{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "*This post was entirely written using the IPython notebook. Its content is BSD-licensed. You can see a static view or download this notebook with the help of nbviewer at [20161029_ReplicatingStatisticsForHackers.ipynb](http://nbviewer.ipython.org/urls/raw.github.com/flothesof/posts/master/20161029_ReplicatingStatisticsForHackers.ipynb).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this post, we will use the framework for statistical testing presented in ThinkStats to replicate the contents of the talk given at Scipy 2016 by Jake Vanderplas: [\"Statistics for Hackers\"](https://speakerdeck.com/jakevdp/statistics-for-hackers)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/jpeg": 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"text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import YouTubeVideo\n", "YouTubeVideo('Iq9DzN6mvYA')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# What framework? What's ThinkStats?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Think Stats (Second Edition)](http://greenteapress.com/thinkstats2/) is an effort by [Allen Downey](http://allendowney.blogspot.com) to write a statistics textbook from scratch. It uses Python for practical calculations. One of the ideas that is worth taking in is the explanation that Allen Downey gives of statistical testing and the practical implementation he provides. His idea focuses on simulating statistical test distributions under the null hypothesis instead of the classical analytical approach.\n", "\n", "His ideas are, I think, best summed up by the following image from his [blog](http://allendowney.blogspot.com/2016/06/there-is-still-only-one-test.html):\n", "\n", "![there is just one test](https://lh4.googleusercontent.com/Bud31guq0w0FvylY57VMR0zHkYqxIpYAfOqgZietyvv1n2ToNEHwHKZWYix8pwct8kDKsZKiwvOWm6PIFEL3gBIQmbakQYHwVT02nn9_H8Fht_zaSBlrRNcqwZa950Vb5nt-5B84)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The framework used in the Think Stats approach mainly consists of this class (taken from the free online version of the book [here](http://greenteapress.com/thinkstats2/html/thinkstats2010.html)):" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class HypothesisTest():\n", " def __init__(self, data):\n", " self.data = data\n", " self.MakeModel()\n", " self.actual = self.TestStatistic(data)\n", "\n", " def PValue(self, iters=1000):\n", " \"Returns p-value of actual data based on simulated data.\"\n", " self.test_stats = [self.TestStatistic(self.RunModel()) \n", " for _ in range(iters)]\n", "\n", " count = sum(1 for x in self.test_stats if x >= self.actual)\n", " self.pval = count / iters\n", " return self.pval\n", "\n", " def TestStatistic(self, data):\n", " \"Test statistic for the current test.\"\n", " raise UnimplementedMethodException()\n", "\n", " def MakeModel(self):\n", " pass\n", "\n", " def RunModel(self):\n", " \"Returns a simulated data sample.\"\n", " raise UnimplementedMethodException()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It mirrors the thinking in the illustration:\n", "\n", "- `TestStatistic` is the test statistic to be used for carrying out the statistical test\n", "- `RunModel` builds datasets that are similar to the original dataset but under the $\\mathcal{H_0}$ hypothesis\n", "- `PValue` runs many simulations and returns the probability that the statistic is higher than our observed effect in our sampled $\\mathcal{H_0}$ hypothetical world\n", "\n", "One of the questions that a statistician might ask you when using such a simulation framework is: how do we know that this way of doing thinks is the same as the established metholody in statistical testing? \n", "\n", "To answer this question, we will work on the sample problems described by Jake Vanderplas in his Scipy 2016 talk and compare results. Slides can be found [here](https://speakerdeck.com/jakevdp/statistics-for-hackers)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# First test: coin toss " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the coin toss problem, the statement is as follows: \n", "\n", "> You toss a coin 30 times and see 22 heads. Is it a fair coin?\n", "\n", "Let's take the steps needed to define our statistical testing procedure (as [defined by Allen Downey](http://allendowney.blogspot.fr/2016/06/there-is-still-only-one-test.html)):\n", "\n", "- our data is a list of (heads, tails): [22, 8] \n", "- our model under the $\\mathcal{H_0}$ hypothesis is that the coin is fair: the probability of it landing heads or tails is 0.5\n", "- the test statistic is the count of the number of heads in the 30 tosses\n", "\n", "Let's implement this!" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import random\n", "\n", "class CoinTossTest(HypothesisTest):\n", " \"\"\"Class for testing if a coin is fair.\n", " Assumes data will be given as a list like: [number_of_heads, number_of_tails].\"\"\"\n", " \n", " def TestStatistic(self, data):\n", " \"Counts the number of heads in the data.\"\n", " return data[0]\n", "\n", " def RunModel(self):\n", " \"Returns data generated under the H0 hypothesis (the coin is fair).\"\n", " n = sum(self.data)\n", " tosses = [0, 0]\n", " for _ in range(n):\n", " if random.random() > 0.5:\n", " tosses[0] += 1\n", " else:\n", " tosses[1] += 1\n", " return tosses " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's test our test!" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "coin_test = CoinTossTest([22, 8])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can compute the test statistic with our real data: it should return 22." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "22" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "coin_test.actual" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Also, we can generate a new random sample of 30 coin tosses under the null hypothesis:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[13, 17]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "coin_test.RunModel()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, let's sample the distribution of our test statistic and compute the p-value for our particular data:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.01" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "coin_test.PValue()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see our p-value is low. But it is not, given that we simulated only 1000 experiments, the exact p-value, which should be 0.008. Let's compare the obtained distribution and the exact distribution of the test statistic under the null hypothesis." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "plt.style.use('seaborn-darkgrid')" ] }, { "cell_type": "raw", "metadata": {}, "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "styles = plt.style.available\n", "\n", "x = np.arange(-10, 23)\n", "y = np.sin(x * np.cos(x**2))\n", "for style in styles:\n", " \n", " plt.style.use(style)\n", " fig, ax = plt.subplots(figsize=(3, 3))\n", " ax.plot(x, y, label='blabla')\n", " ax.set_title(style)\n", " ax.legend()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_simulated_distribution(test, title, bins=30, range=None):\n", " \"Plots the simulated test statistic distribution.\"\n", " plt.hist(test.test_stats, bins=bins, range=range, \n", " cumulative=False, normed=True,\n", " label='simulated test stat\\ndistribution')\n", " ylim = plt.ylim()\n", " plt.vlines(test.actual, *ylim, label='actual test stat\\n(p={:.3f})'.format(test.pval))\n", " plt.legend(loc='upper left')\n", " plt.xlabel('test statistic value')\n", " plt.title(title)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_simulated_distribution(coin_test, \"Coin test\", range=(0, 30), bins=31)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's also plot the analytical distribution:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from itertools import accumulate\n", "\n", "def ncr(n, r):\n", " \"\"\"Returns from n choose r possibilities.\n", " Source: http://stackoverflow.com/questions/4941753/is-there-a-math-ncr-function-in-python\"\"\"\n", " r = min(r, n-r)\n", " if r == 0: return 1\n", " numer = list(accumulate(range(n, n-r, -1), int.__mul__))[-1]\n", " denom = list(accumulate(range(1, r+1), int.__mul__))[-1]\n", " return numer//denom\n", "\n", "def plot_analytical_coin(n=30):\n", " \"Plots analytical distribution under H_0 hypothesis of n coin tosses landing h heads.\"\n", " heads = list(range(n+1))\n", " probs = [ncr(n, h) * 0.5 ** h * 0.5 ** (n - h) for h in heads]\n", " plt.plot([h + 0.5 for h in heads], probs, drawstyle='steps', \n", " label='analytical test stat\\ndistribution')" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_analytical_coin()\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now put the two together:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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uF2ZdSVnX0pvg7q5w9qyuUNEJYQkk0RdBy5at+fzzefj798Xe3p7vvtuVo/38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\nkuiFEMLCSaIXQggLZ7IEghB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npstP9vhPnz5NYGAgNWvWBKBXr1689tpr5RtgPjIyMggK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\nQlg4SfRCCGHhJNELIYSFk0QvhBAW7v8Bl9tYv9Sc8XQAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_analytical_coin()\n", "plot_simulated_distribution(coin_test, \"Coin test\", range=(0, 30), bins=31)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The sampled hypothesis is quite close to the exact one. Can we do better?" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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rmDJlJkuXLiQxMTGrd5kQQmQ5yWIhRHaTAXIGhISc4N13W2BjY4NaraZt24+M\nbopxdi5BxYou9OvXnUWL5v97ndu7BjU8L1ujRs0Xbqd9+5SH05cvX4Fy5Spw7tz/Xqm9x4//TqdO\nnwApj4Vq374Tf/xxTL/82TV4lSpVJikpkbi4uFfajhBC5CTJYiFEdpMBcgYZhrBGY/y4I5VKxcKF\nyxk/fhKFCxdmwYI5LFgwO816ChUq9MJtGD6+KTk5GQsLi3+3/bxMes4wKIou1WvDqUKtra3/u4bJ\nOoUQIi+QLBZCZCcZIGdAgwZuBAQcJDo6Gp1Ox6+//my0/NKlS/Tq1ZWyZcvRs2dfPvmkO1euXAYy\nNo/9zz/vBSAsLJTbt29Steo7ODkV4e+/r5KYmEhSUhLBwc9n0UqpOzlVPfXrN2LHji0AaLVadu/e\nSf36DdPcpomHmQghRJ4hWSyEyG5yk14GNGrUmL//vsqAAb1wcHCkYkUX/TVpAC4uLrRs+T5eXj0p\nVMgWGxsbRoz4GoDGjZuyaNF8k2cbVCoVt2/fon//HqhUaiZN8sXBwYH69RtSs2ZtunfvRLFixahV\nqy5Xr6YEfrVq1VmxYgnjx39N586e+rpGjBjF3Lnf0bv3JyQlJdGggRu9evXTb+e/2xVCiPxAslgI\nkd1MPgc5O5nD8zcNmeNzA/Nzn+Q5yK9GnoOctbLiOcjZydxyGMzvGDK3/oD59cncstjcPh/IeBbL\nJRZCCCGEEEIYkAGyEEIIIYQQBmSALIQQQgghhAEZIAshhBBCCGFAnmIh8p1qrhW5fycit5shhBBC\nCDMlA2SR79y/E5Hup1MIIYQQQmSUDJCFGYsEn6LpKBeV7S0RQoiCyMXFnkePXvRsZ+MZBJ2cFC5d\nis7+RgmRDiavQVYUhYkTJ+Lp6Unv3r0JDw9PVSYqKooPPvgArdb4mXlXr16lbt26qd43N6GhF/n2\n22+yrL4uXT4iLCzUxDYv8P33vhmue+7cWaxevSLV+3fu3Mbbe3SG63smJiaa4cM/zdA66e3Dq/YV\nioKPyvQf0jOIFiL3SA6nj2Rx3sviR49UREQ8TfUnOjoh1XsvHkgLkfNMDpAPHjyIVqtl06ZNjBw5\nEl9f4y9HUFAQXl5eREZGGr0fHR3NrFmz0phj3vxUrlyFKVNm5Og2r127yv37WXcd7p07twkPv/HK\n6z958oSLFy9kaJ309iGr+ypEfiM5nD6SxZLFQmQVk5dYhISE4O7uDoCrqyvnzp0zWq7RaPD396dj\nx45G709xk3FPAAAgAElEQVSYMIGvvvqKoUOHZmFzc1dcXBzTp0/i1q1wVCo1lSpVZvTo8Zw6FcLc\nubPYtm0n06dPwtrahosXzxMVFUnz5u/h5FSEY8eOEBUVxZgx3tSuXZfp0ydRvnwFPD17AqR6DSln\njebPn83Fi+eJjY1BUeCbb7xxdi6Bn98yYmJi8PWdzNixEwgKOsKaNatISkrCxsaGoUOH88471YmN\njWHGjKlcvXqZ114rhlqtxsmpiFG/dDods2ZN48GD+4wc+QWzZy/gf/87w9KlC9FqEwAV/foNxM2t\nCVFRkUydOpHHjx8D4ObWBC+vwfj6TiYhIZ7+/Xvg57fOaLrUM2dOs3DhXBRFQaWCnj37UaVKVaM+\nfPPNt+nuqxAFjeSwsYKWxcuXLyI2Ng61Wi1ZLEQOMTlAjo6OxsHh+fR8FhYW6HQ61OqUk8+NGjUC\nUgLkmYULF9KsWTMqVapELs5kneWOHAkgLi6WVavWo9Pp+P57X27duglgFEKXL4exfLk/jx495OOP\nPfjyy9EsWbKKrVs3sW7dj9SuXTdd2zt//hxRUZEsW7YagHXr/Fm3zp8ZM+YwYMAQDh8+xNixE7h5\nM5wVKxbzww/LcXR05O+/rzFixFC2bNnFypVLsbGxYf36bTx69Ij+/Xvg6lrLaDtqtZoxY7yZN+87\nZs9ewNOnT/H1ncycOYsoX/4tbty4zaBBfVi6dBU//7yX119/kzlzFhIfH8+MGVOIjY1h3LiJ9O7t\nyapV61P1Y9Wq5Xh69qRly1ZcvXqFPXt28O67zY36cO7c/9LVVyEKIslhYwUti5csWU7hwq/x4MGD\nfJnFzs6O6SyppKts8VLOnD9zJUNtECKjTA6Q7e3tiYmJ0b82DGVDhqG0Z88eSpYsydatW3nw4AFe\nXl6sXbs21ToajRpbW6tXbXuOa9CgHitWLGHEiE9p0KAhvXv3oXz58jx5EoVKpcLSUoNGo6ZZs2bY\n29tgb1+KQoUK8e67TbG1taJ8+bIcPPgLtrZWaDRqrKws9P03fK1SgY2NBbVq1aBEidf4+eddhIeH\nExJyEjs7O2xtrbCy0uj335kzJ4mKiuSrr4by7N9BS0sL7t+/y19/neTrr8dga2uFra0zLVu2xNJS\nk2q/29hYolKpsLW14tSpC0RFReLtPQoARQELCw03b16nWbN3+eKLz3jw4B716zfkyy+/olixImi1\ncahUpPl5tm7twdy5s/jjjyAaNGjIiBFfpupD/fp10tXX7JKfjkNDaX2WWSE390d29Sk/kxw2VtCy\neNSoEeh0KRXmlSwu71KGiNv30vFpKel/opAP6Sp73ycizx2z5pbFksPpGCDXrl2bgIAAPDw8OH36\nNC4uLmmWMzxDceDAAf3fW7RowapVq9JcJzlZR2xs/rlxxMmpOJs27eTUqZOEhJxk8OABfPXVaBwd\nC6MoComJySQn6wC1vl+KAomJCrGxWhISktDpUvqcnKwjISFJXy4+PgGtNuW1okB8fBIHD/4fCxbM\nxtOzJ40aufPGG6U5cOAXYmO1aLXJ+v0XH6+ldu16TJo0Xd/WiIh7FCtWHEVRiI9P1G9Hp1ORmJic\nar/HxyeiKCntjI3VUqZMOZYtW42trRWxsVoePHhAkSJF0Gg0bNmyh5MnjxMScpKePbvh6zubYsWK\noSik+Xl6eHxEvXpu/PnnHxw9epSlSxezZs0moz4cOxaUrr5ml/x0HBp69vlktdzcH9nVp9xiZ5f5\n638lh40VtCxeu3a9vlxeyeKI2/dy9XGbee2YNbcsNrcchoxnsckBcqtWrQgODsbT0xMAX19f/P39\nKVOmDM2bN9eXMzxzYUilUmXJz3vZPTlEen6y2bVrG2fOnGbixKnUq9eQqKhIrl27Ss2atTO8PSen\nIoSGptxI8ejRI86cOUWlSpWNypw8eZzGjZvSvn0nEhISWLfuR3Q6HZByzWFSUjIAderUx89vOTdu\nXOett8ry++9BTJkykR07fqJBAzf27dtN7dp1efr0KUFBgXh4tE3VnpT6kgCoVq06N2/e4MyZUzRq\n1IDLl8MYOnQAa9duZdeubSiKwqefDqNJk3e5evUy4eH/UKJECXS65DT7+umn/enduz+tW7ejadNm\ndOr0IU+ePDXqQ3r7KkRBJDlsrKBl8V9/hVC5cnXJYiFykMkBskqlYtKkSUbvlStXLlW5Q4cOpbn+\ni97PqHRPDvGq9fuYDn0Pj3acOvUXPXt2wdrahpIlS9KlSzcuXw574Tov+gerc+dPmDz5W3r06EzJ\nkq//51q4lHXat++Ej894+vbtjlqtpmbNWhw+/H9ASnCuWLGE8eO/Ztq07xg9ehwTJ44DQKOxYObM\nOdjY2ODlNYjvvvOlR4/OFClSlAoV3k6zPWXLlkelUjFoUF+WL/dn6tRZLFo0n/nzE0lO1jFhwhRK\nlixJ167dmDrVhz59PLG0tKJixbdp1coDtVrN229XomfPLixe7Iej4/PryIYOHc68ed+zYsUSVCo1\n/fsPomTJkiQnP+/D4MGf4+MzLl19FaKgkRw2VtCyeN68OcTHJ6AoSp7JYiHMnUrJxbs3YmIS0n0K\n39nZMXtnRvOBiIgnmarCHH+SyIt9Svex4KP8+5xj0+UiIp5mtlm5Ijs+H2dnx0x/FzIjLx5zmVG8\nuIPpQrnI3HIYzO8Yyov9yfIczkhZn6w5TrKSuWVxXjzmMiujWSwz6Yl8xcXFnvTf9JHeGfKicHZO\n32QhMtOTEEJA9sxUGpUySM7SOoV4NTJAFvlKykxLqiy+OeS1dNf36JF5PS5LCCFeTdF0n+1Nv/Rm\nsQLkz1/9RP5hciY98WKHDx9i2LDB+Pkt49dff35pWX//lQQFHUlzmeH67u71ePLkcYbaYTj9Z1ZP\ntSqEEHmdZLEQIqvJGeRMUqlUeHkNNlkuJOQE5cqVT3OZ4fovupHkZQyn/8yNqVaFECK3SRYLIbKS\nDJAzaOXKpfz22y8ULuzEm2+WRlEU/dSk/fv3x89vGUePBmJpaYGjoxPjxk0gMDCA0NCLLFo0H7Va\nzdGjgTx58pjbt2/h5uZOVFSkfmpTRVFYtmwRFy9eABQGDPgUN7cm7N+/j4CAQ8yaNRdA/3rUqG+M\npv/08GjL3LmzWLNmMzEx0cyZM5PLly+hUqlp0KARQ4Z8jlqtpkWLxvTs2YcTJ/4gMjKSzp096dq1\nW+7uXCGESCfJYiFEdso3A+TipZzT/QigV63flKNHD3PkSAA//rgJKysrvvlmpNFZhnv37rJ160b2\n7TuIhYUFmzev5+LF83Ts2IWAgIN07uyJu3szjh4NJCEhgTVrNgMwfbrx45veeKM0X389jmvXrjJs\n2CA2bNgOwH9PaKhU4Oxcwmj6z1OnQvRtmjv3OwoXdmLNms0kJSUxevSXbNy4lh49+pCYqKVIkaIs\nWbKKsLBQPv3Uiw4dOmNpaZmZ3SiEMGN5IYdBslgIkf3yzQA5L8y7HhJygnffbYGNjQ0Abdt+xLZt\nm/TLnZ1LULGiC/36dadhw8Y0bOhGnTr1DGp4foNXjRo1X7id9u07AVC+fAXKlavAuXP/e6X2Hj/+\nO0uXpsyeZWFhQfv2ndi6dSM9evQBoEmTpgBUqlSZpKRE4uLiJJSFEC+UF3IYJIuFENlPbtLLIMPH\nRms0GqNlKpWKhQuXM378JAoXLsyCBXNYsGB2mvUUKlTohdtQq59/LMnJyVhYWPy77edlEhMT09FW\nXarXz2ZoArC2/u+0i/KEBiFE/iBZLITITjJAzoAGDdwICDhIdHQ0Op0u1d3Sly5dolevrpQtW46e\nPfvyySfduXLlMmA8fagpP/+8F4CwsFBu375J1arv4ORUhL//vkpiYiJJSUkEBz+/C/tF03/Wr9+I\nHTu2AKDVatm9eyf16zdMc5u5OF+MEEJkiGSxECK75ZtLLPKCRo0a8/ffVxkwoBcODo5UrOjC48eP\n9MtdXFxo2fJ9vLx6UqiQLTY2NowYkTIlZ+PGTVm0aL7Jsw0qlYrbt2/Rv38PVCo1kyb54uDgQP36\nDalZszbdu3eiWLFi1KpVl6tXUwLfcPrPzp099XWNGDGKuXO/o3fvT0hKSqJBAzd69eqn385/tyuE\nEPmBZLEQIrvlm6mm8wNznJoxr/XJ2dmBDE0UktXlyFvTUpvb9KaQ9465zDKnqabzC3M7hvJif5yd\nHdI/UYhPOitNb1mfvJXDYH5ZnBePuczKaBbLJRZCCCGEEEIYkAGyEEIIIYQQBkwOkBVFYeLEiXh6\netK7d2/Cw8NTlYmKiuKDDz5Aq005HR8dHc2QIUPo1asXnp6enD59OutbLoQQBYTksBBC5CyTN+kd\nPHgQrVbLpk2bOHPmDL6+vixevFi/PCgoiNmzZxMZGal/b/Xq1bi5udG7d2/+/vtvRo4cyY4dO7Kn\nB8JsVHOtyP07piYhkDu8RcEjOSyEEDnL5AA5JCQEd3d3AFxdXTl37pzRco1Gg7+/Px07dtS/169f\nP6ysrABISkpK4xmPQqR2/06E6Rs0TC0XwgxJDgshRM4yOUCOjo7GweH5nX8WFhbodDr9A9QbNWoE\nGD+70d7eHoD79+8zevRoxo8fn6WNFkKIgkRyWAghcpbJAbK9vT0xMTH614ahbOi/z24MCwtj1KhR\njBkzhrp166ZZt0ajxtbWKqNtzrMsLTVm1R8wzz5lVl7aH9n1+eRmH+WYS01yOGPM7Rgyt/5khby2\nP8wti+WYS8cAuXbt2gQEBODh4cHp06dxcXFJs5zhmYsrV64wYsQI5s2bR6VKlV5Yd3Kyzqyes5fW\ncwNDQy+wb99uRo0a+8r1dunyEVOnzqJSpcpG7+/bt4ukpCTat+/8SvX+/nsQFy6cx8tr8AvL/LdP\n/v4rqVjRhSZNmr607vSWy4/y0jGbXc+qzM0+mtvzN+3sMn9pg+RwxphbFqfVn9zP4ty9ZCevHbPm\nlsXmlsOQ8Sw2OUBu1aoVwcHBeHqmzArk6+uLv78/ZcqUoXnz5vpyhmcu5syZg1arZdq0aSiKgqOj\nI4sWLcpQw8zFtWtXuX/f1I1nr+bs2TOUL1/hlde/ePECT59m7CHkISEnKFeufJaVE0KYJjmceZLF\nQoiMMDlAVqlUTJo0yei9cuXKpSp36NAh/d8N7642J4qisGDBHC5cOEdsbAyKAt98480779QgLi6O\nWbOmcurUX1hYWNCkybt06NAZP79lxMTE4Os7GQ+PtsydO4s1azYDcOpUiP71w4dRzJo1nUePooiM\njKRkyVJMnjwDJyenNNty5MhhgoKOcPLkn1hb29ChQ2fWrFlFYGAAiqKjZMnXGTlyDK+9VozAwP/j\nxx9XodGoUas1DB06HEtLC3bv3o5Op2BnZ8/AgZ8a1e/nt4yjRwOxtrbC3t6RceMmEBgYQGjoRRYt\nmo9araZs2fLMmTOTuLg4IiMfULGiC5Mn+7J37y6jcu7uzbL7oxHCrEkOGytoWRwcfASNRoOjo5Nk\nsRA5RCYKyYDz588RGfmAZctWs3btFjw82rBunT8AK1cuITFRy8aNO1i9egPnzp3l9u1bDBgwBFfX\nmowdOwFIfY3gs9cHDx6gevUaLFmyii1bdmNtbc2vv/70wrY0bdqMJk2a0rVrNzp06Mwvv/zE1atX\nWLHiR1atWk/Dhm7MmDEFgMWLFzBq1DesWLGGAQOGcOrUSapWfYePP+5Ey5atUgVyRMQ9tm7dyMqV\na1i7dgP16zfg4sXzdOzYhcqVq/DZZyNwd2/G3r07ad36Q5YuXcXGjTu4ffsWx44FGZQbLoEshMhy\nBS2L167dwIoVaySLhchBJs8gi+feeac6jo5D2LVrG7du3eLUqRDs7OwAOHnyBF9/PRpIucP8hx+W\nAXDnzu101d2liydnzpxm8+b1hIeH8/ff16hWrXq623bsWBAXL17Ay6snADqdQkJCAgDvvfcBY8eO\nws2tCXXrNqBHjz4vrat4cWcqVnShX7/uNGniTt26DalTp55BiZTrHD/99AtOnDjOhg1rCA+/QWTk\nA+LiYtPdZiGEeBUFLYu7d+9K/fpuNGzoJln8L2dnR5Nlipdy5vyZKznQGmGOZICcAceOBbFgwWw8\nPXvi7v4uZcqU4cCBX4CU55AanpGIiLiHjY2N0foqlcroJpqkpET93xcvXkBY2EXatv2I2rXrkZyc\nZFTWFJ0umR49etO+fad/607iyZPHAAwc+Clt237EiRPH2b9/L+vX+7Nq1foX1qVSqVi4cDmhoRc5\nezaEBQvmUKdOXb74YqRRuYkTx6HT6WjRohVubu7cu3c3Q20WQohXUdCy+Pr1KwQFBUkWG/IxXeS+\nT/Zccy4KBrnEIgNOnjxO48ZNad++E5UqVeHIkUB0Oh0AdevWZ9++PSiKglarxdt7DKdPn0Kj0ZCY\nmASAk1MR7t27y6NHj1AUhSNHAvV1nzjxB126dOP991vj5OTEiRPH9XW/iEajISkppe769Ruxb99u\nYmNTHgW1fPlipk6dSHJyMl26fER8fBwff9yRkSO/4Z9/rpOUlGS0vqErVy7Tq1dXypYtR9++/fnk\nk+5cuXI51TZPnDhOv34DadHiPRRF4cKFc/o2v6huIYTIrIKWxeXKlaNnz76SxULkIDmDnAHt23fC\nx2c8fft2R61WU7NmLQ4f/j8A+vcfxKJFc+jbtxs6nY6WLd+nadNm3Lp1kxUrljB+/NdMm/YdH33U\nES+vnhQrVhw3tyb6uvv2HcjChfPw91+JRqPB1bUmN2+G/7tUlUZroGFDN+bO/Q6Anj37cv9+BIMG\n9UOtVlGiREnGjfNBo9EwfPhIJk3yRqOxQKNRM27cRCwsLKhTpx7e3mOwsLBkxIhR+norVnybli3f\nx8urJ3Z2dlhZWTNixNcANG7clEWL5pOYmMjgwUMZO3YkhQsXxtrahlq16ujbbFjOw6NtVn8UQogC\nrKBlcY8entjYFMLGxkayWIgcolJy8XeYmJgEs3rOnjk+NzCn+uTiYs+jR2n/42PEJgriX0vflNM+\nZHk5Jyddutrp5KRw6VJ0OirNnOz4fJydHYmIyNgjp7KSuX2Pihd3MF0oF5lbDoP5HUN5LocBiAKf\n10wX8yF9+ZqRsj6RQNF0VSlZ/GrM7TsEGc9iOYMs8oSUUFalf0CbS9IbtM7OeXtQJIQQ/5VfchjS\nf5Lk0SMzvxZbZJt8M0Bu2rQBoaEXs63+ypWrcOTI8WyrXwgh8jvJYSFEQZFvBsgSmkIIkbskh4UQ\nBUW+GSDnNUuW/EDduvWpV69BhtfV6XQsXDiX48d/JzlZh6dnD/0jgdJb7ubNcGbMmMKjR4+wtbXF\n23sSb71VhnXr/Dl06ID+MUcPHz4kLi6WX345zJYtG3F0dJQbNYQQZiHv5bAPb71VFoBdu7azfftm\nNBoLSpV6nbFjv8XRsbDksBD5hDzm7RWcP3+OGzeuv1IoA+zevYObN8NZt24rK1b8yNatGwkNvZCh\ncpMmedOhQ2fWrdtC//6D8PZOeTB+z559Wb16A6tWrWfBgmUUKlSIyZNnANC58yds2bKRhw+jXrHn\nQgiRN+TNHB4DpExKsnLlEhYv9sPffwMlS5bCzy9lwhLJYSHyBzmD/ApWrVpO585dOXUqhMWL51Os\nmDO3b9/C1rYQY8dO4K23yjJv3vecPXvKaD1LSyuWLVvNkSMBfPxxR1QqFQ4ODrRs+T6//rqfypWr\nGpV/UblixYoTHv4PLVu+D6Q8Ymj27BlcvhzG229X0q+/cOFcGjZ0o379hgCo1WpatHiPdev8GTbs\nq2zeS2ZIk/7Zm+Be9rdHiALsRTlsY2PDlClTcXZ+I9dy2NbWjqSkZGJiorGzsyM+Ph57e3tAcliI\n/EIGyBkUHR3N2bOnmTlzDv/73xkuXQrjiy9GUr26Kz//vJvJkyewcuUao2dZ/ldExD2cnUvoXzs7\nO3PtWurpMF9U7t69exQrVtyobPHizkREROgHyH//fY2goCNs2bLLqFzjxk35+uvhEsyvIhmZvUmI\nPOBlObxr13a8vcexfPmPuZbDjRu7061bT7p374SDgwN2dvYsXbpaX05yWIi8TwbIGXTzZjivvVYM\nC4uUXVexogvVq7sC8PHH7Zk5czpPnjxh1arlnDnzl9G6VlbWLFu2Gp1OZzQVqqKAWq1Jta0XlVMU\nHf99YL2iKKjVz6+Y2bp1I506dcXW1s6o3BtvvMm9e3dJTEzE0tLy1XaCEELkopflcLt2HzNv3ne5\nmsMnTvxBYGAAO3f+TOHCTixePJ9p0yYyc+ZcQHJYiPzA5ABZURR8fHwICwvDysqKadOmUbp0aaMy\nUVFRdOvWjb1792JlZUVCQgJff/01kZGR2NvbM2PGDIoUKZJtnchJKpXq32BModE8D9Rnc65oNOqX\nnrkoUaIkDx7c179+8OA+xYs7p7vcf99PWfZAf5ZDp9MRGPh/+PmtT1WnTqdDrVYbBb4QIm+THDb2\nshx+PsVy7uXwnj07aNKkKYULOwHQsWNXevf2NGqj5LAQeZvJm/QOHjyIVqtl06ZNjBw5El9fX6Pl\nQUFBeHl5ERkZqX9v48aNuLi4sH79ej7++GMWL16c9S3PJW+88SZRUVEkJiYCcPlymP5nuR07tlG9\nuit2dvYvrcPd/V1++mkPycnJPH36lEOHDtC0abN0lmtO8eLOlC5dmkOHfgPg+PHf0WjUVKhQEYCr\nV6/g4FCYkiVLpqrz9u2blCr1uv7MixAi75McNvayHN6zZwc1auRuDru4VOb334OIi4sDICDgENWq\nvaOvU3JYiLzP5LczJCQEd3d3AFxdXTl37pzRco1Gg7+/Px07djRaZ+DAgQA0bdrUrILZ3t4eV9ea\n/PXXSaysrCha9DWWL1/MnTu3KVasGN7ek03W0b59Z27fvkXfvt1ISkqifftOuLrWAtDf6ezlNfgF\n5WoC4OMznRkzpvDjjyuxtrZmypSZ+vpv3rxBqVKl0tz2H3/8TvPm72V2NwghcpDksLGX5XCRIkWZ\nMmW6yTqyM4fbtv2Iu3fv4OXVEysra0qWLMn48T76bUsOC5H3mRwgR0dH4+DwfNpcCwsL/c9DAI0a\nNQKeX17wbJ1nd+za2dkRHZ3986DnpL59B7BmzSq6dev170+Xc4D0z12u0WheeHOGl9fgdJV74403\n+eGHZWkua978vTTDNzk5mQMH9jN37iKTbRRC5B2Sw6m9KIchfVmc3Tns5TXYqJ5nJIeFyB9MDpDt\n7e2JiYnRvzYMZUOG11IZrhMTE2MU7IY0GjW2tlYZbnRuq1+/LsHBh1GpUm7eeNYHS0tNnu7P+vVr\n6dWrF2+8UcJ04X/l9T7lZTmx37Lr88nNz1yOudQkh1N7UQ5D3j6GJIdznmRxxskxl44Bcu3atQkI\nCMDDw4PTp0/j4uKSZjnDMxe1a9cmMDCQ6tWrExgYSN26ddNcJzlZl64zrnnR4MFfAODvv1Hfh/Se\nQc4tHTp8ApChNuZcn6xzYBs5Kyf2W3Z9Prl5HOf171FG2dll/tiWHE5bWjkMefsYkhzOeZLFGZeX\nv0OvKqNZbHKA3KpVK4KDg/H0TLkD19fXF39/f8qUKUPz5s315QzPXHTr1o0xY8bQvXt3rKysmD17\ndoYaJYQQ4jnJYSGEyFkmB8gqlYpJkyYZvVeuXLlU5Q4dOqT/u42NDfPnz8+C5gkhhJAcFkKInGXy\nMW9CCCGEEEIUJDJAFkIIIYQQwoAMkIUQQgghhDAgA2QhhBBCCCEMyABZCCGEEEIIAzJAFkIIIYQQ\nwoAMkIUQQgghhDAgA2QhhBBCCCEMyABZCCGEEEIIAzJAFkIIIYQQwoAMkIUQQgghhDAgA2QhhBBC\nCCEMyABZCCGEEEIIAxamCiiKgo+PD2FhYVhZWTFt2jRKly6tX75lyxY2b96MpaUlQ4YMoVmzZty5\nc4fRo0cDULhwYWbPno21tXX29UIIIcyY5LAQQuQsk2eQDx48iFarZdOmTYwcORJfX1/9sgcPHrB2\n7Vo2b97MypUrmT17NomJifj7+9OmTRvWrl1LhQoV2LZtW7Z2QuRd1Vwr4uzsaPKPEOLFJIeFECJn\nmTyDHBISgru7OwCurq6cO3dOv+zs2bPUqVMHCwsL7O3tKVu2LGFhYVSpUoW7d+8CEBMTg4WFyc0I\nM3X/TgT4pKNgesoIUUBJDovMquZaMSWPX0rJkbYIkR+YTMzo6GgcHByer2BhgU6nQ61Wp1pma2vL\n06dPKVGiBN9//z379u0jMTGRYcOGZU/rhRCiAJAcFpmVrpMVppYLUYCYHCDb29sTExOjf/0slJ8t\ni46O1i+LiYnB0dGRb7/9llmzZuHm5kZgYCCjR49m2bJlqerWaNTY2lplRT/yBEtLjVn1BzLXp9Kl\nrQAlfaFrEwXxr7SZPKlIEQVnZwfTBf8tGx6ufaXtZNcxl5vHsTl+jzJLcjhjzO0Yymx/0p3FZpbD\naIDkKJydi5osmpkcBvPLYnP7Dr0KkwPk2rVrExAQgIeHB6dPn8bFxUW/rEaNGsybNw+tVktCQgLX\nrl3j7bffpnDhwtjb2wNQvHhxnjx5kmbdyck6YmNf/YDMa2xtrcyqP5C5Pj18aA2o0n9WIr3l8oGw\nsGjThf7l7Ozwyvs4u4653DyOze17ZGeX+RvjJIczxtyOocz2J0NZnJ4y+UUy4POa6XI+8PChkql9\nbG5ZbG7fIch4FpscILdq1Yrg4GA8PT0B8PX1xd/fnzJlytC8eXN69epF9+7dURSFr776CisrK7y9\nvZk8eTI6nQ6AiRMnvkJXhBBCgOSwEELkNJMDZJVKxaRJk4zeK1eunP7vXbp0oUuXLkbLK1SowI8/\n/phFTRRCiIJNclgIIXKWTBQihBBCCCGEARkgCyGEEEIIYUAGyEIIIYQQQhiQAbIQQgghhBAGZIAs\nhBBCCCGEARkgCyGEEEIIYUAGyEIIIYQQQhiQAbIQQgghhBAGZIAshBBCCCGEARkgCyGEEEIIYcDk\nVN32skAAACAASURBVNNCiAzSgLOzo8lixUs5c/7MlRxokBBCCCEyQgbIQmS1ZMDHdLH7PhHZ3RIh\nhBBCvAK5xEIIIYQQQggDMkAWQgghhBDCgMlLLBRFwcfHh7CwMKysrJg2bRqlS5fWL9+yZQubN2/G\n0tKSIUOG0KxZM+Li4vDx8eHWrVskJibi7e1N9erVs7UjQghhriSHhRAiZ5kcIB88eBCtVsumTZs4\nc+YMvr6+LF68GIAHDx6wdu1adu7cSXx8PN26daNx48b4+fnh4uLCzJkzCQsLIywsTIJZCCFekeSw\nEELkLJMD5JCQENzd3QFwdXXl3Llz+mVnz56lTp06WFhYYG9vT9myZQkNDSUoKIjWrVvj5eWFg4MD\nEyZMyL4eCJFf6Z92oZh86oU88aJgkxwWQoicZfIa5OjoaBwcHPSvLSws0Ol0aS6ztbUlOjqahw8f\n8vTpU/z8/GjWrBkzZ87MhqYLkc8ZPu3C5+V/7t+RJ14UZJLDQgiRs0yeQba3tycmJkb/WqfToVar\n9cuio6P1y2JiYnB0dKRIkSK0aNECgBYtWrBy5co069Zo1NjaWmWqA3mJpaXGrPoD5tmn/CqtzyG7\nPp/c/MzlmEtNcjhjzO0YMrf+5FWZ2cfmlsVyzKVjgFy7dm0CAgLw8PDg9OnTuLi46JfVqFGDefPm\nodVqSUhI4Nq1a7z99tvUqlWLwMBAqlatyp9//knFihXTrDs5WUdsrDbrepPLbG2tzKo/kNk+WWdp\nWwq6tD6H7DrmcvM4NrfvkZ1d5r8HksMZY27HUOb7I1mcHpnZx+aWxeb2HYKMZ7HJAXKrVq0IDg7G\n09MTAF9fX/z9/5+9+46Oovr7OP7e3TRCEgJKAAVpMTSldwgdDUWlE3oJJagIgtKVUEMLCEivAlIF\nFBUeFX+hSzEISAsI0iEJhAApZLPZ+/wRWTYQsgnpm+/rHI/ZnTsz987Mfrg7e2dmNcWLF6dx48b0\n6NGDrl27opRi2LBh2NnZ4evry7hx4/D29sbW1lZ+2hNCiDSQHBZCiMxlsYOs0WiYMGFCovdKlixp\n+rtjx4507Ngx0fR8+fIxf/78dKqiEELkbpLDQgiRueRBIUIIIYQQQpixeAZZCCGEEMJq6YB45Hab\nIhHpIAshhBA5VIVK7im4DaTKlLrkWPH//d8v+WJhfnK7zdxEOshCCCFEDhV2O9Rix87idCHEc2QM\nshBCCCGEEGakgyyEEEIIIYQZGWIhUs3Dw4mICI3Fcq6uioiITKhQTucQDn6Wxwh6eCguXIi0WE4I\nYf2e5rCyPITCIRweZ0KlcrIU5rCbW8K/bZLF1k86yCLVIiI0hIY+SlFZN7cMrow1GPWK5TJ+EBEh\nF9oIIRI8yWE3N5eUjTFOSZncLIU5HBr6EDc35wyvjsh6MsRCCCGEEEIIM9JBFkIIIYQQwox0kIUQ\nQgghhDAjHWQhhBBCCCHMSAdZCCGEEEIIM9JBFkIIIYQQwozFDrJSivHjx+Pt7U3Pnj25fv16oumb\nN2+mffv2eHt7s2fPnkTTjh07RqNGjdKzvkIIketIDgshROayeB/k3bt3o9fr2bhxIydPnsTf35+F\nCxcCcPfuXdauXcv27dt5/PgxXbp0oV69etja2nLnzh1WrVqFwWDI8EYIIYQ1kxwWQojMZfEMclBQ\nEJ6engBUqlSJ06dPm6adOnWKatWqYWNjg5OTEyVKlCA4OBi9Xo+fnx9+fn4ZVnEhhMgtJIeFECJz\nWTyDHBkZibPz06fG2NjYYDQa0Wq1z01zdHTk0aNHTJw4kb59++Imj1GzWhUquRN2OzSrqyFEriA5\nLIQQmctiB9nJyYmoqCjT6yeh/GRaZOTT55FHRUVha2tLUFAQ165dQylFREQEw4cPJyAg4Lll63Ra\nHB3t0qMd2YKtrc6q2gMvblPY7VB5vGkWeHZfZNQxl5XHsTV+jtJKcjh1rO0YelF7rKmNOcWTbW7t\nWWxtn6GXYbGDXLVqVQIDA/Hy8uLEiRN4eHiYplWsWJGvvvoKvV5PbGwsly9fpmLFiuzatctUpn79\n+kmGMkB8vJHoaH06NCN7cHS0s6r2wIvaZJ8ldRE8ty8y6pjLyuPY2j5HefOm/fMiOZw61nYMvSiH\nramNOUXCNn9+21tbFlvbZwhSn8UWO8jNmzfn4MGDeHt7A+Dv78/q1aspXrw4jRs3pkePHnTt2hWl\nFMOGDcPOLnd/4xBCiPQmOSyEEJnLYgdZo9EwYcKERO+VLFnS9HfHjh3p2LHjC+c/cOBAGqonhBBC\nclgIITKXPChECCGEEEIIM9JBFkIIIYQQwox0kIUQQgghhDAjHWQhhBBCCCHMSAdZCCGEEEIIM9JB\nFkIIIYQQwozF27wJIYQQInNVqOSe8MTSF1K4ublkWn2EyG2kgyxETqAD4rH4D2LBIm6cOflP5tRJ\nCJFhwm6Hgl8yBfzM/hNCpDvpIAuRE8T/93+/5IuF+SV3xkkIIcRL0z05SZH82Xs5UWEdpIMsAPDw\ncCIiQvOCqYmfX+7qqoiIyPg6iWc4hIOfsljMzS1hH124EJkJlRJCpKenWayS/0LsEJ5JNRIm8STs\nk2nh8PjFWRx2W3LYGkgHWQAQEaEhNPRRCsa9IZ3jrDLqFctl/CA09CFubs4ZXh0hRPp7ksVubi4y\nfCK7spTFfpLD1kA6yCIRi+PenkhJGSGEEEKIHEhu8yaEEEIIIYQZi2eQlVL4+fkRHByMnZ0dU6ZM\noVixYqbpmzdvZtOmTdja2uLr60ujRo24ffs2Y8aMwWAwADBp0iRKlCiRYY0QQghrJjkshBCZy+IZ\n5N27d6PX69m4cSPDhw/H39/fNO3u3busXbuWTZs2sXz5cgICAoiLi2Pu3Ln06NGDtWvXMnDgQAIC\nAjK0EUIIYc0kh4UQInNZPIMcFBSEp6cnAJUqVeL06dOmaadOnaJatWrY2Njg5OREiRIlCA4OZtSo\nUTg7JwxONxgM2NvbJ7lskXnkpvNC5FySw0IIkbksdpAjIyNNIQtgY2OD0WhEq9U+N83R0ZFHjx7h\n6uoKwOXLl5k5cyYLFizIgKqL1JCbzguRc0kOCyFE5rLYQXZyciIqKsr0+kkoP5kWGfn0Hn9RUVG4\nuCSchTx8+DCTJk1i5syZLxz3ptNpcXS0S0v9sxVbW51VtUfkTE+OwbQci1l5HMvn6HmSw6mT04+h\nnFx3kSA9cjg95n9ZOf0zlB4sdpCrVq1KYGAgXl5enDhxAg8PD9O0ihUr8tVXX6HX64mNjeXy5cu8\n+eabHD58mKlTp7J8+XKKFCnywmXHxxuJjtanT0uyAUdHO6tqj8iZEo5B+zQdi1l5HFvb5yhv3rQP\nbZAcTp2cfQyl7bMrsof0yOGny8l8OfszlLTUZrHFDnLz5s05ePAg3t7eAPj7+7N69WqKFy9O48aN\n6dGjB127dkUpxbBhw7Czs8Pf3x+DwcDIkSNRSlGqVCkmTJjwci0SQohcTnLYesj1IELkDBY7yBqN\n5rlQLVmypOnvjh070rFjx0TTf/jhh3SqnhBCCMlh6yHXgwiRM8iDQoQQQgghhDAjj5oWQgghhEgv\nOv4bJmN5uEzBIm6cOflP5tRLpIp0kIUQQggh0ks8KR4qE+aX3Hh0kZVkiIUQQgghhBBm5AyylfPw\ncCIiQgOo5L/JOoRnUo1EZnB1Vbi5Oaeo3IULkRbLCSFe3tMcBsniXMQhHPyUxWJubpLF2ZF0kK1c\nRISG0NBHCeOg/LK6NiKzpDRoU9KJFkKkzZMcBiSLc5NRr1gu4wehoQ8li7Mh6SALYU1MF4ckTy4M\nEUIIIV5MOshCWJMnF4dYIBeGCCGEEC8mF+kJIYQQQghhRjrIQgghhBBCmJEOshBCCCGEEGZkDHIO\nV6GSO2G3kxtPavlJPkIIIYQQ4inpIOdAie+pGZJ8YYdwGIXcVkgkKen7JSvc3JIuK/fpFOKpxFmc\nnHDc3FJwyy+R+5juPHQPN7cCz0x8PoslhzOPdJBzILmnpkgvSQWtm5sLoaEPk3hf7tMphLmXus98\nSsuJ3MF056EkvkD58fR48ZP7JWc2ix1kpRR+fn4EBwdjZ2fHlClTKFasmGn65s2b2bRpE7a2tvj6\n+tKoUSPu37/PZ599RmxsLG5ubvj7+2Nvb5+hDRFCpIKF+yU/mSb3S84eJIeFECJzWewg7969G71e\nz8aNGzl58iT+/v4sXLgQgLt377J27Vq2b9/O48eP6dKlC/Xq1WPBggW89957tGnThqVLl7JhwwZ6\n9+6d0W2xKsmPLZZxxSKNkrtfst/TaXK/5OxBclgIITKXxQ5yUFAQnp6eAFSqVInTp0+bpp06dYpq\n1aphY2ODk5MTJUqU4Pz58xw/fpxBgwYB0KBBA7766isJ5hRI8djiJ+OKQX6uE5km6fHKSZeTMXLp\nS3I486R8XHHCsS5Epkh2rHLSJIvTxmIHOTIyEmfnp/8o2tjYYDQa0Wq1z03LmzcvkZGRREVFmd7P\nmzcvjx49SnLZO3f+TGysIdn1Ozo64unZMEWNyelkbLHIdlL46GqNnQalT+gsRES8+BcO83KWyPCO\npzIyh//88xjXr9+yWAcPjzKULFkqjS3JHiz9QgcJHWRLx2tEBEle0CpEukturLI5P0zXkMh45bSx\n2EF2cnIiKirK9PpJKD+ZFhn59NtJZGQkLi4upoAuUKBAopB+VseO7dJa/2wnb96XH+OnFIDzf3+n\n8MzE+BQuPLuXy8p1Z/dymb3u8S/4O1XkzFp6ysgcbtiwfsZWPoskl8Whtyzc/Scjj9/snje5Jeey\nQzlLZV8mi83KmfcpXkZa+jPWwOKDQqpWrcrevXsBOHHiBB4eHqZpFStWJCgoCL1ez6NHj7h8+TJv\nvvlmonn27dtH9erVM6j6Qghh/SSHhRAic2mUhVOV5ldPA/j7+7N3716KFy9O48aN2bJlC5s2bUIp\nxaBBg2jWrBn37t1j5MiRREdHkz9/fgICAnBwcMiUBgkhhLWRHBZCiMxlsYMshBBCCCFEbmJxiIUQ\nQgghhBC5SaY/Sc/SDe9zqrZt25ougilatChTp07N4hq9nJMnTzJr1izWrl3LtWvXGDVqFFqtljff\nfJPx41/6iq0sZd6ms2fP4uvrS4kSJQDo0qULLVq0yNoKppDBYGDMmDHcvHmTuLg4fH19cXd3z9H7\nKKk2FS5cOMfuI6PRyLhx4/j333/RarVMmDABOzu7bLmPrDGLrSWHwfqy2FpyGKwvi60thyGdslhl\nsl9//VWNGjVKKaXUiRMn1KBBgzK7CukuNjZWtW3bNqurkWbLli1TrVu3Vp07d1ZKKeXr66uOHTum\nlFLqyy+/VL/99ltWVu+lPNumzZs3q1WrVmVtpV7S1q1b1dSpU5VSSkVERKhGjRrl+H1k3qb79++r\nRo0aqS1btuTYffTbb7+pMWPGKKWUOnLkiBo0aFC23UfWlsXWksNKWV8WW1MOK2V9WWxtOaxU+mRx\npg+xSO6G9znV+fPniY6OxsfHh969e3Py5MmsrtJLKV68OAsWLDC9PnPmjOnK9wYNGvDHH39kVdVe\nWlJt2rNnD927d2fs2LFER0dnYe1Sp0WLFgwZMgRI+Has0+k4e/Zsjt5H5m1SSmFjY8OZM2cIDAzM\nkfuoWbNmTJo0CYBbt26RL1++bLuPrC2LrSWHwfqy2JpyGKwvi60thyF9sjjTO8gvuuF9Tubg4ICP\njw8rVqzAz8+Pzz77LEe2qXnz5uh0OtNrZXb9ZnIPGsjOnm1TpUqVGDFiBOvWraNYsWLMnz8/C2uX\nOnny5MHR0ZHIyEiGDBnCp59+muP30bNtGjp0KBUrVmTkyJE5ch8BaLVaRo0axeTJk2ndunW23UfW\nlsXWksNgfVlsTTkM1pfF1pjDkPYszvQOcnI3vM+pSpQowfvvv2/629XVlbCwsCyuVdqZ75eoqChc\nXCw/US27a9asGeXLlwcSQvv8+fNZXKPUuX37Nr169aJt27a0atXKKvbRs23K6fsIYNq0afzyyy+M\nGzeO2NhY0/vZaR9ZWxZbaw6D9WWxNXzGrS2LrTGHIW1ZnOlpmNwN73OqrVu3Mm3aNABCQkKIioqi\nYMGCWVyrtCtfvjzHjh0DEh40UK1atSyuUdr5+Pjw999/A/DHH39QoUKFLK5Ryt29excfHx8+//xz\n2rZtC0C5cuVy9D5Kqk05eR/98MMPLF26FAB7e3u0Wi1vvfUWR48eBbLXPrK2LLbWHAbry+Kc/BkH\n68tia8thSJ8szvT7IKskbnhfsmTJzKxCuouLi2P06NHcunULrVbLZ599RuXKlbO6Wi/l5s2bDB8+\nnI0bN3LlyhW++OIL4uLiKF26NJMnT0aj0WR1FVPNvE1nz55l4sSJ2NnZUbBgQSZOnEjevHmzuoop\nMmXKFHbt2kWpUqVQSqHRaBg7diyTJ0/OsfsoqTZ9+umnTJ8+PUfuo5iYGEaPHs3du3cxGAwMHDiQ\nUqVKMW7cuGy3j6wti60ph8H6sthachisL4utLYchfbJYHhQihBBCCCGEmZw74EwIIYQQQogMIB1k\nIYQQQgghzEgHWQghhBBCCDPSQRZCCCGEEMKMdJCFEEIIIYQwIx1kIYQQQgghzEgHWaQrvV7Pli1b\nUj3fn3/+yYULF1JUdvPmzcTHx79w+u3btwkMDAQS7u16584di3Xdvn27aZ700qRJE/R6fbouUwgh\nUkKy+CnJYvEypIMs0lVoaCjfffddqufbunUrISEhKSq7ePHiZEP58OHDHD9+HIDRo0dTuHBhi3Vt\n27YtjRs3TmWtk5dTbhIvhLA+ksVPSRaLl2GT1RUQ1mXJkiVcunSJhQsX0rNnT8aMGcODBw8AGDdu\nHG+++SajR4/m2rVrxMbG0rNnT0qXLs3+/fs5e/Ysb775pilEw8PD+fTTT1FKodfr8fPz4/Tp09y9\ne5dhw4Yxb948vvzyS+7cuUNYWBhNmzbl448/ZunSpcTGxlKlShVWrVrFxIkTuX//PtOnT8fW1hYH\nBwfmzZuXqK5Go5GCBQvSqVMnJk+ezKlTpzAYDAwePJgmTZqY2te+fXvmz5/Pa6+9xv/93/9x/Phx\nfHx8GD9+PHFxcYSGhjJ06FCaNm1qmmf06NG0atWK+vXrs3//fnbu3Im/vz+7du3im2++QafTUa1a\nNYYNG5a5O0sIYbUkiyWLRRopIdLRjRs3VOfOnZVSSs2cOVNt2LBBKaXUlStXVJcuXVRkZKRq3ry5\nCg8PV+Hh4eqnn35SSik1atQotX///kTL2rNnjxoyZIiKjY1Vp0+fVsePH1dKKdWkSROl1+vVjRs3\n1JYtW5RSSsXGxqpatWoppZTatm2bCggIUEop1aNHD3X58mU1ffp0tWrVKmU0GtVvv/2mbt++naiu\n8+fPVxs3blS//fabGjZsmFJKqYcPH6q5c+cmqtOGDRvUggULlFJKDRgwQF28eFEdOnRIHT16VCml\n1PHjx1Xfvn1N9YyNjU3Utn379qlRo0apiIgI1bJlS/X48WOllFKff/65OnToUNp3gBBCKMliyWKR\nVnIGWWSYCxcucOTIEXbu3IlSikePHpE3b15Gjx7NF198QVRUFO+///4L52/QoAFXrlxh0KBB2Nra\nMmjQIACUUiilyJcvH6dOneLIkSPkzZuXuLi455ah/nuSuq+vL4sWLaJXr14ULlyYypUrJ/nT4OXL\nl6lcuTIAzs7OfPLJJ4mmt27dmm7dutGhQweioqJwd3cHYNGiRaafCJOqx7P1uXr1KuHh4fTv3x+l\nFNHR0Vy/fp06deq8cF4hhHgZksXPkywWlsgYZJGutFotRqMRgNKlS9O7d2/WrFnD3Llzee+99wgL\nC+PMmTN8/fXXLFmyhJkzZ2I0GtFoNM+F5JEjRyhYsCArVqzA19eX2bNnA6DT6TAajWzfvp18+fIx\nc+ZM+vTpw+PHj4GE8WZP6vDEjz/+SPv27VmzZg3u7u5s2rQJrVb73Drd3d05deoUAI8ePcLHxyfR\ndCcnJ8qXL4+/vz/t2rUDYO7cubRp04bp06dTq1YtU/A++b+dnR1hYWEAnD17FoCiRYtSpEgRVq1a\nxdq1a+nevTsVK1ZMw5YXQoinJIsli0XayBlkka5eeeUV4uLiCAgIwNfXlzFjxrBx40aioqIYPHgw\nBQsWJCwsDG9vb2xsbPDx8UGr1VKpUiVmz55NsWLFKFWqFABly5Zl2LBhbNiwAaPRyMcffwxAtWrV\nGDBgAOPHj2fYsGGcOHECW1tbSpQoQWhoKGXKlGHJkiWUL1/edHHG22+/zdixY8mTJw86nY6JEyfy\nyiuvYDAYCAgIwN7eHki42vnQoUN07do10TrNderUif79++Pv7w+Al5cX06dPZ+nSpbi5uREREQE8\nvTCkY8eOjBkzhh9//JESJUoAUKBAAXr37k23bt0wGo0ULVqUli1bZtyOEULkKpLFksUibTTqyVcr\nIYQQQgghhAyxEEIIIYQQwpx0kIUQQgghhDAjHWQhhBBCCCHMSAdZCCGEEEIIM9JBFkIIIYQQwox0\nkIUQQgghhDAjHWQhhBBCCCHMSAdZCCGEEEIIM9JBFkIIIYQQwox0kIUQQgghhDAjHWQhhBBCCCHM\nSAdZCCGEEEIIM9JBzkWMRiOrVq2iffv2tG3bltatWzNr1iz0er3Fedu2bUtkZGSK1xUZGUmvXr3S\nUl18fHyIiIh44fSHDx/y/vvvc+bMGdN74eHh9O/fn1atWvHee+/x119/mabt2bOH999/nxYtWjB0\n6FCioqKAhO0ydepUWrRowbvvvsvGjRtN81y9epXu3bvTqlUrOnXqxOXLl9PUpvTUo0cPfv3116yu\nhhAilawtiwGmTJmCr6+v6fXjx48ZPnw4LVu2pEWLFuzevds07eTJk3To0IFWrVrRp08f7t69a5q2\nZMkSUxZ//fXXpveTy/asNnr0aFatWpXV1RDpTYlcY9y4cWrIkCHq0aNHSimlYmJi1IcffqhGjBiR\n7uu6fv26qlKlSpqWUaZMGXX//v0kp+3Zs0e988476q233lKnT582vT9kyBC1ZMkSpZRS586dU56e\nnurx48fq3r17qk6dOuratWtKKaVmzpyp/Pz8lFJKrVu3Tg0YMEAZjUb14MED5eXlpU6dOqWUUqpD\nhw7q559/VkoptXfvXtW6des0tSk9de/eXf3yyy9ZXQ0hRCpZUxYrpdTPP/+sateurQYOHGh6b8aM\nGeqLL75QSil169Yt5enpqe7cuaP0er1q2LCh+uuvv5RSSq1fv171799fKZWQ623btlWPHz9WsbGx\nqnv37mrXrl1KqRdne3YwatQotXLlyqyuhkhnNlndQReZ4+bNm/z0008cPHgQR0dHABwcHJg4cSLH\njx8HEs40TJgwgfPnz6PRaPD09GT48OFotVrKli3L4cOHCQwM5LfffkOr1XL16lVsbW2ZMWMG7u7u\nidY3ZswYHj9+TNu2bdm2bRuXL19m6tSpREREYDQa6dGjB+3atSM6OprRo0dz7do1NBoNb731FhMm\nTGDMmDEA9OzZk2XLllGoUKFEy1+3bh0zZsxg2LBhpvfi4+PZs2cP48ePB6Bs2bKUKFGC/fv3ExMT\nQ8WKFSlWrBgAXbp0oU2bNowfP57ff/+dzp07o9FocHFxoVWrVuzYsQM3Nzf+/fdfWrZsCUCDBg3w\n8/Pj3LlzlCtXLlF95s2bx++//46trS2urq5MmzaNV199le+++47NmzdjMBiIiIhgwIABeHt7s337\ndn755RdiY2O5efMmRYoUoVu3bqxbt46rV6/Sp08fevfuzfbt2/npp59QShESEkLhwoWZNm0aBQsW\nTLT+48ePExAQQExMDDqdjo8++ohGjRpx9+5dRo4cyf379wFo2LAhQ4YMefkDSQiRJtaWxZcuXWLl\nypV8/PHH7N+/3/T+7t27CQgIAKBIkSLUq1ePXbt2UbFiRZydnalcuTIAHTp0wN/fnwcPHrB7925a\nt26Nvb09AO3atWPHjh00b978hdnerFmzRPVZv349mzZtws7ODnt7eyZMmEDp0qUJDAxkyZIlGAwG\nwsPD+eCDDxgyZAhHjx5l9uzZuLm5cfHiRfLkycPgwYNZu3YtV65coXnz5owePZqjR48yY8YMChUq\nxPXr18mTJw/+/v6UKlXque2R0u07ceLElz+QRMbL6h66yBy//PKL6tixY7JlRo4cqaZMmaKUUkqv\n16u+ffuqpUuXKqWUKlu2rLp//77atm2bqlGjhgoJCVFKKTVp0iQ1atSo55Z148YN01kLg8GgWrVq\npc6ePauUUurRo0eqZcuW6uTJk+r7779X/fr1U0opFR8fr7744gvTWd4yZcqoiIiIZOvcuHFj0xnk\nsLAwVbFixUTTP/vsM7V27Vq1ZMkSNX78eNP7BoNBlS1bVkVGRiovLy918uRJ07TNmzerwYMHqxMn\nTqgWLVokWl6XLl3U//73v0Tv3b59W1WrVk3p9XqllFKrVq1Su3fvVlFRUapz586mNpw4ccK0TZ5s\nxzt37iillGrVqpUaMmSIUirh7MiTdmzbtk1VqVJFXb16VSml1KxZs9Qnn3yilHp6BvnBgwfq3Xff\nVTdv3lRKKRUSEqIaNmyobt++rRYsWGBqd3R0tBo2bJjprJUQIvNZUxZHRUWpdu3aqX/++Udt27Yt\n0Rnkt99+W929e9f0es6cOWratGnq559/Nq3niYYNG6rg4GDl4+Nj+sVOKaUOHTqk2rZtm2y2m4uP\nj1dvvfWWCgsLU0op9cMPP6jNmzcrpZTq2bOnKUdDQkJU+fLl1f3799WRI0dUhQoV1Llz55RSSvXr\n1095e3srg8GgwsPDVYUKFVRoaKg6cuSIKl++vAoKClJKKbVhwwbVrl07pdTTM8gvu31F9iRnkHMJ\nrVaL0WhMtsy+fftM429tbW3p0qUL33zzDf3790cpZSpXoUIF3NzcAChfvjy//fZbssu9cuUKVRMn\ntgAAIABJREFU165dY8yYMablxMbGcvbsWerXr89XX31Fjx49qFevHj179jSd5QUSrdcSo9GIRqNJ\n9J5SCq1Wi1LquWkAOp0uye3yZHu9aHnmChUqRLly5Wjbti2enp40aNCAOnXqALB48WICAwO5evUq\n586dIyYmxjTf22+/bTobU7RoUerVqwfAG2+8gV6vN5WtX78+b7zxBgCdOnWiTZs2idb/119/ERYW\nxkcffWTaXlqtluDgYDw9PRk4cCC3bt2ibt26DB8+HCcnJwtbUgiRUawpi8eOHUuPHj0oXbo0J0+e\nTDTt2cx9kp1J5arRaESn0yU5z4syOqks1mq1tGjRgs6dO9OoUSPq16/Pe++9B8CiRYvYs2cPO3bs\nMF1L8iRjX3/9dcqWLQsk5K+zszM6nY78+fPj7OzMgwcPAChTpgxVq1YFoH379kyaNMk0LbXbt1ev\nXom2r8h+pIOcS1SsWJFLly4RHR1t+lkPICQkhC+//JJ58+Y9F1xGoxGDwfDcsp78/AWg0WgsdmLj\n4+NxcXFh+/btpvfu3buHs7MzdnZ2/Prrrxw9epTDhw/Tu3dvvvzyS955551Ut/GVV15BKcXDhw9x\ncXEBIDQ0lMKFC+Pk5JQowO/cuYOLiwsODg689tprhIaGJtomhQsXfu598+WZ02g0rF27ltOnT3Po\n0CH8/f2pXbs2Pj4+dO7cmc6dO1O9enXeffdd9u7da5rP1tY20XKeff2ETqcz/R0fH5/oNSTsJ3d3\ndzZt2pSonq+88go6nY7ff/+dQ4cOcfjwYTp06MDChQtNP28KITKXtWRxSEgIQUFBXLlyhdWrV/Pg\nwQMiIyMZOHAgS5YsoUiRIoSGhlKgQAEgIZPKly9PkSJFCAkJMS3HYDDw4MEDChUqZJrniSd5m1y2\nP2vGjBn8888/HDp0iKVLl7JlyxYCAgJo06YN77zzDtWrV6dDhw7s3r3btL3s7OwSLcPG5mnXyHyb\nJvX+s/mc0u3bq1evl/63TmQOuYtFLuHm5sZ7773HmDFjTFdAPxnnVqBAAezt7fH09GTdunUA6PV6\nNm3aZDqrmVo2Njamb/0lS5bE3t6eHTt2AHD79m1at27NmTNn2LBhA6NGjaJevXoMHz4cT09PLly4\nACQET1L/KLyITqejYcOGpo7i+fPnuXz5MjVr1qR+/fqcOnWKa9euAbB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W1iZry2Jr2z8v\nw2IHuWrVqgQGBuLl5cWJEyfw8PBIspz5mYtq1aqxd+9emjdvzvnz53nttdeSnCc+3pjiU/h792b8\nqf7o6NSV37Pnd7Zu3UzlylUpWrQYbdu2eWF7Vq9ejru7B/XrP/+I0RUrllC0aDHefbclnp41+Pnn\n3RZvBWQu4VZAP/DZZ6M5f/4c3377DZMmTUtdY17A2n5mkfZY5u8/hU8/HZmuy0wNa9tHefPap3kZ\nksPJs/YstrbPBFhfm6wti61t/0Dqs9hiB7l58+YcPHgQb29vAPz9/Vm9ejXFixc3nZ2AxGcuOnbs\niJ+fH507dwZgwoQJqapUTqLRaPDxGWixXFDQsRde2GA+/4su3kjO5cuXCAsLBaBs2XLp1jkWQmQP\nksOWSRYLIdKTxYv0MlJOvDhk+fLF/Pbb/5EvnytFixYjLCyUIkVeo1Sp0vTt25f58+cn+QjQRYvm\nkz9/fgYP/pT9+/fy8OEDbt26Sd26noSH36NUqdJ4e3fH07MG77/flnPnzgKKfv0Sbrmza9dPpkeb\nAqbXn302ikGDfIiKiqJhw8Z4ebVizpwZrFmziaioSGbPns7FixfQaLTUqlUHX9+Ex0Y3aVKP7t17\ncezYYe7du0eHDt506tTlufZa27dIaY9lbm4uhIY+TNdlpoa17aP0uEgvI+XEHIbclcXW9pkA62uT\ntWWxte0fSH0Wy4NCUmH//j3s2xfIN99sZPHilURGRiY6yxAScsfCI0CHmh4BGhsby5o1m/D1/fi5\n9bz+ejFWrlzHuHETmTJlPA8eRABPH236hEaT8IS7fv18qVSpMqNHf/nf+wkF58yZSb58rqxZs4kV\nK9byzz8X2bBhLQBxcXry5y/AokUrmTRpOosXf01cXNrH/gkhREaTLBZCZDTpIKdCUNAxGjZsgoOD\nA1qtllat3k805s/8EaALFsz9b5xbQ7MlPC1bsWLlF66nTZuEe2+WKlWakiVLc/r03y9V3yNH/qB9\n+4SfV21sbGjTpj2HDx8yTX8yBq9MmbIYDHHExDz/2FUhhMhuJIuFEBlNOsipZB7COp0u0TSNRpPi\nR4DmyZPnheswvzo9Pj4eGxub/9b9tExKzjAoZXzutfmTkOztnx2wLs8UFULkDJLFQoiMJB3kVKhV\nqy6BgbuJjIzEaDTyyy87E02/cOFCqh8BmpQnjy0NDj7PrVs3KF/+LVxd8/Pvv5eIi4vDYDCYHpP6\ndNnxzy2nZs06bNu2GUh4VOkPP2ynZs3aSa4zC4eiCyFEqkgWCyEymsW7WIin6tSpx7//XqJfvx44\nO7vg7u5hGpMG4OHhkaJHgCZHo9Fw69ZN+vbthkajZcIEf5ydnalZszaVK1ela9f2vPrqq1SpUp1L\nlxICv0KFt1m2bBFjx35Ohw7epmUNHfoZc+bMpGfPzhgMBmrVqkuPHn1M63l2vUIIkRNIFgshMprc\nxSIdWeNVn9bWJmmPZXIXi/Qld7HIfNZ2DFlbe8D62mRtWWxt+wcy4FHTQuRUFSq5E3Y71GK5gkXc\nOHPyn0yokRBCCCFyAukgC6sVdjsU/FJQzs9yJ1oIIUTqpfREBcjJCpG9SAdZCCGEEBkipScqQE5W\niOxF7mIhhBBCCCGEGekgCyGEEEIIYUY6yEIIIYQQQpiRDrIQQgghhBBmpIOcDs6fP8cXX4xKt+V1\n7Pg+wcHnLazzLLNm+ad62XPmzGDVqmXPvX/79i3GjRuR6uU9ERUVyZAhg1I1T0rb8LJthXvgpyz/\nx72XWLYQIruRLM6OWZzCHJYsFtmMxbtYKKXw8/MjODgYOzs7pkyZQrFixRKVCQ8Pp0uXLvz444/Y\n2dmZ3r906RKdO3fm0KFDid63NmXLlmPSpGmZus7Lly8RFpZ+V/zevn2L69evvfT8Dx8+5Ny5s6ma\nJ6VtePm2FgC/FDyVyk8Bj15i+UJkDsnhlJEszo5ZnMIcBslika1Y7CDv3r0bvV7Pxo0bOXnyJP7+\n/ixcuNA0/cCBAwQEBHDvXuJvfpGRkcyYMQN7e/v0r3UWiYmJYerUCdy8eR2NRkuZMmUZMWIsf/0V\nxJw5M/juu+1MnToBe3sHzp07Q3j4PRo3boara34OHdpHeHg4I0eOo2rV6kydOoFSpUrj7d0d4LnX\nkPCP4ty5AZw7d4bo6CiUglGjxuHmVogVK5YQFRWFv/9ERo/+kgMH9rFmzUoMBgMODg58+OEQ3nrr\nbaKjo5g2bTKXLl3klVdeRavV4uqaP1G7jEYjM2ZM4e7dMIYP/4SAgHn8/fdJFi/+Gr0+FtDQp09/\n6tatT3j4PSZPHs+DBw8AqFu3Pj4+A/H3n0hs7GP69u3GihXrEj0u9eTJE3z99RyUUmg00L17H8qV\nK5+oDaNGfZHitgqR20gOJ5bbsnjp0gVER8eg1Woli4XIJBaHWAQFBeHp6QlApUqVOH36dKLpOp2O\n1atXky9fvkTvf/nllwwbNgwHB4d0rG7W2rcvkJiYaFau/JZly74B4ObNGwCJQujixWCWLl3N8uVr\n2Lx5PXnz5mXRopV06ODNunXfpHh9Z86cJjz8HkuWrGLt2s14ebVk3brVuLkVol8/XypVqszo0V9y\n48Z1li1byKxZ81i5ch2ffz6GsWM/Jzb2McuXL8bBwYFvv/2OiROnce3a1efWo9VqGTlyHK+/XpSA\ngHk8evQIf/+JfPHFJL79diP+/gHMmuVPaGgIO3Zs57XXirJixVoWLFjG9evXiI6OYsyY8djbO7By\n5beJtgXAypVL8fbuzvLlaxg16kuOHz/2XBtS2taM4ubmYvG/CpXcM2z9QiRHcjix3JbFkyf7s2LF\n2lyRxUJkFxbPIEdGRuLs/PT51TY2NhiNRrTahL51nTp1gIRv2E98/fXXNGrUiDJlyiR6P6erWLEy\nS5cuZPDggdSoUYtOnbry+utFCQ0NSVSuXj1PtFotBQq8goNDHmrVSthGr79elEePHqR4fW+99TYu\nLr58//133Lx5k7/+CiJv3rzPlTt27Aj37t1j6NBBpu2t0+m4fv06QUHHGDLkMwBcXV1p0KCxxfWe\nPn2Ke/fuMmbMcDQaDUajEZ1Ox6VLF6lduy6ffz6UkJDbVK9eE1/fwTg65uXhwxc/L75p0+bMmTOd\ngwf3Ub16TQYO/Oil25ph/CwXkZvYi6wiOZxYbsvi4cOHEB9vNC0vO2Rxyp+Ql7pjz83NxWIZeeKe\nyAwWO8hOTk5ERUWZXpuHsjnzb6o7duygcOHCbNmyhbt37+Lj48PatWufm0en0+LomHPGxJUuXYId\nO34mKOhPjh07ytChHzJy5GhcXV3RaDTY2urQ6bTkzZvH1C6NBpycEl7b29ug1Sa02cZGh62tzlRO\nqXjs7GxwdLRDowEHBxuCgg4za9YMevToRfPmzXjzzdLs3Pkzjo522NnpTNtPp9NQq1Yt/P1nmOoa\nEnKHggXd0Gg02Nk9XY+Dg12i9T7h4GCLRqPB0dEOW1stpUqV5ptv1mFrqyMuLp6wsDAKFCiATqfj\np592cfToYY4ePcqAAT2ZPXsur75aEI2GJPent3dnmjVryuHDhzh48ACrVi1j8+atidqwf/++FLU1\nq2WHOphLal+mh6xsZ0a1KSeTHE4st2Xx+vUbiIuLB8g2WZziJ+SlpEwqy4f5hWa7Y9baslhyOAUd\n5KpVqxIYGIiXlxcnTpzAw8MjyXLmZyh+/fVX099NmjRh5cqVSc4TH28kOlqfooqm5nnuLyMl30i/\n//47Tp48wfjxk6lYsRohIaGcPx9M5cpVUUoRFxdPfLwRvd5gapdSEBMTR3S0nthYA0ZjQpudnFw4\ndepvoqP1REREEBQUROnSHkRH61EKHj82cPDgQerW9aRlyw+IjY1l+fLlGAzxREfriY+H2NiE5Vas\nWJXFixdy/vwF3nijBH/8cYBJk8azbdvP1KxZh61bt1KhQmUePXpEYOD/8PJq9dx2j4szEheXsDx3\n93Jcu3aVP/44Qp06tTh58m8+/LAfa9du4fvvv0MpxaBBg6lRox7BwcFcvHiJfPleIT4+Psn9OWhQ\nX3r27EuTJl7UqlWf9u3fIyTkXqI2pLStqZP+4y5TX4eM5eholyF1ysp2ZlSbskrevGk/DiWHE8tt\nWXzkyFHKln2bixeDc2gWp7/sUAdz1pbF1pbDkPostthBbt68OQcPHsTb2xsAf39/Vq9eTfHixWnc\n+OlPRM+OdTJ/Pz1+3kvN89xfavkp+Pncy6s1f/11nO7dO2Jv70DhwoXp2LELFy8Gv3CeF22XDh06\nM3HiF3Tr1oHChV+jatXq5nMB0KZNe/z8xtK7d1e0Wi2VK1dhz57/AVChwtssW7aIsWM/Z8qUmYwY\nMYbx48cAoNPZMH36bBwcHPDxGcDMmf5069aB/PkLULr0m0nWp0SJUmg0GgYM6M3SpauZPHkGCxbM\nZe7cOOLjjXz55SQKFy5Mp05dmDzZj169vLG1tcPd/U2aN/dCq9Xy5ptl6N69IwsXrsDF5enPZB9+\nOISvvprFsmWL0Gi09O07gMKFCxMf/7QNAwd+jJ/fmBS1VYjcRnI4sdyWxV99NZvHj2NRSmWbLBbC\n2mlUFg5Oi4qKTfE3FDc3lwwNZvwgNPTFY7dSwhq/cWXHNqVq7FtKb/OWonJpP0bSW0bsHzc3lyxt\nZ3Y85tKiYEFny4WykLXlMFjfMZQd25PiYyGl+Zqasn6SxRktOx5zaZXaLLZ4BlmI7CbDxr4JIYQQ\nQiAdZJHDeHg4kXBmOCWlw1O41PD/blCfkvUrLlyITOFyhRDCWt0DvwIpKJfSHP6vbIqyODXLFOLl\nSAdZ5CgRERpAk85nkF9J8fIiIqzrdllCCPFyUvqk0tQsM6VZLE/cExnP4oNCxIvt2fPRaZO2AAAg\nAElEQVQ7gwcPZMWKJfzyy85ky65evZwDB/YlOc18fk/PGjx8mPL7cwKcP3+WWbP8//v7HF98MSpV\n8wshRE4mWSyESG9yBjmNNBoNPj4DLZYLCjpGyZKlkpxmPv+LrrROzuXLlwgLS7horWzZckyaNC3V\nyxBCiJxMslgIkZ6kg5xKy5cv5rff/o98+VwpWrQYSimmTp1AqVKl6du3LytWLGH//r3Y2trg4uLK\nmDFfsndvIOfPn2PBgrlotVr279/Lw4cPuHXrJnXrehIefo9SpUrj7d0dpRRLlizg3LmzgKJfv0HU\nrVufXbt+IjDwd2bMmANgev3ZZ6NYsWIJUVFR+PtPxMurFXPmzGDNmk1ERUUye/Z0Ll68gEajpVat\nOvj6foxWq6VJk3p0796LY8cOc+/ePTp08KZTpy5Zu3GFECKFJIuFEBkpx3SQCxZxy9BH/RYs4max\nzP79e9i3L5BvvtmInZ0do0YNT3SWISTkDlu2bOCnn3ZjY2PDpk3fcu7cGdq160hg4G46dPDG07MR\n+/fvJTY2ljVrNgEwdeqEROt5/fVifP75GC5fvsTgwQNYv34rkPAkKHMaDbi5FaJfP1/27Pmd0aO/\n5K+/gkx1mjNnJvnyubJmzSYMBgMjRnzKhg1r6datF3FxevLnL8CiRSsJDj7PoEE+tG3bAVtb27Rs\nRiGEFcsOOQySxUKIjJdjOsjZ4bnrQUHHaNiwCQ4ODgC0avU+33230TTdza0Q7u4e9OnTldq161G7\ndl2qVathtoSnF3hVrFj5hetp06Y9AKVKlaZkydKcPv33S9X3yJE/WLw44elZNjY2tGnTni1bNtCt\nWy8A6tdvAECZMmUxGOKIiYmRUBZCvFB2yGGQLBZCZDy5SC+VzJ+rotPpEk3TaDR8/fVSxo6dQL58\n+Zg3bzbz5gUkuZw8efK8cB1a7dPdEh8fj42NzX/rflomLi4uBXU1PvfaYDCYXtvbP/vYRblDgxAi\nZ5AsFkJkJOkgp0KtWnUJDNxNZGQkRqPxuaulL1y4QI8enShRoiTdu/emc+eu/PPPRSAhwM0DMTk7\nd/4IQHDweW7dukH58m/h6pqff/+9RFxcHAaDgYMHn16FnbDs+OeWU7NmHbZt2wyAXq/nhx+2U7Nm\n7STXmYUPVBRCiFSRLBZCZLQcM8QiO6hTpx7//nuJfv164Ozsgru7Bw8eRJime3h40LTpO/j4dCdP\nHkccHBwYOjThmfX16jVgwYK5Fs82aDQabt26Sd++3dBotEyY4I+zszM1a9amcuWqdO3anldffZUq\nVapz6VJC4Feo8DbLli1i7NjP6dDB27SsoUM/Y86cmfTs2RmDwUCtWnXp0aOPaT3PrlcIIXICyWIh\nREbTqCz8uhoVFWtVz/q2xmeXZ7c2ubk5k6oHhaR3ORShodnnBvUZsX/c3FwIDX2YrstMjex2zKVV\nwYLOWV2FZFlbDoP1HUPZsT1ubs4pf1CIXwoXmtKyftkrh8H6sjg7HnNpldosliEWQgghhBBCmLHY\nQVZKMX78eLy9venZsyfXr19/rkx4eDjvvvsuen3Ct43IyEh8fX3p0aMH3t7enDhxIv1rLoQQuYTk\nsBBCZC6LHeTdu3ej1+vZuHEjw4cPx9/fP9H0AwcO4OPjw71790zvrVq1irp167J27Vr8/f2ZOHFi\n+tdcCCFyCclhIYTIXBYv0gsKCsLT0xOASpUqcfr06UTTdTodq1evpl27dqb3+vTpg52dHQAGgyGJ\nW9gIIYRIKclhIYTIXBY7yJGRkTg7Px3YbGNjg9FoNN0fsk6dOkDiW9M4OTkBEBYWxogRIxg7dmy6\nVloIIXITyWEhhMhcFodYODk5ERUVZXptHsrmnr01TXBwMH379mX48OFUr149HaoqhBC5k+SwEEJk\nLotnkKtWrUpgYCBeXl6cOHECDw+PJMuZn7n4559/GDp0KF999RVlypR54bJ1Oi2OjnYvUe3sydZW\nZ1XtAetsU1plp+2RUfsnK9sox9z/t3fvcVHV+R/HX8xwCxAtg3TLFRXZspRSt7YSV01bu2ypRaFp\nS7EW/n7bTTMvUY630AzTTFtNk9J+inbPLlu2pmllpimrJta6bWokIJKAym2+vz/IcVBkhtsAw/v5\nePSQ4XzPme/3XN59OHPmnDMph6vH2/YhbxtPXWhs68Pbslj7nBsF8oABA9i0aRNxceU3PU9OTiY1\nNZX27dvTt29fRzvnMxezZ8+muLiY6dOnY4whNDSU+fPnn7HssjK7V91nr7L7Bu7Zs5s1a97m0Ucn\n1Hi5sbG3MG3a0/zudxdX+P2aNW9RWlrKoEG312i5X3yxkd27d5GQcP9Z25w+ptTUxURGRtGrV+8q\nl+1uO2eXRkeSnZnlolXDP2WqMe2z9XWvyoYco7fdfzM4uPbX/iqHq8fbsriy8dRnFrunYa9pb2z7\nrLdlsbflMFQ/i10WyD4+PkyePLnC7zp06HBGu08++cTx84IFC6rVCW+2b9+/yc52VfTVTHr6Djp2\n7FTj+b/9djf5+dW7CfnWrVvo0KFjnbVzlp2Z5fom8a6mi3gh5XDtKYtFpDr0qOlqMMbw3HOz2b17\nJ8eOFWIMjB+fxGWXdeP48eM8/fQ0vvlmG76+vvTq9UcGD76dJUsWUlhYSHLyFAYOvIlnn32aV15J\nA+Cbb7Y6Xh85ksvTTz9FXl4uhw8fpk2btkyZMoNWrVpV2pcNGz5l48YNfP31VwQEBDJ48O288spL\nrF+/DmPstGnzG8aMGUfr1uezfv0/efnll7BaLVgsVv7nfx7Cz8+Xt99+HbvdEBwcwsiRoyosf8mS\nhXz22XoCAvwJCQll4sQnWb9+HXv2fMv8+XOxWCxERHRk9uyZHD9+nMOHc4iMjGLKlGTeffetCu1i\nYvrU96YRkWakuWXxpk0bsFqthIa2UhaLeIgK5GrYtWsnhw/nsHDhUgCWL09l+fJUZsyYzeLFL1BS\nUsyKFW9QWlrKI4/8L1dddTV//Wsin376CRMmPMk332w940s0J1+vXfsRXbt2Y9iwuwEYO/Yh/vGP\n97jzzrsq7Uvv3n3YuHE9HTt2YvDg2/nww/f497+/58UXX8ZisfDOO28yY8ZUZs2ay4IFzzFp0jS6\ndLmMLVs28803XxMf/1duvfU2jh795YxAzso6xOrVK1izZi2hoUEsXbqUb7/dxZAhsaxbt5bbb48j\nJqYPCxbM5YYb/sz11w+ktLSUhIQRfP75Rqd2d3pXIFuBsvLHf1YlrG04u3Z875k+iTRDzS2LP/lk\nPSUlhrS0V5XFIh6iArkaLrusK6Ghibz11mscPHiQb77ZSnBwMABff72FsWMfA8pvwTRv3kIAMjN/\ncmvZsbFx7NixnbS0V9m/fz//+c8+Lr20q9t9+/zzjXz77W4SEoYDYLcbioqKAOjf/09MmPAo11zT\ni549r+Kuu/5S5bLCwsKJjIzinnuG0atXDD17/oEePX7v1KL8OuBRox5ky5bN/N//vcL+/T9y+HAO\nx48fc7vPTU7Zr//aqm6Wbaufj3FFpFxzy+Jhw+7gyiuv4Q9/uEZZLOIhKpCr4fPPN/LccynExQ0n\nJuaPtG/fno8++hAov1G/8xmJrKxDBAYGVpjfx8enwrfMS0tLHD8vWPAcGRnfctNNt9C9++8pKyut\n0NYVu72Mu+66m0GDbvt12aUcPfoLACNHjuKmm25hy5bNfPDBu7z6aiovvfTqWZfl4+PD888vYs+e\nb0lP38pzz82mR4+ePPjgmArtJk2aiN1up1+/AVxzTQyHDv1crT6LiNREc8viH374no0bNyqLRTzI\n5X2Q5ZSvv97Mtdf2ZtCg2/jd7y5hw4b12O12AHr2vJI1a97BGENxcTFJSePYvv0brFYrJSWlALRq\ndS6HDv1MXl4exhg2bFjvWPaWLV8SGzuU66+/gVatWrFly2bHss/GarVSWlq+7CuvvJo1a97m2LHy\ne6UuWrSAadMmUVZWRmzsLZw4cZxbbx3CmDHj+e9/f6C0tLTC/M6+//47Roy4g4iIDsTH38uddw7j\n+++/O+M9t2zZzD33jKRfv/4YY9i9e6ejz2dbtohIbTW3LO7QoQPDh8d7JIsvjY4kPDzU5X8NzZ0+\nXhod2dDdlCZMZ5CrYdCg27DZHic+fhgWi4XLL7+CTz/9JwD33nsf8+fPJj5+KHa7neuuu57evftw\n8OABXnzxBR5/fCzTp8/illuGkJAwnPPPD+Oaa3o5lh0fP5Lnn59DaupirFYr0dGXc+DA/l+n+lTS\nG/jDH67h2WdnATB8eDzZ2Vncd989WCw+XHBBGyZOtGG1WnnooTFMnpyE1eqL1Wph4sRJ+Pr60qPH\n70lKGoevrx8PP/yoY7mRkZ257rrrSUgYTnBwMP7+ATz88FgArr22N/Pnz6WkpIT77/8fJkwYQ8uW\nLQkICOSKK3o4+uzcbuDAm+p6U4hIM9bcsviuu+IIDDyHwMDAes9it+4mBA1/RyE33l+Xu0lt+JgG\n/BymsLDIq+6z5433DfTUmKKiQsjLq/x/PhUE5sKJ1u4HeF23CzwMJ85z2bRVK8PevQVuLLR26mP7\nhIeHkpVVvVtO1SVvO47Cwlq4btSAvC2Hwfv2oUaXwwDkgq2162Y23C+m3W1rOwy4zmFQFteUtx1D\nUP0s1hlkaRTKQ9mn8Z+5GO/e/xDy8nT9n4g0LU0mh3H/JImyWGqqyRTIvXtfxZ4939bb8i+++BI2\nbNhcb8sXEWnqlMMi0lw0mQK5sYXmCy/Mo2fPK/n976+q9rx2u53nn3+WzZu/oKzMTlzcXY5vPLvb\n7sCB/cyYMZW8vDyCgoJISrLx299GAOVfCvnnP9cSFHQOl13WjQceGI2fnx+rVq0gNDRU1wSLSI0o\nh93P4bfeep3XX0/DavWlbdvfMGHCE4SGtlQOizQRuotFDezatZMff/yhRqEM8Pbbb3DgwH6WL1/N\niy++zOrVK9izZ3e12k2enMTgwbezfPkq7r33PpKSxgHw3nvv8OWXm3jppWW89NKrnHdeaxYtKn/k\n7O2338mqVSs4ciS3hiMXEWkcGnMOZ2b+xOLFL7BgwRJSU/+PNm3asmRJ+f2YlcMiTUOTOYPcmLz0\n0iJuv/0OvvlmKwsWzOX888P56aeDBAWdw4QJT/Lb30YwZ84zpKd/U2E+Pz9/Fi5cyoYN67j11iH4\n+PjQokULrrvuev7xjw+4+OIuFdqfrd3554exf/9/ue6664Hyb1CnpMzku+8y2Lt3DzExfQgKKr9p\n/h//2I/HHnuY//3fh7BYLPTr15/ly1N54IHRnllZIiL14Gw5HBgYyNSp0wgPv7ABcngG332XQVBQ\nMKWlZRQWFhAcHMyJEycICQkBUA6LNBEqkKupoKCA9PTtzJw5m3/9awd792bw4INj6No1mvfff5sp\nU55k8eJXKtyq53RZWYcID7/A8To8PJx9+858NPHZ2h06dIjzzw+r0DYsLIysrCy6dLmMVatWMGRI\nLKGhLfnww/c4fPiwo9211/Zm7NiHFMwi0mRVlcNvvfU6SUkTWbTo5QbI4XCysrK49toYhg4dzrBh\nt9GiRQuCg0P4+9+XOtoph0UaPxXI1XTgwH5atz4fX9/yVRcZGUXXrtEA3HrrIGbOfIqjR4/y0kuL\n2LFjW4V5/f0DWLhwKXa7vcKTnowBi8V6xnudrZ0xdk6/H6cxBovFwp/+dCPZ2Vk8+OAogoLO4ZZb\nhuDnd2ozX3jhRRw69DMlJSX4+fnVen2IiHhaVTl88823MmfOrAbN4S1bvmT9+nW8+eb7tGzZigUL\n5jJ9+iRmznwWUA6LNAUuC2RjDDabjYyMDPz9/Zk+fTrt2rWr0CY3N5ehQ4fy7rvv4u/vT1FREWPH\njuXw4cOEhIQwY8YMzj333HobhCeVP6L01FOVrNZTgXryltJWq6XKMxcXXNCGnJxsx+ucnGzCwsLd\nbnf678un5RAefgFHjx6lf/+BDB8eD8Du3Tu58MJT28tut2OxWCoEvog0bsrhiqrK4VNPkGu4HH7n\nnTfo1as3LVu2AmDIkDu4++64Cn1UDos0bi6/pLd27VqKi4tZuXIlY8aMITk5ucL0jRs3kpCQUOFj\n/BUrVhAVFcWrr77KrbfeyoIFC+q+5w3kwgsvIjc3l5KSEgC++y7D8bHcG2+8Rteu0QQHh1S5jJiY\nP/Lee+9QVlZGfn4+n3zyEb1793GzXV/CwsJp164dn3zyMQCbN3+B1WqhU6dIMjJ2M3Hio5SWllJa\nWsqyZalcf/1AxzJ/+ukAbdv+xnHmRUQaP+VwRVXl8DvvvEG3bg2bw1FRF/PFFxs5fvw4AOvWfcKl\nl17mWKZyWKTxc3l0bt26lZiYGACio6PZuXNnhelWq5XU1FSGDBlSYZ6RI0cC0Lt3b68K5pCQEKKj\nL2fbtq/x9/d33CUiM/Mnzj//fJKSprhcxqBBt/PTTweJjx9KaWkpgwbdRnT0FQCObzonJNx/lnaX\nA2CzPcWMGVN5+eXFBAQEMHXqTAB+//s/sH37N8THD8UYQ+/efbnzzrsc7/3ll1/Qt2//ul4tIlKP\nlMMVVZXD5557HlOnPuVyGfWZwzfddAs//5xJQsJw/P0DaNOmDY8/bnO8t3JYpPFzWSAXFBTQosWp\nx/P5+vo6Ph4CuPrqq4FTlxecnOfkN3aDg4MpKKj/xzx6Unz8X3nllZcYOnTErx9dzgbcfzSj1Wo9\n65czEhLud6vdhRdexLx5CyudNnLkKEaOHHXG78vKyvjoow949tn5LvsoIo2HcvhMZ8thcC+L6zuH\nExLur7Cck5TDIk2DywI5JCSEwsJCx2vnUHbmfC2V8zyFhYUVgt2Z1WohKMi/2p1uaFde2ZNNmz7F\nx6f8yxsnx+DnZ23U43n11WWMGDGCCy+8wHXjXzX2MTVmnlhv9bV9GnKba587k3L4TGfLYWjc+5By\n2POUxdWnfc6NArl79+6sW7eOgQMHsn37dqKioipt53zmonv37qxfv56uXbuyfv16evbsWek8ZWV2\nt864Nkb33/8gAKmpKxxjcPcMckMZPPhOgGr10XNjCvDAe3iWJ9ZbfW2fhtyPG/txVF3BwbXft5XD\nlassh6Fx70PKYc9TFldfYz6Gaqq6WeyyQB4wYACbNm0iLq78G7jJycmkpqbSvn17+vbt62jnfOZi\n6NChjBs3jmHDhuHv709KSkq1OiUiIqcoh0VEPMtlgezj48PkyZMr/K5Dhw5ntPvkk08cPwcGBjJ3\n7tw66J6IiCiHRUQ8y+Vt3kREREREmhMVyCIiIiIiTlQgi4iIiIg4UYEsIiIiIuJEBbKIiIiIiBMV\nyCIiIiIiTlQgi4iIiIg4UYEsIiIiIuJEBbKIiIiIiBMVyCIiIiIiTlQgi4iIiIg4UYEsIiIiIuJE\nBbKIiIiIiBPfhu6AeLdLoyPJzsxyo6Wp976IiDRX7mWxcljkJJcFsjEGm81GRkYG/v7+TJ8+nXbt\n2jmmr1q1irS0NPz8/EhMTKRPnz5kZmby2GOPAdCyZUtSUlIICAiov1FIo5WdmQU2Nxq600akmVIO\nS225lcWupjc1VqAMwsNDq2wW1jacXTu+90yfpMlweYnF2rVrKS4uZuXKlYwZM4bk5GTHtJycHJYt\nW0ZaWhqLFy8mJSWFkpISUlNTufHGG1m2bBmdOnXitddeq9dBiIh4M+WwSA2U/fqvrer/3PuUU5ob\nlwXy1q1biYmJASA6OpqdO3c6pqWnp9OjRw98fX0JCQkhIiKCjIwMLrnkEn755RcACgsL8fXVlRwi\nIjWlHBYR8SyXiVlQUECLFi1OzeDri91ux2KxnDEtKCiI/Px8LrjgAp555hnWrFlDSUkJDzzwQP30\nXhq1qKgQwLj3sV1gLpyo5w55ihUoyyU8/Dy3mrdqZdi7t6B++yRNmnJYasPtLPamHD4pMBdsrq+t\njopSDktFLgvkkJAQCgsLHa9PhvLJaQUFp3aowsJCQkNDeeKJJ3j66ae55pprWL9+PY899hgLFy48\nY9lWq4WgIP+6GEej4Odn9arxQO3GlJfnA/i4f12bu+0auzLA1tp1OxsUFJwgJCSgxuu4vva5htyP\nvfE4qi3lcPV42z5U2/FUK4vdadOUjHcvi/PyTK3WsbdlsbcdQzXhskDu3r0769atY+DAgWzfvp2o\nqCjHtG7dujFnzhyKi4spKipi3759dO7cmZYtWxISEgJAWFgYR48erXTZZWV2jh0rrqOhNLygIH+v\nGg/Udkz6QpAr5es2oMbruL72uYbcj73tOAoOrv1xoByuHm/bh2o/HmWxO2qzjr0ti73tGILqZ7HL\nAnnAgAFs2rSJuLg4AJKTk0lNTaV9+/b07duXESNGMGzYMIwxjB49Gn9/f5KSkpgyZQp2ux2ASZMm\n1WAoIiICymEREU9zWSD7+PgwefLkCr/r0KGD4+fY2FhiY2MrTO/UqRMvv/xyHXVRRKR5Uw6LiHiW\nnqQnIiIiIuJEBbKIiIiIiBMVyCIiIiIiTlQgi4iIiIg4UYEsIiIiIuJEBbKIiIiIiBMVyCIiIiIi\nTlQgi4iIiIg4UYEsIiIiIuJEBbKIiIiIiBMVyCIiIiIiTlQgi4iIiIg4UYEsIiIiIuJEBbKIiIiI\niBNfVw2MMdhsNjIyMvD392f69Om0a9fOMX3VqlWkpaXh5+dHYmIiffr04fjx49hsNg4ePEhJSQlJ\nSUl07dq1XgciIuKtlMMiIp7lskBeu3YtxcXFrFy5kh07dpCcnMyCBQsAyMnJYdmyZbz55pucOHGC\noUOHcu2117JkyRKioqKYOXMmGRkZZGRkKJhFRGpIOSwi4lkuL7HYunUrMTExAERHR7Nz507HtPT0\ndHr06IGvry8hISFERESwZ88eNm7ciK+vLwkJCbzwwgv06tWr/kYgIuLllMMiIp7lskAuKCigRYsW\njte+vr7Y7fZKpwUFBVFQUMCRI0fIz89nyZIl9OnTh5kzZ9ZD10VEmgflsIiIZ7m8xCIkJITCwkLH\na7vdjsVicUwrKChwTCssLCQ0NJRzzz2Xfv36AdCvXz8WL15c6bKtVgtBQf61GkBj4udn9arxgHeO\nqTE5uW5ruo7ra/s05DbXPncm5XD1eNs+5G3jaaxqs469LYu1z7lRIHfv3p1169YxcOBAtm/fTlRU\nlGNat27dmDNnDsXFxRQVFbFv3z46d+7MFVdcwfr16+nSpQtfffUVkZGRlS67rMzOsWPFdTeaBhYU\n5O9V44HajimgTvvijcrXbUCN13F97XMNuR9723EUHFz740A5XD3etg/VfjzKYnfUZh17WxZ72zEE\n1c9ilwXygAED2LRpE3FxcQAkJyeTmppK+/bt6du3LyNGjGDYsGEYYxg9ejT+/v4kJiaSlJREXFwc\nfn5++mhPRKQWlMMiIp7lskD28fFh8uTJFX7XoUMHx8+xsbHExsZWmN6yZUvmzZtXR10UEWnelMMi\nIp6lB4WIiIiIiDhRgSwiIiIi4kQFsoiIiIiIExXIIiIiIiJOXH5JT0RERMRrWYEyCA8PrbJZWNtw\ndu343jN9kganAllq5NLoSLIzs1y0Mh7pi4hIc6UsrgNlv/5rq7pZts3VehZvogJZqi0qKoS8vEOu\nGwbmwon6709T16qVITy8hVvt9u4tcNlORLxfeQ77AMriOhGYCzbXf0iEhyuLmwsVyFJt5aHs4/Kv\nbcC9Ns2cu0HrThEtIs1DXp4PWVn55ZcF2NyYwZ02zdn41q7b2CAr66iyuJlQgSzSUKyur3k7Kaxt\nOG6dKRIRE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10, 7))\n", "for ind, iters in enumerate([1000, 5000, 10000, 40000]):\n", " plt.subplot(2, 2, ind + 1)\n", " coin_test = CoinTossTest([22, 8])\n", " pval = coin_test.PValue(iters=iters)\n", " plot_analytical_coin()\n", " plot_simulated_distribution(coin_test, \"Coin test {} samples\".format(iters), \n", " range=(0, 30), bins=31)\n", " plt.xlim(0, 30)\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What we see here, is that the sampled distribution, even with as low as 1000 samples, gives an estimate close to the correct answer, which is 0.8 %." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now move on to the next study case." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Second test: difference in means " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The second problem is as follows:\n", "\n", "> A group of start sneeches got the following scores 84, 72, 57, 46, 63, 76, 99, 91 while a group of cross sneeches got these scores 81, 69, 74, 61, 56, 87, 69, 65, 66, 44, 62, 69. There's a difference in means between the two groups (73.5 for the stars, 66.9 for the crosses) but it is significant?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, let's describe our test setting:\n", "\n", "- our data is a list of scores for the two groups: it's a list of length 2 that contains all the values [[84, 72, 57, 46, 63, 76, 99, 91], [81, 69, 74, 61, 56, 87, 69, 65, 66, 44, 62, 69]]\n", "- our model under the $\\mathcal{H_0}$ hypothesis is that there is no difference between the two samples: each group comes from the same distribution of score values\n", "- the test statistic is the same as in Welch's t-test \n", "$$ \n", "t = \\frac{\\bar{X}_1 - \\bar{X}_2}{\\sqrt{\\frac{s_1^2}{n_1} + \\frac{s_2^2}{n_2}}}\n", "$$\n", "\n", "\n", "Let's implement the statistical test for this case using the simulation methodology:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class MeanTest(HypothesisTest):\n", " \"\"\"Test for checking if the difference in means of samples is significant.\"\"\"\n", " \n", " def TestStatistic(self, data):\n", " \"Computes Welch's t-test statistic.\"\n", " group1, group2 = data\n", " n1, n2 = len(group1), len(group2)\n", " s1, s2 = np.var(group1, ddof=1), np.var(group2, ddof=1)\n", " m1, m2 = np.mean(group1), np.mean(group2)\n", " return (m1 - m2) / np.sqrt(s1/n1 + s2/n2)\n", "\n", " def RunModel(self):\n", " \"Shuffles the existing data and splits it into two subgroups.\"\n", " group1, group2 = self.data[:]\n", " pool = group1 + group2\n", " random.shuffle(pool)\n", " return pool[:len(group1)], pool[len(group1):]" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [], "source": [ "mean_test = MeanTest([[84, 72, 57, 46, 63, 76, 99, 91], \n", " [81, 69, 74, 61, 56, 87, 69, 65, 66, 44, 62, 69]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's check that we implemented the right test statistic: we expect a value of 0.932 (taken from Jake's slides)." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.93161477717115826" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mean_test.actual" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's see if we generate random samples correctly:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "([81, 69, 62, 61, 69, 74, 87, 69],\n", " [72, 63, 57, 46, 65, 84, 99, 76, 56, 66, 91, 44])" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mean_test.RunModel()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, let's compute a p-value:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.176" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mean_test.PValue()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What does the sampled test statistic distribution under the $\\mathcal{H_0}$ hypothesis look like?" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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4OTmRlpZmfJx7pJ5XYGAgvXr1YsiQIfz88880bdrUOHl0ixYtSEws/CYenU5L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\nAXN+Zcl1FGtjsitkTEwMPj4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_simulated_distribution(mean_test, \"Difference in means test\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, we will compare the real distribution with the sampled one. Let's write a function that does just that. It turns out that Jake has already put all the information regarding this in his slides. The test statistic has the following probability density:\n", "\n", "$$\n", "p(t; \\nu) = \\frac{\\Gamma(\\frac{\\nu + 1}{2})}{\\sqrt{\\nu \\pi} \\Gamma(\\frac{\\nu}{2}) } \\left( 1 + \\frac{t^2}{\\nu}\\right)^{-\\frac{\\nu + 1}{2}}\n", "$$" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from scipy.special import gamma\n", "\n", "def plot_analytical_mean(data=[[84, 72, 57, 46, 63, 76, 99, 91], \n", " [81, 69, 74, 61, 56, 87, 69, 65, 66, 44, 62, 69]]):\n", " \"Plots analytical distribution under H_0 hypothesis of the Welch t-stat with given sample sizes.\"\n", " group1, group2 = data\n", " n1, n2 = len(group1), len(group2)\n", " s1, s2 = np.var(group1, ddof=1), np.var(group2, ddof=1)\n", " m1, m2 = np.mean(group1), np.mean(group2)\n", " \n", " nu = (s1/n1 + s2/n2)**2 / (s1**2 / n1**2 / (n1 - 1) + s2**2 / n2**2 / (n2 - 1))\n", " t = np.arange(-5, 5, 0.01)\n", " density = gamma((nu + 1) / 2) / (np.sqrt(nu * np.pi) * gamma(nu / 2)) * (1 + t**2/nu) ** (-(nu + 1)/2)\n", " \n", " plt.plot(t, density, drawstyle='steps', \n", " label='analytical test stat\\ndistribution')" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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VIOEuLtjpvvaHHpJWe6B5/fVCduzQ8+uvvi6J8DYJd3FBrFbXmu1T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\n91a3bt3q66J43YgRI9R9+/b5uhgelZ6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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_analytical_mean()\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What if we put both plots together, the simulated one and the analytical one?" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Uyf1We7A6WXTbFYQikGdylyQJLy8voqKiMDAwYO7cudSsWVMzPzAwkF27dj0/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\nN24cSUlJ9OzZk3fffbccQhcVRgELToHxBnSfXub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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_analytical_mean()\n", "plot_simulated_distribution(mean_test, \"Difference in means test\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Both distribution look quite similar. Let's check the impact of the number of simulations on the resulting simulated distributions: " ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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J1MuOuroOomrVakyaNO2/79UJly5dSIECZmzZspMNG7Zy585ttm/fCkB8fBwF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\ngMMBJpPWSKWmGsjJMWAyKex2A2azwmzWfpYvXtQKdlCQVvCNR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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10, 7))\n", "for ind, iters in enumerate([1000, 5000, 10000, 40000]):\n", " plt.subplot(2, 2, ind + 1)\n", " mean_test = MeanTest([[84, 72, 57, 46, 63, 76, 99, 91], \n", " [81, 69, 74, 61, 56, 87, 69, 65, 66, 44, 62, 69]])\n", " pval = mean_test.PValue(iters=iters)\n", " plot_analytical_mean()\n", " plot_simulated_distribution(mean_test, \"Mean test {} samples\".format(iters))\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, we see the approximation by simulated sampling is quite good compared with the analytical test statistic. And even if in this case a thousand samples is not very close to the exact density, it seems enough for a good idea of the p-value." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An interesting side note here is that Jake VanderPlas does not actually use the test statistic of the analytical test, but seems instead to have reverted to a different, simpler statistic, the difference in means between the two samples. Let's see if we can reproduce his result:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class MeanTest2(MeanTest):\n", " \"Changes the test statistic to a difference in means.\"\n", " def TestStatistic(self, data):\n", " \"Computes the difference in means between the two samples.\"\n", " group1, group2 = data\n", " m1, m2 = np.mean(group1), np.mean(group2)\n", " return m1 - m2" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": true }, "outputs": [], "source": [ "mean_test2 = MeanTest2([[84, 72, 57, 46, 63, 76, 99, 91], \n", " [81, 69, 74, 61, 56, 87, 69, 65, 66, 44, 62, 69]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The observed effect is:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "6.5833333333333286" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mean_test2.actual" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This value is similar to the one Jake shows on one of his slides. What is the p-value?" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.157" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mean_test2.PValue()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, we find something close to what Jake has. What does the sampled distribution look like?" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Wrl3L/v37Tcolb9F36NCBK1eu0LFjR7Zv306/fv2yFJQluXz5IrNmBWZcMB3t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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_simulated_distribution(mean_test2, \"Difference in means test using a simpler test statistic\", bins=50)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see what this looks with 10000 iterations (which is what Jake seems to use in his presentation):" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(-20, 20)" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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cvn2bpKQkHBwcjOs1adKEgwcP0qpVKxwcHHB1dWXy5MkopZ7oXJcqVYo+ffpw69YtXnnl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\nYv+EEKIQpLf2s/qvRo2a2W5Vo0bNJ9r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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pval = mean_test2.PValue(iters=10000)\n", "plot_simulated_distribution(mean_test2, \"Difference in means test using a simpler test statistic\", bins=50)\n", "plt.xlim(-20, 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Realizing that Jake did not use the \"official\" test statistic for simulation yields interesting questions:\n", "\n", "- are all test statistic equivalent? \n", "- if not, how do I choose one?\n", "- what if two different test statistics yield two different p-values? which one should I trust?\n", "\n", "In my current understanding, I am assuming that not all tests statistics are equal. For instance if I use $t = \\sin(\\bar{X}_1 - \\bar{X}_2)$, I'm not sure that the result will even make sense. You know what let's actually test this." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class MeanTest3(MeanTest):\n", " \"Changes the test statistic to a difference in means.\"\n", " def TestStatistic(self, data):\n", " \"Computes the difference in means between the two samples.\"\n", " group1, group2 = data\n", " m1, m2 = np.mean(group1), np.mean(group2)\n", " return np.sin(m1 - m2)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.4139" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mean_test3 = MeanTest3([[84, 72, 57, 46, 63, 76, 99, 91], \n", " [81, 69, 74, 61, 56, 87, 69, 65, 66, 44, 62, 69]])\n", "mean_test3.PValue(iters=10000)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_simulated_distribution(mean_test3, \"Testing with a silly statistic\", bins=50)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly, what we see above is nonsense: it has not the intuitive bell shape we expect from a well defined test statistic. So that would answer the first question. However, using Welch's t-test statistic and the simple difference in means of two samples is not the same thing. So where's the difference? Hopefully, someone can point me to good references about this topic. \n", "\n", "Following this line of inquiry, I'm also wondering about the result shown in Jake's slides: using two different test statistics, he obtains the same p-value. I'm guessing this is just a coincidence. Or is it not?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Conclusions " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I won't replicate the other parts in Jake Vanderplas' slides (bootstrap resampling and cross-validation) so that this post just focuses on statistics and hypothesis testing.\n", "\n", "As we have seen, the simulation framework proposed by ThinkStats is very simple to apply to the two problems found in Jake Vanderplas' Statistics for Hackers presentation. Moreover, we found through comparison of the exact solution and the approximate simulation solution that both approaches yield the same result. While trying to pinpoint the difference in philosophy, we also saw how the simulation approch is very flexible and allows easily changing from one test statistic to another, which is one of the hard points when doing real statistics (think of all the different names for all these tests...).\n", "\n", "I think I still have many things to learn with respect to this statistical testing topic and I would be grateful for links regarding the simulation/analytical frontier as well as criteria for choices of test statistic." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "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 }