https://github.com/cran/bayestestR
Tip revision: 68a979e69aa2a1e57017730e1397470d5614d216 authored by Dominique Makowski on 02 September 2021, 23:10:30 UTC
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<title>1. Initiation to Bayesian models</title>
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<h1 class="title toc-ignore">1. Initiation to Bayesian models</h1>
<div id="TOC">
<ul>
<li><a href="#loading-the-packages">Loading the packages</a></li>
<li><a href="#simple-linear-regression-model">Simple linear (regression) model</a>
<ul>
<li><a href="#fitting-the-model">Fitting the model</a></li>
<li><a href="#extracting-the-posterior">Extracting the posterior</a></li>
<li><a href="#describing-the-posterior">Describing the Posterior</a></li>
</ul></li>
<li><a href="#a-linear-model-with-a-categorical-predictor">A linear model with a categorical predictor</a>
<ul>
<li><a href="#data-preparation-and-model-fitting">Data preparation and model fitting</a></li>
<li><a href="#posterior-description">Posterior description</a></li>
<li><a href="#rope-percentage">ROPE Percentage</a></li>
<li><a href="#probability-of-direction-pd">Probability of Direction (pd)</a></li>
</ul></li>
<li><a href="#all-with-one-function">All with one function</a></li>
<li><a href="#references">References</a></li>
</ul>
</div>
<p>This vignette can be referred to by citing the package:</p>
<ul>
<li>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></li>
</ul>
<hr />
<p>Now that you’ve read the <a href="https://easystats.github.io/bayestestR/articles/bayestestR.html"><strong>Get started</strong></a> section, let’s dive in the <strong>subtleties of Bayesian modelling using R</strong>.</p>
<div id="loading-the-packages" class="section level2">
<h2>Loading the packages</h2>
<p>Once you’ve <a href="https://easystats.github.io/bayestestR/articles/bayestestR.html#bayestestr-installation">installed</a> the necessary packages, we can load <code>rstanarm</code> (to fit the models), <code>bayestestR</code> (to compute useful indices), and <code>insight</code> (to access the parameters).</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(rstanarm)</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(bayestestR)</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(insight)</span></code></pre></div>
</div>
<div id="simple-linear-regression-model" class="section level2">
<h2>Simple linear (regression) model</h2>
<p>We will begin by conducting a simple linear regression to test the relationship between <code>Petal.Length</code> (our predictor, or <em>independent</em>, variable) and <code>Sepal.Length</code> (our response, or <em>dependent</em>, variable) from the <a href="https://en.wikipedia.org/wiki/Iris_flower_data_set"><code>iris</code></a> dataset which is included by default in R.</p>
<div id="fitting-the-model" class="section level3">
<h3>Fitting the model</h3>
<p>Let’s start by fitting a <strong>frequentist</strong> version of the model, just to have a reference point:</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>model <span class="ot"><-</span> <span class="fu">lm</span>(Sepal.Length <span class="sc">~</span> Petal.Length, <span class="at">data =</span> iris)</span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(model)</span></code></pre></div>
<pre><code>>
> Call:
> lm(formula = Sepal.Length ~ Petal.Length, data = iris)
>
> Residuals:
> Min 1Q Median 3Q Max
> -1.2468 -0.2966 -0.0152 0.2768 1.0027
>
> Coefficients:
> Estimate Std. Error t value Pr(>|t|)
> (Intercept) 4.3066 0.0784 54.9 <2e-16 ***
> Petal.Length 0.4089 0.0189 21.6 <2e-16 ***
> ---
> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Residual standard error: 0.41 on 148 degrees of freedom
> Multiple R-squared: 0.76, Adjusted R-squared: 0.758
> F-statistic: 469 on 1 and 148 DF, p-value: <2e-16</code></pre>
<p>We can also zoom in on the parameters of interest to us:</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>insight<span class="sc">::</span><span class="fu">get_parameters</span>(model)</span></code></pre></div>
<pre><code>> Parameter Estimate
> 1 (Intercept) 4.31
> 2 Petal.Length 0.41</code></pre>
<p>In this model, the linear relationship between <code>Petal.Length</code> and <code>Sepal.Length</code> is <strong>positive and significant</strong> (<span class="math inline">\(\beta = 0.41, t(148) = 21.6, p < .001\)</span>). This means that for each one-unit increase in <code>Petal.Length</code> (the predictor), you can expect <code>Sepal.Length</code> (the response) to increase by <strong>0.41</strong>. This effect can be visualized by plotting the predictor values on the <code>x</code> axis and the response values as <code>y</code> using the <code>ggplot2</code> package:</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggplot2) <span class="co"># Load the package</span></span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a><span class="co"># The ggplot function takes the data as argument, and then the variables</span></span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a><span class="co"># related to aesthetic features such as the x and y axes.</span></span>
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(iris, <span class="fu">aes</span>(<span class="at">x =</span> Petal.Length, <span class="at">y =</span> Sepal.Length)) <span class="sc">+</span></span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_point</span>() <span class="sc">+</span> <span class="co"># This adds the points</span></span>
<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_smooth</span>(<span class="at">method =</span> <span class="st">"lm"</span>) <span class="co"># This adds a regression line</span></span></code></pre></div>
<p><img src="data:image/png;base64,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" width="100%" /></p>
<p>Now let’s fit a <strong>Bayesian version</strong> of the model by using the <code>stan_glm</code> function in the <code>rstanarm</code> package:</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>model <span class="ot"><-</span> <span class="fu">stan_glm</span>(Sepal.Length <span class="sc">~</span> Petal.Length, <span class="at">data =</span> iris)</span></code></pre></div>
<p>You can see the sampling algorithm being run.</p>
</div>
<div id="extracting-the-posterior" class="section level3">
<h3>Extracting the posterior</h3>
<p>Once it is done, let us extract the parameters (<em>i.e.</em>, coefficients) of the model.</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>posteriors <span class="ot"><-</span> insight<span class="sc">::</span><span class="fu">get_parameters</span>(model)</span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(posteriors) <span class="co"># Show the first 6 rows</span></span></code></pre></div>
<pre><code>> (Intercept) Petal.Length
> 1 4.4 0.39
> 2 4.4 0.40
> 3 4.3 0.41
> 4 4.3 0.40
> 5 4.3 0.40
> 6 4.3 0.41</code></pre>
<p>As we can see, the parameters take the form of a lengthy dataframe with two columns, corresponding to the <code>intercept</code> and the effect of <code>Petal.Length</code>. These columns contain the <strong>posterior distributions</strong> of these two parameters. In simple terms, the posterior distribution is a set of different plausible values for each parameter. Contrast this with the result we saw from the frequentist linear regression mode using <code>lm</code>, where the results had <strong>single values</strong> for each effect of the model, and not a distribution of values. This is one of the most important differences between these two frameworks.</p>
<div id="about-posterior-draws" class="section level4">
<h4>About posterior draws</h4>
<p>Let’s look at the length of the posteriors.</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><span class="fu">nrow</span>(posteriors) <span class="co"># Size (number of rows)</span></span></code></pre></div>
<pre><code>> [1] 4000</code></pre>
<p><strong>Why is the size 4000, and not more or less?</strong></p>
<p>First of all, these observations (the rows) are usually referred to as <strong>posterior draws</strong>. The underlying idea is that the Bayesian sampling algorithm (<em>e.g.</em>, <strong>Monte Carlo Markov Chains - MCMC</strong>) will <em>draw</em> from the hidden true posterior distribution. Thus, it is through these posterior draws that we can estimate the underlying true posterior distribution. <strong>Therefore, the more draws you have, the better your estimation of the posterior distribution</strong>. However, increased draws also means longer computation time.</p>
<p>If we look at the documentation (<code>?sampling</code>) for the <code>rstanarm</code>’s <code>"sampling"</code> algorithm used by default in the model above, we can see several parameters that influence the number of posterior draws. By default, there are <strong>4</strong> <code>chains</code> (you can see it as distinct sampling runs), that each create <strong>2000</strong> <code>iter</code> (draws). However, only half of these iterations are kept, as half are used for <code>warm-up</code> (the convergence of the algorithm). Thus, the total for posterior draws equals <strong><code>4 chains * (2000 iterations - 1000 warm-up) = 4000</code></strong>.</p>
<p>We can change that, for instance:</p>
<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>model <span class="ot"><-</span> <span class="fu">stan_glm</span>(Sepal.Length <span class="sc">~</span> Petal.Length, <span class="at">data =</span> iris, <span class="at">chains =</span> <span class="dv">2</span>, <span class="at">iter =</span> <span class="dv">1000</span>, <span class="at">warmup =</span> <span class="dv">250</span>)</span>
<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a><span class="fu">nrow</span>(insight<span class="sc">::</span><span class="fu">get_parameters</span>(model)) <span class="co"># Size (number of rows)</span></span></code></pre></div>
<pre><code>[1] 1500</code></pre>
<p>In this case, as would be expected, we have <strong><code>2 chains * (1000 iterations - 250 warm-up) = 1500</code></strong> posterior draws. But let’s keep our first model with the default setup (as it has more draws).</p>
</div>
<div id="visualizing-the-posterior-distribution" class="section level4">
<h4>Visualizing the posterior distribution</h4>
<p>Now that we’ve understood where these values come from, let’s look at them. We will start by visualizing the posterior distribution of our parameter of interest, the effect of <code>Petal.Length</code>.</p>
<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(posteriors, <span class="fu">aes</span>(<span class="at">x =</span> Petal.Length)) <span class="sc">+</span></span>
<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_density</span>(<span class="at">fill =</span> <span class="st">"orange"</span>)</span></code></pre></div>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA8cAAAJACAMAAACXE+S8AAAAolBMVEUAAAAAADoAAGYAOpAAZpAAZrY6AAA6kNtNTU1NTW5NTY5NbqtNjshmAABmADpmtv9uTU1uTW5uTY5ubm5uq+SOTU2OyP+QOgCQZgCQ2/+rbk2rjk2r5P+2ZgC2kDq2/9u2///Ijk3I/8jI///bkDrbtmbb25Db/7bb/9vb///kq27k////pQD/tmb/yI7/25D/5Kv//7b//8j//9v//+T///+Xlqn1AAAACXBIWXMAAA7DAAAOwwHHb6hkAAAWA0lEQVR4nO3dDXvbVJqAYUO31JR2KTP9WFi6Q5buzk6gobTk//+1lezEsR1/yNKRdN5z7vu6JjieRETy+6APO/HiFohuMfcPAAymY4hPxxCfjiE+HUN8Oob4EnbsPwkwEx1DfDqG+HQM8ekY4tMxxKdjiE/HEJ+OIT4dQ3w6hvh0DPHpGOLTMcSnY4hPxxCfjiE+HUN8Oob4dAzx6Rji0zHEp2PuLRYewqh0zEoT8e+//y7loHRMq414TckR6Zjb7YyVHJKO2cu4CXnun4dL6Zj9jIUcj455lLGQw9Fx9Q5kLORodFy7gxkLORgd1+5Ix0IORceVO5axkEPRcd2OZyzkSHRcNx2XQcdVO5WxkAPRcdV0XAgd1+x0xkKOQ8cVO5exkMPQcb3OZyzkKHRcLx2XQ8fV6pKxkIPQcbW6dSzkEHRcq44ZCzkEHddKxyXRcaU6ZyzkCHRcpwsyFnIAOq7TRR0LOXs6rtJlGQs5ezqu0qUdCzlzOq7RxRnrOHN9Hp+/floul6/bWzfL5bc/D1kUs7i8YyHnrcfD89dPTbvXyxdNxs2Nm03IHukoemTs3WLy1uPB+fTqbfPx+vmvf/3U7pSvXvRfFLPo1bFdcs56PzbNfngT9MBFMa2eGdslZ6z3I3P1/NdPP7SH1Dc6DqZ3x3bJ2er7wNwsX9+dGm9OkD3GMQzI2C45Vz0flpv7y1w6DmdQx23JCzFnp98jcrN62slxdUQDM96KeSHpbPR6GK7Xzx67zhVQkoz3k557pejzEFwv367+6XmngJJ3vG557tWqXa/nj1/f3fI6kHBGyVjJs+ux+a+XK22/116XGcxYHXtKal5+T6Iq42Us5FnpuCpjdizkGem4JqNmLOQZ6bgiI2cs5PnouCKjdyzkuei4HuNnrOO56LgeE3Qs5JnouBpTZCzkmei4GjoumI5rMU3GQp6HjmsxVcdCnoOOKzFZxkKeg44roeOi6bgOE2Ys5BnouA46LpuOqzBpxjqeno5rMG3GQp6ejmug49LpuAJTZyzkyem4Ajouno7LN33GQp6ajsun4/LpuHhzZKzjiem4eLN0LORp6bh082Ss42npuHQzdSzkSem4cHNlrONJ6bhwOq6Cjss2W8ZCnpSOy6bjOui4aDNmrOMp6bhoc3Ys5AnpuGSzZqzjCem4ZPN2LOTp6LhkOq6Fjgs2c8ZCno6OC6bjaui4XLNnLOTJ6LhYGWSs46nouFg6roiOS5VDxjqeio5LlUXHQp6Ijkul45rouFB5ZKzjiei4UJl0LORp6LhQOq6KjsuUS8ZCnoaOy6Tjuui4SPlkrONJ6LhIOq6MjouUUcdCnoKOS5RTxjqego5LpOPa6LhEOq6NjguUVcZCnoKOC6Tj6ui4PJllLOQJ6Lg8Oq6PjouTXcY6Hp+Oi5Nfx0IenY5Lk2HGOh6djkuTY8dCHpuOS6PjGum4MFlmrOOx6bgwOq6Sjguj4yrpuDB5dizkkem4LJlmrOOR6bgsOq6TjouSa8Y6HpmOi5Jtx0Iel46LouNK6bgo+XYs5FHpuCQZZ6zjUem4JDqulY5LouNa6bggOWcs5FHpuCA6rpaOy5F3xjoek47LoeN66bgcmXcs5BHpuBw6rpeOi5F7xkIekY6LoeOK6bgYOq6Yjouh44rpuBT5Zyzk8ei4FDqumY4LESFjHY9Gx4XQcdV0XIYQGQt5NDoug47r1nPDfvrbr83Hz2+WjRfDFkUCQTLW8Vj6bdjPb563HX/64efBiyKFKB0LeSS9tuvNcrnq+Gb1cdCiSELHleuzXW+Wr9cFX7/YvttDNB8dV67ndl13fPX35vT49cBFMVyYjIU8kiEdf37z3W9NzPche4Rmo+PaDdof7970CM0mUMdCHsXwjj+9ejtoUQyn49ol6Pj+yScP0FwiZazjUQzpeL0ndlw9Ox1Xb9j16vZ5J9e55hYqYyGPYthx9dVyuXw7cFEMpWP8nkR8OkbH4QXLWMhj0HF4OkbH8YXrWMjp6Tg8HaPj8OJlrOP0dBydjtFxeAEzFnJ6Og5Ox9zqODwdc6vj6EJmrOPkdBxbzI6FnJqOY9MxLR2HFjRjIaem49B0zIqOIwubsY4T03FkcTsWclo6jkzHrOk4sMAZ6zgtHQemY+7oOK7IGQs5LR3HpWPu6Tiu2B0LOSUdhxU8Yx2npOOwoncs5IR0HJaO2dBxVOEzFnJCOo5KxzzQcVAFZKzjdHQcVAkdCzkZHQelY7boOKYiMtZxMjqOqYyOhZyKjmPSMdt0HFIhGQs5FR2HpGN26DiiYjLWcSI6jqicjoWcho4DKihjHaeh44B0zB4dB1RSx0JOQsfxFJWxjpPQcTxldSzkFHQcTmEZ6zgFHYdTWsdCTkDH0RSXsY4T0HE0OuYxHQdTXsZCTkDHweiYA3QcS4kZC3k4HcdSZsdCHkrHoRSasY6H0nEopXYs5IF0HEmxGet4IB1HomMO295+f75cPPlXmkUxhnIzFvJAu5vvw2LRP2WPxNh0zBGPNl//lD0SYyu5YyEPcmDrvW9KfppmUaRUdMY6HmR/67W74+9vP/YJ2QMxsrI7FvIQOxvvj2/u98Qfvv5l2KJIrvCMdTzE7vXqr368u6nj/OiYozx/HEXpGQt5CB1HoWOO2zmu/vf1YXWfg+pbHY+r/IyFPICOg9AxJ2w23Zd3i41nwxZFejVkLOT+Du2PEyyKtOrIWMe9uc4Vgo45SccRVJKxkHvbbLg/Xz7558u782PXuTKjY06zPw6gmoyF3JeOA9AxZ+xsty/vnra/8NTzLwl4CEZSUcZC7mlns73/+pc/vnna1jx4UaSjY87Z3mxf3j27/bj43uu58lJVxkLuZ/f3Fp/dfvjqRx3nRcectd9xc2h9+8Hf58pIZRkLuZfd8+Mn/3z5dJXz4EWRio45b+969eLrX/pe5tLxKKrLWMh9eP44czqmAx3nrcKMddzD/nG111fnpcaOhXy5/deBpFoUSVSZsY4vt/+8U6JFkUadHQv5YjrOWaUZ6/hiu6/L7PmM0+NFkYSO6WZni7Uvrk60KBKoNWMhX2zvfcxdr85IvRnr+FKeP86XjulKx9mqOGMhX2p3ezVH1k/+713Pq9Y2fVo6prPd61xf/fjhyb/++MbvO+Wg6o6FfJn9vwfS/u5xh98//vS3X9t/3CyX3/58aFEMVnfGOr7Mo78H0nZ89nr15zfP245vmohvNiHb8knpmO72XwfSdvz+3P642Q23Hf/10+vmk6sXBxbFUJVnLOTL7L8OpOn4w7lXg9wsX9+0HX969bb57Hq1a95fFAPpeO5HIJRH16sXi686vOviuuMffr6/+XhRDFJ9xjq+SM+ttYp3fWq8OUG24RPSsZAvoeMsyVjHF9l6v8XFxvnXVzuuHpeOfxfyJXa21foVIB86nCC7zjUuHf+u40sc+v3js8873XXseaexyHjFRHV26O+BdHhfmBuvAxmTjldMVGdD9sfNMbXXZY5BxneMVFd7rwPpen58dlEMoOM7RqqrA68D6fk25jpORcb3jFRX/o5AfnS8YaY60nF+dLxhpjrScXZk/MBMdaTj7Oh4i6HqRse5kfE2Q9WNjnOj4x2mqhMdZ0bGu0xVJzrOjI53mapOdJwXGe8zVl3oOC863mesutBxXnS8z1h1oeOsyPgRY9WFjrOi48fMVQc6zomMDzBXHeg4Jzo+xGCdp+OMyPggg3WejjOi44MM1nk6zoiODzNZZ+k4Izo+zGSdpeN8yPgIk3WWjvOh4yNM1lk6zoeOjzFa5+g4GzI+ymido+Ns6Pg4s3WGjnMh4xPM1hk6zoWOTzFcp+k4EzI+yXCdpuNM6Pg003WSjvMg4zNM10k6zoOOzzBdJ+k4Dzo+w3SdpOMsyPgs43WKjrOg47OM1yk6zoKOzzJep+g4Czo+z3ydoOMcyLgD83WCjnOg4y4M2HE6zoCMOzFgx+k4AzruxIAdp+MM6LgbE3aUjucn445M2FE6np+OOzJhR+l4fjruyIQdpePZybgzI3aMjmen486M2DE6npuML2DGjtDx3HR8ATN2hI7npuNLGLLDdDw3HV/CkB2m45nJ+DKm7CAdz0zHlzFlB+l4Zjq+jCk7SMfzkvGFTNlBOp6Xji9lzA7R8axkfDFjdoiOZ6XjixmzQ3Q8Kx1fzpwdoOM5ybgHc3aAjuek4z4M2mM6npGMezFoj+l4RjruxaA9puMZ6bgfk/aIjucj455M2iM6no+OezJpj+h4Pjruy6jt0/FsZNybUdun49nouD+ztkfHc5HxAGZtj47nouMhDNsuHc9Fx0MYtl06nomMBzFsu3Q8Ex0PY9p26HgmOh7GtO3Q8Ux0PJBx26bjech4MPO2Rcfz0PFg5m2Ljmch4wQM3AMdz0LHCRi4BzqehY4TMHAPdDwHGSdh4jZ0PAcdJ2HiNnQ8Bx2nYeTu6XgGMk7EyN3T8Qx0nIqZu6Pj6ck4GTN3R8fT03E6hm5Nx5OTcUKGbk3Hk9NxSqZuRcdTk3FSpm5Fx1PTcVrGrjVoK3x+s2y8SLGoasg4MWPXGrQVPv3wc6pFVUPHqZm724Hx3Tz/NdWiqqHj1Mzd7cD4rl9sf2Z7diDj9AzewPiu/t6cHr9Osqha6Dg9gzcsvs9vvvutifk+ZJvzPBmPweQliG9zkmxrnqfjURi94Vvg06u3qRZVPBmPpPrZS9Dx/ZNP1W/L83Q8kupnb8gGWO+JHVd3p+Ox1D58w65Xt887uc7VmYxHU/vwDVv/q+Vy+TbNomqg4/FUPn1+T2I6Mh5T3eOn4+noeEx1j5+OJyPjcVU9fzqejI7HVfX86XgqMh5bzQOo46noeHQVT6COJyLj8VU8gTqehoynUO8I6ngSMp5GtTOo40noeBrVzqCOpyDjqdQ6hDqego4nU+kU6ngCMp5QnWOo4/HJeEp1jqGORyfjaVU5hzoenY4nVuMg6nhsMp5chZOo45HJeHoVTqKOxyXjOdQ3ijoelYznUd0s6nhECxnPpbZh1PF4VDyf2oZRx6OR8Zwqm0Ydj8VB9bzqGkcdj0TFc6tqHnU8CjvjDNQ0kDoeg4qzUNFE6jg9O+NMVDSROk5NxfmoZyR1nJiKc1LNTOo4KTvjzNQylDpOScW5qWUodZyOnXGGKplKHSej4izVMZY6TsTOOFdVzKWOk1BxxmoYTB2noOKsVTCZOk5AxpkrfzR1PJyD6uwtSh9OHQ+m4gBKH04dD2RnHEPh06njQVQcRtmH1joeQsWRlDygOh5AxrEUvEvWcX8OqqMpd0R13JuK4yl2RnXcl4wjKvXQWsc9OagOqsySddyPiuMqcVB13IuMIytwl6zjPmQcXHGzquPLOTWOr7Rdso4vpuIilFWyji8l41KUNLA6vpCD6nIUtEvW8WVUXJRiZlbHF5FxYUrZJev4Eg6qy1PG2Or4AiouURFzq+PuZFymEgZXx53JuFQFnCTruCOnxiULP7s67kbFZYu+S9ZxJzIuXuzx1XEXMq5A6PnVcQcyrkLkAdbxWa5w1SLwBOv4HBXXI+7VLh2fZmdcl6gl6/gUFVcn6BTr+AQVVyjmGOv4KDvjOoU8tNbxMSquVsBJ1vFhdsY1i7dL1vFBKq5ctGHW8QF2xgTbJet430LFtEKVrONdImYj0ETreIeK2RJnl6zjB46o2RdlqHV8T8QcEGSXrOM1FXPEIkLKOr51QM0Z+ZesYxe3OC/3nXL1HdsX003WKVfesYi5QL4p19yxXTEXWyyyjLnejkVMX/m1XGnHdsUMlNeOucaORUwi2cRcXcciJrEcYq6p49X2nvtBp0wzp1xNxxJmZHPul4f9e2+Wy29/TrOo8Szsh5nMTC0P+nfeNBHfbELOruOFgpnD3eBNOusDvvevn143H69eJFhUUgsBk4Epax7yr/n06m3z8fr5r5ctanFS3x9maxFzP37w4PS4p+pgUMc/tIfUN5d2fFrP1c7mYABmMGT+16fGmxNkKcFMdAzxZXdcDVxshutcQGIlPu8EtSn5dSBQi2HxXUd4XSYUr5rfk4CC6Rji0zHEp2OIT8cQn44hPh1DfDqG+HQM8ekY4tMxxKdjiE/HEJ+OIT4dQ3wpOwamNULHwEx0DPHpGOLTMcSnY4hPxxCfjiG+mju+2f7r25s/xf3p1XL54vg3RbGzco2r7347cG9Mh9dt+0Zgh1euGc/l2xPfVXHHO++G0b5L1eqTm2azfX4TPuTdt/pop6Mdh/17Yzq8bts3Aju8ctftvadCrrfjnXen+vzmdXvPi7t7N+89F9XeW28169eOw/69MR1et+0bgR174F7cnn7g6u14790ib9cdr98LNrz9lbv+7j+bcXi8yhEdXrftG4EdXjkdH7f37s23dwcvz//7zXL5er4fK429lWs+bU+zHq9yRIfXbetGZEdWznH1UeuTkIdTkZtVvtfLZhOu//MX2e7KtQdr7Tjsr3JMh9ft4UZoR1bu7AVKHT9snb9++u63629L2GXtrdx1Mwqldny/bg83QjuyclfNQH56deIwsd6ODxxkNptvfWayPksJbGflVp8Uely9u27xOz6ycmcvbFTc8eNt09y13oLhr3btrFz73GPrbYHXuTbrtrkx80830OGVO38gVW/HO1f415uvifjzm7sbc/5owz1+humq2OedinodyOGV24zn0e+rt+PdZ9w3Y369mffQHr3i46rc14GU1PGRlXN+fMLdSzHvnpy7Pya7WRbwvNPeyt1uvbwvfMbH1u22iI6PrNzVmamsuWMohY4hPh1DfDqG+HQM8ekY4tMxxKdjiE/HEJ+OIT4dQ3w6hvh0DPHpGOLTMcSnY4hPxxCfjiE+HUN8Oob4dAzx6Rji0zHEp2OIT8cQn44hPh1DfDqG+HQM8ekY4tMxxKfjUr1frDz519Z9H5493P7jm+/vvnDnSw5rvvHLu6dpf0AS0nGp3n/9S/Pxz5dblf75smfH7TfqOGc6LtW649sPX/24uUvHxdJxqe46/rhocv3QHGA/a8pdLJo736+Ptg90vP6ypthn7+8OyNt//teT/22/8R/v/u3d3mE62dBxqbb2x+3//vjm2Xp/3Gbb7lsfd3z/ZV/eNe3/+fLpehkfmnbX++P7e8mPjku17viPb56u2mwq/fqXNsd1vs0njzrefNmXd+09zd2rL2k/W3d8d+9M68MpOi7V3fXqZv/5cXWK3ER5d37c7FkXBzrefNn6TLi5e31u/f6+46e3Os6Vjkt1d1x9uz7tba07ft9GfGh/vPmyh45Xi/ig4/zpuFQPHX+8v2Td5vhxcXf0fGR/fHt7a38cj45L9dDx+sS3yXTVcdvml3dHz4+b/39T7N75sY7zpeNSPXR8+75pt73SvL7O9bQ9hD7Q8ebLHordvV6t43zpuFRbHa9OfZ/ervv92D59/D9f/dh2vHpy+e6C2LPNl20V2z5//B/NjQ/t88c6zpeOOeO9p4zzp2OOWu2uVx/InI45rj3Q3np9NtnSMcSnY4hPxxCfjiE+HUN8Oob4dAzx/T/TadC3l5cGpQAAAABJRU5ErkJggg==" width="100%" /></p>
<p>This distribution represents the <a href="https://en.wikipedia.org/wiki/Probability_density_function">probability</a> (the <code>y</code> axis) of different effects (the <code>x</code> axis). The central values are more probable than the extreme values. As you can see, this distribution ranges from about <strong>0.35 to 0.50</strong>, with the bulk of it being at around <strong>0.41</strong>.</p>
<blockquote>
<p><strong>Congrats! You’ve just described your first posterior distribution.</strong></p>
</blockquote>
<p>And this is the heart of Bayesian analysis. We don’t need <em>p</em>-values, <em>t</em>-values, or degrees of freedom. <strong>Everything we need is contained within this posterior distribution</strong>.</p>
<p>Our description above is consistent with the values obtained from the frequentist regression (which resulted in a <span class="math inline">\(\beta\)</span> of <strong>0.41</strong>). This is reassuring! Indeed, <strong>in most cases, Bayesian analysis does not drastically differ from the frequentist results</strong> or their interpretation. Rather, it makes the results more interpretable and intuitive, and easier to understand and describe.</p>
<p>We can now go ahead and <strong>precisely characterize</strong> this posterior distribution.</p>
</div>
</div>
<div id="describing-the-posterior" class="section level3">
<h3>Describing the Posterior</h3>
<p>Unfortunately, it is often not practical to report the whole posterior distributions as graphs. We need to find a <strong>concise way to summarize it</strong>. We recommend to describe the posterior distribution with <strong>3 elements</strong>:</p>
<ol style="list-style-type: decimal">
<li>A <strong>point-estimate</strong> which is a one-value summary (similar to the <span class="math inline">\(beta\)</span> in frequentist regressions).</li>
<li>A <strong>credible interval</strong> representing the associated uncertainty.</li>
<li>Some <strong>indices of significance</strong>, giving information about the relative importance of this effect.</li>
</ol>
<div id="point-estimate" class="section level4">
<h4>Point-estimate</h4>
<p><strong>What single value can best represent my posterior distribution?</strong></p>
<p>Centrality indices, such as the <em>mean</em>, the <em>median</em>, or the <em>mode</em> are usually used as point-estimates. But what’s the difference between them?</p>
<p>Let’s answer this by first inspecting the <strong>mean</strong>:</p>
<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">mean</span>(posteriors<span class="sc">$</span>Petal.Length)</span></code></pre></div>
<pre><code>> [1] 0.41</code></pre>
<p>This is close to the frequentist <span class="math inline">\(\beta\)</span>. But, as we know, the mean is quite sensitive to outliers or extremes values. Maybe the <strong>median</strong> could be more robust?</p>
<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a><span class="fu">median</span>(posteriors<span class="sc">$</span>Petal.Length)</span></code></pre></div>
<pre><code>> [1] 0.41</code></pre>
<p>Well, this is <strong>very close to the mean</strong> (and identical when rounding the values). Maybe we could take the <strong>mode</strong>, that is, the <em>peak</em> of the posterior distribution? In the Bayesian framework, this value is called the <strong>Maximum A Posteriori (MAP)</strong>. Let’s see:</p>
<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a><span class="fu">map_estimate</span>(posteriors<span class="sc">$</span>Petal.Length)</span></code></pre></div>
<pre><code>> MAP Estimate: 0.41</code></pre>
<p><strong>They are all very close!</strong></p>
<p>Let’s visualize these values on the posterior distribution:</p>
<div class="sourceCode" id="cb21"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(posteriors, <span class="fu">aes</span>(<span class="at">x =</span> Petal.Length)) <span class="sc">+</span></span>
<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_density</span>(<span class="at">fill =</span> <span class="st">"orange"</span>) <span class="sc">+</span></span>
<span id="cb21-3"><a href="#cb21-3" aria-hidden="true" tabindex="-1"></a> <span class="co"># The mean in blue</span></span>
<span id="cb21-4"><a href="#cb21-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_vline</span>(<span class="at">xintercept =</span> <span class="fu">mean</span>(posteriors<span class="sc">$</span>Petal.Length), <span class="at">color =</span> <span class="st">"blue"</span>, <span class="at">size =</span> <span class="dv">1</span>) <span class="sc">+</span></span>
<span id="cb21-5"><a href="#cb21-5" aria-hidden="true" tabindex="-1"></a> <span class="co"># The median in red</span></span>
<span id="cb21-6"><a href="#cb21-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_vline</span>(<span class="at">xintercept =</span> <span class="fu">median</span>(posteriors<span class="sc">$</span>Petal.Length), <span class="at">color =</span> <span class="st">"red"</span>, <span class="at">size =</span> <span class="dv">1</span>) <span class="sc">+</span></span>
<span id="cb21-7"><a href="#cb21-7" aria-hidden="true" tabindex="-1"></a> <span class="co"># The MAP in purple</span></span>
<span id="cb21-8"><a href="#cb21-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_vline</span>(<span class="at">xintercept =</span> <span class="fu">map_estimate</span>(posteriors<span class="sc">$</span>Petal.Length), <span class="at">color =</span> <span class="st">"purple"</span>, <span class="at">size =</span> <span class="dv">1</span>)</span></code></pre></div>
<p><img src="data:image/png;base64,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" width="100%" /></p>
<p>Well, all these values give very similar results. Thus, <strong>we will choose the median</strong>, as this value has a direct meaning from a probabilistic perspective: <strong>there is 50% chance that the true effect is higher and 50% chance that the effect is lower</strong> (as it divides the distribution in two equal parts).</p>
</div>
<div id="uncertainty" class="section level4">
<h4>Uncertainty</h4>
<p>Now that the have a point-estimate, we have to <strong>describe the uncertainty</strong>. We could compute the range:</p>
<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a><span class="fu">range</span>(posteriors<span class="sc">$</span>Petal.Length)</span></code></pre></div>
<pre><code>> [1] 0.33 0.48</code></pre>
<p>But does it make sense to include all these extreme values? Probably not. Thus, we will compute a <a href="https://easystats.github.io/bayestestR/articles/credible_interval.html"><strong>credible interval</strong></a>. Long story short, it’s kind of similar to a frequentist <strong>confidence interval</strong>, but easier to interpret and easier to compute — <em>and it makes more sense</em>.</p>
<p>We will compute this <strong>credible interval</strong> based on the <a href="https://easystats.github.io/bayestestR/articles/credible_interval.html#different-types-of-cis">Highest Density Interval (HDI)</a>. It will give us the range containing the 89% most probable effect values. <strong>Note that we will use 89% CIs instead of 95%</strong> CIs (as in the frequentist framework), as the 89% level gives more <a href="https://easystats.github.io/bayestestR/articles/credible_interval.html#why-is-the-default-89">stable results</a> <span class="citation">(Kruschke, 2014)</span> and reminds us about the arbitrariness of such conventions <span class="citation">(McElreath, 2018)</span>.</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">hdi</span>(posteriors<span class="sc">$</span>Petal.Length, <span class="at">ci =</span> <span class="fl">0.89</span>)</span></code></pre></div>
<pre><code>> 89% HDI: [0.38, 0.44]</code></pre>
<p>Nice, so we can conclude that <strong>the effect has 89% chance of falling within the <code>[0.38, 0.44]</code> range</strong>. We have just computed the two most important pieces of information for describing our effects.</p>
</div>
<div id="effect-significance" class="section level4">
<h4>Effect significance</h4>
<p>However, in many scientific fields it not sufficient to simply describe the effects. Scientists also want to know if this effect has significance in practical or statistical terms, or in other words, whether the effect is <strong>important</strong>. For instance, is the effect different from 0? So how do we <strong>assess the <em>significance</em> of an effect</strong>. How can we do this?</p>
<p>Well, in this particular case, it is very eloquent: <strong>all possible effect values (<em>i.e.</em>, the whole posterior distribution) are positive and over 0.35, which is already substantial evidence the effect is not zero</strong>.</p>
<p>But still, we want some objective decision criterion, to say if <strong>yes or no the effect is ‘significant’</strong>. One approach, similar to the frequentist framework, would be to see if the <strong>Credible Interval</strong> contains 0. If it is not the case, that would mean that our <strong>effect is ‘significant’</strong>.</p>
<p>But this index is not very fine-grained, no? <strong>Can we do better? Yes!</strong></p>
</div>
</div>
</div>
<div id="a-linear-model-with-a-categorical-predictor" class="section level2">
<h2>A linear model with a categorical predictor</h2>
<p>Imagine for a moment you are interested in how the weight of chickens varies depending on two different <strong>feed types</strong>. For this example, we will start by selecting from the <code>chickwts</code> dataset (available in base R) two feed types of interest for us (<em>we do have peculiar interests</em>): <strong>meat meals</strong> and <strong>sunflowers</strong>.</p>
<div id="data-preparation-and-model-fitting" class="section level3">
<h3>Data preparation and model fitting</h3>
<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">library</span>(dplyr)</span>
<span id="cb26-2"><a href="#cb26-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb26-3"><a href="#cb26-3" aria-hidden="true" tabindex="-1"></a><span class="co"># We keep only rows for which feed is meatmeal or sunflower</span></span>
<span id="cb26-4"><a href="#cb26-4" aria-hidden="true" tabindex="-1"></a>data <span class="ot"><-</span> <span class="fu">filter</span>(chickwts, feed <span class="sc">%in%</span> <span class="fu">c</span>(<span class="st">"meatmeal"</span>, <span class="st">"sunflower"</span>))</span></code></pre></div>
<p>Let’s run another Bayesian regression to predict the <strong>weight</strong> with the <strong>two types of feed type</strong>.</p>
<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a>model <span class="ot"><-</span> <span class="fu">stan_glm</span>(weight <span class="sc">~</span> feed, <span class="at">data =</span> data)</span></code></pre></div>
</div>
<div id="posterior-description" class="section level3">
<h3>Posterior description</h3>
<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>posteriors <span class="ot"><-</span> insight<span class="sc">::</span><span class="fu">get_parameters</span>(model)</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="fu">ggplot</span>(posteriors, <span class="fu">aes</span>(<span class="at">x =</span> feedsunflower)) <span class="sc">+</span></span>
<span id="cb28-4"><a href="#cb28-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_density</span>(<span class="at">fill =</span> <span class="st">"red"</span>)</span></code></pre></div>
<p><img src="data:image/png;base64,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" width="100%" /></p>
<p>This represents the <strong>posterior distribution of the difference</strong> between <code>meatmeal</code> and <code>sunflowers</code>. It seems that the difference is <strong>positive</strong> (since the values are concentrated on the right side of 0). Eating sunflowers makes you more fat (<em>at least, if you’re a chicken</em>). But, <strong>by how much?</strong></p>
<p>Let us compute the <strong>median</strong> and the <strong>CI</strong>:</p>
<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a><span class="fu">median</span>(posteriors<span class="sc">$</span>feedsunflower)</span></code></pre></div>
<pre><code>> [1] 53</code></pre>
<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><span class="fu">hdi</span>(posteriors<span class="sc">$</span>feedsunflower)</span></code></pre></div>
<pre><code>> 95% HDI: [-0.12, 97.72]</code></pre>
<p>It makes you fat by around 51 grams (the median). However, the uncertainty is quite high: <strong>there is 89% chance that the difference between the two feed types is between 14 and 91.</strong></p>
<blockquote>
<p><strong>Is this effect different from 0?</strong></p>
</blockquote>
</div>
<div id="rope-percentage" class="section level3">
<h3>ROPE Percentage</h3>
<p>Testing whether this distribution is different from 0 doesn’t make sense, as 0 is a single value (<em>and the probability that any distribution is different from a single value is infinite</em>).</p>
<p>However, one way to assess <strong>significance</strong> could be to define an area <em>around</em> 0, which will consider as <em>practically equivalent</em> to zero (<em>i.e.</em>, absence of, or a negligible, effect). This is called the <a href="https://easystats.github.io/bayestestR/articles/region_of_practical_equivalence.html"><strong>Region of Practical Equivalence (ROPE)</strong></a>, and is one way of testing the significance of parameters.</p>
<p><strong>How can we define this region?</strong></p>
<blockquote>
<p><strong><em>Driing driiiing</em></strong></p>
</blockquote>
<p>– <strong><em>The easystats team speaking. How can we help?</em></strong></p>
<p>– <strong><em>I am Prof. Sanders. An expert in chicks… I mean chickens. Just calling to let you know that based on my expert knowledge, an effect between -20 and 20 is negligible. Bye.</em></strong></p>
<p>Well, that’s convenient. Now we know that we can define the ROPE as the <code>[-20, 20]</code> range. All effects within this range are considered as <em>null</em> (negligible). We can now compute the <strong>proportion of the 89% most probable values (the 89% CI) which are not null</strong>, <em>i.e.</em>, which are outside this range.</p>
<div class="sourceCode" id="cb33"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb33-1"><a href="#cb33-1" aria-hidden="true" tabindex="-1"></a><span class="fu">rope</span>(posteriors<span class="sc">$</span>feedsunflower, <span class="at">range =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">20</span>, <span class="dv">20</span>), <span class="at">ci =</span> <span class="fl">0.89</span>)</span></code></pre></div>
<pre><code>> # Proportion of samples inside the ROPE [-20.00, 20.00]:
>
> inside ROPE
> -----------
> 5.28 %</code></pre>
<p><strong>5% of the 89% CI can be considered as null</strong>. Is that a lot? Based on our <a href="https://easystats.github.io/bayestestR/articles/guidelines.html"><strong>guidelines</strong></a>, yes, it is too much. <strong>Based on this particular definition of ROPE</strong>, we conclude that this effect is not significant (the probability of being negligible is too high).</p>
<p>That said, to be honest, I have <strong>some doubts about this Prof. Sanders</strong>. I don’t really trust <strong>his definition of ROPE</strong>. Is there a more <strong>objective</strong> way of defining it?</p>
<div class="figure" style="text-align: center">
<img src="data:text/html; 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AIDgUWtgd0Sjhyg2CUbBBseFOdeYcTshytidkGx6IgYIrYoNhwithwVEbA7FUb6ZUqxvp9EA%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%2FfwQUF1N1BQXs2qUUtvdn1UVQX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3ynlXcqx%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%2BDVmm2s36yewct5GZXitB2HTR2dEDu8RGoWMTQMU4qigIm1fu7khGuTI179JGgQdgut8t4604VmPQyVEp2UiYOWskiUq8kuFdGKlVEfCpIaaAqvud7nufjQEdu9TCSTm8BRopxUlGIOl3K1BJLpl9%2BItJ96HOZUlohlIei8%2FlsoNLMqcwgRieVoHlUUz1Jqe0xwprWaQ9p%2FmaZCJUsNTBGkk9zekUd%2FvVjoLKKx%2FET5nTAvJFlRDA0XdEwpBYH3hxFoIsYetRJRYnM05Vk90a7jssul0w6PWs1cnY9Lhq4l6GCe1J21EmktMKN49MEaH9FkW4N0U8CaMVmVx8HoHQXehLa3YhS1DDFF%2FFz6tqsNGDhHMVQdq5v0F6gTMmY9FbYSSM9qYglAdAXE%2BbUrcvWSq4Xc3p1Xi03MEp5TnFXHe1hxL7kXrmAJLyUlN74zoD0kqxZrdTTZcolo1Jdo1Swk2JWNygt4HFeToQKl1jhVlL8UQ44vWwi0yK4H0bcK6qZOCeRUvQkkjr8M9Ok15VLZLXWSTbu1Rq1XOx3AzunuJF70oiTihisjiXoagK0vzFxD6C1a%2FfaKuUU87LjoLg51kmYU3EWUmOdVLIrdv9g9i5Up0rXqe%2FAnu1ITinpyY42wiJG7QEa66TSYOeLFKwQ5XSkI%2Bl5xZIe9N1Lt%2Bf1GjYYVYxyHnMa66RGZF9m59WuqrTKaCMZmb5Lr1OKHouxR5XSZh3GjnXSFEtsi3a7uLCwsNi1WnkRV1hlTHK1YGxbVBTKq%2FWIk4qcrIvwWJyTplgdpqrKeYn2f1ZqSlRn1%2BefiYBeM0YSet835KQip60HaJyTuGQkVkkNjW7RsHOoGBsZrdit8Mbsmq5TGe%2BkIruil9STSvwf006pbUnOSEaibQ7YKFml2m55bB6GnFTkx95BocY5SdcpulvV2s71ClunFurbOe0KuW96r%2Bmx2WEoHmcWNZOdmZ5e61xvRaFLq%2B%2FSr8TzFH%2F82bt7t%2FcMx%2B87O%2FQzcffw8HBPNyTdgP2%2Be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alt="Prof. Sanders giving default values to define the Region of Practical Equivalence (ROPE)." width="75%" />
<p class="caption">
Prof. Sanders giving default values to define the Region of Practical Equivalence (ROPE).
</p>
</div>
<p><strong>Yes!</strong> One of the practice is for instance to use the <strong>tenth (<code>1/10 = 0.1</code>) of the standard deviation (SD)</strong> of the response variable, which can be considered as a “negligible” effect size <span class="citation">(Cohen, 1988)</span>.</p>
<div class="sourceCode" id="cb35"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb35-1"><a href="#cb35-1" aria-hidden="true" tabindex="-1"></a>rope_value <span class="ot"><-</span> <span class="fl">0.1</span> <span class="sc">*</span> <span class="fu">sd</span>(data<span class="sc">$</span>weight)</span>
<span id="cb35-2"><a href="#cb35-2" aria-hidden="true" tabindex="-1"></a>rope_range <span class="ot"><-</span> <span class="fu">c</span>(<span class="sc">-</span>rope_value, rope_value)</span>
<span id="cb35-3"><a href="#cb35-3" aria-hidden="true" tabindex="-1"></a>rope_range</span></code></pre></div>
<pre><code>> [1] -6.2 6.2</code></pre>
<p>Let’s redefine our ROPE as the region within the <code>[-6.2, 6.2]</code> range. <strong>Note that this can be directly obtained by the <code>rope_range</code> function :)</strong></p>
<div class="sourceCode" id="cb37"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb37-1"><a href="#cb37-1" aria-hidden="true" tabindex="-1"></a>rope_value <span class="ot"><-</span> <span class="fu">rope_range</span>(model)</span>
<span id="cb37-2"><a href="#cb37-2" aria-hidden="true" tabindex="-1"></a>rope_value</span></code></pre></div>
<pre><code>> [1] -6.2 6.2</code></pre>
<p>Let’s recompute the <strong>percentage in ROPE</strong>:</p>
<div class="sourceCode" id="cb39"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb39-1"><a href="#cb39-1" aria-hidden="true" tabindex="-1"></a><span class="fu">rope</span>(posteriors<span class="sc">$</span>feedsunflower, <span class="at">range =</span> rope_range, <span class="at">ci =</span> <span class="fl">0.89</span>)</span></code></pre></div>
<pre><code>> # Proportion of samples inside the ROPE [-6.17, 6.17]:
>
> inside ROPE
> -----------
> 0.00 %</code></pre>
<p>With this reasonable definition of ROPE, we observe that the 89% of the posterior distribution of the effect does <strong>not</strong> overlap with the ROPE. Thus, we can conclude that <strong>the effect is significant</strong> (in the sense of <em>important</em> enough to be noted).</p>
</div>
<div id="probability-of-direction-pd" class="section level3">
<h3>Probability of Direction (pd)</h3>
<p>Maybe we are not interested in whether the effect is non-negligible. Maybe <strong>we just want to know if this effect is positive or negative</strong>. In this case, we can simply compute the proportion of the posterior that is positive, no matter the “size” of the effect.</p>
<div class="sourceCode" id="cb41"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb41-1"><a href="#cb41-1" aria-hidden="true" tabindex="-1"></a>n_positive <span class="ot"><-</span> posteriors <span class="sc">%>%</span></span>
<span id="cb41-2"><a href="#cb41-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">filter</span>(feedsunflower <span class="sc">></span> <span class="dv">0</span>) <span class="sc">%>%</span> <span class="co"># select only positive values</span></span>
<span id="cb41-3"><a href="#cb41-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">nrow</span>() <span class="co"># Get length</span></span>
<span id="cb41-4"><a href="#cb41-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb41-5"><a href="#cb41-5" aria-hidden="true" tabindex="-1"></a>n_positive <span class="sc">/</span> <span class="fu">nrow</span>(posteriors) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
<pre><code>> [1] 98</code></pre>
<p>We can conclude that <strong>the effect is positive with a probability of 98%</strong>. We call this index the <a href="https://easystats.github.io/bayestestR/articles/probability_of_direction.html"><strong>Probability of Direction (pd)</strong></a>. It can, in fact, be computed more easily with the following:</p>
<div class="sourceCode" id="cb43"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb43-1"><a href="#cb43-1" aria-hidden="true" tabindex="-1"></a><span class="fu">p_direction</span>(posteriors<span class="sc">$</span>feedsunflower)</span></code></pre></div>
<pre><code>> Probability of Direction: 0.98</code></pre>
<p>Interestingly, it so happens that <strong>this index is usually highly correlated with the frequentist <em>p</em>-value</strong>. We could almost roughly infer the corresponding <em>p</em>-value with a simple transformation:</p>
<div class="sourceCode" id="cb45"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb45-1"><a href="#cb45-1" aria-hidden="true" tabindex="-1"></a>pd <span class="ot"><-</span> <span class="fl">97.82</span></span>
<span id="cb45-2"><a href="#cb45-2" aria-hidden="true" tabindex="-1"></a>onesided_p <span class="ot"><-</span> <span class="dv">1</span> <span class="sc">-</span> pd <span class="sc">/</span> <span class="dv">100</span></span>
<span id="cb45-3"><a href="#cb45-3" aria-hidden="true" tabindex="-1"></a>twosided_p <span class="ot"><-</span> onesided_p <span class="sc">*</span> <span class="dv">2</span></span>
<span id="cb45-4"><a href="#cb45-4" aria-hidden="true" tabindex="-1"></a>twosided_p</span></code></pre></div>
<pre><code>> [1] 0.044</code></pre>
<p>If we ran our model in the frequentist framework, we should approximately observe an effect with a <em>p</em>-value of 0.04. <strong>Is that true?</strong></p>
<div id="comparison-to-frequentist" class="section level4">
<h4>Comparison to frequentist</h4>
<div class="sourceCode" id="cb47"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb47-1"><a href="#cb47-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(<span class="fu">lm</span>(weight <span class="sc">~</span> feed, <span class="at">data =</span> data))</span></code></pre></div>
<pre><code>>
> Call:
> lm(formula = weight ~ feed, data = data)
>
> Residuals:
> Min 1Q Median 3Q Max
> -123.91 -25.91 -6.92 32.09 103.09
>
> Coefficients:
> Estimate Std. Error t value Pr(>|t|)
> (Intercept) 276.9 17.2 16.10 2.7e-13 ***
> feedsunflower 52.0 23.8 2.18 0.04 *
> ---
> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Residual standard error: 57 on 21 degrees of freedom
> Multiple R-squared: 0.185, Adjusted R-squared: 0.146
> F-statistic: 4.77 on 1 and 21 DF, p-value: 0.0405</code></pre>
<p>The frequentist model tells us that the difference is <strong>positive and significant</strong> (<span class="math inline">\(\beta = 52, p = 0.04\)</span>).</p>
<p><strong>Although we arrived to a similar conclusion, the Bayesian framework allowed us to develop a more profound and intuitive understanding of our effect, and of the uncertainty of its estimation.</strong></p>
</div>
</div>
</div>
<div id="all-with-one-function" class="section level2">
<h2>All with one function</h2>
<p>And yet, I agree, it was a bit <strong>tedious</strong> to extract and compute all the indices. <strong>But what if I told you that we can do all of this, and more, with only one function?</strong></p>
<blockquote>
<p><strong>Behold, <code>describe_posterior</code>!</strong></p>
</blockquote>
<p>This function computes all of the adored mentioned indices, and can be run directly on the model:</p>
<div class="sourceCode" id="cb49"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb49-1"><a href="#cb49-1" aria-hidden="true" tabindex="-1"></a><span class="fu">describe_posterior</span>(model, <span class="at">test =</span> <span class="fu">c</span>(<span class="st">"p_direction"</span>, <span class="st">"rope"</span>, <span class="st">"bayesfactor"</span>))</span></code></pre></div>
<pre><code>> Summary of Posterior Distribution
>
> Parameter | Median | 95% CI | pd | ROPE | % in ROPE | Rhat | ESS | BF
> ---------------------------------------------------------------------------------------------------------
> (Intercept) | 276.62 | [240.03, 310.68] | 100% | [-6.17, 6.17] | 0% | 1.002 | 2793.00 | > 1000
> feedsunflower | 52.73 | [ -0.12, 97.72] | 98.38% | [-6.17, 6.17] | 1.89% | 1.000 | 2860.00 | 0.806</code></pre>
<p><strong>Tada!</strong> There we have it! The <strong>median</strong>, the <strong>CI</strong>, the <strong>pd</strong> and the <strong>ROPE percentage</strong>!</p>
<p>Understanding and describing posterior distributions is just one aspect of Bayesian modelling. <strong>Are you ready for more?!</strong> <a href="https://easystats.github.io/bayestestR/articles/example2.html"><strong>Click here</strong></a> to see the next example.</p>
</div>
<div id="references" class="section level2 unnumbered">
<h2 class="unnumbered">References</h2>
<div id="refs" class="references csl-bib-body hanging-indent" line-spacing="2">
<div id="ref-cohen1988statistical" class="csl-entry">
Cohen, J. (1988). <em>Statistical power analysis for the social sciences</em>.
</div>
<div id="ref-kruschke2014doing" class="csl-entry">
Kruschke, J. (2014). <em>Doing bayesian data analysis: A tutorial with r, JAGS, and stan</em>. Academic Press.
</div>
<div id="ref-mcelreath2018statistical" class="csl-entry">
McElreath, R. (2018). <em>Statistical rethinking: A bayesian course with examples in r and stan</em>. Chapman; Hall/CRC.
</div>
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