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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 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<!-- README.md is generated from README.Rmd. Please edit that file -->
<h1 id="the-pepo-package">The P(e):P(o) package</h1>
<p>This is the alpha release of <code>pepo</code>, a minimal package to calculate the probabilities of hemiplasy (trait evolution incongruent with species tree due to incomplete lineage sorting) and homoplasy (incongruent traits due to convergent mutations). Currently, the package includes functions to estimate the ratio of these two probabilities, which we call the Hemiplasy Risk Factor (HRF), for all branches on a phylogeny. Provided a tree, branch lengths and population-wide mutation rate in coalescent units (2N), the HRF will give an intuition for the relative importance of hemiplasy in the evolution of a particular clade.</p>
<h2 id="installation">Installation</h2>
<p>This package depends on <code>ape</code>, <code>dplyr</code>, and <code>purrr</code>. The last two are part of the <code>tidyverse</code>.</p>
<p>Install <code>pepo</code> from github with: <code>devtools::install_github("guerreror/pepo")</code>.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(pepo)</code></pre></div>
<h2 id="quick-example">Quick example</h2>
<p>In this example we start with a preloaded phylogeny of Solanum sect Lycopersicon from Pease et al (2016). The tree is already of class <code>phylo</code> (from the 'ape' package).</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">data</span>(<span class="st">"tomato"</span>)
<span class="kw">class</span>(tomato)
<span class="co">#> [1] "phylo"</span></code></pre></div>
<p>The two functions you'll need from <code>pepo</code> are: <code>prep_branch_lengths()</code> and <code>tree_hrf()</code>. The former returns a tibble (a tidy data frame) with variables that will be needed by the latter.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">tomato_branches <-<span class="st"> </span><span class="kw">prep_branch_lengths</span>(tomato)
tomato_branches
<span class="co">#> # A tibble: 36 x 7</span>
<span class="co">#> code from to this_branch descendants ancestor sibling</span>
<span class="co">#> <chr> <int> <int> <dbl> <list> <dbl> <dbl></span>
<span class="co">#> 1 20-21 20 21 1.40 <dbl [2]> NA 4.59 </span>
<span class="co">#> 2 21-22 21 22 1.38 <dbl [2]> 1.40 0.596</span>
<span class="co">#> 3 22-23 22 23 1.56 <dbl [2]> 1.38 0.376</span>
<span class="co">#> 4 23-24 23 24 4.42 <dbl [2]> 1.56 2.76 </span>
<span class="co">#> 5 24-25 24 25 0.525 <dbl [2]> 4.42 0.355</span>
<span class="co">#> 6 25-26 25 26 0.616 <dbl [2]> 0.525 1.63 </span>
<span class="co">#> 7 26-27 26 27 1.07 <dbl [2]> 0.616 1.00 </span>
<span class="co">#> 8 27-1 27 1 0.612 <dbl [0]> 1.07 1.00 </span>
<span class="co">#> 9 27-2 27 2 1.00 <dbl [0]> 1.07 0.612</span>
<span class="co">#> 10 26-3 26 3 1.00 <dbl [0]> 0.616 1.07 </span>
<span class="co">#> # ... with 26 more rows</span></code></pre></div>
<p>Then we can call <code>tree_hrf()</code> on that tibble. The function will return the original data frame plus a new variable, <code>hrf</code>. This function assumes branch lengths are <strong>in coalescent units</strong> (e.g., calculated in MP-EST). The call below will assume the default population-wide mutation rate (0.01).</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">tomato_hrf <-<span class="st"> </span><span class="kw">tree_hrf</span>(tomato_branches)
tomato_hrf
<span class="co">#> # A tibble: 36 x 8</span>
<span class="co">#> code from to this_branch descendants ancestor sibling hrf</span>
<span class="co">#> <chr> <int> <int> <dbl> <list> <dbl> <dbl> <dbl></span>
<span class="co">#> 1 20-21 20 21 1.40 <dbl [2]> NA 4.59 NaN </span>
<span class="co">#> 2 21-22 21 22 1.38 <dbl [2]> 1.40 0.596 0.473 </span>
<span class="co">#> 3 22-23 22 23 1.56 <dbl [2]> 1.38 0.376 0.241 </span>
<span class="co">#> 4 23-24 23 24 4.42 <dbl [2]> 1.56 2.76 0.0341</span>
<span class="co">#> 5 24-25 24 25 0.525 <dbl [2]> 4.42 0.355 0.685 </span>
<span class="co">#> 6 25-26 25 26 0.616 <dbl [2]> 0.525 1.63 0.624 </span>
<span class="co">#> 7 26-27 26 27 1.07 <dbl [2]> 0.616 1.00 0.561 </span>
<span class="co">#> 8 27-1 27 1 0.612 <dbl [0]> 1.07 1.00 NA </span>
<span class="co">#> 9 27-2 27 2 1.00 <dbl [0]> 1.07 0.612 NA </span>
<span class="co">#> 10 26-3 26 3 1.00 <dbl [0]> 0.616 1.07 NA </span>
<span class="co">#> # ... with 26 more rows</span></code></pre></div>
<p>Some <code>NA</code> values in the <code>hrf</code> column are normal: the function does not calculate HRF for tips or ancestral branches. This is because the HRF is a property of a branch that has: 1) two descendant lineages, 2) a sister lineage, and 3) an ancestral branch with known length.</p>
<p>That's it. Now we can explore/plot the HRF of all branches in the phylogeny. For example, we can use the <code>ggtree</code> package to plot the tree. The <code>to_treedata()</code> function converts our HRF tibble and <code>phylo</code> tree into a <code>ggtree</code>-compatible object (which allows for easy plotting).</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(ggtree)
solgg <-<span class="st"> </span><span class="kw">to_treedata</span>(tomato, tomato_hrf<span class="op">%>%</span>
<span class="st"> </span><span class="kw">mutate</span>(<span class="dt">cathrf =</span> <span class="kw">cut</span>(hrf, <span class="dt">breaks=</span><span class="kw">c</span>(<span class="dv">0</span>, <span class="fl">0.2</span>, <span class="fl">0.5</span>, <span class="fl">0.8</span>, <span class="dv">1</span>))))
<span class="kw">ggtree</span>(solgg, <span class="kw">aes</span>(<span class="dt">color=</span>hrf), <span class="dt">size=</span><span class="dv">2</span>) <span class="op">+</span><span class="st"> </span>
<span class="st"> </span><span class="kw">geom_tiplab</span>(<span class="dt">color=</span><span class="st">'black'</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">scale_color_gradient2</span>(<span class="dt">limits=</span><span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>), <span class="dt">low=</span><span class="st">'#008080'</span>, <span class="dt">mid=</span><span class="st">'#f6edbd'</span>, <span class="dt">high=</span><span class="st">'#ca562c'</span>, <span class="dt">midpoint=</span><span class="fl">0.5</span>, <span class="dt">na.value =</span> <span class="st">'grey90'</span>)<span class="op">+</span>
<span class="st"> </span><span class="kw">theme</span>(<span class="dt">legend.position =</span> <span class="kw">c</span>(.<span class="dv">05</span>, .<span class="dv">85</span>))</code></pre></div>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAqAAAAHgCAYAAAB6jN80AAAEDWlDQ1BJQ0MgUHJvZmlsZQAAOI2NVV1oHFUUPrtzZyMkzlNsNIV0qD8NJQ2TVjShtLp/3d02bpZJNtoi6GT27s6Yyc44M7v9oU9FUHwx6psUxL+3gCAo9Q/bPrQvlQol2tQgKD60+INQ6Ium65k7M5lpurHeZe58853vnnvuuWfvBei5qliWkRQBFpquLRcy4nOHj4g9K5CEh6AXBqFXUR0rXalMAjZPC3e1W99Dwntf2dXd/p+tt0YdFSBxH2Kz5qgLiI8B8KdVy3YBevqRHz/qWh72Yui3MUDEL3q44WPXw3M+fo1pZuQs4tOIBVVTaoiXEI/MxfhGDPsxsNZfoE1q66ro5aJim3XdoLFw72H+n23BaIXzbcOnz5mfPoTvYVz7KzUl5+FRxEuqkp9G/Ajia219thzg25abkRE/BpDc3pqvphHvRFys2weqvp+krbWKIX7nhDbzLOItiM8358pTwdirqpPFnMF2xLc1WvLyOwTAibpbmvHHcvttU57y5+XqNZrLe3lE/Pq8eUj2fXKfOe3pfOjzhJYtB/yll5SDFcSDiH+hRkH25+L+sdxKEAMZahrlSX8ukqMOWy/jXW2m6M9LDBc31B9LFuv6gVKg/0Szi3KAr1kGq1GMjU/aLbnq6/lRxc4XfJ98hTargX++DbMJBSiYMIe9Ck1YAxFkKEAG3xbYaKmDDgYyFK0UGYpfoWYXG+fAPPI6tJnNwb7ClP7IyF+D+bjOtCpkhz6CFrIa/I6sFtNl8auFXGMTP34sNwI/JhkgEtmDz14ySfaRcTIBInmKPE32kxyyE2Tv+thKbEVePDfW/byMM1Kmm0XdObS7oGD/MypMXFPXrCwOtoYjyyn7BV29/MZfsVzpLDdRtuIZnbpXzvlf+ev8MvYr/Gqk4H/kV/G3csdazLuyTMPsbFhzd1UabQbjFvDRmcWJxR3zcfHkVw9GfpbJmeev9F08WW8uDkaslwX6avlWGU6NRKz0g/SHtCy9J30o/ca9zX3Kfc19zn3BXQKRO8ud477hLnAfc1/G9mrzGlrfexZ5GLdn6ZZrrEohI2wVHhZywjbhUWEy8icMCGNCUdiBlq3r+xafL549HQ5jH+an+1y+LlYBifuxAvRN/lVVVOlwlCkdVm9NOL5BE4wkQ2SMlDZU97hX86EilU/lUmkQUztTE6mx1EEPh7OmdqBtAvv8HdWpbrJS6tJj3n0CWdM6busNzRV3S9KTYhqvNiqWmuroiKgYhshMjmhTh9ptWhsF7970j/SbMrsPE1suR5z7DMC+P/Hs+y7ijrQAlhyAgccjbhjPygfeBTjzhNqy28EdkUh8C+DU9+z2v/oyeH791OncxHOs5y2AtTc7nb/f73TWPkD/qwBnjX8BoJ98VVBg/m8AAEAASURBVHgB7N0HfFRV2vjxZ9ITSAIkdAQpAoIUWQRREEFdEAVBQVCwgKKgixVULLt2EUX56Pqi2BZFRUVEEVeKCwpKUQRRioDSq6GFhPTJf57jf4aZZNLvJFN+530vc+fWc743bp6cc885tnxHEhICCCCAAAIIIIAAApUkEFZJ9+E2CCCAAAIIIIAAAggYAQJQfhAQQAABBBBAAAEEKlWAALRSubkZAggggAACCCCAAAEoPwMIIIAAAggggAAClSpAAFqp3NwMAQQQQAABBBBAgACUnwEEEEAAAQQQQACBShUgAK1Ubm6GAAIIIIAAAgggQADKzwACCCCAAAIIIIBApQoQgFYqNzdDAAEEEEAAAQQQsCQAzc3Nlccee0x27NhRJtHMzEx59tln5brrrpPPPvusTOdyMAIIIIAAAggggEBgClgWgD766KOyffv2Mik8/vjjMmnSJKlZs6ZZynQyByOAAAIIIIAAAggEpEBEVeZ6/fr1MmjQIHnppZeqMhvcGwEEEEAAAQQQQKASBSwNQI8fPy733Xef/Pzzz9K2bVuzXq9ePcnKypJ//OMfcsstt5gaz+bNm0tERISsW7fO1HyOHj1aXnnlFYmKiqrEonMrBBBAAAEEEEAAgaoQsKQJ3pnxG264QXJycqRv374yf/58ueyyy8wu3fbGG2/ItddeK9HR0XLs2DHp0KGDJCYmigaoXbp0kfDwcOdl+EQAAQQQQAABBBAIYgFLa0Bvu+02eeaZZwzXaaedJkOGDJHU1FQJC/srzh08eLBrvx701ltvmZpSrQElIYAAAggggAACCISGgKU1oOeee65L7W9/+5tZ37dvn2tb165dXeusIIAAAggggAACCISmgKUBaEJCgkvRZrOZ9fz8fNe2pKQk1zorCCCAAAIIIIAAAqEpYGkAGpqElBoBBBBAAAEEEECgLAIEoGXR4lgEEEAAAQQQQACBCgsQgFaYkAsggAACCCCAAAIIlEXA5nhH89RLmmU5k2MRQAABBBBAAAEEECiHADWg5UDjFAQQQAABBBBAAIHyCxCAlt+OMxFAAAEEEEAAgYAXePnll+XDDz+0pBzp6emyatWqEq9FAFoiEQcggAACCCCAAALBK/Dll1/K8uXLLSmgTjI0dOjQEq9l6UxIJd6NAxBAAAEEEEAAAT8V0KnCMzIyRMcyj4yMNJ9+mtUSs6WzUFavXl0iIion1JszZ45899138uqrr0rt2rVLzF/l5KrEbHAAAggggAACCCBQdQIHDhyQzMxMVwbc110bA2zl+PHjUq9ePYmOjpbNmzfLAw88IL/++qvozJRaSzlgwABXibRP+osvvigaSNrtdrn++uvl1ltvde3XZvXnnntOtm3bJh07dpR7771X2rVr59r/0UcfmenXGzRoIDk5Oa7tRa3QBF+UDNsRQAABBBBAICQEsrOzPYLPYCm0BpVHjx6V3bt3yznnnCNRUVHy/PPPS61atWTgwIGyZMkSV1Fnzpwp8+bNk5EjR0qjRo1kzJgxsmzZMrN/6dKlcuGFF5rzH3roIfN5/vnny9q1a13nz5o1S7Qpf/jw4a5txa0ETQ2oRvnffvut9O/fv8jy/vTTT7Jp0ybp3bu31K9f33Wc/pWzaNEi0erqSy65xMC6drKCAAIIIIAAAkEtoAFosKa8vDx5+umnRWsm33//fdMkr8GnBqUaWPbq1csUXfdrLBQeHi6jRo2SFStWmM5EPXr0kPHjx0u/fv3M+XrwkCFDTE3oSy+9JG+//Xa56CwJQPfMfVfyc0uubi1PDhv2v1bComOKPfXkyZMybNgwg1ZUADpu3DhZuXKlqTZWSEVv1aqVaG+ts88+W7p16ya///67TJ06VRYuXBjQ730Ui8VOBBBAAAEEEPAQqKz3JD1uWklfYmNjZc2aNSbOcS/n3LlzPXLQpUsXE0c5N2ot6L59+8w7sVqB16xZM5k8ebJzt/n8+eefPb6X5YslAejvbzwvuSfTynLfUh9b96IBElVMAKrvMgwaNEiSk5MlKSnJ63W11lOhd+7caWo5X3jhBYP45ptviq737dtXNIrXpIHoggULzDavF2MjAggggAACCASVgHY6CsYUFxcnNWrUkJSUFPMuaHFljI+P99jtNDly5IhoU762FmtA6kzt27c3sZfze1k/LQlAy3pTK48/ceKEzJgxQ/bv319kNfAvv/wi3bt3N8Gn3lurmzX41KTRu/v7CrpPa0o1KCUhgAACCCCAQOgKJCQkSMHALFA09LVCbU7XpLWXGtu4pwkTJsjpp58ut99+u/vmQuvaNK+1qB06dJAnnnjCtV/fH9URA8qbLAlATxtyk+P+p2b0TN++RQ59+1WZ81Sz47lSo0OXMp2nNZaaPvnkkyLP27Fjh0eUri/fam83TbrPveZU92kPLxICCCCAAAIIhLaABnE6HFOgp5tvvlluuOEGef31182ndhaaMmWK6XRUUtm0JlQ7Jr333numn4x2Ppo/f77ceOON8swzz5R0epH7LQlA98x+s1ATfHlqs4/9vFJ0cU+NBpSuN5X7OQXX9Z2H3Nxc12YdHkDHxtKkP1hF7XOdwAoCCCCAAAIIIBCgAjrkkrYGa8927ROjtZraMemyyy4rVYk00NTm9549e5oaYY2j7r77brnllltKdb63gywJQG2OKl5d/DU1bNjQNZSA5lFrP7XaWZM+BGdtqH7X9ZYtW+oqCQEEEEAAAQQQCHgBrcV86qmnZOLEiSaQLBjn/Pe//y1URh1U3pn0VYRPP/1Udu3aZRbtxF3UYPOPPvqo6FJSsmQc0LCIMAmLCPfJUt7XgrV3uw66qkmHVtLhBLZu3WoGR33jjTekT58+Zp8ORaDvkGpPeo3utVrZOSSBOYB/EEAAAQQQQACBIBDQ1t+CwWdZitW4cWPTp6ao4LMs17KkBjQ8KkLy8yy5VOG8l6ct33EVDThHjBhhajT1vU6N/Dt37ix169aVM888U/TlW006fNPnn39uHoi+rHvPPfdImzZtzD7+QQABBBBAAAEEELBewOboWn+q91A5r79yeDfJzUgv59nFn9b1rSUSWcP78ErFn1l4rw40qz22EhMTC+3U+V8rc87UQhlgAwIIIIAAAgEiYM/NlPSdX0le5uG/chyu86b776t4JbHm2qrLiagOhQ7TIYx0IVkvYEm1pVZSlrOi0voSFXNFnYJKF2+JHzBvKmxDAAEEEECgsEDa9s/Enp16akdelttYOKc2B8pafpj3cMieF7wzJFX1s/EuXtZcOYYpsDkWEgIIIIAAAggEt4DWfnoEn0FQXLstxmspsk46guykOl73sbFiApYEoLYwmyMALW93oRIK4KPLlnBXdiOAAAIIIICAF4F8e56XrYG+qYi3EQOheTdA6S0JQCNiosSW75u54B2hbYDSkm0EEEAAAQSCT8AWFrjvehb1NMLys7zuio4r3GfE64FsLLOAJQEoNaBlducEBBBAAAEEgkrAFh4tYZGe84kHSgHtEuc1q2FFvBvq9WA2lknAmgDUUUXtnLS+THfnYAQQQAABBBAICoHI+NMlruEFAVmWrKwsSd2/PyDzHqiZtigApRNSoP4AkG8EEEAAAQQQQKCyBSwJQM1rmryqWdnPjvshgAACCCCAAAIBKWDJ2ElhUZES5hhf0xeLY4TRgIQl0wgggAACCCCAQFUJ2O12M7vjb7/9VlVZKPa+ltSAhkc6LuOzqTiLzT87EUAAAQQQQAABBAoI6ESXL774ovTp00datWpVYG/Vf7UkABUdhJ6B6Kv+aZIDBBBAAAEEELBMIDc3VzIzMy27XkkXCg8Pl8jIyJIOC4r9lgSgPh2GKSiYKQQCCCCAAAIIBJpAWlqa6FKZqVq1apKcnGxGF9Lm88cee0z27NkjvXv3lgsuuEAWLlwokyZNMlk6fPiwTJs2TRYtWiRa49m9e3cZPXq0NG3atDKzXK57WfIOqJkI3jkhvNWf5SoWJyGAAAIIIIAAAqUT0Pcl/SWlp6dLamqq7Nq1S7p06SIZGRly3XXXyfLly+XKK6+UOXPmuLKq2z/++GMZOXKkjBs3ThYvXiwDBw507ffnFWtqQH05Dih9kPz554e8IYAAAgggEPACeXn+Nb2ojkv6zDPPSIsWLWT27NmiTfNas6kB6bFjx1ze9erVkyeffFI6depktulxV111lfhbeVwZdluxJADVXvD5+b55Z4GpON2eFqsIIIAAAgggYLlAdHS05desyAUjIiJkzZo10qNHDxN8Oq/Vt29fmTVrlvOrvPXWW7J27Vp59tlnZceOHTJ//nzXPn9fsaQJ3hbuGIjeEXX7YvF3QPKHAAIIIIAAAoEtoB1/4uK8T8dZ2SXTvCQmJpqazpo1a3rcXms83VO/fv3k0ksvFX1XVGtL7777bvfdfr1uSQ2oLSJcwvLCfVNQmuB948pVEUAAAQSCQiBjzw+Sm3pAwmNrOsbjrubzMuXbc3x+j6q4QZ06dUyHI30Hs6p6o+t9NRAOc4ws1KRJE/Pep7vFjz/+6Pq6atUq+eqrr0S3OZvg3377bdd+f1+xJAB1dUKqotLud8zf+vXXX0ubNm1cD8E9K1otvXHjRvdNpneZ/tWg6ZtvvjEv+ToPOPvss6Vu3brOr3wigAACCCDglwJHvv8/sWeeeiewUjLp6PcRUSe50K20F3agp+rVq4su/pCGDx8uY8aMMc3sQ4YMMc3r7777rquHe5RjAiA1105KmjZt2iSTJ0826zp8lDbj+3OyJHc2X3ZCKmEmpKVLl8rQoUNFH9SECRPkn//8p4wdO9bD/Oeff5Y33njDtW379u2SkpIiBw4ckJycHNEqbB3ewJkmTpxIAOrE4BMBBBBAwC8F0v/4pvKDT4dEUWFm1slj4vv6V798FD7J1A033CAar9x1111yyy23SIcOHcy6DsOkSSvLbrzxRunVq5doU31sbKz8+9//Nseed955snr1ap/ky6qL2hzRc1E/S6W+xx9TR4k9668IvNQnlfLApv94VcKrJRZ5dPv27eWVV14xL+rqkAWdO3eW3bt3S1EvFOuAslpVrS/s9u/fXzQ41Ye8bt26Iu/BDgQQQAABBPxN4Pi6DyTnyPZKz1Z+eJREJhf+vZwbXluSWwfGEECVjlaOG2pPeE1a06mxiwaYjz76qGzbtk1mzpzpuuKff/5p3hc944wzzDY9T8cHbdCggesYf1yxphOSo5rX5piO0xdLcRWgWsW8detWM/Cq4jZu3FgSEhLMwykKW2tIzz//fBN86jEaeOqLu1qt/dprr1X6gLNF5ZPtCCCAAAIIFCcQFhVf3G7f7cu3SZ6tcF1nfmSS7+4ZglfW8T01Ptm3b58JPnUw+v/85z/SrVs3D43atWuLM/jUHVoB5+/Bp+bTkib4Gp0uMe8h6AU15RzdLxk7fv7rSxn+ja5/hkTXa17gjKJ7IWlNp/YU01cAnCkpKUkOHjwobdu2dW5yfepfBFpbunnzZtc2Hb7AOdTBhg0b5OGHH5b169dL/fr1XcewggACCCCAgL8JhMfWqLIsnYw+S6plrZOw/L9q6bIi6kt4Qusqy08w3lhfLdQxQJs3b25eC9TXBnXA+dtuuy0oimtJAJq2+Xux55yaKzXf7hjQ1S0oLK1U1qHtkp2yy+PwxLP7enx3/6Iv2GotqHvSdzp1Gitv6Z133pE+ffrIaaed5tqtA7g+8cQTEh//11+S+jLvjBkz5IEHHnAdwwoCCCCAAAKBIlCtxSUSHuc5fI+Vec9zvLiXnh4hqbHnS4T9uNhtUWIPc3TeKcfvfSvzFWzX0sq1uXPnOqzTzTBLZ555pqkJDZZyWhKAOqJPkbxTwzKY+sjy/CDmO6bCyvOcDqu4y+h4WDpdlb4bERMTY56J/oVQ1ByoOjzB888/7/Hs9F0Krap2BqCtW7c2g7l6HMQXBBBAAAEEAkQgsuZpEhHvOV6klVk3s+yk73ZUNIVLbngtKy/NtbwIaKWac5glL7sDdpMl74A6BqwSny3F0OpgrTorwPTp081R+peCDp+kY3npXwzuTe1as6lDMRV8d+LTTz911XaeOHFCPvzwQxk8eHAxd2UXAggggAACCCCAQEUELAlAbY4A1FdLSYXTMa9eeukladWqlTz44INmvCw9Z8WKFXLhhRe6TtdZAho1auSq6XTuuPPOO+X48eNmOINmzZqZ4Qzch2RyHscnAggggAACCCCAgDUCljTBR8RGiz2iwqM5eS9RcW3wjjO0yVyb0XVcz+TkUwPjXnzxxWacT+dFO3bs6LVpvVatWvLJJ5+Y3u/6TqmzKd95Hp8IIIAAAggggAAC1gpYEoA6az+tzVrZruYefJbtzL+O9peZD8qTd85BAAEEEEAAAQQCScCSALSqp+IMJHDyigACCCCAAAIIhLqANQGosxNSqGtSfgQQQAABBBBAAIESBSwJQG1hNkcnpFODwZd4Vw5AAAEEEEAAAQQQCFkBSwJQ0eBTa0F9kUrohOSLW3JNBBBAAAEEEEAAAd8JWBKAhsXEOib19FUA6rvCc2UEEEAAAQQQQKAsAi+//LIZb3zo0KFlOa3QsTqRzk8//WTmbm/Xrp2EWmdoa6JG5zugvvgUmvYL/dSyAQEEEEAAAQSqRODLL7+U5cuXV+jeU6dOlRo1asigQYOke/fuouOQf/311xW6ZqCdbEkNqC3cMRB9vjWxbEFAws+CInxHAAEEEEDA/wTS0tLk5MmT/pexUuQozFGBplNealCoc7D7Mq1bt07uvvtueeedd2TEiBGyd+9eue6668yyY8cOiYqK8uXt/eba1kSN+rB8tfgNFRlBAAEEEEAAgeIE7Ha7BOKSm5trZkU8evSoKZ5O333PPfdI27ZtzQyJL7zwgkdwnZ+fLy+++KL06NFDzj//fHnttdc8WFatWmWm9dZJcG688Ub55ZdfXPuXLVtmajw16NRgV2dpHDdunOzfv182bdrkOi7YVwhAg/0JUz4EEEAAAQQsFNAAM1jTiRMnTNEGDBgg8+fPN1N86/pzzz0nEyZMcBV75syZMm/ePBk5cqQJIMeMGSMaWGpaunSpXHjhhaYm86GHHjKfGqSuXbvW7D/33HNl+vTpZt35z8aNG81qnTp1nJuC/tOaJvjoKAkL95GVj6vCfZRrLosAAgggEMIC6X+sktQ1n4rk5fhMISwuVsKrx/ns+kVdODzcV7/wi7pj5W3XGsklS5bI4sWLZc2aNdKpUydz8/j4eJk2bZorIw0aNJBFixaJWowaNUpWrFghWuupNaLjx4+Xfv36yfvvv2+OHzJkiJky/KWXXpK3335bzjnnHNd1dOWzzz6TKVOmmOvUr1/fY18wf7EmADU/jMH7AxnMPwCUDQEEEEDAWoGc4wcldfVH1l7Uy9XyI6K9bBXTBO51h0Ub9X1JfU8xOzvboiv6z2USExPlxx9/NO+Dnn322a6M3XzzzaKLM3Xp0sUEn87v2oy+b98+0aZ77dmunYomT57s3G0+f/75Z4/vu3fvNrWqc+fOlccee8yjhtXjwCD9Yk0AGuG4jM1HVfK+fRc4SB8rxUIAAQQQqCqB9N++rZRb58fWFMlPLXSv7LQjEpXYoNB2KzfUq1dPUlJSJDMz01xWawI1MA3UpDWf2glJazq1XHXr1i22M5Ie556cHZeOHDki+n6oumhA6kzt27eX5ORk51eZM2eOab4/77zzRDsltW7d2rUvVFYsCUBdHZBCRY1yIoAAAgggUISAMxgpYrdlm/PDHL2l8wpfzhadWHijxVs02AzW9xW19vKPP/6QQ4cOucqo73u+9957MmvWrGIltWk+NjZWOnToIE888YTrWG3W19pRTevXr5drrrlGHn/8cbn//vtdx4TaiiV/rjin4vTFp6NqNdSeCeVFAAEEEAhggYjEepWS+zxbdbFHeNbE5cS3kIj40OnI4gvowYMHizbF33fffXLgwAHZunWrCRRjYmJKvJ3+8aEdkzRY/fbbbyUvL08+//xzueqqq0Sb3DV99NFH0rhxY/O+6MqVK8V9CdRhrEqE8XKANTWgvAPqhZZNCCCAAAIhKVBE59nIWk0kLKa6dSQJ9eRkfGeJOrZRwnLTJDe2ruQ6AlBSxQSSkpLkk08+kWHDhskHH3wgGnhqpyIdiqk06ZlnnjHN7z179jRN+jk5OWbcz1tuucWcrr3lt23bZoZvKng9fX/U/d3TgvuD6bvN8a5CfkULlLrlXcn3UU+/hJbXiC3cMdUnCQEEEEAAgQAQSN/6naMH/JxCOa3Vc7RE17fuXb9jx46JLgWT9qSOjvbeQangsXwvWkBrL7X2s2nTpuXy3LVrl+jSqlUrqV27dtE3CtE9ltSA2qIcP+h2S1rzvTwGmuC9oLAJAQQQQAABBHwooB2rKtI5SJvZdSF5F7AkAK3qTkg6e4DOodqmTRvXmF0Fi/vbb7/J9u3bXZu1B5/OUKBJe6vpeF76UvUll1wSMtNguTBYQQABBBBAAAEEKlHAkgBUOx/5rLNQCRWgOuPA0KFDZfjw4WYMrX/+858yduzYQoSPPPKIqQp3VoPrYLEagKanp5v3Lbp16ya///67TJ06VRYuXFjs8AuFLs4GBBBAAAEEEEAAgVILWBKA2h091fOrqLf6HXfcIbNnzza9ye666y7p3LmzmU2g4PsvOs7WF198IS1btvTA0ZeK+/btKzpDgSYNRBcsWGC2eRzIFwQQQAABBBBAAAFLBKx5cTPMMTSBdhRyLrYoE5BqUFqmxRZ56hrOaxVTzNzcXPOCcPfu3c1R+q5FQkKC6V3mflpaWpocPHhQ9uzZI5MmTfLYrzMT9OrVy3W4ruuQCCQEEEAAAQQQQAAB3whYEoCGx9WTiLiGrsUWU8vRJ8lW5sUWleC6hvN6xRVbx9TSsbrcB/3V4RM02HRPOuirjq2lTevaq+3iiy+Wt956yxyyY8cO0XOcqVatWmbcL+d3PhFAAAEEEEAAAQSsFbCkCT4jY49j7tkcz5zZyh7b5uYelyzH4p5ia7QrsnE/wjEFqNaCuicdb0un03JPOmfr3r17XTMa6JRYjz76qGmqj4yM9LiGnl+9uoXjtLlnhHUEEEAAAQQQQAABKXuU6AWtTM3sZWyW93I71ybtyZ6amuqai1Z36KwFOmaXe9LptHRxJh1WQcfmstvtotNm6TnO5O185z4+EUAAAQQQQAABBCouYEkAmucYyt5XS3FF1NpL7UA0ffp0c9jcuXOlbt26pqZTe7dv3rzZbD98+LAZXkm36bj7b7zxhlx55ZVm2KWBAwfKjBkzTBP9vn37ZP78+R7vhBZ3f/YhgAACCCCAAAIIlF3AkiZ4DeosmFCp7Ll3nDF58mS5/PLL5ZVXXhEdNFbnX9W0YsUKGTFihKndbNeundx+++3StWtXyc7ONu98fvzxx+Y4nWpL52nV3vF6/j333GPGEzU7+QcBBBBAAAEEEEDAcgFLpuLcs3tu4XdALcpqo9P6O2oqHb3sS0gpKSmSnJxc7FHa5K7TlmlHo4JJt+u7n/peKQkBBBBAAIHyCjAVZ3nlOC+UBCyJttIycx29yz07A1mFaHc075fmPYGSgk/Nj8505C341H01atTQDxICCCCAAAIIhLjA22+/LXFxcWaimxCn8FnxSxPblXjzPEcTvK+WEm/OAQgggAACCCCAgIUC8+bNM1N0W3hJLlVAwJIa0DxHNaUuPkk+uqxP8spFEUAAAQQQqGKB48ePmz4NVZyNgLu9dmyOj4/3GFs84AoRQBm2JACtyk5IAWRNVhFAAAEEELBMoKjOvzrxCql8AjpzYv369V0n6+g5w4cPl7Fjx0qfPn1c25966inTqfmxxx6TjIwMeeihh8w03nXq1JH+/fvLmDFjTBO+6wRWCglY0gSvlZ++WgrlmA0IIIAAAgggIDpxCslaAR0pR4NOZ9KJbbSTsnO4R92elZVlRuDRYFPTgAEDzBCODz74oFl/7rnnZMKECWYf/xQtYEkNaEZOnuQ6prj0RaIF3heqXBMBBBBAINAFiqoBDfRyVXX+dcpu96RDOt5xxx0mMNWAdMGCBWbs8KFDh8qSJUtk8eLFsmbNGunUqZM5TZvxp02b5n4J1r0IWFIDmu2o/vTV4hhh1Eu22YQAAggggEBoCzBttG+ef2xsrMeFBw8ebGZO1IlqNM2ePds0x+voOz/++KOZ/vvss892nXPzzTebgNS1gRWvApYEoDmOaZB8tRB/en1ubEQAAQQQCHEBrY3T2jaSNQI6VGPt2rUlKirK44I6TKNOeKOBpzbR6+Q11113nTlGxyDXGRhtNpvHOXwpWcCSJng6IZUMzREIIIAAAghYLZCUlCQ1a9aU3NxcM9a11dcPletpAKkBaFGBpDbD66JTfmvMc8UVVxiaZs2ayR9//CGHDh0y04DrRh3CSWdlnDVrVqjwlauclgSgzg5I5cpBCSfRAF8CELsRKIfAZz+tkT1Hj0iz2nUkitm/yiHIKQgULVDz8H7RftR2x7uE+Y4lzPHfmM0R3PgqaeBUsNbOV/cK1ev269fPGOt03UOGDJGYmL9maNTm+fvvv1/uu+8+mTRpkpw4ccJ879KlS6hSlbrclgSgOgh9rmOaSxICCPi3QKaj+ejCSU9JStoJ/84ouUMggAUGOmaFvjM5U3JPZrhKERlfzbXOSuAJaIB/9dVXy2uvvSY33XSTqwBaA/3JJ5/IsGHD5IMPPjCBqQarL7zwgusYVrwLWBKAZufaJcex+CJRA+oLVa4ZqgJ3fTCT4DNUHz7lrjSBJFuuR/CpN845kS7Hjx2ROqeGmKy0/HCjsgvMmTOn0ElNmzaVdu3aSbdu3Tz2XXTRRXLgwAHZunWr6DHR0dEe+/niXcCSAFSDT18FoHRC8v7g2IpAeQQ27N1TntM4BwEEyiBQJ8xzGB/nqQf375Q6Z57n/MpngAhkZmaawea19lMHnPeWwsPDpXXr1t52sa0IAUteStHmd18tReSbzQggUA6BavxlXg41TkGgbAIpRYwPXyupXtkuxNF+IfD888+bnu7nnnuu3HDDDX6Rp2DIhCUBqLMTki8+aYIPhh8zyuAvAqcn1faXrJAPBIJW4EC296LVrOF4OZQUcAJ33XWXaWJ///33JYJOm5Y9P0ua4O2OyDNPo0+fJF9d1yeZ5aII+LVAWJj3seqeumqIhNks+XvUr8tP5hCoDIHaBzeI7FxWGbfiHpUgwID/vkG2JADVXvC6kBBAIDAFBp/TVcJ9OExMYKqQawTKJ5D6S7ocJgAtHx5nhYyAJQFoTq5jJiTH4otUmrh2//798vXXX0ubNm1cc7F6y8v69etly5Ytcumll5qps5zHfPPNN+YFY+d3nVJLZzYgIYAAAggggAACCFgvYEmbW0aeXTIcPeF9sZQU1i5dulQ6duwoP/30k1x22WUybdo0r0p9+vSRiRMnmnlbO3ToIAsXLjTH5eTkiI7Z9corr7iW33//3es12IgAAggggAACCCBQcQFLakC1ltJnr4CWUMY77rjDzM/ao0cP0ReFO3fuLKNGjfIYh2vFihWyd+9e+fXXX83V9JgpU6bI3//+d9m4caOcccYZZuqsEm7FbgQQQAABBBBAAAELBCypAdVOSL5aiiujzn2rA792797dHNa4cWNJSEiQbdu2eZzWtWtXWbVqlWtbSkqKpKenm+/r1q2TFi1ayLvvvmtmOEhLS3MdxwoCCCCAAAIIIICA9QKW1ICe06KTR87+TE2RzXs8g0CPA4r40qR2I2nsWDxSMW3wu3fvlsTERLHZTvXs1WmxDh48KG3btnVdRufJrVbtr2nQ9uzZI08//bRMnz7d7F+7dq2sWbNGtAZ1w4YN8vDDD4u+K1q/PtNVuABZQQABBBBAAAEELBSwJABd8dsaycopYuCzMmT2j4O7RRf31Kl5e/evHus6HpfWgronfafTGWy6b9d1bW6//PLL5V//+pf07dvX7H7yySfliSeekPj4ePM9IyNDZsyYIQ888ID5zj8IIIAAAggggAAC1gpYEoCm5eRKpiPw80XKL2Yuznr16klqaqroNFkxMTHm9jofq87FWjD98MMPMnDgQHn55ZflyiuvdO3W5voGDRq4AlCdSmvHjh2u/awggAACCCCAgLUCdscMiuPHj5dbb71VWrVqVeGLa+WRvlKnv8+bNGlS4etxAd8LWPIOqA5C76ulmBZ4iYyMNDWZzub0uXPnmuGT6tSpY97x3Lx5sxHct2+fqfnUWQzcg0/d+emnn7pqO0+cOCEffvihDB482Pfy3AEBBBBAAIEQFch39F5+8cUXLanw0d/9NWvWlIsvvlhatmxpXsH75JNPQlQ2cIptSQ2o4w8ZRyckHxW6uAjUccvJkyeb4FKHUQoPD5f33nvPZER7vo8YMcJMnzV16lQ5dOiQ9O7d25VJHedTA9M777xTRo8eLTr2p74feu2113oc5zqBFQQQQAABBCpZQGsKtdOsBmz62pl7n4dKzoolt4uOjhbtl2FV0prPYcOGmf4bDz74oGkVHTlypOiirZ4aF5D8U8CaANRRNl/FnyWxaZO5NqNrz/bk5FPz7OpfQtocr0mDVF28pVq1aon+paS93/U/bmdTvrdj2YYAAggggEBlCWRnZ4tOtKLBZ7AkDT71d7UGos60aNEi+fe//20qkJzTXmZlZZnAcuzYsWbIRG3R1L4ZOpyijmwzdOhQGTBggBnhJi8vT+655x4T2NaoUUP0HK0VPXLkiNSuXdt5Gz79TMCSP0P0Pw5fLaX1cg8+S3uO+3H6Q0/w6S7COgIIIIBAVQpoy10wBZ9qqTW6WmGkn8501llnyfz58+WLL75wbpIFCxaY8bnbtWsnOuLNOeecI1FRUfL888+LVhxp7eaSJUvk3HPPNZVNcXFx5lztiPzxxx+bMcEJPl2cfrliSQ1oZm6eoxNSnk8KGDx/9/mEh4sigAACCASpQMFRXoKlmBp8aqDoTDrs4UUXXWQmldHmdE0aROprc7pPazS1c5H249CWSg0+NSjVmRB79erlqjzSyWV0am0N2r/77jvn5fn0UwFLAtA8xzzwuT6aC95P3cgWAggggAACPhXQ9z2DrQZUwbRcGki6J+2zMWbMGDl58qR5b/Pzzz83o9boMTpWd7du3TzO0Sb2gumpp54yTfIffPCBmZpbp+hu1KjA2OIFT+J7lQlY0gTvqx7wet0gevWlyh4yN0YAAQQQCDwBKzvr+FPptQm9YOegQYMGmSx++eWXsnDhQjPGt3PUGm2y12EXvSXtTLxr1y6zS5vp//GPf8g777wjhw8fZoptb2B+tM3zT5ByZizPESXqQkIAAQQQQAABawS89XjXwE1nAAzEpOXRzkf6Lqd2HHJP2g9Dm9a16V37Y2hA6uyQ1KxZM1m5cqX74TJhwgQ5/fTTzTBOs2fPlu3bt7v267ufsbGxoj3kSf4rYEkA6uyA5L/FJGcIIIAAAggEvoDWiiYkJAR+QbyUYPjw4XL11VebpnYdk9uZbr75Zrnhhhvk9ddfN59aSzplyhRTw6nTbmvHJK311GZ8HTVAm+L1HdNLL73UeQk+/VDAkgA019FUrotvkq+u65vcclUEEEAAAQQQKLuAdiLSqbS1BvSSSy5xXUCHXPrll1/MO6Ljxo0zHZKefvpp856nHvT444/LqFGjzH6dGTEpKclMqX3mmWe6rsGK/wlYEoBm5dlFF18kwk9fqHJNBBBAAAEEqk5AXyUo2MFKOyZppyFtind//1Wb7rVWc+LEiWYCGZ3tyD098sgj5t1PHStUA1jdz7CK7kL+uW5JAJqTly/ZPuoFz6ul/vmDQ64QQAABBBCwSkBrLpcvXy6bNm0yY4J6u66+E1ow+HQep1Nxak95UuAIWBKA+rYJPnAwySkCCCCAAAIIlF1AZzfS2Qt1fviieryX/aqc4c8ClgSgdELy50dM3hBAAAEE/EHg+LqFkr7th1JnJa/xuSKRf83wU+qTAvTAr776yry7qT3kSaEhYEkAyjBMofHDQikRQAABBEoWKPhuo/OMzN2/OldL99mgs9giPQ+1556aQchzT2B/0xmPSKElYE0A6ugBr4PG+yL55qq+yCnXRAABBBBAQCTnyF5rGKJiC10nL0gD0EIFZUPQC1gSgOY6OiFpRySfJB9d1id55aIIIIAAAiEvkJ+Xa42Bo/d3oeRtW6GD2ICA/wtYEoBm5NolI9dzVgOriu6YjNOqS3EdBBBAAAEEfC4Qf1YvSdu0rOL30drOKM9f0zaGhqm4K1fwCwFL5oLXINFX/+cXSmQCAQQQQACBUgrE1G0qNc69SsRWwV+xOYWnkgyPiillLjgMAf8W8PzTqpx5ZRimcsJxGgIIIIBAUArU7Hy5JHbqJ3lpRyUssnw9u/enHJXcApO82BxTcZIQCAYBSwJQ7X/koz5INMAHw08ZZUAAAQRCUEBn8wlLSCp/yW3HHef6ZpbB8meKMxGwRsCSAFT7H/loIqRSlXL//v3y9ddfS5s2baRTp05FnvPTTz+ZWRZ69+4t7kM+6AwMixYtMlN/6fyzjENWJCE7EEAAAQQQQACBCgtYUpd/PCdXjmf7ZinpfeulS5dKx44dRYPLyy67TKZNm+YVZdy4cXLrrbeKHq9B6m+//WaOS09Pl/bt28vs2bPlmWeeMdcoagw3rxdmIwIIIIAAAggggECZBCwJQJ01oFoLavVSUh/4O+64wwSPL7zwgqxatUr+9a9/SVZWlgeCzi07d+5cs//111+XCRMmyOTJk80xel7fvn1lxowZZh7atLQ0WbBggcf5fEEAAQQQQACBigusXr1aHn744YpfiCsEvIAlTfADOnSUXPup91R2HT4s3/3+e5lx2jVsKGc5ltKm3Nxc2bp1q3Tv3t2c0rhxY0lISJBt27ZJ27ZtXZf55ZdfzDH6Po6mXr16yZtvvmnWf/75Zxk+fLhZd+5buXKlCUpdG1lBAAEEEEAAgQoL/O6IDbTF8cknn6zwtbhAYAtYEoCu+OMPycjOdkmkO9btJbWdu44+tbI9JUWOOJrES5t2794tiYmJYnMbmDcpKUkOHjzoEYDu2LFDkpOTXZetVauWHDhwwHzXfXqOM+k+DWBJCCCAAAII+JtATk6O7Ny506+yFRkZKfq7Myam5CGirrnmGtGFhIAlTfD7jx+X3UePupayBJHujyDV0RnI/Tq6XlyKiIgQrQV1T/ofZ7Vq1dw3ScHj9Jjq1aubY/Q/HPdruO/zuAhfEEAAAQQQqEQBu1vLovtttZ+CPy3ZjkonrfjR36X33XeffP7556aGs2vXrqKdfr/88ktX9pcsWSI33XST+Z6RkSEDBgyQ77//Xu666y4555xz5M4775Rjx47J1KlTpVu3bnLRRRfJf//7X9f5rASPgCU1oOc2a+aoAXXM2OCDFBkeXuRV69WrJ6mpqaK92J1/eWnNZtOmTT3Oaeho1l+27NSsFHrM6aefbo5p0KCBqzZUN+i+li1bmn38gwACCCCAQFUJFBWAVlV+iruvBsQnT540fSjeeOMN06H3/vvvNyPUXH755bJ48WITjG7fvl0+/fRT8xqcBqzz5s2TtWvXmkB08ODB8uyzz8qcOXNEf2/feOON5nqDBg2SQ4cOmVfsissD+wJLwJIAdPatY6qk1Fp7qR2Ipk+fLtoZSTsa1a1bV+rUqSPau12b6Fu3bi06tJL+VaXvi2rgqf9x9OnTx+R54MCBpgOSfupfXfPnzze95aukQNwUAQQQQACB/y+gr5cF0qgsztfhmjdvbn6var+LK6+8UjTonDRpkglAvT3ckSNHyuOPP252bdmyRd5++21ZsWKFNGrUyASy2r9D+3Kcf/753k5nW4AKWNIEX5Vl197sL730krRq1UoefPBBeeutt0x29If3wgsvNOv6bspTTz0lnTt3Nu+GHnU07WtPeE3Dhg0zf1VpradW9+twTTqeKAkBBBBAAIGqFNBOtYGS9FU35+tvPXr0MONqO/Pes2dP2bhxo/Nroc9zzz3XtU37a5x11lkm+NSNzv4bhx2dm0nBJWBJDWhVkmgNp3YaSnF0YHL+oGp+Lr74Yo+mdX3n5LrrrhN950Q7LjmT1qJ+/PHHpvZT3wvV/4hICCCAAAIIVLVAzZo1TSfbEydOmJpQ/f3kHM2lqvPmfn/9PVqjRg1X3rQl0j1pLW54Ma/TOftkOM9xBrLO73wGp0DQRFvuwWdRj0pnOCpqliP9j4cUeAInszJk+cbVkpWbLXUSkyQiPGh+pH3yMI6l69R+IlHhNgkTm2Q55pkuaaxdn2SEiyKAQKkE9HdToP1+0mZ096QzFWorJQkBdwF+W7trsB5QAvuPHpTXFrznGPLr1Bi0AVWAKsjsXkczVs2YCEcA+tfbNzpc2tFMz5EkqiBb3BIBBIJIYNasWTJ69Gjp0qWLfPDBB2aSl6JmKQyiYlOUMgoQgJYRjMP9R+DD5fMIPsv4OOyO6k5n8Kmnhjk6OSREFT3SRBkvz+EIIICA6Rx8xRVXmF7x+srA2LFjTY92aBBwFyAAdddgPaAEUjPSAiq/fpFZR41nwRQRZnNsKry94HF8RwABBEojoB1+tW/Fhg0b5IwzznANk6jnjho1yiy6Hh8fX6iXvw7D5J5iY2MLHeO+n/XAFQj4XvCBS0/OKyoQyfueZSaMiij8n/xfQ6doEEpCAAEErBHQms927dp5BJ/WXJmrBItA4d9GwVIyyhH0AtVjPGe8CvoCW1DA6lE0eljAyCUQQAABBCoowG+jCgJyetUJOAc9ds9BtZg4Gdjlr0kG3Lez/pfA0cWLJCV9BxwIIICATwR01sGiRpvxyQ25aMAKEIAG7KMj494EIsMjpVXD5t52sc0hEB/zPQ4IIICAzwQCafB8nyFw4VIJ0ARfKiYOQgABBBBAAAEEELBKgADUKkmugwACCCCAAAIIIFAqAQLQUjFxEAIIIIAAAggggIBVAgSgVklyHQQQQAABBBBAAIFSCRCAloqJgxBAAAEEEEAAAQSsEiAAtUqS6yCAAAIIIIAAAgiUSoAAtFRMHIQAAggggAACCCBglQABqFWSXAcBBBBAAAEEEECgVAIEoKVi4iAEEEAAAQQQQAABqwSYCckqSa6DAAIIhLiA3W6XlJQUyc7OlrCwMImIiBBvU+YGClN4eLjozD5aDhICCFgrwH9V1npyNQQQQCAkBTT43LNnj+inM2kgGugpLS1NGjRoYILQH374Qd555x3R+c6bNWsmPXv2lNtvv93s+/bbb2XGjBlyxx13yBNPPCFXX321WTZv3iwPPPCA/Prrr9K1a1cZOnSoDBgwINBZyD8CFRagCb7ChFwAAQQQQCA1NdUj+AwWEQ2ojx8/LgcPHpTevXubGt6nnnpK/v73v8vEiRNl0qRJpqh79+6VTz/9VC699FLJycmR5s2by+7du+Wcc86RqKgoef7556VWrVoycOBAWbJkSbDwUA4Eyi1ADWi56TgRAQQQQMApkJeX51wNuk8t24EDB2Tw4MHy5ptvmtcLtJDffPONrFu3zlXeo0ePyvvvvy/XXHON2TZ27FhTe6rbtBlfg08NSpcuXSq9evVynccKAqEoQAAaik+dMiOAAAIWCwTze5LVqlWTDh06yOuvvy6fffaZrF27VrZt2yZz5syRyy67zCUZHR0tgwYNcn1fs2aNdOvWzeMd0rlz57r2s4JAKAsQgIby06fsCCCAgEUC2uko2JJ2oKpRo4ZoALp161bzzme9evVM7eXFF19sOlu5v/OqAWhMTIyLQTtk6fEkBBAoLEAAWtiELQgggAACFgkkJydLXFycRVer3MtoAOrsxf/aa69JYmKirF692lWjOXv2bI+As2DutKPSypUrPTZPmDBBTj/9dNN5yWMHXxAIMYHg+5M1xB4gxUUAAQT8WUBrRgN1cQaf6qsdifRd0KysLPP5wQcfyP/+9z+zXpT/zTffLCtWrDBN9zoigDa/T5kyxQSgRZ3DdgRCRYAANFSeNOVEAAEEECi3wJgxYyQ2Nlbq1KljerO/99578vLLL8vChQvl6aef9npdHXJp/PjxoufqeKL33HOPOdb9vVGvJ7IRgRAQoAk+BB4yRUQAAQQQqJhA48aN5eeffxYd19MZhOoVtWe7vvcZHx/v6v3uvJPWoOqQTTpc0759+6Rly5bOXXwiEPICBKAh/yMAAAIIIIBAaQVat27tcWjt2rU9vnv7Ur16dYJPbzBsC2kBmuBD+vFTeAQQQAABBBBAoPIFqAGtfHPuiAACCPitQNrWbyXtt/+J2HMdebQ5/v//LyXkOLdGC5FGPUo4it0IIIDAXwIEoPwkIIAAAggYgaxDWyVt00I3jXyRfF3cNhW56r1BzZ6XU+QZ7EAAgdAV8P6/GKHrQckRQACBkBVI37a83GXPj6np9dzM1BSv29mIAAKhLUAAGtrPn9IjgAACbgKlqup0O/7Uan6+97ngbWE0tJ1SYg0BBJwCBKBOCT4RQACBEBeISKhbbgFb5lGv50bHJ3ndzkYEEAhtAf40De3nT+kRQAABl4AtLNK17r4SWbOx2CKi3DcVXo+tI97qQINxjvjChWcLAgiUVYAAtKxiHI8AAgiEmEBix4ESEV+n2FKfOHFCMg8fLvYYdiKAAAJOAZrgnRJ8IoAAAggggAACCFSKAAFopTBzEwQQQAABBBBAAAGnAAGoU4JPBBBAAAEEEEAAgUoRIACtFGZuggACCCCAAAIIIOAUoBOSU4JPBBBAAAHLBbKysiy/pr9c0OaYpjQ6Olro6e8vT4R8BJIAAWggPS3yigACCASYwPHjxwMsx2XLbkREhNStW1dyc3Nl6NCh8vTTT8trr70m3333nTRs2FD+9a9/SefOnV0X/b//+z/55JNPJD09XXr37i0PP/ywxMXFufZ//PHHosfs2LFD2rZtK48++qjH+a4DWUEgwAVogg/wB0j2EUAAAX8QyMvzNgqoP+TMt3nQwPOwY/gp/Zw3b5707dtXYmJi5LbbbpMNGzbIZZdd5srAXXfdZQLS7t27yx133CGLFi2Snj17itPurbfekuuvv14GDhwo06dPlyZNmki3bt1k3bp1rmuwgkCwCFADGixPknIggAACVSigAVioJn3NoFq1aqb4o0aNkscff9ysd+jQQbp06SI7d+6U7Oxs+fe//y0zZ86UYcOGmf0XX3yx1K9fXxYuXCh9+vSRBx980ASmd955p9l/ySWXyMaNG8315syZY7bxDwLBIkAAGixPknIggAACVSgQGxsraWlpVZiDqrt1VNSpWaLOP/98V0YaN25s1vfv3y/btm0Tu90uW7ZskcmTJ7uOqVmzpqnhPPPMM+XgwYPSq1cv1z5d0RpQbZYnIRBsAgSgwfZEKQ8CCCBQBQJaA5iamirB3OnIG2t4eLgkJSW5yq2BeMGUn58vKSkpprOSNtdr5yVnGjFihLRr18404+s2bXYvmPR8EgLBJkAAGmxPlPIgUA6BGcuWSJjbL8VyXIJTgkCgZcZOaVaBcmhzsnauycjIEO2co8FZMCft/a7ve2o5Swq8mzdvbt71vOmmm6R9+/YuljfffFNatmwpycnJZtu3334rWhvqTCtWrDD7nd/5RCBYBAhAg+VJUg4ESiGQ62gC9JbeXLrI22a2hZjAiAZh0qxuxfqmak2o833IEOMrtrgXXXSRqd188sknZcqUKVK9enV54YUXzPLbb79JrVq15PLLLxcNSPUd0cTERFm+fLloAEoTfLG07AxQAQLQAH1wZBuB8gjsPpxSntM4J0QEGibWdJS08LBJmY4ONNVDxMBXxdShljSQ1KGamjVrJpGRkWb4Jt3WqFEjc9tp06bJkCFDpE6dOlK7dm05cOCA6YDUv39/X2WL6yJQZQIEoFVGz40RqHyBrNycyr8pdwwYgWox+v5i4QD0mKNJnQC0+McYHx8vBd/V1PFB3bedc845phOS9mzPzMyUjh07insHJg1Ev//+e9NhSd8VPeuss0xNafF3Zi8CgSlAABqYz41cI1AugbObNJWv1q8t17mcFPwChyRB2soBj4Lao+IlufZpHtv4Un4BfTfW/R3QglfSDkpnnHGGWQru4zsCwSRQsZd9gkmCsiAQAgIPXTFEmiTXDoGSUsTyCPxpi5ecep0lX/7qpZ0fWU1yGvd2dFDjV0V5PDkHAQSKFqAGtGgb9iAQdALaa/f92++Vzfv2yN4jh6VejZr0fg+6p1z+AkXk2SXPni95tVqLLeek5MfUECH4LD8oZyKAQJECBKBF0rADgeAVaN2gkehCQsBd4OjRo2Lmbo+IkXzHQkIAAQR8JUC7iq9kuS4CCCCAAAIIIICAVwECUK8sbEQAAQQQQAABBBDwlQABqK9kuS4CCCCAAAIIIICAVwECUK8sbEQAAQQQQAABBBDwlQABqK9kuS4CCCCAAAIIIICAVwECUK8sbEQAAQQQQAABBBDwlQABqK9kuS4CCCCAAAIIIICAVwECUK8sbEQAAQQQQAABBBDwlQABqK9kuS4CCCCAAAIhKvD999/LfffdF6Klp9ilESAALY0SxyCAAAIIIIBAqQU2b94s77zzTqmP58DQE2AqztB75pQYAQQQKJPAvn37ynQ8BwevQHR0tCQlJUlUVFTwFpKSVYoANaCVwsxNEEAAAf8XyMvL8/9MksMqFcjKypJDhw6J3W43+Zg5c6Z0795dzjrrLBk/frxozad7+uabb2Tw4MHSvn17GTNmjJw8edLsXrx4sYwcOVJWrlwpV199tfTo0UNeffVVOXbsmIwePVo6duwow4YNkwMHDrhfjvUgEiAADaKHSVEQQACBigjk5ORU5HTODRGB3Nxc0UB0+vTpJojs37+/PPzww7J69Wr5+9//LpmZmUZCg8lbb71VOnfuLFdeeaXMmjVLHnjgAbNv165d8uGHH8pNN90kXbt2lRYtWsjYsWNNoKrXv+222+THH38054cIa8gVkyb4kHvkFBgBBBDwLhAeHu59B1sRKCCQn58vjzzyiNx7771y//33m70XXHCBdOvWTdavX2++a5D60UcfmaBSN5w4cUKWL19u9uk/GRkZJgjV2lNNn3zyiTRq1Ejefvtt8z0tLU2ef/55s84/wSdADWjwPVNKhAACCJRLoFatWuU6j5NCSyA2Nlb+/PNP0xSvTefO1KBBA9m5c6d06dLFbIqLi3MFn7rhtNNOE/f3iXW/M/jU/cnJydKvXz9dNUnfNT1y5IjzK59BJkANaJA9UIqDAAIIlFcgIiJCNIhISUkRbQbVGlFdbDZbeS/JeUEkoD8H2gkpISFB1qxZY0pWv379IksYHx9f5D7d4W1/tWrVij2HncEjQAAaPM+SkiCAAAIVFtDezRqEkhAoTqBZs2Zm94oVK6RTp05m/ejRo3LttdfK5MmTizuVfQgYAZrg+UFAAAEEEEAAgTIJ6OsagwYNkmnTpokGoampqTJx4kT54YcfTIeiMl2Mg0NSgAA0JB87hUYAAQQQQKBiAhp8aiB63nnnSb169WTDhg0ye/Zs0XdESQiUJGBz9GTLL+kg9iPgjwL//vI/cuh4ikfWalRLlHsGjPbYxhcEEEAAAd8J7N27V/T94bp16/ruJlw56AR4BzToHikFQgABBBBAoPIEGjZsWHk3405BI0ATfNA8SgqCAAIIIIAAAggEhgABaGA8J3KJAAIIIIAAAggEjQABaNA8SgqCAAIIIIAAAggEhgABaGA8J3KJAAIIIIAAAggEjQABaNA8SgqCAAIIIIAAAggEhgABaGA8J3KJAAIIIIAAAggEjQABaNA8SgqCAAIIIIAAAggEhgABaGA8J3KJAAIIIIAAAggEjQABaNA8SgqCAAIIIIAAAggEhgABaGA8J3KJAAIIIIAAAgjHhWQ4AAAx/UlEQVQEjQABaNA8SgqCgH8LvPzyy/Lhhx9WWiZXr14tJ06cqLT7cSMEEEAAgdILEICW3oojEUCgAgJffvmlLF++vAJXKP2pe/fulfPOO082b95c+pM4EgEEEECg0gQiKu1O3AgBBEoUyM7OlsOHD0tubq6Eh4dLRERg/ycaGRkpCQkJpiwlFt6CA9auXSuLFi2SN998U/Ly8iy4IpdAAAEEEPCFQGD/dvOFCNdEoIoENOjct2+f6+4aQGlAGugpPT1dGjRoYIqRn58vL774osyZM0fsdrtcf/31cuutt5p9//3vf+WDDz6Qd955x1Xk9957T9atWyfPPfec2abB+bRp00yQqdfq3r27jB49Wpo2bWr2f//997J06VKpW7eubNmyxXUdVhBAAAEE/EuAJnj/eh7kJoQFNLgKxqSBdVpaminazJkzZd68eTJy5Ehp1KiRjBkzRpYtW2b27dixQxYuXOhB8Ntvv7n2647rrrtOPv74Y3P+uHHjZPHixTJw4EDXObfffrtoU78GqSQEEEAAAf8VoAbUf59NkTnTmiObLb/I/aGzw83AURvmQAnoogdzk7H+zGrSmlBtItfXC0aNGiUrVqyQVatWSY8ePUr17OrVqydPPvmkdOrUyRyv17nqqqtMc7uukxBAAAEEAkOAADQwnpPJZW7OCTn857eOpsvMAMq177Kam31cOqUdkDYnD4vNEYBujkuSbXHVfXdDH19Z35cMhiZ3b0xxcXFmc5cuXTzeB9VaUPfXDryd677trbfeEn3P89lnnxWtMZ0/f777btYRQAABBAJEgCb4AHlQms3Df35D8On2vJql/ikd0v+UyHy7REi+nHUyRVoe3eV2RGCtBmMNnnaiqlOnjkRFRZmHER8f7/FQbCXUWh89etTj+H79+smll14q2jTfokULufvuuz328wUBBBBAIDAEqAENjOckebmZjuAzK0ByWznZbJh+pNCNGqUH33uU2myttaOBmEoKMN3LpGXMzPSs3ddA05m0qf6rr76SH3/80dUE//bbbzt384kAAgggEEAC1IAGzMNye98xYPLs24xGOWo9CyatCQ22pEFcoC5leRbt2rWT48ePiw5Yn5GRYXrEL1myxHUJrUXVnu+6T9OmTZtk8uTJZl07OpEQQAABBAJHgAA0QJ6VzcajKvioYiMLdzqJjYwueBjfA0Sgc+fOMmzYMLnjjjskMTFRXn31VfnHP/7hyv3ZZ58tN954o/Tq1csMs6RN8To8U/369c2g864DWUEAAQQQ8HsBR98N7T5M8ncBe16WHNz/RaFshofHSWRUzULbQ2FD6rwPxX7Msxk+IiFZThs1JSCLf+TIEUlNTS2U94YNGwZsE3yhwpRiQ0pKihmIX3u8e0t//vmnHDt2TM444wyzOysrywze7xxr1Ns5bEMAAQQQ8C8B3gH1r+dR5txERdeRGrX+VubzguGE9PB5YhfPADQYyhXqZUhOTi6WoHbt2qKLM0VHR7sGundu4xMBBBBAwL8FaNf17+dD7kJEIN+eZ95vDJHiUkwEEEAAgRAXoAY0xH8AKH7VCeSmHZM//m+8ZP+5x2QivGlHie03puoyxJ0RQAABBBCoJAFqQCsJmtsgUFDgj2kTXMGn7svbvk5y/1hX8DC+I4AAAgggEHQCBKBB90gpUKAIZB/aXSiruVt/KLQtK5X3XAuhsAEBBBBAIKAFCEAD+vGR+WATyM/JLlSksMiYQtvYgAACCCCAQCALEIAG8tMj7yEhEBn71zzqIVFYCokAAgggEBICBKAh8ZgppF8KlDAPul/mmUwhgAACCCBggQABqAWIXAIBBBBAAAEEEECg9AIEoKW34kgEEEAAAQQQQAABCwQIQC1A5BIIIIAAAggggAACpRcgAC29FUcigAACCCCAAAIIWCBAAGoBIpdAAAEEEEAAAQQQKL0AAWjprTgSgSoRyMjIkOzswuODVklmuCkCCCCAAAIWCBCAWoDIJRDwpcCRI0dk3759cuzYMddtZs6cKd27d5ezzjpLxo8fL5s3b3bt27ZtmwwZMkRatGgh3bp1k9dee03y8/PNfrvdLgMGDJA1a9bI/fffL6NHj3adxwoCCCCAAAKVJUAAWlnS3AeBCgpoAKo1odOnT5eRI0dK//795eGHH5bVq1fL3//+d8nMzJQ9e/bI3/72N4mLi5Np06bJ9ddfLxMmTJDHHnvM3F0D0Xnz5smIESNk/vz5JkCtYLY4HQEEEEAAgTILRJT5DE5AAIEqE9Dm+EceeUTuvfdeU4OpGbngggtMILl+/XqZMWOGJCcnm0/dd8kll5jaz7vvvlvuu+8+iY6O1s1y5plnypw5c8w6/yCAAAIIIFDZAtSAVrY490OgAgKHDh0SXXr06OG6SoMGDWTnzp3SpUsXUxvas2dP1z5dOe+880zN6ZYtW1zbhw0b5lpnBQEEEEAAgcoWIACtbHHuh0AxArYwW5F7a9asKcePHzf769ev7/W4w4cPS5MmTTz2ub//6dyRmJjoXOUTAQQQQACBShegCb7SyblhsArYszPl4H/fkJwj+yWyRl2JSKhVfFH/f8cg94NiY2IkydGEru96RkZGSljYX38jRkVFme/NmjUzh69YsUI6depk1o8ePSrXXnutTJ48WZo2bSrLli1zv6SsXLlSwsPDpXnz5h7b+YIAAggggEBVCRCAVpU89w0qAQ0+tz0/UvIdn5oydm4sV/nsuTlSvXr1Is+tVauWDBo0yHQw0gC0bdu2MnHiRPnhhx9Mr/cbbrhBbrnlFhN0nnvuuabnvHZauuaaa0RrPfPy8oq8NjsQQAABBBCoLAGa4CtLmvsEtcDBL6e7gs/SF7Rwc3tW+okST9fe7RqI6rud9erVkw0bNsjs2bMlNjZWrrvuOrn99tvNvkaNGknt2rXNMnXq1BKvywEIIIAAAghUlgA1oJUlzX2CWiD78P6yl8/RLC55uZ7nhZX8n2TdunXl22+/lb1790pERITod2ey2WwyZcoUeeCBB0Q7HWmTvHZSciZtine+E+rcxicCCCCAAAKVLVDyb7vKzhH3QyAABSITa0vm7lODwZemCOGN20re9p89Do08/SyP78V9adiwYZG7nTWfRR7ADgQQQAABBKpQgCb4KsTn1sEjEJmYVObCRF0wTMLqn+oYFNnuQqnW9fIyX4cTEEAAAQQQCDQBakAD7YmR34ASaHjNgxJZ81QTuXvm95+0S9yVE8SeelhsUdFii6ku2oROQgABBBBAINgFCECD/QlTvioViEpqIFHJRTSV79hh8haWUPba0yotFDdHAAEEEECgggI0wVcQkNMRQAABBBBAAAEEyiZAAFo2L45GAAEEEEAAAQQQqKAAAWgFATkdAQQQQAABBBBAoGwCBKBl8+JoBBBAAAEEEEAAgQoKEIBWEJDTEUAAAQQQQAABBMomQABaNi+ORgABBBBAAAEEEKigAAFoBQE5HQEEEEAAAQQQQKBsAgSgZfPiaAQQQAABBBBAAIEKChCAVhCQ0xFAoGoEtm/fLn/88UfV3Jy7IoAAAghUSICZkCrEx8kIWCuQn58vdrvd2otW0tV0GtHKnEr0hhtukK5du8pzzz1XSSXkNggggAACVgkQgFolyXUQsEAgMzNTdu3aZcGVquYScXFxkpSUJOHh4T7JwOHDh2XOnDkyb948WbZsmQlAfXIjLooAAggg4FMBmuB9ysvFEQgtgZMnT0pKSors379fhg4dKj/99JOMHj1a2rdvL9dee63s3r3bA2TVqlUyePBg6dixo9x4443yyy+/uPY/88wz8vbbb8u7774r3bp1kxMnTsiePXvk008/ldzcXKlevbrrWFYQQAABBAJLgAA0sJ4Xua0igaw/90jW4f2SczzF65KXlVFFOfO/22ZkZMjx48flo48+kv79+0vLli1l4sSJsmPHDjn//PNF92taunSpXHjhhRIVFSUPPfSQ+dT9a9euNft/+OEHefbZZ+XOO++UTp06SWRkpHTo0EG+/PJLszRu3Ngcxz8IIIAAAoEnQBN84D0zclyJAhl7t8qedx8Ve0kBpuPdTdJfAu7vgo4bN04mTJhgdlx88cXSpEkTmTlzpqkVHT9+vPTr10/ef/99s3/IkCGybds2eemll0zNp27UGs+9e/dKYmKiOYZ/EEAAAQSCQ4AANDieI6XwkcCemY+XHHzqvWMTRDJSy5QLbUJOS0sr0zmBcHCNGjXk4MGDJqs9e/Z0Zbl27drSpk0b2bRpk6kF1eb5Zs2ayeTJk13H6MrPP//s+n7ppZcSfLo0WEEAAQSCR4AANHieJSWxWCD3ZKrYM9NLdVVbfJLkewlAMx1N9lHJDb1eIzk52TQr67uNmiIiIiQsLHDfitGaT+2EVK1aNVcAWrduXY+yay9/7aB05MgR0XXtdLVv3z7XMfquqLo4EzWfTgk+EUAAgeASIAANrudJaapKINZLh5iwcIlMalBsjjTACuYga8uWLaaWUxG0B/u6detk7Nix0qBBA4mNjTXvdD7xxBMuoyVLlrjeEXVtZAUBBBBAIOgEAre6JegeBQXyNwGbrfT/ediSThNbLc+azvBO/SSiWg1/K1al5uexxx6To0ePmhpP7WiUkJAg2qyutaUjR46U9957T7799lvJy8uTzz//XK666qpCPeUrNcPcDAEEEECgUgSoAa0UZm4STALapB7XrINHkXLqtJCcNheKfcsKyU8/JmENW0tYg5Yex4Til7Zt20r9+vXNqwUNGzaU//znP6KfmnSYJW1+1/dE4+PjJScnR+6++2655ZZbQpGKMiOAAAIhJUAAGlKPm8JaIRDTsKXUvfRmj0vpO42pqakS3uYCj+2h/uWBBx6QqVOnys6dO0WDUfektaE6pqcOvK9Lq1atRDsqOZMOOF9c2rBhQ3G72YcAAggg4McCBKB+/HDIGgLBIKC9/QsGn+7l0vE8GdPTXYR1BBBAIPgFSv+SW/BbUEIEEEAAAQQQQACBShCgBrQSkLkFAqEm0KJFC9PxKJh7+IfaM6W8CCCAgJUCBKBWanItBBAwAjqeac2aNdFAAAEEEEDAqwBN8F5Z2IgAAggggAACCCDgKwECUF/Jcl0EEEAAAQQQQAABrwIEoF5Z2IgAAggggAACCCDgKwECUF/Jcl0EEEAAAQQQQAABrwIEoF5Z2IgAAggggAACCCDgKwECUF/Jcl0EEEAAAQQQQAABrwIEoF5Z2IgAAggggAACCCDgKwHGAfWVLNdFAIFSCaSmpspPP/0k0dHR0q5dO9GpO0kIIIAAAsEtQA1ocD9fSoeAXwtMnTpVatSoIYMGDZLu3btLs2bN5Ouvv/brPJM5BBBAAIGKC1ADWnFDroBAkQIpKSmiswIFYoqIiBCdSlM/fZHWrVsnd999t7zzzjsyYsQI2bt3r1x33XVm2bFjh0RFRfnitlwTAQQQQMAPBHzzm8UPCkYWECirQE7qYTmxcaVEVEuU8LgEsWdllPoS+fn5Xo/Nysryuj1QNp48eVIaNGggEydONDWU69evl3nz5km1atVk/Pjx0q9fP1dRjh49Kv/85z9lxYoVUq9ePbnmmmtk+PDhZr/dbpeBAwfKv/71L/noo4/MPPHt27c3NZ4adGpq1KiRjBs3Tq666irZtGmTdOjQwWznHwQQQACB4BMgAA2+Z0qJyiHw55IPJWXRu4XODIsuXS1cdnZ2oXODYUNeXp6kpaXJggUL5I033pDLLrtM7r//ftNMfvnll8vixYuld+/eooFqly5dJCEhQW6//XbR9zrHjh0ru3btMsGrBugauG7dulXCw8PlnnvuMe97Tp8+3YNp48aN5nudOnU8tvMFAQQQQCC4BAhAg+t5UppyCOSmHfMafBZ1qcxjKYV22Wy2QtuCZYOzdrd58+YyY8YM80rBlVdeKdu3b5dJkyaZAPTll1+Wffv2yZo1a0wQqmXXTkUPP/yw3HvvvSbo1G1nnnmmzJkzR1cLpc8++0ymTJkio0aNkvr16xfazwYEEEAAgeARIAANnmdJScopkPbbj97PDAv3uj3P0ZxcMMXHx0tmZmbBzUHxPS4uzpSjR48eHu+z9uzZUzTw1PTdd9/JaaedJq+++qr5rv9oQHrkyBFTC9q0aVOzfdiwYa79zpXdu3fLhAkTZO7cufLYY4+Zdec+PhFAAAEEglOAADQ4nyulKoNAePVE70drrWZcDZGTxzz2h9cqXDun70Tm5OTIsWOex3qcGGBfIiMjpVatWq7OQHXr1vUogdaManO6psOHD4vWAmvQ6Z7uvPNOiYmJcW3STk3uSWtDR44cKeedd55op6TWrVu772YdAQQQQCBIBQhAg/TBUqzSC4RHVyvy4MjzhkjOkv+I5OWYY2x1mkq1rld4PV6HE9IlWNOWLVs8iqbDJbVq1cps0+Z5DUJ1WCVn0prNL774wnRIcm5z/9QOTdpR6fHHHzfvlbrvYx0BBBBAILgF/D4A1U4Qwfx+XWl/vOz5p5p9ne/k4VJavfIdV61lZ7E3PFOiBt4v9n2/icRUl7BGbSUsMrp8Fwzws2bNmiWjR482nY0++OADWb58uUybNs2USt/bfPfdd813rdH8/fffTY92/RnVzkj633HBpL3hGzduLNq0v3LlSo/d2kPe2fTvsYMvCCCAAAJBIeC3AWhGRoYcOnRInMFWUGhXqBC5EhmeLyez8yTXni/a5SUmMlxiK3RNTi5OIPa0VpLuOMBWvZaEt+xW3KEhsa9v375yxRVXmB7vOrapBpY33nijKfuFF15oaj/vuusuU5t54sQJ6dOnj+k5XxTOsmXLZNu2bXL++ecXOkRnRjr77LMLbWcDAggggEBwCPhtAErwWfgHzBl86h4ddTIjJ0+iM09I8Db6FjZgS9UJdO7cWT7++GPZsGGDnHHGGR7vdmqu9H1Prf389ddfJSkpydU8r/v0XdGCf0x+8803uouEAAIIIBCCAn4ZgGrtZ8FfViH4bDyKnJ//V82nx0bHl4zstIKb+I6AzwS05lPnay8q6Tig2qGIhAACCCCAQHECfjlHIO82entk2ujuLfnlI/SWUbYhgAACCCCAAAJGwC9rQAN17mzf/kx5D0CjommA9607V1cBfV+Tudn5WUAAAQQQsErALwPQogqn4xKG6i9Buz1HMlMLy4SFBdQjLFwAtgSEgDatkxBAAAEEELBKIKCiFx2WpWbNmlaVPaCuk5uXJUe8BKABVQgyiwACCCCAAAIIOAR4gZAfAwQQQAABBBBAAIFKFSAArVRuboYAAggggAACCCBAAMrPAAIIIIAAAggggEClChCAVio3N0MAAQQQQAABBBAgAOVnAAEEEEAAAQQQQKBSBQhAK5WbmyGAAAIIIIAAAggQgPIzgAACRQq8/PLL8uGHHxa5f/Xq1fLwww8XuZ8dCCCAAAIIeBMgAPWmwjYEEDACX375pSxfvrxIjd9//11mz55d5H52IIAAAggg4E0goAai91YAtiFQ2QI5OTly4sSJyr6tZfez2WwSGxsr4eHhFb7mNddcI7qQEEAAAQQQKIsAAWhZtDjW7wXyTqbKofmvlCmfOalHy3R8VlaW6BLIKSwsTOrUqSMxMTGSkZEhDz30kCxYsMBs69+/v4wZM0Z05jFN+fn58uKLL8qcOXPEbrfL9ddfL7feeqvZt2TJEpk5c6a8+eab5jv/IIAAAgggUBoBAtDSKHGMXwrk52YXypduS9+6utD24jbYs3O87s7Pt3vdHgwbNZBMSUmRRo0ayYABA2TXrl3yz3/+Uw4dOiSTJ08WbVp/5ZW/AnkNMDt16iQjR440QaoGp23atJEePXrI9u3b5dNPPyUADYYfCsqAAAIIVKIAAWglYnMrawW0ttOSFF3dcZnC18o4clCkqSV38MuL5Obmyv/+9z9ZvHixrFmzxgSZmtH4+HiZNm2aK88NGjSQRYsWmSb7UaNGyYoVK2TVqlUmAHUdxAoCCCCAAAJlEKATUhmwONTfBPKtyVCsBqBeUlhw/30WFRVlAs9q1arJ2Wef7QK4+eabzXbnhi5duni8L6q1pvv27XPu5hMBBBBAAIEyCxCAlpmME/xFIPa0tpZkxRYdK7Ya9TyvFRElcWf1kOTkZM/tQfJNOyAlJSWZZvi6deuKdkwqKmmNqHsq7lj341hHAAEEEECgKIHgruIpqtRsDwqB2pffLgc+fkay9m+rUHk0oIrqc6vkfDNT7Ad+F1tCbYnsPlSi6jSW6tWrm4466enpJkiLiAj8/2S0vNHR0aIdkZo1ayZ//PGHefdTOyVpmjdvnrz33nsya9asCrlyMgIIIIAAAkUJBP5v06JKxvagFwhzNJE3GPqIKac9N0eKrsMrniLT0aP94J8pEj3gbtPju2ANnwadiYmJxV8kQPcOHjxY7r//frnvvvtk0qRJZngp/a7N7iQEEEAAAQR8JUATvK9kuW6lCoRFRIqtvEv4qb/DCgaflVqIKriZNsN/8sknMn/+fGnSpIl07txZOnToIC+88EIV5IZbIoAAAgiEioDNMcafRT05rCPLzs722slBa6Fq1qxp3Y0C6Eq5eVmy9Y9PC+U4MaGZNKhLbVUhmDJsyMzMlAMHDhQ6Q3/WgrXms2Bh8/LyZOvWrdK0aVPTPF9wP98RQAABBBCwUuBU1Y+VV+VaCCAQUALaKal169YBlWcyiwACCCAQuAI0wQfusyPnCCCAAAIIIIBAQAoQgAbkYyPTCCCAAAIIIIBA4AoQgAbusyPnCCCAAAIIIIBAQAoQgAbkYyPTCCCAAAIIIIBA4AoQgAbusyPnCCCAAAIIIIBAQAoQgAbkYyPTCCCAAAIIIIBA4AoQgAbusyPnCCCAAAIIIIBAQAoQgAbkYyPTCCCAAAIIIIBA4AoQgAbusyPnCCCAAAIIIIBAQAoQgAbkYyPTCCCAAAIIIIBA4AoQgAbusyPnCCCAAAIIIIBAQAoQgAbkYyPTCJRe4Pvvv5f77ruv9CdU4Mhdu3bJV199Jb/++qvY7fYKXIlTEUAAAQSCWYAANJifLmWrkIAGUHl5eQG55Ofnu8q+efNmeeedd1zffbFy8uRJ6dOnjzRp0kSGDx8u7dq1kwsuuEBSUlJ8cTuuiQACCCAQ4AIRAZ5/so+AzwSOHz8uugRqio+Pl1q1alVK9p966inZsGGDbN26VVq0aCFa63rxxRfLI488ItOmTauUPHATBBBAAIHAEaAGNHCeFTn1kYB7baGPblEllz1x4oRHAP3NN9/I4MGDpX379jJmzBjRWktNqampMmDAABNAOjO6c+dOs829BnPGjBly9dVXS8eOHeWWW26RBQsWOA+XZcuWyYgRI0zwqRvPO+88ueKKK+R///uf6xhWEEAAAQQQcAoQgDol+AxZgdzc3KAtuzPIPHbsmNx6663SuXNnufLKK2XWrFnywAMPmHJnZ2fLvHnz5PDhwy4HDUp1W0ZGhtn2n//8R+644w5p06aNPPvssxIeHi79+vWTTZs2mf267+abb3adrysbN26UOnXqeGzjCwIIIIAAAipAEzw/ByEvEBkZGbQGYWF//Y2ZlZUlH330kan91MJq7ejy5ctLXW4NUp955hm57bbbzDm9e/cWDUrXr18vZ555pqlZdV5Mj9XgVjsiffHFF87NfCKAAAIIIOASIAB1UbASqgIxMTGiQWhOTk7QEdSoUcOUKS4uzhV86obTTjtN9u3bV+ryapP7n3/+Ka+++qps27ZNVq1aJZmZmYV6ui9atEjuuusu07y/ZMkS0xGp1DfhQAQQQACBkBEgAA2ZR01BixNo2LChaYLWJmetNdSA1GazFXeKX+/TMlSvXl2ioqJMPrVDUlmSNtm7p9dee03Gjx8vvXr1kk6dOsnEiRNl6NChrkN0tABthn/jjTdkwoQJpgZU709CAAEEEEDAmwABqDcVtoWkQFJSUkiW2xmkao2mM+nQTc6kw1Fp8/u4cePk6aefNpt1dADn+6G6QbfrUE+rV6+WDh06OE/lEwEEEEAAAa8CBKBeWdiIQOgIJCQkSOPGjc1wSdpDXoPLSZMmuQC0JliDVA1QdcQAfX/0nnvucY2PqgfOnDlTrrnmGhOUrly50nWuvt6gveZJCCCAAAIIuAvQC95dg3UEQlRAazDnz58vjRo1Mr3btbbTmTQAfeyxx+Tdd981vdobNGggZ5xxhhl2aezYsWaopS1btsjrr78u3bp181iGDBnivAyfCCCAAAIIuARsjhqNU1OmuDZX7Yr2ovXWQSIxMVFq1qxZtZmrorvn5mXJ1j8+LXT3xIRm0qBul0Lb2YBAWQW0hnPv3r3SvHlzr6dqJy0dWkl7vTub7XW8UA1adVgmEgIIIIAAAqUVoAm+tFIch0CQC2hzeVHBpxZdO2YVfL9Tp94kIYAAAgggUFYBmuDLKsbxCCCAAAIIIIAAAhUSIACtEB8nI4AAAggggAACCJRVgAC0rGIcjwACCCCAAAIIIFAhAQLQCvFxMgIIIIAAAggggEBZBQhAyyrG8Qj8v/buPLaKag/g+O92ga6UFixFgVfLI4Cx8IfG5DUgiAQUGheUFIIpSjCiBFDRCgY1EJcSEEhIEDT8USlQEXiuf4BKJEANGFNjQDapcWshAqVQWrvQvv4O7166TOly77Rz534nwd45M3PmnM9p7a9zlkEAAQQQQAABBPwSIAD1i4+LEUAAAQQQQAABBDorQADaWTHORwABBBBAAAEEEPBLgADULz4uRgABBBBAAAEEEOisAAFoZ8U4HwEEEEAAAQQQQMAvAQJQv/i4GAEEEEAAAQQQQKCzAgSgnRXjfAQQcIVAYWGh5OTkdLku586dk3nz5smlS5e6nAcXIoAAAqEqEFQBaF1dXai2E/VGAIEAC5w4cUI+/PDDLudaXl4umzZtkqtXr3Y5Dy5EAAEEQlUgwokVr66utixWVVWVZTqJ9groL9iLFy9KQ0ODhIWFSXh4uL03JHcEbBDweDwSEREhCQkJEhkZacMdyBIBBBBAoKMCjgxA6+vrLcuvARBb9wpo0P/333/7bqptw5NoHwcfglCgsrJSbr31Vl/J9+/fL+vXr5dTp05JRkaGrFmzRmJiYszx77//3jwlPXDggKSlpcm4ceNk/vz5JpD1ZnDy5EmTpk9UR40aJStXrpTbb7/de5ivCCCAAAIWAo7sgo+OjrYoqkhUVJRlOon2CZSVldmXOTkj0AMC+kdURUWFubOO33zmmWfk7rvvlmnTpklBQYEsWbLEHNMxnhMmTJDz58/LW2+9JZMmTZKlS5dKbm5us1JnZWXJkCFDZMGCBXL48GETxHrzb3YiOwgggAACPgFHPgH1la7Fh169erVIYddugbaeRtt9X/JHwE4Bb2+KDvfZsWOHeXKp97ty5YocPHjQ3Prs2bPy+OOPy+bNm83QE03Up6U//vijOe79z7vvvivZ2dlm95FHHpFBgwbJ1q1bTWDrPYevCCCAAALNBYIqAG1edPa6Q0DHzNHl3h3S3KM7BWJjY83ttKtdu8292+DBg6WkpMTsjh49Wj744AP59NNPpaioSH755RfZvXu3TJ061Xu6+Xr//ff79m+77TYZPny4aHc8GwIIIIBA2wIEoG3bcKRR4GYTjnRSBxsCwSLgnYSUmJgo3t6U+Pj4Not/+vRpM+YzJSVF7rvvPpk4caLU1NRIy14BnZjXdIuLi2u6y2cEEEAAAQsBAlALFJLaF9Axby1/8bZ/FWcgEDwCusSSzpg/cuSIb9LRzp07W41F//nnn2XgwIGmYjr2U7vo586dGzwVpaQIIIBADwg0/9O9BwrALRFAAAEnCuhT0mvXromOE9Wv27dvl3379pnPTcurk5Z0vKieozPo9QnozJkzm57CZwQQQACBFgIEoC1A2EUAAQRUQN9ypCtyJCcnS1JSkplYpMs17d27V95++20fks6OT01NFe3OX7dunezatcs8OfWdwAcEEEAAgVYCnsbZoI5bXFPHWXknAjQtsXaH6fitUNzqrlXL6eL/tqp6Qp80uXXAPa3SA5Wga4BavemFLvhACZOP0wV0QpE3CNWy6s+ELgnXdPyo/owUFxfLyJEjfd31Tq8X5UMAAQR6UoAxoD2pz70RQMDxAiNGjGhWxltuuaXZvu7orPr09PRW6SQggAACCFgLEIBauwRNakP9tcZlkv6xrbz1jfmzIYAAAggggAACgRQgAA2kZg/kdbniN9F/dm2R4f+WiLD+dmVPvggggAACCCAQggJMQgrBRu9MlT0S2ZnTORcBBBBAAAEEEGhXgAC0XSJnnNBQX9cjBfF4elvel655SxYSEUAAAQQQQKADAgSgHUBywinh4daBoP1lq7e8RVhYuGU6iQgggAACCCCAQHsCBKDtCTnkeFhYhPSJ/1e3l6a+oarb78kNEUAAAQQQQMDdAkxCCqL2vS3lPxLVO0nKr/wqHglrfJ91Hwnz2PsksrYmVpgIH0TfJBQVAQQQQACBIBAgAA2CRmpaxH6Jw0X/ddfW1kL03XV/7oMAAggggAAC7hOgC959bUqNEEAAAQQQQAABRwsQgDq6eSgcAggggAACCCDgPgECUPe1KTVCAAEEEEAAAQQcLUAA6ujmoXAIIIAAAggggID7BJiE5L427ZYaXblyRTweT7fci5u4TyAyMlKio6PdVzFqhAACCCDQIQEC0A4xhe5JDQ0NlpUvKyuzTCcRgY4KxMXFSf/+/SUnJ0fGjBkjP/30k3z++ecSGxsrL730kkyZMsWXlX6/vf766/Ldd99JSkqKzJw5U2bNmmWOf/3117J7926ZO3euvPnmm1JcXCz33HOPrFmzRvQebAgggAACzhOgC955beKoEtXV9cwrQB2FQGFsEaioqJCqqirZs2ePPPnkk3Ly5El55ZVXZOTIkZKZmSn79u0z962srDQBZWFhoTz33HMyceJEefbZZ+Wdd94xx3///XfJz8+XrKwsmTRpkkydOlW2bNli8rKl4GSKAAIIIOC3AE9A/SZ0dwb19dav4nR3ralddwnU1taaWw0dOlTy8vIkLCxMpk2bJr/++qvk5ubKhAkTZP369VJSUiI//PCD9OnTx5zfu3dvWbZsmSxevNjs65CQQ4cOSXp6utmvqamR/fv3m8/8BwEEEEDAeQIEoM5rE0eVSH/R8xTUUU3iqsLo95duY8eONcGnt3Ljxo0zgafua2A5ePBg2bhxo/ewCUgvXrwo+vRTt/j4eF/wqftDhgyR0tJS/ciGAAIIIOBAAQJQBzaKk4rUr18/qa6uJgh1UqO4pCyJiYniDUAHDBjQrFY69jg8/PprZi9cuGAmvOlT0KbbokWLJCoqyiTFxMQ0PcQEuWYa7CCAAALOEyAAdV6bOKpE2iU6aNAgM1ZPuzV19jKz3x3VREFZGP0+ioi48b+fU6dONavHN998I8OHX3/lrHbPaxC6bt063zl//PGHfPHFF2ZCki+RDwgggAACQSNw4zdA0BSZgvaEgC6Zw7I5PSEfGvcsKCiQp59+2kw22r59uxw8eFDee+89U/k5c+aYSUW6/9RTT8mZM2dkwYIF5g8hnYzEhgACCCAQfALMgg++NqPECLhO4IEHHpCHH35YEhISzEx3DSx1Zrxu48ePN08/n3/+eUlOTpY777xTevXqZSYtmRP4DwIIIIBA0Al4GsdaWS/02INV0a7eluO9tDj6y0nHjbEhgIB7BEaPHi0zZswwyyYdO3ZMhg0b5hvb2bSWly9flqNHj4qOS/Z2zzc9zmcEEEAAgeARoAs+eNqKkiLgagEdb+xdRsmqoroEU0ZGhtUh0hBAAAEEgkyALvggazCKiwACCCCAAAIIBLsAT0CDvQUpPwJBLnDgwAEzpjPIq0HxEUAAAQQ6IUAA2gksTkUAgcALeN9uFPicyREBBBBAwKkCdME7tWUoFwIIIIAAAggg4FIBAlCXNizVQgABBBBAAAEEnCpAAOrUlqFcCCCAAAIIIICASwUIQF3asFQLAQQQQAABBBBwqgABqFNbhnIhgAACCCCAAAIuFSAAdWnDUi0EEEAAAQQQQMCpAgSgTm0ZyoUAAggggAACCLhUgADUpQ1LtRBAAAEEEEAAAacKEIA6tWUoFwIIIICAawSqq6vlxRdflNOnT7umTlQEAX8EeBOSP3pci0CICNTV1Ul9fb2EhfE3a4g0OdXsoEB4eLh4PJ52z9afoW3btsmjjz4qw4YNk+nTp8uYMWNk0aJF7V7LCQi4UYAA1I2tSp0QCKBAaWmp6NMbNgQQaC2gwWdSUpLEx8e3PtgkJTY2Vs6ePetL+e2332TEiBG+fT4gEGoCPM4ItRanvgh0QuD8+fMEn53w4tTQE2hoaJALFy7IP//8I+Xl5bJ27Vq599575a677pIlS5b4fn70eFZWlhw9elTmz59vuuI/+ugjWbZsWeihUWMEGgUIQPk2QACBNgWqqqraPMYBBBC4IaA/K6tXr5YdO3ZITk6OzJ49W3bt2iWvvvqqOam2ttYcO3funDz44IPmqekdd9wh48ePv5EJnxAIIQEC0BBqbKqKQGcFOjK2rbN5cj4CbhTQsaB5eXkybtw4yczMlIULF0p+fr6kpaW1qq4e79evn6Snp8vEiRNbHScBgVAQYAxoKLQydUSgiwIRERGikyfYEECgbYHIyEiJi4szgeeqVaukqKhIJk+ebJ50anc7GwIItBYgAG1tQgoCCPxfoK0noO1NuAAQgVAR8AafukLEhg0bZObMmVJQUGA+L168WF577TVZsWJFqHBQTwQ6LEAA2mEqTkQAAa+Adh+yIYDADYGrV6+aLvjs7GwZO3asOfD++++btT9ffvnlGyfyCQEEjABjQPlGQAABBBBAwE8BXWZJn4CuXLlSKioqTG6XLl2SIUOGmO75ltnHxMTIn3/+adbXbXmMfQRCQYAnoKHQytQRAQQQQMB2geXLl4s+AV2zZo306dPHBKJbtmyxXKh+xowZ5umorge6b98+28vGDRBwmoCncQ2zBqcVqqamRkpKSloVKyEhQRITE1ulk4AAAvYI6JIxVksxpaam2nNDckUgyAXKysrk+PHjpha6zFLfvn3brJH3SalOYGJDINQEeAIaai1OfRFAAAEEbBPQhyQZGRkdyp/As0NMnORSgaAKQPV1gPqmCTYEEOgeAZZg6h5n7oIAAgiEmkBQBaD6KjP9x4YAAggggAACCCAQvAKOnAVfX18fvKKUHAEEEEAAAQQQQOCmAgSgN+XhIAIIIIAAAggggECgBRwZgEZFRQW6nuSHAAIIIIAAAggg4BABRwag+kqzpKQkhxBRDAQQQAABBBBAAIFACjh2EpIu4qtvitA1CDUgDQ8PD2S9yQsBBDogoGsa6uoTbAgggAACCARSwLEBqFYyIiJC4uPjA1lf8kIAgU4I6B9/bAgggAACCARagN8ugRYlPwQQQAABBBBAAIGbChCA3pSHgwgggAACCCCAAAKBFiAADbQo+SGAAAIIOFagqKhIli5d2uXybdy4UXbu3Nnl67kQAQSuCxCA8p2AAAIIIBAyAidOnJANGzZ0ub579uyRwsLCLl/PhQggcF3A0ZOQaCQEEHCmQElJiTMLRqkQsBDQVVR0ZZXo6GiLoyQhgEBPCBCA9oQ690QgSATaei1uTU1NkNSAYiJwXUCX9BswYEAzjjfeeEMaGhpkxYoVvvRvv/1W1q5dK1u3bpW4uDjJz8+Xbdu2if4sTJ8+3XceHxBAwD8BuuD98+NqBFwtUFdX5+r6UbnQErh8+XKzCicnJ8vq1auloqLCl75582YpLy83weemTZtk9uzZEhsbK1OmTJHc3Fz56quvfOfyAQEEui5AANp1O65EwPUCHo/H9XWkgqErkJWVJfpH1pdffmkQ9KULn332mcyaNUtqa2tl+fLlMm/ePPn4449l4cKFcuDAAbl69WroglFzBAIoQAAaQEyyQsBtAjpujg0Btwhol3rTrX///jJ58mTfrPa9e/eaN39pV3txcbGUlpaa495rUlJSZNSoUd5dviKAgB8CjAH1A49LEXC7gAag165dE+261LFy+kTU+8/tdad+7hHQN3olJCSYrvSWtXriiSdkzpw5UllZaZ50ZmZmSt++feX48ePm1NTU1GaXaLc9GwII+C9AAOq/ITkg4GqBxMRE0X9sCLhR4KGHHhKdJf/JJ5+Y7ve8vDxTzbS0NPNVu929Tz118t2hQ4ckPT3djRTUCYFuFaALvlu5uRkCCCCAgJMEdGmmxx57THJyciQiIsJMNtLy6Yx5nXikk5IuXrxoxn7qrHmdTc+GAAL+CxCA+m9IDggggAACQSyg3fB//fWXZGdnS2RkpK8mOgteN+12HzhwoBw+fFh04hIbAgj4L+BpHNfV4H825IAAAggggEBwCuiEo6FDh5pxnyNGjGhWCV3/89ixYxITE2POaXaQHQQQ6LIAAWiX6bgQAQQQQCCYBXQJJp1k98ILL8iZM2dEX7PJhgAC3SNAF3z3OHMXBBBAAAGHCeiTz6ioKDly5IisWrXKYaWjOAi4W4AnoO5uX2qHAAIIINCGgHavl5SUyKBBg9o4g2QEELBLgADULlnyRQABBBBAAAEEELAUoAvekoVEBBBAAAEEEEAAAbsECEDtkiVfBBBAAAEEEEAAAUsBAlBLFhIRQAABBBBAAAEE7BIgALVLlnwRQAABBBBAAAEELAUIQC1ZSEQAAQQQQAABBBCwS4AA1C5Z8kUAAQQQQAABBBCwFCAAtWQhEQEEEEAAAQQQQMAuAQJQu2TJFwEEEEAAAQQQQMBSgADUkoVEBBBAAAEEEEAAAbsECEDtkiVfBBBAAAEEEEAAAUsBAlBLFhIRQAABBBBAAAEE7BIgALVLlnwRQAABBBBAAAEELAUIQC1ZSEQAAQQQQAABBBCwS4AA1C5Z8kUAAQQQQAABBBCwFCAAtWQhEQEEEEAAAQQQQMAuAQJQu2TJFwEEEEAAAQQQQMBSgADUkoVEBBBAAAEEEEAAAbsECEDtkiVfBBBAAAEEEEAAAUsBAlBLFhIRQAABBBBAAAEE7BIgALVLlnwRQAABBBBAAAEELAUIQC1ZSEQAAQQQQAABBBCwS+B/g+6wyqpRkYsAAAAASUVORK5CYII=" /></p>
<h2 id="hemiplasy-risk-in-the-great-apes">Hemiplasy Risk in the Great Apes</h2>
<p>This is a quick calculation of the HRF on the phylogeny of Human-Chimpanzee-Gorilla.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">apetree <-<span class="st"> </span>ape<span class="op">::</span><span class="kw">read.tree</span>(<span class="dt">text =</span> <span class="st">"((((human,chimpanzee),gorilla),orangutan),out);"</span>)
<span class="co">#nodevec <- c("human","chimpanzee", "gorilla", "orangutan", "hcg", "hc")</span>
<span class="co">#two_n_vec <- c(125, 45, 65, 10, 20, 21, 19, 50)*1000*2 #2Ne for each node</span>
two_n_vec <-<span class="st"> </span><span class="kw">c</span>(<span class="dv">125</span>, <span class="dv">45</span>, <span class="dv">65</span>, <span class="dv">15</span>, <span class="dv">15</span>, <span class="dv">18</span>, <span class="dv">19</span>, <span class="dv">50</span>)<span class="op">*</span><span class="dv">1000</span><span class="op">*</span><span class="dv">2</span>
pop_std_vec <-<span class="st"> </span>two_n_vec<span class="op">/</span>two_n_vec[<span class="dv">3</span>] <span class="co">#relative to human 2Ne</span>
time_vec <-<span class="st"> </span><span class="kw">c</span>(<span class="dv">5</span>, <span class="fl">6.5</span>, <span class="fl">1.5</span>, <span class="fl">4.1</span>, <span class="fl">4.1</span>, <span class="fl">5.5</span>, <span class="dv">12</span>, <span class="dv">15</span>)<span class="op">*</span><span class="dv">1000000</span> <span class="co"># times in MY</span>
length_vec <-<span class="st"> </span>time_vec<span class="op">/</span>(<span class="dv">20</span> <span class="op">*</span><span class="st"> </span>two_n_vec) <span class="co"># coalescent branch lengths: MY/(gen * 2Ne)</span>
apetree<span class="op">$</span>edge.length <-<span class="st"> </span>length_vec
<span class="kw">plot</span>(apetree); ape<span class="op">::</span><span class="kw">edgelabels</span>(<span class="kw">prettyNum</span>(length_vec, <span class="dt">digits=</span><span class="dv">2</span>))</code></pre></div>
<p><img 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7frDKi1bNy4UUaNGuUNnHr9aGpqqtStW9cqwm8EEEAAgRAIEEBDgE6VoRU4cfCEnDiYLMU813YGWg5sOiij7xsjm3/cbDbX6lJLdLZz8lPfyW7PDUnH9h2XyU9O8Vz7GSHXDLgm0CFYl8UCMTEx5u71zz//3IRQvftdb9p7++235csvv5SCBQuaGvPkyWOuAz106JDMmDFDunXrJtHR0d5ZUZ391EW/CengwYPmNT8QQAABBOwXIIDab06NIRbYv/6AaUGxKkUDtiT5ULKsHLdKDm45bLYXrVxEug7rIgc27Jf3m/9HXq/6puz4bYfcO/5uKV4tcIgNeGBWXpGAPrdTZ0L12Z+xsbHmzvdPPvlEfK+9HThwoMyaNcucbn/uuedMGT3tbp1yb9q0qbkLvlmzZqJPnmBBAAEEEAiNQITnuiqeqh0ae79a9T+GH374oUyYMMFvPW+uTKBi1YrS4b/tJa2wmZmj61+VozuPSmSuSHMTkrXv6C5j5M0n3/ILQtY2fme9gAZK/XPh9aBWTTo7qne9FysW+B8HOo579+41+/M98JYavxFAAAF7BbgL3l5varNZIDpPtAxp8p4UKhG872w/tOeQXPXuVTb3LHyr04fJ65+0lly5cqUZPnUfDZ08MistPdYjgAAC9ggQQO1xppYQCSz8ZWHQr/XTwFO0aODT+SHqNtUigAACCCDgaAECqKOHh8ZdqYDelKLffMOCAAIIIIAAAs4R4CYk54wFLUEAAQQQQAABBMJCgAAaFsNMJxFAAAEEEEAAAecIEECdMxa0BAEEEEAAAQQQCAsBAmhYDDOdRAABBBBAAAEEnCNAAHXOWNASBBBAAAEEEEAgLAQIoGExzHQSAQQQQAABBBBwjgAB1DljQUsQQAABBBBAAIGwECCAhsUw00kEEEAAAQQQQMA5AgRQ54wFLUEAAQQQQAABBMJCgAAaFsNMJxFAAAEEEEAAAecIEECdMxa0BAEEEEAAAQQQCAsBAmhYDDOdRAABBBBAAAEEnCNAAHXOWNASBBBAAAEEEEAgLAQIoGExzHQSAQQQQAABBBBwjgAB1DljQUsQQAABBBBAAIGwECCAhsUw00kEEEAAAQQQQMA5AgRQ54wFLUEAAQQQQAABBMJCgAAaFsNMJxFAAAEEEEAAAecIEECdMxa0BAEEEEAAAQQQCAsBAmhYDDOdRAABBBBAAAEEnCNAAHXOWNASBBBAAAEEEEAgLAQIoGExzHQSAQQQQAABBBBwjgAB1DljQUsQQAABBBBAAIGwECCAhsUw00kEEEAAAQQQQMA5AgRQ54wFLUEAAQQQQAABBMJCgAAaFsNMJxFAAAEEEEAAAecIEECdMxa0BAEEEEAAAQQQCAsBAmhYDDOdRAABBBBAAAEEnCNAAHXOWNASBBBAAAEEEEAgLAQIoGExzHQSAQQQQAABBBBwjgAB1DljQUsQQAABBBBAAIGwECCAhsUw00kEEEAAAQQQQMA5AgRQ54wFLUEAAQQQQAABBMJCgAAaFsNMJxFAAAEEEEAAAecIEECdMxa0BAEEEEAAAQQQCAsBAmhYDDOdRAABBBBAAAEEnCNAAHXOWNASBBBAAAEEEEAgLAQIoGExzHQSAQQQQAABBBBwjgAB1DljQUsQQAABBBBAAIGwECCAhsUw00kEEEAAAQQQQMA5AgRQ54wFLUEAAQQQQAABBMJCgAAaFsNMJxFAAAEEEEAAAecIEECdMxa0BAEEEEAAAQQQCAsBAmhYDDOdRAABBBBAAAEEnCNAAHXOWNASBBBAAAEEEEAgLAQIoGExzHQSAQQQQAABBBBwjgAB1DljQUsQQAABBBBAAIGwECCAhsUw00kEEEAAAQQQQMA5AgRQ54wFLUEAAQQQQAABBMJCgAAaFsNMJxFAAAEEEEAAAecIEECdMxa0BAEEEEAAAQQQCAuBnGHRSzqJAAIIpCNw4MABKVmypOSNyZtOqcxtSjqcJL/88os0atQocztSGgEEEAgDAQJoGAwyXUQAgfQFdu7cKSUql5C7Jt2ZfsFMbP156M8yefJkAmgmzCiKAALhI0AADZ+xpqcIIJCOQI4cOSS6UNozoKeTT0tU3qg0j3Du3DmJiIjwbs+RkyucvBi8QCBMBMaOHStXXXWVNGzYMEx6fPnd5P8hL9+OPRFAIEwEFo1YLIMqvx6wtxtnbZIPW38kL5R6WT5u96nM/88C0TDKggAC4SUwYcIEufXWW6VMmTLh1fHL7C0B9DLh2A0BBMJDYPWkNTLxb5M8ofLi/m7+cbMM7zJSyiaWlV6T75HKreNk6nNTZe2UtRcXZg0CCLhaQK/5Ll26tPnj6o5mUecIoFkEyWEQQMBdAiePpsj/7h8rX/YYLQXLFQzYuTmD50rl6+Kk/aB2UqZ+GWn5ZAupe2ddWTp6ecDyrEQAgcACX3/9tTRr1kzy588vCQkJ8vHHH/sV/PTTT6VXr14yZ84cadCggTRt2tRsX7p0qTz88MMSFxcntWrVkueff162bt3q3Vf3u+uuu2TLli1yyy23SLFixcwspb73Xb744gu57rrrpESJEqaeY8eOSePGjWXevHmmmB6nVatWvrvIkiVLJDExUTZs2CA333yzvP/++3LkyBGzTvfXJava51exS94QQF0ykHQDAQSyVuD3pbtk6/zt0m3E7ZJ4b6Ln+k7/4yftTpJNntPvV/dr6nftZ6fBHaTrsNv8C/MOAQTSFHjjjTfkjjvuMAFv/Pjx0rJlS7n//vtFQ6G1TJ06VTZv3ix9+/aVG264QXr27Cn69Ip27drJ+vXr5cUXX5R+/frJ6NGjzb6++61YscKEz7Zt28rQoUNl7ty58t5771lFZOTIkeZ4GjDfeecdWblypWjZBQsWSPny5U25adOmSWpqqncffaHhdPny5VKuXDm57bbb5Pjx49KhQwd5/PHHJSYmJsva51epi95wE5KLBpOuIIBA1gmUqlNKHv6tv+TMFSnz3pt/0YGP7Dxq1hWJKyLTX5gpei1o3oJ5pOkDjSX++viLyrMCAQQuFtixY4cMHDhQXn/9dXnsscdMAQ2gixYtkn//+9/SrVs3s07f79692wQ+KxTq9jp16si4ceMkd+7cppz+vu++++TEiRMSHR1tjrNnzx4TKsuWLWvKfPXVV2ZmUt+sWbPGzHhq8HzggQfM9hYtWpjrOIsXL+69nnPhwoVy0003me3WD21TzZo1JVeuXNK8eXNJSUkxs60aQnUZPnz4FbfPqsuNvwmgbhzVS/Tp7bffloIFC0psbOwlSrIZgfAQ0NNxZ86c9utsnvx5/N5f+EZnQHX5pt+3cnDTAUnokCCrJqyWEV2/kK6fn58BXb16tehdsSwIIHCxgD55Yv78+ZIvXz558MEH/QrozOaQIUPMuqNHj5rT3BpUrfCpGwYMGCAPPfSQbN++Xfbv3y8bN26Ub775xpzG1/Bp7ffMM8+IFT51v02bNpnT6/p64sSJUrhwYRNC9b0u+kzgunXrigZQXZKSkkz99evXN++tHxpA9RS8LvpaF98yWdE+c1CX/iCAunRg0+vWa6+9JvHx8VKkSJH0irENgbAR0Ou2Tp/2D6CX6nxKUoopcur4KXlk0cMS6XnsUtt/tvHcEf+xTB04Tep0rS3Lli3zBNszlzoU2xEIS4GoqCjRayV1xjNPHv9/8OnpbD21rcvixYvNkyX0Gk7fZfDgwTJo0CDRGU69drNy5comhNaoUcMUs/br1KmTd7dTp06Z2dDevXubdbNnzzazl9oW30VnZjUE62Idxzdcavv09LteKqCLBlBtg96EZC1Z0T7rWG78TQB146heok/6l/rVV1+VJk2aXKIkmxEIDwENih26nT9tltEexxTLZ4rWub2WCZ/6JjIqUmp0TpCZL88SfW5o165d5R//+IduYkEAgQAC1atXl9atW1+0RWdGrdlFPf2tNw/pTUbWoo880lP2euq8e/fuZhZT/7FXtGhR75c/6H46E+obHDU06j829UYmXfQGIj197rvour1793rL6P8/6HGqVavmLTZr1izzj0vrOBpArddaKKva563QhS9yuLBPdAkBBBAIukBsqfOXsBQoW8CvrtiSXNriB8IbBNIRqFSpkvz0009+JfRxRnqjkN4IpIuGO32wu+8XPWgA1Dvf9RS8nkLXRb95TM9m1K5d27zX/fRUemRkpHmvP3Rdzpw5zbWZ+r5ChQrmbnZ9bS39+/c3L63gqjc5aV3WcfQ5vy+99JI5jhWKdZZUr0e1lqxqn3U8N/4mgLpxVOkTAggEXaBofFHRELpp9ma/utZ+v14KVyqc7rcm+e3AGwTCWEBPj+ujij766CNzE4/OfOqZAz21rXeW63Lh7KKuu/baa821nDNnzhQ9rT5p0iRzJ7tu01Cpi+5nhUizwvNDZ0V11tU65a83LOnd7o888ogJsHo3/vTp002otY6jZfU6U71WfO3atXL77bfLvn37vMfR0/H6db4aTPW3LlnVPnMwl/4ggLp0YOkWAggEV0BPtzft20QWfLRAFg5fLMcPnJC5786TDdPXS6Ne529MCG4LODoC2V9Ag6Y+u/OJJ54wN8Z26dJFOnbs6L0BScOdhj7f09vaa70jXQNq+/btzSOP9DFM+jglXfSmobT20wDqeyw9ht6Brzcv6XWhOtOpp+R9y/Tp08fcmFSxYkVzuYC2Ue9+t8roTVT6aCi9tM26kz6r2mc65NIfXAPq0oGlWwggEHyBq/s1Mdd6Tnlqiox/ZILkyZ9bmngew6TB9IdXZwW/AdSAgAsE9DppvcNdZxl973LXrmm4O3v27EW91JuG9HFKespdt1un4X2/BjfQfr/++qv3WBpU9Y54PY2vz+7URR+lpDfo6s261qKXCegTLXR20/qaTZ2l9V2+++4789xPff6nLlnRPt/ju/E1AdSNo0qfEEAgSwWufrCJ6J8LF70mreUTzaX5Y9fI4W2HzTcm5YjkxNKFTrxH4FIC+kimC8PnpfbR7QUK+F+DnZF9rDJ697xeI6rfuqTfsrRt2zYzi6kPnLdO/1tl9bcVPn3X+b4O9GSZK2mf77Hd+JoA6sZRpU8IIJApgbx588r2Vdtl7N3fZmq/9AovnbhUbn/vjvSKsA0BBEIooI9t0tlPPfX+7LPPmsc5FSpUSHQ2U++6ZwmuAAE0uL4cHQEEsoGAPhdXb36wbiDIiiZH3Bchf/nLX7LiUBwDAQSCJKCPcXrqqafMNyLpaXy9q9262z1IVXLYPwQIoHwUEEAAAY9A48aNcUAAgTAU0IfH+z5APgwJQtJlLlYKCTuVIoAAAggggAAC4StAAA3fsafnCCCAAAIIIIBASAQIoCFhp1IEEEAAAQQQQCB8BQig4Tv29BwBBBBAAAEEEAiJAAE0JOxUigACCCCAAAIIhK8AATR8x56eI4AAAggggAACIREggIaEnUoRQAABBBBAAIHwFSCAhu/Y03MEEEAAAQQQQCAkAgTQkLBTKQIIIIAAAgggEL4CBNDwHXt6jgACCCCAAAIIhESAABoSdipFAAEEEEAAAQTCV4AAGr5jT88RQAABBBBAAIGQCBBAQ8JOpQgggAACCCCAQPgKEEDDd+zpOQIIIIAAAgggEBIBAmhI2KkUAQQQQAABBBAIXwECaPiOPT1HAAEEEEAAAQRCIkAADQk7lSKAAAIIIIAAAuErQAAN37Gn5wgggAACCCCAQEgECKAhYadSBBBAAAEEEEAgfAUIoOE79vQcAQQQQAABBBAIiQABNCTsVIoAAggggAACCISvAAE0fMeeniOAAAIIIIAAAiERIICGhJ1KEUAAAQQQQACB8BUggIbv2NNzBBBAAAEEEEAgJAIE0JCwUykCCCCAAAIIIBC+AgTQ8B17eo4AAggggAACCIREgAAaEnYqRQABBBBAAAEEwleAABq+Y0/PEUAAAQQQQACBkAgQQEPCTqUIIIAAAggggED4ChBAw3fs6TkCCCCAAAIIIBASAQJoSNipFAEEEEAAAQQQCF8BAmj4jj09RwABBBBAAAEEQiJAAA0JO5UigAACCCCAAALhK0AADd+xp+cIIIAAAggggEBIBAigIWGnUgQQQAABBBBAIHwFCKDhO/b0HAEEEEAAAQQQCIkAATQk7FSKAAIIIIAAAgiErwABNHzHnp4jgAACCCCAAAIhESCAhoSdShFAAAEEEEAAgfAVIICG79jTcwQQQAABBBBAICQCBNCQsFMpAggggAACCCAQvgIE0PAde3qOAAIIIIAAAgiERCBnSGql0kwJDBkyRA4dOpShfWJiYuTRRx/NUFkKIYAAAggggAACoRAggIZCPRN1jhgxQh566CFp8bfmGdpr9sA5Eh0dLX369MlQeQohgAACCCCAAAJ2CxBA7RbPZH2pqamS2LWBtH6mZYb2PHUwRXQfFgQQQAABBBBAwKkCXAPq1JHJRLtOJ5/ORGmKIoAAAggggAACoRUggIbW/4prXzRisQyq/PoVH4cDIIAAAggggAACdgkQQO2SDkI9qyetkYl/myTnzgXh4BwSAQQQQAABBBAIkgDXgAYJNpiHPXk0RSY9PkmWjVkhReIKy5GdR4NZHcdGAAEEEEAAAQSyVIAZ0CzltOdgvy/dJVvnb5duI26XxHsTJSLCnnqpBQEEEEAAAQQQyAoBAmhWKNp8jFJ1SsnDv/WXau2r2Vwz1SGAAAIIIIAAAlcuwCn4KzfMkiMsXbpUZsyYIRUqVPA73rFjx6RE0+J+6/Lkz+P33vdN8smT8uyzz8qgQYN8V/u9/v3332Xt2rXSpEkTv/W8QSC7C3w76Vt58eUXJX/+/EHryvFjx2XC2AlSrFixoNXBgRFAAAG3CxBAHTLCffv2lRtvvFGKFCni16L//e9/MuqXkX7r0nuTO3du801IPXr0SLPYX/7yF6lUqVKa29mAQHYVeHPwm3LVXWUkunDeoHVhxVerZMyYMaJ/Z1kQQAABBC5PgAB6eW5ZvlfhwoVF/1y4FC1a1HONZ8Yv8szhKashtnz58hceyvteQ2pUVJT3PS8QcItAzpyRnvAZLVXaxgetS5u+3xy0Y3Ng+wXmzZsnzZo1k2XLlkmtWrXkvvvuk+XLl8uvv/4qU6ZMkfbt28vmzZsvOjtlf0upEQF3CXANqLvGk94ggEAWC5zjOWdZLOqsw505c0b++te/SvXq1U3DFi5cKA0aNPC+1omBChdcGuWsHtAaBLKnADOg2XPcaDUCCGRAYNbrc2TpV8sClixcqbD0GH1nwG26cuOsTTL9XzNkz6q9UrpuKal5S01p3LthmuXZkD0FmjdvLvpHl+TkZFm1apX079/fvPcNo2YFPxBAIMsEmAHNMkoOhAACThMoXaek1Lqlht+f+Ovi5OCmgxJbPF+azd3842YZ3mWklE0sK70m3yOVW8fJ1Oemytopa9Pchw3BEzhx4oS5ubJKlSpmpvKjjz6SqVOneoOj1rxx40bR69tLlSpl/vTp00eSkpK8jdq2bZskJibKunXr5LbbbpOSJUua0+6dO3eWt99+25TT0/A6I+o7A2q91gJ6s+jDDz8scXFx5nT9888/L1u3bvXWwQsEEMi4ADOgGbeiJAIIZDOBKm2reK4HreLX6m8f8dzBXq2YtH+tvd963zdzBs+Vyp6g2n5QO3MNdpn6ZeTo70mydPRyKVAkeHfY+7aB1+cF9BKIu+66y4S/F154QXbu3CnPPfecOS2eI8f5ORQNjjqL2bRpU/nss8/MUz5eeeUV2bdvn4wdO9Yc6LfffpP169fLQw89ZK6R79atm5QrV04mTJggt956qymjM565cuWSmjVrmn23b9/uDaMHDhyQdu3aSd26deXFF1+UI0eOmOA6f/58+f777xkuBBDIpAABNJNgoSiecizF8+D5bQGrLlO/tPT4313e7dsWbhfhLGFAK1YisGnOZlk0fLHcO7Gn5IoOfCNe0u4k2eQ5/d5zXA+/GwA7De5gAL/7G2HDzk/S66+/bgLemjVr5KqrrjJVR0dHm9Pk/fr1M+8fe+wxqV27towfP97cYKlBUWcyH3/8cTNDqTdlarg8evSoCZv333+/2W/OnDmerzI+5w2ZWkZvRNIQqq91sWZAhw8fLnXq1JFx48aJ3sipi/7Wm5Z0hlbbxIIAAhkXIIBm3CokJdu2bSsvDnpRlr4Q+Dq2CxuVKzm3dOrU6cLVvHeQgJ7GK17c/9muDmpetm7KqdOn02z/2dNnZfyAiZLQMUEqXJ32UyKsr7YtEldEpr8w01wLmrdgHmn6QGOJvz7eE1jEzH7p83RZgiuQL18+88iru+++2xs+tUYNmLpoONSgqM9Q1jvWfZ/uoWU0gOqpeQ2gixYtMjObvXv3NvvqD12nwbFatfNf6qHHaty4sdmur/UGpIoVK5r3AwYMMLOnOiu6f/9+c9xvvvnGPHOW8GmI+IFApgQIoJnisr+wXqe0buU6+yumxqAInD171pzC0+vUWLJe4NjpY1JBygU88Ppp6+XQlkPS6d/nZzIDFvKs1BlQXb7p963nWtEDktAhQVZNWC0jun4hXT+/TU56vuxBT+++8847phw/gidw5513yuLFi+Xvf/+7XyU7duww7+vXry9LliyRnDlzSps2bfzK6Jd46KKn2XXRQKkzn76PtdMAqjOnkZGRZlxXrlwpDz74oLe8Ht9aBg8ebL7gY8+ePVKiRAmpXLmyCaE1atSwivAbAQQyIUAAzQQWRRG4UgH9j59et7Zr164rPRT7BxBo3a5VgLXnVy35cpkUqlBIKl5bIc0yuiElKcVsP3X8lDyy6GGJzJlD2v6zjXzY+mOZOnCaVGtdVV599VUeRJ+uYtZsXLFihbz55ptSoEABvwPOnTvXnP7WRyfpNZ46U6kh1Hf55ZdfpGDBguaGIQ2sej3ohSFVQ2mrVuc/M4FuQNLrRHXR60T1NL/+o6N79+6mPj3Fr89pbtSokW+1vEYAgQwKcBd8BqEohgAC2VfgxMETsu77dVK/Rz2/GbBAPYopdv7u+Dq31zLhU8tERkVKjc4JcmjrYTmdcibQbqwLgoA1e6mznNaip8Bfe+01c62mnnLXO9L37t1rbjCyyugs9dChQ+X66683461BU//hZ13PqeX0uk29rtSa5dQyeu2nXgOqp9j1rnmr/KxZs0w9egOT9YUhkydPNpdi6AwqCwIIZF6AAJp5M/ZAAIFsJrBq/Go5ezpV6nWrc8mWx5aKNWUKlPWfdYsteX69uQj0kkehQFYI5M+f3zwy6V//+pd8/vnn5s9NN91kbiaywqHOYMbExIg+EknvkNeZTp251MtdPvjgA9MMPdWuj3CKjf1jDD1rNdSmpqZ6Q6YGUL37PdANSNdee61s2rRJZs6cKadOnZJJkyZJz549zbF5SH1WjDTHCEcBAmg4jjp9RiDMBHav2C0aKL0hMp3+F40vKhpCN832/8rNtd+vF314fVSewHfPp3NINl2BgIZI/TpMvQnorbfe8l4PagVQvTNeZyP1cUh6s5HeNKSnx/W0uTVbqeHSKm81RUOp3sWe1jcgFSpUSCpVqmSKa+jVZ4dqOzTs6mOYRo4cabb5PmvUOja/EUDg0gL+F81cujwlEEAAgWwnsH/9ASlWtWjAdh/wPJR+xoszpeG9DTzXh1Y0p9ub9m0i056fJiVqlJBq7avKklFLZMP09dJm4HVyZMORgMdhZdYLbNmyxYTJL7/80ntwvfNcT6d37NjRu86aodQnE2hwzJMnj3ebvpg4caLfe32j33ZkfeORvtebnazl//7v/0T/WIue6v/qq6/MKXedWbWCLV/TagnxG4HMCzADmnkz9kAAgWwmsH/9fk8ALRaw1cmHkmXluFVycMth7/ar+zWRlk+1lClPTZHX4t+QOW/+KE08j2HSYMpin8CoUaPMaXG9xlPD3k8//SQvvfSSubZTnxBy4aJPl7gwfF5Y5kre681QVvi8kuOwLwIIiER4/lJ7nmrHEk4C+m0h+kiRJk34j6nd467XnOlsis6isGS9wDWtr5GI2uckb6GseSj4udRzknw4WfIWzCsROSJMg6f9Y7q899573AWf9cN30RH1aRH6XGO9Q13vaNfrO5s1a2YeOE8QvIiLFQhkKwFOwWer4aKxCCCQnsBnH34qQ94bKpFJkekVy9w2veTz+J+7JD7TUHwfZv7nFl5ltUDp0qVFH6ekX6Gpd6UnJCT4PZA+q+vjeAggYJ8AAdQ+a2pCAIEgC8THV5G3B78d5Fo4vJ0C+pB4/aYi69uK7KybuhBAIHgCXAMaPFuOjAACCCCAAAIIIBBAgAAaAIVVCCCAAAIIIIAAAsETIIAGz5YjI4AAAggggAACCAQQIIAGQGEVAggggAACCCCAQPAECKDBs+XICCCAAAIIIIAAAgEECKABUFiFAAIIIIAAAgggEDwBAmjwbDkyAggggAACCCCAQAABAmgAFFYhgAACCCCAAAIIBE+AABo8W46MAAIIIIAAAgggEECAABoAhVUIIIAAAggggAACwRMggAbPliMjgAACCCCAAAIIBBAggAZAYRUCCCCAAAIIIIBA8AQIoMGz5cgIIIAAAggggAACAQQIoAFQWIUAAggggAACCCAQPAECaPBsOTICCCCAAAIIIIBAAAECaAAUViGAAAIIIIAAAggET4AAGjxbjowAAggggAACCCAQQIAAGgCFVQgggAACCCCAAALBEyCABs+WIyOAAAIIIIAAAggEECCABkBhFQIIIIAAAggggEDwBAigwbPlyAgggAACCCCAAAIBBAigAVBYhQACCCCAAAIIIBA8AQJo8Gw5MgIIIIAAAggggEAAAQJoABRWIYAAAggggAACCARPgAAaPFuOjAACCCCAAAIIIBBAgAAaAIVVCCCAAAIIIIAAAsETIIAGz5YjI4AAAggggAACCAQQIIAGQGEVAggggAACCCCAQPAECKDBs+XICCCAAAIIIIAAAgEECKABUFiFAAIIIIAAAgggEDwBAmjwbDkyAggggAACCCCAQAABAmgAFFYhgAACCCCAAAIIBE+AABo8W46MAAIIIIAAAgggEEAgZ4B1rELAFoEzZ85ISkpKUOvKmTOn5M6dO6h1cHAEEEAAAQQQyJwAATRzXpTOQoEqCfGyecMWyZ03eAExJTlFtmzZIuXLl8/ClnMoBBBAAAEEELgSAQLoleix7xUJHDtxXB5bPkAKlMl/RcdJb+cRN46SHTt2EEDTQ2IbAggggAACNgtwDajN4FSXMYFz585lrOAFpS53vwsOw1sEEEAAAQQQCKIAM6BBxOXQmRfYMGODLBy+WNZP3yAFryog9XvUl6sfbJLugVJTz8ns1+fI0i+XyrF9x6XqDfGSeG+iVLymQrr7sREBBBBAAAEEQiPADGho3Kk1gMDhHUdkVPevJLpwXrlnXA+p172eTHt+mswb+nOA0n+umvLUdzL33XnS4onm0mNMdzmTcla+unu0pBw79WchXiGAAAIIIICAYwSYAXXMUNAQncXMXzq/3PTGTZIjR4SUTSwr2xdslyVfLpOr+zUNCHRs7zFZ+N9F0uHNm6TenXVNmdJ1SsnQZh/I6omrA+7DSgQQQAABBBAIrQABNLT+1O4j0H7QjXLycLIJn9ZqDZiRUWlP1K8Yt0pyx+TyhM861i4SlTdKBix6yLxf8flK73peIIAAAggggIAzBAigzhgHWuERiMqTU6JKxhqLA5sOyvIxy2XHrzvk5qGd0/Q54jltX6xacdm//oD8OPgn2b18t5SsWUKue+66oN5dn2aD2IAAAggggAAClxQggF6SyH0FDhw4IKNHj5YFCxaEtHNpPYT+0NZD8k7iENO2Km3jpVaXWmm2M2l3kiR7Zk0/6/i5FKtSVMrULy3Lvl4uG37YJP1/7msedP/111/LwoUL0zyGnRtSU1OFO/XtFKcuBBBAAAEnChBAnTgqQW5T9erV5dChQ3L27Nkg15T+4VPPpgYsEF0kn/Sf/6BsnbfVzGp+dP0n0ntaL4nMefGp+JSjKbJ31V5pM/A6uXZAM3O8pg82laFXv29uTDrrCXw7d+50TOjT8EkADTjsrEQAAQQQCCMBAmgYDbbV1XHjxlkvQ/r7izFfBKxfr+nU2Uz9kysmt/zv/rGy4zfPw+SblLuofEzxfBIRIVL3jtrebcWrFZMS1YvLzkW7JDpvXhkwYIA0a3Y+nHoLheiFzoAOHTo0RLVTLQIIIIAAAs4QuHhKyRntohVhKLDFM+O5Z9Uev57Htapk3u9cuNNvvfUm1nPNaE7PtaP5iuWzVpnfsaU815JqMmVBAAEEEEAAAccJEEAdNyTh26BJT06RsX2/9QNYN3W9eV+4UmG/9dabSi0qyunkM+ZmJWvdqeOnZPOPW6RsgzLWKn4jgAACCCCAgIMECKAOGoxwb0riPQ3MXeyz35gj+vilZWNWyOzXZpvT6fFtKhsevTt+9H1jPAFzs3lfoVkFc+PR2L7jZIdnllS3f/vweMmZO1Lq3J72zUvhbk3/EUAAAQQQCKUA14CGUp+6/QQa/7WhHPcEz9lv/CgzX55ltukp+E7/7uB5FmikeZ98KFlWep79GdcqTipea1ZJ9y+7ydgHv5WP237iucFHpFCFQnL7Z7dJsarFzhfgJwIIIIAAAgg4SiDCc0eu5z/ZLAjYL1C8THHp8X33i57XeSbljBzaelj0+s48+XNnuGH61Zsnj5z0O96IG0fJZ28Oc9RNSFFRUSF/AkGGUSmIAAIIIIBAEASYAQ0CKofMmEByUrKM6DhSYgrHZGyHyyi1adFmKVw48PWjl3E4dkEAAQQQQACBLBBgBjQLEDnE5Qns27dPNm8+fy3n5R3h0nsVKFBAqlateumCNpXQxzAxA2oT9h/VTJ48OehfRHDNNddIq1at7O0YtSGAAALZWIAAmo0Hj6ZnPwECqL1jtmfPHilZsqS0+FvzoFY8+805cvLkScmdO+OXjAS1QRwcAQQQcLgAp+AdPkA0DwEELl9AL3EvWLygtH6m5eUfJAN7znv3Z77hKgNOV1pk+fLlUrt2bfnxxx9FZ50DLY8++qhMmTJF1qxZE2gz6xBAwCECPIbJIQNBMxBAwH6By7kHMzWV+zbtH6nzNS5cuFBy5Mgh9erVS7MJV111lTz88MNpbmcDAgg4Q4AZUGeMA61AAAEbBTbO2iTT/zXD881be6V03VJS85aa0rh3Q8+XZ6X97Vkbf9go3w+cLvvW7JU8BfJIrS61pM3A6yRXdJSNLQ/vqjSAJiQkSL58/t985qvy2GOP+b7lNQIIOFSAGVCHDgzNQgCB4AjolxgM7zJSyiaWlV6T75HKreNk6nNTZe2UtWlWuG/tPhnZ7UspWK6g3DOhp7R6uqUsHrVEpjz9XZr7sCHzAnod7dtvvy0tWrQQvYHwhhtukE2bNnkPpAG0QYMG8vXXX0tiYqKUKVNGHn/8ce/21atXm/UrV6406z755BO57rrrZN26ddKmTRspWrSo9OrVy1wu8c0330jjxo3NMf7+9797j7FhwwZzjJ9//lnatm1r2qG/t2/f7i2jL5YuXWpmWuPi4qRWrVry/PPPy9atW71lPv30U7nrrrtky5Ytcsstt0ixYsXk1ltvNe+1kM6+62UE2o8L/4wYMcJ7nEmTJsltt91mnuZRs2ZN+eqrr7zbrBcZKWOV5TcCThEggDplJGgHAgjYIjBn8FypfF2ctB/UzvMtWmWk5ZMtpO6ddWXp6OVp1r/mj3Da+Z2OUr5JOWnUq6HUvaOOLP/fCuGUfJpsmd6gYfLVV181YfHNN980wfG5554zxzl79qwsWbJE5s2bJ++//770799f+vXrJ1rup59+MmV++eUXWbx4sVSoUMG8//7772Xt2rVy5513SseOHeXJJ58UDYbdunWTQYMGSd++fc221157zXvN6Pz5881TE/76179K165d5cUXXzT1asC0lgMHDki7du1k/fr1Zru2Y/To0XL//fdbRWTq1KmyYsUKEz41wA4dOlTmzp0r7733nimTnJwsnTt3NnXccccd0qNHDxNgt23bJtdee/5bNqZPn272j4mJkVGjRhkXbfusWbO89WSkjLcwLxBwkACn4B00GDQFAQSCK5C0O0k2eU6/9xzXw+90e6fBHdKtOG/BvJJ6+qycST7tLZd6NlVy5cvlOY53FS+uQGDChAkmpH333Xdm5lMPpaFTZydPnDhhZkI1tFWuXFnGjx9vHmemT5XQYLhq1Sozm6gzpPrYNesU/aJFi+TUqVNm1lBnKnWGVY+nwXH27NmiwU5nPN944w3ZsWOHVKtWzfvIro8//liaNm1qenTkyBEZMmSImbXUyzSGDx8uderUkXHjxnmffKBPQLjvvvtMW6Ojo0Xr1qcw6Gxs2bJlzXF09lJnTnXRMk888YR5rT/uvvtuOXr0qMyYMUPKly8vu3btMuH03nvvlQ8++MCU09CrYVtDbMuWLTNUxlsBLxBwmAAzoA4bEJqDAALBEziy86g5eJG4IjL9hZny4XUfy39vHSHrp61Pt9KqN1Y1p9/HPTReNszYIHOH/CzLvl4uTfo08guy6R6EjekK6Mxk8+bNveFTC+uM4uHDh01Y03Cpy+DBg0341Nf6HOEzZ85IfHy8vjWhr379+ua17rdx40bRAKfhUxfrzni9SUnDp++6KlWqmPdaj562t8KnrtQZSQ2TeopflwEDBoie9v7999/lt99+MwFXT+nnz5/ftFWDpAZbrccKn7qfXk5QsWJFfem3vPTSSybUfvjhh967+/X5tUlJSWaGVmdxrT96A5b2S5eMlPGriDcIOEiAGVAHDQZNQeBSAvofWv2PUp48eS5VlO0eAZ1BO+mZNbMWnQHV5Zt+38rBTQckoUOCrJqwWkZ0/UK6fn6bVO+YYBX1+x1bIkZu/c8t8mn7z2TT7PNfnhDfNl6uGXD+UUBaj868pXcTk98BeeMnoKfT9fS6nvL2XXw9NRhqeNNZSmvRWUZd9NFM1in6Ll26mHV6Kl4X672+1mPoXfQdOvw5463HKFKkiJQrV85zOUWqOYXve7pd99MZVl1KlSplfmsI1lP4GkpLlChhZmU1FNaoUcNs17r1Gs9OnTqZ9/pDZ2J1NrR3797edfpi7NixopcZ6GzoPffc492m16CePn3azHR6V/7x4uqrrzavMlLmwn15j4BTBAigThkJ2oFABgT01Fz37t2ldevWGShNkb1798r17dt4IVKSUszrU8dPySOLHpbInDmk7T/byIetP5apA6elGUBXT1wtY3qPlXp31ZPEnvVl19Ld8tPbc+W/t4yQu//XXXJE5jDX/PEPAy91pl5oKNQAZs1CWjvraXH9Kl09Xa3hsVmzZtYm81vXaXDUAKkhUU/VWzOguk1PxetNS9aiYVMDrJa3Fl1n7aOzjMeOHfNeQ2qV0WsuS5cuLYUKFRK9VEDvtH/nnXfM30Vtn87C6g1OjRo1Mrto3dpm67i6Up9hqoHStz0auvXUuwZivfbVd9Gwqjcx6en+tJaMlElrX9YjEGoBAmioR4D6EciEgF5npjMuGkRZLi2gXhGecGMtMcXOP76nzu21TPjU9ZFRkVKjc4LMfHmWnDiULNGF8lrFvb8XfPKbFK1STKxrRUvXLS35ikbLlz1Gy45fd0iE5386JgRQL1mmXujspX5Fre8d73q6XGc29Qahhx56yMyQ6t3gvouGRyvQaejTGVPrGaG6rW7dumbG09pHy1jlrXVaTv9Rp4tu10X/4WItesZh5syZJijqOg2jekpf22QteipcrxPV9upi1R0ZGWkVMety5sxprh3Vlbt37zYzpHpNq95gpCHcd9EwrnX5LnpXv94UpTdK6f8PZKSM7/68RsBJAv6feCe1jLYggAACWSwQWyrWHLFA2QJ+R44teX6957yp33rrzfYF26XajeevEbTWxV8fLzk8M6hb52+3VvH7MgU0qF1//fXm8Uo6C6nhU+9C18cs6WOT9L3Obl4YHn0DpYY+DXN6HaYu+t63vIbcZcuW+a3bt2+febySNVOpx9P933rrLRN4t3geoaThVMPhwIEDzXH1elANyhpK9bS6Xgvas2dPs63CH3ffa93WMc0Gzw89dvXq1c0/UnS/m2++WQ4dOiRPP/20uTteb77SP9Z1qnr6Xh/9pNeHalgdNmyYCb19+vQx4VOPm5EyVv38RsBpAgRQp40I7UEAgaAJFI0vKhpCres4rYrWfr9eClfynOotHG2t8vutgXXvmn1+67b/sk1Sz6RK/jLnA4/fRt5kWkDvMtcbgzSkNWzY0Ny8o4EsNjbWhDed3dQZTWvRcHjw4EFv0PMNozprqc/+9A2geope76L3XadBURdrnR5Dg7DeKa+n+/Wa0507d5o7z/W5pLrcdNNN5rmc7du3N+3VGcmRI0eabVrv8ePHzQ1D1jHNBs8P3/bpo6T0kVF6ul8fwaR3t994443mz7Rp08wueu3qyy+/bGaA9dpTDZ466+p753xGylj18xsBpwlEeC6UDvxPfqe1lPYg4AIBvclBTzXqbMzlLPofP33moP7Hj+XSAjpzlFAnQR5d87C3sN7BPu35adLx3x2lWvuqssTzQPmZL/9gvtWoad8mptzS0ctk7Xfr5C9DO0tU3ij55eNfZfKTU8z1onod6M6FO2XGSz/I8f3Hpf+8vvJ6/Fty9MhRTsF7lS//hQY+vdZSr6G0c9G/mxoyn332WRNA9ZFNGnD12s9Ai55y17/Heg1oMBetQx9wr3fT58qVK2BVGSkTcEdWIhBCAa4BDSE+VSOAgP0CV/drIqc9z/Oc8tQUGf/IBMmTP7c0eaCxWOFTW7R7hef5jeNWSee3O5oGNuqVKCePnJSZr8ySqc9PN+tK1ystd33VTXLH5jbv+ZE1AnraPRSLdQOSfiuRLno9b1rhU7dbM6L6OpiLXp5QqVKldKvISJl0D8BGBEIgQAANATpVIoCAfQIpySme6zS3+VVY8doKUv7qcnJs7zGJKR5j7mL3LaMzo/pn98o93v0qNCsv5ZpcJcf2HDOhU4PnyaPnj3361GlvOV5kTwE9Ra6n+a0Amj17QasRyD4CBNDsM1a0FAEEMimgp0ebt2wuS19Ylsk9M1f85ttuTvP0aOaOROlQCejXZepXZ9o1sxmqflIvAk4RIIA6ZSRoBwIIZLmAXjP33fjvsvy4HNB9AsWLFxf9w4IAAvYIcBe8Pc7UggACCCCAAAIIIPCHAAGUjwICCCCAAAIIIICArQIEUFu5qQwBBBBAAAEEEECAAMpnAAEEEEAAAQQQQMBWAQKordxUhgACCCCAAAIIIEAA5TOAAAIIIIAAAgggYKsAAdRWbipDAAEEEEAAAQQQIIDyGUAAAQQQQAABBBCwVYAAais3lSGAAAIIIIAAAggQQPkMIIAAAggggAACCNgqQAC1lZvKEEAAAQQQQAABBAigfAYQQAABBBBAAAEEbBUggNrKTWUIIIAAAggggAACBFA+AwgggAACCCCAAAK2ChBAbeWmMgQQQAABBBBAAAECKJ8BBBBAAAEEEEAAAVsFctpaG5Uh4FKB7du3y4wZMy7Zu9TUVDl37pwMGzbskmUDFdixY4dMmzZN9u7dG2izlC1bVtq0aRNwGysRQAABBBBwikCE5z+G55zSGNqBQHYVKFW2lEQVyyklE0pesgvHjx2TfDExlywXqMDJ5JMSFRUlkTkjA22WX7/4TZYsWSJ16tQJuJ2VCCCAAAIIOEGAGVAnjAJtyPYChYoWkuaDr5HSdUqFtC8H1h2UkydPhrQNVI4AAggggMClBLgG9FJCbEfgCgWCeZIhmMe+wm6zOwIIIIAAAmkKMAOaJg0bELgygd+X/S5zh/ws66aul7wF80q97nWl5RPN0z3oqvGrZPqLP1xUps2zraR6p+pm/dFdR2XyU9/Jxh82SurZc3JVo6uk/avtpHi1YhftxwoEEEAAAQScKEAAdeKo0KZsL3DqxGn5qufXUjaxjNw7/m7ZvWKPTHpiskTkiJAWf7s2zf5tW7BDTieflnrd/K/hLFi+kNlHZzy/6DFakg+ekE5vd5I8sblk5iuzZPhtI6Xf3L5pHpcNCCCAAAIIOEmAAOqk0aAtrhGY+85cOeEJiZ3f7SxReXJKqdql5MiOIzL//fnSrH9TyZk78F89DaqVmleU1v/XKqDFoS2HZNfiXdL5nY5S65YapkxUvlzyWYfPZevPWwPuw0oEEEAAAQScJsA1oE4bEdrjCoENMzdKfJvKJnxaHarWvqonlCbLTk+ATGvZs3KPJ6yev5M+NfXiB1TkKZBHIiJEUpJSvIdIPZNqXueOze1dxwsEEEAAAQScLBB4GsbJLaZtCGRHxPEoAAAVU0lEQVQDgYObDpprM32bGlsqv3l7bM8x39Xe10me9ScOnJD96/fLZ53+K9vmb5PiCcU913feIOWbljflogtHS52utWXe0J8ll2fmM2+hvDLrtTlSul7pi+rzHpgXCCCAAAIIOEyAGVCHDQjNcYeAzlBGF87r1xmdvdTl2L7jfuutN3tW7DYvt83fLjX/UkNaPtncE0iPyzBPGN3tmRm1lpteby96rPEDJprrTI9sPyx3fH6b59mg/HW2jPiNAAIIIOBsAf6L5ezxoXXZVCBHlOdB8Xqu3Gex3qaePuuz9s+XRasWk46DO8i9k+6Rhvc2kBaPN5c+M3vLOc+peJ3l1EVnSd9v/qFEReeSbiNul57jeshVja+S/7T52C+k/nlUXiGAAAIIIOA8AU7BO29MaJELBGKKx8jJw8l+PTl55PwD4nPFBL5Ws2DZApLYs77fPnqc8leXF2t2dO136+Tg5kPy8NfdpUilwqbsVQ3LyuvV3pTFIxb77csbBBBAAAEEnCrADKhTR4Z2ZWuBmBIxcuG1nkm7z1/7Wbji+UcqXdjBw5675Lf/uuPC1ZLTcxe9mVH1bNn+yzYpWqWoN3xq4ai8URLXKk62ek7dsyCAAAIIIJAdBAig2WGUaGO2E4hrUVHWz9AHxZ+/Q107oA+kz+15bmdaX9epM5gf3/Cp7Fu339vfZM+s6abZm6VM3fNf8VnAM0t6eNth0eeMWstZz13wW3/eJvlLn7/JyVrPbwQQQAABBJwqQAB16sjQrmwtkHhPA9FT7lM831iU7DkVv2XuFtFng7Z6upUnhJ4/BX/Ac6f86PvGyOYfN5u+1upSy8x26rcc7fbckKQ3K01+cop5eP01A64xZfTblPRa0tH3fi0HNh6Q/RsOyKTHJ8lxT9lGvRKztRmNRwABBBAIHwGuAQ2fsaanNgrElow1Nwl98+C3suCT3zxfxZlHqneuLo17N/S2IvlQsqwct8qcPq/o+XKkopWLSNdhXWTi45M9Nxr9x5TT0/X6TUrW12wW8nwj0p1fdJMJj06UdxoONWX0UUw3D+kklVvHydxXfvYenxcIIIAAAgg4VSDC89V+Fz/t2qmtpV0IOFSgWu1qcs1rV3tOg8f6tVD/eh3dlSSxnmtCc2TwMUm6j14/qtd95isS7Xc83zfH9x+XMylnTZ0Rf9xiP7zjKJk4eqI0btzYtyivEUAAAQQQcJQAM6COGg4ak10FWrRoIcO7DJcChQsEtQtJSUcld+48kitXroD1nD1xVuLi4gJuYyUCCCCAAAJOEWAG1CkjQTsQyIDATTfdJP369ZP27dtnoDRFEEAAAQQQcKYANyE5c1xoFQIIIIAAAggg4FoBAqhrh5aOIYAAAggggAACzhQggDpzXGgVAggggAACCCDgWgECqGuHlo4hgAACCCCAAALOFCCAOnNcaBUCCCCAAAIIIOBaAQKoa4eWjiGAAAIIIIAAAs4UIIA6c1xoFQIIIIAAAggg4FoBAqhrh5aOIYAAAggggAACzhQggDpzXGgVAggggAACCCDgWgECqGuHlo4hgAACCCCAAALOFCCAOnNcaBUCCCCAAAIIIOBaAQKoa4eWjiGAAAIIIIAAAs4UIIA6c1xoFQIIIIAAAggg4FoBAqhrh5aOIYAAAggggAACzhQggDpzXGgVAggggAACCCDgWgECqGuHlo4hgAACCCCAAALOFMjpzGbRKgQQQCBrBNasWSM7duzImoOlcZSKFStKXFxcGltZjQACCCBwoQAB9EIR3iOAgGsEDh48KAkJCZLQolpQ+7R69hpJSUmRXLlyBbUeDo4AAgi4RYAA6paRpB8IIHCRwKlTp6Rg8YJyxze3X7QtK1e8WPIVSU1NzcpDciwEEEDA1QJcA+rq4aVzCCCQnsC5c+fS2xxwW2pq5vcJeCBWIoAAAmEswAxoGA8+XUcgXAU2ztok0/81Q/as2iul65aSmrfUlMa9G0pERESaJBt/2CjfD5wu+9bslTwF8kitLrWkzcDrJFd0VJr7sCFzAsuXL5fatWvLjz/+KNdcc03mdqY0AghkKwFmQLPVcNFYBBC4UoHNP26W4V1GStnEstJr8j1SuXWcTH1uqqydsjbNQ+9bu09GdvtSCpYrKPdM6Cmtnm4pi0ctkSlPf5fmPmzIvMDChQslR44cUq9evczvzB4IIJCtBJgBzVbDRWMRQOBKBeYMniuVr4uT9oPamRnPMvXLyNHfk2Tp6OVSrX3gm5XW/BFOO7/TUfIViZbyTcrJvrX7TQjtOLjDlTaJ/f8Q0ACqN43ly5cPEwQQcLkAM6AuH2C6hwACfwok7U6STZ7T71f3a+p3ur2TJ0R2HXbbnwUveJW3YF5JPX1WziSf9m5JPZsqufLl8hzHu4oXVyigAbRBgwby9ddfS2JiopQpU0Yef/xx71G3b99u1i9YsMC7Tl/ccMMN8sEHH5h1W7duNWXmzp0r/fr1k5IlS5rT+evXrxfddvPNN0vRokWlc+fOosezliNHjsgrr7xiyuo+vXr1kh9++MHabH7feeed8vnnn8s333wjTZs2Ne176qmn/MrwBgEEMiZAAM2YE6UQQMAFAkd2HjW9KBJXRKa/MFM+vO5j+e+tI2T9tPXp9q7qjVXN6fdxD42XDTM2yNwhP8uyr5dLkz6N/IJsugdhY7oCZ8+elSVLlsi8efPk/fffl/79+5sA+eabb8pPP/1k9v31119FQ2r58uW9x9q/f79MnTpVihQp4ldmwIABkjt3bnn33Xdl48aNJlB26tRJGjZsKEOGDJHp06fLsGHDvMfp27evfPTRR3LrrbfK0KFD5fDhw3LjjTfKnj17TJnTp0/L2LFjZfjw4fLhhx/K3/72N+nTp48MGjRItF0sCCCQOQFOwWfOi9IIhFRA/0Oq/8HT/wiyXFogOTlZTnmez2ktOgOqyzf9vpWDmw5IQocEWTVhtYzo+oV0/fw2qd4xwSrq9zu2RIzc+p9b5NP2n8mm2ZvNtvi28XLNgPM3ypxNPSt33323REZG+u3Hm4wJ6KxkjRo1RMercuXKMn78eImKijKPtnr++edl1apVZmZy0aJFUrp0aSlRooT3wLpOF5051UUDqi4PPPCACZ36Wv++fP/99+bmpkaNGukq8/fI+oKCZcuWydq1a2X06NFm9lS366xqbGysfPfdd9KzZ09ZuXKledartmvKlClaRM6cOSP/+Mc/ZOnSpSbYmpX8QACBDAkQQDPERCEEnCGgpxRz5swphQoVckaDHN4KncWa8eMMbytTks6H0VPHT8kjix6WyJw5pO0/28iHrT+WqQOnpRlAV09cLWN6j5V6d9WTxJ71ZdfS3fLT23Plv7eMkLv/111yeM7Dd+jQgQfRe6Uz96J69ere4Dh48GATPvUImzdvNiEvPj7eHFDDphU0rRo0cBYsWFAqVarkLaPfTKWn0K1l9erV0qZNG7HCpz6zVU/J33XXXaaI3nmvx9m7d6/onfh6av63334z2/R0vC5W0NV/AFrLli1bRB/lpfWxIIBA5gQIoJnzojQCIRV46KGHQlp/dqt89+7d8vTzT3ubHVPs/M0tdW6vZcKnboiMipQanRNk5suz5MShZIkulNdb3nqx4JPfpGiVYqLXiupSum5pyVc0Wr7sMVp2/LrDcxo+h9x+++2SJ08eaxd+Z1JAT39rkKtW7c8bwazQpwFRF32vM5u+y/z586V+/freVRok7733Xu97vbZTzxw8+eST3nXr1q2T48ePe++212PoKX/dV2+A0q9VtWaza9asafbTuvXUv9UWXbl48WKzrU6dOuY3PxBAIOMCXAOacStKIoBANheILRVrelCgbAG/nsSWPL/eM53lt956s33Bdql2YxXrrfkdf3285PDMoG6d/+eNLH4FeJMpAQ1/zZo189tH15UrV85c36nXYuof37CpX386Z84c77pt27bJgQMHpEWLFt7jaEjUWUrfY+txddFj6Wn/9u3bS9myZU1QTUryPBHBc0pdQ2WpUqXMjUZaVve59tpr9aV3sdqnNzWxIIBA5gQIoJnzojQCCGRjgaLxRUVDqHUdp9WVtd+vl8KVCkt04Whrld9vDax71+zzW7f9l22SeiZV8pfJ77eeN5kXsG5AuvD0us46Wus2bNhgDly1alVvBdbNQlYZK1ha77WgHkNnNS+cWdVT9nrqXsPmoUOHRK811XX6ZQQ6azp58mTvbKe2T8v5HlePrfX5BmJdx4IAAhkTIIBmzIlSCCDgAgE93d60bxNZ8NECWTh8sRw/cELmvjtPNkxfL416JXp7uHT0Mhl93xg5/cdjlxr1biSrxq82ZfU0/frpG8y3Imn4rNbOf2bUexBeZFhgzZo1cuLEiYABzwp91uUNeke83vmu14p+8sknpg4rBGrY1FlL/WMtGhJ1NlMfcG8tvsFWT6nnz59fRo4cadqg14t27NjRXA9aoUIFs4uu05lSqy2BjmOt4zcCCGRM4M+/kRkrTykEEEAgWwtc3a+JtHyqpUx5aoq8Fv+GzHnzR2nyQGMTTK2O7V6xR1aOW2VmOHWdhtPWz7SSma/MkkFxr8uI20dJRI4IueurbpI7Nre1G78vU0BDos481q1b13sEvcHn4MGD3hlGDX933HGHefSRXoupNxHpdZ16p7p1k1KgGUnfsKkH19PxelreCq3R0dHy8ssvy6hRo6RAgQLSsmVL6d27t7mr/dixY6Y9eoy02ndhKPV2gBcIIJCuQITnL2Pgi57S3Y2NCCCAgPMF9CakhDoJ8sjK/hc1Vh8kf3jbYfN8zxyRGfu3uNln62HJ67lRSf9Yy0ulX5Wko0nchGSBBPG3zn7GxMRkubWeZt+5c6e55jSIzefQCCDwhwABlI8CAgi4VkDvdNaworNXwVz03/H6TEjrzulg1sWxEUAAATcIEEDdMIr0AQEEEEAAAQQQyEYCGTvvlI06RFMRQAABBBBAAAEEnC1AAHX2+NA6BBBAAAEEEEDAdQIEUNcNKR1CAAEEEEAAAQScLUAAdfb40DoEEEAAAQQQQMB1AgRQ1w0pHUIAAQQQQAABBJwtQAB19vjQOgQQQAABBBBAwHUCBFDXDSkdQgABBBBAAAEEnC1AAHX2+NA6BBBAAAEEEEDAdQIEUNcNKR1CAAEEEEAAAQScLUAAdfb40DoEEEAAAQQQQMB1AgRQ1w0pHUIAAQQQQAABBJwtQAB19vjQOgQQQAABBBBAwHUCBFDXDSkdQgABBBBAAAEEnC1AAHX2+NA6BBBAAAEEEEDAdQIEUNcNKR1CAAEEEEAAAQScLUAAdfb40DoEEEAAAQQQQMB1AgRQ1w0pHUIAAQQQQAABBJwtQAB19vjQOgQQQAABBBBAwHUCBFDXDSkdQgABBBBAAAEEnC1AAHX2+NA6BBBAAAEEEEDAdQIEUNcNKR1CAAEEEEAAAQScLUAAdfb40DoEEEAAAQQQQMB1AgRQ1w0pHUIAAQQQQAABBJwtQAB19vjQOgQQQAABBBBAwHUCBFDXDSkdQgABBBBAAAEEnC1AAHX2+NA6BBBAAAEEEEDAdQIEUNcNKR1CAAEEEEAAAQScLUAAdfb40DoEEEAAAQQQQMB1AgRQ1w0pHUIAAQQQQAABBJwtQAB19vjQOgQQQAABBBBAwHUCBFDXDSkdQgABBBBAAAEEnC1AAHX2+NA6BBBAAAEEEEDAdQIEUNcNKR1CAAEEEEAAAQScLUAAdfb40DoEEEAAAQQQQMB1AgRQ1w0pHUIAAQQQQAABBJwtQAB19vjQOgQQQAABBBBAwHUCBFDXDSkdQgABBBBAAAEEnC1AAHX2+NA6BBBAAAEEEEDAdQIEUNcNKR1CAAEEEEAAAQScLUAAdfb40DoEEEAAAQQQQMB1AgRQ1w0pHUIAAQQQQAABBJwtQAB19vjQOgQQQAABBBBAwHUCBFDXDSkdQgABBBBAAAEEnC1AAHX2+NA6BBBAAAEEEEDAdQIEUNcNKR1CAAEEEEAAAQScLUAAdfb40DoEEEAAAQQQQMB1AgRQ1w0pHUIAAQQQQAABBJwtQAB19vjQOgQQQAABBBBAwHUCBFDXDSkdQgABBBBAAAEEnC1AAHX2+NA6BBBAAAEEEEDAdQIEUNcNKR1CAAEEEEAAAQScLUAAdfb40DoEEEAAAQQQQMB1AgRQ1w0pHUIAAQQQQAABBJwtQAB19vjQOgQQQAABBBBAwHUCBFDXDSkdQgABBBBAAAEEnC1AAHX2+NA6BBBAAAEEEEDAdQIEUNcNKR1CAAEEEEAAAQScLUAAdfb40DoEEEAAAQQQQMB1AgRQ1w0pHUIAAQQQQAABBJwtQAB19vjQOgQQQAABBBBAwHUCBFDXDSkdQgABBBBAAAEEnC1AAHX2+NA6BBBAAAEEEEDAdQIEUNcNKR1CAAEEEEAAAQScLUAAdfb40DoEEEAAAQQQQMB1AgRQ1w0pHUIAAQQQQAABBJwtQAB19vjQOgQQQAABBBBAwHUCBFDXDSkdQgABBBBAAAEEnC1AAHX2+NA6BBBAAAEEEEDAdQIEUNcNKR1CAAEEEEAAAQScLUAAdfb40DoEEEAAAQQQQMB1AgRQ1w0pHUIAAQQQQAABBJwtQAB19vjQOgQQQAABBBBAwHUCBFDXDSkdQgABBBBAAAEEnC1AAHX2+NA6BBBAAAEEEEDAdQIEUNcNKR1CAAEEEEAAAQScLUAAdfb40DoEEEAAAQQQQMB1AgRQ1w0pHUIAAQQQQAABBJwtQAB19vjQOgQQQAABBBBAwHUCBFDXDSkdQgABBBBAAAEEnC1AAHX2+NA6BBBAAAEEEEDAdQIEUNcNKR1CAAEEEEAAAQScLUAAdfb40DoEEEAAAQQQQMB1AgRQ1w0pHUIAAQQQQAABBJwtQAB19vjQOgQQQAABBBBAwHUCBFDXDSkdQgABBBBAAAEEnC1AAHX2+NA6BBBAAAEEEEDAdQIEUNcNKR1CAAEEEEAAAQScLUAAdfb40DoEEEAAAQQQQMB1AgRQ1w0pHUIAAQQQQAABBJwtQAB19vjQOgQQQAABBBBAwHUCBFDXDSkdQgABBBBAAAEEnC1AAHX2+NA6BBBAAAEEEEDAdQIEUNcNKR1CAAEEEEAAAQScLUAAdfb40DoEEEAAAQQQQMB1AgRQ1w0pHUIAAQQQQAABBJwtQAB19vjQOgQQQAABBBBAwHUCBFDXDSkdQgABBBBAAAEEnC1AAHX2+NA6BBBAAAEEEEDAdQIEUNcNKR1CAAEEEEAAAQScLUAAdfb40DoEEEAAAQQQQMB1Av8PE5Ec7Fj2frsAAAAASUVORK5CYII=" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">ape_hrf <-<span class="st"> </span><span class="kw">prep_branch_lengths</span>(apetree)<span class="op">%>%</span><span class="st"> </span><span class="kw">tree_hrf</span>(<span class="dt">mutation =</span>(<span class="dv">2</span><span class="op">*</span><span class="dv">10000</span><span class="op">*</span><span class="dv">10</span><span class="op">^-</span><span class="dv">8</span>))
ape_hrf
<span class="co">#> # A tibble: 8 x 8</span>
<span class="co">#> code from to this_branch descendants ancestor sibling hrf</span>
<span class="co">#> <chr> <int> <int> <dbl> <list> <dbl> <dbl> <dbl></span>
<span class="co">#> 1 6-7 6 7 1.00 <dbl [2]> NA 7.50 NaN </span>
<span class="co">#> 2 7-8 7 8 3.61 <dbl [2]> 1.00 15.8 0.287</span>
<span class="co">#> 3 8-9 8 9 0.577 <dbl [2]> 3.61 7.64 0.907</span>
<span class="co">#> 4 9-1 9 1 6.83 <dbl [0]> 0.577 6.83 NA </span>
<span class="co">#> 5 9-2 9 2 6.83 <dbl [0]> 0.577 6.83 NA </span>
<span class="co">#> 6 8-3 8 3 7.64 <dbl [0]> 3.61 0.577 NA </span>
<span class="co">#> 7 7-4 7 4 15.8 <dbl [0]> 1.00 3.61 NA </span>
<span class="co">#> 8 6-5 6 5 7.50 <dbl [0]> NA 1.00 NA</span></code></pre></div>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">hc_hrf <-<span class="st"> </span>ape_hrf <span class="op">%>%</span><span class="st"> </span><span class="kw">filter</span>(to<span class="op">==</span><span class="dv">9</span>)
<span class="co"># the data here are from Kong et al 2012</span>
<span class="co"># numerators are sums of CpG and nonCpG mutations, from Table 2</span>
<span class="co"># the denominator 2*78*2.583e9 is the number of sites observed (effective bases times transmission events -- two times number of trios)</span>
cpg <-<span class="st"> </span><span class="kw">tibble</span>(<span class="dt">mu =</span><span class="kw">c</span>(<span class="fl">1.2e-8</span>, (<span class="dv">2489</span> <span class="op">+</span><span class="st"> </span><span class="dv">1516</span>)<span class="op">/</span>(<span class="dv">2</span><span class="op">*</span><span class="dv">78</span><span class="op">*</span><span class="fl">2.583e9</span>), (<span class="dv">855</span><span class="op">+</span><span class="st"> </span><span class="dv">73</span>)<span class="op">/</span>(<span class="dv">2</span><span class="op">*</span><span class="dv">78</span><span class="op">*</span><span class="fl">48.8e6</span>)))<span class="op">%>%</span>
<span class="st"> </span><span class="kw">mutate</span>(<span class="dt">nmu =</span> <span class="dv">2</span><span class="op">*</span><span class="dv">15000</span><span class="op">*</span>mu)<span class="op">%>%</span>
<span class="st"> </span><span class="kw">mutate</span>(<span class="dt">hc =</span> <span class="kw">map_dbl</span>(nmu, <span class="cf">function</span>(x) <span class="kw">tree_hrf</span>(hc_hrf, <span class="dt">mutation =</span> x, <span class="dt">mode =</span> <span class="st">'strict'</span>, <span class="dt">pepo=</span>T)<span class="op">$</span>hrf))
cpg
<span class="co">#> # A tibble: 3 x 3</span>
<span class="co">#> mu nmu hc</span>
<span class="co">#> <dbl> <dbl> <dbl></span>
<span class="co">#> 1 0.0000000120 0.000360 5.42 </span>
<span class="co">#> 2 0.00000000994 0.000298 6.55 </span>
<span class="co">#> 3 0.000000122 0.00366 0.521</span></code></pre></div>
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