{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction to Statistical Power\n", "**Author**: Paul M. Magwene" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If viewing this as a live notebook, or using the nbviewer, use the \"Show Code\" button below to toggle the display of the Python code that generated the figures.\n", "\n", "If viewing this notebook via GitHub you might want to use [this nbviewer link](http://nbviewer.jupyter.org/github/Bio204-class/bio204-notebooks/blob/master/inclass-2016-03-09-Introduction-to-Statistical-Power.ipynb) to view this notebook." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%html\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import scipy.stats as stats\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "np.random.seed(20160309)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Outcomes of hypothesis tests\n", "\n", "In standard statistical hypothesis testing there are two real possibilities -- the null hypothesis is true or the alternative hypothesis is true. When you carry out a hypothesis test, there are two possible test outcomes -- you reject the null hypothesis or you fail to reject the null hypothesis. It is typical to represent the different combinations of the reality / statistical tests in a table like the following:\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "| | do not reject $H_0$ | reject $H_0$ |\n", "|------------|:-----------------------------:|:------------------------------:|\n", "|$H_0$ true | okay | Type 1 error (false positive), $\\alpha$ |\n", "|$H_A$ true | Type 2 error (false negative), $\\beta$ | okay |" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When we specify a significance threshold, $\\alpha$, for hypothesis testing, this controls the Type I error (false positive rate) of our test. The false negative rate is often referred to as $\\beta$. In general, there is a tradeoff between the false positive and false negative rate -- the lower the false positive rate the higher the false negative rate, and vice versa.\n", "\n", "### Statistical Power\n", "\n", "The power of a statistical test is defined as:\n", "$$\n", "\\mbox{Power}\\ = P(\\mbox{reject}\\ H_0\\ |\\ H_A \\mbox{is true})\n", "$$\n", "\n", "In words, this is the probability that the null hypothesis is rejected, conditional on the alternative hypothesis being true.\n", "\n", "If $\\beta$ is the false negative rate, then \n", "$$\n", "\\mbox{Power}\\ = 1 - \\beta\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exploring statistical power for one-sample t-tests\n", "\n", "We'll use a one-sample t-tests to illustrate the concept of statistical power. For this example, we'll explore the power of the t-test to distinguish between the null hypothesis that the data of interest are $H_0 \\sim N(\\mu=0,\\sigma=1)$ and a true underlying distribution $H_A \\sim N(\\mu \\neq 0, \\sigma=1)$.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Effect of sample size on power\n", "\n", "First we'll hold the effect size ( $|\\mu_{H_A} - \\mu_{H_0}|$ ) constant and vary sample size.\n", "\n", "Consider the population distributions below for the null hypothesis (red) and true underlying distribution (black). Both have the same standard deviation ($\\sigma = 1$) and differ only in their means ($\\mu_{H_0} = 0$ and $\\mu_{H_A} = 0.5$)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Population Distributions" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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aeXp+fidZ2fE8EDxXK9N3ePDwiBYtWtCiRYt8C0pERGKEc76HCmD1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "muH0, muHA = 0, 0.5\n", "sigma = 1\n", "\n", "fig, ax1 = plt.subplots(figsize=(12,5))\n", "x = np.linspace(-4, 4, 500)\n", "\n", "ax1.plot(x, stats.norm.pdf(x, loc=muH0, scale=sigma), color='red', \n", " linestyle='dotted', linewidth=2, label='Distn under $H_0$')\n", "ax1.plot(x, stats.norm.pdf(x, loc=muHA, scale=sigma), color='black', \n", " linewidth=2, label='True Distn, $H_A$')\n", "\n", "offset = 0.2\n", "ax1.text(muH0 - offset, 0.45, \"$\\mu_{H_0}$\", \n", " horizontalalignment='center', color='red', fontsize=18)\n", "ax1.text(muHA + offset, 0.45, \"$\\mu_{H_A}$\", \n", " horizontalalignment='center', color='black', fontsize=18)\n", "\n", "ax1.set_ylim(0, 0.5)\n", "ax1.vlines(muH0,0,0.5,color='red', linestyle='dashed')\n", "ax1.vlines(muHA,0,0.5,color='black', linestyle='dashed')\n", "ax1.legend(loc='best')\n", "ax1.set_xlabel(\"Random Variable X\")\n", "ax1.set_ylabel(\"Density\")\n", "ax1.set_title(\"Population Distributions\\nfor the Null and True Distributions\",fontsize=18)\n", "fig.tight_layout()\n", "#fig.savefig(\"fig-H0distn-vs-TrueDistn.pdf\")\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Sampling distributions of the mean\n", "\n", "Now imagine taking samples of size n=10, n=25, and n=50. What will happen to the **sampling distributions of the mean**? We've encountered this repeatedly before -- the sampling distribution of the mean should be centered around the true population mean, and should have standard deviations given by $\\frac{\\sigma}{\\sqrt{n}}$ (remember that the standard deviation of a sampling distribution is called a \"standard error\").\n", "\n", "Here is what the expected sampling distributions of the mean look like for the null and true distributions with samples of size 10, 25, and 50." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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0J1mpXNJ7TimllCo+tCdZKaWUUkqpHCoZSbLzA2253S5A0dHRNGvWDB8fH6ZN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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n1, n2, n3 = 10, 25, 50\n", "\n", "fig, (ax1,ax2,ax3) = plt.subplots(3, 1, figsize=(10,12), sharex=True)\n", "\n", "x = np.linspace(-2, 2, 500)\n", "ax1.plot(x, stats.norm.pdf(x, scale=1/np.sqrt(n1)), color='red', linestyle='dotted', linewidth=2,\n", " label='Sampling Distn\\n of mean under $H_0$')\n", "ax1.plot(x, stats.norm.pdf(x, loc=0.5, scale=1/np.sqrt(n1)), color='black', linewidth=2,\n", " label='Sampling Distn\\n of mean under $H_A$')\n", "\n", "offset = 0.1\n", "\n", "ax1.text(muH0 - offset, 1.4, \"$\\mu_{H_0}$\", \n", " horizontalalignment='center', color='red', fontsize=18)\n", "ax1.text(muHA + offset, 1.4, \"$\\mu_{H_A}$\", \n", " horizontalalignment='center', color='black', fontsize=18)\n", "ax1.set_ylim(0, 1.5)\n", "ax1.set_xlim(-1.75,1.75)\n", "ax1.vlines(0,0,1.5,color='red', linestyle='dashed')\n", "ax1.vlines(0.5,0,1.5,color='black', linestyle='dashed')\n", "ax1.legend(loc='upper left')\n", "ax1.set_xlabel(\"Random Variable X\")\n", "ax1.set_ylabel(\"Density\")\n", "ax1.set_title(\"\"\"Sampling Distributions of the Mean\n", "For Samples of Size n = {}\"\"\".format(n1))\n", "\n", "ax2.plot(x, stats.norm.pdf(x, scale=1/np.sqrt(n2)), color='red', linestyle='dotted', linewidth=2,\n", " label='Sampling Distn\\n of mean under $H_0$')\n", "ax2.plot(x, stats.norm.pdf(x, loc=0.5, scale=1/np.sqrt(n2)), color='black', linewidth=2,\n", " label='Sampling Distn\\n of mean under $H_A$')\n", "\n", "ax2.set_ylim(0, 2.25)\n", "ax2.vlines(0,0,2.25,color='red', linestyle='dashed')\n", "ax2.vlines(0.5,0,2.25,color='black', linestyle='dashed')\n", "ax2.legend(loc='upper left')\n", "ax2.set_xlabel(\"Random Variable X\")\n", "ax2.set_ylabel(\"Density\")\n", "ax2.set_title(\"\"\"n = {}\"\"\".format(n2))\n", "\n", "\n", "ax3.plot(x, stats.norm.pdf(x, scale=1/np.sqrt(n3)), color='red', linestyle='dotted', linewidth=2,\n", " label='Sampling Distn\\n of mean under $H_0$')\n", "ax3.plot(x, stats.norm.pdf(x, loc=0.5, scale=1/np.sqrt(n3)), color='black', linewidth=2,\n", " label='Sampling Distn\\n of mean under $H_A$')\n", "\n", "ax3.set_ylim(0, 3)\n", "ax3.vlines(0,0,3,color='red', linestyle='dashed')\n", "ax3.vlines(0.5,0,3,color='black', linestyle='dashed')\n", "ax3.legend(loc='upper left')\n", "ax3.set_xlabel(\"Random Variable X\")\n", "ax3.set_ylabel(\"Density\")\n", "ax3.set_title(\"\"\"n = {}\"\"\".format(n3))\n", "\n", "fig.tight_layout(h_pad=2.5)\n", "#fig.savefig(\"fig-H0sampling-vs-Truesampling.pdf\")\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the figures above we see that as sample size increases, the sampling distributions of the mean for the null and true distributions have less and less overlap, suggesting that as sample size increases the probability that we corrected reject the null hypothesis will increase as well." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exploring power with simulations: varying sample size\n", "\n", "In general one doesn't know either $\\mu_{H_A}$ or $\\sigma$ so these parameters need to be estimated from the data itself. Because of this, in the simulations below we use the t-distribution to model the sampling distribution of the mean under the null hypothesis.\n", "\n", "Each set of simulations below estimates the probability that you reject that null hypothesis, given the alternative hypothesis is true for a fixed effect size. The significance threshold, $\\alpha = 0.5$, for all the simulations." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "For sample size n = 10\n", "the percent of simulations where we failed to reject H0 is: 71.3\n", "and hence, the percent of simulations where we correctly rejected H0 is: 28.700000000000003\n" ] }, { "data": { "image/png": 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O1K1bl1WrVhX4z6AgPv30U1xcXAgLC2Pp0qXFOrYQ1mzJyk9Yve1HPos+aFqO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\n9etDKjHzeDx8++237Nq1q8Ji98BsWKJj47j1/ie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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 10\n", "mu_null = 0\n", "mu_alt = 0.5\n", "sigma = 1\n", "SE = sigma/np.sqrt(n)\n", "samplingdist_null = stats.t(df=n-1,scale=SE)\n", "dist_alt = stats.norm(loc=mu_alt, scale=sigma)\n", "\n", "nsims = 1000\n", "alpha = 0.05\n", "null_left_cutoff = mu_null + samplingdist_null.ppf(alpha/2)\n", "null_right_cutoff = mu_null + samplingdist_null.ppf(1-(alpha/2))\n", "\n", "sample_means = []\n", "sample_zscores = []\n", "\n", "for i in range(nsims):\n", " sample = dist_alt.rvs(size=n)\n", " mean = np.mean(sample)\n", " sample_means.append(mean)\n", " zscore = mean/np.std(sample,ddof=1)\n", " sample_zscores.append(zscore)\n", " \n", "sample_means = np.asarray(sample_means)\n", "sample_zscores = np.asarray(sample_zscores)\n", "\n", "fig, ax = plt.subplots(figsize=(10,4))\n", "x = np.linspace(-2,2,250)\n", "ax.plot(x, samplingdist_null.pdf(x), color='black', label=\"Expected distn of\\nsample means, H0\")\n", "ax.hist(sample_means, bins=50, normed=True, label=\"Observed distn of\\nsample means, HA\",\n", " color='steelblue', histtype='stepfilled', alpha=0.5)\n", "ax.set_xlabel(\"mean X\")\n", "ax.set_ylabel(\"density\")\n", "\n", "min_y, max_y = ax.get_ylim()\n", "\n", "# draw left_cutoff\n", "ax.vlines(null_left_cutoff, 0, max_y, linestyle='dotted')\n", "# draw right cutoff\n", "ax.vlines(null_right_cutoff, 0, max_y, linestyle='dotted')\n", "\n", "ax.legend(loc='upper left')\n", "\n", "failed_to_reject_H0 = np.logical_and(sample_zscores > null_left_cutoff, \n", " sample_zscores < null_right_cutoff)\n", "\n", "How_often_failed_to_reject_H0 = np.count_nonzero(failed_to_reject_H0)/nsims\n", "print(\"For sample size n =\", n)\n", "print(\"the percent of simulations where we failed to reject H0 is:\", \n", " How_often_failed_to_reject_H0 * 100)\n", "print(\"and hence, the percent of simulations where we correctly rejected H0 is:\", \n", " (1.0 - How_often_failed_to_reject_H0) * 100)\n", "\n", "#fig.savefig(\"fig-powersim-n10.pdf\")\n", "\n", "pass" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "For sample size n = 25\n", "the percent of simulations where we failed to reject H0 is: 29.9\n", "and hence, the percent of simulations where we correctly rejected H0 is: 70.10000000000001\n" ] }, { "data": { "image/png": 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ldHS0tLa2lp988onMy8uTu3btko6OjjIuLk5KKeUbb7whP//8cymllEeOHJHV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\naiaEUDoUs9ayfRcc+ysatzJvKh0KERk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 25\n", "mu_null = 0\n", "mu_alt = 0.5\n", "sigma = 1\n", "SE = sigma/np.sqrt(n)\n", "samplingdist_null = stats.t(df=n-1,scale=SE)\n", "dist_alt = stats.norm(loc=mu_alt, scale=sigma)\n", "\n", "nsims = 1000\n", "alpha = 0.05\n", "null_left_cutoff = mu_null + samplingdist_null.ppf(alpha/2)\n", "null_right_cutoff = mu_null + samplingdist_null.ppf(1-(alpha/2))\n", "\n", "sample_means = []\n", "sample_zscores = []\n", "\n", "for i in range(nsims):\n", " sample = dist_alt.rvs(size=n)\n", " mean = np.mean(sample)\n", " sample_means.append(mean)\n", " zscore = mean/np.std(sample,ddof=1)\n", " sample_zscores.append(zscore)\n", " \n", "sample_means = np.asarray(sample_means)\n", "sample_zscores = np.asarray(sample_zscores)\n", "\n", "fig, ax = plt.subplots(figsize=(10,4))\n", "x = np.linspace(-2,2,250)\n", "ax.plot(x, samplingdist_null.pdf(x), color='black', label=\"Expected distn of\\nsample means, H0\")\n", "ax.hist(sample_means, bins=50, normed=True, label=\"Observed distn of\\nsample means, HA\",\n", " color='steelblue', histtype='stepfilled', alpha=0.5)\n", "ax.set_xlabel(\"mean X\")\n", "ax.set_ylabel(\"density\")\n", "\n", "min_y, max_y = ax.get_ylim()\n", "\n", "# draw left_cutoff\n", "ax.vlines(null_left_cutoff, 0, max_y, linestyle='dotted')\n", "# draw right cutoff\n", "ax.vlines(null_right_cutoff, 0, max_y, linestyle='dotted')\n", "\n", "ax.legend(loc='upper left')\n", "\n", "failed_to_reject_H0 = np.logical_and(sample_zscores > null_left_cutoff, \n", " sample_zscores < null_right_cutoff)\n", "\n", "How_often_failed_to_reject_H0 = np.count_nonzero(failed_to_reject_H0)/nsims\n", "print(\"For sample size n =\", n)\n", "print(\"the percent of simulations where we failed to reject H0 is:\", \n", " How_often_failed_to_reject_H0 * 100)\n", "print(\"and hence, the percent of simulations where we correctly rejected H0 is:\", \n", " (1.0 - How_often_failed_to_reject_H0) * 100)\n", "\n", "pass" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "For sample size n = 50\n", "the percent of simulations where we failed to reject H0 is: 5.7\n", "and hence, the percent of simulations where we correctly rejected H0 is: 94.3\n" ] }, { "data": { "image/png": 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mXl5eprbuTUIKujb37t1LVlYWERERwJ3kMCIiokhb6enpzJ8/n0aNGuHg4FAk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\nuaEbIe27WD44C3FyblijP58QlSWVMyG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 50\n", "mu_null = 0\n", "mu_alt = 0.5\n", "sigma = 1\n", "SE = sigma/np.sqrt(n)\n", "samplingdist_null = stats.t(df=n-1,scale=SE)\n", "dist_alt = stats.norm(loc=mu_alt, scale=sigma)\n", "\n", "nsims = 1000\n", "alpha = 0.05\n", "null_left_cutoff = mu_null + samplingdist_null.ppf(alpha/2)\n", "null_right_cutoff = mu_null + samplingdist_null.ppf(1-(alpha/2))\n", "\n", "sample_means = []\n", "sample_zscores = []\n", "\n", "for i in range(nsims):\n", " sample = dist_alt.rvs(size=n)\n", " mean = np.mean(sample)\n", " sample_means.append(mean)\n", " zscore = mean/np.std(sample,ddof=1)\n", " sample_zscores.append(zscore)\n", " \n", "sample_means = np.asarray(sample_means)\n", "sample_zscores = np.asarray(sample_zscores)\n", "\n", "fig, ax = plt.subplots(figsize=(10,4))\n", "x = np.linspace(-2,2,250)\n", "ax.plot(x, samplingdist_null.pdf(x), color='black', label=\"Expected distn of\\nsample means, H0\")\n", "ax.hist(sample_means, bins=50, normed=True, label=\"Observed distn of\\nsample means, HA\",\n", " color='steelblue', histtype='stepfilled', alpha=0.5)\n", "ax.set_xlabel(\"mean X\")\n", "ax.set_ylabel(\"density\")\n", "\n", "min_y, max_y = ax.get_ylim()\n", "\n", "# draw left_cutoff\n", "ax.vlines(null_left_cutoff, 0, max_y, linestyle='dotted')\n", "# draw right cutoff\n", "ax.vlines(null_right_cutoff, 0, max_y, linestyle='dotted')\n", "\n", "ax.legend(loc='upper left')\n", "\n", "failed_to_reject_H0 = np.logical_and(sample_zscores > null_left_cutoff, \n", " sample_zscores < null_right_cutoff)\n", "\n", "How_often_failed_to_reject_H0 = np.count_nonzero(failed_to_reject_H0)/nsims\n", "print(\"For sample size n =\", n)\n", "print(\"the percent of simulations where we failed to reject H0 is:\", \n", " How_often_failed_to_reject_H0 * 100)\n", "print(\"and hence, the percent of simulations where we correctly rejected H0 is:\", \n", " (1.0 - How_often_failed_to_reject_H0) * 100)\n", "\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can repeat this exercise for multiple sample sizes as shown below." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mu_null = 0\n", "mu_alt = 0.5\n", "sigma = 1\n", "\n", "nsims = 2000\n", "sizes = [5, 10, 20, 40, 60, 80, 100, 150, 300]\n", "\n", "alpha = 0.05\n", "SEs = [sigma/np.sqrt(i) for i in sizes]\n", "left_cutoffs = [mu_null + stats.t.ppf(alpha/2, df=i-1, loc=mu_null, scale=j)\n", " for (i,j) in zip(sizes, SEs)]\n", "right_cutoffs = [mu_null + stats.t.ppf((1-alpha/2), df=i-1, loc=mu_null, scale=j)\n", " for (i,j) in zip(sizes,SEs)]\n", "\n", "dist_alt = stats.norm(loc=mu_alt, scale=sigma)\n", "samples = [dist_alt.rvs(size=(i, nsims)) for i in sizes]\n", "sample_means = np.asarray([np.mean(i, axis=0) for i in samples])\n", "sample_stds = np.asarray([np.std(i, ddof=1, axis=0) for i in samples])\n", "sample_zs = (sample_means-mu_null)/sample_stds\n", "\n", "failed_to_reject_H0 = [np.logical_and(i > left, i < right) for (i, left, right) \n", " in zip(sample_zs, left_cutoffs, right_cutoffs)]\n", "\n", "frac_failed_to_reject_H0 = [np.count_nonzero(i)/nsims for i in failed_to_reject_H0]\n", "\n", "correctly_rejected_H0 = [(1-i) for i in frac_failed_to_reject_H0]\n", "\n", "fig, ax = plt.subplots(figsize=(6,4))\n", "ax.plot(sizes, correctly_rejected_H0, marker='o', color='black')\n", "ax.set_xlabel(\"sample size, n\")\n", "ax.set_ylabel(\"Power ( = Probability $H_0$ correctly rejected)\")\n", "ax.set_ylim(0,1.1)\n", "ax.set_xlim(0, max(sizes)*1.05)\n", "\n", "#fig.savefig('fig-powercurve-diff05.pdf')\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Varying both sample size and effect size\n", "\n", "In the simulations above we kept the effect size (the difference between the mean of the null and true distributions in our example) constant. Now let's explore how both sample size and effect size influence power. We'll consider three different scenarios -- $\\mu_{H_A} = 1$, $\\mu_{H_A} = 0.5$, and $\\mu_{H_A} = 0.25$ ($\\mu_{H_0} = 0$ in all three cases). As before, the significance threshold, $\\alpha = 0.5$, for all the simulations." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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V1dWA81zc2trKtm3biIuL89WWnpFmzyRv2rSJrq4uj6NR/aVFsvIl\nu0h2unG9mxoaYM8eSEqyFrMNFiKn/yjQtjqlBo+uri4OHz4MOM/FW7ZsobOzk2nTpjnu9Y0mOTk5\njBs3jubmZnbv3u11OKqftEhWvuTHmeRNm6zPc+ZYhXKkrFq1it///ve0t7dH7kn6SYtkpQaf2tpa\nurq6GD58OCkpKY7GirZ+5Lq6Ol5++WXefvttx2NpX3L00iJZ+U5HRwe1tbWICHl5eV6H083Ob5HO\n8fv27ePgwYPdb3P6gV0ka45XavCwJyvsPdydiLZ+5M7OTrZu3erK7K/2JUcvLZKVL11zzTVceuml\nJEVyyraf7FnUSOd4P568Z3/PmzdDZ6e3sSilBsbYsWNZunQpM2bMcDxWtM0kjxo1ivj4eOrr62lp\naXE0lv096zZw0UeLZOU7iYmJzJ07l8svv9zrULoZM3AzyXaLiZ+K5OHDYeJEaGmBnTu9jkYpNRBy\ncnK49NJLKSoqcjTO0aNHKS8vJy0tjenTp7sUXWTFx8d3v5Pp9F29uXPnkpCQwM6dOzl58qQb4akB\nokWyUn1QUQG1tTBsmFUsRpIfj6cG7UtWSoVn48aNAMybN8/xKXYDya1cnJqaysyZMwkEAmzevNmN\n0NQA0SJZqT4I3fot0vsEjxgxguTkZJqammhsbIzsk/WDPYOuRbJSqj+irR/Z5ua7etqXHJ2i5086\npTw0UP3IACLC5z73OTIzM321VZIu3lNKhcPuxY22Inn8+PHccsstruyyVFJSwi9/+UstkqOMFslK\n9cFA9SPbLrjggoF5on6YPRsSEmDXLmhqgowMryNSSvmdMSbqFu3ZhgwZwpQpU1wZSxfvRSdtt1C+\nsn79ep599ln279/vdSjdOjutXR0AFizwNhYvpaZah6gYAx9+6HU0SqlIMcbwhz/8gVdeecXxfu37\n9++nvr6enJwcCgsLXYow+kyePJmhQ4dSWVnpq+091blpkax8pby8nL179zrecsdNu3bBqVMwYQKM\nHOl1NN7SlgulYl9TUxMHDhygtLSUxMRER2PZ7QUlJSVIpBd0+FhcXBwLgrMs2nIRPbRIVr5hjHF1\n83q3DGQ/st/pDhdKxT57N4f8/HzHhW209iNHgp68F320SFa+0dDQQEtLC0OGDCEzM9PrcLoNdD9y\nKGMMnT46vUN3uFAq9tmTFaNHj3Y8VuhMcjTr6uoiEAg4GkP7kqOPFsnKN9ycvXCTVzPJe/fu5cEH\nH+S1114b2Cc+h8mTrQV7FRVw+LDX0SilIsHumXX6jl57eztbtmwB6G41iEYvvPAC999/P4cdJj17\nNn3jxo10dXW5EZqKMC2SlW+4OXvhlpMnrZ7khASYM2dgnzstLY2TJ0/66uS9uLjTixd1MkSp2BMI\nBFwrkrdv305bWxuTJ08mKyvLjfA8ERcXR2dnp+NcnJubS2FhISdPnqS0tNSl6FQkaZGsfOOKK67g\njjvuYObMmV6H0m3TJggErF0dUlMH9rlzc3OJi4ujrq6Otra2gX3yc7DfNdW2OqViT1xcHPfccw+3\n3nqr433aY6Uf2f5jwY0JC+1Lji5aJCvfSExMpLCwkOzsbK9D6eblor3ExERGjRoF4PhtPjfp4j2l\nYtvQoUNd2as9VvqRI1Eka19ydNAiWalz8HLRHribnN1ivxYbN1qz7Eop1ZtYmUkeNWoU8fHx1NfX\nO96eVGeSo4sWyUqdg9fbv9mLGE+ePOlNAL3Iy4OCAmhshL17vY5GKeVHDQ0N7Nmzh6SkJGbNmuV1\nOI7Ex8eTl5dHSkoKx48fdzTW3LlziY+PZ+fOnTQ3N7sUoYoUPZZaqbOorobKShg61NrVwQvTp09n\n2rRpJCUleRPAWRQXW6/Nhg0wdarX0Sil/GbTpk0AzJkzx3f5Kxy33norqampjndeSktL48ILL2Tr\n1q1s2bKFRYsWuRShioSIzySLyNUiskdE9onIv/Zy+5dEZFvwY42IzAy57WDw+i0iog08McxPC9Ns\n9izyggXWrg5eSExM9OUvGN0vObpoHlZ90dHR4XgvYFus9CPb0tLSXNua1G4/0ZYL/4vor34RiQMe\nAq4CpgO3isiUHnfbDyw2xswCfgg8GnJbAFhijJljjInupiZ1Vm1tbfzoRz/ikUcewRjjdTjdvO5H\n9jM9njp6aB5WfbVp0yb++7//mzVr1jgeK1b6kSPBfk108Z7/RXp+rBj4yBhzyBjTATwL3BB6B2PM\nemPMieCX64HQjRllAGJUHquursYYQ0JCgh4iEiXmzQMR2LYNWlu9jkadh+Zh1SdVVVV0dnaSlpbm\naBxjTMzNJLtJi+ToEenElw9UhHxdyZnJt6evAa+HfG2AN0Vko4h8PQLxKR+wd25wunG9m7q6rN0b\nQIvk3mRkwPTp0NkJW7d6HY06D83Dqk/cysUVFRXU1tYybNgwJk6c6EZoMWXatGkMGTKEgwcPUldX\n53U46hx8s3BPRC4H7gBCu9gXGmMOi8hIrCRdaozp9X2gZcuWdV9esmQJS5YsiWC0yk1+LJL37oWm\nJhgzxtrNwWutra1UVVUxYcIE38y2FxfDzp1Wy8VFF3kdjX+tXr2a1atXex1Gn2geHryam5tpaGgg\nMTGRkSNHOhrLniFdsGCBb/KVG4wxHD9+nLa2NvIc/GKIj49n/vz5vPPOO2zYsIFrr73WxShVb8LN\nw5EukquAwpCvC4LXnSG4SORR4GpjTPf+KsaYw8HPR0TkRay3Dc+bnFV08WOR7Ld+5EceeYTGxkbu\nvvtux7/A3FJcDL/5jfYln0/PYvG+++4b6BA0D6vzsvPw6NGjiXO4UtkukmOt1aKsrIynn36awsJC\n7rjjDkdjFRcXa5E8gMLNw5Fut9gITBKRsSKSBHwReCX0DiJSCPwZ+Ioxpjzk+jQRSQ9eHgJcCeyM\ncLxqgLW2tpKQkEBKSgrDhw/3OpxufutH9vuhIsrXNA+r82pubiY5OZnRo0c7HitWF+3Zr83hw4cd\n7wKifcnRIaIzycaYLhG5F1iBVZA/bowpFZFvWjebR4HvA8OAh8V6X6YjuIJ6FPCiiJhgnE8ZY1ZE\nMl418FJSUviHf/gH2trafPW2nD076pccn5+fT2lpKVVVVcyePdvrcACrJzk1FcrKoL4efPQ3jgqh\neVj1xZw5c5g9ezYdHR2Oxunq6ureI3nBggVuhOYbQ4YMITs7m+PHj3PkyBFGjRoV9lihx1MbY3z1\n+0+dFvGeZGPMG8DkHtf9KuTy14FPLAYxxhwA/FENqIhLTk72OoRuLS2wfbu1N/K8eV5HY/HjTHJi\nIsydC++/b80mX3211xGps9E8rPpCRBzvy15aWkpzczPjxo0jJyfHpcj8Iz8/n+PHj1NZWemoSC4o\nKCA3N5eamhrKysooKipyMUrlFt3WR6ketmyxdreYPh3S072OxmIvEqmtraWzs9PjaE6zZ9r1HUOl\nFMRuq4XNbrlwOmEhItpyEQW0SFaqB7/1I4M1015UVMTUqVNp9dHGxHrynlIqVKwXyWPGjCE/P9+V\nNTRaJPufb7aAU8ov7Hzlt4XZX/rSl7wO4RNCT94zxjpgRCk1eMV6kVxQUMDXvvY1V8YK7UtW/iR+\nOgY4XCJiYuH7GGyOHDlCW1sbubm5JCT45++1SZOgvNw6JGPWLK+j8TdjICcHjh6F/fth/HivI/I/\nEcEYE3N/Tmgejl7l5eUMGzaMrKwsRwvIWlpayMjIwBhDY2MjQ4YMcTHK2NPQ0EB2djbJyck0NjY6\n7gdXfdfXPKztFsozGzZs4PHHH2f9+vVeh9Ktvt4qkFNTrZ5kdW4i2pesVDTr6uri2Wef5Wc/+5nj\nVq4tW7bQ1dXFjBkztEDug6ysLCZPnkxbWxvbt2/3OhzVCy2SlWeqq6sB6+0rv7D3/J03D3w0ue1r\n2pesVPSqq6ujs7OTYcOGkZqa6misWG+1iATtS/Y3LZKVJzo7O6mpqQFwdLyn2/y4aM/vQvuSlVLR\nxc0TT7VI7j/tS/Y3LZKVJ2pqaggEAowcOdJXeyT77RCRno4fP84HH3xAaWmp16F0s88L+PBDcHgO\ngVJqgGmRHJ7y8nLefvttmpubHY1jv1Yf6CyDL2mRrDzhZmJ2izH+n0muqqrijTfeYMuWLV6H0m34\ncJg40TqEZdcur6NRSvWHW7m4vr6e8vJyUlNTmT4IFnSsWbOG9957j8rKSkfjzJw5k6SkJPbs2cOJ\nEydcik65RYtk5YnMzEyKiooY76PtEA4etHZpGDECxo3zOpre2f3bVVVV+GknAe1LVir6GGMYP358\n9+lvTmwMLuiYN2+er3YrihS3TkFNTk5m9mzrUEv7OG/lH1okK09MmTKFL33pS8ycOdPrULqF7o/s\n1/1+MzMzSUtL49SpUzQ0NHgdTjftS1Yq+ogIn/nMZ7jrrrscF7aDqdUC3CuSQfuS/UyLZKWC/N5q\nAdYvNTeTs1t0GzilBrfBXCQ7fVdP+5L9S4tkpYKioUgGd2cw3DJ7trVl3q5d0NTkdTRKqYFkjBl0\nRfLQoUPJyMigra2N+vp6R2OFFsl+aqNTeiy1UgB0dsLmzdZle7cGvyoqKsIYw8SJE70OpVtqqnU6\n4ebN1seSJV5HpJQaKIcOHeLIkSOMGDGCcX5d0BEBCxcuJC4uzvH+0pMmTSIrK4uamhqqqqp8dXbA\nYKczyUphzYC2tFi7NAwf7nU05zZ69GiWLFnCmDFjvA7lDNpyodTgFDqL7ORY62hTUlLCggULHJ8u\nGBcXp4eK+JQWyWpAGWNYsWIFW7duJRAIeB1ON7/vjxwNtEhWKnpUVlayatUqx1uYweDrR44E7Uv2\npz4VySLygohcIyJaVCtHGhsbWbduHStWrPDVjEO09CP7mRbJkae5WLll7969vPvuu+zZs8fxWFok\nO6czyf7U10T7MPAl4CMRuV9EJkcwJhXDQjeu92ORbO/3q/pv8mTIyICKCjh82OtoYpbmYuWK6upq\nwPkhIp2dnWwOLuhY4PcFHT5mF8mbNm2iq6vL42iUrU9FsjHmLWPMbcBc4CDwloisFZE7RCQxkgGq\n2GIXyaNHj/Y4ktNOnrR6khMSrF0aVHji408vetTJkMjQXKzcYIxx7aS93bt3c+rUKSZMmMCIESPc\nCG9QGjVqFGPHjuXkyZOuzO4rd/T5LTsRGQ58FfgasAX4X6xE/WZEIlMxyY/HUX/4IQQCMHOmtUtD\ntHjjjTd47LHHaGtr8zqUbtpyEXmai5VT9fX1tLW1kZGRwdChQx2NNdhbLWpqanj++edZvny547G0\nL9l/+tqT/CLwHpAGXGeMud4Y80djzLeA9EgGqGJHIBBw7S0+N0VrP3JFRQXV1dXdr6kfaJEcWZqL\nlRvcnKwY7EWyMYbdu3ezb98+x2NpX7L/9HWf5MeMMa+FXiEiycaYNmPM/AjEpWKQMYYbbriBo0eP\nOt4yx03RWiTn5+dTXV1NVVUV48eP9zoc4MwiORCAOF1e5jbNxcqxwsJCPvOZz5CVleV4rMFeJOfk\n5JCQkMCxY8doaWlxtGeyFsn+09dfYT/s5bp1bgaiYl98fDzTp0/nsssu8zqUM0RzkQz+OnkvP9/6\naGwEFyZW1CdpLlaOZWdnU1xczAUXXOBonObmZnbu3El8fDxz5sxxKbroEh8fT15eHuA8F8+bN4+4\nuDi2b99OS0uLG+Eph85ZJItIrojMA1JFZI6IzA1+LMF6u0+pqFZbC4cOQXo6TJnidTT948ciGbTl\nIhI0Fys/2rJlC11dXVx44YWkpQ3ef4Zu5eIhQ4YwY8YMurq6+PDDD90ITTl0vpnkq4D/AQqAB4Gf\nBD/+Efi3yIamVOTZhdz8+dbuDNFk+PDhJCcn09TURGNjo9fhdNMiOSI0FyvfGeytFjY3Jyy05cJf\nztmTbIz5PfB7Efm8MebPAxSTUgMmmvdHFhFuueUWsrKyyMjI8DqcbvbvS12g7R7NxcqPtEi2TJgw\ngdtvv92VrU2Li4v59a9/rUWyT5yzSBaRLxtjngTGicg/9rzdGPNgxCJTagBEaz+yzS8L9kLNnw8i\nsG0btLZCSorXEUU/zcXKj7RItqSlpbmWi0uCMzZaJPvD+dot7C0I0oGMXj6U6pNNmzbx+9//ntLS\nUq9D6WZM9BfJfjR0KEydCh0dVqGsXKG5WLniiSee4E9/+hPNzc2Oxjly5AgHDhxgyJAhTJs2zaXo\n1LRp00hLS2P//v0cOXLE63AGvXMWycaYXwU/39fbR1+eQESuFpE9IrJPRP61l9u/JCLbgh9rRGRm\nXx+rosehQ4c4ePCgr1bslpVBQwPk5Vk7Mij3aF+yu5zmYs3DCqC1tZX9+/ezZ88eUhy+xbNx40bA\n2pEhPtoWdPhYQkIC8+bNA06/xso7fT1M5MciMlREEkVkpYgcEZEv9+FxccBDWItOpgO3ikjPPQT2\nA4uNMbOwtjd6tB+PVVHCjyfthc4ii3gbS6zRvuTICCcXax5WNvvgodzcXMeFrd0OsMA+i165Rlsu\n/KOv+yRfaYxpBK4FDgKTgH/uw+OKgY+MMYeMMR3As8ANoXcwxqw3xpwIfrkeyO/rY1V0OHXqFMeP\nHycxMZGRI0d6HU63WGq1CAQCvjqe2l4IqTnedeHkYs3DCnB3smL9+vUAXHTRRY7HiiVtbW0EAgFH\nY+gOF/7R1yLZXuB3DfB8SDI9n3ygIuTrSk4n3958DXg9zMcqn7ITc15eHnE+OoItVorknTt38qMf\n/Yg333zT61C6XXghJCfDRx/BsWNeRxNTwsnFmocV4F6RHAgEuovkiy++2HFcseKZZ57h/vvvp66u\nztE4oUWyMcaN0FSY+nos9V9EZA/QAvy9iIwEWt0MREQuB+4AFoXz+GXLlnVfXrJkCUuWLHElLuWc\nH1st2tthyxbr8vwoP8w3IyOD9vb27rdS/SAxEebOhXXrYNMmuPJKryPyzurVq1m9erVbw0U0F2se\njm1u5eK9e/dy4sQJCgoKfJXXvZacnAxYr3Nubm7Y4xQWFpKTk0NdXR379+9n4sSJboU4aIWbh/tU\nJBtjviciPwZOGGO6RKSZvr3lVgUUhnxdELzuDMFFIo8CVxtjjvfnsbbQ5Kz8ZfHixUydOpWkpCSv\nQ+m2dSu0tVm7MGRleR2NM3l5eYgItbW1dHR0kJiY6HVIgDVDv26d1Zc8mIvknsXifff1ac1zr8LM\nxZqHFQD33HMP1dXVDBs2zNE42mrRu/z8fHbs2EFlZWX34rtwiAglJSW8+uqrbNiwQYtkF4Sbh/vz\n3vcU4BYRuR24CejLr72NwCQRGSsiScAXgVdC7yAihcCfga8YY8r781gVHeLi4hg1ahTZ2dleh9Jt\n3dTPBfEAACAASURBVDrrcyzk+KSkJEaOHEkgEKCmpsbrcLppX3LE9DcXax5WAKSkpDBhwgTE4Upl\nLZJ7Z8+qu/GunvYl+0OfZpJF5AlgIrAV6ApebYA/nOtxwZmOe4EVWAX548aYUhH5pnWzeRT4PjAM\neFis/7kdxpjisz22/9+iUp9kF8mx0k6Xn59PXV0dVVVVjBkzxutwgDO3gTNGdxBxQzi5WPOwctu6\nYALVIvlMubm5xMXFUVdXR1tbW3f7RTjsIvkD3SLIU9KXpnARKQWmGZ92kIuIX0NTPjVuHBw6BDt2\nwIwZXkfj3ObNm1m+fDmXXHKJb/pAjYERI6yFewcOWK+5st5KNcaE9SeDn3Ox5uHBoampiczMTBIS\nEjhx4gSpqaleh+Qrjz32GCdPnuS2224jJycn7HGOHz/OsGHDSE5OpqmpyTdtdLGir3m4rwv3dgK5\nwGFHUSnlA4cPWwVyRobVkxwLZs2axZw5c3y1e4iI1XLx+uuwfr0WyS7RXKw8tXHjRowxzJ49Wwvk\nXvzt3/6tK+tvsrOzueCCC9i3bx87duxg7ty5LkSn+quvv1FHALtFZLmIvGJ/RDIwFRuampp8t4WN\n3WpRUgKxclBUQkKCrwpk2yWXWJ/XrvU2jhiiuVj1W2trK+3t7a6Mpf3I5+bmAnXtS/ZeX2eSl0Uy\nCBWbWltbefDBB8nKyuJb3/qWb4q4YI6PmX5kP7NfY/sPE+XYMq8DUNHnww8/5K233mLx4sWO27G0\nH3ngFBcX8+STT/LBBx/wd3/3d16HMyj1dQu4d0RkLFBkjHlLRNKAGJmDU5Fi78mZnp7umwIZYmtn\nC78rLoa4OGvLvZYW0HdnndFcrMJRWVmJMYbMzExH4xhjdCZ5ANnHU6/TWQbP9KlyEZGvA38CfhW8\nKh94KVJBqdhQWVkJQEFBgceRnNbRYR1uAae3KFORk5FhLYzs7Dz9uqvwaS5W/WWM6c7FTne+2b9/\nP0ePHiUnJ4fx48e7EZ46h9mzZ5OSksLevXupr6/3OpxBqa/Te/cAC4FGAGPMR0D4yzbVoODHInnb\nNmhthQsugOHDvY7GXcYYGhsbKS0t9VUfuPYlu0pzseqXxsZGmpqaSElJYbjDpBc6i+x0r+VY1tXV\nxeHDh7t/B4YrKSmJBQsWAKdfezWw+loktxljurv+RSQBa29OpXoVOnvhpyI51vZH7umxxx7jueee\n49ixY16H0k37kl2luVj1S2gedlrYaj9y35SVlfHoo4+ycuVKx2NdEpxlWKuzDJ7oa5H8joj8G5Aq\nIp8GngdejVxYKtqdOnWKrKwsMjMzGTp0qNfhdIvlRXsi0v0HSUVFhcfRnBZaJPtogjtaaS5W/dLe\n3k56erorkxXaj9w39mtdVVVFIBBwNJYWyd7q62EiccBdWMefCrAc+LVfdo7XTez9q6uri3gf7bM2\nYYJ1sMXWrTBrltfRuG/t2rW8+eabzJ07l+uuu87rcACrMM7JgaNHobzc+hkMZg4PE/FtLtY87F/G\nGAKBgKNcfOrUKTIzMwkEApw4cYL09HQXI4w9P//5zzl27Bjf+MY3yMvLC3ucuro6Ro0aRVpaGidO\nnCAhoa+bkqlz6Wse7tNMsjEmgLU45G5jzE3GmMc0G6q+8FOBXFtrFcjp6bFxyl5v7IU5Tnvh3CRy\nejZZJ0Oc0VyswiEijnPxhx9+SGdnJxdeeKEWyH1g52Kn7+rl5OQwadIkTp06xfbt290ITfXDOYtk\nsSwTkaPAXmCviBwRkf8YmPCUco/dalFcHDuHiPSUl5dHXFwcdXV1tLa2eh1ON+1LdkZzsfKa9iP3\nj5utb9py4Z3zzSR/B2sl9QJjzDBjzDCgBFgoIt+JeHRKuWgw7I+ckJDAjBkzmDt3Lh0dHV6H002L\nZMc0FytPaT9y/4wdO5YJEya40guuRbJ3ztmTLCJbgE8bY472uH4ksMIYMyfC8fWJ9sKpvrjsMnj3\nXXj1Vbj2Wq+jGVyam8E+x6ChwWp5GazC6UmOhlyseTh2GWPIz8/n8OHDlJaWMmXKFK9DGlR27NjB\nzJkzGTt2LAcPHvQ6nJjgVk9yYs+kDGCMOQIkhhucim2HDh2ivLyctrY2r0Pp1tkJGzdal/UQkYE3\nZIi1ULKr6/TPQfWL5mLVb1u3bqWmpsbxvumVlZUcPnyYrKwsLrjgApeiU301bdo0MjIyOHToENXV\n1V6HM6icr0huD/M2NYi9//77PPnkk3z00Udeh9Jt+3brWORJk2DkSK+jGZy05cIRzcWqXxobG3n5\n5Zf53e9+53gs+23+kpIS4uL6unOsckt8fHx3m4seUT2wzvevfZaINPby0QRcOBABquji10NEYnl/\n5Ghhn7ynOT4smotVv9h5OD8/3/EhIu+//z4ACxcudByXCo/2JXvjnBvuGWNidA8AFSnHjh2jpaWF\n9PR0Mu0mVB8YDIv2/K7noSJ6qm3faS5W/eXmZIVdJC9atMjxWCo8WiR7Q983Ua76+OOPAXeOQHWT\nnVcGy0zyiRMnePfdd3311ty4cTBqFNTXg486cZSKSfbWY/Z+veFqampi69atxMfHU1xc7EZog0pZ\nWRmvv/46NTU1jsYpKSlBRNi8ebOvtveMdVokK1fZRXJhYaHHkZx2+DDs3w8ZGXDhIHlj+tSpU6xa\ntYpNmzZ5HUq30ENFfFS7KxVzOjo6qK6uRkQcF8kffPABgUCAuXPnMmTIEJciHDz27NnDhg0bKC8v\ndzROZmYm06dPp6Ojg82bN7sUnTofLZKVqyZMmMD06dMZP36816F0W7PG+nzxxTBYTvQcNWoUiYmJ\nHDt2jObmZq/D6aZ9yUpFXmdnJwsXLmT27NkkJyc7GmtNMIFqP3J4/n/27jw+6up6/P/rZGNJIBBW\n2cK+E0BWAWMA2cviLlpbN2zFtdZP/fxqF237+bbaj59Wa11Q64oIlLKJICJEtrAvYScQ9iRsgZCE\n7HN/f7xnhoCASWYm73cm5/l45JGZyczNgSQnJ/d97r2edhd/nIKqLReVT4tk5Vc9evTgzjvvpGnT\npnaH4uUpkqtTO11ISAjNmzcH/HPik7/o8dRKBV6tWrUYNmwYEyZM8Hks7Uf2TenjqX3dis9TJDup\njS7YaZGsgl51LJLh8uTsFH36QHg47NwJWVl2R6OUup7i4mJvQaYzyRUTExND7dq1yc3N5dy5cz6N\nVXomWQ/uqRxaJKuglp0N27ZZbRbVbc2JE4vkWrWgb19rdwudTVbK2ZKTk8nNzaVdu3aOujpYlZTu\nC/c1F7dv356GDRty8uRJDh065I/w1A/QIlkFtXXrwOWCG2+0Tn2rTlq2bMmtt97KqFGj7A7lMjff\nbL1ftcreOJRS16f7I/tHv379uO2222jXrp1P44gIN7l71rQvuXJokayCWnVttQCoWbMmgwcP9vYm\nO4UWyUpVDbpozz/atWtHXFwcUVFRPo/labnwfG1UYGmRrPzi+PHjzJkzh927d9sdymWqc5HsVIMH\nW9vBbdgAut2nUv61YsUKlixZ4nP/qzHGW4jpoj3niI+PB2CVzjJUCi2SlV+kpqayc+dOjhw5Ynco\nXkVFl46j1hzvHPXrQ/fuUFgIGzfaHY1SwcMYw9atW1m/fj1FRUU+jXXkyBHS0tKoX78+nTt39lOE\nyld9+/alZs2a7N69mzNnztgdTtDTIln5hRMPEdm2DS5ehE6doFEju6NRpWnLhVL+l5WVRXZ2NjVr\n1qSRj0mvdD9ySIiWCk4RERHBwIEDAW25qAwB/84XkdEisldE9ovIC1f5eCcRWSsi+SLy3BUfOywi\n20Vkq4hsCHSsqmJcLpffjkD1J221uJyTtgzSIrlyaR6uHjyTFS1btkREfBpL+5EDwx952NNysXLl\nSp/HUtcX0PPHRCQEeBMYDqQBG0VkvjFmb6mnnQWeAiZdZQgXkGCM8a25SgXUqVOnKCwspF69etSt\nW9fucLw8BVh1L5K3bt3K6tWr6du3r3dltN08RfLatVBSAqGh9sYTzDQPVx/+vKKnh4j4lzGGmTNn\ncuTIEZ599lmfTkLUIrnyBHomuT+QYow5YowpAr4AJpZ+gjHmjDFmM1B8lddLJcSofOTEVgtjdCa5\ntMzMTO/XyQmaN4c2beDCBUhOtjuaoKd5uJrwXNHzNRdnZmayc+dOatSoQd++ff0RWrUnIuTk5JCf\nn+/zfskDBw4kLCyMrVu3kp2d7acI1dUEOvE1B0p/Nxx3P1ZWBvhGRDaKyBS/Rqb8pmfPntx///30\nd9BpHSkpcPo0NGkCPm5NWeXFxsYC1h8z2nJRLWkeribuueceJk6cSLNmzXwaZ9WqVRhjGDBgADVr\n1vRTdMrzx4uvC9wjIyPp06cPLpdL90sOsIC2W/jBYGNMuog0wkrSe4wxV+1Uf+mll7y3ExISSEhI\nqJwIFTVq1KB9+/Z2h3GZ0rPIPrbmVXn169cnKiqKnJwczpw54/OCHn+5+Wb45BOrSH76abujCZzE\nxEQSExPtDsMXmoeriJiYGGJiYnwex/P9ql8//4qNjSUpKckvV/Xi4+NZv349K1eudNyBUU5U0Twc\n6CL5BFD6uk8L92NlYoxJd78/LSJzsS4b/mByVsrzs+CZrazORITY2Fh27drF0aNHHVUkg1UkGxO8\nf8xcWSy+/PLLlR2C5mFVLt999x0At9xyi82RBBfPTPKJEycoLi4mLKziJVh8fDx//etftS+5jCqa\nhwPdbrERaC8isSISAdwLLLjO872/JkWktohEuW9HAiOBnYEMVgUHYy4VyUOH2hqKY3iS89mzZ22O\n5JKOHaFxYzh5Eg4csDuaoKZ5WJXZ+fPn2bZtG+Hh4d6txpR/1KpVi8aNGyMiPufiwYMHIyJs2LCB\nfD2VKWACOpNsjCkRkSeBpVgF+QfGmD0i8jPrw2aaiDQBNgF1AJeIPAN0BRoBc0XEuOOcboxZGsh4\nVXA4dAiOHYOYGOvQCgVxcXF069aNyMhIu0PxErHaYf7zH2s2uUMHuyMKTpqHVXl4+pH79+9P7dq1\n7Q4n6EyePJk6deoQ6uOWPvXr16dHjx4kJyezYcMG744Xyr8C3pNsjFkCdLrisXdL3T4JXG1z3Ryg\nV2CjU74wxlBYWOjTVjaB4JlFvuUW0D3wLU5dfHPzzVaR/N138PDDdkcTvDQPB7fCwkLCw8N93hsZ\nLrVaaD9yYNSrV89vY8XHx5OcnMzKlSu1SA4QLSFUhWVmZvLKK68wY8YMu0O5jLZaVB2e38OJiVab\njFKq/BITE3n11VdJ9sN+itqPXHV4CuNVukVQwGiRrCrs8OHDGGN8Wnzgb8bAihXWbZ0Icb64OKst\n5uhRSE21OxqlqqbDhw+Tn59PVFSUT+NkZWWxZcsWwsLCGDRokJ+iU4Fys3v185o1ayguvtoW58pX\nWiSrCjt8+DAArVu3tjWO0lJT4fhxaNAAunWzOxr1Q0JCLv0x4/njRilVdvn5+WRkZBASEkKLFi18\nGmvNmjW4XC769evnqPUL6uqaNm1Kx44dyc3NZfPmzXaHE5S0SFYVYoxxZJGs/cjXV1xczJEjR8jN\nzbU7FC9PW4wWyUqVn+eQoObNmxMREeHTWNpqUXlycnI4dOiQz+MMGzYMgOXLl/s8lvo+LSNUhWRm\nZpKTk0Pt2rVp2LCh3eF4eYpkbbW4urlz5/LRRx+xb98+u0Pxcud4li/XvmSlysufkxVaJFeOvLw8\nXnvtNT7//HOf2yQ8RfK3337rj9DUFbRIVhWSlZVFVFQUrVu39suKan8ovT+yFslX5zmi2vOL1Qm6\ndLGOD8/IAAfV7kpVCYWFhYSGhvpcJGdnZ7Np0yZCQ0MZPHiwf4JTV+XZL7m4uJjjx4/7NJZnF5I1\na9bofskBoEWyqpC2bdvy3HPPMWHCBLtD8Tp4UPuRf4jnF+mhQ4cwDpm2Fbn0R41eMVSqfH70ox/x\nwgsveP8Arqi1a9dSUlJCnz59qFOnjp+iU9fiycW+Tlg0atSIuLg48vPzWbdune+BqctokawqTEQc\ntUdy6Vlk7Ue+ukaNGhEZGUlOTo6jTt/ztFxoX7JS5RceHu7z4RSJ7gSqrRaVo02bNgB+6UsePnw4\noC0XgaClhAoa2mrxw0Tkstlkp/As3ktMBJfL1lCUqpaWLVsGXOpxVYHlmfk/fvw4RUVFPo2li/cC\nxzkb3CrlA+1HLruOHTtSVFREdHS03aF4tW8PzZvDiROwc6e1f7JSqnKcPXuWzZs3ExER4d17VwVW\nrVq16Nq1KzVr1qSgoIDw8PAKjxUfH09oaCgbNmwgOztb22X8SGeSVVDYv98qsBo2hK5d7Y7G2eLi\n4pg8eTIdO3a0OxQvEW25UMouK1aswBjDoEGDdH/kSnTXXXcxfvx4nw+BqVu3Lv369aO4uFhP3/Mz\nLZJVubhcLjZs2MDp06cds/AL4JtvrPe33qr9yFWV7pesVNmlpaWxZ88ev+xo4Gm1GDFihM9jKXto\ny0VgaDmhyiU9PZ3FixczY8YMx2z9BrB0qfV+5Eh741AVV7ovuaTE1lCUcrxNmzYxa9YsNm3a5PNY\n37hnGW699Vafx1L20P2SA0OLZFUuBw8eBKwt4JyiqOjS7KNOhFRdrVtDmzaQlQVbt9odjVLOZYwh\nNTUVgHbt2vk0VmpqKqmpqdSrV48+ffr4Izxlg0GDBlGjRg22bdvmqJ2LqjotklW5+Csx+9O6dZCT\nYx1K0aKF3dEoX3gmsjxXBpRS33f27FmysrKoXbs2TZs29Wms0rta+LqNnLJPrVq1GDRoEGD1mCv/\n0CJZlVlhYSHHjh1DRLx7PDqBp6DSWeTySUlJYe7cuZw4ccLuULxGjbLeL1libxxKOZlnsqJt27Y+\nt715imRttbBHYWEhq1evZt68eT6PpX3J/qdFsiqzw4cP43K5aNasGTVr1rQ7HC/Poj3tRy6fgwcP\nkpyczD4HnQU9fDiEhkJSEly4YHc0SjmTv9reSkpKvD2sumjPHqGhoaxatYrt27eTlZXl01ieQ0WW\n6qU4v9EiWZVZgwYNGDJkCL1797Y7FK9z52DjRggPBz0oqnzat28PwIEDB2yO5JJ69WDAACgu1iOq\nlbqWnj170rNnT5+L5G3btpGZmUlsbKyjWuiqk9DQUO/X0ddc3K9fP+rXr8/BgwcdlderMi2SVZk1\naNCA4cOHO2pxx/Ll1gltgwaBj1tNVjuxsbGEhoaSnp5Obm6u3eF4eVouvv7a3jiUcqquXbsyadIk\nnw8E8uxqMWLECEftVlTdeP5A8VwhqKiwsDDvFYEl2rPmF1okqypN+5ErLjw83HtEta/J2Z9KF8kO\n2opbqaCj/cjO4Lmql5qaisvl8mms0aNHA1ok+4sWyarKMkb3R/aVv2Yw/KlvX4iJgUOHQK8YKhUY\neXl5rF69GrjUy6rsUa9ePRo0aEBBQQHHjx/3aSxPkbx8+XK/HDRT3YXZHYBSFXXwIBw+DPXrw403\n2h1N1dS1a1fq1avnqN1KQkOtreBmzbJmkzt0sDsipYLPd999R0FBAb1796Zhw4Z2h1PtjR49mlq1\nanHDDTf4NM4NN9xAz5492b59O6tWrdIFmT7SmWRVZZU+ilq396yY6OhounTp4qjdSkD7kpUKtK++\n+gqAsWPH2hyJAqvlonnz5oSE+F6WacuF/2iRrH5QWloa77zzDklJSXaHchlPAaV/KAcfT5G8YgUU\nFtobi1JOsWTJEmbMmEFaWprPYy1evBjQIjkYaZHsP1okqx+UkpLCyZMnHXXUZUEBuNec4M4HKog0\nbw7du0NuLqxZY3c0StnPGMPu3bvZv3+/zztRpKSkcODAAWJiYhgwYICfIlROMWjQIOrUqcPu3bs5\nevSo3eFUaVokqx+UkpICQAcHNYd+951VQMXFQcuWdkejAkFbLpS65OTJk2RnZxMVFeXzUdSeVouR\nI0fqUdRBKCIiwrsYU2eTfaNFsrqu3NxcTpw4QWhoqKMWdy1aZL0fN87eOIJJYWGhI/dL1hyv1OWT\nFb7OJGurhbOdP38e4+P+l9py4R9aJKvr8iTmNm3aEBERYXM0FmMuFck/+pG9sQSL7du38+qrr7Lc\nQcfc3XwzREbC9u2gVwxVdeevK3oXL14kMTEREWGU5y9R5RiffPIJr7/+OhkZGT6N4ymSly1bRqEu\n7KiwgBfJIjJaRPaKyH4ReeEqH+8kImtFJF9EnivPa1XgeRaIeDY7d4L9+63t3xo0sI4wVr5r3Lgx\nJSUlpKSk+DyD4S81a17a//rLL+2NparTPFy1FRUVcfr0aUJCQnw+inrFihUUFBTQr18/Gjdu7KcI\nlb/ExMQAsG/fPp/GiY2NpUuXLmRnZ7N27Vp/hFYtBbRIFpEQ4E1gFNANmCwina942lngKeCvFXit\nCrCxY8fy5JNP0qNHD7tD8fLMIo8erVu/+UvTpk2pU6cO2dnZpKen2x2O1/jx1vuFC+2NoyrTPFz1\nhYeH8/zzz/Poo49So0YNn8Za5E6gY8aM8Udoys86duwIwP79+30ey/M1/lJnGSos0DPJ/YEUY8wR\nY0wR8AUwsfQTjDFnjDGbgeLyvlZVjgYNGlC7dm27w/Dy/LxrP7L/iIhfk7O/jBsHIrB8OeTk2B1N\nlaV5OAiEhob6fNCEMYYFCxYAMN7zF6hylDZt2hAeHk56ejoXLlzwaawJEyYAMH/+fMdcIaxqAl0k\nNweOlbp/3P1YoF+rglRWFqxaBSEhlxZ2Kf/o1KkT4PtlPn9q3NhqqSksvHR4jCo3zcMKgM2bN3Pi\nxAlatGjBjXpMqSOFh4d7W2p8nbAYPHgwMTExHDhwwFF5vSoJmmOpX3rpJe/thIQEEhISbItFBc7i\nxVBcDPHx4G7dUn7Spk0b6tSpQ8OGDSkpKXHM1lDjx8O6dVbLxW232R1N+SUmJpKYmGh3GJVC87Cz\nzZ8/H7BmGH3dIUMFTseOHTl79ixhYb6VaGFhYYwbN45PP/2U+fPn07lz9e2UqmgelkBOwYvIQOAl\nY8xo9/3/Bowx5pWrPPf3QLYx5v8q8FqjlxKqh3vugVmz4G9/g2eftTua4GOMcdwvzx07rP2wGzeG\n9HTrKkJVJiIYYyrtP1nzsPKIi4tjx44dLFmyRHe2cDB/5uE5c+Zw5513MmjQINboyUxeZc3Dgf51\nsxFoLyKxIhIB3AssuM7zSwdc3tcqPzp8+DDp6emO6mMqKAD3HvhM1K7IgHBagQzWyXuxsXDqFKxf\nb3c0VZLm4SrKGENycjIXL170eaxDhw6xY8cO6tSpozP8DufPPDxy5EgiIiJISkri5MmTfhu3ugho\nkWyMKQGeBJYCu4AvjDF7RORnIvIYgIg0EZFjwC+AF0XkqIhEXeu1gYxXXbJ06VKmTZvGgQMH7A7F\ny7N4q2dPcNC5JirARC79UTR3rr2xVEWah6uujIwM5s6dy7vvvuvzhIVnwd6YMWN83iFDVR116tRh\n+PDhGGO8O5uosgt4T7IxZgnQ6YrH3i11+yRw1YOFr/ZaFXhZWVmkp6cTHh5O69at7Q7Ha948631V\n7EtVvrnjDnjjDfjPf+CVV6zCWZWd5uGqae/evYB/Ttnz9CNP1Mtw1c6ECRNYvHgx8+fP5+GHH7Y7\nnCqlinf3qUDwrIJt37494eHhNkdjKSkBd45n0iR7Y1GVb/Bgqyf54EFITrY7GqUqh6dI7tKli0/j\nnDlzhpUrVxIWFqb7I1dDnoWaX3/9NdnZ2XaHU6Vokay+x5OYnbQSdv16OHkSWre2FnGpwDHGsH37\ndmbNmkVRUZHd4QDWoTGeP47+8x97Y1GqMmRmZnLq1Clq1Kjh8xW9efPmUVJSwvDhw6lfv75/AlQB\nd+HCBVasWMGqVat8GqdZs2YMHjyYgoICbbkoJy2S1WVyc3M5fPgwISEhdOjQwe5wvDyF0aRJeqk9\n0ESEDRs2sGfPHkf1pN9xh/V+zhx741CqMuzevRuwWi183Y7x3//+NwB33nmnz3GpypObm8vKlStZ\nv349LpfLp7E8X3vP94IqGy2S1WVCQkIYNmwY/fr1o1atWnaHA4Ax1rZvAHfdZW8s1YXn8u6ePc5Z\no5WQAPXqwa5doPviq2DXunVrbrzxRnr27OnTOJmZmXz77beEhoYySXvVqpSmTZtSr149cnNzOXbs\n2A+/4Dpuv/12AL766ityc3P9EV61oEWyukytWrUYMmQIo0ePtjsUr3Xr4NgxaNECBg60O5rqoWvX\nroB14lNx8ZUnFdsjIgLcp6xqy4UKei1atGD8+PG0b9/ep3HmzZtHcXExw4YNo2HDhn6KTlUGEfHm\nYs+VhYpq2bIlAwcOJC8vj8WLF/sjvGpBi2TleJ5Z5LvvrvoHSVQVMTExNGnShIKCAlJTU+0Ox8vT\ncuH5nlBKXZ+2WlRtpa/q+boN4F3uS7GzZ8/2Oa7qQksO5WguF3h+nu++295YqhvPDIZnIacTjBoF\n0dGwbRs4KCylHOncuXMsW7aM0NBQbtO9M6uk5s2bEx0dTXZ2NmlpaT6NdYd7luHLL7/0ywE11YEW\nycrR1q6FEyesE9f697c7muqlV69eTJ48mXHjxtkdileNGuBurWPGDHtjUcrp5s2bR1FREQkJCTRq\n1MjucFQFiAjjx49n6tSpNG/e3KexYmNj6d+/PxcvXtRdLspIi2QFQElJiaOOoPYo3Wqhu1pUrrp1\n69KxY0efV9b72+TJ1vsZM6xFnUoFk5KSEr+NNX36dADuuecev42pKl+7du389kfOZHcC9XxvqOsT\nJxZG5SUiJhj+HXZat24d69atY+jQoT6vpvaX4mJo2RIyMmDjRujb1+6IlBMUF0Pz5nDqFGzaBH36\n2B1R+YgIxpig+5NP87DvjDG888471K5dm0mTJhEdHV3hsdLS0mjRogXh4eFkZGTo/sgKsI46b968\nOaGhoWRkZBATE2N3SLYoax7WmWQFQHJyMllZWYSFBfyk8jJbtswqkDt2rHqFkAqcsLBL/enawmIk\ntgAAIABJREFUcqGCSUZGBqdOneLUqVNERUX5NNYXX3yBMYZx48Zpgay8mjZtyvDhwykqKtI9k8tA\ni2TF6dOnSU9Pp0aNGnTq1MnucLw+/dR6/8AD2mqhLudpufjiC2txp1LBYPv27QB0797d5zanzz77\nDIAf//jHPselgsv9998PaMtFWWiRrEhOTgas3QycMpN84QLMnWvd1hxvv7y8PJ/36fSnm26yjig/\ncQISE+2ORinfuVwudu7cCUBcXJxPY+3evZutW7cSHR3N2LFj/RGecgBjDOnp6T7vcnHbbbdRs2ZN\nVq5cydGjR/0UXXDSIrmaM8Z4i2Sn9CKDdfRwXh7Ex1vFkLJPcXExb7zxBrNnz+bcuXN2hwNYVxZ+\n+lPr9ocf2huLUv5w8OBBcnNzadCgAc2aNfNpLM8M4Z133knNmjX9EZ5ygB07djBt2jSWL1/u0zh1\n69Zlgvtkps8//9wfoQUtLZKrudzcXOrWrUu9evVo1aqV3eF4eVotfvITe+NQEBYWRocOHQDYtm2b\nzdFc4vnemDPHuvKgVFWWl5dHZGQkcXFxiA/9ZSUlJd5WC89ldRUcOnToQGhoKAcPHiQrK8unsR54\n4AEAPvroI0fubOUUuruFAqCgoIAaNWrYHQYAR49a+yLXrGkt3PNhgbfyk9TUVD799FOio6N55pln\nfPol7k8JCfDdd/Dee/Doo3ZHUza6u4W6FpfLRXFxMRERERUe4+uvv2b06NG0adOGAwcOEKLHlAaV\nf//73+zatYuhQ4cSHx9f4XGKi4tp1aoV6enprF69msGDB/sxSufT3S1UuTilQAb46CPr/cSJWiA7\nRZs2bYiOjiYrK4tDhw7ZHY7XQw9Z7z3fM0pVZSEhIT4VyAAffPABAA8//LAWyEGoV69egLXI05c/\nSsPCwvipu2fN8z2jvk9/gpSjlJTA++9bt6dMsTcWdYmIeHvWndRycccdEBkJa9bA/v12R6OUvU6f\nPs28efMICQnhwQcftDscFQBt27alTp06ZGZm+rzo7iH3LMOsWbPIzs72R3hBR4tk5Shffw3HjkG7\ndjB0qN3RqNJ69epFr1696OugU12ioi7tmayTIaq6++yzzygqKmL06NG0aNHC7nBUAISEhDBkyBCG\nDx9OgwYNfBqrY8eO3HzzzeTm5jJz5kw/RRhctEhWjvLee9b7KVNArxQ6S/369Zk4caKjFnjCpSsO\n//oXFBTYG4tSdjHGeC+bP/LIIzZHowKpf//+DBkyxOcDZ+DS94q2XFydLtyrppYtW0ZRURE33XQT\n9erVszscANLSoFUra3uv48ehSRO7I1JVgTHQuzds3w7Tp8N999kd0fXpwj3lUVhYyPTp0+nevTt9\n+/b1aUHs2rVrGTx4MI0bN+bYsWM+9zar6iE3N5dmzZpx4cIFtm3b5qitYANJF+6payosLGTjxo1s\n2LCBwsJCu8Px+vBDqyd54kQtkFXZicDjj1u333rL3liUKo+dO3dy9OhRduzY4fOOMW+++SZgLdjT\nAlmVVWRkpHcB3z//+U+bo3EeLZKroW3btlFYWEjLli1p3Lix3eEAUFwM775r3X7sMXtjUVXP/fdD\nnTrWAr4dO+yORqkfZoxhw4YNAPTp08ensdLT05k9ezYhISE87vmLUakymjp1KmD1tDvlwCin0CK5\nmimdmAcMGGBzNJfMnWst2OvUCW691e5oVFmcP3+eixcv2h0GYC3g8xwu8vbb9saiVFkcOXKEkydP\nEhkZSbdu3Xwaa9q0aRQXFztyzYAKLM9R1b7o3LkzI0aMIC8vjw/1CNPLaJFczRw8eJCzZ89St25d\nunTpYnc4Xn//u/X+6ad1wV5VsHr1al5//XXvH1xO4JlA++QT0MkQ5XTr168HoG/fvoSFhVV4nMLC\nQt555x0AnnrqKb/EpqqGkpIS3nrrLd577z2fT+B78sknAavlwuVy+SO8oKDlSDWTkZGBiNCvXz/H\nbDS/aROsXWsdHKLHUFcNnu2lNm7cSFFRkc3RWLp1s65C5ObCtGl2R6PUtRUXF3P27FlCQkJ83lJx\n7ty5ZGRk0LVrVxISEvwToKoSQkNDadq0KcYY7x9dFTVu3DhiY2NJTU1l8eLFfoqw6nNGlaQqzZAh\nQ3jmmWcctdft669b76dMsS6bK+eLjY3lhhtu4OLFiyQnJ9sdjtcvf2m9f+MNcNCaVKUuExYWxuOP\nP85jjz3m0zZexhhee+01wJoJdMpx8ary3HTTTQBs3ryZ/Pz8Co8TGhrKE088AcD//u//+iW2YKBF\ncjUUHR1NzZo17Q4DgBMnYOZMq8XCfbVHVQEiwqBBgwBISkry6XhUfxo1yppRTkuzvq+UcioRoYmP\n2/gkJiayceNGGjZs6N2hQFUvzZo1o3Xr1hQWFrJlyxafxnrssceoW7cuiYmJjmqls1PAi2QRGS0i\ne0Vkv4i8cI3nvCEiKSKyTUR6l3r8sIhsF5GtIqJfsSD02mtQVAS33w6xsXZHo8qja9euREdHc/bs\nWfY75ExoEXjuOev2a69ZeygrzcPB6pVXXgGsXuTatWvbHI2yi2c2ed26dZSUlFR4nOjoaH7+858D\n8Oqrr/oltqouoIeJiEgIsB8YDqQBG4F7jTF7Sz1nDPCkMWaciAwAXjfGDHR/LBXoY4y57jIc3cS+\najpzxiqML16ELVusAyFU1bJ582bOnDnDwIEDiY6OtjscwDp1LzYWTp60jjkfOdLuiC5X2YeJaB4O\nTtu2baN3797Url2bo0eP+nxEsaq6jDHMnj2bjh070qNHD0JDQys8VlpaGm3atKGoqIh9+/bRoUMH\nP0bqHE45TKQ/kGKMOWKMKQK+ACZe8ZyJwCcAxpj1QLSIeK5BSSXEGPSc+ovrjTesAnnMGC2Qq6o+\nffowatQoxxTIADVqwLPPWrf/8AedTUbzsGP4Mxd7ZvqmTJmiBXI1JyLcfffd9OrVy6cCGaz2jQce\neABjjPYmE/jE1xw4Vur+cfdj13vOiVLPMcA3IrJRRKYELMogt2rVKmbNmsXp06ftDsXrwgX4xz+s\n27/+tb2xqODzxBMQE2MdLrJ8ud3R2E7zsAOUlJTw/vvvs3LlSoqLi30aa//+/cycOZOwsDCe8/QX\nKeUnzz//PCLChx9+yNGjR+0Ox1YV35yxcgw2xqSLSCOsJL3HGLP6ak986aWXvLcTEhJ0Kxy3/Px8\nkpKSyM/Pp3///jRq1MjukAD45z/h/HmIj4chQ+yORgWbOnWs3uTf/AZefhmGDbP6le2QmJhIYmKi\nPZ/cPzQP+8H27dtJS0ujsLCQm2++2aexXn75ZVwuFw8//LAeHqL8rnPnztx7773MmDGDP/3pT0wL\ngj01K5qHA92TPBB4yRgz2n3/vwFjjHml1HPeAVYYY2a67+8FbjHGnLxirN8D2caY/7vK59FeuGtY\nvnw5q1atIjY2lp/+9KeO2CLo3Dlo29YqkpcuhREj7I5IBaMLF6B1a+v7bflyGDrU7ogsNvQkax62\nWXFxMf/4xz+4cOECt99+Oz169KjwWDt37iQuLo7w8HBSUlK0SFYBsW/fPrp27UpISAj79u2jbdu2\ndofkV07pSd4ItBeRWBGJAO4FFlzxnAXAT8CbzM8bY06KSG0RiXI/HgmMBHYGON6gkpuby7p16wAY\nPny4IwpkgL/+1SqQhw7VI6iDzdGjR0lLS7M7DADq1r2008Vvf1ute5M1D9ts06ZNXLhwgcaNG9O9\ne3efxnrppZcwxjBlyhQtkNVVFRUVsWXLFp9OzuvUqRMPPPAAxcXF/PGPf/RjdFVLQItkY0wJ8CSw\nFNgFfGGM2SMiPxORx9zP+Qo4JCIHgHeBqe6XNwFWi8hWYB2w0BizNJDxBptVq1ZRVFREx44dadmy\npd3hAJCRcenwkP/3/+y7BK78b/v27Xz44YcsWrTIMYtFn34aGja0epPnz7c7GntoHrZXQUEBq1at\nAmDYsGE+TVZs2bKFOXPmULNmTX6tiznUNXz22WcsXLiQrVu3+jTOb3/7W0JDQ/nkk0/Yu3fvD78g\nCAV8xbIxZokxppMxpoMx5i/ux941xkwr9ZwnjTHtjTE9jTFb3I8dMsb0Msb0Nsb08LxWlV3NmjWJ\niIhgqFOuMwN/+pO1o8XEiTBwoN3RKH/q0qULUVFRpKWlsXOnMyYb69aF3//euv3CC9ae3NWR5mH7\n5OXl0aRJE1q0aEHHjh0rPI4xhueffx6AqVOn0qxZM3+FqIJMv379AFixYgUFBQUVHqddu3Y88sgj\nuFwufvWrX/krvColoD3JlUV74a6toKCAGjVq2B0GAHv2QFwclJRAcjL4eNVROdDWrVtZsGAB0dHR\nPPnkk4SF2b82uKjIOoUvJQXeegsef9zeeCq7J7myaB6+Pl9z8fz585k0aRIxMTGkpKQQExPjx+hU\nMDHG8MEHH3DixAni4+N9mig7efIk7du3Jycnh2XLljF8+HA/Rmofp/QkK5s5pUA2xtq7trgYpkzR\nAjlY9ezZk8aNG5OVlcX69evtDgeA8HD485+t2y+9BFlZtoajqilfcnFBQQG//OUvAasnWQtkdT0i\nwkj3KUpJSUlkZ2dXeKwmTZp4W3uee+45n070q4q0SFaVYv58ayeLevWslgsVnEJCQhjh3q5k27Zt\nPi0c8afbb4fBg+HUKfjd7+yORqnyefPNNzl48CCdO3f2Hhus1PW0atWKLl26UFRU5HP72y9+8Qti\nY2NJTk7mgw8+8FOEVYO2W6iAy8uDrl3h8GHrAJEnn7Q7IhVoW7dupWvXro65kgGwfTvceKN1e9Mm\n+0551HYLVR7Hjx+na9euZGdns2jRIsaOHWt3SKqKOH/+PBkZGXTu3NnnsWbNmsU999xDTEwMe/bs\noXHjxn6I0D7ablENZWdns2vXLsfsLODxP/9jFcg9eoBOglQPvXv3dlSBDNCzp7Xbhctl9SU7ZJJb\nBaG9e/dy/vx5n8cxxvDEE0+QnZ3NpEmTtEBW5VKvXj2/FMgAd911FyNHjiQzM7NanfKoM8lBwhjD\nrFmz2Lt3L8OHD2eIQ46x27oV+vWzCpJVq6xL3krZ5cIF6NIF0tLsW8SnM8nB7dy5c7z99tsAPPHE\nE0RHR1d4rDlz5nDnnXdSp04d9uzZQ/PmV54mrlTlSU1NpXv37uTl5fH11197+56rIp1JrmZ2797N\n3r17iYiIIC4uzu5wAGtXgYcftnazeOopLZCV/erWvbRP93/9Fxw8aG88KrgYY/jyyy8pKiqiU6dO\nPhXI58+f56mnngLgL3/5ixbIynZt27bl9+49NX/+85+Tk5Njc0SBp0VyEMjNzWXx4sUAjBgxgrp1\n69ockeWVV2DbNuto4P/5H7ujUXYqKiri9OnTdocBwJ13wj33QG4uPPig9UecUv6wdetWUlNTqVWr\nFqNHj67wOMYYfv7zn5Oens5NN92ki/WU35w+fZri4uIKv/65556jV69eHDp0iGeffdaPkTmTFslV\nnDGGefPmkZubS+vWrenTp4/dIQGwbp213RbAe+9BVJSt4SgbXbhwgWnTpvHZZ5+Rn59vdzgA/POf\n0LQprF4Nf/ub3dGoYHD69GmWLFkCwJgxY4iMjKzwWJ999hkzZ84kMjKSjz/+mJAQ/VWtfLdt2zbe\nffddli9fXuExwsPD+eyzz6hRowYffPABc+fO9WOEzqM/eVXcxYsXycrKolatWtx2220+HXnqL+fP\nw+TJ1gzdc8/BrbfaHZGyU1RUFDVq1ODChQssXLjQEQtLGzQAz05GL74IGzfaG4+q+k6ePInL5SIu\nLo4ePXpUeJzU1FSeeOIJAN544w06dOjgrxBVNdeoUSNcLhdJSUkcOHCgwuN069aNV199FYApU6aQ\nlpbmrxAdRxfuBQHPpWwnHFNqjHUpe/Zs6NMH1q6FiAi7o1J2O3v2LNOmTaOwsJBRo0Yx0CFnkj/1\nFLz5JrRqBVu2WMVzoOnCveCVkZFB/fr1K7yzS15eHvHx8WzatIk77riD2bNnO2LiQwWP7777jsTE\nRGrVqsXPfvazCvfNu1wuxowZw9KlSxkyZAjffvstEVXol70u3KtGwsPDHVEgA7z2mlUg16kDX3yh\nBbKyNGjQgEmTJgHwzTffcPToUZsjsrz2GgwYAEePwgMP6LZwyjdNmzatcIFsjOHxxx9n06ZNtG7d\nmmnTpmmBrPwuPj6e9u3bk5eXx+zZsyvcnxwSEsInn3xC8+bNWb16tfdEyGCjRbLym0WL4Fe/sm5/\n9BG0b29rOMphunTpwk033YTL5fLpUp8/RUTArFnWDPLixeA+fVWpSvfmm2/y8ccfU6tWLebNm6dH\nT6uAEBFuu+02oqOjOXPmDJmZmRUeq0mTJsyZM4eIiAjv92+w0XaLKsYYgzHGcQs5du2Cm26C7Gz4\nwx/gt7+1OyLlRCUlJezevZvu3bs7apZs2TIYMwaKi+Hdd+GxxwL3ubTdIji4XC6/5eFFixYxceJE\nSkpKmDFjBvfee69fxlXqWtLT0wkNDfXLyXnvv/8+U6ZMITw8nCVLljBs2DA/RBhYZc3DWiRXMcuW\nLePs2bPccccdhIWF2R0OYJ2mN2QInDhh9SPPmAEOqn+UKpMPPoBHH4XQUFi40CqaA0GL5KovNzeX\nTz75hPj4eLp16+bTWElJSQwfPpy8vDxefPFF/vSnP/kpSqUqzy9+8Qv+/ve/U6dOHVauXEmvXr3s\nDum6tCc5CK1evZo1a9awf/9+x6wmTU+3dq84cQLi4+HDD7VAVlXTI49YO12UlMDtt4MPuySpIJaf\nn89nn33GqVOnWLNmDS4fGtl37drFj370I/Ly8nj44Yf54x//6MdIlao8r732Gvfccw/Z2dmMGTOG\nlJQUu0PyCy2Sq4ikpCS+/fZbACZNmkSrVq1sjsgqkEeMsE4t69PHmn2rVcvuqFRVlJ2dTYkDTvX4\n4x9hyhTIz4fx4+G77+yOSDlJfn4+06dPJyMjg5iYGO67774Kt1xs376dhIQEMjMzGT9+PO+++66j\nWpBU9XT+/PkKvS4kJISPP/6Y4cOHk5GRwS233MLevXv9HF3l0yLZ4YwxJCYmsnTpUgDGjRvn0x6c\n/nL4MNx8s9WL3LUrLFliHfmrVHmdO3eODz74gNmzZ1NUVGRrLCLwzjvw0ENw8SKMHWt9byuVm5vL\nRx99xPHjx4mOjuaBBx4gqoKnJG3atImhQ4dy5swZRo8ezcyZMx3TPqeqr40bN/Lmm2+yc+fOCr2+\nRo0azJ8/n6FDh5Kenk5CQkKFx3IKLZIdzuVycezYMUSEiRMn0rdvX7tDIjnZ6kH2zCAnJkLDhnZH\npaqqvLw8CgoK2LdvH59++ikXL160NZ6QEOuUyAcftArl8eOt3VpU9ZaVlcW5c+do0KABDz30EPXq\n1avQOIsWLWLo0KGcO3eOCRMmMG/ePGrpJTjlAOfPn6ekpIQ5c+aQlJRUoYOfIiMj+fLLLxkxYgQn\nT5707qFcVenCvSqgsLCQ48eP07ZtW7tD4T//gZ/8BHJzrR7khQt1Bln57tSpU0yfPp0LFy7QoEED\n7rnnHho1amRrTMZYW8L95S/W/RdfhJdfthb2+UIX7lVdx44do379+hWaQTbG8Oabb/Lss8/icrm4\n7777+PDDD6vUAQwquBljSEpK4ptvvgGgb9++jB49mtAKJL38/Hzuv/9+/vOf/xAWFsY777zDI488\n4u+QK0x3t1B+VVxsFQiehdcPPADTpkHNmvbGpYJHdnY206dP5+TJk0RERPD0008TGRlpd1i8+SY8\n84x10MjIkTB9um9XTrRIrn6ys7N5/PHHmT59OgAvvfQSv/vd77QHWTnSzp07mTdvHiUlJfTq1YuJ\nEydWaByXy8V///d/89e//hWARx55hDfeeIPatWv7M9wK0SK5CjLGkJeX54hvoNJSU+HHP4akJOtS\n9CuvwC9/qbtYKP8rLCxk4cKFxMTEMHToULvD8fr2W7j3XjhzBlq0sLaLGzmyYmNpkex8Fy9epFat\nWn4pYjdv3szkyZNJSUmhdu3avP/++0yePNkPUSoVOMePH2fBggXcfffdNPSxn/Jf//oXTzzxBPn5\n+XTv3p3PP//c9rVVWiRXMWfOnGHRokUUFBTwyCOPVOjyhr8VF8Nbb1mXmXNyoHlz+PRTcFDtooKQ\n52fZabNsx45Z+4AnJVn3f/Yz6w/G6OjyjaNFsnMZY9i2bRvffPMNCQkJ9O/fv8JjXbx4kZdffpnX\nXnuNkpISevTowaxZs+jcubMfI1YqcIwxfsvDycnJ3H333ezbt4+wsDB+/etf8+tf/7rCx7j7SvdJ\nriIKCgpYvnw5b7/9NocPHyYrK4szZ87YHRZr18KAAdZl5pwcuPNOa8GeFsgq0ETkmok5JyenkqO5\npGVLWLkS/vxnCA+3Tubr0MGaVfZhq1zlEOnp6Xz88ccsWLCAvLw8UlNTK7RwyRjDnDlz6NGjB6++\n+ioul4tnnnmG9evXa4GsqpRr5eGLFy+We8vOuLg4Nm3axNSpUykuLuYPf/gDPXv25Msvv6zQz1ll\n0ZlkG23fvp2lS5d6V/P37t2bESNG2LrSOTkZfvMba0EeQKtW8I9/wIQJtoWkFAApKSnMnDmTvn37\nMnjwYOrUqWNbLDt2wOOPw5o11v24OHjpJZg40WpJuh6dSXaWoqIiFixY4N2qKjIykpEjR9KjR49y\nzaIZY1ixYgW//e1vWbt2LQDdu3fn/fffZ8CAAQGJXSk7zJw5k1OnThEfH0+PHj3KvVf4ypUrmTJl\nCvv37wdg2LBhvPzyywwZMiQQ4V6VtltUAcnJycydO5eWLVsyYsQIWrZsaUscxljbuP31r7B4sfVY\nZCQ89xy88IJ1Wym7LV++nFWrVgEQGhpKr1696NevH02aNLElHmPgiy/gV7+C48etx+Li4OmnYfJk\nuNbSAi2SncUYw0cffcSJEyfo168f8fHx5ZqoKC4uZsGCBbz66qusX78egMaNG/Pyyy/z6KOP6v7H\nKqjk5+fz3nvvkZmZCUBMTAwDBgwgLi6OmuVYyV9YWMjbb7/Nyy+/zLlz5wC4+eabef755xk7dmzA\nf260SHaQa/X1GGNITU2lbdu2tvRfHj9u9Rh/9BG4/6CjVi149FGrD9mm2kOpa8rIyGDlypXs2bPH\n+9h9991Hhw4dbIspPx/ef99qw/CcFh8dbe2z/PDD0KPH5YtctUi2z7Vy8enTp4mIiCC6HA3m+/bt\nY8aMGbz33nukub/wDRo04Nlnn+Xpp5+mru6NqYJUSUkJO3bsYOXKld4CNzo6mmeeeabctcy5c+f4\n+9//zhtvvOE97a9Zs2Y89NBDPPLII7Rp08bv8YMWybYrKiri0KFD7N+/n0OHDvHYY4/Z1qBe2v79\nsGgRfPklrFhhzYYBNG1qXT6eOlUPBlHOd+rUKTZt2sSBAweYOnWqI2br8vNh9mxrseu6dZce79AB\n7rjDervxRggN1SK5Mp0/f579+/eTkpJCvXr1GDduXIXGMcawa9cu5s2bx6xZs9ixY4f3Yx07dmTq\n1Kk8+uijjti2UKnK4HK52LNnD5s2beKGG25gZEW3/AEuXLjAe++9x7Rp07xtGGDt1Txp0iQmTpxI\nt27d/Dah6JgiWURGA3/HWiT4gTHmlas85w1gDJALPGiM2VbW17qf55jkvGnTJvbu3cuKFSto1aqV\n9/Hbb7+90rc8MQYOHLAW4a1dC8uXw4EDiUACABERVg/lgw9a21nZVWckJiaSkJBgzye/DifG5cSY\nwL64XC7XVfvhcnJy+N3vfseoUaNo3bo1zZs3r/ARwhWxZYu1j/icOda2cR6NG8OpU5VfJFe3PJyb\nm0tiYiJHjhxhw4YN3tmomjVr8vzzz5dp96Di4mL27NnDunXrWL58OcuXL+fUqVPej0dHRzNx4kQe\nfPBBEhISyvXLW3+Oy86JMYEz47Izpmvl4qSkJBYtWsTYsWOJjY2lSZMm153UMMawatUq3nvvPebM\nmUNeXp73Yy1btiQ+Pp74+HhuvvlmOnXqVO5+aI+yFskBLYtEJAR4ExgOpAEbRWS+MWZvqeeMAdoZ\nYzqIyADgHWBgWV5rh7y8PM6fP0/t2rWvemnuxIkTHDx4kIMHDzJw4EA6duxIhw4duOGGGwIWU3Gx\n1Tpx+DDs2wc7d1pvycngbhvyqlkzkdtvT2DcOBg9GmJiAhZWmTkx2YAz43JiTGBfXNdKkIcPH2bL\nli1ER0ezzj2tGxUVRffu3Rk1alTA47rxRnjnHesgklWrrGJ5/vxLvcuVKRjzsMvlIjs7m/Pnz9Oq\nVavvFagRERFs3rwZYwzHjh1j3LhxdOjQgQ4dOnyvQC4sLOTQoUOkpKSQkpLC/v372bZtG9u3b7/s\nFzTgnS276667uPXWWyt8dVB/jsvOiTGBM+OyM6Zr5eKUlBRWr15NeHg4YBWnjRo1YsyYMbRu3fp7\nzxcRbyH87rvvsmzZMubPn8/ChQs5duwY06dP9x7KExUVRY8ePejZsyc9evSgXbt2tG3bltjYWL+d\nZBnoucP+QIox5giAiHwBTARKJ9iJwCcAxpj1IhItIk2ANmV4bYUZYygpKaGwsJDCwkLCw8Ovepls\n9+7dbN++naysLM6fP09BQQEAQ4cOJT4+/nvPv/HGG2nfvj0FBQVMmTKl3HG5XNaRzzk5l96ysuD0\naWtG6vTpS28ZGVZhfPw4XGs3liZNYPBgGDTIev/VV/CHP5Q7LKWqlE6dOtGzZ0/i4+M5cuQI6enp\n5OTkUFhYeNXn79u3jw0bNhAVFUVkZCRRUVHUrl2bJk2a+PQHbliYtW3i0KHWLjF790LXrhUerqIc\nm4fdn4+ioiJvLo6Ojr7qTO+XX37J2bNnycrKIisrC5d7373nn3/em7tdLhc5OTlcuHCBbt26ERIS\nQkpKCiLCunXrmDdvHhkZGaSnp5ORkUFGRgYnTpy45nZWbdq0oW/fviQkJDBs2DA6depFhXsWAAAg\nAElEQVTkuP27lXKyiRMnkpSURO/evTl27Bhnzpzh1KlT1yxiFy5cSE5ODlFRUURFRXHDDTfw7LPP\n8o9//IMDBw6watUqVq5cyZo1azhx4gRJSUkkeTavdwsJCaFFixa0atWKxo0b06RJExo3bux9K8/h\nKIEukpsDx0rdP46VsH/oOc3L+FqvsWP34XIZjDG4XIb69evTpIn1y82YS2+nT5/i2LETlJS4vP24\nxkDjxk1o0SLysucCnDzZkBMnung/j0go4eERJCU1YNq0y59r3W6JMbBzZwT790NRkfVWWHjp9tXu\n5+VZBbF7N7hyEbEO+mjdGtq1g+7dL721aHH5oqElS8o/vlJVTXh4OPXr1/ee2meMITMz85oFzpkz\nZ0hNTf3e4wMGDLhqkey5BB8WFkZYWBjh4eGEhYXRq1cvbrrppu89f+/evSQnJ9u1g02l5eHRo0fj\ncrkue4uNjSU8PNx738rRLg4cOMDFixe9j3ne2rZt632+57nFxcWkpqaSn59PcXExJSUl3o+98847\nFBYWUlBQQG5u7lXj8sw8XY2IEBsb673q16FDB7p3786NN95IjBMutSlVhUVHR9OkSRMmuPeRLSws\n5NSpUzRu3Piqzz906JB3MWBpU6dOJS4ujri4OJ544gnAytt//OMfOXDgAGfOnCEzM5PMzEzOnTvH\n0aNHOXr0qM/xB7QnWUTuAEYZYx5z3/8x0N8Y83Sp5ywE/myMWeu+vwz4FdYMxnVfW2oMZzTCKaVU\nGVRmT7LmYaWU+j7be5KBE0CrUvdbuB+78jktr/KciDK8FqjcXzhKKVXFaB5WSqkKCPSx1BuB9iIS\nKyIRwL3AgiueswD4CYCIDATOG2NOlvG1Simlrk/zsFJKVUBAZ5KNMSUi8iSwlEvbB+0RkZ9ZHzbT\njDFfichYETmAtfXQQ9d7bSDjVUqpYKN5WCmlKiYoDhNRSimllFLKnwLdblGpROSXIuISEUcsSRaR\nP4jIdhHZKiJLRKSpA2J6VUT2iMg2EZkjIo44O1VE7hSRnSJSIiI32hzLaBHZKyL7ReQFO2PxEJEP\nROSkiCTbHYuHiLQQkeUisktEdojI9xZz2UFEaojIevfP3Q4R+b3dMXmISIiIbBGRoG5ZcFIudmIe\nBmfmYiflYXc8movLwIm52Ml5GMqei4OmSBaRFsAI4IjdsZTyqjGmpzGmN7AIcMI3yVKgmzGmF5AC\n/H82x+OxA7gN+M7OIEodnjAK6AZMFpHOdsbk9iFWTE5SDDxnjOkG3AQ84YT/K2NMATDU/XPXCxgj\nItfctqySPQPstjuIQHJgLnZiHgZn5mJH5GHQXFxOjsvFDs/DUMZcHDRFMvA34L/sDqI0Y0xOqbuR\ngMuuWDyMMcuMMZ441mGtVredMWafMSYFsHuFvPfgBWNMEeA5PMFWxpjVwPc3j7SRMSbDc3Sx+3t9\nD9a+urYzxnh2HK+BtfbC9r4yd/E4Fnjf7lgCzFG52Il5GJyZix2Uh0FzcZk5NRc7MQ9D+XJxUBTJ\nIjIBOGaM2WF3LFcSkT+JyFHgPuB3dsdzhYeBxXYH4TDXOlRBXYeItMaaLVhvbyQW96W0rUAG8I0x\nZqPdMXGpeHTEL4pAcGoudngeBs3FV6O5uAKclIsdmoehHLk40Psk+42IfAM0Kf0Q1j/wN8CvsS7v\nlf6Y3XG9aIxZaIz5DfAbdz/VU8BLdsfkfs6LQJEx5vNAx1OeuFTVIyJRwL+BZ66YtbONe4aut7vP\nc56IdDXG2NbmICLjgJPGmG0ikoAzZuoqxIm52Il5uCxxuZ9TqblY83DwcloudloehvLn4ipTJBtj\nRlztcRHpDrQGtouIYF2y2iwi/Y0xp+yK6yo+B76iEpLzD8UkIg9iXWoYFuhYSivH/5WdynLwgnIT\nkTCspPypMWa+3fFcyRhzQURWAKOxtxd4MDBBRMYCtYA6IvKJMeYnNsZUIU7MxU7Mw+DMXFxF8jBo\nLi4XJ+diB+VhKGcurvLtFsaYncaYpsaYtsaYNliXZHpXRoH8Q0Skfam7k7D6hGwlIqOxLjNMcDfW\nO5Gds2xOPjxBcN4M5L+A3caY1+0OxENEGopItPt2LayZzb12xmSM+bUxppUxpi3W99TyqlggX49T\nc7ET8zBUiVxsd67RXFw+jsrFTszDUP5cXOWL5KswOOeb9y8ikiwi24BbsVZT2u0fQBTwjXv7k7fs\nDghARCaJyDFgIPCliNjSn2eMKQE8hyfsAr5wwuEJIvI5sBboKCJHReQhB8Q0GLgfGObe5meL+xe/\n3W4AVrh/7tYDXxtjvrI5purIKbnYiXkYHJiLnZKHQXNxOWNyYi4Oijysh4kopZRSSil1hWCcSVZK\nKaWUUsonWiQrpZRSSil1BS2SlVJKKaWUuoIWyUoppZRSSl1Bi2SllFJKKaWuoEWyUkoppZRSV9Ai\nWSk3EWkhIqkiUs99v777fqsfeq1SSin/0FysnEKLZKXcjDHHgbeAV9wP/QV4xxhz1L6olFKqetFc\nrJxCDxNRqhQRCQM2AR8CjwK93Cc/KaWUqiSai5UThNkdgFJOYowpFpFfAUuAWzUpK6VU5dNcrJxA\n2y2U+r6xQBrQw+5AlFKqGtNcrGylRbJSpYhIL2A4MBB4TkSa2BySUkpVO5qLlRNokazU5d4CnnEv\nHHkVeM3meJRSqjrSXKxsp0WyUm4iMgU4YoxZ7n7obaCziNxsY1hKKVWtaC5WTqG7WyillFJKKXUF\nnUlWSimllFLqClokK6WUUkopdQUtkpVSSimllLqCFslKKaWUUkpdQYtkpZRSSimlrqBFslJKKaWU\nUlfQIlkppZRSSqkraJGslFJKKaXUFbRIVkoppVSFicifROS0iKRVwuf6vYh86u/nKnU1WiQrpZRS\nDiUih0XkoohcEJF0EflQRGrbHZeHiLQEngM6G2OaVdKnLc9RwbYfKywir4jIGfcfEn+5zvNiRcTl\n/lpnu9+/WJmxqstpkayUUko5lwHGGWPqAjcCfYHf2BGIiIRe5eFY4Iwx5qyfxgsqIvIzYALQA4gD\nxovIY9d5iQGijTF1jDF1jTH/UxlxqqvTIlkppZRyNgEwxqQDi4HuACJyg4jMF5GzIrJfRB51P17D\nPfsc477/oogUiUiU+/4fROT/3LcjROR/ReSIe6b6LRGp4f7YLSJyTER+JSLpwL8uC0pkOLAUaOae\n9fyX+/EJIrJTRDJFZLmIdC71mkPu8bYDOSLyvTpERP4uIkdFJEtENorIkKv+p1yaeZ0iIifcb7+8\n4mk1RORjd3w7ROTGUq9/QUQOuD+2U0QmlfkrUnY/AV4zxqS7v37/Czx4necLWps5hn4hlFJKqSrA\n3dowFtjifmgmcBRoCtwF/D8RSTDGFAAbgFvcz4sHDgOD3fdvARLdt18B2mPNcrYHmgO/K/VpmwL1\ngFbAZTOgxphvgTFAmnvW82ER6Qh8DjwNNMIq6heKSFipl97rfl09Y4zrKv/UDe546rvHmi0iEdf5\nr0kA2gGjgBdEZFipj413jxENLAT+WepjB4DB7ln6l4HPRKTJ1T6BiEwWkXPuwv/cFbczRaTFNWLr\nBmwvdX+7+7FrMcBh9x8J/xKRBtd5rgowLZKVUkopZ5snIpnASmAF8Gd3UXYT8IIxpsgYsx14H2vm\nEvdzb3G3NMQBb7jv1wD6uT8OMAX4hTEmyxiTC/wFmFzqc5cAv3d/joIyxHo38KUxZrkxpgRr5rQW\nMKjUc143xqRdazxjzOfGmPPGGJcx5m9ADaDTdT7nS8aYfGPMTuDDK+JfbYz52hhjgE/d/xeezzPH\nGHPSfXs2kAL0v0ZMM4wx9Y0xMe73pW/HGGOOXyO2KCCr1P0L7seu5gzW1yYW6APUAaZf59+tAizs\nh5+ilFJKKRtNNMasKP2AiDQDMo0xF0s9fASruAL4Dvg/rD7mZOAbrHaJr4EUY8x5EWkE1AY2i4hn\njBDc7R1up40xReWItZk7DgCMMUZEjmHNUHtcq6D0/NueBx4GbnA/VAdoeI2nmyvGO4K7HcUto9Tt\ni0BNEQkxxrhE5CfAL4DW7o9HXufzVFQOULfU/Wj3Y9/j/iPFc5XgtIg8CaSLSKT7Y6qS6UyyUkop\n5WxylcfSgBgRiSz1WCvghPv2WqzZ19uA74wxe90fH4tVQIM1c3kR6OaeDY0xxtQzxkSXGrO8u0Ok\nYc2EltaSywvZa47p7j/+L+BOz4wt1uzr1f4PcD/estT9Vu4YrktEWgHTgKmlPs+ua30eEbmv1I4T\npd88j12r3WIX0LPU/V7ux8rKoLWabfQ/XimllKpi3Jf312K1XtQQkTjgEayWAowxecBm4AkuFcVr\ngZ977rtbEN4D/u6eVUZEmovISB9CmwWME5GhIhLmnhXOB5LK+Po6QBFw1r2o8Hfux67ntyJSS0S6\nAQ8BX1znuZ4iOBJwAWdEJEREHuLyGejLuFtAPDtOlH7zPHat2fFPgOdEpJmINMfaLu/DqwYm0l9E\nOoqlAfA6sMIYk33df70KGC2SlVJKKee63kzuZKAN1szpHOC3V7RlfAeEYi2E89yP4lI/MsALWAvY\n1onIeazdKjpWOFhj9gM/Bt4ETgPjgPHGmOIy/HvAagf5GtgPHMKa6T72A6/5/9m78/imqvTx45+n\nZd93hAKlVAEXVgUUXEBFEcdl3BVUXEbHhdGf4obfikxFRVFEdEZcRlCYQUXFXQS1AiKyCoJAoZQC\nLZtAWdpSaHN+f5wbCCVpCyS5Sfq8X6++ktx7cvMkbW+enDznnJ+wz2E68IIzoDBgiE6cK4CXgLnY\nkoxTgdllPM5RM8aMww4Y/B07aO9zY8xb3v3OrBreGuo2wLfYnvOl2A8XNwU7JlV+Yj9IKqWUUkpF\nDxFJBNYClQPMkqHUcdGeZKWUUkpFq0C1ykodN02SlVJKKRWt9OtwFTJabqGUUkoppVQJ2pOslFJK\nKaVUCZokq4BE5A4R+dG5HufMB9nCuV1dRL4SkVwRmeRse15E/hSR9X6OdZ6I/B7eZ6CUUtFHRHqK\nSLoz/+7lbsdTkvNe0Loc7RJFxCMifnMNERkmIu8HOz7n2O86y0XPdW7fIyKbnde0figes4x4WjqP\nrTXUUUST5AhSYqLyYhHJ99l2Y9lHCAnvdDkeZz5I71yQ1wP1gPrGmAHOCXMwcJIxptURBzHmJ2NM\nhzDF7CoRucXPpPN7nDeLx92OL9hE5BER2SQiO0XkTRHxu5KniLQXkc9FZKvzYeorETnRZ/8dIlJU\nYoL+XuF7JkpFjH8Crzrz737udjAlOe8F68rb/Dj3HzVnQZILgObGmDOdc9JLwIXOa7rzGI9batJf\nGmPMBuextcY1imiSHEF8JyrHLq15qc+2/5VsLyLx4Y/yoERglc8/fGtgy7GefGKJMea9kpPOA0Ow\nc5m+E44YjuUkfoyPcyl2WdfzsPO1tgeeCtC8LnYu17ZAU+ycoZ+WaDOzxAT9P4cmcqUiWiLwx7Hc\nMZTvCy6/5xyN1sA6Y8w+5/YJQFVgxXEeV7BJvfYGVxCaJEcuocQ/ooikishkEfmviOwCBojI+86K\nRN42F4hIps/tBBH5xOm9yxCRewM+oEgjEflSRHaJyBxs0uPdF+98gm4lIs8AQ4GBTm/fLcDXQCvn\n9pt+jl0yrg0i8v9EZKnTAzlJRCoHiOsOEUkTkTFO23SxKxPdLiLrnV7MAT7tq4rIyz77XhORKs6+\nBk4P5lYR2e70bDb3ue8sEXlaRH52nsvXIlLP2VfdifNPJ465ItIg0Ovpc8wzgFHAdcaYbT7PKdN5\njDUicp1P+7tFZIWzb6mIdHC2n+q8DjtFZImI9Pe5z/vO8/xGRPYAZ5f2OgTRLcCbxph0Y0wukIpd\n8eoIxphfjTETjDG5xphiYDRwioiUtZqWUhWGiKzBnnu/dM4BlUWkmYh85pyz0kXkTp/2w0TkI+cc\nkAvcWuJ43Z3/f/HZ9lcRWeJc7yYic5zzSraIjBWfb4Oc8/69IpKOXeDDu62Nc72/iCxy3jeyRGRY\nyacE3OEcO1tEHi7luZ/pnHt3ishiETmvlLbNRGSKHHpvG+xsvx27iuBZzus3CVjp3G2niMxw2rUX\nke+c13SFiFzrc+xqIvKSiKwTW1I4U0SqcWjlwlzn2D38xNVNROY7r8cmERnlbD/YC+08T99vGwtE\nZK3TTkTkced9YZvY93zve1BV5/fsfQ/6VZyVElWIGGP0JwJ/sCsNnV9iWyp2BZ7+zu1q2CVIn/Jp\ncwGw1rkuwGLsikrx2NV81gJ9AjzmFGAS9hN3B2zP5w/OvnigGGjlE8t//D1ugGMfth+7gtIcoDFQ\nH1gF3B7gvncAhdiVhwR4DlgHvAJUBi4BcoFqTvux2B7LOtjVpb4Ehjv7GgFXAFWcfVOAD30ea5YT\nSxvn9Z0J/NPZdy/wiXNfAboCNcr4PTZwfpcP+myr7cTbxrndFGjvXL8R+y1CZ+f2iUCC8zzXAg87\nv4sLgD0+x3gf2A50d25XKe118BPnucBOYIdz6Xt9h/e4fu63DPirz+0mzt9J7XL8jV8DZJX4Pe8B\ntmJ7fIbizMCjP/pTkX6cc0Yfn9sznf/nykAn53+kt7NvmHN+vMy5XdXP8VYDF/jc/hB4xLneFeju\nnNNaAcuBf/i09WBXwKvnPbbzP+4995wLnOpcPw3YBFzu3E507j/JOZ+e5sR+vk/s7znXE4A/gYud\n2xc4txv6eT4CLACedM6HrbEr7vV19t+K/VYKnziKvecToAawHvshX5zXdBuHzsOvAz9ge6AFONN5\n7Q87ToDf3RxggM/jdC8RQ1yJ9pWANOAZ5/YDzjGaOY/5b+C/zr67gM+w79ECdAFquf33Gss/rgeg\nPwF+MYGT5BkltpWWJPcC1pRo/3/AOD+PVwk4ACT5bBvJ4Umyh+Amydf63H4JW4Pn7753AMt9bnd2\nTjb1fLblAqc4J44CoKXPvrOB9ADHPgNbJuK9PQt41Of2YOwyogB/w75ZnXYUv8evgI9KbKuNTTyv\noMQbGjADuMfPcXoDG0ps+xAY6vN38LbPvqN6HY7j73Sd798p9o3Qg60FLO1+rYBs4CqfbUk+f1+n\nYRPlh4MZr/7oTzT8+J7/gRbOubmGz/5nvedfbKKZVsbxUoF3nOu1gb2+54YSbR8APva57QHOK9HG\ng5Mk+7n/aOAl57o3ST7JZ/9I4C2f2L1J8qPAhBLH+ha42c9jdMeWU/hue9znOQZKkuOc29cBP5W4\n/xtAinPuzPd3ni95nADPP815Xg3Lc19sEvy5z+0/OPwDUjNgP/ab/9uwS2d3cPtvtKL8+B1goyJa\nWWvY+2oFJIrIDue2YP/RfvTTtqmzb6PPtiyg27EEWU5bfK7nY3sSytO2ACg29ut93221OFR7tsTn\n28U47IkaEakJjAH6Ymtkxbmfr80l4vLuH489YX3olAi8D/yfCbAcqoj8H5CMTcQPMsbsETsQcwgw\nXkRmAQ8ZY9YALYEMP4drju358JXF4a+Z799Gqa9DEO3F9lR71cXW7O0JdAcRaYLtmRptjPnEu90Y\nk+lzfZnYsp77sR+glKqomgM7jDH5PtuygNN9bpf1vvBf4GcR+TtwFbDQGLMBQEROAl7GnqeqYztM\nFpa4/0YCcEoOnsN+sK3i/Hzk08Rw5PvKaX4OlQhcJyKXeQ/txPJDgLYJft7bZgaK08/9zyxx/3jg\nPey3jdWw39wdizuwH0pWOiUU/zTGfOWvoYjcje2J9y3bSAQ+FRHvuVqwH5KaYt9zWgCTRaQuMBF4\n0tjyNRUCWpMcfUyJ23nYr3S8mvlc34DtOWzg/NQ3xtQ1xlzp57hbsAlUS59tR8xSEQW2YL96bOfz\nvOsZY7y1w49gT0JnGGPqAeeX98DGmAPGmH8aY07B9speBQzw11ZELnQe62pjzF4/x5pmjOmLTWYz\ngHHOrg3YxLqkHA7/3cCh3tiDh/W5XtbrUDLe8+TIGTl8Z5k4ovbOsRz7VaVXZyDbGOM3SRaRhsB0\nbInLqADHPOwu5WijVCzLARo4H/C9SvvfP4IxZgU2Oe2PLen6r8/uf2O/tUl2zolPcuT/XWnHnwRM\nBRKc+4/zc/+S7ys5fo6zAdur7Pt+VdsY80KAtmv9vLdd5qetPxuwve++969jjLkfW+JRgP/zcKmv\nM4AxJsMYc5MxpjHwAjBFRKqXbCci5wDDsaUpvu8R64FLSsRW0xizyRhTZIxJNcacCvQELsOWjKgQ\n0SQ5+v0GXCoi9USkGbY8wOsXYL+IPOQU/MeLyGki0rXkQYwxRdgT3XBn0MJpwM1heQbHxm/y5PTq\nvg2MEZFGACLSQkT6Ok1qY3uHdzkJ27ByP6BIH7GD5wTbg3oAPz2zIpKAfeO43xiz3M/+E0TkL86J\nswj7Qcd7nLeBR0Wks9P2ROd4c4Ai53dZSUTOx9ZiTz7G16Fk+59MiRk5zOGzTPwa4GV5D/ibiLQT\nO4jxSeBdfw1FpA7wHfC9MeaI111E+nkHoYjIKdia5KkBHlepCsHYaTfnAM855/GO2N7Ko51f+L/Y\nUopzOLyntzaw2xiTLyLtgXuO8ri1gJ3GmAMi0h07dsSXACliBz6fii0Z8HfemghcJiIXOYPbqjkf\n3pv7aTsP2CMijzrt4p1z8xl+2vrG4fUl0FZEBjrn08oicoaItDPGGOw57GWxgwO9A+0qY+uWPfhP\noO2DiAzwnnOBXdjE2rdXGBFpCXwA3GKMKfnN4TjgWRFp5bRtLM5c2SLS23kPj6OU9yAVPJokR64y\nP7E6xmNH7mZhZ5g4OFWc8xVMf5z6LeyAiTewJ0V/7sUONNuMHR38n2OMqTyO91gl7+97ewj29Zgn\ndrT3t9gBcGC/VqyHHeQ2G1szXN64mmMH7u0CfscmfP/10+4u7Fd2r/vpkX0V+7XeI9jelG3AWcB9\nAMaYydiavQ/EzmDyMXYu6v3YXoMrsT0drwA3GmO8Xwn6i/vhUl6HoHC+RhyN/ZpzLfZvMdW7X0Sm\nicgQ5+Y12J7mO53Xw/uanODsvwhYJnZ2js+wf8v+epGUinUl/59vxNbs52DPCSnGGH9lc6WZjP1q\n/3tjzA6f7UOwMyXtxiZoJRNYf+cW3233AqnO+er/sMlfybY/YQfWTQdeMMZ8f8QB7YeBK7Afjrdh\nz11D8JOnOJ0Af8GeTzKx721vcXjpV8CYnZ7bi4AbsK9pDvA8tkQN53F/B+Zj3yuex9YSFwAjsKUr\nO5wPBSX1A5Y7r+do4HpjTGGJGM7HDnKe4vP+4F1sawz2/Ped85rOwb6Hg/3mcQr2PWg5tnQyJIux\nKMs70jN0DyDSD/uGHoctqh8ZoF037B/D9d46xfLeVymllFJKqWAKaZLsfCWQjp3ZIAf7qewGY8xK\nP+2mY+uA/mOM+aS891VKKaWUUirYQl1u0R1YbYzJMsYcwH6Nc4WfdoOxXyFsPYb7KqWUUkopFVSh\nTpITOHxqmo2UmObLKcq/0hjzbw4vrC/zvkoppZRSSoVCJMyT/Ap2RbhjJiKhLaxWSqkgMsbE3NR2\neh5WSkWT8pyHQ92TnM3hc+224PC5HcFOYD5ZRDKxo9//5Ux3Up77HhSMlVWC+TNs2DDXY4iWuCIt\nps2bN/PVV19xzTXXMGLECJ5++mmeHz6c3EsvxWCHJ5vkZMydd9qf5ORD2wcMwOTnV5jXKpLjisSY\njIntPNLt1zaa/g40rtiJTeOKvrjKK9Q9yfOBE0UkEbue+w3YqWwOMsa08V4XkXeBL4wxn4tIfFn3\nVSoUmjZtSv/+/Zk3bx4PPPAAM776io5PPUXdVaugdm0YMwZuvRXinM+YHg9MmACDB8OkSbBjB0yd\nClWquPtElFJKKXXMQtqTbOw8vfdj55NdDkw2xqwQkbtF5C5/dynrvqGMV1Use/bsYevWraW2qVmj\nBpd//TVJq1ZB48YwaxbcdtuhBBns9dtugzlzoFEj+OYbuPNOOIpPq0oppZSKLCGvSTbGfAu0K7Ft\nXIC2t5d132jRu3dvt0PwKxLjciMmj8fDhx9+yJYtW7jxxhtJSkryH9cbbyATJkCNGvDtt9Cp05EH\n8+rYEaZNg3POgfffh5494e9/D2rckfj7g8iMKxJjUuEXqX8HGtfRi9TYNK6jE6lx+RPyxUTCQURM\nLDwPFT6zZs3ihx9+oE6dOtx1113UrFnzyEbp6dC5MxQUwOTJcP315Tv4pEkwcCBUrw5Ll8KJQV3k\nTkU5EcHE6MA9PQ8rpaJBec/Duiy1qnC2bdtGWloaAFdccYX/BNkYuPtumyDffLPfBHnfvn3+H2DA\nAJskFxTA3/6mZRdKKaVUFNIkWVUoxhimTZuGx+OhS5cutGnTxn/DDz6AtDRo2BBeeeWwXfv372fq\n1Km8/vrrFBYW+r//6NG2hjktDT76KKjPQSmllFKhp0myqlC2bdvG2rVrqVq1KhdccIH/RoWF8Jgz\ndffzz0ODBoftrly5Mtu3b2fv3r3MmjXL/zEaNYIRI+z1xx6DQL3OSimllIpImiSrCqVJkybcf//9\nXH311f7LLADeeAPWr4cOHeD224/YLSL069cPgHnz5rF3717/x7n9dnuMdetgnN+xqkoppZSKUJok\nqwqnQYMGnHTSSf53FhTAs8/a6888c/hUbz4SEhJo164dBw4cYPbs2f6PFR8Pqan2+siR2puslFJK\nRRFNkpXyNWkSbN0KXbrAZZeV2tQ7jc2iRYsoKCjw3+jyy+0MGZs2wTvvBDlYpZRSSoWKJslKeRkD\nL79srz/8MEjps8OccMIJnHzyyXTp0gWPx+O/kQg8+aS9/uqrdnU+pZRSSkU8nSdZKa9vv4VLLoGE\nBFi7tlzLShtjkDKSaYqKoE0b2LDBrsbn1DOriknnSVZKKXfpPMlKOXJzc/n000/ZsGFD6Q29vciD\nB5crQQbKTpABKlWCe++118eOLddxlVJKKeUuTZJVzFu0aBFLly5lwYIFgRv9/hqquecAACAASURB\nVDtMn26Xn77rruAHceedUK0afP01rF4d/OMrpZRSKqg0SVYxrbi4mMWLFwPQtWvXwA3festeDhoE\n9esHP5BGjeCmm+z1118P/vGVUkopFVSaJKuYtnr1avbu3UujRo1o1aqV/0b798N//2uv33nncT1e\nfn5+4J2DB9vL8eN1OjillFIqwmmSrGLawoULAduLHLB++KuvYPt26NjRTtd2DPbt28fbb7/Na6+9\nRnFxsf9GnTvD6afDrl3wxRfH9DhKKaWUCg9NklXMys/PJzMzk/j4eDp16hS44fjx9nLQoDKnfQuk\natWqHDhwgIKCAlaXVnN88832cuLEY3ocpZRSSoWHTgGnYlpBQQGbNm2iTZs2/hts2WKnfBOB7Gxo\n0uSYH2vOnDlMnz6d9u3bc/3115f9eJs22VplVaHoFHBKKeUunQJOKaB69eqBE2SwtcjFxdC//3El\nyAAdOnRAREhPTw9cm9y0KVx0kZ07+YMPjuvxlFJKKRU6miSriu299+zlrbce96Fq165NcnIyHo+H\nZcuWBW6oJRcqQojIOyKyRUSWltLmVRFZLSK/icixFe0rpVQU0iRZVVwZGfDbb1C7Nlx6aVAO2bFj\nR+rXr09cXCn/WldcAbVqwdy5Omeyctu7wMWBdorIJUCyMeYk4G7gjXAFppRSbtMkWVVcH39sLy+7\nDKpWDcohTz31VAYPHswZZ5wRuFGNGnDVVfb6Rx8F5XGVOhbGmNnAzlKaXAG857T9FagrIk3DEVus\nyszMYuDA4fTpM4yBA4eTmZnldkhA5MYFkRvbzJmzSUq6iHr1Licp6SJmzpztdkgVRthee2NM1P/Y\np6GUtWPHDrNy5Upz4MCB0ht262YMGPPJJ+EJzNdnn9nHPuOM8D+2cpVzvnL9vOn9ARKBpQH2fQH0\n9Lk9A+gaoG3wX6zjsHbtOjNgwNOmd++nzIABT5u1a9e5HZJZu3adSU5+2MBeA8bAXpOc/LDrsUVq\nXJEc208/zTKVKl1zWFyVKl1jfvpplqtxVQTBeO3Lex7W2S1UzPn++++ZPXs23bt355JLLvHfKCsL\nWreGmjVh2zaoXj2sMVJQAI0bQ16ejSXQQicq5kTa7BYikgh8YYzp6GffF8Bzxpg5zu0ZwKPGmEV+\n2kbMeTgzM4u+fceSkTEcqAnkkZw8jOnTB5OUlHhMxzTG/tvm5R35k59fvu2//DKcTZuGODF55VGn\nzigSEoYF4Zkfm+zs4ezeHXlxgbuxGWPweIopLvYccbllyzN4PN6/r0NxxcUNo27dh0scByDw/0b5\n9h+8VUabsvb7b3O8+4N1jEPtAu8vLHwdSKXka9+69V/JzPwu4P18lfc8XKlcR1MqiqxcuRKAdu3a\nBW70ySf2sn//8CfIYB+zXz9b8jF1KvzjH+GPQamyZQMtfW63cLb59fTTTx+83rt3b3r37h2quEqV\nkjLeJ0EGqElGxnAGDBjFLbcMO+rkNi/PJshVq9rP1b4/NWocuc27vWnTw7etWeNh06aaJaKtSfv2\nHt59N8wvko9BgzzMnx95cQHcdFM+S5YcGVtSUv7BhVL98Xg85OXlsWfPHvbu3cuePXuc63vYvdtu\n271792H7vG292/fv30/t2rWpVasWtWvXPni9Tp06fP11Oh7PkXFVrryGe+/9EbCJmHcRK3+X/vYH\n2nfoOkCgfXJwf1nH8X/f0mMt7RjBeozyvB4DBqwnP//I1z43txqBpKWlkZaWFnB/IJokq5iyfft2\n/vzzT6pWrUpiYik9Rt565GuuCU9g/lx1lY3j0081SVZuErzvqkf6HLgP+EBEzgRyjTFbAh3IN0l2\nU3a2h8N7mQBqsnath8WLDyW2detC8+blS3hr1ID4+OOLa+rUOJYuzaNkD9hJJ8VxyinHd+zj0bZt\nHPPnR15cALt2LQaOjG3duh/417/uZ9euXezatYvc3NzDru/Zs4caNWpQr1496tate/DS9/oJJ9Sl\nXr0TqFu3nd/9NWvWDLhSa1LSRaxbd2RczZrl88wzN4XuBVE0abLb72tfr96+gPcp+aF9+PDh5Xos\nTZJVTElPTwfgpJNOIj7QO1pODvz8M1SrZnuSQyA/P58FCxawb98+LrroIv+NLr0UKleGmTNtyUfj\nxiGJRalAROS/QG+goYisB4YBVbD1em8aY74Wkf4isgabqdzmXrTll5AQh7/E6sIL4xg3zqWggNTU\nQcydO+yIMpDU1MHuBRVhceXn57N48WLmzZvH/PnzycmZCQwAJh2MDQZQu/YW2rZtGzAJrlOnTuD3\ngCCYMOEpLrhgEEVF4w/GVanSICZMeCpkj6mscL72miSrmLJq1SqgjFKLr76yl3372qnYQsDj8fDj\njz8SHx/PeeedR1V/s2fUrQvnnw/TpsEXX8Dtt4ckFqUCMcaU2eVljLk/HLEEU2rqIL7+ehg7d7qf\n9PlKSkpk+vTBpKSMIifHQ/PmcaSmHnuddLTHdeDAAZYvX34wIZ4/fz7p6emceuqpdOvWjb59+7J7\n926++uozoDNwArAZWMN55w3gHy5+A3fuuWfz/fdw661/JTe3GvXq7WPChKc499yzXYupogjna68D\n91RMWbp0KStXruTyyy+nWrUA9UlXXgmffQbjxsFdd4UslnfeeYeNGzdy/fXX0759e/+N3nwT7r4b\n/vIXmyirmBdpA/eCJZLOw1u2QNu2WfTuPZ49e7xJ3yDXk9GKzOPxsGbNmoPJ8Lx581i6dCmtWrWi\nW7dudO/enW7dutGpU6fDOhUyMzPp27cvGRkZB7clJyczffp0kpKS3HgqKgaU9zysSbKqWAoLoWFD\nOxJn/Xpo2bLs+xyjmTNn8uOPP9K1a1cuu+wy/41yciAhwQ7k27HDloComKZJcujdf7+tZBo92u1I\nKq7s7OyDyfD8+fNZsGABderUOZgMd+vWjdNPP506deqUeazMzExSUlLIycmhefPmpKamaoKsjkvE\nJMki0g94BbtwyTvGmJEl9l+OncvDAxwA/p8x5mdn3zpgl3efMaZ7gMeImJOzinDTp8NFF0HHjrBk\nSUgfatOmTbz55pvUqVOHBx98MOAAELp0sSv/TZtmY1MxTZPk0Fq9Gs46C1auhEaN3I6mYti5cycL\nFiw4mBDPmzePAwcOHEyGvYlxkyZN3A5VKSBCpoATkTjgNeACIAeYLyKfGWNW+jSbYYz53GnfAfgQ\nONnZ5wF6G2NKWxFKqfLz1iMHaRnq0pxwwgnUqlWL3bt3s3XrVpo2DbBQ2SWX2CT5m280SVbqOD35\nJDz0kCbIR8vbW5udnU1CQkLA3lrvwDrfsonNmzdz+umn061bN2666SZGjx5N69atA3cMKBUlQtqT\n7EwZNMwYc4lz+3HsqOmRAdqfBbxtjDnVuZ0JnGGM2V7G40RED4aKAiedBGvWwOzZ0KtXyB8uPT2d\nOnXq0LRp08BvGLNmwbnnQrt2tvtLxTTtSQ6defPszIrp6XbKNlU+gep+v/76a/Lz8w8rm1i9ejWn\nnHLKYT3E7du3D+lMEkoFW0SUW4jI1cDFxpi7nNsDge7GmH+UaHcl8BzQGLjUGPOrs30tkAsUA28a\nY94K8Diun5xVFFi9Gtq2hfr1YetWqBQhk7sUFdlur127ICMD2rRxOyIVQpokh4Yx0KcPDBwId97p\nWhhRaeDAgUyaNOmI7fHx8bRt2/awOuKSA+uUikYRUW5RXsaYqcBUETkbeAbo6+zqZYzZJCKNgeki\nssIYM9vfMSJlpSfljvfff59q1apx8cUXBx4I4i216NcvchJksLH07QtTptiSi/vuczsiFUTHutKT\nOjpff20/+w4a5HYk0Sc72/8iij179mTmzJlhjkapyBHqTCEbaOVzu9QlTY0xs0WkjYg0MMbsMMZs\ncrZvE5FPge5AmUmyqljy8vJYu3Yt8fHxXHnllYEbTptmL0O0gMhxueQSTZJj1LGu9KTKr7gYHn8c\nnn8+sj7/RoM5c+awbNkyv/tatWrld7tSFUVciI8/HzhRRBJFpApwA3aZ04NEJNnnelegijFmh4jU\nEJFazvaawEWA//9kVaGtXbsWgMTERCpXruy/UWEh/PSTvd63r/82burXz17+8APsC7y0plLqSO+9\nB/XqQaCZFtWR0tPTufrqq7nhhht47LHHaFOizCs5OZnU1FSXolMqMoQ0STbGFAP3A98By4HJxpgV\nInK3iHhXcbhaRJaJyCJgLHCds70pMFtEFgNzgS+MMd+FMl4VnbyDTZKTkwM3+uUXKCiADh0g0CwT\nIWSMYefOnQSs2WzeHDp1sjH+/HN4g1MqihUUwFNPwQsvgE6mULYtW7Zw33330atXL3r06MGqVasY\nMmQIM2bMYMCAAfTp04cBAwboYh1KEYaaZGPMt0C7EtvG+Vx/AXjBz/0ysetQKhWQMaZ8SfKMGfby\nwgvDENWR3n77bXJychg8eDANGjTw3+jCC+3czd9/DxdcEN4AlYpSY8dC9+52bmQVWF5eHi+//DJj\nxozhlltuYeXKlTRs2PDg/qSkJCZOnOhihEpFnlCXWygVUrm5uRQUFFCrVq3SJ6qfPt1eulRqUa9e\nPeBQaYhf3sT4++/DEJFS0W/HDnjxRXj2WbcjiVxFRUW89dZbtG3blhUrVjBv3jxefvnlwxJkpZR/\nuiy1inoHDhxgx44dgRfr2LnTTrEWH2/fVWvVCm+AwIIFC/jqq6845ZRTuPbaa/032rvXTk/n8cD2\n7bbIUsUcnQIueIYMsf82b7wR1oeNCsYYvvzySx577DGaNGnCiy++SLdu3dwOS6mIEFVTwCl1PCpX\nrhw4QQZIS7OJ59lnu5IgAwcHxWRmZmKM8b+wSK1acOaZdqGTtDQobaYOpSq4rCx4910IMDFDhTZv\n3jweffRRtm3bxosvvkj//v119TuljoGWW6jY5y21cKkeGaB+/frUq1ePgoICNm/eHLihN0YtuVCq\nVCkpdrbEZs3cjiRyZGRkcMMNN3DVVVdx8803s2TJEi699FJNkJU6Rpokq9jnHbTn4tRvIkKbNm04\n4YQT2FfaFG9al6xUmZYsge++g0cecTuSyPDnn3/y4IMP0qNHDzp06MCqVau44447qKSTRit1XLQm\nWcW2jRuhZUuoU8fW+br4puHxeIiLK+Nz6f790KAB5OVBdradGk7FFK1JPn79+sFf/gL33x+Wh4tY\nBQUFjBkzhlGjRnHDDTfw1FNPlT6AWSkFlP88rD3JKmqtX7+egoKC0ht5FxA5+2zXl+IqM0EGqFIF\nzj3XXv/hh9AGpFQU+v57WLMG7rqr7Laxqri4mPHjx9O2bVsWLFjAnDlzeO211zRBVirINElWUamo\nqIj333+fF198sfREeeZMe3neeeEJLBi8JReaJCt1GI8HHnvMTvlWpYrb0YSfMYZvv/2WLl268Pbb\nb/Phhx8yZcoU2rZt63ZoSsUkLVhSUSk7O5uioiIaN25M9erVAzf09iR7e2ejQe/e9nLWLFfDUCrS\nfPghxMVBoFkUY9nixYt55JFH2LBhAyNHjuSKK67QAXlKhZj2JKuolJmZCVD6sqmbN8OqVVCzJpx+\nepgiC4JOnaB2bfudck6O29EoFRH274cnn4SRIyvW8tNZWVncfPPN9O/fn6uvvpply5Zx5ZVXaoKs\nVBhokqyi0rp16wBo3bp14EbeUouePaFy5ZDHVB7GGNauXUtaWhoej8d/o0qVbMygvclKOd54A9q1\ngz593I4kPHbu3MkjjzxC165dadOmDenp6dxzzz1UjpBzmVIVgSbJKuoUFRWxceNGoJxJcgTVI4sI\nX375JT/99FPp8yV7y0O8z0GpCmz3bhgxAp5/3u1IQm/fvn289NJLtG3blt27d7Ns2TKGDx9O7dq1\n3Q5NqQpHa5JV1CksLOTUU08lPz8/KuuRExMT2blzJ1lZWTQPNMWbJslKHfTCC3DJJdCxo9uRhI7H\n4+F///sfTz75JJ06deKnn37ilFNOcTsspSo0nSdZxaY//4TGjaFaNcjNhapV3Y7ooN9++43PPvuM\ndu3accMNN/hvVFgIdevayz//hIYNwxukChmdJ/no5ORAhw6weDG0ahX0w4ddZmYmKSkpZGdnk5CQ\nQGpqKpmZmTzyyCNUqlSJF198kXMj7IO9UrGmvOdh7UlWsWn2bHt55pkRlSCD7UkGO8+zMcb/AJyq\nVW3sP/0EP/8Ml18e5iiVigzDh8Mdd8ROgty3b18yMjIObvvkk09o1KgRL730Etdcc40OyFMqgmhN\nsopNEVpqAVCvXj3q1KlDQUEBW7duDdxQSy5UBbdyJXz6KTzxhNuRBEdKSsphCTLYVfN69erFtdde\nqwmyUhFGe5JVbPImyRE0aM9LROjpzF5Rs2bNwA01SVYV3BNPwKOPQv36bkcSHNnZ2X63b9myJcyR\nKKXKQ5NkFXtyc+G33+y0b2ee6XY0fvXo0aPsRmedZaeDW7QI9uyxcycrVUH8/LP90//f/9yOJHgS\nEhL8bg84gFcp5Sott1BRZe7cucydO5e9e/cGbvTzz2AMdO8ONWqEL7hg8y6CUlwMv/zidjRKhVxm\nZhYDBw6nT59hXHnlcO6/P4tq1dyOKnhSU1Np0qTJYduSk5NJTU11KSKlolNWZibDBw5kWJ8+DB84\nkCxngbFg055kFTWMMcyZM4c9e/bQpk0batWq5b9hBNcjH7Vzz4Vff7UlFxdd5HY0SoVMZmYWffuO\nJSNjOFATyOONN4ZxzTWDSUpKdDu8oEhMTKR27dqcdtppGGNo3rw5qamppa8cqpQ6TFZmJmP79mV4\nRoZzpoBhc+cyePp0EoP8v6Q9ySpq7Nq1iz179lCtWjUaN24cuKF3ZotYSZJB65JVzEtJGe+TIAPU\nZO3a4aSkjHcxquCaOnUq9evXZ8aMGfzwww9MnDhRE2SljtL4lJSDCTLYM8bwjAzGp6QE/bE0SVZR\nY/369QC0atUq8Cjwfftg4UIQidh65KPSq5d9Lr/+ap+bUjEqO9vDoQTZqyY5OQGWb48yxhhGjBjB\nk08+qbNYKHUcPJmZfs4U4MnJCfpjaZKsokZWVhZgk+SAFi2C/fvh1FOhXr0wRXZs8vPz+fjjj3nv\nvfcCN6pf366ksH8/zJ8fvuCUCrOEhDjsF6e+8mjePDbepqZNm0ZhYSGX65znSh2bhQvh5puJmz/f\nz5kC4kIwADY2zj6qQtiwYQNQRpI8Z469dKZYi2RVq1Zl1apVZGZmkp+fH7ih97no4D0Vw1JTB5Gc\nPIxDiXIeycnDSE0d5FpMwTRixAiGDh1KXJy+7SpVbkVFMGUKnH02/PWv0LEjg+bNY1hyss+ZAoYl\nJzMoBANgdeCeihr9+/cnKyuLZs2aBW4URUlyfHw8CQkJrFu3jg0bNtCuXTv/DXv2hDfe0CRZxbSk\npESmTx9Mr16jaNTIQ8eOcaSmxsagvZkzZ7Jp0yauu+46t0NRKjrs2AFvvw2vv26X23zwQbjySqhU\niURg8PTpjEpJwZOTQ1zz5gxOTQ36oD0AMcYE/aDhJiImFp6HOk7GQLNmsGULpKfDSSe5HVGZvv/+\ne2bPnk2vXr248MIL/Tdas8Y+lyZNYPNmW6OsopaIYIyJuV9isM7DbdvC559D+/ZBCCpCXHzxxVx7\n7bXceeedboeiVGRbsQJefRUmT4bLLoMHHrBToQZZec/D+r2Pih1r19oEuVEjOPFEt6Mpl5YtWwKw\ncePGwI2Sk6FxY9i61T5HpWJUURGsXw+xNOHD/Pnz+eOPP7jlllvcDkWpyOTxwDffQL9+0KeP7RD6\n4w94772QJMhHQ8stVOzwLbWIkt7WFi1aAJCTk4PH4/Ffryhin9Nnn9mSi+TkMEepVHisXw8nnABV\nq7odSfA899xzPPLII1SpUsXtUJSKLHv32kT41VehenXbazx1KpG0glDIe5JFpJ+IrBSRdBF5zM/+\ny0VkiYgsFpF5ItKrvPdV6jBRVI/sVaNGDW699VYeeuih0gf0nHWWvfQ+R6Vi0Jo1UfMlULksX76c\nOXPmaJmFUr6ysuCRR6B1a5gxA958085MNWhQRCXIEOIkWUTigNeAi4FTgRtFpGSl2QxjTCdjTBfg\nDuDto7ivUod4E8hevUpvF2Fat25NtbJODN7EX5NkFcNiLUl+7rnneOCBB6hRo4bboSjlLmNg1iy4\n+mro2tXeXrAAPvnELpoVod/+hrrcojuw2hiTBSAik4ErgJXeBsYY37mvagGe8t5XVQzz589n4cKF\nnHXWWXTq1Ml/o9274fffoXJl12uYQuKMM6BSJfsc9+yB2rXdjkipoIulJDkjI4Nvv/2W119/3e1Q\nlHJPYSF88AG88ootr3jgAZgwAWrVcjuycgl1uUUCsMHn9kZn22FE5EoRWQF8Adx+NPdVsW/9+vVs\n2bKFAwcOBG7066/2k2nXrra2KdZUrw5dutgBDvPmuR2NUiERS0nyyJEjueeee6hbt67boSgVfps3\nw9NP25KKSZPgmWdg5Uq4776oSZAhQgbuGWOmAlNF5GzgGaDv0R7j6aefPni9d+/e9O7dO1jhKZd5\nZ37wzgTh188/28soqkc+aj172lX3fvkFLrjA7WhUOaWlpZGWluZ2GFEhVpLkjRs3MmXKFNLT090O\nRanwWrQIxoyx8zhefz18/z2ccorbUR2zUCfJ2YDv8mgtnG1+GWNmi0gbEWlwtPf1TZJV7Ni7dy+5\nublUqVKFxo0bB24YhYP2Stq/fz8HDhygZs2Sq9I7zjrLnny0LjmqlPzQPnz4cPeCiWDFxZCZCW3a\nuB3J8Rs1ahS33XYbjRo1cjsUpUKvqMjOvjRmDKxbZ3uLR4+GBg3cjuy4hTpJng+cKCKJwCbgBuBG\n3wYikmyMyXCudwWqGGN2iEiZ91Wxz9uLnJCQEHj2h+JimDvXXo/SJHnhwoV89dVXdOvWjUsuucR/\nI9/lqT0e0OVtVRCISD/gFWz53TvGmJEl9tcBJmI7LeKBl4wx44MdR3Y2NGwI0T7Gbdu2bbz33nss\nW7bM7VCUCq2dO+Gdd+C11yAhwdYb//WvdmxQjAhpkmyMKRaR+4HvOHQCXiEid9vd5k3gahG5BdgP\nFADXlXbfUMarIs+WLVuAQ/MJ+7V8uR3MlpgIzZuHKbLgql+/PsaY0hcVadnSnoiys2HVKjj55PAF\nqGKSzyxCFwA5wHwR+cwY4ztA+j5guTHmchFpBKwSkYnGmKJgxhIrpRavvPIK1113Hc2j9FykVJlW\nrbJzG//3v3DppfDRR9Ctm9tRhUTIa5KNMd8C7UpsG+dz/QXghfLeV1Us5513Hl26dEFKmx7m11/t\n5ZlnhieoEEhISEBE2Lx5MwcOHKByoE/iPXvaE9KcOZokq2AozyxCBvBOp1Ib2B7sBBliI0nOzc1l\n3LhxzJ8/3+1QlAouY+C77+wsFYsWwd1321XxmjVzO7KQ0u9rVcSrU6cOtUub8sybJPfoEZ6AQqBq\n1ao0adIEj8dDTk5O4Ia6qIgKrvLMIvQacIqI5ABLgAdCEUgsJMmvv/46/fv3JymW1tVWFVteHrzx\nhh1899hjcN11djGQf/4z5hNkiJDZLZQ6Lt4p0aI4SQbbm7xlyxays7NJTEz038i3Llmp8LgYWGyM\nOV9EkoHpItLRGLO3ZMPjmWVozRq46abjD9YteXl5vPrqqzqTiYoN69fD66/bmuNzzoF//xvOOy9i\nF/0oy7HOMqRJsopue/famuT4eDuPcBRr0aIF6enpGGMCN+rcGapUsfNN7toFOgerOj7lmUXoNuA5\nAGNMhohkAu2BBSUPdjyzDK1ZA8nJx3x317355pucc845nKxlUCpaGWOnUx0zBn74AW691XZCxcCU\nM8c6y5AmySq6LVxoZ3ro0iXqFxHp1KkTnTt3Lr3+umpVmyjPm2eX9NT5ktXxKc8sQlnAhcDPItIU\naAusDWYQxkBGRvQmyYWFhYwaNYovv/zS7VCUOnr799tV8caMsZ0v//gH/Oc/urIrWpOsItjWrVvx\neDylN4qRUguAuLi40hNkL+9z9dZiK3WMjDHFgHcWoeXAZO8MRCJyl9PsGaCniCwFpgOPGmN2BDOO\nTZvsIlx16gTzqOEzfvx4OnXqRJco/zZLVTBbt9ra4tat4b337Ap5q1bB4MGaIDu0J1lFpL179/Lv\nf/+bWrVq8dBDDwVOHr1Jcvfu4QvObT16wNixmiSroCjHDESbsHXJIRPNg/aKiooYOXIk77//vtuh\nKFU+v/1me42nToVrr7WzVpx2mttRRSRNklVEys62ZZGNGjUq3/RvFSlJ9j7XX3+131NH6UAKpbyi\nOUmePHkyLVu2pFevXm6HolRgxcV2qegxY+w/3P3328uGDd2OLKJpkqwikjdJTkgoORuVj02bYMMG\n+z1t+/ZhiiwCnHiiXe5zyxY7AjnQTBhKRYloTZI9Hg/PPfcco0ePdjsUpfzLzbX1xWPH2inbHngA\nrroqplbFCyWtSVYRqVxJsnfC/m7d7OwWMWLLli0sWrQocD22yOG9yUpFuWhNkqdOnUqNGjXo27ev\n26Eodbj0dFtb3KaNHeD+wQd2fv3rr9cE+ShokqwijjHm4IIapSbJMVqP/L///Y8vvviCP//8M3Aj\n7+A972ugVBSLxiTZGMOIESN48sknyzfgVqlQ866Kd+mlcPbZdorQ33+HSZNi7n0yXLTcQkWcffv2\n0axZM/bs2UOd0oa7x2g9ckJCArt27SI7O5smTZr4b6QzXKgYYUx0JsnTpk2jsLCQyy+/3O1QVEWX\nnw/vvw+vvmq/VX3gAZgyJeqnRY0EmiSriFO9enVuueWW0hfV8HgOlVvEwPRvvhISEvjjjz/YuHFj\n4CmlvB8MFi6EAwf06zMVtbZts3++9eu7HcnRGTFiBEOHDiUuTr+QVS7ZsOHQqng9e9q64z59dDB3\nEOl/t4pYpX6FuXq1nfS8eXMorSQjCrVo0QI4VJftV8OGtuutoACWLQtTR40w2QAAIABJREFUZEoF\nXzT2Is+aNYtNmzZx3XXXuR2KqmiMOVRb3Lkz7NsHc+fCZ5/B+edrghxkmiSr6BSjpRYAzZo1Q0TY\nunUr+/fvD9xQB++pGBCNSfKIESN4/PHHqVRJv4xVYbJ/v60t7tEDbrkFevWCzEx45ZXoXaoyCmiS\nrKJTDK20V1LlypXp0qULPXv2pKioKHBDrUtWMSDakuQFCxawfPlybr75ZrdDURXBtm3wzDN2Vbx3\n34WUFLsq3j/+Eb1LVEYR/RisolOMzmzhddlll5XdSJNkFQMyMqBfP7ejKL9nn32WIUOGULVqVbdD\nUbFsyRK78Menn8I118C0adChg9tRVTiaJKuIsn79enbv3k1iYiK1A60dv2+fXVZTBM44I7wBRpLO\nnaFKFVi50tZn163rdkRKHbVo6klevnw5c+bMYeLEiW6HomJRcTF8+aUtoVi9Gu691142auR2ZBWW\nlluoiLJw4UI+/vhjVq5cGbjRkiV2RoeTT67YXzdVrWoTZWNgwQK3o1HqmERTkvzcc8/xwAMPUKNG\nDbdDUbFk1y4YPRratoXnnoO77rL1xkOHaoLsMk2SVUQp10p7MV5qcVS05EJFsR07oKgoOvKAjIwM\nvv32W+699163Q1GxYvVqW1uclGTf1yZNsjNV3HijTusZITRJVhGjoKCA7du3Ex8fT9OmTQM31CT5\nEE2SVRTLyLC9yNEwa9XIkSO55557qKtlTep4GAMzZsBll9kZKmrXtqvi/e9/cOaZbkenStCaZBUx\nvEtRN2vWjPj4+MANY3j6N19btmzht99+o1GjRpx++un+G/lOA2dMdGQbSjmipdQiOzubKVOmkJ6e\n7nYoKloVFMDEiXYwHsCDD8KHH+qqeBFOe5JVxChXqcWOHfYrqqpVoWPHMEXmjtzcXObOncuy0hYL\nOfFEaNAAtmyB9evDF5xSQRAtSfKoUaMYNGgQjaKhLkRFlo0bbW1xYiJ8/rlNkn//He68UxPkKKBJ\nsooYLVu2pFu3bpx00kmBG3kHqHXtGvM1W74r73k8Hv+NRHRRERW1oiFJ3rZtGxMmTGDIkCFuh6Ki\nibe2uGNHyMuzq+R98QVccIF+4xdFNElWESMpKYn+/fuTXNrqQRWk1AKgZs2a1KtXjwMHDrBt27bA\nDbUuWUWpNWsif7GwV155heuuu47mzZu7HYqKMFmZmQwfOJBhffowfOBAstLTbW1xjx4wYIC9zMy0\nvceR/mlQ+aU1ySq6xPBKe/4kJCSQm5tLdnZ24MGM3tfC+9ooFSUivSc5NzeXcePGMX/+fLdDUREm\nKzOTsX37Mjwjg5pAHjBs8mQGd+tG4tCh8Je/QGlja1RU0J5kFT2MqXAzW3h7r7z12n5162YvFy60\n82kpFQV274a9e6FZM7cjCez111+nf//+JCUluR2KijDjU1IOJsgANYHhxcWMT06GK67QBDlGaE+y\nih5ZWbB1KzRsCG3auB1NWLRr144aNWrQqlWrwI0aNbKvx9q1sHw5dOoUvgCVOkYZGbbUIlLLM/Py\n8nj11VdJS0tzOxQVgTwrVhxMkL1qAh5nliYVG7QnWUUP317kSH1nDbKGDRvSuXNnGjRoUHpDLblQ\nUSbSSy3eeustzjnnHE4++WS3Q1GRpKgIhg0j7o8/yCuxKw+I09r1mBLyJFlE+onIShFJF5HH/Oy/\nSUSWOD+zRaSjz751zvbFIqLv/jHK4/EwefJk0tLSMMYEbljBSi2Oivc10SRZRYlITpILCwsZNWoU\nQ4cOdTsUFUnWrIGzz4a5cxn0448MS04+mCjnAcOSkxmUmupmhCrIQlpuISJxwGvABUAOMF9EPjPG\nrPRpthY41xizS0T6AW8C3mVnPEBvY8zOUMap3LV161ZWrVrF1q1b6d27d+CGmiQHptPAqSizZk3k\njr+dMGECHTp0oGvXrm6HoiKBMfCf/8Djj0NKCtx/P4lxcQyePp1RKSl4cnKIa96cwampJGr9ekwJ\ndU1yd2C1MSYLQEQmA1cAB5NkY8xcn/ZzAd+VJAQtCYl55VpEpKjIDkwDTZL96dLFDhRZvtyOhqpV\ny+2IlCrVmjV2lqxIU1RUxMiRI5kwYYLboahIsH073HWX/YP98Uc47bSDuxKTkhg2caKLwalQC3UC\nmgBs8Lm9kcOT4JLuBL7xuW2A6SIyX0T+FoL4VAQoV5K8fDnk59sBahV01atSS1GqV7eT1ns8sGhR\n+IJS6hhFarnF5MmTadGiBWeffbbboSi3TZ9uB0K3bm2/yfRJkFXFEDGzW4hIH+A2wPfM1MsYs0lE\nGmOT5RXGmNn+7v/0008fvN67d+/Sv7ZXESXHGQ1capJcwUstpkyZQmZmJvfeey81a5YcU+3o0QMW\nL7av1bnnhjdAFVBaWprOkFBCXp5dYd5ZVDJieDwennvuOUaPHu12KMpN+/bBE0/AlCkwYYJdJU9V\nSKFOkrMB37mrWjjbDuMM1nsT6Odbf2yM2eRcbhORT7HlG2UmySp67N+/n61btxIXF8cJJ5wQuGEF\nWmnPn71795Kfn092djZt27b136h7d3jjDR28F2FKfmgfPny4e8FEiLVrISkJ4iKsmG7q1KnUqFGD\nvn37uh2Kcsvvv8NNN0H79rBkCZQ1s5CKaaE+Rc0HThSRRBGpAtwAfO7bQERaAR8DNxtjMny21xCR\nWs71msBFwLIQx6vCrFKlStxxxx1ceeWVVK5cOXDDCrbSXkneXvZSFxXRwXsqSkRiqYUxhhEjRvDk\nk08iFWSKSeXD44HRo+H88+Hhh+HDDzVBVqHtSTbGFIvI/cB32IT8HWPMChG52+42bwIpQAPgX2LP\nTAeMMd2BpsCnImKcOCcZY74LZbwq/OLi4khISCi91GLvXluTHB9vB6hVQOVKktu3twP21q+HzZuh\ntJ55pVwUiUnyd999R2FhIZdffrnboahwy8mBQYPse83cuXaVG6UIQ02yMeZboF2JbeN8rv8NOGJQ\nnjEmE+gc6vhUFFi0yH7K79LFDlCrgHyTZGOM/56u+Hg44wxIS4P58+Gyy8IbpFLltGZN5C0MOWLE\nCJ544gniIq0GRIXWJ5/APffAfffB0KFQKWKGaqkIoGcDFfm85QMVtNQCoE6dOtSqVYv9+/eze/fu\nwA115T0VBSKtJ3nWrFlkZ2dz/fXXux2KCpc9e+COO+DRR+Gzz+CppzRBVkfQvwgV+Sr4zBYAIsKg\nQYOoW7culUo7kevKeyoKRFqSPGLECB5//PHS/7dU7Jg7FwYOhN697YxAtWu7HZGKUFLq3KtRQkRM\nLDyPiiZg2UBJiYm2znbZMjj11NAHFs02boSWLaFePTsJvn51HHFEBGNMzI0MK+95eN8+qFvXTgMX\nCTnpggUL+Otf/8qaNWuoWrWq2+GoUCoqghEj4N//hn/9C666yu2IlEvKex6OgFOUqqjS0tJYunQp\nffr0oWPHjv4bbd5sE+Tate3ANFW6hARo1gw2bbLddYGmi1PKJZmZ9nNvJCTIAM8++yxDhgzRBDnW\nZWTY3uPate04l+bN3Y5IRQHtZlKuyc7OJjc3t/SvOL1lA2ecYQemqdKJaMmFimiRVGqxfPly5syZ\nw9/+pgu6xixj4N134cwz4frr4dtvNUFW5aZJsnKFMaZ8y1FrPfLR08F7KoJFUpL8/PPP88ADD1Cj\nRg23Q1GhsH07XHutnf/4hx/gwQe1BE0dFf1rUa7YuXMn+/bto1atWtSpUydwwwq+0p4/+fn57Nq1\nK3AD7UlWESwjIzKS5LVr1/LNN99w7733uh2KCoUZM6BzZ2jVyp4LO3RwOyIVhTRJVq7w7UUOOHjP\n47Hz/UKFnv7N12+//caLL77IDz/8ELjRGWfYy8WLobAwPIEpVU5r1kTGWg0jR47k73//O3Xr1nU7\nFBVM+/bBQw/ZxUH+8x94+WWoVs3tqFSUipChE6qi2bFjBwDNS6sNW70adu2y9WOllWRUIE2aNAHK\nWHmvbl07yHHlSli6FLp1C1N0SpUtEsotsrOz+eijj0hPT3c3EBVcy5bBTTfBSSfBkiXQsKHbEako\np0mycsV5551Hjx49KHXKKK1HPkLTpk2Jj49n+/btFBQUUD3QCoQ9etgked48TZJVxDhwADZsgNat\n3Y1j1KhRDBo0iEaNGrkbiAoOjwfGjoVnnoGRI+G22+wgZqWOk5ZbKNdUq1YtcJIHutKeH/Hx8TRr\n1gyAnJycwA21LllFoKws+8WQm7Otbdu2jQkTJjBkyBD3glDBs2kTXHIJTJ5sFwm5/XZNkFXQaJKs\nIpf2JPvlnQ2k1JIL72vm/aChVASIhFKLV155heuuu670Ui8VHT79FLp0gbPOglmzIqPYXcUULbdQ\nkamwEH77zfYIeAeiKcAmyQ0bNqRKlSqBG3XsCFWqwKpVkJtrV+BTykWZmVmkpIwnJ8fDwIFxpKYO\nIikpMawx5ObmMm7cOOZ7BwSr6LR3r53O7ccfbaJ81lluR6RilCbJKjL99pstYDzlFChtirgK6LTT\nTqNDWdMZValie1h+/RUWLIALLwxPcEr5kZmZRd++Y8nIGA7UZNKkPObOHcb06YPDmij/61//on//\n/iQlJYXtMdXxy8rMZHxKCp7sbOKqVmXQihUkXnCBfZ+oXdvt8FQM03ILFXY5OTkcOHCg9EZaahFQ\nwCnzStJFRVQ5iEg/EVkpIuki8liANr1FZLGILBORH4/2MVJSxh9MkK2aZGQMJyVl/HFEfnTy8vIY\nM2YMTzzxRNgeUx2/rMxMxvbty5BJkxielsaQadMYW1hIVkqKJsgq5DRJVmFVWFjIW2+9xQsvvEBx\ncXHghpokHz8dvKfKICJxwGvAxcCpwI0i0r5Em7rA68BfjDGnAdce7eNkZ3s4lCB71SQnx3NMcR+L\nt956i7PPPpuTTz45bI+pjt/4lBSGZ2T4fLyC4Vu2MD4lxc2wVAVRriRZRD4RkUudE6pSx8w7I0OT\nJk2Ij48P3FBntjh+voP3SptqT1Vk3YHVxpgsY8wBYDJwRYk2NwEfG2OyAYwxfx7tgyQkxAF5Jbbm\n0bx5eN5SCgsLGTVqFEOHDg3L46ng8fzxh5+PV+ApbXYfpYKkvGeof2FPlKtF5HkRaRfCmFQM811p\nL6AdO+xCIlWr6lKix+PEE+2Avc2bYeNGt6NRkSkB2OBze6OzzVdboIGI/Cgi80Xk5qN9kNTUQSQn\nD+NQopxHcvIwUlMHHX3Ex2DChAl06NCB008/PSyPp4LAGBg7lrg//vDz8QridHYSFQblGrhnjJkB\nzHC+drvRub4BeAuY6PRAKFUmb09yqUnyggX2smtXqFw5DFFFp/Xr15OdnU2PHj2Ii/PzeVfE9iZ/\n950tuWjZMvxBqlhQCegKnI/txPtFRH4xxqwp2fDpp58+eL1379707t0bgKSkRKZPH0xKyihycjw0\nbx5HampoB+1lZmaSkpLCxo0bWbhwIe+8807IHksFWX4+/P3vsHQpg6ZNY9gddxwsucgDhiUnMzg1\n1e0oVRRJS0sjLS3tqO9X7tktRKQhMBC4GVgMTALOBm4Feh/1I6sKqVw9yd5SC61HLtWnn35Kbm4u\nbdq0oWnTpv4b9ehxKEm++urwBqjCwimDu8YY8+Ex3D0baOVzu4WzzddG4E9jzD5gn4jMBDoBpSbJ\nJSUlJTJx4rBjCPHoZWZm0rdvXzIyMg5uGzp0KN26ddOZLSJdZiZcdZWd2WjOHBJr1GDw9OmMSknB\nk5NDXPPmDE5NJVF/j+oo+H5oBxg+fHi57leuJFlEPgXaAe8DlxljNjm7PhCRBUcVqaqwioqKaNas\nGZUrV6Zhw4aBG86day/PPDM8gUWpFi1akJuby8aNGwMnyTp4L+YZYzwi8ihwLEnyfOBEEUkENgE3\nYL8t9PUZMFZE4oGqQA/g5eMIOeRSUlIOS5ABMjIySElJYeLEiS5Fpcr03Xdwyy0wdCgMHnxw5bzE\npCSG6e9NuaC8PclvGWO+9t0gIlWNMYXGGF3pQZVLpUqVuOGGG0pvZIwO2iun5s2bs2zZMrKzswPX\nWnbrZi8XLIDiYihtsKSKZjNEZAjwAT4j5IwxO0q7kzGmWETuB77DjlF5xxizQkTutrvNm8aYlSIy\nDVgKFANvGmP+CNkzCYJAq1GWupS7co8x8PzzMHYsfPghnHuu2xEpBZQ/SX4G+LrEtl+wdWpKBc/a\ntbB9OzRuDK1bux1NRPOWrJT6xt+0KSQmQlYWrFgBp50WpuhUmF3vXN7ns80Abcq6ozHmW+w3hb7b\nxpW4PQoYdZwxhk2gci5dijoC7dkDt94KOTn2G68WLdyOSKmDSp3dQkROEJHTgeoi0kVEujo/vYEa\nYYlQVSy+vcjlXTSjgmrWrBkiwtatW9m/f3/ghlpyEfOMMUl+fspMkGNVamrqEbXHycnJpOpgr8iy\ncqU9PzVuDD/9pAmyijhlTQF3Mbb3oAW2Bu0l5+chQCecVMGnpRblVrlyZbp3706fPn3weEpZlEFX\n3ot5IlJDRP5PRN50bp8kIn9xOy63JCUlcdddd9GyZUv69OnDgAEDmD59ug7aiyRTp9qyiocfhnHj\n7JSfSkWYUsstjDETgAkicrUx5uMwxaQqMk2Sj0q/fv3KbqQ9yRXBu8BCoKdzOxv4CPjStYhc9s03\n3zB27FiuuKLk2ijKVcXFMGwYvPcefPmlzmKkIpqYUlbiEpGBxpiJIvIwtr7tMMaYiBjhLCKmtOeh\n3Ldhwwa2bt1KUlISDRo08N+osBDq1IH9+2HnTrsQhjp+eXn2dRWB3buhhlZKuUlEMMYEtZZIRBYY\nY84QkcXGmC7OtiXGmE7BfJwyYoiY83BmZibdu3cnOzubKlWquB2O8tqxAwYMgH374IMPoEkTtyNS\nFVR5z8NllVt4V4OsBdT286NUufz+++98+eWX/PFHKYPilyyxCfLJJ2uCHEw1a9oBe8XFsPj/s3fn\n8U1V+eP/XydQttJCkaWlpQtlX8QFF0SgFVBERRFHZAoK89VhXMdxnM/4Gy0U0Y8iCg6D46AfFbAo\nijCyI2UpIMgiKig7XQJt2SmUtpQuOb8/blMKTUoKTW7Svp+PRx5Jbk5u3iS3l3dO3uecn82ORrhH\noVKqIaWdGUqpaOCCuSGZ5/PPP+exxx6TBNmb7NhhzLbTpQskJUmCLHzClcotZpReuzbrsgNKqUHA\n+1ycXmjSZY//Hvh76d1zwDNa652uPFf4jiotIiKlFtXv1lth506j5KJ3b7OjEdUvAVgBtFFKzQF6\nA6PNDMgsWmtmz57Nl19+aXYowu6LL+DPf4Zp02DE5dNwC+G9rtSTDIBS6h2lVKBSyk8ptVopdUIp\nNdKF51mA6RgDALsCI5RSnS5rlgr0Lf1Z8A3goyo8V/iA4uJijh49ClxhCib7IiKSJFc/GbxXo2mt\nVwIPYyTGXwI9tdbJZsZklh9++AE/Pz969pQp/E1XVAQvvgjjxsHq1ZIgC5/jUpIM3K21zgHuB9KB\ndsDfXHjercABrbVVa10EzAUuGUWhtd6stT5benczEOrqc4VvOHbsGDabjRYtWlC/shHM0pN8VTIz\nM1m8eDHbtm1z3kgG79VoSqlEjCQ5RWu9RGt90uyYzDJ79myeeOIJlEwhaa5jx2DAANi/H7Ztg+uv\nNzsiIarM1STZXpZxHzCvXFJ7JaHA4XL3M7iYBDvyJLD8Kp8rvFRGRgZwhVKLkychJQUaNoTu3T0U\nWc2Qk5PDTz/9xN69e5036tLFGLCXmgonTnguOOEpnwAhGMtHpyql5iul/mx2UJ5WUFDAvHnziIuL\nMzuU2m3LFujZE/r1M2awCAoyOyIhroqrK+4tUUrtBc4DTyulWgAF1RmIUioWGAPceTXPT0hIKLsd\nExNDTExMtcQlrl1YWBi9e/cmPDzceSN7D+fNN0NdVw9LARe/fGRmZqK1dtyDVreu8d5u2GD06gwe\n7OEoa6/k5GSSk5Pd+hpa67VKqfXALUAs8CeMMrV/uvWFvcySJUu48cYbadOmjdmh1F4ffQSvvQb/\n938wZIjZ0QhxTVzKRrTWryil3gHOaq1LlFJ5uFb6kAmUz4zCSrddQil1PUYt8iCtdXZVnmtXPkkW\n3iU0NLTyXmSQUotrEBgYSEBAAOfOnePUqVM0b97cccNbbzWS5K1bJUn2oMu/tE+YcNXjoJ1SSq3G\nmI3oB2ADcIvW+ni1v5CXmzVrFo8//rjZYdROFy7Ac8/Bxo3GeaZjxys/Rwgv52q5BUAnYLhS6nHg\nEeBuF56zDWinlIpQStUDHgMWlW+glAoH5gOjtNYpVXmuqEEkSb4m5XuTnZLBezXZTqAQ6AZcD3Qr\nnRKu1jh+/DgbNmzg4YcfNjuU2ufwYWP1vOxs41wuCbKoIVyd3eJzjOWp78T4Oe8W4IpDh7XWJcBz\nwEpgFzBXa71HKTVWKfXH0mbxQDPg30qpn5VSWyt7blX+ccJHaH0xcbv9dnNj8VEuJcnlB+95yaIP\nonporf+ite6LMXjvFMYKfGfMjcqzvvzyS4YMGULjxo3NDqV2SU42zi3DhsG8eRAgSyiImqPSFffK\nGim1B+jiNcspXcabVnoSV2H/fqPnISQEMjONleFElZw6dYrjx48TFhZGgLP/pLSG4GA4fhwOHoTo\naM8GKQC3rbj3HNAHuBljBqINwAat9ZrqfJ0rxGDqefjmm29m0qRJDBgwwLQYahWt4f33YdIk+Pxz\nGDjQ7IiEcJmr52FXR0j9BgQDR64pKiEcKV9qIQnyVbnuuuu47rrrKm+klNHjs2SJ8Z5LklyTNACm\nANu11sVmB+Npv/32G8ePHyc2NtbsUGqHvDx46inYu9eY3z4y0uyIhHALV2uSmwO7lVLfKaUW2S/u\nDEz4vpKSEmbNmsXKlSux2WzOG8oiIp5jf4/tX0xEjaC1fhdjxqE/KaWeU0r1MDsmT/r8888ZOXIk\nderUMTuUmi8lBXr1Aj8/Y5CeJMiiBnO1JznBnUGImun48eOkp6eTk5PD3XdXMs5TBu15zh13GNeb\nNpkbh6hWSqkXgD8CC0o3JSqlPtJa/8vEsDyipKSExMREkpKSzA6l5lu+HEaPNlbQe+YZ+eVP1Hiu\nTgG3TikVAbTXWq9SSjUC5Cu7qNThw8ZaMGFhYc4bFRTAjh3GyVaWkXW/W28FiwV++QXy840FRkRN\n8CRwm9Y6D0ApNQljOrganySvXr2a1q1b06VLF7NDqblsNnjzTfjPf2DBAujd2+yIhPAIV2e3eAr4\nBphRuikU+NZdQYmawT7TQqVJ8vbtUFwMXbvKqOhqUmlpS+PGxvKwxcXw44+eC0q4mwJKyt0vKd1W\n482ePVvmRnans2fh4YdhxQpjISJJkEUt4mpN8rNAbyAHQGt9AGjprqBEzeBST7L9Z397GYC4alpr\nEhMTefvtt8nPz3fesFcv41pKLmqSz4AtSqkEpVQCsBljqeoa7dy5cyxZsoTHHnvM7FBqpt27jV+f\nQkNh7Vpo3drsiITwKFdrki9orQvty90qpeoCMueacCovL4/s7Gz8/Pxo1aqV84Y//GBcS5J8zZRS\nFBUVUVRUREZGBh06dHDc8I474MMPL773wudpracopZIx5rIHGKO1/tnEkDxi/vz59OvXjxYtWpgd\nis+zpqUxMz4eW2YmltBQRvfqRURCAkyebNQhC1ELuZokr1NK/QNoqJQaCDwDLHZfWMLXNWrUiGef\nfZbTp09jsTj5wUJr6UmuZm3atOHQoUMcPny48iQZjPdeaxl848OUUg2APwHtgF+Bf9emKeBmz57N\nc889Z3YYPs+alsa/Bg5kQkoK/kAeMP6rr3h+/nwihgwxOzwhTONqucUrwAmMk/BYYBnwmruCEr5P\nKUXz5s2dJ2oA6elw7Bg0bw7t2nkstpqsTZs2AGRkZDhvFBUFLVvCyZPGdE7Cl83CWP30V+BejJVR\nawWr1crOnTu57777zA7F582Mjy9LkAH8gQnFxcz8+mszwxLCdK7ObmFTSn0LfKu1PuHmmERtYe9F\n7tVLejOrib3+OzMzk5KSEsfzxipl9CZ/+63xGcgXFF/WRWvdHUAp9Qmw1eR4PGbOnDk8+uij1K9f\n3+xQfJ4tM7MsQbbzB2xZWWaEI4TXqLQnWRkSlFIngX3APqXUCaXUOM+EJ2q08kmyqBb+/v40a9YM\ni8XCmTNnnDeUwXs1RZH9Rm0qs9Bay6wW1cjSogV5l23LAywyUE/UclfqSf4LxqwWt2it0wCUUm2B\nD5VSf9FaT3V3gKIGk0F7bjF69Gj8/f2d14LDxfdcBu/5uh5KqZzS2wpj3EhO6W2ttQ40LzT32bp1\nKzabjdtkAaJrd+YMo/ftY3xgIBNyci7WJEdH8/zEiWZHJ4SplNbOJ6lQSv0MDNRan7xsewtgpdb6\nRjfH5xKllK7s3yE8q7CwED8/P1RlJRS5udCkifHTf06OLGrhaefPG+9/cTGcOQOBNTKX8kpKKbTW\nNa6+yJPn4WeffZaQkBBee02GxlyTM2fg7rvh9tuxvvgiM8eNw5aVhaV1a0ZPnEhEVJTZEQrhFq6e\nh6/Uk+x3eYIMoLU+oZTyu+roRI22bNkyDhw4wJAhQ+jYsaPjRtu2Gas43XyzJMhmaNgQbrwRtm41\nlgUfONDsiIRwyYULF/jqq6/Yvn272aH4ttOnjQS5Tx+YMoUIpRifmGh2VEJ4lSvNblF4lY+JWiwj\nI4P8/HwCKltBT6Z+M5+UXAgftGzZMrp3705ERITZofiuU6dgwACIiYEpU2TgtBBOXClJ7qGUynFw\nOQd090SAwrfk5+dz6tQp6tatW/kiIjJoz3wyeE/4IBmwd41OnoT+/Y1fjyZPlgRZiEpUWm6htXYw\nf5QQztnn523durXj6cfAKLPYvNm4LT3JbqG15syZMxQUFBASEuK4kf2937zZ+EwqG+gnhBc4efIk\na9euZdasWWaH4ptOnDAS5PvvhzfflARZiCuQ/xVFtTp06BAA4eE1oEawAAAgAElEQVThzhvt32/U\nw7VuDZW1E1ctLS2NadOmsWzZMueNwsKgTRs4exb27PFccEJcpa+++or77ruPQBloWnXHj8Ndd8GD\nD0qCLISLJEkW1aqgoACLxVJ5kiyLiLhd69L5TbOysigurmT6XCm5ED5k1qxZUmpxNY4dg9hYGDYM\nXn9dzrtCuEiSZFGt7r//fl555RXatm3rvJHMj+x2DRo0oGXLlthsNrIqWzVLBu8JH7Fnzx4yMjIY\nMGCA2aH4liNHjAF6w4dDQoIkyEJUgSTJotr5+fk5r0cG+P5741oG7blVmzZtADh8+LDzRtKTLHzE\n559/zsiRIys/t4hLZWUZPcgjR8I4WShXiKqSJFl41okTsHevMU/vzTebHU2N5lKSfMMN0KAB7Ntn\nTAslhBey2Wx8/vnnUmpRFZmZRg/y6NHw6qtmRyOET5IkWXjWxo3G9W23Qb165sZSw4WHhxMcHFz5\nVHz16sEttxi3peRCeKnk5GRatGhBt27dzA7FN2RkGAnyU0/BK6+YHY0QPkuSZOFZGzYY1336mBtH\nLRAUFMTYsWOJjY2tvOGddxrX9s9GCC8jcyNXwaFDRoL8pz/B3/5mdjRC+DRJkkW1yMnJYd++feTn\n51feUJJk72P/LNavNzcOIRzIy8tj4cKFjBgxwuxQvJ/VaiTIzz4Lf/2r2dEI4fMkSRbVYv/+/cyd\nO5fly5c7b5SbCz/9BHXqyKA9b3LHHcZCIj/+CFf6kiOEhy1YsIDevXtXXjYkIC3NSJBffBH+8hez\noxGiRpAkWVQL++Aw+2AxhzZvhpISuPFGaNzYQ5GJK2rSBHr0gOJi2LLF7GiEuMTs2bN54oknzA7D\nu6WmGrNYvPwyvPCC2dEIUWNIkiyqhUsr7Umphffq29e4lpIL4UUyMjL46aefeOCBB8wOxXsdPGj0\nIL/yilFmIYSoNm5PkpVSg5RSe5VS+5VSf3fweEel1CalVIFS6qXLHktXSu1QSv2slNrq7ljF1cnJ\nyeHMmTPUr1+fli1bOm8oSbIpjhw5wtq1a0lNTXXeyP6ZyOA94UXmzJnDI488QoMGDcwOxTsdOGD0\nIL/2mjFQTwhRrdyaJCulLMB04B6gKzBCKdXpsmangOeByQ52YQNitNY3aq1vdWes4urZe5HbtGmD\nxeLkkCosNMotAHr39lBkAiA1NZX169eza9cu543sSfIPP0BRkWcCE6ISWmuZ1aIy+/YZCXJCAvzx\nj2ZHI0SN5O6e5FuBA1prq9a6CJgLPFi+gdb6pNZ6O1Ds4PnKAzGKaxQYGEiPHj3o2LGj80Y//wzn\nz0PHjlBZb7OodvYSGPuXGYdatjQ+m/x8Y3ClECb76aefKCgo4A5Zvr6ivXuhf3944w34f//P7GiE\nqLHcnYCGAuWX+8oo3eYqDSQppbYppZ6q1shEtQkPD+ehhx6iZ8+ezhtJqYVpWrduTd26dTl58iR5\neXnOG9rrkqXkola5UklcuXa3KKWKlFIPeyIuey+yUsoTL+c7du82EuT//V9jNT0hhNvUNTuAK+it\ntT6ilGqBkSzv0Vp/76hhQkJC2e2YmBhiYmI8E6FwjSTJpqlTpw5hYWGkp6dz6NAhOnfu7Lhhnz7w\n8cfG4L2XX/ZskDVYcnIyycnJZofhULmSuP5AFrBNKbVQa73XQbu3ge88EVdhYSFffvklm+0lWsLw\n229w990weTLExZkdjRA1nruT5Eyg/HQHYaXbXKK1PlJ6fUIp9V+M8o0rJsnCy9hs8H3pxyZJsinC\nw8OvnCTbe5K//974zJzVl4squfxL+4QJE8wLpqKykjgApZS9JG7vZe2eB74BbnFnMGlpacTHx7Nz\n505K43Hny/mWX381EuQpU0AWVhHCI9ydJG8D2imlIoAjwGNAZX/dZWdEpVQjwKK1zlVK+QN3A171\nv4tw0Z49cPo0hIZCZKTZ0dRKnTt3plGjRkRHRztvFBEBbdrA4cOwaxd07+65AIVZHJXEXTJIWinV\nGnhIax2rlHLbAOq0tDQGDhxISkpK2baBAweSlJREVFSUu17WN+zYAYMGwT//CY8+anY0QtQabk2S\ntdYlSqnngJUY9c+faK33KKXGGg/rj5RSrYAfgQDAppT6M9AFaAH8VymlS+Oco7Ve6c54hZvY597t\n0wekZ8gUwcHBBAcHX7lh374wZ45RHiNJsjC8D5SvVXb6R3wtZW/x8fGXJMgAKSkpxMfHk5iY6PJ+\napyff4Z774Xp0+GRR8yORgifdLVlb26vSdZarwA6XrZtRrnbxwBHy7TlAje4NzpxLc6fP8/ChQuJ\njo7mllsq+RV27VrjWurEvV+fPheT5GeeMTsa4X6ulMT1BOYqo/ahOXCvUqpIa73o8p1dS9lbZqbj\nSrysrKyr3qfP274dBg+GDz+Ehz0yXlKIGulqy968feCe8GJWq5V9+/ZRUFDgPEm22cD+7S021mOx\niatkr0tetw60lp7/mu+KJXFa67b220qpz4DFjhLkaxUa6njio9atW1f3S/mGbdvg/vthxgx46CGz\noxGiVpKROeKqpaenAxBZWZ3xrl1w4oRRj9y+vUfiEtegUydjzuQjR2D/frOjEW6mtS4B7CVxu4C5\n9pI4pZSjFSq0u2KZOHFihdrj6OhoJk6c6K6X9F5btsB998H//Z8kyEKYSJJkcdWsVitwhSTZXmoR\nGyu9kl5Ca43WTnIdpeCuu4zba9Z4LihhGq31Cq11R611e63126XbZmitP3LQ9g9a6wXuiCMqKopn\nnnmGsLAwYmNjiYuLq52D9jZvhgcegM8+M66FEKaRJFlclfPnz3P06FHq1Knj9GdS4NIkWZhu/fr1\nTJ06lQMHDjhvJEmyMMn69et5++23WbNmDYmJibUvQd60CYYMgVmzjJ5kIYSpJEkWV8XeixwWFoaf\nn5/jRjabUdsKkiR7ieLiYs6dO0daWprzRvYkee1a4zMUwgNycnJYt24d999/v9mhmOP7743Sis8/\nN2azEEKYTpJkcVXatWvHE088Qb9+/Zw32rEDsrON+XdrW4+Ql7L3zNnryR1q2xbCw+HUKWMBAyE8\nYOnSpfTp04cmTZqYHYrnrV9vzF7xxRdwzz1mRyOEKCVJsrgqdevWJTIysvKfQ+0/19t7JoXpwsLC\nqFOnDkePHiU/P99xI6lLFiaYP38+w4YNMzsMz0tONuY/njsXBgwwOxohRDmSJAv3kXpkr+Pn50eb\nNsa05JX2JkuSLDwoLy+PpKQkHnzwQbNDcTtrWhoTRo5kfGwsEwYMwPrww/D119KZIIQXknmShXsU\nF19caU+SZK8SGRmJ1Wrl9OnTzhvZP7N164zPsq6cKoT7LF++nNtuu41mzZqZHYpbWdPS+NfAgUxI\nScEfyAPGt27N8xERRJgdnBCiAulJFu7x009w7hy0awdhYWZHI8q59dZb+Z//+R/uvPNO543CwqBD\nB+Mz3L7dc8GJWmn+/Pk8UguWXJ4ZH1+WIAP4AxOyspgZH29mWEIIJyRJFlXmtJa1PPvP9NKL7HUa\nNmxIgwYNrtxQSi6EBxQUFLB8+XIeqgWLZtgyM8sSZDt/wFabl94WwotJkiyq5OzZs0yePJmZM2c6\nX5ACLtYjS52d77J/wZEkWbjRypUrufHGG2nZsqXZobidpaCAvMu25QGW2rr0thBeTpJkUSUpKSkA\nNGjQAOVsBb0LF4w5PwFiYjwTmKh+9s/u+++Nz1QIN/jmm29qx6wW//43o9PTGd+mTVminAeMj45m\ndG1celsIHyCjcUSVpKamAtC2bVvnjTZtgvx86NYNgoM9FJmodi1bQvfuxlzJmzdDZXNiC3EVCgsL\nWbJkCW+//bbZobjXpEnw0UdEbNrE88C78fHYsrKwtG7N8xMnEiHzyAvhlSRJFi7TWpclydHR0c4b\nfvedcS2T4nu1oqIirFYrrVq1IiAgwHGju+4ykuRVqyRJFtVu9erVdO7cmdY1tdxAa4iPhwULjNl+\nQkOJAMYnJpodmRDCBVJuIVx25MgRzp8/T5MmTSqfqkmSZJ+waNEi5syZw549e5w3uvtu49r+mQpR\njWr0rBZaw1/+AsuWGVMphoaaHZEQoookSRYuy8/Pp2nTprRt29Z5PfKxY/DLL9CwIfTp49kARZXY\nS2bsdeYO9esH9erBjz/CiRMeikzUBsXFxSxcuJCHH37Y7FCqX0kJPPUUbN1qDHxt0cLsiIQQV0GS\nZOGydu3a8cILLzB48GDnjVauNK779QNXphkTprGXzKSlpVFcXOy4kb8/9O1r9IolJXkwOlHTrVu3\njqioKCIiatgyGkVFEBcHaWnG+bBpU7MjEkJcJUmSRZUopahb2eprUmrhMwIDA2nZsiVFRUUcPnzY\necNBg4zrFSs8E5ioFWrkrBYFBTBsmDFweelSaNzY7IiEENdAkmRRfWy2iz3JkiT7BHtv8sGDB503\nsifJK1can7EQ16ikpIT//ve/NStJzs2F+++HRo1g/nz5JU2IGkCSZFF9duww6lbDwqBTJ7OjES7o\n2LEjnTt3pk2bNs4bdelifKbHjhmfsRDXaOPGjQQHB9OuXTuzQ6keZ84YHQMRETBnDvj5mR2REKIa\nSJIsqk/5UgtnA/uEV4mIiODRRx+lU2VfapSSkgtRrWpUqcWJE8ZUiT17wscfQ506ZkckhKgmkiSL\nKzp37hzff/89x48fr7yh1CPXXPbPVJJkcY1sNhsLFiyoGVO/ZWUZg5QHD4b33weL/JcqRE0if9Hi\nig4cOMDq1atZvXq180a5ubBxo/GfxIABngtOeMaAAUYP2aZNkJNjdjTCh23ZsoXAwEA6d+5sdijX\nJi3NmObyiSfgjTfk1zMhaiBJksUVHThwAID27ds7b7R2rTH10a23QlCQhyITHtO0Kdx+OxQXG/O+\nCnGVasQCInv3Gj3IL70Ef/+72dEIIdxEkmRRqeLi4rLFJipNku0/w0upRc0ldcniGqSlpREXF8f0\n6dP58ccfSUtLMzukq7Njh1GDPHEiPPus2dEIIdxIkmRRKavVSlFREa1ataJJkyaOG2kNS5YYtytb\naER4rcOHD/PNN9+wefNm543KJ8laeyYwUSOkpaUxcOBAvvjiCy5cuMDy5csZOHCg7yXKmzcbS7VP\nm2aUWQghajRJkkWl7KUWlU7V9OuvcOgQtGpljPAWPic/P59du3bx66+/Om90003QvDlYrbBnj+eC\nEz4vPj6+wvLnKSkpxMfHmxTRVVi7FoYMgc8+A18vFxFCuMTtSbJSapBSaq9Sar9SqkLxllKqo1Jq\nk1KqQCn1UlWeK9zvxhtvJCYmhq5duzpvZO9Fvu8+Gd3to9q2bUvdunXJysri3LlzjhtZLMZnDLB4\nseeCEz4vMzPT4fasrCwPR3KVli2D4cPh66/l1zIhahG3ZjRKKQswHbgH6AqMUEpdPiHrKeB5YPJV\nPFe4WatWrejXrx8hISHOG9kTpgce8ExQotr5+fnRtm1bAPbv3++8of0zXrTIA1GJmiI0NNTh9tat\nW3s4kqswbx6MGWOc52JizI5GCOFB7u72uxU4oLW2aq2LgLnAg+UbaK1Paq23A8VVfa7wAsePw5Yt\nUL++TP3m4zp06ABcIUm++26oVw9++MH47IVwwcSJE8uWQLeLjo5m4sSJJkXkopkz4c9/NpZkv+02\ns6MRQniYu5PkUOBwufsZpdvc/VzhKUuXGoO4YmOhcWOzoxHXwJ4kHzp0iJKSEseNAgKMkf1aG5+9\nEC6IiooiKSmJuLg4YmNjiYuLIykpiaioKLNDc+6DD2DcOKMWuUcPs6MRQpigrtkBVJeEhISy2zEx\nMcTIz2KeIaUWNUZAQACPP/44oaGh1Klsad0hQ4wZLhYvNn6GFpVKTk4mOTnZ7DBMFxUVRWJiotlh\nuObtt40lptetA29O5IUQbqW0G6dyUkrdDiRorQeV3n8F0FrrSQ7ajgfOaa2nXMVztTv/HbVRUVER\nfn5+lTcqKDBmO8jLM2Y8CA/3THDCXBkZ0KYNNGoEp05BgwZmR+RTlFJorWvc8mw14jysNbz2Gvz3\nv7BqFfhCzbQQospcPQ+7u9xiG9BOKRWhlKoHPAZUNuKnfMBVfa6oRvPnz2f69OlkZGQ4b7RqlZEg\n33ijJMi1SViYMR1cfr6svidqDpsNXnwRli83epAlQRai1nNrkqy1LgGeA1YCu4C5Wus9SqmxSqk/\nAiilWimlDgN/AV5VSh1SSjV29lx3xisMRUVFpKSkcOrUKecLiAAsWGBcDxvmmcCE9xgyxLj+9ltz\n4xCiOpSUwJNPwo8/Gl/8WrQwOyIhhBdwa7mFp9SIn/m8yN69e/nqq68IDQ3lySefdNyoqAiCg+H0\nadi9Gzp39myQwly//grXX28kE1lZULfGDG9wOym38DKFhTBqlFE69O23MgBZiFrAW8othA/au3cv\nAJ06VTIt9fr1RoLcqZMkyDXQhQsX2L17N06Tnm7doH17OHECNmzwbHBCVJeCAuOXsPPnjUWRJEEW\nQpQjSbK4RElJCfv27QOgY8eOzhvaSy0eftgDUQlP0lozY8YM5s2bx5EjRxw3Uuri0rzffOO54ISo\nLrm5xgqS/v4wf74MQBVCVCBJsrhETk4OTZo0oUWLFrRwVpdnsxmjv0HqkWsgpRTt2rUDYPfu3c4b\n2j/7BQuMY0IIX3HmjLEwTlQUzJkDV5rJR3i1yMhIlFJykUuFS2Rk5DUdW1KTLBwqKCiggbOelR9+\ngDvugIgISEszehVFjZKWlsbs2bNp1qwZzz33HMrRZ6w1tG0L6elGycWdd3o8Tl+klNQkm+rECSNB\n7tcPpkwBi/QV+brSvymzwxBeyNmx4ep5WM4OwiGnCTLA118b1w8/LAlyDRUREUGjRo04ffo0x50t\nP62k5EL4mMxM6NsX7r8fpk6VBFkIUSk5Q4iqKSmBr74ybj/2mLmxCLexWCxlAzd/++035w3tJRfz\n50vJhfBuaWlGgjx6NEycKF/whRBXJPM2iapZvx6OHIHoaLjlFrOjEW7Uo0cPioqKiI6Odt7o1luN\nhWQOHYKNG6FPH88FKEQlrGlpzIyPx5aZiaVxY0Zv20bEuHHwzDNmhyaE8BGSJIuqmTvXuH7sMemJ\nqeHCw8MJv9JKihYLjBgBkyYZA6AkSRZewJqWxr8GDmRCSgr+QB4wvmVLnr/3XiLMDk4I4TOk3EIA\nkJqayqpVqzhx4oTzRoWFF2tPpdRC2P3+98b1vHnGMSKEyWbGx5clyAD+wITjx5kZH29mWEKYwmKx\nkJqaCsDTTz/Nm2++WfbYhx9+SHBwMIGBgWRnZ7Nx40Y6dOhAYGAgixYtMitkryFJsgDgxx9/ZOPG\njezfv995o6QkYwGRbt2MixBgrLzXrZtxbKxcaXY0QmDLzCxLkO38AVtWlhnhiFosKiqKNWvWmBpD\n+dmJPvzwQ1599VUAiouL+etf/8qqVavIyckhKCiI8ePH88ILL5CTk8OQIUOqLQar1cpdd92Fv78/\nXbp0YfXq1U7bvvvuu3Tv3p3AwECio6N59913L3k8MjKSRo0aERgYSGBgIIMGDaq2OC8nSbLg/Pnz\nZclx9+7dnTe0l1qMGOGBqIRPsfcmf/GFuXEIUViIJSODvMs25wGW1q3NiEiYxJqWxoSRIxkfG8uE\nkSOxpqWZso/KlJSUVOv+HHE2Pd7Ro0e5cOECncutmmu1WunSpUu1xzBixAhuvvlmTp8+zRtvvMEj\njzzCqVOnnLb//PPPOXPmDMuXL2f69Ol8bZ9VCyPpX7p0KTk5OeTk5LBixYpqj7eM1trnL8Y/Q1yt\nH3/8USckJOhZs2Y5b3TunNb+/lqD1gcPei444TUKCwudP5iaahwbjRoZx4pwqvR8Zfp5034BBgF7\ngf3A3x08/ntgR+nle6C7k/245f2qkuPHte7XT6fHxuq/RkXpXGM2b50L+q/R0To9NdXsCIUbODr2\n0lNT9V+jo6/pGLjWfYwaNUpbLBbdqFEjHRAQoCdPnqzT09O1Ukp/8sknOjw8XPfr108nJyfrsLCw\nS54bGRmpV69erbXW2maz6bfeektHR0fr5s2b6+HDh+vs7Gynr/vOO+/okJAQHRoaqj/99FNtsVh0\nSkqK1lrr0aNH6/j4eL1//37t7++vLRaLDggI0P3799fR0dHaYrHohg0b6oCAgMrP+VWwf/9+3aBB\nA52bm1u2rW/fvnrGjBkuPf+FF17QL7zwQtn98u/NlTg7L7l6HpaeZMHOnTsBYzYDp775BvLyjIFZ\nlc12IGqc4uJi5s6dy5QpUyh0VnMcFWUsMJOff3E1RuH1lFIWYDpwD9AVGKGU6nRZs1Sgr9a6B/AG\n8LFno3TRzp3GbCt33EFEUhLPr17Nu3FxjI+N5d24OJ5PSiIiKsrsKIWHOKxLT0mpUl36te5j9uzZ\nhIeHs2TJEnJycnj55ZfLHlu/fj179+7lu+++A3C8YFOpadOmsWjRIjZs2EBWVhZBQUE842SWlhUr\nVjBlyhRWr17NgQMHWLVqlcN27du3Z9euXQCcPXuWVatWcfDgQcLDw8t6af0crET5wAMPEBQURLNm\nzSpcOyvP2LVrF23btsXf/2IRVI8ePcpe/0o2bNhA165dL9kWFxdHq1atGDRoUFkO4w4yu0Utd+7c\nOQ4dOoSfn98lP7lU8NlnxvXo0R6JS3iPunXrkpeXR0FBAbt37+aGG25w3PDxx2HTJpg5E0aN8miM\n4qrdChzQWlsBlFJzgQcxepYB0FpvLtd+MxDq0QhdsWABjB0L06aVlYNFREUxPjHR5MCEWZzWpc+Z\nY8zE48o+Sp9TYR9VrG3Xl5U7KKWYMGECDRs2dOn5M2bM4IMPPiAkJASAcePGERERQWJiIpbLFsSZ\nN28eY8aMKfv/PCEhgbn2UslK4iufpF8eb3mLFy92KebycnNzadKkySXbAgMDyXLhfRw/fjxaa8aM\nGVO27YsvvuCmm25Ca83777/PPffcw759+wgMDKxybFciPcm1XEBAAC+88AJDhw6lXr16jhulpBjz\nIzdqBL/7nWcDFF7Bnhj/8ssvzhs99hg0aABr1hgLNwhfEAocLnc/g8qT4CeB5W6NqCpsNnj9dXjx\nRVi+XMZLiDKW0FDHdelxcaXFE1e+WOLi3FbbHhYW5nJbq9XK0KFDadasGc2aNaNLly74+flx7Nix\nCm2zsrJo06ZN2f2IiIhKk15PaNy4MTk5OZdsO3v2LAEBAZU+b/r06SQmJrJs2bJLerV79epF/fr1\nadCgAa+88gpNmzZlw4YNboldepIFQUFBBAUFOW8we7ZxPWwYXOGgFjVTt27dWLFiBVarlezsbMfH\nS5MmxjLViYlGb/KECR6PU7iPUioWGAPc6axNQkJC2e2YmBhiYmLcF1BenvHLVkYGbNkCpb1sQgCM\nnjiR8Zs3XzpXdnQ0z0+c6NF9OCujKL/d39+f/Pz8svslJSWXTMcaHh7Op59+Sq9eva74eiEhIRw+\nfPF7r9VqrbSUo6oGDx7Mhg0bHO6zT58+LF26tML2rl27kpqaSl5eXlnJxY4dOxg5cqTT1/n00095\n55132LBhQ1kPujNKqSt+EUhOTiY5ObnSNg65Urjs7Re8YcBITVVSonVEhPG92sVCeVEzLViwQCck\nJOg1a9Y4b7RmjXGstGmjdXGx54LzIXjRwD3gdmBFufuv4Hjw3vXAASC6kn254d1yIj1d6x49tB49\nWuuCAs+9rvBKzo699NRUnRAXp8fFxuqEuLirGrh5rfvo1auX/vjjjy/ur3TgXklJSdm2s2fPan9/\nf71s2TJdVFSkExIStJ+fX9ngtKlTp+qYmBhttVq11lofP35cL1y40OHrLV++XIeEhOjdu3frvLw8\nPXLkSIcD95zFUpVBcVXRq1cv/be//U0XFBTo+fPn66CgIH3y5EmHbRMTE3VwcLDeu3dvhccOHTqk\nN27cqAsLC3VBQYF+5513dMuWLfXp06cd7svZseHqedj0k3R1XCRJdqNVq4zDJDzcSJhFrZWamqrf\neustvXbtWueNSkq0jooyjpmVKz0Wmy/xsiS5DnAQiADqAb8AnS9rE16aIN9+hX255f2qYP16rYOD\ntZ4yRWubzTOvKbyaN+cACxcu1OHh4TooKEi/9957Oj09XVsslksSU621njVrlg4JCdGtWrXS7733\nno6KirpkdoupU6fqjh076sDAQN2uXTv96quvOn3NSZMm6eDgYB0aGqo/++yzSpPky2Mp/7rVyWq1\n6piYGN2wYUPdqVOnSzpbNmzYoAMCAi6JoV69ejogIEA3btxYBwQE6KefflprrfWuXbv09ddfrxs3\nbqybN2+uBwwYoH/66Senr3utSbIy2vo2pZSuCf8Or/TIIzB/vvHT+bhxZkcjTKS1pri42OGI50tM\nnGgcK8OHX5xbW5Qp/WnQa9Z0V0oNAv6JMUblE63120qpsRj/iXyklPoYeBiwAgoo0lrf6mA/7j8P\nf/wxvPYafP453H23e19L+AxXfm4XtZOzY8PV87AkybXUwYMHqV+/PmFhYc7rlbKyIDzcuH3oEMhE\n/MIVhw9DZCTUqWPcbtXK7Ii8irclydXFrefhoiJ46SVj1c9Fi6BDB/e8jvBJkiQLZ641SZbZLWoh\nrTUrVqzg008/LVvP3aH/+z8oKYEHH5QEWbiuTRt44AEjsfnYO6fUFT7k1CkYNAhSU40BepIgCyE8\nRJLkWigtLY1Tp04REBBAlLPJ9YuLLyY4Tz/tueBEzfDss8b1jBnGsSSECyosAbxihbFASM+eRg/y\nZXOtCiGEO8kUcLXQli1bAOjZs2eFicjLLF1qTK3Uvj3cdZcHoxO+RGvtuFynf3+jx2//fli8GIYO\n9XxwwqtY09KYGR+PLTMTS2gooydOvGQFPGtaGv8aOPDS6ba+/JLnJ08m4qWXTItbCFF7SU9yLXP6\n9Gn2799PnTp1uPnmm503nD7duB47Fpwl0qLWOnjwIJ9++hnFj2gAACAASURBVCm//fab4wYWC9iX\nTf3gA88FJrySPQF+ec4cJiQn8/KcOfxr4ECs5RadcbgEsM3GzJ9+MiVmIYSQ7KeW2bZtGwDdu3e/\nZB31S+zYAatWgb8//OEPHoxO+IozZ85w+PBhNm/e7HzAzBNPGKs0rl4Nu3d7NkDhVRwmwCkpzBw6\nFJ57Dh58ENvChdWyBLAQQlQXSZJrmb59+zJw4EBuv/12542mTjWu//AHqGwlPlFr9ejRg0aNGpGV\nlcWhQ4ccN2ra1EiUAd57z3PBCa9jy8x0nACfPm2U5YwejaV3b7ctASyEEFdDkuRapmHDhtxxxx20\ncjYtV1YWfPGF8XP5iy96NjjhM/z8/LjlllsA2LRpk/OGL70EShlLVUuPYK1lCQ11nAD37QsvvABD\nhzL6ww8ZHx1d1s6+BPDoKiwBLIQQ1UmSZHGp6dONqbuGDoW2bc2ORnixW265hbp167J//35Onjzp\nuFG7dvDww1BYCNOmeTZA4TVGT5x4xQQ4IiqK55OSeDcujvGxsbwbF8fzSUmXDO4TQlSdxWIpm+71\n6aef5s033yx77MMPPyQ4OJjAwECys7PZuHEjHTp0IDAwkEWLFpkVstdw+2Iipas5vc/F1ZwmOWgz\nDbgX49w5Rmv9c+n2dOAsYMPJKk+l7WQxkeqQm2ssHpKdDZs2Qa9eZkckvNySJUs4cOAAQ4YMITo6\n2nGjLVvg9tuN6bsOH4aAAM8G6WVq62IiZbNbZGVhad26wuwWQlwtb15MJCoqik8++YS7TJwlqk6d\nOhw4cIC2l3V8FRcXExgYyNatW+nWrRsAAwYM4KGHHuK5556r1hisVitjxoxhy5YtRERE8K9//Yv+\n/fs7bDthwgTefPNNGjRoUDaD0s6dO4mMjKzy617rYiJunQJOKWUBpgP9gSxgm1JqodZ6b7k29wLR\nWuv2SqnbgA8Be8GsDYjRWme7M05R6oMPjAS5d29JkIVL+vfvz7333kudOnWcN7rtNujTBzZsgI8+\ngr/+1XMBCq8RERXF+MREs8MQtUhaWhrx8fFkZmYSGhrKxIkTna8N4MZ9VKakpKTy82c1cPYF4ujR\no1y4cIHOnTuXbbNarXTp0qXaYxgxYgS9e/dm+fLlLF26lEceeYSDBw9y3XXXOWz/2GOPMXv27GqP\no8q01m67YCS7y8vdfwX4+2Vt/gMML3d/D9Cq9HYacJ0Lr6OFcykpKXr37t3aZrM5b5Sbq3Xz5lqD\n1t9957ngRO2wZIlxbLVqpXVentnRmKr0fOXWc68ZFzkPC7M4OvZSU1N1dHS0Bsou0dHROjU11eX9\nXus+Ro0apS0Wi27UqJEOCAjQkydP1unp6VoppT/55BMdHh6u+/Xrp5OTk3VYWNglz42MjNSrV6/W\nWmtts9n0W2+9paOjo3Xz5s318OHDdXZ2ttPXfeedd3RISIgODQ3Vn376qbZYLDolJUVrrfXo0aN1\nfHy83r9/v/b399cWi0UHBATo/v376+joaG2xWHTDhg11QECALiwsdPm9qsz+/ft1gwYNdG5ubtm2\nvn376hkzZjhsn5CQoEeNGlUtr+3svOTqedjdNcmhwOFy9zNKt1XWJrNcGw0kKaW2KaWecluUNZjW\nmqSkJL7++mt27NjhvOGHH8LJk0av38CBngtQ1A6DB8Mtt8CxY8axJoQQbhQfH09KSsol21JSUoiP\nj/fYPmbPnk14eDhLliwhJyeHl19+ueyx9evXs3fvXr777jsAx4sylZo2bRqLFi1iw4YNZGVlERQU\nxDP2eegvs2LFCqZMmcLq1as5cOAAq1atctiuffv27Nq1C4CzZ8+yatUqDh48SHh4OEuXLiUnJwc/\nP78Kz3vggQcICgqiWbNmFa6HDBni8LV27dpF27ZtL5l2tkePHmWv78jixYtp3rw53bt35z//+Y/T\ndu7m7Svu9dZaH1FKtcBIlvdorb931DAhIaHsdkxMDDExMZ6J0Mvt2bOHo0eP0rhxY7p27eq4UX4+\nTJ5s3B4/3piNQIjqpBQkJMB998GkSfCnPxnzcNcCycnJJCcnmx2GELVKZmamw+1z5sxhzpw517Tv\nrCrO1KMvK3dQSjFhwgQaNmzo0vNnzJjBBx98QEhICADjxo0jIiKCxMTECqvmzps3jzFjxpSVUCQk\nJDB37twrxlc+Sb883vIWL17sUszl5ebm0uSyJeUDAwOdvo/Dhw9n7NixtGrVis2bNzNs2DCCgoIY\nPnx4lV/7Wrk7Sc4EwsvdDyvddnmbNo7aaK2PlF6fUEr9F7gVuGKSLAw2m421a9cCxvzIjr4VAkbP\n3vHj0LMnDBrkwQhFTVNSUkJxcTH169ev+OC99xq/VGzZAv/+N/ztb54P0ASXf2mfMGGCecEIUUuE\nhl7+o7UhLi6ORBdr40eOHOkwoW5dDXN3h4WFudzWarUydOjQsoRYa42fnx/Hjh0rS5ztsrKy6Nmz\nZ9n9iIgI0wc1Nm7cmJycnEu2nT17lgAng7g7depUdrtXr178+c9/5ptvvjElSXZ3ucU2oJ1SKkIp\nVQ94DLh8TpFFwOMASqnbgTNa62NKqUZKqcal2/2BuwEna+AKR3bu3MnJkydp2rQpN910k+NG2dlg\nnw7m9delF1lctbS0ND744IOynw8rUArsCeKkSXD2rOeCE0LUKhMnTqww4050dDQTqzDvdnXsw1kZ\nRfnt/v7+5Ofnl90vKSnhxIkTZffDw8NZvnw5p0+f5vTp02RnZ5OXl1chQQYICQnh8OGLFaxWq7XS\nUo6qGjx4MAEBAQQGBla43HfffQ6f07VrV1JTU8nLuzhb+o4dO5z/un0ZM2cvcWuSrLUuAZ4DVgK7\ngLla6z1KqbFKqT+WtlkGpCmlDgIzAHuhTSvge6XUz8BmYLHWeqU7461pdu7cCUBsbKzz0bNvvWUk\nynfdJb3I4poEBgZy9uxZfvnlF44fP+640d13GzNdnDplHHtCCOEGUVFRJCUlERcXR2xsLHFxcSQl\nJVVpZorq2EdwcHDZHMV2lyd8HTp0oKCggOXLl1NcXMwbb7xBYWFh2eNjx47lH//4R9nqpidOnHA6\nh/Gjjz7KzJkz2bNnD/n5+bz++uuVxlfV5HPZsmWcO3eOnJycCpelS5c6fE779u254YYbmDBhAhcu\nXGDBggX89ttvDBs2zGH7RYsWcebMGQC2bt3KP//5Tx566KEqxVltXBnd5+0XZFS1Q8XFxXrHjh26\npKTEcYP0dK3r1zdmHfjxR88GJ2qkpUuX6oSEBJ2YmOi80datxjFXv77WaWkei81bILNbCFGtvPnY\nW7hwoQ4PD9dBQUH6vffe0+np6dpisVT4f3nWrFk6JCREt2rVSr/33ns6Kirqktktpk6dqjt27KgD\nAwN1u3bt9Kuvvur0NSdNmqSDg4N1aGio/uyzzxzObqG1dhhL+detTlarVcfExOiGDRvqTp066TVr\n1pQ9tmHDBh0QEFB2f8SIEfq6667TAQEBunPnznr69OlX/brOjg1Xz8NuX0zEE2Qxkas0apSxXPDv\nfw/XOJBBCIC8vDymTZtGYWEho0aNqjB5fZm4OGP58xEjjOtapLYuJiKEu3jzYiLCXNe6mIgsS11b\nff+9kSDXqwdvvGF2NKKG8Pf358477wTgu+++w2azOW74v/8L9evDl1/C5s0ejFAIIYRwjSTJtVFx\nMdjnWPz730GWhhXV6PbbbycqKor+/ftXmJ6oTEQEvPSScfvpp41jUgghhPAiUm5Rg9hsNi5cuHDl\nuRenTjUSlKgo2LULXJyrUYhqlZcHXbuC1QrvvXcxaa7hpNxCiOol5RbCmWstt5AkuQbZuHEjP/zw\nA0OGDKFDhw6OG2VkQOfOkJsLS5YYizsIYZZly4xj0N8fdu+G8PArP8fHSZIsRPWSJFk4IzXJAoBT\np06RnJxMXl6e8zkRtYYnnzQS5IcekgRZmG/wYHjkEaNX+ZlnjGNUCCGE8AKSJNcAWmsWL15McXEx\n119/Pe3bt3fc8OOP4bvvoFkzY8UzITzIaU/PP/8JTZrA0qXwySeeDUoIIYRwQpLkGmDTpk1YrVb8\n/f255557HDdKTb1Y8/nvf4ODlXqEcIeSkhLWrFnDV1995ThRbt364pe2F1+ElBTPBiiEEEI4IEmy\nj8vNzSU5ORmAIUOG0KhRo4qNiopg5EjjJ+3f/Q5MWP9c1F75+fls27aNffv2sX37dseNRowwjsu8\nPGP+bpntQgghhMkkSfZxjRs3ZtSoUdx1113OB+v9/e/www8QGiplFsLjAgICuK+0/n3FihVkZWVV\nbKSUcWyGhhrH6j/+4eEohRCiZrJYLGVLYz/99NO8+eabZY99+OGHBAcHExgYSHZ2Nhs3bqRDhw4E\nBgY6Xfq6NpHZLWq6BQtg2DCoWxfWrYM77jA7IlFLLVmyhO3bt9O0aVP++Mc/Op6qcMMGiI2FkhL4\n5hvj2K1hZHYLIaqXN89uERUVxSeffMJdd91lWgx16tThwIEDFVZALS4uJjAwkK1bt9KtWzcABgwY\nwEMPPcRzzz1XrTGMGzeOb7/9lj179hAfH8+4ceOqdf/OyOwWwrndu2HMGOP2O+9IgixMNWjQIFq3\nbs2ZM2dYvXq140Z9+sC77xq3R4+GPXs8Fp8QomZJS7MycuQEYmPHM3LkBNLSrKbsozIlJSXVuj9H\nnH2BOHr0KBcuXKBz585l26xWK126dKn2GNq3b8/kyZO5//77q33fbqW19vmL8c8QlzhyROuICK1B\n69/9TmubzeyIhNDZ2dn6iy++0Hl5ec4b2WxaDx9uHLtRUVofPeq5AD2g9Hxl+nmzui9yHhZmcXTs\npaam6+jov2rI1cbckrk6OvqvOjU13eX9Xus+Ro0apS0Wi27UqJEOCAjQkydP1unp6VoppT/55BMd\nHh6u+/Xrp5OTk3VYWNglz42MjNSrV6/WWmtts9n0W2+9paOjo3Xz5s318OHDdXZ2ttPXfeedd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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "def power_sim(mu_null, mu_alt, sigma, alpha=0.05,\n", " ssizes = [5, 10, 20, 40, 60, 80, 100, 150],\n", " nsims = 2000):\n", "\n", " SEs = [sigma/np.sqrt(i) for i in ssizes]\n", " left_cutoffs = [mu_null + stats.norm.ppf(alpha/2, loc=mu_null, scale=i)\n", " for i in SEs]\n", " right_cutoffs = [mu_null + stats.norm.ppf((1-alpha/2), loc=mu_null, scale=i)\n", " for i in SEs]\n", "\n", " dist_alt = stats.norm(loc=mu_alt, scale=sigma)\n", " samples = [dist_alt.rvs(size=(i, nsims)) for i in ssizes]\n", " sample_means = np.asarray([np.mean(i, axis=0) for i in samples])\n", " sample_stds = np.asarray([np.std(i, ddof=1, axis=0) for i in samples])\n", " sample_zs = (sample_means-mu_null)/sample_stds\n", "\n", " failed_to_reject_H0 = [np.logical_and(i > left, i < right) for (i, left, right) \n", " in zip(sample_zs, left_cutoffs, right_cutoffs)]\n", "\n", " frac_failed_to_reject_H0 = [np.count_nonzero(i)/nsims for i in failed_to_reject_H0]\n", "\n", " correctly_rejected_H0 = [(1-i) for i in frac_failed_to_reject_H0]\n", " return ssizes, correctly_rejected_H0\n", "\n", "\n", "\n", "ssizes, power025 = power_sim(0, 0.25, 1)\n", "ssizes, power05 = power_sim(0, 0.5, 1)\n", "ssizes, power1 = power_sim(0, 1, 1)\n", "\n", "\n", "fig, ((ax1,ax2),(ax3,ax4)) = plt.subplots(2, 2, figsize=(10,10))\n", "\n", "x = np.linspace(-4,4,250)\n", "ax1.plot(x, stats.norm.pdf(x), linestyle='dashed', color='gray', linewidth=2)\n", "ax1.plot(x, stats.norm.pdf(x, loc=1), color='blue', linewidth=2)\n", "ax1.set_xlabel(\"X\")\n", "ax1.set_ylabel(\"Density\")\n", "ax1.set_title(\"True diff in means Zscore = 1\")\n", "\n", "ax2.plot(x, stats.norm.pdf(x), linestyle='dashed', color='gray', linewidth=2)\n", "ax2.plot(x, stats.norm.pdf(x, loc=0.5), color='black', linewidth=2)\n", "ax2.set_xlabel(\"X\")\n", "ax2.set_ylabel(\"Density\")\n", "ax2.set_title(\"True diff in means Zscore = 0.5\")\n", "\n", "ax3.plot(x, stats.norm.pdf(x), linestyle='dashed', color='gray', linewidth=2)\n", "ax3.plot(x, stats.norm.pdf(x, loc=0.25), color='red', linewidth=2)\n", "ax3.set_xlabel(\"X\")\n", "ax3.set_ylabel(\"Density\")\n", "ax3.set_title(\"True diff in means Zscore = 0.25\")\n", "\n", "ax4.plot(ssizes, power025, marker='o', color='red', label=\"true diff = 0.25\")\n", "ax4.plot(ssizes, power05, marker='o', color='black', label=\"true diff = 0.5\")\n", "ax4.plot(ssizes, power1, marker='o', color='blue', label=\"true diff = 1\")\n", "ax4.set_xlabel(\"sample size, n\")\n", "ax4.set_ylabel(\"Power\")\n", "ax4.set_ylim(0,1.1)\n", "ax4.set_xlim(0, max(ssizes)*1.05)\n", "ax4.legend(loc='best')\n", "ax4.set_title(\"Power for alpha = 0.5\\n for variable effect sizes\")\n", "\n", "fig.tight_layout()\n", "#fig.savefig('fig-powercurves-variable-diffs.pdf')\n", "\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As intuition would suggest, we need to consider sample size and effect size when considering the power of a test. We can get away with fewer samples of the effect size is very large." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [py35]", "language": "python", "name": "Python [py35]" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }