{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Posterior Predictive Checks\n", "\n", "PPCs are a great way to validate a model. The idea is to generate data sets from the model using parameter settings from draws from the posterior. \n", "\n", "Elaborating slightly one can say that - Posterior predictive checks (PPCs) analyze the degree to which data generated from the model deviate from data generated from the true distribution. So often you'll want to know if for example your posterior distribution is approximating your underlying distribution. The visualization aspect of this model evaluation method is also great for a 'sense check' or explaining your model to others and getting criticism. \n", "\n", "\n", "`PyMC3` has random number support thanks to [Mark Wibrow](https://github.com/mwibrow) as implemented in [PR784](https://github.com/pymc-devs/pymc3/pull/784).\n", "\n", "Here we will implement a general routine to draw samples from the observed nodes of a model." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import pymc3 as pm\n", "import seaborn as sns\n", "import matplotlib.pyplot as plt\n", "from collections import defaultdict" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lets generate a very simple model:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using advi...\n", "Average ELBO = -148.20: 100%|██████████| 500000/500000 [00:38<00:00, 13010.69it/s]\n", "Finished [100%]: Average ELBO = -148.18\n", "100%|██████████| 1/1 [00:00<00:00, 4319.57it/s]\n", "100%|██████████| 5000/5000 [00:02<00:00, 2151.11it/s]\n" ] } ], "source": [ "data = np.random.randn(100)\n", "\n", "with pm.Model() as model: \n", " mu = pm.Normal('mu', mu=0, sd=1, testval=0)\n", " sd = pm.HalfNormal('sd', sd=1)\n", " n = pm.Normal('n', mu=mu, sd=sd, observed=data)\n", " \n", " trace = pm.sample(5000)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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QQ5g4cSJmz57t9g1hWVkZFi9ejJycHCxatAilpaUhjJQQEgy/nW/Ci+8Xormt\nSfvMCf2x+u4cCAXBL8baXfC4XCyfNxZCAR8sC7x9pCygb9cJIV2TkJCA5uZmh+kVFRVISkoKyjoN\nBgPWrVuHyZMnY8aMGdizZ4/LeT/77DPMnTsXEyZMwD333IOSkpIur7+XP7+ERheTW8FMZAWy+1UE\nNnhxEKhEY0OLGjVNyohs5RNIvpx6F2tlAAB5F+qSeSLu1FWusLwZSq0BGr0JdWLPD/2+tErxVVda\nIl0Sybq8fqXG0KtqirJgIZFpHWpnGU1MQGquXayVoVWpw0Unx8ZkZlBVL0dDqxr1kk7nnQ+XBJm6\n43wMZjfyQAt78ollWSxfvhx9+vTB4cOHsXHjRrzxxhs4evSow7xarRbLly/H5MmT8cknnyAnJweP\nPPIIdLre82UhpCcxmRkc+O8lvHm4FAYjAz6Pg6W/H4U/3TwaUfzwjzgTadKSBPjTzaMBWG6C/v1l\neY+/eSWku5g3bx42b96M8vJycDgcqNVq/PDDD9i0aRP+8Ic/BGWdW7duRVlZGfbu3Yv8/Hzs2rUL\nx44dc5ivsLAQGzZswMqVK3H06FHk5OTg4YcfhlYbWTVs6Gpm4am1jVZv8rr4tbsWHb5wFpHEycOq\nLw/o3aFVUaCTdxUiOaqblKhvUTutGxQJ9AYzWhU6j+dYd7v/kKk6Elv1LWq77WtoVaOksgVyNy2b\nQlVw3ldafddaHBpNZpReacWlOtctdXqiinrLaNK2AnWMNW6SQWZzxzpEEpVdtzlPtajaVXaqKxap\n56YzYU8+SSQSjBkzBvn5+Rg8eDBmzpyJqVOn4tSpUw7zHj16FLGxsVi9ejWGDx+O9evXQygU4quv\nvgpD5ISQrqhpUmLTvwvx9W+1AICUhBisuTcPs3IGhDmyyJY3Kh3X51wFADh1UYwfztSHOSJCCAA8\n/vjjGDZsGBYsWACNRoOFCxdi+fLlGDlyJJ544omAr0+r1eLgwYPYsGEDsrKyMGfOHCxbtgz79u1z\nmFcikeDRRx/FrbfeioEDB+LRRx+FXC5HRUWF1+uTKnVgWbZTwfGub0dvIgtAVyWJXIszlRKUXfZu\ntLgrje5Hs3I3IpZHTo7/hdrgjvYViTQ6I+olahiMZjRLNdAZ7B88WZaF0WSGycxAotDafC44rRX8\nKXgvalbhYq0MJjOD4goxLopkjq0yOmFhSaZ5U/y6M43OiMsNCp/2Acuyfie8vOkSqtEbcb46sKMw\n1olVOF3cis7hAAAgAElEQVQhibhBCPQ29amqm1TWfztLKLvDsqxXI+/5w5/vR2OrBuXVUqejVjrT\nOdnDDUM+/GKtTSLJy9Nb3I2vsfxwB5Ceno4dO3ZYfz516hROnjyJ559/3mHekpIS5OXl2U3Lzc1F\ncXExFixYEPRYCSFdZzIz+PznKzj6S7V1OOrRQ1LwyG1jkSiMDnN03cNdN16NC7UyNLRosP/bSxg5\nKBn904ThDouQXi0qKgrbt2/HqlWrcP78eTAMg5EjR2LEiBFBWV95eTnMZjNycnKs0/Ly8vDWW285\nzPv73//e+m+9Xo9//etf6NOnj0+xlVyS4KoUQdeC7ua6+nLZ2yLBthk+FpaEk0isxtB+CdaRtJRe\n1ojx9Eb8Qo0U2cPTvIvLS02tWvRJivXxU6HJZJrMDFrkOiQnxCAmyrcW1q52ZXvNlZpmJXhcLhpl\neowflmL9fWW9pUh1qEbtPVvVgolXp3u9fQajGSKJJQERI+74jEiswsD0eJef0+hMdsk0X7Tvsxa5\nDpOy+nqcn2FZnKtqgdnMYlxmGvg839pP+DtqmadkV3uitfP5rm3ryte+fy7UyJA7Mt3lcrqS8+Bw\nunZt6pwsdYVlWdQ0qcDnczGgj+We83KDEs0yDYb1T0RGivPBgViWhZlhfT5mWr0JcQLnqQqRWOV0\nenuXucsNCowa3PEdZBjWYzLVIvTZJ53RBKPJjCg+z++roKvjrzOYUN2oRFqSwI9rcnCEPflka/bs\n2WhoaMD111+Pm266yeH3zc3NGDlypN20tLQ0n97cEULCp6ZJiXePnkdts+WPRnQUF3fOysTsvIHg\ndtcKq2EQE8XDI7eNxYvvF8JgYvDW4VKsXzIJUfywN2YlpNcbMmQIhgwZEvT1iMViJCcng8/vuJVL\nS0uDXq+HVCpFSkqKw2d++eUXPPTQQwCAV155BbGxvt2MavQmRPv4AAFYWteUXWlFbAwfIwclu5zP\n1Q00w7KQKfWIj41CtI8Jg2Dz96GvtlmF0UMcj5Ez7QknZ6PJdZUqjC0yQvlnX6u3jHIoVehhYhjw\nm7leJT1qmjsecuVqPYAEmBkGcpUBicJorx6o2xMUlxu6XkvGW3K1AX2T3X+/WxU6NEm1SE/uSCr7\nUjumc7Fkf7QnZD2dCjKl3tqVqalVgwE2SbH2hGJSfDQE0Y6PtiYzg0uVgSnKbPt9P1vVYm3R1Hm9\n1Y1Ku5o8vo6EV1Enx6QQDbjjbetHiVyHhlZLAic5PhpCQRSaZRoAlnPbVfKprFoKtdaIMUNTER9r\nqeWqN5pRJ1aBDwZcHxM+Kq3RZfLJdh5b9S1qa4LVPTfnNAu/clN6o9ljIvjURTGuycoIeO27i7Vy\naPRGSFV6Sj45s3PnTkgkEuTn5+Oll17Chg0b7H6v0+kQHW3fMiI6OhoGQ+iGBySE+E5vMOOzny7j\n699qrW9hRw5KxoN/yEJfF3+siHuDMxJw5/Uj8J/vLqGmWYWPT1Ti7huvDndYhPRaWVlZ4Lh5mj5/\n/nxA16fVap3eEwFweV80atQofPLJJ/j+++/x7LPPYuDAgRg/frzX6+zcisbb+2SRWAWtwWT5z83D\nravR6ETNKtS3qMHnepcw6A7kaj0UGgMS45y0+HWzYzngeFUXRKs3gdepD4mrejZ6gxkx0b4n9bpT\nr8vSy612Lc+8bYVm2ypEozfBZGZQ06SyPnTHOkl2+KJZpkWUHwldj7x4im0vhixX+9cdNJTH3/ba\n0znnJRKr0NhqOR7Xjunn8NnqRiW0hq7XPmM7JR9su9J1TnbIfNynnb+rDMtaB+EJtM7XYNsuiWY3\nCUXbbnDnr0i9euHJsCyUbUXkq+oVGJ9paWV5rqoFUdFRAGPGmCGpXseu0RlRIZJ7nrETmZe16Bpa\nND4vW6U1IjbG9fWz+JIYk0b1tSaqW5XOuzZakqv+fatctdDT6DvOS4ZlI+JFf0Qln8aOHQsAWLt2\nLVavXo01a9bYvdGLiYlxuKEyGAwQCHp3M3BCItnZqhbs/fqCtR85tXYKnDmTBuLc5Racq2rFsZO1\nGDM01fqHnRASWps3b7ZLPplMJly5cgWHDh3CM888E/D1ubonAuCyRVNqaipSU1ORlZWF06dPY//+\n/T4lnzgcDvh8Lnhcy000j2f52ROGZa2f4fI41n8DAJfLAcf2gYcDh9YkTVIteFwuWMDp+kxmxqsW\nKLbr7cx2ubbz2U232fZ2WqMZRjPj8DtncXb+7MVaGa4d6/iwbGZYm33MddhfDMOCy+Xgcr0cAh4H\nPC4HJZUSJMfHIHNAEtQ6I8611YSy/azOYHa6D8pqpJjsIanH5XHAY+w/2378Oy9TozdZt7/zPrH9\n2XbbuFzH5YBjeSh3ltRlWRYXamRgWRZZQ1LcJn4ByyNd5+U7i9ETiUKHFoXO+hmDiXE4Pu3b1s7V\n8hUag/XeyFVs3uLxOGBtSvlyeVyPy3AWF6/T99N2WzvjcNzvO72JcVieq/OCy+OA1xa/s7j5PNfX\nHbGsI0Y+nwuTmYFKa0SiMBpcDqdtJDlO27HxvF9tl83aXLsA5+dRe0yeziN3xyNWwHf4vMnMuF2m\ndV/yuPbXUA/rvVytdLlcHtf1NZ3H79hGFo7nvrPP2V37bZZtMrOIgqVYuqtrL4/veA6XXpE6zGe7\nbmfrAhyvo84+C3T8rXE1H7dTkrCxVYPL9QrEOTl+thpaLV0T5So9RGK103kty3cdpzv8tn1l+9my\n6laH73LnEh1Spd76Pe68bcHiV/Jp0aJFuOOOO3DLLbcgISGhSwG0tLSguLgYc+bMsU4bMWIEjEYj\nVCoVkpM7mmdnZGRALBbbfV4ikSA93XUfWkJIeMhVeuz/7hJ+O98x9Hj28FTcf9MopHtoCk68w+Vw\n8NAtY5D/7v+g0Bix+0gp8h+YHDFNawnpTW6//Xan07Ozs/HRRx9h/vz5AV1fRkYGZDIZGIYBt+0G\nUyKRQCAQIDHRvrbM2bNnwePxMGbMGOu0zMxMVFZW+rTOuLgYJMXHQCi1PDDzo6OQlBTn8aY1QapD\n+4BMGiMLobCjO0l7MqVdrFBg7ZrRznb+lBT7m+crDQpUNyhw9aBkXOWmPk3n5XRmu1zb+ZKT4ywP\nSnwuVAYGQqVj66FL9UpkDU11G6er9TubT6c3WedNiI+B2aa5BZfDsbYCqWkrJh7F5yIqOgpqA4PY\nuBg0K/Rut9UZYbwAHA7HZWuG+HiBQ2HhpKQ4pKQI3W5X531i+3NSUhyErZbWHXECPridRrktr1Ug\nPi4KE0c5JsbEUi0sjVk4MLAc9EsVol6sglJjwPABSbhQLUVMNA+CaD6EsVFex+hJq8ro1fyJiR1/\nh93NH+Wi1KWz88IdYbwAJpvuU4mJsS6XodIY0CzVOo1LEBsNIdtxvjXJXZ9Lohbny7BV1aR2+r3o\nPC1eKLCOzOgs7rrWjnV13rbOyyo83wS11ohBXB6GD0hCXLMaSrUBsbHe1RW1XTbLsl4d76SkOAgV\n7nviuDumvOgoCIX2NYkSEmKh0Lnurte+vPj4GLsR1DytNzpGDrhIcMTHx7iMs1VthELrOR5bZqZj\n/8UJ+NZ52o9FbGw0jCwHfVMtvSDs/jbweXbLtF1WZ/yYKCTERVt/z+dxERMbDZ3BjNREAeIT1GBd\nbLOrc6mz5BQhGIYFn9eREC+5LLV+Rih003qUa9mWVrXr60dychyEMp3DddAbSUlx0Nr83WhnG5PG\nyNptq1JjQO1ladt8oeniCfiZfLr22mvx5ptvoqCgADfeeCNuv/12TJs2zeNbB2dEIhFWrlyJEydO\noG9fyx+Xs2fPIjU11S7xBAATJkzA7t277aYVFRVhxYoV/mwGISRIii+J8d7R81C3NdFNEkbjnjlX\nY3JWX7+uE8S1JGE0Hp43FjsOnIZaZ8Ibh85hzb15VP+JkAgxfvx4rFmzJuDLHT16NPh8Pk6fPo3c\n3FwAQGFhIbKzsx3mPXjwIEQiEd59913rtNLSUmuLc2+p1XpwGAbqti4larUezRIVcq7u4/ozOiPE\nLSprl40KD91RWltVMNp0RVOoDdb1AYBUav+AVlZheSl5urwJsXz3f1/UbtZtu1zb+b78sQoA0Dcl\nFoIYvstliBpkbuN0tX5n8+kNZuu8PLBQO+kux+VyEBsbDa3WALVN8u6ySIoGiRo6H0eg+u9v1eAA\nyB2V7rQVmUqlg8Fo33Wptl6GOD7H7XZ13ie2P5881zFaK2MyO+2SqVTpMDAt1iGmllaNdVmSFhV4\nLIPT5ZaXXZVe1sZyFmNXtR8XqUyNc5UtiIni+bX88koxMlLjIJFpUd+ixtB+iU4HZTGZGdRL1JB3\nGv2qps5ybNqJpVpo9CYMyohHSUWLy+6vgdwXzpbnbJ+LGmSQ2xQud/adqKnv6GqlVEZBKu14hO18\njjW31fYpr9IjJY4PjUYPgAOt1uBVnar29TNto3t6s08UCq3H+ZxtVzulxuDweYXA/blj3Zcqvdvu\ncp3Xq1LpXdZ5Uqv14IGxq6lljUfpfhudbZ/J3PH3gjGZIZWqIZZpodUarNev81USRHHS0GTznQaA\nC5f1EEZzERPFg1ZvwtnKFpfbeaFKguFXJdp9/vuTNQCAqwcmQa3SQe1ikAbrftQa3W5ftUiKCzVS\nJMfHIKutXp/X3xeGgVSqdrsPZTINVEqdz9fu9s+WXWl129uWNZvtjpGoWWUXS0S3fHrqqafw5JNP\n4ueff8ahQ4ewcuVKJCYmYsGCBViwYAGGDRvm9bLGjRuH7OxsrFu3DmvXroVIJMIrr7xiTShJJBIk\nJCQgJiYGc+fOxY4dO7B582bcdddd2L9/P7RaLW6++WZ/NoMQEmBGkxkf/rcS3xWJrNOunzgAd84a\njjhBlJtPkq4YOywVC2YMw6f/7zIuNyix/7tLWDJ3VLjDIqTXU6vV2LdvH/r0cZ2c8ZdAIMD8+fOR\nn5+PzZs3o6mpCXv27MGWLVsA2N8/3XXXXVi8eDH27t2LmTNn4vDhwzh79ixefvlln9ZpMJphjuLB\nbFMvR6U1QCzVQq01Iik+Ggk2iSOt3oQzlRKf1nGlQWlXiFunN9mtr711R/sISs5+54rZTZ2f9s8q\nNQan8zW0qDG4b4LLZZjNnmNx9lln85lMjHVes5lxsU5LMobptA8q2ur4+Kp9MLBmqdZpoWpnyQqx\nzDKCm7vt6rxPXO0/k8vtbFtWp4cq2/1iMrMwGMxuj6/L5cL9eeE7y3GpaVRCpvI/kXNJJEN8bJS1\nyHxJpcRpPaPKejnEMsfaQBK5FkZjIjgcDowmBhdqOxJyKm34auU62+fFF8VO57FlO7/ZxNjN4+4c\nM5kYGI0MuHyew3fFleoGBZQaI1RaI8YOS/XqM2Y357ZtLO5+1/nzrr/79svztF2d19v5WtXZ5QYF\nhIIohxaoZpN361FqDKiXqBHF52FwRrzdtcxkYnChRmrtDsYwLMxmBs2tGlxycu06eb4J44f3wZVG\nhdui7WYz6/L6IhKroNO7vj60x10hkrvdvtLLlqL1ErkWJlOSZb1eXjsUaj1qm5Rur4EqjcGujpgv\nTCYGZjPrth5g+/63/dk+ltC8tPa75hOHw8G0adMwbdo0aLVa7N27F6+//jrefvtt5ObmYunSpU5H\nrOuMy+Xi9ddfx6ZNm3D33XcjNjYWS5YswX333QcAmD59OrZs2YIFCxYgPj4eb775JvLz8/Hhhx9i\n1KhR2L17N9V8IiQC1EnUeOvwOYjElqx6kjAay+aNwdih3hcSJP675bqhqKxXoKSyBd8X1yHzqkRM\nG9c/3GER0mu4KjjO4XDw/PPPB2Wda9euxfPPP4+lS5ciISEBf/3rX61lDGzvn8aMGYN//vOf2L59\nO7Zv346rr74a7733nrXFubda5DokOSmQ3f5gK5J0FPw1mRmnD8WeyNV6GIxmRPG5MDOsy9ay5TUy\nvwslu1LdqLSO5uQrV2+ctXoTBNE8j61+GYZFk1QDoSDK48hIwaTVmexqaDW0qB1aPNnyNBR90Nju\nz3DF4Ia3I4i5094NzXaZnVs1t8idFy8G2oeqj7JbjtJF0flIZTIzDvvBHXmnhF/xJTFMZhZCH7oy\n1dqMpFbl7QiFPjQaqWlSor5FjZT4GHA4HPRJErioa+Z+OXK1AUlOWsMFgsFoBmJ9f2lcL1Gjpllp\n/TlR6N0yXA2GAFhq4/E9tGoF3Jfq9mqAAR+OocFo9nnk1eompdvft49q6o/IuwK61qWC483Nzfjs\ns8/w2Wef4eLFi8jNzcXChQvR2NiIDRs24OTJk1i/fr3H5aSnp+Mf//iH09+Vl5fb/Txu3Dh88skn\nXQmbEBJgv5Q24t9flsPQdrM1PjMND94y2vkoPiQouBwOHp43Bs/vOQmJXIe9X1/A4IwEDOrrvgYK\nISQwOhccB4CoqChMmDABgwYNCso6BQIBCgoKUFBQ4PC7zvdPs2bNwqxZs7q8Tm96TpdXS30e7cmW\nWKaFQmOEUmNwKJDazpfEk9HEeLzx9ybx5OsNvqhZBZFEhX6pcRjaL9HtvHUSNeraugsNtOnyotCE\nNlnQ0GrpFpM7Kh0ancnjfvNF5xHB7Pi4c21Pw+704NUVpy42Y9zwNAi9bEnuRQ+zkLvSqPBY97O2\nWYVBfePBMCyKLoodRtl0lyQ436nLpd7ovMi+t9zVUvKHSmtEfYvlOiNtS5S5Gv2sSep+5LXz1a0Y\nOTDZ65Ebu8qba79t4gnwLqHCsu6XrTOaEM/3fM5XulqXh0N4/korRg1OcT9TJ0WXxLhmdIZPnwkq\nLxLwLGtJSF+olSE1IcZhhMVQ8Sv5dPjwYRw+fBj/+9//kJqaigULFuAf//gHhg4dap2nf//+eOml\nl7xKPhFCuq/vTonwf99cBADweRwsumEE5uQNpNpOYSAUROHRhePw0t5TMJgY/PPTs/jb0knU5ZGQ\nEHBVcLyn8aaRSVcST4ClsGx7cqk9IdOuqVWDjLbitO4YjGaodSYkxUfj1MVmj/P72+LJHVFb7I2t\nGo/JJ4lNzR6RWOVmzuAzMQy0ehN0LuoC+etcW7cVX1nqvNiPaNhb7zDOVrVg4oh0xER7bnURtlZp\nbjS2atDY6j6pUiexJJ80epNj4ilCeXM+avUmS4uiALroRzdbozmwMXhLazChttnZtY0FJwDf6BaF\n8ySeykNXNrnGgAYP56QzgWjdGGqVdXLoDCbUt5gwqG/XBo3zl1/Jp/Xr1+OGG27AP//5T8ycOdM6\nyoqt4cOHW7vOEUJ6pqO/XMHHJyzFWJPio/H4nRMwpF94LmbEYki/BNx300j868tyNEu12PXJWTyx\nOIcKkBMSBLt27fJ63sceeyyIkYTOpTr/agr5olnqurve5UaFy+STbTeUksoWmBgGV7loORVonh70\nW108GLXrri9sqhudJ8qkSr3HJIO3ii+JweNykTMiDVHOuk91j/xEwBRXiDF6SKrHLlfOdktXE8O9\njdFNnSFfnamUICU+dKOKBZIlYdH1BH3nlwmRwq+kYARdd7wJhQWgN9rXQwsHv5JPP/zwA1JSUiCT\nyayJp5KSEowdOxY8nuWPQm5urnX0FUJIz8KyLD75oQpHf6kGAKQlCrD6nhz0TfH8NpoE38wJV6G6\nUYnjxXUor5Fhz5fn8fCtY7rtww0hkcrbMgAcDqfHJJ9Cwd9uJOerWzFmaCoS46KtywjEA1M7lZsu\ncGK5+/pWrlooMAyLmmYldIbAtjLqKm8bnDTLnCeY5Gp9QGtymRkGja3ajq7ktiWfAraWwAl2g53z\n1a2Y4qHbT7geLnsSo7f1pry8v5J2oQh9KHU+f8urg/fSIRIatzEsC6WPXZwDO1BB13i7D3k8Dtrz\nbMFo7esNv5JPKpUK99xzD2688UY888wzAIDly5ejT58+2L17N/r3pyK3hPRUDMti/7eX8N0py4h2\nGalxWH13DlITqfB/JPnj765Gq0KHM5Ut+LW0CWmJAtwxKzPcYRHSo/z3v/8Ndwi9UoObhFKrQhe0\neoPBeHCsb1EHrIVQJNHqfWtJoDN6Tr51x24uXeGp3pC1IL+LJ8+KOjmu6YH3ZvQaLfS8+X76i4XX\nubugkcjct0x1Rqnxb2S6cApXnSdbfvXD2Lx5M4YMGYIHHnjAOu2LL75A//79nRa9JIT0HB/+t8Ka\neBqYHo819+ZS4ikC8bhc/Hl+trUb5NFfqvF9cV2YoyKk9zEYDDh16lS4wwiZ0sutQV+HuyLYUkVk\ntCwoviT2PBN6bkIl0CMRApZWVt2lBlAgXKx139qE8VBRvLvvq0isWUVcczuggAemLhZ2d9UC01us\nH+0nLzd6ORJihNAZTFB7qH8VCn4lnwoLC7FmzRqkp6dbp6WmpuKZZ57Br7/+6tOympqasGrVKkyZ\nMgWzZs3Cli1bYDA4b/a2YsUKZGVlYfTo0db/nzhxwp9NIIT44f+dqcexk7UAgGH9E/HMHycGbZhX\n0nUx0Tw8fud49EmyJAf3HruA0xWSMEdFSM907tw5LFy4EGPHjsXo0aOt/02YMCFoNTANBgPWrVuH\nyZMnY8aMGdizZ4/Leb///nssWLAAEydOxPz584PWakupDe9Q7nqTGRKZ+y5wIYkjwIWFiYW1NovN\ns2L43+UHh6fupxK5zmOCRq0z4kxlz/u739CiRvFFMeTq8F5v2kXyOWjytuugjTqJ2mNyszOR02Li\nXmA9J1KJeyzL+pVACwe/kk98Ph8KhWO2T6vV+pylXrVqFfR6PT744APs2LEDx48fx9///nen81ZV\nVWH79u348ccf8dNPP+HHH3/Edddd588mEEJ8dEkkw/tfXwAA9EkS4PFF4xEfS6OoRbqk+Bg8sXgC\nhAI+WBZ48/A5XOg0FDEhpOsKCgrA4/GwYcMGREVF4bnnnsPSpUvB5/OxY8eOoKxz69atKCsrw969\ne5Gfn49du3bh2LFjDvOVl5dj5cqVWLRoET777DMsXrwYq1atwoULF4ISV7hV1Hse3pt0T02tWoeH\naRb+tfLRREArgK7oPKy9Mxdrgj9AQDBIZFqUXnHdirK6SQm9yYzz1cFvaemNSE4+FV0Uo0Ikh0Jj\nwK9ljV59RqM34rfyJlxu8L51j7/F7Fmwnr+/3SOvQrzgV/Jp5syZePHFF1FTU2OdVltbi4KCAsyY\nMcPr5VRVVaGkpAQFBQXIzMxEXl4eVq1ahc8//9xhXoPBAJFIhOzsbKSlpVn/i4qih19Cgq1FrsM/\nPzkLM8MiJoqHVXeMR0KQamqQwOufJsTKO8aDz+PCYGTw6kdnKAFFSICVlZXhb3/7G+655x6MGjUK\nI0eOxJo1a/DUU0/hww8/DPj6tFotDh48iA0bNiArKwtz5szBsmXLsG/fPod5jx49iqlTp+Lee+/F\noEGDcO+992LKlCn48ssvAx4X6RnMEdoSoaFVjcILzaixaWVRJ1H51ar3Qq2sS12F3ImUVgheF8yO\nMO4SyLXiyBwxLVIxLAuJQosyN8k8V5qkwa9Hpzeaw17zqbvrTl1s/Uo+PfvsszAYDJg7dy6mTJmC\nKVOm4KabboLRaMTatWu9Xk56ejreeecdpKamWqexLAul0jGTf/nyZXA4HAwaNMifkAkhftIbzNj5\ncQkUbYX1Hp43BgPbR5sh3cbIQclYecc4awLqtY9KPNaTIIR4j2EYazmCIUOG4OLFiwCAG2+8EeXl\n5QFfX3l5OcxmM3JycqzT8vLyUFJS4jDvwoUL8dRTTzlMV6noIS7cQvFw5w+/u9CEiMHU9W6NeqMZ\n5y63BCCa8PH00NmNnklJL9aicF/wW9XNWykGW0Vd92nt69dod2lpafj000/x888/49KlS+Dz+Rgx\nYgSmTp3q01DeCQkJmDZtmvVnlmWxb98+p13pKisrER8fj9WrV+N///sf+vfvj5UrV2LmzJn+bAIh\nxAssy+LdL85b3zAunDEMuSPTPXyKRKpxw9Ow8o5x2PnxWeiNZrz64Rk8sXgCRg5KDndohHR7Q4YM\nwalTp3Drrbdi+PDhOHv2LABAqVS6rGXZFWKxGMnJyeDzO27l0tLSoNfrIZVKkZKSYp0+fPhwu89e\nunQJv/76K/74xz8GPC7SMyi1BvB51BzBX2pt8EYH80WktMDq6VqVkTHQASGRzq/kEwDweDzMmDHD\np252nrz88ssoLy/Hxx9/7PC7qqoq6PV6zJgxA8uXL8c333yDFStW4MMPP8TYsWMDFgMhpMM3J2tR\nWN4MALhmdF/cet3Q8AZEuqwjAVVCCShCAuj+++/H+vXrAQBz587F/PnzIRAIUFRUZNc6KVC0Wi2i\no+27P7f/7C7Z1draipUrVyIvLw833nijT+vkcjnws9E8CTBu25DZwTwmCo0RPC4db1+0Hxe90Uz7\nLkKE4rsiVxt67PHm87kB37ZQHBPim/ZjEmx+JZ/EYjFee+01FBUVwWg0OhQZ/+6773xe5rZt27B3\n71689tpryMzMdPj9Y489hqVLlyIhwTJs+KhRo3Du3DkcOHAAL7zwgj+bQQhxQ9SswsETVQCAQX3j\n8cAfRvvUspFErnHD0/DY7eOx6xNLAmrHh6fx2MJxyB6eFu7QCOm2Fi1ahOTkZKSkpCAzMxMFBQXY\nvXs3+vfvj+eeey7g64uJiXFIMrX/HBsb6/QzEokEDzzwADgcjsvBXdyJjaVaf5GGjklkouMSeeiY\n+MfAciAUxgRl2XRMeh+/kk/PPfcczp07h1tuucWaDOqKTZs24cCBA9i2bRvmzJnjcr7O68rMzERl\nZWWX108IsWc0MXj7SClMZgZRfC6W3zYWMVG8cIdFAmh8Zhoeu30cdn1yDgYjg78fLMHD88bgmtEZ\n4Q6NkG7pl19+we9+9zvrz/PmzcO8efOCtr6MjAzIZDIwDANu21tpiUQCgUCAxMREh/mbmpqwZMkS\n8Hg87N27165bnre0WgMNiR0huFwOYmOj6ZhEGDoukYeOSdecKm0I+DLpmESeiG759Ouvv+Kdd97B\npGw+TvIAACAASURBVEmTuhzArl27cODAAbz66qt2N22drV27FhwOB5s3b7ZOKy8vx8iRI7scAyHE\n3qc/VEEkVgMA7rw+EwP6CMMcEQmG8Zl98OTiCfjHxyXQGcx463Ap1DoTbpg4INyhEdLtPPjgg+jf\nvz8WLFiAhQsXBn2AlNGjR4PP5+P06dPIzc0FABQWFiI7O9thXq1Wi2XLliEqKgrvv/++3UAvvmAY\nFmame46e1fNYEo50TCINHZfIQ8ck8tAxiTyh6f7o11ri4uKQltb17hmVlZV44403sHz5ckycOBES\nicT6H2B5g6fXWwq4zZ49G0eOHMGhQ4dQU1ODXbt2oaioCPfff3+X4yCEdCivluLr32oAAGOHpuDG\nvIFhjogEU9aQFDz7x1wkxEWBBbD36ws48vMVh+7UhBD3vvvuOyxevBjHjh3DTTfdhHvvvRcHDx6E\nWq0OyvoEAgHmz5+P/Px8nD17Ft9++y327NmDpUuXArC/h3rzzTchEolQUFAAhmGs91o02h0hhBBC\nQoXD+vGEsXXrVigUCrzwwgvg8fzvivP222/j1VdftZvGsiw4HA7Onz+PrKwsbNmyBQsWLAAAHDx4\nELt370ZjYyNGjBiBdevWIS8vz6d1isVKv+MlpKfT6Iz423u/oVWhh1DAxwsPTUFKQnD6eZPI0tiq\nwfb/FKNFYXlYnTNpIO6+8Wpwqc4X6WbS07teDqCrysrKcOTIEXz11VeQyWS46aabsHXr1oCvR6fT\n4fnnn8fXX3+NhIQELFu2zPpSzvYe6uabb8aVK1ccPr9gwQIUFBR4ta4TRSKo1Xp6Sx0heFwuhMIY\nOiYRho5L5KFjEnnomEQeHpeLP8xwrLsdaH4ln9auXYvPP/8ciYmJGDRokMNoK++//37AAgw0Sj4R\n4trbR0rxa2kTAOAvC7IxKatvmCMiodSq0GH7gdNoaNEAACZn9cWyW8cgik8jkZDuIxKSTwBQWlqK\nr776Ch988AE4HA4KCwvDHVKXUPIpstDDW2Si4xJ56JhEHjomkSdUySe/aj4BwK233hrIOAghYXbq\nQrM18XRddj9KPPVCqYkCrL0vD38/eAaVdQqcLG+GUmPAY7ePR5zA7z8XhPQatbW1OHLkCI4cOYLq\n6mpMmTIFf/vb3zB37txwh0YIIYQQElZ+PU1420SbENI9qLRG7D12EQCQmhiDP86hQv69VXxsFJ6+\neyLeOlyK0xUSlNfIsOX/TuGJxTnUBZMQNxYvXoyzZ89i4MCB1qLjV111VbjDIoQQQgiJCH73pWhu\nbsauXbvw1FNPoaWlBV999RWqqqoCGRshJET2f3sJCrUBAPCn32dRK5deLiaKh0dvz8asHMuDs0is\nxua9haiXBKdwMiE9QWZmJt5//3188803ePTRRynxRAghhBBiw6/kU3V1NebNm4dPP/0UX3/9NTQa\nDb744gvccccdOHPmTKBjJIQE0ZkKCX4pbQQATB/XH9nDuz6SJen+eFwulswdhQXThwEAWhR6FOw7\nhYu1sjBHRkhkKigowOTJk8MdBiGEEEJIRPIr+bRlyxbMmTMH3377LaKiogAAO3bswOzZs/HKK6/4\ntKympiasWrUKU6ZMwaxZs7BlyxYYDAan85aVlWHx4sXIycnBokWLUFpa6k/4hJA2Gp0R//6qHACQ\nFB+Nu24cEeaISCThcDi4bfow/OnmLHA5HKh1Jrzyn9MoLG8Od2iEEAAGgwHr1q3D5MmTMWPGDOzZ\ns8fjZwoLCzFnzpwQREcIIYQQ0sGv5FNRUREeeOABcGyG4Obz+fjLX/6CsrIyn5a1atUq6PV6fPDB\nB9ixYweOHz+Ov//97w7zabVaLF++HJMnT8Ynn3yCnJwcPPLII9DpdP5sAiEEwIfHKyBTWZK9S+aO\nglAQFeaISCSaOeEqrLxjHKKjuDCZGbxx6By+LawNd1iE9Hpbt25FWVkZ9u7di/z8fOzatQvHjh1z\nOf+FCxfw+OOPw4+BjgkhhBBCusSv5BPDMGCcDIuoVqvB4/G8Xk5VVRVKSkpQUFCAzMxM5OXlYdWq\nVfj8888d5j169ChiY2OxevVqDB8+HOvXr4dQKMRXX33lzyYQ0uuVXm7FD2caAABTxmRg4tXpYY6I\nRLIJI/rgmXtyER8bBRbAB99ewofHK8DQQywhYaHVanHw4EFs2LABWVlZmDNnDpYtW4Z9+/Y5nf8/\n//kP7rnnHvTp0yfEkRJCCCGE+Jl8mj59Ot566y27BJRMJsO2bdtw7bXXer2c9PR0vPPOO0hNTbVO\nY1kWSqXSYd6SkhLk5eXZTcvNzUVxcbEfW0BI76bVm/CvLy3d7RLiovDHOVeHOSLSHQy/KhHrl+Sh\nb3IsAOCr/9Xgnc/LYDI7vowgpDdzVT4gkMrLy2E2m5GTk2OdlpeXh5KSEqfz//jjj3j55ZexdOnS\noMdGCCGEENKZX8mnNWvW4Ny5c5g+fTr0ej1WrFiBG264ASKRCM8++6zXy0lISMC0adOsP7Msi337\n9uG6665zmLe5uRl9+/a1m5aWloampiZ/NoGQXu2j4xVoUVi6rN77u5FIiIsOc0Sku8hIicO6+/Mw\ntF8CAODX0ia89tEZaPWmMEdGSPjt378fs2fPRk5ODmpra5Gfn4/XX389KOsSi8VITk4Gn98xOmla\nWhr0ej2kUqnD/Lt27aJaT4QQQggJG7+STxkZGTh06BCeeOIJ3H333Zg0aRKefvppHDlyBAMGDPA7\nmJdffhnl5eV44oknHH6n0+kQHW3/gBwdHR2St4uE9CTnLrfg+9P1AIBJo9IxOauvh08QYi9RGI1n\n/jgR49pGRiy7IsXWD4ogV+nDHBkh4XPkyBFs374dCxcutA7GkpmZiTfffBPvvfdewNen1Wqd3hcB\noWl5RQghhBDiC77nWZyLjY3FokWLAhbItm3bsHfvXrz22mvIzMx0+H1MTIzDzZTBYIBAIAhYDIT0\ndBqdCXu+6Ohud9/cUXYDBxDiLUE0HyvvGId/f1WOn842oqZJhZf2nsKTd+WgX2pcuMMjJOTee+89\nrF+/HgsXLrQmm5YsWYK4uDjs3r0bDz74YEDX5+q+CLDcowUDl8uBn+8tSYBZjgUdk0hDxyXy0DGJ\nPHRMIk/7MQk2v5JPS5Yscfv7999/36flbdq0CQcOHMC2bdtcNgnPyMiAWCy2myaRSJCeTkWSCfHW\nf/77/9k78/ioqrv/f+6dO/u+ZbInJCELBBISFq2CTxFF7IPRCqK2ymNFkEd9EIRatD8RtYAVUdsq\nKiqtaHlw36q1QvugbVUMa1giEsISIMuQdSazz/39MZnJrMnMZLYk5/165ZXk3HvP+d57zj33nu/9\nLj+go8dlnXL77BLIiLsdYQgwHBq/uLYMSikfn/z7NPRdZqzbthf3z69AQaYs2eIRCAmlsbERkydP\nDiifNm0aHnvssZi3p9Pp0NnZCafTCZp2vbzr9XoIBALIZPG5/4RC8sxINUifpCakX1IP0iepB+mT\n0UdUyid/1zq73Y7Tp0/j+PHjEQey/MMf/oAdO3bgmWeewVVXXRVyv4qKCmzZssWnbN++fVi6dGlE\n7REIo5VDDXr885Aru90l43SoLiHudoShQ1EUfjqjEAoJH2/+7TgMJhue2r4f9/50AsaPUQ1eAYEw\nQtBoNGhsbEROTo5P+f79+wNiVsaCsrIyMAyDAwcOoKqqCgBQW1uL8vLymLflxmSywukkGS5TAZqm\nIBTySJ+kGKRfUg/SJ6kH6ZPUI6Utn9avXx+0/Pnnn0dzc3PY9TQ0NGDz5s1YsmQJJk2aBL1e79mm\n0Wig1+shlUrB5/Mxe/ZsbNq0CevWrcOCBQuwfft2mEwmzJkzJ5pTIBBGFUazzZPdTi7m4daripMs\nEWGkMbMqGzIRDy9/fAQWmwPPvn0Qd80dh6llumSLRiAkhAULFuCxxx7D6tWrAQAnT57EP//5Tzz7\n7LNxyTAnEAhQU1ODNWvWYN26dWhpacHWrVuxYcMGAPB5h4oVTicLh5Nkt0wNXNZupE9SDdIvqQfp\nk9SD9EnqkRj3x5i2UlNTg88++yzs/Xft2gWn04nNmzdj+vTpmD59Oi6//HJMnz4dAHD55Zd76pNI\nJHjxxRdRW1uLG2+8EXV1ddiyZQuJ+UQgDALLsnjzb8fRaXDFAll4TSkkQm6SpSKMRCaXpmH5TZUQ\n8DhwOFm89OER7NrblGyxCISEcNddd+Haa6/FihUrYDKZsGTJEvzmN7/B3Llzcffdd8elzdWrV6O8\nvBwLFy7E448/jmXLlnnCF3i/QxEIBAKBQCAkG4pl2ZjZun388cd44okn8O2338aqypjT1taTbBEI\nhITy1aHzniDjl5Wn487/HJdkiQgjndPNPdj01gH09NoAANddlo+ay8eQ4PaEhKDVSpPavslkwokT\nJ8CyLAoKCiCRSJIqT6zYva8JRqOFfKVOETg0DbGYT/okxSD9knqQPkk9SJ+kHhyaxrXTA5O+xZqY\nBRw3GAz4/vvvceuttw5ZKAKBEBvO6Y1484vjAIA0pZC42xESQl66FA/9vBpP7zgAfZcZH/3rFMxW\nBxbMLCIKKMKI4vz580HL1Wo1AKC7uxvd3d0AgMzMzITJRSAQCAQCgZBqRKV8yszMDFhAcLlc/Pzn\nP8d1110XE8EIBMLQsNgcePHDw7DanGA4FJbWlEPIj+qWJxAiRqcS4aHbqvH0/x7AOb0Rf/vuLCw2\nB26bXQKaKKAII4SZM2cOqlBlWRYUReHYsWMJkopAIBAIBAIh9YhqJeoOZkkgEFKX7Tt/wLk2IwBg\nwcyxyEtPrisKYfShkPDxy1snYdOOgzjd0oPdB87DanPgFz8pA4dOTGBDAiGevP7668kWgUAgEAgE\nAmFYEJXy6bvvvgt73ylTpkTTBIFAGALfHG3Glwdd7iBVxVrMrMpKskSE0YpUxMOqWybh2bcP4sS5\nLnx9pAVWmxNLasaD4RAFFGF4M3Xq1KDlnZ2d4HA4kEqJ0p8QGQxNwz7KYqBQoMCCpFsnEAiEkU5U\nyqfbbrvNY2buHa/cv4yYmRMIiaelvRd/+uv3AAC1TIA7ri0lcXYISUUkYPDAgkr87t1DOHa6A3uP\nt+EP79XhnhsmgMsQBRRh5PDKK6/g9ddfR1tbGwAgOzsbd911F2666aYkS0YYLqhkArR29iZbjIQi\nF/PQabQkW4wRS1meCsdOtydbDAKBQEBUb/0vvvgisrKy8Oyzz+Lrr7/G3r178cc//hFjxozBihUr\nsGvXLuzatQs7d+6MqF6r1Yq5c+cOaFm1dOlSlJaWoqyszPN79+7d0ZwGgTDiMJpt+N27h2CxOsCh\nKdxdMx5iATfZYhEI4PM4uH/+RFQUugIxH2q4iBfer4PNPrq+8BNGLi+//DL+8Ic/oKamBs8//zx+\n//vfY9asWVi3bh3eeuutuLRptVrx0EMPYcqUKZg+fTq2bt0act+jR4/ipptuQmVlJebPn48jR47E\nRSYCgZBayMW8ZItASCFkotExHrI0IyPT7EgjKsun9evX45FHHsGMGTM8ZZdccgkee+wx/PKXv8Rd\nd90VcZ1WqxUrVqzAiRMnBtzv5MmTePrpp3HJJZd4ymQyWcTtEQgjDbvDieffq8OFi64vpvN/XITC\nLHmSpSIQ+uEyHNzz0wl44f3DOHBCj4MNF7H5g8P47xvKiQseYdjz5ptv4tFHH8X111/vKZs1axYK\nCwvx8ssvx8X66cknn8TRo0exbds2NDU14cEHH0RWVhauvvpqn/1MJhMWL16MmpoabNiwAdu3b8eS\nJUuwc+dOCASCmMtFiB5iqEwg+JKbJsWZ1p5kizFiyNVJcbjxYrLFIIxSonrbb21tRVZWYAwZiUSC\njo6OiOtraGjATTfdhKampgH3s1qtaGpqQnl5OdRqteeHyyWWHYTRDcuy+NNf61F/phMA8OOqLFw1\nOTvJUhEIgTAcGv99QzkqizQAgAMn9Nj8wWHYHcQCijC86erqQkVFRUD5lClT0NLSEvP2TCYT3nnn\nHfz6179GaWkpZs2ahUWLFuGNN94I2Pcvf/kLhEIhVq1ahYKCAjz88MMQi8X461//GnO5CMMbjVyY\n8DZTLdqTRpb4azAaYKJMNKKQ8GMsSWLJ06VW7D+GQ0GnFMW+XpJIJij56cRIxpuoRkllZSU2bdoE\ng8HgKevs7MRTTz2FSy+9NOL69uzZg0svvRQ7duzwiSHlT2NjIyiKQk5OTjRiEwgjlk/+fQr/qmsG\nAEwoUOPWWWNJnCdCysJwaCy9vhwT+1zw9v9AFFCE4c+VV16Jbdu2BZR//PHHmDlzZszbq6+vh8Ph\nQGVlpaesuroahw4dCtj30KFDqK6u9imrqqrC/v37o24/HosXQvLhcznJFiHp0DR5f4oHObro3KCG\n++usdJS4uRGC4yDvtj5E5Xb361//GrfffjtmzJiB/Px8sCyLU6dOQavVRpV2+JZbbglrv4aGBkgk\nEqxatQrffvstMjIycN999/m4/xEIo41vjjTj/a8aAQDZWgnurhlP0tgTUh4uQ+OeGybg+ffrcKjh\nIvb/oMfLHx3BEjJ+CcMUtVqN7du3Y+/evZg6dSoYhsHhw4dRW1uLK6+8EqtXr/bsu379+iG319bW\nBoVCAYbpf5VTq9WwWCzo6OiAUqn0lLe2tqK4uDhA3sFCHQxEnk6Klo74BMbO0khwTm8YfEdCzFHJ\n+KP+2g93ZUeqkK4Sobm9f45IUwgh4HJw7EzkXjLDFdpvMCklfHQYkhtcn8LwHeCxvH40RcE5gNFL\nrLCS2KY+RPWGX1hYiE8//RQPPPAAKisrMWnSJDz88MP48MMPkZ6eHmsZPZw8eRIWiwXTp0/Hq6++\niiuuuAJLly4lQTMJo5Yjp9rx2qeujJIKCQ/3z58IIT8qnTKBkHBcCqhyTChwWUDVft+G1/5Sn5CX\nAQIh1hw7dgyVlZWQyWSor6/H4cOHAQCTJ09GV1cXmpqaPD+xwGQygcfz/aLu/t9qtfqUm83moPv6\n7xcueTppXK1DctIGtpCQi4efGw6PIRZFhOCMz1clW4S44O9uRFEU5FG40An5DGQiHrjDMDbkuHyV\njzKTpimU5YXX33JiMRWAVMRDploc1r4DeVMBwKSxmliIFIYcCWlm2BD1KlUul2P+/PloamryuMHF\nO/bSvffei4ULF0IqdfnOlpSU4PDhw9ixYwcee+yxuLZNIKQadScv4vfv1sHuYMHncrBsXgVUMhI4\nljC84DIc3HNDOZ575xCOne7A10eawefSuG12CXEdJQwrgrncxRM+nx+gPHL/LxQKw9o30mDjNE0h\nSytFTl8Mk3hZKTIMDQGPCZkNM0srhsFki0vb8aKqRIvvjrUOuh+HQ4d1Xd3KP9fv2PUDw4TXfizJ\nS5fiSGPi+3NCoRp1DYGBl8Ptg2BkaSXo7LVF1C9KmSCu1zwZfRqsXYZx/R2pLAxDY2KRBk6WxbdH\nIoufJxVxYTTbAUR/r0iE3Kjmm+pSLXgMB0aTzXPONE1DLR+8v4V8BuML1RGfbzgwXBocDhXzMcHh\nUGDDvL7u+YvDiaxPOAwNUOGNIf/xp5ELoO8ye/4XCrgJuS94vOTcf5GSKHfjqJRPLMvi6aefxrZt\n22Cz2fD555/jmWeegVAoxKOPPhpXJZRb8eSmsLAQDQ0NcWuPQEhFDpzQ44X3XYonHpfG/8ybiLz0\n1ApoSCCEC4/LwX03TsCmHQdx4lwX/u/AefC4HCyYWUQUUIRhRVdXF06dOhWg6KEoCpMnT45pWzqd\nDp2dnXA6naD7Xmz1ej0EAkFAFmCdToe2tjafMr1eD61WG1GbQiEPKqUYSqXry7PYzwKJYWjYh+hi\nUJgth1IpxhWTc9HTa8XhIMoBhUIE8UXTkNpJNFqNFGJx16D7yWQCGCyOsOsVCmNrHaFQiCEWJ9bt\nLi9bCbVaAh5D4+u6CwHbi3OV0KlE+OrAuajqp2kKTmeg+YFSGfxc5TJhyD6YVp6Obw83B5TLxDzk\nZ8og5DP49nBzRP3ikiN+1nzxrj/cdkPNG+HU40Ys7ozoWJmEDyflctOK5l4pzlWCpinUn2oHAKjl\nAlz0UmAMhE7rmoe5fKtnnEmlgrD6Y8akLFAUFfH5uinJU+L708HdGxUKEbrNDhgsrrlaJuah2xid\nFaw3fB4HFmv4cxfg6pNILIPkMiHsDic6e+2D7iuTCX32qy7PxD+95pBE3RclYzToNsVeiThciUr5\ntG3bNnz44YdYs2aNx+Jo1qxZWLt2LTQaDZYvXx5TId2sXr0aFEVh3bp1nrL6+vqAOAYEwkhm3/E2\nbP7gMBxOl8XT/fMnoiRXOfiBBEIKI+AxuH9+BZ7avh+nW3rwt+/Ogsfl4KczCpItGoEQFu+++y7W\nrl0Lm80WYO5PURSOHTsW0/bKysrAMAwOHDiAqqoqAEBtbS3Ky8sD9q2oqMCWLVt8yvbt24elS5dG\n1KbJZEV3twkdPJeyy2j0jb1xaXk6vg6yMI8EyuFER4cRgOt7uH8bANDVZfIpz9CIcEEfn/hTg5Gh\nFuHCxcHb7ugwBj0Xf7r5nLD2o2kKQiEPJpM1qGIlWjo7w5NzMMblK3H0VHixfdz9bUPw/hZwgK6u\nXp9tFBW+O4tKJkB7kHo7Q/RJt4CDXK0Ix4LIbzJagh6TqxUBdgd6rK7FbiT9Eu7YiJZ41x9uu+5+\njlQW93HRHEuzTpjM9qjvla6uXuhUIqgkXHA5NDQKPs6cD61E9lZ0es7XZPPIzedQYfVHZ6drTom2\n37r95khvujp70dPTv51mnTD2Dt3ykM8RhC2v9/zlcITfJ13dJshE3KDt+M8JFhPfZ79uvzkkUfeF\nyWgBnA4YTYMrzJLJjyZmJKSdqJRPO3bswCOPPIKrrroKjz/+OADg2muvBZfLxfr162OqfNLr9ZBK\npeDz+Zg5cyZWrFiBqVOnoqqqCh999BH27dvnkYFAGOnU1rfipY+OwOFkIeBxsOKmShRly5MtFoEQ\nE0QCBg/cXIkn/7wP59qM+OTfp8Dn0vjJpfnJFo1AGJTf/e53qKmpwX/9139F7M4WDQKBADU1NViz\nZg3WrVuHlpYWbN26FRs2bADg+/40e/ZsbNq0CevWrcOCBQuwfft2mEwmzJkzJ6I2nU4WDofTY93k\ncPpaOdntzoCySOH5WU8Fq8/h8G3HYWeH3G60ZGslaGob3FIo3Gvjf26hcSkAnc7wzj3cIO5OR2yu\npVjAhVYh8Ak4HYrB+jvYeCvMlKPBTwkQKhhxqGtqD1HudLCQCLioKtbgu3pfV8lQ/eiwu+4Ld8zC\ncPtloDpjRbzrD4ZSwg9oN9S8MRiDjY+BcDhYjzIokj7pP97Vr+l92T1Z58AylOWpoe8yQasQeuT2\nHmfu+gaTI9pr5Tl+gHnEbnfC4XWfO2Jwz8vFfOSmidHebQ6oSynhQyHho7G526s0svnLA8tCyGOC\nHlNdnAa7w4mWjl7Y7SxUUj5+8Bt//uNRLGDQ3Ru91ReXw4HNMbC1l93hBIeikvaMciMRcGEwh1Yy\nsjH8iDEQUTkgNjU1oaysLKC8tLQ0wKw7UvxdLC6//HJ89tlnAICrrroKa9aswebNmzF37lz84x//\nwCuvvILMzMwhtUkgpDosy2LX3iZs/tBl8STkuxbpRPFEGGlIhFysXFAJncr1ovfu7pP4ovZskqUi\nEAanu7sbd955JwoLC5GVlRXwEw9Wr16N8vJyLFy4EI8//jiWLVuGWbNmAfB9f5JIJHjxxRdRW1uL\nG2+8EXV1ddiyZUtClGQDoU5wnEIBjxm1QXwHC+KuEPORqRaDzx0egdG1CiH4XkHcq4u1MbcCT0Sc\nljF+QblHChq5cPCd4oBY4Bv6hUVioz0LeBzkp8sC5BjplOUpwWU4mFDgG0w9QyVGSa4S1BDiCYkF\nXEgE3D6FduhxxWVoCPkM8tNlKMqWhxW2IXuQeXEwOGGcFwUgPyPx97lCzIeuT2kKuIK1e+OfiTFR\nRGX5lJWVhbq6OmRnZ/uUf/nll57g49Hib5ZeX1/v8/+8efMwb968IbVBIAwn7A4ntu/8Af/Y7/JT\nFgsYrFhQiTFJmMgIhEQgl/Cx6uZKrH9jHy52m7F95w/gczmYUUE+NBBSl1mzZmH37t3Iz89PWJsC\ngQDr16/H+vXrA7b5vz9NmDAB77333pDbTHQctmBfa6OVoLJIgy6DBV1nhh7fxBs+lwOLLbJYJ6lG\naZ5LcRNLF754U5Alx7HT7aApCkwMM6GlKYMvcIW82GYTFgu4ng8tiSJR6eWTFa4xoNkoTlXAY2Du\nc58cbIHub1EY7qUdkyHD2RYD7EmwhokksLREyAVFURDxGbR0DG7FKPC7RwZSFoULRQHlY9RDrido\n3QNsy9NJIeQzYDg09F2uGIPhWHIGtEFRIZX6cjEfXV6uf0IeA5M1tHue99j0aQNUgKK1NE+JptbQ\n1q7j8lU43BgYUzHeRDWL3nnnnVi7di3a2trAsiy+/vpr7NixA9u2bcOvfvWrWMtIIIxajGYbXnj/\nMI71BQ3UqUS4f97EhL+sEAiJRiUTYNUtldjw5j50Gqz402f14HFpXDIuPdmiEQhBWbVqFebOnYvP\nP/8cubm5AUqaYAqi4U6eTorTLT0AAJU0PlZMcgnfR/mUoQovzXZI4rAqLs1V4mCDPub1hks4rh8A\noJUL0dY1cKB2mqagEPPRGUYslAyVGE6WDWtRGg/kYh4mFmjA49IDKkUj7XIhP/jyKL8vscuACpwU\nz5GhkgmQpRHHfbwO5/TyEwvUqDt5ERRFQSUfeF4T8jmDujMFQ6cUIU0hxN7v2wIUUKEUXpVFGhw4\nEV6/Bbv8GrkQCjEvIkXt2CwF+DwOTjf3hH2MN65sdvGHivLGG2iYqqQC8HkupZFEyMWFi8YB9o4N\naUqh55nqT1muEk16I8xBvp1MGqvBvh/C9z5TSQWQCJNjnReV8unGG2+E3W7H5s2bYTab8cgjiaaK\nbgAAIABJREFUj0ClUuH+++/HLbfcEmsZCYRRSUt7L5595xBa+rTsZXlK/PcN5aPOlJcweklTirDy\n5kl48s/70NNrwysfHwOP4aCqOLIMXQRCInjiiSdgNBphtVpx7lx0WbmGA96v+BlqMaQiHpxOFhJR\n5M+maFy8BLzUcwsLpayIhngu2gsyZdCpRLBYHfjhXOgsWqV5SnxzNDBwvFvB2N7jyvallrsWMENR\nPg3VilskiK01UjiU5ilx/Eynr9JgAA2X2/XF/zrl6hKXpbg4W4EuoxU5aZKYWomFIlFKhwD8ms3P\nkHk+4IYLTVOYWKgO28pTIupXPkXiqUlRFMblq3C2tQdpShE4HAot7b3I0gRXsPtbFUVCmkKEgszI\n77Whep6653hRDOfIYET7TWHAw1JIkcxjOJBL+GjSB1eA8YaJuzQQpfLpk08+wTXXXIMFCxagvb0d\nLMtCrY6PORyBMBqprW/F1s+OwdSX6vfHk7Jwy6yxCXlhIBBSiUyNGA8sqMRv/7wfvRY7Nn9wGPf8\ndAIqizTJFo1A8OHLL7/E5s2bMX369GSLEl/8XsgH+npanK3A8aZ+JYdWIURumgRNbUaYLXZkasTQ\nd5lhtYfvssYCASsNlYyPC+3hfZUOtZ7IUInRYbAEdWmIFSU5Snx/tn8hLOIz6LWE115Zngo9Riua\nggQNz9SIQn4t94aiKEiEXFj9XATDtVorzlHgRFPoTF9uNLLwXW28Y5KkOm69oEzEQ3WJFqeae/oV\nSgNoDem+6+7eVyHmIy9d6qO0zNNJ0dRmjFtQYpVMAFUCYqzJxXxwaApycXJiqwl5DAymfiskiZCL\nsjwlzkSYDTMS9+JsrQQOBwuJkBtxnDCRgPGJVSaLU0y6aGNfxcrNWiLkoiBDBpuDxdnWyKyo8sJQ\n0kYrp0TIDTkPx1r3xNB0gJWbViHwcbtLNOFazcaSqFayjz32mCewuEqlIoonAiFG2OxO/PmL43jh\ng8MwWRygKODWWWPx86uLieKJMGrJ1UmxfEEF+DwOHE4WL7xfh0NJdHEhEIKhVCpJAhQ//Be7FChw\nGQ7GZMhQlq8Cw6ExLn/gINH+yi2WZX0WBSI+12cRz+XQA8dpCbEpL12KbG1kLn0KMd/z90DugO5Y\nQUopH2VeC03/ILQDWTbIxTxkacXISQtciKWrRCjOVqA0zIDb/gs1XYgYR9HitoLLVA/RRXKI8BkO\naIoaNNh6NIRa7Ibj/iMSMAHWchlqMSaXaFE1VhsQJyecxXekFGcrIBFywwo6TIEKy+pGKuShLE+J\n4hxFzJQWWZrw+04s4CJXJ8XEAg3UMgHK8lzBr+NtFcJwaBRmyVMrJEYK+j2mKUUhrbpCMalIGxAo\nOxjRjjaKojChYAh6jAgaDma1G++kBoONgtI8BYQ8BrlBnivxIqozzs/Px/Hjx2MtC6xWK+bOnYvv\nvvsu5D5Hjx7FTTfdhMrKSsyfPx9HjhyJuRwEQjJo7TRh/Rt7sXNvEwBAIeHhwVurMGtyTsIDvBII\nqUZhphwrbnIpoOwOFn94rw6HGhIfKJFACMXdd9+N3/zmN2hsbIQjQV8SN27ciEsvvRTTpk3DU089\nFdYxp0+fRkVFRdRtDuVpFOxRJuAxngV7MIsZpZQPATf0wlcs9N3G53Iwaaw2uthQYa7X6L4FS3Gu\nwlPG4wZ/pc7TSX0WN3IJH1NLdZhUpA2wcijJUQxooUBRFGRB3BspioJKJoBCwkdBhgzZGgkml6SF\ndzJxZLBFv1s54M1QXIsAV4B6NxVFGkwaqx1ynW6iXc+H+wpHURR4XA4KM+U+CqfB3gH9lY7hBGdW\nyQQoH6PG1DJdyH24HA6UEj6KcxQoyVFAwGN8rq8/ZXlDzzaY7qXAEfKYsBWHOVoJJhSowWVoiAQM\nxmYrQlpfxdsFLFEk4jzisfwIV0nuHXNpMMRDcL8NdX+Fc7uHujypOMaCnaZYwEVFkQaZESoFh0JU\nV6a0tBQrV67EK6+8gvz8fPD5fJ/t0QTVtFqtWLFiBU6cOBFyH5PJhMWLF6OmpgYbNmzA9u3bsWTJ\nEuzcuTPp6YIJhKHgcrOrh6nP7LN8jAqL5o6Lm/ktgTAcGZutwPL5FXjmrYOw2Bz4w3t1uO/GCUP7\nakUgxIhXX30V58+fx7XXXht0u38236Hy2muv4dNPP8ULL7wAm82GlStXQqPR4I477gh5zIULF7Bk\nyRJYrdFnewvnK7Q3YzJkaLzQDSD0QqaiSI1uozWkW1C6WoRTzd0h2/BRClCulNtZ2uBudAOtpSJx\nePKPv6iRBw8UK+AxAdmlaJoKuqiKReyotDDc2OL9PYsNoaURcBmYbf39EUw5MD5fhb3HWwesXynh\nh9xWnKPAiXNdkIl5oGlqwMxeLBs8S9RQCHZtOXG2XFf4XY9YBRIW8jk+LmFud/dg8cD4DCeiLGqh\nkIv5noxisagvGAWZ8pBZvuTD6L27fIwaNocT+yMINB2MgVw9Q1nyhcq6Fg7+47UsV4kOgyUgk1xh\nVvgxqvytSBNFYVbwsVSaq0RrpwnqBLi6Djeieso1NjaiuroaADzud0OhoaEBDzzwwKD7/eUvf4FQ\nKMSqVasAAA8//DC+/PJL/PWvf8X1118/ZDkIhERjsTqwfdcP+PLgeQCur6k3zBiDOZfkhWUKTSCM\nNopzFFh+U78C6vfv1uF/bpyAcqKAIiSZpUuXJrS9bdu2YdmyZZg0aRIAYOXKlXjuuedCKp927tyJ\nRx55BGlp0VnETCjSoKurN2IFiVomwKkLPWDBhozvI+AxA1qnBDwNvQtY3wU/j3EpdRgOjcoiTdCF\ncmB1rgpCKU3CIWaP7AR4y8T67SLc2FUluYpBs6xxGV9FjbcFW0WhBp0Gy4Dp23lcDsblB1pUDdRe\nuDHHolGGcGgaaQohenqjV/hGg0zEQ3evNWJlcTLJVIshEYY/v3BoOqwYWQzT3285aVLwg1gpjstT\noaPHgkxNZK5z7tisyYCmKfDpobsUahX9inOpkIcek9dYDTLkS3KUYFnWJ57fUJBL+JBL+AHKp0hc\n0kJZng4FThj3u0TIRXVxGhgOhW+PtXjJw0G21s9qLwnLuqE80+JF2Hf4b3/7W9x7770QiUTYtm1b\nTIXYs2cPLr30Utx///0DmoIfOnTIo/RyU1VVhf379xPlE2HYcbq5By99dMQz2SqlfCy5bjyKcxSD\nHEkgjG6KcxS4f/5EPPP2QVhtTvzu3UO4u6acZMEjJJUbbrghYW21trbiwoULmDx5sqesuroa58+f\nh16vh0YTGJB/9+7dWL58OfLy8rBw4cKI21TJBKAcDtjtkQVEZjg0qoo1cDoRtgtFAF4v7cHepRkO\nDa1CiJ5eG/LTB45dESzDnjum4lDe02P1wUgkYIDBY3oPjRh/3CrNVaLuZPuggWujsezK8+pPIT8w\nVtJQEPA4KM5RoP50hycQ8EBxqoK5PA7GpLGapMTsLM5RoNNgCbAyCbpvtgLn9UZPxjY3iV625uqk\nsHkpAgcbpXnpUpw8P/jNwmM4KM5Vorm1GxlqERyOwDOTiXmQRREk3RCGUjEpn5IHuce95zoRn0H5\nGDU4NIXTzb7Wm+5a/K0Dk63TUEkFnqybQOwCowMuF04hnwn7vvVXmEeCv3JoKNd1XJ4KR0+3R19B\nggh7Bt+6dSvuvPNOiET9GuHFixfjiSeeiPormptbbrklrP1aW1tRXFzsU6ZWqwd01SMQUg0ny+KL\n787inf9rgMPpmmWqS7RYeE1pzEylCYSRTkmuEsvnV+DZtw/BYnPghfcP4xc/KcWPyjOSLRphFLNr\n1y4cP37cJ+aT1WpFXV0dtm7dGrN22traQFGUz/uXRqMBy7Jobm4Oqnx6/PHHAbg++CUaLjPEr/Os\n759UkE2FmfKgh8pFPHT1Wj1KJx6Xg+JsBS52m3Gx2+yzr0YuwNlWw6DWFMEWCDRNoThbAaPZDpvd\nidZO14elSNdEOlV4meuGQqwXw66v/GI0DuAamWyKsuQ4ca5fUTE2SwGGQ0MipFFdooXDycJosgUo\nIGiKgrOvw6NZ4EarePJuKxrrBYZDQyMPL5C8OxNeOFaCIYlyUGnkQui7TEOvaBAyNGIIOIDd7oQj\nhmq1+OQm7CddJUJzey8KQsxvoYjoKvZlYwQCFY6h4yElV/s0NluO+jOsJ1NcKOV/nk6KMy0GHyX2\nYGT5WyxFSDhJB+KBTMxDQYYMJy90h53BNBmErXwKNvF99913sFgSlx7QbDaDx/N9KPB4vCHFLiAQ\nEkmX0YpXPzmKw40uzTSPS+PWWcWYPjGDBBUnECKkJFeJlbdU4tm3DsJotuOVT47BZHHgyursZItG\nGIVs3LgRr7zyCjQaDS5evAidTge9Xg+Hw4Gf/OQnEddnsVjQ0tISdFtvr0ux4f1O5P57JL4TeQeu\njjSw7NgcBdq7zT4WIO7F9kW/xbbbVW+wmEOhcNULT4yrcBDyGJisdo+LBk1RyNNJw1ZA5Q6wqCrL\nU+FsS09gMNkIXzekQp6nDpWMD323S1kQzIosFMkOJaCRC32UTyKvcURRFBgOBXkYVkIjmWCp4ONN\nfroUfC4nZHDwAYmR+U1JzhACpcdZB5OfLkOWRhKxdU20d1ueTopDJ8NY23uddyh36nhCURTGZstx\nttUA6QAWiRlqMdKUwrhnlQNcLsJtnSafRBSJJk0pgkzMCzo3p8o6M/VCsQ8An88PeKmyWq0k2Dhh\nWHCksR1bPjmKbqNrDOemSbCkZjwykpyKmEAYzhRmyvHgrVV4escBdBmtePOL4+g12/CfP8pPmQct\nYXTw8ccf46GHHsLtt9+OK664An/+858hEolwzz33ICcnJ+L6Dh48iNtvvz3oOF65ciUA1zuQv9JJ\nKAzP2iEawgmcPDZbgZPnu8Hj0mCG4I7gjUYhgNEsAU1T0PTFz3EvJjg0NWA7DEMjM8SXbE8dnP46\nGIYOa6EyUJscTn8dDGfg61AxVoNesx1SEdfT197H+7fn3ua+FjkaERyO4AoDtVwAtTzwHZnrd44c\nJlBG7+0VY/st6dJUItAcGjyGhtBLgeN93Wivc87PkKGlvRfFOYqAaxvquoSzTzT41xtO3RwODarP\nSj3gGnGo/jHUV597Te6KD0UH9BsA0JyBxywAyCU8z/5yCR+cNmPIfcO9roPBMDRYr9Bdoe6tYPdH\nqHEeTC7vMgGfwZhMr2DRFIKOo2D1+dxnA/Sne95y/2a96uFxaWiVkc2Z3jLQg8w/gGtsBJtrwsV7\n/8Gup/c2n339rqX32GW8ZJJ5jTufNvyuNQvW87+Qzwwqoz/u+GkcL7lCzXmhYBgaY8MIVcKgv56x\n2Qo0tRkwJkMWscxcLmdAGQuz5SjIkoV89+TQwed1/7k4WH+6xw2HpkL2txsJw/M6znfsDTQO450Y\nwc2wUj7pdLqAAOd6vR5aLYnzQUhd7A4nPviqEZ99c9rzUnLV5BzM+4/CIfkJEwgEF9lpEvzq51V4\n+n8PQN9lxvtfNaLHZMPNM8fGLVsOgeDPxYsXMXPmTABASUkJDh06hGuuuQbLly/Hww8/jGXLlkVU\n39SpU1FfXx90W2trKzZu3Ai9Xo/MzEwA/a548XwnkskGX6QplWJk6GQQCbgxfcapVP0KJA6PC7HY\ntRiXSoVQKqP7iCMWuyxdeFzapw53uT88Lg2rzYmxOYoB25QZrDD0BSKWK0RQRpjxyGhzQtzj+7HV\n3R7NZTznzqGpsPrEH4bff/0AQCEPlNH7Gvifa7BzN9lZiLtcFhNyWX+fKJViTAiz3kj2iQbvehUK\nEUSCwUMdaFRiGE22oLIUMgwMFte6JCtdDh6X06cI7IBQyPM5hifg4Vy7y2IsO10B5SAKD6VSDJ6A\nB5Z1uYypVWJ09Fhw8lxgjCOlUhyTayaR8GG19SsyJWJe0LqC3R9CPjPovu7tA8lqszs826WiwPa9\nj5XLRZ4xJ5MNPg+47xWfNkKc40CkaSSeMZGmEg16PNdkg1hscLU3hPkKGPx6upErRBB39LsVS6UC\nn3al3RYYra6+VijEUEj76wjWRpfZgR6zo69MBLPFAXFn37WXC0POn6HONUsnQ3u3GVPGZ3jmHv/z\niOW9711naWHgM3LaxEwcbrgIhZQfsl2To3+Oi0bGsfnA8TMdPmUymQhicb/bqUwqCJj7gf5nlFRq\nhJMKfK6GkqOj144uk0ujLJeL0Nnr+nuo43AoRKR8SvZX5IqKCmzZssWnbN++fQnPMEMghIu+y4SX\nPjyChvMuE3yJkItf/KTMk66WQCDEBp1ShNU/r8bG/92PCxd7sbO2CRe7zFg8d3z0QY4JhAiQyWQe\nd7jc3FxPPMrMzMyQ7nPRkpaWhoyMDOzdu9ejfKqtrUVGRkbQeE+xorvbFNLKxh+DLbo03GHVbbLB\n2Bfro4eh0NER2ipkINx1WBnapw53uT/jytLQa7ZDOEib3d1mTx1dnb2gBgnEHXi8KUAGd3tOloXV\nYoPDySI3XRdRn7hhWdan/s6uXsBPRu/t4Vxfb5nNvRZ0dARXPIZTb6RthwuXYtFpcC3sOjt7YQkj\neHmmUoDjBjPUMkFQWXI1IjAMDaPBDCPg8XcymaxwOlmfY9IVfNgdLBg4wzovft8ldO8r4AQfmx0d\nxphcM4PBAptXQgGaDS5nMBkcNvug+7q3DySrze70bKecge17H9vV1ev5v7vbhA5+8Gc9h0NDJhN6\n7pXB2hgMp83uOV6YJh70eKO5f77ic6Kfr4DBrycA5Ook6O7ynUPk2TKfdnt6vOaorl6w9v75Olgb\nYi4Fp90BLkODtdnR5VV/j9+1D2cs5mpFKM5TwmKyhjyPWN77g0EDKMmWgev3LPCmZ4B5ORz4NIsM\npQBtHSZ09XnBeI9hAOgK0gbQ/4zq6THD2GsL2B5Kjq5u33ukfxwGHuO+T+JNRMqnJ554Anx+v1bS\nZrPhqaeegljsqzlbv359bKSDy7JJKpWCz+dj9uzZ2LRpE9atW4cFCxZg+/btMJlMmDNnTszaIxBi\nxYETerz6yVEYza4JvSRHgcXXjYdSOrpjChAI8UIp5eNXP6vC79+rw4mmLuz/QY8Nf96HZfMmhpXx\nh0AYCtOmTcPGjRvx+OOPo6KiAi+99BJuvfVWfP7551Cpwk/9Hi4333wzNm7cCJ1OB5ZlsWnTJtx5\n552e7e3t7RAIBD6JYoaKw+GMONtdPLDbnZ6g4PYhyMTn0ui12DE2Xe5TR8iA46wrM9Rg7TkcQ5PP\n+/wAVywR7zrKx6hA0xREAi46TNaozl8jF6Clw6UsddgDZfRuP5z6lRI+hDwOaJqCXMwLeUw49Uba\ndrg4naynbpvNCS5n8Lq5HBrj81UhZXEHanZvc1vbutvyPsYdBDjac7I7nEHHpv94ibZ+mYjnCZQP\nAA4HG7SuYDI4HPSg+7q3DySr97n4X7+AY72uRyhZfWV01TdYG4PhcLBe7Q5+vMO7vSHOocGu3ZgM\nqU88M51ShPZus2dfrUIIDkX5tOt97ex+93+o/ikfo+o7B9bnGjqdbFjHe8MwNPhcDnoNzqDjYmKB\nOuHPGg5Fwelg4QwRyEsi4AaM/UhlVEr46DFa0d7TPx78r1ew+4t2uLZlqsU4amgHTVEozJSj8UI3\nsrTikHI47F5j1R7Z/RIvwraHnjJlCtra2tDU1OT5mTRpEjo6OnzKmpqahiSQv3XV5Zdfjs8++wwA\nIJFI8OKLL6K2thY33ngj6urqsGXLFhLziZBS2B1OvPWPE/jdO4dgNNtBAai5fAxW3TKJKJ4IhDgj\nFfGw6uZKTBunAwCcbu7BE6/X4myrIcmSEUY6v/zlL9Ha2orPPvsMs2fPBo/Hw2WXXYbf/va3WLhw\nYczbW7RoEa699lrcd999WL58OW644QafdubNm4fXXnst5u2OJMrHqFFZpEl55bRc4huMmeHQPkHY\nUwGaplBeoMa4fFXSPSVGKhyagoAbv4gpuToJtF4Z8iLJaBar91vvoSPgpX50mFQY68GyGnrLxQSL\nYefdtVGcQrxz3YXjEptoeFwOKgrj7LkS4sK6Y+vLxDxUFGpQVayFWi5AdYk2/NjByR+qACKwfNq2\nbVs85fBw7Ngxn//94x1MmDAB7733XkJkIRAipb3bjBc/OoITTa4vEDIxD0vmjkNZfuy/ehMIhOBw\nGQ4Wzx2HNIUQH//7FNq7LVj/xl4svm48cXklxI2MjAx88MEHsFgs4PF4ePPNN/HPf/4TOp0OEydO\njHl7NE3jwQcfxIMPPhh0+9///veg5VOnTg141xpueK/3hpLwiqaplFzgpsKClhAlcew6iqJQXqCC\nze7EwQZ9zOtnODTyM6Ro63LFoJEKB89AV5KjRE+vFVna2MSPYTg0MtVi9JhsyNOFzuSYTCJRyiWK\nDJUYF9qNQeezeMs7muYrYRiuupHg//wK1VPe5d4yDMdrn3pPXAJhmHL45EW8/PFRGPqCEJbmutzs\nUv2LKoEwEqEoCjfMKECaUog/flYPs9WB371zCHN/lI+ay8eQQOSEuMHn89He3o7a2lqo1eq4KJ4I\nw4dUnWm0CqHH7U4sTD0rg3jgu1BLPQVCODAcGkwcs1JxaBoFGTIYTHZkpw2uUFJK+WFZPYWjyHKT\nm6JKp1QmRyeBXMLzuIHGSkEfCtarUv85Lk8nxemWHqSrYufyPZJIV4lw/qIRNEUFWLWyITorVHkk\nePcTnUSlFVE+EQhDxOF04sN/NuKTf5/2lP3nj/JRc3l+WOmaCQRC/LhsQgY0cgE2f3AY3b02fPzv\nU2hs7sbiueM9L2kEwlB4/vnn8frrr+Ott95CXl4e9u3bh8WLF8NgcLl6Xnrppdi8eTMJERBD+F4u\nZ2kRpkmPFrko/MVzrOExsXexkwi5KB+jBoem4qrMSCXkEh7ae1wZwLhxuKbJRMhjYLLGJsh/mlKE\nNGVMqkJxtgLtPRbkpEkG3zlSvNbjUa+lh6cOMgCaonw+dg9mETPQabuVR+pws3T6NZWhFkMp5aek\nVWkqwONyUF2sBRA498Y6C3qaUogL7S5FV5pShE6DFWarHTm6ONyPYTI6njYEQpzoNFiwcfsBj+JJ\nIuRi+U0V+OmMAqJ4IhBShJJcJR75rykozJQBAA6fbMdjf/wOp5t7kiwZYbizY8cOvPjii7jpppug\nVqsBAA899BAEAgE++eQT7N69G0ajES+//HKSJR1ZMBwaEws0KMtVxt26eHy+CplqMYqy5XFtJxR8\nLgciQXwWcRIhN+ZuJKlMmkKIPJ0UxdmKmC/y3CTLnqAkVwG1TIDibEXc2xqTLoOAx2BcGCElVDIB\nirLkPgpjQvyRirjgczmgKQpZmoEt2PzHbIZajMoiDYqyQs95Tm/FX5DtRPE0MFyGE3QO0ilFkIv5\n0MiEPveXXBzdxw8hn0FFoQaVRRpwGRrjx6gwqVib1PuRrI4JhCg5cqodj762B9+f7QQAjM2W49E7\npmBCgTrJkhEIBH9UMgF+eWsVfjwpCwCg7zJj3Rt78fd9TTExZyaMTt5++2386le/wgMPPACJRIK6\nujqcOnUKt912G4qKiqDT6bB06VL85S9/SbaoIw6RgIE8AW7tUhEPuTppQi1lvBdzxHUldlAUhQy1\nGKpwLTqGEQIeg7HZioScm04lQmWRBrIkWgMmk+HwykBTlCcwddDkBIOcg4DHDGg9pfJytUzEPDxa\noGkKZXlKFGXLIRPxUJytgFYhREHfx9NoEPIZnzGQTJc7gLjdEQgRY7M78O7uk/jbd2c9ZXMuySXW\nTgRCisNlaNw2uwQFmTK8/vn3sNmdeONvx1HXcBF3XFsGWZRflgijl4aGBlx22WWe/7/55htQFIUr\nrrjCU1ZUVITz588nQzwCgUAgjFJomgIdhi1eNEGrhXwGEwvUAChi1RZHVDLBiFOWp8RK2Wq14qGH\nHsKUKVMwffp0bN26NeS+S5cuRWlpKcrKyjy/d+/enUBpCaOZplYDHv9TrUfxJBFysWzeRMz/jyKi\neCIQhgmXTcjAr2+fjMw+U/SDDRfxyGt7UHfyYpIlIwxHvF/ca2trIZfLUVpa6ikzGo0QCuMTl2jj\nxo249NJLMW3aNDz11FMD7nvgwAHcfPPNmDRpEubMmYO33347LjIRCAMx0q1lEpV9yn0dkxmLLFoK\nMl3uXNIhyi4R9cdtHGpd0TIMk43FDJGAGzeXYMLIJSVGzJNPPomjR49i27ZtaGpqwoMPPoisrCxc\nffXVAfuePHkSTz/9NC655BJPmUwWvSkagRAOTpbFF9+dxbu7G2B3uGxVy8eo8IuflJFsdgTCMCQn\nTYJHFk7G2/9owK59Teg2WvHMWwdxZXU2bryigMQrIIRFcXEx9u3bh7y8PHR3d+Pbb7/FlVde6bPP\nZ599huLi4pi3/dprr+HTTz/FCy+8AJvNhpUrV0Kj0eCOO+4I2Fev12Px4sW49dZb8dvf/haHDx/G\n6tWrkZaW5mOlRYgDo3l1GoSiLDnOthmgko6sr/mJpjhHgS6DNSBb1nAgTSGEVMgFnxe5xYx3YHWx\ngOuJcRVJApFE35Le56lVJCZBAoGQqiT97dpkMuGdd97Bq6++itLSUpSWlmLRokV44403ApRPVqsV\nTU1NKC8v9wT2JBDiTVObAds+/x4/NHUBcLnu3PTjIsysykrYFy4CgRB7eFwOfnZ1McoLVNj66TF0\n99qwa28TDvzQhp9fXYKKIk2yRSSkOD/72c+wZs0aHDt2DPv374fVasXChQsBAC0tLfj444/x6quv\n4je/+U3M2962bRuWLVuGSZMmAQBWrlyJ5557LqjyaefOndBqtbj//vsBALm5ufjmm2/wySefEOVT\nHBALuUCH629eNIGt45wmPZnwuBwUZiYnePtIguHQUMuHrwIv2kD3pXlKtHaYPJnYhoNLEod2JUiw\n2R0kPhJh1JN05VN9fT0cDgcqKys9ZdXV1XjppZcC9m1sbARFUcjJyUmkiIRRitlqx0f4EB0VAAAg\nAElEQVT/OoUvvjsLR19ah1ydBIvnjve46xAIhOFPRZEGa++chj99Vo8DJ/S42G3Bc+8cwpTSNNw6\nayx5WSSE5LrrroPVasX27dtB0zSeeeYZTJw4EQDw0ksv4a233sJdd92FmpqamLbb2tqKCxcuYPLk\nyZ6y6upqnD9/Hnq9HhqNr+J0xowZGDduXEA9PT0k42M80MoFsNoc4DF0VItstUyAxgvdrroUqb+4\njjXj8lQ4eaEbGWoSbJ3gC5/LQU5a8tLER4vLPW3oy26lhI8OgwVpiqHdG+xgEceTQLZWgqY2AySC\n8K3YCMOPpCuf2traoFAowDD9oqjValgsFnR0dECpVHrKGxoaIJFIsGrVKnz77bfIyMjAfffdhxkz\nZiRDdMIIhWVZ7Duux/Zdx9HebQHgsnaa+6N8XDMtFwyHxHYiEEYacjEP9904AXu/b8ObO4+jy2DF\nd/WtONzYjp/OKMAVlZnk3icEZd68eZg3b15A+ZIlS3Dffff5vMfEira2NlAUhbS0NE+ZRqMBy7Jo\nbm4OUD5lZmYiMzPT8//Fixfx6aef4n/+539iLhvBFfcnWxv9Apnh0Kgu1gJAQrPseVOcrcCJc11J\nybYnE/NQSSxPCYQAxmYrYDDZfOJdjRSyNGLIxDyIh0kcKS55J4yKpPeuyWQCj+frr+z+32q1+pSf\nPHkSFosF06dPx+LFi/HFF19g6dKleOuttzB+/PiEyUwYudSf7sAHX53E8T4XOwCoKFTj1quKiZ82\ngTDCoSgKk0vTMC5fhXd3N+D/9p+DyWLHm18cxxffncUNMwowpSwt6WlqCcMDnU43pOMtFgtaWlqC\nbuvt7QUAn/enUO9Oweq97777kJaWhgULFgxJRkL8SJbSyY1KJsBkCR80TeY7AsEbqYiL9h4zgMQr\nIGiaiklmXm933lR5paEoalgkJCjIlKOt04Qx6dJkizIsSbryic/nB7wouf/3zw5z7733YuHChZBK\nXZ1dUlKCw4cPY8eOHXjssccSIzBhRPJDUyc++KoRx053eMrUMj5unVWMyrEaEtuJQBhFiAQMbptd\ngkvL0/HG377HmRYDWjtNeOmjI/jrt2dw438UYHy+iswLhLhy8OBB3H777UHH2cqVKwG43pf8lU4D\nZdbr7e3F0qVLcebMGWzfvh18fmQupZxR8qXXO3stE03MpgTg7ovR0ifDBXd/uJR2dMqOn9GE/71C\n05TnHlfI+BH3UVaaBCwAAY8DUQSBzlMJhZSPLqPrmSHgMwkfp8N5/srUiGMafiVVnjeJ6oukK590\nOh06OzvhdDpB9118vV4PgUAQNIudW/HkprCwEA0NDQmRlTCycLIsjjS24297zuDIqX6lk0TIxZxp\nuZhZlR1VJg4CgTAyKMqS45H/moI9x1rw/pcn0dZpxumWHmzacRCFmTJcNSUHVcVa4o5HiAtTp05F\nfX190G2tra3YuHEj9Hq9x53O7Yqn1WqDHmMwGLBo0SI0NTXhT3/6U1TxM2Wy0WEBLBb3K+WUytSO\n8Tha+mS4IRS6lMKpPn5GE973StU4Cj29VhRkyqNadKtVwy/ulDdyuQh8IQ8iPoP0IbgIDxUyfw2v\n500sSLryqaysDAzD4MCBA6iqqgIA1NbWory8PGDf1atXg6IorFu3zlNWX18flxTGhJFLr9mGf9Y1\n4+/7mtDaYfKUiwUMZk/NxZXV2VFn4SAQCCMLmqJwybh0TC5Jw+4D5/HxvxrR3WtDw/luNHx4BEop\nHzOrsnBFZVZEqZ4JhKGQlpaGjIwM7N2716N8qq2tRUZGRkC8J8AVy/Dee+/FuXPn8MYbbyA/Pz+q\ndru7TXA4nEMRfVhgNFo8f3d0GJMoSWg4HBoymXDU9Mlwwa3IMJmscDrZlB0/o4lg9wqfBvgSHrq7\nTYMcPXJRi13vLMkYo2T+6idVnjfuPok3SV9hCwQC1NTUYM2aNVi3bh1aWlqwdetWbNiwAYDLCkoq\nlYLP52PmzJlYsWIFpk6diqqqKnz00UfYt28fHn/88SSfBSHVcbIsfjjbia+PNOOboy2w2vonOpmI\nix9XZeOqyTl92SgIBALBF4ZD48rqbFw2IR1fHjiPnXuboO8yo6PHgnd3n8RH/zqFSWM1mDZOhwkF\namINRYg7N998MzZu3AidTgeWZbFp0ybceeednu3t7e0QCAQQiUR4++23sWfPHmzevBkSiQR6vR4A\nwOVyIZeHn/be4XDCbh/5CwWHs/8cU/18R0ufDDecThYOJ+mbVILcK6kH6ZPh9byJBRTLsknPtWg2\nm7F27Vp8/vnnkEqlWLRoEW677TYAQGlpKTZs2IDrr78eAPDOO+9gy5YtaG5uRlFRER566CFUV1eH\n3VZbG0krPJo412bAN0db8M2RZlzstvhsK8yUYWZ1NiaXpIFLfPIJBEIEOJ0sDp7Q44vas6g/0+mz\nTSxgMKU0DdPG6VCULffx5yfEH612dAQBdTqdeOqpp/Dee++Bw+Fg/vz5WL58uWf7zJkz8dOf/hT3\n3nsvFi1ahH/9618BdUyZMgWvv/562G12dBhHxcvxN0ebPX9fMi49iZKEhmFoKJXiUdMnwwWGoXGo\nsQNGowUOpzNlx89ogtwrqQfpk37czxutQojCzPA/BsUad5/Em5RQPiUSonwa2ThZFo0XunHgBz0O\n/KDHOb2v+SKfx8HkEi1mVmVjTEZgTDECgUCIlDMtPfjq0AV8d6wF3b02n21iAYMJBWpMLFJjQoEa\nYgFxzYs3o0X5lAxGy0KBKJ8I0UKUT6kHuVdSD9In/RhMNnQZrdAphUm1mk+U8on4GBGGPQaTDfWn\nO3C4sR0HT+g92RvccGgK5WNUuGR8OirHasDnkiDiBAIhduTqpPjZVVLcfGURjp3qwNdHWrDvhzZY\nrA4YzXaX9eXRFtAUhcIsGcaPUWF8vgr5GVJiFUUgpCA5WgnO6Y0oykreV2gCgUAgjHwkQu6oihlK\nlE+EYYfRbEPDuS4cO92BY6c7cLbFAH/zPYZDoTRPiUlFGlSXpkEm4iVFVgKBMHrg0DTKC9QoL1DD\nYnPg2OkOHDyhx8ETenQarK7Yc01d+KGpCx981Qghn8G4PCXG5StRmqdEukoEiqKSfRoEwqgnSytB\nhkYMmtyPBAKBQCDEDKJ8IqQ0docT5/VGnDzfjYbzXWg4143m9t6g+4oFDCYWqjFprBbjx6hIxjoC\ngZA0+FwOKos0qCzSgGVZnGkx4GCDHkca29FwrhtOloXJYsfe423Ye7wNAKCU8lGa61JGleQqoJGT\nFMQEQrIgiicCgUAgEGILWZ0TUgarzYFzeiNOt/TgTHMPTjX3oKnNCHuIFJx8HgclOQqU5SlRlqdE\ndpqEvCwSCISUg6Io5KVLkZcuxXWXjYHJYkf9mQ4cbezA4VPtaOlTqHf0WPD1kWZ8fcQVb0YjF6Ak\nR4HiXAVKcpXQygXEMopAIBAIBAKBMCwhyidCwmFZFl1GK5paDTjbZsDZFgPOtBpw4aIRA4W/18gF\nKMySozBThoJMOXJ1EpLOnEAgDDuEfAaTxmoxaawWANDebUb9mQ6PK3F7X2ZOfZcZ+q5m/OuwSxkl\nF/Ncc2CWDIWZcuSnS8EjMewIBAKBQCAQCMOAlFA+Wa1WPProo/jiiy8gEAjwi1/8AnfccUfQfY8e\nPYpHH30Ux48fx9ixY/Hoo49i/PjxCZaYEC49vVZcuNiL8xeNOK834lybEWdbDTCYbAMep5Lxkadz\nWQrk6aTIz5BBLiZxmwgEwshDJRPgR+UZ+FF5BliWRWunCd+f6XT9nO1XRnUZrdh3vA37+tz0aIpC\nulqEnDQJsrVi5KRJkaURQynlg6aJhdRoYOPGjXj33XfhdDoxb948rFq1KuS+X331FTZu3IhTp05h\nzJgxWLFiBWbMmJFAaQmE0QGPS8MIID+dZFUmEAgEb1JC+fTkk0/i6NGj2LZtG5qamvDggw8iKysL\nV199tc9+JpMJixcvRk1NDTZs2IDt27djyZIl2LlzJwQCQZKkH93Y7A50Gay42G1GW6cZ+i4T2jrN\naOsyofli76BKJpqikKEWIUcnQW6aFDk6CXLSJCRAOIFAGJVQFAWdUgSdUoQZFZlgWRb6LjOOn+1E\nw/luNJzrQlObASwLOFkW5/Uuxf63XnUwHAoauRBpSiG0CiHUMgEUEh4UEj7kfb8FPA5x4RvmvPba\na/j000/xwgsvwGazYeXKldBoNEE/3p05cwb33XcfVqxYgZkzZ2Lnzp2455578PnnnyMzMzMJ0hMI\nI5fJZek439wFIY9YphIIBII3FMsO5OgUf0wmEy655BK8+uqrmDx5MgBg8+bN+Prrr/H666/77PvO\nO+/gpZdewhdffOEpmz17NpYuXYrrr78+rPba2npiJ/wIxO5wwmi2w2CywdBrhcFkQ4/Jhp5eG3r6\n/u8yWNFltKLLYIHRbA+7bpmIi+w0CbK1rp+cNAkyNSJwGfJwJhAIhHAxWew4daEbp1p6cLbVgLOt\nBjRf7IXDGf7jnMfQkIp4kIm5kIp4kIq4kIl4kIl5kIl4kIr7/5eKuODQw8fFWauVJluEhPDjH/8Y\ny5Yt87z/fPTRR3juueewa9eugH337NmDXbt2YfXq1Z6yadOmYe3atbjmmmvCbrOjwwi7PXgcRkJi\nYRgaSqWY9EmKQfol9SB9knqQPkk93H0S93bi3sIg1NfXw+FwoLKy0lNWXV2Nl156KWDfQ4cOobq6\n2qesqqoK+/fvD1v5NFpwOJ0wWRzoNdtgNNthNNtgNLmUSkaTDQaz63eP+3+TDQaTHSZL+MqkYPB5\nHGjlAmjkQqSrREhXi5CpFiNdLYJEyI3R2REIBMLoRchnUJavQlm+ylNms7syg7Z09KK1w4TWThPa\n+n53Gaxw+n1nstqduNhtxsVu86DtUQDEQi7k4n5llFTEg0zEhVTMg0TAhVjIhVjAQCzgQixkwOcS\ny6p40traigsXLng+2gGud6fz589Dr9dDo9H47D916lRMnToVAGC32/H+++/DarVi4sSJCZWbQCAQ\nCATC6CXpyqe2tjYoFAowTL8oarUaFosFHR0dUCqVnvLW1lYUFxf7HK9Wq3HixImEyTsQnQYLLDYH\n0OcOwbKu4NrOvt9uNwkny8Lp7PthAaeThcPJwuF0wuFw/e10srA5nLA7nLDbnX1/s7DaHbDanLDa\nHLDZnbDYHDBbHTBb7X2/Hei12GGxOmJ6bq6v5FxIhK4v4gpxv/uGXMyDWi6ARi6ARMglCw4CgUBI\nMFyG9mTU88fpZNHTa0WnwYpOgwWdBgu6e23oMVrRY7Kh22hFd6/VY+Hqbw/NAn0fKGw4pzeGJQ8F\n18cIPo8DAdf1m8uhwXBoMAzd9zcFmnb9cKj+vymKAk253LIpigKHpkDRAIemQFMUhHwGl4xPH9Vx\nANva2kBRFNLS0jxlGo0GLMuiubk5QPnk5syZM5gzZw6cTiceeOAB4nJHIBAIBAIhYSRd+WQymcDj\n+b5Auv+3Wq0+5WazOei+/vslg4/+1YgPvmpMthhhwedxIBEwEAu5kAq5fb95EAsZSIRcSERc128h\nFxKB6ws3n/itEwgEwrCEpinIJXzIJXzkYWCXNKeThdHcp5AyWtHVa0W3sf9/l5LKpajqNlphDWEu\nzwKeDyJdcTinMy0G3DV3XBxqTh0sFgtaWlqCbuvt7QUAn3eiUO9O3qhUKrz77rvYv38/1q9fj7y8\nPFx11VVhy8QhGWZTBndfkD5JLUi/pB6kT1IP0iepR6L6IunKJz6fH/Ci5P5fKBSGtW8kwcbjFQvi\nzusn4s7rifk6gUAgEAiEoXPw4EHcfvvtQa2JV65cCcD1DuSvdPJ/d/JGIpGgtLQUpaWlOHHiBLZt\n2xaR8kkmC103ITmQPklNSL+kHqRPUg/SJ6OPpCufdDodOjs74XQ6QfcFNNXr9RAIBJDJZAH7trW1\n+ZTp9XpotdqEyUsgEAgEAoEQb6ZOnYr6+vqg21pbW7Fx40bo9XqP65zbFS/YO9GJEyfQ2dnpEyOq\nsLAQe/bsiY/wBAKBQCAQCH4k3datrKwMDMPgwIEDnrLa2lqUl5cH7FtRUYH9+/f7lO3bt88nWDmB\nQCAQCATCSCYtLQ0ZGRnYu3evp6y2thYZGRlB4z39/e9/x//7f//Pp+zw4cMoLCyMu6wEAoFAIBAI\nQAoonwQCAWpqarBmzRrU1dVh586d2Lp1KxYuXAjAZdlksVgAALNnz0ZPTw/WrVuHhoYGPPHEEzCZ\nTJgzZ04yT4FAIBAIBAIhodx8883YuHEj9uzZg2+//RabNm3yvDsBQHt7uyc2VE1NDfR6PZ5++mmc\nPn0ab775Jj755BPcfffdyRKfQCAQCATCKINiWf+8NonHbDZj7dq1+PzzzyGVSrFo0SLcdtttAIDS\n0lJs2LAB119/PQCgrq4Oa9aswcmTJ1FSUoK1a9eitLT0/7N35/FNlPkfwD85eh+0pRTLKRRpgdK0\nBdTKpbgCLrDlEJRFXRV19QeoiAeesIsICoIsXqh4wa4LKAp4LHghHshRjnKXltL7SNLc9/H8/kgb\nkjZpkzbJJO33/Xr5kk4mM98nz8xk5pvn4DJ8QgghhJCAslqtWLNmDXbu3AmBQIDZs2dj8eLF9tcn\nTJiAmTNnYuHChQCAwsJCrFy5EkVFRejduzeeeOIJ3HjjjRxFTwghhJCuJiiST4QQQgghhBBCCCGk\nc+K82x0hhBBCCCGEEEII6bwo+UQIIYQQQgghhBBC/IaST4QQQgghhBBCCCHEbyj5RAghhBBCCCGE\nEEL8ptMnn9auXYu8vDxcd911WLNmTavr/vLLL8jPz4dIJML06dNx4MCBAEXpH96U/cSJE7jjjjuQ\nk5ODW2+9FTt27AhQlP7jTfmblJWVQSQS+Tky3zMajXj22WcxatQojB07Fh9++KHbdc+ePYs5c+Yg\nOzsbs2fPxpkzZwIYqe95U/YmR48exZ/+9KcAROdf3pR9//79mD59OnJycpCfn48ff/wxgJH6hzfl\n3717NyZNmgSRSIS5c+eisLAwgJH6XnuO+8rKSuTk5ODIkSMBiNB/vCn7ww8/jIyMDAwZMsT+/59/\n/jmA0Ya+9hxrpH2MRiOmTZvmdI5WVlbi3nvvRU5ODqZOnYrffvvN6T2///47pk2bhuzsbNxzzz2o\nqKhwev2jjz7CuHHjMGLECDz33HMwGAwBKUtnUFdXh0ceeQTXXXcdxo8fj9WrV8NoNAKgeuFKeXk5\n5s+fj5ycHEyYMAGbN2+2v0Z1wr0HH3wQzzzzjP1vqhNufP/99y3ufR599FEAQVAnrBPbvHkzu+mm\nm9ixY8fYoUOH2NixY9kHH3zgct2ysjImEonYxx9/zCoqKtiHH37IMjMzWVVVVYCj9g1vyi4Wi9mo\nUaPY+vXrWVlZGfv6669ZVlYW279/f4Cj9h1vyt+kurqaTZo0iWVkZAQoSt/55z//yfLz89m5c+fY\nd999x3Jzc9nevXtbrKfVatno0aPZq6++ykpKSthLL73ERo8ezXQ6HQdR+4anZW9y/vx5Nnr0aDZh\nwoQARukfnpb93LlzLDMzk23dupWVl5ezrVu3smHDhrHz589zELXveFr+I0eOsOHDh7M9e/awiooK\ntnr1anbttdcyrVbLQdS+4e1xzxhj8+fPZxkZGezw4cMBitI/vCn7xIkT2VdffcUkEon9P6PRGOCI\nQ1t7jjXiPYPBwBYsWNDiHP3LX/7CnnrqKVZSUsI2bdrEsrOzWU1NDWPMdt+SnZ3NPvzwQ1ZcXMwe\ne+wxNm3aNPt7//e//7FRo0ax/fv3s1OnTrEpU6awFStWBLxsoWrOnDnswQcfZMXFxezo0aNs4sSJ\n7NVXX2WMMTZt2jSqlwCzWq1s0qRJ7KmnnmJlZWXs559/ZiNGjGBfffUVY4zqhGtfffUVS09PZ0uX\nLrUvo+sXN95++2328MMPM6lUar/3UalUjDHuz5NOnXy68cYb2RdffGH/e9euXW4fOA8dOsRefvll\np2XXXnst+/bbb/0ao794U/ZPP/2U/fnPf3Za9sILL7AnnnjCrzH6kzflZ4yx7777juXl5bH8/PyQ\nSz5ptVqWlZXFjhw5Yl/21ltvsbvuuqvFujt27GB/+tOfnJZNnDjR6bMKJd6UnTHbsZ6Tk8Py8/ND\nPvnkTdnXrl3LHnjgAadl9913H1u/fr3f4/QXb8r/7bffsnfeecf+t0qlYunp6aywsDAgsfqat8c9\nY7Zr4Ny5c0M++eRN2Q0GAxs6dCi7fPlyIEPsVNpzrBHvFRcXs/z8fPs9SNM5+vvvv7OcnBym1+vt\n695zzz1s48aNjDHGXn/9dae60Ol0LDc31/7+efPmsTfeeMP++tGjR5lIJHLaHnGtpKSEZWRkMKlU\nal/21VdfsXHjxrGDBw9SvXCgvr6eLV68mGk0GvuyhQsXsn/84x9UJxyTy+Vs/PjxbPbs2fbkE12/\nuPPEE0+wdevWtVgeDHXSabvd1dfXo6amBiNHjrQvGzFiBKqrqyGRSFqsf+2119qbCZrNZuzYsQNG\noxFZWVkBi9lXvC37uHHjsGrVqhbLVSqVX+P0F2/LDwA///wzFi9ejGeffTZQYfrM+fPnYbFYkJ2d\nbV82YsQIl92KCgsLMWLECKdlubm5OH78uN/j9Advyg4Av/76K1599VX87W9/C1SIfuNN2WfMmIEl\nS5a0WK5Wq/0aoz95U/7Jkyfj73//OwDAYDDgo48+QnJyMgYNGhSweH3J2+NeJpPhtddew4oVK8AY\nC1SYfuFN2UtLS8Hj8dC3b99AhtipeHuskfY5fPgw8vLysG3bNqdztLCwEMOGDUNERIR92YgRI3Di\nxAn766NGjbK/FhkZiaFDh+L48eOwWq04deqU071QdnY2TCYTzp8/H4BShbYePXrg/fffR1JSktNy\nlUqFkydPUr1woEePHli3bh2io6MBAAUFBTh69CiuvfZaqhOOvfLKK8jPz0daWpp9GV2/uFNSUoIB\nAwa0WB4MddJpk09isRg8Hg8pKSn2ZcnJyWCMoba21u37ysvLIRKJ8OKLL2LBggXo1atXIML1KW/L\n3qtXL6ckm1QqxTfffIMbbrghIPH6WnvqfsWKFZg9e3agQvQpsViMhIQECIVC+7Lu3bvDYDBAJpM5\nrVtfX+/0uTStW1dXF5BYfc2bsgPAG2+80SnGegK8K/vAgQORnp5u//vixYv4448/kJeXF7B4fc3b\nugeAgwcPIicnB2+99RaeffZZREVFBSpcn/K27KtXr8aMGTOcbgpDlTdlLykpQWxsLJ588kmMGTMG\ns2fPDvmxHAOtPecZ8d7cuXPx9NNPOz0QALbPv7XvbFff6cnJyairq4NSqYTBYHB6XSAQICEhodX7\nYGITFxeH0aNH2/9mjGHr1q3Iy8ujegkCEyZMwJ133ons7GxMnDiR6oRDBw8eREFBARYsWOC0nOqE\nO6Wlpfjll18wadIk3HLLLXjttddgMpmCok6Eba8SvAwGg9uHZq1WCwAIDw+3L2v6d9Ngga4kJSXh\n888/x/Hjx7Fq1Sr0798ft9xyiw+j9g1/lL1pu4sWLUJKSgpuv/12H0Xre/4qfyjS6XROZQXcl1ev\n17tcN1Q/F2/K3tm0t+wNDQ1YtGgRRowYgZtvvtmvMfpTe8qfnp6OnTt3Yv/+/Xj66afRp0+fkGzd\n6k3Zf//9dxw/fhwrVqwIWHz+5E3ZL126BIPBgLFjx+LBBx/Ed999h4cffhjbt2/HsGHDAhZzKOvK\n19hg4O7zb/rsW/tO1+v19r/dvZ947tVXX8W5c+fw2Wef4cMPP6R64djGjRshkUiwfPlyvPzyy3Su\ncMRoNGL58uVYtmxZi8+P6oQb1dXV0Ov1iIiIwIYNG1BZWYmVK1dCr9cHRZ2EdPLp5MmTuPvuu8Hj\n8Vq89sQTTwCwnRTNb5Ra+7U7NjYWGRkZyMjIQHFxMbZs2RKUySd/lF2r1eLhhx9GeXk5Pv300xa/\nwAUTf5Q/VEVERLQ46d2V1926kZGR/g3ST7wpe2fTnrJLJBLce++94PF42LBhg99j9Kf2lD8pKQlJ\nSUnIyMjAiRMn8Omnn4Zk8snTshsMBixbtgzLly9vcbMQqryp94ULF+Jvf/sb4uLiANiSj6dPn8a2\nbdvwz3/+MzABh7iufI0NBhEREVAoFE7LHL+z3dVPfHy82ySh0WikuvPSmjVrsGXLFrz++usYNGgQ\n1UsQaPoBYenSpXjiiSdw2223QalUOq1DdeJ/GzduRGZmpsveMnSecKNXr144dOgQ4uPjAQAZGRmw\nWq148sknMXPmTM7Pk5BOPl177bVu+xjW19dj7dq1kEgk9q5zTd2xevTo0WL94uJiyOVyp36MaWlp\nOHz4sH+C7yBflh2wjf1y//33o7KyEh9//HHQj5Hh6/KHsp49e0Iul8NqtYLPt/WklUgkiIyMtF94\nHNcVi8VOyyQSSch+Lt6UvbPxtux1dXW4++67IRAIsGXLFiQmJgY6ZJ/ypvynTp2CQCDA0KFD7cvS\n0tJQUlIS0Jh9xdOyFxYWorKyEosWLXIaR+aBBx7A9OnTsXz58kCH3mHeHvdNiacmoVzvXOjK19hg\n0LNnTxQXFzstc/zOdvedPmTIECQmJiIiIgISicQ+9ofFYoFcLg/Z73wurFixAtu2bcOaNWvs3fap\nXrghlUpx/Phxp+ETBg0aBJPJhB49erS4tlOd+N8333wDqVSKnJwcAIDJZAIA7N27Fw899BCdJxxp\n/v2clpYGg8GA5ORkzs+TTjvmU0pKClJTU1FQUGBfdvToUaSmpiI5ObnF+j/++CNeeOEFp2WnT58O\nyTEyvC07YwwLFy5EVVUVtm7dGpJlduRt+UPdkCFDIBQK7YPFAbbyZmZmtlhXJBK1GFz82LFjToPJ\nhhJvyt7ZeFN2nU6H+++/H2FhYdi6dWunOA+8Kf9nn32G1157zWnZmTNnQvZa53jf9IcAACAASURB\nVGnZRSIR9u3bh127dmH37t3YvXs3AGDlypV45JFHAhqzr3hT788880yLSSTOnz/vchBO4lpXvsYG\nA5FIhLNnzzr90lxQUGD/zhaJRDh27Jj9NZ1Oh7NnzyInJwc8Hg/Dhw93uhc6fvw4wsLCkJGREbhC\nhLA33ngD27Ztw/r163Hrrbfal1O9cKPpx5T6+nr7slOnTqF79+4YMWIEzpw5Q3USYFu3bsWePXvs\n9xgTJkzAhAkTsGvXLmRlZdF5woFff/0V1113HQwGg33Z2bNnkZiYiJEjR3J/nng8L14I2rRpExs3\nbhw7dOgQ++OPP9jYsWPZRx99ZH9dKpXap+usra1lI0eOZGvXrmWXL19mW7duZcOHD2fnzp3jKvwO\n8abs27ZtY0OGDGH79+9nYrHY/p9cLucq/A7zpvyODh06xDIyMgIZqk+8+OKLbOrUqaywsJB99913\nbMSIEey7775jjDEmFovtU2CqVCp2ww03sJUrV7Li4mK2YsUKNmbMGKbT6bgMv0M8LbujnTt3sgkT\nJgQ6VJ/ztOzr1q1j2dnZrLCw0OkcV6lUXIbfYZ6W/8yZM2zYsGHsk08+YZcvX2YbNmxgubm5rK6u\njsvwO6Q9xz1jjKWnp9unzA1VnpZ93759LDMzk33xxResrKyMbdy4kWVnZ7Oqqiouww85rX3exPcc\nz1GLxcKmTp3KFi9ezC5evMg2bdrEcnNzWU1NDWOMscrKSiYSidi7777LLl68yB599FGWn59v39bX\nX3/NRo4cyb777jt28uRJNnXqVLZy5UpOyhVqiouL2dChQ9mGDRucvjfFYjHVC0csFgu77bbb2Pz5\n81lxcTHbv38/Gz16NNuyZQuzWCxsypQpVCccW7p0KVu6dCljjK5fXFGr1Wz8+PFsyZIl7NKlS2z/\n/v1s7NixbPPmzUFxnnTq5JPFYmGrV69m1157LcvLy2Pr1q1zev2mm25iGzdutP998uRJNmfOHJad\nnc2mTJnCfvrppwBH7DvelH3+/PksIyOjxX933XUXF6H7hLd13yRUk086nY4tXbqU5eTksHHjxrFP\nPvnE/lp6ejr74osv7H8XFhayGTNmMJFIxObMmROyCdYm3pS9SWdJPnla9smTJ7s8x5tuEEKVN3W/\nf/9+Nm3aNCYSidhtt93GTpw4wUXIPtOe454xxjIyMkI++eRN2Xfs2MEmTpzIsrKy2MyZM9nRo0e5\nCDmktfZ5E99rfo6Wl5ezO++8k2VlZbGpU6eygwcPOq1/4MABNmnSJJadnc3uu+8+VllZ6fT6u+++\ny2644QY2atQo9vzzzzODwRCQcoS6TZs2tfjOTE9Pt98jlpWVUb1woL6+ni1atIiNHDmSjR07lm3a\ntMn+Gp0r3HNMPjFGdcKV4uJidt9997Hc3Fw2duxY9uabb9pf47pOeIw5DARBCCGEEEIIIYQQQogP\nddoxnwghhBBCCCGEEEII9yj5RAghhBBCCCGEEEL8hpJPhBBCCCGEEEIIIcRvKPlECCGEEEIIIYQQ\nQvyGkk+EEEIIIYQQQgghxG8o+UQIIYQQQgghhBBC/IaST4QQQgghhBBCCCHEbyj5RAghhBBCCCGE\nEEL8hpJPhBBCCCGEEEIIIcRvKPlECCGEEEIIIYQQQvyGkk+EEEIIIYQQQgghxG8o+UQIIYQQQggh\nhBBC/IaST4QQQgghhBBCCCHEbyj5RAghhBBCCCGEEEL8hpJPhBBCCCGEEEIIIcRvKPlECCGEEEII\nIYQQQvyGkk+EEEIIIYQQQgghxG8o+UQIIYQQQgghhBBC/IaST4SQLqeqqgoZGRn48ssvuQ6FEEII\nISQk0P0TIaQjKPlECCGEEEIIIYQQQvyGkk+EEEIIIYQQQgghxG8o+UQICXlnzpzBPffcg5EjRyI3\nNxf33nsvTp48aX993759yM/Ph0gkwsyZM3Hu3DkOoyWEEEII4R7dPxFCAomST4SQkKZWq3H//fej\ne/fueOONN7B+/XrodDrcf//9UKvV+PHHH/Hoo49iyJAheOutt3DrrbfiySefBI/H4zp0QgghhBBO\n0P0TISTQhFwHQAghHVFSUgKZTIa77roL2dnZAICBAwdi+/bt0Gg0eOuttyASibB69WoAwOjRowEA\n69at4yxmQgghhBAu0f0TISTQqOUTISSkXXPNNUhKSsLf//53LFu2DN9//z2Sk5OxZMkSJCQk4MyZ\nM7jpppuc3nPrrbeCMcZRxIQQQggh3KL7J0JIoFHyiRAS0qKjo/Gf//wHN954I/73v/9h0aJFyMvL\nw7JlyyCVSsEYQ2JiotN7UlJSOIqWEEIIIYR7dP9ECAk06nZHCAl5V199NV555RUwxlBYWIhdu3bh\n008/Rc+ePcHn8yGRSJzWl8lkHEVKCCGEEBIc6P6JEBJI1PKJEBLS9u7di7y8PEilUvB4PIhEIrz4\n4ouIi4tDQ0MDcnNzsW/fPqf3/PjjjzRgJiGEEEK6LLp/IoQEGrV8IoSEtNzcXFitVvzf//0fHnjg\nAcTGxuKbb76BWq3GpEmTMHnyZNxzzz1YuHAhbr/9dly6dAmbNm3iOmxCCCGEEM7Q/RMhJNCo5RMh\nJKT16NEDmzdvRlxcHJ5//nk89NBDOHfuHDZu3IhRo0Zh5MiReO+991BfX49FixZhx44dWLVqFddh\nE0IIIYRwhu6fCCGBxmMhNmWB0WjEqlWr8PXXXyM8PByzZs3C4sWLuQ6LEEIIIYQTRqMRs2bNwosv\nvohRo0a1um5lZSWmTZuGd999t811CSGEEEJ8JeS63b300ks4fPgwPvjgA6jVaixevBi9e/fGnDlz\nuA6NEEIIISSgjEYjHn/8cRQXF3u0/vLly6HX6/0cFSGEEEKIs5DqdqdQKLBz50689NJLyMzMxPXX\nX4/77rsPJ0+e5Do0QgghhJCAKikpwZw5c1BZWenR+rt374ZWq/VzVIQQQgghLYVUy6eCggLExcVh\n5MiR9mUPPPAAhxERQgghhHDj8OHDyMvLw2OPPQaRSNTqujKZDK+99ho++OADTJkyJUAREkIIIYTY\nhFTyqaKiAr1798aXX36JTZs2wWQyYebMmXj44Ydp2k9CCCGEdClz5871eN3Vq1djxowZSEtL82NE\nhBBCCCGuhVTySavV4vLly9i+fTtWr14NsViMF154AdHR0bjnnnu4Do8QQgghJOj8/vvvOH78OFas\nWMF1KIQQQgjpokIq+SQQCKDRaLBu3TpcddVVAICqqip8+umnlHwihBBCCGnGYDBg2bJlWL58OcLD\nw7kOhxBCCCFdVEgln1JSUhAREWFPPAHAgAEDUFtb6/E2xGKVP0IjhBBCSBDo0SOO6xCCSmFhISor\nK7Fo0SIwxuzLH3jgAUyfPh3Lly/3aDuMMRrigBBCCCHtFlLJJ5FIBIPBgLKyMvTv3x+AbaaX3r17\ncxwZIYQQQkjwEYlE2Ldvn9OyW265BStXrkReXp7H2+HxeFAqdbBYrL4OkbSDQMBHfHwU1UmQoXoJ\nPlQnwYfqJPg01Ym/hVTyacCAARg/fjyWLl2KZcuWQSwW47333sOCBQu4Do0QQgghJGhIJBLExcUh\nIiICffv2bfF6SkoKkpKSvNqmxWKF2UwPCsGE6iQ4Ub0EH6qT4EN10vXwuQ7AW2vXrkX//v0xb948\nPPPMM7jrrrswb948rsMihBBCCOFM8y5xY8aMwbfffuvRuoQQQggh/sZjjgMAdAE05hMhhBDSedGY\nT/4jk2noV+ogIRTykZgYQ3USZKhegg/VSfChOgk+TXXibyHX8okQQgghhBBCCCGEhA5KPhFCCCGE\nEEIIIYQQv6HkEyGEEEIIIYQQQgjxm5Ca7Y4QYqM3mqEzWMAYg9XKYAUQJuAjITacBpIlhBBCCCGE\nEBJUKPlESJCzWhnK6lS4VK3E5RolLtUoUSvVwtVMAXHRYRiQGo+BqfEY2Cse1/RJQES4IOAxE0II\nIYQQQgghTSj5REiQqpFq8NupWhw8UwuZyuDRe1RaEwpLpCgskQIAoiIEGJ2ZiptyeyO1u/9nMCCE\nEEIIIYQQQpqj5BMhQcRktuL30zU4cLIGpTXKFq+nJETh6tQ4DEyNR1J8JHg8Hvg8gMfnQas3obTG\n1kKqol4Fs4VBZ7Dg+4JKfF9QiaFXJ+Lm3D7IviaZuuYRQgghhBBCCAkYSj4REgTMFit+KazB1wcv\no0F5pZUTn8fD8IFJuGF4Kob0T0RsVFir27khMxWALYlVUqXA/hNVKLgghsXKcPayDGcvy5DWKx53\n3HwN0np382eRCCGEEEIIIYQQAJR8IoRTZosVvzYmnaQOSafeyTEYm5WK64ZdhW4x4V5vN0zIR0b/\nRGT0T4RCbcDPJ6vx84lqyFQGlFQrsXJLAa4f2hOzxqehe7dIH5aIEEIIIYQQQkJPlVgNoYCPnknR\nXIfSKVHyiRCOFFcp8Mn/zqNSrLEv69MjFvljBiBncDL4Puoa1y02An8ZPQC3XtcfPxRUYs/vpdAZ\nLPjjbB0KisSYcn1//DmvP4QCvk/2RwghhBBCCCGeqpFqoDWYMeCqePD53AwPIlXoUSFWA7BN4hQd\n2XqPE3+qkmgg4PNwVSdLgoXc0+b333+PjIwMDBkyxP7/Rx99lOuwCPGYVm/Clr0XsGpLgT3x1KdH\nLBbMyMTy+0ZhRHoPnyWeHIUJ+Zh8XT+s+nsebsrpDR7P1j3vy19L8Y8Pj6C4SuHzfRJCCPE/o9GI\nadOm4ciRI27X2b17NyZNmgSRSIS5c+eisLAwgBESQgghrhlNFpTVqSCW61At0bT9Bj9R60z2f+uN\nFs7ikKkMqKhX4XKt0immziDkWj4VFxdjwoQJeOmll8CYbbL5iIgIjqMixDMFF+qxdV8RFBojACAq\nQojbbkzD+Oxefkk4uRIfHY67JqVjQm5vbN1XhAsVclRJNFi1pQATcvtg5viBiIoIuUsDIYR0SUaj\nEY8//jiKi4vdrnP06FE8//zzePnll5GdnY1///vfeOCBB7B//35ERUUFMFpCCCHEmcXK7P/ubMmW\n9tA4JsEM5jbH/A0lIfeEWVJSgmuuuQZJSUlch0KIx0xmK7b9eBE/HquyLxuVkYK5f7oGCbHcJE97\n94jFk3/NwS8nq7H9pxLoDGb8cKwSx4vFuHtSBrLSunMSFyGEEM+UlJRgyZIlba4nkUiwYMECTJ06\nFQCwYMECfPjhhyguLsbw4cP9HSYhhBDiluMP8E2NS7gWNDODB0kYvhKSyafRo0dzHQYhHquX6/D2\nl6dRVqsCACTGReBvk9ORlZbMcWS2i/347N4QDUrGv78rQsEFMRqUBry+4yRGZ16F22++plNl2wkh\npDM5fPgw8vLy8Nhjj0EkErldb/LkyfZ/GwwGfPTRR0hOTsagQYMCESYhhHQaVitDaa0SUeFC9EqO\n4TqcTsExz2PlLoygERzpN/8IueRTaWkpfvnlF7z99tuwWq2YPHkyHnnkEYSF0QMyCT7HisTY/PU5\n6AxmAMDwgd1x/9QhiIv2fgY7f0qIjcCCGcNRcEGMLfsuQKkx4rfTtThd2oC7JqUjd3APrkMkhBDS\nzNy5c71a/+DBg5g/fz4AYO3atdTljhBCvFQt1UAs1wEAuneLRESYgOOIOhcuWz6xTp32CQ4hlXyq\nrq6GXq9HREQENmzYgMrKSrz00kswGAx49tlnuQ6PEDvGGL76/TK++KUUgC2jP3PcQNx6ff+Aje3U\nHiPSeyC9XwK2/XARv52uhUJjxBs7T+HaISn46y2DER9kSTNCCCGeS09Px86dO7F//348/fTT6NOn\nD7KysrgOixASZBqUejSoDOiXEotwSq440erN9n+bLVZKPhHihZBKPvXq1QuHDh1CfHw8ACAjIwNW\nqxVPPfUUnnnmmeDpm0m6NKuVYet3Rdh/3Da+U7fYcDz0l2FI75fIcWSeiY0Kw/ypQzFqSE98/L/z\nkKkMOHyuHufKZJh3y2CMykihc40QQkJQUlISkpKSkJGRgRMnTuDTTz/1KvkkEITcJMmdVlNdUJ0E\nl85SLyXVSgC2e9qhA0J7nF1f14lAwIOAb9uWUMCHUBjadc2F5nViZcz+mQr43H2mAgHfHkeYkMs4\nAn+MBeqaFVLJJwD2xFOTtLQ0GAwGyOVyJCaGxsM96byMJgve3XMWx4rEAIDePWKweLYISfGRHEfm\nvay07lgx/zps/6kYB05WQ6U14Z1dZ3DkXD3unJSObjHUCooQQrzx888/4/3330dpaSm2bduGnTt3\nol+/fsjPz/frfk+dOgWBQIChQ4fal6WlpaGkpMSr7cTHUze9YBMMdaLWmVAr1aB3j1iaLbdRMNRL\nR8TE2CbDMQNITOwc4xr5qk7iZHoYLLZ/JyREI5Z6BbRbU50YTBbExNgSnrEx4ZwdcxK1ESq9rXK7\nJUQjkaPnN7nODLnWfCWOxGhO4vCHkPqG+PXXX7FkyRIcOHAAERG2i+LZs2eRkJBAiSfCOY3ehH99\nVoiLlQoAwOC+CXhk1nBER4bueGTRkULcc2sGRg1JwcffnodEoUdBkRjny2W4e3IGRmWkcB0iIYSE\nhN9++w0LFy7ElClTcPLkSVitVpjNZjzzzDNgjGH69Ol+2/dnn32GyspKbN682b7szJkzGDZsmFfb\nUSp1sFhoONhgIBDwER8fFRR1cvB0LQCgtEKGkV38viCY6qUjNBqD/d8ymYbDSDrO13WiUunsn49c\nroXJYOrwNr2h1plQXqtCanIMEuO4mTG7o5rXidFksX+mPKuVs2NOqdTb41DIteBZLBzFceUYUyh0\nCAvAWFRNdeJvIZV8ysnJQVRUFJ577jksWLAA5eXlWLNmDR544AGuQyNdnFpnwqv/OY5KsRqAbeyk\nB6cNRZiwc/QDH3Z1Ev45/1p8tr8EPx6rgkZvxttfnsbxoT0xb+JgxIRwgo0QQgJh48aNWLJkCe65\n5x7s3bsXALB48WLExsZi8+bNPk8+SSQSxMXFISIiArfffjvmzJmDLVu2YNy4cdi1axdOnTqFV199\n1attWixWmM2h+0DdGQVDnVistv1bjNzHEiyCoV46oqlOAYR0ORz5qk4sFmb/fMwc1POJi7beFQ0q\nPa4felVA9+1rTXViNluvXEes3J07FotDHByew06fhzm0ryXNhVQn1ZiYGGzevBkymQy33XYbXnjh\nBdxxxx247777uA6NdGFavQmvbTthTzzdlNsbD+dndprEU5PIcCHunJiOJ+fmoHu87ZeWP87W4cXN\nh3G6VMpxdIQQEtwuXLiACRMmtFg+efJklJeXd3j7zcfiGzNmDL799lsAwNChQ/Hmm29ix44dyM/P\nxy+//IIPPvgAKSldu5UKIYSQ4KLWmVAv0/p1H0qNEaU1ShhM3LRs6spCquUTYBujwLHZOCFc0hnM\nWL/9JMpqVQCAW0b2xR03D+rUA3IP6Z+If9x3HT79oQi/naqFTGXAum0nMXFUX9x2YxqEIT7IJiGE\n+ENcXBzq6+vRr18/p+XFxcXo1q1bh7d/7tw5p7/Pnz/v9Pf48eMxfvz4Du+HkM6KMdap798ICVbN\nO5VdqlEiNirMb0OXnC1rAGBLdA0f2N0v+yCu0VMiIe1kMFqwYcdJ+4wgN+X07vSJpybRkULMnzIU\nC2cOR1y07Yth35EKvPKfY2hQ6jmOjhBCgs+0adPw8ssv4/z58+DxeNBoNDhw4ABWrFiBP//5z1yH\n1+UYTRbUy3Uwh/C4PKQlxhjUOhOszLsxUmqkGhw5Xw+JXOenyAgh3tAZ/N8qSaN3Hq/L6bLRyvNc\nIL83modhMod2ay1KPhHSDiazBf/6vBBFjYOLjxmeinkTB3eJxJOj3ME98M/512FIf9uA/yVVSiz/\n8AhOX6JueIQQ4uixxx7DgAEDMH36dGi1WsyYMQMPPvggBg8ejMWLF3MdXpdzprQBl6oVKKlScB0K\ncYExhnNlMpy93OBVIqlSrMHpUikuVsi92l9ZnQpWxlBc7f3xYLUyKDRGrxNehBD3WAAG2W6PS9VK\nFFwQc/Jju0ShQ0GRGCXtuE4Fi5DrdkcI16xWhvf2nMW5MhkA4PphPXHPrRngd7HEU5NuMeFYcns2\ndv1aiq9+vwy1zoT1209i2uirkT9mQJdLyBFCiCthYWF47bXX8Mgjj+DcuXOwWq0YPHgwBg0axHVo\nXZKh8ddjmdrQxpqECw1KAxSNsz1J5DqkeDjVeJXENv5mIOv18Pk6AEBcdDhEg5IDtl/CDa3ezHUI\nAaPVm3CxUoHkbpHo3SPWq/cyxlBUIQePx8M1fbp5/zwQnLkn1Mtt41EVVcoDPuB7ceOPJWK5Dmm9\nOt5dnwuUfCLEC4wx/PeHizh6wTbTRM41yZg/ZQj4/K6dYOHzeZgxbiCu6dMN7+45C7XOhN2/XUa9\nTId7/zwEYUJqZEkIIQDQv39/9O/fn+swCAlqZofZ1kyWIH0KbUalNXIdQqelN5rBGBAVwe2jq9Fk\ngd50JfkUqMZudQ1aKDRGDEiND8wOGxVVKKA3mVEhVnudfJIq9PYkcIMyEt27RXr1/o58tJViNRqU\nBlzTp5tXx4xja6uu/WTnP5R8IsQLew9X4PuCSgDAoN7d8Pe/DIOAT4mVJpkDu2P5vaOw8fNTKKtT\n4Y+zdWhQ6rFwVhZio/wzaCAhhISCjIyMVn/5bT5gOHFPrTOhWqJBavdoxEWHcx0OIcSPTGYLThRL\nAACitGROE1Dny73rzukrpbVKTvbrmGjzltF8JYHsmEz2VEeTT4CtpVAoDijemXvwUvKJEA/9caYW\n238qBgBclRSNR27LQniYgOOogk9SfCSWzsvFpt1ncKJYgqJKBVZ+chSPzRGhp4fN5gkhpLN5+eWX\nnZJPZrMZly9fxpdffomnnnqKw8hCz+lS27iCDSp9wLs9EEICS6G+0qJMqtCjT4p3LXDc0ehNiIoQ\nejRshkZvgkSuh9ZganNdfwp06zoeeO0ee8lp7G5vVvYhncG3XSRpUqWOC0jyafbs2Zg1axamTJmC\nuLi4QOySEJ86d7kBm7+2/SrdLSYcj88RUUueVkSEC7Bw5nD894eL+L6gEnUyHVZ+UoDFc0QBbzJM\nCCHBYObMmS6XZ2ZmYseOHcjPzw9wRIS4Z7ZYUVanQmxUGDc/HDk8jFL3F+JrlWI1KsVqJMVFYnDf\nhDbXPxUkE+lYA9wihsfjsBUOFztuJWOmUBtQVMlNy7fOJCD9ha6//nq88847GDNmDB5//HH8+uuv\nYJ25PRnpVKokGrzxxWlYrAwR4QIsniNCckIU12EFPT6fh7/eMhhzb74GPNi6Saz973GaWYgQQhxk\nZWWhoKCA6zAIcVIpVkMs16G0RglrO594g/VeX6M3QavntgVLsAjklPHBpKlbVoMqtFqytOdcNJmt\nUGiM7TofHVvrev1+x/XbMfkQF1eP1vYZbJNTKLVGnLokhVQRWsdwQJJPS5YswU8//YS33noLAoEA\nixYtwo033oj169ejtLQ0ECEQ0i4KtQGvbz8JncEMPo+HBTMy0a8ntd7zxi2j+uLh6ZkQ8HnQGSxY\nu+0EirycApkQQjojjUaDrVu3IjmZZsgiwUWtvZKcsbbjoVVvNONYkSTovu91BjNOXZKi8JIUBqOF\n63DaVCPV2BKAfkjkKTRGFFwQ42Kwt+ZwyFsEZzrTv+QOSY/2dIErLJHiXFkDqqVar9/rmDLqap99\nIFpcmi1WVNar29Wd8uzlBmj0Jlys8s35G6hZHAM25hOPx8Po0aMxevRo6HQ6bNmyBW+99Rbeffdd\n5Obm4m9/+xsmTpwYqHAIaZPBZMG/Pi+EtLF/792T05E5IPQGrQsGIzNSIBDw8PaXp2EwWrBu+wk8\nMisLQ69O4jo0QggJCHcDjvN4PPzjH//gICISCBcr5bBYGAb3S3A7tozOYIZGb0JSfKRH488EQkcf\nNEtrVDBZLGhQWWC2WCEUBMfkLDLVlQd5ucaAnuHRUAbpLHUGkwVldSoAQHiYAL2TY3y6/fNlMjAw\nSJV6XOPTLRNfqqxXd+j9JostyVpRr/L5MdQar8Z8amsDnVRpjRJSpR6VEnA+fmFxlRy9U7v5fT8B\nHXC8vr4eu3fvxu7du1FUVITc3FzMmDEDtbW1eP7553HkyBE899xzHm/vwQcfRPfu3bFq1So/Rk26\nIquV4d3dZ1BaY/vS//P1/TFO1IvjqEJbzjU9sGhWFjZ+fgpGkxUbPivEopnDkRmCs1AQQoi3mg84\nDgBhYWEQiUTo27dvh7ZtNBoxa9YsvPjiixg1apTLdfbv34/XX38dZWVl6NevHx599FFMmDChQ/sl\nrVOoDfYfsMQyHXomuR476WSJbSavvkaL19OZBytfdueqkWogVxuQ1rsbIvww0UsRRzOYtcXxM9To\nfN9NsL0DSZOu6fSlBlzVPRopng494sW4be09FrV6M6IiBK3OJOuVAJ8S0iAawNxoCkwX3IAkn3bt\n2oVdu3bh0KFDSEpKwvTp0/Gvf/0LV199tX2d1NRUrFy50uPk09dff40DBw5gxowZfoqadGXbfyrG\n8Yu2m8Frh6Rg5viBHEfUOQwf2B2Pzc7Cvz4rhNFsxcadp/D4HBHS+yVyHRohhPiVuwHHO8poNOLx\nxx9HcXGx23XOnz+PRYsWYenSpRg3bhwOHDiARx55BJ9//jnS09P9EhcBTA7JA8dpx92pkWpbJJ+M\nJgsYs03k0VWZLFaYtEZcqlJgiB9aTFMKpm31ch3CBHwkxkUEfN+8Lj7kvLqV8cmaumvFRYe7fN2X\ns71pDSZcqlZ4nnzysyqJBhX1KiTHR2FQH9+32PFZQquDgiUOXwlI8um5557DTTfdhDfffBPjxo0D\nn9+y6e3AgQNx5513erQ9hUKBNWvWICsry9ehEoLvjlRg35EKAMCg3t0wf8qQoGkG3xkMvToJi+eI\nsH77SRjNVrz+WSGevCMHA3vRLHiEkM7ljTfe8HjdhQsXer39kpISLFmyq5LvbQAAIABJREFUpM31\nvv76a+Tl5WHevHkAgHnz5uHHH3/Et99+S8mnINSg1CNMyEdUhBDHLooBADmDegRVAqq8TgWxXOfR\nTGG+ovXBg7SrRJPF2jUH3faUXG3ApWrbZDHZg5LB4/Eg4PM46UoZrIPYc+XM5QYAgCgtGVERLR/r\nm7dAbFDqkRAXEZDnGqea8sPuKuptvVMkSh0Gwf/dxTxNguqNZggF/KDpahxsApJ8OnDgABITEyGX\ny+2Jp8LCQgwbNgwCge2LNDc3F7m5uR5t75VXXkF+fj7q6+v9FjPpmo6er8d/f7gIAEhJjMLCWcMR\nJgyem73OIr1fIhbOHI5/fV4Ig9GC9dtP4Om/5qJPSufobkAIIQCwc+dOj9bj8XjtSj4dPnwYeXl5\neOyxxyASidyuN2PGDJhMLX89V6s7NpYI8T25w3Te/R0mOKmX69DXxXek2WKFwWTxS3e01lRLNQCA\n80HaZc0T9LOiZxTqK2NiSRR6VIrVEPL5yE3vQT/OOrBaGcQKHWKjwhATGRbQfSs0RpfJp+aKKuVI\nTYpB/6sCO3lSqLRe62hXVJXWiDOXGyDk8zEivUdItVoKVFo3IMkntVqNuXPn4uabb8ZTTz0FwDZe\nU3JyMt577z2kpqZ6vK2DBw+ioKAAe/bswbJly/wVMumCiirkeHfPWTAAcdFheHyOCPFumrGSjssc\n2B1//0sm3v7yNDR6M9ZuO4Gl83JxlZsxMQghJNT8+OOPft3+3LlzPVpv4EDnruMXL17EH3/8gb/+\n9a/+CIt0gOO02fo2ZmNjjOH4RQkMRjOGD+ze5gOv2WKFWK5Dt5hwRLexrqcNTNy1GgrEI1eNVAOF\n2oi03vEB+aHQm4HTO1MLHcfn50qxLWFttlqhN5jbPI58vf9gViXRoEpi+3wCPXg0YwxqnQkCPs8p\nCeXqKKxp0AQk+dSZzgFPVdRfOT+MZmurPwqI5bpAhRVUAtIe7OWXX0b//v1x77332pd98803SE1N\n9WqwcKPRiOXLl2PZsmUID6ekAPGdKokG//qsEGaLFeFhfDw2W4SUREqC+NuI9B64b0oGAECpMWLt\nf4+jIYgG3yOEEH8zGo0oKCgI2P4aGhqwaNEijBgxAjfffHPA9utvnf1Bx1X5dAYzzI1jSVXUuW7F\nZmUMMpUBJrNt5rSyOhUKL0m92newPvyX1akg1xjsk8P4yoVyGazNPu/SGiUKLog9ukcxmS04flGC\nc41donyByzoIpdYbbTFbrKht0Ppl23V+2q4nNDozTpdKcbJEApMH48uRtrXnsPfmW6iksSur6+0E\n7vus+bXO3wLS8uno0aPYvn07evToYV+WlJSEp556yj7+gCc2btyIzMxM3HDDDf4Ik3RRMpUBr28/\nAa3BDD6Ph/+bnokBqTT+UKDckJkKvdGCrfuK0KA04LVtJ/DMnSMQGxXYJsuEEOJPp0+fxgsvvICi\noiJYXbQWOXfunN9jkEgkuPfee8Hj8bBhwwav3y8IkjEsBA5jhwqFfBhNFpy6JEVUuBBDB3g2IHXz\nbbRGqtBDwOchwcvBloUCvn0/AgHP7X4c1xE4vEcodP634/ub6oLP5wHgu93+5VolaiRahIfxYTRZ\nnbbXGoGA5zKO5jG3KHPjdvnNyuHt+Cd8h/1fWdbsM2h83WCyQCjkw2yxtlmvQoftChq313w/Sq0J\n9XId+DweYiKF6BYbAYlCDz6fh5JqJVKatdB2fL9AwMflGiVMZisMVga9ydLu+xnn44ffZp15q7XP\nyvG1MBefke09Ap/H5Iqgg59D07kiEPBRIVZDItd7df4D7o93x/NOIOCBwbPzy1NVEo3bfTuSqQ32\n9fQmC6IibY/4jseQI0/j4wt4EDRrq9L8vYwxWBlreY1ofg1wcf2y/9/i4hojbL2uPTl++XzX10V3\n7+XzHWJufr1xcU0SCvkQy3QwmC3onRwDAZ/ntsytxdA8DnefXVvXXW/VSDUoq1VhQGp8wLrQBiT5\nJBQKoVQqWyzX6XRe/VL1zTffQCqVIicnBwDs4xfs3bsXx44d802wpEtR60xYt+0EpEoDAODuyenI\nSkvmOKquZ0JuH2j1Zuw8cAk1Ui027DiJJ+7ICarBVQkhpCNWrVoFgUCA559/HqtWrcLSpUtRXl6O\nf//733j11Vf9vv+6ujrcfffdEAgE2LJlCxITvZ9lND7e/SxHBpMFUrkOyQlRCG9j/CGF2vad2y22\nfTNnxcRceV9iYgwulDUgLDwMZgDhkeGI8eBhv/k2Wou1qsHWPaJnSpxX3YxMjIcYma2lTHx8lNv9\nNMUiFPIRFx8JbeOU1/FxUVDpLW7fr9WbEBVl6wkQFxfpcvuFpTL79sMcOg20VmYAiI1Vgyew3Wcn\nJsRAIOBDZzBDptQjJSna6fNz1LTduFgN0PiglJAQgzAvH460ZoYYpdFpWZiQ7xR3UwxREUIkJsbg\nzCWp23pVNo6JE2+wIEZtK1e3btFITIxxWZaGxnUkKiPG9k5s9XhxfC0+PgpVUp29XuLjo5yOc2+6\n7oVFGBETY2vR5q5+3WlQ6lEjsY3LlRgXgV49Wo4XFhsbYe9e2VaZYjQtx4xLSIj26FzrKDP4iGk8\nBy08Hrp1i25MunonPj4KOhNrUd+efK7ujveEhBjEx4Q3rhNpH+Dbm7pqjeP566lu3aKQ2M12reYJ\nhYiJ0bRYx9P4Yh3K5Oq9jDEUnK+HwWjByKE9nbqZybRmKHTmxpiikZjY8vuj6TslQm9qUc5urVwz\ngdav4U2v8fk8l9tw9944mR4Gi+2kSEiIRqzD8CsNGhOUeueu0FHREagplQEAenTnIT4uClYe3/7+\nyPCWqRa5ygAra/04lKpN9mu/Y322dd31VmGpDNHREahTGBAVoKFmApJ8GjduHF566SWsW7cO/fr1\nAwBUVFRg1apVGDt2rMfb2bp1K8zmKzNdrFmzBgDw5JNP+jZg0iXoDGas334CVY1fztPHDMA4US+O\no+q6puT1h1JjxPcFlSipVuKtL09j0azhNFsEIaRTOHv2LD7++GNkZWVh586dGDx4MP7617/iqquu\nwvbt23Hrrbf6bd86nQ73338/wsLC8MknnyApqX3T1SuVOlgcHkSsjKGyXo3oCCEqxGroDRbERAlb\n/RFHbzTjeJEEACAalIzoSO9vRTUag/3fMpkGcoXOvqxBpoFR3/YDcfNtNGc0WxAuFKC8TmVft6pW\nieRukR7HqXCIS6kUQhbluqxN6wgFPITzrvytjBTY/61QOL9fIOAjLCIMOp0RViuDkMdclsOxnI5c\nretIrdZDq7fdczfINBAK+Dh4uhYAkBQf2eZ2VWo9NDpbwkIut73famVtJg3MFitUWhN0BnOLfQiF\nfKe4m163mMyQyTQoq3Ie/LxpXbFch+JKBYRCPnp1j3b4TLWIFLj/jJo0yNStHi+OrymVtiRJU70o\nFFpYTbbPsV6mxaVqJXr3iHU5eLxcbUC1RIO+KbGIiw5HRf2V/UYKeW3WmaM/GusKAMoAwGJpMSC1\nRmOwJ5/aKpOrz0gu18Kob3lMV9arodaZMKhPN4/v4QxGC8LC+C5bXyiVevv+NRoDjpktSOvt+exm\nAgEf8fFRbsvhyefa2vFuMdqOc7VGD0tj4sKbumrPflujVOjAt1phZQzVEk2bZZbIdVBqTejXM7ZF\nfTmWydV7VVoj6hvHuTp1oc6pXi6USuzHl0KhhRBXvjsc68Risbo83+UKLaKE7q8XnpyTfL7r88bd\ne1WqK8eaXK6FyXAl6apUtTx+6sRXvh8qaxS2cmht7ymvkiM2KszpvDOYLDh2QeyyPI5xOO5L0Vif\nzeN2915vOG6vrR+NfCUgyaenn34a9957LyZNmoT4eFt3JqVSiWHDhuGZZ57xeDvNByaPibFl+fr2\n7eu7YEmXYDJbsPHzQvs4AX8a2QfTRl/NbVBdHI/Hwx1/ugYqnQmHztbh1CUpPvzmPOZPHUKzqRBC\nQp7VarUPP9C/f38UFRVh5MiRuPnmm7Fp0yaf708ikSAuLg4RERF45513UFlZiU8++QRWqxUSiS35\nExkZidhYz2cZtVis9jGGAFuXkKbprpsoNUandZqTKvT2Qaolch16JcegvE4Fk8WKganxHo0v4zjI\ntdlshdXC7MtMJgvMHtxEO25DpzdDKODZ9y2R61BcrUDPxGgI+Dz7umazpdWyNWe2WO3vtViY2/c2\nrcMDHxaH9ziWq/lnDwBqpR5Wq20dd9t3NyB4W+VwjMNstgLsyrbEcvdj2zRt19rs/WdLG6DVm5E5\nMMlla4AmJ4ol0BvNLl/jW65snzHHz4YPs9naoqxN65ZUKmyfkdHqtF7TZ+ruM3LcTvNjzpHja03J\n2aZ6MZuv1FtRhS05VlarRKqLyVVON47F1aDU4/qhV6Gs9kqvEVf135rmZdLqzQhrTCwwxsDj8WCx\nMPvYMo7bblDqnctrcf0ZOZbNcd3LjXHzeTwM7NX2MBYylQEXKmSIiw7HsKtbJsZNJuf910g1TjNB\nekqnN7ktR1vcHSMXymTomRSNlMQop/NVqtAjPjqsw+NltXVsunK+TIboSCE0enOb5z9jDOfLbS13\nLBYrBqTGw8oYisrl4PNtx4i78woATA7nhqnZ8eDYYsrd8du03NV52No1E2j5PeDqNcZ4bV4XVQ4z\nBTpd95rFLJHrXX4WjutbrFc+rwuNn+uojBR7dzml2ujRNbn59bfptfZez91x3J7V2om63XXv3h1f\nfPEFfv/9d1y8eBFCoRCDBg1CXl5epxrEjoQGi9WKd3adsU8PPHr4Vbjj5mvoWAwCfB4P86cMgVpn\nwpnSBhw8U4u46DDcPmEQ1Q8hJKT1798fBQUFmDp1KgYOHIhTp04BAFQqFYxGYxvvblvza+SYMWOw\nevVqTJ8+Hfv27YNer8ecOXOc1pk+fbpXE780MVusUGqMkPlgggiN3oRqqe1X29jIMPRsx4ynPIcf\n69szdOqxIjHiY8IxpL+tK2Jx40CwdTItenW/0p2hRqpFcrfWux4WVcgRHx3ertmkWvuaczVKxcUK\necuFHtLqze1qddYeRpMFSq3tGL9co0JGf/ddPt0lnlqjN7l+j6subhVih4HZObyvqJdpUSPVYkCv\neJczK/trAP3SGiWkCj2GXJ3oNKhxU0IKAIoq239cOYat1bfsqufKxcb9qbSur4OlNS2HbvFWWY0S\nZ4pdtzjpCIPZgvJ6FXQG52PwXFkDBlwV367rWUeZrVb7+eYNhcb2HrFcB3k7WlyF6l26Wmdq0SrQ\nkUShg0xlaNe1CQCMJiuiIhzH6HPNZLagqEKB2Kgwj2cbbeJJq9K2BGrY8cB86wAQCAQYO3asV93s\n2tKeGybStVkZwwdfn8fxi7ZffXMH98A9t2ZQy5ogIhTwsWBGJtZ8egKlNUrsO1KBuOgwTMm7muvQ\nCCGk3e666y4899xzAIBJkyYhPz8fkZGROHbsGLKzszu8/eYDlp8/f97+72+//bbD23dUUqWATO39\nw4krjjMzldYq3T6s6QxmqHQmJMe37PbGc3jsac8zOwODwoOHLU0bD9Ol1Upo9CZo9LYuLAHlZcEL\nL0mQOaB7wCf36MjMSt6+taJe7ZMJZKxW3z+WXWpMqJy93IDrh17l8+27UyeztVorKndOMKl0JpdJ\nMACtPJUynCltAAPD0KuTwOfx/JLPM7ej9U9zl32QwGqNWKGDsNlg0GV1Kk6STx3VlWfLc5X0La5y\nPyudt1o7Pcpq1VDpjFDpjE4/cnhyTumMZsS4GY9Qo7cl14LlWTcgySexWIzXX38dx44dg8lkalGx\nP/zwQyDCIF0cYwxb9xXh4BlbP/ihVyfi738Z5tEsEiSwIsOFeGx2Flb/+xhqpFp8/vMlxEaFYXx2\nb65DI4SQdpk9ezYSEhKQmJiItLQ0rFq1Cu+99x5SU1PxwgsvcB2eV3yVeALQ4obYYLS4nGziZInt\nRyO9oeWvz06baHaPqTeaodQY0b1bZLu+7+VuyqrSGnGpWomrkqLtD5h605XBaAM7eXX71DZoMcjN\n2Dm+bHhz5rLsynZhux9TaU2IiRL69R5MpW275U3zFiuunCuTtbkO1xhjaFAaEBEu8CihaGo2iHR7\nDlip0gCV7kprmZ6JzomWYDkH6mXuu4k2sTIGsNZbpnR2eqPZby3ugllHSuzLT0vq0JLY0vz8bCsO\nN4FU1qtRKVEjKS4Sg/smdCQ8nwlI8umFF17A6dOnMWXKFMTFed8MmZCOYoxh+0/F2H+8CgCQ1jse\nC2cO93r2FRI4cdHhWHJ7Nl7eWoAGpQGf7L2AmMgwjMxI4To0Qgjx2sGDB3HLLbfY/542bRqmTZvG\nYUT+ZTJbUFanRkJMOJIT3HdVa/5jrG0MCvdjNtVI23iQbLbBwhIprIxBpTMhrZfngxQ30bpJTpy5\n3ADAubVWex5bffWwF8yPjM3HKSmvU6OmQYPYqDBkDuju131fKJe12nLGk8SSu2PAHYObboD+JFXq\n7S00Rrm4T/JHSsV5rKuWR2Aw5DGMJgtKqpStzhhntTKcLJbAyhhEg5K79EQ3BRfEiItuZ2tILw4y\nrd4Mq0IHXisHSW2DFjKlHgN6xbc6TlxHeZvoccdgtLS9Uiscu8F6+wOPuxallY2DwTeoPOgiH6Dz\nNSDJpz/++APvv/8+Ro4cGYjdEdLC7t8uY+/hCgBAv56xWDxb5NcLGfGNpPhILLk9G6u2HoNaZ8K7\ne84gKlLockBKQggJZvfddx9SU1Mxffp0zJgxo9NPllJcpYRCY4BEoWs1+dSypYFvH5ObbsrFcl27\nkk/t1uxGvkGpdznDWZfDgJoG2xhfap0J9XIdUlo5PjpCbzRDa2j9icpo7uADo4uHPoW642O4eUss\nv/JwaTQFR7cprcGEepkWKYn+6XpmZQxltSqEhwnQO9n1VPMtWni50KDSw9B4HNQ1aNG7R9c9T81W\nq1eJj/oGXYtlBpMFEc0mfZCrjUhq7DJtZbZkX0xMBHolRiIh1nViUG80Q28EiisVyBzovyR1WZ0K\nRpO1XeP0OVJqjYhz0XVVqTHiQrkcqcnRiPLTs2cwJHo9FZDUbnR0NLp39+8vG4S4879D5dj1aykA\nILV7NB6/PRvRbvrFkuCT2j0Gi+eIEBEugNnC8Mbnp+yDUxJCSKj44YcfMGfOHOzbtw8TJ07EvHnz\n8Nlnn0Gj8c2U3MHkQrnMozGUgJbd7gLB5CbhYLUyqHWeDZLsimNRmrrxNNEZzaisVzvNAOViC263\n15YQevZwcqnad+OpNNeR8aW41lrkOoMZf5ytxR9nazntJsXzIFF8yU9jLVXUq1HXoEWdTIsKFwN+\nN6kSe3d9DeFDpl06UlydwQyJ0jn5VFarwvGLYtRInT/3ernWPmae48xstQ1td4lUNxtrzx9jsDUl\nxL3lSSyltUroTWafDJzvVrMDt0aqwbnG1rnBJiDJp/z8fLz//vuwWDr26wIh3jpwshrbfyoGAPRI\niMQTd+S4H1CRBK0BqfFYNHM4hAIeDCYL1m8/iUvV/h08khBCfKlXr1546KGH8NVXX+Hzzz9HVlYW\n3nzzTYwZMwZPP/001+H5lC/HhPKaB0+P7rpaXSiX4XSptM33N09qXEkAXHkYLyyR2mfNa1IpUaO8\nTu20zNPHKNbGmiqt0fuHMg4etN2Vw2S24tSltj/7K9vp3A6fq3P7WtP4ZwBQL2/Z8qRdGg9diaLl\n9tx91u2d/atBqceFchm0+vZ3T6ySqJ26QzpOBlBep0JJtcI2DpYH3Y0ck2hN57ZCY0R5naqNZHFo\nM1us7U7kmC1Wp+OwSVMSp6xO1eI1pabjLQKLKuQ4eqEelfXqtldu5E2C1nFVT952ocL/48F58htE\n81DL6lRQeDnjYaea7U4ul+Orr77C/v370bdvX4SHOz/8f/LJJ4EIg3Qxx4vE+Ph/ttl+EuMi8OQd\nOUiMc9/nmwS3oVcn4f9mDMebO09Bb7TgtW0n8NTcnA43kyWEkEAbOnQoGGMQCoX4z3/+02UmXjGY\nLP799beZy7Wu9+VuDB9PbtaLqxQtxvYoqpAjKkLo9JDjrjuXRKHDwF4dn4HNlQsVcgzpn9ihbVyq\nVkKpNcJo8tMPxm6ecCrq1W3OJhjKDD76PBuUzskUtdaEnh2rcifNk6OtaW+Suaix9bpaZ8KI9BSn\nZK67CQdcUTsMKF9cpYDOYEG3mHBUN7a6ifWwl4OrFobnymytRowmKwb18V933bJaFZRaIwb3TYBS\nY4RErsPVqfGIivDvI7rZYsWJiy2TR57SdKCFaEc0JRObxjJqi5UxnCiWIDJMgCFeDtlRLdH4fpDu\nDjT09WRyhFAQsEFvpk6dGqhdEYKLlXK8s/sMGANiIoVYcnt2q2NOkNCQPSgZD0/PxNtfnobOYMba\n/x7Hk3Nz0K8nJaAIIcGvoqICe/bswZ49e1BWVobrrrsOL774IiZNmsR1aH7VoNQjKT6yxZTVtpnP\nXL/HZLZCbzS3GEODx2v9F+k6mQ6lNSp07xbZoktHg1LfoW51gOuWITK1gdvWXo087erojsVqRb28\n7W4wrWlrDKfmXWiauOsK6U+B7PDZ2sO6yWxBtcSzz72o2bADHrdWaKOwKo0RKq2pw12aPJlhsImr\n8ZjEch36eDg2mq5Zy6sqiRoy1ZVHW0U7Wto0v7ZIlDoMgn+ST1bG7C2FLtco7deQ82Uy5Azu4Zd9\nNqmRalsdiL89POmGyQWDyQKDyQK1ztTmTJCOM5Z6NEh3APn7hxt/dGd0JSDJp1WrVgViN4QAAKrE\namzYUQiT2YpwIR+Pzhahl5uBCEnoyR3cAw/+ZRje2XUaGr0Za/9rawHl6c0KIYRwYc6cOTh16hT6\n9OljH3S8V69eXIcVEEWVclzTOwEqL7oBHL8ohpUxDOrdDcndPP/xqOmBocrFL+PNH9yDgpf3+yqt\nETqDGalu7mvOXG4AD8CQ/ongeTmeli/Gu7lUrbAln4LzOTQoFVUq2jw3XM0m50sVYvctSTzptmQw\nWXCsSOyyxV+DUo/SGhX69oxtkZhs3q2taU8KjRFavck+k6Sn9A6tEj3tMtfWeeKrVmstOHysjvsw\nBCAR6+r66JV2jNUnVxnA5/E464XS1nFcKVa3uyupp4or2z/GXWvJoVAaqyxgLZ/q6+uxfft2lJaW\n4tlnn8WRI0cwePBgDBw4MFAhkC6gQanHuu0noTWYwefx8ND0TAzqHcDZbUhAjMpIgcUyFO/tOQu1\nzoRX/nMMi+dk+60rAyGEdFRaWhqefPJJjBo1iutQOFEv865FTVNXnIo6tVPyqfl4S2cuNyBc2Dmm\nRm/teY4xW9nPNA4iq9K5fkhqSmJIlXqvknZc82RWMl+TqbhvrQbAo6SsXGPw+hxy1Dx5xWurCaGX\n6lqJrSnpa09MOjhV4jzOF2MMVsbs3d460hhD6WGy2/G8U+tNLVrhtacFFWA7X0+XSpHWq5vX3ehq\npJqgnpW7Pa1kFFojFFojzJaWPxYHQ/KkspUErKfaOpfbM7tmvVyH6Mgwt61GQ01Avq3Lysowbdo0\nfPHFF9i7dy+0Wi2++eYbzJo1CydPngxECKQL0BvN+H/27jw+ivr+H/hrZu8zeyUbcpNADsKRcEo5\nbBFFUYxUQVEBT6zWetUTbGlRC0Wq/r61Kl5YsSJVtBQU8apY6gEIciZAuEI4kmzu7G72nN8fmyy7\n2d1kN9kzeT8ftcBkduaz85mdzLz3/Xl/Xnh/r/tmYuEVBSgZootxq0ikXFScijuuGgaWYWBst+PZ\n9/bE7cwOhBCyfPnyARt46ouenklaTVbUt8TX8IhwOdtlxijPB76utX+6cji5HmuEdC3+HYOJB13t\n4Po2y2Bv9TaoECv+Zo7zV5vLX0H9w6cbo1pvLVhds3w4LrTzvKtQs/0A7yS9VpMVPx6pC3kbAPwO\nY2sz27D3mCHkWQlP1bRGpZh1b+yqqO1T22Id9I1YPbsIqe8o0N9XsZwZ01NUgk8rVqzA9OnT8cUX\nX0AgcI21fO655zBt2jSsWrUqpG1VVVXh9ttvR2lpKaZNm4Y33ngjEk0mCYbjOLz5cTmqO6ZUnT01\nF1NGDozhDAPZxOGpuGf2cNcseFYHnn9/H/b08qaBEEISldVqxaxZs7Bz584e1921axemT58ehVZ1\nwTBB1wTpz4WnO9nsTrSZbT3OYucplOfqFqPV72xU/jg5LvwPJiFsrqIqNsMhHb2seeMZxAl6tsII\nPfe1mKw+QaVA2RXdZSd1xx7hIX/dCfVa0Jv4aTTqtZ01GLv9eaBJEOJRoFpRkR6y1h3P61dPQfeD\nCfhFdbBZT06OCzgD5g/lNTh4siHmQaioBJ92796NW2+91Ssazefzcc899+DQoUNBb4fjOCxatAg6\nnQ4bN27EH/7wB7z88sv4+OOPI9FskkA++f4Udh12BR0uGqbHVROzY9wiEi2j85Nx/5xREAl4sDuc\n+NtHB/DtgXOxbhYhhESF1WrFQw89hMrKyh7XPXz4MB544IGY3Xx2DZ5YbQ6foQ4WmwP7j3sPxelv\n051bbA78eKQWB07Uo7q2y0NpmLKPgskGs9mdMFvs+OmoAfuP1wcMkNQ0mnGgS5+EUyiF0q02B46f\nbUFTDLMnahpNaLfaYbbYewwqRKs9kdTXIvSh6DqsNhq6TkwQCd3V1Oovgh3mGIke3n3EALPFjuY2\nS8Cg+7l6E8pPNkSuhlcMdf5OP1NnxPGzgetKtZqsaI3RTIWdohJ8cjqdcPqJkhqNRvB4wU2nCQAG\ngwHDhg3D0qVLkZWVhalTp2LixIn48ccfw9lckmD2HTPgw23HAQBZKXIsvKKwV2m3JHEV52jw2xtK\nIBXx4eQ4vL65HJv+dyLm0X1CCImkY8eOYe7cuaiuru5x3ffeew/z5s2DTte34ei9va4azTaf4EZN\no8lnRqGmLlkIHIc+TQkeb5wch9O1Fx5EO2e7AlwZK+b2wN/ah3s9NWkSAAAgAElEQVQ2qRaTKzvK\nanfAZLH7HPtOp2tbQ6o3cvBkQ0QeMAHg2NkW1DaZYl483mJzYu8xg0/wtKqmNSbt6U93vX25hU+k\n2/9YBNoS1d5KQ7dDMG0OB87Vm7oN8jW0tqM5hEkvEomp4/fGufqeg+GxPu2iEnyaPHkyVq9e7RWA\nampqwrPPPouLLroo6O0kJyfjueeeg1Tqmvngxx9/xM6dOzFhwoSwt5kkhpoGE1b/+xA4AHKJAPf+\ncgREguADmqT/GJKehMduGg2V3DUt90f/PYE3Py7vd9+YE0ISn9UanhvgHTt2YOLEiVi/fn2PQaHt\n27dj5cqVWLhwYZ/22dssAbvTGdQQs671OGwOR9inBI81Q7P/YRFA8MMrIiFcM223mqwRGzoZKEsq\n2kN+6pv9PwifqYt9JlQwejvkMNL6HpBJnOjTkdNxOPtmFPi7NrSZu/+daLbaeww4W22OiM8KGa+q\nQ5m9kONw8EQD9lbG5kudqJTRf/zxx7FgwQJMnjwZFosFd999N86cOQOVSoUVK1b0apvTpk3DuXPn\n8POf/xyXXXZZmFtMEkG71Y6/frgf5o6Z7e4uK4ZOlTgzu5Dwy0yR48kFY/HC+/tQXdeG/x04j/qW\ndvz6lyMgEwti3TxCyAC3bt06vPbaazh//jy2bt2K119/HXq9Hvfcc0+vtjdv3ryg133xxRcBAB99\n9FGv9tXpVIQzO6JRf4X0Pz9F+UEq1KFoodT26o1EeeTuKUgY66wMf8JVoLqqphXpyTI4nRwqz7QE\nPUytv7M7nH6L6ceDfUHWzUskTW1WtPYQ7IukqGQ+6fV6/Otf/8KDDz6IG264AWPHjsXDDz+MTZs2\nIT09vVfb/Otf/4pXXnkF5eXleOaZZ8LcYpII3v3iqHus/dxpQ1CUo4lxi0g80CjFeOLm0RiRqwXg\nKmT6zNs/RrwmAiGEdGfTpk34y1/+gtmzZ7snX8nLy8Mrr7yCN998M8atIwTx+eTfD9jszoCZUgON\nv5n4vHDwrYMWghR1+L+E7jq0srfO1htxurYNR6ubQ6pz1t+1W+O3BlMiFYIPliNcKa69FJXMJwCQ\nSCSYM2dO2LZXXFwMAHjiiSfwyCOP4PHHHwefH7W3Q2JsV0Uttu9zFZUeW5iCS8dmxLhFJJ5IRHzc\nd90IvPv5UfxnzxmcbzDh6b/vwj2zR6AoWx3r5hFCBqA333wTS5YswezZs93BpgULFkAqleK1117D\nbbfdFuMW9ozHY8Fjo/K9JemCz2cBBu7jz7KMx5/h6ZN471+GZcCLzvfmvda1XzhcyMqK5LHl85i4\n7rtOdgfXbTsZlkFtk7nX78Vssfu8NhKfld5qNlphtTkToq8iqbNPeDwWzUZrWI4Hj8eA54zva1gk\n8fkseDwWTA/BJV6Aa0Vnn0RaVKI1CxYs6Pbnb7/9dlDbqa+vx549e7ymCB4yZAhsNhva2tqgUqn6\n1E6SGBpbLfj7pxUAALVChIWXF1CBceKDx7K4+bJ86DVSrP/qKIztdjy3/ifceGk+flHau4xLQgjp\nrRMnTmDs2LE+yydMmIBly5bFoEWhqTrfglaTDTKZKNZNGZBa2x2oqG7xOf4SiTBs+6hrsVL/hkln\nv1TXm6NyTBUKMWxc4t8LWxxcn46XHQj4+nB+VvpCEB/NiAtSqRAOZ9/6vJONA1g+DzL+wKz9q1bL\ngjrHFQoxjNbY1XyLSvCp69A6u92OU6dO4ciRIyEVvqyursZvfvMbbNu2DSkpKQCA/fv3Q6PRUOBp\ngHDNZHYIxnY7GAB3XjWMavmQgBiGwWXjMjFIK8UrGw/AbHFg7dbDOFtnxA3ThwzYb0cIIdGn0+lw\n4sQJZGZmei3fs2eP+54mnp042wKz2QpnjFP2iQvLMpBIhNQncSZW/WKkYVwB0Wcl/nT2iclkhc3u\ngNHc/4a3RVtDQ1tQ14EzdjvaLb5DHftV5tPy5cv9Lv/b3/6G8+fPB72dESNGYPjw4Vi8eDGeeOIJ\nVFdXY9WqVbj77rvD1VQS5z7bcdo9XvzyCVkopCFUJAgjcrVYMn8s/u+DfahtMuPL3dU432jCPdcM\nh0REw3UJIZF3/fXXY9myZXjiiScAAMePH8f27dvxwgsv9HkGOn8MBgMUCgVEovBlXTidXNzOkjXw\nuL48oT6JN9Qv8Yf6JP64+qSp1QKRgKV+CYPK6uagjqPRHGid6HwhH9Ov/cvKyrBly5ag12dZFi+9\n9BKkUiluuOEG/O53v8OCBQtw8803R7CVJF5U1bTiw2+OAQCy9HLMnpob4xaRRJKmk+HJhWPdNZ8O\nnmjA8nd2o6GFioASQiLvzjvvxMyZM/HQQw/BbDbjrrvuwjPPPINZs2bhV7/6VZ+333X4+eTJk0O6\nxyKEEEKirT8W9Y6FRJlYieG42E1tsWnTJjz99NP44YcforbPurrIThFMIsPucGLZWztRXWeEgM9i\n6S3jkKaTxbpZJAHZHU68vfWwu2C9WiHC/deNRJZeEeOWEULCITk5vj/LZrMZlZWV4DgOubm5kMvl\nsW5SULbtrobRaKFvqOMEj2Uhk4moT+IM9Uv8oT6JP9Qn8YfHspg5JS/i+4lZwfG2tjYcPnwYN954\nYzSaQBLclu9PobrONfXq3F8MocAT6TU+j8WtVxQiOUmMj/57Ao2tFiz/x278+prhGJ6rjXXzCCH9\nyNmzZ/0u12pd15qWlha0tLQAANLS0qLWLkIIIYSQaItK8CktLc0nHVwgEODmm2/G1VdfHY0mkAR2\n1mDEpm9PAgCGZiThF6NppjLSNwzDYNakwdAlSfDmJ+WwWB144f19WHT1MIwv0se6eYSQfmLatGk9\nzsbKcRwYhkF5eXmUWkUIIYQQEn1RCT6tWLEiGrsh/ZDTyWHNlnLYHRz4PBa3XFEItocbeUKCNXF4\nKtQKEf764X6YLXas/vdB2B1O/Gz4oFg3jRDSD7z99tuxbgIhhBBCSFyISvBp586dQa87bty4CLaE\nJJqvdlfj2BnXkISyyTkYpKXhdiS8CrPVeHReKf6y/ie0mW14Y7Mr2Dl1FA2BIYT0zfjx4/0ub2pq\nAo/Hg0IR3/WpCCGEEELCJSrBp/nz57vTzj3rm3ddRmnnxJOh2YwN244DALJS5JgxPivGLSL9VXaq\nAo/OK8Wq9/agxWTDW1sqYLM7ccmYjFg3jRDSj7z++ut4++23UVdXBwDIyMjAnXfeiblz58a4ZYQQ\nQgghkRWV4NMrr7yCp59+Go888gjGjx8PoVCI/fv3Y9myZZg9ezZmzpwZjWaQBMJxHN7+9DAsNgdY\nhsGtM4vA57GxbhbpxzJS5HjsptFYuW4Pmtus+MfnR8BxHKaPzYx10wgh/cCrr76Kl156CfPnz0dp\naSmcTid+/PFH/OlPfwIACkARQgghpF9jOM9UpAiZMWMGlixZgqlTp3ot37VrFx599FF89dVXkW6C\nW11da9T2RXrvu4Pn8dqmQwCAmRdl47qfR37qR0IAoKbRhGfX7UFDiwUAcOdVwzBxeGqMW0UICVZy\ncnwOZbv44ovx4IMP4pprrvFa/sEHH+DVV1/FZ599FqOWBWfb7mqaFjuO0FTl8Yn6Jf5Qn8Qf6pP4\nw2NZzJwS+eftqKSS1NbWIj3dd4YyuVyOxsbGaDSBJJA2sw3vfXkUAJCiluDqSTmxbRAZUPRqKR69\ncTSSZEIAwBsfl2NvpSHGrSKEJLrm5maMGjXKZ/m4ceNQU1MTgxYRQgghhERPVIJPJSUleO6559DW\n1uZe1tTUhGeffRYTJ06MRhNIAnn/P5VoNdkAAAtmFEAo4MW4RWSgSVFJ8ND1JZCK+HByHF761wEc\nOd0U62YRQhLYJZdcgrVr1/os37RpE6ZNmxaDFhFCCCGERE9Uaj49+eSTWLBgAaZOnYqcnBxwHIeT\nJ08iOTmZpiEmXg5XNeK/+84BACYWp2JYjibGLSIDVWaKHPfPGYm/vPcTrHYn/t8H+/DYjaXI0sfn\nkB5CSHzTarVYt24dfvzxR4wfPx58Ph8HDhzArl27cMkll+CJJ55wr7t8+fIYtpQQQgghJPyikvmU\nl5eHTz75BL/97W9RUlKC0tJSLFmyBBs3bkRqami1VGpqanDfffdhwoQJuPjii7FixQpYrdYItZxE\nk83uxN8/PQwAkEsEuP6SITFuERnohmaocM/s4eCxDMwWO577514YmsyxbhYhJAGVl5ejpKQESqUS\nFRUVOHDgAABg7NixaG5uRnV1tfu/UFmtVsyaNQs7d+4MuM6hQ4cwd+5clJSUYM6cOTh48GCv3wsh\nhBBCSKiikvkEAElJSZgzZw6qq6uRmemaPUogEIS8nfvuuw8qlQrvvvsumpqasHjxYvB4PDzyyCPh\nbjKJsi3fn8L5BhMAYO4vhkApFca4RYQAI/N0uP3KIry66RBajFa88ME+LL55NKTi0K9fhJCBy9+Q\nu3CwWq146KGHUFlZGXAds9mMRYsWoaysDCtWrMC6detw11134YsvvoBYLI5IuwghhBBCPEUl84nj\nOKxatQrjxo3DVVddhfPnz+Oxxx7DkiVLYLPZgt7O8ePHsW/fPixfvhx5eXkYM2YM7rvvPmzevDmC\nrSfRcK7eiM3fnQQAFGapMGkEzS5G4sdFxamY8wvXDBBnDUb87aMDsDtodg5CSGiam5uxd+9e7Ny5\n0+u/Xbt29Wp7x44dw9y5c3vMlvr4448hkUjwyCOPIDc3F0uWLIFMJsOnn37aq/0SQgghhIQqKsGn\ntWvXYuPGjVi6dCmEQlc2y/Tp0/HFF1/gxRdfDHo7ycnJeP3116HRXKgDxHEcWltbw95mEj1OjsPf\nPz0Mu4MDn8dg/owCMAwT62YR4uXy8Vn4ealr1s7yU434+5YKcBwX41YRQhLFhg0bMGXKFNxwww2Y\nP3++z3+9sWPHDkycOBHr16/v9nq0b98+jBkzxmvZ6NGjsWfPnl7tlxBCCCEkVFEZdrd+/Xr8/ve/\nx6WXXoqnnnoKADBz5kwIBAIsX74cDz74YFDbUSgUmDRpkvvfHMfhnXfewc9+9rOItJtEx9d7zrhn\nErvqZzkYpJXFuEWE+GIYBjddOhT1ze3Yf7we/ztwHslqCa6eNDjWTSOEJID/+7//Q1lZGW655Zaw\nDXWbN29eUOvV1tYiPz/fa5lWq+12qB4hhBBCSDhFJfhUXV2NoqIin+WFhYWoq6vr9XZXrlyJiooK\nbNiwoS/NIzFkaDbj/a+PAQAykuWYeVF2jFtESGA8lsWvyoqx4h+7cbq2Df/67wnoksT42fBBsW4a\nISTOtbS04Pbbb0dOTk7U993e3u7OPO8kFAppwhZCCCGERE1Ugk/p6enYv38/MjIyvJZ/88037uLj\noXr22Wexdu1avPDCC8jLywtHM0mUcRyHtz89DIvVAYYBbp1ZCD4vKiNBCek1iYiPB+aMwtNv70Jj\nqwVrPqmAWi5CUY6m5xcTQgas6dOnY9u2bTEJPolEIp9Ak9VqDTkDi2UZRKliA+mBqy+oT+IN9Uv8\noT6JP9Qn8aezTyItKsGn22+/HX/84x9RV1cHjuPw3XffYf369Vi7di0ef/zxkLf31FNPYf369Xj2\n2Wcxffr0CLSYRMO3B87jwIkGAK56OoMHKWPcIkKCo1aIcP91I7HiH7vRbnXgxY8OYPHNo5GeLI91\n0wghceqRRx7BrFmzsHXrVmRlZfnUNly+fHnE9q3X630yzQ0GA5KTk0PajkRCs9DGG+qT+ET9En+o\nT+IP9cnAE5Xg07XXXgu73Y6XX34Z7e3t+P3vfw+NRoMHHngg6HoFnV588UWsX78ezz//PC699NII\ntZhEWlObBeu+OAoA0KslKJtMdXNIYsnSK3DP7OH4f+/vg9lix/Pv78WS+WOhVohi3TRCSBx6+umn\nYTQaYbVacebMmajue9SoUXjttde8lu3evRt33313SNsxm61wOmmihXjAsgwkEiH1SZyhfok/1Cfx\nh/ok/vSrzKfNmzfj8ssvx/XXX4+GhgZwHAetVhvydo4dO4aXX34Zd911F0pLS2EwGNw/0+l04Wwy\niSCO4/DOZ0dgstgBALfOLIJQwItxqwgJ3fDBWiy4vABrPqlAQ4sF/++DvXjsxtGQiKJyaSWEJJBv\nvvkGL7/8MqZMmRKV/RkMBigUCohEIsyYMQPPPfcc/vSnP+H666/HunXrYDabccUVV4S0TaeTg8Pp\njFCLSWhcQ1WoT+IN9Uv8oT6JP9Qn8Sc6wx+jspdly5a50701Gk2vAk8A8OWXX8LpdLpv3qZMmYLJ\nkydH7UaOhMf2/eew+4jrfJg2Oh35maoYt4iQ3psyMg1XT8oBAFTVtOHlfx2A3UG/SAkh3tRqNdLS\n0iK2/a7D+CZPnowtW7YAAORyOV555RXs2rUL1157Lfbv34/XXnstbLPuEUIIIYT0hOE4LuK5bnPn\nzsUtt9yCmTNnRnpXPaqra411Ewa08w0m/HHNTlhsDqSoJVh6yzjKEiEJj+M4vPFxOb49cB4AMKYg\nGb8qKwaPpSKKhERbcrIi1k3wa/369di6dSt+97vfISsrCzxeYmX8bttdDaPRQt9Sxwkey0ImE1Gf\nxBnql/hDfRJ/qE/iD49lMXNK5Cdxi8pTf2FhIR5++GG8/vrryMnJgUjkXRMlkkU2Sfyw2Z1YvfEg\nLDYHeCyDu64upsAT6RcYhsEtVxSizWzDvmP1+PFwHdZ8UoHbriwCy0RnDDUhJL698cYbOHv2bMAv\n4srLy6PcIkIIIYSQ6InKk/+JEycwZswYAPCZbYUMHB99cxynalyZZ7+cmkuz25F+hc9jcc81w/HC\n+3tRUdWEbw+ch0jIw82X5vsMhyGEDDyhFvcmhBBCCOlPIhZ8WrlyJe69915IpVKsXbs2UrshCeLA\niXp8uqMKADAsR40ZE7Ji3CJCwk8o4OG+60biL+t/wrEzLfjP7jMQC3i47ud5FIAiZICbPXt2rJtA\nuhAL+Gi32WPdjAFHKuK7J50hhBAycEQs+LRmzRrcfvvtkEql7mWLFi3C008/jZSUlEjtlsShFqMV\nr292DSeQSwS446phNBSJ9FtiIR8PzhmFle/uQVVtG7b8UAWOA+b8ggJQhAx0X375JY4cOQKHw+Fe\nZrVasX//fqxZsyaGLRuYRuZpsaOiJtbNGHCGpCdh3/H6WDeD9CMiAQ8Wm6PnFSNg8CAlTpxricm+\nCUk0EQs++atjvnPnTlgslkjtksQhm92Jv320Hy1GKwDgtiuLoJKLengVIYlNKhbgoRtK8Od/7Ma5\nehM+3VGFNrMNC68ooCLkhAxQq1atwuuvvw6dTof6+nro9XoYDAY4HA5ceeWVsW7egMSyvl8IjMjV\n4uCJBjgjPx/PgCUVC2LdBNLPFGWr8VOlISb7llL9WhJjfJaFPUEKt9NTEIkYjuPw9qcVOFrdDACY\nMT4TJUN0MW4VIdGhlArx2E2jkZPqmnlr+/5zeOmjA7DZY/PNHCEktjZt2oTFixdj+/btSElJwbvv\nvovt27dj9OjRyMzMjHXzBhytUuyzbJBGBplYgNKh/f9eJSslPmeFJPEnTSuLdRN6JOCzMaslS1nt\nPfN3vQ03fseXu4M08X++htvYwsQZVUbBJxIxW36owv86pp4fmafFnJ8PiXGLCIkupVSIR+aVoihb\nDQDYc9SA5/+5F2aqdUHIgFNfX49p06YBAAoKCrBv3z6oVCo8+OCD+OSTT2LcuviRrpOHtP5Fw1ID\n/mxkri7gg3O6znd5dmpnQCY+HyYFvPDdtqvkwrBti/RvWXqF+8E+ngn5vLBub0KRHhnJPV+PQi0l\nIpcIBlz5ESYK19SSoTqMyNVCo4zOCJvMKATwE+FzF6qIviOKBA9cu4/UYcPXxwAA6cky3HV1sd/0\ndkL6O4mIjwfmjMKY/GQAQEVVE5a/8yNqm8wxbhkhJJqUSiVMJhMAICsrC5WVlQCAtLQ01NRQ3aFO\nIiEvbA+RUjE/4INzd/eo8Xr72h9mCc4IMbgYrJG52ohsN9KKczSxboIXhSQxg5KRCG4wDAMBv+dH\nZak4tGF3WXoFxMIBNlQvCtdUPo+FTCyIWvwhGo+1akX/K1UT0TP/6aefhkh04aDZbDY8++yzkMm8\nv21avnx5JJtBouzU+Va8uukgOAAKqQD3XzsSEhoPTQYwAZ/F3dcMx9tbK/DN3nOorjPiqbd24q6r\nizE8QW+YCSGhmTBhAlatWoWnnnoKo0aNwurVq3HjjTdi69at0Gji6wE01lJUElQb2sK2vZF5WrSY\nrKhrNKPZ5KpBSSWdImf4YC3aLXZUnm2O2j4jUUeqZIiuV3WE8jKSsO9wbVDrKqRCFOdocPBkQ8j7\nSRTd1aPRKMTgsQzUChGOVDf5XSczWQ6FTIhDMThGEannxLn/zy+lVIiWjutUfxGn8fyo0yklMLSE\n8OVzmA+cgMfC5ohtbaiIZT6NGzcOdXV1qK6udv9XWlqKxsZGr2XV1dWRagKJgXP1Rrzw/l5YbU7w\neQzu/eUI6FSSWDeLkJhjWQYLLy/E3F8MAcMAxnY7nn9/Lz75/pTfCRoIIf3Lo48+itraWmzZsgUz\nZsyAUCjEpEmTsHLlSixcuDDWzYuJoemqqOxHKOBBlySBxqPuCJ8XP49DGclyjCtMQXGOBrndZDf1\n9hv9/IzwHedg6v/IJYIe7/0SIYtLLORD1ouglkIaWvZQqOtHEtdNUKS31ApRwOFr+Zkq5KUneX02\nu0pPlkMZo2MUqb7p7ravMEsdkX3GEq/L9VYpEyJTr4BCGtzni8+yEAWZERuvmauA73GItu4+Z9ES\nsXSUtWvXRmrTJE6dqzdi5bt70Nwxs92tVxRhaBhveAhJdAzD4PIJWcjUy7F640G0mW344OtjOHmu\nBbdcURRy6jYhJHEMGjQI//rXv2CxWCAUCvGPf/wD27dvh16vx8iRI2PdvLilVYrR0GIJ+qFYIRGC\nz2OQopb6/CxFLYHN7oRQyINQ4HqQyUxR4HRtq1eQIdoPL50P5gqpEAqpEMcDTNve23ZplGIM0shw\nrsHY2yYCcD0AioXBD4ns7lt2vVoKkYCHiqrGoLdXkKnG4dPBrx8OxTkanK5tC/rYxSrTn8eycMTr\nbFeM6xx3ODi0W+1obHPNfB7Nukf8LvXSWIYJekbL0qHJMJptUClEqKxuRkNre5/a0tNeo1GmRKMQ\n9/l9dKVVilHf4n+b6To5zjeY3P8epJUiNz0JZ873nB2pUYiRn6kCx3GoONXozl4NJNDRU0iEaDXH\nNqMs1HO+LzWfBDwWBVlqiAQ8HD7dCIvViYxkGWoaTT2/OIIStoqV1WrFrFmzsHPnzlg3hcA38LTw\n8gJMHB64CCghA1lxjga/XzgWWSmuB45dh+uw9M0fcDiEm3BCSGISiURoaGjAf//7X2g0mj4FnqxW\nKxYvXoxx48ZhypQpWLNmTcB1t2/fjrKyMpSWluK2227DiRMner3faFLLRRhTkBz0+hIRHwVZar+1\nMhiGQUaKHCkeWTlpWimKczQYlnMh2yAaxXF7w7NVKWoJRhem4KJiPUbm6qCQCrstjhyuB9q+ZrN7\nPniHEsgCXBk0ej9BxUjI1ruKCbMsA5kk+IDSsMG9y1rRJfX+uOqUEozO1/UqSysSxEI+CjI9jkNH\np2enKpCbdiHjLVrtTU+WYdwwvdcyjaL7DBDPDD+RgAeNUtxt4CBQRmBmigJiQZfzJw6y3S9MrhA+\neelJfpePyNVCwGdDziIbW5CCUXk65Ge6EhkYhkFREDXSAmWIdncN1ClD//z1phuTVaFlHvGDqDnW\nHblEAAGfxfDBWpTm6yDokj3mWV8xPTk6swQmZPDJarXioYcechfrJLHlL/B0cUl6jFtFSHzTqSR4\nYv4YTOoI0ta3WLDy3T3YsO0Y7DEej00ICZ+//e1vmDBhAk6dOgUA2L17Ny677DLcd999uOmmm3Dr\nrbeivb1330D/+c9/xqFDh7B27VosXboUL774Ij777DOf9Y4ePYpf/epXuPTSS/HRRx+hqKgICxcu\nhNkc+sQHPT20hSLYL4G7Zi2EY5sX1megkArB8/yGuZtt9KUgs1ou6ltgq8ubU0iFYBgGUjEfxTka\n6NWBH6A8X+nzMBwAyzA+QZFwZqv0Zhhhkiy8w6DGF+r9Lud5nHOh9Flvi+VLQgzEeUpPloHHshgR\nhhqSWV1m8MpNcwUUAgUWuho8SImSIbqYDC/yV8KgIFONLL3CnenYSSy68G/PIX08lsWEIj2y9KEF\nZwKtn66T+QQvOfSc/RRp3Q077mnY36g8nd/lga4Noo5jP9gj4BVMIIrPY4POJMwOpr+6iRYNyUjy\n+zlXyUQoytZAxOchJ9V7qHAwfdh1qGBfatMFClB3DqsuyFQjuZsvB/z1T2GWCjyWhVouCvmc762E\nCz4dO3YMc+fOpVpRcaKqphUr11HgiZDeEAl4uP2qYfhVWTGkIj44AB9/dwrPrP0RZwx9Gx5BCIm9\n9evX45VXXsHcuXOh1boeDBcvXgyxWIzNmzdj27ZtMBqNePXVV0PettlsxgcffIAnn3wShYWFmD59\nOu644w688847Puu+9957KC0txb333oucnBw88sgjUCgU2LRpU8j7VUV49p2uN6axeEjr7rG5eLCm\n10WIC7LUIWf7eJJ7PMSmanufAZSmC+61RdlqDAky6NApmKnpOwUbntAoxEHVrQq1LpBWKQbLMpD0\nMPOYWiGCkM8Dn2XdM9d2Gj64f00aIhLy3IGBoiy1O0tQrRChZIj/oEO8GpyqDDhbWJpWBo1CjDSt\nDMM6aq0NTlViTEFy2GZLk0tcgYaugRGum+hTtDL7+iKYGQABIC8tCcNyNO4vD6RiAUbkajEqTxdw\nG5kpCuSkKkP6XPFZFoM8Ms8CdV9vfpfkpSchSSZEaX4yUjVSFGapoZKJgmrf4EFKlOYHn7Xrj+db\nUUgFKMpSY1i2xh1IEgv57jpOaoUIeWmhXa+lYgHG5CejINfuNCMAACAASURBVIp1xhIu+LRjxw5M\nnDgR69evpyK9MbbnaB2Wv7MbzW0UeCKkL8YX6bHs9vEozHLdXJ8634o/vLkDH35zHDa7I8atI4T0\n1vvvv4/HH38cv/3tbyGXy7F//36cPHkS8+fPx5AhQ6DX63H33Xfj448/DnnbFRUVcDgcKCkpcS8b\nM2YM9u3b57Pu6dOnMWrUKK9l+fn52LNnT+hvKsI0SrH7Cy0AMDT7ZoVpO262vYb2RFHxYA1SNRce\nEvtSlyMUPJbF6KHJGJXXtyFWDMNAIuJDKup+G50Pz6HoKZDjic9jg8oqys9UuR+wurv1DyVDDriQ\n0ST08yAs8NgWyzIoGaJDyVDfYSuCEPYZjiLrwWat9RaPZTAsW40x+SlIknsHbsRd+jZJ5v3zzgyK\nbrfvcbz0mjBOSNTlNBqkkUGvCRzIYVkG+Zkqd7ZHiloKvUbaY2Zf12dPbYACzoNTle7rk1DAw8jc\nC4E7hVQAicg3CD04VYksffDB277o7nMXTPaegOd/Hc/X6pLEPgFhmVgQMJspI1mONK0UqRppt9ee\nrplZncPyOgUKHvYUNej6slSN1CdIppKLUJithlwi6DELM9ARztYrgr5OquQX9qGUCpEkF0EpE2JE\nrhYZOjmKsgP/DsxICe5cikaNMU8JV9123rx5sW7CgMdxHLbuOI33/1MJDq7UzVtnFmFiMdV4IqS3\nNEoxHp5Xis92nMaH3xyH3eHE5m9PYkd5DRbMKMCwIMa5E0Liy7FjxzBp0iT3v7///nswDIOLL77Y\nvWzIkCE4e/ZsyNuuq6uDSqUCn3/hVk6r1cJisaCxsRFqtdpreU1Njdfrz507B5UqepOCqOUiWGxO\nSES8gEVph6QngWUZWD2C7hab6+9iIR/tVrt7vZxUhTsQEO7po3vKfOCxLLL1CigkQohFPFSc8j9F\nvD/BfG3a3VTrXYcPBa3LW2IYBiNyNfihvMbv6vkZKp/jkNrNw3ynnibO8Hx4Z1kGw3LUqDzT7O5n\nf+3wen04c+ECdLNOKfHJmGFZBmzHC6QiPkwW17koCiGTTa+WQq+W4tjZZtQ1mZGiunA8g31XQzOT\nsP94vdeycCTqJCdJIJMI3AE8Ab/njSbJhEjTSsHns+DzWLAMfIJzXbEMg1F5OrRbHV4P1qGIh+ni\nOwXKDOwa+JKK+RiZqwOPZcDnsRg8SInGo3UBX6NLksDQHPqwaL1aGlxBaY/u1aulqG00uz9bUjEf\n2XoFrDZnwEL7w3LUOFdvQm2T9776kheiVYqDyjpTdQlwKrsEgQIFhHVJYrT2UKzcU0+BcblEgIJM\nNVgGKPdXszXAexmklWGQVobvD533+ZlaLnIX5AdcmUlF2Row8J7MQCLiBwwulQ5NRrvF7nNc4kXC\nBZ9IbNkdTqzdehj/3XcOgCt6f+8vR9CsdoSEAdsxG15pvg5vf3oY5acaUdtoxqr3fsJFxXpcOzUP\n2qTYT5NKCAme5830rl27kJSUhMLCQvcyo9EIiST0DACz2Qyh0PvmsvPfVqv3DfbMmTNxzz334Mor\nr8SUKVPw73//GwcOHMCECRNC2ifLMuCxjHd9pB5k6eVQSIXuG+FjZ5rdr+fzWa9t8fk81zIeC57D\n9RTD4zHg8131bM7VG5GskkAg4EHgEYQpyFaj/GSj1/p9NUgrQ22j78Of57b1HUPfeDwGTq7nfbre\nm+/x69rewmw1Tp1vhVohwtHqZr/rdWaQeGaScIDfvukMDnT+zPMYdV2/KFsNm92JZI/6UaX5yWgz\n2ZCsloBluu9/hccDD8sy4HG+79XzfaiVYgwX8fHTUYPf7UklAu/3zbIB36M2yTtrzm/7pAK0mmyu\n1/DYC+ebxzYLc7rPqCvK0eD42RboksQ+5zCPx4JDZzaB/37Oz1QhTSeDXCJwXx/4PP/vq6skucjv\n+ROoP4NV0E0GhSfvzysLbYAaM5511JLVEq8+VPCFUPipbRyo7Z2vHVOQAlO7HWarHadr2nzWkYj5\n7m3IpRfOm87PiGef9PYa0fVc8bwOdT02XSk9gm18PouLilOxs7zW72u0SWI0tloQqmSVBG3tNrRb\nus+aFwp4yM9UocVoQ1aqHPUt7eA4xt2OzI6MsNom32ugQMBCLOJDIRN6fZHQeX3rvBYKugmUe16/\nOo+bQMAG3S+dr2FZ/9f7kXk6GNttOHmuFYCrLppGKUZVl/PGs+2D05Tu9V1t6/l3Sed1klftO2uf\noPP6EuC88He+F+dq8d2B817rh3rfz+ezkHWTORawPSFmjvYWBZ9I0AxNZqzedBDHzrimAE7TyXD/\ndSO7LW5GCAmdXi3FwzeU4PuDNVj35VG0mW34/mANdlXUYfqYDMycmN2r4RCEkOjKz8/H7t27kZ2d\njZaWFvzwww+45JJLvNbZsmUL8vPzQ962SCTyCTJ1/rtrMGvKlCm499578Zvf/AZOpxMTJkzANddc\ng9bWVoRCIhEiO0ONrHQVmtosMJntOFPn/2a+0/B874LOylYrjFZX1kJSkhQy2YWHmySlBGq1FHJZ\nC/gC18OTRMyHWu16Uk3V+x+2xPF4kMlc38ArlRL3+n0xVi2D08mhsbUdB45dyDTxt+30VCXq/ASq\nulKrZZBJW8DjO3yWd6VPcb3Xs43t3a6n9JilyWZ3QCbzHfakVsvQ0u6AzOgKuiQlSd3b6rr+4Czf\nLNuuYQl/+/DXRplcDLvdO0PFX/+oO9rEsgx2HPTOBkhKknp9g29xArIm38w5tVoGlUoKG8egIUBm\nHQDkZqpQebqpoy1iqNUyyA0m2D2yHHo6f9QA0lIvZLzkZqpR02DCsMFaKJUSNLdZIPFTmN5zu12P\nsmf/dLtvtczn+KtVMog7siK665uethsMz+339FmbJBHCavMOZAa7bX9t6zwPz9cb0dDmfazUKhm0\nGgY2joHN4URBltoni8azT3p7jdCb7LB6nNJe57tH+4M/nq6gBcN4v8bGMZA1hj4RRZJKCnmbFTy+\nvdv11GqZd9urW9xZS57L87LUOF9v6vJaOXgdQ7W6vme5XASrzemznUAkEiE6Vvc6j3vSuV+5VOB3\nP53LBumVaDPZkJ4sB8sy4Hg89+e/6/oqlRQCkQBn61zZXooQfpf4O3eTVFKo1dKA50Wga3VvzqNQ\nRHr7PaHgEwnKzopavLWlAuaONOPhuRr86urhPaZXE0J6h2EYTByeihF5Wny47Ri+2XsOdocTn+6o\nwra9Z3HlxGz8ojQ96JlACCHRd9NNN2Hp0qUoLy/Hnj17YLVasXDhQgBATU0NNm3ahDfeeAPPPPNM\nyNvW6/VoamqC0+kE2/FNpsFggFgshlLpG6S56667cNttt6G1tRUajQYPPPAA0tODr9NYkp+MtrZ2\ntJtc38ZLeAzqjO0wGrv/dr6x0XvYRkuL2f0az78DQHOzCQKGQ5vRAovVFaBx2O0+2+iqudVyYZsi\nXo/rh4IFvNrob9s6uRDGNgvq/GQJeGpsNKK5xQx7R1aXXiNFskrcbXsD7ZvHY6FUStDSYoajYwiS\nze70Wp9hXPtobDTCabe7f2az2Nzbajdb4XByfvcRiErKx5k6/+t5vr6trR0Oh/c4nJYWPholgX9v\nOWx2tFsvBOeamoxwWG0e/zb5nHMFWSr3fuUiFqe7OSdbPc45k8R1rrS1tsPYkTGlUYpCPn/0SSKo\nZXzw4URLixlgWZjNVjid3u+9u+02d/ksBNLYaPRZr6nZ5J5RzPNneelK9xfGwWw3GJ5939pqRqOw\n+2wJfgjb9mw7j8fA4eDA57M+rxcynM8xaGw0gmUZaGSuL+aaPIaDdX5WPPukt9cIpZgN+Jns6Trh\nj0zIoq7JjKJstddrWlp6vrb609xkcl2ne8h86to+o9HiDj55/qy11bcdTR3HGgAEDIemNitUciEa\nG41obbO4A87dHYPOPjGZrO7te57HPdHIBKhvaccglaLHYy0Xsmhudp0PrNPh97h2boN1XriGtrbw\n0NgY3Be9/rbZ0mzyOVcDnS+6JDE0SrHP5zucv8v87dff75RIo6cW0i2LzYH3vjyKbT+56lEwDFA2\naTCu+llO1AuUETIQySUCLLi8EJeOy8SGbcex+0gdzBY7Pvj6GD7+7iSmjEzDtDEZ7hlpCCHx4+qr\nr4bVasW6devAsiyef/55jBw5EgCwevVq/POf/8Sdd96JsrKykLddVFQEPp+Pn376CaNHjwbgGtY3\nfPhwn3U//vhj7N27F4sXL4ZGo0F7ezt++OEHrFixIuj9JclFcNrsXpksdrsTDmf3tVe6Zr44HJz7\nNQ6H9+vtDifsdiecXuuwPtvw2YfHdhwd2wgnrzb62TYDdNSgYnG61pVNJhUJIJPwvQJSdrvTq7ZR\nVkfNju7a29O+Pd+vZ38IeCxGDdGBz3MdP7lYgMwUOVgGEAt47tfkZ6pw4ER9t/voapBGiqoa/1lz\nnq/37EfPn3e3j4JMFXZ71MKxdVnfs68zUxRIUUkg4F84RxxdzkkhnweO49w1giRCPuRiPix2J1LV\nUtcx89hmmlbWq/OHBeN+HY/Hg9Ppeu9apRgc55olstt+DuKzBLiOn0IiQJPHA6Td7gSvI8un6/kS\naJtda8sE+54Zj304HFxYP2uebR0+WAdDczuSVb7Zc53tsHd5rz09l3T2Sef64Win53Z6+qz6k61X\nILMjK8frs+P0/ewE1TaHEw6792vlYgHa2r0zxbq2Tyriu+vMBfq8eS5jna5jPXiQEi1GK5Lkwo5r\ntzOkY+z52XM6nLAHWcAsVSN116ALpS9ZhgHHcXB2KU7l7xoayvntr686Xx/M+dI5GUF364dLpLff\nEwo+kYCOnW3Gmx+X41xHuqVGKcKiWcU+swoQQiJvkFaGe385ApVnmvHBfypxpLoZZosDn+08jc93\nnkbJUB1+XpqOomx1yDP+EEIi57rrrsN1113ns/yuu+7Cb37zG6/C4KEQi8UoKyvD0qVL8ac//Qk1\nNTVYs2aNO6BkMBigUCggEomQk5ODxYsXY9y4cRg6dCieffZZpKWleRU+DxfPwuD+yCV81HaMevD5\nlrvjeUAk5KHd5tpGuq7nYQGejys9zVYVSek6GdRyESQiHhiGgbHd5g4+db7XzBQFTte2BjXLm6dg\n3pf3KozP7wJ/BcN7M4Q72Knoe1N7WCjgoTBLjYqOAr4+s0J5bNRV4LrL7zuPtqWopMhNU6LiVKM7\nWMMwrppNgYTj/FHKhEiSCWFqt2PwIGVQv5NDOVYFWSqvQvHBtFiXJIFIwINSKoDJYkeySoLTtW2o\naTT5zGIXrEh+0iQiPjK7ma1rWI4G+45fqBMWw499n/kLmvF6+QV/14LvqRop0rQyr4Du8MFan9cN\nSU/CyfOtUCl6Hrbp2TI+j3XPRAmEXnDccwKBYK8rfcEyDEqHJsPucOKMwQhDsxl6dc8TKfRGKJMR\n+BOtWVSjLaGDT9E4SQcii82Bjf89ga07q9wXkdH5ybjlikKqM0NIjA1JT8JjN41G5ZlmfL6rGrsP\n18HJcdhz1IA9Rw2QifkYU5CMcYV6FGarel18lBASWXq9vueVevDEE0/gj3/8IxYuXAiFQoH7778f\n06dPBwBMnjwZK1aswDXXXIPi4mL84Q9/wIoVK9Dc3Iyf/exnWL16dZ/370mvlsLp5JCeLMNPlf6L\nRwOugrgWmxNCAeszbFitdD34eN7dBXPfoZQJIRHyYbM7kRZEsCqSPMsRyMQCDB+shclih67jAW2Q\nVgqJkNdtQVh/Qr3njYdb5K7T0ruW9fw6lVyE/AwVBHzWJ7jUm4BWklzoDj75BKsiZNhgTcSyChiG\ngVwiQJu55xpRnSQivjuQm9QxW1h2qgIquSike3uv/ovhOSYV8zGhSI+65nZIRfx+90yokAq6nfWy\nK6VUCJVc5FMOJStFAZZlkDtIiZPnW5GZIvfb350FyLtSyUQ9Difui77MjtdbndeV3DQlUjVSyMJc\nQkavlkLAY93HeUhaEk7VtCK7o4h7T4YP1qK20YxB2sgExWItoYNP5eXlsW5Cv3O4qhFrtlS4Z3gR\nC3m4ftoQTB2V1u8u7IQkKoZhMDRDhaEZKtQ3t+Or3dX4Zu9ZGNvtMLbb8c3ec/hm7znIxHwUD9ag\neLAGwwdrfaaOJoQkNrFYjOXLl2P58uU+P6uoqPD69+zZszF79uyItUUpFQY1Kw/DMH4zGjxnUfN6\nvg3i1oNhGIzM04Lj/GcR9FWqRorzDSaoelHMWS4ReD3ssQzjlSkQrP5yByYUBBf8CXSMPANa/u5L\n/R0nvUYKJwdIhLy4zQyW9qF+Y6DPiGcWjMhP0I1lmJDvC2IQKwiIYZi4KjkweJASJ861ICM5cMZW\nsBiGwbAcDb4/dN7nZ8MHu2b+9JxpLjtVAZnYdZ3h/PRSiloKnUoScmafNkkMh1OJ4+cu1A7r7nkw\nZ5AClWeaIeAFl/XjmeEV7axVtiOIG0hvm9M5hK6TTiWBLoTztOvvjHCTigQwWWwxy6xK6OATCZ9W\nkxUbOooadxqZp8WCGQW9ukkihESHNkmMOb8YgtlTc3HoZAN2ltdi91EDzBZXIGpHeS12dEzlm66T\ndQSiNBiaqQq6sCMhhESaLsnj5twzwBBk2IVhmIhl+2TrFdAoxZCLY5f93ZkVFqxYBKu6e5jRKSWw\nOZzQ+xn6FwrPbDl/E24opAKIBXzYHE5kJLsyfViG6Xb4pjZJjOaODBM+PzZhPm2SGCaLaxaxqtog\nZqEMIgqkVoiQrJKA4xDydO2B9+v52UxMQn5k7n30aim0SnHEA5xyiQBDM1RAdZM7ABUwg8ijk3ob\n3ElRS1FV0+ZVYysQXZIEEhE/6PvL3LQk7Ks0QC4RJHQtYYVUiFaTFbmD/M/IGk8Ks1Soa26HNsTf\nKeFCwacBzunk8M3es9iw7RiM7a76CjIxHzdOz8dFxXrKdiIkQfB5LEbm6TAyT4cFdicOnmzAvkoD\nDpxogKHZdXNyxmDEGYMRn+08DT6PRX5mEoYP1qJ0qK7PDwSEkIFnkFaG2kYzWDb0DIpOhVlqNLdZ\nkZ58ITgQauZTpDEMA6VU2POKEVCQqUaL0fv4JAqxkAdTxyzJQzKSwrJNlVyEjGQ5GABJMt8+YRgG\nI4do4XRyQQcBkjuyEsRCfkyHqndmBAYVfPIS+EOSlxae495JoxTjdF0bACCpF5mAsTRyiBbnDSbo\nNZHLlopmZl3AwHyM09NkIQTppWI+RucnJ3TgCQCKstRot9ohjeEXFMESCnhB1VKMFAo+DWDHz7bg\nnc8O4+T5C7/kJhanYu60IX5/oRNCEoOAz6JkiA4lQ3TgOA61jWYcONGAgycaUF7VCIvVAbvDiUMn\nG3HoZCP++Z9KpOlkKB2qQ+nQZAwepKDAMyGkRwI+i5KhOrAM0+uHB5VcBJXc+yHW81v8gX4pUitE\nvQvsxcFxG5qhwtHqJmgU4c2g72lYE8swYHnBHwCGYZASoaLDvZE7SImqmjboNVKo5EIcPNnQ7frR\n/IxIRHwMH6wFw/S9oHJXIgEPFpsjYoFemViA7NTg6u4kAqVcCEOLq0yKMEAts3CdGpGMZyV64Alw\nvYdECDzFAwo+DUC1jSZs2HYcOytq3csykmW4+bICmsmOkH6GYRjoNVLoNVJcMiYDdocTx8404+DJ\nBhw43uAOPp81GHHWYMTH352CLkmM8UV6XDRMj4xuZpshhBB/3/TzWTaoIRqBSER8tJpdw6AoEJ64\nJCI+RubpYt2MhJOiliJZJYnbcz9S9WiKczRobLNAS+U+AvKsDZacJIbD4YRIwIMwwmUU/E0eQEhv\nUPBpAGkxWbH5fyfxnz1n4HC6LiISEQ/XTM7FtDHpNCsWIQMAn8eiIEuNgiw1fjk1D42tFuytNGD3\n0TpUnGqE3cHB0NyOT74/hU++P4V0nQwThrkCUaEUTCSEDFzFgzWobTS7hzOFKksvh83ugFwiiNsC\n0fEu2FpZJD71FHgKFApQyURoMlqgiNEw0b4QCngRm/a+vxALLzy6MwyDQdruh0/FawAzXlGMLfIo\n+DQAtBit+HzXaXz5YzXarQ4ArtkFflGajqsm5cSsjgEhJPbUChF+XpqOn5emw2yx46dKA344VIOD\nJxrgcHI4YzDiw2+O48NvjmNoRhImFqdibGFKRGfiIIQkNomI36fhLZ1BctIHUXrmVEiFcDicMFns\nyEsPb30hErrBaUoYmszhKzBOEg7FTxKDTilxD5scSCj41I81tLTj0x+q8M3es7DaL6S/jy9KwS+n\n5sbV+HZCSOxJRHxMLE7FxOJUtJlt2FVRi+8P1eDI6SYAwNHqZhytbsY/Pj+Cohw1xhakoHSoLiG/\nYSWEkP6mt0kOGclyVNe1hZSpNipPh8ZWC5JVEvBYBhabw+/scyS6RAIe0nuoiUUIib2cQQpIxXwk\nyQfWPTT9luhnOI7D0epmbPvpDHaU17qH1wFAyRAdZk3KweAEmAaSEBJbconAnRFV39yOH8pr8N3B\n8zhTZ4TDyeHAcVfNqL9/ChRkqlAyNBnDstVIT5ZRmjchhCSQjGQ5tEoxxCEUkJaI+F7BJgo8RRcN\nD4odrVKM+pb2qOwrTSvD2XpjSK/J1itw9EwT+GEsp5KtV+DE+ZawbjMeSUQXroGR/mKVz2ORFsNZ\n52KFflP0E21mG77dfw7b9p7FuXqTeznDAOOL9Jh5UbZ7CldCCAmFNkmMmRdlY+ZF2Thd24Yd5TXY\ndbgONQ0mcBxQUdWEiipXdpRSKkBhthqF2WrkpCqQrpNBwI9sIUxCCCHedZ5C/QqAgkfxK0UlRW2T\nCWq5/1kP6fue6Bo8SAmpWABVFDJWsvQKaJPE2H+8PujXaJPEEAm1IQWTe5KilvgEnPsjqViA3LQk\nOBzO3s0ySnrUv8+gfq6hpR17jhqw52gdDlc1eWU5SUQ8XFScisvGZkKvoeF1hJDwyEyRIzNFjl9O\nzcUZgxE/Hq7D7iN1OF3bBgBoMdmwo7wWO8pds2myDINBOimyUuTQa6TQJYmhVYqhS5JApRDSRAeE\nEBIBFJDoP3IGKaBTianWYpzg81ikRzFjpTcf5XCfKwzDQCkbGMPDUmhynYhKuOCT1WrFH/7wB3z+\n+ecQi8W47bbbcOutt8a6WVFhbLfh2BlXzZVDJxtw4lyrzzp56UpMHZWG8YV6iMIY8SaEEE8MwyAj\nWY6MZDnKJg9Gi9GKiqpGHDrZiPJTDahrcqWkOzkOZ+qMOFPnmzbOAJCK+VBIhVBKBVBIhZCK+ZCJ\nBZCK+e6/y8R8yCQCr5+x9GRFSEj3RJ9//jmef/55nDt3DsOGDcOSJUswbNiwKLeYEBIqlmF8Jgfy\n/BVIMxsSQhJFwgWf/vznP+PQoUNYu3Ytqqur8dhjjyE9PR2XXXZZrJsWVi0mK87UGVFd14YzdW04\nfrYFZ+qMfmcwyEiWY3S+DmMLU5BBRQYJITGglAkxvkiP8UV6AK5ZNqtqW3G6pg2nalpRXWeEocns\nNfkBB8DYboex3Y7zDcHvi2EAmVgAueTCfzIJ3+PvAsjFAq/glVTMh1hEQSvSvwR7T1RZWYmHH34Y\nTz31FEpLS/HWW29h0aJF+PLLLyES0dCC/omudf1ZbpoSB080QCYRgGWpr/szsfDC43qqlkazkMTG\ncFzilKwzm8246KKL8MYbb2Ds2LEAgJdffhnfffcd3n777aC2UVfnmy0UCza7E41tFjS2tMPQ3I66\nJjPqmtpR12xGbYMJLSZbwNcKBSzy0pIwKk+LkvxkSg8khCQEjuPQarLB0NwOQ7MZTW1WtJqsaDXZ\n0Gqyos1sg6ndDmO760/PQFU4MADEIh6kIj4kos7glCswJRUJIO8IYMk8gloKqRAKqQB8Hg0PTBTJ\nyYpYNyEqQrkneuutt7B582Z88MEHAACj0YgxY8Zgw4YNKC4uDnqfjY1G2MP8uSS9w+ezUKtlXn3i\ncDqxs8I15FkqEmBknjaWTRyQ/PVLpNgdTvBYhib56EE0+yRSLDYH7A4nZOL+MfSyP/RJf9PZJxHf\nT8T3EEYVFRVwOBwoKSlxLxszZgxWr14dw1ZdYLM70Wa2oc184UGqxWhFc8d/LUYrmtosaGy1oLWb\n4FJXuiQxsvUKDM1IwtBMFTJT5PQgRAhJOJ01A5QyIXLTep5102Z3wtRu68iOssFodv3ZeZ01mm1o\n7fizzf2fHXaH/xsZDoDZ4oDZ4gBgCantEhEPCokrEKWQCiGXCqCQdmRaiQUdmVh8SMUCSIQ8iEV8\niIU8ulaTiAnlnkilUqGyshK7d+9GaWkpNmzYAIVCgaysrGg2mUSYZxBCKesfD6kkMPr9MnCIBDyI\nBFROhSS+hAo+1dXVQaVSgc+/0GytVguLxYLGxkao1eqw7MfucGL/sXo0G62w2hyw2J2uP60OtFsd\naLc50G61o93qgKndDlMYvqUXCXhIVomRrJIgWSVBmk6G9GQZ0nUyr3RLQggZKAR8FklyEZICzPDj\nD8dxsNqc7uwpY0fwytRuh9lih8ni+rvJYuu4fncucwWuLDaH3+26glZm1DaZQ3oPQj4LoYAHkYCF\ngM+DUMBCwGch4LHg8Tr/ZMBjGbAsAx7j+pPt+DabYQAWDDr+BzBwDx1kGFetD4a5sJxx/8mAZeDa\nJst2/MkgXSdDQZaKvinvB0K5J5o5cya++uor3HjjjeDxeGBZFq+++ioUioGRJTZQsAyD3LQkGM02\nKsNACCEk7iRUVMNsNkMo9C641/lvq9Uatv1s+t9JbPr2ZNi2JxPzoZKLoJQJkSQXQi0XQaMUQ60Q\nQa1w/V0pFdDDACGE9BHDMBAJeRAJedD0nFzlozODtTOrynNYoOvfNrR5/N1otnnNNNqV1e6E1e5E\nW2gxq4haess4ZKdS0CHRhXJP1NTUBIPBgKVLl2LUqFFYt24dHn/8cXz00UfQaDRB75NHmRZxo7Mv\nuvZJWhRn4SK+AvULiR3qk/hDfRJ/otUXCRV8EolExYuI4QAAEM1JREFUPjdUnf+WSIKrexRMLYhF\n147ComtHhd5AQgghhJAoCOWeaNWqVSgoKMC8efMAAMuWLcMVV1yBDz/8EHfccUfQ+1QqqcZkvKE+\niU/UL/GH+iT+UJ8MPAkVbtTr9WhqaoLTeWF4m8FggFgshlLZi6+4CSGEEEISUCj3RAcPHkRhYaH7\n3wzDoLCwEGfPno1aewkhhBAysCVU8KmoqAh8Ph8//fSTe9muXbswfPjwGLaKEEIIISS6QrknSklJ\nQWVlpdeyEydOICMjI+LtJIQQQggBEiz4JBaLUVZWhqVLl2L//v344osvsGbNGixcuDDWTSOEEEII\niZqe7okMBgMsFtesjnPmzMH777+PjRs3oqqqCqtWrcK5c+dwzTXXxPItEEIIIWQAYTiOC1wpNQ61\nt7fjj3/8I7Zu3QqFQoE77rgD8+fPj3WzCCGEEEKiqrt7osLCQqxYscIdYNqwYQPeeOMN1NTUoKio\nCE8++aTXUDxCCCGEkEhKuOATIYQQQgghhBBCCEkcCTXsjhBCCCGEEEIIIYQkFgo+EUIIIYQQQggh\nhJCIoeATIYQQQgghhBBCCIkYCj4RQgghhBBCCCGEkIjpd8Enq9WKxYsXY9y4cZgyZQrWrFkTcN3P\nP/8cM2fORGlpKW666SYcOnQoii1NDKEcz+3bt6OsrAylpaW47bbbcOLEiSi2NPFYrVbMmjULO3fu\nDLjOoUOHMHfuXJSUlGDOnDk4ePBgFFuYWII5np127dqF6dOnR6FViSuY4/n111/jmmuuQWlpKcrK\nyvDVV19FsYWJJ5hj+u9//xszZszAqFGjMG/ePOzbty+KLUwsoXzmq6urUVpaGtS6xFso9wGkb/yd\n09XV1bj11ltRWlqKq666Cv/73/+8XvPtt99i1qxZKCkpwS233ILTp097/fytt97C1KlTMWbMGCxZ\nsgQWiyUq76U/qKmpwX333YcJEybg4osvxooVK2C1WgFQv8RKVVUVbr/9dpSWlmLatGl444033D+j\nPom9RYsW4YknnnD/m/okNr744gsUFhaiqKjI/ef9998PIA76hOtnli1bxpWVlXHl5eXc559/zo0e\nPZrbunWrz3pHjx7lRo4cyW3cuJGrqqrili1bxk2aNIlrb2+PQavjV7DH88iRI1xxcTH317/+lTtx\n4gS3cuVKbsqUKZzJZIpBq+OfxWLhfv3rX3OFhYXcjh07/K5jMpm4SZMmcStXruSOHTvGPf3009yk\nSZM4s9kc5dbGv2COZ6eKigpu0qRJ3LRp06LUusQTzPEsLy/nhg8fzr3zzjtcVVUV984773DFxcVc\nRUVFlFubGII5pjt37uRGjBjBbdq0iTt9+jS3YsUKbvz48XQd9SOUzzzHcdztt98e9LrEW7D3AaRv\nAp3TV199Nffoo49yx44d41avXs2VlJRw586d4ziO486ePcuVlJRwa9as4SorK7kHHniAmzVrlvu1\nn376KTdu3Dju66+/5vbv389deeWV3FNPPRX195ao5s6dyy1atIirrKzkdu3axV122WXcypUrOY7j\nuFmzZlG/RJnT6eRmzJjBPfroo9ypU6e4bdu2cWPGjOE2b97McRz1Saxt3ryZKygo4B5//HH3Mrp+\nxcbLL7/M3X333Vx9fT1nMBg4g8HAtba2chwX+89Jvwo+mUwmbuTIkdzOnTvdy1566SVu/vz5Puuu\nWbOGu/baa93/bmtr4woKCrgDBw5Epa2JIJTjuWzZMu7mm2/2WjZz5kxu/fr1EW9noqmsrOTKysq4\nsrKybh+G3n//fW769Oleyy677DLuo48+ikYzE0awx5PjOG7dunVcaWkpV1ZWRsGnAII9nqtWreLu\nvPNOr2W33XYb9/zzz0ejmQkl2GO6ZcsW7pVXXnH/u7W1lSsoKOD27dsXraYmhFA+8xzHcRs3buTm\nzZtHwadeCOU+gPReoHP6/7d3/zFR138cwJ+keJjD8VPTolUwuRI57g5k2tBGLcHVhEJb0FaZ5moe\nm9Pm9WM7zKICNA2cSr+DrTENhlhrRU2zSTg46C6QrbuRxiSOU0hsx8m49/ePxufrxxPlzLvPHXs+\nNv74vN6f216f1+vz4d57f+4+d/LkSaHVamU3Rp977jlRWVkphBBiz549sl64XC6h0+mk1xcVFYmq\nqippvK2tTWg0Gt5onQK73S7UarU4f/68FDt69KhYsWKFaGlpYV8U4HA4xJYtW8Q///wjxTZv3ix2\n7NjBnihseHhYrFy5Uqxdu1ZafOL/L+Vs27ZN7N692yseDD2ZVl+76+npwfj4ONLS0qSYXq+/5tcW\noqKiYLPZYDabIYTAV199hcjISNx9992BTDmo+VLPP//8ExqNRhZbtGgROjo6/J5nqDl16hSWLVuG\nuro6CCEm3c9isUCv18tiOp2ONb3KVOsJ/PvV0LKyMjz77LMByi70TLWe+fn52Lp1q1f80qVL/kwv\nJE21pjk5Odi0aRMAwO1247PPPkNcXBySkpIClWpI8OWaHxoawq5du7Bz584b7kvefJkH0M2b7Jy2\nWCxYvHgxVCqVFNPr9ejs7JTGMzIypLGIiAg88MAD6OjogMfjgdVqRXp6ujSelpaGsbEx9PT0BOCo\nQlt8fDw++ugjxMTEyOIjIyP49ddf2RcFxMfHY/fu3bj99tsBAO3t7Whra8PSpUvZE4W99957WLNm\nDRITE6UY/38px26349577/WKB0NPZt7MAQWrwcFBREVFYebM/x9WbGws3G43hoaGEB0dLcVXr16N\nH3/8EYWFhZgxYwZuu+02VFdXIzIyUonUg5Iv9YyNjcXAwIDs9f39/YiKigpYvqHi6aefntJ+DocD\nixYtksViY2Nhs9n8kVbImmo9AaCqqgoA0NDQ4K90Qt5U63nffffJtn///Xf88ssvKCws9EdaIc2X\ncxQAWlpa8MILLwAAKioqMHv2bH+kFbJ8qee7776L/Px82YSYps6XeQDdvMnO6cHBQcybN08Wu3K+\n5XA4vMbj4uIwMDCAixcvwu12y8ZnzJiBqKgo/PXXX143DEkuMjISDz74oLQthEBtbS2WLVvGvgSB\n7Oxs9Pf346GHHsKjjz6K0tJS9kQhLS0taG9vR1NTE0wmkxTndaKc3t5enDhxAvv374fH40FOTg6K\ni4uDoifT6pNPLpcLs2bNksUmticeEDhheHgYTqcTJpMJhw4dQl5eHoxGIy5cuBCwfIOdL/VcvXo1\nvv32Wxw7dgzj4+NoaGjAb7/9hrGxsYDlO92Mjo5es/5X155IaRcuXIDBYIBer8fDDz+sdDohLzk5\nGfX19SguLsb27dv5KZObdPLkSXR0dODll19WOpWQ5cs8gG69yeo/UfvrzRNGR0el7cleT1NXVlaG\n06dPY8uWLexLEKisrMSBAwfQ09OD0tJS9kQhly9fRklJCUwmk1f92BNlnDt3DqOjo1CpVNi7dy+2\nb9+Oo0ePoqysLCh6Mq0++aRSqbwOfmL76jvHFRUVSE5Olu42vfnmm8jNzUV9fT02bNgQmISDnC/1\nzMrKwubNm2EwGODxeJCZmYm8vDyMjIwELN/pZrL6R0REKJQRkTen04nnn38eYWFh2Lt3r9LpTAsx\nMTGIiYmBWq1GZ2cnvvzyS6SmpiqdVkhxu90wmUwoKSnxmijR1PkyD6BbT6VS4e+//5bFrpwHTNaf\nuXPnTrpIePnyZfbOR+Xl5aipqcGePXuQlJTEvgSBxYsXAwCMRiO2bduGgoICXLx4UbYPe+J/lZWV\nSElJwfLly73GeJ0oY+HChWhtbcXcuXMBAGq1Gh6PB6+88gqeeOIJxa+TafXJp/nz52N4eBgej0eK\nOZ1ORERESA2Y0NXVBbVaLW2HhYVBrVbj3LlzAcs32PlSTwDYtGkTzGYzTpw4gU8++QSXLl3CnXfe\nGciUp5X58+djcHBQFnM6nYiPj1coIyK5gYEBFBUVYXx8HDU1NfwKzn9ktVrR3d0tiyUmJmJoaEih\njEKXxWJBX18fDAYDtFottFotAGDjxo0oKSlRNrkQ4us8gG6tG80DrjceHR0NlUoFp9MpjY2Pj2N4\neJjzCB/s3LkTn3/+OcrLy/HII48AYF+Ucv78eTQ3N8tiSUlJGBsbQ3x8PHuigG+++QY//PCD9D7b\n1NSEpqYm6HQ63HHHHeyJQq5+f05MTITb7UZcXJziPZlWi0/3338/Zs6cKT00CwDa2tqQkpLite+8\nefO8np3T29uLu+66y+95hgpf6vn111+jtLQU4eHhiImJwejoKFpbW5GZmRnIlKcVjUbj9XBxs9ks\ne/ArkVJcLhc2bNiA8PBw1NbWIi4uTumUQt7hw4exa9cuWayrq4vPK7oJGo0G3333HRobG3HkyBEc\nOXIEAPD222+juLhY4exChy/zALr1NBoNuru7ZXea29vbpXmARqOB2WyWxlwuF7q7u6HVahEWFoYl\nS5agvb1dGu/o6EB4eLjs5itNrqqqCnV1dXj//feRm5srxdkXZUzcUHA4HFLMarUiNjYWer0eXV1d\n7EmA1dbWoqmpSXqfzc7ORnZ2NhobG5GamsrrRAE///wzMjMz4Xa7pVh3dzeio6ORnp6u+HUyrRaf\nIiIisGbNGphMJlitVjQ3N+PTTz+VftnK6XRKjVi7di0OHTqExsZGnD17FhUVFejv70deXp6ShxBU\nfKnnPffcg7q6Onz//ff4448/sHXrVixcuBArV65U8hBCzpU1XbVqFUZGRlBaWgq73Y633noLLpdL\nNgGi67uynvTfXVnPAwcOoK+vD++88w48Hg+cTiecTid/7c5HV9b0qaeeQmtrK2pqanDmzBl88MEH\nsFqt/HVGH0zUc9asWUhISJD9Af/eeLr616tocjeaB5B/LV26FAsWLIDRaITNZkN1dTWsVisKCgoA\nAE8++STMZjM+/PBD2Gw2vPrqq0hISJB+raiwsBAff/wxmpubYbFYsGPHDqxbt072S0d0bXa7Hfv3\n78eLL74IrVYrvcc5nU72RSFLlixBSkoKXnvtNdjtdhw/fhwVFRV46aWXkJGRwZ4oYMGCBbL32Tlz\n5mDOnDlISEjgdaIQrVaL2bNn4/XXX0dvby+OHz+O8vJybNy4MTiuEzHNuFwuYTQahVarFStWrBBf\nfPGFNJacnCwaGhqk7cOHD4vc3Fyh0+lEUVGROH36tBIpBzVf6llfXy+ys7OFXq8XBoNBDA4OKpFy\nSFGr1eLUqVPS9tU1tVgsIj8/X2g0GrFu3Tqeozdwo3pOmDhX6fquV8+cnByhVqu9/oxGo1LphoQb\nnaPHjh0Tjz/+uNBoNKKgoEB0dnYqkWbImOo1f619aWquNw+gW+/q8/Ts2bPimWeeEampqeKxxx4T\nLS0tsv1/+uknsWrVKpGWlibWr18v+vr6ZOPV1dVi+fLlIiMjQ7zxxhvC7XYH5DhC3cGDB73e35KT\nk4VarRZCCHHmzBn2RQEOh0MYDAaRnp4usrKyxMGDB6UxXivKMxqNsnkge6IMm80m1q9fL3Q6ncjK\nyhL79u2TxpTuSZgQQvhj1Y2IiIiIiIiIiGhafe2OiIiIiIiIiIiCCxefiIiIiIiIiIjIb7j4RERE\nREREREREfsPFJyIiIiIiIiIi8hsuPhERERERERERkd9w8YmIiIiIiIiIiPyGi09EREREREREROQ3\nXHwiIiIiIiIiIiK/4eITERERERERERH5DRefiIiIiIiIiIjIb7j4REREREREREREfsPFJyIiIiIi\nIiIi8pv/AaEckTQYCWIFAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This function will randomly draw 500 samples of parameters from the trace. Then, for each sample, it will draw 100 random numbers from a normal distribution specified by the values of `mu` and `std` in that sample." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 500/500 [00:04<00:00, 111.40it/s]\n" ] } ], "source": [ "ppc = pm.sample_ppc(trace, samples=500, model=model, size=100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, `ppc` contains 500 generated data sets (containing 100 samples each), each using a different parameter setting from the posterior:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(500, 100)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.asarray(ppc['n']).shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One common way to visualize is to look if the model can reproduce the patterns observed in the real data. For example, how close are the inferred means to the actual sample mean:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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tNpuOHz+uWbNm+b4k9sMPP+iNN95Qnz59VFRU5Le+2+1WdHR0vfuJj48JSr0I\nDcYncp1ubDyeE4qJcSg21lnreoFyn3SoSZNGatq0UUjal2rehujoKL/bsbFGwH3ExDhks0cFdT9V\nru9M7CfUD+9rkYuxMb+whtvk5GQ5nU6/sx9ceOGFOnjwoFq0aKGvv/7ab/2CggI1b9683v2UlLhU\nVuZtcL0ILpvNqvj4GMYnAtV1bIqKjsvlcsvhPBmSOlwut4qKjstujw1J+1LN21Baaql0+5ROnAh8\nG10ut2x2NaiNClarVdHRUSotPSWv1+trP9T7CXXD+1rkYmwiV8XYBEtYw23nzp118uRJfffdd/rF\nL34hSdq7d69atWqlzp07a8GCBXK73b7pCVu3bvX78lldlZV55fHwQo5UjE/kOt3YeDyGvF5DZd7A\nj2rWxus15PEYIX191LQN3kr3G7qNhlH+/ODsJ+9/avL62jsT+wn1w/ta5GJszC+sE08uvPBC9e3b\nV9nZ2fryyy/10UcfadGiRfrNb36j7t27KyUlRdnZ2dqzZ48WLlyonTt3atiwYeEsGQAAABEs7Bdx\nePbZZzVt2jTdfvvtiomJ0YgRI3T77bdLkubPn69JkyZp6NChatOmjXJycriAA1BHDbk0rt1ukcdz\nQkVFx+Xx1Hy0sbDwsIwQHbUFACAQYQ+3cXFxmjFjhmbMmFHlsdatWys3NzcMVQFnv4ZcGtdqtSgm\nxiGXy+338fzPHfjxe8UlJClBSQ0pFQCAoAl7uAUQOoFeGtdmtSg21imH82St80SPlhxpSHkAAAQd\nJ3sDAACAaRBuAQAAYBqEWwAAAJgG4RYAAACmQbgFAACAaRBuAQAAYBqEWwAAAJgG4RYAAACmQbgF\nAACAaRBuAQAAYBqEWwAAAJgG4RYAAACmQbgFAACAaRBuAQAAYBqEWwAAAJgG4RYAAACmQbgFAACA\naRBuAQAAYBqEWwAAAJgG4RYAAACmQbgFAACAaRBuAQAAYBqEWwAAAJgG4RYAAACmQbgFAACAaRBu\nAQAAYBqEWwAAAJgG4RYAAACmQbgFAACAaRBuAQAAYBqEWwAAAJgG4RYAAACmQbgFAACAaRBuAQAA\nYBqEWwAAAJgG4RYAAACmQbgFAACAaRBuAQAAYBqEWwAAAJgG4RYAAACmERHhdt26dUpNTVX79u19\nPx944AFJUl5enkaNGqX09HQNGjRIGzZsCHO1AAAAiFT2cBcgSXv27FG/fv00bdo0GYYhSXI6nZKk\nsWPHqn0BX57qAAAgAElEQVT79lqxYoXWrVunrKwsrV27Vi1btgxnyQAAAIhAERFu9+7dq0suuUSJ\niYl+yzdu3Ki8vDwtW7ZMTqdTmZmZ2rhxo5YvX66srKwwVQsAAIBIFRHTEvbu3asLL7ywyvIdO3Yo\nLS3NdxRXkrp166Zt27adyfIAAABwloiIcPvNN9/oo48+0sCBA3XNNdfoueee06lTp5Sfn6/k5GS/\ndZOSknTw4MEwVQoAAIBIFvZpCT/++KNKS0vldDr1/PPPKy8vT08++aRKS0vlcrnkcDj81nc4HHK7\n3fXqw2aLiAyPn6kYF8YnNOx2i6xWi2xWS72fa7VaK/301riexVLefiB91K0Oi+x2i+z20L1GatpP\n1kr3A92PFYK5n6obmzOxn1A3vK9FLsYmcgV7TMIebs877zxt3rxZ8fHxkqTU1FR5vV5NmDBBN910\nk0pKSvzWd7vdio6Orlcf8fExQasXwcf4hIbHc0IxMQ7FxjpPv3INoqOjan08JsYhmz2qQX3Uxn3S\noSZNGqlp00YhaV+qeT9V3vbo6CjFxhoB9xGK/VS5vjOxn1A/vK9FLsbG/MIebiX5gm2Ftm3b6uTJ\nk2rWrJn27t3r91hBQYGaN29er/ZLSlwqK6v56BPCw2azKj4+hvEJkaKi43K53HI4T9b7uVarVdHR\nUSotPSWvt+axcbncstmlEyfq30dduFxuFRUdl90eG5L2pZr3U2mppdLtUw3axmDup+rG5kzsJ9QN\n72uRi7GJXBVjEyxhD7cff/yxHnroIa1fv973xbEvvvhCTZs2VUZGhpYsWSK32+2bnrB161ZlZGTU\nq4+yMq88Hl7IkYrxCQ2Px5DXa6jMG8gRx/Lx8Hq9tT7fMMrbD6yPOlThNeTxGCF9fdS0n7yV7ge+\nH8sFdz9VHZszsZ9QP7yvRS7GxvzCPvEkPT1dMTExevTRR/XNN9/on//8p2bOnKm7775b3bt3V0pK\nirKzs7Vnzx4tXLhQO3fu1LBhw8JdNgAAACJQ2I/cNmrUSC+99JKeeuopDRs2TI0aNdKvf/1rjR49\nWpI0f/58TZo0SUOHDlWbNm2Uk5PDBRyAc4TX61Vh4eGQ9lFYeFhGiI48AwDOvLCHW6l8ju1LL71U\n7WOtW7dWbm7uGa4IQCQ4fqxY67cdVHJy/c6QUh8HfvxecQlJSlBSyPoAAJw5ERFuAaAmsY3iFd8k\n8fQrBuhoyZGQtQ0AOPPCPucWAAAACBbCLQAAAEyDcAsAAADTYM4tAJzlzsRZJSQpMTHRd/lfAIhU\nhFsAOMudibNKHDtWrAE9U9WsWbOQ9QEAwUC4BQATCPVZJQDgbMHnSwAAADANwi0AAABMg3ALAAAA\n0yDcAgAAwDQItwAAADANwi0AAABMg3ALAAAA0yDcAgAAwDQCCrc333yz/vznP+vo0aPBrgcAAAAI\nWEDhtmfPnnrxxRfVp08fjR8/Xh9//LEMwwh2bQAAAEC9BBRuH3roIf3jH//QvHnzZLPZdN999+mq\nq67SH//4R33zzTfBrhEAAACoE3ugT7RYLOrdu7d69+4tl8ul3NxczZs3TwsXLlTXrl11xx13aMCA\nAcGsFQAAAKhVwOFWkg4dOqR3331X7777rr766it17dpVv/rVr3TgwAH9/ve/15YtW/Too48Gq1YA\nAACgVgGF23feeUfvvPOONm/erMTERP3yl7/UCy+8oAsuuMC3TkpKip588knCLQAAAM6YgMLto48+\nqquvvlo5OTm68sorZbVWnbp70UUXafjw4Q0uEAAAAKirgMLt+vXr1bRpUxUVFfmC7Y4dO5SWliab\nzSZJ6tq1q7p27Rq8SgEAAIDTCOhsCceOHdO1116rRYsW+ZZlZmZqyJAh+umnn4JWHAAAAFAfAYXb\np556Sr/4xS80atQo37I1a9YoJSVF06dPD1pxAAAAQH0EFG4//fRTZWdnq3nz5r5liYmJ+p//+R9t\n2rQpaMUBAAAA9RFQuLXb7SopKamy3OVycaUyAAAAhE1A4fbKK6/UtGnT9P333/uW7d+/X9OnT9cV\nV1wRtOIAAACA+gjobAmPPPKIRo0apYEDByo+Pl6SVFJSorS0NE2cODGoBQIAAAB1FVC4TUpK0sqV\nK/Wvf/1LX3/9tex2uy6++GL16tVLFosl2DUCAAAAdRLw5XdtNpuuuOIKpiEAAAAgYgQUbvPz8zV7\n9mx99tlnOnXqVJUvkf39738PSnEAAABAfQQUbidPnqxdu3bphhtuUOPGjYNdEwAAABCQgMLtpk2b\ntHjxYmVkZAS7HgAAACBgAZ0KLDY2VklJScGuBQAAAGiQgMLtkCFDtHjxYpWVlQW7HgAAACBgAU1L\nKCoq0urVq/Xhhx+qdevWcjgcfo+/+uqrQSkOAAAAqI+ATwU2aNCgYNYBAAAANFhA4Xb69OnBrgMA\nAABosIDm3ErSoUOHNHfuXD300EM6fPiw/vrXv2rfvn3BrA0AAACol4DC7Xfffacbb7xRK1eu1Pvv\nv68TJ05ozZo1Gjp0qLZv3x7sGgEAAIA6CSjczpgxQ/3799e6desUFRUlSZo1a5b69eunZ599NuBi\nMjMzNXHiRN/9vLw8jRo1Sunp6Ro0aJA2bNgQcNsAAAAwv4DC7WeffaZRo0bJYrH4ltntdo0dO1Zf\nfPFFQIW89957Wr9+vd+ycePGKTk5WStWrNDgwYOVlZWlAwcOBNQ+AAAAzC+gcOv1euX1eqssP378\nuGw2W73bKy4u1syZM9WpUyffso0bN2r//v16/PHHddFFFykzM1NdunTR8uXLAykZAAAA54CAwm2f\nPn20YMECv4BbVFSkmTNnqmfPnvVu7+mnn9aQIUPUtm1b37IdO3YoLS1NTqfTt6xbt27atm1bICUD\nAADgHBBQuM3OztauXbvUp08fnTx5Uvfee6+uvvpq5eXl6ZFHHqlXWxs3btTWrVs1btw4v+X5+flK\nTk72W5aUlKSDBw8GUjIAAADOAQGd57ZFixb6y1/+otWrV2v37t3yer267bbbNGTIEMXFxdW5Hbfb\nralTp+qxxx6rcpUzl8tVZZnD4ZDb7a53vTZbwGc8QwhVjAvjExp2u0VWq0U2q+X0K/+M1Wqt9LPq\nFKQKFkt5+4H0URehbr+2PqyV7ge6H0/XRyCqG5szsZ+sVovsdovsdn5fa8P7WuRibCJXsMck4CuU\nxcTE6Oabb25Q53PmzFHHjh11+eWXV3nM6XSquLjYb5nb7VZ0dHS9+4mPjwm4RoQe4xMaHs8JxcQ4\nFBvrPP3KNYiOjqr18ZgYh2z2qAb1Ec72a+uj8rZHR0cpNtYIeh8NUbm+M7Gf3CcdatKkkZo2bRSy\nPsyE97XIxdiYX0DhduTIkbU+/uqrr9apnTVr1ujw4cNKT0+XJJ06dUqS9P777+u3v/2t9uzZ47d+\nQUGBmjdvXu96S0pcKiur+egTwsNmsyo+PobxCZGiouNyudxyOE/W+7lWq1XR0VEqLT1V7ZdHK7hc\nbtns0okT9e+jLkLdfm19lJZaKt0+1aAagrkd1Y3NmdpPRUXHZbfHhqwPM+B9LXIxNpGrYmyCJaBw\n26pVK7/7Ho9H3333nb766ivdcccddW7ntddek8fj8d2fOXOmJGnChAn64YcftHDhQrndbt/0hK1b\ntyojI6Pe9ZaVeeXx8EKOVIxPaHg8hrxeQ2XeQI44lo+H1+ut9fmGUd5+YH2cXqjbr60Pb6X7ge/H\n2vsITNWxORP7yes15PEY/K7WEe9rkYuxMb+Awu306dOrXZ6Tk1Ov89CmpKT43W/UqPzjrtatW6tV\nq1ZKSUlRdna2xo4dqw8++EA7d+7UjBkzAikZAAAA54CgzuAdMmSI1q5dG5S2rFar5s2bp/z8fA0d\nOlSrVq1STk6OWrZsGZT2AQAAYD4Bf6GsOp9//nlAF3Go8PMjwq1bt1Zubm5DywIAAMA5ImhfKDt2\n7Jj+3//7f/rNb37T4KIAAACAQAQUbs877zxZLP7nU4yKitLw4cM1ePDgoBQGAAAA1FdA4ZYvdQEA\nACASBRRut2zZUud1u3fvHkgXAAAAQL0FFG5HjBjhm5ZgGP93XsWfL7NYLNq9e3dDawQAAADqJKBw\n++KLL2ratGmaMGGCevToIYfDoZ07d+rxxx/Xr371K11//fXBrhMAAAA4rYDOczt9+nRNmTJFAwcO\nVNOmTdWoUSP17NlTjz/+uN588021atXK9w8AAAA4UwIKt4cOHao2uMbFxenIkSMNLgoAAAAIREDh\ntkuXLpo1a5aOHTvmW1ZUVKSZM2eqV69eQSsOAAAAqI+A5tz+/ve/18iRI3XllVfqggsukGEY+vbb\nb9W8eXO9+uqrwa4RAAAAqJOAwm3btm21Zs0arV69Wnv37pUk3X777brhhhsUExMT1AIBAACAugoo\n3EpSQkKCbr75ZuXl5al169aSyq9SBgAAAIRLQHNuDcPQs88+q+7du2vQoEE6cOCAHnnkET366KM6\ndepUsGsEAAAA6iSgcJubm6t33nlHjz32mBwOhySpf//+WrdunebOnRvUAgEAAIC6CijcLl26VFOm\nTNFNN93kuyrZ9ddfr2nTpmnVqlVBLRAAAACoq4DCbV5entq3b19leWpqqvLz8xtcFAAAABCIgMJt\nq1attHPnzirL169f7/tyGQAAAHCmBXS2hDFjxugPf/iD8vPzZRiGNm7cqKVLlyo3N1fZ2dnBrhEA\nAACok4DC7dChQ+XxeDR//nyVlpZqypQpSkxM1IMPPqjbbrst2DUCAAAAdRJQuF29erWuvfZa3Xrr\nrSosLJRhGEpKSgp2bQAAAEC9BDTn9vHHH/d9cSwxMZFgCwAAgIgQULi94IIL9NVXXwW7FgAAAKBB\nApqWkJqaqocffliLFy/WBRdcIKfT6ff49OnTg1IcAAAAUB8BhdtvvvlG3bp1kyTOawsAAICIUedw\n+8wzzygrK0uxsbHKzc0NZU0AAABAQOo85/bll1+Wy+XyW5aZmalDhw4FvSgAAAAgEHUOt4ZhVFm2\nZcsWnTx5MqgFAQAAAIEK6GwJAAAAQCQi3AIAAMA06hVuLRZLqOoAAAAAGqxepwKbNm2a3zltT506\npZkzZ6pRo0Z+63GeWwAAAIRDncNt9+7dq5zTNj09XUeOHNGRI0eCXhgAAABQX3UOt5zbFgAAAJGO\nL5QBAADANAi3AAAAMA3CLQAAAEyDcAsAAADTINwCAADANAi3AAAAMA3CLQAAAEyDcAsAAADTiIhw\n+/3332vMmDFKT09Xv3799NJLL/key8vL06hRo5Senq5BgwZpw4YNYawUAAAAkSzs4dYwDGVmZqpZ\ns2Z65513NHXqVM2fP1/vvfeeJGns2LFKTk7WihUrNHjwYGVlZenAgQNhrhoAAACRqM6X3w2VgoIC\ndejQQY899phiY2PVpk0b9erVS1u3blVSUpLy8vK0bNkyOZ1OZWZmauPGjVq+fLmysrLCXToAAAAi\nTNiP3DZv3lyzZs1SbGysJGnr1q369NNP1aNHD23fvl1paWlyOp2+9bt166Zt27aFq1wAAABEsLCH\n28r69eun4cOHq0uXLhowYIDy8/OVnJzst05SUpIOHjwYpgoBAAAQycI+LaGyOXPmqKCgQFOnTtVT\nTz0ll8slh8Pht47D4ZDb7a5XuzZbRGV4/EfFuDA+oWG3W2S1WmSzWur9XKvVWumnt8b1LJby9gPp\noy5C3X5tfVgr3Q90P56uj0BUNzZnYj9ZrRbZ7RbZ7fy+1ob3tcjF2ESuYI9JRIXbtLQ0SVJ2drYe\nfvhhDRs2TCUlJX7ruN1uRUdH16vd+PiYoNWI4GN8QsPjOaGYGIdiY52nX7kG0dFRtT4eE+OQzR7V\noD7C2X5tfVTe9ujoKMXGGkHvoyEq13cm9pP7pENNmjRS06aNQtaHmfC+FrkYG/MLe7g9fPiwPv/8\nc/Xv39+37OKLL9apU6fUvHlz7d2712/9goICNW/evF59lJS4VFZW89EnhIfNZlV8fAzjEyJFRcfl\ncrnlcJ6s93OtVquio6NUWnpKXm/NY+NyuWWzSydO1L+Pugh1+7X1UVpqqXT7VINqCOZ2VDc2Z2o/\nFRUdl90eG7I+zID3tcjF2ESuirEJlrCH27y8PN1333365z//6Ztfu3PnTiUlJalbt2566aWX5Ha7\nfdMTtm7dqoyMjHr1UVbmlcfDCzlSMT6h4fEY8noNlXkDOeJYPh5er7fW5xtGefuB9XF6oW6/tj68\nle4Hvh9r7yMwVcfmTOwnr9eQx2Pwu1pHvK9FLsbG/MI+8eTSSy9Vx44dNWnSJO3du1f//Oc/9eyz\nz+ree+9V9+7dlZKSouzsbO3Zs0cLFy7Uzp07NWzYsHCXDQAAgAgU9nBrtVo1b948xcbG6te//rUm\nT56skSNHavjw4bJarZo/f77y8/M1dOhQrVq1Sjk5OWrZsmW4ywYAAEAECvu0BKn8XLcvvPBCtY+1\nbt1aubm5Z7giAAAAnI3CfuQWAAAACBbCLQAAAEyDcAsAAADTINwCAADANAi3AAAAMA3CLQAAAEyD\ncAsAAADTINwCAADANAi3AAAAMI2IuEIZACCyeb1eFRYeDnk/iYmJslo57gIgcIRbAMBpHT9WrPXb\nDio52R2yPo4dK9aAnqlq1qxZyPoAYH6EWwBAncQ2ild8k8RwlwEAteKzHwAAAJgG4RYAAACmQbgF\nAACAaRBuAQAAYBqEWwAAAJgG4RYAAACmQbgFAACAaRBuAQAAYBqEWwAAAJgG4RYAAACmQbgFAACA\naRBuAQAAYBqEWwAAAJgG4RYAAACmQbgFAACAaRBuAQAAYBqEWwAAAJgG4RYAAACmQbgFAACAadjD\nXQBwrvJ6vSosLAxZ+4WFh2V4jZC1DwBAJCLcAmFSWFiov236UnFxCSFp/8CP3ysuIUkJSgpJ+wAA\nRCLCLRBGcXEJim+SGJK2j5YcCUm7AABEMubcAgAAwDQItwAAADANwi0AAABMg3ALAAAA0yDcAgAA\nwDQItwAAADANwi0AAABMg/PcAtUI9dXDJK4gBgBAKIQ93B48eFBPPvmkNm/erOjoaF133XUaP368\nHA6H8vLyNHnyZG3btk2tWrXSxIkT1bt373CXjHNAqK8eJnEFMQAAQiHs4fb+++9XkyZN9MYbb6io\nqEiTJk2SzWbThAkTNHbsWLVv314rVqzQunXrlJWVpbVr16ply5bhLhvngFBePUziCmIAAIRCWMPt\nvn37tGPHDm3YsEGJieUh4v7779czzzyjK664Qnl5eVq2bJmcTqcyMzO1ceNGLV++XFlZWeEsGwAA\nABEqrF8oa968uRYvXuwLthWOHj2q7du3Ky0tTU6n07e8W7du2rZt25kuEwAAAGeJsIbbxo0b+82h\nNQxDr732mnr16qX8/HwlJyf7rZ+UlKSDBw+e6TIBAABwlgj7nNvKnnnmGe3evVvLly/Xyy+/LIfD\n4fe4w+GQ2+2ud7s2G2c8i0QV4xKJ42O3W2S1WmSzWkLWh8VS3n6o+mhI+1artdJPb0j6qItQt19b\nH9ZK9xv6WgjmdlQ3NuHcT8FlqKSkUHZ76PpITEzy7cNQiOT3tXMdYxO5gj0mERNuZ86cqdzcXM2e\nPVsXX3yxnE6niouL/dZxu92Kjo6ud9vx8THBKhMhEInj4/GcUEyMQ7GxztOvHKCYGIds9qiQ9RGM\n9qOjo0LeRzjbr62PytseHR2l2NjAT9sWiu2oXF8491MwFRxyadMXhWrRIjTtHztarCH9GikpqXlo\nOqgkEt/XUI6xMb+ICLdPPPGEli5dqpkzZ6p///6SpBYtWmjPnj1+6xUUFKh58/q/KZWUuFRWVvPR\nJ4SHzWZVfHxMRI5PUdFxuVxuOZwnQ9aHy+WWzS6dOBGaPhrSvtVqVXR0lEpLT8nrrXlsInkbGtpH\naaml0u1TDaohmNtR3diEcz8Fv48YOZxxIWnf5nKrqOi47PbYkLQvRfb72rmOsYlcFWMTLGEPt3Pn\nztXSpUv1xz/+Uddcc41veefOnbVo0SK53W7f9IStW7cqIyOj3n2UlXnl8fBCjlSROD4ejyGv11BZ\nCC+yYBjl7Yeqj4a1Xz4eXq+31udH9jY0rA9vpfsNfS0Edzuqjk0499PZ1IfXa8jjMc7I+00kvq+h\nHGNjfmGdeLJ3717Nnz9fmZmZSk9PV0FBge9fjx49lJKSouzsbO3Zs0cLFy7Uzp07NWzYsHCWDAAA\ngAgW1iO3f//73+X1ejV//nzNnz9fUvlf7haLRbt371ZOTo4effRRDR06VG3atFFOTg4XcAAAAECN\nwhpuMzMzlZmZWePjbdq0UW5u7hmsCAAAAGczzocBAAAA0yDcAgAAwDQItwAAADANwi0AAABMg3AL\nAAAA0yDcAgAAwDQItwAAADANwi0AAABMg3ALAAAA0yDcAgAAwDQItwAAADANwi0AAABMg3ALAAAA\n0yDcAgAAwDQItwAAADANwi0AAABMg3ALAAAA0yDcAgAAwDQItwAAADANe7gLAOrL6/WqsLAwpH0U\nFh6W4TVC2gcAAAg+wi3OOoWFhfrbpi8VF5cQsj4O/Pi94hKSlKCkkPUBAACCj3CLs1JcXILimySG\nrP2jJUdC1jYAAAgd5twCAADANAi3AAAAMA3CLQAAAEyDcAsAAADTINwCAADANAi3AAAAMA3CLQAA\nAEyDcAsAAADTINwCAADANAi3AAAAMA3CLQAAAEyDcAsAAADTINwCAADANAi3AAAAMA3CLQAAAEyD\ncAsAAADTINwCAADANAi3AAAAMA3CLQAAAEwjosKt2+3WjTfeqC1btviW5eXladSoUUpPT9egQYO0\nYcOGMFYIAACASBYx4dbtdmv8+PHas2eP3/Jx48YpOTlZK1as0ODBg5WVlaUDBw6EqUoAAABEsogI\nt3v37tUtt9yivLw8v+UbN27U/v379fjjj+uiiy5SZmamunTpouXLl4epUgAAAESyiAi3n3zyiXr1\n6qWlS5fKMAzf8h07digtLU1Op9O3rFu3btq2bVs4ygQAAECEs4e7AEm67bbbql2en5+v5ORkv2VJ\nSUk6ePDgmSgLAAAAZ5mICLc1cblccjgcfsscDofcbne92rHZIuIA9TnD6/WqsPDwadez2azyeE7o\n6FGXysq8dW6/pKRQFotks1oaUmatLBaLbFbLWd1HQ9q3Wq2VftY8NpG8DQ3tw1rpvrWBNQRzO6ob\nGzO8Xs9MH4ZKSgplt4duG2w2qxISYvh/JwJVjAljE3mCPSYRHW6dTqeKi4v9lrndbkVHR9ernfj4\nmGCWhdPIz8/XPz/bp7jGCSFp/6cfvlN8kyTFxjpPv3KAYmIcstmjzuo+gtF+dHRUyPsIZ/u19VF5\n26OjoxQba/z8qQ3uoyEq12eG1+uZ6KPgkEubvihUixYhaV6SdOxosYY0jlHz5s1D1wkahExgfhEd\nblu0aFHl7AkFBQX1ftMoKanfkUE0TFHRcdnsMXI442pdz2q1Kjo6SqWlp+T11n18rLZouVyndOLE\nyYaWWiOXyy2bXWd1Hw1pv65jE8nb0NA+SkstlW437PUWzO2obmzM8Ho9E32Ut3/696aGiDrpkcT/\nO5HIZrMqPj6GsYlAFWMTLBEdbjt37qxFixbJ7Xb7pids3bpVGRkZ9WqnrMwrj4cX8pni8Rjyeg2V\neU93pKt8TLxebx3W/T+GUd52fZ5TX2boo2Ht121sInsbGtaHt9L9ur2e699HYKqOjRler2eijzOx\nDRV/cPD/TuRibMwvoiee9OjRQykpKcrOztaePXu0cOFC7dy5U8OGDQt3aQAAAIhAERduLZbKX+Kw\nat68ecrPz9fQoUO1atUq5eTkqGXLlmGsEAAAAJEq4qYl7N692+9+69atlZubG6ZqAAAAcDaJuCO3\nAAAAQKAItwAAADANwi0AAABMg3ALAAAA0yDcAgAAwDQItwAAADANwi0AAABMg3ALAAAA0yDcAgAA\nwDQi7gplAACcrbxerwoKCmS3x8jjMULWT2JioqxWjk8B1SHcAgAQJMeOFutvmwoVH99MXm9owu2x\nY8Ua0DNVzZo1C0n7wNmOcAsAQBDFxcUroUmiykIUbgHUjs80AAAAYBqEWwAAAJgG4RYAAACmQbgF\nAACAaRBuAQAAYBqEWwAAAJgG4RYAAACmQbgFAACAaRBuAQAAYBqEWwAAAJgG4RYAAACmQbgFAACA\naRBuAQAAYBr2cBcAAADqzuv1qrDwcEj7SExMlNXK8S+cnQi3AACcRY4fK9b6bQeVnOwOSfvHjhVr\nQM9UNWvWLCTtA6FGuAUA4CwT2yhe8U0Sw10GEJH4zAEAAACmQbgFAACAaTAt4RxT/kWEwpD2UVh4\nWIbXCGkfAAAA1SHcRpjV7/9DFntMyNovyP9JcjRR08TQfVHgwI/fKy4hSQlKClkfAAAA1SHcRhiv\n1an4pNYha//IUZecMXEh/SLC0ZIjIWsbAACgNsy5BQAAgGkQbgEAAGAahFsAAACYBuEWAAAApkG4\nBQAAgGkQbgEAAGAahFsAAACYBuEWAAAAphHxF3Fwu92aOnWq/vd//1fR0dEaPXq0Ro0aFe6yAABA\ngM7EpeC9Xq8kyWotP45nt1vk8ZxQUdFxeTzBuUR8YmKir31EjogPt08//bS++OIL5ebmKi8vT488\n8ohatWqlAQMGhLs0AAAQgMLCQv1t05eKi0sIWR8HfvxeVnuUkpNTJElWq0UxMQ65XG55vQ0Pt8eO\nFWtAz1Q1axa6y9kjMBEdbl0ul5YvX66XXnpJqampSk1N1V133aXXXnuNcAsAwFksLi4h5JeCt9gc\nvj5sVotiY51yOE+qLAjhFpEroo+l///27jwmqut9A/gzMCo1P1xZgktrcAEinWERGxZR1BKdukC1\nVqHSKGglqI0psWgLKKi1gnvSdEHRSmOUtgpVI6BGk9pAoSBYWSrUsIgCgxJ2aPH8/micb0e0zm2Z\nARDo6wkAABAqSURBVGeeT2LKnHvuvc/M63XeGY+3paWl6OnpgYuLi2bM3d0dRUVF/ZiKiIiIiAaq\nAd3cNjQ0YMSIEZDL//cF8+jRo9HV1YWHDx/2YzIiIiIiGogG/LKEwYMHa409ftzd3a3zcczNB3QP\nr8XMzAzmZjI9Hl+G9vZWtDbr78NBR3sLzM0HP/ccZmZm6O6So6vrT83C/748/n9hDOf4L8fXtTYD\n+Tn813O0t/3f335uQWtza5+f4994Wm2M4ferIc5hmOfQCsh6IJdbSPpzTdo59P06NaO5eQjkcv29\nFzU3P0BHezPM9Ph+9+Tr9G/fc559/GbI5WMgl784PcZA1dd9mkwIMWAXnly8eBE7duzAjz/+qBmr\nqKjAggULkJOTg2HDhvVjOiIiIiIaaAb0xw1bW1s0NTVpfcJSq9WwsLBgY0tEREREvQzo5tbJyQly\nuRw3btzQjOXl5cHZ2bkfUxERERHRQDWgm1sLCwssXrwYsbGxuHnzJi5duoTk5GS8++67/R2NiIiI\niAagAb3mFgA6Ozuxfft2ZGRkwNLSEmFhYVi5cmV/xyIiIiKiAWjAN7dERERERLoa0MsSiIiIiIik\nYHNLREREREaDzS0RERERGQ02t0RERERkNNjcEhEREZHRMLrmNjExEZ6ennjttdeQkJCg0z6tra3w\n9fXF2bNn9ZzOtEmpzY0bN7B8+XK4urpi/vz5SE1NNVBK09Hd3Y2tW7fCw8MDM2bMQHJy8jPnFhcX\nY9myZXBxccFbb72FW7duGTCp6ZFSm6tXryIgIACurq5YvHgxrly5YsCkpkdKbR6rqamBq6srcnNz\nDZDQtEmpT1lZGYKCgqBUKrFo0SLk5OQYMKnpkVKbrKwsqFQquLq6Ijg4GMXFxdJOJozIkSNHhJ+f\nn8jPzxc5OTlixowZ4ujRo8/dLzo6Wjg6OoozZ84YIKVpklKbhoYG4eHhIfbv3y8qKyvF+fPnhUKh\nEFevXjVwauMWFxcnFi9eLEpKSkRWVpZwc3MTGRkZvea1t7cLb29vsWfPHlFRUSF27NghvL29RUdH\nRz+kNg261qakpEQ4OzuLlJQUUVVVJVJSUsTUqVNFaWlpP6Q2DbrW5u9CQ0OFo6Oj+Pnnnw2U0nTp\nWp+Wlhbh7e0tYmJiRFVVlTh06JCYNm2aaGxs7IfUpkHX2ty+fVsoFAqRlpYmqqqqRFxcnPD29had\nnZ06n8uomttZs2ZpNahpaWli9uzZ/7hPbm6u8Pf3Fz4+Pmxu9UhKbU6ePClUKpXWWHR0tIiMjNRr\nRlPS3t4uFAqFyM3N1Yx99tlnYuXKlb3mpqamirlz52qN+fv783rREym1SUxMFGvWrNEaW716tdi/\nf7/ec5oiKbV5LC0tTaxYsYLNrQFIqc/x48eFv7+/1tjSpUvFtWvX9J7TFEmpTXJysliyZInmcWtr\nq3BwcBC//vqrzuczmmUJ9fX1uHfvHqZNm6YZc3d3R21tLdRq9VP36e7uRkxMDGJjYzFo0CBDRTU5\nUmvj6+uLTz75pNd4S0uLXnOaktLSUvT09MDFxUUz5u7ujqKiol5zi4qK4O7urjXm5uaGgoICvec0\nRVJqExgYiA8++KDXeGtrq14zmioptQGAhw8fYu/evYiPj4fg/y9J76TUJzc3F7Nnz9YaS01Nha+v\nr95zmiIptRkxYgTKy8uRn58PIQS+++47WFpa4uWXX9b5fEbT3DY0NEAmk8HGxkYzZmVlBSEE7t+/\n/9R9Pv/8c0ydOhVeXl6GimmSpNZmzJgxUCgUmseNjY24cOEC69SHGhoaMGLECMjlcs3Y6NGj0dXV\nhYcPH2rNra+v16rd47l1dXUGyWpqpNTG3t4eDg4Omse3b99GdnY2PD09DZbXlEipDQDs3r0bgYGB\nmDhxoiFjmiwp9amursbIkSMRExMDHx8fLF++HPn5+YaObDKk1EalUsHX1xdBQUFwdnZGQkICDh06\nBEtLS53PJ3/+lIGjq6vrmW+o7e3tAIDBgwdrxh7/3N3d3Wt+eXk5Tp8+jfT0dD0kNT19WZsnj7th\nwwbY2Njg7bff7qO01NHRoVUP4Nk16ezsfOrc59WO/h0ptfm7Bw8eYMOGDXB3d8ecOXP0mtFUSanN\nTz/9hIKCAsTHxxssn6mTUp/29nYkJSUhJCQESUlJOHfuHEJDQ3Hx4kXY2toaLLOpkFKbpqYmqNVq\nxMbGQqlU4uTJk4iKisKZM2cwatQonc73QjW3hYWFCAkJgUwm67UtMjISwF8v0pMv2EsvvdRrfnR0\nNDZu3KjzC0X/rC9r81h7ezvCw8NRVVWFkydPYsiQIXpIbpqGDBnS6w+UZ9XkWXMtLCz0G9JESanN\nY2q1GqtWrYJMJsPBgwf1ntFU6Vqbrq4uxMbGYtu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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = plt.subplot()\n", "sns.distplot([n.mean() for n in ppc['n']], kde=False, ax=ax)\n", "ax.axvline(data.mean())\n", "ax.set(title='Posterior predictive of the mean', xlabel='mean(x)', ylabel='Frequency');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparison between PPC and other model evaluation methods. \n", "\n", "An excellent introduction to this is given on [Edward](http://edwardlib.org/tutorials/ppc) and since I can't write this any better I'll just quote this:\n", "\n", "\"PPCs are an excellent tool for revising models, simplifying or expanding the current model as one examines how well it fits the data. They are inspired by prior checks and classical hypothesis testing, under the philosophy that models should be criticized under the frequentist perspective of large sample assessment.\n", "\n", "PPCs can also be applied to tasks such as hypothesis testing, model comparison, model selection, and model averaging. It’s important to note that while they can be applied as a form of Bayesian hypothesis testing, hypothesis testing is generally not recommended: binary decision making from a single test is not as common a use case as one might believe. We recommend performing many PPCs to get a holistic understanding of the model fit.\" \n", "\n", "An important lesson to learn as someone using Probabilistic Programming is to not overfit your understanding or your criticism of models to only one metric. Model evaluation is a skill that can be honed with practice. \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Prediction\n", "\n", "The same pattern can be used for prediction. Here we're building a logistic regression model. Note that since we're dealing the full posterior, we're also getting uncertainty in our predictions for free." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Use a theano shared variable to be able to exchange the data the model runs on\n", "from theano import shared" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def invlogit(x):\n", " return np.exp(x) / (1 + np.exp(x))\n", "\n", "n = 4000\n", "n_oos = 50\n", "coeff = 1.\n", "\n", "predictors = np.random.normal(size=n)\n", "# Turn predictor into a shared var so that we can change it later\n", "predictors_shared = shared(predictors)\n", "\n", "outcomes = np.random.binomial(1, invlogit(coeff * predictors))" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([0, 1, 1, ..., 1, 0, 0])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "outcomes" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "predictors_oos = np.random.normal(size=50)\n", "outcomes_oos = np.random.binomial(1, invlogit(coeff * predictors_oos))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using advi...\n", "Average ELBO = -2,454.48: 100%|██████████| 5000/5000 [00:04<00:00, 1205.88it/s]\n", "Finished [100%]: Average ELBO = -2,434.84\n", "100%|██████████| 1/1 [00:00<00:00, 5974.79it/s]\n", "100%|██████████| 5000/5000 [00:06<00:00, 754.55it/s]\n" ] } ], "source": [ "def tinvlogit(x):\n", " import theano.tensor as t\n", " return t.exp(x) / (1 + t.exp(x))\n", "\n", "with pm.Model() as model:\n", " coeff = pm.Normal('coeff', mu=0, sd=1)\n", " p = tinvlogit(coeff * predictors_shared)\n", "\n", " o = pm.Bernoulli('o', p, observed=outcomes)\n", " \n", " trace = pm.sample(5000, n_init=5000)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Changing values here will also change values in the model\n", "predictors_shared.set_value(predictors_oos)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 500/500 [00:02<00:00, 190.34it/s]\n" ] } ], "source": [ "# Simply running PPC will use the updated values and do prediction\n", "ppc = pm.sample_ppc(trace, model=model, samples=500)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mean predicted values plus error bars to give sense of uncertainty in prediction" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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f09Ojrq4urV+/XgsXLtS///u/684779TPfvYzTZw40XSZubm2D1AjxHCf0DfZif6xliug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\nERER8XgqtSIiIiLi8VRqRURERMTj/Q/SV/dX1TBRLgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.errorbar(x=predictors_oos, y=np.asarray(ppc['o']).mean(axis=0), yerr=np.asarray(ppc['o']).std(axis=0), linestyle='', marker='o')\n", "plt.plot(predictors_oos, outcomes_oos, 'o')\n", "plt.ylim(-.05, 1.05)\n", "plt.xlabel('predictor')\n", "plt.ylabel('outcome')" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [default]", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 1 }