https://github.com/cran/bayestestR
Tip revision: 092b63c552bdf3196413c25583520dc23033769b authored by Dominique Makowski on 30 October 2021, 13:00:02 UTC
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<body>
<h1 class="title toc-ignore">Bayes Factors</h1>
<div id="TOC">
<ul>
<li><a href="#the-bayes-factor">The Bayes Factor</a></li>
<li><a href="#bayesfactor_parameters">Testing Models’ Parameters with Bayes Factors</a></li>
<li><a href="#bayesfactor_models">Comparing Models using Bayes Factors</a></li>
<li><a href="#bayesian-model-averaging">Bayesian Model Averaging</a>
<ul>
<li><a href="#weighted_posteriors">Averaging posteriors</a></li>
</ul></li>
<li><a href="#appendices">Appendices</a>
<ul>
<li><a href="#testing-contrasts-with-emmeans-modelbased">Testing contrasts (with <code>emmeans</code> / <code>modelbased</code>)</a></li>
<li><a href="#contr_bayes">Specifying correct priors for factors</a></li>
</ul></li>
<li><a href="#references">References</a></li>
</ul>
</div>
<p>This vignette can be referred to by citing the following:</p>
<ul>
<li><p>Makowski, D., Ben-Shachar, M. S., & Lüdecke, D. (2019). <em>bayestestR: Describing Effects and their Uncertainty, Existence and Significance within the Bayesian Framework</em>. Journal of Open Source Software, 4(40), 1541. <a href="https://doi.org/10.21105/joss.01541" class="uri">https://doi.org/10.21105/joss.01541</a></p></li>
<li><p>Makowski, D., Ben-Shachar, M. S., Chen, S. H. A., & Lüdecke, D. (2019). <em>Indices of Effect Existence and Significance in the Bayesian Framework</em>. Retrieved from <a href="https://doi.org/10.3389/fpsyg.2019.02767">10.3389/fpsyg.2019.02767</a></p></li>
</ul>
<hr />
<p>The adoption of the Bayesian framework for applied statistics, especially in the social and psychological sciences, seems to be developing in two distinct directions. One of the key topics marking their separation is their opinion about the <strong>Bayes factor</strong>. In short, one school of thought (e.g., the <em>Amsterdam school</em>, led by <a href="https://www.bayesianspectacles.org/">E. J. Wagenmakers</a>) advocate its use, and emphasize its qualities as a statistical index, while another point to its limits and prefer, instead, the precise description of posterior distributions (using <a href="https://easystats.github.io/bayestestR/reference/hdi.html">CIs</a>, <a href="https://easystats.github.io/bayestestR/reference/rope.html">ROPEs</a>, etc.).</p>
<p>The <code>bayestestR</code> package does <strong>not</strong> take a side in this debate, and offers tools to carry out analysis irrespective of the school you subscribe to. Instead, it strongly supports the notion of an <em>informed choice</em>:</p>
<p><strong>discover the methods, learn about them, understand them, try them, and decide for yourself</strong>.</p>
<p>Having said that, here’s an introduction to Bayes factors :)</p>
<div id="the-bayes-factor" class="section level1">
<h1>The Bayes Factor</h1>
<p><strong>Bayes Factors (BFs) are indices of <em>relative</em> evidence of one “model” over another</strong>.</p>
<p>In their role as a hypothesis testing index, they are to Bayesian framework what a <span class="math inline">\(p\)</span>-value is to the <strong>classical/frequentist framework</strong>. In significance-based testing, <span class="math inline">\(p\)</span>-values are used to assess how unlikely are the observed data if the <strong>null hypothesis</strong> were true, while in the <strong>Bayesian model selection framework</strong>, Bayes factors assess evidence for different models, each model corresponding to a specific hypothesis.</p>
<p>According to Bayes’ theorem, we can update prior probabilities of some model <span class="math inline">\(M\)</span> (<span class="math inline">\(P(M)\)</span>) to posterior probabilities (<span class="math inline">\(P(M|D)\)</span>) after observing some datum <span class="math inline">\(D\)</span> by accounting for the probability of observing that datum given the model (<span class="math inline">\(P(D|M)\)</span>, also known as the <em>likelihood</em>):</p>
<p><span class="math display">\[
P(M|D) = \frac{P(D|M)\times P(M)}{P(D)}
\]</span></p>
<p>Using this equation, we can compare the probability-odds of two models:</p>
<p><span class="math display">\[
\underbrace{\frac{P(M_1|D)}{P(M_2|D)}}_{\text{Posterior Odds}} =
\underbrace{\frac{P(D|M_1)}{P(D|M_2)}}_{\text{Likelihood Ratio}}
\times
\underbrace{\frac{P(M_1)}{P(M_2)}}_{\text{Prior Odds}}
\]</span></p>
<p>Where the <em>likelihood ratio</em> (the middle term) is the <em>Bayes factor</em> - it is the <strong><em>factor</em></strong> by which some <strong>prior odds</strong> have been updated after observing the data to <strong>posterior odds</strong>.</p>
<p>Thus, Bayes factors can be calculated in two ways:</p>
<ul>
<li>As a ratio quantifying <strong>the relative probability of the observed data under each of the two models</strong>. (In some contexts, these probabilities are also called <em>marginal likelihoods</em>.)</li>
</ul>
<p><span class="math display">\[
BF_{12}=\frac{P(D|M_1)}{P(D|M_2)}
\]</span></p>
<ul>
<li>As <strong>the degree of shift in prior beliefs</strong> about the relative credibility of two models (since they can be computed by dividing posterior odds by prior odds).</li>
</ul>
<p><span class="math display">\[
BF_{12}=\frac{Posterior~Odds_{12}}{Prior~Odds_{12}}
\]</span></p>
<p>Here we provide functions for computing Bayes factors in two different contexts:</p>
<ul>
<li><strong>testing single parameters (coefficients) within a model</strong></li>
<li><strong>comparing statistical models themselves</strong></li>
</ul>
</div>
<div id="bayesfactor_parameters" class="section level1">
<h1>Testing Models’ Parameters with Bayes Factors</h1>
<p>A <strong>Bayes factor for a single parameter</strong> can be used to answer the question:</p>
<blockquote>
<p>“Given the observed data, has the null hypothesis of an absence of an effect become more or less credible?”</p>
</blockquote>
<div class="figure" style="text-align: center">
<img 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rua3RwrY6qxDDuBWfrH/AAUa+C+i+DLfXv8AhYmi6lZ3krQW9vY+ZcX00i4yotlXzl6jl0UcjnkV9xf8G637Dvgn9mf/AIJM2Pjrx94d8NtceP7m/wDH9/e6tp0MxstNdcWx3sGxD9kgScAYA89jjJNWv+DdL4A+A/jV8FPFX7Wl14P0RfH3x08Ya1qtndTWUTTeHdLhvpbS30+2IGIkUW5LFNpcsM5CJjaOHS6k/wBqT6RX4nwD4Z/4KifB3XNct9Pu9f1Lw1JeNshm17SbjTrV29DNIoRfqxA9696tdZiv7WKe3njmhnQSRSxMHSRSMhlYcEEcgjg1+in7K/7Q/gf/AIK3/CT4taX4s+GukXHhvwT8QNa+HtzpmtiLVYNVWwdF+1FHiVYzIHDeWNxjI4kY81+Q/wCz34Hj/Z0+KH7Q3wo017y78K/Bfx7qFjoS3U7TSWWlOnnw2xdiWYRgOASSTuOazrUlFc1zrwGLnXqeza18jqPjl+1p4B/ZvtrdvGPia1026vQTa2KI1xfXIHdIIwzkf7RAXPGa8+0P/gqD8Hdb1iGxuvEGo+HWum2Qza7pFzp9u7enmumxfqxAHrX3t/wbW/sXeE9S/ZJ0/wDac8V6HY638ZPjReXurT6xqEKXE+iWMd3Pb2tnZsQfJi8mJHOzazb1VsiNAv0f+xl+1R4N/wCCwnwf+Mun+Kvhlo7eF/AvxG1n4cTabrMkesW+uR2KW7C8ZHhQRGQXA/dYcoV/1jdRpHDpHJUzObl7qVj8zfiP8b/Cvwa8Gf8ACSeKfEOl6LoLFVS9nl3RzFxlRHtyZCwBICAkgE9BmvL3/wCCoHwDck/8LO0f/wAArz/4zWd8JP2YrD4Sf8HCHgf9kS0WbXvh98MPiXJ4y0a11E/ak07TToi6tb2jF8mRYnnKqzEkkknkmv6Bz8CPhnHrCWP/AAhPgkXjRG4WL+xbbdsDBS33OmWA/Gr9nfc0qZpK/uJfM/C/xV+218KfBXgnR/EeqfEDw7BofiAuNOuo5muPthQ4k2pGrP8AI2A2VG0kA4JxWTo//BQX4K+J9J1PULL4leGWtdHiWa7M0klvIiFgoKxyIryfMwGI1Y5I9RWZ/wAE5vhVpfgr/g6U8U/CzUdFsbjQ/DfiXxte2WnXdmj28VteWwuIVWNl2hAuCoA4BHrX2j/wcLfsC+Hb74kfsk/FXw74V0Oxh8GfFnR9C12Ky0yKOO4stRvrYI04VcMiTwogDcZumH8WC/ZkvNZX0ivxPkHwD+358HPif4tstD0H4haHf6vqDiO1tjHPbtO54CK0saqWPQLnJPABNdJ8af2nfAn7PcFjJ428U6b4dOpM32Rbje0s+zG4qkas+0ZGWxgEgZzX1R/wczfB7wz4U/Z6/ZxbQfDnh/RLy9/aB8MWzT2VhDbOytbal8rMig7cgHB44FeH/scfCq1m/wCC/Xwz0vxFpul6vaTfC3WZhBdQJcwki7YBsOCM8dazlOCqKm3q+h008ZUlh5VuXZpdbanj1l/wVS+C93ZzO3xM8OzRWqBmEsdykgGQPlDRBpOvRQSOuMDNWNA/4KgfBfxFePb2PxM8NxziJ5d1y01qgVRk4eZFXOBwoO49ACa/Qf8A4Kb/AAW8G6L/AMFHf2E7Sz8I+F7W11HxxrqXUMWlQJHcqNHkIDqEwwB5AOcEA9a8o/4O4PhB4S8Ef8Ej573RfC/h3SLz/hMdKj8+y02G3l2kT5G5FBwcdK09mjk/tWp/Kvx/zPjKb/gp18B5ZGZviZo+5uW/0S85P/fmrMX/AAUl+Bd5p1zcp8TvD/lWu3eHS4jkO44G1GjDv77Acd8V+4PhD4Z/Cv4cfstaX4s8ReD/AAda6PoPhSHVtTuzoEMzQwQ2Yllk2pGzthFY4UFjjABPFflL8c/25P2Wv+Cg/wDwWK/YhsvgTqXhjxRZ6Hr2uJ4htYfCN1pcYEtlGYPMW6tYVlBMcmAu7aVJO3IJfs0H9q1P5V+P+Z4/4N/b8+DPxJ8VWWi6N8RNCu9U1CQQW0EizW/nyMcKitLGq7mJAC5ySQBkmmfEP9u34P8Aww8V32g698QNFsNY09zHc2wSedrdweUZo42UMOhXOQeCBX3D/wAHPPwj8J+Bf2BvBN9onhfw7o95/wALT8PJ59lpsNvLtLT5G5FBwcDiq/8AwbN/Cnwv49/Z7/aOutc8N6BrVzD+0D4nijlvtPhuXRPs2mnaGdSQMknHTJNPl6Gn9pz5OayvfzPhTRP+Cg/wU8VanHaWfxM8MrMwJBu3ksovxkmREH4tXq1tcx6lbxzW8kdxDcKJIpImDpKpGQykcEHsRwa/T3wZJ+z7+2B+0Z8dvgPqXwd8H6hffBWTRYtcXVPDdjNY38eraebu3kh+UnKqJUbIBBTIOCK/I/wj8KtO/ZH/AG+P2hPgXoslxF4L+Hfiix1Hwxb3E7THTrDUrcXX2NGcljFC3yIWJYjJYkkku1jqwWYyrVPZzW/Y4nxB/wAFAPgt4d1a40+8+I2hpdWchilWKO4nVWHBAeONkbHqpIp0H7cfwb1Lw1ea1F8RPDrafYSJFOzO6TKzZ2gQsolfODyqEcHng1+ln/Bsj8FPBvi7/giB8E9Q1bwj4Z1TULg675tzd6XBNNLjXtRUbnZSThQAMngADtXC/t0fsD+G9T/4OPf2N/Elr4Y0OPw3q3hnxCuo2EOnQR2rvpVtcTRyvGFAdjLqNsuSDwi+lXGVjl/tip/KvxPzt/4eE/BOUqq/ETSNzMAM210o6+piwPqeKNS/b8+DGm30lvJ8RNDaSE7WMUdxMmfZ0jZWHupIr+gr9pD9nrwDY/s7+PpofA3g+KaLw5qLI6aLbBlItZMEHZXyH/wbKfBfwd4w/wCCH3wR1DVvCfhnVL+Ya6JLm80uCeZwNf1IDLspJwAAMngCq9o+ov7Yq/yr8f8AM/LHw3+2p8J/Hvii10rSvHmi3OoXsnlwROJbfznJAChpEVdxPAGckkAZNdz4j1Kz8O6bPqGoXlrp9lZoZJrm6mWGGBR1LuxAUe5Ne7f8F7P29v2V/jt8Ctb+BPwmv9CvfjdofxB07TbrRNN8F3tncRTWOo+XeRi5a0SEiMo+WWXawUkFh18o+F/wO8N/tsf8FU/gV8G/FVrHfeBGbVPF/iDTCuIda+xQlrW3lH8UPmgl0OQwJBHQjeNObpOsl7qdvmzto5hKdGdWcV7tvxPne9/b0+HDzXH2O91zVIIWZHvNP0S5uLZiODiQJggeo4rYtP2nfh1qvgGbxJH4v0X+x7V1juJHmKy27tnajwkearHDYG3J2nGcGv3++PH7XXhz9in9oD9nf4N6b4Jtk0340arqOhWT6a0djaeHksrHz1It1jIkDsY4wilAqlmydoRvhf8A4Lx/8E+vhr4Y/bQ/Yv8AjPofhPQ9F8Ra18e/DHhLxF9iso4YfEMNzdi4R7qNQFlkT7LIocgsyzFWLBUC5RrNHHHOqqesV+J+Z+lftl/CjXtVgs7Txxo7XFwwSMSJNCpY9AWkQKPxIqx8T/j94J+DuuRWHiTxDp+j6hJEJkt5lkeTYcgMVRWKg4OM4zjiv13/AODmz4LeDfCH/BD/AON2oaT4S8M6XqEH9heXc2mlwQzR51/TVOHVQRkEg4PIJFfMX/Bu54P0P4of8FJ/2mP7f0LR9Yjh8LeGDDHf2cd0If3Tg7d4OM4GcdcV0RqTdJ1LaJpfff8AyOiObzdKU3BXTS69b+fkfny37anwseXnxppfBBGLa4A/9F03Vf2wfhfp940MnjPSWaNQP3SSzKc8/eRCv4A8dK/fn9u39uz9jX/gnj4rsfCfxguPBfgvxB4h0ttR0+A+BbrUFmgLvEJN9rZyovzow2sQ3GcYIz4Z/wAGt3wj8GePP+CQvhbUtS8K+GdXuJvEWuYubvSoZpHT7fLtyzpuwBgAHoOKy+tS7GX9uVP5I/c/8z8dbL9rf4X6tfRQxeM9Hjds8yCWFDxnBZ0Cjp3NZ8n7W3ww8xtvjXScZyv+j3Gf/RdfpN/wcU/8FFv2QdV/Yk+NvwM8J6x4Xtfjbpd7a6YdItvBd7azRXNtqNu1xGt39jWAbY0kO4S7WAIBOQD+mlj4F+G/wh/Yuh8b6j8O/C2pQ+FvBK65cww6NaeddLb2AmZFLKBuYIQMkDJ5pPEPew/7erWtyx/H/M/nE8GfFrwb8TZxb+H/ABToepXTEhLdZ9lw/BziJwrH6gEV18OnyWq7W29c9NtfrP8Atr/sp/AD/gqj/wAEc9b+M3hf4Z6D4f1+98BXXjXwhrMGlW+m65o97b2jzwxNcQDdtEsQjdNzIwGRkhWH5I/BPxBqPxI+DvhbXrmaFrrVNLgnnYJ96QoN5692zXdg4yxDcVuj3MlxjxjlBxSa1OyvlH/DWP7J/A4+Png8Bsf9Ph71+s3/AAdHf8oKPjn/ANwD/wBSDTK/KC6O79pb9k3vt/aC8IDPr/pZr9X/APg6O/5QUfHP/uAf+pBpleScvGzvmb9EeE/8Gt9kunfE/wDbChVdqx+NdNAAGMD7NPX6ZeG/2YvBPhX9pjxN8WbHT5o/HnizR7PQ9UvDeysk1pau7wIIS3loQzt8yqCc8k1+a3/BsOuz4xftjj/qdtM/9JZ6+gvgFGo/4OE/2hW2ru/4VV4W5xz/AMfN3/gPyrOi704vyR8/mkbYyqv70vzZ81/8FkP+Vib9gX/rvc/+lFfoN/wUZ/4J/wDgz/gpZ+zdL8M/HmteKtA0GTU7XVftnh67gtb5Jrdi0YV5oZUAyefkzwMEV+fP/BZD/lYm/YF/673P/pRX1N/wX7/YW8d/8FEf+Cfdx8Ovh1p+j6n4jk8RabqYt9TvvsdvJDA7GQGTqCQccYOCcGtDhW5+X/7Bf7Y/w3/4IFf8FuP2hfg/4u8TeKr74S+KJNG0tvF3iK7TU9SsdQhsluLeW8eFELQN9quoy6RHy/3G7Ch3r9Yv2w/+Ccfw9/4KP6Db/ETwN8SvGHw38dapof8AZ+k/Ej4Z+J5LOXUbHcZYYbhreQRX1mJtsmwkN8pCSx5Jr80/+CGX/BIDwX8PP26P2gPhZ+0V8G/hLfeItP8ADvh7X9E0Nj/wkFrptrK97HM8Mt0ZJMs4i35JwSg6YFfZX7Kfwq1j9k//AIL1eNfhn8O/Cd14L/Z71L4O23iE6PpWnG18Nx64NTjgW5jCr5SXTw+cjBCrSKmWDeUpULqfE9b+ffz11+8/N/8AYZ/Zr+Mn7Iv/AAc4fAHwF8dvF3jL4h+M9LtfEU+m+K9Z8RXGr2mtaLJoWpm0a0FxmW3CSi7WSJmYCTdjIwz/ALWf8FNf+Ca3gX/gqR8ENA8C+PvEPjTwzpvh3xJb+KLK98MX9vZXy3kFvcwRjzJoJlChbmRvlUNuVCGABB+Z/wBvqPTx/wAHHH7A7x/Z/wC1G0bxyLjGPN8kaLP5W7vt3GbHvu966n/g4r/4J5fEP/gpR+xx4H8F/DfSNB13VvD/AMQrDxJf2Osak2n21zZQ2OoQyIZVww3NcRr8hDYZiCCM0C5ru5+OWneD5vgz47/aT+Ga+IfEXibR/hl4w1nw7o97r12t3qL2sMbqPNlVUDMcZOFUZJwAOB+13/BuR/yhQ+AX/YGuv/ThdV+Ifhb4M65+yp4t+LvwN8ReA/DfgvxX4Bs4bzULfQdUm1CymF9YNcRsJpi0jOse0Hcx64GAtft5/wAG5H/KFD4Bf9ga6/8AThdVjS3l6ntZo74ag+bm0euvRrvqc7/wbtf8mp/Fr/stfjD/ANLRXiX/AATY/wCVoP8Abg/7F7Sf/ROnV9Mf8EMPgh4t+Bn7L/xBtfGHh/VPDd54g+K3irW7K11G2a3uJLOa/YQzGNwGVZAhZSQNyFWGVYE/L3/BMPVItY/4Oef24poWDImiadASDn5o1sI2/JlIrY8M+oP+Cov/AARn+Gv/AAUk8deG/HHjDxx8VPBuu+A9Hu7HT28H61a6b5sUh8yTe0trM+TjHysox1Br5h/4M5fDl7f/APBPPx9461e8utR1rxt49uWubu5ffJOtvaWsakt1PzM/J7k1L/wcQf8ABHz4uf8ABR/9pL4W+Kfh/wCD/BPjLQ/Cfh++03UbPxBr02lqZpZg0bAwskh2jLDDYyMEEdfo/wD4N2f2ftT/AGZP+CRvw18L69a2trr0N3rVxqK20nmxGR9XvNhVu48oRDPtS6la8u/yOg/4JK/HWH9rb9n74vT30y6laWvxb8aaEVYhv9E/tOZ4Yz9LeeIfT2r8kv8Ag08tJvC//BVnxt4RupDNfeAfhXq3hu6cjDM9v4phxkdsI6DHPAFfsf8A8Ewvjz+zH8cPht4uk/Zdbw3/AMIzZ+IZJtfTRdBuNIhbVZYYy8rpNDEZJHjSLLqCCFAzkV+bn/BH34QSfAz/AIOq/wBsjQHCqsnh7UtYiCqVCxX+paRfxjn0S5UZ79e9MFKyaOl/4OeF3/ti/s1cZ/4oP4pn/wAtwV9zf8EJ/wDlD3+zv/2Jln/I18M/8HPL7P2xP2az/wBSH8U//UcFfc3/AAQn/wCUPf7O/wD2Jln/ACNdk/8AdYf4pflA7Kn+50/8U/yge2fsr/steB/2OvhHH4J+HmnTaX4bhv7vUVglvZbxhPczvPM3mSszcyOxxnAzgYr8pP2B/wDgsT8Pf2KP+Cs37WnwW+LWsWfg/wAOeNvipf654e8Q3jhLGHUCkFvc291JnEKvHHaskrhYwUkDOMrX1X/wbaRrF/wS/wBPVVVV/wCE08U8AY/5jN0K8j/4Jx/sTfAX9rr9rb9tib4lfDH4e+P/ABToXxqvkSbXNHgvrqzspbW3MShpFJWNpEuCAOMh64zhPeP2+/8Agj7o/wC2MniHx58I/ix8RvgL8UvFttbzXHiTwP4kurPTfFDQxhLV9StYJFS5CRFkSWNkkCuCWdVCH8Af2vvhX4l+B/7PH7S3g34wXvizWv2hPC+oaHYeKdZ1/wAQS64dasBd25sLqzuJVV/srxnKq43qpQNg/In7rf8ABKLwz4o+Cn/BRn9sn4XWOh6l4b+CPg/UfDNz4E0hbVrfRdJe606SW9TT1wECSSBJJEiOxXJbarSMW/Lv/g67EEX7evxQ+w+Xtk+DvhxtS8r/AJ+B4kwnmf7XlBMZ524qKiuvmjow0uWT81L8mfuN/wAFYv8AlFl+0t/2SrxR/wCmi6r8rf8Ag2Dt2tv29fEgaNo93wB8GOAV27gbe1Ofx9a/VL/grF/yiy/aW/7JV4o/9NF1X5Z/8GyHiW88T/t7+IJLz7ODafs++CbOIQxhAIora1Rc46sQMknkkmh/EvmKC/dSfp+p9Ift8W6XP/Byx+xXvXd5fhbxG6+xFvcYrL/4O2/FreAP2B/hlryx28jaJ8V9Gv1Sd2SJzFDdyAMygkKduCQCQOxqv/wUz8a2/gb/AIOS/wBhu4upfJivtI1nTQ2QAXuEnijXn1d1HrkivQv+DlD4Z+JPif8Asw/Be28M6LquuXdp8ZvDc0sVhbPPJChadA7BQSq73UbjgAsOeRVmB+T37dP/AAdleLv25P2RfH/wl1D4I6F4Zs/HWltp0mpp4gnnayG9X3BDbgMfkxgkcnrX7r/8EZ7Vb7/gkP8As7Qybtk3w60hG2nBwbRAcGuL/wCDifxTa+Ef+CLnx8uLq4jt1utCisYy7hd8k95bxKo9SS+Md66//gjnCtx/wR7/AGe42+7J8N9KU49DZpQBx3/BeHStc+G3/BET426b8Obe30+TSPCcVhHBGGVbbSllgiu0Tb022Pngdhjnivi//g3s/wCCn/wt/ZE0S5/ZR8feLNI8O/ZdVk1v4a6xe3ca2OtaRqjC7gtJZdxWG9WSaTKSbN3mBVywG/79/wCCcvxe0r/gpf8A8EmvBOoeKM6rD448IS+GfFSZ8tri5jSTT9Q6E7d8kcrDuA618W/8G+//AASk+AvjT9gzUNH+KPwg+GXjb4jfD/x1r/hPxDf6roNvd3iXNreELG7yKWwImiZQT9x1xwaXUq6tY9t/4KK/8ENdQ+N2k+KfFH7N3xk+JH7O/wARvEV/Nrt9ZaB4q1DT/CviXUZQPNuLu1t3zDcS7V3XEAyfmZ4pWOR+W/7K/wBt8A/BL4xaT4gHi2z+Lek6jqlj8RD4l1c6vqlxq8NsyGVrnH72JlGUbkH5vmf77fq5/wAEGZ/H2gaF+0h4K8Uafrmm+Dvh78Zde0LwDa6hBJFDp2iRyL5FpZ7wP9DiUgRBSUVX2rhQAPz7/al0Bdf/AOCw37a9lpojNldR6DC+wfu/tUmiKsmcfxbic9+tc+KUfZ3kepkvP9aUYLVp/gr/AKH6cf8ABvtbJaf8EZf2fVjXareGQ5Hu1xMx/Mk1+J/7M/8AwcReI/8AgkN4++Pnw50X4XaL49t/EHxg8SeJ5L2fWZrOS1eWaO18gosLg4FoHyG/5adBiv2U/wCDbrxlH42/4Io/AuZPMWTT9OvtLmjkxvikttSu4CrAdP8AVggHnaVz1rk/+DdH4c+IPhn8Jf2nLTxDouqaLcXf7RHiu6t0vbV4PtMJisEEse4DfGWRwHXKkqwzwa6TyT87f+CEH7RFx/wVK/4OP/HP7QWqaHaeFb+48Bzaq+i2t210unvBb6bowDSPGhbzEJkAA43gZ4Of1k0z9oi6vf8Agu3rHwv+1L/Ztj8D7XXlgzybp9cnjc49ohD0/vHPavIP+CcnhOy8Yf8ABe39vzx9avDcQ2P/AAh3hmCdGDYlTR4/tceR0KSW0akeox1Br6Bg/aA/Zjt/+CoM3giOTw2v7Uk3h/7PKw0G4GqPpflLdeUb7yfKMexVfy/NzwOM8UAfnrN8IP8AhWP/AAej2mqjd5fj7wI/iBF2hVTbpElg2PXLWLMSe7Gv10+OPwf0b4/fDu78K60qSWstzZagowGaCe1u4ru2mAPdJ7eN1PqntXxP+1h8Mv7K/wCDi39k3xntGNd8B+LNEJ297OHzhz3/AOP016545/ag/wCFX/8ABZfwN8Mbu6jhsfip8Mr24tYmxumv9MvTNGq/9u1xesQOuz2oA+Wf+DtvWJ/D37EvwN1C1bbc2Pxy0G4ibOMOlhqrKfzAr43/AOCIvxX1b4s/8F3PBN1rO03dn8OtZgyowpHnBuPzr66/4PA5vs/7AHwekxu8v406K2PXGm6tXwr/AMG8Oqf2p/wXA8JspcqngDWFG8YYDevWvJxFOLx9KdtUpan0mDt/Y2I780T+gT4v/sueB/jf8V/hx4y8TafNeeIvhZqFzqfhmdL2WBbS4ngMErNGjBZcxkjDhgOoxX58f8HhH/KHyb/sdNJ/lcV6z/wVMjV/+Cl37AzFVLL4617BI6f8SZz/AEH5V5N/weEf8ofJv+x00n+VxXrHzZ9/6R8NbD4z/saWvg/VZ7y10vxZ4LTRrya1dUnihuLEQu0ZZWUOFckFlYAgZBHFfiv4j/4Ji+Dv+CWf/Bdf9iHwf4E8cfE/xdoOuXGp3ot/FutQahHppjgkjC2qQwQpEpBO7g52jpiv2M8b/DrUfjB/wTr1fwlo8dvNq3ij4czaRZJO/lxPPcaY0UYdsHapZxk4OBX4Q/sX/wDBJj4nf8E2/wDgp3+xpc/EL4c/D/whJqXiS9019Y0LxJd6peeIbhNPmkMlxHLK0MIVTwIERSScg8VLeuxUdnr/AME/R7/g6eTzf+CfHgZTNFbhviv4cBllIEcfzT/MxPGB1Oao/wDBra8L/s1/tJNbzLcW7ftCeJzHKmdsq/ZdMwwzzgjnnmvXf+C+X7EXxG/b4/Yo0fwd8LrHRdR8UaX4z0vxB5GqX/2K3khthMWBkweSXQYHOCfSvNv+DZn4QeKvgN+z3+0R4V8cWOlab4s03456zJqlpplx9os7aabS9HnKRP8AxIokABPPFL3ufysac0fZcvW/6H1B8NP2XvB37I/7U37RHx61bxpBZv8AGh9Bn1hdUlhstP0CDSNO+xxfvWbnfulkZ3KgblUD5Szfitr3xe0T9qb/AIKYftLfFvwrdxap4M8SeJtN0PQ9QgOYdTXTbRbea4jbo8TSYKOvDKc1nf8ABTj4O+CPi1/wXN/a0bxd4I0vxZc6T/whs+n3V3c3Ub6WDoVp522OOZIZRIAgYTxyAbBt2/Nu6bwjpum+H7XS7HSbOz0/TbURrbW9pGsUUKcHaiqAFHsB61l9YXO4JbHvZRlc2o4pvR3svwP0Y/4NcP8AlBT8Dfrr/wD6kGpV9MfCXQtF/ajs/gv8bCv/ABMNP8N3E9huX5kTU4LYzD2YeQgP0Ir5n/4NcP8AlBT8Dfrr/wD6kGpV1H/BG74/x3X/AARo8J+MdRkiSPwhY+IIJyzcRw6ZqV/Cm49v3NuhP1610HzZ7p4l+IS/Ff8AYW8UeJI23Qa14V1S7gOc/umhnMfP+7tr5k/4Ncf+UFHwM/7j/wD6kGp12X7A2ptrH/BBH4b3LPJI0vwahLM5yzN/ZZBye/IPNcb/AMGuP/KCj4Gf9x//ANSDU6APh7/gt5/wS98Kf8E6Nf8AD/x4+HHxF+K//CSfF/46W8fiHQ77WraTQMasb66u9ltFbRtndCqKZJHIQYO5gGHht7+02v8AwT9/be+FP7RE1m2p+H/At7d6N4lsoXRbqfS79PJke3V2USTREl1jyNxwCVGWGL/wUt/4JJfGb9iX4z/HT9qLxR8PPAWreBYfiRqXiy21dfEkv9rwWeoauFtBHbA+TvVriN/mQspduflGN79jb4b+G/2gP+Cun7O3hf4t+H9H8WeFNetPEMJ0zW7FbiwuroWHmxqyuNryLtQjI6gV6VPOVDByy+om+Z3XZWPZw7X1Gqnrt8r7H7W+IPDXwB/4LVfs36H4i8N+LpNd0/T5mvfD3i7whrMml+IfCF80RUyQTx4mtLkI2GilXBGA8bDAr8cv2xf+Cdv7Q37BH/BUf9lKPxx8avij8bvgx4i+N/hZ/Dmo+I/E15eppd6mox/6PdWszvGLrymfy54yA6JN8q5ZV+8v20/2VLL9gr9ur9j3Uv2Z/hrafD+28X+PptC8df8ACG6KLa11XSnhQvHqCwpseJI/tEqmUHy2jMilWTcPa/8AgtZHYv4N/ZrN55H2hf2i/AJsfMxu87+1ADs/2vKMvT+Hd715p4xyP/B0d/ygo+Of/cA/9SDTK+Sv+DZn/lJD+057+FvDB/8AIclfoL/wXB/ZC8Zft5f8EvPid8J/h/Dp9x4u8Vf2V9gjvroWtu32fVrK6k3SEELiKCQj1IA718If8G6HwW+IX7Pf/BUj9qbwn8UdN0PSfGml+F/DH2220e8N3aIrxO8RWQ8kmNkJHYkiuunWisNOm93KL+5Sv+aOiNSKoyg920/uUv8AM+rf+Cuv/BG/4dft3+I/+FveIvHXxW8H+Lvh74Ru7PTB4S1u102OWKPzrn94ZLaWQkuxB2uo2gcZ5rh/+DTKVpv+CLfgt3Znd9e1pmZjksTfScmvKP8Ag4U/4Ix/GH/go1+2V8PfHHgHwf4H8YeG/DvhJtGvrXXvEE2l5uDdzSggwlZCAsgIIbGSeK9q/wCDWbwvdeCP+CRug6LfRww3mj+K/EFlcJE++NJI9RmRgrdwCpwe4rkMn8K1+Wun6a/ofEP/AAcv/wDBF74Y/s7/ALOvxc/aW8P+M/ihJ438ZeK7a51HR59YtP7CL3t0vmr5EdqspVcDaGmJBVSS2K/Z20+Gcfxq/Yci8GzXr6bD4s8CjRnu0jEjWq3On+SZApIDFQ+cEjOK/ne/4Lgf8EKfjp4Z+MX7Sv7Q934b8EyfD261698TQ6j/AG8w1CCzlnGCtuuFLnfyrAkZPPSv3z+OqLJ/wSj8ZKyhlb4TXoII4I/sd6Bz2Wt9PPTy1+/TQ8M/bA8YfCv/AII7/wDBE7XPhtfeNtNeTw/8Or3wv4bg1O7ij1DxLfyWcsUSxwKdzGSZ9zBARGm4k4Umvx1/Z08LzeAvgJ4N0e+WS3vrHSLdLiNhgxyFAzL+BJH4V83/AAK+DHhHwZ8Dvh/8QdN0OxXXFEMl9PMz3DSy+Y3zqrsyxnAH3QOcGvsQyNcpHIoX51Dc89ef619hwzh4RnJyd3ZbfefpnDOSzwadeq03NKyV9E9fv2MT4oaB4ovrbwB4q8FyaHH4s+GvjvS/GulQaykrafdXFixkjim8oh/LZsbthBIBAK5yO4/bY/4KD/th/wDBSL9l3xJ8G/H+k/s46H4N8ZTWMep32g2urrqVstvewXiGIzXMked9ugIZTlSQCpIYVZLVrLQdo2OTdGSN1Y7WTaeRTNHLGOZe25JD+BxXwrquKdj3cVw7gswrfWKyd9NnbQn/AGev2n/2kP8Agm/8aPihe/Bmy+CuuaL8XNctdQuD4zg1F7q2njgKKiC1miUJ87cncTx0xWn4f/4KH/tn/Dz9sPxl8aYdB/Znbxp400Ox8MalZSwaydPgtrKSR4niUXIcSMZmDEuwwq4Aycw/EKddNK3L8iz1K2k+XqcLzVq6uB4l8UtIq7VmdDIDzuO0ZbPv3FcNPF1Uo3Wmv6WFW4Nyqs6teq5KTd1Z99WcN+0V+0p+1d+1X+2B8KPjl4msf2f9P8dfBOYnw9p+n22rJpd+JGLsbrfO8nynGAjpnJz0r6Ki/wCC5f7fcr7f+ET/AGSxyRk2WvY4/wC3yvKHlZdSmjP8DkAZ+U//AKqsWMLQXOVk3K24sBxu49K0ji5t2OFcG5a3ZKX3nC6z+0r+1hr37eF5+04fEnwu8G/FOx0GDQl0bQrS+l8O69p8ZdngvY5pXlwxKkbGOGjRl2MoavpJf+Do79oaHwwuny/sz+BX8QeUIzrKeOcaWZP+en2TyzOI/wDY83d/tV4m0KXutTx43GSEqA3C8qRz39O1eT2/g2bzbyG4WZbiFCYmx8rYOSK9KipOi6k+54+I4Uw1+WCat57/AH/8Az9f/a8/aU1X/goR4U/av1TxB8P/ABL8WvCy3dnp+hajaXMfhnR7Ge0uLYWsEcUizFUF1O4LSbmdgzM5DbvppP8Ag47/AG4nOP8AhD/2WQ3odP1wf+31fLMcqxySRzLJu2cYHGe1QaxqdjothcNcPcPNcQv9nEAUYcj7xJqafPJtdjL/AFcwjeqfyZnfEz9on4oftJ/tK/FX4k/EFvCuj+J/ijDYWepWvheK4i0+JLKyNmmwXEkkm4pgkFzzkjAIA9K/ZA/4LrftVfsA/s2+Fvg/4R8Nfs/6p4b8DW8lpYXWr2Oqy306PNJNulaO8jQtukP3UUAYHufntNWa3vBE0hVGyiu/Xdzng9/esXU7lhcDd5jKRtQsB046/r+dZ1KvKtFr3O2pkOEnQhSkn7t7a99z7c1r/g6B/bS8S6VdafDoP7Ovh+a6jaFdSstG1SS4siQQJY1mvJImZeoDoy5HII4r5l/Ym/bo+O//AATz/aX8efFbwPdeBfH3jL4oWrL4mvvG9tdy/aLh7n7TLNGtrNDtLyc8kgDgAV56iLJFuVl5yOetE1wqRrlmXJIAA5I47Vz/AFia3Ob/AFdwVuWz+8+7V/4Ojv20GcL/AMIX+zLuY4H/ABK9b5P/AIH1b+A3/Bfv9s/SPBWn+GfDfg/9lmKw0K2WCJZ7HXN7KvViRe8sSck4HJPFfBsMiwH5p3Vj/Cy4xXuPwOtUsfAs18rKLy8lMbt/EoHHT39qca1RszqcO4FQur39Tp/+Cb/7Sf7Tv/BI7wB4k8M/Cq1+BPijTfGGpprWpT+JrbU3ntbnyVjaOPyLiIeUoUckFiSTxwK6zwX+1J+1n8Mf+CgPjL9qLS9J/Ztb4jfETw/F4X1fT2t9Y/sj7NF9kEdwi+eJfPK2cKktIV2r93JGKIma2tWVUVm52oDljgd//r11lvfSXWjWUzRqhbDNsbPOOnpXWr81rnNUyHCKCkk7+ppfGDxN+0N/wVB+Kfhvxp8cl+DfhrTvhj4c8UaRpi+CINRWe8k1jTTZyGYXUsilY1AdSpU5yCG3Ar1n7Fv7c/7dX7M/wI8D/CLwXon7Kl9oPg3To9H0y61eLXGu54YgcPM0dwq7j1O1FHoBWv8ADCYp8JteZflVlmycekef61ufBI7vHent6s5GO3ymv1DEcN4VU8JSSfv3b17pX/JH0lThXBWwdCztO7euvvW/yRxn7L/x/wD25v8Agmx8EbL4deEtN/ZW1jQft1/rSXOqJrkl0Zry5e6nUlJ412rJKyphc7VXJJyTzf7OehftSfs2fFL4j/tMeD/Gnw3h+J3xL12e78X+CJrS8bwfq0DFGiEbNJ58c8UhlKPuyFmK79pYP9CfHebN7po9Lcn6/NTdCh8n9n+/Zv4rs4/OKsp8OYGGPrYez5YxutdnYzqcJ5dTxtbDpNpRdrt6O2n4keuf8HBH7WOuaVJpWj/sv/Dnw1rmPLXW9Y+IMeo6XG443ta26pcFScEKHBxwTnmvjv4n/sUePP2y/AnxKPi7xlH4s+OPxsurKS91qaDyLGFrWVHtrCCNQTHbII9gIH907flwfZ55PK1WXq26Q9B05FdP8KvGdr4H8a6LrFxbyXcWn3kU7xxSBGlCt9zPYGvzbHR9nax8/RyfD0k2ru6tq+jXlYwf2ov+ClX7dvxv+C3jj4X+KND/AGT7PRfH2hX/AIZ1O50yHXPtNtbXlvJbSyRM1y6h1SRipZGAYDKkcV43+zh4r+On/BOH42x+MfghJ8I/Ec2o+A9H8Fal/wAJrBf+Wv8AZ8aIJIEtpYz+88tW+ZjjJGO9ej/FH4iLqPiLUns7PbI0sjKDwkRY5+Uf3fzrjNL8UzR6iJbqL5pFA+6OO469K58wxPsZKMNn1Or+wcIqbjFOz8+xn/tV6X8ff+CnPxe8K/E/40a58Nvh7rvw20ySPwfe/DiO/ju7PURcx3EF1KLqVyPKkj3AxurHgcfeH15+zv8A8Flf23NH0SHw/q/7P/w9+PGqWu2FNf0LxfB4We6UA4kuILlWTzXxk+UEQHICgYr538P+IG8Ql7hodrqNqqDkY788cV9kf8E4o7nwb4w/tqFbm8ghytxFC+5Y4yPmJHPyjrk4xg18zis6xFKovZtO/dafg1+ZyYrIsNDD8yTv3vr+TPIf23v2df2jv+ClXhZW/akuvDHw38BW9jdTeHfhx4PvTcldTeB4rbUNUvGJFw1u0rMsUOI22r93Ll+X/Zv/AGxv29/2U/2evB/wv8N6J+yXfeHfAmjW2g2E+oprz3lxbwRiJHlZLhFMjKoLbVUZPAA4r7v/AG1viP4T8b+H7aby9SXxBCDHbIGXyViLff2k8qw6OmT68V8teblmwfvHpWX9uV7uSe/lp8jLCZLQnTtWi0/U+d/2FPiR+2l/wSu+C1z8NvhzN+zn4u8M3+rz+IFn8TwaubmxnuY4vOt4vImjXyFeNmUsCxaRySAQq2/gL8fP2yv2WP2iviJ8WtBn+B97efFjVo9Y8UfDi1jv7fw9LPHDFC95ZzyyNJBeTLGS7MxRmfLBgqIns/iabfNEvcK4P5ViyPv1VG9ULfTmvSoZpWnG7a+4JZJhvauKT+86zxj/AMFxv2x/iX4bm0nwv+zp8Nfhbq1xHsHiDxD45i1+1tc4BdLW1VHLgEld5K527gwBBxf2ZP2OJvgxoGtXWueKL7x18QPHGqyeI/FXiS+iWObV7+UDOEH3IUAwiZwuWxgHaKacTRq3KsV/mK+jrGwWG9hbHG4Y9uBXw3HHEOMpeyp0Jcqb18z9C4KyDBUFPEKPNPZN629Ft+Fz53+BvhD9pL/gmB438TX37P7eCvHXwz8YahNrepfDfxTcvYDSLyQAyy6ZeKdkQkYDKS/uwBjaSQ45v9qb/g4q/atvvDl94a0P4LeAPgjrcimObXdT8WQ+KpbVWB+a3ht1WPzh1BlDp6qeo+q/jXc/2L4B1K+VtjWdnJPkdwqk4PtnFfjd8XfE114n1yS4xvkvnEmSxyMk/wCP5V6PD/E2Mq4W1aSk07ba2t/XQWL4Fy2vV+spNXu2k9L39Lr5NeRtfsFf8FL/ANo3/gmNb+PNP+G9r8LPHq/EPXT4j1fXvHFvqdzq99dtGquXeC6jUjdvbJDMWkYluQA7R/2zf2mNZ/4KU/8ADXEWj/BdfiedN/sY6VJaakugi3+yfZfM2/aPO8zZ283Gefam+EPhvHY2iPIpc8Es38JrsotJFvEojXy2TkDPf3warFcVYuGlNrTyJlwHlXM24y183Zen/BPRPiL/AMFd/wBs74mfGP4c/EDUvB/7L6eIPhnLfy6O0NprQVlvrQ206Sg3ZLIV2sArL88aHJAIPlv7Q/7eH7Vf7Rv7Ynwr+PWtR/BTw749+Cvmx+H7bRLXU10/U45yRcQ3gluHk2NGzofLZCVkYZBww6CS68q3b5F2qQR32jGCc/0rC191S3dgqqx60qfFGPlC9479uhlDgXKu0v8AwIof8FE/+Cjf7TH/AAU/+FvhbwT8VNF+Ceh+GfC/im18VpP4UtdSivnnt4bmBUJuLmVChW5kyNobIU5wCD4r+zN+058Sf2Af2p9L+LnwztPBWseJtP0e70Q2niiG5mtDDOylnC28sTlxjAy+B6Ht6Brzq6MzfMCMMRyB7en9a8f8eIttcnbgrvP4gYxx+depgs2xNeXtJ25ktNCsRwrgcPh5YaKfLJpvXXQ+hfjp/wAF3v2ov2ivjf8ACTx/r3hf4C2mtfBnVbvWdChs7DVktbua5tmtXW5DXjMyBGLKEZDuAySMisL/AIKMf8Fh/wBpD/gqR+zo3wr+Iuh/A/RPDsuowasLnw7ZanDeiaAPsXM91Kmw7yDlM9MGvne3uhc3Lc7ckEZwD078VTEbJqC7Q27cAVY5J75r15ZjVvZu3yPFhwnlzd0nb1P0s+BP/BwZ+3H4u8K2Wj+F/A/7M18ui2KQRW50vXZLlooo8ZIW95IVCT06GvJf2h/+CyP7WX7Qnxn+EvjjXvDP7PsOr/BnWLjXdCi06y1dba7uJ7ZrZ0uVe7ZmQI5YBGQ7lHJGRXlv7KXxDvPhu2sLYyRxtqFqyLuYruO0jAIOeVJ44+77mm6vpf29vtrTeY9wgdVCqvyA8HA4/SuSGcVrNTav6GNThPAxjza/efUzf8HMv7biH5vBP7MK/wDcN1v/AOT687/Z9/4Lmftc/s+a98SL/wAP+GP2dLq4+KHi6bxnqsd9Z6u6wXktpaWbJAFvFKw7LKIhXLtuZzuwQF8HuYfsj7juwCCSwwDiobGzXV7hI42XznOxQpySPbHPvRPOK8XfS3oc8eGcDs7/AHnbXPxa8b/tFftRfEj43fFaPwjpXir4nS6bbXNv4eS4h022Wyso7SMxiZ5JPnSNCQXb5gxGAQB794e1GJbKxnh+eGPahBP3WChufw5/GvnX4i3r6f4ftdLt1SERAGTbhjITgnnBx+Feqfswajb3sV5a3677Wa1djGZWiCyKBtb5evTHWvLw2YVHiVXqfa0dvlb8j2o5fChhVSp7Lbv3/U6z9iP9v79sP/gnJ+zH4d+DPw90r9nDXfBvg2S9Gm33iC21dtSuEub2e7YzeTcxx533DgBVGFCgliCx4/4D/tZ/tafst/sU+LfgXoMfwDv/AAJ4ki1j7XqOpRas2qWSamJDdCFkmWNdjTSGPcjcnLbskV1Wo6gvmtt3eXuygPYH8T6etcj8WPELaP8ADq+2yeW906QL8oOQTk/y5+tfo1P2bTcr7XPkf7Dw/MlZ/edx+xV/wUz/AGyF/Z00n9n3wlpH7Mv/AAiPhXwsPDqatrlvrKXBshCYFeSSO5CmZl6BYwM/wgVzv7GX/BT39rj/AIJqfs5aD8D/AId6P+zv4q8I+Bpb5NO1PVrPV5L27S4vZ7t5JGjuoowPMuHCjYvygDkgk8HF46uPA3wqNpo7NZ3utIs1zcxov3GyGG/G5Tkjgds/SvP9J8ULaSSxyBttuA0aiY7WPqfX9DXPRjy2eIejV1Y9OjwvhOTmnf7z2P8Aby/4K7/taft//sveI/g/8QvC/wABdH8I+MTajUL7QbDVV1C1W3u4bpTG0t3JHnfCoIZCCCRwcMPDvEGoa9q95omtaFr2seH/ABN4Q1KPWvD+t2biS40e9j+47AnlOMMpGGHUHGKpXustLNJN5zbpO4dwePXr+fel0TxJ/pCq0wfzGG88c4GOee2e9eXiMR73uvbY9nB5PgKMJ0oJ2nvfXb8tz9DvhR/wc4ftK+DtGg0LxZ8Bfh78TNehhU/2xoXi4eH4rlAMb5Le4SXEjcFthVc5woGAPnn9q39tj9qj/goJ8Yfh38QPEGqfDrwyfg74q0/xf4T8B2sdzJokl9ZzrMk9/OH82aTA8v5CFCO4Tyi7FvLfB/iVUvlimt41Zo9glwPnjHQ59fYV3Hg3VhZavuV1VZlZMBc4yOP19K6crxSxEZe1Vmjwcw4ZwlGV6V2n3f8AwEe/D/g4e/bpk1fULGLwf+ypNdaaqNIi2OtgvuJAC5vhk8c188eBv+Cw37VvwK/bP+Jvxwh8K/AlfGnxb0/TNN1ezvbHVv7NtotPi8mA2yi7VwzL98vI4JAxt6VQ8X2t54N8Yf8ACRaesV1FNHsvLYDkg/x8g9K3m+Iul/FLTIINRNrDtJwktmis3fJZeo9ga9bE0aOHk4V52d007acrS38073+R6VDhHA1YRdNSbtrZ9T0i6/4Ojf20LIfvPBn7Ma9P+YZrf/yfXln7FP8AwW7/AGpv2Hfg7c+A/B/h79ny80n+1NQ8QGXWrHV5biS4vrl7maNWiu0XaryMqgqDtAyWOScnxf8AstafrlpJcaTcW+xFM8j2shdQo67kPQDHUGvnzX7BdOu5o7G9W8VckMFKhhntXlVakopunNSMavCeDg7OMvvPrn9ov/gtz+1x/wAFDvgJ4x+DfiXw1+zvpOgeNdONlqV1p9hrEN5bwl1YtEXu5FDgqMbkYGtn4gf8F7/2xNX+D+rfCnUvCf7NlvpOoaG/hieaKx1kXCW0tsYC6sb0rv8ALbIJUjODtI4r498K+NNa8MyW9xZsjNBkgSIGznsePb8K6HxP4xXxw8uoTRx2dzJGhdFbLBk6kHHQ8cVlVx0Y0U18V36W6Hdg+E8qqtqSltp7xB4Y0K38O/s/+CfC9rPM+oyTxW87xnEM+xyC4B5B5x9DX05p1u0FoqIrKqDaM4yccV82/BrUIvEnijwvppj3/wBnXs1yzkZLAjI59jj9K+ltkcYCsA23od55B57fWv0zg+mqsXUXZH0VKjZKC+ykvuOb+FvjOHX7CPS7qSSKRSfIdvulvukH0DZxXUWUctu12uxt0ajKkcgbhXhvg/VfsV5jYzRyMCzBvmODn8MetfQXh3XLDxv4VjuLVZ4dUh/dXO45W4U4w/sR71+ZYml7P5mWX4xc3JIg+I92NR0XUH5VfODD/gKDFW/A15G15byblmWSNSvbOUp3iK1ivLO7gVtytM4J9tg5p3wm0JdW02xbztrwQjaMf3c5JPfFc9OP7mx6U9W0iY6VNceILi3ij3jY03ynqAASfwp1kSy53bsKxB9cDvW7Lod5aeNbm309WEzExqi8l8rlqh0TwZJd+GtW1GOSzjj03yhLEzhJpDLuUFF6kDGDjpU06yc0kXh1ezOWsp1h8SSeY0o3wrynU57ZrE13UFs9eaHbuTJX7vzHcCM/Wtu2DweJm2+WreUgAcZyAT0PY1m+O9E+xRzahx5camWRTzvxzt+p6V1UMROpTVB9Xv6GcsO/eqJHnPiG20u1EP8AaV8bFQpPmJB5ryAHsvT2ryjxn4mj13UJvs7QiDafKAQcjoNxz8pPWuo8T6BrnjycXH2V44HJPzIUCjt1PSuS1TwS1pBJ50kKsvQBdwk4x07D61n/AGpTo15U4yvfT0PL9m97HK+cs0itJx5JMj4H8uKhutuFMfzDYHCk5z9D/SjVQdOu9qsybhgNjg1WSaHakitlsFRgYyeM/hWPtkzgluaJeOK2Ubl3MxOQuAvtUbXDi4V9u0DOWHpVe6kbzioEfXHyjFOR1ZSq7mbOCAOoHarbvaxPW5ctJo4pflZnDHncc5HtX0L8NbNtE8BabDKqrcsrSum35oyzDHPfj8q8c+EPhWbxd4oiby/OtbV1mmB+5tUjAP16d6+jtZ18a3JFDHZ28CwMTmNfmzxkZwOOKUudVFBLTuYVuVR03Gx2nmabOX+aS6TaSe+e+a7ILHY6XYxKysE2ohHY4Brj2Xz7yOH+GQ811Or3K/Z7eNmCtIQefwr2MPG8rvyOOpJygov+rqx634ClWP4J6wy8/vJs5PLZSMf1NbnwFl83x7Y5/ebUlII4x8vP864Xw/4ts/DXwBvJLm5jja4mkjSHcPMk+ePoPTCnn2r591z9oDxBHr7NpWr3mmwW8hWA2kph+UMOQRzzjPP41+z5rjqVB4STatGPfuj6zF4iMJYOa15Iq/yPub47XAF/p/8As2IYfXca3Nqx/sdwSbV3T6o4DEcjkA/+givmn4T/ALROqfGzRZINeuIbjUNKgEQlWPyzPFk4cjJy2c5P0r6BHxK8KwfBDw34P1XXv7L1C5u3u5VW0luvs0e84dwmMAgjgEmvCxWbUJYuviHs47fKx5tbGwq4yriF1T0/A8Xl23OtMB0ErZ+bHNWba0kuWto7dJJ5J5FSOJVJkdieFVQMsT7V7N8NvhD4J1VptUmnudY0m3k2nUrqX+zUu/8AZghTLuOvzMRyOfSus8XeL/hF8O/D+k658L47y18UX0/9nJe6jM08ejM2FlnwwJV1GNrD5cH7ua/H86zGFGKunptpueHTTVqai3p+R87/ALRvwGv/AISeFtMuNcv7W18UTuvm6BF+8nsbVo9yvcODtWRz/wAs8ZHevEVud0/3s+XgZPf0z6V3/wC0HbeIvhN4+1Kxn1SG6kjJDzw5kS9jkG4Sb5MyPkH7zYxXmUcbOzn5jg9T3HavFjiq9ek6mId1va99OnRfd0PUqUlCKinfS+x23w9eXVZU021Aa4uphBGuMAuxwOR7nkfWvo7xb8ZLL4b/AA41b4Y+Czdya1e2aweIddjO03UgILW0WBlYxll3DrzXgv7O9+PCGq6jrAkVrqztXFmJULKHYfM49wOB9a7z4AW8OuWHiC8vrV2uppUZpXYEANuIX13cV4eL96fso6Ja/ea+xjGmqk1c9B8JyTWng3T4ZFliaGIRmN5SzRDHC5/u/jUqXgjPPcmsWTS4A7ZUnvyT0/OqOqQwQGFYfkkZxwOcjvVYalGUFTTOKpUldtrc1Nfud9zC394sP0rHgkJ1Dd3aOmT3MOnRqWVV28YJqDQ9Wj1DWtqrhUTr7V7EYeypW3OGNpVec0xckXMI/vOuePcV9PxDN3ED93g4/AV8wS69ofhCGHUNWt7y8jRxlbaYR+URghj/AHvTHtXong39tnwr4l8RR2FwraazEvDcTEhG7BfQH3r5PizJcRiqUK9PaOu259xw9jIUYOlLqex/EHS4te8HX1rNt8m4tZY33DIIKHtX4/8Axj+H1x4S8aWCvDthjuxC57bS2VJ/4DX696/qUOp+FLq4glSSKS0kZWVsgjYelfC3i/w/pfigeTqFvFMkcizb2O3y9uecgZ461x8JYWrUp1IrRxZ6mIx7w9GPNs3+p5bdWqQxxqydwVYDoKhjVA/zDbHjr0pviP4kaQ16YLaSPAYIgIxxnH6+pqj4r1H7N4V86Fo/l6Agn8Qc1y4zBzjWlCW9zq9op7CXuoQWzEyXCwxrzlzjc3oPp71yGv8AxB0u4RoYrgSMvGUUnBrzfxJq95rZ/fS3E8MpACDqB6cn9akfWrjSbz+zW0VbeRV3fN1IPQ8jqa9WjgFGluccqtpKMjoJbtbzd5bbt/c/xV5z8TdJktUkbblcZH+z7evevTtEX+0bJGuI44WZAwyKp+NfDlvqFm29l8tlJyo78cV1YPFRozSZpWoqpoup4DAjSLG2GHy7VBOcH8K3LbwjdarYpMrxxSD/AFaH78mPU9vxpW8Nx6Zq0kTZwsgKj+96/iOn413Ogafa3Ol/uxtkj5weM9umeev1r18XinDVanj4PA8zfQ5/wjq7WM+xt0Ukb7dufmGR1P06H/er0S/v1tbCObcwjvEBRmXaqMT9z/gJrzDVJll8Q3CrMOJPL2jkMPSvSvhPfW/inwbcabqDFWt3V4R/dJG1se/ArmqRdo1JdVc58Qrx5O2n3GHqWqNM+W3buchvun8ff+lanw5gEl1NfN5heEeWpReoJydp/T8amvvh7ZXMzRtfXTJG2UVY8kjP1/UVvw2cOn6KllZq1vuTlMgyKe5YnPXt0OKqpiIcnKjzaVPnnYqNYt4n1aeTezSRkRjIwuBxgfUgkCvQ/hnEuleWufvI6MRwf85rj/AVvHJsVo9zRTD5S2VRsEBvXgkGu28P2DWt2i72Ubd4GR19OlclKUpVIw80d2JpRhD5HQNd73Cg/dGBXn3x+1fZa6RbjbsaSaY7hkEbQvr6126TyF1VSQVxyB83fPPWvLf2l9clbxFptq3mLHb2+ViHRC7HJI7njrX6dKfLSkn2sfK05J1LdrszWi/tDQLNTOzXEkQiSBejt61i6z8ONUsBG/ls+7Ocdvf3Haus+CsEEen3eoaku2OxjVIG6gN6d+a2LjVrfxCzNBNHMe6Kwz9D0rnz6sqdGlKO3KfQYeipU1F6M8XaGZCyyLIn8LAr1I45ogtpMbVO1D97aOT9PUV66nhyO6mLSiItty2E3KR6nNcz8RPCEVhD9pjV1iB+coBjJxwVJHWvjqOYxk+V9SvqXI29yDwxJCLS1yD532hY4wG6j+L9O1eseE/DU19qlv8AZVY3EMocA/KGAYcE9uteU+A4Y117TrbEmWZrhzkHZtB29egzx1r334UiOLxXaRyMyyTxMgDEYBwOpHrX0eUKcU5LW7R4uZ4m/u9jKv4i0hjkjK+SWEik56k55xyK5zVvBVlfxTTKzWZCHAjj/d59xwRn2rofETSPq07YyvmMAQe281vfBvwonjL4i6Pp1xHHNa3V0qXEat8zRjlh69K/VMywdHEU0qsU7pfIvAY6eGS5JWNbx18etH+HH7Ktx4V8O+G9L1aTxFb+UdXlZ1ntWX7xjRTuznI+bg9a+L7jwDqRBnNtcNHyQSBn8frX0x4+j8vW7qGxt/Kt4XkEMZABVdxAHSuFv76GzuXEzRRNnA3OByevGf6V+N5rXoYOs6VBI+hdF1I3k7vueEz+dbzujmZCTnpzitzwlp8OpQtHL5jMeEIHzDPXnp2rvvHnw+TXNNa6tIZHlUbj5ZALD+tcbY203hi1eT5hJjBiPJbseh7V58cbOtSXLpYVCLgzW/Z08Ozf8LaZoZI98Nm8qMRkdQDxx619BSLqEZXbeKvygnESgE492zXzCvimbQtWgvoTLDct1IH3SMEdcZHHQ8V9AeB/2o/DOoaBG2uaFq0mpxnZNJZX6wQykAfMEKNg+uDiv0bhbimlhqXsasXfy1+/ax6OHwcXeTkkWvh/+yJeePdQSwi8SaRYXEx2wtcKxjZvTcMdTxnOK6rxp+zp8Sf2Vfs2rapYrHpMzmA6lA6z2cnZdxGdmR614fP+0LrNtfLJG08aryCjEYx7ZxX1B+y3/wAFEdY1BpNC8SWenarpd4v2a7t7uP7RFqURHKSq2RnuGxkECvHzasvaP2SvH9D4urOvSlzxRh6bPb+IdOa8tZAY5EO7IAKsy8jGeR3Bq7+z5bPcaPZrtzzLGB7fNx+lep+L/wBlbw74f0abxV4I1a7bw7qUTSDTpIxM1lKeTEWHJQc8npxXkfwm8VJ4K8HQ6jJDLP8AZbxkMcf3id5GP/rV5OExUailDquh9Rl9f6xD3N0tf0PYvhvpQv8A45s8kW4W6zSE5I+6nH+favOX077TqVzK3XzGOQgz1OB+Ga6LSPjvp2geLtR1K203VoJbyBoYo5oi2xnwD06HrisOHXLOK4kMknliV8bZI2XHPfPGa8KnjoxqXl0PtMvyDETXNydE16mHaaLIdQ875QUCqGJywPzHgfhWmsdrDBLLdJC4VTiOTozE9SPal1DWtP0rR7y+uriNLWyMTttI+Y/OMD35FeL+Gfi7N4z8c63FLMy20MSSRg/dQBsFdvTkck16OErVoQlXj9m9r/j81ubZ1gFgoKMo2ckejXcAvt0X7rywuQdvy8V5B8WfA66VPJIlu0kO3LMMnZzn0rs1+INqLxrO1ka6uI32yjHEZ9PrUl9qqarDJFKFkH8Qcbvyr4mjia0K3tZJu/Xb7/PufI1aa2Z8h+KtLKapJgPt3Zxng/QGsZbbcf3bF3XIb/ZNe6/Gb4Q29pa/bLX92sxJI2gACvPfh/4F+06+sl1iS1h+bawyjn3Hevt6OZRlR9rNo8b6nOc+WBxMUkqSt2VclgOjN61e05VNyskmQijLkdVHt716R8dvAVnpel2uoWNpZ23nn941sojVvYpjj615jaXDbvl43H7p+7x6jp+dduCxKrw50ZYmjKjNQl+B9JeBdE0vwzo6/wBmpuhmiMhkdss5OK6Bniito2kk27pMdwWORxxXK/C5VPgWyDD+FuH64yMf59K6POF+b7nBI55Hr/XNdPNK11uckY05VbT2JNQ8WRaBq4lKGR/LMhTdtWPBwcnH8q5jxD8cNQ1IL8yrDE2NiDlR6Z75qv478JX40f8AtKKFriFm8oPuyy+gOOox3rhAzv8AL8y45bnao/3ec5rttUhGKqRtdX10Mq2Hpufuu67rb5dfU29W8aXWs3skk00zPISxXOFXPoPyFVUut8mVXczHHy9+nKisvPnOqsdq+uflP416B8I/BY1b7Rq12imG3i32inEcYI6u3OTjHbrXsZVh8ZmddUtZdW77JHRGlKTvujY+GOlzeH9ThvrzWW0GJFJQqhaa57iMKAdpOOrcV6NrH7Remi4muYvDFjc3k8RTEuq3M8aHgK21QBuXrjOOa8V1i8ll1G4mLLMsrbyxXbu/vEc8Vp6IG1uWOCGNZJGIA+Uf5x9OK+ezTHewk4p9bPz1OyngadveVvmfT3hH9pPQ/jN9j0XxAbzw3Hb2qiOTw1CbtBJ/CkkE0iYyeSVcfQ1f1L4coNTt9HXUIY47bfP5rThWkOFPIDEK3HK5OOa8T+HnwX8SXUkt94dt45BDGvnrcHyiB0IDY5XGefwra+M8beFPEFr5cnltDYJLeQwy4VZPukgjHIHfGa+QzjFVq9ZRukl3Kw+HjGq2n0dj0TxP4RS+h+0NfRalGYQC0km5/LwAFP0riYvC0w1aSJY2kUsVRQOCO1cF8FPjBPpnj3Sp9eYy6feBI7uAykxuBxls5znryK+oE+KfhHwrJZXmuaLZ6Hpk1v5sV8iSOb47mCqu044wOW456V0VsRClR+q1Y2qLy0ffX9DPER5bN9jyTxVb3nw5sIElt5rJbpiv79WDHpjgjp+Ne5eBtHXwt4VWHcjNdYnkK/xkqCPyycV4X+1n8cbXx3YaT/wit9p9z9laT7UzqWldioKB9vBUHHT0r1iw+IVjf/DLTPEU11GlnNZRb3t4ZWRHVQsny8tww7+ox3r5+UqjlzfeOvUTowUfmbWq6uID5UTAyycAf88werGsHVNai0GfG7dNKNxOc5+vpUlxG8PhwazbfaLmzvW2xzPbPGsjYyCA3IrkIbz7XdM0wVvnC4A5Ynjn6Zr6DARXJzvU8K0p1HE0bdLzxdqvkWsbXNzIQqoh9fXOMfU8e4q54Q8QeHfDupquq+JtLs23FJZCS8cagnGGX7x+gx6E03xFrFv4Z8D3Wnwo3nX3yM68ZX6+leE674ehgRpLdflUknjqK9mrTUKSdTS//ANaWFklfqemftG/F7Q/Eken2Ph2Zri0sVDPOFZGmY9WII5HpntXlces/Z3yrDMZLcfzrFlvFK+W0m1uvJ5P+elQfbNw6987ewrj5nOPK3ob0qk4u1z6b/ZK/aVufCrX3h3UJmm0rVIWSEuc/Z5mR9rfQk9PaqLq0t15Zj+Zsoy89Twfz5rxT4fTb/FNkfMaPbMreZ1KnIH5+9ez+e8urTksz7WYjd657ivOwWFpwnP2b1b1PRxWKqSwsebWzPFfjp8E9U0hIbjSbSxhtZrMXlvc3D+U1xhsPGpbhnX0Gfw6Vi6FpuoXnwutZ9SZVmmZo4I+pCDqxr6+/aE0231z9n74a2ckcckix37AlQ23NwRgf57V89/EyWx0bTLHTVwBaQhicfxE8/XiuDFYNRpzrON3016nv5dUqVVFtnicPhrypZY5EjaPAKk54H96taHw75su+dpJGj5yzbzgcDqfSqs2sC0uI4zhvnPDfMxz07nFbpuMQLtXy2YZIHFeHVnUVNJaHrVKN9ZGZcxpajczfPj5WHQc5x9TWHrmrRi3ZW2eYPu8cj/6/FXPEupiEMq4jYDHyjcTj+VcR4i1V3mmGWYPjbxjPHf8c5rXA05OequClyLUyL6P7Trm5o2kSbleRlH781uXF2uk2C7kTauSBjB4HrXLWV6kN/8AMhyBuAPQn39ql8ReP7TVLBtPt47oSMdsjkkL05Ar150nJrmTOKnUhGMrM49L9rjUbqbdthkkMi7vm284wK7b4Xa3HLqMSTNiC5mELHdtbaynLZ9AeK43UJ4kKQR7gsIA2qeGIP0q94dZRJ/C0cZyW7KOp6/n9a9WtBKlaL6HhYeUnLTzPfdR8A3UGxkupDHuz9/5Y17E9zkelGm6Itmu1S2zOQxPDEHGT78d6vfD/wATt4x8H6fNdZaaOH7PlP4ynRu/UYq6qiKT5lGGPfo31/pXzdOs+W0jWFGKlzPcboOljTryadY/9cBuBHBORn+ldN4XsJr/AFBbdcu2f3Y/HFZNvH+/254T5iM9RgfrXZeBLaQa7a+U0dvMZVIkfgID1OfpXdldPnqpsyx9ZRpN9dhvijwrdeE5tt8MLJho2TO32y31rwf9oa5mn8bxrcSBpIbaJWZvvDJOOa+svFUMaeH5reedLpsvMG4IjQZ6H3OOfrXxP8VtXOr/ABA1CXdG0Ym2gNz8q9K+4eIcsK5T3uj5mth7TconpWmaZa638KrVV8pZpHad2BK7n6DODyfasvSfDreHC1wyv5Uecktyx+n9Kb8NdUjXwDtLALauyPjqp4/Oq994yimVbOO4aSPJKFhtyT74ry80lUlyq10oL7z3qMeenF9Swt3e6hrDKJGhtyD8xLHpzjC84NbHjrSVuvDFjt8y3W4uQX86TcVwvC9O5x+Gap6ArM0bFSp4IznAB65JrbY6t8VdRk03w5ozXsln+7kvrlttpanHLjnDMO3evmq1WFOprZI65UopO7OQ+Gtotz4l1e4jZljs38lP4i2SeQfw/WvZ/hf4a1DW/EtncrDKLW3k8ySQLtVRx3PUVW8HfDzwv+z7oUf9qXy6tqjfvX+UCLJHTHr9ayfHv7U0lzD9n01mtbXhdka7Vx9B1raXEyp0vZ4aDb2u+5wUspdT3qi0PRtd8M6B4avp5b/UlmV2JVEwuMnPWseH496L4EuFudFsZLe6jyEnaQl1zXz3qnja41qdpJJ5pBnJDSMwX86zZ9TkuV8tSqo2GOzisMZxBmmJa9rUcV5HpU8upU/s/eeyan+0xPcy7beGGNc8log28985FYt18fneWSS402zPlklwYh8xzxXn2nyRwGRm2ScqAhGd3rS6sI2GI7eJtowOh47V4rhzSvKTbPS51tY9s8I/HHwlqaxRanoluh6hoP3Zz+FaGpfA7wD8Q5HutL1y6tbqRjJFZXDK0bN1+Y56A9j1r5pujJp7ZWXbuGcI2OMDrT7PxpdaYwZLiRduGUZNVTliYRXsX3vcz9jSfU9V+NfwN1i61OwkXTzcsoMHmW4GwcYycYAGMn8Kx9J+C0cNkqS3Me9PlJUjDY79a6f4DftQ/wBnXsVrrjtdWcjESI/Iwe4Br3vxB8Nvh/47u49S0y6ktbWeJcRRyBFRupAA4HWujB4ytVqezxL5bdU2vx6mNStKi/h5r+h8P394BE0nBUDdjPUelU9N8XyeHdWW4gMkLbw6yRsQUrmZ/EGYmDSN8oOVHQ57U3+01Fqqv8zN056D0r9GVGcbts+Y9tCV7n6G/sHf8FCNF+HXhx9K1NRqU90GjeGdduM/xKR0468VvfEXT7XW9PuhoOl6bbpqV19pimjYjyxncflHHfFfnBpusvp+Jo5GVo8kleDivsT9lDxIviP4YM1xcG6uorjOxySNnIBB/wAK8TE4aMKirpbs7cnpSjiE6LV33PbvAtu2iWNul54V8Ja4IQVaW6kuBI/OeeQMjPXHeulT4g2domP+Fa+G1VW3MsNzPkgc8ZY1xa3CwKqtHESBn5iTUV54sj8O6TdXkzJHDDC7uQx5x0Aye/SvisVwPgcxxa0kpSf8zt9x+04XMq6p89SKt1aqSXzSUl92h5P+2D8R7HxDd/YdN0G38Ow6aC0saXDyfaJW6sd3bHAA6Z7183+HfEMdnr2mw6dJK2pTXiRPGq54YjGT3Hb2rU+OnxNl8aa3c3HnCNrtiyqTyF7Vwvww8V2Pw98dQ6lqCNeLCjbWU8RyY4J9QPxr9Hw2Swy3BwwuHTlyR1bbbberv+Fn2PhM8zani8Qp3enm3+bf5nvXjX4W6tea1v0aZmjaRjID94HjJ/Otzwt8PZPCVvuvLiaWZuWRj8oJrF8P/FHUr+ytdQtVjt7KZSQ5lUpIPYY4NWJfim+r7o0C7lPODmvi8T9ZjL2XKv69Djlg6VSftXr8zW8XQR6jp7WyncuMAFc1z+keDYhYpnyo4kf94T8pwK1v7X+3srDgsOeOtV9V8u4tRbs3yueVHf8ArWEJNUnCVxy/du9jzn9ovxBavpy2tmfMhj6MDjvXkvhnSG1rVbe23bVunKMem0c857fWvQfjtYhbiG1j/don3Wx1+taPwQ+Fem3gvLjU9ZtdNmjOLcld3B6nnsP619Vl9anhsNeozxMdzTq853WlahZS2EMMMcMMlkqwvGn3WxwHH+0T1rXkeSOeFI3McjERkjsO/wCdchqen2vhLWrf7DrEOoQyPiR449rLz37flXZ3ukTadr1qtwVU5Jicjh8Y5H1z3r2qFSFSkpR1ujxa14zZo+O5FsfC0dotxFhWz5QGCQePrXk/iPRlns5n8va6Yzjv9DXVfGHRvN1u2mZpZJmVfMjDnAX14P8AKsHTo2lt/LaOSIL90u7Z/D/65rbNMw9rWjyRsoxSPRpRbpxg10M/wF4m0PRri1F5pEM13G/ltcTEyKR0Hy5xXda/rjadZtZ2dxBDuCtIxwRH6BQO9eZ3Ojzal4ggtbWPzJLgg4X7y4OSTXZeNdQjtS1rEAzRJsGwcttxhj+P516uS46OD9pXd+aS7m9GM3BpIb8OfBOo+PdfmtbWS3kdUe5bzAUyADn1HP4V9bfBX4ReDdL0u10fXtP0fSdSuVDudVleKe2LKFWRZVIGCTnaeK+TvBupTaZoF3cf6VG0yeRGyAhd3cHI561Lr3xw8VWWkzaSuqre2MyeW8MsaMwG3ufvZHrn0r4bNsK6yXst73evncqdOU1a+x2HxV+LbaV4gtodL1K6/wCJcJbW2SO4PlqFbG4Hv2IzXlvxV8fy6rL9omuZbq8df38jPlpc8kH3ribia48vzGaRWJJTk8c81ILFry2VnSZt3G5SOT+NdCqOnBp2+aKpRUWmw1vW5rvTIrzdKAq4Dnr789q6JfjJq48LW+l3Fx9qtoUAjWf5wg69DxXHyWFxbafeafPIdkuXjz0U1T02Yantjkm+dI9rbf4iOhrlqUlJc9R3d/zLlJSdzo/BnxMuPCGrXxEccg1CN42j3bIzuwQcLxxivVf2bf2oU8F+IY9N1C6ki0lpAxDSF1HsVPB6n6V8+y2zm4eOR/3iqCjeoNbHgHw217rNv5iPIpb5ivNc+JwtGonf/IyqUVUjZH6meOfH/wAJ/EXg+wuNJufFEmoGJWuWa4kfT0T0VAMDJ44NcOnh2ztNT00QyNb215Kyl5ULCPnlhnBIGfX+VeR/BXxgumaVc6Csazie1e2tVdurMQTx7V7BeeKI/EPg3TdOvtJtI9T0+2S3ivbaVo3kUZ+V4ySuR/eGCa4ctxHsJuE02u3Q4sPgnGpqeffEy/e51rULePzljhIEBxwy/wD1+tcxpltIg8u7h2joQxxV74h+Knn8TNBcN5ckarGFVdvAGBVFbvahaWYtuODuGc16mZYiNWps121OunTjFanN+JtBEmqEWse5ccY/h61z+pWE2kTIJh8zYPXpk121xqlnCzKG3HIPXqKzfAHhp/i58U49OXcLaMG4mdQSBFHgkevXj8ainU5YtrZHPHCOc1Thu2rEfge9S31P59rZRWH1DjBx+Fe0QXCvqMjLlt2Wz9a8Sv8AwzdeHvGMtq0csMtsQ7LJwQp2sobsM7v0r2PRW3Hc2Fbb09KvDxXtPaRfQnGU50aHsam6Z7n8XPBx1H9j7wNr1rEzXGltcIwxu+SSVzz9CRXw38X55Lq9nt7i4kZMldn9wE9Aetfp74B8Mx+LP2JLOwcf66xuWQjqriWTaR+KivzO+K1nJ/bF3GLZprxcgRluAVbByfSvCxUYVm+Z6Rb6nvZDXtFQXQ8mTw9/Yl4ZLW02KrDDYJDe/wBa6qPxAbiBI5vlbGGPQmueutF8SSEHUbq1tx0CW4JKn0GePzqKKxezWRpbppGUn5SPy6d65MRTu9D6KUJNXHeMZlEqsx3dwAcYrz3U70x3TYJwew/E5+p/pW34w8TrJ8pk+YcYK4xj1/GuG1TU3MreX8rZyd3f3HtXsYHDuyPKxWI5VZDZ9Qb7eOflbGQe9QeM5JLOFZhHuG44ReFP/wBeqEl473PzbdwIxgEmuo8YKE02FflI4GcdeM/0r0ZJKUUup5MpSnGcU+tzlYIZZow3ywO4+Zh1X/CtXQrsWE0UMLJ80g3OehbvmsqGyk1NiVYqGJwOx9/oPSum0bwatnDDPv3MxCIWJB9yavFSi4Xlp+pxYeLU+a59F6BYRJ4StrrT1+y2Uy7ViMoaQlfvFvQE5IpbCf7dc7d25mPGenPvXB6P8TdN8HeG1tZmluLveSUThU7YJP0qxovxk86Vrj+yZGtN5UuHXr2wOK8WhldebTUfd7ndOtGCtfU9bh8MSRsouJdqspXIUnI9PY1r3VhcWml+esMiw7f3ayDCuFGOvesfwd8ZtF1bQrjVVuo1j08F54ZIsSRDvkY+Y8cY461Y8S/EPSfFPhCzuLPxJ4cs4dSlcJbXGo7br5efnjVWaMHjhtuevQ19pl+Xcii0rX7nzuIrTqO0jmvFXxIvLTQNWuJr2Vd9v9mSB5NyEngcY9M186avdtPeySNnezHA/urjnFd98X9ahZbfTtLk8+1tctJMG+SeQ85DE9AMjGK4fTrCS4bzSyqrcIQByPr6162ZWVNR00VzP2U1sbXw4vbjSbu6+ZmhkwrKG+8eOlbsul2+qX7LHNLtmIUQ5++2enr+VUNEszDIFXZtY84UH/Jr3T4W/Dyz+HHh5fFWtQxzXxTNtbyjKxnoGP6V8HjsydGNk7tnvYOi+Xk7Mm8CfCq38K6Amp+JpkhiCnybUt+8l7gtnoPwqv41+O4stPWx0SOHT7OFSmyDjH19TzXA/EL4q3niu+kLKzLubPPTv+lcbJq7TwHcqtzu4P8Anmvk5wq1n+83R7Hso9VsXPEvimbWbto5pmlVm8w55/X+lZpmZT8qrtxzgcipvIeZ1dfl7gdcfXuTV+w0rELfL8zgZ3Z55966IOMYW6mkp9DJi037WdxZVUnB7bxVm3sMOyKy5U9TWt9lZY4laMlsY2gDAHbPemRab+88yMxFhxt55o9pczlK5D/ZzWcOXXO7nPtVbUGlmt2Tjy2jHOPeugttHkkII/eKxBAY9PUVDq2mrHDs28Acj3//AF1nGtG5F9Tjprf9zu27cn5uDz0rKvlUxMVbdtOCOmB/k10VxZNBF5bfxkn9BWPqOjiESfK7Y5ODwwrroySVy+VJXMGSWW1fzI23KpONx64//XWrofxN1TS7BYLfUJreKMnCZPFUrnTJLpt+R8x388beKbb6RG8KtlfmGTkgfzNa13CSXOtOljCpd6I4mOVg0e5mZ2cNndx1qyl+RNGzZIU9B+VZ6QyQvu2nawwpNWLMGSdmO3avD5OOe1fpktmz8+jJ3R0OnSid4+o5K89CPevqP9hctJp+sxtI729uIVjC8qeuT/hXzD4etsRYYclSOD717j4U1K7+D3wz0e80fVkt7zWpJvtkSxYktTGw2bi4KkFWOMCvPrU+dwgurR9NltSNKSqO+jPry+ZDcttb5WjH9a8F/au+K39iaYukxMsY4lnIb72eAo/mc1Y8CftKrb+GL2TXFkury22mJoEAN1uz1wMA4Gc181/FX4hN488aXuoXTLDG0m5YmbcTkYAH6V25fgamFk8RVj3s/U+kx2eL6taMt/Iy5ba61q8mumkWCHGAzjkiuY1C7aa6EPnrJCh2g7dpJq/rPiSS8hWDcyL/ABKBt2+n51i3ckcucBfl6EV3acrm/U+NrVOaO9rHr37ON02v3eoaXb26zSsPOimnc7bRF6hUHHPrXrsvhC08ORNt2tI3+sdmzk/l+lfKngr4gaj4C1b7ZYsu4xmKRefmU9eneuqi/aIvb6dmuoXKsc/u3/pXzmeYKriKqqR7LyPbwOZRjR5ZvU9quvES2cjMr/KvHvVzw9FNrGoK+/C7c8VwPgW4XxpYLexs7KzkOhGPLPYGvWPDdhHptgWY7Cq5yR8oHck18njIOHuW1O/mbiptmH4r8CR6/fedJt/d8An/APVXM+I9BXRr1raPbtjJUj7ueAeK0vHn7Q2j6FcPZ6ev9p3CjMm04jUez9z7Vw8nxkbxZq8n2qz8hZmyGX+E4xXsZTLERV6i07Hi5hiKbtyPU18/Z0RpFdSeAWUqp/z+deseDPjVZa5fWen6xa2sMKp5cF5Ah2xt/C0gPPBGCffpXmFzdTXGmxQyzzNbiUPHEJDsyfb3q9eWvliGTnaYzGAOmV6/zr3HU91KOh5lV6uTNfxUt9pniFvOCvI0jNI4bdE6Ho65x8p61BrWqqmmoiR4DKSAo5HtRe6zca74Zj/1Mlxp5CF2bbI0Q6KF6NgVzt5rP2ckyMq4zyRiuTFYe1RX1ukz1qVRcidzNk8Y3Whi6W3lWFJGUu+wbjz0B6jNWLszapYx3TNskuow21jjoSODntj1rnr/AFOzutQiSa58m3kZWZkG5kHJPHv0rbt/Eum6/Ctla+ZFDHlIUccsueue3U1rXkowUbMeHrXbgmvvPYvgXNZ614BvIdY1SW3hhl2JDI26NAQcyHj73A4yeteY+LWgiu5vJ8rdbu2GJx5qg/p61ueCtJGiWO9fMkgl5ZVmKeT7gd+3BrB8ZIIL1oTG6qfnDEllYHvnNcdH967K+hsoygznZ7iO7BaR1UqeB68Z4re8B2EuuXdvawrtkkbfuKg4B9qybnR1eSPa0bNtwBiu8+CdlCfFMbZXco2oT6+9efjq1SnTlboaU2uZRZ1erfBZdTsv9It1kmZchlG3+lcRqf7PP2N2aKIq2Plxxj1r6YmO6zQ7Q3PQVyniFN07futuOK+Yp5hWSunb5nbGMb6o+frb4JSWr7pG8wJnjHOCfpXQaZ4dTQnhZY1UoeqjnHvXdPF5kzoeB6YrB8XapZ+HLLzZUkV2yAgXLNjHbv1rtqYytOpZ67Gq9nHSxi+HtU/sL4nWFxHNJ+8mRVwceWS4r6jvY2guGLD5i5bP97gHNfFHj7xbfO1jqRtGt7azuEACHJPzDqPWvt7xnps/h6HR5XKS2+o2MNyZVcMI9yDIIB4NVjKMklJHnVpJVGkzg/iVpDLqK3iw+YsifMwGShrzfxFrjacWj2urdgGySa9f8WeIbGwgha5ult4QpkkYjcNo9B3rzD9oiMaXfafFLpv9k33lh5IZcrcsjrujeQchWI/hr6DCUXVoqct/M8etVcZuJxr62/muONjL1H3qjsNcm0x3a3muIZJAys0chjYgjGMjBx3x61kyzs7fLjpjpTrafA/2lJ9+wraVKycbrXQinWnzXTOj0fxHeJqq3DTSTTOys/muX8wggAEnr0HX0r3fR5GMyyN/EQzc5wTyf5mvE/hV4G1L4g+ImttNt/Pa3iN1cMW2pDGgJLFvyr2PSb1ZGZePuqOPoKKcoc3slYmUasqHtKmt31Pvr9nkKP2XfD8bbW3W0wPt++lr86P2ptIfwf8AG6RrNNsN1NJLtC/d57k9q/Q/9ndsfsx6D/16y/8Ao6Wvkj9q7wd/wk1rd3EEEIu7V2Al3fOyE8rt96+eo0lOrOL2ud2V4hUqi5tmfGvjSK51HXZHjkYYJZgOeOlYPiDVmtbZYRvHmpjJH3v8+9dD4iu5IbidWiZTGzAgrjac/wCe1ef+IdUO9925dw5bGaiNFuWqt0PqpVtLRdzkfE90xl2vznoP7w9awrmfzIt20sTwSAMe1dFqtn/aSF2yyL8w+XC9evtjtUOk+DLrUbvcynYpHOf9Yx7/AKV7EK0aUdTx6kalSVktLmb4b8ONe3BkaMLt5BBK7v8A61dP4n0RrmwjVVG5Tmul07w+LOzWMR7TySMZ+bpVyHQWvn8tgpjjX52HIauGtjndyXTb5npRwsKdNuW7POPDXgy8uGV0iZYIyVyfUV2fhvwa3/L088flr5cABHzsT1PpXZR2UNpGF8tfLVQPLPUk8du9RW1lvk3bWW4k52rycA8KT0rP+0Jq02tvM8a0V8JyFx4HbRHknvIG8hZfLUzYCyv1xnufp2rK16yurtRMtrd/Z1wE8u2cxpjkYwvp3r6T+CHxZ8SfBHVJbjQrq2jvLhNjNPZQ3SxDn7vmo2Dz1GK+nPgP8TPF2p6YfEvjfxRbWfh9gwhF7EGubl+/kQJtBXr8zDaK9z/XCFOCpeyWvW54OOp1HXck+iZ+Y2hTuIbqSOVSscfz7pMcZ9OhPt2q3YG0hDvcStyCwmmbhSeRtzgdsV+q17+054cvL2WPQ/Cfh2zLEM+oS6Rarc3IH8RcR8E88DJ4qDxF+1uthaNH5en3RkO4wvp9vMAR04ZDn6d6mtxbDljHkTXqcUYV2rp21Pyyvgk9sgjkjmi3qpYMGLHBPH/1hTdJsm1XVrWFnbyYyVwBt9/zr7m+IHxY8P8AxBmMeufDnwTrFqBkxNp4snDHPIktjGR39QDg4OK87v8A9lnwJ8TbtZvAmpzeHvEMYaRvDus3AliumxgJa3A6sD0WTGfWj/WOjXfs5Ll0fmehSnVVlPXU8v8AhV8O28S+NrW3VmmRX8x2VcYRTyfxre+M/ii58Saq1vDNJ9khJjVFOFjA4/Gu4/Z78F6n4T1fxJ/aFlJZahp9sLaSCZTGULfe4PNc/wCI/ArQ3Ek5Vm3PtAUbWOK8fFYSTpe3nsj6LAyhdtM8kuvDEm9m2ybGJYNu4x1qzY6RCpXdFuZerY/pXb33hnbNnb5hyc7TjFS2fhRGXdu2HjjNfLVMY+bQ9VtPU5y10mGSTPljnpxjFX4NHXLNtIxxkiunt9IFvb4Co2Bjdiq8qMI1Yx7gqgll9K5lim9DNyWxhyaRCtuy4x2QE8D61WeCOzg/1MG7r8p6D1rQuj9pl3SMqbThQOo9DzWXczSTq2MMzdiTgj0ranNswbJBqIJjO3buBUACq+rOmWkzgvkL6L6moTGWURdhzkHkH/PFTRQiMzcZ3KeCevr+VVzKMrBY5PU2Zn28fLk57duBWfcL5Jy3fuO1dNqdjHPE37tWZeVX145FYVwivavt24Xpj+X4Gu6jK6sinJ8piXULyj5mRY+Ay46Yz0NUZ7aN5TuliG3gc9vyrRv2Kwru4+bGdvTg1Tjsd6fMqZ/2hgiurmUlaRKV9Tz6WOVF2sjLnI4HAos7WeebysYjb7xYGtx9OnJ2sm7aQpw3zH6D3rRt/Ct1cOzLZsVYhgd/QV+k/W9D4aOCqyfLysi8FW00epeXtDD7oPTP516N431hYPslhH8q2Me0P1yx6/lXL6PAmg3JZo2WRYyQjetXIBNrt3DHtVZJGwWc8YPf60YfDudZYiW0UrfM9qclTo/V4fE/0Lh12NfDqRvJumyQT93NczcBXEmNpbBIA5rW8dacND1p7E7ZGhAJK9ie3+fWsI3jFtqqVbpwORX0NbGOtGGi0OWpe/J5GJN4ZvotFfVLiOT7LJJsVSOM/Xt+NQt4cuL7ShPbw+ZCr8EMBtx+NeoaPealN4BvNLVo3tbsAsHXO09j+pqHWPBV1pnhezjQr+7AJCDG814eOrVKUeafXY7cPgVVt2PH7u1aORVfzEZTnA71ZQqm1PlXzOuBjFdjrHgi9udUiZBHsZQGDDkVrXvwyt9F8LNqVxbTeT5hjWVvlUnGeCev4VnHFc8b2em7Wxi8tnSc5OyXmL8IPibH8LhdNeWsl1Y3aDZGoBw46nn1pfHnx11T4gQrb227TdPz80ELnMo7bie3sPSufurW4uIVjePy42JYA0610j7K3GG2oW+uMV59bB09a9jmrYqrb2aejCy0i4vpUhiheUyMFAjH3z6D617p8Iv2aI47yyuNem8mO6Kho0txI0cZ6g7mClgOetXP2cPhrBYaQNdmj8y6mJW3XvGo7gf1r17S9dvNFvluIliaZehmiEmCRjIB6f8A1q+dzDMqqqctNe7ff5I7cPlqlTtPcuftNf8ABN3VvgF8OrLxt4X1iHxl8P75SVvFg8i7sHwSY54gSu1ezjOK+fbmUy6PCXVl2u+zKfeUkcjj+VfdXw4/4KhePPBng9vCuu2Ph7xF4XkiMMltd6cquqHhtrAgfdzgEV8xftWeCdL0fVbPW/DytH4a14vPDGDuWwkP3o93bJyQPavUwOaUqjVPqzzaeFxFBy9oly9Dy3SjG2qvC+HjmOwZPbuPrXOavZw33iHVIbNb2Wzs0VCY8NIkndgSfu1Z1rxB/Zll5wfY+BsVhzuzwc1haPY3Vhof2uG48lpCXlbzCuM9mHevsMmw8HW9rUWkVb5mcZuMdDndVg/sy4aNnDSgZL5yy+2egpug6g1jrlnNn7sy8nvkjP8AOqt7MJ9Q3MpjSTcXY9Rjp+dO06ya8vowrMVzvfb8pOCM47dqwqU3ztJWM41mpqR7PeT2OlaRDJcSTorZUxKrfvDuyTn8RVJPE/8AwnVvJbwxy7bGN2yqmRsZAGT2UetcT4r8V7v3cbM8bJsKMSCg44yO9VfBGszadqjLDdS2jXIMLtG5USJkHDe1L+z6FCMZJttrW56dTMPa1r200OotdQFg+7j5kYJ7544rtvgtpzXfitXV8YBJB4xXBofNDfu2aXGELAZYeua6T4MXjWHxK0+N5HRZHVSCeuTivlM2px9nNLsz06bvNM+n9Vv5odOX7LCtxKw2oSMgntxXjnxZ17WPDOn3N1q2stZpHt/dWdsJJOTjBY/Kv1zmvpO7t/7J0fZBHGrKCFfbyPevHPiN4Bmj0C6shcNc2942+WJxuVznPOe+a+HyucITtPud2rWkjD+CsOleK9IkuLe9vnmIOPtLZJb2rjPi+0iax9mu/tC2rKyl4s7lOPqOOldz8F/h3/wj07TTcZf5Yx8v41r/ABb8JLqvmXDxiNSBjd1NehCtCGJbWzNqdO7948I8NeBRqPhm6t2AkdoflcnklSCDyevHevYvhf4onvfDtnHczyM0I8sKzbsYOO1crZWEelyYT7q+nTFWvA2q/ZriS3ZdpgmdOmMjqDXpc7nCUVr1OXGUYQUXJdT0zx9caTb+GhqOpqZVtcwiEAnzgw47cfNxzXhfi3xddeN9ZuNSu3LXF028hv4V7Lk+lezeJYY9b+Ht9G0fmYh3g57r81eEvE2pOCx9wMcn2r0MtrRlS5OqPBzKk+e66gkvm+Wo5bbjAFTZaNTuVVwMZIwamtx9lgbbHygG4DqCeKutcNIPLkVTkYw2c/XGea3lUi+hgk0df+zt8SZvhz8QFmjxJb6lBLp1zGHAVlkTaCfo2016bpkf2a8aN9xaMCMlhgkgYrwJbb7BNDcK2zy2X5f9rqCRn2Ne3eGtXGs2Ud5/z8R+Zn0cEA1Ps4Rnzx7F/WJypRpS6XP0H/Z9uY0/Zf8ADKFgrtaTYz/13kr5s+JHhrVPFuvXVvpKWaSNLiS5vrqOzs7FC335ZpPlQew5Ne7fCnX7Pwv+yFouqajdRWdjaWczPJK4QY82Unr9McV8X678AfFv7bPim91C3uJNI8G285YatqkbWtiIev7uPBa4kPtkVy5ThbOpiqjtGPUxnPlpJeR6Zqb/ALNfwG+HrahceLvh38VvHVwWRYbrSry+062kxyAkZiXJPHmHrnoa+Z/jr8O7zwx4ei8a+JvDfhvRLbxXeBtIsbO3Nv5UPBLiBwXWPDDG7nOetfS2n+H/AIW/sD/Dq88VaVpY8SeJtLjMdvrOsQJIstwBlfItzwiqcHJyTivl39qnXfFX7QkepxSTtrHia10+DW5AeZZ5JvnkRVxyFHQAAAACuipmuGndQVrmmTwqxqc9RtrzZzOpeA9Nt4G8m3h2sD229uOKpL4SWCF3jVduOg7Y/n+FL8JPG7eLfAUKXKtHqGmk2tzG67ZAU4XcOoNd3oXg9r+086YbUZTtH8RHr9K+NxVWSruMXoj7z6zTgrtaWOA0/wAFfbJizMYbfPL9z9P8asRQQS3B8uNkhjY/Ko6n1yT9a6bxxcro4S1hAjLbVAH3m9/pXO2sB+zK21juwCP4mPPT2op1ZrmctnY8XFYiU3ZPQryW4WbdyW6omc7z/e+laGl2CoAc4mb7z/3v9nPpVqz0Cbfuby/MbO8+nGcDj9K2NO0qOQHev3fvD+lOpiP3fus4aivEk0fTYZtrKqqFxgMvOa6bSJZr541Z93ljanpGM8is3TLdpJFUL6YPqBXQ2Fl9jto1Vi0gcuxP8PQ4rzMRLn2kwqRjbYsl/Jt1OPvZ5z1xWLq19tk+982QcetaOqzEP0PPPHcnJyfyrEmsjqNzG826OHGAP4j7+wpRq2imc9S6WhXkga7dlC4Gcrxw3r+VZdzoNxLc+ZHHNI0J3blwvPbnripvGnxQXRoVt9NjF9qTt5Udso5GfX0HH615/qml+JPGO6TWNUGmwx8pBbYQRn0Ynk4r0cNzWbbQU4Setz6o+GWqvrXw53ar/wAf7ERebJ+8nMa8KpfGXXuM965zxB4etWaWXcGjjB2tnGfbmsn4U2k2kfDKwtVuJp9qkiVzllbPXPcVf1CVprVo0cMrDBGM5PcivpMbnVJZZHCQXR3PWweFdm7nEas8bs+3AVGwdoqikW1cr05z+tdDPozfdVemV5H51FPpCmBfm2MPmAx1r87lV5tj23ZGMs21BuyVxkDoR71g3199obbGzsy5JAPTnv71savDJpuVZSytwCBXORXTXF0zeV1HA24PvVU48urZEqfUqXSvIJEKjzGUYVTnPNVXhczfKvXnmt2WESffSRvUYBxUGq6cwuHmj6MQcHoPWtqdaLfusnlS1aMWC1bexcbefWm3EbQF3jDdcHjsTz+dbkNtHMueQvTPqaqXEARirblYk9+h7V0OaZhKN3dbGNfeWo3bj84wvynjHesHUbVY3by/JWQ5zn1OOeneus1Fdtuqv2B5x09axrqBRF8u1lHIJBzzmuilUaI30ZyWpljbklUcq3KqNpHX1rNkufLfbIu5vUHGa1PENwsqlvutgbiOrda5l5GnP3vu/L9a9ejHmV2ZyqJOyRxdx47vbqQSeZFCxweE5/Pvitbwn8SdVXUoLf7QjRyOIwrpgAscfhXN6boFxqnmeTG0eAcPJwD7j6VoWegzaZMkss0chjOcDnP+H1r9ZlSw+sLH5pRx+MT5uZnuXij4R6tYX011ctZxxAgI/mht4IB4GDWD4M2jV7Vs5j81Sf7230FZOvftG614gsrK18mztbewQRrtDM02O7knmsXQviZDpVwWaJZMcuB/Sul4eFWChT06Hr4fGQVRVKm7Sueh/HfQY7XXYNTt9jNeIyyDHy7xyD+WK4qztrrUpoVtY5WuJH+VIlBZuecA8V0Fx8UbHx3pX2GW1kjSQZhm3BVjYdCx/nXsHwd8Kab8I/BLakp0/Vda1SPeLiI+bDGvfb6N2P41lg4qFObrSUeT8T1I0fb1uak9DjfBXhW4h8OuLmNbe6imO+KRg8ij/eyfyrU8TpHeiNXUKm4DCnp+NVtU8bNYeIZJmjVbfUDiU4xsY96xvEuvv9ldjuDBjtPUE18fmWLq4mdntHY+jwlP2Ud9jufhz8PbHxDr0i3UzR2MSbpCHySPSuG/aD+IkPjPxQun6Ttt9F0YtDbW6L+7dx1cqONx5GetZ9x8UJrHRpobOZkmuk2sQeUxVf4WeGv7U10XNwFaOAmRmduDgAkmvoMNnE8Llrw1JKPN8TS1fzPMx1eVep7OLvHqU9a0ZvD0FnHK+66eMSSL/DAGGQvuat+BPCsnj7xdb6erZXdulJ52x/8A18VR17XP7a1m8ul+VbljINxzsA+6B9BxXov7MOmKtpqGpMh82UiNXz0IwT/OvEx2KeHwftIb7ryZ5tJwq1vZpHumn3EHhDw6trZq2YQFV8YYLWdea+0w3NI25uuW7d6ytX8Srho/4jxjPSqaX63B+8Bt657V8PicdicQo05P3Y7adz6WMeV6l/WZvtEDfNncM43dqpPrP9veANY0G6/fQlFuoWY8xOnPA6c+1Olk82xPPzbT+XpWbpF4tpqpjkA8qZGjc9SAR2HrTyu8a0XHe6FKn7SlKD7Hh2rvJrWtTKvEMZxkHO9vTnj8Kg8S32zTmjB6gZweevX6Vs6raJb6reRwq23eQNy4ZiDkMfwrJbWV02VrlYYpLqRdqvIAxib6V+/UcMqNBKT+K34nxFapK9mzKjOm6bBHJN9ou9QYnNtNDsghP8Ll8/vFPIK9BgGqN94hfWXL7UgXbsRE4AWi9n8yylmlZpJJn+Vm68cnPbuay45flViNvOOef/1V8vOTu9e5zpSvuTTSyEKN7HHH3ulWNJvtlwrM2SCE3dD9MmqckiydGxioJFmWVfJ2tuGSX5GaxjJcyKUrNM9S0Z8afDc7FWOQDDMcnPNaFlqH9i67b6hHujNrJHJvPAGDzzXBfD/WfIdbVmdIZgCq8lWf1x2+tdhcRtxDJuVc/Nu7g15eKoQnN39D38LV51e+x9+eH9ZtfGXhq1vYWO26iV8Zzjj/ABrn/Fnh1Z0bajOR155FeYfst/EzztATTJJmLWbeX0zxnjmvZ3uPtUZYMy+YSPpivy7GxqYWtKnNbO/Q9rDxTipHldxMdA1DzJEaRUPKbtu8DnbnP+cVyPxG+LFzrFrdQMsam4B8pfIwbZeMfNk5P5V0fxl8TyeDLqKSHT7jUvP48qNMvn1x6V5B4s8UXN4J2uNJvI5pCAmX8tEXuCuMnt37V24GmqrUz1sNRlOVrF3QvEKvaLHcfNKF25Hr/nmvLvin8VvEHhvxvqFnZ3SW8bSxusiRjzMY57Hj/CtjQNJlg1SS4maTa2dkRJKx/SuA+J13BqvjG+3Bg1uy/MOM/LX1WXU17WSfY8fPoOFNa9T2X4VftB6pdeDGsbmWC+nZXSVph+8YY9MVWiZpNruyR9gV6fpXh2mavJp8xMMzRtH90jowr1rwLrreJNKWaRrOFhkygy7W/AdcGvS+qqm/dSPm6lR1Em3sbjMRMoZ2fd68Z/T/APXWhp7+Wu6TdtLcZHX6en0xWdYbZv8AU3FrLjjZkqwP0NXZHmjjZm+990kD7xxx34xXnyikxLVBrd75VpHCvzK5LBh1xnpnHH1r1L4G6jceIdNGnQpLcXkcirDAg3NIH6KB68dK8c1mdJLhM7lWGPJIxx65/Kvr39jbwPJ8DvhJdeONSh26x4iBh0ONxkxQKB5k+MAjLHAPpU4rFwow5pdjCompKMep734s1nw34U+BXgvw74qtxqV/oULXD6YJf3ckxLMnmdmA3ElW4ya8k+Jnx01TxxiNpJIbSBRHHDF+5iiHTYqrwq49K53VNSutf1F576ZpLh2Jbd82M89SawPFN3HpthM7Mqqils5GM9PWvkK2OqVmqLfudjojh4t+9qef/HXxm3xX+ImnaGzzTaNoCJPcJ5nDMOFG1Rj5jj61x3jKPWNf/auiuvDt7LZTWIa5eVQfmiCBQjAY+XAIAPpWh8O7aXUoL/V2DGTVLz7x6iNDtXH86679nfQZNY+N/iq8aJ2W3t4Y1bblUJd8/icirqVHCMl2TPUvGnBxibHjD4PWfjW80+9j22Wsbg11LbIF+0R5+bd754zVrxTJb6BZzTRrHGsC/KPQjjGe5/xr0jUdPWK3KqF3ZyWA2sTXh/xd11rjWl0y3+by2KnB43cEj3A/rXlUKntXzMxo1p1PcZxd/wCZ4g1O6u5maRQ24Bz0HNXNKtFN35iqrRqAkeRnkjrj2/rQlqt7dLYw/wCrVsykD+L/AArorHSlgKsY8RxDaoHT/JrvqVHGPJfQ2i76Fe309UCx8bj/AKwH7zf1zU0cCyzLHFuWOP5Oeh/MVLqEw0+ByEjMknDFuo/GpPDULTx7pDjtjH3RWD/h6E1FeJo6faLaRLcY+6uBH0xWvokS3VtvzukuCJWJ6Kvb6Vj6lIs9/bWa/dLb25xjHP4Vq6bfJcm8vM7Y8CFBjGQoyax9mr2sTUiQ6hFvuFmkZo42LE46k/3R7muJ8TeKbnXtQfTdPby1UZmnAz5A6Dj+I1Y8V+KLzxNrKaRpm4h18x51O0WydCxJ7/4VLbeCmeyTT7NhYI5zPcYzI+OsnsD2PrXTGiqcbrUnlajdGHbaPb6TNcQafMPtUKj7XeyHeVY8/icZwO1cR4h8CjxlqChZrhLWE4d3J3y++c8c9q9M1bQraytYdM0yDybW3OQFz8zHO5iTzknms6bT4tHtlVW86SbkkfeHPJNdDxU1Nx2+SOiO12d38FNH/s34ZwWqySzQ28zRRMxyQvXuentVrU18vUl8vzArfe64b9ePrUnwb0prjwDccMrR3P3Cwyvy1au9KaMbmyvY59vevNx1Tlhyo9rLYqUWmZcQ8she7fMW9z2q4dLW5ncKinJzwdvHse/1rI1TVk08MWEnGTkDp9abYeMFg+7skK/eUH7vr2rx43OrE07axRqXXgdbp285RIMZx1P86yrj4UQKrSKPLxgEgcN6Cun0fx/DJhXTGOWG3Kkdqt6vrMOoKqqeW5A6BQKrnexwuvUTPL9b0X7DlYwdygdto6+tYmqWHnW7bdy8cKvcdq7vX7NUZo3+9ySx6c57VxXiST7CrSbv3aPtJx0FVRjZ2idkanNHUyo42tk8oru8skjjrVG9tme9blm2/Nk+vpUN14o829ZV3bSetWEJkCkN94E59K9JeZPI3sVLzc0TbS2fvHHauT8R3zWq7fNZODn5sf5616HH4auNSQLHHL83G5RwecVdtf2cLXxA0i6rfLu7Qq+1gPfH9azp4unTbvsbYfBur2PnnUdXjkzh1YqcEZ6fX86zpYUQgLuYY6p0Ndj8UfglJ4flnfT948s5cA7g2M4rypvEFxbu0Ui4kiO1gOxr7PLp068Oam9Dz8zwVXCzSa0ZrT+MrW40q1jhDs9u7qTGgwR2rNvGuLsbzCtuh4Hmvzj1xWDceKLcb5ls3aTG5mL9ew49ves+58WT3YZY18ssPmLNjFfpsMPPc/L5YyK+F/gbF1KlvHtNxvbnIC4A71l6hr1vCzLCh5OeO/41nyie92t50nzD5dxwvAp1vp21VONkjdyoIAHr/nmtvZydrnPLE8yLVvqNzfPujZrcKcFVPf69e/TpXoXww+NGoeCdCk01itzatIWTzm/1IPXb+NcCkbId67V29DjHU96lOQTjqpwDn8aUsLTnG01cuhmFalrBnr7fE3SfENu0M0k0RcffI+XPaq8viKO4tFRblWZmK7c/eA715f8AbnRv97rU8V25jVlkbePujpWFTLsPy7WseuuI61tUjtbK1F/q628Q2s5r0HxDKvgzwTHZwhRdX8ZVyOSUPVv6cVlfBbQYdWtP7Tcqyx/fI5ZMDmsP4g+KxrOs3MsbRiG3AjtyDyoB5/PrXz1SSqV/YJtJLXTqe17SNDDOb+KSvoZc+oIGTau45G5c9PavbP2e9RhHgeaPdljcMCmcbePX6Ac14GAwWNt0ZMhLYC4+ldr8IPF0ejaubWRtsN4pwD2b1/Ssc3ouphuWJw5Xil9YvI9C8XeLZLKRWVDt6nnrWl4b10a3Yo6t8rfeX6Vz3iCCPUWKllZkGAD3qr8Nbl7bUprOTquWjJPUGvmvYctPXV2Pr+Zuep6ZDd7FYMflXt+tZt/N86zJ8rK4YH0xTp5BIygdiMf1qrdgwwFv7xyMVwUnye8uh2U4q9jhfHcR07V7thkCU+aP+BDJ/wD1dK4XVJAbmZWZmhkHCjjkV6F8V52XTLW7CKzITExP5r+teU6jqCxFeT5oBC46V+r0sydXC09bu34nwGY0XGvJS26DNSkjkRQ7Mu0DjH+FULlhLbL/ALJx9aGucNmTlm5OKjR/Omb+6ePwrnje12efs9CSB/ITPl7t3BJJ4PrUMs00MjjcvcZz2/lTophuZWzx93jtUd6QG7bevT6Vjfqac5NDrEhTcpk+XAIXg5H8vwrqLX4kzKIY5ommO3btY/Nj6jmuPCpjdnavdj0Fa1h4XZbT7Vet9ntJBlMHbJL/ALp7USp3jzMqNWd9D0r4XfHaPwt4nguHZrezEqmZWHzYz7elfZ2ieOLa8sopmlXy5YVmTacghhkHPuPwr89B4u099EZrW1aGZQxihRcRQAfxb+rMeh4r139m79qO10vwfa6JryzSNZsUilL5Voj91GH+zyB7Yr4/ibh+9KFamve62etvM+mynGyleM2j6k1C5s9WSRZGjbevB5LD05rzr4iaM9zEMYeNlwGx93pVv7dp+qWH2rTdS3qVLqI5AcfXnivHPiv+0TN4RupLCzuIbyXHAY5VSeua+ZwWAxNWUYwVj3ljPYvnkxfELjRLWZpJsmP7pwB06V4Fruo/b9evLgBmWZ8kZP0q74u+KmreK/OW4mCwtwyoMZ+lZMDsI1UemcgfMPxr77L8BKjTtJ3Z81nOYKu0khsUwR1Xlv7h/u/4/jXTfD3xnH4d1RZLnTLfUoZjtkXzDGyjvtIxz6Vzykyllfoo/OkEsbJu3Bfc/wAPvXp1KMZSVzxedrY988J2f/CU6RJqFlb3Mlisxj82RD+5PXax55AIGa0fDGqveXb6dcTf6vd5LyH7pHqQMY69q8W8CfErW/AV01xo+r3Vn5h+aIS70kHT5kOVYH3Gfeu38FfGq31PU92oW0drfXDLGtzbrtjQlufk7bj3HTNcFbDtQbUfxNY1O59ifstfs8eF/C1rp/i7x5D/AGtqV5m703QiGEVuoO1HuMYLbvvKo4wOQa9U+KXiq48cXazTH93HGUjQJsWJBwFUf3R0AHpXPaakiz2qzP8AvEhjBD/OceWpHPp1q5eXWbSORTxnCn2zX5/jsVUqScZPS+h0UaFn7Tr+Rz8kP7zkD90u7GeR/WvPfj7qj6X4DuG3NukYBexr0aS48pLiViCqrjCr904NeW/GxW13XPD+jttYXVygcE/Kqg5OR6YrkpxTqNnVS+Jtk3hTQV0DSdKs1fd9ngUscDn5Sefxr0D9nNd3hTVjHGqyNqTgsP8AloBjGfoK5S7nBur6RT/q4yiknHP9K6n4I3Ufhj4bzb5j50k7yyLjPljJxn61lipylpEqpdosfFnxlF4J0OTypM3En7uM8HnBzXhM8i2umSXlzIrX1wMbR/yzXJyf5V0fivWpvHHiOa4lY/Y7cEIrA7Rg8/U1zlvAuv69MxVTb2ih5Nv8XoD9cH8q6MPy04bJHRRiorQueF9GNpa+dIf302CV9B2/x/Gukaza0tlO7aF5z1yf/wBVM0VftE7BtqhAGUbentTfEeorHbeVuxtOR79a5ZycmCvz3Ma8nNzetznjrj061rWLLBbJM67S33VxWBHM8k0cY+UsfmPselWdY1QW1pHEu4sq7j82cGtZWUbIupFpWNKwnWaK+un+bgQx85+c/wD66o+LPEzeHtFh063Ek14z+UqQ9WlblifX37cVoadp7aRoy5wfs0Zudw/v9v51c8A+E916+vXkYkmYmGzh9M9X/HrTjL3t9CJSWrZQ8P8Ah5vAGhSW6wLfa/qDb5X2jart91D7fpxWvp+jzeF9Hb7RcSXGp3TZuZW+bcT0jUD+BAO/pXQSaWuixeY7rcXjklnJ+6Owri/GOvraozO3zDODu4xU1uaT5UFP31oVdb1eOxhZ92515JIGT+Nczpt7NrupM2DIGbcM9qw7/WLrxHqX2WNztfgAdzXcaHpcPg3TFllyJ2AUr/d963jGKWq1Npcq06m54J+JL/DW/mhuNstjOd06DjOOp/8A1V6ZcanZ+KvDn2vS1+0Q3SboR6CvnyW+OpTyBguJPl2uc5/Guk+G/iW48G/DrT1aRG3yOUXfjA3HHasMdgqtSl7SFtD0cDKfNyrsj0PSvhTDru6bX7x7WOUArGDj8Miuz0v9l/wu9t5tteOp2gj94Tn9a+ePGfx2vbrdiRo/LfJJY4H0qx4a/aht9Q0+K3uNajtZ8lVMitnj6V4ccHibanqVoTvrOx7tc/s82umbvseoLuzkqScj9a5zWfDbaSik7VZcp0zuHrXAab8WtUOouV1CSaEtmJiSC/HXHp2rVl8e6hqh23Dhl+8MDv0/rWcqc4yszKVOSWpB4ul+Rj9Dz61wevSmaxmRjuViVI9RXTeItVkn+WRVJYd65e9iZ+Mda7sPHU2hDRHA6urxzIVj8tgw5HO4CtrR77y5Yyzfu85IwOlW9T0hHG/Khh61WtrNREflG7H3h/Ou7RrU39lfQ9i+HfxD0JbP7LN5cMm3AdvXP/168/8AD/8Awj+q/EDVYtQvNQs7hbhykkZzFIM8ZJ56Y6VS1/wg1n4KnvEkZH4O7vxXNQ+Lpp57eNrH7XcNhF2D5z7k1x06VPklKF15nfhMNGK03NL4g2Q8D+OI2huheWV8pHXPGCR/KvnfxZpscviK7kRflkkLDFe1fExbjRrJZLsbZFjJUd1z0FeCX2tTC6YbuQea+oyWm+S99Dl4irJQhFPVHKAbLfdH93HUjG+q8U0JmYsrq2MEYyPyqxI+dygsrMMjcPb/ABqOGE2tynylm3YyTwe/Sv2/1P57UrBuzDhmYiP7uVPQ0941gVmDL82MYGfpxUcc7I7bt0bd2GSTUscbJLubDNj7v9aQcw6GXaM9Y1JDZGOfpUxI2D+8o5+lQusathpG3H5snP0pSzRDcNreZwSenFBRKgZs42n8cUpZkQjO1uvXgCmQnLlT5e70U06WRlRl2r0IrGo76Bq9Edn4D+IVz4f0LUrBFX/TiANp6dzjnv0pn2QyxySBFC8Mw644rkdLuf3nWugh1hreNY/vBui+teViKSjOUoLc9eOKnOKUuisaF3Ows4pA25V4A/u59aZpk+wrulMMkZ+8P4T1FVBeCOz2lvmV8getRrIvn4Y4G3Kn+8a5PZpx5Wa0pNPmR3lr8T5bdPs18qyfLhZkP3s+vpVrRfFNtZ+IrO5imjaNv3LEHPJ/GvOhesZFVVDK4+aqU1xJaTBo2aGNXwFA+771xSwEHG12j1qeZVFJcyTPqQ6xAkAkaaJI+7udoFZevfFHRbaKQreLJgj7i7/r3rxRdVutdYefdTOu3cFB4q/a2yw2u35fm4+leR/YsIvWR6n9uVGrRVjsvE/xC0nxVo17YxSSLJtVogy7dxJxXmfiCQPMq7myo2n61cvLZYZmwcqgB3Vk3rHdtXnYcZ/v+9e9gqMaUFCJ4+OxU60+efaxDIMH5e3JHfFQxP8AvPlztzznrTZtqNkNzj3pPuAsv0K56+legeai7cSiN1wu7byAO5quJGv7jy1hk8xm2KgOWYnj8OajhvfPBkZWjZecGr+lSyabHcXUSxtI42RMTypPWqp0lN8pXMdB4b8EWeh+HpNa1S4ErW4byLNFz9okHUluyqetc14h8R3GuX7h5Y5Ax2uwzsAHQL7AcVp+K9U2WtvZmQOtrCqYB6ZGSfxzXOQ2bCeNPveY+eOwFGJnyL2a6FQbuaWpXCxaQ0Ks2yQlCQuKbZXC6RqEcMnyq6YP9Ks3FnJql9p1rsO3zRnHc9TVLxcyzatJsyWDgqMcHHH16VhiKzlLlvpa1zuw8Z+ydRd/yLb61eQxeUtzPDHk52Nt/kaoXTLJKpz5kjcDCnJr07w94T0HX/BEc02nyR6lbkZcN8siHv8A/r5qxo2h6To9jPNDbr5u07d/PPtXlfXaVN2S1Wh7TwFScU5PzPNoPDM0z+fMphjUc7+M1EIpjMzKqx7flODnNb3jDVPMaTOUEgAwO1ZEsrFEUKOFz8vf6+9dtOpOUefoeTjIRjLlREsiiVWLMrL3IyKkgMN4R8q7vQUQKCcsrfkacqs0aybdpXg4rdRurnHZj54UaUDaPMKk7u5x0+lPsl+xXNvKy/NHIjYUck7gaheTaWyrFiCv0FWUZHUxbl3NkDJ6cYHNY1fhaCMro/TbwtqjHTLWX7vmWsUgUnd1jUde9P1G+efSWC/NtbacjHGaydF1GMaLYiNt0bWsSh8feHlrz/8Aqq1HJ5unybeVMmAenpX5LiKajP5s9aMrQT8ijHdST21w0q7d8m1eOMdP6157rMS6n+0RbyeSZYtLt5CMgnDYxXpoh3qit8u8lufQe9eXeCJn1X4peIZvveWPLHPXmtMK3G7N6fX0/M3NJRZ7LVWbcdpPyleSdvNN1nWbfwZ8LdL0vT23XuqRm5uJFzuJz/F7Y4xUmkXKmDUvOKovzOxPVRjqRXM+GkTU9UkvtjR2dlkJk7gRz+HXn6Vnyt3uOMG0ivr8y6Bp0cMLZklG8qRk5Py/n/8AXqbT9KfSbGOGQ/vesu1fvE9j9P61lWEn/CS+NvOkVTa6fmaUA/KT0Ufj1ArpYZTeZkZVR5GLgA9fQUV+WH7ux02sLAv2Q5Vmbv8A/rrG8TXBKu27b/Wrt3f/AGadox16qfWuW8TalMJtkjDy16H1oo076jpxZa0llaWZsMpIxj0qfTbYarr7MrHykfzGz2UdayNN1DyopN3HGa2vD8i6Tp7S5bzLgiEDGSQSBW04a3Np+Z1hs5NdNlYRq23UJArkdQmef0A/WvQotPht4hJGoZIV8uL+6AOM/Wub+H+mef4iurv5ylnEIo8j+LvgfjWt4y8TxaFZ7d25dnyqo5X3rhiuZ6HmzjzS5TnPG3ii28P28hkk3SKmSexzXkEVrqHxI1CQW/7mzUkGaYbVB9j3raW1f4n6zJPcyS/2RbuQpHBnPcKfbHOfWtjVruO003yLOJYoIwUwOnHNaUpJRUktTroxjCyiZsVtY+DYFhslaa828yvhs+uOntWNqOoSauzMzMATggVPdQefH8wYtjIGen41GlssSBcFQ3Dc5xXQop6yOmMbO42zhMSLuG7bwC3vW/rFikVjZ2vyqttGCM98+tZ/h63N/rUELL/Ec49utT67I0t9KTu2xsU/KumvJwwkkr+9oepldFuTlHoY934OluCzMqc85xxVax+F9pfD7PND1bcsgxuOffFbOk+K1067aOaFpIyeCa9C0XSorywhmjT93Jypr5qpi5Utz3pwlvJHK6F8No9L2qu6UqAAzAtj6V2ek+BJrmBdu5m78dq6rw5YMr+ULVH2jIbI5rcgtWh/1kbKqjntXDWxEpyuzza7auzybxR4Ua0Q71ztP93NcZrEu19u1dvrXqvxIv48MsbY4PA9TXkGqneJXY45GOa3oa7nRh/ejdnPa/OWZdvAyRWXotxJNdKpZivHAqXWNxk+Vse1VtOWS3dpGZdwJXH0r06e2h3SppHfH4Z/8LV8Pw2/9sPax2827ywfv9OD+Vb0fwMj8LG3kt7m3by1JZ8/crzfQPi7J4CtJVWzS83EEBm24681pa98aNY8UeFZoYo7exjl+95WSW/E1xSwuJlywlLS4oVvZ6nmf7SXjVpNS+wpIskathiG4yMivD5rG4vJmkXbgn612Hj1Z57jEq+Y0bEs351zboYz/q2554OK/QcBRhSpKET5jOazrVFJM5eJGKN93cuGPOfwpwuGjdSvLL93/aqvCggaT5txkGcg9FH9akhiaeRduW2/c9SfQV+tH4tfQmaZmmVm+QZ9PvDGfzqSJwo3H7o6k9V+tQsrOfmc/wCsDkbc7eMH8aciPPKvUMvIY8AelJlxJZ4lFz8zqpVMkH8aZbxM1sy/LtLbgCc7hUlsu9+hKjjOOv8AnJqOe2UAlmO1Tt+Xr17UK9igkRZNzKu1u+OKILjbsXHcDJqPzW/1Y3R9gSvJ96a8O4r5bfPH8zZ43VjOMtxcrLlt+6mG4LtY8EDHNaU821Ayjc2OB/drLVzLCyyMPVdp5BqSO+8u5Cs37sgZZux9M+9c9TzOijK0WmWhc74fvd+tEN+JDuznbx1qOfTpId27CxsflI6H6UfYfs6I23HHTZnca8+ro7HdGT6FoyeZH8rbWY4HtUvl+XF8/wA31Oc1SihZkK7W68fL0q5FZTOmFVuOoI6Vlc1pylc0NFucxt97gZB9vStq1kVyqs24EZ+lc3Z2jQNtMLD+IvnArStrr5lZcrGRgM3BJ9vauetHS6OiNVpmpIiSK6g7QxxXP3k7CdhtGeO/61tLPthZsfL0z6e9YOtyKihxhs4HHfFVQKqSbWpQubjy5Bx1ODmnmSNCCo3bepz+tV5z9pOD80cfJI6/SpLOMNj5flfjp0BOP61181tWYxjdWNzTfCGp63p63kduzws2N5GNwq9D4RvNPMKyW7Hy5A7jBr6m/Zw0bwz4y/Zz0trqxuIbizZ4JplGVdlPX6102nfBPQ9dWRrPUIpGbgCUjI9PpXyWK4qWHqOLjqmfaUeG6c8OqsZanxLrVlLrGq/ZoYWkuJmComwhia2m+E+uaKRI1jtZl3hc5K/hX2L/AMMzHSZUv7a3jmurc5QgZAPTOa5G48D/AGbXr06oZoZEQKFVSfMLHJ57cVniOKKM6Uakfie6NKXDVP7Unf5HzRo1ncWurPNLA8K2kLfMy5G4/LXO6pbZ1QSHl+BkV9O6z4asZLKRVKzKykbSuC1eY+MvhGl5I11p/wDrFOTGeQfYV1YXPKc3ytWJqZS4UWoa6vQr+F72RfDEb7owrJsIJ6lTWVqXiFUtxDg7dxzgdfxqn4r0nUtCsYYZLO4t7dQSJCCqlj3rCF69kY2cx7GypOM5989utehTo05ty+YVazguVq2xH4muPPlVdsrbgWye9R275k2fNtjA24OM0a2zS30fLsjIduDkmlghUQKyn5sYJfvXoUYxVPU+bxrftW/QmgRrmTbtkPuDT7hG8xVXHPbOKZFLMXXyo4y3IPzYGKHE10Nwj8vd8uc/rVRl7ujOTmuPEGy8G44GMqwHP+FJs3JOxYxoqsDhtvGCOpOKbdQyLFGrOqhnwoAz0xmvSv2UvgXJ+0J8UxY+Xcf8I5oyi/1u8AISG2DjCFugeQ/IoPPXHSufFVoUqfNUFyLXU+xPh/IrfDrwyVTy92kWzYY5bmIEZ/Oui0c/a9Lk/h54/KjxxNFd6jHdWv7mFYUiW3XH+jxoAkacDsgUfXJ703wc2/T5Oc/vAOa/Kq0lOfMvP8z1I83s1cm1aYWcMkg2ttjI5GcGvHfhNqG7xbrucBmldcjuR/SvVvGt21jot/JlV2gbCuD19B1NeH/Bi7KeKby4lJWFnneRnPCAA9+9XRgmmzvpwvC5s63O1srWcayeZqDbQWxu8v0JHrU/iW5XwT4WWxj/AHbt1c9Mnr+GOKd4atV1rVptWkj+Vcm3yMbUz8o9/rXM+LLybxz41hsfmEcjgl/RQc//AFquJrZWRoaFZ/2B4VWaRg02oP57D1Q8Jk+w5q/HrEVtEBJkeSu0MPWsrUr6ObUp1X95bQN5Kg9gvTGKr3rqbLdlgZnDYbuKdTV3ZtCCbHap4i85ZPnbLZAOK57Urz7Yy7pPmUYBPpUtzIfOK7SdqknPvxVEAI49e9VTulobWsaVpGLhPL8zcH447V0Gnyrf+JdOs1z5cJ84hTyAvP8ASsHSCq3itwqx9f8A69XfBkn2zXL68J8toYRGhxyWZgAB74P5US1WpnUkj23wLMdG8JC6m3RNeNJKQ/OATxXBa79o+I2vy2MMrfZ1G6aRWxhc9AfU10njjVzZ6dY6Xas0k8yKijZliSBkAe1T6LoMPg7RIbFWVrmRi8z45LeteXGTWxw6bmfd2Nt4b0+G1hjRI40KhAOP/wBfv3rnNRlgkh4DKq/KQB1ro7ywe9lMjyMu4/dI29Ky9T06G2Rlbtz7E9aqMmtEaR2Odv4Mwxtt2qvy57+1Z91J5a4UfN13VpakwYbGb5lORz1PbNZN9I0sf3Y156D7wrthLudVO/U2/ha0a+No/MmihWYELJKQqKWPc17nr3wL0Hwhpv8AaWqXUF0txhwlvIu2Qn0JNfLet6idK8LXtyw2/ZoWkGfbmvmO7+IutateM0upag0ZlMnlGVmVQMEADOK7qGR1cbF2naK/r1OmOarCJ3P0V8WeDPD9jb+dN4euY7eRd0UyTq2M8jgf0qr8Kcwr9nK7YmclFk+baO2K5z4HfEax+L/wgsri31KC3k0tI7e4glIXYQijIHbPrXVeGP7LsNVjMmp2DBiG+STds9zzxXxmZYGdCo6a1+/9T7GnV9tQVSCPRNP0eaELJiMPg8Diq+svJGGjkLtlc9eldX4V8T6PqsUdtDf2s4xt3Iwb+tQeJvD6wyllKtG3SQenoT+VeK8RJaNHlzbu7nifjPT3aNirLn0Jrgbzw60+VZgwbngV734g8HLdMzplVIwQo4FcP4g8MtbMzbSqrx0wK6KOKfodVOScbHimueEXgDScqqn061y+vv8AYIG+cg53fnzXrPimzdbeTc25B2zzXjXxAmy8nltxkY3Ht7V9FgKnPrI0lK61Md2bUzCu77pwfevRNK0X/ilWfavyjp61wWgxMI4W2rndyVH869P0t410cruUccgnjNdmIqW2OfVrQ8Z8a6Oy3UkixgLv5z9DXn9/YkXLfNn8Ole1eNtKZJZGwzK3JOOB7V5Vq8KG9b92q9sYr6bL6nuHmYujG12eZsBCjHy2+VsFVGQB1/yKsQxbJWPJZsZIGAPpU/kNHKVVpFhY7sY4GOp/KowqpI2JD83zEe9fsDPwenrCyJBCGT7v8Gzr+v1ps8HyddvPrzTWjjlPEm0p97nr6CpIbv7Om2NY/QA9M1jUk7qx0xfcgB4O4ngfw8ZpJEMfO0uzr0/lVllW7KszK+D8pXgD/PNMaN9+5fnx+grRystSinPEQ8e5VJC4yTUc1qxLSrGqqq8tn1qU+WwZvMKqD0J6etLOBDHJuJZWXHXtWMqjJ5n1I7BxDLuZi27hR6mrUY8zDjEbDp6596owARwKGPzSDcPfmr0Q/wBFVuVYn1rnnUv0NYzSRraVdeZbL5vzbeAP61clKTv8ygYX5QOx5rG0+TDBm+h+lWb268idf9nH/wBauWtTT1PRo1EopWNqJlFr+8bbkDjH0qw12qSeWY4yygdR0rBOrbm3P5mV5zgAVI2oMWRvmfdzye1efKk76HWnZ3ZtJd27O33cp94dhUMtvGUVlXaq5wQMq3fArNbU2jfcu1WH6VJbap8yszLu6ZB5qY0Wt2D1WhsQOUsmAUq2M7h15rn9fm2ywxhW2e1XnuASzKyhP4wzHJrPvZZLhl+XanStqMeVlydxunbT5x3MoxnaFpY5clW5Xa2FI9KrmX7JM/zN83HU9KS3n4VWXbt+4Sa65rm2M9rs+gv2Rv2i/EHga4Xwza6db6xYXTO3lsuWjJBJOPwr3rQfGWn+Ltfl0ubTXs71gZAYxtUcdS3T/wDVXyz+yJ4tv/Bnx88P3Wl21ve3U0xt/Jc5Uq4IJ/AV+jXjX9njw/r9j/allcTWV7tzcR7MIpx1HqM+tfnHE2Hw9Csq9SO/mfd5Di19V5JSZwenWGuaRoz/ANg6nDeiM5MLvu2+1dRB4Yh8RWS3uoWcbzTQCO6Kr9w9yPevOtb/AGXfEGk2s2qaDqUisJMjaxIc/TpXf3MeteHrCGRVDQsi+cjHocDP618XiHBzXs9j3ea2l7mV/wAMx6ZfRpLZ3E00ExJCSAfIPU1ynjD9j64s7Oa806bMeScK4616l4f8YeTJasVaLd95R0Ir0S20iy8T6RMbXcGVM7V6URxlamldnL7SzvI/Pfxd4TvNF1j7DqUcjRzEJiRQwA9q5fVv2bL3xKN2jyQyJksIpGCsOeeenavp749/DW4+2SXU4kkW1O8AjHTP9a8Z0i6m0WSIbVAyXJJPygntX2WX5xNU0lqebibOTPFfG/wY8S+FZlmutIuFhRD+8T519+lcqIXSH/VtgtkZ+XHtzX2VovjZogpSRvu7Tj7pH06GqHin4f8Ahv4mWrLd2EUbsCPNgAjlz7Y6/Svbp59SilGcfmeDiMHKUnJHyFHOYXXarIzcFh1FWba5neJdtuqbu5O0ivb7X9iLUtb1aRNL1rS2s5D8v2pnjlA9CAD06dab4n/Yl8S+F7Z2t9a0LULmJciCOVvMI7gErya9qniaVSPPFnHLCzXQ8J1iSS3khaTaMr9xVwX4GOfqa+zv2dDD8E/gNZ6W+I77Xyuo3524kLvkRKSOqqoBAPGSTXx34t0q48N+KPsOoQSW93a4Esci42f/AK/WvqrwHPafGDwHo2qWl5HHeWsMVvc2rfeVovl5B4O5eRXi8Rc8qSUW2rpGmChCdS09z2Z7wG9WOeVVa4QEj3+Xn8cVseBo/O0m6Yfwzt0rkfG+q/2dquksfuwsitx0UgD+eK9N8MaCtvoE8jLxIGkAzzngA/SvkvqFSony9DoaslLucH8WJP7O8D3lwGJ8uMZUnr1ryj4a2CT+D49qBptQO0ue6A5I/E8H1Fep/tDWEkHwt1DafmO5F/BTj8q4T9n2yWbQ4N7hVs4gNx5G4/41VOm6dJpo7Iy9w1fE0i+EvDAjVmbI3Hbhdq4xmuQ8BP8AZYNV1q6T95GmyMZBJySBn+fHrWj8UNQbWrxbOLa8bNgnAwI/ek8Rouk+FrbTow6ySfNIVA/AVzxsotdyr6JGNoNu7WRz/rGy5z/ETT9UXyYYt42vszg1bSweCGFVJHIRjjrgcVmeIFaS4eQsc52qPXH/AOuqk7vQ7qL6GXPN80nc7QM1ntKXnq0VYR7mDBlyx44qrHtL9O3rXRGLsVKV9i41w1pYTNn5mGK6b4O6b/aQjkchhNdCRh6LGOc/iK4jU71sLHt3I3J969L+EdvInhlXK/vGXyQoGMeYwJP5Vlirqnqc9Z2jc9C8LWn9oazf6zIqtyIrVWGQD03D8K1NQtYrJfOkGZPMIOT92rmYdC0+GGPH7uMDPrXO67diYsxZju5IzXBGyWqPLcnKV0UdX1pg8yoEwDjOK5HUtWYSN1Yk856VqX9wHlZecc5rm76IvLIc/L1FTHe6O2mU7m4aWU8/Wqc0hkkz7etWrhVWDd3Y4qhOTv2x/KetdkFqdpwv7QvihdG+GV5GHZZr9hboB78n9Aa+cPOkeNWVlX/CvYv2rb5hDpNgy7cF5yU+73Uc9enFeLwNJGfLSHzM85r77JqKjhl63Pn8walNJ9Fb5nr37Lvxntfhh4juYtUXdpd4gWRVPCngbiK/QD4f/C7wr4v8O2OtW+rfaLS5jEsaRxhFZT29+lfljboU2xyLtZjnGOp9K/QD/gnumoa58C7KO+2QQrdSx6c7nm5RT8236EgV8vxhl8qkPrMH8J9BkmdVYcuFqSsmeu6ppWk+F42ForQqPuFcirPw/wDiJ/aF1caVdM8trIpMblTlTkf40zU/h/faxM3E3XjmotL8MN4XuFaRZFzwCT/n0r8mlUcoJNPvex9HzxcXZ3OmsroWd61uzM0XOG29K5H4mahb29pIyqm0nd71D44+JMPh+GRpJWT5c89OOnPWvmn4u/HtrkuouFUMcL823A611YHA1K9RKKCnywfPNmt8SvF6sv7mRM5OQD2ryTWpWvGds/dBAz3pbG8uNef7QrJJHIv8Jq8nhqX7Ors2FKgn2r7Gjh1QXs57l+2jJXjsR+HLJo3Rsjcex6V11ncbVVVbIj5ZfU1h2NsLNV3Nu/u9sU641aOEyfvNrKac6alLQzjpqjJ+JHiO2trKSa4maBMFiSOBjtXg2ufGHSX1OT/SWHOOFNdF+1NrE1z4W2xyMsTNlwT1Hzd6+dnjZnLIilW5/eE5r9A4byunUo+0mfD8SZ3KlVjRjG/U9mmsFmO1dq7WDYPU/wCfSsvUrGWGYtsZW6nNdNDEpLbVXcMkHvn1qvf6bNNukjKyMxyU/Cv0PWx+X0pJHLbjjcVTzOeWPHTHPrUsFy2M7W8z+6v3a1pPs88wgkhWGQqT06mub+Ihm8NeCtQvrV1M1tGMN1CksFz+uazje12jZy0uaIuQJ1yJFb7qc446/wAyalSf7KWZsNtJ4znIr9iPA/8AwZz2vjHwXo+sf8NMeKITqtjDeeX/AMIjAfL8yNXxn7V2ziofiR/wZ423gD4d69ry/tL+J7ltE064vxCfCMCiUxRNJtz9q4ztxUzlfY5/7Qh2Z+PHkJN+82Bd3PvVSW3e2jlZZPkaTBHtX62fsif8Gnkf7Tv7KHwv+Jc37RniTR5viJ4S0nxNLp8fhWCZLJr2ziuTCrm4XcEMpUNtGcZwOlcL/wAExP8Ag2Z/4eI/sJ+AfjJe/H7X/C9x44t7qaXSoPDENzHaeTeT22BIZ0LZEIb7o+9j3rPlCOYU1umfmTby+bPt+UsvC89BV2IMj53bhnbX2v8A8Eyv+CDh/wCCgv7VH7T3w7uPjNrPhWH9njxPF4bttQg8Pw3D66j3epwedJGZlETYsFbAZ/8AWEZ4yfrT4i/8GeVv8P8A4d69ri/tL+J7j+xdPuNQEJ8IwKJTFEz7c/auM7cVm6T6DeY0+zPx5ikyV29xnNW7+E3kUe3HHPNcp4LnvvHGneF7VbptPm8SanZaZJdxxB/I86YRs6oSAWA5xnH0r9xP+INGIdP2oPFWB0/4o+Dj/wAmqz9m5LQ7ZZlSpWTT1Vz8YIIfMdV2t8rc/NVuVR5pz93tX3//AMFLf+DbX4mf8E7fgLq/xW8J/Ee3+L3hLwrGLrxDp11ow0vVLCzH+suoissiSrHnc4JUhQWwQDjh/wDgjp/wRUvP+Cwvhb4jeKJPizqXw70bwZrFvothFY6JHf8A252t/OlZy0qbSN8eAM/ePTiuf6rPmsdX9s4f2fPr2t1PjgWiH+IBiNw9asXenbXhdo/l/vHjFfoP/wAFSv8Ag271D/gm5+xV4n+Mml/HbxB4zbwnPZC606bwzb2wNvPdRW8kiv57/MnmhgMc7ccUf8FEP+De6b9jP/gnb4g/aG8MfHrX/iVaeHbLTdZtNHufC8NvDqNpdXVtEXaRJ2KhIbgyk7Twh6dRP1Sr0t+P+RnHPcPazT/D/M/PJrX5u7buRkdR7UT/ACxqq9EO0/0r9EPgx/wbsDxx/wAEytJ/aX8eftCeIfCdrdeCJPHd9pVj4Wguls7QW73SRxs06F2aEJgbRlmxz1PX/sP/APBrK37YX7Hvw0+KVx+0Z4k0Kbx/4ds9ck06PwrBMlk08SyGJX+0LuCk4B2jOOg6Vt9VYf29R7P8P8z8vI181yvcDOe1d18AfAPgvxxqOpL408WN4Ts7WPzIHW3eV7psj5RgcHr+VfW3/BVb/g3w8Sf8E4Ph38ONV8GfFjWPip4n+I3jiy8E6doV74fisYpZrqKdo28xZ3IIeJR0AwxJIA5+tvh3/wAGjPwp8HfDTTbz46ftBfERfE2oXNtZPN4b1Kw8P6OLu4kWGG0hW5t5mld5nWNCSrSMygRhmxR9WlczqZ1RcbpO/wAj5P8A2LvgP8NdN8fXGueF/EF74mms4PJT7TbtCkLPwHGRyfp05r27xfqXjOwnuLPSbdVsZI2zN5qs/wB3uG61B+2T/wAEsfFn/BDY6b8R/CvjzVPiZ8CtX1ez0LX7LX4EXXPC3nuI7e6FxEFjuIvOYK+UjI3ooVi29aXxx1HxV8Ufjt8Afg54L8YXHw8k+K3ia602/wDElnYx3t3aRwWvmhY45CFIZmG45B+UYOMg/FZ1RnLMKeDdOL517re2mrvvt6H1eT5pQhl0sUpy9y3MtL7q1vX1Pjm+/aL+I/7NPxMktoNUmVPPad7W8ffFcDdnlT0+g4r7g/Z0/aU8N/tmeCg1vbtpXiCzKpcwtG5jlOOSjEBTnrjt0r1Txn/waeeIviJr39qa3+1p4r1LUMY8+bwRZlv/AEor5/8AgJ/wTD+LHjT/AIKh/E/9ljTf2jtZ0PQfhL4as/EQ8U2nhGzW+1GW7SzKWzxiQAIgmlIbeT8nQ5+V5jwjVxFKMKcYRkuqb/8AkRR46wqqOfLP5pf5nTeJfhNqWmXLIFkWNPlBHp60eC9f1bwJrUbZee3UbCuOB9a9f/aO/wCCF/xw/Z7/AGdfHnjzSf2xPHHijVPA/hzUdestIu/CFl5WqzWttJOls7NM21ZGQJkg43ZwcV84fslj4mf8FdPH3h3wD8ItU0vwDBb+EdM8R/EfxtNY/bP+EdkvEDR2djblgslxIVkwXIARWIZWT5vm8ZwXmUatOlTcXzX1Tdlbq7rb0uehh+NMDVpTq1E0o20sru/Ra7+tjqP2kvFNjrPhaWe1Y/apGEUkJGPLUjJP518y6jpjWV18mPmwv4V+l2rf8GzXwk1nxRceHl/ap/aLk+Ii6cNWNjceMdOn8uNmMS3bad9lD/ZzIGUfMFyCofIr4lk/4JBfG+P/AIKieH/2X/GnxUj0PR9X8O3/AIn0P4gaLoUcs/iC1gKqsc1u8gWGaNtyuqN0ZD84YMfdo8G4ymknOMu+6t+B5kuNsHUbk4SXbZ3/ABPJLc7XZF+X+HPrV/SbtmvWbLYyBwetfeX/ABCb+I9+7/hrnxnuPOf+EPtv/kmvm/8A4KHf8EVvit/wTsf4R/8ACAfGLVPjJ4p+K3jaDwXY6DrPh+Gxs1kntp5BPJLHK7qkZiDMRtAQMxICkHplwnirX5ov7/8AIzjxlg20nGS87L/M8tTWmhlYqjZzyN1NsPEDSatG0zyOyt8pLdq+9PCv/Brt4H0nwZot18b/ANpz4tReMNauYbHPhjW7Hw5pEl7NnbZ2sU1vK8rFgVTkO4XOxSSo+K/+Czn/AATF+Kv/AARq+Gy+NfDfja4+KXwu1u4/siDUdXtlTXPCl7IrGEzlB5dxEwR8SFQBJtUquV3lbhXFKn7kk321Q6PGODcnGUZJd9H+Byfxf+A2l/Fq1s7qaZ9P1CGMxrdogkLggcSDjcByR9a7b4f/AA0j8I/CmHQftVpdx2vNveR24hlaQHOSM9/T3r6x+Hn/AAbE+M/Hfw50HWD+1542t11jT7e+8keELU+UZYlfaD9o7Zx+Fcd+1d/wQg+P37DvwQ8QfEjwH8aLX43Wvg+yl1XVPCmveGl0+7vrOJfMnNrPDK5adY0ZkjI+bkDc21G76OTZhTpeylOLXRJv9Uc1PirAud3GS87L8dT558Xa75q2bS7d8Jj80H0yBzXvmkwPY+EYRIdzSICT67un6V8I/E34y3PjT4baXq3hzUJNFsfEmpaSsmpeQs82mWd3cLG8qxsdhkVmUYJxnPQ4I++/+CgH/BGj4sfsCfsa+O/jFZftXeLPGU3w709dUj0TUPCdpHa6gqyxoY5GEzELtYnIBPHGOtYZblk61GdSDs9VZ6ao6szzyhhakaUk2rXurbP5nnnx1shefDK6CjODIefpivJfhJfrpHw7eQt+8b5Aw5zgd+1fTH7DP/BEL4rf8FBv2MvA3xa179qLxR4Nl+JOnHWH8P6f4UtprPT4pZH8uONzMrFTEEPIzzznqfnn/gl5/wAEsviN/wAFGfjJ+0D8OtT+N2tfD+z/AGefEI8KC9sPDcNw/iCU3V/FJJMGlXY6i0UlVJAEg6HlssRwvi5vSUdV57/ccseLcKlbll9y/wAyj4b097mdtQ+ZlmlOQRgBR/jUVz/xOPFiuD+7hVuf7npX0b4L/wCDfnxd4k/bI8cfBm3/AGsPGMcPgnwjoniOS/Xwna+ZLJqN1qUJtyvn8CNLCNwdxz55GBty3jHxk/4JRePPgn/wWA+D/wCyfb/tEeIr7T/i54bu/EU/iZ/DVsl3prW0GpyiJIvMO5WNgoJ3r/rDwcc8n+puLW04/e/8h/63YV/FGX4f5nP3eoqrqz7gGJJGOhI4rlNcvHmKyKzL5IJB9Wr2f/gqb/wSY8Xf8EnPhx8N/Hr/AB7174n2/i/4gad4MutI1Lw7BZRLDdQXczTB1ldty/ZgAAB9/OeMGL/glf8A8EafFP8AwVk/Z58QfE64/aA8QfDxbXxdqOgRaLYeHILy3ijtvKKsHaZDkiTnI7dTRDhXEKr7Nyjtfr6djsjxbhI0vbcst7dO1+58+6lcJFJuXc245PHJz1qvFOq7g0cnzHI3Him/Ez4Sat+zJ+1j8X/hJqXiq68bL8M9bg0+31m5sks57xJbZJTujRmAwxwOST69APUP+CbP/BOLXP8AgrB+0P8AFHwrD8WdW+F9j8NdN0m8gNhosWoNqDXgnL+YXkQrt8oAYyCD2xzjTyerPFSwaavHr06eXmelV4goU8FHGtPllolpfr526Hk6s2oanErISd2OP4T7V9HfCHw4Lbw6twwxtkYqf71fSsX/AAaP61BP5i/taeMVkBzn/hD7br/4E1w13/wQw+I+h/t3aB8B4f2sPGX2DVPh/qPjkaqPClossD2uo2NkLYJ53KuLxnJ3DBjHBzkd2I4RxE48sZr53/yPFrcaYaStGEvw/wAzz3XL1ZJ9m0MrHLGuf1e7C7+u5jggDt2r67f/AINc/HUjZb9sjx03/cn2v/yRXzF/wTI/4I//ABB/4KV+Bvilrt/+0x4o8Jv8NfiRqvw9iitPC9rMuoR2EVq63bfvU2PJ9oOV+bG0fMa8/wD1Ixt/jj+P+RhT4swkVrCX4f5nA6jc7T6N0GfQ9f6ViXLo0rZ+6v3SR1rz79tnwP42/Yn/AGoviz8Cj8RLzxdc+Dte8LaRY+KrrS4re7WPV7OK5lbyVZlzH5m1csc4JyMjH2V+3z/wb4+MP2If2NviL8W7X9qPxZ4juPh/o0urxaZc+FLWOK9ZCMRs/nNgHPXafpRQ4RxcnKPNH3Xbd66J9vM7XxXhKShJxk+ZX2Xdrv5HzVqD4ljU7fLUZGBVGV1Ev4ZzWBf+JtR1X4WPqmnJB/bN1o5vbWN8mIXLWxdFx127yB64r6Q/Zi/4Ib+Iv2sv+CZmj/tDeFv2mvF11f6z4PudeXQP+EStmj/tK2jlE9gH87lRdQyQh9gyADtGcVz5ZkdbGczptLl3vf8ARM9nNeIKOA5Paxb5trW6W7tdz4S/aSuhf+NVt1lZls4FTB9Dk15rYO32zLfwjP4V99/8ElP+CEviH/gsb+y3d/GzxJ8ZNS+HL6hr1zpdlpuneH472GeC2jhUz7mmQqTM067cNgRg7ucA/wCCUf8Awbw6t/wUU1rxl4t174o69onwL0HxLqOgeHdV07T4rbXvG0VrO8Jul3GSK1iBUDdiUlxImBt3195hctnToxpux8zieKsJOblGL+5a/ifEdmqzuy7FGeST3roj8e/GngLwfotnpmuSW9n4akaTTsL/AMem9gzAD3Ir9Zfin/waS/DbxX8N9UuvgH+0J4/k8W6TeT2Tf8JVqllr2jtdQMUls5xa28TwSLINrn52jIIMZNfn9/wTB/4JU+Jv+Cn37VvxQ+D/AIy8Zan8Hdd+EtgV1m1tNJj1AvfJeNbTRHdKnygrlSrMCD1PUksqcnyVLOLHHifBOPteVqUdlo7nd/Cz/gtBZ2OhW1t4k8Hf2rfRRgS3VpdBPNIGN2CvU96xvjl/wVu1Rvss2h+AY7ezkUgTXU/mqvBI4C8nj+dep/Ez/g2At/hd+358JfgpD8fPEFxb/Ezw/rutyaqfDEKSaedO+zbY1j+0EOJPtBySw27Bwc8cp/wVm/4IxX3/AASJ8CfDfXY/jFqvxLs/GviX/hH5tM1Hw/FZRWyfZpZvNV1mc7gUAAwPvHnsfDqcD5XBusqSvu9X+Wx1Yfjic2qMU1eyT006Hxj8Tf27fG3xIaSWRrO1aY9I/wCEfQivJdc8d6pr6M19cXEkhbOVfaMV9lf8Ezf+CVln/wAFa/2w/GXgE+Orr4c2fhXwtFr6XNlpMd+107XMcRRlaRNoAkzkE9K7j9sf/g3ltP2U/wDgox+zv8Cbf4ya1rVr8c5LtLjWJPD8UMmkeTjGyLz2Em7POWXHvXtYHKcLCnGVGmkedmHE9ZVXSqSb5dOn+Z8V/BP45XfgjVYLe4k+0ae7YMb8eX7g19YeGPFNj4l0WOa1kUxyxghs8jgH86+4T/wZRaOxGf2lPEnHT/ij4f8A5Kr86P2tfgRN/wAEr/8AgoB4t+BsnjG68baL4ctbC5i1S7sBZysbm1jmK+WsjgKu/HU5xnjpXiZ/w9zwliKfS2h63DvFydaOFqJ2lovU6TW5WYt1dQep7Vh3LrAQ275VbqR6iuntlt9S0hbj7RE6Om7cnQ+4ryb4kfEeO2lmt7FVkZOd7DKj8iK+IwWGnOo1Zq3dH6HisZClT5mYfxouYtR0uS0dgzSjAGfYjNeQ2ehR2luscjfMv8q6q7lk1S7aaaSRmwenO3n+VU7iLD/u23Lj+7X6JgYyw1NQR+W5xi1iKyqL0O5n0912srfL1x61St9Sjsn/AHjONzFSR1Wt2RdyHlVHUEc5rA1eySeaSRT/AKsfvPVT9K+0lJXPm6cUipr2nNcxtJDJvXruI+YZrl9eg/tXSLrT7rc1vcrskC/KfUEe4IBroZrrZArrIe+QR1rPvZY7mPExjeTH8P8AEaynWS3NuW6P2V/4NP8A9r/4tfH/APac+L3hr4gfFDxt490Xw74V06XTLXXNTkuo7FmnKkxqxIU7QFyOoFZP/B2t+2X8Xv2eP2nfh34b+H/xO8aeB9B1rwJqF3qNjo+pyWtvfus8q/vEU4YlRtyecVyP/BnRGI/22Pj0ArL/AMUlpnDdR/pBrF/4PNCo/bR+FO7/AKJzqeOM8/aJai6tc8OUF7bl8z9q/wDgk7/yiy/Zp/7JV4X/APTRa1zf/BFn9lbxh+xL/wAEx/hZ8L/H1rY2fi7wpa3sWoQ2l0t1Chl1C5nTbIvDfu5UzjocjtXSf8Enf+UWX7NP/ZKvC/8A6aLWs3/gkP8Ati+Jv2/f+CdPw1+L3jCw0LS/EnjK2u5r220aGWGxiaG+uLdfLWWSRwCsKk7nbkntgUHOfBn/AAbY/wDKTb/gpV/2Uu2/9OfiOsH/AIOVvA37ax+P83jD4Fal8SNP+B3h34ZG68VyaF4qt9MsYZ4LjUprySSCSZXkYWfk5KRksAigkjbW9/wbY/8AKTb/AIKVf9lLtv8A05+I65j/AIOcP+Cz/wAUP2OvjLqX7OnhjR/hrN4L+KXwpkl1TUNdt7w6jbnUJ9S0+YQSRXCRjEUSMgaJsNuJLDCgKim3ZH4f/DNrUa78NBZiSO1bxLpBiRzlsfaUOT7881/Wz/wWE+CHij9pP/gmT8Z/AvgrR5PEHivxN4dks9M06OWOJrqYuhChpGVB0JyzDpX8knw101dM8T/DeNLiO6jj8R6OiyJ918XCcg+hr+ur/gq3+0R4m/ZM/wCCdPxc+JHgy4tbXxR4P0CTUNNlubcXEKSq6AFo24YYJ4NY0djszCPLUSfZHmn7fXxG0X9lX/giX4x0X4weKNHt9em+EN54buFvtTXzvEGqNo5tnggZyHnklncKCvJLgnHJr5+/4M9/hk3gT/gkOurSWzQSeMfGeqaoHYf65Y1gsw30BtWH4V9XfHL4R+E/+Clv/BLuG4+I3hPw/qkvjb4errcSSWqzHRb2601ZhNaSSAtFJHIwKODuGwZJri/+CFXwYvvhZ/wRA+Ceg6fOlvqmseDW1q3nmGFSXUnmvo2bbzhftK8jnCjvWxwmF+1V40tf+Ck3/Bvh8UPFFrDNqUfjH4eaxrdhFGCzzzWnn3FuqBcE/vLaMAd+ARyRXjX/AASq8SXX/BU//g2QvPh/50V14qt/BusfDk7h8sV1axSR6eTyScQNZMT3bdX15/wTJ/YZ1z9jX/gmt4T+BPjjWtH8T33h+w1DSri+02ORLa5t7i5uJEUCQBsiKZVOR1U44r8xv+DM7xPq3gPxb+018J7yZprLwzqOnXqxbBH9ku1kvrKfKgctIltbEn1j7kk0Ae1f8HMHxRtf2HP+CGvhn4N+HPLhuvFy6R4EsrZMb4dNsLdZ53VWz8gjtIoj3H2hee9fZf8AwRQ/5RHfs5f9iBpP/pMlfkL/AMHenxL1Lxd+3b4F8CzM39h+C/hXf+KLaPccPd31zdWkjFenyx2ceD6k9O/69f8ABFD/AJRHfs5f9iBpP/pMlRGd5OPY6KlBxpRqv7V/wsfhRrVz+2J+yn+3v+zn4j/bC1r4hWPwrT4uWV7p0nibxZa6lp0EkcrATCKKaQxGOGZjvbChS3Tmv3N/4LAfsY+Lf22P2X9E0rwLPpv/AAlngXxjpHjjTrK/uWtINYfT5TIbM3Co/kNIrELIUZVYLuABLD+ev9tn/gpx8YP+C+Xxj+E/wS8XWvwg8KxyePjpOkXOk2t+txBLcObUSXSSXE26IDDfIAScY9K/VT4beNf2lv8Ag3v/AGcfDt78ffiX4T+O3wXh1zT/AAzGsEF3H4m8ORXL+WkkFxINtzBCqsfImy5G1UljVQhoxlFq1z5J/wCC3P8AwXO+Kf7QfwI8cfsp/EX9lXWPgr4v8YNp8kWo6n4yS+jhS01G2vDNABZRx3UbfZmQPDMV5JBbaVPJ/sufGWH4p/8ABVL9jiKGTctn4tvXYZyQzWIB/lX6kf8ABzN+zP4c+PP/AASV+IniO+0+xbxT8MbeHxL4c1doQ1zpkkdxCZ1jfghZoA8bLnaSUYglFx+G/wDwSL8TyeI/+CuP7LTSMrL/AMJNNIoC427rJ+K8jG4NVcbQry+xzW+asz6PLa9OOVYun9p8n/pWn6/ef0Bf8F1fBP7QXj/9h+PT/wBmqTxZH8Rv+ElsJXPh3WYdJvTYKJfPAnldFCn5ARk5OOCAa+P/APg2H+F3xQtP2pP2svFPxpTxhN8RLG80Dwtf3HiXV4tX1BZIbaaWSB7mL5JNkb2uNvG1kHavr7/gux/wUQ8b/wDBMX9htfiV8P8ASfCus+IZPElhoy2/iCCeaz8u483c22GaJ9w2DB34GTwa84/4Nrvi34i/al/ZI+Jvxt8XWGhaf4l+MPxM1HWrqHR4ZY7KNYLOxsAsQlkkfbutJG+Zycu3QYFev1PnNeXyPqX4DfGnTf2vbH446CzC607wr4y1DwHcrnKfutPszMgI5+9cOD3Dbh2r8w/+DNj4az/DnwN+01Z39s0OqaX40s9AufOBE6fYoZ0WJ88gJvYAdsmv0K/4Js/sT+Mv2NfEHx6ufFfiTQ/EFv8AFj4lal4701dPjlRtPjuwimGXzBy4EScrkda8I/4IjfDQfBj9tH9vfw1hlb/hb511FIACxajbm9jUAdgs2B7Ae9Mk841/9orwH+zf/wAHUvjrXPiR468I+AtDn+AEGnW2oeJNat9KtJJ21aykWBJZ3RDIVSVwgOSEc4wDjwH/AIONv26/D3xW/aQ/Zn1P9nX4+aHN4g0jTPGkWqaz8O/FNrfXmmQtbabNFHM9tI3lpK1u4AfG7a+MkGt/9vL/AIJmeCf+CsP/AAcieNPhj8QNb8XaFoGl/Bix8TRzeHZ7aC6kuYL+G2RWaeCZfL2XkpICgkhecAg/Mv8AwVI/4I7fDv8A4Iz/AB1+DWnfDHxH46163+Lmk+LYtcXxNcWd15SafY20sHkmC2hKZe4fcSWztUDGDnjx9SdPDVJw3SbX3bnZl9OFTE04VNm0n9+x+0//AAQz+K/ib44/8Em/gn4s8Y69qnibxNrWiyTX+qajcNcXV44up1DO7csQqqMnsBX4+/8ABLX9pz4sftGf8F7/AAFpXjz4meOPGvh3Q/HXjqTTNF1bU5Lix0lrSwvIIZIkY4BEd1Ig/ujgYr9Yv+Dd/wD5Qtfs/wD/AGAJf/Sy4r8aP+CJ9x9j/wCDgTwp91vtPjj4jw4J+7i2ds/pW1WTUoJdX+jf6EUIKUKjfSN1/wCBRX5M/W3/AILujOp/sb+37R/hg/8AkC/qv/wdEWEN/wD8ERvjD50ayeQ2kyx7hnaw1S0wR78mrP8AwXc/5Cf7HP8A2cf4Y/8ARF/TP+Dn44/4Ii/Gb/d0r/062lbHMfQ/j7wVqXxK/wCCZuteHNHsW1TV/EHwxn02xswyKbuebSmjjiBchRuZguWIHPJArmP2TNEvv2PP+CRHgXT/AIvT2+i33w9+GltB4oa/vkkjsTb2AEySTbih2BSuQxXjgkYNdf4m8fal8Kf+CceoeKNFkih1jw38NpNVsJJYxIiTwaWZYyynhgGUEg9eleR+FPhr4a/4LIf8EdvA958afDWh6zefETwJa6zcvDbCM6XqEtoG+1WbNuaCRZCWUqTgZU7lJBAP54fhx8JppP8AgkRrmoXDyRaouhi/tnH341t9RN5Gyn/rmFH0Nf0Sf8FDdet/2jP+CEvxU8QQ+XdW/if4OXevwsh3K4bSjdowI6jgEGvwj/Zr8WyfF3/gm1Z2t40d1eal4a1DTJl4LfuzcW6Fh/tLGnPev25/4Jn6bD+2j/wb2fDnwvukjj8VfCN/BLMCFZfLspdLYg9OsZI/CvluG8RUnUxNKpvGbf3t/wCR9HxBTSjQnHZwSXokv8z6R/YV+GknwZ/Yo+EXhOaEQT+G/BukadNGOiSRWcSOP++ga+af+CMfwSj+FPxq/bYv1jeNte+PmrT/ADg5dZLOyvcg/wB3dfPivVP2pf2m0+Dv7d/7LHwziu1sYfiZfeIy0AGFnj0/SGdU9OJJ4jj2HpXrfwV+FEPwy174g3kMPkt4w8USa7Lx/rHaztLfd+Ith+VfUnzh8X/sB/Eib4hf8F7/ANuuFplmtPDeleB9HtAAP3apYXEki+/76WY/jjtXkH7af/K3j+x//wBk31f/ANIvEdYX/BvP8RI/it/wWA/4KI67C5khuvFtpHEx7pFfarEuPbCDHtW7+2n/AMreP7H/AP2TfV//AEi8R0Abf/B2s4T9ir4FseAvxz0Ak+n+garWl/waWv5n/BMnxK3974ma6f0tqw/+DvLUrfRv2D/gveXc0dta2vxs0OaaaQ4WJF07VizE+gAJrX/4NH7qO+/4Jea/NDIssM3xI1t0dfuupW2II9iK5VF/WG/7q/NnY5L6ql15n+SPzE/4KBtt/wCCvP7VQzjd4rsh16/6AleH+O/iT8Qv2XdI8YePPhf8TPHPw31rUrC3i1UaBqbWkeqrAxSESbcHKCR8YPGT6kn1j/gpB450fw1/wWP/AGoLK+1Wxsb6/wDFVn9minnEbT4sYwQoPU5IH415j+0P4HvvEn7KvjnVUXZZ6bp4kkmJ4ZvOjAQeuc/pXyWI9rTzZyp3V2vmtLn32DjRq5IoVUnaMn6PW3zP6cfib451nS/+CaXiDxLb6pew+ILf4ZXOpxaikpFxHdLpTSCYP13hxuz681+O3/Bs/wDGz4kfG7/gqhY6t8SPiV4y+JF9qH7P15qlvL4gvmu303zvEGnI8MRYkhD5Ct6kn2r9dPi5/wAonPE//ZJLr/0zvX4yf8Gp8vmf8FL9D/2f2bph/wCXHaV9fUqNVIR73/I/PaUE6c5Pol+aPvb/AIOFvhX+198Stc+CjfsryfET7LY/24PF0fhTxVa6C8m8af8AYfNe4kVXwy3ODtbaN/3d2Tw3/Bndr9z4q/4J5/FzVLy41C7vNS+M2sXU89/MJruaR9N0lmeWQAB5CSSzAAFiTXf/APBwN/wWE+J3/BK7xR8EdN+HNh8LZ1+Jg17+0rrxtFeG2s/sC2DRbHt54tm77VIDuD5Pl428584/4M1rc2n/AATc+KURuLO8Mfxg1ZDPaMWt58aXpA3xk8lD1BPJBFac0ee3W39eRnyy5L9L/wBeZ+dv/Bcg/wDG639oT/sc/hv/AOmi0r9yf+C8n/KHb9ob/sT7n+a1+FH/AAXU1+xsv+C5nx20+a8t4r6+8YfDyS2tmbElwsekWW8qO4Xcuf8AeFfuv/wXlOP+CO37Q3/Yn3P81rDDJqpVv/N/7bE6cVJOnSt/L/7dI/Az4dRFfh74fbrt0y1bn/rilfqD/wAGpfxijm+Cfxt+B9587fDbxb/a+nROuF/srV42liRcn5tssFxuxwPMGetflH8F/H+ieNvAOlQ6PrOn6jNY6dbQ3SW8wke2YRKMMvUcgjn0NfXf/BCrxtd/C/8A4LW+H7GwYNZ/FDwFqemanCRgBrF0uoZh6t8uz6Ma+G4ZrOlj50JXTlfT01/K5+h8WYeNXLIV4NPla1XZ6P8AGx9v+KvD83/BDH/g3I8W6PHdLZ+IvBegatp+nXQKl31LUb+4jtZ8N8rsr3UUhGMEIcDHFeo/8G5GhReHf+CKHwCt4YPs6yaNdXRXHVptQupWb/gTOW/4FXx//wAHmfxh1LRv2ZPgt8ObYNHpvjXxXdavfzJKVZxp1qPLgK4wyM94HOTw0CcHt9mf8G8l/wD2j/wRd/Z/k2qu3w/JFwc/cu7hP/Za/Q762PzJ02oKfdtfdb/M5/8A4IDf8kN+PX/ZfPGv/pcteD/8EzNPh0z/AIObv25o7eNIo20XSJSqrgF3hsnc/UsxJ9STXvH/AAQG/wCSG/Hr/svnjX/0uWvA/wDgm/qJT/g6P/bctQqss3hvSpS2ehSHTBj/AMfP5UyD6K/af/5Tx/sq/wDYh+Nf5afXzH/wd7rv+AH7Pwxuz8Rug7/6BcV9OftP/wDKeP8AZV/7EPxr/LT6+Z/+Duz/AJIT+z3ndj/hY/OO3+gXFYYrSjN+T/I6cH/vEP8AEvzPm/8A4NToGt/+CpXxgVhj/i29vxjoPt9vX0//AMFfv+VhT/gn/wD9d9T/AJrXzJ/wauW7W/8AwVW+Mm6TzN/w4t2HOcD7fbcV9N/8Ffv+VhT/AIJ//wDXfU/5rWWX/wC7Qv2Rtmjvi6jXdn09/wAF2vBH7QnxA/YSk0/9mWbxRD8TT4gsZFfQdWi0u7+xr5nnfvpJI12/cyu7J44IzX8sP7VDfFnSP2o/F1l8drzxJqHxe0meCw19tb1JNRvI9kKeUhnRmRwIygG1iAMCv6o/+C5v/BQbxx/wTQ/YeHxI+HuleFdY8RyeJNP0VLfxDBPNZeXcFwxKwyxPuG0YO/AyeDX8sP7Z/wAbfF37T/7XPjr4keOLPw9pfi7xnfJeX9poizJYQMkSQ/uhK7vgiMEhnPJPQcDatKDapvd9C8rjNVVVS0XXt2Nb4VfGy/0qwbQ7rfNCy4hlB+71yP5VNqdw13uBXqSeOPzrhfhIGn15lVXYRru6btvX+f8ASu/lti77s53Ejj6V8xXpU4VXY+0pYqtVoKM3cxtptQWU/e+Umo5Yokb5t2WGeK1GtBPtUfxH8qo3xC3G1UZgoxkVrTV2ctrNtneaP4I8Qa7p6XFvYRRw5DRyTSbNw+n9BRdfC7ULK4uLi4mtwzkFkiBYn9K9a+F1s1r4Ot4rj5mjQMA304FVfFJVt2IWX6Vh/bWInUaurFRwNNas8I1Xw5HpxYqtxcDOcN8q+/FYkqLE5AUDHYHHNdx41tVtlaRpMZbOBXA391CLlmWMgMeuelerRrTqbhOnFaQPvz/g2m/bu+Ef7Bv7W/xi1j4veN9N8C6f4h8Nafa6dNfRzSC8kSdmdV8tG6D1xWP/AMHO/wC3D8J/29v2qfh9rXwh8aab460zQ/Amo2N9PYwzKLadppGVCJEU5IYEYz1r4Lult7mRvMWGTB48yMNj8TVmxso7cbo7aKNdvOFCK/fJxXoRqPltY8X+zeas6rl1vsf0a/8ABOf/AILwfsjfB/8A4J8fAfwj4l+N/hjSfEfhf4d+H9I1WxltrtnsruDTbeKaJisJXckiMpwSMjrXlf8AwQh/4LT/ALLf7Lf/AASe+EHgPx98YvDvhrxd4ftL6PUdNuLe7aW1aTUruVAxSJl5jkRuCeGr8IzZwXG3bY2casMhBbqfx6ZP1pDpcM07M1raMernyx8w6DJxVfWEc8clu7Kf4f8ABP1k/wCCF/8AwVP/AGff2XP29v27vFXj74oaH4b8O/FDx5BqnhW+uILlo9btV1DXJDLGFjLBdlzAfmCn94OM5x92/Fr/AIK2f8E1Pjz4jj1rxv4w+CHjLWoLVbKK/wBd8InUbmOBWd1iEk1ozCMPJIwUHALscZY5/m3XS0utvnW9u3ljaoaNSU9AOOlTJpNntYNY2eVAz+5TnP4VMsUl0NVkEm9J/h/wTmPhdqNv4asfA+qXjraaXpviWzvbiZo22wW63xcyYAztC88Dpiv6fP2hP+C1H7AH7UnwY8R/D3xz8bPC2seEvFVobHVLJBqdqbmEkEr5sMayLkgcqwNfzbJarJEySKr44JI+UrjpipItCsYsN9hs+uGzboRj8q5I5hGLtbc68Rkcqii+a1klt2+Z/QF+2p/wcb/sjfB39ijxZ4f+Fvjm08Z+IP8AhF7nRPDHh3w9pN1shf7K0MG9pI0jit4htZyWyscbbVdtqkg/4Lk/sofBD/gmcngHwX8f/DcPjDwh8MRoGhfYra8SVL+20ryLfyiYAoYSom3PAOK/Ef8AZu0q1j+NvhZYbS1jjk1CNZYxEqrINyjaQOCDyMHtXvfhsf8ACI61qENhpfh+Ly7mTZ/xLLfMZDEDYduVxgHOetfP5lxh9Uq+zVLm0/mt+jP0jg/wTrZ/QlVo4pQlHdOF9HbrzI+7f+CGv/Bfr4d+Cf2HhYftUfHpoPitH4gvWki8SQ3Ul/HZMsJgyUhI2kFivPQ14f8A8EdP+CjX7OH7HH/BVP8AbU8WeI/ix4d0vwH8SNei1PwpqrW119n1WKW8vbl1jCxFv3X2hUO4DkcZFfInxQSDxndatfaxbW+o3y2rbp7iJJHbb0+YjNePaN4ZsbyRYZLW3dYId8atEpVTz0GOlduW8SfWqblKnytb63/Q5OMfB2pkNaNKWKU+a9vcts+vvM+oP+Dg39r34c/t4f8ABRT/AISz4P8Aiuy8deHbX4Opoc97YQTKiXov9RlMGJEU79ksbcDHzjnOQP0y/wCCVn/Bc79kz4Ef8E2/gf4N8WfGzwzovibwz4M03T9TsJba8aSzuI4FV42KwkZVgQcEjjgmvxD+yW+k3atZwwwrJhysUYQZx6CqOr6RDdSyMNN00tyd5t0ZnJ6knFdVHNk6j93f9D5vEcJOWHp01V1jfp3d+5+mX/BYv/goh+xdp/wE8GeJ/wBmFPg9qXxg8JfEbRPEtrD4b8KLpuoXkdtM80imZbVG2OwUONxzu6Gvr34m/wDBQr9hP/gtl+yJp/h3x98ZvD/gfSf7U0/W7zQvEXiO18LazYXVrKJPs0n2ltrqfmjdoGcFXYpIrbXX8AvFWj2umPaSw21nGyxKoeKBUbPOeQK53VdB0vWWkkvtL027lyNsk9ursMe5Ga9B4y3Q8afC8krKpr6f8E/b7/g4M/4LefBT4gfsTeMPgT8H/GWj/Ezx18R4ItLlufDkyX+k6FZCeJ7iae6Q+Ud0SuiLGzEMwJwAA35K/wDBPP4w+Ev2af8AgpT+z54y8Ya1ZaB4N8J6/JLqOqTK7RWkf2R0UvsDNycDgH+deUxQW+k2i2+n29nbI3/LO3jWMHjpjAqjqNkt3bgXEe6PIVQybufTuDUyqOU4ztsdVHJlTw86HNrK13001P2I/wCDlT/grj+zr+2n/wAE34/Bnwp+KWh+NPFv/CXaXfx6ZZW90szxR+dvYb4lHG5e+ea9K/4IV/8ABX79k/8AYy/4JXfCf4f+MfjN4V8P+LtNs7q61jT3trtntbi4vJ5yrlYSu4LIoOCeQeTX4U/2Tb2Cho7eJWVsKywbW9xwKbN4fhmdi1vZhsFj5kagn8SK2+sdbHDHhuT932n4f8E/ZP8A4Iof8F9fDvhT4k/tBS/tMfH28XQ9S8QQXHw8Ovx3MkU2m+ffq72uyEkRkCAc4+6BjINdH8Nf+C5fwC/Z7/4LPfGbxtY+KJvE3wT+NHhnw02q+M9I0u7uLHwtrFiLm0iiux5YdEljc5dVY7jEMY3FPnTQ9A0nWvBPg20vNJ0vUIbfQrUQPcW0cuxSucLuBwPau/0bw1p+m/C+4WxsdNt9PuEktbyyjt0jilbPVkA2txjqO1fE1+OfZycPY6p2+L/gHof6m9fa6f4f+CfoMv7UX7DHg/8AbL1r9qBf2kfhM3jjUPAyeDrqKHx9ps8J05LpbsslmjmdrhnSNeNx2xqFQEsW/MP/AIKVftz2/wDwVn/a6h8ceCtN1OH4S/C3wzqeh+E72/s3t7nxRf3q4uryGJvmW32RRIm4BjjJAJZE4W+/Zz+HdrqP9oW/gXwjFfLJ5qzLpFvvB9fu9a7zw/pYuyqq3l/LtRdo+XHTGOgrjzTjH6xQdChTcb6Nt9OtvXv+B05fwv8AV6yrVp81tUkuvn6H1t/wRU/4LY/ssfsz/wDBLb4N+A/HXxk8O+HPF3hvR5LbU9Nuba7MtnKbqdtjFYSudrA8E9a/KH9nL9oK9/Zv/al0n9pLwfp8niq18F/FjxBrcNrbqyvr2iX0jW915G4D52gL7Cw+VgSQcYr6E8dfCfSZdRW6l0LSbmb5jNI9lEzSE/xEkZJ+tcP4o02Oyh8uNVhiiXakaoFVAOgAHA/Cuipxh9Y5VSp8ri097901st7m2X8Iwg5qrUupRa2t1Tvu9rH7EeMP+Cg/7Dv/AAUr8D/CzxNr3x+8B+Hx8PfFmn+PNK07WfFVn4d1C11K1jlVIbq3u2V2RfPcOq8FlG1yOT8K/wDBzB/wWi8A/tbfsoax8DPgLqR+IsclzBq3jLxHpSmTR9OsbV/NW3jn4WaV5RE5Me5FSNuSSdnwhrnwy8L+LdUN1qfhvRb64bhpLixid2PqSRXY+DbKy0LSY7WxtLWztVYqsNvEscYz1+UADmvSqcWe5enT183ocseCHGo1Uq+75LX8/wDM/Wz4r/8ABdz9kfXP+CdviXwdZ/HDwvceJLz4c3Wjw2S215vku20xoliBMOMmQheuM1gf8Ezf+C4f7J/wV/4Jg/BzwL4q+NfhnRfFXh/wLY6XqWnzW14ZLO5S2CPExWEjKtkHBI44zX5reHfD2hpNGw0PRxJnIYWMOVPrnbUPjvwjo+o280jaNpLyTMWaRrKJnLdyTtySazjxlFu3sv8Ayb/gGP8AqZK9va/+S/8ABPkv9lX4jat8L/hJotxblgvlS7reQfJKjTysM+mVbI9Qa/ZP/g3y/wCC0v7O/wCyj/wTE8KfDf4sfFbQ/B/izwhquq2f9n3ltctKLd72WeJ8xxMuCJSBzn5a/Ij4ir9kvbqMbR++YBR2xjFerfsdWXh/WNF1DSdU0vS2vEuFuI7qa2iklcFcfKWBPB/Cqp5ksHCpi+S/O7tJ+b8vM9PMsl+s06WGU7ezVr230S7+R9hf8FWv+CuPw7+Nv/BYD9lX4n/C/wAc2Pif4Y/A2e2v/FOt2dhctBpUWoapFa3wkLIrZ+xqGGAehxk5Ffps3/BxR+xWgP8Axf7wp8vpaXx/9oV+Rdh4RXR9Ilt9PGi/YbgHzIDYpFvJ4+YKPm445Brm7rwJp6JGk/hXRtyzBwYLGFzgf8BBrnhxq3Jp0eunvf8AAPOfBbsrVfXT/gmz/wAGw3/BQr4Z/sPfGX9oHxJ8ffG+l/D+6+J9vo2saa19bXBXUi8uoTTNGERztUzKOf73GcHHsX7U3/BV79njx3/wcp/sz/GfSfijod98L/BfgbUtM1vxAkFyLbTrmW11xI4nBjD7ma5gAwp/1g98fO3iKw0+/wASX2l295s4Q3Vmsmz1wWBwD7VlX8Ghmyazi03SFgkxI8P2WJUYjOCVxgkeuK0p8ZXir0tfX/gDlwX71o1dP8P/AAT9k/iz/wAFt/8Agnv8fPD1vo/jr4ofCvxppNrcrewWWveH5tSt4Z1R0WVY5rZlWQJJIoYDIDsM4Jr55/4JMf8ABY/9kL9lnwT8btD1D4q+DPB+k6t8ZPE2teHLC30+4htjpE8sX2WSGOKDbHEyL8qgDAHQV+YepeCdHub5Vj0XTGaZgFVLKI5JPbAr1H4ffsraTbzW2oeJNH0vy4QGjtXtY2ZwM4DccDpxXoUeJPaK/s9PX/gHPLhCUXZ1f/Jf+CfTP/BeX9uf9iD9rj9g/wCIlr8JdW+FPib45+KtS0Y2V5pnhfy/EGoONTs/NK3bWyyb/IRwSZASgK85wfm//goNJAP2QPiFpWk27eTb6W+yOLBxGk0bs2B6KrMfQA12Ag0XTL3z7PQdFsZosiGS2sIonj7YBVQR/Os691LzWYqqxyvncSc4X2Hr/SvFzbiWEpQ9jvF6rvqtPwPWyzInh6VSm5359NttH5+Z+g/xJ/4Ltfsj6z/wTp1/wba/HDwvN4kuvhvcaPFZC2vN73baW0SxAmHGTIQvXrX5n/8ABAT9rv4c/sF/t1eGfF3xg8U2fgXw3qHwDfRra+v4JTHLePrltOsAEaMdxiRn6cAc9Rm1/wAIV4feUs2haIufm3Pp8TNuH4d+uetUddt7HWpVivtP0+8hjb5BPCsu0/3sMDiipxgp1YT9l8N+vdW7HLT4PlGnKHtfit07O/c/Wj4wf8Fkf+Ccv7Q0mmt4/wDH/wAHfHDaMJRp58QeGJNTNiJdnm+V51q3l7/Kj3bcbvLTOdox8z/8EYP+CvH7Jv7I2hftLaTrPxP8H+CtH8S/HrxL4h8KWMOnzw282iTRWKWk0EcUO2OEiJlVcLgJjAFfC934U0Iy7f7C0VVYED/QIeP/AB2q+oeHNHvk3S6RpM2z91HvsomMajoq/Lwo7DpXV/rrG9vZP/wL/gGceCJv/l7/AOS/8E+6P+Cyf/BSH9g79or9k/xpqvgnxN8Jde+Mmqar4euYNZg8NFdcmW31fTvNf7Y1sJfks4XX7+fLTaOMCvsPxt/wXv8A2EfiP4V1DQfEXxo+H+v6HqkRt73TtR0q6u7S8jPVJIntyjqfRgQa/ERfCGjxSl49J0lWwRlLOJSPX+Gq7eCtFjdj/YmkM3YLYxcD3+Wn/rpH/n0//Av+AargWTV/bL/wH/gndf8ABQL4qfAv41f8FS7vXP2c/wDhDW+HNv8ADeys7pvC2jrpdguof2hOzq8axRAymMod20kqAM/LgXv+Cf8A+034E/ZC/wCCsvwl+IHxK8RWnhHwbY6Dr9pPqt3HI8CSyW6pGn7tWOSx9O9cFpmmWulwOtnZ2tumCxjhiWNT3zhQBmvIP2hr6LUfE9nYzrG8NumWidQy7iMg4NYZbjvrma/WuW2m1/Kx6eKyf6vlLwXPfre3nfa59nf8HPP/AAUc+CP7fdz+z7a/B/4g6T46m8L6jrU2rJYwzobOOaG0EbN5kajDeW44z92vYv8Ag22/4LffCf8AZ4/Zc039nP40eJtP+HeqeCry7bwzrusyGDStasLm4lutj3LfJDNFJNIuJCiFDGFYsGA/HPW9Jt9P1JY4YY49i5JjjC7gfpS2ugw6zp91HcQwTx7QNsqBl/I19ZLGOM22tD5mORqUPq/Pqm2nbulp+B/Sl4d/4KT/ALD/APwSx+CHjO88P/HXwd4stfE/irVvGFxpfh7xJZ+JtWvNR1Cdp5IYIbRiVj3YRDLtVQF3yE5Y/j7/AME9f+Cu13+zh/wV98aftTfEzQNUTwj8ahqGmeI7Wxie6uvCVhLPby2c2wYMohW0hR+NwjLkKXwh+NtH8JaXpd0slppOm203TfHAqsPxAzXp3w2sWe4hDDd5nAUD7ua4sVnEoJSpr/gns5bwVCpGSrz1a0stvPz9P6X9E13+3L+xL8bvj58PfjtJ+0l8J4fEHgfQ9T0zSIbrxvp+nj7PqP2ZpjPaTss4lUW6hQQhHmSBlY7dv5x/8Fjf25PD/wDwV8+O/hHRfhPLd6x8Ifgmt9q+peKWtngs/EOszRCKK3sy4DSJCm8s+ACWfqPLZ/zR/aS8E+HYPFTOmg6OrxRKJXSzjDM2AcnA561+k/wg8Nw6l8AvD62lvHHay6WiosSBY1GwjAA4HJ6V81xVxZPD4FewhrU016J7/MeUcIxp45+3nzKm07JbvoeWf8EGv22PhX+wZ/wUf+JniL4u+MNO8C6LrXgODTrC6vYppEu5xewsUXy0Y5Cox/CvZv8AgpZ/wVe/Z3+NX/BaP9jT4k+F/inoWseB/h1NqDeJNWiguVh0gSFdnmBogx3YONoPTnFfnT+07bX3gzVr5LK0tZGsbpkYTQJKUBPUBga4nwJ8cWsdIaPUNH0me3dwska26KsnuwC84r3MHnE44SEo076Lrb9GeXmeQqWLnLnsm77f8E/Xn/g4j/4K1fs6ftvfsB6f4F+FPxT0Txp4um8baNeRaZZW10s0kUckm9hviUcbh371+Of7Vfgz7H4iXUohiK6+82O5yevrXrvhf4jeDdTvI5LO2sbG8ZNuI7VI2UnsCBmp/if8PF+JPhKOGNVMqNmNs9fSuTEZzN4mEnDlS877/I3weVKjRnHmvfyseFfs+aI0lne3uPuKB092rrNY/dk7eOMnj2rrPhv8Lrn4f+GWtb+JUklfqD1HP+NZ+t28TXLLH5YC/IAw71yVMV7Wq5I76OH5KEX1ZytlGolY4XbtOCetZd9bxtcsd6rnqM963tStPI01s7f3rZyvVeDXLamfInVfvfKOc16mHlc462i1PqXxt4y0fwDrOo6T/aFjL9luJI0aKQPuAJxgjg+1eZ+JfjPZq0qQedMzYAyNvev1Y8Qf8G0Pw2mLf2f488Zaf12/aYIZQvp0x/SuF8Tf8GzNvlm0v4ssoPCfa9DDA/irE181g8wwFOK5nJteRlUxlR6qP4n5L+KfFU+rzOkkbRrnjB3NWHGGubpd3ln1A/wr9RvEf/BtP48t9w0/4jeD75c5VZ7O4h/TkV5zrn/Bul8eNIbfaX3gnVAvRodQMefwMa/zr3qOfYCO0mjmnUnNdvlc+ALq2SSdn2javBp+nYlDLnbngFQSo+vv7V9keJP+CF/7RWhRt5Pgm3vGb732XUIWLD1GWBxXnPjD/gl/8dfh7C7ah8N/Enlxjl4YRIq4/wB3Oa76OcYWp8NTQ2pxZ4OYZN+4hcKuCSOuOn5ZpbKdpU3H5s9cgc9+a6DX/hlrXg7UGtdW0u6sLpRvME6FHz06H0zVWPRJ9m0K25f7wB6dSK63Vpv4Tpp05Nq5WCK8S7FVWznIq1axPMW3fKG4zjqR0FFnp80KfNHJG3GdyY3YrQtLVXILKy99uPv/AE54PvWdSpF7HTTunqQR2DCRif4CMflVmGwDL97aFbnIznNWY9LVwvytj1Ixmrq6Srfu/L3bwcZ/CuGd76nVTpdGdh+zLp3nfHXwijfNu1KHr3G9c1754e0M6t4/1Daq7VuZ3Ax7mvCfguk2g/EzRbyNfLe1uldCf4CCP/119XfCvwTL/wAI5PdtHJJcXDvlsffLc5/Wvy7jCTjiIyj9/wA2f094MTVLAVpvd2j+T/I+f/G1mDa6xgf8u0g47fNXP/sYfsjeLf28v2x9C+D/AIQ8UaP4L1LWNEvdWbVtR09r5EW3C/uxGGHLZPJz/j6Z8UvBs2n6Nq3nwyIfs7Y+U8rnBrx34Y/Ej4j/ALNPxch+J3wp8ZP4F8beH9Ku7SPUf7ItNUR7aQAvH5VyjxgnbjdtyM19RwfiqXJzVHpfX7v8z5Dx3qVKs6ccG/f5dLPzT36aH6DL/wAGlPx2Rgf+Gi/AeR0z4Rk/+Lrzj46/8G4vxq+C3xO+E3hW7+Onge+m+LPiSfw3a3EXhV4xprxaXe6iZmG/5wy2TR49ZAexr9kf+CL37Q/jL9rD/gl/8IfiJ8QNZPiDxl4o0qa61PUDaQWv2mQXc8YPlQIkS4RFGFQDjPXJr8ff2KP+Clvx8/a9/wCC8Xwl8E/Ev4iL4o8D+G/ih4vj0TSDoGm2Tac9jpWo28TefbwRyyfubllw7EHGTuOCP0n6vQi17q+4/lWOa5hJNqrKyV37z7pd+7Rwv7dn/Bvx8X/2NtK+GNzrHxp8GeIl+JXxA0n4fWyweGnt/wCz5r8Tbbpvn+ZU8k5Xqd1R/wDBQr/g3X+LH/BPD9j/AMZ/GTWPjN4N8V6f4Lit5ptKg8Oy20l6JbqK3CiTf8uDKG+ikV+z3/BYn9nHxx+0f4b/AGeIfA/h248RS+Dfjj4a8U60sNxBD9g0y1F19ouW8103KnmJlU3Od3CnnHJ/8HMH/KEb45f9eem/+nSzrX2MOxh/aWLe9SX3s/MH9kX/AINgvi1+0P8As8fDv4pWnxl+G9va/EDw3pviaDTdR8Ivd/Y0vLWO4WFyXw5QSbScYJBrc+OH/Bv78SPgX8Vfhp4d1j4kfAEXHxg8QSeG9Pu4/hmkcWnXUWnXd8p2Bwp80Whi5BO6Rcd6/Y3/AIJK/wDKK79mr/slnhn/ANNVtX86/wC0L/wUb/bI0pfhf4t/aY1L4x6brHw48W2vjbwtonij4TWnhTS9UvbCYGWKPUY4YZpSbOSXdGYdn7zDZwpO0Yc2iOeWKqvVyf3s9D/b9/4J6+Ov+CWvxI+FPgfxFonwH+LutftAX82heG75PB8umf8ACP30d1YQlpFhmRZVdL3gNnDID90FWk/4KVf8ETfGn/BMT4M6X8RPFnxC+F/i6HW/ENl4YsPDmmeFZtKk1Ke5ZmISWKUeWUhimk3HI+TBBJFftP8Atx/sr6f+3l8SP2Q/HukhNT0PwP8AEG28afa0J2/Yf7MubqCUY7NdQ2PX+9XwB/wctfGj/ha37f8A8GfhLAxk034a+H7rx7qwVt0bXV3I1naRtg/LJGsMkmCM7ZRjqa6cDh/rGIhR7vX06v5LUqnXq8ySk/vPnn4Bfs6/E79tf9s62+Bvwz8ZeHPht/wjXw3j8Wy6lqmjnVWulW8itBbgFvlAEysGAz8pBzkY9M+Lf/BM39p34VftTfCT9n+7+O3w5vrz4wWet6pZ63H4L8s6QNLhhlkjZA4WTzvOAyQSu0+1d1/wRMhWD/gvb4uVf9X/AMKDTZ7j+2LDFfoL+09+zx408df8Fcv2WviJpOgz3vgvwHofjC01/VFniWPTZb21tUtVZGcSN5jRuBsVsY5wOa+aw+U4CrD2nsou7bvZd2etmGaYyOIlCNWSSe12fjV/wVW/Ye/aB/4JH/Bzwv4z8RfFj4f/ABCh8ZeI4vC1vaxeFWsn0+WWCeYXIZXAbaISNrZB3Dg19U2//Bup+1TZTM0P7TXw59AT4DXOPpu4rpf+Dyb/AJMh+C//AGVWy/8ASC+r9Gv+Chni/wAfeAP2Gfixrfwri1Sf4kaV4Xvrnw1HpumDU7x79YWMIitmjkEzl8YQo27pg1t/YuAvd0Y/cjieb45qzqy+9n416p/wSW/aYT9t3T/gFJ8ePh3Jq+qeBbvx+Nd/4QsbY4IL+2sDZ+Xux8zXIk34yNhGcGvH/wBv39hn4tf8E0vjd8IfDfxC+IvhX4kWnxg/tlYX03QTpkmltp0VtITkNh95uVGCOAh9a+hv+CCH7RX7R3x+/wCC1epN+0xJ4+HjDS/gXfGxt/F3gS38IXkFtJr2mbvKghjj8+AypIFmZQWZXXC7SK7r/g6Xtjeftf8A7Fca9Wk8an8rTSzXBmGU4CGDq1KdKMWoyd7Wd0n8z0MrzXG/XKUJVZNOUU1e6abR8nf8E6P+CNvxp/4Ki/s02/xg8N/GHwX4F0nWNUv7CDRrrw015JbLbTtDky7vmLbc/j+A9l8Z/wDBtH+1V8PfD9xqnhv4tfCX4gahaxtIujajpFxo4utvOyKaPcBI3IXzNqA4yQMkfYX/AAakf8odfDH/AGM2u/8ApfJXoX/BIjW/H2rftC/tkx+KbrxNdeGbP4xXsPhj+1XmeCGHyUMsdqZOBCDs+WP5AScDJNejHKcG4cvs4/d+u5ySzzH87l7aX3u33bH8/wD4j+OOuaN8O7qaSGLwXr2i+IY/DXiUarD5/wDwicwuhbXTyRgjzPKY9MjOeemK+rP+Ckn/AASo+PX/AAS9/ZY1H4xeJ/i14J+JHh3RdRs7S/0i08MGwmMVzMsIlWVW4KsyDB4O78D4H+3F4HtfGH7bv7YnhyzW3Fvq3xG1lVww2i5kIdj9RNyfQ1+uPhR9W/4LCf8ABr9BpthI2oeM9c8CJpM28l5p9W0mZY335wd8stnuPH/LXIyMZ8nLsrwTnWoSgm4y3a1s1prvpqexmmZ42MKGKhNrmjrbRXT10210Pzi1/wD4IB/Fa5/YG/4aW8U/GzwT4d0dvA48d3Oinw1LJJaRPZi6W13h/mkIKpnnLHjNWv8Agkt/wQt+NX/BR/8AZqs/HuteL9D+CngLX7gXmj3lvo39peIda8oeWZlDOi29ozb9mX3uVJKlNjt9xf8AB178bbX9lL/gkD4f+Dvh+TyZvH17YeHbeBTiVdL0xEupmHOdoNvao2M/LKQeGr74/Y/0OPwN/wAExfhfptislrFpHww0q3twCVeIR6VEq89cjA565r3vqWHa5XBW7W/Q8F5pjGtaktfP9f8AI/KP9p//AIN6v2iP2TfhLqXi74Z/GS3+OQ8P2sl7feFvEGh/2df3cMalmFjNFJIWn2g7Y2KhugLHCt4r/wAEyf8Agn38dv8Agrv8BNb+KHgr4ueE/hn4fsvEd14eh0e/8Nm/uv3EUEnmvLu+8wnUEDgFTX62/wDBu7M03/BFr9n9nZnb+wJVyxzwLy4AH4AAfhXA/wDBuHoFn4T+AP7Q2l6fbx2un6b+0D4vtLaGMYWGKN7VUUD0CgD8K5ZZLgZVPaulG/orfdtfzLjnOOjD2aqytvvr9+/yPz9+CP8AwSM/aQ+O37U/xs+EVr8dvAWm6h8C7jRbW+1STwiZl1s6lp63yMsZYiPylbYcYyea8e/aw+DfxC/4J5ftg/8ACn/iJ4o8L/ES8vvCkPii21jTNF/s426yXMsHkMmSG/1ZbcOeRX7Ff8E/P+UyP7fn/YT8C/8AqNx1+b//AAcM+G9P8Q/8FyvDjapJcDT9P+FdlczQwZ8y5xqV2Agx7kE57CuXH5Rg1hpclOMX3StbU9PJc0xlTHU4TqSkm7Wu307HnH7BH7KPxg/4Kc/G3xRoXwuvfDXgHwt4DEFv4i8Z6tYfbnt7mX51tbG2GFlm2AsxchVHUqSm/wCxfF3/AAbQfGjRNFnvvC/7XV5ruvxjfDZeI/BsMem3bdSsjxTPJGp6bkViB0rtP+DUbxXpuofs/ftFaSs0S65a/GLUdSntDhZreyubGxW0LL1CnyJ1U4wfLbHQ1a+LP7SfiT/giL+2H+1D8YPiZ8Mfiv8AEH4UfGbVdD1nSPEPguzttTtdBW1sPsk8WoiW4ie0IfyUR2BidQgDhvkHXg8tw0KCiop3Su7bnHmGbYyWJm+dxs2kk2rWZ+c37Ov7Pvx+/bJ/4KD+KP2Y5NT8L/Bz4ifDbQbrV/El9daadXs9RkhubaFPsgJyIJYruGZGb5sEg++v+31+yJ8Yv+CU/wAVvhXpPj/4ieE/iZp/xVTWREunaAdMl046dbwS53BsNvM6jBBwFPqMfQn/AASC/bO8P/8ABQj/AIOXfiZ8YPCfh/xV4b8N+MPg3vsLfxBaxW95MsF1pFs0u2KSRCjSQuFIc5C9jxXQf8HbEvkfHD9kZj0U+M//AEi0+uLGZPgY4So4U1opO/W+vXfRm2EzbHTxlNTm9ZRVtlZtdNtUeH/sC/8ABHz9oj/go1+x/wCDfjNo3xy8B+D9L8dR3NzBo0vhH7Q9gIbua22eZuy+fJ3ZPPzY5xmuV/4Kbf8ABK/4+f8ABLj9mtfiZr3xk8C+OLO61mz8PjTofCrWrK90XCzbw/8ABsztOQc8g9K/Vr/g2i/5QffAf/rx1P8A9PF9X4k/8FmP2uP2zPHviLxh4P8Ajb/wtPT/AINx/E+W28MJrHwxtdI0W7SG8mNiItVFvFJK5tkkdVBbzEQsSwyR2SyfAJWdGP8A4D/X3nHHOMe3dVpf+Bf8H8D7em/4Niv2kpSf+MlPh+w7E+CcEj/vqvnX4sf8Em/jr8Jv+CiXwr/ZpufjJ4Hvta+LGjahr1t4iXwsyppqWcNxI0DRb8OH8g/NjILe2D+9X/BQjxd4+8A/sN/FjWvhZFqk3xI0rwtf3XhqPTdNGpXj6gkLGARWzRyCZy4GEKNuPGDX4P8A/BLL9o39pT9oL/g4W/Z5f9p9vHUPjbS/Deu/YLTxV4Hg8KXUNlJpd/ho4ooYjNE0yTASsnWNgOhAcsowF0nRj/4Cv8hxzjMLNqtL/wACf+f5HvX/ABDA/tJIrFf2kvh6zY4DeDCAfYndXyp+1p+yZ8Y/+Cc/xw8O+C/jNb+GL6y8cQ3EvhnxP4YlmbTNSktwGmtpo5gHhuFQq2CNjbwFLYJH7K/8FiNf+IWifFv9jmP4e3HiKG4vvjpo9vrkelNLtn0gwXJvluFThoBbiRm3/KAueCAa+cf+Ds+3iPwd/ZwnG37ZH8UYY4jn5gjWVxvx7ZVM/hXHmWSYKWGny01FpNppW1S8juyvPsdHFU1Ko5JtJpu+jduux+bZt1MYZcgzLsHPc185/FG8+3+P76QScCbYNwzjHFfROo3MVjot1JP8sduhkdj/AAAZO4ev/wBevnG+0db68kmEm5ZGLAjuCcivluG6cbyqP7z9PzSMnBRiZV5pEOowC4VW+YbSQc06Hw79i8P3U0UhlbeNykYwtXtJsFiuVguvMk3ckx/KMmug1XQ20kR223fFchlBZvlJA/WvscVyctzwMDRk2r79TirFGkkJVVaRT8o7E9q9N+GVnJ/a1irbVd3DqFPQZGa850qNEj27FWQPlgD0PtXqHgezaXxVZF8hVjHPvzXzWOjayWx9jlsWrp9jifirdf2n4hugNrBrySM7h1A46/hXffs1/t5eKP2flh0sx/8ACQ6Cr7fsVwzF0GR9wg9BjH41xr+Fbrx14thsbWJ2upNRkj+YbhjnmqfxT+CPib4b6o0V1pd1JDH0kijLD8vxqsbh8LiaMcNildWWj/Q+eqSxEK1StR79D0f4q/EvQ/jb48uPEGn6dNYWerHMttcndsY9Rn0zXn2tfAKz1CxhudNuFt5JCSyORtBpvwvhd9JuY5I5EaOYEKykMfXivTPD6s+nyY3dcHmuD20cNT9jQ0X3nJX5qsuarv6WPI9E/Z41pdXjuGntUjtznKHG4da9U8NRtY2q27r5hUks4PpWktuiOFYMNq4VjzipHsxHar/FxgY9a4K2MnN6s41TsZ/iLUBLZx7uWK8GvP8AULJjcNt27S3cetdnrtmzjcdyhc1gS2aedtZvmIzXXQaig8jj/E9l5UYh27sc4Nef+IJmt7/awC4QcfnXpXiuN7iZvmMnlrjHoK81125WK/Kt8pwO1fQ5c1K5w4qF3qftB4x/4OD/ABPc+Y2lfCiC1iOcy6hqO5QP+Arz+deaax/wXn+LGr3CxWeheAdN87O3e7SsB7A45r4dsviXY2G2K38m3h258u1uJHyPcdqu2Hiq61S6DWdjrF95gwBFpjXAx9dteD/Z8aerpq3na35npPB4aC96S+8+qPEP/BW79obWGZotc0HT4F7WukCVgfbk/wA64nVP2/fj14timkuPihrVluYBhDbLZt+BK4/WvNNH+H/jPxFOn2HwD4nut3zfuNEmQfXpiu78Jfsd/HTxC/8AoPwz8cNGehe38pf/AB8j+dRalFXSivncObBx6owta/aD+LWvzqt18TPHF2qrwqa5tyCSNxCsCfoPSsjVP+El1+23X3ifxxqEn3XFzqlzIuM8fdcjp6ivfvD3/BLn9o7xdAF/4V39lX+H7bcxRY469Sa7zQP+CHH7QmrjdJa+E9LZvmAk1J259TtTr9K5qmJgouMbI0+vYSC/4B8Z2PgqzuZwb+3FxIu355ZZFZQTjkuPm+ma1E+GVnJua3t13MQxQ20UwAxk9DkV9/aD/wAG/wD8XtRaFtV8ceELJk7xLPLjgdOBXf8AhH/g3U1J5Q2s/FCFmP3hZ6aQF9wXbr7dKz+vJxVpP7jmlneFht+R+aEHgLT3jVZLO36A7VhdB/UVen+FWlPC7Lp8K89FkXkfiAa/Wrwt/wAG9PgWwdW1Lxx4svmxhhGsUK/oCa9D8Lf8ELfgboAVr638S6zJtxm61Riv/fIArFYqpze62c8uIsPfRfgfihb/AAW0e6uvLjg3zNlVjX94SenQc559K9I8Cf8ABODxJ8QpozDpctjauN/2i6YQRqOOe7Hr0xmv3L8Af8E+vhP8NbaOPSfCdha7P+WnWRsdDu613dn8B/CNgQI9DsifUxbv5muv63UlrqccuIY20ikfkX8Bv+CMejaPfW/iLxJ4wjm0XTbmP+0FsohEYixxhTK2XA4PCnjNfUVp/wAEyfh/4d+FseqWPxI1KHSVuFQXV1ZwbJGZ8AZ2qScccelfZXiD9nDwj4h1O2vLjTfJuLXCKbeRolcA8BkXCt+INY/jzTfhjZ+E5NJ1rUdDt7WzvIi8ckkbSQzj7nykHBH04rkq5Vh8W+bFU+ay095r8jty3jzNMAlDCV5QXMm1G1nb1T1PhD4qf8E4/hb8RPBmsaZ4e8W6t4g8eapamDT2WLy7SI9SWjC8+hOSckV8kfEb/giz8VPCHgrxFfRro+oWttpt67GOYxsFSJiflYdcA96/aLw5+zn4B1m3+3aQ100h3Il/Y3rwy7T95VdMDB9vzrY+JHguHw98BvFWn6dBM2NBvkjXe88shNvJ1Y5LMTj3JqsLg/q8FChG2vqcuYcY47FVHOvWlLp72v5WPBv+DdU5/wCCKvwB/wCwHP8A+l1zX4rf8Ep/DN9Y/wDBf/4W6tLa3Een6j8XfiRb29wyYjmkisJDIqnuVEqEjtvHrX6if8EGv+Ci37Pfwd/4JF/BHwz4u+O3wZ8L+I9J0aaO+0rV/Gum2V7Zuby4YLLDJMroxVlOGAOCK/OP9g74+eC/A/7fv7OPirXfEeh+H/Buk/HP4v6lc+KdT1CCz0IwXmmWKW0i3sjiFlkaJgp3YYlQpYnFfq1aVpw9f/bWfGUeblnyrpr5K6/Wx+6v/BQX9uKb9hvR/hLdQ+F4vFH/AAs74l6N8PnR9SNj/Zq34nJuwRFJ5pj8n/VfJu3ffXHPiX/BzB/yhG+OX/Xnpv8A6dLOvFv+C2X/AAUH+AXxd8N/szw+Ffjl8HfEkmh/H/wrrGpLpnjTTbr+zrGEXYlu5tkx8qCPeu6V8Iu4ZIzVn/g4T/4KG/AD42f8EfPjJ4Z8G/HP4OeLPEmpWlgLPSdG8aabfX12V1K1dhHDFMzuQqsxCg4Ck9Aa6DA+y/8Agkr/AMorv2av+yWeGf8A01W1fiR+0b/wUJ17/g4H8W/B6TVvhh4W+Gvg3wdJrst25+IFnrV/qsN1a/Y3iWwWKG5hKspId02kNuBGF3fqR/wTD/4KZ/s3fD//AIJs/s+6Dr37QXwP0XXNF+G3h2x1DT7/AMd6Xb3VhcRaZbpJDLE84aORGBVkYBlIIIBFfAf/AAV2+F/7Dvw8+H/wXvv2Yb74Cv8AEV/i94eiuP8AhBvElnqGqf2e32jzsxwTu/kl/JDHG3JUHqK7MvlTWIg6seZXWl7dfR/d+JnVu4ux+i3/AAbvfGLVvjN/wSD+Ec+uSfaNU8M2974VlnBYiePTb2ezgfLEkkwQxZz/ABbuAMCvyT+MM2oftTft/wD7UnxHv5PKmbx9e+CrVXIJt7LRgtpFjjgvjcRzzivuj/g3p/b4+BP7P3/BMfw/4X8efGr4R+CfE1n4k8QvcaRr3jDTtNv7ZX1a6ZDJBNMsiblIYblGQQRwQa+L/wBlfTrf4yfEX9ou/wBBurDWtJ1f4xeLb/T7+ynW6tb+2e8DJPDKhKSRMpDK6EqwOQTXdlOIp4WpXxFTaFOdvmuX9Tow9OdStThDdyR7t/wRWsmsP+C+HiyNt23/AIUChXPp/bFhiv0++NP7aknwj/b0+CXwTXw1HqEfxg03xBqD6ydQMTaT/ZcEEoUQeU3neb52M+Ym3bn5ulfkz/wTT/ag+GfwB/4Lm+ItY8efEDwR4H0iL4Groh1HX9dtdNtJbwazausCyzSKpl8pC2zO7CMcYBNfSn7WP/BQv4AeI/8Ags3+yL4s0/46fBu/8L+G9A8bwavq9v410yWx0qSe0slgS4mWYpE0rBggcjeVYLnacfH5HU58BSn3VzuziNsbUXmcX/weTf8AJkPwX/7KrZf+kF9X6W/ts/tHt+x/+yJ8SPikmjr4hb4f+HrzXRpjXf2UX3kRNJ5Xm7H2bsY3bGx6GvyE/wCDr/8AbZ+DH7R37HXwl034e/F74W+O9S0z4mWV7eWnh7xXYancWtuLG9UzSRwysyxhmUFyAoLKCckZ/S74o/8ABRP9jn41fDrWvCPir9oH9nXXPDfiOzk0/U9PufiDpJhvLeRSrxsBcA4IJFeseafnv/wSD/4KN6p/wVC/4L733xH1bwHp/wAPJLf9nKTSYNOtPFMHiFZ4R4jtLlZ2lhjj8lz9pKmB13r5YJxvAGh/wdH6vZ6H+2N+xTdX91a2NpHL40Ek9zKsUSZtNLUZZiAMkgDJ6kV3fwL+IP7Cf7Fn/BUrwjrnwi+IH7OHgfwvqvwr8TWGt6jpHjTTFs5bz+1/Dz2sM0v2gospjS6aNSQzLHKQCEbHv/7VHxs/4J6/tvNoJ+LXxT/Zd8ef8Iv9o/sr+1fHukyfYftHledsxcj7/kxZz/cFcuIw7rYeVCb+JNXS7q21/wBTow9dUa8a0F8LTs32d97foedf8GpRDf8ABHfwyVO5f+Em13BHf/T5K8J/bR/4Obvil8L/ANoX4tfCr4c/AnwvNqXw71+68PQ+Kdb8WNLZtJESFlexSCOU54bYsxA5G49a6T/g25/bz+AP7PP/AAS90bwz4v8AjV8H/BerWvibXJV0rWPGWnWF1FA9/KYm8qWZXCsmCpIwykEZBBr8xPjp4u0T4qf8FCv2mfEHhzWtJ1/w/rHxEvLrT9U028ju7K/iYZWSKaMlJFIIOVJHNY5liJ4fDudPVqy7/qjvyXB08Xi1Sq3s7vTyOR8JW+qjUNe1/wASal/bPivxhrV54i1/URH5YvL+6lMszhR0G48fyHQfq7/waV/FK8i8GftEfC590mk+EfGFt4h052dm8kapa5kgUE4VFa1DAKAN0sh6mvzKuND3RbznyYx82Aeua+z/APg2r/aq+Ff7LXxz/afX4lfEv4e/Dr+17rw8dPXxP4ks9Ja+CWtxvMQuJEMgXcuSuQu5c4yK+fyCtKeLnKW7Tb+9dD6niqjSp4GnTpqyi0l6Wf8AkeQf8Hcnxkvvi1+3xD4Jmymi/CT4eNeWkb4O+91OTdNKvoDDBAhz3j96/d39n29/tL/gnl4HuNuz7R8OrCTaTnbnTYzj9a/ng/4L1/FHwR+1P/wVQ+JWpeBvGvhHxh4d1XwJpVjFrGiaxb6jY+cFkVl86F2Tcp6rnI9K/Wj/AIIVf8FVfhT+2D+wf4J+Fut+LtH8OfFPwL4etvB2t+H9S1CG1v777NbrbLeWqu37+OVFVy0YOx3KkAbS301OqnWnC+qt91j5DEUGsLSqpaPmu/O/+R6X/wAG7P8AyhX+AH/YCm/9LbmuI/4N2777V8Kv2n49u37L+0b4yjJz97LWjf8As2PwrqLv9pj4B/8ABAT/AIJ3+F/A/iH4j2OtHwHoktvomlG7gbX/ABVMGeQJBaxnOXlkC78eXHvUu4HNfAH/AAbbf8FVvDf7NuvfEv4Z/tAalp/w21v4u+LLn4laFrGsTC00u9uL6ONbuyed9scEqGCNlVyAxdlyG2K/Q5xTUW9WcUaM5QdSKdla77X2uffP/BPz/lMj+35/2E/Av/qNx1+a/wDwcaXL2v8AwWu0do22sfhRZjp1/wCJld1+vngfwL8Jv2Rfjd8cPj9qvxQ8P6fp/wAZ5dGvtTuNV1a0tdL0xdO05bOLypmYAiRELksTz04r8E/+Cjn7Y/hv/goz/wAFPvGXxZ8LyXcvw78N6Ra+DfDeoPC0X9trA7yTXSK3IjM0j7M4JTaSFbco87OKihg562b0Xrc+i4PozqZvR5Fs235JJnXf8Ejv2eP2uvip8evF3xu/ZX1j4b+Gbfwvqv8Awhview8U6lcC38WvDHFcD7TbRwurKqzKqSK6Sr8wVhk5/cD9in9uSL9rbxh8VPhT408M2Hh34q/ByWx07xvo1pdnVNGmXULZp7eW0uXjjM0MsSuGSSJGjZWUhl2yP+Uf/Bup/wAFIPh1+xH8Zvi18Jfil4m0vwRo/wARNWh8XeFdb1aZLXTZ7gwrBdWs1y7BIpP3cJQPhSEf5ssgb9RPhX8Bfg/+xv8AtN/Hj9pDUPihodlB8b10afUp9X1e0tdJ0eLT7RoVMc7MARLkuzO2BgAYAJO+X8v1aHK7qy8zgz9VVmVf2y97mfS3XR/Na367nxJ+w5+xD4T/AGEv+Dp/4l6D4F0+30Pwj4u+DFx4r0/SLZdlrpH2nV7GOaCFOkcX2iCZ0jUBEWQKoCqAOY/4O27mwtfjj+yG+qahb6Xp/m+MVmu5/wDVwA2mnDJ5HcgAZ5JFU/2av+CtnwZ+Pf8AwcneNvijceOvDHg/4V6R8HJvBeh+KPE+ow6Jp/iCaDV7SaRreS6aMPmWS4CAHcyQFsAA4+3P2qPjd/wT2/beGg/8La+Kf7Lvjz/hFzOdK/tXx5pMn2Hz/L87Zi5GN/kxZ9dgratSVWlKn0kmvv0POo1ZUqsai3i0/u1KP/BtF/yg++A//Xjqf/p4vq/I/wD4L1f8Fktc/wCCi3w/1D4Tt8K9H8I6L8I/i/8ANr58cW15danJYNeadsXTTDFOok+1rJvBdV2FctyR+kf/AAQq/wCChX7OvwN/4JZ/DPwp4i+OnwW8J6to82tRvpOp+NtNs7qzjbWr94Q0Uk4dQ0TRsuRyrKRkEGvl7/gu74K/YGuf2H/H3jH4P61+znqnxk1HxBpmpLd+HfFmn3us3DzatbveSpHHcMzZjeVnIUgKWJwBkaS5vsmcbdT9iP21v2jW/ZC/ZG+JHxSTR18QN8P/AA9ea8NMa6+yi++zxNJ5Xm7H2btuN2xsehr8PP2MP+Ci2rf8FQ/+Dmf9nX4mat4Bsfh01p4C1PQodNtvFEGv/aI0sNXu1naSKOPyiwvQvlMu4GMknJKr+u3xQ/4KKfsc/Gn4da34R8VftBfs6654b8R2cun6np9z8QdJMN5byKVeNgLgHDKSOK/OHxNrP7Ev7Jf/AAWv/ZJ8T/BPxf8As++FPB8Om+MV8W6voPi7T2sLWRtLEdmLyYXDJEWaSRY95XeWYDJGBQRcbO616f1bX8D75/4LJ/8ABU7Uf+CU/wAG/A/ibSvh3H8Sr/xt4pi8MQaa+vDRvKeS3mlV/NaCVTzFtwQo+bO7ivxl/bR/bq+LP/BU/wCNPg/xF8StD8N+BvCPw7e5uvD3hPR7lr+Q3VwgQz3d0wCyyIoAXy1VRjgDLE/VX/Bzh+2b8Hv2nPgX8B9J+Gvxa+GfxA1bT/ipY3dzZeGfFNjq11bQfZLtTM8cErssYZlBcjaCygnkZ+K/BOl+dZ7XZsr6nkHj+fSvjeLM0r4eKoU9pLXv2/rQ+44QynDVk8XWTbhJW102vf8Ap28jn/i+q2Xw9v0kZ9t0v2bPfDH/AOtXjVhZLDaYwFWJdvHqOK9b/adupNP8P2NmqqsdzKHJzzkBsV5VZSGfEMcbSGQ4ZccA/WuPIoxp4fmn1PtcZNzqcse1ylLYf2lJsjBWQHCgdWPpXVa/ptpF4fto2Zt1js3GU/MpYYP6itXwX4Mt9MjN9eSD7ZkqgUbkTHce/vVTx1aR3ejXzM27zVGdw5yDxXr1Kjqwsmc2FwkqdVux5RPbrp+qFhIreWxJAB554r1D4fmS51ax+bdxlvVfWvMrcPHcq+VdeEIIzjFek/CiffqjSc7pD8o64615GY2aUmfRYFSUtj1v9kn4bQap8Y5byVSI7MvLkjq3zY/nX1Jr3g/T/EsZW4t4ZOS3zjOc/wD6q8z/AGWPDB0Xw9cahN/rL+XAyOi9sV6g82C5+8q9a/P+LMZUU0qcmtCsLT9nF83c8G+M/wAD7WOzlvNNs44bmJicRqBvXuOlePeF9O+zXU1vJCbdl/vnmvrrxJbR3iHzNy9uD0rw/wAf6Ha28z3SxL5icl/4m9OK5MpzSaj7Orr5nPmGBlVXPT6Hneq/u327cMpwc1Iw+zWLbT0G7J9ay73xzptzrD295I1pLG3O7G1j9akTUrS5lkH223kjbO1RICMduK+qjFyXMj5OtSnB2kiOaT7Y6xsGwy7iSf5VlXNg22aUJ8qDYp45q40scYBjdG5I4I6U+aLztMZgvytxzXXTlokY8rTR5j4lUPNN12jO45ryXVrVrnUJGAbAOBhu1e2eNNKj0mz8x5FRCDv6Mfxry9NHsdRklkkvFjbeQBjqK+gy2rGEXJnnYyMm7I/Yf9nPxDpogjWLwh4Mt+VTMelLkDOO5NfWPws12FVjEekaHDxwY7FFx+VFFePmFGGr5V9xhKEee1up7V4a1OR9mBHH8g+4u3+Vdxo8r/Z/vtj0zxRRXgyhFRVkKrGKtZG5ayM7qC79B1NalnDjncx9jiiisluzz60nexpQKN6/TPFaFnwfwFFFbxk7Hm1pPuWoRlvwp7LjFFFdFLXcw5mKvzGs3xN4UtPGumNp98boW9x94291JbyDHIw8bKw/OiitPsFWRzPhn9nrw14Q1VtRsl1z7VC3mKbjXL24XOA33ZJWUjPbFdbbpHelvNhhk+dT8y7ucLzz9aKK6qDdmY1ZNNWLaRrF8qqFXeRheO/tTp22KMdz19KKKqpJqF0TGTc7M/NP9pT/AIJr/Af4nftCalJqHwl+HcOydppRZ+GbC2N055LSOkIdie+WryL4q/szfD7xx4l0H4b3ng3w2ngTSbkpZ6FDp0SWNsd5JdYtu0OSzZYDJ3H1oor4/GYyu5u83ptq9D9gyWhTWCTUVqnfTf1O8/aq/YD+BX7M37Nkc3hP4M/C+11LxDMmlXWoz+GbS4ulgkUB1RmQhSwJBOK2/wDgnh/wSh/Z7stJfxdL8LPB99rWig3NpLc6VbssUiDIcAIOc/hRRXZgcVXeIpxc3Zxu1d6vXVnnzoU1ltWair829lfp1OR+Nv7A3wFm1u6vo/gj8J7WXUomuJFg8MWqorl+So2fLnJrxO1/ZY+GPwx8Sw6t4d+HngvQ9Utdxgu7LRoIZoTyMq6qCp9xRRX9ReHsVPCqU1d93qfjmK0dVL+f9GcT4/8A2Yvhr4x8Q3mqat8P/Bmo6leP5txd3GjwSTTv/ediuWPuea+0/wDgjV8LvDlvrPiKwt9E0u1sLDT/ACbe1t7dYYYVZhnaigAflRRX03HlGnDh3EzhFJuDu0tTz8FUksZR1+0fRfxs/wCCRH7NPxxulufFHwZ8DaleSOUNyNOWGbB6nfHtOfrXzl8Zv+DZj9ky70S6k0/wfreg7sFl0/V3VWIJIJWQOOM+lFFfyPgcRVTaUnb1Z93Tk5Vk5an5dfts/wDBO34f/sg+Jbqz8IrqP2eZ/srreR2khaMggqzLArMDjkMSDXzhZfCTw6mpSWraLokkeAQW0m03D8RED+dFFfVYSpN0eZt3v+iPpMLTg9Gkdv8ADn9lPwP421mG1u9FsY45Z1RjDaQIeSBn/V47ntX6/fsvf8Gyn7KPxN+GWm63rfhnxBeXl1CryBdTEMZPsqIuKKKqdap7Rav7zz84pxj8KPZ9P/4Nif2NbQ7pPhjNeNgDdcaxctnHA6OPSu18M/8ABAr9kvwRpX2XT/hHp0dsrFxG2pXrLu9ced196KK6K3vxSnr6nzMqk4u8W0y5c/8ABKD9m/wzp8qw/B3wnMqnhbnz5vT+9Ia5LxT/AME2P2a70yTXf7PPwfvpoU2LJdeH0mcKOQNzEn9aKK5acIwleKt6DVepJqMpNrTqZ3hf9mn4L/CvT2h8O/Af4K6TFO4kkWHwlbYdueTkHP41+Vv/AAWA8CeEfHP7Smt2d34H8G21nZ2dpHbQWGlpYrbBt+QjQ7WXJGcBgM0UVeIbjDnjv36/efa8LUKdTGeznFNW2aTXTofFC/DHw78KNYivPD+j2un3anck5LTyQnHVGlLFT9K734Zabb/Fi4u4/EkMWuQLGP3N4gmjJP8AFtYEbvcdKKK5syqSeEVRvXv1+8+kp0oU8S6NNJRu9ErL7tjmfiN+zV4B8IwSahYeF7CK5wW+eWaaPJ9I3coPwXivT/B3hqz0f4a6fHbwqkfkbtg+7k89KKK8vB1qlanetJy9Xf8AM97D4WjQa9hBRvvZJfkedfZbXxn8UI9L1axstQ0+SBt0FxCJEPJ5we/v1pbP9lv4fadrc1xH4Xsmk/eYWWaaWMcf3Gcp+nHaiivQo1p06sYwbSd7pOxljsJQq05TqwUmtm0m16Nn0l4E+EnhX4h/BXw/Hr3hrQdYh02N47SO8sY5ltl44QMDtHsOK+qfgR+wV8Edf8J2Ml58I/hxcSNdxqzyeHrVmYFhkElOlFFfO4zFVozkozaV31Z8BUpwc7tI9p/a2/4JyfAHRfglqeq2vwW+F9vqX2cyfaYvDVokm7A5yIxXiFx+w78GdF+BFhq1r8Kfh3DqTWr7rhfD9r5jbkIOTs7gkfjRRXi4jG4hKKU5b935G2HoU7x91fcfm/ffAzwXF+0lZaevhPw6LCW6YNb/AGCPyiOONuMY9q6j9rT4E+BtA+NN1p2m+DPC+m2IghPkWmmRQx5AbnAGM+9FFfcYXEVXXinJ/wAKT3e99z6CjhaOvuL7kY/wx+FvhnSEhu7Pw9otneY+W4gs40lTtwwGRmvoz4Y2Ub2EgZc+Tgrz7ZoorwcdUlNNydzshTjCPLBWXkeV/tlaRG95p7bpMQfKi7vlG5Sx4+org/C9mlvb2sabgs0e5ueSaKK96n/uUScN/vXyOttL149HhjG3azk9KyvF377wteswG5eBiiivpMMl9WubS+JnlIi+eb5m+5uxnvXonwLj+0XgVicbSePoaKK8HMvgR1YNvmPuzwXpUWl+BtNWHcqm3R+vcrmrekOZZplbkYJoor8w4m/3iJ6C/hmP4jhVlXr8w9a8e8erm3m6j92TxRRWOWL30ZTbUV/XY+WfjDbRyax5uxRJgDI4zXmuuXMkUx8uSSH5uSjEE0UV+v4GEfYw0/q58Xmkn7WX9dDN8Q67qFu4kj1C8jbb2krG0z4m+IHuZoTq155YIG3f7UUV7EqMFFWit+x4zqSbV2b7aldanbfv7q4kGzkF+vIrNkXzJpP4cNjC8UUVy1opN28jlqSd0f/Z" alt="Bayesian analysis of the Students' (1908) Sleep data set." width="80%" />
<p class="caption">
Bayesian analysis of the Students’ (1908) Sleep data set.
</p>
</div>
<p>Let’s use the Students’ (1908) Sleep data set (<code>data("sleep")</code>). The data comes from a study in which participants were administered a drug and the researchers assessed the extra hours of sleep that participants slept afterwards. We will try answering the following research question using Bayes factors:</p>
<blockquote>
<p><strong>Given the observed data, has the hypothesis that the drug (the effect of <code>group</code>) has no effect on the numbers of hours of extra sleep (variable <code>extra</code>) become more of less credible?</strong></p>
</blockquote>
<p><img 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jbSb3Bvq3927t//6XfeHb5W6DOkj6wtoW8j/Qb3tPrt3aeuC/0K0kfWltC3kX6Dl1t977POf/2vx68V+gzpI2tL6NtIv8FLrT6+s3vx+M61N0+O3949/4zXCn2G9JG1JfRtpN/gpVZ/cvs08vd2L55s39u/Mn6t0GdIH1lbQt9G+g3uCf31d08+PPtm/sHN594fvlboM6SPrC2hbyP9BveH/jzxZ78cvVboM6SPrC2hbyP9Bi+3+u7ulfP3b05zL/RLSB9ZW0LfRvoNXm71h7tr3zm+s3v+/eO7O2/dLCF9ZG0JfRvpN7in1Xd31999cPPs85V+M3YJ6SNrS+jbSL/Bfa3+ye+8e/Lg5d3ua+OP0Qt9ivSRtSX0baTfoJ91U0D6yNoS+jbSb/Byq99+4edXfa3QZ0gfWVtC30b6De7/eOUVXyv0GdJH1pbQt5F+g0JfQPrI2hL6NtJvcN8PNXt+/4cqf/FHR0ff+uHF1wp9hvSRtSX0baTf4OUfavbvb+x23/i9c79/Ifm/PNrc+t6F1wp9hvSRtSX0baTf4J63bnZ7fx79o7du/e3Jox8cvXThtUKfIX1kbQl9G+k3uOc7+n/+zL989h39x6++drLl/tsffPZaoc+QPrK2hL6N9Bv8nK1+9Nb5d/Q3zgh9hvSRtSX0baTf4OhTN3s+gHP/6C/O/lvok6SPrC2hbyP9Bkehv/zTK//z4lv03rpJkT6ytoS+jfQbfKLVx3d2T3ryp1c++v7RhXfohT5G+sjaEvo20m/wyVZ/+GTnrz3x0ysfvXX02pOvFfoM6SNrS+jbSL/Bp1r93z/76e3r//qzc0/+rYev3/ruU68V+gzpI2tL6NtIv8HLH6/8y9/f/wdj37v4Z6XOXyv0GdJH1pbQt5F+g1du9cevnv3J2KNv/uiz1wp9hvSRtSX0baTf4OXv6P/js19/9Nufferm/pHQp0ofWVtC30b6De75eOULj9+6Of4H/3LwNaSPrC2hbyP9Bi+H/s7u2ne2X3z08uNf/N+vFfoM6SNrS+jbSL/By60+/UZ+99w7x3+/272w/3dlP3ut0GdIH1lbQt9G+g3ua/Xp9/Knvv6MfzW40MdIH1lbQt9G+g3ub/Xd3e7am89+rdBnSB9ZW0LfRvoN/h/f0V/7xm73m89450boU6SPrC2hbyP9Bve8R3/+7vyPbz7zzRuhD5E+sraEvo30G9z7qZuzwB+//axv6oU+RPrI2hL6NtJvcM/n6D+t+09e9jn6JaSPrC2hbyP9Bod/Mvb474R+Bekja0vo20i/wS/SaqEPkT6ytoS+jfQb3Nvqn7zxjV9/95O/eudZrxX6DOkja0vo20i/wT2tfrD9eanr735ye/fiM14r9BnSR9aW0LeRfoOXW30a+Bf+6fb1d7ePWb6y5xUXXiv0GdJH1pbQt5F+g5dbfXf3/ON/Q/i9018NXyv0GdJH1pbQt5F+g5c/dXPn2puPQ//AjyleQ/rI2hL6NtJvcM/n6E/rfh768/8cvFboM6SPrK0b9HHosY3tCb3v6FeTPrK2Dt0evkKHHtvYvvfoXzwP/fFd79GvIX1kbR26PXyFDj22scutfnBz95s/vX3933768rN+VLHQh0gfWVuHbg9foUOPbWzf5+hv7s5dG3+6UuhTpI+sLb8Z20b6De5r9fE/fOM081/7w58/67VCnyF9ZG0JfRvpN1jtZ90c+v9/4ytz6KldgdC3kb7HYqE/dHz4Ch16bM8m9G2kz7Fc6P+LHtIvayP0baTPUehZU/plbYS+jfQ5Cj1rSr+sjdC3kT5HoWdN6Ze1Efo20uco9Kwp/bI2Qt9G+hyFnjWlX9ZG6NtIn6PQs6b0y9oIfRvpcxR61pR+WRuhbyN9jkLPmtIvayP0baTPUehZU/plbYS+jfQ5Cj1rSr+sjdC3kT5HoWdN6Ze1Efo20uco9Kwp/bI2Qt9G+hyFnjWlX9ZG6NtIn6PQs6b0y9oIfRvpcxR61pR+WRuhbyN9jkLPmtIvayP0baTPUehZU/plbYS+jfQ5Cj1rSr+sjdC3kT5HoWdN6Ze1Efo20uco9Kwp/bI2Qt9G+hyFnjWlX9ZG6NtIn6PQs6b0y9oIfRvpcxR61pR+WRuhbyN9jkLPmtIvayP0baTPUehZU/plbYS+jfQ5Cj1rSr+sjdC3kT5HoWdN6Ze1Efo20uco9Kwp/bI2Qt9G+hyFnjWlX9ZG6NtIn6PQs6b0y9oIfRvpcxR61pR+WRuhbyN9jkLPmtIvayP0baTPUehZU/plbYS+jfQ5Cj1rSr+sjdC3kT5HoWdN6Ze1Efo20uco9Kwp/bI2Qt9G+hyFnjWlX9ZG6NtIn6PQs6b0y9oIfRvpcxR61pR+WRuhbyN9jkLPmtIvayP0baTPUehZU/plbYS+jfQ5Cj1rSr+sjdC3kT5HoWdN6Ze1Efo20uco9Kwp/bI2Qt9G+hyFnjWlX9ZG6NtIn6PQs6b0y9oIfRvpcxR61pR+WRuhbyN9jkLPmtIvayP0baTPUehZU/plbYS+jfQ5Cj1rSr+sjdC3kT5HoWdN6Ze1Efo20uco9Kwp/bI2Qt9G+hyFnjWlX9ZG6NtIn6PQs6b0y9oIfRvpcxR61pR+WRuhbyN9jkLPmtIvayP0baTPUehZU/plbYS+jfQ5Cj1rSr+sjdC3kT5HoWdN6Ze1Efo20uco9Kwp/bI2Qt9G+hyFnjWlX9ZG6NtIn6PQs6b0y9oIfRvpcxR61pR+WRuhbyN9jkLPmtIvayP0baTPUehZU/plbYS+jfQ5Cj1rSr+sjdC3kT5HoWdN6Ze1Efo20uco9Kwp/bI2Qt9G+hyFnjWlX9ZG6NtIn6PQs6b0y9oIfRvpcxR61pR+WRuhbyN9jkLPmtIvayP0baTPUehZU/plbYS+jfQ5Cj1rSr+sjdC3kT5HoWdN6Ze1Efo20uco9Kwp/bI2Qt9G+hyFnjWlX9ZG6NtIn6PQs6b0y9oIfRvpcxR61pR+WRuhbyN9jkLPmtIvayP0baTPUehZU/plbYS+jfQ5Cj1rSr+sjdC3kT5HoWdN6Ze1Efo20uco9Kwp/bI2Qt9G+hyFnjWlX9bmBn0cemxjQs+a0i9rc+j28BU69NjGhJ41pV9WWx5MIqFnTXoSyoNJJPSsSU9CeTCJhJ416UkoDyaR0LMmPQnlwSQSetakJ6E8mERCz5r0JJQHk0joWZOehPJgEgk9a9KTUB5MIqFnTXoSyoNJJPSsSU9CeTCJhJ416UkoDyaR0LMmPQnlwSQSetakJ6E8mERCz5r0JJQHk0joWZOehPJgEgk9a9KTUB5MIqFnTXoSyoNJJPSsSU9CeTCJhJ416UkoDyaR0LMmPQnlwSQSetakJ6E8mERCz5r0JJQHk0joWZOehPJgEgk9a9KTUB5MIqFnTXoSyoNJJPSsSU9CeTCJhJ416UkoDyaR0LMmPQnlwSQSetakJ6E8mERCz5r0JJQHk0joWZOehPJgEgk9a9KTUB5MIqFnTXoSyoNJJPSsSU9CeTCJhJ416UkoDyaR0LMmPQnlwSQSetakJ6E8mERCz5r0JJQHk0joWZOehPJgEgk9a9KTUB5MIqFnTXoSyoNJJPSsSU9CeTCJhJ416UkoDyaR0LMmPQnlwSQSetakJ6E8mERCz5r0JJQHk0joWZOehPJgEgk9a9KTUB5MIqFnTXoSyoNJJPSsSU9CeTCJhJ416UkoDyZRudDTxqHHxl4eTCKhZ1WHHht7eTCJhJ5VHXps7OXBJBJ6VnXosbGXB5OoXOgP/XuEfEX0JJQHk0joWZOehPJgEgk9a9KTUB5MIqFnTXoSyoNJJPSsSU9CeTCJhJ416UkoDyaR0LMmPQnlwSQSetakJ6E8mERCz5r0JJQHk0joWZOehPJgEgk9a9KTUB5MIqFnTXoSyoNJJPSsSU9CeTCJhJ416UkoDyaR0LMmPQnlwSQSetakJ6E8mERCz5r0JJQHk0joWZOehPJgEgk9a9KTUB5MIqFnTXoSyoNJJPSsSU9CeTCJhJ416UkoDyaR0LMmPQnlwSQSetakJ6E8mERCz5r0JJQHk0joWZOehPJgEgk9a9KTUB5MIqFnTXoSyoNJJPSsSU9CeTCJhJ416UkoDybR52j1//zp0dEf//Dia4Weg9GTUB5Moqu3+uHrR6e++aMLrxV6DkZPQnkwia7e6vtHf/LBox8cvXbhtULPwehJKA8m0ZVb/eitb3/wq//81WuFnoPRk1AeTKIrt/rh6y9t//Xe+Xs3N84IPQejJ6E8mERXbvXHr569aXP/1ve2/xJ6DkxPQnkwif6foT9/rdBzMHoSyoNJJPSsSU9CeTCJPsd79Gehf+/C5yuFnsPRk1AeTCKfumFNehLKg0l09Va/t32O/vs+R08GPQnlwSTyJ2NZk56E8mASfc6fdfMtP+uGDHoSyoNJ5KdXsiY9CeXBJBJ61qQnoTyYRELPmvQErkzoWZPQw5UJPWsSergyoWdNQg9XJvSsSejhyoSeNQk9XJnQsyahhysrF3raOPTYYBlCz6oOPTZYRrHQ96R5wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQFyD0wIjQAxQn9ADFCT1AcUIPUJzQAxQn9ADFCT1AcUIPUJzQAxQn9ADFCT1AcUIPUJzQAxQn9ADFCT1AcUIPUJzQAxQn9ADFCT1AcUIPUJzQAxQn9ADFCT1AcUIPUJzQAxQn9ADFCT1AcUIPUJzQAxQn9ADFCT1AcUIPUJzQAxQn9ADFCT1AcUIPUNwXCz0AkWaFXulD3Lhx6K8AfsUaU0wLPRlu3Dj0VwC/Yo2JhL4Ap0UOa0wk9AU4LXJYYyKhL8BpkcMaEwl9AU6LHNaYSOgBihN6gOKEHqA4oQcoTugBihN6gOKEvoL3Xjr0VwBnfvFHR0ff+uGhvwqeJvQF3D8SeiL88mhz63uH/jp4itAv79H3j4SeCI/euvW3J49+YI9xhH51D1+/9WevOywSfPzqaydb7r/9waG/Ep4k9Kt7+DcfPBR6gjx6yx7TCH0BQk+S+0d/cegvgacIfQFCT5D/9BZ9HqEvQOiJ8ej7R96hzyP0BQg9KR69dfTaob8GLhP6AoSeEA9fv/XdQ38N7CH0BQg9Id7zZ6UyCX0BQk+Gj189+5OxR9/80aG/Ep4k9AUIPRnuHwl9JqEHKE7oAYoTeoDihB6gOKEHKE7oAYoTeoDihB6gOKEHKE7oAYoTeoDihB6gOKEHKE7oAYoTeoDihJ5ejt/e7b7+zr3diycnH+5e/PHN3dffPDn56I3dbvfCO9vfv7v9nZOTe2Bh1m4AAAIDSURBVLvnt1+/8uDl3bU/fP+wXzJ8UUJPK8d3TpO+u/a756H/jZu73XPvn3x4c3f2f33l5OnQ/8HZ33n+wF80fEFCTyv3dtf++uSjl3fnod8qf3Ly4ObuhZ9v3+pfe/Pp0O+ee+fk9Lv+Vw78VcMXI/R0cvoN/Rbt07SfhX4r++Oon2xdf/7p0F9/9+zXz3nzhqUJPZ08uHne7LvnoT/7i8fxf/zXT4b+7Nef3D7rPSxL6Onkw8ffvN+7EPpPbp9/Y38e9Kd+M3b79fGdx/8ALEro6eSp0J/9xaffsAs9VQk9nTz+Jv6p0PuOnuKEnk6eeo/+LPTPfI/+wU3v0bM2oaeTx1H/5PaF0D/5qZvzvzj9585Cf/Y/C/d8kJ7FCT2t3Ns+Uvnp5+jPA37+Ofr/fuPs05Yf7nbfOfnozu7x5+iff9/n6Fmf0NPKk38y9vF36hf/ZOz5P3D9H89D/3tnf+PFg37J8IUJPb2c/6ybu0+E/uLPujk5fmP7Bz58/Juxp9/Of+07h/tqYQqhp6O7V3o35mr/FMQTejp5/AGaTz9ROSb0FCH0dPLJ7e23V4/vXu2n1wg9RQg9rfx4d/77rlf6E1BCTxFCTy8/+a3TzD/+fddnEXqKEHqA4oQeoDihByhO6AGKE3qA4oQeoDihByhO6AGKE3qA4oQeoDihByjufwFCAzwuAe8LjQAAAABJRU5ErkJggg==" width="100%" /></p>
<p>The <strong>boxplot</strong> suggests that the second group has a higher number of hours of extra sleep. <em>By how much?</em></p>
<p>Let’s fit a simple <a href="https://easystats.github.io/bayestestR/articles/example1.html">Bayesian linear model</a>, with a prior of <span class="math inline">\(b_{group} \sim N(0, 3)\)</span> (i.e. the prior follows a Gaussian/normal distribution with <span class="math inline">\(mean = 0\)</span> and <span class="math inline">\(SD = 3\)</span>), using <code>rstanarm</code> package:</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">set.seed</span>(<span class="dv">123</span>)</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(rstanarm)</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a>model <span class="ot"><-</span> <span class="fu">stan_glm</span>(</span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a> <span class="at">formula =</span> extra <span class="sc">~</span> group,</span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> sleep,</span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a> <span class="at">prior =</span> <span class="fu">normal</span>(<span class="dv">0</span>, <span class="dv">3</span>, <span class="at">autoscale =</span> <span class="cn">FALSE</span>)</span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
<div id="testing-against-a-null-region" class="section level3">
<h3>Testing against a null-<em>region</em></h3>
<p>One way of operationlizing the null-hypothesis is by setting a null region, such that an effect that falls within this interval would be <em>practically</em> equivalent to the null <span class="citation">(Kruschke, 2010)</span>. In our case, that means defining a range of effects we would consider equal to the drug having no effect at all. We can then compute the prior probability of the drug’s effect falling <em>within this null-region</em>, and the prior probability of the drug’s effect falling <em>outside the null-region</em> to get our <em>prior odds</em>. Say any effect smaller than an hour of extra sleep is practically equivalent to being no effect at all, we would define our prior odds as:</p>
<p><span class="math display">\[
\frac
{P(b_{drug} \in [-1, 1])}
{P(b_{drug} \notin [-1, 1])}
\]</span></p>
<p>Given our prior has a normal distribution centered at 0 hours with a scale (an SD) of 3 hours, our priors would look like this:</p>
<p><img src="data:image/png;base64,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" width="100%" /></p>
<p>and the prior odds would be 2.2.</p>
<p>By looking at the posterior distribution, can now compute the posterior probability of the drug’s effect falling <em>within the null-region</em>, and the posterior probability of the drug’s effect falling <em>outside the null-region</em> to get our <em>posterior odds</em>:</p>
<p><span class="math display">\[
\frac
{P(b_{drug} \in [-1,1] | Data)}
{P(b_{drug} \notin [-1,1] | Data)}
\]</span></p>
<p><img 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" width="100%" /></p>
<p>We can see that the center of the posterior distribution has shifted away from 0 (to ~1.5). Likewise, the posterior odds are 2, which seems to favor <strong>the effect being non-null</strong>. <strong>But</strong>, does this mean the data support the alternative over the null? Hard to say, since even before the data were observed, the priors already favored the alternative - so we need to take our priors into account here!</p>
<p>Let’s compute the Bayes factor as the change from the prior odds to the posterior odds: <span class="math inline">\(BF_{10} = Odds_{posterior} / Odds_{prior} = 0.9\)</span>! This BF indicates that the data provide 1/0.9 = 1.1 times more evidence for the effect of the drug being practically nothing than it does for the drug having some clinically significant effect. Thus, although the center of distribution has shifted away from 0, and the posterior distribution seems to favor a non-null effect of the drug, it seems that given the observed data, the probability mass has <em>overall</em> shifted closer to the null interval, making the values in the null interval more probable! <span class="citation">(see <em>Non-overlapping Hypotheses</em> in Morey & Rouder, 2011)</span></p>
<p>All of this can be achieved with the function <code>bayesfactor_parameters()</code>, which computes a Bayes factor for each of the model’s parameters:</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>My_first_BF <span class="ot"><-</span> <span class="fu">bayesfactor_parameters</span>(model, <span class="at">null =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">1</span>, <span class="dv">1</span>))</span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>My_first_BF</span></code></pre></div>
<pre><code>> Bayes Factor (Null-Interval)
>
> Parameter | BF
> -------------------
> (Intercept) | 0.103
> group2 | 0.883
>
> * Evidence Against The Null: [-1.000, 1.000]</code></pre>
<p>We can also plot using the <code>see</code> package:</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><span class="fu">library</span>(see)</span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(My_first_BF)</span></code></pre></div>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAABegAAAOECAMAAADt/iG0AAABmFBMVEUAAAAAADoAAGYAOjoAOmYAOpAAZrYAr8cAv8QZqL4ep70ftrkltLc6AAA6OgA6Ojo6OmY6ZmY6ZpA6ZrY6kLY6kNtNTU1NTW5NTY5Nbm5Nbo5NbqtNjshmAABmADpmOgBmOjpmOmZmZgBmZjpmZmZmZpBmfJBmkGZmkJBmkLZmkNtmtttmtv9uTU1ubk1ubm5ubo5ujshuq8huq+R/f3+OTU2Obk2Obm6Oq8iOyOSOyP+QOgCQZgCQZjqQZmaQZpCQkGaQkJCQtraQttuQ2/+pfoyrbk2rjm6rq26ryOSr5P+tzeCu2++2ZgC2Zjq2ZpC2kDq2kGa2kJC2tma2tpC2tra2ttu229u22/+2/9u2///HdYHIjk3Ijm7Iq47I5MjI5OTI5P/I///L0+XM4/bTgXrY5OPZ9fbbkDrbkGbbtmbbtpDbtrbb25Db27bb29vb2//b/9vb///kq27kyI7kyKvk5Kvk5P/k///4dm3+6+n/tmb/yI7/25D/27b/29v/5Kv/5Mj/5OT//7b//8j//9v//+T////7chqKAAAACXBIWXMAABcRAAAXEQHKJvM/AAAgAElEQVR4nO3d/aMcV33Y4SvARG0iA068tsEEWlyaBMttYrvFpk7aGpSW1LROy0uxkgaMJQenIeXSFtuyMcWS/u3u7jl79212d3Z3Xs5853l+kHT3andW98797NGZObMXDwEI7aLvJwBAu4QeIDihBwhO6AGCE3qA4IQeIDihBwhO6AGCE3qA4IQeILg+Q3/hVYaCvPDVn3Tpqy/0/Q9mPIQeEqEnLKGHROgJS+ghEXrCEnpIhJ6whB4SoScsoYes087/5Cd9/3MZEaGHTOiJSughE3qiEnrIhJ6ohB4yoScqoYdM6IlK6CETeqISesiEnqiEHhILpghL6CEResISekiEnrCEHhKhJyyhh0ToCUvoIRF6whJ6SISesIQeEqEnLKGHrNPOWzBFh4QeMqEnKqGHTOiJSughE3qiEnrIhJ6ohB4yoScqoYdM6IlK6CETeqISekiKWTD17kyX/3LCE3pISgn9u1mn/3hiE3pIygj9u0sd//sJTOghKS70Sk9ThB6SIkKfCv+e0tMooYeknNC/N6X0NEjoISkh9FedV3qaJPSQFBD6d1dC/57Q0xihh6zTzlcumFrtfCp9518EQhJ6yHoP/XrnhZ7GCD1kRYT+vfeUnsYJPWRCT1RCD1lxoVd6GiL0kPUd+neFnpYIPWQlhP6995Se5gk9ZD2HvqLzQk8zhB6SvhdMVYVe6WmE0EPSc+grO295LI0QekiKDL0hPU0QekiEnrCEHhKhJyyhh6Tc0Cs9ZxJ6SPoN/fZqKaGnMUIPSf+hr+i80tMEoYes085vLJjaNaAXepog9JCVGXqHYzmf0EPWY+j3dN6QnvMJPWSFht6QnrMJPWQ9h35X54Weswk9ZEJPVEIPmdATldBDJvREJfSQ9Llg6mDolZ5zCD0kPYZ+70k3hvScTegh6Tn0uzsv9JxL6CEpO/RKzxmEHpL+Qn9g5saQnnMJPST9hn5f54WeMwk9JIWHXuk5ndBD0lvoD87cGNJzJqGHrNPOryyYOtx5oec8Qg+Z0BOV0EPWU+hrzNwIPecResh6DP2Bzgs95xF6yISeqIQessJDr/ScTOgh6yf0daboDek5j9BD1l/oD3Ze6DmL0EPS04Ipoad9Qg9J8aFXek4l9JAUHXpDes4h9JAIPWEJPSRCT1hCD0k/oa93dqVJes4i9JD0F/oanTek5xxCD4nQE5bQQ9Zp5xcLpoSeDgg9ZH2Evu4UvdBzDqGHrK/Q1+q80HMGoYdM6IlK6CErP/RKz2mEHrIeQl9/it6QnjMIPWQ9hb5m54We0wk9ZEJPVEIPSR8LpoSeTgg9JEMIvdJzEqGHpPTQG9JzMqGHROgJS+ghEXrCEnpIegj9MafRm6TndEIPSU+hr915Q3pOJvSQCD1hCT1knXZ+vmBK6OmG0EPWeeiPm6IXek4m9JD1EvojOi/0nKqF1v7iucnkqa//cvsT9yZPr29b6CmJ0BNV4619cGsy94Wt0n90U+gpmdATVeOtvZw88dJ0VH9z8vzGJ2avAEJPwboO/bFT9ELPqZpu7ccvTl6e/X5v8uSP1z9zORF6itZH6I/pvBVTnKrp1i4CPx2/v7z2iY9uPvkfhJ6SFR96Q3pO1HRrby9ifnu96rOR/qXQU7DOF0wJPV1pPvR5bv5y/XDsrPtCT8mEnrAabu2DW4vQ31sL/fwjoadkQk9YzYc+T82vhf7jF5/49kOhp2gDCb3Sc7xuQp8mdISekg0g9Ib0nKaTqZs8Xy/0lEzoCauLg7Ef3ZxN3Ag9ZRN6wmq6tZcVp1deTpZWj9AKPSXpI/RHdt4kPadpfsFUSvnqgimhZxA67fxPfnLCgN6QntN0dwkEUzcUTuiJqruLmgk9hRN6omr5MsW3V+dqhJ6iddv5N4SezjTf2gerbzwi9AxH96E/uvNCz0m8lSBkQk9UQg+Z0BOV0EMm9EQl9JB0u2DqjdmCqdNCr/QcS+gh6T70x3fekJ6TCD0kQk9YQg+J0BOW0EMi9IQl9JAMJ/RKz5GEHpJhhN6QnhMIPSRCT1hCD1mXnf/JG2+cchq90HMSoYdM6IlK6CHrtvNvnNZ5oecEQg/ZMEKv9BxP6CETeqISesiEnqiEHjKhJyqhh6zbzgs93RF6SLpcMDXt/FdfEHq6IvSQCD1hCT0kQk9YQg+J0BOW0EPSYejfEHo6JfSQDCn0Ss9RhB6SoYTekJ6jCT0kQk9YQg9ZZ52fh/7NUzsv9BxN6CETeqISesiGFHql5xhCD9lQQm9Iz7GEHjKhJyqhh0zoiUroIeu280JPd4QeskGFXuk5gtBD0t2CqXnoT18wZUjPsYQeEqEnLKGHROgJS+gh6Sz0bwg9HRN6SDoN/ZtCT4eEHpKBhV7pqU/oIRlQ6A3pOY7QQyL0hCX0kHXU+Rz6MxZMCT1HEnrIOuy80NMpoYesw9C/KfR0SeghG1DolZ6jCD1kQk9UQg+Z0BOV0EMm9EQl9JAJPVEJPSRdLZjKoT9rwZTQcxShh0ToCUvoIRF6whJ6SISesIQeko5CvzgWK/R0R+ghGVzolZ66hB6SQYXekJ5jCD0kQk9YQg9ZJ52/Cv15C6aEnmMIPWSddV7o6ZjQQ9ZZ6N8Uerol9JANLvRKT01CD9mgQm9IzxGEHjKhJyqhh0zoiUroIeuq80JP14Qekk4WTC07f+aCKaHnCEIPidATltBDMrDQKz31CT0kQk9YQg+J0BOW0EMi9IQl9JAIPWEJPSRCT1hCD1kHnV8J/bkLpoSe+oQeMqEnKqGHrNvOCz3dEXrIhJ6ohB6yAYZe6alF6CEbWOgN6alN6CETeqISesiEnqiEHpIOFkytvO3I+QumhJ7ahB6SjkL/ptDTOaGHZJChV3rqEHpIBhd6Q3rqEnpIhJ6whB4SoScsoYek/dC/IfT0Q+gh6Sb0bwo93RN6yNru/Hroz18wJfTUJfSQDS70Sk9NQg+Z0BOV0EMm9EQl9JAJPVEJPWRCT1RCD5nQE5XQQyb0RCX0kAxvwZTQU5PQQ9J66NcH9EJPd4QeEqEnLKGHROgJS+ghGWjolZ7DhB6SAYbekJ56hB4SoScsoYek7dC/IfT0Regha7fzGwP6RhZMCT31CD1kQk9UQg/ZQEOv9Bwk9JANMPSG9NQi9JAJPVEJPWTtd17o6YfQQ9Z+6N8Uenoh9JAJPVEJPSQtL5jaDH0jC6aEnlqEHpJBhl7pqUPoIRF6whJ6SNoN/dZJN0JPd1po7S+em0ye+vov12578Fc3J5N/+R83ti30FKT90L8p9PSj8dY+uDWZ+8Jq6T9+Md349Fr+hZ6SCD1hNd7ay8kTL01H9Tcnzy9vm8b/8z/avFHoKYvQE1bTrZ2O3V+e/X5v8uSPr25cfHC5Ps4Xekoi9ITVdGsXTZ8O4l++uvFy8vTaJxfbFnpK0mbnt0PfzIIpoaeOplt7Ozd9+YcVRvSUrO3OCz19aT70eRp+I+oPZ2feTJ749tq2hZ6StB36N4WenjTc2ge3FqG/txH6e5PJ/Ijs6raFnpIIPVE1H/o8Nb8V+qf+xbT0RvSUa7ChV3oO6Cz0D7fnboSeogwy9Ib01NDZ1E3+7OoRWqGnKEJPVB0ejN26UegpitATVdOtvdx3euXGMF/oKUmrC6a2Q9/Qgimhp4bmF0yllK8umFrO5xjRUy6hJ6xOLoFwmT+YfnL1YjdCT0kGHHqlZ79OLmo2DfzsFPr/fdPKWMo10NAb0nNYy5cpvp1+/+hmuvHzq5e6EXqKIvSE1XxrH6y+8UgO/cP/N3vjkc13IxF6StJm6CtOuhF6uuOtBCEResISekiEnrCEHrL2Ol8V+qYWTAk9hwk9ZAMNvdJzkNBDJvREJfSQtdt5oac/Qg9Zu6Hf7LzQ0x2hh0zoiUroIRN6ohJ6yISeqIQekhYXTFWFvrEFU0LPQUIPSXuhrzzpRujpjtBD0m7ot2ZuhJ7uCD0kQk9YQg+J0BOW0EMy6NArPfsIPSSDDb0hPYcIPSRCT1hCD1lbna8OfXMLpoSeQ4QeMqEnKqGHTOiJSughG3TolZ49hB6ywYbekJ4DhB6ybjsv9HRH6CETeqISesiEnqiEHpLWFkxVh77BBVNCzwFCD4nQE5bQQzLg0Cs9+wk9JG2FvvL9pYSeLgk9JG2GvuJYrNDTHaGHROgJS+ghEXrCEnpIhJ6whB6ydjq/K/RNLpgSevYTesja67zQ0y+hh6y90Fd1XujpjtBDJvREJfSQCT1RCT1kAw+90rOT0EM24NAb0rOX0EMm9ES13drf/P4f/KCjbQs9BWlpwdSu0De6YEro2asi9F+8uLj2WBetF3pKIvSEtd3a+68/enHRSeuFnpIIPWFVtvb+X36pi9YLPSUResLa1dr77+TWf7/FbQs9BRl86JWeXfa09v47X563/g9/3ta2hZ6CtBP6nSfdNBt6Q3r22dfav3/lxsU89V9radtCT0GEnrB2tvadV9Jw/mevT2v/bDvbFnoKIvSEVd3aPGmTD8a+ffFIK7M3Qk9R2uj87tA3u2BK6NmnorWp8hfLw7C/+eInftjKtoWekgg9UVUvmLr47Ktrtwg9I9BW54WevlWF/lOvrs/UfPjdds6xFHqK0lboqzvfcOiVnj1c1AwyoSeqQ629/7MWty30lEToiapq6mZlRv6DG+1Mz6dtCz0lEXqiOhD6to7Dpm0LPSUReqJab+3rzzzzzFduXPvcMwuPXgg9I9HGgqk9J900vGBK6NljvbUfpGserHq8xW0LPQVpK/Q7BvRCT3c2Wvudz3zm0YuLT35m4bOtXdHsodBTFqEnrANz9O1uW+gpiNATVsU7TP3pP2txFL+2baGnIEJPWBZMQSL0hLXW2vt/972fT3/57qrvtTe8F3pKEiD0Sk+1tdbOp+fnFzVbcnolIzHw0BvSs5vQQ9Z85/eFvukFU0LPbuut/dU/zH752ap/aHHbQk9JhJ6oHIyFTOiJSughE3qi2tPa+3/33e+1u22hpyTddr6V0Cs9lSpb+86f/TC/peC1b7a5baGnJAMPvSE9O1W19rXZqTb3v9H2STdCT1mEnqgqWvv+PO8f3Lj49MMPv+HqlYyG0BNVRWtfm8f97fm0zQc3HrEylnFoYcHUvtA3vmBK6Nmp6uqVs8Lf/8bFLPHeYYrREHrC2nWZ4g9uzMf1Qs9oNB/6Pe8vJfR0aVfo08yNqRvGo53Q75yibz70Ss8uFdejnx2AzTM3098+3eK2hZ6CCD1hVZ9188kbszeLvf/6jVZPpBd6SiL0hFXV2u/MTqCfDuhnS6ZaPLtS6CmK0BNW9crYZ555dXbKze8/9oNWty30FEToCctFzSBro/O7Q9/8gimhZxehh6yN0O/uvNDTnV2t9cYjjI7QE1VVaz98xVsJMkJCT1QVrf3ghveMZYyEnqgqL2p28di//+7C96yMZSSEnqiqLoHQ6snzq9sWekoSIvRKT4Vd17rpZNtCT0kGH3pDenYQekgaXzC1P/QtLJgSenaonKN/tqNtCz0FEXrCqjzrpsVLE69tW+gpiNATVkVrf/XTi2uPOeuGsWk69Aem6IWe7lSedeM8ekYoSOiVnm1CD0mA0BvSU61q6uZnq1zrhpEQesJy9UpIhJ6whB6yZjt/KPRtLJgSeqpVt/bDVx6dTc7/5p94hynGo/nOCz1lqGrt/e/ko7C/+WKra6eEnqI0H/p9nW8t9ErPlqrWvnZx8al/fmMa+vvfuLj2zRa3LfSUJEDoDempVNHa92d1T1e8mZa+xStZCj1FEXqiqrzWzeNXlzZ7/6LFyyEIPUUReqKqWjA1m67JoW/1UpZCT1GEnqh2XaZY6Bmdxjsv9BTiwIj+gxtCz0g0u2DqYOdbWTDltBsqHZijf+3i0y1uW+gpSIjQG9JTpfKsm4uvpdDPTqhv8UR6oackQk9YO86j/+RXblz7d1+5uGhzQC/0FEXoCauytd+5ukjx77b5XlNCT0mEnrCqW/ur1x+dVv6Tj7V6qRuhpyhCT1iuXgmJ0BOW0EMSI/RKTwWhh6zJzh8OfTsLpoSeKtutvf/Ol2/MjsNe+9yrbW9b6CmJ0BPVZmvvv35j+cbg1/6o3W0LPSXptvNCT3c2Wnv/G9O+f/YPvvvd7/63P52deNPitSuFnsIIPVFttPa11VPnZwtjLZhiNISeqNZbO7/6wdrH3mGK0RB6olpv7dY1zF474R2mfvHcZPLU13+5dtuv//zm9o1CT1GEnqjWWnv/G5sD+OPfYerBrcncF1ajfplum3z+x2vbFnpK0nDnhZ5irLV2+21Gjr8e/eXkiZemo/qbk+eXt310c/LH/3d+49Nr2xZ6CtLkgqkanbdgiu4cCP3R7zD18YuTl2e/35s8uRy9386Bvzd54tur2xZ6ChIo9ErPuqZDvwj8g1sp+Gt/Xr3xodBTliChN6RnW9OhXwzel39YIfQUTOgJq/nQ57n5y/XDsXMf3TR1Q7GEnrAaDv10zJ5Df68i9LfXbxN6StJg6OucdCP0dGcj9Nc+98yarxx51s1ycqYi9JeTtZkboacoDYf+QOeFng5thP5iS3Ohn3b++bUbhJ6SRAq90rNmPfRf/syWzzY1dTPt/B9vbFvoKUljna8V+rYWTBnSs63p1u46GPvgrzbH80JPYYSeqJpu7WX16ZXTkf5swezGtoWekgg9UTXd2sWMzfop87POf3vr7wo9RRF6omq6tZWXQJh2/skfVWxb6CmJ0BNV462tuqjZ5Wr1V7Yt9JRE6Imq8dauX6Z4vkRqOsq/sjpxL/QUJUrolZ5Nzbf2weobj8xD/9FNoWcAhJ6o+myt0FOS5hZM1ep8awumhJ4tQg+J0BOW0EMi9IQl9JAIPWEJPSRCT1hCD0ljoa9zNXqhp0tCD0mjoT/YeaGnQ0IPidATltBD1lDna4a+5QVTSs8KoYcsTOgN6dkg9JAJPVEJPWQNdl7oKYrQQ9Zg6Gt0XujpjtBDJvREJfSQxQq90rMk9JDFCb0hPeuEHpKmFkzVDH2LC6aEng1CD4nQE5bQQyL0hCX0kAg9YQk9JJFCr/SsEXpIGgp93ZNuhJ7uCD0kQk9YQg+J0BOW0EPWSOdrh77VBVNCzxqhh0zoiUroIWus80JPYYQessZCX6vzQk93hB4yoScqoYdM6IlK6CGLFnqlZ0HoIYsUekN6Vgk9JI0smKp/0k27C6aEnlVCD0ljoa83oBd6uiP0kAg9YQk9JPFCr/RkQg9JrNAb0rNC6CFpIvT1j8UKPR0SekiaCn29zgs9HRJ6SISesIQesvM7f0zoW14wJfSsEHrIYoVe6VkSesia6bzQUx6hh6zbAb3Q0x2hh0zoiUroIRN6ohJ6yISeqIQeMqEnKqGHpIEFU8eEvu0FU0LPktBDIvSEJfSQRAy90jMn9JCcH/qj1ku1HnpDeq4IPSTNhL5u54WeDgk9JEJPWEIPidATltBDEjL0Ss+M0EPWROfrh771BVOG9FwResg6HdALPR0SesiEnqiEHjKhJyqhh0zoiUroIWug82WFXunJhB6ybgf0Qk93hB4yoScqoYfk3AVTR4a+/QVTQs+C0EMi9IQl9JAIPWEJPSRCT1hCD4nQE5bQQyL0hCX0kJwZ+mPXS3UVeqVH6GGhgdAf0flOQm9ITyL0kJ3V+aND38WCKaEnEXrIhJ6ohB4yoScqoYfs7M6XGXqlR+hhodsBfSehN6RnTughE3qiEnrIhJ6ohB6yY7r+W1veeOMfLwk9RRF6SGosmNrO+w41at/JgilHY5kTekj2h75249dr33foDemZEXpIdoe+TtW/9a1/tFRnaC/0dEfoIakM/c6w/6d135r6iyt1ai/0dEfoIdkIfZ287wr9Ve1/a3fthZ7uCD0ka6E/ovG7Ql8xtF+tvdDTHaGHZBn6IyO/J/R7ai/0dEfoIZmH/oTGHwx9de2Fnu4IPWSbma/Z+EXn94d+u/a/8zu/I/R0Q+ghuX5y5msM6Ctqf/369Q5ab8UUD4Uekml2T638kaHPsZ+FvovUCz1CDw/nlb8K/bGNPyn0s9b/9m9fX7S+zdoLPUIPOfMp9Cdlvu4U/bo7v71Ifasje6FH6Bm760snVv60Af009FMrrW8r9UKP0DNuK5m/fvfkzp8e+tT65SROS6FX+rETekZrrfJT/YR+bWDfRuqFHqFnrDYzf/eFr3Ya+q++cOdOReubn8EReoSeUdqq/FmhP+lY7Ebo20u90CP0jFBV5s8N/bGd3w796gxO06FX+pETekamuvJFhL6l1As9Qs+o7Mx8GaFftr7B+RuhR+gZkd2VLyf089Y3Olcv9Ag9I7In8yWFfpr6Jg/LCj1Cz2jsq3xhoV+kvpG5eqFH6BmJA5k/Z8HUSaH/i72db/KwrNAj9IzB3jmbc0N/0mn0h0J/p7nDskKP0BPeviOwTYX++M4fDv2dhg7LCj1CT3j1Ml9k6Bs5LGvFFEJPcDWH86WGvonDskI/ekJPaPUzf3LoT5yirx/6sw/LCv3oCT2R1a/8eaE/ofO1Q3/n7MOyQj96Qk9cR2W+5NDfOe+wrEn60RN6ojoy8ycvmDox9AcWTFWk/vTDskI/dkJPSMfMzZ8X+lOn6I8O/RmHZYV+7ISeeOqeON9Y6E/o/EmhP/WwrNCPndATzymZH0Lo75x6WNYk/dgJPdGcNJwfSujvXB2WNaSnPqEnllMzP5zQXx2WFXrqEnpCObXygwp9Tv0R8zdCP3IttPYXz00mT339l1u335u8vLFtoadZZ2R+WKE/dv5G6Eeu8dY+uDWZ+8Jm6T+6KfS06qzM3z11wdSpoT9ywVT1oL5u6oV+5Bpv7eXkiZemo/qbk+fXb592Xuhp07mdPy30p55Gf3boj5q/EfqRa7q1H7+Ycn5v8uSPV25+8NfTzgs97Tk782eE/qTOnx/6O/VPtRT6kWu6tYvAP7i1mvWPnptM/uSW0NOWBjI/wNDXH9Q7kX7kmm7t7cnTG3+YuTf5/I8eCD1taaTzJ4X+9JmbRkK/SL0hPXs1H/o8N3+5ejj213+zOcafb1voaUIzmT899Kd1vqHQ1yy90I9bw62d1jyH/t7meTdCTyuayvxQQ1/vTEuhH7fmQ59rLvR0ornODzX0tY7JmqQfN6FnyBrM/EkLps6Yoj9vwVRl6g3p2cHUDcPVZOZPD/2JA/omQ19j+ZTQj1o3B2NnhJ5mnXz1soihP3impdCPWtOtvaw8vXJG6GlUw5kffOgPzN+YpB+15hdMpYH8dtaFniY1nfnhh/7A/I3Qj1lHl0B4KPQ0qfHhfIjQ752/Efox6+yiZkJPc9rofIjQ75m/Efoxa/kyxbeXh2SFnqa00vkYod89f2OSfsyab+2D1TceEXqa10rm756yYOqM0+gbXDBVmfrt+RuhHzFvJcjQtNX5E0N/aufbC/2O+RuhHzGhZ1jambaJFfrq+RtzNyMm9AxJ04ukzgv9WTM3rYa+cv5G6MdL6BmQNjN/YuhP7nzLoa+YvxH68RJ6BqPdzEcL/fb8jdCPl9AzEG1nPl7oN+dvhH68hJ5haL/zR4f+vCn6LkK/Pn8j9OMl9AxBB5k/fsHUeZ1va8HUZuqX8zdCP15CT/m6yHzU0K/M3zi/cryEnuJ10/mwoV/O3wj9aAk9heso84FDfzV/I/SjJfQUrbPMhw79Yv5G6MdK6ClYqwthzw39mSfddBv6PH+j9CMl9JSry8yfFvrTO9916POg/t3rfX9T6YPQU6xOMx8/9Iup+r6/rfRA6ClVx50/dsHUmTM33SyYUnrmhJ5Cdd75E0J/Tuf7CL3Sj5XQU6Rup+dHE/q33npL6sdI6ClQp2fbjDH0Uj8yQk95esn8kaE/e4q+r9AvSi/1YyL0lKanzJ8Q+rM631vo795V+tEResrSW+ZHFPpF6vv+XtMZoacoPXb+qNCfP3PTW+iVfoSEnoL0mfnjFkyd3/keFkzdWQ7pTd+Mi9BTjF4zP7bQL0ov9aMg9BSin1MqTwx9AzM3/YU+l96gfkSEnjL0nfnjQ39e53sK/cqQXupHROgpQu+ZH2XopX4shJ4SFND5EYVe6UdH6ClBAZ0fSeg3h/RSPwpCT/9KGM+PN/RSPwJCT9/6PwybHdf5c0Pfy4Kp6tA71TI8oadnxXT+yNCf2/mSQm9QH53Q06tyMn9E6BsZ0JcVehdFiE3o6VFJmR9T6JV+bISe/pTV+dqhb6bzfYV+55Be6QMTevpSWOaF3kR9XEJPP4rL/HGhP7/zvYZ+f+mlPhyhpxcFdn4sod8zpDeoj0ro6UGJma+/YKqZ0Pe1YGp/6KU+JqGnc0VmfmSh31N6qQ9I6OlaoZ0fT+gPDOlN1Qck9HSr1MzXD31DJ90UHHqD+nCEni6Vm/njQn9+58sOvZPqgxF6OlRy5+uGvqEBfemhV/pQhJ7OFJ15od+k9IEIPR0pPPN1Q99U5/sOfe3SS30EQk83iu98zQVTjYW+vwVTdUPv7Js4hJ4uDCDzR4S+kc73GPrapTeoj0Load8gMi/0laQ+BKGndQPp/IhCX/NwbCL1AQg9LRtK5kcX+mNLL/UDJvS0ajiZrxf65o7F9hr6o4b0BvXDJ/S0aUidrx36Zjo/pNA7qX7ohJ72DCrztULfYOeHFXqlHzahpy0Dy3ytBVMNhr7HBVOnhN70zaAJPS0ZWufrhL7JAX3/oVf68RB6WjG4zAv9QUo/XEJPCwaY+ZGF/qTSS/1gCT2Nuz7Izgt9DUo/UEJP04aZ+bGF/oTDsTNKP0xCT8MGmvk6oW9wtVQZoT+h9M6zHCShp0kDnbWZqxf6pjrfe+hPHNIr/SAJPY25fn3InT+8YKrRzve8YOqM0Ju+GSChpzED77zQ13Vd6odG6GnI0DN/MPQNd37AoTeoHxyhpxHDz/zoQn9W6aV+WISeJgy/8neF/khSPyBCz/lCZH58oW+o9FI/AELPuYJk/r7wKMAAABApSURBVFDoGz2JvpzQn1N6g/rBEHrOEmFufqHbAX0BoT93SH/XSfVDIfScbugnzq/bv2Cq8c73vmCqkdAr/TAIPaeLlHmhP5HSD4HQc6pQw/m7B0LfeOfDhN5E/RAIPaeJlvlRhr7R0kt9wYSeE8Sr/F2hP4PSl07oOVasQ7BL+0Lf+LmVhYS+qdJLfeGEnuNEzfzh0Dfb+YJC30jppb5oQs8Rrl+P2/l9oW+h84WEvrEhvdIXTeg5QuDM3923YKqN0JewYOpOk6GX+oIJPbWFrvzdPaFvpfMBQy/1xRJ6aoqe+RGHXunDE3rqiF/5uyMNfcNDeqkvk9BzUOyZ+aV9nY8b+sZLL/UFEnoOGEvm94e++c4XFXqlD07o2Sf0+ZSbuu18MaFvfkgv9cURenYbVeZ3hb6liZuCQt9G6aW+LELPLuOq/M4FU211vpAFUzPNT97cdamzsgg91caW+V2hb21AX1DoWxnSG9SXROipML7K390R+m8J/RmUvhRCz5ZRZn5f6NvofHGhV/rIhJ51IzsAu6Iq9O11vqjQtzakN31TCKFn1Xgzvzv07XS+rNC3Xnqp75fQc2XMlb9bGfoWOz+W0C9Tr/U9Enpmrq9r6Ue+bNuhb3HiprTQt1l6qe+f0LOZ+bZ+3IvXaedLWjA109rx2LnrWt8voR89g/mFbjtfWOhbHdLfXd3D+t7hR0noR07ll8Yd+nZLr/X9Evox0/g13XZ+bKGX+j4J/UiZsNnWbeeLC337pdf63gj9KKl8lW47X2bo2y691PdD6MfHYH6HsYe+m9JrfR+EflSub2r/p3pAuu38eEMv9d0T+hHR+L1WFkx10fnCFkzNvdVZ6u+u74x9/2iEJ/RjYSh/yDL0XXS+yNB3WfqN1Gt9q4R+FFS+hqvQt3cN+uJD393szZzUd0Xoo9P4uhah76bzJYe+w9RvjuvVvh1CH9jWoVeZ3yeHvqPOFxr6bmdvMq1vndDHtN14lT8khb6rzhcb+o5nbzKpb5fQh1PVeJGvYRb6b3XW+cJD333qjevbJPSRaPw5pqHvsPPlhr6X2ZvMjH1LhD4IjT/ft7rsfIkLpq70Naif2d6N+/7ZikDoh0/jm/FWt50fQOh7Sn1F69X+TEI/aBrfmGnVOs180aFfpr6370flrt33z9twCf1QaXyj3sqh767zZYe+70F9ovZNEfqBqdz1Nf5MKWmdZr700BcwqM927vKSX5/QD4fGt2RRtG47X3zoy0n9XbU/l9CXbvcervFNuJqieOtOt50fQOiX8zcltH5f7SX/AKEv04FdWuOb8daKO0JfobDU3z1Ye8WvJPQlqbEP63tj3lrP/J0Xvtpp5wteMLVq9YvU93dsg+TX10Jrf/HcZPLU1395+Eahr5d2jW/BZuXvCP1ObxUc+zq11/0WQv/g1mTuC788dOM4Q3/UfinvLXhrw1XPhH6nza9Z39/DSsf/aPUdgw413trLyRMvTQfwNyfPH7oxdOiP3+nkvW2btVrPvNDvV/G16/sbusvZP3x916MFTbf24xcnL89+vzd58sf7bxxy6M/ek3bp+0ckoMq8b0V+RugP2POl7Pu7vEMrP6R91+ckTbd20fIHt1Lbd9/YZ+hb+f6fpu8fhVD2lOhQ5e8IfS2Hvqx97wJ79f3DvtR58ppu7e3J0xt/2HXj2aHv+3t1or539rDOSHwi9HUNtvTr+k7BYWcFck3zoc/T8JcrR14rbwwe+r534vE5vfCZ0B9n8KHfpe92rDirkKsaDv2DW4um31s2vfLGh4MO/VlPnFa8u0Pfz2sMxvTVHmZomg99noVfD/32jQ97Df1ZG6ZI48gMEXTfqQGHHoA6Bjx1A0AdAz4YC0AdTbf2supMysobhR6gE80vmEpj9o0FUxU3Cj1AJ1wCASA4FzWD5IUXIm+OUWv5MsW30+8uU0z5hJ6wmm/tg9X3GLm9mJ33xiOUTugJy1sJQiL0hCX0kAg9YQk9JEJPWEIPidATltBDIvSEJfQAwQk9QHBCDxCc0AMEJ/QAwQk9QHBCDxCc0AMEJ/SQWDBFWEIPidATltBDIvSEJfSQCD1hCT0kQk9YQg+J0BOW0EMi9ITVb+gBaMVabPuq/HzjALRirbV9RR6Abgg9QHBCDxCc0AMEJ/QAwQk9QHBCDxCc0AMEJ/QAwQk9QHBCDxCc0G+7N3l58cdfPDeZPPX1X/b5bAry4NYkefLHfT+VcthFttlRKvSbFaHf8tHNxXdksb9+wY/x3Mcv+vndYBepYkfZ1nNWhH7T9Buy+I5cTp54afrye3PyfL9PqRQf3dSzDXaRKnaULX1nRejXPfjr6Tckf0em45L5H+4ZmCSXk6f7fgqFsYtUsqNs6D8rQr/mo+cmkz+5lb8ji+/Eg1vL2bVRu23cusEuUsmOsq6ArAj9mnuTz//o6htwezEuuW2AMvPg1hPf7vs5FMYuUsWOsqGArAj9ml//zcor7dW45NKxtpmPX3zyf/zryeSJP/bFWLCLVLGjbCggK0K/ZfEdmf6evyP3/BTPzI4nzRmvZXaRSnaUCj1nRei3rHxH8hyan+K5y8kTs3N//8+/cuQxs4tUsqNU6DkrQr9F6A/4+EXH2hK7yF52lBVCXxpTN4eYkM7sIvvZUZZM3fQvzSkuJhQdjF23/tWZUbUFu8hedpQlB2P7tyP0l86dmxH63ewie9lRlnrOitBvebBc2ZB2U6th5pb/51S1BbtIBTtKlZ6zIvRbrr4B1revu8xfh+XlmUbPLlLFjlKh56wI/ZblK60rVq2Z7qGf/9H86+E/5At2kQp2lAo9Z0Xotyy/I65Bu+7eTV+PDXaRKnaUbT1nRei3rMydPfCuEmt+/efTn+CnXvL1WLKLVLGjbOk5K0IPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9ADBCT1AcEIPEJzQAwQn9IzZu4d1+GyuH9bhsyEQoWfMhJ5REHrG7N1339uv49Df3U/oOY3QM2ZCzygIPWMm9IyC0DNmQs8oCD1jJvSMgtAzZkLPKAg9Yyb0jILQ07XXLrJrn3315+mmD25cPLv9F+//5x+ufpj+0m++ePH4vkdPd6p+wG1CzygIPV27Cv3Up745v6myyz+98YnjQ5/v1GPo7//Dzk/95ovXvrnvrmeG/tDDM15CT9deu/h0+sOvfnrjYk+a3r5YD31yIPTVd9qp+dD/9MbuVxihpydCT9euQj+v9u4uDzL0979R778SlUzd0BKhp2sroZ9NsezMttALPQ0Rerq2GvrpB4/8fDml/vdfvri4+OQfzg7Rvp8m8Z+dfu4T//07s9n85Rz9h69cXFz73fmB3KvJ+Pdns0Ard8o3vzN7xM+++nDxdz+cffzYDxabF3pGQejp2lro531edPntfIh2NihfDf0/nd92FfrP3Ugn7cwmpPeH/v538iPOXxWmNz6zcteZuqF/f/p69Lc3li8R919/dPGKlD9IrybpX/D44sb8avT+xePv35i+VC0m0Vfvvfjc7M+1Q7/+dOo+POMl9HRtLfSpyFe/zsL4zo30F/IszPTWi9/7+f3vLc+6ubj2tdlBz7X/C+RXjJU7PTvf1OwRZ7n/dH6kT33/4f3/cnH1DKah33uN4pXQ/5v0EvFsftbLF4zpIP5i0fer0H/4pZW/8f78temRn+cSr9178bnZw05Dv/caxauhX3k6dR+e8RJ6urYW+jTlnrr8dg5SjvWy2Y+szNLMQr+I7eMHQn91BODtxf8b0gT+a1cT+fVDP3/JmOZ7ds/pc/jUdPz+P7+U/+9xbfrB/b+df5Cnbqa/TV9SHn74yuJ/J4/84OHP8mkxm/dOn5s5IvSrT6fuwzNeQk/X9oR+7UDqstmp1lehz+PT+fT+3tBfPeDVVh7Pf/eE0D++fKDF46aP1v49OfRvL5/k4/N7P5v+/uw5rt978bmZY0L/+PZDHHp4xkvo6drO0L8/m1leLjdan4XZXjA1//y+0E+ju9hS5YvCw2NCn18aZgWfPu7VU5g+7NsXF7939axT6JeHZGez6Vf3npd4497vr7y6HRH6ladT++EZL6GnaztDn9bMXnvs++lTO0N/1dBp1w6EfnEm5tu7Q1/7YGz+wyd+uPoUplubTSZdXHwundmTEp9uujqyvLj3vMQb935/ZQL9qIOx2w9x6OEZL6GnazsPxj58+NNH02HEr80+ODv0K6fcV47+H54Q+g9urIb+g/kFFxbn9syOJB8T+vm9zwv92kMcenjGS+jp2u7TK6fu/+WX0wmSwxnRz/z9v300nW1zFfrVmXEjenom9HRtz4KpJJ852dEcfc3Q756jz+7Pt3E1R7+6fHetxFuT6CeFfn2Ovt7DM15CT9c2LoHw7MOtLqda7wz9p1ce5+qzr9U66+b00O886+aqrO8vQz/7Gz/I/5TNEm+dFnNS6NfPuqn38IyX0NO19YuaPZLXrK52+bX9I/pU6XTi4KL7i5sPnEd/Rugvfm/zPPp3vpRfkK79UVrn9fjVWH72dF5Ns/fPbpZ4/d6nhn7l6dR9eMZL6OnaVeh/9vriMsVXDZ+tMsp1XOR4O/SrK2NnZ+pMkzfN2mIl6OqdtlbGnh76T31p5eIJ1StjF88n/0/jarnsRok3l66eFPrVp1P34Rkvoadra288kiY4coLfX9Txd/ONs05uh/4P0l/71Hz4/2E6weUT//ViWbmrO21d6+aMg7H/6zs3Fteu2bjWzcOffma6iU9+bf7R/VdS8dO1bhYXo1kr8cbFaE47GLvydOo+POMl9HTtKvSffOzVfNMiwR++cmPlRPrpoL0y9M/Or165qOzsPtPiLeK9cad09crvr23lnLNuWnX8WTdQi9AzZkLPKAg9Yyb0jILQM2ZCzygIPWMm9IyC0DNmey9dmXT4bPZeujLp8NkQiNAzZkLPKAg9QHBCDxCc0AMEJ/QAwQk9QHBCDxCc0AMEJ/QAwQk9QHBCDxCc0AMEJ/QAwQk9QHBCDxCc0AMEJ/QAwQk9QHBCDxCc0AMEJ/QAwQk9QHBCDxCc0AMEJ/QAwf1/63AlX6QxBHcAAAAASUVORK5CYII=" width="100%" /></p>
<p>Note that <strong>interpretation guides</strong> for Bayes factors can be found in the <code>effectsize</code> package:</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>effectsize<span class="sc">::</span><span class="fu">interpret_bf</span>(<span class="fu">exp</span>(My_first_BF<span class="sc">$</span>log_BF[<span class="dv">2</span>]), <span class="at">include_value =</span> <span class="cn">TRUE</span>)</span></code></pre></div>
<pre><code>> [1] "anecdotal evidence (BF = 1/1.13) against"
> (Rules: jeffreys1961)</code></pre>
</div>
<div id="testing-against-the-point-null-0" class="section level3">
<h3>Testing against the <em>point</em>-null (0)</h3>
<blockquote>
<p><strong>What if we don’t know what region would be practically equivalent to 0?</strong></p>
</blockquote>
<p>Or if we just want the null to be exactly zero? Not a problem - as the width of null region shrinks to a point, the change from the prior probability to the posterior probability of the null can be estimated by comparing the density of the null value between the two distributions.<a href="#fn1" class="footnote-ref" id="fnref1"><sup>1</sup></a> This ratio is called the <strong>Savage-Dickey ratio</strong>, and has the added benefit of also being an approximation of a Bayes factor comparing the estimated model against the a model in which the parameter of interest has been restricted to a point-null:</p>
<blockquote>
<p>“[…] the Bayes factor for <span class="math inline">\(H_0\)</span> versus <span class="math inline">\(H_1\)</span> could be obtained by analytically integrating out the model parameter <span class="math inline">\(\theta\)</span>. However, the Bayes factor may likewise be obtained by only considering <span class="math inline">\(H_1\)</span>, and dividing the height of the posterior for <span class="math inline">\(\theta\)</span> by the height of the prior for <span class="math inline">\(\theta\)</span>, at the point of interest.” <span class="citation">(Wagenmakers, Lodewyckx, Kuriyal, & Grasman, 2010)</span></p>
</blockquote>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>My_second_BF <span class="ot"><-</span> <span class="fu">bayesfactor_parameters</span>(model, <span class="at">null =</span> <span class="dv">0</span>)</span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>My_second_BF</span></code></pre></div>
<pre><code>> Bayes Factor (Savage-Dickey density ratio)
>
> Parameter | BF
> ----------------
> group2 | 1.24
>
> * Evidence Against The Null: 0</code></pre>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(My_second_BF)</span></code></pre></div>
<p><img 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" width="100%" /></p>
</div>
<div id="directional-hypotheses" class="section level3">
<h3>Directional hypotheses</h3>
<p>We can also compute Bayes factors for directional hypotheses (“one sided”), if we have a prior hypotheses about the direction of the effect. This can be done by setting an <em>order restriction</em> on the prior distribution (which results in an order restriction on the posterior distribution) of the alternative <span class="citation">(Morey & Wagenmakers, 2014)</span>. For example, if we have a prior hypothesis that <em>the drug has a positive effect on the number of sleep hours</em>, the alternative will be restricted to the region to the right of the null (point or interval):</p>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>test_group2_right <span class="ot"><-</span> <span class="fu">bayesfactor_parameters</span>(model, <span class="at">direction =</span> <span class="st">">"</span>)</span>
<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a>test_group2_right</span></code></pre></div>
<pre><code>> Bayes Factor (Savage-Dickey density ratio)
>
> Parameter | BF
> ----------------
> group2 | 2.37
>
> * Evidence Against The Null: 0
> * Direction: Right-Sided test</code></pre>
<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(test_group2_right)</span></code></pre></div>
<p><img src="data:image/png;base64,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" width="100%" /></p>
<p>As we can see, given that we have an <em>a priori</em> assumption about the direction of the effect (that the effect is positive), <strong>the presence of an effect is 2.8 times more likely than the absence of an effect</strong>, given the observed data (or that the data are 2.8 time more probable under <span class="math inline">\(H_1\)</span> than <span class="math inline">\(H_0\)</span>). This indicates that, given the observed data, and a priori hypothesis, the posterior mass has shifted away from the null value, giving some evidence against the null (note that a Bayes factor of 2.8 is still considered quite <a href="https://easystats.github.io/effectsize/reference/interpret_bf.html">weak evidence</a>).</p>
<p>Thanks to the flexibility of Bayesian framework, it is also possible to compute a Bayes factor for <strong>dividing</strong> hypotheses - that is, for a null and alternative that are <em>complementary</em>, opposing one-sided hypotheses <span class="citation">(Morey & Wagenmakers, 2014)</span>.</p>
<p>For example, above we compared an alternative of <span class="math inline">\(H_A\)</span>: <em>the drug has a positive effects</em> to the null <span class="math inline">\(H_0\)</span>: <em>the drug has no effect</em>. But we can also compare instead the same alternative to its <em>complementary</em> hypothesis: <span class="math inline">\(H_{-A}\)</span>: <em>the drug has a negative effects</em>.</p>
<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a>test_group2_dividing <span class="ot"><-</span> <span class="fu">bayesfactor_parameters</span>(model, <span class="at">null =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="cn">Inf</span>, <span class="dv">0</span>))</span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a>test_group2_dividing</span></code></pre></div>
<pre><code>> Bayes Factor (Null-Interval)
>
> Parameter | BF
> -----------------
> group2 | 20.53
>
> * Evidence Against The Null: [-Inf, 0.000]</code></pre>
<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(test_group2_dividing)</span></code></pre></div>
<p><img src="data:image/png;base64,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" width="100%" /></p>
<p>We can see that this test produces even stronger (more conclusive) evidence than the one-sided vs. point-null test! And indeed, as a rule of thumb, the more specific the two hypotheses are, and the more distinct they are from one another, the more <em>power</em> our Bayes factor has!<a href="#fn2" class="footnote-ref" id="fnref2"><sup>2</sup></a></p>
<p>Thanks to the transitivity of Bayes factors, we can also use <code>bayesfactor_parameters()</code> to compare even more types of hypotheses, with some trickery. For example:</p>
<p><span class="math display">\[
\underbrace{BF_{0<b<1\text{ vs. }b=0}}_{\text{range vs. point}}
=
\underbrace{BF_{b<0\text{ vs. }b=0}}_{\text{directional vs. point}}
/
\underbrace{BF_{b<0\text{ vs. }0<b<1}}_{\text{directional vs. range}}
\]</span></p>
<p><strong>NOTE</strong>: See the <em>Testing Contrasts</em> appendix below.</p>
</div>
<div id="si" class="section level3">
<h3>Support intervals</h3>
<p>So far we’ve seen that Bayes factors quantify relative support between competing hypotheses. However, we can also ask:</p>
<blockquote>
<p><strong>Upon observing the data, the credibility of which of the parameter’s values has increased (or decreased)?</strong></p>
</blockquote>
<p>For example, we’ve seen that the point null has become somewhat less credible after observing the data, but we might also ask which values have <strong>gained</strong> credibility given the observed data?. The resulting range of values is called <strong>the support interval</strong> as it indicates which values are supported by the data <span class="citation">(Wagenmakers, Gronau, Dablander, & Etz, 2018)</span>. We can do this by once again comparing the prior and posterior distributions and checking where the posterior densities are higher than the prior densities.</p>
<p>In <code>bayestestR</code>, this can be achieved with the <code>si()</code> function:</p>
<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a>my_first_si <span class="ot"><-</span> <span class="fu">si</span>(</span>
<span id="cb16-2"><a href="#cb16-2" aria-hidden="true" tabindex="-1"></a> <span class="at">posterior =</span> <span class="fu">data.frame</span>(<span class="at">group2 =</span> posterior),</span>
<span id="cb16-3"><a href="#cb16-3" aria-hidden="true" tabindex="-1"></a> <span class="at">prior =</span> <span class="fu">data.frame</span>(<span class="at">group2 =</span> prior),</span>
<span id="cb16-4"><a href="#cb16-4" aria-hidden="true" tabindex="-1"></a> <span class="at">BF =</span> <span class="dv">1</span></span>
<span id="cb16-5"><a href="#cb16-5" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb16-6"><a href="#cb16-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb16-7"><a href="#cb16-7" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(my_first_si)</span></code></pre></div>
<pre><code>> Support Interval
>
> Parameter | BF = 1 SI
> ------------------------
> group2 | [0.15, 3.04]</code></pre>
<p>The argument <code>BF = 1</code> indicates that we want the interval to contain values that have gained support by a factor of at least 1 (that is, any support at all).</p>
<p>Visually, we can see that the credibility of all the values within this interval has increased (and likewise the credibility of all the values outside this interval has decreased):</p>
<div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(my_first_si)</span></code></pre></div>
<p><img 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" width="100%" /></p>
<p>We can also see the this support interval (just barely) excludes the point null (0) - whose credibility we’ve already seen has decreased by the observed data. This emphasizes the relationship between the support interval and the Bayes factor:</p>
<blockquote>
<p>“The interpretation of such intervals would be analogous to how a frequentist confidence interval contains all the parameter values that would not have been rejected if tested at level <span class="math inline">\(\alpha\)</span>. For instance, a BF = 1/3 support interval encloses all values of theta for which the updating factor is not stronger than 3 against.” <span class="citation">(Wagenmakers et al., 2018)</span></p>
</blockquote>
<p>Thus, the choice of BF (the level of support the interval should indicate) depends on what we want our interval to represent:</p>
<ul>
<li>A <span class="math inline">\(BF = 1\)</span> contains values whose credibility has merely not decreased by observing the data.</li>
<li>A <span class="math inline">\(BF > 1\)</span> contains values who received more impressive support from the data.<br />
</li>
<li>A <span class="math inline">\(BF < 1\)</span> contains values whose credibility has <em>not</em> been impressively decreased by observing the data. Testing against values outside this interval will produce a Bayes factor larger than <span class="math inline">\(1/BF\)</span> in support of the alternative.</li>
</ul>
</div>
</div>
<div id="bayesfactor_models" class="section level1">
<h1>Comparing Models using Bayes Factors</h1>
<p>Bayes factors can also be used to compare statistical <strong>models</strong>. In this statistical context, they answer the following question:</p>
<blockquote>
<p><strong>Under which model are the observed data more probable?</strong></p>
</blockquote>
<p>In other words, which model is more likely to have produced the observed data? This is usually done by comparing the marginal likelihoods of two models. In such a case, the Bayes factor is a measure of the <strong>relative</strong> evidence for one model over the other.</p>
<p>Let’s use Bayes factors for model comparison to find a model that best describes the length of an iris’ sepal using the <code>iris</code> data set.</p>
<div id="for-bayesian-models-brms-and-rstanarm" class="section level3">
<h3>For Bayesian models (<code>brms</code> and <code>rstanarm</code>)</h3>
<p><strong>Note: In order to compute Bayes factors for Bayesian models, non-default arguments must be added upon fitting:</strong></p>
<ul>
<li><code>brmsfit</code> models <strong>must</strong> have been fitted with <code>save_pars = save_pars(all = TRUE)</code></li>
<li><code>stanreg</code> models <strong>must</strong> have been fitted with a defined <code>diagnostic_file</code>.</li>
</ul>
<p>Let’s first fit 5 Bayesian regressions with <code>brms</code> to predict <code>Sepal.Length</code>:</p>
<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(brms)</span>
<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb19-3"><a href="#cb19-3" aria-hidden="true" tabindex="-1"></a><span class="co"># intercept only model</span></span>
<span id="cb19-4"><a href="#cb19-4" aria-hidden="true" tabindex="-1"></a>m0 <span class="ot"><-</span> <span class="fu">brm</span>(Sepal.Length <span class="sc">~</span> <span class="dv">1</span>, <span class="at">data =</span> iris, </span>
<span id="cb19-5"><a href="#cb19-5" aria-hidden="true" tabindex="-1"></a> <span class="at">prior =</span> </span>
<span id="cb19-6"><a href="#cb19-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_prior</span>(<span class="st">"student_t(3, 6, 6)"</span>, <span class="at">class =</span> <span class="st">"Intercept"</span>) <span class="sc">+</span> </span>
<span id="cb19-7"><a href="#cb19-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_prior</span>(<span class="st">"student_t(3, 0, 6)"</span>, <span class="at">class =</span> <span class="st">"sigma"</span>),</span>
<span id="cb19-8"><a href="#cb19-8" aria-hidden="true" tabindex="-1"></a> <span class="at">save_pars =</span> <span class="fu">save_pars</span>(<span class="at">all =</span> <span class="cn">TRUE</span>), <span class="at">backend =</span> <span class="st">"rstan"</span>)</span>
<span id="cb19-9"><a href="#cb19-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb19-10"><a href="#cb19-10" aria-hidden="true" tabindex="-1"></a><span class="co"># Petal.Length only</span></span>
<span id="cb19-11"><a href="#cb19-11" aria-hidden="true" tabindex="-1"></a>m1 <span class="ot"><-</span> <span class="fu">brm</span>(Sepal.Length <span class="sc">~</span> Petal.Length, <span class="at">data =</span> iris, </span>
<span id="cb19-12"><a href="#cb19-12" aria-hidden="true" tabindex="-1"></a> <span class="at">prior =</span> </span>
<span id="cb19-13"><a href="#cb19-13" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_prior</span>(<span class="st">"student_t(3, 6, 6)"</span>, <span class="at">class =</span> <span class="st">"Intercept"</span>) <span class="sc">+</span> </span>
<span id="cb19-14"><a href="#cb19-14" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_prior</span>(<span class="st">"student_t(3, 0, 6)"</span>, <span class="at">class =</span> <span class="st">"sigma"</span>) <span class="sc">+</span> </span>
<span id="cb19-15"><a href="#cb19-15" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_prior</span>(<span class="st">"normal(0, 1)"</span>, <span class="at">coef =</span> <span class="st">"Petal.Length"</span>),</span>
<span id="cb19-16"><a href="#cb19-16" aria-hidden="true" tabindex="-1"></a> <span class="at">save_pars =</span> <span class="fu">save_pars</span>(<span class="at">all =</span> <span class="cn">TRUE</span>))</span>
<span id="cb19-17"><a href="#cb19-17" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb19-18"><a href="#cb19-18" aria-hidden="true" tabindex="-1"></a><span class="co"># Species only</span></span>
<span id="cb19-19"><a href="#cb19-19" aria-hidden="true" tabindex="-1"></a>m2 <span class="ot"><-</span> <span class="fu">brm</span>(Sepal.Length <span class="sc">~</span> Species, <span class="at">data =</span> iris,</span>
<span id="cb19-20"><a href="#cb19-20" aria-hidden="true" tabindex="-1"></a> <span class="at">prior =</span> </span>
<span id="cb19-21"><a href="#cb19-21" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_prior</span>(<span class="st">"student_t(3, 6, 6)"</span>, <span class="at">class =</span> <span class="st">"Intercept"</span>) <span class="sc">+</span> </span>
<span id="cb19-22"><a href="#cb19-22" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_prior</span>(<span class="st">"student_t(3, 0, 6)"</span>, <span class="at">class =</span> <span class="st">"sigma"</span>) <span class="sc">+</span> </span>
<span id="cb19-23"><a href="#cb19-23" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_prior</span>(<span class="st">"normal(0, 3)"</span>, <span class="at">coef =</span> <span class="fu">c</span>(<span class="st">"Speciesversicolor"</span>, <span class="st">"Speciesvirginica"</span>)),</span>
<span id="cb19-24"><a href="#cb19-24" aria-hidden="true" tabindex="-1"></a> <span class="at">save_pars =</span> <span class="fu">save_pars</span>(<span class="at">all =</span> <span class="cn">TRUE</span>))</span>
<span id="cb19-25"><a href="#cb19-25" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb19-26"><a href="#cb19-26" aria-hidden="true" tabindex="-1"></a><span class="co"># Species + Petal.Length model</span></span>
<span id="cb19-27"><a href="#cb19-27" aria-hidden="true" tabindex="-1"></a>m3 <span class="ot"><-</span> <span class="fu">brm</span>(Sepal.Length <span class="sc">~</span> Species <span class="sc">+</span> Petal.Length, <span class="at">data =</span> iris,</span>
<span id="cb19-28"><a href="#cb19-28" aria-hidden="true" tabindex="-1"></a> <span class="at">prior =</span> </span>
<span id="cb19-29"><a href="#cb19-29" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_prior</span>(<span class="st">"student_t(3, 6, 6)"</span>, <span class="at">class =</span> <span class="st">"Intercept"</span>) <span class="sc">+</span> </span>
<span id="cb19-30"><a href="#cb19-30" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_prior</span>(<span class="st">"student_t(3, 0, 6)"</span>, <span class="at">class =</span> <span class="st">"sigma"</span>) <span class="sc">+</span> </span>
<span id="cb19-31"><a href="#cb19-31" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_prior</span>(<span class="st">"normal(0, 1)"</span>, <span class="at">coef =</span> <span class="st">"Petal.Length"</span>) <span class="sc">+</span> </span>
<span id="cb19-32"><a href="#cb19-32" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_prior</span>(<span class="st">"normal(0, 3)"</span>, <span class="at">coef =</span> <span class="fu">c</span>(<span class="st">"Speciesversicolor"</span>, <span class="st">"Speciesvirginica"</span>)),</span>
<span id="cb19-33"><a href="#cb19-33" aria-hidden="true" tabindex="-1"></a> <span class="at">save_pars =</span> <span class="fu">save_pars</span>(<span class="at">all =</span> <span class="cn">TRUE</span>))</span>
<span id="cb19-34"><a href="#cb19-34" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb19-35"><a href="#cb19-35" aria-hidden="true" tabindex="-1"></a><span class="co"># full interactive model</span></span>
<span id="cb19-36"><a href="#cb19-36" aria-hidden="true" tabindex="-1"></a>m4 <span class="ot"><-</span> <span class="fu">brm</span>(Sepal.Length <span class="sc">~</span> Species <span class="sc">*</span> Petal.Length, <span class="at">data =</span> iris,</span>
<span id="cb19-37"><a href="#cb19-37" aria-hidden="true" tabindex="-1"></a> <span class="at">prior =</span> </span>
<span id="cb19-38"><a href="#cb19-38" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_prior</span>(<span class="st">"student_t(3, 6, 6)"</span>, <span class="at">class =</span> <span class="st">"Intercept"</span>) <span class="sc">+</span> </span>
<span id="cb19-39"><a href="#cb19-39" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_prior</span>(<span class="st">"student_t(3, 0, 6)"</span>, <span class="at">class =</span> <span class="st">"sigma"</span>) <span class="sc">+</span> </span>
<span id="cb19-40"><a href="#cb19-40" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_prior</span>(<span class="st">"normal(0, 1)"</span>, <span class="at">coef =</span> <span class="st">"Petal.Length"</span>) <span class="sc">+</span> </span>
<span id="cb19-41"><a href="#cb19-41" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_prior</span>(<span class="st">"normal(0, 3)"</span>, <span class="at">coef =</span> <span class="fu">c</span>(<span class="st">"Speciesversicolor"</span>, <span class="st">"Speciesvirginica"</span>)) <span class="sc">+</span> </span>
<span id="cb19-42"><a href="#cb19-42" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_prior</span>(<span class="st">"normal(0, 2)"</span>, <span class="at">coef =</span> <span class="fu">c</span>(<span class="st">"Speciesversicolor:Petal.Length"</span>, <span class="st">"Speciesvirginica:Petal.Length"</span>)),</span>
<span id="cb19-43"><a href="#cb19-43" aria-hidden="true" tabindex="-1"></a> <span class="at">save_pars =</span> <span class="fu">save_pars</span>(<span class="at">all =</span> <span class="cn">TRUE</span>))</span></code></pre></div>
<p>We can now compare these models with the <code>bayesfactor_models()</code> function, using the <code>denominator</code> argument to specify the model against which the rest of the models will be compared (in this case, the intercept-only model):</p>
<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(bayestestR)</span>
<span id="cb20-2"><a href="#cb20-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb20-3"><a href="#cb20-3" aria-hidden="true" tabindex="-1"></a>comparison <span class="ot"><-</span> <span class="fu">bayesfactor_models</span>(m1, m2, m3, m4, <span class="at">denominator =</span> m0)</span>
<span id="cb20-4"><a href="#cb20-4" aria-hidden="true" tabindex="-1"></a>comparison</span></code></pre></div>
<pre><code>> Bayes Factors for Model Comparison
>
> Model BF
> [1] Petal.Length 1.27e+44
> [2] Species 8.34e+27
> [3] Species + Petal.Length 2.29e+53
> [4] Species * Petal.Length 9.79e+51
>
> * Against Denominator: [5] (Intercept only)
> * Bayes Factor Type: marginal likelihoods (bridgesampling)</code></pre>
<p>We can see that the <code>Species + Petal.Length</code> model is the best model - with <span class="math inline">\(BF=2\times 10^{53}\)</span> compared to the null (intercept only).</p>
<p>Due to the transitive property of Bayes factors, we can easily change the reference model to the full <code>Species * Petal.Length</code> model:</p>
<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a><span class="fu">update</span>(comparison, <span class="at">reference =</span> <span class="dv">4</span>)</span></code></pre></div>
<pre><code>> Bayes Factors for Model Comparison
>
> Model BF
> [1] Petal.Length 1.30e-08
> [2] Species 8.52e-25
> [3] Species + Petal.Length 23.38
> [5] (Intercept only) 1.02e-52
>
> * Against Denominator: [4] Species * Petal.Length
> * Bayes Factor Type: marginal likelihoods (bridgesampling)</code></pre>
<p>As we can see, the <code>Species + Petal.Length</code> model is also favored compared to the <code>Species * Petal.Length</code> model, though to several orders of magnitude less - is is only supported 23.38 times more!)</p>
<p>We can also change the reference model to the <code>Species</code> model:</p>
<div class="sourceCode" id="cb24"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a><span class="fu">update</span>(comparison, <span class="at">reference =</span> <span class="dv">2</span>)</span></code></pre></div>
<pre><code>> Bayes Factors for Model Comparison
>
> Model BF
> [1] Petal.Length 1.53e+16
> [3] Species + Petal.Length 2.74e+25
> [4] Species * Petal.Length 1.17e+24
> [5] (Intercept only) 1.20e-28
>
> * Against Denominator: [2] Species
> * Bayes Factor Type: marginal likelihoods (bridgesampling)</code></pre>
<p>Notice that, in the Bayesian framework the compared models <em>do not</em> need to be nested models, as happened here when we compared the <code>Petal.Length</code>-only model to the <code>Species</code>-only model (something that cannot be done in the frequentist framework, where compared models must be nested in one another).</p>
<p>We can also get a matrix of Bayes factors of all the pairwise model comparisons:</p>
<div class="sourceCode" id="cb26"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a><span class="fu">as.matrix</span>(comparison)</span></code></pre></div>
<pre><code>> # Bayes Factors for Model Comparison
>
> Numerator
> Denominator
>
> | [1] | [2] | [3] | [4] | [5]
> ---------------------------------------------------------------------------------
> [1] Petal.Length | 1 | 6.54e-17 | 1.80e+09 | 7.68e+07 | 7.85e-45
> [2] Species | 1.53e+16 | 1 | 2.74e+25 | 1.17e+24 | 1.20e-28
> [3] Species + Petal.Length | 5.57e-10 | 3.64e-26 | 1 | 0.043 | 4.37e-54
> [4] Species * Petal.Length | 1.30e-08 | 8.52e-25 | 23.38 | 1 | 1.02e-52
> [5] (Intercept only) | 1.27e+44 | 8.34e+27 | 2.29e+53 | 9.79e+51 | 1</code></pre>
<p><strong>NOTE:</strong> In order to correctly and precisely estimate Bayes Factors, you always need the 4 P’s: <strong>P</strong>roper <strong>P</strong>riors,<a href="#fn3" class="footnote-ref" id="fnref3"><sup>3</sup></a> and a <strong>P</strong>lentiful <strong>P</strong>osterior.<a href="#fn4" class="footnote-ref" id="fnref4"><sup>4</sup></a></p>
</div>
<div id="for-frequentist-models-via-the-bic-approximation" class="section level3">
<h3>For Frequentist models via the BIC approximation</h3>
<p>It is also possible to compute Bayes factors for the comparison of frequentist models. This is done by comparing BIC measures, allowing a Bayesian comparison of non-nested frequentist models <span class="citation">(Wagenmakers, 2007)</span>.</p>
<p>Let’s try it out on some <strong>linear mixed-effects models</strong>:</p>
<div class="sourceCode" id="cb28"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb28-1"><a href="#cb28-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(lme4)</span>
<span id="cb28-2"><a href="#cb28-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-3"><a href="#cb28-3" aria-hidden="true" tabindex="-1"></a><span class="co"># define models with increasing complexity</span></span>
<span id="cb28-4"><a href="#cb28-4" aria-hidden="true" tabindex="-1"></a>m0 <span class="ot"><-</span> <span class="fu">lmer</span>(Sepal.Length <span class="sc">~</span> (<span class="dv">1</span> <span class="sc">|</span> Species), <span class="at">data =</span> iris)</span>
<span id="cb28-5"><a href="#cb28-5" aria-hidden="true" tabindex="-1"></a>m1 <span class="ot"><-</span> <span class="fu">lmer</span>(Sepal.Length <span class="sc">~</span> Petal.Length <span class="sc">+</span> (<span class="dv">1</span> <span class="sc">|</span> Species), <span class="at">data =</span> iris)</span>
<span id="cb28-6"><a href="#cb28-6" aria-hidden="true" tabindex="-1"></a>m2 <span class="ot"><-</span> <span class="fu">lmer</span>(Sepal.Length <span class="sc">~</span> Petal.Length <span class="sc">+</span> (Petal.Length <span class="sc">|</span> Species), <span class="at">data =</span> iris)</span>
<span id="cb28-7"><a href="#cb28-7" aria-hidden="true" tabindex="-1"></a>m3 <span class="ot"><-</span> <span class="fu">lmer</span>(Sepal.Length <span class="sc">~</span> Petal.Length <span class="sc">+</span> Petal.Width <span class="sc">+</span> (Petal.Length <span class="sc">|</span> Species), <span class="at">data =</span> iris)</span>
<span id="cb28-8"><a href="#cb28-8" aria-hidden="true" tabindex="-1"></a>m4 <span class="ot"><-</span> <span class="fu">lmer</span>(Sepal.Length <span class="sc">~</span> Petal.Length <span class="sc">*</span> Petal.Width <span class="sc">+</span> (Petal.Length <span class="sc">|</span> Species), <span class="at">data =</span> iris)</span>
<span id="cb28-9"><a href="#cb28-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-10"><a href="#cb28-10" aria-hidden="true" tabindex="-1"></a><span class="co"># model comparison</span></span>
<span id="cb28-11"><a href="#cb28-11" aria-hidden="true" tabindex="-1"></a><span class="fu">bayesfactor_models</span>(m1, m2, m3, m4, <span class="at">denominator =</span> m0)</span></code></pre></div>
<pre><code>> Bayes Factors for Model Comparison
>
> Model BF
> [m1] Petal.Length + (1 | Species) 8.24e+24
> [m2] Petal.Length + (Petal.Length | Species) 4.77e+23
> [m3] Petal.Length + Petal.Width + (Petal.Length | Species) 1.52e+22
> [m4] Petal.Length * Petal.Width + (Petal.Length | Species) 5.93e+20
>
> * Against Denominator: [m0] 1 + (1 | Species)
> * Bayes Factor Type: BIC approximation</code></pre>
</div>
<div id="bayesfactor_restricted" class="section level3">
<h3>Order restricted models</h3>
<p>As stated above when discussing one-sided hypothesis tests, we can create new models by imposing order restrictions on a given model. For example, consider the following model, in which we predict the length of an iris’ sepal from the length of its petal, as well as from its species, with priors: - <span class="math inline">\(b_{petal} \sim N(0,2)\)</span> - <span class="math inline">\(b_{versicolors}\ \&\ b_{virginica} \sim N(0,1.2)\)</span></p>
<div class="sourceCode" id="cb30"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb30-1"><a href="#cb30-1" aria-hidden="true" tabindex="-1"></a>iris_model <span class="ot"><-</span> <span class="fu">stan_glm</span>(Sepal.Length <span class="sc">~</span> Species <span class="sc">+</span> Petal.Length,</span>
<span id="cb30-2"><a href="#cb30-2" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> iris,</span>
<span id="cb30-3"><a href="#cb30-3" aria-hidden="true" tabindex="-1"></a> <span class="at">prior =</span> <span class="fu">normal</span>(<span class="dv">0</span>, <span class="fu">c</span>(<span class="dv">2</span>, <span class="fl">1.2</span>, <span class="fl">1.2</span>), <span class="at">autoscale =</span> <span class="cn">FALSE</span>),</span>
<span id="cb30-4"><a href="#cb30-4" aria-hidden="true" tabindex="-1"></a> <span class="at">refresh =</span> <span class="dv">0</span></span>
<span id="cb30-5"><a href="#cb30-5" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
<p>These priors are <strong>unrestricted</strong> - that is, <strong>all values</strong> between <span class="math inline">\(-\infty\)</span> and <span class="math inline">\(\infty\)</span> of all parameters in the model have some non-zero credibility (no matter how small; this is true for both the prior and posterior distribution). Subsequently, <em>a priori</em> the ordering of the parameters relating to the iris species can have any ordering, such that <em>a priori</em> setosa can have larger sepals than virginica, but it is also possible for virginica to have larger sepals than setosa!</p>
<p>Does it make sense to let our priors cover all of these possibilities? That depends on our <em>prior</em> knowledge or hypotheses. For example, even a novice botanist will assume that it is unlikely that petal length will be <em>negatively</em> associated with sepal length - an iris with longer petals is likely larger, and thus will also have a longer sepal. And an expert botanist will perhaps assume that setosas have smaller sepals than both versicolors and virginica.</p>
<p>These priors can be formulated as <strong>restricted</strong> priors <span class="citation">(Morey, 2015; Morey & Rouder, 2011)</span>:</p>
<ol style="list-style-type: decimal">
<li>The novice botanist: <span class="math inline">\(b_{petal} > 0\)</span></li>
<li>The expert botanist: <span class="math inline">\(b_{versicolors} > 0\ \&\ b_{virginica} > 0\)</span></li>
</ol>
<p>By testing these restrictions on prior and posterior samples, we can see how the probabilities of the restricted distributions change after observing the data. This can be achieved with <code>bayesfactor_restricted()</code>, that compute a Bayes factor for these restricted model vs the unrestricted model. Let’s first specify these restrictions as logical conditions:</p>
<div class="sourceCode" id="cb31"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb31-1"><a href="#cb31-1" aria-hidden="true" tabindex="-1"></a>botanist_hypotheses <span class="ot"><-</span> <span class="fu">c</span>(</span>
<span id="cb31-2"><a href="#cb31-2" aria-hidden="true" tabindex="-1"></a> <span class="st">"Petal.Length > 0"</span>,</span>
<span id="cb31-3"><a href="#cb31-3" aria-hidden="true" tabindex="-1"></a> <span class="st">"(Speciesversicolor > 0) & (Speciesvirginica > 0)"</span></span>
<span id="cb31-4"><a href="#cb31-4" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
<p>Let’s test these hypotheses:</p>
<div class="sourceCode" id="cb32"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb32-1"><a href="#cb32-1" aria-hidden="true" tabindex="-1"></a>model_prior <span class="ot"><-</span> <span class="fu">unupdate</span>(iris_model)</span>
<span id="cb32-2"><a href="#cb32-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb32-3"><a href="#cb32-3" aria-hidden="true" tabindex="-1"></a>botanist_BFs <span class="ot"><-</span> <span class="fu">bayesfactor_restricted</span>(</span>
<span id="cb32-4"><a href="#cb32-4" aria-hidden="true" tabindex="-1"></a> <span class="at">posterior =</span> iris_model,</span>
<span id="cb32-5"><a href="#cb32-5" aria-hidden="true" tabindex="-1"></a> <span class="at">prior =</span> model_prior,</span>
<span id="cb32-6"><a href="#cb32-6" aria-hidden="true" tabindex="-1"></a> <span class="at">hypothesis =</span> botanist_hypotheses</span>
<span id="cb32-7"><a href="#cb32-7" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb32-8"><a href="#cb32-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb32-9"><a href="#cb32-9" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(botanist_BFs)</span></code></pre></div>
<pre><code>> Bayes Factor (Order-Restriction)
>
> Hypothesis P(Prior) P(Posterior) BF
> Petal.Length > 0 0.50 1 2.02
> (Speciesversicolor > 0) & (Speciesvirginica > 0) 0.24 0 0.00e+00
>
> * Bayes factors for the restricted model vs. the un-restricted model.</code></pre>
<p>We can see that the novice botanist’s hypothesis gets a Bayes factor of ~2, indicating the data provides twice as much evidence for a model in which petal length is restricted to be positively associated with sepal length than for a model with not such restriction.</p>
<p>What about our expert botanist? He seems to have failed miserably, with a BF favoring the <em>unrestricted</em> model many many times over. How is this possible? It seems that when <em>controlling for petal length</em>, versicolor and virginica actually have shorter sepals!</p>
<p><img 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" width="100%" /></p>
<p>Note that these Bayes factors compare the restricted model to the unrestricted model. If we wanted to compare the restricted model to the null model, we could use the transitive property of Bayes factors like so:</p>
<p><span class="math display">\[
BF_{\text{restricted vs. NULL}} = \frac
{BF_{\text{restricted vs. un-restricted}}}
{BF_{\text{un-restricted vs NULL}}}
\]</span></p>
<p><strong>Because these restrictions are on the prior distribution, they are only appropriate for testing pre-planned (<em>a priori</em>) hypotheses, and should not be used for any post hoc comparisons <span class="citation">(Morey, 2015)</span>.</strong></p>
<p><strong>NOTE</strong>: See the <em>Specifying Correct Priors for Factors with More Than 2 Levels</em> appendix below.</p>
</div>
</div>
<div id="bayesian-model-averaging" class="section level1">
<h1>Bayesian Model Averaging</h1>
<p>In the previous section, we discussed the direct comparison of two models to determine if an effect is supported by the data. However, in many cases there are too many models to consider, or perhaps it is not straightforward which models we should compare to determine if an effect is supported by the data. For such cases, we can use Bayesian model averaging (BMA) to determine the support provided by the data for a parameter or term across many models.</p>
<div id="bayesfactor_inclusion" class="section level3">
<h3>Inclusion Bayes factors</h3>
<p>Inclusion Bayes factors answer the question:</p>
<blockquote>
<p><strong>Are the observed data more probable under models with a particular predictor, than they are under models without that particular predictor?</strong></p>
</blockquote>
<p>In other words, on average, are models with predictor <span class="math inline">\(X\)</span> more likely to have produced the observed data than models without predictor <span class="math inline">\(X\)</span>?<a href="#fn5" class="footnote-ref" id="fnref5"><sup>5</sup></a></p>
<p>Since each model has a prior probability, it is possible to sum the prior probability of all models that include a predictor of interest (the <em>prior inclusion probability</em>), and of all models that do not include that predictor (the <em>prior exclusion probability</em>). After the data are observed, and each model is assigned a posterior probability, we can similarly consider the sums of the posterior models’ probabilities to obtain the <em>posterior inclusion probability</em> and the <em>posterior exclusion probability</em>. Once again, the change from prior inclusion odds to the posterior inclusion odds is the <strong>Inclusion Bayes factor</strong> [“<span class="math inline">\(BF_{Inclusion}\)</span>”; <span class="citation">Clyde, Ghosh, & Littman (2011)</span>].</p>
<p>Lets use the <code>brms</code> example from above:</p>
<div class="sourceCode" id="cb34"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb34-1"><a href="#cb34-1" aria-hidden="true" tabindex="-1"></a><span class="fu">bayesfactor_inclusion</span>(comparison)</span></code></pre></div>
<pre><code>> Inclusion Bayes Factors (Model Averaged)
>
> P(prior) P(posterior) Inclusion BF
> Petal.Length 0.60 1.00 1.91e+25
> Species 0.60 1.00 1.25e+09
> Petal.Length:Species 0.20 0.04 0.171
>
> * Compared among: all models
> * Priors odds: uniform-equal</code></pre>
<p>If we examine the interaction term’s inclusion Bayes factor, we can see that across all 5 models, a model with the term is <em>on average</em> (1/0.171) 5.84 times less supported than a model without the term. Note that <code>Species</code>, a factor represented in the model with several parameters, gets a <em>single</em> Bayes factor - inclusion Bayes factors are given <strong>per predictor</strong>!</p>
<p>We can also compare only matched models - such that averaging is done only across models that (1) do not include any interactions with the predictor of interest; (2) for interaction predictors, averaging is done only across models that contain the main effects from which the interaction predictor is comprised (see explanation for why you might want to do this <a href="https://www.cogsci.nl/blog/interpreting-bayesian-repeated-measures-in-jasp">here</a>).</p>
<div class="sourceCode" id="cb36"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb36-1"><a href="#cb36-1" aria-hidden="true" tabindex="-1"></a><span class="fu">bayesfactor_inclusion</span>(comparison, <span class="at">match_models =</span> <span class="cn">TRUE</span>)</span></code></pre></div>
<pre><code>> Inclusion Bayes Factors (Model Averaged)
>
> P(prior) P(posterior) Inclusion BF
> Petal.Length 0.40 0.96 2.74e+25
> Species 0.40 0.96 1.80e+09
> Petal.Length:Species 0.20 0.04 0.043
>
> * Compared among: matched models only
> * Priors odds: uniform-equal</code></pre>
</div>
<div id="comparison-with-jasp" class="section level3">
<h3>Comparison with JASP</h3>
<p><code>bayesfactor_inclusion()</code> is meant to provide Bayes Factors per predictor, similar to JASP’s <em>Effects</em> option.</p>
<p>Let’s compare the two:</p>
<ol style="list-style-type: decimal">
<li><strong>Across all models</strong>:</li>
</ol>
<div class="sourceCode" id="cb38"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb38-1"><a href="#cb38-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(BayesFactor)</span>
<span id="cb38-2"><a href="#cb38-2" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(ToothGrowth)</span>
<span id="cb38-3"><a href="#cb38-3" aria-hidden="true" tabindex="-1"></a>ToothGrowth<span class="sc">$</span>dose <span class="ot"><-</span> <span class="fu">as.factor</span>(ToothGrowth<span class="sc">$</span>dose)</span>
<span id="cb38-4"><a href="#cb38-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb38-5"><a href="#cb38-5" aria-hidden="true" tabindex="-1"></a>BF_ToothGrowth <span class="ot"><-</span> <span class="fu">anovaBF</span>(len <span class="sc">~</span> dose <span class="sc">*</span> supp, ToothGrowth, <span class="at">progress =</span> <span class="cn">FALSE</span>)</span>
<span id="cb38-6"><a href="#cb38-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb38-7"><a href="#cb38-7" aria-hidden="true" tabindex="-1"></a><span class="fu">bayesfactor_inclusion</span>(BF_ToothGrowth)</span></code></pre></div>
<pre><code>> Inclusion Bayes Factors (Model Averaged)
>
> P(prior) P(posterior) Inclusion BF
> supp 0.60 1.00 140.99
> dose 0.60 1.00 3.21e+14
> dose:supp 0.20 0.72 10.12
>
> * Compared among: all models
> * Priors odds: uniform-equal</code></pre>
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2FTKI2Ci5bBUrY8IgYjZRRx%2FyUg2PCRQxGyTIGAQbBIYDAJAMBsmTAYcKRa30%2BEKH0yi5D6dyDYJznMGA1UUMAiUD6YUqh9PhAuHCKGKgBtRS48IkKbQpyqBs7pVKbOCgU2HZAuHHdFDArK0p9NAhsRSmysKBT6Y2Uq5wQ%2BnwopDZwgXHcKKQ2IENqKU2hRUzZwUCGw7IENmrLK4IbEqpmwqLSm1SLSGzx2UyqWCAG0KFTNo20RambWRQYfeoR5YAHDLtK5UwC1GVBa3xQpwFWaoLTsgpbY%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%2BnypVb6aUD6aUbBCtgnOczY8IBjwhAxUqxsUAwQDBCl%2BnwyNcjfTKIXAqKGBRcZDAKAfT5UA%2BmqFPpjZRaXBAMOEhS4qKU2qKU2IENqkUptKBTagQ2KmCGw0WctENh2SHMU%2BmdkCmw7KZXCZsUi4IfT5QpTZupnDWMpmxSCZ9PhKqZs4UCG3hFIbOyKniQ7qZXCZtdQTusKKmbdGUVM2KKXE7IPJYeK7YcOQ4tcqiwtooGFvDBawyqLeyCltp7bKphW21%2BdkFBatYwzlQWFCqCzRkS4OLFUqosQUFiuDKgsTCZyoLOFUOLOEKcWDZXBk4t4VjJxYgcWgaIU4tGyIYWuhnBxZwqhxYgYW8OgYWnZA2B2VT4nHp7pUHBCmwQMLCqUR6aJTD0wgYWDZUwOI2UgZikBxKsBwKIbBFHBQMLeFYlbDhMGcmwOyfE%2BA4FCjghyjglBwQjYIDhwhBx4VBw4CDYqKOJQbBEwOKK2BQo4FCtgdkKOB2QrYKFHBCh9NUo%2FTUK30ylAwQHDhBsChAxKhGxT4rORsTsg2J2QbE7INidlBseEUMUGxSLQwUGwCFbC1ChgEyYDDgKDYoFxOyK2JQDHhADahC4BADYiwuHCmcmMBgdkaDA7ImAw4UilPppClwSLS%2FTQKfTUC%2FTGyQD6Y2UyuCH0xsikNhChgptUUhs4RSG1AhtRSGzhQIfTKKQ2Hbuoqd1iipmwqZyENiLjKZ9MKKmbNlFTNvCKmbOFAhCmcKndafwUVI2oSlb3U0UivGFq71wqgtVRYW8JgycWuzaqotbaPvVRQWpgyoLVWcrC1kDi3uiKC1WIoLVYZypbbREqotNKq8hynFpVQ4sKqHFhKqKj01KHFiBxYgcemESmFoEMqhxZwqHFiBxZwkS%2FAwtViHFqYwoi1WIbBAwsCpnBsRsoQcSdFcpgwsKZMZN9MoG%2BnygOClDYKoOAQNgNkyco48IZwOKEHEoo47JUg4oo48Oqg4cKA4oDjwgOKJytirSDiosbFSLRxCqQcRshnDY8IQceEwRsUi8zYoQWQjY8Ikw2PBRcxsTsosHHhBsTslSDigGCA4hFbEKDYhEjNwgzcIc7Nwis3CAMg2KDYhQDHsiwMUGwQgfTOyAYHZRaGB7oNgqBhypFbAKIGA2RQwGyQuWw4RSmxRcFNqIDKqDbqUgYhCAbOEUhsOyZMFw7KKBsKBfp8sopT6fsEoU2KKQ2cKBTYNkMZhDZwovOQ2MikNqiwhsUEzayqkNqixM2cIENnCy0mbOFBM%2BmSipmzdRUzZ%2BKhUjYi85DYCpVSutCKmbRRlBPEPRZi14wC7uCotMQtMqC0nRUq1tqFVFlFcJlS2yiqK22dglRUWDXwRFbbBsmTGVBYBo%2FC0igs4VRUWJEUFqsDi1EyoLFU5Ti3ZIHFiooLG0SIcWHQKwOPTKYMnw6KpkwsRKcWIGHpq0OPTCIfEDRSgtwqQwtRDCxRTCxKQwtVQcUyYMLeEIItegVDYHZReQRYqlNgiURYEKOI5Sg4jZAcRshBxQgi1Fg4pgzhsUBxCIItHVFHDhEoiw7JRsOAlBwKVRw5RK2A3Sg4DlQo4jZVK2I2UyuGYbKozDZRWbhAW4QZgi8rMiMyK2IVRmCitj1QHHhBsFItb6Z4VhWw6IVj6aFbBIUMAorYBVGw4CAYnZRWYhEZlMYXIMhGYJBseEWtg%2BnioB9PhDGQPp%2BOiKH0yotKbNygGCDYhQgYDZADYNkAwQKbNlGiYoAyAYhQLhwqFwOyjRTZwopTYdUQuCKU%2BmsqmfTVoU27qKQ2BQqZs4UyuMkNqikNvCGMpG1FIbXSCZsKipG3hRUzapFTNhFFFSNnHZQTuseVOZedI26IuEzZCLhPFSLXji3Rd3nVFvZWCgt2VxhMq22qxFrbUFRYyrOcq22cIK22LTKgsVFR6aCgsVRUWURKcWBEUFnCqKizhA4tCEOLSVUOLAgcWrUQ2CmDKg9PhVLg4sQNhwimxKVDD0zqhnJh6Y3RD4BCmFg6olHEbOnKpseEQwsVIbBAcUBxQgi1DODY8FCDgdlQcEBwUwZMLFStgFKDgFUoi0dUKOA2UoOHAQpsVUbHlRRxQjYqo2IUWDiFSNiEgzDZRRx4VQceEI2J2SKOJSDYpBseUBxCQy2ISGBxGymeQ52x4SDMhjDMixmCJBZAMQgOI2RWw4UGwVGw5Uo2G5SgYHdBsEo2HDqVQxGyDYBRWwGgCqBgooYIBiixsShGY7IQMeEGw4UAwShfplRQPpoYyH0whS4BT%2F4v%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%2BmiUp9MqZaxkMCiExUy1gMQgU2AqBTYikxQKbe6BTaikNnCZMENhUjRDbupBM2JAl1hCipm3hTOFTu9NFwmbFFTPpqCRsRcZTNiLUrrFFSutGqmVSus2UXCJtUypMZUHjCwru4KixtVamVrbN0FhaeyuEytbYNlUVttfogtbbwtMqC1UVFqIqLURQWqmVBZwiRS2w7KoqLG0RDiwlUqlvpqlUFiJaYWohxYopxYFUNiNgiGAVhTC07IU4sQMLeEQ2PCAsiwcVUhsVQws4hQHDhXmTnNgf8ACgYWHgIDgd0QcEUcAkBFo0dWA4cIGFnCAi1EjC3eUUcRCEHHhAWQbE7KVRxOyrI4lSq2KUHFKNh4pSjiNlKDiNko2A2TBkceAgOJ6INioNiqNjyg2KA4lMmGxKlVsSlBxPARK2B4SjY8qVWx7pRsE5TkHDhUrYgaKLzhiNkLBYbK1Ax5QbGEoGJRWxKXBysxSkDHhKRsUK2CFY27KLWxQbEoA1VFDDgJChjoyLGYeChnDY8IkBhshAI7qLANvCoU2FFwBsOykKXEpFDFIRseFIFNiBT6fCBD6amWsBgqlKbFlSmxCkNnCjVKbGRKU2hDlIbEVM2bKKQ27oqd1igkbW5TK4TNqgkbSFlpM2uiom1Sqldb4JlcYSutQwjdayipXWKLUsSo1XkC3YOuzzq22HZVF7bCeiGFrbGVSqizlXCZWtsGiuEyrbYrUVFg2RFrbBsiKi3ZXGDKgtVRUWomTgKwUtsVTKgtRDC1CHFqGTi3h0Q4tJ0VwZwYWHZA49M9OFRQWfeiGwCQo4qoYWSgYWDZ0WmFiqCLeFA%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%2BCi4LjyhAxO3dAGKitiiBh9zqLnJTb2ShTYi%2F7i4qLQxCIXAKKQ2KBTYikNqEKbVBM2pViZtRcENqgmbNkawkbWUi1M2qCN1qKkbVFRutUhUrrVFRutRUbrVFqWMqNPIttouzguLRsrhF7bdWWsYZysLeEFrbYRMrW2q4Ra21VFRarhMqi07KkUFnCCws3CvIycWnogpb6ZQzlQWJhMnFrqnMoLEooLBsiHxGyHKIt4VSHFrophb2RDi3hVBFqYyZwYWhCGbhAcTsqGwQoi1CiLSaqUNjRKDgiUcVKDiEBxGgQFkBZUxhmQjNwiwUSMhBxOqK2JQHEoXA4ojYpQcfJAcQhhmUoOPDoDjwg2J2QHEoRhadkMtidkGxKijgVYNiUMYbE7oRsDHmg2BKc5zDgUGwJQHA8INh0QHB0o2J6pRseEowt4TBlsfJCMxfVSrG6hVIzBRQYbIMAEMswQZvFFDEoVmKDMUVmQjNCEbEbKUgYeCDYdGQDEpRmQZlCs3dAMRslGwj3IBilIDbqkDHZQwGPCLyFxEooG1lAFYgECiypTagU2%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%2FFDCN1sqLjKZCKhdaoqVwUELgpGkbrVFwjih8HnW28Loxle207Ksr22FKi9thVFhZolRa2xWpla2wKorbYNlUqwtA0VTn51BamEysLQAiHAVFLbVUyoLeOigZlQ4t%2FBUhxb9wRDYomMHFuyKYWqoOO6BhbsiGFiUEWiYZSrkcUBYOgItKqQ2I1KEEAbdFFjIGbhVBFpQy2KKLIkFkBwOyA4FAcAhzCLRshzDj96iiyqMyUFuEGZBmRYLVSIzd0GYKjMkG8tlFbhAVRpQZCMyDMpgyzbShBZKRm8EVmaqVOdm8EGbVTmW0WGqtRm%2FBRWbhKCx2VRmUI3dFZCChGRIzIrMpBuio3VQZAKaKKyoKIEaqKzBVANvLKKBBQBj9qqMgCi5ZkKDVQBUZRQZ9EAbZCA1XQBIAykGIHZAG1CtQpG6BSKsi4yBt7IENrfcpFoIFNqgQivGiLSEfgi0jKLkhtQTNqhUyFIqd1qCRFYUaSIQRutUXGUiFFRutTK4QuCyqFwSKm0rK8rgtHC6Yw55WtCqZXtCuEXtthDOF7bYWmXTZ6Hq3B7fTuuB%2FiALLOdppxz5w1jZ6s82Mun0%2FwBH%2BpvfD9P6t7VAsJ%2BCzniNnp59WOnDWNhtNXNpz0ZdNn7d%2BuuLW%2Fo%2FXuJoB6dz%2B5Yzxmxxi%2F79PThccJts5n%2BzV0ZdNv7T%2B5a%2Ft36n%2Fur%2FALFj%2FIcNvNHax1t%2F0PEbvV2c9TpH7H%2B8Q37R%2BsO3%2Bg9T%2FNWf8rwm%2B0drT1tf4zi91r7Oep0Wfy9%2B%2B3h7P2X9fcN7f03qn%2FmrGfOeB08%2B32eP59PW1jyjjdXLjYbTsaup0Wfy1%2B%2Fkgf7j%2FXh9T%2Bn9QDxNqmfPOAx%2Bvs%2B3p61x5Nx%2BeT%2Fo2nY1dS4%2Flb%2BYtP2T9b1%2Bjf8AYs%2F5%2FwAv3%2Bz7WGseRcfuNfZyvZ%2FKP8yXBx%2By%2Fqu%2Fpl%2FBc8%2FcXl2P19HS6Y%2B3%2FMM%2Fo6%2Bhf0%2F5O%2FmW8sP2b9QCzzaLX8SFnV9zeW4%2FX09K6ftzzHP6OpUfyX%2FM%2FwD%2Bn9aObf8AOWfVHlm%2B0%2Fj1NemfMtzq%2FDrX%2FwD%2BF%2Fmqv%2B6L%2B%2Fqel%2FnrHq3yvfY6NXU3j7V8y3OenT1q2fyF%2FNl%2F5f2g%2FwDG9b0R4P6gWdX3h5Vp%2FW7uvwtaftPzPP6Pe09a39v%2FAObf%2FwBT1%2F0%2F6f8A1iz6y8p33d1%2BFfSPmm572jxK%2FwBu%2FwCbGH%2Fl1k6fW9L%2FADlz9a%2BVbzPZ1dTp6O8z3eO1p6z2%2FwBOv5pN2J%2FQ%2BnbvcfW9Nh4XEqZ%2B9vK8Y5Npns6uox9m%2BZ5%2FJjtaetb%2B2%2F8ANAj%2FAGb0B%2F21qx638sz%2BbV2cunozzL5dPawpZ%2FTX%2BZ73f0%2F01h0B9YH3ArOr758sx8dWf5WtP2V5jn4acfzHH9Mv5nYHH9Kx%2FwCtp%2F7Kz688t%2F59n%2BK%2BiPMP%2BPT%2FAAXH9Lv5ih%2FV%2FRAmtp9W5x4WFYz9%2FwDl2PhtOzjxN%2BhuPz8dHTnqNb%2FS%2FwDmEkf6b9CJbI%2Brf8PTdTP7geXY%2FLtOjHiXH2Lx%2Bfjs%2BnPhUH9LP5gf%2FwC8%2FbwJn6nqtH%2FZLn7heX%2FJtejT43T0Hx3z7Pp1eFS3%2Blf74Tdn%2Bu%2FQWgNS71bnf%2Fswpq%2FcPgfhs9p0afFldP2Fxvx17Pp1eFT%2B1X7yB%2F6h%2BiPQ%2Bp%2FmLPuHwe72nd62s%2FYPGbzR3uow%2FpX%2B7v8AN%2B4%2Fo7RoR9Qv%2FwCwFM%2FuJwnw2Wvu9a4%2BweL%2BO00d7qV%2FtT%2B5mn7n%2Bmivy3%2B9mWPcTht1r6cNe3%2FE73R0ZEf0p%2FciQ%2F7p%2BmAJqLbyZUz%2B4nDbrX04XH2BxG909GVh%2FSj9XT%2FfHo%2F91d%2FnLHuLsdzq7WOpv2%2F22%2B09Geth%2FSn9Wf8A8t6L7fSu%2B1PcXY7nV046j2%2B22%2B09Geta3%2BlHrn%2F81YNx9Ax%2F8xc%2FcbRuM9r6XT2%2B17%2FHZ%2Bpj%2FSn1nA%2F31YQYf6Br%2FwB4nuNo3Ge19J7fa9%2Fjs%2FUsP6TXMH%2FfQCaj%2FZoH%2FwA0LGf3HxeTh%2B%2F9DeP29zOXiO59Tf2mJLf7%2B1n%2FAMLp%2FwB8p7j%2FANv3%2FoPb3%2B47n1ns%2FpPY5%2Bp%2B%2FXNo36YW%2B%2F1Ss6v3Hz8OH7%2F0taf29x8dv3PqP%2Faj0XP%2FAJ3fVv8AoB%2FrFn3G17jHaz4Wvb7Rv89n6hH9J%2FRdj%2B9%2BpGv%2Bzj%2FWJ7ja9xjtfSvt9o3%2Bez9TD%2Bk%2FoBif3u8iMh9ADzzKZ%2FcbafDYY7Weo9vtnv8APZ%2Fip%2Faj9G%2F%2FAKt61P8A4Vv2rHuLttzp6c9Tft%2Fsd9q6MdYj%2BlH6N2P7v64f%2Fq7ftT3G22509Oeo9v8AY77V0Y6wP9Kv0QLH949cR%2F8ACtf3p7jbbc6enPUe3%2Bx32rox1rf2q%2FbP%2FwBn%2BqdtrPcy5%2B4vE7rR05b9AcPvdXRhj%2FSr9rH%2FAOT%2FAFVWfGz7FPcTid1o6cr6A4be6%2BjDf2p%2Fa2%2F9U%2FUvwLNOye4nE7rR%2BPWegOH3urowpb%2FSz9mxe79w%2FW3Xat9MeWBWM%2FuHxl5Nns%2B91t4%2BweEnLtNfd6h%2FtZ%2Byn%2F8Av%2FrXff092%2FwKe4fGbvZ97xL6C4Tea%2B71B%2Faz9llv3D9aSKT6f%2BYr7h8Zu9n3vEnoLhN5r7vUJ%2FpZ%2Bymn7h%2BteIf09f8AiJ7h8Zu9n3vEegeE3mvu9Qf2t%2FZiW%2F2%2F9a%2Bk%2Bn3%2FAIE9w%2BN3ez73WegeE3mvu9Qn%2Blv7LbX9w%2FWePp9%2F4FPcPjd3s%2B94j0Dwm8193qE%2F0s%2FZRP8AvD9aQefT1%2F4ie4fGbvZ97xL6B4Tea%2B71B%2Fa%2F9lkH9f8ArQ38T%2Bm3BmxX3D43d7PveJPQPCbzX3epX%2B137BAP6z9eCQ7%2FAFPS930viuef3C4%2F5Nn0avG36C4H59p06fC39r%2F5fdj%2Bs%2FcAYLfU9L%2FUqe4XmHybLo1eNfQXA%2FPtOnT4W%2Ftf%2FLzT%2Bs%2FcGP8A1npcf9SnuDx%2FybLo1eM9BcD8%2B06dPhEf0t%2FYCx%2F2v9wD0%2Bf0v9UnuFx%2FybLo1eM9BcD8%2B06dPhb%2B1%2F8AL7Fv1f7if%2B09L%2FVJ7hcf8my6NXjPQXA%2FPtOnT4S%2F2u%2FYWP8A4z9f0Pqel%2Fqk9weP%2BTZ9GrxnoPgfn2nTp8Jv7X%2Fy%2BxP%2B1%2FuMf9Z6X%2BqT3B4%2F5Nl0avGvoPgfn2nTp8Lf2v8A5f8A%2FwDL%2FcHnH%2FSelp%2F2Se4PH%2FJsujV4z0HwPz7Tp0%2BEl39Lv2Nhj%2Bu%2FXWlpe%2F0i9Kf6MLWn9wuO%2BOz2fRq8TOr7C4L4a9p06fCH9rP2b%2F8AYfreC%2Fp%2B7BX3D4zd7PveJn0Fwm8193qA%2FwBLv2bT9f8ArCWkP6df%2BQr7h8Zu9n3vEeguE3mvu9Tf2u%2FZm%2F8Av%2F1zyCx9P%2FMT3C4zd7PveI9BcJvNfd6m%2Ftd%2BzMT%2FALf%2BtOon0%2F8AM1T3D4zd7PveI9BcJvNfd6m%2Ftd%2Bys%2F8At%2F63kP6f%2BZKe4fGbvZ97xJ6C4Tea%2B71N%2Fa79lj%2Fx%2FwCt8fTo3%2FAT3D4zd7PveJfQXCbzX3eoP7Xfs8f%2BP%2FWks7g%2Bm3nYnuFxm72fe6z0Fwm8193qKf6WftbuP3P9WLZYY2E%2B5bx%2B4nFfHZaPx62M%2FYPDfDa6%2FwAOov8Aa39rr%2FvT9SxDgG30x8FfcTid1o6cp6B4be6ujAD%2Bln7aW%2F8ANP1Lk%2F4bNn2T3E4ndaOnJ6B4fe6ujAXf0r%2FQP8v7t%2BoAOh9Own3hbx%2B4u3nLsdPTlnP2BsLybbV0YJ%2Fav9EI%2FwB7%2Bu%2F%2FAPFa3vV9xdtudPTnqT0Bsd9q6MdYj%2BlX6KP%2FADb1wTp9O2I6p7i7bc6enPUegNjvtXRjrJf%2FAEp%2FTv8AJ%2B8%2BraG%2Fi9G0z%2Fywtaf3F2k5dhjtZ6mNX7f7O8m2z2cdaY%2FpV6JD%2FwC%2B7%2Bf9AC3%2FAMxX3F17jHaz4U9v9G%2Fz2fqN%2Faj0CP8A1y%2Fp9Af6xPcXXuMdr6T2%2FwBG%2FwA9n6k7v6U2FhZ%2B%2BEA6n9OC%2FT%2FSBax%2B42r48P3%2FAKcs5%2Fb7Hw2%2Fc%2Bop%2FpQQP%2FXf%2FwDV%2Bz1lr3H%2FALfv%2FQz7ff3Hc%2Bsp%2FpUZb9%2Bn%2BEH9Ka7f9Krj9xv7fv8A0Ht9%2Fcdz6if2q9aP%2FOrOf9Af9Yt%2B4ujcZ7X0se3%2Bvf47P1E%2FtX6pp%2B9enR%2F%2BhLf%2B%2Br7i6NxntfSnt%2Fr3%2BOz9SX9q%2FwBZP%2Fm%2FouP%2Bru%2B1b9xNjudXTjqY9AbXfaejPW39qv1pdv3f0ILH%2FR3af8ZPcTY7nV046j0Btt9p6M9aJ%2Fpb%2B5v%2FAOpfpuuN%2FwBi6e4fDbrX%2BDHoHiN7p%2FEP7XfuLOf3P9MOcb%2Feye4XDbrX04PQPE73R0ZS%2Ftd%2B8EOP1%2F6PHSfU%2FwAxb9wuD3e07vWx6C4veaO91B%2Fa395dh%2Bv%2FAEQ0r6n%2BYnuFwe72nd6z0Hxe80d7qSu%2Fph%2B%2FB2%2FWfoCB%2Fl%2BqD%2F8AS5W8fuDwHx0bTo0%2BJzz9icbjm17Pp1eED%2FS%2F9%2FFpP%2B0%2Ft5Oto9T1X%2F8ApK4%2FcHy%2FP5Np0afEmfsTjvn2fTq8KX9sf5hL%2FwCl%2FRQf%2Fi3%2FAOrXT195d%2FptOjHiZ9Dcf%2Fro6c9SV%2F8ATX%2BY7aH9JeBU2%2BqY8bQtafvzy7Pz4%2Fl%2Fixq%2ByPMMfJn%2FAPf4FP8ATf8AmQQ36arf9Lv%2FAMVX115b%2FwA%2Bz%2FFPRXmH%2FDp%2Fggf6efzMH%2F8AD%2BjczuR6tq6et%2FLfm1dnLGfszzH5dPawW7%2Bnf8zin6X0rz%2FhHrWfEhax97%2BWZ%2FPns5Zz9m%2BZY%2FJjtYSP9Pv5pgH9BZx%2FpvT%2FAM5b9a%2BV7zPZ1dTPo%2FzPd47WnrSu%2FkH%2BagWH7aL4qPX9Bp63hax95eVZx%2F6z%2BXX4Wc%2FaPmeM%2FwDl3tPiSu%2FkL%2BawD%2F5SYq3regfL6i1j7w8qzyf93d1%2BFM%2FafmeOX%2Fq72jxIn%2BSP5pH%2FAOIvH%2Fael%2FnrfqzyvfY6NXUx6W8y3OenT1o3fyb%2FADMCRd%2B0eq9uxsPmLlrH3R5Znl%2F7tP49TGftrzHGf%2FHV%2BHWlf%2FKH8yWs%2FwCz%2BuXowB9xW9P3N5bq%2FX0%2Fj1M5%2B3PMdP6Or8Otzn%2BVP5jf%2FwBH%2FVf8ha9R%2BXb%2FAEdKen%2FMNzq6ET%2FLP8wiv7L%2Bs%2F7m%2FwCxb%2Fz3l%2B%2F0drDH%2BD4%2Fca%2BzlG%2F%2BXP3604n9k%2FXE7D9P6h91q1jzvgM%2Fr7Pt6etnPk3HY%2FQ2nZ1dTnv%2FAGD98tD3fs3660bn9P6o%2FwCatY844LPJjb7Pt6etnPlPG459jtOxq6nOf2b93Yk%2FtX6wAVP0PU%2FzVr%2FKcJnm22jtaetn%2FG8Vj9LX2c9Tmu%2Fav3Gf%2FL%2F1P%2FdX%2FYt%2F1%2FDbzT2sdbP9DxG71dnPU5j%2Bh%2FWAn%2FwnrBoI%2BndHkt44vY55tenpwxnhdt8dGroy57%2F0vr2lr%2FQ9S07G0j4LWNvs845NWOnDOdjtMZ5dOehy%2Bp6V9jZ2XWvuGW9OrGrmzhM6c458Oe4IiFwRUbgsrhFpSK%2FSPp%2FtH7Vbc9v7Z%2Blt0j0fTH%2FNXwPV5jxWccu115%2Fmz1vuWny%2FhtPNs9HZx1O30v2z9vtuBt%2FQ%2Fp7TMj07A3ksZ47iM4mdpq6c9beOD2GM3GjT0Ydtn6H9IGP%2Byei4m35A76aLnnitrn8%2Brpy3jhtlj8uOjDut%2FT%2BjH%2BisfX5RHkuf%2Fbr%2FANc9LeNlp%2F0x0Ou21mB2grm6Omy0gB42UHRbbpXbQqKrbadSWfyQVttPytXQH7kqui214Zvb7VBYW6CA%2BygsLTDGKMgYSSB2ZWBxaQQ0g%2B9KKgMRX7FA4tJfhw7oHtFO6mQzOHEg1KKYWsQGg16ohsXINxIZ%2FPkIKMBAknT2CgAtYf4hAYQw1VocAgM07jnwUUWNwI3iVBmIgHx07KkGSCRrx56ICAbtGGgMopmcA8QSgGFzCkSOqAuxd6jWPaqAsQNRQczqgOJO7Q4MfegbFqBxx4oARpIB1ozfggYW8kmeiDOTIpqZFaUQbgCBTzQY3UALyB4pEEk6s4lhv8EUCQHYsdHogIoA8x28UADg8bxO6DPdsedNe%2FvQGjvoICAA3kBhWpkoMBQ1cxttVA0nEQfDkIMQZevfRKMbINDOp328UoAADh9A%2Bmn2JQRazAkPoY3pVKNjMWhtendKA35dXNQ%2FtogaJLkBnGygNA80l%2BUAAtf8oJBgdEG0m12MaoMQILVYEbahAbbQBAjU0QbEP3mUoXEC1z8zePeqUaHi0Bi7oMwAyL2isQe6oN1ujPPIUowZ3iTXmnKDYgNuddtdEAYw4l5I0VGa38p3gPyg2JgOZp4apRmmpB1J2HglCsXEyKE7MdOyAkB8X5Z0GwJ145SjMxilS0sgwclwxEjJuiAmRIBfRAIN0V1YoMCADL8nVAoJDB3PjFVUa3EUe2rindA5Lcb91FATIGMwgW4APJcAttsqjANIgOfl61eqijiDJtrz9qBTaGDgwXMA7nRAJ1qLXJQC4OTEatJQagGw0O7oNiBIDk6oExhrav8Al9%2FuVGa4EDF4kjR%2FwUAZ2Jky%2ByAAXUJjLSea8IjAEh209oQhQcrS4x%2FwzPiUQXFwJA2cuyKUi6Q%2B7OiAbaWkYkCNQeFQpdizEMVFTxmrTrv1VQOCKVCKTGPlBEflZKiZBZhOw0fqqExLky0gWoJ3DYcyVQpfsNS2kFIJ3WBwDM1UCXWk00h0HNjW7WW9gtCVwcGDu6COHVvtRIh6loc7tIfdMIhdbUU28FRy%2BpZZda1wF1p0uDhaxnOM3CZxjPO5L%2F03oXZA%2BjZc%2FwCYYgv5Lpjba8c2rPSxnZaM8%2BMdDjv%2FAEP6Mv8A%2BF9FjX%2FR208FvHFbbH59XTlz%2Fptln8mnow5P92ftzt%2FsH6fr9Kxvcun9dxG81drPWx%2FRbDd6ezjqVstee1F5c5ep1WW613Uo67Rw7e9QXtBgv3Sq6bLa66KVXRYKU4FVEXtmIce3xRVhbE0eUqr2W1JgNVSiotegaD9ilF7QSQxjQ%2B9SigBNIksFQ4kMJJpt1SigteCGIkqUNawtcSGjsqKW6zN1AdnUoZhaATSHI4UFMWc0qSZjzSqbWKgOiGxBcEy8NVKCA5h25Hm7KUOwLEiSlUJImLSW0%2BKAgN0FRbHVWqNo02060SjYAC4fwu5tShmHynkl9j5JUNUGBSX4bhKoWviARj1iEBxl3c6h2ShjaCMSZoSfaUoLl6SNQ2qDEU1tKUYmhILExbqgwLfK8Bg4GvVABJD%2FAJnLdISguzyAR%2BY7OgwyeaHTtwlB0MMRUHyUozaAUZwfsVoIH5pYXFx5KUCkMeWlKM1ptmXLt0ShrRaRu4iJlM5BLyB4k91KAMiBURVWjPIDA7jT3KAvkdRi1DugzSDA6VSgMTjq1W2SjCRbLA156pQHALSDbDzsqNaC1XcNIShqGbmfnyUoQCLixLn82ytBLYv%2BLoCAxcggtDUCUYkChd5JPsEGccAw4d9WSjQD8oZpuaOyUYQA5gMBuxQYNpERv26JQTDh6a0%2FFQYUAEPV69koWpDaByRXwroqDL46s8CFKN8rgsxAgfYqM%2BogbmlfvQC55ALi4bVqYKAvqDWQTpuUBElxBox08FKM%2BuTQQ6ASJE8EiuyoIkEDSAezuoA%2Bpt6A79SqM1Q8vHs6UKBbaADt5pRrgDLuBr1TGRiNQzDXoEo0gbmAJh9VaAwektN2qUbKt1LeYFUBtJOMPAc%2BKBHDs5BuZ2p49kQwoHLPMdQlUHYgAyXOO5fdAQ5ca6HTghKNUNqP4Z%2FFKAwc5SeRHu5SjG01tNS5Jn3JQJ0c%2B%2BfsQAE0IPU6DRApYl688JQMaMSADI56pQsux3n3pRmFMvy1l6pRhvLajUcMogHkO%2Bn4pQDDh59veUoFJYnbl1aFOJhmLoEuZpNDBQIbSH2ShCxyFr7E%2BZVqEbcM%2FwCY%2FilErrQ53eo8VaEIDgksZcO%2FZKJs%2FwApFPblMhSBIIZ6dOylEbrXmRqzVVojeHdnfeioheCXDdExkRLPdxp%2BCI57rZIZpVo5vUAEsz6FXGUc9%2FsVaOe8aHsERz4F%2B1VaOex4KK67Aw82Kg6bNnrTdB0WmmxqorosBgVI1UHTaTu70AUVa0U0ajTQqmF7ciWnZ1FdFuTbuoLWvT26qCgkvU6D26KikwB3HVQPaDAmJ28UFANKW2wyBgGDUPnKgpbV2cE%2BcophubWIL2vxuiKyR8v2dUUXYOTAE7%2BSgYZPBdBhbucqwfBAQQbQCWDSH26oM0s1NHoGQEEW3QIb83EKwO5NfAxPVRWJJ3J0cKjEQ4hxBLAdUQw%2FMJ%2BaUUSSSwJGhcbIA5dyYkAe8eSIx%2FiuckioPDoC5MhiN%2BRsisLi7Cm3TRIDboxJDCPbopkAC5q0%2FM%2BiAuDqaS1JkIH3aTx1UANACWGp9oAQY6yx3b7NVQXk5UDMXUGdxdNabIFBJAAIeZYeKoZwZy2kbfioBkXxBLvt4lIMKkiMQ2SAgloLvr9iAFy%2FzAG6oIdigLkknR3fp%2BCAA2g7PvWEGyuIAaoI4SAlgWZzJZkGkNoGJxrKEYm4iC%2BgLfYg3FpFp1j4IQACzEB2Da06oQH1BrLiv2qwa00LO4fWuiBiXi5QZyGDjRwKoAMgWgszdPuQNxt2HbxQKb2IBJEVaO1UgxJJjUV0QZ3I0JLkINkQ4DckoCXNZhwW8YQYXEmrsHhIN%2BV2rqgxLOxq2qAZQQflBjp2QY3H%2BEZZflEU7pAXNDz3D0QZySMg5I2QAEhxHTb3IC%2BReQf8TfagFxJa0Frmf3JgYGkmWDkbdeqDXFiCbqAEDp4Kgu1C32qDElhLA1Jj7EAuy%2FhtkMARoqGq8cNwVAuumRFNYVCkMDcCYeIjVCMZOgNLSPFAJAi4sZB6qg69II%2BCAFyHf%2Fgzrp5oQDeRDl9%2BUgFQwDAwdC6JDFrt9noig4LAMWmZQAB%2F4g9WGqELdkMgQwoSOURnIg1ltiilalTNAW%2BzVEbR7aCCCVBi5fUmgNEAY8uRL08kANQCJPHtuoFi4Sa0J52VIRyAWPSde0qoS4Egs769%2BiKQw0tTb4DhEBwQQa0O6KmQRDz7oq6qJ3ONXPCCVRMEe2qoUiKnkugkQWpN2yggcgTLg6KiFxL7AVQQud9ix9qLSZS9QPWD7bJgc1%2B1DVEct4Jnw6LQhc%2F2BEc%2F8XxbyVHN6emr6qjrsH2rNHSKAVlm1UV020fQU04RXTYJah0PmpR0WOGed303UFrYq4BZM5VawTqTKDotA1hqaUWVWtDGvVEVenSDKBgC2xfqlVQCgthpLmfilRXEGlWYtzVSqe0N7vwQUtcNDUgTCBgx7U55QEAkn5uQ9VAbXc3M%2BgZBU8QdB8FBvzaEgluyo3yhiNfBiqofnmoaI8pTmGrp%2BapMa6IKEGCAHMMdeiBndqFt2ooMT2Z3uZAKEmpFG0j7koLatQ6JQoOVXmhNOiob5idH12PClwCGYRo4NYNfJKMwNrkPPu1OyUOTTR9CoA8FrXfT7eroAzkS9rwCPsVozlsgPlqdyoDL7zThACXJdmZiNUBo0uCacIB8pFpuYjf23QBid33H2QrQzggEOW08%2FcoMKFtKfcgAJIqSSRNOUBbIu0DWPBKByBJ0aoJ8EoNWf5hBZAAZxdrWZuqAw1p376IFa4swLGhEM6oYPDuIkS8qAhzIalUGxaMfCPxSjC2AxZvYJRgCCAA3PRBiKPDGmhKBmcOxb%2BDRAMQWBOXB%2BxKMRaQwdneiDG0OwBoGP3hBiLQIMhgH99EAuBctRnch6VQA2s4mTo3TqlGa4V1hvvQEg7FpLadkAkEOGYQxHdBsfzABy09dnSjH5nkwZHxhAOCDHVKC9uggUIFEAuIBDgktGtHQEmSPEGnPvQA4ki54q%2BytBjJjXaWZQYsHf3%2Bb1QCRaACMjAuPjqlBq7GGg1fpKDCTALPzVtXQEnj5TU%2B9AA%2FykGlSWjhAIqSSLqkUCAsAJPyiCK9EoP8A70sD1QAkiNNSfgyAEvBGsbvVAGDMbQCzEhnr8VaMbRoNmq%2B%2FsyUJUQYGk91aGOgqSXr3UAdyAXltlRouMOAX0jugNNKCilABJBYEAeMKjM7w5EzA1dQJcGd36VDdOUAmkGwCdUoxh3NBDaDx3QKDRydAwOtUQD8xL9RUcIA0QYP5Y2%2B9ApEQAGp9miDXBtCzGRVAjPoREUZlRIgfmMEOlCOdfPQRVBO6h0I0KokS4PEOyIWazBgFBK7%2BICoNd0Erg0V96K577flIh1qohcWZg2k%2FYmBG6szylRzXAEw5ZUc94F3LHTlUc90DdqhERYZNqqjlsDfFB12gPSdCoq9tWLyfYIOq3rH3qZV02wHo6mR0WwQ4qouFrAH5feqDottLDV9NgoL21O%2B0qKoBDUI9tVUPaBk2nuUVQOxkzA68KiweXkmFkOJl3YzwgcEB7rZGyCgD9D7bIHgEu4eUGDMS72iBvogaMnILUOohQG2jOABokUwMgbnwZAtoJIkyI5HZUU0khzDb%2B3RAXrod7fFQbUGZGmsfcqCXDMztUqBQHMgPL86UVGJcCoLwgYWOJAiG2frwpRhbDj5S0BolA7a1BUAFxLaBpf21QAO7sSDLO8%2B3CBgweGAFUUDW6f8AhFkRsQzQYHL%2FAHIMXDSQKUf7UDSAA7e0IpIIpSBRj7wqg7gyK%2FYoMTJxECkxuEBoSD%2FF7MijiYmpd43RDYwZoaBFDEdDv08kQwE0IbeX2RQcQQH47FEBjAAZgIDfegYuWFvV9DqgDal321YoCa0%2BVn7lBnkbEsdkVrKCY7SdUyhSQQ4qQwarqg0eGA0ZQEEyJB8WQABxPzS87oMJDgkho5PigJ1JctIAQKwgHXSnl3QNi8%2FmLu2j8QgDhxIh3D6lBhVzPhxRBocMC5AoGeio1pYMXpOvCgIth63fwvo2iAQJLx%2BY1CAwYAYCG5QAuTIoe%2B6A2tzMgdaoEYwzDGs7dFQSQS0ZM9PeoCLQDoG%2BKKUCGIxJYNKqMQ5AN2MSA0MoDiRJlpL6dEAFpBkyHcNy8FACaauWA3b8EBigEeCKRwSQWyGldWVQTkadYLlQbU1q2yA1rNpjYorOTIGviiAWqLgzgluyAsIIjYjXqgGU4MDSOdhTZAflhx72bp3QBzDwSwf4yEGAyEwZBIjVAuNNIb2ZWgOPzEkRy3ZUZwXat3SfeoBIHXcuFQeCCxl6oASRp0avDiEGNo0GsjSZlQTJYgVLUdjKoxr%2FAJTS%2FsHQY1LGuoUQpdgLXhjcKIMQKkA9dECEV%2Fw6g%2FcqFuAlnAuKBCNolqa7oJ3HXxLIEIJehcVfRUTuDEnU6%2B3RBHUuenKBQDLl2TKYSYVE90VC4TOvwVRzGCwoXcDwVESNi0PCIjfR68K4HLcHBjofYq4HNdUhvFBJjk3mjLk9PFnA5DarWR12e%2BizlV7dxXQorrtHGyg6LSJu3%2BCmRa1hyNKfBFdFgh3AO%2Big6AGB1YexRV7awYUDhpA7omDi0wwqavulVcAGGpT4KUMHe40GsoLWgXON6jogaT8rhxXwQM9Tw7MUDM8mem6UPSgDYsQYpuoG63AOJ2dFYHWHP8PCDDQVOgoPuQUh3l7aj7HQAOQAQ2xgwqCXOrA%2Fl4Oig1ammvJ0IQAObi8XA0G7CVQwAGUtj%2BYKUOzPc00A6qVQ1JuDbbyiMKsGcB2afFAoOpDlncasfigf80GWqNEAFGDEEdkVopN4PxRGIgMBDG0bIMbS4LdtAlGYF99BXxFEoNhuu0YDSqZDAER0HPVAuJLxIEPuKHVAwAAEEk18PBBiQXFDbPt2QEgkCARUgz1ZnQF2Ichh7UQBg7iprd06pRhi1tQ8OYMboGaGnX3opXGINDi%2B6I1rULPby%2BpCZCuwh4OnxBVDgsw%2FCaKAQWMbgAPPvQakEBh%2BZtgNOiA6uQeAemiKX8xIfSWRDEPSCAGQByCz5C6QHHRAHDPSZujXdkBqB7E90CtBtNz8%2B8qhpnUjTR%2BygIZncAeUINkzirksXQKN9ndudYQZquGyYBxpRkBEMf4jXR26INEOWNCaOg38MkAET33QAw4H5WILN3QYlySN8Rzx5oD%2FAJOpd7ttigxMkuwDDhBmMtA014QDU%2FwnetX5QNBho8kUrsXxtyIjfuiGFXBfYaMgAcmRy0oMQCXZo2%2FBBsXkH4opWufcEsQ4hEKbTLmQGfhKC4Ji75RM%2FegzOxl4f4yOiDcFtvZ0UALaPsAdR9iI0vc4BIimiBmFaEvKKUkWsHPM7wiMAxyDMZJ3SgORDEkOANa1hAxxeWM7oJkEDUQ90K0Coa3%2BGIfgcqjQHYEN4AqAkvrIgdwgxIobnrwgBtBuLu%2Fj96BADaQN9Pjugwc3F9OrFBpBjSs9UCzLiTQyoicWuxLWj8u3VaG6FiRQoEuabSW2HHggQuYdte6CVwAM0JogQg0JPmrRMiCasgjo2oMgFVMkuDhzWjlRULiGubUP9quEc9wYFo1AKCBDOSXaSqIXBoZtvBEc14DyQTwtDlvFvmdFRJi7%2BbKMuOw9CrnCumy6BqVIOqwjYy0%2BaK6LC8iPPRSDqsu1aCFmC1pBPcPqFYro9My0O9OikF7btAK1CmcKvZcK0DMkDO5iHoPYIKWkEkVYedEHQDiCanQKQNaTV4adfZ1IKi5stBQH3pA9pLGjs79eiQYyGxIep%2BxUUEPFa6Dus5Gc1knW0H4SrA2WptbKoPCRRehI7DcoHBttABbYBIGyFBJP2JApuyYYtpt2hINkHcmsWnrskBNziQZhhykBB1LhtAG%2BGqgd2LggAbqKUXUa1m%2FMA3h4qxByAcsW2fnqykVn1IA2c0VRsmNxm5qJBsgHto5jfwSASa1MbHdBsqAWgEHz1SA5Ro7QXiSkGyB2YT8UimlhkSKexKRDAtLGfthSDG4O5tIectfcrBnucmS4YSg2TD5jJgDk7KQDID5WbQgzGzqwHNsizBngxqfNIBk1rCjSa%2B3ikB53kndBjcZNtuQO32pAchbS2dBrypFC4hw4BeATGvKuEC64mgo%2Fy1NExgA3CtdZaOUgd5MAtQ691FK8uzvroQ1fNVGBJuJxgD2hAciATozgEpAMyDEghwY8UgwZzB3tnQoNmMQKEVmQkByYgsJhzHZikGeeedgUVheSBcYBl%2FblIACA%2FUFhCINtzn8rOKPDdEgxugl4MBp%2B1IGMijFRSky5EGC6Ixu4L6nRWDZCfmkiNQkGBgDEZEDybqkGNxFAza7e5IC4cHwL1Uigbg9GYxMUorEDLUQQKc90gd3YHvyopXeAG6e9EYXR%2BVgHfXsrAcgCHDloevtKkVjcWdg%2BlvwSIAukHRmDUqrBiSaTbqDq%2FKAwDSbtIZxKig4ufGG7F1UA0LQ1C%2FeiQKchDeE7cIFBGNoLXC08F%2FFAQaSxtj4IMSwh3ckDkx8UBfRg%2B%2B2zqRQyIeDdrb76qwHL%2BKgAn2ZIFBDXR2BJRAclvlcDUP8AFIGeCGZ7iwFUBF%2BpEN8s18VIpCCGLcMaNqqhcgDq8lzR2CsBzNo0FeiQC69jsAapAQSR4ueaIFdySCCQwrKQJkA8Npd4DZIAbsiwraXSAW3OLiIdpJ%2B5TOEY3AswYkv5JAj6WgETQtRagW4yzFm1NVIEuIAHytowSCZul3gwCkCXEsHHUdVcCNxuIIg7EQrBN8niC0KCd9zAG7VmKsErrg70cJjA5yTD1aVRzXGWbjaPBWIjddXc0DpEc110tWrqwctxMnX4KwQmnd%2BVUcdkiRGlw%2BCI6rXbfd1Kros3Z6HZkquqw6aCGUo6LZAZrtIUHTa3yk7pWl7DAeN67aKC9sVnUn4KUXD%2FADtVSghjcHB3f3K0WtpIlqdVKKiAxZgYPTlSioIAFHNAgIZgBI1G7q0VqwIDv8qlDProTTdA7sHaOfHlQMDPaTzsigBi8PNPN1aCxeS%2BpqPilFaBnIlShXJnFwDO6oImBc7yfJKMaNaWgy%2ByUC4GB3BnR9ExkOdAAwZmFXUo2RBORjTf3oDbJNNvCvvUoAcEB6VAaOXhWhqADs6isHe6K0PsyULSloBkl57q1B%2BYtMN3UozvNvVt6MqN8sG3t8WShrRLXB6kOpVNuwerAFh0CUCagggRa32lWoLNq4IZm0GiVQGI%2BYyGcFkqC%2FZy%2FwBxUUQ7k0c%2FdKUAPUOZo%2B6UEPBoGp8AlABJAOhFXnogIAIa1gKgijpRgauG0bx1QZhUAT8UoUHZ3PBffVVGBhx%2BYhA1oLEXTvt5qZypSXucbflJbXZVBaG%2FKJmg8EoBD3B5LOB1Sgt%2FEBJLufBSjPbLyJcvsgwg1NzOXjTwVqjlGTAv7BQLa2zBmII06q1GD94y8Eo2jEE3SACz8TRKMSAYDBw%2BjaOgIEFqbBmPailBBdyY0KKTQgGZPsVahizAEuTQxKgAuORJoNacjRUEcTTVi6g0s9ZesJRtiTiDLK0As5BAYtRKMAKyxkkJQwOhgtThRQBD3giT%2Bb8VUY3AHnbqoBAgwKDrV9laC7gEgTQ0dRQLNAdgId44VqMTqYZ5E0QEwWJcHQ6%2FBBpb5o3I81KC8gjZjxsigQ7iAlCAh22Jcu0%2BKBdgAfl7N0VqG7Et7V7qKAaX%2FKeyVGId7iC4p20VoIbsKMN1KpS4NGD4g90RnpqNOsz5KhnJIgiHdRQfUy7P0QAAGYJE%2BTVVqEGRL%2BfG0OrQQzgTEh5ShQYuB1j7uyB60e3inKilDsQ4jQTXRVEwaM1JhASWBhqygQOGLPEnkyVM5RmeSQXodeyUIdS7irHlWhbmLAyQZPZKFLdC8mvZ0olcAQW1Na%2BKUTuFIke1VcZE7ibiRvp96CUww7IEPBHBSiFxdmdgS4VwOe8h3BmaKohcXIimqojcSTBYio4RHNdBow1KUcl9DC1RJ5rG76ojjt1mqqOq2exhRXTY0Grsyiumw6Me6g6LXaQ5aCmR0WzzKjS9mpmC7%2BSgvbpc2rPRMi9tSASXOvKge2WL13p2QVtedf8AEEFQQ2x0P3KBwSRNrA1lBS2LcTMR%2BCCo3kCg196DOB%2FEwB6oKOCx0mNpqsjWs4NsbRvKq4B3FGMEPMPXdUMHA3LU2%2BCB5YgU0MuoCRk0s0n8CgwpBe0%2Fmh5QEUrxkR2ZBsgGeuw0PsUimBoCamC%2F2qAl2Z23Blh1QaaFmuAGOj1KAvFpAjc6BBjc2rHmiQBgCB3M%2BCBQ5LCLCxDBEYBqxEcIHJhtRXSqKV5IyYtA0RBEEUEmUU4kWuTNbgd0QXbXJ3IbYooGkF7aElEFyDbkdPxQa6AYIeSaoo99Y%2BCBWDmHgOKdSiDaQIGmhO5RQDy4dpB1k0QZnYlydRXZEY1t2BcHzlAZoQQ5rsigxLEVg1imqINI8%2FvRSs4tdiBQDy8EQTbI%2FwAWpZAQwc9wNepPKKDuQWckM9sxr5ojNrUGBEAIrGKzOj%2BLIgxR8W%2FKH19iit8zagiGJnrygzh2AJZp0qgAYgir66n2qiMazSeBR0GnEkCojp2RWA%2BaTBp70BJcZAtFBqgBNooSC7tUojESW02AroEBDucQwENCKAkwCAeGY%2BwRGclsXo4gIppGnB16IAGNWNpmJfvwiAA71BoxneqDC7oQPzDd%2BEgIHzQwADAIoSLon%2FJdy3L8oGMD8ooxeA3mgABtZy4cNDMiFcM4l6mQOdEDGdBawh9OiKBgtWYI328ERmIYPQSNB4oC%2Bhd9xCKxMNTT4IIngviHI9t0Q0h2L2iD0RWYAhywOjs2yDOIAkD2jsgLiTUGuqAamMWEalAQWABk%2FegECsRJhEZnFu7ObTygwq4tYmt3R4RQIIAmgmpRCQaBjPloFQpYPDwHD7aMyoYTWd6UZQHSJeCSJ%2BCKBa20gHrNH3REyKSdRkPNAflZ3dy%2FXRAvzCIbiiIBMcCR0lAheAAHNQ234qhbg0tLV%2B9BO6A1XLkdEC3YlhvLBQRNGrrvRUIQ1Rlz38VRETs5od0CElwfLzQQuIZ2nurhEbyH2JPxRXNdvzELSI38AGKKYRzXs8zs%2FmqOX1BWrw7KiGuPl8VUcfpmntJTKOq00ALNVRXRaWHaOyVXXbqA3DbrI6bZaHISi1ruQ1Gb7Uqui2eG0UqugF6g%2FepkVDggklzolFQSxY6QVBQEOG4YCk6pRUGvB7h0FAJLV0Cge0uBb47exSigLmjw4ShiCMpLmUoayDWA5dTOQxeLd4bblKGJMPHdGgYAbkyT96tQRcKTMA7ToyBmoGDO59xYJQwZn%2Fi1r7lKoOBiwYbqo1WY6wRvqlGt%2BW5nYElgmchxcAMhIGg9pWVMXMAt8EoVyCII0Ar47KozU0bT3bbKUbQMOdCA1KJVEOBEhtISjB9wSGFfbdKFpazjLQsQCPYq1Bcu7UPl71FYxG4qA9G2ShnMGS9SPBKMLnxcO1XrwlDZPP5WDgFAdnqanVKNQAAsfYpQMoNQ0c%2B0oMGGuRDEqoMk0gROqlVuTXUapQRzJJpVkoW65raaaSyqMaTB6OW1UUfyi6XILj70ozi16TQ7tugznQ6M9UG1LeDJRiRBaYr1%2B9KA4IBOoyJ8zylQGYC1mapNCrQQRWQxE7%2BKiieWIMHdKA5tBeWmRSOFQQQHD4tPRQAEh7ZJ3%2B9ASIIfYUHuSgFnkEb7dUo35QR%2BYAszPXRKMznmpHTv0SgioNQBB3fqlBZmcvSvglAau5Md4dKAHA%2BZneo9%2FmrQQ8AjcnhSjUDiO1T5pRodzEta2qUEVpIgFKAAem46pQCwrcfmBlKMCcm0P5njuFQcplwXZlACCXINQwIKUEVZ%2FwDhBKNwQxIlAAzC7FgHbulQX3iZPGiKUnEOBI5j7EoXWTQiKpQdiXAdAGIA4EsPclBkxBZ6zwlCsQboGLTNd%2FcrUE4gfNIAYk6gKVSn8xuya3UfFlahiSSw6j2bhRRIDiu4CUYbmlQUoXIiSGA3hUKxcu9zUSjAGAKDn20ShQw%2Fyd2%2BPirUM2MBgKkqVQFwe4vFFQLiHfmVKJkwbmJ4BKqDMF2h7koX8txiKm56AqVAuIBbFuEwFmCHJIrwrQpIPQ%2BEpRO6Tszz70oS4muo9mQSJDgbv8wnzCoiToPbxShXBgCdQgjc06gQ4VoncWNOjJjI5biQ5FGrVURuJftTWVajnvDF9NvxSo5r2LsRqFRzXnjhWiL%2FADM%2FtVKjhsNA79FR1WFh4qDpti6hPtyorqtJ3bRQdFpAmZ3QdFpFBzKirWNoeoKmVdNmhc9T7lMi1h0YhpPPgoKaM1FQ9rsADIFUFrCbgDXcJkOGa3FneNUFQRFSeeFkMC7Cj0I3CooCCHqABTdQM50JJofeimcEZuwURoteal3KKIfToake9UE5MCJimqKd7uhqx%2B5AQwBbQhj7FBgRoIJem5QYEjVwD7hKAvQs7weOEGtg1kgFMgPaWNA8katx2SIpR3l6AU8lFByCZcOSRqgzN%2BYOHqUBdyxgs8H3KAAkC6pYwTqXVBMl3AHXxogDQQCKFw7Ud%2FMoA9Cx0Zq9KohjSDpDMorBjLM1UAAa4kQ5o6obIkBy5qbT7cIMCTyDRBhdWIp22QOLrXggadh%2BKg0FnIkBh8FQJ%2BZyBsdkG%2BUuCKnmS26DNBe0R%2BXaEBipI6kKDFjBqacPrKoHLfLcX4QF6%2FK2ooFANCGAJ09zqgi4OXOxHfhSAG6TXjTTdUH%2BHRw2LoMGoDUT8GQBoLEBjXw1QaHDmszHtVAfmDbDfRAIuILmDSmqDSSAZLSWQYXWuWEhmfwSAtJIAJFa8IAxLzLSAIpTZAS7OSxGvTiUBIJY0q5hx71AtsCJGg253VGMSzA7V5EINBMdepr8EGBunIEtIAZAdXq5fSIqgFRczToKnugxJk21Z3aD0QZzLCKkblkCk6RPyx7FEOKHQ3b%2B2iig4IeNiQ%2FuQAXwAC5aRuqNlVwAH8UCm64AkeI51hAXnln691AopBDav4P0VGJkSHGj%2BKDbwK1G%2FQoA5cVj8zeVEB%2F4rgU435QEuQGNWJP2KAC1tzjIfToqM5I0IMcIDHNaNOygVw5DgB4bgKhQWdgS0t14VG%2Fi3u4KAXAgEhwAPzatqiG4aA0nhFAFw8ULHbugDAOAcXnKiIVySRQEsZk8eSARtUOX7orNIeRsiBJ1lm1ooFyAcFqO4norAtXkh0QLiAwcDaECEiCwaiBHYOJf2KCReXkifF1oTuu7mjn7kEbmoeHOiDGmj1ZQc5gUymiolcDxx8VRz3GrS%2FvVHPdcJBoKOiI33OC8AVZVHLfQidh7FUc190ttVIIsc3iqtRwWXAblyqOqy4EuzyoR023NJpRRXTZf7exRXTZfD8QoR0W3CnkoL23hxqQVFX9O8Oz6KCwuAkOYgIKi7tVm3Qh83Y7mm4QWtvJ0%2BU9FFh7S48sfwVpD23M4pvH4qZFQRWbhRQh82Lu%2FFPehFMrfGvhqgEO2L7IQwIuIban3qcxDZOWbWPNBnypG5aHnQq1RyHIPRkGF4YRBbYQ33IRTN2%2BbE7cn3oMbiCYnp4IMbqQzAECD2CAOGYFjQgVhCNvptoZbzQhnbICuhQjZkwzBoIFFIDkLhUh9NYlCGe2SZ69VCM4qA1DCEA32u5Yc%2FBUF6PaW2jzUGcngnVCMSAxekv0qhAdgDi21ux%2B9UjM0hz5JSC4lxyTFVCMTQgF3nw8kIBapJGpPbRUjAg5Pb%2BbwLhCDkxerVpDfaoBmQIMES9CqQxvAEhgDTdlAMiSajUt08FSDmLWf%2BI7oQwvEj5mhoUWBnboCxk8uiRsxpUy34KkY3gk1BFWgygY3D5hbqKHwooQcg58kWFytnXXLqiQcrWd2EsSWQgA23M%2B8FCCLnE2kBtd0AoQwkRa4jyVIxuYF3IME7uoNkJe2akDhUYgAUadD5hSkZ7Rabdaxo6pANwaHcboQ2Vtsy7UjT8VFjZWnsQ%2FtKJC5T0cA1r3lUjZ2AsHBPvQgZnUQZJY%2BEVQEepbL2u5g1cBQDIEYm01BYtDyqRswdC5p7VUIxvtBNrByI8%2BioN18Aij%2B9QhcwavEbchCFe0uzHQH4KkEXPuHJZ0BBJaOhPwUILw5ltojxRYR7SRD6Y92VQzhy%2FBFuqhABADFiHpSB96pBcQcd2ajKBXcUIc1HTVUgkgRBDwDoyEC675XB6jQR0Qa0%2FKSATB08qoQ7h5Mj2oosIDaxO4D6%2BeyqRs3JZ%2BtKJApIlixMyemyoBJYfxHUcaoQwumQRRggUEgTNadZQhiavR5UIRxaa8sA%2FdWkY3AhnIxiqEKbnZgQXkgfagDvNsA1CUAXGIfihUQMm%2BYTHzShALGWJerKkC68WuS8SgmSD80yJaAhE3rcQ4EjRUhMnOrAxVAuYEUArsgibw1HbTmsOhEyQGn2KqRO4gaOzbOhEiX%2BaQ%2BnkhELrwC5glm9yohddoCRzqqIm4T1REL7gHL1og5byJ6y3itEcpugzKqIv8AM%2Br1blB59umj1VR1WR41UV1WXMA7qDotu1BpJUV0WkRNNd0HVafx5UVUEkB4fyUF7bpA32eEVcFzWDpRlBa0yKHbuoKhhI1KAu7ih2QVtLSIfX2KCoZjU6EIGBpMaHZA9vys5qXlRThwxYRLBA4IJEi3UPtsgM2zUVPRA7ijDrxopAQdOIBKgIBEGhNK6K0Yy0ToVVGrmf8AJ%2B3zUBF1CXIuLqhgXJYMRTSDRQABgwDu86eSoLMxrzvsgYCej%2BagUwXJ0Ymk8qgACA4JMGdp%2BKBssSNH8t1IGyLQH60SDChoxp00DICTowMT8FAAKzq8RXog0QRqdPYIMAD8wcZPBG9UB2LPsDugLGLqHUIMGA%2BURuKboF%2FMzh3h990BtB5Y9imRiAWB%2Fhn7EAJalIfqN2QEkEggiH1QAmTUkUd%2B3FUBnQVPQd0A1BJDk09mQGdiTSfegABIo13s%2BnwQYOzsa0130QYORc%2FzA0OjICwJ%2BZwQ7z8UGL6FoqgBud%2BKDy5QAHIhjAeW16qh5tGzmBTsoMSwDjkBApu%2FMSTDEtp0KA%2FM5aAK8e9AA7sXHPU8boCCdQSaA6x9qAECT%2FCYbRAHB%2BUyYZ9e6o1vzOD8suBrKBi4LGXoGqygBctMgtaXZz2QEksCNNYQbJxFAWYhIMBNpLkjX3oAasZP8Q08UBIDyeQCHhBuMXtO0oBN0AgjxQF67SzFkG5kP9roAZbfSNW5EICSAa11hAAHj5WeNw2%2FRBtw4%2Fym2lAXucEMAIPXyQapIYhxIqgF2xq2zpgYEEyBIhtlRhcDT%2Fja9lIFFw0Alzl3furBmMPJq7IM%2FDvp0NEAeh%2FNsX1VG5brb0QDn%2BE19mQG4OQ12LFMDE0AJPM12dQKXuh2HmqFAdhOOr790AItrUdkGBJFrOdz%2BKmUrEvaXDlnIQKS3zCZEoAA5BedBsFQjiJFdD7kALuGoHcoJm6QAWGvLIEJihAGnsVRMuLiHrTdEKSBHiTsdHRUSQ9QQIA6IhSW6DbhBI3czugiSGMxLaKiF1zmAY3VErjo5eRoiZc9xZ20lUc9xBMU4VwOe403VRzXkS3cboiLz5qjgtOnRBey4kbEVGio67LmjusjotILEDpsouHRbdXnyQdNtwiXGiiuiw9Nn2UFQ3jBSqvaQwO2%2FvUFgQ0CnhCC1hatApVO4%2FhlyA9UQzj8paKOgsLnG3tsopw06lq6cK0PkzNMcqBhUlhNT8EofNi7vQcqBxdQOztKDBrqyTUKh8mYCmrqDAiS8vACBy9AIOte6lC7sxFR15VoYXUbzEAaorbkTDIAHBLOAJ9grQ4uAEuJ%2BbZ1AXB%2FirIND5oNjDlnma9EoaSJcRXYoMSAdBugEAxJqT%2BJ1SjOxJuLhoB4QAQ2lAwQb%2FJctEjcVZA70YAAaqAPbVhBY7hUZyHALvDtVAwYuA8u51hQFyG68j7kAECHcvG0IMbrp1aS2z%2FcnICwEUl6JQpBcc0EjqlBaTAcwD7cJQddJG%2B%2FuQCks%2BMjfmUoYuDVqv0QD%2FJ0L4ilPNBh%2Fkhnl4TOQANCPy0SjfKA1YDb8IM%2FzOxcCj86INQMSIgPwlDO7fLMA61QLV2i4Q4%2FBKDSAw03hKAXajzA47pRt7WYuXPHggDEAziSfHRKGcQ1QW8UGMsdz8PNKAxktk%2Bh4Sgh%2BDHy9W0QaZLtsN9n6oBNSWLgM7INRwT35CDEEyBNCD1dKDjaH0IDk8eSUaQGMAsPHolG5obqv7kAAIJEEHsyUFgzM5YkxD0SgA2nr11QE0BEdeUoANpbj8ohkDEnRp1qEAi126jZxCUAk1cWtRBoBJJ1lnQDIO%2FjogUkzkKGCH3qyoLgmXgwgx3dpd%2FwSgGCHa4Ma8V0QaoYEF5380GFTrFdX3SgO7hoeVQYmpqBPKgPUhxTolCG7cAvQ%2FBADc5k0LR0QKXrAA3PgVaM4qLhrPvjspRnYAgHE1ZKjABiASC7P1UoV8S4D6eSoBLFycQgWATRz%2BX8FQLrgYIcB%2FmqgmSDFtAYQKZq23hslCEm41HcUVQDWrk1KVUriKUqyUSykh2brPREK7SPw%2BKCd12oAoWCCdxZ9ZGSYVC64Se7qoidz%2BCtELriTBB3LojnuuE7Es6ohfdBIh5VHMSQ%2Flsqy57yJ02TAg%2Fz%2FBUcNh4QXtNPJB02EwenZQdNhgPHfVQdNpAPWqir2HbSohTKui0sXNG9iguC7RFXUFRcXd2H8I5SKtaW7SVBedNJoiqAg67OVBTKHZuapgEXWkS816%2BwViK5As8ifJRTvDl28wgclg%2FLhBnYhxNGFOB5qIrlvw5UU766GppCAi6m4gbFUEkia%2FBATBNG9nUDC4EVJ%2FwhICCSS4BGyDDQu4BnryoCKlux3GvvVWi5c%2BKDCWJAHPdAPmYsfmFDCB8mlhSu%2ByA5W3DsenZAWaP4Wk%2FYgwc1YNBG%2B6BWMAt9jbKghv4gwFCW8FBqtQcEVVBcy1JDqDO4JB%2F5MlBqsYPtzsgwNaOwBCAuYcToDKAGgdy7x2QHMuAd%2Fl37skGdyYYj%2BJ%2Fi7oC4drY0cqAgyRLM59ggwLi4sw0PxQHQPazSihZwYDUkdkyg6HEhz4P96BTaCHfkNHSSgJcCAKdHZAdQ5rQIAzuDShLoMZfia88ICSWYaQR%2BKAM2nzXVQGCKV1E0%2FBBmioI25q6AAzwK8NPxQYxWBd0qKIGJLginigSLWMV6tvKc40kMLWDGWmiAhi5BYmh0ICAA7watIdAzQQwmpaEAtta0jLWXHwTIxFzk1eDOiAF9DsO9JQM5DA6%2B3KBXBcbQG37INkCCR0fvyyQGCGagQKSwdvm1uH2qwLmCzEguGHwSA5FtXrMT7BIAROQLj7WQaQXGsHsgYkiGfkxRApALyXaG6oC8Eg5TH2IMBUnQu40QEiWMx0QBjLAQ7asgDSS7hm31QA3h3Fr7nnZAQTo8jXRAlHEAmSd0BcSNRtOiBXBMl2luqDSzg8nuiDIdug8tlAlpA%2FyQGg%2Feg1zmdqGkqgVZ33YoFl3baWVAy%2BUkPq%2BmpQKbiJu1o0lQLk413QTdiS%2BR2%2FFUK8TdAiOyoU3EDikwgmSaab0QJk%2BsVJVgQzSYUoW%2B6vRMYErjEliaqjnuuYVZoICIhdcDr3VxgJdczyx1CIhcW44VHNddroKhUQuIejIiF9w67lVHLfSQqOdy%2BXkqOGy7nWQqOq09hqsi9lzBnGqDptLN1ooOq0vrPCiremSdZ%2B1FXtuIDbwoL23O%2FwAUFxd96iqAmRQsJQWtu7cxpEqCwMAE10KCttzan%2Fg%2FcoKQaAkEymFF8WDx2V50OLgXbeg51hRTi4QKDUGeUFDcd2EUTAYOOpllARoCWek7IHzDZaa86ICLtTpTiuiB7TMgvvv2UBFDMmoM%2FYqCQQPzNsXZAcj0ippKkBYUYc9HQFjcB8VAQWmm6AOxfQ7096oIL6sGYN70WtqCzNLinO6AmASKmsFAQTONwJZ2QYXXUPEcdkBJNJf%2FABBARdTnWnigwFdrvE%2BKAmWmN6U8EGmpoJG6BcmIJDMKhWBgxf5Z6VdQZ2Zq%2B27IA%2FYwCO2iAQZIm6gd%2FDRA0s38JEEa1QaXjWjzSqDF2JqW3p3QF2uEs%2FmUAFwdn%2FKYFa0QYPpe4aorXogzu5obY6IA5tJYO%2BnXlA2RYvtDlICDA%2FijyUCuQ7AuAdKkqggtQNaPyoNnQs7aUZIGyYCIAbhlIBkXJYEavVWBYgEBiaCA6A6HU06dEGygQCGkT7kgGQkU3J25lICDq8W%2Fm29mQB63A0BHtCBgbntfaB9qDZGtWgJAlxOhZzr4pgFyHq%2F%2BIINqLiAxqemqDAF9CdfZ0G%2FLOjyNuUGJo7R%2BZAGMOAYo6DFhOm8ICQMpMtDoMSADO7nUcoDo0hhEIAAYP5uD7FAAImnMOgJLMWa7RzXugV%2FzEtAmKsgJuDFwRHaECEmhck1ID86qjEs9zna4iNIUGJoLQ5GsIMIfkMbvxQLUEAIggsdRsis4rVqs9QogktJLCSgmbh3Z3VgGR4Dltm2Vg0ZEEmjv8HQK7HrDjeqAEuPloWIMoASCZ1qgQ3RBx3%2BMoFJFS5Ya9UCk3Pta1FQpuGgcvTT2lAhu%2FwAp7h7UQTuI%2BwcDRETeTuSCD1p5qgEtDNlp7BQIbpIJ%2B5BI3ANMqiV1zxq0oI3XSdeFRElpEaP9qIjddJJPboqOe66QHfb4KiFxhn7fFBK65hp9iI5b7h74VRzX3HuahURnbyVR59t7NzRI06bLxGnVSDotuGrd1EdFl%2FCK6bLmbXdTJF7b9d4P2KRV7b5SC9t4D9a7qRV7bmf5oOsBBYXuJBo4UFLb7RDzskVWy5g21PemcEXtuBEud3lQhhfQ09tkgqLgwdjo%2B6hDO8g9OqpDAl3Ad6O6kByAh32mXQPbcHcflPsIQVzBIccuYogJuxpTVIGBAl2LUUhD5M8EhvJRWzq0nY6KwG28AvbtI5RD%2FU1aD2lIrWsRBLmpLVZEhnDSHANSgIuLgMQ3RSKwvG1NjMcJBhcDqzy9EiGBd%2Fmnz3UWBk9B2b8KqjR8xqx%2FLQezIGyBkSwE6R1QYlyXjf3IoltWcCT9yEbKHALkJBjc51tpISDC%2BcZpBPs6DG9nOm41kKkNmHYCQIHtRQgi4ESOI6INkALmD9tX2SDChfn5RwhGMEyeAHhCNGoJLF0IPygDxHCEY6jQUHnCED5XAY8ARyhGdq0pT3oC4cDWnavdIBENUCDqhBBDs0NRCCC80fVCFFwf8xLQwSAAmflYGAqGoNyNT03UIAud4%2BV2hIjAuNbnAn7kVhc4ly%2BujeaQEmBE%2BJQbJtDokGcOxPLdSgxkHV6gBCMCzljMkalBnli5b%2BJAHckaVY8oRhNrh2IjVvN0IJajG48oRjcGpFSyQCQXD6hzX2dCNlABM78gKwHUSWM%2B7ooRtuB0QjC4Fn1MDzlIBkAxduIQgZSQAS8EaOyEb6jmJFEgGRIuYMX1%2FFAM%2BX2SDPoWIEY7JAuTOSzEQPuSBwbQBqbY5QKb3FC%2FtuyRGFxiCJcqAZS0gbaN3QbIUDlmYinkkAzAmrnqKwkCm8G4NUvLOrEYXGhHAqEgV2H5Q%2BsdlRs7JGrUSDG%2BZaRpuopcixhhWFUhcwSGpo0aIFyG7Ws%2FZFhcsWkxUUSIV6gTEj2KpGybncosTNwALU2O6JCZaswJfQIFJJd4YwgU3B3Ylj%2BbZUTN476%2BNVAl1xAqQ8kmVYJ33EAtJ1O%2FZCI3XhpqzEhWCZuES5r1QSJFrsHOvt3TnRG6%2BWfpburEQuvmndIIX3kRxX7lRC64STroiOe%2B8SGfVlcYEL75bhiqOa64OTrwqiP1A9fbqkV5wu1Wh0WXGNlB02l9ZUyL2Hsg6Bc7CnKiui256%2B%2FyQXsNQzgyoLW3Gru8htUVe26XJnQdFBYXkUkioQWFzgOK6cKB3AYaiQiq231aSD7kirW3vr82kKCoNNCDRQMCTpTQQCgplMQBLe9QPkYL1ZuVUM566GFCjO7inKKIuMB22ZUOC1QwoFBRx0c6oMbjyWYR5pAwMvMmVBstTt14QPkBx5dUBBY8En26IGyMw1PM7IDlE1EPKBoPJoUAAMfws1D5IGm2hjWEABLiGAMIGyrDEDnVSDFmcSaBAaMIHDIM%2FLOw6%2B9FZv4dH2SjVuLiHmfglGcB3cQSwPc%2B9UM4dhEO52CisxIEkaoBpcwoxAVRtKEDQdeiDEkEgXSzse6A51AMceKQEEkBrpbiiKUGIaDXkohjcZDs0ugxIFs1qgZ3JDHvIRQu0IjQlpCIOQY86fFRS%2FLD6u6qGLMxID69UAcMJYaFBnA5iEGyx2IP5qoA4BM0JnZBgbdbgWfI09qoGe0AaAaj4qKDgUkEgv3VGcCskl%2FGiIzWkB9NduiUAF4JqGeJZAcrY2erNKDXEAcGAPuQLk%2Bjy2qDEksYtGp19nQbNg5LAFgPhqgxNzSXLV2%2B5FaRJOTkDbtCIFxltRr3QYD%2FABGnt5oGYQ%2FYaBRStRtD5aKgXADgGo0RBcXM55kT0UG9iDRKA%2BrIVuAe5qgBZnYfNqIoURhAcl3rKDOBqYNaIA4IOqoXK4sKxLO%2FgkDBiHBijoFJEvABFeUCvbTQRX23QA3nbGQ2tKpACZLnhh5IFyYEi2jtPigAJaHHXpogVw%2Bpd3OyBctXFpqOSrBriQxqaOUCPt8uqonkxAFRTXhAMiYq1TshQdmDtx%2BKIE0gkMAgmbmhpanARSEh9zLoEytNCXJdBI3FoiVRM36gnU%2FckREkihd6KhDeN%2B6QRJaIGwVRC66SMp2QQJFXHLKiRJBYn2CI577ndq0KDnvuMjfdVELrt3O4Co57ywaGdMCOerndUedbfpDaKo6QW%2BKiumy6k%2BwUyrosugAaKIsLqDyQdFt3kiui24001UF7bn9veoKi%2FuUVYXmN9HhQXF%2Fn%2BKiqW3OwBYRDaIigJqO3wCVVLbiGO9RoEyKW%2BpTmh67KKrnE0QPbcdz7eKgpbeXYjrrKB8jBlm9tVKGBES54VqQzxs87IMLjActTaiBxcep3G0qKbIlmLv7QrQRe8QHkeKgYEMSHtag2KAuXAFDI%2B5A%2BWm0FQEXl4MfxeCA5EAwQalvggNpoA9tZ0QEXEfxOedUBN8vi5Ghqg2Rt8YbmVQRXYuXea0UoYEl2DABtkGybtQ7%2BwQYEgkiQTIQHJhMaugNpB37saqA5CR4kR7URRc1cFzHKAOwiSIAp2lBiXdixO2roDqGZz0olAJd5d%2BNkpRBl7paQSlGJYkm13En4USgk7n7Iq5ZKBlIhiX%2B5CjAIfR2SgFhqZYMFaoBiXEm4yaQlQwuDOKeXdRWJbbLQdVRgdtaH3lkBd8gILUKgWj0PEDxZWo1WActr4QiszByPmYT7OlRiXL6N%2BaiDGK6b76JQXOhrpy%2FVFZ5gvEAIAZEN0OgHdEYwbaTAAQGOpGilVnDBi%2FT7kQCRMzq9aJRiSHOr6fGqUAtUtwXborQS%2BkkGaa8lSjOzDEjbfxSjF%2B%2B9H%2B1KACTr2bfdKCSWqHA1%2BxKMXJZnfV0oGVS4cH8UQpOjGPt4VGyaWZhHRAci8kP7UUUoNavpCqMbiHYSfgg0WuwYsKJQNPzZe1O6ULkDo0wxZUbMuxECH1hQYksJd9UC5NAZ2lj4ooZXP10KIU3mZir8DZUKbwKv4mEGJeAQAa90ANwtkzPUygU3EMwc0ShM7gaSduqoBuJI21MhQJcZp8CqgSHlhoNNUCuzGmzsGSkKb5%2F5yKQ3kPtJLoEJJ1qgQ3GN%2FNUTN%2FzAUQSN5Ys71KombxqXendEqd1zzoK8IIm6mpGqqIG4sS5BnoqJXXmdjvCGco3XO50CIhdfuKKjnuvZ2M0VETdq8oiF91Zog577mHwVVzZl1UcNt1PeqjosuLB4UF7Lmg90V02391FdFt9C7cqRF7bmZvFBW2%2FQIrosv1Md1M4Fxc1TGg1UFRcxPvRVBds1Z7IL23uPe8LIqLtjOpf3oKi4GlRuHRTg3NvuFFUF5YacOkFBc1SeqCgvejka%2B9A4vp3b7FAwvIoxGyQOLoLD7UDgxo9SyiQRdkN5f2dAXJBqR%2FCVQz%2FKwHUcKKYXiKDp7kByblwYQNk9DwSgIuc3B3F3tsgMDoKDZAzzR32UBdxV9bXQEXCSZeTtRARfWg%2B5AXAB5YR8aoGtuNRqabdXRRFxq%2FG6Agu3iCEGBaWLbD2CIOVtXqYZBoJO3mgwIIYNHKAs5Id%2FbhAXcmh2CkVg9styeyIO8TQ3IpQflNz1d2%2B9WIZ2ABruSpFZw4J0cMkABA4AaJ17IGcAuavCAAjzejH4IDkJYuAHZ596DOJJYtJQb5Q4dn35QYEVgywKg0EE%2FwAOrVVRiC5gEAflFUUwbjnrRQLqC7AVJ8VQXnWKjfzUGx27iqABxW2ZoqM7nY0OiBXDEO1KndEMLgzu7OT3lIrMMefeUANwtJklqpEGHqG8T7kUruxduAYRBcaS1B8EAyNdNQdkgwMzazlwNeqRWfWjVOzBkAF0Yt3ZEAE3Nx2qKqjAM0voW2HRASBXYx2RQcFi%2FIO4RABAMPu1EC5FzdV9NPjogLk1YXFn9yAEuJrps6AZB3fTYvCBcgNNoHCDZXBoeafggGQAIOjBAj2mGZjvvoqDkaAMalSDEl5nYKhCedK8HlACREQUCm9%2BjvHHVAuQLhmCBXNNQZKAVoRNURiRALMNCgU3NrUSPwQhDeJBDaTCRSXXuSJcKwIbh8xiNECm%2BR8zcIJm8ikA1%2FFBI3EhquqEycgPoURM3ASOjcqid13LkoiRuDtTjzVETeewQRNz18RyqiRvh9BoEETerBz33ly32JgQuO7cqolfcR96DmvuaWVwrmuuBJoqhMkSvMtvb4KjpsuoPFQdAucNqlF7b2ijKK6bb%2B%2FRRV7b36iqiLW3M0pRYXe3KKtbfQbKC1vqD7W%2B9BYXCJp%2BYKKoLqcGQyUVtvpyJ%2BKC4udgeqzVUF7kzT8UDi53cNPigplL%2BW6VTj1HPtRQP9QPa%2FYGsoHF8hy7nr5oKG%2BAz8tKA5kNUnb2CCgunpyoHyoNpUoIu0h%2BNuVaQzvFOqDWx93xRDZF9izsotEXs1PdPRUEXOHkTQ6qUHKAXBG9FaDkLWeY8%2BEocXB93NW1ClGegd%2BffCBsyBPn%2BCDZVggoMbg9oiGhA2bsMnNQ6gxLg5DHXslDO2s%2B2qVRDMdCaslAcSx0EaylQ4uD1BmT1SqF1xE7OwNUQzkS3sUqg4HQCLhwlQ2Q3c6Hr0RQfafwSoI4oN57JVAXWgEwwqyqDDkwWrp59FKrC05Eg7%2BKVGbEAVHilGkfMxJb5bde6Kzi1311EVTnBeXcAUBPHVBiagFruCgBdgHcmnxSoMtB4aiVRd9Sgzk1IHd0CgmvDjSOUQSSS9WEjUJRgfeKlFBmks9UqMYl6UFEqi8UYtrM9EAiBtLMlQdnPwSgEiguYvR39mSjEiBDUKVQBiCeW9ilRnBDCXqyUAk%2F4X4PXdKDlMxu1JSqDl30FD1SgZyHdAHDOTRy%2FKVAJHyiIiUqgCKNXRKjOTbSu%2BqVQN7C0P3fREDIXFw5aiKGY6MqgF3G1uh12QBzuzz8KFADcKAdiFaBkG0nXRKBddo7UbVSgC5gBL7JQuREnSs7pQt1JltD9quMjO0mI9pUKXggdVakbKu%2B6VYTKmwepUoU%2BprR6EKiZLyI4JQKbmBPEP5q0Ib2FTw6UTNwJMj7igmb3LAPOvkqFuJkulCXXgMw7IhDfI%2FDyQSN7ZHwKojdewarbKold6g3%2BxBM3Rv5oI3XM4Bd5CtRzm7o6tEjfI02QRuvd211RELrhQFtm4Vohdd3VVz33DfslRC64B5nZWolnz7Og84EKovZeISK6bTTyWRe24EQaoq1twfdQXtvcxpCRV7b94OqguLq0PKIsLnIUVS2%2FkNuguLxBBHI0UgsLoo%2FUoKC6hZ9lFUtvoxdggsLxEztXRRVAdjOh0QUF7NEbBBQHwCgLyGr7e9FUFwA21I4QOLgDz8KoKfUoQHOpCkDA03ZkDggiYQEXA8bHokD5NUu9Ad1BQXblzoygwugVejmoVDOwklgKoC4M0Iq%2BiILh58N0WtwS5ZwgzwBQGSUDEvUxsfNA4voAWhwFFEXFqto9aKozvd49UURcDLtxuiMGcMXbQcIGe5o13UUQTVi7R7QgxuFBroffCQaCK5ceSIPMA7OimdyZnVtYUAfUBVBdjOsvqFFFxX8zxvEoNlqWGz6eSAuJ2KBXHzGm569VQQ4YO5IjhAXEfM0nVQZ3cC4M71VDEmQ46eagWKtFSXVBBpM08FBpoS77oNJYv0JLIBOTO7aKg8SNj5KDaSWgh%2FegGRaC%2B%2BkDdVBd2IuIGiijlO7eKAGWYuAOEAg6iBLboNkKguIbSUAd7iduXQHK0BmYeXdAou3G%2Fi6DZ1faQ2qqNbdRqCQTUplRFwLb8e2qgQXtrTWOisRi0AGpnfZFbIS9NUgAIuBaJnWU5gAajrHgkAe6rxLN96oBIgRaZd0QMpI2FWQMbtPBlFI7V6Ame6qFJBapb4dEAJDyHNtEGclhTcBAjhoZzt7BAQe4iUKWAQPGK6IgEgww6fdCAEh%2Bu3j5osBwARI20QIbpc3TodECm4EEs43okC5B23oVQl14diWqgBuDIIm%2FaN9a9FYFJBcmW3QI9D4klEKbwJJZ0hUzeC3NFYIm7XfTp4IiZuIG5KonddLAsYJRU7i4L%2B3iiJXXAQINRvsqiJv0PbZII3XipLbBUSNwL7IIG4gEP3V50SuLcsioXXb9FRz3XB2HsERG64NWlVRz3XUYzurhEckHm23k60WmV7biWe7RRV7bzvRIrot9Q7tupB0W3neAoK23kaoL2%2BoYmtCKKRpa31DXLSgUFhfuURcXdSVFUzP3oK2%2BoQWeKBBYeoZnuFBUXnUxogoLzvEsotVFxiS5qUFB6hIIBnR9eykU31DLFyzwiK53dZkoqn1CaHhSB86dUDC7Is8EIGzJivaPNFpheXckSfdwge31C7gxSNtFBQepc7kuKMUDC44mWIQE3khn%2BKBxdcB%2BZpUB%2BoaAjmHSBhcNTOoQHK5vzA7goQwIIlh23SkM9WuqdN0B%2BZ%2BEAycNyzQgwvLTDiZ0QHIvV0BzuZnbogP1KtAQHMt%2BYF6nRA2ZAkyJMIALmdoZygY3NAJfQoMLi5uccoMC1CH1HxQEXFqlpLkoCLjNr9R70ByuLtBNSFFDK4O5cH4oNlcAzDV0QRfcwDzsitk5mKP0QNlDEtFVAMiJLknTRVC5kEBteNEgbOTEakwkUAWMFnDx7kByrIfaI2Ugz1kF36qg5E9FBsneQW8fBAuRLE1NFRjcz13NKINlrVvggIvJL8VSAC81Hc6cpAc7gWhmhIFF2LkCTqiBmXY66MPPxVgIvuIqQdWHXqpBhdcwZwHdigDmJI4Z9FRnIjIOKOg2RqJmGZRQyJdpDCPgqhcySSaVH3INncHLkPNH7IBmRJvHKKGRdzDs6IXMw4g1DaaIML7gILgGjIA9zBzWoLeaDAlm2qyDZEjadPwQAlxWkM6DfUgYl0C5l5IcCRCBc2Z7hugXO4vID18EAN5g5bwkC5EPKBDeZaHOoVCi81yjRkyE%2BpcSS8GhQTNzlgXdUA3k1JbnVApJH8TDZKhD6jNvq26QqZ9S5g5bZmdWBTfcAPbwQTPqefmiJn1CJy3Vgmb7mm7vRBM%2BoXI9yFSN50LblVE7rz03%2B9BG71bvaisErry4kxqgldfqNIQRuv8VURu9QjWEVE33KohdfV0EbrzR4VRz3XnfyVELryXD9FRHIv8dUR59ty1lF7bt67KKvbf24UFrbj1RV7b%2BWhQdFt%2FlopBa2%2FYu%2BikVa26jd0Frb534UVYXyBXWqQWF%2B5fhQVyhwQOUFLb4r30QUtvYzFOiCtt53DPBUFh6lJ0dlIHFw1ZtUWqAkSKIGF%2Bh9nRVcwdZ0dQOL6seUD5Unuge31JclgpBQE8e5QMLgXGo0VBfo2oRTZFo9vFA4vJ1aVIGz53Y8oCLyw23QO7iZ2ZARcTUhzHdIDk8abaJA4uY9VATeQ8MBsimF%2BLCUQcrqjXyQHIGof4IMLgHdyftQMQDMB4dBgHcvHgg2g0ZhugaXh6qKXLSrCaEqoJIo4ZobzQFzQEG7dAHd%2Flrt7bINlq2roHzcP3qorZmRoBThUFy4nqiNMHx0KAi94AgeSg2RdneXNfbRVQNx1IaqIOWniNUAG7DhKGF00oaqKBurruOiqMSWgCPYIC%2B4oXQK5G25QF6FjB1QZ%2FyiAUAButHxHvQF%2B5NAUUDexFN26og5NDdkUCTDOQ%2FsUQM3JlyPJFDIjffr4IgOWY0CDZGDQiHqgDnQQ2nkgzkyPfCAOWaST2QEw5csdlAHDw44pwqBUMIf7GZAfyuW2p1RQyOzNQIgZVj7ZQDJgC3RpQA3mNW9qKKXIlnAYvJlVAN0cawgQ3R8xfqqAbrnBFPZ0gV2IamroFN7u1N0AzrudTr7kCZVjsKIFyNRuwPVUI5lvlq7ogG7l6QKoUmcc1lIFuvAGgGzpAhuMsfFUIboApWiBLrmER04QSuv0VQmTjcIJm%2BpBdEpDfNegQSuvAeqoldcX25%2BCCV16ondcxDmUEieyCN18wa7KwRuv%2B1BI3M502VRG68pEc917l1oQvv8lRG66r%2BKIjdcyCOU1lVHCC9DKtVUXtXdEdFt%2F4KKvbe%2FZQVtu1B7IL23wfMKKtbdMIL237dlkWF6iqW3KiwvLg8qKuLxuygpbe48KIKZCATXRA9t9PBBUXmJEQSoKi%2Bal2hBQXnbzUFcx32RTC6YrUoHyL8UZ0Di%2BstOzMop8g8xow2ogYepNWejhEUFzM8j4qKf6mrkhqpA%2F1BUwaBARdGoNIQNlV9aNFNEoLkayBKKYXXUqDVAx9QBuKbypAc31L7jZA4v1p1QNnt1aiA5vUO3vQEXAw4fUH2CA5xXuNFA2YFYBpogIvodUBzYE7Ul0BF7gEeNaoGy3Pf8FFbNydkQR6gkx4hUAlpM%2BdEByDwEBBFXbsoMDk4neY9mVGe0EOWfdBnDSYKAns4KgM0oSae9BnLs51CowOx4IUGfTTRAAS0nnsqGc7vqe6ig5aoLOgORk02BhEDKPtH2qjZHQnpqoM8tl2HiyAFyK1q6o2RpRy9ZGiAvMzIUGLy0ooOCdy6IxL7dEArQgDaqoJNoc8zCgBIlj2Z0o2Qq8VlVWyFsmC6iBbcIoH0TIGZr4KjH1GMmqgUXVkH8KxuqpTeHgjlyiNk3V3dAM7mu9zV3QKbyCJbg68oBnq4A38lQDdzAQDKhpEqBchGWgqFQn1DUxLT5IBdcBqw4p0QLkYYdRxoqA9xl24U5ApuYkmay%2ByqUuZrR6bRygX6ndygX6jO6BDcakoEy2LkVVCZPwzONECG%2Bh1ogS664irKoQ3aHs23ZAh9SfeURM%2BoW5VEjeAKwPwQTuvLxu5LoJG%2Bu5VCG6ZPmgmb%2FNBG6%2FbsNFRG71D2nugkb0ETc3DhVEbrw%2FIVRG655Mkaq8wjf6nkmBC66JVRG69kgjdeqJZoOK25EWFwKiqW3FUWtuCgvbfypBa24aFBW29vcoq9t4%2B5Ba29meikFrbtB3UVUXCJdCqi6NkVW2%2BkzsoKi%2FSr6aIKi%2Bmu6gcXMILIKC7qx2QUF7wCgoLwQON1BQeoNIoSkDi9wzOygpkH6%2FBFNbc%2BrEmUDZkPXcsgceoQz9winF4NWflQPlSfsCAi6rVOn3FA4vAGg26KQPlViYCBxcDp%2BKgOQHQGSgL1Y61VqmN%2FNd1CiLoZ%2Bu6BhdXyCA5liGqgYX8t0QNnIrwSigLhL1FSEQ2TwY2lAchR2N0FARe7Tq6gOYoQJ0KQFyQzQZqimF79tUgGe1ddUgJ9Rm2SDZgzrPTukQRedex9nRRyAL6DpyoCbyRNCzQgw9RueIqg2T6SDRVBzIcuGMeCigLwXL9w9FUH6jksYCK2etEGy3rp%2BCIJvFY4UUBfAdnpsqjZM%2BrBBjcWYnuoNmKQPhyqoG9oo77%2BKI31KAGtaIoi4%2FNJIOigGWmpmNUC5B4pUuqC9p43DqBc5dwW3oqNmd%2BERjfqO5bZIoZcEvUMiBlEkRL1SAPJLhyWPVADcHkyOFQLi5fbRMDZAPNHl0UDfQ7KBfqfNEDUKoB9SheqKXMVB096IBviuvdAjxNWY91RjcwEPSQgBu4rCgXNme5viqhTc9Ke%2FhAv1GhzyUgQ36CvG%2FdIFN2gL9S6oXIAoEN8NSY6KwIbxpXhAh9R%2Flp18EiUhut1OqFKb2l35QJd6lZkHoiJ3XhhLvAVxgTu9RtezoJm4CQWVCZa71LIJm4O7uQyCd14Vgkb6zzKCV1%2FbR3QSuuqdd1RI3BETu9QTqRokELr6tqqiN16ojdc7z0QRN2%2FZVEbr%2B7qwRuvEpBC65UI44TlRxW3BUWtIUFhcGQOC3IQXtuG6iq23aoLW3DrwoKi7wRVrb1Be24Rwoqovb3uiKi%2BAHUgrbdFUVQXs2hSKoLm8FBUXu24QVF1PIKCgu0egr0QO57IGF7auge2%2Fdmr7FMiovBgyNlA%2BfMGiQOPUkiVA4u5cU8EU2UuNoKFM51A9tEU%2BRjU7oGF40LMaBA2TauRpRA4uEB2ah%2BxQML5JeNvBAwvL8DX3qQMbhV5QML9a6pA2RZQEXwK88oGyFXpVAH1rNSfbZVaJu3JZ%2FghTi7WpUAF24beXVgbJ9e6gObOO%2ByBsg5Lvx0RRFzBhBaWRAygh2eJ1CBhczDwfRFE3hoIfxIRGFwgxygOoYMwZvvQDJ206IGe06t4hQAkFhWZZUE3aExMKAu01I1KoAukS%2B8oM%2Br9dnQYEAkg8M6KwgEOW1RGdy4LAc1QYFnAMjlBif8rSbnAQYkbtLHlBgQ8E%2BxRQdq3ayiM4AaGaiDPEB%2BsoA8HQBy46IBkGoxoEBztrDS%2FLoAboDkBtkUMgKO5UQHakHY0VAyEmp0CDG7YsZQTN1KnzVByllAM9AaUNdFYUMjSv3IA7ULV%2FFEAlzv9miAG7VjGigXLVhq7TVUDPUd%2B6BTedQPgkC5GtTuUCm%2FlmgTurAmQLAnRApv8pCoU3tSen3IFN8gIEc11bVEKS1NWhApuAeWJ1QIfUL%2FABREzcKEto6sCG4Eb8oJm9jwdVRM3OOqBTcZ0mOiBMx3CCZvMh%2BjqwSuvl9kwJm%2BuvKQSNwI3V5ghu%2B8IlSuuhiUEbvU%2B5WIjdfXzVgjde78IJG51SpXXSiI3XOghdfKsEiSa0VRO66uqCb%2FADIrhB5VRUXcoLW3U96gtbcoqgO0qiguRFrbwoq1t%2FioKi4HWlUFbb29zKLVbb0FRd5ILW3w1VBYX0HmopxcPBBQXS%2BpRVLb5rRQUF%2BlSB7kFReDL0UD56%2BCBxc%2BwdKKZH70DC7V2ZQPbfTVUPmN%2FbsoHF4dhEdUD57kcEKBxfV44RTZCJogYEVoaIUz0cTygYX9jsopheANxv8AiqCLw4Y0dA%2BYkcQFICLrqk16oGF43GjIGyepf%2FCoDmw7oGyB6%2FagOes1%2B1Aw9QTqdQpBsgzEPqUDZPL9OqAgwHNUABNSRyEBcTQdKpVbJn1hUog0lwEAF2wLmoQpgXr2JUGzBnQUdATczac%2BaDZFifAfg6A5MBABKAZaTRggYXggMYbXZIBnz0BQEX0makfFBhe4YgEbIBmCZLvQMyA5g6sDogU3MQxjZvigIvihHCQbJoBZAuZFDrqXVGNzsCRyPxUGylvBBsncjug2XLNsgGXgKsgAuO7lkKGTawNSFSs4hqEqDZQJ7BELkIPmqAS4OjFo2UGPqNwEgxuLN7SgQ3kjY6KgZh9xoUCm5n2KBTfUvUCFQMoIfglApvEkHwQKSB4wgXPsQqBmTXp2UCv%2BCqENwcuS40QpTcJNSUCm%2BrVRC5aP0KBDfXrKoTMUJdBP6jvzUqhTdXVBPKo0p4oEN5DZHugU3sHeuqCZvYTTUoJm%2FwC5USN7jZBM3Pr1KoQ31colTuvG%2FRBG71HoqiRvVgldeBTsgjkS6BDcByiI3XOqI3XqiF13dVEyWQTuueiCN1xZ0VN9XVRxi5%2FtRFAUVUXKKsL4QVF50UFRc%2FCBxcR0RFbbqaoqwvKgrbfo7qCoukNCCgvLToirW3qB7b9EFhfDarKqW38oKC9BQXS7qKcXvXRBQXvrATmFMwJKCgv13UgcXt96BxdDu2qBhdVA4uNOyBh6nNKlQOL%2BWmUD5pA2T0L7uophe0v0QOLq6bnXZAwveD0ZAXAMSgYFyOJQo5EEBxPiiiLyDWEDm%2FV%2BFAfqQ79GVBzqBrHRQMLzDmXkhINmT2qBukD5HQvOygObfagOZpM0YoAb36BUPmLQS9BXooNk9D1KBsywkg6GqDfU2kjR0gOb3CWGiDZ6aNRAc3%2BIKDH1GqWmqQbLvKQNkDXwUgwIaZ1ZIAbiHYqjfU3LJCsbngdEGytI9wdBnkbBpQHINAPQqQDIt7grAMndmFDyyQA3tQuduEgbL3uoBm7iK6KwA%2BoxDpAPqNDhjqgGfNdUAzFCxBpVBvqEVKBcyXPYFAMjMvcgzjwpWEAyIFYAZAubaz1VgGQPxSBTe8wYd9kgBvakE6oFzI44QDLzqqFN2phlACeYVQMg9eGQoG8DXzQIfUoN%2ByBDe%2BuqBTcaaIhTewLTurAhv%2FBApvPdFTyM1mIVQhI1KBchPzQ9ECm%2FSiCZvcmqQIfUZ%2Fegmbup1VCG8s57oJm7sFRM3%2BKJUjfyqJm9666IJ3Xz0SCV1%2BmisRK65UTNyIldfygkbueFRE38pBI3EmqoS65kErrkEbr1RG650QjyqOIXeK0KW30UyLW3pkVF1FlVBcVRQXwoqttyCou8VEiguQUF1PIoVUXfeiq23%2BepUFRe4HKkFBfxKCguoyLVLb9VMqpb6m%2BmqQUF%2BtFBQXnpNEgoL9SzoHy5bZRTi5m8UFBefBA49SdkDi8791BQX8dEBFw02olDC59eyB8jLS2igIvZthqVQ4vMVhRT%2FU7bIgj1Nan7UgcX1UgbI6mlEU2Z9t0BF5nUGqBs2D6lAchImEDZQ%2FKgOQ%2BKFEXFhQgqqwJfuoDmfJUNm3bhQbOm4D9EDD1G6hAc9kBPqeSQbNj3bVIDmB3080gAvfbnlIGzPQJAXgCdqqDG4kHTsrBhfseyg2Uma6fag2f%2BUOUgOTbxQ%2FakAyuq8ahBvqamldEhWzbVgKQkBF0BkAzq0b8INnMk%2FY6sGNxLSRukAzhyTKQA3MY2o6A5PqVAuerUoOqsGF7aUglIBmQweldEAPqDdtHSAfUOzjVAM%2FDQAIBkdCzIFF1NBV1RsjrqoUhuapNvO6qVsmBINd3QrG4MdFAp9SO0qhTfQ6oFN5ADEg%2BKIU3B0UuYoNKqwL9TVIFN4EVHX70QmfLcfagU3wZgvRULdcZ5TAXKJPcIFzAoXRSm9n9qohTeJ96Kmb3REzfu%2FBqqEN0l%2FFAmb8oEN%2ByIkb37KiZ9SKsgnddXfdUIbuSgmbvLRVKmb6gIJXX%2BCRErr9lRI3%2BSombtaIiZuQSN3EoJm9VUjegkbifsVRM3BBK69ETzmqo5AVRUXIHF1PeoKi8JBYXKQOCiqW3IKC77lBYXqKoLtXRFBdygcXIK237aqZVS2%2F70FRf%2BKgpbed%2FFBQXjwRacXa%2BaBxf06KKoPVivVIKW3xVlBQX%2BXvSBxfvRQOLtaIHyoQYJRTfUP2pBT6jtNVAReOQ1UFBdzUSimF6IYXg9tEDi5qHpsoo5btyqgi5mksCgYXw71UDC9zuQgb6lfIoG%2BpzOiRRzcdNkgYXAto0hEMLiorC96RzQqob6laB9H1UUc36IDnQ%2FBAcw1Q2qAi8MHkoDluZ0QbIMz9kKwLOH6IUciRVrkBBYMCGQHI7wotE3yeKoBkYadEByIAMcngINlLQgwvu4CDZnXxQbMuAD1lAMrqvzCoORp5qAZND1QF4%2BCAZVDV2hBsgYq1AqBlcX7Qd0ShkdT1QrZ6dki1stT4olbJQoZCYd6iFQMxv1QA3hnE6oB9Rojp9qAZuw8AQg31GMmSgXMBtTqgQ%2BrWWCsRvqaeSQKb2LkDqigfUEbV6IFzk68IhMzwNmQDOunRULk%2FfRRSuxOiqAbxv3UC56eaqlN%2BtAiEN25HOqBTeKbopDezz5qoQ36pAmTPPUoFN3fmEEzeDGuqqFN%2FLtRSCRvfnzVCG%2FlBM38qwIb9URM3tqqlTN9UE7r5rTRMYErr9aKid1%2FKCZv7KwTN34oiZubVBM37VVVM3pBE3OqhCVBM3KokbpQSNyoTJUcwLohnQVFyiqC5BQXqCttyCguBUVQXMgoL0VQXIKC9QUF2yiQ4uVooLlKp7b2AbTRBS2%2FfwQUF1N1BQXs2qUUtvdn1UVQX8vuED5nZFOL%2BXUDi%2FzQUFw35KBxfO%2FCgcX7w%2BqBxfALdQgYXE6simFzIGzYbclA4vrKBhfQKBhdPWnZA9t8QwGuzKKbPempKIOTopspd%2ByVByAFXZFNkZNEqALw0E9O6obJi7zqophe0xwgJv69UQTfHvSqb6gG8BQH6hPXVOQN9QbRugOYavJQDKXLHl5QEXjQk6bogm8hgJhFHIPVygw9SjeOqBs4r0UC5VMDchUEepSS40dAc3l%2FbupQR6h4YoALywb2ZKDmdISjZlya7IMbyAPigGcTU0lBs67jlAM6sQSqNmYHLBAD6mhLmpPRBsz20Cg2ZVAN4DOZ0HCAZgkz1lAueSIOaKXN9eycgGaBR6gI381QPqN8UQBfFZRSm%2FUSCgXIQ26qAbieqlAJDMS6tGNwOp56KUKbxFQ2qoGZOrTKilN4KIX6mjsqpDeAPgiEN408VQpvL1pooFyJ1V5AhuBk12QA3gMiEN5nVAhvndAhv4VEz6joJm%2FtogQ3nRUIb90SkN6tRM3oJm8boJm9UTN78oEN3KCZu28UqENypEzfyipG5UTN6CZLoiZuRE7r1RI3coJm77gqJm5UI%2FKg5wVUUFygZA%2BUJFUF1FA4u%2FFUVtuUzgVFyiqAoGFxCCgvBUVQXcoKC4b9lBQXcpA4uoiHF33oHFyiqC%2Bkud0Di%2BsugoLqSoKC8tVA4vetUU4v581CnFze90U4u%2B8IG%2BpRIKD1KbCrpA2YCgoL2FUDC%2BRrypA2T0qEDC7lkU2XvhA2fKAi6vmgcXs%2FKimF6IOcmaIGF4qPBkDD1BR6QUimzUGzp5lVBFwp4Iovs8ICDz4INlsQdkDC4tuyg2bbxoiNnAnx4RRyNXZ6jlAcueiDZRWiA5w7g8FARe%2BqAZy2T7h0Bzn3ygw9TR2O3CA%2FUJbVIjZ7l3oisb%2FAMAg2ZFUBy5YIFzfUazsg31K68IDnz5oB9R4eQgxvO7IEzViDmVIrG47sgGfikAz7uYViBlR%2FJRWyZgGA0KAZWjWNFQDcTqeQg2dW7FAM66bpAuew6JAue%2FvQKb9awg2Y3ZAhuHHKqFPqAcdEgU36SWCQLn2QDPlkKQ3D7VShmygTPdVCm9izoFzr5ugnmOh3VCm%2FugQ3%2BVEEzd7tVUKbncOhSG9pQTN%2FwBqIQ3oJm8VVCG%2FaEEyeVQhu5QIbiiJkosIb9kgmbpq6omb0EyXZVCZAIJm9ESN0KiZPZUIboUEyXVwEJRMly47oOcOqHBKZDgnlQUdAwKKcE8oKAnYqClpKCgJmCyCgJ2KinHgUDgnZFPaTsgqCdAoHBOxUFASdEDgnYqIcEzBCoZzsop3u2PKCgN2xQODcNDygoDdsfgoHBuGjhA4uNGoopgTVigZzs6BgTEFFUBu2fZAwuu%2FwlA2R2QODdDA8qBgbtigYG4aE7oHBu0HVQEkxCKYE7VQF7pgoCCeaoC91GKBwb5a3uii9wqCdnQFzEFEF%2BPJA73agqKz3ag8IjEl5DnR1Q73MYUUAb5g90Q2V2x6IrPdsUQSSzEP7dUVnumJ7ojPxCAudB02RWc62lBnZ6xxwgznQRqOEQXLMxRWc7FQB3o46bKozn70UX2B6hQBzt%2BCqA5aiDORpVBgbtujIASa3AtsUVnuFAeEGyuMAFtUAJueiAE3bEnRAHucBkAe7YoA921yBXuYwiA5Gh8FRsrqsZUikN10QfB1QCTsW1qiFOT0lADlFUCvc8glAHOgKBSbho6IV7tBHCoBN2yBCbnoe6Bcrpg%2BCBCbnoVQhN2oIKBCbmoUCudvJEKSdkCG4iGJ7KhCTsiFJOxRU3uahbogQm%2FYqokSdpTAVzsqEJOxKIUk6COFBNzsqpCTMFBMk7FUTJOgKqEJOqKQlEISZgoJEnZVEyTsUCEnbuipknY9VUIXQITwiEJPLoFnlUf%2F2Q%3D%3D%22%3E%0A%20%20%20%20%3C%2Fdiv%3E%0A%20%20%20%20%3Cdiv%20class%3D%22position%2Drelative%20d%2Dblock%20my%2D0%20mx%2Dauto%20overflow%2Dhidden%22%20style%3D%22width%3A%20940px%3B%20height%3A%20370px%3B%20clear%3A%20both%22%3E%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22404%20%26ldquo%3BThis%20is%20not%20the%20web%20page%20you%20are%20looking%20for%26rdquo%3B%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dxrange%3D%2220%22%20data%2Dyrange%3D%2210%22%20height%3D%22249%22%20width%3D%22271%22%20style%3D%22z%2Dindex%3A%2010%3B%20left%3A%2072px%3B%20top%3A%2072px%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAAQ8AAAD5CAMAAAAOTUC8AAAAA3NCSVQICAjb4U%2FgAAABDlBMVEX%2F%2F%2F%2FMzMzFxcUAAAC2traTk5MAAADW1tbMzMy7u7uvr69mZmZUVFROTk4AAADW1tbMzMyZmZlCQkLW1tZra2tmZmbW1tbFxcWvr6%2BFhYXe3t7W1ta2traZmZne3t7W1tbFxcWlpaXe3t62travr6%2Fm5ube3t7MzMzFxcW7u7vm5ube3t7MzMzv7%2B%2Fm5ube3t7W1tbv7%2B%2Fm5ube3t739%2Ffx9Pbv8vTv7%2B%2Fm5ub%2F%2F%2F%2F39%2Ffx9Pbv8vTv7%2B%2Fj6e3i6Ozf5ejV3%2BTU3uHR2%2BDH1NvG09nF0de6ydK6ydG3xs%2BsvcedtL6RqLWEna10lKVpipxmiZxbgJNafpRQdYxKc4tCa4M9aoM2YnsyYXowXXjFq0N%2FAAAAWnRSTlMAERERIiIiMzMzMzMzMzNEREREVVVVZmZmZnd3d3eIiIiImZmZqqqqqqq7u7vMzMzM3d3d7u7u7u7%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F9H2B9VAAAACXBIWXMAAAsSAAALEgHS3X78AAAAHHRFWHRTb2Z0d2FyZQBBZG9iZSBGaXJld29ya3MgQ1M0BrLToAAAIABJREFUeJztXY1jE7eSTx53vNwX3OGWuxcO7siDd7xcoYQXrpVCaQNrB%2Bw4MSHx7v7%2F%2F8hp9DkzGq29tgm0RS3Yu5Y0Mz%2FNjEbS7LK19dnKYLAXy2Dw%2Bfj4AsrOg6cvtdbKFv%2Fx8tmDnc%2FNV6%2FymLDvv64gws7eIe8olP%2FbW6G%2FxypjbCW%2B%2BpZD7WhqnWgf9O5l8Cy21hIkT3tbzmGCQ4cu%2B%2FPVuwwi99r9gY9Ht2716mTnWRxIjoUO9571G9tBrh26N18rlH1JgDu3bvbp48EhapwpR0BEP1iBL03%2B9ORrlRLNxf8H5fmtWzeW72H7wLOeGYpm3w%2B2e%2FCF2gfN7cfXSmXXEyQD%2B7CPWt4%2BwLohuA507%2BB2L75Md9ir9eNrtfJU4PuHWz3U8vahb4jVQ2d9%2BnL0r0t2%2B0zooBdfq5VtBoel%2Fl0Ptdw51JnYNABhv%2F3j0nzx9roPXyuWByorWn27vFpuH3TrAwnOrAL9%2BPd9%2BCLd9eBr1cLFsRz3UMunSerglMmNBEWMcb5fni%2BK8jWYyw4dBvfRY5LfFbQrVxJ2%2Fefl%2BMrc0TUEH3uSHMtP8ttoUoxWzidZ9MVNY%2Fqfe%2FCFsLym4MMTjXR7TPIhlkNTi9bcTMLkEyvq5wv7T%2FFdWgNcQ%2FBxOxLz2gn8Lz%2FJ31aCfZBARituLPbqTws7FsKYawg%2B9tMwRDF6eK3o9DS1Eio8vvS68mIBhX2hm2vwpkktEeHlJ%2Fkd2pIG13QhE%2B3Jf3zTTeIwjz16BUUrlrsqmr6OIvxpabVko5hkf%2FHk%2Fv1v79y%2F%2F9fvj5SSVEc%2F7xzquxKUy%2FO1cnlKCLq%2Flw8%2Btg8Rz0gFnpuwKZQ7T45yZQGI7nT1%2FAzVDA37BEUrlm3NldqUvy6tlruspXcOfwIcbt68YXq5cePGzW9%2BjMqHqz%2FqEG471kLr7uX5WrlkwRSQX36Sf0YbIjhID%2F%2F0o9MIOul836H8u7jX%2FnytXA7oxGgvvl96GLbFSAzgYB38wxHHHMqdMpkDaly21fJ8rVx2sjFQfSb5XWlR%2B10OB6zNUIwWLKdsMHjaiuUago89skTw6r6819rH2hGizzviMB4KA%2F68KN8erhYwvIbg46Wgxj0m%2BbD9jZwybFBIbD%2BgAvrwqkToJdHb3nytWm4nU4kTol5%2BkidaHYaxsEGxjSEPa51vCwN%2Bm651bMMefK1c9oli9A0%2B8tnWfBSbH8RqSdRHBQlJlHd9wQeO1eMKtMck%2F1jl5bvSKD5gJqCtbS3kK5ZrCD5YTOzKt8sPwwFu6dvfLzUfUELWEF7IIt5VPBIz37759OrxFOPgl%2BV9JvlDtC4Jq%2FpyzMT0w17KlZ9FxFLNawg%2BtnMGe23ISfvfP5TZ9tu0eC5SdyQ82H6%2Fw%2FwaNgp306SARmx5tRyEYQxe0vz%2FtzLbz%2FgSxjS4L9WW1hDXEXxk%2B%2Bqq3ynlXcqx%2FXhSxmOP66LB8aFU%2BwAPku7P14plBwkTS59Jfg839d%2BelIcxTjDI%2Fz4RpNzJuDLAXUPw8YDRBbXvtSG3F6RDrBenF2NeKPgIUZaExwOMmQ8Tr2WjUDPuVM9JnqxBfWddeKis6L8J1V%2ByRZHuy9dq5XYkGuNFmORvUd7TmOY9HPCFsQJ7K%2FK9w4wA%2FhLwuE3sxP0fFwGDbD4U%2BFqt4OAyrMHjJE%2FH0oIm4IH4DqVrHJXiu4aSfjxmCEPJ%2BELT%2FIbg2DrERho2JILXQngEDckdGoNMu1plPIRcCCEgO4xVUqgi8aUixY3AcTdKkfy9jsHlAJPUfuRlPOhIdnHH68JVhsdd9HPc5UZ8kSAGMNsQHvtUFEskTfJ4HLyCCHjkxtyJR4w1u%2BqnpW3yp4wvehiwGTy2GV%2B27%2Fuxbz4X2N2pDI%2F4K%2FYfZZq5O83rbwcY8BEw5YsGahvCYzeQRXijSX6QhdYL%2FIcvP3ZxdxDDWF3EYzfhq8M6APNFIx4t6u0qhe9fw7z2JDnDAVFJZ%2BkSHpragFnAd%2BKRaIWvvP6BUnwgFOGLMC3r7Qplhw2T%2FfJN6nqQD5OEBw%2Fn1IuuMPJAcKis1xCjJMg0SZFieMjjtEKhsbqj%2FgLFxIPkzTwoXfaSpFyEB5JD1Dq865wwRnyF4CChtRE8UF54HGC8wzAIaCT%2BcrrITsKfJfEo9nqIfsqCD8SXKvawUrnNaZLgYyvoh14Wj8jkMnh09Hobj4L23onwRdRWbwqPvwimT3YYwlZP5zgwTOHrj0vph0ry0F7%2FgrANcxHnizv6TeAh5Zrcxx3zdUJXPBamRStAFx5p0Esoo0cCgtvK%2BSJmupH59i4TFgjTHYZBik0Cd0vEH1qIvzM8FJlwSa93SWdZULSVxYkbml%2F2M5D5aeAAjbuv1jHfpjHvjAZyWZg0hC9fcr5Q683gsU1lcFffkH6xveiSXrLAeaE1a9Kp%2B4br5%2Fv9mudnD3BzvSE8dvkYqOw0cMC4EukeaLLMWLj6FpLISDy7i%2BnpIl90kbEBPKTnutjxxgANoirRTcdzqfKfytzR028nDzmeeEb6c984Xzmka%2BPBc02ySX5L3Oss4IGy9k1kLx%2BokD5TTKzofmHiCxmiwBfL21wbD5qJ4Qo%2F3qDzWoHuHhlJV%2B6X98cGvK7S5HjiAV8cSnxprtnrr%2BcOkrVEqHkqEo7X%2FZGygAdHVckHKkFeVE3H6gmPA7Ss8bSzvHG27t5EPHZbZUNv%2BHryP3u44AQMHaq4n9ITo7sItFD3uzIeeyo6mqgpjxIeaF89kZX5wgQFvvqVxyhGxyevufePzKPZTan0TPEgyRWbdCxgntKZWbmgOFZ%2FzOQURs2xzG4HLV71LQE4Vs%2BfDsXiyZ%2F%2FESXYZr9bh1rGgz3uZNvdSep0qPo%2BERB%2FArqIr36lRCbjQHyoR2OPKT2BXEoJ84R1%2BqOtM7xBfu6EIovVCPkOT96NR%2FJI2Dex4BFTQxv%2FmswgByR0cpXEE3soA%2BLE3QUOx7CIJOBiSBAcksHqlfEQhkBCvqQ%2BiO5jUl37GbJA9zGerHxf31E8JLLSY4q5B1GdM303HpqQovMbBqOgPYjubmAvaY8xgQJbB7xPpfD0EswpfxCC8sPQ2QAepMuC9hGuKXuILsvUcJ0%2BlB0ImU6js8F4RJn5TkOGTF70mniQrsQpJiXCJoPI%2FFZ8Lhs5%2BxeywezHnpNMJNmsJC%2Bf5Qrsr%2B0%2F8HQlkxI5I3T3cQcBv%2FsSX2KC%2FnMcW3aQlCc6P1Lh1GRt%2FSDemdFCzOC6nO5daTx%2F%2BBeB6gGvB0QfUjxyAw2M4AiSMRfPQzZlL1QiaaahoGG6Ysam%2Bj5nbJ%2B43NAjWbxm5HDNsrW4v9fxH3xGyGaTyIUwIzC6T8UZ4fu%2Fy%2BCQZgSaYour9NNYd72efmRictiliSenezf73aq03sUU75LEzqT5dPFK%2BSqrBIUllY3YC%2BIxV2iRATYOh3iIUIvD%2FQeDwfbWYLC7%2F1Lx4nuiW4ES3cCSsDGZlU3gQUe%2BAASuojkee7yFSj5Psz%2BsPKF7PWm2EHhYQpXXi8dSeCFNZoqohEJ8cj%2BO3%2B5Q4liYWgCzO3QnR%2BAh3llm1DY0vyxSCcUHiNHdU1oENcvzYvQg2%2BRmB18l%2ForrmVXx2Nq6tbjcz%2FlKPxK62yFGzbUtgSHJeSfb6FueLxyMFfj6hHg4cUp0HySN6rHagIxjvtBZki%2FW5%2Fp4LFEGSTcT3ULdbN8rAtGBzotbK%2B0D53nCm8o%2FXUBXUyNVHefoOymiYGGT8FoY36f%2BdrXhHJBNiu5x2mQZUMGU6jrnIMfyGMTyfvXDFZ9X4OcN14gHV%2FYOuv%2BV0CPBWXHL79Fq1sLOyfTCE%2BONlQGm6ETrovu%2FUWbBZeSm93xl5zdIbIU%2BrxMPLFcn3f9m2RMZIlhnHq0%2BFwxoZ9doL9nuYTfd%2F8wDrvgdeyFldz1WftgpzyO%2FRjyohAvo%2FtsLUTu8eieTefHtOpEC9qcL%2FfwGywAT1UuNw40%2F%2F1CwGHT1w6P1AqeIRwLkuvSDvVhoCbo3H%2F3QfQrs0FjnwcAsv%2FCLnG9DuXHr4XO%2BRE4fzx%2BuH1UPyNPd1%2Bk%2F6BAvS%2FeGWWI8eZGv8F88ub%2BRNcYgG6brwWN78O%2F3WVmS7o2bRuo79x8%2BieXh%2FTt%2BwXVz7RXX6nytW27ki8ulm968mTe%2BuT4Y6%2FK1JuGs9Gx%2BM5aeTT8pX1%2FL1%2FK1fC1fy9fytXwt11%2Fu7h%2BEJWZajZRKcZuLXPE9L755JHctnKzRRV86ZMrIkZoFKqHawf7dMho74vEI2tdAtzALPfb%2FGO9sWSt2QrkgP5f21fIuRHZd84M%2FFuB4UMpgpL0K28DZjcK5I%2F6qhbucSJI722LJ%2B46Vkf4sl2gv%2F7tMfyHNlstD4AIgHc6rdHUgQ5X3zX9PnHICTE3ERLvA12MBjnuBFB6UkuJ2fco0A%2BeETfI4rkCHCbFOCj%2Bryijey%2BD4w0tcFzfAnQjjLOi9rA1s1GXZSk9oxN%2FJbzq%2F6W8kvaI2LollymH2D3ftyiMkeYLoZviwSpRElyP7l47EXsQOGi%2BEVEaG8Jbjz692OR77GY%2FchRWsv%2BSxsipFb7hikkwar%2BWjAqXEqVyrfY4HMZfrUNGoYh1yMAX8hLP8S45Hltv1K1H0jJXCD5R9nd3heBDYaKOc8yzBFZ1lFxhkPWX6RQwg45k2XyYlO1YkfXKWkhgZHli2JVI4kfT9cvzzWyzHv6CAC%2FrtIimBgdPK4LOEh8hNrocIDUW%2Fdqg0j5RVAkFJQsuCUl1PFpANuxgDsz7juEt4cMxiDwIpFZU1t3bsORYNnswnJUgG4ROtB4v2klDxF7%2BPIFXWDzqiRSeEnQv%2BkQ0AYiy2%2FVI9b44HNwrxIt39jbnd8ny7sK%2FPbeqUclmTWLVuhRTwwJ2jYRV6SSQkNog1%2FFpskK9wEWOfxmFRnohEosIlwyckZZ0rUEHM5ZUoxvpejseXsLAqNtGkHTElolNYu4j1Un3Uitin%2BbjH8PjNrtUE%2FjAXsd97XD%2FkMctMWEeOCSeUjQIYxAPkP6TLAv9YlEzY5NCEEL3AK0b3XoaHQFgLd9M17%2FST7vtSuoIKZJIriX2hlsoA6bMWROJk9WVijLTES5wlllB1vlgpoYkIBtFK%2BNtayGQiYaKGv7s9s3sIDzw2RJm5AL9lyO5h%2FcgnIcoWMZGyGRLOugXnFlq01WRFuR%2Bk7K0Zrt3D8XpZx5j3UGrWtm09yWvJiirJJoOZydvhog0PTTPZrIv2JpOxSBfmIH3TNPbvumnPHR7tBHepG3SDx7mTpm0ECJaKc4eGIhsKR%2Be8qeErtwlyRbGKJDvi3HtkPSfpkKFsgGgtHjX8NdPqdG7wmZCKpsqkoJmAR73qYVNlOk4%2FaGDGgXB6BUOA1U0Ssqy1qTJRwXthvU%2Bsk7jRmYUDVAMAaWZWfMsW8jkNwwPb2KQBmVbzOUOjBlhzz5NSAMnN%2B5x76R%2BQyOvaMmvad6NqalCpqmFbz%2BBHozJUPyaTyUgU2NyozI9F%2F5TrJrHukUEeV58lu4wmyrRS%2FpoE47tDrMKAzreppv9bGzzMHaP0wFgT8KgnCb%2ByPhZMUOAbDyDaPZkwPJCfMpozIf5gIwuMgz90PKpvv74dVQqUHhRXvR2%2BgXvJn37izTKKh7Z%2BystnrHciU1tjs8zAUX6lhq9kRTGMNUkg61%2FN%2F2fWSMDFBD7HH1rrf9vQ68g6Y3vx03TufmtC3zBTXb4%2FMz3N3vvexxe2ysXYNKl8X62nO%2FOO3Y6Fc%2FNNc1Z5PqFl3c6nR1jsfgs9gGMrq8a%2B244mbe1FhP8tGDDjtGO4nrV2sCxsVt7a2pjtorIzNXTy07yGORuECP2f214sts3YEgM9tLXAGKrW%2F%2B4ZOfd0bdzhfDx051tCPABN56%2BSAP0CvoNttH4RXL9OnVrFjVUMYSdEPf%2FZXJ5%2BbJyDfQ1Q2CFsgwm%2FOYeZCfCYthao2mAXuDi9bBMir6GD0LP581q9mV36zlz901nAw1w49YC6V9DyZ6965s4UjSOTqHPtaLUDvdAafQYYIngTHAiA%2F5hW1QiGxPkRN55gVfVkWI18ZUfcmpopxlg%2BjEZVFVyC9j01Z6PhqQtg1MTAOamGI1BHe206fouYA2mP3JWBdWp6mzS%2BpdGOibm%2BMPgka0B2Qdx%2FZi9KBThKrxihtUH0dFVHG%2FZhhwtIbK0ja0BNah6gNLKcwqfR%2BrSqNA0gotG1i65ADXUEGPBxyhGKF14j2t6fBNRP29Si1%2BZTgGOL20pEEHfn55cwqj78sp8wvbQuOHpv9ON88oaOi4vHlLown9OTnyg%2FMGtqJH9QHm%2BA%2FjoZqh8IHXhQCQ9D5ecxxEkXHAQV%2FSrDBd2NcEgvgOeeV6dAwONRW58GWm2b%2B3FTH60v%2FDitUOswcmMb77ezyU%2BxW6W9xVlcVFBDHTUwqqUfpMYu4lTEwaumtvbSXNbWf4xd%2FWAlmgyPHyTsN3TyHcRekmHRTzu%2FNGkKNVIEXQ3%2BI0yCx3M77TTNaWpumwLNqfOG9eXbhHbjpeL6EfxJdKYOEDcQkSS6NbF9J3daMAydwMUFwSH9gzXcgIIhYynsnBfiMq%2FeSr8%2BvbQRA0yCHrxJXfvZZnxmJ472Mno4HVYhAY8QbMCKQON4zA0MWih4jxuRg8mmaechHMlGlhWyUMBwLPdq4OAE7B0dzCPoh44Bq6kdjdjrOJmqhxODV3sSqQXL8yvm5D8a2GHRAZ8w30WCyUSbOrY8mxyn8cylCB%2FE2cJfByTncqnmdBMjxETenyY%2F17R2fXPaxhjUL32sAHZt%2FKpNPtF5IOtHnAVG%2Fai9P609Wc%2B9VRvPQ%2B1stqnt3tTY1KxUr0Qp5Xsm2kHOo1AlhIy1l9YH3Voh8aP6hsVE214NhyYIaJt5HATTtHYuYl6Z3ybBEdrfWzRzm3snxq9OTaWpofAOpDQUpqPhq8DYpen4pDq2pPzU63k4umrrD%2B%2BqkSHxS1L2aJfINzJAmHbwV86KqI7PIfK7PHV3bFTZnB%2BffrTzhb1htHd2bJXYRfLg1Sx6x3Z30TRV4Ze2rl%2F7nk9t%2FDl7C06nraGDyxj6Wifz6speVH6QIF5rG0cS4vqZ48Eq3sSvZ0JIVBpZemH%2BotpB4g9dyAmaOB85cz%2FNWrvGqM7d6sqGX%2FD70BqQ20m7fOXZGbW29sxOoa3behwrHzW7%2BLupZi7Irwx8Vz5cnx9bfsY2CB8GRl5BEAN8zBy01czNZ8DY1G1qOjx6HLFv5XhwzeCQTJwkM%2BXxgIVkM5q5u3bLyDJn7QbE94tM6GZkWYRtE7eYM0H7iQrK7Ncjw5ldiFixf5nOTa359LUnPTxzPXurPgJ%2FPPM81C3wAE2trCdnjo9JbhNIrmzAOR6SQij1m0sDUtKKHz4zPAp8JihIP8z1yuT5z1qpzqVlzj%2FV1qwG8o8q9q0Kux2pliaN3Z8iHuUmcsH4eYHFKl0dELELs6I4LmoTTwNZDrrw6NIrnaTG%2FWZCaMQtZVmTFp9047Xcc5bZUfAfn8d4vwCQBTwIBh1DQ6xDRUZF604VMi0V%2B15Oji7mwt2eE4FoLzr7G0mV9pSQ0Wr0PyYSx6vLqPF46nQn44L4CC7XhvIJCv6Dm9XvJmEqt5cv1rQFabDyruY%2F%2BUB32IvQ1W8%2FJivNL7xDZmaa6iInPHSxO1PQJZZTAteiTek4HpIu5ffELgRyUvyxASbcudPSTEQNSG5Fk37jaIRhYJ4M81IcwwVXSrQX7BwCOfa1s0t3t2rdWhcJy1oHfSX0xD41lb1oolJXUncZ7qQs0I98xZ%2BbXOI5DqF6NQ2bYsibkDbUvUZamvdHe1aRN2aLtFeF1LlYg4nqruX5dn3vD3t9RPSNeP8I4Seb5iU8Ev%2FUikvySOtPvOXMDXmd9WeHmNjfSEzKzBOuC3gIrdhQLIyB8F54cSCxAiG1cASwUpOhSfT8XcGENWnr6yMFy7gI5ArzLWIo9gJf3LlGq3xygbJphk4Txhf2yMNnXPhNRXMd9grdpFPDjtnlqatk89Da5uK9pzm%2BCPkO7cx3aTq%2F8l0qtxFm%2Fh%2FaLcW6GWq7hQbbYFfTn5XbqzR9xi1HDF2GEAWxhAdHmha7N2jkd3uTLRw9wZav9ruIcHt%2B5PSjdrunzUWQpvI3AMgP9qbbGAybvvrUnWFaRM59lzYD5OqVl8PJW8NmLfRj5D2aN35nen7kck8sXo6VKgw8c0lMNHyZz7eisQTXfz6HMZ%2Bp2VVb1%2FOZNp9NMz%2BHXI3W7RW39RRIQo6CFbX2m%2BvKba7bHdV0QFP7VjC4r60Qtg%2FYvTdd%2Bj3yJiRxKLv1Dpv5div%2B%2FFhBHokfG6h0%2BhHUw260w1b9MVOOJeLlkj%2FFbgEb2lHrjogn%2FnNsPo%2BUPbJrJqNhPGwB%2FzEcjdLhCzSHU4BRNXx%2FaUwGro24NnEkHU9CusfUn4bC0fekgiSOeH6jlK%2Frj7i1umrbi2oUDnl0yC0Ag6ZJ09KsKNhOIf5QWYMw6Zy17Zn5BpZuPtWZ%2B4hni6c%2BLnW5Gy6VKKpsONyHTBm4VTc4YTNMSf4YX4dUkdNwTKc8Hg6XZoLxCSlt4VCsaUOuHS2L5oXcXhiWBENtjwKNQry2VnukjmqnJo6f1ynjwgujg3AKg4byJfQv42nAo3VH%2FxE1wAe6bFESB0v0CEec8QiVJudwIDSPdjOkcv3A07j7Rmb%2BV%2Fa43ma6NWNtzUU7IdpLZ%2F5j5fXC4ZESCDEe7mY1vXTW747vm4bVaj%2FG%2FICAh8VO21QRraOexLPehuDBhFiiZPqxcJI%2BA8%2F1wc63Z8pZj3LCNNY%2FTv11TUUPF8GY4BoO0ez8RI7z%2FVBbe3Guchp7cHjYs2F6aDyp3blwSFaK%2FoNFInhBtQweFADJ5YxhajPsnBthXrdNGxIcW5dxMXT1g%2FEbXGqMh5fYasLYTjfzs9amM8SsRYeaTQUAJbyKSRzeBWO%2F4XDRLoNOpfsxKaVvdCf6DyUvhVw5Ak9qBPnFkJ5ZJxLkP5u8waLbXKcJdoZeWYKnND75avw26HhUef9pU83OJscKjzFPMcP%2B1DaufU5I0BudYklSdPgt%2BBV%2FvxyP8dax1ZnVYrCVxn7aMrbhUaIb%2BDORYnKGYbKZwYF9TOvQPnljbMb%2BTWoK13CoTZnwub4jrB%2FOBN2zD5DjqSH288koXbogRfoyHtJkHa%2Bsmrfv1IkNJJ256FcmMPtwYgKBqvo5%2BHvz%2FQw%2FG2RH3sQkACRkS1w17eVJNRqFpA2Iw06qaupn459MIH7x3nQygiQOz4dpczGsxvMwj0Dc8a6q3s39JDS3fYznDXroQpSjsErriD%2F40IRyBHPt3NKO5uK024aKwMdbn4EAl%2FOUVDlpQ677FTQ7a5qwXGkg1jz12Q2wAPBzRuPSAJJoUx%2BdN86v%2BsGxf8Ywz01dvA%2F52y4%2BVUlBcgCCh01Fnm8xFNT8%2FAzTgMuHyOBMhS6nXhhgflS7rBCYMd%2Bk3iAPz96%2Fspwez13OCPxdD0030wBI64W34X0Q3XZzNPcwe3uxTPiYHiq8%2BuABgdujyFwORGGTMsODzC5K3AMGwzZLUsiwR5GBOjlzkgEerZfsYnIUW7uMZeMA4s3jM48I2JHt2SePhOy0d2dOoSaxC%2FUaUkIuU3K4Hn8AdbgYe%2F6OpmaN83Fi10%2BVSsMb4wg03pnWCPaC97EoNnknmvWo0zlNPiAqOdniXG5vhew0TC9jxK1T4h0edvowSie2ctPg%2FsD%2BVfSnpLbYFH1Q%2F5stCsJ3kmypRd60j04ErEjtJnvIVRoCOfKSReuYX3RWX55wuNzCaOOvmgQj4Qfu5%2FVF45Z54XfSoSf03qccpl7QQDGl5cOH72dwSfHYupvr1NTQrxEP4sgSrbdmbh2eNXUzztsGmV7BnD6eQ5AswZ8MWdIwYsrcgor2IiG6AUVx%2B0EfTwuWAE8r%2Bkn6IjTC%2FHvYR34DzZlLFkSsqyiy%2FyCCrAt5%2BD50ws6or8QA%2BgzDiyMkCPfZI%2FsgWO2n14wVfiGwnBRY8NlL4%2BEu1zkpqFwsNstlCFzNIG3yQo4rAyH7GB0sG4l06Yr5LCbxQte%2FAA9FtUILPgUzW%2Frkl8j3cC0OGw6SLmYjIBw4ynR17DpQ0ZpXtRQ78MBKm81LgusQGCn8JDshWluvkFxRDYdHUqWcD4lrSyzHQ%2FSFnHjGfa4JrvLILk%2FkSRPddLa0ni%2BcQCg%2F5D9zRaMWlY1MKR5bWsEy%2BpGM%2FWtol15CFcpRZQ8niIdr08q4QAUxp9yzg%2FEIKlbrq99C%2FCHIrfOmQodCLfXmoo7Lsw79evuhSdVcrQa9wmKhfrlHbk0JS5YV9MuWQvxB%2B8jYJ3xlP6RLuGZBKTe%2FcB02XFWYvNhrZzKwNf0b1gInEYSVD4IFPKRhZu3pcGV3kdvX6SlJHatJffOHSeGtGRUy2UVBc3jYMNxEUjAckJ0RSe39hfMt7aCIksBicHNYUDSbMlxitS4SHb9Z2MU1Ylp0Y9WgaqIDc0U8ZGdBuVtqTpz4R%2FQDxaI8yKyo8SMWPh2eHpHS%2FFJwP1q5fa%2Fmg3sq0q4mJtN56x8TdEkPNkMhOgZ4YxA0%2FXlqd3%2BupnY3FDZ2XELEa18N5he%2FPwb70LV7hBSi%2FHoy%2Bdi2l%2BG5ItfSnYv7%2BaRyCRBuyh5%2FsJtMF3avCtYAH0%2FgTAMOJKRRJvcW6kdoFIC3Hbs9Te1ecWQ4D%2BmEE%2Fdaoba5OoojFQzb7vTZI3t4B4U%2Bmvs9tNrupcJeYg14%2BEy886Z1Jyt21eM3TS9sLskv85An0TQRj9ZvEyrYT6r9vizgOfPf2bQfhKM2s%2BD5lxwWpVu%2FAexeSXHsyTV2j%2B91G1mZxkg8nKxO6%2Fierqn2G8NOLtiL9Qe9Z3Z79Nw%2BIujkeeNzOSxJu4ibtqmcv3F6%2FnZ26Z%2Ff07%2FUfmfbKNAv7ilF99wanubSKDMZC3gwv4RaQMrCcDSJ5whwUHhxUs3hON%2B%2BbmJUVR9ckoPXDz%2FfwonAEDIiXPrCvK1tosIHe%2BkTAeym9IddFYEYAAAHAklEQVRXtm0bnkSFXfn5uDq59HkPc5viMBr6IwXv7UEr3lpgbdrEqIosAuhno2qO39GRiRkmPikeo2AwH%2BgXqAkPGxTqc4gewsu0IFSMAW14uN2fRAfHFw5aXaKCdgeORmkav9qP8an2FILh6Sa89cC%2FT0IR2FNmYxvxgAcY7Ws3iFvOnKusH11nlb6RS0IIeLjX4QRs3I%2FNBfIfDcXDMd74BA50attOjc6f%2BTechJM47U97zad%2F9B%2BNOwrYwG0HdXLrpdYdbeqa1FNRo7Kzyi7%2FkQMYghebo9AkPOKz624EL52pj0P1%2BMaP1j9d7gEg8EC12p70p6P8FmtgRM7%2FAB2Fp9sdoZjgGTfx%2BRGvvRnYCpCkwdedeLC2qUxb96qeBmlz%2BA1kq%2B3P00QpZDw06SS%2BQVxC4p37tOkS6cC2QfZSJ0G1e0uIwcEf9QezjPZi8dbOAWmVFkIlncc%2BtRyf6gQJfpwFEmCaen4Wz4sdHzpMJVDmKEMhpbl4AMLhfoP9h297FZ%2FEtsPbIItEwIahiK%2F1sn%2Fg4XXLq31DQKqnlcOPzCQKK4XCU0aXfqRWqZ8Lw%2FL4ODFFEl5AJpehgDqx%2Fg3U2528B%2FFiIosPT0DfxzHGSPih1BqvATFlKrxPwvKH%2Fakz4JAqUtfiux4jHGTQRTw4lqiXJr5IgVk3FDhcrrheBnEoAFEq%2BDnCBLoU3hXiK2iNNQg%2BL%2F2pMTrn1tRe6gSoToSTYGF8MzlL%2F%2F5LACDfgJ7XJvqthpV%2FxY%2BNBltfx2UonJi5f1S9jpbt39qhISh5P6xOrky8opyinQyr9yFRwflDiNK8S00UUv4lOAYFr%2BM6NSy0bH7x%2FvS9cUPTyr4lo7FHVuHo2wgzm52fZiIRRGR7KefSn7m40DqK2THEpzVkz8YJt4F1BxoRd%2BgC6bXjJqYm2MTVeFmPlY7VzPqnvjoNb804fwsUGsjwPvZv2dAmXo8B%2FCRw%2BiaSsfrj41F4S4Z7y9v5OKgMOvqLPgQZUUk%2FkGWR82D3jqTWBe0VrBtgrjkPvbukh5DMpv1b9lwMN3XnDbVXgGnI9YDLoVuSnKufPjqezx1YlXvloUFmmE4rjq%2FCkiT6Bf8yPyvs2yu%2FEJjDC3PgLYBNetOTe00HdiH0CEWKx2iMErF0DY7PrmIGSmX3PQno7yAjqKnjayaqICioxAUsLS5CigRk77fthzH0O3LJ3ecuKWSm3Ytn4V0fkBllBnsGn%2BbLDMbo5%2BllE%2FMgdMTDvr9Yh5WzXTi7lPfwdiHtWCXaQURcKn9Mr7L1v1TJ%2FRnpQNrmiNU0i0%2FzTjpIan4n0FmwP5bvJJPodhmxuXqWuF7s%2Bjn7LU8R28TR2YL4Q7YbgUhyMclLaSJEBCa4p5LkJERgcKKr9y2ctohKLzJO2S%2BNMMdj3UGTGVhz0Fi1o2oEKYb2LUsMdGJqOaE4U2B%2BSBH0o9sBF8zkOp92gwet7Hx6EoQq981%2FT5xyAu57If7Iuenh6MplDUfnf4XPyk017Vhsvd7LAxbNLwz6HNuC3mQDrIXbkfF%2Bx0dDmEDn0%2BOcHu458afTnYwLIpAWzys%2Fu7zht08hLyZFvI9vIeqHZCmMjaAtOquTlTiZkINX3BDZQxHjDLi8WvYzuyE5Pq7%2FOR5fhIsIv3JwNuEiMoXEZVE8htGXRggNtcoglETHVZiCZ0qT6iYSCbplpBRYToYlaHcxPs1PagTquMoXNytn6pXpGu4k%2FF6IP6QecWMyaKK7iT8Sm5DGJBcJo5A6kRUiViBaqvhlgVL2k4hHHLovfDIoSsVvSJjI7cv6kQ%2BgQEro9HOsZaQrdKMIHUdGPm9AHP7a%2F3XO3lZU8KefS10F0jq%2FqzGe8VPHaoucBL5O6lrwH0x1dWiUg5FqdoKzmUBJ818%2BTeBc8h9Uf3stEXOjIPUQSOVxFP2VBKusDASOgo1Qywq3OuMx3%2BAL2%2F7AXza9%2FVF8P8zv1FwWvB%2BXMZWzTW0n1MSV%2BYDkN%2F2NBDqFn2sAud9tcWyoaIgqKXrpfUq%2Fs0kWFcFeeCcaS5sjJJqpbCU6DmqXF%2BICsi4EchsMADkeh78r75nT5Xi8DDUk3Spa6%2BeNoQTcc2ZURCfqCVEo9%2Bclx2Nfkd%2BTIkrKKsuATSpJKqy3xdCAC0a1tTzAyzkJikGuL%2Fscj13cyW%2FSIiKs0jJtl%2BPxhx8okUL%2FzH5%2BKz73cJvjsXUPk8GKII6QxAbZ4hDYVVFiyjxqRgXN1%2BX4go9dh1Fr4WfPsrt9L4Nja%2BuxKCRhtUjhV75r%2BFiAY2tr71em5EmxELAZGW7HjCBc7YlwbG398eBT7ujLGufHXkKQd51Y0fSGQtCE%2B5k%2BoJqUysFOAQ5wIvsHvhFCpItJTDLjQBAxOI%2FSaHJgCtqDfl9vpjt4JrmOra3%2FB72L99CCrFH3AAAAAElFTkSuQmCC%22%3E%0A%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dxrange%3D%2210%22%20data%2Dyrange%3D%2210%22%20height%3D%22230%22%20width%3D%22188%22%20style%3D%22top%3A%2094px%3B%20left%3A%20356px%3B%20z%2Dindex%3A%209%3B%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAALwAAADmCAMAAABYgh8IAAAAA3NCSVQICAjb4U%2FgAAABgFBMVEX%2F%2F%2F9SOCxSOjH%2Fwp8AAAD%2BwJ4ICAhWPjL%2F7tDMQjj%2F%2F%2F%2F66834vZuZmZmVcl%2BbdmN7KCIxIRr39%2FdUQjpRS0nFQjhKMihptaVQRUEzJyAyIx46KSF8LSdAKyJSOCxUQjqcincQEBBSOjFSOjHzp4tSOCz%2FxqZSOjFkTEBUQjpSOjG7qJP%2F%2BPQpHhpSOjFSOjH87%2Bjz4cRqUURDMSlTSURQRUFUQjr%2F1r%2F%2F0bAaEg9UQjqHZFL%2F59nOTENTSURSOCyNfGojGhddV0wpKSnGl3yWlJKUh3d4YlM5OTkQEBDez7fLvKWdj4hzW0xIQj%2F05%2Bbbp4nWZlZTSURTSURSOjFSOjHo17yMgn5%2BbFwZLSlWPjL358v%2F4sL5w6XWxKyJcmF3VkYhFxIzMzP86MynnIi1jHRXmYwhISEYGBhSOCwICAj50rvehn%2BSblqRMClWPjIICAgAAACLZWJAa2I2XVRRS0kQEBBUQjpLOC%2Fxt5blqqWvhnBNh3spRD4ICAhWPjKmNNozAAAAgHRSTlMA%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FRBH%2F%2F%2F8i%2F%2F%2F%2F%2F%2F%2FuZv%2F%2Fd4j%2F3f%2Bq%2F1WZ%2F%2F%2F%2FZrv%2F%2F%2F%2F%2FIjN3%2F%2F%2F%2FM%2F%2F%2F%2FzPM%2F%2F8RM%2F%2F%2F%2F%2F8RiP%2F%2F%2F%2F8R%2F%2F%2F%2FEUTM7v%2F%2F%2F%2F%2B7%2F%2F%2F%2F%2F%2F%2F%2F%2FyL%2F%2F%2F%2F%2FRGa73f%2F%2F%2F%2F%2Bq7u7%2F%2F%2F8id5mq%2F%2F%2F%2F%2F%2F%2Bq7kFCNkwAAAAJcEhZcwAACxIAAAsSAdLdfvwAAAAcdEVYdFNvZnR3YXJlAEFkb2JlIEZpcmV3b3JrcyBDUzQGstOgAAAgAElEQVR4nMVdh0PUyBo32U2C7gLC0vvCozcBQREbFlTUs%2FfeFfXOe%2Fq84on%2F%2Bpv2lZkkm6x3nCNuSzL5zTe%2Fr8zMl2TXrsTSNrny2%2Fz8%2BPBgZX%2FyDv9e6Tp6rXKongMGPV0i%2BTI%2BeXWngGWUrsmpGxrGt2u5DxrxfIPel3%2B%2Bd2ywbQcxJpa2ym8DHit5hV9B6JGvP%2Fq%2BP145saNgrdJWmcKeV%2FLzvBs5xXfds4togUDvfRv5l%2Fhf%2Bc3Xvc763%2FNWch3b5bFjtOhNB3jjR3cY965dhzTN7aJ0L5fo57CxrPHw4Vh%2Bzfke5ILnvoNZ%2F%2BBH3mSeGqboCHV8RE2R%2F69Xdgj58oiloT7DLYXoX89TyXXebMZ7UJ0dkX7X8CjKyPfQTkAzVEvy8GYAm%2Bzro6EZRKJjdXmNbORzowytz87ma8lrEHl4g%2BqJGgu1iC%2BRadebfwz%2B1cFjFsURboy6v2dX1uazupSRjEhhwfCLjeP%2Fq11N1%2F5rlcrcysrwsPirXDvUldTrR1euE%2BqIREZv%2Bqzq%2B0AO8NhlkW1rfOgFKCNxOG37D1UGV6bujlr6AowbuDs%2BPCyadHT%2F%2F7r2L1eGx2tplniNfLua2uJS5494x%2BGJgUNIIfF%2FYO5aV9f%2Brv9VKpXJleH5eY93mpaYj8eyhoAsXBEDJyPEjhUq9cu2cye4cD2fNMCczo%2FYRgMjAl7yQyMmRdYkhg9%2B841Y9Aki4qkPnNe1DGfzBipTVUe%2BLSPeEj8muiSc%2FAPgswkR%2BbTVwGfHRsSt8ZzgtTx58f0EkFYA4kMfeMgAjipLhdRhXGljxMqhsVSlj5Jyz%2BvZtbqidrhvH%2Bfi9W0hcZ0AmgKkbDd1w1YoFhdDk2I89lJtcxJuEKvv0U54Ch90hfalmrsywYPPqFMqhmeugQNIYAd919LEFQfa7hgqL4%2B5eWPAcTLbCmTO6runBrvIdMySOjdc0lsTK2N7M%2Fn5aBz8wUzwvxjoltLwvuUA8Iw%2BmUDeIOgqiE886gVqTBSDzFvDOmokE%2FwUOxT5weqJuA0mYYGZt%2B2FhYP2jzxXx3lXxQ6Eo7Nt5UimAByzwtTSJcI%2F7OPmM8Gv6DPqIQBR1RlSghHynf9Og0mqrLeiyNpOW%2BLKazXTG80EP%2Bd9Bxv%2Fpc7IBD9p65rjCJnVifcI281qVIoAqANAa2JnUR8pUMv0UpP%2FgITidAVE3xeSmbco00tVoEZXBk707XPDYgTIxBwfxil4VEeER%2BBXlEliHCVK5tRLRVcVAQIK9hgzVAMtE2k1y%2BBKHkjbcrAoynoscpqmDsgcfFYStF3hwNA15hk5ENv%2FpEiQ9CSuEjy2cWPyzPigAtX73j8Rx%2BI3NiLjfVjXUDBzAqHyfSMFQKHtvwlcCAVYFmpFFA%2FhuAzs3jE%2FZgY3k17mzIEtniRr6LOT%2Bgwytzs8msiaOTDVZYIf%2FHsGgcB19M7OzvbMzvb2LnFQf0ejMkexw4YhkVOHJZU4GiZNeWD3algsFuV%2FXcLq6uxsP%2BsJvV%2BdUV5mWDluwdXHmblOV3I%2BBbke0ESet381DBVy86Y%2FqPfV2SUGCWvkNdeYe%2FktC%2Fw3u7U%2BVpU3HO%2BvorjNa0g%2FyNas9zo9ljsAmsrAfpUYEVcfP3WEhnt0rBZD4ouWPmOP7oJw1qnaMgDp9iIroJ%2F0Yqj52pSXETr0hiRs0wgjf6YDYrOGX2%2FokDXX%2BuZvDeWekJBrc0fA7yAB5OXOL7WxL%2FusMs%2FuSS9z%2BvEJx6slr1%2BgP7ANgj9hi6lZK2UE4vbNeQwK3p6M1ZHr3zOfYnbrWNXcCFkDGNvJ8IS6FFfzmC7qey%2FDVg7bpsmZFvasLW6%2FdBhItn1n1KcOgS1Vgu0lTAsn9EuNuBKXMdVx9QVcHSHyBGXNxB9SM4hIxWqHZ9WeGYwPpA%2BmjjFvmWNURuAjIXcuai5h3gKus%2BpLVVUV2TOzHtgC6mgPbEWqzsI4JNmC84pM5YzxVcaXkCMnNTWcKlp7PsEeJHbWnMFKC4tHI0veqJwWvy3ziRr8xGJLGBZDuxNCCzO3m90coE9St6TGYH1LToKokDlHcWiGZA6ze7jUUcQEWPcA3xiiViw5XjGiZkT2%2BfQ%2ByRbnGIPsk8g551OWjfqLaGjItIeED%2BnD2oXKLbwVqA6xkpxfnAtJcwjXOEmYNDAeAMJEakGWaxiGYoQqJNaDFjgdgvJfhZPyKXUfxc97WGFJ0tk3cU4Ys5O1MrXO8Vh6i8yxgjXud%2BX%2FWa%2B%2B8WZ8TbPLpYg1McO70t7Pl6QpukY%2B3o74RgrV%2Bplc4qbO%2Bs1PZP2I5UoTUKbOmIY2GO5U4yyxrCVyC2iChLd0zgCJUPiup2obYNpCr352rDNrCZHLOMwd66znH6bJL%2B5YtsL4HS81PFSHY8Pr8VDUjF6sP88ayzcH%2FG82WDKYxiRaLWGKFD0JwbyEYNKtIIzsumtsQmyisfbY4ySmlGlBe9KyTdvAhBkNHMYkW7MOznWSd4zr9herA9SxVZSIE1RxJmOxR%2BKV%2BA5cxumue9UJHUHwIRN2yBlSLPLAmf6v25h5S%2BI2wg4upxzkeZdgOwAcOSYrKkaVRbNO%2B4RWi4s9xgPWHuAbKNaUq7PunR0ReHrE8IRByR8RAGLLpIZ4whzRIZ8E6YpvtsQd1wVfe9eqRXfH8HCeA6EsDQmtHarWrG3tdT2%2BtjaIpi8iI5Uj8WPWRkyxo%2BNRQ6MAjgrzqEETJ%2Ff4jaXX%2FsJ%2B9%2BqYha868iVOuyFBnkFhsY5BISP9DWpiqnmiLTh3uWQxJCSVZGpqhQ1xvli7rFvW3IcGeAlzlyOc8gxu%2FtXVJ4ztFn2toACBuwaUN0sfu%2BTlXTs8Zll5ZBN2ExlEs01rA3O34GXqMIgMLm%2BCKVWrj3nX26Gl%2BIzgV3gDE2lj96f50IO6Z4mf2G3PsTLV4OaIYVcxDjt5rRkMHE%2FdNXvWmbexagPlcrSNO%2BgE9o%2B1iTf8CWMqnTxpQR01doDg1ZHD0zG7vr7%2B5Elv9ypxx26ALVZsB9Bsvbu3W5TeHhZxdjjGMXWKepD09XtWFx83idL8JQgKhYL8f%2FnUl6a1Cb93NTXEXO%2BdWFxrenHqsjigXNBFHlkon2o%2Bo0xXOJt35XnY1leGPVdSxPvm5qbm5lMIIdBAVDOaRTMWJyYmuruXxOvE4vumJgkZwAbwV9bfymVx8IvF3qoYjTPR%2BbF1QoIBAcJgDW7gIpnpOurVqFnIvbn5clAAIRIy8RIE5UAL2PwYBHwXLXA4rCx2Dy6LjpyYtbhhwbHY4N014CG5yWd%2BDA2LbbKY5pwRyAX8sjo5hxYooAHrCfld7QdtoQ1mL7GhXG6WPIzQoHlks%2BEL8zsQ3cxnCdn8ZE9ANEnoTV%2B%2BS8jyB%2FkaYBPlty%2BSh4%2FjQmbUIYUYYMYmTirWX2yKCed0Iyn3puZTdPIAcAcGbEDtgEYE8KEcAOvhiELhhazxMSpcZDse0mD9yYCHDkmYWIr5BhwprCnszZeJ7UEZVRHABhZ1At4jvFmyqeLrKUmbNUOQzNQBjf0q4IaIINcCnUQu%2FizpEoXxU5koXmaQA%2FMF2yrfLwstal7LmxzDRiIxgDEPi%2FWp2oWtkdi%2FlJkcOZIA2gToA7JEll6w98tSjR5zvhJL4pOOGvyyhzTzPBZ31TQ%2Ba5I0TcbKazDEg%2B80PhK8Ulgu81TjY8eUaYvmUAdENYr5zdpQXtYiLJPHIWxaK7UpItpos4ikKkOvKcmLvly0tK3GZD35KE4n7lbT8vknmjcunD59%2BsKBMbJ0ZGoMSRS8MvdcBbSPJO%2BxZ4f3zew7fMBIfiJvpKLBD1u%2Bx%2FnCq2Au4lGjKuf37DmMxC0DS6hIx19Gm1JAEqFqBw8O7zFl5v5lqUWR587Qeeh0NXZtGQfsaD6xAR70ml3faQ1%2BU570YAGQMyOJOhpIS47OwGCWPynzeGBmD5VNSUSSF5oOUEhrRm%2BUogPHrGflSixq7I2X9mj0EhGz8mQHUeDgnrSOGpUoH2gF4PLD5mmhSNTVqGZJntN7A%2BDt%2BMUWs2U6YcMtA16fe%2BZgGQwON%2BvM2aIhRWKpb2%2F3cOytm42nm98DaJOEQGd1ktJM%2BsoUp0m%2BcPg0Ul6VfdwOYhc4UQ1pLQQGYzMSdWsr4N9sbLywRhJMD4dlMdMHU3VfraJZc%2BvWeej1w4GKuIyQA3JI5QLiRZuPjnefOXzm8D3Fv4ei0jP6DNmJYYMo%2BXw9hRsEa07%2Ft2%2Fv3vYjl6XwBIYxsNWgkGXF7MAQPEDWY0gglFVDv%2FRutyhX%2Ftyz57wAv1jLQCuQ5qcK0QbhMQGnj92F1Pv69vb1yZMeVnw9bA1IHOtYpk30U9kI%2Fu2R3e2728XflUsSvDX8T8w%2BMB2yTApr9Q98AefmKvvFxgt9EvzP4rS7j6ge3%2FMAuexEORg5BGAqTWigtfWtFHu7%2Bn9FclFJrfYkqwZmJitXoDU%2B5xU3785S1a1GQRlRft6tOlwJ8Bk61gAMeoABQYE1RzdAcF55p0tH2ndjWRNstERYK5nCLC9MQmPyOubG%2FwrKCPDmvH9qgwMaikyHuEu%2FBXY%2FFMZapba8283K3luNtwxbfDypRQKCBQOpimfD9Ow%2BirHpzGkl%2BL6fzTk1ccasyFJLvUyiN3SSbSurjco%2FLZgqlBja%2B%2Foaj1uSI2njb%2BAzId2sy0GZ5WZv%2FXcvsaYdRH%2BgTjerFF0IXuqqacHevltnuIrVcrOQpXjC7pdaCReqEsP4vcjWK9rUB%2BQ70Rtpu17GyJ2asE%2BwZoaTRoDfuzbBBAgsTUy%2BwSnuUc9iOl9cUS9abyAl%2FvZpjb2PVE3yZl%2BgGcHsDHAGgmYarYgPrWBqdpPk9%2FZRoGLmM4Cs3EfKF1wE%2F40zi%2FVUcpLQhVsSOdgadeq3Uop1jTvKY5I1f3Lw7T8L66tPnpgkBO8azRyAX0le6TPHaouJOZsT2tb0EeUN6a2QvYz2HA1Owdgi3a6DMpqxbM3un4VMmHTTvIxeysNUs0HWouTCfNhxAX4vGErT4Ze1uUGiayMPgIMgYZQuY4PWK0h3Bj71%2FB4z%2FDTDPenFWoeAYxHS6cY1y1DK8k4iGeOhL40I2bxImUXHyr9eofYr8H19XsLyk0bjs94Q%2Fxl4J%2FikVtjXbIi%2FicbGtT5S13YELyVPYQDXVgjJ4LNqwwEZA1%2FZzYsCb3mXGuuSFUabyEGeOmo%2F3ig5b7NG0EaE5Q90OCmRlQMiiY7pywFTCEvyRBygjYPfpY7%2BGfM%2BRrz8yQanNfg%2Bpq6gsJruAcEGwcNbmfAHUmH3vGtXdbQj5x0M1ADf%2BsnHoFLlJHKmOMdYl69OyEGIlDyLp5Sp3DNDFp0FYwUdhCHtcRiIppJzXprKyLLZ%2BMm1mCD5Ey5yz2N6o19gdHVbgJdOqs9i6z7lpGj2CdleY3TFnJRlKnPaDlgMPMoCTwPcjupY1sFxGXM%2F3suNfLsMD1rlcIRiAHK0LCA2LTA7yQbPHIFYXoHv2%2FvYYxEAN9BAXvwdcg%2BGLeSs6QnZKhsS%2FH8pNGg3lG9tPVAoGIMelGHqGCdsiPzow3Rg1s6qkYFZjmwV%2FQK5laNO%2F7gtYN%2BjZgn%2BdN%2FPnPJH9kkcY9yka67XnCw7IMe%2B91j%2FtQvwjYt57%2FlgxiLLjCK8j8DG8Nn6xaYLSvSWuv4pse8LkOh8AMhMPU4a6O0P1CjwHZP87j49GLFwp83Wt5GhZDGb%2BcDMkxn3yrWKi02KN41XEH27Hga23gegEBWzPiDrif63EOiA%2FtIRhv69GgbG5muoNcxlGtbcQM5Y3Ipwf%2Fb7WrPizflLR1DR1DiqVUc2AbC%2BAO9lWjErwzDLbHqrZpveHkFXfUXO21y0U5IY0634YCBhEJi8dkblfXPTkJqivATO8colPfXB%2BZJj7UzanH1qyuftEQ29%2Fd3MTelELKNiJR3w1IJRCOZjWsp6AGMi%2FVUuh6gpytbWP%2BVJj%2FzZqqcZHzCn5AxWA7Q7aCe1Ih%2FUk3z73slulJNOl0TVFzxyk5RdE7sy39x8AvCCP%2BW%2BODaskkveG43nBXapo3qSTpb7ZaK2kXOOYdVhmKS8tKBmulsFeLOsQ1zRn9xh1RTamhotdCI2tQJ4YVNKW4scJlrLIO%2BCCRw1Q%2F64cuVdOUiL2MZmcJZVtUGAH5LTxNj56cvv%2Bg6Qc2lJXMQY1BJfr3o3L8CktCkzY8Zrwuo2yPs%2Fyg38oXkCIxLUYBOdUV2tjRdE%2FbqXU0dyWsR6IPW7LWjPGlCRpzY1vleraA9mtOiN3GYOkhdSbhYboC3qFYgNbF8bwJQfTnHvmZbVL%2FrW%2BS2zjZt0OD9gdwxNIXvg1SJWyZpaOFb9TZx5wJcPAmS0eDce2ORWIHAzcSx3edtq5KAc3Qu5PLqWx3DvN%2Fpaz8VFaxL7C3HSZzNGZDPPHqSvV2oPdMWeN6DQU34fOwzqM3Og8EXScs2zAZMNpBklX18sZS5YoBsievYhVj3eohTNKTkyGjugFyDHTI5BOWAeVvukQkE7%2F%2F%2BwBdoyCB4G5uXC2L3D%2B%2FbtO%2FxW%2FPRFJh%2B8Z%2B7ex7Q3br5974a2lG84UCs2c37WcYa16p2dRCNM%2BJF3VogA41imADjA%2BkPlM6xh%2F6dLdBwG37ZsPWgcqQlfF30vRHOKJiCz54QhKCgXaJEh4G8BzegryjdNcCFaaWUEydwrt200xhGLLKwP5VeZFHfKGu4FyHOVKGaYbadu5VspOaUznRLjEjCEpg0w5VTJFZFBDZGmTYLNzh%2BRBeVyEB%2B5BC9UworLWTci02hx%2BD0SD2rANLo94qvMsi9Jk74F6n0m18T1HNzHTOKrj398kZxZzLGeI0epdNXFL3xLQmcx7%2BXL2KyZtFMBKgesERhLIqMpnAFTBHoLRcC%2FLCjzfpHo6cjfg1BFayC%2FkP0XaJ5vtNOSuOXcfG%2BiuekPNIrklgJQT6sdRrwBabKhTxm9rvzpjxdNOksoZ0qwdUHvMPVL9g0aHje9sMjyXUkHpLRK7M3NkOCUnXQggnn78roKT%2FBzKES3TjE7nGn%2BI1uq5f%2FYxRjLoICHQOcIsTef4ZBNTOLkybBEP%2Feuzm1TddwT6PGLrEi9EBzZbZcraQubQuxrEdpAy7ty7KC9fuJdbo5et9iBeBOI4y2esgCYTqDWCOLEwNtO2EyLjD04tXGbx1ZuPBMzH2l36KmMMtTWMW6qkBdNHzh4cGwMwcRThYIYbQpOqtDYwfvPHl64zdIn%2BQlSU4VSb0o1OcpaGyXUSSIYKpUaSs%2FuyzaQcWQ2U8c2haDgaK9xWAcPPGsoLTy%2FHdUR0sodBmrdyuzQeAbh0AZcfNjQIBogyrP7b2ULTFCv%2BVBmfcBUQQfEB%2B%2FLw0rnH%2FGACs7o2z%2FYCpBwF2qrdA1aN6OukZg5dK9BgRc4RCccODhGuotqHJAFNU15cOCZOurmEE1k5Lz72Hz2HWZ37dq%2FcgyOZnLwuSiUOZqYLmnksoh31QBypNCMMuPN2H3dX6XpRWZcct2B95fcD01ouzYyCjyssSp65qFCYpogPyy8HUtf1zmooZcaNs%2FEPIkdCTAx6Y8jeaTOG1AZGWWVJdPx0abCrNivcJVK9w%2BOxRRUfn5wH7TkueVHs29oMT%2F5XQ86uTo5NZCRgXN8s4GKwibx40jJ2FDBddM3DTfPQMvJGtZYqR%2Bv9YiWn15vFYvF7XOvfkrZoUs2gJ%2FP9eAAv2Re5PvDxTAMZ%2BWVRN3qcqrFBeig8xMWSfBTUl7h9ZXlFFCGHFv6MqA71eK5k6l77R8cT7P6sgG3zwNoMEANDZsXq3h11Oo0dsoQ70LLyjsz26MjlUyyPFXXMX3t7Ox8GRa30uHv2rU8OJ%2BehHRxWhHe6oKbi%2BYSu6VN%2BGnhDE%2Bn4dN0XDSj44OH8j0OZ0teivVRgO9cF63Yflpr3xPL8vkO7iSgFtbi83tGH0H4pYZpdRuQ2%2FdK2BzOP5%2BTxLxdnxo8mibwtlefXznSPal69uvHT1V9fd7rjMaeWB4%2BZtkC4I4XDd1UNp8p70JUDC%2FoPhFfb06kz%2BPeuDsyWKn5WIWTH0QvVrfPWj%2B%2BpqtAq18%2FfQ230zSXNaAyPM%2FIQ7J79LAB7b7W0NvTaIoWFp29VZsH5kfmKokPw7DLU4nwZedfWzb6p9twBeJLRf3tzIpU2V%2BZm4IkKbp548VpQxHdAQv38OO9i1xX%2FA6v481wJb%2FvOSdB%2FtXZ%2BZcL77W5klVs6%2FxLED93jbsq3f396kpKWuW%2FSNJv2FwAM1Rq2ECpd%2FT39rR0txzLrp6VDxJgVYj3zitny8lftfCrd5R9O5e%2FzmGBoqVnie7EJ16mSyrgETZ9gTT4PCJv6e5pkUfVBf6svs6z%2BvGv6pa77ekWuwNAmKm1VNpaROkR%2F3o70P5FzzXm6QUTMcimXNTY%2B8Xu3d0tvT09vb31gD%2BJ18iHxZhFPLtlcN%2F5%2BPLjnV%2FPJlWQWLyOpaXebtmEln64FHfiubQ60wvAHvE3LTd19Lb0tvT3635iWW65wNOVwXHRPv2VlLazmpv2J4y961jq7%2BnpVuIXjv7RdMO96Zsl5nTPeFGHEDe2T%2BrstzoejHeyaK7g%2F%2Fg1SSefflB3T%2Fv6svPlp7DoakVa6UJPIxvQK%2BGLxkxsbE4%2F1LzXpmbT9%2FolcqMWZp0x%2B3b4WF6ZUOOO0NgY6eV2fh%2BOntF8D3zDq6yMREUD5I3Jjg9Nl0rM2w519BudtsZH2Y9RsMGHoQhkPhWTdvhMdx%2BbFd4jV6feReQY7SwJCZ8ZWmgooehLDRMdsN33%2BM0vczwwh4MvFoXkP4WJbnQbiFWVghnNMQToSh4LdUwMbUKALBtwk3cOjiTlX17058wF%2FeHLzjvFRHNyVnmCYvWTurOY%2FyYb%2FQhDYwEcOg%2FjW9mIaR4WQECm3qN8zPkJb5pQvRMWkwMYRfvi%2BldzpsyHY3S54kSQG9MsPi5tOOky1E4%2FGs8zxjtHN%2BIQ%2F1J22lYa2wPxXtY9mMc9YK%2BbAHD8uRn2qb%2BL1CnxlM3R7ADnFdxkRrmpJGsjy1lFLTpV7U6d8wi1T8SR%2BI9fKFFY0xBBEJk8%2FZ5FfBm9GCv4sfNOmBq9fBY7rLLBxniNIc0hm%2BYckH98yMzQqBkma7eE0epozYcRvqI7mihLmTre%2B0lynsO4nmrvlwdqXIz3aOgeDktUUFZjCCw3zac%2Bk6DtdZHirr9SfJQpn%2FFmdECGlBnCyRt8%2BsJ%2BEbQZuodzgWBsOLviCRqjc0nn6fp9lt965i8RsteIGn%2BCeyuRbG4MxsZnJ47eTZGhkf1x4aVwNue5LQ0DmewPNOTNoDWm6pLTXi14KxnZhjufwl9rWadzVatCfbpjg8SetqNzdzPvS3B8CCfSRHDA2mgcFGuJMVN01rt3f5mfP2bUuspvOyPfaobrZ6sp%2BUPyqYVTd%2B8yGRIJkAjQ5o0hbWnUiPw4p7zPeoGTzjQfh5XKmPo9GLGYO%2Bhs1XYL275Vpx8%2FK7Ek9dYQGxfAxoty2%2FFgebtA1L7Obgv1sfNjMSvcnQN3AxY8V6oj6aAaTQ09hzkyIfkzKGWf18KQu7ZIX9YiKnpClBGW5mPm%2BPoa07uEAv4mLkb2PRqa1gNAVS6y%2FSwrwz2bJRucea2GcBMxEU92Zg%2FxKraE67jxP2yJvItD0%2BheGxoWc2UqW5VBX9BN%2F%2B50vryT7p9s8J7FPqs5IKcayzGPhs7TMKphIseVb9AFznw6TAnoWbHsiYGKnSz0Xcq2MbTJRlITeXKb4YTWvQ89xfbqRzGsDnNNyVR85wzmlDUywt2GRUPSRwH8kqshbE%2FA7dQFY61%2BJXk5KVAthp%2BzsWva%2FB0z6fkXh54jaUQTorp7Dmxcvxn6ieFTmGsyqYLScKkN4vadc1gWRJbbQ9MwApTFURwzAnRahN6J98OsYvunr2H4IVNXEbzPqojZYHYm0Da7AdHxoYcUzpcavISHP8QOYmE%2B1uh3f%2Bz8qh1rzhkqnlKPp%2BD8ZOdlvGG4RGSzUCqRl3LAMk8VW1l3bqf89a%2FOr8LYbPV01wW%2BDnPmWcuDsqiwDGfLFupuPDqprx8FY7a6W3pacj0%2FXt%2BJnhH7ex6P%2BcgaBC442T%2BjlXEr%2B4cdyGuS79Vwq6Wlp6elpSXnc%2BsPeShQrKrOx0s%2Bem4mPhRtFvh2X93m8%2BrKQILVxx%2Fwt9EWOaMsZ3FzLkMc5TXFHD%2Be0IiMtYMc%2F%2B3nuCAiGnDTqsw32XmV33MklPW2SORyQj%2FnIvgyIbcpkSgq4r3hkPx28TkAL8H42yO%2FDffduzo3yqrBavk9cfu71TpEd29LPuz2g15coLampZg9b%2BK5ga7%2BNs2%2BAPAGo%2BgUmn63PiN5tXQh%2FnKCv2odbkdnvvUr%2FuRqnX%2BBpvoaNHiPUYSfrW3QpIdpEjnX1%2FW3dHf3yKWLNznB7wIg3FnD6XP6ro2SWZFViQhmhwhqcM63PJXqu5aEvirO554MH7UU3pGH6trRqbkRz4Po3s2BFaqycY%2FZ%2BfMkWo0spnxtmF8F9RlV6mgxJaellLfr8QGZbX81J80Ey4pX45KNRwu4lF8S4J0l8yTLsTwFDsua%2BVSkF8YmL3Z42Cc35uQYx0EGXTUco3d70xBevk7bPPNTHkfeNnmM9gNh9CtTWceyZ9u3BI%2BnQY3Q9FObR1EZcge%2BLWJgJpcFbSPr%2B6lZNF0j3zxm8cWHpZ5eGRzUsXA4h8n%2FVi77wLDV314NzxudZ5x%2FrpCwnIkaccqJyetWSzukl%2Brpzo9d3c%2BPeR9dfnd1BsQNpLBOOm1S%2FmC2z9OS0IFSbTm2TY57aPm9%2Fl5hLfMvvMmyf4Tjjrz5ufjymsUr8J7ww3OUu5ztc6xXJpYTFUgNE36qu7e%2BLAVZuiZXxudFGVlJyd9BMjB9RPOzwVLONnx22YF8y36Wujx%2FZXBYABgfnqwzLTFXIVEmWKfbmFXWUDruhu3ZjyPf8VLzruOL93CCu%2FTI8z37psc%2FGroxlWkZev7NBpztO8Nap6%2FUzre6vqPgaTAUc%2Fu1If8AAAMJSURBVAue9xAFb7JV%2BHRhbme%2FU%2BUq5zgKHH%2BB3DLB%2BQluadRe9SSr7EjZb1wXBlMQUuofhihLdAJ%2Bh9mqOhImdqh0GUhWB%2BAqk%2F8Ix4ENlOUMCl5HrsrOlKPcvjvgpLmh%2BXkPolQMtwayq9%2FZcg3D1sRMzwim%2B0r3aBuapjpynHak0HwsyNOitQcRvZz58NwLaGpduPKvgK%2B1JAW2sqSnbYBN6IB%2FtLmZ9NxiRzfnQV9vJhjUzEd67zz4%2BFQFK9MwfbCQsHrwo6MblLy77mGWao6flwmtpXsPN5Iux%2Fmuq0D%2BuaKn8Z0n9DJuyKQBufB4LuS4ofxgjV220fiI0OBcD0MN3knE0Pz5wRp7FGe4mSFhmYezYRHAJ8xeZTyQfKfLChOzj1ynJsisAZmGdy7s9yCmJPHfyKx%2FJ8v%2BrGfRrhZDlYZ3rtjLYKPd2YmxXe4yXjucV49eVQlVr2WyoB3Oy6%2BDWSfYwbIcZbDGF6xRKRonZc5afMXz96wz7GB5w%2Bc7jOKiUkqk%2FZCUdLa4yjsES74roXakDBCDuX0kdPKht3rddytkv5Oz%2FYFDQTMnlJ6cWC0Wf9W7fi522CMWXaZqn2DnysmtdUc9zTsGAh2CNSbR4Wmxx8JtFP0HDUjOyozjfkuMKFlY0pcuCi5M2V712LIIkCd9rngny9Mt8xxjK5yPeDs8PyxSyu%2FJsMPsYF3W%2BCMihLYt8wS99aX0rC0RlX2gLPdzT6zeMVr7I0j%2Fij0HfrV7ySOfymx5aOUQtm31Jyj1jwD%2FFBN7w61zJ3e1HVq5zqmvssl6UVvNMWEH7QGN%2FSGB5dPP29vb5z6%2FPom8aDs0MsAb0BG6V0eeFNGZMxgc%2FYFeyimwGiZLTxhPZTv562w%2Fb5839YPHUnY5F8729vf3d8vMqoR0sKdbQkVaWpb6%2B5f6u0d%2BiJlML08xYTnlUvKfztEzQOu47PNfKa%2FhwaofUjMIT27h9fj%2FJrIc5bPObv%2F1da2rsE9um1T%2Bfw1WvvLTtuBLjVsnmHL21faH8EPeyyZrlf8DbgJ4SzuJtLoAAAAASUVORK5CYII%3D%22%3E%0A%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dxrange%3D%2210%22%20data%2Dyrange%3D%2210%22%20height%3D%22156%22%20width%3D%22440%22%20style%3D%22top%3A%20150px%3B%20left%3A%20432px%3B%20z%2Dindex%3A%208%3B%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAAbgAAACcCAMAAAA6Xk4VAAAAA3NCSVQICAjb4U%2FgAAADAFBMVEX%2F%2F%2F9NmcCTfmuUe2OQd2KMdWGGcFqEbVqEa1JNmcCbhGucf2ibhGucf2iUe2NHhaiQd2KfinFJm8ajhWubhGucf2iDeW2Qd2KBdmuMclqKbllzYExJm8ajhWubhGucf2iMclqKbllJnctEnMubhGucf2icfWKQd2JChaxJnctEnMujhWubhGuegWWcf2iQd2KjhWubhGuegWWcf2iUe2OMclqKbllIodGjhWubhGuegWWUe2OMclpEpNdBoNOnimujhWuegWWUe2M8iriMclpsWkhDp92ljXOnimujhWulhGSegWWcfWKUe2M4i76VeF2Uc1mMclqOb1NCq%2BFDp92tjXCnimujhWulhGQyi8WMclpPrdxLrN1Cq%2BFAquM9quM%2FqOOvkG87peCtjXCtjGunimuqh2o2n9ujhWurhGSlhGQ2ltKcfWIvktAvjs0yi8Uqi8sticWUc1mTcVRpUkJkUUFardVTrdhPqNSvkG%2Byj3CtjGutiWenimuqh2qrhGSegWWcfWIyi8UxiL%2BUc1m9poq9pIa1nYJgrdNirNBardVqqsezmn2wmX5aqtCVnZWtlXq0k3NapMxTps%2Bsk3a0kW6yj3CvkG%2BzjmymkXZTositjGuljXNSncOtiWdQm7%2Bnimuqh2qfinFNmcCrhGSchnOjhWtQlrx5jpGlhGSbhGuUhHWegWWmfmGcf2iMgniVgW2ifF2cfWKTfmtIjrVCjLSceluUe2ODfnhAiLeVeF2PemR6enqQd2I7h7qZdFlChayUc1mMdWE6hbZ0eXw6g6%2BTcVSMclqOb1M6gKaGcFpqdX2KblmMa1OEbVphc4GEa1JecX%2BEaE4yeaKDZk98aFSDZEwxdJ5RbYF5ZFJ7YkswcJZ1YU9DaoN5XklzYEwubJN0XEkpapM5ZYFzWUNsWkhrV0MzYX8tX35pUkJoUj5kUUEpXH1jTzxgTj9hTDpbSjpRQjZSQjNMPzNLPDFHOS1CODBENyxANCs9NC86MCo3LSgwKSktJycvJyUrJCR%2F7i4wAAABAHRSTlMAEREREREREREiIiIzMzMzM0REREREREREREREVVVVVVVVZmZmZmZmZnd3d3d3d3eIiIiIiIiImZmZmZmZqqqqqqqqqqqqu7u7u7u7u7u7u7u7u8zMzMzMzMzM3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d7u7u7u7u7u7u7u7u7u7u%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FWBVVlgAAAAlwSFlzAAALEgAACxIB0t1%2B%2FAAAABx0RVh0U29mdHdhcmUAQWRvYmUgRmlyZXdvcmtzIENTNAay06AAACAASURBVHic7Z0LYFtl2ce7DS8MxsdgE0VwoOxTUWFsMHCICKKuXJSbOoG0xSGKjG0OAbmo3NwYKDbYnKWkBjsGmtoOEyXIGNRUvrVOOktpCy2jI5hmTbuypDljY03p97z39z3nJM2lJIPmaZqce855f%2Bf%2FXN5zkpSUHBB20OzZcxacsuCURaWlpYtgYPbsaYXepaKlsumfWHBO6Q9%2B5LKyH5R%2Bfkah969oZptx0jnf%2FYUlMcl%2BfsHcQu9n0bhNnbOg9Ae14zEjtsFz57kfKPQOFw10tmB8mQmr9SC788wiuoLa1LnnZAANDGPzBNpfWHV4ofd98tqMLy7JCBrj9kI0FtP1gYWF3v9JaVPnlv48U2rUTwZjcV2P6%2FHo8YU%2BiMlns865PXNqLpcbc9P1WDyO4A1%2FvNDHMcns89ZF2viGuLWD2PS9%2B%2FfpMdBcoY9kUtmcLFykAOcHXvrIWCIxsgcGvlbog5lEdkrW2LDgQroO3MbGRscSe8BZFvpoJo%2FNzZ4binB%2BSEv2AbWxxNjY28CwKLk82fTMqjbFUErZAwEOmCFLjAG43YU%2BoMlipdlzQ56yfliPv4X8JLb9QK6YWObFDsuBGwLXoseGEwkc4ZC7LPrKfNlXcuCGQtx2Pb4HgCVGsbsc3avrNxX6kCaH3ZEjuKGYvo85SnjZH48VS7l82Cdy4IZzk1h8%2BO3RUUINnOXIcFz%2FcKEPajLYolzAbYBiIK7H9icgn0wkcIwbgRq8mJ3kwc7PBRy6mhOP6YgbqQbAYvF4MTvJg2XbR8nAtUH5jZJKym5sbE8xrcyLZd9LScC1AzhwkaOjOMSNjo3u0eM%2FLfRBTQbLodsEg%2BvS43GeUiKL63oRXB4sF24IXAdU3KSESyRwcrm3CC4vlksZR1xlTB9D5FiGsne4CC4flqurbIP0H4U45i6LMS5P9oMcwbXo%2BvA7VGyjkF4m9sSK5UA%2B7Ls5gtuEygGUmIyi7koAFyuWA3mxnHpO0PXvmB4fSZDrqOgawTvgOos36eXBcrj8Te7wig7r%2B%2BklnTHc5aXHi11eebCpaX46wMo2IHB9qB7A1HAHyv6YHiv0MU0Oy%2FjOZWH4HuY2dOfCKHaTyGHuLd67kCebkyM4vx6L7UdOchTjA09ZzE3yY1kXBBvIpz0G9fheEt8gsxyJx2PFEJcfm5UlNzfh5umAAuAd7CdH8bWB4gXwfNnnswNHuXm8wzHUeYJvGBop3iuUT5uTTb8XE5zH0wOJ5H7c3%2FUOupO5eONC%2FuyQzPtPajk3j28YdLYfFd9747FYUXB5tTnXZqs3sFYAF9u7fx8UBvqbhT6SSWdzMlKdR7FeQBZDH4%2FTo8WUMv8244vpxrpaj8GCyFvG9fhw8ROphbFZX0nj5iETNrDmaFyP6T89utAHMIlt%2BnhfumCBDVmg44pc5XbEEcd88pOfOvHEY%2F5nQo5kEtqMk0pZsuJ2j6s2bHede1QObzjliM9%2B%2BXJbuQ2svLzMZvv%2B5d%2F86meK%2BLKzGSed8d1fuOvBEJja2g0GVA0N9cQ8njtzoXbwMad%2F3VZeVlFuQ39ltvIKgGezVfzwhu999TMTdziTzA6pT8tOznLzUwBaWXk51hogKwO1lYPkkOoqyst%2FuHLlim8W2WVn6YG7KJtNT%2FnUly9D2kLkkMjK8T96YIYw8P3lK5ev%2FMlXiz4zC7szLXC%2BjL%2FG6%2BDPngWgyiuQvIjGsKsko%2BXEb1bYgNxKYFeUXeZ2V3qS%2B3RGGz34xK8jjVE%2BjBiWHFabjfhKCHaYHKD7XhFdhrZswn3llE%2BeVUZ4lSE0FQhhBXDC4Q3Toy%2BY7Q9XIndZRJexpQnurnS3d8zplwEs7BrLylhcox4SMcTRrgKll%2FhhK7%2BBSA7sm8VYl4FdlB64%2BuPS2djBn70cyayM0qqwEV6kAEAShEEmN1zUAdsfrsS2YvnyIrpM7Nw0wX1r%2FE0dc1YFJSIlIrYKChEqOQyLukqUtZRhjMup4lYgfl9994%2F4fWJnpgluPF855cTLy1n4QukHfiYe0kYrORbgysqI6pDnBA1ev5ImKPjle0XRpWenpgmuPmXfyRFfvqyszCalHsRb4jgGcMrKKFQ8BXd7oQEcA23fB2jLl9M4VxRdunZyuuDOTbqJKZD8Y1woaFWgBBKRw%2B6yrIJnkjYqP6ZLEuGQ01xO9UaEt7wourTsuHTBJfOVR5x%2BGe7KwjKiAJnCsMO0sX4utESFjURAlr6glxuo1JjkVq4sVgbj2%2BHpgrP2lcecJUoyBK%2BsDDRH0eAYV0b7TigmhBQXAwwtzL2BQaMVXdFdpmMfSBvcmaZ1p3zq61hURGi44K6wUXVVkHSkgl4WoB6yjFIus4mcxXb9cllv5LXoLse1tMEtM6w45cTLKLQKkoiUEQGV2cpInxaurytQtCvDAiOdzTaMWs5krmfEhK%2BE4qBIbhxLs7MSTPnVgYNPv7yiolxKOCoqSD9yGVVWWUUZ86FoHgtyVI%2FkEgHpx7x%2BpWyM3k%2BK5FLbsrTBnSpWOuIs2gViY30g5bR2oy82lFrCE4tvmFoFzVfoarRiKL%2BeslpBanAa71asKKYoKS3dPq%2F6%2Bju%2FsfjqxYu%2FAY8rr7rKRpqfyAklJTbGyMZkxy8H2OjFbyY9RBGVDTSJuV6IjSCEkmAFGiySS2FHXpg2uHqHww6P3z5w3333rb0P2%2F0P3nzLLbdceSVwvKqCwSKlAetHriBdJlDS2fAF8DJSfuM0hXRm3kD1Rvu%2BlmNyaLjoLSWbeuSRJ8ybd%2FY3Fi%2B9%2BupbHWCu9MG5GDbGDQbI0FrydP99999y8y1XXXkl8pI4kJH%2BShYJcTJjIxklml2BU9Ablq%2BglcBy0oeykjOc7OSmH3nsvHmLF199td1hx6pBT1g%2FDvu69MF5KDZrW4sea8kL1eP999%2BCBIkdK7pqYOPXw2HCVT8j9rvn%2FvnPp%2F%2BJ7Ll7nrvnnrvvRgGOOs0VUwrddIWwmZwWAsSI2SkwB%2BFnd6QP7k8PSCpTEKn41irjYvT%2B%2B5FjvQXB%2Bt1D%2BO93Dz30u4f%2Fz2D%2FAIL3gPZWrFi%2B8nuFbsQ82qHHzjtj8beXElYUl4O%2BCGyYJnle53rcMz61uj%2F98dGHDIgQlLX3SQTXqk8GpGuVldeCIG%2B%2B%2BeafPYzVhoAp%2BP55z93Id06CPpTps%2BadvXjpbURV5OFgGkPI7OSZDiiigyEN3QubGtsjjzxsAnefte4k52mpPRnu75988mlkTz739HPECEdQ3j3gNd%2FHqeX0mUDsahG2qDGx8QehSL0l056D%2BlEy4nRZ8wNsjz76yKOPCBJridpMzNZK2hP%2F0oJr%2BWQ6%2BiiCBg%2FK72ky%2BvTTz8HjuXvuvueUY2ceObXQbTzBNvNzoDEHp8JwMCp2iaPiM%2B2K4tgCwqFqTldtrSCIsD2CHw8aSBlwyAqjU34P9ujf%2Fvbkk%2F%2F4F9jLr776%2Bqvw%2F%2FquXbv60X%2F%2Fq6%2B%2B8carL7%2F80r%2F%2BBZ7yack4xj%2BRnbx16dJvL1589rx5nzvyyEML3fDZ26EnnEFEZmfeT0QwO%2FOQdsFMcYsO7i0ZX7G%2BQYyac91vH3gYDAF4%2BOEHefJoYQ%2FBIo8AoicRIuDzOnDZRQmRVzIOL3QSfmWzib3%2Bxhsvv%2FwybAB85ZNPIxU%2BWa2EaXpmakuXLl28ePG8efNmHjnrvSHIY%2BctXqplryZ82FyOQquyx5RWggLAWk0PAiYC6aXXX3%2F1DS6hXYxVv4RkJ5nWT6ftFKAYWvLYScZ29hPI%2Ff2vv%2FHyS%2F8wOnTxIg7hVszxjHnzTpg588AT5PTPnb1Uama73S6UhYeZppTM0W6XDlEkK0xhKj05d7E7fvsAzf3x84NIUBjU6wRLvwGAEBXj1s%2FI9DN99bOF%2BvlyQoFknZ0SUTSrxs49iJ3to90uOxh6RMLX3MYd68xZMwsLbdYZ37nVIUjIslCHpQMxzZNTSWVd1ShJUm4%2F9PtHQVgv0bjUL2BhFqLNmXIUpNIIVyDFhtftZ64TD4LSELV%2BBh0vuvPv8o7Zxemm%2BhGLQxBh3r506TXEsR47a%2Bb0PFI74exbxa6rHs3Y%2Flkfm%2Bwl0WDlA3%2F8279eelVQEGIRUus3jlBf2M8IcTq7%2Bvu5h%2Bxn7IRzZVvY2S%2F5UZjwyhPKycYOgz3bxf4qh2bnh%2B4wHB4%2B4luXXvMdIshZ72Kmc8J3bjMhko5BsJGkxOcpaYjKmrtMaYxupGFLxyu7WCOK5t%2FJ1dNPfRpTxi7h3tBinAiRUj%2Blv5OKqR8vL9FluPvlc%2BS%2Frzz%2FZ4VF0vM12WnMYr7KVTlu8nLNNd%2FGAfLYCcR4wq34PZzaOg1SPCfYOvyHHurearJDZJOUY5GyyWQHDYs4uwYG3uR%2BETfyTtzS%2FXScQlBdIs04cFrBVSPAMx%2Ba1tnw39defP4JiGyaeT%2FFeSaa3q7Rg9PUk5THfqlVDPQ189mgXXMNaPFz2SM8aNacBfNLx%2F%2BJlXXrnMobc3CmRNHukJuCHa3iWPCru%2BHvm1988bXXdrIG30XhGXJ3PqFfTkr6WX7ZT5UlgpxEqJ%2BnmExm%2Fbtee%2B2V%2F%2Fx785%2FXy%2BeZlCuRfdc0A0XpSBUHw4SlHJrZUpz04E7nnZAJv0Pmzi%2F9UYZf4%2BTkSGSHr%2FFpmvFINbHPVucp2cy6xx77%2B%2BZ%2Fv%2FjKa%2F%2Fl6cROpipGZKegwtJGlj%2BqpCXPSJT1Gth%2F%2FgOsNj%2Fx2GM1bE%2BZu%2BY7IyvPLrGRTkI1gskDMmJNLCu5T6U%2FV24kNuHW75xxwrgJzbQ5i76b9TfOO8WbSyCMg6ldv2axPDm89Y89sfl5LESLCEbJqJU1L8%2F6ESKQ04vwt3nz5r8%2FBpzUd9AMb6cJoXEBGRKRiTxBZV9k541j5%2B1hR%2FQ%2BkbzOn1Z6e7bQGLtxkxFNnqbxpqEuU1qDP8QWNLaoHaSI7InN2P79Ith%2Fnt8s25%2FJEutoG09I%2BLEYnoAz0rACO11U74mHrznjWEtus3L6dQej7OyG3StouFD2J70cSRplO60RAcnnXh5OUsUd3Ha2md0hE8HN5fG4yfsqISAX06zGNHlUS754UhP7ZL2ClmTu%2BJu3mxYx76QyT1Oz1%2FHe4fYzVJ95UE4%2F9UaNfFlJ0rd%2B77ZWMkt9HHzzFpbybDZm32wCXemcaRK4Bbljq%2FV4NgV3vxlpc5l3xdMWjASDbW2BTR4P3RVFldQPpdEM5iMzKk6Tjpcp1HxOaJrG6JpmGt5Sna%2FJ20%2B9r1beQmNHqiU7YDZLS7Z5113iJtOpt%2BeKjfz48zD6mruhx1nb0LdydYYjkcggsvAgvG4Ptr2waZOnVmpXtq%2BaeT%2BVcanxjAevJWtOaWuauTk0eU8Nrtg8QTO%2Bp3lXNXVc2rZmVrtYSt15vhGLhT1e77JDKLhTctabx1M%2FpMdj6GvuYlG3chS1IUSL%2FiOAEUIwMhgO9mxr3uTzuOTD15TDNYvTyDdJHLQUhOVprplwyVswn0rG08VIj6uev591ELAMCWxNumMWO7zBC3bXxwi4XCMc6K1hKK7H0deBgkXk08UVHCRqGyTkBtURMt4X7Gxr3lTvcRpOT%2BWoNe5nkuhKos3e3%2FIU5%2BpOGhs18aJuWjktNONqyZyo7KKtdtzBdsiwkvwmZLbbg7h5fXdhzc3InZsnCF5yeO%2F%2Bt%2FfqILuAdLp1ErVFJGJYcaqFw1SUOyAUgh%2F1WJ9uppaQXYwmPZSmVZaxEJgsG4t1pVhpcqLKuHyOJTu1lMXVzRn2QVkD74YLqPnwA7zlRKQmkE62ILGNJBJjo%2Ftiw3pUvGM995MUkEAmCzGs8kSYg70YYa3xICQ1pm1JpWWYaxk1DUsY9iFPHsGJteZD0Ag79N10F%2BQIDhxlFAQ3gn%2Bdb2xvTB%2F28x3YgWBQdlR4EYaGq09aJDLIl2Vow9t72logFLqNB5i5WYU4c1i0jnbGZY26UM4F68A2%2FulmpVSnizhIrDT26luWe4jz4F%2Fs1vGP4MDfO5CgBB1OhxNd%2BvERBmEOjKmK5JmRSFiSGQ%2BCimvFI2E0I9LX2wElBQqFEAzhCf2j98HmQP02eI4GYxqejlsXz9XwXCduG6fG1iDr41EHz%2FTJJtEKbCk8xofxdumGNbQf8E%2F3RCNHzd4LT3TQt3GQ9eHNHJqT7aeD74qDHoHmZHsA7%2BJyb%2FDItBg7GPWX5PgjtDjCRfX4Hvx7YaOgur3x4Sg5Gs3Zo%2FjESAQDI7AixhSFTli%2FurKq7qnmzu19IgulNMNcq0EaCp2s2fETvKGGGwC%2FoofGkBI2DrKURhqdrkea3kHbkzWyg54JGmlc0p6apvE3c%2FLV6TJ8Fn3FAOh0ypTtH56JBzUHm%2Buge47nI2INAIqT8spDePiDJdNzExxEuEA8pu9PEGyJMfTjRR5yWroiHJhIISNcceFBiR%2BDG179K2a%2Frnysrmnr9iCTY4RtSQqPwR5aFTo1RlFqfidmCVPdbtKxU1uLv1AYEdA0rjiNnfgaWYW1N5qDFyVLaFjDggPXj1CmRrZH%2FzBqHP34OaSx93Ly3SUKRjNdeDcbaBjzcWI%2BiR3RnvdbOSeV0BohSCXxb7yRX%2BmLxWPN5Jh9SiaiJpbgP8ODEeYzKWCUuzT9ymRrKmvqnm3q3q6Ax%2BuFuVz7emkoFJ5NahfS4C5XLXIQ%2BOAbGhpgcIMbgyRujumOtjrFZ%2BHZNKoz6leopjQHV7%2FG3tRBh5mbpN6QsUaDyGuhgsojqJicozQdm%2F9LHywpmZ0zuOG4%2FvYY%2BT1MkFxiTzzeQ07TZo6EiSvCBQM5iQVNVXImW11ZTd0oC3%2FCCQ%2BG6ZaDO9pwKFzHG4spUaON6FwHbYW%2BvFs6pxWQGheXxs8DIhXijkWopGGMh1o0m3pFTUziz%2BQFocI%2FaNIgwTCYTwlqsp%2F03fu1D6FqIDdw8P4B9CO0BBv6RdPEPl0Pkp3sMTDh4SyMJSOrjSYhaKAuOThhv6msq2vahgimyEpJKHzc42SujkpF462p0dMdncVen98PD%2FKE24ySxJrUmHSFpySnAY1vXHlc7w6NvRMWFRa7x9vgha2j8OXze%2FF74XdF4QxPRqPkBXYAT0ZLIfPiWX5%2FIByNRm%2F6WknJoTmBg%2FO2Jx7Xqdrw72LuH9Z3k0MIch9IuimFoxscpMEqzCQX4ZlkdzrgJDe6vq6pmbpR6oS5vrngd6BQ6EehkHopLhHuUeFYaiElaED8%2FDjG%2BMkDs4QWqwf%2FKkRJciCabPC45SBncy0RNJY0OQ%2F89IxAo3COwAvess%2Fr53MxFi97N3IKIX4%2BpDy0Ip7XGiX28ZKpuYILxXQdaW0MgQPVjcT1KDmMMMv6OZcIC0kRXgdEBDIyMbwmI3KKG23q7A7z80NKebgMw5DNNAd8HpdTU%2FMEjeuF5ggUmdfHWtzPz30iST%2Box%2BuhhkKUwINmC15eCYyEieqaAPH5DCt6qRrRal6yLhqn3G760UdLSnK6iArgduv6PlLDoV9WTCRGYnECzjW%2BugYFWN4PHU7LV6awSuxGu4MsaEpxVPTNhENBVBU2eFgSIjJ3rkJM0GvQgU80vg%2FJhg1yKIq6iI%2FzKtMliOoaRF2Cq9%2BrLIH85JsIW%2B%2FPq6o%2BUlKS%2BS%2B8SfYH9DvrUAyMkbQSQlxiRI8PY9dei5uKFG5SfwnJTSJcZqZiwSKvzM6YGxVBkJ84sgsXVSEjpwnnh%2FyhG5dVvAV97MXn83nldlbamyzklSZzLfn8NMDJMQxsy5bWjq5QKNS7RVGmdFIMALbB%2BqpqDG5RLuA8nno9po8kaFaJdDeix4bxIddKZ7kgI%2FV28VRC0l3GQS4dQ270mabO7WFZdRJK2sEzGEI9pAEE0cUTGmFuiIFeqUU5GC9zpF4f1ySWKI5RfKZfWo9LqbGlpa2jN9Q3MBCVrK9RBudlTrYNcftDFbKP5FjIeTz%2BOPoFWvIb6yjGje1nMc5tKt9EyR1J0YR9Ew5OGLjRvzZvw90yTO2DQo9h5tYRxiD40hcCUBp65DwG5OdpIJHIJ3Pw%2BaQkUQLDvJ1wgTAQ2NLa1hMMRRRYiu0OsK3J4XII5tRVMXDZ%2F%2BozBrdJB3CIGjVwlRgcHCTvpsKuEkuK9ZhwTGEFHC4IBlNUchNmvwY32ry1O5hmP2oQVYdEjI%2Bvw%2F2%2BjAdpVtnj%2BalHVEYDLVva2jt6gwMDg0lpyTYkTgpaO3h9KDNpQ9TAVUJyUjI3J3ABXY8TYgksu8S%2BmD6IP1%2BwLigHFBbhwiLSKWm7pLns0sosbXVlTd0zzZ3d9M4K4SFSXoMK7tgRDoWCoZ6u9vaurq72LS3YAi0taKgVT21v74AlBsIDQ2mhwhYOd3fv2I2Gggp3TDAEk2uI4DC4ktKsubkxOJ3%2ByDqR3Fu6HiaepY0Dk%2Fq1hODIqR3mC3HLKzhhKBtFCPuUMl6xiDIjfR7jqCvc19nZ1LSxjoipqqYPTQ34jQZAe6jgsKssmZr1lR2oBvzcVSZwnEvs1fUeAq5ZuEBx7Dif5EkmTTHDg8KrFgycsNW4okD5qFoKyr4CxnbnhKsv3Nm9tfmpuhpCAj9Vo0d1VU0kKkuOxrgtMLG%2BSlZcyUHZlgRQevr0eHwEZZO4iIMnGH8Bu0qnh3hGcvBheuzhMO0exg3AUgEl2Sw4OMnWQEJa14xrCtNlpizADYWD3Z1Nz26sYwCqqqurqxg3zq8OLdtoEFw7TKtmC32E3umVZU2AOg2G4%2FH9Y7izCzvMd3Q9Vk%2BzsJAIZJlILx%2FJSRb2a4iGf21u6uzuDpLdTi92QbAMdndva276y8aaKiurVhRHnrphxS4DuJ5oNMRX%2Bii7uXJONh0ouEMuGtffRld0UIwDyb0diw27MLZ1zgBhxXt9DfAi5pMYB%2F5CE0rLflNZWd3c3LwVOMKjGyQJ1tdJRjqbkf21DlBVW8ISepP4SSSR5MJ%2BtboP0ZxSBVdy0KLaTLmR31qP6PF9YwlCLjGa2KPHwqzucfWReyjDCjRDzI%2BQ2ywHmfYGOwvNJG2rFHqRBSTEQ9FUq55Q4aXIrrqaDUGUe1MJcn5%2FOBp9li8uwJWUHJJpdkn6V3sgOxklPSejo4mReFxv4RXrJt4DqWZmxkxtkMVBNPhsoXmkbZUKqmSiMujJer5hpLotasoroVx%2Fii8ggyspObQ0E9XR3xHeQm%2FNGxtFYe6tuB5zg6t04T9njzmn5n0WvHKTXClylzWF5pG2%2FToFAmtWxmmKp2SI0eBGANeugoOQupEv%2FpES1aZ%2FMe1YRxylx9MwHIu%2FRYqB0bERPa6HMDIU51xOd1BKGdXbYuXYhy8e0JKu7wDNTSxsjWViUW3wn9V8jqVZ67UawPWYwD3O6X60xGQnpdcFxrh5PGEd91bipHKfPhz3w1wn01xtj0g9pKwkHDFmKnxka6FxpG9rkoCQ%2FKOIbYKnhXOUQiBdBIJcyFR%2F1%2FHljIrDNvuc8WUn%2FXZ3QI%2Fpe0mQG9FjcZ6aUNEFQplV4b8pNI70bY2kLLNqpFkp5JZMsUGUVhoVx%2BvvKgvFYZtbmvp2S49sQ%2FHh2F7MDX3Syitzw6%2BeQGtPUHBKfV11W6FpZGCrjfoyZI1ydikGZYrJY16nCRwkJz6%2BzWTgSkqmzV2SNFOpVbh5AsPoswP796FPyOkdNL4xblh26Mnjb27fwa%2Ba0ktw0jVOIr2%2BA6nbZDxbbfRzCiVlptE9Wk3mrNG6W9kVAm4RlFWOpzhsU%2BdeYOUzDdg86MM6sRhoDf0PXSuk6uRP0sreQFtPkN%2BjZ%2FrgznsnpURG29ngL41ckvjMpM61GqFrikYjKjgowLfypVKCQ3bYoiVKu5upgdVDER4HfxmP7%2F4QaHX2%2FK%2Bcfy1m5hTkOEA8UL%2BppWPHwCCvvXGNjof6upvqaioLTSRNq04JwpRZsmmqRK3BPxuN7lbB9UajvXzJccEhw19dU2vNjJIL6dhP3vRhsdaMOQvOX2IZKTlDjy%2FQ1tsnkkop7QR%2Bf1l%2FwPOTkFQr%2F9VGmVklMcZCgNUNePpTJlfZBSj5smmBQ3b4yecuuzM5OU8g%2BObQTz9useLskxadf%2B3tjJZT5YdH3Q2B1o4d1lctd3Q3bzyA%2BZlxmAaqiaJSdVkac9Mk4FqgtHucLZA2OEJvzqnnXris3grcsnM%2F%2FYEUa06fveArS65NluwQ%2BW1qbtvOLzuHxU20WH%2FNf11feeBV5gYJmYBYjFjXD9VGKVY9Y8oqG6OszytjcNSmHnXyqWdedNFFS5YtW3bhhReee%2Bqnj0oFTbJD584%2F%2F9qUhUZtPSQvITnyDbIMJnzA8VudkpGx%2FDZBNaUu8kAzJCfkilwjGH5FNTnTZFbgcrWDZn8B3Kcb35ZPHvhjEC786sITGja1tAUHknS1AL%2BnDgh%2Bqw2gUvhDQ0ln4mzqatmGe04aGTYYQBfkon%2BgC1j2nOTJDpkz%2Fxxwn26ZoNslRtwujz%2FQ3qN%2BZFW6qSjc3VRgfqtFP5asnmqJkgrLWI1Xs8VFWsLmdkMOSZAhePg1EBVX5AqiONUOmzu%2F9Lo7XIwW0h8nR17qIXkJRnjaydBRPwr5Z6H85xojGcvyLbu6HPxiO%2BFFwDWSSi66nix0AIAjNm32F845%2FzomN%2BI73W5JgK4GX0t7L78Nk2uP3f5XCP2tkRo%2BRUWXatS4ATZeA4xamOAINn8jul1oAN%2F%2FUJ1mUpE3g%2BLvgiW%2FIAEPBz0KksnQtQGSl47goCo%2F6ZMIfdvzyM9wPS4JPnNvJRs0CFQehaRyd2MjCXDkBQ31InL1VVXrTy40qCQ2C4q%2F6%2B5ws6AnQh81Vz1EP%2FzBVJ6yyNV7eDC8PR%2F%2Bs9Ioltx7utjgdpRUMmp%2BDjBE70C6qdCEUtr0WSR7cblkZjJC1HMWFB8EZxdshRRBf3XvHj85wzCwS57sJ6GnGvKUPY2CGn9l5D48fvMV3Gb87%2Fzzl%2FzSrZgcAt0bcMc1728Rt0rTEBgJb9%2F6zLvAb7WxAkijIyXNHpWtwGaLX0BjCP2N7ehm2ejAhwpNJX1Dxd91bp5uGs3lbvAHOnr6eN1A07ooEQAAA8RJREFUnSbvB4URzG%2FirhupF8CN92lZic3UUWlZNIDgdqN%2BE8ZKGEa5pbWr695C08jYcPF3nSI7g3kDULurn%2BCS7v9D%2F91bn50Qfr%2BxVougKKBQTCZ9VVfJrpbXCujDA22Cm8BHKvHGxosLzSFbmzF3%2Fvk%2F%2FqWbdbqY%2FWetD9znDrV2pxU8Y7g9R35qv0mVrCALPEmEZ6oVAG4NZCboYhzlJEU4LryPFRpAbjYNXXr4sdtl1h6bAO6zrTc0GGF3%2Fpuz0Oz5rTE3feaX3cxg67biKNYqKCnksPq%2BVOiWnxg7bM58VvwlMeDX2iH8J75qG%2BGFILr7Jbx9W1NdXWUmdypVjpMbVlcpLtNCXvJyVY9vbN7WzT9IEmxMYe8TbsxmzwX53ZGMHfafKP71ivKPfAkVc6G0gu%2FuhBKiZvwcdE1yIAZxWfc%2B8z6SjU1bu4OGD9uFkzHb1Nh473GFbul3xabNRsVfUvnhmtC7CfLPYMR41U88Y18a7N7anEKElQYASdnwC9tqrllT92xz946w5Sd8epOr7V70PV7vY5sxZ36psfgzmRciIMpAkxYQpCgMb7cQ4RoDIakLK%2FUHPeqeam7r7rMGFo3uHgr1tgeSYzvt%2FY2NG2QvpdeNg8%2Ft9ngDre29wQH6NQzSh4vozWjsQ35UhKDC1VZSs%2Bq7IhNr6kBfW7u3J%2BMFJXUo2NPekiqyNd573nGFbs882yFzFvDiL7UEvYFAe0eQ9KJFFOUpV5TQ57%2FDYQiHnc3Nz2zcWLexrm69jK5m40Y09dmmpm0Aqy%2FVR1cHwqGu9taUwLCtOu%2F4QjdjwQyKvwt%2BPJ77FAi34K%2B3GGQ3UShf%2BJfbx78psJ6O1i3jE8PQPv0e6uJ6t2za7C8suuDH6eFD5sMqJAgjpCDM5QsXBgdCvV2tyaOYkdnFpx03ScJamob7ztKUH1OhL4AuBgbDGXxxCbXdkYFQqKenNXUQU%2B1eYPZeuAhQGJudgftktgF19La2d3X1hkKhoaHIkBnk0MDAUATD6upqTSOCGXV2aZFZWoaKv9J03WdD8gZvSTNoJbd7rzjv5Pd4R2QB7DB048Q4%2FDZ4c0STFNmqSxYeX5RZLnYYuM9k4S%2BF3LK2VVect%2FBjxbRxwgyFvyXXbngX5bbqiksWHnd4oY%2Fz%2FWoHzZ5LHehEYQsAsNNOPrqosfzYtKOOX7jw0kuvuHFVVrRuvPGKS85beNrxRxersgLa4Ucft%2FC08y655NKLV91446pVN95roISmwuPSiy%2B%2B%2BLyFC4%2F7WNEdHtj2wTwm8v8Pkm%2BrFsKSnCYAAAAASUVORK5CYII%3D%22%3E%0A%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dxrange%3D%2210%22%20data%2Dyrange%3D%2210%22%20height%3D%2249%22%20width%3D%22166%22%20style%3D%22%20%20top%3A%20297px%3B%20left%3A%20371px%3B%20z%2Dindex%3A%207%3B%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAAKYAAAAxCAYAAABQ69KMAAAAGXRFWHRTb2Z0d2FyZQBBZG9iZSBJbWFnZVJlYWR5ccllPAAAHXRJREFUeNqEXW%2FEbld2X2u%2FrxBCCCEk7kjdunVJ3XHHMBVCKoRUxjC0OqaUofphVNMvjaE1NbSG9ktDCaH6IRKlY9IZMzoavVq9xFyuiUYuISbmaoiGEC7h2avrnL33Wr%2B19j5vbjx5z%2FOcc%2FbZZ%2B%2B115%2Ff%2BrP5h6%2F8KRUSov2j%2F2cmkUIsQsxVf2X9z8%2Fp%2F%2FZjpqr%2FFf1vu6bYNVs72%2Fft63b9dn78fvxPr4f22tUMbbYnCv5f%2B5H7V7Xfhavdsb8Hz%2B1t%2FdPXg2s59E%2F78bj24yHozwP6uWLtTn1rzxpNcW8F297HpN3zkd77wRjPbZy1vVt8wfj4e7RxEmJruZ3n8J77HLHsfaz7Pds8nGjd%2F7L3jtMc5fFqv0j%2Ff%2Bl3nvb29%2Bu2Bqr3o9JZeCb%2B83PFxinT2TkSpQ0CiT0AL2bBAadO0P12FnhAhQnyiWFcAPtgSyfGUyCqcRwHUGwi9uP%2BPKSpQJTc%2B0F0TS%2B6T9u51k9d1d%2Fv19MPax8u9Ql8RK95dPRzvFeBd6W0RGLfYEJgMdjQwKQjAW5EuWjvM23j7f4u97SP72x91H7d0XY%2B1d%2Fu6nUf6t%2F39fPxePa4vxGJz0Ve6IPI23zUNp87w5HDd2yLWPyerW9jzMcYdRoYRLe%2FG8cWfQyq0wmctbnXs%2BdErbH2UrW9mFBqdLxre7Hx4rSv1NiB8EL7X%2B7DUoG4qROW2KpqE9GuLX3gCNoaK3PiopWvabuXdYA2jnZJf7usnwdZ6lX9fn%2FmLsilkYBspLd%2BCRKKDtNGvAcT18bA7y%2BhzcFdauj3ipvA%2Bfu0jev2O9cnURLxxNHkjrb3qR7f1q58ov28oz%2Fe1o%2F%2B5U9ojJ10RrqNbSfOIRHau5XAdHDhsfWx2oJq0rOzC%2B600NsS5hXfP3jfQbBj%2FNrx%2BWDJBA%2FfxbmtKGgWuAFyOOnk59du955s%2Bga3bNwYWXgTqU4gPkAM5%2FXLA53wtgm73MXqZT11dbxIHADxQTcFIIvfg0kQiSKxCPxWYLWLccpGaFn8cTs%2F1Ixt8XdOg20MFSAuEpQ0oD5xXRHylT5%2F18dP%2Fu71o41A9Vi5Lr3diJXe0%2Bl9f4hjJwzvU1aJdsnWJZxJCKk2rkVAfPMJORn0B%2BcJVSdJdNO%2Bn89CarBYgcFtEyzsehHDgwdhj4kb322F2co7WVeNa3AQ0PfrPV%2FexK0eX9PjK3r6ih4%2FwhQHPagZ%2Fbm167Zb30oifO73chKp2F7kp9XGb3AHTmJxfPf3dXHHSUXa3l3qggjLzI2jxGmiefSBgmKD11WzD4DRPNw%2FT0Z9VT7Te97WFt7ZOO6mJugzbqqOeHdrtpg%2BK%2FZpDIATIVGwIUzn7GM%2B%2Bl%2BM6JFIV5zZ7ZXzqGQ3pTnoK5n9CiWi4DDZqGyjiiBGNGEyL%2BsTv6J%2Fv6wD9qQ%2B%2B5qLx5om2XUmVxEqiN9BTDh4tdN9VxFoVhGODK0qTUS5qGPj5iUYIDLxuaUB03Ve15TXKkIkINBNRSYVYTAQBr39yOAA1aCpCyTXuwTy9lnuams39bFv6Xve1Pl7S9v%2BjKyfMi0cNLSkc9rKpS8blIDIEGQyToPOKMAxZYilxMZdoQc2TrXT91Cu2YwYXA1utZlBdEkH9Fk9fkZPP9VWsyRr1pV3Rs6Kkz4WkJRm%2BUsWy2TiPC4wDhM58ADTs6Vzp%2B1dVCS5uOuLduduTWSZASazJjWrNTUYOn3JWL99ol19GhyHko4tNs6nRMA1EOWRJAgLRSZx%2Bqg%2B4%2Bv69%2BvO2eoN%2FfOm0sANpYsbUQLunAbEv4t873vijDImWpbqy%2BjTeeYYwwgx8QAK6XiFQbwFpgGNm43b7Fac8P369Gf1l2e1vY0YH0c9w59RTBMMnKy%2F7DTQXao1Ec1GDhW4yNCNBiG1SRMYqAEZDU58MopiUEVsgLvRQGixy7zqMxdGLumwi4tAvH8seJ4seDZuPxlNXCedlG3RNChoydlFApd3hsRJRO8M5KmOkmxGlhKn%2FEx%2F%2B4FO%2BAfURfxY8gWMKzGpBu%2BUFhwlzIXHmPzrK3%2Byd2qILVxJjlNy4pTFROPi34P6UWLk39Vrnm1644G4Cvjn6Bxa%2FAhr9IE3LFWgT7Q0HPA5JFG3C%2FAUcOW9fcPjuC%2ByutAB4xJziKtMXHmFsV6MV9LnYoGZI08GE0fi2%2Fu1UB2iYRLRzBkWi1q4qiK3lPm8oXTwekcBJgOn0ZMbwf4%2BbKpjXjiNUXQuWRAKoGIcx14SMSeuJlY6pd%2BnLWwi4Ef6%2BT%2F9vKbNf22DazgJNwHwYXC3apNZAxY3rq27yCYwACStOJ6mq4lbJ6IsNhyeiqgEiRPlgK4yiD70JFQTSodfRhvtWhufgNGKLW6XHEIO4fjknMK7be8ki3fFMR1QDSIJNtYSNeHmAKEgDbu1B6qFJEeIYxr6jOtKN9%2FVo3f1vd7VG%2F9Cf34kM5FqRtApMLZBR7zA0cv8ohwUJk4QysZBdqu8NXhVz%2F%2BtHv1Kifif9crntINnbTUUIA6fRoRvULxlCL0NDoD1ImCE0MQp86SxiaWIz41n7lIC%2BkEJq6Pk5XDCOZu9PeBwaP0d%2BpPrkNt9u6rBZKJ8qAZu4fOEOGCfd%2BB6YZAy9tiA7QISKHMlNKikj4Vr4FG1QIZSk43C4IXbIbzv6jv9r575kfb3eW3%2FjAGrdpYyoxB5HkrmZkIIi5TJEus6n4pq%2Bk%2F99X%2F02wt6x8PjJZuHoBHG1qHokcAn%2Bcv7ZJBN%2FJjYedVKGOBhiOwvL5zwXJm4qkFaE%2BGUlYUAepujCS5R6mT4BBCcx%2BKS7g0Z%2BJ5M%2BmGFsV4B0yiumxJ11t%2BJE9ccALgEaBy5Z%2FKhdclYgmwbiw7Rh%2FHetS9SJgFdv0uZsv%2FynH7%2FoR78Sj9%2F3tU7wGQ5oRVOeUNnLdEt5P5QF3Ft0HqnvqbHP9fjn2zYWNPdsp4ny5cb%2FndJBOCck4NP10QS1bCWMqENQhFyfQWJDPvWxGiyAhPWlrkuT%2B4DWLjMafI4Ep5IIP72Gx9oirIU1cihKSyj08QNwwIWwJ%2Bh3wPOi%2BOLcB9P3j0jRlucCw%2FYWEQ16Pcq1uWv9Vm%2F1OPv6eehRrhAH4KSR0xNKpJWU2Si3JwfVJ%2FSSfqF%2FvAvOiDX0deZDQoTKv3lxoANKCqMnRTUjpKokAjVLCZTEBFAX7DM4mJX8rkmJZt2ztImiQ3tdIJwWH%2FlZhsLzRfbyiXH0X0LhCoTsHQC7A%2BdFyUs3ov%2FRa9dvsdUDUlcFqQWwzg57lwnr9m8aKLHxxejPKjH39E2f6nH39Er7gsL34zGjhJvhqIEnU1scAfF6%2FE%2F6d%2F%2F0FNP4EAzGBhoUNiAcyOo3RvBbCKDGNqY3IkUjBaii9x1KSAC3GeTiAXgOd7TJ0j68hE2vzHCTnsblZdGC%2BK1JholCMX2Tot3jRYuEmoFRkEA%2BZAbFYixjjNSlj5pzoiCSICJogRxl3Sc31ndCR4vKRculq6%2FPqDtfk9b%2FoUePy1JvRoLYDfGSwexax8c%2BLfBPe%2FqTd%2FM%2BFzuGBIUupd4QBaSFW%2BhgYJm4nbCiBw0DopcsFJlNmjM2i0L7h6NFupgtXRdaFjRPHSfrMQLHRgtEtQN7iLS9NOuc5txVhPKwAJPKROURlTDmKAqEz1MURkqaQ55IYVEOATYBDdtJnsI94vBiV2C2YITpKErevzv%2BtmY3v0UEJ7uVh3cxF1vdKYvvFnar21Kq%2BDDF9YwAsBZD%2BRueXLQg6JxseuI3YIXC%2BHqA8Rsv8%2BDUvpE82Qhr1ZwsUCFDp%2BwTP4aBMQHsF%2B4ggZZzc%2BPQRzRuMCFKoELDiPBiFPExsh1Vu6OLQF%2F9CkYH0gowbgUn1gGCGi2ASCUcAoVFAt%2BGf1qc7BGUff5Yj58xvCmYUgkQIjf1N%2F%2BW48eRzRkN5xxYBv10r9px17wlV2J%2BZhFIxeMkzNHxGTPicESYMEPg2rXyYSDch5xQA%2FOCMHC4%2FksUx8HsaTVC9wIpYZAgG%2FkQua1YUrhYtFnfYQDcuJ2PJCMjmy43dG5tkmjOoEtQTXhGgKoaXG1v3OZdV3hpVcpEP0CvWChSZ%2BPqgMBE4mSucXJ8s83Yxqx8QIiYlOEXttk%2F%2BQPhVW%2BDMtaKNFECwuZ6xzymzidrWIGkIoBlC%2FiLrdkySHRsOFzEDCwIPIBJrdraDKcgovTruPJ6l6pDoMb%2BjvWJZF4DOrQyYff2IF2N8bEPHRHvMI5epbXkoJxOCExcsh%2B2tyJhSNGw0oORT5io43DC3ju%2BuyxPLQ5Z%2FT4iTFHZaxI%2FfHv9bLn%2BcCrwlQPQBsBOKlMCrJHHNEUsCCTSB1GU0nGGE2ruhktZck53JMihvU1YDt6oXYxzTXERNbgaSmgj0YYSYKTgBe%2BbbdqkYOhfj5Ep0NqjRgN%2BJ68P%2BBgEFnAbY4LB8eAyIyLdkJDo2sgDLPTpSYm4otfmA7uoaBbBjxUVlKXH9RzP2kQEzUcUz%2FP6RP%2BeOVnJgh0FSqTDjHyeob%2BVQh0ruFeWoSJxZUKxF%2B5p1ycAVH0%2FBWJoWPMx6kPA6pyNaMupNXczvDICEROFQg8yJjvalFQ8j2vIK9hHaNHrHBEAnzcxNJPUAJ4ny52QqwJBr17Yvp%2BkAy8Fu3oKg7pIZxw4JwHZoE5dUJGuvR9VD%2FfN6VHT35%2Ftnjjimw6k4tf4zIQp4cuyMBZhh%2BOUGcSEDmQV9QnB1MuBnRRuIZBmMQicDac9HVUTYZWSvCETO67AB9FXQt1NgbDDY2f4HOnMi3Qi4I0CCJ3MESR86IL3J4Xi6aAa7mE9BFKILxQDEyOTouYRsIH4XV1wmORuMu0cPpY%2FL7O41XV2MqT2wGKpzHBWdQUiBUc1liMpu6%2BZCabnLEinIAl5I6ESagdGskrdQFdDNbn8EZMCEO1oYKoqQCGS1c9gh%2BYKWW6lBD0IBBwEqLIJeKrA8vMqRYXGZEVUYbRtoxYzAODJxhoh7azqUct2asapmw5SUAwjkJIQDWyKxM9VYN7en8avSxBeHTCTIAVn%2Bl0vrCJ8qdXWXaSpAAnrjjEU%2BB6TJYhxws9CO%2BvpoVh3ktvR2gKt0VIA1MJPDyOAmfx1GGG3J%2BsmNd%2BLobHoY%2Bcekzqyv3aHAgYreTIxD5pwiZyObgPI9eQvpCHYWcKVRtEijH5C6s4hL3NVoB53pLUARHqgS0shqG6JOCsABizwEg0RB3cGD0dLEheqmKtX%2FTU1tKjCIwO60%2BozPpIWpUleon66j4DhsYgtkoYxIHwx2iWNUAdXXuYoTi%2F87DGMTrblXa0kN2TU2n2G8%2FIhEwii1N8I8I6Iy9%2Fwz1k4aUJrtQRrZWMlPY7T%2F7sHJzhzEImRwctJF5WKRAZQIeI47pue7QFVwIN7M8UXiIUY4FmaIohumpysrBc2s7cc5Y6%2FLXVQN05Vq5OCrGsuFvtVqZdXxeDEXUyg0kAoEaYJHsYOBCL666mizGHELhchIBTTGVW8mnSq0pSXWTponNssi0QxGiDFc6cgiBm3TJPdkxym8PHPDGQJySEJnEMDCYk9on5rEOoYsdnBxwmNiqnEEuaxyTgoUzBeK20ylOSe1tLd7IoDH5YBENZDvygMhFd00FpAZPUoEsZpzQ%2FtQRvhUfRtG%2Br5K3heXAiLSmnBaahpXwAB59z1V13qokb1gVxHJstwcuTC0t01QD1%2BGig0NKzFSe%2FTAsi6%2BDZykZGgFFgqIeiRPO5lRCmVzCoOzseEoQ1heQFF2mO%2BdzPvb25JN%2FQzykmt8ME15kb2oukUPoQgT6tRNDkWA70TdTlZGEg1PBsEykSLdARMLtaZF5lRA6MEI%2B0ljkMd9buJGO3nALDZOmFGf6raaFBqsHIaXK0Ik%2BkWKT8ygtEyUAJ%2BfEiIfGNl8lhtDSy8lgMHNtD6WT2NMEiY6HlIoPF%2B4PNJXlXr3zVNbwOJXDPAl6AwzkkXkJuJC%2F1DPfEsLndDBLqf9t1EfQOE8wcn820dvElH3WemByUa8o%2FWO8eh8lmqXKo8tNUlZGUhzGFAb7JgbGmckRuvPL5Z1GOoHks5VOX6kAMpcsqB0%2Foh0iZkYK9ryXEIOQI1aH%2BDacH6rliKED18etpM4UqRFCYdLmrn38oHYp4Ubv1iQWhcg0BnEexKAN0j0aDxzfmgShc3Z2XCB4j2d1rQwGfNHEm4HOWNVSyAsDHREwBIUygV1MgMFMRhGIFDsIQPjm2MBN3ZlyIUmBixXTEI%2Bw1BzrEsRCQJiVx7bUbNCarpcJcRlSnGMFaZKnKYFkut9alG3%2BzY4IxdkGCd%2FEv9eheaZ4O3qj097SVUyDGXvSqBpeYE%2BxYKSs9YhZ94mVSwCs0IohQRCDc4AOW6xwNmCbpUQEvjFYrogZzwO%2Fs98XgVWIJETsIi%2BAzs9VqYWsyA8qlQzh4PcJ2GN2zcuLlsXBpUqkZ18Uj1i%2FwhR9BTdyDqBm8eRTE8ME94pmtAzpcMbQJdGd%2BXb%2B90iLYO3alF%2F9Ub%2FlWcPj3qOscsznnupSlAn%2BRRwND9zOXyGB4nhjUq3LM5spqxXSNldXqPv2kkwparZOC7glt4oBS45I0caa14ZiirLrox5yi4OSQFA3KvDDYohTIkNFcX2kVkFig7zEqjJdFC2nCTEM%2FJYYFooQAx8VPdZz%2BwCrujUiePmH%2FqE19Vf9%2BGnOTeeHSuwjgPZqEE6STZtFCEEfIMDweeo9prrQIWi1JH8v6GhpykoyioQth1mBJ5QTX7%2BeE6PBVjVFIh8ZW9qHPsY3ZSPG%2BY9aoWDZpxEhdJYoitACawlNYnxzGbHqkfYlxlRNK4uZdCXCRqxuEMZsv611Kd%2BWzYUS766FPut72hn75on674w%2BWoAMugwFC%2FUOZ%2FKUClTcqFGwK4DHXUJ3Dc5M78UsSK6k3Pmld701cCgu1ogvWjKKerFYWabqrXHK0HZDAxlW5XudMlF5ORVKOe3ZhVsxQDMaOeP9qArLF1ZTot5YJbVgFIs9Sqpqw84UvSV0beV11GdmUDOeNEP9o%2B%2Bw1ktBjNPSBWASG3tOLv6S3v0TJ9I%2BFBGTh%2B3QOJL3y14wXQjGDrmNlQwX96Ty5sOTAkvT40V3tEOfEwfIFx5KH30XcrqAFynWpToQUZJbkaz4OpvWyM0JEcwXPKZ4SKjeX7M5EzxkuPOR0PZwuRMiHynV1CfOEcLpR%2BkWcI%2BfwP5RyGVxfLM7b2t5v6a8v10XYXMHqbgUSkbTprU7Ntzfuqd9vodUYSa1M9X1GOL13PoLDJVQlPpmSvXRBGtjMk%2FhFvC4bLzFCfoZNRrDsWr9lIoQ4unXqizJXzShLw61CqFeMbcVwPAruzmEUoLHi%2Beq%2BQKZCY0txmrxZlSFSPpZlzFY%2FLWJMTSXpXi0vWsYHkmsF%2BvMnek7pir%2Bo7d1a6%2FBm1AKYXDnUCtK%2Ft%2FX7l7TNb%2Bnx%2BwLpoaEKcciBcUA2exMQ3kBrPIrDXgZwCbtwCMnyGMW1qVUPMgfDX8lGUFm6KEsotlWWVTMQZLaA3ZIJMVu1fKHljF6tYkhGOYwpCB4wzCEfqSjB1Zg5eVmYNrwKT4N40QouzEIHNaXu6T0qgek39NxLWQUQkBS9dI2A%2FiaAL6bKuKJmPMuv6zXf0M%2FbFvLGvPRyILuvIdKcJn1qPw%2BF5UU8GWzlJ0Y4BWMCV5mchnJIWaaYDghrCq5gBi7O4KU6CwMvHHVr9K6Yw0DmwNtRyGpO9qcLC1mN9OoSUhxmw2ykfXDwZJVkzCRJMTJEVyFqVJY6PXr5Sk%2B2qzEAaKsb%2F3d6%2FAXaJbB8uEJgQvSViFc3yBAQB9%2BppTicdLBf1cZ%2BU899Vf%2F%2BeH6L2ZtQFpl4pu%2BMQgQIsbDQsp5RTiPgdaKV764AQsbyzTml7p5AxwWPSu9CtTqgJ7h%2BRilWNZAy1wh4pcXLyTIdZW1g1oVXKG26cIjjSlAFeBUtNRXlLYeespnT%2BrP6mLyv7byov39Bf%2FsznfCP1u9XQrEyY1orR%2Ft4ZXcN8ir66A1t6Hf081hD6%2BmuTBYjQTBqLKs3ezMqAnBzQDCUd2GoELeK2cQkq1xzUro17cSApf9QJ0ZHZYW6P2WxINZRQvm3kirmoTPiKG51RaSxekqNKQ1QojHjuBGyO9J7EQiVCfDHRR1dj3s797T9V%2FXdfluPf00%2Ff6N3fjxqj1YpM3KBBhIjB2ZZxAlCSWvGUoF5vZpv86%2B0k4%2FpGGuH%2BKW%2B3UcopJrxubqo8lZT9d0wgTyXvA6QToriWa9q18Hcul2BxPUg%2B1NS6USadMfMHZF7E0R3YxprsfFx%2F%2F%2FKETBlaY6YRqEAue26nvDk0o3v8nkIh1icaJgLJijFMyAf%2BrGe%2B0P9%2B5jOyTf075u5fM8usYqAPl3AzoB0mD4m54MIRhKWKfpcl3F%2BVsx11B3CgWR6Ux%2F0ph5%2FW%2B%2F5il73PO0VPbZKwgRh2VHMFDCO5nA1YPljhWGmXxY%2FHRvM%2BiZPVdOIiMr0naCQ%2FUUuvJJKU08uzeHOkzUMhvgp5pKvtm0ZkgaT1oSyTQBzZQVpS0AniNYbKeS8n2yxLzZS%2BFTb3KoKv6qf7e8nIT5XeL5H1s6WqULyKHWN%2BTpWo1c41Vx3w8YJeM0pwFK9qd9u6nNe1C%2BPs%2Bx115%2FRyXpaZ%2ByhodvZ9huhAoWXreZFTXezBmUOgsVwLyxStdpVLRe4ctBJltao9VNiBQ6%2FMu4gx1IDr5twXyjYgruboajEeut8YCkjV15VRHEVC7BXce5qxb4gh6ukKnl66ob%2BdkPn7Ibe9%2Baq2nILWRS3IWRd0tu3A6FUjtUjts6DNcRQ49IaknksWLoq40n9Y4ejOLhm1Gww08v6rJf7ith2S3hGr922TvmK3vxIqEBBEV%2BM9Snr5xS%2Bd104hrChjhlLZ6PICvvvbKKnFvBI%2BSP2ySqu8iQXW4JXYp15SjlAjZgL1EIXdznykdSoqX67E0TccQ25OhYfqyGvP%2B0%2B8pmO8Vs6xspc6L%2BUUDbR%2FKnHXA7O7fhC1qstS7X3kRc0ZdxevGr18ISdD0gjuskqbKx0mv3kkN8tYDxUi4qGPQ%2FZ3WLg%2BbmlE3DLV5tc0mep6D%2FthMptq4%2F7UPFueSVt0RSKosp356IAbsft6vJODnIoOn0Hj7PA0UMEe1A5eBKV%2BfuqTjovAk2CGJ5C6WTJgYK6Ilj2WnyjqL2mal0Q7n79e3q8gd0bId7UuXmrQBQY5ugzBK8YkSUJGne1OMrhgvHmWV04R9%2BzVTwb7LvUxXYhfdVImXxtBSxstNBtZUIN8I3biAXRygc6MR9op14HTrhtNDp2QXtCj6%2Fqs7bjh91TBQVH5SxZn6nimfRnhnxpDs4BOtjhYS7dSostWlLwhKEBdQraiHnrtNDt3B%2FdJGL00dewD2eFEgslbD5LM6x1SwntjrawEeK2S9qdfas%2FaqtvqD1jbnLtSlPnsJAYxwV2vGclhY1agw48kmlANThf56%2BwBQvPK3%2BOZFltJIS%2BbtvL0KJtyHQROhjs5mXaNvLkn7XB5hF8sJUSUQLla7T%2FpSvKTS9z29LvALjtJZiFpvykuBlV3GkhKuZ1Odi4zSDRvL9O3K2CPR9feHLxVtTtko8Atygpy6BkGjtDfKxtvKfXbftJvrNxQz3eCPC9DB0JGEACW%2FexZHdIXUihbn1U3mNHim2oRYEIc9l0NP7yBqwF1Irzw4CMvLvsAl6wjjJuRrrewJMBErGkNYsckuCUm2OiCbaf3ixAeYv23bso43TXu9i6ohdvWzlf2jms0EO6KB7XCdiq2V0N26eERSUhcJjJ9wMaBWFXbkOckChqxSY9MACJADcsxknfg%2F592KG5LSTxjj70pL%2Ff7rz0Hb3%2FHvcdeSURBG7klbfIs1pRY8FUV4tWUfkhEknE3JzZtRvF9wzm07SVChNuyHqeO37EAacBA0KksBHdabEpEy0gE4aa7LKMHMqbKg0D63hHXbrVjahbBOgCc3af7e%2B5bRN91tUDIGLTqR7Q4ytjb0V%2FJ74eYwli5t%2B80ZLhfh%2Fobx9RTIf9WLv4PqgkW8du9zbe0fP39J6d2OI23dy2Zk5qC6cM0zGcdez01t8t68EehUS2t6W5ZIVgN7YK0U4npeEzYyfHaE1Uk2yBjBjYNO9jD8%2F%2FF2AADp%2F9%2FkGB8WMAAAAASUVORK5CYII%3D%22%3E%0A%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dxrange%3D%2210%22%20data%2Dyrange%3D%2210%22%20height%3D%2275%22%20width%3D%22430%22%20style%3D%22top%3A%20263px%3B%20left%3A%20442px%3B%20z%2Dindex%3A%206%3B%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAAa4AAABLCAMAAAAf1ZMtAAAAA3NCSVQICAjb4U%2FgAAAAXVBMVEX%2F%2F%2F%2BznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGvF0qvAAAAH3RSTlMAEREiIjMzRERVVWZmd3eIiJmZqqq7u8zM3d3u7v%2F%2F6qauNwAAAAlwSFlzAAALEgAACxIB0t1%2B%2FAAAABx0RVh0U29mdHdhcmUAQWRvYmUgRmlyZXdvcmtzIENTNAay06AAAAnhSURBVHic7V2Lmqo4DF6Og%2Bggg4hYkWne%2FzGXW9skjddRATVn9xsubUn%2FP0nTFvW%2F%2F8YmQRjOw0ZmQ2vyESrzMIrjJMtypfZKKd0JtP%2B1R6CV2m7SVRgMrep7ShBGqzjNskIp0OZfx1FPUU9YyxWgC2qbrqKPwz1DapJqJ9qqA%2BaEydE7YNlrpCyyeBkO3aGXlJ6k0gKPvaUngR9inmQG26ulyn6W80%2BIvIeEi1W6Vb8MYhz6ulPABIAdtFyUhJ5LRpw7q1SexuHX0B2epsyiON10zgQOVuhocDyB40XTsoQVdxc0vUmZbUTtsjj6hMgLZbZMsn3psAULPqCwZnIHYLxwhqgLMkZdezx06nZgS5afLPKoBGG83irMhAhvj7BFGTCNzMfuQHe1z%2BoQ%2BWENSRDFWVE6mGz2Bgw87YYpfIu5Cq1AYqV0Lh860jvjUPk6%2FuT%2BYZy5PAIYdvjEOYr9w11OINcd21REuIezkjPTg3L3rrl%2Fw5Rg0x5CJCaSgOaVhv4%2FUwE4WZgc25DgkZxc%2Frw293%2BbEDlbpsrHSJNBy2V8GHSwTPGZlMUfgJ5jdngNO%2FghWnBAFf3YXety%2F5cOkVFaVAjhv1k5bcAMNAx%2FC%2B%2FpOHfkBvZqppQlfJ9nqxfM%2FcOfAo9BGBB%2F3QEAxTzARbk74IvnSGGjkz9AIsVITUdSz70fFspik7zMwBauS9JfBgV3HJ8boIXIuEaJesTsmdwkxdH6cWthlcrSVfhvaLz%2FIkFSepGNgmCt9kRokoKhUBxMWOSXJWvwHRLcrAzFPTqx4A%2FF%2FmaCgtqm8WKSi1pxRbvJwdDYkrt4iXl0to5asKFNYB%2FDTI8AGQTRhY9yJEgep%2BoYg9A%2FCia47p9aq3vWYoTvO8wxj609oUM6kaPeT0zNG%2BskmzyoLJnIun9BIRfBBs2jJPAopUWIHSrmKTRlQHD71NAZnOhEaFyy%2Bad7MKnsndgIYJX7rXP%2F1chz%2FyAtwTAgGjacQNRHkcQpi%2Fmgqx3eba844NCstcqzMS9qzdfH43wPCTd47m8IQOtUQnhDf1zjAgmeJl5Mow8AXI%2BVEubsiOkTM5du3X9ocnwJFEN3uo7hLss%2Bf0OmWalNMqZ1%2F%2BWh9xUfIAq%2BtEtPMAeTcXkWTsH2DEBwsb4iMCWGG2P3%2BVDv%2FITLOA5bNw%2BiBG03Wp1Hta3l%2BwbT56mZpKpz%2F%2B9nhUizezW1pI0bAq8K3FXRerPUAUlwc66TR7YYyv0m%2BX5o7h8s8%2BrdI9q9DbBqtkbnjwiRSfXyJt%2Fv0SCWHrarRhuoB7bNfQe2iMMA4smjFuk8p7EVHaiTT%2F3vmfuvKvcUo4C1GRqkSCFBhDiIHQB13MOCs3zf1STUH1NniBXOSmV%2Fz%2F1nWxBUAk2ugt%2F3XqlDscnW8Sr%2ByQ%2Bmf6dDmpQ5YrPQtAV3jVKPEea8GafkPkjGXxDrOvCtHlIHHKWmJWyNuHekq%2B151az7R7ev%2B4f5CTrA%2FeN0qIzaSp3%2B5%2BpDB3om6SeQ%2B%2FXAVty6od0ShrpxSQioUjkch6tMWXVxyOFp5d82OTQv7ed79jlCby6OHifMVX7eteZaqhteZv1KK9cwCJ3Gurl%2Bqm2ykDKfecMZSHUdYIJBTn54cnWutc1mQ%2Fua9%2F2D1UEMDjhfQEgi1apis5I4C%2BO0%2BNVceO7PnklyMwMOiFza%2BwgrIP%2FLRoeptYbjuYxvs4x9qjHWhkwruBpnllX3l6%2F7L%2FJKEwESJo4o2J0URx4x%2B27eo%2Fqk%2B6YSdUrCK27lsEuX50kL4r2kqGvTmTpXtzzR7GyZ7pglcBjYkgW6Z3p51LhNbeDzbTSMOG2l9RvUin30UaNCjfWqEXvxIxQAUYXphqo4PrubVZFG5973CdcVge%2FiNO5cktNw5t7W0dNK44CrpPFziesBaRWXpST6TyBKGVWL%2BFwa8s2DIvUnirSVi3LSJtk%2FMI21fuX1Q%2FdgUtk7QVGA%2B192NixGGfExwbIJrPXf4hK2HGel9pskrTtoGSb6DUPk9vw7kO6lUAOND69Tf3ft4krvZ2OPRd5NUhx5NXJUQAHAZYkGR78xqif2A1umWl4A6SyxM17aS6%2F36xuXwvpJtWtxPPNXe436h9OAoIvLPGS5Jb0Iz1lSsM5za6ylmN9GVi%2FzeKOclthtGIQGP%2BYxvjcy96IO6AlHV7PidIBj1outCc9CuGK0qqAMUplEE%2FPU5EI0%2Fy271INQjnDa3mVvYB5ne5LhHIcXa8IijlSvm2gjzIUgx7DB0AkgXzGku%2BBIypIQIvfPk8thrgea9kNDfrAo4ntuv9WT6l31iYWi2cHuOizDJK%2FAtV9P4%2FLvR7yW8PXtJtUOX6a9S70QA7yDpNfsjNQAygK7iQ%2FR86zhEHd94McPrwd7FiVZsf8tlcoe%2BwmbelJN%2FPkNs3e8wNEeLR6I9z3kXz9Bk%2Bflzn5JwNQkmBLEkG8BRWgS8%2FLV0HxcIsGi4QzbKwi9cX19kcRCU7obuWTuNQ5pF0IwBR6yOM7zm6T406a29hmSXWGlQHtxwkRD17FaJvZBwSBadRM0RhMPgsBuY5Ic9II%2F4VMAB5nvzjIDBGtDFkJeKA7GLX318TOaYvnQ%2BN8kYcPZi4Y7opQ1xu5vNd4PK52V9htZSPLx6unIbzQ05n8Vs%2BtJhyaNgyAZRDzUgB9qqbiHuCmP4qQ%2FojGD%2BOvksRrhR8pukY4z8LuMFxeIP7DUgxk9D5U8NgI9lMOwMEM2nJnwhh6AfZe2YsksJpZmnJavflI9tggmNOVUEovx0N02fNH2ydTka5lsS95vfkwABI0zP1LER98CyCo4t8GOR4ZKYP513VJnmUz6C1pOSr9T7VxKsHJ5VCLoMtYGnJIXr%2BhZVAK7eOWzIS0VskwBxOsax0rkPY98E0%2BlE87er5N%2FUbLBX784tUGszJfj%2BaT6s8R%2BZSYHa5Rr7kazQ37XbcSJSbMQ4gwfNEcRkTL4rkq5TaL38ypfmlf26fuTBj9vrGKQ0vxA4geTbDxHs%2F1j4ka%2BErX8XvSm9TvJzE7QOHAnUzYv46CH3mjVkewzjHhkc2W1eefwd1KaN0J%2Bn5rhaVQPUIlWyjwZ%2Bz7x8DJbrrelJWugja%2BqSBefgepiqSdo25Kn0Bxl7Gy0GM7BifuRVrxQCT1Tn4HqJmleJSa%2FZMCHLkyA24ZyWR8jkKUwwG630e%2BllmwHkK%2FvNC85uoyL3ttsfo5D37E0nbhVVWSrF9kJGYMEi5%2FO0eSE0AY97Dh4H82bGrjK9XzqE%2FweIuYHef42OFmpmm%2B0eN1F9bFIuGy%2BJ4R6F8tITq8rdr%2Fg8SHqmTIL42RT7BkpJ1fmK1VkSTyN78h%2BVQnCMI7T5keezW88A15p0krtsmwdx4tPKjFOmfU%2FoP48L%2FofeFiF96pE5uQAAAAASUVORK5CYII%3D%22%3E%0A%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dinvert%3D%22true%22%20data%2Dxrange%3D%2250%22%20data%2Dyrange%3D%2220%22%20height%3D%22123%22%20width%3D%22304%22%20style%3D%22top%3A%2073px%3B%20left%3A%20467px%3B%20z%2Dindex%3A%205%3B%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAATAAAAB7CAMAAADEzSzaAAAAA3NCSVQICAjb4U%2FgAAABgFBMVEX%2F%2F%2F%2FjyZz02KW2pHvdxZu2pYLny5fv1qWFel7Vu4OlmnasnHuyn3uKfmLexZbVvpSEe2Lkx5Ts27LSuIXGs4vFsIrZxJbs0aLPvJO6p4Pp2rHlzZ3WvY3Puo7dy6DayaHOtoTdwZJuaFvJsn6llXPw1KC2o3fWxZ3ErYSomnuekm%2FHsoSekm%2BAdmKomnucjm3OtYvn17GcjnOllXO6p4PKsIjSuIt7c2O8rIWEfGmSh3ONg2V1cGGUinTt0Jydk3FzbGHPuo7kz6GJf2vn1q3q1aTfz6majnm2pHuyn3u2pYKyn3vPuo7s0aLOtYvSwJm8rIW3lXKllXq9q4ndxZvVvpTexZbPuo7SuIXErYR7c2N1cGGEe2Komnu2pYLPvJPGs4vWvY3OuJF8dWmNgmxybFuOhHG6p4OsnHvOuJGsnHuEe2LFrn3Gs4vHsoTFsIq6p4O2pYLKsIi2pYLZxJa2pYLayaHZxJbGs4usnHvbv4%2BvnHalkG6Jf2t%2FeWx8dWl0XqRGAAAAgHRSTlMA%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FEbv%2F%2F3f%2F%2F%2F%2F%2F%2F0Qid%2F%2F%2F%2FyJE7v%2F%2FIu4iRP8iRP%2F%2FEcz%2FM%2F%2F%2F%2FyJ3d4iqu8zd%2F%2F%2F%2Fd4iqu%2B7u7u4RESJEmarM3f8iMzNEVXeImZmqu7u7u7vMzN3d7u7u7v%2F%2F%2FxEREdqVUEYAAAAJcEhZcwAACxIAAAsSAdLdfvwAAAAcdEVYdFNvZnR3YXJlAEFkb2JlIEZpcmV3b3JrcyBDUzQGstOgAAAUrUlEQVR4nO1dC0MTVxbeMDNOrGQmEUgIECCKiooFQeUhKj62iI%2Buimhti692pbi2dq2P2tb2r%2B99nce9MwNJVIJdDiTzzGTuN9%2F5znfvjPiPf2z7%2BPe%2Bdp%2FBpxX%2FPv2fdp%2FCpxU7gDUZO4A1GTuANRk7gDUZT07%2Fcnvo9cr6artP5BOJtdeX9vZdGhw6NPhyB7LN4931vX17%2B%2FokYkODhx7sOLJN4i%2BJl4pLg4NDg0PnF9p9Rts7Fgy%2F%2BjRiIi8ftPuUtnesH9%2BrEZOTQYnY0Fq7z2k7x%2BLxvX0Csr3HJWp7Lw0NHRoafL0jY9mxLsXreB%2B8SYINDu2Uyux4LRX%2FeN%2Fx4zovv5BJObijYpmx8IWKQxD%2FUvGm3ae1bePi08ePe3sfPybAulXcmm%2F3mW3XWJRqL0OL%2Ft4vhNsXsaP6WfFOar4qkyr6vhhS5rXdp7WNQzvWPqn4ErEhJfor7T6rbRy3dbeoT7PskmCXiMvtPqttHIt3Z5TH1zEzMyg59le7z2o7xy9vtdxL1C69eiUB%2Bz%2B0YdPz383N3bpy5cr98zoevXn08MWLhw9%2Fui9WXvlhbm563lTCp2%2BPHzd49Q2%2BfSU0%2F%2FWf7T35LYz5i3O37j%2B%2FG0d%2Bf6VDRtjB48DZXRhRVB%2B4%2B%2BLZlan%2FvtWeQiA2OHRCMOz%2FomO07%2BKtpz%2F%2FGkccJwOWnIQIXMhBU3G087UwX%2BVyLMOrHvrb4zU9d%2Bvqr7FfQR6FOA0JrpBtrRBmJQlYKe7VEfd61d7z7W7Qx4yLt652x9EFCw787WAQhrANaHdWoyXiZOeuOFZoife%2FM2ACrIlyP4fK0qzQAszBTsVZSMldKht7dUr2lkuPlifb3bgPHfuePP017udcCm3NSgAU2pwzeta%2Fq37y9z9u1no1XDIl47JK1UfLs%2B1u5AeLfWeu1nJJTiUByQi248mbN2%2F%2BcWS8psCSqHUKhmEdvbb2d%2BiDP7ka51JajyJFW0KiV8j3gfew4%2BbN04X8kZFir4JLMcyLJ4apgpYeLX3amE3%2FcLcfWstSzyWXpV8mKuKH5tTPqT%2Fy%2BXxxZCSv89GkpGDdKHMdpfOff7KYzT3MIQqivTL6ReT6c34uJ19%2BVI5UlCO%2FXC7ruahsVkLoRbG2HAjA8gKwWFVImZJC9Cfyp%2F%2B4eaokgjAba3fTW4mlN%2F0CHwmMbLIvMRLRryGrXKiYCCmIUqF0aWpZr9O7VTqL%2BaICTOdjr7IVE8V8%2FvTRU8OnZAyI%2BO23en3gpzPtbn9z8c1yJLC5YPBI2CqeiEzVcE0Y0hqmYrWiYljR1Ejlw%2BJuSbvCyM0Bya1SVBcx8NvAwKlfr3w6qfnnAxuVkL071ssW%2FzQzwXePC5CSvdqIqZQUwiYgu%2Bl0oXaV6j99324kGop3t1MkPcNNhIldWekMk%2Bj1%2Fy4B0%2FoV665Rt8IrXywMu4gJzO5OtRuNTWPxtp12YXrbQw5kAsTUaqpz2veUhvVqJ2YYJqM4kARMxN3tXTQnb3dYqmOlmpuShAq5e7dbae%2BhZvqrWvBlpawSYL%2Fb3NqFRXPgh4V2w5IVbjK6TU7jXjqV0uYRN%2FHR%2FkhrWPWGAWw8JSExTt1qNzKp8fU6B4L71DCRYkki4b58x1QgYXJB%2BLme7nJt%2FPffR%2BtZWBme3d2GLmMtgz1pTU%2FtSbpkSoxksJTlH%2B%2FnyNBsyVodfbnNKubi9fTWZ9gEzsMUkBvpmBNuLmCpHCvF97eR%2Bv%2B1niLpYeKdVQIqAwypkP264G7ke23ASjQtWeu3T16udTjhjEMkYHTUyAEomYwuQno33HIgya9SGudKPy%2B0GyoZ39zOUpctI91ZO%2FscqrE124Fkqy4TnIqXZk5dsnQkwnJkYUeY2mmi7S5CmXJWv9JuvNabYUImXpScIa1J8NHJVXbIswTJZqC9aKv2%2F%2BkUx7TIqn7ppTAMzS9hmVkzQ%2FiEULHG483F9uG1aLEjzSWkN3dz2xBativ1cxbdeN6B4Ce1TC9GbTP%2Ba851phzMUqWNANpwU5iGG7v1e5ZgKSVdrFUNBKL324OXK18diZalAoayllYO4ICpRyES84xVrwMN6FeJoHveDrxuu21JX3A0jFdGO5%2BzInTdRkjAIeQVCYaViClwsU1tkH4u96HTPJsPDd8xSlsbgpYxxBhUuGojZqVh%2BOUWI7ZwvdlC1kikpGiDClnZMCPbj9jC9Q5KlA6SnSyrGtqk2SBrM3HM3k0i2IyvAMS2ErDrvAEWPDZWYWqXKdl6W8SdLXiERFbTlx5wiFRyZ0rJQZ8tfO5nJdU2WLMND2dZZc9dkbgMWR3O%2FmTelZKosXk5ebZVeD1IRSixziZEkhfpaLt11D50aukISfNT1KrE%2FYS9fWlr8FpHIbYqYoe72EAkiLXhAbK7TWGGTm3izUpbMnixukGr2pWXZwGeJvOy9M3Hx%2BvrClxecEJ4uZM4JnxTYtOG4xjpkTQpYRZem8ajjw%2FYS6t1WUmZDVuWlr1Pya1YQKXKlbMdN35o4X83OTm5qF%2BLk4vi94Fsc0UzrFLpqByoHBChHsRRs%2Bq9olao1WrxQn9FPsqjHncSczrUXL96Bkr9Vvpz6ske9StftdHRHvEjQ75P1B7XMmLipIjukypO1QbskMu12sApNVeDdXUTv93%2FPBHvo2x39GNKfs43z3TpiHxc9tWPnvi%2Bfu7LLOtdc7552MlsMQc0G9VCBBvMjvow3YHneYH6kVMvCAI9xRVqRi8Faqv5AG40n8C9vIAtsb0DOKaa%2Fvc9CIbt81ljJTBq2WeIqXb6gK0Fp8%2BOksshmrA%2FAk1IqjU90HYLMY8BEcDqgBqtNuoVgKjBxuyl8fVclIMAVgTV1gFbVW2LWEuoPZxjRAzebp%2Bv83MMKAMX4seZitET2KzwGIUYgzRAQcBJ4xAOYCJsGMSGuMA08V79rmXA1oEu2A5fE0yuiNgm4gjSiNCVOZcjUvo%2B7acTUrOW4apePYxc1CTOEVxDOzE%2BJvKP75FIVITe86pzLQO2AnQyVMEkguTEzNITBydb5wBgH5IR3hFwHzMeGBZQ4zBlHBCRVQRMgGARDCiGsArz0OPfIH%2BqrY9h3wGQGHlyvM0cH2sf1nYHSVUHUOsiJzMRUl8CZlOBpU1gsQbzLyDZI9AshNkmyErYkaZXW8XrXRIqyB4f1Rp2iajZFgcpB%2FFgzgJlNV0LsTDqMXVnOHgWmYxied2xLN39Fy5c%2BOc%2FL3Q2EPxI%2BiIgA1%2B1CtiaaVwE4sPUzKIUJi3DgSkV0I3A9sFSRFg%2BuD9R4I9yDnGSEaEgwcTMKMM%2B%2Bmzz6OTIswoiX9VWBxfXc1bwksj5ZnPFKXdsQddbKrDioxEDk%2BirdxhFqCzNDizAwEUFVfZ9DQEG%2FoTlIyxUW%2F2HSytcWVywInjLgfNkdAIUrKQjAGGGXEYS3NwoShJLQKvIsTZ6XkRXsUGGsXrCDiRVv1Wvf4dzhzkI34fciohqJrkiqKjQfqyrmIc%2Bw5TvAplpIB5lZQ5duOXu0VLIaUx%2BsZyF0sjIns7OPYeBYWgo0PSaL%2Fm8Nbwm2%2Bhateg341onkKW%2BZlghL3%2Fy%2BUKhoJ%2Fll289Pd3dAWNYwrWqL2ixc7RGOqRiw56fDSqlF2LF0DS9S8xim4yw143Gen6mPxN0G5H0gWEFCVChWDCPpecVegKvHg2YXX3Rm%2BmcbA2wdZswKZUfCJdjswllsvZitcBUYF0JCF3gm3%2FD8hBO5afeHyj2DfgGHwEr5PVvoaiIJkETgHUzwAJ%2BBTxjOPbsCRZaAmwlu9uSUgkBF2IVdKNA6ejjvsNLNk%2Bw3fBYojAPwS0FcEK%2BRXhdkGH5okRJZ6aCrICAfbYnNYxHa%2B0R4shQwE0qn6sV5RVAQIzjCPHEY3XRZh4b2JCAUQ%2FaUIr8GIxRGNmRrazjeTCG6XTUUibJ1tPd0%2B2dOzI%2Bvof6Suj%2F1cEUYC11jiZt7mxFbwg79jKqHrVAZwqPw2ZyGKkxEZfrcVm81ePx8XNHjiit16AVJbkAMK1hafTCY3lPWwFsTZ%2F7xx6UyMzuwE2UTmb3SauxNHTDIaJYM6xg4MoX1T%2FfUpBJhgUjR86d27NBdnveL60Atu5zVCR0AJ7VZM4lH6yERa%2Bcb61ixZF9Xm%2FjV6cKHW2LaC7DaFKN63Ec1%2BU%2F6j0iCAYM00ABcErDRkR0BjAyZncc3qNz9DKjIVThIN8%2BzoB1p40J8gw6NaxfrmZ050j%2Bc%2Bd4RDFMOQmslHnDMFYls21L9VgLgPnAq5yl5BuZc%2BIeS9yIOGXLIB4cP8A1X2gYXn3o72Wbc7kigotlRL8A1lVqmHYVOiWh8w19Lxy8xi9spXO0SPbbmHs0A1xzyI%2BB4rMEBcOmIfFpN%2FsoNFyBn5Apye1EABYVRvBxXNBDAGO4kAYwJV0mKw3TGGAeaVZyILKVMrm2NeaBV1ud7UC2qmserBzkK0xrJ%2BCCQNcoTy6sqB1%2FgbpGHh6akRgdSwtjiA9QpyJqlaVdDClX5p3sopLgI8c4oFY6A6ROQbTHUCGB0KSJn244ETKu%2BlUg3WcMs8ByR3dPNA%2FYSwWUsgNRAoacGeWzeEdo%2Bh8CbDh5yBp39BVKG7ZzFL47AlthOpAF2aPUmFFf0gYbq6RRgObL5DfUCjaqh0yhhjntlaOCPmqWbRrAn1rJrYsCLwZ6n4hreoAMYz7fI0LojXAB2GgF2n2dnXkrJbFA8tEKvara9D9%2FWH2fm9Y5BiiyDzfZGZgxdBHFVops5AGQJ2VTT4BhEqIi2Vc5dMFsBRNAGmpDvWz6r6tcdrOwdTFKHIgN3WbfRo8Sl52Pr3o4JMaUe8CcETFMewo1WFHEviSlpAbHtsS6s9XZdOfowZbkHfHV50jKtygj7xjpiHt67YTBGzVMm1UYrFCAQUpalhj7XuBWWugc3SE8GFJIgchHs4D%2BymxkyYuOAcoHpaXPduYZDx%2BNYp6CODLKRw0Dt7sU1OXfNeIDiIUC2HxjXhVgR8blaAVLSNIxGGbzmh1D%2FHoryZRjltfAF%2FnRRoMULjWUIgVV%2BVeg6qJHKbuS4wU15Jo3Bsx0xUnDiExYUvg3BtPNAbZKNsHp1WQ8a2OzkTjjs%2FJqPu4r0Ih8ZO4ZxcoxoQEko%2Fs6aPxZYQjknSN1GHD6haIeyjdjrmpMH2zFZy701gUImu4cXUYgGC6MArSIKWYTxgKOSqCV3yxd2f6GfxHIFk7QUSQNumlnLVLesYwaVtAWjPrfajxM8m%2BP3XtXs5xhnU12jlYwnSKGFruFhGzzuVTZXUurSjDjQXhnyJ2clAEiZwDxsDWIYQ9lTJTr5Tiu18bH5fAOqL2imevDPrNT%2FDA%2FjMrwJjtHdzZvUQpZLCh84JXZEe9hyk10Q5M%2BbPUVclGaUgX8STAiGIA6qhjm2zdBwL0WdF9S2Ipz546oIerAKilYefVbc52jdzlLV3AkYQuLZgSApIp%2FogqofaryTy6X6wOCYefOQfcRiSYLJe8aBUz3vUTRbK5ztIqXH0pji2M0CCISUm%2Fa%2FGGxOMkwbs2hCFhjNOYBC%2Bp8mxtHaMRkSvbgeBjdC2Z9VQSsqc7ROjSXewnOK1vDk2Q0295jpLaMzosKv2kejVkwF6s2lNX3QJXETIRBnoLVl2QpSCMiWIibK5MrCfXa6JYryRYg5TMq0udhH8tR4Ed4JVWAMfI4t1zZ6IKHKKrOkb5MhmFF6EkWjK0oJAYQvcwht%2BYesLhjTh1yiz%2BGZLiTs0I7AaZihoZcwQibRp7JKyO1PDKYAJCzAMlkxhAjlpJF8K%2FCixXZbbZO9nniL9o6saqZByzeNezHuUtgEm7hyKYGzQhxz7YtdfBcrh%2F3sMPtcYqp16g6ELvzbYiFOqaqJGmYxyMgLqucbAKwtVbdJiUlFgiGL7MW7Eh2CcZ6EvMhF3SZSbeJQidfVXUEdPr0LIrWsXyRj7hCkmNusuyXx2ri6XN49JDyCaVnS4Z25DRubmjH6JjKDEpJa2gnRcPotkCAagbaWH3SOGArQC5UGdvGEolo5kM%2FZRdjnrHbbUzCGLlYoYsZw%2FJ47xsHeqzOt3Vkqi6I4s9TU98fW2gMMGwZEcnpO3LKWcnILYb5HKamhqex%2B%2BcxFUHkFZkMrAZcfkTU5BGoL6kFrADPo%2BRt0bcPx%2B5EKbJWR7t27%2B7q6vpq%2F%2F6Dl6fGvp%2FdxMm%2Bm5ycWltbW19fP7%2By8qbceC75SDzcaJdKFEffvSjEYl8wjCSMyj4jQmounZQf5k8gFtHvqyEeAswhmIxqtXpCxL3Ro8MiugReKsxULAvsLh9slHf7ZicnV9fWlpfXH1w7%2F7IcWdXzQz%2BIImZj3rmzPBnhlxjoF2Uy5%2BcsW0EPohStu0ZVFSdmZmaOHj06fHS4a3h4NyCEWCFaFnLyTWIneXes8R7U%2FPzk6urq5eXlB9eunZd%2F3h2KJ2YVKRdLN7YOIaO90abkYoSKOyaQLtJ%2FrALaCzDAlNYrhp0WMT4%2BPjLydmbm3r0bXvXGqKQQA6JLTbrMbFcSpi5rxZf79z87eFCQTbCtCcjsWJie%2Fl4guLy8%2FPzatbsCwTJPMSaKDrPUcvLWUUyJxwyEw6jkrSP5vIDWMImPiBOCP4pAXTYCLn0ALURPwgY7vJAAXT44NjU2e2wzLWs59n03Pz03tbp0ZfnZj9fO1%2BJYkLCJznscEHcCpshpD1igAM2cuDc8UTtVlSAZ3eF4dNlM6epymQOxf%2F%2F%2BKwcPLo2NjR2bbd9%2FzzI9P31x7sza0tLy8x9%2FrA30qjT2UeQgMY3dH8BETNp9BU%2B1%2Bkoo0D2pQEKgh5EYu52USglLzrs0QDLDxkQtPPZ12wDaLPZ9Nz175szc0tLSsx%2Bff1mrDcSghJJ%2BNV4bg2qgCCQVWifYbrfNkEpdu51UA11ia74yEiQAOja7BX%2BK4WPF%2FPT8k7kzt35Yuv%2Fz84c9J17NnHh1T%2BNjANLMAf50ucg4DCIJAo0em%2Fq2dY3e7jHboNykpZrIsPsHLwsJmjo228qzhJ9k7OOJlrBDFphKoy8fXBNF7Njst%2B0%2B8bbFV1k8EhL0k9Jo6Ru%2F3b4avdWxH%2FllJEhk2Oy3f1sJev8QJmhMaHS7T6OB%2BB%2BC%2FKOr0h4pdAAAAABJRU5ErkJggg%3D%3D%22%3E%0A%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dinvert%3D%22true%22%20data%2Dxrange%3D%2275%22%20data%2Dyrange%3D%2230%22%20height%3D%2250%22%20width%3D%22116%22%20style%3D%22top%3A%20113px%3B%20left%3A%20762px%3B%20z%2Dindex%3A%204%3B%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAAHQAAAAyCAMAAAC6RQ9kAAAAA3NCSVQICAjb4U%2FgAAABgFBMVEX%2F%2F%2F%2FkyZm1pIDexpr73qqnmnallnGnmnn33aqjlXn12anszpi7p4PUvZPu1aXPuo6tm3zr0aLfxZbNt4xxbWOUim6yn3l7c2NsaF2%2BrIStm3yom4C2o3v22KSznW%2BrnIGejGuqlm3ZxJZxbWN0bFvUvZPv0JvnzZ2MfmPArYq7p4PXvo7Qu5LFsoq%2BrIRsaWDx057ErYKznXCsmnKFe2qom4CPgWSMhG3Qu5Kck3OllnGjlXl7c2NzcGeJf217c2OJf23FsoqUim6%2BrISck3PArYp%2FeWl%2FeGWfknrGsIzArYrGsIyck3PNt4zXvo67p4Pr0aLQu5K7p4Omk2zfxZbZxJbErYL12anu1aWwm2753KfmzaHny5aMg3N%2FeWmfknqajnmUiXSMhG2Mg3OrnIGjlXmUim6UiXSMhG2EeGN%2FeGW1pICajHOFe2rGsIy7p4OVhme%2BrIStm3ynmnmejGuUim6VhmfUvZPQu5LNt4zexprPuo7GsIy7p4Oyn3mmk2w%2B%2FMV0AAAAgHRSTlMA%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FRP%2F%2F%2FyJ3%2FyIR7v9E%2F%2F%2F%2FRHe7%2FxEiu%2F%2F%2FRHfu%2F%2F%2F%2F%2FxH%2F%2F%2F%2F%2FIjNEVaqqzMwRESIzVXeIu8zdIiIzZmZ3d4iZqru7u7vM3d3u7u7%2F%2F%2F8RESIiIiIiMzMzMzMzM0RERFVVVWZmZmZmZnd3d4iIiIiIiOmar1cAAAAJcEhZcwAACxIAAAsSAdLdfvwAAAAcdEVYdFNvZnR3YXJlAEFkb2JlIEZpcmV3b3JrcyBDUzQGstOgAAAFzUlEQVRYheWXh3saRxDFvSzHHQsczUEKCFVkiINKFEW25RZFcVwjJFvNTu%2B99%2Bp%2FPfNmCwfcxYosf8n3ZcB3gjvv797sm9nl1KlHxNyjbngCMf7U%2FwU6929Al%2F5L6X3nq43f5ud%2Fuf3ZpScARXp%2FGB%2F68q1fD4IHYXP5TC73em731psnDYXS9dMDX729nVZBmkIpVc4hXr188tCLA9CfAiIqftM%2F1WwTda90otC5IeilbahkoYAG9Ocyiz1J6JDSNw41Kg0wvRTOTVC3HgvzwcbG7ZJrfoNKLx8qTms6IBxT%2BcPyY1JvHqgmxrhlPpPSq54rm21WyFyXZDzGGVC%2FOSby8jYP1KRBdq9Y6Dnvgrn8cwACZRc%2B4rklU8FXIZv4xvGg20qLeEDUPS576kjnfAN9D5cUpxZYfeJsa6m7x2J%2BCSIkBCFV%2FZaFWqVbSrtI6dwq7SjODc9q7liFc2Dmyzw6EtxP71IjDKkdNFUzRDT5tkDBUUobOLd3VND46urqjQZi6mYYlsvl18oIQbE3T1ERUkiEwEngjIOsdrvdgrQx%2ByzHt6c5xuil3wlbgBJGEGY0Gk84hP4k%2Bidh%2BPxnPnWkGIuH2tG0AIvQWAsXRqFRiy%2BOxkyE2oGlyd%2BwPP1IfeE6wSeh9B%2FnmKB5sZjJZjNeDGuh6lPUk6BTFiVdIqWFWqR0avsZZ2g1m6FXDLRYoQuZzEQSVESsaU%2Fmi7JyEepTwE0%2BVRBaaYFGzmYnYqCyhku11PUE9zrvGJ3WREKG6HFK2TVFVyadU1QrZwGVkENDx0AXAa0nKG1EjCP7J6GhKtrfbc8LSKnQ0BryW4%2BDVmm2s36yewct5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ticon%2Dcheck%20js%2Dclipboard%2Dcheck%2Dicon%20color%2Dtext%2Dsuccess%20d%2Dnone%20m%2D2%22%3E%0A%20%20%20%20%3Cpath%20fill%2Drule%3D%22evenodd%22%20d%3D%22M13%2E78%204%2E22a%2E75%2E75%200%20010%201%2E06l%2D7%2E25%207%2E25a%2E75%2E75%200%2001%2D1%2E06%200L2%2E22%209%2E28a%2E75%2E75%200%20011%2E06%2D1%2E06L6%2010%2E94l6%2E72%2D6%2E72a%2E75%2E75%200%20011%2E06%200z%22%3E%3C%2Fpath%3E%0A%3C%2Fsvg%3E%0A%20%20%20%20%3C%2Fclipboard%2Dcopy%3E%0A%20%20%3C%2Fdiv%3E%0A%3C%2Ftemplate%3E%0A%0A%0A%0A%0A%20%20%3C%2Fbody%3E%0A%3C%2Fhtml%3E%0A%0A" width="100%" /></p>
<ol start="2" style="list-style-type: decimal">
<li><strong>Across matched models</strong>:</li>
</ol>
<div class="sourceCode" id="cb40"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb40-1"><a href="#cb40-1" aria-hidden="true" tabindex="-1"></a><span class="fu">bayesfactor_inclusion</span>(BF_ToothGrowth, <span class="at">match_models =</span> <span class="cn">TRUE</span>)</span></code></pre></div>
<pre><code>> Inclusion Bayes Factors (Model Averaged)
>
> P(prior) P(posterior) Inclusion BF
> supp 0.40 0.28 59.19
> dose 0.40 0.28 1.36e+14
> dose:supp 0.20 0.72 2.57
>
> * Compared among: matched models only
> * Priors odds: uniform-equal</code></pre>
<p><img src="data:text/html; 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lDC5Fo%2FTKI2Ci5bBUrY8IgYjZRRx%2FyUg2PCRQxGyTIGAQbBIYDAJAMBsmTAYcKRa30%2BEKH0yi5D6dyDYJznMGA1UUMAiUD6YUqh9PhAuHCKGKgBtRS48IkKbQpyqBs7pVKbOCgU2HZAuHHdFDArK0p9NAhsRSmysKBT6Y2Uq5wQ%2BnwopDZwgXHcKKQ2IENqKU2hRUzZwUCGw7IENmrLK4IbEqpmwqLSm1SLSGzx2UyqWCAG0KFTNo20RambWRQYfeoR5YAHDLtK5UwC1GVBa3xQpwFWaoLTsgpbY%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%2BnypVb6aUD6aUbBCtgnOczY8IBjwhAxUqxsUAwQDBCl%2BnwyNcjfTKIXAqKGBRcZDAKAfT5UA%2BmqFPpjZRaXBAMOEhS4qKU2qKU2IENqkUptKBTagQ2KmCGw0WctENh2SHMU%2BmdkCmw7KZXCZsUi4IfT5QpTZupnDWMpmxSCZ9PhKqZs4UCG3hFIbOyKniQ7qZXCZtdQTusKKmbdGUVM2KKXE7IPJYeK7YcOQ4tcqiwtooGFvDBawyqLeyCltp7bKphW21%2BdkFBatYwzlQWFCqCzRkS4OLFUqosQUFiuDKgsTCZyoLOFUOLOEKcWDZXBk4t4VjJxYgcWgaIU4tGyIYWuhnBxZwqhxYgYW8OgYWnZA2B2VT4nHp7pUHBCmwQMLCqUR6aJTD0wgYWDZUwOI2UgZikBxKsBwKIbBFHBQMLeFYlbDhMGcmwOyfE%2BA4FCjghyjglBwQjYIDhwhBx4VBw4CDYqKOJQbBEwOKK2BQo4FCtgdkKOB2QrYKFHBCh9NUo%2FTUK30ylAwQHDhBsChAxKhGxT4rORsTsg2J2QbE7INidlBseEUMUGxSLQwUGwCFbC1ChgEyYDDgKDYoFxOyK2JQDHhADahC4BADYiwuHCmcmMBgdkaDA7ImAw4UilPppClwSLS%2FTQKfTUC%2FTGyQD6Y2UyuCH0xsikNhChgptUUhs4RSG1AhtRSGzhQIfTKKQ2Hbuoqd1iipmwqZyENiLjKZ9MKKmbNlFTNvCKmbOFAhCmcKndafwUVI2oSlb3U0UivGFq71wqgtVRYW8JgycWuzaqotbaPvVRQWpgyoLVWcrC1kDi3uiKC1WIoLVYZypbbREqotNKq8hynFpVQ4sKqHFhKqKj01KHFiBxYgcemESmFoEMqhxZwqHFiBxZwkS%2FAwtViHFqYwoi1WIbBAwsCpnBsRsoQcSdFcpgwsKZMZN9MoG%2BnygOClDYKoOAQNgNkyco48IZwOKEHEoo47JUg4oo48Oqg4cKA4oDjwgOKJytirSDiosbFSLRxCqQcRshnDY8IQceEwRsUi8zYoQWQjY8Ikw2PBRcxsTsosHHhBsTslSDigGCA4hFbEKDYhEjNwgzcIc7Nwis3CAMg2KDYhQDHsiwMUGwQgfTOyAYHZRaGB7oNgqBhypFbAKIGA2RQwGyQuWw4RSmxRcFNqIDKqDbqUgYhCAbOEUhsOyZMFw7KKBsKBfp8sopT6fsEoU2KKQ2cKBTYNkMZhDZwovOQ2MikNqiwhsUEzayqkNqixM2cIENnCy0mbOFBM%2BmSipmzdRUzZ%2BKhUjYi85DYCpVSutCKmbRRlBPEPRZi14wC7uCotMQtMqC0nRUq1tqFVFlFcJlS2yiqK22dglRUWDXwRFbbBsmTGVBYBo%2FC0igs4VRUWJEUFqsDi1EyoLFU5Ti3ZIHFiooLG0SIcWHQKwOPTKYMnw6KpkwsRKcWIGHpq0OPTCIfEDRSgtwqQwtRDCxRTCxKQwtVQcUyYMLeEIItegVDYHZReQRYqlNgiURYEKOI5Sg4jZAcRshBxQgi1Fg4pgzhsUBxCIItHVFHDhEoiw7JRsOAlBwKVRw5RK2A3Sg4DlQo4jZVK2I2UyuGYbKozDZRWbhAW4QZgi8rMiMyK2IVRmCitj1QHHhBsFItb6Z4VhWw6IVj6aFbBIUMAorYBVGw4CAYnZRWYhEZlMYXIMhGYJBseEWtg%2BnioB9PhDGQPp%2BOiKH0yotKbNygGCDYhQgYDZADYNkAwQKbNlGiYoAyAYhQLhwqFwOyjRTZwopTYdUQuCKU%2BmsqmfTVoU27qKQ2BQqZs4UyuMkNqikNvCGMpG1FIbXSCZsKipG3hRUzapFTNhFFFSNnHZQTuseVOZedI26IuEzZCLhPFSLXji3Rd3nVFvZWCgt2VxhMq22qxFrbUFRYyrOcq22cIK22LTKgsVFR6aCgsVRUWURKcWBEUFnCqKizhA4tCEOLSVUOLAgcWrUQ2CmDKg9PhVLg4sQNhwimxKVDD0zqhnJh6Y3RD4BCmFg6olHEbOnKpseEQwsVIbBAcUBxQgi1DODY8FCDgdlQcEBwUwZMLFStgFKDgFUoi0dUKOA2UoOHAQpsVUbHlRRxQjYqo2IUWDiFSNiEgzDZRRx4VQceEI2J2SKOJSDYpBseUBxCQy2ISGBxGymeQ52x4SDMhjDMixmCJBZAMQgOI2RWw4UGwVGw5Uo2G5SgYHdBsEo2HDqVQxGyDYBRWwGgCqBgooYIBiixsShGY7IQMeEGw4UAwShfplRQPpoYyH0whS4BT%2F4v%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%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%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%2BCi4LjyhAxO3dAGKitiiBh9zqLnJTb2ShTYi%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%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%2FFDCN1sqLjKZCKhdaoqVwUELgpGkbrVFwjih8HnW28Loxle207Ksr22FKi9thVFhZolRa2xWpla2wKorbYNlUqwtA0VTn51BamEysLQAiHAVFLbVUyoLeOigZlQ4t%2FBUhxb9wRDYomMHFuyKYWqoOO6BhbsiGFiUEWiYZSrkcUBYOgItKqQ2I1KEEAbdFFjIGbhVBFpQy2KKLIkFkBwOyA4FAcAhzCLRshzDj96iiyqMyUFuEGZBmRYLVSIzd0GYKjMkG8tlFbhAVRpQZCMyDMpgyzbShBZKRm8EVmaqVOdm8EGbVTmW0WGqtRm%2FBRWbhKCx2VRmUI3dFZCChGRIzIrMpBuio3VQZAKaKKyoKIEaqKzBVANvLKKBBQBj9qqMgCi5ZkKDVQBUZRQZ9EAbZCA1XQBIAykGIHZAG1CtQpG6BSKsi4yBt7IENrfcpFoIFNqgQivGiLSEfgi0jKLkhtQTNqhUyFIqd1qCRFYUaSIQRutUXGUiFFRutTK4QuCyqFwSKm0rK8rgtHC6Yw55WtCqZXtCuEXtthDOF7bYWmXTZ6Hq3B7fTuuB%2FiALLOdppxz5w1jZ6s82Mun0%2FwBH%2BpvfD9P6t7VAsJ%2BCzniNnp59WOnDWNhtNXNpz0ZdNn7d%2BuuLW%2Fo%2FXuJoB6dz%2B5Yzxmxxi%2F79PThccJts5n%2BzV0ZdNv7T%2B5a%2Ft36n%2Fur%2FALFj%2FIcNvNHax1t%2F0PEbvV2c9TpH7H%2B8Q37R%2BsO3%2Bg9T%2FNWf8rwm%2B0drT1tf4zi91r7Oep0Wfy9%2B%2B3h7P2X9fcN7f03qn%2FmrGfOeB08%2B32eP59PW1jyjjdXLjYbTsaup0Wfy1%2B%2Fkgf7j%2FXh9T%2Bn9QDxNqmfPOAx%2Bvs%2B3p61x5Nx%2BeT%2Fo2nY1dS4%2Flb%2BYtP2T9b1%2Bjf8AYs%2F5%2FwAv3%2Bz7WGseRcfuNfZyvZ%2FKP8yXBx%2By%2Fqu%2Fpl%2FBc8%2FcXl2P19HS6Y%2B3%2FMM%2Fo6%2Bhf0%2F5O%2FmW8sP2b9QCzzaLX8SFnV9zeW4%2FX09K6ftzzHP6OpUfyX%2FM%2FwD%2Bn9aObf8AOWfVHlm%2B0%2Fj1NemfMtzq%2FDrX%2FwD%2BF%2Fmqv%2B6L%2B%2Fqel%2FnrHq3yvfY6NXU3j7V8y3OenT1q2fyF%2FNl%2F5f2g%2FwDG9b0R4P6gWdX3h5Vp%2FW7uvwtaftPzPP6Pe09a39v%2FAObf%2FwBT1%2F0%2F6f8A1iz6y8p33d1%2BFfSPmm572jxK%2FwBu%2FwCbGH%2Fl1k6fW9L%2FADlz9a%2BVbzPZ1dTp6O8z3eO1p6z2%2FwBOv5pN2J%2FQ%2BnbvcfW9Nh4XEqZ%2B9vK8Y5Npns6uox9m%2BZ5%2FJjtaetb%2B2%2F8ANAj%2FAGb0B%2F21qx638sz%2BbV2cunozzL5dPawpZ%2FTX%2BZ73f0%2F01h0B9YH3ArOr758sx8dWf5WtP2V5jn4acfzHH9Mv5nYHH9Kx%2FwCtp%2F7Kz688t%2F59n%2BK%2BiPMP%2BPT%2FAAXH9Lv5ih%2FV%2FRAmtp9W5x4WFYz9%2FwDl2PhtOzjxN%2BhuPz8dHTnqNb%2FS%2FwDmEkf6b9CJbI%2Brf8PTdTP7geXY%2FLtOjHiXH2Lx%2Bfjs%2BnPhUH9LP5gf%2FwC8%2FbwJn6nqtH%2FZLn7heX%2FJtejT43T0Hx3z7Pp1eFS3%2Blf74Tdn%2Bu%2FQWgNS71bnf%2Fswpq%2FcPgfhs9p0afFldP2Fxvx17Pp1eFT%2B1X7yB%2F6h%2BiPQ%2Bp%2FmLPuHwe72nd62s%2FYPGbzR3uow%2FpX%2B7v8AN%2B4%2Fo7RoR9Qv%2FwCwFM%2FuJwnw2Wvu9a4%2BweL%2BO00d7qV%2FtT%2B5mn7n%2Bmivy3%2B9mWPcTht1r6cNe3%2FE73R0ZEf0p%2FciQ%2F7p%2BmAJqLbyZUz%2B4nDbrX04XH2BxG909GVh%2FSj9XT%2FfHo%2F91d%2FnLHuLsdzq7WOpv2%2F22%2B09Geth%2FSn9Wf8A8t6L7fSu%2B1PcXY7nV046j2%2B22%2B09Geta3%2BlHrn%2F81YNx9Ax%2F8xc%2FcbRuM9r6XT2%2B17%2FHZ%2Bpj%2FSn1nA%2F31YQYf6Br%2FwB4nuNo3Ge19J7fa9%2Fjs%2FUsP6TXMH%2FfQCaj%2FZoH%2FwA0LGf3HxeTh%2B%2F9DeP29zOXiO59Tf2mJLf7%2B1n%2FAMLp%2FwB8p7j%2FANv3%2FoPb3%2B47n1ns%2FpPY5%2Bp%2B%2FXNo36YW%2B%2F1Ss6v3Hz8OH7%2F0taf29x8dv3PqP%2Faj0XP%2FAJ3fVv8AoB%2FrFn3G17jHaz4Wvb7Rv89n6hH9J%2FRdj%2B9%2BpGv%2Bzj%2FWJ7ja9xjtfSvt9o3%2Bez9TD%2Bk%2FoBif3u8iMh9ADzzKZ%2FcbafDYY7Weo9vtnv8APZ%2Fip%2Faj9G%2F%2FAKt61P8A4Vv2rHuLttzp6c9Tft%2Fsd9q6MdYj%2BlH6N2P7v64f%2Fq7ftT3G22509Oeo9v8AY77V0Y6wP9Kv0QLH949cR%2F8ACtf3p7jbbc6enPUe3%2Bx32rox1rf2q%2FbP%2FwBn%2BqdtrPcy5%2B4vE7rR05b9AcPvdXRhj%2FSr9rH%2FAOT%2FAFVWfGz7FPcTid1o6cr6A4be6%2BjDf2p%2Fa2%2F9U%2FUvwLNOye4nE7rR%2BPWegOH3urowpb%2FSz9mxe79w%2FW3Xat9MeWBWM%2FuHxl5Nns%2B91t4%2BweEnLtNfd6h%2FtZ%2Byn%2F8Av%2FrXff092%2FwKe4fGbvZ97xL6C4Tea%2B71B%2Faz9llv3D9aSKT6f%2BYr7h8Zu9n3vEnoLhN5r7vUJ%2FpZ%2Bymn7h%2BteIf09f8AiJ7h8Zu9n3vEegeE3mvu9Qf2t%2FZiW%2F2%2F9a%2Bk%2Bn3%2FAIE9w%2BN3ez73WegeE3mvu9Qn%2Blv7LbX9w%2FWePp9%2F4FPcPjd3s%2B94j0Dwm8193qE%2F0s%2FZRP8AvD9aQefT1%2F4ie4fGbvZ97xL6B4Tea%2B71B%2Fa%2F9lkH9f8ArQ38T%2Bm3BmxX3D43d7PveJPQPCbzX3epX%2B137BAP6z9eCQ7%2FAFPS930viuef3C4%2F5Nn0avG36C4H59p06fC39r%2F5fdj%2Bs%2FcAYLfU9L%2FUqe4XmHybLo1eNfQXA%2FPtOnT4W%2Ftf%2FLzT%2Bs%2FcGP8A1npcf9SnuDx%2FybLo1eM9BcD8%2B06dPhEf0t%2FYCx%2F2v9wD0%2Bf0v9UnuFx%2FybLo1eM9BcD8%2B06dPhb%2B1%2F8AL7Fv1f7if%2B09L%2FVJ7hcf8my6NXjPQXA%2FPtOnT4S%2F2u%2FYWP8A4z9f0Pqel%2Fqk9weP%2BTZ9GrxnoPgfn2nTp8Jv7X%2Fy%2BxP%2B1%2FuMf9Z6X%2BqT3B4%2F5Nl0avGvoPgfn2nTp8Lf2v8A5f8A%2FwDL%2FcHnH%2FSelp%2F2Se4PH%2FJsujV4z0HwPz7Tp0%2BEl39Lv2Nhj%2Bu%2FXWlpe%2F0i9Kf6MLWn9wuO%2BOz2fRq8TOr7C4L4a9p06fCH9rP2b%2F8AYfreC%2Fp%2B7BX3D4zd7PveJn0Fwm8193qA%2FwBLv2bT9f8ArCWkP6df%2BQr7h8Zu9n3vEeguE3mvu9Tf2u%2FZm%2F8Av%2F1zyCx9P%2FMT3C4zd7PveI9BcJvNfd6m%2Ftd%2BzMT%2FALf%2BtOon0%2F8AM1T3D4zd7PveI9BcJvNfd6m%2Ftd%2Bys%2F8At%2F63kP6f%2BZKe4fGbvZ97xJ6C4Tea%2B71N%2Fa79lj%2Fx%2FwCt8fTo3%2FAT3D4zd7PveJfQXCbzX3eoP7Xfs8f%2BP%2FWks7g%2Bm3nYnuFxm72fe6z0Fwm8193qKf6WftbuP3P9WLZYY2E%2B5bx%2B4nFfHZaPx62M%2FYPDfDa6%2FwAOov8Aa39rr%2FvT9SxDgG30x8FfcTid1o6cp6B4be6ujAD%2Bln7aW%2F8ANP1Lk%2F4bNn2T3E4ndaOnJ6B4fe6ujAXf0r%2FQP8v7t%2BoAOh9Own3hbx%2B4u3nLsdPTlnP2BsLybbV0YJ%2Fav9EI%2FwB7%2Bu%2F%2FAPFa3vV9xdtudPTnqT0Bsd9q6MdYj%2BlX6KP%2FADb1wTp9O2I6p7i7bc6enPUegNjvtXRjrJf%2FAEp%2FTv8AJ%2B8%2BraG%2Fi9G0z%2Fywtaf3F2k5dhjtZ6mNX7f7O8m2z2cdaY%2FpV6JD%2FwC%2B7%2Bf9AC3%2FAMxX3F17jHaz4U9v9G%2Fz2fqN%2Faj0CP8A1y%2Fp9Af6xPcXXuMdr6T2%2FwBG%2FwA9n6k7v6U2FhZ%2B%2BEA6n9OC%2FT%2FSBax%2B42r48P3%2FAKcs5%2Fb7Hw2%2Fc%2Bop%2FpQQP%2FXf%2FwDV%2Bz1lr3H%2FALfv%2FQz7ff3Hc%2Bsp%2FpUZb9%2Bn%2BEH9Ka7f9Krj9xv7fv8A0Ht9%2Fcdz6if2q9aP%2FOrOf9Af9Yt%2B4ujcZ7X0se3%2Bvf47P1E%2FtX6pp%2B9enR%2F%2BhLf%2B%2Br7i6NxntfSnt%2Fr3%2BOz9SX9q%2FwBZP%2Fm%2FouP%2Bru%2B1b9xNjudXTjqY9AbXfaejPW39qv1pdv3f0ILH%2FR3af8ZPcTY7nV046j0Btt9p6M9aJ%2Fpb%2B5v%2FAOpfpuuN%2FwBi6e4fDbrX%2BDHoHiN7p%2FEP7XfuLOf3P9MOcb%2Feye4XDbrX04PQPE73R0ZS%2Ftd%2B8EOP1%2F6PHSfU%2FwAxb9wuD3e07vWx6C4veaO91B%2Fa395dh%2Bv%2FAEQ0r6n%2BYnuFwe72nd6z0Hxe80d7qSu%2Fph%2B%2FB2%2FWfoCB%2Fl%2BqD%2F8AS5W8fuDwHx0bTo0%2BJzz9icbjm17Pp1eED%2FS%2F9%2FFpP%2B0%2Ft5Oto9T1X%2F8ApK4%2FcHy%2FP5Np0afEmfsTjvn2fTq8KX9sf5hL%2FwCl%2FRQf%2Fi3%2FAOrXT195d%2FptOjHiZ9Dcf%2Fro6c9SV%2F8ATX%2BY7aH9JeBU2%2BqY8bQtafvzy7Pz4%2Fl%2Fixq%2ByPMMfJn%2FAPf4FP8ATf8AmQQ36arf9Lv%2FAMVX115b%2FwA%2Bz%2FFPRXmH%2FDp%2Fggf6efzMH%2F8AD%2BjczuR6tq6et%2FLfm1dnLGfszzH5dPawW7%2Bnf8zin6X0rz%2FhHrWfEhax97%2BWZ%2FPns5Zz9m%2BZY%2FJjtYSP9Pv5pgH9BZx%2FpvT%2FAM5b9a%2BV7zPZ1dTPo%2FzPd47WnrSu%2FkH%2BagWH7aL4qPX9Bp63hax95eVZx%2F6z%2BXX4Wc%2FaPmeM%2FwDl3tPiSu%2FkL%2BawD%2F5SYq3regfL6i1j7w8qzyf93d1%2BFM%2FafmeOX%2Fq72jxIn%2BSP5pH%2FAOIvH%2Fael%2FnrfqzyvfY6NXUx6W8y3OenT1o3fyb%2FADMCRd%2B0eq9uxsPmLlrH3R5Znl%2F7tP49TGftrzHGf%2FHV%2BHWlf%2FKH8yWs%2FwCz%2BuXowB9xW9P3N5bq%2FX0%2Fj1M5%2B3PMdP6Or8Otzn%2BVP5jf%2FwBH%2FVf8ha9R%2BXb%2FAEdKen%2FMNzq6ET%2FLP8wiv7L%2Bs%2F7m%2FwCxb%2Fz3l%2B%2F0drDH%2BD4%2Fca%2BzlG%2F%2BXP3604n9k%2FXE7D9P6h91q1jzvgM%2Fr7Pt6etnPk3HY%2FQ2nZ1dTnv%2FAGD98tD3fs3660bn9P6o%2FwCatY844LPJjb7Pt6etnPlPG459jtOxq6nOf2b93Yk%2FtX6wAVP0PU%2FzVr%2FKcJnm22jtaetn%2FG8Vj9LX2c9Tmu%2Fav3Gf%2FL%2F1P%2FdX%2FYt%2F1%2FDbzT2sdbP9DxG71dnPU5j%2Bh%2FWAn%2FwnrBoI%2BndHkt44vY55tenpwxnhdt8dGroy57%2F0vr2lr%2FQ9S07G0j4LWNvs845NWOnDOdjtMZ5dOehy%2Bp6V9jZ2XWvuGW9OrGrmzhM6c458Oe4IiFwRUbgsrhFpSK%2FSPp%2FtH7Vbc9v7Z%2Blt0j0fTH%2FNXwPV5jxWccu115%2Fmz1vuWny%2FhtPNs9HZx1O30v2z9vtuBt%2FQ%2Fp7TMj07A3ksZ47iM4mdpq6c9beOD2GM3GjT0Ydtn6H9IGP%2Byei4m35A76aLnnitrn8%2Brpy3jhtlj8uOjDut%2FT%2BjH%2BisfX5RHkuf%2Fbr%2FANc9LeNlp%2F0x0Ou21mB2grm6Omy0gB42UHRbbpXbQqKrbadSWfyQVttPytXQH7kqui214Zvb7VBYW6CA%2BygsLTDGKMgYSSB2ZWBxaQQ0g%2B9KKgMRX7FA4tJfhw7oHtFO6mQzOHEg1KKYWsQGg16ohsXINxIZ%2FPkIKMBAknT2CgAtYf4hAYQw1VocAgM07jnwUUWNwI3iVBmIgHx07KkGSCRrx56ICAbtGGgMopmcA8QSgGFzCkSOqAuxd6jWPaqAsQNRQczqgOJO7Q4MfegbFqBxx4oARpIB1ozfggYW8kmeiDOTIpqZFaUQbgCBTzQY3UALyB4pEEk6s4lhv8EUCQHYsdHogIoA8x28UADg8bxO6DPdsedNe%2FvQGjvoICAA3kBhWpkoMBQ1cxttVA0nEQfDkIMQZevfRKMbINDOp328UoAADh9A%2Bmn2JQRazAkPoY3pVKNjMWhtendKA35dXNQ%2FtogaJLkBnGygNA80l%2BUAAtf8oJBgdEG0m12MaoMQILVYEbahAbbQBAjU0QbEP3mUoXEC1z8zePeqUaHi0Bi7oMwAyL2isQe6oN1ujPPIUowZ3iTXmnKDYgNuddtdEAYw4l5I0VGa38p3gPyg2JgOZp4apRmmpB1J2HglCsXEyKE7MdOyAkB8X5Z0GwJ145SjMxilS0sgwclwxEjJuiAmRIBfRAIN0V1YoMCADL8nVAoJDB3PjFVUa3EUe2rindA5Lcb91FATIGMwgW4APJcAttsqjANIgOfl61eqijiDJtrz9qBTaGDgwXMA7nRAJ1qLXJQC4OTEatJQagGw0O7oNiBIDk6oExhrav8Al9%2FuVGa4EDF4kjR%2FwUAZ2Jky%2ByAAXUJjLSea8IjAEh209oQhQcrS4x%2FwzPiUQXFwJA2cuyKUi6Q%2B7OiAbaWkYkCNQeFQpdizEMVFTxmrTrv1VQOCKVCKTGPlBEflZKiZBZhOw0fqqExLky0gWoJ3DYcyVQpfsNS2kFIJ3WBwDM1UCXWk00h0HNjW7WW9gtCVwcGDu6COHVvtRIh6loc7tIfdMIhdbUU28FRy%2BpZZda1wF1p0uDhaxnOM3CZxjPO5L%2F03oXZA%2BjZc%2FwCYYgv5Lpjba8c2rPSxnZaM8%2BMdDjv%2FAEP6Mv8A%2BF9FjX%2FR208FvHFbbH59XTlz%2Fptln8mnow5P92ftzt%2FsH6fr9Kxvcun9dxG81drPWx%2FRbDd6ezjqVstee1F5c5ep1WW613Uo67Rw7e9QXtBgv3Sq6bLa66KVXRYKU4FVEXtmIce3xRVhbE0eUqr2W1JgNVSiotegaD9ilF7QSQxjQ%2B9SigBNIksFQ4kMJJpt1SigteCGIkqUNawtcSGjsqKW6zN1AdnUoZhaATSHI4UFMWc0qSZjzSqbWKgOiGxBcEy8NVKCA5h25Hm7KUOwLEiSlUJImLSW0%2BKAgN0FRbHVWqNo02060SjYAC4fwu5tShmHynkl9j5JUNUGBSX4bhKoWviARj1iEBxl3c6h2ShjaCMSZoSfaUoLl6SNQ2qDEU1tKUYmhILExbqgwLfK8Bg4GvVABJD%2FAJnLdISguzyAR%2BY7OgwyeaHTtwlB0MMRUHyUozaAUZwfsVoIH5pYXFx5KUCkMeWlKM1ptmXLt0ShrRaRu4iJlM5BLyB4k91KAMiBURVWjPIDA7jT3KAvkdRi1DugzSDA6VSgMTjq1W2SjCRbLA156pQHALSDbDzsqNaC1XcNIShqGbmfnyUoQCLixLn82ytBLYv%2BLoCAxcggtDUCUYkChd5JPsEGccAw4d9WSjQD8oZpuaOyUYQA5gMBuxQYNpERv26JQTDh6a0%2FFQYUAEPV69koWpDaByRXwroqDL46s8CFKN8rgsxAgfYqM%2BogbmlfvQC55ALi4bVqYKAvqDWQTpuUBElxBox08FKM%2BuTQQ6ASJE8EiuyoIkEDSAezuoA%2Bpt6A79SqM1Q8vHs6UKBbaADt5pRrgDLuBr1TGRiNQzDXoEo0gbmAJh9VaAwektN2qUbKt1LeYFUBtJOMPAc%2BKBHDs5BuZ2p49kQwoHLPMdQlUHYgAyXOO5fdAQ5ca6HTghKNUNqP4Z%2FFKAwc5SeRHu5SjG01tNS5Jn3JQJ0c%2B%2BfsQAE0IPU6DRApYl688JQMaMSADI56pQsux3n3pRmFMvy1l6pRhvLajUcMogHkO%2Bn4pQDDh59veUoFJYnbl1aFOJhmLoEuZpNDBQIbSH2ShCxyFr7E%2BZVqEbcM%2FwCY%2FilErrQ53eo8VaEIDgksZcO%2FZKJs%2FwApFPblMhSBIIZ6dOylEbrXmRqzVVojeHdnfeioheCXDdExkRLPdxp%2BCI57rZIZpVo5vUAEsz6FXGUc9%2FsVaOe8aHsERz4F%2B1VaOex4KK67Aw82Kg6bNnrTdB0WmmxqorosBgVI1UHTaTu70AUVa0U0ajTQqmF7ciWnZ1FdFuTbuoLWvT26qCgkvU6D26KikwB3HVQPaDAmJ28UFANKW2wyBgGDUPnKgpbV2cE%2BcophubWIL2vxuiKyR8v2dUUXYOTAE7%2BSgYZPBdBhbucqwfBAQQbQCWDSH26oM0s1NHoGQEEW3QIb83EKwO5NfAxPVRWJJ3J0cKjEQ4hxBLAdUQw%2FMJ%2BaUUSSSwJGhcbIA5dyYkAe8eSIx%2FiuckioPDoC5MhiN%2BRsisLi7Cm3TRIDboxJDCPbopkAC5q0%2FM%2BiAuDqaS1JkIH3aTx1UANACWGp9oAQY6yx3b7NVQXk5UDMXUGdxdNabIFBJAAIeZYeKoZwZy2kbfioBkXxBLvt4lIMKkiMQ2SAgloLvr9iAFy%2FzAG6oIdigLkknR3fp%2BCAA2g7PvWEGyuIAaoI4SAlgWZzJZkGkNoGJxrKEYm4iC%2BgLfYg3FpFp1j4IQACzEB2Da06oQH1BrLiv2qwa00LO4fWuiBiXi5QZyGDjRwKoAMgWgszdPuQNxt2HbxQKb2IBJEVaO1UgxJJjUV0QZ3I0JLkINkQ4DckoCXNZhwW8YQYXEmrsHhIN%2BV2rqgxLOxq2qAZQQflBjp2QY3H%2BEZZflEU7pAXNDz3D0QZySMg5I2QAEhxHTb3IC%2BReQf8TfagFxJa0Frmf3JgYGkmWDkbdeqDXFiCbqAEDp4Kgu1C32qDElhLA1Jj7EAuy%2FhtkMARoqGq8cNwVAuumRFNYVCkMDcCYeIjVCMZOgNLSPFAJAi4sZB6qg69II%2BCAFyHf%2Fgzrp5oQDeRDl9%2BUgFQwDAwdC6JDFrt9noig4LAMWmZQAB%2F4g9WGqELdkMgQwoSOURnIg1ltiilalTNAW%2BzVEbR7aCCCVBi5fUmgNEAY8uRL08kANQCJPHtuoFi4Sa0J52VIRyAWPSde0qoS4Egs769%2BiKQw0tTb4DhEBwQQa0O6KmQRDz7oq6qJ3ONXPCCVRMEe2qoUiKnkugkQWpN2yggcgTLg6KiFxL7AVQQud9ix9qLSZS9QPWD7bJgc1%2B1DVEct4Jnw6LQhc%2F2BEc%2F8XxbyVHN6emr6qjrsH2rNHSKAVlm1UV020fQU04RXTYJah0PmpR0WOGed303UFrYq4BZM5VawTqTKDotA1hqaUWVWtDGvVEVenSDKBgC2xfqlVQCgthpLmfilRXEGlWYtzVSqe0N7vwQUtcNDUgTCBgx7U55QEAkn5uQ9VAbXc3M%2BgZBU8QdB8FBvzaEgluyo3yhiNfBiqofnmoaI8pTmGrp%2BapMa6IKEGCAHMMdeiBndqFt2ooMT2Z3uZAKEmpFG0j7koLatQ6JQoOVXmhNOiob5idH12PClwCGYRo4NYNfJKMwNrkPPu1OyUOTTR9CoA8FrXfT7eroAzkS9rwCPsVozlsgPlqdyoDL7zThACXJdmZiNUBo0uCacIB8pFpuYjf23QBid33H2QrQzggEOW08%2FcoMKFtKfcgAJIqSSRNOUBbIu0DWPBKByBJ0aoJ8EoNWf5hBZAAZxdrWZuqAw1p376IFa4swLGhEM6oYPDuIkS8qAhzIalUGxaMfCPxSjC2AxZvYJRgCCAA3PRBiKPDGmhKBmcOxb%2BDRAMQWBOXB%2BxKMRaQwdneiDG0OwBoGP3hBiLQIMhgH99EAuBctRnch6VQA2s4mTo3TqlGa4V1hvvQEg7FpLadkAkEOGYQxHdBsfzABy09dnSjH5nkwZHxhAOCDHVKC9uggUIFEAuIBDgktGtHQEmSPEGnPvQA4ki54q%2BytBjJjXaWZQYsHf3%2Bb1QCRaACMjAuPjqlBq7GGg1fpKDCTALPzVtXQEnj5TU%2B9AA%2FykGlSWjhAIqSSLqkUCAsAJPyiCK9EoP8A70sD1QAkiNNSfgyAEvBGsbvVAGDMbQCzEhnr8VaMbRoNmq%2B%2FsyUJUQYGk91aGOgqSXr3UAdyAXltlRouMOAX0jugNNKCilABJBYEAeMKjM7w5EzA1dQJcGd36VDdOUAmkGwCdUoxh3NBDaDx3QKDRydAwOtUQD8xL9RUcIA0QYP5Y2%2B9ApEQAGp9miDXBtCzGRVAjPoREUZlRIgfmMEOlCOdfPQRVBO6h0I0KokS4PEOyIWazBgFBK7%2BICoNd0Erg0V96K577flIh1qohcWZg2k%2FYmBG6szylRzXAEw5ZUc94F3LHTlUc90DdqhERYZNqqjlsDfFB12gPSdCoq9tWLyfYIOq3rH3qZV02wHo6mR0WwQ4qouFrAH5feqDottLDV9NgoL21O%2B0qKoBDUI9tVUPaBk2nuUVQOxkzA68KiweXkmFkOJl3YzwgcEB7rZGyCgD9D7bIHgEu4eUGDMS72iBvogaMnILUOohQG2jOABokUwMgbnwZAtoJIkyI5HZUU0khzDb%2B3RAXrod7fFQbUGZGmsfcqCXDMztUqBQHMgPL86UVGJcCoLwgYWOJAiG2frwpRhbDj5S0BolA7a1BUAFxLaBpf21QAO7sSDLO8%2B3CBgweGAFUUDW6f8AhFkRsQzQYHL%2FAHIMXDSQKUf7UDSAA7e0IpIIpSBRj7wqg7gyK%2FYoMTJxECkxuEBoSD%2FF7MijiYmpd43RDYwZoaBFDEdDv08kQwE0IbeX2RQcQQH47FEBjAAZgIDfegYuWFvV9DqgDal321YoCa0%2BVn7lBnkbEsdkVrKCY7SdUyhSQQ4qQwarqg0eGA0ZQEEyJB8WQABxPzS87oMJDgkho5PigJ1JctIAQKwgHXSnl3QNi8%2FmLu2j8QgDhxIh3D6lBhVzPhxRBocMC5AoGeio1pYMXpOvCgIth63fwvo2iAQJLx%2BY1CAwYAYCG5QAuTIoe%2B6A2tzMgdaoEYwzDGs7dFQSQS0ZM9PeoCLQDoG%2BKKUCGIxJYNKqMQ5AN2MSA0MoDiRJlpL6dEAFpBkyHcNy8FACaauWA3b8EBigEeCKRwSQWyGldWVQTkadYLlQbU1q2yA1rNpjYorOTIGviiAWqLgzgluyAsIIjYjXqgGU4MDSOdhTZAflhx72bp3QBzDwSwf4yEGAyEwZBIjVAuNNIb2ZWgOPzEkRy3ZUZwXat3SfeoBIHXcuFQeCCxl6oASRp0avDiEGNo0GsjSZlQTJYgVLUdjKoxr%2FAJTS%2FsHQY1LGuoUQpdgLXhjcKIMQKkA9dECEV%2Fw6g%2FcqFuAlnAuKBCNolqa7oJ3HXxLIEIJehcVfRUTuDEnU6%2B3RBHUuenKBQDLl2TKYSYVE90VC4TOvwVRzGCwoXcDwVESNi0PCIjfR68K4HLcHBjofYq4HNdUhvFBJjk3mjLk9PFnA5DarWR12e%2BizlV7dxXQorrtHGyg6LSJu3%2BCmRa1hyNKfBFdFgh3AO%2Big6AGB1YexRV7awYUDhpA7omDi0wwqavulVcAGGpT4KUMHe40GsoLWgXON6jogaT8rhxXwQM9Tw7MUDM8mem6UPSgDYsQYpuoG63AOJ2dFYHWHP8PCDDQVOgoPuQUh3l7aj7HQAOQAQ2xgwqCXOrA%2Fl4Oig1ammvJ0IQAObi8XA0G7CVQwAGUtj%2BYKUOzPc00A6qVQ1JuDbbyiMKsGcB2afFAoOpDlncasfigf80GWqNEAFGDEEdkVopN4PxRGIgMBDG0bIMbS4LdtAlGYF99BXxFEoNhuu0YDSqZDAER0HPVAuJLxIEPuKHVAwAAEEk18PBBiQXFDbPt2QEgkCARUgz1ZnQF2Ichh7UQBg7iprd06pRhi1tQ8OYMboGaGnX3opXGINDi%2B6I1rULPby%2BpCZCuwh4OnxBVDgsw%2FCaKAQWMbgAPPvQakEBh%2BZtgNOiA6uQeAemiKX8xIfSWRDEPSCAGQByCz5C6QHHRAHDPSZujXdkBqB7E90CtBtNz8%2B8qhpnUjTR%2BygIZncAeUINkzirksXQKN9ndudYQZquGyYBxpRkBEMf4jXR26INEOWNCaOg38MkAET33QAw4H5WILN3QYlySN8Rzx5oD%2FAJOpd7ttigxMkuwDDhBmMtA014QDU%2FwnetX5QNBho8kUrsXxtyIjfuiGFXBfYaMgAcmRy0oMQCXZo2%2FBBsXkH4opWufcEsQ4hEKbTLmQGfhKC4Ji75RM%2FegzOxl4f4yOiDcFtvZ0UALaPsAdR9iI0vc4BIimiBmFaEvKKUkWsHPM7wiMAxyDMZJ3SgORDEkOANa1hAxxeWM7oJkEDUQ90K0Coa3%2BGIfgcqjQHYEN4AqAkvrIgdwgxIobnrwgBtBuLu%2Fj96BADaQN9Pjugwc3F9OrFBpBjSs9UCzLiTQyoicWuxLWj8u3VaG6FiRQoEuabSW2HHggQuYdte6CVwAM0JogQg0JPmrRMiCasgjo2oMgFVMkuDhzWjlRULiGubUP9quEc9wYFo1AKCBDOSXaSqIXBoZtvBEc14DyQTwtDlvFvmdFRJi7%2BbKMuOw9CrnCumy6BqVIOqwjYy0%2BaK6LC8iPPRSDqsu1aCFmC1pBPcPqFYro9My0O9OikF7btAK1CmcKvZcK0DMkDO5iHoPYIKWkEkVYedEHQDiCanQKQNaTV4adfZ1IKi5stBQH3pA9pLGjs79eiQYyGxIep%2BxUUEPFa6Dus5Gc1knW0H4SrA2WptbKoPCRRehI7DcoHBttABbYBIGyFBJP2JApuyYYtpt2hINkHcmsWnrskBNziQZhhykBB1LhtAG%2BGqgd2LggAbqKUXUa1m%2FMA3h4qxByAcsW2fnqykVn1IA2c0VRsmNxm5qJBsgHto5jfwSASa1MbHdBsqAWgEHz1SA5Ro7QXiSkGyB2YT8UimlhkSKexKRDAtLGfthSDG4O5tIectfcrBnucmS4YSg2TD5jJgDk7KQDID5WbQgzGzqwHNsizBngxqfNIBk1rCjSa%2B3ikB53kndBjcZNtuQO32pAchbS2dBrypFC4hw4BeATGvKuEC64mgo%2Fy1NExgA3CtdZaOUgd5MAtQ691FK8uzvroQ1fNVGBJuJxgD2hAciATozgEpAMyDEghwY8UgwZzB3tnQoNmMQKEVmQkByYgsJhzHZikGeeedgUVheSBcYBl%2FblIACA%2FUFhCINtzn8rOKPDdEgxugl4MBp%2B1IGMijFRSky5EGC6Ixu4L6nRWDZCfmkiNQkGBgDEZEDybqkGNxFAza7e5IC4cHwL1Uigbg9GYxMUorEDLUQQKc90gd3YHvyopXeAG6e9EYXR%2BVgHfXsrAcgCHDloevtKkVjcWdg%2BlvwSIAukHRmDUqrBiSaTbqDq%2FKAwDSbtIZxKig4ufGG7F1UA0LQ1C%2FeiQKchDeE7cIFBGNoLXC08F%2FFAQaSxtj4IMSwh3ckDkx8UBfRg%2B%2B2zqRQyIeDdrb76qwHL%2BKgAn2ZIFBDXR2BJRAclvlcDUP8AFIGeCGZ7iwFUBF%2BpEN8s18VIpCCGLcMaNqqhcgDq8lzR2CsBzNo0FeiQC69jsAapAQSR4ueaIFdySCCQwrKQJkA8Npd4DZIAbsiwraXSAW3OLiIdpJ%2B5TOEY3AswYkv5JAj6WgETQtRagW4yzFm1NVIEuIAHytowSCZul3gwCkCXEsHHUdVcCNxuIIg7EQrBN8niC0KCd9zAG7VmKsErrg70cJjA5yTD1aVRzXGWbjaPBWIjddXc0DpEc110tWrqwctxMnX4KwQmnd%2BVUcdkiRGlw%2BCI6rXbfd1Kros3Z6HZkquqw6aCGUo6LZAZrtIUHTa3yk7pWl7DAeN67aKC9sVnUn4KUXD%2FADtVSghjcHB3f3K0WtpIlqdVKKiAxZgYPTlSioIAFHNAgIZgBI1G7q0VqwIDv8qlDProTTdA7sHaOfHlQMDPaTzsigBi8PNPN1aCxeS%2BpqPilFaBnIlShXJnFwDO6oImBc7yfJKMaNaWgy%2ByUC4GB3BnR9ExkOdAAwZmFXUo2RBORjTf3oDbJNNvCvvUoAcEB6VAaOXhWhqADs6isHe6K0PsyULSloBkl57q1B%2BYtMN3UozvNvVt6MqN8sG3t8WShrRLXB6kOpVNuwerAFh0CUCagggRa32lWoLNq4IZm0GiVQGI%2BYyGcFkqC%2FZy%2FwBxUUQ7k0c%2FdKUAPUOZo%2B6UEPBoGp8AlABJAOhFXnogIAIa1gKgijpRgauG0bx1QZhUAT8UoUHZ3PBffVVGBhx%2BYhA1oLEXTvt5qZypSXucbflJbXZVBaG%2FKJmg8EoBD3B5LOB1Sgt%2FEBJLufBSjPbLyJcvsgwg1NzOXjTwVqjlGTAv7BQLa2zBmII06q1GD94y8Eo2jEE3SACz8TRKMSAYDBw%2BjaOgIEFqbBmPailBBdyY0KKTQgGZPsVahizAEuTQxKgAuORJoNacjRUEcTTVi6g0s9ZesJRtiTiDLK0As5BAYtRKMAKyxkkJQwOhgtThRQBD3giT%2Bb8VUY3AHnbqoBAgwKDrV9laC7gEgTQ0dRQLNAdgId44VqMTqYZ5E0QEwWJcHQ6%2FBBpb5o3I81KC8gjZjxsigQ7iAlCAh22Jcu0%2BKBdgAfl7N0VqG7Et7V7qKAaX%2FKeyVGId7iC4p20VoIbsKMN1KpS4NGD4g90RnpqNOsz5KhnJIgiHdRQfUy7P0QAAGYJE%2BTVVqEGRL%2BfG0OrQQzgTEh5ShQYuB1j7uyB60e3inKilDsQ4jQTXRVEwaM1JhASWBhqygQOGLPEnkyVM5RmeSQXodeyUIdS7irHlWhbmLAyQZPZKFLdC8mvZ0olcAQW1Na%2BKUTuFIke1VcZE7ibiRvp96CUww7IEPBHBSiFxdmdgS4VwOe8h3BmaKohcXIimqojcSTBYio4RHNdBow1KUcl9DC1RJ5rG76ojjt1mqqOq2exhRXTY0Grsyiumw6Me6g6LXaQ5aCmR0WzzKjS9mpmC7%2BSgvbpc2rPRMi9tSASXOvKge2WL13p2QVtedf8AEEFQQ2x0P3KBwSRNrA1lBS2LcTMR%2BCCo3kCg196DOB%2FEwB6oKOCx0mNpqsjWs4NsbRvKq4B3FGMEPMPXdUMHA3LU2%2BCB5YgU0MuoCRk0s0n8CgwpBe0%2Fmh5QEUrxkR2ZBsgGeuw0PsUimBoCamC%2F2qAl2Z23Blh1QaaFmuAGOj1KAvFpAjc6BBjc2rHmiQBgCB3M%2BCBQ5LCLCxDBEYBqxEcIHJhtRXSqKV5IyYtA0RBEEUEmUU4kWuTNbgd0QXbXJ3IbYooGkF7aElEFyDbkdPxQa6AYIeSaoo99Y%2BCBWDmHgOKdSiDaQIGmhO5RQDy4dpB1k0QZnYlydRXZEY1t2BcHzlAZoQQ5rsigxLEVg1imqINI8%2FvRSs4tdiBQDy8EQTbI%2FwAWpZAQwc9wNepPKKDuQWckM9sxr5ojNrUGBEAIrGKzOj%2BLIgxR8W%2FKH19iit8zagiGJnrygzh2AJZp0qgAYgir66n2qiMazSeBR0GnEkCojp2RWA%2BaTBp70BJcZAtFBqgBNooSC7tUojESW02AroEBDucQwENCKAkwCAeGY%2BwRGclsXo4gIppGnB16IAGNWNpmJfvwiAA71BoxneqDC7oQPzDd%2BEgIHzQwADAIoSLon%2FJdy3L8oGMD8ooxeA3mgABtZy4cNDMiFcM4l6mQOdEDGdBawh9OiKBgtWYI328ERmIYPQSNB4oC%2Bhd9xCKxMNTT4IIngviHI9t0Q0h2L2iD0RWYAhywOjs2yDOIAkD2jsgLiTUGuqAamMWEalAQWABk%2FegECsRJhEZnFu7ObTygwq4tYmt3R4RQIIAmgmpRCQaBjPloFQpYPDwHD7aMyoYTWd6UZQHSJeCSJ%2BCKBa20gHrNH3REyKSdRkPNAflZ3dy%2FXRAvzCIbiiIBMcCR0lAheAAHNQ234qhbg0tLV%2B9BO6A1XLkdEC3YlhvLBQRNGrrvRUIQ1Rlz38VRETs5od0CElwfLzQQuIZ2nurhEbyH2JPxRXNdvzELSI38AGKKYRzXs8zs%2FmqOX1BWrw7KiGuPl8VUcfpmntJTKOq00ALNVRXRaWHaOyVXXbqA3DbrI6bZaHISi1ruQ1Gb7Uqui2eG0UqugF6g%2FepkVDggklzolFQSxY6QVBQEOG4YCk6pRUGvB7h0FAJLV0Cge0uBb47exSigLmjw4ShiCMpLmUoayDWA5dTOQxeLd4bblKGJMPHdGgYAbkyT96tQRcKTMA7ToyBmoGDO59xYJQwZn%2Fi1r7lKoOBiwYbqo1WY6wRvqlGt%2BW5nYElgmchxcAMhIGg9pWVMXMAt8EoVyCII0Ar47KozU0bT3bbKUbQMOdCA1KJVEOBEhtISjB9wSGFfbdKFpazjLQsQCPYq1Bcu7UPl71FYxG4qA9G2ShnMGS9SPBKMLnxcO1XrwlDZPP5WDgFAdnqanVKNQAAsfYpQMoNQ0c%2B0oMGGuRDEqoMk0gROqlVuTXUapQRzJJpVkoW65raaaSyqMaTB6OW1UUfyi6XILj70ozi16TQ7tugznQ6M9UG1LeDJRiRBaYr1%2B9KA4IBOoyJ8zylQGYC1mapNCrQQRWQxE7%2BKiieWIMHdKA5tBeWmRSOFQQQHD4tPRQAEh7ZJ3%2B9ASIIfYUHuSgFnkEb7dUo35QR%2BYAszPXRKMznmpHTv0SgioNQBB3fqlBZmcvSvglAau5Md4dKAHA%2BZneo9%2FmrQQ8AjcnhSjUDiO1T5pRodzEta2qUEVpIgFKAAem46pQCwrcfmBlKMCcm0P5njuFQcplwXZlACCXINQwIKUEVZ%2FwDhBKNwQxIlAAzC7FgHbulQX3iZPGiKUnEOBI5j7EoXWTQiKpQdiXAdAGIA4EsPclBkxBZ6zwlCsQboGLTNd%2FcrUE4gfNIAYk6gKVSn8xuya3UfFlahiSSw6j2bhRRIDiu4CUYbmlQUoXIiSGA3hUKxcu9zUSjAGAKDn20ShQw%2Fyd2%2BPirUM2MBgKkqVQFwe4vFFQLiHfmVKJkwbmJ4BKqDMF2h7koX8txiKm56AqVAuIBbFuEwFmCHJIrwrQpIPQ%2BEpRO6Tszz70oS4muo9mQSJDgbv8wnzCoiToPbxShXBgCdQgjc06gQ4VoncWNOjJjI5biQ5FGrVURuJftTWVajnvDF9NvxSo5r2LsRqFRzXnjhWiL%2FADM%2FtVKjhsNA79FR1WFh4qDpti6hPtyorqtJ3bRQdFpAmZ3QdFpFBzKirWNoeoKmVdNmhc9T7lMi1h0YhpPPgoKaM1FQ9rsADIFUFrCbgDXcJkOGa3FneNUFQRFSeeFkMC7Cj0I3CooCCHqABTdQM50JJofeimcEZuwURoteal3KKIfToake9UE5MCJimqKd7uhqx%2B5AQwBbQhj7FBgRoIJem5QYEjVwD7hKAvQs7weOEGtg1kgFMgPaWNA8katx2SIpR3l6AU8lFByCZcOSRqgzN%2BYOHqUBdyxgs8H3KAAkC6pYwTqXVBMl3AHXxogDQQCKFw7Ud%2FMoA9Cx0Zq9KohjSDpDMorBjLM1UAAa4kQ5o6obIkBy5qbT7cIMCTyDRBhdWIp22QOLrXggadh%2BKg0FnIkBh8FQJ%2BZyBsdkG%2BUuCKnmS26DNBe0R%2BXaEBipI6kKDFjBqacPrKoHLfLcX4QF6%2FK2ooFANCGAJ09zqgi4OXOxHfhSAG6TXjTTdUH%2BHRw2LoMGoDUT8GQBoLEBjXw1QaHDmszHtVAfmDbDfRAIuILmDSmqDSSAZLSWQYXWuWEhmfwSAtJIAJFa8IAxLzLSAIpTZAS7OSxGvTiUBIJY0q5hx71AtsCJGg253VGMSzA7V5EINBMdepr8EGBunIEtIAZAdXq5fSIqgFRczToKnugxJk21Z3aD0QZzLCKkblkCk6RPyx7FEOKHQ3b%2B2iig4IeNiQ%2FuQAXwAC5aRuqNlVwAH8UCm64AkeI51hAXnln691AopBDav4P0VGJkSHGj%2BKDbwK1G%2FQoA5cVj8zeVEB%2F4rgU435QEuQGNWJP2KAC1tzjIfToqM5I0IMcIDHNaNOygVw5DgB4bgKhQWdgS0t14VG%2Fi3u4KAXAgEhwAPzatqiG4aA0nhFAFw8ULHbugDAOAcXnKiIVySRQEsZk8eSARtUOX7orNIeRsiBJ1lm1ooFyAcFqO4norAtXkh0QLiAwcDaECEiCwaiBHYOJf2KCReXkifF1oTuu7mjn7kEbmoeHOiDGmj1ZQc5gUymiolcDxx8VRz3GrS%2FvVHPdcJBoKOiI33OC8AVZVHLfQidh7FUc190ttVIIsc3iqtRwWXAblyqOqy4EuzyoR023NJpRRXTZf7exRXTZfD8QoR0W3CnkoL23hxqQVFX9O8Oz6KCwuAkOYgIKi7tVm3Qh83Y7mm4QWtvJ0%2BU9FFh7S48sfwVpD23M4pvH4qZFQRWbhRQh82Lu%2FFPehFMrfGvhqgEO2L7IQwIuIban3qcxDZOWbWPNBnypG5aHnQq1RyHIPRkGF4YRBbYQ33IRTN2%2BbE7cn3oMbiCYnp4IMbqQzAECD2CAOGYFjQgVhCNvptoZbzQhnbICuhQjZkwzBoIFFIDkLhUh9NYlCGe2SZ69VCM4qA1DCEA32u5Yc%2FBUF6PaW2jzUGcngnVCMSAxekv0qhAdgDi21ux%2B9UjM0hz5JSC4lxyTFVCMTQgF3nw8kIBapJGpPbRUjAg5Pb%2BbwLhCDkxerVpDfaoBmQIMES9CqQxvAEhgDTdlAMiSajUt08FSDmLWf%2BI7oQwvEj5mhoUWBnboCxk8uiRsxpUy34KkY3gk1BFWgygY3D5hbqKHwooQcg58kWFytnXXLqiQcrWd2EsSWQgA23M%2B8FCCLnE2kBtd0AoQwkRa4jyVIxuYF3IME7uoNkJe2akDhUYgAUadD5hSkZ7Rabdaxo6pANwaHcboQ2Vtsy7UjT8VFjZWnsQ%2FtKJC5T0cA1r3lUjZ2AsHBPvQgZnUQZJY%2BEVQEepbL2u5g1cBQDIEYm01BYtDyqRswdC5p7VUIxvtBNrByI8%2BioN18Aij%2B9QhcwavEbchCFe0uzHQH4KkEXPuHJZ0BBJaOhPwUILw5ltojxRYR7SRD6Y92VQzhy%2FBFuqhABADFiHpSB96pBcQcd2ajKBXcUIc1HTVUgkgRBDwDoyEC675XB6jQR0Qa0%2FKSATB08qoQ7h5Mj2oosIDaxO4D6%2BeyqRs3JZ%2BtKJApIlixMyemyoBJYfxHUcaoQwumQRRggUEgTNadZQhiavR5UIRxaa8sA%2FdWkY3AhnIxiqEKbnZgQXkgfagDvNsA1CUAXGIfihUQMm%2BYTHzShALGWJerKkC68WuS8SgmSD80yJaAhE3rcQ4EjRUhMnOrAxVAuYEUArsgibw1HbTmsOhEyQGn2KqRO4gaOzbOhEiX%2BaQ%2BnkhELrwC5glm9yohddoCRzqqIm4T1REL7gHL1og5byJ6y3itEcpugzKqIv8AM%2Br1blB59umj1VR1WR41UV1WXMA7qDotu1BpJUV0WkRNNd0HVafx5UVUEkB4fyUF7bpA32eEVcFzWDpRlBa0yKHbuoKhhI1KAu7ih2QVtLSIfX2KCoZjU6EIGBpMaHZA9vys5qXlRThwxYRLBA4IJEi3UPtsgM2zUVPRA7ijDrxopAQdOIBKgIBEGhNK6K0Yy0ToVVGrmf8AJ%2B3zUBF1CXIuLqhgXJYMRTSDRQABgwDu86eSoLMxrzvsgYCej%2BagUwXJ0Ymk8qgACA4JMGdp%2BKBssSNH8t1IGyLQH60SDChoxp00DICTowMT8FAAKzq8RXog0QRqdPYIMAD8wcZPBG9UB2LPsDugLGLqHUIMGA%2BURuKboF%2FMzh3h990BtB5Y9imRiAWB%2Fhn7EAJalIfqN2QEkEggiH1QAmTUkUd%2B3FUBnQVPQd0A1BJDk09mQGdiTSfegABIo13s%2BnwQYOzsa0130QYORc%2FzA0OjICwJ%2BZwQ7z8UGL6FoqgBud%2BKDy5QAHIhjAeW16qh5tGzmBTsoMSwDjkBApu%2FMSTDEtp0KA%2FM5aAK8e9AA7sXHPU8boCCdQSaA6x9qAECT%2FCYbRAHB%2BUyYZ9e6o1vzOD8suBrKBi4LGXoGqygBctMgtaXZz2QEksCNNYQbJxFAWYhIMBNpLkjX3oAasZP8Q08UBIDyeQCHhBuMXtO0oBN0AgjxQF67SzFkG5kP9roAZbfSNW5EICSAa11hAAHj5WeNw2%2FRBtw4%2Fym2lAXucEMAIPXyQapIYhxIqgF2xq2zpgYEEyBIhtlRhcDT%2Fja9lIFFw0Alzl3furBmMPJq7IM%2FDvp0NEAeh%2FNsX1VG5brb0QDn%2BE19mQG4OQ12LFMDE0AJPM12dQKXuh2HmqFAdhOOr790AItrUdkGBJFrOdz%2BKmUrEvaXDlnIQKS3zCZEoAA5BedBsFQjiJFdD7kALuGoHcoJm6QAWGvLIEJihAGnsVRMuLiHrTdEKSBHiTsdHRUSQ9QQIA6IhSW6DbhBI3czugiSGMxLaKiF1zmAY3VErjo5eRoiZc9xZ20lUc9xBMU4VwOe403VRzXkS3cboiLz5qjgtOnRBey4kbEVGio67LmjusjotILEDpsouHRbdXnyQdNtwiXGiiuiw9Nn2UFQ3jBSqvaQwO2%2FvUFgQ0CnhCC1hatApVO4%2FhlyA9UQzj8paKOgsLnG3tsopw06lq6cK0PkzNMcqBhUlhNT8EofNi7vQcqBxdQOztKDBrqyTUKh8mYCmrqDAiS8vACBy9AIOte6lC7sxFR15VoYXUbzEAaorbkTDIAHBLOAJ9grQ4uAEuJ%2BbZ1AXB%2FirIND5oNjDlnma9EoaSJcRXYoMSAdBugEAxJqT%2BJ1SjOxJuLhoB4QAQ2lAwQb%2FJctEjcVZA70YAAaqAPbVhBY7hUZyHALvDtVAwYuA8u51hQFyG68j7kAECHcvG0IMbrp1aS2z%2FcnICwEUl6JQpBcc0EjqlBaTAcwD7cJQddJG%2B%2FuQCks%2BMjfmUoYuDVqv0QD%2FJ0L4ilPNBh%2Fkhnl4TOQANCPy0SjfKA1YDb8IM%2FzOxcCj86INQMSIgPwlDO7fLMA61QLV2i4Q4%2FBKDSAw03hKAXajzA47pRt7WYuXPHggDEAziSfHRKGcQ1QW8UGMsdz8PNKAxktk%2Bh4Sgh%2BDHy9W0QaZLtsN9n6oBNSWLgM7INRwT35CDEEyBNCD1dKDjaH0IDk8eSUaQGMAsPHolG5obqv7kAAIJEEHsyUFgzM5YkxD0SgA2nr11QE0BEdeUoANpbj8ohkDEnRp1qEAi126jZxCUAk1cWtRBoBJJ1lnQDIO%2FjogUkzkKGCH3qyoLgmXgwgx3dpd%2FwSgGCHa4Ma8V0QaoYEF5380GFTrFdX3SgO7hoeVQYmpqBPKgPUhxTolCG7cAvQ%2FBADc5k0LR0QKXrAA3PgVaM4qLhrPvjspRnYAgHE1ZKjABiASC7P1UoV8S4D6eSoBLFycQgWATRz%2BX8FQLrgYIcB%2FmqgmSDFtAYQKZq23hslCEm41HcUVQDWrk1KVUriKUqyUSykh2brPREK7SPw%2BKCd12oAoWCCdxZ9ZGSYVC64Se7qoidz%2BCtELriTBB3LojnuuE7Es6ohfdBIh5VHMSQ%2Flsqy57yJ02TAg%2Fz%2FBUcNh4QXtNPJB02EwenZQdNhgPHfVQdNpAPWqir2HbSohTKui0sXNG9iguC7RFXUFRcXd2H8I5SKtaW7SVBedNJoiqAg67OVBTKHZuapgEXWkS816%2BwViK5As8ifJRTvDl28wgclg%2FLhBnYhxNGFOB5qIrlvw5UU766GppCAi6m4gbFUEkia%2FBATBNG9nUDC4EVJ%2FwhICCSS4BGyDDQu4BnryoCKlux3GvvVWi5c%2BKDCWJAHPdAPmYsfmFDCB8mlhSu%2ByA5W3DsenZAWaP4Wk%2FYgwc1YNBG%2B6BWMAt9jbKghv4gwFCW8FBqtQcEVVBcy1JDqDO4JB%2F5MlBqsYPtzsgwNaOwBCAuYcToDKAGgdy7x2QHMuAd%2Fl37skGdyYYj%2BJ%2Fi7oC4drY0cqAgyRLM59ggwLi4sw0PxQHQPazSihZwYDUkdkyg6HEhz4P96BTaCHfkNHSSgJcCAKdHZAdQ5rQIAzuDShLoMZfia88ICSWYaQR%2BKAM2nzXVQGCKV1E0%2FBBmioI25q6AAzwK8NPxQYxWBd0qKIGJLginigSLWMV6tvKc40kMLWDGWmiAhi5BYmh0ICAA7watIdAzQQwmpaEAtta0jLWXHwTIxFzk1eDOiAF9DsO9JQM5DA6%2B3KBXBcbQG37INkCCR0fvyyQGCGagQKSwdvm1uH2qwLmCzEguGHwSA5FtXrMT7BIAROQLj7WQaQXGsHsgYkiGfkxRApALyXaG6oC8Eg5TH2IMBUnQu40QEiWMx0QBjLAQ7asgDSS7hm31QA3h3Fr7nnZAQTo8jXRAlHEAmSd0BcSNRtOiBXBMl2luqDSzg8nuiDIdug8tlAlpA%2FyQGg%2Feg1zmdqGkqgVZ33YoFl3baWVAy%2BUkPq%2BmpQKbiJu1o0lQLk413QTdiS%2BR2%2FFUK8TdAiOyoU3EDikwgmSaab0QJk%2BsVJVgQzSYUoW%2B6vRMYErjEliaqjnuuYVZoICIhdcDr3VxgJdczyx1CIhcW44VHNddroKhUQuIejIiF9w67lVHLfSQqOdy%2BXkqOGy7nWQqOq09hqsi9lzBnGqDptLN1ooOq0vrPCiremSdZ%2B1FXtuIDbwoL23O%2FwAUFxd96iqAmRQsJQWtu7cxpEqCwMAE10KCttzan%2Fg%2FcoKQaAkEymFF8WDx2V50OLgXbeg51hRTi4QKDUGeUFDcd2EUTAYOOpllARoCWek7IHzDZaa86ICLtTpTiuiB7TMgvvv2UBFDMmoM%2FYqCQQPzNsXZAcj0ippKkBYUYc9HQFjcB8VAQWmm6AOxfQ7096oIL6sGYN70WtqCzNLinO6AmASKmsFAQTONwJZ2QYXXUPEcdkBJNJf%2FABBARdTnWnigwFdrvE%2BKAmWmN6U8EGmpoJG6BcmIJDMKhWBgxf5Z6VdQZ2Zq%2B27IA%2FYwCO2iAQZIm6gd%2FDRA0s38JEEa1QaXjWjzSqDF2JqW3p3QF2uEs%2FmUAFwdn%2FKYFa0QYPpe4aorXogzu5obY6IA5tJYO%2BnXlA2RYvtDlICDA%2FijyUCuQ7AuAdKkqggtQNaPyoNnQs7aUZIGyYCIAbhlIBkXJYEavVWBYgEBiaCA6A6HU06dEGygQCGkT7kgGQkU3J25lICDq8W%2Fm29mQB63A0BHtCBgbntfaB9qDZGtWgJAlxOhZzr4pgFyHq%2F%2BIINqLiAxqemqDAF9CdfZ0G%2FLOjyNuUGJo7R%2BZAGMOAYo6DFhOm8ICQMpMtDoMSADO7nUcoDo0hhEIAAYP5uD7FAAImnMOgJLMWa7RzXugV%2FzEtAmKsgJuDFwRHaECEmhck1ID86qjEs9zna4iNIUGJoLQ5GsIMIfkMbvxQLUEAIggsdRsis4rVqs9QogktJLCSgmbh3Z3VgGR4Dltm2Vg0ZEEmjv8HQK7HrDjeqAEuPloWIMoASCZ1qgQ3RBx3%2BMoFJFS5Ya9UCk3Pta1FQpuGgcvTT2lAhu%2FwAp7h7UQTuI%2BwcDRETeTuSCD1p5qgEtDNlp7BQIbpIJ%2B5BI3ANMqiV1zxq0oI3XSdeFRElpEaP9qIjddJJPboqOe66QHfb4KiFxhn7fFBK65hp9iI5b7h74VRzX3HuahURnbyVR59t7NzRI06bLxGnVSDotuGrd1EdFl%2FCK6bLmbXdTJF7b9d4P2KRV7b5SC9t4D9a7qRV7bmf5oOsBBYXuJBo4UFLb7RDzskVWy5g21PemcEXtuBEud3lQhhfQ09tkgqLgwdjo%2B6hDO8g9OqpDAl3Ad6O6kByAh32mXQPbcHcflPsIQVzBIccuYogJuxpTVIGBAl2LUUhD5M8EhvJRWzq0nY6KwG28AvbtI5RD%2FU1aD2lIrWsRBLmpLVZEhnDSHANSgIuLgMQ3RSKwvG1NjMcJBhcDqzy9EiGBd%2Fmnz3UWBk9B2b8KqjR8xqx%2FLQezIGyBkSwE6R1QYlyXjf3IoltWcCT9yEbKHALkJBjc51tpISDC%2BcZpBPs6DG9nOm41kKkNmHYCQIHtRQgi4ESOI6INkALmD9tX2SDChfn5RwhGMEyeAHhCNGoJLF0IPygDxHCEY6jQUHnCED5XAY8ARyhGdq0pT3oC4cDWnavdIBENUCDqhBBDs0NRCCC80fVCFFwf8xLQwSAAmflYGAqGoNyNT03UIAud4%2BV2hIjAuNbnAn7kVhc4ly%2BujeaQEmBE%2BJQbJtDokGcOxPLdSgxkHV6gBCMCzljMkalBnli5b%2BJAHckaVY8oRhNrh2IjVvN0IJajG48oRjcGpFSyQCQXD6hzX2dCNlABM78gKwHUSWM%2B7ooRtuB0QjC4Fn1MDzlIBkAxduIQgZSQAS8EaOyEb6jmJFEgGRIuYMX1%2FFAM%2BX2SDPoWIEY7JAuTOSzEQPuSBwbQBqbY5QKb3FC%2FtuyRGFxiCJcqAZS0gbaN3QbIUDlmYinkkAzAmrnqKwkCm8G4NUvLOrEYXGhHAqEgV2H5Q%2BsdlRs7JGrUSDG%2BZaRpuopcixhhWFUhcwSGpo0aIFyG7Ws%2FZFhcsWkxUUSIV6gTEj2KpGybncosTNwALU2O6JCZaswJfQIFJJd4YwgU3B3Ylj%2BbZUTN476%2BNVAl1xAqQ8kmVYJ33EAtJ1O%2FZCI3XhpqzEhWCZuES5r1QSJFrsHOvt3TnRG6%2BWfpburEQuvmndIIX3kRxX7lRC64STroiOe%2B8SGfVlcYEL75bhiqOa64OTrwqiP1A9fbqkV5wu1Wh0WXGNlB02l9ZUyL2Hsg6Bc7CnKiui256%2B%2FyQXsNQzgyoLW3Gru8htUVe26XJnQdFBYXkUkioQWFzgOK6cKB3AYaiQiq231aSD7kirW3vr82kKCoNNCDRQMCTpTQQCgplMQBLe9QPkYL1ZuVUM566GFCjO7inKKIuMB22ZUOC1QwoFBRx0c6oMbjyWYR5pAwMvMmVBstTt14QPkBx5dUBBY8En26IGyMw1PM7IDlE1EPKBoPJoUAAMfws1D5IGm2hjWEABLiGAMIGyrDEDnVSDFmcSaBAaMIHDIM%2FLOw6%2B9FZv4dH2SjVuLiHmfglGcB3cQSwPc%2B9UM4dhEO52CisxIEkaoBpcwoxAVRtKEDQdeiDEkEgXSzse6A51AMceKQEEkBrpbiiKUGIaDXkohjcZDs0ugxIFs1qgZ3JDHvIRQu0IjQlpCIOQY86fFRS%2FLD6u6qGLMxID69UAcMJYaFBnA5iEGyx2IP5qoA4BM0JnZBgbdbgWfI09qoGe0AaAaj4qKDgUkEgv3VGcCskl%2FGiIzWkB9NduiUAF4JqGeJZAcrY2erNKDXEAcGAPuQLk%2Bjy2qDEksYtGp19nQbNg5LAFgPhqgxNzSXLV2%2B5FaRJOTkDbtCIFxltRr3QYD%2FABGnt5oGYQ%2FYaBRStRtD5aKgXADgGo0RBcXM55kT0UG9iDRKA%2BrIVuAe5qgBZnYfNqIoURhAcl3rKDOBqYNaIA4IOqoXK4sKxLO%2FgkDBiHBijoFJEvABFeUCvbTQRX23QA3nbGQ2tKpACZLnhh5IFyYEi2jtPigAJaHHXpogVw%2Bpd3OyBctXFpqOSrBriQxqaOUCPt8uqonkxAFRTXhAMiYq1TshQdmDtx%2BKIE0gkMAgmbmhpanARSEh9zLoEytNCXJdBI3FoiVRM36gnU%2FckREkihd6KhDeN%2B6QRJaIGwVRC66SMp2QQJFXHLKiRJBYn2CI577ndq0KDnvuMjfdVELrt3O4Co57ywaGdMCOerndUedbfpDaKo6QW%2BKiumy6k%2BwUyrosugAaKIsLqDyQdFt3kiui24001UF7bn9veoKi%2FuUVYXmN9HhQXF%2Fn%2BKiqW3OwBYRDaIigJqO3wCVVLbiGO9RoEyKW%2BpTmh67KKrnE0QPbcdz7eKgpbeXYjrrKB8jBlm9tVKGBES54VqQzxs87IMLjActTaiBxcep3G0qKbIlmLv7QrQRe8QHkeKgYEMSHtag2KAuXAFDI%2B5A%2BWm0FQEXl4MfxeCA5EAwQalvggNpoA9tZ0QEXEfxOedUBN8vi5Ghqg2Rt8YbmVQRXYuXea0UoYEl2DABtkGybtQ7%2BwQYEgkiQTIQHJhMaugNpB37saqA5CR4kR7URRc1cFzHKAOwiSIAp2lBiXdixO2roDqGZz0olAJd5d%2BNkpRBl7paQSlGJYkm13En4USgk7n7Iq5ZKBlIhiX%2B5CjAIfR2SgFhqZYMFaoBiXEm4yaQlQwuDOKeXdRWJbbLQdVRgdtaH3lkBd8gILUKgWj0PEDxZWo1WActr4QiszByPmYT7OlRiXL6N%2BaiDGK6b76JQXOhrpy%2FVFZ5gvEAIAZEN0OgHdEYwbaTAAQGOpGilVnDBi%2FT7kQCRMzq9aJRiSHOr6fGqUAtUtwXborQS%2BkkGaa8lSjOzDEjbfxSjF%2B%2B9H%2B1KACTr2bfdKCSWqHA1%2BxKMXJZnfV0oGVS4cH8UQpOjGPt4VGyaWZhHRAci8kP7UUUoNavpCqMbiHYSfgg0WuwYsKJQNPzZe1O6ULkDo0wxZUbMuxECH1hQYksJd9UC5NAZ2lj4ooZXP10KIU3mZir8DZUKbwKv4mEGJeAQAa90ANwtkzPUygU3EMwc0ShM7gaSduqoBuJI21MhQJcZp8CqgSHlhoNNUCuzGmzsGSkKb5%2F5yKQ3kPtJLoEJJ1qgQ3GN%2FNUTN%2FzAUQSN5Ys71KombxqXendEqd1zzoK8IIm6mpGqqIG4sS5BnoqJXXmdjvCGco3XO50CIhdfuKKjnuvZ2M0VETdq8oiF91Zog577mHwVVzZl1UcNt1PeqjosuLB4UF7Lmg90V02391FdFt9C7cqRF7bmZvFBW2%2FQIrosv1Md1M4Fxc1TGg1UFRcxPvRVBds1Z7IL23uPe8LIqLtjOpf3oKi4GlRuHRTg3NvuFFUF5YacOkFBc1SeqCgvejka%2B9A4vp3b7FAwvIoxGyQOLoLD7UDgxo9SyiQRdkN5f2dAXJBqR%2FCVQz%2FKwHUcKKYXiKDp7kByblwYQNk9DwSgIuc3B3F3tsgMDoKDZAzzR32UBdxV9bXQEXCSZeTtRARfWg%2B5AXAB5YR8aoGtuNRqabdXRRFxq%2FG6Agu3iCEGBaWLbD2CIOVtXqYZBoJO3mgwIIYNHKAs5Id%2FbhAXcmh2CkVg9styeyIO8TQ3IpQflNz1d2%2B9WIZ2ABruSpFZw4J0cMkABA4AaJ17IGcAuavCAAjzejH4IDkJYuAHZ596DOJJYtJQb5Q4dn35QYEVgywKg0EE%2FwAOrVVRiC5gEAflFUUwbjnrRQLqC7AVJ8VQXnWKjfzUGx27iqABxW2ZoqM7nY0OiBXDEO1KndEMLgzu7OT3lIrMMefeUANwtJklqpEGHqG8T7kUruxduAYRBcaS1B8EAyNdNQdkgwMzazlwNeqRWfWjVOzBkAF0Yt3ZEAE3Nx2qKqjAM0voW2HRASBXYx2RQcFi%2FIO4RABAMPu1EC5FzdV9NPjogLk1YXFn9yAEuJrps6AZB3fTYvCBcgNNoHCDZXBoeafggGQAIOjBAj2mGZjvvoqDkaAMalSDEl5nYKhCedK8HlACREQUCm9%2BjvHHVAuQLhmCBXNNQZKAVoRNURiRALMNCgU3NrUSPwQhDeJBDaTCRSXXuSJcKwIbh8xiNECm%2BR8zcIJm8ikA1%2FFBI3EhquqEycgPoURM3ASOjcqid13LkoiRuDtTjzVETeewQRNz18RyqiRvh9BoEETerBz33ly32JgQuO7cqolfcR96DmvuaWVwrmuuBJoqhMkSvMtvb4KjpsuoPFQdAucNqlF7b2ijKK6bb%2B%2FRRV7b36iqiLW3M0pRYXe3KKtbfQbKC1vqD7W%2B9BYXCJp%2BYKKoLqcGQyUVtvpyJ%2BKC4udgeqzVUF7kzT8UDi53cNPigplL%2BW6VTj1HPtRQP9QPa%2FYGsoHF8hy7nr5oKG%2BAz8tKA5kNUnb2CCgunpyoHyoNpUoIu0h%2BNuVaQzvFOqDWx93xRDZF9izsotEXs1PdPRUEXOHkTQ6qUHKAXBG9FaDkLWeY8%2BEocXB93NW1ClGegd%2BffCBsyBPn%2BCDZVggoMbg9oiGhA2bsMnNQ6gxLg5DHXslDO2s%2B2qVRDMdCaslAcSx0EaylQ4uD1BmT1SqF1xE7OwNUQzkS3sUqg4HQCLhwlQ2Q3c6Hr0RQfafwSoI4oN57JVAXWgEwwqyqDDkwWrp59FKrC05Eg7%2BKVGbEAVHilGkfMxJb5bde6Kzi1311EVTnBeXcAUBPHVBiagFruCgBdgHcmnxSoMtB4aiVRd9Sgzk1IHd0CgmvDjSOUQSSS9WEjUJRgfeKlFBmks9UqMYl6UFEqi8UYtrM9EAiBtLMlQdnPwSgEiguYvR39mSjEiBDUKVQBiCeW9ilRnBDCXqyUAk%2F4X4PXdKDlMxu1JSqDl30FD1SgZyHdAHDOTRy%2FKVAJHyiIiUqgCKNXRKjOTbSu%2BqVQN7C0P3fREDIXFw5aiKGY6MqgF3G1uh12QBzuzz8KFADcKAdiFaBkG0nXRKBddo7UbVSgC5gBL7JQuREnSs7pQt1JltD9quMjO0mI9pUKXggdVakbKu%2B6VYTKmwepUoU%2BprR6EKiZLyI4JQKbmBPEP5q0Ib2FTw6UTNwJMj7igmb3LAPOvkqFuJkulCXXgMw7IhDfI%2FDyQSN7ZHwKojdewarbKold6g3%2BxBM3Rv5oI3XM4Bd5CtRzm7o6tEjfI02QRuvd211RELrhQFtm4Vohdd3VVz33DfslRC64B5nZWolnz7Og84EKovZeISK6bTTyWRe24EQaoq1twfdQXtvcxpCRV7b94OqguLq0PKIsLnIUVS2%2FkNuguLxBBHI0UgsLoo%2FUoKC6hZ9lFUtvoxdggsLxEztXRRVAdjOh0QUF7NEbBBQHwCgLyGr7e9FUFwA21I4QOLgDz8KoKfUoQHOpCkDA03ZkDggiYQEXA8bHokD5NUu9Ad1BQXblzoygwugVejmoVDOwklgKoC4M0Iq%2BiILh58N0WtwS5ZwgzwBQGSUDEvUxsfNA4voAWhwFFEXFqto9aKozvd49UURcDLtxuiMGcMXbQcIGe5o13UUQTVi7R7QgxuFBroffCQaCK5ceSIPMA7OimdyZnVtYUAfUBVBdjOsvqFFFxX8zxvEoNlqWGz6eSAuJ2KBXHzGm569VQQ4YO5IjhAXEfM0nVQZ3cC4M71VDEmQ46eagWKtFSXVBBpM08FBpoS77oNJYv0JLIBOTO7aKg8SNj5KDaSWgh%2FegGRaC%2B%2BkDdVBd2IuIGiijlO7eKAGWYuAOEAg6iBLboNkKguIbSUAd7iduXQHK0BmYeXdAou3G%2Fi6DZ1faQ2qqNbdRqCQTUplRFwLb8e2qgQXtrTWOisRi0AGpnfZFbIS9NUgAIuBaJnWU5gAajrHgkAe6rxLN96oBIgRaZd0QMpI2FWQMbtPBlFI7V6Ame6qFJBapb4dEAJDyHNtEGclhTcBAjhoZzt7BAQe4iUKWAQPGK6IgEgww6fdCAEh%2Bu3j5osBwARI20QIbpc3TodECm4EEs43okC5B23oVQl14diWqgBuDIIm%2FaN9a9FYFJBcmW3QI9D4klEKbwJJZ0hUzeC3NFYIm7XfTp4IiZuIG5KonddLAsYJRU7i4L%2B3iiJXXAQINRvsqiJv0PbZII3XipLbBUSNwL7IIG4gEP3V50SuLcsioXXb9FRz3XB2HsERG64NWlVRz3XUYzurhEckHm23k60WmV7biWe7RRV7bzvRIrot9Q7tupB0W3neAoK23kaoL2%2BoYmtCKKRpa31DXLSgUFhfuURcXdSVFUzP3oK2%2BoQWeKBBYeoZnuFBUXnUxogoLzvEsotVFxiS5qUFB6hIIBnR9eykU31DLFyzwiK53dZkoqn1CaHhSB86dUDC7Is8EIGzJivaPNFpheXckSfdwge31C7gxSNtFBQepc7kuKMUDC44mWIQE3khn%2BKBxdcB%2BZpUB%2BoaAjmHSBhcNTOoQHK5vzA7goQwIIlh23SkM9WuqdN0B%2BZ%2BEAycNyzQgwvLTDiZ0QHIvV0BzuZnbogP1KtAQHMt%2BYF6nRA2ZAkyJMIALmdoZygY3NAJfQoMLi5uccoMC1CH1HxQEXFqlpLkoCLjNr9R70ByuLtBNSFFDK4O5cH4oNlcAzDV0QRfcwDzsitk5mKP0QNlDEtFVAMiJLknTRVC5kEBteNEgbOTEakwkUAWMFnDx7kByrIfaI2Ugz1kF36qg5E9FBsneQW8fBAuRLE1NFRjcz13NKINlrVvggIvJL8VSAC81Hc6cpAc7gWhmhIFF2LkCTqiBmXY66MPPxVgIvuIqQdWHXqpBhdcwZwHdigDmJI4Z9FRnIjIOKOg2RqJmGZRQyJdpDCPgqhcySSaVH3INncHLkPNH7IBmRJvHKKGRdzDs6IXMw4g1DaaIML7gILgGjIA9zBzWoLeaDAlm2qyDZEjadPwQAlxWkM6DfUgYl0C5l5IcCRCBc2Z7hugXO4vID18EAN5g5bwkC5EPKBDeZaHOoVCi81yjRkyE%2BpcSS8GhQTNzlgXdUA3k1JbnVApJH8TDZKhD6jNvq26QqZ9S5g5bZmdWBTfcAPbwQTPqefmiJn1CJy3Vgmb7mm7vRBM%2BoXI9yFSN50LblVE7rz03%2B9BG71bvaisErry4kxqgldfqNIQRuv8VURu9QjWEVE33KohdfV0EbrzR4VRz3XnfyVELryXD9FRHIv8dUR59ty1lF7bt67KKvbf24UFrbj1RV7b%2BWhQdFt%2FlopBa2%2FYu%2BikVa26jd0Frb534UVYXyBXWqQWF%2B5fhQVyhwQOUFLb4r30QUtvYzFOiCtt53DPBUFh6lJ0dlIHFw1ZtUWqAkSKIGF%2Bh9nRVcwdZ0dQOL6seUD5Unuge31JclgpBQE8e5QMLgXGo0VBfo2oRTZFo9vFA4vJ1aVIGz53Y8oCLyw23QO7iZ2ZARcTUhzHdIDk8abaJA4uY9VATeQ8MBsimF%2BLCUQcrqjXyQHIGof4IMLgHdyftQMQDMB4dBgHcvHgg2g0ZhugaXh6qKXLSrCaEqoJIo4ZobzQFzQEG7dAHd%2Flrt7bINlq2roHzcP3qorZmRoBThUFy4nqiNMHx0KAi94AgeSg2RdneXNfbRVQNx1IaqIOWniNUAG7DhKGF00oaqKBurruOiqMSWgCPYIC%2B4oXQK5G25QF6FjB1QZ%2FyiAUAButHxHvQF%2B5NAUUDexFN26og5NDdkUCTDOQ%2FsUQM3JlyPJFDIjffr4IgOWY0CDZGDQiHqgDnQQ2nkgzkyPfCAOWaST2QEw5csdlAHDw44pwqBUMIf7GZAfyuW2p1RQyOzNQIgZVj7ZQDJgC3RpQA3mNW9qKKXIlnAYvJlVAN0cawgQ3R8xfqqAbrnBFPZ0gV2IamroFN7u1N0AzrudTr7kCZVjsKIFyNRuwPVUI5lvlq7ogG7l6QKoUmcc1lIFuvAGgGzpAhuMsfFUIboApWiBLrmER04QSuv0VQmTjcIJm%2BpBdEpDfNegQSuvAeqoldcX25%2BCCV16ondcxDmUEieyCN18wa7KwRuv%2B1BI3M502VRG68pEc917l1oQvv8lRG66r%2BKIjdcyCOU1lVHCC9DKtVUXtXdEdFt%2F4KKvbe%2FZQVtu1B7IL23wfMKKtbdMIL237dlkWF6iqW3KiwvLg8qKuLxuygpbe48KIKZCATXRA9t9PBBUXmJEQSoKi%2Bal2hBQXnbzUFcx32RTC6YrUoHyL8UZ0Di%2BstOzMop8g8xow2ogYepNWejhEUFzM8j4qKf6mrkhqpA%2F1BUwaBARdGoNIQNlV9aNFNEoLkayBKKYXXUqDVAx9QBuKbypAc31L7jZA4v1p1QNnt1aiA5vUO3vQEXAw4fUH2CA5xXuNFA2YFYBpogIvodUBzYE7Ul0BF7gEeNaoGy3Pf8FFbNydkQR6gkx4hUAlpM%2BdEByDwEBBFXbsoMDk4neY9mVGe0EOWfdBnDSYKAns4KgM0oSae9BnLs51CowOx4IUGfTTRAAS0nnsqGc7vqe6ig5aoLOgORk02BhEDKPtH2qjZHQnpqoM8tl2HiyAFyK1q6o2RpRy9ZGiAvMzIUGLy0ooOCdy6IxL7dEArQgDaqoJNoc8zCgBIlj2Z0o2Qq8VlVWyFsmC6iBbcIoH0TIGZr4KjH1GMmqgUXVkH8KxuqpTeHgjlyiNk3V3dAM7mu9zV3QKbyCJbg68oBnq4A38lQDdzAQDKhpEqBchGWgqFQn1DUxLT5IBdcBqw4p0QLkYYdRxoqA9xl24U5ApuYkmay%2ByqUuZrR6bRygX6ndygX6jO6BDcakoEy2LkVVCZPwzONECG%2Bh1ogS664irKoQ3aHs23ZAh9SfeURM%2BoW5VEjeAKwPwQTuvLxu5LoJG%2Bu5VCG6ZPmgmb%2FNBG6%2FbsNFRG71D2nugkb0ETc3DhVEbrw%2FIVRG655Mkaq8wjf6nkmBC66JVRG69kgjdeqJZoOK25EWFwKiqW3FUWtuCgvbfypBa24aFBW29vcoq9t4%2B5Ba29meikFrbtB3UVUXCJdCqi6NkVW2%2BkzsoKi%2FSr6aIKi%2Bmu6gcXMILIKC7qx2QUF7wCgoLwQON1BQeoNIoSkDi9wzOygpkH6%2FBFNbc%2BrEmUDZkPXcsgceoQz9winF4NWflQPlSfsCAi6rVOn3FA4vAGg26KQPlViYCBxcDp%2BKgOQHQGSgL1Y61VqmN%2FNd1CiLoZ%2Bu6BhdXyCA5liGqgYX8t0QNnIrwSigLhL1FSEQ2TwY2lAchR2N0FARe7Tq6gOYoQJ0KQFyQzQZqimF79tUgGe1ddUgJ9Rm2SDZgzrPTukQRedex9nRRyAL6DpyoCbyRNCzQgw9RueIqg2T6SDRVBzIcuGMeCigLwXL9w9FUH6jksYCK2etEGy3rp%2BCIJvFY4UUBfAdnpsqjZM%2BrBBjcWYnuoNmKQPhyqoG9oo77%2BKI31KAGtaIoi4%2FNJIOigGWmpmNUC5B4pUuqC9p43DqBc5dwW3oqNmd%2BERjfqO5bZIoZcEvUMiBlEkRL1SAPJLhyWPVADcHkyOFQLi5fbRMDZAPNHl0UDfQ7KBfqfNEDUKoB9SheqKXMVB096IBviuvdAjxNWY91RjcwEPSQgBu4rCgXNme5viqhTc9Ke%2FhAv1GhzyUgQ36CvG%2FdIFN2gL9S6oXIAoEN8NSY6KwIbxpXhAh9R%2Flp18EiUhut1OqFKb2l35QJd6lZkHoiJ3XhhLvAVxgTu9RtezoJm4CQWVCZa71LIJm4O7uQyCd14Vgkb6zzKCV1%2FbR3QSuuqdd1RI3BETu9QTqRokELr6tqqiN16ojdc7z0QRN2%2FZVEbr%2B7qwRuvEpBC65UI44TlRxW3BUWtIUFhcGQOC3IQXtuG6iq23aoLW3DrwoKi7wRVrb1Be24Rwoqovb3uiKi%2BAHUgrbdFUVQXs2hSKoLm8FBUXu24QVF1PIKCgu0egr0QO57IGF7auge2%2Fdmr7FMiovBgyNlA%2BfMGiQOPUkiVA4u5cU8EU2UuNoKFM51A9tEU%2BRjU7oGF40LMaBA2TauRpRA4uEB2ah%2BxQML5JeNvBAwvL8DX3qQMbhV5QML9a6pA2RZQEXwK88oGyFXpVAH1rNSfbZVaJu3JZ%2FghTi7WpUAF24beXVgbJ9e6gObOO%2ByBsg5Lvx0RRFzBhBaWRAygh2eJ1CBhczDwfRFE3hoIfxIRGFwgxygOoYMwZvvQDJ206IGe06t4hQAkFhWZZUE3aExMKAu01I1KoAukS%2B8oM%2Br9dnQYEAkg8M6KwgEOW1RGdy4LAc1QYFnAMjlBif8rSbnAQYkbtLHlBgQ8E%2BxRQdq3ayiM4AaGaiDPEB%2BsoA8HQBy46IBkGoxoEBztrDS%2FLoAboDkBtkUMgKO5UQHakHY0VAyEmp0CDG7YsZQTN1KnzVByllAM9AaUNdFYUMjSv3IA7ULV%2FFEAlzv9miAG7VjGigXLVhq7TVUDPUd%2B6BTedQPgkC5GtTuUCm%2FlmgTurAmQLAnRApv8pCoU3tSen3IFN8gIEc11bVEKS1NWhApuAeWJ1QIfUL%2FABREzcKEto6sCG4Eb8oJm9jwdVRM3OOqBTcZ0mOiBMx3CCZvMh%2BjqwSuvl9kwJm%2BuvKQSNwI3V5ghu%2B8IlSuuhiUEbvU%2B5WIjdfXzVgjde78IJG51SpXXSiI3XOghdfKsEiSa0VRO66uqCb%2FADIrhB5VRUXcoLW3U96gtbcoqgO0qiguRFrbwoq1t%2FioKi4HWlUFbb29zKLVbb0FRd5ILW3w1VBYX0HmopxcPBBQXS%2BpRVLb5rRQUF%2BlSB7kFReDL0UD56%2BCBxc%2BwdKKZH70DC7V2ZQPbfTVUPmN%2FbsoHF4dhEdUD57kcEKBxfV44RTZCJogYEVoaIUz0cTygYX9jsopheANxv8AiqCLw4Y0dA%2BYkcQFICLrqk16oGF43GjIGyepf%2FCoDmw7oGyB6%2FagOes1%2B1Aw9QTqdQpBsgzEPqUDZPL9OqAgwHNUABNSRyEBcTQdKpVbJn1hUog0lwEAF2wLmoQpgXr2JUGzBnQUdATczac%2BaDZFifAfg6A5MBABKAZaTRggYXggMYbXZIBnz0BQEX0makfFBhe4YgEbIBmCZLvQMyA5g6sDogU3MQxjZvigIvihHCQbJoBZAuZFDrqXVGNzsCRyPxUGylvBBsncjug2XLNsgGXgKsgAuO7lkKGTawNSFSs4hqEqDZQJ7BELkIPmqAS4OjFo2UGPqNwEgxuLN7SgQ3kjY6KgZh9xoUCm5n2KBTfUvUCFQMoIfglApvEkHwQKSB4wgXPsQqBmTXp2UCv%2BCqENwcuS40QpTcJNSUCm%2BrVRC5aP0KBDfXrKoTMUJdBP6jvzUqhTdXVBPKo0p4oEN5DZHugU3sHeuqCZvYTTUoJm%2FwC5USN7jZBM3Pr1KoQ31colTuvG%2FRBG71HoqiRvVgldeBTsgjkS6BDcByiI3XOqI3XqiF13dVEyWQTuueiCN1xZ0VN9XVRxi5%2FtRFAUVUXKKsL4QVF50UFRc%2FCBxcR0RFbbqaoqwvKgrbfo7qCoukNCCgvLToirW3qB7b9EFhfDarKqW38oKC9BQXS7qKcXvXRBQXvrATmFMwJKCgv13UgcXt96BxdDu2qBhdVA4uNOyBh6nNKlQOL%2BWmUD5pA2T0L7uophe0v0QOLq6bnXZAwveD0ZAXAMSgYFyOJQo5EEBxPiiiLyDWEDm%2FV%2BFAfqQ79GVBzqBrHRQMLzDmXkhINmT2qBukD5HQvOygObfagOZpM0YoAb36BUPmLQS9BXooNk9D1KBsywkg6GqDfU2kjR0gOb3CWGiDZ6aNRAc3%2BIKDH1GqWmqQbLvKQNkDXwUgwIaZ1ZIAbiHYqjfU3LJCsbngdEGytI9wdBnkbBpQHINAPQqQDIt7grAMndmFDyyQA3tQuduEgbL3uoBm7iK6KwA%2BoxDpAPqNDhjqgGfNdUAzFCxBpVBvqEVKBcyXPYFAMjMvcgzjwpWEAyIFYAZAubaz1VgGQPxSBTe8wYd9kgBvakE6oFzI44QDLzqqFN2phlACeYVQMg9eGQoG8DXzQIfUoN%2ByBDe%2BuqBTcaaIhTewLTurAhv%2FBApvPdFTyM1mIVQhI1KBchPzQ9ECm%2FSiCZvcmqQIfUZ%2Fegmbup1VCG8s57oJm7sFRM3%2BKJUjfyqJm9666IJ3Xz0SCV1%2BmisRK65UTNyIldfygkbueFRE38pBI3EmqoS65kErrkEbr1RG650QjyqOIXeK0KW30UyLW3pkVF1FlVBcVRQXwoqttyCou8VEiguQUF1PIoVUXfeiq23%2BepUFRe4HKkFBfxKCguoyLVLb9VMqpb6m%2BmqQUF%2BtFBQXnpNEgoL9SzoHy5bZRTi5m8UFBefBA49SdkDi8791BQX8dEBFw02olDC59eyB8jLS2igIvZthqVQ4vMVhRT%2FU7bIgj1Nan7UgcX1UgbI6mlEU2Z9t0BF5nUGqBs2D6lAchImEDZQ%2FKgOQ%2BKFEXFhQgqqwJfuoDmfJUNm3bhQbOm4D9EDD1G6hAc9kBPqeSQbNj3bVIDmB3080gAvfbnlIGzPQJAXgCdqqDG4kHTsrBhfseyg2Uma6fag2f%2BUOUgOTbxQ%2FakAyuq8ahBvqamldEhWzbVgKQkBF0BkAzq0b8INnMk%2FY6sGNxLSRukAzhyTKQA3MY2o6A5PqVAuerUoOqsGF7aUglIBmQweldEAPqDdtHSAfUOzjVAM%2FDQAIBkdCzIFF1NBV1RsjrqoUhuapNvO6qVsmBINd3QrG4MdFAp9SO0qhTfQ6oFN5ADEg%2BKIU3B0UuYoNKqwL9TVIFN4EVHX70QmfLcfagU3wZgvRULdcZ5TAXKJPcIFzAoXRSm9n9qohTeJ96Kmb3REzfu%2FBqqEN0l%2FFAmb8oEN%2ByIkb37KiZ9SKsgnddXfdUIbuSgmbvLRVKmb6gIJXX%2BCRErr9lRI3%2BSombtaIiZuQSN3EoJm9VUjegkbifsVRM3BBK69ETzmqo5AVRUXIHF1PeoKi8JBYXKQOCiqW3IKC77lBYXqKoLtXRFBdygcXIK237aqZVS2%2F70FRf%2BKgpbed%2FFBQXjwRacXa%2BaBxf06KKoPVivVIKW3xVlBQX%2BXvSBxfvRQOLtaIHyoQYJRTfUP2pBT6jtNVAReOQ1UFBdzUSimF6IYXg9tEDi5qHpsoo5btyqgi5mksCgYXw71UDC9zuQgb6lfIoG%2BpzOiRRzcdNkgYXAto0hEMLiorC96RzQqob6laB9H1UUc36IDnQ%2FBAcw1Q2qAi8MHkoDluZ0QbIMz9kKwLOH6IUciRVrkBBYMCGQHI7wotE3yeKoBkYadEByIAMcngINlLQgwvu4CDZnXxQbMuAD1lAMrqvzCoORp5qAZND1QF4%2BCAZVDV2hBsgYq1AqBlcX7Qd0ShkdT1QrZ6dki1stT4olbJQoZCYd6iFQMxv1QA3hnE6oB9Rojp9qAZuw8AQg31GMmSgXMBtTqgQ%2BrWWCsRvqaeSQKb2LkDqigfUEbV6IFzk68IhMzwNmQDOunRULk%2FfRRSuxOiqAbxv3UC56eaqlN%2BtAiEN25HOqBTeKbopDezz5qoQ36pAmTPPUoFN3fmEEzeDGuqqFN%2FLtRSCRvfnzVCG%2FlBM38qwIb9URM3tqqlTN9UE7r5rTRMYErr9aKid1%2FKCZv7KwTN34oiZubVBM37VVVM3pBE3OqhCVBM3KokbpQSNyoTJUcwLohnQVFyiqC5BQXqCttyCguBUVQXMgoL0VQXIKC9QUF2yiQ4uVooLlKp7b2AbTRBS2%2FfwQUF1N1BQXs2qUUtvdn1UVQX8vuED5nZFOL%2BXUDi%2FzQUFw35KBxfO%2FCgcX7w%2BqBxfALdQgYXE6simFzIGzYbclA4vrKBhfQKBhdPWnZA9t8QwGuzKKbPempKIOTopspd%2ByVByAFXZFNkZNEqALw0E9O6obJi7zqophe0xwgJv69UQTfHvSqb6gG8BQH6hPXVOQN9QbRugOYavJQDKXLHl5QEXjQk6bogm8hgJhFHIPVygw9SjeOqBs4r0UC5VMDchUEepSS40dAc3l%2FbupQR6h4YoALywb2ZKDmdISjZlya7IMbyAPigGcTU0lBs67jlAM6sQSqNmYHLBAD6mhLmpPRBsz20Cg2ZVAN4DOZ0HCAZgkz1lAueSIOaKXN9eycgGaBR6gI381QPqN8UQBfFZRSm%2FUSCgXIQ26qAbieqlAJDMS6tGNwOp56KUKbxFQ2qoGZOrTKilN4KIX6mjsqpDeAPgiEN408VQpvL1pooFyJ1V5AhuBk12QA3gMiEN5nVAhvndAhv4VEz6joJm%2FtogQ3nRUIb90SkN6tRM3oJm8boJm9UTN78oEN3KCZu28UqENypEzfyipG5UTN6CZLoiZuRE7r1RI3coJm77gqJm5UI%2FKg5wVUUFygZA%2BUJFUF1FA4u%2FFUVtuUzgVFyiqAoGFxCCgvBUVQXcoKC4b9lBQXcpA4uoiHF33oHFyiqC%2Bkud0Di%2BsugoLqSoKC8tVA4vetUU4v581CnFze90U4u%2B8IG%2BpRIKD1KbCrpA2YCgoL2FUDC%2BRrypA2T0qEDC7lkU2XvhA2fKAi6vmgcXs%2FKimF6IOcmaIGF4qPBkDD1BR6QUimzUGzp5lVBFwp4Iovs8ICDz4INlsQdkDC4tuyg2bbxoiNnAnx4RRyNXZ6jlAcueiDZRWiA5w7g8FARe%2BqAZy2T7h0Bzn3ygw9TR2O3CA%2FUJbVIjZ7l3oisb%2FAMAg2ZFUBy5YIFzfUazsg31K68IDnz5oB9R4eQgxvO7IEzViDmVIrG47sgGfikAz7uYViBlR%2FJRWyZgGA0KAZWjWNFQDcTqeQg2dW7FAM66bpAuew6JAue%2FvQKb9awg2Y3ZAhuHHKqFPqAcdEgU36SWCQLn2QDPlkKQ3D7VShmygTPdVCm9izoFzr5ugnmOh3VCm%2FugQ3%2BVEEzd7tVUKbncOhSG9pQTN%2FwBqIQ3oJm8VVCG%2FaEEyeVQhu5QIbiiJkosIb9kgmbpq6omb0EyXZVCZAIJm9ESN0KiZPZUIboUEyXVwEJRMly47oOcOqHBKZDgnlQUdAwKKcE8oKAnYqClpKCgJmCyCgJ2KinHgUDgnZFPaTsgqCdAoHBOxUFASdEDgnYqIcEzBCoZzsop3u2PKCgN2xQODcNDygoDdsfgoHBuGjhA4uNGoopgTVigZzs6BgTEFFUBu2fZAwuu%2FwlA2R2QODdDA8qBgbtigYG4aE7oHBu0HVQEkxCKYE7VQF7pgoCCeaoC91GKBwb5a3uii9wqCdnQFzEFEF%2BPJA73agqKz3ag8IjEl5DnR1Q73MYUUAb5g90Q2V2x6IrPdsUQSSzEP7dUVnumJ7ojPxCAudB02RWc62lBnZ6xxwgznQRqOEQXLMxRWc7FQB3o46bKozn70UX2B6hQBzt%2BCqA5aiDORpVBgbtujIASa3AtsUVnuFAeEGyuMAFtUAJueiAE3bEnRAHucBkAe7YoA921yBXuYwiA5Gh8FRsrqsZUikN10QfB1QCTsW1qiFOT0lADlFUCvc8glAHOgKBSbho6IV7tBHCoBN2yBCbnoe6Bcrpg%2BCBCbnoVQhN2oIKBCbmoUCudvJEKSdkCG4iGJ7KhCTsiFJOxRU3uahbogQm%2FYqokSdpTAVzsqEJOxKIUk6COFBNzsqpCTMFBMk7FUTJOgKqEJOqKQlEISZgoJEnZVEyTsUCEnbuipknY9VUIXQITwiEJPLoFnlUf%2F2Q%3D%3D%22%3E%0A%20%20%20%20%3C%2Fdiv%3E%0A%20%20%20%20%3Cdiv%20class%3D%22position%2Drelative%20d%2Dblock%20my%2D0%20mx%2Dauto%20overflow%2Dhidden%22%20style%3D%22width%3A%20940px%3B%20height%3A%20370px%3B%20clear%3A%20both%22%3E%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22404%20%26ldquo%3BThis%20is%20not%20the%20web%20page%20you%20are%20looking%20for%26rdquo%3B%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dxrange%3D%2220%22%20data%2Dyrange%3D%2210%22%20height%3D%22249%22%20width%3D%22271%22%20style%3D%22z%2Dindex%3A%2010%3B%20left%3A%2072px%3B%20top%3A%2072px%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAAQ8AAAD5CAMAAAAOTUC8AAAAA3NCSVQICAjb4U%2FgAAABDlBMVEX%2F%2F%2F%2FMzMzFxcUAAAC2traTk5MAAADW1tbMzMy7u7uvr69mZmZUVFROTk4AAADW1tbMzMyZmZlCQkLW1tZra2tmZmbW1tbFxcWvr6%2BFhYXe3t7W1ta2traZmZne3t7W1tbFxcWlpaXe3t62travr6%2Fm5ube3t7MzMzFxcW7u7vm5ube3t7MzMzv7%2B%2Fm5ube3t7W1tbv7%2B%2Fm5ube3t739%2Ffx9Pbv8vTv7%2B%2Fm5ub%2F%2F%2F%2F39%2Ffx9Pbv8vTv7%2B%2Fj6e3i6Ozf5ejV3%2BTU3uHR2%2BDH1NvG09nF0de6ydK6ydG3xs%2BsvcedtL6RqLWEna10lKVpipxmiZxbgJNafpRQdYxKc4tCa4M9aoM2YnsyYXowXXjFq0N%2FAAAAWnRSTlMAERERIiIiMzMzMzMzMzNEREREVVVVZmZmZnd3d3eIiIiImZmZqqqqqqq7u7vMzMzM3d3d7u7u7u7%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F9H2B9VAAAACXBIWXMAAAsSAAALEgHS3X78AAAAHHRFWHRTb2Z0d2FyZQBBZG9iZSBGaXJld29ya3MgQ1M0BrLToAAAIABJREFUeJztXY1jE7eSTx53vNwX3OGWuxcO7siDd7xcoYQXrpVCaQNrB%2Bw4MSHx7v7%2F%2F8hp9DkzGq29tgm0RS3Yu5Y0Mz%2FNjEbS7LK19dnKYLAXy2Dw%2Bfj4AsrOg6cvtdbKFv%2Fx8tmDnc%2FNV6%2FymLDvv64gws7eIe8olP%2FbW6G%2FxypjbCW%2B%2BpZD7WhqnWgf9O5l8Cy21hIkT3tbzmGCQ4cu%2B%2FPVuwwi99r9gY9Ht2716mTnWRxIjoUO9571G9tBrh26N18rlH1JgDu3bvbp48EhapwpR0BEP1iBL03%2B9ORrlRLNxf8H5fmtWzeW72H7wLOeGYpm3w%2B2e%2FCF2gfN7cfXSmXXEyQD%2B7CPWt4%2BwLohuA507%2BB2L75Md9ir9eNrtfJU4PuHWz3U8vahb4jVQ2d9%2BnL0r0t2%2B0zooBdfq5VtBoel%2Fl0Ptdw51JnYNABhv%2F3j0nzx9roPXyuWByorWn27vFpuH3TrAwnOrAL9%2BPd9%2BCLd9eBr1cLFsRz3UMunSerglMmNBEWMcb5fni%2BK8jWYyw4dBvfRY5LfFbQrVxJ2%2Fefl%2BMrc0TUEH3uSHMtP8ttoUoxWzidZ9MVNY%2Fqfe%2FCFsLym4MMTjXR7TPIhlkNTi9bcTMLkEyvq5wv7T%2FFdWgNcQ%2FBxOxLz2gn8Lz%2FJ31aCfZBARituLPbqTws7FsKYawg%2B9tMwRDF6eK3o9DS1Eio8vvS68mIBhX2hm2vwpkktEeHlJ%2Fkd2pIG13QhE%2B3Jf3zTTeIwjz16BUUrlrsqmr6OIvxpabVko5hkf%2FHk%2Fv1v79y%2F%2F9fvj5SSVEc%2F7xzquxKUy%2FO1cnlKCLq%2Flw8%2Btg8Rz0gFnpuwKZQ7T45yZQGI7nT1%2FAzVDA37BEUrlm3NldqUvy6tlruspXcOfwIcbt68YXq5cePGzW9%2BjMqHqz%2FqEG471kLr7uX5WrlkwRSQX36Sf0YbIjhID%2F%2F0o9MIOul836H8u7jX%2FnytXA7oxGgvvl96GLbFSAzgYB38wxHHHMqdMpkDaly21fJ8rVx2sjFQfSb5XWlR%2B10OB6zNUIwWLKdsMHjaiuUago89skTw6r6819rH2hGizzviMB4KA%2F68KN8erhYwvIbg46Wgxj0m%2BbD9jZwybFBIbD%2BgAvrwqkToJdHb3nytWm4nU4kTol5%2BkidaHYaxsEGxjSEPa51vCwN%2Bm651bMMefK1c9oli9A0%2B8tnWfBSbH8RqSdRHBQlJlHd9wQeO1eMKtMck%2F1jl5bvSKD5gJqCtbS3kK5ZrCD5YTOzKt8sPwwFu6dvfLzUfUELWEF7IIt5VPBIz37759OrxFOPgl%2BV9JvlDtC4Jq%2FpyzMT0w17KlZ9FxFLNawg%2BtnMGe23ISfvfP5TZ9tu0eC5SdyQ82H6%2Fw%2FwaNgp306SARmx5tRyEYQxe0vz%2FtzLbz%2FgSxjS4L9WW1hDXEXxk%2B%2Bqq3ynlXcqx%2FXhSxmOP66LB8aFU%2BwAPku7P14plBwkTS59Jfg839d%2BelIcxTjDI%2Fz4RpNzJuDLAXUPw8YDRBbXvtSG3F6RDrBenF2NeKPgIUZaExwOMmQ8Tr2WjUDPuVM9JnqxBfWddeKis6L8J1V%2ByRZHuy9dq5XYkGuNFmORvUd7TmOY9HPCFsQJ7K%2FK9w4wA%2FhLwuE3sxP0fFwGDbD4U%2BFqt4OAyrMHjJE%2FH0oIm4IH4DqVrHJXiu4aSfjxmCEPJ%2BELT%2FIbg2DrERho2JILXQngEDckdGoNMu1plPIRcCCEgO4xVUqgi8aUixY3AcTdKkfy9jsHlAJPUfuRlPOhIdnHH68JVhsdd9HPc5UZ8kSAGMNsQHvtUFEskTfJ4HLyCCHjkxtyJR4w1u%2BqnpW3yp4wvehiwGTy2GV%2B27%2Fuxbz4X2N2pDI%2F4K%2FYfZZq5O83rbwcY8BEw5YsGahvCYzeQRXijSX6QhdYL%2FIcvP3ZxdxDDWF3EYzfhq8M6APNFIx4t6u0qhe9fw7z2JDnDAVFJZ%2BkSHpragFnAd%2BKRaIWvvP6BUnwgFOGLMC3r7Qplhw2T%2FfJN6nqQD5OEBw%2Fn1IuuMPJAcKis1xCjJMg0SZFieMjjtEKhsbqj%2FgLFxIPkzTwoXfaSpFyEB5JD1Dq865wwRnyF4CChtRE8UF54HGC8wzAIaCT%2BcrrITsKfJfEo9nqIfsqCD8SXKvawUrnNaZLgYyvoh14Wj8jkMnh09Hobj4L23onwRdRWbwqPvwimT3YYwlZP5zgwTOHrj0vph0ry0F7%2FgrANcxHnizv6TeAh5Zrcxx3zdUJXPBamRStAFx5p0Esoo0cCgtvK%2BSJmupH59i4TFgjTHYZBik0Cd0vEH1qIvzM8FJlwSa93SWdZULSVxYkbml%2F2M5D5aeAAjbuv1jHfpjHvjAZyWZg0hC9fcr5Q683gsU1lcFffkH6xveiSXrLAeaE1a9Kp%2B4br5%2Fv9mudnD3BzvSE8dvkYqOw0cMC4EukeaLLMWLj6FpLISDy7i%2BnpIl90kbEBPKTnutjxxgANoirRTcdzqfKfytzR028nDzmeeEb6c984Xzmka%2BPBc02ySX5L3Oss4IGy9k1kLx%2BokD5TTKzofmHiCxmiwBfL21wbD5qJ4Qo%2F3qDzWoHuHhlJV%2B6X98cGvK7S5HjiAV8cSnxprtnrr%2BcOkrVEqHkqEo7X%2FZGygAdHVckHKkFeVE3H6gmPA7Ss8bSzvHG27t5EPHZbZUNv%2BHryP3u44AQMHaq4n9ITo7sItFD3uzIeeyo6mqgpjxIeaF89kZX5wgQFvvqVxyhGxyevufePzKPZTan0TPEgyRWbdCxgntKZWbmgOFZ%2FzOQURs2xzG4HLV71LQE4Vs%2BfDsXiyZ%2F%2FESXYZr9bh1rGgz3uZNvdSep0qPo%2BERB%2FArqIr36lRCbjQHyoR2OPKT2BXEoJ84R1%2BqOtM7xBfu6EIovVCPkOT96NR%2FJI2Dex4BFTQxv%2FmswgByR0cpXEE3soA%2BLE3QUOx7CIJOBiSBAcksHqlfEQhkBCvqQ%2BiO5jUl37GbJA9zGerHxf31E8JLLSY4q5B1GdM303HpqQovMbBqOgPYjubmAvaY8xgQJbB7xPpfD0EswpfxCC8sPQ2QAepMuC9hGuKXuILsvUcJ0%2BlB0ImU6js8F4RJn5TkOGTF70mniQrsQpJiXCJoPI%2FFZ8Lhs5%2BxeywezHnpNMJNmsJC%2Bf5Qrsr%2B0%2F8HQlkxI5I3T3cQcBv%2FsSX2KC%2FnMcW3aQlCc6P1Lh1GRt%2FSDemdFCzOC6nO5daTx%2F%2BBeB6gGvB0QfUjxyAw2M4AiSMRfPQzZlL1QiaaahoGG6Ysam%2Bj5nbJ%2B43NAjWbxm5HDNsrW4v9fxH3xGyGaTyIUwIzC6T8UZ4fu%2Fy%2BCQZgSaYour9NNYd72efmRictiliSenezf73aq03sUU75LEzqT5dPFK%2BSqrBIUllY3YC%2BIxV2iRATYOh3iIUIvD%2FQeDwfbWYLC7%2F1Lx4nuiW4ES3cCSsDGZlU3gQUe%2BAASuojkee7yFSj5Psz%2BsPKF7PWm2EHhYQpXXi8dSeCFNZoqohEJ8cj%2BO3%2B5Q4liYWgCzO3QnR%2BAh3llm1DY0vyxSCcUHiNHdU1oENcvzYvQg2%2BRmB18l%2ForrmVXx2Nq6tbjcz%2FlKPxK62yFGzbUtgSHJeSfb6FueLxyMFfj6hHg4cUp0HySN6rHagIxjvtBZki%2FW5%2Fp4LFEGSTcT3ULdbN8rAtGBzotbK%2B0D53nCm8o%2FXUBXUyNVHefoOymiYGGT8FoY36f%2BdrXhHJBNiu5x2mQZUMGU6jrnIMfyGMTyfvXDFZ9X4OcN14gHV%2FYOuv%2BV0CPBWXHL79Fq1sLOyfTCE%2BONlQGm6ETrovu%2FUWbBZeSm93xl5zdIbIU%2BrxMPLFcn3f9m2RMZIlhnHq0%2BFwxoZ9doL9nuYTfd%2F8wDrvgdeyFldz1WftgpzyO%2FRjyohAvo%2FtsLUTu8eieTefHtOpEC9qcL%2FfwGywAT1UuNw40%2F%2F1CwGHT1w6P1AqeIRwLkuvSDvVhoCbo3H%2F3QfQrs0FjnwcAsv%2FCLnG9DuXHr4XO%2BRE4fzx%2BuH1UPyNPd1%2Bk%2F6BAvS%2FeGWWI8eZGv8F88ub%2BRNcYgG6brwWN78O%2F3WVmS7o2bRuo79x8%2BieXh%2FTt%2BwXVz7RXX6nytW27ki8ulm968mTe%2BuT4Y6%2FK1JuGs9Gx%2BM5aeTT8pX1%2FL1%2FK1fC1fy9fytXwt11%2Fu7h%2BEJWZajZRKcZuLXPE9L755JHctnKzRRV86ZMrIkZoFKqHawf7dMho74vEI2tdAtzALPfb%2FGO9sWSt2QrkgP5f21fIuRHZd84M%2FFuB4UMpgpL0K28DZjcK5I%2F6qhbucSJI722LJ%2B46Vkf4sl2gv%2F7tMfyHNlstD4AIgHc6rdHUgQ5X3zX9PnHICTE3ERLvA12MBjnuBFB6UkuJ2fco0A%2BeETfI4rkCHCbFOCj%2Bryijey%2BD4w0tcFzfAnQjjLOi9rA1s1GXZSk9oxN%2FJbzq%2F6W8kvaI2LollymH2D3ftyiMkeYLoZviwSpRElyP7l47EXsQOGi%2BEVEaG8Jbjz692OR77GY%2FchRWsv%2BSxsipFb7hikkwar%2BWjAqXEqVyrfY4HMZfrUNGoYh1yMAX8hLP8S45Hltv1K1H0jJXCD5R9nd3heBDYaKOc8yzBFZ1lFxhkPWX6RQwg45k2XyYlO1YkfXKWkhgZHli2JVI4kfT9cvzzWyzHv6CAC%2FrtIimBgdPK4LOEh8hNrocIDUW%2Fdqg0j5RVAkFJQsuCUl1PFpANuxgDsz7juEt4cMxiDwIpFZU1t3bsORYNnswnJUgG4ROtB4v2klDxF7%2BPIFXWDzqiRSeEnQv%2BkQ0AYiy2%2FVI9b44HNwrxIt39jbnd8ny7sK%2FPbeqUclmTWLVuhRTwwJ2jYRV6SSQkNog1%2FFpskK9wEWOfxmFRnohEosIlwyckZZ0rUEHM5ZUoxvpejseXsLAqNtGkHTElolNYu4j1Un3Uitin%2BbjH8PjNrtUE%2FjAXsd97XD%2FkMctMWEeOCSeUjQIYxAPkP6TLAv9YlEzY5NCEEL3AK0b3XoaHQFgLd9M17%2FST7vtSuoIKZJIriX2hlsoA6bMWROJk9WVijLTES5wlllB1vlgpoYkIBtFK%2BNtayGQiYaKGv7s9s3sIDzw2RJm5AL9lyO5h%2FcgnIcoWMZGyGRLOugXnFlq01WRFuR%2Bk7K0Zrt3D8XpZx5j3UGrWtm09yWvJiirJJoOZydvhog0PTTPZrIv2JpOxSBfmIH3TNPbvumnPHR7tBHepG3SDx7mTpm0ECJaKc4eGIhsKR%2Be8qeErtwlyRbGKJDvi3HtkPSfpkKFsgGgtHjX8NdPqdG7wmZCKpsqkoJmAR73qYVNlOk4%2FaGDGgXB6BUOA1U0Ssqy1qTJRwXthvU%2Bsk7jRmYUDVAMAaWZWfMsW8jkNwwPb2KQBmVbzOUOjBlhzz5NSAMnN%2B5x76R%2BQyOvaMmvad6NqalCpqmFbz%2BBHozJUPyaTyUgU2NyozI9F%2F5TrJrHukUEeV58lu4wmyrRS%2FpoE47tDrMKAzreppv9bGzzMHaP0wFgT8KgnCb%2ByPhZMUOAbDyDaPZkwPJCfMpozIf5gIwuMgz90PKpvv74dVQqUHhRXvR2%2BgXvJn37izTKKh7Z%2BystnrHciU1tjs8zAUX6lhq9kRTGMNUkg61%2FN%2F2fWSMDFBD7HH1rrf9vQ68g6Y3vx03TufmtC3zBTXb4%2FMz3N3vvexxe2ysXYNKl8X62nO%2FOO3Y6Fc%2FNNc1Z5PqFl3c6nR1jsfgs9gGMrq8a%2B244mbe1FhP8tGDDjtGO4nrV2sCxsVt7a2pjtorIzNXTy07yGORuECP2f214sts3YEgM9tLXAGKrW%2F%2B4ZOfd0bdzhfDx051tCPABN56%2BSAP0CvoNttH4RXL9OnVrFjVUMYSdEPf%2FZXJ5%2BbJyDfQ1Q2CFsgwm%2FOYeZCfCYthao2mAXuDi9bBMir6GD0LP581q9mV36zlz901nAw1w49YC6V9DyZ6965s4UjSOTqHPtaLUDvdAafQYYIngTHAiA%2F5hW1QiGxPkRN55gVfVkWI18ZUfcmpopxlg%2BjEZVFVyC9j01Z6PhqQtg1MTAOamGI1BHe206fouYA2mP3JWBdWp6mzS%2BpdGOibm%2BMPgka0B2Qdx%2FZi9KBThKrxihtUH0dFVHG%2FZhhwtIbK0ja0BNah6gNLKcwqfR%2BrSqNA0gotG1i65ADXUEGPBxyhGKF14j2t6fBNRP29Si1%2BZTgGOL20pEEHfn55cwqj78sp8wvbQuOHpv9ON88oaOi4vHlLown9OTnyg%2FMGtqJH9QHm%2BA%2FjoZqh8IHXhQCQ9D5ecxxEkXHAQV%2FSrDBd2NcEgvgOeeV6dAwONRW58GWm2b%2B3FTH60v%2FDitUOswcmMb77ezyU%2BxW6W9xVlcVFBDHTUwqqUfpMYu4lTEwaumtvbSXNbWf4xd%2FWAlmgyPHyTsN3TyHcRekmHRTzu%2FNGkKNVIEXQ3%2BI0yCx3M77TTNaWpumwLNqfOG9eXbhHbjpeL6EfxJdKYOEDcQkSS6NbF9J3daMAydwMUFwSH9gzXcgIIhYynsnBfiMq%2FeSr8%2BvbQRA0yCHrxJXfvZZnxmJ472Mno4HVYhAY8QbMCKQON4zA0MWih4jxuRg8mmaechHMlGlhWyUMBwLPdq4OAE7B0dzCPoh44Bq6kdjdjrOJmqhxODV3sSqQXL8yvm5D8a2GHRAZ8w30WCyUSbOrY8mxyn8cylCB%2FE2cJfByTncqnmdBMjxETenyY%2F17R2fXPaxhjUL32sAHZt%2FKpNPtF5IOtHnAVG%2Fai9P609Wc%2B9VRvPQ%2B1stqnt3tTY1KxUr0Qp5Xsm2kHOo1AlhIy1l9YH3Voh8aP6hsVE214NhyYIaJt5HATTtHYuYl6Z3ybBEdrfWzRzm3snxq9OTaWpofAOpDQUpqPhq8DYpen4pDq2pPzU63k4umrrD%2B%2BqkSHxS1L2aJfINzJAmHbwV86KqI7PIfK7PHV3bFTZnB%2BffrTzhb1htHd2bJXYRfLg1Sx6x3Z30TRV4Ze2rl%2F7nk9t%2FDl7C06nraGDyxj6Wifz6speVH6QIF5rG0cS4vqZ48Eq3sSvZ0JIVBpZemH%2BotpB4g9dyAmaOB85cz%2FNWrvGqM7d6sqGX%2FD70BqQ20m7fOXZGbW29sxOoa3behwrHzW7%2BLupZi7Irwx8Vz5cnx9bfsY2CB8GRl5BEAN8zBy01czNZ8DY1G1qOjx6HLFv5XhwzeCQTJwkM%2BXxgIVkM5q5u3bLyDJn7QbE94tM6GZkWYRtE7eYM0H7iQrK7Ncjw5ldiFixf5nOTa359LUnPTxzPXurPgJ%2FPPM81C3wAE2trCdnjo9JbhNIrmzAOR6SQij1m0sDUtKKHz4zPAp8JihIP8z1yuT5z1qpzqVlzj%2FV1qwG8o8q9q0Kux2pliaN3Z8iHuUmcsH4eYHFKl0dELELs6I4LmoTTwNZDrrw6NIrnaTG%2FWZCaMQtZVmTFp9047Xcc5bZUfAfn8d4vwCQBTwIBh1DQ6xDRUZF604VMi0V%2B15Oji7mwt2eE4FoLzr7G0mV9pSQ0Wr0PyYSx6vLqPF46nQn44L4CC7XhvIJCv6Dm9XvJmEqt5cv1rQFabDyruY%2F%2BUB32IvQ1W8%2FJivNL7xDZmaa6iInPHSxO1PQJZZTAteiTek4HpIu5ffELgRyUvyxASbcudPSTEQNSG5Fk37jaIRhYJ4M81IcwwVXSrQX7BwCOfa1s0t3t2rdWhcJy1oHfSX0xD41lb1oolJXUncZ7qQs0I98xZ%2BbXOI5DqF6NQ2bYsibkDbUvUZamvdHe1aRN2aLtFeF1LlYg4nqruX5dn3vD3t9RPSNeP8I4Seb5iU8Ev%2FUikvySOtPvOXMDXmd9WeHmNjfSEzKzBOuC3gIrdhQLIyB8F54cSCxAiG1cASwUpOhSfT8XcGENWnr6yMFy7gI5ArzLWIo9gJf3LlGq3xygbJphk4Txhf2yMNnXPhNRXMd9grdpFPDjtnlqatk89Da5uK9pzm%2BCPkO7cx3aTq%2F8l0qtxFm%2Fh%2FaLcW6GWq7hQbbYFfTn5XbqzR9xi1HDF2GEAWxhAdHmha7N2jkd3uTLRw9wZav9ruIcHt%2B5PSjdrunzUWQpvI3AMgP9qbbGAybvvrUnWFaRM59lzYD5OqVl8PJW8NmLfRj5D2aN35nen7kck8sXo6VKgw8c0lMNHyZz7eisQTXfz6HMZ%2Bp2VVb1%2FOZNp9NMz%2BHXI3W7RW39RRIQo6CFbX2m%2BvKba7bHdV0QFP7VjC4r60Qtg%2FYvTdd%2Bj3yJiRxKLv1Dpv5div%2B%2FFhBHokfG6h0%2BhHUw260w1b9MVOOJeLlkj%2FFbgEb2lHrjogn%2FnNsPo%2BUPbJrJqNhPGwB%2FzEcjdLhCzSHU4BRNXx%2FaUwGro24NnEkHU9CusfUn4bC0fekgiSOeH6jlK%2Frj7i1umrbi2oUDnl0yC0Ag6ZJ09KsKNhOIf5QWYMw6Zy17Zn5BpZuPtWZ%2B4hni6c%2BLnW5Gy6VKKpsONyHTBm4VTc4YTNMSf4YX4dUkdNwTKc8Hg6XZoLxCSlt4VCsaUOuHS2L5oXcXhiWBENtjwKNQry2VnukjmqnJo6f1ynjwgujg3AKg4byJfQv42nAo3VH%2FxE1wAe6bFESB0v0CEec8QiVJudwIDSPdjOkcv3A07j7Rmb%2BV%2Fa43ma6NWNtzUU7IdpLZ%2F5j5fXC4ZESCDEe7mY1vXTW747vm4bVaj%2FG%2FICAh8VO21QRraOexLPehuDBhFiiZPqxcJI%2BA8%2F1wc63Z8pZj3LCNNY%2FTv11TUUPF8GY4BoO0ez8RI7z%2FVBbe3Guchp7cHjYs2F6aDyp3blwSFaK%2FoNFInhBtQweFADJ5YxhajPsnBthXrdNGxIcW5dxMXT1g%2FEbXGqMh5fYasLYTjfzs9amM8SsRYeaTQUAJbyKSRzeBWO%2F4XDRLoNOpfsxKaVvdCf6DyUvhVw5Ak9qBPnFkJ5ZJxLkP5u8waLbXKcJdoZeWYKnND75avw26HhUef9pU83OJscKjzFPMcP%2B1DaufU5I0BudYklSdPgt%2BBV%2FvxyP8dax1ZnVYrCVxn7aMrbhUaIb%2BDORYnKGYbKZwYF9TOvQPnljbMb%2BTWoK13CoTZnwub4jrB%2FOBN2zD5DjqSH288koXbogRfoyHtJkHa%2Bsmrfv1IkNJJ256FcmMPtwYgKBqvo5%2BHvz%2FQw%2FG2RH3sQkACRkS1w17eVJNRqFpA2Iw06qaupn459MIH7x3nQygiQOz4dpczGsxvMwj0Dc8a6q3s39JDS3fYznDXroQpSjsErriD%2F40IRyBHPt3NKO5uK024aKwMdbn4EAl%2FOUVDlpQ677FTQ7a5qwXGkg1jz12Q2wAPBzRuPSAJJoUx%2BdN86v%2BsGxf8Ywz01dvA%2F52y4%2BVUlBcgCCh01Fnm8xFNT8%2FAzTgMuHyOBMhS6nXhhgflS7rBCYMd%2Bk3iAPz96%2Fspwez13OCPxdD0030wBI64W34X0Q3XZzNPcwe3uxTPiYHiq8%2BuABgdujyFwORGGTMsODzC5K3AMGwzZLUsiwR5GBOjlzkgEerZfsYnIUW7uMZeMA4s3jM48I2JHt2SePhOy0d2dOoSaxC%2FUaUkIuU3K4Hn8AdbgYe%2F6OpmaN83Fi10%2BVSsMb4wg03pnWCPaC97EoNnknmvWo0zlNPiAqOdniXG5vhew0TC9jxK1T4h0edvowSie2ctPg%2FsD%2BVfSnpLbYFH1Q%2F5stCsJ3kmypRd60j04ErEjtJnvIVRoCOfKSReuYX3RWX55wuNzCaOOvmgQj4Qfu5%2FVF45Z54XfSoSf03qccpl7QQDGl5cOH72dwSfHYupvr1NTQrxEP4sgSrbdmbh2eNXUzztsGmV7BnD6eQ5AswZ8MWdIwYsrcgor2IiG6AUVx%2B0EfTwuWAE8r%2Bkn6IjTC%2FHvYR34DzZlLFkSsqyiy%2FyCCrAt5%2BD50ws6or8QA%2BgzDiyMkCPfZI%2FsgWO2n14wVfiGwnBRY8NlL4%2BEu1zkpqFwsNstlCFzNIG3yQo4rAyH7GB0sG4l06Yr5LCbxQte%2FAA9FtUILPgUzW%2Frkl8j3cC0OGw6SLmYjIBw4ynR17DpQ0ZpXtRQ78MBKm81LgusQGCn8JDshWluvkFxRDYdHUqWcD4lrSyzHQ%2FSFnHjGfa4JrvLILk%2FkSRPddLa0ni%2BcQCg%2F5D9zRaMWlY1MKR5bWsEy%2BpGM%2FWtol15CFcpRZQ8niIdr08q4QAUxp9yzg%2FEIKlbrq99C%2FCHIrfOmQodCLfXmoo7Lsw79evuhSdVcrQa9wmKhfrlHbk0JS5YV9MuWQvxB%2B8jYJ3xlP6RLuGZBKTe%2FcB02XFWYvNhrZzKwNf0b1gInEYSVD4IFPKRhZu3pcGV3kdvX6SlJHatJffOHSeGtGRUy2UVBc3jYMNxEUjAckJ0RSe39hfMt7aCIksBicHNYUDSbMlxitS4SHb9Z2MU1Ylp0Y9WgaqIDc0U8ZGdBuVtqTpz4R%2FQDxaI8yKyo8SMWPh2eHpHS%2FFJwP1q5fa%2Fmg3sq0q4mJtN56x8TdEkPNkMhOgZ4YxA0%2FXlqd3%2BupnY3FDZ2XELEa18N5he%2FPwb70LV7hBSi%2FHoy%2Bdi2l%2BG5ItfSnYv7%2BaRyCRBuyh5%2FsJtMF3avCtYAH0%2FgTAMOJKRRJvcW6kdoFIC3Hbs9Te1ecWQ4D%2BmEE%2Fdaoba5OoojFQzb7vTZI3t4B4U%2Bmvs9tNrupcJeYg14%2BEy886Z1Jyt21eM3TS9sLskv85An0TQRj9ZvEyrYT6r9vizgOfPf2bQfhKM2s%2BD5lxwWpVu%2FAexeSXHsyTV2j%2B91G1mZxkg8nKxO6%2Fierqn2G8NOLtiL9Qe9Z3Z79Nw%2BIujkeeNzOSxJu4ibtqmcv3F6%2FnZ26Z%2Ff07%2FUfmfbKNAv7ilF99wanubSKDMZC3gwv4RaQMrCcDSJ5whwUHhxUs3hON%2B%2BbmJUVR9ckoPXDz%2FfwonAEDIiXPrCvK1tosIHe%2BkTAeym9IddFYEYAAAHAklEQVRXtm0bnkSFXfn5uDq59HkPc5viMBr6IwXv7UEr3lpgbdrEqIosAuhno2qO39GRiRkmPikeo2AwH%2BgXqAkPGxTqc4gewsu0IFSMAW14uN2fRAfHFw5aXaKCdgeORmkav9qP8an2FILh6Sa89cC%2FT0IR2FNmYxvxgAcY7Ws3iFvOnKusH11nlb6RS0IIeLjX4QRs3I%2FNBfIfDcXDMd74BA50attOjc6f%2BTechJM47U97zad%2F9B%2BNOwrYwG0HdXLrpdYdbeqa1FNRo7Kzyi7%2FkQMYghebo9AkPOKz624EL52pj0P1%2BMaP1j9d7gEg8EC12p70p6P8FmtgRM7%2FAB2Fp9sdoZjgGTfx%2BRGvvRnYCpCkwdedeLC2qUxb96qeBmlz%2BA1kq%2B3P00QpZDw06SS%2BQVxC4p37tOkS6cC2QfZSJ0G1e0uIwcEf9QezjPZi8dbOAWmVFkIlncc%2BtRyf6gQJfpwFEmCaen4Wz4sdHzpMJVDmKEMhpbl4AMLhfoP9h297FZ%2FEtsPbIItEwIahiK%2F1sn%2Fg4XXLq31DQKqnlcOPzCQKK4XCU0aXfqRWqZ8Lw%2FL4ODFFEl5AJpehgDqx%2Fg3U2528B%2FFiIosPT0DfxzHGSPih1BqvATFlKrxPwvKH%2Fakz4JAqUtfiux4jHGTQRTw4lqiXJr5IgVk3FDhcrrheBnEoAFEq%2BDnCBLoU3hXiK2iNNQg%2BL%2F2pMTrn1tRe6gSoToSTYGF8MzlL%2F%2F5LACDfgJ7XJvqthpV%2FxY%2BNBltfx2UonJi5f1S9jpbt39qhISh5P6xOrky8opyinQyr9yFRwflDiNK8S00UUv4lOAYFr%2BM6NSy0bH7x%2FvS9cUPTyr4lo7FHVuHo2wgzm52fZiIRRGR7KefSn7m40DqK2THEpzVkz8YJt4F1BxoRd%2BgC6bXjJqYm2MTVeFmPlY7VzPqnvjoNb804fwsUGsjwPvZv2dAmXo8B%2FCRw%2BiaSsfrj41F4S4Z7y9v5OKgMOvqLPgQZUUk%2FkGWR82D3jqTWBe0VrBtgrjkPvbukh5DMpv1b9lwMN3XnDbVXgGnI9YDLoVuSnKufPjqezx1YlXvloUFmmE4rjq%2FCkiT6Bf8yPyvs2yu%2FEJjDC3PgLYBNetOTe00HdiH0CEWKx2iMErF0DY7PrmIGSmX3PQno7yAjqKnjayaqICioxAUsLS5CigRk77fthzH0O3LJ3ecuKWSm3Ytn4V0fkBllBnsGn%2BbLDMbo5%2BllE%2FMgdMTDvr9Yh5WzXTi7lPfwdiHtWCXaQURcKn9Mr7L1v1TJ%2FRnpQNrmiNU0i0%2FzTjpIan4n0FmwP5bvJJPodhmxuXqWuF7s%2Bjn7LU8R28TR2YL4Q7YbgUhyMclLaSJEBCa4p5LkJERgcKKr9y2ctohKLzJO2S%2BNMMdj3UGTGVhz0Fi1o2oEKYb2LUsMdGJqOaE4U2B%2BSBH0o9sBF8zkOp92gwet7Hx6EoQq981%2FT5xyAu57If7Iuenh6MplDUfnf4XPyk017Vhsvd7LAxbNLwz6HNuC3mQDrIXbkfF%2Bx0dDmEDn0%2BOcHu458afTnYwLIpAWzys%2Fu7zht08hLyZFvI9vIeqHZCmMjaAtOquTlTiZkINX3BDZQxHjDLi8WvYzuyE5Pq7%2FOR5fhIsIv3JwNuEiMoXEZVE8htGXRggNtcoglETHVZiCZ0qT6iYSCbplpBRYToYlaHcxPs1PagTquMoXNytn6pXpGu4k%2FF6IP6QecWMyaKK7iT8Sm5DGJBcJo5A6kRUiViBaqvhlgVL2k4hHHLovfDIoSsVvSJjI7cv6kQ%2BgQEro9HOsZaQrdKMIHUdGPm9AHP7a%2F3XO3lZU8KefS10F0jq%2FqzGe8VPHaoucBL5O6lrwH0x1dWiUg5FqdoKzmUBJ818%2BTeBc8h9Uf3stEXOjIPUQSOVxFP2VBKusDASOgo1Qywq3OuMx3%2BAL2%2F7AXza9%2FVF8P8zv1FwWvB%2BXMZWzTW0n1MSV%2BYDkN%2F2NBDqFn2sAud9tcWyoaIgqKXrpfUq%2Fs0kWFcFeeCcaS5sjJJqpbCU6DmqXF%2BICsi4EchsMADkeh78r75nT5Xi8DDUk3Spa6%2BeNoQTcc2ZURCfqCVEo9%2Bclx2Nfkd%2BTIkrKKsuATSpJKqy3xdCAC0a1tTzAyzkJikGuL%2Fscj13cyW%2FSIiKs0jJtl%2BPxhx8okUL%2FzH5%2BKz73cJvjsXUPk8GKII6QxAbZ4hDYVVFiyjxqRgXN1%2BX4go9dh1Fr4WfPsrt9L4Nja%2BuxKCRhtUjhV75r%2BFiAY2tr71em5EmxELAZGW7HjCBc7YlwbG398eBT7ujLGufHXkKQd51Y0fSGQtCE%2B5k%2BoJqUysFOAQ5wIvsHvhFCpItJTDLjQBAxOI%2FSaHJgCtqDfl9vpjt4JrmOra3%2FB72L99CCrFH3AAAAAElFTkSuQmCC%22%3E%0A%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dxrange%3D%2210%22%20data%2Dyrange%3D%2210%22%20height%3D%22230%22%20width%3D%22188%22%20style%3D%22top%3A%2094px%3B%20left%3A%20356px%3B%20z%2Dindex%3A%209%3B%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAALwAAADmCAMAAABYgh8IAAAAA3NCSVQICAjb4U%2FgAAABgFBMVEX%2F%2F%2F9SOCxSOjH%2Fwp8AAAD%2BwJ4ICAhWPjL%2F7tDMQjj%2F%2F%2F%2F66834vZuZmZmVcl%2BbdmN7KCIxIRr39%2FdUQjpRS0nFQjhKMihptaVQRUEzJyAyIx46KSF8LSdAKyJSOCxUQjqcincQEBBSOjFSOjHzp4tSOCz%2FxqZSOjFkTEBUQjpSOjG7qJP%2F%2BPQpHhpSOjFSOjH87%2Bjz4cRqUURDMSlTSURQRUFUQjr%2F1r%2F%2F0bAaEg9UQjqHZFL%2F59nOTENTSURSOCyNfGojGhddV0wpKSnGl3yWlJKUh3d4YlM5OTkQEBDez7fLvKWdj4hzW0xIQj%2F05%2Bbbp4nWZlZTSURTSURSOjFSOjHo17yMgn5%2BbFwZLSlWPjL358v%2F4sL5w6XWxKyJcmF3VkYhFxIzMzP86MynnIi1jHRXmYwhISEYGBhSOCwICAj50rvehn%2BSblqRMClWPjIICAgAAACLZWJAa2I2XVRRS0kQEBBUQjpLOC%2Fxt5blqqWvhnBNh3spRD4ICAhWPjKmNNozAAAAgHRSTlMA%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FRBH%2F%2F%2F8i%2F%2F%2F%2F%2F%2F%2FuZv%2F%2Fd4j%2F3f%2Bq%2F1WZ%2F%2F%2F%2FZrv%2F%2F%2F%2F%2FIjN3%2F%2F%2F%2FM%2F%2F%2F%2FzPM%2F%2F8RM%2F%2F%2F%2F%2F8RiP%2F%2F%2F%2F8R%2F%2F%2F%2FEUTM7v%2F%2F%2F%2F%2B7%2F%2F%2F%2F%2F%2F%2F%2F%2FyL%2F%2F%2F%2F%2FRGa73f%2F%2F%2F%2F%2Bq7u7%2F%2F%2F8id5mq%2F%2F%2F%2F%2F%2F%2Bq7kFCNkwAAAAJcEhZcwAACxIAAAsSAdLdfvwAAAAcdEVYdFNvZnR3YXJlAEFkb2JlIEZpcmV3b3JrcyBDUzQGstOgAAAgAElEQVR4nMVdh0PUyBo32U2C7gLC0vvCozcBQREbFlTUs%2FfeFfXOe%2Fq84on%2F%2Bpv2lZkkm6x3nCNuSzL5zTe%2Fr8zMl2TXrsTSNrny2%2Fz8%2BPBgZX%2FyDv9e6Tp6rXKongMGPV0i%2BTI%2BeXWngGWUrsmpGxrGt2u5DxrxfIPel3%2B%2Bd2ywbQcxJpa2ym8DHit5hV9B6JGvP%2Fq%2BP145saNgrdJWmcKeV%2FLzvBs5xXfds4togUDvfRv5l%2Fhf%2Bc3Xvc763%2FNWch3b5bFjtOhNB3jjR3cY965dhzTN7aJ0L5fo57CxrPHw4Vh%2Bzfke5ILnvoNZ%2F%2BBH3mSeGqboCHV8RE2R%2F69Xdgj58oiloT7DLYXoX89TyXXebMZ7UJ0dkX7X8CjKyPfQTkAzVEvy8GYAm%2Bzro6EZRKJjdXmNbORzowytz87ma8lrEHl4g%2BqJGgu1iC%2BRadebfwz%2B1cFjFsURboy6v2dX1uazupSRjEhhwfCLjeP%2Fq11N1%2F5rlcrcysrwsPirXDvUldTrR1euE%2BqIREZv%2Bqzq%2B0AO8NhlkW1rfOgFKCNxOG37D1UGV6bujlr6AowbuDs%2BPCyadHT%2F%2F7r2L1eGx2tplniNfLua2uJS5494x%2BGJgUNIIfF%2FYO5aV9f%2Brv9VKpXJleH5eY93mpaYj8eyhoAsXBEDJyPEjhUq9cu2cye4cD2fNMCczo%2FYRgMjAl7yQyMmRdYkhg9%2B841Y9Aki4qkPnNe1DGfzBipTVUe%2BLSPeEj8muiSc%2FAPgswkR%2BbTVwGfHRsSt8ZzgtTx58f0EkFYA4kMfeMgAjipLhdRhXGljxMqhsVSlj5Jyz%2BvZtbqidrhvH%2Bfi9W0hcZ0AmgKkbDd1w1YoFhdDk2I89lJtcxJuEKvv0U54Ch90hfalmrsywYPPqFMqhmeugQNIYAd919LEFQfa7hgqL4%2B5eWPAcTLbCmTO6runBrvIdMySOjdc0lsTK2N7M%2Fn5aBz8wUzwvxjoltLwvuUA8Iw%2BmUDeIOgqiE886gVqTBSDzFvDOmokE%2FwUOxT5weqJuA0mYYGZt%2B2FhYP2jzxXx3lXxQ6Eo7Nt5UimAByzwtTSJcI%2F7OPmM8Gv6DPqIQBR1RlSghHynf9Og0mqrLeiyNpOW%2BLKazXTG80EP%2Bd9Bxv%2Fpc7IBD9p65rjCJnVifcI281qVIoAqANAa2JnUR8pUMv0UpP%2FgITidAVE3xeSmbco00tVoEZXBk707XPDYgTIxBwfxil4VEeER%2BBXlEliHCVK5tRLRVcVAQIK9hgzVAMtE2k1y%2BBKHkjbcrAoynoscpqmDsgcfFYStF3hwNA15hk5ENv%2FpEiQ9CSuEjy2cWPyzPigAtX73j8Rx%2BI3NiLjfVjXUDBzAqHyfSMFQKHtvwlcCAVYFmpFFA%2FhuAzs3jE%2FZgY3k17mzIEtniRr6LOT%2Bgwytzs8msiaOTDVZYIf%2FHsGgcB19M7OzvbMzvb2LnFQf0ejMkexw4YhkVOHJZU4GiZNeWD3algsFuV%2FXcLq6uxsP%2BsJvV%2BdUV5mWDluwdXHmblOV3I%2BBbke0ESet381DBVy86Y%2FqPfV2SUGCWvkNdeYe%2FktC%2Fw3u7U%2BVpU3HO%2BvorjNa0g%2FyNas9zo9ljsAmsrAfpUYEVcfP3WEhnt0rBZD4ouWPmOP7oJw1qnaMgDp9iIroJ%2F0Yqj52pSXETr0hiRs0wgjf6YDYrOGX2%2FokDXX%2BuZvDeWekJBrc0fA7yAB5OXOL7WxL%2FusMs%2FuSS9z%2BvEJx6slr1%2BgP7ANgj9hi6lZK2UE4vbNeQwK3p6M1ZHr3zOfYnbrWNXcCFkDGNvJ8IS6FFfzmC7qey%2FDVg7bpsmZFvasLW6%2FdBhItn1n1KcOgS1Vgu0lTAsn9EuNuBKXMdVx9QVcHSHyBGXNxB9SM4hIxWqHZ9WeGYwPpA%2BmjjFvmWNURuAjIXcuai5h3gKus%2BpLVVUV2TOzHtgC6mgPbEWqzsI4JNmC84pM5YzxVcaXkCMnNTWcKlp7PsEeJHbWnMFKC4tHI0veqJwWvy3ziRr8xGJLGBZDuxNCCzO3m90coE9St6TGYH1LToKokDlHcWiGZA6ze7jUUcQEWPcA3xiiViw5XjGiZkT2%2BfQ%2ByRbnGIPsk8g551OWjfqLaGjItIeED%2BnD2oXKLbwVqA6xkpxfnAtJcwjXOEmYNDAeAMJEakGWaxiGYoQqJNaDFjgdgvJfhZPyKXUfxc97WGFJ0tk3cU4Ys5O1MrXO8Vh6i8yxgjXud%2BX%2FWa%2B%2B8WZ8TbPLpYg1McO70t7Pl6QpukY%2B3o74RgrV%2Bplc4qbO%2Bs1PZP2I5UoTUKbOmIY2GO5U4yyxrCVyC2iChLd0zgCJUPiup2obYNpCr352rDNrCZHLOMwd66znH6bJL%2B5YtsL4HS81PFSHY8Pr8VDUjF6sP88ayzcH%2FG82WDKYxiRaLWGKFD0JwbyEYNKtIIzsumtsQmyisfbY4ySmlGlBe9KyTdvAhBkNHMYkW7MOznWSd4zr9herA9SxVZSIE1RxJmOxR%2BKV%2BA5cxumue9UJHUHwIRN2yBlSLPLAmf6v25h5S%2BI2wg4upxzkeZdgOwAcOSYrKkaVRbNO%2B4RWi4s9xgPWHuAbKNaUq7PunR0ReHrE8IRByR8RAGLLpIZ4whzRIZ8E6YpvtsQd1wVfe9eqRXfH8HCeA6EsDQmtHarWrG3tdT2%2BtjaIpi8iI5Uj8WPWRkyxo%2BNRQ6MAjgrzqEETJ%2Ff4jaXX%2FsJ%2B9%2BqYha868iVOuyFBnkFhsY5BISP9DWpiqnmiLTh3uWQxJCSVZGpqhQ1xvli7rFvW3IcGeAlzlyOc8gxu%2FtXVJ4ztFn2toACBuwaUN0sfu%2BTlXTs8Zll5ZBN2ExlEs01rA3O34GXqMIgMLm%2BCKVWrj3nX26Gl%2BIzgV3gDE2lj96f50IO6Z4mf2G3PsTLV4OaIYVcxDjt5rRkMHE%2FdNXvWmbexagPlcrSNO%2BgE9o%2B1iTf8CWMqnTxpQR01doDg1ZHD0zG7vr7%2B5Elv9ypxx26ALVZsB9Bsvbu3W5TeHhZxdjjGMXWKepD09XtWFx83idL8JQgKhYL8f%2FnUl6a1Cb93NTXEXO%2BdWFxrenHqsjigXNBFHlkon2o%2Bo0xXOJt35XnY1leGPVdSxPvm5qbm5lMIIdBAVDOaRTMWJyYmuruXxOvE4vumJgkZwAbwV9bfymVx8IvF3qoYjTPR%2BbF1QoIBAcJgDW7gIpnpOurVqFnIvbn5clAAIRIy8RIE5UAL2PwYBHwXLXA4rCx2Dy6LjpyYtbhhwbHY4N014CG5yWd%2BDA2LbbKY5pwRyAX8sjo5hxYooAHrCfld7QdtoQ1mL7GhXG6WPIzQoHlks%2BEL8zsQ3cxnCdn8ZE9ANEnoTV%2B%2BS8jyB%2FkaYBPlty%2BSh4%2FjQmbUIYUYYMYmTirWX2yKCed0Iyn3puZTdPIAcAcGbEDtgEYE8KEcAOvhiELhhazxMSpcZDse0mD9yYCHDkmYWIr5BhwprCnszZeJ7UEZVRHABhZ1At4jvFmyqeLrKUmbNUOQzNQBjf0q4IaIINcCnUQu%2FizpEoXxU5koXmaQA%2FMF2yrfLwstal7LmxzDRiIxgDEPi%2FWp2oWtkdi%2FlJkcOZIA2gToA7JEll6w98tSjR5zvhJL4pOOGvyyhzTzPBZ31TQ%2Ba5I0TcbKazDEg%2B80PhK8Ulgu81TjY8eUaYvmUAdENYr5zdpQXtYiLJPHIWxaK7UpItpos4ikKkOvKcmLvly0tK3GZD35KE4n7lbT8vknmjcunD59%2BsKBMbJ0ZGoMSRS8MvdcBbSPJO%2BxZ4f3zew7fMBIfiJvpKLBD1u%2Bx%2FnCq2Au4lGjKuf37DmMxC0DS6hIx19Gm1JAEqFqBw8O7zFl5v5lqUWR587Qeeh0NXZtGQfsaD6xAR70ml3faQ1%2BU570YAGQMyOJOhpIS47OwGCWPynzeGBmD5VNSUSSF5oOUEhrRm%2BUogPHrGflSixq7I2X9mj0EhGz8mQHUeDgnrSOGpUoH2gF4PLD5mmhSNTVqGZJntN7A%2BDt%2BMUWs2U6YcMtA16fe%2BZgGQwON%2BvM2aIhRWKpb2%2F3cOytm42nm98DaJOEQGd1ktJM%2BsoUp0m%2BcPg0Ul6VfdwOYhc4UQ1pLQQGYzMSdWsr4N9sbLywRhJMD4dlMdMHU3VfraJZc%2BvWeej1w4GKuIyQA3JI5QLiRZuPjnefOXzm8D3Fv4ei0jP6DNmJYYMo%2BXw9hRsEa07%2Ft2%2Fv3vYjl6XwBIYxsNWgkGXF7MAQPEDWY0gglFVDv%2FRutyhX%2Ftyz57wAv1jLQCuQ5qcK0QbhMQGnj92F1Pv69vb1yZMeVnw9bA1IHOtYpk30U9kI%2Fu2R3e2728XflUsSvDX8T8w%2BMB2yTApr9Q98AefmKvvFxgt9EvzP4rS7j6ge3%2FMAuexEORg5BGAqTWigtfWtFHu7%2Bn9FclFJrfYkqwZmJitXoDU%2B5xU3785S1a1GQRlRft6tOlwJ8Bk61gAMeoABQYE1RzdAcF55p0tH2ndjWRNstERYK5nCLC9MQmPyOubG%2FwrKCPDmvH9qgwMaikyHuEu%2FBXY%2FFMZapba8283K3luNtwxbfDypRQKCBQOpimfD9Ow%2BirHpzGkl%2BL6fzTk1ccasyFJLvUyiN3SSbSurjco%2FLZgqlBja%2B%2Foaj1uSI2njb%2BAzId2sy0GZ5WZv%2FXcvsaYdRH%2BgTjerFF0IXuqqacHevltnuIrVcrOQpXjC7pdaCReqEsP4vcjWK9rUB%2BQ70Rtpu17GyJ2asE%2BwZoaTRoDfuzbBBAgsTUy%2BwSnuUc9iOl9cUS9abyAl%2FvZpjb2PVE3yZl%2BgGcHsDHAGgmYarYgPrWBqdpPk9%2FZRoGLmM4Cs3EfKF1wE%2F40zi%2FVUcpLQhVsSOdgadeq3Uop1jTvKY5I1f3Lw7T8L66tPnpgkBO8azRyAX0le6TPHaouJOZsT2tb0EeUN6a2QvYz2HA1Owdgi3a6DMpqxbM3un4VMmHTTvIxeysNUs0HWouTCfNhxAX4vGErT4Ze1uUGiayMPgIMgYZQuY4PWK0h3Bj71%2FB4z%2FDTDPenFWoeAYxHS6cY1y1DK8k4iGeOhL40I2bxImUXHyr9eofYr8H19XsLyk0bjs94Q%2Fxl4J%2FikVtjXbIi%2FicbGtT5S13YELyVPYQDXVgjJ4LNqwwEZA1%2FZzYsCb3mXGuuSFUabyEGeOmo%2F3ig5b7NG0EaE5Q90OCmRlQMiiY7pywFTCEvyRBygjYPfpY7%2BGfM%2BRrz8yQanNfg%2Bpq6gsJruAcEGwcNbmfAHUmH3vGtXdbQj5x0M1ADf%2BsnHoFLlJHKmOMdYl69OyEGIlDyLp5Sp3DNDFp0FYwUdhCHtcRiIppJzXprKyLLZ%2BMm1mCD5Ey5yz2N6o19gdHVbgJdOqs9i6z7lpGj2CdleY3TFnJRlKnPaDlgMPMoCTwPcjupY1sFxGXM%2F3suNfLsMD1rlcIRiAHK0LCA2LTA7yQbPHIFYXoHv2%2FvYYxEAN9BAXvwdcg%2BGLeSs6QnZKhsS%2FH8pNGg3lG9tPVAoGIMelGHqGCdsiPzow3Rg1s6qkYFZjmwV%2FQK5laNO%2F7gtYN%2BjZgn%2BdN%2FPnPJH9kkcY9yka67XnCw7IMe%2B91j%2FtQvwjYt57%2FlgxiLLjCK8j8DG8Nn6xaYLSvSWuv4pse8LkOh8AMhMPU4a6O0P1CjwHZP87j49GLFwp83Wt5GhZDGb%2BcDMkxn3yrWKi02KN41XEH27Hga23gegEBWzPiDrif63EOiA%2FtIRhv69GgbG5muoNcxlGtbcQM5Y3Ipwf%2Fb7WrPizflLR1DR1DiqVUc2AbC%2BAO9lWjErwzDLbHqrZpveHkFXfUXO21y0U5IY0634YCBhEJi8dkblfXPTkJqivATO8colPfXB%2BZJj7UzanH1qyuftEQ29%2Fd3MTelELKNiJR3w1IJRCOZjWsp6AGMi%2FVUuh6gpytbWP%2BVJj%2FzZqqcZHzCn5AxWA7Q7aCe1Ih%2FUk3z73slulJNOl0TVFzxyk5RdE7sy39x8AvCCP%2BW%2BODaskkveG43nBXapo3qSTpb7ZaK2kXOOYdVhmKS8tKBmulsFeLOsQ1zRn9xh1RTamhotdCI2tQJ4YVNKW4scJlrLIO%2BCCRw1Q%2F64cuVdOUiL2MZmcJZVtUGAH5LTxNj56cvv%2Bg6Qc2lJXMQY1BJfr3o3L8CktCkzY8Zrwuo2yPs%2Fyg38oXkCIxLUYBOdUV2tjRdE%2FbqXU0dyWsR6IPW7LWjPGlCRpzY1vleraA9mtOiN3GYOkhdSbhYboC3qFYgNbF8bwJQfTnHvmZbVL%2FrW%2BS2zjZt0OD9gdwxNIXvg1SJWyZpaOFb9TZx5wJcPAmS0eDce2ORWIHAzcSx3edtq5KAc3Qu5PLqWx3DvN%2Fpaz8VFaxL7C3HSZzNGZDPPHqSvV2oPdMWeN6DQU34fOwzqM3Og8EXScs2zAZMNpBklX18sZS5YoBsievYhVj3eohTNKTkyGjugFyDHTI5BOWAeVvukQkE7%2F%2F%2BwBdoyCB4G5uXC2L3D%2B%2FbtO%2FxW%2FPRFJh%2B8Z%2B7ex7Q3br5974a2lG84UCs2c37WcYa16p2dRCNM%2BJF3VogA41imADjA%2BkPlM6xh%2F6dLdBwG37ZsPWgcqQlfF30vRHOKJiCz54QhKCgXaJEh4G8BzegryjdNcCFaaWUEydwrt200xhGLLKwP5VeZFHfKGu4FyHOVKGaYbadu5VspOaUznRLjEjCEpg0w5VTJFZFBDZGmTYLNzh%2BRBeVyEB%2B5BC9UworLWTci02hx%2BD0SD2rANLo94qvMsi9Jk74F6n0m18T1HNzHTOKrj398kZxZzLGeI0epdNXFL3xLQmcx7%2BXL2KyZtFMBKgesERhLIqMpnAFTBHoLRcC%2FLCjzfpHo6cjfg1BFayC%2FkP0XaJ5vtNOSuOXcfG%2BiuekPNIrklgJQT6sdRrwBabKhTxm9rvzpjxdNOksoZ0qwdUHvMPVL9g0aHje9sMjyXUkHpLRK7M3NkOCUnXQggnn78roKT%2FBzKES3TjE7nGn%2BI1uq5f%2FYxRjLoICHQOcIsTef4ZBNTOLkybBEP%2Feuzm1TddwT6PGLrEi9EBzZbZcraQubQuxrEdpAy7ty7KC9fuJdbo5et9iBeBOI4y2esgCYTqDWCOLEwNtO2EyLjD04tXGbx1ZuPBMzH2l36KmMMtTWMW6qkBdNHzh4cGwMwcRThYIYbQpOqtDYwfvPHl64zdIn%2BQlSU4VSb0o1OcpaGyXUSSIYKpUaSs%2FuyzaQcWQ2U8c2haDgaK9xWAcPPGsoLTy%2FHdUR0sodBmrdyuzQeAbh0AZcfNjQIBogyrP7b2ULTFCv%2BVBmfcBUQQfEB%2B%2FLw0rnH%2FGACs7o2z%2FYCpBwF2qrdA1aN6OukZg5dK9BgRc4RCccODhGuotqHJAFNU15cOCZOurmEE1k5Lz72Hz2HWZ37dq%2FcgyOZnLwuSiUOZqYLmnksoh31QBypNCMMuPN2H3dX6XpRWZcct2B95fcD01ouzYyCjyssSp65qFCYpogPyy8HUtf1zmooZcaNs%2FEPIkdCTAx6Y8jeaTOG1AZGWWVJdPx0abCrNivcJVK9w%2BOxRRUfn5wH7TkueVHs29oMT%2F5XQ86uTo5NZCRgXN8s4GKwibx40jJ2FDBddM3DTfPQMvJGtZYqR%2Bv9YiWn15vFYvF7XOvfkrZoUs2gJ%2FP9eAAv2Re5PvDxTAMZ%2BWVRN3qcqrFBeig8xMWSfBTUl7h9ZXlFFCGHFv6MqA71eK5k6l77R8cT7P6sgG3zwNoMEANDZsXq3h11Oo0dsoQ70LLyjsz26MjlUyyPFXXMX3t7Ox8GRa30uHv2rU8OJ%2BehHRxWhHe6oKbi%2BYSu6VN%2BGnhDE%2Bn4dN0XDSj44OH8j0OZ0teivVRgO9cF63Yflpr3xPL8vkO7iSgFtbi83tGH0H4pYZpdRuQ2%2FdK2BzOP5%2BTxLxdnxo8mibwtlefXznSPal69uvHT1V9fd7rjMaeWB4%2BZtkC4I4XDd1UNp8p70JUDC%2FoPhFfb06kz%2BPeuDsyWKn5WIWTH0QvVrfPWj%2B%2BpqtAq18%2FfQ230zSXNaAyPM%2FIQ7J79LAB7b7W0NvTaIoWFp29VZsH5kfmKokPw7DLU4nwZedfWzb6p9twBeJLRf3tzIpU2V%2BZm4IkKbp548VpQxHdAQv38OO9i1xX%2FA6v481wJb%2FvOSdB%2FtXZ%2BZcL77W5klVs6%2FxLED93jbsq3f396kpKWuW%2FSNJv2FwAM1Rq2ECpd%2FT39rR0txzLrp6VDxJgVYj3zitny8lftfCrd5R9O5e%2FzmGBoqVnie7EJ16mSyrgETZ9gTT4PCJv6e5pkUfVBf6svs6z%2BvGv6pa77ekWuwNAmKm1VNpaROkR%2F3o70P5FzzXm6QUTMcimXNTY%2B8Xu3d0tvT09vb31gD%2BJ18iHxZhFPLtlcN%2F5%2BPLjnV%2FPJlWQWLyOpaXebtmEln64FHfiubQ60wvAHvE3LTd19Lb0tvT3635iWW65wNOVwXHRPv2VlLazmpv2J4y961jq7%2BnpVuIXjv7RdMO96Zsl5nTPeFGHEDe2T%2BrstzoejHeyaK7g%2F%2Fg1SSefflB3T%2Fv6svPlp7DoakVa6UJPIxvQK%2BGLxkxsbE4%2F1LzXpmbT9%2FolcqMWZp0x%2B3b4WF6ZUOOO0NgY6eV2fh%2BOntF8D3zDq6yMREUD5I3Jjg9Nl0rM2w519BudtsZH2Y9RsMGHoQhkPhWTdvhMdx%2BbFd4jV6feReQY7SwJCZ8ZWmgooehLDRMdsN33%2BM0vczwwh4MvFoXkP4WJbnQbiFWVghnNMQToSh4LdUwMbUKALBtwk3cOjiTlX17058wF%2FeHLzjvFRHNyVnmCYvWTurOY%2FyYb%2FQhDYwEcOg%2FjW9mIaR4WQECm3qN8zPkJb5pQvRMWkwMYRfvi%2BldzpsyHY3S54kSQG9MsPi5tOOky1E4%2FGs8zxjtHN%2BIQ%2F1J22lYa2wPxXtY9mMc9YK%2BbAHD8uRn2qb%2BL1CnxlM3R7ADnFdxkRrmpJGsjy1lFLTpV7U6d8wi1T8SR%2BI9fKFFY0xBBEJk8%2FZ5FfBm9GCv4sfNOmBq9fBY7rLLBxniNIc0hm%2BYckH98yMzQqBkma7eE0epozYcRvqI7mihLmTre%2B0lynsO4nmrvlwdqXIz3aOgeDktUUFZjCCw3zac%2Bk6DtdZHirr9SfJQpn%2FFmdECGlBnCyRt8%2BsJ%2BEbQZuodzgWBsOLviCRqjc0nn6fp9lt965i8RsteIGn%2BCeyuRbG4MxsZnJ47eTZGhkf1x4aVwNue5LQ0DmewPNOTNoDWm6pLTXi14KxnZhjufwl9rWadzVatCfbpjg8SetqNzdzPvS3B8CCfSRHDA2mgcFGuJMVN01rt3f5mfP2bUuspvOyPfaobrZ6sp%2BUPyqYVTd%2B8yGRIJkAjQ5o0hbWnUiPw4p7zPeoGTzjQfh5XKmPo9GLGYO%2Bhs1XYL275Vpx8%2FK7Ek9dYQGxfAxoty2%2FFgebtA1L7Obgv1sfNjMSvcnQN3AxY8V6oj6aAaTQ09hzkyIfkzKGWf18KQu7ZIX9YiKnpClBGW5mPm%2BPoa07uEAv4mLkb2PRqa1gNAVS6y%2FSwrwz2bJRucea2GcBMxEU92Zg%2FxKraE67jxP2yJvItD0%2BheGxoWc2UqW5VBX9BN%2F%2B50vryT7p9s8J7FPqs5IKcayzGPhs7TMKphIseVb9AFznw6TAnoWbHsiYGKnSz0Xcq2MbTJRlITeXKb4YTWvQ89xfbqRzGsDnNNyVR85wzmlDUywt2GRUPSRwH8kqshbE%2FA7dQFY61%2BJXk5KVAthp%2BzsWva%2FB0z6fkXh54jaUQTorp7Dmxcvxn6ieFTmGsyqYLScKkN4vadc1gWRJbbQ9MwApTFURwzAnRahN6J98OsYvunr2H4IVNXEbzPqojZYHYm0Da7AdHxoYcUzpcavISHP8QOYmE%2B1uh3f%2Bz8qh1rzhkqnlKPp%2BD8ZOdlvGG4RGSzUCqRl3LAMk8VW1l3bqf89a%2FOr8LYbPV01wW%2BDnPmWcuDsqiwDGfLFupuPDqprx8FY7a6W3pacj0%2FXt%2BJnhH7ex6P%2BcgaBC442T%2BjlXEr%2B4cdyGuS79Vwq6Wlp6elpSXnc%2BsPeShQrKrOx0s%2Bem4mPhRtFvh2X93m8%2BrKQILVxx%2Fwt9EWOaMsZ3FzLkMc5TXFHD%2Be0IiMtYMc%2F%2B3nuCAiGnDTqsw32XmV33MklPW2SORyQj%2FnIvgyIbcpkSgq4r3hkPx28TkAL8H42yO%2FDffduzo3yqrBavk9cfu71TpEd29LPuz2g15coLampZg9b%2BK5ga7%2BNs2%2BAPAGo%2BgUmn63PiN5tXQh%2FnKCv2odbkdnvvUr%2FuRqnX%2BBpvoaNHiPUYSfrW3QpIdpEjnX1%2FW3dHf3yKWLNznB7wIg3FnD6XP6ro2SWZFViQhmhwhqcM63PJXqu5aEvirO554MH7UU3pGH6trRqbkRz4Po3s2BFaqycY%2FZ%2BfMkWo0spnxtmF8F9RlV6mgxJaellLfr8QGZbX81J80Ey4pX45KNRwu4lF8S4J0l8yTLsTwFDsua%2BVSkF8YmL3Z42Cc35uQYx0EGXTUco3d70xBevk7bPPNTHkfeNnmM9gNh9CtTWceyZ9u3BI%2BnQY3Q9FObR1EZcge%2BLWJgJpcFbSPr%2B6lZNF0j3zxm8cWHpZ5eGRzUsXA4h8n%2FVi77wLDV314NzxudZ5x%2FrpCwnIkaccqJyetWSzukl%2Brpzo9d3c%2BPeR9dfnd1BsQNpLBOOm1S%2FmC2z9OS0IFSbTm2TY57aPm9%2Fl5hLfMvvMmyf4Tjjrz5ufjymsUr8J7ww3OUu5ztc6xXJpYTFUgNE36qu7e%2BLAVZuiZXxudFGVlJyd9BMjB9RPOzwVLONnx22YF8y36Wujx%2FZXBYABgfnqwzLTFXIVEmWKfbmFXWUDruhu3ZjyPf8VLzruOL93CCu%2FTI8z37psc%2FGroxlWkZev7NBpztO8Nap6%2FUzre6vqPgaTAUc%2Fu1If8AAAMJSURBVAue9xAFb7JV%2BHRhbme%2FU%2BUq5zgKHH%2BB3DLB%2BQluadRe9SSr7EjZb1wXBlMQUuofhihLdAJ%2Bh9mqOhImdqh0GUhWB%2BAqk%2F8Ix4ENlOUMCl5HrsrOlKPcvjvgpLmh%2BXkPolQMtwayq9%2FZcg3D1sRMzwim%2B0r3aBuapjpynHak0HwsyNOitQcRvZz58NwLaGpduPKvgK%2B1JAW2sqSnbYBN6IB%2FtLmZ9NxiRzfnQV9vJhjUzEd67zz4%2BFQFK9MwfbCQsHrwo6MblLy77mGWao6flwmtpXsPN5Iux%2Fmuq0D%2BuaKn8Z0n9DJuyKQBufB4LuS4ofxgjV220fiI0OBcD0MN3knE0Pz5wRp7FGe4mSFhmYezYRHAJ8xeZTyQfKfLChOzj1ynJsisAZmGdy7s9yCmJPHfyKx%2FJ8v%2BrGfRrhZDlYZ3rtjLYKPd2YmxXe4yXjucV49eVQlVr2WyoB3Oy6%2BDWSfYwbIcZbDGF6xRKRonZc5afMXz96wz7GB5w%2Bc7jOKiUkqk%2FZCUdLa4yjsES74roXakDBCDuX0kdPKht3rddytkv5Oz%2FYFDQTMnlJ6cWC0Wf9W7fi522CMWXaZqn2DnysmtdUc9zTsGAh2CNSbR4Wmxx8JtFP0HDUjOyozjfkuMKFlY0pcuCi5M2V712LIIkCd9rngny9Mt8xxjK5yPeDs8PyxSyu%2FJsMPsYF3W%2BCMihLYt8wS99aX0rC0RlX2gLPdzT6zeMVr7I0j%2Fij0HfrV7ySOfymx5aOUQtm31Jyj1jwD%2FFBN7w61zJ3e1HVq5zqmvssl6UVvNMWEH7QGN%2FSGB5dPP29vb5z6%2FPom8aDs0MsAb0BG6V0eeFNGZMxgc%2FYFeyimwGiZLTxhPZTv562w%2Fb5839YPHUnY5F8729vf3d8vMqoR0sKdbQkVaWpb6%2B5f6u0d%2BiJlML08xYTnlUvKfztEzQOu47PNfKa%2FhwaofUjMIT27h9fj%2FJrIc5bPObv%2F1da2rsE9um1T%2Bfw1WvvLTtuBLjVsnmHL21faH8EPeyyZrlf8DbgJ4SzuJtLoAAAAASUVORK5CYII%3D%22%3E%0A%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dxrange%3D%2210%22%20data%2Dyrange%3D%2210%22%20height%3D%22156%22%20width%3D%22440%22%20style%3D%22top%3A%20150px%3B%20left%3A%20432px%3B%20z%2Dindex%3A%208%3B%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAAbgAAACcCAMAAAA6Xk4VAAAAA3NCSVQICAjb4U%2FgAAADAFBMVEX%2F%2F%2F9NmcCTfmuUe2OQd2KMdWGGcFqEbVqEa1JNmcCbhGucf2ibhGucf2iUe2NHhaiQd2KfinFJm8ajhWubhGucf2iDeW2Qd2KBdmuMclqKbllzYExJm8ajhWubhGucf2iMclqKbllJnctEnMubhGucf2icfWKQd2JChaxJnctEnMujhWubhGuegWWcf2iQd2KjhWubhGuegWWcf2iUe2OMclqKbllIodGjhWubhGuegWWUe2OMclpEpNdBoNOnimujhWuegWWUe2M8iriMclpsWkhDp92ljXOnimujhWulhGSegWWcfWKUe2M4i76VeF2Uc1mMclqOb1NCq%2BFDp92tjXCnimujhWulhGQyi8WMclpPrdxLrN1Cq%2BFAquM9quM%2FqOOvkG87peCtjXCtjGunimuqh2o2n9ujhWurhGSlhGQ2ltKcfWIvktAvjs0yi8Uqi8sticWUc1mTcVRpUkJkUUFardVTrdhPqNSvkG%2Byj3CtjGutiWenimuqh2qrhGSegWWcfWIyi8UxiL%2BUc1m9poq9pIa1nYJgrdNirNBardVqqsezmn2wmX5aqtCVnZWtlXq0k3NapMxTps%2Bsk3a0kW6yj3CvkG%2BzjmymkXZTositjGuljXNSncOtiWdQm7%2Bnimuqh2qfinFNmcCrhGSchnOjhWtQlrx5jpGlhGSbhGuUhHWegWWmfmGcf2iMgniVgW2ifF2cfWKTfmtIjrVCjLSceluUe2ODfnhAiLeVeF2PemR6enqQd2I7h7qZdFlChayUc1mMdWE6hbZ0eXw6g6%2BTcVSMclqOb1M6gKaGcFpqdX2KblmMa1OEbVphc4GEa1JecX%2BEaE4yeaKDZk98aFSDZEwxdJ5RbYF5ZFJ7YkswcJZ1YU9DaoN5XklzYEwubJN0XEkpapM5ZYFzWUNsWkhrV0MzYX8tX35pUkJoUj5kUUEpXH1jTzxgTj9hTDpbSjpRQjZSQjNMPzNLPDFHOS1CODBENyxANCs9NC86MCo3LSgwKSktJycvJyUrJCR%2F7i4wAAABAHRSTlMAEREREREREREiIiIzMzMzM0REREREREREREREVVVVVVVVZmZmZmZmZnd3d3d3d3eIiIiIiIiImZmZmZmZqqqqqqqqqqqqu7u7u7u7u7u7u7u7u8zMzMzMzMzM3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d7u7u7u7u7u7u7u7u7u7u%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FWBVVlgAAAAlwSFlzAAALEgAACxIB0t1%2B%2FAAAABx0RVh0U29mdHdhcmUAQWRvYmUgRmlyZXdvcmtzIENTNAay06AAACAASURBVHic7Z0LYFtl2ce7DS8MxsdgE0VwoOxTUWFsMHCICKKuXJSbOoG0xSGKjG0OAbmo3NwYKDbYnKWkBjsGmtoOEyXIGNRUvrVOOktpCy2jI5hmTbuypDljY03p97z39z3nJM2lJIPmaZqce855f%2Bf%2FXN5zkpSUHBB20OzZcxacsuCURaWlpYtgYPbsaYXepaKlsumfWHBO6Q9%2B5LKyH5R%2Bfkah969oZptx0jnf%2FYUlMcl%2BfsHcQu9n0bhNnbOg9Ae14zEjtsFz57kfKPQOFw10tmB8mQmr9SC788wiuoLa1LnnZAANDGPzBNpfWHV4ofd98tqMLy7JCBrj9kI0FtP1gYWF3v9JaVPnlv48U2rUTwZjcV2P6%2FHo8YU%2BiMlns865PXNqLpcbc9P1WDyO4A1%2FvNDHMcns89ZF2viGuLWD2PS9%2B%2FfpMdBcoY9kUtmcLFykAOcHXvrIWCIxsgcGvlbog5lEdkrW2LDgQroO3MbGRscSe8BZFvpoJo%2FNzZ4binB%2BSEv2AbWxxNjY28CwKLk82fTMqjbFUErZAwEOmCFLjAG43YU%2BoMlipdlzQ56yfliPv4X8JLb9QK6YWObFDsuBGwLXoseGEwkc4ZC7LPrKfNlXcuCGQtx2Pb4HgCVGsbsc3avrNxX6kCaH3ZEjuKGYvo85SnjZH48VS7l82Cdy4IZzk1h8%2BO3RUUINnOXIcFz%2FcKEPajLYolzAbYBiIK7H9icgn0wkcIwbgRq8mJ3kwc7PBRy6mhOP6YgbqQbAYvF4MTvJg2XbR8nAtUH5jZJKym5sbE8xrcyLZd9LScC1AzhwkaOjOMSNjo3u0eM%2FLfRBTQbLodsEg%2BvS43GeUiKL63oRXB4sF24IXAdU3KSESyRwcrm3CC4vlksZR1xlTB9D5FiGsne4CC4flqurbIP0H4U45i6LMS5P9oMcwbXo%2BvA7VGyjkF4m9sSK5UA%2B7Ls5gtuEygGUmIyi7koAFyuWA3mxnHpO0PXvmB4fSZDrqOgawTvgOos36eXBcrj8Te7wig7r%2B%2BklnTHc5aXHi11eebCpaX46wMo2IHB9qB7A1HAHyv6YHiv0MU0Oy%2FjOZWH4HuY2dOfCKHaTyGHuLd67kCebkyM4vx6L7UdOchTjA09ZzE3yY1kXBBvIpz0G9fheEt8gsxyJx2PFEJcfm5UlNzfh5umAAuAd7CdH8bWB4gXwfNnnswNHuXm8wzHUeYJvGBop3iuUT5uTTb8XE5zH0wOJ5H7c3%2FUOupO5eONC%2FuyQzPtPajk3j28YdLYfFd9747FYUXB5tTnXZqs3sFYAF9u7fx8UBvqbhT6SSWdzMlKdR7FeQBZDH4%2FTo8WUMv8244vpxrpaj8GCyFvG9fhw8ROphbFZX0nj5iETNrDmaFyP6T89utAHMIlt%2BnhfumCBDVmg44pc5XbEEcd88pOfOvHEY%2F5nQo5kEtqMk0pZsuJ2j6s2bHede1QObzjliM9%2B%2BXJbuQ2svLzMZvv%2B5d%2F86meK%2BLKzGSed8d1fuOvBEJja2g0GVA0N9cQ8njtzoXbwMad%2F3VZeVlFuQ39ltvIKgGezVfzwhu999TMTdziTzA6pT8tOznLzUwBaWXk51hogKwO1lYPkkOoqyst%2FuHLlim8W2WVn6YG7KJtNT%2FnUly9D2kLkkMjK8T96YIYw8P3lK5ev%2FMlXiz4zC7szLXC%2BjL%2FG6%2BDPngWgyiuQvIjGsKsko%2BXEb1bYgNxKYFeUXeZ2V3qS%2B3RGGz34xK8jjVE%2BjBiWHFabjfhKCHaYHKD7XhFdhrZswn3llE%2BeVUZ4lSE0FQhhBXDC4Q3Toy%2BY7Q9XIndZRJexpQnurnS3d8zplwEs7BrLylhcox4SMcTRrgKll%2FhhK7%2BBSA7sm8VYl4FdlB64%2BuPS2djBn70cyayM0qqwEV6kAEAShEEmN1zUAdsfrsS2YvnyIrpM7Nw0wX1r%2FE0dc1YFJSIlIrYKChEqOQyLukqUtZRhjMup4lYgfl9994%2F4fWJnpgluPF855cTLy1n4QukHfiYe0kYrORbgysqI6pDnBA1ev5ImKPjle0XRpWenpgmuPmXfyRFfvqyszCalHsRb4jgGcMrKKFQ8BXd7oQEcA23fB2jLl9M4VxRdunZyuuDOTbqJKZD8Y1woaFWgBBKRw%2B6yrIJnkjYqP6ZLEuGQ01xO9UaEt7wourTsuHTBJfOVR5x%2BGe7KwjKiAJnCsMO0sX4utESFjURAlr6glxuo1JjkVq4sVgbj2%2BHpgrP2lcecJUoyBK%2BsDDRH0eAYV0b7TigmhBQXAwwtzL2BQaMVXdFdpmMfSBvcmaZ1p3zq61hURGi44K6wUXVVkHSkgl4WoB6yjFIus4mcxXb9cllv5LXoLse1tMEtM6w45cTLKLQKkoiUEQGV2cpInxaurytQtCvDAiOdzTaMWs5krmfEhK%2BE4qBIbhxLs7MSTPnVgYNPv7yiolxKOCoqSD9yGVVWWUUZ86FoHgtyVI%2FkEgHpx7x%2BpWyM3k%2BK5FLbsrTBnSpWOuIs2gViY30g5bR2oy82lFrCE4tvmFoFzVfoarRiKL%2BeslpBanAa71asKKYoKS3dPq%2F6%2Bju%2FsfjqxYu%2FAY8rr7rKRpqfyAklJTbGyMZkxy8H2OjFbyY9RBGVDTSJuV6IjSCEkmAFGiySS2FHXpg2uHqHww6P3z5w3333rb0P2%2F0P3nzLLbdceSVwvKqCwSKlAetHriBdJlDS2fAF8DJSfuM0hXRm3kD1Rvu%2BlmNyaLjoLSWbeuSRJ8ybd%2FY3Fi%2B9%2BupbHWCu9MG5GDbGDQbI0FrydP99999y8y1XXXkl8pI4kJH%2BShYJcTJjIxklml2BU9Ablq%2BglcBy0oeykjOc7OSmH3nsvHmLF199td1hx6pBT1g%2FDvu69MF5KDZrW4sea8kL1eP999%2BCBIkdK7pqYOPXw2HCVT8j9rvn%2FvnPp%2F%2BJ7Ll7nrvnnrvvRgGOOs0VUwrddIWwmZwWAsSI2SkwB%2BFnd6QP7k8PSCpTEKn41irjYvT%2B%2B5FjvQXB%2Bt1D%2BO93Dz30u4f%2Fz2D%2FAIL3gPZWrFi%2B8nuFbsQ82qHHzjtj8beXElYUl4O%2BCGyYJnle53rcMz61uj%2F98dGHDIgQlLX3SQTXqk8GpGuVldeCIG%2B%2B%2BeafPYzVhoAp%2BP55z93Id06CPpTps%2BadvXjpbURV5OFgGkPI7OSZDiiigyEN3QubGtsjjzxsAnefte4k52mpPRnu75988mlkTz739HPECEdQ3j3gNd%2FHqeX0mUDsahG2qDGx8QehSL0l056D%2BlEy4nRZ8wNsjz76yKOPCBJridpMzNZK2hP%2F0oJr%2BWQ6%2BiiCBg%2FK72ky%2BvTTz8HjuXvuvueUY2ceObXQbTzBNvNzoDEHp8JwMCp2iaPiM%2B2K4tgCwqFqTldtrSCIsD2CHw8aSBlwyAqjU34P9ujf%2Fvbkk%2F%2F4F9jLr776%2Bqvw%2F%2FquXbv60X%2F%2Fq6%2B%2B8carL7%2F80r%2F%2BBZ7yack4xj%2BRnbx16dJvL1589rx5nzvyyEML3fDZ26EnnEFEZmfeT0QwO%2FOQdsFMcYsO7i0ZX7G%2BQYyac91vH3gYDAF4%2BOEHefJoYQ%2FBIo8AoicRIuDzOnDZRQmRVzIOL3QSfmWzib3%2Bxhsvv%2FwybAB85ZNPIxU%2BWa2EaXpmakuXLl28ePG8efNmHjnrvSHIY%2BctXqplryZ82FyOQquyx5RWggLAWk0PAiYC6aXXX3%2F1DS6hXYxVv4RkJ5nWT6ftFKAYWvLYScZ29hPI%2Ff2vv%2FHyS%2F8wOnTxIg7hVszxjHnzTpg588AT5PTPnb1Uama73S6UhYeZppTM0W6XDlEkK0xhKj05d7E7fvsAzf3x84NIUBjU6wRLvwGAEBXj1s%2FI9DN99bOF%2BvlyQoFknZ0SUTSrxs49iJ3to90uOxh6RMLX3MYd68xZMwsLbdYZ37nVIUjIslCHpQMxzZNTSWVd1ShJUm4%2F9PtHQVgv0bjUL2BhFqLNmXIUpNIIVyDFhtftZ64TD4LSELV%2BBh0vuvPv8o7Zxemm%2BhGLQxBh3r506TXEsR47a%2Bb0PFI74exbxa6rHs3Y%2Flkfm%2Bwl0WDlA3%2F8279eelVQEGIRUus3jlBf2M8IcTq7%2Bvu5h%2Bxn7IRzZVvY2S%2F5UZjwyhPKycYOgz3bxf4qh2bnh%2B4wHB4%2B4luXXvMdIshZ72Kmc8J3bjMhko5BsJGkxOcpaYjKmrtMaYxupGFLxyu7WCOK5t%2FJ1dNPfRpTxi7h3tBinAiRUj%2Blv5OKqR8vL9FluPvlc%2BS%2Frzz%2FZ4VF0vM12WnMYr7KVTlu8nLNNd%2FGAfLYCcR4wq34PZzaOg1SPCfYOvyHHurearJDZJOUY5GyyWQHDYs4uwYG3uR%2BETfyTtzS%2FXScQlBdIs04cFrBVSPAMx%2Ba1tnw39defP4JiGyaeT%2FFeSaa3q7Rg9PUk5THfqlVDPQ189mgXXMNaPFz2SM8aNacBfNLx%2F%2BJlXXrnMobc3CmRNHukJuCHa3iWPCru%2BHvm1988bXXdrIG30XhGXJ3PqFfTkr6WX7ZT5UlgpxEqJ%2BnmExm%2Fbtee%2B2V%2F%2Fx785%2FXy%2BeZlCuRfdc0A0XpSBUHw4SlHJrZUpz04E7nnZAJv0Pmzi%2F9UYZf4%2BTkSGSHr%2FFpmvFINbHPVucp2cy6xx77%2B%2BZ%2Fv%2FjKa%2F%2Fl6cROpipGZKegwtJGlj%2BqpCXPSJT1Gth%2F%2FgOsNj%2Fx2GM1bE%2BZu%2BY7IyvPLrGRTkI1gskDMmJNLCu5T6U%2FV24kNuHW75xxwrgJzbQ5i76b9TfOO8WbSyCMg6ldv2axPDm89Y89sfl5LESLCEbJqJU1L8%2F6ESKQ04vwt3nz5r8%2FBpzUd9AMb6cJoXEBGRKRiTxBZV9k541j5%2B1hR%2FQ%2BkbzOn1Z6e7bQGLtxkxFNnqbxpqEuU1qDP8QWNLaoHaSI7InN2P79Ith%2Fnt8s25%2FJEutoG09I%2BLEYnoAz0rACO11U74mHrznjWEtus3L6dQej7OyG3StouFD2J70cSRplO60RAcnnXh5OUsUd3Ha2md0hE8HN5fG4yfsqISAX06zGNHlUS754UhP7ZL2ClmTu%2BJu3mxYx76QyT1Oz1%2FHe4fYzVJ95UE4%2F9UaNfFlJ0rd%2B77ZWMkt9HHzzFpbybDZm32wCXemcaRK4Bbljq%2FV4NgV3vxlpc5l3xdMWjASDbW2BTR4P3RVFldQPpdEM5iMzKk6Tjpcp1HxOaJrG6JpmGt5Sna%2FJ20%2B9r1beQmNHqiU7YDZLS7Z5113iJtOpt%2BeKjfz48zD6mruhx1nb0LdydYYjkcggsvAgvG4Ptr2waZOnVmpXtq%2BaeT%2BVcanxjAevJWtOaWuauTk0eU8Nrtg8QTO%2Bp3lXNXVc2rZmVrtYSt15vhGLhT1e77JDKLhTctabx1M%2FpMdj6GvuYlG3chS1IUSL%2FiOAEUIwMhgO9mxr3uTzuOTD15TDNYvTyDdJHLQUhOVprplwyVswn0rG08VIj6uev591ELAMCWxNumMWO7zBC3bXxwi4XCMc6K1hKK7H0deBgkXk08UVHCRqGyTkBtURMt4X7Gxr3lTvcRpOT%2BWoNe5nkuhKos3e3%2FIU5%2BpOGhs18aJuWjktNONqyZyo7KKtdtzBdsiwkvwmZLbbg7h5fXdhzc3InZsnCF5yeO%2F%2Bt%2FfqILuAdLp1ErVFJGJYcaqFw1SUOyAUgh%2F1WJ9uppaQXYwmPZSmVZaxEJgsG4t1pVhpcqLKuHyOJTu1lMXVzRn2QVkD74YLqPnwA7zlRKQmkE62ILGNJBJjo%2Ftiw3pUvGM995MUkEAmCzGs8kSYg70YYa3xICQ1pm1JpWWYaxk1DUsY9iFPHsGJteZD0Ag79N10F%2BQIDhxlFAQ3gn%2Bdb2xvTB%2F28x3YgWBQdlR4EYaGq09aJDLIl2Vow9t72logFLqNB5i5WYU4c1i0jnbGZY26UM4F68A2%2FulmpVSnizhIrDT26luWe4jz4F%2Fs1vGP4MDfO5CgBB1OhxNd%2BvERBmEOjKmK5JmRSFiSGQ%2BCimvFI2E0I9LX2wElBQqFEAzhCf2j98HmQP02eI4GYxqejlsXz9XwXCduG6fG1iDr41EHz%2FTJJtEKbCk8xofxdumGNbQf8E%2F3RCNHzd4LT3TQt3GQ9eHNHJqT7aeD74qDHoHmZHsA7%2BJyb%2FDItBg7GPWX5PgjtDjCRfX4Hvx7YaOgur3x4Sg5Gs3Zo%2FjESAQDI7AixhSFTli%2FurKq7qnmzu19IgulNMNcq0EaCp2s2fETvKGGGwC%2FoofGkBI2DrKURhqdrkea3kHbkzWyg54JGmlc0p6apvE3c%2FLV6TJ8Fn3FAOh0ypTtH56JBzUHm%2Buge47nI2INAIqT8spDePiDJdNzExxEuEA8pu9PEGyJMfTjRR5yWroiHJhIISNcceFBiR%2BDG179K2a%2Frnysrmnr9iCTY4RtSQqPwR5aFTo1RlFqfidmCVPdbtKxU1uLv1AYEdA0rjiNnfgaWYW1N5qDFyVLaFjDggPXj1CmRrZH%2FzBqHP34OaSx93Ly3SUKRjNdeDcbaBjzcWI%2BiR3RnvdbOSeV0BohSCXxb7yRX%2BmLxWPN5Jh9SiaiJpbgP8ODEeYzKWCUuzT9ymRrKmvqnm3q3q6Ax%2BuFuVz7emkoFJ5NahfS4C5XLXIQ%2BOAbGhpgcIMbgyRujumOtjrFZ%2BHZNKoz6leopjQHV7%2FG3tRBh5mbpN6QsUaDyGuhgsojqJicozQdm%2F9LHywpmZ0zuOG4%2FvYY%2BT1MkFxiTzzeQ07TZo6EiSvCBQM5iQVNVXImW11ZTd0oC3%2FCCQ%2BG6ZaDO9pwKFzHG4spUaON6FwHbYW%2BvFs6pxWQGheXxs8DIhXijkWopGGMh1o0m3pFTUziz%2BQFocI%2FaNIgwTCYTwlqsp%2F03fu1D6FqIDdw8P4B9CO0BBv6RdPEPl0Pkp3sMTDh4SyMJSOrjSYhaKAuOThhv6msq2vahgimyEpJKHzc42SujkpF462p0dMdncVen98PD%2FKE24ySxJrUmHSFpySnAY1vXHlc7w6NvRMWFRa7x9vgha2j8OXze%2FF74XdF4QxPRqPkBXYAT0ZLIfPiWX5%2FIByNRm%2F6WknJoTmBg%2FO2Jx7Xqdrw72LuH9Z3k0MIch9IuimFoxscpMEqzCQX4ZlkdzrgJDe6vq6pmbpR6oS5vrngd6BQ6EehkHopLhHuUeFYaiElaED8%2FDjG%2BMkDs4QWqwf%2FKkRJciCabPC45SBncy0RNJY0OQ%2F89IxAo3COwAvess%2Fr53MxFi97N3IKIX4%2BpDy0Ip7XGiX28ZKpuYILxXQdaW0MgQPVjcT1KDmMMMv6OZcIC0kRXgdEBDIyMbwmI3KKG23q7A7z80NKebgMw5DNNAd8HpdTU%2FMEjeuF5ggUmdfHWtzPz30iST%2Box%2BuhhkKUwINmC15eCYyEieqaAPH5DCt6qRrRal6yLhqn3G760UdLSnK6iArgduv6PlLDoV9WTCRGYnECzjW%2BugYFWN4PHU7LV6awSuxGu4MsaEpxVPTNhENBVBU2eFgSIjJ3rkJM0GvQgU80vg%2FJhg1yKIq6iI%2FzKtMliOoaRF2Cq9%2BrLIH85JsIW%2B%2FPq6o%2BUlKS%2BS%2B8SfYH9DvrUAyMkbQSQlxiRI8PY9dei5uKFG5SfwnJTSJcZqZiwSKvzM6YGxVBkJ84sgsXVSEjpwnnh%2FyhG5dVvAV97MXn83nldlbamyzklSZzLfn8NMDJMQxsy5bWjq5QKNS7RVGmdFIMALbB%2BqpqDG5RLuA8nno9po8kaFaJdDeix4bxIddKZ7kgI%2FV28VRC0l3GQS4dQ270mabO7WFZdRJK2sEzGEI9pAEE0cUTGmFuiIFeqUU5GC9zpF4f1ySWKI5RfKZfWo9LqbGlpa2jN9Q3MBCVrK9RBudlTrYNcftDFbKP5FjIeTz%2BOPoFWvIb6yjGje1nMc5tKt9EyR1J0YR9Ew5OGLjRvzZvw90yTO2DQo9h5tYRxiD40hcCUBp65DwG5OdpIJHIJ3Pw%2BaQkUQLDvJ1wgTAQ2NLa1hMMRRRYiu0OsK3J4XII5tRVMXDZ%2F%2BozBrdJB3CIGjVwlRgcHCTvpsKuEkuK9ZhwTGEFHC4IBlNUchNmvwY32ry1O5hmP2oQVYdEjI%2Bvw%2F2%2BjAdpVtnj%2BalHVEYDLVva2jt6gwMDg0lpyTYkTgpaO3h9KDNpQ9TAVUJyUjI3J3ABXY8TYgksu8S%2BmD6IP1%2BwLigHFBbhwiLSKWm7pLns0sosbXVlTd0zzZ3d9M4K4SFSXoMK7tgRDoWCoZ6u9vaurq72LS3YAi0taKgVT21v74AlBsIDQ2mhwhYOd3fv2I2Gggp3TDAEk2uI4DC4ktKsubkxOJ3%2ByDqR3Fu6HiaepY0Dk%2Fq1hODIqR3mC3HLKzhhKBtFCPuUMl6xiDIjfR7jqCvc19nZ1LSxjoipqqYPTQ34jQZAe6jgsKssmZr1lR2oBvzcVSZwnEvs1fUeAq5ZuEBx7Dif5EkmTTHDg8KrFgycsNW4okD5qFoKyr4CxnbnhKsv3Nm9tfmpuhpCAj9Vo0d1VU0kKkuOxrgtMLG%2BSlZcyUHZlgRQevr0eHwEZZO4iIMnGH8Bu0qnh3hGcvBheuzhMO0exg3AUgEl2Sw4OMnWQEJa14xrCtNlpizADYWD3Z1Nz26sYwCqqqurqxg3zq8OLdtoEFw7TKtmC32E3umVZU2AOg2G4%2FH9Y7izCzvMd3Q9Vk%2BzsJAIZJlILx%2FJSRb2a4iGf21u6uzuDpLdTi92QbAMdndva276y8aaKiurVhRHnrphxS4DuJ5oNMRX%2Bii7uXJONh0ouEMuGtffRld0UIwDyb0diw27MLZ1zgBhxXt9DfAi5pMYB%2F5CE0rLflNZWd3c3LwVOMKjGyQJ1tdJRjqbkf21DlBVW8ISepP4SSSR5MJ%2BtboP0ZxSBVdy0KLaTLmR31qP6PF9YwlCLjGa2KPHwqzucfWReyjDCjRDzI%2BQ2ywHmfYGOwvNJG2rFHqRBSTEQ9FUq55Q4aXIrrqaDUGUe1MJcn5%2FOBp9li8uwJWUHJJpdkn6V3sgOxklPSejo4mReFxv4RXrJt4DqWZmxkxtkMVBNPhsoXmkbZUKqmSiMujJer5hpLotasoroVx%2Fii8ggyspObQ0E9XR3xHeQm%2FNGxtFYe6tuB5zg6t04T9njzmn5n0WvHKTXClylzWF5pG2%2FToFAmtWxmmKp2SI0eBGANeugoOQupEv%2FpES1aZ%2FMe1YRxylx9MwHIu%2FRYqB0bERPa6HMDIU51xOd1BKGdXbYuXYhy8e0JKu7wDNTSxsjWViUW3wn9V8jqVZ67UawPWYwD3O6X60xGQnpdcFxrh5PGEd91bipHKfPhz3w1wn01xtj0g9pKwkHDFmKnxka6FxpG9rkoCQ%2FKOIbYKnhXOUQiBdBIJcyFR%2F1%2FHljIrDNvuc8WUn%2FXZ3QI%2Fpe0mQG9FjcZ6aUNEFQplV4b8pNI70bY2kLLNqpFkp5JZMsUGUVhoVx%2BvvKgvFYZtbmvp2S49sQ%2FHh2F7MDX3Syitzw6%2BeQGtPUHBKfV11W6FpZGCrjfoyZI1ydikGZYrJY16nCRwkJz6%2BzWTgSkqmzV2SNFOpVbh5AsPoswP796FPyOkdNL4xblh26Mnjb27fwa%2Ba0ktw0jVOIr2%2BA6nbZDxbbfRzCiVlptE9Wk3mrNG6W9kVAm4RlFWOpzhsU%2BdeYOUzDdg86MM6sRhoDf0PXSuk6uRP0sreQFtPkN%2BjZ%2FrgznsnpURG29ngL41ckvjMpM61GqFrikYjKjgowLfypVKCQ3bYoiVKu5upgdVDER4HfxmP7%2F4QaHX2%2FK%2Bcfy1m5hTkOEA8UL%2BppWPHwCCvvXGNjof6upvqaioLTSRNq04JwpRZsmmqRK3BPxuN7lbB9UajvXzJccEhw19dU2vNjJIL6dhP3vRhsdaMOQvOX2IZKTlDjy%2FQ1tsnkkop7QR%2Bf1l%2FwPOTkFQr%2F9VGmVklMcZCgNUNePpTJlfZBSj5smmBQ3b4yecuuzM5OU8g%2BObQTz9useLskxadf%2B3tjJZT5YdH3Q2B1o4d1lctd3Q3bzyA%2BZlxmAaqiaJSdVkac9Mk4FqgtHucLZA2OEJvzqnnXris3grcsnM%2F%2FYEUa06fveArS65NluwQ%2BW1qbtvOLzuHxU20WH%2FNf11feeBV5gYJmYBYjFjXD9VGKVY9Y8oqG6OszytjcNSmHnXyqWdedNFFS5YtW3bhhReee%2Bqnj0oFTbJD584%2F%2F9qUhUZtPSQvITnyDbIMJnzA8VudkpGx%2FDZBNaUu8kAzJCfkilwjGH5FNTnTZFbgcrWDZn8B3Kcb35ZPHvhjEC786sITGja1tAUHknS1AL%2BnDgh%2Bqw2gUvhDQ0ln4mzqatmGe04aGTYYQBfkon%2BgC1j2nOTJDpkz%2Fxxwn26ZoNslRtwujz%2FQ3qN%2BZFW6qSjc3VRgfqtFP5asnmqJkgrLWI1Xs8VFWsLmdkMOSZAhePg1EBVX5AqiONUOmzu%2F9Lo7XIwW0h8nR17qIXkJRnjaydBRPwr5Z6H85xojGcvyLbu6HPxiO%2BFFwDWSSi66nix0AIAjNm32F845%2FzomN%2BI73W5JgK4GX0t7L78Nk2uP3f5XCP2tkRo%2BRUWXatS4ATZeA4xamOAINn8jul1oAN%2F%2FUJ1mUpE3g%2BLvgiW%2FIAEPBz0KksnQtQGSl47goCo%2F6ZMIfdvzyM9wPS4JPnNvJRs0CFQehaRyd2MjCXDkBQ31InL1VVXrTy40qCQ2C4q%2F6%2B5ws6AnQh81Vz1EP%2FzBVJ6yyNV7eDC8PR%2F%2Bs9Ioltx7utjgdpRUMmp%2BDjBE70C6qdCEUtr0WSR7cblkZjJC1HMWFB8EZxdshRRBf3XvHj85wzCwS57sJ6GnGvKUPY2CGn9l5D48fvMV3Gb87%2Fzzl%2FzSrZgcAt0bcMc1728Rt0rTEBgJb9%2F6zLvAb7WxAkijIyXNHpWtwGaLX0BjCP2N7ehm2ejAhwpNJX1Dxd91bp5uGs3lbvAHOnr6eN1A07ooEQAAA8RJREFUnSbvB4URzG%2FirhupF8CN92lZic3UUWlZNIDgdqN%2BE8ZKGEa5pbWr695C08jYcPF3nSI7g3kDULurn%2BCS7v9D%2F91bn50Qfr%2BxVougKKBQTCZ9VVfJrpbXCujDA22Cm8BHKvHGxosLzSFbmzF3%2Fvk%2F%2FqWbdbqY%2FWetD9znDrV2pxU8Y7g9R35qv0mVrCALPEmEZ6oVAG4NZCboYhzlJEU4LryPFRpAbjYNXXr4sdtl1h6bAO6zrTc0GGF3%2Fpuz0Oz5rTE3feaX3cxg67biKNYqKCnksPq%2BVOiWnxg7bM58VvwlMeDX2iH8J75qG%2BGFILr7Jbx9W1NdXWUmdypVjpMbVlcpLtNCXvJyVY9vbN7WzT9IEmxMYe8TbsxmzwX53ZGMHfafKP71ivKPfAkVc6G0gu%2FuhBKiZvwcdE1yIAZxWfc%2B8z6SjU1bu4OGD9uFkzHb1Nh473GFbul3xabNRsVfUvnhmtC7CfLPYMR41U88Y18a7N7anEKElQYASdnwC9tqrllT92xz946w5Sd8epOr7V70PV7vY5sxZ36psfgzmRciIMpAkxYQpCgMb7cQ4RoDIakLK%2FUHPeqeam7r7rMGFo3uHgr1tgeSYzvt%2FY2NG2QvpdeNg8%2Ft9ngDre29wQH6NQzSh4vozWjsQ35UhKDC1VZSs%2Bq7IhNr6kBfW7u3J%2BMFJXUo2NPekiqyNd573nGFbs882yFzFvDiL7UEvYFAe0eQ9KJFFOUpV5TQ57%2FDYQiHnc3Nz2zcWLexrm69jK5m40Y09dmmpm0Aqy%2FVR1cHwqGu9taUwLCtOu%2F4QjdjwQyKvwt%2BPJ77FAi34K%2B3GGQ3UShf%2BJfbx78psJ6O1i3jE8PQPv0e6uJ6t2za7C8suuDH6eFD5sMqJAgjpCDM5QsXBgdCvV2tyaOYkdnFpx03ScJamob7ztKUH1OhL4AuBgbDGXxxCbXdkYFQqKenNXUQU%2B1eYPZeuAhQGJudgftktgF19La2d3X1hkKhoaHIkBnk0MDAUATD6upqTSOCGXV2aZFZWoaKv9J03WdD8gZvSTNoJbd7rzjv5Pd4R2QB7DB048Q4%2FDZ4c0STFNmqSxYeX5RZLnYYuM9k4S%2BF3LK2VVect%2FBjxbRxwgyFvyXXbngX5bbqiksWHnd4oY%2Fz%2FWoHzZ5LHehEYQsAsNNOPrqosfzYtKOOX7jw0kuvuHFVVrRuvPGKS85beNrxRxersgLa4Ucft%2FC08y655NKLV91446pVN95roISmwuPSiy%2B%2B%2BLyFC4%2F7WNEdHtj2wTwm8v8Pkm%2BrFsKSnCYAAAAASUVORK5CYII%3D%22%3E%0A%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dxrange%3D%2210%22%20data%2Dyrange%3D%2210%22%20height%3D%2249%22%20width%3D%22166%22%20style%3D%22%20%20top%3A%20297px%3B%20left%3A%20371px%3B%20z%2Dindex%3A%207%3B%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAAKYAAAAxCAYAAABQ69KMAAAAGXRFWHRTb2Z0d2FyZQBBZG9iZSBJbWFnZVJlYWR5ccllPAAAHXRJREFUeNqEXW%2FEbld2X2u%2FrxBCCCEk7kjdunVJ3XHHMBVCKoRUxjC0OqaUofphVNMvjaE1NbSG9ktDCaH6IRKlY9IZMzoavVq9xFyuiUYuISbmaoiGEC7h2avrnL33Wr%2B19j5vbjx5z%2FOcc%2FbZZ%2B%2B115%2Ff%2BrP5h6%2F8KRUSov2j%2F2cmkUIsQsxVf2X9z8%2Fp%2F%2FZjpqr%2FFf1vu6bYNVs72%2Fft63b9dn78fvxPr4f22tUMbbYnCv5f%2B5H7V7Xfhavdsb8Hz%2B1t%2FdPXg2s59E%2F78bj24yHozwP6uWLtTn1rzxpNcW8F297HpN3zkd77wRjPbZy1vVt8wfj4e7RxEmJruZ3n8J77HLHsfaz7Pds8nGjd%2F7L3jtMc5fFqv0j%2Ff%2Bl3nvb29%2Bu2Bqr3o9JZeCb%2B83PFxinT2TkSpQ0CiT0AL2bBAadO0P12FnhAhQnyiWFcAPtgSyfGUyCqcRwHUGwi9uP%2BPKSpQJTc%2B0F0TS%2B6T9u51k9d1d%2Fv19MPax8u9Ql8RK95dPRzvFeBd6W0RGLfYEJgMdjQwKQjAW5EuWjvM23j7f4u97SP72x91H7d0XY%2B1d%2Fu6nUf6t%2F39fPxePa4vxGJz0Ve6IPI23zUNp87w5HDd2yLWPyerW9jzMcYdRoYRLe%2FG8cWfQyq0wmctbnXs%2BdErbH2UrW9mFBqdLxre7Hx4rSv1NiB8EL7X%2B7DUoG4qROW2KpqE9GuLX3gCNoaK3PiopWvabuXdYA2jnZJf7usnwdZ6lX9fn%2FmLsilkYBspLd%2BCRKKDtNGvAcT18bA7y%2BhzcFdauj3ipvA%2Bfu0jev2O9cnURLxxNHkjrb3qR7f1q58ov28oz%2Fe1o%2F%2B5U9ojJ10RrqNbSfOIRHau5XAdHDhsfWx2oJq0rOzC%2B600NsS5hXfP3jfQbBj%2FNrx%2BWDJBA%2FfxbmtKGgWuAFyOOnk59du955s%2Bga3bNwYWXgTqU4gPkAM5%2FXLA53wtgm73MXqZT11dbxIHADxQTcFIIvfg0kQiSKxCPxWYLWLccpGaFn8cTs%2F1Ixt8XdOg20MFSAuEpQ0oD5xXRHylT5%2F18dP%2Fu71o41A9Vi5Lr3diJXe0%2Bl9f4hjJwzvU1aJdsnWJZxJCKk2rkVAfPMJORn0B%2BcJVSdJdNO%2Bn89CarBYgcFtEyzsehHDgwdhj4kb322F2co7WVeNa3AQ0PfrPV%2FexK0eX9PjK3r6ih4%2FwhQHPagZ%2Fbm167Zb30oifO73chKp2F7kp9XGb3AHTmJxfPf3dXHHSUXa3l3qggjLzI2jxGmiefSBgmKD11WzD4DRPNw%2FT0Z9VT7Te97WFt7ZOO6mJugzbqqOeHdrtpg%2BK%2FZpDIATIVGwIUzn7GM%2B%2Bl%2BM6JFIV5zZ7ZXzqGQ3pTnoK5n9CiWi4DDZqGyjiiBGNGEyL%2BsTv6J%2Fv6wD9qQ%2B%2B5qLx5om2XUmVxEqiN9BTDh4tdN9VxFoVhGODK0qTUS5qGPj5iUYIDLxuaUB03Ve15TXKkIkINBNRSYVYTAQBr39yOAA1aCpCyTXuwTy9lnuams39bFv6Xve1Pl7S9v%2BjKyfMi0cNLSkc9rKpS8blIDIEGQyToPOKMAxZYilxMZdoQc2TrXT91Cu2YwYXA1utZlBdEkH9Fk9fkZPP9VWsyRr1pV3Rs6Kkz4WkJRm%2BUsWy2TiPC4wDhM58ADTs6Vzp%2B1dVCS5uOuLduduTWSZASazJjWrNTUYOn3JWL99ol19GhyHko4tNs6nRMA1EOWRJAgLRSZx%2Bqg%2B4%2Bv69%2BvO2eoN%2FfOm0sANpYsbUQLunAbEv4t873vijDImWpbqy%2BjTeeYYwwgx8QAK6XiFQbwFpgGNm43b7Fac8P369Gf1l2e1vY0YH0c9w59RTBMMnKy%2F7DTQXao1Ec1GDhW4yNCNBiG1SRMYqAEZDU58MopiUEVsgLvRQGixy7zqMxdGLumwi4tAvH8seJ4seDZuPxlNXCedlG3RNChoydlFApd3hsRJRO8M5KmOkmxGlhKn%2FEx%2F%2B4FO%2BAfURfxY8gWMKzGpBu%2BUFhwlzIXHmPzrK3%2Byd2qILVxJjlNy4pTFROPi34P6UWLk39Vrnm1644G4Cvjn6Bxa%2FAhr9IE3LFWgT7Q0HPA5JFG3C%2FAUcOW9fcPjuC%2ByutAB4xJziKtMXHmFsV6MV9LnYoGZI08GE0fi2%2Fu1UB2iYRLRzBkWi1q4qiK3lPm8oXTwekcBJgOn0ZMbwf4%2BbKpjXjiNUXQuWRAKoGIcx14SMSeuJlY6pd%2BnLWwi4Ef6%2BT%2F9vKbNf22DazgJNwHwYXC3apNZAxY3rq27yCYwACStOJ6mq4lbJ6IsNhyeiqgEiRPlgK4yiD70JFQTSodfRhvtWhufgNGKLW6XHEIO4fjknMK7be8ki3fFMR1QDSIJNtYSNeHmAKEgDbu1B6qFJEeIYxr6jOtKN9%2FVo3f1vd7VG%2F9Cf34kM5FqRtApMLZBR7zA0cv8ohwUJk4QysZBdqu8NXhVz%2F%2BtHv1Kifif9crntINnbTUUIA6fRoRvULxlCL0NDoD1ImCE0MQp86SxiaWIz41n7lIC%2BkEJq6Pk5XDCOZu9PeBwaP0d%2BpPrkNt9u6rBZKJ8qAZu4fOEOGCfd%2BB6YZAy9tiA7QISKHMlNKikj4Vr4FG1QIZSk43C4IXbIbzv6jv9r575kfb3eW3%2FjAGrdpYyoxB5HkrmZkIIi5TJEus6n4pq%2Bk%2F99X%2F02wt6x8PjJZuHoBHG1qHokcAn%2Bcv7ZJBN%2FJjYedVKGOBhiOwvL5zwXJm4qkFaE%2BGUlYUAepujCS5R6mT4BBCcx%2BKS7g0Z%2BJ5M%2BmGFsV4B0yiumxJ11t%2BJE9ccALgEaBy5Z%2FKhdclYgmwbiw7Rh%2FHetS9SJgFdv0uZsv%2FynH7%2FoR78Sj9%2F3tU7wGQ5oRVOeUNnLdEt5P5QF3Ft0HqnvqbHP9fjn2zYWNPdsp4ny5cb%2FndJBOCck4NP10QS1bCWMqENQhFyfQWJDPvWxGiyAhPWlrkuT%2B4DWLjMafI4Ep5IIP72Gx9oirIU1cihKSyj08QNwwIWwJ%2Bh3wPOi%2BOLcB9P3j0jRlucCw%2FYWEQ16Pcq1uWv9Vm%2F1OPv6eehRrhAH4KSR0xNKpJWU2Si3JwfVJ%2FSSfqF%2FvAvOiDX0deZDQoTKv3lxoANKCqMnRTUjpKokAjVLCZTEBFAX7DM4mJX8rkmJZt2ztImiQ3tdIJwWH%2FlZhsLzRfbyiXH0X0LhCoTsHQC7A%2BdFyUs3ov%2FRa9dvsdUDUlcFqQWwzg57lwnr9m8aKLHxxejPKjH39E2f6nH39Er7gsL34zGjhJvhqIEnU1scAfF6%2FE%2F6d%2F%2F0FNP4EAzGBhoUNiAcyOo3RvBbCKDGNqY3IkUjBaii9x1KSAC3GeTiAXgOd7TJ0j68hE2vzHCTnsblZdGC%2BK1JholCMX2Tot3jRYuEmoFRkEA%2BZAbFYixjjNSlj5pzoiCSICJogRxl3Sc31ndCR4vKRculq6%2FPqDtfk9b%2FoUePy1JvRoLYDfGSwexax8c%2BLfBPe%2FqTd%2FM%2BFzuGBIUupd4QBaSFW%2BhgYJm4nbCiBw0DopcsFJlNmjM2i0L7h6NFupgtXRdaFjRPHSfrMQLHRgtEtQN7iLS9NOuc5txVhPKwAJPKROURlTDmKAqEz1MURkqaQ55IYVEOATYBDdtJnsI94vBiV2C2YITpKErevzv%2BtmY3v0UEJ7uVh3cxF1vdKYvvFnar21Kq%2BDDF9YwAsBZD%2BRueXLQg6JxseuI3YIXC%2BHqA8Rsv8%2BDUvpE82Qhr1ZwsUCFDp%2BwTP4aBMQHsF%2B4ggZZzc%2BPQRzRuMCFKoELDiPBiFPExsh1Vu6OLQF%2F9CkYH0gowbgUn1gGCGi2ASCUcAoVFAt%2BGf1qc7BGUff5Yj58xvCmYUgkQIjf1N%2F%2BW48eRzRkN5xxYBv10r9px17wlV2J%2BZhFIxeMkzNHxGTPicESYMEPg2rXyYSDch5xQA%2FOCMHC4%2FksUx8HsaTVC9wIpYZAgG%2FkQua1YUrhYtFnfYQDcuJ2PJCMjmy43dG5tkmjOoEtQTXhGgKoaXG1v3OZdV3hpVcpEP0CvWChSZ%2BPqgMBE4mSucXJ8s83Yxqx8QIiYlOEXttk%2F%2BQPhVW%2BDMtaKNFECwuZ6xzymzidrWIGkIoBlC%2FiLrdkySHRsOFzEDCwIPIBJrdraDKcgovTruPJ6l6pDoMb%2BjvWJZF4DOrQyYff2IF2N8bEPHRHvMI5epbXkoJxOCExcsh%2B2tyJhSNGw0oORT5io43DC3ju%2BuyxPLQ5Z%2FT4iTFHZaxI%2FfHv9bLn%2BcCrwlQPQBsBOKlMCrJHHNEUsCCTSB1GU0nGGE2ruhktZck53JMihvU1YDt6oXYxzTXERNbgaSmgj0YYSYKTgBe%2BbbdqkYOhfj5Ep0NqjRgN%2BJ68P%2BBgEFnAbY4LB8eAyIyLdkJDo2sgDLPTpSYm4otfmA7uoaBbBjxUVlKXH9RzP2kQEzUcUz%2FP6RP%2BeOVnJgh0FSqTDjHyeob%2BVQh0ruFeWoSJxZUKxF%2B5p1ycAVH0%2FBWJoWPMx6kPA6pyNaMupNXczvDICEROFQg8yJjvalFQ8j2vIK9hHaNHrHBEAnzcxNJPUAJ4ny52QqwJBr17Yvp%2BkAy8Fu3oKg7pIZxw4JwHZoE5dUJGuvR9VD%2FfN6VHT35%2Ftnjjimw6k4tf4zIQp4cuyMBZhh%2BOUGcSEDmQV9QnB1MuBnRRuIZBmMQicDac9HVUTYZWSvCETO67AB9FXQt1NgbDDY2f4HOnMi3Qi4I0CCJ3MESR86IL3J4Xi6aAa7mE9BFKILxQDEyOTouYRsIH4XV1wmORuMu0cPpY%2FL7O41XV2MqT2wGKpzHBWdQUiBUc1liMpu6%2BZCabnLEinIAl5I6ESagdGskrdQFdDNbn8EZMCEO1oYKoqQCGS1c9gh%2BYKWW6lBD0IBBwEqLIJeKrA8vMqRYXGZEVUYbRtoxYzAODJxhoh7azqUct2asapmw5SUAwjkJIQDWyKxM9VYN7en8avSxBeHTCTIAVn%2Bl0vrCJ8qdXWXaSpAAnrjjEU%2BB6TJYhxws9CO%2BvpoVh3ktvR2gKt0VIA1MJPDyOAmfx1GGG3J%2BsmNd%2BLobHoY%2Bcekzqyv3aHAgYreTIxD5pwiZyObgPI9eQvpCHYWcKVRtEijH5C6s4hL3NVoB53pLUARHqgS0shqG6JOCsABizwEg0RB3cGD0dLEheqmKtX%2FTU1tKjCIwO60%2BozPpIWpUleon66j4DhsYgtkoYxIHwx2iWNUAdXXuYoTi%2F87DGMTrblXa0kN2TU2n2G8%2FIhEwii1N8I8I6Iy9%2Fwz1k4aUJrtQRrZWMlPY7T%2F7sHJzhzEImRwctJF5WKRAZQIeI47pue7QFVwIN7M8UXiIUY4FmaIohumpysrBc2s7cc5Y6%2FLXVQN05Vq5OCrGsuFvtVqZdXxeDEXUyg0kAoEaYJHsYOBCL666mizGHELhchIBTTGVW8mnSq0pSXWTponNssi0QxGiDFc6cgiBm3TJPdkxym8PHPDGQJySEJnEMDCYk9on5rEOoYsdnBxwmNiqnEEuaxyTgoUzBeK20ylOSe1tLd7IoDH5YBENZDvygMhFd00FpAZPUoEsZpzQ%2FtQRvhUfRtG%2Br5K3heXAiLSmnBaahpXwAB59z1V13qokb1gVxHJstwcuTC0t01QD1%2BGig0NKzFSe%2FTAsi6%2BDZykZGgFFgqIeiRPO5lRCmVzCoOzseEoQ1heQFF2mO%2BdzPvb25JN%2FQzykmt8ME15kb2oukUPoQgT6tRNDkWA70TdTlZGEg1PBsEykSLdARMLtaZF5lRA6MEI%2B0ljkMd9buJGO3nALDZOmFGf6raaFBqsHIaXK0Ik%2BkWKT8ygtEyUAJ%2BfEiIfGNl8lhtDSy8lgMHNtD6WT2NMEiY6HlIoPF%2B4PNJXlXr3zVNbwOJXDPAl6AwzkkXkJuJC%2F1DPfEsLndDBLqf9t1EfQOE8wcn820dvElH3WemByUa8o%2FWO8eh8lmqXKo8tNUlZGUhzGFAb7JgbGmckRuvPL5Z1GOoHks5VOX6kAMpcsqB0%2Foh0iZkYK9ryXEIOQI1aH%2BDacH6rliKED18etpM4UqRFCYdLmrn38oHYp4Ubv1iQWhcg0BnEexKAN0j0aDxzfmgShc3Z2XCB4j2d1rQwGfNHEm4HOWNVSyAsDHREwBIUygV1MgMFMRhGIFDsIQPjm2MBN3ZlyIUmBixXTEI%2Bw1BzrEsRCQJiVx7bUbNCarpcJcRlSnGMFaZKnKYFkut9alG3%2BzY4IxdkGCd%2FEv9eheaZ4O3qj097SVUyDGXvSqBpeYE%2BxYKSs9YhZ94mVSwCs0IohQRCDc4AOW6xwNmCbpUQEvjFYrogZzwO%2Fs98XgVWIJETsIi%2BAzs9VqYWsyA8qlQzh4PcJ2GN2zcuLlsXBpUqkZ18Uj1i%2FwhR9BTdyDqBm8eRTE8ME94pmtAzpcMbQJdGd%2BXb%2B90iLYO3alF%2F9Ub%2FlWcPj3qOscsznnupSlAn%2BRRwND9zOXyGB4nhjUq3LM5spqxXSNldXqPv2kkwparZOC7glt4oBS45I0caa14ZiirLrox5yi4OSQFA3KvDDYohTIkNFcX2kVkFig7zEqjJdFC2nCTEM%2FJYYFooQAx8VPdZz%2BwCrujUiePmH%2FqE19Vf9%2BGnOTeeHSuwjgPZqEE6STZtFCEEfIMDweeo9prrQIWi1JH8v6GhpykoyioQth1mBJ5QTX7%2BeE6PBVjVFIh8ZW9qHPsY3ZSPG%2BY9aoWDZpxEhdJYoitACawlNYnxzGbHqkfYlxlRNK4uZdCXCRqxuEMZsv611Kd%2BWzYUS766FPut72hn75on674w%2BWoAMugwFC%2FUOZ%2FKUClTcqFGwK4DHXUJ3Dc5M78UsSK6k3Pmld701cCgu1ogvWjKKerFYWabqrXHK0HZDAxlW5XudMlF5ORVKOe3ZhVsxQDMaOeP9qArLF1ZTot5YJbVgFIs9Sqpqw84UvSV0beV11GdmUDOeNEP9o%2B%2Bw1ktBjNPSBWASG3tOLv6S3v0TJ9I%2BFBGTh%2B3QOJL3y14wXQjGDrmNlQwX96Ty5sOTAkvT40V3tEOfEwfIFx5KH30XcrqAFynWpToQUZJbkaz4OpvWyM0JEcwXPKZ4SKjeX7M5EzxkuPOR0PZwuRMiHynV1CfOEcLpR%2BkWcI%2BfwP5RyGVxfLM7b2t5v6a8v10XYXMHqbgUSkbTprU7Ntzfuqd9vodUYSa1M9X1GOL13PoLDJVQlPpmSvXRBGtjMk%2FhFvC4bLzFCfoZNRrDsWr9lIoQ4unXqizJXzShLw61CqFeMbcVwPAruzmEUoLHi%2Beq%2BQKZCY0txmrxZlSFSPpZlzFY%2FLWJMTSXpXi0vWsYHkmsF%2BvMnek7pir%2Bo7d1a6%2FBm1AKYXDnUCtK%2Ft%2FX7l7TNb%2Bnx%2BwLpoaEKcciBcUA2exMQ3kBrPIrDXgZwCbtwCMnyGMW1qVUPMgfDX8lGUFm6KEsotlWWVTMQZLaA3ZIJMVu1fKHljF6tYkhGOYwpCB4wzCEfqSjB1Zg5eVmYNrwKT4N40QouzEIHNaXu6T0qgek39NxLWQUQkBS9dI2A%2FiaAL6bKuKJmPMuv6zXf0M%2FbFvLGvPRyILuvIdKcJn1qPw%2BF5UU8GWzlJ0Y4BWMCV5mchnJIWaaYDghrCq5gBi7O4KU6CwMvHHVr9K6Yw0DmwNtRyGpO9qcLC1mN9OoSUhxmw2ykfXDwZJVkzCRJMTJEVyFqVJY6PXr5Sk%2B2qzEAaKsb%2F3d6%2FAXaJbB8uEJgQvSViFc3yBAQB9%2BppTicdLBf1cZ%2BU899Vf%2F%2BeH6L2ZtQFpl4pu%2BMQgQIsbDQsp5RTiPgdaKV764AQsbyzTml7p5AxwWPSu9CtTqgJ7h%2BRilWNZAy1wh4pcXLyTIdZW1g1oVXKG26cIjjSlAFeBUtNRXlLYeespnT%2BrP6mLyv7byov39Bf%2FsznfCP1u9XQrEyY1orR%2Ft4ZXcN8ir66A1t6Hf081hD6%2BmuTBYjQTBqLKs3ezMqAnBzQDCUd2GoELeK2cQkq1xzUro17cSApf9QJ0ZHZYW6P2WxINZRQvm3kirmoTPiKG51RaSxekqNKQ1QojHjuBGyO9J7EQiVCfDHRR1dj3s797T9V%2FXdfluPf00%2Ff6N3fjxqj1YpM3KBBhIjB2ZZxAlCSWvGUoF5vZpv86%2B0k4%2FpGGuH%2BKW%2B3UcopJrxubqo8lZT9d0wgTyXvA6QToriWa9q18Hcul2BxPUg%2B1NS6USadMfMHZF7E0R3YxprsfFx%2F%2F%2FKETBlaY6YRqEAue26nvDk0o3v8nkIh1icaJgLJijFMyAf%2BrGe%2B0P9%2B5jOyTf075u5fM8usYqAPl3AzoB0mD4m54MIRhKWKfpcl3F%2BVsx11B3CgWR6Ux%2F0ph5%2FW%2B%2F5il73PO0VPbZKwgRh2VHMFDCO5nA1YPljhWGmXxY%2FHRvM%2BiZPVdOIiMr0naCQ%2FUUuvJJKU08uzeHOkzUMhvgp5pKvtm0ZkgaT1oSyTQBzZQVpS0AniNYbKeS8n2yxLzZS%2BFTb3KoKv6qf7e8nIT5XeL5H1s6WqULyKHWN%2BTpWo1c41Vx3w8YJeM0pwFK9qd9u6nNe1C%2BPs%2Bx115%2FRyXpaZ%2ByhodvZ9huhAoWXreZFTXezBmUOgsVwLyxStdpVLRe4ctBJltao9VNiBQ6%2FMu4gx1IDr5twXyjYgruboajEeut8YCkjV15VRHEVC7BXce5qxb4gh6ukKnl66ob%2BdkPn7Ibe9%2Baq2nILWRS3IWRd0tu3A6FUjtUjts6DNcRQ49IaknksWLoq40n9Y4ejOLhm1Gww08v6rJf7ith2S3hGr922TvmK3vxIqEBBEV%2BM9Snr5xS%2Bd104hrChjhlLZ6PICvvvbKKnFvBI%2BSP2ySqu8iQXW4JXYp15SjlAjZgL1EIXdznykdSoqX67E0TccQ25OhYfqyGvP%2B0%2B8pmO8Vs6xspc6L%2BUUDbR%2FKnHXA7O7fhC1qstS7X3kRc0ZdxevGr18ISdD0gjuskqbKx0mv3kkN8tYDxUi4qGPQ%2FZ3WLg%2BbmlE3DLV5tc0mep6D%2FthMptq4%2F7UPFueSVt0RSKosp356IAbsft6vJODnIoOn0Hj7PA0UMEe1A5eBKV%2BfuqTjovAk2CGJ5C6WTJgYK6Ilj2WnyjqL2mal0Q7n79e3q8gd0bId7UuXmrQBQY5ugzBK8YkSUJGne1OMrhgvHmWV04R9%2BzVTwb7LvUxXYhfdVImXxtBSxstNBtZUIN8I3biAXRygc6MR9op14HTrhtNDp2QXtCj6%2Fqs7bjh91TBQVH5SxZn6nimfRnhnxpDs4BOtjhYS7dSostWlLwhKEBdQraiHnrtNDt3B%2FdJGL00dewD2eFEgslbD5LM6x1SwntjrawEeK2S9qdfas%2FaqtvqD1jbnLtSlPnsJAYxwV2vGclhY1agw48kmlANThf56%2BwBQvPK3%2BOZFltJIS%2BbtvL0KJtyHQROhjs5mXaNvLkn7XB5hF8sJUSUQLla7T%2FpSvKTS9z29LvALjtJZiFpvykuBlV3GkhKuZ1Odi4zSDRvL9O3K2CPR9feHLxVtTtko8Atygpy6BkGjtDfKxtvKfXbftJvrNxQz3eCPC9DB0JGEACW%2FexZHdIXUihbn1U3mNHim2oRYEIc9l0NP7yBqwF1Irzw4CMvLvsAl6wjjJuRrrewJMBErGkNYsckuCUm2OiCbaf3ixAeYv23bso43TXu9i6ohdvWzlf2jms0EO6KB7XCdiq2V0N26eERSUhcJjJ9wMaBWFXbkOckChqxSY9MACJADcsxknfg%2F592KG5LSTxjj70pL%2Ff7rz0Hb3%2FHvcdeSURBG7klbfIs1pRY8FUV4tWUfkhEknE3JzZtRvF9wzm07SVChNuyHqeO37EAacBA0KksBHdabEpEy0gE4aa7LKMHMqbKg0D63hHXbrVjahbBOgCc3af7e%2B5bRN91tUDIGLTqR7Q4ytjb0V%2FJ74eYwli5t%2B80ZLhfh%2Fobx9RTIf9WLv4PqgkW8du9zbe0fP39J6d2OI23dy2Zk5qC6cM0zGcdez01t8t68EehUS2t6W5ZIVgN7YK0U4npeEzYyfHaE1Uk2yBjBjYNO9jD8%2F%2FF2AADp%2F9%2FkGB8WMAAAAASUVORK5CYII%3D%22%3E%0A%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dxrange%3D%2210%22%20data%2Dyrange%3D%2210%22%20height%3D%2275%22%20width%3D%22430%22%20style%3D%22top%3A%20263px%3B%20left%3A%20442px%3B%20z%2Dindex%3A%206%3B%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAAa4AAABLCAMAAAAf1ZMtAAAAA3NCSVQICAjb4U%2FgAAAAXVBMVEX%2F%2F%2F%2BznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGvF0qvAAAAH3RSTlMAEREiIjMzRERVVWZmd3eIiJmZqqq7u8zM3d3u7v%2F%2F6qauNwAAAAlwSFlzAAALEgAACxIB0t1%2B%2FAAAABx0RVh0U29mdHdhcmUAQWRvYmUgRmlyZXdvcmtzIENTNAay06AAAAnhSURBVHic7V2Lmqo4DF6Og%2Bggg4hYkWne%2FzGXW9skjddRATVn9xsubUn%2FP0nTFvW%2F%2F8YmQRjOw0ZmQ2vyESrzMIrjJMtypfZKKd0JtP%2B1R6CV2m7SVRgMrep7ShBGqzjNskIp0OZfx1FPUU9YyxWgC2qbrqKPwz1DapJqJ9qqA%2BaEydE7YNlrpCyyeBkO3aGXlJ6k0gKPvaUngR9inmQG26ulyn6W80%2BIvIeEi1W6Vb8MYhz6ulPABIAdtFyUhJ5LRpw7q1SexuHX0B2epsyiON10zgQOVuhocDyB40XTsoQVdxc0vUmZbUTtsjj6hMgLZbZMsn3psAULPqCwZnIHYLxwhqgLMkZdezx06nZgS5afLPKoBGG83irMhAhvj7BFGTCNzMfuQHe1z%2BoQ%2BWENSRDFWVE6mGz2Bgw87YYpfIu5Cq1AYqV0Lh860jvjUPk6%2FuT%2BYZy5PAIYdvjEOYr9w11OINcd21REuIezkjPTg3L3rrl%2Fw5Rg0x5CJCaSgOaVhv4%2FUwE4WZgc25DgkZxc%2Frw293%2BbEDlbpsrHSJNBy2V8GHSwTPGZlMUfgJ5jdngNO%2FghWnBAFf3YXety%2F5cOkVFaVAjhv1k5bcAMNAx%2FC%2B%2FpOHfkBvZqppQlfJ9nqxfM%2FcOfAo9BGBB%2F3QEAxTzARbk74IvnSGGjkz9AIsVITUdSz70fFspik7zMwBauS9JfBgV3HJ8boIXIuEaJesTsmdwkxdH6cWthlcrSVfhvaLz%2FIkFSepGNgmCt9kRokoKhUBxMWOSXJWvwHRLcrAzFPTqx4A%2FF%2FmaCgtqm8WKSi1pxRbvJwdDYkrt4iXl0to5asKFNYB%2FDTI8AGQTRhY9yJEgep%2BoYg9A%2FCia47p9aq3vWYoTvO8wxj609oUM6kaPeT0zNG%2BskmzyoLJnIun9BIRfBBs2jJPAopUWIHSrmKTRlQHD71NAZnOhEaFyy%2Bad7MKnsndgIYJX7rXP%2F1chz%2FyAtwTAgGjacQNRHkcQpi%2Fmgqx3eba844NCstcqzMS9qzdfH43wPCTd47m8IQOtUQnhDf1zjAgmeJl5Mow8AXI%2BVEubsiOkTM5du3X9ocnwJFEN3uo7hLss%2Bf0OmWalNMqZ1%2F%2BWh9xUfIAq%2BtEtPMAeTcXkWTsH2DEBwsb4iMCWGG2P3%2BVDv%2FITLOA5bNw%2BiBG03Wp1Hta3l%2BwbT56mZpKpz%2F%2B9nhUizezW1pI0bAq8K3FXRerPUAUlwc66TR7YYyv0m%2BX5o7h8s8%2BrdI9q9DbBqtkbnjwiRSfXyJt%2Fv0SCWHrarRhuoB7bNfQe2iMMA4smjFuk8p7EVHaiTT%2F3vmfuvKvcUo4C1GRqkSCFBhDiIHQB13MOCs3zf1STUH1NniBXOSmV%2Fz%2F1nWxBUAk2ugt%2F3XqlDscnW8Sr%2ByQ%2Bmf6dDmpQ5YrPQtAV3jVKPEea8GafkPkjGXxDrOvCtHlIHHKWmJWyNuHekq%2B151az7R7ev%2B4f5CTrA%2FeN0qIzaSp3%2B5%2BpDB3om6SeQ%2B%2FXAVty6od0ShrpxSQioUjkch6tMWXVxyOFp5d82OTQv7ed79jlCby6OHifMVX7eteZaqhteZv1KK9cwCJ3Gurl%2Bqm2ykDKfecMZSHUdYIJBTn54cnWutc1mQ%2Fua9%2F2D1UEMDjhfQEgi1apis5I4C%2BO0%2BNVceO7PnklyMwMOiFza%2BwgrIP%2FLRoeptYbjuYxvs4x9qjHWhkwruBpnllX3l6%2F7L%2FJKEwESJo4o2J0URx4x%2B27eo%2Fqk%2B6YSdUrCK27lsEuX50kL4r2kqGvTmTpXtzzR7GyZ7pglcBjYkgW6Z3p51LhNbeDzbTSMOG2l9RvUin30UaNCjfWqEXvxIxQAUYXphqo4PrubVZFG5973CdcVge%2FiNO5cktNw5t7W0dNK44CrpPFziesBaRWXpST6TyBKGVWL%2BFwa8s2DIvUnirSVi3LSJtk%2FMI21fuX1Q%2FdgUtk7QVGA%2B192NixGGfExwbIJrPXf4hK2HGel9pskrTtoGSb6DUPk9vw7kO6lUAOND69Tf3ft4krvZ2OPRd5NUhx5NXJUQAHAZYkGR78xqif2A1umWl4A6SyxM17aS6%2F36xuXwvpJtWtxPPNXe436h9OAoIvLPGS5Jb0Iz1lSsM5za6ylmN9GVi%2FzeKOclthtGIQGP%2BYxvjcy96IO6AlHV7PidIBj1outCc9CuGK0qqAMUplEE%2FPU5EI0%2Fy271INQjnDa3mVvYB5ne5LhHIcXa8IijlSvm2gjzIUgx7DB0AkgXzGku%2BBIypIQIvfPk8thrgea9kNDfrAo4ntuv9WT6l31iYWi2cHuOizDJK%2FAtV9P4%2FLvR7yW8PXtJtUOX6a9S70QA7yDpNfsjNQAygK7iQ%2FR86zhEHd94McPrwd7FiVZsf8tlcoe%2BwmbelJN%2FPkNs3e8wNEeLR6I9z3kXz9Bk%2Bflzn5JwNQkmBLEkG8BRWgS8%2FLV0HxcIsGi4QzbKwi9cX19kcRCU7obuWTuNQ5pF0IwBR6yOM7zm6T406a29hmSXWGlQHtxwkRD17FaJvZBwSBadRM0RhMPgsBuY5Ic9II%2F4VMAB5nvzjIDBGtDFkJeKA7GLX318TOaYvnQ%2BN8kYcPZi4Y7opQ1xu5vNd4PK52V9htZSPLx6unIbzQ05n8Vs%2BtJhyaNgyAZRDzUgB9qqbiHuCmP4qQ%2FojGD%2BOvksRrhR8pukY4z8LuMFxeIP7DUgxk9D5U8NgI9lMOwMEM2nJnwhh6AfZe2YsksJpZmnJavflI9tggmNOVUEovx0N02fNH2ydTka5lsS95vfkwABI0zP1LER98CyCo4t8GOR4ZKYP513VJnmUz6C1pOSr9T7VxKsHJ5VCLoMtYGnJIXr%2BhZVAK7eOWzIS0VskwBxOsax0rkPY98E0%2BlE87er5N%2FUbLBX784tUGszJfj%2BaT6s8R%2BZSYHa5Rr7kazQ37XbcSJSbMQ4gwfNEcRkTL4rkq5TaL38ypfmlf26fuTBj9vrGKQ0vxA4geTbDxHs%2F1j4ka%2BErX8XvSm9TvJzE7QOHAnUzYv46CH3mjVkewzjHhkc2W1eefwd1KaN0J%2Bn5rhaVQPUIlWyjwZ%2Bz7x8DJbrrelJWugja%2BqSBefgepiqSdo25Kn0Bxl7Gy0GM7BifuRVrxQCT1Tn4HqJmleJSa%2FZMCHLkyA24ZyWR8jkKUwwG630e%2BllmwHkK%2FvNC85uoyL3ttsfo5D37E0nbhVVWSrF9kJGYMEi5%2FO0eSE0AY97Dh4H82bGrjK9XzqE%2FweIuYHef42OFmpmm%2B0eN1F9bFIuGy%2BJ4R6F8tITq8rdr%2Fg8SHqmTIL42RT7BkpJ1fmK1VkSTyN78h%2BVQnCMI7T5keezW88A15p0krtsmwdx4tPKjFOmfU%2FoP48L%2FofeFiF96pE5uQAAAAASUVORK5CYII%3D%22%3E%0A%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dinvert%3D%22true%22%20data%2Dxrange%3D%2250%22%20data%2Dyrange%3D%2220%22%20height%3D%22123%22%20width%3D%22304%22%20style%3D%22top%3A%2073px%3B%20left%3A%20467px%3B%20z%2Dindex%3A%205%3B%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAATAAAAB7CAMAAADEzSzaAAAAA3NCSVQICAjb4U%2FgAAABgFBMVEX%2F%2F%2F%2FjyZz02KW2pHvdxZu2pYLny5fv1qWFel7Vu4OlmnasnHuyn3uKfmLexZbVvpSEe2Lkx5Ts27LSuIXGs4vFsIrZxJbs0aLPvJO6p4Pp2rHlzZ3WvY3Puo7dy6DayaHOtoTdwZJuaFvJsn6llXPw1KC2o3fWxZ3ErYSomnuekm%2FHsoSekm%2BAdmKomnucjm3OtYvn17GcjnOllXO6p4PKsIjSuIt7c2O8rIWEfGmSh3ONg2V1cGGUinTt0Jydk3FzbGHPuo7kz6GJf2vn1q3q1aTfz6majnm2pHuyn3u2pYKyn3vPuo7s0aLOtYvSwJm8rIW3lXKllXq9q4ndxZvVvpTexZbPuo7SuIXErYR7c2N1cGGEe2Komnu2pYLPvJPGs4vWvY3OuJF8dWmNgmxybFuOhHG6p4OsnHvOuJGsnHuEe2LFrn3Gs4vHsoTFsIq6p4O2pYLKsIi2pYLZxJa2pYLayaHZxJbGs4usnHvbv4%2BvnHalkG6Jf2t%2FeWx8dWl0XqRGAAAAgHRSTlMA%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FEbv%2F%2F3f%2F%2F%2F%2F%2F%2F0Qid%2F%2F%2F%2FyJE7v%2F%2FIu4iRP8iRP%2F%2FEcz%2FM%2F%2F%2F%2FyJ3d4iqu8zd%2F%2F%2F%2Fd4iqu%2B7u7u4RESJEmarM3f8iMzNEVXeImZmqu7u7u7vMzN3d7u7u7v%2F%2F%2FxEREdqVUEYAAAAJcEhZcwAACxIAAAsSAdLdfvwAAAAcdEVYdFNvZnR3YXJlAEFkb2JlIEZpcmV3b3JrcyBDUzQGstOgAAAUrUlEQVR4nO1dC0MTVxbeMDNOrGQmEUgIECCKiooFQeUhKj62iI%2Buimhti692pbi2dq2P2tb2r%2B99nce9MwNJVIJdDiTzzGTuN9%2F5znfvjPiPf2z7%2BPe%2Bdp%2FBpxX%2FPv2fdp%2FCpxU7gDUZO4A1GTuANRk7gDUZT07%2Fcnvo9cr6artP5BOJtdeX9vZdGhw6NPhyB7LN4931vX17%2B%2FokYkODhx7sOLJN4i%2BJl4pLg4NDg0PnF9p9Rts7Fgy%2F%2BjRiIi8ftPuUtnesH9%2BrEZOTQYnY0Fq7z2k7x%2BLxvX0Csr3HJWp7Lw0NHRoafL0jY9mxLsXreB%2B8SYINDu2Uyux4LRX%2FeN%2Fx4zovv5BJObijYpmx8IWKQxD%2FUvGm3ae1bePi08ePe3sfPybAulXcmm%2F3mW3XWJRqL0OL%2Ft4vhNsXsaP6WfFOar4qkyr6vhhS5rXdp7WNQzvWPqn4ErEhJfor7T6rbRy3dbeoT7PskmCXiMvtPqttHIt3Z5TH1zEzMyg59le7z2o7xy9vtdxL1C69eiUB%2Bz%2B0YdPz383N3bpy5cr98zoevXn08MWLhw9%2Fui9WXvlhbm563lTCp2%2BPHzd49Q2%2BfSU0%2F%2FWf7T35LYz5i3O37j%2B%2FG0d%2Bf6VDRtjB48DZXRhRVB%2B4%2B%2BLZlan%2FvtWeQiA2OHRCMOz%2FomO07%2BKtpz%2F%2FGkccJwOWnIQIXMhBU3G087UwX%2BVyLMOrHvrb4zU9d%2Bvqr7FfQR6FOA0JrpBtrRBmJQlYKe7VEfd61d7z7W7Qx4yLt652x9EFCw787WAQhrANaHdWoyXiZOeuOFZoife%2FM2ACrIlyP4fK0qzQAszBTsVZSMldKht7dUr2lkuPlifb3bgPHfuePP017udcCm3NSgAU2pwzeta%2Fq37y9z9u1no1XDIl47JK1UfLs%2B1u5AeLfWeu1nJJTiUByQi248mbN2%2F%2BcWS8psCSqHUKhmEdvbb2d%2BiDP7ka51JajyJFW0KiV8j3gfew4%2BbN04X8kZFir4JLMcyLJ4apgpYeLX3amE3%2FcLcfWstSzyWXpV8mKuKH5tTPqT%2Fy%2BXxxZCSv89GkpGDdKHMdpfOff7KYzT3MIQqivTL6ReT6c34uJ19%2BVI5UlCO%2FXC7ruahsVkLoRbG2HAjA8gKwWFVImZJC9Cfyp%2F%2B4eaokgjAba3fTW4mlN%2F0CHwmMbLIvMRLRryGrXKiYCCmIUqF0aWpZr9O7VTqL%2BaICTOdjr7IVE8V8%2FvTRU8OnZAyI%2BO23en3gpzPtbn9z8c1yJLC5YPBI2CqeiEzVcE0Y0hqmYrWiYljR1Ejlw%2BJuSbvCyM0Bya1SVBcx8NvAwKlfr3w6qfnnAxuVkL071ssW%2FzQzwXePC5CSvdqIqZQUwiYgu%2Bl0oXaV6j99324kGop3t1MkPcNNhIldWekMk%2Bj1%2Fy4B0%2FoV665Rt8IrXywMu4gJzO5OtRuNTWPxtp12YXrbQw5kAsTUaqpz2veUhvVqJ2YYJqM4kARMxN3tXTQnb3dYqmOlmpuShAq5e7dbae%2BhZvqrWvBlpawSYL%2Fb3NqFRXPgh4V2w5IVbjK6TU7jXjqV0uYRN%2FHR%2FkhrWPWGAWw8JSExTt1qNzKp8fU6B4L71DCRYkki4b58x1QgYXJB%2BLme7nJt%2FPffR%2BtZWBme3d2GLmMtgz1pTU%2FtSbpkSoxksJTlH%2B%2FnyNBsyVodfbnNKubi9fTWZ9gEzsMUkBvpmBNuLmCpHCvF97eR%2Bv%2B1niLpYeKdVQIqAwypkP264G7ke23ASjQtWeu3T16udTjhjEMkYHTUyAEomYwuQno33HIgya9SGudKPy%2B0GyoZ39zOUpctI91ZO%2FscqrE124Fkqy4TnIqXZk5dsnQkwnJkYUeY2mmi7S5CmXJWv9JuvNabYUImXpScIa1J8NHJVXbIswTJZqC9aKv2%2F%2BkUx7TIqn7ppTAMzS9hmVkzQ%2FiEULHG483F9uG1aLEjzSWkN3dz2xBativ1cxbdeN6B4Ce1TC9GbTP%2Ba851phzMUqWNANpwU5iGG7v1e5ZgKSVdrFUNBKL324OXK18diZalAoayllYO4ICpRyES84xVrwMN6FeJoHveDrxuu21JX3A0jFdGO5%2BzInTdRkjAIeQVCYaViClwsU1tkH4u96HTPJsPDd8xSlsbgpYxxBhUuGojZqVh%2BOUWI7ZwvdlC1kikpGiDClnZMCPbj9jC9Q5KlA6SnSyrGtqk2SBrM3HM3k0i2IyvAMS2ErDrvAEWPDZWYWqXKdl6W8SdLXiERFbTlx5wiFRyZ0rJQZ8tfO5nJdU2WLMND2dZZc9dkbgMWR3O%2FmTelZKosXk5ebZVeD1IRSixziZEkhfpaLt11D50aukISfNT1KrE%2FYS9fWlr8FpHIbYqYoe72EAkiLXhAbK7TWGGTm3izUpbMnixukGr2pWXZwGeJvOy9M3Hx%2BvrClxecEJ4uZM4JnxTYtOG4xjpkTQpYRZem8ajjw%2FYS6t1WUmZDVuWlr1Pya1YQKXKlbMdN35o4X83OTm5qF%2BLk4vi94Fsc0UzrFLpqByoHBChHsRRs%2Bq9olao1WrxQn9FPsqjHncSczrUXL96Bkr9Vvpz6ske9StftdHRHvEjQ75P1B7XMmLipIjukypO1QbskMu12sApNVeDdXUTv93%2FPBHvo2x39GNKfs43z3TpiHxc9tWPnvi%2Bfu7LLOtdc7552MlsMQc0G9VCBBvMjvow3YHneYH6kVMvCAI9xRVqRi8Faqv5AG40n8C9vIAtsb0DOKaa%2Fvc9CIbt81ljJTBq2WeIqXb6gK0Fp8%2BOksshmrA%2FAk1IqjU90HYLMY8BEcDqgBqtNuoVgKjBxuyl8fVclIMAVgTV1gFbVW2LWEuoPZxjRAzebp%2Bv83MMKAMX4seZitET2KzwGIUYgzRAQcBJ4xAOYCJsGMSGuMA08V79rmXA1oEu2A5fE0yuiNgm4gjSiNCVOZcjUvo%2B7acTUrOW4apePYxc1CTOEVxDOzE%2BJvKP75FIVITe86pzLQO2AnQyVMEkguTEzNITBydb5wBgH5IR3hFwHzMeGBZQ4zBlHBCRVQRMgGARDCiGsArz0OPfIH%2BqrY9h3wGQGHlyvM0cH2sf1nYHSVUHUOsiJzMRUl8CZlOBpU1gsQbzLyDZI9AshNkmyErYkaZXW8XrXRIqyB4f1Rp2iajZFgcpB%2FFgzgJlNV0LsTDqMXVnOHgWmYxied2xLN39Fy5c%2BOc%2FL3Q2EPxI%2BiIgA1%2B1CtiaaVwE4sPUzKIUJi3DgSkV0I3A9sFSRFg%2BuD9R4I9yDnGSEaEgwcTMKMM%2B%2Bmzz6OTIswoiX9VWBxfXc1bwksj5ZnPFKXdsQddbKrDioxEDk%2BirdxhFqCzNDizAwEUFVfZ9DQEG%2FoTlIyxUW%2F2HSytcWVywInjLgfNkdAIUrKQjAGGGXEYS3NwoShJLQKvIsTZ6XkRXsUGGsXrCDiRVv1Wvf4dzhzkI34fciohqJrkiqKjQfqyrmIc%2Bw5TvAplpIB5lZQ5duOXu0VLIaUx%2BsZyF0sjIns7OPYeBYWgo0PSaL%2Fm8Nbwm2%2Bhateg341onkKW%2BZlghL3%2Fy%2BUKhoJ%2Fll289Pd3dAWNYwrWqL2ixc7RGOqRiw56fDSqlF2LF0DS9S8xim4yw143Gen6mPxN0G5H0gWEFCVChWDCPpecVegKvHg2YXX3Rm%2BmcbA2wdZswKZUfCJdjswllsvZitcBUYF0JCF3gm3%2FD8hBO5afeHyj2DfgGHwEr5PVvoaiIJkETgHUzwAJ%2BBTxjOPbsCRZaAmwlu9uSUgkBF2IVdKNA6ejjvsNLNk%2Bw3fBYojAPwS0FcEK%2BRXhdkGH5okRJZ6aCrICAfbYnNYxHa%2B0R4shQwE0qn6sV5RVAQIzjCPHEY3XRZh4b2JCAUQ%2FaUIr8GIxRGNmRrazjeTCG6XTUUibJ1tPd0%2B2dOzI%2Bvof6Suj%2F1cEUYC11jiZt7mxFbwg79jKqHrVAZwqPw2ZyGKkxEZfrcVm81ePx8XNHjiit16AVJbkAMK1hafTCY3lPWwFsTZ%2F7xx6UyMzuwE2UTmb3SauxNHTDIaJYM6xg4MoX1T%2FfUpBJhgUjR86d27NBdnveL60Atu5zVCR0AJ7VZM4lH6yERa%2Bcb61ixZF9Xm%2FjV6cKHW2LaC7DaFKN63Ec1%2BU%2F6j0iCAYM00ABcErDRkR0BjAyZncc3qNz9DKjIVThIN8%2BzoB1p40J8gw6NaxfrmZ050j%2Bc%2Bd4RDFMOQmslHnDMFYls21L9VgLgPnAq5yl5BuZc%2BIeS9yIOGXLIB4cP8A1X2gYXn3o72Wbc7kigotlRL8A1lVqmHYVOiWh8w19Lxy8xi9spXO0SPbbmHs0A1xzyI%2BB4rMEBcOmIfFpN%2FsoNFyBn5Apye1EABYVRvBxXNBDAGO4kAYwJV0mKw3TGGAeaVZyILKVMrm2NeaBV1ud7UC2qmserBzkK0xrJ%2BCCQNcoTy6sqB1%2FgbpGHh6akRgdSwtjiA9QpyJqlaVdDClX5p3sopLgI8c4oFY6A6ROQbTHUCGB0KSJn244ETKu%2BlUg3WcMs8ByR3dPNA%2FYSwWUsgNRAoacGeWzeEdo%2Bh8CbDh5yBp39BVKG7ZzFL47AlthOpAF2aPUmFFf0gYbq6RRgObL5DfUCjaqh0yhhjntlaOCPmqWbRrAn1rJrYsCLwZ6n4hreoAMYz7fI0LojXAB2GgF2n2dnXkrJbFA8tEKvara9D9%2FWH2fm9Y5BiiyDzfZGZgxdBHFVops5AGQJ2VTT4BhEqIi2Vc5dMFsBRNAGmpDvWz6r6tcdrOwdTFKHIgN3WbfRo8Sl52Pr3o4JMaUe8CcETFMewo1WFHEviSlpAbHtsS6s9XZdOfowZbkHfHV50jKtygj7xjpiHt67YTBGzVMm1UYrFCAQUpalhj7XuBWWugc3SE8GFJIgchHs4D%2BymxkyYuOAcoHpaXPduYZDx%2BNYp6CODLKRw0Dt7sU1OXfNeIDiIUC2HxjXhVgR8blaAVLSNIxGGbzmh1D%2FHoryZRjltfAF%2FnRRoMULjWUIgVV%2BVeg6qJHKbuS4wU15Jo3Bsx0xUnDiExYUvg3BtPNAbZKNsHp1WQ8a2OzkTjjs%2FJqPu4r0Ih8ZO4ZxcoxoQEko%2Fs6aPxZYQjknSN1GHD6haIeyjdjrmpMH2zFZy701gUImu4cXUYgGC6MArSIKWYTxgKOSqCV3yxd2f6GfxHIFk7QUSQNumlnLVLesYwaVtAWjPrfajxM8m%2BP3XtXs5xhnU12jlYwnSKGFruFhGzzuVTZXUurSjDjQXhnyJ2clAEiZwDxsDWIYQ9lTJTr5Tiu18bH5fAOqL2imevDPrNT%2FDA%2FjMrwJjtHdzZvUQpZLCh84JXZEe9hyk10Q5M%2BbPUVclGaUgX8STAiGIA6qhjm2zdBwL0WdF9S2Ipz546oIerAKilYefVbc52jdzlLV3AkYQuLZgSApIp%2FogqofaryTy6X6wOCYefOQfcRiSYLJe8aBUz3vUTRbK5ztIqXH0pji2M0CCISUm%2Fa%2FGGxOMkwbs2hCFhjNOYBC%2Bp8mxtHaMRkSvbgeBjdC2Z9VQSsqc7ROjSXewnOK1vDk2Q0295jpLaMzosKv2kejVkwF6s2lNX3QJXETIRBnoLVl2QpSCMiWIibK5MrCfXa6JYryRYg5TMq0udhH8tR4Ed4JVWAMfI4t1zZ6IKHKKrOkb5MhmFF6EkWjK0oJAYQvcwht%2BYesLhjTh1yiz%2BGZLiTs0I7AaZihoZcwQibRp7JKyO1PDKYAJCzAMlkxhAjlpJF8K%2FCixXZbbZO9nniL9o6saqZByzeNezHuUtgEm7hyKYGzQhxz7YtdfBcrh%2F3sMPtcYqp16g6ELvzbYiFOqaqJGmYxyMgLqucbAKwtVbdJiUlFgiGL7MW7Eh2CcZ6EvMhF3SZSbeJQidfVXUEdPr0LIrWsXyRj7hCkmNusuyXx2ri6XN49JDyCaVnS4Z25DRubmjH6JjKDEpJa2gnRcPotkCAagbaWH3SOGArQC5UGdvGEolo5kM%2FZRdjnrHbbUzCGLlYoYsZw%2FJ47xsHeqzOt3Vkqi6I4s9TU98fW2gMMGwZEcnpO3LKWcnILYb5HKamhqex%2B%2BcxFUHkFZkMrAZcfkTU5BGoL6kFrADPo%2BRt0bcPx%2B5EKbJWR7t27%2B7q6vpq%2F%2F6Dl6fGvp%2FdxMm%2Bm5ycWltbW19fP7%2By8qbceC75SDzcaJdKFEffvSjEYl8wjCSMyj4jQmounZQf5k8gFtHvqyEeAswhmIxqtXpCxL3Ro8MiugReKsxULAvsLh9slHf7ZicnV9fWlpfXH1w7%2F7IcWdXzQz%2BIImZj3rmzPBnhlxjoF2Uy5%2BcsW0EPohStu0ZVFSdmZmaOHj06fHS4a3h4NyCEWCFaFnLyTWIneXes8R7U%2FPzk6urq5eXlB9eunZd%2F3h2KJ2YVKRdLN7YOIaO90abkYoSKOyaQLtJ%2FrALaCzDAlNYrhp0WMT4%2BPjLydmbm3r0bXvXGqKQQA6JLTbrMbFcSpi5rxZf79z87eFCQTbCtCcjsWJie%2Fl4guLy8%2FPzatbsCwTJPMSaKDrPUcvLWUUyJxwyEw6jkrSP5vIDWMImPiBOCP4pAXTYCLn0ALURPwgY7vJAAXT44NjU2e2wzLWs59n03Pz03tbp0ZfnZj9fO1%2BJYkLCJznscEHcCpshpD1igAM2cuDc8UTtVlSAZ3eF4dNlM6epymQOxf%2F%2F%2BKwcPLo2NjR2bbd9%2FzzI9P31x7sza0tLy8x9%2FrA30qjT2UeQgMY3dH8BETNp9BU%2B1%2Bkoo0D2pQEKgh5EYu52USglLzrs0QDLDxkQtPPZ12wDaLPZ9Nz175szc0tLSsx%2Bff1mrDcSghJJ%2BNV4bg2qgCCQVWifYbrfNkEpdu51UA11ia74yEiQAOja7BX%2BK4WPF%2FPT8k7kzt35Yuv%2Fz84c9J17NnHh1T%2BNjANLMAf50ucg4DCIJAo0em%2Fq2dY3e7jHboNykpZrIsPsHLwsJmjo228qzhJ9k7OOJlrBDFphKoy8fXBNF7Njst%2B0%2B8bbFV1k8EhL0k9Jo6Ru%2F3b4avdWxH%2FllJEhk2Oy3f1sJev8QJmhMaHS7T6OB%2BB%2BC%2FKOr0h4pdAAAAABJRU5ErkJggg%3D%3D%22%3E%0A%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dinvert%3D%22true%22%20data%2Dxrange%3D%2275%22%20data%2Dyrange%3D%2230%22%20height%3D%2250%22%20width%3D%22116%22%20style%3D%22top%3A%20113px%3B%20left%3A%20762px%3B%20z%2Dindex%3A%204%3B%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAAHQAAAAyCAMAAAC6RQ9kAAAAA3NCSVQICAjb4U%2FgAAABgFBMVEX%2F%2F%2F%2FkyZm1pIDexpr73qqnmnallnGnmnn33aqjlXn12anszpi7p4PUvZPu1aXPuo6tm3zr0aLfxZbNt4xxbWOUim6yn3l7c2NsaF2%2BrIStm3yom4C2o3v22KSznW%2BrnIGejGuqlm3ZxJZxbWN0bFvUvZPv0JvnzZ2MfmPArYq7p4PXvo7Qu5LFsoq%2BrIRsaWDx057ErYKznXCsmnKFe2qom4CPgWSMhG3Qu5Kck3OllnGjlXl7c2NzcGeJf217c2OJf23FsoqUim6%2BrISck3PArYp%2FeWl%2FeGWfknrGsIzArYrGsIyck3PNt4zXvo67p4Pr0aLQu5K7p4Omk2zfxZbZxJbErYL12anu1aWwm2753KfmzaHny5aMg3N%2FeWmfknqajnmUiXSMhG2Mg3OrnIGjlXmUim6UiXSMhG2EeGN%2FeGW1pICajHOFe2rGsIy7p4OVhme%2BrIStm3ynmnmejGuUim6VhmfUvZPQu5LNt4zexprPuo7GsIy7p4Oyn3mmk2w%2B%2FMV0AAAAgHRSTlMA%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FRP%2F%2F%2FyJ3%2FyIR7v9E%2F%2F%2F%2FRHe7%2FxEiu%2F%2F%2FRHfu%2F%2F%2F%2F%2FxH%2F%2F%2F%2F%2FIjNEVaqqzMwRESIzVXeIu8zdIiIzZmZ3d4iZqru7u7vM3d3u7u7%2F%2F%2F8RESIiIiIiMzMzMzMzM0RERFVVVWZmZmZmZnd3d4iIiIiIiOmar1cAAAAJcEhZcwAACxIAAAsSAdLdfvwAAAAcdEVYdFNvZnR3YXJlAEFkb2JlIEZpcmV3b3JrcyBDUzQGstOgAAAFzUlEQVRYheWXh3saRxDFvSzHHQsczUEKCFVkiINKFEW25RZFcVwjJFvNTu%2B99%2Bp%2FPfNmCwfcxYosf8n3ZcB3gjvv797sm9nl1KlHxNyjbngCMf7U%2FwU6929Al%2F5L6X3nq43f5ud%2Fuf3ZpScARXp%2FGB%2F68q1fD4IHYXP5TC73em731psnDYXS9dMDX729nVZBmkIpVc4hXr188tCLA9CfAiIqftM%2F1WwTda90otC5IeilbahkoYAG9Ocyiz1J6JDSNw41Kg0wvRTOTVC3HgvzwcbG7ZJrfoNKLx8qTms6IBxT%2BcPyY1JvHqgmxrhlPpPSq54rm21WyFyXZDzGGVC%2FOSby8jYP1KRBdq9Y6Dnvgrn8cwACZRc%2B4rklU8FXIZv4xvGg20qLeEDUPS576kjnfAN9D5cUpxZYfeJsa6m7x2J%2BCSIkBCFV%2FZaFWqVbSrtI6dwq7SjODc9q7liFc2Dmyzw6EtxP71IjDKkdNFUzRDT5tkDBUUobOLd3VND46urqjQZi6mYYlsvl18oIQbE3T1ERUkiEwEngjIOsdrvdgrQx%2ByzHt6c5xuil3wlbgBJGEGY0Gk84hP4k%2Bidh%2BPxnPnWkGIuH2tG0AIvQWAsXRqFRiy%2BOxkyE2oGlyd%2BwPP1IfeE6wSeh9B%2FnmKB5sZjJZjNeDGuh6lPUk6BTFiVdIqWFWqR0avsZZ2g1m6FXDLRYoQuZzEQSVESsaU%2Fmi7JyEepTwE0%2BVRBaaYFGzmYnYqCyhku11PUE9zrvGJ3WREKG6HFK2TVFVyadU1QrZwGVkENDx0AXAa0nKG1EjCP7J6GhKtrfbc8LSKnQ0BryW4%2BDVmm2s3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on%20octicon%2Dcheck%20js%2Dclipboard%2Dcheck%2Dicon%20color%2Dtext%2Dsuccess%20d%2Dnone%20m%2D2%22%3E%0A%20%20%20%20%3Cpath%20fill%2Drule%3D%22evenodd%22%20d%3D%22M13%2E78%204%2E22a%2E75%2E75%200%20010%201%2E06l%2D7%2E25%207%2E25a%2E75%2E75%200%2001%2D1%2E06%200L2%2E22%209%2E28a%2E75%2E75%200%20011%2E06%2D1%2E06L6%2010%2E94l6%2E72%2D6%2E72a%2E75%2E75%200%20011%2E06%200z%22%3E%3C%2Fpath%3E%0A%3C%2Fsvg%3E%0A%20%20%20%20%3C%2Fclipboard%2Dcopy%3E%0A%20%20%3C%2Fdiv%3E%0A%3C%2Ftemplate%3E%0A%0A%0A%0A%0A%20%20%3C%2Fbody%3E%0A%3C%2Fhtml%3E%0A%0A" width="100%" /></p>
<ol start="3" style="list-style-type: decimal">
<li><strong>With Nuisance Effects</strong>:</li>
</ol>
<p>We’ll add <code>dose</code> to the null model in JASP, and do the same in <code>R</code>:</p>
<div class="sourceCode" id="cb42"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb42-1"><a href="#cb42-1" aria-hidden="true" tabindex="-1"></a>BF_ToothGrowth_against_dose <span class="ot"><-</span> BF_ToothGrowth[<span class="dv">3</span><span class="sc">:</span><span class="dv">4</span>] <span class="sc">/</span> BF_ToothGrowth[<span class="dv">2</span>] <span class="co"># OR:</span></span>
<span id="cb42-2"><a href="#cb42-2" aria-hidden="true" tabindex="-1"></a><span class="co"># update(bayesfactor_models(BF_ToothGrowth),</span></span>
<span id="cb42-3"><a href="#cb42-3" aria-hidden="true" tabindex="-1"></a><span class="co"># subset = c(4, 5),</span></span>
<span id="cb42-4"><a href="#cb42-4" aria-hidden="true" tabindex="-1"></a><span class="co"># reference = 3)</span></span>
<span id="cb42-5"><a href="#cb42-5" aria-hidden="true" tabindex="-1"></a>BF_ToothGrowth_against_dose</span></code></pre></div>
<pre><code>> Bayes factor analysis
> --------------
> [1] supp + dose : 59 ±4.5%
> [2] supp + dose + supp:dose : 152 ±1.5%
>
> Against denominator:
> len ~ dose
> ---
> Bayes factor type: BFlinearModel, JZS</code></pre>
<div class="sourceCode" id="cb44"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb44-1"><a href="#cb44-1" aria-hidden="true" tabindex="-1"></a><span class="fu">bayesfactor_inclusion</span>(BF_ToothGrowth_against_dose)</span></code></pre></div>
<pre><code>> Inclusion Bayes Factors (Model Averaged)
>
> P(prior) P(posterior) Inclusion BF
> dose 1.00 1.00
> supp 0.67 1.00 105.74
> dose:supp 0.33 0.72 5.06
>
> * Compared among: all models
> * Priors odds: uniform-equal</code></pre>
<p><img src="data:text/html; 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bBUrY8IgYjZRRx%2FyUg2PCRQxGyTIGAQbBIYDAJAMBsmTAYcKRa30%2BEKH0yi5D6dyDYJznMGA1UUMAiUD6YUqh9PhAuHCKGKgBtRS48IkKbQpyqBs7pVKbOCgU2HZAuHHdFDArK0p9NAhsRSmysKBT6Y2Uq5wQ%2BnwopDZwgXHcKKQ2IENqKU2hRUzZwUCGw7IENmrLK4IbEqpmwqLSm1SLSGzx2UyqWCAG0KFTNo20RambWRQYfeoR5YAHDLtK5UwC1GVBa3xQpwFWaoLTsgpbY%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%2BnypVb6aUD6aUbBCtgnOczY8IBjwhAxUqxsUAwQDBCl%2BnwyNcjfTKIXAqKGBRcZDAKAfT5UA%2BmqFPpjZRaXBAMOEhS4qKU2qKU2IENqkUptKBTagQ2KmCGw0WctENh2SHMU%2BmdkCmw7KZXCZsUi4IfT5QpTZupnDWMpmxSCZ9PhKqZs4UCG3hFIbOyKniQ7qZXCZtdQTusKKmbdGUVM2KKXE7IPJYeK7YcOQ4tcqiwtooGFvDBawyqLeyCltp7bKphW21%2BdkFBatYwzlQWFCqCzRkS4OLFUqosQUFiuDKgsTCZyoLOFUOLOEKcWDZXBk4t4VjJxYgcWgaIU4tGyIYWuhnBxZwqhxYgYW8OgYWnZA2B2VT4nHp7pUHBCmwQMLCqUR6aJTD0wgYWDZUwOI2UgZikBxKsBwKIbBFHBQMLeFYlbDhMGcmwOyfE%2BA4FCjghyjglBwQjYIDhwhBx4VBw4CDYqKOJQbBEwOKK2BQo4FCtgdkKOB2QrYKFHBCh9NUo%2FTUK30ylAwQHDhBsChAxKhGxT4rORsTsg2J2QbE7INidlBseEUMUGxSLQwUGwCFbC1ChgEyYDDgKDYoFxOyK2JQDHhADahC4BADYiwuHCmcmMBgdkaDA7ImAw4UilPppClwSLS%2FTQKfTUC%2FTGyQD6Y2UyuCH0xsikNhChgptUUhs4RSG1AhtRSGzhQIfTKKQ2Hbuoqd1iipmwqZyENiLjKZ9MKKmbNlFTNvCKmbOFAhCmcKndafwUVI2oSlb3U0UivGFq71wqgtVRYW8JgycWuzaqotbaPvVRQWpgyoLVWcrC1kDi3uiKC1WIoLVYZypbbREqotNKq8hynFpVQ4sKqHFhKqKj01KHFiBxYgcemESmFoEMqhxZwqHFiBxZwkS%2FAwtViHFqYwoi1WIbBAwsCpnBsRsoQcSdFcpgwsKZMZN9MoG%2BnygOClDYKoOAQNgNkyco48IZwOKEHEoo47JUg4oo48Oqg4cKA4oDjwgOKJytirSDiosbFSLRxCqQcRshnDY8IQceEwRsUi8zYoQWQjY8Ikw2PBRcxsTsosHHhBsTslSDigGCA4hFbEKDYhEjNwgzcIc7Nwis3CAMg2KDYhQDHsiwMUGwQgfTOyAYHZRaGB7oNgqBhypFbAKIGA2RQwGyQuWw4RSmxRcFNqIDKqDbqUgYhCAbOEUhsOyZMFw7KKBsKBfp8sopT6fsEoU2KKQ2cKBTYNkMZhDZwovOQ2MikNqiwhsUEzayqkNqixM2cIENnCy0mbOFBM%2BmSipmzdRUzZ%2BKhUjYi85DYCpVSutCKmbRRlBPEPRZi14wC7uCotMQtMqC0nRUq1tqFVFlFcJlS2yiqK22dglRUWDXwRFbbBsmTGVBYBo%2FC0igs4VRUWJEUFqsDi1EyoLFU5Ti3ZIHFiooLG0SIcWHQKwOPTKYMnw6KpkwsRKcWIGHpq0OPTCIfEDRSgtwqQwtRDCxRTCxKQwtVQcUyYMLeEIItegVDYHZReQRYqlNgiURYEKOI5Sg4jZAcRshBxQgi1Fg4pgzhsUBxCIItHVFHDhEoiw7JRsOAlBwKVRw5RK2A3Sg4DlQo4jZVK2I2UyuGYbKozDZRWbhAW4QZgi8rMiMyK2IVRmCitj1QHHhBsFItb6Z4VhWw6IVj6aFbBIUMAorYBVGw4CAYnZRWYhEZlMYXIMhGYJBseEWtg%2BnioB9PhDGQPp%2BOiKH0yotKbNygGCDYhQgYDZADYNkAwQKbNlGiYoAyAYhQLhwqFwOyjRTZwopTYdUQuCKU%2BmsqmfTVoU27qKQ2BQqZs4UyuMkNqikNvCGMpG1FIbXSCZsKipG3hRUzapFTNhFFFSNnHZQTuseVOZedI26IuEzZCLhPFSLXji3Rd3nVFvZWCgt2VxhMq22qxFrbUFRYyrOcq22cIK22LTKgsVFR6aCgsVRUWURKcWBEUFnCqKizhA4tCEOLSVUOLAgcWrUQ2CmDKg9PhVLg4sQNhwimxKVDD0zqhnJh6Y3RD4BCmFg6olHEbOnKpseEQwsVIbBAcUBxQgi1DODY8FCDgdlQcEBwUwZMLFStgFKDgFUoi0dUKOA2UoOHAQpsVUbHlRRxQjYqo2IUWDiFSNiEgzDZRRx4VQceEI2J2SKOJSDYpBseUBxCQy2ISGBxGymeQ52x4SDMhjDMixmCJBZAMQgOI2RWw4UGwVGw5Uo2G5SgYHdBsEo2HDqVQxGyDYBRWwGgCqBgooYIBiixsShGY7IQMeEGw4UAwShfplRQPpoYyH0whS4BT%2F4v%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%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%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%2BCi4LjyhAxO3dAGKitiiBh9zqLnJTb2ShTYi%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%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%2FFDCN1sqLjKZCKhdaoqVwUELgpGkbrVFwjih8HnW28Loxle207Ksr22FKi9thVFhZolRa2xWpla2wKorbYNlUqwtA0VTn51BamEysLQAiHAVFLbVUyoLeOigZlQ4t%2FBUhxb9wRDYomMHFuyKYWqoOO6BhbsiGFiUEWiYZSrkcUBYOgItKqQ2I1KEEAbdFFjIGbhVBFpQy2KKLIkFkBwOyA4FAcAhzCLRshzDj96iiyqMyUFuEGZBmRYLVSIzd0GYKjMkG8tlFbhAVRpQZCMyDMpgyzbShBZKRm8EVmaqVOdm8EGbVTmW0WGqtRm%2FBRWbhKCx2VRmUI3dFZCChGRIzIrMpBuio3VQZAKaKKyoKIEaqKzBVANvLKKBBQBj9qqMgCi5ZkKDVQBUZRQZ9EAbZCA1XQBIAykGIHZAG1CtQpG6BSKsi4yBt7IENrfcpFoIFNqgQivGiLSEfgi0jKLkhtQTNqhUyFIqd1qCRFYUaSIQRutUXGUiFFRutTK4QuCyqFwSKm0rK8rgtHC6Yw55WtCqZXtCuEXtthDOF7bYWmXTZ6Hq3B7fTuuB%2FiALLOdppxz5w1jZ6s82Mun0%2FwBH%2BpvfD9P6t7VAsJ%2BCzniNnp59WOnDWNhtNXNpz0ZdNn7d%2BuuLW%2Fo%2FXuJoB6dz%2B5Yzxmxxi%2F79PThccJts5n%2BzV0ZdNv7T%2B5a%2Ft36n%2Fur%2FALFj%2FIcNvNHax1t%2F0PEbvV2c9TpH7H%2B8Q37R%2BsO3%2Bg9T%2FNWf8rwm%2B0drT1tf4zi91r7Oep0Wfy9%2B%2B3h7P2X9fcN7f03qn%2FmrGfOeB08%2B32eP59PW1jyjjdXLjYbTsaup0Wfy1%2B%2Fkgf7j%2FXh9T%2Bn9QDxNqmfPOAx%2Bvs%2B3p61x5Nx%2BeT%2Fo2nY1dS4%2Flb%2BYtP2T9b1%2Bjf8AYs%2F5%2FwAv3%2Bz7WGseRcfuNfZyvZ%2FKP8yXBx%2By%2Fqu%2Fpl%2FBc8%2FcXl2P19HS6Y%2B3%2FMM%2Fo6%2Bhf0%2F5O%2FmW8sP2b9QCzzaLX8SFnV9zeW4%2FX09K6ftzzHP6OpUfyX%2FM%2FwD%2Bn9aObf8AOWfVHlm%2B0%2Fj1NemfMtzq%2FDrX%2FwD%2BF%2Fmqv%2B6L%2B%2Fqel%2FnrHq3yvfY6NXU3j7V8y3OenT1q2fyF%2FNl%2F5f2g%2FwDG9b0R4P6gWdX3h5Vp%2FW7uvwtaftPzPP6Pe09a39v%2FAObf%2FwBT1%2F0%2F6f8A1iz6y8p33d1%2BFfSPmm572jxK%2FwBu%2FwCbGH%2Fl1k6fW9L%2FADlz9a%2BVbzPZ1dTp6O8z3eO1p6z2%2FwBOv5pN2J%2FQ%2BnbvcfW9Nh4XEqZ%2B9vK8Y5Npns6uox9m%2BZ5%2FJjtaetb%2B2%2F8ANAj%2FAGb0B%2F21qx638sz%2BbV2cunozzL5dPawpZ%2FTX%2BZ73f0%2F01h0B9YH3ArOr758sx8dWf5WtP2V5jn4acfzHH9Mv5nYHH9Kx%2FwCtp%2F7Kz688t%2F59n%2BK%2BiPMP%2BPT%2FAAXH9Lv5ih%2FV%2FRAmtp9W5x4WFYz9%2FwDl2PhtOzjxN%2BhuPz8dHTnqNb%2FS%2FwDmEkf6b9CJbI%2Brf8PTdTP7geXY%2FLtOjHiXH2Lx%2Bfjs%2BnPhUH9LP5gf%2FwC8%2FbwJn6nqtH%2FZLn7heX%2FJtejT43T0Hx3z7Pp1eFS3%2Blf74Tdn%2Bu%2FQWgNS71bnf%2Fswpq%2FcPgfhs9p0afFldP2Fxvx17Pp1eFT%2B1X7yB%2F6h%2BiPQ%2Bp%2FmLPuHwe72nd62s%2FYPGbzR3uow%2FpX%2B7v8AN%2B4%2Fo7RoR9Qv%2FwCwFM%2FuJwnw2Wvu9a4%2BweL%2BO00d7qV%2FtT%2B5mn7n%2Bmivy3%2B9mWPcTht1r6cNe3%2FE73R0ZEf0p%2FciQ%2F7p%2BmAJqLbyZUz%2B4nDbrX04XH2BxG909GVh%2FSj9XT%2FfHo%2F91d%2FnLHuLsdzq7WOpv2%2F22%2B09Geth%2FSn9Wf8A8t6L7fSu%2B1PcXY7nV046j2%2B22%2B09Geta3%2BlHrn%2F81YNx9Ax%2F8xc%2FcbRuM9r6XT2%2B17%2FHZ%2Bpj%2FSn1nA%2F31YQYf6Br%2FwB4nuNo3Ge19J7fa9%2Fjs%2FUsP6TXMH%2FfQCaj%2FZoH%2FwA0LGf3HxeTh%2B%2F9DeP29zOXiO59Tf2mJLf7%2B1n%2FAMLp%2FwB8p7j%2FANv3%2FoPb3%2B47n1ns%2FpPY5%2Bp%2B%2FXNo36YW%2B%2F1Ss6v3Hz8OH7%2F0taf29x8dv3PqP%2Faj0XP%2FAJ3fVv8AoB%2FrFn3G17jHaz4Wvb7Rv89n6hH9J%2FRdj%2B9%2BpGv%2Bzj%2FWJ7ja9xjtfSvt9o3%2Bez9TD%2Bk%2FoBif3u8iMh9ADzzKZ%2FcbafDYY7Weo9vtnv8APZ%2Fip%2Faj9G%2F%2FAKt61P8A4Vv2rHuLttzp6c9Tft%2Fsd9q6MdYj%2BlH6N2P7v64f%2Fq7ftT3G22509Oeo9v8AY77V0Y6wP9Kv0QLH949cR%2F8ACtf3p7jbbc6enPUe3%2Bx32rox1rf2q%2FbP%2FwBn%2BqdtrPcy5%2B4vE7rR05b9AcPvdXRhj%2FSr9rH%2FAOT%2FAFVWfGz7FPcTid1o6cr6A4be6%2BjDf2p%2Fa2%2F9U%2FUvwLNOye4nE7rR%2BPWegOH3urowpb%2FSz9mxe79w%2FW3Xat9MeWBWM%2FuHxl5Nns%2B91t4%2BweEnLtNfd6h%2FtZ%2Byn%2F8Av%2FrXff092%2FwKe4fGbvZ97xL6C4Tea%2B71B%2Faz9llv3D9aSKT6f%2BYr7h8Zu9n3vEnoLhN5r7vUJ%2FpZ%2Bymn7h%2BteIf09f8AiJ7h8Zu9n3vEegeE3mvu9Qf2t%2FZiW%2F2%2F9a%2Bk%2Bn3%2FAIE9w%2BN3ez73WegeE3mvu9Qn%2Blv7LbX9w%2FWePp9%2F4FPcPjd3s%2B94j0Dwm8193qE%2F0s%2FZRP8AvD9aQefT1%2F4ie4fGbvZ97xL6B4Tea%2B71B%2Fa%2F9lkH9f8ArQ38T%2Bm3BmxX3D43d7PveJPQPCbzX3epX%2B137BAP6z9eCQ7%2FAFPS930viuef3C4%2F5Nn0avG36C4H59p06fC39r%2F5fdj%2Bs%2FcAYLfU9L%2FUqe4XmHybLo1eNfQXA%2FPtOnT4W%2Ftf%2FLzT%2Bs%2FcGP8A1npcf9SnuDx%2FybLo1eM9BcD8%2B06dPhEf0t%2FYCx%2F2v9wD0%2Bf0v9UnuFx%2FybLo1eM9BcD8%2B06dPhb%2B1%2F8AL7Fv1f7if%2B09L%2FVJ7hcf8my6NXjPQXA%2FPtOnT4S%2F2u%2FYWP8A4z9f0Pqel%2Fqk9weP%2BTZ9GrxnoPgfn2nTp8Jv7X%2Fy%2BxP%2B1%2FuMf9Z6X%2BqT3B4%2F5Nl0avGvoPgfn2nTp8Lf2v8A5f8A%2FwDL%2FcHnH%2FSelp%2F2Se4PH%2FJsujV4z0HwPz7Tp0%2BEl39Lv2Nhj%2Bu%2FXWlpe%2F0i9Kf6MLWn9wuO%2BOz2fRq8TOr7C4L4a9p06fCH9rP2b%2F8AYfreC%2Fp%2B7BX3D4zd7PveJn0Fwm8193qA%2FwBLv2bT9f8ArCWkP6df%2BQr7h8Zu9n3vEeguE3mvu9Tf2u%2FZm%2F8Av%2F1zyCx9P%2FMT3C4zd7PveI9BcJvNfd6m%2Ftd%2BzMT%2FALf%2BtOon0%2F8AM1T3D4zd7PveI9BcJvNfd6m%2Ftd%2Bys%2F8At%2F63kP6f%2BZKe4fGbvZ97xJ6C4Tea%2B71N%2Fa79lj%2Fx%2FwCt8fTo3%2FAT3D4zd7PveJfQXCbzX3eoP7Xfs8f%2BP%2FWks7g%2Bm3nYnuFxm72fe6z0Fwm8193qKf6WftbuP3P9WLZYY2E%2B5bx%2B4nFfHZaPx62M%2FYPDfDa6%2FwAOov8Aa39rr%2FvT9SxDgG30x8FfcTid1o6cp6B4be6ujAD%2Bln7aW%2F8ANP1Lk%2F4bNn2T3E4ndaOnJ6B4fe6ujAXf0r%2FQP8v7t%2BoAOh9Own3hbx%2B4u3nLsdPTlnP2BsLybbV0YJ%2Fav9EI%2FwB7%2Bu%2F%2FAPFa3vV9xdtudPTnqT0Bsd9q6MdYj%2BlX6KP%2FADb1wTp9O2I6p7i7bc6enPUegNjvtXRjrJf%2FAEp%2FTv8AJ%2B8%2BraG%2Fi9G0z%2Fywtaf3F2k5dhjtZ6mNX7f7O8m2z2cdaY%2FpV6JD%2FwC%2B7%2Bf9AC3%2FAMxX3F17jHaz4U9v9G%2Fz2fqN%2Faj0CP8A1y%2Fp9Af6xPcXXuMdr6T2%2FwBG%2FwA9n6k7v6U2FhZ%2B%2BEA6n9OC%2FT%2FSBax%2B42r48P3%2FAKcs5%2Fb7Hw2%2Fc%2Bop%2FpQQP%2FXf%2FwDV%2Bz1lr3H%2FALfv%2FQz7ff3Hc%2Bsp%2FpUZb9%2Bn%2BEH9Ka7f9Krj9xv7fv8A0Ht9%2Fcdz6if2q9aP%2FOrOf9Af9Yt%2B4ujcZ7X0se3%2Bvf47P1E%2FtX6pp%2B9enR%2F%2BhLf%2B%2Br7i6NxntfSnt%2Fr3%2BOz9SX9q%2FwBZP%2Fm%2FouP%2Bru%2B1b9xNjudXTjqY9AbXfaejPW39qv1pdv3f0ILH%2FR3af8ZPcTY7nV046j0Btt9p6M9aJ%2Fpb%2B5v%2FAOpfpuuN%2FwBi6e4fDbrX%2BDHoHiN7p%2FEP7XfuLOf3P9MOcb%2Feye4XDbrX04PQPE73R0ZS%2Ftd%2B8EOP1%2F6PHSfU%2FwAxb9wuD3e07vWx6C4veaO91B%2Fa395dh%2Bv%2FAEQ0r6n%2BYnuFwe72nd6z0Hxe80d7qSu%2Fph%2B%2FB2%2FWfoCB%2Fl%2BqD%2F8AS5W8fuDwHx0bTo0%2BJzz9icbjm17Pp1eED%2FS%2F9%2FFpP%2B0%2Ft5Oto9T1X%2F8ApK4%2FcHy%2FP5Np0afEmfsTjvn2fTq8KX9sf5hL%2FwCl%2FRQf%2Fi3%2FAOrXT195d%2FptOjHiZ9Dcf%2Fro6c9SV%2F8ATX%2BY7aH9JeBU2%2BqY8bQtafvzy7Pz4%2Fl%2Fixq%2ByPMMfJn%2FAPf4FP8ATf8AmQQ36arf9Lv%2FAMVX115b%2FwA%2Bz%2FFPRXmH%2FDp%2Fggf6efzMH%2F8AD%2BjczuR6tq6et%2FLfm1dnLGfszzH5dPawW7%2Bnf8zin6X0rz%2FhHrWfEhax97%2BWZ%2FPns5Zz9m%2BZY%2FJjtYSP9Pv5pgH9BZx%2FpvT%2FAM5b9a%2BV7zPZ1dTPo%2FzPd47WnrSu%2FkH%2BagWH7aL4qPX9Bp63hax95eVZx%2F6z%2BXX4Wc%2FaPmeM%2FwDl3tPiSu%2FkL%2BawD%2F5SYq3regfL6i1j7w8qzyf93d1%2BFM%2FafmeOX%2Fq72jxIn%2BSP5pH%2FAOIvH%2Fael%2FnrfqzyvfY6NXUx6W8y3OenT1o3fyb%2FADMCRd%2B0eq9uxsPmLlrH3R5Znl%2F7tP49TGftrzHGf%2FHV%2BHWlf%2FKH8yWs%2FwCz%2BuXowB9xW9P3N5bq%2FX0%2Fj1M5%2B3PMdP6Or8Otzn%2BVP5jf%2FwBH%2FVf8ha9R%2BXb%2FAEdKen%2FMNzq6ET%2FLP8wiv7L%2Bs%2F7m%2FwCxb%2Fz3l%2B%2F0drDH%2BD4%2Fca%2BzlG%2F%2BXP3604n9k%2FXE7D9P6h91q1jzvgM%2Fr7Pt6etnPk3HY%2FQ2nZ1dTnv%2FAGD98tD3fs3660bn9P6o%2FwCatY844LPJjb7Pt6etnPlPG459jtOxq6nOf2b93Yk%2FtX6wAVP0PU%2FzVr%2FKcJnm22jtaetn%2FG8Vj9LX2c9Tmu%2Fav3Gf%2FL%2F1P%2FdX%2FYt%2F1%2FDbzT2sdbP9DxG71dnPU5j%2Bh%2FWAn%2FwnrBoI%2BndHkt44vY55tenpwxnhdt8dGroy57%2F0vr2lr%2FQ9S07G0j4LWNvs845NWOnDOdjtMZ5dOehy%2Bp6V9jZ2XWvuGW9OrGrmzhM6c458Oe4IiFwRUbgsrhFpSK%2FSPp%2FtH7Vbc9v7Z%2Blt0j0fTH%2FNXwPV5jxWccu115%2Fmz1vuWny%2FhtPNs9HZx1O30v2z9vtuBt%2FQ%2Fp7TMj07A3ksZ47iM4mdpq6c9beOD2GM3GjT0Ydtn6H9IGP%2Byei4m35A76aLnnitrn8%2Brpy3jhtlj8uOjDut%2FT%2BjH%2BisfX5RHkuf%2Fbr%2FANc9LeNlp%2F0x0Ou21mB2grm6Omy0gB42UHRbbpXbQqKrbadSWfyQVttPytXQH7kqui214Zvb7VBYW6CA%2BygsLTDGKMgYSSB2ZWBxaQQ0g%2B9KKgMRX7FA4tJfhw7oHtFO6mQzOHEg1KKYWsQGg16ohsXINxIZ%2FPkIKMBAknT2CgAtYf4hAYQw1VocAgM07jnwUUWNwI3iVBmIgHx07KkGSCRrx56ICAbtGGgMopmcA8QSgGFzCkSOqAuxd6jWPaqAsQNRQczqgOJO7Q4MfegbFqBxx4oARpIB1ozfggYW8kmeiDOTIpqZFaUQbgCBTzQY3UALyB4pEEk6s4lhv8EUCQHYsdHogIoA8x28UADg8bxO6DPdsedNe%2FvQGjvoICAA3kBhWpkoMBQ1cxttVA0nEQfDkIMQZevfRKMbINDOp328UoAADh9A%2Bmn2JQRazAkPoY3pVKNjMWhtendKA35dXNQ%2FtogaJLkBnGygNA80l%2BUAAtf8oJBgdEG0m12MaoMQILVYEbahAbbQBAjU0QbEP3mUoXEC1z8zePeqUaHi0Bi7oMwAyL2isQe6oN1ujPPIUowZ3iTXmnKDYgNuddtdEAYw4l5I0VGa38p3gPyg2JgOZp4apRmmpB1J2HglCsXEyKE7MdOyAkB8X5Z0GwJ145SjMxilS0sgwclwxEjJuiAmRIBfRAIN0V1YoMCADL8nVAoJDB3PjFVUa3EUe2rindA5Lcb91FATIGMwgW4APJcAttsqjANIgOfl61eqijiDJtrz9qBTaGDgwXMA7nRAJ1qLXJQC4OTEatJQagGw0O7oNiBIDk6oExhrav8Al9%2FuVGa4EDF4kjR%2FwUAZ2Jky%2ByAAXUJjLSea8IjAEh209oQhQcrS4x%2FwzPiUQXFwJA2cuyKUi6Q%2B7OiAbaWkYkCNQeFQpdizEMVFTxmrTrv1VQOCKVCKTGPlBEflZKiZBZhOw0fqqExLky0gWoJ3DYcyVQpfsNS2kFIJ3WBwDM1UCXWk00h0HNjW7WW9gtCVwcGDu6COHVvtRIh6loc7tIfdMIhdbUU28FRy%2BpZZda1wF1p0uDhaxnOM3CZxjPO5L%2F03oXZA%2BjZc%2FwCYYgv5Lpjba8c2rPSxnZaM8%2BMdDjv%2FAEP6Mv8A%2BF9FjX%2FR208FvHFbbH59XTlz%2Fptln8mnow5P92ftzt%2FsH6fr9Kxvcun9dxG81drPWx%2FRbDd6ezjqVstee1F5c5ep1WW613Uo67Rw7e9QXtBgv3Sq6bLa66KVXRYKU4FVEXtmIce3xRVhbE0eUqr2W1JgNVSiotegaD9ilF7QSQxjQ%2B9SigBNIksFQ4kMJJpt1SigteCGIkqUNawtcSGjsqKW6zN1AdnUoZhaATSHI4UFMWc0qSZjzSqbWKgOiGxBcEy8NVKCA5h25Hm7KUOwLEiSlUJImLSW0%2BKAgN0FRbHVWqNo02060SjYAC4fwu5tShmHynkl9j5JUNUGBSX4bhKoWviARj1iEBxl3c6h2ShjaCMSZoSfaUoLl6SNQ2qDEU1tKUYmhILExbqgwLfK8Bg4GvVABJD%2FAJnLdISguzyAR%2BY7OgwyeaHTtwlB0MMRUHyUozaAUZwfsVoIH5pYXFx5KUCkMeWlKM1ptmXLt0ShrRaRu4iJlM5BLyB4k91KAMiBURVWjPIDA7jT3KAvkdRi1DugzSDA6VSgMTjq1W2SjCRbLA156pQHALSDbDzsqNaC1XcNIShqGbmfnyUoQCLixLn82ytBLYv%2BLoCAxcggtDUCUYkChd5JPsEGccAw4d9WSjQD8oZpuaOyUYQA5gMBuxQYNpERv26JQTDh6a0%2FFQYUAEPV69koWpDaByRXwroqDL46s8CFKN8rgsxAgfYqM%2BogbmlfvQC55ALi4bVqYKAvqDWQTpuUBElxBox08FKM%2BuTQQ6ASJE8EiuyoIkEDSAezuoA%2Bpt6A79SqM1Q8vHs6UKBbaADt5pRrgDLuBr1TGRiNQzDXoEo0gbmAJh9VaAwektN2qUbKt1LeYFUBtJOMPAc%2BKBHDs5BuZ2p49kQwoHLPMdQlUHYgAyXOO5fdAQ5ca6HTghKNUNqP4Z%2FFKAwc5SeRHu5SjG01tNS5Jn3JQJ0c%2B%2BfsQAE0IPU6DRApYl688JQMaMSADI56pQsux3n3pRmFMvy1l6pRhvLajUcMogHkO%2Bn4pQDDh59veUoFJYnbl1aFOJhmLoEuZpNDBQIbSH2ShCxyFr7E%2BZVqEbcM%2FwCY%2FilErrQ53eo8VaEIDgksZcO%2FZKJs%2FwApFPblMhSBIIZ6dOylEbrXmRqzVVojeHdnfeioheCXDdExkRLPdxp%2BCI57rZIZpVo5vUAEsz6FXGUc9%2FsVaOe8aHsERz4F%2B1VaOex4KK67Aw82Kg6bNnrTdB0WmmxqorosBgVI1UHTaTu70AUVa0U0ajTQqmF7ciWnZ1FdFuTbuoLWvT26qCgkvU6D26KikwB3HVQPaDAmJ28UFANKW2wyBgGDUPnKgpbV2cE%2BcophubWIL2vxuiKyR8v2dUUXYOTAE7%2BSgYZPBdBhbucqwfBAQQbQCWDSH26oM0s1NHoGQEEW3QIb83EKwO5NfAxPVRWJJ3J0cKjEQ4hxBLAdUQw%2FMJ%2BaUUSSSwJGhcbIA5dyYkAe8eSIx%2FiuckioPDoC5MhiN%2BRsisLi7Cm3TRIDboxJDCPbopkAC5q0%2FM%2BiAuDqaS1JkIH3aTx1UANACWGp9oAQY6yx3b7NVQXk5UDMXUGdxdNabIFBJAAIeZYeKoZwZy2kbfioBkXxBLvt4lIMKkiMQ2SAgloLvr9iAFy%2FzAG6oIdigLkknR3fp%2BCAA2g7PvWEGyuIAaoI4SAlgWZzJZkGkNoGJxrKEYm4iC%2BgLfYg3FpFp1j4IQACzEB2Da06oQH1BrLiv2qwa00LO4fWuiBiXi5QZyGDjRwKoAMgWgszdPuQNxt2HbxQKb2IBJEVaO1UgxJJjUV0QZ3I0JLkINkQ4DckoCXNZhwW8YQYXEmrsHhIN%2BV2rqgxLOxq2qAZQQflBjp2QY3H%2BEZZflEU7pAXNDz3D0QZySMg5I2QAEhxHTb3IC%2BReQf8TfagFxJa0Frmf3JgYGkmWDkbdeqDXFiCbqAEDp4Kgu1C32qDElhLA1Jj7EAuy%2FhtkMARoqGq8cNwVAuumRFNYVCkMDcCYeIjVCMZOgNLSPFAJAi4sZB6qg69II%2BCAFyHf%2Fgzrp5oQDeRDl9%2BUgFQwDAwdC6JDFrt9noig4LAMWmZQAB%2F4g9WGqELdkMgQwoSOURnIg1ltiilalTNAW%2BzVEbR7aCCCVBi5fUmgNEAY8uRL08kANQCJPHtuoFi4Sa0J52VIRyAWPSde0qoS4Egs769%2BiKQw0tTb4DhEBwQQa0O6KmQRDz7oq6qJ3ONXPCCVRMEe2qoUiKnkugkQWpN2yggcgTLg6KiFxL7AVQQud9ix9qLSZS9QPWD7bJgc1%2B1DVEct4Jnw6LQhc%2F2BEc%2F8XxbyVHN6emr6qjrsH2rNHSKAVlm1UV020fQU04RXTYJah0PmpR0WOGed303UFrYq4BZM5VawTqTKDotA1hqaUWVWtDGvVEVenSDKBgC2xfqlVQCgthpLmfilRXEGlWYtzVSqe0N7vwQUtcNDUgTCBgx7U55QEAkn5uQ9VAbXc3M%2BgZBU8QdB8FBvzaEgluyo3yhiNfBiqofnmoaI8pTmGrp%2BapMa6IKEGCAHMMdeiBndqFt2ooMT2Z3uZAKEmpFG0j7koLatQ6JQoOVXmhNOiob5idH12PClwCGYRo4NYNfJKMwNrkPPu1OyUOTTR9CoA8FrXfT7eroAzkS9rwCPsVozlsgPlqdyoDL7zThACXJdmZiNUBo0uCacIB8pFpuYjf23QBid33H2QrQzggEOW08%2FcoMKFtKfcgAJIqSSRNOUBbIu0DWPBKByBJ0aoJ8EoNWf5hBZAAZxdrWZuqAw1p376IFa4swLGhEM6oYPDuIkS8qAhzIalUGxaMfCPxSjC2AxZvYJRgCCAA3PRBiKPDGmhKBmcOxb%2BDRAMQWBOXB%2BxKMRaQwdneiDG0OwBoGP3hBiLQIMhgH99EAuBctRnch6VQA2s4mTo3TqlGa4V1hvvQEg7FpLadkAkEOGYQxHdBsfzABy09dnSjH5nkwZHxhAOCDHVKC9uggUIFEAuIBDgktGtHQEmSPEGnPvQA4ki54q%2BytBjJjXaWZQYsHf3%2Bb1QCRaACMjAuPjqlBq7GGg1fpKDCTALPzVtXQEnj5TU%2B9AA%2FykGlSWjhAIqSSLqkUCAsAJPyiCK9EoP8A70sD1QAkiNNSfgyAEvBGsbvVAGDMbQCzEhnr8VaMbRoNmq%2B%2FsyUJUQYGk91aGOgqSXr3UAdyAXltlRouMOAX0jugNNKCilABJBYEAeMKjM7w5EzA1dQJcGd36VDdOUAmkGwCdUoxh3NBDaDx3QKDRydAwOtUQD8xL9RUcIA0QYP5Y2%2B9ApEQAGp9miDXBtCzGRVAjPoREUZlRIgfmMEOlCOdfPQRVBO6h0I0KokS4PEOyIWazBgFBK7%2BICoNd0Erg0V96K577flIh1qohcWZg2k%2FYmBG6szylRzXAEw5ZUc94F3LHTlUc90DdqhERYZNqqjlsDfFB12gPSdCoq9tWLyfYIOq3rH3qZV02wHo6mR0WwQ4qouFrAH5feqDottLDV9NgoL21O%2B0qKoBDUI9tVUPaBk2nuUVQOxkzA68KiweXkmFkOJl3YzwgcEB7rZGyCgD9D7bIHgEu4eUGDMS72iBvogaMnILUOohQG2jOABokUwMgbnwZAtoJIkyI5HZUU0khzDb%2B3RAXrod7fFQbUGZGmsfcqCXDMztUqBQHMgPL86UVGJcCoLwgYWOJAiG2frwpRhbDj5S0BolA7a1BUAFxLaBpf21QAO7sSDLO8%2B3CBgweGAFUUDW6f8AhFkRsQzQYHL%2FAHIMXDSQKUf7UDSAA7e0IpIIpSBRj7wqg7gyK%2FYoMTJxECkxuEBoSD%2FF7MijiYmpd43RDYwZoaBFDEdDv08kQwE0IbeX2RQcQQH47FEBjAAZgIDfegYuWFvV9DqgDal321YoCa0%2BVn7lBnkbEsdkVrKCY7SdUyhSQQ4qQwarqg0eGA0ZQEEyJB8WQABxPzS87oMJDgkho5PigJ1JctIAQKwgHXSnl3QNi8%2FmLu2j8QgDhxIh3D6lBhVzPhxRBocMC5AoGeio1pYMXpOvCgIth63fwvo2iAQJLx%2BY1CAwYAYCG5QAuTIoe%2B6A2tzMgdaoEYwzDGs7dFQSQS0ZM9PeoCLQDoG%2BKKUCGIxJYNKqMQ5AN2MSA0MoDiRJlpL6dEAFpBkyHcNy8FACaauWA3b8EBigEeCKRwSQWyGldWVQTkadYLlQbU1q2yA1rNpjYorOTIGviiAWqLgzgluyAsIIjYjXqgGU4MDSOdhTZAflhx72bp3QBzDwSwf4yEGAyEwZBIjVAuNNIb2ZWgOPzEkRy3ZUZwXat3SfeoBIHXcuFQeCCxl6oASRp0avDiEGNo0GsjSZlQTJYgVLUdjKoxr%2FAJTS%2FsHQY1LGuoUQpdgLXhjcKIMQKkA9dECEV%2Fw6g%2FcqFuAlnAuKBCNolqa7oJ3HXxLIEIJehcVfRUTuDEnU6%2B3RBHUuenKBQDLl2TKYSYVE90VC4TOvwVRzGCwoXcDwVESNi0PCIjfR68K4HLcHBjofYq4HNdUhvFBJjk3mjLk9PFnA5DarWR12e%2BizlV7dxXQorrtHGyg6LSJu3%2BCmRa1hyNKfBFdFgh3AO%2Big6AGB1YexRV7awYUDhpA7omDi0wwqavulVcAGGpT4KUMHe40GsoLWgXON6jogaT8rhxXwQM9Tw7MUDM8mem6UPSgDYsQYpuoG63AOJ2dFYHWHP8PCDDQVOgoPuQUh3l7aj7HQAOQAQ2xgwqCXOrA%2Fl4Oig1ammvJ0IQAObi8XA0G7CVQwAGUtj%2BYKUOzPc00A6qVQ1JuDbbyiMKsGcB2afFAoOpDlncasfigf80GWqNEAFGDEEdkVopN4PxRGIgMBDG0bIMbS4LdtAlGYF99BXxFEoNhuu0YDSqZDAER0HPVAuJLxIEPuKHVAwAAEEk18PBBiQXFDbPt2QEgkCARUgz1ZnQF2Ichh7UQBg7iprd06pRhi1tQ8OYMboGaGnX3opXGINDi%2B6I1rULPby%2BpCZCuwh4OnxBVDgsw%2FCaKAQWMbgAPPvQakEBh%2BZtgNOiA6uQeAemiKX8xIfSWRDEPSCAGQByCz5C6QHHRAHDPSZujXdkBqB7E90CtBtNz8%2B8qhpnUjTR%2BygIZncAeUINkzirksXQKN9ndudYQZquGyYBxpRkBEMf4jXR26INEOWNCaOg38MkAET33QAw4H5WILN3QYlySN8Rzx5oD%2FAJOpd7ttigxMkuwDDhBmMtA014QDU%2FwnetX5QNBho8kUrsXxtyIjfuiGFXBfYaMgAcmRy0oMQCXZo2%2FBBsXkH4opWufcEsQ4hEKbTLmQGfhKC4Ji75RM%2FegzOxl4f4yOiDcFtvZ0UALaPsAdR9iI0vc4BIimiBmFaEvKKUkWsHPM7wiMAxyDMZJ3SgORDEkOANa1hAxxeWM7oJkEDUQ90K0Coa3%2BGIfgcqjQHYEN4AqAkvrIgdwgxIobnrwgBtBuLu%2Fj96BADaQN9Pjugwc3F9OrFBpBjSs9UCzLiTQyoicWuxLWj8u3VaG6FiRQoEuabSW2HHggQuYdte6CVwAM0JogQg0JPmrRMiCasgjo2oMgFVMkuDhzWjlRULiGubUP9quEc9wYFo1AKCBDOSXaSqIXBoZtvBEc14DyQTwtDlvFvmdFRJi7%2BbKMuOw9CrnCumy6BqVIOqwjYy0%2BaK6LC8iPPRSDqsu1aCFmC1pBPcPqFYro9My0O9OikF7btAK1CmcKvZcK0DMkDO5iHoPYIKWkEkVYedEHQDiCanQKQNaTV4adfZ1IKi5stBQH3pA9pLGjs79eiQYyGxIep%2BxUUEPFa6Dus5Gc1knW0H4SrA2WptbKoPCRRehI7DcoHBttABbYBIGyFBJP2JApuyYYtpt2hINkHcmsWnrskBNziQZhhykBB1LhtAG%2BGqgd2LggAbqKUXUa1m%2FMA3h4qxByAcsW2fnqykVn1IA2c0VRsmNxm5qJBsgHto5jfwSASa1MbHdBsqAWgEHz1SA5Ro7QXiSkGyB2YT8UimlhkSKexKRDAtLGfthSDG4O5tIectfcrBnucmS4YSg2TD5jJgDk7KQDID5WbQgzGzqwHNsizBngxqfNIBk1rCjSa%2B3ikB53kndBjcZNtuQO32pAchbS2dBrypFC4hw4BeATGvKuEC64mgo%2Fy1NExgA3CtdZaOUgd5MAtQ691FK8uzvroQ1fNVGBJuJxgD2hAciATozgEpAMyDEghwY8UgwZzB3tnQoNmMQKEVmQkByYgsJhzHZikGeeedgUVheSBcYBl%2FblIACA%2FUFhCINtzn8rOKPDdEgxugl4MBp%2B1IGMijFRSky5EGC6Ixu4L6nRWDZCfmkiNQkGBgDEZEDybqkGNxFAza7e5IC4cHwL1Uigbg9GYxMUorEDLUQQKc90gd3YHvyopXeAG6e9EYXR%2BVgHfXsrAcgCHDloevtKkVjcWdg%2BlvwSIAukHRmDUqrBiSaTbqDq%2FKAwDSbtIZxKig4ufGG7F1UA0LQ1C%2FeiQKchDeE7cIFBGNoLXC08F%2FFAQaSxtj4IMSwh3ckDkx8UBfRg%2B%2B2zqRQyIeDdrb76qwHL%2BKgAn2ZIFBDXR2BJRAclvlcDUP8AFIGeCGZ7iwFUBF%2BpEN8s18VIpCCGLcMaNqqhcgDq8lzR2CsBzNo0FeiQC69jsAapAQSR4ueaIFdySCCQwrKQJkA8Npd4DZIAbsiwraXSAW3OLiIdpJ%2B5TOEY3AswYkv5JAj6WgETQtRagW4yzFm1NVIEuIAHytowSCZul3gwCkCXEsHHUdVcCNxuIIg7EQrBN8niC0KCd9zAG7VmKsErrg70cJjA5yTD1aVRzXGWbjaPBWIjddXc0DpEc110tWrqwctxMnX4KwQmnd%2BVUcdkiRGlw%2BCI6rXbfd1Kros3Z6HZkquqw6aCGUo6LZAZrtIUHTa3yk7pWl7DAeN67aKC9sVnUn4KUXD%2FADtVSghjcHB3f3K0WtpIlqdVKKiAxZgYPTlSioIAFHNAgIZgBI1G7q0VqwIDv8qlDProTTdA7sHaOfHlQMDPaTzsigBi8PNPN1aCxeS%2BpqPilFaBnIlShXJnFwDO6oImBc7yfJKMaNaWgy%2ByUC4GB3BnR9ExkOdAAwZmFXUo2RBORjTf3oDbJNNvCvvUoAcEB6VAaOXhWhqADs6isHe6K0PsyULSloBkl57q1B%2BYtMN3UozvNvVt6MqN8sG3t8WShrRLXB6kOpVNuwerAFh0CUCagggRa32lWoLNq4IZm0GiVQGI%2BYyGcFkqC%2FZy%2FwBxUUQ7k0c%2FdKUAPUOZo%2B6UEPBoGp8AlABJAOhFXnogIAIa1gKgijpRgauG0bx1QZhUAT8UoUHZ3PBffVVGBhx%2BYhA1oLEXTvt5qZypSXucbflJbXZVBaG%2FKJmg8EoBD3B5LOB1Sgt%2FEBJLufBSjPbLyJcvsgwg1NzOXjTwVqjlGTAv7BQLa2zBmII06q1GD94y8Eo2jEE3SACz8TRKMSAYDBw%2BjaOgIEFqbBmPailBBdyY0KKTQgGZPsVahizAEuTQxKgAuORJoNacjRUEcTTVi6g0s9ZesJRtiTiDLK0As5BAYtRKMAKyxkkJQwOhgtThRQBD3giT%2Bb8VUY3AHnbqoBAgwKDrV9laC7gEgTQ0dRQLNAdgId44VqMTqYZ5E0QEwWJcHQ6%2FBBpb5o3I81KC8gjZjxsigQ7iAlCAh22Jcu0%2BKBdgAfl7N0VqG7Et7V7qKAaX%2FKeyVGId7iC4p20VoIbsKMN1KpS4NGD4g90RnpqNOsz5KhnJIgiHdRQfUy7P0QAAGYJE%2BTVVqEGRL%2BfG0OrQQzgTEh5ShQYuB1j7uyB60e3inKilDsQ4jQTXRVEwaM1JhASWBhqygQOGLPEnkyVM5RmeSQXodeyUIdS7irHlWhbmLAyQZPZKFLdC8mvZ0olcAQW1Na%2BKUTuFIke1VcZE7ibiRvp96CUww7IEPBHBSiFxdmdgS4VwOe8h3BmaKohcXIimqojcSTBYio4RHNdBow1KUcl9DC1RJ5rG76ojjt1mqqOq2exhRXTY0Grsyiumw6Me6g6LXaQ5aCmR0WzzKjS9mpmC7%2BSgvbpc2rPRMi9tSASXOvKge2WL13p2QVtedf8AEEFQQ2x0P3KBwSRNrA1lBS2LcTMR%2BCCo3kCg196DOB%2FEwB6oKOCx0mNpqsjWs4NsbRvKq4B3FGMEPMPXdUMHA3LU2%2BCB5YgU0MuoCRk0s0n8CgwpBe0%2Fmh5QEUrxkR2ZBsgGeuw0PsUimBoCamC%2F2qAl2Z23Blh1QaaFmuAGOj1KAvFpAjc6BBjc2rHmiQBgCB3M%2BCBQ5LCLCxDBEYBqxEcIHJhtRXSqKV5IyYtA0RBEEUEmUU4kWuTNbgd0QXbXJ3IbYooGkF7aElEFyDbkdPxQa6AYIeSaoo99Y%2BCBWDmHgOKdSiDaQIGmhO5RQDy4dpB1k0QZnYlydRXZEY1t2BcHzlAZoQQ5rsigxLEVg1imqINI8%2FvRSs4tdiBQDy8EQTbI%2FwAWpZAQwc9wNepPKKDuQWckM9sxr5ojNrUGBEAIrGKzOj%2BLIgxR8W%2FKH19iit8zagiGJnrygzh2AJZp0qgAYgir66n2qiMazSeBR0GnEkCojp2RWA%2BaTBp70BJcZAtFBqgBNooSC7tUojESW02AroEBDucQwENCKAkwCAeGY%2BwRGclsXo4gIppGnB16IAGNWNpmJfvwiAA71BoxneqDC7oQPzDd%2BEgIHzQwADAIoSLon%2FJdy3L8oGMD8ooxeA3mgABtZy4cNDMiFcM4l6mQOdEDGdBawh9OiKBgtWYI328ERmIYPQSNB4oC%2Bhd9xCKxMNTT4IIngviHI9t0Q0h2L2iD0RWYAhywOjs2yDOIAkD2jsgLiTUGuqAamMWEalAQWABk%2FegECsRJhEZnFu7ObTygwq4tYmt3R4RQIIAmgmpRCQaBjPloFQpYPDwHD7aMyoYTWd6UZQHSJeCSJ%2BCKBa20gHrNH3REyKSdRkPNAflZ3dy%2FXRAvzCIbiiIBMcCR0lAheAAHNQ234qhbg0tLV%2B9BO6A1XLkdEC3YlhvLBQRNGrrvRUIQ1Rlz38VRETs5od0CElwfLzQQuIZ2nurhEbyH2JPxRXNdvzELSI38AGKKYRzXs8zs%2FmqOX1BWrw7KiGuPl8VUcfpmntJTKOq00ALNVRXRaWHaOyVXXbqA3DbrI6bZaHISi1ruQ1Gb7Uqui2eG0UqugF6g%2FepkVDggklzolFQSxY6QVBQEOG4YCk6pRUGvB7h0FAJLV0Cge0uBb47exSigLmjw4ShiCMpLmUoayDWA5dTOQxeLd4bblKGJMPHdGgYAbkyT96tQRcKTMA7ToyBmoGDO59xYJQwZn%2Fi1r7lKoOBiwYbqo1WY6wRvqlGt%2BW5nYElgmchxcAMhIGg9pWVMXMAt8EoVyCII0Ar47KozU0bT3bbKUbQMOdCA1KJVEOBEhtISjB9wSGFfbdKFpazjLQsQCPYq1Bcu7UPl71FYxG4qA9G2ShnMGS9SPBKMLnxcO1XrwlDZPP5WDgFAdnqanVKNQAAsfYpQMoNQ0c%2B0oMGGuRDEqoMk0gROqlVuTXUapQRzJJpVkoW65raaaSyqMaTB6OW1UUfyi6XILj70ozi16TQ7tugznQ6M9UG1LeDJRiRBaYr1%2B9KA4IBOoyJ8zylQGYC1mapNCrQQRWQxE7%2BKiieWIMHdKA5tBeWmRSOFQQQHD4tPRQAEh7ZJ3%2B9ASIIfYUHuSgFnkEb7dUo35QR%2BYAszPXRKMznmpHTv0SgioNQBB3fqlBZmcvSvglAau5Md4dKAHA%2BZneo9%2FmrQQ8AjcnhSjUDiO1T5pRodzEta2qUEVpIgFKAAem46pQCwrcfmBlKMCcm0P5njuFQcplwXZlACCXINQwIKUEVZ%2FwDhBKNwQxIlAAzC7FgHbulQX3iZPGiKUnEOBI5j7EoXWTQiKpQdiXAdAGIA4EsPclBkxBZ6zwlCsQboGLTNd%2FcrUE4gfNIAYk6gKVSn8xuya3UfFlahiSSw6j2bhRRIDiu4CUYbmlQUoXIiSGA3hUKxcu9zUSjAGAKDn20ShQw%2Fyd2%2BPirUM2MBgKkqVQFwe4vFFQLiHfmVKJkwbmJ4BKqDMF2h7koX8txiKm56AqVAuIBbFuEwFmCHJIrwrQpIPQ%2BEpRO6Tszz70oS4muo9mQSJDgbv8wnzCoiToPbxShXBgCdQgjc06gQ4VoncWNOjJjI5biQ5FGrVURuJftTWVajnvDF9NvxSo5r2LsRqFRzXnjhWiL%2FADM%2FtVKjhsNA79FR1WFh4qDpti6hPtyorqtJ3bRQdFpAmZ3QdFpFBzKirWNoeoKmVdNmhc9T7lMi1h0YhpPPgoKaM1FQ9rsADIFUFrCbgDXcJkOGa3FneNUFQRFSeeFkMC7Cj0I3CooCCHqABTdQM50JJofeimcEZuwURoteal3KKIfToake9UE5MCJimqKd7uhqx%2B5AQwBbQhj7FBgRoIJem5QYEjVwD7hKAvQs7weOEGtg1kgFMgPaWNA8katx2SIpR3l6AU8lFByCZcOSRqgzN%2BYOHqUBdyxgs8H3KAAkC6pYwTqXVBMl3AHXxogDQQCKFw7Ud%2FMoA9Cx0Zq9KohjSDpDMorBjLM1UAAa4kQ5o6obIkBy5qbT7cIMCTyDRBhdWIp22QOLrXggadh%2BKg0FnIkBh8FQJ%2BZyBsdkG%2BUuCKnmS26DNBe0R%2BXaEBipI6kKDFjBqacPrKoHLfLcX4QF6%2FK2ooFANCGAJ09zqgi4OXOxHfhSAG6TXjTTdUH%2BHRw2LoMGoDUT8GQBoLEBjXw1QaHDmszHtVAfmDbDfRAIuILmDSmqDSSAZLSWQYXWuWEhmfwSAtJIAJFa8IAxLzLSAIpTZAS7OSxGvTiUBIJY0q5hx71AtsCJGg253VGMSzA7V5EINBMdepr8EGBunIEtIAZAdXq5fSIqgFRczToKnugxJk21Z3aD0QZzLCKkblkCk6RPyx7FEOKHQ3b%2B2iig4IeNiQ%2FuQAXwAC5aRuqNlVwAH8UCm64AkeI51hAXnln691AopBDav4P0VGJkSHGj%2BKDbwK1G%2FQoA5cVj8zeVEB%2F4rgU435QEuQGNWJP2KAC1tzjIfToqM5I0IMcIDHNaNOygVw5DgB4bgKhQWdgS0t14VG%2Fi3u4KAXAgEhwAPzatqiG4aA0nhFAFw8ULHbugDAOAcXnKiIVySRQEsZk8eSARtUOX7orNIeRsiBJ1lm1ooFyAcFqO4norAtXkh0QLiAwcDaECEiCwaiBHYOJf2KCReXkifF1oTuu7mjn7kEbmoeHOiDGmj1ZQc5gUymiolcDxx8VRz3GrS%2FvVHPdcJBoKOiI33OC8AVZVHLfQidh7FUc190ttVIIsc3iqtRwWXAblyqOqy4EuzyoR023NJpRRXTZf7exRXTZfD8QoR0W3CnkoL23hxqQVFX9O8Oz6KCwuAkOYgIKi7tVm3Qh83Y7mm4QWtvJ0%2BU9FFh7S48sfwVpD23M4pvH4qZFQRWbhRQh82Lu%2FFPehFMrfGvhqgEO2L7IQwIuIban3qcxDZOWbWPNBnypG5aHnQq1RyHIPRkGF4YRBbYQ33IRTN2%2BbE7cn3oMbiCYnp4IMbqQzAECD2CAOGYFjQgVhCNvptoZbzQhnbICuhQjZkwzBoIFFIDkLhUh9NYlCGe2SZ69VCM4qA1DCEA32u5Yc%2FBUF6PaW2jzUGcngnVCMSAxekv0qhAdgDi21ux%2B9UjM0hz5JSC4lxyTFVCMTQgF3nw8kIBapJGpPbRUjAg5Pb%2BbwLhCDkxerVpDfaoBmQIMES9CqQxvAEhgDTdlAMiSajUt08FSDmLWf%2BI7oQwvEj5mhoUWBnboCxk8uiRsxpUy34KkY3gk1BFWgygY3D5hbqKHwooQcg58kWFytnXXLqiQcrWd2EsSWQgA23M%2B8FCCLnE2kBtd0AoQwkRa4jyVIxuYF3IME7uoNkJe2akDhUYgAUadD5hSkZ7Rabdaxo6pANwaHcboQ2Vtsy7UjT8VFjZWnsQ%2FtKJC5T0cA1r3lUjZ2AsHBPvQgZnUQZJY%2BEVQEepbL2u5g1cBQDIEYm01BYtDyqRswdC5p7VUIxvtBNrByI8%2BioN18Aij%2B9QhcwavEbchCFe0uzHQH4KkEXPuHJZ0BBJaOhPwUILw5ltojxRYR7SRD6Y92VQzhy%2FBFuqhABADFiHpSB96pBcQcd2ajKBXcUIc1HTVUgkgRBDwDoyEC675XB6jQR0Qa0%2FKSATB08qoQ7h5Mj2oosIDaxO4D6%2BeyqRs3JZ%2BtKJApIlixMyemyoBJYfxHUcaoQwumQRRggUEgTNadZQhiavR5UIRxaa8sA%2FdWkY3AhnIxiqEKbnZgQXkgfagDvNsA1CUAXGIfihUQMm%2BYTHzShALGWJerKkC68WuS8SgmSD80yJaAhE3rcQ4EjRUhMnOrAxVAuYEUArsgibw1HbTmsOhEyQGn2KqRO4gaOzbOhEiX%2BaQ%2BnkhELrwC5glm9yohddoCRzqqIm4T1REL7gHL1og5byJ6y3itEcpugzKqIv8AM%2Br1blB59umj1VR1WR41UV1WXMA7qDotu1BpJUV0WkRNNd0HVafx5UVUEkB4fyUF7bpA32eEVcFzWDpRlBa0yKHbuoKhhI1KAu7ih2QVtLSIfX2KCoZjU6EIGBpMaHZA9vys5qXlRThwxYRLBA4IJEi3UPtsgM2zUVPRA7ijDrxopAQdOIBKgIBEGhNK6K0Yy0ToVVGrmf8AJ%2B3zUBF1CXIuLqhgXJYMRTSDRQABgwDu86eSoLMxrzvsgYCej%2BagUwXJ0Ymk8qgACA4JMGdp%2BKBssSNH8t1IGyLQH60SDChoxp00DICTowMT8FAAKzq8RXog0QRqdPYIMAD8wcZPBG9UB2LPsDugLGLqHUIMGA%2BURuKboF%2FMzh3h990BtB5Y9imRiAWB%2Fhn7EAJalIfqN2QEkEggiH1QAmTUkUd%2B3FUBnQVPQd0A1BJDk09mQGdiTSfegABIo13s%2BnwQYOzsa0130QYORc%2FzA0OjICwJ%2BZwQ7z8UGL6FoqgBud%2BKDy5QAHIhjAeW16qh5tGzmBTsoMSwDjkBApu%2FMSTDEtp0KA%2FM5aAK8e9AA7sXHPU8boCCdQSaA6x9qAECT%2FCYbRAHB%2BUyYZ9e6o1vzOD8suBrKBi4LGXoGqygBctMgtaXZz2QEksCNNYQbJxFAWYhIMBNpLkjX3oAasZP8Q08UBIDyeQCHhBuMXtO0oBN0AgjxQF67SzFkG5kP9roAZbfSNW5EICSAa11hAAHj5WeNw2%2FRBtw4%2Fym2lAXucEMAIPXyQapIYhxIqgF2xq2zpgYEEyBIhtlRhcDT%2Fja9lIFFw0Alzl3furBmMPJq7IM%2FDvp0NEAeh%2FNsX1VG5brb0QDn%2BE19mQG4OQ12LFMDE0AJPM12dQKXuh2HmqFAdhOOr790AItrUdkGBJFrOdz%2BKmUrEvaXDlnIQKS3zCZEoAA5BedBsFQjiJFdD7kALuGoHcoJm6QAWGvLIEJihAGnsVRMuLiHrTdEKSBHiTsdHRUSQ9QQIA6IhSW6DbhBI3czugiSGMxLaKiF1zmAY3VErjo5eRoiZc9xZ20lUc9xBMU4VwOe403VRzXkS3cboiLz5qjgtOnRBey4kbEVGio67LmjusjotILEDpsouHRbdXnyQdNtwiXGiiuiw9Nn2UFQ3jBSqvaQwO2%2FvUFgQ0CnhCC1hatApVO4%2FhlyA9UQzj8paKOgsLnG3tsopw06lq6cK0PkzNMcqBhUlhNT8EofNi7vQcqBxdQOztKDBrqyTUKh8mYCmrqDAiS8vACBy9AIOte6lC7sxFR15VoYXUbzEAaorbkTDIAHBLOAJ9grQ4uAEuJ%2BbZ1AXB%2FirIND5oNjDlnma9EoaSJcRXYoMSAdBugEAxJqT%2BJ1SjOxJuLhoB4QAQ2lAwQb%2FJctEjcVZA70YAAaqAPbVhBY7hUZyHALvDtVAwYuA8u51hQFyG68j7kAECHcvG0IMbrp1aS2z%2FcnICwEUl6JQpBcc0EjqlBaTAcwD7cJQddJG%2B%2FuQCks%2BMjfmUoYuDVqv0QD%2FJ0L4ilPNBh%2Fkhnl4TOQANCPy0SjfKA1YDb8IM%2FzOxcCj86INQMSIgPwlDO7fLMA61QLV2i4Q4%2FBKDSAw03hKAXajzA47pRt7WYuXPHggDEAziSfHRKGcQ1QW8UGMsdz8PNKAxktk%2Bh4Sgh%2BDHy9W0QaZLtsN9n6oBNSWLgM7INRwT35CDEEyBNCD1dKDjaH0IDk8eSUaQGMAsPHolG5obqv7kAAIJEEHsyUFgzM5YkxD0SgA2nr11QE0BEdeUoANpbj8ohkDEnRp1qEAi126jZxCUAk1cWtRBoBJJ1lnQDIO%2FjogUkzkKGCH3qyoLgmXgwgx3dpd%2FwSgGCHa4Ma8V0QaoYEF5380GFTrFdX3SgO7hoeVQYmpqBPKgPUhxTolCG7cAvQ%2FBADc5k0LR0QKXrAA3PgVaM4qLhrPvjspRnYAgHE1ZKjABiASC7P1UoV8S4D6eSoBLFycQgWATRz%2BX8FQLrgYIcB%2FmqgmSDFtAYQKZq23hslCEm41HcUVQDWrk1KVUriKUqyUSykh2brPREK7SPw%2BKCd12oAoWCCdxZ9ZGSYVC64Se7qoidz%2BCtELriTBB3LojnuuE7Es6ohfdBIh5VHMSQ%2Flsqy57yJ02TAg%2Fz%2FBUcNh4QXtNPJB02EwenZQdNhgPHfVQdNpAPWqir2HbSohTKui0sXNG9iguC7RFXUFRcXd2H8I5SKtaW7SVBedNJoiqAg67OVBTKHZuapgEXWkS816%2BwViK5As8ifJRTvDl28wgclg%2FLhBnYhxNGFOB5qIrlvw5UU766GppCAi6m4gbFUEkia%2FBATBNG9nUDC4EVJ%2FwhICCSS4BGyDDQu4BnryoCKlux3GvvVWi5c%2BKDCWJAHPdAPmYsfmFDCB8mlhSu%2ByA5W3DsenZAWaP4Wk%2FYgwc1YNBG%2B6BWMAt9jbKghv4gwFCW8FBqtQcEVVBcy1JDqDO4JB%2F5MlBqsYPtzsgwNaOwBCAuYcToDKAGgdy7x2QHMuAd%2Fl37skGdyYYj%2BJ%2Fi7oC4drY0cqAgyRLM59ggwLi4sw0PxQHQPazSihZwYDUkdkyg6HEhz4P96BTaCHfkNHSSgJcCAKdHZAdQ5rQIAzuDShLoMZfia88ICSWYaQR%2BKAM2nzXVQGCKV1E0%2FBBmioI25q6AAzwK8NPxQYxWBd0qKIGJLginigSLWMV6tvKc40kMLWDGWmiAhi5BYmh0ICAA7watIdAzQQwmpaEAtta0jLWXHwTIxFzk1eDOiAF9DsO9JQM5DA6%2B3KBXBcbQG37INkCCR0fvyyQGCGagQKSwdvm1uH2qwLmCzEguGHwSA5FtXrMT7BIAROQLj7WQaQXGsHsgYkiGfkxRApALyXaG6oC8Eg5TH2IMBUnQu40QEiWMx0QBjLAQ7asgDSS7hm31QA3h3Fr7nnZAQTo8jXRAlHEAmSd0BcSNRtOiBXBMl2luqDSzg8nuiDIdug8tlAlpA%2FyQGg%2Feg1zmdqGkqgVZ33YoFl3baWVAy%2BUkPq%2BmpQKbiJu1o0lQLk413QTdiS%2BR2%2FFUK8TdAiOyoU3EDikwgmSaab0QJk%2BsVJVgQzSYUoW%2B6vRMYErjEliaqjnuuYVZoICIhdcDr3VxgJdczyx1CIhcW44VHNddroKhUQuIejIiF9w67lVHLfSQqOdy%2BXkqOGy7nWQqOq09hqsi9lzBnGqDptLN1ooOq0vrPCiremSdZ%2B1FXtuIDbwoL23O%2FwAUFxd96iqAmRQsJQWtu7cxpEqCwMAE10KCttzan%2Fg%2FcoKQaAkEymFF8WDx2V50OLgXbeg51hRTi4QKDUGeUFDcd2EUTAYOOpllARoCWek7IHzDZaa86ICLtTpTiuiB7TMgvvv2UBFDMmoM%2FYqCQQPzNsXZAcj0ippKkBYUYc9HQFjcB8VAQWmm6AOxfQ7096oIL6sGYN70WtqCzNLinO6AmASKmsFAQTONwJZ2QYXXUPEcdkBJNJf%2FABBARdTnWnigwFdrvE%2BKAmWmN6U8EGmpoJG6BcmIJDMKhWBgxf5Z6VdQZ2Zq%2B27IA%2FYwCO2iAQZIm6gd%2FDRA0s38JEEa1QaXjWjzSqDF2JqW3p3QF2uEs%2FmUAFwdn%2FKYFa0QYPpe4aorXogzu5obY6IA5tJYO%2BnXlA2RYvtDlICDA%2FijyUCuQ7AuAdKkqggtQNaPyoNnQs7aUZIGyYCIAbhlIBkXJYEavVWBYgEBiaCA6A6HU06dEGygQCGkT7kgGQkU3J25lICDq8W%2Fm29mQB63A0BHtCBgbntfaB9qDZGtWgJAlxOhZzr4pgFyHq%2F%2BIINqLiAxqemqDAF9CdfZ0G%2FLOjyNuUGJo7R%2BZAGMOAYo6DFhOm8ICQMpMtDoMSADO7nUcoDo0hhEIAAYP5uD7FAAImnMOgJLMWa7RzXugV%2FzEtAmKsgJuDFwRHaECEmhck1ID86qjEs9zna4iNIUGJoLQ5GsIMIfkMbvxQLUEAIggsdRsis4rVqs9QogktJLCSgmbh3Z3VgGR4Dltm2Vg0ZEEmjv8HQK7HrDjeqAEuPloWIMoASCZ1qgQ3RBx3%2BMoFJFS5Ya9UCk3Pta1FQpuGgcvTT2lAhu%2FwAp7h7UQTuI%2BwcDRETeTuSCD1p5qgEtDNlp7BQIbpIJ%2B5BI3ANMqiV1zxq0oI3XSdeFRElpEaP9qIjddJJPboqOe66QHfb4KiFxhn7fFBK65hp9iI5b7h74VRzX3HuahURnbyVR59t7NzRI06bLxGnVSDotuGrd1EdFl%2FCK6bLmbXdTJF7b9d4P2KRV7b5SC9t4D9a7qRV7bmf5oOsBBYXuJBo4UFLb7RDzskVWy5g21PemcEXtuBEud3lQhhfQ09tkgqLgwdjo%2B6hDO8g9OqpDAl3Ad6O6kByAh32mXQPbcHcflPsIQVzBIccuYogJuxpTVIGBAl2LUUhD5M8EhvJRWzq0nY6KwG28AvbtI5RD%2FU1aD2lIrWsRBLmpLVZEhnDSHANSgIuLgMQ3RSKwvG1NjMcJBhcDqzy9EiGBd%2Fmnz3UWBk9B2b8KqjR8xqx%2FLQezIGyBkSwE6R1QYlyXjf3IoltWcCT9yEbKHALkJBjc51tpISDC%2BcZpBPs6DG9nOm41kKkNmHYCQIHtRQgi4ESOI6INkALmD9tX2SDChfn5RwhGMEyeAHhCNGoJLF0IPygDxHCEY6jQUHnCED5XAY8ARyhGdq0pT3oC4cDWnavdIBENUCDqhBBDs0NRCCC80fVCFFwf8xLQwSAAmflYGAqGoNyNT03UIAud4%2BV2hIjAuNbnAn7kVhc4ly%2BujeaQEmBE%2BJQbJtDokGcOxPLdSgxkHV6gBCMCzljMkalBnli5b%2BJAHckaVY8oRhNrh2IjVvN0IJajG48oRjcGpFSyQCQXD6hzX2dCNlABM78gKwHUSWM%2B7ooRtuB0QjC4Fn1MDzlIBkAxduIQgZSQAS8EaOyEb6jmJFEgGRIuYMX1%2FFAM%2BX2SDPoWIEY7JAuTOSzEQPuSBwbQBqbY5QKb3FC%2FtuyRGFxiCJcqAZS0gbaN3QbIUDlmYinkkAzAmrnqKwkCm8G4NUvLOrEYXGhHAqEgV2H5Q%2BsdlRs7JGrUSDG%2BZaRpuopcixhhWFUhcwSGpo0aIFyG7Ws%2FZFhcsWkxUUSIV6gTEj2KpGybncosTNwALU2O6JCZaswJfQIFJJd4YwgU3B3Ylj%2BbZUTN476%2BNVAl1xAqQ8kmVYJ33EAtJ1O%2FZCI3XhpqzEhWCZuES5r1QSJFrsHOvt3TnRG6%2BWfpburEQuvmndIIX3kRxX7lRC64STroiOe%2B8SGfVlcYEL75bhiqOa64OTrwqiP1A9fbqkV5wu1Wh0WXGNlB02l9ZUyL2Hsg6Bc7CnKiui256%2B%2FyQXsNQzgyoLW3Gru8htUVe26XJnQdFBYXkUkioQWFzgOK6cKB3AYaiQiq231aSD7kirW3vr82kKCoNNCDRQMCTpTQQCgplMQBLe9QPkYL1ZuVUM566GFCjO7inKKIuMB22ZUOC1QwoFBRx0c6oMbjyWYR5pAwMvMmVBstTt14QPkBx5dUBBY8En26IGyMw1PM7IDlE1EPKBoPJoUAAMfws1D5IGm2hjWEABLiGAMIGyrDEDnVSDFmcSaBAaMIHDIM%2FLOw6%2B9FZv4dH2SjVuLiHmfglGcB3cQSwPc%2B9UM4dhEO52CisxIEkaoBpcwoxAVRtKEDQdeiDEkEgXSzse6A51AMceKQEEkBrpbiiKUGIaDXkohjcZDs0ugxIFs1qgZ3JDHvIRQu0IjQlpCIOQY86fFRS%2FLD6u6qGLMxID69UAcMJYaFBnA5iEGyx2IP5qoA4BM0JnZBgbdbgWfI09qoGe0AaAaj4qKDgUkEgv3VGcCskl%2FGiIzWkB9NduiUAF4JqGeJZAcrY2erNKDXEAcGAPuQLk%2Bjy2qDEksYtGp19nQbNg5LAFgPhqgxNzSXLV2%2B5FaRJOTkDbtCIFxltRr3QYD%2FABGnt5oGYQ%2FYaBRStRtD5aKgXADgGo0RBcXM55kT0UG9iDRKA%2BrIVuAe5qgBZnYfNqIoURhAcl3rKDOBqYNaIA4IOqoXK4sKxLO%2FgkDBiHBijoFJEvABFeUCvbTQRX23QA3nbGQ2tKpACZLnhh5IFyYEi2jtPigAJaHHXpogVw%2Bpd3OyBctXFpqOSrBriQxqaOUCPt8uqonkxAFRTXhAMiYq1TshQdmDtx%2BKIE0gkMAgmbmhpanARSEh9zLoEytNCXJdBI3FoiVRM36gnU%2FckREkihd6KhDeN%2B6QRJaIGwVRC66SMp2QQJFXHLKiRJBYn2CI577ndq0KDnvuMjfdVELrt3O4Co57ywaGdMCOerndUedbfpDaKo6QW%2BKiumy6k%2BwUyrosugAaKIsLqDyQdFt3kiui24001UF7bn9veoKi%2FuUVYXmN9HhQXF%2Fn%2BKiqW3OwBYRDaIigJqO3wCVVLbiGO9RoEyKW%2BpTmh67KKrnE0QPbcdz7eKgpbeXYjrrKB8jBlm9tVKGBES54VqQzxs87IMLjActTaiBxcep3G0qKbIlmLv7QrQRe8QHkeKgYEMSHtag2KAuXAFDI%2B5A%2BWm0FQEXl4MfxeCA5EAwQalvggNpoA9tZ0QEXEfxOedUBN8vi5Ghqg2Rt8YbmVQRXYuXea0UoYEl2DABtkGybtQ7%2BwQYEgkiQTIQHJhMaugNpB37saqA5CR4kR7URRc1cFzHKAOwiSIAp2lBiXdixO2roDqGZz0olAJd5d%2BNkpRBl7paQSlGJYkm13En4USgk7n7Iq5ZKBlIhiX%2B5CjAIfR2SgFhqZYMFaoBiXEm4yaQlQwuDOKeXdRWJbbLQdVRgdtaH3lkBd8gILUKgWj0PEDxZWo1WActr4QiszByPmYT7OlRiXL6N%2BaiDGK6b76JQXOhrpy%2FVFZ5gvEAIAZEN0OgHdEYwbaTAAQGOpGilVnDBi%2FT7kQCRMzq9aJRiSHOr6fGqUAtUtwXborQS%2BkkGaa8lSjOzDEjbfxSjF%2B%2B9H%2B1KACTr2bfdKCSWqHA1%2BxKMXJZnfV0oGVS4cH8UQpOjGPt4VGyaWZhHRAci8kP7UUUoNavpCqMbiHYSfgg0WuwYsKJQNPzZe1O6ULkDo0wxZUbMuxECH1hQYksJd9UC5NAZ2lj4ooZXP10KIU3mZir8DZUKbwKv4mEGJeAQAa90ANwtkzPUygU3EMwc0ShM7gaSduqoBuJI21MhQJcZp8CqgSHlhoNNUCuzGmzsGSkKb5%2F5yKQ3kPtJLoEJJ1qgQ3GN%2FNUTN%2FzAUQSN5Ys71KombxqXendEqd1zzoK8IIm6mpGqqIG4sS5BnoqJXXmdjvCGco3XO50CIhdfuKKjnuvZ2M0VETdq8oiF91Zog577mHwVVzZl1UcNt1PeqjosuLB4UF7Lmg90V02391FdFt9C7cqRF7bmZvFBW2%2FQIrosv1Md1M4Fxc1TGg1UFRcxPvRVBds1Z7IL23uPe8LIqLtjOpf3oKi4GlRuHRTg3NvuFFUF5YacOkFBc1SeqCgvejka%2B9A4vp3b7FAwvIoxGyQOLoLD7UDgxo9SyiQRdkN5f2dAXJBqR%2FCVQz%2FKwHUcKKYXiKDp7kByblwYQNk9DwSgIuc3B3F3tsgMDoKDZAzzR32UBdxV9bXQEXCSZeTtRARfWg%2B5AXAB5YR8aoGtuNRqabdXRRFxq%2FG6Agu3iCEGBaWLbD2CIOVtXqYZBoJO3mgwIIYNHKAs5Id%2FbhAXcmh2CkVg9styeyIO8TQ3IpQflNz1d2%2B9WIZ2ABruSpFZw4J0cMkABA4AaJ17IGcAuavCAAjzejH4IDkJYuAHZ596DOJJYtJQb5Q4dn35QYEVgywKg0EE%2FwAOrVVRiC5gEAflFUUwbjnrRQLqC7AVJ8VQXnWKjfzUGx27iqABxW2ZoqM7nY0OiBXDEO1KndEMLgzu7OT3lIrMMefeUANwtJklqpEGHqG8T7kUruxduAYRBcaS1B8EAyNdNQdkgwMzazlwNeqRWfWjVOzBkAF0Yt3ZEAE3Nx2qKqjAM0voW2HRASBXYx2RQcFi%2FIO4RABAMPu1EC5FzdV9NPjogLk1YXFn9yAEuJrps6AZB3fTYvCBcgNNoHCDZXBoeafggGQAIOjBAj2mGZjvvoqDkaAMalSDEl5nYKhCedK8HlACREQUCm9%2BjvHHVAuQLhmCBXNNQZKAVoRNURiRALMNCgU3NrUSPwQhDeJBDaTCRSXXuSJcKwIbh8xiNECm%2BR8zcIJm8ikA1%2FFBI3EhquqEycgPoURM3ASOjcqid13LkoiRuDtTjzVETeewQRNz18RyqiRvh9BoEETerBz33ly32JgQuO7cqolfcR96DmvuaWVwrmuuBJoqhMkSvMtvb4KjpsuoPFQdAucNqlF7b2ijKK6bb%2B%2FRRV7b36iqiLW3M0pRYXe3KKtbfQbKC1vqD7W%2B9BYXCJp%2BYKKoLqcGQyUVtvpyJ%2BKC4udgeqzVUF7kzT8UDi53cNPigplL%2BW6VTj1HPtRQP9QPa%2FYGsoHF8hy7nr5oKG%2BAz8tKA5kNUnb2CCgunpyoHyoNpUoIu0h%2BNuVaQzvFOqDWx93xRDZF9izsotEXs1PdPRUEXOHkTQ6qUHKAXBG9FaDkLWeY8%2BEocXB93NW1ClGegd%2BffCBsyBPn%2BCDZVggoMbg9oiGhA2bsMnNQ6gxLg5DHXslDO2s%2B2qVRDMdCaslAcSx0EaylQ4uD1BmT1SqF1xE7OwNUQzkS3sUqg4HQCLhwlQ2Q3c6Hr0RQfafwSoI4oN57JVAXWgEwwqyqDDkwWrp59FKrC05Eg7%2BKVGbEAVHilGkfMxJb5bde6Kzi1311EVTnBeXcAUBPHVBiagFruCgBdgHcmnxSoMtB4aiVRd9Sgzk1IHd0CgmvDjSOUQSSS9WEjUJRgfeKlFBmks9UqMYl6UFEqi8UYtrM9EAiBtLMlQdnPwSgEiguYvR39mSjEiBDUKVQBiCeW9ilRnBDCXqyUAk%2F4X4PXdKDlMxu1JSqDl30FD1SgZyHdAHDOTRy%2FKVAJHyiIiUqgCKNXRKjOTbSu%2BqVQN7C0P3fREDIXFw5aiKGY6MqgF3G1uh12QBzuzz8KFADcKAdiFaBkG0nXRKBddo7UbVSgC5gBL7JQuREnSs7pQt1JltD9quMjO0mI9pUKXggdVakbKu%2B6VYTKmwepUoU%2BprR6EKiZLyI4JQKbmBPEP5q0Ib2FTw6UTNwJMj7igmb3LAPOvkqFuJkulCXXgMw7IhDfI%2FDyQSN7ZHwKojdewarbKold6g3%2BxBM3Rv5oI3XM4Bd5CtRzm7o6tEjfI02QRuvd211RELrhQFtm4Vohdd3VVz33DfslRC64B5nZWolnz7Og84EKovZeISK6bTTyWRe24EQaoq1twfdQXtvcxpCRV7b94OqguLq0PKIsLnIUVS2%2FkNuguLxBBHI0UgsLoo%2FUoKC6hZ9lFUtvoxdggsLxEztXRRVAdjOh0QUF7NEbBBQHwCgLyGr7e9FUFwA21I4QOLgDz8KoKfUoQHOpCkDA03ZkDggiYQEXA8bHokD5NUu9Ad1BQXblzoygwugVejmoVDOwklgKoC4M0Iq%2BiILh58N0WtwS5ZwgzwBQGSUDEvUxsfNA4voAWhwFFEXFqto9aKozvd49UURcDLtxuiMGcMXbQcIGe5o13UUQTVi7R7QgxuFBroffCQaCK5ceSIPMA7OimdyZnVtYUAfUBVBdjOsvqFFFxX8zxvEoNlqWGz6eSAuJ2KBXHzGm569VQQ4YO5IjhAXEfM0nVQZ3cC4M71VDEmQ46eagWKtFSXVBBpM08FBpoS77oNJYv0JLIBOTO7aKg8SNj5KDaSWgh%2FegGRaC%2B%2BkDdVBd2IuIGiijlO7eKAGWYuAOEAg6iBLboNkKguIbSUAd7iduXQHK0BmYeXdAou3G%2Fi6DZ1faQ2qqNbdRqCQTUplRFwLb8e2qgQXtrTWOisRi0AGpnfZFbIS9NUgAIuBaJnWU5gAajrHgkAe6rxLN96oBIgRaZd0QMpI2FWQMbtPBlFI7V6Ame6qFJBapb4dEAJDyHNtEGclhTcBAjhoZzt7BAQe4iUKWAQPGK6IgEgww6fdCAEh%2Bu3j5osBwARI20QIbpc3TodECm4EEs43okC5B23oVQl14diWqgBuDIIm%2FaN9a9FYFJBcmW3QI9D4klEKbwJJZ0hUzeC3NFYIm7XfTp4IiZuIG5KonddLAsYJRU7i4L%2B3iiJXXAQINRvsqiJv0PbZII3XipLbBUSNwL7IIG4gEP3V50SuLcsioXXb9FRz3XB2HsERG64NWlVRz3XUYzurhEckHm23k60WmV7biWe7RRV7bzvRIrot9Q7tupB0W3neAoK23kaoL2%2BoYmtCKKRpa31DXLSgUFhfuURcXdSVFUzP3oK2%2BoQWeKBBYeoZnuFBUXnUxogoLzvEsotVFxiS5qUFB6hIIBnR9eykU31DLFyzwiK53dZkoqn1CaHhSB86dUDC7Is8EIGzJivaPNFpheXckSfdwge31C7gxSNtFBQepc7kuKMUDC44mWIQE3khn%2BKBxdcB%2BZpUB%2BoaAjmHSBhcNTOoQHK5vzA7goQwIIlh23SkM9WuqdN0B%2BZ%2BEAycNyzQgwvLTDiZ0QHIvV0BzuZnbogP1KtAQHMt%2BYF6nRA2ZAkyJMIALmdoZygY3NAJfQoMLi5uccoMC1CH1HxQEXFqlpLkoCLjNr9R70ByuLtBNSFFDK4O5cH4oNlcAzDV0QRfcwDzsitk5mKP0QNlDEtFVAMiJLknTRVC5kEBteNEgbOTEakwkUAWMFnDx7kByrIfaI2Ugz1kF36qg5E9FBsneQW8fBAuRLE1NFRjcz13NKINlrVvggIvJL8VSAC81Hc6cpAc7gWhmhIFF2LkCTqiBmXY66MPPxVgIvuIqQdWHXqpBhdcwZwHdigDmJI4Z9FRnIjIOKOg2RqJmGZRQyJdpDCPgqhcySSaVH3INncHLkPNH7IBmRJvHKKGRdzDs6IXMw4g1DaaIML7gILgGjIA9zBzWoLeaDAlm2qyDZEjadPwQAlxWkM6DfUgYl0C5l5IcCRCBc2Z7hugXO4vID18EAN5g5bwkC5EPKBDeZaHOoVCi81yjRkyE%2BpcSS8GhQTNzlgXdUA3k1JbnVApJH8TDZKhD6jNvq26QqZ9S5g5bZmdWBTfcAPbwQTPqefmiJn1CJy3Vgmb7mm7vRBM%2BoXI9yFSN50LblVE7rz03%2B9BG71bvaisErry4kxqgldfqNIQRuv8VURu9QjWEVE33KohdfV0EbrzR4VRz3XnfyVELryXD9FRHIv8dUR59ty1lF7bt67KKvbf24UFrbj1RV7b%2BWhQdFt%2FlopBa2%2FYu%2BikVa26jd0Frb534UVYXyBXWqQWF%2B5fhQVyhwQOUFLb4r30QUtvYzFOiCtt53DPBUFh6lJ0dlIHFw1ZtUWqAkSKIGF%2Bh9nRVcwdZ0dQOL6seUD5Unuge31JclgpBQE8e5QMLgXGo0VBfo2oRTZFo9vFA4vJ1aVIGz53Y8oCLyw23QO7iZ2ZARcTUhzHdIDk8abaJA4uY9VATeQ8MBsimF%2BLCUQcrqjXyQHIGof4IMLgHdyftQMQDMB4dBgHcvHgg2g0ZhugaXh6qKXLSrCaEqoJIo4ZobzQFzQEG7dAHd%2Flrt7bINlq2roHzcP3qorZmRoBThUFy4nqiNMHx0KAi94AgeSg2RdneXNfbRVQNx1IaqIOWniNUAG7DhKGF00oaqKBurruOiqMSWgCPYIC%2B4oXQK5G25QF6FjB1QZ%2FyiAUAButHxHvQF%2B5NAUUDexFN26og5NDdkUCTDOQ%2FsUQM3JlyPJFDIjffr4IgOWY0CDZGDQiHqgDnQQ2nkgzkyPfCAOWaST2QEw5csdlAHDw44pwqBUMIf7GZAfyuW2p1RQyOzNQIgZVj7ZQDJgC3RpQA3mNW9qKKXIlnAYvJlVAN0cawgQ3R8xfqqAbrnBFPZ0gV2IamroFN7u1N0AzrudTr7kCZVjsKIFyNRuwPVUI5lvlq7ogG7l6QKoUmcc1lIFuvAGgGzpAhuMsfFUIboApWiBLrmER04QSuv0VQmTjcIJm%2BpBdEpDfNegQSuvAeqoldcX25%2BCCV16ondcxDmUEieyCN18wa7KwRuv%2B1BI3M502VRG68pEc917l1oQvv8lRG66r%2BKIjdcyCOU1lVHCC9DKtVUXtXdEdFt%2F4KKvbe%2FZQVtu1B7IL23wfMKKtbdMIL237dlkWF6iqW3KiwvLg8qKuLxuygpbe48KIKZCATXRA9t9PBBUXmJEQSoKi%2Bal2hBQXnbzUFcx32RTC6YrUoHyL8UZ0Di%2BstOzMop8g8xow2ogYepNWejhEUFzM8j4qKf6mrkhqpA%2F1BUwaBARdGoNIQNlV9aNFNEoLkayBKKYXXUqDVAx9QBuKbypAc31L7jZA4v1p1QNnt1aiA5vUO3vQEXAw4fUH2CA5xXuNFA2YFYBpogIvodUBzYE7Ul0BF7gEeNaoGy3Pf8FFbNydkQR6gkx4hUAlpM%2BdEByDwEBBFXbsoMDk4neY9mVGe0EOWfdBnDSYKAns4KgM0oSae9BnLs51CowOx4IUGfTTRAAS0nnsqGc7vqe6ig5aoLOgORk02BhEDKPtH2qjZHQnpqoM8tl2HiyAFyK1q6o2RpRy9ZGiAvMzIUGLy0ooOCdy6IxL7dEArQgDaqoJNoc8zCgBIlj2Z0o2Qq8VlVWyFsmC6iBbcIoH0TIGZr4KjH1GMmqgUXVkH8KxuqpTeHgjlyiNk3V3dAM7mu9zV3QKbyCJbg68oBnq4A38lQDdzAQDKhpEqBchGWgqFQn1DUxLT5IBdcBqw4p0QLkYYdRxoqA9xl24U5ApuYkmay%2ByqUuZrR6bRygX6ndygX6jO6BDcakoEy2LkVVCZPwzONECG%2Bh1ogS664irKoQ3aHs23ZAh9SfeURM%2BoW5VEjeAKwPwQTuvLxu5LoJG%2Bu5VCG6ZPmgmb%2FNBG6%2FbsNFRG71D2nugkb0ETc3DhVEbrw%2FIVRG655Mkaq8wjf6nkmBC66JVRG69kgjdeqJZoOK25EWFwKiqW3FUWtuCgvbfypBa24aFBW29vcoq9t4%2B5Ba29meikFrbtB3UVUXCJdCqi6NkVW2%2BkzsoKi%2FSr6aIKi%2Bmu6gcXMILIKC7qx2QUF7wCgoLwQON1BQeoNIoSkDi9wzOygpkH6%2FBFNbc%2BrEmUDZkPXcsgceoQz9winF4NWflQPlSfsCAi6rVOn3FA4vAGg26KQPlViYCBxcDp%2BKgOQHQGSgL1Y61VqmN%2FNd1CiLoZ%2Bu6BhdXyCA5liGqgYX8t0QNnIrwSigLhL1FSEQ2TwY2lAchR2N0FARe7Tq6gOYoQJ0KQFyQzQZqimF79tUgGe1ddUgJ9Rm2SDZgzrPTukQRedex9nRRyAL6DpyoCbyRNCzQgw9RueIqg2T6SDRVBzIcuGMeCigLwXL9w9FUH6jksYCK2etEGy3rp%2BCIJvFY4UUBfAdnpsqjZM%2BrBBjcWYnuoNmKQPhyqoG9oo77%2BKI31KAGtaIoi4%2FNJIOigGWmpmNUC5B4pUuqC9p43DqBc5dwW3oqNmd%2BERjfqO5bZIoZcEvUMiBlEkRL1SAPJLhyWPVADcHkyOFQLi5fbRMDZAPNHl0UDfQ7KBfqfNEDUKoB9SheqKXMVB096IBviuvdAjxNWY91RjcwEPSQgBu4rCgXNme5viqhTc9Ke%2FhAv1GhzyUgQ36CvG%2FdIFN2gL9S6oXIAoEN8NSY6KwIbxpXhAh9R%2Flp18EiUhut1OqFKb2l35QJd6lZkHoiJ3XhhLvAVxgTu9RtezoJm4CQWVCZa71LIJm4O7uQyCd14Vgkb6zzKCV1%2FbR3QSuuqdd1RI3BETu9QTqRokELr6tqqiN16ojdc7z0QRN2%2FZVEbr%2B7qwRuvEpBC65UI44TlRxW3BUWtIUFhcGQOC3IQXtuG6iq23aoLW3DrwoKi7wRVrb1Be24Rwoqovb3uiKi%2BAHUgrbdFUVQXs2hSKoLm8FBUXu24QVF1PIKCgu0egr0QO57IGF7auge2%2Fdmr7FMiovBgyNlA%2BfMGiQOPUkiVA4u5cU8EU2UuNoKFM51A9tEU%2BRjU7oGF40LMaBA2TauRpRA4uEB2ah%2BxQML5JeNvBAwvL8DX3qQMbhV5QML9a6pA2RZQEXwK88oGyFXpVAH1rNSfbZVaJu3JZ%2FghTi7WpUAF24beXVgbJ9e6gObOO%2ByBsg5Lvx0RRFzBhBaWRAygh2eJ1CBhczDwfRFE3hoIfxIRGFwgxygOoYMwZvvQDJ206IGe06t4hQAkFhWZZUE3aExMKAu01I1KoAukS%2B8oM%2Br9dnQYEAkg8M6KwgEOW1RGdy4LAc1QYFnAMjlBif8rSbnAQYkbtLHlBgQ8E%2BxRQdq3ayiM4AaGaiDPEB%2BsoA8HQBy46IBkGoxoEBztrDS%2FLoAboDkBtkUMgKO5UQHakHY0VAyEmp0CDG7YsZQTN1KnzVByllAM9AaUNdFYUMjSv3IA7ULV%2FFEAlzv9miAG7VjGigXLVhq7TVUDPUd%2B6BTedQPgkC5GtTuUCm%2FlmgTurAmQLAnRApv8pCoU3tSen3IFN8gIEc11bVEKS1NWhApuAeWJ1QIfUL%2FABREzcKEto6sCG4Eb8oJm9jwdVRM3OOqBTcZ0mOiBMx3CCZvMh%2BjqwSuvl9kwJm%2BuvKQSNwI3V5ghu%2B8IlSuuhiUEbvU%2B5WIjdfXzVgjde78IJG51SpXXSiI3XOghdfKsEiSa0VRO66uqCb%2FADIrhB5VRUXcoLW3U96gtbcoqgO0qiguRFrbwoq1t%2FioKi4HWlUFbb29zKLVbb0FRd5ILW3w1VBYX0HmopxcPBBQXS%2BpRVLb5rRQUF%2BlSB7kFReDL0UD56%2BCBxc%2BwdKKZH70DC7V2ZQPbfTVUPmN%2FbsoHF4dhEdUD57kcEKBxfV44RTZCJogYEVoaIUz0cTygYX9jsopheANxv8AiqCLw4Y0dA%2BYkcQFICLrqk16oGF43GjIGyepf%2FCoDmw7oGyB6%2FagOes1%2B1Aw9QTqdQpBsgzEPqUDZPL9OqAgwHNUABNSRyEBcTQdKpVbJn1hUog0lwEAF2wLmoQpgXr2JUGzBnQUdATczac%2BaDZFifAfg6A5MBABKAZaTRggYXggMYbXZIBnz0BQEX0makfFBhe4YgEbIBmCZLvQMyA5g6sDogU3MQxjZvigIvihHCQbJoBZAuZFDrqXVGNzsCRyPxUGylvBBsncjug2XLNsgGXgKsgAuO7lkKGTawNSFSs4hqEqDZQJ7BELkIPmqAS4OjFo2UGPqNwEgxuLN7SgQ3kjY6KgZh9xoUCm5n2KBTfUvUCFQMoIfglApvEkHwQKSB4wgXPsQqBmTXp2UCv%2BCqENwcuS40QpTcJNSUCm%2BrVRC5aP0KBDfXrKoTMUJdBP6jvzUqhTdXVBPKo0p4oEN5DZHugU3sHeuqCZvYTTUoJm%2FwC5USN7jZBM3Pr1KoQ31colTuvG%2FRBG71HoqiRvVgldeBTsgjkS6BDcByiI3XOqI3XqiF13dVEyWQTuueiCN1xZ0VN9XVRxi5%2FtRFAUVUXKKsL4QVF50UFRc%2FCBxcR0RFbbqaoqwvKgrbfo7qCoukNCCgvLToirW3qB7b9EFhfDarKqW38oKC9BQXS7qKcXvXRBQXvrATmFMwJKCgv13UgcXt96BxdDu2qBhdVA4uNOyBh6nNKlQOL%2BWmUD5pA2T0L7uophe0v0QOLq6bnXZAwveD0ZAXAMSgYFyOJQo5EEBxPiiiLyDWEDm%2FV%2BFAfqQ79GVBzqBrHRQMLzDmXkhINmT2qBukD5HQvOygObfagOZpM0YoAb36BUPmLQS9BXooNk9D1KBsywkg6GqDfU2kjR0gOb3CWGiDZ6aNRAc3%2BIKDH1GqWmqQbLvKQNkDXwUgwIaZ1ZIAbiHYqjfU3LJCsbngdEGytI9wdBnkbBpQHINAPQqQDIt7grAMndmFDyyQA3tQuduEgbL3uoBm7iK6KwA%2BoxDpAPqNDhjqgGfNdUAzFCxBpVBvqEVKBcyXPYFAMjMvcgzjwpWEAyIFYAZAubaz1VgGQPxSBTe8wYd9kgBvakE6oFzI44QDLzqqFN2phlACeYVQMg9eGQoG8DXzQIfUoN%2ByBDe%2BuqBTcaaIhTewLTurAhv%2FBApvPdFTyM1mIVQhI1KBchPzQ9ECm%2FSiCZvcmqQIfUZ%2Fegmbup1VCG8s57oJm7sFRM3%2BKJUjfyqJm9666IJ3Xz0SCV1%2BmisRK65UTNyIldfygkbueFRE38pBI3EmqoS65kErrkEbr1RG650QjyqOIXeK0KW30UyLW3pkVF1FlVBcVRQXwoqttyCou8VEiguQUF1PIoVUXfeiq23%2BepUFRe4HKkFBfxKCguoyLVLb9VMqpb6m%2BmqQUF%2BtFBQXnpNEgoL9SzoHy5bZRTi5m8UFBefBA49SdkDi8791BQX8dEBFw02olDC59eyB8jLS2igIvZthqVQ4vMVhRT%2FU7bIgj1Nan7UgcX1UgbI6mlEU2Z9t0BF5nUGqBs2D6lAchImEDZQ%2FKgOQ%2BKFEXFhQgqqwJfuoDmfJUNm3bhQbOm4D9EDD1G6hAc9kBPqeSQbNj3bVIDmB3080gAvfbnlIGzPQJAXgCdqqDG4kHTsrBhfseyg2Uma6fag2f%2BUOUgOTbxQ%2FakAyuq8ahBvqamldEhWzbVgKQkBF0BkAzq0b8INnMk%2FY6sGNxLSRukAzhyTKQA3MY2o6A5PqVAuerUoOqsGF7aUglIBmQweldEAPqDdtHSAfUOzjVAM%2FDQAIBkdCzIFF1NBV1RsjrqoUhuapNvO6qVsmBINd3QrG4MdFAp9SO0qhTfQ6oFN5ADEg%2BKIU3B0UuYoNKqwL9TVIFN4EVHX70QmfLcfagU3wZgvRULdcZ5TAXKJPcIFzAoXRSm9n9qohTeJ96Kmb3REzfu%2FBqqEN0l%2FFAmb8oEN%2ByIkb37KiZ9SKsgnddXfdUIbuSgmbvLRVKmb6gIJXX%2BCRErr9lRI3%2BSombtaIiZuQSN3EoJm9VUjegkbifsVRM3BBK69ETzmqo5AVRUXIHF1PeoKi8JBYXKQOCiqW3IKC77lBYXqKoLtXRFBdygcXIK237aqZVS2%2F70FRf%2BKgpbed%2FFBQXjwRacXa%2BaBxf06KKoPVivVIKW3xVlBQX%2BXvSBxfvRQOLtaIHyoQYJRTfUP2pBT6jtNVAReOQ1UFBdzUSimF6IYXg9tEDi5qHpsoo5btyqgi5mksCgYXw71UDC9zuQgb6lfIoG%2BpzOiRRzcdNkgYXAto0hEMLiorC96RzQqob6laB9H1UUc36IDnQ%2FBAcw1Q2qAi8MHkoDluZ0QbIMz9kKwLOH6IUciRVrkBBYMCGQHI7wotE3yeKoBkYadEByIAMcngINlLQgwvu4CDZnXxQbMuAD1lAMrqvzCoORp5qAZND1QF4%2BCAZVDV2hBsgYq1AqBlcX7Qd0ShkdT1QrZ6dki1stT4olbJQoZCYd6iFQMxv1QA3hnE6oB9Rojp9qAZuw8AQg31GMmSgXMBtTqgQ%2BrWWCsRvqaeSQKb2LkDqigfUEbV6IFzk68IhMzwNmQDOunRULk%2FfRRSuxOiqAbxv3UC56eaqlN%2BtAiEN25HOqBTeKbopDezz5qoQ36pAmTPPUoFN3fmEEzeDGuqqFN%2FLtRSCRvfnzVCG%2FlBM38qwIb9URM3tqqlTN9UE7r5rTRMYErr9aKid1%2FKCZv7KwTN34oiZubVBM37VVVM3pBE3OqhCVBM3KokbpQSNyoTJUcwLohnQVFyiqC5BQXqCttyCguBUVQXMgoL0VQXIKC9QUF2yiQ4uVooLlKp7b2AbTRBS2%2FfwQUF1N1BQXs2qUUtvdn1UVQX8vuED5nZFOL%2BXUDi%2FzQUFw35KBxfO%2FCgcX7w%2BqBxfALdQgYXE6simFzIGzYbclA4vrKBhfQKBhdPWnZA9t8QwGuzKKbPempKIOTopspd%2ByVByAFXZFNkZNEqALw0E9O6obJi7zqophe0xwgJv69UQTfHvSqb6gG8BQH6hPXVOQN9QbRugOYavJQDKXLHl5QEXjQk6bogm8hgJhFHIPVygw9SjeOqBs4r0UC5VMDchUEepSS40dAc3l%2FbupQR6h4YoALywb2ZKDmdISjZlya7IMbyAPigGcTU0lBs67jlAM6sQSqNmYHLBAD6mhLmpPRBsz20Cg2ZVAN4DOZ0HCAZgkz1lAueSIOaKXN9eycgGaBR6gI381QPqN8UQBfFZRSm%2FUSCgXIQ26qAbieqlAJDMS6tGNwOp56KUKbxFQ2qoGZOrTKilN4KIX6mjsqpDeAPgiEN408VQpvL1pooFyJ1V5AhuBk12QA3gMiEN5nVAhvndAhv4VEz6joJm%2FtogQ3nRUIb90SkN6tRM3oJm8boJm9UTN78oEN3KCZu28UqENypEzfyipG5UTN6CZLoiZuRE7r1RI3coJm77gqJm5UI%2FKg5wVUUFygZA%2BUJFUF1FA4u%2FFUVtuUzgVFyiqAoGFxCCgvBUVQXcoKC4b9lBQXcpA4uoiHF33oHFyiqC%2Bkud0Di%2BsugoLqSoKC8tVA4vetUU4v581CnFze90U4u%2B8IG%2BpRIKD1KbCrpA2YCgoL2FUDC%2BRrypA2T0qEDC7lkU2XvhA2fKAi6vmgcXs%2FKimF6IOcmaIGF4qPBkDD1BR6QUimzUGzp5lVBFwp4Iovs8ICDz4INlsQdkDC4tuyg2bbxoiNnAnx4RRyNXZ6jlAcueiDZRWiA5w7g8FARe%2BqAZy2T7h0Bzn3ygw9TR2O3CA%2FUJbVIjZ7l3oisb%2FAMAg2ZFUBy5YIFzfUazsg31K68IDnz5oB9R4eQgxvO7IEzViDmVIrG47sgGfikAz7uYViBlR%2FJRWyZgGA0KAZWjWNFQDcTqeQg2dW7FAM66bpAuew6JAue%2FvQKb9awg2Y3ZAhuHHKqFPqAcdEgU36SWCQLn2QDPlkKQ3D7VShmygTPdVCm9izoFzr5ugnmOh3VCm%2FugQ3%2BVEEzd7tVUKbncOhSG9pQTN%2FwBqIQ3oJm8VVCG%2FaEEyeVQhu5QIbiiJkosIb9kgmbpq6omb0EyXZVCZAIJm9ESN0KiZPZUIboUEyXVwEJRMly47oOcOqHBKZDgnlQUdAwKKcE8oKAnYqClpKCgJmCyCgJ2KinHgUDgnZFPaTsgqCdAoHBOxUFASdEDgnYqIcEzBCoZzsop3u2PKCgN2xQODcNDygoDdsfgoHBuGjhA4uNGoopgTVigZzs6BgTEFFUBu2fZAwuu%2FwlA2R2QODdDA8qBgbtigYG4aE7oHBu0HVQEkxCKYE7VQF7pgoCCeaoC91GKBwb5a3uii9wqCdnQFzEFEF%2BPJA73agqKz3ag8IjEl5DnR1Q73MYUUAb5g90Q2V2x6IrPdsUQSSzEP7dUVnumJ7ojPxCAudB02RWc62lBnZ6xxwgznQRqOEQXLMxRWc7FQB3o46bKozn70UX2B6hQBzt%2BCqA5aiDORpVBgbtujIASa3AtsUVnuFAeEGyuMAFtUAJueiAE3bEnRAHucBkAe7YoA921yBXuYwiA5Gh8FRsrqsZUikN10QfB1QCTsW1qiFOT0lADlFUCvc8glAHOgKBSbho6IV7tBHCoBN2yBCbnoe6Bcrpg%2BCBCbnoVQhN2oIKBCbmoUCudvJEKSdkCG4iGJ7KhCTsiFJOxRU3uahbogQm%2FYqokSdpTAVzsqEJOxKIUk6COFBNzsqpCTMFBMk7FUTJOgKqEJOqKQlEISZgoJEnZVEyTsUCEnbuipknY9VUIXQITwiEJPLoFnlUf%2F2Q%3D%3D%22%3E%0A%20%20%20%20%3C%2Fdiv%3E%0A%20%20%20%20%3Cdiv%20class%3D%22position%2Drelative%20d%2Dblock%20my%2D0%20mx%2Dauto%20overflow%2Dhidden%22%20style%3D%22width%3A%20940px%3B%20height%3A%20370px%3B%20clear%3A%20both%22%3E%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22404%20%26ldquo%3BThis%20is%20not%20the%20web%20page%20you%20are%20looking%20for%26rdquo%3B%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dxrange%3D%2220%22%20data%2Dyrange%3D%2210%22%20height%3D%22249%22%20width%3D%22271%22%20style%3D%22z%2Dindex%3A%2010%3B%20left%3A%2072px%3B%20top%3A%2072px%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAAQ8AAAD5CAMAAAAOTUC8AAAAA3NCSVQICAjb4U%2FgAAABDlBMVEX%2F%2F%2F%2FMzMzFxcUAAAC2traTk5MAAADW1tbMzMy7u7uvr69mZmZUVFROTk4AAADW1tbMzMyZmZlCQkLW1tZra2tmZmbW1tbFxcWvr6%2BFhYXe3t7W1ta2traZmZne3t7W1tbFxcWlpaXe3t62travr6%2Fm5ube3t7MzMzFxcW7u7vm5ube3t7MzMzv7%2B%2Fm5ube3t7W1tbv7%2B%2Fm5ube3t739%2Ffx9Pbv8vTv7%2B%2Fm5ub%2F%2F%2F%2F39%2Ffx9Pbv8vTv7%2B%2Fj6e3i6Ozf5ejV3%2BTU3uHR2%2BDH1NvG09nF0de6ydK6ydG3xs%2BsvcedtL6RqLWEna10lKVpipxmiZxbgJNafpRQdYxKc4tCa4M9aoM2YnsyYXowXXjFq0N%2FAAAAWnRSTlMAERERIiIiMzMzMzMzMzNEREREVVVVZmZmZnd3d3eIiIiImZmZqqqqqqq7u7vMzMzM3d3d7u7u7u7%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F9H2B9VAAAACXBIWXMAAAsSAAALEgHS3X78AAAAHHRFWHRTb2Z0d2FyZQBBZG9iZSBGaXJld29ya3MgQ1M0BrLToAAAIABJREFUeJztXY1jE7eSTx53vNwX3OGWuxcO7siDd7xcoYQXrpVCaQNrB%2Bw4MSHx7v7%2F%2F8hp9DkzGq29tgm0RS3Yu5Y0Mz%2FNjEbS7LK19dnKYLAXy2Dw%2Bfj4AsrOg6cvtdbKFv%2Fx8tmDnc%2FNV6%2FymLDvv64gws7eIe8olP%2FbW6G%2FxypjbCW%2B%2BpZD7WhqnWgf9O5l8Cy21hIkT3tbzmGCQ4cu%2B%2FPVuwwi99r9gY9Ht2716mTnWRxIjoUO9571G9tBrh26N18rlH1JgDu3bvbp48EhapwpR0BEP1iBL03%2B9ORrlRLNxf8H5fmtWzeW72H7wLOeGYpm3w%2B2e%2FCF2gfN7cfXSmXXEyQD%2B7CPWt4%2BwLohuA507%2BB2L75Md9ir9eNrtfJU4PuHWz3U8vahb4jVQ2d9%2BnL0r0t2%2B0zooBdfq5VtBoel%2Fl0Ptdw51JnYNABhv%2F3j0nzx9roPXyuWByorWn27vFpuH3TrAwnOrAL9%2BPd9%2BCLd9eBr1cLFsRz3UMunSerglMmNBEWMcb5fni%2BK8jWYyw4dBvfRY5LfFbQrVxJ2%2Fefl%2BMrc0TUEH3uSHMtP8ttoUoxWzidZ9MVNY%2Fqfe%2FCFsLym4MMTjXR7TPIhlkNTi9bcTMLkEyvq5wv7T%2FFdWgNcQ%2FBxOxLz2gn8Lz%2FJ31aCfZBARituLPbqTws7FsKYawg%2B9tMwRDF6eK3o9DS1Eio8vvS68mIBhX2hm2vwpkktEeHlJ%2Fkd2pIG13QhE%2B3Jf3zTTeIwjz16BUUrlrsqmr6OIvxpabVko5hkf%2FHk%2Fv1v79y%2F%2F9fvj5SSVEc%2F7xzquxKUy%2FO1cnlKCLq%2Flw8%2Btg8Rz0gFnpuwKZQ7T45yZQGI7nT1%2FAzVDA37BEUrlm3NldqUvy6tlruspXcOfwIcbt68YXq5cePGzW9%2BjMqHqz%2FqEG471kLr7uX5WrlkwRSQX36Sf0YbIjhID%2F%2F0o9MIOul836H8u7jX%2FnytXA7oxGgvvl96GLbFSAzgYB38wxHHHMqdMpkDaly21fJ8rVx2sjFQfSb5XWlR%2B10OB6zNUIwWLKdsMHjaiuUago89skTw6r6819rH2hGizzviMB4KA%2F68KN8erhYwvIbg46Wgxj0m%2BbD9jZwybFBIbD%2BgAvrwqkToJdHb3nytWm4nU4kTol5%2BkidaHYaxsEGxjSEPa51vCwN%2Bm651bMMefK1c9oli9A0%2B8tnWfBSbH8RqSdRHBQlJlHd9wQeO1eMKtMck%2F1jl5bvSKD5gJqCtbS3kK5ZrCD5YTOzKt8sPwwFu6dvfLzUfUELWEF7IIt5VPBIz37759OrxFOPgl%2BV9JvlDtC4Jq%2FpyzMT0w17KlZ9FxFLNawg%2BtnMGe23ISfvfP5TZ9tu0eC5SdyQ82H6%2Fw%2FwaNgp306SARmx5tRyEYQxe0vz%2FtzLbz%2FgSxjS4L9WW1hDXEXxk%2B%2Bqq3ynlXcqx%2FXhSxmOP66LB8aFU%2BwAPku7P14plBwkTS59Jfg839d%2BelIcxTjDI%2Fz4RpNzJuDLAXUPw8YDRBbXvtSG3F6RDrBenF2NeKPgIUZaExwOMmQ8Tr2WjUDPuVM9JnqxBfWddeKis6L8J1V%2ByRZHuy9dq5XYkGuNFmORvUd7TmOY9HPCFsQJ7K%2FK9w4wA%2FhLwuE3sxP0fFwGDbD4U%2BFqt4OAyrMHjJE%2FH0oIm4IH4DqVrHJXiu4aSfjxmCEPJ%2BELT%2FIbg2DrERho2JILXQngEDckdGoNMu1plPIRcCCEgO4xVUqgi8aUixY3AcTdKkfy9jsHlAJPUfuRlPOhIdnHH68JVhsdd9HPc5UZ8kSAGMNsQHvtUFEskTfJ4HLyCCHjkxtyJR4w1u%2BqnpW3yp4wvehiwGTy2GV%2B27%2Fuxbz4X2N2pDI%2F4K%2FYfZZq5O83rbwcY8BEw5YsGahvCYzeQRXijSX6QhdYL%2FIcvP3ZxdxDDWF3EYzfhq8M6APNFIx4t6u0qhe9fw7z2JDnDAVFJZ%2BkSHpragFnAd%2BKRaIWvvP6BUnwgFOGLMC3r7Qplhw2T%2FfJN6nqQD5OEBw%2Fn1IuuMPJAcKis1xCjJMg0SZFieMjjtEKhsbqj%2FgLFxIPkzTwoXfaSpFyEB5JD1Dq865wwRnyF4CChtRE8UF54HGC8wzAIaCT%2BcrrITsKfJfEo9nqIfsqCD8SXKvawUrnNaZLgYyvoh14Wj8jkMnh09Hobj4L23onwRdRWbwqPvwimT3YYwlZP5zgwTOHrj0vph0ry0F7%2FgrANcxHnizv6TeAh5Zrcxx3zdUJXPBamRStAFx5p0Esoo0cCgtvK%2BSJmupH59i4TFgjTHYZBik0Cd0vEH1qIvzM8FJlwSa93SWdZULSVxYkbml%2F2M5D5aeAAjbuv1jHfpjHvjAZyWZg0hC9fcr5Q683gsU1lcFffkH6xveiSXrLAeaE1a9Kp%2B4br5%2Fv9mudnD3BzvSE8dvkYqOw0cMC4EukeaLLMWLj6FpLISDy7i%2BnpIl90kbEBPKTnutjxxgANoirRTcdzqfKfytzR028nDzmeeEb6c984Xzmka%2BPBc02ySX5L3Oss4IGy9k1kLx%2BokD5TTKzofmHiCxmiwBfL21wbD5qJ4Qo%2F3qDzWoHuHhlJV%2B6X98cGvK7S5HjiAV8cSnxprtnrr%2BcOkrVEqHkqEo7X%2FZGygAdHVckHKkFeVE3H6gmPA7Ss8bSzvHG27t5EPHZbZUNv%2BHryP3u44AQMHaq4n9ITo7sItFD3uzIeeyo6mqgpjxIeaF89kZX5wgQFvvqVxyhGxyevufePzKPZTan0TPEgyRWbdCxgntKZWbmgOFZ%2FzOQURs2xzG4HLV71LQE4Vs%2BfDsXiyZ%2F%2FESXYZr9bh1rGgz3uZNvdSep0qPo%2BERB%2FArqIr36lRCbjQHyoR2OPKT2BXEoJ84R1%2BqOtM7xBfu6EIovVCPkOT96NR%2FJI2Dex4BFTQxv%2FmswgByR0cpXEE3soA%2BLE3QUOx7CIJOBiSBAcksHqlfEQhkBCvqQ%2BiO5jUl37GbJA9zGerHxf31E8JLLSY4q5B1GdM303HpqQovMbBqOgPYjubmAvaY8xgQJbB7xPpfD0EswpfxCC8sPQ2QAepMuC9hGuKXuILsvUcJ0%2BlB0ImU6js8F4RJn5TkOGTF70mniQrsQpJiXCJoPI%2FFZ8Lhs5%2BxeywezHnpNMJNmsJC%2Bf5Qrsr%2B0%2F8HQlkxI5I3T3cQcBv%2FsSX2KC%2FnMcW3aQlCc6P1Lh1GRt%2FSDemdFCzOC6nO5daTx%2F%2BBeB6gGvB0QfUjxyAw2M4AiSMRfPQzZlL1QiaaahoGG6Ysam%2Bj5nbJ%2B43NAjWbxm5HDNsrW4v9fxH3xGyGaTyIUwIzC6T8UZ4fu%2Fy%2BCQZgSaYour9NNYd72efmRictiliSenezf73aq03sUU75LEzqT5dPFK%2BSqrBIUllY3YC%2BIxV2iRATYOh3iIUIvD%2FQeDwfbWYLC7%2F1Lx4nuiW4ES3cCSsDGZlU3gQUe%2BAASuojkee7yFSj5Psz%2BsPKF7PWm2EHhYQpXXi8dSeCFNZoqohEJ8cj%2BO3%2B5Q4liYWgCzO3QnR%2BAh3llm1DY0vyxSCcUHiNHdU1oENcvzYvQg2%2BRmB18l%2ForrmVXx2Nq6tbjcz%2FlKPxK62yFGzbUtgSHJeSfb6FueLxyMFfj6hHg4cUp0HySN6rHagIxjvtBZki%2FW5%2Fp4LFEGSTcT3ULdbN8rAtGBzotbK%2B0D53nCm8o%2FXUBXUyNVHefoOymiYGGT8FoY36f%2BdrXhHJBNiu5x2mQZUMGU6jrnIMfyGMTyfvXDFZ9X4OcN14gHV%2FYOuv%2BV0CPBWXHL79Fq1sLOyfTCE%2BONlQGm6ETrovu%2FUWbBZeSm93xl5zdIbIU%2BrxMPLFcn3f9m2RMZIlhnHq0%2BFwxoZ9doL9nuYTfd%2F8wDrvgdeyFldz1WftgpzyO%2FRjyohAvo%2FtsLUTu8eieTefHtOpEC9qcL%2FfwGywAT1UuNw40%2F%2F1CwGHT1w6P1AqeIRwLkuvSDvVhoCbo3H%2F3QfQrs0FjnwcAsv%2FCLnG9DuXHr4XO%2BRE4fzx%2BuH1UPyNPd1%2Bk%2F6BAvS%2FeGWWI8eZGv8F88ub%2BRNcYgG6brwWN78O%2F3WVmS7o2bRuo79x8%2BieXh%2FTt%2BwXVz7RXX6nytW27ki8ulm968mTe%2BuT4Y6%2FK1JuGs9Gx%2BM5aeTT8pX1%2FL1%2FK1fC1fy9fytXwt11%2Fu7h%2BEJWZajZRKcZuLXPE9L755JHctnKzRRV86ZMrIkZoFKqHawf7dMho74vEI2tdAtzALPfb%2FGO9sWSt2QrkgP5f21fIuRHZd84M%2FFuB4UMpgpL0K28DZjcK5I%2F6qhbucSJI722LJ%2B46Vkf4sl2gv%2F7tMfyHNlstD4AIgHc6rdHUgQ5X3zX9PnHICTE3ERLvA12MBjnuBFB6UkuJ2fco0A%2BeETfI4rkCHCbFOCj%2Bryijey%2BD4w0tcFzfAnQjjLOi9rA1s1GXZSk9oxN%2FJbzq%2F6W8kvaI2LollymH2D3ftyiMkeYLoZviwSpRElyP7l47EXsQOGi%2BEVEaG8Jbjz692OR77GY%2FchRWsv%2BSxsipFb7hikkwar%2BWjAqXEqVyrfY4HMZfrUNGoYh1yMAX8hLP8S45Hltv1K1H0jJXCD5R9nd3heBDYaKOc8yzBFZ1lFxhkPWX6RQwg45k2XyYlO1YkfXKWkhgZHli2JVI4kfT9cvzzWyzHv6CAC%2FrtIimBgdPK4LOEh8hNrocIDUW%2Fdqg0j5RVAkFJQsuCUl1PFpANuxgDsz7juEt4cMxiDwIpFZU1t3bsORYNnswnJUgG4ROtB4v2klDxF7%2BPIFXWDzqiRSeEnQv%2BkQ0AYiy2%2FVI9b44HNwrxIt39jbnd8ny7sK%2FPbeqUclmTWLVuhRTwwJ2jYRV6SSQkNog1%2FFpskK9wEWOfxmFRnohEosIlwyckZZ0rUEHM5ZUoxvpejseXsLAqNtGkHTElolNYu4j1Un3Uitin%2BbjH8PjNrtUE%2FjAXsd97XD%2FkMctMWEeOCSeUjQIYxAPkP6TLAv9YlEzY5NCEEL3AK0b3XoaHQFgLd9M17%2FST7vtSuoIKZJIriX2hlsoA6bMWROJk9WVijLTES5wlllB1vlgpoYkIBtFK%2BNtayGQiYaKGv7s9s3sIDzw2RJm5AL9lyO5h%2FcgnIcoWMZGyGRLOugXnFlq01WRFuR%2Bk7K0Zrt3D8XpZx5j3UGrWtm09yWvJiirJJoOZydvhog0PTTPZrIv2JpOxSBfmIH3TNPbvumnPHR7tBHepG3SDx7mTpm0ECJaKc4eGIhsKR%2Be8qeErtwlyRbGKJDvi3HtkPSfpkKFsgGgtHjX8NdPqdG7wmZCKpsqkoJmAR73qYVNlOk4%2FaGDGgXB6BUOA1U0Ssqy1qTJRwXthvU%2Bsk7jRmYUDVAMAaWZWfMsW8jkNwwPb2KQBmVbzOUOjBlhzz5NSAMnN%2B5x76R%2BQyOvaMmvad6NqalCpqmFbz%2BBHozJUPyaTyUgU2NyozI9F%2F5TrJrHukUEeV58lu4wmyrRS%2FpoE47tDrMKAzreppv9bGzzMHaP0wFgT8KgnCb%2ByPhZMUOAbDyDaPZkwPJCfMpozIf5gIwuMgz90PKpvv74dVQqUHhRXvR2%2BgXvJn37izTKKh7Z%2BystnrHciU1tjs8zAUX6lhq9kRTGMNUkg61%2FN%2F2fWSMDFBD7HH1rrf9vQ68g6Y3vx03TufmtC3zBTXb4%2FMz3N3vvexxe2ysXYNKl8X62nO%2FOO3Y6Fc%2FNNc1Z5PqFl3c6nR1jsfgs9gGMrq8a%2B244mbe1FhP8tGDDjtGO4nrV2sCxsVt7a2pjtorIzNXTy07yGORuECP2f214sts3YEgM9tLXAGKrW%2F%2B4ZOfd0bdzhfDx051tCPABN56%2BSAP0CvoNttH4RXL9OnVrFjVUMYSdEPf%2FZXJ5%2BbJyDfQ1Q2CFsgwm%2FOYeZCfCYthao2mAXuDi9bBMir6GD0LP581q9mV36zlz901nAw1w49YC6V9DyZ6965s4UjSOTqHPtaLUDvdAafQYYIngTHAiA%2F5hW1QiGxPkRN55gVfVkWI18ZUfcmpopxlg%2BjEZVFVyC9j01Z6PhqQtg1MTAOamGI1BHe206fouYA2mP3JWBdWp6mzS%2BpdGOibm%2BMPgka0B2Qdx%2FZi9KBThKrxihtUH0dFVHG%2FZhhwtIbK0ja0BNah6gNLKcwqfR%2BrSqNA0gotG1i65ADXUEGPBxyhGKF14j2t6fBNRP29Si1%2BZTgGOL20pEEHfn55cwqj78sp8wvbQuOHpv9ON88oaOi4vHlLown9OTnyg%2FMGtqJH9QHm%2BA%2FjoZqh8IHXhQCQ9D5ecxxEkXHAQV%2FSrDBd2NcEgvgOeeV6dAwONRW58GWm2b%2B3FTH60v%2FDitUOswcmMb77ezyU%2BxW6W9xVlcVFBDHTUwqqUfpMYu4lTEwaumtvbSXNbWf4xd%2FWAlmgyPHyTsN3TyHcRekmHRTzu%2FNGkKNVIEXQ3%2BI0yCx3M77TTNaWpumwLNqfOG9eXbhHbjpeL6EfxJdKYOEDcQkSS6NbF9J3daMAydwMUFwSH9gzXcgIIhYynsnBfiMq%2FeSr8%2BvbQRA0yCHrxJXfvZZnxmJ472Mno4HVYhAY8QbMCKQON4zA0MWih4jxuRg8mmaechHMlGlhWyUMBwLPdq4OAE7B0dzCPoh44Bq6kdjdjrOJmqhxODV3sSqQXL8yvm5D8a2GHRAZ8w30WCyUSbOrY8mxyn8cylCB%2FE2cJfByTncqnmdBMjxETenyY%2F17R2fXPaxhjUL32sAHZt%2FKpNPtF5IOtHnAVG%2Fai9P609Wc%2B9VRvPQ%2B1stqnt3tTY1KxUr0Qp5Xsm2kHOo1AlhIy1l9YH3Voh8aP6hsVE214NhyYIaJt5HATTtHYuYl6Z3ybBEdrfWzRzm3snxq9OTaWpofAOpDQUpqPhq8DYpen4pDq2pPzU63k4umrrD%2B%2BqkSHxS1L2aJfINzJAmHbwV86KqI7PIfK7PHV3bFTZnB%2BffrTzhb1htHd2bJXYRfLg1Sx6x3Z30TRV4Ze2rl%2F7nk9t%2FDl7C06nraGDyxj6Wifz6speVH6QIF5rG0cS4vqZ48Eq3sSvZ0JIVBpZemH%2BotpB4g9dyAmaOB85cz%2FNWrvGqM7d6sqGX%2FD70BqQ20m7fOXZGbW29sxOoa3behwrHzW7%2BLupZi7Irwx8Vz5cnx9bfsY2CB8GRl5BEAN8zBy01czNZ8DY1G1qOjx6HLFv5XhwzeCQTJwkM%2BXxgIVkM5q5u3bLyDJn7QbE94tM6GZkWYRtE7eYM0H7iQrK7Ncjw5ldiFixf5nOTa359LUnPTxzPXurPgJ%2FPPM81C3wAE2trCdnjo9JbhNIrmzAOR6SQij1m0sDUtKKHz4zPAp8JihIP8z1yuT5z1qpzqVlzj%2FV1qwG8o8q9q0Kux2pliaN3Z8iHuUmcsH4eYHFKl0dELELs6I4LmoTTwNZDrrw6NIrnaTG%2FWZCaMQtZVmTFp9047Xcc5bZUfAfn8d4vwCQBTwIBh1DQ6xDRUZF604VMi0V%2B15Oji7mwt2eE4FoLzr7G0mV9pSQ0Wr0PyYSx6vLqPF46nQn44L4CC7XhvIJCv6Dm9XvJmEqt5cv1rQFabDyruY%2F%2BUB32IvQ1W8%2FJivNL7xDZmaa6iInPHSxO1PQJZZTAteiTek4HpIu5ffELgRyUvyxASbcudPSTEQNSG5Fk37jaIRhYJ4M81IcwwVXSrQX7BwCOfa1s0t3t2rdWhcJy1oHfSX0xD41lb1oolJXUncZ7qQs0I98xZ%2BbXOI5DqF6NQ2bYsibkDbUvUZamvdHe1aRN2aLtFeF1LlYg4nqruX5dn3vD3t9RPSNeP8I4Seb5iU8Ev%2FUikvySOtPvOXMDXmd9WeHmNjfSEzKzBOuC3gIrdhQLIyB8F54cSCxAiG1cASwUpOhSfT8XcGENWnr6yMFy7gI5ArzLWIo9gJf3LlGq3xygbJphk4Txhf2yMNnXPhNRXMd9grdpFPDjtnlqatk89Da5uK9pzm%2BCPkO7cx3aTq%2F8l0qtxFm%2Fh%2FaLcW6GWq7hQbbYFfTn5XbqzR9xi1HDF2GEAWxhAdHmha7N2jkd3uTLRw9wZav9ruIcHt%2B5PSjdrunzUWQpvI3AMgP9qbbGAybvvrUnWFaRM59lzYD5OqVl8PJW8NmLfRj5D2aN35nen7kck8sXo6VKgw8c0lMNHyZz7eisQTXfz6HMZ%2Bp2VVb1%2FOZNp9NMz%2BHXI3W7RW39RRIQo6CFbX2m%2BvKba7bHdV0QFP7VjC4r60Qtg%2FYvTdd%2Bj3yJiRxKLv1Dpv5div%2B%2FFhBHokfG6h0%2BhHUw260w1b9MVOOJeLlkj%2FFbgEb2lHrjogn%2FnNsPo%2BUPbJrJqNhPGwB%2FzEcjdLhCzSHU4BRNXx%2FaUwGro24NnEkHU9CusfUn4bC0fekgiSOeH6jlK%2Frj7i1umrbi2oUDnl0yC0Ag6ZJ09KsKNhOIf5QWYMw6Zy17Zn5BpZuPtWZ%2B4hni6c%2BLnW5Gy6VKKpsONyHTBm4VTc4YTNMSf4YX4dUkdNwTKc8Hg6XZoLxCSlt4VCsaUOuHS2L5oXcXhiWBENtjwKNQry2VnukjmqnJo6f1ynjwgujg3AKg4byJfQv42nAo3VH%2FxE1wAe6bFESB0v0CEec8QiVJudwIDSPdjOkcv3A07j7Rmb%2BV%2Fa43ma6NWNtzUU7IdpLZ%2F5j5fXC4ZESCDEe7mY1vXTW747vm4bVaj%2FG%2FICAh8VO21QRraOexLPehuDBhFiiZPqxcJI%2BA8%2F1wc63Z8pZj3LCNNY%2FTv11TUUPF8GY4BoO0ez8RI7z%2FVBbe3Guchp7cHjYs2F6aDyp3blwSFaK%2FoNFInhBtQweFADJ5YxhajPsnBthXrdNGxIcW5dxMXT1g%2FEbXGqMh5fYasLYTjfzs9amM8SsRYeaTQUAJbyKSRzeBWO%2F4XDRLoNOpfsxKaVvdCf6DyUvhVw5Ak9qBPnFkJ5ZJxLkP5u8waLbXKcJdoZeWYKnND75avw26HhUef9pU83OJscKjzFPMcP%2B1DaufU5I0BudYklSdPgt%2BBV%2FvxyP8dax1ZnVYrCVxn7aMrbhUaIb%2BDORYnKGYbKZwYF9TOvQPnljbMb%2BTWoK13CoTZnwub4jrB%2FOBN2zD5DjqSH288koXbogRfoyHtJkHa%2Bsmrfv1IkNJJ256FcmMPtwYgKBqvo5%2BHvz%2FQw%2FG2RH3sQkACRkS1w17eVJNRqFpA2Iw06qaupn459MIH7x3nQygiQOz4dpczGsxvMwj0Dc8a6q3s39JDS3fYznDXroQpSjsErriD%2F40IRyBHPt3NKO5uK024aKwMdbn4EAl%2FOUVDlpQ677FTQ7a5qwXGkg1jz12Q2wAPBzRuPSAJJoUx%2BdN86v%2BsGxf8Ywz01dvA%2F52y4%2BVUlBcgCCh01Fnm8xFNT8%2FAzTgMuHyOBMhS6nXhhgflS7rBCYMd%2Bk3iAPz96%2Fspwez13OCPxdD0030wBI64W34X0Q3XZzNPcwe3uxTPiYHiq8%2BuABgdujyFwORGGTMsODzC5K3AMGwzZLUsiwR5GBOjlzkgEerZfsYnIUW7uMZeMA4s3jM48I2JHt2SePhOy0d2dOoSaxC%2FUaUkIuU3K4Hn8AdbgYe%2F6OpmaN83Fi10%2BVSsMb4wg03pnWCPaC97EoNnknmvWo0zlNPiAqOdniXG5vhew0TC9jxK1T4h0edvowSie2ctPg%2FsD%2BVfSnpLbYFH1Q%2F5stCsJ3kmypRd60j04ErEjtJnvIVRoCOfKSReuYX3RWX55wuNzCaOOvmgQj4Qfu5%2FVF45Z54XfSoSf03qccpl7QQDGl5cOH72dwSfHYupvr1NTQrxEP4sgSrbdmbh2eNXUzztsGmV7BnD6eQ5AswZ8MWdIwYsrcgor2IiG6AUVx%2B0EfTwuWAE8r%2Bkn6IjTC%2FHvYR34DzZlLFkSsqyiy%2FyCCrAt5%2BD50ws6or8QA%2BgzDiyMkCPfZI%2FsgWO2n14wVfiGwnBRY8NlL4%2BEu1zkpqFwsNstlCFzNIG3yQo4rAyH7GB0sG4l06Yr5LCbxQte%2FAA9FtUILPgUzW%2Frkl8j3cC0OGw6SLmYjIBw4ynR17DpQ0ZpXtRQ78MBKm81LgusQGCn8JDshWluvkFxRDYdHUqWcD4lrSyzHQ%2FSFnHjGfa4JrvLILk%2FkSRPddLa0ni%2BcQCg%2F5D9zRaMWlY1MKR5bWsEy%2BpGM%2FWtol15CFcpRZQ8niIdr08q4QAUxp9yzg%2FEIKlbrq99C%2FCHIrfOmQodCLfXmoo7Lsw79evuhSdVcrQa9wmKhfrlHbk0JS5YV9MuWQvxB%2B8jYJ3xlP6RLuGZBKTe%2FcB02XFWYvNhrZzKwNf0b1gInEYSVD4IFPKRhZu3pcGV3kdvX6SlJHatJffOHSeGtGRUy2UVBc3jYMNxEUjAckJ0RSe39hfMt7aCIksBicHNYUDSbMlxitS4SHb9Z2MU1Ylp0Y9WgaqIDc0U8ZGdBuVtqTpz4R%2FQDxaI8yKyo8SMWPh2eHpHS%2FFJwP1q5fa%2Fmg3sq0q4mJtN56x8TdEkPNkMhOgZ4YxA0%2FXlqd3%2BupnY3FDZ2XELEa18N5he%2FPwb70LV7hBSi%2FHoy%2Bdi2l%2BG5ItfSnYv7%2BaRyCRBuyh5%2FsJtMF3avCtYAH0%2FgTAMOJKRRJvcW6kdoFIC3Hbs9Te1ecWQ4D%2BmEE%2Fdaoba5OoojFQzb7vTZI3t4B4U%2Bmvs9tNrupcJeYg14%2BEy886Z1Jyt21eM3TS9sLskv85An0TQRj9ZvEyrYT6r9vizgOfPf2bQfhKM2s%2BD5lxwWpVu%2FAexeSXHsyTV2j%2B91G1mZxkg8nKxO6%2Fierqn2G8NOLtiL9Qe9Z3Z79Nw%2BIujkeeNzOSxJu4ibtqmcv3F6%2FnZ26Z%2Ff07%2FUfmfbKNAv7ilF99wanubSKDMZC3gwv4RaQMrCcDSJ5whwUHhxUs3hON%2B%2BbmJUVR9ckoPXDz%2FfwonAEDIiXPrCvK1tosIHe%2BkTAeym9IddFYEYAAAHAklEQVRXtm0bnkSFXfn5uDq59HkPc5viMBr6IwXv7UEr3lpgbdrEqIosAuhno2qO39GRiRkmPikeo2AwH%2BgXqAkPGxTqc4gewsu0IFSMAW14uN2fRAfHFw5aXaKCdgeORmkav9qP8an2FILh6Sa89cC%2FT0IR2FNmYxvxgAcY7Ws3iFvOnKusH11nlb6RS0IIeLjX4QRs3I%2FNBfIfDcXDMd74BA50attOjc6f%2BTechJM47U97zad%2F9B%2BNOwrYwG0HdXLrpdYdbeqa1FNRo7Kzyi7%2FkQMYghebo9AkPOKz624EL52pj0P1%2BMaP1j9d7gEg8EC12p70p6P8FmtgRM7%2FAB2Fp9sdoZjgGTfx%2BRGvvRnYCpCkwdedeLC2qUxb96qeBmlz%2BA1kq%2B3P00QpZDw06SS%2BQVxC4p37tOkS6cC2QfZSJ0G1e0uIwcEf9QezjPZi8dbOAWmVFkIlncc%2BtRyf6gQJfpwFEmCaen4Wz4sdHzpMJVDmKEMhpbl4AMLhfoP9h297FZ%2FEtsPbIItEwIahiK%2F1sn%2Fg4XXLq31DQKqnlcOPzCQKK4XCU0aXfqRWqZ8Lw%2FL4ODFFEl5AJpehgDqx%2Fg3U2528B%2FFiIosPT0DfxzHGSPih1BqvATFlKrxPwvKH%2Fakz4JAqUtfiux4jHGTQRTw4lqiXJr5IgVk3FDhcrrheBnEoAFEq%2BDnCBLoU3hXiK2iNNQg%2BL%2F2pMTrn1tRe6gSoToSTYGF8MzlL%2F%2F5LACDfgJ7XJvqthpV%2FxY%2BNBltfx2UonJi5f1S9jpbt39qhISh5P6xOrky8opyinQyr9yFRwflDiNK8S00UUv4lOAYFr%2BM6NSy0bH7x%2FvS9cUPTyr4lo7FHVuHo2wgzm52fZiIRRGR7KefSn7m40DqK2THEpzVkz8YJt4F1BxoRd%2BgC6bXjJqYm2MTVeFmPlY7VzPqnvjoNb804fwsUGsjwPvZv2dAmXo8B%2FCRw%2BiaSsfrj41F4S4Z7y9v5OKgMOvqLPgQZUUk%2FkGWR82D3jqTWBe0VrBtgrjkPvbukh5DMpv1b9lwMN3XnDbVXgGnI9YDLoVuSnKufPjqezx1YlXvloUFmmE4rjq%2FCkiT6Bf8yPyvs2yu%2FEJjDC3PgLYBNetOTe00HdiH0CEWKx2iMErF0DY7PrmIGSmX3PQno7yAjqKnjayaqICioxAUsLS5CigRk77fthzH0O3LJ3ecuKWSm3Ytn4V0fkBllBnsGn%2BbLDMbo5%2BllE%2FMgdMTDvr9Yh5WzXTi7lPfwdiHtWCXaQURcKn9Mr7L1v1TJ%2FRnpQNrmiNU0i0%2FzTjpIan4n0FmwP5bvJJPodhmxuXqWuF7s%2Bjn7LU8R28TR2YL4Q7YbgUhyMclLaSJEBCa4p5LkJERgcKKr9y2ctohKLzJO2S%2BNMMdj3UGTGVhz0Fi1o2oEKYb2LUsMdGJqOaE4U2B%2BSBH0o9sBF8zkOp92gwet7Hx6EoQq981%2FT5xyAu57If7Iuenh6MplDUfnf4XPyk017Vhsvd7LAxbNLwz6HNuC3mQDrIXbkfF%2Bx0dDmEDn0%2BOcHu458afTnYwLIpAWzys%2Fu7zht08hLyZFvI9vIeqHZCmMjaAtOquTlTiZkINX3BDZQxHjDLi8WvYzuyE5Pq7%2FOR5fhIsIv3JwNuEiMoXEZVE8htGXRggNtcoglETHVZiCZ0qT6iYSCbplpBRYToYlaHcxPs1PagTquMoXNytn6pXpGu4k%2FF6IP6QecWMyaKK7iT8Sm5DGJBcJo5A6kRUiViBaqvhlgVL2k4hHHLovfDIoSsVvSJjI7cv6kQ%2BgQEro9HOsZaQrdKMIHUdGPm9AHP7a%2F3XO3lZU8KefS10F0jq%2FqzGe8VPHaoucBL5O6lrwH0x1dWiUg5FqdoKzmUBJ818%2BTeBc8h9Uf3stEXOjIPUQSOVxFP2VBKusDASOgo1Qywq3OuMx3%2BAL2%2F7AXza9%2FVF8P8zv1FwWvB%2BXMZWzTW0n1MSV%2BYDkN%2F2NBDqFn2sAud9tcWyoaIgqKXrpfUq%2Fs0kWFcFeeCcaS5sjJJqpbCU6DmqXF%2BICsi4EchsMADkeh78r75nT5Xi8DDUk3Spa6%2BeNoQTcc2ZURCfqCVEo9%2Bclx2Nfkd%2BTIkrKKsuATSpJKqy3xdCAC0a1tTzAyzkJikGuL%2Fscj13cyW%2FSIiKs0jJtl%2BPxhx8okUL%2FzH5%2BKz73cJvjsXUPk8GKII6QxAbZ4hDYVVFiyjxqRgXN1%2BX4go9dh1Fr4WfPsrt9L4Nja%2BuxKCRhtUjhV75r%2BFiAY2tr71em5EmxELAZGW7HjCBc7YlwbG398eBT7ujLGufHXkKQd51Y0fSGQtCE%2B5k%2BoJqUysFOAQ5wIvsHvhFCpItJTDLjQBAxOI%2FSaHJgCtqDfl9vpjt4JrmOra3%2FB72L99CCrFH3AAAAAElFTkSuQmCC%22%3E%0A%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dxrange%3D%2210%22%20data%2Dyrange%3D%2210%22%20height%3D%22230%22%20width%3D%22188%22%20style%3D%22top%3A%2094px%3B%20left%3A%20356px%3B%20z%2Dindex%3A%209%3B%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAALwAAADmCAMAAABYgh8IAAAAA3NCSVQICAjb4U%2FgAAABgFBMVEX%2F%2F%2F9SOCxSOjH%2Fwp8AAAD%2BwJ4ICAhWPjL%2F7tDMQjj%2F%2F%2F%2F66834vZuZmZmVcl%2BbdmN7KCIxIRr39%2FdUQjpRS0nFQjhKMihptaVQRUEzJyAyIx46KSF8LSdAKyJSOCxUQjqcincQEBBSOjFSOjHzp4tSOCz%2FxqZSOjFkTEBUQjpSOjG7qJP%2F%2BPQpHhpSOjFSOjH87%2Bjz4cRqUURDMSlTSURQRUFUQjr%2F1r%2F%2F0bAaEg9UQjqHZFL%2F59nOTENTSURSOCyNfGojGhddV0wpKSnGl3yWlJKUh3d4YlM5OTkQEBDez7fLvKWdj4hzW0xIQj%2F05%2Bbbp4nWZlZTSURTSURSOjFSOjHo17yMgn5%2BbFwZLSlWPjL358v%2F4sL5w6XWxKyJcmF3VkYhFxIzMzP86MynnIi1jHRXmYwhISEYGBhSOCwICAj50rvehn%2BSblqRMClWPjIICAgAAACLZWJAa2I2XVRRS0kQEBBUQjpLOC%2Fxt5blqqWvhnBNh3spRD4ICAhWPjKmNNozAAAAgHRSTlMA%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FRBH%2F%2F%2F8i%2F%2F%2F%2F%2F%2F%2FuZv%2F%2Fd4j%2F3f%2Bq%2F1WZ%2F%2F%2F%2FZrv%2F%2F%2F%2F%2FIjN3%2F%2F%2F%2FM%2F%2F%2F%2FzPM%2F%2F8RM%2F%2F%2F%2F%2F8RiP%2F%2F%2F%2F8R%2F%2F%2F%2FEUTM7v%2F%2F%2F%2F%2B7%2F%2F%2F%2F%2F%2F%2F%2F%2FyL%2F%2F%2F%2F%2FRGa73f%2F%2F%2F%2F%2Bq7u7%2F%2F%2F8id5mq%2F%2F%2F%2F%2F%2F%2Bq7kFCNkwAAAAJcEhZcwAACxIAAAsSAdLdfvwAAAAcdEVYdFNvZnR3YXJlAEFkb2JlIEZpcmV3b3JrcyBDUzQGstOgAAAgAElEQVR4nMVdh0PUyBo32U2C7gLC0vvCozcBQREbFlTUs%2FfeFfXOe%2Fq84on%2F%2Bpv2lZkkm6x3nCNuSzL5zTe%2Fr8zMl2TXrsTSNrny2%2Fz8%2BPBgZX%2FyDv9e6Tp6rXKongMGPV0i%2BTI%2BeXWngGWUrsmpGxrGt2u5DxrxfIPel3%2B%2Bd2ywbQcxJpa2ym8DHit5hV9B6JGvP%2Fq%2BP145saNgrdJWmcKeV%2FLzvBs5xXfds4togUDvfRv5l%2Fhf%2Bc3Xvc763%2FNWch3b5bFjtOhNB3jjR3cY965dhzTN7aJ0L5fo57CxrPHw4Vh%2Bzfke5ILnvoNZ%2F%2BBH3mSeGqboCHV8RE2R%2F69Xdgj58oiloT7DLYXoX89TyXXebMZ7UJ0dkX7X8CjKyPfQTkAzVEvy8GYAm%2Bzro6EZRKJjdXmNbORzowytz87ma8lrEHl4g%2BqJGgu1iC%2BRadebfwz%2B1cFjFsURboy6v2dX1uazupSRjEhhwfCLjeP%2Fq11N1%2F5rlcrcysrwsPirXDvUldTrR1euE%2BqIREZv%2Bqzq%2B0AO8NhlkW1rfOgFKCNxOG37D1UGV6bujlr6AowbuDs%2BPCyadHT%2F%2F7r2L1eGx2tplniNfLua2uJS5494x%2BGJgUNIIfF%2FYO5aV9f%2Brv9VKpXJleH5eY93mpaYj8eyhoAsXBEDJyPEjhUq9cu2cye4cD2fNMCczo%2FYRgMjAl7yQyMmRdYkhg9%2B841Y9Aki4qkPnNe1DGfzBipTVUe%2BLSPeEj8muiSc%2FAPgswkR%2BbTVwGfHRsSt8ZzgtTx58f0EkFYA4kMfeMgAjipLhdRhXGljxMqhsVSlj5Jyz%2BvZtbqidrhvH%2Bfi9W0hcZ0AmgKkbDd1w1YoFhdDk2I89lJtcxJuEKvv0U54Ch90hfalmrsywYPPqFMqhmeugQNIYAd919LEFQfa7hgqL4%2B5eWPAcTLbCmTO6runBrvIdMySOjdc0lsTK2N7M%2Fn5aBz8wUzwvxjoltLwvuUA8Iw%2BmUDeIOgqiE886gVqTBSDzFvDOmokE%2FwUOxT5weqJuA0mYYGZt%2B2FhYP2jzxXx3lXxQ6Eo7Nt5UimAByzwtTSJcI%2F7OPmM8Gv6DPqIQBR1RlSghHynf9Og0mqrLeiyNpOW%2BLKazXTG80EP%2Bd9Bxv%2Fpc7IBD9p65rjCJnVifcI281qVIoAqANAa2JnUR8pUMv0UpP%2FgITidAVE3xeSmbco00tVoEZXBk707XPDYgTIxBwfxil4VEeER%2BBXlEliHCVK5tRLRVcVAQIK9hgzVAMtE2k1y%2BBKHkjbcrAoynoscpqmDsgcfFYStF3hwNA15hk5ENv%2FpEiQ9CSuEjy2cWPyzPigAtX73j8Rx%2BI3NiLjfVjXUDBzAqHyfSMFQKHtvwlcCAVYFmpFFA%2FhuAzs3jE%2FZgY3k17mzIEtniRr6LOT%2Bgwytzs8msiaOTDVZYIf%2FHsGgcB19M7OzvbMzvb2LnFQf0ejMkexw4YhkVOHJZU4GiZNeWD3algsFuV%2FXcLq6uxsP%2BsJvV%2BdUV5mWDluwdXHmblOV3I%2BBbke0ESet381DBVy86Y%2FqPfV2SUGCWvkNdeYe%2FktC%2Fw3u7U%2BVpU3HO%2BvorjNa0g%2FyNas9zo9ljsAmsrAfpUYEVcfP3WEhnt0rBZD4ouWPmOP7oJw1qnaMgDp9iIroJ%2F0Yqj52pSXETr0hiRs0wgjf6YDYrOGX2%2FokDXX%2BuZvDeWekJBrc0fA7yAB5OXOL7WxL%2FusMs%2FuSS9z%2BvEJx6slr1%2BgP7ANgj9hi6lZK2UE4vbNeQwK3p6M1ZHr3zOfYnbrWNXcCFkDGNvJ8IS6FFfzmC7qey%2FDVg7bpsmZFvasLW6%2FdBhItn1n1KcOgS1Vgu0lTAsn9EuNuBKXMdVx9QVcHSHyBGXNxB9SM4hIxWqHZ9WeGYwPpA%2BmjjFvmWNURuAjIXcuai5h3gKus%2BpLVVUV2TOzHtgC6mgPbEWqzsI4JNmC84pM5YzxVcaXkCMnNTWcKlp7PsEeJHbWnMFKC4tHI0veqJwWvy3ziRr8xGJLGBZDuxNCCzO3m90coE9St6TGYH1LToKokDlHcWiGZA6ze7jUUcQEWPcA3xiiViw5XjGiZkT2%2BfQ%2ByRbnGIPsk8g551OWjfqLaGjItIeED%2BnD2oXKLbwVqA6xkpxfnAtJcwjXOEmYNDAeAMJEakGWaxiGYoQqJNaDFjgdgvJfhZPyKXUfxc97WGFJ0tk3cU4Ys5O1MrXO8Vh6i8yxgjXud%2BX%2FWa%2B%2B8WZ8TbPLpYg1McO70t7Pl6QpukY%2B3o74RgrV%2Bplc4qbO%2Bs1PZP2I5UoTUKbOmIY2GO5U4yyxrCVyC2iChLd0zgCJUPiup2obYNpCr352rDNrCZHLOMwd66znH6bJL%2B5YtsL4HS81PFSHY8Pr8VDUjF6sP88ayzcH%2FG82WDKYxiRaLWGKFD0JwbyEYNKtIIzsumtsQmyisfbY4ySmlGlBe9KyTdvAhBkNHMYkW7MOznWSd4zr9herA9SxVZSIE1RxJmOxR%2BKV%2BA5cxumue9UJHUHwIRN2yBlSLPLAmf6v25h5S%2BI2wg4upxzkeZdgOwAcOSYrKkaVRbNO%2B4RWi4s9xgPWHuAbKNaUq7PunR0ReHrE8IRByR8RAGLLpIZ4whzRIZ8E6YpvtsQd1wVfe9eqRXfH8HCeA6EsDQmtHarWrG3tdT2%2BtjaIpi8iI5Uj8WPWRkyxo%2BNRQ6MAjgrzqEETJ%2Ff4jaXX%2FsJ%2B9%2BqYha868iVOuyFBnkFhsY5BISP9DWpiqnmiLTh3uWQxJCSVZGpqhQ1xvli7rFvW3IcGeAlzlyOc8gxu%2FtXVJ4ztFn2toACBuwaUN0sfu%2BTlXTs8Zll5ZBN2ExlEs01rA3O34GXqMIgMLm%2BCKVWrj3nX26Gl%2BIzgV3gDE2lj96f50IO6Z4mf2G3PsTLV4OaIYVcxDjt5rRkMHE%2FdNXvWmbexagPlcrSNO%2BgE9o%2B1iTf8CWMqnTxpQR01doDg1ZHD0zG7vr7%2B5Elv9ypxx26ALVZsB9Bsvbu3W5TeHhZxdjjGMXWKepD09XtWFx83idL8JQgKhYL8f%2FnUl6a1Cb93NTXEXO%2BdWFxrenHqsjigXNBFHlkon2o%2Bo0xXOJt35XnY1leGPVdSxPvm5qbm5lMIIdBAVDOaRTMWJyYmuruXxOvE4vumJgkZwAbwV9bfymVx8IvF3qoYjTPR%2BbF1QoIBAcJgDW7gIpnpOurVqFnIvbn5clAAIRIy8RIE5UAL2PwYBHwXLXA4rCx2Dy6LjpyYtbhhwbHY4N014CG5yWd%2BDA2LbbKY5pwRyAX8sjo5hxYooAHrCfld7QdtoQ1mL7GhXG6WPIzQoHlks%2BEL8zsQ3cxnCdn8ZE9ANEnoTV%2B%2BS8jyB%2FkaYBPlty%2BSh4%2FjQmbUIYUYYMYmTirWX2yKCed0Iyn3puZTdPIAcAcGbEDtgEYE8KEcAOvhiELhhazxMSpcZDse0mD9yYCHDkmYWIr5BhwprCnszZeJ7UEZVRHABhZ1At4jvFmyqeLrKUmbNUOQzNQBjf0q4IaIINcCnUQu%2FizpEoXxU5koXmaQA%2FMF2yrfLwstal7LmxzDRiIxgDEPi%2FWp2oWtkdi%2FlJkcOZIA2gToA7JEll6w98tSjR5zvhJL4pOOGvyyhzTzPBZ31TQ%2Ba5I0TcbKazDEg%2B80PhK8Ulgu81TjY8eUaYvmUAdENYr5zdpQXtYiLJPHIWxaK7UpItpos4ikKkOvKcmLvly0tK3GZD35KE4n7lbT8vknmjcunD59%2BsKBMbJ0ZGoMSRS8MvdcBbSPJO%2BxZ4f3zew7fMBIfiJvpKLBD1u%2Bx%2FnCq2Au4lGjKuf37DmMxC0DS6hIx19Gm1JAEqFqBw8O7zFl5v5lqUWR587Qeeh0NXZtGQfsaD6xAR70ml3faQ1%2BU570YAGQMyOJOhpIS47OwGCWPynzeGBmD5VNSUSSF5oOUEhrRm%2BUogPHrGflSixq7I2X9mj0EhGz8mQHUeDgnrSOGpUoH2gF4PLD5mmhSNTVqGZJntN7A%2BDt%2BMUWs2U6YcMtA16fe%2BZgGQwON%2BvM2aIhRWKpb2%2F3cOytm42nm98DaJOEQGd1ktJM%2BsoUp0m%2BcPg0Ul6VfdwOYhc4UQ1pLQQGYzMSdWsr4N9sbLywRhJMD4dlMdMHU3VfraJZc%2BvWeej1w4GKuIyQA3JI5QLiRZuPjnefOXzm8D3Fv4ei0jP6DNmJYYMo%2BXw9hRsEa07%2Ft2%2Fv3vYjl6XwBIYxsNWgkGXF7MAQPEDWY0gglFVDv%2FRutyhX%2Ftyz57wAv1jLQCuQ5qcK0QbhMQGnj92F1Pv69vb1yZMeVnw9bA1IHOtYpk30U9kI%2Fu2R3e2728XflUsSvDX8T8w%2BMB2yTApr9Q98AefmKvvFxgt9EvzP4rS7j6ge3%2FMAuexEORg5BGAqTWigtfWtFHu7%2Bn9FclFJrfYkqwZmJitXoDU%2B5xU3785S1a1GQRlRft6tOlwJ8Bk61gAMeoABQYE1RzdAcF55p0tH2ndjWRNstERYK5nCLC9MQmPyOubG%2FwrKCPDmvH9qgwMaikyHuEu%2FBXY%2FFMZapba8283K3luNtwxbfDypRQKCBQOpimfD9Ow%2BirHpzGkl%2BL6fzTk1ccasyFJLvUyiN3SSbSurjco%2FLZgqlBja%2B%2Foaj1uSI2njb%2BAzId2sy0GZ5WZv%2FXcvsaYdRH%2BgTjerFF0IXuqqacHevltnuIrVcrOQpXjC7pdaCReqEsP4vcjWK9rUB%2BQ70Rtpu17GyJ2asE%2BwZoaTRoDfuzbBBAgsTUy%2BwSnuUc9iOl9cUS9abyAl%2FvZpjb2PVE3yZl%2BgGcHsDHAGgmYarYgPrWBqdpPk9%2FZRoGLmM4Cs3EfKF1wE%2F40zi%2FVUcpLQhVsSOdgadeq3Uop1jTvKY5I1f3Lw7T8L66tPnpgkBO8azRyAX0le6TPHaouJOZsT2tb0EeUN6a2QvYz2HA1Owdgi3a6DMpqxbM3un4VMmHTTvIxeysNUs0HWouTCfNhxAX4vGErT4Ze1uUGiayMPgIMgYZQuY4PWK0h3Bj71%2FB4z%2FDTDPenFWoeAYxHS6cY1y1DK8k4iGeOhL40I2bxImUXHyr9eofYr8H19XsLyk0bjs94Q%2Fxl4J%2FikVtjXbIi%2FicbGtT5S13YELyVPYQDXVgjJ4LNqwwEZA1%2FZzYsCb3mXGuuSFUabyEGeOmo%2F3ig5b7NG0EaE5Q90OCmRlQMiiY7pywFTCEvyRBygjYPfpY7%2BGfM%2BRrz8yQanNfg%2Bpq6gsJruAcEGwcNbmfAHUmH3vGtXdbQj5x0M1ADf%2BsnHoFLlJHKmOMdYl69OyEGIlDyLp5Sp3DNDFp0FYwUdhCHtcRiIppJzXprKyLLZ%2BMm1mCD5Ey5yz2N6o19gdHVbgJdOqs9i6z7lpGj2CdleY3TFnJRlKnPaDlgMPMoCTwPcjupY1sFxGXM%2F3suNfLsMD1rlcIRiAHK0LCA2LTA7yQbPHIFYXoHv2%2FvYYxEAN9BAXvwdcg%2BGLeSs6QnZKhsS%2FH8pNGg3lG9tPVAoGIMelGHqGCdsiPzow3Rg1s6qkYFZjmwV%2FQK5laNO%2F7gtYN%2BjZgn%2BdN%2FPnPJH9kkcY9yka67XnCw7IMe%2B91j%2FtQvwjYt57%2FlgxiLLjCK8j8DG8Nn6xaYLSvSWuv4pse8LkOh8AMhMPU4a6O0P1CjwHZP87j49GLFwp83Wt5GhZDGb%2BcDMkxn3yrWKi02KN41XEH27Hga23gegEBWzPiDrif63EOiA%2FtIRhv69GgbG5muoNcxlGtbcQM5Y3Ipwf%2Fb7WrPizflLR1DR1DiqVUc2AbC%2BAO9lWjErwzDLbHqrZpveHkFXfUXO21y0U5IY0634YCBhEJi8dkblfXPTkJqivATO8colPfXB%2BZJj7UzanH1qyuftEQ29%2Fd3MTelELKNiJR3w1IJRCOZjWsp6AGMi%2FVUuh6gpytbWP%2BVJj%2FzZqqcZHzCn5AxWA7Q7aCe1Ih%2FUk3z73slulJNOl0TVFzxyk5RdE7sy39x8AvCCP%2BW%2BODaskkveG43nBXapo3qSTpb7ZaK2kXOOYdVhmKS8tKBmulsFeLOsQ1zRn9xh1RTamhotdCI2tQJ4YVNKW4scJlrLIO%2BCCRw1Q%2F64cuVdOUiL2MZmcJZVtUGAH5LTxNj56cvv%2Bg6Qc2lJXMQY1BJfr3o3L8CktCkzY8Zrwuo2yPs%2Fyg38oXkCIxLUYBOdUV2tjRdE%2FbqXU0dyWsR6IPW7LWjPGlCRpzY1vleraA9mtOiN3GYOkhdSbhYboC3qFYgNbF8bwJQfTnHvmZbVL%2FrW%2BS2zjZt0OD9gdwxNIXvg1SJWyZpaOFb9TZx5wJcPAmS0eDce2ORWIHAzcSx3edtq5KAc3Qu5PLqWx3DvN%2Fpaz8VFaxL7C3HSZzNGZDPPHqSvV2oPdMWeN6DQU34fOwzqM3Og8EXScs2zAZMNpBklX18sZS5YoBsievYhVj3eohTNKTkyGjugFyDHTI5BOWAeVvukQkE7%2F%2F%2BwBdoyCB4G5uXC2L3D%2B%2FbtO%2FxW%2FPRFJh%2B8Z%2B7ex7Q3br5974a2lG84UCs2c37WcYa16p2dRCNM%2BJF3VogA41imADjA%2BkPlM6xh%2F6dLdBwG37ZsPWgcqQlfF30vRHOKJiCz54QhKCgXaJEh4G8BzegryjdNcCFaaWUEydwrt200xhGLLKwP5VeZFHfKGu4FyHOVKGaYbadu5VspOaUznRLjEjCEpg0w5VTJFZFBDZGmTYLNzh%2BRBeVyEB%2B5BC9UworLWTci02hx%2BD0SD2rANLo94qvMsi9Jk74F6n0m18T1HNzHTOKrj398kZxZzLGeI0epdNXFL3xLQmcx7%2BXL2KyZtFMBKgesERhLIqMpnAFTBHoLRcC%2FLCjzfpHo6cjfg1BFayC%2FkP0XaJ5vtNOSuOXcfG%2BiuekPNIrklgJQT6sdRrwBabKhTxm9rvzpjxdNOksoZ0qwdUHvMPVL9g0aHje9sMjyXUkHpLRK7M3NkOCUnXQggnn78roKT%2FBzKES3TjE7nGn%2BI1uq5f%2FYxRjLoICHQOcIsTef4ZBNTOLkybBEP%2Feuzm1TddwT6PGLrEi9EBzZbZcraQubQuxrEdpAy7ty7KC9fuJdbo5et9iBeBOI4y2esgCYTqDWCOLEwNtO2EyLjD04tXGbx1ZuPBMzH2l36KmMMtTWMW6qkBdNHzh4cGwMwcRThYIYbQpOqtDYwfvPHl64zdIn%2BQlSU4VSb0o1OcpaGyXUSSIYKpUaSs%2FuyzaQcWQ2U8c2haDgaK9xWAcPPGsoLTy%2FHdUR0sodBmrdyuzQeAbh0AZcfNjQIBogyrP7b2ULTFCv%2BVBmfcBUQQfEB%2B%2FLw0rnH%2FGACs7o2z%2FYCpBwF2qrdA1aN6OukZg5dK9BgRc4RCccODhGuotqHJAFNU15cOCZOurmEE1k5Lz72Hz2HWZ37dq%2FcgyOZnLwuSiUOZqYLmnksoh31QBypNCMMuPN2H3dX6XpRWZcct2B95fcD01ouzYyCjyssSp65qFCYpogPyy8HUtf1zmooZcaNs%2FEPIkdCTAx6Y8jeaTOG1AZGWWVJdPx0abCrNivcJVK9w%2BOxRRUfn5wH7TkueVHs29oMT%2F5XQ86uTo5NZCRgXN8s4GKwibx40jJ2FDBddM3DTfPQMvJGtZYqR%2Bv9YiWn15vFYvF7XOvfkrZoUs2gJ%2FP9eAAv2Re5PvDxTAMZ%2BWVRN3qcqrFBeig8xMWSfBTUl7h9ZXlFFCGHFv6MqA71eK5k6l77R8cT7P6sgG3zwNoMEANDZsXq3h11Oo0dsoQ70LLyjsz26MjlUyyPFXXMX3t7Ox8GRa30uHv2rU8OJ%2BehHRxWhHe6oKbi%2BYSu6VN%2BGnhDE%2Bn4dN0XDSj44OH8j0OZ0teivVRgO9cF63Yflpr3xPL8vkO7iSgFtbi83tGH0H4pYZpdRuQ2%2FdK2BzOP5%2BTxLxdnxo8mibwtlefXznSPal69uvHT1V9fd7rjMaeWB4%2BZtkC4I4XDd1UNp8p70JUDC%2FoPhFfb06kz%2BPeuDsyWKn5WIWTH0QvVrfPWj%2B%2BpqtAq18%2FfQ230zSXNaAyPM%2FIQ7J79LAB7b7W0NvTaIoWFp29VZsH5kfmKokPw7DLU4nwZedfWzb6p9twBeJLRf3tzIpU2V%2BZm4IkKbp548VpQxHdAQv38OO9i1xX%2FA6v481wJb%2FvOSdB%2FtXZ%2BZcL77W5klVs6%2FxLED93jbsq3f396kpKWuW%2FSNJv2FwAM1Rq2ECpd%2FT39rR0txzLrp6VDxJgVYj3zitny8lftfCrd5R9O5e%2FzmGBoqVnie7EJ16mSyrgETZ9gTT4PCJv6e5pkUfVBf6svs6z%2BvGv6pa77ekWuwNAmKm1VNpaROkR%2F3o70P5FzzXm6QUTMcimXNTY%2B8Xu3d0tvT09vb31gD%2BJ18iHxZhFPLtlcN%2F5%2BPLjnV%2FPJlWQWLyOpaXebtmEln64FHfiubQ60wvAHvE3LTd19Lb0tvT3635iWW65wNOVwXHRPv2VlLazmpv2J4y961jq7%2BnpVuIXjv7RdMO96Zsl5nTPeFGHEDe2T%2BrstzoejHeyaK7g%2F%2Fg1SSefflB3T%2Fv6svPlp7DoakVa6UJPIxvQK%2BGLxkxsbE4%2F1LzXpmbT9%2FolcqMWZp0x%2B3b4WF6ZUOOO0NgY6eV2fh%2BOntF8D3zDq6yMREUD5I3Jjg9Nl0rM2w519BudtsZH2Y9RsMGHoQhkPhWTdvhMdx%2BbFd4jV6feReQY7SwJCZ8ZWmgooehLDRMdsN33%2BM0vczwwh4MvFoXkP4WJbnQbiFWVghnNMQToSh4LdUwMbUKALBtwk3cOjiTlX17058wF%2FeHLzjvFRHNyVnmCYvWTurOY%2FyYb%2FQhDYwEcOg%2FjW9mIaR4WQECm3qN8zPkJb5pQvRMWkwMYRfvi%2BldzpsyHY3S54kSQG9MsPi5tOOky1E4%2FGs8zxjtHN%2BIQ%2F1J22lYa2wPxXtY9mMc9YK%2BbAHD8uRn2qb%2BL1CnxlM3R7ADnFdxkRrmpJGsjy1lFLTpV7U6d8wi1T8SR%2BI9fKFFY0xBBEJk8%2FZ5FfBm9GCv4sfNOmBq9fBY7rLLBxniNIc0hm%2BYckH98yMzQqBkma7eE0epozYcRvqI7mihLmTre%2B0lynsO4nmrvlwdqXIz3aOgeDktUUFZjCCw3zac%2Bk6DtdZHirr9SfJQpn%2FFmdECGlBnCyRt8%2BsJ%2BEbQZuodzgWBsOLviCRqjc0nn6fp9lt965i8RsteIGn%2BCeyuRbG4MxsZnJ47eTZGhkf1x4aVwNue5LQ0DmewPNOTNoDWm6pLTXi14KxnZhjufwl9rWadzVatCfbpjg8SetqNzdzPvS3B8CCfSRHDA2mgcFGuJMVN01rt3f5mfP2bUuspvOyPfaobrZ6sp%2BUPyqYVTd%2B8yGRIJkAjQ5o0hbWnUiPw4p7zPeoGTzjQfh5XKmPo9GLGYO%2Bhs1XYL275Vpx8%2FK7Ek9dYQGxfAxoty2%2FFgebtA1L7Obgv1sfNjMSvcnQN3AxY8V6oj6aAaTQ09hzkyIfkzKGWf18KQu7ZIX9YiKnpClBGW5mPm%2BPoa07uEAv4mLkb2PRqa1gNAVS6y%2FSwrwz2bJRucea2GcBMxEU92Zg%2FxKraE67jxP2yJvItD0%2BheGxoWc2UqW5VBX9BN%2F%2B50vryT7p9s8J7FPqs5IKcayzGPhs7TMKphIseVb9AFznw6TAnoWbHsiYGKnSz0Xcq2MbTJRlITeXKb4YTWvQ89xfbqRzGsDnNNyVR85wzmlDUywt2GRUPSRwH8kqshbE%2FA7dQFY61%2BJXk5KVAthp%2BzsWva%2FB0z6fkXh54jaUQTorp7Dmxcvxn6ieFTmGsyqYLScKkN4vadc1gWRJbbQ9MwApTFURwzAnRahN6J98OsYvunr2H4IVNXEbzPqojZYHYm0Da7AdHxoYcUzpcavISHP8QOYmE%2B1uh3f%2Bz8qh1rzhkqnlKPp%2BD8ZOdlvGG4RGSzUCqRl3LAMk8VW1l3bqf89a%2FOr8LYbPV01wW%2BDnPmWcuDsqiwDGfLFupuPDqprx8FY7a6W3pacj0%2FXt%2BJnhH7ex6P%2BcgaBC442T%2BjlXEr%2B4cdyGuS79Vwq6Wlp6elpSXnc%2BsPeShQrKrOx0s%2Bem4mPhRtFvh2X93m8%2BrKQILVxx%2Fwt9EWOaMsZ3FzLkMc5TXFHD%2Be0IiMtYMc%2F%2B3nuCAiGnDTqsw32XmV33MklPW2SORyQj%2FnIvgyIbcpkSgq4r3hkPx28TkAL8H42yO%2FDffduzo3yqrBavk9cfu71TpEd29LPuz2g15coLampZg9b%2BK5ga7%2BNs2%2BAPAGo%2BgUmn63PiN5tXQh%2FnKCv2odbkdnvvUr%2FuRqnX%2BBpvoaNHiPUYSfrW3QpIdpEjnX1%2FW3dHf3yKWLNznB7wIg3FnD6XP6ro2SWZFViQhmhwhqcM63PJXqu5aEvirO554MH7UU3pGH6trRqbkRz4Po3s2BFaqycY%2FZ%2BfMkWo0spnxtmF8F9RlV6mgxJaellLfr8QGZbX81J80Ey4pX45KNRwu4lF8S4J0l8yTLsTwFDsua%2BVSkF8YmL3Z42Cc35uQYx0EGXTUco3d70xBevk7bPPNTHkfeNnmM9gNh9CtTWceyZ9u3BI%2BnQY3Q9FObR1EZcge%2BLWJgJpcFbSPr%2B6lZNF0j3zxm8cWHpZ5eGRzUsXA4h8n%2FVi77wLDV314NzxudZ5x%2FrpCwnIkaccqJyetWSzukl%2Brpzo9d3c%2BPeR9dfnd1BsQNpLBOOm1S%2FmC2z9OS0IFSbTm2TY57aPm9%2Fl5hLfMvvMmyf4Tjjrz5ufjymsUr8J7ww3OUu5ztc6xXJpYTFUgNE36qu7e%2BLAVZuiZXxudFGVlJyd9BMjB9RPOzwVLONnx22YF8y36Wujx%2FZXBYABgfnqwzLTFXIVEmWKfbmFXWUDruhu3ZjyPf8VLzruOL93CCu%2FTI8z37psc%2FGroxlWkZev7NBpztO8Nap6%2FUzre6vqPgaTAUc%2Fu1If8AAAMJSURBVAue9xAFb7JV%2BHRhbme%2FU%2BUq5zgKHH%2BB3DLB%2BQluadRe9SSr7EjZb1wXBlMQUuofhihLdAJ%2Bh9mqOhImdqh0GUhWB%2BAqk%2F8Ix4ENlOUMCl5HrsrOlKPcvjvgpLmh%2BXkPolQMtwayq9%2FZcg3D1sRMzwim%2B0r3aBuapjpynHak0HwsyNOitQcRvZz58NwLaGpduPKvgK%2B1JAW2sqSnbYBN6IB%2FtLmZ9NxiRzfnQV9vJhjUzEd67zz4%2BFQFK9MwfbCQsHrwo6MblLy77mGWao6flwmtpXsPN5Iux%2Fmuq0D%2BuaKn8Z0n9DJuyKQBufB4LuS4ofxgjV220fiI0OBcD0MN3knE0Pz5wRp7FGe4mSFhmYezYRHAJ8xeZTyQfKfLChOzj1ynJsisAZmGdy7s9yCmJPHfyKx%2FJ8v%2BrGfRrhZDlYZ3rtjLYKPd2YmxXe4yXjucV49eVQlVr2WyoB3Oy6%2BDWSfYwbIcZbDGF6xRKRonZc5afMXz96wz7GB5w%2Bc7jOKiUkqk%2FZCUdLa4yjsES74roXakDBCDuX0kdPKht3rddytkv5Oz%2FYFDQTMnlJ6cWC0Wf9W7fi522CMWXaZqn2DnysmtdUc9zTsGAh2CNSbR4Wmxx8JtFP0HDUjOyozjfkuMKFlY0pcuCi5M2V712LIIkCd9rngny9Mt8xxjK5yPeDs8PyxSyu%2FJsMPsYF3W%2BCMihLYt8wS99aX0rC0RlX2gLPdzT6zeMVr7I0j%2Fij0HfrV7ySOfymx5aOUQtm31Jyj1jwD%2FFBN7w61zJ3e1HVq5zqmvssl6UVvNMWEH7QGN%2FSGB5dPP29vb5z6%2FPom8aDs0MsAb0BG6V0eeFNGZMxgc%2FYFeyimwGiZLTxhPZTv562w%2Fb5839YPHUnY5F8729vf3d8vMqoR0sKdbQkVaWpb6%2B5f6u0d%2BiJlML08xYTnlUvKfztEzQOu47PNfKa%2FhwaofUjMIT27h9fj%2FJrIc5bPObv%2F1da2rsE9um1T%2Bfw1WvvLTtuBLjVsnmHL21faH8EPeyyZrlf8DbgJ4SzuJtLoAAAAASUVORK5CYII%3D%22%3E%0A%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dxrange%3D%2210%22%20data%2Dyrange%3D%2210%22%20height%3D%22156%22%20width%3D%22440%22%20style%3D%22top%3A%20150px%3B%20left%3A%20432px%3B%20z%2Dindex%3A%208%3B%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAAbgAAACcCAMAAAA6Xk4VAAAAA3NCSVQICAjb4U%2FgAAADAFBMVEX%2F%2F%2F9NmcCTfmuUe2OQd2KMdWGGcFqEbVqEa1JNmcCbhGucf2ibhGucf2iUe2NHhaiQd2KfinFJm8ajhWubhGucf2iDeW2Qd2KBdmuMclqKbllzYExJm8ajhWubhGucf2iMclqKbllJnctEnMubhGucf2icfWKQd2JChaxJnctEnMujhWubhGuegWWcf2iQd2KjhWubhGuegWWcf2iUe2OMclqKbllIodGjhWubhGuegWWUe2OMclpEpNdBoNOnimujhWuegWWUe2M8iriMclpsWkhDp92ljXOnimujhWulhGSegWWcfWKUe2M4i76VeF2Uc1mMclqOb1NCq%2BFDp92tjXCnimujhWulhGQyi8WMclpPrdxLrN1Cq%2BFAquM9quM%2FqOOvkG87peCtjXCtjGunimuqh2o2n9ujhWurhGSlhGQ2ltKcfWIvktAvjs0yi8Uqi8sticWUc1mTcVRpUkJkUUFardVTrdhPqNSvkG%2Byj3CtjGutiWenimuqh2qrhGSegWWcfWIyi8UxiL%2BUc1m9poq9pIa1nYJgrdNirNBardVqqsezmn2wmX5aqtCVnZWtlXq0k3NapMxTps%2Bsk3a0kW6yj3CvkG%2BzjmymkXZTositjGuljXNSncOtiWdQm7%2Bnimuqh2qfinFNmcCrhGSchnOjhWtQlrx5jpGlhGSbhGuUhHWegWWmfmGcf2iMgniVgW2ifF2cfWKTfmtIjrVCjLSceluUe2ODfnhAiLeVeF2PemR6enqQd2I7h7qZdFlChayUc1mMdWE6hbZ0eXw6g6%2BTcVSMclqOb1M6gKaGcFpqdX2KblmMa1OEbVphc4GEa1JecX%2BEaE4yeaKDZk98aFSDZEwxdJ5RbYF5ZFJ7YkswcJZ1YU9DaoN5XklzYEwubJN0XEkpapM5ZYFzWUNsWkhrV0MzYX8tX35pUkJoUj5kUUEpXH1jTzxgTj9hTDpbSjpRQjZSQjNMPzNLPDFHOS1CODBENyxANCs9NC86MCo3LSgwKSktJycvJyUrJCR%2F7i4wAAABAHRSTlMAEREREREREREiIiIzMzMzM0REREREREREREREVVVVVVVVZmZmZmZmZnd3d3d3d3eIiIiIiIiImZmZmZmZqqqqqqqqqqqqu7u7u7u7u7u7u7u7u8zMzMzMzMzM3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d7u7u7u7u7u7u7u7u7u7u%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FWBVVlgAAAAlwSFlzAAALEgAACxIB0t1%2B%2FAAAABx0RVh0U29mdHdhcmUAQWRvYmUgRmlyZXdvcmtzIENTNAay06AAACAASURBVHic7Z0LYFtl2ce7DS8MxsdgE0VwoOxTUWFsMHCICKKuXJSbOoG0xSGKjG0OAbmo3NwYKDbYnKWkBjsGmtoOEyXIGNRUvrVOOktpCy2jI5hmTbuypDljY03p97z39z3nJM2lJIPmaZqce855f%2Bf%2FXN5zkpSUHBB20OzZcxacsuCURaWlpYtgYPbsaYXepaKlsumfWHBO6Q9%2B5LKyH5R%2Bfkah969oZptx0jnf%2FYUlMcl%2BfsHcQu9n0bhNnbOg9Ae14zEjtsFz57kfKPQOFw10tmB8mQmr9SC788wiuoLa1LnnZAANDGPzBNpfWHV4ofd98tqMLy7JCBrj9kI0FtP1gYWF3v9JaVPnlv48U2rUTwZjcV2P6%2FHo8YU%2BiMlns865PXNqLpcbc9P1WDyO4A1%2FvNDHMcns89ZF2viGuLWD2PS9%2B%2FfpMdBcoY9kUtmcLFykAOcHXvrIWCIxsgcGvlbog5lEdkrW2LDgQroO3MbGRscSe8BZFvpoJo%2FNzZ4binB%2BSEv2AbWxxNjY28CwKLk82fTMqjbFUErZAwEOmCFLjAG43YU%2BoMlipdlzQ56yfliPv4X8JLb9QK6YWObFDsuBGwLXoseGEwkc4ZC7LPrKfNlXcuCGQtx2Pb4HgCVGsbsc3avrNxX6kCaH3ZEjuKGYvo85SnjZH48VS7l82Cdy4IZzk1h8%2BO3RUUINnOXIcFz%2FcKEPajLYolzAbYBiIK7H9icgn0wkcIwbgRq8mJ3kwc7PBRy6mhOP6YgbqQbAYvF4MTvJg2XbR8nAtUH5jZJKym5sbE8xrcyLZd9LScC1AzhwkaOjOMSNjo3u0eM%2FLfRBTQbLodsEg%2BvS43GeUiKL63oRXB4sF24IXAdU3KSESyRwcrm3CC4vlksZR1xlTB9D5FiGsne4CC4flqurbIP0H4U45i6LMS5P9oMcwbXo%2BvA7VGyjkF4m9sSK5UA%2B7Ls5gtuEygGUmIyi7koAFyuWA3mxnHpO0PXvmB4fSZDrqOgawTvgOos36eXBcrj8Te7wig7r%2B%2BklnTHc5aXHi11eebCpaX46wMo2IHB9qB7A1HAHyv6YHiv0MU0Oy%2FjOZWH4HuY2dOfCKHaTyGHuLd67kCebkyM4vx6L7UdOchTjA09ZzE3yY1kXBBvIpz0G9fheEt8gsxyJx2PFEJcfm5UlNzfh5umAAuAd7CdH8bWB4gXwfNnnswNHuXm8wzHUeYJvGBop3iuUT5uTTb8XE5zH0wOJ5H7c3%2FUOupO5eONC%2FuyQzPtPajk3j28YdLYfFd9747FYUXB5tTnXZqs3sFYAF9u7fx8UBvqbhT6SSWdzMlKdR7FeQBZDH4%2FTo8WUMv8244vpxrpaj8GCyFvG9fhw8ROphbFZX0nj5iETNrDmaFyP6T89utAHMIlt%2BnhfumCBDVmg44pc5XbEEcd88pOfOvHEY%2F5nQo5kEtqMk0pZsuJ2j6s2bHede1QObzjliM9%2B%2BXJbuQ2svLzMZvv%2B5d%2F86meK%2BLKzGSed8d1fuOvBEJja2g0GVA0N9cQ8njtzoXbwMad%2F3VZeVlFuQ39ltvIKgGezVfzwhu999TMTdziTzA6pT8tOznLzUwBaWXk51hogKwO1lYPkkOoqyst%2FuHLlim8W2WVn6YG7KJtNT%2FnUly9D2kLkkMjK8T96YIYw8P3lK5ev%2FMlXiz4zC7szLXC%2BjL%2FG6%2BDPngWgyiuQvIjGsKsko%2BXEb1bYgNxKYFeUXeZ2V3qS%2B3RGGz34xK8jjVE%2BjBiWHFabjfhKCHaYHKD7XhFdhrZswn3llE%2BeVUZ4lSE0FQhhBXDC4Q3Toy%2BY7Q9XIndZRJexpQnurnS3d8zplwEs7BrLylhcox4SMcTRrgKll%2FhhK7%2BBSA7sm8VYl4FdlB64%2BuPS2djBn70cyayM0qqwEV6kAEAShEEmN1zUAdsfrsS2YvnyIrpM7Nw0wX1r%2FE0dc1YFJSIlIrYKChEqOQyLukqUtZRhjMup4lYgfl9994%2F4fWJnpgluPF855cTLy1n4QukHfiYe0kYrORbgysqI6pDnBA1ev5ImKPjle0XRpWenpgmuPmXfyRFfvqyszCalHsRb4jgGcMrKKFQ8BXd7oQEcA23fB2jLl9M4VxRdunZyuuDOTbqJKZD8Y1woaFWgBBKRw%2B6yrIJnkjYqP6ZLEuGQ01xO9UaEt7wourTsuHTBJfOVR5x%2BGe7KwjKiAJnCsMO0sX4utESFjURAlr6glxuo1JjkVq4sVgbj2%2BHpgrP2lcecJUoyBK%2BsDDRH0eAYV0b7TigmhBQXAwwtzL2BQaMVXdFdpmMfSBvcmaZ1p3zq61hURGi44K6wUXVVkHSkgl4WoB6yjFIus4mcxXb9cllv5LXoLse1tMEtM6w45cTLKLQKkoiUEQGV2cpInxaurytQtCvDAiOdzTaMWs5krmfEhK%2BE4qBIbhxLs7MSTPnVgYNPv7yiolxKOCoqSD9yGVVWWUUZ86FoHgtyVI%2FkEgHpx7x%2BpWyM3k%2BK5FLbsrTBnSpWOuIs2gViY30g5bR2oy82lFrCE4tvmFoFzVfoarRiKL%2BeslpBanAa71asKKYoKS3dPq%2F6%2Bju%2FsfjqxYu%2FAY8rr7rKRpqfyAklJTbGyMZkxy8H2OjFbyY9RBGVDTSJuV6IjSCEkmAFGiySS2FHXpg2uHqHww6P3z5w3333rb0P2%2F0P3nzLLbdceSVwvKqCwSKlAetHriBdJlDS2fAF8DJSfuM0hXRm3kD1Rvu%2BlmNyaLjoLSWbeuSRJ8ybd%2FY3Fi%2B9%2BupbHWCu9MG5GDbGDQbI0FrydP99999y8y1XXXkl8pI4kJH%2BShYJcTJjIxklml2BU9Ablq%2BglcBy0oeykjOc7OSmH3nsvHmLF199td1hx6pBT1g%2FDvu69MF5KDZrW4sea8kL1eP999%2BCBIkdK7pqYOPXw2HCVT8j9rvn%2FvnPp%2F%2BJ7Ll7nrvnnrvvRgGOOs0VUwrddIWwmZwWAsSI2SkwB%2BFnd6QP7k8PSCpTEKn41irjYvT%2B%2B5FjvQXB%2Bt1D%2BO93Dz30u4f%2Fz2D%2FAIL3gPZWrFi%2B8nuFbsQ82qHHzjtj8beXElYUl4O%2BCGyYJnle53rcMz61uj%2F98dGHDIgQlLX3SQTXqk8GpGuVldeCIG%2B%2B%2BeafPYzVhoAp%2BP55z93Id06CPpTps%2BadvXjpbURV5OFgGkPI7OSZDiiigyEN3QubGtsjjzxsAnefte4k52mpPRnu75988mlkTz739HPECEdQ3j3gNd%2FHqeX0mUDsahG2qDGx8QehSL0l056D%2BlEy4nRZ8wNsjz76yKOPCBJridpMzNZK2hP%2F0oJr%2BWQ6%2BiiCBg%2FK72ky%2BvTTz8HjuXvuvueUY2ceObXQbTzBNvNzoDEHp8JwMCp2iaPiM%2B2K4tgCwqFqTldtrSCIsD2CHw8aSBlwyAqjU34P9ujf%2Fvbkk%2F%2F4F9jLr776%2Bqvw%2F%2FquXbv60X%2F%2Fq6%2B%2B8carL7%2F80r%2F%2BBZ7yack4xj%2BRnbx16dJvL1589rx5nzvyyEML3fDZ26EnnEFEZmfeT0QwO%2FOQdsFMcYsO7i0ZX7G%2BQYyac91vH3gYDAF4%2BOEHefJoYQ%2FBIo8AoicRIuDzOnDZRQmRVzIOL3QSfmWzib3%2Bxhsvv%2FwybAB85ZNPIxU%2BWa2EaXpmakuXLl28ePG8efNmHjnrvSHIY%2BctXqplryZ82FyOQquyx5RWggLAWk0PAiYC6aXXX3%2F1DS6hXYxVv4RkJ5nWT6ftFKAYWvLYScZ29hPI%2Ff2vv%2FHyS%2F8wOnTxIg7hVszxjHnzTpg588AT5PTPnb1Uama73S6UhYeZppTM0W6XDlEkK0xhKj05d7E7fvsAzf3x84NIUBjU6wRLvwGAEBXj1s%2FI9DN99bOF%2BvlyQoFknZ0SUTSrxs49iJ3to90uOxh6RMLX3MYd68xZMwsLbdYZ37nVIUjIslCHpQMxzZNTSWVd1ShJUm4%2F9PtHQVgv0bjUL2BhFqLNmXIUpNIIVyDFhtftZ64TD4LSELV%2BBh0vuvPv8o7Zxemm%2BhGLQxBh3r506TXEsR47a%2Bb0PFI74exbxa6rHs3Y%2Flkfm%2Bwl0WDlA3%2F8279eelVQEGIRUus3jlBf2M8IcTq7%2Bvu5h%2Bxn7IRzZVvY2S%2F5UZjwyhPKycYOgz3bxf4qh2bnh%2B4wHB4%2B4luXXvMdIshZ72Kmc8J3bjMhko5BsJGkxOcpaYjKmrtMaYxupGFLxyu7WCOK5t%2FJ1dNPfRpTxi7h3tBinAiRUj%2Blv5OKqR8vL9FluPvlc%2BS%2Frzz%2FZ4VF0vM12WnMYr7KVTlu8nLNNd%2FGAfLYCcR4wq34PZzaOg1SPCfYOvyHHurearJDZJOUY5GyyWQHDYs4uwYG3uR%2BETfyTtzS%2FXScQlBdIs04cFrBVSPAMx%2Ba1tnw39defP4JiGyaeT%2FFeSaa3q7Rg9PUk5THfqlVDPQ189mgXXMNaPFz2SM8aNacBfNLx%2F%2BJlXXrnMobc3CmRNHukJuCHa3iWPCru%2BHvm1988bXXdrIG30XhGXJ3PqFfTkr6WX7ZT5UlgpxEqJ%2BnmExm%2Fbtee%2B2V%2F%2Fx785%2FXy%2BeZlCuRfdc0A0XpSBUHw4SlHJrZUpz04E7nnZAJv0Pmzi%2F9UYZf4%2BTkSGSHr%2FFpmvFINbHPVucp2cy6xx77%2B%2BZ%2Fv%2FjKa%2F%2Fl6cROpipGZKegwtJGlj%2BqpCXPSJT1Gth%2F%2FgOsNj%2Fx2GM1bE%2BZu%2BY7IyvPLrGRTkI1gskDMmJNLCu5T6U%2FV24kNuHW75xxwrgJzbQ5i76b9TfOO8WbSyCMg6ldv2axPDm89Y89sfl5LESLCEbJqJU1L8%2F6ESKQ04vwt3nz5r8%2FBpzUd9AMb6cJoXEBGRKRiTxBZV9k541j5%2B1hR%2FQ%2BkbzOn1Z6e7bQGLtxkxFNnqbxpqEuU1qDP8QWNLaoHaSI7InN2P79Ith%2Fnt8s25%2FJEutoG09I%2BLEYnoAz0rACO11U74mHrznjWEtus3L6dQej7OyG3StouFD2J70cSRplO60RAcnnXh5OUsUd3Ha2md0hE8HN5fG4yfsqISAX06zGNHlUS754UhP7ZL2ClmTu%2BJu3mxYx76QyT1Oz1%2FHe4fYzVJ95UE4%2F9UaNfFlJ0rd%2B77ZWMkt9HHzzFpbybDZm32wCXemcaRK4Bbljq%2FV4NgV3vxlpc5l3xdMWjASDbW2BTR4P3RVFldQPpdEM5iMzKk6Tjpcp1HxOaJrG6JpmGt5Sna%2FJ20%2B9r1beQmNHqiU7YDZLS7Z5113iJtOpt%2BeKjfz48zD6mruhx1nb0LdydYYjkcggsvAgvG4Ptr2waZOnVmpXtq%2BaeT%2BVcanxjAevJWtOaWuauTk0eU8Nrtg8QTO%2Bp3lXNXVc2rZmVrtYSt15vhGLhT1e77JDKLhTctabx1M%2FpMdj6GvuYlG3chS1IUSL%2FiOAEUIwMhgO9mxr3uTzuOTD15TDNYvTyDdJHLQUhOVprplwyVswn0rG08VIj6uev591ELAMCWxNumMWO7zBC3bXxwi4XCMc6K1hKK7H0deBgkXk08UVHCRqGyTkBtURMt4X7Gxr3lTvcRpOT%2BWoNe5nkuhKos3e3%2FIU5%2BpOGhs18aJuWjktNONqyZyo7KKtdtzBdsiwkvwmZLbbg7h5fXdhzc3InZsnCF5yeO%2F%2Bt%2FfqILuAdLp1ErVFJGJYcaqFw1SUOyAUgh%2F1WJ9uppaQXYwmPZSmVZaxEJgsG4t1pVhpcqLKuHyOJTu1lMXVzRn2QVkD74YLqPnwA7zlRKQmkE62ILGNJBJjo%2Ftiw3pUvGM995MUkEAmCzGs8kSYg70YYa3xICQ1pm1JpWWYaxk1DUsY9iFPHsGJteZD0Ag79N10F%2BQIDhxlFAQ3gn%2Bdb2xvTB%2F28x3YgWBQdlR4EYaGq09aJDLIl2Vow9t72logFLqNB5i5WYU4c1i0jnbGZY26UM4F68A2%2FulmpVSnizhIrDT26luWe4jz4F%2Fs1vGP4MDfO5CgBB1OhxNd%2BvERBmEOjKmK5JmRSFiSGQ%2BCimvFI2E0I9LX2wElBQqFEAzhCf2j98HmQP02eI4GYxqejlsXz9XwXCduG6fG1iDr41EHz%2FTJJtEKbCk8xofxdumGNbQf8E%2F3RCNHzd4LT3TQt3GQ9eHNHJqT7aeD74qDHoHmZHsA7%2BJyb%2FDItBg7GPWX5PgjtDjCRfX4Hvx7YaOgur3x4Sg5Gs3Zo%2FjESAQDI7AixhSFTli%2FurKq7qnmzu19IgulNMNcq0EaCp2s2fETvKGGGwC%2FoofGkBI2DrKURhqdrkea3kHbkzWyg54JGmlc0p6apvE3c%2FLV6TJ8Fn3FAOh0ypTtH56JBzUHm%2Buge47nI2INAIqT8spDePiDJdNzExxEuEA8pu9PEGyJMfTjRR5yWroiHJhIISNcceFBiR%2BDG179K2a%2Frnysrmnr9iCTY4RtSQqPwR5aFTo1RlFqfidmCVPdbtKxU1uLv1AYEdA0rjiNnfgaWYW1N5qDFyVLaFjDggPXj1CmRrZH%2FzBqHP34OaSx93Ly3SUKRjNdeDcbaBjzcWI%2BiR3RnvdbOSeV0BohSCXxb7yRX%2BmLxWPN5Jh9SiaiJpbgP8ODEeYzKWCUuzT9ymRrKmvqnm3q3q6Ax%2BuFuVz7emkoFJ5NahfS4C5XLXIQ%2BOAbGhpgcIMbgyRujumOtjrFZ%2BHZNKoz6leopjQHV7%2FG3tRBh5mbpN6QsUaDyGuhgsojqJicozQdm%2F9LHywpmZ0zuOG4%2FvYY%2BT1MkFxiTzzeQ07TZo6EiSvCBQM5iQVNVXImW11ZTd0oC3%2FCCQ%2BG6ZaDO9pwKFzHG4spUaON6FwHbYW%2BvFs6pxWQGheXxs8DIhXijkWopGGMh1o0m3pFTUziz%2BQFocI%2FaNIgwTCYTwlqsp%2F03fu1D6FqIDdw8P4B9CO0BBv6RdPEPl0Pkp3sMTDh4SyMJSOrjSYhaKAuOThhv6msq2vahgimyEpJKHzc42SujkpF462p0dMdncVen98PD%2FKE24ySxJrUmHSFpySnAY1vXHlc7w6NvRMWFRa7x9vgha2j8OXze%2FF74XdF4QxPRqPkBXYAT0ZLIfPiWX5%2FIByNRm%2F6WknJoTmBg%2FO2Jx7Xqdrw72LuH9Z3k0MIch9IuimFoxscpMEqzCQX4ZlkdzrgJDe6vq6pmbpR6oS5vrngd6BQ6EehkHopLhHuUeFYaiElaED8%2FDjG%2BMkDs4QWqwf%2FKkRJciCabPC45SBncy0RNJY0OQ%2F89IxAo3COwAvess%2Fr53MxFi97N3IKIX4%2BpDy0Ip7XGiX28ZKpuYILxXQdaW0MgQPVjcT1KDmMMMv6OZcIC0kRXgdEBDIyMbwmI3KKG23q7A7z80NKebgMw5DNNAd8HpdTU%2FMEjeuF5ggUmdfHWtzPz30iST%2Box%2BuhhkKUwINmC15eCYyEieqaAPH5DCt6qRrRal6yLhqn3G760UdLSnK6iArgduv6PlLDoV9WTCRGYnECzjW%2BugYFWN4PHU7LV6awSuxGu4MsaEpxVPTNhENBVBU2eFgSIjJ3rkJM0GvQgU80vg%2FJhg1yKIq6iI%2FzKtMliOoaRF2Cq9%2BrLIH85JsIW%2B%2FPq6o%2BUlKS%2BS%2B8SfYH9DvrUAyMkbQSQlxiRI8PY9dei5uKFG5SfwnJTSJcZqZiwSKvzM6YGxVBkJ84sgsXVSEjpwnnh%2FyhG5dVvAV97MXn83nldlbamyzklSZzLfn8NMDJMQxsy5bWjq5QKNS7RVGmdFIMALbB%2BqpqDG5RLuA8nno9po8kaFaJdDeix4bxIddKZ7kgI%2FV28VRC0l3GQS4dQ270mabO7WFZdRJK2sEzGEI9pAEE0cUTGmFuiIFeqUU5GC9zpF4f1ySWKI5RfKZfWo9LqbGlpa2jN9Q3MBCVrK9RBudlTrYNcftDFbKP5FjIeTz%2BOPoFWvIb6yjGje1nMc5tKt9EyR1J0YR9Ew5OGLjRvzZvw90yTO2DQo9h5tYRxiD40hcCUBp65DwG5OdpIJHIJ3Pw%2BaQkUQLDvJ1wgTAQ2NLa1hMMRRRYiu0OsK3J4XII5tRVMXDZ%2F%2BozBrdJB3CIGjVwlRgcHCTvpsKuEkuK9ZhwTGEFHC4IBlNUchNmvwY32ry1O5hmP2oQVYdEjI%2Bvw%2F2%2BjAdpVtnj%2BalHVEYDLVva2jt6gwMDg0lpyTYkTgpaO3h9KDNpQ9TAVUJyUjI3J3ABXY8TYgksu8S%2BmD6IP1%2BwLigHFBbhwiLSKWm7pLns0sosbXVlTd0zzZ3d9M4K4SFSXoMK7tgRDoWCoZ6u9vaurq72LS3YAi0taKgVT21v74AlBsIDQ2mhwhYOd3fv2I2Gggp3TDAEk2uI4DC4ktKsubkxOJ3%2ByDqR3Fu6HiaepY0Dk%2Fq1hODIqR3mC3HLKzhhKBtFCPuUMl6xiDIjfR7jqCvc19nZ1LSxjoipqqYPTQ34jQZAe6jgsKssmZr1lR2oBvzcVSZwnEvs1fUeAq5ZuEBx7Dif5EkmTTHDg8KrFgycsNW4okD5qFoKyr4CxnbnhKsv3Nm9tfmpuhpCAj9Vo0d1VU0kKkuOxrgtMLG%2BSlZcyUHZlgRQevr0eHwEZZO4iIMnGH8Bu0qnh3hGcvBheuzhMO0exg3AUgEl2Sw4OMnWQEJa14xrCtNlpizADYWD3Z1Nz26sYwCqqqurqxg3zq8OLdtoEFw7TKtmC32E3umVZU2AOg2G4%2FH9Y7izCzvMd3Q9Vk%2BzsJAIZJlILx%2FJSRb2a4iGf21u6uzuDpLdTi92QbAMdndva276y8aaKiurVhRHnrphxS4DuJ5oNMRX%2Bii7uXJONh0ouEMuGtffRld0UIwDyb0diw27MLZ1zgBhxXt9DfAi5pMYB%2F5CE0rLflNZWd3c3LwVOMKjGyQJ1tdJRjqbkf21DlBVW8ISepP4SSSR5MJ%2BtboP0ZxSBVdy0KLaTLmR31qP6PF9YwlCLjGa2KPHwqzucfWReyjDCjRDzI%2BQ2ywHmfYGOwvNJG2rFHqRBSTEQ9FUq55Q4aXIrrqaDUGUe1MJcn5%2FOBp9li8uwJWUHJJpdkn6V3sgOxklPSejo4mReFxv4RXrJt4DqWZmxkxtkMVBNPhsoXmkbZUKqmSiMujJer5hpLotasoroVx%2Fii8ggyspObQ0E9XR3xHeQm%2FNGxtFYe6tuB5zg6t04T9njzmn5n0WvHKTXClylzWF5pG2%2FToFAmtWxmmKp2SI0eBGANeugoOQupEv%2FpES1aZ%2FMe1YRxylx9MwHIu%2FRYqB0bERPa6HMDIU51xOd1BKGdXbYuXYhy8e0JKu7wDNTSxsjWViUW3wn9V8jqVZ67UawPWYwD3O6X60xGQnpdcFxrh5PGEd91bipHKfPhz3w1wn01xtj0g9pKwkHDFmKnxka6FxpG9rkoCQ%2FKOIbYKnhXOUQiBdBIJcyFR%2F1%2FHljIrDNvuc8WUn%2FXZ3QI%2Fpe0mQG9FjcZ6aUNEFQplV4b8pNI70bY2kLLNqpFkp5JZMsUGUVhoVx%2BvvKgvFYZtbmvp2S49sQ%2FHh2F7MDX3Syitzw6%2BeQGtPUHBKfV11W6FpZGCrjfoyZI1ydikGZYrJY16nCRwkJz6%2BzWTgSkqmzV2SNFOpVbh5AsPoswP796FPyOkdNL4xblh26Mnjb27fwa%2Ba0ktw0jVOIr2%2BA6nbZDxbbfRzCiVlptE9Wk3mrNG6W9kVAm4RlFWOpzhsU%2BdeYOUzDdg86MM6sRhoDf0PXSuk6uRP0sreQFtPkN%2BjZ%2FrgznsnpURG29ngL41ckvjMpM61GqFrikYjKjgowLfypVKCQ3bYoiVKu5upgdVDER4HfxmP7%2F4QaHX2%2FK%2Bcfy1m5hTkOEA8UL%2BppWPHwCCvvXGNjof6upvqaioLTSRNq04JwpRZsmmqRK3BPxuN7lbB9UajvXzJccEhw19dU2vNjJIL6dhP3vRhsdaMOQvOX2IZKTlDjy%2FQ1tsnkkop7QR%2Bf1l%2FwPOTkFQr%2F9VGmVklMcZCgNUNePpTJlfZBSj5smmBQ3b4yecuuzM5OU8g%2BObQTz9useLskxadf%2B3tjJZT5YdH3Q2B1o4d1lctd3Q3bzyA%2BZlxmAaqiaJSdVkac9Mk4FqgtHucLZA2OEJvzqnnXris3grcsnM%2F%2FYEUa06fveArS65NluwQ%2BW1qbtvOLzuHxU20WH%2FNf11feeBV5gYJmYBYjFjXD9VGKVY9Y8oqG6OszytjcNSmHnXyqWdedNFFS5YtW3bhhReee%2Bqnj0oFTbJD584%2F%2F9qUhUZtPSQvITnyDbIMJnzA8VudkpGx%2FDZBNaUu8kAzJCfkilwjGH5FNTnTZFbgcrWDZn8B3Kcb35ZPHvhjEC786sITGja1tAUHknS1AL%2BnDgh%2Bqw2gUvhDQ0ln4mzqatmGe04aGTYYQBfkon%2BgC1j2nOTJDpkz%2Fxxwn26ZoNslRtwujz%2FQ3qN%2BZFW6qSjc3VRgfqtFP5asnmqJkgrLWI1Xs8VFWsLmdkMOSZAhePg1EBVX5AqiONUOmzu%2F9Lo7XIwW0h8nR17qIXkJRnjaydBRPwr5Z6H85xojGcvyLbu6HPxiO%2BFFwDWSSi66nix0AIAjNm32F845%2FzomN%2BI73W5JgK4GX0t7L78Nk2uP3f5XCP2tkRo%2BRUWXatS4ATZeA4xamOAINn8jul1oAN%2F%2FUJ1mUpE3g%2BLvgiW%2FIAEPBz0KksnQtQGSl47goCo%2F6ZMIfdvzyM9wPS4JPnNvJRs0CFQehaRyd2MjCXDkBQ31InL1VVXrTy40qCQ2C4q%2F6%2B5ws6AnQh81Vz1EP%2FzBVJ6yyNV7eDC8PR%2F%2Bs9Ioltx7utjgdpRUMmp%2BDjBE70C6qdCEUtr0WSR7cblkZjJC1HMWFB8EZxdshRRBf3XvHj85wzCwS57sJ6GnGvKUPY2CGn9l5D48fvMV3Gb87%2Fzzl%2FzSrZgcAt0bcMc1728Rt0rTEBgJb9%2F6zLvAb7WxAkijIyXNHpWtwGaLX0BjCP2N7ehm2ejAhwpNJX1Dxd91bp5uGs3lbvAHOnr6eN1A07ooEQAAA8RJREFUnSbvB4URzG%2FirhupF8CN92lZic3UUWlZNIDgdqN%2BE8ZKGEa5pbWr695C08jYcPF3nSI7g3kDULurn%2BCS7v9D%2F91bn50Qfr%2BxVougKKBQTCZ9VVfJrpbXCujDA22Cm8BHKvHGxosLzSFbmzF3%2Fvk%2F%2FqWbdbqY%2FWetD9znDrV2pxU8Y7g9R35qv0mVrCALPEmEZ6oVAG4NZCboYhzlJEU4LryPFRpAbjYNXXr4sdtl1h6bAO6zrTc0GGF3%2Fpuz0Oz5rTE3feaX3cxg67biKNYqKCnksPq%2BVOiWnxg7bM58VvwlMeDX2iH8J75qG%2BGFILr7Jbx9W1NdXWUmdypVjpMbVlcpLtNCXvJyVY9vbN7WzT9IEmxMYe8TbsxmzwX53ZGMHfafKP71ivKPfAkVc6G0gu%2FuhBKiZvwcdE1yIAZxWfc%2B8z6SjU1bu4OGD9uFkzHb1Nh473GFbul3xabNRsVfUvnhmtC7CfLPYMR41U88Y18a7N7anEKElQYASdnwC9tqrllT92xz946w5Sd8epOr7V70PV7vY5sxZ36psfgzmRciIMpAkxYQpCgMb7cQ4RoDIakLK%2FUHPeqeam7r7rMGFo3uHgr1tgeSYzvt%2FY2NG2QvpdeNg8%2Ft9ngDre29wQH6NQzSh4vozWjsQ35UhKDC1VZSs%2Bq7IhNr6kBfW7u3J%2BMFJXUo2NPekiqyNd573nGFbs882yFzFvDiL7UEvYFAe0eQ9KJFFOUpV5TQ57%2FDYQiHnc3Nz2zcWLexrm69jK5m40Y09dmmpm0Aqy%2FVR1cHwqGu9taUwLCtOu%2F4QjdjwQyKvwt%2BPJ77FAi34K%2B3GGQ3UShf%2BJfbx78psJ6O1i3jE8PQPv0e6uJ6t2za7C8suuDH6eFD5sMqJAgjpCDM5QsXBgdCvV2tyaOYkdnFpx03ScJamob7ztKUH1OhL4AuBgbDGXxxCbXdkYFQqKenNXUQU%2B1eYPZeuAhQGJudgftktgF19La2d3X1hkKhoaHIkBnk0MDAUATD6upqTSOCGXV2aZFZWoaKv9J03WdD8gZvSTNoJbd7rzjv5Pd4R2QB7DB048Q4%2FDZ4c0STFNmqSxYeX5RZLnYYuM9k4S%2BF3LK2VVect%2FBjxbRxwgyFvyXXbngX5bbqiksWHnd4oY%2Fz%2FWoHzZ5LHehEYQsAsNNOPrqosfzYtKOOX7jw0kuvuHFVVrRuvPGKS85beNrxRxersgLa4Ucft%2FC08y655NKLV91446pVN95roISmwuPSiy%2B%2B%2BLyFC4%2F7WNEdHtj2wTwm8v8Pkm%2BrFsKSnCYAAAAASUVORK5CYII%3D%22%3E%0A%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dxrange%3D%2210%22%20data%2Dyrange%3D%2210%22%20height%3D%2249%22%20width%3D%22166%22%20style%3D%22%20%20top%3A%20297px%3B%20left%3A%20371px%3B%20z%2Dindex%3A%207%3B%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAAKYAAAAxCAYAAABQ69KMAAAAGXRFWHRTb2Z0d2FyZQBBZG9iZSBJbWFnZVJlYWR5ccllPAAAHXRJREFUeNqEXW%2FEbld2X2u%2FrxBCCCEk7kjdunVJ3XHHMBVCKoRUxjC0OqaUofphVNMvjaE1NbSG9ktDCaH6IRKlY9IZMzoavVq9xFyuiUYuISbmaoiGEC7h2avrnL33Wr%2B19j5vbjx5z%2FOcc%2FbZZ%2B%2B115%2Ff%2BrP5h6%2F8KRUSov2j%2F2cmkUIsQsxVf2X9z8%2Fp%2F%2FZjpqr%2FFf1vu6bYNVs72%2Fft63b9dn78fvxPr4f22tUMbbYnCv5f%2B5H7V7Xfhavdsb8Hz%2B1t%2FdPXg2s59E%2F78bj24yHozwP6uWLtTn1rzxpNcW8F297HpN3zkd77wRjPbZy1vVt8wfj4e7RxEmJruZ3n8J77HLHsfaz7Pds8nGjd%2F7L3jtMc5fFqv0j%2Ff%2Bl3nvb29%2Bu2Bqr3o9JZeCb%2B83PFxinT2TkSpQ0CiT0AL2bBAadO0P12FnhAhQnyiWFcAPtgSyfGUyCqcRwHUGwi9uP%2BPKSpQJTc%2B0F0TS%2B6T9u51k9d1d%2Fv19MPax8u9Ql8RK95dPRzvFeBd6W0RGLfYEJgMdjQwKQjAW5EuWjvM23j7f4u97SP72x91H7d0XY%2B1d%2Fu6nUf6t%2F39fPxePa4vxGJz0Ve6IPI23zUNp87w5HDd2yLWPyerW9jzMcYdRoYRLe%2FG8cWfQyq0wmctbnXs%2BdErbH2UrW9mFBqdLxre7Hx4rSv1NiB8EL7X%2B7DUoG4qROW2KpqE9GuLX3gCNoaK3PiopWvabuXdYA2jnZJf7usnwdZ6lX9fn%2FmLsilkYBspLd%2BCRKKDtNGvAcT18bA7y%2BhzcFdauj3ipvA%2Bfu0jev2O9cnURLxxNHkjrb3qR7f1q58ov28oz%2Fe1o%2F%2B5U9ojJ10RrqNbSfOIRHau5XAdHDhsfWx2oJq0rOzC%2B600NsS5hXfP3jfQbBj%2FNrx%2BWDJBA%2FfxbmtKGgWuAFyOOnk59du955s%2Bga3bNwYWXgTqU4gPkAM5%2FXLA53wtgm73MXqZT11dbxIHADxQTcFIIvfg0kQiSKxCPxWYLWLccpGaFn8cTs%2F1Ixt8XdOg20MFSAuEpQ0oD5xXRHylT5%2F18dP%2Fu71o41A9Vi5Lr3diJXe0%2Bl9f4hjJwzvU1aJdsnWJZxJCKk2rkVAfPMJORn0B%2BcJVSdJdNO%2Bn89CarBYgcFtEyzsehHDgwdhj4kb322F2co7WVeNa3AQ0PfrPV%2FexK0eX9PjK3r6ih4%2FwhQHPagZ%2Fbm167Zb30oifO73chKp2F7kp9XGb3AHTmJxfPf3dXHHSUXa3l3qggjLzI2jxGmiefSBgmKD11WzD4DRPNw%2FT0Z9VT7Te97WFt7ZOO6mJugzbqqOeHdrtpg%2BK%2FZpDIATIVGwIUzn7GM%2B%2Bl%2BM6JFIV5zZ7ZXzqGQ3pTnoK5n9CiWi4DDZqGyjiiBGNGEyL%2BsTv6J%2Fv6wD9qQ%2B%2B5qLx5om2XUmVxEqiN9BTDh4tdN9VxFoVhGODK0qTUS5qGPj5iUYIDLxuaUB03Ve15TXKkIkINBNRSYVYTAQBr39yOAA1aCpCyTXuwTy9lnuams39bFv6Xve1Pl7S9v%2BjKyfMi0cNLSkc9rKpS8blIDIEGQyToPOKMAxZYilxMZdoQc2TrXT91Cu2YwYXA1utZlBdEkH9Fk9fkZPP9VWsyRr1pV3Rs6Kkz4WkJRm%2BUsWy2TiPC4wDhM58ADTs6Vzp%2B1dVCS5uOuLduduTWSZASazJjWrNTUYOn3JWL99ol19GhyHko4tNs6nRMA1EOWRJAgLRSZx%2Bqg%2B4%2Bv69%2BvO2eoN%2FfOm0sANpYsbUQLunAbEv4t873vijDImWpbqy%2BjTeeYYwwgx8QAK6XiFQbwFpgGNm43b7Fac8P369Gf1l2e1vY0YH0c9w59RTBMMnKy%2F7DTQXao1Ec1GDhW4yNCNBiG1SRMYqAEZDU58MopiUEVsgLvRQGixy7zqMxdGLumwi4tAvH8seJ4seDZuPxlNXCedlG3RNChoydlFApd3hsRJRO8M5KmOkmxGlhKn%2FEx%2F%2B4FO%2BAfURfxY8gWMKzGpBu%2BUFhwlzIXHmPzrK3%2Byd2qILVxJjlNy4pTFROPi34P6UWLk39Vrnm1644G4Cvjn6Bxa%2FAhr9IE3LFWgT7Q0HPA5JFG3C%2FAUcOW9fcPjuC%2ByutAB4xJziKtMXHmFsV6MV9LnYoGZI08GE0fi2%2Fu1UB2iYRLRzBkWi1q4qiK3lPm8oXTwekcBJgOn0ZMbwf4%2BbKpjXjiNUXQuWRAKoGIcx14SMSeuJlY6pd%2BnLWwi4Ef6%2BT%2F9vKbNf22DazgJNwHwYXC3apNZAxY3rq27yCYwACStOJ6mq4lbJ6IsNhyeiqgEiRPlgK4yiD70JFQTSodfRhvtWhufgNGKLW6XHEIO4fjknMK7be8ki3fFMR1QDSIJNtYSNeHmAKEgDbu1B6qFJEeIYxr6jOtKN9%2FVo3f1vd7VG%2F9Cf34kM5FqRtApMLZBR7zA0cv8ohwUJk4QysZBdqu8NXhVz%2F%2BtHv1Kifif9crntINnbTUUIA6fRoRvULxlCL0NDoD1ImCE0MQp86SxiaWIz41n7lIC%2BkEJq6Pk5XDCOZu9PeBwaP0d%2BpPrkNt9u6rBZKJ8qAZu4fOEOGCfd%2BB6YZAy9tiA7QISKHMlNKikj4Vr4FG1QIZSk43C4IXbIbzv6jv9r575kfb3eW3%2FjAGrdpYyoxB5HkrmZkIIi5TJEus6n4pq%2Bk%2F99X%2F02wt6x8PjJZuHoBHG1qHokcAn%2Bcv7ZJBN%2FJjYedVKGOBhiOwvL5zwXJm4qkFaE%2BGUlYUAepujCS5R6mT4BBCcx%2BKS7g0Z%2BJ5M%2BmGFsV4B0yiumxJ11t%2BJE9ccALgEaBy5Z%2FKhdclYgmwbiw7Rh%2FHetS9SJgFdv0uZsv%2FynH7%2FoR78Sj9%2F3tU7wGQ5oRVOeUNnLdEt5P5QF3Ft0HqnvqbHP9fjn2zYWNPdsp4ny5cb%2FndJBOCck4NP10QS1bCWMqENQhFyfQWJDPvWxGiyAhPWlrkuT%2B4DWLjMafI4Ep5IIP72Gx9oirIU1cihKSyj08QNwwIWwJ%2Bh3wPOi%2BOLcB9P3j0jRlucCw%2FYWEQ16Pcq1uWv9Vm%2F1OPv6eehRrhAH4KSR0xNKpJWU2Si3JwfVJ%2FSSfqF%2FvAvOiDX0deZDQoTKv3lxoANKCqMnRTUjpKokAjVLCZTEBFAX7DM4mJX8rkmJZt2ztImiQ3tdIJwWH%2FlZhsLzRfbyiXH0X0LhCoTsHQC7A%2BdFyUs3ov%2FRa9dvsdUDUlcFqQWwzg57lwnr9m8aKLHxxejPKjH39E2f6nH39Er7gsL34zGjhJvhqIEnU1scAfF6%2FE%2F6d%2F%2F0FNP4EAzGBhoUNiAcyOo3RvBbCKDGNqY3IkUjBaii9x1KSAC3GeTiAXgOd7TJ0j68hE2vzHCTnsblZdGC%2BK1JholCMX2Tot3jRYuEmoFRkEA%2BZAbFYixjjNSlj5pzoiCSICJogRxl3Sc31ndCR4vKRculq6%2FPqDtfk9b%2FoUePy1JvRoLYDfGSwexax8c%2BLfBPe%2FqTd%2FM%2BFzuGBIUupd4QBaSFW%2BhgYJm4nbCiBw0DopcsFJlNmjM2i0L7h6NFupgtXRdaFjRPHSfrMQLHRgtEtQN7iLS9NOuc5txVhPKwAJPKROURlTDmKAqEz1MURkqaQ55IYVEOATYBDdtJnsI94vBiV2C2YITpKErevzv%2BtmY3v0UEJ7uVh3cxF1vdKYvvFnar21Kq%2BDDF9YwAsBZD%2BRueXLQg6JxseuI3YIXC%2BHqA8Rsv8%2BDUvpE82Qhr1ZwsUCFDp%2BwTP4aBMQHsF%2B4ggZZzc%2BPQRzRuMCFKoELDiPBiFPExsh1Vu6OLQF%2F9CkYH0gowbgUn1gGCGi2ASCUcAoVFAt%2BGf1qc7BGUff5Yj58xvCmYUgkQIjf1N%2F%2BW48eRzRkN5xxYBv10r9px17wlV2J%2BZhFIxeMkzNHxGTPicESYMEPg2rXyYSDch5xQA%2FOCMHC4%2FksUx8HsaTVC9wIpYZAgG%2FkQua1YUrhYtFnfYQDcuJ2PJCMjmy43dG5tkmjOoEtQTXhGgKoaXG1v3OZdV3hpVcpEP0CvWChSZ%2BPqgMBE4mSucXJ8s83Yxqx8QIiYlOEXttk%2F%2BQPhVW%2BDMtaKNFECwuZ6xzymzidrWIGkIoBlC%2FiLrdkySHRsOFzEDCwIPIBJrdraDKcgovTruPJ6l6pDoMb%2BjvWJZF4DOrQyYff2IF2N8bEPHRHvMI5epbXkoJxOCExcsh%2B2tyJhSNGw0oORT5io43DC3ju%2BuyxPLQ5Z%2FT4iTFHZaxI%2FfHv9bLn%2BcCrwlQPQBsBOKlMCrJHHNEUsCCTSB1GU0nGGE2ruhktZck53JMihvU1YDt6oXYxzTXERNbgaSmgj0YYSYKTgBe%2BbbdqkYOhfj5Ep0NqjRgN%2BJ68P%2BBgEFnAbY4LB8eAyIyLdkJDo2sgDLPTpSYm4otfmA7uoaBbBjxUVlKXH9RzP2kQEzUcUz%2FP6RP%2BeOVnJgh0FSqTDjHyeob%2BVQh0ruFeWoSJxZUKxF%2B5p1ycAVH0%2FBWJoWPMx6kPA6pyNaMupNXczvDICEROFQg8yJjvalFQ8j2vIK9hHaNHrHBEAnzcxNJPUAJ4ny52QqwJBr17Yvp%2BkAy8Fu3oKg7pIZxw4JwHZoE5dUJGuvR9VD%2FfN6VHT35%2Ftnjjimw6k4tf4zIQp4cuyMBZhh%2BOUGcSEDmQV9QnB1MuBnRRuIZBmMQicDac9HVUTYZWSvCETO67AB9FXQt1NgbDDY2f4HOnMi3Qi4I0CCJ3MESR86IL3J4Xi6aAa7mE9BFKILxQDEyOTouYRsIH4XV1wmORuMu0cPpY%2FL7O41XV2MqT2wGKpzHBWdQUiBUc1liMpu6%2BZCabnLEinIAl5I6ESagdGskrdQFdDNbn8EZMCEO1oYKoqQCGS1c9gh%2BYKWW6lBD0IBBwEqLIJeKrA8vMqRYXGZEVUYbRtoxYzAODJxhoh7azqUct2asapmw5SUAwjkJIQDWyKxM9VYN7en8avSxBeHTCTIAVn%2Bl0vrCJ8qdXWXaSpAAnrjjEU%2BB6TJYhxws9CO%2BvpoVh3ktvR2gKt0VIA1MJPDyOAmfx1GGG3J%2BsmNd%2BLobHoY%2Bcekzqyv3aHAgYreTIxD5pwiZyObgPI9eQvpCHYWcKVRtEijH5C6s4hL3NVoB53pLUARHqgS0shqG6JOCsABizwEg0RB3cGD0dLEheqmKtX%2FTU1tKjCIwO60%2BozPpIWpUleon66j4DhsYgtkoYxIHwx2iWNUAdXXuYoTi%2F87DGMTrblXa0kN2TU2n2G8%2FIhEwii1N8I8I6Iy9%2Fwz1k4aUJrtQRrZWMlPY7T%2F7sHJzhzEImRwctJF5WKRAZQIeI47pue7QFVwIN7M8UXiIUY4FmaIohumpysrBc2s7cc5Y6%2FLXVQN05Vq5OCrGsuFvtVqZdXxeDEXUyg0kAoEaYJHsYOBCL666mizGHELhchIBTTGVW8mnSq0pSXWTponNssi0QxGiDFc6cgiBm3TJPdkxym8PHPDGQJySEJnEMDCYk9on5rEOoYsdnBxwmNiqnEEuaxyTgoUzBeK20ylOSe1tLd7IoDH5YBENZDvygMhFd00FpAZPUoEsZpzQ%2FtQRvhUfRtG%2Br5K3heXAiLSmnBaahpXwAB59z1V13qokb1gVxHJstwcuTC0t01QD1%2BGig0NKzFSe%2FTAsi6%2BDZykZGgFFgqIeiRPO5lRCmVzCoOzseEoQ1heQFF2mO%2BdzPvb25JN%2FQzykmt8ME15kb2oukUPoQgT6tRNDkWA70TdTlZGEg1PBsEykSLdARMLtaZF5lRA6MEI%2B0ljkMd9buJGO3nALDZOmFGf6raaFBqsHIaXK0Ik%2BkWKT8ygtEyUAJ%2BfEiIfGNl8lhtDSy8lgMHNtD6WT2NMEiY6HlIoPF%2B4PNJXlXr3zVNbwOJXDPAl6AwzkkXkJuJC%2F1DPfEsLndDBLqf9t1EfQOE8wcn820dvElH3WemByUa8o%2FWO8eh8lmqXKo8tNUlZGUhzGFAb7JgbGmckRuvPL5Z1GOoHks5VOX6kAMpcsqB0%2Foh0iZkYK9ryXEIOQI1aH%2BDacH6rliKED18etpM4UqRFCYdLmrn38oHYp4Ubv1iQWhcg0BnEexKAN0j0aDxzfmgShc3Z2XCB4j2d1rQwGfNHEm4HOWNVSyAsDHREwBIUygV1MgMFMRhGIFDsIQPjm2MBN3ZlyIUmBixXTEI%2Bw1BzrEsRCQJiVx7bUbNCarpcJcRlSnGMFaZKnKYFkut9alG3%2BzY4IxdkGCd%2FEv9eheaZ4O3qj097SVUyDGXvSqBpeYE%2BxYKSs9YhZ94mVSwCs0IohQRCDc4AOW6xwNmCbpUQEvjFYrogZzwO%2Fs98XgVWIJETsIi%2BAzs9VqYWsyA8qlQzh4PcJ2GN2zcuLlsXBpUqkZ18Uj1i%2FwhR9BTdyDqBm8eRTE8ME94pmtAzpcMbQJdGd%2BXb%2B90iLYO3alF%2F9Ub%2FlWcPj3qOscsznnupSlAn%2BRRwND9zOXyGB4nhjUq3LM5spqxXSNldXqPv2kkwparZOC7glt4oBS45I0caa14ZiirLrox5yi4OSQFA3KvDDYohTIkNFcX2kVkFig7zEqjJdFC2nCTEM%2FJYYFooQAx8VPdZz%2BwCrujUiePmH%2FqE19Vf9%2BGnOTeeHSuwjgPZqEE6STZtFCEEfIMDweeo9prrQIWi1JH8v6GhpykoyioQth1mBJ5QTX7%2BeE6PBVjVFIh8ZW9qHPsY3ZSPG%2BY9aoWDZpxEhdJYoitACawlNYnxzGbHqkfYlxlRNK4uZdCXCRqxuEMZsv611Kd%2BWzYUS766FPut72hn75on674w%2BWoAMugwFC%2FUOZ%2FKUClTcqFGwK4DHXUJ3Dc5M78UsSK6k3Pmld701cCgu1ogvWjKKerFYWabqrXHK0HZDAxlW5XudMlF5ORVKOe3ZhVsxQDMaOeP9qArLF1ZTot5YJbVgFIs9Sqpqw84UvSV0beV11GdmUDOeNEP9o%2B%2Bw1ktBjNPSBWASG3tOLv6S3v0TJ9I%2BFBGTh%2B3QOJL3y14wXQjGDrmNlQwX96Ty5sOTAkvT40V3tEOfEwfIFx5KH30XcrqAFynWpToQUZJbkaz4OpvWyM0JEcwXPKZ4SKjeX7M5EzxkuPOR0PZwuRMiHynV1CfOEcLpR%2BkWcI%2BfwP5RyGVxfLM7b2t5v6a8v10XYXMHqbgUSkbTprU7Ntzfuqd9vodUYSa1M9X1GOL13PoLDJVQlPpmSvXRBGtjMk%2FhFvC4bLzFCfoZNRrDsWr9lIoQ4unXqizJXzShLw61CqFeMbcVwPAruzmEUoLHi%2Beq%2BQKZCY0txmrxZlSFSPpZlzFY%2FLWJMTSXpXi0vWsYHkmsF%2BvMnek7pir%2Bo7d1a6%2FBm1AKYXDnUCtK%2Ft%2FX7l7TNb%2Bnx%2BwLpoaEKcciBcUA2exMQ3kBrPIrDXgZwCbtwCMnyGMW1qVUPMgfDX8lGUFm6KEsotlWWVTMQZLaA3ZIJMVu1fKHljF6tYkhGOYwpCB4wzCEfqSjB1Zg5eVmYNrwKT4N40QouzEIHNaXu6T0qgek39NxLWQUQkBS9dI2A%2FiaAL6bKuKJmPMuv6zXf0M%2FbFvLGvPRyILuvIdKcJn1qPw%2BF5UU8GWzlJ0Y4BWMCV5mchnJIWaaYDghrCq5gBi7O4KU6CwMvHHVr9K6Yw0DmwNtRyGpO9qcLC1mN9OoSUhxmw2ykfXDwZJVkzCRJMTJEVyFqVJY6PXr5Sk%2B2qzEAaKsb%2F3d6%2FAXaJbB8uEJgQvSViFc3yBAQB9%2BppTicdLBf1cZ%2BU899Vf%2F%2BeH6L2ZtQFpl4pu%2BMQgQIsbDQsp5RTiPgdaKV764AQsbyzTml7p5AxwWPSu9CtTqgJ7h%2BRilWNZAy1wh4pcXLyTIdZW1g1oVXKG26cIjjSlAFeBUtNRXlLYeespnT%2BrP6mLyv7byov39Bf%2FsznfCP1u9XQrEyY1orR%2Ft4ZXcN8ir66A1t6Hf081hD6%2BmuTBYjQTBqLKs3ezMqAnBzQDCUd2GoELeK2cQkq1xzUro17cSApf9QJ0ZHZYW6P2WxINZRQvm3kirmoTPiKG51RaSxekqNKQ1QojHjuBGyO9J7EQiVCfDHRR1dj3s797T9V%2FXdfluPf00%2Ff6N3fjxqj1YpM3KBBhIjB2ZZxAlCSWvGUoF5vZpv86%2B0k4%2FpGGuH%2BKW%2B3UcopJrxubqo8lZT9d0wgTyXvA6QToriWa9q18Hcul2BxPUg%2B1NS6USadMfMHZF7E0R3YxprsfFx%2F%2F%2FKETBlaY6YRqEAue26nvDk0o3v8nkIh1icaJgLJijFMyAf%2BrGe%2B0P9%2B5jOyTf075u5fM8usYqAPl3AzoB0mD4m54MIRhKWKfpcl3F%2BVsx11B3CgWR6Ux%2F0ph5%2FW%2B%2F5il73PO0VPbZKwgRh2VHMFDCO5nA1YPljhWGmXxY%2FHRvM%2BiZPVdOIiMr0naCQ%2FUUuvJJKU08uzeHOkzUMhvgp5pKvtm0ZkgaT1oSyTQBzZQVpS0AniNYbKeS8n2yxLzZS%2BFTb3KoKv6qf7e8nIT5XeL5H1s6WqULyKHWN%2BTpWo1c41Vx3w8YJeM0pwFK9qd9u6nNe1C%2BPs%2Bx115%2FRyXpaZ%2ByhodvZ9huhAoWXreZFTXezBmUOgsVwLyxStdpVLRe4ctBJltao9VNiBQ6%2FMu4gx1IDr5twXyjYgruboajEeut8YCkjV15VRHEVC7BXce5qxb4gh6ukKnl66ob%2BdkPn7Ibe9%2Baq2nILWRS3IWRd0tu3A6FUjtUjts6DNcRQ49IaknksWLoq40n9Y4ejOLhm1Gww08v6rJf7ith2S3hGr922TvmK3vxIqEBBEV%2BM9Snr5xS%2Bd104hrChjhlLZ6PICvvvbKKnFvBI%2BSP2ySqu8iQXW4JXYp15SjlAjZgL1EIXdznykdSoqX67E0TccQ25OhYfqyGvP%2B0%2B8pmO8Vs6xspc6L%2BUUDbR%2FKnHXA7O7fhC1qstS7X3kRc0ZdxevGr18ISdD0gjuskqbKx0mv3kkN8tYDxUi4qGPQ%2FZ3WLg%2BbmlE3DLV5tc0mep6D%2FthMptq4%2F7UPFueSVt0RSKosp356IAbsft6vJODnIoOn0Hj7PA0UMEe1A5eBKV%2BfuqTjovAk2CGJ5C6WTJgYK6Ilj2WnyjqL2mal0Q7n79e3q8gd0bId7UuXmrQBQY5ugzBK8YkSUJGne1OMrhgvHmWV04R9%2BzVTwb7LvUxXYhfdVImXxtBSxstNBtZUIN8I3biAXRygc6MR9op14HTrhtNDp2QXtCj6%2Fqs7bjh91TBQVH5SxZn6nimfRnhnxpDs4BOtjhYS7dSostWlLwhKEBdQraiHnrtNDt3B%2FdJGL00dewD2eFEgslbD5LM6x1SwntjrawEeK2S9qdfas%2FaqtvqD1jbnLtSlPnsJAYxwV2vGclhY1agw48kmlANThf56%2BwBQvPK3%2BOZFltJIS%2BbtvL0KJtyHQROhjs5mXaNvLkn7XB5hF8sJUSUQLla7T%2FpSvKTS9z29LvALjtJZiFpvykuBlV3GkhKuZ1Odi4zSDRvL9O3K2CPR9feHLxVtTtko8Atygpy6BkGjtDfKxtvKfXbftJvrNxQz3eCPC9DB0JGEACW%2FexZHdIXUihbn1U3mNHim2oRYEIc9l0NP7yBqwF1Irzw4CMvLvsAl6wjjJuRrrewJMBErGkNYsckuCUm2OiCbaf3ixAeYv23bso43TXu9i6ohdvWzlf2jms0EO6KB7XCdiq2V0N26eERSUhcJjJ9wMaBWFXbkOckChqxSY9MACJADcsxknfg%2F592KG5LSTxjj70pL%2Ff7rz0Hb3%2FHvcdeSURBG7klbfIs1pRY8FUV4tWUfkhEknE3JzZtRvF9wzm07SVChNuyHqeO37EAacBA0KksBHdabEpEy0gE4aa7LKMHMqbKg0D63hHXbrVjahbBOgCc3af7e%2B5bRN91tUDIGLTqR7Q4ytjb0V%2FJ74eYwli5t%2B80ZLhfh%2Fobx9RTIf9WLv4PqgkW8du9zbe0fP39J6d2OI23dy2Zk5qC6cM0zGcdez01t8t68EehUS2t6W5ZIVgN7YK0U4npeEzYyfHaE1Uk2yBjBjYNO9jD8%2F%2FF2AADp%2F9%2FkGB8WMAAAAASUVORK5CYII%3D%22%3E%0A%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dxrange%3D%2210%22%20data%2Dyrange%3D%2210%22%20height%3D%2275%22%20width%3D%22430%22%20style%3D%22top%3A%20263px%3B%20left%3A%20442px%3B%20z%2Dindex%3A%206%3B%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAAa4AAABLCAMAAAAf1ZMtAAAAA3NCSVQICAjb4U%2FgAAAAXVBMVEX%2F%2F%2F%2BznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW%2BznXGznW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2F%2F%2F%2FyJE7v%2F%2FIu4iRP8iRP%2F%2FEcz%2FM%2F%2F%2F%2FyJ3d4iqu8zd%2F%2F%2F%2Fd4iqu%2B7u7u4RESJEmarM3f8iMzNEVXeImZmqu7u7u7vMzN3d7u7u7v%2F%2F%2FxEREdqVUEYAAAAJcEhZcwAACxIAAAsSAdLdfvwAAAAcdEVYdFNvZnR3YXJlAEFkb2JlIEZpcmV3b3JrcyBDUzQGstOgAAAUrUlEQVR4nO1dC0MTVxbeMDNOrGQmEUgIECCKiooFQeUhKj62iI%2Buimhti692pbi2dq2P2tb2r%2B99nce9MwNJVIJdDiTzzGTuN9%2F5znfvjPiPf2z7%2BPe%2Bdp%2FBpxX%2FPv2fdp%2FCpxU7gDUZO4A1GTuANRk7gDUZT07%2Fcnvo9cr6artP5BOJtdeX9vZdGhw6NPhyB7LN4931vX17%2B%2FokYkODhx7sOLJN4i%2BJl4pLg4NDg0PnF9p9Rts7Fgy%2F%2BjRiIi8ftPuUtnesH9%2BrEZOTQYnY0Fq7z2k7x%2BLxvX0Csr3HJWp7Lw0NHRoafL0jY9mxLsXreB%2B8SYINDu2Uyux4LRX%2FeN%2Fx4zovv5BJObijYpmx8IWKQxD%2FUvGm3ae1bePi08ePe3sfPybAulXcmm%2F3mW3XWJRqL0OL%2Ft4vhNsXsaP6WfFOar4qkyr6vhhS5rXdp7WNQzvWPqn4ErEhJfor7T6rbRy3dbeoT7PskmCXiMvtPqttHIt3Z5TH1zEzMyg59le7z2o7xy9vtdxL1C69eiUB%2Bz%2B0YdPz383N3bpy5cr98zoevXn08MWLhw9%2Fui9WXvlhbm563lTCp2%2BPHzd49Q2%2BfSU0%2F%2FWf7T35LYz5i3O37j%2B%2FG0d%2Bf6VDRtjB48DZXRhRVB%2B4%2B%2BLZlan%2FvtWeQiA2OHRCMOz%2FomO07%2BKtpz%2F%2FGkccJwOWnIQIXMhBU3G087UwX%2BVyLMOrHvrb4zU9d%2Bvqr7FfQR6FOA0JrpBtrRBmJQlYKe7VEfd61d7z7W7Qx4yLt652x9EFCw787WAQhrANaHdWoyXiZOeuOFZoife%2FM2ACrIlyP4fK0qzQAszBTsVZSMldKht7dUr2lkuPlifb3bgPHfuePP017udcCm3NSgAU2pwzeta%2Fq37y9z9u1no1XDIl47JK1UfLs%2B1u5AeLfWeu1nJJTiUByQi248mbN2%2F%2BcWS8psCSqHUKhmEdvbb2d%2BiDP7ka51JajyJFW0KiV8j3gfew4%2BbN04X8kZFir4JLMcyLJ4apgpYeLX3amE3%2FcLcfWstSzyWXpV8mKuKH5tTPqT%2Fy%2BXxxZCSv89GkpGDdKHMdpfOff7KYzT3MIQqivTL6ReT6c34uJ19%2BVI5UlCO%2FXC7ruahsVkLoRbG2HAjA8gKwWFVImZJC9Cfyp%2F%2B4eaokgjAba3fTW4mlN%2F0CHwmMbLIvMRLRryGrXKiYCCmIUqF0aWpZr9O7VTqL%2BaICTOdjr7IVE8V8%2FvTRU8OnZAyI%2BO23en3gpzPtbn9z8c1yJLC5YPBI2CqeiEzVcE0Y0hqmYrWiYljR1Ejlw%2BJuSbvCyM0Bya1SVBcx8NvAwKlfr3w6qfnnAxuVkL071ssW%2FzQzwXePC5CSvdqIqZQUwiYgu%2Bl0oXaV6j99324kGop3t1MkPcNNhIldWekMk%2Bj1%2Fy4B0%2FoV665Rt8IrXywMu4gJzO5OtRuNTWPxtp12YXrbQw5kAsTUaqpz2veUhvVqJ2YYJqM4kARMxN3tXTQnb3dYqmOlmpuShAq5e7dbae%2BhZvqrWvBlpawSYL%2Fb3NqFRXPgh4V2w5IVbjK6TU7jXjqV0uYRN%2FHR%2FkhrWPWGAWw8JSExTt1qNzKp8fU6B4L71DCRYkki4b58x1QgYXJB%2BLme7nJt%2FPffR%2BtZWBme3d2GLmMtgz1pTU%2FtSbpkSoxksJTlH%2B%2FnyNBsyVodfbnNKubi9fTWZ9gEzsMUkBvpmBNuLmCpHCvF97eR%2Bv%2B1niLpYeKdVQIqAwypkP264G7ke23ASjQtWeu3T16udTjhjEMkYHTUyAEomYwuQno33HIgya9SGudKPy%2B0GyoZ39zOUpctI91ZO%2FscqrE124Fkqy4TnIqXZk5dsnQkwnJkYUeY2mmi7S5CmXJWv9JuvNabYUImXpScIa1J8NHJVXbIswTJZqC9aKv2%2F%2BkUx7TIqn7ppTAMzS9hmVkzQ%2FiEULHG483F9uG1aLEjzSWkN3dz2xBativ1cxbdeN6B4Ce1TC9GbTP%2Ba851phzMUqWNANpwU5iGG7v1e5ZgKSVdrFUNBKL324OXK18diZalAoayllYO4ICpRyES84xVrwMN6FeJoHveDrxuu21JX3A0jFdGO5%2BzInTdRkjAIeQVCYaViClwsU1tkH4u96HTPJsPDd8xSlsbgpYxxBhUuGojZqVh%2BOUWI7ZwvdlC1kikpGiDClnZMCPbj9jC9Q5KlA6SnSyrGtqk2SBrM3HM3k0i2IyvAMS2ErDrvAEWPDZWYWqXKdl6W8SdLXiERFbTlx5wiFRyZ0rJQZ8tfO5nJdU2WLMND2dZZc9dkbgMWR3O%2FmTelZKosXk5ebZVeD1IRSixziZEkhfpaLt11D50aukISfNT1KrE%2FYS9fWlr8FpHIbYqYoe72EAkiLXhAbK7TWGGTm3izUpbMnixukGr2pWXZwGeJvOy9M3Hx%2BvrClxecEJ4uZM4JnxTYtOG4xjpkTQpYRZem8ajjw%2FYS6t1WUmZDVuWlr1Pya1YQKXKlbMdN35o4X83OTm5qF%2BLk4vi94Fsc0UzrFLpqByoHBChHsRRs%2Bq9olao1WrxQn9FPsqjHncSczrUXL96Bkr9Vvpz6ske9StftdHRHvEjQ75P1B7XMmLipIjukypO1QbskMu12sApNVeDdXUTv93%2FPBHvo2x39GNKfs43z3TpiHxc9tWPnvi%2Bfu7LLOtdc7552MlsMQc0G9VCBBvMjvow3YHneYH6kVMvCAI9xRVqRi8Faqv5AG40n8C9vIAtsb0DOKaa%2Fvc9CIbt81ljJTBq2WeIqXb6gK0Fp8%2BOksshmrA%2FAk1IqjU90HYLMY8BEcDqgBqtNuoVgKjBxuyl8fVclIMAVgTV1gFbVW2LWEuoPZxjRAzebp%2Bv83MMKAMX4seZitET2KzwGIUYgzRAQcBJ4xAOYCJsGMSGuMA08V79rmXA1oEu2A5fE0yuiNgm4gjSiNCVOZcjUvo%2B7acTUrOW4apePYxc1CTOEVxDOzE%2BJvKP75FIVITe86pzLQO2AnQyVMEkguTEzNITBydb5wBgH5IR3hFwHzMeGBZQ4zBlHBCRVQRMgGARDCiGsArz0OPfIH%2BqrY9h3wGQGHlyvM0cH2sf1nYHSVUHUOsiJzMRUl8CZlOBpU1gsQbzLyDZI9AshNkmyErYkaZXW8XrXRIqyB4f1Rp2iajZFgcpB%2FFgzgJlNV0LsTDqMXVnOHgWmYxied2xLN39Fy5c%2BOc%2FL3Q2EPxI%2BiIgA1%2B1CtiaaVwE4sPUzKIUJi3DgSkV0I3A9sFSRFg%2BuD9R4I9yDnGSEaEgwcTMKMM%2B%2Bmzz6OTIswoiX9VWBxfXc1bwksj5ZnPFKXdsQddbKrDioxEDk%2BirdxhFqCzNDizAwEUFVfZ9DQEG%2FoTlIyxUW%2F2HSytcWVywInjLgfNkdAIUrKQjAGGGXEYS3NwoShJLQKvIsTZ6XkRXsUGGsXrCDiRVv1Wvf4dzhzkI34fciohqJrkiqKjQfqyrmIc%2Bw5TvAplpIB5lZQ5duOXu0VLIaUx%2BsZyF0sjIns7OPYeBYWgo0PSaL%2Fm8Nbwm2%2Bhateg341onkKW%2BZlghL3%2Fy%2BUKhoJ%2Fll289Pd3dAWNYwrWqL2ixc7RGOqRiw56fDSqlF2LF0DS9S8xim4yw143Gen6mPxN0G5H0gWEFCVChWDCPpecVegKvHg2YXX3Rm%2BmcbA2wdZswKZUfCJdjswllsvZitcBUYF0JCF3gm3%2FD8hBO5afeHyj2DfgGHwEr5PVvoaiIJkETgHUzwAJ%2BBTxjOPbsCRZaAmwlu9uSUgkBF2IVdKNA6ejjvsNLNk%2Bw3fBYojAPwS0FcEK%2BRXhdkGH5okRJZ6aCrICAfbYnNYxHa%2B0R4shQwE0qn6sV5RVAQIzjCPHEY3XRZh4b2JCAUQ%2FaUIr8GIxRGNmRrazjeTCG6XTUUibJ1tPd0%2B2dOzI%2Bvof6Suj%2F1cEUYC11jiZt7mxFbwg79jKqHrVAZwqPw2ZyGKkxEZfrcVm81ePx8XNHjiit16AVJbkAMK1hafTCY3lPWwFsTZ%2F7xx6UyMzuwE2UTmb3SauxNHTDIaJYM6xg4MoX1T%2FfUpBJhgUjR86d27NBdnveL60Atu5zVCR0AJ7VZM4lH6yERa%2Bcb61ixZF9Xm%2FjV6cKHW2LaC7DaFKN63Ec1%2BU%2F6j0iCAYM00ABcErDRkR0BjAyZncc3qNz9DKjIVThIN8%2BzoB1p40J8gw6NaxfrmZ050j%2Bc%2Bd4RDFMOQmslHnDMFYls21L9VgLgPnAq5yl5BuZc%2BIeS9yIOGXLIB4cP8A1X2gYXn3o72Wbc7kigotlRL8A1lVqmHYVOiWh8w19Lxy8xi9spXO0SPbbmHs0A1xzyI%2BB4rMEBcOmIfFpN%2FsoNFyBn5Apye1EABYVRvBxXNBDAGO4kAYwJV0mKw3TGGAeaVZyILKVMrm2NeaBV1ud7UC2qmserBzkK0xrJ%2BCCQNcoTy6sqB1%2FgbpGHh6akRgdSwtjiA9QpyJqlaVdDClX5p3sopLgI8c4oFY6A6ROQbTHUCGB0KSJn244ETKu%2BlUg3WcMs8ByR3dPNA%2FYSwWUsgNRAoacGeWzeEdo%2Bh8CbDh5yBp39BVKG7ZzFL47AlthOpAF2aPUmFFf0gYbq6RRgObL5DfUCjaqh0yhhjntlaOCPmqWbRrAn1rJrYsCLwZ6n4hreoAMYz7fI0LojXAB2GgF2n2dnXkrJbFA8tEKvara9D9%2FWH2fm9Y5BiiyDzfZGZgxdBHFVops5AGQJ2VTT4BhEqIi2Vc5dMFsBRNAGmpDvWz6r6tcdrOwdTFKHIgN3WbfRo8Sl52Pr3o4JMaUe8CcETFMewo1WFHEviSlpAbHtsS6s9XZdOfowZbkHfHV50jKtygj7xjpiHt67YTBGzVMm1UYrFCAQUpalhj7XuBWWugc3SE8GFJIgchHs4D%2BymxkyYuOAcoHpaXPduYZDx%2BNYp6CODLKRw0Dt7sU1OXfNeIDiIUC2HxjXhVgR8blaAVLSNIxGGbzmh1D%2FHoryZRjltfAF%2FnRRoMULjWUIgVV%2BVeg6qJHKbuS4wU15Jo3Bsx0xUnDiExYUvg3BtPNAbZKNsHp1WQ8a2OzkTjjs%2FJqPu4r0Ih8ZO4ZxcoxoQEko%2Fs6aPxZYQjknSN1GHD6haIeyjdjrmpMH2zFZy701gUImu4cXUYgGC6MArSIKWYTxgKOSqCV3yxd2f6GfxHIFk7QUSQNumlnLVLesYwaVtAWjPrfajxM8m%2BP3XtXs5xhnU12jlYwnSKGFruFhGzzuVTZXUurSjDjQXhnyJ2clAEiZwDxsDWIYQ9lTJTr5Tiu18bH5fAOqL2imevDPrNT%2FDA%2FjMrwJjtHdzZvUQpZLCh84JXZEe9hyk10Q5M%2BbPUVclGaUgX8STAiGIA6qhjm2zdBwL0WdF9S2Ipz546oIerAKilYefVbc52jdzlLV3AkYQuLZgSApIp%2FogqofaryTy6X6wOCYefOQfcRiSYLJe8aBUz3vUTRbK5ztIqXH0pji2M0CCISUm%2Fa%2FGGxOMkwbs2hCFhjNOYBC%2Bp8mxtHaMRkSvbgeBjdC2Z9VQSsqc7ROjSXewnOK1vDk2Q0295jpLaMzosKv2kejVkwF6s2lNX3QJXETIRBnoLVl2QpSCMiWIibK5MrCfXa6JYryRYg5TMq0udhH8tR4Ed4JVWAMfI4t1zZ6IKHKKrOkb5MhmFF6EkWjK0oJAYQvcwht%2BYesLhjTh1yiz%2BGZLiTs0I7AaZihoZcwQibRp7JKyO1PDKYAJCzAMlkxhAjlpJF8K%2FCixXZbbZO9nniL9o6saqZByzeNezHuUtgEm7hyKYGzQhxz7YtdfBcrh%2F3sMPtcYqp16g6ELvzbYiFOqaqJGmYxyMgLqucbAKwtVbdJiUlFgiGL7MW7Eh2CcZ6EvMhF3SZSbeJQidfVXUEdPr0LIrWsXyRj7hCkmNusuyXx2ri6XN49JDyCaVnS4Z25DRubmjH6JjKDEpJa2gnRcPotkCAagbaWH3SOGArQC5UGdvGEolo5kM%2FZRdjnrHbbUzCGLlYoYsZw%2FJ47xsHeqzOt3Vkqi6I4s9TU98fW2gMMGwZEcnpO3LKWcnILYb5HKamhqex%2B%2BcxFUHkFZkMrAZcfkTU5BGoL6kFrADPo%2BRt0bcPx%2B5EKbJWR7t27%2B7q6vpq%2F%2F6Dl6fGvp%2FdxMm%2Bm5ycWltbW19fP7%2By8qbceC75SDzcaJdKFEffvSjEYl8wjCSMyj4jQmounZQf5k8gFtHvqyEeAswhmIxqtXpCxL3Ro8MiugReKsxULAvsLh9slHf7ZicnV9fWlpfXH1w7%2F7IcWdXzQz%2BIImZj3rmzPBnhlxjoF2Uy5%2BcsW0EPohStu0ZVFSdmZmaOHj06fHS4a3h4NyCEWCFaFnLyTWIneXes8R7U%2FPzk6urq5eXlB9eunZd%2F3h2KJ2YVKRdLN7YOIaO90abkYoSKOyaQLtJ%2FrALaCzDAlNYrhp0WMT4%2BPjLydmbm3r0bXvXGqKQQA6JLTbrMbFcSpi5rxZf79z87eFCQTbCtCcjsWJie%2Fl4guLy8%2FPzatbsCwTJPMSaKDrPUcvLWUUyJxwyEw6jkrSP5vIDWMImPiBOCP4pAXTYCLn0ALURPwgY7vJAAXT44NjU2e2wzLWs59n03Pz03tbp0ZfnZj9fO1%2BJYkLCJznscEHcCpshpD1igAM2cuDc8UTtVlSAZ3eF4dNlM6epymQOxf%2F%2F%2BKwcPLo2NjR2bbd9%2FzzI9P31x7sza0tLy8x9%2FrA30qjT2UeQgMY3dH8BETNp9BU%2B1%2Bkoo0D2pQEKgh5EYu52USglLzrs0QDLDxkQtPPZ12wDaLPZ9Nz175szc0tLSsx%2Bff1mrDcSghJJ%2BNV4bg2qgCCQVWifYbrfNkEpdu51UA11ia74yEiQAOja7BX%2BK4WPF%2FPT8k7kzt35Yuv%2Fz84c9J17NnHh1T%2BNjANLMAf50ucg4DCIJAo0em%2Fq2dY3e7jHboNykpZrIsPsHLwsJmjo228qzhJ9k7OOJlrBDFphKoy8fXBNF7Njst%2B0%2B8bbFV1k8EhL0k9Jo6Ru%2F3b4avdWxH%2FllJEhk2Oy3f1sJev8QJmhMaHS7T6OB%2BB%2BC%2FKOr0h4pdAAAAABJRU5ErkJggg%3D%3D%22%3E%0A%0A%20%20%20%20%20%20%3Cimg%20alt%3D%22%22%20class%3D%22js%2Dplaxify%20position%2Dabsolute%22%20data%2Dinvert%3D%22true%22%20data%2Dxrange%3D%2275%22%20data%2Dyrange%3D%2230%22%20height%3D%2250%22%20width%3D%22116%22%20style%3D%22top%3A%20113px%3B%20left%3A%20762px%3B%20z%2Dindex%3A%204%3B%22%0A%20%20%20%20%20%20src%3D%22data%3Aimage%2Fpng%3Bbase64%2CiVBORw0KGgoAAAANSUhEUgAAAHQAAAAyCAMAAAC6RQ9kAAAAA3NCSVQICAjb4U%2FgAAABgFBMVEX%2F%2F%2F%2FkyZm1pIDexpr73qqnmnallnGnmnn33aqjlXn12anszpi7p4PUvZPu1aXPuo6tm3zr0aLfxZbNt4xxbWOUim6yn3l7c2NsaF2%2BrIStm3yom4C2o3v22KSznW%2BrnIGejGuqlm3ZxJZxbWN0bFvUvZPv0JvnzZ2MfmPArYq7p4PXvo7Qu5LFsoq%2BrIRsaWDx057ErYKznXCsmnKFe2qom4CPgWSMhG3Qu5Kck3OllnGjlXl7c2NzcGeJf217c2OJf23FsoqUim6%2BrISck3PArYp%2FeWl%2FeGWfknrGsIzArYrGsIyck3PNt4zXvo67p4Pr0aLQu5K7p4Omk2zfxZbZxJbErYL12anu1aWwm2753KfmzaHny5aMg3N%2FeWmfknqajnmUiXSMhG2Mg3OrnIGjlXmUim6UiXSMhG2EeGN%2FeGW1pICajHOFe2rGsIy7p4OVhme%2BrIStm3ynmnmejGuUim6VhmfUvZPQu5LNt4zexprPuo7GsIy7p4Oyn3mmk2w%2B%2FMV0AAAAgHRSTlMA%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FRP%2F%2F%2FyJ3%2FyIR7v9E%2F%2F%2F%2FRHe7%2FxEiu%2F%2F%2FRHfu%2F%2F%2F%2F%2FxH%2F%2F%2F%2F%2FIjNEVaqqzMwRESIzVXeIu8zdIiIzZmZ3d4iZqru7u7vM3d3u7u7%2F%2F%2F8RESIiIiIiMzMzMzMzM0RERFVVVWZmZmZmZnd3d4iIiIiIiOmar1cAAAAJcEhZcwAACxIAAAsSAdLdfvwAAAAcdEVYdFNvZnR3YXJlAEFkb2JlIEZpcmV3b3JrcyBDUzQGstOgAAAFzUlEQVRYheWXh3saRxDFvSzHHQsczUEKCFVkiINKFEW25RZFcVwjJFvNTu%2B99%2Bp%2FPfNmCwfcxYosf8n3ZcB3gjvv797sm9nl1KlHxNyjbngCMf7U%2FwU6929Al%2F5L6X3nq43f5ud%2Fuf3ZpScARXp%2FGB%2F68q1fD4IHYXP5TC73em731psnDYXS9dMDX729nVZBmkIpVc4hXr188tCLA9CfAiIqftM%2F1WwTda90otC5IeilbahkoYAG9Ocyiz1J6JDSNw41Kg0wvRTOTVC3HgvzwcbG7ZJrfoNKLx8qTms6IBxT%2BcPyY1JvHqgmxrhlPpPSq54rm21WyFyXZDzGGVC%2FOSby8jYP1KRBdq9Y6Dnvgrn8cwACZRc%2B4rklU8FXIZv4xvGg20qLeEDUPS576kjnfAN9D5cUpxZYfeJsa6m7x2J%2BCSIkBCFV%2FZaFWqVbSrtI6dwq7SjODc9q7liFc2Dmyzw6EtxP71IjDKkdNFUzRDT5tkDBUUobOLd3VND46urqjQZi6mYYlsvl18oIQbE3T1ERUkiEwEngjIOsdrvdgrQx%2ByzHt6c5xuil3wlbgBJGEGY0Gk84hP4k%2Bidh%2BPxnPnWkGIuH2tG0AIvQWAsXRqFRiy%2BOxkyE2oGlyd%2BwPP1IfeE6wSeh9B%2FnmKB5sZjJZjNeDGuh6lPUk6BTFiVdIqWFWqR0avsZZ2g1m6FXDLRYoQuZzEQSVESsaU%2Fmi7JyEepTwE0%2BVRBaaYFGzmYnYqCyhku11PUE9zrvGJ3WREKG6HFK2TVFVyadU1QrZwGVkENDx0AXAa0nKG1EjCP7J6GhKtrfbc8LSKnQ0BryW4%2BDVmm2s36yewct5GZXitB2HT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width="100%" /></p>
</div>
<div id="weighted_posteriors" class="section level2">
<h2>Averaging posteriors</h2>
<p>Similar to how we can average evidence for a predictor across models, we can also average the <strong>posterior estimate</strong> across models. This is useful in situations where Bayes factors seem to support a null effect, yet the <em>HDI</em> for the alternative excludes the null value (also see <code>si()</code> described above).</p>
<p>For example, looking at Motor <em>Trend Car Road Tests</em> (<code>data(mtcars)</code>), we would naturally predict miles/gallon (<code>mpg</code>) from transition type (<code>am</code>) and weight (<code>wt</code>), but what about number of carburetors (<code>carb</code>)? Is this a good predictor?</p>
<p>We can determine this by comparing the following models:</p>
<div class="sourceCode" id="cb46"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb46-1"><a href="#cb46-1" aria-hidden="true" tabindex="-1"></a>mod <span class="ot"><-</span> <span class="fu">stan_glm</span>(mpg <span class="sc">~</span> wt <span class="sc">+</span> am,</span>
<span id="cb46-2"><a href="#cb46-2" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> mtcars,</span>
<span id="cb46-3"><a href="#cb46-3" aria-hidden="true" tabindex="-1"></a> <span class="at">prior =</span> <span class="fu">normal</span>(<span class="dv">0</span>, <span class="fu">c</span>(<span class="dv">10</span>, <span class="dv">10</span>), <span class="at">autoscale =</span> <span class="cn">FALSE</span>),</span>
<span id="cb46-4"><a href="#cb46-4" aria-hidden="true" tabindex="-1"></a> <span class="at">diagnostic_file =</span> <span class="fu">file.path</span>(<span class="fu">tempdir</span>(), <span class="st">"df1.csv"</span>),</span>
<span id="cb46-5"><a href="#cb46-5" aria-hidden="true" tabindex="-1"></a> <span class="at">refresh =</span> <span class="dv">0</span></span>
<span id="cb46-6"><a href="#cb46-6" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb46-7"><a href="#cb46-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb46-8"><a href="#cb46-8" aria-hidden="true" tabindex="-1"></a>mod_carb <span class="ot"><-</span> <span class="fu">stan_glm</span>(mpg <span class="sc">~</span> wt <span class="sc">+</span> am <span class="sc">+</span> carb,</span>
<span id="cb46-9"><a href="#cb46-9" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> mtcars,</span>
<span id="cb46-10"><a href="#cb46-10" aria-hidden="true" tabindex="-1"></a> <span class="at">prior =</span> <span class="fu">normal</span>(<span class="dv">0</span>, <span class="fu">c</span>(<span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">20</span>), <span class="at">autoscale =</span> <span class="cn">FALSE</span>),</span>
<span id="cb46-11"><a href="#cb46-11" aria-hidden="true" tabindex="-1"></a> <span class="at">diagnostic_file =</span> <span class="fu">file.path</span>(<span class="fu">tempdir</span>(), <span class="st">"df0.csv"</span>),</span>
<span id="cb46-12"><a href="#cb46-12" aria-hidden="true" tabindex="-1"></a> <span class="at">refresh =</span> <span class="dv">0</span></span>
<span id="cb46-13"><a href="#cb46-13" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb46-14"><a href="#cb46-14" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb46-15"><a href="#cb46-15" aria-hidden="true" tabindex="-1"></a>BF_carb <span class="ot"><-</span> <span class="fu">bayesfactor_models</span>(mod_carb, <span class="at">denominator =</span> mod, <span class="at">verbose =</span> <span class="cn">FALSE</span>)</span>
<span id="cb46-16"><a href="#cb46-16" aria-hidden="true" tabindex="-1"></a>BF_carb</span></code></pre></div>
<pre><code>> Bayes Factors for Model Comparison
>
> Model BF
> [1] wt + am + carb 0.811
>
> * Against Denominator: [2] wt + am
> * Bayes Factor Type: marginal likelihoods (bridgesampling)</code></pre>
<p>It seems that the model without <code>carb</code> as a predictor is <span class="math inline">\(1/BF=1.2\)</span> times more likely than the model <em>with</em> <code>carb</code> as a predictor. We might then assume that in the latter model, the <code>HDI</code> will include the point-null value of 0 effect, to also indicate the credibility of the null in the posterior. However, this is not the case:</p>
<div class="sourceCode" id="cb48"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb48-1"><a href="#cb48-1" aria-hidden="true" tabindex="-1"></a><span class="fu">hdi</span>(mod_carb, <span class="at">ci =</span> .<span class="dv">95</span>)</span></code></pre></div>
<pre><code>> Highest Density Interval
>
> Parameter | 95% HDI
> ----------------------------
> (Intercept) | [28.10, 40.09]
> wt | [-5.48, -1.72]
> am | [-0.81, 5.86]
> carb | [-2.04, -0.38]</code></pre>
<p>How can this be? By estimating the HDI of the effect for <code>carb</code> in the full model, we are acting under the assumption that this model is correct. However, as we’ve just seen, both models are practically tied. If this is the case <strong>why limit our estimation of the effect just to one model?</strong> <span class="citation">(Bergh, Haaf, Ly, Rouder, & Wagenmakers, 2019)</span>.</p>
<p>Using Bayesian Model Averaging, we can combine the posteriors samples from several models, weighted by the models’ marginal likelihood (done via the <code>bayesfactor_models()</code> function). If some parameter is part of some of the models but is missing from others, it is assumed to be fixed a 0 (which can also be seen as a method of applying shrinkage to our estimates). This results in a posterior distribution across several models, which we can now treat like any posterior distribution, and estimate the HDI.</p>
<p>In <code>bayestestR</code>, we can do this with the <code>weighted_posteriors()</code> function:</p>
<div class="sourceCode" id="cb50"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb50-1"><a href="#cb50-1" aria-hidden="true" tabindex="-1"></a>BMA_draws <span class="ot"><-</span> <span class="fu">weighted_posteriors</span>(mod, mod_carb)</span>
<span id="cb50-2"><a href="#cb50-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb50-3"><a href="#cb50-3" aria-hidden="true" tabindex="-1"></a>BMA_hdi <span class="ot"><-</span> <span class="fu">hdi</span>(BMA_draws, <span class="at">ci =</span> .<span class="dv">95</span>)</span>
<span id="cb50-4"><a href="#cb50-4" aria-hidden="true" tabindex="-1"></a>BMA_hdi</span></code></pre></div>
<pre><code>> Highest Density Interval
>
> Parameter | 95% HDI
> ----------------------------
> (Intercept) | [29.03, 42.43]
> wt | [-6.66, -2.14]
> am | [-2.80, 5.04]
> carb | [-1.69, 0.00]</code></pre>
<div class="sourceCode" id="cb52"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb52-1"><a href="#cb52-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(BMA_hdi)</span></code></pre></div>
<p><img 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" width="100%" /></p>
<p>We can see that across both models under consideration, the posterior of the <code>carb</code> effect is almost equally weighted between the alternative model and the null model - as represented by about half of the posterior mass concentrated at 0 - which makes sense as both models were almost equally supported by the data. We can also see that across both models, that now <strong>the HDI does contain 0</strong>. Thus we have resolved the conflict between the Bayes factor and the HDI <span class="citation">(Rouder, Haaf, & Vandekerckhove, 2018)</span>!</p>
<p><strong>Note</strong>: Parameters might play different roles across different models.</p>
<p>For example, the parameter <code>A</code> plays a different role in the model <code>Y ~ A + B</code> (where it is a <em>main</em> effect) than it does in the model <code>Y ~ A + B + A:B</code> (where it is a <em>simple</em> effect). In many cases centering of predictors (mean subtracting for continuous variables, and effects coding via <code>contr.sum</code> or orthonormal coding via <a href="https://easystats.github.io/bayestestR/reference/contr.orthonorm.html"><code>contr.orthonorm</code></a> for factors) can in some cases reduce this issue.</p>
</div>
</div>
<div id="appendices" class="section level1">
<h1>Appendices</h1>
<div id="testing-contrasts-with-emmeans-modelbased" class="section level2">
<h2>Testing contrasts (with <code>emmeans</code> / <code>modelbased</code>)</h2>
<p>Besides testing parameter <code>bayesfactor_parameters()</code> can be used to test any estimate based on the prior and posterior distribution of the estimate. One way to achieve this is with a mix of <code>bayesfactor_parameters()</code> + <a href="https://cran.r-project.org/package=emmeans"><strong><code>emmeans</code></strong></a> to <a href="https://easystats.github.io/blog/posts/bayestestr_emmeans/">test Bayesian contrasts</a>.</p>
<p>For example, in the <code>sleep</code> example from above, we can estimate the group means and the difference between them:</p>
<div class="sourceCode" id="cb53"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb53-1"><a href="#cb53-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(emmeans)</span>
<span id="cb53-2"><a href="#cb53-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb53-3"><a href="#cb53-3" aria-hidden="true" tabindex="-1"></a>(group_diff <span class="ot"><-</span> <span class="fu">emmeans</span>(model, pairwise <span class="sc">~</span> group))</span></code></pre></div>
<pre><code>> $emmeans
> group emmean lower.HPD upper.HPD
> 1 0.79 -0.48 2.0
> 2 2.28 1.00 3.5
>
> Point estimate displayed: median
> HPD interval probability: 0.95
>
> $contrasts
> contrast estimate lower.HPD upper.HPD
> 1 - 2 -1.47 -3.2 0.223
>
> Point estimate displayed: median
> HPD interval probability: 0.95</code></pre>
<div class="sourceCode" id="cb55"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb55-1"><a href="#cb55-1" aria-hidden="true" tabindex="-1"></a><span class="co"># pass the original model via prior</span></span>
<span id="cb55-2"><a href="#cb55-2" aria-hidden="true" tabindex="-1"></a><span class="fu">bayesfactor_parameters</span>(group_diff, <span class="at">prior =</span> model)</span></code></pre></div>
<pre><code>> Bayes Factor (Savage-Dickey density ratio)
>
> Parameter | BF
> -----------------
> 1 | 0.287
> 2 | 21.37
> 1 - 2 | 1.26
>
> * Evidence Against The Null: 0</code></pre>
<p>That is strong evidence for the mean of group 1 being 0, and for group 2 for not being 0, but hardly any evidence for the difference between them being not 0. Conflict? Uncertainty? That is the Bayesian way!</p>
<p>We can also use the <code>easystats</code>’ <a href="https://cran.r-project.org/package=modelbased"><strong><code>modelbased</code></strong></a> package to compute Bayes factors for contrasts:</p>
<div class="sourceCode" id="cb57"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb57-1"><a href="#cb57-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(modelbased)</span>
<span id="cb57-2"><a href="#cb57-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb57-3"><a href="#cb57-3" aria-hidden="true" tabindex="-1"></a><span class="fu">estimate_contrasts</span>(model, <span class="at">test =</span> <span class="st">"bf"</span>, <span class="at">bf_prior =</span> model)</span></code></pre></div>
<p><strong>NOTE</strong>: See the <em>Specifying Correct Priors for Factors with More Than 2 Levels</em> section below.</p>
</div>
<div id="contr_bayes" class="section level2">
<h2>Specifying correct priors for factors</h2>
<p>This section introduces the biased priors obtained when using the common <em>effects</em> factor coding (<code>contr.sum</code>) or dummy factor coding (<code>contr.treatment</code>), and the solution of using orthonormal factor coding (<code>contr.orthonorm</code>) <span class="citation">(as outlined in Rouder, Morey, Speckman, & Province, 2012, sec. 7.2)</span>.</p>
<p><strong>Special care should be taken when working with factors with 3 or more levels</strong>.</p>
<div id="contrasts-and-marginal-means" class="section level3">
<h3>Contrasts (and marginal means)</h3>
<p>The <em>effects</em> factor coding commonly used in factorial analysis carries a hidden bias when it is applies to Bayesian priors. For example, if we want to test all pairwise differences between 3 levels of the same factor, we would expect all <em>a priori</em> differences to have the same distribution, but…</p>
<p>For our example, we will be test all <strong><em>prior</em></strong> pairwise differences between the 3 species in the <code>iris</code> dataset.</p>
<div class="sourceCode" id="cb58"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb58-1"><a href="#cb58-1" aria-hidden="true" tabindex="-1"></a>df <span class="ot"><-</span> iris</span>
<span id="cb58-2"><a href="#cb58-2" aria-hidden="true" tabindex="-1"></a><span class="fu">contrasts</span>(df<span class="sc">$</span>Species) <span class="ot"><-</span> contr.sum</span>
<span id="cb58-3"><a href="#cb58-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb58-4"><a href="#cb58-4" aria-hidden="true" tabindex="-1"></a>fit_sum <span class="ot"><-</span> <span class="fu">stan_glm</span>(Sepal.Length <span class="sc">~</span> Species,</span>
<span id="cb58-5"><a href="#cb58-5" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> df,</span>
<span id="cb58-6"><a href="#cb58-6" aria-hidden="true" tabindex="-1"></a> <span class="at">prior =</span> <span class="fu">normal</span>(<span class="dv">0</span>, <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">1</span>), <span class="at">autoscale =</span> <span class="cn">FALSE</span>),</span>
<span id="cb58-7"><a href="#cb58-7" aria-hidden="true" tabindex="-1"></a> <span class="at">prior_PD =</span> <span class="cn">TRUE</span>, <span class="co"># sample priors</span></span>
<span id="cb58-8"><a href="#cb58-8" aria-hidden="true" tabindex="-1"></a> <span class="at">family =</span> <span class="fu">gaussian</span>(),</span>
<span id="cb58-9"><a href="#cb58-9" aria-hidden="true" tabindex="-1"></a> <span class="at">refresh =</span> <span class="dv">0</span></span>
<span id="cb58-10"><a href="#cb58-10" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb58-11"><a href="#cb58-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb58-12"><a href="#cb58-12" aria-hidden="true" tabindex="-1"></a>(pairs_sum <span class="ot"><-</span> <span class="fu">pairs</span>(<span class="fu">emmeans</span>(fit_sum, <span class="sc">~</span>Species)))</span></code></pre></div>
<pre><code>> contrast estimate lower.HPD upper.HPD
> setosa - versicolor -0.017 -2.8 2.7
> setosa - virginica -0.027 -4.0 4.6
> versicolor - virginica 0.001 -4.2 4.5
>
> Point estimate displayed: median
> HPD interval probability: 0.95</code></pre>
<div class="sourceCode" id="cb60"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb60-1"><a href="#cb60-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(<span class="fu">stack</span>(insight<span class="sc">::</span><span class="fu">get_parameters</span>(pairs_sum)), <span class="fu">aes</span>(<span class="at">x =</span> values, <span class="at">fill =</span> ind)) <span class="sc">+</span></span>
<span id="cb60-2"><a href="#cb60-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_density</span>(<span class="at">size =</span> <span class="dv">1</span>) <span class="sc">+</span></span>
<span id="cb60-3"><a href="#cb60-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">facet_grid</span>(ind <span class="sc">~</span> .) <span class="sc">+</span></span>
<span id="cb60-4"><a href="#cb60-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">labs</span>(<span class="at">x =</span> <span class="st">"prior difference values"</span>) <span class="sc">+</span></span>
<span id="cb60-5"><a href="#cb60-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme</span>(<span class="at">legend.position =</span> <span class="st">"none"</span>)</span></code></pre></div>
<p><img src="data:image/png;base64,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" width="100%" /></p>
<p>Notice that, though the prior estimate for all 3 pairwise contrasts is ~0, the scale or the HDI is much narrower for the prior of the <code>setosa - versicolor</code> contrast!</p>
<p><strong>What happened???</strong></p>
<p>This is caused by an inherent bias in the priors introduced by the <em>effects</em> coding (it’s even worse with the default treatment coding, because the prior for the intercept is usually drastically different from the effect’s parameters). <strong>And since it affects the priors, this bias will also bias the Bayes factors over / understating evidence for some contrasts over others!</strong></p>
<p>The solution is to use <em>orthonormal</em> factor coding, a-la <code>contr.orthonorm</code>, which can either specify this factor coding per-factor:</p>
<div class="sourceCode" id="cb61"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb61-1"><a href="#cb61-1" aria-hidden="true" tabindex="-1"></a><span class="fu">contrasts</span>(df<span class="sc">$</span>Species) <span class="ot"><-</span> contr.orthonorm</span></code></pre></div>
<p>Or you can set it globally:</p>
<div class="sourceCode" id="cb62"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb62-1"><a href="#cb62-1" aria-hidden="true" tabindex="-1"></a><span class="fu">options</span>(<span class="at">contrasts =</span> <span class="fu">c</span>(<span class="st">"contr.orthonorm"</span>, <span class="st">"contr.poly"</span>))</span></code></pre></div>
<p>Let’s again estimate the <strong><em>prior</em></strong> differences:</p>
<div class="sourceCode" id="cb63"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb63-1"><a href="#cb63-1" aria-hidden="true" tabindex="-1"></a>fit_bayes <span class="ot"><-</span> <span class="fu">stan_glm</span>(Sepal.Length <span class="sc">~</span> Species,</span>
<span id="cb63-2"><a href="#cb63-2" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> df,</span>
<span id="cb63-3"><a href="#cb63-3" aria-hidden="true" tabindex="-1"></a> <span class="at">prior =</span> <span class="fu">normal</span>(<span class="dv">0</span>, <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">1</span>), <span class="at">autoscale =</span> <span class="cn">FALSE</span>),</span>
<span id="cb63-4"><a href="#cb63-4" aria-hidden="true" tabindex="-1"></a> <span class="at">prior_PD =</span> <span class="cn">TRUE</span>, <span class="co"># sample priors</span></span>
<span id="cb63-5"><a href="#cb63-5" aria-hidden="true" tabindex="-1"></a> <span class="at">family =</span> <span class="fu">gaussian</span>(),</span>
<span id="cb63-6"><a href="#cb63-6" aria-hidden="true" tabindex="-1"></a> <span class="at">refresh =</span> <span class="dv">0</span></span>
<span id="cb63-7"><a href="#cb63-7" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb63-8"><a href="#cb63-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb63-9"><a href="#cb63-9" aria-hidden="true" tabindex="-1"></a>(pairs_bayes <span class="ot"><-</span> <span class="fu">pairs</span>(<span class="fu">emmeans</span>(fit_bayes, <span class="sc">~</span>Species)))</span></code></pre></div>
<pre><code>> contrast estimate lower.HPD upper.HPD
> setosa - versicolor 0.000 -2.98 2.67
> setosa - virginica 0.032 -2.73 2.81
> versicolor - virginica 0.003 -2.91 2.67
>
> Point estimate displayed: median
> HPD interval probability: 0.95</code></pre>
<div class="sourceCode" id="cb65"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb65-1"><a href="#cb65-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(<span class="fu">stack</span>(insight<span class="sc">::</span><span class="fu">get_parameters</span>(pairs_bayes)), <span class="fu">aes</span>(<span class="at">x =</span> values, <span class="at">fill =</span> ind)) <span class="sc">+</span></span>
<span id="cb65-2"><a href="#cb65-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_density</span>(<span class="at">size =</span> <span class="dv">1</span>) <span class="sc">+</span></span>
<span id="cb65-3"><a href="#cb65-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">facet_grid</span>(ind <span class="sc">~</span> .) <span class="sc">+</span></span>
<span id="cb65-4"><a href="#cb65-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">labs</span>(<span class="at">x =</span> <span class="st">"prior difference values"</span>) <span class="sc">+</span></span>
<span id="cb65-5"><a href="#cb65-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme</span>(<span class="at">legend.position =</span> <span class="st">"none"</span>)</span></code></pre></div>
<p><img src="data:image/png;base64,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" width="100%" /></p>
<p>We can see that using this coding scheme, we have equal priors on all pairwise contrasts.</p>
<p>There are other solutions to this problem of priors. You can read about them in <a href="https://solomonkurz.netlify.app/post/2020-12-09-multilevel-models-and-the-index-variable-approach/">Solomon Kurz’s blog post</a>.</p>
</div>
<div id="order-restrictions" class="section level3">
<h3>Order restrictions</h3>
<p>This bias also affect order restrictions involving 3 or more levels. For example, if we want to test an order restriction among A, B, and C, the <em>a priori</em> probability of obtaining the order A > C > B is 1/6 (reach back to <em>intro to stats</em> year 1), but…</p>
<p>For our example, we will be interested in the following order restrictions in the <code>iris</code> dataset (each line is a separate restriction):</p>
<div class="sourceCode" id="cb66"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb66-1"><a href="#cb66-1" aria-hidden="true" tabindex="-1"></a>hyp <span class="ot"><-</span> <span class="fu">c</span>(</span>
<span id="cb66-2"><a href="#cb66-2" aria-hidden="true" tabindex="-1"></a> <span class="co"># comparing 2 levels</span></span>
<span id="cb66-3"><a href="#cb66-3" aria-hidden="true" tabindex="-1"></a> <span class="st">"setosa < versicolor"</span>,</span>
<span id="cb66-4"><a href="#cb66-4" aria-hidden="true" tabindex="-1"></a> <span class="st">"setosa < virginica"</span>,</span>
<span id="cb66-5"><a href="#cb66-5" aria-hidden="true" tabindex="-1"></a> <span class="st">"versicolor < virginica"</span>,</span>
<span id="cb66-6"><a href="#cb66-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb66-7"><a href="#cb66-7" aria-hidden="true" tabindex="-1"></a> <span class="co"># comparing 3 (or more) levels</span></span>
<span id="cb66-8"><a href="#cb66-8" aria-hidden="true" tabindex="-1"></a> <span class="st">"setosa < virginica & virginica < versicolor"</span>,</span>
<span id="cb66-9"><a href="#cb66-9" aria-hidden="true" tabindex="-1"></a> <span class="st">"virginica < setosa & setosa < versicolor"</span>,</span>
<span id="cb66-10"><a href="#cb66-10" aria-hidden="true" tabindex="-1"></a> <span class="st">"setosa < versicolor & versicolor < virginica"</span></span>
<span id="cb66-11"><a href="#cb66-11" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
<p>With the default factor coding, this looks like this:</p>
<div class="sourceCode" id="cb67"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb67-1"><a href="#cb67-1" aria-hidden="true" tabindex="-1"></a><span class="fu">contrasts</span>(df<span class="sc">$</span>Species) <span class="ot"><-</span> contr.sum</span>
<span id="cb67-2"><a href="#cb67-2" aria-hidden="true" tabindex="-1"></a>fit_sum <span class="ot"><-</span> <span class="fu">stan_glm</span>(Sepal.Length <span class="sc">~</span> Species,</span>
<span id="cb67-3"><a href="#cb67-3" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> df,</span>
<span id="cb67-4"><a href="#cb67-4" aria-hidden="true" tabindex="-1"></a> <span class="at">prior =</span> <span class="fu">normal</span>(<span class="dv">0</span>, <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">1</span>), <span class="at">autoscale =</span> <span class="cn">FALSE</span>),</span>
<span id="cb67-5"><a href="#cb67-5" aria-hidden="true" tabindex="-1"></a> <span class="at">family =</span> <span class="fu">gaussian</span>()</span>
<span id="cb67-6"><a href="#cb67-6" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb67-7"><a href="#cb67-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb67-8"><a href="#cb67-8" aria-hidden="true" tabindex="-1"></a>em_sum <span class="ot"><-</span> <span class="fu">emmeans</span>(fit_sum, <span class="sc">~</span>Species) <span class="co"># the posterior marginal means</span></span>
<span id="cb67-9"><a href="#cb67-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb67-10"><a href="#cb67-10" aria-hidden="true" tabindex="-1"></a><span class="fu">bayesfactor_restricted</span>(em_sum, fit_sum, <span class="at">hypothesis =</span> hyp)</span></code></pre></div>
<pre><code>> Bayes Factor (Order-Restriction)
>
> Hypothesis P(Prior) P(Posterior) BF
> setosa < versicolor 0.51 1 1.97
> setosa < virginica 0.49 1 2.02
> versicolor < virginica 0.49 1 2.03
> setosa < virginica & virginica < versicolor 0.11 0 0.00e+00
> virginica < setosa & setosa < versicolor 0.20 0 0.00e+00
> setosa < versicolor & versicolor < virginica 0.20 1 5.09
>
> * Bayes factors for the restricted model vs. the un-restricted model.</code></pre>
<p><strong><em>What happened???</em></strong></p>
<ol style="list-style-type: decimal">
<li>The comparison of 2 levels all have a prior of ~0.5, as expected.<br />
</li>
<li>The comparison of 3 levels has different priors, depending on the order restriction - i.e. <strong>some orders are <em>a priori</em> more likely than others!!!</strong></li>
</ol>
<p>Again, this is solved by using the <em>orthonormal</em> factor coding (from above).</p>
<div class="sourceCode" id="cb69"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb69-1"><a href="#cb69-1" aria-hidden="true" tabindex="-1"></a><span class="fu">contrasts</span>(df<span class="sc">$</span>Species) <span class="ot"><-</span> contr.orthonorm</span>
<span id="cb69-2"><a href="#cb69-2" aria-hidden="true" tabindex="-1"></a>fit_bayes <span class="ot"><-</span> <span class="fu">stan_glm</span>(Sepal.Length <span class="sc">~</span> Species,</span>
<span id="cb69-3"><a href="#cb69-3" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> df,</span>
<span id="cb69-4"><a href="#cb69-4" aria-hidden="true" tabindex="-1"></a> <span class="at">prior =</span> <span class="fu">normal</span>(<span class="dv">0</span>, <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">1</span>), <span class="at">autoscale =</span> <span class="cn">FALSE</span>),</span>
<span id="cb69-5"><a href="#cb69-5" aria-hidden="true" tabindex="-1"></a> <span class="at">family =</span> <span class="fu">gaussian</span>()</span>
<span id="cb69-6"><a href="#cb69-6" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb69-7"><a href="#cb69-7" aria-hidden="true" tabindex="-1"></a>em_bayes <span class="ot"><-</span> <span class="fu">emmeans</span>(fit_sum, <span class="sc">~</span>Species) <span class="co"># the posterior marginal means</span></span>
<span id="cb69-8"><a href="#cb69-8" aria-hidden="true" tabindex="-1"></a><span class="fu">bayesfactor_restricted</span>(em_bayes, fit_sum, <span class="at">hypothesis =</span> hyp)</span></code></pre></div>
<pre><code>> Bayes Factor (Order-Restriction)
>
> Hypothesis P(Prior) P(Posterior) BF
> setosa < versicolor 0.49 1 2.06
> setosa < virginica 0.49 1 2.03
> versicolor < virginica 0.51 1 1.96
> setosa < virginica & virginica < versicolor 0.17 0 0.00e+00
> virginica < setosa & setosa < versicolor 0.16 0 0.00e+00
> setosa < versicolor & versicolor < virginica 0.16 1 6.11
>
> * Bayes factors for the restricted model vs. the un-restricted model.</code></pre>
</div>
<div id="conclusion" class="section level3">
<h3>Conclusion</h3>
<p>When comparing the results from the two factor coding schemes, we find:<br />
1. In both cases, the estimated (posterior) means are quite similar (if not identical).<br />
2. The priors and Bayes factors differ between the two schemes.<br />
3. Only with <code>contr.orthonorm</code>, the prior distribution of the difference or the order of 3 (or more) means is balanced.</p>
</div>
</div>
</div>
<div id="references" class="section level1 unnumbered">
<h1 class="unnumbered">References</h1>
<div id="refs" class="references csl-bib-body hanging-indent" line-spacing="2">
<div id="ref-van2019cautionary" class="csl-entry">
Bergh, D. van den, Haaf, J. M., Ly, A., Rouder, J. N., & Wagenmakers, E.-J. (2019). <em>A cautionary note on estimating effect size</em>.
</div>
<div id="ref-clyde2011bayesian" class="csl-entry">
Clyde, M. A., Ghosh, J., & Littman, M. L. (2011). Bayesian adaptive sampling for variable selection and model averaging. <em>Journal of Computational and Graphical Statistics</em>, <em>20</em>(1), 80–101.
</div>
<div id="ref-kruschke2010believe" class="csl-entry">
Kruschke, J. K. (2010). What to believe: Bayesian methods for data analysis. <em>Trends in Cognitive Sciences</em>, <em>14</em>(7), 293–300.
</div>
<div id="ref-morey_2015_blog" class="csl-entry">
Morey, R. D. (2015). <em>Multiple comparisons with BayesFactor, part 2 – order restrictions</em>. Retrieved from <a href="http://bayesfactor.blogspot.com/2015/01/multiple-comparisons-with-bayesfactor-2.html">http://bayesfactor.blogspot.com/2015/01/multiple-comparisons-with-bayesfactor-2.html</a>
</div>
<div id="ref-morey2011bayesinterval" class="csl-entry">
Morey, R. D., & Rouder, J. N. (2011). Bayes factor approaches for testing interval null hypotheses. <em>Psychological Methods</em>, <em>16</em>(4), 406.
</div>
<div id="ref-morey2014simple" class="csl-entry">
Morey, R. D., & Wagenmakers, E.-J. (2014). Simple relation between bayesian order-restricted and point-null hypothesis tests. <em>Statistics & Probability Letters</em>, <em>92</em>, 121–124.
</div>
<div id="ref-rouder2018bayesian" class="csl-entry">
Rouder, J. N., Haaf, J. M., & Vandekerckhove, J. (2018). Bayesian inference for psychology, part IV: Parameter estimation and bayes factors. <em>Psychonomic Bulletin & Review</em>, <em>25</em>(1), 102–113.
</div>
<div id="ref-rouder2012default" class="csl-entry">
Rouder, J. N., Morey, R. D., Speckman, P. L., & Province, J. M. (2012). Default bayes factors for ANOVA designs. <em>Journal of Mathematical Psychology</em>, <em>56</em>(5), 356–374.
</div>
<div id="ref-wagenmakers2007practical" class="csl-entry">
Wagenmakers, E.-J. (2007). A practical solution to the pervasive problems ofp values. <em>Psychonomic Bulletin & Review</em>, <em>14</em>(5), 779–804.
</div>
<div id="ref-wagenmakers2018SI" class="csl-entry">
Wagenmakers, E.-J., Gronau, Q. F., Dablander, F., & Etz, A. (2018). <em>The support interval</em>. <a href="https://doi.org/10.31234/osf.io/zwnxb">https://doi.org/10.31234/osf.io/zwnxb</a>
</div>
<div id="ref-wagenmakers2010bayesian" class="csl-entry">
Wagenmakers, E.-J., Lodewyckx, T., Kuriyal, H., & Grasman, R. (2010). Bayesian hypothesis testing for psychologists: A tutorial on the savage–dickey method. <em>Cognitive Psychology</em>, <em>60</em>(3), 158–189.
</div>
</div>
</div>
<div class="footnotes">
<hr />
<ol>
<li id="fn1"><p>Note that as the width of null interval shrinks to zero, the prior probability and posterior probability of the alternative tends towards 1.00.<a href="#fnref1" class="footnote-back">↩︎</a></p></li>
<li id="fn2"><p>For more, see <a href="https://philstatwars.files.wordpress.com/2020/09/richard_presentation.mp4">this talk by Richard D. Morey, minute 48</a><a href="#fnref2" class="footnote-back">↩︎</a></p></li>
<li id="fn3"><p><a href="https://doi.org/10.1016/j.jmp.2015.08.002">Robert, 2016</a>; <a href="https://doi.org/10.1080/01621459.1995.10476572">Kass & Raftery, 1993</a>; <a href="https://doi.org/10.1016/S0304-4076(00)00076-2">Fernández, Ley, & Steel, 2001</a><a href="#fnref3" class="footnote-back">↩︎</a></p></li>
<li id="fn4"><p><a href="https://arxiv.org/abs/1710.08162">Gronau, Singmann, & Wagenmakers, 2017</a><a href="#fnref4" class="footnote-back">↩︎</a></p></li>
<li id="fn5"><p>A model without predictor <span class="math inline">\(X\)</span> can be thought of as a model in which the parameter(s) of the predictor have been restricted to a null-point of 0.<a href="#fnref5" class="footnote-back">↩︎</a></p></li>
</ol>
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