https://github.com/cran/bayestestR
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<body>

<h1 id="1-initiation-to-bayesian-models">1. Initiation to Bayesian models</h1>
<ul>
<li><a href="#loading-the-packages">Loading the packages</a></li>
<li><a href="#simple-linear-model-aka-a-regression">Simple linear model (<em>aka</em> a regression)</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>
<p>This vignette can be referred to by citing the package:</p>
<ul>
<li>Makowski, D., Ben-Shachar, M. S., &amp; 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">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>
<h2 id="loading-the-packages">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"><a class="sourceLine" id="cb1-1" title="1"><span class="kw">library</span>(rstanarm)</a>
<a class="sourceLine" id="cb1-2" title="2"><span class="kw">library</span>(bayestestR)</a>
<a class="sourceLine" id="cb1-3" title="3"><span class="kw">library</span>(insight)</a></code></pre></div>
<h2 id="simple-linear-model-aka-a-regression">Simple linear model (<em>aka</em> a regression)</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>
<h3 id="fitting-the-model">Fitting the model</h3>
<p>Let’s start by fitting the <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"><a class="sourceLine" id="cb2-1" title="1">model &lt;-<span class="st"> </span><span class="kw">lm</span>(Sepal.Length <span class="op">~</span><span class="st"> </span>Petal.Length, <span class="dt">data=</span>iris)</a>
<a class="sourceLine" id="cb2-2" title="2"><span class="kw">summary</span>(model)</a></code></pre></div>
<pre><code>&gt; 
&gt; Call:
&gt; lm(formula = Sepal.Length ~ Petal.Length, data = iris)
&gt; 
&gt; Residuals:
&gt;     Min      1Q  Median      3Q     Max 
&gt; -1.2468 -0.2966 -0.0152  0.2768  1.0027 
&gt; 
&gt; Coefficients:
&gt;              Estimate Std. Error t value Pr(&gt;|t|)    
&gt; (Intercept)    4.3066     0.0784    54.9   &lt;2e-16 ***
&gt; Petal.Length   0.4089     0.0189    21.6   &lt;2e-16 ***
&gt; ---
&gt; Signif. codes:  0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1
&gt; 
&gt; Residual standard error: 0.41 on 148 degrees of freedom
&gt; Multiple R-squared:  0.76,    Adjusted R-squared:  0.758 
&gt; F-statistic:  469 on 1 and 148 DF,  p-value: &lt;2e-16
</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> (beta = 0.41, <em>t</em>(148) = 21.6, <em>p</em> &lt; .001). 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="cb4"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb4-1" title="1"><span class="kw">library</span>(ggplot2)  <span class="co"># Load the package</span></a>
<a class="sourceLine" id="cb4-2" title="2"></a>
<a class="sourceLine" id="cb4-3" title="3"><span class="co"># The ggplot function takes the data as argument, and then the variables </span></a>
<a class="sourceLine" id="cb4-4" title="4"><span class="co"># related to aesthetic features such as the x and y axes.</span></a>
<a class="sourceLine" id="cb4-5" title="5"><span class="kw">ggplot</span>(iris, <span class="kw">aes</span>(<span class="dt">x=</span>Petal.Length, <span class="dt">y=</span>Sepal.Length)) <span class="op">+</span></a>
<a class="sourceLine" id="cb4-6" title="6"><span class="st">  </span><span class="kw">geom_point</span>() <span class="op">+</span><span class="st">  </span><span class="co"># This adds the points</span></a>
<a class="sourceLine" id="cb4-7" title="7"><span class="st">  </span><span class="kw">geom_smooth</span>(<span class="dt">method=</span><span class="st">&quot;lm&quot;</span>) <span class="co"># This adds a regression line</span></a></code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></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="cb5"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb5-1" title="1">model &lt;-<span class="st"> </span><span class="kw">stan_glm</span>(Sepal.Length <span class="op">~</span><span class="st"> </span>Petal.Length, <span class="dt">data=</span>iris)</a></code></pre></div>
<p>You can see the sampling algorithm being run.</p>
<h3 id="extracting-the-posterior">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="cb6"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb6-1" title="1">posteriors &lt;-<span class="st"> </span>insight<span class="op">::</span><span class="kw">get_parameters</span>(model)</a>
<a class="sourceLine" id="cb6-2" title="2"></a>
<a class="sourceLine" id="cb6-3" title="3"><span class="kw">head</span>(posteriors)  <span class="co"># Show the first 6 rows</span></a></code></pre></div>
<pre><code>&gt;   (Intercept) Petal.Length
&gt; 1         4.4         0.40
&gt; 2         4.5         0.37
&gt; 3         4.3         0.41
&gt; 4         4.4         0.40
&gt; 5         4.3         0.41
&gt; 6         4.3         0.42
</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.</p>
<h4 id="about-posterior-draws">About posterior draws</h4>
<p>Let’s look at the length of the posteriors.</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb8-1" title="1"><span class="kw">nrow</span>(posteriors)  <span class="co"># Size (number of rows)</span></a></code></pre></div>
<pre><code>&gt; [1] 4000
</code></pre>
<blockquote>
<p><strong>Why is the size 4000, and not more or less?</strong></p>
</blockquote>
<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 rstanarm <code>&quot;sampling&quot;</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 is <strong><code>4 chains * (2000 iterations - 1000 warm-up) = 4000</code></strong> posterior draws. We can change that, for instance:</p>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb10-1" title="1">model &lt;-<span class="st"> </span><span class="kw">stan_glm</span>(Sepal.Length <span class="op">~</span><span class="st"> </span>Petal.Length, <span class="dt">data=</span>iris, <span class="dt">chains =</span> <span class="dv">2</span>, <span class="dt">iter =</span> <span class="dv">1000</span>, <span class="dt">warmup =</span> <span class="dv">250</span>)</a>
<a class="sourceLine" id="cb10-2" title="2"> </a>
<a class="sourceLine" id="cb10-3" title="3"><span class="kw">nrow</span>(insight<span class="op">::</span><span class="kw">get_parameters</span>(model))  <span class="co"># Size (number of rows)</span></a></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>
<h4 id="visualizing-the-posterior-distribution">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="cb12"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb12-1" title="1"><span class="kw">ggplot</span>(posteriors, <span class="kw">aes</span>(<span class="dt">x =</span> Petal.Length)) <span class="op">+</span></a>
<a class="sourceLine" id="cb12-2" title="2"><span class="st">  </span><span class="kw">geom_density</span>(<span class="dt">fill =</span> <span class="st">&quot;orange&quot;</span>)</a></code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>This distribution represents the <a href="https://en.wikipedia.org/wiki/Probability_density_function">probability</a> (the y axis) of different effects (the x 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 posterior distribution.</strong></p>
</blockquote>
<p>And this is at the heart of Bayesian analysis. We don’t need <em>p</em>-values, <em>t</em>-values or degrees of freedom: <strong>everything is there</strong>, within this posterior distribution.</p>
<p>Our description above is consistent with the values obtained from the frequentist regression (which resulted in a beta of <strong>0.41</strong>). This is reassuring! Indeed, <strong>in most cases a Bayesian analysis does not drastically change the 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>
<h3 id="describing-the-posterior">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>
<li>A <strong>point-estimate</strong> which is a one-value summary (similar to the <em>beta</em> 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>
<h4 id="point-estimate">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? Let’s answer this by first inspecting the <strong>mean</strong>:</p>
<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb13-1" title="1"><span class="kw">mean</span>(posteriors<span class="op">$</span>Petal.Length)</a></code></pre></div>
<pre><code>&gt; [1] 0.41
</code></pre>
<p>This is close to the frequentist beta. But as we know, the mean is quite sensitive to outliers or extremes values. Maybe the <strong>median</strong> could be more robust?</p>
<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb15-1" title="1"><span class="kw">median</span>(posteriors<span class="op">$</span>Petal.Length)</a></code></pre></div>
<pre><code>&gt; [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="cb17"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb17-1" title="1"><span class="kw">map_estimate</span>(posteriors<span class="op">$</span>Petal.Length)</a></code></pre></div>
<pre><code>&gt; MAP = 0.41
</code></pre>
<p><strong>They are all very close!</strong> Let’s visualize these values on the posterior distribution:</p>
<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb19-1" title="1"><span class="kw">ggplot</span>(posteriors, <span class="kw">aes</span>(<span class="dt">x =</span> Petal.Length)) <span class="op">+</span></a>
<a class="sourceLine" id="cb19-2" title="2"><span class="st">  </span><span class="kw">geom_density</span>(<span class="dt">fill =</span> <span class="st">&quot;orange&quot;</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb19-3" title="3"><span class="st">  </span><span class="co"># The mean in blue</span></a>
<a class="sourceLine" id="cb19-4" title="4"><span class="st">  </span><span class="kw">geom_vline</span>(<span class="dt">xintercept=</span><span class="kw">mean</span>(posteriors<span class="op">$</span>Petal.Length), <span class="dt">color=</span><span class="st">&quot;blue&quot;</span>, <span class="dt">size=</span><span class="dv">1</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb19-5" title="5"><span class="st">  </span><span class="co"># The median in red</span></a>
<a class="sourceLine" id="cb19-6" title="6"><span class="st">  </span><span class="kw">geom_vline</span>(<span class="dt">xintercept=</span><span class="kw">median</span>(posteriors<span class="op">$</span>Petal.Length), <span class="dt">color=</span><span class="st">&quot;red&quot;</span>, <span class="dt">size=</span><span class="dv">1</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb19-7" title="7"><span class="st">  </span><span class="co"># The MAP in purple</span></a>
<a class="sourceLine" id="cb19-8" title="8"><span class="st">  </span><span class="kw">geom_vline</span>(<span class="dt">xintercept=</span><span class="kw">map_estimate</span>(posteriors<span class="op">$</span>Petal.Length), <span class="dt">color=</span><span class="st">&quot;purple&quot;</span>, <span class="dt">size=</span><span class="dv">1</span>)</a></code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></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>
<h4 id="uncertainty">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="cb20"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb20-1" title="1"><span class="kw">range</span>(posteriors<span class="op">$</span>Petal.Length)</a></code></pre></div>
<pre><code>&gt; [1] 0.35 0.48
</code></pre>
<p>But does it make sense to include all these extreme values? Probably not. Thus, we will compute a <a href="https://easystats.github.io/bayestestR/articles/credible_interval.html"><strong>credible interval</strong></a>. Long story short, it’s kind of similar to a frequentist <strong>confidence interval</strong>, but easier to interpret and easier to compute — <em>and it makes more sense</em>.</p>
<p>We will compute this <strong>credible interval</strong> based on the <a href="https://easystats.github.io/bayestestR/articles/credible_interval.html#different-types-of-cis">Highest Density Interval (HDI)</a>. It will give us the range containing the 89% most probable effect values. <strong>Note that we will use 89% CIs instead of 95%</strong> CIs (as in the frequentist framework), as the 89% level gives more <a href="https://easystats.github.io/bayestestR/articles/credible_interval.html#why-is-the-default-89">stable results</a> (Kruschke, 2014) and reminds us about the arbitrarity of such conventions (McElreath, 2018).</p>
<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb22-1" title="1"><span class="kw">hdi</span>(posteriors<span class="op">$</span>Petal.Length, <span class="dt">ci=</span><span class="fl">0.89</span>)</a></code></pre></div>
<pre><code>&gt; # Highest Density Interval
&gt; 
&gt; 89% HDI     
&gt; ------------
&gt; [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>
<h4 id="effect-significance">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 important. For instnace, 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, isn’t it? <strong>Can we do better? Yes.</strong></p>
<h2 id="a-linear-model-with-a-categorical-predictor">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 exampe, 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>
<h3 id="data-preparation-and-model-fitting">Data preparation and model fitting</h3>
<div class="sourceCode" id="cb24"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb24-1" title="1"><span class="kw">library</span>(dplyr)</a>
<a class="sourceLine" id="cb24-2" title="2"></a>
<a class="sourceLine" id="cb24-3" title="3"><span class="co"># We keep only rows for which feed is meatmeal or sunflower</span></a>
<a class="sourceLine" id="cb24-4" title="4">data &lt;-<span class="st"> </span>chickwts <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb24-5" title="5"><span class="st">  </span><span class="kw">filter</span>(feed <span class="op">%in%</span><span class="st"> </span><span class="kw">c</span>(<span class="st">&quot;meatmeal&quot;</span>, <span class="st">&quot;sunflower&quot;</span>))</a></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="cb25"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb25-1" title="1">model &lt;-<span class="st"> </span><span class="kw">stan_glm</span>(weight <span class="op">~</span><span class="st"> </span>feed, <span class="dt">data=</span>data)</a></code></pre></div>
<h3 id="posterior-description">Posterior description</h3>
<div class="sourceCode" id="cb26"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb26-1" title="1">posteriors &lt;-<span class="st"> </span>insight<span class="op">::</span><span class="kw">get_parameters</span>(model)</a>
<a class="sourceLine" id="cb26-2" title="2"></a>
<a class="sourceLine" id="cb26-3" title="3"><span class="kw">ggplot</span>(posteriors, <span class="kw">aes</span>(<span class="dt">x=</span>feedsunflower)) <span class="op">+</span></a>
<a class="sourceLine" id="cb26-4" title="4"><span class="st">  </span><span class="kw">geom_density</span>(<span class="dt">fill =</span> <span class="st">&quot;red&quot;</span>)</a></code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>This represents the <strong>posterior distribution of the difference between <code>meatmeal</code> and <code>sunflowers</code></strong>. Seems that the difference is rather <strong>positive</strong> (the values seems 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> Let us compute the <strong>median</strong> and the <strong>CI</strong>:</p>
<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb27-1" title="1"><span class="kw">median</span>(posteriors<span class="op">$</span>feedsunflower)</a></code></pre></div>
<pre><code>&gt; [1] 51
</code></pre>
<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb29-1" title="1"><span class="kw">hdi</span>(posteriors<span class="op">$</span>feedsunflower)</a></code></pre></div>
<pre><code>&gt; # Highest Density Interval
&gt; 
&gt; 89% HDI       
&gt; --------------
&gt; [13.52, 91.37]
</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>
<h3 id="rope-percentage">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 around 0, which will consider as <em>practically equivalent</em> to zero (<em>i.e.</em>, absence of, or 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><em><strong>Driing driiiing</strong></em></p>
</blockquote>
<p>– <em><strong>The easystats team speaking. How can we help?</strong></em></p>
<p>– <em><strong>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.</strong></em></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="cb31"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb31-1" title="1"><span class="kw">rope</span>(posteriors<span class="op">$</span>feedsunflower, <span class="dt">range =</span> <span class="kw">c</span>(<span class="op">-</span><span class="dv">20</span>, <span class="dv">20</span>), <span class="dt">ci=</span><span class="fl">0.89</span>)</a></code></pre></div>
<pre><code>&gt; # Proportion of samples inside the ROPE [-20.00, 20.00]:
&gt; 
&gt; inside ROPE
&gt; -----------
&gt; 5.00 %
</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>Although, 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 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M5hVnPk8hjlYQmRkxNAjeTO4c8WSIsLpKbF/UmG6e1b0NMZtFuiWz5C05wi+nuQt4+gykMc36tQP7qPpZ0DxQp1jFifFTg/F/gYHfzpEquDJeSshOcIVPKPTVBRwCEwv5ZeL/u3uqcgnf5GYipsjuOr0aiXiVQ7+iy/7bXr+em6a//bf82R3C/RU7yMe/gN1vCCv20xQX/O26V2/X4eRC+XD3juQNjsH6mevcBNV6hQ+BaoCEPPH3QVeBGv9Op/2AZw+7fNPWLsmN6IGlOfxtpXverEsj3O2D6UdEOkllcbrmYE+5VS0zLpCiqjLqpib06dk5JeYFJouI5AICUoNegaB2UKyDzrLZhcRJb3HqN9mpPgWy+2UqzO912AS2HDExVsot92NVTXq/IJgHacwuRZCBWTZdGT9+2GG9vAWfqCKZEhQiuByi9gu3PI1iNZAeE8C6HSlmfqHbrOom0aHN79iG2gyLQqBofQNgik5O8cdOrFYPW6gfARCjkq8nOVEW51jpVdYHb7+zgyJWYHt7E+bXF2cR+rtkEXSoQLB30vQ9O1mM/nyAlc5z04J5Dcc2qfgtGtpRQnWoXAqVT5Ji51W9sUKnrttN0ujOKpsd78el3fgW/bSP9l++hNxxAjML2hNYLTsfZVV0/O1K1kMETQTdD/e8BEwK1ekzephClPMDUTIBnmSLarC+Qlgc8EJ/qROY3drXXIUoaKfU9zxKAhUw9ASTHPTFHufhL6pc5fDtssEDZWSkobVssH65hAw11TGn/7DsGSYCr0IBq9Mp+f4z0kBeuHBOUkdIgIzSncxSO07RJTcwcyRhhtIKRCUBFRSjhtEFTedym7DkEERNsidB1824D4CFpqXi6BbwK21KGl7RftHCmsEHQCqg/ZMQC1hbYCftFidX6Ok9tTfO9PfgD94fuIWjI1QTvPYJIEWm1rEQn8ltkl73Qrkrqq2n+aWiMuqQDbjirdRmA61tta+wKR3+Z3600Wnz0/KdtH7UujNALTG1Iv+rD0B9b1bt91X2Hue/Vvu6r56mjnmWSNze80RiaAQ9G8iYkn/YiYupDWBkQzhTEKhZIsNkqelO8tXGvhOVzJIokIbXJIQTSACZQsIFUBpQskH1jwH0hFTxmdxA+N8jL6VFOrdmNPJbejHLmJqYuO/UZTtOC800TUl54XboRhbCvVFJK2IfUBAWQLpamrSABztULgqFBwt5PiUslyini0WTXhfH3aPgKlCdQhDb3AykcEn/oxUwdkGdlZlWT6DLdawBIHalLi5GjKllqUy0+5+Z7AY1EiK0scHB3ju9/9I7R33uuFV1pCECc1pk0SlWfqAgFTNuTfjObpRuCUACwZ9JMV1VVe6hacXo05HWusfdXrPL5e9h246zLxks7i2yqIehtqZ1X+zjXIgdzz9u25KTnM8fjyY8dO6Vj7qBcRzXvDdzCoI0U7w1MGPApKltCF5DhOApAUMUqglMAfgymyfoLrM+3zCcykB6QBOT9f5xlk1xHRGpEAnAfc9oKL2NUEthSQK40QPAubCK8a1Zvoh+jQrpcIobdZorQpL3uZltIKRhlYZEjGIiYPz93YCJlPUUxOkKLpk5c4fz+wut9aogRoZCqDKjMYR6tybCkVQwMZQp/fT6KpmPi1qiqxPCqRIKtrWd1PnFhZaNhY4+DwLlojYVON4u49HJ8cI+aH+P3ZGW7dvccAk/xWt2lW1DFWZXHZGd2GCdBIn8b3WzN+eh4B1K0H6vPCKXYoGOCIjzXWTa7XOcJ//sJ8/J69uTV2TK+5XnaV+O58aIa+WMdR5bddV0/SW0sm6k46byFTD36MLlCVkZiXkJQElQwnKylDXFDPHFQCl76bIyUNo0sU+RQQOToSUlFmvYgMrKgbSVGh1DVlQ/kN55RiT3OKXqNtoZE0dVcFpSOpvntLHdPQsPqewahUlxF4ggVEtBhD/5CCYK6q8NRwLWCqEwCUNPUEwrvegD8mNtGnbCgayXNaE22T69DWc4RuzfcLAuZRgHaNjiTIUgyIqVTqQbVrPbonc2QfXKCtNRYrkmVFZCe3kSkJiAmEmKANDrmqkJNP68bHlGgIKsv6UXzXXY7lt+8HAVTi8hIgvX1ywkCUc/5D+JKYbfxqHetNr9cZMPO2Txief31vKo4YgekNqPHqbax91auOLb4vCiTZJydRZ5LAI3FCSQiVmQouLLjTSd1D4oAK7RBTIJkRki5gQsU4k8b4MRnu4EkjQFg2kkdp1NyRjLHdjOQJeGZszcSCJAaskZcpCDBKMuj3DBgJJJe57m2jCNAp0Y/+txU9crKJEhEWFq2t0VjPjAFFnFORQebHCGGJlBq2ccqMZHsoZyPqNdlVGThH3qc1Yltz2pQhUVYknq2Hli1CphAM2bhJXq5OiiL+0VmLw7MvUGctVrWGmc5QTQ4QpIEpbuH4+AMs4gJRip6HSsBW9MInsqHb8ke3HVJsqBX0vhA4bdsWmdYM7re+p1uR1HakPyLTsd7Wehc4pkPbsYurzLex//a5fa96/ghMb0iNyvyxXmdtTwh9t46n7T049X4DDntvU8l+ooG7m5JJnRo+OGpuEl0UeVaRXgkIEt5FqIxsmjSEEfDwWC/XrKhP6ADheuqAEhDK9EKrbdeWbJxyDaMSj/WpS0qNR2kUg1TvU98lpefHHsyRWj/HmpX4JJBK7Rqhs7ytWtBNoU6aBPZIpKrXQEbgOgk0bYvVxRxHH30ILRximyHEDgUBQ2fQUHyAbZGhQzYruYtLXqXkPEA2ViovoEyO5tF9vPfhAczkALGYojITeJ3BJ4N67VHcqhhU0/ZmUkFsbKFC6icBW9N9uv+q+IkeQ8D00aNHODk5wXQ6fQpGxxrrLax9jvHf1u/S57UD23rTO8PXDkx39QEbKjlwPA75mImB5+/6NfEy/7bL9e/5ABvaP/t+f4ZbPqO4Y9d60TG0BTjRrRio0dhcE+jTmkftgW2VPESQKKgtKUm0lGBbAk0kdPKQukNr254DaQNUBKpYQrsMrnFYr1YQ/j6ycgYUhwgyYzsoYSIyUcOghUMOY4gD2keQWj7RKmotcic1UHdSGBZBURdTBsVAlARZUgY0BGypm1pWyISGbZ6gWywZPFJ39ZBy7d0arRKwqgCxWEtaZxLIGoPuk08ZEBag+/pIU0FG+bckRJUg22OETkKdRlRCwUkBWVK4U4vWr3F4MUMtzpDfLaEnM3gfYYoKRZ4DooNGzjGrRINIug/P8Im6xL1waVJJ0nqhY15Bgu+ouywhQoZpkePBxT+j8BKlJCCf8eeBcDzdqEst2BVhrOuq6z9/vl31/Llq1/37InrAt+eROuxjntKO60ivRhjpJaP77U8F9cLnbWtoH4QBACSGANJAvWz/jR3TG1Zjp3Ss11nUrYx8svZXrr57NwgW5VDeKHdPBQMq9t6kjml0fS4a8THTJp0J4BG0a1o0qzXq1RpFlqAqzZGkMCUxVqFo4YLYq4lTmxiI8XrjJvAhMv+T/kYArshyqIoU/r1IidwCMq165brIsFgt4ZoOUgiUpkQrHVbLBouuxZRFR5KXQ1SCTGl03sHZNURG/NmIpl6iWdeIImB6MIGmqFSf0DYSpQpoXcf2UYrIrNTB1bKnLwRFQn/2RYVtYILtlf2CXpfmsALqNlP3V5BgaZMiR04APUlXwAfyYu39Y+lLjEVaRGNQkp+vVYnFfM3xrgezDCH0AF4rxe+BGrVPY431tWt0s7jZ9cYD012TDXZd/reRVTwC0bGuqxjouN4knzicvfBIMMiTRm4U9YmBGmEpAk0MTr2HDy13JilfX/GVPUWFkidnn+yUFQlFdYTq4ATTg0NIU8CFxKCM1O5im3wm5Ga5PcraJoEwYA7kO+ohveRuZnC+H/UHGn8rFE7CXaxBmVCabJYiCZUMrLQIQsJrgywvEBpKdQrQIsJ5kik1OLhTYPnFIyIpoCwk2sZhdbGCch5qMsHs5C5Eu4ZNa7TrFtJayGigKdnK9d3VcERh/ARMW0jfQYYOPlCn1AMmZ9C+PYdszfGvdmyil0yRMFpzl3rL82Vr/xRwPL2NxWqFZmUxKUi0pYhNwQEG3o8c07HGus4a7Njue9ve0s//2DG9AfU6VYljjXW1LsU38Ozr+bRjKrh7SYA0kFiHAGLsj01yc6IRD4mVjMjgneWuYQwWSgRoBUymGav5y9k9ZEUJpQz7d4qwPaZlf1IVG//RS5V5YMoAdQ5p27JcM9ezs65fH0V1SgVnW9RtDX/hEZztVe2+g2PwmFBMKlRVxV6kJfE6nUfbLUCyfd+uEFOL6azCokqc15+FHhQvL9bwIWGiClRZBVta5D7vuaBLC08Rq5AwoA6u4S4nW1kR6HQtbL2AkxpBaUwIFBf9c7eg9GpyE1s/iZz3ATkXRCbr0pi/hSMOrYuYZHdRmQJd3WI1X+Lo1gn7vHrq0tIb4cdzxFhjvaqet8h7ttm068hhqPO66+fz1ds32Pjd++lhaP99M6reCExvUL1QAPWu75Sx9loEGD35k8anHb3tyYZAF2UeMf1RbEzxIyuQoAX3RzmRqWtr2LbmTmmeUVJUBkWm9AQii4qfX9crBOospj52k3ikZGtfGH153BMo7f06w+W2VAWJlRRs8CzIotG/5khTzSNzrail25v/t3XL1IKsIAspzbSCSFQFQsoi9XGknUNXL2ADbXeO6Xu3gM6jWXUIlL0/KaCoc7tqUK9apDtZL0qi5aGGs54c92HIborU+yz4ipDkHNDV8BwnCiRFYQMFiqLgbw/6AnEE3v1Tyyey1ELMyWWVo0mfJjyR4r9hQO5XAnlZomsbXCDi+PYJe7gu1steKDVysMca66U1FMm8q4Zh6Pt5EJbtqmofWP6udV2Uh+s32H/Da+f999xx9yJwutfa0Q5irDe7tCI7JsNm9jTWp8YjASMCjpEtojLu0OmQ2GA+uD65iHim9P+WkpBcDwhJkFRyalHOo2kCkc72NlDSW8C1PUUAJILSfOwTxbJfn+iPRQKkHLMZ+KRLyyY1elHkvcE/dWfJk1QCVZFBzhL8gmJSV2ibdc87LSoGzYvlCjIJOBHY69RUBtH6PtaUvELPzhCrAooiU7McaSLhYw1bWyjfd3dDd8IglEA22Vd516Bt+phVRyC9LcjtH7FZs2iK+aQi49E+mfGTsp6ALa4IL7Z+pMwVRc+3JUcE0HYqwMDAOurGdlgsHuBE3WZxGqVWeeKxZgaKUqs4pGC8dL3WGs+f+61vya7o1V3TsW5avf0c0x17jiPHdKy3uaTozd2FUz2/kXLYZcZiHYrmNJR7T/nw1DUlb83gufNIN3Ba0wpaCgaJlFREXTziqRKYJPBUdx1yBeZ2ZoKVP4S/kFRPFehTnXpfzu1nlTir2KhZyWOUnEe5m7qhC6TgWUAV2VHDoSN1v+ggVYJRxF3tqQkQlpRJcNJzFzc3JezKIXclTIhIa4vu9ALlbAozK0GmqK1tuAuayYiJMkAwvN5E/qVKQsiIplvxGoQ0mISC1xFWdR9GoBSyWYKh+61F1zQQRcGAWWrN0a9iaxFFhvtyQ2MgagSFC/CFAQUWELgPgLlA0zxifi69J6eP7+Pw5B7KyZS3k6NaxxprrG9WacdR/iC+DTu+MQPbNwgd9mwvN7T/hrDN6GN6c2v0MB3rumobcYmNOGcbe7k949IInxTgZAxP9FDZT8V7gMUJUWQKrxmUFnk/trebkX3QCZ0PyIsMSgYGUTT6p2hQqSOEzpGUfqarcfX3ns9quOtInFICbjRSF0rCdS3qukUMHYPQvMz6dE7y/6yXrJzPFIHthnmy1KlNREMViU3sZVaiJUHRWsDaFa9DHJYojg8gZwXCcsXLV1bCtn1WPwH4LNNorUMUDsoYVvmToX+0DmgS1GRK/WA+sbJQy7lLg/yriU1ukwJFY3wp+78zhYFayGIDTk0OU0mcnp2imh7zzv/888/gosRH3/sh2i4MmMGMNdZY++yO7ip++hqJ5S8sNYqfvpmBzlIAACAASURBVFntu+M4+PwBn9Kdl79jhe2h9/xmbg3QBy54otpt/w75uI51vTX0/oeBC1ZWvW/GxrgC+LZjZbZsouGxyeF8h6azgOyYHykyBU3pSaxRoit/23dCyyl7ajrnkaUCRhJApZjODm1X96rxknLsPQuAonNY87ZIyGzCXFFev+2gdEQivim9UKV7myoarScPFT0WtmM/07SBYCH2LgDJKFbH+7ZDVnkY0yCwOX+CkyWsquBMhsN4H8E1wAWp8mugWXIPw5cS6f0p4ozU/AaNbzA5njDv8/x0iUlZMs0gNY9gSuqc5hCxBNQEYXmOtV/BwGG+qlCaSQ/uLeXqt/C2hkwKprzNyVEUE9V1ZMqfE4pnAC1CA5CzgaNELMVgmxNWqTtNy9IZWxgqdwuTSYl6uYT3j1FNj6CiQ7Oco5zMkOpnO6ZfusB9yz/fQaZnvC63zIbtxyLumYUnB5a/a7/sTa9dz1+D+GFg/2hxdQWS0+b6Jz49Ql5VQ8DzRcDw6janoeNvEF4M4ZuhZ+/m0z5Y4tX7bwh4x5e8vrFjOtZY70BdqsClfKYzSXxRrRVymSPEnE31OZmIeZCCR++UvkQG8cSrlFpBBdVzRVPEZJLDNQ0aynZvGwZaJD7KjIBmhVSf7qQuVeh9NzZtrsWo25l4jC03pyjJPM1IQDQCOp9AXSrZEwy3bGPfjdQB61XL22S0gTY5QmiRXAcRBIPexWrOwJCoBD24lmzyT44BBEJVoZgSoL1AkSR3U/X0ADlxbwmsxwt0DY3dPQwp6EPkTuqqrWF8BlV0rN4nCkPSAd46tHUD6TqUMsJkGYIQ6LoOwVoWMlEHORUFd327tmPOKK2X3BEokYpfq9r4veocedkDTsrVJ6HacnGOopygLDLEq7n5z1lRjeLJscYa602sEZje8No1OGKsd/v9pyv+rS/odkIvtn/bdFIVj+t1D44243xSsxMQJZETdeUTq6J6PipxShWBRMpjcks42/AoW4P4qQmKeKPrAJsisskRg0ECZxwTv0kLSalPdgKN9Gl7qAvK3T3D2ywDpclL6CLn18GgFhs1O/XBNHFVAw7vKEjXItYX6OwCzWrB4/BiChwUBRalZkslytPnWT4kJ0iBWaAEi9ewdQu3btB6QJK1FfFgc8nbkVWmfx+IW0tJWEIgzwo0pPi3QI01c3ItqfUNcUQzmPkFwuQUQU9xePcYWV5eglPL1lwTFlSRYt9by/u7Y9BJXNbQ74fYz1Ki1JA5UGoF3ayxmi8wP33AXercANXk7jM+qVe7Nf3vIzTdZ43n51fXt3H++jaff/nx2H4s3vH376Ymk127Kn9Ux726dpV2Xf/+HSKXX3f2983evqF376u+vc931bagVKjetokU9o5AUejV8DQup+akJ5ETsyZ7vmlCL1TSIiAkC0tCINdBEwhlb9IAopNy1j4BzzxwqhRn8XM+foTa8EppjCMIBNL1MQFPrThmk77NkkoQ1CnVWU8f2NhVcUcw9KlTQkXMygphvUJLpvT1koFc9BbJN1AuQzUt4ayApi5kII9QAWETglD8WlThOdVJugh7tkLUNXufNoVi+6iKup6UHmUTGhIyIcfRwTEnYi3XDcppzrGBJGYqsgyH1RTl4Qyk9NLBYk3xqLcLTKoKLiWs12ssvMOkyvjxYTJBvVphvV7xPqaxPXm3kq1U29ZoKRUKEYUC81u1Adplg/n8MXely+rOM93w7Xu7/dvbfnYVm5Syp//f/NwypPa8A76tz+fbWrvvn119Rq/7+2Wsb1Jjx/SG15i1/G7Xru9/Ettu6VPwgi0XMQpWf8fk0bW279pZy/ZJDCx1nwTFHU5I9toMlGSUIncVVeg40pPZkeQjSqIgGlfnOQ4ODpDlOWqy6qSNYHd+T8apm86thOTcUdXzwJWGVAaCbujjTalrGJRhpTvdCEoyzYBar8nzl46jaFQysp8ecUxpWUxQz8+YVjBfXHCnMnSegakRPIlHJGCtSzbqLzIBFRKyLsIvVkhtQMwiU9BUmXMcKQVguWDR+gaZBIyukKkcmfLwybKPqo7EQ9UMfoVzUJ7Snzp0sWCQSZ3maTXZdEdb3tdqI8SCvMJ3o0hTAs+UxCUTOwJ42zDdoZBAntPIX0PKCOsaHv9zF1vrZ8RVY72eGs/Pr66dz18D9w82bq4+4OrCvuoF/Vd72Btbu+7ffdUITMca6y2uq90zzrOX8pnOGrVFKRVpyysloBNIdRMoLpMiRcse7CjNPprcZeWUow7R1ugWC47JJAV8JLBEAgNaJomhaNxMfp8iMGeURD1S9Z1RKqINSFVA0qxaZv1N948TG+4BcUEld0t7DgIlS/F2b1QHMSokQSalBYNZGpGXQqOrlwhdC9tYWLakChC0XgKcSkAXBkrnaFZztATGKU2J+jNSIMsKzsAnP9aOACsLxySDQhKTUboUcXMpw/+iXWBCvFRdMu/1/PEjnNslys7iCArl4V3er13TQuQZptMpcqJM2Jrz+UnERe9LNZsi+t59wHd9PCw5EOTkFRuJAtCxCwA5INBjtSmRVRMGuARut+/vlj/87gBUOfDtOnbMxrq+2tlA/7on2js+/5u+vhGY3vAa4ujceH/tIZ+zAVXf3uuGb9+u7/8zCtErI/ztzSXfm7urXvgTmDsZuYsqed/EzUhYcXcz0fKIb2k7+GaFZr5CRbzMogTJ8QlbklqnE6TStzg2CpLy+MmjU2ro3k2faQOc0pQd9pZRBC45TQncHYw0yk+ReaX8HoTe65NBFzY/Y+pBtlbw0cBG4oCWkBOFPKs4IlTOayi1hIweRiZ40TLQJOETeYgSELc+ICMerVHMQyXBUu06hNZD6gpKJahKwpB7gCWBU8f7XUnDQQI5RZoSBSESsO8Q2wbB1kBo+DUK4pWSHZX3nEjFhvtRMwhtG9/7l1KKlVToUuC/ZwSUk+YOLYFwtuqiuFJ69bS/jEEyGdtcUdEypZTPvNdj93T/9cafn/dcu++fHX08r/v7ZaxvVCMwHWust7jSZQZ9L47BBpASYKKfLVk+GVK198DU6z7Kk0oR0ImbjquSl9ZrnF4Ue0/SQvVdRNs6NNShjAlTAqrGICqJQGp0Gv9LwQA4JY0UPbwnTqvHVJbcTY3oOZ8995Su1AOE8FA+420PYuNFyt3ciOQDb0PbtchMAZUXkGxNZYGu6f1ULaVRTZA88UtbKMrJl5ZBN/FUSXB169YtGBJZhYQagkF0lhksmnXvTJAf4GBSwAiBmhTz0fe+ozLwiL2Oa5ALVeYbGCVRzBRkpTiMwDY17GqFA02+qQlt0yA0iVOsjBLsb7pYrZCC49dLQQTUEZVRMU+2bSyyCYFfMvzvhVsdAekg4GVEpDhU6RiUbu3AxhrrbapvYtd0tZ75VIivz/l9W31Ct7Xr/t1X6V3JxWHwhb36hCkHOlZRDDnBvXoDIqXQXPW5u1xv/zPccNXq1+mIvaiufVQweEm8X4twOXTiGnrAwPYNLn/H3Tv49CGbPAKDftOt5OQhahJbeN9iVc9hwiHa1SPM3TkvTIkppCyQlEcnLlDoj7hzGdoFkm0g7Ap2dY72fA3fRnQ4xHFeoEANHdY9cOxWiAuJLJ+gO5ohuI6PQy1JIO+QWvo9Q1UcQFE6KYmbFNkt5RCqFztRp4MoA2u5Ztsk2b8YdgkAUQqch6AuKFlDpYDA9k+9FRYlQElhIUSD2jQMQk3t4RcNwrrjBKeMREtC4TwsEVSfTa8rjYxAeBQ4Oj6BcwFzNcdqknplvTqC/+KCxPcQJuLcNzhoS8QUsGwfIRmNw9ktZEFALhuk8gLe/BfU7R2Yow+hZ7d5BO9r8jDtMMkNpuoEKazgu8cIds4WV1lRIuVTuERBAgohNhDKQpuEIpMwHA/bQbQBNhOcMMWWXgSAlUGgNCgRGbzq9Hb3HvjVveAzsO3UiX1HEOz5/Lrr+Xvf56fB5Q8tYGD9ekcfT/38+5+ed6sY8km93u/PfX9/q8HPx6vx17eRfPmiGjumY431FlcP1CSLmOImh14bwd1RsiuSUcI3QLKh1yfJ0BvYU5eTDKA2I3dOr6ffnWNeIxnpk3/p8eEh20Mt6wVcu2LBE3mAsqgpyf7CNPU+VUbl/LfIIqwcMit6s36pkGTOF5G9jRWBzsBOAWTcv02awsYuijmo1CVMJH7vn0froHF3YheB3kGAAG42m8LGFbxPUAcVZKYhiF4wm8BQ/n4r0BEVgLxRmwaWQB8C5/G7FDDLDiFUgTyfwhwYdE9WWM7nPMY/unWAWm4subRkjqqm7qtPSMRtna+QihItcixbIJ3XOLhzF8cHBMglLKVZZSWbwAdq9DJFwkJasozquItcZIfQOuPAA6X6nH3SfhnyTs0msOhdDq6K22IUl4K30S1qrLGe1khveTPq2oHpYKTXyOEZa4fat2r2pqtyn4piZB+DyV6XEkrr/u/SQkjX20NBbQz4E6cRUdrSlouauJO4yaunnPe2RSBwevEEtW9QdwsII1HdPsD05DZMfsD8zM496S19JMWSFvyTLJsk2UDlJTyBKm04d54DOqkbGjro4FmZziaeZCCQYh+DujHbp/MCiaKgem5q8L3PKLkDkLKdHyAMA2VrPGIuoeg2SQwi06REKDKYpdsAww4d8TWDZxETxapSxzSeO8TaQb9f4vD4BPLDiPtti3q9QsbepYo7ugT0E4nIrENILdA5rDrPnerb2QGyDLhYXuCxbWDrY1STnDvIqA6g6TWgQog12tr3RvqhQwwS6tDAu8SJVzT6z8wEOiugswkyUwFhjrRJ0toCUwandEEwfgm/8/Wun/92rX0D2TcdKO9r+3cGpoOT0J19yIZe+K7LH2ust7uu2ghtf6fOGwlnvJ3DurY32SfH9pgY5CEZvl36YdK4nXAgXQmSRVNybBWlfA1BQqVJCTMpUR0cQmUlCLMlEvFQJiF18AT1XzOQ2ylzSaE2XqJ9bCo396jjCcfLT6mDFgltu+XIxk3nNPA2YkNTELQM+j89mQzqyc90w7dM0kA6snLScATUqLNqJAuQgtLoXETmCHCTPZWBFqaXF5GIS0lo8l+9sOwzStuc6RzV4QwnH97F+UOgXq6AlPVdSdmnXMXO9cui1+xbiFUD1TQwlYNNwLJ2OHcN1lWBsswpKR85jecp238y6UfwjYOwHp55wBdwJLiqE8rqAIcHCiafwMeAbr2Azrdd1H7ktk32GjulY431bD0Por4KqNr3KH1fo/A3Zfkvq70b7O/bIH5XC+m3vbX/ro8u9u3TdlN94LbFYqIUr8SR9o20zlosl0s09SP+e56XzMfzkcb0DZSoYMqc89ppGTJtuEb00zvI6GBEQl2vGKwdzGYw1QRGFwyUnItMBzAseuJZN1Kk8btEoM4rccd9hPTEKfU9r5Q5pJ67spSVT+Kk4PsLzy0TisJKew/W1ANTApGbY5yAs6B1kXVVKjgZ27QWxicEF+DJaSAzfXwoJFMRYkPbIJAlAy1LiEwyUI45pVpFRBUg53Pm1N53f0A5LdnG6fjkFguSVivPr1dqDZP3F+oZK/WzPlUrBFw8eAC5WsMc38LJ4QlaCXRdgyY5NK1FURgUpWa/VEn+qLmGEg5BOEDOmVuq6CIBjr1UQy2ZqhB8QomyZ4rp9Iy5/livp256R+1dP//hGwLSsa63bjzHNA50RPdMbR9roK77im3X2vcpat/L/yr7N13hZ/YgbjOeJyDDivCKleBEMnVdDdt1yCnrXh5yZ44oAIQbacRs+f6afUwJPF54h4zykJKC64iL2oKopIqV6Bq09Eh8T4olhdisk/iTvbo9rSWEzXv7I/S8y+Q7Ns531FfV2aZj27+WuNmjUfSyBO6KInCGfiJkymJLhZhp7pDq1jPvk0CqDR6SRuK6N+0P6BBFzh1UmQUOF6CkK7EJEvApQhcKE19ALTzq0wXOzheophPkBIg9Ccp67i1vo1ZMA6DuLNk/0QVBM7+AqGto22FG9AlDfFrNQHZSFkyJoPeg7QSs7ikB+cZvNkmJtu24U1pWh4gph409JSMjZf80Y2W+Mdmll+n2feXfbwBIvek+jfvq+GzrusVP133+HWxMvebtG0Hpm1E7A9PBt3nfPpE33SdzrLGusdhwnS2fnv5O4IX4ioeHh9BYQqBgvqJUHs6vIDoLCIsEy1zTLc+U1PWu7eDIjslZFikdfvABJpMpiA7aLtaAaJAflBBVzuFMlMiUEnFcNwKdvlcJpAaSlrkGoskg8gpRmt4KiiiiUbJFFIE0BrMb71Jsfheb4P/AF67psosKGuWT8IrBrIGoZN/1Ja4tdUULA6np+YFv6WDCXeCkI3xq4ckGioRXKsCRJRO9MOFRkm+pl1g4i7pdohOa+aSYaBaD9V+wAl1w8F3DoiQCrHARhZhCuQ7r88dsqRXJTmtygKANTGfZYov8S8lHtZxOIKuCPVoJgHqbI+oSIj+A1hUDWpUZqEwxyPWpQVVVKMpyI3yKl1/2+wZdY431ttfIMX113ViO6a41RrqNtc/at0/bTfWB2xafOMTTE0jPR0w8ztbmCCqtgJhD6wJSEZxawbqaM+xj9Czswda7lBX6ji2b6D7imLrMwBJftKnRLGsURYZCH0JXBKgiLPE6WXXf81QJBFJ6E42lKW9fRQuZ+rhR4mkqmSFRR1Ns+OupNywhNwFKpGL7q80+7+P4E4/32ULKdgxMSbwVKXGKkqAyAZ8L7lKazECTv+qm+9u5FvFgxvsDitDwBDony6x++dp7aLvGer5EaBtoBxRRod6AUIUMPng26aciH1VPmn7muSqmLEzLgvfV/Pwx4jLH8T2B2XTGYPbBJ59BC4kmeNSUgjWp+H3KyfopJV6uUceIXYF1ksgnOSaHR/yziy2aeo1pmaMsS+RFwSIo68LGE+f6jrmxbk696+e/qzV2S9+c2j8wvdKxvCrAuKxdG5oDHdGXfTBuMiC+un+GPkz7Ntbet0/q0PN37foMivN23L6h5V/3eXlrA7y1UZI8sRdoLf0vh6x+hFsnJeDnuH//t1gs1nCuRJYdw4oJCuVZV6Qpq14X6EDRThTZOUEbA+5Wh2jvP0b7+CGqWQlzfIBFTilJFY+6i1gjeAFtInsKkrF+13hed5lyRGER7Jr5lWXee3G2LqJNJFKiDqpFJiWKJKCocxsEj8odjarJozisePQupIc2stdlRcc2VRSTulA1upyInyUEpThJzZ1eHxvmax48/gITytdfW6RGIyvvIshEKffIj3JMlgrp1hTL9W/QdA+A2EIrjVooNELBLhw0i53AgqVJVCBaLBn9k7doiFNolXCSF8gLDTiL9vEp0vQ2bh+/j88f/wGLtsbBe7dRR4vGNpALicPpDIcHt+HtKZbLM1Q4Qj4F2uUadauJyIq1bXCsP0KsBdbdAtPjGfs+ns+XmB4cosqnbPD/yuNj4AC+6eKMwfXv6NM4uPxrfn1Dy9+V6nbTz3+D3z/P7IEvc01ZbLnTBmQDDxj4fhZ+YPlDEO3VE2Mh7MDzd1z/0PYP1UuW/1o7plvu0/ZgGq9gvlzjPhnrdZbeJD3Zes0qfe4Dsmem4oQk9sSUT4U12xuPqYNHQ8lOIjBPU5mcgR9/HRBYpJAmTnvq6QDeW/jQj5r7ZFIywlccERpcZPW5loJtqwRzUSNHfiYf0fkAGXsQkTZcSk+RpMzv3HROfeSfYpOtT53UWVvCdAFd5+HCGlEpBsBwpKD3OF2tscrsxspbwlJnlhqwkTqWDaa3P0ZObFeyxEoe3dk5Yus5ulQLBX1Pw3cWbkURrR1HnYrUR5uSserazjF77zbbRTVtA1NUqI6P0agc9588wQ//9K+xqBewImH9+CG6LuBolsNaj3p+ivIICMZgHRya+Rn7w8qiQHU4QVkZPJ7P8d2T77Eoi9B9t26YpkG0hvnpE5R5MX6exnrn6+UCqOt29dn3+t/M5e8dmD4PQq/+f+RA7V7XDWR3JsffcCD+tl8oUASmtTUWixXntpPvpskLjg71KUGpDEoZaC0Z1NFPjsDUvYp+3aw4w12WOWSR84kqkgiKkpeoX6ITj+XTZjRN3qC9zZPkbp3WJQKRUWk+HwVbQhmlem9S9ACW1PTB90lQJHLiWTvzZQN0Euxn6skQn9T35Aol04aKEFGRDylZLzUdA0OdCVS3DpFTfKjUaGTL0aZFnkPqnB0ECq15u3ywOI8NsjKDuXWMyrZkSADp5jBWcGpKk1bMvSXLLeLvGpVxTr8miT6JsaYnUNMKZ+s5Hp0voJ3AYXGMVgk8WdZ4/A+/xtHxMT78zof43vQYp48foVlbiOAxm0yx7ObIc7KRIgsrAZ1lbN2qk8VBlsPcu8vpewRQyZuWQGlVTVGaDNK5r3D8Xq84ae+frx2T83atsdFwzZVeBUrHuqn12jqmz9uYjKD0y3UTP0DXPcrfd9307dt7EU+UOqbdZmSvc2hFJviSBTi9uJAERE8vJJWSfIuUcBQtVKGhMw1TTohoyXxP6fuEIv7c08hd6E23NfTjLe5y0si92ozUZG+7ZB2SIi+O3kuUx/QbiygCjWS7T7xM4qkS4M3ipktK9lFKc5eUl4PeaP+iIw4t5epbJL/qrazqgIzoBiRREg7etZBaMQVguWygBTArC94v86XARAAVgecygyTu7FKha1qEkCBXCrGWsLVAiAYhI0BLMaWaVouz2OLi0/u4f/8+LhZLOJmhTr9EAwOYEl3d4c6dO/jF3/41/uLnP0Oz6rBo19Ay4f337iF1HUpdwDoy/reQ5DO7bPkxvszw83/9EyAvoNYN0xtom2K0DLy1VIOD6rfVB/Err3/fyx+/5661RlD6ZtbegemLDoSrH9bxQBk/PGNdX8UN91Rrw8p8AjMEAPtxu2BOqGRAmBCaFtZa7jDGjTjKUBczL2AI0OZV710aEndVabzvIi49VLmbSqpxGo1TF5SAr+96n1MR2Tapa1cQlAZFXdpkekN/kXorptCfN8jrlHw+qadK9laBvUsNdws1+aR2DWRIzFs9nXnoEKCNg0EHX6+xuFgwVaGxHfz5BYTJMS0K5OUhopVIBGzJKip43CZbJrKdovVT1zckdErBl0t0ncMfHsyxqD3Olh0WtkablugS0PqEzgU8WK/QNA1aZzlvPymP83WDtaVM/CnuFga/+93v8Iff/gq//sc/x62jGY6PKjTNmsHsv/r5T9Cs51jMV+yGUGqJbn6G5ZMvQHEA939/hr/6xX+Duz/8MVCUOF2s0XWWO6ZjjTXW03rR9+owB3mgBr+rh+4fWP8gFNhx+bsufk/L390u6iuCqOfB6Fe9knzXQNoISsd6nUUqezrmiFdKkZ4EyojfSPBR5WRen21sptwzHpl9l9MjLFfw7CGaUaApJBvyR1ZFBBMhne4TnVJicEcdUxq3Ux59jAFKRSgte39Vwf1OFmopGTnlSVjHnFNFHFB6TCABVIsYaojYYbWYQ+UliskRtMqRAvFbqfPasuI/uDW/JkUK/HaJermA9xE2SdRNiyMB5KpCQI6gSsRcYTVf4vHFHLZuMF+v2A3AxgjrHRzZOzUturphbum/+6fPUNsO57bFwpG6PqCL5BLV0wpSF9jOSWU5GqIpIEM1K5DRvk4JmXA4qjRKDVw8vI+jXGL24V2EYPGHzz7FMSVycSiAweGsQknOBPUS6vwMfr3Cr37zKeSTR/jh3/7X+M5f/i2ODg4xZ0mDYGupHbU9Y431VtQLQelIJ7yx9Vo6plfH+KPw6dutkWO633oXjlPqZlLHMxiLzjWwNE4nARH5ZTKvVLO3aNzksHPzc2PSj7ZBKiqEPPQd0CRZh+oZtjoUIu8tquD7Lqrqn8sjfeaRekh+Trj0JCb7KEp/IpAZbEPPRBIFIHuQDNcgNAu4bo75eo4DfRcQFRv8+7oG1nPE5RPY5QWWy5rTl2LdYj1fYN11QD7hUfrposUFKfxNwOq3F1glhaV1ePzoFOcPHsG2HebzObro0RDY3JzHNNEJAlh49bD17D/qjYTTCi71vqsmAoWkmNGcO7mua9HWNXy3RiEFSnrdAMppgR//6EP81Z//HAflBHfu3cWH3/0YXgnMV0t88ct/5qSp9957D9+5dxtxfQa1egJ1UCEJhz86zLD4/Df4l/8AHN+5h+M//yvkHAnrEIJHyTn8r6qRY7rPGr/nrrlewDHFGyV+2tV1Z9fXN7T+/Sz/tXBMr4LS8Srl5TWexMZ63SU2MZ59F7Qf4zNPEf2YfjvWv3rrFfaeU5oO5QGnDsEY7uxJMgmlcw1ZJZE3qO+9U7ERIz0d3UQWWrFoaHM+YNCrniYY0fOMb+GiRpIWJp8io4QjRDj6e0tj6zXnxNNHh3w924sLpMU5uidfYP7gM4R5zmr+dr3E+cUCVinkt0oslcCD04B/+cf/jAvr8C+Pz/HYOejpIbsDULe01BkCxYemhI5U+jTSlwaVkCiThCGBGKVO6QzTKmcfVgKzsWkhbWCrurVxqBsSbUncO57iNkWawqLUCSfTCWbvvYfbJ7fwl3/2E+4Gk7MBjfHzoxluv/8eDokeISPu3buLSaXx8OI+LtZzqOSRFRLF2RkWVmCFDI8/+wTTj38AFBV0kSM5ycsca6x3tV4NSse6qbX3rPyXpZC8toNDDHAg0n5nXYM+pAGXo9Ht1d23CtwHfMYEXt1RSWnPHQX5ah85MirfbQW7+bSJgeMnDR0/e/J5+6rLH3p/JQhQdQiaxtBztGkFU2SQccK+nk5doO8RRjTtAueP76N78hAT3+H96hBm+h7qzgEXNSo94dx8UvQ71yEnwc7FBWZlBZc6NpWnKM1kA0dpKlLmV7cRvYWWAZkRkNHD2wAKGs2zAmH5CKeffAFTzHD8oz+Gz3Is2xW8sggiYvb+T2Cchf78U5TNHDassGhbLNc12jaH6D5DYzXqrsIX3SF+e7rCF7/5Fjh7mAAAIABJREFUHR6FBk8a4m4C9XrFhvt5JqHXNbrgQZ4CHRIOWo/b8gTL9QVw28FqD/o1nx4BuUPjFKzrMEkaZQSWqzl7xx4eHrObwfszgfePj/DdkwPmk04oelUAF6sGT+ZLSJvjbn6A9fIcaZqjmGgYJZGaNbKQkHSOyd1DtJnDxf1PIc6f4ChmiIkiSqc4PznCxfoJhD/D4pf/D8xP/ww+fw9RZcjaDpADdlFxyAdx4PM/4JOY4quPv93FlUMt0Ve/vqFT7c7ipp3PP/te/65c5F19Onf0AR2o9CLv0q/z9Tpk1DpoiD7QURxc/o7P37kGXt9gQ/Wbvb4bn5X/ttf+uS/XPaoYqjfdx+261/9tLf/50VY/bo8bU3u6giJfURYyURRoimhdgGjrvkuYkVfoAYwr2buU6QApoPYCmY0saMoKg6KaIFMSS++wJI7nvRmLqLxdo/MNC670tIB3Acu6Rh40gqjQNQmPz9aodA6jpzC5hooF2q5BLBLuhwaLi8fA+QrHncR0HbGuO/z+dIZ/+PQLfB4uEG7dxf0K+KeHn+LBg89gXYIhEDktcHhSICOHAVgcHs94O7krvGyQ3zqCPvkYnz/8NU7nFzj54B6cTeyLeiQMCpUwdQ2OC4U//cE9fP87H+OjD95HnmW4fe8WJlqicBZucYbF2QUuiJdLHFllodoa7fkTmEoi04eIRJswAtFotskqjyYwKsERZWK9QqpbaEt2UhYqJZQmR6xmWHUN1mfnaE+fIBydIBjFAHf/CQ83/fxy3fW2n39u+vqf1tgpfXNqBKY3qMYPzlivu0ioxJ6iQrFClTvEqRcn9Zn0Wd8VDp6ha6HJr7QCkkUMFsm11BaDUQJ50Ud+WhfRsW1RwuyjP+KulicFvHNYrObwrlf2k/9o/bs/sLAnJorYXEIpgYOjYxgCXACWUeHko+9AJoOYZQySif8KJyC8wTFWeLhcYeXXyHSOkozqHz3GZ2TRdH6Ovzst8U+fPsYnp2ew6p8Qk0UlPP78w7v4kz/6GD/48U9w9/gA9w6mEPWCO5XvHR2hMBkefPEQv/rtpwh/8sf4N//j/4Df/+e/x//6P/0v+I+//QSpLHAy1ThZLPCLv/kL/PSHH6FEhwIOtw9nOJplyHKNztTQqRdsebuA7S7gfYusELhVTpDmnvmysp2hSMegIBrqWE+qGYu+grKwbQu/PEM8O4NcXCCu1/BNjZgSqmRwPJmyrdTqySnmjx9h+oMf9RQMek9H1tRYY72wvsr3bdozB3vX5Q89f9+16/a97Pl7H+XjFYlPr2XdA/ffVK/QkYs71ussAqVSZpDCcnoRi5soupMApuvjNn3bcKIQCaIoz95HB0djeKFRVgUmkwlUngHesyqcVPSt7/jqN7kabnkB1y6Z8zkpC8yKGeonXyBOCkhJAqVzrCmysz1DNTvi7Pny9gEO6XEXS6xWc3JEQllOIHIDJRXc/BNk6w63vYFoM3z6xQL/13/6Lf7973+Dz7sV/uE0YGIKHN+e4f3pDD/+6AP8xc9/hF/87V/gT3/2I4QnLdrlGcJyjtVjgdWTFtPYIazWSBcPcLdp8G//w/+J6U+/h5+d3MXPPv4hfvuwQ1fmOD7I8Itj4L/76Y/w/Y/v4uLx51hePIa9OMXatVBHh5B2zZZb0QaAKA/MwVXcRyJObsg7NG4FR1GkIrFZvjAaZlpyIpZPC4i1Bc7PkK9XMD7ABgvXrdmOKqsFjidHmGqDblHDLpcoNPV96a3a2QxnrLHe+BrtGN+8GjumN6T2R9Le7atp/6rZIY7brivY1Sdu4OmDG3jDfeSw5TiTCb5hQVJMpMoP7Ddar1v2BI11B7dcAE0D6RM8xY3SmL9z0NUUlTI83vddx6Io8gFVpFJfnMK7DqJZIjRz7g4miupUCivqmBLflLqzOiJR1r0SSG6BzK14nK7DIVanD9Gczxn0HpUT5GXEuqmZLrB2Hbqlw5PfXeAf/ukz/Ltf/gp//+kfcNY2UEbjv70zw8/+9E/xNz//S/zZz36KH/74B8inOZ4sn+CTJ5/j9O9+iS8+/T0WTx7Arudo6gsWc5HFE72eH+V3UX/6Kf63//l/x7/67o9RugLSF+gWFkFp/Ku/+T5MfY7P//kx+63OZscQxiAKDa8PUfg5HOFRK5BCyVGrFJ3qgwOchyyByD5SAibLYCYVTJUh5uhV9eTd6hrEuoG2gWkQMVO984G3nJd/6GcojEYuOnTrBZTsE7RIa6aGKKK7fsAGP7/7du3YbwDA7s+/4eefnU+w+17/t7t9Iyh9M+q1qfKfT34aD5C+XnY197q6pcPk+ute/01Phnptm/KN6qt8zhiUSsViHfpJgkACRSRccOQjShn0XYvQ2R5MEXNNaQSVw0nP8ZtRSDSdQ3IeIgSUmYAxFPtZ4dFnT7B48Ani+oIz9Iu8QkepSIs15LzBcr1AVAlHd45xfOcu8qoEagep1qg/yJC5iFmu2XrJrRdYN2skL1DlBfL3foB//x//b/zb/+Pv8Pe/+hwXAA6qCn9z/D6+X87w3//r7+EvfvFf4eijD3BaL/G7X/+/WD44w6///v/D7/7xV1hfrJmSQDzOsuiTo7rQwNSBo0J//fnneP/gLvJHS/yXX/4a0/wYXevxwd3b+N7dKQ4PS5w+vs+m/x9//DFODo+x6BxWyxY2NCjsGs6SiwBgfULbBs7+J7W8VBFJCebL8sVBAHJ6L4hz28zhosVBAjoy1z+7QKrXEErCMZOhT8FyUvbm/RrQSmA9PwechRDkXrD7OXb4+Nnt87HvZLnr3r5da0yW+vZqxBxvTo0d0xtU+/ngDJHPr/vENrR9u7om7Nsnbtf1D9WuPnJD37zEMdUcGbq9kT8meJz/NNeeFPToJ/wMSmlIHDJ67ASqOgTyqvcxBRnpBza5F65FFxRW5+v/n703/bXsOs/8fnueznznoVgzZ1KkJFKDZSmJlU47QNtAPgZGkAac5EP8IQmQb/kb8g90N/pDgADuBPEQI0nHHastyxZlS6IpziySxSpW3fHMZ8/TCta6RZqiWXUoHl7dKvI8QKFQde/Ze+2111n73e/7Ps/D6HBCPhko69CgKavZHoMxWP2CJBNkZUY0HBD1NdpdlDSUEAWl4bDZatLxGkRRRD8a4K1J6aQWcVxw8zDmr159n794/QZJUfPIhYd4eqPLo4HBBd/C9m3SLOa1l37OT174O45v7uNnGl4kWMmgatdsrm0qe9M8jZVKRn88pb8/YDSI2ey5uJrPo2tbvDvcYz8dIqSH1PiQ2J3RXLlKksUUSUQ06XN90lfEKE2X7lU22kpTergqW1ak4D/SNSvD0GSLQ02cumi1RXY8ZVDdohVmGE0L4VZotiDTm0SHA+KjEY7MYrcCCkmMskxq3SI3dcZZSs/UlBtsFE6p0wzdCjBV9vu0Ffbv9/3lrPGg7z8P+vnvjk/XY7r4MU7z+Gf97Vp0fHftMV1gTEucIpY9pkv8OvCBVJkiPykS1Af/Fio4re7YcxpKPF+o8rA4kcNX5XzTcdFtV+mPShkkKZUve0irPCZLI+rapahMDNMjKw2O946I8iFhYXAwmHA47eO6tvSBUnJSftBg96ErbG3u4roN3vxff8jzjz/OUw9fxvIsWttrnHvoUd67dcCf/NG/5ZWXD3l97za232FFM3kInbV0TGGHXM8TOm/W9G8MCUdDssGAni6NPDXqtkOwts53r7bY2Vinv3/IjXevK3H67fUtDvsTleEcGn30PKdrW9RGjbvqY02ByZDnn30GIwhor61QTg2S8YAynNJrNHB0h/7xbY5YU9ajpuWq3tAkn1GWstyeK3UDj4YKdBOZOU76WJWOk1pofo3XtkgLQTKOyKNEBdm6a2MIAzPKkI2kSVoj0piG52JKu9I8VfdMUdl0nbpaWj8tscSyz/TBgnnqb2x3dNr+0TL4IOY6ZZ21uYWeuQt0ng7eYjp79YfOFNo/Gq2SNj3l4PS0dUrnn3/e9Z2t3NKi41u8FLfY9c+7v5WUgSpLHNOkEXQUcSmJpV2mhVHlaHVbMfSHySE6ObZV4JgGWqzTdnuIqM/6RhO7ZXEcpuiOx9H+jJd/+hJNL0BvtTgKdX7+TsYLr7zPwdExZqWjpwXJOOTIiLA9V7UKdNttVtB5e3/EpmiR5n2uv3mb/++tPr71MzbWt3n2G9/gn1/+j/m/X/kp/+O//Fc4aZOHz+9g67IEnyrB+ySegnDoj1qc55CxbqpMYpxk2FJKqdFkgGB2PGBFDChfegfTCMjqgHiSsNLSWO04pHu3IO5RBA4pKdtGlx3bpbee89DjFzlnzBDXr+NZLm5nl5m3zvHBIZFeK8msuNTRaoMySqCSfyqMNCXJa1LDIlZ9oRpZEZNXBUaVMAlTmkYXu/aIZDvD+F20qkC3K6xmgGdbaJMUYxaqgDlNpnitCxSaj2kliCTEKkC3PELJ/p9Xyl4w57Lo/rT45xfrQZ2vUzw35zPn+Iv1YJ72+RdtlRBzeowXx2LHX7R9UD9l+uC848+7P/rC63cxzNs/5o3vbjCXqf4llvgSQ5byObEalaQfzw8khZ5JGjGZhUiD97LOMYsQoy7Ik4iqKFSvqC21Mns7vHp7RHGYcO39PX72i9c4OhqSTGNs08ZfucZbb73FrZs3TzJ5ko1jCtY3ujz91GWefORZ2oGHXuWKqT8aTtUxbvziRfqjiE7X5/i4z1uzd9Df/gX7/Wtc6BX4kz6//8hl3r49VQQjkxSj1VFjKnODqrKoM53r9TEtqZ1qSbtQm+NRn+ODfY6znGlZsVdltOwm22u7KgPcHxzQNAUPdxp0REmrOCLLbYq6UjJTa50mW22H7Z022w+t0+z6DA4GjOORepG03ZIoHJFIif6OoJLNpcrG1FBqBpLg5OpQKlq+JJxVOIaOJnSyImXUz4miEK/RwHVdmRLFlw5RnQaGbRDNZhRJgqYLClFSFAVJkqi5k1BcqbK4k92uPxdy3BJLLLHErxPLUv4Z414lho8Txpb44t//szq/jGF0TcN1fQxdEMczChnlzPYps1yVhB3Pp7u+qVyZZIDUn0558doRf/U3P+b9wz6DWcjBwZBabSsmRZZT6S+y5sOzjzzCs1cf49K5TdZ3O+w+vMXWhTUafQ9RZIyO9tBEwTBMCfKYHxcFnhD06wLXt7nc3UbPQlbSY45//G+52Gvzu49f5OhyyXg44uWbB9xOCqpUIDQfizZOaVGva0R5TiErF46BZjh0203JRKLo92m567TsgCBoUuYFiWnScjR21ta43G1jRX36aUo1GhGnOWaeYto+/sYawaXzjESO6TdpVRp+rZMMBtx+720ODm+S5wmOdNWSWS3TwjZMdMvE1k/Y8sLUMWX7hG3gYqqM7iyOKOIK37EJmg2sKlAtBXp2YhErHbgaDR+zrrg1GiklAGlwIEqBsCyqO1JRli5fN+ZnS06flf5g4375ft6vx18+n5Y4DSwD0/sYyz7TBx/3O6tWv1MKlC5Hsq9EOi9JmaZ2b1VJMsXJCLyAKMq4eTgEEale0Pfee49XX32Vv7h2zGw6Vk5Ejm3hO6bKEga+x7nHLvP9//ASX3/sWZ7auYoRZowO9plODrn1o7/m53+2R7qX41s60eiQqi7x2l1miYaTzggoORQpvmWx6QTYccx5odERgrWtdbauXOJJT5AeDWn/6Bf88OV9Ss2h5beUR79uShKSpXz14ypXAZxktT90dZdnNrY5HI148drruHVKoxjgugZPPrrGriRPbfRYNQ0M0eR4FrIz6jKdRKx0V2lv99h55DIPPfM4mdai4Xq4uoEWRQyuX2ccFbjHMZ6ZE0pbUBn4lxXCcdT5P6g+G7Xs05XldhfTkASzGqOqEHWFKV8EgKLSmI4m2GFMQ/rsW4ayNfUCHzdwsUydtCypVWCq4bQ6CNdBk9nYXJvLzF+8lPtg70+nfX0Lk2NO+fxf9vt/v+PL+uJgnroE86I6jKc+sae98Xy6rMWHfvlLLPFrxEetjMtK5jp1xSYPml3VSxmPDlSGsD+4xf/5lz/nxs0D+sMBYRwyGAzw1y/h+yVmPGHNhd2VFhd2t/n2b3yT559/npaZMjwe8dJf/zmv/ewVbr99nTqMaTkGTc/F8lw66yv02j2KLMUwPILApm7VtElpuR5FpmPVJrrt8fBjF/n+7/42F597Dm1tk4PjnxJ0muy+fcjuewm53UDXIvrHB1S2izmuWW01CDyLfv+IKI3Zbvk8++TDaLrNYzstXKETyB7bToPedo/VXhMtDZntH5DFGV7L59zONvEkVpnlQgZ+mkFSVdhlSVTMqNo+za02frWO+bKPjUlDWGQUlKJWmqh5LaW2PkIwE3fMCmTZXZKUpOWrOCn/J2HE1LSU7FQcTllpt8BxiOKUMs1pd5qsbu4SDQ4oJpAnmfLHb3ZW0DxP+XZJ0trnoBi1xBJLnBKWgf8n40ufMV1cB2/5xrjEgw3lf6/0S08y9FWtq0yj6zUx2j3CsOTnb97gz37wAnFy0tfYaPk0Nrcphn16jsY3n36U7z/3GDttTwV2W9vbTPau8YMfv8T1G+9x48b7xHGMLUx6foud9XNc2Nph4/wGRZYoOaoyz5VclQz+qhjM2THWZMrM8JlZGomnMbFr9LUuld9mJPX+XZ/heMJYltrjlExzwJSl+4ROw8KNbTbaXVbX2uysdxBGxaOPXeLy7qo618rmt/BlOT2TblUFetNBs3QmYcQwEzQMA93QsQ2LPIRZOCNNQ+LBkOnRiHJ4jUKrsbou3W4LZGbTr2g1bYqDMZ7rUpQlhS7uqG0JJZll6roSwTfdE09++UcaHFimg6gN6qImjVIMu0bTK7IsoSoDXMtTvbtSgd+SDlHWAFOryJKcwtTY6K2Aa5OUOc6pSxEtscQSS3z++DWQnxbVYfxiY57A/jKL+sXGfXF/T6QhlMC+JPkUVa3YlrVusrq+hufnKrMng6Xd7R2E5L7X0llJ4+JWm2cfvsQ3ruxydbVBOhlydHibg3euc/v4mNdvlIz7U2ajiMDS2N3dZPf8Zbob29Rei//n2iscHw3xvYbqk9SLio1WkzpPqfWczU6A7zRpuj5JVlPMDklHe2TRRXJjBTNMyQ6GVGnOcTylX9U88+QFLm12KI77hIlUHcjQjZJzu5t0VjsErYBJcowhdUDbAY4MyKtCBc5imiF0gyrXaDXXqZKhmpOqrBQ5STLrW17AeqNJz3SxtnqE0ZRkNGTvzdcZHwwwUwOv2SGPBU6VqbmVNq+l0jcQaHJ+xQmjvKgFWVZRFKUiK9V3tmRR65SFoNm1EbVPHeVE0xmNtSbNRlfdm6o6sY2V1qx1VlOVNc1uDyybLM9pGLpMwt4Tyx7De2PZY3q6nz9tLBNHDya+9BnT+xXL/tIlfl2QAZEMmWR/qcqYqnWnKbtJ6XF/+fxFnnv2ab7yxKNsbGwRhmMOD2+QpFN++9vf4isXH2Jy/RpvvPsqq502w1nI9cGYw2nMa4MmAQa7q+d56tImF66eJ7J1fvjG6/zNy69xK0zwG02eeuKrzIYh777yMluBzflug5aFClTlWFYbLa421rGy2/SqGJGNSV2D1uGEToHSIjVbQxLd5tGvfo1HKHnxj/6MSR2jWxB0Gmyd28Bs2AwmA0hhY2uHqBxjagaWKDC1XGUrMymXNStwKoNUuloVmXrBruUzWFTKdjU8HJAKgd22SYcDzFlCfXtK/81blLWFv7JJbndw06MPS/eyt1RUtZLoksQk2WMqNEtlaiv1VTdAr9F1C6FLhpRJFE8JGj41BuksYTKcoGsOTqON7beYKaUDGyEDBM3AbTYVwarKU6UAUKXLr9ESSyzxYMH8pSazT0I9541o3ufnNjktGHzNG9+8sy+ogzd//ubrZC5kQzpPB3YO5p9x3rvLvVMy2ryMuVjw3WjB618Uc1f/nOsT2oLztyBM4VBZglKkCKugLqWlqIlvN3EMn7LR5aVXX+Wrzz3L6mab16+9gmZa7A9GNLptHrmwQs+NqcwJ+qrH9VHC9WnNL/amWJ7P+mpCFYd0Nnd47LlvUOk+f/5XP+Unr8fc6HeJXQ8yA0fagXoRgZeze34T32zyystvct5ucemxFs89+zi2XhFH2ySNixi6h+vXHEpBfylLpdX87lOX+Bc/+Ck3r9/mN37r65TNiBXDprXVZf0rj9C4tMrtm9dora1A0cA0z7G1OlJSWVVWQpJhFOAkOZWVSeYRvusRhwnhWGaI25jdFk3XI+/POL72HtHhMbZtkxcFk9kUoWv0eg0aVomu19TNHaJ4Rj4eS2spTFOocn5R5SDlttKU1UaDKEsJ4whJ2S+kikCVIWyDbVdKXVnkTkWa5IySAXpq02s2lMyUoIdWjZkkI/zdxwlWt9DSiq7hKz9/nMXWz6KvxqfPEJijI3za+8+CEHP2r7PORy76dF/8/Is5Z3308auLf8jwfjjuOTqssq3ok7RQP/UzW/9llZ2PQ7rb3fP8xr05OPqc8c+RUZ+7/uY9/+cf/94/v9vnlxnT+wjLsv0Sv26cZPNQFqPqb+1ko1Nl5boiHk9V/2UymeGbNtfeuMb66hpGXRMfj7h265jmxS2soMvx/oDBOKKobTzbYzKb0C40nnnkKr2Ox89//Je8cesWN8MY0/HxvAnruoeRxYx+8VN6gcF/9o0n+OZTz5JOUraylK3eLpeeeJjzF7cZjaQsfo7tOqp303KktFVNbtdkWoKpCR596BxvvfQ67z/9GDvPfpfDv/sx602X9aaPCGM2gw5VXmM32mxs73BrlGCYGrbuErgNKhER5ZEKaFrtBpNiSO1UOB2LvNCYDcZoJEpL9ObNd/FSiKQ0k+3Q7HUImk08L1AtSqKsqKtCBbd0aqbTmlkUkhcZtm3i+MGH7RPyoSUDXEmU+mAfyJIUrbWCYUrnrFr9rlZpVFlKojzxK9ViUek6tuMRNFsYtuwsPbmHuqEtbOi7xBJfFHyW5+vymXw2+NIHpot73Z6x3MaizhsLf+/mnP+0uxFO3XlkDh7w+atFfec0Qr19KycSXVOBWV0X2FVNy/exdY1/+v3fUoHpwcEh4WjC1voa/++PX0KvNR7udiitnMF0zM3hiAyBa1gEnQ5TUXB0e59oekyZp1zptemt94iTJv7mRb7y1MP0miZWndK2TewKcs9i8zvPkE5rPCtnuP8eqSjprHVotBsqaIuTFHM6osymVFqqsohPn9vk//rJ6/zdz1/nm999Hg7eRogSq6yoogrX0onrGtczCcsYhEeZllSVJD+VipgkAztZbo+KRPWeImpc06S2TKZJwvDokCqJKYcDNLuB5li0uy3Wzp0jaHcpy5o8yhW7vkpmGJaObVr/kG0xDAzLUYYGcguO4kRlFkzTpsgyNFkFqjWSKCXNNVzHw3F0HDNRga48dyY09DLH9kxyXcNyHTqra5iSbCX7gStOgtZF95dF1/dpf/+1M95/FsZ9Pv5TLnjOP//nub9/5GLuZE/Fr3CBp6ExPjcjfJ87a50WvvSB6VljnsD+EkucJpS+pqmpjClCOhEJ9UfTakRdoIuSduCSFjXf/a3v0eqt8Md//Mf8yZ/8CVkeceM456///k1uNx1IciZpRSE0fM9F0wsqQ3A8G+L7Jt/8/m9x+eI5TDSaXhPXcuk3Gzz+6CWKeEqdTKjjiNH+AabuENhtOlZOLFJmoyHuWo/Oaps4jTg6PCatNdZmBWFWofkOXd1nbRjySK/J6z/7KQ8/+xgP/+Zv8LOX3+Cd/SM219tUWazaJ0y7pDYmbG61ScOIcf+YPMvoNHzaW5tMp2Om0ynJMKHtt5geT7n55nWy0ZSmFOE3G6xu+YRFQnOlS3dnh2BlBUybOq3Qs5M2I0O6POUps3CiHJqUu5YTYFgmtdAwTEM5Ypm2heM45PmJh74M6mXGNU4Eqz0fx7RJzZli6ifJFFGUSt/V6fpMZabbsmj2VpWkljBMqKStbLWUi1riS48Pn6l3HqeqSvQpJ+Vewefy+Xx6WAam9zE+3RvZgjq0C2dEFvWKXhRnbLk4r4dmwQOcOitXF6p8X8gSsjBUdlAGpdQlRRlx6+036axuUFtSBL7me//Jd+hstDE9wR/+4f/BNIGep+MUPraUOdJlYFSrVgBLeh7tH/Hst5/j6W99nSe++SzOaodhGKpASpafG2lEimDvuE8eTlU/apWWrLU6GHZOevSeeqIYoqTh2miaYBJOsAyX1W6PQvZoZQl6UZKNY8x0wqWOraScrr/0Av/kf/h9srVdhv0BUVkgoil+w2Dv4Bor5y9ji4Qsn5HEfeqsoiGvxWlTG65qD9i88jQXz1/mtZ+9zPFL77K1eYEnr16BLGIyGmLGx7R6XWw/UD2iQstwTAfJXQrTCOpCOWDlSaokoWQbggxCZda00nQMXUc3peyTjambyltakrFkwCr/lgoJhumqFwSpMxtnqVIgOLGPddV5pBwVspTfXUFIKSnTQhQ5dV2iyX8vtEDO9OMLD/C+L8XO8RI/89EvvL+d9gDm3H9+Oav7q66Hj/76aQSi2jyv+1NPWT+gGdO5pegzrjV8EXpAlgL7S5wVTFOW7nWlXar6IsWJVFRV52R5zI2f/ITB+gaXnn6GMInQ9Jorl7f4r/7r/4Lh8BblRNDVBenhnjRbwrBNyigmnIzZWGnw3H/6m/zG977L5oXzCM8jymUi0VXZ2dEsoWudkH06wQphAf3jKXUqqHwd12lQdJqE/SHDwQC328FbK2gHDVqddXy3yX5V4KQh0XDI8eFNDK3C01O+/cRlDo9v8+Lfv8Jzz3+LW+/v8eaLL+CWJesbPY4PD9D8I8qqSZlk0mlEWa4amk2aV2B5dDcbaEET0VnB2trkwvPP8+SVq5zbXufWtTdJrhc01wLVA5qkKeEkVL2vzY4HNpQiQ69LLEPHcx2yslDZUUlDKQc7AAAgAElEQVRiMlwb13NVsKpK7lWlMqplUag/VXlCSqjSjDxNlHtVmMQUAnTbRvcD3E6XNJucaKA2bBqdLpUs42u64oSKZYfpEkt8iE96vv4qBjmfRHiaHx/dG4tSW+edf/7VnbLB0Gf88Zc+Y7p4j+lix1/8LWzBYHY+rXyx45/6G98ZB/Nzh39/X9+HGYU76hayy1TXpCe7fFcv0W/e5sab12hKK9BLl5ikCXm7ydXtLf7b//L36HW3uPHy3/O//Yt/Sf94QNDWMB0TR1js7Gzxnd/7Z6x2VznujygnQzpBSzkSyWVl5TmzrqlcjizdUN7wweVL0h+VcDIky0O2Hn+c4U/+juksYbfSsDVLZXWl4LyUTkpFSJ1niKjC1mxqq8RuVGxtreIOLX76p3/EumZj+S0m+yNiEbPRg06wjS7a3LoxxSgEIqkxypSJPaQ2LCrHxgxc4v19Dt+/BUXNuXNbNNou4+kRURVitkzM5gpGUaBXUxwjxywqRBoqMm7QNBGzE0KTXdiqVJ9UxQnZqTrpUZP9rKblqJ5ZWcYXKlkttU1T5aMviVdSJ7XKEtIix21INQGT2naYlhVlHKvjN72ARrtHpZkn2W95/7RPk3GZgwe+WnnWTZLzTn+fJyPu9/s/l/Z999/9NJKMCynmfCqc9fPrM9LmTxlf+sB0iUWxmJzHEmc7fzJTJzcf+ZeOpbgGUj7J0E0MQ2cTnTdffYMX45Rv/u7v0Lt0gWQ0YlCkPHnpIvtHA773nW9QHN7mhz94gVev3SYta1baAY889jD1KCQrdcrhRG3yuVYxiScIW+D40qWpg961aQZtyjjFkjqqWcqkGNNY7XE4itkbjolTyW73qYuSw8NDvEYKhUahj6mjKVZRsrW6yfWD23jdrmK/b3XW2LR9bv7tC6w89AhGUnB7b4/h4ZCHv/p1fNvjyoXHsKXQ/Tgkmk5Umd1uB1SuSWHUdHyHOIpUNpWy5varLxPPBniuRcfSCG1L+eT7DXCzknQyZjLoY/rS1tWjrjTCJKWqChUoOo6nCFZSdzQvawLXV/Nd5sWHzHzZW5pGMaV0lHJ1Kunzn6fIhlW/3ZQNpcySjOq4T5tItU04nocbNFB6AvVJg4s87hf/27fcf77Y+Hzur3bylvbL/+ZTkIvuyPmdna74l3N9m/pcr/p5P16sx6+e80qmz7MEnfP5+TKliy02fU6PyNzr008WnhLf5oMsykd+Puf8846/eHvAvPm/d7nQWNDydVHMYyXPH9+io59XallQZ3LB9VuaJ3JRpnpFPQmOSpm1011aqxcpzj9B741f4JUm+iAmmvyQeHWT8vJXCa+/SXH7RdLt3+F3/6f/HnP7X3Prf/5XWNMG0SCjHIdM01cgbUJkoVktNDfAsXuqXN0WLQ7GAt91KOVOJEzCyYgiigjMBiKuMKS//XCPrQvruF3ZUynoSa962X7gWbhSP1Qk1FZNEdfsBGsktSAWGoN0Sq0CRB3LG/H8ty8xSy6R1z5OcxfHWyWrb5JW0Fhrsb5zjlqXZfIGRrMl417ickRxuMfkndcRB7cwZxFmlDKbacS2j374KjQbYFmkZs7MrtBrG8du4JsBo3pMViZospzvW+gyGyvtVytdBZC2EEzHY5I4VHuAJItZgYNHoALiRF7fZIZVVXgYNISO7Wp4iqsWcjAZ0KuamN0N0t01KY2KE0WUjkFm2hjzZJYXXF/z9qdFmwnmd8Dd+wwL1ytOu8d7wc9/2ozfZ0V9yvvn/PHP0Smdf4IPz/PRlVJ9cNq58Y320X98MKgP/+tXCRvFnXF89Jo/eP7fHfde39WcBb5oqX3e42Vu/DH3+ffJn19mTJdYYom7YvPqLm/+Ox3fNtFEwWw2wwh6aEmK7rhYkcs7P/kb/LU23/ntf8bR633+4n/5NzTWu1TdNpvBLvHxFLMA27OUsHzh2BjNJolt8VC3TZRGTGZjxfKnKAl8D7vWyKOEt996h0bQYWNzm1o3yCulg4QwDTRZGh/F6uXDsC3KOFeM/UR6zweu0hbVUkGapwzEUPXRNje22Nm+iruyQ60HZHqDcBpRVBqG08KUbHjLUHafcldumg18v4fdXCWfhFS5wE5rZU2qKZvSgjROMIycQor0y6heoJj+ZZpRFJXKSsusZlmX1PK4uqUITaZtk2aZ+pnKyNSVIkmp3y1OhLc9z1N/S7KU5zTxmw1s1yKdFAwHfaUarhsGdqOhjAYMzTwxPj3xPF0u7CWWuM+wdHWcj2Vgep9j7hvPcoEvcYrY+soVXMk610pEHiqCTmMaYaQx+moT015l79WXuKbrXP727/D7/90f4MeH7N26yWNXr1BYPrN8SqOuaEidUJHQbDbprm2qfMPta28oHdDAd3C8gMquMIqaaDJlcnDMJMm5/PAjnLtwjihNqCwTz/cRtofbauGkPSZxQSJi9fZtN3x0TZMFbkbxjOqwRKYNZ8GEySykVwlEo0Oz6SHsFC9o4+k+ZSUVBRzVo2nIHlvpQS8KbOGgu230zibT2QzyEksGoEWKyCqsRqAmX+QCo6xxhakCy6LISaIEw3GVLqwMGmWfqtJLrQSmZuIYtvLOlyV6ybKXwv91VSHqWmVS5P9ZxomurO/7dIMAJ5CapjaNsmQ8nVAXNZrnqfYF2atKddK3KqTslzj9FraFyRenvH8tvfy/3Ljf5ueDoPTTBqenz1G5P89/5oHp/MBrwc+fsdzFote3xBJnieChTXafeJrxq29RxGPFOhdJgp2n1EaDWIrely6zH73Bi/sV3/tvfo9/+gf/OT/6wz/limVQbPRoy17J/pBwuk90GGPu3SR0WtSZwG66CMlOL3xK5VqkUSYl44MR71+7yc4Tj7F94QKWY5AmMb5j41o2WSUILIdQN1QgJglFldRdrU5sCCdxyPFogDk26K13CPAoJilHb77DbDilc+4W7fVNGp02zd4mrt8jFyV1LU7qc3WJqEvywsKSAasfUDaaiCpXLPuSIeU0wjEsyiynkHJQks0v+0cFyjVL2ruWWnni5iSDT132j5onDybdVKX72tQRlUZZywxsrTRepQ6p3DcqmTmtcmxTxw18dNc+Cc5rqcPqEPhtwuEQXA93fUXJROmlRq6r+BRLSH//M5ZTW2KJJX4JHw1Ol/hkLDOmSyyxxF2hN1e4/Jvf529vvE+ZRnQ3zzGepWhlRBG3mO3fJLBWcPyc8a23+PG/+ddc+s732Lr6ODdf+hl0HmXLdiGNmA4OqKWrlKiJ0hQXh2zFpzRkFOVgtjt02h2ptKQyjZM84dITVxVL/2g4IMlS2lobLc8poxRhusSTROmGWqtrZGLM6LhPGKaU0grUtgnzBN/22WiukFcJw+mIcPAOHI3wHxoz8gvExjnclU205gpuaxXNclWJXWYuS0ujNAW5LO83W1i2jtVsUNsWudknGodKV7RKCkRengSlGioYrdBU5lSW8KWov2aaqj/U0Ax0w8GSovlpRF6VZPJ8eaHIT9Ilqs5l1rXAMC0lByXbHWQbhJS28j0PRzcp8xLXcNGCBs7aqjqfdI1SxlGGdlaE2iWWWGIOlkHpvbEMTB9wLBf4EqcK0WT9699h5WcvYI328NwWiWNT1CHZYEIryQldHa3hcKW7y3tv3+DAeANd93k3HnLx2j6i26PKakV+ctc71EFAUQo8x0ff3qW1skFjbVMRo6TWp1bk9DwTe6NJY5Zw68a7RKMBlqx6S4vQNEYkKcmoj15pFNJSNMvVd0FKMsmeTinSn9UVZsPC9E1VGncqi4awySYTouktRmGK1hSk+wP0VpP2zjl2Hn4Mo9kly6oTPVBKaqGfsOoNHVOV0335v1g6GLmg1i0EGTJdq/RIy5xKMv1FrUr4prI5rVQmt77T7i9Z+UI3VBuDUdiYsalK/TLglIGpDFbl9ZimTkXFcDJWeqe+4xPopiJOidqg53ep2y3slRVkV6ou+1mNE4KGXguq+zxher+3AnzZsXy+fH44jbk86/tzWudfBqb3OZY9pkucKcom9dYql7/9m0z/3Z9KbhLty5tEsyH6LMZd2WYWTynSHM3c5uL6FaaDCdbqKue/+l0mb77F6OAWTqvD+sOP0XrkMnrTU+Xwtu1hdVroTgPMExLS4GhIWU7xbSmBZBO+/BbRrX2agYvrGMTjIVXDR+gWk2yMmRWMB0Oi/kj5+ttSF1SW9/OMeDymd+4irbU2umGS5AlIQwHLIJ6GHBwd0tAuYtgeZR4SRW+giZz27jkK00OYnnLmkS5VxAmEMcLQVeAny+267+O2muR6TC17V0WJVmjoQgaiOaUAW7o4WTqGUVOJmqTIybJSGf6UknDrGbieh9WSlKVYtQLUd3pMVfbUttFMQ2WLoyxXfvqSX2XpJp1mh1UrIGx3cbodlTEVMmNqaCcqOPXp7w1f9B7T+z3wPesexPsdD/r9X/aYLrHEEkt8DFppM9MMdh9/gus//HPiNGdje53onT5OJRh123jxISu2zcHNIa2dbXyvotNrcfHcd8gfe5I3Xn8HM+hy6flv4WysE2cxRp6iZSWj9wfE0TEaNo2gzYXmGrrRYDbd4/DWTcJr1ymmY7pXLqiG7BuDI3zRwe/1iIqUDd2l6TdwuxpmUVPKHswyp+H5mGsGZsej0Q0QOSSTirSuSHWNSKuJyhTf3qG3uU2SH3Lj9muk1WtsVjlud10RrALTQRg2WpRRz0JymUW1DbI6V1ItMjuaxBHZZIYuSVHo5Cf5UYSmk6YpjivtV+0T6ZciV9lQpSMjLUdtA880sFyXLM7JpH5pkVPoJz1opqHhygwzNZNozGQ2xah1NK/JaqtDy2pQBD625yoilXxOSIvZJZZY4uyx7CX9bDDnTdpcnSoxR0lMv3ctSZ8TcFcfUQL76Fg/rSPDPB3Uua/0+ief58OxzMlK1Pqc+Sn/sSXpR4f0IMjnfjjuj90ToTJHn8+xP/vn5+jgnbLzygdz8fHr+LTXNfeNdOH5+ZiS3J3j1Scnx6hmyj40P3cZ8+nvkL/+Asfvvk1htGg0bNzJEYVvE/seVllSMEF31zmeJezEA9qPPM0z564wG0/oH9yg3nsH2zYxLGmdWbPub6K3anLTwt9YJYqmiOkYO8uYvf0eqaaz+fjDJLZGOp7gCxsrBn/Nx+35pHqbzrlttNExs1vXyQ8SpH1+XVjkBXTMHJFOFOO9YcvgNMKsc7bXuhwc7dN/7wXWdp7j0e8+T3bN49pLf4/77i1210IaTZfDIsO2XHy3RSBZ9LVA1yw8R1eBZ+7UCKld6mlYhqX89pXkk44KKKs0RisqLNek1Wiqcnya9gnTGbXIaNhrpMmMNBphWwKrKSim0vNfQy806sAnD8FIPHZaNsdH15kmfVZ3LpIngjcsja9+/Wl82a8qNAzfoinHMM3IWg5avljFRZuzQc/TCV4UYkHLx19lfJ/4fJmzf4h6Ma/+uTqec+a/nvf8nae0Oef65gnQizkvQWLe+OaSl+99/LvpYH5emBsfLagj+1F2/sefFR9n7n/S+pyHRW2JxTwDgrmfn7e+P/n4y4zpEgvhXl+Q5ZviCT5rUHo/oGo4mOMIr9Nk/WvP0p/cID8Y4bkloyzEb7QpypqsPNHidHwPz7OIi5zJ8JDopoXrS7vMBm6rQVZWGIZG4HpYjoUQFoHMDpY5cTZG5BPyWZ+jG+8w2N9no7epStlhGpMWJZbfobt1nta5hymCBmmZo2UhZVog/B54JVoeo1sFtlMwGY7Qagdds9EwqTSDrDjR+bSEgaDkxnvX6V59iMuXL7Pd6RIPjjg8vM3+YMDquW3C4ZRYj2i3VrCl+1Sek0vTelErGSeRFZS5vK8VeZWr4FP2oMqSvJR8KquKOE0Quo7ch6U2qWTWF1IaqihxDBNsB0SpXsWl7ahWG+RpRRLP0GxNOUY5rk0QNCnykOPJDHtzlStf+ya9nQvopq9eckV152EvTkw7lt/AJZZ4MLB8Xv4DFg5M570xfR5TfT/fsPnOUnPmR/vHmdgPDvkg9Qd9/G3uvhn7gm98i+JB32wio6Zdm5CDefUq7dFXSX/w7+HwmNwT5F4Hw/GxHUu5WMkKSxROqGSmprAZ3HyX9tYW7WAX/Ca60kjSqKROJyZHZYLjaBTVlHh0RKvOEeMjlZW101yRmeRXpCpKJbDvdtZp7lzB33yUyPRpOzHlZESaVxjjCJyMUpSKrCTJQVQmSVyRVjFZXjObRORJQUvqoeoesVYgKJjORipw9pptPMtWjkuHx4es5DXtoIFlmNRFpowAck0gpO6oqOnZrgpEK9Og0ioqTZyw4mW1oCzxfReRZeQym1wUOA2fXqerekejOMaU0k+ShS+zsUWtCjCapeNYLppVYual8he1XFv2VWBZNnFmsj8M2brc5dK3/wPMnXOUOJSZlLgSJ354ulCkKX3RLf6Mvz9nhX/Yv+Zd/ynvc/Pmf9F99kt6f+8nfNLz8nPr7XxAn3/3fcb0y/wW8Wmu/azn57Qt8RbF/TY/v+p4znr8WZLSaa+SJiFjB3aefp7J23vc/tEPsDsaQ1wagae0NKWiaF0WFHmEKV9YMwtbbyCSkDRLVGAqXE/GV8RxQpSE0LRUBpLpgGLvXbIio//GO9z82Utsd9cpwwS7MtCSDK0qqepUaYNqRq3sN5FsedmzKXu5ZABb5qTRhHw6U9nDXAjCRFp3jjgajZUEVNf1lFOSrxsEbY+dy+cI2i0Gkvlem6x3Omxcehh6q4zfv47rWHhmdZLRFBWBd+IqlWa50jCVmVElESWDUimmL/32xYm+qsyYCtkOVJ44OcnIU7LuPcdVwbZRGyp7KmWeDN2mEiVZniOMEsM1aFk2qdTzV375OY4d0Os6zEqDjauPYu5eAtslKWtEKU5Kp1qNUDv7/IfSg76/Puj7y1l//rSxNDg42+Pf7/HB3TA3MJ3PCp+bMvxMA5t3/rv17n3Op/8cMH9+1DV8pMf0QcMn9ZjeP1nT012fvwo+qaR/v2fFPdmj6FckhqCMa/xgBeeZr3H0zlske+/gr51kDKMoIfAsmkEDzzIps5jZ8Ah/xcLRK1zTRJPBmOMov/s6TdXM19MpZTik7N9A3LxBPJtx9No14oMjvNVd2q6PaxvYecYoi0lG+xzc0InLKcL0seuSKompZ2PK2ZAqGlPHE2RjpiU04tpjGMcMJiHSSbS7ukKn08KxLRqeR7DdpvfQLq21NXzDJgtTJnmJHXisPHSewrDZv/Uex6Mjem2ftU5HZTvjtCAPYzTTOvnuSra//OOAZ1l3LEhP9ExN00Q3DfKiVP2nGCVFWUIltU0hj3Ml/yTbIqwqJ076iDQlCDwVjKZCkAodrapZbbexPBez1AjW10mUzql0lBKYhnESnKtt2ZjbPvjpcP98f84GZ339C7vpL3j8perLaeKTnKDu1mP62XDa6+d0MJf8JOYMbE7v99x39k/j3LTIzVlYLmLOzx8EctISZ4sHuce0ZbqMZKDnmrRrW5LKsS5dZetb3+KV//02QV0q4o2y2dQtJZtUZAVGLVQmM5kOcXsrOKJCSI3NMCaLI/QkwigyqtEB+eCA7Pb7pPt7pMMR0WhGZ2OLYGuLfjigkzvoRUnL8rFMQZkMSQ+kcL2Quv3odYVeVlRxhFZmaLpkxFeK+BKmOtNZpEiYG5vrXHjkkrIjjeOxshPdePSK0gBNHYtGq4vtFhzu7RPnCV5gsXr5EUrfZXL8PlU8pT8b39FOrYhmMb3VrponKSNV6SeuU6aUkpKST1mpektd9yR4l0RMmR01NKH6Sk1HY1YU5HWlSD6OG2DXDo4VUtWZ8s6XPbGGE0Ap9U1PbEalD/+sghv7t9mpa5UFtmRrhK3fkZsSipmvFcug4rPgboSTJZZYrs9fDx4I8tOnZeA/iPikoEV7gK7149lSPvYW+GXHgz4HwpC6nBVaLbOePnFa0fCbrD35NfyXXqOevo1pSxKTpjKASVaQziKarqEC1Wk8wxkPMY/76LlOVhsUMppMxmhFglmH6MmUbDggPB5zdHBM5XlsPPYEyXqb48N3OTzOKIaxIgA1tnr4todTobKlk70Dtdbk+WXmMM4FMRazWiOJIobjiCQvMAJf9at213p0tlc4HBuUnom1sYXRaTGW7k1FQeBYOO0GtSFIybidVzQ3d9nsNRjeeJP+u9eVzFXLadJp9pT1qNQcleodJSf9pVKj9YO7Ll2bpKuTDExllV3+LUv58jO1UTMQmRLZl6oBcZohRTwcWf6Xxy0KasOR9H7qtMKS2dEoIopDvLVVbN/C1gRFXWLIfUOSrpTdqYYuM6aytK+XZ7yC7m98kZ8tSzwY+KTn5d2Ubh40nGGP6byc6GJyBQ8+Ptv8PAhl3gcD99f6fNACVZnRa3cazMZH5FJv3mmQ5IJGZ5WNZ7/K4C/fIg+nDMMUv9mhGbSwLUcx1mfhDKvtqfL1+OgIMzNw/AAH2YeakIYDRrMDxGTGaNAnHE+YZgUbl69w5dvPM9U1Nh7pcO0nr/L6L64xHoQ01tfYeGiDra0uvgHZ0RFlpZHLwBSDohKEJQzSmmmY0XKb+J0OTjPAbPqsrK1y5SuP0Uk3KPWSrLAwPF/JQMkA0XUC1adZ6SWJDE31DnmdYJo+zZU1Zv1jor0+GQV+o0GlC1Wql6V4wzIV696RwWRVq6VlFIZyg5IleQ39Q2eq8g4ZSndMpYiT5imT8QypE2DpmvLgT5OMmWz1sQqirKJjeSqglT29F59+ime/9x0MraaqixNZP81SPbWWZuPK7LWoKFg0MP2y7+9nff2Lklfmje/Lfn+/6Djt9XM6MOfplC468Pml7nk6bXf5wQcP+DmqAOUcHbV5t+2u5//UQeO956fS/kHHlDuakr/ejOPp9BjdPwHYvBX45SZnzbt+2xGkSYnl9NRUGvlJoJPisPWtf8L0+E2qvQPMwyl5MiLdDbBbHcqkj15MsCMdx5yipxq1PibNfAzdoY5LqqhGm+mIfkEnNzgejrFXAqydFmLFQZQVvnuB7Wd96sYaN157i8H7ewxv3absD3EMHau2saQmqihU+X2aJxyHMzI03I117DwksxIuPv8EnQvn0TfXyKTnveagFQWNrY76jre8E9ekSMZ3bhO9rOlZa4T5CM2yEfYqzoV1Nhvb3LL/lnS0h7uaE5YOUVmTYiKk2YDjYGmQzsZEZYTlNTGiCjuRsbpOVJYMsgmaluGaOnpxHuoMz5ICUzGWbBItavJU9ow2WS1zJge3aQctZv4WT/7zP1DZ5EbLp9IzZKuqbronN6tWLa5qb8qrRKUdtIXX9/39/ZmPT7e/3V0j8qyvf9FmsblPuDk/X/T6TlvVYNHxzWO/Lzb/c80utOrO7/2jM985/535+cjPf+l353J8FgssPylB9tF/63fRIf2k3/1VsNQxXWKJJe6KeYHz7tUnuDGc4nZalEWh2Ptew8UUBpbuk40jqkpDyysqN0S3PGzDQi91SDLiUR8jnDEZDpXOp2Z5XLzyGLUw6fZWFcnIX9/kifVtnvnmt6njmHQ0Vq5Qe7dus/fOe1Bk5NEEUaaKBb/R9lX52wlaPLT9JFrgculrX6FueBSGTpHlFEmsxpvPAvwgQDNtoiQmzUps2wXLJNE0mmWXQuqd6iaNZpN2s636Pw/e0dmvYy5sX1B2odM4U4SnhusQWCa5J3tFTeJMsuQLldmUWVWz1jHKAk0IdPNELk7c2cDlJm+ZBoa0K5XNpLWGZRt0Zak/aKCvrrC1sc7q+vod4XWDLF2u3SWWWOL08ElC/6ddzV0GpkssscRdMS8wXbnwOO+++gZEE+ooJ0kmeDMbN8kxEqjSCsMs0PQMLS/QjRxDN1VGUqQZ1XRMPg0ZDodEFezsnmf13CXGpoXtr1CaJXmRIaM6yWA3u03VZ2qdX6c5uczD6TcIj/bZu/YqR+++TRmnNKVW6Po5mt11jNV1gm6b7u4FUqNiEoXkMjDUK2UEMDk+xpJqn56DVgvyMldSUKZtKovPyQyCdlP56cdUOLpLe/MiSZIxPLjJwSyj01the7dDXZfksxm50nHVsBwXS5KwkpPWgFoG3ujomklZlCee97bMWWlUmnSSMrFMG11WUKQWaynIpKSU1EmtSrSqwNQ1lYXJiwRDlemXW/gSSzywOG2d2lPCaQeny11tiSWW+Ozw12nuXuBg/D5WbWJpBdFwiFkaiKiisizQbUWEUjFufeIXLz3tJTvfLAVRHDGYxRRBwIWvfJ3U8DD9FmlmIDQb23ExTClYnyiFAE0GiO0mzW4bUQjctR4ENpVlMDk8xmmusXLpUXobD3Ek23kCl7GuK/H73NApqwzTlElVl+l0SpqP8E0fV6uVSYBZaDjWiZ3uqF2iuzFVmVAmFQ3Toem2WF+9gJYahNMBwmvi9dZU+a3WdLI0Ia9qiqJUvTpJnlLlqQpUTc/GlvFkWEFWojuVGktlmooAJWWfpDh/VVfKrkAexzIMNU5t0Gd0fETrQqKOKRUKZJC/xBJLLHGa+CwmAItguastscQSd8W8t+Lc9Dn32NMc3HgJzSjpuBqD60cYdksJxudWjSlZ6nITK3PqKkfkJ6X0JA7Ra5c0qzgKQ84/8RS9K48y0S0afpskSfE0C0OvsWV5WyuUd36u+lwFhqGTlFL/c4Pdxzv0Ns8zG41xgy7d9V0MO8CsU/KqINNKRQbSJGEqTlSu0SlNml2deLZPGRnY0iIgzpmVFaltY9gOwbkORXRMJUxcu4HnrODYLvXKKk2hsdFrUZsGk2moRO0dv0lvQ8pAlYzChKpIKdKMIk8xAwev4aFVNlouqNKUoozRDXmNOkUtSGSwKov7SvIJrEZTyURpaazmL5qO0Ksa13awLFMRqJZYYonTwelzAOZ76d8bv34d7l8lU3pmrPzPzTpric80v4ti3u1ZSj59sbHo17OoDYLNczTXt0lvxYqNbihueYUuk2QnZwoAACAASURBVKWmpTQ6q7wgz08CNCmFJKWdilojnSYM05zCb/Lot36DWgrIux7CMvG1Bg2hMQuHDKYTapGrLKJvebhOE11zqcoxRV5iWj52d5fAW8V2PCXkPwqnNCV1vywIp2OVaZUFeukmVdcFaVpQZH32371JOYnwhUU8DpVZgJBi9bqOs9Zh5/wFNs9doNATDg6OcTtdDM8jNDOyvZuYjQZmp4NmuMg8pyQ5IcNcw6dIp1RZSqnM9EvF1ZQKTpLzoBWQEaI5PnVZqzmRCWVTB8PUMKTNqW5Sy3FbOpqpE04nVGWJ6QToqqy/lIO6F77s+9tZX//9Pv/L8OTeuFum9NMaHC3JT0ssscTnjnkbj7TdlNJHOxev8s7hHuOjYzwvIIpmVNLxSTSxq5NgTJbCZaZQit2bmqOcko6LMfvjGZee+Rrnn36WutHC9B2qrKDpuVRZSC5ShF7gOqY6tmO3oPYoUo2eNSKuZMBpU+suhqhxhEZQVRhFyuHLN3BNg2w8UUL8MmaMpdtUWRLqguHBbY7fv40IM1wZmE4jEtlqoOtMkoiBCHjkkTGXHx5TajWTeEx7bYXO6gpJmXP8wt9y8amnuPDsV/C8Nkmaq8C2LsGxG5Jgj6UZyvnJkEljaZka5xRxBpkAs6SuCspSUMpflixmSz8hM8uMsAy6xQmxyqJm2D8mCWe4nqcC2eV74xJLLHGaOAvpymVgusQSS9wV8wJTySAPo4TNhy5y66UXmSW3WWt06A/7CKuglXqKiS5J5FYOdamrTGRtmGgys2o5HE1D/qPnnsdbWSVvBkRSokVUShM0IaeyCoQhqM1KecZXSSZp6xS5Trj/NhUWfnsNUZv09/bR05i2IchnY7LBhEavhzOeKMck6W8/GAyIJbs/z8gnIfF4RoCJbmiYmY5vN0mkw1IUsac3eP3f/z3dv32Zy9srbLQcysZtMs+iVpnYAdFwgyKc4Xe7qsRuNJrUqaCsDITtQRBQlQa24yBFoeqiVL2xNqbSLDVkZ6sMmpUAv6bIUbp0rxJCBf6VqBVjX85HGoeqfO9rMveb3/diTUssscS98GDojP66mfnmoipp8zbG+Zan94a+YKp4bsZnwc9/cIPuNo5PU6o40THVP/K7+kcyIae78BbNuCw6//OxmM7cF79Ut+j6nXf8OTrAQjoSdRF6gNfaxrRfJ8uP8Fs2BwcxlRjT7nYxfItEF2R6hW1oiCIjnoUY/fc5f2Gb9uVLFK0m09GYlu3iai7ZRGYELcy4gWN0cIIGpZURTY/Ij15BHPV55b1X2VnfhvEBN6+9h1VbmMKkubKFIWwaM5/R8YCiyrj+/jvUUlJKrzneu03T8/CCGt3KsYVBXRuMC50xLns1vDmxue4dKU3W7bxivQMXV9dwySnDFCEq7FnKaqtNa22VynLRSh03EEyrkL5IsaSbaGEhCqko6qDHUo0gpzAL8nZFZDSVp7/l6HQV+75AaKmK+IWp0c4qzEabWe0S1yUi7jMb7dE7f4FJYtFwsnvfwDPG6e8P98b89X2245uH0/5+n/X4Th/zzj/v+TFPp3NeBDUvwrm/DQzudX9PMzhdZkw/Jyydmpb4MkKue6kdqpkaaxtb7OkGWZJjaRqtVossTckdge0airEuUo2sLinKlCiPGUcZbq9FS/rpBz5amRAXIXlloguTrCf1Pk2qMGG0f0g2G1MP+4xef4uDV17jwvZlmqOMShywXtpopoXVaJAMZ6RlgT45Zv/4iL3BEdI63jZMOn6DixceJ5nG/Oz4JoHXZrW3xSyteXH0HteHB8w8l0lQ0R1Oabsul1daXOi0aaJj5PmJUxT8/+y92bMkd37d98l9q6pbd+3be2PfBjPADAYzgyFnMAvJMClRDikcoeCDbT04wm9+cMiSQ2GFn+wIv9n+F0yFyAjLNi2JJilSGgapITkrAQwwWAZA7913qzX3zfH9Zd3b1Y3bXQ0U7vSCOjONultlZWZlZZ78fr/nHDaffIpgfR0MW6U7VUkB0Zjxzg7h3hYdETC5jrKEkkpnXdR4tqNmSaViK7OkygRfzh9acyEoyoKizIX14+sdBoMBRsebVE1NWq2WuuDKcxdYYIEFHjaYn3Vxy1Fu/2dh397rbVwcv/d2+3WxNKoqbE1ndeMYlutTxANluyRkdWxkWFaOZjtoSn0ubeyCOqmotYpeWnHu2Cn8pRXSsiAtQsgTrMrAsjx2L54nkBb3YMT1t9/l/Btvkl3bYyW3WCkddns9qlpXefSmY7Pbu4xt2+zs7ioid+3KBxidFv7mBl94+WU02yeLa1b8Lm//7G3e3N2hGhbYyXXCOOWD3ha9JEQrXEpD42s2nNlY5bET66y1XbQqRoTwYrgvc6MnXnyRzskz1K4jMXMg8aDy/GiME8eKDOuOtP1r0jgS/ZPyKg0cjSqvyHWDuqzUDGlVlsqvVP2jVvuntCRadUS34yuXgDTLFAGWSo+MUdzvuN8/n4v1mw+L8+/9vf3zVrTnLbbdw6z8e4t5D4xPoxVxlB5fD/uBP3v5cz190co/4u2XuUcREhW6hrm0jCOq+jKkHI1Jwgjd0dDE7sisG3P4Uvw6S4wa9S+3HNrrx6j1it3tayT5gK5vYVUaaTLCe+193n3zZ+xe/BBbHOnTHEtEVI6N013H9BPSOuTaeI/hVkycl7SXVyg8R0WMnn3lVVbOnmbj6cfpnD7DW+cv8KOfvMbe+Qt8+P6H/PzidcLRGFuHZc/hmKHzWLfLiu/iGAYvrXZZXe6wutLCdgziwiapCjTXVZXZ5cefxl5bVRVTygRN2WFFGGlKu6wYStb9xERb3quyKGV8VlF6mUdNdYlCFSss1CxpqbxQmyhRXRM7rARMS1VcPbfNpf6It99+i40nnsVxPMg+2+eHebFYv/lw/6/fPX35BT4hFq38TxGLdv4CnzXoWt1k1cv1x/Pxlpapoj2MssSrIdBNPNtuTjT1hITlBWVSUKYlfrdDd6VNVaZk4x0cPaFV+IS9kAu/uET+vZ/w4ds/IxoPOHPyGCfWNqkDg3FSsjOKMK7tktsWqeuSe2s88+pX6J45Rz/L+Pm77/Pa1g75e9epL+3wwcXf5/wHH7J7+TKD6z2OdTq86C3jb3Y5JgQ0cDGyECsOWfUc1tpt2ueOicEUpmdhdzx8xySzTexOl9byKvrKCrVjU0vFU8RUWUgSjsjCEUaUYDgehbT+i1K14fOyYBwPMXQL1/clYV8lQonLvsyrSZW0Lir0slaxpWldsSyvYbo4bkDv4nVef/11Xvr2rxHYLguzqAUWWOBhw4KYzol9Mjr9uMACnxWkcYLueMqrlNJE83wGSULLgKXljko80gxdVfzQNRX3afgaZiZSIINTgU2rY6EVY/wyph716F+8wOX3LvPjH77J7msfEpUJhm1TjyriKsTXXWXJdH13jw8MDbvbwXQdrg9S3vnFVZJ3r3L12h6v//R1KEYk4xFtERP1+jy2ssLXNs7hBSd45twjnNZ0LNfCcA1KEkYhRLZYU+l0V2yVs59lYyob3OWWmod1XQ9nqUt37RihZigCWWc5WlEosUltNPGioru3hIhnZTO+UJQqDjVMM3SjorAkg7+xkpIxB83QSMUJtcyVSl+TGFLfo7XUIdMs0rxUUaiSAjUY9NF9Bwtv8VlbYIFPiIf9ej3v9t2r/TP3jOmDXiE86hnTh72Cupgxvbe419svBEp8jmS80jE0ltc32KprkjzDa7uI+6a0p8XE03ICHNNRZM1ey/GjDLvcIxptsXPpXaVIH1z8kKtvvMPuxQGDX1zjcqZxoTdkNwkJ3F3OrGxwLGgRhwMub13he8OEVncJzTYVYbP+/Z8RoLNiemwYNpqV0zZNTne7PHL2HI+urnBmeRlP2TTVFPGYKBmw3euRVBm6b6K3bfLAYbxkQ5pQ6gZe4GO2fdXCr4yGZEuGvbqzl2pokWJqpSKS9coyWiz+pCZpbxcmFeIkiinFc9V1lBZ3lCf4hqsMYyQ1qpBWvvyrJKRAjPbFbsoik+V7Pte2d1W+/vHNTXa3ryNxA6eOP3rPj8E7YTEjOR8W63d/YzFjemd8ZmdM7wcsWvgLfFbhui5xVZNJLrxlceL0GS60W5R7MZlEkHpWo2A3LbRWgB20MXWnEf6kOfGH17h69QPGVY7nmGz9/Oe8/5PXcBKfdc3lzSQhrEwiv0viuuz0B2jXr9Jedll+4jh/95KtCHBcJ7RPnSYL+6w6Fq264sz6Bprlsbm0zHrQ4vjqKqPBLkmZsXH2OFd2trhwPaLUC0ZlqUzuPdfAcCRK1aY2bVq1jue7LHVXCFodUq0mTwvsLFeE1HEM9CqlUtGgFaZjqeSqxHIotIh0HCvLOwkMkGpnbZj47UC16GW2VbKiRI2fi4isyJS4Sa8qHNPEFfsoyckfjVj2O2xt7yg1/qlTp+j390i0+5+YLrDAAgt8XJhod/bhqiY2W7cy3/3vNf3OhGzu4ej6qH3u7uxTVtX5bdex2bbJ79TDrTFdYikzywetPvjb/edqWv3R5d9+CTN+f29xqynvNBpCf+fVm33Dda+3f973Z97je97tn2/969JFy1LWWoGan6zWnuWpb/4Ob//R75Jcewf30U3WV1YZhjm1tKY1Q0I70W0L25RK5DLG5Sto+SVyiR/9YJu2s4blOGxd3eHlTsHz3sSQ3zaoa5+Os8Yjp05y8tgGxuMVbZVrb5AGFtWJYzinzmC6yxSZhldlBLpGFY6Uwr8/7JGLNf31q5i2waoLYVkqKyvsgE6wQnupQ1pljHfGOG1YOXeGtKUTRn20vCbNc1zDojD30DaWqQ2fPokSdS2VBfmV80Tnf67Ia6uzQb/fZ5gkVKauHANEhS9tehkvyC0Tx7QQ632tyinynEKiW60Sw7JJC0uR1svb29S2PN/B8Bx022O3H/LaX/+QJ556ks7qMqV8WHSDcZYSp4mq8mp5RuC4at/H0ZhWq0NVayRpgeu1qLLwnh4/Dz/u9ed7Fh7u909ie2/lINPf7395O34z26d0PoP82cs/WsziZ7puTNZzep9NP2de/nf4/ruriunt3rTPGm4crHeXgHA3xGvWfn9YCrGLY+jhRE2NZZSURaKIkW27dDc3Ofbok1wbXicZRZiIzVGpFPq5J+bxjlLzC7qbq6R1ruJCJYLU8Uy2r+yytzPAL22C2qPd6eK1O0pxH4cRHb/NqbVjdHyfkQODKCIrI9xglc1HT7DyyDnGac21S1tUgz1GaUrS6xOPemiuhWcskdUZwyTGsF2WWl3WTjvqIhOGIcO4pyrBJ09t4AUurlQ4i0jl6GtFhd1uqbnZrd4uWmmwtr5Ot+0QjVMG/V3iKERzXEWus35JliUUZYZpNdudi4tBWSg7q7KsKMhU0pW4G+yfS0RMJhZSWh2RxQmV63HtymUe+9KXOb55krFuUCZDLlw7z89/8ba6KXj0icf5yldfoWM7KobV1E21jUmV4tiWUvUncYZmGCphKo5GOOa8yTMLLHB/Y1Zq0eLadP/BpL7ziWm/endbzHj+bGZ1nx8Eavv213HyuL9N8ii/n/5++u/U491XjB/WD8Tig//wQqtjDKMizzNqy6YyHKy145x4+gWunP8FXr6DVmp4pq0iOV3LUnOTuumiizF/WeKXBeG4j97x2djokjkw0mKWZRa0l+P6FmsbHbygTTxOiIcJUTxWhM3QHQxxBhCSF0b0PviQZBSSZCXj3piqTLAk5tMGe8nD1D1M26Zl6XQ1GPa2cBwHx7GU6X+6l2MaCaZZYVol9voKmuNg1ZkiruIo4HgB7bVVolFElQ/Iwhrb86kLychPsTwXrdMmGg3QqqxJc5pErAqEgJZVqYIJdGnlVyjv0kpsqDQNwzIVaZUqrp6P0KuCstCJk5DjJ07QXuoSRwmabnLs+DoXLlzk+3/xV/z+7/0up0+f5etf/zqvfOUVHn/6aZY7K9R1oXxepf0gZFleQ5Fe87NezVzgs4qFWPnucK9GFD/2jOnHfSMf9Df+YGThFgI5fVAfdpB/nO1u2vcffZ2HAQtS+nCj0ktl9F7nGToWSVkQGA7+qUcwNx8hfXeLIo+UNVKdFSThmDqX6im4pk177SwBDvgtTJnXtE1WH9Vx1tbQZb6zH6sqpmXbtDtCCNuM+zGjXkwW5eQSYdpt47QDCguifl8RPz8I2Gw7lL6rREqCsqzJiko5BJTS4lMVXgPfc6nrmLQXkZsl1pKtZjzFumms11hZgllqtEyXQZWr6qTMkQa6zfDyO4RlCK2lxgoriVV1tDY0xlWJncaYlryOzNrKXCoqk9/QDFUt1SY+sHmeUshMrhBGEWWVIoLKoIwJ/BZXxyEnTp7m2PHTDKNYVaDFB3VvtM3G8XWefvoJ3nnzTf70j/6Q93/2Jj//0U944rHH+M5v/qecOvcIruMTJTGaMPQ6pyhyPNchzxaGUws8/Lid1/itvOuXfb16EK+Hv4x1Nmdnwd7Icj38TTvaLPv7Z4bwdut5558/6FnN8+JOLZPb/ezBwrzrf79nSd8ZpdKX61jC/TQxoC+INIugvcbaE59j652fkCYpjlNS5RllVKuxdk0z8XUdw1nHX7Jw2+uU+ZhxOMBbPcWxsx2qokSL+gx6e4x6e1yP+hi1QbDapbuyxHiUYJxco3ZMEttCcyy8TktFdu4b/7cch2E4ZpwkqpUeLK8oa6YkSYnjGLqrWG0XswyJkyG1IcTRxOp0CFotBo5NVdfkcUoZpYrYalVNnOak44TtKxfx/RZ2rWNZLtloxKjfE+qLaZpk+QDHNak0i8EwIq+lAtxB0zWiKMYwK4o8I0tT1eJnam5fPjs6BYamcW1vjy988zdYPrbJcBSR67pS7S8vLzXb2Wpx+vRJrl++yqWLF7DRGPcHnL90gV999Tv8yrd/Db+1pGZPhQTbhkaeRGiGc0+Pn4cf9/v++ey8f4eN4h32++nvF6Lme4PFjOld4NZq5q2+pdOP3PL3n+TAnt6/D+uMKRx+x7rAg4USU7WgdUk+osasTepKDONtTj32NNHqBntbV5WIspaseFGc24ESBbq6TRhnqq3vOh7hCJJ8pFr+htuBvGIvHBJqOqltUpaaIpNpBrbZpmoZbFotUtsmdW1Ky8G1PWXllOQJ4yQjq3XiWqPyWmiBD62WigT1tCXWdYtenpOPB0R7Y+qsUvOr4itqdtpUQYfuclfFrg6G8roF3tIS3rENTNtiMN7DqiySQcJeeo1Op0tbtyl1izCKqbSCmhzLsikqQ93ki/JfqqJC4uXR0TUKdfNdNTGuhq4ETLUKI6hIa5MkTEl1h1NPPIe/tMogzRWdyNOEKBoj01Zra2s8/4UX2bq2zWs/+innL19WVWrPT/j//u3vUZsV3/3Nv48hoxR1ievaJKMh5gMQa7rAAp8Ut6+ULmZM7wazCktHhZnEdPEmHS0+izOmt/vZAg8eKtMiz0pFsMSv09Vdal0jywpVnVw6tsm17WuqaulotaoiWmYAVUTuxlRuSNDyseya0jPoLrcpikp5kvpeC8texrQyrKCm1e1QxjGjYayqizKHGfX3MDfWCJakctpCy3WxGsFx23RWdRLANw1011brlSQJozhVSnXfd2gtdRmEY8LBiHJ3iC/iqOUV6k6XzLVZ9sUVtSa0bPQgoH18A2tlBU238HSpwG6yfX2Hqx9eJ2pHnNg8Rku3iOKEvExwJRWrLpS7h2npqroZx6Fqqcv6C+lVzHKizpXPhW5YyrlAmlVJ7bITFjzzxa+xcvIclfieylm7KkizGN0wlLK13fZZXl1Ft1360uovYSNOefzcEu+cv84PfvjnrJ48xfNf+Aqe60n8lhJ4LRr5CzzsmCVQXuDjY1b1eV6Ys+0ObrYz+OgbOev584qfyhm/P1qIvc1H13W/Mrr/s+nvb922u7OD+KzMmN7uZws8mNA0m7JK1GmgSgoMv1YVy2EcK2uk0489xvWrl6jHfYwiwrFsWq5DoVtYmkFUjhRZLfIUXc9Y6Qbs7OzS641xXYfVpU2csiLpF1TxEKvWWFvqEEUlvX6ItrFEueZTrgXgLmHWdqPptHQqWyeISsIsIa1KReIMr0lKKvOS8XhILuvTaaO3l9m7eo2wN8LsdAk6y3grq4S7l3AsU6nkHc/FdBxFZKli7LpxxrdNlzLJ2RtvY5UVuSj4x338lqdmWMW/NM9LpYRXZDqOVfKT5/kkyZgsSUjTrDHWry10qZZqE8N9yyfXNb789W/SWlpjkJcUVa2IqVZX2JbH9vauEnCtrW7wzLOf4+133lM/k/b/9vYFNX+6E+X89Q++z8lzj7O+tEGvN2B5uQv1gpou8PBjljJ/+ucL3HuY9S0npo+WtWcRzzsTx/nf56M+UGYR5xvE8rCbgzvdMDS/mzWDWx3S0r6xz2fYxFLpUxXXQ54z/eGr9k0Fpp5/1Ht31gd91vExa/vLj+F68Elw1MkXM9/fOd+geZc/PWN+GOw8A9NF7OUJ5D+5+r/v+4jnvPXor1C98zZ2KyTv17jBBrHWJjNLxsmHOP01IqtFrXv4lk+8e5lsd4/u+iZprbEXfoil5+R6CaWG47QxDJMsHZGasEPKit2mYx6nzEzicJfaLLC6AZXhkVQjJaqysgKrakSGe1GqhEmicG+tnGIvr+HRM7hWxvbb77DZ8YlGe9iBTTBO6I0GSvDkrC5RS0U1qUjDMXGakSU96kDH32yzd3GbSx9cou23sZZOkrgO7mrFSmERbY+5cP4Ke0miqreODUk6oKoidkcjsDt4rSVl56SnKZ5ZoWUxRWuJ73zru3SOrTHMM+K8VmIuyd13bJco7qsqb5TWVJbH409+ka+9dJ0/+8M/4LG1gJUTXyQvSpZaNXtXfsprf9PlO7/2D5T9Vi3JWCK6qpvqs7gBiMdpkQsxtrAsU4mv7nwAfbzCxq3QZ7i61Pqs8+e8yTaziPl8H8CbCxuHvf7Rnr9kHvpOmPX5nz8ZaFZhadb2zWtndvv1a667Nx+fH23737mpPOv8OPv9m/cKPN/nb5aP6s2rfzsv0zs9f5aG6fDXv+lZi7uFBRZY4FNF0ObMY0+RZOAZHnkYE+7tkEdjJJ1ey8WYXtKRKmV4X2gSZ1pQYqiqpWP56uJQVjp5VRMWJWMRILk+nY1jHDv7CEF3VVk6han4iI7UfKbrBFRpqcYGTDNQrfMSDdNxaS21CNq+jHIy2t3G0JvEps1TJ+msrxAliWpz53GE4/nKHsr2AxUlKmfqUhKawhHZcIBV6uhpAWlFleZEozG9Xo+iylleXcEJPJyWj99q4bUCtVzLMLE1A8toWv5BEGDrNVUS4tngSPKUGEmZDk+/+BLHzj6K3eoo4ij7SEYCxMZPzvlSKVUjAbrGeDRgbXWJxx9/jOMnNjl9+jS25SorK3l0HI+3336b11//W1zXUCb7hu0psl9jksQFRVYpUZUjs67FvTX/XmCBBT6buOPtwEKccm9w0w3Cp1ixO+y+Y3ErcmcsbtbujJn7R7M4+eiz/OLH31Mt6mqUUObifWrjrnbQxWopG1NZJllWIWoct9PFCtrobosgTUhLjdLNlIBIDthc/D1tm07Qwl3uoDldDK+NV4p7fYdOu4WtW8TDIY7dbpKO8lrNijqBji2jBOOMJB5TpQW6C2mZoAcumQ7xYI+1s6cV2ZNZzUoYrKlTmzp5XZBFY4rhgGwUUhc1qdg+JTmeYRHnGYPxCGN9iZNtn7AYQ5GR5amKbRU/UalS6TLKUFWTyqRFlccq+cm2ffqSq1/DyuYpHnvhqwTdNXLDJM0LKiGkVUldZirUQBNRGIVMT5CJNZXk+VPQ7XY4ffa0TNtiWQZhPMS2fAZ7PX764x9w8uRZVleOE6Y1rm1jWQGWWVNkOVVZYtQ0IxYzSmqzK2rzHT8zB8HmrSjO7AjeGfcqS/x+wez1v9vkw8Mx//5ZEJgHEYqYLlRp9w6zxE/ztnIfdMzc/gf8vHPU7+9RL3/W4mMx11/eZOXY4wxf/wnBOMOW+ckwo4oN1aYv4wGZZiiDe2kfHztxEj1YJskrLN3FczW0DhS2p1o/cjETsljZHqNCw5IKYq4MQlla7mJoJYO9AWmY41gGGkbj36nnSlSUpjHjYQ9TA482g0GI6WvEdU1SZJRppMinVEijOCOvJmp5gZDQIkfPc6w8p395QK7X6KZJa5KRvzvoE8Zj5YNqtTzKfkaUNf6ncqGWNZIRC7HXN0xPzZhqZYZjWaRpRJjXdE4/xhNffgV79Ti5ZjLOMrKiMeAXpb8IqmT54hQg6n5ZXtuzGPW3ef8X77C23mXj+AaaYSIeWOLhKjO/KysOW9cv8zd/9ed897u/juNsyiYp7ZXYUpmmTVVkTWyqlh/5netn/fx21Fjs3wUeRJgLUnrv8TAb7C/wGYewP93l5FOf5/xf/wjinK4rcZoZ0VCImU1ZGxJsila56J6Fo3nkSUquSJyObjnYXrupXIqlUoWqUpaFJi791JquVPxmWeC6mvI93RmO8TorBK6LGvPT7KZlUJVkUUQehk3LPLzOzmCbU4+eJk0THEP8UD36W1v4nRa65iGjluI7ahUVtSQoSaxnXirTfWl3J1mC4ZjK8N5QcZ8GhmVgew5B22EU7jRxo5WmqqNi7G8IPa0qknGIluf4lk1W5PTigs6Zx3j+V77Fo1/4Mv3aUj6qUrmU5dqmriqaqNfxGI9jtUwx5++2Xd5/7yLReI/Pf+E5OkstMUpQFlvdpRUyMezXNPK85q3X/5aO7/LKq38fTXxaM0117qVKKuSUKiHPUjQZhl1ggYcU81fcH/aK9715ffNu/uiTLPjTwlGPEszbijpyfMaJ6lG38u41jjqwd97lzyvekhNMkhUsnzyHtbJOPDhPUJZYukmeVMTliCSp8d0ulm2RhhnJcEyheXRWTlNLcpNpU2s1hpgblaJcr9EVudPRbB/LRP/vnAAAIABJREFU9dXcpVUXeLUImxLqKsMUEpcM0GzxDE0bH9GypsxSXM1g2fbJkx5GGlOFI5UaZRdlE28ajzFbLrWVKQJZJynFqCQdjgl3h6QDadGXuK0242FJmCaKfGZlge2Y+L6L51ugl1RZqeyzlN+xWEHVlWr553nBaBjS9mxqw6I/jklNl6eefYEzz71I5nXUvlAzpKLY1/TGWUp0YLWuBFCm3axvFccUeU443GVjfYVz584QpxGmYRNFQ9Y3H2E0GtHv91lZWVaq/b/8i78gTuHpp57n1NmnVLxyIdq1YlIhts3ZkdNzHj/3PrB6PvHIfX/+mSU+PfIVmBV5vphjXuCjuIsZ08WMxi8bNxvsP9gzpg/68XOvVf33O2YS16xARj/xAx7/4pd499oW/XGP1eUucV5hxBlhEmGsJuCYGHWuqpGShqQ5yxSeZBhpqDKpmNFnGXmUYdWG8iqt8kr9/eqSJEWFDC5fgipjZWWJwoBx/xpex0eCSMuyRNcMjKLAKMEqNGxLZ6MTkPZ6JLt9OppBOg5xu76yUiolFCCrqKOMtB8x2hsz6g+Js1yNCEjiUi6jrTWKwMo6SstcFxFXGKHpBXmUYFTgur4ipUJi0ywhE7sn01Jirf44p3SXOPfM5znz7BfJ3IDdYYglaVC6jlY26vHa0FWluCiFlpsYulRiS2zLoHd9mzgccObUJkWZkMkcqpZheTpJGqlj0bIcDGzafoerw8t874//FaPdLTVWcOzUE4oEp6q3D6ZliWfVHd/fo54xnbWAeVXj86qmj3rG9H4/f8x/fry3y1/g/sTB7cyipb/AAgt82hDlvWPblIbB4y9+EcP3GYQhRakRjtOm+peVpFFKPByrimjbc/EM8eAfq6qfzGvGmcSBpio3v7ezy2Bnj2wcUsYpw50dkmGfrSuXef2Nn7C7t0W721IZ9VoV4YhnqIVS30tOvFR5a1HQ94ck0ZCO61LHGYFusRo0Jv4i/hkNetR5RJ2F1LLOw5CsPyIZZ+RZTS52VqMBkZBH01CpSiKskkqtGPnvbF+nv9MjGo5UvKpqk1uWuF6RVSKaKlheWiLNS3aGI7rrJ3nxa99g89xjRHmllPmObmLrmjizotWlqpiKYEclbemusksTQZWo85Mkoq4KVla7arSh3W6jaSXrG8v0ertqFvXY2jGiUUiVl5w4dgLPKnnnZz/iT/743/DOz95QPMyW8QhTErPyxedhgQUW+KXjtln5+3ca82bZH3VW/mxV5bzNourQSNL9x0/q03Xw6nO2Wma7yE2bmh6y/KmfHeZzer9j3lb/zIrEjN/Pen1zxjs4y4d13lEObc7112f4MM5yKTTEFzPVqK0lqmWP53/nP+dH/9e/4P13fsrnNlfYdm1c00YfDinqFn3DIDEgsGwIB6RXNGW55G8sUxk2436kLJe64i84HrCjDeiur1CWBdnuZbyoxJbW9iCl0+2Qux7RIESzXHy31RjXuzX1ckUsk63uGVXZ7BxfoeM4SvTU0kridKSiSwfbKWatoaU1WV4qcqwCBZQ6PkerLbriKWpIqlPObjwiNkuCtonhm1jjMXWVqznPOhGiadPJTTTNIvc0XCsnHCS0n3iCE1//NvmxcwzEKssRcVQsSfkURUllNK17MeEX4ZPKeK1Sof34gcvupfeJR2NOHTuOY7noVkAkRWjvBOJm1eo45FnCVm8bTeyxZAbW1Dh3/CkG4wEX3v8J17bf5fNXv8rLr3yHdmcTo/bIK029nm0WKgBBqrOmYalbjiIuqKWqethxtR/PrM/ygZzvbHPUFUV9Sj10+PnxiFvlR11RnXP5N5nWTx5v8tGe4UM7y+d1FqqZ/MK4sZ43md00z9Nn+LzOmmSZ5cN71OKzWaNUtX7n/Ttr/+narONrPv53u0/IXWXlL7DAAgt8Itimmo/MylzZFh07eYbPvfxV3k/GvHvhfcxOB8eq8AOpJjogMaUUqoOs5kElBckq0QoP3dBxTINKqo5lTV7kGIWuKp91VuA4LqvrG2o5hS5zmKXyLq1FmW5IepPYTenKu1MJDuuKyjFZanfxdJMiDKFI6a5tkMU2/cEuVZgwjhLycUQeNxVEy7Epi5wkS/ECT51bSxEQVaW60RCfUs9ycYWwlpYKHIgpqRxNkUGZLc3GI5V29W6dsnrqEZ76yquc+9zzGJ2uqsCKV2pZZkq0VasRhEbJL2MNtfxX5k1FRS8n/kncqfihWlqFputK4W8FAXnajABIEr+sl8yp6pNQDxV/amt4QYtMK+mNRvzFn/8H3v/gAl/92rd44YWvKOIpWivTaOZNR9GAokgI/Da255GJGOwzEq28wMOHeWegFzgaHDkxPfoZoPsbi5P0Ap9pyJxmVSpiJK1vu73MuRe+Rrw34C8vbXE81cnTXKUgSdJRHdpYLUcZ5osBvYyWmuJalNhUhoGpFei2Ls5PZLqOKS35MKb0M3y/Q7AslVWL0jTJqgrbsFWlUbM8Sml/i9Lfk7a7q6qOsZlT2o56TpGkqoWupyV1JqmjJdUoJgtDolGsCKKIl6RIIkEAsvzANdXVK8vSxmqqrDE1Cz2vKUcZ25d2ENmWt9QhqSBMEsJsrEipW9W4Jx/nyZd/lSdf/Crm0iojqcpmmfIiDTyHcVw0ZvoyZqvVk6S4+uBntlYR9vuEw4GaD7WcJmdf0pyqMldCMaoava4RJ1cM1EyrtPVF3b/bH2CYGp32Eq12R4UDXH7/Xf59b8C7b/yY7373t/FbHUw3oKp0PGcFs22oC/YoGRNMVUw/mpqjLS7sC9zXmDeZ8NP0GT988XPOWH+itfo4mM/n+HaYm5je78Pb973qfgY+zhur3fLIXXywPs7fPoyYd5RiFmZpTrVZ4oo5X/9e3xhJ+7hWhMlRdklSATWWNzn++a9wZi8m/smfNar3okRLK9JeJB18Jf7BX8JYysmtipCcDMRKHscO1J4r9QojCtHzStlNFbpky9vonkfp2OSUuIaF4XhguCpNqhLJkJBSq1TETNrlI5m5NG3MCuJRSnj1GlYRYxYl6d5YrZ+l6WQivlIyKh3LdtCl9S/vcJkrpX9S5qp1bZsOVVIwurZHJab24YhxkqIblhIZ6VL1laFXy+Hzr/4dHn3mWYzOCr0wViIq09AwVDKUiWXdEKAKmZSvp0eJbC1jq7/NoN9T6n7XDZRfapqESvy0FnQR3VSpnqOpFnw9sZ+SLmZ7pauOUrGhkop2O2gRjoaKoL792t+QRBEvf/nrPPX8y+imRZnVRNLCl3UUW6mpI3R65Gn/63LGB+B+v3GfJR6d+fxPd3U+uvwj3n/zXn+O+vI67/bP22q/1z6x877+/frpW7TyF1hggSODaVti8oSpGRRGRZqU+LZN99zTvPDdgB9d/wnx9i5mVXKs3SUzDa7s7rHXH1MFJi0hgkXBeDBU2fmWENZWpcz0pSVeRxGO6WNK5GipkRo6rudhuj7EIVVVN7ZSE6N5XTOVSEla43VR4BZy8cwkHwlDb3xJRVBlJSlZPCaLYtWeLzSdytTQLVtFg4rYSebXBsmIMi+Ui4DMr9qei2N7lGnNYGfIuO1jOy5BZaiRg2vXtxnkKRtPPMpTL32J9hPPYXVXVdJTgYbn2YhTUxqPCeMI0/IVkRRHAXUXPbHK2r/gJ+M9imSsnJ1832/GGCiwbIk91TB1DRkJbbxiUdVjRayF1NYVhudgW1ZT3cwyVWVdarc4trFGnqf0RjEXLr6P7bQ4fe4pLM+nynVFej3bpcyiGW38RcdogfsXD3vH9kHFPSemizd+gYcZ996n8R5D7JCKnCxP1GddZhwLIYuOw/LZc3zht36bn/35X7Dz87fwsoLu0hIrtU6/F5LmNWaYUlcmZV0p4mZ0DWojVHOjEnFaSLypbmOJbl3SnWwX3Q0wHQc7SUmSGHHYN3ULXdrOpolhO5ia3syujka4tqU8VKsoR7MMuitLlHsFly/uYNsOcZoQlyma4eA48rc2RVEpQZNnW2RSxRSyahgqAarUNDIJCMhzrmcJj2ycUH6N1y5dZy+MOfbcszzzjW9x6nPPEZUtUkmyqiocGVHQaiXkktAATdKtqsb/tJL51YlllESlCuEWsrp7+YIilEudFq7vkeaZ8lMNXAfXs0nDVFVxpUpba4aq2hqmpR6l9V/rhfI6tW1XZeRL4pNExlakalzgpL+svE0vXvmAMEt44slncfxAzfbqVaGiYadRT6q6sm7yqBuHi6MWWOB+wCzxjzGz5Xi0Hbej9gGeKZ6auQHz+Rzfrqd4z2dM58WD3opf+MQu8DBDSJtUN8s0USd58fgsqoIoz1Qr+MRLv0FWL0FpM7j2IXU4UlZPtmcTDmLirFGFy9ylwFezopYiWiJCygwpjEYU2hDTamHaPobpKjcB17QYphGFkNHSx7RrdN1oRD96Ix7KzJJeNEDPTFzTQF920I02WTZgqCWs2l2VZy89s8oyyDRJnCpUMlURpyw7bdBKKtOgKCsJCyXLczTpk2s6q1aL3etb7Fy9rqrBL/z6d3nx27+BsbbJ1VHIcsdU4w5CAqW6mcZxI1QSgi2CrCRsTnISETpREKsAKxFQpSnxeA90E8NoKXIrZNgwDeVcYIgQSmL+LQPTcdENk1pmbmWkwPXUOIJnl6RpSZZritgbtoHhuVIjVtGnuhmwttZS9lPbu+fJ3xyzunKMVmuJTntF2YBN789Fgt0CDxJmz5je3z628/oAHzU+qU/wopW/wAILHBmSsiSQ+U3HVibx4q4mBFUqc0JmhnQ49+I3WdEsfvwn/yd7e+dxuxZBV6p/Q0Y7qDZ5JNGddYkrM6RomK6pWt5SoezvDSGz6SxtYAsJVkQOZc0kRqni7anRJCdJtRElxqoxdBFC2VzqXVf37Y+cPYO52iIpxqQuGCs+o16M5ljYlkOu1cp8vs4irFrDcTwlmJL1E7KdS6Wwak7GUoH0HJfRMKY32MFoBXzp5Zd5+stfQ2+vME41loJNdC0hzxNcu5lNzfNGnCSViCjJmK5HNvZ0mqpGClGXiq0jqVYiZioLVSmVndJqeXiuwWjcJ2i31Xyv6wdohk0lb4BUmD1fuRjk0Y7yO0VzyAtdXcd0S2sSq+qcbnuDMBqw198mTWM2NlYw9IzB7jbD3R6a11L+rOKjKmRYbjwkItUwm0uLiMEWWOB+xeIG6v6EKReHO+FufDhvZfXT3+szfLRmLX8WZq//rDuOO7/AYT5rN6oC89/x6DQXG2UDM1nWdHvh43xw9p9VfozP2sf52/sRR65qPOI7ziP3YZ3XJ3fO/dcSGbjMR4roRkijMj7V8YS4lDUdvVT3x53nv87ngmP88I/+gHdf+yvOBRVPby7xzok1BoOhytY3sZQyfO/ydao05tEzJ8mCDNcxGaQ7lPVxOl2HUZYzHBcc766zevwJLrz7BhfffYtnv/AS7snHGNeGUpon4RCjaHFm/SmV7hTQZicsGMcGnr2MVbqMox2sQuqHObrt0Gr7pHVMGI7wHBs9c4njiNaSTVJGqt3dXuoqsjhKQy4Mr7K0eZazL3yVs1/8OvXyGv00VnOtLUssozRc11P7OcoKRR5FSS+Rqo4prbaMcZJR6x7Yvvp529Mo4h5XfvEjLDNoTPtlL5o1QdBC91xyyyQIlnGMVkMUJ5VNIZHW/kxpXmN76weVTlMvm0z/slZZ/obhYpUZdlnTcjr4VgvfW8YWhb6eKjFbHG2r93k8ORfLsoWkyj95rdbSyuRIaOymavlXaQfk27Kb83et/pdT18XksVJpX4bWPjjOqrIh7fJvv0oLxZEevzN9hmfgfhcvfprnt09y/Zl7++5y/W9NU7zb1xXf4INlTB6N6bPmzILgnf9g1ijBLMx7dMzymZ2ZfDZr+TM/f4fzt0+lYnorOV1EmS6wwAJ3gziLVeVRbsrWHnuEX/+H/xnvfn+Ziz/9Pu9GMd7JGi/o4Do1Vy9f49pugStq+Nrk9St7rK7bOK6LH3Rw3EBZIpm2qeYzkzxT7Xfx4hQeNIokvWlIqgcYmqmqnSrb3nUa3qSBYemsrK0S+DajlVVG17cxHF1VeNNkrEiTzH2SZsRppuyZiiIjjdVAGoHfAcPn+m6PvcGY1uoJXvrGt3nii68wwmZvNMZ1bTzPmgiHnJsulNOKeyYuBLYTEKeNsb5raYSjEb2d6+iUtDsdTNPC8Vwsz8X2fCzXwbAcRdx8u90kTplmM+NrGAfEVLX+i/Tg5n56HeTv9sksE9I5vRw1n4qmvFPryYzs/j+p5ErylaDX76vqse8HeG6A7bbUfmpm03TCKMYQhb9S+WsYemPe3xDVkuqAd9Y3ORJomjnZb4uP2QK/PKjPw4LaHDmOrJW/IKd3h8OjYG++SC2wwMMKwzbJJB9fRDIizNnc5MlXfx1tucVbP/0hbnyJJb/L0qrP3o7JxQ+uIrVTwwuw/Ra6bbCk6XSXVwk6q2iWrSqIukSehiF228PpdsjSEXlVY6Ui2KnRxW+0qol0HW+pi5ZnTaSnVuN1AlqugSORnrZOrVUqvakqElKJURUiljVm+xFjNR8qM61iwTQelQz7fTLb5/Evf4FnXniJY6cfoXbbxONYVVCEGFqmuPIbinjdeg7YJ2BKRCT7RURJ5CrXX2xTL+/tsLN1Hd916K6soAnZdFxFSG3HU7O3MuIgM6qW6XyEmMo/9Triy1obN1V1ZFnqDCRkdTI3KmRTniNV0H1Sq2ZKdUONQ+yv8zQ53be2yvJICd+kwmyathKTCUF1XV8tK5CAAvY7RRVFUe+bD0iUgRoNuLFPSrVcqaRq4mcr5LiaV3yxwAIPLmZWJB/QLfvUiOlhRHQxvzEfFvtvgYcdtmaodpY0zKI0VYlHS8vrnPnyN8lb65z/4e9zbTBmzWpx5sRJXM1je2fAIC2V+Ghrt2QU6tT+Jqumh2Y51Gr4FEUoS9PFaS1R52kjwqJWqUgSFSu+nJFKSbLJR6UipsNwiFaY1FnKMEmwXYssTZRAyZqQtDTNFSFyvYDKqLFMjySHq7sDYt3CO3aC088+zde/82tsnH6UK1vbXL6+g+W1mnnOulRVRWu6I3jIZ135jWqOytkXghY4Jsl4l1FvR/39+voafmdJzZUqAmpbqjop852aCLl0UfnrN1U/p6uisi2H3xjf8CLdV9gLsfU8Ty1nv8Krq/SpSbSj3owJTK+78lktdSXISpKU0XikqqTiAiAkV9Z1/dimItBCWnUJJjClOq2r2dRK/lU3d0M1ff/1UBlYi1v3BX5ZOOyzMqsTftSjHPfa7uqolj6TmH4sg13t41f6FuSLgxnTw/pS9/v+ud994OZ9/QfJAPx+XP7M58epMqqXzGpPszEDj7LKKbUWz730DY6vGPzVn/w7fvb6a9hRQtswWRavzzJmnET0Iria9sgMn83nPs+6YalIU60qMcRDtdaVwb7lBeSZmPgXWF6lxEO+oaHZtmr/S1UvSyOyZEw/qcjSUs18iuencgQoCmWzpNTzIiKybGrTJSEjihK298YMooLHX3iWL3zzVTonjkOwxPmtXWXs3+ouqwqhoMwSyrxSVv0qJXWKDE639feFTlWV0/I8qjzh+tUrylT71JmzrK51wWujGbpqge9XRoXkobL1dYxJxXS/SrpPOBUprfWbZrzkZYVgHsSV6jpFlqu/lXUXcdP+c2/F/s9uHUWQ0qcl6xQYBL6ntqfIS8pCErAiesOeWm671aXdXsaX7dFt5VAgzD3Ls8n61IqUNsttqqp3c1V82D//8+JhT1b8NLqOt7t5W+Do8KkkPx0aRbdoQy+wwAKzoJlKQS8wpdJZgyHVSNtXhvgrj36ZZ74CYVTxix/+JZf6V+lYrmrVK5GO5ZMmEXu9HcbhkGNCxmpdmfK7uoiCTFXRNNyAQToikxjQGpIix7cdNb+p56lq7YtdlO84kMWKyHW6K1x5/70mZnQS4ykic01sqiqbnXHK1mCL3ijC6qxy5sUX+MJ3f41Hn3ueqMiJipI4L2j5gap4SuWwLvMDoijG/LeKMvZx8PMixRXiWZf0ezuEwxGra5ucfuSkIo6VYR+QSMNoRE6Gbt6okBrN16rtfcg5WQjnfnVzetZ0/18Sxep3MscrVc6DSqvRLE/Tb59MxbT4Vb/xGrL9+38TxQlVkdHb3aK/t4fr+LSEpLZkZlisv5qWvSYiOvFWmLx+WTT7x7iztnaBBebCoaR06mM0ywf0QRcXz8Ks7f+kOBLx0wIfb9999PvF/lzgs4HadZQfp20ZqjIYD0K8VqA8TsMwptYrNh57hq8vuTz63KOMrl1k58Jl3n3jXYa7I9btHNfWKNOYcb+H+C1JtGaqyK6o13OcWleEJ3VLNNdBty3Vmi9NHV1U4kWtRghMagLTJC0MCXYiCNrUhUYmEZx6iWUYSowUFbATxVzeHbLX20UPOnz5pa/ypVe/y/rZs4y1xiar0/IJxKc0iUnCSL2f0nJX7XDli2oq4jldZdz/ep9IumpUQCML+8oL9tjmBhsnjtNZWSVV5vtNO95UVliGssRqiKip1MOS6X8wUzpZ/u2Smg6NFC1LtS7uhJgmWWP4r9Kn1CxoOXlO015vypg3lmNqZlMlLYqDsADV9p+MF3i+r9r84/GYOB6TJCFxMiaKA2Vn5S/5qhpsiU2YZivRk0YjkGpwZ1X+Ags8zHhYq7dHNmO6IKvzYbH/FvgsYEiJ7djEda4IWKvbIc1S4ijFD1qM05K98YCheGg+9wRf+vbXOP/We1we/SvOD97GHe5QY5PGI/q7OyQqxrOLjD5qJQzHQzpWjetK5dRWlk/COrOkJK9LpR63koQ0jMijMVkWk0cJeqlTpOJ/apKIXZNZ0wlaZBUMxhFX+zFXByMsw+Hs40/z+Vd+hY0nHmOUl+hlgSV5+IVElUYYWo1r64o0ipJdolQzlVXfUCwOqZbuE8jANdWMaRSGeLbNibOn8TpdwqrEtAOqYqR8XZtUraYyKkROPcoNrqEdVELrSazpQate2SGVSnR0U5VT2vuTv9uvcu5bTu0TQW0Si3pYlXeaaGd5U/GUeVLlQEBDUvM8I01TsqqZX5XZ2263O5nhTYmTAcPRDsa48ZD1vS6+38axOmpd1DhrfbvcmAUW+PSxaOH/8mDezqZk+uvb3VU3f3P7N6v5k1mnjlm9mHKunXGYD+nHWf5h+4Db7K/DX//OB3Ox72OqTSoZ2o2J6eb7GfuvnqFKPeLna3NHks2JWds3C7O2fxaO+vVnvn/T95bV3T3nU339j+8jPH0OCQgxlI28pVr3cuw7poVRNtXTQXSFctyj2Npja8um6z/N2c89w6//gw3eu/C/8K//+j0219bJtq9x9S++z/GnnuW5l14kMzViF1YKW0WgpkaL9uZJxnHEsD/Eb7uUtofXu8gwSuhTMk51rNSnWzsMfvEOP/v+X6KZFqZYLvk2v9jtg+UwTODD96+ysn6Cl3/nt3nxSy+xur5B2NtTNk0YNomIdiwPt56Q0aJQVVTDKBWx8gzUXKuaV51SsSvB0pTSndIiz2OWNk6yvr5K0HJI0wSriKjTEFN3J238pkranEsagor6ej9iv26CDWiqnOKVaijlhkmapwfzr0IKJSlKRg/E1WA0jllZWcGxvSZVShwIxFFAqp9VqfbP7d5f9bVdT+hvecNtQM51poEp//avHxKxOvGGsgwTK2g1+6CQ2NmCUbzLcHdHOS74vq9sqsSFwLU2JufJyfWoqm46Zyt3ARHBSUTqxJVUZQyomwTxa23Wf3pudrpiLBZd8xz/c2Pu88us2tOs5c/avjnX75dwfbrTNXpen3BjztrRkfvUzvj9rPWf7XM6awU+2Q6641G7uENYYIEF5sHt1Ob7j4ZhK9P1SjnvN1n6cpNWk1JWCVSJsm4a1gVp3oiFhIQ88dxz/Lf/3T/hf/qfE/7sT/+UKq3QTYff/d3f5Tt7e3z5V14hHAxZ8jxc0yQvC0bDnpqNXA4cijJn98olnDomjhOVStVyLeosYefqBa59+C5ZMiIrKlodqeYtc2W3zy8uXEDz2jz++ef55q/9Bme+8kWCdouibEiXpTfKcdswlLUTuXZg09RUICtVMWwUveZBZXRf7c5kn+0r6YUXST6/H3iKjBnG5O91S71OVes3xYFqt8SCNsS0/shs3HRVdlqxvy+gkt/laizihjk/B8vV1SVv+rVuh2nd/HQRZLoae7vjQ2A6sj46RmU0QjBqkrSxoJLZAcdO1IiB77VU618TQZuyZGiqvmmSNPvS1JSoCrUEMU6XSnHJtI7rwJ910al6qLDo5j54UMT0bt+0Wwf1fznE9ahfY/byP1olrj/GwT0zW+fmv7vpDlGf/450gQXuE0x/Zg5ImKqWNgRKtd8lCarKVRxpGPWJ+lvkotIvIhx3iTTPSYd9Wq7LuWef5b/5p/9UKeT/7I/+hDffe49LW1sqbnN1fZ1TZ06zO9ij0+mga2J7lKDlNaOoohD7KDGAT0eUojwvSnxdJ89Crn74cy5+8HPsMmsSkHQYxRkfXtvl6jDlhc9/hZe+8St88WtfJbUcZf0kpMm1bfWJzZNIzVOW8QAv6B4QHuFgIqQqVeW0MboX8ndrlXS/dS4EsVJjCC5B4GPZBpnMxsquM0x0Nataq6qg5N837h4T9b2qFBoTAjmpIioVftV0qeryoLoqHfp9cus4jVhKKqdiiyWG/brVqPyFxO2fjRQ5Ne7iGvCRitdkPnXyv+n51488Va0zDUHXGwJdVOVBhbkZCdgmSU2S1MOxJWY1mHi3Omr/iGhrsjCq6saMbTODKw4O5UcI9rSP7G2CaRZ4wLEgp/c3zDu12mahvlvPjgXuAO1mUqq+nDobztsqOvLnz3vmvset+Hlx1K9/37//H2NRh8wjlqWmxDDGwcuUFGVIlg5J00ETkxmPlWK/1Wlh+y6l6YFps9sbcvzMI/yX/9WKjAWPAAAgAElEQVR/jed3+KN/868ZhBFvvPEma2t/zre+9S3ap1dUxntVpuh1QT6O2bl2XSU5nTl5mpHMk1YlZTRS85B5b4e4t0ORjul2Wjh2h0vbu+xc3iWsbZ5++QV+9e/8PU4/+RgjXSMJE4qipBV4tAOfIkuxDYkH9aCU9n0Tu6wb1YE6nom4Sb4XYspUlfQGid0nipIS1WTQN/OZVePt2Ri1YghBnfy9VGAbTFVQ1ff7BLVU1WlFTqdGnKYrrvvrIOslxG9pqT0x1Tcm40aG+sw2M6qzJfGHiTtvIn63WGV95LnlzcvZ90pVtlVyE5D1qeucOExJIjlOXGwZoXB9ZZsVtJf3dwm6eLLWzfiZJrGounaw7fuoqpvnbe/5+e9en99mYs5W/y/p/HTb42tOVA84/Zm1/jPLakfk43poK/92b9hn8Q7j1mop3NwG+9RwGCldVEwXeMBx68z6re3mqpiarS5zijIiTcdkeUhZxYTjGE/T2dra5kovpnPmeQLPVaIZSXka7Y343AtfxLRcNcv5x3/4h5y/fIV33nmHYytrPNf5ohJVuWaNXudk8YA8GqDXFtk4xMgyjCon3NlltLtNFQ4hT1WlTXdddqOC87sDqtYqz3/jazz/yq9y+qmnyHWIxiHd9jpWXagKYn8YksURji2enxp5mmP5gSJ5jVG8Nklgaqp0UsGb3h/TcaH7tkyu72JYJqUaAchVdrc2mSVF2SVpB6S0ed50G19HEwI4IZINqZwipxMipmynqupgPYSQ7o8bSJKU+Lc2JW0Dzaia1xCSKm9aNWvG3rjpPLnvQ7o/YjB9fjuMPJiWflA5VRVPbWoZE1P/ZhugKiuKMlERsVE8Vs93h/1JxbmN7Xpqf8nBpsYCcg5m+w+Ox0lv/27GFBZ4sHCrnmaB+xc3EdNZH8RP8sbOnEGauag73xHtJ48c1fKnXunWJd/l82Zgv+p8KCm9m/U76uH1+7xiesSvP/v4ndfAe9bxO+/Fcb73f5Z4cN8u6G5w2CiQYVXN3F9ekKQxeTYmzSLVSi7SjKJyCJYD+sM36ccxXzHEm1RjNByy0W2z4rUZxyGPPfEM//C/+Ef47RZ//u/+lDffeputrS3+ww++z9e++iW+8fUv4fqGUvd7jkPLaanXDLeuoyUJgysX6F+5Qp3GpFFMVulc7ye8dXnM8smzPP3yV3nySy/R2jzBOE9VS9mxnEYQJC1mIU6ahd9dV0RIUOqJahnr+qT9LFMKeqUIYyVVWmXFdMPMfjo6dD9xyfOcxrezbOYhm+VNJSyJkeAkPrRmSjTFRPzE/k3vfq58Q06l5X9jpnX/PW7y63MxwC9rPK/xX71RUa2buVht3yJK1vPO4qBbCd50xfTQ0Y5brjHThFl5v04cBGR/yDq6tteQeKlMG/LzamJPlarnSmhCHDmE0UAJuEzHVY+u6ylbsVvFt9pHAgRmXX9mif/u+OtP4fx7tJj//Dff9s17flTz6kfos/6gU9xZ63+3g4if9Pe3w23FT7dToX8WcdiH82hnVBaDTQs8HLhZiHOjErjfMtWqWBEhSVeSOU+0plJnKMKg47dXuHT9Klu7Y1rLx5okI3RlWt/oqW2ScE9k1nzppZdZXV9hbW2NP/x//oC33n2H6rW3qcOIE8sB585uKEJra01req8/YO/8BfLxkGxvh2IwVGQ4rSQeFbZHI6ruSZ595ds89dLnMboBSZ1SlRqe4RBoHqM4JmhLNc5VhvCW4xElKUmcYbdWKUa7E7V8o0ov8koJcRqv4ptnSqfTmYSgCsGVnzX7qiGDjUiKg7+rtOkZyUkn55bzhzbxHN0XLKnLzcGspX4TeVRkLsvUclqt1sE6cVD9rBv3BG1CGA8RL92Mj1Yep8+d0xXKQ62nyqJZ3wmBN9SYwqSAS42p+UrIJP4moqA3VQpWrR7VTGwlFdeMJJa8/qF6LxyvRavVURGruu6qfT8dLrAQQD1cWMyTPngw/vn/8M/+x/21PqxtfevvPopZdyyz9sm8FaejXT6HXFw/TdQHyzUOHg+gfjnvPcm89zyznj/v/pi3Yjrv688bqXo/Hb/7jGV6m2YRh1nbP9/zueVzs3+R2G8Xb21dYDQeEkex2he+7xF4jvpaqorvfbjH7/3Lf8kP/uZvCJZWcNtrVLrBSqdNONzDtdr4Uv1ybeIsxrJtnvvcszzz9FN0gjZ+ZRMJ8YxHaFqhZkAtwyLNCj748CLFzhXivR56muBJSxyTvDYY5xo745jPffPv8vgXnkdvuQzyEMPScG0HV7NxsbBaHn4g7fqK6zt7vP7WO/zbP/5Tvvcf/5qLV7d48tTGZLbUULOm+wbz+/OmIpKSqqQoy6dz6OV7IU7CAQupDqpZAF1ViORrVR2VVr1+Q8yj9vFUBak5l2g3FPQHXnTawXGnTTkC7L9PIuaS75eWlqg1Q9k71RNR/42va3XwGre4Adz6j0likxor0PYjULWDR6hues708aIIunHD+mr6eGriVk2KxGyU9XUTp6qr0YZ6QpwrZQtl2ya2bWGIt2xVE6cxo9GQXq8nSbNN5Oxk1nYaDUGdfWzPh1nnv6MeJ5j38z9vxfRo+cP0cX7zzxdjGneDe7WftCJPZ3z07nxgVTNK6fqcGzbbJ3TWhXG+6uO8PqWzUN00d7dfMdGnqiKzWhn3d1b9AkeLWa302T6+d4ZYNjVEwJgQm4YcHbRjjXRyaZhUnOoJ4ZjY9aimzKRIV+WxUtqPxnsk8UhZNhVJSeB3lR+m69usbbbZ2tnm937v/+UnP3qbH/7gP9LrDRiNRlimy9raBidPnubE8VMsLy/z67/1Gzz//POcOnVSXWLTslBEY3d3l63tbeKL73D5g3fI+3tUox7lOOTYyiauG3Dp4hWi8++z1LJwrQLTqhnlFT8/3+dqaOKvnOZb/+i3CFptLNdrDPG9gKXuCqbrKSFSPEj58Pz7/PSnP+WNN97g4sULivBEyqw/41u//ff45//9P2bVE+/Sing8xLIcLNdnZ6/P6uoqrmeiW9KCzpqUJb+NbQXUtYFlFAcK9KadfzORM7Sbm163ft4rbk6V+kjLXNPJ00RZZYkAbVv2WZLR6q7iBS2KJLlBGPX9ims1VWGdfdG/yVd0qmrePN55FEDXP7ruN2/gDbHS9N8cVGQnX1dN+bR53fJGdOogHDdVVDsgCDq0W01ev/Kj1XSy4mBSYsKBCiVCawhdhaH76r1RVmGWNbVaN3xp58GDfn6ft1I57/bd/PqTY2XK+1SbIeCbd//f75Xaoz5+Pun2L4jp3K+/IKYL3DscNTGt6mxSbdsXsRzuO9m055tibaPsPvit8p0cS1U0HJJmoYoe1RS5kcHMEtcRIuDS6bYI0z7/6//+v/Ev/o//mytXhix3A0XwRPnezEVqB96T8v3pR8/w1FNP8eqrr/LNb73Kk08+qdTWMvsplciot4ut1bz3tz/ig7/9Ma//5ff48K03OX3sGGvdJeJru7iOycpqo/h/b2uXty7vsfLo53nlO7/J6qk10jxjb9Bnd6/HKE7IipzBKKQ36PO3P3yNKIoYDockSRM7qhs3qm9Oe5l/9k/+Mb/9n3yHdLRHWeQNOTMslUIljgDtto/lymxn47kZtLu4bkuNDOjkNxHTW0nexyWmH3l/pSFeFniWeMnm7O3tUVYoYmraDtWkmqhNwj72Z01vvPd3JqXTM6XTvz8gizNnnOuPENObhKe3ENNbt7XSG4HWYeRUwRKLMLmZKf5/9t78x5LsOhP7bqxvza32pburN5JNUmxxEylxGQ0leUBLFCXDA1mbaWqkmbFm5ldDgA3Dhv4BwxgYNozBwIBmNGPJtoSBKI0tihIlUk1xa/bCbjZ7qe7qrq4lq3J9Wyz3GufcuBE34sV7L7Mys7aO03idlS/jxXrjxXe/853vQKYO20x1O8vo95fQbnXhdTq8mDn3GqQ62ZlVUJm/qlIqdzQwk4eDglI0wPTQgSm/ZzXVaYDp3QlMD9yS9KgPbPH6j/bC3+03fgM839lx1NffdUL+qTIfSBNG50d2oFTpzCbmGTOaThI2QCdwuDO6xj/jJAIjnoxtk1mRSitM4fjGUgkIfR8bNzaxuz2C77QY9BFbyzrAvO+6zPw3XVx85VW8/IOX8NRTT+FLX/oSLly4AMdzOQ398MMP46d/9hdxbHkJ33jhDbz49A8ROB2snTqDpX6AzeuXsLM5RnepD4y7nLZOls7i3Y99GCff9X44Z0/hS1/6Mt66+hZeefVVvHXlLQalhPUjsoIaj7nXvrF+MueBwJTpC3/jzcv41te/js/99E+yfRF7hMqEuy2trS7DZS/OGLFMOeVMRTnG4F6I4uvNZhurqe9biRwgSsUAXkC3Z6Xzy1pZ39cOAJUU+qyYxZpWi5ns9/ai5TRm/sWrnN6VxtFBbyRjxDIBA4PFrEBMGveH7DxyGb+CFBI+tYv1AsQR+dvG2B3c5AlU4LfgtkN0Oj2ttxUuF1yRv6vr+mz8TzMxU7CGmg5SdxqYvdOj0Zfem3FovfKbaKKJOxFH7aOqX0oiA6apttgx+U3TUEhpTWg8GWA42sFwsMP+oaN0Oy/uCTjV6SNNFGIjDKQWnYGHyThhtq7T9fHJH/8EnvrrZ/DGxZvMaNngRoONokMRVVYTeL1+9W381Veu428y03ra3vLqCp596SLe98QT+JM//0u89Mz3cK4X4lzfxZIIsT6MMQodjBwHV25s4+r2dTj9VVxYfRDXXnkd3/4Pf4L177+BwWiX7YekUNyFyfU0GPeEzggR2NTgBHkFvchA1FK7heee/h6n+j/60Y8gkVQYtcvsLDGQ5FF6c2OdMyf9/gksLa8iTiTieMJAFhVAdxBQWgcyaULAQDhO2AmBgoqu6L0kiisZL8NUToPM6r/t/UUNQCiWnc9YLcoY2Y0J6kAwnKINKkPcTBfL7zkKCTVRyK5fEDhIYj3xSdMJhqMJBltDtpqKJmtYWlpjOQm1TOX7TuqWpUKIXIup5bBmP9KmkPUuiOJ66H2pHSdN3F3X7KCpfLXI7uFW9mpfcXfbbSyKg6bym2jiKCOJlLYJcpxiLApdJW78JIkdHY0GmIx2EScjTg0LJ/OWdDOGSgrImABXwql4z/G5raZ0N9HrHIeDAFE0RLvjYXd3iC9+4V/gr/7qW1haW8nTx4VNUMrgk376boB+v8+tRtmsPuvtTP+OkgS9Tgtnzj2Aq9duYmtjC4FMsRI6ePjkGlQ0gOhQMQyxYAI3NscYRArLJ05Ceg4uXX4LHbQYwBA7RgBaE20R0gyQGLsoxykedrSvprjJGQGj8Ri/9Cu/jP/xd/8HjOIhNrc3cOLEGoOiwcYGn4+l5WXWzvphC1E84vUSCEaK/Lir6Xg+L2q6At8OaYHIajqd9z+V6LRCRMMdbG7c4H0mDa0TtDGaRBU/QfNda7OCdtX+9Le98Ui1LaKm0/mzY5HGVM7ImOWpfLPPRldq6UvJ49UNkI0nM57JE7Y4pjFdo8EQaSLQ763g+LGz6HVXs65btP24tG95+9Z8LBxMSnOvx93FGE9rTO/+BgbvzGgY0yaauKfjaKUuLk09KUfvZGboKuV2nsSGku5xku7qopwkQkrWPiplRpGM0T3hYJSSHIBFl0hlzFpRw7yRbVKrtcJbISN3rTkd4fjaEt7z2AW8/P1XsJ0gtzriYhNuM0nMa4sZWuqRTxnVOI0RTUa8FLGlxKS2WgEGm+v4/voNeGzHREDYRey18fLGENFoAoRjtnZyRIgg6Oj0+4113s5qqwM3DLidKQUZt1MalzRqlP4mZjHxkowNNK0yNcChxgHKSbgzU6IknnnheWzs7GJpuQff3UHoehjeXMerr76MRx55DKdOnWFQmjLg1kCYio1UWmYcpxjKPVSN1wFS85OAI10/0vHS78aiKmGPVW3Qb63M/KO8D5Xt1e1D9We+Twu7RxVp/MKU31r3zOPOPi10Zy3lOnAodc/4WlWAMgHKoiOXlppo0Ow7LrqtNgNXKhK7/OYb8L1rWF5exQoXwbn5Xuj++wk7Aeg9V3s4viZuZ/DYa874XR9HrzE94hnTUbPxd7u4+V4XXzdxsDji24/1n9QiJ40TBmaUYiZGL2EgmnKnHQIyQdCC5+iHsO6qkyAmwJPG8DzToYgAo2DbJnAnowi91gk4iir+PdY4KknM3Tre854L+MqXXexu66IbBgZxxOA0CCmF7+XASndWkrkfZUxWVGNtwxSQZdSSg+X+Eoa7u9jdGSCWPuIEEFR5nbrwwh73TFe+i143RExepqMRFx8NdjfYuqnFPqUeb1sl2tx9tDvSxvYGZDkqs23KWDkCQJ5AZ7mLq+s38LVv/B1+9rP/AN1WF5vXruGVF76P7lqf3QWoAp7Y0WiSQPhZX/gk4g5VJupA5q2GYS49z0USRwxMKZ3dyYp9aNLhUo/8ZH7VvL1ve/m9mkbdaw3BLK3gos+T5MToTSmd77L3q2RwCm5pmrCGOQy8XBbAVmYy0gVnSvLY7rQDLpC6eXMDN2+uY2d3E6PxLpaPHWNbL9/zeQIm1eF26mu+3w8Wjcb03oyGMW2iiSZmRhpPuHCJUvVUdZ7KCMJJtcbSd1kXqdknqu5WDNiQSCjpQSiBXhdsC0XAJ40muSbPc3SP/NEwwurqCar5Z2DQ7S3h5s0r+PBHnkQ7FBgMBgwMCWQSC0pFRSQT0OxkgnZm15OkiTap93SBlMwYsTTocvefeH0dcjzUfedDB5vJRLcxHXoI2h5GkwEG0Q6k1ObyRHR1lzoIhWRtbRKPMRmTL6aP0At14U4KOJ6fNwwgLobSwARQjdZ0NJnA8X1cuXYN/9+X/wKf+clPM5N88eLreO7pp/HL//QfYW1tjWcQ5IVKqV/fI546Ys1n27IgwiECUhN0HBEXlCVohT6fwzjR++6HDmsyMQcAzWNIZ21bWV2fFlWuG6A3a/vVXt/VbZsCK8cAFKVbsBJIJSKcQKfZL+N+QMuRvpfGHTkT7O7usrcr2XwdP05AdIjNzU289toP0V5fx4kTJ3Dy5EkGqPZ+OGKxD2oTRx91+uYGrN7d4e2tKnJOHPQCL5oRLvi4s0AjIp2DUUoLj+6AlNWsgoa9Pn+aG+ydHYuuP+khoZzS2LI1can0teE71zJJtm+SVFFPqfpogs1oi5fj8ekJTm0S85mnPLlNpjaPT1UMSVX3oYIgsEP6ywTwuPUouKPSZJLy4KYOScRCBsEuokmE8dhBq7uCRCn2OQ3CEKce6OOZV9fhuD4UsZwxKdp9SERwvBidto/JOMJgPGBwsLW1BY98JpVEt9tioOGlY8SKDOoVuqvHGXjsjsfodkIMhxvwwjakM4YXRFAEnuMUgdOGAskAEoSOxyybZ3VJUonWfNIxypbSx+wao/qU0+AMvoglXl3Fzs1tdPwQrz77Al5++hk89vBZfO3rf4lPfurHcO7cw/o6JBMGtC5V9GcsZdvv5dds1vWrfj0rlNP9ruNNWS1Jq9o+Hm0jmozhtclbtYuJFIhJZ0n9+WVSUuirHAUW6WlpeZrOAqmzirW4q9UChjFPi9dYRlF4FbusqVQ/O0FY4Fo4ef7f1rjm6/PK6xsNdnkS5XUClmnQ+Al8idWVNpKej2i8jatvrGO4fQWPPPou9qAltUqckONEB5KyA9qUi1P9nhNAEAuuiB2X8Fv3NyN6d7kKZKM591g+jLi3a1wgFmREDqrBFQvOz4z1N4xpE03cx0F2T9WHOk02nbzFo35Op2mMyXiClEBpNEY8HjHT6YZFm0wDzEptLFXxNxhjcVm0z0SmubS9Ho29EusblYcw7LAVFGlAx8MhfAE21D+11Mfx1SUuMqHe9O0wgOs5XKxELK4bK9ZwBsxqDeD7AW8jDFtcsEL7ZdL79JOYL/o7a0OThNPWu4MJWm5W4e/1dHV96iGJdcegBCOWBrBcIJH5OoN2wIVX9Dfu0imV7shk2WoJR2C4uY21Th9OIvHqSz/A33z1r3Hp4kk89PDD+NiPf2JfA28vTE8VCNgp86pGFVnamt93pnva73WfDrLMwlR81bfU+r3ueKZizukSlfajddXa5ZasIh/LZgz3ukssPyEf24sXX8Ppsw9w8ZjrBlwUSGOaC6DYFUAgjlKGKp7nI2g5uoNWE000UQqv8Ulroon7O/Q9LvLZvZ0+VYo0o7pwiPSjVMSkiAmkmbSL3KPRfhlgypGWAQ0DUOgHt2npqDsW8Za5yERbPQX8wFYqhOe2uU1oPIkRj4ZoC4md69fw0MkTQPICp88FeX8SYFZZU00vQEKlWeMUve4K61MDP9SsqdsClIfl5RVs79xk8EU+lJSaTTKQSalZAqYEZin9Tub2SiYsRUgnE95fMlpPCHv7LssWTMo+VgpRNObjbXstljEQ2DcV2crqQ69GA7RYyxhBxhG+861voLf0CXzmY5+G02pl12BOZ6MsbjUdaYO3qnWT6YtP4bnensEoSoBy70C5Cib3BCwXrLtO22qfl3LtVr2nah3oNUHj1FwbOl9062hSla63RJva03Y7GAyoq9kIV99+iz+5snIMoU86YVd7p7J0hcatzIvkHMe5HbY1TTRxz8VCxvSogetB54tqUap+QSwUlx9w/xrxehN3MqjjozHDz2U5WQU5pZ23d65rCybSbsrM6iiglH2gjeIxDUxLQEcVdkYmLVpa1rILEpnnp2ExOZwWpPK5+juNI6STIXxH4ObVy1hp9/D4Ixfw8quvYXd7gv7KMvrtPoZUnJQQA+shmexABpIlPUIKtPwWFxFRinc8GKPV6mTWUlo3SFX1pAU8efI03n77bQSh6UzEpdtZhyvF3amieBcpuQxkPpduoPWeBqDy51hPy305ya+d3yPwa9LlPc9BvLML33Vx4vwZXLt+BU9+8Efx0Y//BFtbpbHcFyCt/m3R70rpVHa1cIqAEbko0L6yNjdjsOcVJVWBpbA8TevAb91+ThVw7ZFx3Sson0rlW3ZNxXZnfy6v5s9+Z3swWb5G5lwhO/pO2OFxJpwNbG/vIHr9NUTjIbeb9bxV5AtKPSl0PIczFON4xK1Qm2jijsVR22UtXH+Tym+iiXdcsKzOEKZULS4Trm6fRNruSSYTXsihl5elLq1UvaPqQalhkYhpI9aNi5uMxZCVFta6S5WDOcOk5n93dLGSUNrUXCr6d4ob6xv8pfVf/7N/jm9/+9v4xt99Ey+/dhEbm9fgB20uQBqNxuwHSil6Wh/ZUbXaAf9O6fobN9exsrbCQJSKVQhc0j584AMfwE/91E/hT//0T/G9Z56BEB6zrEokDGQ6HUrRj7nwarnVR5qkSMYjTFItUaD9Z6BKXZyoAkpmxVbmnKFoAtAOQ7zn3e/CJ3/84+j1W+xS8Omf/BQSBZYf9IKCNcUMFnERMJsHUE2BURVUmkIfc41Mylqvt14OgBnAc14cBmM6L5VfBaLz7KTqGNO9hq1HNWl8Wt9wPMKNjZss56DKfKru39hYx/bWTayvruKRC+9Hq92jKjm+F5OJYqcLGh+6LdW+d6WJJu77uOeBaXNfN9HE7HDd7A5RCRvfx/GIQelkMmY7onYryBk1wcg004pCMdjiKvPaApYsvak0wNFaRd1FyLGsG0k7SuSSyxlNmTFNDgNAWl/AYJHS/5KN7KVL7KtE4nho91fxX/xXv4F/+Cu/hlde/SH+8A//AL/3e/8Gr/7wLfS6fax2etjd3WQASZZLMfurJjh79jQ+//nPc7r+9//9/8UWTEks0W6FXMDDnaeilF/alknvN5modzsd/PjHP4R3v/tR7mA1uLrD1fEEdkn3SlIB0hPS7yQf8FohV3xTARgBYJIMLC0tcUtU+vdnPvNTePjBB3Hm9Bqefe5pPPHEE5z63R1NsNxbQxoNpwp6ZsWsVLQdU0CPrJEYmHL1kpZBMLubIE4mBRvMhvEZ+HLcKfBbt40q4zkLtM5lTBcE11sZEArzb1PIJMpe6XV2UqhhTDH9GTHr92LJPPNga6Q9L+ZxQOdtbWUVa8tLmAwH2Nq8iRvRiOUbZ888hLVTD0I4Ptde8YSArMUWFRY30cQRx6IGELp72UHiFhnTRmPaRBP3cYiURJ7sPRrFQySJtmxyPcmFREHWXjFFRq2S7hPQBT1kqVNTWW0DAPZ6NFXo1t8NC5fGMk/hV0GJLjgSmMQEahPWtY6TCSZpgrWzD+DM8ZO4fmMHni/wrvc8gd/+7X8KkSb43//Xf4UrV7YQMssrcf7caRw/fhw3btzA9evX8bmf+yz+u//2d3Dp0iX82f/7F7hy5Qq63S5bThFY/e53v4sf/OAH/P7K2jLvv+c6rCulvuif/exn8YXf+DVuvypHussUgQ8CwARM19fXce3aNf43NRpgxjczpycwSp2oVlZW+N8D4aPXCpAkQ5x+4Aze/8H3wSEgSJZMSswFpbMAXd3v+wkjvaDjagVhDkzjTI4hnII9nbUJMx4W7cEsScCsY95vzDtHeiPzt1vWW08zs4AoMc7K6l7F49z3WatMkxea6JFko99rQyU9fu/qlR8iinY5o3Di5AV4rTaE9FgqIl3ZpCybaKImmvuiiSbu65CcluaWocTOgfrIO9osnkzFoxabiJMHKbOkKaWkncwHlAo96u3MzMOdwE1R7GO8IgvrHeqWA8tP0oQpDvIcMn9K2eB+kkwwSiIkUuHU+Yfw6KOPI1xawWDnBnZHIwZ7X/jCr+NjH/wwvvWN7+Dbf/ddLJ0/wVZRBBxfeOEFZoN/7GMfQW+lj7/8vb/gPvrEbp45c4bBgbaoChjAPvDAAxiOB8wqEzDb3B0yWKXlwediArQ7EL7DEoHOsRWcdS/o46czmcQIyHF0PObtExCh80EvA8b73WVEo12MbmzhyY/8KLdOHYyGXFhFWll/AUDbDwCdRTLUXTcDTg0oLQGv0rILGNk97s8stveoNfxiD+d31kEt1eMAACAASURBVD5qZllOnT+T1jc/vWzCQxOjVuAz2KfuZKPBDoJWivXrb2IwiJGqAOcefJTT+MTck1+s1zSGaqKJqfDu9VT4fu1Tpj4/Y7m9ppsWfU0vPL9N8VMTc0KqSf5HKl4yqck8BaM9w/V7VlaEqsw1ULquQaBLPqEtOE5Hp+yFQJRoapSgiHKzocjAJAVJ4IxWlIpj6KdhRw1I1Zo7mfWgJrZNL8vpfCp6StlomD9D4WSV32zGz0pMBynZ6IRdTMYx0tEujnkhXn7rVfh+H72TDyFMXYTd48xGDcYJzl54AmcvPI4nP/UJ/Myli/jrL38F8XCMgVJ44sLD+OlP/SQ+/ff+Pt64egX/xx//EXYH21he6WM42s3PzSRK0V/qYmd3C57fhiskAiGx1guQxENE4wnP2SU6IBtY6gBF2teE/FDdpEjjkh2U7EIGLe6ZnmKMRA2hHImwFbAsoI8YT7/0fXS7bSx1ViDpc6SeIDCeDCD8oBb4mJdPrgj59RdFg84aTWrdd1ZK1xIh4oi6Hek2qqPxNsbDAftxtjtLumArlty1iuyNVNa1irvQVn0I80lKNvgwnb5X1r5Kkwl0CncImWmeWf+6wMeUxgryr0lhgWV9rFKUz4W9L/yTdqC6jCiWSZ1i+7kNGt0BVBBIr0mimX26B7KxTGORZCu8/zJFy3Mh2y2ehMWpRCcIEIolqN0hT/paXYHNjct44fs7CPwxTpx7DEJQwRmNe7IvE7xPtN5iglBkGZq49VgkR7ELNqt/w57wxaJU+MHwyVH7pC7aP3P/zTo/B13/rFU1jGkTTdzFQcVBsL4gzBeReUCbd3XnoZQrypMkxmg84DRzKyyq6o12cFEldPWLxzZkL4z1C8YIVkGItoLy8gcsqkDBSgMzeOXCoWJZA2INwHW9zHrKpdajwGA44D78/f4S3v2u90LEKRvYE0v18IMXsHL8BLx+H//97/4unnvmWYRO+cFRPTb2J03TvDjL7H9eeS/LhvY2W0bnWsgIAQEIl7joBGHgoh12tWZVxvjbv/4qEqHw8NnTCAgURmNdCc/+q8GBRfKLHhIG3PD14Wun8oIoPyu8smNav7p4BxfqXO9g7IdxtouqTJhJlgbrBYixnSjsqn27qIzN+qWLaDRGt9tnZ4jnn38e75I+zj7wGDd9oIyEfd7MtrTRQwNKm3hnRgNMm2jirg59i7Izk6oh2LNmNlRcRF6ZQ+rkE48ghG4p6fut7PMCEoXFDQwIqVQ2Txc5FcCs/OAs2jciA0AEJo31UBW08jotAGqALGntmD21pAH0wO9R/3HfRyrHDFw1c+syK0tsHriSPsC7Hn+P7u8uPLz64ovYeWuCN69cxX/44z9GIKYZp6mHvSr2hQ3T+x0uXKJiJt9xMI4npfNTZjRTBpfUxpRY15VeCz55kyqFq5ffxBtvvIGN3W08/OijOH3ubIldZBDMkonZjMjCbE0lFV63PBWf6esguCiN9MWGmaMWm/Yko6qxNOzhXlPhRxnCquiv28+69/ayv9XPqlIjCtJBW2NZyNJyZnzDum8MYKWxRMVwg3EE11fwhYPt7V1O63tBB72lNfSX17TBvnByr1/tjkD7k2STiAacHmXs5R47SNzrk4s7tf/3fFmgqPFYrNPENdHEvRgyLV42e1cACcW+pClV2o92EI13oNIRfE+i03JL9kzztKKz7iW78w0qbBEB05yNs6q7DdgxaX+zD7BYKQMEq2CC5Af0OQKbtD7qGU9tVQlQETDQn/MZoEdRjE6vx5rQi6+9gu99//sYxQn+5utP4erbVzDaHU5d8SrIqu4bFUlRVT1KfHT5/MAGMDKCI2NQgyzS7ibDHVy59CquvPkGRjtbeN+PPInHn3gCXtjBhChf5XCrSvrqlbLOd7N8/hf9ve6alj+vXQcUpwSpMcAkM9V38naldedn1vqq+1KNw/7Otbdb/Xkr79Xtf939YE+gbHa0Wvxk3yemnamxRaMxLOCj31/mzmU0Iej1uti8eQ0v/eAZxNEuj2/i2jXzCshFmdsmjjzUHhpevJPjcM+Pqn01jGkTTdwDYbxIRa6vy9KHKmFgRrZJCglabQ+tVg/CSdk+iVhFzHkwqwVgwqkY5JuHtKnEN8DO6C7tZYj9tPV8VeY1Bx2qAKzGD5XYJmFV85OF1HgcscY2DNsIw4AZ1cHOOl557TX2Kf3YJ34CQdDCV7/6Vexs7WCp1eHe+/OCGCuVsb+0bdougVMyn5clM3mzvzZ7Sr3UB/wZWtPN69fYCWCwu832Ve//kfei11+F1+lwC1UqxArbLX1OoxiK+rjPoAYWpaBngdap5ZiNTjLwLZGkYwb5gUdSidZM4LtIm7eXv5lrexhxEMZ00bmqjs86cG5S+TaYZdeJNC5lBmg5Gvcme+D4PjdeoGVIbkLvjcYJ1q9fxssvPYtH3/0EQkdLP0gBwAR61jSGOqg1Sc0m3onRGKk10cRdHIQnuHOhk7k5UTGKSJDKCEk6wubWNQyGG0jSCYMmzVqSdtGHTP2pA5vFPu2NfSuYUsMKGZbUNs03ujvDmGJKm1kvFxBZgRX9m9km3qbD6XvS5/EyDtfDs2Thxs0rePvtK3jwwQfx8OPvwqmz5/Bv//3/ia8/9RRafoC1/motwLLfsxlT2h6xpWtrazPBmX0++JjJB1VK9jZdv7nJx3js+EmcPnOGJQHkMEAtXukChixPCBhk08tRYmp/6q7NvL8vumbELpMXLVWCO65kIEX7TeCeJi1VILYXxnPW9mb9vpd1LXrVnZf9vFf3+6z3ZoWqdDij82jfD2ZdBEyNzrTV7mIwGMJ1fHS6VCA1QuBThzLghy8+i63tdaRqwp/1eBJWaG2kPKiHZBOLYlY2oIni/jja8yNrX810rIkm7ubIvw9kxnhRb/sxs6H08BvvbjAL0+20NEMDD2lEWrUWWn4bcJL84MjQe4p1mgESUdHRmc8YM32RVeu72UdtYFoHDAxYRQ1DZRhYkUkAROYJykxpYlpCmlaQwHg8wGC4w76ixG6uHjuJThLhW9/7Lv7vP/ojZjCXwh7evHQJwXJvLkDRLFchRSCmk4ApaUwFb1dWzokNvATCdldbRJEMoN/H6rE19Dpd/vv2cIB2p8/+oNTOlDxj2b0gIdcDh435ZaXqdor9qwGlVU1k3XEVUYBu04bUTGC4Qr5GJ2lfm9wCbEbcrgf6rTKm1QnGPHA6izE1GYE0L3QqnCnsZYy+2kyu9Dju8PsyKtoAO0iY+VcywmsXX4YjAhxfK+QduhmFw04QTdyZsKUc82Jx1fn8++NelQvUZRUOMxpg2kQTd3FooKY4rUegggqbCJiNJ0MGRN3QZaaFCoO4glj4rGsj6x9OGTuFTZKEeQAXxzuLnVOWX2OV9TTV62yhk7E6VRavYCJVaV1VQ/NCWydzz0n6PBUVMePnEOOnWKaQSurAtMNepUHg4OzZk2h7fVy7dhX9Y6t45ZVX8Nbbl3X70b6DpV4fkTOfJWO5gUy5OIUiDEMGxcgcAnKgIsrA1KyHCrf8MMBq6zjSOGEnhAmncj0sLa/C9QOMowmSaMItS4k99YULz/cBSuXXPJfmpdL38nd7OdYo8/nNOn8lEx4jUIXGtXrtyjpLUQv85m3zMGOvx7qX/drremxWX6Ao+EulmWClJQmLWa9J3xuJC092hIuVteNYv/wGxsMh24aRjno82MHp0yfxxhsXsbJ8Akv9kxDKyyZgpvCs0Tg28c6MhZ2fDjojuNdiv1+CB/3qsNOIdswgTJq430LE/PBX0tXsljJpe5lBST13nIwHiCZUcb/D3qaBkyBsU5eekwx4EtYSAp5LD8UESqSsUGMQkg9WlRufqiytPosRsKvvkd0XxAQRkLM1pUkGNkWmOUhpOam4F7wUDnwU6Xs/0J8BpZQRa71mFIJckwbYBpwYUaywdvwCnHAZ0vOhMoN+neoMsNQ/VtrP4USyjnN3Y4hvfvUbuPr6WzqFL4AJVVHDLQEuG2zzPlHHJ0X60jGC0MMxYjyXuoiSMdzQY1bL4ZuxWE9xv7pceEZmmgydE62PVQ77fGmPzWjCV1Cfeu2pSdc8kQn/26lxSjA+n3pDrrU9+wvCXCeL6auAKvo9GkV83l2hkDoKKytLUG6AWEiMyU2g43CLVmKmXSWyNpkKKTG7iuQG0+NDZW4OPHEwgF0U7T+VU+wzdfNC6QirX5r1hXh179nnQFnOCKW15ctkXrt8M5m/yspPlMaFzZKZc5hA+56y6oJatpJfLW1TidzRwaT0aXli683vZLofhF3QHR522hhPtnFze4utwmgCFA0HWHXaeP7vnsaF80/AbQGTmKY6lMpM4KgYSkxbejVxNFHHuB90UnTwSdXRqi33g9/qzs/B11//90Zj2kQTd0GIzLRcE3eaIaXH4GhEhU0b7EtKFdXsWgMfrhPCc9u848KqjK9W4aPCdNqei7A0lnthTumnYUqNv6Mdi6o1p4Ed8kpmsy2TEuU0fpqW/lYXtDx1XSKNJzGm5liIlaoCmbow6VdTRU3doKilKP0exdGev4Bt/ax9Pg8a1XNmM3WGrSsznOXrTWDbvMfss9fiyY6HAG23DbLvl9EESMcIAnJyoAmA1ni1/LB07arXclHcjjTlUTC0pXVadk16kmM7STglMGuuid1JS2StdykDQK/ivsmuqRPD8yWuXXlLP4yVhOu4iKMUcKY14k008U6IJpXfRBN3MDSTloHS3Ks0zV+D4c2sq5KE4PaILusfXUezWxKFXY0NTE3UAUwTwvIlNWEzpCrreW8XfNgP32rYAHZWiEpFPj2oI6lZNcNkmjR+dT31xUgOg9CXX34Zzz77bP7gJ3aX2Ku4IjWoBlXie7w/Drc8vXDhgmZ+k4j3x8UMxtI6h0YnmwNT15nJRB8k6kA/NVOoA/wmfFdhkkgkmUcm+ZoSJUu6RprcjAdb2Lx+FTu7N7hFLbkaKOmj3VrC6srJ2nXeKstSG4eAXavyg7JmtLwfRhtcfG56PYu0umYSCWsyZcKMBeT3A/Jx7nkBHGfEPry0DLHRyk0QhA4uvfkyjp8+C9dps2okjlTuQdxEE++0aIBpE03cwVBZb/Liwcld2qG4I1ICz9cm21SgI6TN5Ljcb5ueYqJS0WzHLNawjtWrsqN2sYkBjQb42g9g1ABg5A9xVxcQZdpMAkaadXJNn8r84T7JqplnyVuq+2rOFwGup556ClevXkWv18uB+iJQpJnVCEGnxfZJ1HP/7NmzSDObq1bYgpwkpeXrwmaiNXNms9Z2R6HyeoyGcXq/pjdid9qywT/JIcw1qTLl+nMx64BTxbbtxPnBdQK40gGSGJvXrmLj2lu4cfMyyz9c6kjlLePE8QfR9fvwuvM7Z6nioGYWJ92OqE5k5u1D3T0x+77RQFah8ORVyssmidMMq2k0gUyjrC3T2AMqHwNJnLArgxQSfocY0xDb29dw49olnD7zKD+WycqLNSHi6FnnJpq422IhML3fNKRNNHFXhXJKTe41sJMMSglUEJtCAJQZyxRWsVCmF/Us66JKGt7WVlYZtarushrKqpg3YMgGjNXPzdLqmUb+NnAu7au1bgKlxH6adXiuB5nEpXNT/Tethvbxb//2bwvdK7X89H1dHY1pgGKDCVs2cPz4cZw+fVqnyEXmAbrg+8+WSMBK6R4WY2qf07oXsZxVFtoGaTKNGWzScCH9r8vG+oIoOUx2B1i/egnxeIBW4PJQJKsx0j8Sa0193j0UwPRufBbUMesmTPGWvWz1s1XK1m62kL2jtalKT7II2juOYr0pFEqZAzN548YQ2T03ntgA1s3XrW/nFC4D3oS12Fffeh0nj50BXSWSYJDjlNtQR028A6MZ9k00cQdDVNpmFmn8hP06CZTqtoRO9n6WnszBWzjlI1pNZ6IC6uZpL22QoxZ4j9bpUqcYU+Vmz37F6XLtFuDlx22zsQQkTTtHQBcGGeFB3XGYz5Kp/UsvvaRbk2aV9rQOLtTyvdL5qO4/Vc+TdjeeRDh27Bh7j1JZNFWwjyZDhKJe55cDv4oNls1c2uehvA97ZxSrk4wq4PW8aZ2vzaj6xJF6AQNtSfl8h0uiEI82sL2xjniyC8eRCNwAwnMRtrro909geWWNrbgSGZWucfX8GWBnmH/erihPHI465rGli1j36tievlY6W8GFiOb8KyeX3FQnAoatL9adrR+ZBtXxId1Ud96CxxNQBwqdlo+tm+vY3riG1eMBXN+jvAmmBTNNNHH/RwNMm2jiDkYB6mAVPWUvAqLS49Q+M6R59XWSPfCpGKk71XUJFkgynorVIpkqwBGVYinz0zbJN2HbKFWZOnt9vA057dNZXdbW5NGxGA/TqsenCRuEUOXz1772NWxt6Wpns14DcFXNZ6rHIjLfVNKXErhVBJBl5q3qB3O3XzVcP8zCJ8woGCv/lFPXtrxM7nHFBf7kh0AOD9ubl7Gx/iaEL9m2itwb/KCHfn8NSysn0el1IXwBjOeB0r3t/9w4YIFU3QQAFjgtb39ah1q3r+X7gO6TNGdOeUKV24e5OWCFNeZL9wXK40Ez6r5mXsmUIuWkhy4ClCNcefsSjh0/xdZomi5t6pObeOdFA0ybaOKOx2x2U1tIZVVRrMlMMn9Dmesr7WIkm70TmYF6XVGSrRmtA4smbPbHdHMynW7oPeP5WY1ZDGsdgDUsG7IqfUol037FqgxM64qhqM3nd77zHW36r8ApaGNyTmn6SVYcVLd/yIDlUq+DlaVlPPbYY3w8cZLACzz0ghAqnm9yXjrftefxYMCrThJgaznJ27Z6XKX9SMnGKkVM15G6ISiyMdrE9tZVbG5ehrfUBxwPrU4Px4+fxcrxM3CDNqIkxmi4g5YbTm2/yrjfrXIvlTUIKKLq0Tod1cmZHSWpxLy/lfTWhVyF6vCqmQspta2Y4OyHwMaNaxCOxGQyRtDuHVpL1yaauJfiNgDTRTO+elYkD2H9PffU28csUiTz/66mmaP9xWHNaKsPs0bb+44ILWbUfqYigpK6M4+DEMIJ4PgxF0ro4n0HKqXe2y5cz81AmO7fTq0mbZaMDNVz18YMUCrLzqiO8URN8VJVO6l7emstKKXKyaaJAKABhFUgRalKktC6dkGSErkNT4QhuqGD4W6ClgiQkJHRyipiks+Srs/TnpCeH+D6+jpWVtbgeC62Nrc51Xz92hU89+z3AJWg0+lzN6gwbDEonyQTZqfsqAJHz3eYdX3f44/jkQcvIIlipK72fx0nMcJYWoVUGTspk0J36xbFR3XH75hJhyPy7wppt5B3Zk9K+Hp5kj1hR5MIruOhE3SoZxDG0QCeQ3rGsDTx0B8XxYs8RdMYoc9iEGztbuHtNy9hsLmN9tIx7Li60xXJGFphB4lykEYJf9an9L4oW1LpmN8KVQqbtV3QOcexOmtVtMvMoNd+D6r8xQWBma9q9qHSPsmSFMGwl36+Ddctr19rt61zKEfa85eut31vOJ5+zyk8XWlcqlTfa5QpoDHfchVfO9KLOnTt2jGinZtQ6Q5c38Fq7yQmwwQ7uxGOn1jFOBngB699F+969ycxSeh+K+QZVfB7N08KmmjiINEwpk00cQdDZCBFp+jth79kTaaywGI1Tb+fAptFWrtZ+lG7uMM8FI33qLGSMqCs+uCUcvakswrA8oInz5sCylqOIDjNzv6iUZT/+3vf+x52d3c5NVrq1JQVNs3ZhSKk4lairU6bgaLnuQzqCfAXjHGaH6PpVKUBs1sL0m41qqnpna0Bs7jdoA3f8ZFKAjED9DptOJ6ft62cxfRRG01BLgEkAImH2LqxzpMJ4fho95bQXz3LAJ/OJ+kfTcFQfk1QX7VejJsDH/LMOGzQtZf1VfWq8/6eT9ysbmCoKVDL7xmHxnILKRWWxQlre40LBS3DPfbjlCdXo8kAQRDm26nKDJpo4n6ORsDSRBN3PHQlvsoq8k1xzHRacNrMey8PrFt9mFUBV/VBSyl3AjQm9Q5LZ6kqtlN21P1ulqd1GTBsliMAaMAovUeG+u1Wm3WlX/nKV7CzPbB6lJt1CvaNXBQOnW8h8eCDD6K/3Gdm0yW7H5kw46WPxQa8WVqWi9PSkn/svGPcy7muO++rSysIXR9OlDKHl+wM0Q9acNwAuzc2plL31WsWkxMr6WRVjBvX3sT61TeZ6VtaPYHeifPsQkD+rYHfmmI4q2zpYQLwvZ6Leds9iM51r8eyaLv22K02seBJVRrl9wyNE8os+H7IBYAyFYiSKGvupf14aQzv7mzh5o3rsMncw9YuN9HE3Rz3P2Na01KvHAeUGjTRxCEEP9xUUqnYntZYmgdc0UFmenzWFYCIGf6SqsZ7spwKnQaX9nK0H0Z3OnXnsEF9fVT1rqbQithBw5qqLEXLetM4zVilKP/siy++iG9/67t5FT5pKfUD3NWuBnsBh0qhHYR46JEL6PR7WlnhAGmUwuV12Q4HKcsqDNggRrbOO/RWo+7aqESx9+vz33sazz/zDC5fvoxTp07jZ/7BZ3Hy1KmcY68CW/OT+vgDCYY7m7h+5TKS8QgnT57DsdMPwgv7CIOAr512RDATHy9LZc9OF+fn9pCx0ryxeKvrm/4pasdztXBsL8vw9ZcWQ5oBUxrL+r6IuMe+ylqjUhaEx6cUSGIJ5VCRU0uP/0jC8QU3TdjdWoc68zCECGbuQxNN3K/RMKZNNHEnQyBn5GAePkKWKoirYVfhzwJF1Qdo9d+oANhqVBnbOrBa7RJV97KjjtGz0/70IOeUcp4yz9pqBkHuMEDLUEcnim9/+9u4du1axiB7mWY2A7XZg39ROKnE6uoKHnroIYTtFpSj09ekI0WWJtcssD7uSTTK0q8CYRjMNLY/jKD1kv71z//0S/jyf/wTuHKCQCT4/d/71/hf/uX/DJmW0/h1+0Bf8IPhFq6vX+Vzt3b8JM6cO8+MqRu2+VgI2BPw11II65rfocfDvHF9K6xtHcjdCwNbt63q79XMhV0gWHbESJkkoWvquQGPVyF8Hm+p0pM6GrOB67F2eDjYxmS4MROENuC0ifs53gHA1Dngq4kmjjbyBxd0sV/BjEwDK7vLz6KopmDrYtEDTlT6s1fBpV2VjkoXpCpgmgUqpMUyVRlTlVlIGWaW/k1p/JsbN/Hd736XGUw3cyHXHqkOVz+LSq/9maEUzp89h9Nnz1AzLcB1mBHl+h2puIjMnGp6X9tLaf0qaTyraV3UMG2L0u2zluX3XOBvvvZXkGqCT3/6x/DgueMYj7axuXUD28PtmWy22Y94vIkbVy9je3eIVQKlDz6CVncFSWIaNmjZg2bi/WKikM7Wli4aU/uJOqnHYcasMTgrFh1v3fpM2KDU/BRZ/ZkZw9Tytd3uohX2EPghXM+ZyjZQdX482sbW5vWST24TTbxToil+aqKJOxjlB7OlLRWSmybV6ftsz9JF2OBWAem8z9j7YaqFbbuqEjA1Gd+ZwKAAoEZjSutNjd1PZrxvPsMp+zTBxYsX8cILL1gANtsHqiqXaV6YtSio6vv8+fNYW1vRaXxXIIk0GHVFwQKTzEIDCMVFKbrt5HQnqlsFWbOY7XE6xgc/9iQeOLaEF1/4Lr78lS/hRz/8PnzuP/88Vk4d40rxumtk/r178zLSeIz+8hKOnTqDbnuZLbTiKIbHTmSFPIRSzNrWSBVjEdPAu7qPhxV7AYxT+7CH8z2LebVlLPM+O2+/pK6Ey1P39ovPJZfjOxAZs+oJDy51dosjiDRB7E4wGccIHd26N54kcDyFWI6ws3EDayfSEiNf1fw20cT9GA0wbaKJOxi68jnNQabIbIkwg/Gcl4KsK5TCHh5gs0CVYUTt9ZtlqoVXpuDJXm4Wy1S3fZsdFfQgzjSOWl8a5+0c6fNUtfzGG2+w3lLkwFX3KE8TlXuYaq3kfLs42tLq2nIuD3DhIpYTeFTJrgoFrwEatD8kLRAkHUgjNkGfd/72a0RZAqgQWF5awmd++u8j3V7HU5dfxec//3P46E98GjLoc6MFpZypz9n7Mti6iU6vh/7aKYTtZS6GitKYAR0B7yiXAxRWXlIWWl0BNXM83crx3UocBgCbBU5hgVT7/bprad+PdmEeMouoauETM9bJhB0QvExiwuPb85g9jbP32NmCWg+nKRdAUUuNJPUwHG2X7r9Fx9NEE/dLeAdNVy+6QaiDRd2DyczEF2UpBHz7lwNFvZZumvVACRTMPz97fejv9/ONhujeiL0+IKpG7ObB5ThjrTElCEQMaSIgHN1dRiCFjDWwIubQMHUuWc+Y1LmyjfMNC+SWAIOwPERVxWw/B4OWptPIBOyOTHbhlTlm0zUpfxgnMVe5uyKF4K5VxPxoEBvQPruO9vMUhT0WHa/jBBDQBTeeNm5kVpRSyw4xTUpw6tn3fK0lTYd489IlbG1ssybVHJcGsAKtwMsKdxIst3tswk9g1vc8dHu9HAy4wofnjfGRH/0RuNT3XLlIycfS9TBRMVdFtz0fw+GAXQG8MNBdqVyXu1IpJ3PZrAAZx6oLSkQ9u2V+p8KmlNgzT5/XSTxhdtYPdNGLp1z0OicgW8fw0//wPfraGHN9qZh9U8JDIh2kSqBFMgjEmGxe4yp8d+U8Ov0+Wp0uDwkZT/gb1Ql8Xo+jvDLIoi5EfsZ+qxieqAe+ZlzA+rv5LnXzgjFl7GqnwHtxvuzv12nW2NZfV/+GzHfUtjE1/qN5ViH3hC6D6el1Fvtp72PC45TW48MRmUMD8fkqhkxjvj5EMDupYBY6Jc/SSFfXk6epbhmrQE20AsdFGIRwul04nocRpfs31tEOQ7picKh1rOojkjG8QGF3tI7rV17AAw+9D3FMbhH6eTUe76ATdAHqCufd2efEQZ9/Tdzdcav45aBx5IzpvTqza2akTRxWzGabpg3t7QdnnVaxFDUMzryoLmcXMM3S3xkfz7plDlsfWLd9U/RkAa1mQQAAIABJREFU9I/GUuf5559nkK4qrSfpeJLMJJ3+ffHtq1hdXcXq6dMMvEZRhPF4wH8PQ4n3njuHEydOsJcngWDyBdXA3GXvTwK7Brzblj1qH+bms0Ap72MS5+lgsw0Cq8TkpmxlZckmRJld5kmE0I1s9T47iNMYKhpiTEDaD9FdXtbyCPbEtX1ZVe77ijkPoFnvz5Ie2J+rS7/bn7nVsbOX9dWlu6v/vvXtFxM7Gh+sJ43HWRFZlHdGIxGvnsx57I7ARXyebopBY5cmHwFPQDy+jq4jGGjL/PoqjEYDpDE1ighy8Kw9UZv6hybu37hjqXw9D73z4G/Wl9y8vzfRxK1E3QPc7shkUvkKBfCopsRzXd0+7XpEjSeqsvwXq4VNZjnDnlbvgyoorQM4et+dqf1XlfXY+yj0SSj9nfbP952c6bx+/Tq+8Y1v8EPdBtZGTmCSIPT78VOn+d/r29sMHLrdNvrHVhElE/ZDPffgAzh28gT8LJVPn2eWUOg+/wSEkYEBz/f3DWgWglcGooVG1+dCLqmZvlQiSsb5eohtNoypCTp8IsiJ3XUgMUkiROMxv9ldXkOXmNLs+9Y+V6ZQZ9b+LXp/L6DcsOLzzo1Se1tX7bprxt+s7dSl7fd3Laet21TmaUuWUDS2iFVPMqDKRYzZNmiCQF21aIJA7V+pGMoLQrTbHYwGLW3TpQS/77ik26aMiJ4g7WxtYjjcRW+5r7eLVGPShjdp4jbEnSLojh6Y2hqo7HmaP/is/9+paITkTdyOmDW+qowlLDBmj03blsiETqWWH7jVn5jxALaBaZ2Wtbqcnc6337c7Q82a5O013Ze7DWSssQGidjco+vezzz6L119/nU3h7faqRmpACfYccMeSmcceWfS029wGcjwcYDyZcEX0yuoqWgRKCawpMxHQFflpZqXE7JaRUNjfGRBzgVdd1DHCgNZ1JmnMMgBqL0sgR+sWC0siN/Dz85CfqyTNjNjJ4iqFSnUnoaDbQ9hq5YDUvs7VazWPFSU5Rq0Uaw4bepDzsWiZqfFotSctxmfxEsKbWs9+AKkQurAu3zZMs4U0u3cLPThdQ34vc9agCQfJcnQ1fgDXD/N71jSooExAyqw56YVtf2JywXCwu7OBne0NdHsnWe4RkcQlOx2EfxvitIn7MZpUfhNNHGHUpfFNmHTqrH71pvDBtoiqAoJ5D1lh6VmrD/dqkcasz99K1LGgZTZ2Ou0qatqs0nuk26PCJLY3ypb92te+pgucPA2MTTrVtT6vmawEydbbuhDK9+AkHiRtP4nRdh102330lpcyE3oF0wOe0CAzX7Hus557VVpA9FbOTV1KP04TeK6n21FGWo+fxBPE44nerh+UukvVAlsC1ckYcRRxFbhPn6F2lo6PJJmUtmeDVOOqULefVQBalxKfPgc1rHkFuE9/Zr7Gft6EjseNPJgbwqLQ65X5Ueh7Jyl1eaI2sWmqLaJk5klKl4WAKclDyFbM8bXnbWomPlT45PoI/DbiSK+PitlgOyEoFzIdYri7ydfX9dr6HPN6pDbtb6KJ+zBuQyp/+uYpf4fc3eLtJpo4iqhW8GJGVf0strSOEa1jS2eNdVUxyLffR87kTQMSG+zOA7azdKl1MYsxRXaehAVkr169iu985zvMNlX324BRKgoyEon3PnoCT37wQ2h1enj2uRfw4suvIHA8tDs9eE6Ak6dPcccnZE4ApMWkzjsE8KifOYFaZmwrgHk/UQdITfDxuZpBIyaMQGpCWkMCLb1ePjmh7SuRjRu7PS3pYhMquhkjiSLu9c8ssnAwSqjgpmgVa0947GsMa3JQ3U9R2efDljntlb2cJUUBysVRLB3hewXcBKHK8u9XioH8OE3hYGqB0gRxlsbniUUScecnPYQ9bQ/Vamu2nSY29KJxad3T5GlKcpGIit6oqQNcXWwl9f0e+g6Ggx1MoiG6rZD1qQ603tjz7/jjs4kmjiRuG2N6t2o1675oG11pE4cVs9LoRuM3K8VeBWs5MBWFdyODlT3s56yH+iyNqLknDKM2D+TWgerqOmexbtV9MCC8+ru0Gg1Q0dObb76ZgSaRd9fRjGbGpCVp3pf8Y5/+AH71V38ZH/r4p/Ctbz6N/+lf/m/40pf+ApsbER544CGcOnOaK/thd7SiHKlU7CTghZlnaZbqz3Zsz2n8RSBWuMUEgBPS1Ct9ewfxJMIxx4XT6xYV5aZdrX1eybGAgdGYC2g8P+BxEVPxlCCWtQBSsCYK1Wu0aP8Pwp7vVa+6iLmvjmMG7dbYsLdTVOXPzi7s5XueK/AZlJLpazY+VMJFcvlEiCUXBVNqUve+56DV6cCngidO0ZObgwO+5KTvdZ2KHCXNWuASONVFcMJVnMof7G6j3V/KjknqNL7rNS1gmjjS2KsM67DjthU/3cpM9U7GolRSE03sN+oZnyLq3i+l+e2xmP8+Rx84R0aAPYIG2zJKWOb+2OOX0l6Azbx7zaTqdf97hZdffpntnwgQtEKf2SZu88g2SbpKms4LMaq9Xg8f+okfwVZ0AzuTm/jIT34MP3vlCp569nm8/sY1HHvgPHpLS/ACnyutqde+kVfQupgtJVDquCWLIWJVb0VfWneMWrcIPo7RYBejnV1cev0ig9OTx4/jiQ9/KJ+YmKr8nEWHnjiwc0AqWVPqhKQrdZFSZb/TAhDlpu+LWqfOYk3nXTfbv7bu7xD7X++imAUu6+QHtka2yp7uZ3u6pej0xM6k+kWmb6axQaA0DH22J2NHBG5B6jOby83FXMF2Y7pTmcdZRcPK6mvrsgzDdQIkscJgsMN2Z8t0HwS6VWySpvDdPex8E03cg+HdTuBVv63bd3ctZC8WWKAcxTabuLdj8QPOpOxdLmbQeDJFIoeI0xGzXMIR/OKlZdE9hseP5zINQ6BEW4BqQKqygo882WoBAGHr1KiwRk13pTH7HWR+mQa42FX4JpUYTyYMnOg4DBuUe50KLwc8kkGArnAUGTMkmLXTD2BWaarCbofXIByEPrC7tZ3tUwdIW/ADiViM4AcuV893Wj1cu3YdP3jhBYy2d7G0tMT6Qi+zPyKWkwqH6KUILKWSWccHw3O4cOphOEqzimGri/HuGCc6AmLjNayunARSSrNKhI7ioqPh9gZbTBEoZd9VVFPfKnMVAYxRp74u+SnPlkLJJ7kuQjKnhETgAlujLbz5+qvYvHEVy90Oem0JL3SYP+DUbkqAWMJxqZ3omH1G1zeGDH7aSysQtL/ZtfMxBtQYNHDIZYDBEI1DYhmlygHxLMCYgy5nev8L4EeJ9LRGJupY56HsyrDXKLZRAF/yyKV9J/cBmSbMOlKTAx5/LkkhHE6hsyeuEkilPu4ykC1S8xSu8rhYKV+G261Bs5caciIldjTTjwpmamNElLqPYzixBFuJunqqwmpU4cLze2i1+lAeFa21WFMqU8njgfbfRYS2LzCKByzF8ESAwG0BqcctdYnpTuWQtB1odxPcXP8hHn78caioDZJb91pArLbgYGnP5/Qoosku3t9xp65vkwloookjjLqHskJZV1qXXq/Tlc6KOuaueK+cxrRT89WimuqLw+p2RKCUPkvgjV7MTtZY96CGvbL1jdXUavVv9osAM3d0Uim2t7dx6dIl3g/TX7xuveZ9Wubq+hZWVtb4vcFwB9/+zt9hZ3cLOztj9HorhUG/BdjzyujbMKkcR7GuwA7aaHeX0ep10Vtaw4kz5/HAw49k7K0B/llrVm5fKbCzM9DaVKvpQXUczZNh7PX9g0StbnUGSD3MtKGoKeCq3Y4opAAqlwWU5QEOTzr0e+yeQEV1bA81nmpBqidi+t6lSU21aM0e87l+2LhJWMsW19DJvXxlNOYhaYwwGtKjifs1mpakTTRxxCFyCxsdNngwz5Y6YHcrTFM1bNBqgB5XsLtuDmrqXAHMz4T6zntUWaxfpgKe1uy55WxHnWbUXqftm1ktvKl9kcKPUtRBG3EScxtSSuXTPpNkckrfaj2sjf7vX/3rfwd3qYWPf+YjGKkdfPnP/wxpFGO5v4zzDzyKlbVV1vpR4YphqalK32GmerZU4rDC9QJypmQmNGj3cPrcw1g7PsLqUh/+ygqSVPtlcrNUYuX4tGl/1ck4Qmepa1kMFefTgBtR6aY0S29ZF0ajedCYNY73sg/2mJryALAndzyBUrl3aCF9mS91KbY/Q46QSmZKeTnTepTvIXMfULewbF8cYwPVhhe0eEIlckcHKkgrd1yz3RHqQKnMjon+lqQRbt68gePHVuC4WRter8nlN3F/RsOYNtHEbQhbIlplRk3UMYqLwOk8naPxsFSWkb5hBY0us6oZNdvOC2a46MPR/b7dgIs1CCiSYTj92973urCBor39umM0YbNLul87FfhIPP/cC7h+fZ3ZQs3eTmsKhVVARQ/v7zz3Er7xze/hzIMXuIvOpYsXOeXbarXZfodS9sikDAY4U2pcuLfnoU/tWKnJZUwtV8MWjp8+izPnH0JreRVQXuZzqSvAhUdp7Ri729sYjyO0Wh34fgjPCzINrsjOiZP/rEb1XFX/Xff7vKhj2ueN2+r7+9W01umwyxO9sr3avPUW79kMcyZzIRCJlAGh6YfPjKrRm9qtZ9k1weNrQS1rg3aLx5DvhVNs6XT2JIVwiu0xCEaa/1v7mbrM1N7cuAaptIWZdqtogGkT92c0jGkTTRxxiKzDTTVExbuz+oBFXbFMBYjWFX9UH9oGENpdpgxLM6sYxOxHkAE0lbGJnHK0evWTIG4WYCg9gGv+VtLEVl66NafD2lviwba2ttgmSoNlMCtF2lPqlJOvWxUPfwIRzDgFHVxZ32SQ982nvg2hBILAx3AwRr/f5wIp28uTPuv7XsbPHb2+SsqIt8RV2/pMIXWyXvVCa2V1qpc6USXcBWg0GiLwfXQ7S6xBLI55b/tbOvc1f7vdUR2Ds8akCZtRRJYOt50K7Ir8umMrr3calDIwzHS4BEip8l9moJSr7/k93d2JujSpTNPNGQg/5Cp8h4qduPxeTu2DfdZt27jaTlxK99qnr4jtnQ3E8QShMepveKUm7tNogGkTTRxhzGMS61LnquYBOysEtIXRTDbVAqUmBT9Lz4YaYMDherl+DtDekE5W7Vyn6zQvp+b46pZbxM6RZQ4t9+qrF/Hcc88zg0jgoJYNq2HSxgTmohh/+Rd/jf/4pa9wcYknfE7dv//J93I3pZj0qq6jfS+pEM11F3DRhxdCZjpdKrLJWozCuDFAMJMacgOAFIPhFgbDAaeIO+0em+9zsQ3vqO6sJ2xArVACXnbY52zqPFohay5NSaK54EyomuYOs6IKrus+Z4NSbRdVpPnze8Z48Gb/1clkyu8V2ma2guJxbTILpO3VZ5WM9MmKLJX6XuI0P+2DAx6XZKTP7hCuafKg2KN21rnQ92aSFQNKZkXt+14vqidZQehhPN7FaLyLsLNUtN9dcP6baOJejGbK1UQTRxhVptAOYRUkVTvyGA3ozJToHh9Jhokxfosia4doWonWGffbryqriQqwxIJjnAVKbVBbpy+txjPPPMMaU3Df+oCLr4hNUhULoGrjgo9/6sfx2f/0ZyEQ4INPfhxtfxlpBCwt9XHh0Qf4c3RuzPk2LULnHdNhBskEXYKkScTm6/S7TyCZ+gClEVxHW1mNJwOWItDuUcGWT33X1fSkApVJT13sJ01/GDHruu7l/NaNPft+qXq05kVrFT3t7LCKn2A8X5OygwUDyFgXPZnUvtQ2UTRuuGVtS6fx/aDF44gmOkoUxU/2MdsTRi5qqux/OZvh8HJkP0WAeDzZZY0rAeHbMT6baOJORMOYNtHEEUaVJTFhHrbEkpiosqUuVV/vgber24b90LLT+HahBWpATF0BhgGz1e2ZauG6bdbtXxVE6fR7GZCWKvNF1o/f8fHaa69xOp90lZ2wg2iiwaTdBcl8lt43qdif/4Wfx6/8+q9BqASf+sR/gv/nD/4cuzuXcP78eSyvdHPg7jhhdj2mu2EdaaQTtjjySD4gNFPLKWPaPtlh+QEzZTu7O/x+O9MvMk2Xls97HQtfDXuyMYudrPv9VmM/jCnmsKazmHlUOp6JvNBwPktqf6a6TvtF1fcqs1sjtlTLB7Qtms48hHB8B2HLY/AYhKT5pXawQeamkE7rSms031VQmh97Zm/FTR4w4QkZO1V4pDtteKUm7s9ogGkTTRxh6JSbeVBqZ0SqtHUYfEhdrWsBsrLudLbO0QBWm41BxqSaoid+6EUJEKcQieQic64Pth6AdSnSkk5PFbZN+batz9jLVKUILBsQli9q3sFI8MOdQHlMoFmSFRWlJzewu7OO/moPEC0kccDr2N3Zwcsvvcz/7nbbGAyGzE5RlXo8SLC0soIbN27knqy07+NozD9ff+UZjEYjvPbmVfzb3/9DXBluYSRH8FyB82sPIE0naLd9Bh9kbO55WtO3Z83mAp9Sm9k2NmH2el1vSbdAjSUCX2hwqlK4GcBO06sYDDaRRAmWl9fQ6epiLZVojaEo1b+oYiJjmoQlRYMEVEEdSwlkSfdYTfFPva83Yy1Xc8yWPjrdRxp/ajssYXbZu5ROMzkUxGRTFo3Z+1NlHZeEH8L1WlBeCzE8uEry+XMIUNr64cp+0O+RMkBWQLHVk+L7VYNC8k1NWUYh1IR72VPxGa1RKl9/BjFcEcB3PHhum9vckvzEdXQq3pm47O+UCgepQ56oCcs1qLyJJnu6Y5Rk9wnaJo3hNC2YYD+cIB1TwdsIXuohGmzB9xLWtpIJf614vYk9R90kaD8TqSaOJhpg2kQTtyn0l5wGpObB41Qqa8vsyt6+FG0waIMfAyhzNsk5HAuqOvZpL+njui/5OiYJFXD71ltv4dq1a/ye3cHILEPA08u67NA66Pdut8sdov7kS3+Gp599ETvDBG++fRXD3RGnwy9cuMDLzLLKOuywme8yeyzztK3K9IrIJhvUr38cj7n6ut0OcuC9l5a0t3IcBxkTpTFoM7L7XGeVGdUhS36j1eXqGEk1Q39ZKydQxqNUF1PpRgRWUR+mNdhm4kjXhBtOWH6ypX3hjhJp6b7kez9OGGSr3CGjPFEEkHUzowml5G3Q+KCCP5J0tHutpk1+E/dtNMC0iSaOOGal8fSDezoVe6vAsY4VywuXnIwF9ayiJ+uzVZ1pNeqAm72fdWyD+XsdSLJTr7X+jW4BAF588UXuj2/kBMbonwq66N/0sCaQefLkSU737+zssA6TgOnNzR1cuf40XL+Nja0trC6vYRLHOH78eOExaR3b9Hk42se/Bia0HwrahShj1qVEFI8xHkXwPB/tdhdeZs+lMiN3OPW7N09ScdjAuw7oTafWb329NsBUWVV8oU+WtfdLcZx7OFZlpCPaEiqVuqgprQBTW2JC3agclsO4mrn3fQSZtpSr8UkSwow1yXEkM6wptCUUVfgrmbAEZjIZ5efJy+7LfPybNrRSM7haNqCws7PJDSLavWO3dF6bqI/q+DksKUsTtxaNSKWJJo4wZun4ZoG2Ent3C6CoxMqQybxMuXKb1+tpIIYZVjp7ZT738rd5QLcqBagDp/nDQQi89NJLuHnzJoMAs6zpEU/aO/o3WT89/vjjJaBJP4ejGCsrx7Hc72Ol14Pn6Pp3MtYPWuFUZ555ustbCWWn12vONzLYwknzrJpbpQkm0YhN9B1Hg57cM9Zokp1pXemsqGUJZxzjrU6MbNBb/TkvFm/L7sxk7Jxk7iUqSlXs84vW5p4HqW2i6PzKbDuUxjeSGLvIyngA84uN9MMSKFVs95VdS5H1EjZTDjPO6DomhT1UVcqTn1NJcg7FxVfErg9H29glvTG1ZW0o0wPHrPF3FJO4Jqaj+tzJnwfNuWqiiaMLmw1F5UY0DIkNxKrG4LOKMqpaQfv3uip/AqX64VkUPmX+9FP7hgXA0n6vuh+z1lddj7280bvaoNJEmiS4ePEiF31oTZ7M9a60rCm+OnbsGB555BFejtZDLKr2lexgNIlYg9oOA0wG23j04YfwgQ9+AKIV1Boe3c4HksgKrlQGTimISSNQSu932ksI/I42zU8LDbBOkael9aACChc9XBcd5+1kjerkFPn+CZlZKpUZUzpntpn+rAlG9TzYv7Pm2rQizQrmWNOaMaY2KLXvUVONn9+vmdhXZR60mq8V3O1JUjqfJkRmMkF9+GlbqR67VdcMc3/SNl03YCkHd3pyyDs1QRQPj5zJb6KJOxkNMG2iiSOMOrbQTgvaUcf+7CWqoNQGp2RbQ686UFqXlp8HJuveq9ozVdc3bz02IC/bNRV/e/311xmY6kKgNGdKzfIE4OjfBEqXl5cZmNI66H36+/LqCbhOCN/10CbLnTjBpz71CXzyk5+8K77+tKTCdNmSSJOIQQgxgr7vIqQOVa7HKV32xSQRKp9KrY00Xp2LYhFrepC0O2ZMava6vlljAxlLWixYjG2VgXK7kK9aCIgFx60jA6XMkmaMqQG/JdlAMYGicZVrS4kldbysN34BSs0kI4V2WJCZHIAK3RiExkmpMM1owe1jAtuJtRAEITOmjqsQhh6SZMLWUU6TbT5wNIzp3RmNxrSJJo44bBbHWDcllJrjLunuXEC3nzDrsYGiYSJtRlKbBJht1oOIOtBc937J3qmilbUtqealV53MjsqzCkg0IwZ885vf5P74xE7RexqMxvk2aHnSl37oQx/ioqfqebyxsY2W73Bf/8loiA9/6El8/uc/h+Vjx2DMy6tROtYDPvxnncf875A5c57E2g6IABi3tCSLIGowQCbsUnCPdDaPN9dvRnFRnT4TR/SwrY6L/YLTeX/X6zQ63wyUGgBZ035UCGOov3jdpW2ogh1VefFTUpKT0ITAbI98dH020/e56InHuWvrtotzksiY9cDUTz+mgqfJBPFojMl4yMVPqdVRzWZ8zTFRKp8AcBRP2KLK84HReIDd3V30ljqLL1ATewpRY2fXxJ2LhjFtookjjGr6WrMmSZ6+syN/mB8ADVVTufkDzzz0LJqlrqvPfqKqCZ2Vzt/L/s5Kxz733HO4fPlyzqZyH/vs73QO2+02lpaW8MQTT/D5NABW+z5qM362jxqPGcz86q/+Mn7qZ34Gk+GQrYTqQPXtDA0edetKAqXEBpvjdIMQ4PR9dk7JHiiz37rbbIIOwpjuN4pxVi5+2q/WNnszvy+FYWMtKYydujevXF+aTaT0PeZlY9di/KG10KnlWUrXN4rGfK3pp9mGuU/tLAKN4YR1qG5u/E9BVfmD4Q7SRmTaxH0aDWPaRBNHGdLNWTdB/oTxGMlkQM0mtW+llSLMtWUWi+csqLpOspakzM4kCT/4WI+WPeykxUjaDz5mfoSTG/zXgcrqv+3t2+vJdZ81ff6NhtJOidrsRErgmfxVA5/BMxVrsXOAcPHySy/ha3/+VfT9Lqe0R5Mhr8cLXIyTERzPQTyM8Kmf/STOP3Qev/cH/wY3hpvodjqE5zAaTrAUKHiU2k8kPvoTfw+/9F9+ETGdX7KXdGSNUm+fD3u1CHyZnvSFv6w5B47QQIbYc5IeKOEg7HQ1uObzRrrEOMeiEnExaTEFNcouDppmZym9rJQqirBEmQnOpRP6A/nninWmM86KmQDVgFDjc6pQMUOrOTszLMTM+mLujKS4dacuAKLxoplgakCROgHcsA3XIyeDRLfLJf9UBoRUHW+xkEanqpLMR1dikrGwqdJG+nSOISJOm5M0NEqzwjQRAI4H4QRQTgC4LRq0oMGre+VLPVcwTSN4vEfwgw63v1Vywl6onjMmm3zETozISRFn7L/ve/k9KqXF3LUiRNKBTx3LkgitloArXWxurOPsqUdvU+PcOxfzZB6HEbPG3918/HbM+t42sehcLSITjpo9nrX+Bpg20cQRhu1XbqqKTbC5/pxiobqYlxK32ZZqkVUd2Dzol84s/ele9KUmDLAVWTqT/h1NJgxOySbqrcuXGbRRqtTIINh43PeQKomTJ4/jySef5PWsr69zOt9RAqEXYrnfxWRnB0ni4MKFh/A7v/Pf6KKVsMVAZ2ewg163e6BzsNcwAGL6y78A+ObnYUf1QbNIN7zfqH72MB/s1X2vMttTY5iXKTs+1EUhe0kgE1PgFHO7T+6ZwIBfMROqMw0Za+qUpTFqQYMFWr+yGFPNlEbsY2rYUltTXr2P7Zymyo6Niqd4vYd1kpto4i6LJpXfRBNHGdlzUaoIqYwgZZSxXI7u3HPAwpNqMVV1Bmxr1+ztHFRveNC0ra2lMw9hNhFXKn94f/3rX8f1mzcYpBqmkQFEBiTiSYSz507jyQ9+AONogt2dAfqdHlwCu3HE3Z2CwEd/uY9//i9+Gx/6sR/LvFAdBrW+H9zy8e/nOKtgwzHpXu6Hn+TnwTBmR50Kr+7fYYLSw46qPlvKaU1wtiOlAkDsYcLH419m/qKV9WoG2dHA1PVZEkIvN2M2aUzSa9E5kNk+k2Y1jiOWlIwnQ8TxpFY+Yt/LesImOWtCzDTpjCH1Mmk8wXiyc6Tnvol3TtxOlnQv0QDTJpo44qBWhmkacftLqWJLG1cPGmEBR34WZS+u8K38Dguc2g9tuzioypja21gUe0l11QGpWWCg7rNmG7Z+lCQJzzzzDAPOsN3KGwR4IisKSSW3O33/k+/DAw+e5+r9ra0dtII22mGLe4nHkyGidIJf+MWfw6994dcw2NmEGwTY2dnmc98KWrdt6OcgBGUQYqqxC61i/bU6rJinyZz33qxXNQ5732020QamdaCzOkmrO54qK0myANdonLN2vZyy93x+Uc976ofvUqtR12NwSkC12jFsVqisEYDp9pREE6RRrE30K84Y1XutxBArh9lSmQHTmJsv7B7qub5X4qCT+SaKmDdpu5MAtQGmTTRxxEFpt1ROkKQj7q0t2OSdHBS92gd+NapfEnW/13ktVouJbjXm6U/rmNN5Kf66YzOsKWkrTXFV0o6GAAAgAElEQVTJ9vY2tyLlZo6OYC2tObaWH/AX14ljx/CJT38cveUeXnjhBbz91hUMBiMGr4HnYDzYxokTq/jN3/wNbvnY6WogSkb2nusjnsW+HUGUJh1Qtbrb2w1KF427W1n/vN8PEtXJl824879nFN/ZYQPS/PzLmKvykRv2uzw+BOtJPTjC1y/PZ9sxZEVOhCqVqB8/5eyF5EmULoKKM3CdsOJYZPrr6ueE7WghtbSA35cZK0ydo+JRw5g2cd9GA0ybaOKIgwqMEmZLKY2fFCAE/lzwqAs1VGbWnZnmVH63l50HSheB21lhlqkrrKn+uwpOF7Gm5sFsWoza/o2XLl1iSxw/CPiYaVkCp8Sk0qcpjf/g+Qfw2GOPclqUGFO2kVIOgxQZRei2Wvgn/+wf49F3PYbheAjhag9IYmYpoiiZ2rejiNLxqqLi29YYYs65Poyom1DsZUK0l6h+/ijYLJsNNaEN6At7MRN191MdKNWykIhfyuhMoVuAKuHyy3FDfhEodXxiT/2Ss0WVgZ3aTkL3foRkMkESxVygZT4tUM5wVM8fHxf5tQpK5zvaMkzp+4MmuvE7AJjWSZSaOLxoGNMmmngnhtBMCWtLkXDnFvIj1L6I7oFZK1HThlEs6CCFGYzSrJj1BTWLMa1bbtZ7xCCZtqImXUvgk9qQkh7PDwNtoeRqPV9usZVKPPGud2NptYfr16+yCb/nBuj3l5FMIoS+i1/43GfxxS9+AXEyQa/fxXC0y1X/pEdkla9/9LWf5tw5lo2QXcRV8m219JGH9WCYJ7uYx3DuB5QeZcyTkhgJhP27mNHetpYtNRrTrB1pfh8a+ydmSYPMr5T+7bFzhCO8uQ9ze/0alGptKdlDGd9SSD0O7ElkdV05m0r7qISedJHggCc3erLbRBOHEbdy7x9lNMC0iSaOMLRtTMoWNfRTg9JbA6H7ZbCqbOlhfeEcBIxUP2vAmdk/U7lMaXyuXpaSdaa21pCALLGejz3yKNaOrWBzewtvvP4mL+87Lga7I6ysrOC3fusfodvvIwg8ZlE77Q7CIMy2fLRp85oj5//X6SDr3scRPCDqgOhRaEKPKuo0mFUQuuiYqgDV4fvRsPXItL5+XuTEul/h5T6lpUxEBfyiso8qs3AzxXw0wdKaYsnfB/Q3YxVX3e98nSW5SfG41pX50ZGd6yaauJPR2EW9w2Nv4v0mZgU91AyzYViPUs9r8qecjODSe+SPDo+Nscmz0vNbSDHMU7pc7QvyYNSf9xyPmZxEJrk3KVduk/+okrlJv3mJzJTb9Rz2vkxVgsBrl/rL2/vJl14W7RD5c5xez7bleqBGRIo7LgnuXOP5ukCHHrJhEDBzqZ+fWnZgxgy3PBVmfOlfZKrNy80+CEeg3e7i5s0NdDotPtZWt4VrVy9j/c2L6KoUERVw0ToSBQ/kHSkxGA7R6bWwdmYNPeccNm48h+10BBHGSMbXsRwq/NY//g2892MfgxIeueybMjF+eXz4E4S3YVouMs9NYsuTRDdXYBtV0tIyY5siwzjWvWhYbRQtM4s1ln4ja6z8Hq3+ZAAza8/0uag6uYrKT7mg2UNhh6ZygFgnT5j9efN30zjA3h4VuSlQp09BPqMyRjsUrNkc7Iy445dHUg/oseQG2n6Nu7vyPSK0Rpn+T+OfPFHTCUQaQSQxPKkwERm4Uy57lDogZrTF7LvjuHBaZpIni+vD3WALH1c3Y/PpXqD7lzx4yZs2jVOICaAiCUQJFHV+isZI4jHfY0FAXbyC/NiLc6avuUvthNHmY1POBPBS9uAlb9SW62KwuY7h1gDd5V42TlKzG1pycJ99fzfPIh2LtNS3uq7DWuetRHWbDTBtookjjDgZaRYwTeA5kltjGj9ExodWD3gDLmFskYRkcOg6Pqed+UtEgYEtAUE2N1dO/vc8hU/aOKped518nXYPelvbqNPk2uDbgFKdYgRSaoHoBXnKVLfPNKBFYhIN4Ym9Wy7ZwMXsi7IYU5k1C6B9GgwGzDIJv5VZPOmg4yCMce7cOZw6dQrwBafn00kEXzjYvLmDX/+lX8TnfvE/43N7N4RCfcvWw4i74WFts4W3flyZhZpQFji1euNnhUSAWzqX85N+3KE+S4VnANW0cs06n/F9QeCeWEtqEGz5lDoaEc88pipLqkpWT2neFCBJi9ajhnE11fW8iRovUxPTLLebv/gY1O3RSTfRxO2MBpg20cQBo1p8UdbACTjUq53SgVTF6+guQClSxAQCozjzsPTz9eQdoKTEaJRkD0oDHE1lsssAMZoMs21mKUa4zCARYGU5peNkLdXNw89+oIJBKXLtpmFui+073B1JZUU72hQ88ENOj5N2ViXT6VXUAKZZGtSi+EmzunSstC8ETPlvbHnlaRZMaW0uLUMtSC9cuADlSjz33DNwU4lASrz/A+/FF774RZx9+AIpegnG3NHhzT2BlLGFyphiFOngRXtXV8RTXf+8WAhcD4iPDwqMy59XxU9l7qGUze5LExrmQY0m1C2NLaUd6Hk8cZmg3fveFJzR/eG42iMUPiSl8EWg0/VuwJNB9imldTvTlfel1D2zsyoHvKZ1KIFR0jbzK474d3NvkzQAILCq2KGjKuuwt2EmZcWkxuH7wThZxPEIkB12CyhAuix9pokm7rVogGkTTRxCVKtqDdOzO9zVlbVsEONBSQeKdGWcu5VoBb0cXMSJbicaBAWj6rWLlBwDXXrPLRi3MOjxTwNYq4UUUsUW65QBVIs5dbPONpzUVU6ugdV/jxmYasCg18uauXjCTA8/TBdoWOuKu6o6PDcz0FeWZRQyX9NEFbY6pv0lvf+e97wHZ86cwUQluPTG65hsbWEpCPFPfvO38KGPfRRxGkN6bgbf71wYtlRPJjQYdYQFTA+MHcogpPpzEYG5CLzsFzjzONfu9HtkTw3wcwrWFCgxp3psGZa/GGfUhpRBpkIGRu1XmjHyKYNSZIBRGXEC75vL/ewdzih47FPKek/PzQCklsTY57SqJ+Xe+CynkCU9OTOlSYQJeelS+j6JLC2rLnxUmc506pzXaGn5DDkuSww8t5V3TItimsD1M+bXzZZ1MrZZ5sxqE03cS9EA0yaaOGDUFV8UYERwqp0YDa29dFj3GbTacIzeVOl0tu+FrA0zFdz/P3vvAS3JVV4L74odbpo8ykISEhJBQiAMlghLAlmAH/EZMPCbnyUDMiDDIzo9HsKE94wtDDZeCxsw4EdOzxIGk3mACIafZERUIgkhjWY0c0OnSv/a3zmn+nTd6nBn7p3pO1Nbq9Q9Haur+1bt2t/+9tfpdlCvmWYdHtQGFRV7Jr5qzrDGFuakwFHlSbdPkmB1iVNx4etSxRHPaqQmU9FLGgQNTXgzrZT6oiZxWlGWJkPlttXkqD8a1e46N+tn/5ufpdFoYG5uTpZ9iys5qVZe1hQLC1tFLZ2dncW+1gFkaQ9Lix084rKL8OjHPBp+LYTj19DmMIMjHMKd2d3VppTrHO7Gq8OHgy/np6XklIq+KYNL/q9jJoVl+RQvAaVLx5wExIqEyg8m6qum2ruZOugnYlC15H+0w/BsS07UPNXY5Khfp10RWV0RcHOF15BSpZhSLe2gF3UQJ8pType3PbR8H+P/Lp689fcjiV5XpbQGUq2oS0WEVZdub1mio1ynps8i3Nw/LKoyKmJaYfOhIqYVKqwDiuV8mI5zP5SDCZVAskPXDfS9jiikJKPM67zttl/g17/+teRx/upXv5JLLlGUYN++ffjNb36DvXv3iv/SoEj4DAEisTvhhBOwc+dOzMw0sH37dpx88smy0Jt5yimn4LTTTpP7g0DNiqeq5Ps1+H5DGGAiweOOeGLZcNTptMF3phfVdVTOo3peMnLjFQ+0ZbaH4oG52Wxi69atcnnXUkuXwV05OPM6ldJdu3ZJrM+tv/wFfnnLzbjnGSfhmX/4TGw5+QQkDv2vbfhkAkd4D2cHwjvO4LSgSUqtRk3PUK6imYYXGIuGdamfOOYNDlWyLbOxOLlyOpakmpD6zC2QU+QKs/Ifx/n6GoKpLCBGRTUh+0mulkoShi6hS9ySWkE9blR1nClCqk8WPNV9j/z7SfPtmZXkqBrwvc19imjGkq3b67UQxx1RT5W/1VUd+eJLUd7wTDc6wiL1g3/XsT4pdcXvTVJaC5vyntwXKMXU7BMcM0u1JOm4wtGIo9WuURHTChU2CNxpzM7vUC/uuFjcv4Tbbr8VP/zhD/H1r38V119/vVzfs2cPWq2WVbLrl81tldHAKYmp4UGaj1e+1DZuuukm3HLLLflzPd1kZYO3Xfigh+C4447D+eefh9/+7d/GOefcQ6KWwrAhZcx2axmNZhP1uo8eEwZSvk+Sl9XdIYRp1A6zSE5z+4KnFCSW6qmGmpSBbqeXkxR2/pNccx1JIH5x0w1oLS7ij57zbFxy2SPURB542H/XIk7YvnMVoTvcsL9T4wNGZvkUN1g43Twe00ST08TySiY5kTMTk5LEzVMkxLFCsgdlN7EJpFIuEzg60D6T3w/y0r3E2zsQK4v8vQW6jF8ylKK8hG8eo5VSvifzaVPV7MTSPf2lCYml2GMw8FkM8XS8wQgqm5SqRr8sT2zg+oVBXcgpzwfTxEUnOaBOIvPt2f9OD8fvq0KFjUBFTCtU2CDwwHDNR/8V11//Q3zmc1/E//fNb2Gl05LSuiQgJT3U66GEb0PUyEBUENM1jwHFzU4DGvQPites1880VCV9kxEa6EB35T0zmYnmtq9/7ZsSR/Xhj3xEnuu5rhA/ktQLLrgfLrrot3Hf889FvdFAENSFrIZUbLTSE/WisRuv6DMtKmyxEGa1XoyU4gE5DENZRxLuTtYVu4E8N82wbds2UYWJvbffgfPudU/83u/9HvxmA+2kh04WY/euXUBKVXf8+m0kbBWsbODBpFVvRzzKa8s3NR7gzY6BSU0O8izQ4mctJZK5dSXVKr/+u9IbxjQSOZJkoYipIblykjMmW9ZYBIQ4czExbkJOVXYxCr5zE6yv0jnKh2sU/1YMMeXfA5dEYqlSJHGk3+PwjdetUGGjURHTYxzHeuemIT/dbn9UJQ8ovK04NtLOKe13zPYjkNh9+41vfAPXXnstPvWpT+H73/9+6fa1FQ5DSiF+z/7tRXWz7Gsa9tXZAivLiIOfd/AAFqUrA/+OU+Dnv7xZlvd/8D1yW71ex8UXX4xHPepRuOSSS3DmmWfKe9dqIYJwh4z5TNIOPCdVY1edRKKuiNCtIep21QG1HiDudhDTN+dmaryom8ELffTSTOKtkiyVTNPQz+ClHdWZ77moBx4W9+/HzAzLmF2ccvqJ6MTL2LXzeDznBS9EY9d2ySttIEMDgSIg3mE4WOtSuF1ytyf/BH69/1jr++qTVG/Va9kkI0PRKjFIZjMEfZJrbBVU6DKdCHDIpfpxsELfLV+z+W2OJd6ZleGZP7ZPBFfiFdSCJt3Y4iN10w66nWW4bhNhbbt+e8ZMJZITy/GiSdzTZfhUnaWp9FqpWrALH54PX8cuuZ6Vu+pkuTWlr2hbzVbiRdWvZ5oNvVidTCYdlV3KhqcO1zFC0kuUp9TKEeb3zmlmfG6UxJLPioze7QZ8/VtJ6E9Nu3BcNaWMhLQWzqDemEO9MSse6ox/O1zXlQBxOwNmgRgRUs9H4DqMbJXXPNIVgwrrj2J6w6FgtQ1nfaYCrhXF16mIaYVjGiaOxZBSMy7SdIhnOsMTdme8lY9J3+enP/1pfPSjH8XXvvY1mViEIxRSvBEQxbLTwRe+8AX8+7//u7zDWWedhUc+8pF47GMfiwdf+BDU6jX4HCuaRGh3VPc8P73PkG/HRRCE6HY7yLqZdFKTSLDMKttXcilTPUWnrxTzPqUOOeikbTlxaDTqCGu+KLpC/OIM5513npT16zPKK0sSkDmqeKuIw+H5Hopq5tHa3HS4QTIYR13V9Z5leWWgVmsoQqrzTdOsfzJgq9HqBEAvjqujokwDmpsH55dFNa2+bt1vRuimyYC/VA276EmgvzQu6dcs86DnJ7vZYMyT8SPTIp3E6jF+GEiknHQxmud7/RNl87yKh1Y4GlAR0wrHPJaWlqTRRnW3uzlJhVY47MYHkiUeHD/+8Y/jne98Jz7xiU+URr6Y5212Rdqsv63m0r/6d3/3d3jLW96CU046DU94whPw1Kc+Beff776YmQlENer1utL0dWDfXumur83MIo0juT2RzHMSDnpLA6U2WpmefE+W6rmtWyvLqhObymnoY/v2reKDZamfB+kTTprV3oUUMUeYalJLUH11N7gr2ZTYhyURVDg0MIii0+vl25UnSY7rozk7oyY+6UanJFUnlEmsG6H0tDFGQKkvREc0OSo4n2V7lSk8evxXkZjmxDe3FzCKSnm7Ez1+lL/DYqWi2PDm5MMmlL2AlYNcKddkmTYcnrMFYQP1GsfpNvREJ2UzUKQ7VUQ4i+UzqUlezmC6QYVNi8N1/CiemB3pfVf1y61wTINNRyRO/ENkd7z5g+z1erl6Ct0odPPNN+NFL3qRdLc/8YlPFAXRkFIZJ2r9MZtpTpsd5jPY1gJ7G914881445v+Dve74AE44+5n4m/+5o1YWu6g0ZxDHLtY2LZDdjO9dqRIQ6oCwsOQ0Vhh7rkzB3xD6DlukuSz1erIJZVSljjPuedZOOusMxH4IXxHHaQzdkFzFnne3e8e9pioYtd20VNa4eBAwZvleRJQuhJ4gsTfw8zcgpyQ0OqgckP7EVGOySUlAfVMPmkAx1MqvEuftaebj/SsfDUaNbX8mqmOahpMUSguJKDy+xViHMnAjKJPvBgFZaAyhYP+kAD6YGEUWPpbPRlbTHW40ZhF2GiqCo9+vGmYEjJsnRxnyPLXq1BhFIadQB9pUaXac1Y4pkGlVB1gEukEB/oHPxNY/573vEe8lSwbv/GNb8Sdd94pqqpREaWBJ45zYsX7jGq32WGsCzKXXNsezEFQfcYMUazKqzff/DO87GUvw/HHn4inP/3/xde+9k3ONYXL7MXGDILajKiovW6K5aUW4igdsE5k1tQrnizw9XlQznQMUHOmhosveQhOPOl4tb11odSRUmco290L+kUgx9v43ZutltpQpKNSTA8VnvhlU5W3r7dzrdFEozkr6mcqpfRkkJQ6aoyvygQO4bk1IaXS+Of1O+Dtr6eswanYtFd2EOfcfi6SiBGpiU+pJAGkcJ3V6nmRrJpoLZ1epS0L/dzeRn0OtcYcglpDouUcMxCDi6vm6TPAn4soqY6xA2TDTegVKkw5KmJa4ZiGUewM6eJ1EqI77rgD//RP/ySNPn/wB38gHksSUdMU1dUNPdBle+M7NR3yJupps4PbgtuEI0INITWfVYi5EwPSpKFHmrqulFvf+9734uJLLsElj7gU117zb1K25wHYrzUwv3U7mrNbpAnFwLHm6NuKKcuX3NYcgXr/C87DxRc/FI3ZGZ1TyXK9cneKSuqq5yYZo8fTfIjARqIYJYQBUloR00NGlsCXCLBE/U35nhBTOL7YQVRUUzwQy2U61zkhSX5jngnN9/LA+cxRkVL93NP+YhRTM6LXhv19i7KJVCKhkl63r5Rmq5WoYYqp7S/NoP6ezIQoTnmqN+dQ5wmd35DcXhkCYJ1w8XNKnqn23jraXFKp9RUmwbQqppXHtMIxD5sUUQ19+9vfjje96U1CTpEHeWd5OZuEKct0V/nAlCfkcUxGQd3sMKqwlEBdN7c4mM8qHfiJ/pwuiamTR/nwcdd9+av4v//3Szj77LPw0pe+FM985jOklMpy/sL8VvS6B5BFPZXbmvQVKyrZ3M58f14/97yz8fSnPw13O+0UOYizoYpj+o3a6kgckC6pw8wkN1NwNg5lDS0V1g9ZHAkPi+JEpiixAUh5wJngwKZ5NWaUSiE9lhLB5AW5Kppk/cSEPCyfv5VUK/RDoqCKcU0mesompXnTU6S8pVw/2krEL5og/zsY1u2cE1N56URIOJ/DIRw8IavXm5iZWZDsUpJSyWx10rz0z9+5H7jotroDHvA+Kp/pZse4Y8h67W9W/daPMKpfbYVjGibImgvL9Pe6173wF3/xFzkpRZ5V2P9j5UHIJqW23wtWqftoUC2MOhrrxg47kUD5aPNqpBxgmeUo4qU8LpHxpSSIP/7xT/GsZz0H5513Pj7+b59AWKvJqFOST0N6DUwiglKDEplideGFF+K/PObRYjrstVvyhsxhNQ1rLNF64in08teKD0O2o60sDCv3Vjh4UI0UEibh+okmnvo3maYD0Vrm71B+E1RJZQao6shX8yCc/skLKyVY3X1fPCgXFVJ7URFd6oSV+wNzkqSfOZHH3JBM++RWIqWCQIgp/z5oT+mPFtXTsPTnMAM4uJ1UtFjlK62w+TFWMR23kx3HrofFpxS7FCtUOBiQMBk/pzlomAYamyjwwGHK0sXGFHbXk5T+53/+Z/7btMvKww4w5rdrNwbZ14+G5qdinmrx32XHQRF/dP6mbimRSxLNH/34p/gvj3kcfvd3fxdXXXWVhPjPNGfR63YwG/rodFfUhJu5Gnp+hBNO8XDRw+6DRz/uMji1GTX73+fYmx5qvpufW2d6BKPcso7EcNj+q7/fslUxM3LH0faCgx35aZ/QrB6DOfjvNM82zVwzEaw/IjMYEpeVv0bmW7f1Z9LnazIu29Ca/Y6sb2Mwf3f5KFEL9mvFmTkOQDchaTtGGun4pW1o9+5E6rckt7bmnYAgPA4HOivI3AhpT01s8gIvP0nJ5H31dCivP2iAKin0dX5EN0M+wcz4PDFwbOKtIRwZIRrr9IdExvdmSRcxS+jdFrqdtnTpe0yPkAxR+kwdZTfIFX1Hcnpd1zTJJToS6oDqvoeHJK5L3moYzmNubgcWFrbKyFT5CWVq1r4jkzMi+ClQd2poOfvR67WRdDsyhS3qdOHXZ3XlwKuUp0PEofKfjX7/jXiv9cxJPdjtV/1uK2xqkGwaBdP4y4xqYpfU+W/GQnmWonbjjTfiQQ96EF7ykpfkpLSo3B0O3H777fje976Ht73tbdJkdbTBnDjwuzDElnFbD33oQ3Hl8/4Ye+64E2GtLiRhfss2dNox0sTBWWeeg/POuy8uvPAinHHGGaq7v9uBR2+v66Hbbqvmow0u14/yGY563Ea9/7ADR7FJZ5RiP0mYdlm25yhlsexxZZjk/vw6+rPkTWXDKJUkePxtGRVVTVLyRKG3H1t8v3Hvv3pDpKueZ06CjVJqUjhWZam6apGO+8ycZJg4KKXoJnEqiRVcX8ZC0V9NtZQNW/Z3YF7fvJf5W+JrSpXGSgKoBJ8KmxkVMa2w6WGXT00jgNmJG4LKHTU7vdmYw2aaV77ylTj77LPxH//xH7jrrrvkuVI2o2/STHrxNjYDk/j93/997Nq1S+bVm+tHG0zKgdmehkRwpv9b/vHtuP/9Hoh3vP1fUGsuoNdOsHXbTmzfdhzuf78L8djHPh4XXPBbaDTnVSk2dSQvkgGPpvlsI5ETOAx22RtyMqp0v5HkYBgBsUlpcf76sNcYhTJCOtD8M4TwjSuLm8WQOhVMr6YomUvVTKTK0yzlc3yn5zh6u3uiaOale8tKU3zPssvi9hradZ+ZCkE/TsomiIYkDrN0OEJq+ZhIPoOdHkDCKkppqpT/IKxjfn4eCwsLqDUb+YmF2X/Z2928r1lf7vMyXS2yJ9ZVqHAkMWr/MWr/WDU/VdjUMKqJQTGmyYwaNZ7QG264Ac997nPx1a9+ddUfBh9j33Y4SvHMQyXe/OY349WvfrVMVTqaQNLAg6g9y99unmLA+a2//g0uf9YV+NjHPoa3//NbsXXrFhx/8hm4+JIGZmZ9+U677Z4Q0Vq9bmrk8hpUznKUEZNDPDYPkFGU71SL3dfrK+AaclJGqiCkJ7MCse1LVcLuE1inZPrQwGPzz1EesF1+IBn+YeXxVpZmkcTK2kcWqbOUSWaCyt9fyl9ILEMb8tfRXlM/CwYIuiyF76hYni9+5pHrbqzTq0ghybNaMstjnvtOrcYplbOa6PVS44Lz1+Nncxhx5ggpnZ3ZgtnZBdQaM+okLhtlIel/Dr4393NyIu57SM06GON3hQqbDJViWmFTw5BHuyvVKApUXkhKFxcXZd77q171Kpx77rn4yle+MqCK2gdzEzWDw1QOu//97y+XH/jAB+Typz/96VH1gzQ2CqNoGbVUOqYT1RzFcZKBH+D/XHMtzjn7XvjC578EpC52H3+yROWEQUO68L0glASAXqfDLqtVJxIbmds4MSndQIxSPu37bNV0nCI48ee3y+sjFNRhi1EXbXXU2GyKCqSxfChVUEU6dbttIYSZvj/0Q1HhbWW4DEXl2G52NL/DkdtFGTxVlBT6aqlZf7vhadhn75NcTzc7cfFl8YMGms2tWJjfjrm5LQjrTRkOwCisFINKdPG7NZ/LREZxfRx9WxUXVWEzo/r1VtjUMDtg++DAzE2zw4b2Nj74wQ/G6173uvxgVpx/b55r+yA3GvSTnn766aLeTkJI6UGlH5UTqkiuWfqfdphmNHu0qzmYq+8ngee7eZPMHXfuwcMf8XC8/OV/KrsnvzYDx6/LFBzOxk+lCzoTj2m9ObPqO1x/ctpX5AzRgKVUbXQnvurGdgcWNcbSzTu0i4R02G35a5ZcH3ebwSQENSvEKQ0jrvwdFInjqnVOI4mDiqMeUj1lKYli8ZIGTpCf9OTeUqdPOm0rThlBL9tWZZ930KqQqNxSIcgqr7j4mezrQkZlCWTSWeDXEQYzqIXMJ51Hs7GAmZl5SykN1MjeNF31Uy47KTJ/R8b6YN+XZlWH/qHiYEvRFQ4NVSm/wqaG2TnYKiebB3hwooeRDU5sstm/f7/cbw5EPGhQRaXn1OBwNw487WlPk8uvf/3rYx/7wQ9+EE960pPyfzM+icv27dvxD//wDxu6nocCRyciGLAsb5ROadhwWNpXZVqG6PqZjfgAACAASURBVPd6seRW/u0br8Z1X/kSrvno/8HO43aJikTVLKwp4pFEPVGwPITy3FJi6KxPKTPDICnFgNK+8Qd/M4+/DLYyVvb7XV2mX9vv2ykkVNh+x+Lr2Zd5w5JVMi96JQlPOt2lZq2ixzJj58xErExkBnwsJBBZkP9uit922fYRcpaWq9vDPmc5+gS7Tzr78VC2gmkgv1ESb0+PPYXKV+UUKjWSty5ZpTzH4HWPWaWcZGVSCjjbX28be7sNI/d2yL75HEpZPjom0FXYnBi3rxla6ai+7wqbGcUDZaaz/UhKr7nmGindU2GEJkVm505iUSSlxfLXRjc/XXzxxXL5j//4j3JJBbSsM//5z39+Tko/9alPybryEha5nWbY6pU5eObb1gHCmr4vilGvh3JApir6rW99C5dc8ghc98UvS4dynSccjj9gvxjABp9QrFKsqFji8IweLb5HUeEcR7omeo+DaJIqklL79qwQ2YaiGmplBA8rg9uvN/gcRWSLHfFlZfRRy/hto9fBSQc+a2Y1v9mpADxB5n7GLJ4bynhUnliRlNKSUgtnMNNcwNzsFhm56/qhCs9PDfl3V1kUBj2uycAC7dsWa4RlHTga4uoqHJtwx/3hHqqUPWxnV0nhFSaBveM1GaRG8bTLqWbHzAMDr7/hDW/AU5/6VHmuCby3lbtiuT7THcL2b3IjS/pscmIZ/+abb87L+A94wAPwh3/4h/jc5z4nJXuSVFjkk6H/j3zkI+X6D37wA7mkajrNyKzO6+K2FqRAr5PkSlmnw/Koctf1ogQ/+PGN+K9PeRo+9enP8dQC8Grww1kkjodu7KCXtNGNWxJK2em1ZVZ5FHXEIhD12tIcNbBkGFwscjl4uyP3ZUlPpg85aYLA9VDzAwScLMRzehlJ6eiZ/dZJjf1Ch4jM+q8I9bfgCUkrW7hOceoiShy5TDIPKXxZMieQJTX5p7J4ajH3yWNdWTiXHq4vl/Yi4fWF9zZ2A5KxOAKS2JFF7BipKmtz4Rz7KHVU+ixfE25eIud8fOZycuJRq5WiUduJRjAPN43gpR1EKwcQZh6yTgcuo+IY29TpyZLFqeqjSjKrE74/blTlpWYSS+pZxXazmIxTWToe3MSXdXV9H47HZIBElgCRvI4hwL4fyujQwOcI0VnUawsIwjk0mlvRnNuGmYUFNBbmUF+ow20AXb8Dx2d3fqLGozIaK1NZpS5JJaddZQnilAN2E52Nq8eVOi48J0PWC5BGPdSDGK3WfjhOCCSqeuQHh8eSVGHzYqOtCuMsNMOWqpRfYaph1DEzo972+BFUPVmSp3fUkNPnPe95eOtb3yqNT+xWnUZcccUVslacwW/APNVvfvOb0qn/sIc9DOecc44QWEM+v/jFL+aPZaTMOFx99dXyuJNOOkkawPj8aS77l4GEjIT8CU94Aq6++q/x3Oc+R25jWbTXW0ZztqlIrusp/7DnSfA5bws4unKsaDRq55sN/N42urnpYFEsQ6/132tFUcUrHsjsg02ZkmrDUXEDQ726QVBD5HfRc1oSE9aLWshWHERZjKCzIkRSbDyem4fle9as+MwdnkYg1ZVs0KO+GoNeT1k/12QlB1BOAcsjm8++N9mrusFKe2GLKujA6xbWrX+TpfwaxTSN8jK+sZTQXqCIt6vf26+a8itMNYb93fnTurOtUAFatbTzKu2DF3/UJJ9GKSWJfdazniWz7vmYaSWlBIP9ife+970Dt7///e+XBVpVvfTSS/P7PvrRj+bXSVoJMxigDC9+8YsHbmUCwGYjpq4SJsWawVn7jWYNT3vaUxEGPrYu7ETcW5axpY7DhhR66lSqQt8ysAaPndkX6rno0KXTgeYce3+5Th7WjUAZOUXJJKtJCWrRY1pE0U5TPK4MO844zqAVok/wMl0mV5OP5KQ06aGXRugmHbR7y3DDGrbM7kCCEL7WWBzPB5wYqeMr4lmynsNQRrLZeJXZ/lzdWOUHNVHgld/V7u43OchqO9nTqEblrSrySfVUX1pxU/mM/jwVILYqSDpOzM0QRV2kcQeO21S3VU69CpsU1S+3wtSjTCk1HfRGTaWP9MorrxRSSrABalphVFCW8T//+c8PXUuW+Ldt25b/2yasRkX9yU9+UvpcPobbgpYGA1ud3SxQPj41U7/V6uCK5zwX7373exAnqSx+2ITvB3KA5gGdUVIqz9EZGK05FIaEFpCVhKajGMEzRSf1w7yhRRVy2L/X2rVe9jo2hhFA8zxbPSx25duvl0YqlimNdUB9RvLVRhQvI+4twQ0YueQhCH0EtVAa6LzQQxDQ7+mKamgimoqJBvk42xHJAiYuKtEjdo1SSiXXZ9OSPXXKJARY6mjxM65Gao2dTXMCump9kAw8RiHLP4PrOojijpDTKimqwmbBsL+96idcYaph1FKzczdduZmOSTF5gn/2Z38maiAbDvg4EtVi2P604ClPeYqsyezsbO4jHYZ9+/atuuflL395fv0tb3lL6TNJaqkemzQClKizmwEkF7YnlV37Vz7/Bfjnt78LvlcTP6HyMGaoNZoqbkc/1jkYj6cmqsXmnWkiocMwym4wjqBO8tplzyubMDVssUlaWf6ofd3uLDdjP2kctZ/L2fGsmIiVp1aX634tRODVpITu+oMEcZJ4r1Xk1EnF3ymE0NH7Ia2YhkETHvc3gS+L43vKUuDqk5jCeGObrK8+GCcDl/ScypKqS3OfbCdX/Rxlf5g6WtUHIiHsbeMiyK0NFSpsNlQe0wqbAuZAYk8Ngiauf/3Xfy2Tk0hEbXXVbnaaJjBMf8uWLVLOZ8PTKHzmM5/J7yWJPXDggDRIQXfoj1JciYsuukgux6mz0woSEx50TbMbD9DdboSrrvpLnH/+/fGAC85HfSbEyuJ+UUk5R5/NSsofKjxhMlg5qHZJOidPWba6bC8xR0d2w5VFSTmFiCYcYgm/+LqjyG/ZdQwhts6YKVnyXmCpPJX4KMkudT3djOXD59Qkn4vyFmfSyAZ9WMtkbC2VRPvzDn7uTObXY5Ry46jmsxT9r198o14GJ3AQZqFuADMqq36PzEzeWv2ZTDe/NM5ZvlRFPGkFiLWyq2OwBpRSO6mAJFa9N0l6N+qoxj9JENCe24qbVphiDN2XZGP2UFXnfIUjCUNISERN96shpfQdMt/zmc98Zj76EpqsktDYt21msImp6Bcl0XzUox41NpifyjFtDR/60Ifw5Cc/eU1bgUT4MY95jDz/e9/7Hv7+7/8+txMcLrAkSw+pyThVUOrX3NwcvvT5z+Dc88/jnEq0W4vwA0c8hnyeIie1wTUt7ggtX6kdtWMuGf7fL/W7/XGo5nFHuOaUjxwtMLxh++3i7eMjhVbfP0De4uETsYb5XAeUUeZ1ZmaaUk9Gj5qufEjOaYy79t2J1uJ+IaW0dKQkbwyrD5s44dQz5YSUzUUy8pP01FF6CwPmXWeQeBave9ZELzu6ytzmuSliR21d4XmZ+q24UYIsSdFFJ4+tUj5Ys431Z030+5vt4VgnB66D0Ki4sNXcfkxdIu/ZTwvJUj0Zq9dVlaNeiJX2HUicFSy1OzjrzAdg93FnIU19Vehfh2SIChUON6pSfoWphmlqMuVc021LUnrTTTfhRS96UR4RxZIetMrm6AipowHs1mf0FT2jbHbi5RlnnCGklMSc24aXRbziFa/IvbZ249Qk4OtRmd21a5e8Bj2t73vf+yRT9XCCpJTlfJJSlmpNBzRLmAcOLOH5z/9j3ParX0vZlN+/sX7wu59MMbcanmCuWuqirpsWiRem7KR9VM7pIb/2kPK34zilmaE2ygjhsMeijDhLOTuxRnt6oog6CGXOPL3FqgFIe0gZKSaXHuAEq5uZxsThrCKvluKaPz5T8VkkkCTFZoxx0TZgT6Aalkna95CWK7dw+icGZjuUNT9RPY01qe9/PwfxZVeocBgx1PqT2qMxjgDG7UArxfbYhiGkPADw0qile/fulYD673//+8f09jGKKMew0rNqw0yLYtzS7t27J35Nkk9aI6DtAsxO/eQnP4nLLrtMxqcae8C04JnPvBzveIdqemu1F9FsBLjzrtuwY+sWaFte6X5GSq1uqMv31nQfu0nHO8Sj+zif30EqWkUiOmwyVNHXOOy2gdceMiWKXeg5adJKYJz0Vj3XXlSEUXk0ktxP8VlIlvKRponyU7paMY1SjiBtY++eXyHtdbB161akmY8ENezcdQIWdp44cjv1MkfyPnMYhVirkG6a5CRxYK69XscoG/Qq9xuTdPUmHZxmZauu5nMXX9t+vNmf2dtswHvratU51TnLWpnl9pfXcCN0Wl20lztodyOccuoZOPG0s8TuQBNEkG3skJAjjYo/HBqmdftVimmFqQb/cEhKSbw8CdtuyeqytH3DDTcc818ep0aReJrpUTaYhYpC/ukk2GyB/h/96IfxgQ98SK43G010o64QmOX28uoHj/BB2revtTnocCMr/DcMB/MZyhTFUQS3SMzscZllvk2bvFHVNg2M9nWzCNIszzPudntIMgeNxgzCemPsZ3EtK4KTK57Jqs8z7PO6JvBeHyztEH5vhIGzrNGsLOmguN2L61Omrha3sWxnqAECJsvUfPoKFTYjquanClMNo5I2myqbj5cf+chH8C//8i/VF6fL/FyK4HhTluGJoqrMKKlh3tSNDPTna/O+9W7C4nv96Z/+KR7ykIuwdesCGo0GevGKkBd6IFc17Th9j6juVskr+qYDv08eNr/i4gyZd481KCKKFFkl7ZISubkcJGWrfZ026AOFpSjmyqJWTH1Oj9JTlRKvi24vxkzDx9z8FtQbc2PXP1dnh3hMbSXT/hz9bTRklrdOCJn0pMBWiTMrH9d+X2ONGLg9Xb29B8j9wIS6TEr5aRrBcYPDMiq3QoWNQHVKVWGq4VjjR7kjpop31VVXySpv9Cz7zQxuJ2aYsvT+6le/euCTMG6K25INTcW5/Ica6E9fKkv+tBAUG7YYk8Vxq/QGj4vJmhSqyQn42c9+hj//8/8uZJT5pp7HEr067y4lL3nTU2p1Z6tpO2IrdTG1Hr0yRW29Sm7DXnvYUqYAjnp8cZZ9mS+zuEguLVVKhua7HuqNGcwsbIXr10Z+FgPH3jZaLWVDEdJ46PYrU1Bt0mrH1w28V0n2q3lsMd+0GJdV3EbDvuPBS1dbAmg7SSXLNNb2iYqYVtisqBTTClMNuwOfShhVueuvv166c810nwqrQVWyTJmkakk1leD40+JjDjXQn3FWhpAWA/1JkBmTVSSsh4I4T2Jw8a53vQvPeMb/g4sveYh0OS+ttDBT88pLp4WDvONaHeOFaUTThGHqHkrUShtlqmkRw0r39m1FclRGzoaRvDICaNTBNC0QOjPS0+mP4XSlwW0WM3Nb4QczSISujm5wdC3Nm7FTqSalw5TfVdsNBdHcPM4Zvq3z546xjRS3p70OTj75qf9vFTGF/FLdrrNhfUNM2+j1OvCD+WoaaYVNi0oxrTDVMDtrktIf/ehHElkECVqvSOnB4B3veIc0S7GpiQH8RRyuQP/1mkJV5BMvetFLxAXIls5mY3Y1KS2SESfVE6JSXXZOC8v0YBiJKSOMBuMI9qpc0XXAKB9l0WdZ9E8WFyczVZNMpjjNLSxgZnZeMkCTCbO6SG4dnQOak1I2WelGq2Hbw8ZaVOphntKiajqp3xQlJw35YgXsOw49u22Z/rReCnqFCkcClWJaYarBBgg2P3FH+7d/+7einPLfbJQweaUVJgO77al8shxvmpqK2OhAfw4VwDpOoeJwL6ZCOXo0LT/bP//zO3H55c9Q9fiscAJTIBVukZQZ9dHS2Y4kygL0UUZAy0gg+upjhnKPqf38gyEzkxI1FFRb8+9kDCEm6WJ+qby+66I5Mwc/bCAi1WRk09jvp39ywUYo+VdqKabIVpFDex1dCcpH318LFY5fOnBhhDJdfA+jFGd24H6JT9esp5MNbuvcDqEn4QW+Iw1Qvag7tYNFKlSYFJViWmGqYUr5LCFT7TPTnaBJa4XJwUake9zjHjjvvPOGPofKp5mvT0Jqyu4kmi94wQtG5qYSD37wg+XyW9/6Vun9fG/6X9erAcocg01HN3dpV1/9tzIdahTNGiBSBVI6zRhFHg+GWBYJ06SqqXlcMZN0GEHNiV5hdvxE/lITqQQVsE8yGkcMRNoYXWXYNih+xnEnB2VK9KQd+gZFT25xoZJc7Mpn9muFCpsZR1wxrUoORzcONSfNPP9Vr3pVHpw/TPWpMB7jJkVBd/rTf/qIRzxCRqbyuin7P/rRjx64tDEu0N/c/4lPfGLdvil78pGaEhXhhz+8Hu95z/tw+eWXA04DUdSSiVAs40ZxF0FYh4cAnXYH7kxJA439szrEyTljf/9jnID2/WUE0s7LzJ9jFDdnuOJqvVD/qi53uyQ5+jkOvD4hg1EJM2SOTjKIXfOm+vH5iitF1KidOvnAJmLqdROZ1sQIqJgNaFoZTKXZiVFxIaLeMtykjZmFOrLaDDrwwQFfQdZC5oyxW+i8z3wyk2wvV8LxVejCMJVXXaZOr09EnRLSnTca6e2Owdek/aAPJb26MsnOlXm5vTjLx42KHzZLlX2BWnIG1Bx3MBqK057SfqNe5rRQ5zZZBmp+A5kfoddqwXMSpDFn8h7dDVDVMWA0ir5lFPYj07r9KsW0wlSDf0Q33ngjPvvZz8pq8t/M2fzud78rXeVf+cpXpPGmwvqCjU8ko1Q4bS/qqNzU+9znPnLJ+8tGl5oy/1qnUI2COUGhqmaXMN/5znei0+nItJxMyrFOf/wmiU+SiPp2tGFV49EhtMCM8q5OCskBTTO5NNmfdg6oEFXp6EnzeC5RUoXAZvkse36/gV9TE5Zgutkn9wAPUypHKZej7AkHi1UnKq7ltzUnG9aYVJtQryrjy22qKcxMnuLj2fzE7Sjkt0KFTYjql1th6nHNNdfgzjvvzEeTMjz93HPPxXHHHSfTjiZRActAz6XpUK8wGaimcopUWXbquEB/lvmHkdaDhU2cjG+Pv5Mvf/nL+OEPfyjjI6mO9Q/suuEmi+EGm99iP6rsPKpbfpJ4p0les4zMjXr8qsem/bGbrlZZDSlVJx3KD0riVas14DuBIqZ8cDp+5LC9DqOsA0MbwPh7SdVl2cL4Ki6p46665JJkkIUKcMbb9CVcTxZ5b2+wGQqS7zpITIsnCfYAA0cUWPXZmGPa7XalpF+NJK1gsBlUUhsVMa0w9WAMEXTZ0sxCJz72sY+N9EsOA0vKHOXJsZuc/3777bcPEFRme5K0Vkrs5BgV6A99P8v43/nOd9b1fY1aKk0y7ISyfMn0wbpeKEpbEqdKq7MJyFF65C7zQg7zfY47SI1VDUkqTbKBvk6/Y35dZsL2L+1FPJGpGkXKkjvVbdWcpggnX5KvRZLlylz6msrthCFw44lp8fMW/a2Tej2Lr7EWBXaUxzQnx76aqc/yvvlekkJawfDvSCcOOP2hAXl1oMIxjXEpE9OKiphWmGp8+9vflpgok5fIcu3pp59+0KtM0vmXf/mXQpLYwc2FhIod6IaI0ipA0sqGK/MHTCJbkdfhGBXoTzzxiU+US1ov1hM2uTLNcIwSI0kVZTYlAfWRpi5cL8h31J7vAunR0b1cpoaMa9RZC8Z13I868BnPpZNngqpc0nyJE2RxjCRR3sk0jVXpH6lWUmOt/lFJDZBmasioSvIc3+Rjq6VrIY39+5Ti3velDi5mGoPjeuWXni/KKC/txdwm5Xuj2mrllOQ0c4c3Ug0SW0VEE/1bVkUDdusna7I6VKgwTaiIaYWpxr/927+JSsqdL7NMYY3HpMd0rTCZnCRSVFu5cA4/iaq5jw0/RfD+7du357dOQl4PFpvRYsAue5b3jY/UgASe5J1lfm7nMtJ6qDCd2/3RjGpM489//nN897vXSzmfU4MgJU89LYwnOunR1b1cRkqL948rxQ97zeL1/vOKua+jF1WaVyqoWmJVqtZ+SUeX9k1EEv9nGpY8N5C+ovx7PojGtFE+0mGqctlSZgWYJHGgTLWV61oxdXXOqZxwucVGsdVEW37Pxgrh9n/fKkqqIqbHOirFtEKFDQBHWBpCarryix3Ja4GJM7J9kByRCWvs5hlnnCGX9gGJMUt2xuck5HWtGGcxwARK7bQpuW9961uFvFOVvu6669b99cuIlint8wB/zb9eK93NkoWbpDJD/FjAuDJ+cZsNUxTHWQEwhNya55gmJ9MEJcQzSVW3fJyYB+fqnhp2wGZyNx94IH5gafAJtXppuuAnL+UPI6Rl/s1R26RYhjcKKrvvi5dc+Fv0LLK5agypnVRgvKZDxpUW5/rL62lvKU/ejc0pTnoSsl+V8ysYbDaPaRWwX2GqwSYW/iE1m020Wq2JfHGjYOKMfvnLX656FBupSOz4GKp7JmCeHejFBiubvBocChk0FgNY8+jZ4MV1oJ3BvD+VWhN4b8B1Zec8S9fj7ufrGVJNwvjkJz/5oNd5EjzqUY/CFVdcgXvd6174wQ9+sCHvYcbT2qqp+Z186UvXIYpSBDUfca8F39O7PJaMqZpuyBpNH7IR40qHwdFd8usNu6ucPDOD1fzkcpis1fykG5xI8khMZWq+fIzJSOmkatHwfYqrX2dwG+bE3YqryoqX8nhv8H2K9gHoGK1MEczUkFSqpZzqVDjBsDv0Dfi752hSIaZOKifwqjGK2+jYOBGrcHTBX0sp50hg2I6lwubAJGqNXYI15IKXHFtpnk9Sar57Q6yMgkmFkCqjIXTQQe5F8HEGDIwvgylFk5wagkdi9Vd/9Vd5GXpS8roWFC0GBNVTYzEwkU3jlNpx97O8fdJJJ+Gyyy7DbbfdtuG/IW6Tsg7+9YQZT2t+R/bv6Qtf/BzgynwhMNbRZVRmwtGQPGB7cEw53+xmJLZnLStnq1KaxBzGQtR4khVbt5vGmv76iYJZyOG0yZPr9pXTssxUftZB5XJQ+exZVQ5zspDySyDx5GokMRw2sKkUVWm0FxWRHeuOCzerw63NIvY8tLIYTQeopcz/7CDww/z9sszJL+0Kdurr9WHLFD83Z/KnrrynSgtVv52yE95htgd7m/tGwdW5sfa2YlSXSRoYfOH+4xyvBoeRZhyjCyrDnHCVAjFzXYHM4+9ZNZRJuqubqWRaTVCj2EMYhEg6PSyt7EFYc9CJUuy5Yz+2LtztkOLCKmx+jKp0TIJxjx2nyq/1ZNigKuVXOOIw5a58wovjSJPTOIXNEMG9e/fmpJSqJ5XGMnDyURkYO0UwSJ7NOVdeeaUsTAMw/tM/+ZM/yRXRInnldCSqmizFHywmsRhgApvBuPtJrplmQPzqV7866n/8VKGMOk5FyWSd8jJN1tbVPa0o7vxHHQwO5qR+lA+zzINqK3zDSojFCKdil/qANy41z9Mk0/54PDBSedU2AclLJSGECqxPUgdZ4iCJnXxKUr98X35QXUtc1jCUefuG+f2K227Y9i2Cr2VbEcRC4PjwcxtEhQqbE1Upv8IRBQmCo+ecG1+g6cD/8Y9/PNGqsURdlo1JonjqqafKXHYzApOKJP2O559/vvyb6qeJOaKayMfZ4zJ5m+niv/TSS4UMG/JK8HVMFBLJ6wc+8IGDUk7HWQwwgVK7EUruZkeSJpJnevrpp8hvjDmPXhDATRI4nMpzlHXm24TP/PtgVQsUSGZp81QJcc2GzJHHCHJnSKlZX/vf/aYpW6nN1OR7wy3zuwbJppeFWgWmYpqq0numpk1NslUOpTo3qvvffM5UD+KX7YJy9bu47e3XdUVtVtmpyAJ4boqI06qSGHES95v9KlTYABzKvmUUNiUx3WxG3grDwaYUExSd6Tgo3sbv+Gc/+1np86hwknyNg/FsUnE0ZJNqIVVOkkkSt8c//vFyOwkr1USqojaR27JlS36dyix0B/o48roWTGIxwAQ2g0lsCMciuE15kEamO8DN7y2OdbzO5sUoQmrQvw+ljx2FYYqojUkarcrU1EyTslGRTTA2AdM0pYaVWveZkamJ9R59Jdx3Z3NbAW0NJKdMEGO8krIuuKWfqb+ug6r66m3mlT5/LV743D+q80jLpjwNsxXQMy0eU09ZNFyP1oQe4qSDTnsJM7NbhrxrhQrTi0oxrTA1MN3U0CXYPXv2lK4aFU6SDRI6lqiHEUFThr/11lvz217/+tfj4osvlixUluDN4174whfKdZbkGUPF7NT5+fl8Jjzfz6iyk5DXq6++WmKtSH7HeSxpMaBHtgjbYgCdATpKqZ1UyTVq8XqH3U8r6E/mAZwZmWyUMmpVHCf5tKjNjuEEtf/Bykrrk6qGw0jpqOfYvlIMIbCjiGx+n57UJVmdtF+I91QRNjf1ledS8lH1iYelsDppS7qqVGe8Gqog37njIRYLwPDJVcPWq3BL6eNGle1XvZ6dEGDNxU8LAfv2NjXgKHxXtkAAj75dj6qpqxXTNvdOY9ehQoVpw9QT04HyTTVj7ahDUQ2wJztxDOkwkFiSzJGIDSOmj33sY0Uttb2lfCx9mKbMb5e7TTTThRdeKIsBSemzn/3s/N+TkFcqlSSFDJ0vQ9FmMM5igAmUWn7O9VRyjwY4cAZOcHw/gOmO8Rmyv8lDyCdRTG0ocrP297BffxJyOiyeaZUCO0a9VbkJVLkzJFEszVIklfI5MlNpUfsQIXNZJCcgqjSeIO7eAZeNVDpOyfUDlWlrPO1DIqcMCSx+1EmIqV2qH6cgw/q+RB1NEvkcZinGWRW3ryi/0sEPIaWByTZ1U7hrnIxVocK0oFJMKxxRGE+pDYmRcZyhzTmTnqAUiZyNstI2SSVJJ0mcIYif/exnB/yrk5BXo1SSbA5TS4s2g3EWA0yg1E6i5B5rID2hV5llUnbvk4zy18Z54mFQx9Fiwdsoj6lNslAmFKzRSjXML1n0Y9r7BTY1JVkq/mCSNddP+usSq1gkGYPKln5WXLJYPl4t6wAAIABJREFUEc4sQxwvq6zRxEMU1+D5dfghZ+7XdZj9aPuBaSLqP2Zw/e19V1YWJ2UR1OI2lNtcNcPKLt3bxDQr5JfaKrRc538yulX9rrm+riQcMP+1t6bvpkKFtWKjUp0qYlrhiIKZe6opRcXaONZ0HhMDdDhBYjdKWZyEvJrxm+9+97uHvk7RZjDOYoAJlFrGS41TcgnGRRF83NGOwA+wf/9+iR6q1+taIXWQtFrwmsFR0/w0CqUl/EMkq2X/nlQltC9dq9HJfr1iyZrkM88+FaU1kc4rFQ2myveqjK9VVKi4Jt+PZTwn/ZdZnCFjRlUcwHVTNTZ0RM+Cut1qVBoyu37Ydfv+4nYZ5tO1PaVl3lJ73Xif76rwfpqlHfu1heAe/b/tCkcnnDRND47SVqiwDjDjJM2O2JBSNkGRSNg5aZsl05YEkVFPZVmqBizVF20GsEr8xY56KqnstDfd+wZGqTXz/ofdbyvHJK+M1DoWrDEOfDz+cY/FRz/6YckzbbUW0WyGQlZ44A6Kk6CKJeixm2h1jqn9pINRFAaIkjT7FNYJg4pj8XXs6+NyBu3mHsc6FOQDR01ZfEhzUyTxTBZhS2JdZlfvm5pXcszz7fJ0Ag+BpTJmaoJRoLrxebLa7ixicf8BKeVvnd+K+S070JidQ+y5aPcihLFdzqdyGvU7+J0MXkzSphqE4IVCTDmj3vVDIXRJtnqaUm4LSFOEmS+d/IrwJohl/WMkmfqcbtYsIdFl1iSdt4pkYDvWslCU4CjuIIrbcjLOfV/Uy1R+adrN16sYpyXbv5fJv9kwajKg+dr8Nyfm7TjxXOt3kJovWr8mpJO/wsFjoxTDYx2VYlrhiMKe7WyDO9a73e1uQqyG+eamlViZeKdRGGYzGNY9P4lSO+7+YxGe66lsVzdDHEX5SRBJD4PJsQnOyyXqaKI2pdUYR1zt24rvMLGXdMjDFDk0SuHqpid1/+Dji0saR6vK4KIqOv1800EvqCuEy9Wd+H69ocd8+gAVUtdDJmNEHfGqSjOVnbmqc/LV9ClXPpsE8zvQYfVqbr+T+dKQRZ+rLqj3t4m9EZJUv65+D2hfrSbTiSbqfU9prFVT9TndEq+usTqpz65OhsxttpWgeFJvf51Vv0aFaUZFTCscUdjdpjKSLzVn8w527NiBW265pfqCNMbZDMbdT9X1EY94RN7tfyyAzSE7dmzTn5RKkoc4jjTBSIs0YupRnOQzjjyOitYzjVDDiOqkKC1TWxFIZtvDJqSr1s9WFB1NzmI1ECFVvkmlZEZC4NR7JqKAymvSqylKtZ+PM3WkG78hZFTeR+bZO+LHTHOSFw+s06CloL9+DmdTsckocxCRqLqxTJHK0sFu+VXqqXwe8/FtK4Bu2OL40LSHhP7ZKEYaJ7JkqWr4Mkdom5jb28/zuM9MkKSp/ryeske4mfz2FWEtZs/KHNj8+69QYdpQEdMKRxTFEj6vs/zFkhYJVJnpv8LBgeNKTb6pPb71aAdju7qdDmo1XxpC4oQ2EVXOdzfJLrBstOQwr2hZR3xZ4w3WoJ4Og62YDpT789D4/icovodCmqt5isR5OVk0SiJLz1QGSdjibg9x2JXoJzmZ1cRUgurhFcrdGVKvnm8TV9RF1WxEMkfV3KXHOFMjPgGdRmUTzNRFpome8sMGQuxilvjdDFHSXnVyjVKlejUpVdYHNnTFWjGN8hn35mm2Olr8PosnHWbfaewDQnzTLjw3yNervz/1hk6+qlDhSKMaSVrhiII7TAmILpBO5k3e+973XrVqVQnq4MGEAHNAG+V/PZoQ+B7OPOsMhKEvBMeQns3yKzpUNRND/maG/R2t9bXX8vhypdTcYEhSfx6/ELQ0VvPm2YAf99DtKR8mmZvvueoI5qrZ+mZx6SFl8LzfkKagfMlXJEUax2pJonyhahlHXUS9jiy83u2uIOquIOl15f35OK4rx35yUTmimSQCiL+WcVZpUrJksmRpIpFQ5j1JjqOolycOpNq7KqqvOzhCtWx7F2835NjsU0l6JbEAdlnfRFFUh/8K04lKMa1wRFFUBPJ8viTB2Wefnd+eDYliqVBhFKI4wt3vfnc4risHfx60GRkVxT0hGJJpOeUoU0bLiMokZHN1B3354yb9+8qGjNK077f/blf5HCWA08lL3WaSkiFSpmlHytFpiqjbQ9DoyW0ulUBd4lev62pl1Bd11JFLPbpT/m8mfvWQxRGcmAplN1cvTUc89AlzSmIXqdxUFdDvw/FZKuekJVfNptdjU8ssCqu8sbmfNOo3gHVTIY9U8VnSN2qzk3ny2aIhiql5D55oKTLq5PYUiYzSirI0+AV2g5Np0NNLdZ5fYQpREdMKRxRmPn7Rn0ViSsW0VquJqmC6TVGpphXWgOOP3y1eZdN8I2XezJWS/sE2FB1JTHoyZv5GyrryB0vA5nJQRZ70fQwxRYEw5dt2ROrAsLfIPaIkd0kkpXNfyvA6QilRpM6Hvc8wLUueyi01UVDiKNXkmQollc9eV3k6pXzezUmkIaey3YznPYvks8SJqxIEkgDgdKUskNcMSFCpwEL5acXOmVoWBuOBzUx4virXm5GoSU/bCkhWmb+q2aKDfpSVbRGwCbAhtzI4wM59tSL3lAKrRreqwNN+cG+h96xChalBRUwrHFFwp2q8ZEZ9gC7l3/e+983P9lVeYR+VWlphEjzwgQ/EzOwskrgr1VwqpSQJ0pHPw/ImsdkNU00PNq5mbFPUGtet7H3Ue6xO0iieYKp/m65yi9y62nNuuujRD6N3UjXZCXnclyNz7zMhdKZEza76nmpxYzxY1EPU7SDqrKjc5DRG7CQD/vW8CcpRdNb1GNjPE2cqu/Qke5o4J6Kgupk7cEJdbAJTzWXpQOe9nGib7vvYEfKrGpUS3XDlynvlCrAVD2Wrs8VmURvmOdV+ssJmxIYT00NVt6o/rKMbRSO/TU6Jhz70oTIP3wbJLLt17R1zhWMTPIGh55CZt51OR7aB8dfxt3HZw3+XFVwhJkAMFzG8wBf1ij7EzC3uX4r/HuPDy1aHtGNIp3sZygii/VzXsb2RmRK9cuKoJvyghAT2ldDVYynt1/fh9COdStZ7WDd4ruQhkTglpd7piUxcJ0Pw/H7pmPerrNREYpTU5lPxS55b00TSge8Fomi3Wi10uy0kfg2uX5PorzhVgzeSqI3Ay5C6db0P8eA5OhJKus4z9b1HIbKkix79or0lRHELcdJBmnWFDAd5tcZF5rKxKRCN1ZhXm94svLAmDUSZ50rUlMv1c1xFMgMHkduTvNY07sJjQ1HWE29sRiIKZTdNkkwNpUodpImLJAo0UV3S29WRbWDIZBzFSl3NUm0jcPOqkU2kw4DPS+WkKwxrqDdmpMrEdY9j5sRm8Fz9W0kUyRVyT+LrZZZ1Yjox7u/oSFfPjjQ/OdI5qhvF7yrFtMJU43GPexw+8YlPyCqachVJqT0tqsKxC5IUHrhJSk3AOBdeJ1l62MMeovhOokx1SaonBUm0UCzzxTcFJpimtN4H6WxI/mi5x9vEPaUDt3HiEkqsjIZYqe8s0xUTJydh9InypCMmoY16CNw23NABmWm3R+V7Ds0gpNPUinVKdYd9L585H7eWRI0Ukpd2kSKC40bwXUUGk8RVWqsbwCcBZpnerYkaygiqRliXufpC3lM1+hNsrhLPKMRWQJItTUqRal6SMKpUdfqnmWeppZmempoilk78VOWtmu2o/bb8KJ7viC8aiZOfZBmVdKD7nydb4pv288WT37SDJKuEnQqbExUxrTDV+J3f+Z189Sp1tEIZaPewrR5GXTrrrLNw9r3PEQLKJhE/UEJdHKdKVcrcYdnw04W+/DlytQ6VhBQJ6KjbBt4z608zyqOTdDxSX4VNNalNVWi9JpJqemYqRXq7cmKImBcGSHoRep0VIahwAtQbNTiBr5RUxjbpDn5OY+L3zJxadtTzN9Bu3WZ9Lh3p5EE3R1FxnBOi6XshfD+EH9Tg84fCRqcBtZzd/akouhK15CjVmoKvJ5YQRa45uz/JVOST8ZryZMiOg5LJUbrbPhg4mVB2BUU8dcaobs4zv2/TcW+IKXeJnh8iCGoIwrq6DEIk3HbMg82jrKbsNz0hqn6CYxMVMa0w1TjxxBPxW7/1W/jGN74hqyk78yCoSvmbEAz43759+6oxrIcC/ga63e7ApBv+Pnjb5ZdfLqS0tbyIWt2B43nwMk8f5E2O45Qf+CYkpaufdnAxTlhVti8fRZqTVPQnJ/VzMdPB+0lOUx3/pO+HJh3S9JOqEZpMSyBZjBPGJ3XED8wRuyvJAXRbbUToYW5+K7Zs2YLm/FawUO1nTr6OEr+UdBFFbd3cFMMP/bxUDrFG+MobKtUXH2F9myJ5Ekyvbkee1OAhSiKtUkLUX+N1Nb8alu6pkLqUT+NE9ktUUaWRKVUEXRRTrdrSoqC2UyI+1TSzDsGZ9oZC+0plI3l9sm9FQZnvgOooF18IqSKl/J27Ir6uHrd6ML+PChUONypiWmGqwQPW8573PCGmpvxn1IKKmG4OPP/5z8eb3/zmfF3Xk5iag7ZpouN1klKOhSURZie252XwfB9J3FHz2VnmT0giEoSNcLq34RgCUfRkY2S5fdTbrB4Hqu8pfWx+XcyjqfW4wXnsfY+uySdVyp9QO+bKSjnbk+8vb9bRf+O8rR74aHE8Z+Jgdn4e23ediC3bjwfcOroDmaf9dZaSNgNGQSVxS389Mh3x5ASabHpInEEPsXySRHXZZ9Ilb9y8OmBfX5fopzhGb+UusZNwgEOv2xZ7kZ07ilTP7ofJKCVjjIWw0rqQJKv3X+Y7tRuY7MEBAx7kAimF/lwqh8AdXJcC7OEIFSpMEypiWmGqwR3r4x//eOzcuRN79uyREiyJB0o69SscObztbW+TyVIG5557rkyXYpA/m9euvPJKPO1pT8OFF16ISy65BJ///OfXZV2NT5GEwCQ48DfD0aunnnoqkCyj1ggR9dqI4rYcjBvNBqvP8LzpLxNOQizXO9fXJnkDPV0WSSoSV1W2T/M80n52qUV2tboqz0eilUE1VlOmNGXKMx7ye6SdNOmis38fkk6Mxtw27Dr5TGzbdSIgjVKsrHdzT6sq0RvCWVfElDX7zLGyO101H9/p3+ZZzWGZo4hzyilP2oYgof26318RzFS8owzg73W6OLD3VqvbPu3nk+rXdNlp75owq0QTeRVy72gfqJ3zKtQ3U3FRxkpQFhllSCp9uKGU8EO4vlKDJSArU01lZqBEhQqbCdXohwpTDRIOjpR89rOfLatpGp7KlKIKGwMqj5/85CexvLyM22+/HR/84AfFv2mDo05JRs1ig/P7qZL+6Ec/klvPOeecDVlPc6IyPz+P5zznOXI9irsybafdWRECmxMuKnJh7aj4xZSpnXZY/Fpfq+x6MWe46P1z3L5i2n9stup50KqpXZ42RNdkGpvGxsXFRdx6ww0y+en4E07H1t1nIHEXkGShipFKocPkTQnck656B1TBOYq0hjh1ESUZemyaiiN0ow463RY63UVZsl7EHwlSDlxg6D4VdckjTaWxiN31adyRdIBOaxGtpf1Y3n8nlvbdgQP7bkdneT96nSUkUQsQotwTpZURULKgjQxdwOnpKCxFGNl8x/GrnnhbqXbWZeF1Lrydi01K7Tn+/C0ziYKklN34XqBK+g69sY6nUgLgrPoOsXZXyBGF/fspWyocnaiIaYWphlHBXvrSl+ZNLabjutoxrR2TkEwbvI9q6GWXXSZ+v127duFJT3oS3vGOd6x67M033yzKKJfDNfbU/CZMKZ/LPe95TzzqUY+S613mVkZdITq1elN5UelFjKINX7eNhp29aRPS1eX4yVDW8FSGYeNEBwloIV/T6Zfy+++TrlpvU75ut9tSIbnt57egEYTYcfwpSJ0GlnpAJ1bTnRzJ/cxyAiyaZAKwR6rbThC1DBFkYT6SiCjGRfWiJXR6B9Du7kd7pYX2yrJ4WLutFXR42W4h7rQRdTpynSc17ZUlLC3ehaUDe2VZ5OVddwJuBNdJ4bkq89R1ValelFeqlSSq6KmIrHwbsMPfFQcEY6i4SPOVXsxtns5oLSP3/L2zemSUUjZumZg0FFT06gS+wmbDhpfy15JDVtb1WZGPYxwSPk1/2Rxe8aq/xKv+x/+A66sGFt/LKHYMxdHoQR1VMh8HQzJJMAlekmSyweyiiy4qffZrXvMaedwdd9yBhzzkIbjiiivw4he/WEry9I5SCeUlQbK7d+/eoWtx4MABuTz99NPXbXv4rgemSGZxjAYVdb+JP/tfr0WGRTh7bkHXnUEHs3CaO7DSjjAjoy1bcP0munGM0B+XUzp6/zNs/7Re+63cAlnaLc/0pKT0vfpTgLwSomo/PtHl+kwrev1L9RwPWBUBlamSNjKdS+qqnFiZae+qMn2mKhq9ZAkhFUDHY28QEk5OoreSpXskqLlUJCMEYUON/GRup99DL7oNN//8q+jMHo+TzrmvSChevIgtoY9Ot43E8dBBF7Uk6JM2LxP/J0vtQknp5Yy7KquTsUuxB495TXGENFpCGrewFN2mAu+jrhBlWgAUOVbWgyhy8xiyXqcn5XpRLzkHituBtgJHdb+bao5MYmIkVBzDc2a1vUF180vfUtZXMj03lhGnrpPlDVnqC3blec1gRgiuOenyfQdBzQfP10l4XX9e/KVmX+fo1/EQAUkHnt+A44a5SsvN5DrQcWnp1GtTG02q+5aVQgVgk4y9PtLrd6jvP2w/WSmmFaYajlHEPB8v/OPnY3ZuRjpfIWX91Wtux6lsNlJ6qCXzcbBJ5j3ucQ+84Q1vkGcYklmGhz3sYXLrxz72MSnJv+QlL5Hnw7rPgOvzvve9TxZ+hquvvnrgfiqqBK0Z6wUhNYFL3iG61IUPvhCXPuzBcNDB9f/xJSRLd8CPljHjO6IwZV4IpMp7SAIxLSjbwa/FX4phZc80k1L4sAVDrADDlLa1NlOxHM2ue5I0pYgqb69ENnmqIiKlZxKvBOh2E7SWI/jeHI7ffQbufe79MTu/XRtAGcuk8kTpv5QO9IKSaJe9RU3nfkKIqqtSGXQkVFCrw6/PwKs15ZIL/BDdJMNyp4cDKx0sLrWx3G5hcWVZcnLlJMDT+5iAVhA1KpULTQSl1z1vIGPULPzckkQgXfWeXoI8w7Xf+BSpkwFXealVziqXEK4u9Q/7XZQprRVG/w2V/bvC4cfUENNKJa1Qhna7KwZ/er3mZ2fwP1/7GolhYbRMECpiUfy92CWt9QYbd0jieDkK01gyXwvJNOB6FHHjjTfKLSS39jpRueUCrcZSWR1GeNcL/AUkVPWoajk+3vWud8CNlrB4yw9QX9mLvTd9F/G+XyKkSuo6yIImEM4KQZ2WAQ2HQgBRKKGXERKbZI573eLjyp5rE9fi31mR2PpeE2niS7g8S9kymMmJVWkbjIZS2isJF1VT32/C8+awdcspuNc9L8K9730BwO8sNvKxq9U+ksJGKRk3J6eKyNXU4gdwwxB+vQG/XoffmEc4s4Da7BbMb92JbbtPlGV2627UZreixvvmtqPebCCs1+DWQtRnmrKwmY6kNKwH8OkTTV25DODnS/5vicFSpXYhpJI5GuilZo0bdQe8wcbakDgRMi+RwH1OLONz/GAGfjAL35sZGFdqvn/o7WBO0Mv2hVV5X6HiGtOJI05Mh52ZV2d6FSAKKGN+YhzYe6eM1rvi8mfi0osfiiROJe7HHITsYG6jzqw3vve97+Fzn/ucRB+xw3wY1kIyDSZRM4sl81Fl8zJMSjLHwTQxnXHGGXLJcj6vkyBzefjDH46VlRW57zGPeUz+ama07Ho2P8kOzFXz0V/16tfi1JOPQy2I8esffQ/7fnEDfnH9f2DpVz9BtrwXLueRw0PqhNIYgpJxneuNUWqkKYnLnFFrGbhNxyeVKZmiSFI71Gqofd0sqis7yRdViu9ftzGquWkYsS1vbrLWNTVEEvJ+aRoh4sx65n0y2itW8+6DegON2Tk0SQrrWxE2j8f2XWehubAbSH1EMjreFdKlJhspP2lxPW21lPeFfl0p49KQ76gJnH4AJ6jBC2cRNueBsInUbyBsbMXWXSfi+JNOw64TT8XWXSdg247dmFvYhpm5BczMzqPRnEVQr0nwvxv4WuX0dZk+yP/NhWTUpfeTBJTlfb6v78FhgL/ns45v/duVSVMceSqXricLK/sc60oiHNRChLUG/LABL2jA9ZoDnfrF7WDU2kHian13057hewRQcY7pQFXKrzDVCGs1yQn0PRf7fv1LBPUAV73yf6DRqMkBz6gL9g7lYDuSJ8VTn/pUPOtZzxr66CNdMl8LiiSzCFN+P+mkk1bdZ8hnEYyCokpMzM3N5ffycxHMGF0vhI6PtBvjgosejP/23GcDrbvQuuVHWNn3G7TbK8jai9j/m5tx1603Il3ZL73KnSQTr2AYTF9aXpFgDCO0ZfmUZV35mV7UqM7+9XwpIaQ2uTsY2K/F7QzNKZVC2lOz7iV3n+rhDJpUJ+sN6SincsrpTkh8RB2yyVBK/K4eC8pIKVZLJH4+VfFKhmCVkWROgWK+aK+7Igu78nv0mNJvyeYiN0S3l2JxqYXFVgtJRg/nrKxTozmPenMrao0tCGuzcMMmXL8uanvqqg54dsTTUsBLLrVafeDfRrX0PFOet2bTZ26upHo64F+RSaWqslLE5Igg1FOdhJTWxIrgCeENhn5HRjGVk3YUTzIO9td5dKMipdODSjGtMNWIogyNZhNzszP4xlevQ7K4Hxc+5MF43etel/98ix29GwWSQOLb3/72yHeY1pL5wZDMG264QS7PPPPM/DbGMRG/+c1v5JIKMa0LsNRi0+D09a9/fex6HQpaWYzawgze9Nd/g/nZJnD7z/GLH34HO3dtxd3ve75su7i1gl/86NvY96sb4KU9BJ47Rd3Kab9zPFcxU0vZ7JPQ4mUZEe1nasY67L2/GKV08HpaeiJn52aiQDaHoVhO52WS9GT6FmTKUU+mHzmOizCYRS3Ygpm57ZiZ2wLPr6mUT3bmeK6M1ExVkKioiB7tPE4snfVq8FGa59Ca1FDH+s9sk/bSfrQW70J7+QA67QPodpbQ67ZEsaW9gCe39VoTs7PzonYuL69g/+J+2XZh2ECtvg3Nme1ozO5ArTYPL6TVoKHW1wng1epww5osyibQkNu4BI2mVkp9OFRHqayS8GuvKG9j05Qety+WBol4ko/tK+Jbm0NYn0dYnxVySmJKpdbxuZ3635H9mzDM054SVWE4Kq4xfag8phWmGpJNKT+NDOff59649ec/A5IYL/zjF+B3LrtMzTy3fj8b6S816uKll1468nFHumQ+DJOSTFoWSMJJNkmuoTvpqczSW2vI9Te/+c18e1C95Xfwk5/8RBq0iE996lNCym2QHA9TZw8Gqe/iFa/4C1x4wX2BPbfh0+9+B84+41Rs2bET3rad2HniqWg0GmjddQf2/OIGLN5xK5y0pzJN4+mJjCpTP1EgHGVk1FY/M2kgSsT6Ypac9VgLG6Kkmz7pE1nb12ijrLw/qqlmFTl1IzjsvM86SNKe3NZszGN+difmZnegXluAi5r2WCYyIx7iOQVq9ZoKi3fUCM+E4zzZbc4ljaSTPVs1ukj68nNLT9JuIem0kHSXgaQFJG3JJeUs/binxoeGoY/ZRhMzJJIZJDqq1WpJtqnjNhHUFxQ5ndmGeoPXt6JeX0BYm5Gmu2FL6q72vBpvqVFEzXhU0/ykfKjqfu7buH2o1gbhjOScqhB92hJSiaoq7R6fgJhWHlOFimtMJ6pSfoWpBnsmkl5Pmlt23/10nHD8btx1221SG3zP+94vc7MNOR12cJ0GHM6SuUGx2WpSkkmrAJVYTk8iGSbBJKjM0mNL4s31ff3rXy+387NRwaUqzOWrX/2q2Bce+chH5u9NkkvCu3v37jyuaj3w5Kc/FS978cuQtVbw1tdchQWSmNYy7tx/AN2ggaVuIuR728Is2ov7cNsvbsbigf3wXUdKodOAYaQUYzyqxcfYiqpRT8c931ZM7b+fUZWsYeta2ojkZdLsRFIax5qYNmcxM7uAoDbHPkYhnxFJcsYAqRi9uI0uA+uhmtPYDZ+JnhrnxJWWAGTpqnWw10vilZDBcxLJGfXcFJ5Mp0okXozEk5m2rZUVLC0vSmRUvU4yGGB5cQk/+9nNWF7pIurRjxxI6Z9Kb705h5mZeSHYcZrJunPh9eKSbwddps/JpyaoPGmyl2azKX8ftLtwCcImAr8h+aZwtV/UVf5jEyVW1qg27PuqUGEz4IibrMZ1DGaWD2rc88pQnRlubsw2fCwutzHvNMEBKv6OuwFuD7+Jl7B7axNf+9frcN9LHgAPXbRqQIM5fh1gqVkDWiQey0M//8FGShVzOO0yOkkaSRsfs9aSOZ8zTs283/3uh/e///1y/eUvf3lpyfymm26S29m1b3yd0IorlVU2ZZFkcoEmxYZkskGJ/+ZB8bOf/azcRoJJIkuiCk1i+Xjz2iTIkyYDcN3XAvY4J06qxlnSEsjyZ0+Nvjz3fvfDn/zTPyDsdLH0mn9A78OfQPTqp+PXJ80hS9qYdV0wYz2bb8DJVhAv7UH39v9EMhMgde8Db2Y3Yqct/mU1CjJF5qgJQglcdHoJZg5xlH6+m8p02Lse3Znv1zJPHIADBC9/riN6YJ9sxpp89Ju20rAhtxsS6pgAexNe7/kD+1CzGALqJamKXWL5PM4QZ6lq5tF5mmm3I1OdZNKao2biZ06ar0PN9XUTl+4qlxxRR4u4GZpOhnaUYWUpQxDOY2HHKWg0F9DjlCTaKlyVk+qLsqfUPXagK3DyUoTQ035M7gNkDVJpCOJEezetqwxVxzSMcdRpgsBLZATosruIHtXVNEQQ1eA6TQnEj90UPT8C4i5qYROhNwMv9UR1dj0fqZ/Ifmbfr75n+olqAAAgAElEQVSJ7Tt3Idh2HFxfZZbGSYAsDOAFTTRrC+iuLKG3tBdJe1nlsAYhUq8u+cvG35lpz67HhiarWz7T7NJ4eo3CyW3XS1MENZN8wAiqfv5pqr27PclEdZEmDrJYfXbPS1EP2WjFLNRarimr8bDQ7+dXXtMp4AfjeMw0rV9ZA+ShnvgM+3zVrPwK0400Q73ZlBnXWZSJ6kLxYKc/wyl/OPWCu+PNH34XLv/dx8lxqdXNZAfuBCFqToRuYSxfPx8wWzMp/c53viOXdg5n8Q+LZHASklkE1UwSRqNmfvzjHy9VM5kIwLK5DbtkTpLM1yABJhEtYhzJ5GWZqlssya8VJKRrJaVE6HtoxRFqM030VloIpK/eQbhjG6797GdwaljHndd8Gp/+3/8b0dIytswuIG1n2L3tRCzftk/cmszApYeQ5esDS/vxsxuuRzcNcdJpAby5OcSJCjAP6AUUhY4Te3zUhRFtbOe+GaM6DONUsCyJRPVj2Z5laZigdhmpCSEqJiwf+hZ6PJlwwdtCNt64nhBKkjqVABBJ2Dy3SS1UXDqF6qKnbunosHgmtRuCNNBwZSmu3STBgf1L8j2wukFVMEljObEIvdqqZABYntGyz4tVB8hIpRhkqohvIqWQl7IDGRGapGo7k/QmqSsEkvsWsakKqe8gdWpCkD2/DsdNhKwvRiu4a99+tDpdzG1hfNQ8fJJSOXS6lJwROBliJ0JnBeh1WjL+lNvd8fyBdTaWCfpb88/kevnJQt6sZO2f7Fn6ZlsM/B5MQ1WaaYcqrQOBeHnTKEYws2UtP8cKFaYCFTGtMNWIO12gHqBLDYtEIfDgpj3gwBJ++pmv4azHPRSPffRleNM/vRkv/qMXIuLB0nXgtjtYcD3syZxcGbV9qOMIwaRgyZpElVONqDSaSKRxJJOK54c+9CEhgezwn0TNNCXz4447Tv5N3yqVUps0btu2TS6vu+66oZ/gUEnm4YRR5rqtFhpegHrmyozwz37hi9i1sBW9z/87rv2r/4nWrT9Gc66J7dt2YW5+N9o/34dasA3deFm6usMgwPzcDDqtfbhrz63Y69ewUHfRmLkgJwUyN0gTAT+fa74OMERiTJZoMQpKLU5OLFPpismsqT2s6lJVTJBJM48ij0I6zQlYGuWv1VfklGInIjHVw6zb95pCqccZy9w8cas52hag3pf3G0XVdVwZw5l/JicVdXWAmLYy9KIUcwtbML9lm5xgchwss0V1e9NIDFNk8u0kIz/19dRVlNRRn1G+16AuHld255tmMJeqpUymcuGnHSnr9+h/9SM49HLWQgT1WaR+gPmkh7v278HyXXuQODG2BRnC2jzknNYJQVHSrdeRufPieVW+1jYc9OQEGVp5Xv29GhU71pcOUo5atoipqKa0MWmUeXx9yXJ2hJjK9+VxwlYiaivXZcv6uWYqHMMoqqQbreRWxLTCVENGTroOlrtt1HyGVruoc/JJ3MPKz27Dt198Fe73Vy/DFc9+DhruHJ575ZXwagHcqCsHksAJ5ECrDkqKnB5ssLrxido5nGUkj6rjOJJpvJwE1UuqietRMj/11FPl0vhJNzs6UA1KVPXaaYLejI/Pf/nzuOfZ90D6q9/gw6/471j68U8xiwwzx+/A7K6dWFzpIPQbiLopvCxAt9tGih4avottW+fgOC2gdTtuu6GHmXALtu3YicbsVukEj2OWgX1FAJNYOsQPBc6Y/XcZ8RrosIajFUA1NUnGSrr9UZIBS9dyMkZiRvKq7AKpPvGK4j7xETUuU2M/M01sIkeNEDWRa76eO89YJp4UtLuRfi+W8qmu+lLqlrxOx0cQuqWky9wWRV3ML3jYumOnRC11O13VZe95aLXaaDbqpdsiL4Fb9xWVVGUhiK3tRHLm6tn5vhDUWn1ePKJJdEBm3tM5UJ+ZRc2vIUoTuEmiPKJxD+j1ZN8QZE1RRf2ggca2XUicBPsP3I5Wbwnhio85iYrykHKfghiB70r53mO+aNiBGylrBRusTIXGXBablewTZruCY7ZhJxokpnacl2yTRNuRaGVwXRnRLNsAKke1QoVDwTACOklKB0Y8fxwqYlph6uHK+MEAPn1u7MuNI/jNJk477TT86M9fi8UTT8bcnzwLv3/5H0jm3wv+2x+jUWuiG0VoSAlNzbfudrvyUYc1dowDiSEmzOEcRzLLvJxYBzWTvlY2H5WV8TcjMl1Nb9TqWHZ6+OKPv417nHgycNMtuPbPXos7vv891F0PwWwNS36KpbSH5U4HQTuRAUNpt4ukF6nYIj+V8vz2hSYWF5ex97abcUdcR3LG2TjhbneHP7NViKiQBTbjxD2J/FkX2GqpYytoo7vdqephgJBp8qJ9qiSK0BmZSRKqxh6pvWe6YcjNX9tkakqBP0mlXJ94hhil8FhZyGLxp5qyc5LFEhIfBL6QfZmiRGKWB8lbByYrqsh8vpkFTlGaw+wc7S8BOr0VBKx6SBlclbeLGap9OPlnN9vNhjwvMwqO+btOxdfr6SapIGSjlYu418HygX1CtoMwRBg01LaHL47iGJFquoq78KMO6s1Z1BpNmdS0dftu0HVw4MBetDptNJo9NJiB67joxqlSkqkeM15qJlaNXCuL6HXaEgtlk1M7ED+TyViOjGzlevPEIkkHbRFx1E+OMK+R6YX/7mZAL+6Kcu0HAXpJih6LTPV5bKvK+BU2KSpiWmGqkWSq4aJBlTRNRBlaTmM0HGDu9BPxgONOwjf/7l140H+9FOmZp+Gpv/97qIcuXvXaq2RGdtyN0O50VEi/7ws5NVNnNhqjSOYwL+ehwu6EP5pAv993vvUdnH3iKajvuQ0f/pOX4c5//yJ2zM3i53sWgTkXTiNUMT+NEHf95g40wjqy1jIc8U6morq3u/QVuoizGE7WRefXP8HtyQpCJ8bu0+8Fr7GNfTZIo1ROhg69nD9acbVVsmLUEhmWNNDwtoGXsZ4jjT+xqJiBtliKSqsJqlvr5q9tv6eofaIWqoYYbpNMussjRL0OskQ1FNVnt6MWNsQ+4YkC5+lyvprpPkCalYV1QNlsNLei2+uyvUmfYNakmZ6ENPebFraHrKusbr9Zp+iz7L+lOYRlUGKxJuY0ZrCRza8hFMtGC+3WInq9rsy951hPsTR4TWRejICqM8P3ex3ZR7BBSghrYxZ+UMeWLbvAIVV8breTIPQjIfK10FeNX3DhhR5qmSOfLeqsoBPHsq+xG5qKxNRzkSco5GNIzUmBWCuSgd8GLQhmke3QpSrdkZOuJInRi0iMAzSbAWr1vhe+QoWDwaE2nx8svFe+8pVXbYZv7HBvmArTAQZSp1RAkgzJckvGAcbcm/sOgoV57L3uc2ju6WH51J1YOP9sZHGG0846Aw966EPwi1t+jrm5WZnAAt0hLX7TLD1o1fQZz3gGTj75ZDzlKU/BBRdcgGuvvbb6pWwgmDb0gAc+EJ/69Kdwr1PvDv+2vfjI5X+E1le/ihP9GMu9BF0nwb7lGKeddzZOvOCeuO3WX2B7nKK1/062L0tJPk4j9JIEnV5XTlIYU+SHIZrRAXSWl7C83Ebq1mQsJomIqFyHWMaHKUnnKqL2Y9rEEn2iYhOUPPopVwJhkUAry1RGrKpRllROhYxxehLL9v8/e28CL8lZlos/tS9d3X36rLOvmUwyARMyISQQYkjYCaAgIAgJRtxFISj+FcErGo2KCgoiYbsICMLVq4CKLGETEQlLEgiZZPb97L3WXl/9f+/7VfXpc+ZMEiG5mUn6za/TZ87ppbbueup9n4U6qbrNZvCDN1Uz+zeabcsoTZ2XhDp01GEmzbuhGajWNsK2qtAtj0U2bItU0gNIOZSvto2UpRtTBeQmoG1q6EbhHpBDJ/X6gMPA4Jh76TbwqsrSq/NLE1gjagLUPt2BtxuN9yEtpgQsDlTQiQvLllURBLcliSNL0aQuG9qr9FpaJgF9lgDE16XjRjN522iqKVOfMg1xlPK1ASdQaUaxR2g9Nb4wIH5uGgXyJk7l4w2CTyIoDAYipAWYpRtHKxN/mDqq0leLb/LfMsVLREphm5UhYXcGsA1XrbYGtdr4D338DuuhrbMJxzzQ8f2DUcOO6bDO6EqylE881J1REo5HQarm6KQB1rgVJM+8EJ27DsOaX0AW+RCRjtwxcN7O8/AHv/d7+MCH/hbHjh7DsWPHMTc7ywpbwRy8Jc/H/0l985vf5Ee32+2+Sn9YD1094/Kr8N5/+j+YGB9D8K278JkbfwfGbbdjvRqhm/ow9AYbpts0gg9T9E7OwkgDBP48HFtHprsIgpB5goophTFRmnIXy7VtNCKB3vwcjrZCNBMNiV7Bpu0uDMtiA3bN/CGTc+7n4oe8VPPC6omFM1m2rEuh6k7BmVzeOe1bRlEHMpfqcB7HEzBVi2OaqIe6tvz16D/CsIbko1osdqLPFXl7RggUFWTbSR1Eok8QyFFM2Tmmt4zCAGmWQDNUmMhhGvetriGOK43DhciQiRw6x3iqSKOY35NH0yvG/4P3mjpgd9WPH80HYjblsnFXnAPxyaUgZRDLkajsygBOTCKvX4on9XsRFCWApjvcNSXRFL0mx4EaBCwFg0rq9EJzEUUJql4drl2HsFWEwTx3VT1KGsspPEDlvqbgdVH6HFqa0IRRskx4xqB8gK4h0kSCzCzl40AM3mifqvkAxUHeBoGBnjm8j4mCkcYxFN2GY1fgPFgUlGEN62EoRRDB5SyuM90HbFgPXfHJ/Bt7ce+v/hwmn3Q59Df8MhTLhBJrSEyFzbWzNMNnvngr7vz6N3H8wEEcmZ3GwQNHIPwYJ7otiDjm7kRZZNZP/34os/YfbUUj8bLLVn4eKfWGFcemCVA3K8rhCWnOFCgZqpqFG1/1i/jld/4ZJuIE+LfP4vM3/SEW7v0+SdmQ6Tr8OINv5YgXQ7TVHJuvfTw2PmknNQ5RNxvIMwsRdQI1Ai6CFdyanrFgR9VS7lz67R7zEUUcsY1QZWwd1uy4GI2Nu6BXJ6AS8OKRuoDg7qLOYCfNciiaBodfJeFlkq6jFANE9j0EmCzAOAmRqohzem4FmmpAJRAY9JBFAZrBcUTkFZpnsFwHpulBKDbS3CaGJJJkAa7nFIKkDLoOaUJPIETJYWUyWGGlsX3/d4bZB0XqMiVWKRiKGDuTh2lCop1U2g2V6UNSbKUW9IGU7drSLOSxMe1Lx6tAVSw2oM+FXoDnnB9LEaQlkJKdY3C+PaPGotMq1Li/rMByfiV3THtdtqViFwBD55x4pXBQADs9SeulIp1U2melcR/gc4gCCZUUg8VtQbeNsDULhB3oeQy3vo1jRFNdQ0xUISWCpsRIgwX4nUVkCe0Tm2ORK94ITMdFRtzOMOHuu+NUWKCpc6s0RxJG8Ls99DpdOfZPe8uSn1aKoMjHlsR5aRbJiFhySBDyZ/mSVgHJ5XNJ0MQepEUnloyr/KAD29PZ17Xth9iw/jys33ge4kiFYZ7ZHblH+/n70b7+p6thx3RYZ2kVsXtbxmFs34qWrqPeCqBNOBCaRDgEIMjS5ulXX4PNm7fgC5//HJTv3QPTcnDPPXsxGvYwF8t4SgJK1AUpBVJ0Uh4ErMP6wYqAfrlNB7dr3wbHilHtSNjjux5UP8So4uGW//NhPP35z0PVj3Do7z6Kb73vA+h9/26MVyz4qYIgy9j2RxG+BE2FTQ69lx6n8CMNmuoiJEdSU2PBDVEiVd2AZursVZkhg2lm3PWiLh5diyS9Hk7s34NOL4E3sQEjGy+A5dg8HqdreMJ2BnUUNWlmnuY6d7wIRBAvkbxSqdtFFAQYxNtUGERRcg9xEuk5Qa+JmWOHMT99ApHSQ2txEd1eG5WKg3XrN2PN2k2oeAY03YDuTTIflkVCJNSh9CHqxikpr6tp3vdXOF0QlHZpKgaN/QsupyZ4X9B4mpTsxCcl6gttWxoZU/c1Z4V+odqnSEzNHhg9ZzwmV5Vy1J73b6UxvDKgWuKghEI5j/s4KZcnbALrxBsOgx53Bt2KAstx+CKAOOSC+bGQDp48jie3AA1ZHjItgaygiOWg6FI8ScejsBzEsY84UaDFPk31oWgW7x92HaB9abjI7JRpEnEao7kY8JSEBFEkjKLvkIplsA1VjAQJAeo0YxpEnJAnasadaR265JyynVcmRZy6vjStoU5yJvcvcYVLizDeTwX9QYq0Vo+AZQFV8XoEvCn3n/jAOMvGxMMa1mCdNRzT09Xww/forNLFMLF1iKOHALcG69ztEK5djE/zIqUGfHIcHx3D1nPPZdPpxYVFpNRtijK04pDH+oNdUjp5nKnRpmdblarr8lb6x5afWzcGQlthBb2W5HjMc56Kf/mvW3HlYx4HK/Rx8M1/gjs/9o/wv3sXxuhEbyhoR2QixUgQQdJDFueIDAXGhjEYozZiv4e0F7HCmUzjKUiIRs/UPSOOsk6Z6JbFYMQmXmYmjeUtSoASGcJuD2GnjbTbQisSsC0TtldjyyoS64gsgipklzRXHbZr0hSNh+LkC5oxz1EUSTsqNN3lC6QoDjA7ewJz00ewuDCN0G8iU3K4FReNUYq4dNgsP6Ss9m4LQWsBpuvxeN51qrCIDyloROzC0skZwoZpCmi6xolYlCikcD590eXkSFC936nT1AFwUxzbNJYPgxgx8UpVDY7tQjMs5oaSK4GqJez9STcJ/Og9TAZ/1MVLskj6ZpA3qFqmSkkgqyrqgO2TBPUSkGUMLBUGlPmyDm9Zfc9h6nYKSXNIGMBJ1wBKfpIuHYoE0ZzFkUvDekKEtK/o/TLJJ6bXNg0dhqYwKCcrJxIKUfeZLipI0a4bGm9LjYRFueSvmtS1zAR3tf3ARxKFyOiClUftCdtMxXHAxvph5LNwjH5PHXppYar0OaTlSL+kL3BXl3jFovCghSjEW5KWoTJvQyvAfemuIF0V8kK9T9tUNVQOhaD1rNXHMTI2BcNw2dJC+eFp0g9pPdrP34/29T9dDYHpsM7aYgNqug/aUOIc2pb1yCvWKqsjuw/EKTzvvPPhmhbm5qaxENKJJO2DUgKkdNIoPU9LTtiwfvAaVCGXI83BCwCKG7UToLp+E17/5zfjHW/5EzQcC8meO/Cdl/8G9n7ps8DJExglUErc4ixGZhnQLRthL0aGmAGIb5nIJj04o670owwjVpFXKgZMS4dpmdAtC6pFfpNFB1QzUVFV7hgmoQ89VxicEncyC3oImzNYbM5DEwk7PUhvS4tBYBkxSiNi6VnUd9yEouWFcX0CVXEYgJF1UHN+Gq35Ewh6CxCxD4gQ09OzcCs2GiMjsBwTWUoJQm10FmYxP3MM7W4baRJipOpBMU1kCY2pqXNpFd29lEVJEgSqEjAO/MwpRQwaJWgl8MhCn+K7M2aHChk6YVk23+SoPWcQqKiJ7Jgy2IYEbJCxrbIzmfYtr/h1lQGRkqIsuRIUyUylkT9HfxKIXfbYVT65Wcr2TmR6z76eoY8oDhlkU2eXQgc0RevHrAoO1JABAAxQ80L1T1GhtO6ayh1W6rYSZT2Ku4z96G96kcLEoVDshqAjTwMpbWLeqMrLnIsUUdiD320zTzcl1wESTBXRqLJ7TtuU/JPzZVz28gKt/B2lbNF2ZpsuiD5wl1xUaRcmr7PL5xVJXEK+Lm1TEpFJv1oN45PrCtGTwV1k9Qw/PT7az9+P9vU/XQ2B6bDO3iKwI3IEIoBod6CsnYTqOKdfHR6NKWxCf+kll+DemcPwF7t9P8TBNKiVRtjD+sGqFHtggD/Y3x30b8vDRVc9BZ/+6MfxvKc9BRp6iD/+Sdz2s7+JtH0Smghh0tBdxAiRwddyZLqBLMnIwBFCTxArOtqmBb9OhugeHPL0jFM2Undcg83PVboRQZM6fgbxWg0J1KgryIArZ4BB3TTqkilZhLjbgWtknIO+OHcSYRDAJkEQjZI1E7lqsBqalNM00s04ErTw1VRyjsE0NAdR4KOzOIuwtQARdiDCHoL2IprzC9LuSaQIw4hvdHxahg6RRAg6bSy25rAwd4JHz55rwXIsBkYEZFTu/qXLjtmVN1Eq+dmBSRSRo3lfXBMnGQM8163wmJs3hpDgiJYlE2G/Syd9NUVh6QTuxpaAXHDkpwR/klcqhUDyvgBlDExJcR4z2OWUKEVbtvxY8Z0uMhpVG1BJwZTLkTh1O7krKxIp8OJ0VI07xfxeivQVJWDKxgpFvCqBXE2R3WT2d9VM9LoL8jkFyFOK9C+QYl8xkcZt7h5zV7zkiLIyXtptlT4LBFp1XYOuycdyQChxRrPlWfgrv1NKvi5HiAoJ2hNO3crkBYNuFtZcZXSp2u+glmN+zdARpyl008Xk5DqYVgUp0TD44uHM/uJ6tJ+/H+3rf7oaAtNhnaUlu6B8ctAyZM0ulNERKANJMqtWLi2oKp6HH/3RKzE+MoZDhw4jTWJUqh6P9enE4lW8voDi/0UE2yO1BlXXKOJgqSgidP26dfidP/0zvPemm9FoOMCJ4zjy6t/HN//sHaDdmLYWEGoyQpKGv8LQEeRAQPGSYQgzV9HNE/SEghNZjpNqBnfEg6cbSMIYGhmkOxbbKGkMRlUeRRN3U9MLL0gk8LwKbBK1EEc1DBmomBqNfhWM1j3EvQ7mpo+iOXsSYa+DiDqs5OqgUp4+KccFv5bEfbJbKYR0fjCJxp/ESHpNtGeO4sTBfZg+fAh+uwsyOhp1bVQrFbiVCknHmX6QkRdlFEPEKYPUudk5nDx+ApquY83UGhbrEDAlEMTj6gJS5aU9k6IUYErrc0NRAEOUPqYFr5G6r5ZpswuBVNsIHu8T+iKwReJBAkOqqhUdSTluVtmwH4VdkgScUsCTc948J0XlStE9LZT0pAujfZfFDOZZJKVKu6XVhFvgKHmNqRHUKWbxV9nxjCP0Oh3JlRUZdyfpsTz6z6WVEncTNTnmV8gvVcjlpsfldGGhmYj9Dq8jRbpyV5Vbybo8TgxTcmzJ0bSgE6RMTSGlvwGT3AqEPKbJBksvJi6iGNNTspRSCMLKOjUZq9fnmIpirC/H/nK7UQdb7XNfS8qExv+WnyUh93musTirMb4GmiaPIzLh14bA9IyuR/v6n66GwHRYZ23xKD+PmUOYRAG5eUPhE+z9HTTyjkZ3u87fhauvfgps28HJkydRqVQ4jYm6XSSIAoOpsgP0g3mfPpqr3F7UjSuB/to1a/BLv/iL+OAHPoCrLrgIyNpo/eMn8NXrfgVi3z5Yjo7MT9hjMhIR0USRhCmSHAipC2nqUFLBgK+rCrRSBQeTFEeTEN54HROehyRIKC4KdrUClUfBFo+ECTxwihF3v2i5VO44ERBJc0iRikj5MU6lgihj5ihEFCDuLSDsNnnUTqN54hsCPlR6PPtdWlBylbt8Oft9Cu6OtuZncPLgvTh41x3Y+73v4fihw4h7ITRFx8zhe3kUbVdrnBwUkNOAHyNLhfQXzSiE18TsbBPzcx14tQbqlDnPAEU/5Xhc+X2oqdoS4CsN8AeAKYl4WNDE3bysb1lV8kQVlMlFJShCAQLBPErA5C6pyBOEtE2oA03qcfJI7XdORd++SYhYRsRyRxbsDXq65Cup8Nfk8hajeF2XCnzqWFKXmmgbGfPEZTQoec8q/QQoCYypa2jQiJ15vypfUAjV4Bsn9hPHnEz1C/sq5udqsrvO4E+VKU/lFwdzeIu/ka+pCnlj66lcXiAIXneN93HJJx2cyPQ5pggHts/S30q7KbXYf2XHlLulJVWDgKqmsKMChwCMTsKrjjAFgXm1qiRdnMn1aD9/P9rX/3Q1BKbDOmuLVMMhJbQkJBjpQNUtKLZ5n2rfweKEmjzn7ujjn3AprnjSk3gcR/6FtXqdeYnUFeFR4kCs4LDuuwbTi+hGAJ/V4YqCV77ylXjPLbfghS94AUxFwcnbvoK7fvetOPHej6CKBPNJEyGNQoUJN63wqD6PKF40h2W7nB3OHak04i5YbJnowcDxVGAGOSbXjWHT2Cgy8s/0PDgjNZi2y0pu07Z5f5KSnfazRl1BS0Pg++gFPqua85Jbqagsejq6GEE3dLiGAksVfE8Kf3p9v9fGibkZiFTAMSswdJcFM8RPZHAqcrQXTmLPd2/Ht//rqziy915E3Q7SIEZzoYXjx2agizZSel86dg0Hhl2FZTmSJwlg4Wgbk5Pr0W6HuHffISiqhdHxKRmpCer+nmoTtdr3oxQfib6JP00ICIR7tTHeLwTySGHP42eR9pXkpllhgCU9VVW+SCNgSr6hZAdFdkYcS6oQoO5wshJ17EzDZlArwwTyJWCaxZyuRGN5Ho1rSwry1daBuqXUKTZof+kqA9K8oBnYpIoPeiw84phizSjSugqDJU1HIiSgLXmfzNpRNKRkHwUNNdtiUBoHPjsmcIdVk+CVkHPMHVKNhXPUWTbZfqug/nCC1pLnKqXU5UUoiFoCS2h87BOPeVAIWO4HXRfLPivljZ5Ln5uE4qaKK4oycKDsplKRYIseY1oeRhrjsJwKpHSqeM0z/Lvq0X7+frSv/+nqrAemD3etxuu6rxPFsB6kKmwYe3kCI0+Qh6kcw9sWn1AeSPEpM/CRd7oQhgq3MYKLdz8eT7j8SjTsER5TNqo2ezW6VZcBDZ0sNFuedEzqvtBJmjoTZqGa1RTmsdGUshi09cfXWPFFRK/xcPulrhy1YzCTuxAslX8v3QpWFj2+FI7RunJ8JXl8Og4ryOkkff3LrsPHPvVJPPclL0a95kH70m3Y/xc34fAf34L06EHkqkCUCxgKRc9SbGiKRPH5woNoegQWYkHduBxJHiFWEwR6Di3XcagbYs7SIDwdO87fCs3IeMxcpU6pNw7HtmAZ1HUiH1PBAhgSx2iWDS020CXLMBJHUQBkuwmLMvJtBe24B8+cRH1iElltFB3LRlarw61WoKc+RPMkosN3w4maOLznOwiaxxElHYRJwIB4rtnCwdv+G1/47Oex795DCKMcnTRgRGUAACAASURBVMUQOkxMeKNQenRBdRTz04uwVQeebaLq6VAtA61AhTd2LhJ1EQePHcDGjetwz913YfrEMdQaVaJAwhvx2G+U0BaNmJM4KyyPVPby1IiPS1zDIimIgCdxcwkwG9QtNGwe2xMoXfIPzQuPTOmd2R+pc+eOfZc4NYl9WnNKkupJ7rbiwKTReNhBq3WSzeKdiscuAmSdxEbx5D+bJ1AopjMVMFIFsSrtjsgGi2gQaqE8p26sQlGrBUCXWjPpcpBz91JHrpiUyImM1P1JhCyhZYlpFIJc10D9bJNAKZEmFBO5YvPzqKNqKCksLUGcK0hIFZ8G7EJA1CDuR5JbA1mD2SPc9SSqBoFi8oLVdVoOAvYBXOIDZ1LARF12EqUJsggTigSlosuxooXcTHJdOYY15vXLyD+XRvf03VWSHjLB1lO0LIZpSEZpwS/ViPtKanvaUrmKiiYQ9iK4FQ9jk2v5O4svWKjDzdze4Tnooayz/fx/f8v/UK/f6V536GM6rLO6apmChdSH4uhQ2zEU4v5pDyyth05QgjokxCNrdjhrXbNtrJ2s4sdf8hw88dor8f1vfxvf/M63MXviJBbmFtlqan5hHq3FFnISggRdRFHM4ztfSWSqkKUyx4s6JbQ8K0d4q/38cFXf47LoCA/yalHwEUvv0dLXtQSi9FgJunNOmlGLlhQLhEyDgemvvPq1uPbaZ2Pj2ARyAgxRhMPfuxP73vh7iKb3w4XWF5/kZX+tzDov3l92ozLuSKW5TA+nST7xK6Mkgm5JQcq6ySlkUYjUkOCOltEiuyiSALGwpBC4kQpaTZGnBlv72MRD1RUGGNTlIw6kiGnEL1ON6Dm2qWFNtcHcyzQI0Gt3kQQhbEtnnuLCzCJ6vR68+TkIswL3wBiOHDuBz33knzA7O8vbwqzXIPIAKnUakcD2QiiVCaS5iTBPcejYEfSUFOddtBuj4+M4eTLgcXiWy9HwRY/bjc9/8Yv4xje+iYn165HEMQMl2h8EMonnmEYEdmO5T3Jbgvl86djLywuLPuBcEuQMitTKY7M8Hgatjvom8XTs0BhbGoEOWCHRaLyHpNeCURljkEv8TRKEqQUFgfZnmMYcRpBnOgNeVSk8O1nAVLQGV5z7Bk9eauFLShzTOEs5598PI5hawBc4iqExyMvZOcuQlIwyo14qnJY6+o7LIQtpJj+zxDklgZSIA+4Qa0qx/nS5mVvQjQw2+bES0Od9wKROafckl3QFRWFp2VmcJfL+566s8rOIgQtY6V+L/rIKplcofTs8uhiR3VV7IB0K/UcMa1hnYw2B6Q9ZQ87hw1TFNy+pVrNuAsMia5ceRJIUEYoPrIgrBlcCGzp5ZmQGT1/wuo5xr4InX/lkXPqES3Ho4CF851vfwbEjJIJZxNzcPOabTSz0Oui0WgjCCFavB4PECyS8oJOuUvgqKgqDujORo1omMq3shA6KvsplphNgvxTJG5WjcYtpD8TPdV0H27Zvx/XXX48nPvGJDA4dS2eBSbiwgLwTwlxowQ0i6EGKTFP4ZCsGwKjSb5GV1jglOE374JSsfmKyiaJkSyNndfuGtZPwqPNtaqg6FM1oQxUBqOWapRpnwxPIU3MJDMirKElDzsxPi76WU60DuoOIvCi5G6bA97vQeoClSJ/ToLWIoNdhPmNj7ThbSFXsFkTURDDtI04zJLYNf2YWDdWHZufwgzZ6SQ+jEyPYtG0UE5M15GqC0Q3no1qbgF1pYK61iOOzxzB94jC2bh+HrQke6zcaY+j6ATZt2wbza1/DnXfeiZ0X7EK9MYZc+HxsUQxlozFO+h4kieBRehQKpGpKfc9TREV9WsoAMFrtool4shi4QCjBFF2QyN1EsJ94sDoDTqYWEN806qDdNjBWqTPQlH7C0maKMvylAX4E0AUAdQJVgykAkKZJBaqStlyrcVDLTr5pSGBKFxVRmMEPIsR5F46ig/qjQte5wyhnF6XlksrHETl6MCXAtqG4VSRhgKDbYaGVWYi9dOq4Ei/ZNLlZrFB8aa7A0CnxyuaUJk2PpK+pIi92Od0jl2ECfZ4rTVXUYuQvlraxehphlHQ+UDhqVun3UkWR3rV0C6MMhlOB41ZQGKfKfTec1g3rLKjTnQ+HwHRYZ2WVxt0JdRGiEJrr8egLPomg7Ac8zl+mOihOhPJ7fwmQkYL83HN3YMc556DdbGP/PXvx/bv34PjsNGYWW1icnkGz1UQcp1icm2Uz7igJmd8WdXweoYJfUvQ7JaX44UypsgvWj4IsAEEpWiIAygbukOk/ckyvcVRjvV7D2rVrcfU11+BZz3om23EtlcBicwFqRN6iCTQ/gOh1YJgacrK54ZOwzG1HOXgszqtqYZqesxF7xv8lfBMshIop3csAgiSHN1LBmFdBra6g7iioOA4fAuQXmiYqVMNhkRyDMWqhcVcshIqEu3Uk3CEVfL1CY/IcGZns0/5SQmTdANF8E1mnCyVLOYmJuKlurYrcqsOpV7GexuJhgG6nxTGULvFXqyqmrvgR7N1/GPfce5gYjBidHEdlfA2cNQ3Up2pQ7XGMT21BrdrAehoT36VjenoGaybmsXX9ZsAg0Onhnnvugd7tYudjHoOvf/3r+Np/fBWTk5NojJiYn59nsL5xw1aM1MdgGh5s20Xgx9DINH4QmBb7hTP1qUO+yolhcExXJksNBk6Uuf4M8ujCLi8E/eVrKYKFYb2siWrQZcEZXUDyKJu7i+zvxPs1J86wpvN4WyGFPls5LWX75/nyk9cSKEUfvBmGBWELjomlNKwsorCALl+saI7H3FjOci09RNlDSZMAmGgNmgU4Hgyrx8CWHAbURMaCQk2gkURKc+WYPNc4IUwhvwVadY4+Vnk9yGVAQFp5MZdVKP1I1kFgSmr5rDDIF/lS/GrZMb2/i9el/aMgFkDFrbA1GgnFxECvtNx+wxrW2VZDYDqss7q0TEGoREh0GzXqcM0t0jc1FPc+/Ezvq0r18uAorASpioJao4bHPWE3Hrv7Qkw3F3Dgjj04fPAQZuZnMTczi976dWiz/+QiOt0e/EqAIAg4VpG4ZJRHzuPCQsxAJ9KHu4s6yBUqvRpLAQaV6zqFmblglbfjOgxMCZA+45nPxJOf/GRcdtkTECcRg1cSj83MTGN0dLRQXlN0qEbtN2IZwg+68PUcia5CJAQ3RR+MYACciqLLxqpsflSGVMl4jJ/kGvMDfTVDrAObtm6CoQMVihaNe8hMnR9rG2p/GcjHlEARjfvp4iGGAm/EgZabnP6UBD66cQ5DaHKESjGmpOimHPUshd9sMjC1PJuFMCQ86WY6tIRU3A7FxUOzIli5dHSgbZhpGtaLcdg1D25tDRobtiFzXRiNOka3bkYctJAaLqZbPibH69i2cyfiNEGv18XUJDAxvhYzYoatgGYWFrFt+w7s278f9+zZg+/dfgeuueZyeBUHC0wvmWZP1IqXoeLVi/hQ0QemeaGcWdaZU049DgaPR71wplAHnjsInihBjf6WCuZJSIAlpf+cstbrUNZ/HZZuFYlFKo/9SUyUZjpEGiJLdQZ2uSYV+vzZUMqB9ek/G2VHkaYSuunAEoq0FSNhVxRAyWJYxFHNyTyfdw53FTWmRghphk8Hk0oZ/A53HlU/QBYJmXRFiU9hxDQQWndDl6K0HDLQgF0TrIwjammcLziIAP1tyJx3TeuP8UvguYyjl6/SxS6KH68sxZGeyu+jbq4Nt1KDZXvFhXWRESVOpUEMa1hnSw2B6bDO2mI/wSBH1TLR1FLknoV832GaMUPdsqHojBTz4AdjtJXnZdApq5PXjU9g/TWTiJPLMLewgMOHDuPePfdgYW4e7fkFBN0A04vzWGw20Wm32UCdgKjf6zEvlYzGoViFr+Tykaky4J36QH6+v1rt5Me2NwM8O+rqcDSjpvPPpIY2DenPiEL8tGXLZlx00UVMcdi9ezeP8JlTSNGMSYywE6LT6cgTM/dvtL5CnQQ6ZO1DQhHVc5Gygbvo8/5QMjSUge1dJN9QZy/NM+5WxkJFRKN8oWI6zmBOVLF+8wakeiwFNiKGYoI7mRXHgOk60F2XVf1kuB51W/AX5gACL2ItC3Mo3lLEMRa7bTiqyY8n1Xcc5mxqb4yNwMwzBqaabQB0M1VYugK/1+UxMLIYpk4WVSaPlpMk4+7p2NQIqg0dilHH5OaNGN92AfLaGBLNhOfEsHUXs9OziLMAVsXD+NQa+K2Yj5v6mk04OTOP9Zu3Ij16GLZXwZo163D4wEF899u346JdO7Fm/QSr3aOog5nZEHbXR8WrwTJrRVd+afTdv8gqeafa8lH+KYIGIZamCoo0HyJRFYrjNFZiCFLti8I7lMbjJL7hxqmObmeRjy3Lrcl4TRK3aSlSugDSFaSR5POmGvE2E2nVVPJeIS2s7vsjmUugSz6itgYrB4WMQqQ+0ihCFDoM2AhElhZW6Jv6L2XS5wRu7QpMlyYcIUSasABPpCrCNGDnBdMivrXDnVNFV7jzyU826ESq8fGNVC9UlezCf8ryrqQjqIXArOyYlt8B5d/j4iL2dIITx63CdmtQdJn0pBQfILbjOtNNTIc1rNPUEJj+kPVAxi7DeqhKYdPsBokp/AzCqwKhD23vYWhjYxD1CvL77Ln84FWe5OlMYGga1k1OYt3UFC7ZfTG6nS7mZuZw9OAR3L13D5qLi1hcbKHVamJhYRE96qT2euj1KF87QJpkRRpOzulBK8emGRuDq8tOYIMAFtwgEf0T2CCwLR0Bynuj4N8S+CQVsVqo6C3TZIDoui6DTUPX+ff09wsu2IXdF+/G7kt2Y926dXLkT1zPNEW310UQBtyBJABCt8ZooziJyrEsAWACGyqna0GKxnjZdKQcKrtUvNbF//g/si8qbY7ylOkRscgRpxqD08wB1m3fBrNagaHRNUmK6tgEvNFx1CdG4RqUjW9xWhPREnQCrV0KjQqQhW3E3TpUylCvODDVnFXqlKlumTmCuMOdvFShOFINI2vGGGwE1JFTidtnw8k6susdy/WwTLKlskAWp6qWQk/IizSHCFtoLcyxAKw6NYVaY4xN+jWtCig2JqYcdNrTyEUbjYlJCHQhNKJN2Bgfn6RUfua8Uvdu09Yt2HPnnTh26DC+/p+34VnPfioqposo6rHqvdvL0WrPwbFTGLbBKva+YGnFd5NyGo5pWaXF0RIfteA7qqVDZsIAjS8eGESqLCDTeMBtIgzbSOI6BNmFse2ahrxIcspDNo5FKhREJFiyHI6KpW5pvizmFcuWcfBGXWHiDaccLqBxzj/5ymYi4OOMIkypS65r5CCQMS+4LHZpVVS+KBSqAsN0YDtVJEEHCfHVsxS6WpOOB2HCbgQk5NKMlNeVjl5FTyXnRC9CFlSC05b8nNI2UZJlEa3LObIETFfnnQ9elCqrtD5LgaDr1WA7Hp/K6QJQ0wY42rky7JoO64yu0+GjITAd1tldjoHMF8gWO0hqJpTWApS9J2Fs2whltAZTCBw9dhSTkxN9j8MHpfpjT0gQlcs4Q7LqqdfrqI+MYPvOHbjymivRaXfYvP/AgYO49969/DOB18XFRf5bGIbMcYxjqXwvU2CYA1hw+UpxUtn5Ghy7EpglvicGu14DJ0CzWG/qgLI1j6ZyoAArxU0D1VqV/Rkt28L69euxafMmbNu6DWvWrMHmLZv7an0eTVNUInL2q5ybm2PQSGC2Vqsti10EljepqWNKgjGbfC6pG1skDRXTzFOqBKjSsFxGZNJ0ktX4Wc4Cs0xoGF0zic07tiNUM1SqLrxKhg0bJ6AQyCGAbdGI1oXpuHBsHSbN210TOdlLJWwECREnhCjhEmj3bHiOjURNOavesxrc6abhb9V1mMdHwJRAjetZyOaPsr16xTAZlimpgjzKGUCahoaqVkfgd1AzNbimioX5I7j967dicxBh43kXM1ex2fIxUh9BtT7G9koUo9rrCRY8TeQqNm3eiiMnj2JiapJtmKJely8a5k9M46479+CKKy6HW9c4JYrAK22XMOoiCELOTlfVpU55KbbRiwsdoSrLj5uBGhS+8fE4cGz196tCF02ZzKbv/552qsZAjnxRibNJaVaMZ9leTVqLpaK8CEuhEcWFHC3MJYqB9CI4feU8Xic6gBRpZWX3lMbnOoH4GEEcQ9flZ4q2HY3t6bWzQkwEzr6nCyUVqm5KkZO2xKsl71sy8SdwyrxaWi1W4BOXVJdhA4oEpNQQVoVeAEKFu8fEiO5vq0GwWYJTcohYMSUpLwb48eqp+2TpE0PdfBeaaUBKrhRoA4+TAQgPzKFkWMM6k2oITH/IOtM7ove3fGe6q0AJyuSXeWFhIxLZAaKTi6ag4juY9WZwaO+/orpwCKP7WtC/9l1o529ibuOXv/AlvPXP34ZXv+ZX8JznPgeNRuNBXMD+/+S2FPmSkrgQ21QbddQbdZx/7k4o1z4HnSSC3+zi6N4DmFucw8EDB3Fg/34sNltsxE0cwzLLnOIv6bXiKOp3PaUYyewLUDj7mxTEdDIm8Fqc9PgEzWP6wjrJshhE0t8mJiawceNGbFi/HmPjYxgfH8f4xFifS6sUwqOU1c4Rv2fMdjoZRkcbsltTcfl1S17qqqNgAIePHMFH/vbv8Dfvejdu//d/Q0JOBa4tHRFOg0yVYntGRohAxPBFxl1Iakz2AMxrOVpOhsuedC4Sp42J0RGMjjfg1hy2iqIOp2EosB1DipmUEO1UkXzLkXVQtDqSTg+9zjEYmQEkJvvP9qKU6RcV3cKYPomg7sEbs5H0AvhBAFfXUXVVhH4L4ew8ggjwPBeGZiCli4owhlmMcNM4hq8YMC0dLnF2ab3VFLPdWcwf+j4aIy6qW86FamhMUxC5AlP10OvOY6LuYbozgyhNYMOBaztYbPksEqp6dXgjY6iMBYiCWRzYfw8ueNyFMKxxZuuaxIlt92AbJqKFY8jdKszqGJv4s/G6SFiEZJC/aK4vHcYD3wf5AK/6lH0zAE6dvC4/n4QOKbc/15FmFPQaQDNiGJmOwO/CqXZZZMSpSMRVNiqw7QyLYQ9xlDIf1UgS6ORxShcuis5OCdoqFlblMtBx5ycS7Bp6Dj2TcamwLWRqDTFxVls+4l6ArpinyykpEtJJCGeSBwOg+Lz96RgkP1ciIVTsKoQfoNcjSojgJCUYsiucRJJ7ahDdRaMLJB+W6cHSqshomcl6TqULlx5SQQlX1YLPSt1aGRxLh4cgEVXGtOviKyPl0AKVM/dNFk6xcwQBfOrC0lieqAVZyp1W03BhmRbGJteXOw6m2k9qlt31H+Z77Syps/389nDXw719hqr8YZ21VZ6UNG3JezEvPA65u2FYmD9wHJ1jR1GhEw2N4vYdhtrzkTk1rNuwnruVN/7ar+MNv/VG/H+//Zt4yUtfzOKcB7WWZnZL3DXu0kgxB3EqlTRBRdVRGWtgYny0MM6W4zoejXfkaLzdanNHkv7W83s4ceIEd1PJq7Ic77PhfVaAduKH8njeYK4nKXWp40ljeQKsBMYrXqUPUDlOsfS1VGTnN6Fxq7qkhKb3ozE1SgV0Ya1TAha22Vkl3xzFPrvj9jvwkQ9/FO97z/tx8cUX4a/+4i3QbYPtdxQSRJVRPKuYLvI/KavdzxBTR0k32G2hk/lYzDJUNqzBll3beR0dypuve6hWK7AqJicz0U0zpPpeMxUeIVOKD2W1U9vVpsjRkRqQdSUH0rL4ooDU6g5FltI2DnrQcwdV14LmOIi6PpI4RJiEyHQDtu3BTLuy+8jcRZmMpKi25MlqKuquhzwLobCSX0fNriDqJoi7Czhy93expTGJemMjd2Utx0CU+exJmWcqDMNmo3wS4liW3G9hIGBYJl9INBeaSFqSSsAes9qS9yz5d5Kdlk7bQI+hxiEM3WR+pHQmyNgHdiUN8XS85cFuX1/qvQIUnCrOWXruSlCZD/jhUqu5/ExzDr+q4oHMoMvPAcutBrqOfFwVyUu5bSEl/jN1TiPyvLVZJCcvvbLiIkwpsv81PhaEZSEyTUS6dAtAf5wu+rxUaWlVOlgs0WfkxbPC0bR0GdSnUCgF/UZb4pSmIu8LoAb5v8smDXk+sCVUBrlMJ9BNDjAY1rAeiTUEpo/weiRcMQ4afPdVu5Ajr4THgjk6R04gn5lDWjEgzBTpwcPw5ppIN1UxNTXFr3PDq34aj/mRx+Cv/+qduPkP/xhv+l9vxMuv+yk+4T/oVZ5dNGWZ9RSP3PKsr8YlMEh/IsBJ3U0CWJVqBVNrJrFj5zl9Y6xMSCOYwVH58j271Ola1sEdeFSel3zbXEZQZumyvwFSxFEuuxz7a6eMIMtXPF08K3m+vu61v44vf/EreOrTn4qP/9+/x5MuuwxKEiNutqDS9tYKYNrPiRxYzqJbm4gMjl2DH/ZwotfFLMVLOjkmd2zDhsftwviObaiYMSzbYA9V26ZRrMrCFFaks+WURo0mHimr1JUiXiK5bvJYW2Cc4j1NkwVZaTjPnFJKnqKI2/bsAkTWBiZ68CojPO5N6Ri0KhxxatkmtDjjbimzKxUTqmkxdUCwYj1EngpE5DwgIniGBqdioa6omJtvYqHZRG3zDjRGN7CoSoXL3qOW7iKlqF3VQhB04EQWPNeVkZdZDlPTsXnrFszMzOD49AEWm5Hzg1lxZKpVLrcffT6CKIFQQ8AIWZVuu1rRhVT4okY2rZeDyLLKfb2av+lq3qKrgVIhlmJQB6s/zlboGJOdziQJmZNr5LYUzQk5yl5NBNi3NaPpAr9O6YFb+IYapkw/EnRxkyPOIgRhD5ppMZVAN2n/G6csUxkFWiaZkQiqn59frBdZcxFVQyfQmBeAk0b5iihM8EtRoc4/y89K8dkpaDHKQAypKIBtP/ygEA2W33UskSoyVclXly4uiFdaHxl/8L+3hvU/qmFH9qGpITAd1hldg/Yq+QqzbQJNlI2TpxEsP8aYZiJxgF41gXXXceiHpiHWb8DaqTX8nDCK8PJX/BRe8MIX4CMf/gh+6/W/jf/4ylfxzlvewd2/h6xOM24qQSSBpiAK+KRIXU86w6aFSp86PcTP7Gdv5/Ikzyd6BQUAUzkrvGhDMd+UnpOk0k+RR+3Kkj9kCTZOp/Qta7XtPvDXZf8qjfppee763l0MSm+6+Q/wqp/7GX7uPd+/myNc14zUodrm0phYU1eRp8mOFAl+5npNLIgEYTXHxIYJbL9gJ7Y+ZifcqVHERg5LqRQdT0NmuBfxm1ksRTm6YSIhcCaKhBzqpKpgxbYfBwj9iAEtHWfdbpffveq57OgQtFrotlpok8VUmsOs1GE4HnRNlSb/ecad6YzjPmWH1LIrsFwPEY2VKXKz22KQStZWPZFxgpBFAQB6ztZEc4f2YduGc+F4a6WAje2IBGJq1KkGi4dC32LP1Hp1hEXydK2zdft23HPP3TiSZZw4RcDU8lxp8UWduByF2CzjYwh+T0bgGpq0gGI/T/20+375MbpU/ZSwVQDqYCoUBi4oy+NV5notcR75wiYrwh0oTz6Xx6qdSc/QQkt1yjFZdhhlilck16W4lXSX8vuBKMXUYWbBnRDo9Toc01pxFViOJi8aFQnkxcDFX18hn8ZMOZHbSpVHKtmJcWpcDoPCG2jUrlAcrI6SbipjW8HvlRdevVjFD3bw87eU+pT3LaZolN//mcCqqnMn3fVGUBkZG6Y7DesRWUNgOqwzugY7pTTSZBGOtmSwbyBEqzkDGwKV6ghm9ADdMRvIZuHfeTe0qy7DSKMBz/MYMOWsPHfwMz97A0bHRvHzP/ML+OjfPRmvvOGVD8tmkLntSyf3HPmyViidXAWLGHLu6tHKF3p13gZ8MlNL3h/6/qgStGpLoooVp7D7AqQra5moZeCOjN2/9IUv4zOf/gzf7txzB3RDGsRTnbtzB75527fw3ne/F//w8X/EV774WVJgcQxsTDGuWSzjSPtiJxkZSYAvSDN08wRBNYc1MYILHrsVWy86j+kXHCGrh3AqNiruKG8jo1Bbk/1QFIYMBEioIshVv1Q/k/qaACVZOaURYuLP9rrIEvk1yFQJTedxLy0WdT5HTeLSVuE1xmDUGhAU+0k4KgwRBF1UiOsbJpwURaiElPSMfAu+I3m+anYViZogo/1IGezUCXYtmLmCQ0f34Mg9G7DpkikkUQzLsvmeumgEJJWYOJg9tmdSVQMV4osaGjZu3oSxyQnu9tNyxwUXWS0sjNgRieM4ZYJRFgdIAh2pTttKYaEPG8aLbOnYWwFCywunQSC1NHIvRswDx9Dghc5K4VQfkCn5KR1Y3i+0/TLB3qYkltKKjqMcn59a/S5sSvp4eYyT0p9tUjO1sByTSn0SMBGtI05C6YKRCuawWgzQtX7EZzlGHwTYRN0glwFmP/BGleN0dsnIFb5gUfizmEp6SmFFxc4Emib9XYsjfBCU9oEzvac4/YUhddzp+M0Uue2I76pTx94mNwdzmDs6rEdkDYHpsM74Wk0tXP4u6O5HcHQ/n8Ao/alqVpBuFAgrc5i//U5M9nwYtoNLL7sUt37uVrzyFT+Nn3nVDfzvpz7tGn6ND/7th/vAdO+9e/GhD34YszOz2LJ1Cx7/+Ev4sSQaeqjqvgDiUv542e3M+yNHrDJSHaz/Cfg8fQ06sMv/HTt6DO97z/vw9re9nZfriVc8Ea/9jRvhFpy3Y8eO8T1xeo8cPoLn/djz8IlP/iO2btuGJIk4vYm8RPMoKKJaJWCkkzjxSRMCcHUL3sgotly4CfamCVS3TsGoOchJ3Z1IwOfUqhCKdAqgLpVJCvui06UpGhzLQUpAk8a6BI6SkEfjBFAUU4PpmjBCHVnRoWV7LPKOJPsx3YRwPMTdeVheDst2YHgefM5Gz2A5Nnc/o16CRAMyXe4XokhEcZeBInlpqhZZEDkwjQpiBimCLc5U8nonMdCxwzi69w5sOu8SCKPCRvAyjVOBZurQSQSXxUiTLOaxmwAAIABJREFUkNXXlHJEY+HxqUms27CWnRWEEEtCuMLKqxwNq6bNfFIaSSdhD4khVeu6Y0gOrihTyZaLnk4RQRVVTjBOJ3Rb2QHUeHnyAeX5gNUaH996n5upkeE90mKZFKZIAOEpr18uFwNe8hwVEoBrTEQxWdjFFAC1yKhXNZkOpQjoacqRo3HYQ6gbsCo12SWlbih3PsFBDCWNhV6fE6qIepIprOjnJVdkJ5OuC8mvVlFSKTjsJ2CpTFMgRwDZCV0a5feXH0tj/bITfEqV6xnLwDLLqcB2q9Aspzh9D5HpsB55NQSmj/C6Pw7Mme4qUI7U+l2agkNGo2s6+c/s/xbqnXlURj3Eeo66YaM1IbBQ05DtvRdrDxyGct45OHfnuQxMqX7ix1/Mnb16rc7/PrBvP9/T6730xS/DoYOHly2D51Xw+t96PX7qFS9DtVr9f74N8AD204O7H1eCUfQ7Zx/7+4/hta9+DdtK/dXfvB1XP/UaVvVz5RI4Hz50hP9JwP8V178Cu87fKce5HR8RJSiFATrzC1DJ6F5oLNaKqANGRuUjDrypCaw9dyvW7dyGZtqFs2EMWqPK1kauZaDqVKDZJmIlR8I+mTEDVLXoIGcJ8TQNOKaDpOIiiyOW85dim1wTUAxKzVGRhm0EacwA0qrWYVgVaOR5WVEx5jVw/I4OemGGVi/kyEoaN9umCccxuTu6EHWhWjocYSFLYyQiQNbrsTDGUlNE5L6exkCmIaMLCotcA8iiyGCA3HBydJrTmDm6F2M7LkLIQIi8XzMGa0RooA4rUROgZexrKvIEjuNifGpcAulYintWgsgS/BBLkacNSYQo8GWnVHeQkxDqPr4f5Ost/Tz4+/L+FILHCuCoFRzRPjBd8Rq01wjtUZ6+nIpkfPFikLG8Zi4ZI63sshavSXn7DPyKmFNSv7NTldAkL5PBYMoAT0bpWhwdTM/rtBeRayYM24Kq6QXndQV4TBNO72IbKAqEkLYX0nGDtitj6IwvsLjLasgOvRy/q/1tohQd2HzAi5hsp07H0S23Y+m0IakAKodE1OtjnPREsbzDE/jDW0NXgIemHmCg+LCG9fCUMuDt1x/rFwp24ta1pvdj0tQwtWENQJnRmoNY07GoxOjNTePer/8HdCPH1q1bePl//fWvw9e+8VU8+9nP4lF0rV7DzX96M//t6JGjfVD64Y9+EAeO7MPXbvtPvO71r8Ob/9fv4/nP+THsJxBbdHzIwikMgkfIkaH0b612C1/8wheZf4tiUEldr7f9xV/i1b/wK3jF9dfhc1+5FS/6yZdgbHycH5OmWdFJUrBnzz3cbbrp5ptw/q7z+aTdaTbRWljkuFLi09K/g06IZuyjp2XQ1taxZvcunPP0J2Hr0y6DsWsDjhsJRtdthOU2YJgj8JxxaFoNXV9FJ9SQmSNwXRrT6v2ULwIp9H50fJDwqVKtMWghr1jqW9GFRWNslM3xwyyBbaswtByarjLXVLdMRAoQUwfNrmDbOTtZZBKneZGjTuCQxFM5sshHblgwnSrcWg22a3FHNE19KCKESa9r6EiyFL0wRBxLQZNuedT6QqpaGKNIVESYmT7KHcwwDoi0IZOuyNaJVPm55O9SB46KOsv0GSDBF60nrRsp81fGXQ6O52kATZ6ZBE4JxNLzVstlX9kxXfm7+/r7ytfBaU7cK1+nHPUzeBbygpP2obgf0CzdB+S+lj6lov/7sug4JN9bej3KsqeuOIFTehzFBNO24/cqxVRYWqbSTzhni6bslHUvt6/I0F/+pW2qFAKu5eP7lfzbZZ/AVTjfpiHDL/Sii2vbLqd6UTTwsFk6rEdqDYHpI7zKUfDpbmd6dYgqRyM4LYda8q0SFQ55Wx68A645gdk1DXTDANVRF7NOAKdmYdvjH4v/7C4i2HMc6kKAdRs38JrOTM9g+znb8c53/zVe/JMvYlumrdu28t/KFJzLn3gZnvaMp7G90vbt2/DLr/4lfPbWf8eJ4yfxohe8GNPT0wxMD+4/iE3rtuI5z7gWf/Dmm/CJf/oE9u3dt+zEeOZWocwWhYq/j0sVfPKfP4UXv+AlnMnOPS5Fwa2fvxV/+OabcN0N1+MP/vgPUSu7zfsP4JZ3vgtXX3FVHxTe9d3v4XG7H8cnWIpn/eAHPoyrnvJM7Jufx+KJk8DcIqazAK00wYERgfpVj8XO51+OsUvWA1MqIsuH6ZKx/DoYGyfgjY9gom5iXU2Hq3Qxf/wuLBy8C15nAb3IQLU6AZu6a0EXnqmiUXehmgYEdUczD7qSQVcWkPoH0Jk9iHChAzU1YWg1zE9shjG2FZ6oAC2fE38yNYISBPDmO0jzJiytDS+dg7F4GFg4DjJUVQwPaXUCI1UVqiFYrQ97FEZ1LTTyExUmJZQiz6nbBlSUDE7aRrZwFFnrBLSoC9FrYd73MJpomL3ty2id/D4814PSUlEXDrI8hGmPY6EVotnusQCuF4RQNQdJZmK0sRXjUxu4izriVICuDz2M4egmFN1CZjnICLCmFOVqIIGFKFWZw6qEHRhhi7vQJDJLcsFUA7pPC+EZ/Yw8Gbhlhem9wjcWA+WDIjlpNUbjeYr/ZLt3QX6pBrI4ZYCosoWSxjG3pJA3jAS6lhTAjl7P4BjOgJKXlIjBHhsvKSTo05FnhRUT5dJnIWJonB1GFxkRpXRR95uek8sbuSGQKI5SnRTFQQZyhHBhVqqwa1UWQ3Wai/DbbYgwgiAubuQjFiFycngwdaRE2YgDRHEHikg4a19NFOS+NPjXiSuaAXGYIeaEqByaStOdBLZh8428SfnyIJeqerJ7Yr41+7+qzB1VYPM6EpWcPpfUPVZEIC8ich2V6hqMTmzkjj7RNfRVkrEebXW6i6blE7b77kr/MHV/7z+sH6yGk4BhndmVyxQd9gwsvkcIAxBHjJJdTKsCXbdYeZ2nNKqrwh5z0WnMIVJ9fP2Ln8GO61/IYPN33vQGzMzM9ke65Gf6sY9+HH9y85/iY//wUUxNTfLrK+qpX1gXPOYCvONdb8dP/sRL8Zd/8VesOPeqklP5jf++jT07Kf8ehejnVT//KrzoxT/BXS2qI0eOYHJy8qGxprrfWr4+xJ99//v/N779zW+zIOwf/vkfcM6Oc/oNmGazxfeUXkVPpc7R77/pzczr/O03vqHPb73upS/Hv//rp/nniy5+HHenZmdn+d9excPb//LteOtb3gpN1/DK666Dq6mIghbm54/heDiHyriNZ7zgGWiMjQC2iszI4dQ8mLYHVbNhuh40x0WWhEjCGO0sxsLcSQSdJhyngl5zjv1EFeFAJ/sryupPM/hxBqGRyboCv9NGj7w+55uIW3PIIhWGl8KZmEDumKi7NdhJgCQPEPghhKVBsYB2y8fidBvQI+lxmoRIsxwjk2uQ+xFCsQjDtPl9VBLB5FrfV5dy2xW7Al2kPCYO/S4Cn5TzPfhhzMr+0YkpTK7biObxo4jaC2g2m5g9dgybJ7fx9u6Fvb5KnDqBQeBz55R9Mil4gXL+FQVTG9cjDHx2BhDFHqRwhjzJ5Ri9CD8YzGEvOal0EaHrhThn5Zi9+PegaO6Uk/l9GfBj8GGnP1HTuqZioHuaJRC0XATGQODr/juu9wUAlpTup4IRFiAVZ8A0ThAK4rlmSNKAx/0E6Ak0EiGCX0dIASbUlMVNlKyUJMtdQwa5vjJp7lRbrcEOahkvLDObhIx07dshqwziRSKYesRxwSTY4hXLi4CpYebosB55NQSmwzqjyyiVxsRXoy96FjMIBidIAtiVOjTFgEVWQQQItASGmsLZMIl1l+zAga8exJ7vfAM7n/tC/OqrXyOtWFQp+tiwcQN+4Zd/Hn/zjnfh+3d9H7su2IUXvugFrCCnMf/Y2NiyTfOUq6/CYy98LN59y3vxutff2AemBMgOHDuA40eP4Tvf/g5uedd78PobfxOf/pdP4wMf/gAsy8RTnnwNd2d3PWYXZ89T6tLUmils2rQR1xQirAejTpw4iTtvvxMzs7OYmZ7G057+NF7mwTpx8iTecvNb+r956Yteiv/7qX/C+g2yq0wgiYqiVWmD7/n+Ht4+P/uLP4dGEUpAI1BSyL/lbX+OX/+1GxnYUs3PzfM9UQH27NmD1934Glz9pCug5cDC3DR6rZM42TwOd+s4835H1jSQajkyLYNTb2B03ToYlocwEpyrX6eu1mKMNEiQ+k2EnRasPEVFE8h6TfitLuDacmSqAKbnIaNuHannORmMTXagUVcqViECICfDfcWA7roYcxpozvYwO9tCrguMTY3DcB0k6GCxs4DGmo3sK5ssziNNejIxKBKI4x4qdQO+bRW6cYVFXCS0gelwd5O8NWO/A7/dlNQCVYVh2RCKhoAM9FMF1YqH1GjC73VwfP8+nHPRk9hovxPIJK+gG/Dr8riaO2cZA1wSNk1MjGPb+edi79170IvDPt2F+aiZwt64wijtmwoQRyAsixEnGrtb5Lp9CmgbHIeryvIx9OBjlFVG+qeMq6U52RKIXOGrW7iiDThvkJooZYCq5lnRzS/b+acC0nLcjhWAtUwOgxgQDbIXqYzgL28c2kGpYnGKIBTSjk2QOCrqW6D1aQM8WEihUf498XMLCkuZfFYC/mWUClXvXxQsuSYsre/qnTu173sq+IKHYmo9VEcaMHSrGHRmDJI17UGMWR7WsM6QGgLTYZ3RpZZcLtI36JIvpuUxmgsnkPoL0J1N1FeBbVWh2xaiqA0/CuFMjWP3tdfA7nwKt33ls3B3nI/t51/Mj0mUVAoTcoGfevnLGJh+7rOfZ2D6yhuuZ2D6oQ98CL92468t2zS0HE980uUM/Pbt24/dl+zm37NXZJRg8+bN2LJlC5597bPxutf+Bj7yoY/g1s99Hs96zrO4W0rA9LzzdjI39hP//El2ALj0CY8/LTB90+/8Lj7z6c9Km6iiDMNkMEtOAS97+cuwZs3Uso7oO/7qr3HLO2/p/3t+bgGPvfBH+OcSEgQFL5ZESwQkyRD/hutuwIc//ncyUagApiPUMQWwf78Uh23ctKn/usTVe+s7/hJ33nEn/3vDxo18PzczgyuuvALXX38dLt19MXqBj2B2EZ3ZGcxPH0ISL2Jy3MPmp1yKczasw6HWHI9ZnWod7kgdiukgU3WYFo1uC0ET8TapaxoFrK4fqbmo2CaSsAPRXEC3p3EcpOFVYNXHUPGqyAybR9EueaaaOlTdhmXVENMI2qrCMmxo5HvbCRH1yAtTZ69QMvSnMalj2Vi7YR2Mya2wLB0VwwK6LRbC+ORtaRiSA6paHB9JSn2yDyLQqRKtgIAKqfQ7CwxWqOvpeBWMeHXAqiLMFMwsLGINgRxdYx/M2f17kbdbcLwGfF9HEklBXhj5ULptBqSk5GcXAiioVT1sPvccHDp6mPP7sxKgURqYUGEoKgvEBrt0fdEQ+YaSIMyMGCTJLngBKLFk60Tj+ZXOD6fwJJXlIo9lllEMJgf4miuIkSoDN53N6dmDlLvPGVTO5pe+rqvVSn7qSouq1bqog48rn0frmaWCO6TsfcvdYrltMk5V0ziIQLCzAQHehPP2VYWNZvn5K71JszJXn7qm5oAAaiAjf+lnHdK7P5Gy+74gSuPfB3EK3fZQGxlj2zIUrgvyO3E4Kh7WI7OGHNNhndGlFP6TpaF8lqcIey34zRlkUVNywtKI+VqU6SNiBQnx0DwH6y/YiUuuuRTN+RO4+7+/hrmjB5GT7Q6fKPj/2HneTvzLv38KrVaLAdulT7gUP/9LP4ebfv+P8KlPfOqUTTM3O8f3AXH9VLUvqvrCrbdyEg9HJOZ5v9t67717+b5Urr/mxtfgf3/w/fjP//4PHJ0+jPd94L2n3fxHDh9lsdWFF16I5z7/uXj+jz+faQJfuPWLuPmmP8Zrf/XGpUhPBZhfWMC7/+bd/NyfftUNfE+2TpTBn5cPUhT4vgSmN7zqZ5gzSvWdb30bv/6rr2N/0Vazzb+r1mpyXYvH/9M//CPHpFL1uj18+Ytfwp/8oRSOcVc2z3Hx7ovxkb//O1x15RUQcYgg83Fs5iBmTx5A2pxD3cixfeMUzt+1AzESjI2NYGysgdGxMdimhaAXIvZ9FpzQyb/TbiLxQ1aTR0HI41HX8dhTshcksB0TlUoV9dFReI1J6KTYt1yYtsVgK/XbCDot9DptqZwmCx8CjTS6bbcxfegQA6J1W7djasMm5IqJbidkc/updesQ2xbadFXkVWE26mimMVppCNgGYk5NovcxmEdJzTdOlCI/S7Kb0gw41RHURkah2w56QcRJTBXHYVCpq0CXaBNqjprnoHvyOGYP7KcxASj4nI5H6uD12h3Mz88iDCmuVIdtGgzXsyzmzjsJutjzVNf6gIc9MtXlYA0rxIS0PYhvmiUSOA92EtlxCcvH3iu7e6uJoDDQDVxN4HTK8nCggMoAGCWrgEREScwpXAMvfsr7YBWAOugAQDfaH2RZxRe4uaRBlLecAWQo/XSzRILn4p6btWL5OrMgSiT9m8jjvpVb+Z4lbYJegwRppTBLDEamDoDTpXvZWaXjc8lHVUMsVO6W1uoN6JohgzcocEPhTLPhyWtYj8gadkyHdWYXCwmkjyAVjScXe22ItAc7DyGCRSTUgaITcyA7PI7pslCD7FTGLtiBS2FgdnEaX/v8J3HhZZdjy64LoFkeJ7rQ9/zjL72Eb2W98Xd/B1ma4YbrX8UxppSrv2HDBnzjG7dxN5Wq9DXduHkj5/D/9CskEFRWGJVvLERXo6MNvv+v//ovFjUQEBsbG8VkwWtdrRoN2bG87qevw5U/emX/EcRnfepVT8PnP/t5BsjkZUnv+Nl//xy/9zOe/UwGnO9/z/v4pPiVL30Zz/2x5/U7Yn4gvSFNy8Ib3vRG5preefsd+Ld/+Vd+Dnlxgm2yJFVhzVqZnPWt276FC7afh81bNnOXleonXvIifOlrX8F5u87n8TItS9TrwW930Gu2cGx+P9rzx7HG1lBxajCtFGnkA66FlPh7ZGFEfpuaAYtEM+RnSay+JIQfBBCaCUuTnDrqljvE3XQchGEMoWecYW/XG6g0JpDqNoJCke9YJtM7gsUF9NpzCHtt2DmBusIXNooQJxECvwXLGkVu6UhpPGu78FQDcauJBT+C8GIGKx7Fj+oup0VlZBVEpu2Ow5ZGKpEGyLifxXkZc5QFcQOp+6eacEdIjOVgfnYa7cUmLMeFXanBNjQGheSTPtqoojk/jZN778HkhY+F6kg1v6GBBT22W0G14sI0dKQi5W4yRIqRShVVtwLH1CSnkYCPqfNXe8L+sOkA+Ck7nzmPgcloPg9D5i0OdvFW6zYuF5Qs/71yGgBbdkypw7fMZH+g2Ic2y5EmCQN7lY4JkbOdUxKFvN2KZP1TBC3l+2GgE8wBHAX1R0aJKqcA2WUAOY+RQ3qSqkoRW5EvpVip0OVzyBkhL4FvKgMBeCtby9Z9JZdX1eK+on6l8IYfW2Tql+BUxpGWv8thO1VU66Ow3RoDeOreLg/kGNawHnk1BKbDOqNLL0zdiTPYF+e0FpBGXWRxG4ibSFUBLbc4NlCl7hWd3OIudIoFnBzD7uokDuybxr3Hj+Ge7/wHbEfF6MadML0GjwyzFVntdKL+gz/6feaU/tFNN+N973n/sk1EfMoLHrOLf6YRPdXb3v5WHv8RF/PQoUM8BnzylVfg2dc+h/9egjzing7Wa278Nfz2G39r4DfLT/LFD8v8RKNYdpJ2nr8TtuMW2fIC7333e/j3L3zxT+D8XbtYkESd0I999GN47o89v/+6vSJ6kziyI40R3PL+d+Papz+bx/q/+4Y3YdNmObKv1aRn62VPvBw/dd3L8eG//RB34s7ZsQO/+OpfxlVXP0U6GhRm7sSBjIOAAWl7fg6tuTmE00ewoWJga2MUahZAsYGTs8fRSXTURsfQPXEAfkDpSwoMxWITeSDgTlbYaSLR66iOj0HoKgLi3tkue3AmugF3rAFhZ4BXh1Ib45N55veg8qgb3HFToy5zkXM14fx03TY5Sz8jTmbSgWlkiPMYYdiBrimoOxWYjo2oF6PTDGApXbimDiMOGSBWibuaaxBhDKvSQCK434eMjN6jgL1MoRtQafSvqmjFCjxNh0FG+64Hv9tG2G0xkNVSmbPfSVqwSdyCHMcP7MP5kc+UExJdsYF8RolUBDw1xGQnlSscwUrCmKAdkn8UTFuKYhKRwbAs5kASD1hfIbTBoDk9dwB9mWVE7VtNdtSVAb5orixFiK6spa4oljidp7FFWg2UgjmsEsAnWQ5TCF5PlnHRlCSNi+esDr9W48X2R/sl8CziWXnsXXBPVRTuAXQvp/G876FrMv9AyZAJnbvgnDJG4FEoAwlRGQPVPMv7QJg+F4M0gXKZqCtdLmv5mJXdZ943ii7z9ln8VJrHqmiMjcOrNiRtgDwNtOIyoDDtH9awHok1BKbDOqOLFMb0ZVyqd0mwsTA3i6jVhAgXUXNGkKQaTJ1OzgaSMEPSi2AkwGi1gTlF4RPe+edsweZz1uEb37sdd337a9gmLEyd48JmY+1Tlb10siHLqKufejXzKEnURHZR4xPjeM61z+bOIAZG9Fu3bcFll1922k1ZAtM/f9tbGNiSbRWN/uv1kVOiPlfWv33q35gSQCP17935/7P35k+S3vd52PPeZ59z7u4sdhe7C4AACICkwEukTIqHKFJUSkocy5LKkuIcrlJSiVP5F+yUk6pUqvJLyrIOO0mxUpLoWIosUaIS62QoirRACiBBYLHnnH2//d5n6vP5vm9Pz+wsIImCtCD6ixrMzkxP99s93f193ufzHH+Oz//K53kz+yf/7J8ufufPvvpneOHfv8D/Pnf+PL78pS/j+mPXGZj+9m9+gRlOYjppkcYVNQCn9ejVq/hXn/vf8cOf+iF+nOmyBIqsmhUmJu5/+l/+Z/yT/+G/5383rnwsgEfJDuaEQOlshulwiPFgAG8wxLVuBzu9HrQ4gheFOH/pEhI549rQVFVxbm0Du4dDFGGCQJ5wVFBVxtBUQggZAhqjr/UWjueykpFWVGuqwun1YW5YyCoJKQXGU+COJENHAaVIkHhTFNGc5Ruk36hIt6oKBjKJfITBCEbLgqxV0BwbpaZj6kcsHSCzend9G5NbL8PsdpDkMR+baTkMFIOhh67dR6lXYgycxMgIYHO8kcXSEn6yKgbrBNNS1MlyX32e8TFpxKpKlBvrwVFUyHmB8f4+goBC+9v890n8mP9eku5xl39FVZqGwYY6Ykz9yQxZFKMyNdZIppoqTuYUmRlT7YxmsBNAkZnTfNFn39RkNms5oWJZU/p667T56awIn2ZRjFLztQB4smjU5/SBYnEdpw1CD5IWnJYLPMi5vwDpXC1K/iKJQ/kbs5ZK9bLErJf0N8prBrM8cVuiJvgYmKLWm7PsqL6N5jEtawb3L/K4SUtu+063D8O2mC0tIMxa9JIoyUynrJR4q/XduVbA9Lt8/W1nqb1RnMkbHV9V1+5VeQJNFps3JjNMXrmJfrtE1NOhKyqi2UwYowwLlSYhKQwUqSY6plsmm1uczMDT15/Eq6/cw8Gffgl2FMJ+5nmhXWUzQXlf/A1tKs+96zn+OGv1emJEP5/7r3s/KBOV1vrGBt7/gQ/UD86JR6q+v8v3XXyPuuZPr09/9jN4/r3vW/zev/7Vzy8u8dlPfvq+y//ub/8O/pP//D/lfzfAtImyovU9730e/+Jf/gJ+5id/avH16dWA8cXxNeNT0ioGBEqnmA4PMB7vQq08XL9owNZS6G3SBruwN9qIoKHtrCMoRkJKmVvIxzESigiKc6RhhDyNoZgWN/e46yV6roEo96Gf71FCPsKogNvrckyYoqyxvCMj3WSWQpMIlEbI5kOk3gBBKMGwtlD6A2hliTQ+RBTmkPUWCtVGtP0I3J4JuaR80ALTpEJWStiwXPiHB8B4gLE3htZuQXJsjNIEkmGg3XYQpBFsaw1F4MM/PIQfDiDZGix0oKcFLMmCmkYc4xSlEcJQREAZFmWUlvCnE3SUHrob57H36k107C3s3/Nx9xu38Pj3P4+DbI58foA8muPlewOgtHHp6uO49tg1RIHPffuJ2WIZQlVFbBgjTWtMcuzUR1+rkFe1654dSvUTjswzjVueaz1z5GnKo/6KkLty7OSnyCsO9pc0ZjfZfEMwSRYNSxLdVimzJIZfq8T6kflLITlDCSQJ/8x0XI5iEjpKUSPLY3NqeOJsT4PTFBK6LbVkKURAubSdTGhuIZjUsj5uzlEtBSNJJ0X8POS/fcHNXwq1eymUxZrV7viTYJlrWyXSoDq1CaqApBR8C2S+ykkNQCdgmTgZKpdyf1mTKktcc4oqQUonJakCRdZYF0oglk5ANFXn2l0O/i/FCF7WFGZpCyZzJRSqxHFqaRZCKjKOQUuzig2dvf4m3M5282bAEhfUwBWauhrj/wXWG+0v3+n+tFpvzloB09V6qBfHudQuVApNp93QaXUw9XzshXO0OkMeo8pZzO7lTm8LjtXhTus8ydDqPYKS2oaCEGqZod/p4vrlEru7B7j90lcw13VcfOKpY/fvA7IZH7T+47/3d3H+/Dl0u53XvVy7JYxEaZ112vTOL3FTuO+f9edf+bXP4wPf+0E2aH3hN38L//hn/2v821//DfzGr//fPLanaKufq534/+V/81/hez/8YWZ2CUh+7EMfYRPGL/3CL+Gn/uHPMND2axDdgOVmEdj9N7/566x7vXzlyuveH5E5KeojY9+HPxggnE1QFD46Vol218F2y0KSqBycnqQZb9o0srZsHVWqIQxmeHX/Lvwq4SrH4WyE+XgKihrPrQR5nKK/sQZJ1jmv1qxymKbF7JZttaCrFhRdYpayZJd5xBFDOjG4zHipfGLiOi0oSoYs8jCdTDkW6NLlHTxyaRtjWYGRV8JoZBpwrRY3MKnBHMHRHvzZFIplwHEMuHolNdPsAAAgAElEQVQHqmlCMkxuiKLu9XkUQyHdnyJzaDoBJ8oYJcCUliGSPODnMLGteRzA0g10LJO1pYkXYZhESI0SrmOg9DPs7t3GzZe/icc//Cw6bgeBMUOepKjyghlUkovcunULklTg0auXOFg+iCNsuO6CtdNVTTC3NRg6K7/ztEu/Yfrk2ixEY/0TrOQSC9p8rsqqDtU/1oA2a6HRVBVqUuXHhxHZiWc8AcuUNc3N7YvjrKOqGsZRrRhEHutCT5qNzmKCl936zc/OAiHL4/+FvGHJrKQRyCYnlCSkROJ+Cz1o83gvslIhdL7NzVCahlLrQBuzGTeUEfBf0srSiR2/vykasrQACVFs0xGtZau1Wm/DtQKmq/XQL47bIRdqJUwNdqeN4XSGONzHY1vnYCmbQieXpcgUyjI1oUgqco59UaHLGkzHQBF6kKoI57e7sPUCu4Mxxt/8GnoXzsNpr7PL9XSczRstykL9sR//sTe8HIXT0/rZf/Sz+Of/68+xNnPnkR1snzuPj3/i4zi/c76+5NmgmBgYcvr/+E/+BL72p1/F//aL/4rNSgRMv/iF31mAgv/sH/0XC7MSrR//Bz+BX/y5X8DL3/wWvv7CC3jXu98N3dDxU//wp/Ho1Ufvux3Sk77R4o2fgGAcwffHCMcj5HMPlpTD7qigYboSeSj9ALLa5WzPlm3wicNgsAulJGYzZ3bTWu8gKlLEQciMUMuy6LeBrEA095FVCqhMhwL35SKDBAO6pkClv7FqoMojEfeTxAyUVYXAkApJM1DqNnL4yPKCK0Xp7U7VHJCdRlMtzjK1CGRQAX6uocg06LpNtiHkwRT5ZB96y2RHPQX/m66F0jDZiEcGmDjOkUOHLYMvY1YRYilGmoQowhxKWiHTcu7tV2QZBrUBpTGSsceB7uU8gaLmKOIMLaeNuR4gTTwc3HwV5TyCbbYwJ0CTptB1Ay3XhmWZHE1WShWiMMVgMsZgOMTFdXGSQeyh7RDrlkIhQ9YD/paLsTGEYYud5rlU6xtJDnDS5Y/FZ5zIEz3r+droWdnwQ45/Seglq1qLXCmyKM0gsF6IylWqYW2MRU2eaZMeIBHAVHACmDbgU5KXjU0EKBW+L0qpnhifnzZ1HQPW+wP7T4N4ButcL1pxLBgzvYvfL+v82LzWkFas/UUlACu3QjVgN035xEVRBStNcV65TPFjeQ1MZSRJBsVw0On12Ym/Wqv1dlwrYLpaD/UiLiLLc67+40QZat9ZW4fd6sCQAvjDA1gyVZSWhA4QVxK8vIRmtlm/5tSB4/TGH6cFJjMPLRq3dhxs0Gb1rVuY3rgB4zEHqmOJcT7wl2JN/yLrBz71A9jc2uI+fmK8br52C1/4rd/GdDLBr/zar+L8zoX7rkUE3FMDZnLi+//gZ36agemv/1+/xi1OP//PRUQUufGXQSmtv/+TP4F3PvMMpwqcPy9u4x//d//tX/l+NKCUmozmE6pyPIBZlVjvuLAouF5NEfsRZqMxxocH6F55FxS95E77Ik0xGxxCQYaeaxKljcnREfIwgkYSjShHNPI4VslUDZjEStltdrbT+FcqRVUj5YRyRijBqkywk8SKgxk0nWSTSDIKTRcVmsQyRkHKb3ayYkOhnnTSfY4pl1SD07a4jSlWRU9+kRNb60FXYxSWC40c+eSgp//YkEMua9TxW3ldeamjyjUGWhnVdlYpx5LlKjUY5TAlA7osw/fmODoa83PTUnT010wceR4Ht6uugstXz0OK5vAPBrDPbSELUyRhhLjIMRoNIekUh2WI9IMMbLQ7Gg1RFDsCeBVkIBL6VrU4Dog//TdcNirx10W5CJRvvk+tSzSOZ/C35MaXlkBquWhtwglg1wDTnEfnCqolYxCxvVWeIUvpZCJhLSkZyDi3lCpcOd5JgDsCdGrdPH+avT3utxdmJKlUa8e8Un8mNlU7cZ9wanzLecZntEkds6GFSA7gfNWyrvCthFuf/l1mNdMrn9KzFsygcvA+xHShyo//DipJIxrwTsYoSURmUeFri5IWumuQNQurSfJqvR3XCpiu1kO9SAvGb+CaJmIOFRWdjXO4+viTsMMeDndfw2gwhOlHMJwOnLxCQm5ZK4Fh25C9CfaGY+RkGul0oZg2csNEokkoHRnbO33c2buLcP0iNMsQWYdvQs0fBe+T+Yj3mbrJhjakIAxPmImW1w9+5tPsrn/02klm853PvJPNSqj1ov/0f/xnnGW5sbFx33U8+9yz/PHXsQTzk/PonvrFiQFyNA1brouWpiMO50iTBHKmQEk0xOMUyVqESsqRBzKyzIctV9zlrqUlJoMJspGHkAw88xhKXqFMS5Qp4EsRO5Gvnr8A3SWRagqCTTRaVXRdtPjQGJcC4EkvmCdsQAoD8NibHhf60Am0ErCIEgZJaZKzHtXuS9B1DV6aQpEMGLbBVaKcClBKSKoIsiHDp2pQMqzTeJ7c/JQMoBtQLJfzS9NkzsdVBXOkccwt8xqnB+gwSGaglCijHEkcisYoP0Se5NBcnUfzxLBR93oUp5AdE48/eQV3j3wM79zG5Z0duib4Uw+TpMCdW69hPI8gaRYeuXQVa+vncef2bc5kJSMVgZsGaErM1J0NSpc/K3U4UWPYud9ZrzC4l040QGEBTIkxxNIYvWEzG0NQKisMDpt2JP79ss4LpaiwJEJexEISwNFM8kIe0DCmD2Jmxc+zxQieSgqqSmHm9LQBahmUngTl9z8my/dfBN03EVBNSL+yKBWglihig8VFSj4xkdjwRCZBeo6K+ClmgZvHiJICOItUpAGQ9KJinSwVV+gcpm9wPNSDExFWa7W+m9cKmK7WQ724PcXQhU6rEoYgCppeP3cB0jDBWpEhDiJMRjNoXgypktmVTKxXHE6QHAwwjTPo3S10t8+hs7XN7E2WxzBUA3pLhv6yj/HkAOZ6G5ZuCtZUeYNN4Y0AbLPJLWgmPnhmfhbgVJJOGJBOr+ff917+OL3oMSF2tFmX65D/N3MRAKGRcuR7SPwZVMr2dEwYsgxXNxn4RXEMRSYdqYNENmBUBubjAdptG5pOrvEEUhQjI3YuyRCPAuhJhdk0QkKja6PFj/0w9KG6Li5cfgStjQ02oRCj2OgWFVVCzuYVYjCBLMuRUwj/nJIaIh6Tc5NPniOeTphlJ5DqdnvodrqQLBt2x2EdMh1vUUYoM+pF19hQVMoFxlHMzLBlt2FYBgxdZZkHjchJHxomOQOoQklAgbnlPECeRZAcDbplQFV0aKoEHRLi0kcwC1D4ETOBrU4bsqFhlngIDgnoqCgoUqrlwDGB6t4BpoNDHnkTyI3DkA1IGjntkwi79w5QVTp63U2M7u2jYzqwDRMGAV1NQ1JkUFQZeYFFxuiDTRy1O78A8qqAUolxtMLmJfCxETBtXg6ngSkWbGOjvyxPsKYUk0X6TEUzTsRVUZIBGa7SOEBOzwsS41AyAWlRGz1qVct4Ttee3hcPlS8B0XKRO1qUVEWrHYP1MxhTinVb1pU2nxcaVpKG8PHn3PQlQa3zURU+RgFUKwbwx+C8uQ2VBAr8PGMGuj4JIFAquljF13RiWpSCpaXWLxrhEyhNC+5ZWK3VetutFTBdrYd+SXX6YJzlDBDyuICqmxjMPGydv4LQ8xGFN3Gwt4fQD3Dh0gVYbQdpWcCAiu3z56D3tqFoOsI4YcNFlYcwyA3L8UcF9ue7WPO2YKwbPDKu6mrAM8FnrXPj9aCf3/d9aVHzeLJT5+FezYZPzUv+ZMQms3XXhC5pCPw5ZEvG3B8gm0fsyFZ1BfF0jjCcU5AoktkYuqsBcYr54T7GgyNUYQYpKiGlEu7t3oKlmtCtFuZxhr3xFL4i4cknruGdn/okJENDEAecSZoVGWfTEhDIipj/TtQFUOUSm8FlAjrelEffdMykdi1nMwFUw4RlAdRNr3ZbzE5O4wAGjXIJHCUTxHkB2Zsh82J4e0ewsxJmS8QvCQ+0DJPxkoIqK5gdLvIhStKazkI+cdKqNrO5HDVEk15ZQxFJyCJidanUQINq6cgUwI9T2LmOTrsP1TaBjoF4PIKuFBzaT9WneVrw8ZN7O81iuK0+TMNGFKV48aVvY3h3D089eh6WrDJrWuka/DSBQwUGGZitw+toLMvs2CAkKlUlHus34Ex9QJg9zohgOp1XSpc3DEuwzLIMmmSTxpa0r0lCWtyIzXPEeorO93Lxe1JdQ9xEWanakq60OgaTx7d1XL3aVK7ySa1anTj25fv/IDb5xGXK4zD8ZrxPxqfG/Lfckc+3pwng3rC5i+uSOXBKHEdZsRaYs1pJnyyJ+loqXuivb0A3XaR0GQK/K+/9ar0N1wqYrtZDvUQOoIyEsh8rAVFpTKmbFuZhiL5kwGlTMPsBjg6HONrf4+iX7Z1NlEoFrXMRGhlLkgzTu/fgttpot2zoVcobnJu0MQwiHIZDXDjYhkT1f06rHumf9chIosi3OAVO30gMVr31ArFpwyWW1Pc8TAaH6FoqtrsOxxfRRtxzLESVhzAccV2o7Tqc2Tk4vItwcgBXKaHLFZJwjsPJIXbv3YZCYfCFimSSoIioB9wBFA23dw+wdzjEuceu45Of+UFce+97YG70mFGLMxqPpuL0ROEJvjhxkIVbmoxMmh6yWSejkXQUMltKAKIlS3AsExq91eUZhkcDSEmANXsHnX4Xwf4IoEifbI5wMoFfHSLxYsz3jtBpt3C0v89OfDdJYfd63NhkmTaPc5MoxdHuTZRhxtmn1GSlOBYyAq1FhigvkEsGonkKpZBhGS5UnaLMcgamGjn9sYFOaw1Fy0LcKjEfH8JxbD7mIPbZkV9mOUbjGfziz3HtSQ39tUdgWC3WKc8GI1jXLzHY4RGxJPFrxZJNjjzSqmOW8vSiy+YEJJdyRHHmOFu6D9gtB8njDI1mc3vkNBcMplT3z0sMTNM44QIAwWRWEMoMWUS/8thf4dfMgsGslipNl4P0pWXNa1kzlwXrSxt5woNWAzirpSrR089/OjGQ5AYwiyxTcd8rbs4yDIlH8MJw1QBXcT3i9uUT4fpyk15QlospUPOYcz5tq8XvE+TO1wxlhUtX6225VsD0O1xvdg7aWz1n7Ts9PlUOIZUtqDSS0yvmVKrKxCPXn8KNF7+I0fwuLl99AvMbGl68OUA7ldCVp8Ash7vlQCp8GPIhu72lMEY0uoe504LZ6kPVDVjZi/CCGZRIx0HHgxOlyI0CiqaK7MPqJOMiNfmixJTUY8XFZr58X1+XST1uy3kz9Kx/HYu7vuMYs/EIWTTDxY0OOoaGIvQhc+4kucInsOMhB9aXco4irUCR/Zu6gYEsYTTYQ/fyc/DuDRHuDaDSuFvKkOkaj4plOcVw2sGLr72CSRbj3R/9KH7g7/0Irjx1BVEZYh4NYKRzdE0N/jSH3O4idl1M0hRtxUZ25DEw1tII6eAIwb17iEczxH6CslKgmgryTIZrWDDyEMndISRrhtxQcbi7i/Xz25grBBorqHkF1ZcRTYbQiwobbh+DqYd2IiN1gCCdQ3E6aJ1zeADrDyfIvAD9sgVPClE4NNYHQiRoURKEJiKbijBGr+MiK0xMqBQiBza0Flp0THGMsCNDaweIDAl27wrUUQjbPcRLL/y/uLi2Dk2bwi9UBGkH5zYuskxg/2AXjh3i9u1vwPcPoXdcRJKNDCZMKpagTFA/hSpRXmq2BC7FE+MY4FVCJtHEFlUiH5SKLNS6Ur5AzhmeKldyShzXRiRzWeeikuY4o954ZjYzwQKS8QiU4+mwRlYmgFYkrLGl1i06eQijAHEa1RGlOqRKBwoNMhUllLK4VbUS159l0M0CqqqgJHNZLtz8hP9yykOVhB2JU534HspAJnFFbKZmDPhIDwwGguI1yoYkuoNZWWeTim78Mq9qQ5cYtMtKJl7WlRjpoy77oMdS1aixyeT2sLIidjRHmgWQCxUKGfYod1kn3p4yYHVOqxD2pozzTyukyJMClWzB7e6gtX4RFUx+3A0t43SIarVFv6nr7b4/P6zHv3rWr9bDv0ifRW2BkjBBUFag3GpjbWOTDS+UDXj5scdw6ckn8Sdf/AoGwbdw+fGrcLwc2698DVeuXcWFyzuQyFldJkiiAomcQMlNtOeUVzlBkqvwx0NMj4Y80qR4IMMymbmpakcy709lrXGTpJP8ZxPOf5o9PTXyl5b6rfnevElmq7/KanR41FvuzTwEPrUbybCsFtqGhipNULIrPUNSxIjjAIWkwidDVKlCzWUeqWdJhSTOEcYF5l//Cuy2i0QDQi+DHpDe18U9pcCLvofDP/0mzj16EZ/5O5/E937qY7j4xKPwcx+BP2GdJKGPghjINIZMziaCFFnGLuncn7K0IJ178HYPML93BMQxAwhySZdxAi/2MQ9oZC+MJtSqNB9HMEOHtX2pXIle/9EUUpwxiLUti9m9LEqRtttQ2jbUfoe1ztS05A3HmO8P+PKOUqBSZVjEwrs2FEMUPhCoD2c+fD+GY9lw6TrjmEGWyn3sglXM5nPk7iY6bhdl4EMKQ2SwcedwDLx2B9stwcyZpg3TNJiZa9k2XMdG4M0F21c/ocplxrJ+rkI+ubmcxWour7MuK1Xlfd/nUb7URDyVx4ajWuNJOsqyKjiqq3n90H0v6vE8JynUZjqKqaLw/qJmSDmQqRKvDXk5N/V16MNlZpc1oEva2uW0gIXRqY68Wn7lvV56AViOQEynyuB68fPi7Mex+Tm1fNEfiAB6JUu15KCqBy8KpLyCYdjc7tSYIPmthO6r/NaasKzWav11rRUwXa23xpJE5iLxDfyGbTkcqTInpiyM0d3s4xP/4Q+j0z2Pr3/1JXz9tof49gxX7QC3xjOc3z/AxkYfvfUubNdAnvoI0xQ37k5xGEWI3Q2kvo9oOkLLtCk4FHlRQm85vHmpSr1pSCUDAIaVFY43ywaQPghkLn60VKGI2m38twxOhV6u5DaegluAEiTBDFttB22q3EzInOShIk2dKjEDlFYxMhqZSgoqzYBCsTlRyvWa4d4R5gMySSU4Gt7B2qQLU3K4uehuGWOwP8aeP8PRbIbtiy184Ae/D5/8oU+jf2Ebfhog8EeoypQVE9SYVCUlojiAUuTQshAgwxsZsUZjVF6KMooRHY6RTOcwVQ1uy4Kk6eRJQqG5rAXVbQttt4X5fIZ8JsNxXTiGCT2IIMUVglnIulHH6cCkxp684KSDaqcPd62P9tY6FzxMhyOM7+whPhzDkTWEliKKH+QcZRFDM0rIFMJPYKsg4FEi8XwkQYgsilju4Jo20jzDeDiC2bKgKV04WguT3RuY3r2Le8MEBzMZ22GCWRnDm81B/NqcTqKSORx3G4bmcvSUrgozGMsR2Y8jnptK/fzKH/T3XjIpNeusoPoFOKvESF0WxCLndtLonJ4T4Ggm0W9PI3cCpUX9PTKeLfSspXiOEShtoqnEqJ4MT9WZ4BfLAFG6/340xqsm5WLh/Mex3vTMmtIzgCnOAO5n6U6JNaaIKgF0JY6GEqX7tbShzmxlRrnMxMkDHZFMFbEKn2Dz70oKdMOA7bbhuG2e0pSLt5OVvnS13r5rBUxX66Fe5AoWYixwZiTXh+YKSPaVQYM/j6B1hGv46hNXcO38ZWz2fw+f/ze/xU79F5Qc6r0jtIcedtb6uLa9jou9DlpqBSlPsTcJcUAAtLtJckX4/gzm2IBpkOmFGA+To6ooiqesdaJSzUJVtdOe1zJb2nxeBpxNSHm9idLv/m3zIc3GTAxpQKA8DNk57+oq+noFLRohnqVM4ZA7WdU13lSTLEQU+UiTgCslKShcTTJE4zFmd/cwubuLeDBgwKgFwDwIMUCJu0mGbxweYDCdY8e28J6ty/jgT30/nn3u3Whf6GPkjzCZDRlO6bLo38/iFFVaQqVsyTThNIAyDrllyhsPUBLINHRYpomy1eIIJr3Thmrq0KsKwe4AWZwgNXWu7tQUFx3XhGkZSChYfh4yg2lqOtIqBUWgB+EcQRrDbrnQtrpwzm2h3e4gnHoIBxOWC6hJgZbjwM8FGMvzEHkxZ0c5AVoaHxdJxQA3nPsM1kj7qZM21Q4R5xmzsr2yBdfooUxlSFRtOhrjW6+FQHcbrqLDD+aoqFM/L0EEMgE4ilkaD4aYT2cMrnlUretCfqKrUBrPTc1anjQtoWYjG8r+wc8NEW2UM4ASek4xoseiHLSo80LF34puC8WxS15oUKVavynVhqDyRJe8eB0d6z3p8ePv80GWJ0By82JbBpziuiScml8sQOWyy/7EtOIMALr80ehnq+o4SJ9zRssl1z4KKDSeb0CktJzkUUdMkSmKpj2ykAHnFNVfNRWxFezWGhy3C5WqlJvf5HNvudalr9bf5nqjUfdqvTlrBUxX66FexNEwCUSNMEpVb1oSv9NHBdiAYmg6h3aPB3dgxBKubBv4wNMX8OrNFH84ivnNhS47i2a4szfFmqFwXeZGy8bhZIaZruDizkXstBzIloZZ6EGbmYAuQY10uGTG4OEabZolKtKXFiICSlpmTXFKM7o0vm/YlZI2aOmYXKmp4L/RxZvqIvtRQpYkzOZRladtaNDKEGaZoko8VJnM0gnqRU/TEHEWclc49dE7pKmcHCJLc24qSkdjZEcjFJMh4pnH7vjM0zAyFLySzvDawQEqv8Bzj5zHRz/yATzznmew9ewlSIqKiT9mJs51HQTBGGkUwdAkVEEoHPYUzRPGSKMYRRzAnxwhDDxUsNG2HRhuH5kmMxsXqhW7uJlBDBNIlGtLo2RNhtHromWazAofHRxCThM2ppS6xiP53NQQlzlSVYfZcerxq8QtVIe37uLw9l3WllqaySC4KmP+8ymM4UquUY1pXG0kDDyTNIKjm3Adh6thg7mPOE1YF9rbWIdaEXufYzIeofQC+GGBu/sDXFnfQTQfwu13ceXydewNZjAMBd3NLlSpi7u3h5iNJ9jcsfj5T9WfpSLVcJEeL+ECz5cMPaed6GVtwHmQsWnBqnJQv8zsOKs/mXHMGKw1gHQZlIrnV15XCWsPvF7+noS62rQ57kr04TfymaWWJ0jSia8bxz6D3yUj03JqwDIw5Z+feqEtX9/pj5NLFqH5krJIAGC97SK54/4Ej+ZE4Phrql2l9zSFDZykQbVbfWimWxe0Mg/LJyCcplAIFny1VuvttlbAdLUe6sWmhnqKRxpBEbJPSesGJMNhUDKbTNFS+7yZDI724Zglnn/2IjRpDC+xMKac0yBDKAG+UuEgjPGq58EyFKybbbx69w6+cjTCrhfh05/4QTz71HMw3RamcYhNq8PNUQlJvnSNWUN2ftfjOVG3eMbIbcnJzEFDJZh1pHgYuRBMZfm3cDbesKQctVMUmPkzRJ4HStUhptSWCqhVzKB0PhvAkm2UuYYslhAXCQMPg0aSecyZoXYWI5xOEB6OkE4CVAE1+pQYzRMcjma4HVYIohBxkuBiv4v3feTd+L6PfQiPvuMyVEdDTPu5LHOXvNAmlhx7xI9TWWFy7w4kWYOuGoiGHoqJD6UsEKYBPSFgdAwots4beqoqCNMEcR5DTzKomsysp2sbMDY7MDd7sFyL7/90/xBxFEEhaUaeI5EraJYJo0NspwqrKqCaBnI/QjyYwPcjHL12h6OwHIvMKl2orRZahcmxQTSyp+cBsc+Uc0qg1TBNqJboT6fnCgWpE9wpNME+q46JKrUxHuzh9v4u9m/fxss37iEIPXTMFIl3hK1HHsXFRzSM59/GcDRAlHvY6GtICfRTPq/qQlNlBksFVfCWEoNChT7XbCWWG56qhl+UmJXLUN73/FgGa1WRc/QVudEVlLV5qGZMK7YQCTayZmebsf/iehbMI07khOa1WYq/x+xhCbUo2MxE8JEnCnRCoi1rPY8BJP0+fQgmlH+jBp8nX4vN5R/0Wlju3T8NTJelDhLLnbU6J1Wpj6eESIRqzjSbE9E6h5VOZKnytpIXx8KFryolSdjQdWK7O8JISScR1F5VVx6IX1CYIV+t1Xq7rRUwXa2HfjWEhICpVPAoQyFHvdOBjAJREKDorcHtrkOKgdL3YEoZ1h89h0+qEl66eQ/f3BthTNuX7VATOsJkDj+IEPoyVLPPmsU/+uIfYvfFW3jf8+/HBz/+MTz1/Ls5PJ6ahnzqOE8jmKbJo2u5jpjJKLaoapxRDQtUH3BRm09oQyL3FlVkZwUo5ahU5AdPUhcGjQcvqWZYpGYiW8sHFtf5gFSAirR9VYWIDEPTKaJoDEOScHH7HHRyS88mKPIAulUgLTNoecgbcUFaCdo484Tjn8golngzfiwCYp0Pp5gOphhPEuxNYtwbxxj6EmZKgA1Lw9NXLuL5D7wbT3/i/dikeCNqZxpMUKoK2t0OFyOMJmM2i1C1KRFwY2+M+d4eFMOG7HYRDmaIj6YwSf+rVjDWOnAcC3mRIQgpfijlsbbjUsA9UZgpkrYFY6PH5QlwDHhJhOndfYxu3kE6mSOpuFeTQSNlblI8kCoLJiycBTBQwfdSROMZosEEliQC8tW2g0SXuaSBpAJISqg5ZVKWoqZUl2C4FhS1hTxO4IcBs+ukddW6LjJb45zdQjWhJHNsb/XxB1/7Jl64fYQLXRcdNWTH9jdffhWGto3rjz+GSvdw4/bLKKJd+F4OqShh6YYwzSiygJiVsNNTgxKB4cUI+5Se9PQ6YQw63R2/AJpNs1I9xudRfnUmKBVSgYK3GAEMT+o1G3DJ7V1lrUGtL1PibO1ncx0NwF2uUD1LCyotMazLP29eK8ud/Ms61GVg2sQ8cdATM6XqUrOUxIBd6FvlpVestAjZlyuVaeHmpIBfn7IG0+7AdbqomFGWICxfdepHI7VYheuv1tt0rYDpaj3kqx5115tJXlJUjAqNWCfDxGA8wPYTT0KxW/DjCglM+FmAsJTQv3oNfXuGUk8QqQWUaYppktJMGpasw205iKsWMrlEkQT8/cNX7+JXX76JP/nqC/QNm/AAACAASURBVHjvJz6Cv/9DP4JrTz6Bjc1N+FnMG7FC48s44zaiSq2BabPpV4LkoC9zYuEqjfWvCXFTWQqr0hBpImycxq1Cp3oKiJ5RkYhjPmZRBSlxBaX4PpmXRA5luXisOEFgEfZdMGChtp35dMptQvPZFK12gXO9dST+GFkco99tYUBVoUnKoHs6GwGkWzRM1srloY9kPEQ+HgBRgNtHAao0RzDysHd3iNfujHB7mmAGE7newkd7Lbzz77wH7/rU+7B+aZNZ0HQ6g6KbMDe3MNvfYzkG5VwSK0o6ySKNMR5PcXSwB4f0v3W7VET6zEzcr4p69DWT44aSIEIw80Hz+v7aOs5tdCkJEkkyxz2pYKZU7znIqhLz4QA3X34F3o272NAdZKbG4K7f7qDdbiMnV3iUcFQYHQcyYmczduInQQCl3UJWFpxIQOkOXUeHlBWwNDJd2VBIg0ssY5VzjBZJARrdJGW9kq7VsqjlyYBu6ggDBdsdE0++7/34wjf2EH79Ns5td6CXcz7h+r0/+T186Hs/i0985jM4f6WFX/n8/4HXXhlyBihJBajtiRhZBlCKvBgtExvKTvCyOAFKH+TGP73uMwBx3mkNQlE75OtEgBLlfddb4VhHusxYLueF0uU1+nsXAvg1xiXxGYsaVJwBTBtwunDj46RspunWL8v7AevyeiOt6VmXbXSmbGoi89+ph1M6PpPmcT9/j9rOJPHGICkGTKsF0+1xOxedUfBon0FuibKouIHrLRZ7vFqr9de2VsD0O1x/kTf572S92df/sC+11AT5SOajXOPRnqZkbFBpnX8Kd7f60HodZtpyL4StyVBcRQSTlwkiy8H2zkW8Gyb6r+3j7mCMiVYh0mUkegndH3CrD2VzFobGTBaBpNf27uLFn/95/PFv/Ft84IMfxKc/+8N493vfD7e3hpRGplomKhzZLnMMAlkHJ4noHrF3p0iKmgNSdUTcs1hyoiEkudbr1SrVJW1cVbv+cWKzF6uOQl1Um1ZNb/giaPw4Ooh2PjG6zzmuKPZmyCMf3v5drLdd2FqIwvehSSYURcXMm3BnfBoXMDIDcXqAaJqgZZOL3YB3eIR4sA/fH2A6HWF2cw1H/gy3ZkPsTgcIghBrroT37mziiYsX8Y7Pvgu9rYtorZ1DhTZKw4DcolzQGWazXbh+gMPZDDBs2O0O8qzg1qXsYIR+XECzDVSUbal1oPfpmGLk/oSrQdeLNnLSliYzlFkMWdOQu8CRSYyTBsPeRKeVs7mpPBxjvnuIwc3bqIYzuK7Lx9K3bAZHslqiVFKYjoU0r+B5lEyQwedqUgrI1KE6OpK8QHo440pRarmazmfod4SMZBbEqOKS26m0TIYRAda2jTijGlYZCWWFyiUkha4v4+dsOPbwG1++iVTfwZXWBvr0PJTWERWb2O63cf2SB6ltIzTI/d/F0+/6BL5567cxCl6CUfrIrQq5nMO2bU4BUCWV0xIoBquQchTVkkixNt4tzmboqzJbAMJmzL7MFOaFAlZYy5U4EasE4y7VhZpJKXI+aRQtuvlltu2TFpNOyBqg2fTMF3ljRCogKwXSLOGaT0q9kOX6nIpkJhSxpPB5wWIszs9xbo2KuP6WwK+q1ECRTrwklUPuSbsJNhuVbDrKpZJfq6jlC/xQFKK5S5PlBfvaRFiJBqe6yrTUBUNKr/JS5BywtrasUwnymCuSVUVUr9KQhEPz6+Y4VUo4uzamkb5uot3bwNrWOdhOS5in6rQP8bepKVIZrxuNtVp/c+u7ff99o/v3Ruav5ZPOsyp//6qP3wqYrtZbYh23z9SNMrIw5fQ6fWaiVEPF+rktSGWBvd051eqgbXWYATNKGWY7gNUxYIcawqhESpiN/keufyK16nEc67uIGVIl3uTv3LqBV779LfzKL/8ynnz2OXz8U5/Ghz7yETx67TpabgtxelKf1rwQZUlcX8XaSaGL5dFqJdhNAorM8qjNCFCqNXQVb3zLrGnzMj8xom/GkWJ+y6O/oga05SJCp+KO+vncY6CeRgHmZLJJAuiqgo2NDSTxgdikc58OjGvKhXYuRRKHsPwEo9kR9g9vwdYMtAsVsldh9nKCG68O8GJ2C7FH1vscF5wWHn3H03jsPU/h6nvegfVL25CLAJViIMkB2oNlqmXNciBJYFQV4iJCFCRI53NkQQCTQFKSoEyo+97HhY0WBrMIw/FNZNQuReCGuurnIfwohD5WEY9nhHShWjKycYA8ytholPkJ/CKFRg9nQvWoHoKZh7KQoBHTaBjQNZeBThBNMfHm/P2ikpFQl3+S8xhepTpKenyznIsBTM0SXfJlibbZYi1gnJcsNNEcHQppZpMUQTRDO9COwR4BFVmBJWvMsoZeiIPbA7z60rewu//zmMclFLlE2zWwvtXHdDbEeOxhR1URRRF+93d/F5PJjIGU53m4+th1bG5uMihdrsVsxsYZtaVJxxrTZi2zpw172Wwwyy1Py2725jNOsa6LcX9ZHZ8MnYp9Es9p6cS4vPl9SWrG3mfPrUmm0IBkkRJw/Hv0/aIJw5dqtrhuWjp9fMvHs3hdERjPi/teuzjBjkb1a6+u1uDbUPi2CbBSAD8BUao5ZrAtNV36dXZrTNrREqpmoNXqotfrs2SEADxFZ6nyagterdU6vVavitV6qFeTuNRUDwpLO40ADe4Mtw0HYRDDUUyYtsF95xrVjsoKTFllZo5YETuJ0PYddJIA0bREHlUgdJpLouGpaeqmhEKlqjiQXaJcwbYLRTOQFSVe/OpX8JUv/THO7VzE+z70ITzzzDP48Mc+yvFAbh0RRIuNHfWGR4Yn2rTzRaajwryIrOqiZYdYrWJpU6wE4CTwKhiaYsGmHoeGNw5lQEmrRatPA2qrupubNusw9uHP5+ysDrwJyiyBqWtY663DabdhKgqSeIogPEA6H0AuEh6Pk9SgSHOMEw89RYY+8jG6dxOH8wLjQMa9wwjDkYawPcfGehtXH7+Id1x5DNefegf6TzyCYstGoJfolW2kLAXU2RmfhD7S0INCDUmGgtDUYRU5ZD9BPjqCF6eIZlMEkyEi34N3uIcwNzAPC9AVrTkSUn+KrJTg2B0ew9MJBvXVl1mICY3hDY1Zu3A2x8F0zhpJOS/ZdKbQ31rTmeUifV/ol5j5IXx/iooqVHVGzyjyih8DOmGxDJMf2zSO+GTIck1+zAn45WGJSs+YQSNspVoaFENFqReApSJIYo4a44zYrGTfXhmI8P7ZZAyEEbbaHbx65x4q00HH1RAlUyRJgFt3buPeboy13X1M/90fIJ4PuFM+DCMYhoajwR1cuPBhZn8b4LbMYLAGU9FOMBn3A9TjvE8sjdqXr28BCut1ApiiqnNLa9BZP5ebKXxZt5ydBqanj0Ewq2r9/K4nB6XM0gjOL6YWraJ22RODXes8i6IGqmfcv6oO6afjo8SABizy9ZP0hQcKxYnOfZy6f1TIIaQBtda0UvikUzDPGmvFm2MivbuslMz+skKnrBDRSZBqw2n3sL5xDnanz5OSvBATk9Vare+GdZol/U5jtlbAdLUe7tXItWoXbDPuohEYteGohgtEMxRJBt+bgQZ8RqsLx+wgOJpCth1281uZj5bvoBVZiIqKNzqlKDHOKzZfUM6iKlfMcMplzl8rssJO7zyLOXy9bapwTB1FNMeXfvcL+Mrv/z/4pV/8F7h0+TKefvppPP7447hw4QI2NtbR6XS585xYNGowotE9VSnSCDqt43cIAKh6iTzLud2Ho+s1TdzHQsQPyZq8MDhhEQzejE1rU0kpmFMaZ+a8yYqaRbr80XQMna6Dsi8P9rCzvYGdnQtYW+uLqke5hZJY22CAYD5EOdiHmhGgNpDLOvxohDWlB2mi4ZuvzvC1wQA3KVtUMrHZXsP7zu/g0SeexOPveQ+2H70Oo9dGoUhIKOd04KHYusj1kWmSoUwiqMTKkvYy8RHOIgaBjq5Al4HJeIzh3gG86ZibngjIDPcHMNvrmM0pzzSGveagyFPkZDqqKjiqRsNVjprKkxyj6QTQdVgkm5jNEY98wVRChqmr0A2d27zyUmKj03zgc2JAUUrQDUUAqCzn0TP9nm5YzI6hqsNBpWWTDIH9BJYrM/FOGa8yMeQ0Cm4ZaBku/IOIdZ78t0lSxEGOLMmF3tX3UEUF2rqDthGjd/ECnL7F2VMEiOj5bbd1TGce7F4fl3cu4s9f+hYmozl6Gz3sj26zLpaeM8QsSqrQmnINhXzMei4Hzy8v3kBk6STTf0oDehYwPeFyrwQoXQTs16zmIi90KdK3WcstTVU99j95fMcazYWWlF4jJEdJY2R5Klqk0qTWaMviBLAGjyLsvqn+Pem2Xwbcy3FSOGNzFZKatJ6tlyJTGcqCoeUgfQK7igxNkeq60brWoBLxcKrRQbvTwcbmNuxuT8RuiVk/M+urEP3VeiuvBwHQ71QCsQKmq/WQr7IOuV52FwuwpmsGOtuPYO69wp3ksmUwkIOhQikoZ0blyB9JLWDkLqy1NtwgRJiUQttWFZj4dR5jJbIf+ZZKEVVDejRiW6hi0iBxKzufqSKyQpTESKk3Pi/w7RdewItf/VNmNC3bxs6FC7h+/TqD1EcevY5ev4+trS30emswLROKZXFoP1Wk+sGUARMlw5D+LqPaT97kGyHpceTUfcaMqkIi1eCB3iQUCaqmcDwNgStibdd6HWioMNobQkkjbHZdtCyNczzjJEWSqby5Fmohguv3D6HMYlSKiVyzkc5n+MP5Hl64M8CN8RzzXMgTdpwcT1808YMf+Sh61x6Fff0SIsfBgDSLWQlLUbBptZHSiJninaI58jhC19LgajK8SYC9mzeguy731JMhanRnD+OjAaIoAQkd6CFw2xugEs/pdAhbAUxzDaQEyCoJkygGcg0x9e5bJiSV+voVBv+UMxvGCXRJY4ZLoxMNdlSLik9y8pNe0QsKmLqMVrsLi25AEs1EdDmVRu6GwqCS2okMU+MYKLmWO7DpqAFDsmCpoYk80byunkxJt0iNWYWor0yJESbdKofmV9BUA/58ijTOWVJx8cI2FKPCZDBHWchQNB3dfg//0Y/+XXT0Cnv3drmudDL3cenKIwys6HiJq6fjWbCmdZVuhbPZi+qMsfvyz05frjoROn/MKJZLTOkClHKUWr0WOaqnzEk1WCZmWpYFOBXAUq5PuET7kcTBFsdyGTZh0TSijpqCghPXJy2H3FeySBQoBGiuZDFp4L9nUZy4T8vHtjzuPwbMDUNciOanStSw0okVsdgESOk6KUouryQYigNV09HeOI9Ouwe70xagthRmMXnFlq7Waj1wrYDpaj3US1pU1Jy1VDjnLyN/5RZyb4iNrg3d0uDFAarCwFqnjVk5QKWbkNBCFHfR8mNEcYEspc0mhp7VQIQ2LnLY1pWL4GnfSS0cb4gQWsGOYzNLNfYTaKoK27CYOSJd5Mvf+AZ/0CZruDbW+n2c29hmTWd3fQP9jXW01vuwWi2c29hiKUCr5fCImTSGKm2QqjiGNBcbo7I0Yj2hn5MyBsqkf6y48rFCnmbsuifn9pDyRecjJN4Ijz16DpsdA8F8BD/NUMk6EtI1aglneSqVDC1VkHg5vCzErAqxO5vi9+7cxp8fxehpOp7SO7jkruPxdz2CZz/2HB595kOQXQeJpnOGJz+O5FrPE0RZDH/PQ6/XQb9lYpbO4Q0HSMoC6WSG3AuQzGLkQQBvOIQ/niDPCyjEhuYlV83S6DTKSK+ZobfmcpB8XlTobm5j59p1oJ2zppSinFIap+oaTNmEoxrs5I8DkStKmlkw+5bx+Jd0f1ktk9BtB26LGr6obCBmMKRKGo/7SQOc5MLoQlFhNEKnkwrKUKUTAVmlAW7GsgfdMlhaQMcYkW7Vj7ibnwApNT4RM09d8WlZAynN5FYnt7sBI1Bw4+Yt6L0K165fgjebYf/OAIm7ju2t8zjaP0IgxXBtm1nR6WyCc901HteTntaqHeqNkUetmdDTAe2ntZfVKW3l8kh/WVu6rDE9occslzNP69+tr+s4fB5nAlM0zUqVfOL7DC7rEHsypjFjLYnYKjYd1SepJMsg+6FgedUlUNpcp8jIbZhRRVEWKQHLRq8H5ZyKY9FOfE9ERdX3v5KhlyZrs0upYEaXa4y1NhS7D9vuYn3rAp/MLAAxvX/QqJ8Y/rxkrfJqrdZbdZ1olTvjfeavOtJfAdPVeqgXAdNqkYHYGDWaTQOQe+vQ3TbS3TtIB0coEo2NTbrahWmswafcUNpkbRutzhrCsECclMjI7qsUcDMgCDIGSwUzJMSq6cx6FGR6kcQmTdNu3shohJhnzEhmSNBvdXmT43FjVULRNbQsU4SqyzL8cIb50SG83V28SJerJMi2AcU0UVDPeUF5rCa2Ntfx+BPX8NRTT2B9owvPn3JZwO5eImQFirIwgWAJWGRVxsCao4iIDfYDbimiHnUCpuTJj/0RHn9kA4//9I8hnB4hJpZKMxETGPU8lGrKmaRpkCFPFYSJgjuTGV4LfHwzrjCel3jSMfHs1nk8ub6BnSvncPFDz2D7PU9gnBnc3ESRWeRMbnPPfAI/8OHNZzxOd7QCbdfkRqnpZIDxdAYpSsGOqDBnME+mJGKhUWeIJqWEOANm05kIeCfTUMsVkTuKjI2d87hw/Rr8aA+pNcU42MdsNGaHFdWNkr7YsW0cSB6KMGe5BAFmWW5AUcHMr+mosB0FqikhT2Lu5C9SQGMBooJKKRjMchuoojDI4EgrWYyr0zJicFWI2T9HX8mJzKwo/V3SOGGZBZmQCBDHdEJALjDSGZYFJuMZJHUNYSFh5kc4ODrE+poDBRqkUsPa+iabZT73uc+hJSVw2w5arg27ZfO/7RqoNmt5ZL1cwbm8lnM7KdaqGd8vfx/1/W2ui57fZ12mMSM12lJ+hS6P6h/w5nKa/V9oOLlZqazDAyQ++WNmlZnuXJxkLFWaEmNJ0owFs1mJYbrAwceyhAaINid2y41QZ2lfm69FqH7zvTrbqR7X0//lTLDsBEwJBOumC7u1iW7nAhx3Dbqp1u9ZJQ8/5DrvVMgBXqcTdrVW6y20ThMm3+laAdPVesjX0pP9RB6jMP9Umov+xja8m69gdO8uUrtC2etAshXMqatcTyHLOpulDMuF244R+iG7nMsyg+NTtqeEhBw6ZGaQheuWQSo5bCl6J825ppJZGpVAosHuf9rcAt/j42Hwyg5i8ZLK0ph/Tu53drqzCFHl2stCpmOjHNEQWtXG3p3b2L9zE7YBvPPJKzDUHIe7N/DHf/yH+J0vfn3puo/dyc2HtgDOipAicIWkYHVJ8FC4FpL5CMWWC7XMce/WDRhk1lo7h8lojAt5Dj8I4B8NMB/OUMwzjP0UN0YzvDA4QFKdw5PyFj56eQvPfM9ltN99Gb1nnoTdPodoEEFd6zDDnLHWMGfHfRkESOZzKslHx1Thj48wGyYM6nVZNF5Rf3448eFk1H5UcG4jCRISZjdDJLmCrFLR7juCPYXHbUnUpmS0TFiui8ncQzgZwR97mB0NMZ/MuJGJ4r7mSYC8lDHVUyR+yE1JOgCH46F0ZrkIKFquDsfVoesy8lRUbEqlqL0lsxLpWRsxf1NFKTNTV4kTgjTgBh+KNqIO+9lwjJRHxbWjHKImlDJHSVpAKQ6qZTGTGRFYVnUcjCZ47c49rF3oYG1tDZPJBAhdaJLBmunxbMrGOq0qsdbrQ1vbxJ39O3Bdm9l2IS84Zh2Xny/F6wCfBmQu6zuPAVkTIbUEck+N7yFaeU8kRzRLqp9/5anbO+vjQUuSREkA5+8W4vGmx7EgBrtuCpNlZXF8pxe/XiVhTuIDJYmOXINpShHIi8VJ7+mmp2OpQ7NFVkCdzcoaUv53xaY6CscnYpVyeI1WB+3uJtzuFqdQUBtXA4ibEwg6sRVfS2eWxq3War3d1xsC0zeiamX5zdXKfLfniK3W66+q3hhk6TS5IJ4XauXi0jvfjz959SW8+vLX0NELrNG+I2l4dXYPF7vrGEUD6C0HdruFtLCRlV1mOZIkxHqn4t6VrAL8pBAB+SVFTNFoO0KkqwxIlFJknco8HRVZjWqlYEQjXkkmfgtqSmH7GTvtaVNSyEyTKaLOkOKFpLIJu4JW6bBkFdMyQadPTT9AWyNmJ8A8roFGKmGzt44wjlhvSWwsbW5U2amzRpFYmvI48icXG6cmHwNYN28jsVTcOZxj14/w1KVt7N27jUuaDDOcIRy9hvHuFPPDCEVp46ho4ffvvYpv7+/B7nXwI+cSbFy5jIvvehbOE09C29xCpLaRpyr0/jrMJICf+EjzAJUs6iTzKEYaC/a1MCtMXr0LeTTHhfV1yKaKwWiC2WSIjuXgID4i2hFhViKobGbD9bhAi0AjueTXAStXYLQ7hPz4vvY3uiiHd+CP7+DuYI7JaAZvFqDIdcyGIVTZh+voMNsWnjCvYC85QLqWYZbMkagyTNeANBOmI91OYGsVwqCAN6ERv41CIpY6hNMmlleBFwUcql+aXe6WJRNXHiUMmGZyhfO9NoKpz8H8qiSer4ZtwfMCRIohwjhzVcST8XNWQ5WUKEMfYUSAS8H6uXXk+QwtMjJJBfa9ELvzBP4rNzD3xvi+7/8oFP0C4lhG5nuY7N4FntyBvdaFRgY/3UCWZByqT2kVxMzSc7r2QN0fZ0bTgBooke6xqEGZqugLoEfgWgBDDiFjRhA1GEUNSPMTriYB10RMap3rWyxsUPVovWRJA4/IKUZJ1WtmNePGLMoezTIRr6QqJhIqo6DbL0hKI4u4CGK+pRxpEUCtLtSM6WkDVcnXn4taNL5/KTGujV625j6L6pidFcY2dhE2d4eD77lmlhhj1pbSa59YVA2arGKuHkKVW7DsLXR7j6DT3+Z0ELqFtEwgSyYf29JbFmtSgTPlvau1Wn+j60H687P+/Rddf5nx/fJ0Z3mtGNPVeksvhXRlqo6nvud7oeURXnnhy0gHE2yrNrQwwTe+9Se4eO0KJEXD2NsjGgtd00Tp2ADleM4PkJgaIkvjusU4LXhkRxtWVbNjgp0VGx1tTDmXosq8c1mKxBmXMsrFSFRWdGSyaMhpsg+lU5q7RjlLukWJXfrVYmxJI0tihuhNQedczZKBqayp9+dH1n886QHvH6kcUWIQxpMD3LrxbTz/1KNYVwyMv/0qUj/EXhXi6JV7wLDAIM7x+3dfwwAJvufD78Pzl6/jHecNrD+yg9bOORStFmDaMGwXGlQeWyd5wICCgs7TNEEYhHy9clLB0jVMJkOUMbGWc+zHESpDZkaQzE/+JIFfZZBLBZM4x9HEZ8Df1wz0HQvdlgW1a8PIZUz2DrGxtY61i48Q8mbj2a0br2ES+lAoTN8wkFa1vtLW4Wz20dvocpzThf4OCrnA0fCQwTvJMIgx11ttdNbbSBOJ2VcviIXOl8jtvEISxNRwD0XSYVrk9LdRJhWbs4i1Y7lGAczHPkI/Yh1pWmRI8ww6RQUlGVLM+TYJjGi6yqaueRWydMQvE2RyG+M0wdE8RL9vY/uRK5DzFMPpPiQ1hWwa+P5PfQo//KM/gi9/+Rv4Pz/3axgcHSCLU1imiel0ygH1GmWr1gBoOTbqxFj/jA1nAU4fsAEts6Snv3/W75zeYI6JiyYOTV6A4rIkM1AjQ5AXl9c0hfNkSc9bNc78vECWJ8gySlDI+LUl12a2B22kzcnZslQhq0Hmoj2qPK5Q5Wg2/veSnrYSmlZVlbnjniYTaZKzhjsIAvQ3+3Bb6/XofgOKYfDJVSWVrIFdme5Xa7X+8msFTFfrLb1yzjRU4Vx9Gu8wTOSqiRtf+xJe+urX4WoKHM3G6OY9QDuC2XHhdNoMHErfh1xk6Lsm5Eq4iWWkvEFFHPmjoGKjRJ1xWEeoymy8EJspbXYtlcMORS04u2Y0MdouS3boWkumDzZe1NmOPESsmRrWp6oKLMtigEWbJ+tDa0MLj/BJS6eqi8zEcmn/XwalSp0JKdzMEnI1h6FJSGfAl37/j3DBsXF1YxPJaILh3T0cpCVeffUIt/cPEBQF3K01fPb5D+IDH3g/Lu5sw6VjNDTklo5SVdnxHo8PoZQy9+QTa5UXCYfUp0mILIiAMIVSahyW34OOdps0sz58qkKdi7ikJJLhRQl8rURcFLhxd4jdgynatomd9R6CIobpHeGDj30f4umcqzxbW5vQuz3c3d2FXgJJRjy1Jlz2ccqgtrvRwyYd92aHolMhxSls08TsaILQm/HfibrtoyRFZ02HajvwIh9hliAvM+LB2GkvSxp0SWY2k3r8kclIY2GaCcOUo78UpYDp2PCGPmuWFddFWkjwSbKQS0glBaZuIyIAmlUIpQpxCU4RyGQDKTFuaYWjVMKAfr80MYkqWHQypJApysGH/4MfxRPPPYd//+JL+NM/+zOWMOhTk8fG3VZ3AbSaJVhRwQI2rnc8YOJ1lgt9+fvSUsf+6WrRxfU9YIR+/6Tt/nQAcb3KotWJr7/pmFcaUCuxRITSKrIk4JMfMkDxkH9Jc33Wqur6UBGdVdWJDDl/NPdrcd/RZJkuAXCJ2NuI0xlYvlE0UoIKFUVEWSb6a5fRbq3B6WxyOxizxmQCkwuW06zWaj3M6/SJHE6dXL7ZE+sHvX5XwHS13tqrKJHx6NqAefEJvOfjbcyGE/z5H/1/uNxz0e5ts0PabDnctjPePeCtx7B06EWJNrl+yWEPBYacQpcCTFEhovGrpKDIohNuYdqg5Bos0sZplBlXHpYcPSohLYUsICV3fFHBVmXITV5kXRVa1H3jhXQMEIgZbYwsYRIgDEPeBPmDWmU0lcErAw/6qI9DqqqFxEFpQHC1JEZXNHa1u50ubu2O8cv/+ov44LNPo6vouPPt1zCdFLgxH2Cqlbj27GP4+Pd9CO9/z7vQ3WghlnJIisv1j3mZQyVXdJ4infusrbN1DVEewPep130GhVhEW6R65AAAFq1JREFUqoTMKuRxiFlWQkpIEiE2fbpPcz+CT6N7v0QYFbjhDVE4LcxVG52tFq5dvYKLl9ZReQP4927j7o0bDHC3N7potTT48yG82QBWoaFtt5BHBcJYGL2IfXZ7Lvo7GzD6LhKKdFISzI+mGE6OkAYR6zYNzYS+bsPutFAqOle5kkxCt+p++ToqTJUMjnUidjXyQ2haBs3QGQzTc4h1yXKBmZfw417JGZJKgE8vSjlcf9PpI4wkxEmGIM0xTQv4hYwQMvy0QJR6CHIZYV4hPJrg17/4hzjftmHoDirVQGdrG2kl49/9wZfwwp+9hEvnr/LJS7fbhWtbnGPaPG/KojE+HZ8IFWdQdsvAcdmZvuykXWYZ8YAN7EFr+XqOwWwDAE+2PymyUacDSMKlTnIQWRwP5d8Sg10WpDuOUeQJ57tWi9xR9URG62kw3PwMOKlvXQakQucpHPbC3NQoY2tjUlmyrpxmE3GUIAoTNqP11zc4/q3XuQiFDVK6uJvl8ePDsVCr7WW1VuuBawVMV+u7clGLEQGBkEkiE+76RVx79v148Y/+AJP9/7+9a/mRrL7O330/6t1d/e6eHgbMwMw0xAZsDA4RUQyJgyx54V0UKVnkL0gWUVbZR7K8yiYrx4tIieJkFUsOAhKThAQ0AgzIMAM90zPdXd1dz/t+R+fce7tv1/QEHIwYUB1UCDX1uHXrVv3O7zvf4yZ8YcJNi7/Xyxf0uRaPgh3LgqQoILCJMpg6NYOtflSFxEo2BpaLMEqhihWPxCLukFAethcVcv9GiRGufORPKGnEPqgiZGpecXpB5ywn4tHReJ60yJLMKB2N8ctRIzWj5QgS5aI6pR7mBbbC7xazHOspm1KpWKgJ8UsSGY3OHCLXxc7Qw8tXr0Ehb9ECQWzWavj933sW3/jObyLraHBUAXUJqFkJRnrEavMsyuBZE6S+ByHw2AFg4rlIVIHHmrHrcLMa0kbBieBZIYvG4rHDaUqeb2MyceHZHjekfiSyH+R8ZxVvHfaw27dwcf1+PP7k09h66hHc+OBtvPbPQ/zyg/dwYW0NW098FUnq4qjfR1sT4B2OkAQZHDfiXH9BUaE2TUiGghAxN83tBqWC9TCm404yLC+uQQjzdKbW0jx7lJLdrSA6rJqXlDzonCx/SPjkBy4E1WSKaE47TBlFS1UJmSIgk2X0Jw77wZIAipT/RCP1kWLsjWEFPm7fHuabGEVGkAI2nUeomEQiW41RRn9AnOFGC1EwwbvvDyDeB2xuLjCy/Iu338VkMubrgrxwCR0dDvs4t9bFwuI8pz7RdV1ttvi6EfKQhWn0s1p3+5twhiH/tP2LUKWknPEcuGPcf5IUhWrzC6lASkVuTqmTy5vi4jnCGGlAThgUuBDmKVC0QaLHC8oJfaZyvNXjlpXCLiqNTpBYKXdIOE1PKD1aqylQaf5d582fCEUzoBstNFptLC6sotZoAlmd3xq/hQQF0suvXDS6s5rVrH7V+twb05m4aVafrmKkYQLZ0LiB8APg/JWv4dFnn8eP//oHWJZrePihhzDcP8DtWzdgNJq0ZODgqA/VIN9Qk70SCbFsqBKEusael2kcwBEimJmRjwCLNSz3u89zwQmhkhWD0UtCptI44oaGPEFpwVWyYtxYvD+hyAUnD82cN0oG/nmzSV6U4/GY0TnDNFidTTdz12dbobiyoKOCDlFDKpZT1XIMWnm91HMxN99F4CewSVRUb+PQ82GPjtBp1HF/U8ez330O3/7+d9DdWMRgeABrOEKUhFCNGuLJgKM4SVEv0bn2XDjjATeppC7WDZMjXJVEYEGQNbIxHFhwyespkxGNJ2zvROP62Acb4gtxClXKoBgyRo5G5FkYpoZ4MsHV//kvYLWGzQcewre/38bNN/4V6WTErgbW8AjBeAi93oDrTGAQ/zOSmPOZySnmmwbmVubQ6jT5nEQTB4PdQwz2hohGIWRZhzOaQG8YWD6vQTREDC0ftu3CsiwOJlAkuiZkpog4xJXVE+jU9Ooac1NJCBWGQKbJgKYgVGVIWgMa5dULIlQpjyoVAwEra0uc/kWpQEkSoHfUh98bQIoS1HUTgqJg4oZsTUVxmaZRQ+IHaLdXoWoNDOwelCTBQxcuYHNtGW+8/hZubu8hij20WkvcSJeenJKUHkd78udeWCKRyKjasJ01tseUiLXa6HGs6Rk1jU5OI5G4A7FMjzdmJ/cjs3wp3/AVlmi0QaPvYs63FthuKww9drlIyccLycn0okBMq683fTzCVFRrtYHlv5cjfPZjTSq87aJRTUVEYcSJYZ25BY4VNWpNCKJMAaTFd44ihnHqfLD9FQccz9a3Wc3qbnU3cf0MMZ3VF7xCSOR7SH6gnJ4kAu0uLn7rt7D55uu48c47ePL8BXzlym/gtVdexs6H12GaOlSjzp0c22mGPjSfjPJzYKcmxOiYCgyVFiVKEkpybhnn0OdoaZIV3oqZzIlNXhaxTRDZw4hCBo2sv7MifZ/9HfOGMiuUwHGBmArEGc1SeJSdPh5zM7E4NwcxzbC3fRu63ofjuXma0V2iE1Ha9hQSkipCpqsRVCmEbdkQSJSTabxYdlsNzDVrePrB8/j6U1uImymu7/wSq6KJttDA7sTFbj1E3R7BHQyRhiE0U4UYhUjI+9R3YRoawonD9lQZGb27HtzhBC6FGIQcNA/fc2HFCSwvhZSIaJFQJxOhyyl0M4PuKdAkCefXlnDR7KLTbGJxZRWPPvPbqI9T7Dz0AP79J/+I19+/BjmcMJ81tSK4QYxY1YBYRBykLG5SahqaCx2Yho7+/iEOdw/QPzqCc+TAPnIxycgtwIXqiDDnKYErw0HPw7Df59Ql2kREZJLOBF2ZObV+GuQCb6J1EMeQxsqKDNGQAUJeF+YZTaWQBYqDJZlbPBnB0Bt48ltPY+vpr7ObwKi/h7evXkX46uvY3j5AGiUwBAMTn1BZBeOBjZpmoC4ZCEIBR/0JREnBansOj11+GGEW443XXsfe7Y8QxS5kDRhaR2hFS9DUEkkvRUq5LRKP4k+lh2Z3XENVD9SyqmP9qvdnFU3FGY3gWSVg6j7FpXs8emffUhSm+SfoJ9h7NEJE/rzELQ1cpFkueqIRPp0bSdL/Twuq/PVOp1SVufjlLSlRzfQkyCO3BcuPIU4k3o1qqol2ZwH1Zpd/A0LiKlPilhIy7UOsJCcLZSTqjGI6q3u8Pk6V/3nVrDGd1Re7khCabrDBPJnWUxIPoV0rl7bwx3/25/jRD3+Av/+Xn+K+7iK+srqKwWAEe9RHx9BZQS7TY4OAR9OSEBXcUQlNQ0VDNDAYxJz4lLBLTQZBJtschVFCQjxHlocgjRBmERIxhSaT4EUCZU2pmQA3ze7QhzDaWizSnHNOAqsg4OaXqlar8fGgwtNj5ErK1cziXXwbp4uaYbOWYTi4CREaLmxswLcdWNYR1rpt1MUYy49uwp7sw756CFr2qaknFHk8DBHujZB6O+wBSoiVxxn8MS/IcRbBiUPAExHYNgLHQUyj+zK3v/AkdQIPfSfEYBJBhwbNbMCk86NTfKsIcZ+oBHU8/tgjeGHrCRiLXTSe/AZqjUUc3tqBuHwBE6WJ9z7YxYISwzAEFkJJioHx2IHST5FKKfNF5boBN/Q4ZKC3vYOjnX24VsjxkGkggnoMs95EKgXY7+3Cjy0MDlMevRLKSsb5/eGYI091rQbJNCHEDkLOZmd8DAbZjnU7ENs1RIoIozkH13FYUOW7MfwwxOGgz1Zb5y5sItPmOfJ02WhiMg7x4fs99HaIDiFBVRoIGwGUVhPx4SE0UeZ8fTpQGms/cOki2qaJv/vR3zL9gIILFrtdZKmHRqcGqaA1HouTklzcQ0ijokp8bYXB6RjRaaS0rDsauqJKnmnZhJYiqPLv04r4adQ0OY4xTSuWTBXfUEYVk2NBIT00KTZ4TG0hjnUQcD5+lkX8Hci53rlncClkys6ITM2FhVFxjvIxfSkWO26wjxvlIupYzJhnnCOrZOJhsqNCszOHeq3F3yrWW2Z0DdPsJUCCkGkTuaKfpHP5ByNklRisWc1qVp+45E/qOTWN0twNgp2uT9t9/yqeWJ9Hfdz7u9eP/+N8au/58y+1GOhQdRwjRRBp/G5gdfMJ/Mmf/iX+6od/gZ/8+B9wv7CB5cYyHNnErtfHemcB8cSGIgvQ9BpUTYCsqmyC70QRXM9HrBGrTcp9FEUFMST4UcaRnk5A6nMBhqKgQ/xUNndMIMSkoFdZsDQvpHDCBGEqI1E0zo6n6ExCGDWFFsEECam4efSnsIhrNLEQhCRYIk1/xEk41BSRR6ZC40sk3MyydbuqF2BPxlxXkRGb/P7EMw0n1Jx2IWhabofkROjIJtq1Nh68/CAsUrPfugVVCGDKKkQng6434VsDTok6IKN8QljnW5iMxnAsmzPnR0MbdaPGDQfRD1xqHkiRHgvoTQLsDWwMbR+mE6Ohq7ivVoMpUtqShUCQ0GmvYXVjA/vBdYg3Hcw/8Aiibz6D7toSFleWYNljvHX7fYgfvofB/i3sjsc4imOsLS5AVWsI3Bi2n2JJyqDX6mipLSRHMW4Od+A7LuyxjdBLYas6bziUZTp3CYtdiJs48kK4roiWLCNVRG5GLeLdqipcRLDFkP1AG3MrLHgi9b3eoMSlOquxUzHNc/ADwPYG2Ot/xP6Wvqcg9GWIXobbO7ewsHEezoQ2Ih4ExYEuOWioKqyJC6EhYslswIsFrOhtGPTh+XtY7pLwTIas6VAW2xh+dID+zgF8jxB+GZ4L1NQ2OrV51IwuN3dkYUTfWVnOE8KYMhLl10GWnnCUUSB7YuHcQLSAk6pEg+LEC3e6CaUxO4o0pWqVtminqABpfGqUfkwrYOcDEZmSFDAjOMqVYl55IhEXDgihyygpcYBpOkHfAVkxGTEldJua1jJlrTzeEhXNHS1UZFmMJPUYcSVrM7Ewtk9TEVrF15ReXyEhE3FQaaJBaHHUx2Acozk3D0Gh75rCgRlk8SazUK7cHYDpCHf+QH3Wv4CzmtX/vz5vdPRur/+ZI6b3emPzaevL/v6+6DW/ch/+4A//CAu6jms/eweHN/YRGiFCIUTg9dEyZR5JUwikTIun75JDIvtNhqmEfr/PxvrMQSPBRJxngitZhoYsMD9Oo+aI0nby1pjHwGQnQ1AcoankaUoc0ZjThvIFmpOaRKkw7j6x5CkRqVIEdZbCGMdNQM4lRJY3GifJWCdfdkM3EUBkVJiEJG1RxPrGMh57/BFsfe0KVF1FEgwwOrqBg14f456HZq0NQabnDZER0pgGGB1ZGI7GsG0bApnOT2yM5QCCouVxqXIDURphZE3Q641wMLLgRYBCpqCiAN00OC9fpnNBaTgCMJqMUddUzDeaMCQZnZqJg93b+I9XXoRWb2Jx9Rye+N4LcJ0BDm9ch9Xbh+c5sMcjpkE0Wx2IcQxBkZgaYZEYi9Brx0MS5dnodTLsl1XIYoo4IlTThx9Tln8KylOQ2zW2EGssdKG1WpBrOvOQFxeWMEeUCk3mz42QUC90eVzP/yQJ245JCcVmCugPDjE8cuA5CfOMQ8fHoHfEnyUhe0RvIN9LelzJo6T/PhiMoNTnoGoGTF3C+vllbop6/T6WkhQ3btzg+9NtODxgPi09lhwISJFfNofVcXtZPIav+t+fgZJWEc6zKCLTSGr1Vs3Pr1Y1RemsuM+zuKjl36qpZmc1vtPHSU1pmYhWfkemUdxp54EiRC7/lyzlLhfF61Vfk+57eLCLVNQrze6JQ1Ye0zobOs5qVr/umn2rZvXlLl/GpctfxfCp9zF89wb2e7cQGyKiVEOQ1XHouqhlCdyIRtAB4jDKF8ZMYOWvazlQZeJBEjcy9zFVpIwFTwIjPArn6DN7lKiuqci3mNCgTEIgJAhJHU+xlEkEv2hMOXddkuEhTzOiTP5ygaXxJKGQJMip5oLnzgDCsddjyd8TKl6p+f8/aSQoQScSchSVuhRFEbCw2Mb6Bgk5aojTFrw0giSYSPw+Dvo9DNGHYZB3aghEJsLQR5SFmNhj9u9UdAOpoLEgyQ5Vfm4yPqfj7fWHOBzZiFIJqqZzpCs15eRCIKj5JiBIQ+ZqHo2HsPtDnFtahyELCC0Lezsf4dWXXsTFy4/gyqUtxCyjFyAbEiNeqqzDrDXh2B4S32Gv0MRPEMsJFMq2J8V2knAAABnaE8qbGRpgqIhVBTH7zCocgqCJEhqba1g/v4n7H34Yi+vrkHWdFdu0MSD6oRM5fC7lOIZBdAqhDELIz2/iTCBIKba3t9G7PUbgExIpI7Ij7N/c53NSa3ePP9Myc56eI0pDigeD60WQdQ3t7hK++73fxd7+Tey/9Ao+3N7BN5/5HaydW8HuXg8/Hb8Ea3SAbrfLN9psKLU7R/CnGsn07I3NWfZP043pNGezrLLBi9nL9cRL9KxJWtlwnoWMMDWg4LiWj5vOsK+6CpTX/fG1ziileOo1qg0xCgrBnc1pESOXZRi5NnRNg6ZrHF9KAj5y7KDPLacHCdDrKnsMs/1Wkpvt5wEBZwvDZjWrWX26uucR03tdtf9JPf1m9flUSiN44oypQH1eRX3ewNidoDcO0VLqMFUZWSww4iaRcTbdMpHtX1jUomgcPUiZ9yTSkaVigRczTneJRQVClpvekw8jeWcmvKiSfpisgBIkpPIm5X1xH7omVH4u4qMxUQCyeJKlXW1Mq4vtceNZoKPTccDVxbtEhsh3MVJFjkelxlAk0/DYRX+wB1zzYdYeRuCOEXkR4jiDb3lwwwixTo2pD0NZZzN6x7PZiJ6aTI3ImrICMYpxrXeU58nHeUMfpQIUrcHNXUbusLrEKnVCUin6E6iT3gVhGrOobLHdhqMq+M+XX8bQ9fHYk4/jheefg6TX8N6bb+Jvfv5PUOIIy+vLSK0xBNtFp9lATdXZR5Q5iITAkgCKNgmKyAb5TJLIMphLbW4ghsQTJb/YuTksrJ/H/Ob9aMx3cfnKFUi6yu+HkFRCRwWJxDUa0wNtO2bUV9Jo+JzkQQyFTRg1Ue2uznn5ZHyfZhL76hK9w/UCFl+RoK3eWTj+bMuGq0TGKUrU9hLEQYTrH27zbWINGQ2eX9/gz5Ia0BJBpGvCUHOLKLJBa1Qat2lxUn4tRaebu8rv0rQY6fT/O32/6eav+j6mf++qt9IG7W7RgzgDMS2RyxOF/OljPAv5LRva6vPkxy2dIY4qfpdpLynl3sMJbRrCHG0nTjVtUCnRbWFhAXp9Dq1Wi6kHISPeYkETkGaxorOa1WdQM8R0Vl/qEol7Ksi8kJeLJI3IyexdFC2kWoaMTNMVATpl4jOapeYLWkpIpwhVlKGf0ZjSbeyF9/Tp46QbOl4SjSQxIiTH6Td0I6RPFiwYQnA8YqacdRrZB+EIGnH0pJSbSfbLTJPc2mowhOeGOLDl3IWAzk9xjimPiUIHCDlmfcm0r2WxmJfRlPv7+3hnb4zG2gaem38em+dWMXYD/OK9a1hZWcGl+85jxTDx3z97EVf/7ec4PDzkNB5q3tRWC7EQMWoJJU/rYe/LOG9OREFi/8+VjXVGRNur6zDmFoF6G4kkM5f3OBST0DdCdgtUmh5PRvZEuaCPmwzfaQNyshGJoarC8Tg5HyPnTVVJxfi44mAFQYDnJ9ju7eLVV19l54H64iK2trYwGAxwffsDTCyHzyMhd/T+qeG9fOkigllj9KmKwgkIGR2Nx3AmFl87pqoxjaPVaMBJ3bs21DnoMKNyzWpWv9YC8L8bp2S2nkgOFQAAAABJRU5ErkJggg==" alt="Prof. Sanders giving default values to define the Region of Practical Equivalence (ROPE)." width="75%" />

<p class="caption">

<p>Prof. Sanders giving default values to define the Region of Practical Equivalence (ROPE).</p>
</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 (Cohen, 1988).</p>
<div class="sourceCode" id="cb33"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb33-1" title="1">rope_value &lt;-<span class="st"> </span><span class="fl">0.1</span> <span class="op">*</span><span class="st"> </span><span class="kw">sd</span>(data<span class="op">$</span>weight)</a>
<a class="sourceLine" id="cb33-2" title="2">rope_range &lt;-<span class="st"> </span><span class="kw">c</span>(<span class="op">-</span>rope_value, rope_value)</a>
<a class="sourceLine" id="cb33-3" title="3">rope_range</a></code></pre></div>
<pre><code>&gt; [1] -6.2  6.2
</code></pre>
<p>Let’s redefine our ROPE as the region within the <code>[-6.2, 6.2]</code> range. <strong>Note that this can be directly obtained by the <code>rope_range</code> function :)</strong></p>
<div class="sourceCode" id="cb35"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb35-1" title="1">rope_value &lt;-<span class="st"> </span><span class="kw">rope_range</span>(model)</a>
<a class="sourceLine" id="cb35-2" title="2">rope_range</a></code></pre></div>
<pre><code>&gt; [1] -6.2  6.2
</code></pre>
<p>Let’s recompute the <strong>percentage in ROPE</strong>:</p>
<div class="sourceCode" id="cb37"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb37-1" title="1"><span class="kw">rope</span>(posteriors<span class="op">$</span>feedsunflower, <span class="dt">range =</span> rope_range, <span class="dt">ci=</span><span class="fl">0.89</span>)</a></code></pre></div>
<pre><code>&gt; # Proportion of samples inside the ROPE [-6.17, 6.17]:
&gt; 
&gt; inside ROPE
&gt; -----------
&gt; 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>
<h3 id="probability-of-direction-pd">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="cb39"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb39-1" title="1">n_positive &lt;-<span class="st"> </span>posteriors <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb39-2" title="2"><span class="st">  </span><span class="kw">filter</span>(feedsunflower <span class="op">&gt;</span><span class="st"> </span><span class="dv">0</span>) <span class="op">%&gt;%</span><span class="st"> </span><span class="co"># select only positive values</span></a>
<a class="sourceLine" id="cb39-3" title="3"><span class="st">  </span><span class="kw">nrow</span>() <span class="co"># Get length</span></a>
<a class="sourceLine" id="cb39-4" title="4">n_positive <span class="op">/</span><span class="st"> </span><span class="kw">nrow</span>(posteriors) <span class="op">*</span><span class="st"> </span><span class="dv">100</span></a></code></pre></div>
<pre><code>&gt; [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="cb41"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb41-1" title="1"><span class="kw">p_direction</span>(posteriors<span class="op">$</span>feedsunflower)</a></code></pre></div>
<pre><code>&gt; pd = 98.15%
</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="cb43"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb43-1" title="1">pd &lt;-<span class="st"> </span><span class="fl">97.82</span></a>
<a class="sourceLine" id="cb43-2" title="2">onesided_p &lt;-<span class="st"> </span><span class="dv">1</span> <span class="op">-</span><span class="st"> </span>pd <span class="op">/</span><span class="st"> </span><span class="dv">100</span>  </a>
<a class="sourceLine" id="cb43-3" title="3">twosided_p &lt;-<span class="st"> </span>onesided_p <span class="op">*</span><span class="st"> </span><span class="dv">2</span></a>
<a class="sourceLine" id="cb43-4" title="4">twosided_p</a></code></pre></div>
<pre><code>&gt; [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>
<h4 id="comparison-to-frequentist">Comparison to frequentist</h4>
<div class="sourceCode" id="cb45"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb45-1" title="1"><span class="kw">lm</span>(weight <span class="op">~</span><span class="st"> </span>feed, <span class="dt">data=</span>data) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb45-2" title="2"><span class="st">  </span><span class="kw">summary</span>()</a></code></pre></div>
<pre><code>&gt; 
&gt; Call:
&gt; lm(formula = weight ~ feed, data = data)
&gt; 
&gt; Residuals:
&gt;     Min      1Q  Median      3Q     Max 
&gt; -123.91  -25.91   -6.92   32.09  103.09 
&gt; 
&gt; Coefficients:
&gt;               Estimate Std. Error t value Pr(&gt;|t|)    
&gt; (Intercept)      276.9       17.2   16.10  2.7e-13 ***
&gt; feedsunflower     52.0       23.8    2.18     0.04 *  
&gt; ---
&gt; Signif. codes:  0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1
&gt; 
&gt; Residual standard error: 57 on 21 degrees of freedom
&gt; Multiple R-squared:  0.185,   Adjusted R-squared:  0.146 
&gt; 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> (beta = 52, p = 0.04).</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>
<h2 id="all-with-one-function">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="cb47"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb47-1" title="1"><span class="kw">describe_posterior</span>(model, <span class="dt">test =</span> <span class="kw">c</span>(<span class="st">&quot;p_direction&quot;</span>,<span class="st">&quot;rope&quot;</span>,<span class="st">&quot;bayesfactor&quot;</span>))</a></code></pre></div>
<pre><code>&gt; # Description of Posterior Distributions
&gt; 
&gt; Parameter     |  Median | CI |  CI_low | CI_high |    pd | ROPE_CI | ROPE_low | ROPE_high | ROPE_Percentage |          BF |  Rhat |  ESS
&gt; ----------------------------------------------------------------------------------------------------------------------------------------
&gt; (Intercept)   | 276.853 | 89 | 247.820 | 305.534 | 1.000 |      89 |   -6.175 |     6.175 |               0 | 2.43536e+11 | 0.999 | 3537
&gt; feedsunflower |  50.991 | 89 |  13.516 |  91.371 | 0.982 |      89 |   -6.175 |     6.175 |               0 |       1.575 | 1.000 | 3535
</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_GLM.html"><strong>Click here</strong></a> to see the next example.</p>
<h2 id="references">References</h2>
<div id="refs" class="references">

<div id="ref-cohen1988statistical">

<p>Cohen, J. (1988). <em>Statistical power analysis for the social sciences</em>.</p>
</div>

<div id="ref-kruschke2014doing">

<p>Kruschke, J. (2014). <em>Doing bayesian data analysis: A tutorial with r, jags, and stan</em>. Academic Press.</p>
</div>

<div id="ref-mcelreath2018statistical">

<p>McElreath, R. (2018). <em>Statistical rethinking: A bayesian course with examples in r and stan</em>. Chapman; Hall/CRC.</p>
</div>

</div>

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