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@josef-pkt
Last active August 29, 2015 14:15
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new get_prediction
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"metadata": {
"name": "",
"signature": "sha256:67e2e09f081d2e1cec5ebd0dcdf605ff612623d86f935d73711941287c650d02"
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"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Prediction Confidence Intervals"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is currently mainly converted notebook from my try out and test python script\n",
"\n",
"The plan is to extend the prediction facilities in statsmodels 0.8.\n",
"The current version in PR is focused on the confidence interval and setting up the structure.\n",
"\n",
"`predict` as method stays simple so it can be used in a loop for example for cross-validation without extra overhead. All additional predict features will be added as a result instance of a new `get_prediction` method.\n",
"\n",
"The discussion for the design for enhancements is spread out over several issues on github.\n",
"\n",
"I'm not yet happy with some of the names of the attributes or columns in the data frame."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# -*- coding: utf-8 -*-\n",
"\"\"\"\n",
"Created on Sat Dec 20 12:01:13 2014\n",
"\n",
"Author: Josef Perktold\n",
"License for Code: BSD-3\n",
"\n",
"\"\"\"\n",
"\n",
"import numpy as np\n",
"from statsmodels.regression.linear_model import OLS, WLS\n",
"\n",
"from statsmodels.sandbox.regression.predstd import wls_prediction_std\n",
"from statsmodels.regression._prediction import get_prediction\n",
"from statsmodels.genmod._prediction import params_transform_univariate\n",
"\n",
"import matplotlib.pyplot as plt\n",
"plt.rcParams['figure.figsize'] = (10.0, 8.0)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# from example wls.py\n",
"np.random.seed(123456)\n",
"nsample = 50\n",
"x = np.linspace(0, 20, nsample)\n",
"X = np.column_stack((x, (x - 5)**2))\n",
"from statsmodels.tools.tools import add_constant\n",
"X = add_constant(X)\n",
"beta = [5., 0.5, -0.01]\n",
"sig = 0.5\n",
"w = np.ones(nsample)\n",
"w[nsample * 6/10:] = 3\n",
"y_true = np.dot(X, beta)\n",
"e = np.random.normal(size=nsample)\n",
"y = y_true + sig * w * e\n",
"X = X[:,[0,1]]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 29
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Linear Regression - WLS"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"minimal version"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mod_wls = WLS(y, X, weights=1./w)\n",
"res_wls = mod_wls.fit()\n",
"\n",
"pred_res = get_prediction(res_wls)\n",
"pf = pred_res.summary_frame()\n",
"pf.head()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>mean</th>\n",
" <th>mean_se</th>\n",
" <th>mean_ci_lower</th>\n",
" <th>mean_ci_upper</th>\n",
" <th>obs_ci_lower</th>\n",
" <th>obs_ci_upper</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td> 5.138253</td>\n",
" <td> 0.198164</td>\n",
" <td> 4.739818</td>\n",
" <td> 5.536688</td>\n",
" <td> 3.744384</td>\n",
" <td> 6.532122</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td> 5.306936</td>\n",
" <td> 0.191008</td>\n",
" <td> 4.922888</td>\n",
" <td> 5.690984</td>\n",
" <td> 3.917112</td>\n",
" <td> 6.696761</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td> 5.475619</td>\n",
" <td> 0.183983</td>\n",
" <td> 5.105697</td>\n",
" <td> 5.845542</td>\n",
" <td> 4.089632</td>\n",
" <td> 6.861607</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td> 5.644303</td>\n",
" <td> 0.177102</td>\n",
" <td> 5.288214</td>\n",
" <td> 6.000391</td>\n",
" <td> 4.261943</td>\n",
" <td> 7.026662</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td> 5.812986</td>\n",
" <td> 0.170385</td>\n",
" <td> 5.470404</td>\n",
" <td> 6.155568</td>\n",
" <td> 4.434044</td>\n",
" <td> 7.191928</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 30,
"text": [
" mean mean_se mean_ci_lower mean_ci_upper obs_ci_lower obs_ci_upper\n",
"0 5.138253 0.198164 4.739818 5.536688 3.744384 6.532122\n",
"1 5.306936 0.191008 4.922888 5.690984 3.917112 6.696761\n",
"2 5.475619 0.183983 5.105697 5.845542 4.089632 6.861607\n",
"3 5.644303 0.177102 5.288214 6.000391 4.261943 7.026662\n",
"4 5.812986 0.170385 5.470404 6.155568 4.434044 7.191928"
]
}
],
"prompt_number": 30
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# ### WLS knowing the true variance ratio of heteroscedasticity\n",
"\n",
"mod_wls = WLS(y, X, weights=1./w)\n",
"res_wls = mod_wls.fit()\n",
"\n",
"\n",
"\n",
"prstd, iv_l, iv_u = wls_prediction_std(res_wls)\n",
"pred_res = get_prediction(res_wls)\n",
"ci = pred_res.conf_int(obs=True)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 31
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from numpy.testing import assert_allclose\n",
"assert_allclose(pred_res.se_obs, prstd, rtol=1e-13)\n",
"assert_allclose(ci, np.column_stack((iv_l, iv_u)), rtol=1e-13)\n",
"\n",
"print pred_res.summary_frame().head()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" mean mean_se mean_ci_lower mean_ci_upper obs_ci_lower obs_ci_upper\n",
"0 5.138253 0.198164 4.739818 5.536688 3.744384 6.532122\n",
"1 5.306936 0.191008 4.922888 5.690984 3.917112 6.696761\n",
"2 5.475619 0.183983 5.105697 5.845542 4.089632 6.861607\n",
"3 5.644303 0.177102 5.288214 6.000391 4.261943 7.026662\n",
"4 5.812986 0.170385 5.470404 6.155568 4.434044 7.191928\n"
]
}
],
"prompt_number": 32
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"pred_res2 = res_wls.get_prediction()\n",
"ci2 = pred_res2.conf_int(obs=True)\n",
"\n",
"from numpy.testing import assert_allclose\n",
"assert_allclose(pred_res2.se_obs, prstd, rtol=1e-13)\n",
"assert_allclose(ci2, np.column_stack((iv_l, iv_u)), rtol=1e-13)\n",
"\n",
"print pred_res2.summary_frame().head()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" mean mean_se mean_ci_lower mean_ci_upper obs_ci_lower obs_ci_upper\n",
"0 5.138253 0.198164 4.739818 5.536688 3.744384 6.532122\n",
"1 5.306936 0.191008 4.922888 5.690984 3.917112 6.696761\n",
"2 5.475619 0.183983 5.105697 5.845542 4.089632 6.861607\n",
"3 5.644303 0.177102 5.288214 6.000391 4.261943 7.026662\n",
"4 5.812986 0.170385 5.470404 6.155568 4.434044 7.191928\n"
]
}
],
"prompt_number": 33
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"pf = pred_res2.summary_frame()\n",
"c = pf.columns\n",
"dir(c)\n",
"cols = pf.columns.tolist()\n",
"cols.remove('mean_se')\n",
"ax = pf[cols].plot()\n",
"ax.plot(y, 'o')\n",
"#ax.fill_between(np.asarray(pf.index), pf['obs_ci_upper'].values, pf['obs_ci_lower'].values, facecolor='blue', alpha=0.1)\n",
"#ax.fill_between(np.asarray(pf.index), pf['mean_ci_upper'], pf['mean_ci_lower'].values, facecolor='red', alpha=0.1)\n",
"ax.fill_between(np.asarray(pf.index), pf['obs_ci_upper'].values, pf['obs_ci_lower'].values, alpha=0.1)\n",
"ax.fill_between(np.asarray(pf.index), pf['mean_ci_upper'], pf['mean_ci_lower'].values, alpha=0.1)\n",
"\n",
"# there should be a pretty plotting method in `get_prediction` results"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 47,
"text": [
"<matplotlib.collections.PolyCollection at 0x8f3aed0>"
]
},
{
"metadata": {},
"output_type": "display_data",
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F4e7uzqFDh2o9JRcREcGaNWuIiYnBzc2NUaNGMXHiRL766iuCg4PZvHkzU6dO\nZe/evfj5+bFv3z5effVV9u7dS1BQEABHjx5l7NixbNu2jS5durB27VqefPJJTp8+jaWlJQBRUVHs\n2LEDV1dXlEqJvU2V5NCYN3Ppv59/jiYy8jVGjLhxp9P69drn+l4y42aacg3n1p0jbe45NFZKHCd7\n4zSwqcmkNKhUkgN1T/4+ie38d7A+eohzY94i7+N/obE0zeKmJhlA1Sb40YcDBw5QUFDAW2+9BcBj\njz3GoEGDiIyMRKFQMGjQIB599FEAPvjgAxwdHUlPT8fKyoqrV69y6tQpAgICaNWqVbXnUavVRERE\ncPDgQZo2bQpAt27dat3u9evX60azAObNm0fbtm1ZvXo1QUFBTJs2DY1GQ2xsLG+++aYuEX7v3r30\n6tULgBUrVvDKK68QEBAAwKhRo5g7dy4HDhygZ8+eKBQKJk+ejKenZ63bKYSoP77/fmmF4AlgxIgE\nNm9eZpAASl2m5lzEOdLmnwPHBjhN98Wxj7vJBE7iHqUm0WjBTOx+3k768NfIee9raHTnxZvrkgwj\n3CQjI4NmzZpVeK158+akp6cD4OV1I5Pf1tYWZ2dnMjIyeOyxx5g4cSITJkzA3d2dV155pdpE8Ozs\nbIqKivD396/yM3cjMzOT5s2b67a9vb0pKysjKysLf39/bG1tOXbsGLGxsQwaNAgPDw9Onz7Nvn37\ndAFUSkoKixYtwsnJSfc4d+4cGRkZuuPe+rMRpskcRi9E1cyl/xSK4ire0W+1Z3WJmuRPk1H5xXHu\nv1k4z26Bz9YAGvd9wCSDJxl9uksXs7CePgG3JzqTb/cAf35/lpzxM00+eAIJoCrw8PAgLS2tQrJ4\nSkqKbtQlLS1N93p+fj45OTl4eHgAMGnSJA4fPsxff/3F6dOn+eijj6o8j6urK9bW1pw9e1Zv7b55\nMcTU1FQaNGiAu7s7AL169WLjxo2Ulpbi4eFBr169WL16Nbm5uboFnr29vXnnnXfIzc3VPfLz83nu\nued0xzXFf6yEEHVDo2lYxTv6qfZcXlRO0sdJ7PdVkRmVjeuiVvhsDsAx2E3+LaoP8q5g9cFbuAU9\nTFF+KX9uOMnFf3+E2sGprltWYxJA3aRbt27Y2NiwYMECSktLiYmJYdu2bQwfPhyNRsP27dvZv38/\nJSUlvPvuu3Tv3h1PT08OHz7MwYMHKS0txcbGBmtraywsqi7WplQqCQsLY+rUqWRmZlJeXk5cXBwl\nJSW1avcDLiz8AAAgAElEQVTw4cP5+OOPSU5OJj8/n7fffpvnn39el6fUq1cvli9frst3Cg4OZvny\n5bqpOYDx48fzxRdfcOjQITQaDQUFBURHR5Ofn1+rNom6I2upmTdz6b+nnprM+vUVR9HXrfMnNHRS\nFXvUTFlBGQkfJqDyieP8Dzm4f9aa5hu64NDD9Z6OaywqVUwdt8C0aa5dw2rZPNwCH6Q8IYW/1hzi\n/DsrUDfxqOum3TWTzIGqK5aWlmzdupVXX32VefPm4eXlxdq1a2nZsiUKhYIRI0YQHh5OXFwcnTt3\nZt26dQDk5eUxZcoUEhMTsba2pl+/frzxxhvVnmvhwoVMnz6dgIAA8vPz6dixIz/99BNw9yM9YWFh\nZGRkEBQURFFREf369WPZsmW694OCgsjPz9cFUD169KCwsFC3DdC5c2dWrlzJxIkTOXPmDI0aNaJn\nz55mM50ghDCu63lOmzcvQzttZ80LL9y52nNVSvNKSV6STOay81j9ww73VW2w62Q+oxHiDsrKaLD2\nPzgunUt+q078/dluSlt2qOtW3ROpRC5MglwXQtyfSnNLSVqcxPnPsmgYaI/La77YtK7+LmZhRtRq\nLDatx3HhLIrcPDn36jxKOvUwyqmlErkQQoh6p/hiMUkLkriw6iINgx3w3NSRRi3s67pZQl80GpQ7\nt+Iw/x3KlZYkvfkphYH96rpVeiU5UAbUpk0b7O3tb3tERkbWaH87O7tK99+/f7+BWy7Mmbnk0IjK\n1ff+K8os4q/X/uJgy4PkpZbi9UMnmi3vUG+CJ5Uqpo5bUPcUqhgcBgfiEP4GaS/N4My6I3USPGVm\nWhAfb7hxIhmBMqA7VSO/E0ngFkLUF4VphSTOTeRS5CWsBznjtaMz1t6mf6u6qDnFH4exnfc2Vmf+\nJi1sBlefGgvV3FBlKElJEBEBsbHOzJx5mT59DHMeyYESJkGuCyHqp4LEAhI/SCLnuxxshrjiNsEX\nK49Gdd0soUeKs3/TaN472Bz6lXOj3uDKc5PQWFVV5sJw/v4bvvwSjh6F55+Hxx+/QJcuJZIDJYQQ\nwnzkn84ncXYSudtysXuuCc1jumLVRD81ooSJSE+j0Uczsdu5hYxhk0h6ezUaW+NPxR4/DqtWQXw8\nvPgihIdDo0aQnW3YP8olB0qIeqa+59DUd+bef3kn8zj23B/8/shRSh2t8I3tRtOZD903wZNKFVPH\nLTCCSxdp+O5k3EI6UGDlxJ+bznDpn+FGDZ40Gjh0CP75T3j7bejZE7Zs0QZQjYw0wCkjUEIIIe7Z\nlaNXSAhPJD82H7vR7vioWtPA0bKumyX06WoeVp8uwPGrz7j42NP8FXWccveaTY/pi0YDv/6qnaq7\ncgVeegn69QPLOrjUJAeqhsaMGUOzZs10C/EaSmpqKm3atCEvL+++Wq7AXK8LIe53uYdySQxPouC3\nAuzDmuIa5oOFnfxtXq8UFWG5aimOXyzkcudgzv9rDmXNWxq1CWo1/PyzNnBSqyEsDB5/vPocdakD\nZSIUCoVRAhpvb+9qFyIWQghTcCn2EknvJ3PtRCEO45vi+0l7LGzkV0q9UlZGg/UrcfzkA/IfbEf8\n0h8pffgfRm1CaSn89JP2rjo7O+2UXc+eYArjC3K13wUZIbldeXl5tev+CeOLiYmRJXjMmKn338Xd\nF0l6P5nixBIcXvHEb4U3yoaSTnudShVDYGBwHbfiHqnVWHwficPCWRQ7u3N2TiTF/+hp1CaUlMDW\nrbBmDTRtCv/3fxAQYBqB03Vy1d/i1KlTBAcH4+TkRNu2bdm6davuvezsbPr27YuDgwPBwcGkpqbq\n3psyZQru7u44OjrSvn37O9aAKiwsZNq0afj4+NC4cWN69uxJcXExycnJKJVK1Gp1tfv7+PiwZ88e\n3fasWbMYOXIkgO4YK1euxNPTEw8PDxYtWlThs8888wzPP/88Dg4OdO7cmePHj+vez8jIYOjQoTRp\n0gQ/P78K6+pd33fkyJE4OjqyZs2aO/xEhRDmTqPRkBWdxcFuh/h77GkaDmiC3/7uuI31keCpPvlf\n9fDGfTphs/wjkqd8TOLKWKMGT4WF8PXXEBoKe/fC7Nnwn/9A166mFTyBjEBVUFpayuDBgxk3bhy7\nd+8mNjaW0NBQDh8+jEajYf369Wzfvp2uXbvy5ptvMmLECGJjY/npp5+IjY3lzJkzODg4EB8fj6Nj\n9Ws5vf7665w6dYq4uDjc3d05dOjQXU0R3jqlWNm+MTExnD17loSEBHr37k3Hjh15/PHHAfjhhx+I\niopi/fr1LFmyhKeeeoozZ86gUCgYPHgwQ4YMYcOGDaSlpRESEkKrVq3o27evbt9vv/2WtWvXUlRU\nVOM2C+Mw5dELcWem1H8ajYas77NInpNC2RU1Dq964fWMJ4oGEjRVxVxHn5QH9mH3wVsosy+S9nI4\nBf2GGzViuXoVNm6EyEjo1AkWL4aHHzba6WvFJAOoGEXMPR8jWBN81/scOHCAgoIC3nrrLQAee+wx\nBg0aRGRkJAqFgkGDBvHoo48C8MEHH+Do6Eh6ejpWVlZcvXqVU6dOERAQQKtWrao9j1qtJiIigoMH\nD9K0aVMAunXrdtftvVll04vvvfcejRo1om3btrz00ktERkbqAqguXbrw9NNPAzB16lQWLVpEXFwc\nlpaWZGdnM2PGDAB8fX0ZN24cUVFRugAqMDCQJ598EgBr6/vj1mQh7icatYaMDRmkfpBGeTk0ntgM\np1APFEoTGwIQ90xx/Ai2897BKv5Pzo2dQV7oWGhgvNDg8mVt0LRxI/TooR1t8vMz2unviUkGULUJ\nfvQhIyODZs2aVXitefPmpKenA+DldSOT39bWFmdnZzIyMnjssceYOHEiEyZMICUlhaeffpqFCxdi\nb195TYzs7GyKiorw9/c33JeBCt/F29ubEydO6LZv/i4KhQIvLy8yMjJQKBRkZGTg5OSke7+8vJyg\noKBK9xWmx9RzaET16rL/NOUazq07R9rcc2islDhO9sZpYNP76o7ge6VSmUcOlCIhnkbzZ2BzYC/p\nI1/n8odbjFo9/OJFWLdOm+fUu7c21+mWX78mT8Zhb+Lh4UFaWlqF0ZyUlBQ8PT0BSEtL072en59P\nTk4OHh4eAEyaNInDhw/z119/cfr0aT766KMqz+Pq6oq1tTVnz56tdVttbW0pKCjQbZ8/f/62z9yc\no5Wamqr7Hrd+F7Vazblz5/D09KRZs2b4+vqSm5ure+Tl5bFt2zbAeHcjCiGMR12qJnVFKqoWcaR+\nkknj6b74/NgV50Ee8v97fZOehvWUMFwHd+eKx8P8ufksuaPeNFrwlJkJ8+fDsGFQXq4dfZoxw/yC\nJ5AAqoJu3bphY2PDggULKC0tJSYmhm3btjF8+HA0Gg3bt29n//79lJSU8O6779K9e3c8PT05fPgw\nBw8epLS0FBsbG6ytrau9M02pVBIWFsbUqVPJzMykvLycuLg4SkpKatzWjh07EhUVRVlZGYcPH+a7\n77677R+6OXPmUFhYyJ9//snq1at57rnndO8dOXKEzZs3U1ZWxpIlS7C2tqZbt24EBARgb2/PggUL\nKCwspLy8nJMnT3L48GFA7kQ0BzL6ZN6M2X/qYjXJy5JR+cVxLiIL5w9a4LM1gMZ9H5DAqZZMdvTp\nevXwx9tzzcKek9/Gc+lf76OxczDK6VNStEusjBgBtrbw3Xfw+uvg7m6U0xuEBFA3sbS0ZOvWrezY\nsQM3NzcmTpzI2rVradmyJQqFghEjRhAeHo6LiwtHjx5l3bp1AOTl5fHyyy/j7OyMj48Prq6uvPHG\nG9Wea+HChbRr146AgABcXFyYPn26LjipyT9cs2fPJiEhAScnJ2bNmsWIESNu+0yvXr148MEHCQkJ\n4Y033iAkJER3/NDQUDZs2ICzszPr169n06ZNWFhYYGFhwbZt2zh27Bh+fn64ubnx8ssvk5eXp9tX\n/mEVwryVXSsjcWEi+31VZG68hNsnD+HzXQCOvdzk/+/65moeVvNn4NazFSWXCvgr6jgXXv8EjbOb\nUU5/5gxMnw5jx2rLEXz/PUyaBM7ORjm9QUkl8nooOTkZPz8/ysrKUCpvj5HDw8M5e/Ysa9eurYPW\nVU6uC/2RHCjzZsj+K7taRvKyZDKXZGLZ3hbn13yw61wPfpOZEJXKRHKgbq4e/o9e2urhPtXf4KRP\nJ09qq4afPKldn27oUO3IkzFJJXKhdxKoCHF/Kb1cStLHSZz/NAurrnY8sLY9tu2qL7UizNTN1cP9\njVs9XKOB33+HVasgORnGjIG5c6G+3qwtAZQBtWnTpkIi93UrVqxg+PDhd9zfzs6u0uH0H3/8kR49\nelS7b3XD8DINV7/J6JN502f/lVwqIfGjJC6svEDDRx3w2NABm4eNk/Nyv6qz0Se1GovNX9+oHj77\na4o7B915Pz3QaCAuDv77X8jJ0S7wO2BA3Szwe7Ockgsk513GG8PcOS5TeMIkyHUhhP4UnS8icX4S\n2WsuYh3ihOtkX6z97eq6WcIQNBqUu7bhMP8dylFy7l9zKHx0oFGKYKrVEBOjnaorKdEu8BsSYtQy\nUpU6kX2IyKSP2X9xO+8GzuDN3tXnJF93t1N4EkAJkyDXhf5IDpR5u5f+K0wrJHFeEpe+zsZ6oDOu\nk3yx9jZy4sl9TqUyXg6UQhWD/dzpKC9dIu2VcAqeeN4ogVNZGezcqV3g19paGzj16gWVpNwaTbmm\nnN1pG9mQ8gmZRamMeugVnvUbTStvJxwdazbqKjlQQghxnylILCDxgyRyvsvBZogr3rsDsPJoVNfN\nEgai+OMwtvPexurM36SFzeBqaJhRhn1KSmDbNm3RSzc3mDIFunev2zXq8kpy+S7xC75N+5wmjR5g\nXLvJPNnyOSyVlhQU5APVryt7L2QESpgEuS6EuHv58fkkzE7kcvRl7J5rgss/fbBqUk8zdgWKs3/T\naN472Bz6lXOj3uDKc5OMUgCzsFBbfmDtWu0yK2PHaterq0tJeX/zdcJidp3fSM+mIbzcfgoBHoEV\nPlNQkE+TJur6MwLl5OQkCcziNjcvHSOEqF7e8TwSZyeRtycP2xFN8I3tRgNnq7pulqghlSqaXbuW\nolQWo1Y3pE+fyQQGDqzy84r0VKwXzMRu1w9kDJtE0tur0dhWvlSYPuXnw7ffwtdfQ9u28NFH0KaN\nwU9bJY1Gw/7zO9iQvJRTeYd57sGX2PPocTzt66aMudEDqJycHGOfUtSC5NGYL+k781Zd/10+fJnE\n95PIV+VjN+YBfPa3poFjHd/qJCpQqarPgVKpoomOfo3RoxN0r61Zo31+WxB1MQvrJXOw/24dWU++\nRMqmM6gbu+i/0be4cgWiouCbb+CRR+DTT6FFC4OftkqFZdfYmryab1KXoVQqCGs9kTUPb8LG0qbu\nGoXkQAkhhMnLUeWQGJ7EtaOFOIxriu+idljYyj/f5mjXrqUVgieA0aMTiIpadiOAyruC1bJ5OK5b\nwcXeQ0n75iTlTTwrOZp+XboE69drp+uCg7VJ4t7eBj9tlc5fSyMqYSlb0yNo79KF2T0+Jtj7CZOZ\nxZL/A0WlZATDfEnfmbeb+y/752ySZidTGF+Ew8ue+H3ujdK66nU2Rd270x14SmVxpa8rFEVorl2j\n4apPcPzPYnK6Ps6pNQcp8zb80E9mpja/accO6NdPG0Q1bWrw01bp2EUVkUkfc/DSbkJ9n2PLk7/y\noPNDddegKkgAJYQQJkSj0XBhxwWSZ6dSkl6Cwz898YjwRmFVu3vE7zbfRhiWWl1F0ve5LNwCH+Tq\nQ//g7892U9qyAwBHjkSjUt3ov8DAyXTurJ/+S0vTjjL98guEhmqn7NyMs0TebcrUZexMiyIqeSk5\npecZ8/CrfNJ3BY2tTTc/VgIoUSnJozFf0nfm68rvV1g/fD3tSjvi+KoXXsO8UDSofXGdu8q3EXqh\nUlWfA9Wnz2TWrEmo0CdrP2hA6AULTs//lpKON+4kO3IkmtjY1wgLu/HZL7/UPr+XICohQVv8Mi4O\nnn0WNm+Gxo1rfbjb3E3Qd7n4Et8mfsZ3af/By86bCZ2mMejBZ7BQmv5IqwRQQghhIhLeS8SirT1+\nS7qjsLj3PI8a5dsIowoMHAgaDRuWvUuDjHjUJQ0I6vU6Xi/OpOSWz6pUSysETwBhYQmsWbOsVgHU\nqVPadeqOH4fhw2H6dLDTc4H6mgZ9Zy6fIDJxCXuyvqO3Z3++7LuJTg901W9jDEwCKFEpGcEwX9J3\n5qm8qJyrMVfp9+uzegmeoPp8G2EYd8yB2reLfvPep//VItJeWcO1kGeqrERZVf8plXfXf0ePagOn\nhAQYORJmz4ZGBqqzWl3Q949/DCA2M5qo5CWcuXqc4S3GsjfoLx6w8zBMYwxMAighhDABF3+6iGUr\nayzd9FcIs6p8G41Gim0am+LIAezmvU2D5ATSxr9H/qDRYFH9NFVV/adW37n/NBo4eFAbOGVlwZgx\nsHgxWBm4XFhVQV928Vme/rkVDRtYMa7NZJ55aBvWDcz7OqzDlWuEKYuJianrJohakr4zTxc2X6RR\nH2dUqhi9HVObb+Nf4bU1a/wJCZmkt3OIilSqmIov/HUc21GDcQ4bwoUeofy9+Qz5oWF3DJ4AAgMn\n8+WXFftv1Sp/AgOr7j+1GvbuhdGjYeFCGDIENm2Cp582fPCkPX/lQd+l4it82PMzfhl2ghfbvmz2\nwRPICJQQQtQ5jVrDle2X8fjWFy6c09txr+c5RUUt094mr7Fm4MBJkv9kDMkJNFrwLrZ7d5LxwhRy\nwqOg0d0t7Hw9Z2jNmmUolUWo1dYEBU2qNP+pvBx279Ymh1tYaJdbeewx4y/wGxg4mc9XnuRf4zN0\nr/33y2ZMHf45gd4hxm2MgRl9LTwhhBAV5ezP4a/R8fjt617XTRH36nwG1otmYb/tWzKHjOfSS9PR\n2OvxFrdblJZq6zdFRGjvpBs7Fnr0uPMCv/ouj1CqLuXHlK/ZkLqUq2fSaHfZCU97NywUdoSE1E3Q\nXu/WwhNCCFFR1uYLWD9uuvVuRA3k5tDwkw9w2BDBhX4vkLrxL9SuDxjsdMXFsGULrFmjrRb+9tvQ\npcudAyfQb3mEnKILbEz8lM3nVuJj78+//zGd/s8OMYsyBPdKcqBEpSSPxnxJ35mfnK252PdrAlSS\nQyNMW/5VrBa+h9ujLSjNuMiatz4j6/+WGyx4unYNvvoKnnwSVCqYPx8+/xwCAmoWPEHVd8qpVMtq\n3I7TuX8w68gYhvzSkgvlCXzVbyvfD4llUAvzqOGkDzICJYQQdSj/dD7luWXYBcgIlFkpLsbyy6U4\nfr6QKx16cGrlr5T5PYz6cIxBTnf1qnaB3w0btCNNy5ZBy5a1O1ZtyyOoNWr2ZWwlKnkJiQV/MaLl\neMKDT+FuW4frvtQhCaBEpaSWkPmSvjMvWZuysH6sMQqldvjgTnWERB0rK6NB5Cocl8wh37c1p5dE\nU9K6i+7tLl2C9Xq63Fzt2nSbNkHPnrByJfj63tsx77Y8QkHpVbYkr+KblOXYWNowru1khj40koYW\nVSxLc5+QAEoIIepQ9pYc7MY1q+tmiDtRq7H4PhKHhbMoaezG2fC1FOs5WLrZhQvaBX63bYM+fbTP\nPT31c2xteYSECtN4q1b5ExRUsTxCen4SkQlL2J65li5uPVgQ9AU9mz1+Pdn6vicBlKiUrKdmvqTv\nzEfxhWKKThbi+diNFVxVqurXUhNGptGg3LkVhw9nUI6S5CkfU/jowCoTjg4fjrmnUaj0dG1i+K5d\nMHiwdsquSZNaH65S1ZVH0Gg0/H4xlsikxRzJ3ccQ3xfYFnoQP6cW+m1EPSABlBBC1JGsLVk07G6P\n0vr+SLo1N4pff8Z+/jsoL10i7ZVwCp54vuaZ2ncpKUlbiuDXX2HoUO2UnZMB0+I6dx5Y4Y67UnUJ\nPyStZkPKUvLLc3mp9QQ+7/cV9g1rVgLgflSTK+FLYCBwAWj3v9c+AgYBJUAC8BJw5Zb9pA6UEEJU\n48jAo1gGu+A6wruumyJuojh6CNv572B1Np60sBlcDQ2DBoYZb4iP1y638vvv8Pzz8NxzYG9vkFNV\n6noZgk1pK/BzaMH4dv/mCb/QenEnnaHrQNXkgz2BfOArbgRQfYA9gBqY/7/X3rplPwmghBCiCmXX\nytjvrsJn/yNYut5dMq5KFc2uXTeKIPbpM1mqi+vD3yex+XAGjY4cIH30/3Hl2VfRWBkmUfr4cW3g\nFB8PL76oXWrFxsYgp6rU6dw/+DrxY3658D19vAbzSocptGvyD+M1wAhMoZBmLOBzy2u7bnp+EBha\n0xMK8yB5NOZL+s48ZP+UjeXDjW4LnlSq6nOgVKpooqNfY/ToGwnAa9Zon0sQVUspiTRaMBO7X3aQ\nPvw1kt5dh8bGrlaHqi4HSqOB337TLrdy7px2vboFC6ChkW5mu7UMwYstX+b94L9pYmu4gp/1mT7G\nJMOASD0cRwgh7hsXvr+ITYjzXe+3a9fSCsETwOjRCURFLas3AZTRRtiyMrFeHI79D99wfsg4Ur4/\ni9pB/4lHGo02t+nLL+HKFRgzBvr3B0tLvZ+qUreXIXiNoQ+9eN+XIbhX9xpAvYM2D+rryt4cM2YM\nPj4+ADRu3JiOHTvq/jK+Xi1Ztk1z+/prptIe2a75dnBwsEm1R7Zv3/7l5184seUEg7aGATeqjwcG\nBhMYGFxh+9b3lcpijh0DgI4dtf89dgwyMs5zXXX7m/q2ShXNf//7Mv36Zei+3/z5J/nzz4mMHz9d\nP+f76QcsN69nwN5dXHhiOJtm/Be1ozNd/hc8Hf5fMczrI0l3s92lS7Buu1OnYH7+GT79NAa1GiZO\nDObxx+Ho0Rj++KN2x7+b7aYPNScyYQk/7P+SVo3bsvDZFfTweoy4uL0cORhnEv1tyO0OHbT1uar6\n//H68+TkZGqjpnN9PsBWbuRAAYwBxgOPA5WVL5UcKCGEqETOrzn8FRaPX8zdLx4cHv4Ew4fvvO31\nqKgnmDnzR300r04Z9PsV5GP1xUIcv1zGpR4DyXolnHLPe6xKWYnSUvjpJ+1ddba2MG6ctgimMcon\n3VyG4HDOXp72G8H4Dv/Gt/GDhj+5iTGFHKjK9APeAHpRefAkzNzNo0/CvEjfmb6sTVUvHqxSVZ8D\n1afPZNasSbglB8qfgQMnVbmPOalqmRGF4h5+1dy67MqKfZT5t6n98apQUgLLl8cQExPMAw/Am29C\n167GCZxK1SXsSPmaDSlLuVqWw0utJ/BZvzU4NHS852PLTQuVq0kAFYk2UHIF0oD3gOmAFTeSyeOA\nVw3RQCGEqG9ytubitrBVrfa9/osrKmoZCkURGo01AwdOqje/0KpaZkSjqXyZkWqVldHg65U4fjK3\n0mVX9KWwEDZv1lYLb9IE3n//xvSqoeUUXWRj4nI2pa3A1+FBpnR+m/7+Q/RWhkBuWqiaIeNimcIT\nQohb5P+dz+9Bx/D/vYdu/TtxQ+W/sP0ZOPCTmv/CVqux2Pw1DgtnUezsTvqr8yjuHKT3tl69Chs3\nQmSkNmAKC4OHH9b7aSp1Ovc4kYkf8/OFzYR4DuTlDlPo4K7/4NCcp4xNdQpPCCFELZzfdB7rxx0l\neKrCPY2waTQof9yCw4IZlCstSZ72CYU9Buh9Du3yZW3QtHEjBAbCF1+Av79eT1EptUZNbMY2IpOX\nkJB/khdajmNf8CncbZsa7JwGmVKtJySAEpWSPBrzJX1n2i5tycH+laorj6tUshZeYODAu54eUuzb\njf38t1FcydMuu9JnmN4Dp4sXYd06+OEH6N1bu2Zds1vWgb7XtfAqc600ny3JX/JN6nKsG1gxrs1r\nPPPwKKOUIdDrlGo9IwGUEEIYSVFWEUV/FeEZ7HbnD4saURw5gN28t2mQnMC5cTO5OngMWOh3GZLM\nTG2w9NNPMGCAdvTpASPUnszITyYqcSnbMlbTyfURPuz5KT2bhVyfajKK+n7Twr2QHCghhDCS1P+k\nkrH5Et5fdqrrppg9xV9/YDN/BtZ/HObcmOnkPfNPNJZWej1HSgqsXg0xMTBkCIwYAS4uej1FpY5e\n3M/XiYv4LecXnvIdzvgO/8bfqaXhT1wFlSqa3btvTKmGhJjHTQumsBZebUkAJYQQNznS/3csH3fF\n9QVZPLjWEs9gs+BdbH7dQ8YLU8gZ/m9opN9F5M6c0VYNP3RIu7jvc8+B471XA6hWmbqMn9Ii2ZC8\nlJzSLF56eAIvtn0Fx4aNDXvieszQAZSylu0S9dzNlVqFeZG+M01l18rI/zWfxv2qn/tRqWKM0Rzz\nk56G9dSxuA16hCtufvy5+Sw5YW/rNXg6eRKmToUJE7R30/3wA7z88t0FT9ergNfUleIc/ntqNoN3\n+7A5/TMmdJrGwReSmND5/yR4MnGSAyWEEEZw8ceLWLZuRANn/U4z1XvZF2j4yRwcvl1H1sCRpH77\nN2rnJno9xe+/w3//C8nJ2gV+584FawPnSCdc/pOvEz9md9a3PObRj1V9vuMfTR8x7EmFXskUnhBC\nGMHxkSco97bBfYIR7nevD/KuYLV8Po7r/sPFx57m4suzKHf30tvhNRqIi4NVq+DSJe0CvwMHGnaB\nX41Gw/7zO4hMWkL81d95/sEwwtpPxsNef99L3CB1oIQQwsxpyjVc3nEZry1+dd0U03etAKuVS3Bc\n+TE5XUM4tfogZd4t9HZ4tVqbFP7ll9qlV8LCICQEGhjwt2Fh2TW2Jq/mm9RlKBQwts0k1j78PTaW\n+s3dkiVXjEsCKFEpqSVkvqTvTE/O/hyULg2w9rW942dVqvu0DlRJCZZrPsPx0w/Jax3Aqc9+pqxl\ne70dvqwMdu3SLvDbsCGMHQu9eoFSz5nAN9eBunAtnaiET/ghPYK2zp0I776I3j79DVKGQJZcMT4J\noIQQwsCyNl2gUUjliwff98rLaRD1JQ5L5nCtWQviP/qe0nb6ywUqLYVt27TlCNzc4N//hu7dDbvA\n75tOaCUAACAASURBVInsQ0QmLUaV/SMDmz/Ld4NjaOWi/8WLb7Zr19IKwRPA6NEJREUtkwDKQCSA\nEpWSEQzzJX1nenK35eL28UM1+ux9M/qkVmOxJQqHReGU2DuTODOCooDeejt8URF8/z189RX4+cGs\nWdDJgOW3yjXl7Dn3HVGFS8g8msLoh/7JwpBPcW5khMJRyJIrdUECKCGEMKC8P/Mov6rGtpOMQAHa\n9ep2bsVhwbuUqyF50kIKgwbpbUiooAC+/RbWr4d27eCjj6CNAQd/rpZcYXPyf9iY8hnO1q6Mb/ca\noS2fx1JpwGz0SsiSK8YndaBEpaSWkPmSvjMtWRuzsO7duMaLB6tUMYZsTp1S/PozDoMDcQh/g7SR\nb3Hm62MU9hqsl+DpyhVYsQKefBLi4+HTT2HRIsMFT6lXz/LhsYk8uceX+IIDLO+9jp+ePYxHTjOj\nB09wfcmVind4rlnjT0iILLliKDICJYQQBnD58GUSw5PIj8vngQjD5r+Yugrr1YXN4GpomN7Wq7t0\nSTva9P33EBysTRL3NlChd41Gw+ELvxCZ9DHHLu/nGf9R/PT0EbwdfQ1zwrtwPc8pKurGkisDB5rH\nkivmSupACSGEHuXE5ZA4K4lrRwtxGNcUl5eaY2F7f/6tqluv7vgRzo1+S6/r1WVlafObtm+Hfv1g\n1Cho2lQvh75NqbqE7Snr2ZDyCdfKrxLWZiIvtB6HnZW9YU4o9ELqQAkhhBnIjskm6f1kCk8V4fCK\nJ36fe6O01s8oi7lRJMTT6MN3sVH9QsaIqeSEb9Dbkitpado76n75RTtd98032rvrDCGn6AIbEz9l\nU9oK/Bxa8HrAe/TzC0WpkOwXITlQogqSR2O+pO+MR6PRcPGnixzq8RunXozH6nFX/FSBNHnZt9bB\nk0oVo88mGpUiPZVG/34J18HdyXugpXa9upem6yV4SkiAGTO0S624ucGmTdqSBIYIns5cPkH4kZcY\n8ktLLpQn/D975x3eVNmG8V/SvSfQ0g2i7A0iCqKAqICKqIgIBcT1IeAWx4cfyt6jgCCr7L2RJVBF\noiK4UEChTbpXunczzvfHYVMgbdM2ad/fdXGZdc55T09M7jzv/d4P657Yz84B3/Nk4wF3FU8qVZT5\nBySwSEQFSiAQCMqJJEmk7ktF80UcunQ9HqMDCXghEIVdHf1NmpaC47xJuO3cQGr/4Wi2/YPkbR5l\nc/68nBr+xx8weDCMHw+urmbZ9Q1IksSJ5P1sVM/lUv5ZXrp3FN/3OE8DlyqaFxQA1p2eLjxQAoFA\nYCKSJJG8PZnYyfEY8o24jw7EZ2AgCpuq/Ci1YLKzcFg4BfcNK0jv9Rzpr36OoX6AWXb9+++ycLp4\nEYYOhQEDwMnJLLu+gSJ9IbvVK9kaH4Gd0oZRLcfxXNNhONqK5f9VTdnp6Y3p23e+WUSU8EAJBAJB\nDSMZJZI2JhE7OQ6jpMDzrSC8nm5ocjRBrSM/D/uvZuGxKoKMrk9ybu1pDIGV7/MnSXDqlNzgNyVF\nbvA7axbYm8d3fgNphYlsjJ7HnsRVtPHpxOQH5/Nw8GNV0mZFUDbWnp4uBJSgTEQ/NetFXDvzYdQb\nSVybSNzUBHBU4vluKJ5P+FXpl6xKZcG98IqLsVuxAI+vZpHdrhvnv/4BfaNmld6tJMGJE7B8ORQW\nyg1+H3usahr8ntWeYkPMbH7MOEy/kOfZ/dQP3ONtWkq8KahUFnz9LAxrT08XAkogEAhuwqgzkrAy\ngbhpCSh9bPH6rBEePevX3eqEToftuqV4LJhKfpPW/LPgILpm7Su9W4MBjh6Vp+qUSrnB7yOPmL/B\n79U2K5p5pBTHMazp68x5bAlejt7mPZCgXFh7errwQAkEAsFljCVG4pbGkTAzEWWgPV7jQnHv5lt3\nhZPBgM2WSDzmfUmRXwiJb0ymtN2Dld6tTgcHDshxBB4esnB68EHzN/jN1+WyQ/1VjbdZEZSN8EAJ\nBAKBlaMv1BO3KI7EOUnY3utEvflNcetSPU1gLRJJQrlnMx4z/0epizsxHy+juEvvSu+2pAT27IHI\nSAgKgo8/ho4dzS+c4vOi2RgzjwNJ6+nSoDsLH11Ll4Bu5j2IoNJYe3q6qEAJykT4aKwXce1MR5+n\nR7NAQ/L8ZOxau+A9LhTXDjU7raNS1aCHRpJQHtmH24z/yv6vN76k8OGnKq1wiopg+3ZYtw6aNpUr\nTq1amWnMl5EkiTPp37FRPZdfs04wsNEQXm3zDiEelTe3lweVSnigLIUzWWm4ext52N/PpNeLCpRA\nIBDcBV22DvUcNSmLU7G/3w2/ta1xaeVR08OqUZTfH8F1+mcos7KJf/VzCvq8WGkzUl4ebN4s/+vQ\nARYsgHvvNdOAL6Mz6jgYu4FNsfPJ02cyovlovnp8LW4Opk3bCGofP+ZlsDBTwzl9IbM8q05AiwqU\nQCCoM5Skl6CeqSZteToOD7vjMyYM56Z1+4tWceokrtM+xTZeQ8Ir/yWv//BKN/rNyoING+SqU7du\nchxBmJn77eaUZLIlJoLt8UsJdg1lVMtx9L1nIDbKutk+p64jSRKHc1JZnB1HqlHHewENeTUoCOdy\nLOUUFSiBQCC4ieLkYmKmxaCN1OL4mBeBu9vh2LgK4qytCMWfZ3CZ9hkO5/4kYcTH5Dz7Omf+PIxq\n8ZNXU6G7dh1Lhw6m+1HS02HtWti7F3r3lm8HmCdX8yoxOedZHz2Hb1O38kjDx1n12E7a+XU270EE\nVoNeMrIzM4mvchJAKfFRUCAvBwRga+6lnGUgBJSgTISPxnoR1+4aRfFFxEyJQbsxA6d+3gQe7IBj\nsEtND+uOqFRV7KH552+cZ/wX51MnSRz6HtlTdyI5OHLmzH5OnBjHyJHXVkStXCnfvpuISkyUjeFH\njkD//vKUXf365huyJEn8nHqE9eq5nMs5xaAmIzne7S8augWa7yBmQqUSHqjqoNhoYENGPF/nJtLA\n3o6p94TydIMG1bpiVggogUBQ6yiILiBmsprMHZm4POtLyNFO2PtXQR8Qa0J9CadZn+N6/CCJL45B\n/Ukkkovb1adVqgU3iCeAkSOjiYxceFsBpVbDqlXwww8wcKDc4NfLy3xDLjWUsC92DZtj56OXSnml\nxRgim2/D2c6yRbCg6sjV61idEcvKvBTaODuxqtl9POrrWyNjEQJKUCaigmG91OVrl38hn+gvY8j+\nJhvXF+sT+l1n7OpZRyjfFcxevUiMx3H2RNwO7CB5wKvE7rqE0f1WlXO7VGil8tZU6H/+kcMvz5yB\nF1+E3bvBza2MjStIRlEqW2Ii2JGwjHs9m/PJ/VPoHdYPpcLymzWL6lPVkK4rZqlWw8aCdB5xc+NA\n65Z08PSs0TEJASUQCKyenD9yiPlSQ96xXFyHNiDshy7YelVBAzVrIi0Fx/mTcduxntS+Q4nbfgGj\n9+3n1W6XCm00XhOgZ8/KfeouXICXX4bPPwdnZ/MN+d+sP9kQM4fjabvoE/QUm548RIt6bc13AIHV\nEVtcwOIMNXsLMxng7cXP97XjXlfL8C9avpwX1AhRUVE1PQRBBalL1y7rVBa/9vuNP3r+iRTmTKiq\nC34f3WvV4kmliqrcDrIycfjiA+o93Jzi3BLObT5L2vvz7yieALp2HcvKlY1veGzFisY88MAYTp2C\nN96Qgy8ffFCuOL38snnEkyRJfJ+0jzdP9mT0qV6E+QRy4oULLOi1xirFk0oVVcMjqB2cK8xldPwf\nPJlwBm8XJX937sSqVq0sRjyBqEAJBAIrJPNkJjET1RT+UYT7q/6EzW2FjUsd/zjLy8X+q1l4rIog\n46F+nFt7GkOg6Rk4V3xOkZELUSqLMRod8fEZw6JFfcnJkaMInngC7MzUBaVIX8hezWq2xC3ERqlg\nVMtxPN90P4621jXlKjAvp/IyicjS8HtpAaP9GrAitBne9pb5g0jkQAkEAqsh/Wg6mi9iKb5Ugvvr\nDfF5ORilY93O/ZEKC3FYMR+PpXPI6tCDlDe+RB/WtML7Mxrh2DHZ42Q0wsiR0LNnpaOhrpJWmMSm\n6PnsSVxJS+92vNrqbR4NfaLu9hsUIEkSR3PSWJwdR4KxlHca+vNGcDAu5chwMgciB0ogENQqJEki\nbX8amkmxlCbrcH8jkIaDg1DY13EHQmkpdpGL8Vg0ndzmHbmw6Ai6+yo+5aXTwaFD8qo6Fxd5yq5b\nN/P1qTuf+Svro2fzg3Y/TwYPZFu/4zT1bWmenQusEoMksScriSU58egUEh8EBhAeGIhdNWQ4mQNR\ngRKUicgSsl5qy7WTJImUnSnETopDn2vE/T+B+DwXgMLWOj5cK4pKdZccIb0e2w1f47FgKgXB95L4\n5mR0re6v8PFKS+Xgy8hI8POT+9R17mwe4WSUjHyftJcN6jnEFf7Ly01fY0TLt/Bxrlf5nVsoKpXI\ngbobpZKRjdp4luUm4m1nw/jgIAb6+6Os4SqkqEAJBAKrRjJKJG1KInZyPEYJPN8KwuuphiiUdXyK\nx2DAZttaPOZ8QXG9AC79bw0lHXtUeHdFRbBzp5wW3qQJfPEFtDWTZ7tIX8Au9Uq2xC3A0daRV1u+\nzXNNh2JvY5leFkH1kG/QE5kRy8rcZO5zcmRp0yb09vW12ulbUYESCAQWgVFvJHFNInHTEsBJieeY\nEDyfqN5kYYtEklDu2YzHrInonNxIfPNLih7oU+Hd5eXB1q2wcaMsmEaOhGbNzDPUtMJENkbPY0/i\nKtr6dOL1Nu/SLahXlV5DlWo/R44suNp+pnfvsXTtanr7GUHVk6kvZVm6mvUFaTzo6sqnYaHcb87E\nVTMhKlACgcCqMJYaiV8RT/z0BJT17fH6byM8Hq0vhJMkoTy4G/eZEzBICmLfmk5h9/4VnlvLzpZF\n09at0LUrfPUVNG589+1M4VzmadZFz0alPUC/kBfY/dQP3ONdcSO7qahU+9m/fxzh4dcS1CMj5dtC\nRNU8iaVFLNGq2VmopZ+nF9+3bUML99rTvFtUoARlUlt8NHURa7l2hmIDcUviSJidhG2oA15jQnDv\nVnu9MaaiOnmch0pLcJv+X8jPJ+G1/1HQ+4UKC6f0dFi3DvbsgUcfleMIgoIqP06jZCQqcTcb1HNI\nKIpmWNPXGd7qLbydfCq/cxOZOLEPgwcfvuXxTZv6MGHCwWobx/WoVMIDdbEoj0UZGg4XZzHEx5eP\nGoUR7GT5rZREBUogEFg0+jw9sRGxJM1LxraFEw0WNcO1k3dND8siUJw8jvNnY3EvLCRh1ATyn3y5\nwvkBycmyMfzQITm/aeNG2SReWYr0BexUL2dL7EJc7F0Y1WIcA5u+XCP+ptu1n1Eobm0/I6h6fsvP\nIiJTw6nSfF6rX5+Lbe6nnkPZCfe1ASGgBGViDRUMQdlY6rXTZetQz1WTsigV+06u+K1uiUubmu1l\nZSkoTv+I6/TPsIu5SJPhH3NhwKtQwQyc2FhYvRqiomDAANi2DXzMUBRKLUxg4+X8pva+XZjZfSkP\nBT1ao1Ott2s/I0k1F8ZZ16pPkiRxIk/LoqxYLumLebuhP1tCWuFWzRlONUHtP0OBQFCjlKSXoJ6l\nIe3rNBy6u9Nwcxucm9UeH0RlUPx5Bpfpn+Hw9x8khI8nd84bSHYVq+RcvCiHX546BYMGwa5d4OFR\n+TFe8zcdpF/I8+x56mS1+JtMoXfvsURGRt/kgWpM375janBUdQOjJHEwO4VF2XHkYOCDwABGBgXh\nYCUZTuZAeKAEZWItPhrBrVjKtStOKiZmegzaNVocH/PC960wHBtbTh+rGuXcnzjPnIDz6R9JHPoe\n2YPGIjnIVZPTp6PoWI54gr/+koXTX3/BkCHw3HNyEGZluNnfFN7sDcJbjq5Wf5OpqFT7+fbbhSgU\nxUiSI716jalRA7lKVbs9UHrJyNaMRJblJmBvo2B8cBAvNmyITS1Y9CE8UAKBoEYp1BSinqpGuzkD\n56d8CDrYEYcgM3SdrQUoov/BacYEnH84StLgcaj/uw7JuWKi8tdfYfly0Ghg2DCYMgUcKzlzJec3\nrWBz7AJc7F14teXbPHvfEIvOb+ratW+VCCYRj3AjhQY96zPi+ToviWB7e2Y3aUTf+nV7tayoQAkE\nArOQfzGfmElqsvdk4TzQF9//NMLeTzSGBSA2BqfZ/8P1230kPT+azJffR3Ir//yaJMGPP8KKFaDV\nyivq+vWrfIPfK/lNuxNX0s6nM6+3eY9uQT3r7Jdj2fEIjenbd36dE1E5eh0rtRoi81No5+zMZ2Gh\ndDOHqc4CERUogUBQreSezSVmkprcw7m4DKlPyPf3Y+dTe1felIvEeBznfIHbN9tJeeYVYndewuhR\n/hWHRqNsCl+5EkpK5PDL3r0r7DO/yvX96fqGPM/up36gibeZUjWtmCNHFtwgngDCw6PZtGlhnRFQ\naaXFLM3QsKkgnV7u7hxu05q25jDV1SKEgBKUiaX4aATlp7quXfaZbGK+UJN/Mh/XcD9CVc2x9ahk\nKaS2kJqM47xJuO3aSOqTLxO37TxGnwYmbXq9B0qvhyNH5Aa/dnZyn7oePaAyPl2jZORE0j42qOcQ\nW/gPQ5u+zvSeF2t1f7ryUpl4BJXKuj1QmuICFmvV7CvKZKC3N780bc89lTXV1VKEgBIIBOUi82Qm\nMV+oKfytCPdR/oTNaoWNi/goAUCbhsOCKbhvXUP6Y4OI2/wXxvoNy70bnQ727ZPjCHx84O234YEH\nKtfgt0hfyF7NajbFzsfB1o5XW74j+tPdBkuMR6hqzhXmEJGh4buSHIbXq8e51p1pWFlTXS1HeKAE\nAoFJpB9NR/NlLMUXS3B7rSG+Q4NROlYs5LHWkZWJQ8RU3DesQPvIANJe/RyDf3C5d1NcLMcPrFkD\noaFyxal9+8oJJ21RCpui57MrYTktvdvzRpt3eTj4sTrrbzKFuuSBOpWXSUSWhj9KC/iPvx9vh4bi\nVVlTnZUiPFACgcBsSJJE2v40NF/GUpqqx/2NABquDkJhX/1ZL5ayKuqGcZTa8ERBPfoeOkJG1yc5\nt+YXDEHlbzBXUCAHXq5fDy1bwowZ8n8rw79Zf7I+ZjZRabt5IngA2/odp6lvJXdaR7jyvtq06Vo8\nQt++NRuPYE4kSeJoThqLs+NIMJbyTkN/dge3xqUOhF+aE1GBEpSJ8EBZL+a4dpJRInl7MrGT4zEU\nGnF/MxCfgQEobGsmJM9SKgJljmOmCw89MJt2T75e7v3l5MDmzfK/zp1lc3hOTvlyoK5HkiROphxg\ng3oOF/P+5OX7XmNkqzHUczHNfyWoPCqV5XqgjJLEnqwkFufEU4rEh0EBhAcGYleHwi/vhKhACQSC\nCiMZJBLXJxI3JR7JVoHH6GC8+vujUNbsdI+lrIo6cmjureP4oIDIyJ20w3QBlZEhV5t27YKHH5ZX\n14WEyM+dPl3+cZUaStgXu4ZNmnlICiOvthzLC8324WgrPCwCKJWMbNYmsDQ3AU87GyaEBfOcvz9K\nMY1bKe4moFYCfYE0oNXlx7yBzUAIoAFeALKraHyCGkJUn6yXilw7o85IwqoE4qclgKctXh+F4fFY\nA4vxydR409jiYuxWR+Dw+/cw5NanlUrTxpGSIvubDhyAPn1kEeXvf+NrylN9yixOZ0tMBDvil9LE\nsxn/7TKdXmF9Lea61UUsqfpUaNCzJiOO5XlJNHF0ZEnTJjzm6yveH2bibgJqFbAQWHPdY+OBI8AM\n4KPL98dXyegEAkGVYig2ELc0jsRZSSiD7PGe0gT3bpb3AVtjq6JKS7Fb+xXuEdPJv6cV+SHtgZ/L\nGN+dxxEfL6+oO3YMnnoKtmyBepVIDVDnXmDdpdkcTd1Gz8C+bHjiAC3rt6v4DgW1iix9Kcu1Gtbm\np9LF1ZXtLZrzgHf588cEd+ZuE58ngKybHnsKiLx8OxJ4xtyDEtQ8UVFRNT0EQQUx5drp8/VET4tG\nFfojKTszqTe/KaHbOuHRvZ7FiSe40jT2RnN2ZGRjevWqoqaxOh22kUvw6XoPtvt2c3HqVmIXHuSB\nPv9l5cobx7FiRWO6di17HNHR8NlnEB4uxxHs2AHvvHNn8XT6dFSZj0uSxC+pxxj3Y19GqR7Ez8OT\n48//xaLe64R4siBUqqgaO3ZyaRGfJ53jIfVPpNgUcbxtG/a1byfEUxVREQ9UAyD18u3Uy/cFAoEV\noMvWoZmrIXlRCvYdXWmwogWu7bxqelh3pdpWRen12GxZjcf8yRTXD+LS/9ZQct2UWocO8vEiIxei\nVBZjNDrSvfuYq49f4fx52df0++8weDB89BG4uVVwSEY9h+I3skE9lwJDDqNajmVV8y0424lwQ0vi\nyurM5ORUjhxpUK2rRGOK81mk1XCgOJNBPj6cadaBRiL8ssqprIlcuvyvTIYPH05oaCgAnp6etG3b\n9qo/48qvZHHfMu9fecxSxiPum36/R48etzx/eOdhUjanEHo4DIfu7sR/nItDiIHgy+JJpZJff8W/\nYZn3XZgw4eANz1+h0vv/4SjK74/wxL7tlHr4smngaEqbd7zqR7pSFerYsQcdOvRFklyu3r/+eVvb\nHqxYAX//HUWfPrBnTw+cnG7c/ub93Xy/Y8cenD4dRaE+nxivv9katwjXJFf6h73Au4MmoFQoLeR6\niPtX7n/99VR+/DGC8eOTAFk4L1/+F7CMrl37Vtnx3du2Y2GGhqifvuNJL0/+eeEFGjg6EhUVRRyW\n8Xlkyfev3NZoNFQEU2r1ocBerpnILwA9gBTAHzgONC1jOxFjIBDUMEWJRainqdGu1eLYxwvft8Jw\nbOxa08O6So1nOxmN2OzaiPucL9E5u5Hw2kSKH3yiXMmVkgSnTskNflNS5Om6/v3B3h7OnNmPSnXt\n/Lp2HXtLtepmkvI1rI+ezTdJ6+nq9whvtn2fjv4PVPZMBVXIxIl9GDz48C2Pb9rU56roNyc/5WWw\nMFPDOX0Rb/k1YGxoKB51NPzSnFRHjMEeIByYfvm/uyqwD4GFc331SWBdREVF0SmkEzFT1GRuzcT5\naR+Cj3TCPsCppod2A2VnO8m3q1xESRLKPVtwnzMRg60jmjEzKerer9zC6cQJWL5cDsIcMUJeWXfl\ne+zMmf2cODGOkSOvnd/KlfLtskTUWe3PrIuZier0IV7oOZyDz54mxKNRpU5TUD1cv0r099+hbVv5\ntjlXiUqSxLc5aURkx5FqLOW9gIYcCA7G0UZ0A6gp7iagNgIPA75APDABmAZsAV7hWoyBQCCwAPIv\n5HNpcjSK00pcX6hHyPHO2DewzCygGsl2kiSU+7fjPucLDEaIe30yhY88Uy7hZDDA0aOyx0mhkMMv\nH30Ubv4eU6kW3CCeAEaOjCYycuFVAWWUjEQl7ma9ehbJxbGMaD6alz2G0/vhfpU+VUH1UZWrRA2S\nxO6sJJZkx2NQSnwUFMjQgABslSL8sqa5m4AafJvHe5l7IALLQlSfrIuc33OI+VJN3vE82g15iHpz\nw7D1rpkmsaZOy1VrtpMkoTy0B7fZ/0MqKSVu1OcU9n6+XMJJp5Pzm1avlg3ho0fDQw/dfhe3Oz+l\nspgifSG71SvZHDcfZztnXmv5Ds82HYKdUkzDWCPyKtFowsOjr1af5KT8iq8SLZWMbNLGszQ3ER87\nGyY2CuZZEX5pUYgkcoHAisn8KRP1lxoKfinAbbgfYVNaYONWc1/C5ZmWq5ZsJ0lC+e1+3Gb9DwoK\nSBg1gYLHBkE5fr2XlMCePRAZCQEBMH48dOp0d+11u/PT5MbR/9sQWnq3Z3q3xXQL6mWR0REC0zHn\nKtECg57IjFhW5CbT1MmRZU2b0EuEX1okoheeoEyEB8qy0R7Top6kofhCMW6vNsRnaDA2zvLvIZWq\n5npxlcdMW6X97SQJZdQhXGd9jjIzi4RR/yX/iSHlEk5FRbB9O6xbB/fdB6+8Aq1bmz6EsjxQXyxU\nYNP0EcYPmkcz31ZlbqdSWW4vNcHdUakqdv2y9KV8fTn8squrK5+FhXK/l+VHjNQmRC88gaCWIkkS\nafvT0EyOozSpFPfXA2i4MhiFveV4IcozLVdV2U7K7w7jOvNzlNp0EkZ8Sn6/YbcalO5AXp6cFL5x\nI7RvD/PmQdOy1hnfhfbtn+SfrN8YP38eenLwcgjipQETefLRoeXfmaDWklxaxBKtmu0FWp709OS7\ntm1o6e5e08MSmICoQAkEFo5klEjenkzslHgM+Ubc3wzE57kAFLaWI5yuUN3Lua9H8f23uM36HJuU\nZBJGfkpev3CwNf03YlaWLJq2bZO9TSNGQFhY+cdxLfhyDgWGXF5tOY7BzV8RwZeCG4guzmeRVs3B\n4ixe9PHho9BQwkT4ZY0iKlACQS1BMkgkrk8kbko8kq0Cj9HBePX3R6G0XC/E9WbaK1TWTHs3FD8c\nw3XW59gmxpMw/BPynh5ZLuGUng7z5+8nLm4Bfn4lPP64Az17jiUsrHyVsHxdLjvUX7E5NgJ/5wDe\n7vAJfe8ZiFJheUJXUHOcLcghIlPNyZI8Xqlfj39ad6aBo2WulBXcGSGgBGUiPFA1h7HUSPyKeBJm\nJoKXLV4fheHxWAOTTaQqVc15aKqt5Qqg/Ol7XGZMwDZOTUL4ePKeGXUthMkEkpLkFXXHj+/nwQfH\nERFhWl7TzaQUxrPh0lz2Ja3m/vrdWdJzI50bPlju87mCSiU8UNaMSlX29bsSfvm3vpAxfn6sC20h\nwi+tHCGgBAILQV+oJ25JHIlzk7EJccBnShPculnf6puuXftWaRCm4ucfcJ05ATv1JRLCx5M74NVy\nCSeNBlatkkMwn30WHn98Aa++eue8prI4n/kra6NnotIe5OmwQex7+mcaeTWp6GkJaiFXwi8XZceR\nbCzl/YCG7A9qg3M5KqQCy0VcRUGZiOpT9aHL1RG7MJbk+cnYtnKhwaJmuHaqePf02lq9UJw6icus\nz7G/eIHE8I/Infs6kp3pWVf//iu3WzlzBgYNgl27wN0dFi26fV7TzUiSxMnkb1inno264BzDlnM8\nAAAAIABJREFUmr7BrF4ReDv5VPi8bqa2Xr+6QteuPTBIEnuykliSE49OIYdfDhPhl7UOIaAEghqi\nNKMU9Ww1qUvTsO/iht/a1ri08qjpYVkcil9UsnD69zyJwz4kd9Z+JPuyM5bK4uxZWTidPw8vvwyf\nfw7Ozteev11ek9F4zZeiM+r4JnYtGzRzMGLgtVZv80Kz4TjYmD4OQe2nVDKyWZvA0twEvOxs+F+Y\nCL+szYhVeIIyER6oqqM4uRj1DDXpq9NxeNQT37FhODVxM9v+Vara4aFR/KLCZfb/cLjwNwnhH5I7\n8A2ThZMkyZWmFSsgPh6GDYOnnwaHMjYvK69pxYrGdO8+n3tbPcS2mMVsjosgzK0xb7R5n8fC+lfp\ntKpKVTuuX12i0KBnTUYcy3OTqH/ub2YMfJbeIvzS6hCr8AQCC6VQU4h6qhrt5gyc+noT+E0HHEPE\nsuWbUZz+EZdZ/8Phwl8kDvuAnBl7yyWcTp6U+9RlZclRBE88cWeL1BWfU2TkQpTKYoxGR1p2HsQx\n20O8f3QoD/o/ysreO2jvf785Tk9Qi8jSl7L8cvhlF1dXdrRsTrFRT4969Wp6aIJqQFSgBIIqJv+f\nfGImq8nak4XLc774vhmGvb9TTQ/L4lCc+UkWTufPysLpuTdNFk5GIxw/LlecDAY5Nbxnz3LlZwJw\nLvMM66JnotIeYkCjl3ij7XuEeDSqwNkIajMppcV8pVWztSCdxz09+CQsjFYi/NLqKW8FSggogaCK\nyPkjh5gvNeQdzcVlSH18Xw/Fzkd4Zm5G8evPuMz8HIfzf5I49LJwcjAtF0evh8OH5YqTs7MsnLp1\nK1fHluuM4bPQFFwgvNmbDG/1Fl6OFTfyC2on6uICFmnVfFOUyQve3oxvFEYjEX5ZaxBTeAKzIDxQ\nFedqg99TBbgO9yP0x+bYuldf3otKZR0emmsVpz9JHPIuOdN2mSycSkth3z45x8nPD95/H+6//+4N\nfq9HNoavu2wM11uMMVylso7rV5c4V5jDwgwNJ0pyGVGvHhdad8bvNuGX4rOz7iAElEBgJq40+C06\nX4z7qw0Jm9/6aoNfwTWueZzOyhWncginoiI5fmDtWmjcGCZOhHbtynf8fF0u22KWsCU2giC3ED7u\nPIk+jZ4Shl/BLZzKyyQiS8MfpQWM9vcjMrQ5niL8UnAZMYUnEFQCSZJI3ZdK7KQ4SlN0uL8egO9L\nltXg11K4flVd4rAPyBn4hsnCKT8ftm6Ve9W1bi1P1TVrVr7jpxYmsP7SHPYlraZL/YcZ3e4jOvh3\nqcCZCGozkiRxLCeNxdlxxBtKeSfAnzeCg3ER4Ze1HjGFJxBUA5JRInlLMrFT4zAUSbi/GUjgQMts\n8FvTKE6dlIXTP+fKvaouOxs2bZLF0wMPwJIlcuWpPPyb9Sdro2dwIn0//UOfF4nhgjIxShL7spJZ\nnBNPEQY+DApkeGAgdiL8UnAbhIASlImYxy8bo95I4ppE4qcnINkr5Qa//Syrwa9KZZqHRqXaz5Ej\nC1AqSzAaHejde6xZW7BcEU5yAOYH5M7cZ7Jw0mph/XrYvRseeUT2OgUFmX5sSZL4Je0Ya6Jn8E/e\nbwxr+gbTHv0XH2fLX16uUgkPVHWik4xszUhgaW4izjYKPgkL5oVKhF+Kz866gxBQAoEJGEuMxH0d\nR8LMRJQN7PH8tBEePetbrW9GpdrP/v3jCA+/Fh4ZGSnfrqyIUvz8gyycLl6Qk8PLIZySk2HNGjh4\nUM5v2rBBNombikEycCR+C+vUs8jXZ/Nay7dZ03wnznbOd99YUKcoNOhZlxHP8rwkQhzsmdekEU/W\nt97/pwXVj/BACQR3QJ+vJ3ZxLElzk7Ft4oTXmBDcH/St6WFVmokT+zB48OFbHt+0qQ8TJhys0D4V\nqihcZ0/EThNN4tAPyH32NZOFU1ycXGWKioJnnoEhQ8CnHO3livSF7FIvZ2PsPLwcvOlDT3L//g0b\nm9Iqqa4JrJdcvY4VWg2R+Sm0c3bms7BQupXnzSaotQgPlEBgBnTZOjRzNSQvSsG+vSsNvm6Ba3uv\nmh6W2VAqy26gq1Dc2kD3bihOHMV1zkTs4jQkhI8nb94ok5v8XrokZzj9/LPc4HfnTvAoRzvA7JIM\nNl6az46Er2jl3YE5Dy9HEVfIN9+8XSXVNYH1kq4rZqlWw8aCdB51c+NQm9a0K8+bTSC4CSGgBGVS\nV+fxi1OLUc/UkL4iDYfuHjTc1Abn5taVMKxS3d1Dc7sGupJk2qo4AOX3R3CZPRHbpAQShn1E3jOj\n7twz5TrOnZNTw8+elatNn34K5ckjjM+LZt2lWRxK2USvwH5s7vstzX1bAzBxZZ8bxBNAeHg0mzYt\ntAoBpVLVTg9UVXvubkd8SSGLtWp2F2YwwNuLn+9rx72urlV2vLr62VkXEQJKIACK4ouImaomY4MW\nx8e9CNzbHsdGVfchW9P07j2WyMjom6o0jenbd8ydN5QklFGHcJ3zBTapKSQM/5i8/sNNFk6//SYL\np5gYucHv5MlwmzzCMjmXeZrIS9M5lXmU5xsP49hzZ2noFnjDa8xZXROYh6r03N2OfwpzicjQcLQk\nm2G+vvzVshOBTqKFksB8CAElKJO68gsq/998YqaoydqVhfMAX4KPdMI+wLo/ZE2pXlz50tq0aSEK\nRTGS5EjfvmNu/2UmSSiOfoPb3C9QZmSQOPxj8vqFgwnZOJIEP/0kC6f0dBg+HObONVlzIUkSP6Ye\nYk30DDQFFxjRfDQL+yzH3aHs6RdzVNdqktpYfTpyZEG1VQV/y88iIlPDL6X5vNagPsvCuuBjb9qU\nsjmoK5+dAiGgBHWUnD9yUE/SkPttLi6D6xH6/f3Y+datPnVdu/a9+5eXJKE8vBe3uV+iyMkmYfgn\n5PcbZlKXXqMRvv9eFk7FxTByJPTubZLmAkBv1HMofiPr1LPQScW83updBjUbgb3Nnb8MK1xdE1QZ\n1VEV/CFXS0RWLBf1RYxr6M+WkFa43fRmO3ZsP7t2LUChKEGSHHjmmbE8+qjlT+sKLBMhoARlUlvn\n8TN/ykQzKZb8n/LlPnWq5th61K7WDCqVGTw0koRy/3bc5k+GohISR3xM/uMvmSScDAY4ckQ2h9vZ\nyanhPXqY3uC3SF/ATvXXbNTMo75zAz7o+DmPN34GpcK0HZS7umZhqFS1zwNVVVVBSZI4lJPK4uw4\ntEYdHwQGMCo4GIcy3mzHju1n48ZxDBlyTVivXy/fNqeIqq2fnYJbEQJKUOuRJAntMS2aSbEUXSjG\nfZQ/YfNaiT51ZWE0oty7Bfd5kzEaJRJGfkZB7xdMUj86HXzzDaxaBd7eMG4cdO1qeoPfzOJ0NkXP\nZ0f8Utr4dmT+I6vpGtijQqdhUnVNUG2YuypokCR2ZSaxOCcelBIfBwfxUsOG2N7hfbpr14IbxBPA\nkCHR7Ny5UFShBBVCfIMIyqQ2/IKSJInUvZf71KXKfer8VwajdKjdrRkqVL0wGLDZuQG3BVMx2NoT\n98rnFPYcaJL6KS6GPXsgMhJCQmDCBGjf3vRDJ+THsPbizKsr6rb2O0Yz31blP4daQm2rPoH5qoKl\nkpGN2niW5ibia2fDlHtCeaZBA5PCLxWKsqcRwbyLC2rDZ6fANISAEtQ6JKNE0qYk4qbGYyiRcP9P\nIIHPij51ZaLXY7NtLe4Lp6Jzdidu9DQKu/c3STgVFsK2bXLLlRYtYPp0aNnS9EOfz/yVyEvT+Dnz\nW55r9DJHn/uTALdy9GsRWBWVqQoWGPREZsSyIjeZZk6OLG/ahJ6+vuVKDZek23kcrWNxgcDyEAJK\nUCbWOI9v1BlJiEwgfnoCONvgMSYYryctq09ddaBSmeCh0emw3bwK94jplHj6onlnLkUPPmmScMrN\nlRv8btkCnTpBRAQ0MbE375Uedaujp3Ep/0+GN/0P8x5biqdj7QkprSwqVe3zQFWULH0py7Ua1uSn\n0tXVlV2tWnC/V8XeK888M5b166NvmMZbt64xL71k3sUF1vjZKagYQkAJrB5DsYG4pXEkzkpCGWCP\n14TGeDwqelqVSUkJduuX4b54JkV+IajHL6Ho/t4mCafMTLnatHMnPPywvLouJMS0wxolI98mbGNd\nzExy9Bm80epdBjffi6Ot+PUvuJWU0mK+0qrZWpDOE56efNe2DS3dKxdoe8XntHPnQuRpO0deemmM\n8D8JKozohSewWnS5OmIjYkmen4JtMye8x4bi1sXye1rVRCKzVFiI/ZrFuC+dS0FYM5JHfkZJxx4m\nbZuaCmvXwv790KcPhIeDv79px9UZS9kVs4INsXNxsXPmP20+4OkmL2KjvPtqPkHdQ1NcwCKtmv1F\nmbzg7c34RmE0Kk9EvUBQCUQvPEGtpzSjFPVsNalL07Dv4obf6pa4tPGs6WGZRLUnMufnYb9yIe7L\n55PXrCMXp22jtM0DJm2akCA3+D16FJ56Sp6yq1fPxMPqctkavYjNcQtp7HEfUx9ayMPBj4mqoKBM\nzhXmsihDTVRJDiPr1ed86874lyeiXiCoAYSAEpSJJc7jFycVEzM9Bu0aLY49PQnY0RanJm41PSzA\n9KpSdSQyq1RRdG3ZDvtlc/BYvZjstg/yz7xv0DXvYNL2MTFyFMHJk/Dcc7BjB5hqO8koSmX9pdns\nSlzBAw0eZtVju2jn17nC51IXUanqjgfqdH4mEZmx/Fqaz2h/P1aGNsfL1Ih6C8USPzsFVYMQUAKL\npyC6gJipajK3ZeL8lA+BBzrgGGw5Zf3yVJWqPJE5MwO79cuoF3WIrE49Ob/4KPp7W5u06YULcvjl\nb7/B4MHw4YfgZqI+jc+LZs2l6RxJ2cqTwc+y9+kfaex1byVORFBbkSSJE7laIrJjidEX805AQ3YG\nt8LF1Ih6gcBCEO9YQZlYwi+o3L9yUU9Wk30wB9dB9Qk53hn7BpZX1i9PVanK+rSlpfDLxDf49uJ+\n9PW92d2nGQ/0DKeDCeLp999l4fTvv3KD34kTwdSeqxeyfiPy4jR+yjzCoHtGENXtb/xcG1buXOo4\ntbX6JEkSB7JTWZQdSy4G3g8M4JWgIOxNjai3Eizhs1NQPQgBJbA4sk5loZ6kIf9kPq7DGhB2sjm2\nnpZb1i9PVcnsfdoS43FcOJUz+yPZ9YAN4RF6IA1IY+XKcQB06HDr1KAkwalT8kq6lBTZGD5rFpja\nc/V0WhSRl6bxT/5vchRBn6V4OFiHD626SSotwtfOAXsTW9HUNvSSkR0ZiXyVm4CtjYLxoUEMbtgQ\nG+GHE1g5QkAJyqQm5vG1x7WoJ8VS9HeR3G5lditsXCz/LVqeqpLZ+rSpL+G4YApuB3aS2vdlNvTp\nSPhr3wNyRaltWxg5MprIyIU3CChJghMnZOGUnw8jRsgr6+5mOzlzZj8nTy4gT59IbF4CqQH2vNb/\nMyKb78DZzrl8Y68j/FWYw8IMDQeKshjr3pD3/e48pXnFR5ecnIq/f4NqWZ1ZlZQYjWzIiGNZbiIN\n7O2YcU8Y/U1MDbdmhAeq7mD5306CWo0kSaTuSyV2chylSZfbrSy3rnYr5a0qVapP2z9/4zR/Mq5R\nB0l++hXidvyD0bs+ykU9yny5UilXwQwGeTXdypVy5NPIkfDooyb1BubUL3s4EvUqY15Pu/rY6sjG\nNCtoLMRTGfycl0lEpoY/dQWM8ffjPa8AXjh3gbHSPbetQl3vo7sigKt0dWYVkn9dangLJydWNbuP\nR319a3pYAoHZEQJKUCZV/QtKMkokbb6u3cqb1ttuxWxVpTugOPsrTnO/xPnnEyQ/P5rYXYswul9b\nGnd9Faxt22vbGQyO7NkjxxG4u8Po0fDQQ6Y1+C0xFLMjZhmH933E/PdunI4cbuaVg9aOJElE5aYT\nkRVLgrGUdwMasjeoNc6XjdFNHR3YnpHIYN+yW9Vc76O7cv3MvTqzqsnSl/K1VsPa/FQedHVlT6sW\ndK5garg1I6pPdQchoATVilFnJGF1AvEzLrdbeat2tFupVFXpDihOncRl3iQc/vqN5MHjUH+6Bsnl\n1qVxXbuOZeXKaEaOvFYFmz+/Mb/8MgZ/fxg/Xm67YopwyivNYVP0fLbELaKFV1ta1rsP+OPWsZlr\n5aAVY5Qk9mUlsyQnnkIMfBQUSHhgIHY3GaPfDQ7is2gNL/oEljmFVeWrM6uQqkgNFwisASGgBGVi\n7nl8faGe+GXxJM5OQhloj/f/7sG9R71a74eoEJKE8rvDuCyYgl2smqQh75I9eTs43X667IrPadWq\nhfz7bwr5+X44OIxh0qS+tDYtxQBtUQrrLs1mT+IKHvTryYYnDtCqfnsm/tbnNsO0vBWR1YVeMrL1\nsjHa2UbBx2HBvODvj/I27+enGjTg3egYVHkZPOh+63TW9RXEK1N4YNl/Y/V1qeGDfLw506yDSA1H\neKDqEkJACaoUXa4OzXwNKQtTsG3lQr0FzXC737umh2WZSBLKA7twWzAFRXYWiUM/JO+pEXd3eAN5\nefD7733Zu7cvYWFRfPxxD5o2Ne2wCfkxRF6cdjXDad/TP9PI61p3YLOvHLRiio0G1mfEsyw3kSB7\ne+Y2aUTf+nfvu6hUKBjT0J/lqfFlCihr+hufK8wlIkPNdyU5jKhXnwsiNVxQRxG98ARVQkl6CerZ\nGtK+TsOhqxveb4Xh0sqjpodlmRgM2OzcgFvENIySgqTw8eT3GWySwzsrCzZuhG3bZG/TiBEQFmba\nYS9mn2XVxSn8mHGI5xsP4812H+DvGlDma1Wq/Xz77TWPV69e5vV4WTp5Bh2rtbGsyEuhrbMTn4WF\n0t2nfH0X8/R6QlQ/sjewPWGOt1ZqLP1vfCY/k4VXUsP9GvB2WJjVp4YLBNdT3l54QkAJzEpRQhEx\n09RkrNPi2McL37fCcGzsWtPDskx0Omw3rcRt8Ux0bt4kjfiEwh5Pm2RUSk+XG/zu3Qu9esk5ToGB\nph32T+1PrL40mT9zfiK86Zu82uYdPB3rntnXFDJ0JSzTalhfkEYPNzc+DQulg2fF867GnTtHXiFM\natjcfIOsQiRJ4kSelkVZsURfTg1/MzgYV5EaLqiFCAElMAvlncfPv5hPzGQ1WbuycB7gS73/hGEf\nYGKcdR1DKizEfu0S3JfNozCgESkjP6Xo/t4mCaekJHlF3ZEj0K8fDB0K9evf+JrTp6Po2LHHjceU\nJE6lHWXVpSnEFv7Dqy3GEd7yP7jYC3FbFkmlRSzRqtleoOUpLy8+aRRGU9fK/63UBQW0P32Gnxo9\ngJtN2dUblarme+FJksTB7FQWZceRjZ4PamlqeFUgPFDWS3kFlPgZIagUOX/koJ6kIffbXFxeqkfo\nd52xqyf8EGWSk439ivm4r1pEXrMOXJq0kZJ2D5m0qUYjN/g9cQKefRa2bwdvE6xkkiQRlbSb1dFT\nyNZp+U/rDxjc/BXsbUyMHK9jRBfns0ir5mBxFi/5+PJni04Em9rXxgTCXFzo7ubG+ox43qjfyGz7\nNRcGSWJnZiJLchJQKuFjkRouENwWUYESVIhMVSbqSRoKfinANdwP31dCsfUQfogySU/F4atZuG9c\nQVbnXqSO+ATdfW3vvh2wZ4+cTl1SUoKXlwP9+o2lW7e7+2IMkoGDcRuIjJ6GUglvtR3PgHtfwkZp\nQnJmHeTvy6nhP5TkMqp+Pd4LDaVBFRmjv8/IYOi5C/zQqKvFCJNSychGbTxLcxOpZ2fLp6HBPF0H\nUsMFgusRFShBlSFJEtrDWtSTNZREl+I2yp+wBa2xcRZvozKJ1+C4aAZuuzaifWQA51f9hD7kzu08\nrnD2LERE7MfDYxyTJ19bmbVyZTTOzmX3twPQGUvZFbOCtZqZ+Dr68vH9k3m80dPii/A2/JKfycJM\nDX+UFvCWvx9rQ5vjUcXG6G7e3vjY2XIgK5l+3jXbeLnAoGdNRizLc5Np5uTIiqZNeNTXV7xfBAIT\nEBUoQZlcP48vGSWSdyQTNzUeXZYBjzcC8XkhEIW98EOUheLSBRwXTMH1yD5Sn3yZjGEfYmhwd4e3\nJMGZM3Kfurg4aNu2Dx99dPiW10VG9mHMmIM3PFakL2BbzGLWa+bhm1qPCYNm0S2op/giLANJkvgu\nV0tEloY4QynvBPjzZnDw1dTw6iAyPp4l8SnsCO10y3MqVdV7oLL1OpZr1azJT6WLqyufhYbQxZQ5\nYcFdER4o60VUoARmw6g3krgukfhpCRhtFHiODsKrf0MUNtb7pXylYatSWYLR6GDWhq2KP07jtGAK\nLj9+R9LA19Fs/wfJu95dt5MkOHlS7lOXlSVHETzxBCxbVnY69ZX+diCnhm+8NJet8Ytp69OZ5b23\nUaouoWtwD7OcU21CkiQOZKcQkR1HPgY+DApkeGBgjRijXwoIYLwmlj8KsmnjUvFVfeUlrbSYpRka\nNuWn0cfTg2Nt29BapIYLBBVCCCjBLRhLjIT+FYoq/EeUDezx/LgRHr3uHhZo6VzfsPUK5mjYqvjh\nGC4Lp+Jw4S+SB41B/fFqJNe7fykZjXD8uFxx0uvhlVfkSIIr8U/Xp1PfuJ0jmcVprLs4i12Jy3nQ\nryebnjxMi3qXfVX+FT6VWoleMrIjI5EluQnY2yj4ODSIQTVsjLZTKnndrwHLM+NYeJOAqorqU1xx\nAYszNOwpzOA5b29Od+xAY5EaXiWI6lPdQUzhCa6iz9MTuyiWpHnJ2N7nhNdbIbg/WHu6qE+c2IfB\ng2+dEtu0qQ8TJhwsY4s7cDk13HXRNGzS00kc8h55A0Yh2Zcteq5Hr4fDh+WKk7MzjBwJ3bvDzYWQ\nM2f2c+LEuBv62y1bHkJGcEt+dDnJY0FPMa7DJzT2uq98Y68jlBiNbMyIY2luIg3s7fgsJJj+FmSM\nTi8p4Z6ffiYqpDMN7KvGsH6xKI8FWjVHS7IZ5uvLR2FhBJhxVaFAUJsQU3iCclOaUYp6tprUZWnY\nd3alwYoW/Fn0ByFda494AjM1bNXrsdm+DrfFMzCiJGnYR+Q//pJJqeGlpbBvn5zj1KABvPcedOly\n+/inK0bxyMiF6KQs4vIS+ds3nb4tgzjS7jeCPELL3E6lqvkcoZqkwKAn8rIxurmTI6ua3cejvpb3\nXq7n4MCz3l6syohlvP81EaxSVf76/VGQzcIMNadK83m9QQOWhXXBx15EV1QHwgNVd6iMgPoYeBkw\nAmeBEUDZ31ACi6QosQj1dDXatVoce3oSsL0tTk3c5CdVNTu2quB2U2ImNWwtLsZu/TLcls6hxNef\nuP9Mo7B7f5PCL4uKYOdOWLcOGjeGiROhXTvTxuzZOJQUozeqjFO8eM9IFrR7n/oufqZtXMe43hj9\ngKsru1u14H4vy05YfyckhJ6//8HbxntwNEPEhCpXS0RWLBf0Rbzd0J/NIa1wE6nhAkGVUNFadihw\nDGiGLJo2A98Akde9RkzhWSj5F/NRT9WQuSMT52d88H0zDIcg55oeVpVTtgeqMX37zi/TA6VS7efI\ngTnYpEVjo0mml10L7nljDiU3pXzfjvx82LpV7lXXurU8VdfcxA4e5zN/ZeXFSfya9R3hTf/Dq23f\nwctRrJIqi5uN0Z+GhdHKiozRj/5ymscd6vOyb3CFtpckiW9z0liUHUeqsZQPAgMYFRSEowlVUYFA\ncI3qmsLLBXSAM2C4/N/ECu5LUE3k/J6DevLl1PDBdS81/IpI2rTpWsPWvn3Lbtiq+mYt3+wbw7C3\nc64+tnJlLt0UBXS4y3Gys2HTJlk8dekCixfDPfeYNsY/tD+y8uIkzued5pXmY1n8+GrcHKxHDFQn\n1xujB1qxMfrd4CA+uKhmiE9QufxZRklib1Yyi3Li0CkkxgcFMjQgAFvRbkUgqBYq46Z8DZgNFAGH\ngKE3PS8qUBZC5slM1JMvp4YP98N35N1Tw1WqOuqjibmI46IZfP7nagYu0t/ydFkZTFfQamH9eti1\nCx55RI4jCAoy7bC/pB5j5aXJxBb+w+st32FoyzdxtqtYVVClqt3X7mJRHgsz1Bwtlo3RH1q5MVqS\nJO5T/cQX3vfQ3aPeXa+fTjKyNSOBJbkJuNvY8ElIEAP9/VFaiDm+riM8UNZLdVWgGgNvI0/l5QBb\ngSHA+utfNHz4cEJDQwHw9PSkbdu2V99YUVFRAOJ+Fd0/fvw42b9kE7A3kJKYUv7pFYv7vAY89EgT\nQP6ShWtLpm++//ffv9/x+dp2/8d1S3HYvoE+/5wl5alXiA5owu+/n6ft5WSA3+U/x9UMptOn5e07\nduxBcjLMmhXFqVPQv38PNmyAxMQoUlMhKKjHLa+/cl+SJEoCClkZPZnEczE83fhFNr90AHsb+xr/\ne1ji/ZjifL67J5CfSvN4XKNmtb8/T1+eE63p/98qc1+hUPB4fCwzfj9L9wGv3fb8SyUDF5s04uu8\nJLz+Osvrfg344JlnUCgUFnU+4r64by33r9zWaDRUhIr+ZBkE9AZGXb4/FOgCjL7uNaICVQNIRonk\nbcnETo3HkGvA/UpquJ0o69+CJMkZThHTcDh/luRBY8h64S0kNw8WLuxDePidU8Dj4uQVdcePwzPP\nwJAhYMpiL0mSOJ64i1XRkyky5jG69Uc832wYtkph9i2Ln/IyWJCp4by+iHH+frwVEoJ7FbdbqW4K\n9HqCVT+yK7AdjR1db3guz6BjlTaWlXkptHN24rOwULr5+NTMQAWCWkx1VaAuAP8FnIBioBdwqoL7\nEpgBo85IwpoEEmYkItkp8BgdjFd/fxRKUda/BaMR5Tc7cF00A5sMrZzhNGMvksM1P1jXrmNZuTL6\nhgymFSsa0737GC5dkjOcfvoJBg2Sp+w8PEw4rGTkcPxmVkVPQamUGNv2E56+90WUCiFub0aSJI7l\npBGRHUeSsZT3AxpyMDi41hqjXWxtGV6vHsszYpka0AKADF0Jy7Qa1hek0cPNjYNtWtHelDeaQCCo\nFirz7fohEI4cY/ArcjVKd93zogJVDegL9cQviydxdhJKf3s83wrGo2flU8NVqlrooylydUH0AAAg\nAElEQVQtxXZrJG5LZqO3cyBp2IcUPPbibTOczpzZj0q1EKWyGKPRkcDAMfzwQ1/OnoWXXoLnngNX\n1zI3vQGDZOAbzToi1dNwtnPi7Xaf8UTjAVUW6KhSWe+1M0oS+7OSWZwTTyEGPgoKJDwwEDtl7ReZ\ncUVFtD71CxMS8vj7vjC2F2jp7+XFp43CaGrKG01gEUQJD5TVUp1BmjMu/xPUALocHZoFGlIWpmDb\nwpl685vi1sVyy/pV2YPuruTnYRe5GPcVCykMbIzm7dkUPfjkXTOcOnToS4cOffntN7ndyoEDMHQo\nTJoEpniWdUYdezSrWBMzHV8nXz7vMpNeYX0tJgnbktBLRrZnJPJVbgIO17VbqUvG6GAnJ3q6u/Nx\n+q+MbBvK7807Eupc++NFBAJrRbRysTKKU4vRzNaQtjwd+wfc8BkbhkurminrmyqKypu/ZDbSUrBf\nNgePjSvIbteN1GHjKW3dxaRNJUmeoluxAtLSYPhw6NcP7E0Icy41lLAj5mvWaWYS6BrMO+3/S/fg\n3kI4lUGJ0ciGjDiW5Sbid7ndSj8LardS3WTrdOiMRuo53L0lkEAgMC+ilUstpVBTiHq6moyNGTg+\n7kXg7nY4Nq65sn55GvMeObLghtcBhIdHs2nTwqoRUJejCNz2b0P7yADOr1ChDzWtX5zRCN9/Lwun\noiI5/PKxx8CUMOcifSHbY5awXjOXezzuY8EjkXQN7FG5c6ml3NxuZWXTe+lZr15ND6vG8axl5niB\noDYjBJSFk3c+j5jJarL3ZeMy0Jfgbzth37DqM29Uqjv7aMojiszSg84EFH+cxmnBVFx+PE7KUyOJ\n2/I3xvoNTdrWYIAjR2RzuK0tjBoFPXrc2uC3LIr0BWyOjmCDZi4tvduxrNcWOjXsWrmTqQQqleV6\noKyx3Up1Izw01o24fnUHIaAslKxTWagnacj/IR+Xl+sTeuJ+7Hwsp6xfHlFUqR50d0OSUH5/BJeI\n6dj/e47kQWNQj1+J5GbatKZOB998A6tWgbc3jBsHXbua1OKOAl0em6IXsCl2Pu187yeyzx7a+XWu\n5AnVTtJ1xSzVathYkM5j7u4ca9uG1lbUbkUgEAhuRggoC0KSJLTHtGimxFH0VxHur/gTNqsVNq7V\nf5nuVsEojyjq3XsskZHRZXigxlR8gAYDNrs34bpkFor8AhJfeof82SOR7E0TmcXFsGcPREZCSAh8\n9hl06GCacMorzWHjpblsiVtE5/oPsfGJQ7Ssb2J34GrAkqpPiaVFLEqPYVdhBs96e/NL0/bcY4Xt\nVqoTUb2wbsT1qzsIAWUBSJJE6u5UNJPj0KXpcH8tAP/lwSgdLHfpdnlEUXl60N0NqbAQ+43LcVs2\nl1KPesQP+4TCngNNm2sDCgth2zZYtw5atIBp06BVK9OOnVuaxfqLc9gav5iH/Hqytd8xmvmauHEd\nI7o4n4VaNYeLsxjq68tfLTsRaMXtVgQCgeBmxCq8GsSoN5K4PpH46QkYjeDxZhDeAxqisK154aRS\n3d1Ho1Lt59tvr4miXr0qJopMIjMD+xXzcV/zFXlNO5AS/hElHe88vuvJzZUb/G7ZAh07yubwe+81\nbdvskgzWXpzJzoRl9Gj4OO90/C9NvJtV7DyqAZWq5jxQfxfmsCBDg6okl1H16/N+WKhYUVZOhIfG\nuhHXz3oRq/CsAGOJkbiv40iYlYjCxw7P98LwfNz6lm537dq36rOc4tQ4LpmF284NZHTry4VF36K/\nt7XJm2dmyg1+d+6E7t1h+XK43J7x7tsWp7Pm4gx2J6ygd1A/9j79E429TFRddYzT+ZksyNTwR2kB\nY/z9WBfaHA+xokwgENRiRAWqGtHl6ohbFEfS/GRs73XC660Q3B8yoXlaHURx9lecIqbj8v0RUvsO\nJePl9zH4BZm8fWoqrF0L+/fLMQTh4dDQtAV5ZBSlEnlxOnsTV9Mn+Gne7vAZoZ6NK3YitRhJkjiR\npyUiKxa1vph3AhryZnAwLqZkPggEAoGFISpQFkhJegnq2RrSvk7DvrMrDVa0wLWdWLp9C5KE8rvD\nOC+eicOFv0h+7k00u7/C6G763yohQW7we/Qo9O8vT9mZGi+kLUph9b9T2Z+8lieCn+XQs2cI9gir\n2LnUYiRJ4lBOKouy4siU9HwYFMArQUHY14F2KwKBQHAFIaCqkKL4ImKmqclYr8WxtxcBO9ri1MSt\npodlEipVNfpo9Hpsdm3E9avZKAoK5RV1s/abvKIOQK2WM5xOnpR71O3YAabGC6UVJrH64lS+SVpH\nv5DnOTzgV4I8Qit2LhaASlU1184gSezJSmJxdjxGpcTHIUEMCQjAxsqmni0d4aGxbsT1qzsIAVUF\n5F/IJ2aymqy9WTgP8CX4SCfsA8QKpFsoyMdu3VLcli+gxLch8SMmUPjIMyavqAO4cEEWTr/+Kjf4\n/fBDcDNRo6YVJrLy3ykcTN7AM2EvcvS5PwlwM32asK6gk4xs+X979x1eVZX1cfybmxBCGi2UQBIS\nEBWQZiJqUEQBEWMvg6gMCs6M+gpYx97GPooCAQlIC0WKWJFRxBJBAyrNRk8hBEJII73f8/5xqBow\nN7kpJ/f3eR4ec0/u3WfHpbDYe521s1KJyUulpYc7z3cN4YbAQJc6p05E5I9UA+VEhzceJvHFJArW\nFuBza3sC/hlKswA9gfQnGel4znqLlktmk9v7QtJH/5vScy92aIiffzaPW9m1yzzg94YbqnfAL0B6\nUSpzd77E6oNLub7rrUwIf4JA3841+EGathJ7JYuyUpiVd4AuzT15sksII9q3t9zDDiIi1aEaqAaQ\n+XUmSS/tpfi3YvzGBhL22jm4++kJpD9yS9hJ8+mv479qBRmXXc/2Weuo6Fr9dgCGAT/9ZCZOBw6Y\nheGvvw7VfUr+YNE+5ux8gTUH3+PGrrcTd/PvdPStZmW5CymsrGBe1l7m5KXRx7sF7/Y8m0Ft2zb0\ntEREGhUlUDV0tPnl3pdTKEu3RvNLR8THO6+Oxu3H7/Ge/hreP33HwWvGkbJiO/Z2gdX+vGHAunXm\nVl1entnDafhwaNYMNm1aRXz8VGy2Uuz25kRGTiA8/OTWCicmTjd3G823f9tGB5/q399q4uNrFrvD\nFeW8k5nEwoJ0Bvr6sqrPOUS0auXs6clfUA2NtSl+rkMJlIPsFXYOvHuAlFf3HWt+GdRIml82KnY7\ntv99gG/MJDzS9nPglvEkPrMYw+evC5SOJkVubqVkZDRnx44J2GxRjB0Ll10G7u7H37du3UTGjj3e\nDX3uXPPr8PAo0gpTmLPzRb5Md43EqaYOlZUQk5XMsoJDXNGqJXH9+nKOzqkTETkt1UBVU2VJJfve\n2UfqpP3YAprR6t4QWg63XvPLOldSgsfSufi9M5kKzxYcuO0hCq+4FarZG2jTplWsXTuRceOOJ0XT\np3dj2LApREScvLIUHT2cMWO++NMYs+YOonjQmXyVvoKbz/g74899nPY+HWv3czVBJ55Td2ObNjzR\nNYxuOqdORFyUaqCcrDyvnL3T9pI25SAePVoQ8PpZ+A9U88s/yck+dtRKQfc+JD8cTfEFl1fvdN4j\nSkvhgw+m8uijCSdd/7//SyA2NvpPCZTNVlrlODvzv6efXz/WXrJdiVMVEkoKmHbknLrbAwL4/Zzz\n6Kxz6kREHKJ9p1MoPVTKjkd3sj5sA5nfF9Ax9hy6vBvuMslTfHxc9d64NxGvx+6l3YXdqNy+m53R\nq0mevobiC4dXO3kqLjaPW7n2WigqqjopstlK/nTNbq+6erxvwMW8cPEUl02e4uPjqry+rSiXu/f9\nzLWpWwj192TX+ecT3bOnkqdGJi4urqGnILWg+LkOrUD9QVFyEUmvJZG1JAuv4a0J+qg/Xt18G3pa\njY7b5h9oMf2/+MR/Q3rUaPYt/cWho1YA8vPhvfdgyRLo3x8mT4Y1a6pOiux2rz9dO6v/SN6YsZ6H\n78k/di02thtRUQ879sM0cZsLcpianczmsgLuC+zIgtCetNI5dSIitaIaqCPyfs8j6eVkDq86jM+N\nAQTcE4ZnJ/3N/CR2O7bVn+AT8wbNUpJJG3kfh2+8B8OvpUPD5OSYSdOKFXDRRXDnnRB25MSUqgrD\n58zpxqBBU449XZdWmMLsnS/wVfoKLi2/mLb782nuYWAYXgwdOr7uDzi2iO/yzHPqdlcU80CnQP6v\nSxedUycicgqqgXJQzg85JL2YTEF8Ab63dyDsuwvwaOPZ0NNqXEpL8Vg2F79ZU6h09+DArQ9RcOXt\nZh8BB2RkmAf8rlwJQ4fCggUQFHTye44mSbGx0dhsJdjtXgwaNJ7w8CgOFu1j9o4Xjj1VpxqnPzMM\ng69yDzHtcArp9jL+HdSZu0JCaK5z6kREnMolV6AMwyDzi0ySX95L8a4S/McF0nZMF9x9XD6fPCY+\nPo7IHn2OFYYXdjuHtNseomTgCIcKw8FsehkbC198AVFRZufwDh2q//k/9nG6L/xxtSP4A7thsCon\njWm5+8jZvJH/XHcNf+/cGQ8lTpajPkLWpvhZl1agTsOwG6StSCPl1X2UH67E/19BdIoNws1Tf8ic\nJGkPnrPepN2GdWRHXsHOKZ9R3uNch4dJTob582HtWvOolfffhzZtqv/59KJU5ux8kS8OLuOmbrer\nj1MVKg2D97NSmZGXiqe7G0+GhdC+rIjLgnWmn4hIXXKJFSh7uZ3U2FRSX9+P0cyNlvcG0/rqTri5\nq4fTidx+iqfFjNfxWf8t6VGjybrtISoDQxweZ/du87iVjRth5EjzlyN9Gc1Dfl/i87Ql3Nj1dsaH\nP64jV/6gzLCzNHMfMXn7ae/pwVNdQri6g/qSiYjUlKMrUE06gaoorCAlJoUDb6VhC/I0m18O0WGo\nJzmxY/iBVNL+dh+Hb7zb4cJwgF9/NY9b2bYNbr8dbrwRvL2r//mM4jTm7nyJz9IWc13YKCZGPKlD\nfv+gqLKChVkpzM5P4wyv5jwd2oUhAQH6b1pEpJa0hQeU55STPDmZtLcP4tnXh3bTeuA3wIG9Ixdg\nFBXRbNlc/GZNpqKFL/tvffCkjuEbN8YRETH4r8cxYPNmc8Vp717zgN9XX63+Ab8AmcUHmbfrJVYd\nWMS1YSP5+qZf6eQX9NcfdCH5leXMy9zL3Pw0wn18WN6rBwNPsR+qGgxrU/ysTfFzHU0qgSo5UELi\nf5PIjM2g+eCWdFrSF++eOtPrJBnpeM6eQsvF75DXI5ykx2IoGTDE4cJww4D4eDNxyskxWxGMGOHY\ng3nZJYeYt+tlVu6P5aouN/PVTb/Q2U+1OyfKqShjVmYyiwrSGeTnx+d9+3BuS8dXB0VExLmaxBZe\nwa4Ckl5JIvvDHLyvbkPbe8Pw6qIzvU7ktns7zWe8gf+q98m89DoO3fYQFd17OzyO3Q5xcWbiVF4O\n48aZLQmOHvBbHdklGcTufpVPUucxIuR6Hoh4muCWoQ7PpSk78YDfEa1a8WRYKL10wK+ISJ1xqS28\n3M25JL6URP7X+fiMakeXuAF4tv9zx2qXZRi4ff8N3jGTaLHlBw5eO46UFduxt3P8SbaKCrMNwbx5\n0KIF/OMfMGgQOPKU/OHSLGJ3vcpHqXMYHnItn9+wkS4tuzo8l6bsjwf8bowI1wG/IiKNkCUTqMxv\nzB5ORT8X43dHB0Jf6oWHv46mOKaiAvePluA76y3ccnNJu2UiuS8shxbV/4P4aA1UWRl8+qnZjqBD\nB3jwQbjgAsd2/PLKcojd9Rof7JvFkKAo/nf9j4S1OsPxn6sJSywpIDozidUlOdzeNoDfzjmPoBqe\nUacaDGtT/KxN8XMdlkmgDMMg/ZN09r6cQllaOf7/7EzXmcHYvBzYO2rq8vNotiAG/3nTKGnfmX2j\nH6doyI0OLRNt2rSK+PippKWl88EHHfjllwmEhUXx/PPmeXUOTacsl0W73+C9fdO5tNMIPr1uA91a\nn+ngD9W0bS/KIzoribWledzVvh27+p5Pe0cq8EVEpEE0+hooe4Wd/Yv3s++1VOx28L87iLY3dMbN\nQ80vj3Lbn4JnzCT831/I4fBLSL/tEcr6RTo8zqZNq/j224ncddfxc+hiYroxZMjxc+iqo7A8n8W7\nJ7EsZRoXBQ7h4fOeo3ubHg7PpynbUpBDdHYyG8sK+L/AjjwQGqoDfkVEGlCTqYGqLKlk36x9pE7a\nj61dM1o9HEbL4WoUeCK3nzfS4u3X8Vm7hkPDR5Ea+xOVwd1qNFZuLixbNpWnnko46frddycQGxtd\nrQSqqLyAJQlTWJI8mQs6XsL7V8VxdsA5NZpPU7UhP4up2cnsqCjm/k6BrOjSG18d8CsiYjmN7nfu\n8txykqckc3DaQTx6ehPwxln4Dwxo6Gk1HnY7ti9W4jNzEp5Je0i7+f9I/jgGu3/rGg2XmQmLF8PH\nH0NEROmx61u3Qr9+5tc2W8lpxyiuKGJZQjSLk98kot2FLI/6kp7t+tZoPk2RYRiszctkak4yqfYy\nHgnqzD+Dg/Fy5NFFB6gGw9oUP2tT/FxHo0mgSg6WkPR6MhnzMmh+kT8dF/bBp7f63RxTUoLHkjn4\nzZlKhUdz0kY9QOGVt2E086zRcGlpsHAhfPaZ2b9p8WJYsaLq2hu7veonG0srS1ieMI1FSZPoGxDB\nuyM+o3d7x8/Ma6oMw2B1bjrROXvJo5JHg4O4MyiIZjrgV0TE8hq8BqowoZDEV5PIfi+bFlFtCLgn\nFK+uvnU4LYs5dBDPOVPxf3c2+Wf159DtD1F8/jCHG18elZJiPlH3zTdw3XVw220QcGSBb9OmVaxb\nN5GxY49v482Z041Bg06ugSq3l7EiIYbYpNfo2boPj5z3PP07DqjNT9mk2A2DT3IOMP3wPuw2gydC\ngrm1c2fctf0sItJoWeYsvNytuSS9lEzel3n4jGxH23+F4tlBPZyO2fEbLWa8gd/nH9Wq8eVRe/aY\n59T98AP87W9wyy1QVUNr8ym8aGy2Eux2LyIjxx9Lnsrt5XyUOJv5Sa/QreWZPBLxH87r5HixelNV\nYdhZkbWfGXmp+LrbeLJLMDcEBmJT4iQi0ug1+gQqa20WSS8mU7S1CN8xHQkYG4pHSz19BIBhYFu7\nBu8Zk/D6bTNp1/+DnJETsAd0rPGQ27aZXcN//RVuvRVuugl8q7HAd+JZeBX2ClYmz2de4ksE+Ybw\ncMTzRAYNrvGcmpoyw867mSnMzNtPJ09PngoN4cr2DXdotWowrE3xszbFz7oa5VN4x3o4vZJC2X6z\nh1PY231x9240JVgNq6wM9/cX4ffOZCgu4cAtE8l75UNo4V3jIbdsMROnxEQYPRpefNHsIO6ISqOS\n/yUvYm7ii7RtEcAbg95hUMjQGs+pqSmqrGBhVgrv5B/gbC8v5vU4i8sC9MCDiIgrqNMVqMrySvVw\nOp2cbDznT8M/NobCkO6k3/ogRYOudux8lBMYBmzYYCZOhw7BHXfAVVeBp4N15nbDzuqUpcxJeAFf\nT18eCX+ey0JHqIXEEfmV5czL3Mvc/DQifHx4OiyUC9u0aehpiYhILTSqFaj4buvVw6kqCbvwinkD\nv5XvkR15Bbve/ISynhE1Hs5uh7VrzcSpuBjGjoXLLwdH2wsZhsFXqe/zzp7n8HRvxtMXvMblYVcr\nbkccrihnVmYSCwvSucTPj9V9+9C/qkIyERFp8uo0gVIPpxMYBm7xcXjPfBPvjfEcvOZO9i37lcoO\nQTUesrIS1qwxi8M9POCuu2DwYMcXsAzDYO2Blcza/SyVlPFwxHO0ORTAwK6X1nhuTUlGeQkxmcks\nLTjEiFatWNuvL738/Rt6WqekGgxrU/ysTfFzHXWaQCl54oSDfSdjO5xD2i0TSHxuCYZ3zVs1lJfD\n//5ntiNo3RomToTISMc7GxiGwfr01czc9QyFlbk8eO4zXHfmKGxuNuIz4mo8v6biQFkx0zOS+LAo\nkxvatGFjRDjdfKp/ILOIiDRddVoDtX9/7c/Cs6zcw3gujMFv3nRK2geRNuoB82DfWnSfLimBTz6B\n2Fjo0sXcqgsPr1lLqJ/SvyZm19NklR3k/v5PcfPZf8fdpoOZAZJLCpmWmcT/SrK5tW0Aj3cNI9jR\nCnwREbGURlUD5ZKSE/Ca9Rb+Hywm+/wh7H55OWV9L6zVkEVFsGIFLFoEvXrBq69C7xq2hNqS8T0z\ndz1FanECE/s9yaie4/Cw6T8DgN3F+UzNTOLr0sOMbdeeHX0G0NFLvclEROTP9CcnEB+/ijVrpmKz\nlWK3N2fYsAlERv714bkncvvhO1rEvIHPhrWkR41m37tbqOwUWqt55eXB0qWwfDlERMC0aXDmmTUb\n69fMH5m562kSCn9jfJ/HuP2cf+HpfurH8+Lj44iMHFyzm1nM70W5TM1KIr40n7s7dOCdsAto4+ij\ni42IajCsTfGzNsXPdbh8AhUfv4pVqyYyZszx40tiY82v/zKJqqjAfeVyfGZNxj0jnbSR95H05AIM\n39oVGGdnm2fTffghDBoEs2dDaGjNxtqZs5WZO5/m97yfuKf3wyzq/TFeHlpVAdhckMPU7GS2lBUw\nIbAji0N74d9MTV1FROSvuXwN1PPPD2fUqC/+dH3p0uE888znVX8oP49mC2LwnzeNkoBADo56gMKh\nN9eqvgkgPd084HfVKrMNwZgx0KlTzcZKzN3OzJ1PsynnW/51zoOM6zMB72YqgAbYkJ/FlOxkdlUU\n82DnTtwbEoKPoz0fRESkSVENlINsttIqr7u5lfz54t5Emr/zFv7vL+ZwxCXsfmEJZf0HnnJs81y5\n41uDkZETTjqU96jUVPOJuq++gquvNrfs2rWr2c+Tkr+HWTueZX3W59zZ8z6mDZ+LX/PG+8h9fTEM\ng2/zMpmak8wBexn/DurMP0JCaF7DpqUiIuLaXD6BstubV3ndMI5vc7n9+L1Z37T+W9KvvI3UhRup\nDOp62nE3bVrFunUTGTv2+Nbg3Lnm10eTqMREmDcPvv/ePKPugw/MtgQ1kVaYwqwdzxGX8RG3n/lP\n3hi2h1ZeNRyMplMDZRgGq3PTic7ZSz6VPBYcxJigIJo14cRJNRjWpvhZm+LnOlw+gRo2bAKxsQl/\nqIHqRtQV9+L+0RJ8Zr2FR/pB0v52H0mPz8fwq17n6fj4qSclTwBjxyYQGxuNj08Uc+fC5s0wahT8\n+9/g51f9OZ+4slVcDhmdvPnRfwMjz7iD7y7dSVvvGi5fNSF2w2BlThrTDqdgtxk8GRrCqE6dcFdX\ndRERcQKXr4ECs5D8yy+jcXMrwSj3YHhFMCPWfE1pmw7H65scrJGZPn0wo0d/+6frzz57Cdu3x3H7\n7XDjjY4f8FvVytabMf5cHRVN1JC/OzZYE1Rh2Hk/az8z8lLxdrfxVJdgbggMxKbESURETkM1UDUQ\nGRlFZFBPms9680h9kx8J/1lMaf+LajzmqbYGfXy8+PhjaF71t//S2u8mMe4PK1sP3p3H0qXvunQC\nVW7YWZK5j5i8/bT39ODN7l2Jat9e5/iJiEidaLqFINXk9uP3eI+9nnbDwykpgm0LfmLf6x/WKnkC\nuPDCCUyf3u2ka7Nnd+P668fXKHkqLM9n5rZn2Z63tsrvV1n0Xgvx8XFOHa+ulNgrmZ2RxMDE9XxW\nlsHss7vzw4DzuKqD6x5eHRcX19BTkFpQ/KxN8XMdtVmBagXMBnoBBjAW2OCMSdW5E/o3eRxyvL7p\ndCorzafp5s2LorISJk2Kpl27EgzDi0suGV/lU3inU1xRxLKEqSxOfpMB7S/m7NbnA/F/et+JRe+u\noKiygvlZe3knL42+3i1Y2qsHF7Vp09DTEhERF1Gbv6LHAt8CczETMR8g94TvN74aqLxcmi2MwX/e\ndLN/0y33Uzjsb7Xu3wTmAb+ff24+VefnB+PGwcUX1+ycOoByexnvJbxNbOJr9Gkbzr8H/Ife7c89\nRePPbkRFTXG4e7oV5VWUMyczmfkFB7nA15enw0IZUNNHF0VERI5wtAaqpglUS2ALcLpn+RtPAnXC\n+XQ5Ay4j/daHKOsX6ZShS0th5UrzgN/AQDNxGjCg5olThb2CDxPfYX7SK3RreSaPnvci4YEXnPSe\nk4reDS+GDh3f5JOnnIoyZmYksajwEJf5+fN011D6tqz9iqGIiAjUXwLVD5gJbAP6ApuAiUDRCe9p\n2ATKMLD9sI4WMZPw/mEd6VGjyRp1P5Wdw5wyfHGx2bdp4ULzfLqxY6Ffv5qPV2lUsip5IXMSXqCD\nd0cePe9FBgZf6pS51kR8fOPoA5VRXsKMzGSWFRwiqlUrnurWlbN9fRt6Wo2a+tBYm+JnbYqfddXX\nU3gewLnAfcBPwGTgMeCZE990//13EBwcCoC/fyt69ep37A/l+Pg4AOe/HnAR7h8tYfNbL2DLz6P7\n6IdJfGohP+3YDGl7iTiSQG3caL4/ImKwQ6/POmsw770HCxbE0b07vPXWYHr0ML+/caPj44WHX8Ka\nfcuZsvoRvDxa8PIt0VwWOoL1678lfl9c3f/7OsXr33/fWq/3++PrlWtX8+HhNDb06MqNbdowvaiQ\nToads337AMcLNY/+RqXXeq3Xeq3Xeu3I66NfJycnUxM1XYHqCKwHji7nXISZQF11wnvqdwXqcA6e\nsW/jFzuDko7BpN3yAEVDbnRKfRNATg4sWQIrVsDAgXDnndD19M3IT8swDNYeWMnM3c9guFXwSMQL\njOh6ncs+OXbU3pJCpmUmsaokm1vbBvBE1zCCHG2WJSIi4qD62sIDWAvcBewCngNaAI+e8P36SaAS\nduE16038Pl5GzgXDSL/tIcp7n++04TMyzG26lSthyBCIiFjF7t1/fb7d6Ww4uIaYXU+RX5HDQ+HP\nct2Zo9iw/jPWrDk+7rBhE5p8XdOJEkoKmJKZyFclh7mjXTseDQujo5drPVkoIiINpz4baY4HFgOe\nQAJwZy3Gcoxh4Pbd13jPfBPvzRs4eM2d7Fv6C5Udg512iwMHzMLwL76AK680V8zCnfgAABgbSURB\nVJ/27//r8+1OZ0vGd8TsfIq0kmTu7/80I3vcgbvN/RRP1plfN1QSFR9fPzVQ24vymJKVxHelefyr\nfXtm9ruAtp6edX7fpixONRiWpvhZm+LnOmqTQP0MnOesiVRLWRnu7y/Cb/YUKCwkbeR48v6zDMPb\neUXFyckwfz6sXQvXXWdu2bVta37vvfdOfb7d6RKobdkbmbHjKfYU/sqEvo9z+zn/opmt2bHvr1kz\n9aTkCWDMmASWLo1usqtQvxQeZnJWEhvLCrgvsCMLQnvSqlmzv/6giIhII2CNo1yyMvCcNw3/RbMo\nCu5OyrjnKBp8Ldic10h9926YOxd+/BFGjoSPPgJ//5PfY7OVVvlZm63qLuB7Dv9GzM6n+CV3PXef\n8xAL+3yEl8eft6VONa6zuovHx69yeHuwrlaffirIZkpWEr9XFPNAp0BWdOmNr4PnDMrp6W+/1qb4\nWZvi5zoa959cO37Da+ab+H/2AZkXRbHzzU8p7xnu1Fv8+quZOP3+O9x2Gzz1FPj4VP3eU51vZ7ef\nnBSl5O9m5o5n2ZC1mnE9JzBzxCJ8PE+9SnaqcZ3RXbyxbA9+n5fJ1JxkEitKeDioM58GB+OtxElE\nRCyq8Z2FZxi4fbkK35HDCLjpUgq82/Pb8m0ceHGx05Inw4BNm+Dee+HRR+GCC+CTT2DMmFMnTwCR\nkROYO/fk8+3mzOlGZOR4AA4W7eM/m8cx5vvz6do2hPhRCTw44NnTJk8Aw4ZNIDb25HFjY7sxdOj4\nmv2AJzjV9uCXX0af9nPx8XG1vrdhGHyTe4jrkn/i4cydjAoMIGlgJA+EhSl5qkMnPqIr1qP4WZvi\n5zoaz59iJSV4LJuH75xoDLvBgZETKPjvSozmznsSyzAgPh7mzIHsbLjjDoiKguqW3hytc4qNjcZm\nK8Fu92LQoPF06RnOa1vv47O0xdx8xt9ZN3gHAd7tqz2voytBS5ce7y4eFeWc7uJ1vT1YFcMwWJ2b\nTnTOXvKp5LHgIO4ICsLDiVuuIiIiDakumw5Vr41Behqes6fQcskc8s/qR/qo+ykeeGXNz0Kpgt0O\ncXFm4lRebnYNHzoUarsIkluazfxdr/DR/jlEhdzEQwOeJdC3s1Pm7CzPPz+cUaO++NP1pUuH88wz\nnzv1XnbDYGVOGtNzU6hwM3gyJJhbO3fG3cV7W4mISONXn20MasXtl014zXwTvy9XkXHZDWyf8TUV\n3Xs79R4VFWYbgnnzwMsL7roLLrmk9rXnheX5LNz9Bu+lTGNIUBSfX7+RLi1r0VWzDpnbgwlVHD5c\n++3BoyoNgw+z9zMtdx9e7m48ExbCTYGB2JQ4iYhIE1W/CZTdju3zj/B5ZzKeibs5eMM/Sf5wN0ab\ndk69TVkZfPqp2Y6gXTt44AG48MLaL2qVVpawZM8UFidP4vwOg/jomu/o3qaHU+ZcV2q6PRgf/9d9\noCoMO8uzUnk7N5U2zdx544wwru7QweW7qTc09aGxNsXP2hQ/11E/CVRBPs3enY3f3GmUe/uRNnIi\nhVfehtHMuQ0Ti4vN9gMLF0JYGDz3HJx7bu3HLbeX835iDPMTX+WcNv1YMmI157TvX/uB60lkZJRT\nn7grM+y8m5lCTN5+gjw9efusMxjerp0SJxERcRl1WwO1IYnm70zGf8UCcvsO5NCtD1AScalT65sA\nCgrMhpfvvgvnnAPjxkGvXrUft9KoZGXSfOYkvECIfxiPnfcS53WKrP3AFlVir2RBZgqz8vZzVgsv\nng4L5bKAgIaeloiISK3V51l4f8Uo82vFoStGkXXrA1SEdHf6DXJzYelSWL4czj/fPOC3uxNuYzfs\nrE5Zyjt7nqe1VysePe8lBoUMrf3AFlVYWcG8rL3Mzkujv3cLnu0aRmSbNg09LREREadpVEXkv61M\nwvBr5fRxs7Jg8WL48EO49FKzSDwkpPbjGobBtwc+IWbX07i7u/Hsha9zedjVLrk1FR8fxzkDBjIn\nM5n5BQe5wNeX//U5h4hWzo+nOJdqMKxN8bM2xc911GkC5ezk6eBBWLAAPvsMrrjC3LILDHTO2D+k\nf8mMnU9SUJnLw+c+y7Vn3uKSiRNATkUZ72alEJfszmV+/nzZtw99W7Zs6GmJiIg0GnW6hbdpUzX6\nQFXDvn3mKtM338A118Dtt5tP1znDz5nrmbHzCQ4UJ3F//6cZ2eMO3G3uzhncYjLLS4nJTGJJwSFG\ntGrF013D6OHn19DTEhERqXONaguvthISzHPq1q+Hm282t+yctYO0I2cLM3Y8xc78LUzo+zije99N\nM1s1W5I3MQfLSng7M5EVhZlc17o1P0WEc8bpzrQRERFxcY3ybI3t2+Hhh+Huu+GMM8xz6u65xznJ\nU3LeTh798Wbu+/FyBoUMIn7UHsb2He+SydP+smIe3/87l+39EfcWBr8MOI/5fXpzho+PznOyMMXO\n2hQ/a1P8XEejWoHassVccdqzB0aPhhdegBYtnDP2gYJkZu58lnUZK7nj7PuYNnwOfs39nTO4xSSX\nFDI1M5HPS3IYHRDAtt4D6OTlvDMHRUREmroGr4EyDPjhB/OcuvR084Dfq64CTyf12MwoTmP2jv/w\nRfoybjljLOPDH6dNi7bOGdxiEkoKmJyRyNelhxnbrj3/DgulgxInERER69RA2e2wbp2ZOBUVmT2c\nhg+v/QG/R+WWZjNv18t8vH8u14aOJO7m3+ng46RH9ixme1EeU7KS+L40j3+2b8+srhfQ1lkZqoiI\niAuq9xqoykpYvRpGjYKZM2HMGLMRZlSUc5KnwvJ8YrY9yw3fdKfI7RCrr9/Eq4NnuGTy9GthLuNS\ntjDywM/0b+NN4oUX8MrZZ1UredI+vnUpdtam+Fmb4uc66m0Fqrzc7N80fz60bAnjx8PAgc471aW0\nsoSle6ayKPkNzu8wiI+v+Z4z2pztnMEtZktBDpOzk/i5vJD7AwNZHtobP2ct7YmIiEjd10CVlsLH\nH5sNMIODYexYiIhwXuJUbi/ng8RZzE98hZ5tevPYgJfo3d4JJwhb0A/52UzJTmJnRTEPdu7E/4WE\n4K3ESURE5C81qhqohQth0SLo0QNeeQV693be2HbDzqfJC5id8B86+wQRM2Qp53e+yHk3sJB1eRlM\nzd5Lir2UR4I686+QEJrbGmWHChERkSahThOo33+H6Gg480znjWkYBl+lvs/M3c/g4+nDfy+eweAu\nw513A4swDIO4vAym5OzlkL2MR4ODuCs4mGZOSpx0npN1KXbWpvhZm+LnOuo0gXr1VeeOF3/wc2bs\nfIpyo5jHB7zIiG7Xu9x5dYZh8EVuOlNz9pJPJU+EBPP3zp3x0IqTiIhIvWnwPlDVsfnQOt7e+QSZ\nZQd4sP8z3NRjNDY310oYDMNgVU4a0bn7KHez82RIMLd27oy7iyWQIiIidcHRGqg6TaDuuONyIiMn\nEB4eVaMBtmdv5u2dT5JQ8CsT+z3Jbb3+gYfNtYqi7YbBxzkHmHZ4Hx7u8GSXEP4WGIhNiZOIiIjT\nOJpA1ekyzpgxX7Bu3UQ2bVrl0OeS8nbw6I83MXHjCC7rchnxo/Ywpvc9LpU8VRoGyzP3cWnSBuYU\npPLyGaH8csH53NKpU70kT+plYl2KnbUpftam+LmOOs9Ixo5NIDY2ulqrUEfPq/su41Pu7Hkf06+Y\nh6+nX43uGx+/ijVrpmKzlWK3N2fYsAlERtZsJaw+lRt2lmel8nZuKu08PXire1ei2rd3uVovERGR\nxqxelnRstpLTfj+z+CCzd77A6oNLGNV9HN8N2U1rrzY1vl98/CpWrZrImDEJx67FxppfN9Ykqsyw\nszgzhZi8/XRp7snMs7szLCCgwRInPUViXYqdtSl+1qb4uY56SaDs9qoPrF23YRkff/0ouZWp+DcL\nZNI1U7hy4Oha32/NmqknJU8AY8YksHRpdKNLoErslSzMTGFW/gHO9GrOgh5ncWlAQENPS0RERE6j\nzh9lmzOnG5GR40+6VlRewIsf3sYnX9/KM/ftZdLESp69N5Xvv3qe+HjH6qWqYrOVVnndze30K2H1\nqaiyghmHEohMXM93Fdks79WDb86LaDTJk/bxrUuxszbFz9oUP9dRpwlUbOxwBg2acqz+qayylEW7\nJnHd12eQvu1Lnr7PftL7x4xJ4Msvo2t9X7u9eZXXDaPqlbD6VFBZQXT6HiKT1rO5MpePe/diTUQ4\nA9vUfMtSRERE6ledJlDjx39OeHgUFfYK3k+cxfVfd2fj4S9YeMWn9Gnfo8rPOGOVaNiwCcTGdjvp\nWmxsN4YOHX+KT9S9vIpy3jy4m8ik9Ww38vm8bx9WhZ/L+a1bN9icTkf7+Nal2Fmb4mdtip/rqNMa\nKLthZ3XKEmbteZ6AFgFEX7qAyKDBAHxUh6tER+ucli6Nxs2tBMPwIipqfIPUPx2uKGdmZhILC9K5\nzM+fr/v1pY+/f73PQ0RERJynThtpdn+jNx7uNh4770WGhEad9ERZ1U/KdSMqakqjK/SuiazyUmIy\nk3i3MIMrWvrzTNeu9PCrWUuGhqDznKxLsbM2xc/aFD/rcrSRZp2uQD0Q/gTXdB9Z5aP4jWmVyJkO\nlZUwIyuJ5QUZXNO6NT+e25/uvr4NPS0RERFxojpdgdq/3zln4VlBWlkx0zOT+KAwk5vatOHJrmGE\n+fg09LRERESkGhrVCpQr2F9WTHRGIp8UZTEqoC2/9jqP4BYtGnpaIiIiUofqvA9UU7W3pJCHUn9j\nWMpPtPJxY9v5A5jRq1eTSZ7Uy8S6FDtrU/ysTfFzHVqBclBiSQFTM5NYU5LDne3as7PPADp4NXx/\nKREREak/qoGqpt3F+UzJTCSuNI9/tG/Pw2GhtGtedSsGERERsZYmXQMVH7+KNWumYrOVYrc3Z9iw\nCXX+1N62ojymZCURX5rHPR07MCesJ62bNavTe4qIiEjjZpkaqKN9o0aN+oKRI79l1KgvWLVqolPO\nzqvKb0W53JWyhVsO/ExEG28SL7yAF88802WSJ+3jW5diZ22Kn7Upfq7DMitQa9ZMPanpJphn5y1d\nGu3UVagtBTlMyU5ma3kB9wcGsiy0N34elvnXJCIiIvXAMpmBzVZa5XVnnJ0HsLEgm8lZSWyrKObB\nToF82KU3Pi6cOKmTrnUpdtam+Fmb4uc6LJMh2Ovo7LwN+VlMzk5mT0UxD3XuxP+69MPL3b1WY4qI\niEjTZpkaqGHDJhAb2+2ka7Gx3Rg6dHyNxvsuL5ObkzcyMWMHfwtsS9LASB7q2lXJ0xHax7cuxc7a\nFD9rU/xch2VWoJxxdp5hGKzNy2RyTjIH7WU8FhzEXcHBNLNZJo8UERGRRsAl+kAZhsFXuYeYengv\n2UYFTwQHcUdQEB5KnERERIQm3gfKUYZhsDo3nak5eymkkidDghkdFIS7W13mjSIiItLUNcklGMMw\n+DT7AFck/8h/DyfxcGgQOyIv5I7gYCVP1aR9fOtS7KxN8bM2xc91NKkVKLthsDInjejDKbjZ4KnQ\nYEZ26oRNSZOIiIg4UZOogbIbBh/lHCD6cApe7m483SWEGwMDj+5nioiIiJyWS9VAVRoG72elMj0v\nFX8PG/89I4xrOnRQ4iQiIiJ1ypI1UBWGnXczUxiUuJ7FRWm81b0rG88fwLUdOyp5chLt41uXYmdt\nip+1KX6uo7YrUO7ARiAVuLr20zm9csPO0sxU3s7bR2dPT2LO7s7lAQFKmkRERKRe1TbzeBAIB/yA\na/7wPafVQJUZdhZnpjAjbz9hzT15NiyUoe3aOWVsERERkfqsgQoCrgRewkyknK7UbmdRVgoxefs5\n06s5i3qcxeCAgLq4lYiIiEi11aYG6i3gEcDupLkcU2KvZOahRCIT41lbnsWyXj345rwIJU/1SPv4\n1qXYWZviZ22Kn+uo6QrUVcAhYAsw+FRvuv/+OwgODgXA378VvXr1IzLSfHt8fBzASa9L7ZVsPzOU\nd/LSCNn+O08HBnLvIHNn8Oh/lIMHD9breni9devWRjUfvdZrvdZrvdZrZ74++nVycjI1UdMaqJeB\n0UAF4AX4A+8Dfz/hPdWugSqsrGBu5l7m5B9ggK8vz4SFMqB16xpOTURERMQxjtZAOePxtUuAh/nz\nU3h/mUDlV5YzOyOZ+QUHifT15dluXTm3ZUsnTElERESk+hxNoGxOuq9Dj9vlVZQz6eBuIpM2kOBW\nyJq+ffj43P5KnhqRE5c4xVoUO2tT/KxN8XMdzuhE/u2RX3/pcEU5MzOTWFiQzhB/f+L69aW3v78T\npiAiIiJSf+rlLLzsijJiMpJYXHiIK1r680zXrvTw86vDW4uIiIhUX6M6Cy+zvJQZGUksLTxEVKtW\nbDi3P2f5+tblLUVERETqnLNqoKo0KPkHijzL+SkinEV9+yh5shDt41uXYmdtip+1KX6uo05XoDZH\nhNPVx6cubyEiIiJS7+q0BsownHMWnoiIiEhdaqg2BiIiIiIuQwmUVEn7+Nal2Fmb4mdtip/rUAIl\nIiIi4iDVQImIiIjLUw2UiIiISB1TAiVV0j6+dSl21qb4WZvi5zqUQImIiIg4SDVQIiIi4vJUAyUi\nIiJSx5RASZW0j29dip21KX7Wpvi5DiVQIiIiIg5SDZSIiIi4PNVAiYiIiNQxJVBSJe3jW5diZ22K\nn7Upfq5DCZSIiIiIg1QDJSIiIi5PNVAiIiIidUwJlFRJ+/jWpdhZm+JnbYqf61ACJSIiIuIg1UCJ\niIiIy1MNlIiIiEgdUwIlVdI+vnUpdtam+Fmb4uc6lECJiIiIOEg1UCIiIuLyVAMlIiIiUseUQEmV\ntI9vXYqdtSl+1qb4uQ4lUCIiIiIOUg2UiIiIuDzVQImIiIjUMSVQUiXt41uXYmdtip+1KX6uQwmU\niIiIiINUAyUiIiIuTzVQIiIiInVMCZRUSfv41qXYWZviZ22Kn+tQAiUiIiLiINVAiYiIiMtTDZSI\niIhIHVMCJVXSPr51KXbWpvhZm+LnOpRAiYiIiDhINVAiIiLi8lQDJSIiIlLHlEBJlbSPb12KnbUp\nftam+LkOJVAiIiIiDlINlIiIiLg81UCJiIiI1DElUFIl7eNbl2JnbYqftSl+rkMJlIiIiIiDVAMl\nIiIiLk81UCIiIiJ1TAmUVEn7+Nal2Fmb4mdtip/rqE0CFQx8A/wO/AZMcMqMpFHYunVrQ09Bakix\nszbFz9oUP9fhUYvPlgMPAFsBX2ATsAbY7oR5SQM7fPhwQ09BakixszbFz9oUP9dRmxWog5jJE0AB\nZuLUqdYzEhEREWnknFUDFQr0B35w0njSwJKTkxt6ClJDip21KX7Wpvi5Dme0MfAF4oAXgY9OuL4H\n6OaE8UVERETqWgJwRn3drBmwGri/vm4oIiIiYmVuwALgrYaeiIiIiIhVXATYMQvJtxz5dUWDzkhE\nRERERERERFzHFcAOYDfwaAPPRU5vLpAO/HrCtTaYPb12AV8ArRpgXlI9p2poqxg2fl6YTy5vBbYB\nrxy5rthZizvmDszKI68VP+tIBn7BjN+PR641aPzcMZ/AC8UsMt8K9KjPCYhDLsZsQXFiAvVf4N9H\nvn4UeLW+JyXV1hHod+RrX2An5v9viqE1eB/5pwewAbM0QrGzlgeBxcAnR14rftaRhJkwnahB43ch\n8PkJrx878ksar1BOTqB2AB2OfN3xyGuxho+AoSiGVuMN/AT0QrGzkiDgS+BSjq9AKX7WkQS0/cO1\nasevLg4T7gzsO+F16pFrYh0dMLf1OPLPDqd5rzQeoRxvaKsYWoMNc5U+neNbsYqddbwFPIL5QNVR\nip91GJgJ8EbgH0euVTt+tTkL73QTkqbDQDG1Al/gfWAikP+H7ymGjZcdcwu2JWZPvUv/8H3FrvG6\nCjiEWT8z+BTvUfwat4FAGtAOs+7pj6tNp41fXaxA7ccsbD0qGHMVSqwjHXPpEiAQ8zcJabyaYSZP\nCzl+GoBiaC25wCogHMXOKiKBazC3gZYAl2H+P6j4WUfakX9mAB8CA3AgfnWRQG0EumNuJ3gCIzle\nXCfW8Akw5sjXYzj5iB5pXNyAOZhPcU0+4bpi2PgFcPwJnxbAMMzVDMXOGp7AXCAIA24BvgZGo/hZ\nhTfgd+RrH+ByzFrgBo/fCMyngfYAj9f3zcUhS4ADQBlm7dqdmE8lfIkew7WCUzW0VQwbv97AZszY\n/YJZSwOKnRVdwvGFAsXPGsIw/9/bitkC5miuoviJiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiI\niIiIiIiIiIg0cv8POVj/TfiCALsAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x8c39570>"
]
}
],
"prompt_number": 47
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also calculate the confidence interval for a different significance level than the default 0.05. For example, we can get the confidence intervals with a coverage of `1 - alpha = 0.9` by specifying `alpha=0.1` as keyword argument."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"pf01 = pred_res2.summary_frame(alpha=0.1)\n",
"print(pred_res2.conf_int(alpha=0.1)[:5])\n",
"print(pred_res2.conf_int(obs=True, alpha=0.1)[:5])\n",
"pf01.head()\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[[ 4.80588804 5.47061803]\n",
" [ 4.98657249 5.62730001]\n",
" [ 5.1670392 5.78419975]\n",
" [ 5.34726223 5.94134314]\n",
" [ 5.52721209 6.09875972]]\n",
"[[ 3.9755207 6.30098538]\n",
" [ 4.1475774 6.4662951 ]\n",
" [ 4.31946127 6.63177767]\n",
" [ 4.49117085 6.79743453]\n",
" [ 4.66270478 6.96326703]]\n"
]
},
{
"html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>mean</th>\n",
" <th>mean_se</th>\n",
" <th>mean_ci_lower</th>\n",
" <th>mean_ci_upper</th>\n",
" <th>obs_ci_lower</th>\n",
" <th>obs_ci_upper</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td> 5.138253</td>\n",
" <td> 0.198164</td>\n",
" <td> 4.805888</td>\n",
" <td> 5.470618</td>\n",
" <td> 3.975521</td>\n",
" <td> 6.300985</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td> 5.306936</td>\n",
" <td> 0.191008</td>\n",
" <td> 4.986572</td>\n",
" <td> 5.627300</td>\n",
" <td> 4.147577</td>\n",
" <td> 6.466295</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td> 5.475619</td>\n",
" <td> 0.183983</td>\n",
" <td> 5.167039</td>\n",
" <td> 5.784200</td>\n",
" <td> 4.319461</td>\n",
" <td> 6.631778</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td> 5.644303</td>\n",
" <td> 0.177102</td>\n",
" <td> 5.347262</td>\n",
" <td> 5.941343</td>\n",
" <td> 4.491171</td>\n",
" <td> 6.797435</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td> 5.812986</td>\n",
" <td> 0.170385</td>\n",
" <td> 5.527212</td>\n",
" <td> 6.098760</td>\n",
" <td> 4.662705</td>\n",
" <td> 6.963267</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 52,
"text": [
" mean mean_se mean_ci_lower mean_ci_upper obs_ci_lower obs_ci_upper\n",
"0 5.138253 0.198164 4.805888 5.470618 3.975521 6.300985\n",
"1 5.306936 0.191008 4.986572 5.627300 4.147577 6.466295\n",
"2 5.475619 0.183983 5.167039 5.784200 4.319461 6.631778\n",
"3 5.644303 0.177102 5.347262 5.941343 4.491171 6.797435\n",
"4 5.812986 0.170385 5.527212 6.098760 4.662705 6.963267"
]
}
],
"prompt_number": 52
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The confidence interval depends on the covariance matrix of the parameter estimates and on whether we use the t or the normal distribution. The distribution can be selected with `use_t`, where `use_t=True` requests the use of the t distribution and `False` requests the normal distribution. We can also choose a covariance matrix of the parameter estimates that is robust to heteroscedasticity or correlation across observations by using the `cov_type` argument.\n",
"\n",
"As it turns out. using the heteroscedasticity robust covariance implies in this case slightly narrower confidence intervals than the nonrobust covariance."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"res_wls_n = mod_wls.fit(use_t=False)\n",
"pred_wls_n = res_wls_n.get_prediction()\n",
"print(pred_wls_n.summary_frame().head())"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" mean mean_se mean_ci_lower mean_ci_upper obs_ci_lower obs_ci_upper\n",
"0 5.138253 0.198164 4.749859 5.526647 3.779512 6.496994\n",
"1 5.306936 0.191008 4.932567 5.681306 3.952137 6.661735\n",
"2 5.475619 0.183983 5.115020 5.836219 4.124561 6.826678\n",
"3 5.644303 0.177102 5.297188 5.991417 4.296780 6.991825\n",
"4 5.812986 0.170385 5.479037 6.146934 4.468795 7.157177\n"
]
}
],
"prompt_number": 35
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mod_ols = OLS(y, X)\n",
"res_ols = mod_ols.fit(cov_type='HC3')\n",
"pf = res_ols.get_prediction().summary_frame()\n",
"ax = pf[cols].plot() # cols defined before\n",
"ax.plot(y, 'o')\n",
"print(pf.head())"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" mean mean_se mean_ci_lower mean_ci_upper obs_ci_lower obs_ci_upper\n",
"0 5.239191 0.186230 4.874186 5.604195 3.253283 7.225098\n",
"1 5.400867 0.179019 5.049996 5.751739 3.417509 7.384225\n",
"2 5.562544 0.172015 5.225400 5.899688 3.581568 7.543520\n",
"3 5.724221 0.165245 5.400347 6.048094 3.745460 7.702981\n",
"4 5.885897 0.158737 5.574779 6.197015 3.909184 7.862610\n"
]
},
{
"metadata": {},
"output_type": "display_data",
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q2rOtuLjjIgeiDrDv/n243uFKx+MdafJhE2r7lZwuspf+sysnT8Izz0CHDtCk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\nD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"text": [
"<matplotlib.figure.Figure at 0x78da370>"
]
}
],
"prompt_number": 36
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"res_ols = mod_ols.fit()\n",
"pf = res_ols.get_prediction().summary_frame()\n",
"ax = pf[cols].plot() # cols defined before\n",
"ax.plot(y, 'o')\n",
"print(pf.head())"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" mean mean_se mean_ci_lower mean_ci_upper obs_ci_lower obs_ci_upper\n",
"0 5.239191 0.277531 4.681178 5.797203 3.160356 7.318025\n",
"1 5.400867 0.269166 4.859672 5.942062 3.326483 7.475251\n",
"2 5.562544 0.260899 5.037972 6.087116 3.492435 7.632653\n",
"3 5.724221 0.252738 5.216057 6.232384 3.658208 7.790233\n",
"4 5.885897 0.244694 5.393907 6.377888 3.823803 7.947991\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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Nyi2AaS3jVyNotfDCC2qOk7+/OgP19tvg7GyW5iWAKsHb25vk5ORSyeIXLlzA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\nREREREREREREREREREREREREgtz/B3vZ2zh2WqerAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x74a15d0>"
]
}
],
"prompt_number": 37
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"GLM"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also estimate the same linear models using Generalized Linear Models, GLM, which defaults to the normal distribution. GLM corresponds in this case to OLS and there is currently no WLS equivalent in GLM since it does not yet allow for user specified weights. In the following we rescale the variables to take account of the weights. Note, this implies that we get the same parameter estimates and their covariance matrix, but we prediction and other statistics are for the transformed model and differ from WLS.\n",
"\n",
"We only have linear prediction in this example since it is a linear model. The prediction for nonlinear link functions is a nonlinear transformation of the linear prediction. The confidecne intervals in this case are defined by default by endpoint transformation, which means that we calculate the confidence interval for the linear predictions and nonlinearly transform the lower and upper bounds.\n",
"This is supposed to have in general better coverage than the delta method. The delta method uses a local linear approximation as is not yet implemented for the prediction interval.\n",
"\n",
"There is another difference between the linear model with the assumption of normally distributed errors, and general nonlinear and nonnormal models like those in GLM or in `discrete`. In the linear normal model the sampling distribution of our parameter estimate and the distribution of the error term, or equivalently of an observation, are both either t or normal distributed under our assumptions. We can therefore combine those and calculate a confidence interval for a new observation based on either the normal or the t distribution. This is not the case in nonnormal models. Take as an example the Poisson distribution, a observation for given parameters is Poisson distributed, but our parameter estimates are (asymptotically) normal distributed. We would need to combine those distributions in order to obtain confidence intervals for a new observations. This is not possible in a closed form, but we could simulate it based on our estimated model or by bootstrapping.\n",
"Currently only the confidence intervals for the \"mean\", that is, for the conditional expectation, is available for non-normal models."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from statsmodels.genmod.generalized_linear_model import GLM\n",
"\n",
"w_sqrt = np.sqrt(w)\n",
"mod_glm = GLM(y/w_sqrt, X/w_sqrt[:,None])\n",
"res_glm = mod_glm.fit()\n",
"pred_glm = res_glm.get_prediction()\n",
"print(pred_glm.summary_frame().head())"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" mean mean_se mean_ci_lower mean_ci_upper\n",
"0 5.110110 0.213037 4.692565 5.527655\n",
"1 5.275544 0.205344 4.873077 5.678012\n",
"2 5.440978 0.197792 5.053314 5.828643\n",
"3 5.606413 0.190395 5.233246 5.979580\n",
"4 5.771847 0.183173 5.412834 6.130860\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"GLM uses the normal distribution for parameter inference by default. We can use the t distribution by setting the keyword argument `use_t=True`."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"res_glm_t = mod_glm.fit(use_t=True)\n",
"pred_glm_t = res_glm_t.get_prediction()\n",
"print(pred_glm_t.summary_frame().head())"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" mean mean_se mean_ci_lower mean_ci_upper\n",
"0 5.110110 0.213037 4.681771 5.538449\n",
"1 5.275544 0.205344 4.862672 5.688417\n",
"2 5.440978 0.197792 5.043292 5.838665\n",
"3 5.606413 0.190395 5.223598 5.989227\n",
"4 5.771847 0.183173 5.403553 6.140141\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Parameter transformation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is not really prediction but uses parts of the same code.\n",
"\n",
"This is or will be equivalent to Stata's `eform` for exponentiated parameters.\n",
"\n",
"....."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"rates = params_transform_univariate(res_glm.params, res_glm.cov_params())\n",
"print('\\nRates exp(params)')\n",
"print(rates.summary_frame())\n",
"\n",
"rates2 = np.column_stack((np.exp(res_glm.params),\n",
" res_glm.bse * np.exp(res_glm.params),\n",
" np.exp(res_glm.conf_int())))\n",
"assert_allclose(rates.summary_frame().values, rates2, rtol=1e-13)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Rates exp(params)\n",
" mean mean_se mean_ci_lower mean_ci_upper\n",
"0 165.688573 35.297780 109.132780 251.553230\n",
"1 1.499773 0.034228 1.434167 1.568381\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from statsmodels.genmod.families import links\n",
"\n",
"# with identity transform\n",
"pt = params_transform_univariate(res_glm.params, res_glm.cov_params(), link=links.identity())\n",
"print(pt.tvalues)\n",
"\n",
"assert_allclose(pt.tvalues, res_glm.tvalues, rtol=1e-13)\n",
"assert_allclose(pt.se_mean, res_glm.bse, rtol=1e-13)\n",
"ptt = pt.t_test()\n",
"assert_allclose(ptt[0], res_glm.tvalues, rtol=1e-13)\n",
"assert_allclose(ptt[1], res_glm.pvalues, rtol=1e-13)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[ 23.98697085 17.75989187]\n"
]
}
],
"prompt_number": 11
}
],
"metadata": {}
}
]
}
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