anova.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analysis of variance (ANOVA)\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For generating random variables.\n",
    "import numpy as np\n",
    "# For handling data.\n",
    "import pandas as pd\n",
    "# For plotting.\n",
    "import matplotlib.pyplot as plt\n",
    "# For t-tests and ANOVA.\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Make the plots bigger.\n",
    "plt.rcParams['figure.figsize'] = (20.0, 10.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set parameters for two populations.\n",
    "popA = {'m': 1.6, 's': 0.1}\n",
    "popB = {'m': 1.8, 's': 0.1}\n",
    "\n",
    "# Create two samples, one from each population.\n",
    "sampA = np.random.normal(popA['m'], popA['s'], 100)\n",
    "sampB = np.random.normal(popB['m'], popB['s'], 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# x values for plotting.\n",
    "x = np.linspace(1.25, 2.25, 1000)\n",
    "\n",
    "# The probability density functions (PDFs) for the two populations.\n",
    "pdfA = stats.norm.pdf(x, popA['m'], popA['s'])\n",
    "pdfB = stats.norm.pdf(x, popB['m'], popB['s'])\n",
    "\n",
    "# Plot the population PDFs as shaded regions.\n",
    "plt.fill_between(x, pdfA, color='g', alpha=0.25, label=\"Population A\")\n",
    "plt.fill_between(x, pdfB, color='b', alpha=0.25, label=\"Population B\")\n",
    "\n",
    "# Plot histograms of the two samples.\n",
    "plt.hist(sampA, density=True, color='g', alpha=0.25, label=\"Sample A\")\n",
    "plt.hist(sampB, density=True, color='b', alpha=0.25, label=\"Sample B\")\n",
    "\n",
    "# Display a legend.\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-12.91230805280065, pvalue=4.523197046239019e-28)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate the independent samples t-statistic for the samples.\n",
    "# We also get the probability of seeing samples at least as different as these given the population means are equal.\n",
    "stats.ttest_ind(sampA, sampB)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "#### T-tests with Iris"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepal_length  sepal_width  petal_length  petal_width    species\n",
       "0             5.1          3.5           1.4          0.2     setosa\n",
       "1             4.9          3.0           1.4          0.2     setosa\n",
       "2             4.7          3.2           1.3          0.2     setosa\n",
       "3             4.6          3.1           1.5          0.2     setosa\n",
       "4             5.0          3.6           1.4          0.2     setosa\n",
       "..            ...          ...           ...          ...        ...\n",
       "145           6.7          3.0           5.2          2.3  virginica\n",
       "146           6.3          2.5           5.0          1.9  virginica\n",
       "147           6.5          3.0           5.2          2.0  virginica\n",
       "148           6.2          3.4           5.4          2.3  virginica\n",
       "149           5.9          3.0           5.1          1.8  virginica\n",
       "\n",
       "[150 rows x 5 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('https://raw.githubusercontent.com/uiuc-cse/data-fa14/gh-pages/data/iris.csv')\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = df[df['species'] == 'setosa']\n",
    "r = df[df['species'] == 'versicolor']\n",
    "a = df[df['species'] == 'virginica']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ttest_indResult(statistic=-39.46866259397272, pvalue=5.717463758170621e-62)\n",
      "Ttest_indResult(statistic=-49.965703359355636, pvalue=1.5641224158883576e-71)\n",
      "Ttest_indResult(statistic=-12.603779441384985, pvalue=3.1788195478061495e-22)\n",
      "Ttest_indResult(statistic=-34.01237858829048, pvalue=4.589080615710866e-56)\n",
      "Ttest_indResult(statistic=-42.738229672411165, pvalue=3.582719502316063e-65)\n",
      "Ttest_indResult(statistic=-14.625367047410148, pvalue=2.2304090710248333e-26)\n",
      "Ttest_indResult(statistic=-10.52098626754911, pvalue=8.985235037487077e-18)\n",
      "Ttest_indResult(statistic=-15.386195820079404, pvalue=6.892546060674106e-28)\n",
      "Ttest_indResult(statistic=-5.629165259719801, pvalue=1.7248563024547942e-07)\n",
      "Ttest_indResult(statistic=9.282772555558111, pvalue=4.362239016010214e-15)\n",
      "Ttest_indResult(statistic=6.289384996672061, pvalue=8.916634067006443e-09)\n",
      "Ttest_indResult(statistic=-3.2057607502218186, pvalue=0.0018191004238894803)\n"
     ]
    }
   ],
   "source": [
    "print(stats.ttest_ind(s['petal_length'], r['petal_length']))\n",
    "print(stats.ttest_ind(s['petal_length'], a['petal_length']))\n",
    "print(stats.ttest_ind(r['petal_length'], a['petal_length']))\n",
    "\n",
    "print(stats.ttest_ind(s['petal_width'], r['petal_width']))\n",
    "print(stats.ttest_ind(s['petal_width'], a['petal_width']))\n",
    "print(stats.ttest_ind(r['petal_width'], a['petal_width']))\n",
    "\n",
    "print(stats.ttest_ind(s['sepal_length'], r['sepal_length']))\n",
    "print(stats.ttest_ind(s['sepal_length'], a['sepal_length']))\n",
    "print(stats.ttest_ind(r['sepal_length'], a['sepal_length']))\n",
    "\n",
    "print(stats.ttest_ind(s['sepal_width'], r['sepal_width']))\n",
    "print(stats.ttest_ind(s['sepal_width'], a['sepal_width']))\n",
    "print(stats.ttest_ind(r['sepal_width'], a['sepal_width']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "#### Problems with t-tests\n",
    "\n",
    "Some links about the main problem we encounter with t-testing.\n",
    "\n",
    "***\n",
    "\n",
    "**[Website: Multiple t tests and Type I error](http://grants.hhp.coe.uh.edu/doconnor/PEP6305/Multiple%20t%20tests.htm)**\n",
    "\n",
    "*[http://grants.hhp.coe.uh.edu/doconnor/PEP6305/Multiple%20t%20tests.htm](http://grants.hhp.coe.uh.edu/doconnor/PEP6305/Multiple%20t%20tests.htm)*\n",
    "\n",
    "Webpage about multiple t tests and Type I errors.\n",
    "\n",
    "***\n",
    "\n",
    "**[Wikipedia: Multiple Comparisons Problem](https://en.wikipedia.org/wiki/Multiple_comparisons_problem)**\n",
    "\n",
    "*[https://en.wikipedia.org/wiki/Multiple_comparisons_problem](https://en.wikipedia.org/wiki/Multiple_comparisons_problem)*\n",
    "\n",
    "Wikipedia page about the multiple comparisons problem.\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(r['sepal_length'], label='Versicolor Sepal Length')\n",
    "plt.hist(a['sepal_length'], label='Virginica Sepal Length')\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.45963991233736334"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1- ((0.95)**12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "F_onewayResult(statistic=1179.0343277002194, pvalue=3.0519758018278374e-91)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.f_oneway(s['petal_length'], r['petal_length'], a['petal_length'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(s['petal_length'], label='Setosa Petal Length')\n",
    "plt.hist(r['petal_length'], label='Versicolor Petal Length')\n",
    "plt.hist(a['petal_length'], label='Virginica Petal Length')\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "### About t-tests\n",
    "\n",
    "When performing an independent sample t-test we assume that there is a given difference between the means of two populations, usually a difference of zero.\n",
    "\n",
    "We then look at the samples to investigate how different they are, calculating their t-statistic.\n",
    "\n",
    "We then ask, given the hypothesised difference (usually zero) what was the probability of seeing a t-statistic at least this extreme.\n",
    "\n",
    "If it's too extreme (say, less that 5% chance of seeing it) then we say our hypothesis about the difference must be wrong.\n",
    "\n",
    "***\n",
    "\n",
    "### Errors\n",
    "\n",
    "Of course, we might, by random chance, see a t-statistic that extreme.\n",
    "\n",
    "We might reject the hypothesis incorrectly - the populations might have the hypothesised difference and the samples just randomly happened to be as different as they are.\n",
    "\n",
    "We call that a Type I error.\n",
    "\n",
    "We also might not reject the hypothesis when it's not true - that's a Type II error.\n",
    "\n",
    "![Type I and Type II images from https://en.wikipedia.org/wiki/Type_I_and_type_II_errors](https://github.com/ianmcloughlin/images/raw/master/typeitypeii.png)\n",
    "\n",
    "***\n",
    "\n",
    "### Calculating the t-statistic\n",
    "\n",
    "From the WikiPedia pages for [Student's t-test](https://en.wikipedia.org/wiki/Student%27s_t-test#Equal_or_unequal_sample_sizes,_equal_variance) and [Variance](https://en.wikipedia.org/wiki/Variance#Sample_variance).\n",
    "\n",
    "Note that we are using the calculations for two samples, with equal variances, and possibly different sample sizes.\n",
    "\n",
    "$$ {\\displaystyle t={\\frac {{\\bar {X}}_{1}-{\\bar {X}}_{2}}{s_{p}\\cdot {\\sqrt {{\\frac {1}{n_{1}}}+{\\frac {1}{n_{2}}}}}}}} $$\n",
    "\n",
    "$$ {\\displaystyle s_{p}={\\sqrt {\\frac {\\left(n_{1}-1\\right)s_{X_{1}}^{2}+\\left(n_{2}-1\\right)s_{X_{2}}^{2}}{n_{1}+n_{2}-2}}}} $$\n",
    "\n",
    "$$ {\\displaystyle s^{2}={\\frac {1}{n-1}}\\sum _{i=1}^{n}\\left(Y_{i}-{\\overline {Y}}\\right)^{2}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of sample A:         1.6070\n",
      "Mean of sample B:         1.8008\n",
      "Size of sample A:       100.0000\n",
      "Size of sample B:       100.0000\n",
      "Variance of sample A:     0.0120\n",
      "Variance of sample B:     0.0106\n",
      "Pooled std dev:           0.1061\n",
      "t-statistic:            -12.9123\n"
     ]
    }
   ],
   "source": [
    "# Count the samples.\n",
    "nA = float(len(sampA))\n",
    "nB = float(len(sampB))\n",
    "\n",
    "# Calculate the means.\n",
    "mA = sampA.sum() / nA\n",
    "mB = sampB.sum() / nB\n",
    "\n",
    "# Sample variances.\n",
    "varA = ((sampA - mA)**2).sum() / (nA - 1.0)\n",
    "varB = ((sampB - mB)**2).sum() / (nB - 1.0)\n",
    "\n",
    "# Pooled standard deviation.\n",
    "sp = np.sqrt(((nA - 1.0) * varA + (nB - 1.0) * varB) / (nA + nB - 2.0))\n",
    "\n",
    "# t-statistic\n",
    "t = (mA - mB) / (sp * np.sqrt((1.0 / nA) + (1.0 / nB)))\n",
    "\n",
    "print(f\"Mean of sample A:       {mA:8.4f}\")\n",
    "print(f\"Mean of sample B:       {mB:8.4f}\")\n",
    "print(f\"Size of sample A:       {nA:8.4f}\")\n",
    "print(f\"Size of sample B:       {nB:8.4f}\")\n",
    "print(f\"Variance of sample A:   {varA:8.4f}\")\n",
    "print(f\"Variance of sample B:   {varB:8.4f}\")\n",
    "print(f\"Pooled std dev:         {sp:8.4f}\")\n",
    "print(f\"t-statistic:            {t:8.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Critical values\n",
    "\n",
    "For a two-tail test (e.g. $H_0$: the means are equal) we reject the null hypothesis $H_0$ if the value of the t-statistic from the samples is further away from zero than the t-statistic at the ($0.5 / 2.0 =$) $0.025$ level."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.9720174778338955\n"
     ]
    },
    {
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ql7ScX3YdBQAAHBPKIQAAcORupW8pFoq5joEm9UX7dHX9qlpxhDkAADh8lEMAAOBIbVW3NL0xzULUbaQn0qNMKaN0Ke06CgAAOAaUQwAA4EhNZ6flGU+e4bajncRDcY2lxlzHAAAAx4C7NAAAcGRqjZpurN/QUHzIdRQc0EBsQHO5ORWqBddRAADAEaMcAgAAR2Yxv6h6UFfYD7uOggMyxsgznqaz066jAACAI0Y5BAAAjoS1VtfWrqk/1u86Cu7TcGJYN9dvqtaouY4CAACOEOUQAAA4EqliSrlKTolwwnUU3KeQF1I9qGsxv+g6CgAAOEKUQwAA4EiMpccUD8Vdx8ADGogN6NraNba1BwCgg1EOAQCAQ1eoFjSfm2f7+g4QD8eVq+SUKqZcRwEAAEeEcggAABy6meyMfM+XMcZ1FByCeCiuW+lbrmMAAIAjQjkEAAAOVT2o6+b6TQ3GBl1HwSHpj/VrLjenreqW6ygAAOAIUA4BAIBDtZxfVrVRZfv6DuIZT57xNJubdR0FAAAcAcohAABwaKy1upG6ob5Yn+soOGSD8UHdWL+hRtBwHQUAABwyyiEAAHBosuWsUsWUeiI9rqPgkEX8iKqNqlYKK66jAACAQ0Y5BAAADs3UxpQifsR1DByRnkiPbqRuuI4BAAAOGeUQAAA4FJV6RROZCRai7mC90V6tFdaUK+dcRwEAAIeIcggAAByKxfyiAhvI93zXUXCEwn5Y09lp1zEAAMAhohwCAAAPzFqrG+s3NBAbcB0FR2woPqRb6VuqNWquowAAgENCOQQAAB5YupRWrpJTPBx3HQVHzPd8NYKGlvPLrqMAAIBDQjkEAAAe2GRmUrFQzHUMHJPeaK9upG7IWus6CgAAOASUQwAA4IGU62VNZ6fVH+13HQXHpCfSo3QprWw56zoKAAA4BJRDAADggSzkFiSJhai7TNgLayY74zoGAAA4BJRDAADgvllrdSN1g1FDXWgoPqTxzLiqjarrKAAA4AFRDgEAgPuWLqVVqBZYiLoL3V6YeiW/4joKAAB4QJRDAADgvk1mJhUNRV3HgCO3F6YGAADtjXIIAADcl0q9opnsDFPKulhPpEeZUoaFqQEAaHOUQwAA4L4s5hdlrWUh6i4X8kKazc66jgEAAB4A5RAAADgwa61upm6qP8aooW43GB/UrfQt1YO66ygAAOA+UQ4BAIAD2yhvKFfOsRA1FPJCqgd1FqYGAKCNUQ4BAIADm96YVsgLuY6BFtET6dFYesx1DAAAcJ8ohwAAwIHUGjVNbkxqKD7kOgpaRE+kR2tba8pX8q6jAACA+0A5BAAADmSlsKJG0GAharzBGCPPeJrfnHcdBQAA3AfKIQAAcCA3UzfVG+11HQMtZjA+qLHUmAIbuI4CAAAOiHIIAAA0LV/JK1VMKRlOuo6CFhPxIyrVSlrfWncdBQAAHBDlEAAAaNpcbk6e8WSMcR0FLSgejmsyM+k6BgAAOCDKIQAA0JTABrqVvqXB+KDrKGhR/bF+zW3OqVwvu44CAAAOgHIIAAA0ZX1rXaVaSRE/4joKWpRnPFlrtZRfch0FAAAcAOUQAABoymRmUvFw3HUMtLj+WL9upm7KWus6CgAAaBLlEAAA2Fe5Xtbc5pz6Y/2uo6DFJcIJZctZZctZ11EAAECTKIcAAMC+lvPLstbKM9w6YH9hL6y53JzrGAAAoEnc4QEAgH2NpccYNYSmDcQGNJ4eVz2ou44CAACaQDkEAADuKVfOKVPMKBFOuI6CNhH2w6oFNa1vrbuOAgAAmkA5BAAA7mluc05hP+w6BtpMIpzQRGbCdQwAANAEyiEAAHBXjaChW6lbTCnDgfVGe7WQX1CpVnIdBQAA7INyCAAA3FWqmFKlXlHEj7iOgjbjGU+y0nJh2XUUAACwD8ohAABwV5OZScXDcdcx0Kb6Y/26mbopa63rKAAA4B4ohwAAwJ4q9YrmNueYUob7lggnlC1nlavkXEcBAAD3QDkEAAD2tFJYkbV2e3oQcJ/CXljzm/OuYwAAgHvgbg8AAOxpLD2m3miv6xhocwOxAd1K3VIjaLiOAgAA7oJyCAAAvE2+kle6mFZPpMd1FLS5sB9WpV5RqphyHQUAANwF5RAAAHibhc0FppPh0MTCMU1np13HAAAAd8FdHwAAeAtrrW6lb2kgNuA6CjpEf7Rfs9lZVRtV11EAAMAemiqHjDEfMsaMGWMmjDGf2OP4U8aYy8aYS8aYUWPMTzV7LQAAaC2ZUkbFWlHRUNR1FHQI3/MV2EAr+RXXUQAAwB72LYeMMb6kT0r6sKQnJX3UGPPkHad9Q9J7rbXvk/SPJH36ANcCAIAWMpOdUdgPu46BDtMb7dV4Ztx1DAAAsIdmRg59QNKEtXbKWluV9DlJT+0+wVpbsNbanYdJSbbZawEAQOuoB3VNbUxpMDboOgo6TDKc1NrWmraqW66jAACAOzRTDp2RNL/r8cLOc29hjPk7xpibkr6k7dFDTV8LAABaw/rWuupBXb7nu46CDmOMkTFGS/kl11EAAMAdmimHzB7P2bc9Ye2z1tonJP2ypN86yLWSZIx5eme9otH19fUmYgEAgMM2uTGpRDjhOgY6VH+0X2PpMb054BwAALSCZsqhBUnndj0+K+muf/Kx1n5H0juNMScOcq219hlr7QVr7YWRkZEmYgEAgMNUrpc1vzmv3miv6yjoUPFwXPlKXtly1nUUAACwSzPl0EVJjxtjHjPGRCR9RNJzu08wxrzLGGN23n+/pIikdDPXAgCA1rCcX5as5JmmNjMF7kvIC2k+N7//iQAA4NiE9jvBWls3xnxc0lcl+ZI+Y629Zoz52M7xT0n6FUm/ZoypSSpJ+ns7C1Tvee0RfS0AAOABjGfGGTWEIzcQG9B4Zlw/dvLHWNsKAIAWsW85JEnW2uclPX/Hc5/a9f5vS/rtZq8FAACtJV/JK7WV0sN9D7uOgg4X9sOqNCpKl9I6mTzpOg4AAFBz08oAAECHW8ovMYoDxyYWiml6Y9p1DAAAsINyCACALmet1a30LfXH+l1HQZfoj/ZrNjerWqPmOgoAABDlEAAAXS9bzqpQLSgWirmOgi7he74aQUOrhVXXUQAAgCiHAADoevO5eYW8ppYhBA5NIpzQVHbKdQwAACDKIQAAulpgA41nxjUQG3AdBV2mL9qnxfyiSrWS6ygAAHQ9yiEAALpYqphSpVFR2A+7joIuY4yRrLRSWHEdBQCArkc5BABAF5vJzrDWEJzpjfZqPDPuOgYAAF2PcggAgC5Va9Q0k51Rf5RdyuBGT6RHqa2U8pW86ygAAHQ1yiEAALrUenFd9aAu3/NdR0EX8z1fS/kl1zEAAOhqlEMAAHSpqY0pJcNJ1zHQ5fqifRrPjMta6zoKAABdi3IIAIAuVKlXtLC5oN5or+so6HLxcFz5Sl65Ss51FAAAuhblEAAAXWi1sCorK89wKwD3Ql5I85vzrmMAANC1uCMEAKALjWfG1Rth1BBaQ3+sX5PpSQU2cB0FAICuRDkEAECXKdaKWiuusd4QWkbEj6hYLypTyriOAgBAV6IcAgCgyyznl2WskTHGdRTgDRE/ornsnOsYAAB0JcohAAC6zHhmXH2xPtcxgLcYiA1oamNKjaDhOgoAAF2HcggAgC6Sr+SVKWWUCCdcRwHeIuSFVAtqShVTrqMAANB1KIcAAOgii/lF+cZ3HQPYUzQU1Ux2xnUMAAC6DuUQAABdwlqr8fS4+mP9rqMAe+qP9ms2N6tao+Y6CgAAXYVyCACALpGr5JSv5hULxVxHAfbke74aQUPrxXXXUQAA6CqUQwAAdIn5zXmFvbDrGMA9JcIJTW1MuY4BAEBXoRwCAKALBDbQZHqSKWVoeb3RXs3n5lWpV1xHAQCga1AOAQDQBTZKGyrVS4r4EddRgHvyzPbt6Wph1XESAAC6B+UQAABdYH5zXiEv5DoG0JSeSI8mNyZdxwAAoGtQDgEA0OEaQUOTmUkNxAZcRwGa0hPp0UphRaVayXUUAAC6AuUQAAAdLl1Kq9KoKOyzGDXagzFGkrRSWHGcBACA7kA5BABAh5vNzrJ9PdpOb7RXE5kJ1zEAAOgKlEMAAHSwelDXTHZG/VF2KUN7SYaTShfT2qpuuY4CAEDHoxwCAKCDpYop1YO6fM93HQU4kNtTy5byS46TAADQ+SiHAADoYDPZGaaUoW31xfo0scHUMgAAjhrlEAAAHarWqGkuN6e+aJ/rKMB9SYQTypayylfyrqMAANDRKIcAAOhQ68V1NYIGU8rQ1jzjaTG/6DoGAAAdjXIIAIAONbUxpUQ44ToG8ED6on2ayEzIWus6CgAAHYtyCACADlSpV7SwuaDeaK/rKMADiYfjylfy2qxsuo4CAEDHohwCAKADrW2tyVorz/CrHu3PM54WNhdcxwAAoGNxxwgAQAea2phSMpJ0HQM4FAOxAU1sMLUMAICjQjkEAECHKdfLWiosqTfClDJ0hmgoqmK1qGw56zoKAAAdiXIIAIAOs1pYlaxkjHEdBTg0vudrIc/UMgAAjgLlEAAAHWYiM8FC1Og4A7EBTaYnFdjAdRQAADoO5RAAAB2kWCtqbWtNyTDrDaGzRPyISvWSNkobrqMAANBxKIcAAOggq4VVSUwpQ2cKeSHNb867jgEAQMehHAIAoIMwpQydbCA2oMkMU8sAADhslEMAAHSIreqWUsUUU8rQscJ+WNVGVeli2nUUAAA6CuUQAAAdYjm/LCPDlDJ0tLAf1nyOqWUAABwmyiEAADrExMaE+mJ9rmMAR2ogNqCpjSk1gobrKAAAdAzKIQAAOkC+ktdGaUOJcMJ1FOBIhbyQakFN6RJTywAAOCyUQwAAdICVwgrTydA1oqGoZrOzrmMAANAxKIcAAOgA45lx9Uf7XccAjkV/tF8z2RnVg7rrKAAAdATKIQAA2txmZVO5ck7xcNx1FOBY+J6/PbWMXcsAADgUlEMAALS5pfySPMOvdHSXWCimmeyM6xgAAHQE7iQBAGhj1lpNZCbUF2WXMnSX/mi/ZnOzTC0DAOAQUA4BANDGNiubylfyTClD1/E9X/VGXetb666jAADQ9iiHAABoY4v5RaaUoWvFw3GmlgEAcAiaups0xnzIGDNmjJkwxnxij+N/3xhzeeffS8aY9+46NmOMuWKMuWSMGT3M8AAAdLPbU8oGYgOuowBO9EX7NL85r1qj5joKAABtbd9yyBjjS/qkpA9LelLSR40xT95x2rSkn7XWvkfSb0l65o7jP2etfZ+19sIhZAYAAJJylZwK1YKioajrKIATvuerETS0XmRqGQAAD6KZkUMfkDRhrZ2y1lYlfU7SU7tPsNa+ZK3d2Hn4A0lnDzcmAAC40+LmokIm5DoG4FQ8HNfUxpTrGAAAtLVmyqEzkuZ3PV7Yee5u/rGkL+96bCV9zRjzijHm6YNHBAAAd3pjSll8wHUUwKm+aJ8WNhdUbVRdRwEAoG018+dGs8dzds8Tjfk5bZdDP7Xr6Z+01i4ZY05KesEYc9Na+509rn1a0tOSdP78+SZiAQDQvTbKGyrWiuqP9buOAjjlGU/WWq0V1nS2n8HrAADcj2ZGDi1IOrfr8VlJS3eeZIx5j6RPS3rKWpu+/by1dmnn7ZqkZ7U9Te1trLXPWGsvWGsvjIyMNP8VAADQhRbzi/I933UMoCUkwglNZZlaBgDA/WqmHLoo6XFjzGPGmIikj0h6bvcJxpjzkj4v6R9Ya2/tej5pjOm9/b6kD0q6eljhAQDoRoENNJmeZJcyYEdvtFeLm4uq1CuuowAA0Jb2nVZmra0bYz4u6auSfEmfsdZeM8Z8bOf4pyT9S0nDkv6LMUaS6js7k52S9OzOcyFJn7XWfuVIvhIAALrERmlDpXqJ9YaAHZ7Z/nvn2taazvWf2+dsAABwp6a2OLHWPi/p+Tue+9Su9/+JpH+yx3VTkt77gBkBAMAui5uLCnnsUgbslowkNbUxRTkEAMB9aGZaGQAAaBGBDTSxMcFC1MAdeiO9WiosqVwvu44CAEDboRwCAKCNZEoZVeoVRfyI6yhASzHGSFZaK6y5jgIAQNuhHAIAoI0sbC4wpQy4i55IjyY3Jl3HAACg7VAOAQDQJgIbaDLDLmXA3fREerRSWFGpVnIdBQCAtkI5BABAm0gX06o2qgr7YddRgJa0s0Ou1raYWgYAwEFQDgEA0Cbmc/OsNQTsozfaq4nMhOsYAAC0FcohAADaQCNoaDo7zS5lwD6S4aTWttZUrBVdRwEAoG1QDgEA0AbSpe0pZSxGDdzb7allq4VVx0kAAGgflEMAALSB2eysoqGo6xhAW2BqGQAAB0M5BABAi6sHdc1kZ9QfZUoZ0IxkOKlUMaWt6pbrKAAAtAXKIQAAWly6mFY9qMv3fNdRgLZwe2rZSmHFcRIAANoD5RAAAC1uJjvDlDLggPqifZrcmHQdAwCAtkA5BABAC6sHdc3mZplSBhxQMpJUuphWoVpwHQUAgJZHOQQAQAtLFVNqBA2mlAH3wchoOb/sOgYAAC2PcggAgBY2k51RLBRzHQNoS32xPk1ssGsZAAD7oRwCAKBF1Ro1zeXm1Bftcx0FaEuJcELZUlb5St51FAAAWhrlEAAALSpVTLFLGfCAPOMxtQwAgH1QDgEA0KKmN6aVCCdcxwDaWl+0TxMZppYBAHAvlEMAALSgaqOq+c15ppQBDygejitXyWmzsuk6CgAALYtyCACAFpQqphTYQJ7hVzXwoDzjaSm/5DoGAAAtiztOAABa0NTGFFPKgEPSH+vXRGZC1lrXUQAAaEmUQwAAtJhKvaKFzQX1RntdRwE6QiwU02Zlk6llAADcBeUQAAAtZm1rTdZappQBh8g3vhbzi65jAADQkrjrBACgxUxnp5WMJF3HADrKQGyAqWUAANwF5RAAAC2kXC9rMb+o3ghTyoDDFA1FtVXdUracdR0FAICWQzkEAEALWSusSVYyxriOAnQc3/hayC+4jgEAQMuhHAIAoIVMbkyqJ9LjOgbQkQbiA5rKTDG1DACAO1AOAQDQIkq1klYKK5RDwBGJ+BEVa0VtlDdcRwEAoKVQDgEA0CJWCiuSmFIGHKWQF9JCjqllAADsRjkEAECLmNyYVG+UhaiBo9Qf69fExoQCG7iOAgBAy6AcAgCgBRRrRa0X15UMs4U9cJQifkSVekWZUsZ1FAAAWgblEAAALWClsCIjw5Qy4BiEvJDmc/OuYwAA0DIohwAAaAETmQn1RphSBhyHgdiApjam1AgarqMAANASKIcAAHCsUC0oXUwrGWFKGXAcwn5Y1UaVqWUAAOygHAIAwLHl/LI8w69k4DhF/IjmcnOuYwAA0BK4EwUAwLHxzDi7lAHHrD/Wr+mNaaaWAQAgyiEAAJzKV/LKlXNKhBOuowBdJeSFVAtqShVTrqMAAOAc5RAAAA4t5ZeYUgY4Eg1FNZOdcR0DAADnuBsFAMARa63GM+Pqi/a5jgJ0pf5ov2Zzs6oHdddRAABwinIIAABHNiub2qxsKh6Ou44CdCXf89UIGlrfWncdBQAApyiHAABwZDG/KN/4rmMAXS0ejmt6Y9p1DAAAnKIcAgDAgdtTygZiA66jAF2tN9Kr+c15VRtV11EAAHCGcggAAAey5ay2qluKhqKuowBdzfd8BTbQWmHNdRQAAJyhHAIAwIGF/IJCXsh1DACSEuGEprJTrmMAAOAM5RAAAMcssIEm0hNMKQNaRG+0V0v5JVXqFddRAABwgnIIAIBjlillVK6XFfEjrqMAkOQZT1ZWq4VV11EAAHCCcggAgGM2n5tX2A+7jgFgl55wjyY3Jl3HAADACcohAACOUSNoaGpjiillQIvpifRopbCiUq3kOgoAAMeOcggAgGOULqVVbVRZjBpoMcYYSdJKYcVxEgAAjh/lEAAAx2g2O8v29UCL6o32ajwz7joGAADHjnIIAIBjUg/qms5Oqz/a7zoKgD0kw0mli2kVqgXXUQAAOFaUQwAAHJP1rXXVG3X5nu86CoA9GGPkGU/L+WXXUQAAOFaUQwAAHJPpjWklIgnXMQDcQ1+0j6llAICu01Q5ZIz5kDFmzBgzYYz5xB7H/74x5vLOv5eMMe9t9loAALpBtVHV/Oa8+qJ9rqMAuId4OK5cOafNyqbrKAAAHJt9yyFjjC/pk5I+LOlJSR81xjx5x2nTkn7WWvseSb8l6ZkDXAsAQMdbK6wpsIE8w6BdoNUZY7S4ueg6BgAAx6aZO9QPSJqw1k5Za6uSPifpqd0nWGtfstZu7Dz8gaSzzV4LAEA3mNyYVCLMlDKgHQzGBjWeGZe11nUUAACORTPl0BlJ87seL+w8dzf/WNKX7/NaAAA6Trle1lJhiSllQJuIhqLaqm4pW866jgIAwLFophwyezy3559RjDE/p+1y6J/fx7VPG2NGjTGj6+vrTcQCAKA9rBRWJLs9VQVAe/A9X/Ob8/ufCABAB2imHFqQdG7X47OSlu48yRjzHkmflvSUtTZ9kGslyVr7jLX2grX2wsjISDPZAQBoC+PpcfVGe13HAHAAA7EBTWQmFNjAdRQAAI5cM+XQRUmPG2MeM8ZEJH1E0nO7TzDGnJf0eUn/wFp76yDXAgDQybaqW0oVU0qGk66jADiAiB9RpV5RppRxHQUAgCMX2u8Ea23dGPNxSV+V5Ev6jLX2mjHmYzvHPyXpX0oalvRfdobM13dGAe157RF9LQAAtJyl/JKMDFPKgDYU9sOazc7qROKE6ygAABwp04q7MFy4cMGOjo66jgEAwAN7fvx5SWKnMqAN1YO6sqWsfvlHf1khb9+/qQIA0PKMMa9Yay/c+Xwz08oAAMB92KxsKlfOUQwBbSrkhVQNqkoVU66jAABwpCiHAAA4IgubC/IMv2qBdhYPxTWTnXEdAwCAI8UdKwAAR8Baq/HMuAZiA66jAHgAfdE+zWZnVW1UXUcBAODIUA4BAHAENsobKlaLioairqMAeAC+5yuwgdYKa66jAABwZCiHAAA4AvO5eRawBTpEMpLU5Mak6xgAABwZyiEAAA5ZI2hoIjPBlDKgQ/RGerWUX1KpVnIdBQCAI0E5BADAIUuX0qo2qgr7YddRABwCY4wkaaWw4jgJAABHg3IIAIBDNpOdYa0hoMP0Rfs0nhl3HQMAgCNBOQQAwCGqNWqayc6oP9rvOgqAQ5SMJJUuppWv5F1HAQDg0FEOAQBwiNaL62oEDfme7zoKgEPmGU9L+SXXMQAAOHSUQwAAHKKJzIQS4YTrGACOQH+sX7fSt2StdR0FAIBDRTkEAMAhKdfLWswvqjfa6zoKgCMQC8VUqBaULWddRwEA4FBRDgEAcEhWCiuS3Z56AqAzhbyQ5nPzrmMAAHCouHsFAOCQjKfHGTUEdLiB2IDGM+MKbOA6CgAAh4ZyCACAQ1CoFpQqppQMJ11HAXCEwn5Y1UZVqWLKdRQAAA4N5RAAAIdgcXNRnvFkjHEdBcARi4aimt6Ydh0DAIBDQzkEAMADstZqPDOu/li/6ygAjkF/tF+zuVnVGjXXUQAAOBSUQwAAPKBsOat8Ja9YKOY6CoBj4Hu+GkFDq4VV11EAADgUlEMAADyg+dy8Ql7IdQwAxygRTmhyY9J1DAAADgXlEAAAD6ARNDSeGddAbMB1FADHqC/ap6X8kkq1kusoAAA8MMohAAAeQKqYUqVeUdgPu44C4BjdXnx+ubDsOAkAAA+OcggAgAcwnZ1WLMxaQ0A36o/161b6lusYAAA8MMohAADuU7VR1Wx2Vv1RdikDulEinNBGaUOblU3XUQAAeCCUQwAA3KfVwqoCG8j3fNdRADjiGU/zuXnXMQAAeCCUQwAA3Kdb6VvqifS4jgHAocH4oMbT4wps4DoKAAD3jXIIAID7sFXd0trWGuUQ0OUifkSlekmZUsZ1FAAA7hvlEAAA92EpvyTPeG/sWASge0X8iGayM65jAABw3yiHAAA4IGutxtJj6ov2uY4CoAUMxAY0tTGlWqPmOgoAAPeFcggAgAPKlrPKV/KKh+OuowBoAb7nqxE0tLa15joKAAD3hXIIAIADmsvNKeSFXMcA0EKSkaQmMhOuYwAAcF8ohwAAOIBG0NBEZkIDsQHXUQC0kN5Ir5bySyrWiq6jAABwYJRDAAAcwHpxXZVGRWE/7DoKgBZijJGR0dLmkusoAAAcGOUQAAAHMJGZUCKccB0DQAvqj/XrVvqWrLWuowAAcCCUQwAANKlcL2thc4FdygDsKR6OK1vJKlvOuo4CAMCBUA4BANCk5fyyrLXyDL8+Aewt7IU1n5t3HQMAgAPh7hYAgCaNpccYNQTgngZiAxrPjKsRNFxHAQCgaZRDAAA0IVfOKVPMKBlJuo4CoIWF/bAqjYrWi+uuowAA0DTKIQAAmjC3OaeQF3IdA0AbSIQTmshMuI4BAEDTKIcAANhHYAONp8c1EB9wHQVAG+iL9ml+c17letl1FAAAmkI5BADAPlLFlMq1siJ+xHUUAG3AM55kpaX8kusoAAA0hXIIAIB9TG1MKR6Ou44BoI30x/p1M3VT1lrXUQAA2BflEAAA91CpVzSTnVF/rN91FABtJBFOKFvOKlfJuY4CAMC+KIcAALiHpfySrLXb00QA4ADCXlhz2TnXMQAA2Bd3ugAA3MNYekx90T7XMQC0oYHYgMYz42oEDddRAAC4J8ohAADuIlfOKVPMKBlJuo4CoA2F/bCqjarWttZcRwEA4J4ohwAAuIvZ7KzCfth1DABtLBFOaDwz7joGAAD3RDkEAMAeGkFD45lxDcQGXEcB0Mb6on1a3FxUsVZ0HQUAgLuiHAIAYA/rxXVVG1VGDgF4IMYYGRktbi66jgIAwF1RDgEAsIdb6VtKhBOuYwDoAP2xfo2lx2StdR0FAIA9UQ4BAHCHYq2oxc1FdikDcCji4bg2K5vKlDKuowAAsCfKIQAA7rC4uSgjI2OM6ygAOkTEj2g6O+06BgAAe6IcAgBgF2utbqRuaCA+4DoKgA4yGBvU1MaUqo2q6ygAALwN5RAAALukS2kVqgXFQjHXUQB0EN/z1QgaWsmvuI4CAMDbNFUOGWM+ZIwZM8ZMGGM+scfxJ4wx3zfGVIwxv3nHsRljzBVjzCVjzOhhBQcA4ChMb0wr6kddxwDQgXqjvRpLj7mOAQDA24T2O8EY40v6pKSfl7Qg6aIx5jlr7fVdp2Uk/VNJv3yXD/Nz1trUA2YFAOBIVRtVTW1M6UTihOsoADpQT6RHy/ll5co59cf6XccBAOANzYwc+oCkCWvtlLW2Kulzkp7afYK1ds1ae1FS7QgyAgBwLJbySwpsIN/zXUcB0KFCXkhzm3OuYwAA8BbNlENnJM3veryw81yzrKSvGWNeMcY8fZBwAAAcp5upm2xfD+BIDcQGdCt1S/Wg7joKAABvaKYc2msfX3uAz/GT1tr3S/qwpF83xvzMnp/EmKeNMaPGmNH19fUDfHgAAB5ctpxVppRRMpJ0HQVABwv7YVUbVa0WVl1HAQDgDc2UQwuSzu16fFbSUrOfwFq7tPN2TdKz2p6mttd5z1hrL1hrL4yMjDT74QEAOBTTG9MKe2HXMQB0gWQkqfHMuOsYAAC8oZly6KKkx40xjxljIpI+Ium5Zj64MSZpjOm9/b6kD0q6er9hAQA4CrVGTROZCQ3GB11HAdAFeiO9WsovqVAtuI4CAICkJnYrs9bWjTEfl/RVSb6kz1hrrxljPrZz/FPGmNOSRiX1SQqMMb8h6UlJJyQ9a4y5/bk+a639ypF8JQAA3KeVworqQV0hb99fiwDwwIwx8o2vudycnhx50nUcAAD2L4ckyVr7vKTn73juU7veX9H2dLM7bUp674MEBADgqN1M3VRvtNd1DABdZDA+qLHUmN49/G52SAQAONfMtDIAADpWrpxTqphST6THdRQAXSTiR1Sql7ReZCMWAIB7lEMAgK42m51lOhkAJ5LhpMZSY65jAABAOQQA6F71oK5b6VssRA3Aib5on5byS9qqbrmOAgDocpRDAICutZJfUS2oMXIIgBPGGHnG02xu1nUUAECXoxwCAHStm2kWogbg1u2FqRtBw3UUAEAXoxwCAHSlXDmn9a11FqIG4BQLUwMAWgHlEACgK81kZ5hOBqAlsDA1AMA1yiEAQNepNWosRA2gZfRF+7SYX1ShWnAdBQDQpSiHAABdZzm/rHpQZ+QQgJZgjJFvfM1mWZgaAOAG5RAAoOvcSN1gIWoALWUwPqibqZssTA0AcIJyCADQVTZKG0qX0ixEDaClRPyIqo2qVgorrqMAALoQ5RAAoKtMbUwp7IVdxwCAt+mJ9Ohm6qbrGACALkQ5BADoGpV6RROZCQ3Fh1xHAYC36Yn0aHVrVblyznUUAECXoRwCAHSNxfyiAhvI93zXUQDgbYwxCnthTWenXUcBAHQZyiEAQFew1ur6+nUNxAZcRwGAuxqKD+lW+paqjarrKACALkI5BADoCqliSpuVTcXDcddRAOCufM9Xwza0lF9yHQUA0EUohwAAXeFW+pbiIYohAK2vP9qv6+vXZa11HQUA0CUohwAAHW+ruqW53Jz6Y/2uowDAvhLhhLLlrNKltOsoAIAuQTkEAOh4s7lZecaTZ/i1B6A9xEIxjafHXccAAHQJ7pIBAB2tHtR1Y/2GBuODrqMAQNMGYgOayc6oWCu6jgIA6AKUQwCAjraSX1GlUVHEj7iOAgBNuz3acSY74zoKAKALUA4BADqWtVbXU9fVF+1zHQUADmwwPqgb6zfUCBquowAAOhzlEACgY22UN5QqptQT6XEdBQAOLOJHVGlUtJxfdh0FANDhKIcAAB1rPD2uqB91HQMA7ltftE/XU2xrDwA4WpRDAICOVKqVNJWdYiFqAG2tJ9KjVDGljfKG6ygAgA5GOQQA6EizuVl5Yvt6AO0v6kfZ1h4AcKS4YwYAdJx6UNe1tWuMGgLQEQbjg5rKTrGtPQDgyFAOAQA6DtvXA+gknvHkiW3tAQBHh3IIANBRrLW6tn6N7esBdJTb29rXg7rrKACADkQ5BADoKJlSRulSmu3rAXSUiB9RpV7R0uaS6ygAgA5EOQQA6Ci30rcUC8VcxwCAQ9cf69fV9atsaw8AOHSUQwCAjrFV3dJMbkYDsQHXUQDg0CUjSWXLWaWKKddRAAAdhnIIANAxJjcm2b4eQEdLhBO6mbrpOgYAoMNw9wwA6AjVRlU3Uzc1nBh2HQUAjkx/tF/zuXltVjZdRwEAdBDKIQBAR5jLzqkRNBTyQq6jAMCRMcYo7Ic1mZl0HQUA0EEohwAAba8RNHRt/ZoG44OuowDAkRuKD+lW+pbK9bLrKACADkE5BABoeyuFFW3VttilDEBX8D1f1lrNZmddRwEAdAjKIQBAW7PW6uraVfVF+1xHAYBjM5QY0rX1a6oHdddRAAAdgHIIANDW0qW0UsWUeiI9rqMAwLGJ+BFV6hUtbi66jgIA6ACUQwCAtnZj/YYS4YTrGABw7Ppj/bq6dlWBDVxHAQC0OcohAEDb2qxsaj43r4HYgOsoAHDsEuGEsuWs1rbWXEcBALQ5yiEAQNu6lbqliB+RMcZ1FABwojfaq6trV13HAAC0OcohAEBbKtaKGt8YZ/t6AF2tL9qn1cKq0sW06ygAgDZGOQQAaEuTG5Py5Mn3fNdRAMCpeDium6mbrmMAANoY5RAAoO1UG1XdWL+h4cSw6ygA4NxgbFCz2VltVjZdRwEAtCnKIQBA25nNzqoRNBTyQq6jAIBzxhhF/IhupW65jgIAaFOUQwCAtlIP6rqydoVRQwCwy2B8UBMbEyrWiq6jAADaEOUQAKCtLGwuqFKvKOJHXEcBgJbhe74842kiPeE6CgCgDVEOAQDaRiNo6PLqZQ3EBlxHAYCWMxwf1s3UTZXrZddRAABthnIIANA2lvPLKlQKiofjrqMAQMvxPV+BDTS1MeU6CgCgzVAOAQDaQmADXV67rP5Yv+soANCyhhPDurZ2TdVG1XUUAEAboRwCALSF1cKqNkobSkaSrqMAQMsK+2HVgppms7OuowAA2gjlEACg5VlrdXmVUUMA0IwTiRO6snZFtUbNdRQAQJtoqhwyxnzIGDNmjJkwxnxij+NPGGO+b4ypGGN+8yDXAgCwn/XiulLFlHoiPa6jAEDLi/gRVeoVzW/Ou44CAGgT+5ZDxhhf0iclfVjSk5I+aox58o7TMpL+qaT/7z6uBQDgrm6PGuqN9rqOAgBtYyg+pNdXXlc9qLuOAgBoA82MHPqApAlr7ZS1tirpc5Ke2n2CtXbNWntR0p1jV/e9FgCAe0kVU1otrKov2uc6CgC0jWgoqnK9rIXNBddRAABtoJly6Iyk3WNSF3aea8aDXAsA6HLWWl1ZvcJ0MgC4D4PxQb2++roaQcN1FABAi2umHDJ7PGeb/PhNX2uMedoYM2qMGV1fX2/ywwMAOlm6lNZyYZmFqAHgPsRCMRWrRdYeAgDsq5lyaEHSuV2Pz0paavLjN32ttfYZa+0Fa+2FkZGRJj88AKCTMWoIAB7MQGyA0UMAgH01Uw5dlPS4MeYxY0xE0kckPdfkx3+QawEAXSxVTGmpsMSoIQB4APFwnNFDAIB9hfY7wVpbN8Z8XNJXJfmSPmOtvWaM+djO8U8ZY05LGpXUJykwxvyGpCettZt7XXtEXwsAoEO8sdZQmFFDAPCgbo8eOtd3Tr7nu44DAGhB+5ZDkmStfV7S83c896ld769oe8pYU9cCAHAvqWJKS/klneljDwMAeFDxcFzZfFbzm/N6dOBR13EAAC2omWllAAAcG2utLq9eZq0hADhEg/FBXVq+pHpQdx0FANCCKIcAAC1lvbiula0V1hoCgEMUC8VUqpc0n2PtIQDA21EOAQBahrVWr6+8rt5Ir+soANBxhuJDurTC6CEAwNtRDgEAWsbq1qrWttbUF+1zHQUAOk40FFW5UdbMxozrKACAFkM5BABoCYEN9Nrya0wnA4AjNBwf1utrr6vaqLqOAgBoIZRDAICWsJxfVqaUYSFqADhCET+iar2qqY0p11EAAC2EcggA4FwjaOi1ldc0GB90HQUAOt6JxAldWb2icr3sOgoAoEVQDgEAnJvfnNdmZVOJcMJ1FADoeGE/rMAGGs+Mu44CAGgRlEMAAKfqQV2vLb+mofiQ6ygA0DVOJE7o2to1FWtF11EAAC2AcggA4NTUxpTK9bJioZjrKADQNXzPl298XV+77joKAKAFUA4BAJyp1Ct6feV1DSeGXUcBgK4znBjWrcwt5co511EAAI5RDgEAnBlLjymwgSJ+xHUUAOg6nvEUC8V0ZfWK6ygAAMcohwAATmxVt3R9/bpOJE64jgIAXWswNqjZ3KxSxZTrKAAAhyiHAABOXF2/Kt/48j3fdRQA6FrGGPVGe/Xa8muy1rqOAwBwhHIIAHDsNkobmkhPsNYQALSAvmif1rbWtJRfch0FAOAI5RAA4FhZa3Vp5ZKSkaQ8w68hAGgFQ/EhvbL8iupB3XUUAIAD3JUDAI7Vcn5ZS/klDcQGXEcBAOyIh+Paqm5pemPadRQAgAOUQwCAY9MIGnp15VWKIQBoQcOJYV1auaRyvew6CgDgmFEOAQCOzfTGtPKVvJKRpOsoAIA7RPyIAhvoxvoN11EAAMeMcggAcCzK9bJeW3mNRagBoIWdSJzQjdQN5co511EAAMeIcggAcCxurN9QYANF/IjrKACAu/A9X7FQTJdWLrG1PQB0EcohAMCRy5azurF+QycSJ1xHAQDsYyg+pIXNBS3nl11HAQAcE8ohAMCRstbqteXXFA/H5Xu+6zgAgCYMxgc1ujzK1vYA0CUohwAAR2pxc1FL+SUNxgddRwEANCkRTmiruqWJzITrKACAY0A5BAA4MrVGTaNLoxqKD7mOAgA4oJHkiC6tXNJWdct1FADAEaMcAgAcmZvpmyo3yoqH466jAAAOKOSFFDIhvb76uusoAIAjRjkEADgSm5VNXV29qpHEiOsoAID7NJwY1vTGtFYLq66jAACOEOUQAODQ3V6EOhqKsgg1ALQxY4wGYgO6uHSRxakBoINRDgEADt3i5qIWNhdYawgAOkAyklS+ktd4etx1FADAEaEcAgAcqmqjqh8u/ZBiCAA6yEhyRK+vvq58Je86CgDgCFAOAQAO1bW1a6o1aixCDQAdJOSFFPEjenXlVVlrXccBABwyyiEAwKHJlDK6vn5dJxInXEcBAByyofiQFnILWtxcdB0FAHDIKIcAAIeiETT08sLL6o32sgg1AHSo4cSwXl56WZV6xXUUAMAhohwCAByKicyENsob6ov2uY4CADgisVBM9UZdl1cvu44CADhElEMAgAeWr+T12sprOpk86ToKAOCIjSRHdCt9S2tba66jAAAOCeUQAOCBBDbQ6NKoIn5EIS/kOg4A4Ih5xtNAbEA/WPiBao2a6zgAgENAOQQAeCAzGzNazC+ydT0AdJFkJKlirajr69ddRwEAHALKIQDAfduqbml0aZTpZADQhUYSI7qydkXpYtp1FADAA6IcAgDcF2utRpdH5Xu+In7EdRwAwDHzPf+N6WX1oO46DgDgAVAOAQDuy0x2Rgu5BQ0nhl1HAQA40hPp0WZlk+llANDmKIcAAAdWqBb0w8UfaiQ54joKAMCxk8mTurJ6RaliynUUAMB9ohwCABxIYANdXLyosB9mOhkAQL7nqz/Wr5fmX2L3MgBoU5RDAIADmchMaCm/xO5kAIA39ER6VKwWdWXtiusoAID7QDkEAGharpzTK0uvsDsZAOBtTvac1I31G1rOL7uOAgA4IMohAEBT6kFd31/4vhLhhMJ+2HUcAECL8YynofiQXlp4SaVayXUcAMABUA4BAJpybe2aNkob6o/1u44CAGhR8XBcQRBodGlU1lrXcQAATaIcAgDsayW/oitrV5hOBgDY14nECc3mZjW1MeU6CgCgSZRDAIB7KtVKenHhRQ3Hh+V7vus4AIAWZ4zRqeQp/XDxh8qWs67jAACaQDkEALireiPQ869dUhAEiofjruMAANpE2A8rEU7oS5cuqlhme3sAaHWUQwCAu3rh4oy+872qRpIjrqMAANpMf6xf114P64++cct1FADAPiiHAAB7GptL64vfWlaPP+Q6CgCgTfWGB/TiaE4vXllwHQUAcA+UQwCAt8kWyvqvz43rxFCYdYYAAPfNGKOzp2P6o6/OaWF903UcAMBdUA4BAN6i3gj0+1+6oWo10GBfxHUcAECbi8d8JROePv1nN1l/CABaVFPlkDHmQ8aYMWPMhDHmE3scN8aY/7Rz/LIx5v27js0YY64YYy4ZY0YPMzwA4PB96aVJjU1t6fzDCddRAAAd4uRQTBvZmj77tZsKAus6DgDgDvuWQ8YYX9InJX1Y0pOSPmqMefKO0z4s6fGdf09L+p07jv+ctfZ91toLDx4ZAHBULo2v6ivfW9WjZ9mZDABwuB45k9ArV3P6xuiM6ygAgDs0M3LoA5ImrLVT1tqqpM9JeuqOc56S9N/sth9IGjDGPHTIWQEAR2gpldfvPzeph0eiioRZZwgAcLg8z+ixs3H92V8saWwu7ToOAGCXZsqhM5Lmdz1e2Hmu2XOspK8ZY14xxjx9v0EBAEenUKrqd//8pmJRT709YddxAAAdKhLxdXI4rE8/e0trG1uu4wAAdjRTDpk9nrtzovC9zvlJa+37tT317NeNMT+z5ycx5mljzKgxZnR9fb2JWACAw1BvBPrvz99QaqOqUydiruMAADpcf+/2Zge/ywLVANAymimHFiSd2/X4rKSlZs+x1t5+uybpWW1PU3sba+0z1toL1toLIyMjzaUHADywL7w4oSu38nqEBagBAMfkzKm4VlIVFqgGgBbRTDl0UdLjxpjHjDERSR+R9Nwd5zwn6dd2di37q5Jy1tplY0zSGNMrScaYpKQPSrp6iPkBAA/g+1cX9dXvremxc3F53l6DQAEAOBqPnInrlas5ffGlSddRAKDrhfY7wVpbN8Z8XNJXJfmSPmOtvWaM+djO8U9Jel7SL0iakFSU9A93Lj8l6VljzO3P9Vlr7VcO/asAABzY+HxGf/ilGZ1/KKZwiAWoAQDHy/OMHjsX11e+s6pTgwn9xI897DoSAHStfcshSbLWPq/tAmj3c5/a9b6V9Ot7XDcl6b0PmBEAcMhWMgU98/kxDQ+GlYg39asAAIBDFwn7OvtQVP/9i9Ma6ovp8XNDriMBQFdqZloZAKCDbG5V9Kk/vS7PMxrsi7iOAwDocol4SMODYT3zp2NayRRcxwGArkQ5BABdpFyt63f//Lpy+boeGmFnMgBAaxjsiygUMvqdP7mubKHsOg4AdB3KIQDoEvVGoD/4yg1NzhfZmQwA0HJOnYgpX6jrmWevscU9ABwzyiEA6AJBYPUnf3FLr17L6R3nKIYAAK3p/MMJLSxX9Ptfuq5qreE6DgB0DcohAOgCX3xpUt++mNI7zifYsh4A0NIePRvX1fGCPvu1mwoC6zoOAHQFyiEA6HDfuDijL39nVY+diyvk82MfANDaPM/onecTevnyhv7oG2MURABwDHiVAAAd7MUrC/qTry/okTMxRcK+6zgAADTldkH07YspfeHFCddxAKDjUQ4BQIe6eGNJf/DFGZ1/KKZYlGIIANBeQr6nd5yP68vfXdXz3590HQcAOhrlEAB0oFfHVvRf/2xK507HFI+FXMcBAOC+hEO+3nEuri98c0Vf/eG06zgA0LEohwCgw1waX9XvPjuhM6ejSsQphgAA7S0S9vXY2Zie/fqivnFxxnUcAOhIvGoAgA7y6tiKfvfZCT10MqYkxRAAoENEIr7ecTauP35hQYG1+vkPPOY6EgB0FEYOAUCHGL25rE9/frsY6klQDAEAOsvtgujzX1/Sl38w5ToOAHQUXj0AQAd48cqC/vCLMzpzOsqIIQBAx4pEtqeYPfeNJVVrDf3tn3yXPM+4jgUAbY9XEADQ5v7ilVn98dfmdf4hFp8GAHS+SMTXY+fj+sp31lStBfqVv/4jFEQA8IB4FQEAbSoIrL740qS+/J1VPXImznb1AICuEQn7escjMX3z5XVtler61Q8+oUiY34MAcL9YcwgA2lC9EeiPvjGmL39nRY+di1EMAQC6Tjjk612PJHXxSla/+9xVFcs115EAoG1RDgFAmylX6/rMF67pO6MpvfORBH8pBQB0Lc8zeuf5hG5Mbuk///FlZQtl15EAoC1RDgFAG8kWyvrkH1/W1fFNveuRpEI+P8YBAN3N84zecT6hlfWK/v1nL2splXcdCQDaDq8qAKBNLKxv6t/+99e1uFrWO84lWXwTAIBdzj+cULUW6N/+wVWNzaVdxwGAtkI5BABt4OrUmv7tf7uqhrU6/3DCdRwAAFrSqeGY+pK+/tNnb+h7l+ddxwGAtsFuZQDQwoLA6hujM3r2G4s6PRJVX0/YdSQAAFpaf29EkbCnP/zCrJbWi/rln3kX6/MBwD4ohwCgRRXLNX3u62O6eDmrx87GFYlwYwsAQDPisZDe+WhC376Y0uJqUf/wl35UAz0x17EAoGUxrQwAWtBKpqB/94eXdOlGTo8/mqQYAgDggEK+p8cfTWp+paR//fuva3Jxw3UkAGhZlEMA0GJGby7rt//rZeWLDRaeBgDgAZ1/OKGQb/Tv/+C6vnFxRkFgXUcCgJbDtDIAaBHlal1/9u0JfetiSmdPx9ST4Ec0AACHYWggokTc15+8sKDJxbw+8vM/or5k1HUsAGgZvPIAgBawsL6p3//CLa2kKnrXIwmFfAZ2AgBwmGJRX48/mtT1ybx+e+mSfu0X36V3nx92HQsAWgKvPgDAoSCw+tarc/rXv3dVhWJd7zyfpBgCAOCIeJ7Ro2e2p5n9xz+8oT//7riqtYbrWADgHCOHAMCRVK6oz31tXNfG8zr/cEzxGD+SAQA4DoP9ESUTvl54aU3XJzb193/hXTp/qt91LABwhlciAHDMgsDq+9cW9acvzMkY6fFHWXQaAIDjFgn7etcjSa2my/o3v3dVv/CzD+lv/vgjioTZIRRA96EcAoBjtLaxpf/5wriuTxR09qGokvGw60gAAHS1U8MxDfY29MVvLevSjQ396offpUdOM4oIQHehHAKAY1CtNfTt1+b0xe8sK+QbRgsBANBCIpHtxarXMmX969+7or/xEyf14b/2mBIx/ogDoDtQDgHAERubS+uPXpjSynpV5x6KKRZluDoAAK3o5FBMg30NfXt0Xa9c39Df/VuP6H2Pn+IPOgA6HuUQAByRVK6o5747pdErWQ0PhPX4o0nXkQAAwD7CIV/vOJfUZqGmT39+Uu9+x7J+5W+8U2dH+lxHA4AjQzkEAIesWK7pW6/N6Wsvrsoz0jvOJ9ieHgCANtPXE1ZPIqSFlbL+1Weu6GcunNAHf+IRDfTEXEcDgENHOQQAh6TeCPTy9SU99615FUuBzpxiChkAAO3M84zOnIqrVm/oxVfT+sHraX34px7ST7/vnGIRXkoB6Bz8RAOABxQEVpfGV/Xcd+a0nqrpoVNRPTTCj1cAADpFOOTrsXMJlcp1/fk3l/T1l1f0t3/2rD7wow8rEuYPQQDaH69eAOA+BYHV1el1feHbc1pcLWtkOKLHH2NdIQAAOlU8FtK7HgmpUKzrfzw/qy9/b0m/+NNn9eNPnKYkAtDWKIcA4IDqjUCXJ9b0/PfmtbRe0YmBiH7ksR7XsQAAwDHpSYT0+KM92izU9AdfmtYXv7ugD//Uw7rwxENMNwPQlvjJBQBNKlfrem1sVV9+aVHpjaqGByL6kUcphQAA6FZ9PWH19YSVL9T0P56f0xe+vaC/9ROn9df+0hn1xCOu4wFA0yiHAGAf2UJZL11Z1DdfXlOxHOjUiYgepxQCAAA7envC6u0Ja6tU059/c0nPf3dZP/m+E/qpv/ywTg9xzwCg9VEOAcAegsBqejmr71xa0mvXs5I1Oj0S0ZnT/NgEAAB7S8bDetcjYVWrDX331ZS+NbquJ97Ro5+78LDefX5YId9zHREA9sSrHADYpVCq6tL4qr51cUXLqariUU/nHoopHGKRSQAA0JxIZHt3syCwWlwt6Xf+aEz9vWH99Qsn9eNPnNZQX9x1RAB4C8ohAF2v3gg0Pp/R96+s6PWxnBoNaXgwrMcfYecxAABw/zzP6NSJmE6dkArFur7wrWX9+TeX9MQ7evRT7zutJx4ZZgFrAC2Bn0QAulIQWM2vbeqVsVX98HJGhWJd8Zivs6cZJQQAAA5fTyKknvMh1RuBFtdK+vTnJxSNTOnCjw3o/U+c1DvPDDLtDIAzlEMAusbtQuj1iXW9fDmtbL6uiG908kREp0diruMBAIAuEPI9nRqO6dSwVK02NHotq++9mlEy4esDPzak9/7ICT328ABFEYBjRTkEoKNVaw1NL2d1ZTytV29uKFeoK+QZjQxHNDIUdR0PAAB0sUjE17mHttcfKpXreulSWt8aXVc86uk97+7XX373iN7x8IASsbDjpAA6HeUQgI6ztrGl6aWcXhtL6eZ0QfWGVcT3dGIorJPDFEIAAKD1xGMhnT+z/fKsXGno9bGcXr68Id+X3nkuqfc/Max3nBnQ6aEeeZ5xnBZAp6EcAtD2soWy5lY3dWsmq8sTWWVzdVlZ9SR9PXwyqkiYNYQAAED7iEV9nT29PaKo3gi0mq7of35lTsbMKxH39GPv6tOPvXNI50/16UR/wnFaAJ2AcghAWwkCq1SuqKVUQbfmsroxmdP6Rk1GUiTiaWggpHec5yYJAAB0hpDvaWQo+sZ0+FK5rsu3cnr5SkaePPX2+HrisV498eigzoz0MLIIwH2hHALQ0ja3KlpOF7S4XtD4XE6T80WVKw0FgRSNeBrsD+tdbDkPAAC6RDwW0pnYmy/jiqXtsuiHVzZkZBQOS488nNC7H+3X2ZM9emi4R0N9cYeJAbQDyiEALSEIrDL5klYzW1pJb2lqMa+ZxaI2C3UZScYYJZOehvrDikXZWQwAAECSEvGQEvE3X9ZVaw2tZyqanFuWtVKgQMl4SI88HNc7z/bpoRNJnRxM6ER/gh3RALyBcgjAsao3AmU2S0rntv/NLhe0sFbUynpFjcBK1kjGKpnw1ZsIsaMYAADAAUTCvoYHfQ0PvvlcudLQ4mpZY9MF2UCSkYwnnRyM6OzphM6d6tHJwYSG+mI60Z9gvUagC1EOATh0xXJN2UJZuUJF2UJFq5miltaLWktVtLFZV2CtjIwkq2jUU0/C18OnogqHuBEBAAA4bLGor1jUf8sf3eqNQMVSQ9cn8xq9mpWM5MkosFZ9PSGdGo7q4RMJnT4R10BvTAO9UQ30xJSIhlnTCOhATZVDxpgPSfqPknxJn7bW/qs7jpud478gqSjp/7DWvtrMtQDaRxBYFSs1bW5VtFWqKV+qqlCsaX2jpLVMWelcRRubNVUqVp4kme0bh1BIisd8JeKeHjkT54YCAADAsZDvqa/HU19P+C3PB4FVpdpQaqOqueWSqtVAMpK128fDIaOBvrCG+sM6ORTXiYGY+pIR9SYiSsbD6ktElYiFmbIGtJl9yyFjjC/pk5J+XtKCpIvGmOestdd3nfZhSY/v/PsJSb8j6SeavBaAI9VaQ+VqXcVKTaVyXeVqXaVqXaVyXbmtijZyVeW2qspu1rRVaii/1ZCk7TE/1m6/IykS9hSNeIpFPJ0aZut4AACAduV5RvFYSPGYNLTH8Vq9oUrVajVV0exSSZWqlWRltTPyKLAyxigR99Sb9NXXE9ZgX0R9PREN9ESViIUUj4aUiIYVjfhKxMKKRUKKRZjUArjUzHfgByRNWGunJMkY8zlJT0naXfA8Jem/WWutpB8YYwaMMQ9JerSJawE0qd4IVK01tt/WG288rtV33u56XKk2tFmsqlxpaKtUU6nS0FaprlJ5ewhxqRLs/PKWZI2Muf1rXbKBFA55CoW330YjnnqTIQ0PRBj1AwAA0MXCIV/hkNSTuPtLySCwqtcDVaqB1tIVLayWVata1RrB9gk7U9hsYBUYK2ONjGeUiHlKxH1FI54SMV89iZBiEV/JRFjJ2HaBFI34ioR9hX1PkbCvkO8pHHrz/Uho+23I97hvBQ6gmXLojKT5XY8XtD06aL9zzjR5LbCnILBvfWztXY/vPnb7+dvP7XVeENi3HQ+s3fN9a988/87jgbXbx3c9bjTsW863kirVuuoNq0qtoSDYPqdaa6ha3y5oqrVA1VqgWj1QI7Cq1azqDataLVCltv3LtV6XJKvASt7OKF2zM3Rn938aq+1MnmcU8ow8f3v4b8g38nyjcMjTQF9YJ0KG4b4AAAA4dJ5nFIn4ikSaH01+u1CqNQKVKw0VtupaWi+rXt++d6439OZNr7n9ZudeOLCSt31P7hmj7QHuRqGQFAp5CoeMwr5RKLx9LxwOmZ1CabtAioQ9RUKefP/N56JhXyHfyPe2yyfPM/KMkedt/1H1dvnkme3Ht49Jb76/+/zb/128nQd3vn/7ujuP3e34G8fMWwuwOwux/Y4DtzVTDu31/x7b5DnNXLv9AYx5WtLTknT+/PkmYrW+b4zO6srExn1de2cxctSsPfjnu7OsefsHvfsPnr0+315f8tvPe/Nj7v78u8+zwa7r33jOvuXxnZ/LBm9+vO2Ptf15tssd+8bvIbs9albB7Y9pjYKd49buPN45qRFICrbPfRDGSL5n5Hnb27nv/nn+xpex6zmjN38B1YPtsNXa8f7/CZ0lGs9ppbDiOgYAoA0V1VB2Nb73qwLgoO4oOt64w72jPDFm+968UpWK5bru46XOW3g7/7P9d9Wd4sZsT58zO6OgZKyMZ3bW3XwzrjHb9+dvljJ259ibBZDZ9ffa26fdPtvsPLH7K999vjF3L4rufOlt7iyK9vi+vPOctx6893/It3/+/d3z8x2R+ynITg3F9NEPPnEEaVpHM+XQgqRzux6flbTU5DmRJq6VJFlrn5H0jCRduHChI17J/vR7z+ovvfOE6xh7epDGuJlv+nt9/LtdT4sNtCbP215UHACAg3rqR6RGw3UKAHu524CEew0CaGYQw76DCO4jk2s98YjrCEeumdv9i5IeN8Y8JmlR0kck/eod5zwn6eM7awr9hKSctXbZGLPexLUdKxL2dXIw6ToGAAAA4AZ7VABAW9i3HLLW1o0xH5f0VW3/eP+MtfaaMeZjO8c/Jel5bW9jP6Htrez/4b2uPZKvBAAAAAAAAAdm7metmaN24cIFOzo66joGAAAAAABAxzDGvGKtvXDn82xVBAAAAAAA0MUohwAAAAAAALoY5RAAAAAAAEAXoxwCAAAAAADoYpRDAAAAAAAAXYxyCAAAAAAAoItRDgEAAAAAAHQxyiEAAAAAAIAuRjkEAAAAAADQxSiHAAAAAAAAuhjlEAAAAAAAQBejHAIAAAAAAOhilEMAAAAAAABdjHIIAAAAAACgi1EOAQAAAAAAdDHKIQAAAAAAgC5GOQQAAAAAANDFKIcAAAAAAAC6GOUQAAAAAABAF6McAgAAAAAA6GLGWus6w9sYY9YlzbrOgY51QlLKdQigDfC9AjSH7xVgf3yfAM3hewVH7RFr7cidT7ZkOQQcJWPMqLX2guscQKvjewVoDt8rwP74PgGaw/cKXGFaGQAAAAAAQBejHAIAAAAAAOhilEPoRs+4DgC0Cb5XgObwvQLsj+8ToDl8r8AJ1hwCAAAAAADoYowcAgAAAAAA6GKUQ+haxpjfNMZYY8wJ11mAVmSM+TfGmJvGmMvGmGeNMQOuMwGtxBjzIWPMmDFmwhjzCdd5gFZkjDlnjPmmMeaGMeaaMeafuc4EtDJjjG+Mec0Y80XXWdBdKIfQlYwx5yT9vKQ511mAFvaCpP/FWvseSbck/T+O8wAtwxjjS/qkpA9LelLSR40xT7pNBbSkuqT/y1r7o5L+qqRf53sFuKd/JumG6xDoPpRD6Fb/XtL/LYlFt4C7sNZ+zVpb33n4A0lnXeYBWswHJE1Ya6estVVJn5P0lONMQMux1i5ba1/deT+v7Re9Z9ymAlqTMeaspP9V0qddZ0H3oRxC1zHG/JKkRWvt666zAG3kH0n6susQQAs5I2l+1+MF8YIXuCdjzKOS/rKklx1HAVrVf9D2H7ADxznQhUKuAwBHwRjzdUmn9zj0LyT9v5I+eLyJgNZ0r+8Va+2f75zzL7Q9LeAPjzMb0OLMHs8xGhW4C2NMj6Q/lfQb1tpN13mAVmOM+UVJa9baV4wxf91xHHQhyiF0JGvt39rreWPMX5L0mKTXjTHS9jSZV40xH7DWrhxjRKAl3O175TZjzP8u6Rcl/U1rLS98gTctSDq36/FZSUuOsgAtzRgT1nYx9IfW2s+7zgO0qJ+U9EvGmF+QFJPUZ4z5A2vt/+Y4F7qE4V4f3cwYMyPpgrU25ToL0GqMMR+S9O8k/ay1dt11HqCVGGNC2l6o/W9KWpR0UdKvWmuvOQ0GtBiz/de435eUsdb+huM4QFvYGTn0m9baX3QcBV2ENYcAAHfznyX1SnrBGHPJGPMp14GAVrGzWPvHJX1V2wvs/hHFELCnn5T0DyT9jZ3fJZd2RkYAAFoII4cAAAAAAAC6GCOHAAAAAAAAuhjlEAAAAAAAQBejHAIAAAAAAOhilEMAAAAAAABdjHIIAAAAAACgi1EOAQAAAAAAdDHKIQAAAAAAgC5GOQQAAAAAANDF/n/3T/ZRqqkbUgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# x values for plotting.\n",
    "x = np.linspace(-5.0, 5.0, 1000)\n",
    "\n",
    "# The probability density functions (PDFs) for the t distribution.\n",
    "# The number of degrees of freedom is (nA + nB - 2).\n",
    "pdf = stats.t.pdf(x, (nA + nB - 2.0))\n",
    "\n",
    "# Create a dataframe from x and pdf.\n",
    "df = pd.DataFrame({'x': x, 'y': pdf})\n",
    "\n",
    "# Plot the overall distribution.\n",
    "plt.fill_between(df['x'], df['y'], color='g', alpha=0.25)\n",
    "\n",
    "# Plot the values more extreme than our |t|.\n",
    "crit = np.abs(stats.t.ppf(0.975, nA + nB - 2.0))\n",
    "tail1 = df[df['x'] >=  crit]\n",
    "tail2 = df[df['x'] <= -crit]\n",
    "plt.fill_between(tail1['x'], tail1['y'], color='b', alpha=0.25)\n",
    "plt.fill_between(tail2['x'], tail2['y'], color='b', alpha=0.25)\n",
    "\n",
    "print(crit)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "At a level of 0.05, there's a one in twenty chance that we incorrectly reject the null hypotheses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "52"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = 10.0\n",
    "s = 1.0\n",
    "t = 1000\n",
    "a = 0.05\n",
    "\n",
    "sum([1 if stats.ttest_ind(np.random.normal(m, s, 100), np.random.normal(m, s, 100))[1] <= a else 0 for i in range(t)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## End"
   ]
  }
 ],
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