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Last active April 28, 2018 10:28
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# State space model in Stan,PyMC and Edward"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"http://www.ie110704.net/2018/04/21/edward%E3%80%81pystan%E3%80%81pymc3%E3%81%A7%E7%8A%B6%E6%85%8B%E7%A9%BA%E9%96%93%E3%83%A2%E3%83%87%E3%83%AB%E3%82%92%E5%AE%9F%E8%A3%85%E3%81%97%E3%81%A6%E3%81%BF%E3%81%9F/"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/apple/Library/Python/3.6/lib/python/site-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
" from pandas.core import datetools\n"
]
}
],
"source": [
"import pandas as pd\n",
"from datetime import datetime\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"import statsmodels.api as sm\n",
"import numpy as np"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Nile dataset"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"data=pd.read_csv(\"https://raw.githubusercontent.com/statsmodels/statsmodels/master/statsmodels/datasets/nile/nile.csv\",index_col='year',)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"http://www.hirotsuru.com/category/Python?page=1504314845"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>volume</th>\n",
" </tr>\n",
" <tr>\n",
" <th>year</th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1871</th>\n",
" <td>1120</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1872</th>\n",
" <td>1160</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1873</th>\n",
" <td>963</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1874</th>\n",
" <td>1210</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1875</th>\n",
" <td>1160</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" volume\n",
"year \n",
"1871 1120\n",
"1872 1160\n",
"1873 963\n",
"1874 1210\n",
"1875 1160"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data.head()"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x115bbc320>"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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gAMDvbP5YSCEojVoAQgCu3hCEzaK6fSqlgAJAtyYAlApKEPUT1zaVK6EvmMBW/ZSVzeOv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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x115bb2dd8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data.plot()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"y=data[\"volume\"]\n",
"n=len(y)\n",
"T = 1000\n",
"N = len(y)\n",
"T = 1000"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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osGE4lLq/X4cOHSIuLo4HHniAlJQUT6yLhsbFygUpWgICAvjkow886ffdZB49\njJ9/AGERkUy8djo3/mU2R4+ks23LZn78fiWvPV99J4XD4aCk2EhIWFi1dovdSVFIb0yH/uDfE2O4\nc0R3/H30PPe/NPJPsZDgEVdwb1F+fpPOW/e/lXgZDAy77AoM3t7Me/QZHHY7nbpE0zehuj++qMLK\n/K92s/t4KXNHxTC4dTkZe7ZiMZvpHhnIPaNi2JdTxqvr07HYmycC7A5JiclO1ZhcRYG8MivHS2oP\nnqwLh1Mhq7jhcxQFjhnNzQ4EVv/yrXmuzXn6hYsQguXLl/PFF18QExNDjx498PX1bXB3T0REBO+/\n/z7Tp08nPj6ewYMH1/pgW79+Pf0SEkhJTuLLZV9w5113A3DbX/7KgP6J3HjTjUTH9OSRxxYy8cpx\nDEhKZML4seTkZGN1KAQEBPD777/Tt29f1q1bVyNmBmDs2LE4HA569+7N/PnzGTSoYRfnokWL2Lp1\nK/Hx8cTGxvLmm28CMG/ePP7v//6PxMTEart85syZQ0VFBb179+aRRx6pEQdUFaPRSHx8PxYtWsSz\n/3oeSc3Pdv6DC7DZbPRP7EdSv3ieeOwxAP42azaVFZX0j4/jyYULSawldiY2tg/3z5/PmMtHMTC5\nP48+8jAAEyZO5OUXXmDwgGQOHzqRTsDX15c3336Xm264npT+Ceh0Ov56u2oNk1Drd++ll16ib9++\nxMfHYzAYGDfu1LJYa2ic74hzOa9GcnKybG4Ohu4xMUTF9ObFtz+iuNJGkJ+BuTOvJy/nOF/88EuN\n/i8/+zgfvP0KX/9xhN3HyzB46UiK0DGyfw8efOLfXH/r3zx9v/kzm3c2Hib34/t5741XiE9MJrvE\nzL2f76R9az+emxyPt1fT9aDdZmNAj3Y4nU5efX8pl44aU2u/0uJi7r39Ju6470GSBw1BSsmES5Po\n2CWaNz/+0tNv0XNPENMrlnFXnwgILDXbeeDLXRgrbcwf24v+XUJYs2oF9826hU9XrqdPv0QAlmzJ\n4NM/juFr0DEwOoyRPSNJ6hLS5Guqi06hfo12P2UWmSg1N34rdXgrb9oFN620wL59qUR371Hrg82N\nQa/DoD87Ol+REgHNckFKKbE6VFdIc4kMbV3rrqSWRErVXeL+DAQCIVT3n+KKNdILgVcjPoOoqCh+\n2/I7QSGhp3XNVcnKOEpZaQlt2rUnLCKyyed76QTeXk0PKE9NTaV3797V2oQQ26SUyU0eTEPjHOeC\ntLQAxPbpS3raPtbuy2PmB3/w5s+HyDhyiE5RXWv0Tc+v4GjrBNr87V3u/HQnb244zCvr0jlwTDWT\nV909ZHcqLN+RRY9wH6zHU9lZw72sAAAgAElEQVS9QxVV7Vv7ce/lPUjPr+DtjYebteaMI4c8W0wL\nC+regrxtyya2/raJuX+9gUMH0kjfn0rm0cNcPm5CtX5/f+DhaoLFbHPy+Mq9FJRbeXRCLP1dIqRn\nb3UH0f7U3Z6+0wd05ulJfRneI5LtGcU89u1efj9ibNZ11cbxEjM2xwnrRbnFTm4ttZTKLPYmCRaA\nwnJbtbEbgyJlvYIF1M/ebHNic6gZTs+k4Lc7lWYJD0U5dcFSdayWxO5QMNudmG1OzDYHZrsTi8OJ\n1aFeq8Xh9LTZnIoaU9IEq5c7VuRMYXclArRZa6/I3hAORWqZczU0GuACFi1xlHUZxsvrDuJn0LN6\nXy55lU66RHfz9NlypIi5S3dw7+c7OeIMwXp8H9f29OPZyXHoBPx8SI1RCQ0/IVp+2p9PYYWNGwZ3\np33HTp6MuQCDuoZxbf+O/LA3l3VpqugoKylp9C+xw+kHPO+L6siDAZC6dxc6nQ5vbx/umHEtSz98\nDyEEI68YX+c5DqfCs/9LJT2/gnlje9KnfbDnWMcuUfgHBLJ/7wnRIoQgrmNr7hrZnQ9mDiDE38Da\n1JbJ5QKqKyfTaMLuVDhmNHG00ERBuZWiCmuVPpLsJrqS3DQkdL7++mv8/f1ZsGAB5eXljX6oS1cA\npc0lIurKE6NI9QFkcyieeAmr3dksoeNUJE5FuoJCnTjriYGofp6C1eFsEcGSbyzB1oJCzZ3iXrrE\nYlNGtTmVBuOtDqQfJiw8rN4+LY3NVRPsVLIYnwlXpIbG+cwFKVoqrQ52BiQRNPBaBrb14rUb+uOt\nF7S65AY6RUUDcCCvnGe/T8PuUJg9vBvzk70pXPEcXb2M9GkfTP/OIewokCB0hISqosWpSL7cfpyu\nEQH079ya/gMvYfvvv1b7RX7ToC70bR/Emz8f5nixievGDePFZx5t1LqPukSLr68fRfVYWtL27CKq\nWwyvvf85JcXFfP7ReyQkD6rTJJ2aU8Zj3+5le2YJd47szsDo6r/MdTodMb1i2b9vj6dNURRS9/wJ\nqG6R4T0i+OOokbImWj3qw2xzsj+3nJIqWXRzSi1UWtUYhrxyC3ZH8x6SDYmWHTt2YDabefrpp4np\n0QNTZWWT51CkxOo4YXmxO1SRYLGrL5tTwaEoni3UTimbFdxc9RyJWojvZPGiKBK7Q61zo1ovHFgd\nJ4ednhqq0GiZER3OU1ub3algc9QuAhUpGy3sWgrFqeB0xd7YbM2ztLixO+sWwxoaFzsXpGgps9gp\nsPtgXPMmve0HCAnwZmCYA/8egyGsK+UWO8/9L43QAG/+NaUfV8a1o3OHdgAU5OUAMKZPW0yKHr+u\nyYSGq7uH1qXlcbzEzNSkTgghSBo4BGNhQbV8LXqd4B+je6LTwbPf7SE7O5s1K1c06i/Uw+kHaN+x\nE207dKSwoO5A3LS9u+nVJ57Y+ASef+O/6PV6rpp8XY1+u7JKmPflLuZ9uYvDBZXMGd6NK2Lb1jpm\nj959OZi217POj999nWnjhnuubWTPSByK5Jf0wgavoymcfFukhIwiE2UWO0UVzf+LVXXj1P3gKigo\nIDw8nF9//ZX2HTpSUmzEamleELXb8mJXFI9FpL6+VUVIQw9Yp1K7a8fpilMxuwSSxeF0bdWVLuvF\n6cHRAg9UxWU5OuW1KBKL/YRloqp160w/8u0uK4u3jw92m+2ULFIS6hRkGhoXOxekaGkX7Me3d1+K\nPXUd6fvVxFVtK9NxVBjZWOjLi2sPYKy08cDYXgT6qqlqwiPaAFDoSi+e3CUEb2klsN8VBLcOIbfU\nwjsbj9CnfRCDu6qWiqSBlwBUcxEBRLTy4a6RMRwtsRE8ZDr5eTn8vm0Ha/blsquebdGH0/cT3b0n\nYeERFNUhWoxFheTlHKd3XzXZ1bDLruDnnYe49sZbq/VLyynj0W/2UlRh5fZhXVl8awrj49rVOXev\nPnGUl5WRnZWJyVTJ4jdeBk7UXooOD6BLqD/r9zdtV1NzcCqSjEJTDUHTVMosdVtb8vPziYiIYODA\ngTz41H+A5sciNBW3lcBtkbG6LCS1iZeG4jKkrF8ktTTu/Can8kC1Ky0nKiSqYDTbHB7r1pm8H27c\n352AwFYA2G2nZpHU5IqGRu1csMnlAnwNdO/ZmwOparXVnIxDmHb+RHrgLCiyMPvSrvRo08rT39vH\nh9YhoeTnqcG3XnodYRVHsHZLwWhy8MKa/egE/OPyHp4EaV2iuxEWEcn2LZu49oZbqs0/tHs4H9qz\nkYOm4heVyJO/VoJQrRaX9Yrkr0OjaeV7IhGaoigcTT9I8sAhFOTlkrZvN4qUGCtthFfJ9Jq2R81L\n0avviUygQScVbzNW2njm+zQiWvnwwtQEjzCrjx6xfQE4sG8PmUcPYyxUY2ryc1XLkxCCkb0ieX/z\nUbJLzLRv3bTdOWeDUrO92r2rSkFBAZGRkZRbHbTr0IXyrNRTNus3hZPdLKqrSaITEnf+PfeumXMN\nKVWh4FNlp4uU7ribE7t/vHQC/UmJ+VrKylJjTS0+YtNwW1oCA1tRXFSI3WbF2+f0lLLQ0LiYuSAt\nLW5iesVyMFV1eWQePUxY5RF6tmnF6N5tarU6RLRp63EPARiO70Do9Dy8Yg+pueXMHt6NyKATmTtV\nF9ElNSwtHrZ/ia4sF/9WwXgd+JGXpiUwLbkTP+3P584l2/lhby7FrmyxudlZWCxmusb0JCwiAmNh\nPq+uS+cvH/xBev6JraZpe12iJbb29OV2p8Kz36dSaXPw4LjejRIs7nslhGDntt/575uLSBk8FCEE\neTnHPX2G94hAwBmxtrQEJquzzhgSt6Wl1GQnqHVrhBCnFEDZUrjjRhyKGgNzruJ0ubmkK06nWgyP\nS5i4LUj2KgHJ1ibu6jpfsNls6HQ6/FyJAM+kANbQuJi4oEVLj959KCk2Upifx7GMI3TpEsW/r43n\n76Nias13EdGmHQUuSwtARfZhDCUZHC8xc2lMBCN61gx07T9gMDnHs8jOyqzWLqUkdefvJJb+wsTg\nLA59/RIBjlJuGtSFF65LIMTfm1fXpzPjv78zd+kOlmw+BDovorv3ICyiDfQcxZrUPKSEpVtPjJ22\nZxftO3UmOKRmzhS7U+GNnw6RmlvO3FExRDWhfpC/fwCdo7ryyeI3MRYWcNf9DxEWEemxtICahj++\nYzA/7S84Y/72P7f/wW3XjudA6p6GO9fCyYHD7m27BQUFqmhxHffy8vJsWdVoHA6ngsWu7uSp69ug\nuESNJyD5NNtEzCYTGYcPIc9wIKvNZsXb2wcvL8M5I4A1NC5ELmjREtMrFlArGB/LOELn6G71JueK\nbNPW4x4CKDYW0rZ4NwOiQpkzolut57jjWrb//mu19uysTEpLiomNS2DEaDWL5Ya1PwDQLSKQF6cl\n8NK0BGYM6oKvl56f8w20u+VFCO2MKbgLISNvo397P65L6cRvh40cKVR3t6Tu+ZPefapbWaSUbEov\nZM4n21iTmsfUpI4Mi6lZeqAhesT2xWa1MnjYSBJTBhHZph15OdnV+ozsGUlumYU92S1bBbk2Vq/8\nmr9eN4FtWzbz9qLnmzWGW5RY7E4OF1SQmltGtrGCoqIigkLCPHEzei+van8d780ubdFXY3ntlUUk\nJyaQlBDPwocfoqJMvc+9e3QnpX8Cg1KSGDp4IKAKr8tHDic5MYFvV6zwjHHdlMnkZGfXOn5L8tqr\nr5AY35fbbrmZy4YPq7XPU088zksvvACAzWrjYNo+7NbT90AvLyulsqKcysqKOtfkpqSkhLfffKNF\n5rXbbGqtMAHe3j414qMiQ1vXcaaGhkZTaFC0CCEWCyHyhRB7qrSFCiHWCCEOuv4NcbULIcQiIUS6\nEGKXEKJ/lXNucfU/KIS4pba5WpqYXn0A+GXdauw2W62J5aoS0aYdRQV5ngRvxsICOvo5efiqWAJ9\nanezdO8ZS6vg4Bouon271RoqfeITie7eg05dovlpzfee4xZTJZE+TqYmd+K5KfF0L/gFr4BgHl99\nlJ/K22DLO8yEzgqT+nXAz6Bn6dZjVFaUk3HkEL2qiJZKq4MFX+/h2f+l4WfQ8/jEPswYHNXkewXQ\nu28/AGbf+wAAbdq1Jz+3+sPvkm7hhPgbeGfj4VOqTVQfUkree+1F/jnnVmLjE7jm+pv58ftvyc3O\navJYJpuTrGIT6fkVVFqdKAocyFCtRz6tTlir9HqXpeUsemT27t3DfxcvZsOmzWz4ZTPr169j794T\nFqbvV6/ltz+28cuvWwD4Yuln/OVvt7Nh02Zee3URAKtWrqRfQgLt2rc/7et95623+HbV9/z3g49Y\n9/PGBvubKiuw22xUVNSsy9NSuHeAVVaUN7im0pIS3n7rrUaNKxUFxen01GE6GZtbtAAGH2/Naqeh\ncZpojKXlfWDsSW3zgR+llDHAj66fAcYBMa7X7cAboIoc4FFgIDAAeNQtdE4nIaFhRES2Zd0PqwDo\n7MrRUhcRkW1wOp2UGIuw2+2UlZbUqDt0Mnq9nsSUQTVFy64/8fLy8sSKDL98LL9v3oDJVMmWTT9z\n1aVJ3HDVZZ6/yIr3/Ezotv9yWa9IQv10FHz1BOXGAgJ9vbgqvh2b0wvZuE1N/uYOwnUqkn/9sJ99\nOWXMGd6Nl6Ylkti5+bd12oy/8PaSr0lMUWvGRLZtX8PS4uet544R3TlSWMmybU0XEY1h59YtvPzs\nQsZOnMLbS75m1tz7kVKy9MP3mjyWlFBcWb0GkrFI3bYd1PrEZ+vl5YWUEoej5fLQNJX9aWmkDEjB\n398fxemkf//+rPpuZZ39DQYDZpMJq9WKTqdWBn71lUXce98/653nk48/YkBSIgOT+/OX29S/Hxa9\n9CJJCfEkJ/bj1UUve/pmHD1K//g47pwzi+SEfkwYPw6z2czf77yDI0cOM2niVbzy8kvVLAn/evYZ\n+vWJ5fKRwzlw4ETCRJvNyqpVqxg/9goGpSRx9x1zcDqddc5R11o/XfIJlw4ZXG0MN1brCdHiXlNd\n4z/y0AKOHD7EoJQkHpz/QJ1jZxw9SlxsL6ZPm0pKYgJzZv2Nt9543TPnEwsf48MPPsDb24dp107h\n2ilTuPrqiSx+9516PwcNDY2m06BokVJuAE7O33418IHr/QfApCrtH0qV34DWQoh2wBhgjZTSKKUs\nBtZQUwidFmJ69/EEk3aOrt3F4yaijZrDJD8vhxKjWrm1tgrPJ5M0cAhHDx2stk05dfdOuvfsjY+v\nGrg7fPRYbFYr8+6Yye3TJ2EwGMg4coiP3lV/+R1JP0D36M7MHdWDp8ZF4Swv8ox3dUIHfAw6Vu5T\nPwa3RWTxpiNszyxm9qXdGB/XzrOrqbm0Cgpm0LARnp/btGtPWWkJZrOpWr9BXcMY3iOCpVuPcaSw\n5evRHHUVjZw7/xF8fH1p37EzI8dcybJP3q+xluZgdFXQripI9XrVknY2YxFiY/uw+ZdNFBUVUVpa\nwubNm8k+rn53BYKJV45jyKABnofhdddPZ+W33zJh/Fjuf2A+b7/5BtNvvLHeqtD79u3lX888w6of\n1rBl63b+/Z8X2bF9Gx998AFvv/UWK775lvcXL2bnzh2ec9LTD3L77Dls3fknrVu35uvlX7Hotddp\n1749369ey91z7/H03bF9G198vpRf/9jKVyu+ZXuV2mGpe/eyZs0aPvjgQ377Yxt6vZ7PPl1S5xy1\nrTUtNZUvv/iCH3/aUGMMqUhsVis6vR6LuXom5drGf/zJp4ju2o3f/tjG088+V+/YR48eZfI117B5\ny+/MufMuvvpymWfsr75cxujRo/H29uaNt9/hfz+s5oMPPuD1V1/1VIDW0NBoGZob09JGSumO0MwF\n2rjedwCOVemX5Wqrq70GQojbhRBbhRBbC+pJZd9Y3HEtPj6+RLapO08JQERbd4K5XIqN6l/jVesO\n1YU7ruWX9WsA1b2xd9cOesclePr0H3AJrYKC2PDjD0y8djrL121h5BXjeXvR8xxI3UOxsYjobjEA\nhLmEklu0BPsZGN+3HRmOINpf+xB/GgVfbc/imz+zmdivPWP71p4w7lSJdN2PqsG4bm4f1pVWPl68\n9OPBFk877p6v6ud1422zKC0p5rvlX5zy+MVFNQWp3rV9134Wd3306t2bf/zzn0y8chw33TCdHj16\neLxVa9f/xOYtf7D8m5W89eYb/LJxI8HBwXy14ht++XULCYmJrPruO66ZPIU758zixuunseW3X2vM\n8fP69VwzZQrhrtIUoaGhbN60iTFjx+Ln54der2fipEls/uVEUdGoqGj69VO/ywn9+5OZkVHnNWz6\n5RcmXj0Jf39/goKCGH/VVZ5jGzduJC0tjWnTrmNQShI/rV/P0SNH6pyjtrX+tH4dO3ZsZ9glg2qM\n4bayhISoYrRqsHhUVDR9+/St9xrqGltKSbt27YiLi6O8tJSEhEQK8gvIyc5m164/CQoKom3bthi8\nvXnjtVcZc8VoZs6cSVZWFofSD9Z5rzQ0NJrOKedpkVJKIUSLRQJIKd8G3ga1yvOpjtejtxrX0rFL\nNDpd/Rot0mNpycXbW83vEdoI0dInPpFefeJ47T/PcMWEazAWFlBaUkyf+ERPH4PBwOPPv4YiFUaP\nvxqAfz78FJNGDeSBu/4KQHRMT7WvtzfBrUOqZcWdmtyJFSu+RtcpjkXr1HwvyV1CmDmkfpfXqdCm\nnRoXkZ+bXa1mE0CQn4E7RnTj6e/TeGV9OneN7N5iFZDzcrMJDY/wxAgAJA0aQs/YvixZ/BZTps9o\nVrVjNycsLSc+W73eC4fTcdZ3fdxy20xuuW0mGYfS+de/niMyMhJFUWjfQdX4kZGRTLx6Elv/+IOh\nw04Emj779FPMm/9/fLH0MwZfMoRrJk9h+nVT+ea7VRgLCjAaC4nu1qPOeZ1OVwr6WhLsefucyHWj\n1+mxOJpRD0qC3WFnwoSJ3HHHHLr16OWxQmYcPdroOaSU3HjTzTz+5FM1jrlFS3BICMXF1S0cBoMX\n+/ftoUvX7nWOL6Xkhhtu5PEnn0JU+V1xIC0NX9day8tKCYuM5JopU1j+1Zfk5eVxlUuY/fbbr6xf\n9yNrflxPTk4Oc+bcQUFJ5SknSdTQ0DhBc58yeS63D65/3U/X40CnKv06utrqaj/tuC0tXaLrD8IF\n1K3GqKn83XEPjREter2eBxY+R252Fotff8kThBtbxdICMGrcBI9gAegUFc2Mv93FoQNpAHTtfuKh\nEhYRSVHhCdHijZPML55ipG0Li65P5O7LunP/mJ6n7BKqj8i2qmg5Oa7FzeBu4Vyf0ol1afk8smJP\ni9Ulys/N8Vh53AghuOG2WaTv38fvmzec0vjFRYXodDqCW5+I/xFC4GUwnPUAyvx89TPPyDjK+vXr\nGTt2LCXFxZSXq8GrlZWV/Lh2DbF9+njOST94kOzjx7l0+HBMJhM6nQ4hBBaLmbKSEnJzjmOzWikp\nNjJ85EiWf/mlx21hNBq5ZOhQ/vf9/7BYLJQUF/PNihVcMnRos9Y/ZNgwvv1mBWazmfLycr7/7jsA\nHA47KcnJrFu/DqPRiNlswmg01mu1qW2tIy67jK+/+spzn6qO4Q7C9fHxJSAgsJqlxeGqC2SuUmMq\nsFWrakHBw4YN54vPl7J315/VxnYLuaDg1phMlTgdDqZMncqyLz7n66++YvQVY/Dy8qK8rJzWrUMI\nDm5NZl4xf+7YSpnFTkaR6awnv9PQuFBorqXlG+AW4FnXvyuqtN8lhPgMNei2VEqZI4T4AXi6SvDt\nFcD/NX/Zjadr9574+voR3b1ng30NBgMhYeEU5OXSKkitguyuO9QQSQMvYeyEybz/xiJGjZvgCcJt\niL/d/Q++XfYpZaUltOtwQteFRURWi5FJP5CKw+Egtm880eEBRDchB0tzaVOPe8jNjQO70L61H4t+\nPMg/l/3JYxP6nHK23PzcbCLb1dz9Mu7qa3nm4Xms/+E7Bg4Z3uzxjUWFBIeEotfrq7V7e3t7tj1X\nrYJ9Jrnx+usoKipCcTp59LGFtGrViuzjx/nLzFsBcDqcXHf99VwxZoznnIWPPsKjCx8HYOq067l+\n6hRe+Pe/uX/eAxw/loF/QABSSoqNhcTG9uH++fMZc/ko9Hod/RISePvdxUyYcBW33KIGus6acwcJ\nCYk11tYYEhP7c+3U6xiUnEREZAT9k5MBsFqtdO3alQcXPMTdd9+NEDr8/P148eVFtGlTu3uzrrU+\nsnAhE68ch6IoGAwGXnx5EZ27dMFqseDj44vQCQLd6fStNiorKjw7fiyWExaWsLAwBg2+hOTEBK4Y\nM4Y5s2cze/ZsZsy4GS+DwTO2l1D/tguPaENZaQnlZWXExvahvLyc9h3aE9I6GEWRjB4zhnffeZvE\nfnF0jOpGv4T+RAR646UXakC4yU6Iv6HmhWpoaDQa0VCSMCHEp8AIIBzIQ90F9DXwOdAZyACuk1Ia\nhWqzfxU1yNYE3Cal3OoaZybwoGvYp6SU/21occnJyXJrlUC+plBqspNpVIM2D6TuoV2HTh4hUh9T\nxwylTfsO9Owdx+LXX2Tb4YIG3UpucrOzmDg8BYvFTK8+cXz+v4a3gYKa4+Xo4YNMvn6Gp+2Bu/7K\n3j+3s3LjdgA+/2gxTz74D1b9spOOXaIaNW5LMKRPZ66aPI3/e+Lf9fZLzSnjiZX76BzmzzPXxKEo\narZUL6+m6+Lh/bpx+fiJPPzMizWO3X7DJArz8/lqbR1ZiBvBvbffzNFD6Sz/8UTMh1Kchb+/H6aK\ncmJ696nn7NOP1WLh0IE02rbrQG7Ocdp16Nio2Kqq2KxWjqQfwMvLQFS3GMrLS8k+lklU1+74BwZW\n66s4naTt3Y2Pjy9Wq4XuPXtXc9e0BMVFReQcP0ZMrz4czzwKAqJcMVwtRfr+VHx8fenUJRqb1Ur6\n/lTadehEsbEQxenEx9cPq8VC9169a5xbWlzM8WMZePuoOVZ6xsZ54pwyjx7GbrPRrUcvDqbtw9fX\nz1MtHuBg2j78/QPo0LkLADklFiqtNvQVBUR3U92qOaUWzDYnnUP98dI3zjrqZ9A3yg2amppK797V\nr0kIsU1KmdyoiTQ0ziMas3toupSynZTSIKXsKKV8T0pZJKUcJaWMkVJeLqU0uvpKKeWdUspuUso4\nt2BxHVsspezuejUoWFqSHr37NkqwgJqrpTAvD2NRAa1DwxotWADatu/IX+68F6BaEG5D9B8wuJpg\nAQgLj6gW07Jr+x+Ehkd4fjGeKSLbtq/X0uKmd7sgbhjYmb3ZZew6Xsqdt1zHI/fd0eT5bFYrxcYi\n2rStPc9IyuBhpO/fR1FhAdklZix2Z6396sNYWEhoLVvZvb29sdvtZzyb6sm43RF+AQHNzq5akJeL\nBDpHd0XvpSc4OASdXo/RWHM3i3unjbuG1ekoHGmzWRFCYDAY8PXzU+dswdvs3jnk66PGnnj7+OBl\nMFCQl4vFbCaiTVv8/Pyx2awoJwWOO+x2crKz8PcP8Fg7q+5Ss1os+Piq1sNWQcFUlJcj3blaZJXE\ncoDFrlBpc2BQrNitJ6qGRwT6IIHCCi29v4bGqXBBZ8RtDmr9oVyKiwoJCW3aX7cAt8y6m8vGXMn4\nSdee0jrCI9tgqqzAZFJ98H9u/4P4xORTCkBtDm1qydVSF1fEtiUswJslWzLZveMPVn+3gsomJhLL\nd9V+OjmmxU2/gUMJTBjHP7/ay6yPt/H3z3ZwqKBp266LjYW1bmX3dj143MXvzhZuF5WPjw8G76Yn\nKlMUhbKyUoKDQzwPU6ETtA4Jpby0BKcrvsON22USFHwaRYvVqlpvBPj6+aMoSovW5/HcM98TrsnA\nwFY4HHZ8fHwJbh2Kj596rKqLCCD7+DGkImnfqbOndpDZ9f9OcSrYbTZPIG6rVsEIbz+OF1dSVGGj\nuMKC8PbDy6BapoyVNvQ6gb9eweGwe9xSXnpBqL+BCquDcpP1jJXB0NC40NBEy0lEtmlLUWE+Bfl5\nhIY3XbT4+vnx0rufnFLMBaiWFgBjQQElxUYyDqcT3z/llMZsDpFt2zXK0gLg7aVjalJH9uWUYQ9R\nTfQbflxdZ//V363ghqsuq5YczC2QImuxtOSWWXh5lyRszJ2YKiuYMagLNofC/cv+5H97chv9ICgu\nKqzV3eJl8EYYfDlWaqeg3MrZMrhYrVb0Xl7o9Hq8Dd5NFlHlpaVIRalRnyokNAwpJSXF1dMuWcxm\nvLy88PH1RafXY7VZMVbYmmXFqgub1erZkefrFg/mZuxCqgNPEK7viYKmAa3UuJaINm1BgJ9r3nKz\njaNFJoor7WqG3rIyIiLb4O3jg06nw9fXj0qLjWNGM8dLzKDzwsdlwVEMvniFtMPqgBKTnSKzA0No\nB4xObw4VVGKyOQjx98bHda1VBWdrf28Meh25pSYKC4uw2J1UWB3UkmC30WjiR+NiQxMtJxEe2RZF\nUTh0II3QZlhaWgr3Tqaiwnx279wGQL+k0ytavPQCb6/qX4k27dpTWJDn2X3REKNj2xLkDcFDbgDg\nh++/ZcOBAn7an18jn8sv61az58/t5GSdSOHjFkhtTgrEdSqS/6zej0ORROz9HPM3jzM1uRMvX59I\n3/bBvPZTOv/dfLTB9dntdkpLimtmOtYbMJtN6ANDAbVmUabRhMnWcg/uxmKzWj0PveZYWkpLijEY\nvPH3rx6s7ePri39AAMWl5ZhsTkw2J2abE4vFgq/LQuHj44tZ+GE02cgusWC1t0AOHqlaQtwPfh9f\nX4QQLZIo0I17u7NbGAEEB4cQ1S3G4/bSexkwBLehXDEgpaSo0kpeqSqcWgWr7mNFkeiCwnH4heJU\nJDanxDu8E3j5UGFxkF9mQafYseYfxlF4BEqysRuzCfXzItjP4Hm5Y4KqWnWEgFZeCkJvoFT6klVs\nJrfUogqjZmgPKSVFRUUeK5CGxsXAKedpudBw52oxVVY0y9LSUoRFqJaWwvw80vbuQqfTVcv70pKE\nBBho7e9NgLcehyI5VD/CGPgAACAASURBVFCB3aH+Fo1s2x5FUSgsyKNtu1rzAVbD20tHnG8xmzr1\nodetz3CgVSf+vXo/AJ9syeT6lE6M6BmJXic4dFBtP3LogCe42F3r6GT30NI/MknLLef+K3qS7uzG\nSys/pDA/j/DINjw6oQ9vbTjE8h3HiW0XxKCudZdeKHVZGU52D4nAMDLycjFbLHhLB4EB/hRZHBxX\nJAE+egK8z9x/lbzcbHx8fLE7FSrKyygvKwWdV6Ncg4riJC8nm8BWrTh4YH+N48UVFuxSkFeyt8pJ\nDryFE6vdQWFZJUqJmQAfPRa7Ql6mJMTf+5S21judDgoKCrA5HJS6CkCWlJRSWlZGWVn97sPKinKX\nFaj+HWnFxkLsdjvpBw/UOOZUJFangsXmxKFIhOMYESHBVFgd5Nmc4LCzP/0wNoeCzamABMVmIjQ4\nEFOlCSte5OvUz9+gFwT66LDabDgdDhwOh7pdvkqqqpL/Z++8w6Oq8j/8nukzmUkmvVeSkFAC0hEF\nC3YQe13brrr6s7Duqmuvq2tfe9l1XbA3EFFxAVFhUUB6bwmBhACppPfM+f1xJ0NCJqQTEs77PHky\nc+6Ze8+ddj/zrQBogqKquhpfv0MWr/LyUsorq9HrDfg5nTS4JLnV9RR6eY8Z9TraesktFgtRUVFH\nnqRQ9COUaDmM4CZVWNuKaQl3WtALQUVtPRU1DdTWd19l2CCPpSWfDWtWkZQyCJuPvY1HdQwhINrf\nhl+TNEyjXhAb4ENGfjlSHrJ45O7f51W05O7fR2BwSLMsIZ/8TdTXpFAVOoSanb9x5cmppI0cy0e/\nZfHyop18t3E/T184hMx07QKTmb6Dk08707M/q80Hu8PXs7/N+0r4bFU2pw0MYWJyMAGVWlG1lcuW\ncs60i9HrBDednMDO3HJeWbSTAcF2gh3es1+8FZbTngw9Ty4uYEdmNgN2zeLlt2ega3Dx+o/p/Lh9\nP1eOjuaqsT0fBF1VVclZZw7h9rsf5Obp9/C/n7/g/jtvYs6PK0hIajtt//MZ/+Lph+/hywW/4Bd7\n6GJWWVvP0/O2sn5vCXVr5xBMGfc9+Rwbtmcw85ddGJ1hhPlWcqC0mqJF/2LRx29TVgN/nb0Bg07w\n7MVphDg694t+2c+LuPWai/nPl/MYOTYFgLeeeZ4f5s1lyYZdgJahEx4R1Sxr6VP3uQwZPpKPv1l0\nxGP84eKLiUtI5OV3P/KMZRdV8tS8rZolA4gOsOGb+TM/znieZdv2YnW5uPD66djGXwUUEeZrYXSc\nP4MdNdx6/sk8+eIbzJvzJQfLyhl35+uU19Rzz5kpmEx6TK2soyn3/+EmpJS8/9V8z9iTD9zA/G+/\nwmAwsGL7PiwmE28t2M7S9AO8cMkwEkMOfcZTInzR9WAdJoWiL6LcQ4cR3KRmxJFqtJgMOoLsZvx9\nTET520gKsWM2dt/T6R8YhBCC/Nz9bFy3mrQRY7pt3wA6HcQH+TQTLI1YTXqi/bWAxEOl/FsG434z\n61POGjfE0z+pkb2ZGfDjy7xz9Qjqf36THT/NYkx8IC9fNpw/nZ7Ezrxy3ly4hfIy7Vd3ZsahUud5\nuVphuUarQmVtPS8t3EGIw8IfJ2kFAlOGpGF3+LJy2aGUcqNexz1nDaTBJXlhwXYaWglIKfKU8G8u\nWlZkFrEjtxz/A6vYn5Xp2eedpycxOTWET1Zm8/GK1guhNZKxYxvffz2L//24gLUrl1NY0LFWFNm7\ntYt4Y5+syOgYANJ3Z3ltl7Bt8wZW/LLYE9sw7+svSUoZ5KkEDXCwspYHv9rExpwS7pqcxNXjE1i/\n4DPqD+zAXrSDfe/eypQkG5W19Yz3K6Vs1ddk78kkwmnlifMHU1XbwHP/bf05bYs9mVoF56ZVlVOH\nDKOk+CBv/eMZLpo8nqkTR3LV1NPISN9BYXkNi378iWcfuw+L1cbWLZtYnXGAz1dl82tGQYv919XW\nkpWZQUJSimdMSsnbSzIorarj1kkDePfaUbx51QjGJ4VSXV1FVmYGm9evIX/Jx1wRfpA3rxrBP68Z\nyc0TBzB+WAoOPz82rF1Fxo5tJCUO4M9nDOSRKYOxmvQtjt8aQ4aNYOvG9dTVHSq6uGXjOsxmC/X1\n9ezepT0vt0wcgJ/VyEs/7OjWHz4KRX9EWVoOIzA4BCEEUsojdng+/Je8TieICbCRkV/epcC6RgwG\nA86AQFYuW0p5WSlpI7qv5IJeJ0gI9sFibP0L2M9mJBor1bFaCujhGUSzP32fx++djpSSNSt+5YZb\n7vRsy969i5iQACL8fTjt7Cl8//Usd9qohdNTQ9ldWMGcdfuwJo6lIXsdmek72JFbxqrdReTm5TWL\nZ/lg2R7yy2p47uI0bG7zucFgYMTY8az8tXkdnAinlf87ZQAvLtzB56uyuXJMTIvzKnKLiKaipcEl\n+XD5HiL8LERbK/lv1iFxotcJ7jhNqyfyycps1u0tYXScP6NjA4gNtHnE1f6cbN544Wm+mfVps+DI\nkLAIFv62ud1ZX3syMwAtVRkgIioGndWXd7ab+LZwPQ+ck0qYn2bxaGho4E83Xs2+vdmcOPE0rvr9\nH1m3agXT73vUs7/MgnKe/G4rJVV1PHTeIEbHBVAZfS3vvPwc/3nzZaJi4jAb9Pzh9DT+aDCwZcM6\nPkUTGkkpg4gPsnPLJO05/Wb9Pi44oW0X4eFkZWbgY3cQGBziGUsclIZz0vV8uUvgO+EmRl4QRm5J\nJdO/y0Ho8wAjUXfNwmEWlFTV89j36Z7HXjMulktHRnme06zdu6ivr2dA8iFL1MrdB9mwt4Q/Tkzg\n3KGHrKcDBw8FYPuWTWTs3IZOp2Pq6Sfj6zzUZFKn0zF0+Ch++fkH8nL3kziw7SKR3hgyfCQfvPsm\n6du3kDpkGKXFxWTvyeScaZfw/ddfkr59K0kpg7BbDEw/LYlHv9nMe79k8seJCUc9S1Ch6CsoS8th\nOGxmgtxfrq11eDbohdfKlhajnihn6x12O0pgUAjrVq0A6LbMoUYLy5EESyNOm4lRA2Mxm82UFOZ6\nxj+d+S6P3XMnJ046ndPPmcq2zRs926SU7Nmd4bEUnHHuNCoryvl1yY+eOdeOj8Mpqgg8dzqjzriI\nfcGjufuL9XyyMpvCmFM8jSt35Jbx3cb9nJcWTkr4IXcRwJjxJ7MnM6OFmDplYAhj4wP4ZsM+r5aB\nxkaYTa1ov2UWsqeokqvHxhIVHUNpSTGlJcWHnjOhCZcbToyjtr6B95ft4Y5P13Lf7I3sKazgo/fe\nZuqkUfz3m9lce/PtfLngFz74eiGX3XY/FQHJvDF/PU/N28Lz87dTUVPP/pxsnn/8Aa+pxdm7NStP\nTJwmWoJCQvE/6SpqpY68smru+nwdq/ccBGDJovns25vNlIsuY+P61dx+/eUAnDPtYgCW7Srk3lkb\naHBJnrlwKKPjtCBjm4+dK6+/iR/nf8dPC+aRODDV495rFEtZmbs8a5qUHMzY+AA+WL6HfcWHAku/\n/uJjXnjiwTaDtHfvyiAmvvmFeLcIw2/cJcSNmEjs4BEEhUcxdnAitpxVFM5/g+plH3HmQH/SYgKp\nWP9fTqjdxPu/H8MpycF8sHwPM37d7RGHjW0wBiRrlpb6Bhfv/ZJJpNPK2YObV9tNSByIwWBg+5aN\n/Lr4R4YMH+kJ1G1K2ohR7HMHiCcObFmMrj0MHT4SgE3rtAKRje09plx0GQaDgZ3btnjmjoj154Lh\nEXy3cT9frT0qHU4Uij6JsrSg/ZoOspvw99FSEqMiI8jPy221CmmQ3dzqLyE/m5GgOhMFZV2v9REU\nEkL69i34+jmJS0js8v6EgNhAnw6ZuIUQREZGUpx/ANDqxTz90N1Mmnw2L749k09m/JNF339DYUE+\ngUHBlBQfpKykhBh3xdDRJ56Mr5+Thd/N4dQzzwU0t0v0gSUcDJhEzuCrMEnJ6cn+OGxWvuJE6qoD\nqG9w8fpP6QT4mLhmXMtYktEnNsa1/I8pF13ebNupA0NYkVnEpn0lDItqfkEqKihAr9d7apIA/LQ9\nH6fNyITEIGoztGPtzdrdrHeUTgguGhHFRSOiKCyv4deMQj5ZmcX0T9dSvGI7Q0+9gItuuosavZ3Z\ne8rZvM9FsX0CQVMnsDC9jAh/G/tLqimpqiVs13d88O6bnDBmHJPPOb/Z+vZkZhAQFOyJ6ckrr8U+\n7GycxTt4/s6refr7rTz+zWbOGRrOqs+/IiQsgidefJMDBUW8+N5nVJoC+M+GcoqWrWNHbjlJIXYe\nPDeVQHtzy+CVN/yRme+8TvaeTC668lBhQ7vDl8DgEPbsOmTZEEJw66QB3PbJGl79cSdPXzgUnRB8\n9v6/2bRuNQf25/D3V/+F0ei9RH1WZgZD3Bdw0Fx+s9bsZXi0kyenDWk2t37qUGZ9PJNhI0eTMjgN\ngHWvryRn+Vb8/3wLd52RjI/ZwOy1ORRX1fHHiQls3bQenU5HXIJmEft+0wFyiqt4+LxBGA5r4mky\nm4lPTOa3X//H5vVruHn6PV7XnHbCoR8JickpXue0RWRMLE7/ADatW82lv7uBzRvWAjBsxBhiExLZ\nuW1zs/k3TIinsKKW//y6Gz+rkcERvt52q1Ac1xwXlpbWitoKoQXTpoQ5CPG1eLoUR0Ro7omQkJaW\nFr1OEOhz5DC8MF9Lh4RBawQGaRaftBGju2wubgy6tZs7rlMjIyPZv28fNpOOV/7+GAFBwTz7+ruY\nzGZShw4DYNumDYBmqgeIdlsKjEYjEyefxdKffvAU2gLYt2UV9u3fEWNzceDDe5noX8bUZB8q039j\nh2UgryzaSWZBBX+cmOBxCzVl4KCh+AcEsvSnH1psGxnrj9mg45f0Ar776nNe/vtjnm0HiwqaVTou\nr65n5e4iJiYFo9cJBqYORQjBou+/bbZPKSVff/4Re/fsJtBuZuqwCN66eiShtftxjLmYgmHX8M/f\nCpi5bDc7cssYHu3k1onxFHz4Z8YVzOOtq0dy52mJrN9bwuJiTTB9//UsGlyS/LJDxcayMjOaxX58\ntGIPIKnf8C1hfhaeuziNMweHMX/TfvKGX0fUNc/zzPwd3DF7J+m+J1DqN4D9xdXYTAYuHhHJ3y8a\n2kKwgOYeu/CK3wGQMmhos20xcQM8bqpGAu1mbjwpgc37Svluw35cLhfp27cSE5fAgm/ncPct13m1\nHNXV1rJvb1azhqVz1++jtLreqxg1GAxcfu0fPIIFtIrRG9asoramBp0Q/HFiAleOjuanbXnc9vEa\nvl+xhXEnnYLJYiGrqJJPfstiWJQfo+P8W+wfNBfRxrWrcLlcTJh0utc5jVYSH7uDsIjOZecIIRgy\nfCQb3ZaWzRvWEh0bj6/TSdLAQaTv2Npsvk4I7pqczPBoJ6/+uJMft+V5261CcVxzXIiWCD8rvtaW\nF75wPwtBdnOLCP2IiAgMBgOx4SEtHhNkN7UZ0S+EIDrA2ma6Yls0xgB0JZ5FCAi0m0gOdXgNum0P\nUVFR7N27l7XLFrNq+S/cfOfdnkymxovL1k1aZ9ws98Wu6YV3/MmnUnywiO1bDrmRdu3cTqqfi/tP\nj6V23zYyM3aQf2A/Bd++iJ/Rxc878hkbH8D4Ad6tXTqdjlPPOo+fF37fokiZxahnZKw/y3cVMm/u\nLGa8/SolBzWXyuGVjn/dVUC9SzIpWROo0XHxnDXlQj7891ueTt8AP3w/l4f/chvTb7zKUzfF6Kph\n87/vIWrnbO47O4VXLh/OZzeP473rRvOXMwZyblokyRGBbHHX2TktJZQrR0dRHTKEoHP/xHp9Mr/7\n93J+P3Mlj8zdTGZBOVmZuzyuocyCchZvzyesIp0DGZs953b7qYmMLvyBkiUz0TkCSc8r57yh4bx4\n6TA+vnEsr181gienDeH6E+MxG1oXzzfcOp2RY0/kpFPPaDYel9BStACcnhLCqFh//vNrJss27KS6\nqpI/3HYX9z/5HD8tmMe9t/2+RbGzvVm7cblcxLothWXVdXy1Noex8QEkhzpaXVtTRowdT01Ntce9\nIoTgqrGxPHdxGrKuGuPpd1A36U6u+tdybvt4DVV1DfzhpPhWhf7AVM264+vnZPCwEV7n+PlrNV6S\nUgZ16QfDkOEjyNixlYryMrZsXOex3iUOTCUna0+LitFGvY77z0khIcjOiws7H/ysUPRX+r1oMRl0\nOG1GIp3WZrUmfMx6r79AAW6++Wb+8Y9/EGBvblGxGHWtptIejtmgJ7KL3Y4bRcuwTmYO2S0GUsN9\niXBaWxSN6wiRkZHk5OTw9yceJTI6hkuuut6zzdfPSVRMHNs2H7K06HQ6IqMP/YpurA68YukSQOuy\nXHywiISkgYRHRWMym8lM30nugX3ImgpuGOrDxKRgbpl0SPh446wpF2rxMotbpsNOGBDEwco68mot\nuFwulv3vJ8+xmwZYL96eT4SfhaQmqaa3/vk+aqqreO/NlwGtVsizj95PcEgYO7dt4Z+vvQDA7E8/\noLSkmFuuu5IJiUEkBNtbWIWGnjCSrZvWe4TOYGM+Zev+i8/QyZhihxOuK+OqMTFk5JUz/dN1uEZd\nQV38BL5el8NbP2fgYzZwgqOCwvw8jzirqqpk3uf/YVxQA+/dMI4ZN4zhxpMTSA51dOgCGxYRxX++\nnNeiAWdM/AAK8/M82V2NCCH40+RkfC1G3lp+AGGykZQymCuvv5nb//oYSzdm8O43S/jktyw+dMe/\nZOzc5tknwOw1OVTVNvC7DqSPjxhzIgCrVzRvkpkS7otz5bvUrJmDv7+Tk5OCueO0RN68egTxQa2X\nBxjotiyNO/mUIzb0fPrld3jgb0duFNoWQ4ePRErJr0t+ZF92FoOGabWWGjvAp7vjcZpiMxl4dOog\nZt4wpkv1cRSK/ki/Fy3BDi3+xKDXeUSETgdR/q0HzI4aNYrbb78ds0GPj1n7pSqEVuehIxcFfx8T\nflYjQoCf1Uh0gJVAe3sqPGiMHncSI8aM71QlXJNBR0yArVu+9KKioqipqWHNmjXcff/DLToApwxJ\nY+vGRkvLLsIim9fbCAkLZ0ByCsuX/gzALvcXdULiQPR6PbHxA8jM2OGphjskIZJ7zhpIUCuispHR\nJ56M0z+ABd993WLbqDh/jHpBuZ8WW7P0p4WAJloC3QHWheU1bMwpYVJycLPXNT4xmSkXXc5nM98l\nP/cAb730DPm5+3npXx9w3oWX8e/XX2LLhnV8+O6bnDB6HMOOECQ9dPhIamtq2LFVs5Ss/W05RfPf\n4MmzYmj46j5qlrzLlWNi+Oc1oxhsLcEndRKbRSzvLs1k64EyrhwTTWyU5q7cn6MFhn7/9ZeUlZRw\n2bV/OOLz01liEzSB0TQYtxE/q5F7z06htE5H0LnTiU8ayI/bcllmP5Hwa15gbpaeT37L4ovV2dzy\n4Wpe/zWPsDHnkUUIM3/dzTcb9nFyUjBxQT4t9t0aAYFBxCcms+a3Zc3GC/JyWbJwHmclWHnh0uHc\ndmoiZw4KI9zvyD8WBg0djsPPj7OmXnjEeUOGj2jmpuoMjZaczz94T7ufpllaklK0lPT07Vu9Ps5p\nM7X5/lcojkf6dSCuyaBrluXjZzPirDbiYza02/IQ4GOioqaKUF9LuzJuDifK3wpYPS4lp0374t97\nsKrNmgxDho/g07nzqe5gKXUt4LZ7BAtolhaAwYMHc/21vyP7YPPYhdQhw/hh3lxKS4rJ2n3IvdGU\nsRMmMvuTD6itqfFUwm1MUY1PTGbbpg0kpwxBr9c3S409EgaDgdPOnsJ/586muqrK09MGtF+rJ0Q7\n+bV4OCBY+rMWU1NUmO+xtCzZmY9Eyzg6nFv+9FfmzfmCh/9yGyuW/swlV1/PsBGjiY0fwPKlP3Pz\nVRdQWlLMXx975ohrHHqCFhuxcd1qBg87gbUrlxETF8/wpBjOnnoRH/zrDYoPFlFdXcWSl24lMTWN\nNz6cTePvCbvFwNpaLXU7JzuLvNz9vPXSsyQOHMTIsSe263nqKLHxmitnT2YGg9JadisfFO5LwP7l\nyIETuP2LLRSU1zAg2IeU+kw+e/1JXn3ldQaNOpGXPp3PGnsY5lNv5Z1fstDrBLEBNq+xLG0xcuyJ\nzP9mNg0NDej12udw7pefUF9f3yyQuD34Op38b0Nmhzq4d5aAwCAiY2JZsXQxoH1WAHdzRp8WwbgK\nheLI9GtLS6OVpSmRTisBbQTSNqWxl0h73UKHo9OJFjEwPmYDSSF2ovytOG3GVsVFqK+ZmEBbh2Nj\novytnRJYrTFkyBAMBgPPPfccfjYzBn3zBTV+EW/fspGszAxi4lq6dcaedArV1VWsX/Mbu3Zuw+Zj\nJ9RdYTd+QBJ7s3azN2s3QSFhnotSeziSi2h4mAWDI4jUiVMpqYGHP1+O/cInqAgaTINLsnhHPkkh\ndiK8uPGiYuO44PLf8eviRfg6/Zn+V632idM/gAefeoHSkmJiExKZdMY5R1xfeGQ0gcEhbFynBX6u\nXbmcEWPGA3D2+RdRX1/Pgm/n8Pi906mrq+dvL7yG3WLCbjFgt2i/KSKiNNHy/BMPcNMV0zCbzTz+\n/Gs9VssjOjYenU7Hjq2bWp1TuPRT7MUZmPSCe84cyEuXDeeuay4g0CT51yvPoK+tYMkr0wle9TbP\nXZzGv68bxaxbTuSVK07w1JnpCCPGjKestNRzkZdSMvuT9xkxZjzxA5I6vL+jIVgaGTpME66xCYk4\nfP08xx+QnNKqpUWhUHin34oWo8F7LZWOlsUWQhAT2H21V5quw9/HRHSAjUERvkQHNI+5cdqMhPha\nMBv0+FnbF0BrNGgBwE5b+0VZe0hJSaG0tJRzzz0XIQTOw57X1CGaCX3F0sWUlhR70p2bMmrcBPR6\nPSuWLmZX+g4SEpM9F924Acm4XC5WL/+lRc+htjiSiyjGVIlsqMM84VoibnqLjfl1oNOzXp/IHz9c\nRUZ+BacMbL3q8c133k1s/AAe/NsLzWp5TD7nfO5/8jn+9tKbbV78hBAMGTaCTevWkJm+g+KDRR7R\nkjI4jbgBSbzy7OP88vMP/PmBx4n28twFh4ZhsVjJ3r2Lm+64my8X/OKx4PQEFquVMRMm8t9vZjfL\n+GqksrKCrN27mOizn3euGcXE5GB0QmAym7nx9j+zduVybr/hckpLinnwiWdIDfclxGHpkuWv8Tlb\n89sypJT88vMisnbv4uKrruv0Po8WQ4ZrLqKmKfQASQNTm9VqUSgUbdNvRYvN1L4Gc8cKTpuJpFA7\nvlYDVlPzIN62rDxCaFaZ5BBHtwuWRqxNXC9axtWhbYHBIYSERTD/m6+AQ+nOTXH4+jFk+EiWL13M\nrh3bm/XRiU/Ufinn5x1o0d25LRpdRN6yiCqLC6jKXMtBlwVTwU6KP/oz+9+7nSlhZViNeixGHScn\nti5awiKimLt4FWdOuaDFtiuvv5lhI9sXID30hFFkpu9g8SKtB01jYKkQgnOmXUxZSQljJkxsNUZF\np9Px5gdf8uWCX7jj3oeaucF6ivMvuZKcrD2sXbm8xbZdO7YjpSQ5ZXCLbRde/jtCwyNZv/o3rrju\nRpJTh7SY0xkiomIIj4zizRf/zoTBsfzftZfg6+fkjHOndcv+e5LGGjWDD3O1JaYM4mBhAYX5LVOb\nt23ewPz581uMKxTHO/1WtPRFjHodsYE+JAT5NLMIWYytW1uE0CrchvhajlpzNaNeR8RhwY6pQ9I8\nabJN052bMu6kSWxat5r8vAMkNCnY1bRwXkctLdC6iyg/7wCF37/KAycHMzngIMU52vpGRfvxyhUn\nMOP6Mfi34SrsDuHbWPPj4/feITA4pJk15aIrruXUM8/liRdeP6LVZtS4Ce1qmNhdnHb2FKw2H76Z\n9WmLbTu2aW6jJC+ixWQ2c88jTzH0hFH8358f6NY13XDLdIYMH8mUiy7n3sf+zgdfLzwqAq6rDBs5\nhjvufZipl1zZbDzJ3R5gZxMXkZSST2e+y++mncG9997j1dKlUBzPKNFyDOJNfIT4ere2RDqt+HSi\nYFxX8fcx4bAcOm6K20UkhGiW7tyUsSed4vkSTkhM9ozbfOyeAl4hYR2ztIDmIvJz+vPzwu+bjRfk\n5+GqLGZYYqSnizRowZE6IY7a8zbYneaad2AfI8aMbyaEQsMjeOXfH3viVo4VbDYfzjj3fBZ8O6eF\nBWvnti1YrLYWqdKNnDnlAj6a+4PX8vhd4Yrrb+LtD2fxwN+e53d/uLVTsSy9gV6v56Y7/oJ/QPNe\nZo1pzwu+/Yp1q1awe1c6f7nlOp5+6G7GnDiRH35YdFRjbxSKvoD6RPQRLEZ9i1iSIIepTUtBTxLh\ntHrcRIPcwbjhkVGYLd4DLYeNGI3FqsUHDUhqXhq98QIU2glLi8FgICllUIuCaIV5uVhtPth87AxO\nO8Fz0Witp1RP4evnJN4t0hpjM/oC5196JeVlpfy0YF6z8R1bN5M4MFVdULtIYHAIsfED+PKjGVx7\n4VmcP2kUP83/jrsefILXZ3xGcPDRfZ8qFH0B9a3Th4gOsJES7iA6wEqor7nNehQ9jclwyE3UWM7f\nWzxLI0aTiVHjJmA2W4iIbm5ZaIxrCe2EpQUgKiaOnCbdmQHy83IJDgkFtF+7J046HYPRiMPPr1PH\n6AqNwZh9SbSMGncSYRFRzVxEUkp2bt1McmpL15CiOe3xLH4xfymzf1jGG+9/wSPPvsLH3/7IDbfc\nqQShQtEK/bpOS3/EqNf1WLBtZ/D3MaETAogkIiq6zWJct9/9ILvSt7dIa050+/fDo6I7tY7I6Fjy\ncvc3q9dSmJ9LYHCoZ84d9z7EmedN65ULwpQLL6e8tLTbAlOPBjqdjikXXc57b/6D/NwDBIeGUZCX\nS/HBIo9rQ+EdISAxxE5NnYsDpdWt1mSyWK0kDkztdCdpheJ4Q4kWRZfxsxkZYLDzxfeLMZrbqEaa\nNtxrwbLzL7mS6Lj4VuNh2iIyRnvc/pxsjyumID+v2cU1Iiqm12JHxk88lfETT+2VY3eFqZdcwbuv\nv8jH/3mHO//6zyGOHAAAIABJREFUiCdFV1lajoyf1YjFqMdi1ONrNZBXVkNeacuGkgqFomMo0aLo\nFmwmA6NSYtmRW4bsRI83k9ns6VHUGRrFzt7sPYdES94Bxp98Sqf3qdBijc44bxr/fuMfFObneZ5n\nb5lDCg0hmgfOCyEI9bVQVl1PVW1DL65Moej7KNGi6DZMBh0BPiYKy2uP+rEbL6aNcS3VVVWUlZY2\ncw8pOsdzb7zH24nP8M4rzyOEICQ0HKd/QG8v65jFaTN67a4d6bSSnlfeCytSKPoPKtpL0a1orRN6\n/jh6nSDAbvK0FAgKCcVstpCTrYmWwgKtYFdjIK6i8+j1em67+0HemPk5Dl8/ho8e29tLOmYRAkIc\n3rPnrCZ9i87xCoWiYyhLi6JbMep71tpiNuoIcZjxtRjR6QShDjPZB6sor64nIjqGvVm7Aa0DMEBg\nJ0SL0SCoq++Ej6ufc/JpZ7JgRev9iPoSBr2gvuHIr7FeJ3BJ2cLd6Ws1EOVvo7beRW29i5qGBs9t\nm+nIzVjDfC2UVNbR4FLvL4WiMyjRouh2gh1miipqOxXbciSEgJgAW7NmkAa9jvggH3JLq4mMjvVY\nWhpFS1A7O0Y3PUZCkJ2a+gZyiquOS/EihObKKKyobRGDYfOx99Kquo9Au4lwPwv5ZTXkthIc67QZ\nCfezUO+SZBVVUuPutO5rNRATYEMIgdWkx2rSA+3rDQaaEIr0t1JeU49RLzDodOwvqUIVvlUo2ocS\nLYpux6jXEWg3UVBWi9moI9BdAC+/vKZLIiDC2Xr36lBfCwMS4lm/5jdAyxwCCA4J69AxAnxMmAw6\nTAYdySEG9pVUcbCirtNrPtYQQusd1ehWc7kkBeW1nl/+QkC0vw0/mxGHxUBmQQXVdf3jiqrXCaIC\nrPhaNJER4qs1cdxXXA1o524z6Qn1tXiqJRv0MCDYTs7BKiTSI1i6QmPn+KbkHKxqZbZCoWiKEi2K\nHiHYbsZhMWJvUio/wMdEYUUtuaXVHf5l6Wc1EtBG9d/BAxOZWVJCaXExBXkH0Ol0+AcGtfsYWjzC\noawPnU4Q5W/DoKsmv6zvp6sKoRUoPPyCGWg3k1dWTWF5LVH+VvzclZcNeh1xQT5k5Jf3WYuTQS/w\ntWoCzG4ytGiREWg3YzTokC6wWwxeO1HrdVqndylljzRhDfAxUVpVR1l1fbfvW6HobyjRougRDHod\ndn1z374QgiC7GaNeR1ZhZbv3ZTRoJvW2GDBAa9SYs3c3Bfl5+AcGtShidySCHWYM+pbxCGF+FoSg\nT9fZ0OkgLtDHa78lvU4Q7mclxGFpcdE26nXEBfqQnlfe7e6+nkYISAj28ZrJ05RGy0vb++u5CPNI\nfys7c8tVrItC0QYqe0hx1PGzGjuURRHhtHr9BXw48fFa9+TKwgMUNCnh3x50Os1t0hqhvhZCfY9O\nZpQ3TAZdu54DbxgNggHB9jYbRLa2f4tRT5if94yY7kII7Rx9zHr8fYw4bUZ8zHrMRm0s1NdMfLAP\ngR143wTaTW0KlmMFo15HpPPY71itUPQ2ytKi6BXCfS1U1tR74iW0i5ShhW/fz2ps9y/hRtFSsD+7\nRQn/tgi2m9sUBSG+FoIdZspr6imrru9wsLEQdNpaEelvxagXZBdVUlXbft+a1aQnNtCG0YsFqSME\n2c2UVNVRWdN9xdEi/a04rUaEaL8Vw27WXDhtWb30OtFq6vGxip/NSEi9uU9b9BSKnkaJFkWvoNMJ\nogNsZBVVEu5nweEWJnUNLs+Xtk4H4c72X3icTidOp5PMzEyKCvIYkNz+fi7t7ZYthMBhMeKwGAmy\nm9lfUkVpVctYBItRh4/ZgM2kx2zQYzboqKprILOgosPCxW4xeGKDEoLs5BRXUVx55OBgvU7gazUQ\n6bR2m1sjyu3C6A43kdmow99m7NTaQn0t6ITgQEn1Eea0LUKPRUJ9LdQ1uPpV8LdC0Z0o0aLoNSxG\nPcmhjmZjob4WqmobKKuuJ8zX0mELQUJCAhkZGeTn5RHUzswhH7O+U5YIk0FHbKAPJVV1VNU2eLKO\nLAad19gYH7OBaH9NqHWEMN9Dwq1R7AXZGyisqPGIFx+zAadVs1YZ9aJH4i/MBi2z5khiob2EOixd\nWmOww4zFqPOalm426toM2j6WiXRaVWyLQtEKSrQojjmiA2zsK64i8AgxJq0RHx/P4sWLqaurIzSs\nfe6hrnbN9pbC2upcm5GwhkMXfqtJh9mgp6SqzqsFw2kzumuBNMdq0hNlshHuJ5FSehVJPUGww0xZ\ndR0VXXATWU06T4ZSV3BYjCSHGDhQWk1RRS0Wox6bSY+/zdSjQbM9jRCCaH9bi0wnhULRRdEihNgN\nlAENQL2UcpQQIgD4DIgDdgOXSSkPCu1b5BXgXKASuF5KuaYrx1f0T/Rua0JniI+PZ9asWQDEREW0\nOV8I2i04uotghxmzUYfVeMjCE1rvIre0upnb5/DGe97QXCBH9+IWHWAjPa+8zYqyrRHi232xJjqd\nIMJpJaKfBbEqwaJQeKc7LC2nSikLmty/D1gkpXxGCHGf+/5fgXOAJPffWOAt93+FottoDMYFSIiJ\nanO+o5XaHD3N4cHFJoOO6AAbwY4G6l2a9USvE8dk9otRr611d5P4HKNB4G8zYXa7yKSEooraFhYk\nq0nf7sBqhUKhOJyecA9NA05x354J/IwmWqYB70spJbBcCOEUQoRLKff3wBoUxylNRUtcdCQNbfQR\nclqPrdiH1ir+HmvYzQZCHGYKymsJdpgJsrd0yfiYDYQ1uCitqsOg12mC5ii5sRQKRf+kq98gElgg\nhFgthLjZPRbaRIgcABoDCyKB7CaP3esea4YQ4mYhxCohxKr8/PwuLk9xvJGQkOC5HRYW1uJXfWP5\netCykxwWFdbVWUJ8LQwMc7g7e3u3VmktHcz4WY1YjHrl9lAoFF2iq9/YJ0kpc4QQIcBCIcS2phul\nlFII0SHHt5Tyn8A/AUaNGqVC6BUdIjY2FgAfHx8cDge6mnoKy2vxMeuJcFoxG3QUVtSSX1aD3dyy\nrLuiY/TFtGKFQtF36ZJokVLmuP/nCSG+AsYAuY1uHyFEOJDnnp4DRDd5eJR7TKHoNiwWCxEREVit\nWmCmj9lAbJCtmcUlyG4mwGaiXqWVKhQKRZ+i0+4hIYSPEMLReBs4E9gEzAWuc0+7DvjafXsucK3Q\nGAeUqHgWRU+QmpraLLbFW+CnTicwGVR8hUKhUPQlumJpCQW+cvuyDcDHUsr/CiFWAp8LIf4A7AEu\nc8+fh5bunI6W8nxDF46tULTKjBkzensJCoVCoegBOi1apJS7gGFexguB072MS+C2zh5PoWgvUVFt\npzorFAqFou+h7OMKhUKhUCj6BEq0KBQKhUKh6BMI2R0tW3sIIUQ+WlxMRwgCCtqc1f9Q5318oc77\n+KKj5x0rpQzuqcUoFL3FMS1aOoMQYpWUclRvr+Noo877+EKd9/HF8XreCsXhKPeQQqFQKBSKPoES\nLQqFQqFQKPoE/VG0/LO3F9BLqPM+vlDnfXxxvJ63QtGMfhfTolA0RQhxPXCjlPKk3l6LQqFQKLpG\nf7S0KI5hhBC7hRCTe3sdxztCiDghhBRCqDbXCoWiz6BEi0KhUCgUij5BvxEtQoizhRDbhRDpQoj7\nens9PYUQIloI8ZMQYosQYrMQYrp7PEAIsVAIsdP937+319pRhBBThBDrhBDFQohfhRBp7vG/CiG+\ndN/WCyHWCiEyhRCvCiHihRCrhBClQogqIUSOEOJvQgh9O495kvtYxUKIbLc7CSGEnxDifSFEvhBi\njxDiISGEzr3teiHEL0KIf7gft0sIcaJ7PFsIkSeEuK7JMWYIId52vy5lQojFQojYJttPFEKsFEKU\nuP+f2GTbz0KI54QQBUKIBiFEufu93vh6Z7vXUCKEWC+EOOWwxz7pXmuZEGKBECLIvXmJ+3+xe5/j\nO/Oa9SRCiLvc7/FNQohPhBAW9+u9wv05/0wIYertdXYHQoj33O+bTU3GvH6m3U1nX3U/BxuEECN6\nb+UKxdGlX4gW9wXqDeAcYBBwpRBiUO+uqseoB/4ipRwEjANuc5/rfcAiKWUSsMh9v88ghDgBeA/4\nIxAIvAPMFUKYgU+Bc4XWVXw6sA0IBz4GngVcwCfAR8DLaB3Hb2zHMWOB74HXgGBgOLDOvfk1wA9I\nACYB19K8yedYYIN7rR+71zgaSAR+B7wuhLA3mX818CRakbB17rUihAgAvgNede/rJeA7IURgk8fe\nCvwDsAOrgbPQXt+VgA34CngbuBuYJYRoWlTsKve6QwCTew7ARPd/p5TSLqVc1tbzdTQRQkQCdwKj\npJRDAD1wBdrr/Q8pZSJwEPhD762yW5kBnH3YWGuf6XOAJPffzcBbR2mNCkWv0y9ECzAGSJdS7pJS\n1qJdQKb18pp6BCnlfinlGvftMmArEIl2vjPd02YCF/TOCjvNzcA7UsoVUsoGKeVMoAYYJ6XcA6wB\nfg+c577dAKxAa845DPgT8G9gMtoF/op2HPMq4Acp5SdSyjopZaGUcp1bBF8B3C+lLJNS7gZeBK5p\n8thMKeV/pJQNwGdANPCElLJGSrkAqEUTMI18J6VcIqWsAR4Exgshot3ns1NK+YGUsl5K+QmaKJvq\nfpweqAOellJWuY+VivZ6u9C6pz8AXCClXAisQuum3sh/pJQ73I/9HE2Y9RUMgFVocTc2YD9wGvCl\ne3tffJ97RUq5BCg6bLi1z/Q04H2psRxwCiHCj85KFYrepb8E4UUC2U3u70X7JdyvEULEASegXbxD\npZT73ZsOAKG9tKzOEgtcJ4S4o8mYCYhw3/4YeATtIv83IAfNMlEJ+KNd0ASaNWI8zd8PrRENZHgZ\nDwKMNG8hsQftfdZIbpPbVQBSysPHmlpaPOuRUpYLIYrc5xZBy1YVTY9lBUqA/wghhgGl7rWFAgHA\npWgCx08IUeze9lOTfR1ocrvysDUds0gpc4QQLwBZaM/lAjQrU7GUst49bS/NX5P+RmufaW/fd5Fo\nnwGFol/TXywtxx1u18Ms4E9SytKm26SWx97XctmzgaeklM4mfza35QGgGE1M5AInA/vc4/VoFpkg\nYAiwVUrpK6Uc3M5jDvAyXoBm3YhtMhaDJpQ6S3TjDfdrF4B2DvsOO87hxxLu+29JKU9AO9eoJuv/\nQErpRLuYO6WUPlLKZ9qxnmP6/eGO35gGxKMJOx9auk+OG/roZ1qh6Hb6i2jJoclFAe1LvSsXmGMa\nIYQRTbB8JKWc7R7ObTQRu//n9db62oHRHVTZ+GcA/gXcIoQY6w409BFCnOeOYwEYiiZQdgJmNJfg\nK4ADWIjmvkkGcoQQA4QQk9qxjo+AyUKIy4QQBiFEoBBiuNvl8znwlBDC4Y59+TPwYRfO+VyhBf2a\n0GJblksps9HcO8lCiKvca7gcLS7rW/fjaoCDUsoV7vur0KwluWjWh6lCiCuBPPdzeYoQIoq2yUdz\nLyV04Zx6ksloLrh8KWUdMBuYgOYKabQQ9+vPOa1/po+r7zuFoin9RbSsBJLcmQUmtHiEub28ph5B\nCCHQYje2SilfarJpLtCYsXId8PXRXlsHmIdm8m/8e0xKuQq4CXgdLcAyHbi+8QFSyvvd2y3Au8CP\nUsqr0VwhX6G5kr5GCzD9Ei1Q94hIKbPQ4j/+ghZPsA4tPgbgDqAC2AUsRXNPvdf5U+Zj4FH3cUai\nBesipSwEprjXUAjcC0yRUjZ29K0FioQQA933B6G5eeYCZ6BZI55Cs8ZkA/fQjs+1lLLS/bhf3NlH\n47pwbj1BFjBOCGFzv+dPB7agvd6XuOcc6+/zrtLaZ3oucK1b3I8DSpq4kRSKfk2/qYgrhDgXLXNE\nD7wnpXyql5fUIwghTgL+B2xE+6UMWiDmCjTrQAxaTMRlUsrDA/v6Be603rullFOEEAlogdcBwFrg\nd+5g12MGIcQMYK+U8qFOPn44mlAzoYmoG9CESb9+vYUQjwOXo1nY1qJlhEVyjL/enUEI8QlwCodc\noI8Cc/DyGrtF3Oto7rJK4Aa36Fco+j39RrQoFMcqXRUtCoVCodDoL+4hhUKhUCgU/RxlaVEoFAqF\nQtEnUJYWhUKhUCgUfYJjurhcUFCQjIuL6+1lKBQKRZ9i9erVBVLK4LZnKhR9i2NatMTFxbFqlQqK\nVygUio4ghDi8yrJC0S9Q7iGFQqFQKBR9AiVaFAqFQqFQ9AnaFC1CiPeEEHlCiE1Nxp4XQmwTQmwQ\nQnwlhHA22Xa/ECJdCLFdCHFWk/Gz3WPpQoj7Dj9Od1Nd10B1XUNPH0ahUCgUCsVRoj0xLTPQqi++\n32RsIXC/lLJeCPEscD/wVyHEILQS+oPRmpz9IIRIdj/mDbSy43uBlUKIuVLKLd1zGi2pqXORfbCS\nEF8zwXYzQgjqG1xU1GhCxmzUYTbo0IpLto2UksraBhqkxNdi7Kll9xj1DS70OtHu81X0berq6ti7\ndy/V1dW9vRRFD2KxWIiKisJo7HvfSQpFZ2hTtEgplwgh4g4bW9Dk7nIO9QKZBnzqLqudKYRIR2ts\nB5AupdwFIIT41D23x0SLtk7ILamhpLIOiSZkmiIE2Ex6nDYTflYjel3LC3p9g4t9xdWU1dThcj88\nOsCK02bqyaV3CSkl5TX1lFTVUVXbQG2DC5dLE2rhfhYcfVB0KTrG3r17cTgcxMXFKaHaT5FSUlhY\nyN69e4mPj+/t5SgUR4XuyB76PfCZ+3YkmohpZK97DLRmbk3Hx3rbmRDiZuBmgJiYmG5YHlQfJlYa\nkRIqahqoqKliX3EVAT4mQn0tHvFSU9/A7oJKauubP37vwSoEAj/bsXfxzyurJr+sxiOwmlJT52J3\nQSV2i4EofytGvQpp6q9UV1crwdLPEUIQGBhIfn5+by9FoThqdOmqJYR4EK2Z2UfdsxyQUv5TSjlK\nSjkqOPjolRmQEgrLa9mRW0ZxZS0VNfVk5FW0ECyNc7MPVlJaXXfU1tcWUkr2Hqwkt8S7YGlKeXU9\new9WHZ2FKXoNJVj6P+o1VhxvdNrSIoS4HpgCnC4P9QLIAaKbTItyj3GE8WOK+gZJdlHbF3QpIbuo\nkgHBdixG/VFYWes0uCR7Cis88Trtoby6nvyyGoId5h5cmUKhUCgU3UenLC1CiLOBe4HzpZSVTTbN\nBa4QQpiFEPFAEvAbsBJIEkLECyFMaMG6c7u29N7H5YKsokoaXL3Xv6muwcWu/PIOCZZGckurqapV\nGVaKnsFut/fYvmfMmMHtt9/udducOXN44okneuzYrTFjxgz27dvnuR8XF0dBQUGn93fKKad4imtO\nnjyZgwcPdnmNCkVfpz0pz58Ay4CBQoi9Qog/oGUTOYCFQoh1Qoi3AaSUm4HP0QJs/wvcJqVskFLW\nA7cD84GtwOfuuX2emjoXew9Wtj2xJ45d30BGfnmrMTttIWXviy6Fort57rnn+L//+7+jftzDRUt3\ncs011/Dmm2/2yL4Vir5Ee7KHrvQy/O8jzH8KeMrL+DxgXodW10coraont7SaUF/LUTtmVW0DmQUV\nXRYctfUuCstrCDmKa1ccXR7/ZjNb9pV26z4HRfjy6NTBHX5cfn4+t9xyC1lZWQC8/PLLjB8/noSE\nBNatW4fTqZV8SkpKYunSpeh0uhbzJ0yY0Or+d+zYgdlsJigoCIAvvviCxx9/HL1ej5+fH0uWLGHG\njBnMmTOHiooKdu7cyd13301tbS0ffPABZrOZefPmERAQwLp167jllluorKxkwIABvPfee/j7+3sd\nX7RoEatWreLqq6/GarWybNkyAF577TW++eYb6urq+OKLL0hJSaGiooI77riDTZs2UVdXx2OPPca0\nadOoqqrihhtuYP369aSkpFBVdchNff7553PyySfz4IMPdvg5Vyj6Eyp9pJvIK60hp7iKQ+E9PUdd\ng4vdhV0XLI0UlNfiUtYWxVFg+vTp3HXXXaxcuZJZs2Zx4403otPpmDZtGl999RUAK1asIDY2ltDQ\nUK/zj8Qvv/zCiBEjPPefeOIJ5s+fz/r165k795BHetOmTcyePZuVK1fy4IMPYrPZWLt2LePHj+f9\n97WSVNdeey3PPvssGzZsYOjQoTz++OOtjl9yySWMGjWKjz76iHXr1mG1WgEICgpizZo13Hrrrbzw\nwgsAPPXUU5x22mn89ttv/PTTT9xzzz1UVFTw1ltvYbPZ2Lp1K48//jirV6/2rNff35+amhoKCwu7\n4VVQKPoux3TDxL5GUXkttfUuYgJsXmu+dAdSSrKKKqlv6D6R0eCSFFXWEmRXQbn9kc5YRHqKH374\ngS1bDpVnKi0tpby8nMsvv5wnnniCG264gU8//ZTLL7/8iPNbY//+/TTNOpwwYQLXX389l112GRdd\ndJFn/NRTT8XhcOBwOPDz82Pq1KkADB06lA0bNlBSUkJxcTGTJk0C4LrrruPSSy9tdbw1Go85cuRI\nZs+eDcCCBQuYO3euR8RUV1eTlZXFkiVLuPPOOwFIS0sjLS2t2b5CQkLYt28fgYGBrR5PoejvKNHS\nzZRX15OeV46v1YDNaMBq0mMydJ9Ba19JNZWdCLpti4LyGgJ9TCqFUtGjuFwuli9fjsXS3B05fvx4\n0tPTyc/PZ86cOTz00ENHnN8aVquVkpISz/23336bFStW8N133zFy5EiP9cJsPiTQdTqd575Op6O+\nvr5L59iUxv3q9XrPfqWUzJo1i4EDB3ZoX9XV1R4LjkJxvKLcQz1Abb2LgrJasooq2X6gjMyCCipr\nu/5FWFRRS1F5bTessCV19ZLiymOn7oyif3LmmWfy2muvee6vW7cO0OqNXHjhhfz5z38mNTXVY01o\nbX5rpKamkp6e7rmfkZHB2LFjeeKJJwgODiY7O/sIjz6En58f/v7+/O9//wPggw8+YNKkSa2OAzgc\nDsrKytrc91lnncVrr73mcSWvXbsWgIkTJ/Lxxx8Dmvtqw4YNnsdIKTlw4ABxcXHtWr9C0V9RouUo\nUF6tFarLLKjgYEUtNfWtW0pcLkldQ/NsICklB0qqyenhgnD55TU9un/F8UVlZSVRUVGev5deeolX\nX32VVatWkZaWxqBBg3j77bc98y+//HI+/PBDj2sIOOJ8b0ycOJG1a9d6BME999zD0KFDGTJkCCee\neCLDhg1r9/pnzpzJPffcQ1paGuvWreORRx454vj111/PLbfcwvDhw5sF0R7Oww8/TF1dHWlpaQwe\nPJiHH34YgFtvvZXy8nJSU1N55JFHGDlypOcxq1evZty4cRgMyjiuOL4RRyNwtLOMGjVKNtYp6Cgl\nlXVkFfVOKnJ7MOgFFqPmOjLpdUgk5dX1VLrrpvhajATaTZgNOrKKKjtVh6UzxATYjsn2BIqOsXXr\nVlJTU3t7Gb3C9OnTmTp1KpMnT+7tpXQb06dP5/zzz+f0009vsc3bay2EWC2lHHW01qdQHC2UbO8l\n6hsk5Q2tu4xKquooqapDCK2eytEiv7xaiRZFn+aBBx5gxYoVvb2MbmXIkCFeBYtCcbyh3EPtpLC8\nhh+25PLZyqxuiU9pL10VLA0uSX5ZDRtzSsgtrW5zflWt65jqqaRQdJTQ0FDOP//83l5Gt3LTTTf1\n9hIUimOCfmtpKfASn7G7oIKv1+dQWF6LyaDDbNAR7mdlZKw/yaEOr2nKq/YUMfPX3ewuPORqWptd\nzGNTB/d6z6HWyC6q5NeMApbtKmRPYSX17hosep3gvKHhXDk6Brul9Zc+r7QGX4uytvR1pJQqG6yf\ncyy79xWKnqBfxrQUV9ZywhMLCfW1MDTKj4GhDlbuLmJFZhEWo47YAB9q6huoqXeRW1qNS4LDbGBC\nYhBXjYnB38cEwMItB3j9p3Qi/W1MTglhRIw/WUWVvLhwO2lRTh4+b1C3pjN3lbzSap6dv40duVod\ni9QwB4Mi/AjztRDiMLNsVyELthzAx2TgxpPjOS0ltNV9xQf7YDf3W03b78nMzMThcBAYGKiESz9F\nSklhYSFlZWXEx8c326ZiWhT9lX4pWkqq6vho+R4W78hn074SKmoacJgNTB0WwZS0cBxNrAjl1fWs\nzT7Ib7uLWLqzAKNex6Ujo6h3ST7+LYsRMU7uOzsVq+mQVWXR1lxeXrSTUbH+PHBuKkZ97wuXnbll\nPPndFmrrXVw1NpYJAwIJ9FIsLrOggrcXZ7B1fylPXTiUoZF+XvfnY9aTENxzDe8UPUtdXR179+6l\nurptl6Ci72KxWIiKisJobG4ZVaJF0V/pl6IFDmUPNbgkOcVVBNvNzYSHN/YVV/HeL5msyCwC4LSB\nIdxxWiIGL6Lk+037efPnDM4dGs6tkwZ0ao3dxYrMQp6fvx0/q5FHpw4mJsB2xPlVtQ386bO11Da4\neOXyE/C1encFDQjxwWZS1haFoq+hRIuiv9Lvr0h6nWjzIt5IhNPKQ+cNYv3eYg6UVHPmoNBWTevn\nDAnnQEk1s9fmkBRsZ/Kg1l0tPcn3m/bz1s8ZJIbYeXjKIPxtpjYfYzXpueesFO75cj2v/bSTB85J\n9XqeheW12AL6/VtEoVAoFH2E3vdrHIMMi3Jy1uCwNmMBrh0fx7AoP95cnM6O3LYrYXYnUko+XZnF\nmz9nMDLWn6cvHNouwdJIYoid68bHsXxXEd9vOuB1TklVXbc1ZVQoFAqFoqso0dIF9DrBPWel4G8z\n8ffvt1J4lCrKuqTkn0t28dGKLE4bGMKD56Z2KpPp/OERjIjx571fMimpapnmLCUcrOyZtgEKhUKh\nUHQUJVq6iJ/VyAPnplJeU8/dX24gs6D1DrTdxRersvl2434uGB7B9MlJXmNu2oNOCG48KZ7aehff\nrN/ndU6xEi0KhUKhOEZQoqUbGBBs55mL0pBS8tdZG/nNHcjbE6zaU8RHK7I4JTmY30+IR9fFdNbo\nABvjEgL5duM+r0XzqmpdVNUenRYCCoVCoVAcCSVauokBwXZevHQYkU4rf/tuC4/O3cSHy/ewIrOw\n2y76+4pPJIy2AAAgAElEQVSreGHBduKDfLjt1MRuq79xycgoKmoa+G8rsS1FytqiUCgUimMAlRrS\njQTazfz9oqF8uHwP6/cW88XqbE/hugtOiGRKWninU4graup5et5WdAju72QMS2skhzoYHu1kzroc\npqRFtCiYV1xZS7ivBZ2XisEKhUKhUBwtlGjpZixGPTeenABAdV0D23PLmLM2hw+W72HO2hxOGRjM\n4Ag/BkX4tsj2aXBJMvLLKa2qY3i00xOrsqewgr9/v40DpdU8MmUQYb6Wbl/3JSOjeGjOJhZty+Wc\nIeHNtrlcUFpdh7MD2UkKhUKhUHQ3SrT0IBajnmFRToZFOdmRW8bnq7KZvzmXbzbsByDIbiLU10Ko\nw0JNg4sN2cWU1dR7tp03NAJ/m5G3l2RgMep56oIhDI7wXsG2q6RF+pEcamfWmr2cOSisRR+mvLIa\n/KxGVRJeoVAoFL2GEi1HieRQBw+dN4i6BhcZ+eVs2VfKnqJKckur2ZBTDMDo+ABGxPhjNuj4dsM+\nZi7bDUBKmIP7zk7xWpa/uxBCcOnIaJ6at5X/7cznlIEhzbbX1LkoKK8l2NFza1AoFAqF4kgo0XKU\nMep1pIT5khLme8R54xICySyoYE9hBRMSg45Kf6Mx8QHEBdr4fFU2E5ODW2Qm5ZZW47QZj4leSwqF\nQqE4/lBXnw4gBBj0R889Eh/kwykDQ46aSNC5rS3ZB6tYllHYYruUcKBENeBTKBQKRe/Q5tVQCPGe\nECJPCLGpyViAEGKhEGKn+7+/e1wIIV4VQqQLITYIIUY0ecx17vk7hRDX9czp9AxOm5GYABup4b4k\nhzqwGI99rWc0CALtJqIDrCQE+5AS7iAm0NYiM+hwJiQGEeFn4fPV2XhrpllcWUd5Tct6LgqFQqFQ\n9DTtufrOAM4+bOw+YJGUMglY5L4PcA6Q5P67GXgLNJEDPAqMBcYAjzYKnaONw2Ig0t9KbJCNASE+\nxAXZCPE1Y7cY8BZjGuG0EB1gw89mRK8T6HWC+CCfY1a4OCwGBoT4kBLmS4TTitNmwsdswKjX4Wc1\nkhxqJ8zP4vVcQWtNcOmoaHblV7B6z0Gvc3IOVqmeRIrjBiklxZW1HCipprC8hrLqOqrrGqhrcHkV\n9gqFoudoM6ZFSrlECBF32PA04BT37ZnAz8Bf3ePvS+2TvFwI4RRChLvnLpRSFgEIIRaiCaFPunwG\n7UQICPezeA1mdViMANQ1uMgtraa4UuvDE+2viZXDMeh1xAX5kFlQQU2dq2cX3gGCHCbC/axHnCOE\nINhhRq8T5Bys8jrn/9s78zg5izLxf5++u+e+c04ukpCD+xZQLrlE0BVF1vU+Vl1dZfW3orKKiLcu\nHut6s4oKiMhCdAVFQe4gVxICBHJnkkzmvrp7+q7fH1U9eTPTPdNzpXsm9f185jP9XvU+9dbzVj3v\nU09VnbOigdv+vofbn2rhpEU1I0YMJVIZWrqjLK4vmzLZLZZikskoIokU0USajFJ4XC68biGWzNAd\nSYxqpDtfjzK/h8V1ITvKzmKZJiYaiNuklGo1vw8ATeb3fKDFcd5esy/f/hGIyAfQXhqam5snKJ7G\n5QK/x4Xf46ahwj/mhGxet4sFNSHqy9OkM4oyf/7H43W7WFQXYnt7pOheh9EMsnzUlvkIx1I5F0r0\nuF286cQF/OCh7Ww5MMCquSODhgdiKdr6YzRNw5wxFstUkkpniCbTxJMZ/F4XIa8bj9tFIpWhP5ak\nbzDJYCLNRJ0mzuvCsRTtA3H7Xlgs08SkRw8ppZSITFmrrZT6MfBjgJNPPnnC6VYGPawJTWxOk0Jn\nm/V73CysDbKrMzqh+0wFInr9oKrgSI/QWMyvCRJNpkimRj7mc1c28vPHd3H/i205jRaA9v44Aa97\nQve2WKaLTEYRTqQYiKUIx1IkUiO9oR63kEpPz8dGe3+ckM895MG1WCxTx0QDM9pMtw/mf7vZvw9Y\n6DhvgdmXb/+0cbjcsxUBL01VxZm7xOXSI4wmajS4XcLCmlDO+Jagz81Zy+t5ZFtHzoUUs+ztiRJL\n2gUVLaVBLJlmy4EBdndG6Q4nchoswLQZLFlaugfz3ttisUyciRot64DsCKB3Avc49r/DjCI6Hegz\n3Uh/Ai4UkRoTgHuh2TcraKwIHHZvg8ctLGsoH7ULqxDK/B5qynJPz3/hqiZiyQyPbuvMe30mAzs7\nI7aCthSdZDrDrq7id9eCXpKjpad4HliLZbZSyJDn24AngJUisldE3gt8FXitiGwFLjDbAH8EdgDb\ngJ8AHwYwAbhfBJ4yfzdkg3JnCwtrg9SUHR7DRQQzgmlqFk2sL/fl9LasnFPBwpog97/YNur1qbRi\nd4k0FpYjk3RGsaszkrOrs1hE42naB+y8RhbLVFLI6KGr8xw6P8e5CviXPOncDNw8LulmECLCgpoQ\nfk982idgW1ATnNJVnv0eHZeSHTWVRUS4YFUT//P4Llq6oyysDeVNI5bMsLsrQkOFn5DPM2LtovHS\nMRAnmtDxCGmlmF8dnNYYAaXUrBvxEU+liacyJFIZlIKakHdoEc7ZRDqj2NkZIVZCI/mytPfHqfB7\nCfqm7n21WI5k7DT+U4wepeSiN5pk0IxYmErqyn3TstpyQ4V/hNECcN7Rjdyyfjf3v9TGe85cMmoa\nkXiaSFy7xP1eF7VlPurKfOMyBpRS7O0ZHCHLrs4ojZV+Giv8U2ZcxFNp+gaT9A+mSKYzLK4rmxWN\nSzSRoq0/Tjh2aCxSW3+MqqCX+nL/rMgnmC6hEjVYQI8saumJclRDOa5JGvIWi8VO4z8tVAS8LKwN\nsaKpgtXzKplTFZi05wGgzO9mbtX0DKUMeN1UBEbasNUhH6curuXBLe2k0oU3DPFkhtbeGFvbwwzE\nRhpDuch+MecynkB/te7qik7JhF7JdIZt7WHa+uIMJtKk0ortHYXLWopE4il2d0XY3h4ZYbCAbkB7\no0m2tYdp6Y6SHEd5liLxVJrtHeGSNViyxJMZ9vUO2onoLJYpwHpaphm3S0/mVlfmoyuSoG8wQSyZ\nGfecENUhL/Org9PahdFQ4WcgR2N34eomntjRxQMvt3Ph6jnjSjOezLCrM0rI76a+3D8UsJxKZ+iP\npYjEU2SUIqP0pHVjBfSGY9qLMGeSxltrb4zMsFspBbu7ouOe86aY6Nlak3RF4gwmCm+8e6NJ+mNJ\nGsr91Jb5Dlu3UXt/jLgpY6VAcfBFcIngcetZp12S/QOfx0XQ6x7S/VhSe8i6wqNP+lZK9EaTxFMZ\nmmvHXkrDYrHkxxothwmXMV4aKvykM4poIkUsmSGR1g21AOUBD+V+HQ/SHUnQFU6QUeqwNaJlfg8h\nv5to/NAhzCcuqmHVnAp+8fguXrW0nvIcHpmxiMbT7IlH8Xlc+DwuIvHUhCfz6hiIE/RNfH6YATOh\nWC6Ugv29MaKJNPOrgyXr0s9kFN3RBB0D8QkP381koK0/TvtAnKqgl7pyHyHf9FUJLd3RvF60sRDR\n3kClVMl7VvIxmEizrT3Mwtrpjc+yWGYzUsouy5NPPlk9/fTTxRajaCiliKcyUxp0OxYDsWTOyfJ2\ndIS55o4NXLJ2Lh98zbLDJk8+XC44qrEcv2d8zyaTUWxtDxc0RNvvddFcGzqszz9LNJGipXsQESj3\ne6gIeFBoz1UinaF/MDnlc41kR6VNdhj9cPLFKR2piEBzXYjKaTRcROQZpdTJ03YDi6VIWD9lCSMi\nh73BrAjkHumwtKGcS9fO5d7NrezoCB9WmXKRyegv98w4uwc6wvGC55SJJ3Xcy87OyJjrz0wVSina\n+2Ps6NBz38STGbrCCXZ1RtndGeVAX4zucGJaJkdTCvZMcaxLJqPYMwkPy2xEKdjTFbWrpVssE8Aa\nLZYRNFTk7op62+mLqAh4+eFD28mUgIduMKEDHAulJ6K7U8aDUjqOZl/PIC+19rOjI0z7QIzBRJpE\nKkMsmWYwof9iyTTxVHrchlSWgViS7R0R2vrjE+46myx6zp2pCXaOJdNs6wjTP2gb5+EoBbs6I6PO\nNm2xWEZiY1osI6gKegl4XSNiB8r9Ht51xmK+88BW/vh8K5cdO69IEh6kN5ok5IuPGfPTGY7T2ju5\n+XOUyg7rTtNGfuNHx1+4CPp0jFJlwJMzgFopRTKtiKfSdAzEicRLYzmEwUSavT2Do87LMxZ90SR7\ne6Mjgp1nIi09Uf78QptZINTPnMoADRV+KoNeqoM+yv2eoQBij0sKDpZXSs8mXVvmoybkG/KqhuMp\neiIJFtRMb+C9xTITsUaLJScNFX5aukd6Mc5b1cjjOzr56aM7WVJfxpp5E1uUcipp7YsR9LnzBpG2\n98do6x+fh2UyKKW9QIOJBN3hBB63UFvmI+RzM5hME42nGUymp339m8nQG00iEmVBTeGGSyyZpjea\npHcwUVIz045FOqOHu7+4v58XW/tJZTJUh3xUB71sOTDA8/v6cLuEOZUBntndQ2KU7rPqoJcbrljL\nkvqygu6dyUDnQILOgQQBr4u0UkPPTo8WnJIsWiyzBhuIa8nLK20DOSfHC8dTfOKODQwm09z0luNL\nYniwxy05lzY40Bcbd5eQ5SDVIe+oX/zZ4cd9g8kpn0hxKgjHU2xrD7O1bYC9PYPMqw6wck4li+pC\nbDkwwOPbO3lqZzeRhPZyza0KEPS6h4yvhgo/F62ZwwWrmqgJ+YaGmHeE40P5DsdTpDOKVEbxf5v2\nU+b3cNNbjp90PNqaeZUTHr1mA3EtsxVrtFjy0hWOsz9Pl8rurgifvHMji+vK+PIbj8FbAtPDi8DC\n2tDQUOjWvkE6BxJFlmrmUxX00ljpP6QRjsRTtPXHSqZLK4tSih2dEZ7a1c1Tu7rZ2hYemgmmJuSl\nZ1hAcLnfw2lLajlpUQ2r51YeYoBnlEIY34rxG/f28h93b+a8oxv5+AUrJpUXa7RYLCOx3UOWvFSH\nfLT2xXIGhS6qK+Pj56/gq/dt4fsPbuNj5y8vev97dlRGU6WfVEbRFbYGy1SQ9Sj4PC7KAx4SqUzO\nGXeLjVKKmx/byd0b9iPAiqYKrj61maPnVLC8sYLygIdwPMXWtgF2dkZYUl/GMfOr8k6s55qAPh+3\noJq3nLKQ3zzVwnELqzl3ZeMkc2WxWJxYo8WSF7dLci6kmOXMo+q5+pSF3PZUC02VAa4+tfkwS5ib\nwxm/ciSRSGXoLmFD8M5n93L3hv1cvGYObzutOecaXeV+Dyc013BCc820yXH1Kc1s3tfHf/9tGyub\nKphXHZy2e1ksRxrF9+lbSpqastEXZ7z61GbOO7qRW/++h7++1Dbl909nFP15Zq+1WLLc/+IBbnli\nN69e3sCHzlk2LYuKForbJXzywpW4XcK3/7p1xiw1YLHMBKynxTIq5X4PPo8r74RsIsJHzj2KrnCc\n7z24je5IgjXzq1iaIyi2UFp6ovzi8V3s7RmkrT9GKqM47+hGPvSaZdMy2V48laYnkpz0ekalRCSe\nYtPeXvb3xdjXO0g8meHcoxs4sblmQt0epcxj2zr5rwe3ccLCaj5+wfKSyF99uZ8PnL2Mm/7yCus2\n7uONJywotkgWy6zAGi2WMakJeUftcvG6XXz6klVc//sXuGX9bgBcAicvquXdZy4e17DZl1r7+eIf\nXgSBY+dXccbSOuKpNH/Y1Mq29jDXXnz0pOYPyZJKZ3h4ayfrd3Tx7J4e4qkMbzh+Hu8+c0lJNHoT\nJZZM8/uN+7nruX1DM65WB70o4OGtHcytCvC6Y+Zy8do5414CoRS5d3MrP3xoOyuaKvj0JatKIiA8\ny7krG3h8eye/XL+bkxfXsnAc74HFYsmNHT1kGZNEKsPLBwYKOrcnkmBr+wAvtvZz7+YDxFMZXnfM\nXK4+pXnMhRaf3NnF1+97mbpyHzdcvvYQz8dze3r41v2vEE+lue7S1Ry3sHpSefrRw9v5w6ZWast8\nnL60jmQ6w/0vtvGqZXX822tXzLgGfSCW5E8vtHHPhn30DiY5eVENbzpxwdBaQsl0hvU7uvj9plZe\nau2nscLPe85cwquW1RU9gHoiKKW4/akWbv37Hk5eVMOnLj66KGtEjUVPJMG/3Posc6sDfP1Nx+Ee\nx2ggO3rIYhmJNVosBbGzMzLuESO90QS/enIPf37hAAGvmwtXN3HZcfNoKPezeX8fj27tZMuBfhIp\nvQhgdyTBsoZyPv/6NTlXcO4Kx/ncuhfoiSb4zlUn5F1uYCy2tYf5xG83cNGaOXzwNctwiaCU4p6N\n+7n50Z2snFPBZy5dRU0R4yIKZXdXhN9v3M+Dr3SQSGU4bkEVbzttEavmVua9ZtPeXn7yyA52dUVZ\nO6+SK09ayAnN1dPuYdrdFeHmx3YSjqdIpfW8JhmlUEobISGfh8qgR69/5XXjNyuCN1UGWNFUQXNt\niMFkmvXbu3jw5XY27evjvKMb+ei5R+UdAVQKPLK1g6//6WVes6KBj52/vGBvkDVaLJaRWKPFUhDh\neIqdHZEJXbuzM8zvnt3Ho9s6UUpR7vfQH0sR8LpYO6+KkM+DzyPUlfm58qQFo34x7+sZ5Jo7NrCo\nLjSh+WHSGcX/u3MjHeE4P3jbSZQPW9H4sW2d/Of9r1Dmd/PJC1dy7ILJeXQmQ/tAjHK/J+dMv9va\nw9zxdAtP7OjC53Fx7ooGXnfsvIJnYk1nFH9+8QC3PrmH3sEkjWYStcuPmzctHovtHWH+457NuEVY\n2lCO10x77xIh2y5HE2n6Y0n6B1NmHaeMXsvJVFFBr5tkOkMqo2iq9HPp2rm88YT5M8JTdMfTLfxy\n/W6OX1jNpy85Ou/szU6s0WKxjMQaLZaCaZnkar2d4Th/fL6VjoE4py+t46RFNRNqIB/d1snX7tvC\n5cfN4/1nLx3XtX98vpUfPLSdT7x2BefkmUNjV2eEr963hda+Qd56SjNvPmnBYf2ST6Yz3PLEbu7e\nsA+3S1g1p4ITm2tAtNG2pzvK1vYwZT43rz9uHq8/dh6VOTxThd5r/Y4u7tt8gE37+jhtSS2fuXTV\nlHpdXmkb4HPrNhPyefjSG9Yyt6rwIcBKKVr7YrzcNsArBwbweVyceVQ9yxvLZ4Sx4uQvL7XxvQe2\nsriujOsvXzOmJ88aLRbLSKzRYimYZDrDK20DJbEI3o8f3s7vN7XyqYuP5qyj6gu6piea4EO/eoZl\njeXceMXaURu9wUSa/35oG397uYOKgIczl9Xz6hUNrJ5bOa64hPGytyfKN/78Mjs6Ily0uomKgJdn\n9/Swo1N7uWpDPuZVBzixuYZLj5lLmX/qYunXbdzPTx7ZwT+e2jxlc+5sbOnly/e+REXAw5ffcAyN\nlbNnhNZEeGZ3D1+59yWW1I89k7Q1WiyWkVijxTIuOgbiHOib3GrJU0EyneHTdz3P7u4I33rz8TSP\nMaIoHE9xw+9fYGt7mO9efUJBIzmUUjy7p5cHtrTz5M4u4qkMFX4PxzdXc+LCGmrKfKYbQ09l7/O4\n8bld1Jb5WFQXGlfX1UAsyV3P7mPdpv34PS7+9bzlnL60buh432ASr1sK6laYKEopvv3XrTywpZ3P\nXrrqkPtPJK07n93Lr9bvZn5NiBsuX0N9CaxRVQpkY1zG8hRao8ViGYk1WizjQinF1vZwSSyO1xWO\n8/HfbKDM7+Fbbz4ur9ehN5rg8+teYE93lE9euJIzC/TMOIkl0zy1q5und/XwXEvPiDVshuN1C8sa\nyjlmfhUXrGoaMSvqQCxJZzhBdyTBywf6uWfjfgYTac5e3sB7zlxctEUoE6kM1961ib09g3zjymNZ\nVFdYjIyT7kiCHzy0jfU7ujl7eT0fPXc5QV/pjewpJj95ZAfrNu7n3y9aydnLG3KeY40Wi2Uk1mix\njJtIPMXOzkjONYkON8/v6+O6u5/n1CW1fPqSkbEYneE41929mY5wnM9csoqTFk1++nalFHu6owwm\n0vi9rqHh0cl0hngqQ1t/jFfawrzSNsCWA/1kFBy7oIrjF1SzozPCy20DI1aePm1JLW87bVHBgbTT\nSWc4zr/dsYGMgi9esbYgmcLxFOu3d/HQ1g427e1FRHjPmYt5/bHzZlzsSS58HhcBr55kMZ7KTFr3\nU+kMn7l7Mzs7w3zzyuNyGofWaLFYRjIpo0VErgHeByjgeeDdwFzgdqAOeAZ4u1IqISJ+4BbgJKAL\nuEoptWu09K3RUrp0huO05lkB+nBzz4Z9/PTRnbzpxPm844zFQ4bLgf4Yn/3f5wnHU3zustWsmVd1\n2GXrjiS4/6U2/vzCAdoH4tSX+80CfuU0VgaoK/PRWOEvmmclH3t7olx392YSqQxfuHwNy5sqRpwT\njqd4Ynsnj23vYmNLL6mMYm5VgNesaODclY0zbs0dt0so87txiZBMZ0hnFH6Pm9py34hRZikziil7\nXkbpVaEj8RT9g4VNDdAVjvPxOzaQSGX4+AUrOGNYd5w1WiyWkUzYaBGR+cCjwGql1KCI3AH8EbgU\nuEspdbuI/BDYqJT6gYh8GDhWKfVBEXkr8Eal1FWj3cMaLaXNZEcTTRVKKb7/t+386YUDnL60lmsu\nWEFvNMln795MLJnmhjyN7uEknVGE46mc88+UKgf6Ynz2bm30vf/spZyyuJaqoJdIPMW6jfu5e8M+\nook0TZV+zlxWX9Kjerwewe9xE0+lSaZ0nScCIZ+byqCXcr9nSoZ6ZzKK7R1hYgV2n7b3x/jKfVvY\n1h7mH07QRnc20NsaLRbLSCZrtKwHjgP6gbuB7wG/BuYopVIicgZwvVLqIhH5k/n9hIh4gANAgxpF\nAGu0lDaZjGJHZ5jBRPHjW5RSrNu4n5sf28mCmhDhWIpUJsMXr1jL0obyYos3Y+kYiPP5dZtp6RlE\ngKMay2ntixGOpzhjaR1XnrSgJA0Vr0eoCHjNPDfuQ4Kik+kMsWSaoNc9LUPZY8k029rDBXchJdMZ\nfvLIDu7dfICGCj+nLa7llCW1vOXkBQQnGHhtjRbLbGWy3UMfA74EDAJ/Bj4GrFdKHWWOLwTuVUqt\nFZHNwMVKqb3m2HbgNKVU57A0PwB8AKC5ufmk3bt3T1g+y/STSGXY3hEmlS6BABf0ENuv3bcFt1u4\n8Yq1EwoktRxK2ngPntndw3MtvVQHvVx1ykKWlaAx6HYJi+tD0zrKqhAm0n26fkcXf3mpjedaekmk\nMqyaW8G9H3v1hO5vjRbLbGUynpYa4HfAVUAv8FvgTrQ3ZcJGixPraZkZDCbSbO8o/Mtyuukb1F1W\nM6krxjJ5RGBpQ1nRDZYsuzojDIxz6QvQq45vbOmjocLH5cfPn9C9rdFima1Mxjd6AbBTKdWhlEoC\ndwFnAtWm+wdgAbDP/N4HLAQwx6vQAbmWGU7Q56a5LkSp9BBUBb3WYDnCEIFFdcX3sDiZXxPENYEa\n1u9xc+qSWi47dt7UC2WxzHAmY7TsAU4XkZDoDu3zgReBB4ErzTnvBO4xv9eZbczxB0aLZ7HMLCoD\nXuZVB6dsttjygIfGSj8La4Msqg/h95bugniljNejR8SMtcL2TEYEFtQEqQiUlqHqdbvGtWSBxWIZ\nmwnXZEqpJ0XkTuBZIAU8B/wY+D/gdhG50ez7mbnkZ8AvRWQb0A28dTKCW0qP2jIftWU+EqkMg4k0\nXZE4kXh63Ok0VvppGjbde5nPw76ewaGun6lABMr9HiqDXrxuYW/PYMnE5kwGt0toqPBTV+Y7ZPRJ\nIqVX0u6OJEhnZn4+QZfhwtpQyXrWast89EYTE3oPLBbLSOzkcpZppW8wyYG+GIlUYSOM5lUHRp2z\nZKqWEXC5YHljBT7PQQ9OIpVhV1ekJGb7nQhul1Bf4aO+zD/qUNl0RtE+EKMrnCiZOKSJ4HLB4rqy\nKV1/aTqIp9JsbRt/zJcd8myxjKS033bLjKcq6KUy4KE7kqArkjjEIAj63JT7PbgERGRoezQaKvzE\nU2l6IpPzuDRWBA4xWEDPerqsoZzdXZEZ9WUc9LmoK/NTHfIWNPTY7RLmVgWpCflo648VPBnaVFAZ\n9ODzuBAEEXBKm1aKVFqZydr0hG1KqREz0Iro7sjGSv+UzK0y3fg9bpoqAyWxZpfFMtOxRotl2hER\n6sr1rK/9sSTxZIaqoHeE0VAo86uDxJLpCc8PE/C6qC/35TzmdglL6sto64+PmGq/1Cjzu2msDIxp\n6OUj4HWzqK5sqNuoJ5qY1u6x+grfhGM8Ysk00UQatwgVAc+EPRDFoqHCTzqjSl6nLJZSxxotlsNK\nZcALgbHPGw0RYWFtiG3tYTITsFvm1wRH9UiICHOqAoT8bvZ2DxYl/sPjFubXBFEZ6I8liSS0N8Tv\nceP3uKgKeqesW8TncTGnKkB9uY/tHZGCu/LGQ644pfEQ8LpnhFdlNOZUBVAoOgcSxRbFYpmxWKPF\nMiPxe9wsqAmxpys6rutqyrwFD4utDHhZ0eSmJ5qkbzDJYOLwdBlVBj3Mrw4OzdZaFTo8QaYet4tF\ndaFxzeZaCE1VfhorJmmpzhLmVgVRCrrC1nCxWCaCNVosM5aqoJeGCn/BLveQ3z3u7gmP20VDhX8o\nlmYgliIcSxGOp4Ya9qzTZrINvdcjNFUEqCnL3XV1OAh43SysCbGne3zGYC5cLj2yp7LEhiIXm7lV\nAaKJVEksf2GxzDSs0WKZ0cypCjCYTBMeY+bR8oCHRbWhScVC+D1u/OVu6sv9KBMomg0izpLJKBJp\nPeQ7auQaq7vF4z44RLkU1vCpCnlpSBZuDOYi6HOxsDaE3zOzu3SmAxFhQc3Ue7QsliMBa7RYZjwL\na4Js6wgPrd47nMqgh+ba0JQaBCKCO0dyLpcQcOn4ixqzLxxP0R1OEEmkCHrdhPxugl69iJ/X7Zqy\nCfmmkjlVATJKjasbQ8TMRhzyUuH3lIQBVqoEvG4aK/y09dvAXItlPFijxTLj8bhdLKotY2dnZETQ\nbHXIy4IxAm+nm3K/Z8IjfIrJvOogLpFRPS7Z4cdVQe+MHNVTTBoq/PQNJonN0HmBLJZiMPNqUosl\nB1U7+yYAABTISURBVEGfm2WNZezpig41AtUhLwtrQ0WWbGYzpyqAS6B9IH5IV0a2S6s25LOGygTJ\ndhOV0mKjFkupY40Wy6zB73GzrKGcvT2DuN3C/Gq77stU0FgZoL7cTziRYiCWwud2jVgiwDIxgr6p\nC3y2WI4ErNFimVW4XEJznfWuTDUul1AZ8NqRQNNAVchLU9pPW5+Nb7FYxsIunWuxWCxFprEiQE2Z\nNQgtlrGwRovFYrGUAPOrg1QGrfPbYhkNa7RYLBZLCSAiNNeGqApaj4vFkg9r1lssFkuJoNfVCiI9\nxZbEYilNrNFisVgsJYQeCl3cuYUsllLFdg9ZLBZLiWENFoslN9ZosVgsFovFMiOwRovFYrFYLJYZ\ngTVaLBaLxWKxzAhElfCiFyLSAewe52X1QOc0iFPq2HwfWdh8H1mMN9+LlFIN0yWMxVIsStpomQgi\n8rRS6uRiy3G4sfk+srD5PrI4UvNtsQzHdg9ZLBaLxWKZEVijxWKxWCwWy4xgNhotPy62AEXC5vvI\nwub7yOJIzbfFcgizLqbFYrFYLBbL7GQ2elosFovFYrHMQqzRYrFYLBaLZUYwa4wWEblYRF4WkW0i\ncm2x5ZkuRGShiDwoIi+KyAsi8jGzv1ZE7heRreZ/TbFlnQ5ExC0iz4nIH8z2EhF50pT7b0TEV2wZ\npxoRqRaRO0Vki4i8JCJnHAnlLSLXGB3fLCK3iUhgtpa3iNwsIu0istmxL2cZi+a75hlsEpETiye5\nxXJ4mRVGi4i4ge8DlwCrgatFZHVxpZo2UsAnlFKrgdOBfzF5vRb4q1JqOfBXsz0b+RjwkmP7a8BN\nSqmjgB7gvUWRanr5DnCfUupo4Dh0/md1eYvIfOBfgZOVUmsBN/BWZm95/xy4eNi+fGV8CbDc/H0A\n+MFhktFiKTqzwmgBTgW2KaV2KKUSwO3AFUWWaVpQSrUqpZ41vwfQDdh8dH5/YU77BfCG4kg4fYjI\nAuB1wE/NtgDnAXeaU2ZdvkWkCng18DMApVRCKdXLEVDegAcIiogHCAGtzNLyVko9DHQP252vjK8A\nblGa9UC1iMw9PJJaLMVlthgt84EWx/Zes29WIyKLgROAJ4EmpVSrOXQAaCqSWNPJt4F/BzJmuw7o\nVUqlzPZsLPclQAfwP6Zb7KciUsYsL2+l1D7gm8AetLHSBzzD7C9vJ/nK+Iis7ywWmD1GyxGHiJQD\nvwM+rpTqdx5Tehz7rBrLLiKXAe1KqWeKLcthxgOcCPxAKXUCEGFYV9AsLe8atEdhCTAPKGNk98kR\nw2wsY4tlIswWo2UfsNCxvcDsm5WIiBdtsPxaKXWX2d2WdRGb/+3Fkm+aOBO4XER2obv/zkPHelSb\n7gOYneW+F9irlHrSbN+JNmJme3lfAOxUSnUopZLAXWgdmO3l7SRfGR9R9Z3F4mS2GC1PAcvNyAIf\nOmBvXZFlmhZMHMfPgJeUUv/pOLQOeKf5/U7gnsMt23SilPq0UmqBUmoxunwfUEq9DXgQuNKcNhvz\nfQBoEZGVZtf5wIvM8vJGdwudLiIho/PZfM/q8h5GvjJeB7zDjCI6HehzdCNZLLOaWTMjrohcio55\ncAM3K6W+VGSRpgUROQt4BHieg7Edn0HHtdwBNAO7gbcopYYH9s0KROQc4JNKqctEZCna81ILPAf8\nk1IqXkz5phoROR4dfOwDdgDvRn9wzOryFpEvAFehR8w9B7wPHbsx68pbRG4DzgHqgTbg88Dd5Chj\nY8T9F7q7LAq8Wyn1dDHktlgON7PGaLFYLBaLxTK7mS3dQxaLxWKxWGY51mixWCwWi8UyI7BGi8Vi\nsVgslhmBNVosFovFYrHMCKzRYrFYLBaLZUZgjRaLxWKxWCwzAmu0WCwWi8VimRFYo6UARORdIvLo\nFKUlIvI/ItIjIn8XkbNF5OWpSHs6EZHFIqIcU6jPCETkbSLy52LLMdMRkXNEZG+x5RgPRl+PKrYc\nMxURuVdE3jn2mcVHRHaJyAXm92dE5KeOY28UkRYRCYvICSKyUkQ2iMiAiPzrYZKv4HporHPH02YM\nb7vMM1hayLWFIiLNJl33VKabj6IZLUbJ2s2Ktdl97xORvxV4/d9E5H1TJMsL5qGHRSQtIjHH9mem\n4h4OzgJeCyxQSp2qlHpEKbVyrItyISLXi8ivxjjnIyLytIjEReTnE7nPTCGXYaWU+rVS6sJiylUq\nzETDoxSZyrqnlFFKXaKU+sVUpzvdH0BKqS8rpZzl803gI0qpcqXUc+iV4h9USlUopb47HTLkkKng\nemj4ucON78m0GeYZ7JjItQ55hgxEk+Yek256MukWSrE9LW7gY0WWAaXUGvPQy9FT5GcVvFwp9eUp\nvt0iYJdSKjLWiVP0Uu8HbgRunoK0phXjhSq2Th5WZprnyjJzsLo1xCLghVG2LTMJpVRR/oBdwLVA\nN1Bt9r0P+JvjnFehF0PsM/9fZfZ/CUgDMSAM/JfZfzRwv0nzZfRaHeOV62/A+4btexfwKNpi7wF2\nApc4jlehFzFsRa+2eiPgzpH2e43MaSP3F9Drjewd9lw+BWwC4oDHbO8DBky+zkevO5IAkiatjWPk\n60bg52Oc4wKuQ69z0g7cAlSZY4sBBXwAbQi1otf/yV57KvA00I9eO+U/HcdOBx4HeoGNwDnDnveX\ngMeAQZPXp4fJdQ2wzvx+HXrNmX6gBbjecd4eI2PY/J2RLbuxdMohyxeNLAPAn4F6cywA/AroMvl4\nCmjK8xyvBbabNF4E3jhMlx4DbjJp3Wj2vwd4Ca1ffwIW5Uk7Ww7vNPntBD7rOO5Hr8G13/x92+wr\nM88343g+83Kkf6mReQCtc580+89Brzj9CaMbreg1b5zvwC1AB1p/rgNc5thu4CTz+21G/jWOd+Ju\n8/t69Fo7t5j7vwCcPI539/8Zufab56mAo3K91zn0oqC6g/x1T169mqB+/JdJawtw/jAd/Qrwd/Q7\ncA9QO0w33mt042Gz/3LzLHvN9avM/mUmvyea7Xmm/M4Z/sw4VG970WtgvcrsbzE68U6HnON6T8fz\nDphz347Wqy7gs+h68wKHHv0Krfdhc6+IeeYPDCu/FaPpBiAmz+0mL88Dax3v2jdNftqAHwLBPPIO\npWm2FfBBYKt5nt/n4LI6zvs/7JA/jF6L6xwObTPG0qfh9z3KlHXY8RcFlEMvHjDPthP4NQfb6F+i\n65BBc92/c1DvPA49WofWrW3A+x33v55JvONKqaIbLRegl5zPVtxDRgt6QbQeo5we4GqzXZenEipD\nvxzvNuefYB74anP8H4FNBch1SLqOgk8C70d7hz6ErhizSva/wI+MDI3oCuWfC1Te4Qq4C9iAXno+\nCKw0+ZrnqJiWOV/OAp93IUbLe4ySLQXKTdn80nFfBdxm8nkMuoLLVhRPAG83v8uB083v+WjlvxRt\nFL3WbDc4nvceYI0ptyqjzMsdcj0FvNXxvI4xaR2LrizeMExGT54KqBCd2o6uyIJm+6vm2D8DvwdC\nRgdOAirzPMc3o19cF7qSiQBzHfKkgI8aGYLAFea5rzL7rgMez5N2No8/MdcehzZusw3RDcB6tB42\noI3FL+bStTzptwJnm981HGzQzjFy3wB4TXlGgRpz/BZ0A1phZHwFeK/j2CfM7x+bZ/whx7FrHPoc\nM2m70Y3z+gL1+2KjC2vR+nkrBRotjFF3jFVHMIZeTVA/rjHP+Sq08VLruPc+Rz5/h6kDHLpxizkW\nROtyBP3eedGNzDbAZ655P7qhC6ENhW/myqdDrnebsrkR/d5+H914X4h+b8sn+J6O5x1YjW4wX23u\n/Z9GtkOMFsf5Q3qQp/xG042LgGeAarQBs8pRVjehG+datN7/HvhKgfW+Av5g0m1G16UXj3KuU/5z\nOLTNGEuf8qbl2P9r4Dbz+yi0vvjRdcjDwLcd5+7KPutc5WnO/2/0h97xJm/nTfYdH7rfeE6eyj8O\nGi1r0S9lA4caLW8H/j7smieAd+VRtKuAR4ad/yPg8+OU65B0HQW/zbEdMoU0B2hCNxpBx/Gr0X2m\nhSjvcAXcBbzHsX0U2sq/APAOS+t6ptZo+SvwYcf2SrSx5nEo5tGO418HfuZQ1C9gPBOOcz6FMXwc\n+/6E+Sozz/uGYcd/BXzO/F6OrgxDeWT+NnBTrpdn+PMuUKeucxz7MHCf+f0etAFw7AR0fQNwhUOe\nPcOO34tp4M22C20QLMqRVjaPCxz7/s5Bo247cKnj2EXo7sgRupZH1j1oA61y2P5z0F9Xzmfbjvai\nudFev9WOY//MwXf5vRz0lL2Efs9vN9u7OWgYXQ/8xZHGamCwwGd8M8bANNsrKNxoGVfdkSOtUfVq\nAvox9EHkKN+3O+7tzOdq8+zdDt1Y6jj+H8Adw3RrH4d6O9ehPQibAH+ufBq5tjqOHWPu1eTY1wUc\nP8H3dDzvwOey+mO2y8wzmA6j5Ty0AX46xnNo9gvaOFjm2HcGsDNP/ofSdMh0lmP7DuDaUc7Na7QU\noE+jGi3oOvoZ8nuJ3gA859jeRR6jBf2xnQYqHMe/gml7mMQ7nv0revyAUmoz2uK8dtiheegKzclu\n9Jd7LhYBp4lIb/YP7YqeM0WiHsj+UEpFzc9yc18v0Oq474/QX7oTpcVxr23Ax9GF3S4it4vIvEmk\nPRrDn/lutCI25ZLNHM/K8l50Q7FFRJ4SkcvM/kXAm4eVy1nA3Dxpgv5Kvtr8/kd090EUQEROE5EH\nRaRDRPrQLtb6CeYvmwenTh1w/I6iyxi0W/RPwO0isl9Evi4i3lw3EZF3mNEJ2fyuHSbj8PwuAr7j\nOL8bXSnm0/XR5MxVhuPRlzehv4J2i8hDInKG41iXUiqV47716Hdg+H2z8j8EnC0ic9GN6x3AmSKy\nGO1Z2zBKvgIFxmbMY6RuFspk645x1VUF6Mc+ZWp0R1rOMhyeTy/59esQ2ZRSGXPcKdtPjAzfU0rF\nc8lsaHP8HjTpDd9XbvI43vd0PO/AIWWtdHxg1yhpTxil1APorrrvo+vfH4tIJfojOwQ845D5PrO/\nUPK9w+OiAH0a7dpL0HGlb1BKDZp9Taad2Sci/eiPyPHUsd1KqQHHvrHq2ELfcaD4gbhZPo92Uzoz\nth+tyE6a0V8JoC07Jy3AQ0qpasdfuVLqQ9Mi8aH3jaM9DNn7Viql1kwizUPyppS6VSl1Fvp5KOBr\nuc6bAoY/82a029VZMS0cdny/kXGrUupqtLH2NeBOMzKsBe1pcZZLmVLqq450hufjfqBBRI5HGy+3\nOo7div4yXKiUqkL3I0uedMbKXzYP+3KcewhKqaRS6gtKqdXovvzLgHcMP09EFqEbgY+guweqgc0O\nGXPJ2YLuTnQ+o6BS6vGx5MpBrjLcn+e+I1BKPaWUugJdjnejDYyx6ER75Ibfd59Jcxu6cvooOs6i\nH11xfQD9FZgp4B5j0cpI3XQSQTcyWZwGyXjrjuHPsWC9KlA/5ouIc9tZhjAyn0l0GeSS7xDZTLoL\ns7KJSDnaC/Iz4HoRqR0u8wQZ73s6nnfgkLIWkRBQNwlZR9MNlFLfVUqdhPYKrEDHTnWijbQ1Dnmr\nlB7McdgoUJ/yXbsS+AU6fstp6H4ZXUbHKKUqgX9i9PrLyX6gVkQqHPsKqmMLpSSMFlOp/QZwjpn/\nI7BCRP5RRDwichVaaf5gjrehYy+y/MGc/3YR8Zq/U0Rk1TTL3ooO2PyWiFSKiEtElonIa6YifdFz\nCpwnIn50X2A2mBL0M1g82ogb8+wC6C9ct4iMZtXeBlwjIktMZfZl4DfDvq7/Q0RCIrIG3b/9G3Of\nfxKRBtMA9ZpzM2gr/fUicpGIZO9/jogsyCezUioJ/Bb4Brq/+H7H4Qq0JR8TkVPRnpgsHeae+eYh\nGEun8iIi54rIMaLnIuhHNxS5Gtsy9EvdYa57N/rLZzR+CHzaPFNEpEpE3jyWTHm4DbhORBpEpB7t\nSs8Oi28D6kSkKteFIuITPUdElSmDfnLn8RCUHup4B/AlEakwFem/Oe4L2tvyEfMftEveuT0mIvJz\nyT9s/w7gXSKy2jRinx92fAPwD0Z3j0J7BrOMt+4YXveMR68K0Y9G4F+NHG9Gx1H80XH8nxz5vAG4\nU+UfbnoH8DoROd94Bj+B/sjKGgPfQQe+vw/4P7QuTgXjfU/H8w7cCVwmImeJiA/9DCbTluXVDaMH\np5lnF0HXwRlTz/0EuElEGs2580XkoknIkY/h+uZkIvUNxlt0DzqIf/gcZBXomKE+EZmPNtIKkscY\nP48DXzF1/bHo5znq1BzjoSSMFsMN6AIAQCnVhf6a/QTa9ffvwGVKqewXxXeAK0VP0vZd4466EHgr\n2to7gP7i98PQhD3TNcztHYAPHdDWg36p5o56ReH4ga+iLfsD6Art0+bYb83/LhF5Ns/116ENnWvR\nFvOg2ZeLm9HdIA+jR0jF0F/HTh5CB8z9FR20l50E6WLgBREJo8vmrUqpQaPEVwCfQb9YLeiXYCzd\nuxUdx/PbYUbTh4EbRGQA3SAPeQJMF9KXgMeMq/R0Z4IF6NRozEGXaz86LuMh9LM6BKXUi8C30DEN\nbei+/8dGS1gp9b9oXb3duGM3A5cUIFMubkSP4tqEjlN41uxDKbUFbdTsMM8nV7fR24FdRo4PortJ\nCuGj6Ep9B3qk3a0cOsz+IXRl+HCe7UJYSJ5nqZS6F+0xeACtnw8MO+UmdNxDG/rr8teOa0etO3Iw\nvO4pWK8K1I8n0bFcnWh9vtLcI8svgZ8bOQMc+rE3/H4vo9/775n0Xg+8XimVEJEr0O9t1qP0b8CJ\nIlJomY/GuN7T8bwDSqkXgH9B61grus6dzPxDeXUDqEQbJz0cHK30DXPsU2hdW29k/gs6DnCquR74\nhXlWb3EemEh9YzgRLetNcnBOsrA59gVzvA9tyN417NqvoD+MekXkkznSvhod57IfPUjl80qpvxQg\nU3ZCw1HnRsuOfrFYLJaSxXxRb0QHQieLLc90ISLvQgeFnpXn+N/QQaY/zXXcYpnt2MmHLBZLyaOU\nSqC7SSwWyxFMKXUPWSwWi8ViseTFdg9ZLBaLxWKZEVhPi8VisVgslhmBNVosFovFYrHMCKzRYrFY\nLBaLZUZgjRaLxWKxWCwzAmu0WCwWi8VimRH8f11cgg3St4VRAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x13e00df60>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"model_sm= sm.tsa.UnobservedComponents(y.values, 'local level')\n",
"result_sm = model_sm.fit()\n",
"fig=result_sm.plot_components()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Stan"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"import pystan"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2.17.1.0\n"
]
}
],
"source": [
"print(pystan.__version__)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_19c7f6adbb1d4d8f65e4ad86cc022f5a NOW.\n"
]
},
{
"data": {
"text/plain": [
"Inference for Stan model: anon_model_19c7f6adbb1d4d8f65e4ad86cc022f5a.\n",
"3 chains, each with iter=1000; warmup=500; thin=1; \n",
"post-warmup draws per chain=500, total post-warmup draws=1500.\n",
"\n",
" mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat\n",
"muZero 1099.7 16.24 93.31 914.72 1041.9 1102.1 1161.6 1279.8 33 1.06\n",
"mu[0] 1097.9 16.05 78.62 916.47 1051.9 1101.1 1150.4 1243.5 24 1.09\n",
"mu[1] 1097.1 16.05 71.78 918.33 1057.3 1101.8 1146.6 1226.1 20 1.11\n",
"mu[2] 1087.0 14.39 67.51 917.35 1050.1 1090.6 1132.8 1205.3 22 1.1\n",
"mu[3] 1100.7 17.42 67.47 918.24 1065.6 1107.5 1143.7 1215.3 15 1.15\n",
"mu[4] 1099.7 17.2 66.61 918.07 1066.1 1105.6 1140.6 1218.4 15 1.15\n",
"mu[5] 1091.6 16.31 65.25 917.61 1056.3 1097.4 1132.5 1205.2 16 1.14\n",
"mu[6] 1074.8 13.24 64.85 916.34 1040.1 1080.1 1115.3 1197.9 24 1.09\n",
"mu[7] 1107.0 19.09 68.85 916.74 1073.6 1111.2 1151.6 1228.9 13 1.18\n",
"mu[8] 1118.1 21.03 75.81 916.66 1080.7 1121.9 1163.5 1264.3 13 1.19\n",
"mu[9] 1091.5 16.63 66.54 916.95 1056.1 1095.4 1135.3 1212.4 16 1.15\n",
"mu[10] 1060.5 11.42 60.43 916.06 1025.1 1065.0 1101.1 1167.6 28 1.09\n",
"mu[11] 1042.0 8.63 59.8 914.07 1006.1 1045.4 1083.9 1152.2 48 1.06\n",
"mu[12] 1041.2 8.71 60.35 913.29 1004.2 1043.6 1083.3 1151.7 48 1.06\n",
"mu[13] 1030.9 7.5 58.12 911.56 993.31 1033.8 1071.0 1135.8 60 1.04\n",
"mu[14] 1026.3 7.1 57.67 910.71 992.01 1027.3 1064.9 1138.0 66 1.05\n",
"mu[15] 1023.5 7.31 58.0 910.48 986.04 1024.8 1061.8 1136.6 63 1.05\n",
"mu[16] 1032.0 8.27 60.24 910.23 992.98 1033.1 1071.0 1156.4 53 1.06\n",
"mu[17] 1013.9 6.06 61.17 891.85 972.06 1018.0 1054.9 1127.8 102 1.03\n",
"mu[18] 1030.3 8.36 60.27 908.98 990.9 1032.3 1071.7 1148.5 52 1.05\n",
"mu[19] 1062.6 14.74 64.23 914.46 1024.7 1066.0 1106.5 1181.9 19 1.12\n",
"mu[20] 1080.4 19.95 69.12 914.68 1041.9 1079.8 1126.0 1208.8 12 1.16\n",
"mu[21] 1100.0 23.94 75.7 914.87 1059.2 1103.3 1150.0 1233.3 10 1.2\n",
"mu[22] 1106.9 24.82 78.49 913.87 1064.5 1110.7 1159.3 1244.5 10 1.19\n",
"mu[23] 1114.4 27.82 83.45 913.27 1068.4 1121.5 1171.3 1264.2 9 1.21\n",
"mu[24] 1107.0 26.33 83.25 913.32 1060.8 1110.9 1162.2 1255.8 10 1.2\n",
"mu[25] 1079.5 22.74 75.43 912.26 1031.8 1084.8 1128.1 1224.4 11 1.17\n",
"mu[26] 1033.5 13.95 60.81 910.27 994.6 1033.0 1073.0 1155.5 19 1.13\n",
"mu[27] 994.23 8.57 55.52 898.42 953.26 992.92 1031.5 1108.8 42 1.05\n",
"mu[28] 937.4 3.19 55.52 821.25 903.94 937.48 973.86 1045.9 303 1.0\n",
"mu[29] 907.66 3.89 55.74 788.78 872.77 910.73 944.89 1007.4 205 1.01\n",
"mu[30] 885.99 4.78 55.38 767.1 850.26 891.08 924.2 983.32 134 1.03\n",
"mu[31] 864.32 6.95 58.98 742.45 825.17 869.32 907.76 963.79 72 1.05\n",
"mu[32] 867.88 5.58 54.13 752.44 832.76 871.4 907.11 963.9 94 1.04\n",
"mu[33] 856.93 8.73 55.89 738.65 818.13 860.59 899.63 955.05 41 1.05\n",
"mu[34] 847.77 9.0 56.94 734.34 809.35 851.52 889.52 948.65 40 1.05\n",
"mu[35] 860.98 5.67 53.18 746.26 828.18 862.94 898.54 956.82 88 1.03\n",
"mu[36] 862.49 5.61 53.54 752.64 827.51 864.23 901.6 957.58 91 1.03\n",
"mu[37] 890.15 2.39 52.63 788.7 855.24 889.97 922.8 996.07 486 1.0\n",
"mu[38] 896.74 3.75 55.45 792.53 860.71 895.94 929.29 1014.8 219 1.01\n",
"mu[39] 877.43 3.38 51.7 774.53 843.09 877.98 909.61 987.61 234 1.02\n",
"mu[40] 843.95 7.23 53.14 735.11 808.56 844.82 883.43 938.15 54 1.05\n",
"mu[41] 811.5 13.0 61.0 685.76 772.7 813.23 854.52 917.01 22 1.1\n",
"mu[42] 787.7 16.95 71.89 638.05 740.58 790.52 837.27 914.13 18 1.12\n",
"mu[43] 816.95 11.44 58.35 696.64 780.93 818.71 856.19 918.22 26 1.08\n",
"mu[44] 840.43 7.42 52.98 735.91 803.66 842.0 878.46 939.24 51 1.04\n",
"mu[45] 884.66 3.56 55.99 777.34 846.03 885.28 916.89 1006.4 247 1.0\n",
"mu[46] 892.2 4.04 56.25 792.44 853.78 889.48 925.34 1017.1 194 1.01\n",
"mu[47] 864.89 2.27 51.08 764.92 830.0 863.89 899.22 970.08 506 1.0\n",
"mu[48] 845.51 4.82 51.49 746.1 809.6 846.04 882.65 941.57 114 1.02\n",
"mu[49] 838.79 5.86 52.42 735.98 802.9 840.78 874.06 935.02 80 1.03\n",
"mu[50] 832.37 7.24 53.66 722.51 796.32 833.19 870.61 930.1 55 1.04\n",
"mu[51] 836.14 5.43 53.25 726.88 800.49 837.36 875.39 929.13 96 1.03\n",
"mu[52] 836.43 5.2 54.03 718.63 801.81 837.72 873.25 934.5 108 1.02\n",
"mu[53] 830.13 6.46 55.96 714.9 792.58 832.37 867.69 932.28 75 1.03\n",
"mu[54] 816.9 8.97 58.16 694.78 779.7 818.49 856.27 924.91 42 1.05\n",
"mu[55] 822.59 8.03 56.18 702.65 784.99 827.31 859.93 924.92 49 1.05\n",
"mu[56] 822.91 6.68 55.49 709.32 785.05 825.7 861.34 922.45 69 1.05\n",
"mu[57] 837.26 3.55 53.3 727.15 803.35 835.99 873.84 938.97 226 1.03\n",
"mu[58] 857.7 2.8 50.16 758.78 823.41 857.52 892.81 953.11 320 1.01\n",
"mu[59] 844.35 4.29 51.48 740.49 811.83 844.81 879.51 938.48 144 1.02\n",
"mu[60] 846.29 3.62 54.64 736.9 811.04 847.77 885.03 944.18 228 1.02\n",
"mu[61] 857.44 2.82 52.89 756.11 820.58 857.72 892.29 960.18 353 1.01\n",
"mu[62] 867.61 2.35 51.57 768.0 833.43 865.33 901.81 969.87 482 1.0\n",
"mu[63] 880.88 2.9 53.64 774.95 845.43 879.91 913.72 991.17 343 1.0\n",
"mu[64] 886.41 3.44 54.22 784.41 849.8 884.97 921.01 1002.8 249 1.01\n",
"mu[65] 875.97 2.78 52.38 774.1 841.98 874.87 907.7 989.22 356 1.01\n",
"mu[66] 864.29 2.37 51.93 765.58 828.52 863.34 898.48 971.35 479 1.01\n",
"mu[67] 858.22 2.65 52.78 751.47 822.8 857.33 894.51 960.07 396 1.01\n",
"mu[68] 825.46 5.83 54.34 719.53 789.59 827.09 862.64 926.68 87 1.03\n",
"mu[69] 801.77 10.14 60.86 674.61 760.62 803.62 843.87 911.75 36 1.06\n",
"mu[70] 796.17 11.45 61.65 674.52 755.87 797.2 838.58 911.96 29 1.07\n",
"mu[71] 813.79 6.97 54.41 701.7 776.72 814.8 850.04 914.33 61 1.04\n",
"mu[72] 820.35 6.51 53.71 714.04 783.83 819.36 857.39 918.67 68 1.03\n",
"mu[73] 824.95 5.3 52.72 709.97 791.04 825.65 860.73 928.05 99 1.02\n",
"mu[74] 843.56 3.13 50.97 739.13 809.48 845.44 879.3 936.54 265 1.01\n",
"mu[75] 868.53 3.25 53.14 765.23 834.03 865.75 902.8 975.21 268 1.0\n",
"mu[76] 864.56 2.34 51.62 764.34 830.31 864.94 898.28 971.02 486 1.0\n",
"mu[77] 863.64 2.5 52.05 761.96 829.18 863.22 899.01 967.58 434 1.0\n",
"mu[78] 858.84 2.55 51.39 754.64 825.44 858.86 895.0 960.17 406 1.01\n",
"mu[79] 859.48 2.1 53.74 747.36 826.51 861.6 895.15 964.93 652 1.01\n",
"mu[80] 848.88 4.3 56.35 724.4 812.86 849.81 886.79 953.35 172 1.03\n",
"mu[81] 853.59 4.1 55.4 737.57 818.57 854.91 892.04 956.94 183 1.02\n",
"mu[82] 876.05 1.72 53.52 767.79 843.68 877.49 910.71 977.73 971 1.0\n",
"mu[83] 903.05 3.63 54.11 797.9 866.72 902.11 937.19 1015.7 222 1.01\n",
"mu[84] 903.9 2.85 53.84 796.74 871.04 903.68 936.41 1011.2 358 1.0\n",
"mu[85] 906.53 2.57 52.65 804.07 873.04 905.71 938.77 1012.4 418 1.01\n",
"mu[86] 896.4 1.77 51.2 793.53 863.85 897.05 929.16 996.4 841 1.0\n",
"mu[87] 905.03 2.08 52.27 802.42 870.12 904.96 938.93 1015.1 632 1.0\n",
"mu[88] 910.83 2.49 51.74 808.45 877.57 909.68 943.86 1015.9 433 1.0\n",
"mu[89] 908.29 2.25 50.91 810.23 873.6 907.66 941.98 1013.8 511 1.0\n",
"mu[90] 920.28 4.08 54.44 818.43 884.61 919.06 953.51 1038.0 178 1.01\n",
"mu[91] 916.93 3.77 53.14 820.47 879.63 915.09 951.62 1025.6 199 1.01\n",
"mu[92] 917.29 4.23 55.05 814.44 879.94 915.17 952.72 1030.8 169 1.02\n",
"mu[93] 925.42 6.05 62.61 820.96 882.21 917.59 965.31 1064.0 107 1.03\n",
"mu[94] 893.25 2.26 54.44 794.79 856.89 892.02 926.42 1011.3 580 1.0\n",
"mu[95] 859.39 1.83 52.33 753.11 825.84 860.13 893.49 963.08 822 1.01\n",
"mu[96] 845.74 3.28 54.36 737.19 810.2 847.2 883.35 946.24 274 1.01\n",
"mu[97] 815.02 9.66 61.1 685.82 776.19 816.19 857.71 926.03 40 1.05\n",
"mu[98] 800.94 11.42 64.6 669.21 757.95 801.93 846.84 921.13 32 1.06\n",
"mu[99] 794.36 12.11 72.68 648.11 742.73 795.72 846.41 920.96 36 1.05\n",
"sigmaV 1.6e4 1257.7 4534.7 9364.2 1.3e4 1.5e4 1.8e4 2.9e4 13 1.19\n",
"sigmaW 2438.2 329.47 2057.5 1.22 1078.6 1973.2 3246.4 7999.7 39 1.1\n",
"lp__ -921.3 26.04 78.11 -994.0 -959.9 -941.2 -917.5 -606.9 9 1.34\n",
"\n",
"Samples were drawn using NUTS at Fri Apr 27 09:27:35 2018.\n",
"For each parameter, n_eff is a crude measure of effective sample size,\n",
"and Rhat is the potential scale reduction factor on split chains (at \n",
"convergence, Rhat=1)."
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model = \"\"\"\n",
" data {\n",
" int n; \n",
" vector[n] y; \n",
" }\n",
" parameters {\n",
" real muZero; \n",
" vector[n] mu;\n",
" real<lower=0> sigmaV;\n",
" real<lower=0> sigmaW;\n",
" }\n",
" model {\n",
" mu[1] ~ normal(muZero, sqrt(sigmaW));\n",
" for(i in 2:n) \n",
" mu[i] ~ normal(mu[i-1], sqrt(sigmaW));\n",
" \n",
" for(i in 1:n) {\n",
" y[i] ~ normal(mu[i], sqrt(sigmaV));\n",
" }\n",
" }\n",
"\"\"\"\n",
"fit = pystan.stan(model_code=model, data={'n': N, 'y': y}, iter=T, chains=3)\n",
"fit"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
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XEY6TkdL3Of5n6/4RUvdIYqBr0lvmTbU+wnGDwgwPe1q6qO8Ic8q0HFoC+0chb+1uBmDq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\nhYVFVPn/7M0KbBxNamEAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x142225f98>"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
},
{
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OirO9ODShMAOm5Hp5aVsjmV5XzwvCufOt2IVg1OD9iv2lipdNz2VilpcJWSmk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\nhYVFVPn/7M0KbBxNamEAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x142225f98>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fit.traceplot()"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [],
"source": [
"la = fit.extract()"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"def plotseries(y,mu_samples,title,ax=0):\n",
" #axis=0 stan, 1 pymc\n",
" mu_lower, mu_upper = np.percentile(mu_samples, q=[2.5, 97.5], axis=ax)\n",
" pred = mu_samples.mean(axis=ax)\n",
" plt.plot(list(range(len(y)+1)), list(y)+[None], color='black')\n",
" plt.plot(list(range(1, len(y)+1)), pred)\n",
" plt.fill_between(list(range(1, len(y)+1)), mu_lower, mu_upper, alpha=0.3)\n",
" plt.title(title)\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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MhBME1lCSxCUjAM6CAIRDfmKR6YPAoM8E0E6+eipmpXnARhqaWkpmAlSZTPz2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\ngEQikSxSpABIJBLJIuX/A32YuqXERGENAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x143feacf8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plotseries(y,la['mu'],'stan',0)"
]
},
{
"cell_type": "code",
"execution_count": 103,
"metadata": {},
"outputs": [],
"source": [
"import pickle"
]
},
{
"cell_type": "code",
"execution_count": 104,
"metadata": {},
"outputs": [],
"source": [
"with open('nile_stan_nuts.pickle', mode='wb') as f:\n",
" pickle.dump(la,f)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# PyMC"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/apple/Library/Python/3.6/lib/python/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
" from ._conv import register_converters as _register_converters\n"
]
}
],
"source": [
"import pymc3 as pm"
]
},
{
"cell_type": "code",
"execution_count": 101,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3.4.1\n"
]
}
],
"source": [
"print(pm.__version__)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"logp = -876.02, ||grad|| = 60.474: 100%|██████████| 31/31 [00:00<00:00, 331.74it/s] \n",
"Multiprocess sampling (2 chains in 2 jobs)\n",
"INFO:pymc3:Multiprocess sampling (2 chains in 2 jobs)\n",
"NUTS: [sigmaV_log__, mu99, mu98, mu97, mu96, mu95, mu94, mu93, mu92, mu91, mu90, mu89, mu88, mu87, mu86, mu85, mu84, mu83, mu82, mu81, mu80, mu79, mu78, mu77, mu76, mu75, mu74, mu73, mu72, mu71, mu70, mu69, mu68, mu67, mu66, mu65, mu64, mu63, mu62, mu61, mu60, mu59, mu58, mu57, mu56, mu55, mu54, mu53, mu52, mu51, mu50, mu49, mu48, mu47, mu46, mu45, mu44, mu43, mu42, mu41, mu40, mu39, mu38, mu37, mu36, mu35, mu34, mu33, mu32, mu31, mu30, mu29, mu28, mu27, mu26, mu25, mu24, mu23, mu22, mu21, mu20, mu19, mu18, mu17, mu16, mu15, mu14, mu13, mu12, mu11, mu10, mu9, mu8, mu7, mu6, mu5, mu4, mu3, mu2, mu1, mu0, sigmaW_log__, muZero]\n",
"INFO:pymc3:NUTS: [sigmaV_log__, mu99, mu98, mu97, mu96, mu95, mu94, mu93, mu92, mu91, mu90, mu89, mu88, mu87, mu86, mu85, mu84, mu83, mu82, mu81, mu80, mu79, mu78, mu77, mu76, mu75, mu74, mu73, mu72, mu71, mu70, mu69, mu68, mu67, mu66, mu65, mu64, mu63, mu62, mu61, mu60, mu59, mu58, mu57, mu56, mu55, mu54, mu53, mu52, mu51, mu50, mu49, mu48, mu47, mu46, mu45, mu44, mu43, mu42, mu41, mu40, mu39, mu38, mu37, mu36, mu35, mu34, mu33, mu32, mu31, mu30, mu29, mu28, mu27, mu26, mu25, mu24, mu23, mu22, mu21, mu20, mu19, mu18, mu17, mu16, mu15, mu14, mu13, mu12, mu11, mu10, mu9, mu8, mu7, mu6, mu5, mu4, mu3, mu2, mu1, mu0, sigmaW_log__, muZero]\n",
"100%|██████████| 1500/1500 [02:16<00:00, 11.02it/s]\n",
"There were 2 divergences after tuning. Increase `target_accept` or reparameterize.\n",
"ERROR:pymc3:There were 2 divergences after tuning. Increase `target_accept` or reparameterize.\n",
"The acceptance probability does not match the target. It is 0.4238921757976004, but should be close to 0.8. Try to increase the number of tuning steps.\n",
"WARNING:pymc3:The acceptance probability does not match the target. It is 0.4238921757976004, but should be close to 0.8. Try to increase the number of tuning steps.\n",
"The acceptance probability does not match the target. It is 0.510485232585227, but should be close to 0.8. Try to increase the number of tuning steps.\n",
"WARNING:pymc3:The acceptance probability does not match the target. It is 0.510485232585227, but should be close to 0.8. Try to increase the number of tuning steps.\n",
"The gelman-rubin statistic is larger than 1.05 for some parameters. This indicates slight problems during sampling.\n",
"INFO:pymc3:The gelman-rubin statistic is larger than 1.05 for some parameters. This indicates slight problems during sampling.\n",
"The estimated number of effective samples is smaller than 200 for some parameters.\n",
"ERROR:pymc3:The estimated number of effective samples is smaller than 200 for some parameters.\n"
]
}
],
"source": [
"with pm.Model() as model:\n",
" \n",
" muZero = pm.Normal(name='muZero', mu=0.0, tau=1.0)\n",
" sigmaW = pm.InverseGamma(name='sigmaW', alpha=1.0, beta=1.0)\n",
" \n",
" mu = [0]*N\n",
" mu[0] = pm.Normal(name='mu0', mu=muZero, tau=1/sigmaW)\n",
" for n in range(1, N):\n",
" mu[n] = pm.Normal(name='mu'+str(n), mu=mu[n-1], tau=1/sigmaW)\n",
" \n",
" sigmaV = pm.InverseGamma(name='sigmaV', alpha=1.0, beta=1.0)\n",
" y_pre = pm.Normal('y_pre', mu=mu, tau=1/sigmaV, observed=y)\n",
" \n",
" start = pm.find_MAP()\n",
" step = pm.NUTS()\n",
" trace = pm.sample(T, step, start=start)"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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ZfNBmYSCzlCWza9BtERGOAeiWXJoHbDqk4st30b4AxFWFciZ+VgzAF4Bjx48H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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x16f6aa4e0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mu_samples = np.array([trace['mu'+str(i)] for i in range(N)])\n",
"plotseries(y,mu_samples,\"pymc\",1)"
]
},
{
"cell_type": "code",
"execution_count": 105,
"metadata": {},
"outputs": [],
"source": [
"with open('nile_pymc_nuts.pickle', mode='wb') as f:\n",
" pickle.dump(trace,f)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Edward"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/Cellar/python3/3.6.3/Frameworks/Python.framework/Versions/3.6/lib/python3.6/importlib/_bootstrap.py:219: RuntimeWarning: compiletime version 3.5 of module 'tensorflow.python.framework.fast_tensor_util' does not match runtime version 3.6\n",
" return f(*args, **kwds)\n",
"/Users/apple/Library/Python/3.6/lib/python/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
" from ._conv import register_converters as _register_converters\n"
]
}
],
"source": [
"import tensorflow as tf\n",
"import edward as ed\n",
"from edward.models import Normal, InverseGamma, Empirical"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1.3.5\n"
]
}
],
"source": [
"print(ed.__version__)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python3.6/site-packages/edward/util/random_variables.py:52: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
" not np.issubdtype(value.dtype, np.float) and \\\n",
"/usr/local/lib/python3.6/site-packages/edward/util/random_variables.py:53: FutureWarning: Conversion of the second argument of issubdtype from `int` to `np.signedinteger` is deprecated. In future, it will be treated as `np.int64 == np.dtype(int).type`.\n",
" not np.issubdtype(value.dtype, np.int) and \\\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"1000/1000 [100%] ██████████████████████████████ Elapsed: 51s | Acceptance Rate: 0.000\n"
]
}
],
"source": [
"muZero = Normal(loc=0.0, scale=1.0)\n",
"sigmaW = InverseGamma(concentration=1.0, rate=1.0)\n",
" \n",
"mu = [0]*N\n",
"mu[0] = Normal(loc=muZero, scale=sigmaW)\n",
"for n in range(1, N):\n",
" mu[n] = Normal(loc=mu[n-1], scale=sigmaW)\n",
" \n",
"sigmaV = InverseGamma(concentration=1.0, rate=1.0)\n",
"y_pre = Normal(loc=tf.stack(mu), scale=sigmaV)\n",
" \n",
"qmuZero = Empirical(tf.Variable(tf.zeros(T)))\n",
"qsigmaW = Empirical(tf.Variable(tf.zeros(T)))\n",
"qmu = [Empirical(tf.Variable(tf.zeros(T))) for n in range(N)]\n",
"qsigmaV = Empirical(tf.Variable(tf.zeros(T)))\n",
" \n",
"latent_vars = {m: qm for m, qm in zip(mu, qmu)}\n",
"latent_vars[muZero] = qmuZero\n",
"latent_vars[sigmaW] = qsigmaW\n",
"latent_vars[sigmaV] = qsigmaV\n",
"\n",
"inference = ed.HMC(latent_vars, data={y_pre: y.values})\n",
"inference.run(n_iter=T)"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [],
"source": [
"qmu_sample=np.array([ _qmu.sample(1000).eval() for _qmu in qmu])"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(100, 1000)"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qmu_sample.shape"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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20//w4cO58cYbOe+88wDfbqCqqipaWlooLS31LHEYaZwWAEQ+EshpAdgPCFu3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\nUWIUFQBFUZQY5f8DOq91Pt0jz/AAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x147ad1588>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plotseries(y,qmu_sample,\"Edward\"+ed.__version__,1)"
]
},
{
"cell_type": "code",
"execution_count": 106,
"metadata": {},
"outputs": [],
"source": [
"with open('nile_edward_hmc.pickle', mode='wb') as f:\n",
" pickle.dump(qmu_sample,f)"
]
},
{
"cell_type": "code",
"execution_count": 108,
"metadata": {},
"outputs": [],
"source": [
"qmu_sample3=np.array([ _qmu.sample(1000).eval() for _qmu in qmu])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plotseries(y,qmu_sample3,\"Edward HMC run1000+3000\",1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# SGHMC"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [],
"source": [
"def nile_st_SGHMC(y,N,T):\n",
" muZero = Normal(loc=0.0, scale=1.0)\n",
" sigmaW = InverseGamma(concentration=1.0, rate=1.0)\n",
" \n",
" mu = [0]*N\n",
" mu[0] = Normal(loc=muZero, scale=sigmaW)\n",
" for n in range(1, N):\n",
" mu[n] = Normal(loc=mu[n-1], scale=sigmaW)\n",
" \n",
" sigmaV = InverseGamma(concentration=1.0, rate=1.0)\n",
" y_pre = Normal(loc=tf.stack(mu), scale=sigmaV)\n",
" \n",
" qmuZero = Empirical(tf.Variable(tf.zeros(T)))\n",
" qsigmaW = Empirical(tf.Variable(tf.zeros(T)))\n",
" qmu = [Empirical(tf.Variable(tf.zeros(T))) for n in range(N)]\n",
" qsigmaV = Empirical(tf.Variable(tf.zeros(T)))\n",
" \n",
" latent_vars = {m: qm for m, qm in zip(mu, qmu)}\n",
" latent_vars[muZero] =qmuZero\n",
" latent_vars[sigmaW]= qsigmaW\n",
" latent_vars[sigmaV] = qsigmaV\n",
"\n",
" return ed.SGHMC(latent_vars, data={y_pre: y.values}) ,qmu"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python3.6/site-packages/edward/util/random_variables.py:52: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
" not np.issubdtype(value.dtype, np.float) and \\\n",
"/usr/local/lib/python3.6/site-packages/edward/util/random_variables.py:53: FutureWarning: Conversion of the second argument of issubdtype from `int` to `np.signedinteger` is deprecated. In future, it will be treated as `np.int64 == np.dtype(int).type`.\n",
" not np.issubdtype(value.dtype, np.int) and \\\n"
]
}
],
"source": [
"inferenceSGHMC,qmuSGHMC=nile_st_SGHMC(y,N,T)"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1000/1000 [100%] ██████████████████████████████ Elapsed: 24s | Acceptance Rate: 1.000\n"
]
}
],
"source": [
"inferenceSGHMC.run(n_iter=T)"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [],
"source": [
"qmuSGHMCsample=np.array([ _qmu.sample(1000).eval() for _qmu in qmuSGHMC])"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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BOLuA2tvbqa6uHvIC4M4CgODMA3iyAAZKSmhlAURFRfXKAjh06BDLly8H8LiU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\nYAAeowAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x15b99ad30>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plotseries(y,qmuSGHMCsample,\"Edward SGHMC run1000\",1)"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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ctTiFum5jaY9aut3AYshY95SwcWCp3MJiMQ0i8ol+v9g+iL93N69npy12Nxrm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\ns3yPT7Y8oxl6J3Az6w+iRw9E9/Bd+6bwVz96D+fi8ohHFwYj2wBjY+i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0lsqEnlMobXQC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\nyyLbEwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x15bdf5128>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mu_lower, mu_upper = np.percentile(qmuSGHMCsample, q=[2.5, 97.5], axis=1)\n",
"pred = qmuSGHMCsample.mean(axis=1)\n",
"plt.plot(list(range(1, len(y)+1)), pred)\n",
"plt.fill_between(list(range(1, len(y)+1)), mu_lower, mu_upper, alpha=0.3)\n",
"plt.title(\"Edward SGHMC run1000\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
@xiangze
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xiangze commented Apr 26, 2018

add libraries version info
add long(3000) run of edward

@xiangze
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xiangze commented Apr 28, 2018

add SGHMC result

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