzgy3K4y+wKVsqtdRX8tqvKXoBkNR77zzTi2FUkqplOAnn3zSNaLLly83KaSSSw1o2KinVF/Vmr+qBlEy6qdeCqUt+aRYKp1kJpgHJbdwAypFV8q4hpykjOvFk7iyPuxf6SmdXI0UUL1gpORqKkFi/nKND/8QgEB+CEiZC88BDacSzIkM2+lebZLahsAE7Z6es2kLNcytVe9S8GQ0WqLpQatXr3bPyf7oQzzcNoX9JMqZrF0P+9d9eHg9WJgk2WWvn9IKfolh1b6Gw6tTQyabvCfGxXPxCTQtvghI0NgI6MtdQ0UajpZRg6GGT8MzMmp09SWvr101hhpqT+wNdB5Df/7f//t/Loy+voOvdymD+rpWI6R41MOpXtVwA6Uo5E+KWLDiXPdqONX4BQ1YkJQaMimhGoIPGnoNNamnVfJKsVOjLeVOaUqplPzpjHp4NQdKYfT1LuVV4RKNFFwp4UpXvJRWJiN5ZSSzjNJQD7KGqpJNRXCe+AMBCDRIAvoYDnoa1a4EI0RSzLJpC9Vmqe1V76uM2jS1N+qBTGw3cwWUTbsuOdXmauRIJtj5Q50BasuCZ42IBW1aWA6Nkqkdl6xy11Ql3WeT93A83PtBgB5QP8qhUUkhBUuNo+ZQyqiBU2+fVm7LqKFSI6IhaTVIUphkl04JVc+peg4/8YlPuMZTw0b6StZiIn3BSwlUQ/T222/b0aNHXTrhP1rJqQn6Cq/GT8NYUiqlqGneVNiot1KK7D/8wz+4yfaKV4qj5oLKKI2vfOUrrgdVMkghTmckjxTnL33pSy4+pa80gkY4CCsW8qP01EMRKOyBe7Kr0ldvs+aCae6s0lLPiqYIBHNuk4XDDgIQaHgENPdTc+bV/sgEQ9a6z6Yt1Mp1tQ9f/vKXXVuhzgItHtIiH30AaxpQXU2qdj0cn9p6zdeX/OoY0L0+8GU06qS2XJ0X+pBO7F2VH32Ua4qRwstdU5TUoZBN3hUe4xeBJmdeYPErIfySLxJptOIum3kokSRGJHEE1KOnFZNBT13YUQqY7JO5hf2F7zWcroYr0SgdKXCZjBTjsIIq5VjDWsmMFEHFG/Yf+JNbML8zsMvmmkr+IKy+6vVL1vgGfpJdw/nodWaRlLZayaQYJ4sHu/oRUDmMHDmyfpHkOfTMmTPznALR55uA2p7wFkTh9LJpC9XGqP0N2tJw+xGOqy73ydr166+/3i2wDNpSya82Lpn6kamNlEypwmeT97rkiTB1I6CPmqvPTGlLZegBTUUG+0gIpFMKc1WyJFDQYCYKly6dsN+gAQzsUimfclfjmOg/CCe3VLIEfpJdM4XJVSEP0lA+pBRr6oD+6VMtKAj8c4UABBougVTKp3KUTVuodibcFqVrB3OlFG7Xpehq1Enxh9vSdPKH5UqVdqrw2eQ9VZzYF54ACmjhmZMiBPJCQEqxhtg09zPYSSAvCREpBCAAgSwIqGdVc/MXLlyYhW+8lBoBFNBSK3Hy26gJaEcADAQgAAEfCKinUicuYSCQjACr4JNRwQ4CEIAABCAAAQhAIG8EUEDzhpaIIQABCEAAAhCAAASSESiJIXitjEvc7zEZjHR2ml+nRR4+GN9kERPY1K4ZvpUTZVS7jKK20aIL301920Llj7qdvJThkpqLXGiDavNpzHVGOxqkMyWhgGoeilYG18foVJpgY/X6xBNFWK0SzFSwUaSTTRxa2aiJ5toWo9hG/8hagemDLGJBnUleI7QoQR+FqjfFNlqdq3qTuCdrXeXSSTA+G/1/SAkINvyui6xiptXGwWbmdYkjyjA+tYe+/c+rLfRB6dM7WPVG2+D5YKgzyUshSi5qV9XWpzMloYDqRTdw4MB0HDK6aVNvnc7gg9EKZ51c4YPRyRpqVKLoValvfrS1iDYw9uVDgTqTvES1+bTOl5YSWmwjRUr1JtgMu77yPP/88/WNIu/hdZJXfdpDMdNuC8EpPHkXOEMCPrWHPv3P63QhnffuQ6+8NotXvUl32EiGYo7UmTqTHGeUXNSuLlmyJHlCf7MtmAKqU110es0ll1xi3bp1iwmlf9hwr4EqaJ8+fZy7No9XmF5nNta+4IILYmF0oxMQdPLCgAED3NFicY48QAACEIAABCAAAQh4S6AgCui8efNszpw5pvO8db3wwgtt/PjxDsovfvELdxyXekRk+vbt6xRQHTk2adIkd5zjz372M7vlllvs2muvdX6mTZvmjkaUovrQQw/Zgw8+6E3vpBOQPxCAAAQgAAEIQAACKQnkXQHVvI/f/OY3NnXqVHeG60033WQ33HCD3Xzzzda+fXu3R9h9991XS4GcPn26TZkyxfr16+f8jxkzxoYPH+56S3WOthRZDS3MmjXLdLTcxIkTU2YSBwhAAAIQgAAEIAABfwjkfcmm5l8+9thjTvlUtrVoRfNBpJhqguq+ffts9+7d9vjjj9u2bdscGU2U1716Q2U010gT3rdv3+5OeZF9MK9FQ/Br1651/vgDAQhAAAIQgAAEIOA/gbz3gApBsEBFk1JnzJhh11xzjZu3+de//tVNTH7ttdfcIgANy48ePdr69+/vwoRX72nRjZTVnTt3xi3Aadu2rWkhTNhIUQ2fCCOld+vWrWEvOd9HEUfOiaYIIAVdE8x9MFo1p4+BqFYR1zdPYqMFEj4Y6kzyUtBiBLEJPiKT+yqMrdokrdaMakW+8oaBAAQgAIHMBAqigEoMNcz33HOPa+zvuusuJ9lFF11kc+fOdUPxsjj//PPt0Ucftcsuu8z1kDpPf/sjxUKrrfWiUO9pYGSfuIJVW4yEFzotXrzYzjnnnCBIna5SYOsbR50SThIoypVqSaLPyUofBVHss5pToik8S5nwaRU8dSZ5QTXmVfAcO5i8zLGFAAQgkEigIAqohtrvuOMOtxfn97///Vhvg3qq1JOnuaAy2uZILyc9S5GQ0hps1SJFR4rlrl27bNWqVbF8yD6sbMpBPafh3tPE51jgNDeHb74pzrXDmaeqOBuz1o/NTLApzGNd8pNPyXyRJ5BDV1+ML7IEbHzgEsjiAxufZPGhbFLJMHtG+g2lFe4fv1OTKjj2EIAABGoRyPscUKX4wx/+0G2j9IMf/CCmfMpePXnf/e537ciRI65n9Omnn7arrrrKbbI+ePBgmz9/vry5vaSklOqn/etWr17thtTV+7lgwQIbNGiQ88cfCEAAAhCAAAQgAAH/CeS9B/Stt96yV155xf2eeOKJGJGf/vSnbpHRddddZ2PHjnUn2Gg+5+TJk52fcePG2YQJE9wQveaKaUsmGfmRf62K14bKPXv2tFGjRjk3/kAAAhCAAAQgAAEI+E8g7wqo5nlq26RURtsxfeMb33Ar46VcBkaK5ezZs92CkmCP0MBtxIgRNmzYMDdEr5MeMBCAAAQgkB0BHYuo0aeoTT7izEbGTMf9ZRNHVH40KlcsDol50Mii5sX7MNVFiw59YkOdSawt//ccJRfVPf3SmbwroOkSD9zUwxlWPgN7XROVz8BNZ9z6cuZ3IBNXCEAAAr4TULuZj6N88xFntiyLmXZYRimfvsgixdOXozi1eFhrOnxhozLzRRaf6kyUXKR8ZtrppCBzQMP/oNxDAAIQgAAEIAABCJQ2ARTQ0i5/cg8BCEAAAhCAAAQKTgAFtODISRACEIAABCAAAQiUNgEU0NIuf3IPAQhAAAIQgAAECk4ABbTgyEkQAhCAAAQgAAEIlDYBFNDSLn9yDwEIQAACEIAABApOAAW04MhJEAIQgAAEIAABCJQ2ARTQ0i5/cg8BCEAAAhCAAAQKTgAFtODISRACEIAABCAAAQiUNgEU0NIuf3IPAQhAAAIQgAAECk7Ai6M4853rkydP5nw+b7MshCrWmb9RnteaRTbTetEZv+Krc36LbXT0l457y3T+bKHk5Ozj5KRVRocOHTLVnWIblZHqS01NTSSi+PB/EElGiAQCEIBAngmUhAKqc2hzPff1cBbgc40ziyiz9lLMtMNC6oVbXl5uFRUVYeui3EuRqKqqsjZt2hQl/cREG+sZv4n5zPVZiqfKqKysLNegkfsPPlhatmwZSdzNm5dEkxoJKyKBAARKmwBD8KVd/uQeAhCAAAQgAAEIFJwACmjBkZMgBCAAAQhAAAIQKG0CKKClXf7kHgIQgAAEIAABCBScAApowZGTIAQgAAEIQAACEChtAsyYr0f5H775prShWz82M607jhCAAAQgAAEIQKAUCdADWoqlTp4hAAEIQAACEIBAEQmggBYRPklDAAIQgAAEIACBUiSAAlqKpU6eIQABCEAAAhCAQBEJMAe0iPBJGgIQgEBjITB7xllps/KP34nmtKm0ieAIAQg0GAL0gDaYokJQCEAAAhCAAAQg0DgIFEwB/fDDD+25556znTt31iK3bt06e/bZZ23Pnj1xbnp+5plnTO6JJlWYRH88QwACEIAABCAAAQj4RaAgCui8efPs29/+tm3cuNHuvvtumz59eozCtGnTbOrUqbZy5Uq79dZbbcuWLc5Nz6NHj7Z33nnHJkyYYHPnzs0YJuaBGwhAAAIQgAAEIAABbwnkfQ7oyZMn7Te/+Y1TMnv37m033XST3XDDDXbzzTfbgQMHbOnSpTZnzhxr2rSpzZo1y2bOnGkTJ050SuqUKVOsX79+zv+YMWNs+PDhtmPHjpRhvKWMYBCAAAQgAAEIQAACMQJ57wFt1qyZPfbYYyblU+bo0aN2+PBhk2K6YcMG69u3r1M+5TZgwABbu3atnThxwrZt2+bcZN+lSxdr1aqVbd++PWUY+cNAAAIQgAAEIAABCPhPIO89oEJQUVHhSJw6dcpmzJhh11xzjXXq1MnNB62srIxRatu2re3du9c++OADF6ZJkyYxN/nbt29fyjAxj2du1Ev63nvvxayk9EqhzcW0y8VzCr+5ppkimlrWx48ft0OHDtWyL4ZFTU2Nk0VzfH0w+nhRz7oPpi71Ll9y+1RnxEU/fZwW26hNOn36dGSyHDt2LKssrV+/3rZu3WqXX365tWzZMhZG4V9//XVT2zdw4EBr0aJFzE3z3jdv3uw+1NV+BiZdmMAPVwhAAAK+ESiIAqpMq5G85557XGN/1113OQ56AaknNDBSHtQYJ9rLXW7l5eW13IIwQRy6du3a1Tp37hyzevHFF6179+6x52xuqrPxlMFPrmlmiC7mLAUrrLjHHIpwo4+CsrKy2EdGEUSIJSlloqqqytq0aROzK+aNPkDyVQdyzZdPdUYfmKq/qjfFNmqXVG/CSmB9ZNKc9Uzme9/7nmvHzjvvPHv44Yft9ttvt0GDBtmRI0fsm9/8pl1yySXuI/rJJ5+0+++/3ymjmiu/Zs0a69Onjz300EP24IMPWo8ePdKGySQH7hCAAASKSaAgCmh1dbXdcccd9rGPfcy+//3vx3obpCSuWrUqln8pM926dbOOHTs6RUIvh+AlJTe9zHft2pU0TCySMzeaT6pfYBKfA/t8X8MyRJlWsfKTLA/qqfFJHp9kEa981YFkZZHOzicuPtWZoHyCazqGUbitXr3adu/e7ebFK74LLrjAzX2XAjp79mwbPHiwjR8/3iV122232YoVK9wHdaq58qnCqGcVAwEIQMBnAgVRQH/4wx+6hvZb3/pWHAsNMWlIXkNRUjwXLFjgegKaN2/uGuL58+fb9ddfb0uWLLH27du7X6owcRHzAAEIQMBDAhdffLE98sgjMcnUM63pCDIalh86dGjMLZgTrw/4xLnyCxcuTBsmrIAG0wwUIBhxkl2hTb7S1BSKfMVdF0a+yOITF8nimzy+lJPqmC+yRFlG2eQp7wroW2+9Za+88or7PfHEE7H/55/+9KeuUR07dqxphXuHDh2sZ8+eNmrUKOdn3Lhxse2X1DsxadIkZ695oqnCxCLnBgIQgICHBNSWBcP9moqgHUI0KiSj0R21b4HRvaZxaBQoPOUmmCufLkwQh65a2KkRJBmlr6F+zZMvtMlXmprfrIWtPhh9TOQrn7nmT1wOHjzopnDkGjZq/5oqJ4Uk+NiKOv5c46POJCcWJRcpsyr3dCbvCuhFF13ktk1KJcSIESNs2LBhbo5o69atY96kjGp4af/+/dauXfySoFRhYoG5gQAEIOAxAe2JrGlJ2us46K1MnPsezG9PZa/spXMLsn/ppZcGt+6F8PLLL9s555wTsyvUTb7S9Gl+s/axzlc+cy0nKZ96pxZqekk6+fSBoCl1ml7ng6HOJC+FKLnogyO8GDxZih9NlEzmWiA7rfQMK5/hZBOVz8AtXZjAD1cIQAACvhHQqNB3v/td+7d/+zfTx3RgtLI96KmUXTDvXXPlE+01ZUkmVRjnyB8IQAACHhPwQgH1mA+iQQACEIiMgI4X1slumhd/1VVXxcV75ZVX2qJFi9wwpfwtX77c+vfv77Zj0uIlzZVXr2gwV16BU4WJi5gHCEAAAh4SyPsQvId5RiQIQAACRSGgefCaVvSd73wnlr7mvz/11FM2ZMgQW7Zsmd14441u2HTkyJGxAzxSzXtPFyaWADcQgAAEPCSAAuphoSASBCDQOAlocaV+yYx2/5g8ebI72EELlfQcmFTz3tOFCcJyhQAEIOAjgY9aOB+lQyYIQAACJUYg1UEKmvcePhkpjCVVmLAf7iEAAQj4RIA5oD6VBrJAAAIQgAAEIACBEiCAAloChUwWIQABCEAAAhCAgE8EUEB9Kg1kgQAEIAABCEAAAiVAAAW0BAqZLEIAAhCAAAQgAAGfCKCA+lQayAIBCEAAAhCAAARKgAAKaAkUMlmEAAQgAAEIQAACPhEoiW2YTp48aTrjNBfTLBfPKfzmmmaKaGpZV1dX17IrlsXRo0dNfHVCS7GNzp7VecO6+mDEJF91INf8+VRnVEaHDh1yJ/7kmo+o/auMVF9qamoiidqH/4NIMkIkEIAABPJMoCQU0GbNmlllZWVOKA/n5Du551zTTB5Lctt8xp08xeS2euGWl5dbRUVFcg8FtJUiUVVVZb7siSjl05dyUjH4Ios+WlRGZWVlBawdyZMKPli08XsUJrx5fBTxEQcEIACBxkqAIfjGWrLkCwIQgAAEIAABCHhKAAXU04JBLAhAAAIQgAAEINBYCaCANtaSJV8QgAAEIAABCEDAUwIooJ4WDGJBAAIQgAAEIACBxkoABbSxliz5ggAEIAABCEAAAp4SQAH1tGAQCwIQgAAEIAABCDRWAiigjbVkyRcEIAABCEAAAhDwlAAKqKcFg1gQgAAEIAABCECgsRJAAW2sJUu+IAABCEAAAhCAgKcEUEA9LRjEggAEIAABCEAAAo2VQEGP4jx8+LC9+eabdsUVV8R4btmyxXbs2BF77tixo/Xp08c979mzx9544w3r1auXXXDBBTE/ulm3bp1t3rzZBgwYYJ06dYpz4wECEIAABCAAAQhAwF8CBVNAdf7zj370I2vatGmcAvqLX/zC3n//fWvXrp2j1LdvX6eArly50iZNmmRDhw61n/3sZ3bLLbfYtdde6/xMmzbN1qxZ4/w99NBD9uCDD1qPHj38pYxkEIAABCAAAQhAAAIxAgVRQDds2GB33nmnVVZWul8s9TM37777rt133321FMjp06fblClTrF+/fnbDDTfYmDFjbPjw4a63dOnSpTZnzhynzM6aNctmzpxpEydODEfLPQQgAAEIQAACEICApwQKMge0urra7rrrLrvxxhvjMMh+3759tnv3bnv88cdt27Ztzv3EiRPuXr2hMl26dLFWrVrZ9u3bTcqs7NWTKqMh+LVr17p7/kAAAhCAAAQgAAEI+E+gID2gl156qSPxwgsvxBF577337NixY/baa69Zy5Ytbfz48TZ69Gjr37+/VVRUWJMmTWL+1XsqZXXnzp1xvaht27a1vXv3xvzpRn42btwYs9Pwf3ieacwhzU3bNG7ZOuWaZrbx1tTUWFVVVbbe8+pP5SdZDhw4kNd0son89OnTpo+XQ4cOZeM9737EJl91IFfhfaozR44cMcnTrFmzXLMRuf+TJ0+a6k3z5tE0hSpzDAQgAAEIZCYQTaubOZ2kPi666CKbO3eutW/f3rmff/759uijj9pll11mejGEjRSL8vJy99IKu8leymvYnH322bE4Zf/SSy+Z7HIxR3PxnMJvrmmmiKaW9cGDB02Ktw/mww8/tLKyMtdDXWx5Tp06ZepVb926dbFFcemrxz5fdSDXDPpUZzTioQ/Ks846K9dsRO5firDqjdqWKIwPeYoiH8QBAQhAIN8EiqqA7t+/3/RiDBRQLSTSgiQ9q1dNvQlSbmTU+9m9e3fbtWuXrVq1KsZF9t26dYs960Y9K+HeFQ3XR9XDEZdQhod8pam85SvuDFmq5Sy2vsgjRcIXWQRKPfi+lJNPXHyqM/qYjbKcwqM2tf5ZsIAABCAAgRiBoiqgGrb93ve+Z1pIpB6Ip59+2q666irXMzJ48GCbP3++XX/99bZkyRKnlEoxHThwoM2YMcO2bt3qFM8FCxbYoEGDYhniBgIQgAAEUhM4fvx4UabM5GuajkY9fDEakctXPnPNo6a66KPch48iTYPziQ11JnltipKL6p5+6UxRFdDzzjvPrrvuOhs7dqyrnBpWnjx5spN33LhxNmHCBDdErx4TbckkIz/yr1XxHTp0sJ49e9qoUaOcG38gAAEIQCA9gRYtWsTNo0/vOzpXTbvIl8ln3LnILOXTF1mkeGo6kt6fxTYagdGIpi9sxMMXWXyqM1FykfKZqe4VVAG9+uqrTb+wufnmm+0b3/iGaZP68LxGKZazZ882DdMHe4QG4UaMGGHDhg1zFdqX+X6BbFwhAAEIQAACEIAABNITKKgCmkoUaclh5TPsL1H5DNz0Fa8fBgIQgAAEIAABCECgYREoft98w+KFtBCAAAQgAAEIQAAC9SSAAlpPgASHAAQgAAEIQAACEMiNAApobrzwDQEIQAACEIAABCBQTwIooPUESHAIQAACEIAABCAAgdwIoIDmxgvfEIAABCAAAQhAAAL1JIACWk+ABIcABCAAAQhAAAIQyI0ACmhuvPANAQhAAAIQgAAEIFBPAiig9QRIcAhAAAIQgAAEIACB3AiggObGC98QgAAEIAABCEAAAvUkgAJaT4AEhwAEIAABCEAAAhDIjYAXR3HmJnLuvk+ePGkHDhzIKWCznHwn95xrmsljqW1bXV1d27JINkePHjXxPXHiRJEk+CjZU6dO2bFjx0xXH4yY5KsO5Jo/n+qMyujQoUOmulNsozJSfampqYlEFB/+DyLJCJFAAAIQyDOBklBAmzVrZpWVlTmhPJyT7+Sec00zeSzJbfMZd/IUk9vqhVteXm4VFRXJPRTQVopEVVWVtWnTpoCppk5Kyqcv5SQpfZFFiqfKqKysLDW8ArkEHywtW7aMJMXmzUuiSY2EFZFAAAKlTYAh+NIuf3IPAQhAAAIQgAAECk4ABbTgyEkQAhCAAAQgAAEIlDYBFNDSLn9yDwEIQAACEIAABApOAAW04MhJEAIQgAAEIAABCJQ2ARTQ0i5/cg8BCEAAAhCAAAQKTgAFtODISRACEIAABCAAAQiUNgEU0NIuf3IPAQhAAAIQgAAECk4ABbTgyEkQAhCAAAQgAAEIlDYBFNDSLn9yDwEIQAACEIAABApOAAW04MhJEAIQgAAEIAABCJQ2gYIqoIcPH7Zly5bVIr5u3Tp79tlnbc+ePXFuen7mmWdM7okmVZhEfzxDAAIQgAAEIAABCPhFoGAKqM5//tGPfmTz5s2LIzBt2jSbOnWqrVy50m699VbbsmWLc9fz6NGj7Z133rEJEybY3LlzY+FShYl54AYCEIAABCAAAQhAwFsCzQsh2YYNG+zOO++0yspK9wvS3LRpky1dutTmzJljTZs2tVmzZtnMmTNt4sSJNn36dJsyZYr169fPbrjhBhszZowNHz7cduzYkTJMEC9XCEAAAr4TePvtt628vNx69eoVE/XYsWP2+uuvW5MmTWzgwIHWokWLmJtGfTZv3mwDBgywTp06xezThYl54gYCEICAZwQK0gNaXV1td911l914441x2Zdi2rdvX6d8ykEN69q1a+3EiRO2bds25yb7Ll26WKtWrWz79u2WKoz8YSAAAQg0BAIbN26022+/3d56662YuEeOHLFbbrnFFi9ebI8//rgb+Tl9+rRzTzXqky5MLGJuIAABCHhIoCA9oJdeeqnL+gsvvBCHYOfOnXE9om3btrW9e/faBx98YBUVFa4XIAig3tN9+/ZZqjCBP1137drlegoCO/UQKFwupk0unlP4zTXNFNHUsq6pqTEp9T4YTa2oqqqygwcPFl0cvaz18aK5xj6YutS7fMntU52R0nT8+HFr1qxZvrKbdbwnT5401ZvmzaNpCsU5k9E0pF/96ldxbZ/CzJ492wYPHmzjx493Udx22222YsUK69q1a8pRn1RhLr/88kxi4A4BCECgqASiaXXrmAW9gPQCCIyUh5YtW7oXU9he7nLTcFWqMEEcunbs2NGkzAZm+fLlcUNWgX2667F0jlm6hYfJsgySlbdDhw5ZmzZRqMhZJZfW04cffmhlZWWuhzqtxwI4njp1yinmrVu3LkBqmZOQMpKvOpA59XgfPtWZ3bt3O+XrrLPOiheyCE8qI9UbtS1RmPCQear41Mb98pe/tAceeCDuI3v9+vU2dOjQWLBgREgfm4kjRQsXLnT+UoVBAY1h5AYCEPCUQFEV0M6dO9uqVatiaNTD2a1bN6dAqldNPUhSbmTk1r17d9e7mSxMLJIzN3oJhF8Eml8afg77TXUfhQKaa5qpZEm0lxKer7gT08r0LFnUe+SDPFIkfJFF3DSPzwcukoU6Iwq1jeqMflGVk8o8kwkrmcEQu8Jo5Cb84ax7TUVSG6gRoMAEI0XpwgR+dVV7qZElGcmndjVY7OksC/QnX2mqc+LAgQMFykX6ZDQilK98pk+5tqu47N+/v7ZDEWzUoaT/M73XfTDUmeSlECWXYEQyeUr/Z1tUBVST7GfMmGFbt251iueCBQts0KBBTonQUNT8+fPt+uuvtyVLllj79u3dL1WYdJnEDQIQgIDvBFKN7qSyV37SuQX5Ve9pYPSCefnll61Hjx6BVVbXl7Pyld5Trmmmj+0jVymfYQX9I5fC30n5zFc+c82NpkVpNEgdMMU2mhalDx+NTvpgqDPJSyFKLvrg0Fz3dKaoCqi+5MeOHetWuHfo0MF69uxpo0aNcvKOGzcutv2S/oEmTZrk7NOFSZdR3CAAAQj4TEDTNTTSExjdn3vuuU65SjXqkypMEAdXCEAAAr4SKKgCevXVV5t+YTNixAgbNmyY+zoKz92TMqoJ9hpCaNeuXTiIpQoT54kHCEAAAg2IwJVXXmmLFi0yXdVjpLnr9957r+s1SjZSpKylCtOAso2oEIBAiRIoqAKairHmX6Wag5WofAZxpAsT+OEKAQhAoKEQGDJkiDspTtvVadRn5MiR1rt3byd+qpGidGEaSr6REwIQKE0CXiigpYmeXEMAAqVM4O67747LvhbQTZ482bRjgVbKh7eGSjXqky5MXOQ8QAACEPCMAAqoZwWCOBCAQGkTSLXFWrpRn1RhSpskuYcABHwmUPzlcT7TQTYIQAACEIAABCAAgcgJoIBGjpQIIQABCEAAAhCAAATSEUABTUcHNwhAAAIQgAAEIACByAmggEaOlAghAAEIQAACEIAABNIRQAFNRwc3CEAAAhCAAAQgAIHICaCARo6UCCEAAQhAAAIQgAAE0hFAAU1HBzcIQAACEIAABCAAgcgJoIBGjpQIIQABCEAAAhCAAATSESiJjehPnjxpBw4cSMehlluzWja5W+SaZrYpVFdXZ+s17/6OHj1q4nvixIm8p5UpgVOnTtmxY8dMVx+MmOSrDuSaP5/qjMpIp/2o7hTbqIxUX2pqaiIRxYf/g0gyQiQQgAAE8kygJBTQZs2aWWVlZU4oD+fkO7nnXNNMHkty23zGnTzF5LZ64ZaXl1tFRUVyDwW0lSJRVVVlvpwKI+XTl3JSMfgiixRPlVFZWVkBa0fypIIPFh19GYUJH58ZRXzEAQEIQKCxEmAIvrGWLPmCAAQgAAEIQAACnhJAAfW0YBALAhCAAAQgAAEINFYCKKCNtWTJFwQgAAEIQAACEPCUAAqopwWDWBCAAAQgAAEIQKCxEkABbawlS74gAAEIQAACEICApwRQQD0tGMSCAAQgAAEIQAACjZUACmhjLVnyBQEIQAACEIAABDwlgALqacEgFgQgAAEIQAACEGisBFBAG2vJki8IQAACEIAABCDgKYGSOAnJU/aIBQEIQKBkCMyecVbGvP7jd6I5EjVjQniAAASKTqDoCuiWLVtsx44dMRAdO3a0Pn36uOc9e/bYG2+8Yb169bILLrgg5kc369ats82bN9uAAQOsU6dOcW6+PBy++aaMorR+bGZGP3iAAAQgAAEIQAACjYlA0RXQX/ziF/b+++9bu3btHNe+ffs6BXTlypU2adIkGzp0qP3sZz+zW265xa699lrnZ9q0abZmzRrn76GHHrIHH3zQevTo0ZjKhbxAAAIQgAAEIACBRkug6Arou+++a/fdd18tBXL69Ok2ZcoU69evn91www02ZswYGz58uOstXbp0qc2ZM8eaNm1qs2bNspkzZ9rEiRMbbSGRMQhAAAIQgAAEINCYCBR1EVJ1dbXt27fPdu/ebY8//rht27bNsT1x4oS7V2+oTJcuXaxVq1a2fft227Bhg8leyqeMhuDXrl3r7vkDAQhAAAIQgAAEIOA/gaL2gL733nt27Ngxe+2116xly5Y2fvx4Gz16tPXv398qKiqsSZMmMYKVlZVOWd25c6fpPjBt27a1vXv3Bo/uqiH9rVu3xuyUxq5du2LP2dy0zsZTBH5ylUtJ1tTU2JEjRyJIvf5RHD161PQhcejQofpHVs8YTp8+bfp4qaqqqmdM0QSvS72LJuXasfhUZ1RfVE7NmjWrLWiBbU6ePGmqN82bR9MUijMGAhCAAAQyE4im1c2cTlIfF110kc2dO9fat2/v3M8//3x79NFH7bLLLjO9GMJGL6zy8nL30gq7yV7Ka9goPvWYBmb//v3WoUOH4DGra6FeI7nKJeGl7LVp0yarfOTbk9ieddZZcbzznWaq+E+dOuUUc328+GCkgNalfPMhu091RuWkD0fVm2IbKYySR21LFKZFixZRRJPXOI4fP24HDhzIaxp1jbwucumDxhej91Fd8pAP+dVJobod7sjJRzrZxKmOCp/YUGeSl1qUXFT39EtniqqASnk5ePBgTAHVQiL1XkqBVC+WXuBlZWVOfg3Vd+/e3fVkrlq1KpYn2Xfr1i32rBu92MIvNw3Xh5/jPKd4KJQCmqtcEle9NXUJlyKr9bJWL5Zeuj7Io8qul6sPsgiqGn5fZKHOJK/m6v1UvYmqnHx42SfP6Ue2+n8NjyJ95FL8u7rKVddwUedYyqcvsqgutm7dOjZdLeq85hKf3hN6n/vCRrL7IotPdSZKLmpXg6mSqepKUeeACvx3v/td12ulF8HTTz9tV111lXsZDB482ObPn+/kXrJkiVNKpZgOHDjQVq9e7YbY9UW1YMECGzRoUKr8YQ8BCEAAAhCAAAQg4BmBovaAnnfeeXbdddfZ2LFjXfe8huUmT57sEI0bN84mTJjghuilRWtLJhn5kX+titfwZs+ePW3UqFHOjT8QgAAEIAABCEAAAv4TKKoCKjw333yzfeMb37DDhw875TJAJsVy9uzZpmH6YI/QwG3EiBE2bNgw16WvIQYMBCAAAQhAAAIQgEDDIVB0BVSo1MOpns1kJlH5DPxoHlNDmPAfyMsVAhCAAAQgAAEIQOD/CBR1DiiFAAEIQAACEIAABCBQegRQQEuvzMkxBCAAAQhAAAIQKCoBFNCi4idxCEAAAhCAAAQgUHoEUEBLr8zJMQQgAAEIQAACECgqARTQouIncQhAAAIQgAAEIFB6BFBAS6/MyTEEIAABCEAAAhAoKgEU0KLiJ3EIQAACEIAABCBQegRQQEuvzMkxBCAAAQhAAAIQKCoBFNCi4idxCEAAAhCAAAQgUHoEvDgJqfSwk2MIQAACEEgkMHvGWYlWtZ7/8Ts1teywgAAEGh6BklBAT548aQcOHMipdJrl5LvunnOVSylVV1fXPcGIQx49etTE98SJExHHnHt0p06dsmPHjpmuPhgxqUv55kN2n+qMyujQoUOmulNsozJSfampiUap8eH/oNhMSR8CEIBANgRKQgFt1qyZVVZWZsMj5udw7C6/N82+PS5jAq0fm1nLT675qRVBRBZ64ZaXl1tFRUVEMdY9GikSVVVV1qZNm7pHEmFIKZ++lJOy5YssUjxVRmVlZRHSrltUwQdLy5Yt6xZBQqjmzUuiSU3INY8QgAAEcifAHNDcmRECAhCAAAQgAAEIQKAeBFBA6wGPoBCAAAQgAAEIQAACuRNgvCh3ZgUPcfjmm+LS1PzUxCkCyYbp4wLxAAEIQAACEIAABDwhQA+oJwWBGBCAAAQgAAEIQKBUCKCAlkpJk08IQAACEIAABCDgCQEUUE8KAjEgAAEIQAACEIBAqRBAAS2VkiafEIAABCAAAQhAwBMCLELypCDqK0biQqXE+FiklEiEZwhAoCESyOa0pEz54jSlTIRwh0D+CaCA5p8xKUAAAhCAgEcEslFiUVI9KjBEaZQEUEAbZbHWzlSmHlKFoJe0NjdsIAABCEAAAhCIngAKaPRMiRECEIAABBo4gUy9pPSQNvACRvyiE2iwCui6dets8+bNNmDAAOvUqVPRQTYGAbLpJU3Mp07zPn3mF2yMTy9qIiGeIZBfAjrP/vXXX7cmTZrYwIEDrUWLFvlNkNgdgVQK6sshPiipIRjcQiCBQINUQKdNm2Zr1qyxPn362EMPPWQPPvig9ejRIyFrPBaDQF2U2GRyosgmo4IdBOIJHDlyxL75zW/aJZdcYjt27LAnn3zS7r//fqeMxvvkqRgEUimpuciCEpsLLfw2JAINTgHdtGmTLV261ObMmWNNmza1WbNm2cyZM23ixIkNiTuyZiBQV0W2yZl4c+mNzZQOinCGgsK5qARmz55tgwcPtvHjxzs5brvtNluxYoVdfvnlRZWLxKMjEIUSK2miUGSjkCUKOaKjS0zFJNDgFNANGzZY3759nfIpcBqCX7hwYRzDDz74wLZt2xaz0xDV+++/H3vO5qYiG0/48ZpAJuUyG+HrE0eHMwkEynA2aeXTT7McZDnyz/8SiSgtf/5w0nj0v3X8b7+kHkKW1T+4K/SU/LbVvT9O7pCD7fv/3/05+E7ttaamJrVjHlzWr19vQ4cOjcWs9nDt2rVxCuh7771nBw4ccH40TH/06NGc28NYAtw0WAJRKI9RZN4XOaLISxBHv8/ODm6TXt9c/I9J7QPL8LSNwC7Z9VPDFiWzzsnujWe+mNH/1SO3ZvSTycOpU6fs5MmTab01OAV0586dVllZGctU27Ztbe/evbFn3cj9rLPOitnJvV27drHnrG4eeTTOm9Lt1q1bnF2xHg4dOmRt2rQpVvJx6e7fv9/KysqsZcuWcfbFeFCF15BkRYUfnw8Ntc5ENoNw4KCk1UD/j6q/4f/RpB7PWH70n57Kxxn7hP/VND5rOUlhVL1pV15ey60uFs2bF7ZJ3bVrl6kNDIzuwx/fsu/atat17NjReVFeDx48mHN7+LV/ORQkYWKmNiiIM+ZQpBuf2kOf/ucPHz5srVq1inXWFKl4XLLV1dV2/PjxuHd3MeUpdJ3pfcFH/z+J+S50nTk39L+cKEuUXNTWaJQ6nSlsa5lOkizdmjVrFqdVnzhxopbyI4VIv8AoTPg5sM/lKpD1jSOX9NL5VQ+GL7LohatFDz7Iowqv+uCDLCo/6kzyWqz/RymfvpST6k1UsmRqcJMTqbttNu1h+INM/x9R1Mso2tS65zo+pE/tYRRs43NX9yeN/KleF7pOJpNYymeU/2fJ0sjFjjqTnFaUXFTeGnFJZ9Krp+lCFsmtc+fOtm/fvljquvelZzImFDcQgAAECkBAO4Aktofdu3cvQMokAQEIQKB+BBqcAqptRlavXm1bt251vV0LFiywQYOSD/XVDw2hIQABCPhN4Morr7RFixa5eZ179uyx5cuXW//+/f0WGukgAAEInCHQ4IbgNcdp7NixNmbMGOvQoYP17NnTRo0aRWFCAAIQKDkCQ4YMsWXLltmNN97ohlpHjhxpvXv3LjkOZBgCEGh4BBqcAirEI0aMsGHDhpnmuLRu3brhUUdiCEAAAhEQ0BzsyZMnu0VBWghY6EVQEWSBKCAAgRIl0CAVUJWVFr5w4keJ1lqyDQEIxBHwZVeMOKF4gAAEIJCGQINVQNPkqZaTVn4uXry4ln0uFtreR/vp+WCUH196OrQli1bE6ldsc/r0abdDgi9sqDPJa4RGLvTx6MPqXK3UVL2Jqv5qWzLfjfZJrk97KGZa1RzVzgH15eVTe+jb/7zqdaaVyPXln014lZHqTTZbr2UTX339UGeSE4yaS6a61+RM46ujvDEQgAAEIAABCEAAAhAoCIEGtwq+IFRIBAIQgAAEIAABCEAgbwRQQPOGloghAAEIQAACEIAABJIRQAFNRgU7CEAAAhCAAAQgAIG8EUABzRtaIoYABCAAAQhAAAIQSEYABTQZFewgAAEIQAACEIAABPJGAAU0b2iJGAIQgAAEIAABCEAgGYGS2Ad05cqVdvDgwWT5xw4CEIBAZAS0t6nOZ/fZvPjiiz6Lh2wQgEAjIdCxY0e79NJLU+amJBRQbby8Z8+elBBwgAAEIBAFgag2tI9CllRxbNu2LZUT9hCAAAQiI5Bpm3mG4CNDTUQQgAAEIAABCEAAAtkQQAHNhhJ+IAABCEAAAhCAAAQiI4ACGhlKIoIABCAAAQhAAAIQyIYACmg2lPADAQhAAAIQgAAEIBAZARTQyFASEQQgAAEIQAACEIBANgRKYhV8NiDwUxwCzZs3t169erltsrRbQdh07drVysvLbdOmTWHrSO67d+9unTp1Mq0IrqiosK1bt6aNt3fv3rZlyxY7efJknD/JePjwYfcLO1RWVlrnzp1jVsePH7e9e/fW8hfzkOKmrKzMzj777IzypQiONQQgAAFr27ata0cSUajt2rVrV6I1zxAoCAF6QAuCmURSEZCCNWjQIPcL+2nSpIn9/d//vX3yk58MW0dy365dO7viiivsxIkTJgX43HPPzRjvgAEDTLImmo9//OOmvc4STZcuXeySSy6x9u3bu9/HPvYxGz58uJ1//vmJXtM+t27dOu0+amkD4wgBCEDgDAF9xGo/xqA9Cq5qXzAQKBYBekCLRZ50YwSkCMpIMdy/f7+7V4N59OhRO+uss9xz8Ec9ovrpyz0IJz81NTXWqlUr5626ujrwblJk1Rt57NgxO3LkiHtW4/vhhx/a+vXrTT2TQZpBIDXKp06dsnA8gVtwbdOmTVp3+VMar732WhDEevbsaf369XPpylJ7RiqeQDbZSV7Za0Nz3Sca5VW9sIk9sYn+eIYABCAQJqB2Ltwehd30Ia42T+1O0L7KXaNDajflJhO0tbJX26l2V+2UntUmh02ytjrszj0EUECpA14Q2Lx5s/Xo0SOmDPY6Myy/6czQu3oYZdTI6YQZNXRS2NTruHz5ctu+fbvrWdy9e7dzkxKqofI33njDWrZsaUOGDLFDhw45NzXAf/3rX+3CCy90yupll11m69atc72vixYtco3rZz/7WdcIq6GVArlkyZI4PmpUv/CFL7iGV/dBwxznKcWDNuVVoy2jnlD1kEomTQXQFIBXX33V3Usu9bYq7mXLlsViEx8psH/6058yKr+xQNxAAAIQyEBA7Yo+vNVmqu3RwS2BMir7l156ydTGahRHU6Xkr0OHDrZ69WrT9CS1a1Ji1Y7KpGqrM4iBc4kRQAEtsQL3NbtSQK+66ipbtWqVUzbVA/ruu+/GFFD1YqqRCxq4iy66yDV8UkBlDhw44BpJKahf+cpXnAKqYW8pkWo81ZiqkVWvppRQKYBSYMPD51Lw5F+KoBReySPlMHyKVv/+/d28UR3vKiX1uuuuS4lUsigdxSX5Fb/SlunWrZtTJNVrIH9f/epXXbpyk9958+a5nodAPk0T+MQnPmHPPfecs5c/DAQgAIFsCahNHTFiRJz3P//5z7Zjxw5n16JFC/vDH/7gFNCvf/3rrj3SKJE+2DV6IwVURtd33nnH+vTpY/pY/t///V/XKTB06FA37129ounaahcJfyBwhgAKKNXACwIHDx50w8oahlcvpibGh3sX1VO4du1ak+KpIXQphlI6AxMoolVVVc5KX+M7d+50856+9KUvuZ7SDRs2xIbtg3DhqxpZmU9/+tPuqh5OKY1hBVTprlixwrmroQ0aZWeR8EcKqmSV0XSCl19+2cmk51deecXFrcZdfqSkSkmWkVKqYa/AaJhec1aV/7B94M4VAhCAQCYC+/bti7Vdgd9wexK0ZRph0vSmQDGVHymvgQkWi6qdUpzyLyN/6hmVe7q2OoiHKwRQQKkD3hAIhuE15KPez7DRop5ACdOwuRo59XAGRspgopEyqp5ENZ5SJIcNG2bPPvtsore4ZzW6QQMrh8R4NfcyfN53WEmOi+jMQ+Ic0MBd4aUUawW+0luzZo3rSZUSKhPMbQ386/mFF16wz33ucyZGYcU78MMVAhCAQDoCakc0HSmVCaYHBe6p5pmH26dkfjK11UH8XCHAKnjqgDcEpFypF1I9gsHXeCCceh7Vo/n222+77Yy0jVLQYxj4SbxqbtLAgQPt/fffd5Pv1csq5TaVUfpKR1/12jLp4osvjhuiVzgpp0FPqXpI1djmatTDq3lWwfBXEEeggCbGp54FyaTpCeqdTeUvMRzPEIAABApNoC5tdaFlJD0/CNAD6kc5IMUZAhrS0VcFiz8HAABAAElEQVS4FMZEs3HjRjcnUwuApHjKj3o10xktRup1ZjGTehvV66geSfU4SnlNZqSAaq7l1772NTespJ5G2YWN5n5qbqjmmcpIMczVqBdCsn3xi190+VU6stNQezqjeVdSfrV4SZP/MRCAAASyJaARo1GjRsV5V7uzYMGCOLv6PtSlra5vmoRvmASanFmZe7phip691M8880zcPL7sQ+LTNwLBNiC5yBUMmScbLkoWT7AlSbrhdU3YTxyyShZXOrts0kkXHjf/CKiujRw50j/BQhLNnDkz9MQtBPJDoC5tdX4kIdZiEdBHz9VXX50yeXpAU6LBwUcCiXMys5ExW8UziCs8xymwS7zWV/lUfNmkk5guzxCAAAQaAoG6tNUNIV/IGB0B5oBGx5KYIAABCEAAAhCAAASyIIACmgUkvEAAAhCAAAQgAAEIREcABTQ6lsQEAQhAAAIQgAAEIJAFARTQLCDhBQIQgAAEIAABCEAgOgIlsQhJey5q70UMBCAAgXwSCHZcyGca9Y2btrC+BAkPAQhkQ0A7IaQzJaGAasXyOeeck45DRrds9mnMGElEHnT0mZRqH4yOmNRLV9sSFdtoRzGVdaZKXyg5qTPJSVdXV7v664Oyph0SVG+0JVYUJji+MIq48hGHdl7QPrqp9sLNJk0xUxvkiyLrU3vo0/+8VqGrXfbh4Aq1y6o3OrzDB0OdSV4KUXJRu6q2Pp2JptVNl4IHbnrR6USc+hhtHJ5p4/P6xJ9LWG1cXllZmUuQvPnViUFqVCoqKvKWRrYRa99OHb+ZaUP3bOOrrz/qTHKCOkSgXbt2XnxEqcFVvdEZ1lGY559/Popo8hpHhw4d6tUeitn+/fvrdApYPjLmU3vo0/98cPJbphPj8lEmiXHqkBHVm44dOyY6FeWZOpMce5Rc1K4uWbIkeUJ/s2UOaFo8OEIAAhCAAAQgAAEIRE0ABTRqosQHAQhAIAsCGq5dvHhxnE/1Ei1btsyWL19e66StdevW2bPPPlvrVLd0YeIi5wECEICARwRQQD0qDESBAARKh8D9999vv/71r2MZPnLkiN1yyy1OKX388cdtwoQJbn6qPEybNs2mTp1qK1eutFtvvdU01CuTLozzwB8IQAACnhIoiTmgnrJHLAhAoEQJqCdz8+bNcbmfPXu2DR482MaPH+/sb7vtNluxYoV17drVli5danPmzHELiGbNmmU6z33ixImWKszll18eFzcPEIAABHwjUBIKqFbfaXJtfYxWj9Y3jvqkHw6baWVZ2G++77UKXnx9ONdck541HKmrD4Y6k7wUVEYaflbdKbZRGam+RHVudTb/B1qE9dvf/ta+9a1v2YMPPhhDsH79ehs6dGjsecCAAbZ27Vq3krRv375O+ZSj7BcuXOj8pQoTVkB37doVW40a7BShRUR1NVrRrDKsTxx1TTtZOPUCK18+GJW/T1zUNvuwCl71xTc21Jna/zFR/i+pXc30Li4JBVSr4Ou7ajzK1WG1iz13m/rmJ/cUk4dQo8Iq+ORsqDPJuUjx1E4FPmwlFnywRLUKPtN2TmqQf/zjH7tezsT8S1Fs27ZtDJrut23b5jiF/99lr90nZFKFiUVy5karoBNXQic+h/1nuldYKTX1iSNTGrm4+ySL5PaJiy9sJIcvsqiMfJLFtzpTyPpbEgqoCjhX03X+pbWD/CXeatdXVsdb8AQBCEAgDYHf/e53duGFF9onP/lJe+utt+J86kNZPVaB0cedFONU9vKXzi2I5+yzzw5uXS/U1q1b4xTdmGOam65P/yGN6/857RpxTUY/+fCgnqyw4p6PNLKNU72fvsgimVu3bu2FQiylRh97vrChziSv0VFy0cd2JmUWBTR5OWALAQhAIHICv//972337t321FNPuWFjvZS/+tWv2rx586xTp062b9++WJq6P/fcc93ozapVq+Lsu3Xr5p5ThYl55gYCEICApwRYBe9pwSAWBCDQ+Aho8ZAWIOn3wAMPWO/evZ3yqZxeeeWVtmjRIjc3ds+ePW4rpv79+7tN41evXm3quVSv6IIFC2zQoEEOTqowjY8cOYIABBobAXpAG1uJkh8IQKBBEhgyZIjbA/TGG290Q1cjR450CqoyM3bsWBszZozpFKOePXvaqFGjXB7ThWmQEBAaAhAoGQIooCVT1GQUAhDwicBFF11kjz32WEwkLWCaPHmy2yFAcz/DC5pGjBhhw4YNc/PoNK8vMOnCBH64QgACEPCRAAqoj6WCTBCAQMkS0A4ByUyLFi1Mv2QmVZhkfrGDAAQg4AMB5oD6UArIAAEIQAACEIAABEqIAApoCRU2WYUABCAAAQhAAAI+EEAB9aEUkAECEIAABCAAAQiUEAEU0BIqbLIKAQhAAAIQgAAEfCCAAupDKSADBCAAAQhAAAIQKCECKKAlVNhkFQIQgAAEIAABCPhAoOAK6OLFi90+d+HMr1u3zp0MotM/wkbPzzzzjMk90aQKk+iPZwhAAAIQgAAEIAABvwgUVAFdsmSJTZo0Ke6842nTptnUqVNt5cqVduutt9qWLVscIT2PHj3a3nnnHZswYYLNnTs3Ri5VmJgHbiAAAQhAAAIQgAAEvCVQsI3o1Zv56KOPWrt27WIwNm3aZEuXLrU5c+a4o+dmzZplOit54sSJNn36dJsyZYr169fPbrjhBncM3fDhw23Hjh0pw8Qi5gYCEIAABCAAAQhAwFsCBekBPX36tN177732rW99y8rLy2MwNmzYYH379nXKpywHDBhga9eutRMnTti2bducm+y7dOlirVq1su3bt1uqMPKHgQAEIAABCEAAAhDwn0BBekDVw3nuuefaZZddFkdk586dVllZGbNr27at7d271z744AOrqKiwJk2axNzkb9++fZYqTMzjmRspqu+9917M6ujRo06hjVlEdCMluRjm+PHjtebRFkMOpVlTU+Nk+fDDD4slQixdfeicPHnSDhw4ELMr5k2+6l1d8uRTnREX/Zo1a1aXrEQa5tSpU6Z6E5Usx44di1Q+IoMABCDQWAnkXQHduHGjLVq0yP77v/+7FkM1+lIYAqOez5YtW7qXQdhe7nJT72mqMEEcunbr1s31mgZ2L774onXv3j14zO7658zeco4zc5RZ+Th48KBJWffB6KOgrKzMfTAUWx4pE9XV1da6detii+LS1wdKsepIIgCf6ow+MPVBqXpTbCOFUfVG7U4URnPWMRCAAAQgkJlA3hXQP/3pT7Z582b78pe/7KQ5cuSIm8/54x//2Dp37myrVq2KSSllRspjx44draqqyvRyCF5SctPLfNeuXUnDxCI5c9O0adPYsL7s1ZMqu6hNPuLMRsZ85SebtBP9BLIUi0UqeRLti/UMl9rkfaozQfkE19rSYgMBCEAAAvkgkHcFdMyYMU7hDIS//vrr7Sc/+Yn17NnT1CszY8YM27p1q1M8FyxYYIMGDbLmzZvb4MGDbf78+Sb/Wj3fvn179xs4cGDSMEH8XCEAAQhAIDUBTcfIxzSVfMSZOhcfuWjUwxejkbpicUhkoM4e9e7rg6/YRlNufGJDnUleI6LkorqnXzqTdwU0XeIaRh47dqxTUDt06OCU0lGjRrkg48aNi22/pN4Jbd8kky6M88AfCEAAAhBISaBFixZxc+9TeszRITyfP8eg9fZezLTDwkv59EUWKZ6ajuRD776mzmlE0xc2KjNfZPGpzkTJRcpnprpXcAX0ySefDP+/2ogRI2zYsGGucobn7qmHdPbs2bZ///64rZsUOFWYuIh5gAAEIAABCEAAAhDwkkDBFdBkFPRFrl8yE943NOyeLkzYH/cQgAAEIAABCEAAAn4RiH5ljl/5QxoIQAACEIAABCAAAc8IoIB6ViCIAwEIQAACEIAABBo7ARTQxl7C5A8CEIAABCAAAQh4RgAF1LMCQRwIQAACEIAABCDQ2AmggDb2EiZ/EIAABCAAAQhAwDMCKKCeFQjiQAACEIAABCAAgcZOAAW0sZcw+YMABCAAAQhAAAKeEUAB9axAEAcCEIAABCAAAQg0dgIooI29hMkfBCAAAQhAAAIQ8IwACqhnBYI4EIAABCAAAQhAoLETQAFt7CVM/iAAAQhAAAIQgIBnBLw4Cz7fTE6fPm3Hjx+PPJl8xJmNkCdPnsxLfrJJO9GPZDlx4oQX8pw6dcobWcQpX/UusQyyefaxzjRtWvzvX9Vd1Zuo/pdV5hgIQAACEMhMoGQU0Jqamsw0cvSRjzizEUEvzWKlnShfoID6IE+ggPogizhJHl9k8anORKnwJdbHXJ+leEppjKqclDcMBCAAAQhkJlASCqh6WioqKjLTyNFHPuLMRgQpE8VKO1G+o0ePWnl5uRfyBC9/X9g0a9bMCy4qM5/qzOHDh61ly5ZWVlaWWJ0K/nzs2DH3oSB5ojAq82zMmjVrbNeuXfapT33K2rVrFwsieV5//XVr0qSJDRw40Fq0aBFzW7dunW3evNkGDBhgnTp1itmnCxPzxA0EIAABzwgUfwzMMyCIAwEIQCCfBP7jP/7Dfve739natWvttttus23btrnkjhw5YrfccostXrzYHn/8cZswYYLrnZXjtGnTbOrUqbZy5Uq79dZbbcuWLRnDOA/8gQAEIOApgZLoAfWUPWJBAAIlRmDjxo1uvulPfvITl/Pq6mp77rnnnOI5e/ZsGzx4sI0fP965STldsWKFde3a1ZYuXWpz5swxjebMmjXLZs6caRMnTrRUYS6//PISI0t2IQCBhkYABbShlRjyQgACDZZA7969bcaMGU7+/fv325tvvmn//M//7J7Xr19vQ4cOjeVNQ+3qJZWS2rdvX6d8ylH2CxcuTBsmrIAqfLDISnO2NVVFw/ZRm3zEmY2Mylux0k6UL19sE9PJ5jng4sNiP8miuudLOQVssuGYbz8+1pko8qx8ZVqUiQIaBWnigAAEIJADgWeffdbuu+8+u/DCC+2KK65wITUntG3btrFYdK/hec2VraysjLPfu3dv2jAxz2dudu7caQcOHIhZacGVlN+oTT7izEZGKTVSbnwwmmtdLA6J+Vc5S9HSfOJim0ABzaSQFEpO6kxy0lFykQKqXzqDApqODm4QgAAE8kBAPZ2f+cxn7IEHHrApU6bYPffcY1rAFFakpMxocVQqe4mVzi0Q+7zzzgtu3WK0l19+2bp06RKzi+omH3FmI5uU67CCnk2YfPnRC7xYHBLzdPDgQWvdunWs5zzRvZDPWngoNh07dixksinTos4kRxMlFymfWjiZzrAIKR0d3CAAAQhESOD999+PNcqtWrWya6+91q16VxJa2b5v375Yarrv3r27de7cuZZ9t27dnL9UYWKRcAMBCEDAUwIooJ4WDGJBAAKNj4DmY/7gBz8wbV8moxXv559/vru/8sorbdGiRc5tz549tnz5cuvfv7/bjmn16tW2detW14O5YMECGzRoUNowzpE/EIAABDwmwBC8x4WDaBCAQOMioEVIX//6123s2LFu+FzPUkhlhgwZYsuWLbMbb7zRDZuOHDnS5C4j/2PGjLEOHTpYz549bdSoUc4+XRjngT8QgAAEPCWAAuppwSAWBCDQOAn80z/9k1Mg1QuqYfjANG/e3CZPnmyHDh1ycz/1HJgRI0bYsGHD3Dw6zesLTLowgR+uEIAABHwk8FEL56N0yAQBCECgERLQ1jhh5TOcxTZt2oQfY/c6FSl8MlLM4cxNqjBhP9xDAAIQ8IkAc0B9Kg1kgQAEIAABCEAAAiVAAAW0BAqZLEIAAhCAAAQgAAGfCBRMAf3ggw/sD3/4g+koukSjvaK0MbNWfoaNnp955pnYtiVht1Rhwn64hwAEIAABCEAAAhDwj0BBFNCnn37avv/977tTPf7zP/8zdoyccEybNs2mTp1qK1eutFtvvdW2bNniKOl59OjR9s4779iECRNs7ty5MXqpwsQ8cAMBCEAAAhCAAAQg4C2BvC9C0tFb6t28++67rVevXtavXz978MEHbfjw4bZp0yZbunSpzZkzx207MmvWLJs5c6ZNnDjRpk+f7k4Ikf8bbrjBbUGiMDt27EgZxlvKCAYBCEAAAhCAAAQgECOQ9x5QnUOr4+akfOo8WO1zp3uZDRs2WN++fWNHhQ0YMMDWrl3rNlvWGchyk9HRZloxun379pRhnEf+QAACEIAABCAAAQh4TyDvPaABAZ1Le9NNN9mRI0fs5z//ubPeuXNn3Bm+bdu2tb1795rmi1ZUVJiU18DorF8dTZcqTOBPVymv7777bsxKaQZD+zHLCG7yEWc2YumMaJ3Z6oPRR4W2lNGZ1D4YnaX94Ycf+iCKO9GmWHUkEYBPdUZnQut/UvWm2EbnFctEJUtwwlGx80X6EIAABHwnUDAFVMrl/PnzbcmSJXbbbbfZvHnznNIihSEwekm2bNmylr3c5VZeXl7LLQgTxKHrOeec436B3fPPP289evQIHrO7/iWzt5zjzBxlVj6kfEoh98Hog0Hlog+GYhspE1VVVd7siSjls1h1JLEsfKozOg+9Xbt2VlZWlihmwZ+lDKveqN2Jwqxfvz6KaIgDAhCAQKMnkPcuiJqaGnvllVccSPVoXnXVVe7ls2bNGuvcubPr1Qwoq4ezW7du1rFjR6dI6OUQGLl17949ZZjAH1cIQAACEIAABCAAAb8J5F0B1ckdDz/8sL366quOhLZPUq+ZzjMeOHCgrV692rZu3ep6OBcsWGCDBg0yHS83ePBg12OqQOo1bd++vfulCuM3ZqSDAAQgAAEIQAACEAgI5H0IXr2e48ePd0roI4884obdtCJevZ8yY8eOdSvcO3To4JTSUaNGOftx48bFtl/S/KxJkyY5ew3lpwrjPPAHAhCAAAQgAAEIQMBrAnlXQJX7T37yk04BPXz4sLVu3ToOyIgRI2zYsGGm4fawm3pIZ8+ebfv373dD9uFAqcKE/XAPAQhAAAIQgAAEIOAngYIooEHWwwpmYKerhun1S2a0WCGZSRcmmX/sIAABCEAAAhCAAAT8IFBQBdSPLCMFBCAAgdIloK3T8rGNWz7izKaUqqurs/FWED8+bXemrc60w0N4O8OCQEiSiLYn84kNdSZJIZ2xipKL6p5+6QwKaDo6uEEAAhBoZAQ0epSPbdzyEWe26IuZdlhGn7Y7k+KpUceo9rgN5zPXe+0TrWl2vpST5PdFFp/qTJRcpHxmqnt5XwWfa0XFPwQgAAEIQAACEIBA4yaAAtq4y5fcQQACEIAABCAAAe8IoIB6VyQIBAEIQAACEIAABBo3gawV0C984QumbZQSza9//WsL9u5MdOMZAhCAAAQgAAEIQAACiQTSLkJasWKF/fGPf3RhXnrpJbv33nvdud9BJDrH/amnnrI+ffoEVlwhAAEIQAACEIAABCCQlkBaBfT888+3733ve271mrbuWLhwoWk1W2C0mrJXr1525513BlZcIQABCEAAAhCAAAQgkJZAWgW0Y8eOtmzZMhfBV77yFfvtb38bd1pR2phxhAAEIAABCEAAAhCAQBICaRXQsP/58+e7ntAtW7a4a9hNe41169YtbMU9BCAAAQhAAAIQgAAEkhLIWgH9n//5HxszZow7mz0xpuuvv96eeOKJRGueIQABCEAAAhCAAAQgUItA1grouHHj7Gtf+5r967/+q3Xo0CEuolRnvMd5KuKDduQ/ePBg5BLkI85shNQRaz4cryZZdcSaFqPpV2yjctZpG6dPny62KC59HT1XrDqSCMCnOqMy0o4auhbbaG676ouuURgf/g+iyAdxQAACEMg3gawUUL1EP/jgA7vvvvvs7LPPzrdMkcev46DyoSTnI85sMi9Fq1hpJ8pXU1NjZWVlVlFRkehU8GdxCY6fK3jiSRLcv3+/N+XkU53RecOtWrVy9SYJtoJaqf6KTXl5eSTphhdpRhIhkUAAAhBopASyUkDbtm1rvXv3ttdff92+9KUvNUgUmc4krUum8hFnNnJIySpW2onyBbL4Io/k8EUWsfJFlqCcEsuvGM+BLD6wkSyBPMVgQZoQgAAESpVAVgqo4EyZMsW++93v2rZt25wy2rz5R0HVK3rJJZeUKkPyDQEIQAACEIAABCCQA4GPtMgMgTQH9MCBA3bbbbfV8skipFpIsIAABCAAAQhAAAIQSEEgawX0/fffT7m4g3lPKehiDQEIQAACEIAABCBQi0DWCui+fftSKqAtW7a09u3b14ocCwhAAAIQqE1g/fr1tnXrVrv88stN7WdgtDOA5tprXurAgQNNp80FZt26dbZ582YbMGCAderUKbB2uwmkChPzxA0EIAABzwhkrYBedNFFbgg+mfwMwSejgh0EIACB2gR0vLFGjc477zx7+OGH7fbbb7dBgwaZtsr65je/6ebT79ixw5588km7//77nTI6bdo0W7NmjfXp08ceeughe/DBB61Hjx5pw9ROGRsIQAAC/hDIWgF96aWX4vZ6PHTokP35z392jaG2Z8JAAAIQgEB6AqtXr7bdu3fbb37zG+fxggsusFmzZjkFdPbs2TZ48GAbP368c9N8+xUrVljXrl1t6dKlNmfOHLergvzPnDnTJk6caKnCqGcVAwEIQMBnAlkroJdeemmtfHzmM58x7en3X//1X/bzn/+8ljsWEIAABCDwEYGLL77YHnnkkZiFFnbqMAcZDcsPHTo05qah9rVr17o2tm/fvrEtvWS/cOHCtGFQQGMYuYEABDwlkLUCmkp+nQH/1FNPpXLGHgIQgAAE/kZAe58Gcz51uId6Qr///e871127dpn2XA6M7rXtnQ56qKysDKydn71796YNE/N85ubNN9+0wL/S1zzTLVu2hL1Ecp+POLMRTCeOSZH3wehjolgcEvMvLjoMwwejE8J04ENVVZUP4hh1JnkxRMlFJ8wpvnQmawX01VdfjYtMEavB/PGPf2xXX311ujRwgwAEIACBEIGNGzfaHXfcYaNHj3YLkeSkeaHhozzVxkpZTWWfLkwoKevXr1/sUXG+/PLLbv5ozDKbm1VrM/rSnNRiGCmfYQW9GDIEaUr5LBaHQIbgqhMMdWKeDwc+BEfvduzYMRCvqFfqTHL8UXLRB4fauXQmawVUQ0PJvjI1DD958uR0aeAGAQhAAAJ/I/DWW2+5+Zs62OOqq66KcdHKdu02Ehjdn3vuuU65WrVqVWDt/GjkSSZVmJhnbiAAAQh4SqBptnLpy07d+eHf8ePH3eT4Ll26ZBsN/iAAAQiULIE9e/bYhAkT7Ic//GGc8ikgV155pS1atMjNCZW/5cuXW//+/d12TFq8pG2b1IO5YMECt2gpXZiSBUzGIQCBBkMg6x5QzUeS8vnb3/7W3nnnHbcyU43jZz/7WTvrrLMaTIYRFAIQgECxCDzxxBOuHf3Od74TE6FDhw5uHv2QIUNs2bJlduONN7ph05EjR7pjj+Vx7NixNmbMGJPfnj172qhRo1z4dGFiCXADAQhAwEMCWSugGgLSMLxORNKKTG0lsnPnTrvmmmts7ty5Vl5enjZ7H374ob3xxhtuj7tg+CgIkGqDZfUCKEyvXr1M25WETaowYT/cQwACEPCJgI401i+Zad68uZvOpC3uNPdTz4EZMWKEDRs2zC0g0ry+wKQLE/jhCgEIQMBHAlkPwesL/NOf/rQbBtKqyu3bt7t9QN9++22bMWNG2rzNmzfPvv3tb7sJqXfffbdNnz495l8bLE+dOtVWrlxpt956a2wFoZ41QV+9rRqykpIbmFRhAneuEIAABBoqgTZt2sQpn0E+dCpSWPkM7HVNFSbsh3sIQAACPhH46BM7jVTa61NHvakX9JxzznE+dVSchuB1qsfTTz/tVnQmi0KrOrXViJTM3r1720033WQ33HCD3XzzzW5RU6oNlqWkTpkyxa3glH8NPw0fPtx0QkiqMMnSxw4CEIAABCAAAQhAwC8CWSmg2sZBezpJEU002tdLE+NTGW0h8thjj1lFRYXzon3StCWDFNMNGza44fxgm4hgg2XFp/3vNNQvo0VOrVq1cr2uWtafalNm5/nMH4WvqakJHt3+Y1owFbXJR5zZyCh2xUo7UT7JIt4+yKM66hMbyeMDF5WZT1yCOhP83yfWqUI+q+5qu5CoyklljoEABCAAgcwEslJANb9Te31q37p7773XLrvsMjcXafHixfbAAw+44fV0SQXKpxp6Dddr3qi2D9Ec0vD+bVropA2TtUGzwqiXNTDyp21JUoUJ/OmquaObNm2KWenlIruoTT7izEZGKdfaTNoHow8K/ZJ9nBRavkDh05naPhiVU7HqSGL+faszagv0cVpsI2VY9SY837I+MoU/fOsTD2EhAAEINHYCWSmggvDwww/btdde67b/6Ny5s+vF1Iv+y1/+st1+++0ZOUlhuueee1xjf9dddzn/qTZYTrSXZ/VUSBFOdJN9cLJIIITOTtYvMM8//7wlLnwK3OpzzUec2cgT5Wax2aSXzo8+GFQuwUdGOr/5dpNSox55zYfzwWjrsmLVkcT8+1RntJCxXbt27oSfRDkL/ax2SfUmsQ2pqxza4xMDAQhAAAKZCWStgPbp08etSP/jH/9oWoEupePCCy+0z3/+8xlTUe+Yek8/9rGPuWPngp4PKbLJNljWaQlSJPRy0DF0Mur97N69uzt9KVmYjELgAQIQgAAEIAABCEDACwJZr4LX0Pe//Mu/uCFF9Xjecsstbi86rUhXL2Q6o02XtY3SD37wg7hht4EDB1qyDZY1HDZ48GCbP3++i3bJkiXWvn1790sVJl36uEEAAhCAAAQgAAEI+EMg6x5QHRunobOJEyc66TVkpZXqd955p9sY+brrrkuaKw1JvfLKK+6nTZgD89Of/tQtJkq1wbL2ygu2X9JihUmTJrmgmieaKkwQN1cIQAACECgsga5P/yFtgrtGXJPWHUcIQKC0CGSlgGpi/TPPPGNr1qxxw+BCJKVQJ3Zo02SdjpRKAb3ooovctkmpsKbaYFmnfcyePdudGqL5YmGTKkzYD/cQgAAEIAABCEAAAn4SyEoB1Wp0rSTX5vOahxk2Bw8edPMzw3a53muDZf2SmUTlM/CTLkzgJ9/XrvMvTZvErq+sTuuOIwQgAAEIQAACEChFAlnNAZWy97nPfc7N4dy6dWuMkzan1xxQbauEgQAEIAABCEAAAhCAQDYEslJAFdGvf/1rt99jjx493N6dmgOqBUHaH1SnIWEgAAEIQAACEIAABCCQDYGshuAVUYcOHdxcTm3B9Je//MXNAf3EJz5hF198cTbp4AcCEIAABCAAAQhAAAKOQNYKqHxr4ZEWFemHgQAEIAABCEAAAhCAQF0I5KSA1iUBwkAAAhCAgD8EdPJTMY7yzVeaWiCbr7hzLbVisU0mp/bnFhd1HBXbqIx07K0v5USdSV4jouSi/wUdc5zOoICmo4MbBCAAgUZGQC+FTC+GfGQ5n2nmM+5cWfgii+QIfrnmIR/+fZJF+fOlnBqrLNnwRQHNx38acUIAAhDwlICOQtZRyoU2+UpTvWr5ijtXRupt9EUW7d8tWXzoAVVvrHrEfGFDnUles6PkovLWFp7pTPH75tNJhxsEIAABCEAAAhCAQKMjgALa6IqUDEEAAhCAAAQgAAG/CaCA+l0+SAcBCEAAAhCAAAQaHQEU0EZXpGQIAhCAAAQgAAEI+E2gJBYhafuHAwcOFLwk8pVmdXV1wfOSKsGjR4+67TU0ybzYJtgCRVcfjJjkqw7kmj+f6owmuh86dMidrJZrPqL2HyyO0IKNKIwP/wdR5IM4IAABCOSbQEkooFr1WVlZmW+WteLPZ5r5jLtWRtJY6IWrlY0VFRVpfBXGSYpnVVWVtWnTpjAJZkhFyqcv5SRRfZFFHy0qo7KysgwE8+8sZVj1RkcLR2GaNy+JJjUKVMQBAQiUOAGG4Eu8ApB9CEAAAhCAAAQgUGgCKKCFJk56EIAABCAAAQhAoMQJoICWeAUg+xCAAAQgAAEIQKDQBFBAC02c9CAAAQhAAAIQgECJE0ABLfEKQPYhAAEIQAACEIBAoQmggBaaOOlBAAIQgAAEIACBEieAAlriFYDsQwACEIAABCAAgUITQAEtNHHSgwAEIAABCEAAAiVOgF2TS7wCkH0IQKA4BN5++213iEOvXr1iAmhj/Ndff92aNGliAwcOtBYtWsTc1q1bZ5s3b7YBAwZYp06dYvbpwsQ8cQMBCEDAMwL0gHpWIIgDAQg0fgIbN26022+/3d56661YZo8cOWK33HKLLV682B5//HGbMGGCnT592rlPmzbNpk6daitXrrRbb73VtmzZ4uzThYlFzA0EIAABDwnQA+phoSASBCDQeAnMmzfPfvWrX9U6GnX27Nk2ePBgGz9+vMv8bbfdZitWrLCuXbva0qVLbc6cOda0aVObNWuWzZw50yZOnGipwlx++eWNFyA5gwAEGgUBekAbRTGSCQhAoKEQ0Lnzv/zlL61Pnz5uqD2Qe/369W54PXjWUPvatWttw4YN1rdvX6d8yi2w132qMHLDQAACEPCZAD2gPpcOskEAAo2OwNChQ2N5CobYZbFr1y5r27ZtzE3327Zts7KysrjeUtnv3bvX+UsVJhbJmZtVq1bF/GtuqeaMBkP4YX/5vs9XmidOnLADBw7kW/ys4j969GhR2CYTTlz279+fzKngdidPnrRTp05ZVVVVwdNOliB1JhkVsyi5qG1TfOlMQRXQw4cP25tvvmlXXHFFnEypJtfv2bPH3njjDdMk/QsuuCCrMHGeeIAABCDQQAg0a9bM9KIOjBpv9Zamspe/dG5BPOo9DYzifPnll61Hjx6BVXbXVWuz85fGV85ppokr7CTls7KyMmxVtHsp2fnKZ66ZOnjwoLVu3TrWc55r+Cj9692vD5+OHTtGGW2d46LOJEcXJRd9cGiuezpTsCF4fRn+6Ec/Ms1/CptUk+s12X706NH2zjvvuMn4c+fOjQVLFSbmgRsIQAACDYyAVrbv27cvJrXuu3fvbp07d65l361bN+cvVZhYJNxAAAIQ8JRAQRRQzWHS6s5Dhw7FYdi0aZObXP/II4/YHXfcYTfeeKObXC9P06dPtylTpti///u/m9wfffRRq6mpsXRh4iLnAQIQgEADInDllVfaokWLTB/rGv1Zvny59e/f323HtHr1atu6dasb0lqwYIENGjTI5SxVmAaUbUSFAARKlEBBhuCrq6vtrrvucvOQfv/738dQJ5tcv3DhQtfIau5TMHTUpUsXa9WqlW3fvt116SZOyFeYsJGiG577omEnDUcU2uQrTW29orlcPhi9LDVsGB46LJZcmnOiYZ7wvLpiyaJ0i1XvkuXZpzqjMgqG5JLJWkg7lZGGio4fPx5JsvX5PxgyZIgtW7bMfYhrtfvIkSOtd+/eTq6xY8famDFjrEOHDtazZ08bNWqUs08XJpIMEQkEIACBPBEoiAJ66aWXOvFfeOGFuGzs3Lkzbu5OMLn+gw8+sIqKijglS3N8NCSVKkw4Yr0E9JILjBSS+rwYgnhyveYrTb0w8xV3rnkUW1/k8UkWcSxWvUtWhr6UUcDFF3n0fxRlOSmubM3dd98d57V58+Y2efJkN1KkuZ96DsyIESNs2LBhrl3TvL7ApAsT+OEKAQhAwEcCH7VwRZAu1QT6RHuJpp6K8vLyrCbdt2vXzvQLjCaGt2/fPngs2DVfaap3xJdJ91IkVC76YCi2kSxaZdmmTZtii+LSV098vupArhn0qc5oKo0+NrW6u9hGH6qqN1L4ojBhpbGu8aWqvzoVKXwyUjj+VGHCfriHAAQg4BOBgswBTZXhVJPrtVJOikS4FzObCfmp0sEeAhCAAAQgAAEIQMAfAkVVQHXWcbLJ9epF0Ikg8+fPd6SWLFniepLUm5QqjD9IkQQCEIAABCAAAQhAIB2Bog7Baxgu1eT6cePGxbZf0vDhpEmTXD7ShUmXUdwgAAEIQAACEIAABPwgUFAF9Oqrrzb9wibV5Hqt9NQ5x1rNHp7PqbCpwoTj5R4CEIAABCAAAQhAwE8CBVVAUyFIN7k+UfkM4kgXJvDDFQIQgAAEIAABCEDAPwJFnQPqHw4kggAEIAABCEAAAhDINwEU0HwTJn4IQAACEIAABCAAgTgCKKBxOHiAAAQgAAEIQAACEMg3ARTQfBMmfghAAAIQgAAEIACBOAIooHE4/v/2zgTKqurK+6cooCjmQcKggkQNDgkGOgxpm0g6CCYQjWk7C+lMDsG1TH+JphONZsXEYIbVfhGjbXcn30qnk2iikW4HRDRRHIgoimMjiIKCgAwCFnNRFNRX/5O+j/tuvXvfUPfdd967v8Mq3h3OsPfvnLffvme6nEAAAhCAAAQgAAEIlJsADmi5CZM/BCAAAQhAAAIQgEAWARzQLBycQAACEIAABCAAAQiUm4AT+4CWW0nyhwAEIACByhIY+sBDeQXYMvOcvHGIAAEI1AYBHNAy1uPQ+z+YN/ct567IG4cIEIAABCAAAQhAoJYI4IDWUm2iCwQgAIE8BA4dOmR27dqVJ1Zlbpci1/79+ysjbI5SW1tbnWF74MABc+TIEVNXV5dD0mQvNTc3G5fY0GZy13+cXNT29BcVcECj6HAPAhCAQI0R0GuM+/Xr56RWpcpVarq4IciBdkUWOZ69e/c2XbpUfqlHfX29OXjwoDNsVO+u1JNLbSZOLnI+87W9VDighw8fduapNGjwqv2JX0+24qun20oHNXgZuXxPXUnJyRN/btKqoz179hi1nUoH1ZHaS0tLSyyiuPA9iEURMoEABCBQZgKpcED19OXK006wPkuVq9R0wfI7e64f3B49ephevXp1NqtOp5cjsW/fPtOnT59O5xVHBrX6ZNtZNnI8VUcNDQ2dzarT6b0HlsbGxk7npQy6dk2FSY2FFZlAAALpJlD5vvl080d7CEAAAhCAAAQgkDoCOKCpq3IUhgAEIAABCEAAApUlgANaWf6UDgEIQAACEIAABFJHAAc0dVWOwhCAAAQgAAEIQKCyBHBAK8uf0iEAAQhAAAIQgEDqCOCApq7KURgCEIAABCAAAQhUlgB7hlSWv+F1nRWuAIqHAAQgAAEIQCBxAjigiSOnQAhAAAIQyEVg6AMP5bqcdW3LzHOyzjmBAASqkwBD8NVZb0gNAQhAAAIQgAAEqpYADmjVVh2CQwACEIAABCAAgeokgANanfWG1BCAAAQgAAEIQKBqCTAHtAqqjoVKVVBJiAgBCCRCIN88UeaIJlINFAKBThPAAe00QjKAAAQgAAFXCORzUCUnTqortYUcaSZQtQ7o6tWrzfr16824cePMMccck+Y6tLrn6yXdcu6K1DMCAARqkcDBgwfN8uXLTV1dnRk/frzp1q1bLaoZq044qbHiJDMIlESgKh3QefPmmVdffdWcfPLJ5rbbbjO33nqrGTFiREkASAQBCECgWgkcOHDAXHzxxeb0008377zzjrn77rvNTTfdZJ3RatWpWuQOdWJfWZlRgZ7WDAoOINCBQNU5oOvWrTNLliwx8+fPN126dDF33nmnueOOO8w111zTQTkuHCWQr4f0aMzyH9EbW37GlJAOAnfddZeZOHGiueKKK6zCl112mVm2bJmZNGlSOgCUUctQB7OIMuPIAye2COBErSoCVeeAvvnmm2bMmDHW+RRpDcEvXLgwC/q2bdvMpk2bMtc0RLV169bMOQeVJeCSM1x2Ei8VVsKtH/hh3oj/5/Xv5I3z/075vznjtLa2mq5bu5qvvPbNnPeLvXj/Gb/Om2TXod054xxoPmC672ow9e0PkPlCQ5eGfFFMj/roOOsPbAzN48iRI6at/d/HB50ZGqeYGy0tLcVE73TcNWvWmGnTpmXykT1cuXJllgO6du1as3v30bpobm7GHmaIuX8QhxPrvpaVkfCXo0/KW3BjfX3eOAcOH46Mc8nqNZH3TXuveVyyRBdkTI8udaFRDh06ZLq99545sbExNE6hN2RbD+fhUnUO6ObNm02/fv0yDPr27Wt27NiROdeB7nfv3j1zbfv27VlpMjciDtZNW551d8uWLWbo0KFZ1yp1snfvXtO7d+9KFZ9V7q5duyzrxhgabFbGJZy0tbUZDUn27NmzhNTxJ4m7zXz6hOklC+m1mXUjstt1yRl2IqG+r3369Mn6jnYiu7xJx5jTQ+PI4MpQNjREO7GhGQRudO2arElVG5MN9IKON27MdriHDBliBg0aZKNIV31n/TbUSxv1uW7qlMxtOdlqTwMHDsxcq+SB17YrKYNXdtzfeS/fUj737dtnbaHmBlc6yC6r3RTb7sold9JtZt3xx4Wq4lKbiZOLbI1GqaNCstYySpIC79W3P434vWr17ASdH/2Y+H9QlKZHjx4FlpA7mkB2No/cORd/VT26rsgiIydn3wV51ODVHlyQRbVKm8ndtuWkBb+juWOW/6p+nNVu4moz+Qxu3BoVYg/9D6v6fnTWHoqZHIq4mHWWiUv20KXvvBw+fc+SbpO56lPtLs7vWa4yirlGm8lNK04uqu98Dz/R7mluGSt6dfDgwWbnzp0ZGXQ8bNiwzDkHEIAABNJCQDuABO3h8OHD06I+ekIAAlVMoOocUG0zsmLFCrNhwwbb27VgwQIzYcKEKq4CRIcABCBQGoHJkyebRYsWGc3r1FSjpUuXmrFjx5aWGakgAAEIJEig6obgNcdpzpw55tJLL7VzkEaOHGlmz56dIDKKggAEIOAGgalTp5qnnnrKXHjhhXaoddasWWbUqFFuCIcUEIAABCIIVJ0DKl1mzpxppk+fbjRfwT+/KUJPbkEAAhCoOQKaTzt37lyzZ88eOxc+6UVQNQcUhSAAgcQIVKUDKjp62wdv/EisnVAQBCDgMAHtKkCAAAQgUE0EqtYBLQayVuA99thjxSTpEFerPrWfngtB+rjS06FtbLTKUitrXQgusaHN5G4RWp2r9uvC6lyt1FSIS5ampqbcSjt0Vfskd8Yeipm+Z/6t7iqpHt/53PRd4qKda9RuXOk0colNLf9O5FsFX9e+d2Jb7ubLVQhAAAIQgAAEIAABCMRPoOpWwcePgBwhAAEIQAACEIAABJIkgAOaJG3KggAEIAABCEAAAhAwOKA0AghAAAIQgAAEIACBRAnggCaKm8IgAAEIQAACEIAABHBAaQMQgAAEIAABCEAAAokSwAFNFDeFQQACEIAABCAAAQikYh/QF1980ezevZvahgAEIFBWAtoP92/+5m/KWkZnM3/iiSc6mwXpIQABCOQlMGjQIPPBD34wNF4qHFBtvLx9+/ZQCNyAAAQgEAcBV17IEKXLxo0bo25zDwIQgEAsBPJtM88QfCyYyQQCEIAABCAAAQhAoFACOKCFkiIeBCAAAQhAAAIQgEAsBHBAY8FIJhCAAAQgAAEIQAAChRLAAS2UFPEgAAEIQAACEIAABGIhgAMaC0YygQAEIAABCEAAAhAolAAOaKGkiFcSgWOPPdYMHDgwK21DQ4MZMWJE1rVCT7xVxieccILp2tX9TRy0DcXxxx+fpV6PHj3Mcccdl3XNOznmmGNM//79vVM+IQABCHQgILt60kkn2b8TTzzR2hNX7WG12OoOkLlQdgI4oGVHnO4CTj/9dDNlyhTTvXv3DIjevXubM844I3Ne6MFf/dVfmeHDh9voY8eONXLkXA8TJkww48ePNz179syI2qdPn9C90UaOHJnRMZOAAwhAAAI+AqeddpqRrRgwYIDRQ+4HPvAB85nPfMbItroWJGe3bt1cEwt5HCCAA+pAJdS6CEeOHDEf+chHItVUr6jfSVNkOa11dXXWqKrns1+/ftaQdelytNn26tUrpyMq51Q9if5eAR0rrT779u1r8/YL5cmgMoMGU4bdL5/iKB/JqHS5gn4cVN6bb75pTj755A5RdE9y+PXxIinPXD8muh6UPVi+p6eXF58QgEDtEVizZo157rnnzLPPPmsWL15stm7dantEPU1z2QrPNsi2yIYpyIYFbaW/w0BxgjYml31VPNljPWB7eeva008/bZqbm3Vog2f3/HG88mRj/XbWS8NnbRJwfwyzNrmnSquXXnrJjBs3zmjYaNOmTVm6NzY2mo9+9KPWwMnINTU1Gb2pRRvYzpw5055rCP+1116zT/uKs2/fPpvHxIkTraGT8ZST98ILL9jzyZMnW0N48OBB2zuwdOlSW656XWUgFb+lpcU6kA899JBpbW01kyZNMkOHDjWHDh3KGMtHH33UGuePf/zj1kmUkXzvvffMk08+aTRULqda8sjBvv/++7P00omGxjZs2GDefvtt87d/+7fmlVdesXrpnvSeMWOGLUsG+/HHHzc7d+7ULTs9QcNrYnDgwAHz2GOPmcOHD5sPf/jD5v3vf7/Zs2ePNdL60dm7d6/NR8dipzBt2jSzbNkys2PHDnvOfxCAQDoIyK4p5LIVshu6rgdY2dS33nrL2gjZRdk19aTqrYHr1q0zn/70p82iRYvM/v37rU294IILzO9+9zubd5h91RvA5NhKBtlZ2STZatm5P/3pT9ZWaeRKU5LkkMrRlG3btWuXjfPuu+/adLoum/n888/b8vivdgnggNZu3TqjmQySHCI5jA888ECWXHJM9ZrU5cuXW0P3iU98wgwZMsRs2bLFxpMDJ0OmIKdv7dq19klf57r3+uuvW4P6yU9+0jqg6iWVEynjqXDqqaeaUaNGZRxfOXues3jOOeeYYcOGWUdPeeu6nEkZUu+JX3NVZZzVy6An9rPOOsvKobxV1n333WedRJ37g57yT2ifpyoHV06iHEkZXhlWBRnZBQsWWN1Hjx5tNL1ARlpB5eieHNCpU6faXg39KCi/e++918oo51bDbjLS+iHRPTn6cq5VNs6nRcl/EKhZArJdGqnR6NDgwYPt1B3ZUdmuMFshGLIv8+fPt1xkb/XgLlsqp1R2MCqE2Vc5j+pgUL56WJZ90kO211mgPDXvXfZUvwGKI7t3yimn2N8G3Zcj+uc//9k6oeeeey4OqKDUeMABrfEKdkU99Xxu3rzZ9hquXr06I5YMnoZoFORwyRDKeHoOqF6jGhY05KQgB1ZGVcZYvYArV660jqeGwJW/DJsX3nnnHe/Q9iQqjXoEJJ+cTwU5id6QueYvKaiXVkFDTzKiktNzLO2NwH8yttLHW2yk3ljl6TmgkklyK+jViOoZ8ILOlVZB8koHGWzJJydeQUNp6rGQAyqnXD8kckDlbKs3mAABCNQ2AT3EysbJLmj0RN9/Pehq9CTMVoiInEUvyHb89V//tb0mm6aH2agQZl/VySBbpXmosqXKK/j6a9kxxZEtU5At/NCHPmQf7nXujY55TqtsnEanCLVLAAe0duvWOc3kLGlYXcM6XtCxeuy8oKd5/3mUAfIMmZdWn+o9PfPMM60TKkdXDqyezL0gR9ALnpMnoy1D7gVvPpJ3LqPpd4RlbOWIRsmmHwGlk2OsIId6zJgx1tnVuefs6lg6y5n1gieXd09DZwr6VI9vMMiRFUfpLuddva4ECECgtgnIeVy/fn1OJcNshSJrhMgLGlmRnZKN1PQejaosXLjQ3vZslxxBL0TZ1yVLllj7ppEeTU+STV2xYoWX1Noov52V3dOfZ+9kVwnpInD0lz9deqNtBQh4Q/EaFveCDKh67WTsZOjUu+h/Qvfi6VMOpwxWVNBTtnpaNWdUw9BaNe93aHOlVY+jhrM0f0nOp5w4L0g+5akeBuWn1afqeYwK6pnQkJgc7lWrVtk/9cqqHK9nVUNZXj7SXz0GXtCPgYbRpKt6UHVPfxoiU++A5FCvrWTxgno9NZdLPRRyqAkQgEA6CeSzFX4qH/vYx6x9U8/nM888Y22gbLEe1DWdR8H/AB9mX/VArs4F2adXX301MzXKX5bkkj32pjfJ7jFVyE8ofcdHH23SpzsaV4CAhln01C1DpqBjPTGfd9551gmVk/bGG2/klEy9kNrWKMoJlSHVPM2zzz7bOp4appdTGxVkNOUoar6lehPlxGmuqIIcUMmnoSUZZQ2de05pWJ7qSVCvQvCJXj0W6p2VjipHw/oy9nKstQjJCyrnU5/6lL0nXpqDqiCnWnOjlFa9BvrB8II4ah6pN53Bu84nBCCQLgKyH1G2wk9Ddk+9lRoK14OzHpplW+REamhetlEP394q9jD7qvu6J7ulHlZ1JqhH1B/0YCwbKFuvY9lHLegkpJdAXXtj+8tksxpm8PDDD3eYj1LD6lalapqLKUfMPzSdSxH1ZuaLo3TqyQw6gLny0zX1fGrVpjenVBPj9fTvd/BkUFVuIWWHlZPrunoD9IMRDNJTf8FhfjmsYhXUTde02tRbSBXMj/NkCOjhaNasWckUVmIpd9xxR4kpSVZNBMJsRS4dctlL2R+1Z/+QvZc2V/xC7ilOVL5eHnzWBgH1nk+ZMiVUGXpAQ9FwI0kCuYxcrvILdQCDDlquvLxrehpX76ee4BVOaB+CDz6ZBx1BL21nP3M5n8ozzNnV82JQN604Va+reo4L5dNZuUkPAQi4TSCXrQiTOGhTFC/MBulervi6rhB1T/ej8tV9QnoI4ICmp67RNISAel4ffPBBuw+ons7/+Mc/VtU8Sm/BgaYGECAAAQhAAALVQAAHtBpqCRnLTkBP7d4WSWUvLOYC/Cv0Y86a7CAAAQhAAAJlIcAq+LJgJVMIQAACEIAABCAAgTACOKBhZLgOAQhAAAIQgAAEIFAWAqkYgtdKY20xQYAABCBQTgJRW4SVs9xi8sYWFkOLuBCAQKkEtFtCVEiFA6oV1v7NdKOAhN3Tm2q0XY8LQfMV81VsUnJq/zdtUaS/Sget+tRqdW1J5EKgzeSuBe06oPbrgrOmBWgKccmilyC4HPT90EI7vXih1CBmskF617cLwSV76NJ33tuPU9sxVTpIFrUbbVjvQqDN5K6FuLn433qYq8TKew25pIr5mn5ctIF5Z4IWqOTb0Lwz+ReTVpuh6006LgS9yUJGRftoVjpoew9tnOxtIl9peWgzuWtA+61qn1XvjSi5YyVzVdtgqd3E5UwtXrw4GcE7UYreqNUZeyhmelmDXsvoQnDJHrr0ndcLK9RpogeOSgc55mo33tvfKi0PbSZ3DcTJRXY1uJ1hsNTKt8ygRJxDAAIQgAAEIAABCNQ0ARzQmq5elIMABCAAAQhAAALuEcABda9OkAgCEIAABCAAAQjUNAEc0JquXpSDAAQgAAEIQAAC7hHAAXWvTpAIAhCAAAQgAAEI1DQBHNCarl6UgwAEIAABCEAAAu4RSMU2TKVgP//HwVQjghfMPdd0uMQFCEAAAjVHoGnq2iydGtrPmszerGv9Hzkx65wTCEAAAlEE6AGNosM9CEAAAhCAAAQgAIHYCeCAxo6UDCEAAQhAAAIQgAAEogjggEbR4R4EIAABCEAAAhCAQOwEmAMaO1IyhAAEIOAuAb2XW6/cizuUI89CZMz3vulC8ogrTmtra1nYliLfgQMH7GtmXXgXfHNzs3GJDW0md4uKk4texam/qIADGkWHexCAAARqjEC3bt1Mv379itKqyWzPG7/YPPNmWESESpbtFzPOd2n78y3lWI6nK++Cr6+vt++Cd6WexNMVWVxqM3FykfPZpUv0IHv03VJaPWkgAAEIQAACEIAABCAQQQAHNAIOtyAAAQhAAAIQgAAE4ieAAxo/U3KEAAQgAAEIQAACEIgggAMaAYdbEIAABCAAAQhAAALxE8ABjZ8pOUIAAhCAAAQgAAEIRBDAAY2Awy0IQAACEIAABCAAgfgJpGIbpsOHD5ewN1v+bUrY984Y7e8mvtrjrdJB2z4cPHgw795jScnJvne5SauO9uzZY9tO7hjJXVUdqd20tLTEUqgL34NYFCETCEAAAmUmkAoHVHuQlWPPr3LkWWh9V7Jsv4z6we3Ro4fp1auX/3JFjuVI7Nu3z/TpqNXfeQAALZxJREFU06ci5QcLrdX93YJ6FnuuhxbVUUNDQ7FJY4/vPbA0NjbGknfXrqkwqbGwIhMIQCDdBBiCT3f9oz0EIAABCEAAAhBInAAOaOLIKRACEIAABCAAAQikmwAOaLrrH+0hAAEIQAACEIBA4gRwQBNHToEQgAAEIAABCEAg3QRwQNNd/2gPAQhAAAIQgAAEEieAA5o4cgqEAAQgAAEIQAAC6SaAA5ru+kd7CEAAAhCAAAQgkDgBHNDEkVMgBCAAAQhAAAIQSDcBHNB01z/aQwACEIAABCAAgcQJ4IAmjpwCIQABCEAAAhCAQLoJ4ICmu/7RHgIQgAAEIAABCCROAAc0ceQUCAEIQAACEIAABNJNAAc03fWP9hCAAAQgAAEIQCBxAjigiSOnQAhAAAIQgAAEIJBuAjig6a5/tIcABCAAAQhAAAKJE8ABTRw5BUIAAhCAAAQgAIF0E8ABTXf9oz0EIAABCEAAAhBInAAOaOLIKRACEIAABCAAAQikmwAOaLrrH+0hAIEKEFizZo157LHHzIEDB7JKP3jwoHnqqafM0qVLzaFDh7LurV692vzxj38027dvz7oelSYrIicQgAAEHCKAA+pQZSAKBCBQ+wS+8Y1vmJ///OdGDuWXv/xl8+yzz1ql5YzqXI7p7bffbq666irT1tZm782bN8/ceOON5sUXXzSXXHKJefvtt/OmqX2SaAgBCFQzga7VLDyyQwACEKgmAitWrDDvvvuu+e1vf2vFHj16tLnzzjvNhAkTzF133WUmTpxorrjiCnvvsssuM8uWLTNDhw41S5YsMfPnzzddunSx8e+44w5zzTXXhKaZNGlSNWFBVghAIIUEcEBTWOmoDAEIVIbAaaedZn7xi19kCt+1a5dpbm625xqWnzZtWubeuHHjzMqVK83+/fvNmDFjrPOpm7q+cOHCyDR+B3Tv3r2mtbXVxj9y5Ig5fPhwpkx7Mab/PD1iyq7gbDRVoVJlB4UUX1dkERdNz6irqwuKmfi5ZFEbdImNK7K41mbi4iK9vBGcsAaHAxpGhusQgAAEYiagHszGxkab67Zt22xP6Le+9S17vmXLFtO3b99MiTreuHGjaWhoMP369cu6vmPHjsg0mcjtB1u3bjW7d+/OXJIzIMe3mNBQQORi8ywgy4KitLS0WKe6oMhljiQnq1IcgqqJi/fgEbyX9LnanB58XAm0mdw1EScXOaD6iwo4oFF0uAcBCECgDATeeustc/XVV5uLLrrIeL2V9fX1WT/Sch7krIZdl1hR9zyxTzzxRO/QOiRPP/20GTJkSOZaIQdNZm/eaMXmmTfDAiPI4fM76AUmK0s09ThWikNQIT109O7dO9NzHryf5Ll64cVm0KBBSRYbWhZtJjeaOLnI+dQ896iQ2CKk9957zzzyyCNm8+bNHeQJW92p1Z4PP/xwTiXC0nTInAsQgAAEHCKwatUqc+WVV5qvfvWrZubMmRnJjjnmGLNz587MuY6HDx9uBg8e3OH6sGHDbLywNJlMOIAABCDgKIFEHND77rvPfO1rXzN66r/++uvNzTffnMERtrpTqz3VO/D666/b1aD33HNP3jSZCBxAAAIQcJCAHqq1uv173/ueOeuss7IknDx5slm0aJGdJ6d42opp7NixZvz48UaLlzZs2GB7MBcsWGAXLSlxWJqsjDmBAAQg4CCBsg/Ba96HVnxqC5FRo0aZf/iHfzCf+9znzJe+9CU7VyZsdaec1BtuuMGcccYZNv6ll15qZsyYYd55553QFaEO8kUkCEAAAhkCf/jDH0xTU5P5+te/nrk2cOBAc++995qpU6faPUAvvPBCO2w6a9YsazMVcc6cOUY2UHFHjhxpZs+ebdNHpckUwAEEIAABBwmU3QHVHKVf//rXplevXlZ9rbDSfBA5pm+++WbO1Z2a+6TJ91r5qaA5NT179jSbNm2yvahhK0JtZP6DAAQg4CiByy+/3OgvV+jatauZO3eu2bNnj537qXMvaKh++vTpdh6d5vV5ISqNF4dPCEAAAi4SOGrhyiid53xqUurPfvYzc8455xjNXdJ8UP/kca361OpOrQ5VGv/2EYqnOVFhafziy3l94403Mpe0wbO3cXPmYt6DEXljFJ9n3iwLiuDSSkutbtTKXj1ouBD0YKP5xi4EPWxVqo0E9XepzWgxgr6TajeVDt4qzbhkiWMLkz59+uTE0q1bN6O/XCEsTa64XIMABCDgAoFEHFApqh+dH/zgB3ZfqO985ztW97AVnMHriqwf0B49ehS06vO4444z+vPC4sWLzYgR+R1KL36hn+XIs5Cy41ypVkh5UXH0wKB68R4youKW+56ciX379hlXfozlfFaqjQRZu9RmtC1Q//797fZCQTmTPpddUrvxtkbqbPnay5MAAQhAAAL5CSTSBaGNlL/5zW9ax0BDTN27d7eSha3u1FYNciT04+CFQlaEenH5hAAEIAABCEAAAhBwl0AiDqhWfOqVc9/+9rezhmrDVndqXpNeSXf//fdbck8++aQZMGCA/QtL4y5iJIMABCAAAQhAAAIQ8BMo+xC89rx75pln7J9WgHrhX/7lX+wio7DVnZqor+1KtP2S5mddd911NqnmiYal8fLmEwIQgAAEIAABCEDAXQJld0BPPfVUu21SGIKw1Z3aauSuu+6yW5Zovpg/hKXxx+EYAhCAAAQgAAEIQMBNAmV3QAtRO2p1Z9D59PKLSuPF4RMCEIAABCAAAQhAwD0CicwBdU9tJIIABCAAAQhAAAIQqBQBHNBKkadcCEAAAhCAAAQgkFICOKAprXjUhgAEIAABCEAAApUigANaKfKUCwEIQAACEIAABFJKAAc0pRWP2hCAAAQgAAEIQKBSBHBAK0WeciEAAQhAAAIQgEBKCeCAprTiURsCEIAABCAAAQhUigAOaKXIUy4EIAABCEAAAhBIKQEc0JRWPGpDAAIQgAAEIACBShHAAa0UecqFAAQgAAEIQAACKSWAA5rSikdtCEAAAhCAAAQgUCkCOKCVIk+5EIAABCAAAQhAIKUEcEBTWvGoDQEIQAACEIAABCpFAAe0UuQpFwIQgAAEIAABCKSUAA5oSisetSEAAQhAAAIQgEClCOCAVoo85UIAAhCAAAQgAIGUEsABTWnFozYEIAABCEAAAhCoFAEc0EqRp1wIQAACEIAABCCQUgJdU6o3akMAAhBIJYG2tjbT2toau+7lyLMQIQ8fPlwWfQopOxinXGyD5RRyfuTIEculS5fK9zOpjjx5CpG93HFoM7kJx8lF9Z0v4IDmI8R9CEAAAjVEQD8yzc3NsWtUjjwLEfLQoUNl0aeQsoNx9KNbKQ5BWVpaWoycTxccUNWRHlBcYUObCbaWv5zHyUXfBT2QRQUc0Cg63IMABCBQYwS6du1qevfuXZRWTWZr3vjF5pk3wwIjyKGuVNlBEXfu3OmMLHIAxMUFB1Sc6urqnGFDmwm23L+cx8lF7U91HhUq3zcfJR33IAABCEAAAhCAAARqjgAOaM1VKQpBAAIQgAAEIAABtwmkYgheXcH79u0rsiZ65Y1ffJ55sywowsGDB0vQp6Csi46keUauBNWz5hi5MuSk4YxKtZFgnbjUZjTP6MCBA04sHJEsmqekthNHUJ0TIAABCEAgP4FUOKCah9DQ0JCfRpExPn9LtJN697fiX2kqEeVMlEOfItW30TWfrFu3bk7IIydCDoArbOQIuyKLS22mvr7edO/e3f6V0ubiTCPboHYTVz258vATJyPyggAEIFAOAqlxQOUoJR3KVaZ+wMuVd7GM9IPrijxyJFyRRRzl3LhSTy5xcanN6IElznpSXgQIQAACEMhPgDmg+RkRAwIQgAAEIAABCEAgRgI4oDHCJCsIQAACEIAABCAAgfwEcEDzMyIGBCAAAQhAAAIQgECMBJKfGBmj8GQFAQhAAAJuEGiaujZSkP6PnBh5n5sQgEC6CNADmq76RlsIQAACEIAABCBQcQI4oBWvAgSAAAQgAAEIQAAC6SKAA5qu+kZbCEAAAhCAAAQgUHECOKAVrwIEgAAEIAABCEAAAukigAOarvpGWwhAAAIQgAAEIFBxAjigFa8CBIAABCAAAQhAAALpIoADmq76RlsIQAACEIAABCBQcQI4oBWvAgSAAAQgAAEIQAAC6SKAA5qu+kZbCEAAAhCAAAQgUHECOKAVrwIEgAAEIAABCEAAAukigAOarvpGWwhAAAIQgAAEIFBxAjigFa8CBIAABCAAAQhAAALpIoADmq76RlsIQAACEIAABCBQcQI4oBWvAgSAAAQgAAEIQAAC6SKAA5qu+kZbCEAAAhCAAAQgUHECOKAVrwIEgAAEIAABCEAAAukigAOarvpGWwhAAAIQgAAEIFBxAl0rLgECQAACEEghgddee8306NHDnHDCCRntDx48aJYvX27q6urM+PHjTbdu3TL3Vq9ebdavX2/GjRtnjjnmmMz1qDSZSBxAAAIQcIwAPaCOVQjiQAACtU/grbfeMv/0T/9kVq1alVH2wIED5stf/rJ57LHHzO23326uuuoq09bWZu/PmzfP3HjjjebFF180l1xyiXn77bft9ag0mYw5gAAEIOAgAXpAHawURIIABGqXwH333Wd+9atfmX79+mUpedddd5mJEyeaK664wl6/7LLLzLJly8zQoUPNkiVLzPz5802XLl3MnXfeae644w5zzTXXmLA0kyZNysqbEwhAAAKuEUjUAd27d695+eWXzZlnnpnFIWxoafv27eb555+3Q1SjR48uKE1WJE4gAAEIOEagsbHR/PKXvzS33HKLHWr3xFuzZo2ZNm2ad2qH2leuXGn2799vxowZY51P3dQQ/MKFC228sDR+B3Tr1q02Dy/jQ4cOmV27dnmniX2Wq0zxcSW0trZWhG0u/dU7fuTIkaw2liteEteam5uNS2xoM7lrPU4uanv6iwqJDcGrAX7/+983evr3h7ChJQ01XXTRReb111+3Q1H33HNPJllYmkwEDiAAAQg4SkBO5qBBg6x03hC7TrZs2WL69u2bkVrHO3bsMJs3b87qLfWuR6XJZBI48JcXuMUpBCAAgUQJJNID+uabb5prr73WGlH/sNO6detCh5Zuvvlmc8MNN5gzzjjDfO5znzOXXnqpmTFjhnnnnXdC0yRKjsIgAAEIxEigvr7eHD58OJOjeozUWxp2XRGj7nkZDRkyxDu0vVCbNm3KcmgzNyMOmsz2iLuF3fLb/sJSFB6rnHkXLoWxvZ+uyKKFbL179870nBejR9xx1U61WM4VNtLPFVk0MuCKLHFyUe+npgxFhUQcUHXrfuc737FP8w8++GBGHjmmuYaWZHg3btxo7ymyDGjPnj2NDKcm7+dKk8m0/aClpcU2du+aQOhacaF7cdFzxC6+zByZ5LgkPuXKO0dxkZf0g6khPRfkUT27xEa9TS5wUQW6xMVrM/qBrHRQ21W70Q9kHKEzPYxa2b5z586MGDo+/vjj7Y/TK6+8knV92LBh9jwsTSYyBxCAAAQcJZCIA/rBD37Qqv/4449nYQgbWtq2bZvp1atX1twVPSHIIIel8Wf83nvvZVaJ6rp+ZPyG3R83/Hho+K0C7xRfZmEZy6mRTi4ETa3Qk60+Kx304y8ukseFoHoqVxsoVj/X2ozqKi6nr1gW/vhyhiVLXHOfOvO9nDx5slm0aJHRp+bLL1261PzkJz+xw/U/+9nPzIYNG4wczwULFpgJEyZYNcLS+HXkGAIQgICLBBJxQMMUDxs+Cl5XevXgaM+84D1d1zCVP6jH1D/stHjxYruS1B8niWOtXi1HcKnLXnPUVC96YKh0UE/Wvn37TJ8+fSotii1fTl+52kCxCrrUZrQopn///qahoaFYNWKPr4cVtZugDSm1oO7dSx85mTp1qnnqqafMhRdeaIeuZs2aZUaNGmVFmTNnjp2GNHDgQDNy5Egze/Zsez0qTak6kA4CEIBAEgQq6oAOHjzY5Bpa0gR9ORL6cfB+pNSTNHz4cDtRP1eaJGBRBgQgAIG4CFx//fVZWXXt2tXMnTvX7NmzxzrEOvfCzJkzzfTp061N1Lw+L0Sl8eLwCQEIQMBFAtEzRMsssd70sWLFCju0pJ5Mb2hJRlX74d1///1WgieffNIMGDDA/oWlKbOoZA8BCEAgEQLqwfc7n16heiuS3/n0ruszLI0/DscQgAAEXCJw9BG7AlJpO5GwoaXLL788s/2SVlJdd911VsKoNBVQgSIhAAEIQAACEIAABIokkKgDOmXKFKM/fwgbWtI8J73lo6mpyc4XKySNPw7HEIAABCAAAQhAAAJuEkjUAQ1DoKEl/eUKWqyQK0SlyRWfaxCAAAQgAAEIQAACbhCo6BxQNxAgBQQgAAEIQAACEIBAkgRwQJOkTVkQgAAEIAABCEAAAgYHlEYAAQhAAAIQgAAEIJAoARzQRHFTGAQgAAEIQAACEIAADihtAAIQgAAEIAABCEAgUQI4oInipjAIQAACEIAABCAAARxQ2gAEIAABCEAAAhCAQKIEnNgHNFGNKQwCEIAABBIn0DR1bd4y+z9yYt44RIAABGqDAD2gtVGPaAEBCEAAAhCAAASqhgAOaNVUFYJCAAIQgAAEIACB2iCAA1ob9YgWEIAABCAAAQhAoGoI4IBWTVUhKAQgAAEIQAACEKgNAjigtVGPaAEBCEAAAhCAAASqhgAOaNVUFYJCAAIQgAAEIACB2iCAA1ob9YgWEIAABCAAAQhAoGoI4IBWTVUhKAQgAAEIQAACEKgNAjigtVGPaAEBCEAAAhCAAASqhgAOaNVUFYJCAAIQgAAEIACB2iCAA1ob9YgWEIAABCAAAQhAoGoI8C74MlbV+T/On/k91+SPQwwIQAACEIAABCBQSwToAa2l2kQXCEAAAhCAAAQgUAUE6AGtgkpCRAhAAAJxEWhtbTX79u2LK7tY8ylFroMHDzqjz+HDh52RRVzq6upMly6V72dqbm42hw4dcopNKW0t1sb+v5m51mbi4nLkyBHT1tYWiQwHNBIPNyEAAQjUFoH6+nrT0NBQlFKHiopdeuRi5VJJcrRKSVe6lOEp5ey5IoscPsniggOqhx45I66woc3kbsNxcpEDqgegqJAKB1RPGLt27YrikONevxzX4r9UvFzG7N+/P35BSsxRT7biKwNT6aAGry+QPl0IYlJK/ZZDdpfajOpoz549Rm2n0kF1pPbS0tISiygufA/yKaIfha5d3TT9pcglh7qUdPk4lXLfJbZyPMXFBQdUdeTJUwrXuNPQZnITjZNLIb/Dblqh3GxKviqo/fol41AWK2SpcpWarlj58sXXD26PHj1Mr1698kUt+301eA0f9OnTp+xlFVKAnE9X6knyuiKLHE/VkQu9Id4DS2NjYyFVmjeOK45QXkGJAAEIQKDCBCo/OaTCACgeAhCAAAQgAAEIQCBZAjigyfKmNAhAAAIQgAAEIJB6AjigqW8CAIAABCAAAQhAAALJEsABTZY3pUEAAhCAAAQgAIHUE8ABTX0TAAAEIAABCEAAAhBIlkAqVsEni7S40nhdZ3G8iA0BCEAAAhCAQPUToAe0+usQDSAAAQhAAAIQgEBVEcABrarqQlgIQAACEIAABCBQ/QQYgq/+OkQDCEAAAjVBoGnq2rx69H/kxLxxiAABCLhPgB5Q9+sICSEAAQhAAAIQgEBNEcABranqRBkIQAACEIAABCDgPgEcUPfrCAkhAAEIQAACEIBATRHAAa2p6kQZCEAAAhCAAAQg4D4BHFD36wgJIQABCEAAAhCAQE0RwAGtqepEGQhAAAIQgAAEIOA+ARxQ9+sICSEAAQhAAAIQgEBNEcABranqRBkIQAACEIAABCDgPgEcUPfrCAkhAAEIQAACEIBATRHgTUhVUJ3n/zgoZL/ghbzn91yTNwoRIAABCEAAAhCAQCIE6AFNBDOFQAACEIAABCAAAQh4BOgB9UjwCQEIQAACzhPI9b74JrO9KLl5n3xRuIgMgbIQoAe0LFjJFAIQgAAEIAABCEAgjAAOaBgZrkMAAhCAAAQgAAEIlIUADmhZsJIpBCAAAQhAAAIQgEAYARzQMDJchwAEIAABCEAAAhAoC4GqXYS0evVqs379ejNu3DhzzDHHlAVOLWXacSunjtoVslVTx3wGZWVUSB5ZCTiBAAQ6ReDgwYNm+fLlpq6uzowfP95069atU/mlIXGuhUzF6s1CpmKJER8C2QSq0gGdN2+eefXVV83JJ59sbrvtNnPrrbeaESNGZGvGWdEEOjqXRWdRUIJCysGRLQglkVJO4MCBA+biiy82p59+unnnnXfM3XffbW666SbrjKYcTdnVz+XE9m0vtcmsjbVsHN1YcZKZQwSqzgFdt26dWbJkiZk/f77p0qWLufPOO80dd9xhrrmGndZdaFeFOJdxyJm7HM0o6VNU9vkc3dzlZBeRL4/s2JxBID4Cd911l5k4caK54oorbKaXXXaZWbZsmZk0aVJ8hZBTRQnkcnQLFWi3eTcTNSlHNkze+nZJmtr/JSVHRnEOnCVQdQ7om2++acaMGWOdT1HVEPzChQuzAL/77rtm48aNmWsaotq2bVvmvLCD9xUWjVhlIVCI4xdHwXGUE56HS73yhb8967vn78iLdu492VMv8ibIijAk6yzq5PKzm6Ju23vHDWiNjHPtH6Km6DTYtD+/pFj7kLvIlpaW3DfKdHXNmjVm2rRpmdxlD1euXJnlgK5du9bs3r07E6cUe9g9k5qDaiUQ5hgWo8+hK3vkjZ5vAkghchRUzrzmvLJERSh279iovDpzL85e80M/6plXlG7X7o+MIy4tvyuuIydXhkeOHDGHDx/OdStzreoc0M2bN5t+/Y7+mPbt29fs2JH9g6lrJ5xwQkbJ7du3G10rJvz+yuzGvWXLFjN06NBisihb3L1795revXuXLf9iMt61a5fp3r27aWxsLCZZWeKqwWtIslevXmXJv9hMq7fN5OcX/H4Uw0bf1z59+th2kz9d/h+8fHlEySqHsa2tzTQ0FGcfwsrs2jVZk6o25rdtOvY/fEvOIUOGmIEDB1qR9R3Rd9afJkyXrOsPHOUjZrJBXp5Z8Spw4pI9dOk7v2/fPmuXNVIYVyjo2/iJjqXJLqvd+H+7O8Y6eqXUco7mEH1Uq22mIG4PDAiF43EpKJ/QXP5yQ7YmX9tL1lrmEbiQ2/X19VledWtrawfnp6Ghof0H5S89G8pTaXr06BxSgexsHoXoV0gc9WC4IouMnBxQF+TxnrhckEX1SJvJ3ZrlpAW/o7ljlv+qFu6o3cTVZvIZ3Lg1KsQe+h9WZS87aw/FTA5FXMw6y8Qle+jSd14On+oo6TaZqz7V7uL8nuUqo5hrtJnctOLkovqWrYgK8T0aRZUS473BgwebnTt3ZnLU8bBhwzLnHEAAAhBICwHtABK0h8OHD0+L+ugJAQhUMYGqc0C1zciKFSvMhg0bjJ6qFixYYCZMmFDFVYDoEIAABEojMHnyZLNo0SLT3NxsNNVo6dKlZuzYsaVlRioIQAACCRKouiF4zV2aM2eOufTSS+0cpJEjR5rZs2cniIyiIAABCLhBYOrUqeapp54yF154oR1qnTVrlhk1apQbwiEFBCAAgQgCVeeASpeZM2ea6dOnG81X8M9vitCTWxCAAARqjoDm086dO9fs2bPHzoVPehFUzQFFIQhAIDECVemAio7e9sEbPxJrJxQEAQg4TEC7ChAgAAEIVBOBqnVAi4GsuaKPP/54MUk6xNWqT+1B6kI4dOiQM863VlpqVa3+Kh20nY72HXOlF4g2k7tFaORCD48urM7VSk21m7jab1NT/n1Lc1NJ7qr2Se6MPRQz2SD/TiPJSd+xJJfsoUvfeW/Hg3wrkTsSjf+KtwpeO6a4EGgzuWshTi6yq/naXl17pLbcotTW1c6qKYM9ZcqU2oISgzavvfaa6d+/vzN7pMagUmxZPPHEE+ass86KLb9ayeiFF14wJ510UvF7UVYBgHwG1wUVOmsLtY+oHsZZ7NSxNvmd6MhEV7Q/qtrN6NGjc0dI8dVabjP57GEqekDVtvOBKKT9x5FHIeVUWxxxgU3HWtMPPVw6cvGuwMYjkexnZ7l76b3PZKV3vzS4hNcRbHKzSSuXqtuGKXf1cRUCEIAABCAAAQhAoFoIpKYHtLMVog3wCR0JaPGDK29E6ShdZa+8733vq6wAjpY+YMAAZ+YwO4rIabE0f1d1SOhIgN+Jjkx0Rb8RmjtM6EggzW0mNXNAO1Y7VyAAAQhAAAIQgAAEKkGAIfhKUKdMCEAAAhCAAAQgkGIC9d9vD7Wq/+rVq41W3Pbr18/07NkzVM2weHq13ZIlS+zWPnrnsj/EmcafbxLH2gZn2bJlZuPGjXb1etgWNHHrv2bNGvPyyy/bMr09XPfu3WvrSLJ4f8cdd1wSGHKWEVav/shR/MKYhaXJp38h8vhlK9dxmF7B8sLihemv9LnS6HW7a9euzbQJtQ29bnLQoEEmH7OgTJwb+9KOQr7zUfUU1haj0uSqW9VHVJqk6ytMxqAcpegflkbb3Tz33HNmx44dZsiQIZnFim+//bZZtWpVpt1rWye1+UqEQusoil+Y/mF5R+kflqYSbML0CsoSFq9YZlH2MIpZUB7XzmvWAZ03b5659957jfapvO2228yZZ55pHdFgBYTFe/HFF80VV1xhtxj6+c9/buewnHrqqTZ5nGmC8pT7XAbtoosuMvv27bOv8HvsscfsW6WCq/Di1v8b3/iGdTQ1D+jmm282eoXqsccea2XQ+bZt24y2dNLf2WefXW4MOfMPq1d/5Ch+Ycyi0ug1imH6FyKPX7ZyHYfpFSwvLF6U/mFp7r77bvuQ5LUJnWuP149+9KNOtZkgAxfPo/j75Y2KF9YWo9KE1W1UGr88SRyHyRgsuxT9w9JoS6KLL77YOp2vvvqq0e+L3u6n/Yt/+tOfmj//+c9m3bp11hZq/8wxY8YExSn7eaF1FMUvTP+ovMP0j0pTdhiBAsL0CkQzYfFKYRZlD8OYBeVx8rx9q5iaC2+99Vbb+eef39b+g2V1+/3vf9/2ox/9qIOeUfG++MUvtr300ks2TbvBaGs3EG3tT2BtcafpIFSZL/zqV79qa/9iZEqZM2dO29NPP5059w7i1P9//ud/2j7/+c97WbctXry47corr7Tn7ca37T//8z8z9yp1EFWvfpmi+IUxi0oTpn+h8vhlK9dxmF7B8sLiRekflsafd/vTf9tnP/vZtvZ9BO3lMGb+NBwfJRDF/2istraweFFtMSyN8g2r26g0fnmSOA6T0V92KfpHpbnlllvafvnLX2aK+O53v9u2YMECez5r1qy29evXZ+5V6qDQOgrjF6V/VN5h+kelSZJRlF5+OaLilcLMn3fQHoYx86dx9bgm54Bqk2Q9NXpvWhk3bpxZuXJlhweAsHh66tSQn/fkqSESDeFv2rTJbsCcK+9S0nQQKIELGgYXDy/kYlOKLlFpTjvtNPOLX/zCK9JuSKzhVIU33njD9O7d2/zud7+zQ1LtX5RMvCQPwtpCUIYwflH6h6VR3mH6FypPUL64z6P08pcVFS9M/6g0Xt4admt/eDRXX311ZuP6MGZeGj6zCYTxz45lTFi8qLYYliaqbsPSBOUp93mUjP6yS9E/Ks1ll11mvvCFL2SK0Abt6uHbv3+/2blzp9Gbqm6//Xb7G5SJlPBBIXUUxS9K/7C8o/QPS5MwltDf/6AcYfqXyszLP2gPo5h5aVz+rEkHdPPmzVnD7X379rVzbYIVERZPw8G9evXKzMtROs0jlXGIM01QniTONfwjHl7IxSZu/fUg0NjYaItU3r/97W9N+1OgPZcz8cwzz9jX+v3mN78x3/rWtzzREv0Mq9egEGH8opiFpVHeYfoXKk9QvrjPo/TylxUVL0z/qDRe3o888oj97k2YMMG7FMosE4GDLAJh/LMitZ+ExYtqi2Fpouo2LE1QnnKfR8noL7sU/aPS6HWU3hz49tEg62h+8pOftHOe5WBobqimm2gK2MKFC/2iJHZcSB1F8YvSPyxvzfkO0z8sTWJA/regKL38soTFK5WZl3fQHkYx89K4/FmT+4BqUY2+wF7QU4fnAHnX9BkWL3hdcZWH9jIL3vPyDl4vJI3iJB2Ccnry++UIxtG9zujv5d0+LGF7sjQHddKkSfbyf/zHf9h5tnJSP/3pT5vzzjvPGuSkFyIFdc7FRQKHxQteV9x8zBQnTP9gfmHyKI9yhqAcKsvTy19uVLzgPU+X4PVced9///3mggsu8BcVyizpNpMllMMnQc4e/6DIYfHCrit92L3gdcX12k3wXpg8SlPOEJRDZXky+ssNxvPLG3Yv7Lo/X7Vt9XTedNNNdhRIawzuueeezB6rel2t7MOMGTP8yRI5LkT+YBwJ5vEL3iuEWZT+UfklAuR/CylUjrB4weuFMvN0DNrDKGZeGpc/a7IHVBu7qrfSCzoeNmyYd5r5DIunVYdapKOnMS8oj+HDh5s403h5J/mp1fxBNtLLH+LWX3lrZWf7vE/z1a9+1U641zUtEGuf75SZKqGeAU130NNu0iGsXoNyhPGLYhaWJkr/QuUJyhf3eZRe/rKi4oXpH5VGeWt1p6a9TJkyJVNUFLNMJA6yCITxz4rUfhIWL6othqWJqtuwNEF5yn0eJaO/7FL0j0qjvDUK9Ic//MHceuutdkGmrjU1NZn33ntPhzaMGDHCbN26tSIbuBdSR1H8ovQPyztK/7A0HqukPqP08ssQFq9UZso7lz2MYuaXx9XjmnRAx48fb7RtwYYNG+wTWfsEb+MN4WmujZwehbB4Wo04ceJEo6cNhSeffNI+lertH3GmsZkn/N/kyZPNokWL7JY22gpi6dKlZuzYsVYKrbzU3My49Vc5V111lfne975nzjrrrIzGGobS07+G4BXkpGpbkg9/+MOZOEkdhNWryve3mTB+UczC0kTpHyVPUkxUTpReul9ImwnTP1/eWgF/yimnZIYrVV4UM90ndCQQxl8x9d3Un0JYvKi2GJYmqm7D0lghEvwvSkb/d74U/aPSPPjgg+bRRx81//Zv/2YfuD2VNRdUD+kqW3PhH3jgAWsvvbUMXrwkPqPqyGszUfyi9A/LO0r/sDRJsPCXEaVXIW2mVGaSIZc9jGLml9vV45p9E5K+vHq6HDhwoH3CvOGGG+yP6fLly80PfvCDjHMZFk9OqpwmdZnLAFx33XXmAx/4gK3HONMk3TA0FHL99ddbB116ta+gM3//939vxdA8pJ/85CfmjDPOsE56XPr/67/+q2nfiSBrTq3qRdtkPf/883aBkvbF0+T7b3/723bLrKS5qLywevW3mSh+YW0mKk2U/mHyJM0mTC/JUUibidI/Km8tXFPayy+/PEvlKGZZETmxBKL433jjjdap13zDqHhhbTEqTVjdRqVJusrCZPR/5yVTKfqHpdGUEvVs+re++7u/+zvz9a9/3fz61782mucnRpqfP3fuXFOJV/pG1ZG/zYTxK5VZmP5R8iTdZsLqtdA2Uwoz6RhmD8OYJc2llPJq1gEVDDk1GkbXKuuoEBVPXdz9+/fvkDzuNB0KKPOFPXv22HmxeiKLCnHqH1WOnuRkcP1GOSp+ue5F1au/zCh+Ycyi0oTpX6g8ftnKdRymV7C8sHhR+oelCebtPw9j5o/D8VECUfyPxjImLF5UWwxLo3zD6jYqjV+eJI7DZPSXXYr+UWn8efuPtVeyXrbgXyzqv5/kcaF1FMYvSv+wvKP0D0uTJBOVFaWXX5aoeKUw8+ftP45i5o/n2nFNO6CuwUYeCEAAAhCAAAQgAAFjanIOKBULAQhAAAIQgAAEIOAuARxQd+sGySAAAQhAAAIQgEBNEsABrclqRSkIQAACEIAABCDgLgEcUHfrBskgAAEIQAACEIBATRLAAa3JakUpCEDAdQLaN3D27NmZjcZ3795dlMjFxH/hhRfsnrtFFUBkCEAAAmUkgANaRrhkDQEIQCCMwOOPP27f+qX9eP/xH//R3HLLLWFRO1zXZubnnHNOh+thF7R3ql76QIAABCDgCgEcUFdqAjkgAIFUEXjooYfM9OnTrc7Lli0rSne96U2vCyZAAAIQqFYCOKDVWnPIDQEIOElAr5b94Q9/aPRmlEsuucR86lOfMj/96U/N4cOHs+R9+OGHbS+m7umVpvfdd5/58Y9/bOMo7r//+7+b888/35x77rm291KbWis88cQT5r/+67/Mxo0bzVe+8pXM+8P1yuGLL77YfOITnzBf/OIX7St3bQL+gwAEIOAgARxQBysFkSAAgeol8MYbb5ibb77ZfOELXzDHH3+8mTRpkrn22mutU+ppJYdTczjHjBlj33ffq1cvc+yxx5rTTjvNRpEjqdfSnnzyyeYjH/mIfUWuXnuqd4Tr1YzHHXec6dmzp5kwYYLp3r27ue222+x80ve///3mS1/6ktm/f791fJ977jmvSD4hAAEIOEUg+j2MTomKMBCAAASqg8D27dvN4sWLzYc+9CEr8KZNm8yf/vQnc91119lzDb9PmzbNvnp2xowZ5vvf/751NM877zwjp/E3v/mN7RFV76eCnE85m+ol/cxnPmMmTpxo1qxZY3tAdX/btm22l3XOnDk6tc7o4MGDjXpjx48fb6/xHwQgAAGXCOCAulQbyAIBCNQEgcbGxozzKYVGjBhhnn322YxuckBnzZqVOfcfvPjii6ahocEOpXvX1Qs6dOhQ65zKAQ2G66+/3mzevNn893//t3nttdfMyy+/bLTKvrm5ORiVcwhAAAJOEGAI3olqQAgIQKCWCGh43B+00l3D5wqay6kV8GeffbY/Sua4qanJ9O/f32hY3gt1dXV26D04j9S7ryH/UaNG2Tmk6g294IILbHzvPp8QgAAEXCOAA+pajSAPBCBQ0wSWLl1qRo8ebQYNGpRTz5NOOsls3brVvPTSS5n76t185ZVXzNixY+01OaReUE/n1VdfbW688UbbQypn9LOf/awdlj9y5IgXjU8IQAACThHAAXWqOhAGAhCodQL+7Zc8XeWMrlq1yg6ja77nyJEj7XxRLWjSanc5mFp89LGPfcwmGThwoI37+uuv23Ol37Jli93UXguQvva1r5mDBw8yBO8B5hMCEHCOAA6oc1WCQBCAQC0TkAMa3ERe8zrnz59vFxpp/qi2VNLCpVNOOcWoR3TlypXm0UcfNcOGDbNo5IjW19fbnlTN9/znf/5nc+edd1onVXNFe/fubeeYaj4pAQIQgICLBOra5yX9ZWKSi9IhEwQgAIEaI6BN5LXdkuaF+kNLS4tpbW212yt513fu3GlXyg8YMMC7lPXpzRf1Lqq3VA5o166sL/WY8AkBCLhJAAfUzXpBKghAAAIQgAAEIFCzBLIfwWtWTRSDAAQgAAEIQAACEHCFAA6oKzWBHBCAAAQgAAEIQCAlBHBAU1LRqAkBCEAAAhCAAARcIYAD6kpNIAcEIAABCEAAAhBICQEc0JRUNGpCAAIQgAAEIAABVwjggLpSE8gBAQhAAAIQgAAEUkIABzQlFY2aEIAABCAAAQhAwBUCOKCu1ARyQAACEIAABCAAgZQQ+P/PwxGr3AKGmAAAAABJRU5ErkJggg==" /><!-- --></p> <p>There are very long tails to the right for these novels (those extremely common words!) that we have not shown in these plots. These plots exhibit similar distributions for all the novels, with many words that occur rarely and fewer words that occur frequently. The idea of tf-idf is to find the important words for the content of each document by decreasing the weight for commonly used words and increasing the weight for words that are not used very much in a collection or corpus of documents, in this case, the group of Jane Austen’s novels as a whole. Calculating tf-idf attempts to find the words that are important (i.e., common) in a text, but not <em>too</em> common. Let’s do that now.</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>book_words <span class="ot"><-</span> book_words <span class="sc">%>%</span></span> <span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">bind_tf_idf</span>(word, book, n)</span> <span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a>book_words</span></code></pre></div> <pre><code>## # A tibble: 40,379 × 7 ## book word n total tf idf tf_idf ## <fct> <chr> <int> <int> <dbl> <dbl> <dbl> ## 1 Mansfield Park the 6206 160460 0.0387 0 0 ## 2 Mansfield Park to 5475 160460 0.0341 0 0 ## 3 Mansfield Park and 5438 160460 0.0339 0 0 ## 4 Emma to 5239 160996 0.0325 0 0 ## 5 Emma the 5201 160996 0.0323 0 0 ## 6 Emma and 4896 160996 0.0304 0 0 ## 7 Mansfield Park of 4778 160460 0.0298 0 0 ## 8 Pride & Prejudice the 4331 122204 0.0354 0 0 ## 9 Emma of 4291 160996 0.0267 0 0 ## 10 Pride & Prejudice to 4162 122204 0.0341 0 0 ## # … with 40,369 more rows</code></pre> <p>Notice that idf and thus tf-idf are zero for these extremely common words. These are all words that appear in all six of Jane Austen’s novels, so the idf term (which will then be the natural log of 1) is zero. The inverse document frequency (and thus tf-idf) is very low (near zero) for words that occur in many of the documents in a collection; this is how this approach decreases the weight for common words. The inverse document frequency will be a higher number for words that occur in fewer of the documents in the collection. Let’s look at terms with high tf-idf in Jane Austen’s works.</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>book_words <span class="sc">%>%</span></span> <span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(<span class="sc">-</span>total) <span class="sc">%>%</span></span> <span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">arrange</span>(<span class="fu">desc</span>(tf_idf))</span></code></pre></div> <pre><code>## # A tibble: 40,379 × 6 ## book word n tf idf tf_idf ## <fct> <chr> <int> <dbl> <dbl> <dbl> ## 1 Sense & Sensibility elinor 623 0.00519 1.79 0.00931 ## 2 Sense & Sensibility marianne 492 0.00410 1.79 0.00735 ## 3 Mansfield Park crawford 493 0.00307 1.79 0.00551 ## 4 Pride & Prejudice darcy 373 0.00305 1.79 0.00547 ## 5 Persuasion elliot 254 0.00304 1.79 0.00544 ## 6 Emma emma 786 0.00488 1.10 0.00536 ## 7 Northanger Abbey tilney 196 0.00252 1.79 0.00452 ## 8 Emma weston 389 0.00242 1.79 0.00433 ## 9 Pride & Prejudice bennet 294 0.00241 1.79 0.00431 ## 10 Persuasion wentworth 191 0.00228 1.79 0.00409 ## # … with 40,369 more rows</code></pre> <p>Here we see all proper nouns, names that are in fact important in these novels. None of them occur in all of novels, and they are important, characteristic words for each text. Some of the values for idf are the same for different terms because there are 6 documents in this corpus and we are seeing the numerical value for <span class="math inline">\(\ln(6/1)\)</span>, <span class="math inline">\(\ln(6/2)\)</span>, etc. Let’s look specifically at <em>Pride and Prejudice</em>.</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>book_words <span class="sc">%>%</span></span> <span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">filter</span>(book <span class="sc">==</span> <span class="st">"Pride & Prejudice"</span>) <span class="sc">%>%</span></span> <span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(<span class="sc">-</span>total) <span class="sc">%>%</span></span> <span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">arrange</span>(<span class="fu">desc</span>(tf_idf))</span></code></pre></div> <pre><code>## # A tibble: 6,538 × 6 ## book word n tf idf tf_idf ## <fct> <chr> <int> <dbl> <dbl> <dbl> ## 1 Pride & Prejudice darcy 373 0.00305 1.79 0.00547 ## 2 Pride & Prejudice bennet 294 0.00241 1.79 0.00431 ## 3 Pride & Prejudice bingley 257 0.00210 1.79 0.00377 ## 4 Pride & Prejudice elizabeth 597 0.00489 0.693 0.00339 ## 5 Pride & Prejudice wickham 162 0.00133 1.79 0.00238 ## 6 Pride & Prejudice collins 156 0.00128 1.79 0.00229 ## 7 Pride & Prejudice lydia 133 0.00109 1.79 0.00195 ## 8 Pride & Prejudice lizzy 95 0.000777 1.79 0.00139 ## 9 Pride & Prejudice longbourn 88 0.000720 1.79 0.00129 ## 10 Pride & Prejudice gardiner 84 0.000687 1.79 0.00123 ## # … with 6,528 more rows</code></pre> <p>These words are, as measured by tf-idf, the most important to <em>Pride and Prejudice</em> and most readers would likely agree.</p> <!-- code folding --> <!-- dynamically load mathjax for compatibility with self-contained --> <script> (function () { var script = document.createElement("script"); script.type = "text/javascript"; script.src = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"; document.getElementsByTagName("head")[0].appendChild(script); })(); </script> </body> </html>