diff --git a/ch_5/notebook/Chapter5.ipynb b/ch_5/notebook/Chapter5.ipynb new file mode 100644 index 0000000..7dcb1fe --- /dev/null +++ b/ch_5/notebook/Chapter5.ipynb @@ -0,0 +1,515 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "from scipy.stats import triang, beta\n", + "import matplotlib.pyplot as plt\n", + "\n", + "plt.rcParams['lines.linewidth'] = 2\n", + "plt.rcParams['lines.color'] = 'r'\n", + "plt.rcParams['font.size'] = 15\n", + "plt.rcParams['axes.labelsize'] = 20\n", + "plt.rcParams['axes.titlesize'] = 10\n", + "plt.rcParams['xtick.labelsize'] = 15\n", + "plt.rcParams['ytick.labelsize'] = 15\n", + "plt.rcParams['legend.fontsize'] = 15\n", + "plt.rcParams[\"axes.edgecolor\"] = \"black\"\n", + "plt.rcParams['axes.titlesize'] = 22\n", + "# plt.rcParams['figure.figsize'] = 13, 13" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def barplot(x, y, title=None, xlabel=None, ylabel=None, width = 0.015, \n", + " color = 'lightsteelblue', ynbins=5, ax=None, **kwargs):\n", + " if not ax:\n", + " fig, ax = plt.subplots()\n", + " ax.bar(x,y,width=width, color=color, **kwargs)\n", + " ax.set_title(title)\n", + " ax.set_xlabel(xlabel)\n", + " ax.set_ylabel(ylabel)\n", + " ax.locator_params(axis='y',nbins=ynbins)\n", + " return ax" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def bi_likelihood(theta, outcomes):\n", + " z = np.sum(outcomes)\n", + " n = len(outcomes)\n", + " return np.multiply(\n", + " np.power(theta,z),\n", + " np.power(np.subtract(1,theta),(n-z))\n", + " ), z, n\n", + "\n", + "def evidence(likelihood,prior):\n", + " return np.sum(np.multiply(likelihood, prior))\n", + "\n", + "def posterior(likelihood,prior,evidence):\n", + " return likelihood*prior/evidence\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Figure5.1 Bayes’ruleappliedtoestimatingthebiasofacoin.Therearediscretecandidatevaluesof θ. At each value of θ , the posterior is computed as prior times likelihood, normalized. In the data, denoted D, the number of heads is z and the number of ips is N." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "theta = np.linspace(0,1,11)\n", + "theta" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0. , 0.04, 0.08, 0.12, 0.16, 0.2 , 0.16, 0.12, 0.08, 0.04, 0. ])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pTheta = triang.pdf(theta,.5)\n", + "pTheta /= np.sum(pTheta)\n", + "pTheta" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "barplot(theta, pTheta, title='Prior', xlabel=r'$\\theta$', ylabel=r'$p(\\theta)$');" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "data = [1]\n", + "pData_t, z, n = bi_likelihood(theta,data) # likelihood of data given theta\n", + "pData = evidence(pData_t,pTheta) # evidence of data\n", + "pTheta_d = posterior(pData_t, pTheta, pData) # prob of theta given data (aka posterior)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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cOWjMzCxXDhozM8uVg8bMzHLVqetoJAmYCLwf2B8YBWwDvAw8CSwGfgP8OiIer2+pZmbWE1UVNJK2BE4F/p0ULspW/Z0UMFsAY4G3A8cA/ynpBuDbEXFPvYs2M7Oeo+KhM0knAY8A3yDtucwk7dEMjYgtI2JkRLyFFFq7AP8GXAMcDtwt6ReSRuU1ADMza27V7NH8GLge+GZE/G+5jSIigOXZcqmkIcAngS8DJwJnd7laMzPrcaoJmpaIeLCzbxwRLwDfkfQjYHRn+5uZWe9QMWhqCZmi/n8n7eWYmVkfVPWsM0kjgP2AbYFXgT8DyyLisZxqMzOzXqCayQADJH0feBy4GrgY+AFwE7BK0hpJ35XUUo+CJO0i6U5J6yWtlXS2pP5V9j1a0v9KelnSM5JulTSoHnWZmVltqtmjmUma1vwYcB3wDDCQdD3N3qQ9nE8BUyXdDHym1r0cScOAO4BlwCTSdOlvkwLxzAp9TwYuAc4HpgPDgIPxM3fMzBqqmh/hfwWWAuMj4qW2RkkbgPcAbwYOA04CjgAelHRkRNxfQz1TSdfkHJ1NJpibzV6bIen8rK0dSdsAs4DPRsSPClZdV0MNZmZWR9XcgmY4cGNhyBSKiJci4pqIOAqYAKwDbpK0XQ31HA7cVhQoV5HC54AO+n0se72shs80M7McVRM0q6lyenJE3EcKhP7A12uoZ2eKZqhlh+HWZ+vKeS/wMDBZ0l8kbZB0v6T31VCDmZnVUTVB83Pgw5LGV/OGEbGGNGngyBrqGQY8V6K9NVtXzrbATqTzOF8CPgi8BNwq6a011GFmZnVSzTma80mHpm6XdDrwo4h4rUKfl0g326xFlGhTmfY2/YCtgI9GxK0Aku4B1gDTgK+1e0NpCjAFYNQo3yHHDGDOglXt2iZNGNOASqw3qbhHk11wORFYAXwXWC3pfNIeRDuSdgM+AfyphnpagaEl2rem9J5Om2ez13ltDdl5nkWk+6+1ExGzI6IlIlqGDx9eQ6lmZlaNqqb+RsRfJe1DmjZ8WrYEgKQlwFrgFdIhrL1I52i+WEM9yyk6FyNpB2AQHd9d4KGsHhW1C9hYQx1mZlYnVT/4LCI2RMQ3gLeR9lh+Tro7wLuBQ4EPka6rWQH8S0T8rIZ6bgEOlTS4oO1Y0l2j53fQ70ZSqBzU1iBpa1LoLamhDjMzq5NOX8yYHUq7MlvanlWzPbA58NeIeKYL9fyA9NybayWdR3rGzQzgosIpz5JWAvMjYnJW00JJc4AfS/oy8DRwOrCBdLjPzMwapMtXzUfEetLzarosIlolHUK6wv8G0nmZWaSwKTSAdHiu0CeAC4CLgC2BBcDBEdFaj9rMzKw2TXd7lohYRrp1TEfbjC7Rto50K5xP5VOZmZnVomLQ1PnpmM+Vu42MmZn1TtXs0aym42tYOmMmftKmmVmfUk3QnE39gqajmWNmZtYLVfOEzRndUIeZmfVSVV9HY2ZmVotOzzqTtCMwnnSrmGeAhyPiD/UuzMzMeoeqgyZ7JPKPgY+WWLeWdO3LJeWeW2NmZn1TZ/Zo5pCub1kP3Evam9kaeCcwBvgGcIqkSRGxtN6FmplZz1RV0Ej6EClkfgscGxFPF61/B/AV0uOc50naK3tgmZmZ9XHVTgY4Hvg7cHxxyABExMrsvmMnAG8GarmhppmZ9ULVBs1ewG8j4smONoqI/ybda2zfap/IaWZmvVu1QbMtHT8PptA3Sc+mOaamiszMrFepNmgGAVXdoywiniVNFvAejZmZVT3rTHTuNjRLgaM7X46ZAcxZsKpd26QJYxpQiVnX5XVngFbSBZ1mZtbHdeY6mq9LOg5YBCzMXn9X5gLNjcAWdajPzMx6uGqD5k7gn4Cds+XjWftGSStIodO2/K7eRZqZWc9VVdBExPsBJI0FWgqWfwLelS3/km2+EfBtaMzMDOjkTTUj4lHgUeDqtjZJ7+SN4TMOGEL9nmFjZmY9WKfv3lwsIlYAK4ArASSJtIezV1ff28zMer4uB02xiAhgWbaYmVkfV3F6s6Quzx6rx3uYmVnPVM11NKskfU7Smzr75pL2kDQHOK3zpZmZWW9QTdDcTrpR5hOSvi/poI72UCSNlfQpSfcCDwJ7kB4vYGZmfVDFczQRcYKki0kPNpuSLa9Jegh4gnQXgIHAW4CdgG1It6z5G3AGMCsiXsmnfDMza3bVXkezEPiApP8DTAYOIU1jfnfRpk8B1wLXANdExIY61mpmZj1QZ6+jeQT4MoCkLYHtSXsyLwNPRsQTda/QzMx6tJqnN0fEeuCRbDEzMyuppqCRNBI4FdgF2Ax4DLgN+HVEvFq/8szMrKfr9GMCJB0IPAx8ETgCeD/pvM0vgBWSJnWlIEm7SLpT0npJayWdLal/J/r3k7RIUkg6qiu1mJlZ19XyPJrzSI8AuIQ0dXkksG/WPgi4VtL0WoqRNAy4g3SftEnA2aRAm9mJtzmZdO7IzMyaQC1BszswNyI+FxF/iIi1EXFPRHwVeCcwF/iWpENqeO+ppBA7OiLmRsQPSCHzBUlDKnXOguo/SNOqzcysCdQSNK9Q5pkzEdEKHEO6vub0Gt77cOC2iHihoO0qUvgcUEX/c4AFpOfnmJlZE6glaH5PujCzpOyJm3OA8TW8987A8qL3ewxYn60rS9LuwEn4djdmZk2lllln3wMul7RPRNxbZptXqO15NMOA50q0t2brOvId4LsRsVLS6EofJKntLgeMGjWqc1VanzFnwap2bZMmjGlAJWY9Vy17NOOBlcDNkj5evDK7kPNDpENYtSgVUCrT3vaZx5H2ss6t+kMiZkdES0S0DB8+vPNVmplZVWrZozm14M8/k/QN0jU0q4GhwEdKbFet1uw9im1N6T0dJG0GXECa9dZP0lDSEz4BBkkaHBEv1lCLmZnVQS1BMwHYs2DZBTglWxekvY/FpJlivyNNHPhDlRdyLqfoXIykHUjTppeX7JHWjSTdYfqionVXAX8C3lHFZ5uZWQ46HTTZeZlN52YkbU66uWZb8OwF7Ea66Sak8HlN0kMRsUeFt78FmF60F3Is6V5q88v0WQccVNS2LfBz4KvAb6oZl5mZ5aPLj3LO9lQWZQsA2ZX8u/LG8Nm9irf7AemQ27WSzgPGAjOAiwqnPEtaCcyPiMkR8Q9gXuGbFEwG+ENE3F/LuMzMrD66HDSlRMRrpGnQvwcuBZCkKvq1Zhd6XgLcQDovM4sUNoUGAFXflsbMzBonl6ApJSKqmu4cEcuAgytsM7rC+tWkc0VmZtZgtUxvNjMzq5qDxszMcuWgMTOzXDlozMwsVw4aMzPLlYPGzMxy5aAxM7NcOWjMzCxXDhozM8uVg8bMzHLloDEzs1w5aMzMLFcOGjMzy1W33b3ZrCvmLFjVrm3ShDENqMTMOst7NGZmlisHjZmZ5cpBY2ZmuXLQmJlZrhw0ZmaWKweNmZnlykFjZma5ctCYmVmuHDRmZpYrB42ZmeXKQWNmZrly0JiZWa4cNGZmlisHjZmZ5arpgkbSLpLulLRe0lpJZ0vqX6HPeyT9VNLKrN/Dks6SNLC76jYzs9Ka6nk0koYBdwDLgEnA24FvkwLxzA66Hpttex7wCLA7cE72ekyOJZuZWQVNFTTAVGAL4OiIeAGYK2kIMEPS+VlbKedFxFMFf58n6e/ADyXtGBFrcq7bzMzKaLZDZ4cDtxUFylWk8DmgXKeikGnzu+x1RP3KMzOzzmq2oNkZWF7YEBGPAeuzdZ3xPmAj8HB9SjMzs1o026GzYcBzJdpbs3VVkbQtcAbws3KH2yRNAaYAjBo1qvOV9lFzFqxq1zZpwpgGVGJmPUWz7dEARIk2lWlvv6G0OXA1sA74fNkPiZgdES0R0TJ8+PCaCjUzs8qabY+mFRhaon1rSu/pvIEkAZcDuwITIqK1vuWZmVlnNVvQLKfoXIykHYBBFJ27KWMWaVr0+yOimu3NzCxnzXbo7BbgUEmDC9qOBV4G5nfUUdJXgM8Cn4iI/8mvRDMz64xmC5ofAK8A10qamJ2wnwFcVHhSP7sDwI8L/v5x4Bukw2aPSxpfsPgEjJlZAzXVobOIaJV0CHAJcAPpvMwsUtgUGgAU3pbmA9nridlS6CTg0vpWamZm1WqqoAGIiGXAwRW2GV309xNpHzBmZtYEmu3QmZmZ9TIOGjMzy5WDxszMcuWgMTOzXDlozMwsVw4aMzPLlYPGzMxy5aAxM7NcOWjMzCxXDhozM8uVg8bMzHLloDEzs1w5aMzMLFdNd/dmq86cBavatU2aMKYBlZiZdcx7NGZmlisHjZmZ5cpBY2ZmuXLQmJlZrhw0ZmaWKweNmZnlykFjZma5ctCYmVmuHDRmZpYrB42ZmeXKQWNmZrly0JiZWa4cNGZmlisHjZmZ5cpBY2ZmuWq6oJG0i6Q7Ja2XtFbS2ZL6V9Fva0k/ldQq6XlJV0h6S3fUbGZm5TXVg88kDQPuAJYBk4C3A98mBeKZFbr/AtgJOBnYCJwHXA/sl1e9ZmZWWVMFDTAV2AI4OiJeAOZKGgLMkHR+1taOpH2AQ4EDIuKurO1x4H5JEyPijm6q38zMijTbobPDgduKAuUqUvgcUKHf39pCBiAiHgBWZevMzKxBmi1odgaWFzZExGPA+mxd1f0yD1XoZ2ZmOWu2Q2fDgOdKtLdm62rpN7ZUB0lTgCnZX9dJergTdZazDfB0Hd6np+hL4+1LYwWPt7er13h3rGajZgsagCjRpjLtNfeLiNnA7M6V1jFJCyOipZ7v2cz60nj70ljB4+3tunu8zXborBUYWqJ9a0rvsVTqN7RCPzMzy1mzBc1yis6pSNoBGETpczBl+2XKnbsxM7Nu0mxBcwtwqKTBBW3HAi8D8yv021bSvm0NklpI52duyaPQMup6KK4H6Evj7UtjBY+3t+vW8Sqi0qmP7pNdsLkM+CPpgsuxwEXA/4uIMwu2WwnMj4jJBW23Au8ETuP1CzafjAhfsGlm1kBNtUcTEa3AIUB/4AZgJjALOKto0wHZNoWOI+31/AS4HFgEfDjPes3MrLKm2qMxM7Pep6n2aJpVX7vRZy3jlfSebKwrs34PSzpL0sDuqrtWtX6/Bf37SVokKSQdlWet9dCV8Uo6WtL/SnpZ0jOSbpU0KO+au6IL//22SLo9G+ezku6Q9N7uqLlWkt4h6YeSlkh6TdK8Kvvl+lvVjNfRNJW+dqPPLoz32Gzb84BHgN2Bc7LXY3IsuUu6+P22ORnYPpcC66wr45V0MnAJcD4wnXSh9ME08e9IrePNZrveATwInJA1Twdul7R7RKzJs+4u2BU4ArgP2LwT/fL9rYoILx0swFdI1+kMKWg7nXRbnCEd9NuHdLHo/gVte2dtExs9rhzGO7xE25RsvDs2elz1Hm/BtsOAp4DJ2ViPavSYcvp+twFeBE5p9Bi6abxTgdeAoUXf9WvApxo9rg7q7lfw518B86rok/tvlQ+dVdbXbvRZ03gj4qkSzb/LXkfUr7y6q/X7bXMOsAC4M4fa8lDreD+WvV6WV2E5qXW8mwH/ANYVtK3L2lTvIuslIjbW0C333yoHTWV97UaftY63lPeRdsPrcR+5vNQ8Xkm7AyeRptT3FLWO972k73GypL9I2iDpfknvy6/Uuqh1vNdk23xb0ghJI0gzYFuBX+ZUa6Pk/lvloKksjxt9dtSv0epSt6RtgTOAn0WZ5wg1ia6M9zvAdyNiZd2ryk+t492WdAz/TOBLwAeBl4BbJb213kXWUU3jjYi1wEGk84t/y5ajgUPL7L33ZLn/VjloqtMtN/psIl2qW9LmwNWkQw2fr2Ndeen0eCUdR/rhPTevonJUy/fbD9gKmBwRV0TErcA/k85ZTKt/iXVVy/e7HekcxyLS4aPDsz/fJGlUHkU2WK6/VQ6ayvrajT5rHS8AkkS6YHZX4IhIF+E2s06PV9JmwAWkmTn9JA0FhmSrBxXdQqnZ1Pr9Ppu9zmtryPZUFwG71Ku4HNQ63umk2XQfiYhbs2A9hhSsPelQaTVy/61y0FTW1270Wet428wiTSOdFBHNPM42tYx3EDCSdHuk1mxZkq27itcnQTSjWr/fh0j/d1t8Ilyk83DNqtbx7gwsjYgNbQ0R8SqwlDRFujfJ/bfKQVO4MfUfAAADM0lEQVRZT7/RZ2fVOl4kfQX4LPCJiPif/Eqsq1rGu450/L5wOT5b91XgX/IptS5q/X5vJIXKQW0NkrYG9uL1kG1GtY53DbBbdhgYAElvAnYDVudQZyPl/1vV6Hnfzb6QToY9AcwFJpKuDVkHnFu03Urgx0VttwKPkk4i/jNp1s7djR5THuMFPk76P96fAuOLlnbX2DTL0pXvt2j9aHrGdTRd+ff5+qzvJ4EjST/UTwHDGj2ueo+XFKAbgJuysR5F+tHdAOzR6HF1MN4tgY9ky72kPbC2v2/ZwXeb629Vw//B9ISFdAz6N6T/C3qCdO1E/6JtVgOXFrUNzX54nwNeAK4Etmn0ePIYL3Bp9kNbajmx0WPK4/stWt8jgqYr4yVNBvg+8EzW9w7g3Y0eT47jPQS4i3R+6llSsB7Y6PFUGGvbv4elltEdjDXX3yrfVNPMzHLlczRmZpYrB42ZmeXKQWNmZrly0JiZWa4cNGZmlisHjZmZ5cpBY9akJG0h6euSlkv6u6Q/S/pGdq81sx7D19GYNaHs7sFzgXcC15EusjuKdPHh7Ij498ZVZ9Y5DhqzJpPdX+se0k0ND42IBVn7VqRbiowEto+IvzauSrPq+dCZWfM5jXSvrS+1hQxARKwj7d30A/ZrUG1mneagMWsikrYgPQvlCWB2iU2eyV637baizLrIQWPWXD5MusHhlVHwLJQCA7PXV7uvJLOuGdDoAszsDY7MXreXNKPE+onZ65+7pxyzrvNkALMmImkNUM0z6cdExOqcyzGrCx86M2sSkgaRQuaPEaHiBRhMevDWXxwy1pM4aMyax/bZ69oy6w8FNiM99dGsx3DQmDWPtufTv1Jm/UnZ60+6oRazunHQmDWPtgsw201dljQeOAK4JSIe6NaqzLrIkwHMmoikZcBOwD9FxO+zth1Jz6vfOmtf3bgKzTrPQWPWRCR9HLgCeBr4b2AQ8DEggCMj4p4GlmdWEweNWZOR9EngdODtpMC5GZgZEY83tDCzGjlozMwsV54MYGZmuXLQmJlZrhw0ZmaWKweNmZnlykFjZma5ctCYmVmuHDRmZpYrB42ZmeXKQWNmZrn6/8DaB5MDuv3FAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ax = barplot(theta, pData_t, title='Likelihood', xlabel=r'$\\theta$', ylabel=r'$p(D|\\theta)$', \n", + " ynbins=6);\n", + "ax.annotate('Data: z=%d,N=%d'%(z,n), xy=(0.05,0.85), xycoords=\"axes fraction\");" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "barplot(x=theta, \n", + " y=pTheta_d, \n", + " title='Posterior', xlabel=r'$\\theta$', ylabel=r'$p(\\theta|D)$');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Influence of sample size on posterior" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0. , 0.001, 0.002, ..., 0.998, 0.999, 1. ])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "theta = np.linspace(0,1,1001)\n", + "theta" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0.e+00, 4.e-06, 8.e-06, ..., 8.e-06, 4.e-06, 0.e+00])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pTheta = triang.pdf(theta,.5)\n", + "pTheta /= np.sum(pTheta)\n", + "pTheta" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "data_left = [1,0,0,0]\n", + "data_right = 10*data_left" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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ykn4i6TZJCyWVvJOKpAskRYnHmN6fvdWDZkkuG3UG3MzMbKDVVYIsaThwIxDA3sApwLHAyRU0vwTYATgcOATYAriy0P82wOXAzcDuwNXAxZJ2zVUbkvXxJnBnN685BxhfeMyvYKxWp5oxoWzGczIzM+tPgwd6AAVHASsC+0XEq8ANklYFJkk6PSvrRNJ44JPA9hFxa1b2NHCPpF0i4sas6onArRExMfv6ZkkbAt8HrgeIiFckrRYRIekYYKcuxvtGRNzdt1O2etHMieTUO+b51tRmZmYVqqsZZNKs7nWFRHgKKWnevpt2z3UkxwARMR2Ylx1D0vLAjsClhbZTgPGShuballxWYc2rmZPjDq1wjmZmZtVQbwnyGNKyhSUi4gnScoeu1vZ2apeZnWv3QWDZEvVmk74PH+7FeMdKelXSIkm3S+oqibc61UqJYyudq5mZWW/VW4I8HHilRHl7dqwv7Tqei/XaC8cr9XfS+uh/Bz4HDCItCdmyXANJR0iaIWnGCy+80MOXs/7QigljK56zmZlZT9RbggzpAr0ilSnvTbvi1+qiffkXi/hZRPwyIm6JiMtIa5WfBr7bRZvJEdEWEW2rr756T17O+kErJ4qtfO5mZmbdqbcEuR0YVqJ8KKVniLtrNyzXrj1XVqxDN/13KyIWAtcAm/WlH6sNJ4j+HpiZmZVTbwnyHAprjSWtA6xE6TXGZdtl8muTHwPeLlFvDLAYeKQX4y3FF/jVOSeG7/H3wszMrLN6S5CvBT4paZVc2QRgIXBLN+3WzPY5BkBSG7BBdoyIWETa//iAQtsJwF0RsaAvA5e0ImnHjJl96cf6j2+cUZq/J2ZmZkurt32QfwVMBK6QdBopwZ0EnJXf+k3SXOCWiDgMICLuknQdcKGk40gzwqcBt+f2QAb4ATBN0k9JNxHZI3vslh+EpN1Js9bjsq/3zw79LSIez7aEuwr4PTAXGAF8HVgb+EyVvhdWRU4Cu9bx/fFeyWZmZnU2gxwR7cDOpB0h/ky6g97ZwEmFqoOzOnkHkmaZfwNcSJrJ3bfQ/+3A/sAuwHXAXsBBEXF9oa9fAn8EDsu+/mP22DH7ehHwAnACad3xZNIa5u0jYkZPztn6n5Pjyvl7ZV2RNFbSTZLelPSMpFMkFWNxqXZDJZ0vqV3SAkkXSXpfiXp7S3pA0luSHpI0oYs+l5E0U1JI+lRfz83MLK9HM8iSREouPwFsB6xLmj1dCDwPzAL+CvwpIp7uzYAi4iG6vnsdETGqRNkrwKHZo6u2V1K4BXUl/ReOvwXs11Udqw9O+HrOd91rTP0dnyUNB24EHgL2Ju0tfyZpouWEbppfAnwEOJz3PuG7Etg21/82wOXAuaRPEvcALpbUXmISg6yvtXt6HmZmlVAlN42TNIQUsI4kBd2OrdHeAl4m3eluWK78HdIM8JkRcWeVx9wU2traYsYMTzb3JyfHfeMkuf9JmhkRbX3soybxWdJ3gG8C63UseZP0TdIyuDULd0DNtxsP3En6hO3WrGxL4B7gEx3L4LJlcstGxE65ttcAq0bENoU+h5MurP428D/Av0fEVV2N3zHXzKDyuNvtEgtJhwKPAj8kzUScTJqhGBYRQyJiZES8jzQbPRb4EmkWYHfgNkmXSFq396di1nNOjvvO38P6V+P4vDtwXSERnkJKwLu6i+juwHMdyTFAREwH5mXHkLQ8aQnbpYW2U4Dx2XUfeT8A7gBuqnDsZmY9Uska5PNI/9P/eESMjYhTIuKm4mxBJHMi4oKI+CywJvAfwDbAIdUeuFk5Tuyqx9/LulfL+JzfNrOj3yeANym9zWbZdpnZuXYfBJYtUW826e/UhzsKJG1CWkp3XIXjNjPrsUoS5LaI2C8i/taTjiPi1Yj4L1LgK84KmPULJ3TV5+9pXatlfB5O6RsqtWfH+tKu47lYr71wHOC/gF9ExNwuRwtIOkLSDEkzXnjhhe6qm5kt0W2CHBH39uUFIuKtiOjqJh9mVeFErv/4e1ufBiA+l7poRWXKe9Ou+LXy5ZIOJF3sd2o3r5caRUyOiLaIaFt99dUraWJmBvRgFwtJa5CuOF4T+BfwJPBQ9hGb2YBx8lYb3t2iftUoPreTLvYrGkrpGeJ8u1LZ6bBcu/ZcWbEOwCuSlgV+QtoBYxlJw4BVs+MrSVolIl7r+hTMzCrTbYIsaTDpI63DKTHjLOkp0k0zzvcewFZrTo5ry0lyfalxfJ5DYa2xpHVIN1XqahZ6Drnt3HLG8N6Wm48Bb2dltxTqLCbtWLESMBI4K3vkTcn6GF3BeZiZdauSNcgnk7YPehr4OemmHT8C/kb6+GtN4GjgHkl/9o4VVitOjgeGb9ldV2oZn68FPilplVzZBNLuGbeUbrKk3ZrZPscASGoj3Sn1WoCIWATcDBxQaDsBuCsiFgCvk3a6yD8+m9X7LvC53p2WmVlnlSyx+ALwILBVRLzRUSjpbWALYDXSrZoPJW3sfq+kPSPinn4Yrxng5LgeeDa5LtQyPv+KtN/yFZJOIyW4k4Cz8rtmSJoL3BIRhwFExF3ZHscXSjqO924UcnvHHsiZHwDTJP2UNLO8R/bYLevnHWBafkCSRmX/fMB/c8ysmiqZQV4duCoffPMi4o2IuDwiPgVsTfpf/tWS1qriOM2WcHJcP/xeDLiaxeeIaAd2BgaRbjRyMnA2adY6b3BWJ+9A0izzb4ALgZnAvoX+bwf2J90N8DpgL+CgMnfRMzPrV5XMIM8HRlXSWUTcLWl70i1Nv0/6aM+sapyQ1R/PJA+o+dQwPkfEQ8BO3dTpNJ6IeIU0i31oN22v5L11yZWMZz7v7XRhZlY1lcwgXwzsK2mrSjqMiMdJ+2ru2ZeBmRU5Oa5ffm8GjOOzmVk/qCRBPh2YC1wv6ShJxY/OSnkDGNGnkZnlOAGrf36PBoTjs5lZP6jkRiFvkdaEPQL8Apgv6XTSZu2dSNoI+Dxpy50ekzRW0k2S3pT0jKRTKgn6koZKOl9Su6QFki6S9L4S9faW9ICktyQ9JGlC4fhykn4i6TZJCyWV3QC/u76sOpx4NQ6/V7VV6/hsZtYqKplBJiL+CYwHTiTtRXkcafsdJN0n6VpJV0q6G/g7aXbi9J4ORtJw4EbSXZP2Bk4BjiVdDNKdS4AdSPuBHkK6gnuptWzZNkOXk7YT2h24GrhY0q65akOyPt4E7uxirJX0ZX3khKvx+D2rrVrFZzOzVqKI7u4QWmggrQDsR9p+ZxuguK/mbODUiLi4x4ORvgN8E1ivY9sgSd8kbSW0Zn4roUK78aRkdvuIuDUr2xK4B/hEx1ZC2VZDy0bETrm21wCrRkR+j05FREg6BviviOh0EUilfZXT1tYWM2b4virlOMlqfL5wr3uSZkZEWxX767f43Ogcc80MKo+7Fc0g50XEWxHxh4j4fHa18sqkj/M2BlaPiA37EHx3B64rJMJTgBWB7btp91xHcpyNczowLzuGpOVJG8tfWmg7BRgvaWiubZf/a+hJX9ZzTo6bg9/H2uvn+Gxm1jJ6nCAXRcSbEfFoRDwYES/1sbsxFG5ZGhFPkJY7jCnZoky7zOxcuw8Cy5aoN5v0ffhwD8ZZzb4sx0lVc/Fd9wZWleOzmVnL6DZBlrRiX1+kB30MB14pUd6eHetLu47nYr32wvFK9KovSUdImiFpxgsvvNCDl2sNTqSal9/b/lHj+Gxm1jIqmUGeJ+lr2bKCHpG0qaSppItGKlVqeYPKlPemXfFrlSmvRI/6iojJEdEWEW2rr756L16ueTmBan5+j/tFreOzmVlLqCRBvh44C3hW0i8l7djVjIOkDSQdLeku4F5gU9JOD5VoB4aVKB9K6Rni7toNy7Vrz5UV69BN/6Ver1p9tTwnTq3D73XV1TI+m5m1jG5vNR0RB0v6OfBD4Ijs8a6k2cCzpGRxBeB9pItBRpBmUp8DvgecHRGLKhzPHAprjSWtQ9q6qNQa43y7bUuUj+G9rd4eA97Oym4p1FlM2ke0UtXsq6U5YWo9vjV19dQ4PpuZtYxK90GeERG7khLAnwD3AWOBXUn7be5N2lII4ArgIGDdiPhxD4PvtcAnJa2SK5sALGTpRLRUuzWzvYkBkNQGbJAdIxvHzcABhbYTgLsiYkGlg6xmX63MyXHr8ntfPTWMz2ZmLaPbGeS8iHgU+DaApCHA2qSZiYXA8xHxbB/H8ytgInCFpNNICe4k4Kz81m+S5gK3RMRh2bjuyvYlvlDScaRZ3NOA2zv2QM78AJgm6aekmeU9ssdu+UFI2p00az0u+3r/7NDfIuLxnvRlpTlBMs8kV1cN4rOZWcvoUYKcFxFvAo9mj6qIiHZJOwPnAH8mreU9m5Qk5w0GirefPjCr+xvSzPhVpGQ73//tWbJ7KnA0aZ/kgyLi+kJfvwTWy339x+z5UOCCHvZlBU6OrYOT5P7RH/HZzKyV9PhOegCSRpKSz7Gk/YCfAK4D/hQR/6rqCJtUK97VyYmxldOqSXK176SX9en4XEIrxlwz66zSuNvjGWRJOwBXky78yN+C+UvAk5K+FhFTe9qvNTcnx9YVzyRXh+OzmVl19OZOeqeRbv18DmmLoJGkC0BOI63bvULS8VUboTU8J8dWCd91ryocn83MqqA3CfImwA0R8bWIeCAinomIOyPiu6RbLN8A/DhbS2wtzgmP9ZR/ZvrE8dnMrAp6kyAvAv5e6kBEtAOfJu2/+c0+jMuagBMd6y3/7PSa47OZWRX0JkG+n7ThfEkR8QYwFdiqt4OyxucEx/rKP0O94vhsZlYFvUmQzwX2lDS+izqLgJ5vj2FNwYmNVYt/lnrM8dnMrAp6kyBvBcwFrpF0UPFgtkH9XsAdfRybNSAnNFZt/pnqkX6Nz5LGSrpJ0puSnpF0iqTinvSl2g2VdL6kdkkLJF0k6X0l6u0t6QFJb0l6SNKEwvEtsn7mZmN4WNJJklbozfmYmZXTmxuF5G++8TtJPyTtsTkfGAbsX6KetQAnMtZfvA1cxfotPksaDtwIPES6ffUHgTNJEy0ndNP8EtLSj8N5706nVwLb5vrfBricNAs+kXRn0oslteduwDQhe93TSDdB2YR0V9NNSOurzcyqojcJ8tbAZrnHWODL2bEg7b05C/iGpL+TLhh5oJU3qG8FTo6tvzlJrkh/xuejSFvI7RcRrwI3SFoVmCTp9Kysk2y5xyeB7SPi1qzsaeAeSbtExI1Z1ROBWyOiI3m/WdKGwPeBjgT5tIh4Idf9NElvAb+WtF5EPF7BeZiZdavHCXJE3AXc1fG1pOWAjXkvIG8ObASM62gCvCtpdkRs2ucRW11xYmy15CS5a/0cn3cHriskwlNIs7nbA3/uot1zHclxNs7pkuZlx26UtDywI51ntqcA50saGhELCslxh45dO9YAnCCbWVX0ZgZ5KdnMw8zsAUC2Jm1Dlg7Km/T1tay+ODm2geAkuXJVjs9jgL8W+n9C0pvZsXIJ8hhgTony2dkxSMsmli1RbzZpCceHgb+V6f/fSMs2Hu5m/GZmFetzglxKRLxL2m7ofuACAEnqqo01FifHNpCcJPdeH+LzcOCVEuXt2bHetNsgV4cS9doLx5ciaU3ge8DvSi3xkHQEcATAuuuu28UQrVl19bfKMcS60i8JcikR4W2FmoSTY6sHHT+H/iPXdz2Iz6XqqUx5b9oVv1aZ8o7lI5cCrwNfL/miEZOByQBtbW3+G9QiKv0bVaznWGJ5vdnmrV8N9DZClfYl6QJJUeIxpthfM3FybPXGP5M1007aCaNoKKVniLtrNyzXrj1XVqxDsf9sxvtC0lKRPbK7BFqLmnrHvKUe1ejHrGYzyJWok22EKuorMwc4tFA2v/szbUwOGlavvOSiJubw3pphACStA6xE6TXG+XbF2EnW15XZvx8D3s7KbinUWQw8Umh7NulvxCcioqvXtibV33+P8v07trSmukqQqYNthHrQF8AbEXF39U6/fjk5tnrnJLnfXQscL2mViHgtK5sALGTppLZUuxMlbRMRtwNIaiOtP74WICIWSboZOAD4da7tBOCuiFjQUSDpO8BXgc909GetYaD+DnkpRmuqtwR5wLcRqqSvPp1hA3JybI3CSXK/+hUpfl4h6TRSgjsJOCsfsyXNBW7dKOPIAAAgAElEQVSJiMMgbT0n6TrgQknH8d6ncrcXJhx+QNrX+KekmeU9ssduub4PAn5IurjwaUlb5do/VmYbOGtQ9fq3x7PLraHeEuR62Eaokr46jJX0KrB81vZ7EdHVTErDqdcAZVaOk+T+ERHtknYGziHF4ldISx0mFaoOBorXjRyY1f0NKd5eRWGyIiJul7Q/cCpwNDAPOKiw/G3X7PmQ7JF3KNmuHNa4Gu1vjmeXm1e9Jcj1sI1QJX1B2pz+HtJ66dWBY0lLQraJiOldjLVhNFqgMuvgJLl/RMRDwE7d1BlVouwVUgJbvGajWO9K3luXXOr4IXROjK3BNdPfGs8uN496S5ChPrYR6raviPjZUgelq0nJ8neBfUoNsJH25GymgGWtyUmyWX1qlb8vTpYbW70lyH3ZRmj1EuW92Uaokr46iYiFkq4B/r2LOnW/J2erBC5rDU6SzepDq/9t8VKMxlNvCXI9bCNUSV9dqcvEtxKtHsCsOfmGIma1578nXfPscv2rtwS5HrYR6ravUiStSNrlYmZPTrheOJhZs/Nssln/8t+R3vHscn2qtwR5wLcRqqQvSUNJV2H/HpgLjCDd6nRt4DPV/Zb0Pwc1axVOks2qx387+odnl+tDXSXIdbKNUCV9LQJeIN3dbw3gLeAu0s1FZvTopAeYA5y1GifJZr3nvxm15WR54CiiYZfMNrS2traYMWNgc2kHOmtl9fDHRtLMiGgb6HG0gnqIuY3KfyvqUz3EsEZUadytqxlkqx0HPGt1nkk2K81/HxqDZ5f7lxPkFuTgZ5Y4STZL/HehsflCv+pzgtxiHATNluYk2VqR/xY0N88u950T5BbhYGhWnpNkawX+O9CaPLvcO06QW4CDoln3fEMRa0aO/1bk2eXKOEFucg6OZmatwzHfesLJcnlOkJuYA6VZz3km2RqNY71Vg5diLM0JcpNywDTrG69Ltnrl+G610Oqzy06Qm5CDp1l1OEm2euG4bgOpFZNlJ8hNxkHUrLqcJNtAcTy3etQqSzGcIDcRB1Oz/uEk2WrBMdwaUbPOLjtBbhIOrGb9y0my9QfHbmsmzTS77AS5CTjAmtWGk2TrK8drayWNPLvsBLnBOdia1ZaTZOspx2mzxptdXmagB1AkaaykmyS9KekZSadIGlRBu6GSzpfULmmBpIskva9Evb0lPSDpLUkPSZrQn331l6l3zHPQNRsgrfq710jxeaB1xOhW/Vkx6069/47U1QyypOHAjcBDwN7AB4EzSYn8Cd00vwT4CHA4sBg4DbgS2DbX/zbA5cC5wERgD+BiSe0RcX0/9VV19frDZNZKWu2GIo0UnweC47JZ79XjUgxFxECPYQlJ3wG+CawXEa9mZd8EJgFrdpSVaDceuBPYPiJuzcq2BO4BPhERN2Zl1wHLRsROubbXAKtGxDbV7qsrbW1tMWPGjIq/Nx0chM3qT28DuqSZEdFW5eH0i0aKz6X0NuZ2xfHYrP9VO2GuNO7W2xKL3YHrCoF2CrAisH037Z7rCJgAETEdmJcdQ9LywI7ApYW2U4Dxkob2Q19V5WBsVp9a5HezIeJzf6v3j4XNms1A/c7V1RILYAzw13xBRDwh6c3s2J+7aDenRPns7BikjwOXLVFvNuk/Ch8G/lblvqrGwdisvrXAxXuNEp+ryrHXrH7UcilGvSXIw4FXSpS3Z8d6026DXB1K1GsvHK9mX0uRdARwRPbl65IeLlWvCyOAF3vYphH5PJuLz7O89fpjIP2kUeLzElWIueCf32bj82wu/RZ36y1BBii1KFplynvTrvi1SpRXs6/3KkdMBiaXOlYJSTMaZb1iX/g8m4vPs6k0Unzuc8yFlnlffZ5NxufZd/W2BrkdGFaifCilZw26azcs1649V1asQ6FetfoyM2sWjRKfzcz6rN4S5DkU1pFJWgdYidLrzsq2y+TXqz0GvF2i3hjSVkGP9ENfZmbNolHis5lZn9Vbgnwt8ElJq+TKJgALgVu6abdmto8mAJLaSGvSrgWIiEXAzcABhbYTgLsiYkE/9FVtffqosIH4PJuLz7M5NER87gfN/r528Hk2F59nH9XbPsjDSZvQ/x9p8/cNgLOAn0bECbl6c4FbIuKwXNlfSFc6H8d7m8c/HxHFjeinAeeQNpbfI6u/W34j+mr2ZWbWDBopPpuZ9VVdJciQbmVKCpDjSWvK/geYFBHv5urMB6ZFxCG5smHA2cC+pJnxq4CJEbHU1Y2S9gFOBT5E2jtzUkRMKdSpWl9mZs2ikeKzmVlf1F2CbGZmZmY2kOptDXLTkzRW0k2S3pT0jKRTJA2qoN1QSedLape0QNJFkt5Xot7ekh6Q9JakhyRN6J8z6Xa8PT5PSVtk5zg3a/ewpJMkrVCoN0lSlHjs1r9nVXLMvTnPUWXG3+nThwZ/P8u9T6F02+KOeheUqdMvN37oZsyjJf1a0n2S3pU0rcJ2DfX72Wocd7ts47jbuW4jv5+Ou53r9er9rMd9kJuW0hq+G0nr+PYm3T3qTNJ/VE7ooinAJcBHgMN5b93dlUBxDd/lwLnARNIavosltddyXXQfznNCVvc04FFgE+AH2fOnC3UXAMXAPLuvY++JPr6fkNZQ3pH7uvhxc6O/n/8D/KVQtg/wLTpfUDUHOLRQNr93I+6TDUnf57uB5XrQrmF+P1uN467jboHj7nscd7sSEX7U6AF8h7SP56q5sm8Cb+bLSrQbT9oEf7tc2ZZZ2S65suuAvxbaXgPc3iDnuXqJsiOy81wvVzYJeLGB389R2Tl9qpv+G/r9LNPX1cDsQtkFwIyBfj+zsSyT+/dlpLW03bVpqN/PVns47jruZnUcd5cuc9zt5jW8xKK2dgeui4hXc2VTgBWB7btp91xE3NpREBHTSRex7A4gaXlgR+DSQtspwHhJQ/s+/Ir16jwj4oUSxX/Pnteo3vCqprfvZ7ea4f0skrQa8Ang4uoOr3oiYnEvmjXa72ercdx13K1IM7yfRY67vX8/nSDXVqfN7CPiCdL/CLta91NuE/zZuXYfBJYtUW826X3+cC/G21u9Pc9S/o300cnDhfJhkl6U9Lakv0var9ej7b2+nuf52XqrZyWdJWnF3LFmfD/3J51TqZ1exkp6VdIiSbdL6tMfuhprtN/PVuO467ib57j7HsfdLjhBrq3hlL4dant2rC/tOp6L9doLx2uht+e5FElrAt8Dflf4X/Rc0kdNnyGtkXsGuHwAgnVvz3MR8AvgMGBn4NfA0SwdwJru/QQOBO6NiOKdJv8OHAv8O/A5YBBwg6QtezHWgdBov5+txnHXcRccdx13l66TP16SL9KrvVL76qlMeW/aFb9WF+37U2/PM1WUliN9LPI68PWlOo74faHun4E7ge8DV/RmsH3Q4/OMiGeBY3JF0yQ9B5wraVxEzOqi/0Z9P9cifSz4rU4dR/ysUPdq0oUp3yVdXNIIGu33s9U47lbAcbds/436fjrulq5X0fvpGeTaageGlSgfSun/CXXXbliuXXuurFiHbvqvtt6eJwCSBFxIdmVrRLR3VT/SqvsrgE262wKnyvp0ngWXZc+b5fqmRP8N935mPkMKSpd0VzEiFpIuotisu7p1otF+P1uN467jbjmOuxnH3c6cINfWHAprhyStA6xE6bU0Zdtl8mtwHgPeLlFvDGktWfHjlf7U2/PscDZpW5u9I6KS+h1q/b/7vp5nXhSem+n9hPQx3+0R8WQPXrdRZlUb7fez1TjuOu6W47jbmeNuxglybV0LfFLSKrmyCcBC4JZu2q2Z7ecHgKQ2YIPsGBGxCLgZOKDQdgJwV0Qs6PvwK9bb8yTbyPyrwOcj4vZKXiyb+dgXuC9yt7ytgV6fZwn7Z88zoXneT0gb9ANbUeFV1NlFM7uTfS8aQKP9frYax13H3XIcd9+r77hbNND737XSg7Qg/FngBmAX0l6TrwOnFurNBc4rlP0F+AewH2l90MPAbYU62wDvAD8FdgBOJ/0vaddGOE/gINL/Xs8n/WLnH6vn6t1C2vB7V1KAviY7z70a5DwnkTZ83y9rdwop6F3eTO9nrvzbpP/Fl9pvdShwG3Ak6cKZCaTN4hcBbbU8z2w8Q0h/NPcH7gIezH09pNx5NtLvZ6s9+vLz20jvax/ikeNuE72fuXLH3T6+nzX9JvgRAGOBv2a/mM+S7lg0qFBnPnBBoWxYFsBeAV4F/gCMKNH/PsD/ZT/oc4ADG+U8SRuXR5nHIbl652W/FAuBN7Jf9N0b6DwPBGaQ7kr1r+wX/xRg+WZ6P3Pls4C/lOl3BdI6xiezc1yQBb2tBug8R3XxMziq3Hk22u9nqz0cd8ufp+Ou467jbumHssZmZmZmZobXIJuZmZmZLcUJspmZmZlZjhNkMzMzM7McJ8hmZmZmZjlOkM3MzMzMcpwgm5mZmZnlOEE2qzFJK0r6vqQ5kt6S9KSkH0padqDHZmbWjBx3rae8D7JZDUlai3RnpA8D/0va/PxTpA3hJ0fEkQM3OjOz5uO4a73hBNmsRiQtB9wJjAE+GRF3ZOUrk26tORJYOyL+OXCjNDNrHo671lteYmFWO8cBmwPf6gjSABHxOmlWYxlg2wEam5lZM3LctV5xgmxWA5JWBI4HngUml6jyUva8Zs0GZWbWxBx3rS+cIJvVxr7AMOAPEfF2ieMrZM//qt2QzMyamuOu9drggR6AWYvYM3teW9KkEsd3yZ6frM1wzMyanuOu9Zov0jOrAUmPA+tWUHX9iJjfz8MxM2t6jrvWF15iYdbPJK1ECtL/FxEqPoBVgLeBpxykzcz6znHX+soJsln/Wzt7fqbM8U8CywJX12Y4ZmZNz3HX+sQJsln/Wy57XlTm+KHZ829qMBYzs1bguGt94gTZrP91bEDfaSshSVsBewDXRsT0mo7KzKx5Oe5an/giPbMakPQQ8BHgYxFxf1a2HnALMDQrnz9wIzQzay6Ou9YXTpDNakDSQcBFwIvA74GVgM8AAewZEXcO4PDMzJqO4671hRNksxqR9EXgm8AHSQH7GuDkiHh6QAdmZtakHHett5wgm5mZmZnl+CI9MzMzM7McJ8hmZmZmZjlOkM3MzMzMcpwgm5mZmZnlOEE2MzMzM8txgmxmZmZmluME2czMzMwsxwmymZmZmVmOE2QzMzMzsxwnyGZmZmZmOU6QzczMzMxynCCbmZmZmeU4QTYzMzMzy3GCbGZmZmaW4wTZ6p6k+ZJC0g4V1L0gq3tIoXxSVj6pn4bZ8TqjsteZX+JYx3mMKpRPq/T86lUznIOZvcdxt/41wznUMyfIZmZmZmY5gwd6AGZV9h3gx8CzAz2QEnYGlgWeHuiBmJlVkeOuNR0nyNZUIuJZ6jNIExGPDfQYzMyqzXHXmpGXWFhTKbcWrps220t6WdK/JH2xcEySDpR0vaQXJS2S9ISk/y6uaavgdUquhSvU2VzSnyS9JGmhpPskHdZF/ZUkfS+r97qkNyTNkvRdSUO6aPdvki6X9M/svP8p6TJJW3XRZoSkcyQ9lX0f/iHpR129jpk1P8ddx91m5ATZWpqkA4HrSJ+m7BkRv80dWxa4DLgY2AZ4CPgT8AZwOHCvpLYqDmc34C5gfeB64F5gE+B/JB1bYuwjsvqnAusAN2Tnsh7wn8CdklYr0e5o4DZgP+CJ7ByfAD4N3CHpyyXarAncA/w/YDnS9+FB4KvATVmZmVm3HHcddxtCRPjhR10/gPlAADtUUPeCrO4hhfJJWfmkXNnxwGLS2rRNS/T146zNLcDIwrFjsmNzgcG58lFZ+fwuzmNUoXxaVh7AlwrHPp+VLwCGFI5dmh27FRiWKx8O3JEdu7jQZlPgbeBd4IDCsQOz8n8BGxWOXZ71dwOwSq58beDh3Pi7fY/88MOP+n847jrutvrDM8jWciQNkvQL4HTS7MRWEXFfoc5qwETgdVJAeyp/PCLOAa4GPgjsXqWhXR4Rvym8zu+B2cCqwJJZE0nrAfuT/tAcERGv5Nq0A1/Ojn1G0jq5LieSZm2mRMQfC681hTSrsSzwtdxrrQvsSwriR0XEa7k2TwPH9eGczWpK0mhJv84+Hn9X0rQavvaJkm6U9GpXH/tL2lrSPdnH/fMkTazVGPuL467jbqNxgmytZghwBfAV4GZg64h4skS9HYEVgVsi4vkyfd2SPY+v0tiuKlM+J3v+QK5sW0DA3RExp9ggIh4CppN+x7fLHdo+e76gzGt1/KHYIVe2Xe61Ol3wEhF/Bl4plpvVqQ2BPYBHskctHUlKlG4uV0HSaNJH9vOAPYFfA2dJOrwmI+wfjrvJBWVey3G3DnkXC2s1Xyf93M8CdouIf5Wpt0H2vKek6KbP1as0tifKlL+aPa+QK1s7e57XRX+PAVvl6lbS7rFCPYCRFbzW48CwLo6b1Ys/R8RUAEmXASNq+NrrRsRiSZ8C9ipT53jgGeDzEfEO8NdsNvEkSedF9hl7g3Hc7bqd424dcoJsreZq0oUf44BvkNa7lTIoe34YuLubPu+pztBY3IO6yp67+iOiLo6Va9dVG7OGFxHd/p5JWgE4BfgssAZpNvE7EXFNf782aenAH7LkuMMU4GhgI+CBvoxhgDjudt3OcbcOOUG2VjMLOJF00cOPJA2JiO+XqNfx8d8DEXFIrQbXAx1r8zboos762XN+g/ynSev3NuC9WYtK2kC6EKac9bo4ZtZoLgO2BE4i/Z58BviTpLaImNVfLyppJdLOCMWP72dnz2NozATZcddxt+F4DbK1nIh4gLS+6yngREk/KVHtRtJVx7tIqsePsG4jzUZsJenDxYOSPgp8nDQ7cmvuUMf6vYPL9Hto9jwtV3Zr9lrjJXX6wyBpT/wxnzUJSTuT1v4eEBG/jIjrI+Jw4E7ge/388h2/R8W1pe3Z8/B+fv1+47gLOO42FCfI1pIi4hFSsJ4HHJdtxK7c8eeAX5AC0J8kjSn2IWm4pMMlvb9W486N73HSFkDLAL+WNDQ3rmGkC3uWAS4tXAzzc+Ad4LOS9s33KekA0kzZ21m9/Gv9ifTx5y+zWa6ONh8Azqju2ZkNqF2Af5L2ph3c8SDtO5vf0WAtSWO6eazbyzGU+yi+EdcfL+G467jbSLzEwhrJuZJe7eL4vl0c6yQi5knalvSH7/8BK0r6cm6d4DdJVzB/Bvg/SbNIgX0F0segHyVt1P5R4LkenUl1HE36yHUH4B+57ap2JM003Uc6ryUi4j5JXwPOAa6QdA/pI7/RpI+UFwPHZLM9eV8h7eW5KzBP0i3A8sBOwP+RNs6v1lXlZgNpBLAmKWEpejf3758An+umr1tYemeC7nTMHBdnBocXjteS4+7SHHdbhBNkayQf7eb48j3tMCKelrQ9aW3cl0jB+uCIeCci3gYmSLooO7Yl6Q5LrwHPAn8AplJ6TVm/i4gXJY0H/oP0x6RjX9BHSbMLP4uIN0q0O1fSfcCxwNbA5sDLpG2YzoiIu0q0eUbSlsDJwN6kK/CfAc7Nyq6u8umZDZSXSes/9+mqUkR8nnRDiaqJiDckPUlKwPI6vu60tVgNOO4uPXbH3RahxtwxxszMrG86tnmLiB1yZbsC15DuatYvCWm2zdufgfUjYn7h2K9J++ZuGBHvZmXnkJKj9Rp0mzezhuMZZDMzaxmShpBuFAJp39lVJe2ffX0NaVbzOuAGSacBD5LuqDYOWCEivtOH196etH/v5lnR7pJeAB7KbjIB7y3d+J2k/wa2IN1g5Ggnx2a14xlkMzNrGdntncvdfGH9iJgvaXngu6REdV3SR+GzgP+KiF5/rJ2tV92+xKGTI2JSrt42wFmkpQX/BM6KiJ+XaGdm/cQJspmZmZlZjrd5MzMzMzPL8RrkATJixIgYNWrUQA/DzAbQzJkzX4yI1Qd6HK3AMXdpr7y+qOyxYSv3eGMKs4ZRadx1gjxARo0axYwZMwZ6GGY2gCQ9PtBjaBWOuUubeke5ZdjJ3luv3+Vxs0ZVadz1EgszM7MW0l1yXGkds2bmBNnMzKxF9CTxdZJsrcwJspmZmZlZTlOvQZY0Fvgv0r3KXwH+h7Tf5LtdtFkO+E9gK6CNtDG8ytTdGzgV+BDwj6zvS6p6Ek2sp7MTXhNnZtZ7vZkRnnrHPMdea0lNmyBLGg7cCDxEuof5B4EzSbPmJ3TRdAhwODAduBPYqUz/2wCXk+6JPpF0Z6aLJbVHxPVVOo2m0teP64rtHbTNzMysPzRtggwcBawI7BcRr5JuG7oqMEnS6VlZJxHxiqTVIiIkHUOZBBk4Ebg1IiZmX98saUPg+4AT5Jz+WseW79fJsplZeX2Jw55FtlbUzGuQdweuKyTCU0hJc6lbfS7R3f3us9uQ7ghcWjg0BRgvaWjPh9t8pt4xr2YXedTytcysbySNlvRrSfdJeje7BXN3bUZJihKPKTUYspm1mGZOkMcAc/IFEfEE8GZ2rC8+CCxb7B+YTfqefriP/Te8gUpWnShXz6BBgxg3bhwbbrghm266KWeddRaLFy/uss38+fP5wx/+UKMRvuell15ixx13ZOWVV+aYY44pW2+HHXagra1tydczZsxghx126PHr7bXXXmy00Ua9GaolG5KWpT2SPXriONJ1JR2PrpbMWZU4rtZGs8TdmTNnsvHGGzN69GgmTpxIqXnHSZMmMWTIEJ5//vklZSuvvHKPx3HGGWcgiRdffBGAiGDixImMHj2aTTbZhHvvvbfHfUJzJ8jDSRfmFbVnx/raNyX6by8cbzn1kqDWyzga2YorrsisWbN48MEHueGGG7jmmms4+eSTu2wzUIF6hRVW4Ac/+AFnnHFGt3Wff/55rr322l6/1hVXXNGrIG5L+XNErBMRBwAP9rDtwxFxd+4xtz8G2EwcCxtHs8Tdo48+msmTJ/Poo4/y6KOP8pe//KVkHyNGjODMM8/s9RiefPJJbrjhBtZdd90lZddee+2S1508eTJHH310r/pu5gQZoNRSCZUpr0b/KlOeDkpHSJohacYLL7xQpSHUj3oMwvU4pka0xhprMHnyZM455xwigvnz57Ptttuy2Wabsdlmm3HnnXcC8O1vf5vbbruNcePGcfbZZ5etV86MGTMYN24c48aNY+ONN0YquYFMJyuttBLbbLMNK6ywQrd1jz/+eE499dSK+i16/fXXOeusszjhBE9a9kVEdD0lZmYNG3efffZZXn31VcaPH48kDj74YK688sqSfXzpS1/ikksu4eWXX67oNYu+/vWvc/rppy815qlTp3LwwQcjia222opXXnmFZ599tsd9N/NFeu3AsBLlQyk9s9zTvinRf8fXJfuPiMnAZIC2trZqJel1oZ4T0Y6x+SKTvtlggw1YvHgxzz//PGussQY33HADK6ywAo8++iif/exnmTFjBj/+8Y8544wzuOqqqwB48803S9YDGDduHLNmzVrqNdra2paUHX/88ey2224A/OQnP+Giiy7qNKbtttuOn//85z06j/Hjx/O///u/3HzzzayyyipLyh9++GEmTJhQss20adMYNmwYJ554IsceeyxDhgzp0WtaVZ0vaTXgeeBi4HsRsXCAx2TWLxox7j799NOMHDlyydcjR47k6aefLll35ZVX5ktf+hI/+9nPOs2Ub7vttrz22mud2pxxxhnssssu/OlPf2Lttddm00037fT666yzTqfXX2uttcqOuZRmTpDnUFhrLGkdYCU6rx3uqceAt7P+b8mVjwEW0/M1dQ2tnpPjPCfKfdexjuztt9/mmGOOYdasWQwaNIhHHin9I99VvWKQzrv00ku59957uf76tCHM8ccfz/HHH1+18zjhhBM49dRTOe2005aUfeQjH+lyTLNmzWLu3LlLZmis5hYBvyDtEvQqsAPwLdI1IXuXaiDpCOAIYKmPYFtJNeOzd7MYGI0Wd0utN+5qVnrixImMGzeOY489dqny2267rWybN998k//8z/9cMta+vH45zZwgXwscL2mViOj4L8gEYCFLJ7U9FhGLJN0MHAD8OndoAnBXRCzoS/+NpFGS4zwH+d75xz/+waBBg1hjjTU4+eSTef/73899993H4sWLyy5tOPvssyuql/fggw9y0kknceuttzJo0CCgujPIADvttBMnnngid99995Ky7maQ77rrLmbOnMmoUaN45513eP7559lhhx2YNm1aj1/fei4ingXyVwJNk/QccK6kcRHR6S9/M39qZ62hEePuyJEjeeqpp5Z8/dRTT/GBD3ygbP1hw4Zx0EEHce655y5V3tUM8vvf/37mzZu3ZPb4qaeeYrPNNmP69OmMHDmSJ598suLXL6eZE+RfkW7gcYWk04ANgEnAWfmt3yTNBW6JiMNyZbuTZprHZV/vnx36W0Q8nv37B6QA/VPgStIV2XsAu/XnSdWTRkyOOzhJ7pkXXniBo446imOOOQZJLFiwgJEjR7LMMsvw29/+lnffTTenXGWVVZYKaOXqlbNgwQIOPPBALrzwQlZfffUl5X2ZQT744IM55phj2HLLLZcq/973vsdRRx3FBhtsAHQ/g3z00Ucvudhj/vz5fOpTn3JyPPAuI92saTOg/JtnVePYWTuNGnfXWmstVlllFe6++24+/vGPc+GFF/LVr34VgHPOOQeg064X3/jGN9hiiy145513lpR1NYMMLLX7xahRo5gxYwYjRoxgr7324pxzzuHAAw/knnvuYejQoT1eXgFNnCBHRLuknYFzgD+T1gWfTUqS8wYDgwplvwTWy339x+z5UOCCrP/bs8T5VOBoYB5wUKvcRa+Rk+MODvRdW7hwIePGjePtt99m8ODBfOELX+Ab3/gGAF/5ylf49Kc/zR//+Ed23HFHVlppJQA22WQTBg8ezKabbsohhxxSth6UXgt35ZVX8vjjj/PlL395SVlXSWveqFGjePXVV/nXv/7FlVdeyfXXX8/YsWO5//77SwbHPfbYY6k/BtaQovBs1tCaJe7+8pe/5JBDDmHhwnpg66MAACAASURBVIXsvvvu7L777gDMmTOHrbfeulM/I0aMYN999+Xss8/u2TeshD322INrrrmG0aNHM2TIEM4///xe9aNu7olh/aStrS06Fs03mmZIjoucKDenV199lcMOO4w//vGP3VceAJJmRkRb9zWbl6TLgBERsUMv2h5FmtDYNCLu76puI8fc3uqvWO14ab31qU99iiuuuILllltuwMZQadxt9m3erMqaMTmG5j2vVrfqqqvWbXLcyiQNkbR/9inc2sDqHV9LGpLVmSvpvFybSZLOlLSfpF0knUL6VPCK7pJjqy7HS+utq666akCT455o2iUWVn3NHhS95MKsZtbgvaVrHTq+Xh+YT+flb3NId9E7HFgReAL4CfCf/TlQM2tNnkE2y2n2/wQMlFGjRi25DWhvLVq0iAkTJjB69Gg+/vGPl9xq7cknn2THHXfkox/9KBtuuCE/+9nPlhybNGkSa6+99pIN8a+55po+jcd6LyLmR4TKPOZndUZFxCG5NlMioi0ihkbEchExOiK+HxGLBuo86pljWWur95j7ox/9iNGjR/ORj3yE6667rk/j7C+eQbaKtFKw9UxyfTrvvPMYPnw4c+fOZcqUKXzrW9/ikksuWarO4MGDOfPMM9lss8147bXX2HzzzfnEJz7B2LFjgXTXpeOOO24ghm9m1lD6K+Y+9NBDTJkyhQcffJBnnnmGXXbZhUceeWTJ9nL1wjPI1q1WSo47TL1jXkued978+fMZM2YMhx9+OBtttBGf+9znuPHGG9l666350Ic+xPTp03n55ZfZZ5992GSTTdhqq624//60FPSll15i11135WMf+xhHHnnkUhu3//73v2fLLbdk3LhxHHnkkd1uQdRh6tSpfPGLXwRg//3356abbuq0Ifxaa63FZpttBqStjz760Y+WvYOTmfVeq8fH/tAqMXfq1KkceOCBLL/88qy//vqMHj2a6dOnV/x9qhUnyNalVg+CrX7+c+fO5Wv/n717j5dzvPf//3oTFF85IMquQxxaEZKNxqmoOpSiOzRUlNahUeq3u6tVxe6uCtum7Dq0pS27zqVJi1KHVJ0iTeoUpWxJkBKnqEasxEaE8Pn9cd2T3JnMWmvWrDXn9/PxmMdkrvu67rnumazPXHPNdTjhBJ544glmzpzJ9ddfz5QpU/jRj37E2Wefzemnn84222zDE088wdlnn80RRxwBwBlnnMEuu+zCY489xqhRo3jxxRcBmDFjBhMmTGDq1KlLdnkqLEQ/ZsyYJT/F5W/XXHMNsOz2of369WPAgAHMmzev07rPnj2bxx57jB122GFJ2sUXX8yIESP46le/SkdHR6dlzczqoR1ibmdbQTcaD7Ew60Y7D7nYeOONGT58OABbbrkle+65J5IYPnw4s2fP5oUXXuDGG28E0u508+bNY8GCBUyePJmbbroJgP33359BgwYBcM899/Doo4+y3XbbAWnNz3XWWQdguZ/uivVk+9C33nqLgw46iIsuuoj+/fsDaaOP0047DUmcdtppfOc73+GKK67o6Uti1vDa/Yt9M2uHmNtXW0FXW0s3kCUNA34K7ETaKOSXwBkR0eXvC5IGABcBB5J62W8DvhkR83J5VgZOBY4gLVP0CnAdcHarTBpxkF2qXRvJq6yyypJ/r7DCCkser7DCCixevJh+/ZYPIYVAVyrgRQRHHnkk55xzznLHxowZw9NPP71c+oknnsgRRxyxZPvQ9ddfn8WLF7NgwQLWXHPN5fK///77HHTQQRx++OGMHj16SfpHP/rRJf/+2te+xuc///muLt3MrObaIeb21VbQ1dayQywkDQLuJu2wdABwJvAd4Iwyik8APkNaTugoYDvSdtJ5PyQ1kH9G2mL658DJwHm9rrw1JH9hWN6nP/3pJT/XTZo0ibXXXpv+/fsvkz5x4sQlP63tueee3HDDDUu2CH3jjTd44YW0e/uECRN4/PHHl7sVfkIcNWoUV199NQA33HADe+yxx3IfCBHB2LFj2WKLLZbsPlXw6quvLvn37373O7baaqu+fjnM2opjYu21QswdNWoU48ePZ9GiRTz//PM8++yzbL/99n36OvWFuvUgK73KewGfBT4NbAisDSwE/gE8DtwL/D4iKhmc8nXSWpmjI+JN4C5J/YFxks7L0krVaydgH2C3iJicpb0CPCRpr4i4O8t6GPDziLgge3yfpI8BhwMnVFDfhuLAV1q79iR3Zty4cRx99NGMGDGC1VZbbUkwPf300/nSl77Etttuy2677caGG24IwLBhwzjrrLPYe++9+fDDD1lppZW45JJL2Gijjbp6GgDGjh3LV77yFTbbbDPWXHNNxo8fD8CcOXM45phjuOOOO5g6dSrXXnstw4cPZ+uttwbg7LPPZr/99uPkk0/m8ccfRxJDhgzh0ksvrdKr0vxqEJ/NrAKtEHO33HJLDjnkEIYNG0a/fv245JJLGm4FC6jDVtPZLknfBI4jBd3C15F3gTdIjdqBufTFwK3A+RHx5x48z2RgTkQcmkvbEHgBGBURt3ZS7kzg2IhYtyj9OeB3EfGd7PE84McRcWYuzw+Ab0TEOt3Vr5G3PXXjuHtuJFtfaLStpmsVn+uhkWNuX6tlDHcstGbTkFtNSzoaeBY4m9QTcQaph2JgRKwWEetHxFqknu1hwFeBG4F9gT9JmpA1cssxlLTz0hIR8SLwTnas7HKZGUXlfgkcJ2lnSf9P0q7A8cDFZdbPmpi/RFirqXF8tiqpdWxyLLRWVesxyJcDDwE7RMSwiDgzIu4pHu4QycyIuCoivgSsC3wL2IU0Jrgcg0gT84p1ZMd6W+5U0ofDFOD/gMnATfke5WbkYFc+v1bWYmoZn83MGlqtG8gjI2J0RDzSk0IR8WZE/BTYFPhNT4qWSFMn6T0t913gy8C/AbuRfpY8PBuiUZKkYyVNkzRt7ty53VTBmoEbydZCah2fzcwaVk0byBHxl16WfzciSg1/KKWDNFau2ABK9xB3V25goZyktYGzgFMi4uKImJx9QJwC/LukkmOQI+KyiBgZESMHDx5c5mXUjht7lfHrZq2gxvHZzKyh1WUVi6wBuSvpp7n3gJeA6dkY4b4yk6KxxpI2AFan9BjjfLldS6QPZelSb5sAK5Fmcuc9RnpNNyLN9LY24dUtrFXUKD5bFdTry7rjn7WimjaQJfUjbdxxDCV6ryW9TNqU48qI6O1044nAdyWtERH/l6WNIU0+ub+bcqdJ2iUipmT1GklqFE/M8ryQ3W8L5H+O/GR2P7uXda8594L2nj8krJnVOD6bmTW0Wo9BPoO0fNArwE+A04FzSI1MkXosjietOXxrL2dE/wJYBNwkaS9JxwLjgAvyk04kzZJ0eeFxRDwA3AlcI2m0pANJO+RNKayBHBGvkXqTz5V0gqTdJX2btHnIbyPCA4zblL9oWBOrZXw2M2totR5i8RXgKWDHiHi7kCjpfdJudWsCnwOOJu1O9xdJ+0fEQz19oojokLQnadm1W0njhy8kNZLz+gHFK1QfmuW9gtxW00V5jgR+kKX/E+lD5VLgP3ta13pzo65vuSfZmlTN4rOZWaOrdQ/yYOC2fPDNi4i3I+LGiPg8sDPwFnC7pPUqebKImB4Re0TEqhGxXkScFhEfFOUZEhFHFaXNj4ijI2JgRPSPiMMi4vWiPG9GxEkRsWl2/s0i4uTccA5rY/7SYU2opvHZWotjnrWaWjeQZwNDyskYEQ+Slk9bkdRTa1XgoFY9fm2tyczG8blpOd6Y9a1aN5B/DXxB0o7lZI6IF0jrau5f1VqZVYk/tKyJOD6bmWVq3UA+D5gF/FHS1yUVj/0t5W1g7epWqz258WZmOTWLz5I2k3SppL9K+kDSpDLLDZB0paQOSQskXSdprZ4+v1WHP1OsldR6o5B3gb2AZ4BLgNmSzgM2L5Vf0lak3er+VrNKmvUxf2hYM6hxfN6SNNHvmexWrgnAZ0hL0R1Fmjx4cxf5zcwqUvONQiLi75J2Im3VfFJ2CwBJfwXmkJZnW5e0rvCKwHdqXc9W50ZbbRVeb69uYY2shvH51oi4JTvvDZTRC53Vax9gt4iYnKW9Qlp2bq/CMpxmZn2h1kMsAIiI9yPibNLyaF8mjX17CRhOCoCjgO1JPQuHR8S19ainmVm7qUV8jogPK6javsBrhcZxdp6HgeezY23LHR5mfa8uW00XZD/pXZ/dkLQa8DFgZeDvETGvjtVrWQ6m9eM1kq1ZNGB8HgrMLJE+IztmZtZn6tKD3JmIeCcino2Ip/oi+EoaJukeSe9ImiPpzHImnpQ7EUTSWtlEk79LWihppqQjeltva23+gmLNqK/jcwUGkTZ8KtaRHVuOpGMlTZM0be5cb3BaC45v1ioaqoHclyQNAu4mjZ87ADiTNFbujDKKdzsRRFJ/YDKwNfBvpAknPyX1rph1yR8iZhWJEmnqJJ2IuCwiRkbEyMGDB1e3ZmbWUmo6xELShn14uvkR8WYXx78OrAqMzvLdlTVqx0k6r7OyPZgI8j1gFWBkRCzM0u7r/WVVlxtmjcPDLayR1Dg+V6KDtNtfsYGU7lk2M6tYrccgz6aTb/oVOIPUK9yZfYE7i4L0eOBc0g5Qt3ZRbrmJIJIKE0EKDeSjgYtyjWOzHnMj2RrIbGoXnysxE9i1RPpQ2nipt0bs9HBcs1ZQ6wbymfRdAL6/m+NDgXvzCRHxoqR3smOdNZC7nQgiaWNgHWC+pDtIa4cuAK4FTo2I98q9iFpqxEBq/jCxhlHL+FyJicBpknaJiCkAkkYCm2THzMz6TE0byBExroZP1+MJHWWU2yT797rZ/XmkXunPAf8MnA0sBk4udWJJxwLHAmy4YV/+mmnNzo1kq7daxudsRYz9socfA/pLOjh7fEdEvCNpFnB/RIzN6veApDuBaySdBHxI+kVwitdANrO+Vtdl3mqgRxM6elCuMLnxqYj4WvbveyWtAXxP0riIeGe5k0ZcBlwGMHLkyL7qqbEW4UaytZF1gN8WpRUeb0wa7tGPtBFJ3qHAhcAVpDh8G/DNqtXSzNpWXRvIkjYCdiRNspgHPB0RT/bR6Tuy8xYbQNcTOsqZCPJGdl88Ke9e0ti7TYG+uo4+4eEVzcGNZGsU1YzPETGb1OnQVZ4hJdLmk+Z/HN0X9Wh2jRzXHcus2dWlgSxpdeBy4Isljs0BLgYujoi3e/E0MylaPF7SBsDqlB5jnC/X3USQvwGlxhkXAn4lu0SZAf5gsfqqUXw2M2to9VoH+RbgEGAhqdf1t8AfST+rfYw0lvevkrbsxXNMBPbJhj0UjMmes6sJJBOBdSXtUkgongiSTcK7C9ijqOyewDvArF7U26yhe4as5dUiPpuZNbSaN5AljSI1LO8DhkTEZyPi0IjYNyI2BT4BXEVqkE7qxdqcvwAWATdJ2iubIDcOuCC/9JukWZIuLzyOiAeAwkSQ0ZIOBK5j+YkgZwLbZDvu7Z1NGjkVODsiFlVY56pwY6s5+X2zWqthfLY24BhmzawePchfAt4FvhQRrxcfjIhZ2azlI4A1SUun9VhEdJB6dFckLel2Bmlyx+lFWTubCHI/aSLINcCjwBeKzv8w8C+k1StuBU4A/gs4p5L6mpXiDxirsZrEZzOzRlePMcifBO6LiH90lSkifiXpn4ETJe0YEQ/29IkiYjrLD4MozjOkRFpZE0Ei4k5Sb3PDcgPLzHqgZvHZesex3ay66tGDvC5dT5LLO4c0TOKg6lXHrLH5g9BqyPHZzIz6NJBXB97sNhcQEW8AD5CWGjJrW24kW404PpuZUZ8GcjkbdeQ9RVo43nrIjarW4vfTasDx2fqU45Y1q3ot89YTnW34YdZ2/GFjDcbx2cxaUr0ayD+QNF3StZJOkLRLtjh9KR8Cq9aycmaNzI1kqzLHZzNre/VYxeIeYBvSznRDgcOy9A8lPUNaUq1we6wO9WsJbkS1Nu+2Z1Xi+NwEmi2+O15ZM6p5AzkiPgsgaRNgZO62DbBFdjs8y/4h4O1MzUrwh471NcdnM7OkbmOQI+K5iPhNRJwcEXtExCBSj8WXgR8DU0lbnfav9DkkDZN0j6R3JM2RdKak4k1BSpUbkO2Q1yFpgaTrJK3VRf4DJYWkaZXW1awSzdaTZM2hFvHZzKyR1WOIRaci4hngGeB6AEki9Vh8sqfnkjQIuBuYDhwAbAqcT/pS8P1uik8ANgeOIfWSnAvcDOxa4nk+AlwAvNbTOlaLG03txT3JVgt9GZ+t/ThOWbNpqAZysYgIUgN3egXFv06aPDI6It4E7pLUHxgn6bwsbTmSdgL2AXaLiMlZ2ivAQ5L2ioi7i4p8F3gF+BuwVQX1NOs1f/hYrfUyPluF3AFiVhs1HWIhqdeznXtwjn2BO4sawuNJjebduin3WqFxDBARDwPPZ8fyddkQOBk4ocw6mVWNPzitN2ocn83MGlqtxyA/ny0btEpPC0r6Z0m3ACeVWWQoRVumRsSLwDvZsbLLZWaUKHc+8JuI+EuZdao6N5Lam99/64Vaxmczs4ZW6wbyH0njdV+V9HNJu3fV4yBpE0nHS3oA+Avwz8B9ZT7XIGB+ifSO7FivyknanTQU4z/KrA+SjpU0TdK0uXPnllvMrEfcSLYK1TI+WxtybLJmUtMxyBFxhKSfAGcDx2a3DyTNAF4lNUI/AqxFmiS3Nmnr09dIDdELI2JRT56yRFo5W6l2WU5SP+AnwFkR8feyKxNxGXAZwMiRI3uynatZj3hMsvVUHeKz9ZAbmGa1U491kKcBe0v6ODAW2BPYGhhelHUucBNwI3BjRLzfw6fqbAvUAZTuIc6XG1wifWCu3Neyx1dLKjzHysCK2eO3K6ivWZ9yI9l6qobx2cysodVtFYuIeBY4FUDSasDHSD0TC4F/RMSrvXyKmRSNGZa0AbA6pccY58stt5xbdq6bs39vDqwPlOo97gC+Avyqh/XtNfcuWDE3kq0SNYjPSBoG/BTYidT58EvgjIj4oIsyQ0gTpotNiIhDe1snqz7HJGsWDbHMW0S8Azyb3frKROC7ktaIiP/L0saQAvz93ZQ7TdIuETEFQNJIYJPsGMDFLG0sF5wKbAwcR5rQZ9YQ/IFkvVGN+NzLdeohTQacmnv8el/VzcwMGqCBLGl94JvAMGAl4EXgTuD3EfFeL079i+y8N0k6l9TAHQdckF/6TdIs4P6IGAsQEQ9IuhO4RtJJLN0oZEphDeSImAXMKrqOo4C1I2JSL+psVhVuJFslqhifK1qnPufpiHiwF89vdeR4ZM2grg1kSZ8BbidN/FDu0FeBlySdEBG3VHLuiOiQtCept/dW0k94F5IayXn9gOLtpw/N8l5B6tG4jfQh0bA8vMK64w8l64lqxmc6X6f+XNI69bdWeN6W5RhvVlu1Xuat2LmkXoSLSUsErQ/skqWvTur9/W6lJ4+I6RGxR0SsGhHrRcRpxePbImJIRBxVlDY/Io6OiIER0T8iDouILn/Ci4ijImJkpXU1q4Vbpj7vD1orVzXjc6Xr1BdcKekDSa9KusAblJhZX6t3A3kEcFdEnBART0bEnIj4c0R8D/gEcBfww6wn2Mz6iBvJVoZqxudK16lfBFzC0hU2LgWOJ/U+L8drz5tZperdQF4EPFbqQER0AAeR1t88uZaVajZu7Fgl/P/GulHt+Nzjdeoj4tWI+EZE/D4iJkXEOOBEYJSkrUvkvywiRkbEyMGDS63eafXi+GONrt4N5CdIS6aVFBFvA7cAO9asRmZtxB9S1oVqxudK16kv5YbsftsK6tEU/HdqVnv1biD/DNhf0k5d5FlE9zvfmVmF/OFrnahmfK50nfpSoujemoRjjzWyejeQdyQtl3aHpMOKD2YL1I9i2fUuzayP+YPKSqhmfJ4I7CNpjVxaOevUl3Jwdv9oBfUwMyup3usg55dOu1bS2aQ1NmeTfn47uEQ+y3HDxvqKl4GzItWMzxWtUy9pHLAGqVH+JvBp4LvATRHxRAX1MDMrqd4N5J1J48YKt2HA17JjQZqw8ThwoqTHSBNGnuzlAvVm1onCFy43lI0qxuderFM/k7SL3jGkJeheBP4b+K+eX15zaPVOEH8xt0ZV1wZyRDwAPFB4LGllYDhLA/Inga2AwuzkAD6QNCMi/rm780saBvwU2IkUgH8JnFG8FnKJcgOAi4ADyW0UEhHzsuMrkoL050kfGpB+3vuPiHik+ys3a2z+0LJqx+eImA7s0U2eIUWPx9PJkm5mZn2p3j3Iy8h6Hh4lN5Ysa4xuybJBeUR355I0CLgbmA4cAGwKnE9q8H6/m+ITSLO3j2HpVtM3A7tmx1cFTgWuBM4hfTB8A5gi6VMRUZOxcK3es2D15Uay5fVlfDbLc6yxRtRQDeRSst7eJ7LbVQCS1FWZzNdJDdnR2Zi2uyT1B8ZJOq9oi9Mlshnb+wC7RcTkLO0V4CFJe0XE3aSJJJtka4EWyt0DPENqKB9d0cWaNRh/cFlXehGfzcwaWr1XsahIRJSznM++wJ1FDeHxpEbzbt2Ue63QOM6e72Hg+ewYEfFBvnGcpb0HPAWsU9ZFmDUJb09tPVFmfLYytNPfXTtdqzWHpmwgl2koRetpRsSLwDsUrb/ZXbnMjK7KSVqF9PPi9B7X1KwJ+APMzMzaRSs3kAdRekemjuxYX5f7j+z4LzvLIOlYSdMkTZs7d24Xp+qeGytWD/5/Z2bV4vhijaSVG8hQemcldZJecTlJ+5MayKdExNOdnjTisogYGREjBw8e3E0VzBqTh1yYVZ//xszqq5UbyB2kxeyLDaB0D3F35QaWKidpO9KqF5dGxEUV1NOsKfkD3MzMWlUrN5BnUjRmWNIGwOqUHmPcabnMcmOTJX0CuB24B/i33lTWrBm5N9nM+pLjiTWKVm4gTwT2kbRGLm0MaYm2+7spt66kXQoJkkaStkKdmEtbj7Tt6t+AL3W3+UhfcgCxRuP/k2Z9p93/ntr9+q0xtHID+RfAIuAmSXtJOpa0jekF+aXfJM2SdHnhcbZ71J3ANZJGSzoQuA6Ykq2BjKRVSY3lQcBZwAhJO2a3bWp0fWYNxb3JZmbWKhp+o5BKRUSHpD2Bi4FbSeOHLyQ1kvP6ASsWpR2a5b2C3FbTueMfBQpbqd5WVPYFYEjvam/WvAqNZG8wYmaV8iZFVm8t20AGiIjpwB7d5BlSIm0+aTe8kjviRcRs0qoWZtYJf8CZ9Zx/hVnKMcTqqZWHWLQkB09rJh52YWZmzcgNZDOrOjeUzbrnv5Hl+TWxenED2cxqxg1lM+spxwyrBzeQzazm3FA2W5b/Hrrm18dqzQ3kJuIAYa3GDWUzK5djhdWSG8hmVneFhrI/AK0d+f99+fxaWa24gWxmDcUNZWsn/r/ec37NrBZauoEsaZikeyS9I2mOpDMlFW8KUqrcAElXSuqQtEDSdZLWKpHvAElPSnpX0nRJY6pzJQ4I1n7cq9zaqh2frbU5Nli1texGIZIGAXcD04EDgE2B80lfCr7fTfEJwObAMcCHwLnAzcCuufPvAtwI/Iy0y95+wK8ldUTEH/v0YszaXPEHoTcPaG7Vjs/Nwg283vNmIlYtLdtABr4OrAqMjog3gbsk9QfGSTovS1uOpJ2AfYDdImJylvYK8JCkvSLi7izracDkiChsQX2fpC2BHwBuIJtVkRvMTa/a8bnhuXHcd7y9vVVDKzeQ9wXuLAq040m9DbsBt3ZR7rVC8AWIiIclPZ8du1vSKsDupJ7jvPHAlZIGRMSCProOM+uGG8xNp2rxuUr17TNuGFdP/rV1DLDeauUG8lDg3nxCRLwo6Z3sWGcBeCgws0T6jOwYpJ8DVyqRbwbpJ8JPAI9UVm0z662uGiH+4GwI1YzPDckN49oq9Xr7b996opUbyIOA+SXSO7JjlZTbJJeHEvk6io4vQ9KxwLHZw7ckPd1FPUpZG3i9h2Waka+ztfg6O7dRNSrSBKoZn5fog5gL/v/banydraVqcbeVG8gAUSJNnaRXUq74sbooT0RcBlzWzXN3StK0iBhZaflm4etsLb5O60S143OvYy60z/vq62wtvs7ea+Vl3jqAgSXSB1C6B6K7cgNz5TpyacV56Ob8Zmbtrprx2cys11q5gTyTojFpkjYAVqf0GLZOy2XyY9/+BrxfIt9Q0rJDz1RQXzOzdlHN+Gxm1mut3ECeCOwjaY1c2hhgIXB/N+XWzdY5BkDSSNL4tokAEbEIuA/4YlHZMcADVVzBolc/FTYRX2dr8XVasarF5ypol/fV19lafJ29pIjuhns1p2wh+unA/5KWDtoEuAC4KCK+n8s3C7g/Isbm0v5AWoniJJYuRP+PiCjeKGQScDFpkfr9svyf80YhZmadq3Z8NjPrrZbtQY6IDmBPYEXSkkFnABcCpxdl7ZflyTuU1ItxBXAN8CjwhaLzTwEOBvYC7gRGAYe5cWxm1rVqx2czs95q2R5kMzMzM7NKtGwPcqOSNEzSPZLekTRH0pmSintISpUbIOlKSR2SFki6TtJaJfIdIOlJSe9Kmi5pTHWupNv69vg6JW2XXeOsrNzTkk6X9JGifOMkRYnb56p7VSXrXMl1Dumk/uNL5G3m97Oz9ykk/Xsu31Wd5Kn5xg+SNpN0qaS/SvpA0qQyyzXV32e7cdztsozj7vJ5m/n9dNxdPl9F72err4PcUJTG3d1NGnt3AGlHvvNJX1S+30VRgAnA5sAxLB13dzNQPC76RuBnpG2w9wN+LamjlkM/enGdY7K85wLPAiOA/8zuDyrKuwAoDswzelv3nujl+wlpDOXU3ONlFjtvgffzl8AfitIOBE5h+QlVM4Gji9JmV1bjXtmS9Do/CKzcg3JN8/fZbhx3HXeLOO4u5bjblYjwrUY34N9J63j2z6WdDLyTTytRbifSIvifzqVtn6XtlUu7E7i3qOwdwJQmuc7BJdKOza5zo1zaOOD1Jn4/h2TX9Pluzt/U72cnqp9K7AAAIABJREFU57odmFGUdhUwrd7vZ1aXFXL/vgGYVEaZpvr7bLeb467jbpbHcXfZNMfdbp7DQyxqa1/gzoh4M5c2HlgV2K2bcq9FxORCQkQ8DDyfHUPSKsDuwG+Kyo4HdpI0oPfVL1tF1xkRc0skP5bdr9N31eszlb6f3WqF97OYpDWBzwK/7tvq9Z2I+LCCYs3299luHHcdd8vSCu9nMcfdyt9PN5Bra7nF7CPiRdI3wq7G/XS2CP6MXLlNgZVK5JtBep8/UUF9K1XpdZbyKdJPJ08XpQ+U9Lqk9yU9Jml0xbWtXG+v88psvNWrki6QtGruWCu+nweTrmm5MX/AMElvSlokaYqkXn3Q1Viz/X22G8ddx908x92lHHe74AZybQ2i9HaoHdmx3pQr3Bfn6yg6XguVXucyJK0L/AdwbdG36Fmkn5oOIY2RmwPcWIdgXel1LgIuAcaSlrq6FDieZQNYy72fpOW5/hIRxTtNPgZ8B/gX4HDSsl53Sdq+grrWQ7P9fbYbx13HXXDcddxdNk/+eEmepFd7pdbVUyfplZQrfqwuyldTpdeZMkork34WeQv49jInjvhVUd5bgT8DPwBuqqSyvdDj64yIV4Fv5JImSXoN+JmkrSPi8S7O36zv53qknwVPWe7EET8uyns7aWLK90iTS5pBs/19thvH3TI47nZ6/mZ9Px13S+cr6/10D3JtdQADS6QPoPQ3oe7KDcyV68ilFeehm/P3tUqvEwBJIm0AsCWwX6RNBToVadT9TcCI7pbA6WO9us4iN2T32+bOTYnzN937mTmEFJQmdJcxIhaSJlFs213eBtFsf5/txnHXcbczjrsZx93luYFcWzMpGjskaQNgdUqPpem0XCY/BudvwPsl8g0ljSUr/nmlmiq9zoILScvaHBAR5eQvqPW3+95eZ14U3bfS+wnpZ74pEfFSD563WXpVm+3vs9047jrudsZxd3mOuxk3kGtrIrCPpDVyaWOAhaStU7sqt262nh8AkkYCm2THiIhFwH3AF4vKjgEeiIgFva9+2Sq9TrKFzP8N+HKk7by7lfV8fAH4a0R8UFmVK1LxdZZwcHb/KLTO+wlpgX5gR8qcRZ1NmtmX7LVoAs3299luHHcddzvjuLs0v+NusXqvf9dON9KA8FeBu4C9SGtNvgWcVZRvFnB5UdofgOeA0aTxQU8DfyrKswuwGLgI+AxwHulb0t7NcJ3AYaRvr1eS/rDzt8G5fPeTFvzemxSg78iuc1STXOc40oLvo7NyZ5KC3o2t9H7m0k8lfYsvtd7qAOBPwHGkiTNjSIvFLwJG1vI6s/qsRvrQPBh4AHgq93i1zq6zmf4+2+3Wm/+/zfS+9iIeOe620PuZS3fc7eX7WdMXwbcAGAbcm/1hvkrasWjFojyzgauK0gZmAWw+8CZwPbB2ifMfCPxv9h99JnBos1wnaeHy6OR2VC7f5dkfxULg7ewPfd8mus5DgWmkXaney/7wzwRWaaX3M5f+OPCHTs77EdI4xpeya1yQBb0d63SdQ7r4Pziks+tstr/Pdrs57nZ+nY67jruOu6VvygqbmZmZmRkeg2xmZmZmtgw3kM3MzMzMctxANjMzMzPLcQPZzMzMzCzHDWQzMzMzsxw3kM3MzMzMctxANqsxSatK+oGkmZLelfSSpLMlrVTvupmZtSLHXespr4NsVkOS1iPtjPQJ4Hekxc8/T1oQ/rKIOK5+tTMzaz2Ou1YJN5DNakTSysCfgaHAPhExNUv/f6StNdcHPhYRf69fLc3MWofjrlXKQyzMauck4JPAKYUgDRARb5F6NVYAdq1T3czMWpHjrlXEDWSzGpC0KvBd4FXgshJZ5mX369asUmZmLcxx13rDDWSz2vgCMBC4PiLeL3H8I9n9e7WrkplZS3PctYr1q3cFzNrE/tn9xySNK3F8r+z+pdpUx8ys5TnuWsU8Sc+sBiS9AGxYRtaNI2J2latjZtbyHHetNzzEwqzKJK1OCtL/GxEqvgFrAO8DLztIm5n1nuOu9ZYbyGbV97Hsfk4nx/cBVgJur011zMxanuOu9YobyGbVt3J2v6iT40dn91fUoC5mZu3Acdd6xQ1ks+orLEC/3FJCknYE9gMmRsTDNa2VmVnrcty1XvEkPbMakDQd2BzYJiKeyNI2Au4HBmTps+tXQzOz1uK4a73hBrJZDUg6DLgOeB34FbA6cAgQwP4R8ec6Vs/MrOU47lpvuIFsViOSjgROBjYlBew7gDMi4pW6VszMrEU57lql3EA2MzMzM8vxJD0zMzMzsxw3kM3MzMzMctxANjMzMzPLcQPZzMzMzCzHDWQzMzMzsxw3kM3MzMzMctxANjMzMzPLcQPZzMzMzCzHDWQzMzMzsxw3kM3MzMzMctxANjMzMzPLcQPZzMzMzCzHDWQzMzMzsxw3kM3MzMzMctxAtqYmabakKLq9K+l5SddI2rredawlSUdlr8FV9a6LmbUmx91lOe62JjeQrVXcCVyd3f4IfAT4CvCIpENrWRFJV2XB8qhaPq+ZWY057lrL6lfvCpj1kR9GxKTCA0mrAv8DHA5cJumPEfFGvSpXQ78DHgQW1LsiZtbyHHcTx90W5B5ka0kRsRA4HngbWAPYp741qo2IWBARMyPi1XrXxczai+Ou424rcQPZWlZE/B/wTPZwo0K6pNUl/Yekv0p6S9Lbkh6X9D1Jq5U6l6S9Jd0u6R+S3pf0hqSZkq6QtG2WZ4ikAI7Mil1ZNEbvqKJzriXpLElP5urxF0nflrRSiTos+QlR0nBJv5X0d0kfSPpWlqfLsXCSPiXpxqzce9n9DZJ27CT/pOx8n5H06ew1eF3Sh5IO7Or1N7P247hb8jocd5uQh1hYq+uf3S8CkLQ2cC8wHOgA7gIC2B34L+AQSXvkfxbMAuyVwIfAQ8ALwP8DNgCOIn0Y/AV4izQWbxdgU2AqMCtXl1m5cw4H/gD8E/AyMIn0hXUH4AJgf0n7RcR7Ja5pZ+AXwCtZuTWAd7p7ISQdD1ycPc8j2euwGXAQ8AVJX4+I/+mk+BeBrwPTSa/Z2sD73T2nmbUlx92lz+m426wiwjffmvYGzCYF2s+UOLY18EF2fPcs7TfZ48nAwFzeQaTAGsCvi87zXJb+qRLPsT4wrCjtqiz/UZ3UedXcOf8d6Jc7tiZLPzzGdXLeAM4CVihx7qOy41cVpf8zKbB+AHyx6NihWfp7wFZFxyblnvPYer/fvvnmW/1vjrvLndtxtwVvHmJhLUfSIEmjgJtI39ofB+6XtBFwMKlH4tiImF8oExEdwNeyY4dI2iB3yo8C8yPiz8XPFREvR8T0HlbxKGBj4DcRcU5ELM6d7w3ST4XvA/8qSSXKzwROj4gPe/Cc3yT9YjQ+In5bdA3jgRuAlYATOil/V0Rc1oPnM7M24rhbkuNuE3MD2VrFfYUxZ8AbwC2kYPgX4MAsqO0KCHgwImYWnyALuA+T/i4+nTv0MDBQaX3PbToJnj2xX3b/21IHI2IO8Czp57SPl8hyS0R80MPn3C27v6qT41dk95/p5PhNPXw+M2t9jrtdc9xtYh6DbK3iTuDv2b8XAXOAPwH3RaTfrICPZffPd3GevwE75vIC/H/A7aT1Pb8CLJD0MOknuWsj4u/LnaVrm2T3vy0j5g9m6YSXghd6+HzQ/bX/rShfsUqe08xam+Nu1xx3m5gbyNYqllmPsxOFqBhl5FkiImZI2py0ZNEepMkauwOfBcZJOigi/tCDuq6Y3d8OvN5N3nkl0hb24LmKdXbt3X1i9OY5zaw1Oe6Wx3G3CbmBbO3k5ex+ky7ybJzdv5JPjIj3gduyG5IGAaeTxo5dTuc9AKW8BGwO/Dwibu9Bud54hTTDexOW9lrklbxuM7Nectx13G1KHoNs7eRPpG/yO0r6RPFBSVuQlvv5kDTbulPZ5JLvZnn/SdLg3OHCEkGdfQGdmN1/sfyq99r92f0RnRw/OrufVP2qmFkbcdx13G1KbiBb24iIF4AbSf/vL5U0oHBM0kDg0uzYbyLipSx9NUknFgXigv2z/G8C83Pphd6ALTqpymWk3owjJZ1RapF8SVtJOnr5ohX7CbAY+JKkLxQ91xeBQ0gzuH/Sh89pZm3Ocddxt1l5iIW1m+OBoaRZw89JmpSl705ak/OvwL/m8q8MnA+cJ+lJ0iznD0k/m43M8pyS/RRYcAvwA+BbkrYi/cQYwBUR8eeIeEvS/qSfDX8AfEPSE6TJLh8l/ew2hLQ4/pV9cdER8VdJJ5AWrL9J0kOkn/w2A7bPrukbEfFkXzyfmVmO467jbtNxA9naSkS8Lmkn4Fukb+/7ZoeeBX4E/Dgi3s4VeYsU3D9DWgB/H9K6la8A1wM/iYiHip7jcUljgJOAT5F2fwKYAvw5y/OkpBGkmdoHANsCHwHmkno5riWtkdlnIuJnkv4KfIc04eWTpKWZbgJ+FBEP9OXzmZmB467jbnPS0pVYzMzMzMzMY5DNzMzMzHLcQDYzMzMzy3ED2czMyiJpmKR7JL0jaY6kMyWtWEa5AZKulNQhaYGk6yStVSLfAZKelPSupOnZmNJS5xst6RFJCyXNk/QHSav3xTWamYEbyGZmVoZsk4a7SSsDHACcSZp4dEYZxSeQJlwdAxwFbAfcXHT+XUjLgd1HmsR1O/BrSXsX5TuGNFFrYpbvGNJkL086N7M+40l6dbL22mvHkCFD6l0NM6ujRx999PWIKLXWa8OR9O/AycBGEfFmlnYyMA5Yt5BWotxOpFUEdouIyVna9qTltD4bEXdnaXcCK0XEHrmydwD9I2KX7PHawPPAiRHxPz2pv2OumUH5cdffuOtkyJAhTJs2rd7VMLM6kvRCvevQA/sCdxY1hMcD5wK7Abd2Ue61QuMYICIelvR8duxuSauQ1sT9ZlHZ8cCVkgZExALSEmEAV/e08o65Zgblx10PsTAzs3IMBWbmEyLiReCd7FjZ5TIzcuU2Ja1zW5xvBulzqrBF8Q7A08BYSS9Lel/SQ5I+1ZMLMTPrjhvIZmZWjkEsu7VvQUd2rDflCvfF+TqKjq8LbA58HzgF+BfgbeAPkj5a/ASSjpU0TdK0uXPndlFFM7NluYFsZmblKjVpRZ2kV1Ku+LGK0lcg7ZA2NiKui4g/AAcCHwDfWO5JIy6LiJERMXLw4KYY6m1mDcJjkM2K3DL1+ZLpB+y8cY1rYtZQOoCBJdIHULqHOF+uVOt0YK5cRy6tOA+5fG9k95MKGSLiTUmPAsO6qIOVqTj+Oe5Zu3ID2dpWZw3hnuT3h4e1kZkUjTWWtAGwOqXHGOfL7VoifShLl3r7G/B+lnZ/UZ4PgWeyxzNIvcliWcryWYU6i4eFdMc6azceYmFt5Zapzy+5NeL5zBrYRGAfSWvk0sYAC1m2UVuq3LrZOscASBoJbJIdIyIWkdY//mJR2THAA9kKFgC3kRrDu+fONQD4JPDXCq7JKK+zwDHO2o17kK0t1CK455/DvS3Wgn5BWobtJknnkhq444AL8ku/SZoF3B8RYwEi4oFsjeNrJJ1E6uk9F5hSWAM585/AJEkXkXqW98tunytkiIhpkm4BLpd0KvA6aW3m94FLqnPZVnDL1Ocd26xtuIFsLa1evR7+WdJaTUR0SNoTuJi05vF84EJSIzmvH1C8/fShWd4rSL9c3kbRmscRMUXSwcBZwPGkDUEOi4g/Fp3ry8B/AxcAqwFTgT0iogPrMfcMm5XmIRbWshoh8DdCHRrBkCFDeP3113t1jkWLFjFmzBg222wzdthhB2bPnt1p3g8++IBtttmGz3/+80vSnn/+eXbYYQc+/vGPM2bMGN57771e1acdRcT0iNgjIlaNiPUi4rSI+KAoz5CIOKoobX5EHB0RAyOif0QcFhHL/YeIiJsjYquIWCUihkbE+BJ53oqI4yNirawee0XEk31+sVaSY1pzqFXMfemll9h9993ZYost2HLLLfnxj3+8zPGf/vSnbL755my55ZacfPLJALz//vsceeSRDB8+nC222IJzzjmnV/WsFjeQreU02pjgRqtPs7r88ssZNGgQs2bN4tvf/jannHJKp3l//OMfs8UWWyyTdsopp/Dtb3+bZ599lkGDBnH55ZdXu8pmDc1xybpSTszt168f559/PjNmzODBBx/kkksuYfr06QDcd9993HLLLTzxxBM89dRTnHTSSQD89re/ZdGiRTz55JM8+uijXHrppV12eNSLG8jWUho54Ddy3UqZPXs2Q4cO5ZhjjmGrrbbi8MMP5+6772bnnXfm4x//OA8//DBvvPEGBx54ICNGjGDHHXfkiSeeAGDevHnsvffebLPNNhx33HFELF3e9le/+hXbb789W2+9NccddxwffPBBZ1VYxi233MKRRx4JwMEHH8w999yzzHkLXn75ZW6//XaOOeaYJWkRwb333svBBx8MwJFHHsnNN9+8XFkz616zxbJm0Ywxd7311mPbbbcFYI011mCLLbbglVdeAeDnP/85p556KqussgoA66yzDgCSePvtt1m8eDELFy5k5ZVXpn///r145arDDWRrGc0QtJutN3nWrFmccMIJPPHEE8ycOZPrr7+eKVOm8KMf/Yizzz6b008/nW222YYnnniCs88+myOOOAKAM844g1122YXHHnuMUaNG8eKLLwIwY8YMJkyYwNSpU3n88cdZccUVue666wAYM2YMW2+99XK3a665BoBXXnmFDTbYAEi9FgMGDGDevHnL1flb3/oW5513HiussDS8zZs3j4EDB9KvX5p2sf766y8J4mbtqJniUDtpxphbMHv2bB577DF22GEHAJ555hn+9Kc/scMOO7DbbrvxyCOPAKmxvfrqq7Peeuux4YYbctJJJ7HmmmtW5wXtBU/Ss6bXjIG+WWaDb7zxxgwfPhyALbfckj333BNJDB8+nNmzZ/PCCy9w4403ArDHHnswb948FixYwOTJk7npppsA2H///Rk0KO0UfM899/Doo4+y3XbbAbBw4cIlvQoTJkzosi6leoulZZfDve2221hnnXX45Cc/yaRJk3pU1szK1ywxrNk0W8wteOuttzjooIO46KKLlvQGL168mI6ODh588EEeeeQRDjnkEJ577jkefvhhVlxxRebMmUNHRwe77rore+21F5tssklPX66qcgPZmlozNo4LmuEDpvDTGMAKK6yw5PEKK6zA4sWLl/TI5hUCaKlAGhEceeSRJSdljBkzhqeffnq59BNPPJEjjjiC9ddfn5deeon111+fxYsXs2DBguV6HaZOncrvf/977rjjDt59913efPNNvvzlL3Pttdcyf/78JXV++eWX+ad/+qeevRhmZlXWbDEX0qS7gw46iMMPP5zRo0cvSV9//fUZPXo0kth+++1ZYYUVeP3117n++uv53Oc+x0orrcQ666zDzjvvzLRp0xqugewhFta0mrlxXNDs1/DpT396yc91kyZNYu2116Z///7LpE+cOJGOjrQC15577skNN9zAP/7xDwDeeOMNXnjhBSD1Zjz++OPL3Qo/IY4aNYqrr74agBtuuIE99thjuQ+Ec845h5dffpnZs2czfvx49thjD371q18hid13350bbrgBgKuvvpoDDjigyq+OWWNq9rjTzhot5kYEY8eOZYsttuDEE09c5tiBBx7IvffeC6ThFu+99x5rr702G264Iffeey8Rwdtvv82DDz7I0KHLbNLZEBqugSxpmKR7JL0jaY6kMyUVr6lZqtwASVdK6pC0QNJ1ktYqke8ASU9KelfSdEljio5vl51nVlaHpyWdLukjJc61s6SHJC2U9LykbxbnsepwgG8M48aNY9q0aYwYMYJTTz11STA9/fTTmTx5Mttuuy1//OMf2XDDDQEYNmwYZ511FnvvvTcjRozgs5/9LK+++mpZzzV27FjmzZvHZpttxgUXXMAPf/hDAObMmcN+++3Xbflzzz2XCy64gM0224x58+YxduzYCq/azMBxuB4aLeZOnTqVa6+9lnvvvXfJGOY77rgDgK9+9as899xzbLXVVhx66KFcffXVSOJf//Vfeeutt9hqq63YbrvtOProoxkxYkRfv1S9plJjTOpF0iDgKWA6aaelTYHzgQsj4vvdlP0DsDmQ36nptYjYNZdnF2AS8DPgd6Rdmr4DfK6wGL2kHwHbA9cCzwIjSDs83R0RB+XOtRnwOGnB+8uyMmcBX4+IX3Z3rSNHjoxp06Z1l81KaMWg3OhDLaw6JD0aESPrXY924Jib9HX8dOyyZlNu3G20MchfB1YFRmdbl94lqT8wTtJ5+e1M8yTtBOwD7BYRk7O0V4CHJO2V2870NGByRBR6eu+TtCXwA6CwW9O5ETE3d/pJkt4FLpW0UUS8kKV/F5gDfDkiFgP3StoQOF3S5dFI3zxaSCs2js3MmlUzzKUwq0SjDbHYF7izqCE8ntRo3q2bcq8VGscAEfEwaavSfQEkrQLsDvymqOx4YCdJA7Jyc1neY9n9OkXPeVPWOM6fa31gqy7qahVq5cZxK1+bmZlZs2m0BvJQYGY+ISJeBN7JjpVdLjMjV25TYKUS+WaQXodPdHH+T5GGbTwNIGl1YINOzlWoj/UhNyDNzHrHcdSsfI3WQB4EzC+R3pEd6025wn1xvo6i48uQtC7wH8C1uZ7tgRWe61hJ0yRNmzu3VEe1mZmZmdVbozWQAUqN3VUn6ZWUK36sTtKRtDJpSMZbwLfLfM5O0yPisogYGREjBw8e3ElRK9YuvR7tcp1m1locu6wVNdokvQ6W9s7mDaB0D3G+XKkW58BcuY5cWnEeis+vtNjfNcCWwM4R0ZE7PL+obEFnvdRWIQdeMzMzq7VG60GeSdH4XUkbAKtTeoxxp+Uy+bHJfwPeL5FvKGl88TNF6RcCBwAHRETxuOi3gZc6OVehPtZL7dg4bsdrNjMzazSN1kCeCOwjaY1c2hhgIXB/N+XWzdY5BkDSSGCT7BgRsQi4D/hiUdkxwAMRsSBX9t+BfyMt4Tali+f8QtEmJmNIDef/7aKuVgY3FM3M+k61Y6pjtrWaRmsg/wJYBNwkaS9JxwLjgAvyS79lu9xdXngcEQ8AdwLXSBot6UDgOmBKbg1kSBt+fEbSRZI+I+k80mYhZ+bOfRhwNml4xSuSdszd8sM4/pu0pNu1knaXdDJwHHCm10C23vAHjZmZWX31aAxyNi53L+CzwKeBDYG1ST28/yDtLHcv8PuIeKWnlYmIDkl7AhcDt5LG8l5IaiQX17t4++lDs7xXkBr+twHLbP0cEVMkHUza8e540jrJhxV20cvsnd0fld3yjgauys41S9LngAtIvcl/B75Tzi561jU3EM16rtrx2cysnZS11bSk1UiNzeNIQbew8sO7wBukjTwG5tIXkxq450fEn/u4zi3B256W5sZx4p2p2kNfbDXt+Fyedo65tYyrjl3W6MqNu90OsZB0NPAsadjBQuAMUg/FwIhYLSLWj4i1SL26w4CvAjeSdpr7k6QJ2RbMZl1y43gpvxZWDsdnM7PqKGeIxeXAzcA5EfFIZ5mycbczs9tVkvoDRwKnkoYqnNlZWTMzq4jjs5lZFZQzSW9kRIzuKviWEhFvRsRPSVs8/6ai2lnbcI/p8vyaWBkcn83MqqDbBnJE/KU3TxAR7xavI2yW54agWWUcn607tY6vjufWKnq8zJukjSSNkXScpIMlDa9Gxaw9OJh2za+P9US147OkYZLukfSOpDmSzixaC76zcgMkXSmpQ9ICSddJWqtEvgMkPSnpXUnTJY3p4pwrSHpUUkj6fG+vzcwsr+xl3iStThrvVrzRBpLmkJZmuzjbZc7MzGqkFvFZ0iDgbmA6aZfRTYHzSR0t3++m+ARgc+AY0s6l55LGTu+aO/8upAmEPyOtyrEf8GtJHUVLcRYcA3ys0usxM+tKT9ZBvgXYA3gHeACYBwwAPgFsTJpF/TVJB0TEU31dUWs97h016zO1iM9fJy0ZNzrbuOmubLLfOEnn5TdzypO0E7APsFtETM7SXgEekrRXbjOn04DJEVFYv/4+SVsCPwD+WHTOQcB/kSYZeu35BnPL1Oe93Js1vbKGWEgaRQq+9wFDIuKzEXFoROwbEZuSgvBVpK2dJ3nZILO+4y8S1pUaxud9gTuLGsLjSY3m3bop91qhcQwQEQ+TNmraN7uGVYDdWX7C4HhgJ0kDitL/E5gK3FPBdZiZdavcMchfIi06/6WIeL34YETMioixwBHAmsC1fVdFa0Vu9Jn1mVrF56GkZeLy536R1Gs9tCflMjNy5TYFViqRbwbpc+oThQRJI0i7mp7Ug7q3JcdZs8qV20D+JHBfRPyjq0wR8SvS1su7SNqxkgrVexKIpJUl/bekP0laKKnkVoOSrsomhxTfuvqgMBy0K+HXzLpQq/g8CJhfIr0jO9abcoX74nwdRccBfgpcEhGzuqwtIOlYSdMkTZs7d2532a0POWZZsyu3gbwupXsASjkHWAQc1NPK5CaBBGkSyJnAd0i7Q3VnAvAZ0sSNo4DtSJNA8ucvTAK5j/TT3u2kSSB757Ktlp3jHaC7bVhnAjsV3WaXUVczs75Sk/icKdVhoE7SKylX/Fj5dEmHkib7ndXN86VCEZdFxMiIGDl48OByipiZAeVP0lsdKDkBo1hEvCHpAaCSHoq6TwKJiPmS1oyIkPQN0ti+zrwdEQ9WcJ1ty70KlfPEF+tEreJzBzCwRPoASvcQ58uVap0OzJXryKUV5wGYL2kl4L9JK2CsIGkg0D87vrqkNSLi/7q+BDOz8pTbg1xOD0HeU6SZ0z3VEJNAsm1ZrY+5cWxWFbWKzzMpGmssaQNSA72rHuzlymXyY5P/BrxfIt9Q0rJwz2TPsz5pmEhHdvtrlm888FiZ19EWHG/NeqfHG4WUqbOehu40xCSQHhgm6U1JiyRNkdRVI96s1/yhZ32g0vg8EdhH0hq5tDHAQuD+bsqtmw1xA0C1OvrAAAAclElEQVTSSNKqGhMBImIRaehb8TrOY4AHImIB8BapkyN/+1KW73vA4RVck1WR45U1s56sg/yDbPzXo8C07P6xThae/5DU69tT1ZgEskkuDyXylZoEUo7HgIdIi+YPJo2VvkvSLlnv9XIkHQscC7Dhhu21Ep4DpVlV1SI+/4K0gcdNks4lxdZxwAX5X/0kzQLuz1bOICIekHQncI2kk1i6UciU3PA3SEu3TZJ0EWn+yH7Z7XPZeRYDk/IVkjQk++eTEfFQBddkZlZSuQ3ke4BtSL2xQ4HDsvQPJT1DCsaFW29/5qrrJJByRcSPlzmJdDupsfw94MBOylwGXAYwcuRID+OwingsshWpSXyOiA5Je5J25buV1NlwIamRnNcPKF556NAs7xWkX+xuIzW28+efIulg0gS840lD5A7rZBc9M7OqKquBHBGfBZC0CTAyd9sG2CK7FX7e+hCodDvTuk4CKbOOJUXEQkl3AP/Sm/O0Ivcem1VPDeMzETGdricuExFDSqTNJ61dfHQ3ZW+maPWhbvLPZmknh2Ucc816rydDLIiI54DnyE10k/QJlg3KW5NmFlfSQ9qbSSC7lkgfytJgm58Ecn9RnsIkkL7gnuEcB+rqcC+yFatBfDbrMccqa1Y9aiCXEhHPkBqX1wNIEqnH4pMVnG4i8N2i5XrKnQRyWjb+d0pWj+UmgUgqTAK5NFc2PwmkYpJWJa2Y8WhvzmNm1lf6OD6bmbWNXjeQi2VLpE3Pbj1V10kgufPvS+q13jp7fHB26JGIeCFbEu424FfALGBt4NvAx4BDKrjuluTe4+pyz4z1VC/js5lZ26jWMm8ViYgOYE/SBI9bSTvoXQicXpS1s0kg95MmgVxD6sn9QtH5pwAHA3sBdwKjKD0J5OfAb4Gx2ePfZrfds8eLgLnA94E7SBPv5pM2KpnWk2s2MzNrZe4ssWbUbQ+ypL5cj2x+Z7vhFTTCJJBS5y86/i4wuqs87c4BsTbci9zeah2frfE59pr1jXKGWMym7yZ0nAGc2UfnsgblAG1WM7NxfDYz63PlNJDPpO8CcFcT7cysAu5FbmuOz2ZmVdBtAzkixtWgHtYi3HtsVjuOz9Ys/EXemk1DTdIzs8r4i4mZmVnfKXuZN0nrkDbjWBd4D3gJmB4RL1apbtZk3Egzqw/HZwPHYLO+VM4qFv2AnwLHUKLHWdLLpDWBr/QSZ2b1458w24/js5lZdZQzxOIM4DjgFeAnpDWJzwEeAUTqsTgeeEjSrX287JA1CfdcNAa/D23H8dmahuOTNZNyhlh8BXgK2DEi3i4kSnof2A5Yk7QT3dGkXen+Imn/iHioCvW1BuSgZ1Y3js9mZlVQTg/yYOC2fPDNi4i3I+LGiPg8sDPwFnC7pPX6sJ5mViZ/YWkrjs8G+O/erK+V00CeDQwp52QR8SCwG2kb6B9UUiFJwyTdI+kdSXMknSmpeFvpUuUGSLpSUoekBZKuk7RWiXwHSHpS0ruSpksaU3R8ZUn/LelPkhZK6nSN0e7O1Q4clM3qajY1jM9mveXPDGsW5TSQfw18QdKO5ZwwIl4AfgPs//+3d/9Bc1X1HcffnyK/pJBQpBMHFQoVM7FFq48OqbGARGLQGqBoGOqMWC3qTMXxF9Yf1YgOU5gRcKaiMiIMioSOoNZKCER+GUAxiIolQaGkUEEKnYcwGIgUv/3j3Mfc3Nx9dp+7u3f33v28ZnY2OXvOec557t7vnufuuefMtTGS9gXWkRa+X0FaBP8DpHl23VwOHEm6WeUU0teLO2wpLWkJcAVwPbAc+C5wmaRjctmendWxFbhllrb2UpfZSPhDaGLUFp/NzCZJLwPks4F7gGskvauXq7nAb4DnVGjPu4A9gRMi4tqI+CJpcPx+Sft0KiRpMbAMeGv2deI3gbcASyQtzWX9J+CmiDgtIq6PiA8BV5O7mhIRjwF/FBHLgG/O0taudbWdB2FmI1dnfDYzmxhdB8gR8RSwFPgF8Hlgs6SzgReV5Zf0Z6TB6b0V2rMcWBsRj+fSVpMGzUd0KfdwRNyUa/dtwH3Za0jaHTiKdPUkbzWwWNK8XNlZt26dS11mo+I/YNqv5vhsNhCOTdYEPe2kFxG/BhaTrpruBXwQWAkg6aeS1kj6lqQfAHeQrk6cXaE9C4FNhZ99P2m6w8K5lMtszJU7BNi1JN9G0u/h0Dm0c5B1NZIDXDP4OLVfjfHZxpTPc7PB63knvYh4GjhT0jnACaQlg5YAf549ZmwEPhMRl1Voz77AYyXp09lrVcodnMtDSb7pwuu9qFSXpFOBUwFe8ILmLkfqYGw2XmqKz2ZmE6PnAfKM7Cu9r2cPJD0bOADYDfh1RPxvn20qm96gDulVyhX/r1nKdzOnuiLiAuACgKmpqSo/z2zOvMPe5KghPpuZTYSepljMJiK2RsQvI+I/BhB8p4H5JenzKL9C3K3c/Fy56VxaMQ9d6i/7eYOqq1F89disOQYcn80Gxp8lNu66DpAl7dnvD5lDHZsozDWW9HzSvLqyOcYdy2Xyc5PvBZ4uybcQ+B3pJpdeDbIus6Hzh1E71RyfbQz53DYbjl6uIN8n6b3Zyg1zIuklkr5NummkF2uAZZL2zqWtBJ4EbuxSbkG2NvHMz54izT9eAxAR20hrFr+pUHYlcGtEbOmxjQOtq0kciJvNx6+V6ozP47CR0yuyeu7J2nC3pE9K2qPXPpiZ9aKXAfI1wDnAQ5K+IOmo2a44SDpY0rsl3Qr8GHgJaTDZiy8C24ArJS3NbmpbBZyTX/otC44Xzvw/Im4F1gKXSDpB0nHApcD6iFiXq//TwJGSzpN0ZLYc0rGkDUnyfVgu6UTgpdn/T8weB861LjOzIaotPo/JRk4rSasInUWKt58H3k+K99Yw/qPdxpm6LPmbMqWrsWcCR2dJz5Duhn6INB93D2A/0tqbzyHdrPYw8Dng3OyKa28NkhYB/0Jatugx4MvAqoh4JpdnM3BDRJySS5sPnAscTxr4/ztwWkQ8Wqj/OOAzwAtJ6ySviojVhTybgfxgeMbbIuLiudTVydTUVGzYsKGXrGPBgaw9fMPe+JB0e0RM9VlHLfFZ0keA04EDZy5YSDqddBFjQWH9+ny5xaRdSY+YWate0iuBHwKvnbmIIWktsGtEvCZX9ipgn4hYkv1//4h4pFD/qcCXgIOynQJLNS3m9qrpsdnxyOrWa9ztaRWLiNgAHCPphcDbSYH4pey4fBDAI8CVpKsAV2RLD81JRNwFvKZLnoNK0h4D3pY9Ziv7LQpXLnqpv2pdZuPGq1q0S43xudNGTmeRNnL6zizldtrISdLMRk7rcpsvnVYouxq4SNK8iNhSHBxn7sie/xjoOEBuo6YPjs3G2ZyWeYuIXwL/CDssH7QfaY7w/0TEQwNvoY2cg3D7eJDcPjXE54XAdYWfeb+kmY2cOg2QB7WR04861P+XpJuj7+7SfhtDjkU2rua8DvKMiNgK/DJ7WEt5cGzWPEOKz2O3kZOkBcDHgK+WTfFoy+ZMZla/SgNkSc8jfRW2iPRX//2km+T+LSJ+O7jmmdmw+MpNOw05Po/NRk6SdgP+FXgCeF/pD/XmTGZW0ZwHyJKOJN1dvAfbgxfA3wEPSHpvRHx7MM2zUfLV4/bzILldhhyf+9nIaf+S9MobOUkScAnwYuBVETHNhGlTfHYcsnFUZSe9s4A9SStNvAR4HrAkS9+LtETbhwbWQjMz69Uw4/M4beR0LmmpuRURMdvPNjOrpMoA+TDg2oh4b0TcGREPRsQtEfFR0o0U1wL/LOno2auxcdamqxM2Ox/rVhlmfB6LjZyy5ebeA7wlItZX6IeZWVdVBsjb2L6szg6yr7n+hrT+5ul9tMtGyAOmyeNj3hrDjM8j38hJ0smkNZ8vAX4l6fDco2wahzWEY5CNmyoD5J+RFpwvFRG/Ab4NHF61UWZWP39AtcLQ4nM2wD4a2IW0pNunSFMdPlnI+qwsT95JpKvMXyENbm8nbeqUr389cCKwlDSgfiNwckRck8s2s6veKcCthcfr59qnpvK5ajZ8VVaxOJ90JWBxdmWgzDa639VsY8iB16zRhhqfR72RU7Z76indW2pN5Jv1bJxUuYJ8OHAPcFX2ddcOsgXq3wjcXKVBkhZJ+p6krZIelHSGpOLViLJy8yRdJGla0hZJl0raryTfCkl3SnpK0l2SVlapS9LFkqLkUXYzilkj+A+kxhtqfDYzmxRVriDntwL9qqQzSV+HbSYtyXNiSb6eSNoXWAfcRbpD+RDgs6SB/Me7FL+c9NXiO0h3PZ9FuhLx6lz9S0jbrJ6fte9Y4DJJ04Wv8brWldnEzldENnfv6Xjy4MjAV3Eabmjx2caD47RZPaoMkF8FvCz3WAT8ffZakNbe/Anwfkl3kG4YubPHBerfRVqi6ITspo9rJe0DrJJ0dtlOSQCSFgPLgCMi4qYs7VfADyUtzd0I8k/ATREx8+FwvaQXA58ArpljXQC/iYgf9NAvs0bxILmxhhmfzYbOscfGxZwHyNm8tt/Pbct2M/pztgfklwN/Brx0pgjwjKSNEfGSLtUvB9YWBsKrSVdwjyDdGNKp3MMzA9qsnbdJui97bZ2k3YGj2PnKyWrgIknzsqWEutbVpQ+N5KsSVuQPquYZcnw2M5sYlbaazsuuPNyePQDI5gy/mB2D8mE9VLcQuK5Q//2StmavdRog5xecz9vI9oXnDyFtu1rMt5E0heNQ4Ec91jVjkaTHgd2zsh+LiNnWAx1LHhxbJx4kN9uA47NZLRx3bBz0PUAuExHPkJYb+hlwMfx+a9Bu9qV8y9Lp7LUq5Q7O5aEk33Th9V7qgvTV5A9J86X3Bz5AmhKyJCJum6WtZo3iD6t26SM+24j5YoZZfaqsYlFJRPS6rFBZPnVIr1Ku+H+VpHetKyI+FxFfiIgbI+IbpKWPfgV8tFMDJZ0qaYOkDY888kinbLVywLVe+H3SbnOIz2a1cMyxUattgNyjadKd1kXzKL+q263c/Fy56VxaMQ+FfN3q2klEPAlcRfrKslOeCyJiKiKm9t9/9Js+OQDZXPj9YmZmk2LcBsibKMzzlfR8YC/K5wV3LJfJzye+F3i6JN9C0lJuv5hDXbPxlRhrLQ+SzUbD555ZvcZtgLwGWCZp71zaSuBJ0jals5VbkK1zDICkKdKc4TUAEbENuB54U6HsSuDWbAWLnuoqI2lP0ioXt3fKM04cbK0qv3fMrA6ONTZK4zZA/iJpG9QrJS2VdCqwCjgnv/SbpHskXTjz/2xpo7WkLVZPkHQccCmwvrBu8aeBIyWdJ+lISWeTNgs5Yy51ZTvtfV/SOyUdne3Gdz1wAHDm4H8tg+WgY/3ye8jM6uBYY6MyVgPkiJgGjgZ2IS3p9ingXOCThazPyvLknUS6yvwV4BLSldzjC/WvJ+0ktZQ0CH4jcHJhF71e6toGPELa3e8q4ALS/OQjImLDXPps1lT+4DKrh881s/rJNy+PxtTUVGzYUP9Y2oHWBs1LwFUn6faImBp1OybBqGLuIDhuO87Y4PQad8fqCrINl4OsDYPfV2bD4/Mr8e/B6uYBspn17ds33+cPMDMzaw0PkCeEBy9WB7/PzGxYHF+sTh4gTwAHFauTryabDYbPo535d2J18QC55RxMbFT83jMzs6byALnFPECxUfPVZLNqfN505t+N1cEDZDMbOn+gmfXO50t3/h3ZsHmA3FIOHjZuZq4m+71pZoPgWGLD5AFyCzlo2LjzQNmsnM+LufHvy4bFA+SWcbCwJvFA2Ww7nwvVOI7YMIzdAFnSIknfk7RV0oOSzpC0Sw/l5km6SNK0pC2SLpW0X0m+FZLulPSUpLskrRxmXXVygLCm8vSLZmhSfLbJ4/hhg/SsUTcgT9K+wDrgLmAFcAjwWdJA/uNdil8OvAh4B/A74CzgW8Crc/UvAa4AzgdOA44FLpM0HRHXDKmuoXNQsDbJv59XvOpPRtgSy2tSfG4ix/HBmPk9OnZYvxQRo27D70n6CHA6cGBEPJ6lnQ6sAhbMpJWUWwzcAhwRETdlaa8Efgi8NiLWZWlrgV0j4jW5slcB+0TEkkHXNZupqanYsGFDz7+bThxUbZK07UNP0u0RMTXqdvSiSfG5zKBi7qA5hg9f2+KG9afXuDtWV5CB5cDaQqBdTbpCcATwnVnKPTwTMAEi4jZJ92WvrZO0O3AU6cpE3mrgIknzImLLgOsaGgdVm0Sd3vf+AKxFI+JzXz2skWN4ffytlFUxbgPkhcB1+YSIuF/S1uy1TgF4IbCpJH1j9hqkrwN3Lcm3kfQV4aHAjwZc18A5qJrtbC7nhT8gK2tKfB5Ljt3jodtxcHywGeM2QN4XeKwkfTp7rUq5g3N5KMk3XXh9kHXtQNKpwKnZf5+QdHdZvlk8B3h0jmWayP1sF/ezswOH0ZAhaUp8/r0BxFzw+7dt3M92GVrcHbcBMkDZpGh1SK9Srvh/laQPsq7tmSMuAC4oe60XkjY0Zb5iP9zPdnE/W6VJ8bnvmAsTc1zdz5ZxP/s3bsu8TQPzS9LnUX7VoFu5+bly07m0Yh4K+QZVl5lZWzQlPpuZ9W3cBsibKMwjk/R8YC/K5511LJfJz1e7F3i6JN9C0lJBvxhCXWZmbdGU+Gxm1rdxGyCvAZZJ2juXthJ4ErixS7kF2TqaAEiaIs1JWwMQEduA64E3FcquBG7NrToxyLoGra+vChvE/WwX97MdGhGfh6Dtx3WG+9ku7mefxm0d5H1Ji9D/nLR00MHAOcB5EfHxXL57gBsj4u25tKtJdzp/kO2Lx/9PRBQXor8B+BfSwvLHZvlfl1+IfpB1mZm1QZPis5lZv8ZqgAxpK1NSgFxMmlP2ZWBVRDyTy7MZuCEiTsmlzQfOBY4nXRn/d+C0iNjh7kZJxwGfAV4I3JfVvbqQZ2B1mZm1RZPis5lZP8ZugGxmZmZmNkrjNge59SQtkvQ9SVslPSjpDEm79FBunqSLJE1L2iLpUkn7leRbIelOSU9JukvSyuH0pGt759xPSa/I+nhPVu5uSZ+UtEch3ypJUfJ43XB7VdrmKv08qEP7d/r2oeHHs9NxCqVti2fyXdwhT+0bP0j6U0lfkvRTSc9IuqHHco06PyeN4+6sZRx3d87b5OPpuLtzvkrHcxzXQW4tpTl860jz+FaQdo/6LOkPlY/PUhTgcuBFwDvYPu/uW0BxDt8VwPmkLVuPBS6TNF3nvOg++rkyy3sW8EvgMODT2fPfFPJuAYqBeWO/bZ+LPo8npDmUN+f+X/y6uenH88vA1YW044APs/MNVZuAtxXSNldrcV9eTPo9/wDYbQ7lGnN+ThrHXcfdAsfd7Rx3ZxMRftT0AD5CWsdzn1za6cDWfFpJucWkRfD/Kpf2yixtaS5tLXBdoexVwPqG9HP/krRTs34emEtbBTza4ON5UNanN3Spv9HHs0Nd3wU2FtIuBjaM+nhmbfmD3L+/QZpL261Mo87PSXs47jruZnkcd3dMc9zt8jM8xaJey4G1EfF4Lm01sCdwRJdyD0fETTMJEXEb6SaW5QCSdgeOAv61UHY1sFjSvP6b37NK/YyIR0qS78ie/3hwzRuYqsezqzYczyJJfwS8FrhssM0bnIj4XYViTTs/J43jruNuT9pwPIscd6sfTw+Q67XTYvYRcT/pL8LZ5v10WgR/Y67cIcCuJfk2ko7zoRXaW1XVfpb5S9JXJ3cX0udLelTS05LukHRC5dZW128/L8rmWz0k6RxJe+Zea+PxPJHUp7KVXhZJelzSNknrJfX1QVezpp2fk8Zx13E3z3F3O8fdWXiAXK99Kd8OdTp7rZ9yM8/FfNOF1+tQtZ87kLQA+Bjw1cJf0feQvmp6M2mO3IPAFSMI1lX7uQ34PPB24GjgS8C72TGAte54AicBP46I4k6TdwAfAP4a+FtgF+BaSa+s0NZRaNr5OWkcdx13wXHXcXfHPPnXS/kmvfqVraunDulVyhX/r1nKD1PVfqaM0m6kr0WeAN63Q8URXyvk/Q5wC/AJ4Moqje3DnPsZEQ8B/5BLukHSw8D5kl4aET+Zpf6mHs/nkr4W/PBOFUd8rpD3u6QbUz5KurmkCZp2fk4ax90eOO52rL+px9NxtzxfT8fTV5DrNQ3ML0mfR/lfQt3Kzc+Vm86lFfPQpf5Bq9pPACQJuITsztaImJ4tf6RZ91cCh3VbAmfA+upnwTey55fl6qak/sYdz8ybSUHp8m4ZI+JJ0k0UL+uWd0w07fycNI67jrudOO5mHHd35gFyvTZRmDsk6fnAXpTPpelYLpOfg3Mv8HRJvoWkuWTFr1eGqWo/Z5xLWtZmRUT0kn9G3X/d99vPvCg8t+l4Qvqab31EPDCHn9uUq6pNOz8njeOu424njrs7c9zNeIBcrzXAMkl759JWAk8CN3YptyBbzw8ASVPAwdlrRMQ24HrgTYWyK4FbI2JL/83vWdV+ki1k/h7gLRGxvpcfll35OB74aeS2vK1B5X6WODF7vh3aczwhLdAPHE6Pd1FnN80sJ/tdNEDTzs9J47jruNuJ4+72/I67RaNe/26SHqQJ4Q8B1wJLSWtNPgF8ppDvHuDCQtrVwH8CJ5DmB90NfL+QZwnwf8B5wJHA2aS/ko5pQj+Bk0l/vV5EOrHzj/1z+W4kLfh9DClAX5X1840N6ecq0oLvJ2TlziAFvSvadDxz6f9I+iu+bL3VecD3gXeSbpxZSVosfhswVWc/s/Y8m/SheSJwK/Afuf8/u1M/m3R+Ttqjn/dvk45rH/HIcbdFxzOX7rjb5/Gs9ZfgRwAsAq7LTsyHSDsW7VLIsxm4uJA2PwtgjwGPA18HnlNS/3HAz7M3+ibgpKb0k7RweXR4nJLLd2F2UjwJ/CY70Zc3qJ8nARtIu1L9NjvxzwB2b9PxzKX/BLi6Q717kOYxPpD1cUsW9A4fUT8PmuU9eFCnfjbt/Jy0h+Nu53467jruOu6WP5QVNjMzMzMzPAfZzMzMzGwHHiCbmZmZmeV4gGxmZmZmluMBspmZmZlZjgfIZmZmZmY5HiCbmZmZmeV4gGxWM0l7SvqEpE2SnpL0gKQzJe066raZmbWR467NlddBNquRpOeSdkY6FPgmafHzN5AWhL8gIt45utaZmbWP465V4QGyWU0k7QbcAiwElkXEzVn6H5K21nwecEBE/Hp0rTQzaw/HXavKUyzM6vNB4OXAh2eCNEBEPEG6qvEHwKtH1DYzszZy3LVKPEA2q4GkPYEPAQ8BF5Rk+d/seUFtjTIzazHHXeuHB8hm9TgemA98PSKeLnl9j+z5t/U1ycys1Rx3rbJnjboBZhPi9dnzAZJWlby+NHt+oJ7mmJm1nuOuVeab9MxqIOm/gBf0kPVPImLzkJtjZtZ6jrvWD0+xMBsySXuRgvTPI0LFB7A38DTw3w7SZmb9c9y1fnmAbDZ8B2TPD3Z4fRmwK/DdeppjZtZ6jrvWFw+QzYZvt+x5W4fX35Y9f6WGtpiZTQLHXeuLB8hmwzezAP1OSwlJOhw4FlgTEbfV2iozs/Zy3LW++CY9sxpIugt4EfAXEfGzLO1A4EZgXpa+eXQtNDNrF8dd64cHyGY1kHQycCnwKPA1YC/gzUAAr4+IW0bYPDOz1nHctX54gGxWE0lvBU4HDiEF7KuAT0XEr0baMDOzlnLctao8QDYzMzMzy/FNemZmZmZmOR4gm5mZmZnleIBsZmZmZpbjAbKZmZmZWY4HyGZmZmZmOR4gm5mZmZnleIBsZmZmZpbjAbKZmZmZWY4HyGZmZmZmOf8PTUDjLQdzI7sAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(3,2,figsize=(10,8))\n", + "axs = axs.flatten()\n", + "axs[0] = barplot(theta, pTheta, title='Prior', xlabel=r'$\\theta$', ylabel=r'$p(\\theta)$',ax=axs[0])\n", + "axs[0].annotate('mode=%.1f' % theta[np.argmax(pTheta)], \n", + " xy=(0.65,0.85), xycoords=\"axes fraction\");\n", + "\n", + "axs[1] = barplot(theta, pTheta, title='Prior', xlabel=r'$\\theta$', ylabel=r'$p(\\theta)$',ax=axs[1])\n", + "axs[1].set_ylim(0,.0065)\n", + "axs[1].annotate('mode=%.1f' % theta[np.argmax(pTheta)], \n", + " xy=(0.65,0.85), xycoords=\"axes fraction\");\n", + "\n", + "#small data \n", + "pData_t, z, n = bi_likelihood(theta,data_left) # likelihood of data given theta\n", + "pData = evidence(pData_t,pTheta) # evidence of data\n", + "pTheta_d = posterior(pData_t, pTheta, pData) # prob of theta given data (aka posterior)\n", + "#small data likelihood\n", + "axs[2] = barplot(theta, pData_t, title='Likelihood', xlabel=r'$\\theta$', ylabel=r'$p(D|\\theta)$', \n", + " ynbins=6, ax=axs[2]);\n", + "axs[2].annotate('Data: z=%d,N=%d'%(z,n), xy=(0.65,0.85), xycoords=\"axes fraction\");\n", + "axs[2].annotate('mode=%.2f' % theta[np.argmax(pData_t)], \n", + " xy=(0.65,0.75), xycoords=\"axes fraction\");\n", + "#small data posterior\n", + "axs[4] = barplot(x=theta, y=pTheta_d, title='Posterior', xlabel=r'$\\theta$', \n", + " ylabel=r'$p(\\theta|D)$', ax=axs[4]);\n", + "axs[4].annotate('mode=%.2f' % theta[np.argmax(pTheta_d)], \n", + " xy=(0.65,0.85), xycoords=\"axes fraction\");\n", + "\n", + "#large data \n", + "pData_t, z, n = bi_likelihood(theta,data_right) # likelihood of data given theta\n", + "pData = evidence(pData_t,pTheta) # evidence of data\n", + "pTheta_d = posterior(pData_t, pTheta, pData) # prob of theta given data (aka posterior)\n", + "#small data likelihood\n", + "axs[3] = barplot(theta, pData_t, title='Likelihood', xlabel=r'$\\theta$', ylabel=r'$p(D|\\theta)$', \n", + " ynbins=6, ax=axs[3]);\n", + "axs[3].annotate('Data: z=%d,N=%d'%(z,n), xy=(0.65,0.85), xycoords=\"axes fraction\");\n", + "axs[3].annotate('mode=%.3f' % theta[np.argmax(pData_t)], \n", + " xy=(0.65,0.75), xycoords=\"axes fraction\");\n", + "#small data posterior\n", + "axs[5] = barplot(x=theta, y=pTheta_d, title='Posterior', xlabel=r'$\\theta$', \n", + " ylabel=r'$p(\\theta|D)$', ax=axs[5]);\n", + "axs[5].annotate('mode=%.3f' % theta[np.argmax(pTheta_d)], \n", + " xy=(0.65,0.85), xycoords=\"axes fraction\");\n", + "\n", + "plt.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Influence of the prior on the posterior" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(3,2,figsize=(10,8))\n", + "axs = axs.flatten()\n", + "\n", + "#small data \n", + "pTheta = beta.pdf(theta,1.05,1.05)\n", + "pTheta /= np.sum(pTheta)\n", + "\n", + "axs[0] = barplot(theta, pTheta, title='Prior', xlabel=r'$\\theta$', ylabel=r'$p(\\theta)$',\n", + " ax=axs[0])\n", + "axs[0].set_ylim(0,.0025)\n", + "axs[0].annotate('mode=%.1f' % theta[np.argmax(pTheta)], \n", + " xy=(0.65,0.85), xycoords=\"axes fraction\");\n", + "\n", + "pData_t, z, n = bi_likelihood(theta,data_left) # likelihood of data given theta\n", + "pData = evidence(pData_t,pTheta) # evidence of data\n", + "pTheta_d = posterior(pData_t, pTheta, pData) # prob of theta given data (aka posterior)\n", + "#small data likelihood\n", + "axs[2] = barplot(theta, pData_t, title='Likelihood', xlabel=r'$\\theta$', ylabel=r'$p(D|\\theta)$', \n", + " ynbins=6, ax=axs[2]);\n", + "axs[2].annotate('Data: z=%d,N=%d'%(z,n), xy=(0.5,0.85), xycoords=\"axes fraction\");\n", + "axs[2].annotate('mode=%.2f' % theta[np.argmax(pData_t)], \n", + " xy=(0.5,0.75), xycoords=\"axes fraction\");\n", + "#small data posterior\n", + "axs[4] = barplot(x=theta, y=pTheta_d, title='Posterior', xlabel=r'$\\theta$', \n", + " ylabel=r'$p(\\theta|D)$', ax=axs[4]);\n", + "axs[4].annotate('mode=%.2f' % theta[np.argmax(pTheta_d)], \n", + " xy=(0.5,0.85), xycoords=\"axes fraction\");\n", + "\n", + "#large data \n", + "pTheta = beta.pdf(theta,47.5,47.5)\n", + "pTheta /= np.sum(pTheta)\n", + "\n", + "axs[1] = barplot(theta, pTheta, title='Prior', xlabel=r'$\\theta$', ylabel=r'$p(\\theta)$',\n", + " ax=axs[1],ynbins=7)\n", + "axs[1].set_ylim(0,.0125)\n", + "axs[1].annotate('mode=%.1f' % theta[np.argmax(pTheta)], \n", + " xy=(0.65,0.85), xycoords=\"axes fraction\");\n", + "\n", + "pData_t, z, n = bi_likelihood(theta,data_right) # likelihood of data given theta\n", + "pData = evidence(pData_t,pTheta) # evidence of data\n", + "pTheta_d = posterior(pData_t, pTheta, pData) # prob of theta given data (aka posterior)\n", + "#small data likelihood\n", + "axs[3] = barplot(theta, pData_t, title='Likelihood', xlabel=r'$\\theta$', ylabel=r'$p(D|\\theta)$', \n", + " ynbins=6, ax=axs[3]);\n", + "axs[3].annotate('Data: z=%d,N=%d'%(z,n), xy=(0.5,0.85), xycoords=\"axes fraction\");\n", + "axs[3].annotate('mode=%.2f' % theta[np.argmax(pData_t)], \n", + " xy=(0.5,0.75), xycoords=\"axes fraction\");\n", + "#small data posterior\n", + "axs[5] = barplot(x=theta, y=pTheta_d, title='Posterior', xlabel=r'$\\theta$', \n", + " ylabel=r'$p(\\theta|D)$', ax=axs[5]);\n", + "axs[5].annotate('mode=%.3f' % theta[np.argmax(pTheta_d)], \n", + " xy=(0.5,0.85), xycoords=\"axes fraction\");\n", + "\n", + "plt.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Exercises" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Exercise 5.1. [Purpose: Iterative application of Bayes’ rule, and seeing how posterior probabilities change with inclusion of more data.] This exercise extends the ideas of Table 5.4, so at this time, please review Table 5.4 and its discussion in the text. Suppose that the same randomly selected person as in Table 5.4 gets re-tested after the rst test result was positive, and on the re-test, the result is negative. When taking into account the results of both tests, what is the probability that the person has the disease? Hint: For the prior probability of the re-test, use the posterior computed from the Table 5.4. Retain as many decimal places as possible, as rounding can have a surprisingly big e ect on the results. One way to avoid unnecessary rounding is to do the calculations in R." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.019434628975265017\n" + ] + }, + { + "data": { + "text/plain": [ + "0.00020858616504854387" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "theta = [0,1]\n", + "pTheta = [.999, .001]\n", + "pPos_theta = [.05, .99]\n", + "pNeg_theta = np.subtract(1,pPos_theta)\n", + "# p(theta=1 | T=pos)? p(T=pos|theta=1)* pTheta / pPos\n", + "new_prior = pPos_theta[1]*pTheta[1]/np.sum(np.multiply(pPos_theta,pTheta))\n", + "print(new_prior)\n", + "# bi_likelihood(theta,[1])[0],evidence(bi_likelihood(theta,[1])[0],pTheta)\n", + "# posterior(bi_likelihood(theta,[1])[0],pTheta,evidence(bi_likelihood(theta,[1])[0],pTheta))\n", + "pTheta = [1-new_prior, new_prior]\n", + "# p(theta=1 | T=neg)? p(T=neg|theta=1)* pTheta / pNeg\n", + "pNeg_theta[1]*pTheta[1]/np.sum(np.multiply(pNeg_theta,pTheta))" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(4995.0, 5094.0, 94905.0, 94906.0, 0.019434628975265017)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "n=100000\n", + ".05*.999*n,.05*.999*n+99,.95*.999*n,.95*.999*n+1,99/(.05*.999*n+99)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(9900.0, 99.0, 499500.0, 474525.0)" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "10000*.99,10000*.99*.01,9990000*.05,9990000*.05*.95" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 dask", + "language": "python", + "name": "python3conda" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}