{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Think Bayes\n", "\n", "Copyright 2018 Allen B. Downey\n", "\n", "MIT License: https://opensource.org/licenses/MIT" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Configure Jupyter so figures appear in the notebook\n", "%matplotlib inline\n", "\n", "# Configure Jupyter to display the assigned value after an assignment\n", "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n", "\n", "import numpy as np\n", "import pandas as pd\n", "\n", "import matplotlib.pyplot as plt\n", "\n", "# import classes from thinkbayes2\n", "from thinkbayes2 import Pmf, Cdf, Suite, Joint\n", "\n", "import thinkplot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Lions and Tigers and Bears\n", "\n", "Suppose we visit a wild animal preserve where we know that the only animals are lions and tigers and bears, but we don't know how many of each there are.\n", "\n", "During the tour, we see 3 lions, 2 tigers and one bear. Assuming that every animal had an equal chance to appear in our sample, estimate the prevalence of each species.\n", "\n", "What is the probability that the next animal we see is a bear?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Grid algorithm\n", "\n", "I'll start with a grid algorithm, enumerating the space of prevalences, `p1`, `p2`, and `p3`, that add up to 1, and computing the likelihood of the data for each triple of prevalences." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "class LionsTigersBears(Suite, Joint):\n", " \n", " def Likelihood(self, data, hypo):\n", " \"\"\"\n", " \n", " data: string 'L' , 'T', 'B'\n", " hypo: p1, p2, p3\n", " \"\"\"\n", " # Fill this in." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "class LionsTigersBears(Suite, Joint):\n", " \n", " def Likelihood(self, data, hypo):\n", " \"\"\"\n", " \n", " data: string 'L' , 'T', 'B'\n", " hypo: p1, p2, p3\n", " \"\"\"\n", " p1, p2, p3 = hypo\n", " if data == 'L':\n", " return p1\n", " if data == 'T':\n", " return p2\n", " if data == 'B':\n", " return p3" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "ps = np.linspace(0, 1, 101);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's a simple way to find eligible triplets, but it is inefficient, and it runs into problems with floating-point approximations." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "from itertools import product\n", "\n", "def enumerate_triples(ps):\n", " for p1, p2, p3 in product(ps, ps, ps):\n", " if p1+p2+p3 == 1:\n", " yield p1, p2, p3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an exercise, write a better version of `enumerate_triples`." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "from itertools import product\n", "\n", "def enumerate_triples(ps):\n", " for p1, p2 in product(ps, ps):\n", " if p1 + p2 > 1:\n", " continue\n", " p3 = 1 - p1 - p2\n", " yield p1, p2, p3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can initialize the suite." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "suite = LionsTigersBears(enumerate_triples(ps));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are functions for displaying the distributions" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def plot_marginal_pmfs(joint):\n", " pmf_lion = joint.Marginal(0)\n", " pmf_tiger = joint.Marginal(1)\n", " pmf_bear = joint.Marginal(2)\n", "\n", " thinkplot.Pdf(pmf_lion, label='lions')\n", " thinkplot.Pdf(pmf_tiger, label='tigers')\n", " thinkplot.Pdf(pmf_bear, label='bears')\n", " \n", " thinkplot.decorate(xlabel='Prevalence',\n", " ylabel='PMF')" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def plot_marginal_cdfs(joint):\n", " pmf_lion = joint.Marginal(0)\n", " pmf_tiger = joint.Marginal(1)\n", " pmf_bear = joint.Marginal(2)\n", "\n", " thinkplot.Cdf(pmf_lion.MakeCdf(), label='lions')\n", " thinkplot.Cdf(pmf_tiger.MakeCdf(), label='tigers')\n", " thinkplot.Cdf(pmf_bear.MakeCdf(), label='bears')\n", " \n", " thinkplot.decorate(xlabel='Prevalence',\n", " ylabel='CDF')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are the prior distributions" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_marginal_cdfs(suite)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can do the update." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "for data in 'LLLTTB':\n", " suite.Update(data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here are the posteriors." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_marginal_cdfs(suite)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To get the predictive probability of a bear, we can take the mean of the posterior marginal distribution:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.22232592246925062" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "suite.Marginal(2).Mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or we can do a pseudo-update and use the total probability of the data." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.22232592246925043" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "suite.Copy().Update('B')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Using the Dirichlet object" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Dirichlet distribution is the conjugate prior for this likelihood function, so we can use the `Dirichlet` object to do the update.\n", "\n", "The following is a [monkey patch](https://en.wikipedia.org/wiki/Monkey_patch) that gives `Dirichlet` objects a `Marginal` method." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "from thinkbayes2 import Dirichlet\n", "\n", "def DirichletMarginal(dirichlet, i):\n", " return dirichlet.MarginalBeta(i).MakePmf()\n", "\n", "Dirichlet.Marginal = DirichletMarginal" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are the priors:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dirichlet = Dirichlet(3)\n", "plot_marginal_cdfs(dirichlet)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's the update." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "dirichlet.Update((3, 2, 1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are the posterior PDFs." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_marginal_pmfs(dirichlet)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And the CDFs." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_marginal_cdfs(dirichlet)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And we can confirm that we get the same results as the grid algorithm." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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55hq2bNkCwJo1a1i9ejXdunVj2LBhVFRUsGfPHnbt2kVtbS0ADQ0NobU9LFGrEBHVVHLQvJP4T8ViA7RixQr+7M/+DIDhw4czcODA5gA1fvx4evbsSVFRESNHjuTzzz/nq1/9Ktu3b6eiooJf//rXnH322W1dPidFrUJEFFPJQcN6Eg0514NKZxguW9qaTuvWrVvz44KCApqamujVqxdr165lyZIlVFZWsnDhQubNm5eNpnopEkN6EUslBw3rSXTkXIDyyde//nXeeOMNrrrqKrZs2cKOHTsYNmwYn3zySavnf/HFF3Tt2pXbbruNwYMHU15ent0GhyRKqeQQ3crkGtKTqFGACtCMGTO4//77GTVqFIWFhVRVVZ3Sc2pp165d3HvvvRw/Hlun/OMf/zhbTQ1VlFLJwf9hPVUml1yhAJUhBw8eBGLbbpxIcigqKjpt+wyI7aab2Dt65513mh8n613lskilkoP3w3pKJZdcoQAlXonEvFMCH4f1lEouuUIBSrIuV+acokDzThJlClCSdVFb6xSVEkaad5Jco3VQknVRW+ukEkYi4VAPSkKlOafM0LyT5CIFKJFWaN5JJHwKUBnQ0NDA/PnzmTFjBrt37+aBBx5QRfMWopYY4ftap7W7/x81O/8fR49HMIKKpElzUBnQ0NDAc889B2R2u41jx45l5Do+iNpiXN/XOv3q4538tvZzauL/neCOH2/jp0SiJed6UMu27El9UgddPfQrrR6fPXs227ZtY/To0QwZMoRNmzZRW1tLY2Mj5eXlbN68mREjRlBXV0dlZSVlZWUsXbqUxx9/nMOHDzN48GBeeeUVevTowaBBg5gyZQpLly5l5syZ7NmzhxdeeIHCwkJGjhzJm2++GdjnC1LkFuMm8HHeqX5PA8db9J7c8eM0/X5fSC0SybycC1BhePLJJ6mtrWXNmjXN+0EBPPfcc/Tq1Yt169ZRW1vL6NGjgVjNvSeeeIJly5bRvXt3nnrqKZ599lkeeyy2VVZRURErVsR2PD3//PP57LPP6NatW85svxG1xAgfJQanL+OVS7p17cKd15eF1SSRjFOACtCKFSt48MEHASgpKaG0tBSAlStXsnHjRsaOje3VeOTIEa644ormn7vzzjubH5eWlnLPPfcwceJEJk6cmMXWd16U5p2inBTxjz+9P+wmiAQi5wJUsmG4MCTbbsM5x4QJE1iwYEGrr3fvfnKu491332X58uVUV1czZ84cNmzYQGFhNP5vi9K8kxbjivhHSRIZUFxczIEDB047fuWVV7Jw4UIANm7cyPr16wEYM2YMH374IVu3bgWgsbGxeSPDRMePH2fnzp2MGzeOp59+moaGhuaitFEQqXknLcYV8U40/hT3XO/evRk7diwlJSWMGDGi+fiMGTOYPHkypaWlXHrppZSWltKzZ0/OO+88qqqquPvuuzl8+DAATzzxBEOHDj3luseOHWPSpEns378f5xwPPfQQ55xzTlY/W6ZEad7Jx6QI0GJcyT8KUBkyf/78044VFRXx85//nKKiIrZt28b48eMZOHAgAFdddRWrVq067Wfq6uqaH3fp0qU5WUIyL8rzTlqMK/lAASpAjY2NjBs3jqNHj+Kc4/nnn6dr165hNyswUUqKAP8X42rOSfKdAlSAiouLqampCbsZWRO1KuW+L8ZNFpw07yT5QgFKMiZyVcoT+DjvlCw4ad5J8oUClAQiSkkRUaA5J8lHClCSV6KcGCGSbxSgpFOUGJFZSowQOUkLdTOkrq6OkpKSsJuRdVGqFgFEMjFCSRGSr9SD8lhTU5P3ZY0iVS2ihSgkRigpQvKZ399+HbB5d3ClgIaf36PN15uampg8eTKrV69m6NChvPbaa2zatIlZs2Zx8OBB+vTpQ1VVFX379uXFF19k7ty5HDlyhIsuuojXX3+ds846i/Lycs4991xWr17NZZddxk033dRccNbMWL58OcXFxYF9xs7wMTEiynNOSoyQfJdzASpMn376KS+//DJjx45lypQpVFZW8stf/pJf/epXnHfeebz11ls88sgjzJs3j1tvvZWpU6cC8Oijj/Lyyy9TUVEBwJYtW1i2bBkFBQV8+9vfprKykrFjx3Lw4EGKiorC/IiRoyKwItGlAJVB/fv3b95CY9KkSfzoRz+itraWCRMmALHaen379gWgtraWRx99tLkA7LXXXtt8nTvuuIOCggIAxo4dy6xZs7jnnnu49dZb6devX5Y/VcSpCKxIZOVcgEo1DBcks1O/ZIqLi7n44ov56KOPTju3vLyct99+m0suuYSqqiref//95tcSt9uYPXs2N9xwA4sXL2bMmDEsW7aM4cOHB/YZ0hG1zL0TfJxzAs07iSSjLL4M2rFjR3MwWrBgAWPGjGHv3r3Nx44ePcqGDRsAOHDgAH379uXo0aO88cYbSa+5bds2Ro0axcMPP0xZWRmbN28O/oOkELnMvQh5aeqVzJ36x0y9tjTspoiELtAAZWbXmdmnZrbVzGYnOedPzGyjmW0ws9NLgkfIiBEjePXVVyktLeX3v/89FRUVLFq0iIcffphLLrmE0aNH82//9m8AzJkzh8svv5wJEya02SP6yU9+QklJCZdccglnnnkm119/fbY+TlK+Z+69vXo3z/zr73hm2e/CboqIdIIl2/W10xc2KwC2ABOAemAVcLdzbmPCOUOAhcBVzrkvzewrzrk9bV23rKzMtSzAumnTplP2YcpH2bwHb6/+P82Pfczce+Zff9fqeqfvj/djiK+tpAhl7kk+MLOPnXNlqc4Lsgf1NWCrc267c+4I8CZwc4tzpgKVzrkvAVIFJ5G0RHAxLigxQqSlIJMkLgB2JjyvBy5vcc5QADP7ECgAfuCc+3XLC5nZNGAawIABAwJprCQX1aQI8DMxQlXKRdITZIBKZ2ugQmAI8E2gH/CBmZU45xpO+SHn5gJzITbE19qbOedOy6LLF0EN054QuX2eIkRDeiLJBRmg6oH+Cc/7AbtbOWelc+4o8JmZfUosYJ2+F3obioqK2LdvH7179867IOWcY9++fYEu4I3CPk9RrhghIq0LMkCtAoaY2YXALuAu4E9bnPM2cDdQZWZ9iA35bW/vG/Xr14/6+nr27t3bySZHU1FRUdYW8PqYFAGqUi6SiwILUM65JjObCSwhNr80zzm3wcx+CNQ456rjr11jZhuBY8BfOef2tfe9unTpwoUXXpjJ5kvURDAxQkkRIm0LtJKEc24xsLjFsccSHjtgVvw/kYyIQmKEkiJEUsu5UkeSGVHO3POdEiNE0qMAJa3yvZyRkiJEcp8ClLTK93JG2kZDJPcpQElKXmbuaRsNkZynACWR52NSBCgxQqSzFKCkmRIjgqPECJH2U4CSZkqMEBGfKEBJs0gmRnjU3VNShEhmtRmgzKzKOVcefzzZOfdqVloloYtEYkQEkiJAiREiHZWqB3VJwuMHAQUo8YKPiRHaRkMks1IFKP3pJ9IBSooQ6bxUAaqfmf2M2Ej/icfNnHMPBNYyEfxPjNC8k0hwUgWov0p4XBNkQyT7opBW7ntihBbjigSnzQClpIjcFomdcj1PjNBiXJHgpEwzN7PJxBIkhsUPbQJ+5px7LciGSfCisFNuIh8TIxJp3kkks1Klmf858D1i+zV9Quw77TLgb8wMBanc4WVauYjktVQ9qBnALc65uoRjvzGz24A3AQUoyTtKjBDJjlQB6uwWwQkA51ydmZ0dTJMkn/metQdKjBDJllQB6j87+Jp4yvfMvSjs86TECJHsSBWgRpjZulaOG/DVANojAfO9IGwU9nlKpMQIkeCkU+roD4CdLY4PBHYH0iIJlO8FYRP5nrUnIsFKFaD+DvjvzrnPEw+a2Xnx174dVMMkeMrcS4+SIkTCkSpADXLOnTbE55yrMbNBgbRI8o7viRGqUi4SjjNSvF7UxmtnZrIhkr98L2ekKuUi4UjVg1plZlOdcy8mHjSz+4CPg2uWZIrvWXuA9+WMEikpQiR7UgWo7wG/NLN7OBmQyoCuwC1BNkwyIxL19hIoMUJETkhVLPb/Av/VzMYBJfHD7zrnfhN4yyQjolZvzxdKjBAJX8pisQDOufeA9wJuiwTMl6w935MiQNUiRHyQKklCJONULUJE0pFWD0oko1QtQkTSoAAloVJShIgkowCVgyKRWu4ZJUWI+EdzUDnI+4KwHlK1CBH/BNqDMrPrgJ8CBcBLzrknk5x3O/AL4I+cczVBtikf+FgQ1vfMPVWLEPFPYAHKzAqASmACUE+sKkW1c25ji/OKgQeA3wbVlnzmS2q57+WMEikpQsQPQQ7xfQ3Y6pzb7pw7QmyL+JtbOW8O8DRwKMC2SNgiVM5IRPwQ5BDfBZy6j1Q9cHniCWZ2KdDfOfeOmf1lsguZ2TRgGsCAAQMCaKpkky+Ze0qMEPFbkAGqzRJwZnYGsT2lylNdyDk3F5gLUFZW5uksRriUudd+qhYh4rcgA1Q90D/heT9O3YW3mFh9v/fNDOAPgWozu0mJEu3nY+Ze1BIjlBQh4pcgA9QqYIiZXQjsAu4C/vTEi865/UCfE8/N7H3gLxWcOsbHzD0lRohIZwQWoJxzTWY2E1hCLM18nnNug5n9EKhxzlUH9d75zpfMPSVGiEhnBLoOyjm3GFjc4thjSc79ZpBtkXApMUJE2kuVJCSvKDFCJDoUoCSvKDFCJDpULDaifEwr9z1rryUlRoj4TT2oiEoWnMKMDVHYiFBEokM9qIhKFpxCTS33cCNCJUWIRJcCVA7wJq08gS9Ze9pGQyS6NMQnOU3baIhEl3pQ0ilRSoxQUoRItChARYiPmXs+ljPSvJNIbtAQX4T4WBDWx3JGWowrkhvUg4oQHwvCJvIlMUKLcUVygwJURPmYuecjzTuJRJcClLRblBIjRCS6FKCk3ZQYISLZoCQJaT8lRohIFqgH5TkfU8sTKTFCRIKiAOU5L1PLPafECJHcoADlOR9Sy5UUISJhUICKkLBSy33cRkNJESK5T0kSkpqH22ioSrlI7lMPStrF16QIUGKESK5RgJLIU1KESG5SgPKML2nlPiZGaN5JJL9oDsozyYJTtuOEj9UitBhXJL8oQHkmWXDKetVyD6tFaDGuSH7REJ/HfKlY7ktiRCLNO4nkPgUo8ZrmnUTylwKUNPMxMULzTiL5SwHKA75k7vmYGKF5J5H8pQDlAW8KwnqYGJFI804i+UUBygM+FIRtKazECM05icgJClCe8SVzLyyqsSciJyhA5TEfkyJUY09ETgg0QJnZdcBPgQLgJefcky1enwV8B2gC9gJTnHOfB9kmOcnHbTQSac5JJL8FFqDMrACoBCYA9cAqM6t2zm1MOG01UOacazSz6cDTwJ1BtUla8GQbDc07iUhrguxBfQ3Y6pzbDmBmbwI3A80Byjn3XsL5K4FJAbbHK76klp8QZrUIrXUSkdYEWYvvAmBnwvP6+LFk7gP+ubUXzGyamdWYWc3evXsz2MTweJNa7gGtdRKR1gTZg0q7KLeZTQLKgG+09rpzbi4wF6CsrCwnvsfDSi33MTEikeadROSEIANUPdA/4Xk/YHfLk8zsauAR4BvOucMBtsdb2Uwt96FahOacRCQdQQ7xrQKGmNmFZtYVuAuoTjzBzC4F/gG4yTm3J8C2yAkeVIvQWicRSUdgPSjnXJOZzQSWEEszn+ec22BmPwRqnHPVwN8APYBfmBnADufcTUG1SU4VVmKE1jqJSDoCXQflnFsMLG5x7LGEx1cH+f4+CStrT3NOIhJVqiSRJWFt5e7LYlzNO4lIe2nL9ywJbSt3Txbjaq2TiLSXelAhCKsgbJiLcbXWSUTaSwEqB/ky75RsWE/zTiKSDg3x5SAf1jqBhvVEpHPUgwpQaPX2PFjrBBrWE5HOUYAKkA/19sKcd0qkYT0RaS8FqABls96eD/NOSiUXkUxSgMqSoDP3fJh3UgkjEckkJUnkCg/mnVTCSEQyST2oHJTNeSelkotIUBSgMiibWXs+zDmBUslFJDga4sugbNbb86XGnlLJRSQo6kFlUFbr7YVYY0/DeiKSDQpQAclmvb1sr3XSsJ6IZIMCVISENe90eo9Jw3oiEjwFqE7KZmJEWGud2lrfNHfqHwffABHJS0pDJtfcAAAJOElEQVSS6KSsljMKaa2T1jeJSBjUg+qkoMsZJRvWC3reSYkQIhI2BagMCiIxwqdhPSVCiEg2KUD5LovDeqf2mpQIISLhUoDqgCATI9rK1At6WC9Zr0mJECISBgWoDggyMSKbFSKUPi4iPlOA6oBAEyOyWCFC6eMi4jMFqE7KRGJENjP12ppnAvWaRMQfClBpCHoxbjYz9TTPJCJRoQCVhiCqlLdZtiiDQ3qaZxKRqFKASkMQVcqT9Zq+Pz6zw3qaZxKRqFKAaqeOzjmlLPQaWK9J80wiEk0KUElket6preG8TPSa0hnKU49JRKJEASqJTKx1CrLX1HqtvNbDqXpMIhJFClBJZGKtU6bnmVL1khKdCEpTry3t0HuJiIRNASpBsmG9dOedgugxKSiJSL4KNECZ2XXAT4EC4CXn3JMtXu8GvAb8F2AfcKdzri7INrWlI8N6ae1y245eU0eG7hSQRCQXBRagzKwAqAQmAPXAKjOrds5tTDjtPuBL59xFZnYX8BRwZ1BtaqlljynZsF6ntlqP95qS7a+U9IeSUFASkXwRZA/qa8BW59x2ADN7E7gZSAxQNwM/iD9eBPwvMzPnXGAbD727fs8pz7sWnr6p8HHn2LRnPwC/29e+6x93sPfLg+zf39h8bNP2E486lhOooCQi+SjIAHUBsDPheT1webJznHNNZrYf6A18kXiSmU0DpgEMGDAgqPYCseC05+Chdv7M6UGpMxSQRESCDVDpVAdKq4KQc24uMBegrKwso72rEwFpX+PhFOd1Pggp8IiIpC/IAFUP9E943g/YneScejMrBHoCvw+wTdww6itBXl5ERDLk9AmYzFkFDDGzC82sK3AXUN3inGpgcvzx7cBvgpx/EhGR6AisBxWfU5oJLCGWZj7PObfBzH4I1DjnqoGXgdfNbCuxntNdQbVHRESiJdB1UM65xcDiFsceS3h8CLgjyDaIiEg0BTnEJyIi0mEKUCIi4iUFKBER8ZIClIiIeEkBSkREvGRRW3ZkZnuBzzt5mT60KKeUx3QvTtK9OJXux0m6Fydl4l4MdM6dl+qkyAWoTDCzGudcWdjt8IHuxUm6F6fS/ThJ9+KkbN4LDfGJiIiXFKBERMRL+Rqg5obdAI/oXpyke3Eq3Y+TdC9Oytq9yMs5KBER8V++9qBERMRzClAiIuKlnA5QZnadmX1qZlvNbHYrr3czs7fir//WzAZlv5XZkca9mGVmG81snZn9q5kNDKOd2ZDqXiScd7uZOTPL2fTidO6Fmf1J/N/GBjObn+02ZlMavycDzOw9M1sd/135VhjtDJqZzTOzPWZWm+R1M7Ofxe/TOjO7LJCGOOdy8j9ie1BtA74KdAXWAiNbnDMDeCH++C7grbDbHeK9GAecFX88PZ/vRfy8YmA5sBIoC7vdIf67GAKsBnrFn38l7HaHfD/mAtPjj0cCdWG3O6B78XXgMqA2yevfAv4ZMGAM8Nsg2pHLPaivAVudc9udc0eAN4GbW5xzM/Bq/PEiYLyZWRbbmC0p74Vz7j3nXGP86UqgX5bbmC3p/LsAmAM8DRzKZuOyLJ17MRWodM59CeCc25PlNmZTOvfDAWfHH/cEdmexfVnjnFtObBPZZG4GXnMxK4FzzKxvptuRywHqAmBnwvP6+LFWz3HONQH7gd5ZaV12pXMvEt1H7K+jXJTyXpjZpUB/59w72WxYCNL5dzEUGGpmH5rZSjO7Lmuty7507scPgElmVk9sM9aK7DTNO+39TumQQHfUDVlrPaGWOfXpnJML0v6cZjYJKAO+EWiLwtPmvTCzM4C/A8qz1aAQpfPvopDYMN83ifWqPzCzEudcQ8BtC0M69+NuoMo594yZXQG8Hr8fx4Nvnley8t2Zyz2oeqB/wvN+nN4dbz7HzAqJddnb6tZGVTr3AjO7GngEuMk5dzhLbcu2VPeiGCgB3jezOmLj69U5miiR7u/Ir5xzR51znwGfEgtYuSid+3EfsBDAOfcRUESseGq+Ses7pbNyOUCtAoaY2YVm1pVYEkR1i3Oqgcnxx7cDv3HxGcAck/JexIe1/oFYcMrleYY274Vzbr9zro9zbpBzbhCx+bibnHM14TQ3UOn8jrxNLIEGM+tDbMhve1ZbmT3p3I8dwHgAMxtBLEDtzWor/VAN/Hk8m28MsN859++ZfpOcHeJzzjWZ2UxgCbHsnHnOuQ1m9kOgxjlXDbxMrIu+lVjP6a7wWhycNO/F3wA9gF/E80R2OOduCq3RAUnzXuSFNO/FEuAaM9sIHAP+yjm3L7xWByfN+/F94EUze4jYkFZ5Lv5Ra2YLiA3r9onPtz0OdAFwzr1AbP7tW8BWoBG4N5B25OC9FRGRHJDLQ3wiIhJhClAiIuIlBSgREfGSApSIiHhJAUpERLykACWSBjM7ZmZrzKzWzH5hZmcF/H7v5+jiYJG0KUCJpOc/nXOjnXMlwBHg/sQX4wsW9fskkkH6hRJpvw+Ai8xskJltMrPngE+A/mZ2jZl9ZGafxHtaPczsejNbeOKHzeybZvZP8cfPm1lNfK+lv27tzVq7Zvx4nZn9dfz4ejMbHj/ew8xeiR9bZ2a3tXUdEV8pQIm0Q7xm4/XA+vihYcS2HbgU+A/gUeBq59xlQA0wC/gXYIyZdY//zJ3AW/HHjzjnyoBS4BtmVtri/fokueYJX8SPPw/8ZfzY/yBWemaUc64U+E0a1xHxTs6WOhLJsDPNbE388QfEymSdD3we3w8HYoVlRwIfxstFdQU+ipfQ+TXwbTNbBNwA/Lf4z/yJmU0j9rvYN/7z6xLet9VrJrz+v+P/+zFwa/zx1SSU7XLOfWlmN6a4joh3FKBE0vOfzrnRiQfiX/T/kXgI+Bfn3N2t/PxbwHeJ1Xxc5Zw7YGYXEuv1/FE8iFQRKz56ytu0cU2AE1Xnj3Hy99lofWuZtq4j4h0N8YlkzkpgrJldBGBmZ5nZ0Phr7xPbQnsqJ4f3ziYW4Pab2R8QGzpszzWTWQrMPPHEzHp18DoioVKAEskQ59xeYhsdLjCzdcSCwvD4a8eAd4gFoXfix9YCq4ENwDzgw/Zcsw1PAL3iKfFrgXEdvI5IqFTNXEREvKQelIiIeEkBSkREvKQAJSIiXlKAEhERLylAiYiIlxSgRETESwpQIiLipf8Pcs2rOKk1SaMAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "thinkplot.PrePlot(6)\n", "plot_marginal_cdfs(dirichlet)\n", "plot_marginal_cdfs(suite)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### MCMC\n", "\n", "Exercise: Implement this model using MCMC. You might want to start with [this example](http://christianherta.de/lehre/dataScience/bayesian/Multinomial-Dirichlet.slides.php)." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "import warnings\n", "warnings.simplefilter('ignore', FutureWarning)\n", "\n", "import pymc3 as pm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's the data." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1., 1., 1.])" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "observed = [0,0,0,1,1,2]\n", "k = len(Pmf(observed))\n", "a = np.ones(k)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's the MCMC model:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\n", " \\begin{array}{rcl}\n", " ps &\\sim & \\text{Dirichlet}(\\mathit{a}=array)\\\\\\text{xs} &\\sim & \\text{Categorical}(\\mathit{p}=f(f(\\text{ps.T},~f(f(\\text{ps})))))\n", " \\end{array}\n", " $$" ], "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Solution\n", "\n", "model = pm.Model()\n", "\n", "with model:\n", " ps = pm.Dirichlet('ps', a, shape=a.shape)\n", " xs = pm.Categorical('xs', ps, observed=observed, shape=1)\n", " \n", "model" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "logp = -5.8985, ||grad|| = 1.118: 100%|██████████| 7/7 [00:00<00:00, 1525.99it/s]\n", "Multiprocess sampling (4 chains in 4 jobs)\n", "Metropolis: [ps]\n", "Sampling 4 chains: 100%|██████████| 8000/8000 [00:01<00:00, 6107.20draws/s]\n", "The number of effective samples is smaller than 25% for some parameters.\n" ] } ], "source": [ "# Solution\n", "\n", "with model:\n", " start = pm.find_MAP()\n", " step = pm.Metropolis()\n", " trace = pm.sample(1000, start=start, step=step, tune=1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check the traceplot" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And let's see the results." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "def plot_trace_cdfs(trace):\n", " rows = trace['ps'].transpose()\n", "\n", " cdf_lion = Cdf(rows[0])\n", " cdf_tiger = Cdf(rows[1])\n", " cdf_bear = Cdf(rows[2])\n", "\n", " thinkplot.Cdf(cdf_lion, label='lions')\n", " thinkplot.Cdf(cdf_tiger, label='tigers')\n", " thinkplot.Cdf(cdf_bear, label='bears')\n", " \n", " thinkplot.decorate(xlabel='Prevalence',\n", " ylabel='CDF')" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_trace_cdfs(trace)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And compare them to what we got with Dirichlet:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "thinkplot.PrePlot(6)\n", "plot_marginal_cdfs(dirichlet)\n", "plot_trace_cdfs(trace)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Using a Multinomial distribution\n", "\n", "Here's another solution that uses a Multinomial distribution instead of a Categorical. In this case, we represent the observed data using just the counts, `[3, 2, 1]`, rather than a specific sequence of observations `[0,0,0,1,1,2]`.\n", "\n", "I suspect that this is a better option; because it uses a less specific representation of the data (without losing any information), I would expect the probability space to be easier to search.\n", "\n", "This solution is based on [this excellent notebook](http://nbviewer.jupyter.org/github/WillKoehrsen/probabilistic-programming/blob/master/Allen%20Downey%20Problem.ipynb) from Will Koehrsen." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1, 1, 1])" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "animals = ['lions', 'tigers', 'bears']\n", "c = np.array([3, 2, 1])\n", "a = np.array([1, 1, 1])" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "warnings.simplefilter('ignore', UserWarning)\n", "\n", "with pm.Model() as model:\n", " # Probabilities for each species\n", " ps = pm.Dirichlet('ps', a=a, shape=3)\n", " # Observed data is a multinomial distribution with 6 trials\n", " xs = pm.Multinomial('xs', n=6, p=ps, shape=3, observed=c) " ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\n", " \\begin{array}{rcl}\n", " ps &\\sim & \\text{Dirichlet}(\\mathit{a}=array)\\\\xs &\\sim & \\text{Multinomial}(\\mathit{n}=6, \\mathit{p}=f(\\text{ps},~f(f(\\text{ps}))))\n", " \\end{array}\n", " $$" ], "text/plain": [ "" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (4 chains in 4 jobs)\n", "NUTS: [ps]\n", "Sampling 4 chains: 100%|██████████| 8000/8000 [00:02<00:00, 3157.96draws/s]\n" ] } ], "source": [ "with model:\n", " # Sample from the posterior\n", " trace = pm.sample(draws=1000, tune=1000)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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5FJT1fInlSaorZtas8DNpjGlWu05kjz8zPg7XLP35WOsQQgieT8H3w12jVEQr8JXCNIP7r1RFcKasmZL6mGaBCKkYzjoc6x1l1dxqnMPDrNo0f4Y6cxL6dkO8Eagee02NeWlOlpcmVWCU+gATnEF+NouIRjGiYwU7BgYCr1BLS8vz7nLHcJ7d3SkuXNzAkqbnJi5GC0FggS+BCR6s6XwfTb1NfudO3J5eIosuGS80ZjpEsOzvw7nAC/ecBNZz7E/ZrTAlMu+WJpHKA7WU5+D0DBGdr07NIftiCREUQswpeK6K8fHXAwdPV3tngkxmH23tX2Pu3BtpafmTE25rWlm++tUP8vi//DthU7H0lhv53Jd/xQ3r/zQQV1LCQ1+AX74XllwG77x3krgqp2nREt74ma+y4dL/y77/nUf379cRYSlHj36JLU9eS3fPnUg59WzjlYuu5BvXf4OB3ADvuO8d9Of6T36yhgE3fxPmrYef/QUMHjj5PhqNRnPm2SuE+HMgJIRYLYT4D2DLbHfqVCgKhe6RsRA9Pzs+pE3ZxwnLSbZBqmNa7dimh5KKnO+PW3h0zEScvjnzZNswD5aFQc000y0aMeW+rjyhB2g6x7Z8OWkGXsqiy8JASlHwuhTem8YxZ8LcGzVd2oayU763xbPZ7k1TdJ4iluvj9B9i965teGVjrcrDuspOOO35/HJghITjle4yWdjEJ7CFy69Y9uFHyD788Lg2BwcHGRwcnFb/bM+fMuTVKtz3eXey/eQrRcI5uRe35MCSU4cITtp+ir/KcXt68SW4Ez/jz1XQSIWfc8e95pd70k6z3pBSsaMjScYa34fjfatYh0fwRwrhlmUTSHZ7D1Z7H27PNGzXs4jTmYM1H3hICPEs8DRBDtbdp7G904rv2+zb/3dEI02cd+5nT5gY2Lrnab72wbcgt7bjrmnivV+7ndff9FcYojDcTh5+/hfwyL/AxrfCW38B8fqT9sEwQlz86tfy55//N2RuPlv+0yaUuIVYbDGHDv0D23e8jnRm6gXVLp53Mbe94jZGrBHed//7GLVHT37S0Sp4848gEoefvgOc6cXBazQazRnkg8D5BJVr/xdIA387qz06RaYla07RYec6Ph17Ewx2ZtiayvHgcBq3mFNRsLyM59BGMjdzOU1T8jzyL5Qn8TMO5r4E5t7EKTV/b2KUJ1OThcz4MDYVCAql8NMO/nG8jH7awU/bpXEOmx7u0PPLd3v40CB7eqZ4npc1fSIBmXc8zAk5NL/e1cPenlF+M5ii3XOn3M/t72f07t+SymS5azDFXXv7eORYnmMZg97E2LmYjlcSMeUW/ZATHLfHdkoeDaUUMpPBsyyUnCxolTN1X6bD0+0jPNM5MulcDVH0PI7f3sq5PD2U5rGRDLkJ60apCSXYS3nxaooDTcFYpUlwPBfbniyC+xMGiZ7s1DtOE7cvh906gjTHRGK7OdbWdI8mLQ8vYZ58wwmkLZfuEZMdHSOF9hQhx0ceGuGJA4McS5zApiz77CjPRUkD6Z2iInyxeLCUUs8qpS5USm1QSq1TSn32dLV1JjjW8Z/kcq2sWfMvRCJTiyE7n+eub36F33zun7Bdm3nveBWf+Mz3mdOwYGyjTD/8942w71fw8s/Ca259zmtOtSxfyVv/+WtsuO6V7Pj5dg78ZC5L530a2x7g6advprX1C/j+5A/sBXMu4OvXfp2uTBcf/P0HsbyTL9aYic6h97p/Rw0dIvurv8Ny/zAXqNNoNGcnSqm8UuqTSqlLlFIXF/4+e1einQal+TspMfftw+nsnGQNpZ6DraCUmmRky4KXwUyZjNqBODKlRDp+WSjPZIWlPInbn0MphePJSQar8jyyjz6Kn0pN2nck54zzIgzYLk+MnKCAQqEfWSHozJ3cwHOUGmeU57YdJXXXlhmzqwan8GaUh2oqKTEOpmjozNG+s5/fbe2cvL2vsNtS2G2jpUtaM2jhTjSmy/CkYiBzYk+UnCDmxl05f+oBUErxwO4uNu8f8wwUPX1Hh7L4SjEkfRyl6Cw3zJXivvZudhhRjg6n8JRiRPpYnj+pMMWWIwn2TSEAjUIPpRrrqw/kt+/A7OrEaT2C09OD09HBcE+WU11bus9ySE8h2koftQmvH9uX4JkjSQDcCe85HZ3j9i15hcoFlvJhYN+UEwPFoyXzNrs7jtDadmTc+yaCvDPF7MYJbuShTCDYlR/kbjndGQ51jNA6kB3nvVUKhroyZJImiuB7YX9vGucEHl7rYBKnO4PM5XCOHSu9njPzyBNMfBiFGRq77NixtIvyJelCaObxGBcCrSSeORd3es7Kswa90NE0yOc76Oi4nXktr6Gp6coptzm64yk2334ruVSSwytM/vzdn+TqldeN36hvN9z5JrBG4U13wnk3PO8+RSpivPw9H2DFpkvY/K3/4O4v/IqXvflvaF6xl86u75AceYLz136V6upzxu13ybxL+OKVX+Qjj3yEjz32Mb5y1VcIlZVitz2f3x8Y5Hf7+nn62Ag9qeCh9nfh1/DB/f/L/9nVyI7a67lgcR3Xr2nh2vPmUl95ehcxdF0Xy7KIxWJEIi/8xec0Gs3MIYR4iCkmY5VS185Cd2aIwDARnotyHLzhYfzRJaWyyoNCcNiDZabN0njFuD1dX5LMOZRnpTgdafyUTeXGyfm35s6dmPOiVG66EG/EwurJgQhE01QeLKcrgz9qY1RF+H1HEtvz+ZP1CxCeRIUN/JER/HQG6+BBqi67bNy+j7YOAbC4McjzeDKVpXMgS6OlWDO/9rij8Ui0gspUlqW11cfdBuDZ0RFqbQvTmU88GsI+3B4ISyWDMuETkErR63ss8AXSEhixCbeRlJAbQlZPHjflS6TtI8dZUeP9WcYEo9XpzozzBExX+HUM5+nNQO2iGmpjUz8DfaVKoqWcvONjmi6VNRWT3rP276d62zNkLg3sGm/YxO7MEHJ9/LIS2btcm3A6z+JYFCEEEsgqSIsQ5cXlFYKJU7AmCs8wyJguMalIK0kcMea1KhS2QClk19OQS+BXLEIB+YOHyPguA1VrcIZDLF/4/Cd4DzgOtu9Pyv8JWSNU5noZSC+noTLKgvognz1fdiWnmGaY8H8hb0gpRPGijvbAYD6IAGLy2AMcGsiSTVtUD0Yw9w0TPz8oQvaAimPF4JqTnJPpS6KGIJGxeah1iPUL61jTUIXyJF7CZChjE7Ymj5nn+GSdoIZhKu/SOpihXficO6+GZM7B8STz6oICar4v8VxJOGKQ27oVaVpEFi3Ckor2jnZE2ue8pqnrERQdeyWBpUCNVTQ5MeWTAoU/pSPwhoZw+weIr193wt2djg5CdXWE6sccIuVFPc4E0xJYU1X/+0Oi9cjnMYwIq1Z9dNJ7Vi7L7+/4Fgcee4h8vcHjL0vyL2/8Bhvnbhy/4YG74BfvDRJA3/W7ILdpBlh50aW8/cvnsvm2/+DR7/+QJes2cOlb/o1jPZ/n6e1/yqpVH2PRwlvGzUS+ctkrSZgJ/nnbP/PFbV/kk5d+krzj893H2/nvLccYzjk0VkV56com3nLZEhbUxYkZGxh6pJN/Hb2DL86/nHs6JPfs6SdkCK5c3cy7r1jBy1Y1ndKaCp7ncezYMXp6eujr62NgYIBsNovrjoUFVFRUUF1dzbx581i6dClr166luvrED12NRvOi5sNlf8eA1wGzX/7uFEjlHdoTOdbWj69uN+zcTyy0CJNgUis7RUnyjuE8KdMhUvgeB/BT470fyvVLuQ5KKpQnsDtGcetqiDHmxZjSg1Vm+NiF0Cn7yAj1PXlGllTh9JkFw+rkzwIhYGjE5IBvnFBgBQ2PhS+6viQSmiyYKrrasYEHDgzw6gsWnDS3qjVv0+17NAw4+JkQRmzCbdO/G4aP4q+4dtL5uH05/LSNF69AFcdJTvYUljMxzGqcHPMs8F36sz52yqI+PiakHE9C1JjkpQIIGQJfKnypCONPEm39oxZbjw5z7cYFk/b1+gPPlSiEvPlZF6kUIVeOE1jCV0hflgxUpSgZvZOkhhpfxOBZI0SkuoaK7hTXb4SHXYs6YbC2OAbF43gOXqKPULoHOSfIR5fA7q4UTm4P86ao8vdMn4mBYP162H4syajpct2ayQUvlOcRaTuMO2dysY+q7kdpGMnTU7WYp48lSxUohSvhBJ8Dt+zcS9dRqsmi2XOYKLBK+5XlbinXxx3Mk0tbmGlFyhaTQiIn3lv3JUaZEw2zyDfYlzXpH1CsaQgmL+y8h92XJ1w/NgF+92BqrDR8of2J5/BYYRKkOA7dB0bwujLMX1GHcgJPt+NJ7tvfTzxt01xMmJsCWfAoT/QAoor3keKBrj6WNNRxTvX44hrjz3Xsey731DaAkwosc08gWYxYMPYpBNVnaRXBbwohosB/A3cqpY7v13uRkUg8RCLxIKtW/j0VFeM/uJ17d3Pvf32V3EiS4U013Nuyn69e9+/jxZVSQbnzB/8JFl4ceK5qnn/Fm6morKvnNR/+FHt+v5mHv3c7v/5sK5e+/gNEFj7E4cP/RHL4Mdau/RKRSENpn7eseQsDuQG+u/cOkollPLZ7HkMZm+vOm8vbLl/GFauaCU2cvlz2A/jG5XzG/Rr/8Pf38mxfjt/t6+dnO7p563eeYs38Wt5/9Upu2jB/2kLL931aW1vZt28fhw8fLsUiNzY2smDBAmpra6msrKSiogLLssjlcqTTabq7u9m3bx/33nsvS5cu5cILL2TdunWEQnphZI3mDwml1I4JLz0hhHhkVjozQ7Qlcliuj/Inf49afjew4rj7+r6PcMHNO1AQWDkrTyQcoRJ4fCRDpCvLeRal+CzpFvJQci4YBtIQ4E8/B6uY4xExfTzXxc+GiLRMvbORHwuFC5XCxBSpvMP+3jSXrWgqhRYVSWRtqtKBONndPcpgVwpic7lk2KShKTC8yw2ySQUmprCrlD8mEI9ndsnRBFgWvmsBQTu5UZuquorS+kRKAkqUvDDP1YQzclnwfeh7FuoO81RuDYOtQ1zbVEvF0RSiMBYhz8TZvZ18OELlJWMVIkNC4KNw8yaRkGCi8ql2hhDJYQYzjQDMrSlb2mUKg3Oq4hyVSZshO4ma3zh26FIcadmxPIEpJor+cclgAIwqWcp9kgTFVLxhC7O/giplULzti3uax0lNyNhjnqNitA0EgsUbypOMG/SmLNZXK4TrEOnvRuaXQnRMzB/PVAkNmRghDyXllFMFP897JCyXBfURZMWYwKIQdpf1FLUAcnLemOP5+EBRQhenP9zeLBnpM2q64IRwenrgvOaxHcuujVsQxUOOx6JQWRRRYZNM0ipMnpTtUwyhdSUYxYjGMsHl+8G6ZeExaWCbLiWrqrCtLOQZpvIOzRWTI5iUChaJlkrR5XsMSJ/XyMlLGDj5DPsGHLotm1VLx68n67g+0vGojIaB4HitoRArCb7jxrVXCFMUU5Q97RlIcTDrklvSwqa8zZqKqb2Jp4NpCSyl1BVCiNXAXwDbhRDbgDuUUvef1t7NMlI6HG79HJWVy1m8+J2l15WUbP3lj9ny0ztpmLcA/80XcNfIr/jMSz/D1YuvHjuAZ8Ndfwu774R1rw/yrSLPba2F6SKEYMN1r2TJ+Rv4/R3f5LEf/ISmRYu54HVvZzh5J09tu4l1675Ofd1FpX3es+4D/GpLA7842MDiZotf3PIyNi1pOH4jdYvgpq/Cz/4C47F/ZeM1H2fj4nr+9vrV/HpXL7c/2sYH/3cn332inU/duJaLlh7/WLlcjh3bd/D09u1kMmkqojGWLV7FOavOZeXq5dQ1VpceLFOhlGJwcJB9+/axd+9efvnLX/LQQw9xxRVXsHHjRsJhHf2q0fwhIIRoLPvXAC4C5s1Sd2aE0jef55KO7SfuLEY6DgqF7SlyhVygHsthpLObSxuqicwvzM7vPUo8PQdvTgrVXIUQgo5EDwAXs5Ahx8NxXM6jLNSszCb3y0XCc1ULCgbTFsOhMKsVlFdXH0xbhAf7ibfux11ZT6SlpSTgJIqdXSnSpstwzqEmFiZWWJvKlwrL9UkOZ1FK0ZcyGYxUMByPEutKcbnMolwXY/6JSpFPPhGzK4YZDcTe8ZLR8zt3YrijsPoavESC3FCa7soFzFsmwUeGAAAgAElEQVQ+FhinlCoLe5LPKd9LKajatY0KvxmWA9b4uWuZGSsc0pzYhhpoxV1x+bhtipOZ2QcfxA4ZKMKMhEN4BN6UJZmd1BHnyaPB+kGv3rCgJGBLHrGxKhNjJfoLoYBFXF8iFYQmPJaLQkkoSTRdyZAN0XOCcXH6cojyHLWywRFlrwkByvaRInhHAidaU2pzYpSqMg/mxDwgL2nh9uXYlcph1UdZXx0HpTBcl/zDD1P9p2NVoAWBR0b6HkaozG6QCkJBPwYcl5rwBG+yJ7Ckg+1EUWYK1AKUAqEUfWmT4WGLGtOl1g8EViidAgKv0K7uFAp4KTAQCdEVCrFKSWqEURrzYmtKgXW4E8IhwoWwvbtDcc5PBwUiwhPG9WSfWSUV/oiF60v8snXuBIL0zp1EB2yqNl049b5K4QAJ2wUVLM1gTyF+d2VMjpk2V1RWklYSgcAqTEgkLJejrqTSlqQbgtc808XaPzzuGNuPJclm89x4XgsoxbGKOK0hA8eBUCqFMTxMY1MQUpl54AGU61J3442T+tKbMrELqSVp78wGNkzbClVKtQohPgVsB74OXCiCT/YnlFK/OF0dnE16ev4X0zzGBRu+jWEEKt3KZbn31q/Q9szTrLniaiJ/vJ6vPvFh3nTum3j9Oa8f29kcgR+9FToeh6s/Dld99PhTJTNI/bz53Pyxf+To9qd4+Aff5vf/vo2WNZtYcEUrO3a8mVUrP8ySJe+mPZHnL/9nB92Dc1m5fB/DsR9jhf8DuPzEDax7HRzeDI9+CVZdB4tfQkU4xBsuXszrNi3i589086+/O8TrvrGFP924gH+4aS1N1RUopRjqzNC6u5s9h55hINuGEpKIXU9tfi1Ru5Fkp8HWJxJsJYFhCOpaKmleWEXTomoWrG6gZVkNRuFLVQhBS0sLLS0tXHPNNRw+fJhHH32Uu+++my1btnDTTTexYsXxZ3k1Gs2Lhh2Mhdd7QDvwrlnt0Qxg+DZ1yQ58I4dZcYzIvhq8OQl6RSUjOQclFWnTYqiji/VtJnU3BcaFcD1QimRXhnBHhpZlxw+9C/Xm8CbYZh5MPzloCg5nLRIVYXJK8NKRHCIWIhaPkbZcQrmgoIXMBcZhMWdIqTHPyZajQbW/YoiS60kIBd6uovHpFZ6lniwLGbphak3t+4Fh6I+MoJx6RNk6Sl6+YPwWHRCWQEk1aXIvt2cvTjaCYwr64y002RJpmchsDrehisygS22NLBQ0KBMRxeNKhTNFOGepWqNlAtPPZXYHB4nMDfLChAiKe7QXvJ6ros08WxsDL8fCsmMa+SyGaZKx5lJXGRic9hSFDUoGviEmxdmqwscs+D0mzrxkkvDwIEqNjZtyJF4yR9QsHFMpfre3n7TtEouGGPX84LrIsbWNAs/I2PWd2ncEOV+SKxvPSYUWCuNaFHfeCe5nIQRDoxbpSBf1C5cDBEVlHAcKIn9PxmRVZWzK/bP5PMe6D7OusgoWrQOlsF2JEiFcX4L0CCcTxA88i7OkiuiyZWXjCaMhgwqlsJSiRlDKYRNlXc4+ESyTU//qi0gWpgOO5iyMSAQ6Mjjh8smSqc+1t7B4uJKKkcJ9bx1OwuoGhOsghWQob1JlORxv2bn97Wn2NlZRPZrDKCRY9aRMLp6wXYcZFNywjo1SNeoilMTxFVIqjqbyWJEIKyuiRE0JleC73piiLBuc6iELO5wCj5L4zilJLTCcSFBdU0M0Gj1pdUlJQcibfimP9Uww3RysDcA7gRuB+4FXK6WeEUIsAJ4EXnQCy/MytB+7lYb6y2hquhqA7EiSX3zh0wz3dHHdX/wVzZdfwBvufgNrGtfwkUs+MrbzyDH44Z8Fv197O2x4wxntuxCCVZdcxvILL+bA4w+z96HN7P7eCEuucjnCv/CrR5/kmwdfRyRk8LVXLeTCpSv5+61b+fvNH+K2G7/D2jnnn7iBG74MnVvgF++Bv3wcKoIV3kOG4A0XL+amDfP5xsNH+eYjR3nowCBvaGliXmeahH8Es7IPgObKJaxZcQEtc+cSq44SjYUQQmDlXfJph/yoTbIvT397mtbtQemYaCzEwnMbWLymkaXrm6gthIYIITj33HM555xzOHLkCPfccw/f//732bhxI694xSuorDx9K5M/X5RSuN3d2IcP4yWTKNNCRCOEGhuJLlpExapV4wwBjUYzNUqp5bPdh5km5XrUZtqpzw1DYyEMCoXK55GF7zMvMUR7XzcNsYqSO0D5irCzALfgSRkdytO0pGbS8V3fw/XBSwxPct+4KFJ5N8j5mWI63PEknifHZZWMs+kK/7gS9j2xC6MqwqZrXhJ4pEobFjpse6X1jsqP4Y06JLoz1IqiMR+MwMQUpPFhgZDxLCLGmFnjeZBMG8iBLInDB2kWQ8y/+orS+8V8lOIQ+JkQ5rNDxC+YgxACx5dElcRODENsXuGYPiTb8FoPIO068mYjUoKd5bghgk8fS9Kftng54wtUHHex6ONQqp+w7Wn6rrqGtdVxDnsO/a5LU8GT4BXvhaEBaBmLIqncuQ0B2C85j2Jwmul6KKUw00lsOxC0Ra9WSWNO4Rwp/y2VwjnWQWX7IBhGIMHK7Ndi0QcRxKORyDlU2CFG3KD0t2XmYHkwCZBr76eOMZFXfv9JKenqdKgwJxvTx8t7C/J8JPkyA3zilmNVBIPxk7kc5rN7cAbjsHx+ILgLxr8rFftzJqvL2rOsHBEvhXLM4CZUipGQwdb6OSxVLlW2hbCCM/Kz48uSh1wJno+XHKE70sygC/Xzqsb1yxsYv/bTllBFcUCCY8C4ta7UxItU+PuJY90YlZXIMrNfquDer9z2OKHGegiDVyZWlVKIwvp7yvcJ5ysYqZFUjatKqvASCSqWBV7drO2xq2OEFU2VmGmHmOXjhMBzfUg/StjJQTjwkBWFjip6Cydcl5BTDMOVGCUve7CPmc9z6NAh1q+fup6BKvss+tIgMRRi4dFR/NoawvVTi+WZZroerFuB2wm8VaVAV6VUb8Gr9aKjo/N2XDfJqlUfRQjBSF8PP/v8pzHTo9z8sX9k8boNvP2+t6OU4itXfYVoMQa2Zwfc+UbwHbjll7DsihM3dBoJhcOsu/p61l19Pan+Plq3P8nmfVu5o/dltMT7ePXw3bT+l08rcDFwMc3ce+9Hub+iglhVNfGaWhoWLKJxwSIaFy5i/qpzqW+ZB6EIXP0J+PX74cdvhU1vh3AMKqqhooZYvIU/qa8lVt3ED4eHub1zgEVGmpfFEly6fgNXX3MVjY2NJ+t+CSvr0n1ohK4DSbr2J2nfnYAfwfyVday+pIWVm+ZSWRtUN1q9ejXvf//7eeSRR3jiiSc4evQor33ta1m+fPZtMLutnczmzeSefBJr/35k5vjliUU0SnzjRmquv46a668nsmBygrJG84eMEOK1J3r/hRpZMZC26PE80lYVyPFrNx3KxdmTixMOKZRlI0Jg+7L0JB9XjhkYkD77hlI0AOWlgAZSQxzNO9RkLKhlQojg2HZF+99yg+prFeEQ2zuShC2fy1aPGe8K8KXHcF8b1W4IGVXIgjejuCByn+1iKxX4VAT4GQe/L4e0PGT1eCPZGbRIVuaoXVBdMhilUoHIZKzQQrmc8VHgu7hyLGSpaCtmczaW69PePUx5IGHxXCctqOwr+nIWfYkcFTJPKO4H5VMA5+hROC+C44dRSgYlusVY0n65rS+lT2dnJ72pYB1LqcbntVm+R2dFjLW5wGB9Mt3GkFg1rivtvsfDhstlZpiudAsrfDgciTCQt6nM5EkXTtJDEJ4gH9oTOdYW+vVkbR1Nrsv5ZZs4ro+nJGZ6hJ6eHhYaTaXrUJrlL+b0WN4kgSszIfyEAyhiTgXEXCYWAxnzxCiU6yGkxChULpZ5FylCY+8Xh7/Qbnl7Vk7iS0X7oQTMj6GURLkuIhJBKUXe9tgzmOFV6+YREgJ8h1jaYthKcNj08f2CR6zgecnn87S1tTFngvdLymByQhY8ZMlRm/qCQX4wZ9KWt4mWfc5WmwepdQZA+QXFKUnmOokZMUZkM13tg8CicW0oAu9aaCSBkR0hGw6TTqSpqqymtnhPFq6D09uHEGA5Po8eGixUXRQlJdU7apFLOjAvsEHVccqmO+3HEIZALFkB0gcjFExs+JK2WHzKpRm8YQtjxEbZDr8/fJBsZRTwxi37EM6ksfbuJrIgQm+VxLebCItgSQYrlSLe3UNm6RJczyeUHQXCpSsthAH4Jyz1Xhwwo7DP2O00WVT32Q62VCyLV9CdyZBzXYQwcKQia2fIps3jLllwOpiuwLoBMJUKJL4IRiVWWH/kB6etd7OEbQ/S2fld5s69kdraDYwODvCTf/o4vufxhk9/gXmrzuGOvXewe2g3/3zlP7O4tpCcd/C38LN3QfUceMdvYc65s3siZdTPm0/Xgpfw3S0xzp8f4a/X/YQwHTTE3kRcXoNrO/SPdPPTvT+iwvW4tuUiyDsMth2hdevjpQ9TfcxjWXyQ82oHWRCXiLaHoe3hUjtd9noez7yLYW8Joao2/rS6mx1+C894i7jPO58rox6NI7vBbYHqFqhsPGnoZKw6wqqL5rLqorkopRgdNDm6c5DD2wZ49EeHeewnrSxe08D5Vyxk2YYmIpEI119/PWvXruVnP/sZ3/ve97jqqqv4oz/6ozNeBEPm86TvvY/UT39Kbvdu0lXVZDdeSPiNb6Zy+XKqVyynqamJpupKcD28xBBuRwfmnr3kHn+MgS98kYEvfJHYhg00vPGN1N54A0bszMy+aDRnOa8+wXuKF2hkhetLjELcXrFqV4Ci34lCFHwJyhaEKstCtZiQsK4UB6TLHMARgkNCMJIYPWGVO4XCHfc/SMvi/keehYYaXrnp3FJzbnmIllI4rgUGZKwUg2HBHMZ7znZlTQYjYV4KWPv2E99Yj0pnUHkLRfXUqSPlHiE52YOFlPjF5HlfErFTICtRUpLI2gxlbEIqNsltURwCv/S/4phhsLjM0LNdiSjs2JbIBUIUEK5PNltB2oni+gLHG0bGjoEzf5LRZ+ZGefDZLPHaJuK1DUipMMqSmPZkTLorKpgXCcRD0smR2LeVemcNNAUNtvlBoF7WjdIIdPWHyM0X+IkEfvsRYrXzycdq2F5Tw2WZdNCFQhNiguE6ICqwci7Uxkrj4BcER0n0FE6horOd4UEfERsLvfQLngZVEBKOJxkZygWhbuEQThiUo/CGTFQ8ilTgOYXrJiVV+3YSidbC0qVjwpkyb40QSD9cqMqoAvFavN+kh69c6hB4o6P4yRT2kT6iS+ahlGLfSI4Ox+VQMsfaUAS/+xlqR336VRX9RgTTjASCoiYoKTEwOIg3fAyzMEYVWY+GjixqRW0p4NiTks7+DLU5BxY2lTxr5Vc5Ll2KZRVVwYMVDKyPSmcxQmUBd+WmjucTGk4gKwTHsgbLoh7nVoJrBT6McseyVIrdI4M42WYcTxINhUqf47ztjSuVfyBnsrLYXPE+LxVkUThHjhJOg1ffiN3Xj3N0K4PRKKGi6CmcoPLHqij6lkVnhUu+IkJRYJVGwfOxhgZI7O7l6LkrqDGWEyaGQJAfHCDsS5CKbNso2Baoygkeb7Ate3Il+wnbGMUCGyV3/eRvjK2pwEO4LF5BznWxfYPdlTWQz2D5Plv6hzgvuYDVTaenFsJEpiuwHgCuB4rlfyqBzZw0YeeFSXv711HKZeWKvyOXGuFnn/8UrmPzxn/8F+YsWUZbqo1bd97KdUuu44blhbWsnv42/PbDsOBC+PMfwxTrZswmP93exUd+9iwvW9XEbbdcTNS4lAMHP87Q0A8JNfWx9tIvsSHySpZddyXv+t27OBx+mO9c8Lcs3vFDvENPkTTDdMsldNjz2ZtYxK6RBdQ31PCGxbuoEmky197O44/HOdaviNamCDVuZcBymROx+Hz8bkR+kA/lbuEDT6zi/ifv57OR/6ZO5MCIBGNV3QK1C8Z+agq/m1dDzdgXvBCC+pZKLnrVMi561TKGe7Ic3jbAoaf6ufdbe6iqr+D8Kxew7o8WsmDBAt73vvdxzz338Mgjj9DR0cGf/dmfUVV1vAjjmWHU9djfP8TOBx9hf2c3x5rm0vnm9zH83jr8iWIypSCVoCpkcH51nItq63n5S5fyklf9MS0f/Xvs9nYyDzzA6K9/Td8nP8ngl75E3etfR+Nb3qK9Wpo/aJRS7zz5Vi88/ME8ETMwYnrMLMt8l+oJCfbF0KyxsBlQrk9PbwrfMIBgFr6YeyKUot8wiAzkkDmntM8YYtyxi0ilyD/1FK3bnqVyUQ0PIZmf2IkdXszRobEohPK8BlGwTt1UCuWEEOFYKVzHLbTjeJJQdw9ycAgv55Gc30jSshnwPC6MjFlaXT0Jkmkb1/eo6E/j9GSIJcsWvJWwt3eUlBLYiVGUimP4MeI7WmmrqUB6PhUoosfRlB4KIT0GcXjGznJVtJJLU6NI2UTS80pjIYvDI4KZ9BFLccSEcAQcfxglQAi/UKZ7bCylH+SWGKEQKenjK4NwWSyUV8wR8gV7u0wSOQM8H2kGRnYqZ9IxOgyhsTB3wxXkU2GskTSW4xB2LYjVIIWgLxolHA6NzdKrYnhpgOOE6T+UYun8GpRSdCVzSBWs3WSEwuAXPIVSEe1qRy2eN87wVYfuRYoI6tzrUQTLCUTCFqEaGKoIkY6EwPCo8yROyiKZE/gOuH4EKgOPUzEtLLhnPWQIqkIGGcsjpQTz5NgEopcOU5OvYhTJkDdKGI/m0WGcvgGUL8gaIfptiSslduFet1XgJszaHiHpgKhiMG1RvMeLdvnWQ31U9h+hoVCMK2x6EA88WH46VKiwFwyhUwi/FMBAyqRmxARXgCrLsysICSX9YNJYgXekC7F6Fd5omq25KOc7PkXTXkiFrbySaOszPZb3m+RGA691eQ7WQctnuxtlcSqBjEeQ2RD+iE0oPl4oKNdl8KntLKmcD8SJFCZqilX3lCxqwcJ9NziILyPIsMQIKWLKRwiB258jzxDDzcG1yHs5siEbm4IjV6pxXxQjZjUD3Sb+aoVfWENPCNgdixaWklBI38fo78XIzUdWBpM5g1mHlGMiHJ9xKhEIOR5hzwQaAFkSnF6u8PmZoNLyzvj8KgUMehX4oRjJChc3D+Eo9GdtVnNmmK7AiimlSrVVlVJZIcTZl9gyA+RyR+nt+wkLF/45YWMuP/riR8mOJPmzT32OOUuW4UmPTz3xKSojlXzqsk8FF3PLrbD5k3DOq+D134Xo6TXgnyu/fbaPj/78Wa5c3cztb7u4UJ2plvXrbqW75we0tn6Bp7a9mrVrvsQ5jZdz24b/w3ue/hxvfezD/HvKZuOl72Lu+Tczd+HFbDIMHDNP67YnOfD4w/z04BBvXd7P6C8+THv+k8TXK7qGjlBpVHLjja9g06ZNJa/Rz/Np/uvB/Xz9yZfxVOhyvrxxiCsrOyE7AJk+GD4C7Y+BPWHV9+p5sGAjLH0ZnPvHgegq0LSwmpfeXM2lf7KcY3uG2fdoD9vuaueZ+zpYc8UCNl6/mJtvvpnly5dz1113cfvtt/OmN72JefNOvciYUooe22Vf1mRPxmRf1mTvaJauYlWdpecRW7iSVdEwV85pZFEsypxomDnRMBXCwFEKV0pGPJ+2vM2ejMl3uhN8o2uIedEIb57fyLsXLab5Pe+h6d3vJr/taUZ++EOS//09kv/9PWpf+Qoa3/EO4hs2nPK5aDQvZIQQNwLnUwrkAqXUZ2evR8+fdMpGWn6h6IMg67tUGIKhEQNZKYq2G5YtQCiqosH/iYNDPD6YoKq6hlX2yPiAGiFQ2FiZfqJGY/k74ybVFZB3LDIjA8SampEKpGUT8myyfi3e0NNAmApriK4RE2JlayUVFvIt5khIBF4iQXTJIkqlH5RCIXk2cYBVTYsYMQwylkuPaRMPBydS1ZnFtjxE2uFYNlUodQ2+neee/hFSOZNIUT8ohecr+uIx6mWh4LeC8PAwtLeVnVWAX1ynqvCS5eRoSO/DsefheYIu12NOKomfmce2TI7VkQjz7UIIpGmAE4xXTo6Nmu8GBzMUoCSKEDuSWRbGo7giC1VhMsKgzXM5qAQXlInlYs+Ub5DzHaQXLnkmZDbHM21PMbRoYVAWvrCxYVt4rseBDhtjNEk0GiJSKJV9LBrGUhZFVVQMMxtXZK7wTyI73juakT4RN4WTH6Du2XaMynLBXDjX3CjukEWHnyBvB561kG+Vjq8Ay8gTz40yEBJ09/YiVJlBXHaz+baP29ODrQRV5zYxlLGp8uGcwjaelJiuLJXpkIX9e/s7Sh64oWgEJRhX8OKxA0NUzK9nTtnZzU+0U291s7sySNmQUuLYeSoBZY6fvPCzLsoVpfsVpXDsMVH/2N4B2pJp6sNQrEivPB/7UBte2sO9ZE1JNAmpMJRPun8QqUJ0jrg0Ja3SmA/7OZQI7EXpKIiD7RbHvbQZvQW3cgdhFhcFXa7g2RQKqSTe6CgqUoOvJAcPdBKbN5YW4Xs+yhFI20CFxwqxSAXZTAgrFqIqXDZx4fi0S5/7e4Y533VplgrHD4bD9CBrudSWPunBGA2OuvQNZriwYFo5rYcwHRuDMEKB6xSEl++BggGhaHU9KqMgbRu7bQtWw2rSVLG4oZK42U/cGgCnAZQipBTm0ChxVfieUWPFUYazDseGcwxmbFpqgwmdsRKYgoiMkPV9IowXrqeb6QqsnBBik1LqGQAhxEWAeZJ9XpAcPfplDCPOsqUf4P5v3Uqi4xg3f/TTLDgnWKn6zgN3siexhy/90ZdojjfDY1+BBz8La18Dr/tOkJ90FvH7gwP8zY92ctHSBm675eJS6VsIvEGLF72NutqN7N33t+zcdQvz3UWsfno3/xNv5v3z5vKuOTb/75wruWHxS0r7ReOVrLniGpQ4jyeHLuOR5Hd5efMDrI7dydahS7hw/TpeccONxCfMroQra/k/r76Mqy9M8X9/vItbtgje/tJL+NgNa4iXLWqInQ0EV7oHBg9A7y7ofQYO3wf3/wM0roT1fwab3gZ1QWKuETJYsXEOKzbOIdmXY+fmDvY90sOeh7txF8bZW6foMtZzwcg+bv3GbewMnUNszhJWzalm3cJarl/bwvwpFjIsopTimOmwPZ1jb8ZkbzYQVClvbGZrad7knK4BbkxZnBeuY3VFI/PtEFg20Fc6lhEPY1RGCr/DhGqihJvihJrmYK+s4BHH5kd9w3ytY4Dbuod4z6I5/OXiOdRf+hKqLn0Jbm8vyf/5Iamf/IT0PfcSv+giGt/xdmquvRah1wHT/IEhhPgmQVTFNcC3gdcD22a1U6dA3vWD9WuKsTqAbQcGfHmInIKSa0W6guz+VjwhyRVKTUvplyx4H/CNTmy/fpzASocENUqUtlNA2swgAN9zeSid5S2FpKFeEUMYIZqFw8RvymA5rfE5O4FBLErvFw37LY1hFgiPg5ke5HAO16uke8RkVXWktG913scYsagcDAocSSEpZCgwKhTNY80A0G+B0xtsWyizgFJl4XFF74bns78vXVrk1nQK4VjSQimBbQj2hgRx0wFfllXRU+AJhFsQUmNFxoMcs2hBiBRCpxxf0j0yREtjMPat0idMmOyEkL1iH/fXVrDBDow/WbimbmII6ToTzhTIDZOMV+CIBvJ5A4mkJtOGSZR4vh/CTUCk5EWB8WuPlR8tKwxsIwQKnsi6GOYhLvc7iLotRMzJofu+VDiepKMrRW/OpMY3qcyNkK2sAgxsH86191KR6KEzcg1mupNwaA5OSBTEtUAqyfDoEM8eMWgAlCxOJiikAL8wtkdSKVzH5cJCQY5iv0uhc6ogIFUhdNGTRHMeNEqODudKAms0ZNCQb8NWLobyONCXpqM9CcrHsMMMpCsRbqhUZKFYeER5FrgmZsZH+RZWNltqfaKNXnQKSal4prWXrONDoTR4xvZosxR56THUaeI0psc8X2VVA4vBsLKwlJlRFuupgN54jMryBL6yPKguJ4dvZ3DMUWREgfQZyowJJt91x0R2+ccCie0ZVEoDQ9moMgVsKsWo6dL//9k773i9qirvf/cpT7n93vRKAiQkEAKBUIIUaYJjxwF1UMA682IZ+7w6o47dcUYZxxkFdVSKDawDCCgoXVoIBEhPbpJ7b24vTz117/X+cc5TboKKjgi+n6zPJ1zuc87ZZ5+997nP+u3fWr9VCXFjw54QOiwo+YpSf4njnkYoohwkCqYKKJWLOL5HxjgYbw6TQYVc+u4YkYYYSxBiSgW2FYfRRYe4exlzO3LYOu1/nNbzEsELLEpGIAf3R9BiGegvYKWb2hUvRNqz6WSo+npJ1ErT/Ls/j4Ag8MwB1ruBG5RS+9Lf5wGveXa69NzZ1NQjjI79ksMOfR+b73qILffdxamvvYSlaxIRyqHKEP/12H9x2oLTOH/J+XDvvyfg6ugL4ZVXgv38qr304K5x/u66R1k5r4P/vuyE6SCmyTo6VnNS1zvp7f0Ae+f0MbZuPksO/XuunfMK3nPXB/mHe/6Bu/rv4kMnfoiuXBd9Wya474btjA2UaVmiedxax8JqL+dYv2Fs2GLn1ke5vzDKKRdeTL79QIng1Qu7uPldp/H5W7fyzft6uWf7GF98zbEcu6grOSHbBtllCVN16AsbF07thW23wZab4K5/SaTil78Y1l0+TUzE7szwxAKH/5lrOGRcs7q/yjH9ikPnz0Id+SLCvgc4obyF4arh9k0z+cEjfXzkZ09x7KIuXnbMfC5cu5COnMtwEHH7eJG7Jks8MFVmJK09k7MUK3JZzheXw4YjDustsqxsk9cAM1A5C2dmSwKiZjpYWbv5+xjjxRgvRhcDoqEKuhROS7xc1erwvi6XF/W4XD8L/n3PMF/vG+H9S+bytsWzcefPZ84HP8DMyy+n8KMfMnHNtQy88124ixbRc8kldF3wKqxnOQzyoB2055GdIiKrlSSCNHkAACAASURBVFIbReTjSqkv8BeafwUwrbZw0y6tb0LCVMAh549QlTyCiwDxlI2xPCI3ix+1IjKG6e9HFixF0hwlPS2BSfCBpzoyLLTVNI8xNgY7MuTKGpD6pk08XoQZrZgYVNmj+aI6mKrnZigmw5AFJP6cQRBf01JWhAr2uZ1kigVaBBxdTXuUWO159dQUTirnXpUYSR2uBhsj7B4rc5jAcDmkf+sgM4whm3YhraGMEcOkN44QAzb9kx5HAnfb2fpd676nUgSBkDWGSjXE0/uxOApkPwetdq02UJ0qo+M2MuEUTjiFG9rsa5uFiMEYoVgtobMZRrxUsW5mKkyAMJmqxoZhROCXIddZSwVKrm+iocqpW14iYCSeYKbdlnbPNAZRwNVVrMDHKY7C7CQnvKYSKAgbW9sIsy7LI8GEcQIfamGlNU+/aW2ERrinWMbrSVk7k4RAGh0zGbiUnMbglP0ipThElAbbQaVhoj4xxhjKlSo1mZQoqhV8VhhUvY+Bbi7HW5ukhIEpeFFtqaHFYHkapQ0EZlpY4/asS87JkIsa2YX3bR2iMhUTuq3ssbO0OTla0ufcXh5DvFEi3yb28oS+j9PmouOIuCDJPfaff5WAldorVntrQyzWT2WpmsR3mEjrmuWKIVFKw8p+aQO6Dqoan/sWVG2bluY1EMRYaY5UVVGfJyFliZqs4oXsKmgW51S9v5C4HQJYoupsZ23+pakHVa1BQUpCIQjOwB5kYoJanqQItFcddo6UwWmrz1XV+Kigisl1gCT3lyDAbrEJY8PgZMhcgd1BSMvAbrpbFiHSidTUQHVEfzmgV2sQw1RQQbuawAil0PD4SJG5RR8Etu+ZwhYFs5riDZVKlUoNouXPia+ecaHhh5VSK4AjSKZmi4j8buH5vzATEbbv+BzZzBwy0WncefVHWLpmLSe+olHb6l8f/le0aD500odQj14Dt38sqQv1qqvAen4xB5sHi7zlmkdY1J3n6jedSEfutzBrcQC/+Cfsh77G4XOPZs7J72X71I/Y3vt5svuu4RNHvYnb5h7LlU9cy1M7t/PKsbcR7MzgzvRh5R72Tg4zd+5cWl72DeybX8frZgxyZ+4SHvvFLWx74D7OecvlLDvxwFS9nGvz0ZcdyTkrZ/P+Gx7ngq/cxyXrlvCec5fTmf8tfe1aDCe+Nfk3uRvWXw2PXgNbb4Ylp1Fe9wGu2jOXb9+3m1IQ88IjZvHqVy7kpPmdbL5jgKfuGsAaizj6rPPo8x+DLZv46JpWVp70Qn65eZRbnhzkE7dv5VNb+2k7pIPRtDjKvKzLqd3tnJDJsqqvyvwNk8hQEQBTGUVP7iKzpJOuC88if9QhWLlnDrRLfsQtGwe5d8Mghf4i8yI4qmJzZCXknAGLc4BH2+Ffl2f5uBnkC0/28+pMK29ZvYBlc9rpufRSui++mNLtdzDx7W8z/OlPM/rlL9P9movovvhi3D9BKORBO2jPc6tFU1TT0iHjJGVb/yKt5hpZApFS3N2ymCNLmqg8SCUbYiRNMtcxifMp3NaaY/akT79nmAcYEoWwcHCIqCtCwpiKimmPNO3JJUSpkEDRVs37P1SqHlYsOHHyQdB01BovYU1ZlKohZu8E1rwsrRvXY44+FWdyDDobohSFOOL+tlZsy2KlSWOLBCyxcCWuh0DWzKSby8OWsAAQY9Am2eE3SurKgTUTgYofk/WGwMxJnXJpOi5YCIEOiAbHERUjdDAeRIxWfaZUKjoROZSsGjMh+J5Q2Ftkw75JWkOL5RaMRDa9xZgOy6KihRwNZ9QAEht2Dvvc+KtNHNUyDyUag6AkSckfnwyoeh6H5QKGlOGGNCxtzcIZaW8b41AKNO0pkBYRrDCiUJ1k1C/XWZlIN+qG1Ua8LmyXDuuMeIAZhSdQWjcPC/2l3eya0rTZ8+vjlStFDOyYonO+nj7GTLeKn7h9ey3TmAyBPUXFaCDYjmrAg3IZYwy2qDR8cvp8CwkrUYoDVF9f/fPA8dGWX2uF/U2MwY8MBS8iSiNIjDTmPhThyarHIsshR3jA9aO2yxM7e5lpx8zICYEfkSv70Cp4CLcO72ZpxqYQO+wpakRFmILHcKFKuK9Cd3GC/WuW1WG6pE+Wdvvx9lnspA3jBhQzDrUCOHZo0HYIYg4QztBAezzGLD0OauX0g9LI8dsxViX/VB8thQo+Vl0xE6EOAjPBBMN08uTGbZSrFgWrjfY8kIbzxrpBaEWRIbSbYqxpyKQfUH7AgDu0D10NIBXxyOscswoZVI66IEzNPF1lzNPsLs1k3G0hNzhIvqjwuhKtgmqs2NzZRWsMp/hesiljJX5gHIeUwxjBIoxDfBuqXqUewrk5DvFzeRZ7iUz+ZDFobBKQ7PtUJcRH01EqTwt5fbbtD6FcTgCWpNesUUohItc8K716Dmx09DaKxQ0sO/wT3PrFL9PS2c2L3/5eVPqH976B+/jFnl/wjmPfwaK+R+Gmd8Ph5yTM1fMMXPVNVLn0mw/RmnG45s0n0dP6W+opTe6BGy5Lwu/WvQPO+WfabZfjuICJifvZ1XsFO3d8hmXK5XMzjmP4iZUUJvrpW7CbFu2QDbKc95LzOOn4k7AsC9yvYF13AWetfopVn72C2678D/7nC59hxQvO4Jy3vJ3s09SjOuXwmdz6ntP5/K1buOY3u7nx8X28/7wj+OvjF+La1gHn1617CZzzMTjjg8gj3yS48wu0fe/lrNWrqS55F3/9V+excl7jLZ/1muUcc9ZCHvjZLjbc2k+ufS5Hrc6xYcOjjE5OMevs82ntVoSTJQQIpgKcUY/TW1r4h5ltzH+qQLCrkOyMxqMEW+5ET22n82VnMeOfLsWd88xFTWJtuHfHGD9+dIDbnhoiiA1LZrSwbs1cVi/s5Kj5HcztyJH1NdGeEsdsHueaJ6f4dbfmX1dkudbyuP3mx5lZNFx80mL++viFdJx/Hh3nn0d1wwYmrr6G8f/+JuPf+jYdL34xPZdeSn7V76ltdtAO2l+u3aSU6gL+FXiUxB35+nPbpT/etCW4URkcw6M9c+ggYLcKWaAqGONQjUsUwxY805IorKf+Ql8gjGKYDxixE+EFkvyGMAoh0xBVgIZjZTWRFF4pYnK8mnzLZ5IqUb8kQ+2MSMCPIx7unEegNfbEGMcqRbRnD874GI4oApU4RkYpUBbVQDNeq11kNFjgiCGK6inzQBIq1jP1BCNmAQvSzx+LLDyBWsa3pA5sIz9Fk/OGyEiO0J+DTSYpgysKg6ShQckDGqXZ42TZ7QcsnAjAhZGSjx02NvQMYCMUSiF2yqq0ZR0mffBioRRr/FhY1FxhQxqMgfaySFzCMpKEaEaa/K5tVLuOQDIZDKCNBmysKGDTlgRYqBRsFOwc+1pn0FZp+BR2qQgt+QQ3pfknu7wMXhSzUAuZKQ+vq4U9RcUicWlTQlFC5seTWLoKSmEEimESdrZjdJyuH93LMWddOg0kgRB68TQUOzDpNZxlLRSGPUxo0mdoWCGYnqvlBFWUCTHVEJMR8toB4ycMloZKYOjRVTwTo2MfPTWFWCMEHcMUrHF8tx3oIgiqhEEMKp8oCtqwV9tIE5jQJlFgDNLPAoRQC72OmwD7aSbsyuchgqlyBataRLXnoeJhuSGaJJ+nVWxq3CIkpRAe2zPF3D23s8r32JFZt1+ryX9FFMoYmrKTsAOXsg31YMDJPViSpb24nUw0hajp6g5GwYJwCxljgVXHy0m0rdHkyoP4ah7YrVQGR8lGMVPKZrLq0+JkkZRFtEyMGxUZiHw8R4EOULQxXPQRchijCSV5SyAJjZyqxMyuOumaVHWGbH8LoxDfxPXgTaFRNNzST3OBCKGOGbRaKNs5OkhAt4hB66iOvUtuwshXgyrDlSkOUcITAxMQa6aCHFEu6Y/ychAbJHVthzIZFnheXeQirFYZnxhD2uYnypTpgjFpjuafy55poeFrgcOAx2gOGYX/LwCWMRE7dn6e1tZl7Ph1mcnBfVz4kU/Xw9v82OfTD36aJR1LeFPXKrjmlbDwBLjo2kSW5HlkE5WQS7/5EH6kueHvTmFB12/JK9p6C/zkb5NZfM11sHK64nFPzyl0dpzM4/fczZ5d36dl/m9YcOKDLAAOD3NMxQ6D4nPTwLe5cbgLx52Ncns4felxnL3x+9xb2s7dZx5K14Y8cv9dPLrxLrac5hD1ZGhxW5jdMpvl3ctZ0bOCNbPX8KlXHs3rTlzMx372FB/68RN8+Y7tvOnUpbzuxMW0Zn/7Mu0rCR/etJaHC//GP8y4l0uiGzij/23w0MVw5j9CR6PqSeesFs57yyqOPafIPT/YxrYNhs3HncnVs3J4OwZZkLF575I5XDS3h9ywx1M37WDBriqt+IwaD3t4PfLEz7HciO5L3kDPxZ/A7up6RvMiImweLPHjR/v56WP7GCsHdOZdLly7kAuOW8iaRV0HVhfvAGa3MvOEuYgRLt5d4KzHRvicV+SnS9tQFc2v7+rlql9s44J1h3DZKUuYsWYNLWvWEPb3M3nttUzd8EOKN95Ifs0aet7wetrPPRflPr/yBA/aQfvfmIh8Mv3fHymlbiIRZSr8rmuezxaLogZ/BIU2SViX092PyCEAjEYOobHoAHQUgK+pyQEUNdwRd7NWBDu0oFqAyhDKjbCCAjoXIVFMHASAi2VU/Us9ijSjgSEqV3CCkOq4g1VtpFsXDYzqCCM2JoiJszF7czlWSa3vklIpdtp/KAURv+kdx5SKWGEAOYXVtG/fEARIQJgbFoAcoYKiUrhNDn9cKIBRaJMwKCrw6iMlen8GK/lpUufNiMaLc3SMTdUdYGNkWn3Tio4wUYVctQ3XN4lghpfBMla9LT9W9EUGJAmnNCTOZW1HXQOqUMCSANfJJCqCYYBOQwBrHI8zNoprV/AcJ+2v4GPISJbQUvXPtElCnJRYuLqTHamTGcQG149wKjHjmRJuFFJVDoORYmdoWOSGdKR86LhRDFUFW8OgbTHetohVQ40CtmOWQvYLK0MlUvw1hzQux0xUQmIdUCwM0yoNV7DgR7i1+gGeT0yIuIaS61LCp5M8SkcIsK8KrX4fc/19WJklFMmlEfIxYsUJMEcQkwQ8Rn4VK9+Cyo6iVJZ+x2Guaay3sh/zq20jTEUx4ukEJLYmKoBq7yDO4rb6WgTwtI3WQuC4TLo5csYkYXoCe6sBni3EpikwUcDzI+xqhf3xRq0QckEZvDhgvkAidLLfIkytJB6mVCETtSF2LSSyPtzEJmRPYQ9z45hmlqzmGeT8MWaUHqbgLiLuOAcL8IxhvByCm6g6Si6Jj5Sgj7bSnVjhGehqCCpDqHU9dLYST9EXTNLJ7EZfjUo2QYC9E5U6MNmPfGR4osBoqJPnbV4yvoW1K2bHzCl6YqYVakiURC1UU5t2oR/P+ORMprHXIjA0McJo/xBTna1sd2MmnbnMyMVIpHHddKwKIdLlgAWe51LSDoQh4vtMDe1DxOAFETEWyjgpq2waoZB/BnumDNZa4Ej5XQU0/oJtYN/38bw9LOj6CPfd8iOOPe8lLF51TP34N5/8Jn2lPq4+5TO4118GnQvhdd+HzPNLSLESxLzx2w8zMOVx3VtO4oi57QeepGP41Sfgvi/B3NVw0dXQc+i0U8QI29cP8+DPdlEY0+SXnM/2sUNBDbBipcPixYZZepjZld2YaByLMSAtiLlQ6C/meGXvekrZKvcftxJZ1Mns20c59hea0Re2MLIIHh95nFt6bwHAtVxOmncSLzrkRVz7lvN5YGeJK+/ayadu3swVv9zGuUfO4aWr53Pa8plkmxSYbn1yiA/88HFE4EMvP47Xn/wqbP+fEuGRB6+CJ38Ep7wTTnlXktdFEkqwuQNufHEPvxxPFJsOG6qycmwjS6sTvPLUl9B65zj+tslEzSgzRum+H6AGNrKzYx63rzqbrpe9lJeceBjdT5NfNm0cRdg+UubmjYPc/MQgO0bKuLbizCNmc8FxCzlzxaxpz/O7TFmK7KFdLDm0i69GhgseH+D/RuPcemIXF+2NiO/s4xX37OalpxzCW09byoyFC5nzoQ8x8x3voPCTnzBx3XcYeO/7cObMoft1r6X7ta99xuDwoB2057MppR4HfgD8QER2AsHvueR5bXHKuAgwGToMT7ZwaCZiZ8tsTAVmRqO061GeVGuSvJ7xfbRZMzAqUeEb04puFBsdC2OX6Rsq0h0bbB0SBZqhwQFM4BFNlWh1XJaUnmBn9gVAcs/+QBgMFTOzBn9qkrhUIE9TfZx0I8iuVFB2hRE3QywK34KNbW20F6oQAhpScTsqkQavAdQSQQhDCUNVDPbkOGb2vGkxafe3WuxoybCyHFCIbDrsGD20h3y5QKm0GY+jcII2PMtJarym13pOUtA3U2iENRljgTIElsKJSuCm/qRIwoYooRLDeGDosTx6qIG1NAdLW2gN42GVMBC6w2xaB0wxhksPhjJREppphNFMhqplsdhokjq6SXtihKBSRUkmZaQaTIeu+GTze5FcJ8qbgegIqlVUSztWuQRisastx2N5wfcVmAaXZ3sKS2vEURTjhspazSne5VgEOiYnGSqWTQ/Tw+/6TUhrqYj0JIWSTXaMIFchjJZPwwgJiRJhl4u4Vrp5K0nYXhSFZJSV5NuFPpKtUnEaUSgq1il4gpX+U1SdDtqlhLazdZDhG4sdUTt+LiQMI3QKbLviLLp7GNsRYAXEFm7oAInEY1wPZUtY2HxrEjIXoyBOgKMlClsUXmgTxwIWhJZNronlGqyGFKjB/rTgVzpM2Sceh54IExkqttCqFF6U5ClqFJ4k7J9lDKJgS6md2bkA7JR1QbEjl+GaMEYhRBpGTGOzUxB87RGKQywxUuPQmsdfYkKBjK6iK2WsFNMC03L0AOzq43hxhUxhDHFyQIaSF9Ni203135pKEIjCiksMSpZ5wJ7RAUquxf766UosRAtDcZax7jyLA4NIiBLBKUJRGezAUI1UHWCJGKIwBhSh0YwREFo5FribWFSdZLtaR2Rgj+8ymolZWC7QHwkDUYayE5ONFa2OTdbUViF4QZnJkX3k5h+PEkUpzKAmxoj8KUaiPKWqQmXqbzBC8ncgqBwYNvps2TMFWE8Cc2mWQvs9ppRaRMJwzSXZjvuaiHzpD+7hs2xRNElv75fo7DiBe799D52z53Da31xWP763uJdvPPENXrboXI779RcgqsKlNyYFcp9HFmnD//nOozzRP8WVrz+eE5Y8Tf+K+5JCyHvvh7VvgvM+C24jRCMKNVsfGOLxO/qYGq6SXxAiK3bSNzXKggULOP/817Fo0aJpTYoIUTSBHwwS+INUKtuZ7HqIrl/fzN9s38JRxxfpOvkyZpz3YW75j69g3bGViy5+I8e/+lWUohKbxjdxT/89/Grvr/jo/R/livVXcNERF3HlpRezewR+8HAftz41xE8f20fGtlg2p40Vc9vZPVZl/d5Jls5o4T3nLmd2R45Hdk/gRZryvLdTOf3VlJ+8hdId25m665MMzTqJLcyivxwQBjFWJOS0gAj9Av3MB+bzzZt20YFihg6ZP7yDRaVBVqxezakfew/5WUsJNgxw3ePDfHP9MC0Zm+MWd7N6YSez27Nk3SRpc7jo8+S+Ik/0TzFZjVAKTlzSw6WvOIqXrJ7/20M2n6Ep1+JFaxdxSjyfTzyxl2tUgYWzevjwUz79dw1wwf17eMXpS3nb6YfS1t5OzyWX0H3xxZTvvpvJa69j9N+/xPjXvk73619Pzxsvw+nu/v03PWgH7flrLycRXbpeKWVIwNb1IrL3ue3WH2e6SSmsHNlkcgaDYizThvIU86NBJk2eWCVqdVkUcVMRXt+22dueozvn0JHZi3HLSDlxkpQfYk+OErW1MOXH9Lj9iZPl+5R9zWghStih1LJli9AoJGxH5V0U8YG1/IChok+QhtMHloWjQcVWPYRHI/XdfoVih9dBMGkxL03019UylZEBMkSoIMm/aeZTipGFUgZxq0lekmgyUZbJbIaH3IWoMWnyRBUT2Tw9Xq0Ng4p9nMjDGMP2cWFBh82IU2WyatEVZzB5GAsUtjSFpacYSxToWBFEifpZpJpjoASpVgnzSQKZSRmt0Ww2BYs63TFXuH4S0jS6bSvWohDJdGGFufq9tNb42sJIUvNHUs9ZiUFFCZAILAtBE6dCDzt0HuMrWo2LaBfs4GlV0mojY6URkzq2KRd0Hcin8C9lX4SgpR+tIeOX8arx9HbSYkp1+CpCrGNccTFpYWyFsMrfQLs2DHAqjgi9GYdSJgdT6WVGqPqGgtJ1TYrN/gxiybIwLIPRCcMjNWntlNkSgVg1+q0N/mClrv5X8CPsyKFUdCnGDXDgkCFvHJrFEU3aZmQcTGgQV2idHMHKWgRWFxJrxE2YqsnYw5kYBKuHUgyzbWjOTFK1JSgGJIvRPQxUq+QsD+wMtk70LWNjwDHsK1hkTQ69PyvWVMcpiA3jBavuqXdEU40TdW3+GmynGztIdRzEwfYSgZgYQzHSBNqj0/axcjOnhaHVueR0XCZSptWYGMuLIU6AdKQhb4OjbZzQoJXCWBZ7WrOcMFHFnaoQ2R4m041EmmbBQz8qszfUVCwHQ8xYxmFni2F+dYiigK1sohTpDQcRcyd2kShh1nqpiJq0SwQIS1M4KkhzUSFSFjqC0tgoE9v2gJ2neYZqpbu84vMPYM0ENimlHqJpd1BEXv47romB94nIo0qpdmC9UuqXIrLpj+/un9527Pg8cVyi2ruWwvCdXPTRz5DJJQtKRPjsQ58lY7l8ZHwC9m2A134PZq94jns93YwRPvjDjdy9bZTPXXA0LzrqaYQNdtwBP34bRB5c8A1YfWH90Ghfia0PDLHlgUGCSkzXYovcsX3sHeqlw3RwwQUXsGrVqiTPaj9TSpHJzCCTmQHtq5g161xYcjly6G7kG2dxzMYJHpavMtD+PV7wlnez8Uc93HXdNymMDnPmZW/j5Hknc/K8k3n/2vezfng9V2+6mq9t/Brf2fwd3rr6rXz8lRfzyVeu4t4dYzywa5z1uyf56WP76opYveNV3vX9x37LyBwLHJvE+4+5iOvRlYWjZ3WxsruVNi2YwQp6qILSUNURW5xJylaMCmHH4hXcHa9KXtCfj3PEnJDTls3kmjeeyEjJ55E9kzzUO8FVd++aptBlW4pls9t40ZFzOXZxF2evmM3sjgMlTf+31ubYfH7NUl4+WeJ9m/Zy+QkWF+51uHJ7wK/u6OOC3+zlkhct4zUnLMK1bdrPPJP2M8/E37qNsSu/yvjXv87Eddcx47JLmfHWt2Ll/zzVzQ/aQftTmojsAT4PfF4ptQz4CPAvwPMrOfYZWrPzg6LuTMOBNVz80NCePmWzn1YDO4m6WYwpVaAtqiuwGRFip0BkPBTgxzYTRY9RY/BC09DCFvBKFhkt2OSwTYyoBABVCXDE4CiL2ISEtodlJ6FNNWamVAix7AC7bzfY2XqblarBxiJKY65io3HDcWJbUKIhDjF+rV5QellTBKBFBi1Czrh1B8rXIUolznCkFCqVJhfAF4MrNioOUZ5hj8pgdxlEW9MG3dSEECFxYIEdvkUdgqSToirV/WZNMEqxMZ9nrCUHU8m9nbDEYXozvRmbYZYjSCq2AZEeJxvMYIo8HcYgRjCp+EAKJdI5T+4rCiwzXWwgwqIUZWhLhUsCY2PVCz439y75LdCCUTGhl6OwOyayK3hWQJZ2NDoFWfBQqZOFcR8r+Q29lW7C7IK0IY0TVXEsH7FrUh/NGUcNq2pFtgmMD2Wy2Dopgp3MZ1K/iea6yGnNLCVgp8IKD0me2QLdCFVVox4jqIUomqTFOPRxTIySLGGcwPlovz8BKp1Dy0QYq9HfQOfRgUFZHkoLkbYYcl3cNFYwEo1bGSNu1ygd1qP3ak9Xy92TOALjUE2TBnMmBKspz7A+UoKRWs6SD7QgVhloTUFf0njRD2kxDsYxoGIW+711YKk1mFDVAwltbWFZGsoR2aCIl7ZTRlPSoGJBJYr8LK7GTOUtqpGhJQ1y3W/6UFFE4Plov1Qn85qfucbvWkawjEuWPFHgozNgPI1qQheWH1BsCOxzqOllmd6WYu0mCURgixknKwGTaT3ZWvmDAd9hkQvtbiPbz4kz2GFSrDlSChVbWMYl1sm6KgclAtdrgCwaIbp/DnumAOuf/9CGRWSQlPESkZJSajOwAHjeAKypqUfYN3g9s7tfw+1fv5ejzjibRUc1irb+uu/X3DtwL1fNOJX8I9+FF34IVvzVc9jjp7fP3bqFn2wY4H3nLue1Jy6efjAO4Y6Pw2/+E2athIuuJu46nKGtkwxsnaT38THGB8pYtmLRqk7CGQM8tfUxrHGLM888k3Xr1pHJ/OGMi+pegrr0Zqxv/RUnb1JsPWERO3Z+gsVnn0373PNY/7ObKY6N8tJ3fRA3l0Mpxdq5a1k7dy07p3ZyxforuGL9FVy/9Xr+8aR/5MwjTsMLNd99YC+tGZtPvnIVaxZ1M1oOCOLGTlyoYEcY8kC5wl3FCmWEnqzDG9xJXr/hMxw6+AhVuZjS4PnEpTZENPHA44Q774Csz/C61/OADqh2DLNghuKiN17Ergmf3+wa5zc7x7n6N7v5xr29rJjbzoVrF/HB81fQ4tpMeRFhbHBsRVfexfldAh1/Yju1u51fnbyCz+0a5BuMcf/CLB/eUOWq8Zgf/HQ7r7qnl3e/ZCVnr5yNUorcEctZeMUVBG/fwdhXvsLYV77K1E9+ypwPfoD2888/MBfsoB2057kppZYAF5EwWRr44HPZn/+NLbRsXBGSjCRBG2E8yJDJ+Nj75UIMehb5nM1sp8YuyAGhQmJgqKUVaIACUQbVOoyEZVTQASgkFoyS5Dsjk95kfAwRpwFiYoVRCkGIiAjikO5MntFgilLPVmx3ATAHgGIo2GJQWpgoTBK1ziKOBTuTsB9RHCf1kUicnmY9AhVFrFXvdAAAIABJREFUkAetLaLYRrkKVCNfC6XQRnAAZVqBMhLHiKuoyy34HojCsxTrZ3UzvyhoMagohgkf05qtO/Q136/mAO8er6AqJUIT4YtQV1EThVEkynyQhulR9z4FqTNvgsVuy2UZMCccYthdzkBRs0xRL2gW+iXKXoWCzGW+Upi0I5YYCo5iW3cn5Yyb9EpNFyRBqOfI1L5tAu1gqQxiGRSGcgyuxOg4xlIJOxYFIZ6jCLMWKpZERl1BYGKc0EcswTIRvla02hm6B/YwfGgCsJSJUSlAae7H/rRZaCyqxkr6lWsclv3U6BRCKVY4no9xG8xg1sRktK6Ho44KaLeNva0zsGODV57AFRDyqDBAKyHWISaq0CpVoIWS9tlrxolNnmYHPhP5YOIEyKdHXJVJcv8yHRjTitYN11i8EhIbgjhPmykkcy01ANz03KJRU7vJuzYeWWbJMPNlK5tlObV3QkcKHVso29R9FiUG3CriTmGpbuJUD0aM4YG2GNeJGc77KO1DkMyVCEQ6XevNGLLGuhpDJIpyJovIdF9EiaYzVMRG4cWGstGQd1IGziI0NiZKVvGgD5TLHCoG2p1pNzIqrTEVJ7XaFArLJOqgKonATOZbINYxg16Wjg4LS0Jm6JGmDk/fEJiSPNta5zKCRb5GO6UHIxG8MMCLG/NpaZNMiTTauW/OfGwNoaXQOiklkLB1Tczrn8GeqUz7XUqpQ4BlInK7UqqFP2B3MP3yWwM8+Md08tkwYyK2bP0I2ex8Nt0YksnlOP31b6of92KPf3noXzgrO5d1j/0Elp4Bp3/gOezx09vX797F1+7exSXrDuEdZx0+/eDIFvjJ29D7nmT08PfR3/06+q8rM7TzHnRsUJZizpIOTr3ocKqZfdxz/+1Uh6sce+yxnHXWWXR0/O4co99rs1fCG2/BuvZVrPjNBnrOuYynJn6Iu3gjp735Yu795i/5wcc/xKv+4aO0djXC1A7rOoz/PPs/eXDwQT7z4Ge4/I7LWeiewpanzuSY+Yv48uvWsKinBU8bxl3YXU4K/z5UqPBUOdmt6HRsXragh5d1trB2bIjo8SrB4Fvor74XFeQx5WHC3bdgxU/Rtm4tc977afLHHsMRlsWaCY/rv3UzfeNP8tV/u4rXXPQaLn/h4Vz+wsOZqobcuHGQH67v55M3beJLt2/jknVLuOwFS5jb+adnqZ6ptdo2n1y2kJfO6uI9W/p4+/HCX1dt/vaBAq+cMFx9zUa+d3gHH37FURw2K8lHyx5+OAu++EW6L76YoU99moH3vJeW669n3ic/RWbhgufsWQ7aQftDTCn1IElO+vXAhSKy6w+49nzgSyTfZ98Qkc/td/wyEnXCgfSj/xSRb/wp+v3bzFGKjKkBrMSKoUsc28wzJcSa7iDEYhEZoRhElJTBURHQYHaisDnPAxKYkjqvKma3FzPgeGSNIVsdhziCpk01ATQWYZzFGA/fTgCXpUKw4lQ+XdCqlvuTgKvRALICPXlQUZ69owHGFzqdAC+GjDhoUVjigLaQ2BBFhqKviCVpSMUho45NzUGupMp+dl2CQFBksYnqIWLjocWjIRyVPkKYiiYM5RyKEmCwCCuCFMIkSaxcwdJ1vcEk7L1YJLTihNNR0xPjTR0sGLSJcUxD2rxkYrokcU7FWEzmMxjPqstmF8MaPyFgh9j5UUx5IWCIBLSysERD7DGcsylI0zyISu9Z+0QjJqmvVduVN+KC46MyFYwRSpFgtAalsETVnVCNYVyX0UrImBxiK7TRRDqeXoeNBChaxuBMTZD1k/GPjY0JLVpr5F7z+aIwJCqWvrGwTEynDBKqbipxSCxWorYHeHFMMfJhNKalq0xNcmR+WKAoMxJmSPvYUqQ3PwsbQ5Q6/w3hBWG8GqFM+qEkoY7lyKNDQairdSCqRKMFDFZayDfpvG/bWLqIUxlFaqWq00mNTQaIGZkJ3YGQyJg8jbqeCBXl0Bf4lMmSlxIGyIvPVHonoyHyFNmost+wpUjdaoTgFpXPJGW0laNQl5tvALPklk2t2CGhMlR1SKlapte18TJ5jFgYsbABK45oicug2thXNsS+Ya1dBGYBQmxcjLHw9vQzlhdiEzGatcl7FuiQqjHk7FZoUkps7k9tE8SJDZarCOIYbQSdrmNt0ndqOspOfiR4ETEJ+NNGiElk8pMi48m8BCqmJIooTqBSzhhy2qU1Za0gCa2csHJMRi4LIc2DTMNKD1CWfPbsmaoIvhV4G9BDoia4ALgSOPsZXNsG/Ah4t4gUn+b429K2Wbx48f6HnzXbu/e/qVS20WVdTv9Tv+bct72Tlo5GvO43nvgGk6V+Ple0UNl2uODrzzs59p9s6OfTP9/MS46ex8dedlSdeTChz/iNV9L/4OP0RxcwGH+M6D4F9DFzURurXriAhUd0M++wTvr27eEXv7iJkZERDjnkEM477zzmz5//p+vk7BXw5ttQ176KObd9jY5zPsgGuZlK5iuc8+7/w11fuZf/+cgnOeuit9LeMQMxYGVtrBaH41qO5hPHfp033/ltdjg7cU7YBvMW8I7dA+zdEjIYNFyQFkuxWmneWZnguF07WL5pK0wolDuPqVkrsXKdSGwj3m7sWQFthxZpW7UXZ+QxMI/A3T+HvjNg0Um0LzqRN7/nVfz61gXc/eAvufa7V3PcoWdy9oVr6GrP8IaTD+ENJx/Chr2TXHXXLv7rzh18675e3n7W4bzpBUvJuc/dOjmpq407TjiCz/cOclXfKLed08FlY/Dm9QVKO3yu+OL9zD91Ie88exntaW20luOPZ+kPb2DyBz9g9N++QO8rXsGcD/1fOl/96oNs1kH7S7BLRWTLH3qRUsoG/gs4F+gHHlZK/c/ThLH/QETe8Sfo5zOyeiFbUdOc12Tj/MD3USFsrri0BxZhVuNkPMSugkpCfl1j192zEJOov0U+GgsRQygRY2HEykovh4xtYFwOYZwZiMBIoFCOIrZjxA4RgT1t7cyrjLLUfYitmcOQ0gnsdEM60pig0UBRCgTXVqnzn0Z1pT7pnoIC2yCiCEzT7vpUmYnYxXegEFUgjFBiGMtaidKhCfBEE2uXcjiXfIo9BIVNLgF5oijFFrFjs085zELXh1AjGKMIY5dI51BiJ4VyDagwRmEjKMb8JNyr5pRDIi4gabHYuqw1yY54aKar7wWpCptSSR2sxFlPjhlj8HRYZ6qMG6FIAKtR1J170zJBuX0SVZydOIVaocUiigxRJpl1AN91gGiaRLq2/YRNIS1kZnTd8VSSXGljsU/5VEXjxq0Jy2HphAWsFACn3qaIIh4vEUqAigKUA1ospkKhO6f2F8rDiEMio6AQDPOjXhaaCTxzPBWTw6RAT7SgTMiaeD0UDQO5xRjakzGNdBLOB1gyfXzVNIl4wdIBpakiSIAJA7TKQBSlmwlp53TioNuRx2CcpVb+WqVAfSKfZZyQrB5BeYmqniMxXWaKMTqwsj7lLp/iRIyEAbHbD3YLxAl1HJosrlg82NHN9pwHUUNJ0EhtvSRPpCo+lu1h01afx9p6ggZ0C5QmsDQOEEQRYlnUovlqJ8ehQTvJL8otEzlVxiuKvXNmI+VyKszX4GxmFkocFlSpdKeiXwqqqpGTJCRFm6t+gUk7kajwCRlP1WqUJNFCJvCIYo3b/AS1oa6FEoo6kE2vyaUri/0XTr1iwH7EoHIKKZDsxqhElGZjlGOoajEjG9MSGzwjeE0MVl61gihiUYxFilmZBIyGoY/fJLbzbNszDRF8O3AiKQMlItuVUr+38I9SyiUBV98RkR8/3Tki8jXgawBr1679s0DLYulJdvX+OzO6z+H+/1rP/OUrOfrMc+vH9xb38q0nv8VXo3byk1vgkp9C+5w/R9eesd25dYQP3LCRdYfO4IuvOQa0sPupcXrveozezRU8vRpYTffsLEesnMnCI7qZv7yLfFvyogwMDPD9G75Lb28vXV1dXHTRRaxcufLZcai7FsObboMbLiN/6yc4ceWFrO9pYVT/B2esew09e84nunmMAXuMR7ttNnXabO6w2NJhM5Kz4JAX1ZvaNOkzO9rH2thhYaHMkoF9LN3Vx7zxCna2DattHnbnElTXUdAFWDHODCF/VCetLzgep/3c6X2rTsDWn8Pmm2DLTbDh2uRzO8uZM5exdMmxfHfvXNbv/gW9H+/n9POOY9VZh2DbFmsWd3PlG45nx0iZf7l1C5+/dSvffXAvH3npkZz3dHlwfybL2xYfO3wBr503g8/s2seXTZHrz+/i9X0R79xk0XfPCH/3yCCveukRXLBmAZalULZNz9/8DW2nn8Hghz/M4D99hNIvb2feZz+D0/P8EnQ5aAet2f4YcJXaicCOGuOllPo+8Aqe4zB22z7wb3DzF+OI3UbsOKAT6fEgzqTOW2qZChJnQMXTLmw4Qhp0iHZUuoufAIW8LmEkJiNlYAalGCZDhRhobStAzkVUkhfRKhMA5HWENorRnEsx24UKA7w44YJMFGKhUNjERhCjp8NDJYTGQlQj/E7VehNOgrQQ4hOQocUEWBITimYkzOOkdYqaC06IUQz42frvoyZDp5R5rCODMkkYUxg38luSmxl6fYu8pPVxVFKnKW+Byk1iMQVxHtsESegkNQCcjFugNI7ETcMsWHGAMrXaQEmjVrprHvse5aqHb7JkgIqdA7GTED2BvuqMxMm1IspxWn9MNLFJwgEbnEtige2glUGFMZKyll2mQECEJWnOnRiQZH3YKDLioEQYUvvl3SiBOCJOPWSFSRgJsahERQwhxBHKMoyHiqpA1QWjTCPUclpzSTu2xMQIWT95BhMnynu1mmaQON5jnk3FCJaVgiulKGUz5FR1ellfafohYGEReVVwEvbKiyMsP2GIts6cOW3ETMoUKitO2dek30ag3+7iUFNGWxZVpTlcttFlShRZDQjLvF6M1YZSCXBVdpCC42RsI2Pj18e0keljxErWX1ofrhQLQ6GDWCkIlIRV1qLpz2TwIw1R8u5N2QkEDJRQ0/5rXgMVHdBmYmpBotUwx3icx3E1oZMhV8/Eqo1dQjepRJEFQRGl6F9JDWAJk2EZ09reWAdNa1wQlDFYxsaWaBqDiySy80JSc89pnqtpU6iwdMj+BZtrXZyW6NVkRgy1um5ebKPcgLiyi51eK6UYyKZ5bcrBkqQnWpK/k4hBG8PA0PAB93y27JkCrEBEwprzrZRyOHDMpplKTv5vYLOIfPF/1cs/oUVRkSef/HsymRmMPHIYfuVeznnr2+sFhWvCFqf7ISft2wkv+Hs49IXPaZ/3t8f6prj8O4+yfE47//bSo3j0pt1svnsPXhVc5XNI+w6WnHoMC08/jdau7LRrx8fHueOOO9i0aRMtLS2cf/75rF27Fsf5Q2pO/xHWOpPghdegf/xRWjZfyxo5hB3Ll7P5iFt5csVS7hxdxLaeGWjbQZFQ8flxn7O0xXlZh8MGp5gzWCEbWqhMO4lYWAtwOMw6HGYJygW7J0dmcReZua1klnTizmtFWb8DNLb0wJrXJ/+MgfEd0P8wjG6G0W0sGb2Hy2WSa9WrGW99gttum+LJm1o49ajNLF41BzX/GA6fezRfv2Qt9+0Y45M3beJvr13PS1bP4+MvP4qZbdnffu9n2Y5ozXH10YfywFSZz+0a5AvzNV9b0MEr+kLetSvgyRu28sZ7d/PeC1ZxzKJEsj2zcAGLv/0tJq+7jpF/+wK9F7yaBVd8kZY1a56z5zhoB+1ZsgVAX9Pv/cBJT3Peq5VSpwPbgPeISN/+J/wpIzEOmdmK8oMmENDsIKasliS74RYKLcnfbiuuQrYpTFlBEOkk5AzqW8RxyyREHQy5HcypDiW7ypKGdsUhU26DodFGUCL0ts6kTZK8j1pYUqgtyqFNNi2so02MUta0nXhbNMXIZtyXxDFVQFOyew1YGW0RWlmUijFGMUIRUYmKmDEha/SjENtMZlcgxsKYpHaSEoPU8qCQtIZY4/6DFDBqNjaJEz3kKzLEFFREXjsoN6k7VogES4QMPp7K13ungLL2iTBUqYVequlMophGqJaAipP6YgrISIASlfRTDEHoEWlJiuaSiHUoSdr0sAmNi1GJVP9g5OIYQ2gpjA4IQo+8ytJ4WkVSvqnRFw/NcfE2UAZltUE9NO7AkDaJgjqzNRWCWIo8jQpszevO9n2M1QTim9iHkTggkPw0sNs8vwbwMFRNgGg7YelSpcRirBJlOFGUwwy1/V0r1lSdpJbVzq5OOqNsQ0FOYCyyaLEkAbsCQU0eEbA1VIISFTlQLc6usSu5EpYVUKvUFNUYxvQ8rYSsJHpuRuIU3Eo6nqaeQ6ca005U8zP8ECEzbV4iEyS5e1HIcKSwLZUCgJTZMoZypNmXzWBVvKRFpfE0lAOwHUnVMxv15cJYN25OAnwibdgcKZZmzH7z0WB3asBUhRGgUKJx4jLGajBdva3tVKxaKKek4ERN08IQYJX3KLbWbHGOZXYAVdsiShUmm8MXp4EFRZ3BbTaDdQAbCtARTrIq7uVBOQVDDoskLBqxwSjs/u0YswqwsXRQH3UlMZakXGVtc0LVRIP+PPZMveq7lFIfBvJKqXOBy4Ebf881LwDeADyhlKrJvH1YRH7+x3X1f2/GxDz51Lvw/X4W9XyK/7n9ata+7AJmLV5SP+dXfb/i8b1388uJMsxaAS/88HPV3ae1naNl3vTth+nOu7zRbeFnn3wIRFiSfZgj569n0Xl/hb32XWBPf71GR0e599572bhxI47jcMYZZ7Bu3TpyuWc/b0iXQqZu3oX32ChW68XIqpNxdn2SI7ffx6Pll/D9pctonSOcMbCLmY/cSxTk2WwdwfvbRjhyy0MEmzcnDc2di/OCUygun8+VpV+wITPCKw6/gL894e9oaW373UDqmZhlwazlyb8m6wqrvG1wE7f86l4e29PH3jjPTx8/kcVP9HJi2wdZkN0E89fwgsPO4saXnclVvYfxH7/u5f4dY/zzy4/i5cfMf05D7U7uauOnxy3j0WKFK/tG+a5Mcd1ClzWTec4bCPneVY/w/dUzee+LVzKrPYuyLHouuYT88ccz8PfvZs8bLmHOBz9A9xvecDBk8KD9/2RPt5j3/4q/EfieiARKqb8DrgbOOuCiP2EkhlIkOTuxgZqqXq1wryHR59XW/uJbdXnn2ok6LGFJRNbESYhgTYjBjiCsBbqZxmaxUinf0uRYGw+0g9gQK0MlBiUeglAMXSZVFjcyVCzNPO3REZXZzZJpz2NCqTvytZZtZWMpu7ahnhwTK3Gwg5gxt5h4ytRycw2ZuvqcAyQFU+3Ywzd5oqfxmbQCiTMEGiYDi5yTwQpjYixCWxHHio70/pbEtBmPlWxmt7WYSWtpOowxvvw/9t48Xo6qzP9/n1NV3X33e3Nzs+97AiEECGFTWRzUEREEQRlHFHWYcZ8ZRR0Z3NcZUVxGGR1xEFFHcEEERBBZBIIsgRCyQci+3n3pparOeX5/nKru6pugzEgS/H3z8AK6+9bynFNV3c/nfJ7n83jsLqjMcROP/bBOKMG9qKWvBVJhYvysC/AM0N9PXCqysquTAsP4NkJMTNp8NVKqqiIoCnrKPpNNRFFbx/JFMSZwQBhxKViOJQuIiSilFFzVl/rbUImpu7lr94swECnQikniAMWAbsAGLXRI5NgGa0B79BR8rI2zI6YcRlibp6wsTemHfgWsB9bD4CX3akSzHcBIC9ZVaWFwPaN0MhYryjFf1qKJCfEAxWDOpys59FDFIywXaPIr+6uEQoxBl7oJCiVCaWFCvAMv6SulEwYkHXc6TVYco1OsA6KWKGFuCsqrm1tlHGOYtWLa03KU7noKW1K2isx7qyCWyEmIi8FWht1zqUN0EOLZihPpEElAsiIN26v9r2oKIgDECmIleMqluSrS/Zwvgzpk2PY7GXNRKBsS2pByPIiIg7EV8WgKB+jH1T+WlCWbmAmwJ5/DhEV87fFYR47lUcjK9jzd8SCaztotMup7CknA1KjjRTbAWp9A4iqxVVbCzLgHEU2LDJMK+mcXUlTCFipbQduYgioxPX6aPczGcdxCb6gZiYV2FFP+vC45/yt7vgDrw8DbgFXApcAtwB8t9BWR+9j/D9ghMRHDU2s+SG/vvcyb80nuvOouWsZ2cdL5F1W3KcUlvvjQF/n0sKGxPARv+lldn6hDbbsHy/ztd1YQlSPO7w/o3bKHoxt/xeJpG2k58VxY+n0IalLbIsKmTZtYsWIFa9euJQgCli9fzsknn0xLy36aEB8AK63upu/GDdiKofn0KTy4uJ1/29bBprZruHzr93jz1hu4sPu3bJ6sWNV5LE/s6qA5foajwpV0bt6NmjefcZddRvOpLyM3cyZKKSYBXzBv56uPfpVrnrqWuwbu4fMv+TxHjD3iwAwi10h++nGc89bjmL9mDTfddBMDwaNsCqexvecTTBk3wvHFXzLpvi8T3PvvvDvXzCvmncsH976S9/1oJb98fAefe91RdLUcOjYL4JjWJv7ziCa2zQ65cVcfP8518/kOD39RgSN7I877wUO8esEE3n/KLPK+R8MRRzDzxhvY8ZF/YfdnP0dp1ZNM/PSn0PlDO47Ddtiylogu/TMwTUTekUi1zxeRm//ErtuAbGO/KcCO7AYi0pN5+22c/PuBtdCtnIfWsQpZgQVFjDYWbW0daFHAYM4n1dmzIsSmwrYhn5kNJawIk8sD7Mx3VdeOU7GGWAw61bpu7EeXXDp8rRbMuLQfMahckRIG0RFYyGuPnkgYQXNSaTeBquyb2mLB+qmymBNbSFksK6oaJVgUI1FSNaIURrmeUi0yRAr9rIAo43pTVYUdFGY/K+IxigGpsLkSEVihvxKgFWgRFgZPsKs4HoJpCB4KaLRl0NAqw/RV51so+x5KJKnmEiQuY0QhhWEUESL1K+8pG5JjBCsWIzEioOKQSHlY5eqT5hfXYuOYjTIPFOwwOSRJMUtl2W0ixODU9xTGD8ETjDS6K69cPVNkg33ARjq1Lph1nZjrarX2WSwTIhtRqQyzK5hMLh6A2KWxNYVFmiriSANJegolZGpfRYHvwvgIQFkHPq2GsLF6bcZHW1BRiWfELWCKtVgSwGNBTA14KJzAgRHtgHQWN+LSz0qRIfJ8QNcprgmgvAj8IlNMN530kj4sSlx6m6RXV0bF/hnsZZAEXgjL4idR+drsVe82ESIbEmOJPEVsPTxpqjKH7ixZ39w/FosWRaidsqOIwiiFWIPZXWakJbl42lTnpXZAx16bBPIMhtql7WWYTZEqyQYIQ1FAW67IYHs3zd3tbt6BWPl0N+QpqRAT2upEj7W7mSHbWaVmMkgrsXby+g5up8guZsAEtHkxRse05VYxLupkM0fSkowyvR77SxHMWs4WCZQH5DIbq3Q0ybVR6ZTXmiMDMQEGg/XLoBRN8S5ED9NGPzuki4qOqMQKhSWQkIbRvS4OoD1fFUGL+3H59oF158BYHI/w1JoPsnfvr5k9+zK2PAg927Zw7oc/RpBhcL6z6jvM2/M0p/d2O8XAycccQq/rbaCvmzdedT/dJc0bhgNOLNzN8cvLNJ30Vudn5suyr6+PtWvX8sgjj9Dd3U2hUOClL30py5cvp6mp6Y+c5YUzscLg7ZsY+t02gsnNrH/1VL7Q28tjazczsyHHZ46cz2tP/xZq73vp+/57mLPpUabs+D2LlzfS8/ASHmto5cGFBU447xymnn0+flC/WpT38nxw2Qd56ZSX8tH7Psqbbn0THzjuA1y04KIDyrIsXLiQKVOmcPvtt7Nq1Soap3ezbXAm29ZexKRZl7JkQQ8z5Xbmrv8lNw5fxzWFc/m3tefyii/t5XPnL+UVR048YL49X5tSyPG+GeN57/RxPDZY5Bfrd3NrZYAtY1tYLyN867bHOLOrjUsXTOLo1lamfOPr9Fx9NXu/chXh5s1M+drXCMb/yRLMw3bYDpZdAzwCnJi83wb8BPhTAOsPwFyl1EycSuAbgIuyGyilJiYtR8A1NF7zQjn9XKbEomzEwvhJelUbu1RLJujYF0gYyVEWwdf1DEZv7CHGY7AsxLFB/BTU1K8eq9wQi+OVUJlKLAYvKCV9odKV8WyQlPbvkTS+x0taGylASzYgdMCgvRKx1dcohCZVW5wxSoitBi8FhbpauWJQWFG02j3Mk03VgMzGFmtiIrFoq+iOoFGPYu8S253z6A1asZHBNAygQx9MTYChS7rZE0+hqCK8QNMW1WYlDUA14uqptMWIdYqCwJ4QKGS2FwWFQUrWY2tYoKWaTpYEhmkKmk6D+lpkr5IaNMcgKrQYZtitbLcKkc7aXCqI23egdAGKjWS5xj+W9OTUB3UVqDvRiNq+beUyEGAxGGt5PDceW3E+hyJ0hy58nzc4RKmjQl8EsQcoYU+oGaQRzy86DbBKC+RKmXMLkRXQENgKrktaIloRhSgKTrdhlLKbFUNgDWUdYMSvAihlDX2hkBNLOq1qlPS7q9GxdJcbGVfZBZn2jlpqgb8Sn5KOafIN4pRDqiIMWVDgWMIaeCEze0srKxK45ARWRmJNbPKgwgT0pKDAp5EiY+0g22lFbIivfKzOkaNcPY8qFfGIGVFRcp59zVbntQTKc3WMNkKJVPUvJLt3UtQU+gYkRAFBNAJBA72FPC05i4hBKoPQ2IRgCfQgYkOazSCDXr2adFlilI1Im8dZAbGGwZzPGNNNrBVeNIJna20h9P5EFzOv54erKWhhmz65bpsGKTHGDICu1bq5RYPazIQqR0yEbRjEeD55U2Yw9lB+/T2VitSwn3TZA2XPV0XwWfYFoYjIrBfcoxfY+vsfZu26yxkZeYa5cy+nwZ7KQz9/Pwtfchqzli6rbrdpYBM/ffw7/KK/COOPhJe+SNqo7HiM/ruv5fWPncAm1cwl0RD/8NqYzpdeBgV340dRxObNm3n66afZsGEDPT1u0XXKlCkJ00IMAAAgAElEQVScc845HHHEEQTB/jKkD4zZ0ND743WUV/dQPGEcX56T52ebtzGlEHDlgqlcMH4MXhzx1LU/Zvc132Pinl30T5zExNMrzOnrYdrCFSw+9h3c/VQj9//PD1hz712c9pZLmbHkmH3A0/KJy7nx7Bu5/L7L+fxDn2flnpV8/KSP0xQcOCDZ0tLCeeedx7HHHsstt9zCnsoq2maPYffgVG69pZXWMa9n8cvey6LJz/D29T/hZas/yfuLb+HS64QLpg1zxUVn0Nw+9oD593xNKcUxbU0cs2wWH48MK+98lls293DnOI9fjAzzi0c30O5p/qqrjZe/7kKWz5lD/2UfYtPrX8+Ub3ydhsWLD/UQDtthA5gtIhcqpd4IICIl9TxWWUQkVkq9G/g1bon7uyKyWin1SeBhEbkJeK9S6mxcYl4v8JYDNorEfA3YIg1SZKodYZfMr/k86mdYiUvdiUVhiVG5muKaTUOSakCR9qQxtfA6079JV3rYE+XAM9g4RGmfWnJidgU5Cd8UoDwC3wOnIYFvSigbIzrAWoOxMU2RhqAZwqx6lxArB1qochwqHRSIEMchOTsMCmKlySlLQUpMskPsCMZQiSxF3Uof4GfTkJLDbCtbBgnIeRWsEnLeCMQeOtkgxmNIYiDAWF0L2RSEEqHFEqv6fKK0+ipnLZXM54FJGiz7FeIwRxFFSxLI++JjVEyIdayRuD5TaTqhAsQvERrHDzRIhTYZxIu3sTNugXwAYhjM5cgrTTlOw7bRqWejzYWiKRMgAlrFyRQbxKtgDXQM9uM3+URaYa0htDmseGiEgVgxrKGSD1AIVgxxckQn9R5jPA8dhCRa2HXBvUhVwA9jhbLNQrtEV08b/MJQHathRViwZw9PdUygmEnFK1bAmvoUxaplPjL5gOHSvoF0RIwlSY/1fXbFEWMahpCiU5C2SZHRZLONPOVEcn7fcykgLYGy6RZKsBgsHogmFuP6ygGgWWpW06wCtqgjiXURTCcVrQiSO8koDSbCy5Uz58mcu5riq7GlEohxz6JXf4+6Jsb1M5SXCg22hOAhBjS1PmDgAJKYArvKvgOLOYMXjxBUQscGejGEDQhOQVKsQuna/VewIWVtGYh8KBhUXKn25xJcumyQ7RSOUDY26Sfnnv4oqfHKPofT7PYqqBIUkcBg5NHmZZp+o6vzNN7splWGyLYoV1JjJlXy3XKw7PmmCB6XeV0AXo+TbH/RmYhl2/YfUC5vo69vBUNDqyjkJ3H0ku/S0X4S11/+z+Sbmjn1zW+v7mPF8vEHPs5HevpoiUM455vgH8REzdFmrVO2e+AbbNvQyzvCj7Ih8Hj/jCbe+45XoT1Nb28vTz/xEBs2bGDTpk1EUYTnecyYMYNly5YxZ84cxo49+EG8GQrpvuZJwp0j3Pqqify7KlLuLvOBGRN497Rx+IMDbL3q6/T+4Hoah/uxrePZdPF7ePl7LiZobmJ49fcI7/wIYx74Jq/IN3Hiuefzywf7+ennPsakeQs58fw3Mv2opXVAqy3fxlWnX8U1T17DVx/7Kmt71/LlU7/MnI45f8TTP99mzJjBpZdeyqpVq7jnnnvY7T1O29wOyuFk7vv5EA/5eWYf+z4Wvm4MPy3/jq/dsYL/2LKMB75wM1cesZFlZ17kZOxfBKYCj6WvnMMR28bzths20N0zzDVdihs6NTdFlp/s6qMQdHH6N67hxOuu4fi3XsKMj32MttecdahdP2yHLVRKVbuJKqVmQ138+5yW1ATfMuqzKzKvPwJ85IVz9U9buVKmrEdXPAAIsdi6wEhhiawrkjeA59VATEVbPCUMo9lVKjA+5zGhbwN7TTtRUyNaYrREpL2HYlNOjpn4YSqUlZAXRawhh6YQR9U+WIhF5wIoC2BRViWAKUnFSgEZoDDYPJiSuG65gPJcXYxTLzPY2LoUOWC23YBXDnmUWS69LvFpVrSBIckzlp3oIOTh/DJ0qa0uZQhA2wrKzyPadRjtiEZYEK8H08AqfSQAER67yzm8FBJke12ZGG2TcFzXwiRjnWz26AoSvZ+gTaVcglgUJkMIugGltTEGweSGwS8h1ICeh6v/KRWGEDGEcQcWRZRI23vYWprkqDoXQRBrKSfn0vkiE/UmOkLL42oGfuMA3eIzNNzO8eZZXhI+w5PeLBSGwMZAayLsUTsHkoJrlZ7BNSnG1dQ5MYEsyErmLLkP4tgJnmR5GY0gfjnDTdRG4InQHFboCZpBQSXSDoRpAzpKiuxq/gAcbVexV01kxGbS2JVbY4iVReIyrViGqZ3OUlPbtEqhgYlmJxWCOkW7FK7ZRCfPJKxbRAxKUbSWnVGZBp2D1t1QCiGGsdJLnzRXxwUQW03Ojb7u3NhMap2IAwSkIKaMsRovSZVtsP2UvE60UsSktVbu3jDi1wHW47wHCCIYDlxNo9rP/ToijQnjJsQJF1aggs4Xk0fW1WzNkE1skw5ias93QxwS6pg49tF+D1Z5kIjEI8LR0eMM2IBHWeQ+CzxMkgWpJFG6VPXsvJVUj9CdxaKr6beDuQAkZmspIN9cQkURFk2zHcmMOstBuk+H83meKRw8suH5pgj2jProK0qp+4Ar9rf9oTSlNBs3Xom1FZqa5jF3zr8wefIb8bxG7rn+e+ze+DRnvf/DdT2vblh/Ax0b7+XMoQE47aMw8ahDN4BN98HtlyPbH+Nx+7d8vPw+1uQN7z9pBmctyvPr23/N008/XWWpOjo6WLp0KXPmzGHGjBnkcocOGMYDFbq/vYrd5ZDPvaaL31WGOaW9mS/Mn8KUndvZdfm/MnTzzXhRyNrx8yn/zXs4/+/Pp62h5nPzEW+hPPsVrPn9JYx96mG61v43b+pqYs+i07j9iW3c+NkrmDhnPiec9wZmLj2u+iOuleZti9/GUV1H8cG7P8hFt1zEFSdewVmzDiwA8DyPo48+msWLF/Pkk0+yYsUKdux4Em+Sz9jGKaxdNcDaB5tp75rOqSedwPGNu7j8t2UueHIZf7/my/zj4gq5U/8ZJrw42KDclBbGv+doGn+3jX+8cwvv6BY++uRuHu/0mbWkiwe14pbzL6bhtW/k5Ecf4qId3+WVb78Y7b24esQdtv+n7GPAbcBUpdQPcAJLbzmkHv0ZtnNgpG6VH61JSmgo66Cmo5Agj9AqquLIyR/jpOGnQhgyLtjsjz3GxpYu6aVX5QhpqgMvqaWL7hVTwmCoKFUNYRVCRzxS3UgpsEE/vj+EZ2KsNGCpB4E2CduM1fjYBDikgaOH8iwSJwqDuQDQFIplQtHUxd02leVITBvQMSFlcpngTOkY0THaeijPpeQVbK1nopf0h4pHpVumqm5ZrKIRYlT1eqiEoxBTcWIXSXwcW6cylz2iVimDaDKTXD/bgTWUEJSyGO0ls1VjFxVCT9n1+GpD1aVCZo8Up9ej6r3QG3k0IaRyDDNkE1qamSgFcjLCDjMRQcjpIRSW8bKX0oBlBjtQlR5QZYSAafYpongMqiZhUT236Hp/XJpnyrQm4A+NRYiJEfGy1QzVFLrhKOcur8pCTKhEoHLufTn2yCnQhSGwgi3V1B5TlqlRSsxUm9huF1WfBWuhL/Jo8y0T4o34WFbKTOIUANQyOBn0GvcB6ySMUE+pgTYUsbL4RMworyPd0yrYEvtsLHvk0TT7DUz0ByGGVgY5xq7CqrRRrmBMIVkNSvtGucbikQWxIbUqMZgsOxFTZLLdg8XDWkXZeGgpowBPKyKzL7udzr8Sk6Sh1hII9/drXf3G0QqNkNOGdoaS8QsQ02QGmah2UZB+1jMXJyuoyMURNsEtU81uBpiY8UYS36TqYzrF9ZAaXP82QcRihWoXO1Ga0XVbCgta6PcUfm6oOoDqeXUEo9JHVVAh9ob2M/oDY883RTBbjKRxjNbBUUn4P9iJJ9xJELSjMl+6Tz+8gj/84gaOevkrmX/iKdXPd43s4rsrvsj/9A4hE49GnfKPh8Jl6N8Kt34I1v0K0zyd37ZezzVbPVYWDKd2hYys+jnXPRrh+36VpZo7dy6dnZ1/+tgHweLeMnu/s4rfFSyfWtZMMarwuXlTeMPAHvZ86EM8c8dviLTPHVOPZfjV53HJ35zO1DGN+z1WoTCRBaffzLMzv87G1V9hxraQcTt/xZsm5OhZfCq3r97Oz77wCcbNmM0Jr7uQOctOqMrsL5uwjJ+85idcds9lfOTej7BpYBPvOvpdB1z9zvM8lixZwpIlS9i5cyePPPIITzzxBGHLJlrGtzEcT+L+X/bjS573LprDb/0i39x8Nnc/sYWvPHUh8xYeDS+7DCYdfUD9fD6mPE3rGdMozOvA//E6vtJteUQHfOjOrZDTvGrZZPSkDu4+5njuCHLM+uXdXLJ4PhdMn0CrfxhoHbaDayLyG6XUo8AJuN/s94lI9yF26/9s/ZVM6K9qUGuc6SbINAVVo0MYcW1qy7ErzSdZCzcIOkk7ErHESjHG9LCLppRjAWp1R2lNi6JGEATaYpJAXYxBmvphGASN6BAMmChEp/U11RXyhJuoohZBq1qvHKUNXq7sYICpX1kWVC0tEeWYOm2w+WGoZH47FBR1LZmxkN+LIk+UbOOpWo2PRUAirAhGjfqueg4WyipVN9du0/rmtwNhrpYSlYxVIeTjNKEuE8BmFNB0MhP1MEWqc6b9CikTEKIoGo84QQDih4gIS80alGmmR6bXRay1matnlGbazTSFg+zwx4ECv3032uRoBdoqZUqBR4MMEikFykcEuuweFDMSIO9V50MCHypxRqeOzFkzr5UTtMiyMoiglc3uBModv9afzVmoYgJI2Dv3t2JyCoN1AEAy8NYmRYEoRmJ3YcpG0cgQ0FQF05DUEOmKU/HLJKtW5yxzXxhxBYeLwg206wgRlzbXn8+x1zjFulhiipEGRt9PquprlXxDsEmNGgi9Jc04VQMFCstMuxVtRiipAiAUYyhVFdprCzHZ27cxrFT/1lUepBSoBKykoMvWLV40hyFDSSqmqjKKbuy1DgRm1DUGPNcnb3cc4CeKfVPNTroo0ePNZbzZQVjliJPvImrfXXbU/Ka+GVtj41I/1KgxphbErh7M4hFhiUVACVOCZ9hGnv54UpUdU0EFz99Xvv9A2fNNEfxS5nUMbAIueMG9eYEsl6vPXuzftZPbvnEl42fN4bSL/676uYjwyfs/wQd376RFLOqcb+4jb37ATQRWXg+3fRisoXzKJ7jh4SP5de9O7i+MYbbuZpHZw6IlS5g/fz7Tp08/pCzV/izuLrHzO6u4apLiuql5FjfmudIr0/bpK9h0110UgwK/mHs6u888h/e+bhlHTGr7k8dUymPWrPcxbtwr2bDhMzyz4x5mbouYsPs3vLET+ucfy73PbOWmKz9L55RpLD/3Auaf9BK09uhq7OI/z/xPPv3gp7n6iavZOrSVT538KXLewZm3iRMnctZZZ3HmmWeyevVqHnvsMbZsWYMar+hsnsjunZ0s6m2jpaWBW/0ZnBV9gcvW3cgla09FH3U+nHGFa858iC03tYVx713KwK82ctyKXfymaxzXd3l8d8V2wthy7IwOFulN3JPzuXzLXj6zdS+vn9jJP0wdx8zGw0qDh+3A2qiFP4BUjGKaUmqaiDx6sH16Icwl9yTCDzg1NYtiVrwlCVzrF4uya7RZwidvI0IsvokJg7AukAmth5Vak1GAnrJHey6pMxrVK6azUKK70gDWECqNMVUazZ19lHS3FYtWVAFiLMb9qyMn4Z1YGmwrbRGjsFZhUQwEDeQJ68L0yGrKOlmJ99140v5OtorgFMeET1FSeVbKGJTKIQK+NQlT4QAWIlXwlngCSb8qMvPvoRyjoQ1pJ1ZPC7FE1IdPUh23CTzE+tgYKp4mCnwSnXwACnGUBIwpEZiu6muUxHVX1ysMgDiAtS3MM1RsppKkWJIr4vuGxqESrTLCKqaTZQmATEpfzUsRAalJeLv+SuKa7wIxllAFIBalDTqGzlKFYoYiqPY4UgqTyAlqlTlTNhAWhVYqYZRSaC1QTWtzphEnXpBcF69hCGVbk+sLJWMJ4/3HZ6IEL2UpVQ2kAoRWO+5GnCS6KHHbKLdAEFuNauyHUiY+EIiUS1NMnxuFqsqDFySkYj3yYl0SpQDiJOefs8RHQZxOoYKwoQ+NhrCWJjdhZBhpFGpiGrXJTKFybJOTKOq2yUlEix3BkxEW9eziybYWUC6V1M1vzdLXWgxYYVzvALtanBC+Dsqo2CbAeDRrlOogquQp8Z0q5qjvixYzQJd9koJUsAjFKvhNxyKIKEbiALC0hhWG8gkjaYXtlRwkizXZO9hQfz+PKw4zTvXTq5sJlcVmQLaP4Si7jntkPOmzqhBUvL/06wNjzzdF8LQD7ciBsuJAPz/9/MdRSvGaf/wIfgac/HDtD2le/2vOGBmGMz4G4xcdZOd64efvhPW3ItNOZuWsD3LbXStZb1dzn57NonbLV1//UmbNnI7W+6pHvRgs2lNk3fdW8eH5Pg+3e7y50ePvvvsVort+x558EzcueAUbTnkV/3jOsZw8539fE9bcPJ+lS69lYNZKtm//AZu2/opJW3uZtPNhzm4VBic3saFpI6tXPsiap9qYPHcpE2cfRZBr5z3zz2BGYxtXPv5ddo3s4qrTrqK90H4AZmH/lsvlWLp0KUuXLqWnp4fHH3+clStXMpjbQW5qnlm5GfzNlg5+k/P5tLyeXza8hq+u+hTTnzoOTnynU7LMHRzVx+cynfPoOHcuhQVj6LtxA29aV+GS0xfxcz/i+oe28v2eJo7t3sA7b7iOW085nR8dfzLX7ejhrHHtvHvaOI5q2T9LedgO2wtgX/ojfxP206/qL8FySaCq/RDr2UQFbt+CfZd+BuNlD3ullVgFabcsBGiNSjQW+1HEFP0GWqKR6r49lQZ6y4UqU5CG5QqpKq1VmS0Jq+/FajwNI7FPQIyxxqniiUGL4Cu/GkKlgVAsML+8jrX+WGxBuRX72gJ51QSwVlejv1LsJwxPjVGIRWVW1IWl4eOs4BRIev7ohJUqSAlrjZPkFoVPVIUxolLwWk/3VBPaEtl6jUoa2oPOl1B6BMpNNZn72q7V2rEUOsTkwMRV+bTU53HSzdGVp/BHQrRSFHG1JTpLF2b8mhDvps3sYm0wkx49hrKyBFIvsOHlSoDvAvxkapW48NexgDUwlO3J5D5LZNIzrFoxATFpY92WuEST10s5rAEznSjIiVerqRKBKBHRqN6tXoTf1AuxECbMm5/WPCmhVYaSOXP3XaYrG7n2PXhhA8gEQAiNh5IKIilkcKPpkD40Qp/UL9x61ZtLu7lQIJ5OcTIIBMZQsbn9giJRQiiCzYg5lI0Hqj5Adz29NAWpoMXgC0kd2+gDJql21UUF48agNMqP8NKrk1n0qGep9+XE0DGq0EPOE46KNlAwEUYKFLwBPGkGz6CyHazS511got3JdjWWYlHYTLNjftLDZpogVxcAlEuV1BhcbzTAA6t1FcTVfE3TCmu+Z8ejEoA12ibYnfSzr0JxlQEzES6J1EGXRhOC1Vgt5FS5uqGq+l5vVglSGt7n8wNlzzdF8J/+2N9F5MoXxp0X1ga79/Czz3+CoZ5uzvvoJ2kbN776tw19G7juwc9zQ+8gMmUZ6qT3Hlzn9q6HH14IA9vYeNzH+fXmBnb/7m72mE7uNbM4akorP/q7k2jIvXhTrqLdI9z5wye57KgcA3nFJx5/gJde/TWG8o1cv+iveezYM3jPq5fwmaMmof/MJsBtbUfT1nY0dsHnGB5+ip177yVYfQsd6x7j2F3bWRxodo4tsGNkIxue/kV1v2nAl6cVWF96kC/e+WrefsJXmdV57J858v+9dXZ2cvrpp3Pqqafy7LPP8vDDD7NmzRq8cR4Xdc5m5Y5Obi0WOJPPcEF+gEvv/CqTV92IOuvLMPflB93f0dawsJPc+1vou3ED5d9s4dw57VzyjhN5arjMzU/M4sf3TeDSG77JJT+7ni+84d3cetRCbtrTzwnNjXxwzkRO7njRZhQftr9Q+0te+Ptj5qehlB8nqc1ubT+tZaoqYiE0UmaObGK8FFipXB9AzxqipG7KF4svMbOGd9MQxHXNQqUibgWbAGuFdgZx6/QOTonVoAyRVyJWIaJaUMCYcJhB8ehUEEiMsXFdSpVkQhuXOmaZU9lKA3t4IqgX9XGiehblheRHQsoNDYRE1XDNT+uXEk1umwnK3CwZwsY8FEsEsUV8lx7ZHFc4yaygNx5Lh+mmV7VUcYtUZ0HVOaIzI3BpjCqZ+WTlW6fgwRBKBJlKlmx4qazzISZlVCAgRollpmxl0AQ0xTGedv2xCEr1SYRSC6bH2j520Ma0eCcDwQRyQYSp1GZbKxewq1wJrYcxI/nakbTGRtaBT1RdmnwqcqBUoi5Y+4tjpDKhvM6PACUopUDDQlBENQ0hOiPhrUDnSrXJEEH5yZx5FSqeRcduDry8qx8iStI491lAUESik0bDjskNbIVjwyfZo8ex0ZuCwqVPLrIbQMesUMfVHaE9rtXaqFwJlKDL9eeZWu5lkezhsdxkesnhKcnwJs7ibBqjcvMKFk8rtIAk6afT7TYaGEINNDGddewoOGCovAgb+24UCfEU53w0QoMt0RBUKNKMUhDp+vbFLVEZdFagPNss2h07NjHjZJCChE6kI1+iHBpUrozWFbzcXgip26/DH2Sm9OKpEp5YIp3Hkie981IoXs8XUVtoyX6aMMRODsXVTcYIrVEFgupDN+rqZkFX+kIxwzzLA3QwWe3CEXVeZh/3YHSO9NPXNqH6uS8xR5pnaDVpl66GKgiOUoiTLfp6sfXBwtVcLQNuSt6/BrgH2HognPpzTUTYsOL33PndbxGHIedc9q9MWVBrQluOy3z4nsv45N4eGrSPOvdq8J7vVLwA9vSd8JO3MqRbuW3ap1n98E48W8bGR3C338L0jgLfe+vyFzW4CncO862b1/DFxTnGRxW+/sXPMHP7Vn46/3RumHc6bzlzMZ962SwKwQs7Bq19WluPorX1KJj9LkdNb7yL3KP/zbS1v2L6ziK7TSerBtsYnLyAOS9bQq69hLf3DuaHu3j28QvY1rSYhbPezdixZxzw2qx9/dfMnj2b2bNn09PTwwMPPMDKlSsZ46/nXVPnc/OuMXy/1MZt5gpes7nIWVdfx/xjfk7TOZ+ExkMr3Ok15+h88yJG/rCLgZs3svsrjzHn3Nn8y18vRF61gGf/7jR2/usV/PvVn+KhaYv59GvexoNzx3LecJFxofD6llYumjueWWObDvq8H7b//5pSqgC8EzgF97t9L/AtESn/0R1fpJZT9Wuvk+Pd7FBd1fdW1fo+pSvCjVIiDY4CiYlUQH3dkBpVWAIVU8sx0hpMGnTXcAZevoxo16g4ZbgUQsGE4MP0ymaaw92s9qeSFVgYncYY+jGKXCpivV/z84PA+LrPNC41Tym3ap5WgQhUG+mOpY8eHBsX2TjxwIIX0y7djAmHGC7UmPRa+qWTJXcQNsMWCM8ZhMUYREIXOFVTFDU5CRkX97CpaSyTBobZ2zhmVPqbZSkr0UEZLzYMhDliH5qIUUHI/vqbSXKOdP98wzAdtp/Z0WYe5CWEo2c5YRLTKF6wLh1T0v5ntlrzpEJLGskPil/na50pi7IWrW0VgFoMR8pTrJIlDFXV8UBEOdBobd19pkUYNq73mFIWlanhUoFLPMxlREjSsa+uTCLGd4ItIuTFbdNm+rF6EoYQ7RUgFrQfor1hGEnV56DT9pN1RIDWSpmK5FEtVGdPRNEZDrFZt9IQVCgDQ7FXvSR1c6xqeZCxKHKZLQTwbIVJuW5aGKHZDqNzFRwciZE4TyQGQwTaR1nLkmgN1gp78ktI16CtiaspmGU/QGf6ZOmmErYYOKl5P0J5MQ02SkBehm3Sppp+u7XcQot2YDOUMlaHaAStINAVlLLYhhBoTi8kvhi8uEJjVH9dqsqYVY+ceZjawookaYR+CWis21KJraZw1hIOnTUbwyCOPZvGDhChWyUxj9hkkUMwNqqlqAJTZSd7pRGUDyR1Wsl3aFHn0SqmjAdSphkhdxCTwZ4vqhgLHCMiQwBKqY8DPxGRt//RvQ6yrb77TjavWsnO9Wvp372TcTNm86p3/xNjp06vbiMiXHH/FSzb/CjHFYfhrK9A5+yD5+TjP0J+9k4eaz2D2ytLCTfvprk4g3xhNtc2lGnxNNe+bTkdTS+uOqusDW4f4rJ71vHzOQEnbHyGj3zjc2yatpiLT3sjRyyZw89fewTTOw9SapvWMOcMmHMGangPrLyecY9+n5d7TxONbGbdDx9h55iTmHfBtxlu38OPHvkgR8SriVZdSmvLUcya9U+MGXPKIQn4Ozs7Oeusszj11FN56KGHePDBBzlF1nPy7CXcur2B75YbuDO6kJN+rznl4WtZ+PIjmH7mGXj+oUsXVUrRfPxECrPa6f2fdfT+cB2lp3ppP3s2s2aMZ+a132LgxhtZ/pnPctN1H2fNRX/P1dMXs6oBvlEZ4pt3d9O5o8RLOltYPrOT0xeMe06xk8N22J6nXQsMAV9L3r8R+D6unchfnIVxiVjXAohO288Or2uf7ZTYahBlMfiNg1RZFRGgPtCNtcsIAxfaWBGKJlXm27fbT1USO+kzIyhEoqT+qGZtMphs78xqjZes6mtPE3gxWJ/RyMqKoPMlakpfdlQ4DK2qiPZDlI6wopOkNyeN7aPRGo6I13GfXpKkxSVpV8Qov4LWETl/CJ+x1VX3GlOVBsYWSdIJq3PbOOAC2oTvyibXpXM+y2xjnNnLg8ExzI0300CFXTShVA4EjFUMmIAOh8Zo8AeIxDGESmlM9vIkjKMSV0szFDTULlbih1LCGDOAFqGZIXrxa7OesF4qV3GqDVBlkFQ6nZLUW3lxjYFQlmFToJUR8BzjaUeJf1Qb82auj0boivcyqCdAYw/Zixsjtb9K+bAAACAASURBVBg6qc8qxj5gyJJjSdsjkPpao8nxLibF21kv80AUpq0PLR6eGDevaCJigkIZ0UNQcXVddYIZVFv84uVcw9tYLLGNCZJ6p2raGQpJr8s+T0HNL3fUmhVjTaO/71PjFYr74vOq3HoNoFQbLgOeGIxS5ClTUNkUtoxUu3bptcbEgMbLhSgdM7ncRzt7MsClumfy36ygh6Vky5jGfsfIxm1126d3uVauPq41THp0JazvQr0GFQhSbq9R6Sh8m5VUT47nh9i4MbkF3LYnRE/wSLBolJ8p6+24Yp+YxiikGAS1+RZBrCFSllYZZpxdx7Btrs6db2Os51oyWCtondR+ag/tj9BYDAnFfTf48cFbd3u+AGsaSZlmYiEw4wX35s+0HevWsG3Nk3ROnsoJ572Bhaecuo989NVPXM2za3/BZ/uHYd4r4di3HDwHH/o25Vv+hV82vYnVg2MY19FJ/PQUWiaM5b+DIpWi5SfvOIHJ7Q1/+liHyLZs7uetK59h9QSfv/3Nr7nwD3fz+ePfwtrxc/nXsxZywXFTDx070TwOTnk/6uT3wdaH8B69loVP3MCR9mf0X3srg03H8ua//hT/sv0amgZXcYG3hZWPv4WxY89g/ryPUyhMOjRuNzdz+umns3z5cu677z4eeughXqUVw7OO4a6dHj8MIu43s1l+C8y/7TYWnDydBS+ZTuek5j998ANk/tgGui5dwtDvtjJ45xYqG/po++tZNB47jvbzz6dh6VJ2fOjDLPzm5/n2KafQdvnl/EfJ47uqh72deW4ZiLj5ng187KbVHDGplVcdOYFzj5nyor73D9uL1uaLyJLM+7uUUo8fMm/+TCuFvZjnYhQgESmwOFWvBJpUAVlG4mBUlDds87Tg6rDG2j6GbAsl42M8LxGtcNu3yyBT7A52hNPROUVBKoyPu+nT4xBcKlAtU68WMFaD9kBQhGDyiFJOeX30b0J1EVuqsZaxcdIjy4X0ooQGqaB0KmRhwI9AQGvHHLmMLSdi4MiFWs1W1jyJ3HGt4AUGZTKr6n5EUxiCqQFHV3+0r2qZzajgjTfdjn3RUa2XFpYmO0JBGlHYJN0u0/QZhRb3rmQCtOTAr8GBI+JnaLXD1fm0ShAraCxTy92MjQcS9rCM0IxPTbxjktnB9mAyVPZJvqpeKQUo36k+AngeqLTRs7Joa8nbiBEvR5ZhiBGsjV2tnR8CHtpatK+Iker8i6eT1FKpCh/I6EkEkqIz9plgYKrZQUHKBMSUU0SmLX5skhl2n4lKbx9LR7m3SsA41s6NQ3u1+zpzFfGUsKiygUDAiMIaBV7tNlWJmmHWFFR7cIlorFdGNZRhpAEEKiqHx/64yHTvBPIl9fTZtEifGJTHArUeT2L6pJlYwfjiABl1fLK1kZ22n0HcwssYGWRA5euuuEqYJGUMaPdMxUnKnuQGIG7KbO+eQ5vMrqdsXRsDSWrHlGeT+wECf8RJoVuFlyxDGOIqqCjHAcXIZ2wQkb0XJ+YHUVFWKdEd31oDQYCWkKZymcjT4NW+0RQOGC9WG4grLeRMzJOeSzluiksMVUXM3HfISBRUn9VldhWxWNaqeajn/mp9we35AqzvAw8ppX6G8/5c3Krhi8pe/o4/Lsd927O3cd0jX+Wm3hG8pnFw9tf3/eI/UHbfV9h5x9f5SfAO+op5Fs04lj0PNjB+bjs/yJXYubvMdW9fzvwJL95alXs37OHvn9lGqVHxyWu/S3NDGxcu/XuOm93FbRcsYUrHi4SJUAqmLUdPWw5//UXiJ25E/e4bLBz+PfLz3/PVYAa/7prCvw5t4x/mnoDuvZ8HV7yS2bM/wJTJb6qT9z+Y1tTUxCte8QpOOOEE7r77bh577A+c4+coLziWO7Yp/scLmWFHWHLfNubctYsJ01uZd/wE5i4bT2PrwWc8ladoPWMaDUd20vfTp+m7YT0jj+ym/dUzyc+ezYwf/4i+H1zP3q98heJrX8vb3/Y23vOWi7l+oMzXtuxhb1vALDwqm4b599vXc+Vv1nPq/HFcdPw0TlswDu/PrNs7bP/P2GNKqRNE5EEApdRy4PeH2Kf/s/k1zMHoOvBsf6HUbKBR+6mpd/VaqnqwQVOgOc1wUoqpsptYeSjAV161ZihHxHR2MBRNYsTXLI43MtEbZI2eBWJQYmmXYWLyVWbE+ebMyw271fFSgBaN8iKwrtYrE+YDwri4h4rKMaBbsMSgY1rt/vvUKHFpSFbVGCVXyaJol34GaaqxUzJ637g6bb4YTEZmvYvddPolhGYH2JRgieiyg1hRKC/pLUZEratX7YqkAtgWCyIsiJ5irNfOdlqTYFXV9RvLNikOrY9NVtuXmY10hLsZ8Jv2gQQaS5sp0mhCLC7VTzLHEoHCKGbRV2lPrYTJyNxMeRsyvbybUtSK9mwCdNy21T5QkoJWF5w36R302xDlOXCrMajqOQWUl9R2pXskvmdAVEul7JrEpmY9UHGGO6kerVpzk5qXoEKTBv7JpCqVMHzpxtqB8JxxnIAoVWusK2B1heYgpLUyzDjbzxozk8h4tMYlFB46P4J4FQhdPFPHanlRgkWyvglb9SQqhLTS6/bQGtGWpFWTmw3lWKg0Ry0F5UJS/6dcSi7Wpz0cRrAMSGeViStIBWMhSi5Ql+3j2WR8id45AGOj4ep1A9J2xohNUuh8TVxND3Y0aiyRyyT1fUQJVmJC7WXGPoqdQrFcPYTRObB5/DrZkdpWIoKVegkMQSGxIMG+0Fd5Bt8fxovKQGOSkuuals+3TzNZ+WgFTXGIFo3nWYo2hybMLCzVwGz2WUtfH8y44nlFkiLyGeCtQB/QD7xVRD57IB37v9gfA1e3b7qdj97zYb7VH9IRVVAXXgfN+6ZdHBD7/VWsueNa/ktdRFQYw/K5Z7L3wUZmLOni5raYJ3cM8PWLjmHZjENbY/NcJiJc/YdnecOW7TSGhm9e+x0ennAs/9J6Au98+Xx+8PblLx5wNdpyTfjHvZm2D6yg/I4H2DL2leRKu3jTzhX87tk9dP3mAR7cMpWG5iNZv/4TrHz8EirhoW2h09bWxtlnn8273vUuFsydTW7T/ZwTrOSSJU1Iewu/aIr5fls39wzs5Lc/Wc/3PnQfv/zqStat2EVY3k+kdYAtGN9E16VH0f66OcS7R9jz9ZX0/GANcW+FMW/+W2bd8iuaTzuN7v/4D3ac+QrOu/1mHjh6Fp+YM4mhnOLJGQ0sPm8u55w2k1XbB3j7tQ/zV1fezQ8f2kI5OniSqoftL9aWA/crpTYppTYBDwAvU0qtUko9cWhd+z+Y1NdgORVBqQKZzF/wE9k47cdMyfdmIhaFp6hLzxlted9kjpQNdRSiYJl5mIKU8ZMOWYEyKCydDFRVxkxcq4cQUdXsNA10hCU6y0NE/hY8v1h37i7TQ7MdYY7ZypFmY7VETOVGOMqsqW6XTRp0caRNAIZjfVQCdxba9TTbYRook6YbCRabrGAHVXnwpF5ELFZi0t5fk3KDaByxItZgMOQkcsfyK6NSx9LkKwcDvAx7uLTyNOBENjyxhMpnpz9xlApkJj0qUfaLMRRsmYLdf48ejcXzwupcp2KLnrIogdZohGapn2MvkwYn7rKigI5wmJyNaZEKjSYkbeyagtd8nQKeoJXBzwe0BH34TUPVi7G/ezINweo6e4ljRXwxo46d2U6EsdEAAHlrXA1Qcs2sgIhNWMgkPdH0cXT0THUuFTDR7EJ0XFNNdCffZy69fBEP61z3NEU8EGGJ2YJC8LRrOaCUJPeZxSZNi7Mpa+n/JGniGxCjsLTISNVPNydSJXo1tUbSNXU/x2qqZDaUjtEIXr3OJQExw+G+C6nKUzUmUKtqb7WaPLuAVoiu9XMLQ0vOGjp1H5PsDtoYTO5mt4UTv1HwHCF1OgKVANzx7N7vdkonDGh20Tq5d0ymp5lRNll2SdohK0MkIYo4SV923F2DlLIO1GoKU7CqlAOKKX5E6m4BpRKS/CDZ/0bZoREYFJFrlFJdSqmZIvLsgXLshTIR4dqnruVLD3+Jz5V8jhzcC2d/DaYcJCW5h77NA7/5Gb/mNUyeNIWZTcez7p4e5p0wnpvzIfc+3s3nX7eYv1o0/k8f6xBY2Vj+6bdP8FMfTt41zLsevYsPTH0FUmjgexcezanz95XUfLFaYfIipr/nx1RGhnj6V9/Ee+IHvNLbzKs33s+zq9uw06bTN/8BHnzglRyx6N8Z23XqIfV37NixXHDBBWzfvp077riDZ9f9jrNb22hadCx3PtXHLwebae4Y4LTOVszOYbZc8xR+TjNzSRfzl09g6sIOtHdw2DilXW1W41FdDN27neF7t1N6spvCgjE0nziJyVdeSfltb2PvVVex59/+De+//otzL3g9b7zwDfww1nxt8x7+EMS8/KyZvDX2ufX+rXzkp6u48jfreevJM3jTCdNpLRzkHnWH7S/FXnmoHXghTU+cAGoTAJ61NKkSXaYXnamPqfFYLhXL90OOrGxAS8zepDB8pmym1fSyQSU99VQ2AJYayyCCjOpjBU6da4LpqX7a1TCMXywTxKYawLREw1QsjK0MJCxONbKhuTKC1QHWGnTCKqQ2J95SJ+NcrZipfpYAIxOD6Or5bDW0q0HCwHFf5IiZY59NT589DL6TFnBzmnhpMIREoBUewgRdxkJST+L6Qbn/ezUGRAmeH5EN7D3lpLatCBID1qM5jOhiCNvo4eVCjKq4wFfpTCtbW61tEa0wOQ/KGWCSBSnJmCMJ8UWhlasz8ayrW8nbiIIq1qXceX6xPtG0OoS0x1eMDkZc0J8JpPMYxoaDdAfNzofkj35rNzsb5hCEpeRwksx8emhbvaZCjVnSkirP7eOKe53s02AqzB7eRbsU0bhrooCcNrTmi8ytbKUlFyNFYZ4ZwiPG05YU6k6yeyGoB+X7M0VaW2ermnyiNR1e0c24WAITEefKRKWAdtmD6CTdTvkZtg9iCXAqjfVsCclxsiM2EqIVeBp8G7tUQe3Yp1StMjWrnEJhrXarNm9uAcFdEyWuftBqyYCKDAMIaY/dKl+GWLCaMXaEJl1ESUQzlo12CXFmX5HkKauyf7VzjKXPgSHlFlYagiG0X0jUEhM/lAbPEIvjt5wsvQOsXlChZHwn1a7q67eyYCl7X7onpt40hhiTsNtuvqyIY6mSBuF+htl11/7gCdo9X5n2j+GUBOcD1+C4/uuAkw+ca3++bR3aymdXfJb7tt/HJ72JvHrXCjjubXDMmw/K+e2j1/HrW37JCk5lwfz5jCkfwbp7ull82mR+W4j5xQM7+MCZ83jD8Ye+qez+bNtImYt/+zirm/Nc8uROZgzv5ZLgWI6Z0s7XLzqGSX+h9TL5phbmXHAZXHAZQ1vWsOu2zzB22+3M3PsExV0B28ePsG7kLazoXURb7kImzz2CCXPm0dDS+qcPfgBs8uTJXHzxxTzzzDPccccd7Fz5W07p6OC82R73rt7ILd2LuVWVOf2YsZykG9iyuocNf9hNQ0vAnOPGM//4CYyb0XJQauN0waftr6bTfOJEhn+/g5GHdtG95kn8zgINi7sYf8WXiHetpfd7/03P1f8J3/4Or375y3nta1/Lj6bP45s7erkjNpxz+hQu1rO56YGtfPG2dfznPRv5h5fN5s0nznhRq2setoNvIrJZKdUBTCXzm/aX2mhYtwWMyTmmoDUuYpVmrt7C6OVkTaJiJ1JdpW40JXISUsanXQbwlZOD8Kpr06puf4srfN9vSJpk2jgBAAg8yyyznSYZYlBcYYiy0BKP0OYVwVOYwCdVrRNsEiA6RikfJ+xMErC1myJ9XkMSxLtidaxrWpqyEK3lEjkf+vKFxKl0DOJqTKzga0HUc1Wt1VirWFnw0lQzoYVhXqIeYRcTsBiawpAwZ+kol6CtwzEXGKzKkVZRebkyTbkBdEbcQKtaAKpQaM+l8BkT0lkRJtpn2ZBrxgJGW2LfjvLO7dtArfje0wlzk73e2mKSxrAKp8aWshUOZqm6oL4tLlLGp+TXmr7XkqegyxtmyORQYtAqbSArVLvypjuIu4Kegor1XKKnEibYbp6RCjkbYrxCsl3CKCT74IEyce3YqKTBcwYyZNCwzlxFX7kaw5aGPvKepa04iPUzapBKUdBxEoRLDVmQ8X+UBU3DKNtY6/MkliXxWhqVoPxGlCe0RsO0RcP/H3vnHWfHVd7973POmZnbtq9WuyqrYlmWLGNcZCxjgTHFsY3BoYX+0hMghEDe9yUhkORNJQRSgJAQCCV0Ykw1BodixwU3LOMuualXa/veNuWc948zt6xMAsRBsoOfz8fe1d25M+fMzJ37/M7v9/weJkyIRFXCrNQ6IJ53smgc2glTzRCSBKdy/ql7DHldEoB2kKoMlKLsGpye3Mts2JNDyFzy2e7+25H1+r9avy+niLKYmhTaoNfXc3U27p51IV/U8D3AFE4MitTbqYsltRYjqm3ioh1ty/kWM6Sjmn9uiK+zaoEcXzPmj9O0gg0aiA4gXQgpBhpVXFyASpjX7gGS4lTS9uARfA2p0TEQ0u/mUIBVmkVusnO9u2bX7mmmHZk4QloWHYKOamCLtFovnJZsxbbt2i266/Pwi46fFco9DzgV2ALgnNsnIo+6YqG5eI4tB7ewv7qfG/bfwFW7ryJQAZ/oP5Mzbr0E1j8HLvirozIWe8elfPMbX+NWTuPM00+HvSu478eHOeOiVdxQTPnUd3fw2rNX8Zvnrjkq4/l547t3PsBb90zRLIS898YH+Z4q8vmZIV6/eRW/e8E6gqPEjPyio2d8PT2//lnipM7Xvvt/GP7xV3jy4TnWHIaJwZt4oLSVb/3DcTRnIwbGljB+0imccNZmlq7fgFJHN9E/7rjjWL16NVu3buWaa65h6z3bWN1b4e+K17Nl3xyXbH86/+YinnbSIl66agR33xx3X7OPO67cQ99IkQ2bl7L+7DEK5V88E6QrIX2/spLeZ4xTv+Mw1R8dYO7q3cxdtRtVCSg9+TfpueDN1G+/mrlvf4nsiiu4sL+fC5/7XL74tPP55OFZvuksL37yKB9/+nF85soHeM+3t/Lxa7fz1mccz4vPWP4/5h58PB5ZiMifAq8GOpoh//Mx2WhYgLQr2TateqEjFkhCNKITlI69DCn/86nJPexWo3QymDw1cY6BZI5UDDNhCY1lQQer7j5J4hvyWpVB7jSosEQlh53J5Xcu83/HJz/zLqKRRjidr66bBOdCfwRrKdWq0OPZJB8tiZ4jUz7JH21MYWxGV/ubPBnuKgxCPNjI8qJ8a5FwHqcmaHfg7WLCnFJolzHcnCVVNVIGAKi4eRKl6HO+3sVi6YubzDjfx6plSd3qveVsxvLGQ4wkDzGl+mkDvS42DSCI5hAUi800jepgW0KosAyms1jC9jucR7D0uSrL4r1M4oFkT5AwE+tuqtLX0uRgQqxv8qzJG/SKZ/lUl/5JOUtPVqduoryNWMu0wqfUWiwxTZ9Mt41TPA9J9xm3nflNNcpU8OfLIYw1D0Bzin2V8fZ90PrZAgztXmaA0gnK5KYHkuUqNGkzdOI6QMm6KpFM4HSF3nSenqzKdFACLb7NkYPl6YEFiTfAYDzDs5NrOKSGOoiy1YJAp3lztoVSxYJKENdgQ30HhcYMHQkomCDOHSb9TSkCg8kUxgVMFodILEihDkkL+LaYEt/kupI1SBNNUvSulwPOSyFXJ7upqVL72rbbhwFWCSprnc+OVLBg6zSlt72tFduW5Xbe7cfebtLdYhXF7y/VNVKZByJCydofGSFj0E3yEC1JrZcet0LjFz46LHI3oMuP0Z0SOYexjqZtetqudZyfAH51VCcwCnEhK7N9OKCUNGgGHUmkl/d5S34dxWTpENo0urC1H5tCYaXhjVccGNckCUCawsrqQYZKR6+c5WcFWLFzzkluySEiR8mD++eLvfN7ecsP3gLASHGEV57wEt50+BClmz8O6y6CF3z8qPS7yu65nK9fegm3cxKbN22ium0xe+45zOYXHc8dZcvffO1enn/qUt797PWPun5ASWb5029dx8cqFVbFwjsf3M27G2Wsg4+84lTOP2n0p+/kMRhhUORXL/wwWzf9Fu+87k9Y9cA1vHSuxpmTEzxx9TQHhs7gnqlB7rr6+9z23cspDwzyhKefx8nPPJ+eweGjNk4RYf369axbt44HHniAa665hlt2zlMolfhT+xUeiCt8ZvuFXHXvQzz7CWP85jtOgd01tl6/nx9+5X5uuuxB1p45yqnPGqd/5Bf/oBGjKJ06QunUEWwtoXHvFI2tkzR3zZHd2QBOorT5JKTgcLWHiG+/m5f9+z9ywVDAF597AZc4+LJM8b82L+GfnrKKj333Pt79tTv52DUP8vsXrue8Exc/6j5Dj8dRj18DjnPO/eQClsdcdORyrRoCh/N1IGIWbFXRk+0GuKFNiTJfpzNop0GlC5a0BQhs5gvt8cxLIUuoa+2ZD7VwW5ebTlgnOO2NAnT3KnlXhuUE9mS9OFFtm3DRCS7Lf29ZoDtN0AUencoTSgGnhSBt0N+sMdXVP1FoK6UIdYoRh+0s93sZmrJYESaln0XUupKtXN6GN1KQLgux9lNDOmxG6mwuTeuYJnRbeAQuw5B1AK2It4Q+4hEkYhl0cxygn7oNqFCjqguUsiZVQkomphYbQudBUjnz/ZIW7EdgPikgxo9BqQ7QCfPGxStrBxhIZr0Vvs4TY9+9GYvNC/o7KM1mSQ5qNRqHCw0u9aYeYdag1+U1TE7afcZa5yp1tivVz2VxEtPPLIdsSmby+4gWaymIOLSztDwVfO8m38HLiSBK8vslr2tz3qGydZVaTFPJNnImpX3awQoj2SQZC+uSIonJnAaBwMYkzrM8tg3Uc8YXB9ZixbZvZRGoUKNB2lV35UHscDzLZMHLb0s0SJ2hnDWZChyJSejVNXqrdVreL63zpl2GshbEMyfj9gBNHKFNqKpWnVSn5ULnbvPvH2jOMBX1YcWC6jZZEVKydt+vVmSSkjkhdGl+5VuOm/6+6Fl0gH2NIkM2I3QxTfELrifGD2IKCVW7NG8L4NGpiCNQGWFUhcRDdG06j1onNq+T6jB2fnSC1QrXAldtCaMH0g0iwtyc3LX+J2BdRkZKMU4opU2mogiHB6FaElTYRCTAAVpiSrbpWTpaJvi+TUAhS6iqCLDeqMZoijbGVI5eOc7Pijb+VUT+CegXkTcArwU+9p+9QUQ+AVwEHHLOnfTIhvmzxcrelXzuws8xUlzE4oNbkX/7Azh4B5zxBjj/L48KuLL3/YCv/uvnuJN1PPWsTUzdtoiD26c495XreLAH/uALt/P0dSO894Unox5lLmm79h7iN66/l1uHerh4V5Uz4pjfOqDZsKTEP7z8tKPX2+oYxrrBdfzlRZ/jun3X8VtbPsz43ht4U32elftuYIXcyHnPejoHep7KTffMccNXvsSNX/1X1m9+Gme94KX0j44dtXGKCGvWrGHNmjXs2rWLm266iTvudlht+U33TXb0rOLrW4Vv37mfF5y2jLe//kTC+ZTbr9zDtusPcM91+zlh0ygbL1hJ36KjI/VUpYDSKSOUTvF1e9lsk3j3HMmhGumhOsmhHiQaxSWWMeDtP4YXs5ePry3wSWv5HMJrN43x6rNX8oHv3cdvfOYWNq0e5A8uOpENS/r+84M/Hv+T406gHzh0rAfy3xHiMoJiFRoLRYEOMM5h298blkpah9ADkNF4itm0iFN5j53uJWbxxeMoQeeJ3EBaJU0yRCKqUqC7CkRMjNZVcH0eNAlkLsZo8BVInYJ5X5RuKamYxYU55qJhphtFAudodgGVqNBgdWM/U2H3wk5LMuYjk4xYEiINsdU58+JXzhWWHl0DZailnhlDCVmj6q2spePxJ60zlifkZgE/4KOQNMnCiGIrec9DtTrwKrCZypP+vNbI5Ql3vj+bNxturcqX0k4RvuAISbiv2s+KbDd9wQxWIhQOk9cOVZIqaxp7OdFuR4eSN0n1F25OylSk1jUuDxCUwFJ3kFJap+AaaBy1LKSHecb0VNe59TVf0KrnUXRXQxVcM5c1+rn0pVUCZTwbdkS49h5V+xWFcHx6PyPuMCY13GY2eObKZeBSRJu8lirtOP+1d9jNqvhrHIh3icRZmgZUbDEu5eTqfe16rPbMlKByd8ZWeKmpI5SM2Cp6VEzYnKXXCVPGy/slJ09DO4vOmxtblaJUp9/ZkbNWrlXn1eWMmIPy3ixhyhhm0yJLs8OEudX/ApzsaLOYpTChqGc53FCozKJdlgM4eyRB3R6DdplnKbvnqQX+g/yxVaM1HM/QFKipSpflumbeFpmxhiFmCcgo6YwGIQPJPIWGw5SStkGG5IeydBY5/G5SMuclg07H2NyMSuE/Cy4HSinim6LnKwcjjWkO9YwgQJYvBNAqsbQ2JwlzkC6WUhYzRUg5bZBlAYGZbQMxLUJka+3zXcwaVI1ngLWzNJwmU5Zys8ZcGFGTgN5AM98yyjgK8TMhDufc+0XkWcAsvg7rD51z3/0pb/sU8PccLTv3uErh2r/l5Nl9sPOHMLUd+sbhJZ+Hdc8+KkOwO67jG5//KHe6dZyzaROHfjTI5L5Zznv9SewoOt7+uVvYuGKAD7/stEeVvMk5xzcvu5F3BAHNvjJ/tPUQVydF/mxfjZedOc4fXnQiheCXp+5FRNi8dDNnLzmbLYe28Fd3fZLlD13BC+bmGN19JUvj73NxcZDkRRdx28Qw1199LVuv+3c2nPMMNr3gJfQOH13jj/HxccbHx5mbm2PLli3ccsM1hPWYF6kfsquygq//GL5+2z5e8+SVvOkFx3Hmc1ez5Yqd3HX1Pu694QBPeNoyzrhoJVHp6JpI6N6I4oaI4obOa846sukmyaEazQcfYvkdVd595wz/a4fin9ZV+LDM0JM4XrOkh3f29nHJrsO84oPX8StnLON32Sgl0wAAIABJREFUzlvLSE/hPz7g4/E/Nd6Dt2q/k45IDOfcc4/dkB5B2CZSsu2Z+M4/lnJaI0JRNyFzlDjB3U+ZSRIUShyJWDJlj0xlAVhiZjlge0DAiGMsmWPYTHOAHkpZk1CmmDIlEEVP0iCUmKaCsmu0U86l8UOkrs6AmmeWhT34HLA4mKUnaDBoZxiPdzLvFm6jdMqgnWFxst+vPnOE6tF5N73WCnQHJlkKtoppOqTkAWZ3PZklzvVDgm8x5OtFeksNag0P5oxkC1JnclairzHHTHEwB2u5HEoJSxsHUAXlXclc6xpIm5XxOaOHckqlDCRziJsnkoxU1BFzc20JXHcY653jlqcHUcotyJdFwEqLf/OgcchOod00s67iGTI7g+QmE8qBto5l2YG2ALNz4r0YU5ECxoMgJSyVffRRWWDOYMno7v/kjhjzQl87R2i9PLXkaqxMdlCTkBTrAW3eqwyb4FSYW4f7yMT7l+usZfnhWG+3s5Vxf0Sl0EoIgdAmngkSaTOS+Zv8mV2Q+fvrszyaoaQtjTQmcR2Ga9qWESWMpQeJkiaZqLzerwOmWkcYbM6QIcxE5dbhuo7iwbtC6KqCQloIrs2n5OYX+c1QDGIUCsklgIPJPC7NUFFeM3VELIRQXYsAJvG8lLMP206UxYkHGQWXUZVWiwSYTYvMpCUGmcjdDS1DQY1JBrGhARKGyzXUvKWctIBIfowcJEouubQ4RrI5mrGHEQPxNCl1UheQEPj5qwylxDPH+fCVtHkmwqyOcVBIazhTyl/1xwhKVQbTOeJmgiIgrGvictI+FRqhZG178oHtGK6UsyZVMSyKJ/1ihkAiBi/dPHq5908FWCKigSucc88Efhqoaodz7moRWflfH9rPGSqAa/8WyiMwsh6e8jvwhF+D4OgkXG7XjVzx6b/lx+4kNj3xVPb+sI/qVI1nv/lk7tcpb/rMLZw41svHX33Go6pIf+Leg/zhDfdy6fIe1szGvGFqlvfut2hV4wMvOYWLT1l6rId4zEJEOH3x6Zy++HQO1w/z/Xv+nvLE5xmdqiN7apx852d5krOcumk9D2bHc+W1V3D31T/gjItfxJN+9YUE4dErpgTo6enhnHPOYfPmzTxw163cduVXMVM7GTQPcbdbykevtnz+xp28+dzjec3zjuO081Zw07e2c9uVu9l20wE2XbyaE89e4mUbxyhECWawgBksUFw3SP+FJwCweO9ejv/y5Wy5aicf2/RkPrhqCZ/rt7w2rvCO3QkP3jzJp2+5jmUbR/nVZ6+lED3uOPhLFP8CvBe4g4cbTT3mwpHitG6bAShpufRlGEJ02mBOvEypIk2mpchQYR6VQJBlpKiO1OyIpKY72jbSznnGK89Uii5B8IYTI+kkkrt5VbIaSqDPeEmOBApin2g+Q9+Kspa5VHNcppl3IdPojtROeVAynu6jZkPmtcYoz6q1hFuDdo6CPSLJVL6nUCltIJkCldE84vFkbQKiWCRTROLZeFGgA03Q9ElXREID777nHFijSYgo67QNhExhDhtbRDmWuykmXR8OoeQaFKlRdE2s8vNRXVJDlZsehFkdZ8IursPliWDOvrhOLZaId/4DRySztEBNRxrm2mzRosYMFhhU08y0L6vDiQcyPiEVAheTSga5KYnrqt/KeUB01ECa/gjGOIrJQgt6S4pSIbTz1iPkZz8xOfWsxWI70ZbZtRs/i8W4GOHI57HDZb72q5VUI3CC7ARl/H5cbnySn5eWrM8ziI5i2qBhehDxUKYnq5M5EO2BzoCdpKHhodR/D7f7cSlpAxN75PwkaZ8ylTfXVe7hALll/JBlMZgiHtjl/dJc2nb7fFh06S6dzRCncNqzkr2u0/+tIwK0DOp5JpWXJiocmCqgcc6x3B4mVhkdVO0vumBR4jxLREvy6ueUtbV6ru3sp3SGKk9TUoqSSdBiKWoHGWxs3kUaCMU4I9YdWryU1gkCg7Xeb7Ngm9S0QTtHLP4eLJmUWCc4XeiaVS45zcdUSufaI3e0pLf+GgeFBirr6ZxzAKVAFEGYy3Wdv6atdQEnFiQlI2gzzf5yu1z6+CgCWM65TERqItLnnJv5adv/vCEivw78OviV+P9ymBDedfCoyAAfFnu3cOW//AU32lN54toT2Xv9IC5NeO7bTmVr2uSNn97CutFePv26Mx81VtPxvnmuvPx23jUasXdZhZfuOMhko8Af7axx9poh3vfCJz5mXQJ/ETFcHObFp/0/mvFbuPm2N9Ec3sIXayETO2qcP/cg65r3sOZ4w0G9hqsv/wj3XPMDnv6aN7L6tDOO+li11qw9eSNrT95IY9ePueeyv+e2Q/dza7iWW5LlvPc7GR+9chtv3Lyc1774RE56ylKu+dd7uepz29h24wGe/sr19C9+dPU1C5cuZeS338CvZBmbr72WK79zKR9atYH3rV/H51YqXn9IeP62BuFNk+y++XriFb2sOnsphRMGUY+iBY3H4xcSh51zHzzWg/jvCtWuY/HgR8QnYNkRteFijF8Nx7tlKaDk6syIZ46ss2ggdNJOsAASUrQKOunOw9ZTXPvlclYn1lEbZCnrgZK4hXbYZZpYZ5HUIkmBphvEGE3m/PedUhYjGiuWclr3rESw0N1ujd0HDlKjsXlC7ozCGfGeBALLk4eYsAMccAPtdyrJAEW/rbabArcilARRloJLmEfAgKQeADnjJ27Ie3wph3fzqzHKJJIJSc6ZFLI6K5O9NHQhb2rblZh79OR/aAuZzi0gOn+OXYDOsnwFHcabE+xPS2Tkjmw5GO2GwS4Hyi1A0QJsQLumaVl2kCZlnBK0hcXZNAdVf369jrhhuq6uy9mxsWzCW2W3/yYcVMMsotML0krCVFLASL0jEWxLGX0UbJOq7nL4yxNlkW5nwCOYJrxVPsrhtJDaDCuO1p3pcJguMwrBkUiKI2U4nSFzmrrrAMHA1jE5u1iXGJxFJHy49E6ptlV9d2Q4rIlJaSAYenWNaVtEOUdvUGPhJV94blMsVjXQYSO/8v47pz+so5pHwFTp+pGbelRsDUPe36zLZfFktYOKqueGNH6fhoSGeDZ1RXqA3XRqwAvW096iHGVVZdqVfd83ZZHMPwcG7Cwr7SEgBN3hcywKUTG92TzGZX6hVTlOtjtJE8uBbBETulMmUs6amDDsMsnI5blt3WbeI856YNe6zVpNoa0SD5COtPjQCkJBxUcuCC0M0RnDbpKGpWtRuMVu+3rBksSk1tdXto5yNLVjPysaaQB3iMh3gWrrRefcWx/pAJxzHwU+CrBx48af/ET4WeNYgKv9t3PtJ/+Aq7MzWLv8OA7dNEKhqHjO20/hjrkav/GZWzh+cYXPvO5J9BWPPbhq7pzloSvu5+91wqdXF1k8X+d1O2b44v2OUtjgTy/ewMvPXPGoqw97tEQUDnP2xi+xd+/n0Q+8l6Un9XKNOZe/euAuzp3Yz3Pm7+MlKzP2JPu49oP3cufJF/DM172ZUl//MRlvYfwUTn3zP3Pqnh/xvO/9NXftuIIr7CYuj0/hPd/fxT9edT8Xro54xXOOZ+2hEa7/yna+9Gc3cebFqzn56csfdfeBaE3lnHN4zjnn8MytW7n8G9/hA4vH+ZMVq/n44oTn2TLLfjTD6TtmmNwxhzOK0vpBik8Yprh+yK+6Px7/0+IWEXkP8A0WSgQfkzbtuG6Q4BkXtMBP6CEuCAbBdDXXNOSbikVhKNEkck0KKoYMQhWjtUVjMQjW+QazymX0ZEm+gqxApUgGvaZGg1J7PCIZ4hzWZqS5eYUTmNa9RBymaGOGkyo1NPuhnegHChqSkTmby7tyIKccPWou3zeYsEmiynlW6nCpn7iIIxBLr20wo2KsJDQlygFWgMFhVYpz3kCglM7RGzZRItQbgpdJqTzhtmhJEOsItaKomkgpw1qLpP57usdWmaAXcAQ24YRsN4f0IIUw9c54eaguOVgrTO7P2B0Zipa7e3dNUaRims6QmhhaDJx4OV43Y9R6dEm+gTjrHfWsL2KxYW6PL26B9f5APE+iM2q61OIx/Lj/g0d7KgvzlJaELrYGm5usiDic1u0BldI6TglVXexyeHco6bBT+gj3OK0UWeb/KOB7TWWtKjGF4Lpq58DYBENG0XVMUiphTNyI8nG2zeqxott1Tb6OSHXc9pSmEApZ03aaZOeSxoVMrzdjEOWoZDVSOgvOC5zmye9l5dDGMyftOUqLRuxsPMAkDzHcZm8BKq5GXxx3wE7OkBrnGdbetEqs1AIbe0Qo542pRS0YjNeM5g2OK6qOK0ZMN6GvWWW5Pdi+btJ+g5e8pih60ioxoEJBEigSe4Ks7Zrsm/kGgaWgUqrdJiPiIDTt6xfRoB5HDMWzbSmndilFnVBMakRHPNRaLphF06DfzYHr9AQzxVYDZ1hVmGBPtQxFv4hkHfTpGtP0tps0N1VAr9SYzDrPLgd0/PB/8fGzIpJv5f89Ht1x8C5u+sTv8r30TFYsWs70lqUMjha56C2ncPPBGd742Vs4blGFz77uTPpLD+/AfbTCOUfzgWlmv7+Lm6aq/PmJIdt7Is7ZsZP7dxk+W4df27iMd5y/juHK0ZW1PRZDRLFs2SsYGnoqd9/ze6yevobTn/gUav2/zwd23kD/nV/l5RMP8ZKVh3lg3x6+/I7reNKrf491Zz3l2A162Ub6Xv0FnnzgTp78o4/zf299J5+On8pns2fx+ftCLr3vLtYFE2w+IWRgrshVX5vl/lsO8oxXncjA6KPT3KS4bh0vWLeOi3bt4itf/gb/NDDK369cw6KzIp6kSlSvOcDZTcWvbJ2gdMdhpGgoPXER5Y2LCZZWHncf/J8Tp+Y/N3W95niM2rQ7mxK2EqcumdcSM4mWEnuzbkMX195Ot6UvvlZlSTDJTDbCarWHQWYYiGosCqbIXANlIlTs5WqtqpPBZJYAzUBQZzIt+8RUCYuCKrtzgCVYlPJW11YUKItLHQ0cVdUgFEeU82pjboJ9pkqi/Sq2VgtZFUPGYDbLpO5hzE5gooyxYIJGptjJEIh6OPuQszlKHIUgo5kAxjKYTBNnBR7SPd62nYzetEEQhRhlSBoNEINW3ljASYqmyahMYQsBNRdRliYqqjLQs58JFBaFsR1wB8JiO0USRawMDzBT72uv2h8Zfaa2wD5bK9ChwcYGsq5V9JxJcuJ8uZJuufz586tdJwENZOH6u7T/76WPD6u9ymVshgxlEyI3i4pdu+HygqIoPMtglfKmJu1juPYRZ7LCAsDXnnkrcc7StkxL5a9HxktNK0mVoq0DUfvvCmmP+UhzCYcf96juuARqm7KscZDdNrdfd74H2mIzy2RdeytKA6IN0p6lP69aQWb9nlObYTyv0z5iLDGpCCZ3+isoLxVU4hhOpuiVOQ6p0Df0zXjYNV/o7SegTF4W6ChISr3rRh5yE4xZRSAFmkBTQpY0pwjULBDQWivJyMgkbl+b0HUMNJQIva5KyTgqukbLmNO1rmvXz16pITpiMim0ZZzdoVzGgJqjljNhRdckIeRAMMxy2YcymhRBum5oJ4qRcI7ABGzTS1jDHpLMUZcCCEwHg5TjSYwcUSMmwkg6SSlMiJIZGvzkfHMomkOnCZnTWGNQicOZBKymrJoogVQneT+tEFyG6IS0EaElxZBRZaECS+f3lT6KfgL/KcASkXHn3C7n3L8crQE9ZmLXDdz2mXdyeXIOo32jVO9YwdLj+7nwTU/gsnsO8o5Lb2fdaA+fed2ZDJSPDbhyztHYNsXs93YydWCeDx0nXHpmheG5WVbePM2Nk4ZnrBvht595PCcvOzYMy2M5isVxTjv1s+zZ8xkeePCvcdM38srxNzJ61s3cuPs6qtf9Deduv4WXl6/j1s//Bh/8zkbOfd3bOGn5qccuuR89CS76WyrP/GPefOelvOnOL3Ldg1N8OP1VbkhO4LYdimGZZ1X/Xsbnt3H/B27ihA1rOOsZT2Rk8QhKPfoYoGh8nJf+zlt43oMPcvkXLuFjQ8v41gkb6H3qIBNNzd/cdICn6YC3DJVY/KODVG/Yj1lcovykUcqnL0YVjgHz/Xj8t4Vz7txjPYb/zshcwtLmflRSbCdTFghU5pmRfFXetZNfjbExSoFRgjghkYBIfMKVGg8QxpIDSAAuDLz/QAse5ODBiWMwnKAk4gEWYEQvkNRUsjquEOAaigyFKEdVCwcKw6jE11K0QJRSljMHt0BgiSdYaFCg8jnZjIqrQQZGoBRmSGy9acMRdSxivNU6yn9eU5cwbGeoIZRcTIa3c9Y4crcLjNGQCJGKWRZNc0hG0Tohc3nSqjJc8RDT9cVUNPSaqpesWT/akBSrNWGWYluJPpbBdIY56c/zd4vuSj6LuklRxVSzAuT1QSJgIkOcBcyaHpApjqyJa4XDMy/DzVmK1lual/TDDRD8ti2B3MNDxJIpsDYlEC8y1KHQtL7xbZu5sBpRGUY0MZYgqpM1c3c70WgyMizOedApIgQ2JdERBpfLLiF0KeWsRlWXvATMKSQ3bihmzXaD584Au26HfAbloEpsC1iEfqr0unmmGMSFYDPTnqnWmT9H8RRDacqsK9BMI0wxIwi9pFTltuZYD/gR8sa8oCXvASeglKAViEtZ29iNDhqkhMzaMq0aSELtEZo/sQtlZvl3+ZJwgnoSoEWwtkJfsYZzCgkN5C57nrkVMAVSl9LjqszZJZRURqSEuih0zm1lOmcjQ912FG2fvbbM0BtIqByqame9nDhU3pWvtbnL3yTKfzZsy3TCN7QumxrWGoSmZ6qUkKoAI94QBVF4R3XVro9yOCI1z6pgjh5S5p1FKeuXJsQzWIFKF4Bn5XLzFoGmjiDpug2Uylm3DoPoX9c40rxO1FBUzXwureuhAM+qt9kpgboUcpltft/iiCVDeh+ZUO7niZ+WWXwNOA1ARC51zr3gZ92xiHwBeBowLCJ7gD9yzn38vzrQR1XcewV3ffGP+Zp9FgPFYdJta1hz2mKe8er1fOL6nbzn21s5e80QH3nF6fQcg5orZx2NuyeY/f5O4v01fjDY5K+eVGSyXGTs7t3MHDBsXruUN7/suMeB1SMMEcXy5a9iZOR87rv/PWzf8UEOHPgaT1j7Bwy98rvUpney+7Lf5rQHruL45DDf+vNtvP/UxZx11oVcuOpCxnsfQd3hI4lCL2x8DbLxNWyeP8Tmrd/i0D1f4+v3Z1wSb+LmdJybgT5psOSePVy27W5WFhOOW7mMFStWsGLFCsbGxtD60VPfVFi9mue/63c5f8sWvveJf+Gzq9Zx7SlnwFMXc/N8xvPunmTjUIE/XjvGyI55Zr75ILNX7KB06giVs5YQPEqZusfjp4eIPBvYALRdjZxzf3LsRvRfD+dSQpWgbYCvnVoATRCBvrgBRhEay2BSZ0DPIkGJoaDKndlK+qSKxdF0TVIl3e4JoFQujRJUoD2Ay7LcyW5hr61l0SxJV71KJavhIoVrKjJRIJpDpVFWyIG2qUIaNMjiIoJjpPkQzsE+8YBtMKhy2JZxCoyKybKQkmtisqw9N6OEctyk7vL5m6wtjxTl0GEKMd78O0/GbBaAQCgZTiyiQSvtWSExOBK0OLTKcJlPVQOXAhbrC0dwxuCsAuk4ybXqNoo0qear7aGL/evKghVMmFCg2hY7lXXsZXM69mCPjoQrDovsNcs53e4A4GA6zIpwv5dCpQth0rT0UVfCquyAP7HtxNOilcVl0KsbNCVgPq9109LhsURZ3/TZtpLzhS2RWzUxLYDlmRfFssoMxfoskwygRHyDWQ8TqZSaMAPltI4o3x+pXujDpYBzXa52DhHH/t4ljB3chlP+Hk5tI5ccghEhyxlUZT3TVNRN4jz31y5DCfQns5QLnoHM3QpQAlYpIuqkkoIroJVDa0FHYI1FNTNUtrAHU0sXabDERnK20x+vbOsoowklRWzney00R+gBEVTLu9yfaJzodu1RICnDQcIe5euY0vx+Cpz/jLXe54yDNMOKRpNSMJpEKyS/XplotPH/UMablDjbgXYlk0AWoPEtElI7w2I9SUoAkuFsmI+2ywK+BbDcEam/Ev85cJ3NMhSB9tRYVZfRzra1kUPJLIRQl5qXtqYQkCJi6VNVRisHUcQEzjJo5plL+shyOXOQN54+ZIZYxER+fE2iLBlZB5TkYw4DRxpDpBKWqhm0MlitGSgfJMUxnRVyHtfXsznxgLA3jElijUORqoCQBOtipPfoLaj+tCN1P9dX/zw7ds699OcfzmMgbvkUW7/5IS7l2ZTNIHrHCZx87jhnPG817/7G3XzpR7t59slj/M2vPZHIHP3ks3HfFNPfuI/0oSY7ZJr3H5dxw5qVlCdmWbJjlldtWMeLX7mcxb2P21n/d0YULeakDX/HkrFfY9u9/4/bbn8DgwObWXP8O1n5yq/DrhspfvkNvCzYyinbJvjIjof4x7Uf5sSRk7hg1QWcv+p8RkpH1969HZUR2PgaRja+hjdkCW/YfRO777iaH2w7zPcnh7k+PZF7ZBQVO0bvnGfx3Xcypn7IWBizYnw54+PjrFixgqVLlxKGx04K24rSaafxnFNO4ZxvfpPbPvhnXLrhVC4/5zziMxfxo2rKBdt3c+FQH3/4jPUU75ikesshqjceIFzVR885yyicMPC4fPAxFCLyEaAEnAv8M/BC4KZjOqhHENZmBCplUWEK50JmGMZluR23CE5DpTCFxD7ZimwHEBR1SqxSYufrpxzentjm/yjoABdmpI2EVFJEg7K52Ew5TJRC3EkLQmVJ3ZErvkLoYiwVQmXB+OQ+3w1J0MBK2gYX0OkD1Bs2uY1VrNU7GSBlX1wBmguswgGWMMVkqpjn4XKsI+tNHOCsIjDCqJ2igSIwBqccs8V+IlVHpr3UarBHs2eadjIseY1QlnsZ2rxgKFXaF+cr3wC2iFAjNwtpyTYF0I5INbE5vBJTBGm0lGn0qTqHzEDOJmjGhmqk8Rx6tjV+tdBl3A8KRMiUYdr1UpNpiiRM6QFgFlGGYpARhg1MrUmfEmYT3+dpJJhjMi7RUFF+rgCTkWUaUeJrs3KQ0WQVaVylZdghkUGVNKavhEwqTJYSiEFhSUmxIpQKET21FIk9+whAqYCq1o9wLYRyVGcK59kf6wkHrVzbAESpzuYt2/3W9UisBnzT4eFkkpquPKzuCRF07gi42uzlYDBKXZUWwsiH3TxeTinikDCAuE5dIgaoIs5hTKs+TeUgEUJdQBwMh3PMKsG6DujMJEUQrChK2hKpOaq9YzTiPkQaKNVqviv0JnOMO1//pEsFSCwmwTNs2lEJa8ybHog7CyoaiJQmVIqmbVctIkAxTGk2IlYn+1CiCVxMWWKCsEYGTCfDfh7iuj5fHfmgza0eldLoLPYgUQMqL7dSGlUQYqAuRbqNckQ7VJCB2Lz2DQo6w6+3GlaGs6hKxuEGlJImZZlgd9oPWUBgfQNs2/qO1aq9eFCKUpJGtzEKDEY1ms0MsVXyzgg4sfSYhMQ5ppud3SRiiEhZVpwhLs2g4hyQO0spbbCMKcYq53G04qcBLPcf/P7LF2kTLv8/3L/l37mE5xFKP4V963nKi9YxunERL/vnG7l11zRvOXcNv/OstUfdHCA5WGXiS7eT7kupNg7zicFDfPas08HBWQ3F723cwJNWDD6eOP6CY3DwyZz5pMvYs/dzbN/+IW666TksGXshq1e/neitN5Nd9Vesu/Zv+ct0iqvuPpkvBjHvm3gf7//R+zl3+bm8+qRXc8qiU47dddIBrDyb5SvP5lXPgVc152g8eANX37iVL941yl1ZLz/WFW6VZRSThGX3zTN0712s0NdS1pbR0VHGx8dZvtwDr56enmMyDVGKvosvZvOznsX6f/44r3r3W/nuk87msotewH0bBvhGavnOj+7lBYv6+cPfPgVz9xTzP9zHxKfuIhgt0/O0ZRSfsAjRj39eHgPxZOfcySJyu3Puj0Xkr4GvHOtB/VdjdNGJ3FrroyCHSDG0O3E6SIixOqOqyhRsnbLA0qDuK040qNDSMz9HQcUU8Q10HyoME0SGdbX9vj5FMpwoGoH2rEDszS4y5Qh0lkuAhEwcB0tLKc0cpLtUQgR6qeIyIdB5wu4gy0FJf2CYRLcrbFrPMgEiBUvLM4Sp9bVIyuUG8Y5AOqYJUTTPWOh4oDGcv+Ta+2jnZa5Tk+ScQpTC2IxUQagUDV1krjLEonS/P30CgwVhsDdhdtrLw4KwicoComKVRj2kbB0EARWjqMUwk5UZlKzLOsUzHa0ouJjRdLc37gCM0hhjUTbDJcrXXhUyJH+LiTQrF5VQDZ96OWnN6gjsoNpr8rnluUChjFRrPs1V3kDBiWVezzIkjrmsQKgyz142YSqqMGT8ea4TUcrrkpRyTMtilqg+nHuwA7AEIhMhhZCoJ2N4qkqkHMO9U+yYWwxKU4mKKBMg3cqF3Gbc4mWJXrLmMEFLHunB01a1ghPsLjQ2l2z5WBT75shGoBA45lOhloY43fSSN5UwF5boldjLQ3XgXaOzHDiEClXPUGGL3crr0VQGzuCUpS+r+44CziKi0MbRKtPaaRaz2E532J08stTgVKdvUlk3GLR1EhsTqFw22QIdoSEASpUmtb4CHBIWJZP02JhDjIFKUVgqIjSdQ7TGZYLW1i9SOEh0QNQv9EzU2WMjWnb7RrTH8kqROAUivrYNX3fZK45MFDVJUUGGMpYszSW8eFbzQLiOweI+kmr+aTIapxU2VMyZEuFs7hApLXzve3XpYgj1BplkWCX02ir7zDDCDGIsqEIuHYQgg+FKlYJxRNkKEg6194fOQA9AMs944xDzRYXL3U7R4MRgXIYJhOPDKVTcub2UOPpNDWlk2Laxisaj/B6oqtxpdYit5dM5e+4qtHhpZ73Yh3MKYz3AikLQP7P1xCOPn3akJ4rILP4JUMx/J/+3c871/kJH92iJqR3w5deyfe8OGWXeAAAgAElEQVRBviAvQmc99M2cxPlvPJW9RXj9h66l2kz5x5efxgVPGDuqQ0umajz40WsoTRZwaYMrsrt537kbme1dxeZikb87eSXLSo8bVxzNUCpkfPlrGBt9Htt3fJg9ez7DgYPfZNmyV7DiqW8mPPmFqM+/igunt3D8bYvYt+lt/HhVxiX3XcIPvv0DTh4+mVdteBXPXPFM1FHs2fATI+qhsP5ZnLf+WTzTOn787fu48vJd7ItiGj37uC0ucYNbyU3pOOujSdZO1dl/8EfccMMNAPT397fB1vLlyxkZObp1XKpUYtFbf4u+5z+fkfe9j+e8/fXct3ETl73idVw+VuYLKuaS6+/mvJ4Kf/GbT2Dgvlnm/n03k1/chv63nfQ8ZSnljYuRX6JG24/BaGW8NRFZAkwAq47heB5RjCrNw5LulnSnJesSENOgYJoY1STJy47EOEbDSUY5jLIQlBSVoRKZa5IlGanxTIsRQ7XveA7NlxmOd+UgSPmkvZTiiCETJFmFCWJEpTjbsXQei6YYCuc5XB8Brch6emjONlENhYuGUQS+niMfc1EFHgDpfCJ5j53RaI6mNEmcpi9/Lkz2DZChGZ1pEhSqqCBjWOZoOg2ivKRMvMzLAgf0EH3poTwZTQBN0YAtgypDwfXSOGSwxqERjrfz3GsN5aiO0SlhahnPDnJIj0MCrlRArCUtl2moMsO1w9DUzLsyPczTk9SpBVEb9AbKdpk1CLNBhZGkitaKpkQkXa58VhSFUtkn2Non725hdQ1ZEuK7BEGoQGnBKQ2mgIsiSLuenzkgLusmZd2krkvUwiIPpkuIdJOh3G59X7qKZYWdFLIaYSBEonGlYQoz29ifDbCIQ4AQqpByUCFSKT2FKSrlkEAVoWa8zbcCldvbo6AcKJIgbeXYzKgySjnEaES36p0yLBorXiI2EM9ilSKO+hmsNGCyffL8/ZErWr1LuMMWg7wnHLSNT3I6KwgdqpKR6DID2hFKjZJJmEsBcZgwxVpL5GoM12NcoOkNGlgVEoSKJPaSsgnTR699CBUaj2gzSOslKMeERiOJP2TZNala2/YayVD0pfOMFWbRDQXG1y9lVtFj6xgloA1iU1ApZR3RtI3250J0xmhYJYoTTACmYIjqNWw18h4lXWytUQGCxjhLqZBRsg1UFLFEN9hejbA28EVOR8T+YIi6LKJf9jFWnMXGmnlTIEsdymjsQJk4q5E0Y6yy7Tq1BSG+OXTgUqwuYJSCqBesr9XDKmyq6Q9qoMOc7coXVrQlrvVQicqsMLsJXEyIofWM65bjrogPMtpbYAJDVk1J6iUYgKxQIKh3FjZQCoq9kGlUoYBtgAnLnBdZBqen24s6abHCrC7h5huEktKnG8hR5Ir+U4DlnPvlziqyFG78CFz55zzolvF59WIkKTASn8oFbzudT929l49ds501I94p8ITRo7Na75zj9q17mPjkv3FcupSSKXD37O38xTnr2DZ6LieUIj61djlPHqgclfE8Hj85gqCftce/i2VLX8727R9i166Ps3fv51i29JWMv/Ey4mv+mdXXvZ9lP/4jwrufwYtf+2mumr+JT9/9af73v/9v1g6s5S2nvIWnLX/ao4J5VEo47dlrGX/iEr73ybuY2FvgwpP6GDvhIN/fup2v7+/nq1PLGaKXi/u3c8Z4P7P0sX37du644w4ACoVCu4ZrxYoVjI6OHpU6rnDZUpZ94O+o3nAjhb/4C9a+7Q28bfNT+OYr38gnIsPlNPn2TVs5zYS865VrOeVgzPzVe5j++gPMfn8Xlc1LqWwae9wQ49EZl4lIP/A+YAs+P/vYsR3SI4igRJGApm6QZSE42KdHGMkOEgq+5gNBhY5yKSGjn7RaJOodwtV30h/NoVNLNtCDnjc4pakMlrGzjsR0WCWHMBcOM1nu45zmdcgSi5lTpHmSa9OIvvIamLkPEZg0vajgEEjCoeIgfXYe8ElwkgzgMsO+XsOa3l727F/CKep6QAiiiD5doVatUzQBlWIG8/lUxRKaOojQr0JmWw5tXY+7UGmKKqYcCARFAlKiqmJRNMEWfSJTlOlTuxGTEbgaoUoYKQRMFIa8FM0YbBDQKn4p64DxwiRpkJGKJiRvJqsErTQDpQGqtUlQAaODSwmbhwjCgBkG6UnmsVaTxUVUJGgReqOMxDkypdBaoSNpsyP79BizpkRTAgzeZEEbQ1pwpNp6f+l2h1QoqmauloqxymG0I8w0TvQCduVAYZiTGttAZ7i8XkiMRfcqZLK1O2mfx6Iuc6C0gpVz96CUQSGkphfTW+Rwo4+RbD+mUMkZToWKCgyp1LNAGPqjmPlmmXOjIZpZnQP5OHqNZeVgie2Hp3kwHsTYBJSihM3nJWixIBpt8w5RJkWhSLXCFA1ZqHFp7kSYW4vb3F2RosGFhmpzMX3s8vNUEOiAUAsFI6QaiPpRKqBP5fdkvjBptJf92TCERgJGMdAT0xgZor43a5+nKdNLpBTHySy2FOAamiyMcMYSmgBNAAYUGhJLKAbBMSsVBmyVFfEhiEr+FlOKzGY0673IEYr5ZlBiTzTA3ZUnMD55F/3qEEorhsIms7k0VAJFq8Sr9TFYXpxhVzyMMZpSWmMorVMsKQq2SWgzflIMmHlioGEK1EtNKo0MrKCU5PmEY39pCYtkGrRGJKNmNHf3rkGCIn2T0xRNiuvCNahuoaCPVqNn/7t3GPTSY7pWhPASxMgvdIBD8vu55SYpAmFZU65UmHJNMhq4nMXrZkydCSAKcOLIxKCVpnWosaWrMBMRUuh8VoYH6szVYgbNnJ+3+wn9Ln5B8Xi28B/Fjuvgit+H/T/mrtEXcunBFUhSYFW4iVUvPoHXff02th6Y4xWbxnnXhSdSPArNTO89OMd3v38rpW98i6dWjmdo+AQms/3806aQb448lVAJf7JqlNcsXUTwKOtf9MscpdJKNmz4a1aufDPbd3yInbs+yp69n2FsxQtZfsIluH/9v5w1fwX3f2ALJ5z5Tr560aV8f9+V/MNt/8Bbr3wrp46cyu+e8btsGN5wrKcCwPCyCi/6vTO47Qe7ufnyHezeWuKp513Eb716CTffeSufuG6GTxw+hc9OJ1xsrucNx80y/JRz2GWOY+eefezcuZNt27YBEIZhu4Zr9erVjI2N/UIZrvKmM1n1lUuZvuQSHvq7D3Dxm17Jq17yYq589kt43+5Zbik3ef6dDzLihDedP8rL7Djx1fuY/c4O5q7aQ+XJY1TOXoouH/uedo+HD+fcn+a/XioilwEF59zMsRzTI4q+pRTKvbiaw6iMwDp6y5Zd2VKOk2mUC0ACVhX3e5c8q3DVXkz/IElWw9Yfats1L6vMUDrOgS5SnusjmfEJaNEUPEugIAsiSuVBRvscc7UmEzkfE1QCevsHmZ4OgNjXTGgvXavriD4aIBqbDdOMQdsahciiTYHjo3n2xytIS5Y1TEBYhmoNJcJI2MMkM6RpgUDH7RwsVIYSAUsL/WT15Th1B6iIfjO7oAeYaMVYbQYpeTMLEs8EDRYS5urQY+oUlKLl9RbPzpHpIl0G5QRa4ZQlNhFh6hkFU3JoqymWI5puyNdgGZ8ilQrCQKGMmmyPop39DmE5XDAIGScM1tiZeZQYhUJfUKMaaGaDXsrMQmByyZRCGYVyAUrKtLLY0eIcldl9lJN5bjNrGSoYXNPRZ5rUlMUF3gShV5oUwgZ7wkHWVL0lvBR7oacXM2VZpGeZkWIOpKFShAllUMU+JEgh8R3UarqCVX6fo4uKlIOm7/2lowWdrRf1NBjvH4CeIQ47fz/8f/bePFqSqzrz/Z1zYo6c8968eeepbs2DqlRSSSokhAQSBoyZbIwxHmgvMM9Du93Pq9frZ3rZ3au73W6/Nm7ANvIIuAHbGGwwYCRLDEISEpprVqnmuvOY8xAZcd4fkXWrShIgQIipvrVi3ZsZkSdOnJj2Pvvb304bLYbdCobsxbX7UVojJBSCFSQ+IQotBb1WmZr2cXQQ0/uIEEQkEybYHSLRjPmBUYTQIaGEMIpLTXeEYtnNQEdyxhvGjlqIegfHcJh2x9jSnqVDbNR7hkUrAlPm8YwWq1ED70Js0ZBoQ9IQNsqQ+LZgqXsCLxRPjkwHIatoJdFmTJcL2j6KIlqeAqkJuvXPTClJWgZHzEFmhGLCnovrka3nOGmi0EXrJpNemRNlh0hKQCMtDcrijL+JDnWK2oQQVNdRkg6IqkCE8e3WUB5OV4fdlBEDThnXcPH8NL6foDVz7DkfI1p2SBkVZoRFSpY55Y0w1D5D+6IOEG3DIVQGtkqTQ6OFoK0sTNfm5imJOauo1i61JS86WFHkoqhyIfoqEQhToKNYoCTslmuIxAW1S3Exd5GYxm9Khewqo+p4eNB+HtFsAKV1JRbTtOJcSyW7zyAouRmcagMEnDOKtN0cI6YN67Xa4minbQp60y1kIAmVfUkh5O8+rjhYlyKK4MQ9cO8fwNkHwC/w4K7/yeeemMFoJ5js28+Tgy7v/j8PU0ja/PnP7eXlW/u+a93RWvPUfJXPH5rj4S89yg33f4rbvCLOplcTCc2X9zn8r75tnG8FvKmQ4d2TA/TZVwy/71f4/iTbt72HsbFf4eyZO5ie/ijn9YfpfcWtjJ27nvGHP0rwxG/x8Fc/xPhr380nXvMPfPrUP/Pex97LWz7zFn5iw0/wb/f8W3rcnm++s+8ylCnZc/soG68tcv8nnubhz57myXvOsfOWYf7kXXuZrjX567se5uOH9vPxY4JXHX+IX3X/kJ/YsRde+zOUczs4c+bM+nL33Xdz99134/s+U1NTTE1NMTk5ieO88GIswjDIvuUtpH7sx1h87/tY/djH2POP/8Tnf+5tHLv19fznp5Y4aIT87pk5/kcEb7k2y6/fMoR17wyVe85RvXcaf18/yZsGUakr9NvvFYQQ1wDntNZz3c8/B7wROCOE+B2t9co3bOD7GI6fJmq7yFAw6tRp2hY6aSGbClGRhEZ8X8Qi2hFGUiNMYodHCDrKxVIWa84WxIXE/S7N1VYW2WwviXYKWQEv5ZDLFzBFd4ZXKKLIxTQkiYSk7Bh0In9dHEF3KVrl9BCBtCgHKXrNCpFOo/wSMjeCSLVoLheQ4gSZRIqFTgJhlNePT69bVMQ0u27fPGkjHQ/RTlEVMOqtkrIblFvdnKSuMkKUsFGqEx9zAGYyjZEyoVHhgmqEFl21RKGQSnbrfQ0gIhMp1vBtg+olsmlCgmu5sR1o9OCaazQuFOWVGsOy4tpGUiKMC4qjgpybhS4Vz9i0B+PYV1FS41hgyxYbMy00NoMpRTvpkM3kKFsKwzSxbYnR8Gk3bZS7jGVEeCLEFLA9sciUayIrIciAFbfDKcZZqjoMiDIVO0kQtFAIIjRGIkFjdBTOnmbAXCFQ+fXxNpRkyM4w5CwTmbPIVnW9NlMris3ARNLHCkoxVc8xCC/k1iQ92uUOUmRAKFJGRMOokbGI89ikD6JNIRFhGQKzbnQLCHeV6GSHnFmNIxiOD+244XxvkuVyg5a0sKM2fjpEdDUhLpRJDs0kDTNWkdQizqvbmqnT0B2ayuuKAgoMYeAaRRrNJp5VREQRtWiNfFSLI74yCVQ5bQ2zjWXMIEDaNqJuIGwTqRSG79IUdUSjhFJmLIKhBUKZeF4a7BrdslTI9Ciq3kG7NroFhiuh1h3rVDIWhjFddMJH6LVuLpJASIGVtqAdR3SkErS7an8Ny1t3XlRXzMaQgkWnh7TVpryaoM+uQBDnXuVzOZRhEpnPMOOFBMNCGgpRj8cxrds4OsA2Q0KT9ZxCS2rayiItDXwDJA1sZZGwkowXU3Sqyzy9epK27yCq8STAmLfKqtFL1qyQaFSRhJw3BkiGFQrhUuyY1mtkBrKszC/RDmqYdnBRthJYs3PoSGLI+L4TCvrc+PmgtcYzPFakg9BxKQlhmASuBYamlfBp5sepiTpNlWG5k2YlcBj0h7nq6imOV3rpLM4ikEhLIXRI00mTtusxxZUXD1ccrHYdph+BI5+Ol8oMpIbo3P77fHamj0efeBzZzFMfuZbfXypRmlviF28Y5zdv20jCfuGHr92JeOL8GncdnufOQ3MEp0/z1mN38R/rZdzdb0MlB5jZmuAPtyX4QrnGFkPxya2jXJ+5Qgf8QUHCn2Lr1v/J5ORvcf78hzk//REWvTWyL9nChiMl9i8/ztxnfp5/+YfdDL70bXz0xr/io7Of5MOHP8ydp+/knbveydu2vA1Tfe+d6UTW5rZ/s409t4/w8GdO8/BnT/PYXWeZuKqXd9ywi994rc9f3neSD94n+UztOl7x8OP8+qO/wo68Zseun2HH/p+G17yGWq3G008/zfHjxzl69CiPP/44Sik2bNjA9u3b2bRp0wuuUKgyGYrv/m2yb/0ZFt/7Xpb/9AMUPvJRPvr2t7N820/wX56Y4wtBk7+Sq3xwfoWXTLi8+8atDD64RPX+aaoPzODv7SNx4xBmj/vNd3gFLzQ+ALwcQAhxE/B7wK8BVwF3EKsJ/mBCE+c5hPFMrG1YyHQN0TWMVswsyncp5kY4d37hkh9KWl4fbmMZx3AYTG3mBGfiJlUaYVRBg5dMkZHDyEoFlEAZEmGmwctBq7Tu/IyMmcxPg65ZXKi6pRFg+YSWzYncZvxVcH0DkUig8oN4iTTSr6MbkpTvk/AcFsrgeu66RPVF3UNwhGI4V6DsD2OObKW5ugreNlTlQTp0kE6WRjvEbTdj6k/Yjvt3mSqEgeNPAE93CyTL2BmLNEpJhJCY3ehbIpVndbkfrQNCmkAdrASm0Jimie/59A1vZbZ5jJTdhzzjIiijEZi+i6HbCH0hRy4WsqCrgtfJDqJFVzVRCExnBciTyXs4YoUASCYTlNN5GnNxRC1lRhBGON1onkDgmD69XhK/k2VaJNGWIlQmQhlE0iIIMqCm4z60U2CUCAw3Nq51LBiSMGJ6aSdwEa7CsPKIzhJ5d5la0KHRVZgjNkVJOQ7tUBMaDoal6GiLMEphpoeRsg51A6kU2rDJuBZJy6RjgKF8ECukPPCdMotND6KIRBiSahq0W0kcVSeyTZTsAWbiU9Z18JQhWbUKbBtcoF3OoRqaQChsDbmUyXRMIENamqH+Cfz5J8iZbfzeCuJ0fMjLI3sYWG1hqi1Y0iRhtzjZSkK56/UIyWJqijC0SFgJ2sol4QRUEzZYHoZdwk5JytkBxIkKRTNEtCRRx8Y2FJ6haFySKydVBsNaxVQGgd2JaXJSISIDnEFMNYPRpYzG0dcLMvcOylLQFmCnsMIIN3RYsicouQ2cIHZiOmEaIUoIw0KHGRJeia35JJ2FtXX6aehnwTAws32wEv8uFtzwIYhdNcsQWIZEWjaOBCtU1LvPENNUWA6EymQ+MciAOIqhyph6GU9JkFlE93oKpYEyBEIbmCokkY1othIkGmCoOmEnSztwCds20gZhOQghUN1okmnEeVpVo4NlVImsAUQLbNskoolnB9iqgxQmOtLYhs2amSErAhxlY1gWbcASCumk8dK9VMtnCAyHcuEG2semKfh5MukUhq/oLMaKq8r3cUdc6sfLlJ1exo219dIOLwZ+dByshSPw2N/EaoCdJjRL8XcrJ+LaCoYDk7fCtv9MaehlfOQj/8D5xSc529rIYbeH5bNL3LSxl//wyk1sG0i/IF3SWrNQaXFopsTB6TJfO73Cw6dXaQQhI/Ulfm36y2w7/iTO9jdgjeynlLX465f28JFmFa/W4L9sGOQXB3viRMor+IGDbReYnPz3jI29i/mFzzI7+wm+tvWr9C0mmTrZ5LXuvZx95Anu/vQ4mfRm3r3hp3ikc4S/+9yfcNeDn+DtV7+Dl0zejO35yO9xPaqeoSSvfOcOlqerHPzyNMe/Ns/xr83jpix2bcryl7fu4J5ShY88ZvDjzat4WfkMv3bPX7Lni/8Nxm7Ev+pn2LXltezatYswDDl//jxHjhzh0KFDHDt2DNM02bRpE9u3b2fDhg0Yxgv36LInJhj6wz+k+c53svhH/5vF97wH9aEP8Z6fexvRa9/IB55a5W+WVvlyHl5x6hyjWcGvvnGUV59pUXt4ntqDc9gbsyRuGMDZmO0qgF3BiwB1SZTqzcAdWut/IKYKPv497Nd3jITnxEnzXdUw03IRxup6ToMW0E6kcSyXC17L4sAu8u0zZMOzpCl3i6u6pJ00pWYJbeYx02u4Mp4MEMBUqkrNM1kv1yhNanZyncYjlYnWmmy7RVSxMbKC9iX5oDs3FqgdnkcIgT8xwHi6HyptLhiiZsJYpwAKKbFUfN8qO7VO2XNTPqY0SfQN0Un3QrUFtoetTJSQWJaLVk0wg4sUo8ggCuMQSrs9BOkWyYLHwky8TSqTRBoWOgxRSpH1HRqdWFLbsBXKAYRJ5A1BM6ZNhmEe16ohpWTTwFVkGxYHmgkMZSIv0OW6NrYggdaCKLIxVAOl4opZnm3iFNOI+iKu764n0kxM7qF88jyyW/x1qTjJ8bMt+poVhJBYOuiOERj5JJYMMKWJ6N9J2jjL+foa0oiwDBupXMJQobwkrYaHJRpYyuZsfhzD7CWRXcRba7JiOdAWcdTIy6OFwao/zoi1SDVOFkJKTdEqkYvqJB3B8sQryXZOQ+VwfLzd+lpG0iNqxqTLxdRmmg2PwPNJiFkKEYh0Hx1RQos6dAvl9ugaK4FCKA+odwfv4qSg7Ip/CHExuko6w9naOKmV0/E5cbIQzqIjST6Zxk8nIVY6x5C96205g4OwehJLdtuX+rKctabyWXD70dVlTGmCciimKkzX4w74SbBzESgLu8dD1mooywBpMZB2EZZNo1Zhwekn2ZhBI5hKFzgWbWGhcQABLJrXIFghcqawxCymEeeRtayAwHaIpTgv3DsC7DRGahRjLlin9ErHItfJYiRcomoJISUiGABRRimF21uktNpB2CbtvikM20H5OYzFA1ideZTp4Zoup60Mg7U5kn6E5Ta5kG22kCwyoiShNkCA5ZqU2k2M7Vtwzq8QLqxgEeKJkMjyEEIQdeJobcGv46QEy2SohQUUyyBilb8L0alalMWLAnqnbqajVhDzX42jjFIhIogMB20FGKkcelEgpSSKBHmvSSfwMYwOWkd0nBRZewXLsElYNtl8kvOLIZ5lUDOci8OoJVbWxkirdYn9Cw8cJWJl0QuiLJ31+n5XHKwXHmvn4OG/AsOOnSnLh95NsP2NUNwBEzejLZ9DBw/x1+/9MIdbGZ6O9tBGcE1fgvfftonrJvLfdDcX8MiZFY7NVQmjiDDSNIKIcjOg1AhYKLeYXmswvVqn3LxILt9cTPL2CZObH/wXEvfejTm2H+fV/4OmNPnIjXnu8Do0mlV+bqCH3xzro9f63kcwruA7h1IeA/1vYqD/TTQa51lcvJNDk58nefhexs5V+NnRJ1hKHedQ0MvkSpLBlRStxyOevPMOnuQOAEzHxUul8FIZ3HSaZK6H/PAIPcOjFCenMO0Xp+5ZfjDBS9+yif1v2sCpJ5Y49cQS54+ucPxr8ySBX7JtjmQd7m2O84bwd9ntt3jH+c9z88n/gGP934jtr0Nd9TOMjtzA6Ogot912G2fPnuXAgQMcPnyYgwcP4jgOW7duZefOnYyMjLxgOVvO5s0M/8kf03jiCRbf/34W3/NHiDv+jHf85E/yW299K3fVTP6/4zMcs+G3yiu82wh41Q1pfqNtIQ+vsvzXh1B5h8R1/XhXFVDJ731NsB9yKCGEobXuALcC77hk3Q/0u802FNqQlEigZJZCcpRFP8DOhIhanOtxQQ0r0oKKnSe0E6SL+5mZPY/QxI6+lIylxnmi+TgLQ3vIn5lBCgPbGoSOwFERxXQbEbFud5i5SdJL54iUDUKy4g1SqQX4jSbC8pFUQEgMaWLZKRoitngN3yPv2pQqc9AVOQg7U3gpg2TYosc9jh95JDyPVmSgxQrSdjCyWfzkTkxvnLVnjIPj2pR6pgjXDl/yrcCTJuVmio6dQRgOleQUItWPxkDQwZFJcukhqrVVTEMisQmjRcAgUg4q5WGmfKp1E92IE/y9Vmvd/resDE7bwehGlKTQKB2uO4sSidYWEOJ7m1Aso6XGsQuAwEpa2I4F9diR6UsN4/pFli0LQ7kMJvqB08yaRfrCDBnzKJGQKEcRBCIuKiYEwrLxBn28qqLZ0XhGAiEFfsJEmA69JoyIJEu1gKSdou4UMPL9pAo5JtoLdBYDVjtJcNMYXjPOvRICXIXOmUhzmJ7lp8lEDUAwPLyPo+fOEgJm2of2xch8RxmX3VRap0DOIewBGtkWa4GDTZWCX0fICCeycBMuHQpQL+OYHkqYBJ0kUnRIOr0E4jhzWl0UThCCybTLwopAGAaRYRN7BwopL0wiGphyBCWGLnZGXm4LeckEyDzVSMMS2D17GW89hWY1Pp/d7VJpiRUpfLMNwkQ7vUTGLFhxrlFHWfQOJjDVVVTnvoxuX9yPJc1uDp2KC/OKHtp9aXKex6o9inQkltnG0LN4SYNGTa9X6LqgimilPJgrX7z5XBdZayJdA90A27DIqIs09JyXp6MEKlSoC+90IVCGQSo5QG9qglKfT3/QpiDT0DgC6zlQmrbpwPA+Rme+gKMiThALgQvTpJXspV06f+EWA2Ui3CTl9BYMq4Wr1nC9kOL2a3hySZKaDREVgTQtWtNFXH2KBbuIyE2wZ+waErlx0mcOEugqui4ROkTZJspPoZWJsGxksAoRNE0XM3QQosZqcTvtToe806HariNlgJ/sJdU3hjRd7PwwAMq1CWtG10NfT82KLwclSNlJWhdSDIRcZyjaa6d4sfAD/RL6lrDxNvh/Z55zVRBG3HvwNB+68xEeXxGs6Y0o4NU7+vnFG8fZPZL9lnf36Sdm+ev7T1/2nakEadck79sMZl2uHs0w2Ztg20CaqahE4y//nNKf/RMqN4b/ut8jDFPcuT3J+0YMZul55FoAACAASURBVDptbs+m+O2JAab8K0WCf1jhukOMjLydkZG3E1xVpjz/JXj4L0gfuZ+Xts6wN6GYn7CZ67UpWynmyiHlqkEiHKInLBKsKipLi0wfOUSrHtMjlGHQP7WZsauuZuN1+8kWB77rx2GYiqm9fUzt7UNrzcpMjfnTZZanq4ycr3LVvOT+Zp2vRfAu+VqGOq/jxhLsvHuOzBe+RMr/HOnxCVI7ryM7Mc6rX/0aXvWqV3Hy5EkOHDjAgQMHePTRR0mn0+zYsYOdO3dSKLwwhZrdXbsYueMOmseOsfwXf8HK3/wNKx/6ELtuuIFP/fSbaVxzPf/1yCyfDqp8wgz5ZFRmYCDi38kk+1dDws+covS5UzhTWbzdBZxNOaT7o/OofRHxUeBLQoglYqn2ewGEEBuAH1iRi04QYOPTBFb9PEoMkBcmOGkitUTGzsaFZoWJ6w6zlkizIl12pEYwyi2icANh2ERIG40gmdiEXj5OZLosFcfJzp/HcYuYtQymPQtC0Mn0Y6zO4vgpMu51jGXbDGQAIalaeWqqTloEoGy0bRG1Hfq8IVa7fR5JDmN6WaBCN8QUrxASYdjsHknRWDhNLcqg0kNQOkMmnSRMrCCsPDI5iGP2cCGXCWBw388ys3oArSWhYyAlpHKTWJV5WpZLPWixOWvj5+oEV08QFK9GRwqhOgihKGZeQkN/FVldwPR9dLNGNTGKym7FKE/HUuJSEYY9QIRnxPLocbctentv45raKc61m3hdIfIoigikQYMUdOW2DdPGUQaRUPh2DgBNoquSFoewZGoAx3Dp6d+OlA69TmzYamEQ9nucWdtCRpZJitWL2f50aXTdYsoXIzKX67iZhU2480kMcxeIGpjDZLM3k3K/SLV+hJA0iwh2bNtIsidPcOAM0jMp9hRYapyNqWpmbOMYRhLlbabqPYhpaqzURbaOOzBM79gEtdYpVpc8bCeLV9mA56epDqQQqwsMBwHnnA7F1jyeM4Kf7mehE587M5jilF8grHyJVFRmT6aHR5Z8zgvNiB87cqoT4Bguo4lFpGXRm3VZmOMyKEaQWBcV6gCkSd/EBuZPPg1AKj+Grs2xlihwtNbD5sxu0muHMPrTZCzFShiAsEi6bfbml5BNh8jeCv4wQRFWGi1KUYbpSgrbNHGtHnJ+DjuSyFJ8XbcSo4iSAWiUZZIvDFHK18imU8jRHpY7mt7OPNRgQ04gXQi8BBvcJF+rC3S3TpWQAh11z7fnkS06WNMOLRMc28RIdFOmhMQwTCxlUnc3cMEq1UJiWDZhu4Pl5EFF+MrENQOCBgxYaczUBOfVWWSpBNLAURGmZRFqjdYOQsBqYSOt8jRem3WJ9WB8N7WF2Olatm0GjVUGijeT7rOZLVWpS4HjJfDNTkx79HJooTCK2xFS0R5+M4nTn6AdrOIm2qSTKXxLsKAFrqWhDqaQaEK0tgjMiEwqTXttjb6JGymuLdOOjtAZ30M7cDFEH0IvoNGYuSTW8DhiMe7rhathtbCZzsoZcpkEK/luAEMIpNGECFSnzouFH4m3fjMIOTxbJuhEtMOIejvk/GqDM0tVDpxZ5OBcnUALwGWQDm/dNcwvvGYTvclvP4H93718I++6eRIlBYYU2IbCMeWz5LaD6WmW/vQ9zH3yk0gvR+oN/4mo088XB2z+YrvH4ajDTsfkvRtG2Z/93hRtvYLvDUwzRX7ox2Hox+E1LaInP4bz2AcZP/MoE2fqtBIdVjMui36Zur9G3T1CtEHQY2RJ+BuwzZ2E9Tyrpzuce3yar3z0g3zlox+kd3Scjfv2s2n/TS+KsyWEID+YID94eZ7gv2mHLMzV+OiDZ/k/B6f5aKvDA+YgLw36Ka4KohUTHpkH5jHNiMJYmuJkjt2TN3LLS2/j7PRJnnzySe677z6+8pWvUCwW2blzJ9u3byeV+s5L9DmbNjH4+79P4Td/k7W//zhrH/8407/26xi9vfz2G9/Af3/Na/iEleYPT84xnTD5rVaIalS5Ohny9kSCnecrNI+tghTYYymcLTns8TRmf+JKAeMXAFrr/yqEuBvoB+7Uep1cL4lzsX4g0W7UcZVLO7eZ5PAw+XP+enmAUrbIiJPAMxMUggDL6mEknSerPLb3bGd66TA97iBrWQdjYYmGlSaR2IR2TwCQc/NkvCZGupcNk3s4+vhjAHTyo8jaGqbbg5LpWN5cGTFnrUvL0wiEiqlXSXUNrhwikx7gzFCdqza+DNMLWVm5v5t7dIGuE4tMAETbX0en9BiZ5CBhpYzRKVE2ywjZfc+a3mXjoAavJ5NxaJx6lEYmSaUZYSQHMGtLJBJpomqNXM8kpcosQsTS3cr2QLcxhENmeBxWvxqLKxgGdn+eVmIULc2L1pihAMloejwe+6g7uy0tlHLoSW2hleqnETZYJc+a1UtgBjTVbtLBfaSMCKUMDKGxbAsdBWgR52bZwgGqsSNgujQ3XAeA644SBHGsLtIuyBqRULSVxXy2j9ScxHSMmN6kDGSYJmUVWDY0eQFPrwmcS0wTY+vt6PAp/GwvZdHAyk6RL/aRyN9OUKnROd1iEUF/op9sZoCne8dgYR51ISIkbaTlcsGpG0mNcXT4KhabFfrmL85TGPke8oPDTJ9UZPt8LGGzZXQiPs0CjFyB1EqAlmfQ9gCRMpGpJFu2jnP0yy6uV6AmTdpY5M12LPpgJcn1mmwdNKis0Y3KCoQNvYkmYxO3crReh1qAbVmYpkn/0AiGZVKXPhdOpMbAMC8yBqQ0CTrDWOYpbCcXq20C0jMwsDCikMgaQLZOo7w02vKQ6VEiHRF522l4kElrRirgWQ201qStNKbpEOokwjBoJcfINDtMV7PgZ0gl82we3kHWzfBV6wx0wBgbxpo7iSlMarkibt8gCbcrpR8HKQmsEIII13QZL2xGTB+l3+9nsTSL5TYZ3X0NJx9aoZlRMU0wmcMZuxo4x4XBn+yBdr6PxOB+Fhe/AmiUsgjcDGZqkHyuSMLwKHcCQGAYJk4iiQh20O6s4ohuVFyIeJy77CilLroIMjNJ/42vxHGKOEAwMk651otOF1g40wKrgL9jF2GjuS6T3z++h4WTDyOzLURTIkUSS7Uh0OT8FiNRSNSJMPwC1XaEld7F8PDLGBrS6CikJO/ET6S70xQGlhwHxgn1KsgjaJl8FuGv6ecpqWvI20029I5SblWoitr6tISWLx6z5EfCwZorNXnDH9//rO9NQlKiyZSsM9w2uGl0ip946y4S2e88QpT2TNJ8fQpf6+RJlv/szyl9+tNIO0nqdf+Rjh7mX3sUf7XN56iKGLcl7xsb4Q19WeT3QR2kK/gewrCRe34e9vw8lKbhyKewT32Z4un7KJ7vqu8AJUPSNEvgzCCMLxKJiF4BUxMmalOGIHCprs6wdt89PPGvJm6uSGHDFvp2XI83uBlSg3Gi+4twvRmWYmAkxb8f2c6vvG4Lf//Ief70iyf44FqDsQmPN2xM8LL6Y6jjj7K4lmT+9GYee3qUqJuAny16DE3tZcctN1DqzHD0+GHuvPNO7rzzTiYmJti5cyebN2/+jpUIzWKR3l/7VXre9ctUv/xlVv/2b1n+wB0s/+kH2D+1gdtvfyVP3nwr728pHrAVj0Sax2fqUK1yrSH4yWySq5bqeJ+JjRVhKazRJPZYGms4idnvX6ETfpvQWn/1Ob576nvRlxcKrVoVpSNwPHRqE9ntTaQpmV45S9vxkdkJ7LU1jFaEEJK+iU0MposAFDdsJF3oI5HLU15aJGjFUZZer5fF+iJb+m+llnwKii/DqNdx1V5sy8dyNO3Rq6A1DOfLuFteDnIFhMTfMETQOkWPm0UlZinYg1RKccRhS34LW/JbANA6xHEGqKpl/PQgdmceJGgnjmx5qc2ozDhrqw+RSKWRy5J5K0nPyCsg2Q+5CbLBII3FwzSb8Sy67XadLiEouxmyUhKYCUaKIBI3smLmoDILQM7JsbLl5WStFIY0IDOCYVqEpkMYRrTyg1jahRCqfj+uapO38yTKZbL9g6zOTq+fA3GJYenueytrJw7jrvnM+yHFZkhvU7FmaLJmiGHb7O4PMJMZfH+Kjt8P1EjLPoqWpOVkQAjS6T0IaeDYRcrlJ/AMl7ZwWZefA0Jp4A4XccsGfX37SeZ7KC2G9Dg3cMO+65ifuZ8eawnL8JipHyUiwu6fZLA4RbP0NKyCP6joHUxC5OMmB9mUnyZlXMzRdfwEJeYpFEcQJx/CMC0s2ySK4jwwz+ljMDHIQmeOSwPBne6Y9G+c4OyxGYR0YPOrIerA9L1YygI0WsSVeiMdF63NKJ8dWzdyohxhJ4tES01cHUJ6iPktLrLZIjuyk8q9v4uUHTIJn5lWCjtlY2c2xvshoLe3l3yxSNIxIKgzOLqLxZk+0EsIKwmN5YvnT4h1URbbcFCWhJGrkFYN5h8n72YpNdpolWZ77w4cbyO+P4HWmrXWGpayeGj2IfqzgDWOCFu0vRqdoISBItIRXjLNzmiNsBPh9hbZumkrjuWgtSZCYxd7qGXTpFaHcI0IM9WDWRiMoyliASnjgrxNPyBsSvqtDCkvi1YGWwcyHFmLM6ecsasR55ZBPInlFHCTLVrWpaJKAt+CYn4CuWkfLN4PRDQK+6g0IDuygeLIJlYXzlAVEincbi6hZjAxhGcnqMiYluqbPknDpbenp9uywOpN014sMZ4ep+gX1/fq5RI42QHs5Aae2FjCySQxEi5Gwl0PJGSK/WRe9loeOX0PpZLNSLOJbTaxs2WStsdoazML5w7R0ZptU9cixm7AcS5O+nr7rqHTGGWJButRcUCJLH72epJOiqfn17p9jXHz8M0cPSswxBJJM0nSTHJanr44XPLFy1f/kXCw+lIOv7wl5NTTx5FCY0ko+DZezUOvpuhJTfHSX9jM6Lbnn2P17aJx8BDLd9xB5a67UPlRUq//T1REP3/Tb/D3Uy7nlWbCNXnvWB+vL2SvCFhcwbORHoTr3hUvUQiLx2DpGGLpOGrhIOX5J+lUZrCjkJQ08IXE1CEinENEHVQEpLoLp+DMA3DmL9eb18pG5CehbzsUt8d/B3bHjtd3CY6peNt1o7x57zD//OQMH3voHP/rgQX+SA5x6+Y9vGG0wY+vfgLj6B+wWE4zF2xlpnkDx786Svve+IGZ6tnO1WNX0bTmOL90kn/8x3/EMAw2bdrEzp07mZyc/I7EMYRhkLzlFpK33EIwv0Dlzjspf/5fWH7/+xl83/v4g8lJzt7+Kj62cy+fG07QHvI50oHfOV2hdrpCvxC8vjfNTZ7D8FqL1r+eWafey4SJ2e93lwRmwcPocZH2j3at9x9FyLWTJCmz0s2xsJ5BL00mkxhKYUexQZkb37puNCjDIJGL32OpnosiAHv79hLpCCUVycRmIJ5DEcLAsBxEV7c501cklRnHCxZhtgpColwbZSkGencxmJ1A5Hdx4oHH6Bsdu6xfQigymb3QGmJt/lGEinOzot4tkEsg3CwOIKSJabsg6+zdcAv++E3rbdh2L6bK06RrLMuL89N2IcvI0Ovwt0eYpx9maHgvPZkRzp1uriuqbkh283K6n6VStC2futNDKdfLUNmBULNt21uwUj7JlbM0lcJJ5boO1oVcoItjnugbRpybgQi0PYGV03inIppOgYQxD8rELIwjDR/TTBPkb4CKQAkXu7WGbadBa1z3kpwhoK9vBM/dhp8+TPXRMzTrWcIwBEvSN7qRvh37MS2b0uJ899zaFAdvonTuKwhg944bCeNqZkgpyDoxaUw/QyXN8VzMyMByYqO8p3c/fnKUbKZI3+A4c6cb6K37aft96+exr+/ViMZdrPVY2I013NoiffmN8fXoxKIHEhfMuM3rBq7DMzwWF0+uT86NpcaI0mP0u+Ocrxzgpi0TlJXPw0ciRAfw8lBeQbkOKX98vb+e44CS1N00SAPlGrh9Pplif7zBxM3QWMFLpfFyPaxVW8+eEEwUgPOXffXKza8gCuu05h9HCoXs3URj7TiGUCTdPmwjPhbvGZFUhq6Or7+Sx3i4wOzBY1iGyfC2HRz76lfY1juJ2zeMYznd8RMM7L2KxlocNfb691KMICpuYVUsEIYNprJTKHOYgeQs1UaEZhNZq0hPz9Xo5RZmJMg7F4RPFCM7rgWxD3vuMWrEUVbHGaDVmgMZM6OU8kBKDFEk0OfRdhZLv4RkOoNtF3DMDrbchhIxE8pwHHr6h9g0sp+55gIFN8fx1XO0GvX191Kh8GO49buwe7MMFS6vwymNBBFgJIZIXN3P18XAbpq6TnToIPXUIIW0ouWeQ4XLiKBLRbSTeKk09E1c/tv+XdCpwdLd6EscLICXjt4MwJPnv8DKYC+Te65eP3+b99xA0GyQLhTpdCrI5FE65TVEBM743q/f1xcYPxIOlmspfvUNL2f25NWcO7LKmcfXqM+1yfR57HnzCBuvLaKMFyZR/rmgg4DK3few+rcfo/61J7AmbiDxk3/AI4kMnxkyubtoUhewL+3xO0O9vLInfcWxuoLnB6mgb2u8AMnuUmqV+NSJT/G5U5/jwNIBAIYSQ+wrXsPudB9DRkAimKdZPkq9fASjVcduRVjNCKMkSNbOkzl6CvvA313cV2EbjF4PozfA6H5IFp/dn+8QliF5w54h3rBniBOLVf7ua+f4h0fPc+fhNq55OzdvfCu3Xl3nxvZ97Dn7V0Rzh1nujDGj9jPNPmYO9NNqJTDZQX+uiU6scPzY0xw6dAjTtNiwYZKNGzeyceNGfN//5h36OjD7CuTe9rPk3vazsbN1111U7v5X+v/8A/xG+728PZ3hi6/7KT511T5ObEjibEhih5JPnKnwxydmERFc3ZfidQMZrvFdeushnfk61ftnoHPRQJIpC7PHxXjGotL2FefrBYAQ4pXAHwEK+HOt9e89Y70NfAi4GlgG3qy1Pv3d7FO6MACdMc4uH7rs++29O4iiEAF4nkd7YAtkb3peM7KxZPLl21muR3FiA8l8L7Xmke52Bl46A20T5g5Abpyt7RwPqlMoZZPc/DIMy+KVb5r6uvsybfuiyJfW2J5/2eRMT/5lRJl9yJ7zqO5z61K46TSV1WVMx6HVCC+K2AhB7+Cm+P/UBCgLFXUQSl50KqZug/I0ZMcA8J2tiHaVKJ9DqyrpVJ5ac4mEm8SxEpAo4CZSkOgjXShCaiuytxdpXIx6K8OIIyI6ZFN+E/s2ewy8ZIB/PhSRXRZoHRH0b0VdqI0lJIuDu6HVoU9Cq1Ak6uZrrY+9lefW7R3SmQ00dIYz9T6efKKCSDls2/3zWI0SdB2iyT3XrDsQojsWludhmRcNeoC8k2cqO0XO6Y51d9tEJsfYxEtw/Jii7Tj9OE5sEBdGx6klNT09/WSTG9f7J4TipqGbaHQahDrEkSaprgOXTG7DlqeQ4iLl+8I+B7a8ngPH/wmWT+GZMW0VYMM1MT0yCzyeztKPAicDZUjZKZRU5Pq2oaXGzu3hFDPoRHx+hhMDzOXci3Q1y4sXoLPhesprJ9jRswPWvoCXzmDt/inIFeCxx3ANl6wd5+FYykIYNrp/HzYuuzbcjtaaMKxjGM9+F0xmJi+7Z9Lpq+iPnmZ11y688RuQSjG2aw+VpUUKhcsdg4nMBIuNRcqtMn2JQWRlHomNlBZh2CDjKqqhpOAWGN+0GdEeI13oQxkmuAWoLZJMT1ApnYzPYXfSJIg2wrFThMonk4knStqrxzAqXTovYMohDD2IMiyEsEj6W2I1wDBcd646g68lMTpKti8+58PWMFHUQSkDJXJkszfjJjxkVzxEWibJ3OX1N/3UFjo734mZGIQzdz1r/C7F7sJuwtNL2DpNUBiD2nSsZtqI68uZI1tgy+uf81kmnyFgMrxlO+WlxfXPo72CVEKRSFx0jL1UGrr5g4aRxC5YRDVJI3UtqfH937CvLyTEM2c7vpfYu3evfvjhh7/jdtqNDp//s4MABO2QWqlNeakBOlYXGdmWZ8v1/Yzv6vmuSSprrWkdO0b5s5+j9NkvIIx+9Pg1PDG5ha/0mHypaDJrCxJS8ppChl8Y7OGqlPfNG76CK/gWMV2d5ovnvsiDsw/y8NzDVIIKEIf/e71eBhMDbPBTDKgO6cYidn0WS61hum2MICJZ7ZAqd8isQbbSWq84H2aGEKP7kaM3wvA+6Jn6rlALgzDioVMrfO7gLJ8/NM9iJZ5tnyok2NtvsV2cZEfjQTYs3Ilbn2OlM8yMvI4ZrmW2OkS1YdK2V2nbKwTOCqGMf5/2eugvDDI2OsbYxBjpvI/jmd/RMyFqNmk8+ii1Bx6gdt/9NI4c4eDERu7c9xLuvfp6Sp6PF3aYqtVhKeD4uRZRU9ObtLllU4FbNvVyfdbHWG3RWWrQWWzQWW7SWaoT1TqX7UvYCpWyUEkLeeGvrRCWQlgSezKD2fv99UwRQjyitX7xphC/AYQQCngKeAXxdPfXgLdorQ9fss3/BezUWv+yEOKngddrrd/8jdr9jt9j9RU4cQ9fW3uK5eE97M8P0+nUAE2rNY9pZtZzeIrF1377+7kEURTQaJzD9yeec3272aCytEh+aOR5tbdw5hT3P3EnQ8khdt94O+pbjBwHzSam49BuL3Hoqx/m2HIbf8MQP77jrZdtF0Yhnz/9efoT/ewu7H5WO7NPH2Ntfo7ihimsXBpPuTQq5diJXG8kiGluJ+6BsZeAc3kZFq01R+//MseqBtfu28NA5hJ61oGPE0UBC30+icQmEolNlFolgiigJxK0a+dYic6Sy70Ey/r6DIBKpcKdJ+7ETbm8auJV33Bsamur2J7P0sq/AN/kGqivxMeX7HvO1WEU0ug0SFjfWh3NThCAjo3jZ+KBmQdwjvxzfD52PLsUXWVlCcc2Mf00QRQgkSipCMMGzeYsvj/BZ09+FuCyseh0KnQ6lcsoZM1WrIDh2MW4pmkUrJ+/dqvJzPlPYrk50vlb8V+AuqVaa2ZqMwz4A8/Kp38u1IM6XrsBJ78Ak7fQEFVKpccxnXG0sZGEsYxl9SAvzQs69xCsnY3/z46vR9AAwiDixOMLKCWZ3FO48CVMPwrZUUgWOXLfl4DYMa8sL63fswunT7I8Hedt9Y1Pkhu4PKIK0GquUF2ukh+8eJ9/9uRn6fV6uaZ4zdc9zoNLByn6RR6afQjgOa/hpbOnWTx3hnRvH6oQ0Gk8Tb5uUI4W0ekifYXnvu611szPf5qZp47hqmvZsv+ll61frC9ycOkgNw3ddDGv8Bn43OH30Tx9lA2pl7L1utd/y8+jZ+L5vsd+KB2sVqPDp/93XAZFGRIvbZEt+hRGkwxMZbCc707gLqzVqD/4OLUHD9E4dI6a2cPR8Y0c6M/xZEbxeFbRUAJbCG7MJnhjMcftPem4qNsVXMGLgEhHnKuc4+jKUU6snWCmOsNMbYaZ6gwrzRUancb6tqlAsKVuMB5J+oyIrBfiZZrkRYNsJSBT6pApBZjdiEtLKRb8FEvpIWp9O7DHXkbf8D76EwMvWFHkKNIcnatw7/FF7juxzBPn1ig1gvX1fb5izG1QiBbIt6fJN8+S0i10mKBNgYYcohIlqdKhLaoIs4ISIabW2IGH3UnhGRlSbo5UIoubMLE9E8c3sD0T2zMu/+wbOL6JaavnfOGG1SrNg4doHHiS6sFD3Fdp8sXRDTy0bRfz+ZjCVVxdYWxujsTMInKlSdiWDE8Ms3XbBHt2jrNltAclBVE9IFiKHa6w1CKqtAnLbcLu36jSRgcXaRS5N2/C2/3CKCu+UPg+c7CuB35Ha3179/P/A6C1/u+XbPP57jYPCCEMYA7o1d/gxfkdv8e0huWnCewU+Lm4bg/Qai+xunI/vb23EQQrGEYSw/jhFz4qLy5w8twRxrddRdp+dg3KelDHVvZzGldBq8na3CzZgSEM89t/BlVWlnASSUzrGcJX04+AsogKGxHCes5ngNb6eRnj95y9h9HUKJOZyefVp1Z7iU5Qwvef3/YvFoIooFWeJeGkn+WsPl88l4P17SCK2gihEOL7I9qvtabZnMa2i0j5dezQpadh9vE4Cjv07Efl/Oky6V4Xx3/u6/n4Q/fTCQI2Xf+SS6TtIWi3mH3qGJlikVTP838vRDpCdAUwvhnmanOstdbYnNv8nOtXZ6dJZPOYjkMQrGKaWYIglqk3za9/rdTrpyHyILQunxx5nnho+ossLjzENfnXUhh57r59K/iRdrBeaDQOLRHVOugoQocaHUZElTrtuVWW1irMBh1mhWTe85jzbU75khNJyawbO04C2GRbXJdPcms+xf5s8opTdQXflwiigHpQp9KuUA2q1IIa9aBOrVOj3qhSmp6hMT+HrkxjtpewdYleWaJfVekJG2QbbRL1cL29tiEoWyYlw6KMTVm7lLRPRWepR2miyEdoD4QZq4+N9uLsHqcTdQiigHbYvrhEbQpegV/a8Uvr7WutObfS4OBMiZOLVU4t1TmzXGO51map2qLS7DzXYX5dSCKM7mKKEAeNrQV2JLEjiRMauNrAiSS2BkcLLA2uEKRsSdqW+A44nsS2wZAhSkUoEaJkh77eFqPZeZrn5zm83OZLOsMjfh9P9I2ykrj4gikuLTA+c47R2WmypTXSzRY9Avotg+FskkyxgJFJIxNJZDKBSibj/30f4foI00WlPKT1/WFYXMD3mYP1JuCVWutf6n5+G7BPa/2rl2xzsLvN+e7nE91tlp7R1jvo1uEaGRm5+syZMy/SUVzBFfzwIQiDWMBDfftKzj+wiCJYORlT8O1vLbIIEHY6tGrVb8sR+WFFGIW0wtaz8+u+TTzf99h3NQfrm/Hbv19xpNrgj87M014rUXvqGJEzRKgsAgkVQ1AxBVVDUB2zCeXlCmWm1owbBtemfLZmfHYkXa5OeaTNH4l0tyv4AYcpTdL/f3t3HyNHWQdw/Pub2d17aXvXlqMvtJW20hoIIRYaqKKCQgCpoSZWU5RYBfkDbfVKrwAAC5lJREFUI1ExMRhiovgXapCYEJEAikReFAlciEqQl5AgbWkF2kILrQXL0XJt73ovvdv3+fnHPHfZu7325rjbvb2d3yeZ7Mzsc7fP/vKb2efZfeaZhtYxvykG4OyxdxdyOQb7eunv6eRg5zZyHS+R7NtHc/oILZl+lg0MkiqeGPE3CuSTQi7pkUt6ZDyPTJdH/4vCgCcMeB4nPGHQ8xj0EmT8JMxawJFUgJechfiN4CWY7SW4qM3nooXJ8BaSGiDFAgR5ctkcvQM5Mrk8hVyBXD5PPp+nkM1SGOylmBmgkMkQ5PP4WWFXsILutNKdT9JdbKQ3aKKfJnr8JDnPI5dQAoq4u1+WC8AfCGgcCEgppFBEhUtzec4o+qxs2MqcOY/hEfBxlFUE3Hhc4VCKzo9dzL5L7+Cto93s1Vb2trSw7dw1FEfdSNkLApozaWalB2lOp2k+fpzGXCdeEOAFAb6Gjx6K54dT+/q+jyYS4B7V91HfbbsFz+fabC+XSBFJJhDfBz+BJHzwfZrXrsWfPfEP/Bo21leyo79xjFIGVb0Xwrt+r127tna+tTRmBpqqEQ8zkudB21kf+c/9RMI6V6P4nk+zV/3h8hVr9bvx7XdTMr5dRNpLx7fXqsFiwM7+NF5RoWU+PoN4DJIKAtpyASuLQmsywdxkMwva2li2oI2lTQ0saUxyWjJhU6qb2EmkUrS0nU5L2+ksPutc4PryQpletOd/FI69Sb5rD4W+gwT9h2Gwm1S6n+bsAP5AFr+QxwuC8r8H4DC8/saE6jb21QdjW//TLiiZohlVyPaT7unkWOchurqP09Xbx5G+NF0DeboGixxPB/TmIB345PDJaYIcPnn1yeOjQH/TIbq9AbppZDuby184gEvOvIT1y5ewfvmS4d1FVY7lChzK5jnQn2ZX1wn29ab5MOdxXHx6U00cTQaohJMSh5MTazhDHAoCsxsSBKqI64CFHdAACQIkV0CCHAQBniqH//kkh1/bNmZsVrQ/hb969ZjPzVAdwLKS7aXA6LvRD5XpcEMEW4Hu6lTPGGPMTFXJn1UuBPar6gEAEXkU2ADUfAfrgtZZ/HvdSb6qN8Z8NI2tyKLzSC467xR3iHOKecj2Q+4EmulDsz0E6W40002Q7UGLWbSYDS9ODwqgRSgWwN17BS8ZTtXsJ8L1oW0vAX4K/CTiJ1EvifgpJDGLxqYzhmdiGiYCjS00LWph2aJVI1rjZVUuFslms2SzWXK53PBjEAThvVGCYHgp3VZVVJXFi8unuvVFWNiQZGFDkjUtzXxlSfmtJFSVvnSBD/sy9GfyDOaKpPNF0rkihUDZeEH5xcxl/6NQIMhk0fWfJchkoFBAi0W0EMZVi0VSy0717mekV4FVIrIC+ADYBHx9VJl2YDPwCrAReP5U118ZY4wxUNkO1hKGbzUNhN8EXjS6UOnYdeCEiLw9iddsA46NW8pYnKKzWEVnsYomznE6c7orMERVCyLyPeAZwmHsD6jqmyJyO7BdVduB+4GHRGQ/4S9Xm8b7vzt27DgmIpO9CCvOOXIyFpORLB7lLCblLCYjTUU8In2OVWySCxH5KnDlqAuIL1TVmyvyguFrbK+VC6hrmcUpOotVdBaraCxOZjyWI+UsJiNZPMpZTMpZTEaqZjwqOZVdlPHtxhhjjDHGGFM3KtnBGh7fLiIpwqEV7RV8PWOMMcYYY4yZVhW7Butk49sr9XrOvRX+//XC4hSdxSo6i1U0FiczHsuRchaTkSwe5Swm5SwmI1UtHjV1o2FjjDHGGGOMmckqOUTQGGOMMcYYY2LFOljGGGOMMcYYM0VmXAdLRK4SkbdFZL+I3DrG8w0i8ph7fquILK9+LWtDhFjdIiJvichOEXlORGrmHjXVNl6sSsptFBEVkVhOexolTiLyNZdXb4rIw9WuY62IcPx9TEReEJHX3DF49XTU09SWqOeieiIiy9yxsMedN77v9s8XkWdFZJ97nOf2i4j81sVop4icP73voHJExHfniKfd9grXttnn2jopt7/u2z4iMldEHheRvS5XPhX3HBGRH7pjZreIPCIijXHLERF5QESOiMjukn0TzgsR2ezK7xORzZOumKrOmIVwsoz/AiuBFPAGcM6oMt8F7nHrm4DHprveNRyrzwPNbv0mi9XJY+XKzQFeArYAa6e73rUYJ2AV8Bowz20vmO5613Cs7gVucuvnAO9Nd71tmd4l6rmo3hZgMXC+W58DvOOOiV8Ct7r9twJ3uPWrgX8AAqwDtk73e6hgbG4BHgaedtt/ATa59XtKziF13/YBHgS+49ZTwNw45wiwBHgXaCrJjW/FLUeAzwHnA7tL9k0oL4D5wAH3OM+tz5tMvWbaL1gXAvtV9YCq5oBHgQ2jymwgPAgBHgcuExGpYh1rxbixUtUXVHXQbW4hvFdZHEXJK4BfEB60mWpWroZEidONwN2qehxAVY9UuY61IkqsFGhx663YfQJN9HNRXVHVw6r6H7feD+whbDyWfp4/CHzZrW8A/qShLcBcEVlc5WpXnIgsBdYD97ltAb5A2LaB8pjUbdtHRFoIG9L3A6hqTlV7iHmOEM4G3iQiCaAZOEzMckRVXwK6R+2eaF5cCTyrqt2u/fIscNVk6jXTOlhLgPdLtjvcvjHLqGoB6AVOq0rtakuUWJW6gbBXH0fjxkpE1gDLVPXpalasxkTJqdXAahF5WUS2iMikTlAzWJRY/Qy4TkQ6gL8DN1enaqaGTfS8XXfcsKU1wFZgoaoehrATBixwxeISp7uAHwOB2z4N6HFtGxj5vuu97bMSOAr8wQ2ZvE9EZhHjHFHVD4BfAwcJO1a9wA7imyOlJpoXU54vM62DNVZPe/Q881HKxEHkOIjIdcBa4FcVrVHtOmWsRMQDfgP8qGo1qk1RcipBOEzwUuBa4D4RmVvhetWiKLG6Fvijqi4lHLbwkMs1E1+x/vwSkdnA34AfqGrfqYqOsa+u4iQiXwKOqOqO0t1jFNUIz9WDBOEwsN+p6hpggHDo18nUezxw1xVtAFYAZwCzgC+OUTQuORLFyWIw5bGZaR/mHcCyku2llA+rGS7jfjJtpfynwziIEitE5HLgNuAaVc1WqW61ZrxYzQHOBV4UkfcIx+22S/wmuoh6/D2lqnlVfRd4m7DDFTdRYnUD4Vh5VPUVoBFoq0rtTK2KdN6uRyKSJOxc/VlVn3C7O4eGdbnHoSHHcYjTxcA17jPnUcJhX3cRDmlKuDKl77ve2z4dQIeqbnXbjxN2uOKcI5cD76rqUVXNA08Anya+OVJqonkx5fky0zpYrwKr3AwpKcKL9NpHlWkHhmb/2Ag8r+4KtpgZN1Zu2NvvCTtXcb1WBsaJlar2qmqbqi5X1eWE16tdo6rbp6e60ybK8fck4eQpiEgb4ZDBA1WtZW2IEquDwGUAInI2YQfraFVraWpNlLypO+46kPuBPap6Z8lTpZ/nm4GnSvZ/080Itg7oHRoOVC9U9SequtR95mwibMt8A3iBsG0D5TGp27aPqn4IvC8in3C7LgPeIsY5QvgZsk5Emt0xNBSTWObIKBPNi2eAK0Rknvtl8Aq376OrxIwelVwIh9K8QzjT0m1u3+2EDV4IGyl/BfYD24CV013nGo7Vv4BO4HW3tE93nWs1VqPKvkgMZxGMEifCn9nvJDzJ78LNZBTHJUKszgFeJpwp7nXgiumusy3Tv4yVN/W+AJ8hHI6zs+Tz6GrC60OeA/a5x/muvAB3uxjtqvfzMeGQ66FZBFe6ts1+19ZpcPvrvu0DfBLY7vLkScLZ3mKdI8DPgb3AbuAhoCFuOQI8QngNWp7wl6gbPkpeANe72OwHvj3Zeon7p8YYY4wxxhhjJmmmDRE0xhhjjDHGmJplHSxjjDHGGGOMmSLWwTLGGGOMMcaYKWIdLGOMMcYYY4yZItbBMsYYY4wxxpgpYh0sY4wxxhhjjJki1sEyxhhjjDHGmCnyf+uVMwBmZmW9AAAAAElFTkSuQmCC\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace);" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "thinkplot.PrePlot(6)\n", "plot_marginal_cdfs(dirichlet)\n", "plot_trace_cdfs(trace)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The results look good. We can use `summary` to get the posterior means, and other summary stats." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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meansdmc_errorhpd_2.5hpd_97.5n_effRhat
lions0.4467500.1550290.0023860.1630300.7447813833.0267590.999522
tigers0.3307350.1501890.0021130.0604510.6161493769.9395440.999898
bears0.2225150.1324490.0023850.0093860.4697373754.1706421.000137
\n", "
" ], "text/plain": [ " mean sd mc_error hpd_2.5 hpd_97.5 n_eff \\\n", "lions 0.446750 0.155029 0.002386 0.163030 0.744781 3833.026759 \n", "tigers 0.330735 0.150189 0.002113 0.060451 0.616149 3769.939544 \n", "bears 0.222515 0.132449 0.002385 0.009386 0.469737 3754.170642 \n", "\n", " Rhat \n", "lions 0.999522 \n", "tigers 0.999898 \n", "bears 1.000137 " ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "summary = pm.summary(trace)\n", "summary.index = animals\n", "summary" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also use `plot_posterior` to get a better view of the results." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = pm.plot_posterior(trace, varnames = ['ps']);\n", "\n", "for i, a in enumerate(animals):\n", " ax[i].set_title(a)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 1 }