{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import arviz as az\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.formula.api as smf\n", "\n", "from scipy import stats" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "az.style.use(\"arviz-white\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Gibbs sampling for simple linear regression\n", "\n", "\n", "For observation $i=1, \\dots,n$\n", ", let $Y_i$ be the response and $X_i$ be the covariate. The model is $Y_i\\sim\\mbox{Normal}(\\alpha + \\beta X_i,\\sigma^2)$.\n", "\n", "We select priors:\n", "* $\\alpha,\\beta \\sim\\mbox{Normal}(\\mu_0,\\sigma_0^2)$ \n", "* $\\sigma^2\\sim\\mbox{InvGamma}(a,b)$.\n", "\n", "To illustrate the method we regress the log odds of a baby being named “Sophia'' (Y) onto the year (X). To improve convergence we take $X$ to be the year - 1984 (so that $X$ is centered on zero)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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yearsexnamenprop
4729521951FSophia1530.000083
4835881952FSophia1100.000058
4941611953FSophia1300.000067
5051031954FSophia1120.000056
5159401955FSophia1520.000076
\n", "
" ], "text/plain": [ " year sex name n prop\n", "472952 1951 F Sophia 153 0.000083\n", "483588 1952 F Sophia 110 0.000058\n", "494161 1953 F Sophia 130 0.000067\n", "505103 1954 F Sophia 112 0.000056\n", "515940 1955 F Sophia 152 0.000076" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dat = pd.read_csv(\"data/babynames.csv\")\n", "dat = dat.query('name==\"Sophia\" and sex==\"F\" and year>1950')\n", "dat.head()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "yr = dat.year\n", "p = dat.prop\n", "\n", "X = dat.year - 1984\n", "Y = np.log(p / (1 - p))\n", "n = len(X)\n", "\n", "plt.plot(yr, p, \"b.\")\n", "plt.xlabel(\"Year\")\n", "plt.ylabel(\"Proportion Sophia\");" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "results = smf.ols(\"Y~X\", dat).fit()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: Y R-squared: 0.929
Model: OLS Adj. R-squared: 0.928
Method: Least Squares F-statistic: 848.2
Date: Thu, 25 Apr 2019 Prob (F-statistic): 5.13e-39
Time: 15:13:10 Log-Likelihood: -37.748
No. Observations: 67 AIC: 79.50
Df Residuals: 65 BIC: 83.91
Df Model: 1
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept -7.1885 0.053 -136.347 0.000 -7.294 -7.083
X 0.0794 0.003 29.125 0.000 0.074 0.085
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 14.668 Durbin-Watson: 0.156
Prob(Omnibus): 0.001 Jarque-Bera (JB): 4.634
Skew: -0.315 Prob(JB): 0.0986
Kurtosis: 1.876 Cond. No. 19.3


Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: Y R-squared: 0.929\n", "Model: OLS Adj. R-squared: 0.928\n", "Method: Least Squares F-statistic: 848.2\n", "Date: Thu, 25 Apr 2019 Prob (F-statistic): 5.13e-39\n", "Time: 15:13:10 Log-Likelihood: -37.748\n", "No. Observations: 67 AIC: 79.50\n", "Df Residuals: 65 BIC: 83.91\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept -7.1885 0.053 -136.347 0.000 -7.294 -7.083\n", "X 0.0794 0.003 29.125 0.000 0.074 0.085\n", "==============================================================================\n", "Omnibus: 14.668 Durbin-Watson: 0.156\n", "Prob(Omnibus): 0.001 Jarque-Bera (JB): 4.634\n", "Skew: -0.315 Prob(JB): 0.0986\n", "Kurtosis: 1.876 Cond. No. 19.3\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "\"\"\"" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results.summary()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Intercept -7.188465\n", "X 0.079399\n", "dtype: float64" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results.params" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(yr, Y, \".\")\n", "y_hat = results.params[0] + results.params[1] * X\n", "plt.plot(yr, y_hat, \"C1\")\n", "plt.xlabel(\"Year\")\n", "plt.ylabel(\"Log odds Sophia\");" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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KLrjsPsz968B0YoRFY1zVcHcsUnAVERERqSFZx51Mn5GHaZ7/3jRh+oy8y555tfaeP3SgIe7deiEFVxEREZEakpFhukOri2mCw2GW/YIyWKePYWVsBcDWteEuEwAFVxEREZEaExFh4+JTWW02CA+vfAQzdycBYET2wQhuW43V1T0KriIiIiI1pHWonenTAt3h1WaD6dMCaR1qr9TrLcvC3L38/GtvuremyqwzfPbkLBEREZH6YHR8Y2Jj/XE4TMLDbZUOrQDW0V3w47fg3wSjy4garLJuUHAVERERqWGtQ+2XFVhdrC+XAWB0HobRKKi6y6pztFRARERExAdZRQX/PXRAywQABVcRERERn2Qd/BgKTkNwGEZUrLfL8QkKriIiIiI+yP1QVvTdGBdvTdBA6V0QERER8TFWznGsb/8BgO2mMd4txocouIqIiIj4GHNP0vkjXtv1xGjZ3tvl+AwFVxEREREfYlkW5pfnlwkYmm0tQcFVRERExJf8+yvIPgh+jRr8Ea8XU3AVERER8SGma+/W6wZjNAn2cjW+RcFVRERExEdYxYWYe1cCeiirLDo5S0RERMTLso47ycgw6eDcxBX5J6BZKEb7W71dls/RjKuIiIiIFyUlFzBo8CkeTDhD6rt/BcAWPRrDrvnFiym4ioiIiHhJ1nEn02fkYZrQIuAE/Vr9C4AT7e72cmW+SVFeRERExEsyMkxM8/zXg8PW428rZt/JLhTmdSTEu6X5JI+D69mzZ3nvvff49NNPycjIIC8vr8x2hmGwf/9+jwsUERERqa8iImzYbGCaMLLdKgA+OnYXD4XrQ/GyeBRcc3JyuO+++/j222+x2+34+/tjWRYhISH8+OOPWJYFQNu2bau1WBEREZH6pHWonenTAvnL619yffMDFJl+dPvZPbQOtXu7NJ/kUZxfsGABhw8fZsyYMaSmpnLnnXdiGAabN29m9+7dvPjii7Rs2ZLo6Gg+/fTT6q5ZREREpN4YHd+YRY//DQCzwx2MHNPGyxX5Lo+C6yeffEKrVq34/e9/T6NGjTAMw32vUaNGxMXFsXDhQjZt2sQ777xTbcWKiIiI1DdWcSFNDicB0LTPvV6uxrd5FFwzMzPp3Lkz/v7+AO7gWlRU5G7ToUMHYmJiWLVqVTWUKSIiIlI/WQf/Bnk/nt+7tVN/b5fj0zwKro0aNSIgIMD9fVBQEAA//vhjiXbBwcEcPXq0CuWJiIiI1G/mjsUA2Lrfh2H393I1vs2j4Nq6dWsyMzPd319zzTUAbN++3X2tuLiYr776iubNm1exRBEREZH6yfrpO6zvUsAwsPW8z9vl+DyPgmvPnj05fPgwOTk5ANx+++34+fnxxz/+kSVLlvDZZ58xefJkjh07Rq9evaq1YBEREZH6wtzxPgBGx/4Yzdt5uRrf59F2WEOHDmXfvn18+eWX3HLLLYSGhvKb3/yGl156iRkzZgBgWRYtW7YkMTGxWgsWERERqQ+s4nOYXy4DwNZzvJerqRs8Cq49e/Zk2bJlJa798pe/pHv37mzatIkzZ84QGRlJfHy8lgqIiIiIlMHavx7yT8AVbTA6DfB2OXVCtR75Gh0dTXR0dHV2KSIiIlIvuR/K6nEfhr1aI1m9pfPERERERGqZ9cNhrPQvwLBh6zHO2+XUGZWK964dBEJDQ7Hb7SV2FKgMHf0qIiIitSHruJOMDJOICJtPH5tq7vwLAEangRjBykmVVang2r9/f2w2G+vWrSMqKor+/fuXOC2rIoZhsH///ioVKSIiInIpSckFTJ+Rh2mCzQbTpwUyOr6xt8sqxSoqwPxyOQC2Xr+o1GvqSiCvaZUKrq4trZo0aVLiexERERFfkHXc6Q6tAKYJ02fkERvr73NBz9r3EZw9CcFhGB0vfVJWXQnktaFSwfX999+v8HsRERERb8rIMN2h1cU0weEwfS64mjvP5yhbj3EYtoprq0uBvDbo4SwRERGp8yIibNguSjU2G4SH+1bUsY4fxMrYBjY7th6XPimrokDeEPnWb1NERETEA61D7UyfFugOr66P1H1tVtL9UNa1d2Bc0fqS7etKIK8tVdo07Pvvvyc1NZXs7GwKCwvLbGMYBo888khVhhERERG5pNHxjYmN9cfhMAkP972HmKyis5i7VwCVfyjLFcgvXuPqaz9bbfEouBYWFvL73/+etWvXAuePdy2PgquIiIjUltahdp8NddbXa6DgNDRvh9H+tkq/ztcDeW3yKLjOmTOHNWvWEBwczIgRI4iKiqJp06bVXRt79+7ljTfeYPfu3RQVFdGhQwfuv/9+RowYUek+CgsLWbBgAWvXriUzM5Pg4GBuvfVWpkyZQkhISJmvWbt2LYsWLeLbb7/F39+fG2+8kcmTJ3PDDTeUamtZFps2beL9998nLS2NnJwcWrduTe/evUlISKBdu3Ye//wiIiJSf5g7/vNQVs9fYFz8+f8l+HIgr02GVdF0aTluu+028vPzWblyJWFhYTVRF9u2bWPChAn4+/szbNgwmjVrxsaNGzl69ChTp07l4YcfvmQfpmmSkJBASkoK0dHRxMTE4HA42LRpE61bt2b58uWlwuv8+fN57bXXaNu2LXfeeSf5+fmsW7eOc+fO8c4779C7d+8S7V988UXee+89QkJCGDBgAEFBQRw8eJAtW7bQtGlTPvjgAzp16lRmfbt27aJHjx6kpqbSvXt3z98sERGReqQ+7llqZe2n+K3+YPPDL3EXRrNW3i6pbrI80LVrV+vhhx/25KWVUlRUZA0cONDq2rWrtW/fPvf1nJwca9iwYVbnzp2ttLS0S/bz4YcfWp06dbKmTp1qmaZZ6vqTTz5Zon1aWprVuXNn64477rDOnDnjvn7o0CErOjraGjhwoFVUVOS+np2dbV133XXW7bffbuXk5JTo67333rM6depkPfXUU+XWl5qaagFWamrqJX8WERGRhuDDpLNW1xt/tDp3+9HqeuOP1odJZ71dUrUoXv1bq/D3oVbR0gneLqVO8+iRtLZt23L27NlqjtD/tXXrVhwOB8OHD6dz587u60FBQUyaNIni4mKSk5Mv2c+KFecXQD/xxBMlTvoaPXo07du3Z/369eTm5rqvJycnU1xczMSJE2nWrJn7eseOHbnrrrtwOBxs3brVff3YsWOYpkn37t0JCgoqMfZtt90GwIkTJy7vhxcREWmgytuzNOu407uFVZGVf/K/D2XFPODdYuo4j4Lr3Xffzd69e/n3v/9d3fUAsH37dgD69etX6l5sbGyJNuU5d+4ce/bsISoqqszlDLGxsRQWFrJnz55S47rGuNDNN98MwI4dO9zXIiIi8Pf3Z9euXSUCMMA///lPAPr06VNhnSIiInJefd2z1Ez9KxSdhdDOGFGlM4ZUnkcPZ02YMIEDBw6QkJDAtGnTiImJKTGjWVXp6enA+WB4seDgYFq0aEFGRkaFfTgcDkzTJDIyssz7ruvp6enuoJqenk7Tpk3LfGjLVYurNoAWLVowdepUXn75ZYYOHUr//v0JDAzk0KFDfPHFF9x77738/Oc/v8RPKyIiIvDfPUsvDK91fc9Sy1mMue09AOz/k1CteelC9XFdcFkqFVwHDBhQ5vXMzEweeOAB/Pz8CAkJKfOXYRgGn3zyyWUV5Zq9vPDj+gsFBQWRlZVVYR85OTnutmUJDAwsMZbr6yuvvLLcMS9uD+dDfKtWrfjf//1fli5d6r5+0003MXLkSPz9/SusU0RERM6rj3uWWgfWw+ljEHgVxg2jamSMpOSCUu/Z6PjGNTKWt1UquB47dqzC+0VFRWRmZlZLQXXN3LlzmTt3Lo8++ihxcXFcccUVHDhwgBdffJHx48fz+uuvc8cdd3i7TBERkTqhvu1Zan7xZwBsvcZj+Fd/mCxvXXBsrH+df+/KUqngevDgwZquowTX7KZr1vRiubm55c7GurjuXzxD6pKXl1diLNfXFY15cfsvvviC//u//+OBBx4osT1Xjx49+NOf/sSAAQOYOXOmgquIiMhlqC97lprHdmM5toPdv8YeyqpoXXB9eA8v5pOLRlzrT8tax3r69GlOnjxZ5vrXC4WHh2Oz2UqsSb2Q6/qFa2AjIyPJz8/nhx9+KNXeVcuF7V0PYF28tyvAlVdeybXXXktmZqZ2FhAREWmAXLOtRte7MJqF1sgYrnXBF6rr64Ir4pM/Va9evQBISUkpdW/Lli0AxMTEVNhHo0aN6NatG2lpaWUuddiyZQsBAQFER0eXGtc1xoU2b95cog2cXyIB5W955boeEBBQYa0iIiJSv1g5x7G+Xg2Are9DNTaOa12wK7zWh3XBFalScD148CDPPfccI0aMoHfv3vTu3ZsRI0bw3HPPsX//fo/77du3L+3ateOjjz7iwIED7uu5ubnMnTsXPz8/Ro367wLn7Oxsjhw5Uupj/jFjxgAwa9YsrAsOCEtKSuLIkSMMHTq0xEf/8fHx+Pn5MW/evBJ9HT58mNWrVxMeHl5ieyvXaVcLFy4sNfbKlSvJyMigS5cu5T4gJiIiIpcn67iTbduLfH5vV3P7QnAWYYTHYAu7sUbHGh3fmE1/a857f76CTX9rXm8fzAIPj3wFeOutt5g7dy5OZ9l/OHa7nYcffpjHHnvMo8K2bt3KQw89hL+/P8OHDycoKMh95OuUKVOYOHGiu+1TTz3FypUrmTlzJvHx8e7rTqeTX/3qVyWOfP3+++/ZuHEjoaGhrFixotTWV/PmzeP1118v88jXP//5zyWCq9Pp5IEHHmD79u1ceeWV9O/fnyuuuIJvvvnGPaP73nvv0bNnzzJ/Rh35KiIiUnl15el5q6iA4lk9IO8n7PcuwNZ1pLdLqjc8Cq6rVq3iqaeeomnTpowbN45hw4Zx9dVXA+d3IPjoo49YsmQJ+fn5zJw5k7i4OI+K27t3L3PmzGH37t0UFRXRoUMH7r//fkaOLPkHUF5wBSgsLGTBggWsWbOGzMxMgoODufXWW5kyZQqtWpV9TvCaNWtYtGgR3377Lf7+/tx4441MnjyZbt26lWpbWFjIokWL2LBhA9999x1FRUVcddVV9OrVi1//+td06tSp3J9PwVVERKRyso47GTT4VKk9Xjf9rbnPfSxu7lqKc+VUCA7Db+o2DLtH2+ZLGTwKrvHx8Rw6dIgPPviArl27ltnm66+/ZuzYsXTq1KlSx7M2RAquIiIilbNtexEPJpwpdf29P19BTC/f2TPdsiyK5w6ErH3Y7vg99psf9XZJ9YpHa1yPHDlC7969yw2tAF27dqVPnz4cOXLE4+JEREREoO48PW+lfw5Z+8C/CbYe47xdTr3j0W87KCiI4ODgS7Zr1qyZHkwSERGRKqsrT8+7Dxy48R6Mpi28XE3949Gii5tvvpmUlBQKCgpo3LjsRdEFBQXs2LGDfv36ValAEREREfD9U7WsExlYB/8GgK1PzW2B1ZB5NOP6xBNPEBAQwKOPPlrmIQEZGRk89thjBAQEkJiYWOUiRUREROD8zGtML988ztTc9i5YFkaH2zFalf9wtnjOoxnX2bNnc9111/HZZ58xZMgQrr/+esLCwoDzuwocPHgQ0zS57bbbmD17donXGobBCy+8UPXKRURERHyEdS4XM3UJULMHDjR0HgXXlStXur82TZN9+/axb9++Uu3+/ve/l7qm4CoiIiL1jbnzfTiXAy07YHS43dvl1FseBdfFixdXdx0iIiIidZJVfA5zy58AsPebhHHx9gdSbTwKrjExMdVdh4iIiEidZO3+EHKy4Io2GNGjvV1Ovab/JBARERHxkGU6caa8BYDtf36N4dfIyxXVb1U6g6yoqIhNmzaRmppKdnY2hmEQEhJCjx49GDRoEP7+vnOShYiIiEh1s/avg5++gybNsfX8hbfLqfc8Dq6pqakkJiaSlZXFxafGLlmyhDZt2vDqq6/qKFMRERGplyzLwrn5TQBsvR/EaBTo5YrqP4+Ca1paGgkJCeTn59OlSxdGjhzp3g4rMzOTNWvW8PXXX5OQkEBSUhKRkZHVWbOIiIiI11lH/gmZe88f79pngrfLaRA8Cq7z588nPz+fp59+mvvvv7/U/fHjx7N48WJeeOEF5s+fz4svvljlQkVERER8ifmvNwCw9fw5RuBVXq671eJJAAAgAElEQVSmYfDo4awvvviCzp07lxlaXcaPH0/nzp35/PPPPS5ORERExBeZ3+/CStsCNj9ssQ97u5wGw6PgeuLECaKioi7ZLioqipMnT3oyhIiIiIjPMjefn201okdjBId5uZqGw6Pg2rx5c9LT0y/ZLj09neDgYE+GEBEREfFJVvY3WAc2gGFg7/eIt8tpUDwKrr1792b//v0sX7683DbLly9n37599OnTx+PiRERERHyNa99W47ohGK06ebmahsWjh7MmTZrEp59+ynPPPcfatWsZMWIEYWFhGIbB0aNHWbt2LTt37qRJkyZMnDixumsWERER8Qrr1FGsPckA2G551MvVNDweBdf27dszb948EhMT2bFjBzt37ixx37IsWrZsySuvvEL79u2rpVARERERbzO3zAezGOOaftiu1l71tc3jAwj69u3LJ598woYNG9i5cyfZ2dkAtGrVip49ezJkyBCaNGlSbYWKiIiIeJOV9yNm6l8BsN0y2cvVNExVOvK1SZMmxMfHEx8fX131iIiIiPgkc+s7UHQWo203jGtu9nY5DZJHD2eJiIiINCTW2dOYW98Fzs+2Gobh5YoapkrNuBYXF3P69GkCAgJo1qxZqfsnT57ktdde4x//+AcnT56kVatW3HHHHTzyyCMEBQVVe9EiIiIitcn8YgEUnIaQThjXD/F2OQ1WpWZcV65cSb9+/Vi0aFGpezk5OYwdO5YVK1aQnZ1NUVERx44dY+HChfzyl7+kuLi42osWERERqS1W/knMzxcAYO//Wwyb3csVNVyVCq7btm3DMAzGjBlT6t78+fPJyMigcePGTJs2jbVr1/Lmm29y9dVX8/XXX/Phhx9We9EiIiIitcXcMh/O5UBoZ4zOw7xdToNWqeB64MABOnXqRKtWrUrdW7VqFYZh8NhjjzFu3Dg6duzIwIEDefvttzEMg7/97W/VXrSIiIhIbbDyfsLc+jYA9gFPYtj0eJA3Verd//HHH4mKiip1/dtvv+Wnn37CZrMxatSoEvciIyPp1q0bhw4dqp5KRURERGqZmfIWFOZD224Y193p7XIavEoF17y8PJxOZ6nrX375JQAdO3akRYsWpe63adOGM2fOVLFEERERkdpn5f6Aue094D9rW7WTgNdVKrg2b96c9PT0UtdTU1MxDINu3bqV+bri4mLtKiAiIiJ1krn5zfP7tl7dHaPTQG+XI1QyuHbr1o3Dhw+zefNm97UTJ07wySefABAbG1vm644cOVLmulgRERERX2adycLcfn43JduAJzXb6iMqtY/ruHHj+Oyzz3jkkUcYMmQIV155JR9//DG5ubmEhobSv3//Uq85evQoaWlpjBgxotqLFhEREalJ5r/mQHEBRngMRvtbvV2O/EelgmtsbCyTJk1i7ty5rF69GsMwsCyLRo0aMXPmTPz9/Uu9ZunSpViWRb9+/aq9aBEREZGaYp06irnzL4BmW31NpYIrwOTJk+nfvz+bNm3i5MmThIaGMnLkSNq1a1dme39/f8aPH88tt9xSbcWKiIhI3Zd13ElGhklEhI3Wob63mb/5rzngLMSI+h9s12gCzpdUOrgCdO3ala5du1aq7ZQpUzwqSEREROqvpOQCps/IwzTBZoPp0wIZHd/Y22W5WScdmKlLALD1/62Xq5GLaRddERERqRVZx53u0ApgmjB9Rh5Zx0tvuektzn+8BmYxRvtbsEX29XY5chEFVxEREakVGRmmO7S6mCY4HGbZL6hl1k9pWLuXA2Dr/6SXq5GyKLiKiIhIrYiIsHHxiak2G4SH+0YccX72CphOjI79sYX39HY5Ugbf+EsRERGReq91qJ3p0wLd4dW1xtUXHtAyj+3G2psMgH3A77xcjZTnsh7OEhEREbmUinYNGB3fmNhYfxwOk/Bw39hVwLIszI//HwBGt9EYYdFerkjKo+AqIiIi1aYyuwa0DrX7RGB1sQ59gpX2Ofg1wj7oKW+XIxXQUgERERGpFnVh14CLWc5inB/PAMDWZwJG87L3pxffoOAqIiIi1cLXdw0oi/XlB/DDIWjSAtstj3u7HLmEKi0V2LZtGzt27OCHH36gsLCwzDaGYfDCCy941P/evXt544032L17N0VFRXTo0IH777+fESNGVLqPwsJCFixYwNq1a8nMzCQ4OJhbb72VKVOmEBISUuZr1q5dy6JFi/j222/x9/fnxhtvZPLkydxwww3ljrNp0yaWLFnC/v37OXv2LC1btuTGG2/kt7/9LW3atLnsn11ERKSuce0acGF49aVdAy5mncvD+enLANhum4rRJNi7BckleRRcc3JymDRpEjt37sSyrArbehpct23bxoQJE/D392fYsGE0a9aMjRs3kpiYyLFjx3j44Ycv2YdpmkycOJGUlBSio6MZNGgQDoeD5ORkPv/8c5YvX14qvM6fP5/XXnuNtm3bMnbsWPLz81m3bh0/+9nPeOedd+jdu3eJ9pZl8dxzz7Fs2TLCw8MZOnQogYGBZGdns2PHDo4dO6bgKiIiDYJr14CL17j60nrWC5lb5kFuNrSIwBbzgLfLkUowrEslzzL87//+L8uXLyciIoKf/exnREZG0rRp03Lbx8TEXFb/xcXFDBkyhKysLJYtW0bnzp0ByM3NZezYsaSlpbFu3ToiIyMr7CcpKYlnnnmGYcOGMWvWLAzDKHE9Li6Ol156yd0+PT2dYcOGcfXVV/Phhx/SrFkzAA4fPsw999xDSEgIGzZswM/vv3l/8eLF/PGPf2TcuHE8++yz2O0l/+EsLi4u0f5Cu3btokePHqSmptK9e/fLeo9ERER8VdZxp0/tGlAWKyeb4tf7QGE+9jF/wnbDXd4uSSrBoxnXzz77jJYtW7Js2TKaN29e3TWxdetWHA4H8fHx7tAKEBQUxKRJk5g6dSrJycn85je/qbCfFStWAPDEE0+4QyvA6NGjeeedd1i/fj3Tpk0jKCgIgOTkZIqLi5k4caI7tAJ07NiRu+66iw8++ICtW7fSr18/AAoKCnjrrbdo164dzzzzTKnQCpQbWkVEROorX9s1oCzmZ69AYT7G1d0xuo70djlSSR4tOsnJyeGmm26qkdAKsH37dgB3QLxQbGxsiTblOXfuHHv27CEqKoqwsLAy+yksLGTPnj2lxnWNcaGbb74ZgB07drivbdmyhVOnTjFw4EBM02Tjxo0sWLCApUuXkpGRcakfU0RERLzAyv4GM/WvANgGP1dickt8m0fTgREREZw4caK6a3FLT093j3Ox4OBgWrRocclg6HA4ME2z3OUEruvp6enuoJqenk7Tpk3LfGjLVYurNoCvv/4aALvdzsiRI0lLS3Pfs9lsPPDAA/zudzp9Q0RExJc4Nz4Plolx/RBsEb0v/QLxGR7NuP7iF79g7969fPPNN9VdD3B+LStQ4uP6CwUFBZGTk1NhH677rmUAFwsMDCwxluvrisa8uP1PP/0EwHvvvUdQUBArVqxg165d/PWvfyUyMpJ3332XJUuWVFiniIiI1B4zbQvWN5vAZsc+6FlvlyOXyaPges899zB+/HgSEhJITk7m+PHj1V1XneB6rs3f35+33nqLbt26ERgYSM+ePZkzZw42m4333nvPy1WKiIgIgGWamH/7AwC2nr/ACOng5Yrkcnm0VOD6668Hzge3Z5+t+L9WDMNg//79l9W/a3azvFnVimZGXVz3L5whvVBeXl6JsVxfVzRmWe0BunbtSmhoaIn2HTt2pF27dmRkZHDmzBmuuOKKCusVERGRmmXtTcLK3AuNgrDd/oS3yxEPeBRca3pfUtf604yMDLp27Vri3unTpzl58iQ33XRThX2Eh4djs9lKrEm9kOv6hWtgIyMj+fLLL/nhhx9KrXN1ram9sP0111wDlL+kwXW9oKBAwVVERMSLrIIzOD/+fwDYbnkcI6jsQ4jEt3m8HVZN6tWrF3/6059ISUlh2LBhJe5t2bIFuPTesI0aNaJbt27s3r2bY8eOldpZYMuWLQQEBBAdHV1i3C+//JItW7YQFxdXov3mzZvdbVxchxF89913pcYvKirC4XDQtGlTrrzyykv9yCIiIlKDzL/Pgtwf4Kr22P7n194uRzzkk2ew9e3bl3bt2vHRRx9x4MAB9/Xc3Fzmzp2Ln58fo0aNcl/Pzs7myJEjpT7mHzNmDACzZs0qccJXUlISR44cYejQoSU++o+Pj8fPz4958+aV6Ovw4cOsXr2a8PBw+vTp474eHh5Ov379yMjIcO8Z67JgwQLOnDnDwIEDtZeriIiIF1nHD2Bu/TMA9uF/xPAL8HJF4imPTs4qS25uLoZhuJ/Wr6qtW7fy0EMP4e/vz/DhwwkKCmLjxo0cPXqUKVOmMHHiRHfbp556ipUrVzJz5kzi4+Pd151OJ7/61a/cR77GxMTw/fffs3HjRkJDQ1mxYkWpJQHz5s3j9ddfp23bttx5553uI1/PnTvHn//85xLBFc5vuzV27Fh++uknbrvtNq655hr279/P1q1bCQsLY9myZWVurwU6OUtERKSmWZaF873RWGmfY1w/FL/73vV2SVIFVZoK/Ne//sX777/Prl27yM/PB6BJkyb07NmTn//859xyyy0e992nTx+WLFnCnDlz2LBhA0VFRXTo0IHHH3+ckSMrd8KF3W5n3rx5LFiwgDVr1rBw4UKCg4MZNWoUU6ZMKTNQTpw4kbCwMBYtWsTSpUvx9/fnpptuYvLkyXTr1q1U+/DwcJKSkpgzZw6bN29my5YttGzZknHjxvHII49w1VVXefweiIiISNVYX6/GSvsc/BpjH/oHb5cjVeTxjOvMmTNZvHix+yN414NIro/YDcNg/PjxPP3009VUav2jGVcREZGaY53Lo3hOPzjzb2z9n8R+e8VHxYvv82jGdf369SxatIirrrqKiRMnctddd5XYfmr16tXMmzePxYsXEx0dzdChQ6u1aBEREZFLMf/5Gpz5N7SIwNZvkrfLkWrg0cNZS5YsoVGjRvzlL3/h5z//eYntoIKCghg3bhzvv/8+AQEBLF26tNqKFREREakM64dvMT//EwD2YTMw/Bt7uSKpDh4F14MHD9KnTx+ioqLKbRMVFUWfPn1K7AogIiIiUtMsy8K57llwFmFcOwjbtXd4uySpJh4F16KiIpo0aXLJdk2aNKGoqMiTIUREREQ8Yh3YgHXkn+DXCPvQGd4uR6qRR8E1PDycHTt2cPbs2XLbnD17lh07dhAeHu5xcSIiIiKXwyrMx7l+GgC2fpMwroz0bkFSrTwKroMHD+ann37i0Ucf5fvvvy913+Fw8Oijj3LixAmGDBlS5SJFRETEt2Qdd7JtexFZx53eLqUEc/MbcPoYNL8a282PebscqWYe7SowYcIEPv30U7Zs2cLgwYO54YYbCAsLwzAMjh49yldffYXT6aRr1648+OCD1V2ziIiIeFFScgHTZ+RhmmCzwfRpgYyO9/7DT9YPhzE3vwWAfcj/wwho6uWKpLp5vI9rXl4es2fPJikpiYKCghL3GjduzOjRo/nNb35TbSdp1Ufax1VEROqarONOBg0+hWn+95rNBpv+1pzWoXav1WWZJs534rAc2zE6DcD+879gGIbX6pGa4fHJWYGBgUybNo3ExET27dtHdnY2AK1ataJLly6VenhLRERE6paMDLNEaAUwTXA4TK8GV3PHQizHdggIxD7iJYXWeqpKR77Cf494FRERkfovIsKGzUapGdfwcI8em6kW1qmjmBv/eL6WO57FaH6112qRmuW9vzIRERGpc1qH2pk+LRDbfxKEa42rt2ZbLcvCufZ3UJiHER6DrdcDXqlDakelZlzffPNNDMNg3LhxNG/enDfffLPSAxiGwSOPPOJxgSIiIuJbRsc3JjbWH4fDJDzc5t21rV+twjr0KdgDsMfNwrBpTq4+u6zgOnToUHdwNQyDyjzXpeAqIiJS/7QOtXs1sAJYeT+dPyELsN02FSOko1frkZpXqeA6c+ZMAEJCQkp8LyIiIuItzg3PQf4JaHUdtn6aJGsIKhVcR40aVeH3IiIiIrXJPPwZ1p4PwbBhHzUbwy/A2yVJLfBoIUhmZianTp26ZLvTp0+TmZnpyRAiIiIiZbLO5eJc/VsAbH0TsF2tvdAbCo+C64ABA3j55Zcv2e6VV15h4MCBngwhIiIiUibzk5nnj3VtEY5twJPeLkdqkUfB1bKsSj2Y5WorIiIiUh1Mx07Mbe8CYL/rVYwAndDZkNTonhEnT56kcWPvn10sIiIidZ9VmIczeTJYFsZN92Jrf4u3S5JaVumTs3bs2FHi+x9//LHUNZfi4mLS0tLYvHkzHTtqawoRERGpOvPjGfDTd3BFG+xD/uDtcsQLKh1cf/GLX5Q49zclJYWUlJRy21uWhWEYPPjgg1WrUERERBo889CnmNsXAmCP/z+MJs29W5B4RaWDa1xcnDu4rly5kvDwcLp3L/spPn9/f1q1asXtt99Oly5dqqdSERERaZCsvJ9wrpwK/GcXAS0RaLAqHVxffPFF99crV66ke/fuOohARESknso67iQjwyQiwstHuloWzjVPQm42hHTCNugZr9Ui3lfp4Hqhp59+mqZNm1Z3LSIiIuIDkpILmD4jD9MEmw2mTwtkdLx3Hra2di/H2r8O7P743f0Whn8Tr9QhvsGjXQVefvllPvvss+quRURERLws67jTHVoBTBOmz8gj67iz1muxTjpwrnsWANvtv8Voe0Ot1yC+xaPg2rJlSxo1alTdtYiIiIiXZWSY7tDqYprgcJhlv6CGWKYTZ9JkOJeLER6D7eZHanV88U0eBdd+/fqRmppKYWFhddcjIiIiXhQRYcN2UTqw2SA8vEa3fi/F3DIPK2MrBARiv/sNDJv31tmK7/Dor3Dq1KnY7XYSExPJzs6u7ppERETES1qH2pk+LdAdXl1rXGvzAS3r3/swP30JAPuw5zFaRNTa2OLbPHo4a9asWVx33XVs2rSJf/7zn3Tu3Jm2bdsSEBBQqq1hGLzwwgtVLlRERERqx+j4xsTG+uNwmISH1+6uAlZRAcUfPgLOIozrh2DcNLbWxhbfZ1iWZV3ui6677rrKD2AYHDhw4HKHaBB27dpFjx49SE1NLXdPXBERkYbEufZ3mNsXQVAIfo/+HSOwpbdLEh/i0Yzr4sWLq7sOERERaeDMr1adD62GgT1+jkKrlOJRcI2JianuOkRERKQBs348gnPVEwDYbnkcW8fbvVyR+KLafURQRERE5CJW0VmKP0iAwjyMyL7Ybk/0dkniozyacXUpKipi06ZNpKamkp2djWEYhISE0KNHDwYNGoS/v3911SkiIiL1lHP9NDi+HwJbYh8zH8NepXgi9ZjHfxmpqakkJiaSlZXFxc93LVmyhDZt2vDqq6/qoSMREREpl7knCWvnX86va71nHkazUG+XJD7Mo+CalpZGQkIC+fn5dOnShZEjRxIWFgZAZmYma9as4euvvyYhIYGkpCQiIyOrs2YRERGpoqzjTjIyTCIiane7qwtZPxzGuea3ANhu+w229jd7pQ6pOzwKrvPnzyc/P5+nn36a+++/v9T98ePHs3jxYl544QXmz5/Piy++WOVCRUREpHokJRcwfUYepvnfAwZGxzeu1Rqswvz/rGvNx7imH7bbflOr40vd5NHDWV988QWdO3cuM7S6jB8/ns6dO/P55597XJyIiIhUr6zjTndoBTBNmD4jj6zjzlqtw7nuGcg+CEEh2O+eqyNdpVI8Cq4nTpwgKirqku2ioqI4efKkJ0OIiIhIDcjIMN2h1cU0weEwy35BDTC/XIa16wMwbP9Z19qq1saWus2j4Nq8eXPS09Mv2S49PZ3g4GBPhhAREZEaEBFhw3bRv/1tNggPr50dMq3Mr3Cufer8uLcnYrumX62MK/WDR3+lvXv3Zv/+/SxfvrzcNsuXL2ffvn306dPH4+JERESkerUOtTN9WqA7vLrWuNbGA1pW7g8UL3kAis5idLwd262P1/iYUr8Y1sV7WVXCkSNHGD16NOfOnaNnz56MGDGCsLAwDMPg6NGjrF27lp07d9K4cWM+/PBD2rdvXxO113m7du2iR48epKamatswERGpVVnHnTgcJuHhtbOrgFVciHPhPVgZ2+Cq9vj9ej1GE30qK5fHo10F2rdvz7x580hMTGTHjh3s3LmzxH3LsmjZsiWvvPKKQquIiIgPah1qr7VtsCzLwlz37PnQ2qgZfuMWKbSKRzw+gKBv37588sknbNiwgZ07d5KdnQ1Aq1at6NmzJ0OGDKFJkyZVKm7v3r288cYb7N69m6KiIjp06MD999/PiBEjKt1HYWEhCxYsYO3atWRmZhIcHMytt97KlClTCAkJKfM1a9euZdGiRXz77bf4+/tz4403MnnyZG644YZLjvf222/z6quvArBs2TJuvPHGStcqIiJSH5nbF2LufP/8IQNj5mGEdPB2SVJHebRUoDZs27aNCRMm4O/vz7Bhw2jWrBkbN27k6NGjTJ06lYcffviSfZimSUJCAikpKURHRxMTE4PD4WDTpk20bt2a5cuXlwqv8+fP57XXXqNt27bceeed5Ofns27dOs6dO8c777xD7969yx3vyJEjxMXF4efnR35+/iWDq5YKiIhIfWembcG58F4wi7ENehb7LY95uySpw3wyuBYXFzNkyBCysrJYtmwZnTt3BiA3N5exY8eSlpbGunXrLnkiV1JSEs888wzDhg1j1qxZGIZR4npcXBwvvfSSu316ejrDhg3j6quv5sMPP6RZs2YAHD58mHvuuYeQkBA2bNiAn1/piWqn08m9996LYRhERkayZs0aBVcREWnQrJMZFM8fAvknMLrFY7/7Lfe/i0U8UaW9Lw4ePMhzzz3HiBEj6N27N71792bEiBE899xz7N+/3+N+t27disPhYPjw4e7QChAUFMSkSZMoLi4mOTn5kv2sWLECgCeeeKLEPyijR4+mffv2rF+/ntzcXPf15ORkiouLmThxoju0AnTs2JG77roLh8PB1q1byxzr7bff5uDBg7zwwgvY7dpEWUREGjbrXB7Ff/3l+dDathv2uFkKrVJlHgfXt956i9GjR7Ns2TIOHz7M6dOnOX36NIcPH2bZsmXcc889vPHGGx71vX37dgD69Su9t1tsbGyJNuU5d+4ce/bsISoqirCwsDL7KSwsZM+ePaXGdY1xoZtvPn9+8o4dO0rdO3ToEG+++SYTJ06kY8eOFdYlIiJS31mmiTN5Mhzff/5krPsWYvhX7bkXEfAwuK5atYo33niDRo0akZCQwKpVq9i5cyc7d+5k9erVJCQk0LhxY+bOncuqVasuu3/X4QYRERGl7gUHB9OiRQsyMjIq7MPhcGCaZrnLCVzXLzxIIT09naZNm5b50JarlosPXiguLuapp56iffv2/OpXv6qwJhERkYbA/McsrP3rwB6A/WfvYgS39XZJUk94tKvA4sWL8fPzY/HixXTt2rXEvWuvvZZrr72WO++8k7Fjx7J48WLi4uIuq3/Xx/cXflx/oaCgILKysirsIycnx922LIGBgSXGcn195ZVXljvmxe3h/MNc33zzDcuXL8ff37/CmkREROo7c9dSzL/PAsA+4kVs4b28XJHUJx7NuB45coTevXuXCq0X6tq1K3369OHIkSMeF+frDh48yPz583nwwQfp0qWLt8sRERHxKvPw33GuTgTAdstkbD3u83JFUt94FFyDgoIIDr70xsHNmjUrd8bzUv3Df2dNL5abm1vubOyFY7valiUvL6/EWK6vKxrz4va/+93vaNeuHY89pq09RESkYbMy9+L84CEwnRjRd2Mb+LS3S5J6yKOlAjfffDMpKSkUFBTQuHHjMtsUFBSwY8eOMh+wuhTX+tOMjIxSs7qnT5/m5MmT3HTTTRX2ER4ejs1mK7Um1cV1/cI1sJGRkXz55Zf88MMPpda5utbUXtj+4MGDAOUeTHDvvfcC5x9kGzhwYIX1ioiI1FXWSQfF7/8cCvMwrrkZe9xs7SAgNcKjGdcnnniCgIAAHn300TIfksrIyOCxxx4jICCAxMTEy+6/V6/z62FSUlJK3duyZQsAMTExFfbRqFEjunXrRlpaGseOHSuzn4CAAKKjo0uN6xrjQps3by7RBuDuu+8u83+ucNu/f3/uvvvuMnc1EBERqQ+s/JMULx4HudkQej32n72D4Rfg7bKknvJoxnX27Nlcd911fPbZZwwZMoTrr7/eHc6OHTvGwYMHMU2T2267jdmzZ5d4rWEYvPDCCxX237dvX9q1a8dHH33E+PHjuf7664HzH9fPnTsXPz8/Ro0a5W6fnZ1NTk4OrVq1KrGEYMyYMezevZtZs2aVOoDAdcrVhR/9x8fH8+677zJv3jwGDBhQ4gCC1atXEx4eTp8+fdzt//jHP5ZZ/1NPPUV6ejq//vWvdeSriIjUW1ZRAc4lD8CPh+GKtvj94q8Yja/wdllSj3kUXFeuXOn+2jRN9u3bx759+0q1+/vf/17qWmWCq5+fH88//zwPPfQQ9913H8OHDycoKMh95OuUKVOIiopyt589ezYrV65k5syZxMfHu6/HxcWxfv161q1bx9GjR4mJieH7779n48aNtGnTptRscFRUFI8++iivv/46I0eOLHHka3FxMTNmzCjz1CwREZGGxjJNnEmPYWVsg8ZX4Df+r9r2Smqcx9th1bQ+ffqwZMkS5syZw4YNGygqKqJDhw48/vjjjBw5slJ92O125s2bx4IFC1izZg0LFy4kODiYUaNGMWXKlDL3a504cSJhYWEsWrSIpUuX4u/vz0033cTkyZPp1q1bdf+YIiIidZL58R+w9q0Fu//5vVpDr/d2SdIAGJZlWd4uoqHatWsXPXr0IDU1le7du3u7HBERqWeyjjvJyDCJiLDROrT6jiN3bn4Tc+PzANjvnostOv4SrxCpHh4f+SoiIiK+Kym5gEGDTytHiowAACAASURBVPFgwhkGDT5FUnJBtfTr3PauO7Ta7pym0Cq1qkoLNouKiti0aROpqalkZ2djGAYhISH06NGDQYMG6SQpERERL8g67mT6jDxM8/z3pgnTZ+QRG+tfpZlXc9dSzI+eAcB261Ts/R6pjnJFKs3j4JqamkpiYiJZWVlcvNpgyZIltGnThldffVUfgYuIiNSyjAzTHVpdTBMcDtPj4Gp+tQrnqicAsPX9FbYBT1a1TJHL5lFwTUtLIyEhgfz8fLp06cLIkSPd22FlZmayZs0avv76axISEkhKSiqxab+IiIjUrIgIGzYbJcKrzQbh4Z6tEDQP/v/27ju+yXJt4PjvSZru0lJGkdEWwTIFBcrmuGWvIqB4hHMEQRARjuN14CuOI6AvDlBQXAfwCMhQhqCIomUXRECGgNhdWmhp6aLNeJ73j5jQkC7ahqRwfT8fPk3v586TOxdJc+V+7rEFy+qpoKnoujyErv/LssGAcIsqJa4ffPABhYWFPPfcc4wbN87p+NixY1m6dCmvv/46H3zwAXPmzKl2Q4UQQghROY3C9Mx6McA+XECng1kvBlSpt1U9HfvXVq5mlA4j0A2eI0mrcJsqJa67d++mbdu2pSatNmPHjuXrr79m165dVW6cEEIIIapmRIwvvXoZSEpSCQ+v2qoCauJeLP8dBxYjSpsB6GPeRdHV3OoEQlypKl0zOH/+vMMGAGVp3rw52dnZVXkIIYQQQlRTozA9XaOrNiFLTT2IZdmDYLqIctMd6EctQtHLJjzCvaqUuIaEhJCQkFBhvYSEBIKDg6vyEEIIIYRwEy31EJYlD0BxPkpkD/T3f4Li5ePuZglRtcS1W7duHDt2jC+//LLMOl9++SVHjx6le/fuVW6cEEIIIcqWnmFhb5yJ9AxLjZ1TTdqP+T8j4WI2SrPO6P++DMXbv8bOL0R1VKnPf8qUKfzwww+89NJLbNiwgcGDB9OkSRMURSElJYUNGzawf/9+/Pz8mDx5ck23WQghhLjurVlb5DT5akSMb7XOqSbsxrLs72AsQInojv6hz1F8AmuoxUJUX5W3fN29ezdPPfUUWVlZTrMLNU2jfv36vPnmm/To0aNGGnotki1fhRBCVEV6hoV7+uU4LXf1/bchVV+n9XSsdSKW6SLKjX3QP/gfFO+AGmqxEDWjyqOse/TowdatW9m8eTP79+/n7NmzADRs2JAuXbrQv39//Pz8aqyhQgghhLCq6Q0G1JNbsSwfD+ZilKi70N//MYpBPsOF56lS4pqfnw9AYGAgMTExxMTIPsVCCCHE1VKTGwyoxzZj+XIiWEwobfqjH/WBTMQSHqtKk7O6dOnC+PHja7otQgghhKgE2wYDur8+xau6wYD629dYVk6wJq3th6IfvViSVuHRqtTjGhQURNOmTWu6LUIIIYSopOpuMKAeWIHl63+BpqLcMhL98HdkcwHh8aqUuLZp04bk5OSabosQQgghrkCjMP0VJ6yapqFufw/1+38DoHT5O/rBb6DoqnQRVoirqkqv0kceeYTffvuNb7/9tqbbI4QQQggX0VQL6jcv2JNWXe8pkrSKWqVKPa6+vr6MHDmSGTNmsG7dOu68805uuOEGfHxKHxcTHR1drUYKIYQQono0UxGWNVPRjm4ERUHX/xX0PR5xd7OEuCJVSlwfeughFEVB0zS2bdvGTz/9VG7948ePV+VhhBBCCFEDtIs5WL74B1rCHtB7ox+xAN3NQ93dLCGuWJUS12HDhjltOiCEEEIIz6NdSMO89AE4ewJ8gtCP+Qzdjb3d3SwhqqRKieucOXNquh1CCCGEqGFaxu+Yl46B3DQIaoTX2C9QGrV1d7OEqLIq75wlhBBCCM+l/rnDuhtW0QVocBNeY5ejhMhSlqJ2u6LE9eeff2br1q2cOXMGb29vWrVqRUxMDM2aNXNV+4QQQghxhSxxS1C/eQFUM0p4NPoHl6L413V3s4Sotkonrk8++SSbNm0CrGvAAWzbto1PP/2Ut956i7vuuss1LRRCCCGuU+kZFhITVSIiKrfBgGYxoW56ETXuPwAoHWLQD5uHYvBzcUuFuDoqlbiuWrWKb775Bi8vL4YMGULbtm0pKChg27ZtHDx4kP/5n/9h27ZtBAUFubq9QgghxHVhzdoiZr1agKpe2tJ1RIxvmfW1wmwsKx9B+3OHdbmru59H12eqTKYW15RKJa5ff/01Op2Ojz76iB49etjLJ02axHPPPcfXX3/Nli1bGDFihMsaKoQQQlwv0jMs9qQVQFVh1qsF9OplKLXnVTt7EvN/x8L5BPAOQH/fQnRt+l7dRgtxFVRqq4yTJ0/SsWNHh6TVZtKkSWiaxsmTJ2u8cUIIIcT1KDFRtSetNqoKSUmqU1315A+YFw+0Jq0hzfB6ZKMkreKaVake1/z8fMLDw0s9ZivPz8+vuVYJIYQQ17GICB06HQ7Jq04H4eGX+ps0TUPd9QHqd6+CpqJEdkd//8coAfWvfoOFuEoq1eOqaRq6MvYxtpWrl381FEIIIUSVNArTM+vFAGwfvbYxrrZhAlpRHpaVj6B++7I1ae38IPpxX0rSKq55so6rEEII4YFGxPjSq5eBpCSV8PBLqwpo6ccwr5gAWX+C3oCu3yx03R6WSVjiuqBotrWtytG6desqvyEUReHYsWNVuu+17sCBA3Tu3JlffvmFTp06ubs5QgghPJx6YAWWDc+CuQiCm6Af/RG6ZvL5Ia4fle5xrUR+W6P3E0IIIYSVZrqIZePzaAeWA6DcdAf6+95H8Q91c8uEuLoqlbj+/vvvrm6HEEIIIUqhZf2JefkEyDgGig7dnc+g+9s0lDLmnghxLZMxrkIIIYSHUo+sx/L1v6A4HwLqox+5CF2LPu5ulhBuI4mrEEII4WG0ojwsm2ai/boSACWiG/pRH6LUaeTmlgnhXpK4CiGEEB5ETdqHZfVjkJ1k3bq1zzR0dz6Foje4u2lCuJ0krkIIIYQH0Cwm1J/eRv35HdBUCGmKfsR76CK7u7tpQngMSVyFEEIIN9Oy4rGsfgwt5QAASsf70A96HcW3jptbJoRnkcRVCCGEcBNN09B++QLL5hfBWAi+ddAPfgNdh2HubpoQHkkSVyGEEMINtAupWNb/D9rJrQCYGvfA74EFKCFN3dwyITyXLAInhBBCXEWaqmLZtxTzgtvQTm7FaDHwzrEZ9Fj8IWt/rO/u5gnh0aTHVQghhLhKtPMJWL7+F1r8LgB+y+7AS7++yp/5LQGY9WoBvXoZaBSmd2czhfBYHp24Hj58mAULFnDw4EFMJhMtW7Zk3LhxDB48uNLnMBqNLF68mA0bNpCWlkZwcDC33XYb06dPp0GDBqXeZ8OGDSxZsoQ//vgDg8HALbfcwrRp07j55psd6mVkZLB582ZiY2P5888/yczMJDg4mE6dOjFhwgQ6duxYrecvhBDi2qCpFtTdH6H+MBdMF8HgR8pNTzNuzn2oXEpSVRWSklRJXIUog8cmrnv37mX8+PEYDAYGDhxIUFAQW7Zs4amnniI1NZVHH320wnOoqsrkyZPZsWMHHTt25J577iEpKYm1a9eya9cuvvzyS6fk9YMPPuDtt9+mcePG3H///RQWFvLNN9/wwAMP8Mknn9CtWzd73WXLlvHRRx8RHh5Oz549qVevHomJiWzdupWtW7cyb948BgwYUOOxEUIIUXtoGb9be1ltKwbc2Bv90Hn4mZrCGzmgXqqr00F4uIziE6IsiqZpmrsbcTmz2Uz//v1JT09n5cqVtG3bFoD8/Hzuv/9+4uPj+eabb4iMjCz3PGvWrOH5559n4MCBzJs3D0VRHMqHDRvG3Llz7fUTEhIYOHAgTZs2ZfXq1QQFBQFw6tQpRo4cSYMGDdi8eTNeXtZ8f8uWLYSGhtKlSxeHx92/fz//+Mc/CAgIYPv27Xh7e5favgMHDtC5c2d++eUXOnXqVKVYCSGE8EyasQD153dRdy4Ciwl8gtD3ewml84OXPo/WFjHr1QJU1Zq0znoxgBExvm5uuRCeyyO/1u3Zs4ekpCQGDRpkT1oBAgMDmTJlCmazmbVr11Z4nlWrVgHw5JNP2v9IAIwYMYIWLVqwadMm8vPz7eVr167FbDYzefJke9IKcNNNNzF06FCSkpLYs2ePvfzee+91SloBunTpQrdu3cjJyeHEiRNX9uSFEELUapqmoR79BvP8v6HGzgeLCaXVvXg9/jO6Ln93/DyK8eX7b0P47OM6fP9tiCStQlTAIxPXuLg4AHr37u10rFevXg51ylJcXMyhQ4do3rw5TZo0KfU8RqORQ4cOOT2u7TFK6tOnDwD79u2r1HOw9crafgohhLj2aVl/Ylk6BsuK8XAh1br71Zgl6B9cghLcuNT7NArT0zVaJmQJURkemVUlJCQAEBER4XQsODiYunXrkpiYWO45kpKSUFW1zOEEtvKEhAR7opqQkIC/v3+pk7ZsbbG1rTxpaWns2rWLBg0aEBUVVWF9IYQQtZtmLESNXYC6432wGEHvja73Y+j+9jiKt7+7myfENcMjE1fb5fuSl+tLCgwMJD09vdxz5OXl2euWJiAgwOGxbLdDQ0PLfMzL65fGZDLxzDPPYDQaeeqpp9Dr5Ru0EEJcqzRNQzu+Gcvm/4WcFACUlnegH/RvlHo3ApCeYSExUSUiQie9qkJUk0cmrrWVqqo8//zz7Nu3j1GjRjFsmGzZJ4QQ1yo15VfU715GS/hr7kNwE/T9X0FpO0AmXwnhIh6ZuNp6N229ppfLz88vszfWxna8rB7SgoICh8ey3S7vMS+vX5KmacycOZP169czZMgQXn755XLbJ4QQonbScpKxfD8b7fBfk4S9fNH1nITutmko3gH2eukZFnvSCtY1WmWDASGqxyMnZ9nGn5Y2jvXChQtkZ2eXOv61pPDwcHQ6XZljUm3lJcfARkZGUlhYyLlz55zq29pS2phZW0/rmjVrGDRoEHPmzEGn88jQCiGEqCKtKBfLltcwv9vbnrQqHe/Da/pO9Pc855C0AiQmqvak1ca2wYAQomo8MruKjo4GYMeOHU7Hdu7cCUDXrl3LPYePjw8dOnQgPj6e1NTUUs/j7e3tsLuV7XFtj1HS9u3bHerYqKrKCy+8wNq1axkwYABvvPGGjGsVQohriGYxYdn7Gea3u6Nufw/MxSiRPfB69Du87nsPJdh55RqAiAgdl/dhyAYDQlSPR757evToQbNmzdi4cSPHjx+3l+fn57Nw4UK8vLwYPny4vfzs2bOcPn3a6TL/qFGjAJg3bx4l91lYs2YNp0+fZsCAAQ6X/mNiYvDy8mLRokUO5zp16hTr1q0jPDyc7t2728tLJq39+vXjzTfflKRVCCGuEZpqQT24CvO7vVE3PgeF56F+S+vyVg+vRWlS/rbejcL0zHoxwJ682sa4yjABIarOI3fOAusmBBMmTMBgMDBo0CACAwPZsmULKSkpTJ8+ncmTJ9vrPvvss3z11VfMnj2bmJgYe7nFYmHixIn2LV+7du1KcnIyW7ZsISwsjFWrVjktfbVo0SLeeecdGjduTN++fe1bvhYXF/Pxxx87JK4LFizgvffew9/fn7Fjx5a6Zuvdd99NmzZtSn2OsnOWEEJ4Hk1V0Y5uwPLj/0HmKWthQD10dzyJrstDKHrDFZ0vPcNCUpJKeLisKiBEdXnk5CyA7t2788UXXzB//nw2b96MyWSiZcuWPPHEEwwZMqRS59Dr9SxatIjFixezfv16/vOf/xAcHMzw4cOZPn16qeu1Tp48mSZNmrBkyRKWL1+OwWDg1ltvZdq0aXTo0MGhrm0IQmFhIR988EGpbWjSpEmZiasQQgjPoWka2u9bsPwwFzKOWQv9QqzrsXZ7GMUnoPwTlKFRmF4SViFqiMf2uF4PpMdVCCHcT9M0tD9+Qv1hLlrqQWuhT5B1pYCeE1F867i3gUIIO4/tcRVCCCFcSVNVtN+/RY19Fy31r+2/DX7ouk9A13syin/pG9IIIdxHElchhBDXFc1iQjv8FZbtC+DcX2NYDX7oosei6zMVJdB5GJkQwjNI4iqEEOK6oJkuoh5YjrpjoX17VnzroOv2MLoeE1AC6ru3gUKICkniKoQQ4pqmFZ5H3bcMdfdHUJBpLQyobx3D2nWcjGEVohaRxFUIIcQ1STt7EnX3R6iHVoPporUwpCm63lPQdXoAxeDn3gYKIa6YJK5CCCGuGfYVAnYvRju17dKBRu3R95yI0mH4Fa/DKoTwHJK4CiGEqPU0YyHaoTVYdi++NOFKUVBa90PX4xGUyB4oiuLWNgohqk8SVyGEELWWlvE76v5lqAdXQVGutdA7AF3nMei6j0cJjXRr+4QQNUsSVyGEELWKZi5GO/oN6r6laIl7Lh2oG46u+3jr+NWrOOEqPcNCYqJKRIRs6SqEq0niKoQQolbQsuKtvasHVkDheWuhTo/Sqi+6rmNRbvwbik53Vdu0Zm0Rs14tQFVBp4NZLwYwIsb3qrZBiOuJJK5CCCE8llacj3Z0A+qvK9ESSvSu1mmMrsuD6DqPQalzg1valp5hsSetAKoKs14toFcvg/S8CuEikrgKIYTwKJqqoiXssiarRzdeWspKUVBa3o4u+h8oUXeh6N37EZaYqNqTVhtVhaQkVRJXIVxEElchhBAeQcuKRz24CvXgl5d2tgKo1wLdraPR3XIfSnBj9zXwMhEROnQ6HJJXnQ7Cw6/ucAUhrieSuAohhHAbLfcM6m/r0H77Gi314KUDvnXQ3TwM5dbRKE07eeRSVo3C9Mx6McBpjKv0tgrhOpK4CiGEuKq0gizUoxvRfvsKLXEvaJr1gKJDafE3dLeORmnTr1bsbDUixpdevQwkJamEh8uqAkK4miSuQgghXE4ryEI7sQX1yHq007GgWuzHlIhuKDcPRdduMEpgAze2smoaheklYRXiKpHEVQghhEtouWdQj21CO7YJLWE3aCUGgzbugO7mYejaD0EJaeq+RgohahVJXIUQQtQYLSse9fhfyWryL44HG7VH13YAupuHotRv4Z4GCiFqNUlchRBCVJlmMaElxaGd+B71xA+QeerSQUVBaRaN0nYAurb9UepGuK+hQohrgiSuQgghrohWkIV26kfUE9+j/fETFOVeOqjzQmney5qstumHEhTmtnbWFNnSVQjPIYmrEEKIcmkWE1rKAbQ/fkb74ye01F8vrQQAEFAPJeoudFF3o7S8HcW3jvsaW8NkS1chPIskrkIIIRxomgbnE1D/+MmarMbvgOJ8x0qN2qNrdQ9Kq7tRmtyCorv2eiJlS1chPI8krkIIIdBy09Hid6HG70T7cztkJzlW8A9FubEPupa3WXtVPWgHq5pQ2nAA2dJVCM8jiasQQlyHtLyzaPG70OJ3osbvgqzTjhX0BpTwaJQWt6NreRvccDOK7trcyrSs4QCypasQnkcSVyGEuMbZLv1rSXGoiXFoiXGOs//BumvVDe1Rmve0Tq6K7IniE+CW9rpCWROsKhoOIFu6CuFZJHEVQohrjGYxoZ05Yl2mKjEOLSkO8s85VlIU6zhVW6Ia0Q3FL9g9DXax8iZYVTQcQLZ0FcKzSOIqhBBuUJ0llkreN6yhDi6kWmf9pxxASz6AduY3MF10vJPeG6VJR5TwrtZ/EV1R/OvW4DNyr6r2qFZmOIBs6SqE55DEVQghrrLKLLFUViK2/st01n20nzZ1jnAh9DA9mv6Gr/nc5Q8BfiEozbpYe1IjuqI07ohiuDaXcapOj6oMBxCidlE0reRifOJqOnDgAJ07d+aXX36hU6dO7m6OEOIqSM+wcE+/HKcevu+/DbEnS7ZELEifQ9u6x3h8+CnahR7DnHwYfW6S0zk1RY9yQzt0TW9FadqJTL9biL8QSUSkV40nYBX1FLtysf7Szl1RPCsTb9t5ZDiAEJ5PelyFEOIqKq0HUFNV0o//ScPMk+SdPkLQ5kNsvPN3GvunWSucAe0M2NKp5IJmHM9py285Hfgt+2amv96d6B7WRf8v9T7mX3FvbkXHKuopduVi/WWdu6Z6VGU4gBC1g/S4upH0uApx/clIzOKpf/5C88DTtKrzO1HBJ7ipzkkCvApLrZ+UH86xC+24+e5bCYzqwJAp4VwovjSJ6kp7F8tLLss7VhM9m1XtrS3v3ID0qApxHZEeVyGEcAGtKA/t3Ck4+zva2RNoGdafoXnpfNqrlDt4+UDDVhQFt2HB6uacyGnFiQutyTPXsSZis0OoH6bnyWedk8vKLphf3kQloNxJTBWdu6Lj1emtLe/cXaMN0qMqxHVEElchhKgiTdMg9wzauVNomafg3B9omX+gnfsD8tLLvmNwE4whrcg2tMK/eTvqtmoP9Vug6A0YgFa+RSwvIxErb3mmimbIl5cAahrlJp4Vnbu84xXN7K/uzH9ZskqI64ckrkIIUQ5N06AgEy0rHrL+RMuKR/vrJ+f/BGPpl/gBCGyIEtYapWErlIatoWErlIZRKL51MABlLe9fUSJWVu9hReM5K0oAyztW0bnLO743zlSt3trKjFOVHlUhrg+SuAohrnuaxQy5qWjnkyA7Ee18Ilp2onW3qfMJUJRb9p11eghtjlK/JUqDlij1W0KDKJT6Laq1oH9VE7Hykt6KEsCKksOKEuqyjlent7ayjy2EuD7I5Cw3kslZQlwdmmqBvHS07GTISUbLSUHLSYacFLTsJMhJAdVc9gkUBeo0Rql3I0q95lDvxku360ageHk73cWVy0JVV3kTlVw1icmdKxIIIa4dkri6kSSu4kpVdRmjmjhe1Xa5mqZpUHQBclLRclPRLqTBhbS/fqaiXUiFC2nlJ6ZgnRwVEo4SGo5SNwJCI1BCwq3JaWgEisGv0m2SJKx0FSXFMvNfCFERGSogRC1R1WWMauJ4ddb2rOj+5R3TLCbIP4uWm2GdBJV3BnLT0XLTrb/npkPemfLHmdrovCC4CUrdZhDSFCWkGUrIX7dDIyGoEYpOV+FpKlLRRKPrWUXDH2ScqhCiItLj6kbS43ptckXPZXXWsazu+pvVWdsTSklsZ/oT078I8s/x8+ZUNqxMJdQ7k/p+mdzdNZuI0Cy0vAzIy4DC85UPnn+o9XJ+SBOU4MbW28FNILixNVkNaoSiu7Je6vKUdd+9cSYefsR5TOxnH9eha7Thih5DCCGEI+lxFeIKVaf3sar3rc4yRtVZfxMqs7anhp++kLo+2YR6n6euz3nyd1zE0jCHgnOZKOvTmB+dTahPFvV8sgg9kIX5oPWyfS+gV+cSD3wetMtyVU3nhcm7IUpwI7zr3YBS5wao08j+M7O4AQnnGxHewnntTnu8/XQ0Cq65nuLy7luZiUZCCCGqRhJXIa5ARb2P5SV51blvdZYxupIZ3V6KiSBDLnV9LnCjwcK5uGwGND5DsPcFgg05hHhb/3mvyMOkz+GW/PPEDczCW29yDNRBUAE/YHCz0mNpNgSTfD6UrOJ6nC+uR2ZxA84V1WfYmHBu7NgYJTCMjbHBvDDbgEXVXYrZwNKGOJjQ6XKuaBeoii7nl3X/iu5b2S1GhRBCXDkZKuBGMlTAM1Xlcr1trcqyLhGHh+uqfF/b5eXKjHHVVJUg7wJefNJC/9uL0YpyoSiXfTuy+P6bcwTo8wj2zuW26EIiwvLhYg5aUS6FWTmohTkEGgqqHLciiw/Zxrr4hTagbtP64F+PQqUei5f7c74olPPF9cgqrke2qR6fr7kR9D4uG+IA5Q+fqCje5Z07MVGt1FAAmWgkhBA1T3pcxTWpqpOBqnq5vqJe0fLuG9ZQR0TjIur7ZuKnL8BfX0iAVwGB3gW0LAJ1fyFacT7DQvK4Z2YeBefzCPLOxzc/H/PiPLTiPIYU5zMoJhfFmI+CBkfBfPTSY3UCOrUv8eCXXZL3Byg5/NK3DvjVRfEPISO3Dgd+D+SCMZgLprr0uDOMW7o3hIBQFP9Q8K9LRn4ISWk+hEfoaVAipnWA5koRSy7vfWxsjWl5PZPVGeJQ3V2gyjt3ZYcCyEQjIYSoeR6duB4+fJgFCxZw8OBBTCYTLVu2ZNy4cQwePLjS5zAajSxevJgNGzaQlpZGcHAwt912G9OnT6dBgwal3mfDhg0sWbKEP/74A4PBwC233MK0adO4+eabXdZOV/HktSTLU52lm6o6+768S8BhDSDihkLq+WbhoxThq7+In9dF/LyKaKHpUY8U0dB0kf88eoGtW3Lx0xXibyjkb93M1N9RRGBeAe93z8VXfxF/fSH+XtZ/9TcXYt5QSD1NY+u9pQRiC1hK/Or31z+Ayy+VOKRNem9r8ukbjOIbBL7B8NdPxS8YfEPArw6Kbwj4BV8q9wux3tZf+tPQBNBX0HvYKAQaNS2l/ZS/cHx1ti915S5Q5Z1bhgIIIYT7eOxQgb179zJ+/HgMBgMDBw4kKCiILVu2kJKSwowZM3j00UcrPIeqqjzyyCPs2LGDjh070rVrV5KSkvj+++9p1KgRX375pVPy+sEHH/D222/TuHFj+vbtS2FhId988w3FxcV88skndOvWrcba6eqhAtVdpqii465aN7SsdmuqBczFbPg6j7feysYLE75exTwxWc9dt2lgNpJ97iIvzjyPQSnGW2/ER1eMr1cxUyfqUSwXWf55LgZdMb66Inz0xfjoi7mzt4qPvpjc84UknS6wl/voi/DTFxHgU4xONVb1v+GKaAZ/zLpAdH6BePkHgk8geFt/Kj6B4B1gTUh9gqy//3Ubn0AU223fOiiGa2PN0Oos41XZ139ZCXllJtrJUAAhhLi6PDJxNZvN9O/fn/T0dFauXEnbtm0ByM/P5/777yc+Pp5vvvmGyMjIcs+zZs0ann/+eQYOHMi8efNQFMWhfNiwYcydO9dePyEhgYEDB9K0aVNWr15NUFAQAKdOnWLkyJE0aNCAzZs34+XlVSPtdGXiWt4YvbAGCqhm1n1dwNy5F1A0C95eJp6e7s2AvnqwmMFiYuv3FrOdqwAAHrRJREFUBXz0cT56zHjrzTz8kJ4+PRWwmNmzu5A1ay4dGzZI4dYOgMUEFjPHfitke2whesWMt95Er65wY6QKFiOYTaQmF/HHiUK8FBPeehM3hlsIDTZjLjKSmnQRg86EQWfEW2fEW2fC12BE0SxlPt+rSdP7YtH7oXj7ofcNAG8/FIM/GPzs/xSfAOttb39rsuntj2LwJ+eiH2ez/ajfJIh6jYL+OhYAPgHg5Vcj64hea6qzaH11k0tJToUQwrN45FCBPXv2kJSURExMjD0ZBAgMDGTKlCnMmDGDtWvX8q9//avc86xatQqAJ5980p60AowYMYJPPvmETZs28eKLLxIYGAjA2rVrMZvNTJ482Z60Atx0000MHTqUFStWsGfPHnr37l2j7XQF2xi9kZErmNJqAT76YrwUM4b3LJixZrMDgYH9StzpsnGRtwO39ylx/DRYTltvRgPRJXPtZFCTL/3aGmgdVeJ4JmiZl35tDDQOK3G8wPrPC4gILOUJXfb1StUUjKo3RosPRtVAUF0/fPx9MOPN76f1GC3eFFt8KVa9Maq+/O2OQPDyYe1GhWKzN0bVhyKLD0bNl8mP1SW4nj94+bBrn57P/gsXzT4Ua748MimUvgODLyWlep9qJZehf/0TlVedReurO85UxqkKIYRn8cjENS4uDsCeIJbUq1cvhzplKS4u5tChQzRv3pwmTZqUep6lS5dy6NAhp3Pafi+pT58+rFixgn379tnbVRPtdBXbGL0bA09T1yenUvcxqV7oDAb0BgMm1YucXB1m1QuzZvjrpxdNmvmgKQZOnFbsZWbVgEkz0KmzL6ENfDl3Xse27diPG1VvzKqBwUMDaRrhS2KKnqXLLZhV6zGT6o1JNTD18RDqN/JmxjNGjBaDNTFVvTFr3ixdVp+GN/iRkeVF/6GFGC1egPXLiK0nOTBMjwH4s5RLvEF/XeIN9C7i/y47VveuS5d/e7eHlgOkl00IIYTwRB6ZuCYkJAAQERHhdCw4OJi6deuSmJhY7jmSkpJQVbXMy/S28oSEBHuSmZCQgL+/f6mTtmxtsbWtptrpKpcmkDzP53+ORVEUpk0LYsDAANDpOZulY3BMPiaLF2bVCxUdOp1iXy4oK8NC33KWGppQ2rF/h+AVpkfJsDB7kfPx++4OQR+mxz/Dwpq5zsdnRodQP0zPsKnOiWdYC2ty2cgfZs70LndiTFUnA5WMnSSsQgghhOfxyMQ1Pz8fwOFyfUmBgYGkp6eXe468vDx73dIEBAQ4PJbtdmho6Rdybee5vH512+lKl5K0YKckLSwA/ud5f2sCiHMCWNHM6fKOVXTfio5XlFxWN/mUxFQIIYSonTwycRU1p7wkrToJYnWTy4qOV2dcoxBCCCGuTR6ZuNp6N229ppfLz88vs5fTxna8ZA9pSQUFBQ6PZbtd3mOWVr+67XQ3V058keRTCCGEEDXJI9fesY0/LW186IULF8jOzi51XGlJ4eHh6HQ6hzGpJdnKS46BjYyMpLCwkHPnzjnVt7Xl8vrVbacQQgghhKgcj0xco6OjAdixY4fTsZ07dwLQtWvXcs/h4+NDhw4diI+PJzU1tdTzeHt707FjR6fHtT1GSdu3b3eoU1PtFEIIIYQQleORiWuPHj1o1qwZGzdu5Pjx4/by/Px8Fi5ciJeXF8OHD7eXnz17ltOnTztdsh81ahQA8+bNo+Q+C2vWrOH06dMMGDDA4dJ/TEwMXl5eLFq0yOFcp06dYt26dYSHh9O9e/cqt1MIIYQQQlSdR+6cBdbF/SdMmIDBYGDQoEEEBgbat1KdPn06kydPttd99tln+eqrr5g9ezYxMTH2covFwsSJEx22fE1OTmbLli2EhYWxatUqp6WvFi1axDvvvFPqlq8ff/yxQ+J6pe28nKu3fBVCCCGEuJZ45OQsgO7du/PFF18wf/58Nm/ejMlkomXLljzxxBMMGTKkUufQ6/UsWrSIxYsXs379ev7zn/8QHBzM8OHDmT59eqnrtU6ePJkmTZqwZMkSli9fjsFg4NZbb2XatGl06NDBJe0UQgghhBAV89ge1+uB9LgKIYQQQlSeR45xFUIIIYQQ4nKSuAohhBBCiFpBElchhBBCCFErSOIqhBBCCCFqBUlchRBCCCFEreCxy2FdDy5evAjgsHmBEEIIIYQna926Nf7+/m55bElc3SghIQGAv//97+5tiBBCCCFEJblzGU9Zx9WNMjMz+e6774iMjMTPz8/dzRFCCCGEqJA7e1wlcRVCCCGEELWCTM4SQgghhBC1giSuQgghhBCiVpDEVQghhBBC1AqyqsBVtG7dOn755ReOHDnCyZMnMZlMzJ49m5iYmFLrx8bG8umnn3LkyBGMRiMRERHExMQwduxY9Hq9Q929e/cyduzYMh975cqV3HLLLU7l27dvZ/HixRw9ehRN02jfvj0TJ06kT58+1XuyNcSVMbPJz8/n008/ZcuWLSQnJ2MwGGjWrBl33XUXU6dOdap/+PBhFixYwMGDBzGZTLRs2ZJx48YxePDgGn3uVeXKmD300EPExcWV+/hz585l2LBhDmXXc8wAcnNz+eyzz9i6dSspKSl4e3vTtGlThg8fzsiRI/Hx8XG6T0JCAm+//TZ79+6lsLCQiIgIRo8ezZgxY9Dp3N/n4OqYpaens3DhQmJjY8nMzCQkJIQ+ffowbdo0brjhhlIfw5NfZxkZGWzevJnY2Fj+/PNPMjMzCQ4OplOnTkyYMIGOHTs63Sc/P58FCxawZcsWzp07R4MGDbj33nt5/PHHCQwMdKqvqipffPEFK1euJDExEX9/f7p168aMGTOIjIwstV2e/Bng6phlZWWxevVqjh49ypEjR0hNTQXgxIkT5bbLU2Pm6njt37+frVu3EhcXR2pqKoWFhTRp0oS77rqLSZMmUadOnVLbVdPvS5mcdRXdeeedpKamUrduXfz9/UlNTS3zD/3SpUv597//TWBgIPfeey9BQUHs3r2bkydP0rdvX+bPn+9Q35a4du3ala5duzqdb+TIkTRq1MihbP369Tz99NPUrVuXgQMHoigKmzdvJjMzkzfffJMhQ4bUbACqwJUxA0hLS2PcuHEkJyfTs2dP2rRpg9FoJCkpibS0NDZs2OBQf+/evYwfPx6DwcDAgQMJCgpiy5YtpKSkMGPGDB599FGXxaKyXBmztWvX2v+4l2Q2m/nwww/R6XRs27aNsLAw+7HrPWa5ubnExMSQnJxM586d6dixI0ajkdjYWJKSkujevTufffaZQzL6xx9/cP/991NUVES/fv0ICwsjNjaWkydPMmrUKF599VWXx6QiroxZUlIS999/P1lZWfTq1YtWrVqRmJjIjz/+SGhoKCtWrCA8PNzhPp7+Ovu///s/PvroI8LDw4mOjqZevXokJiaydetWNE1j3rx5DBgwwF6/sLCQMWPGcPz4cXr16kXbtm35/fff2b59O23atOGLL75wmtX94osv8uWXX9KyZUtuu+02srKy2LRpEz4+PqxYsYKWLVs61Pf0zwBXx8z2uakoChEREWRkZHDx4sVyE1dPjpmr49WrVy+ys7Pp3Lkzbdq0QVEU4uLiOHbsGOHh4axYsYJ69eo5tMkl70tNXDU7d+7UUlJSNE3TtA8//FCLiorS1qxZ41QvPT1da9eunRYdHW2vr2maZjKZtMmTJ2tRUVHaxo0bHe6zZ88eLSoqSps/f36l2pKTk6N16dJF69atm5aWlmYvz8jI0Hr16qV16dJFy8nJqcrTrFGujJnZbNZGjBihdejQQdu9e7fTOU0mk9Pvd999t9a+fXvt6NGj9vK8vDxt4MCBWtu2bbX4+PjqPN0a4cqYleXbb7/VoqKitEmTJjmUS8w0bfHixVpUVJT2+uuvO5QXFxdrI0aM0KKiorS4uDiHYw8++KAWFRWl/fTTT/Yyo9GojRs3TouKiir19Xq1uTJmEydO1KKiorQlS5Y4lG/atEmLiorSHn74YYfy2vA6++6777R9+/Y5le/bt09r166d1rVrV624uNhe/u6772pRUVHaG2+84VDfVv7uu+86lO/evVuLiorSxowZ43CeXbt2aa1atdIefPBBh/q14TPA1TE7d+6cFhcXp+Xl5Wmapml9+/bVoqKiymyPp8fM1fH68MMPtYyMDIcyVVW1l156SYuKitJmzZrlcMxV70v3X2+6jvTs2ZMmTZpUWC82NhaTycR9993nUN/Ly4tp06YBsHz58mq15dtvvyU3N5e///3vDpfdGjZsyNixY8nNzeXbb7+t1mPUBFfG7LvvvuO3337j4Ycfpnv37k7n9PJyHEmzZ88ekpKSGDRoEG3btrWXBwYGMmXKFMxmM2vXrr2i5+cK7nidrVq1CoD77rvPoVxiBsnJyQDcdtttDuXe3t706tULsF6ytImPj2ffvn1069bN4T4Gg4EZM2YAl+LtTq6KWXFxMTt27KB+/fo89NBDDufq378/bdq0YceOHfa4Qu14nd1777106dLFqbxLly5069aNnJwce0+fpmmsWrUKf39/HnvsMYf6kyZNIjg4mNWrV6OVuGBqe01Mnz4db29ve3mPHj3o3bs3+/btIz4+3l5eGz4DXB2z+vXrEx0dXeqwi9J4esxcHa+JEyfSsGFDh7qKojBlyhQA9u3b53DMVe9LSVw9UGZmJgBNmzZ1OmYr+/XXXzEajU7HExISWLp0KYsXL2bjxo2cP3++1MewjVPs3bu30zHbOJ2KxjJ6kqrEbNOmTQD069ePM2fOsHz5chYvXszmzZspKChwOk95MbMlINd6zEqTnp7Ozp07adCgAbfffrvDMYkZ3HTTTYB1XFxJJpOJXbt24evry6233movLy9mHTp0oE6dOtd0zHJycjCbzTRu3BhFUcq8z549e+xltf11ZvuSbPuZkJDA2bNn6dSpk9NwAB8fH7p06UJGRgaJiYn28r179+Lv71/qbka2uJRMLGr7Z0BNxOxK1eaYuTJetnNePlbdVe9LmZzlgUJDQwFISUlxOmYrM5vNJCcn06JFC4fjGzduZOPGjfbffX19efzxx5kwYYJDPdt2sxEREU6PYSurzhv8aqtKzI4cOQJYt66bPXu2Q7IRGhrKO++8Q7du3exl5cUsODiYunXrXvMxK82aNWtQVZXhw4c79VJLzKzjy9etW2efmNS+fXtMJhPbt2/nwoULzJs3z2FMcHkxUxSF8PBwjhw5wsWLF2vFjntXGrM6deqg1+tJS0tD0zSn5NV2H1ucSt6uja+ztLQ0du3aRYMGDYiKigIu/e0ta0JVyb/RkZGRFBYWcu7cOaKiokqd6GY7T2Vj5umfATURs6qorTFzdbzWrFkDXEpGbVz1vpQeVw/Us2dP9Ho9a9as4cyZM/Zys9nMe++9Z/89NzfXfjs0NJRnnnmGTZs2cfDgQWJjY3nzzTcJDg7mzTffZMWKFQ6PkZ+fD0BQUJDT4/v7+6PX68nLy6vpp+YyVYmZ7fLsa6+9xrhx4/j555/ZvXs3M2fOJC8vj8cee4yzZ8/a65cXM7Be/rjWY3Y5TdPsl3ouHyYAEjOwfnlctmwZQ4YMIS4ujk8//ZRly5bZL6Fd3kNWmZgBtSZuVxozPz8/oqOjyczM5IsvvnA415YtWzh+/Djg+Pxr6+vMZDLxzDPPYDQaeeqpp+xJp62tZV3Cvvw1UNn6tjiVvF3bPgNqKmZVURtj5up4HT9+nPfff5969eo5dZC56n0pPa4eqFmzZkyaNImFCxcyePBg7rnnHvss3DNnztC4cWPS0tIcvlnfdNNN9kuSYP3jP2TIEFq3bk1MTAwLFixg1KhRHrGMjitUJWa2sTu33347Tz31lL38oYceIiMjg48++ojVq1fbx+9ca6oSs8vt2bOHlJQUunbtWuq36mtNVWJ2/vx5pkyZwvnz51m8eDGdOnWiuLiYH3/8kTlz5vDTTz+xZs0agoOD3fjMXKcqMXvuued44IEHeOWVV/jxxx9p1aoVSUlJ/PDDD7Rq1YoTJ07U+r9lqqry/PPPs2/fPkaNGuW0hJxwJjG7Mq6OV3JyMpMmTcJisfDWW2/Zr664Wu1+51/DnnjiCd544w2aN2/Opk2bWLVqFY0aNWL58uX2b0J169at8DxRUVF07NiRzMxMhy758r5NFRYWYrFYyvyW5KmuNGa2sjvvvNPpXHfccQdwaThByfplfUPMz8+/5mN2ubImZdlIzGDOnDn8+uuvzJ8/n9tuu42goCDq16/PqFGjePrpp0lOTmbJkiX2+pWJWcl6tcGVxqx169asXr2a/v37c+zYMZYuXUp8fDyvvPIKQ4cOBXD4kKxtrzNN05g5cybr169nyJAhvPzyyw7HbW0t2UNa0uU9WZWtX/I1U9s+A2o6ZlVRm2Lm6nilpqYybtw4zp8/z/z580ud4Oyq96X0uHqwoUOH2v9I2xiNRhISEggJCaFZs2aVOo/tA6GoqMheFhkZyZEjR0hMTHRKTGwJbm3sQbuSmDVv3pzs7OxSF022lRUXF9vLbON8EhMTad++vUP9CxcukJ2d7TDJprao6uvswoULfP/999SpU4e+ffuWWkdiBj///DMhISG0bt3a6Ty2P/ZHjx61l5WM2eU0TSMpKYmGDRs6TajwdFf6OmvRogXvvPOO03meffZZAIfXU216namqygsvvMDatWsZNGgQc+bMceo9tv3tLTkmtaTL/0b7+/vToEEDUlJSsFgsTldJbOcpOVaxNn0GuCJmVVFbYubqeKWkpDB27FjOnj3LO++8Y+/ouZyr3pfS41rLfPvttxiNRodFhMtjNps5duwYiqI4LN8RHR0NwI4dO5zuY5v9XNpGBrVRWTGzJQ1//PGH031sZSWX7ykvZjt37gSu/ZiVtH79eoxGI4MHD8bX17fUOhIza3KWn59f6uoMtlU/Si5fZItHaTE7fPgwubm513zMypKfn8+2bdsICQlxmAhSW15nJROKAQMG8MYbb5Q5maphw4YcOHCAwsJCh2PFxcXs37+fhg0bOiQVXbt2pbCwkAMHDjidzxYXW5xK3vb0zwBXxuxK1YaYuTpeJZPWt99+m7vvvrvMtrjqfSmJq4cqrfv+9OnTzJ07l8DAQCZOnOhw7Ndff3VYbw2sSesbb7xBamoqvXv3JiQkxH6sf//+BAUF8fnnnztMmDh79ixLly6lTp069OvXr4aflWtdacxiYmLw9vbm888/JyMjw+E8H374IWCNk02PHj1o1qwZGzdutE8QsdVfuHAhXl5eDB8+vKaflktdacxKWr16NVD2MAGQmAF06tQJs9nMwoULHcqNRqO9rOTqFc2bNyc6Opq9e/fy888/28tNJpO9B3LkyJE19nyuhiuNWVFREWaz2aHMaDTywgsvkJOTw2OPPeawTW5teJ2VTCj69evHm2++Web4cUVRGDlyJIWFhbz//vsOxz788EMuXLjAyJEjHVZcGDVqFADvvPOOw5ek3bt3s2PHDqKjo2nevLm9vDZ8Brg6ZlfK02Pm6njZktaMjAzeeust7rnnnnLb46r3pWz5ehWtWrWKX375BYCTJ09y9OhROnXqZP9Gc/fdd9u/vcycOZNjx47Rvn17QkJCSEhIYNu2beh0Ot5//32nddFs4zRvvfVWwsLCyMvLsy843bhxYz7//HOnxcLXrVvHM888U+rWdW+88YbTZT13cGXMAJYtW8Zrr71GSEgI99xzD97e3vz000+kpqYyevRoXnnlFYf6e/bsYcKECRgMBgYNGkRgYKB9+7rp06czefJkF0ekYq6OGVjH/o4YMYJ27dpVuID09R6z48eP8+CDD1JQUECHDh3sk7Nsi+i3a9eO5cuXOyRiJbd87d+/Pw0bNmT79u2cOHGCkSNH8tprr12lyJTNlTHbv38/jz/+OD179uSGG24gPz+fn3/+mbS0NEaNGsUrr7zilIB4+utswYIFvPfee/j7+zN27FinpePAGrM2bdoAzttxtmvXjt9//53Y2Ngyt3ydOXMmq1atqvSWr57+GXA1YmYbegLw/fffk5+f75BMPfPMMw7jqT05Zq6Ol22b51tuuaXMz4bHH3/c4XdXvC8lcb2Knn32Wb766qsyj0+dOtX+n75582aWLVvG6dOnKSgooH79+vTs2ZNHH33UaY9ugMWLF7N9+3YSEhLIzs7Gy8uL8PBw7rjjDh5++OEyZyzHxsayePFi+xi7du3aMWnSJPtiyu7mypjZ/Pjjj3zyySccO3YMi8VCy5Ytuf/+++09GJc7fPgw8+fP5+DBg5hMJlq2bMm4cePcvq+3zdWI2axZs1i+fDkvvfQSY8aMqbBN13vMEhIS+PDDD9mzZw/nzp1Dr9cTHh5O3759GT9+fKnrscbHx/P222+zd+9eCgsLiYiIYPTo0Tz44IMeMaPelTFLS0tj7ty5HDp0iMzMTPz8/Gjbti1jxowpczw1ePbrrKJ4AcyePZuYmBj773l5ebz33nt89913ZGZmUr9+ffr27cvUqVNLndSiqir//e9/WblyJYmJifj7+9OtWzdmzJjh0Ntakid/BlyNmLVq1arc8//www9Om2d4asxcHa+KYgXYd+Yqqabfl5K4CiGEEEKIWsH9X9uFEEIIIYSoBElchRBCCCFErSCJqxBCCCGEqBUkcRVCCCGEELWCJK5CCCGEEKJWkMRVCCGEEELUCpK4CiGEEEKIWkESVyGEEEIIUStI4iqEEEIIIWoFSVyFEMINpk6dSqtWrXjzzTfLrffEE0/QqlUr5syZc5VaJoQQnku2fBVCCDc4e/YsAwYMoLCwkFWrVtGuXTunOj/++COTJ0+madOmbNy4ET8/Pze0VAghPIf0uAohhBs0bNiQp59+GovFwgsvvIDZbHY4np+fz8svvwzAK6+8IkmrEEIgiasQQrjNqFGj6Nq1K8ePH+fTTz91ODZv3jzS09MZPnw4vXr1clMLhRDCs8hQASGEcKOEhASGDBkCwPr164mMjOTXX39lzJgx1K1bl02bNhESEuJ0v+PHj/PRRx8RFxdHTk4OoaGh9OnTh6lTp3LDDTc41M3JyWHdunX89NNPxMfHk5mZSUBAAB06dGD8+PF0797d6fyjRo3i0KFD7Nixgx07dvDf//6X06dP4+/vz86dO10TDCGEqID0uAohhBtFRkby2GOPUVxczIsvvojRaGTmzJmoqsoLL7xQatK6ceNG7rvvPjZt2kSjRo248847CQkJYfXq1YwYMYL4+HiH+vv37+f1118nMTGR5s2bc8899xAREcH27dv55z//yYYNG8ps34IFC3j++efx8/PjjjvuoEWLFjUeAyGEqCzpcRVCCDczm83cd999HD9+nA4dOnD48GHuuOMOPvjgA6e68fHxDB06FD8/PxYtWkSnTp3sx1auXMn//u//0rlzZ7744gt7eWJiIjk5OXTs2NHhXIcPH+Yf//gHBoOB2NhYfHx87MdsPa5+fn589tln3HrrrS545kIIcWWkx1UIIdzMy8uL1157Db1ez+HDhwkICGDWrFml1v3ss88oLi7mueeec0haAUaPHk2fPn345ZdfOH36tL08IiLCKWkF6NChA6NHjyYnJ4f9+/eX+ngPPPCAJK1CCI/h5e4GCCGEgPbt23P33Xfz3XffMXr0aBo1alRqvV27dqHT6bjzzjtLPd65c2e2b9/O4cOHHS7rm81mdu3axa+//kpWVhZGoxGAP//8E7COtS1tElhZjyOEEO4giasQQngIf39/h5+X0zSNM2fOoKoq0dHR5Z4rOzvbfjslJYVHH32UU6dOlVm/oKCg1PLLJ3oJIYQ7SeIqhBC1hKZpqKqKl5cXgwcPLrfujTfeaL/93HPPcerUKQYMGMDDDz9MZGQkAQEB6HQ6li5dyr///e8yz1Ny3KsQQribJK5CCFFL6HQ6GjRowLlz53j55ZcrlVTm5OQQFxdH48aNmTdvHjqd49SG5ORkVzVXCCFqnEzOEkKIWqRnz56oqsoPP/xQqfp5eXmAdaeuy5NWo9FY6fMIIYQnkMRVCCFqkfHjx2MwGHj11VeJjY11Op6dnc2yZcvsW8iGhYXh5+fH0aNHOXz4sL2e2Wxm9uzZpKamXrW2CyFEdclQASGEqEVuuukm5s6dy7PPPssjjzxCixYtaN68OaqqkpaWxunTpzGZTIwaNQovLy+8vb355z//ycKFCxkzZgzdunWjTp06HDx4kJycHB544AGWL1/u7qclhBCVIomrEELUMgMHDqR169Z89tln7N69m9jYWHx9fQkLC2Po0KHce++9DuNfp02bRuPGjfn888/Zv38/fn5+dOnShenTp7Nv3z43PhMhhLgysnOWEEIIIYSoFWSMqxBCCCGEqBUkcRVCCCGEELWCJK5CCCGEEKJWkMRVCCGEEELUCpK4CiGEEEKIWkESVyGEEEIIUStI4iqEEEIIIWoFSVyFEEIIIUStIImrEEIIIYSoFSRxFUIIIYQQtYIkrkIIIYQQolaQxFUIIYQQQtQK/w/fs5PpaLuZHgAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot fitted values on the proportion scale\n", "plt.plot(yr, p, \".\")\n", "p_hat = np.exp(y_hat) / (1 + np.exp(y_hat))\n", "plt.plot(yr, p_hat, \"C1\")\n", "plt.xlabel(\"Year\")\n", "plt.ylabel(\"Proportion Sophia\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# MCMC!" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# Priors\n", "\n", "mu_0 = 0\n", "s2_0 = 1000\n", "a = 0.01\n", "b = 0.01" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "n_iters = 3000\n", "\n", "# Initial values\n", "α = results.params[0]\n", "β = results.params[1]\n", "s2 = results.resid.var()\n", "\n", "α_list = []\n", "β_list = []\n", "s2_list = []\n", "\n", "for iter in range(2, n_iters):\n", " # sample alpha\n", " V = n / s2 + mu_0 / s2_0\n", " M = np.sum(Y - X * β) / s2 + 1 / s2_0\n", " α = stats.norm(M / V, 1 / V ** 0.5).rvs(1)[0]\n", "\n", " # sample beta\n", " V = np.sum(X ** 2) / s2 + mu_0 / s2_0\n", " M = np.sum(X * (Y - α)) / s2 + 1 / s2_0\n", " β = stats.norm(M / V, 1 / V ** 0.5).rvs(1)[0]\n", "\n", " # sample s2|mu,Y,Z\n", " A = n / 2 + a\n", " B = np.sum((Y - α - X * β) ** 2) / 2 + b\n", " s2 = stats.invgamma(A, scale=B).rvs(1)[0]\n", "\n", " # keep track of the results\n", " α_list.append(α)\n", " β_list.append(β)\n", " s2_list.append(s2)\n", "\n", "keepers = {\"α\": α_list, \"β\": β_list, \"s2\": s2_list}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plots of the joint posterior distribution" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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vrDT0vcDlf402bDyDjzSCbQi+FyZUeY2UJa6qasHf/9GC1xcrF0PqBeAOBzB2dDLWrGsOet67Kj343zVtXUzGjk5Gv74uDP2VC+VbPIrtSxMoI63hl94veaANwPKykn37PdhV2YJBA5P8NedERESJgMF2HNOrvTVCK9gNnJwYKSMlLmonC4IAPPRgGrp0cSCvvy/o2rHToxs4Bgb1gbxeBAWrXi8wf0ETNm9MQUWFJ2RWPTvbeLMeve0JAnDt2GR8/Adl+7+Zd6fimrGpqKjw4A9rfdeLInDylBdr1gXffs26ZvTr24TNf/QotiP9ohG4Hw6Hr7vJ1OLUkO+l2q8MUgvBJ58KHnkf7q8noTz029NB79O1Y5Px1LxOYW2DA3qIiMiuGGzHOa3aWyO06o0FQT07Hk5AY6TERX6yIGVR5z3V5K+X3rzFozkBUdqncEaze71A1Z7QgTYAf7Afyr79HtXuIIDvOc24JVV1nDoAvLzIjaQkAfMXNPnvL4rQXDA67+lG5Ub+/TiNjV7FCc6yd9x4e7k7ZGmQ1vuVnR3dryeh7NsfnL0HfCdIkyZ6DGe42T2FiIjsjH22E0BujhP5g8P/WV8KdgOHokg12/JthTtx0OignKJCXx/sO25NVXTfCBwqozV4JVQ3EDmHAzj+o6h7H0EAnnjU2C8EpWVuTJxySrNERBT1e3eLIlAyXz2wDocoAnfdU6/5S0WooTVa71deXpKlPdh3VbaoXr57t/rlchzQQ0REdsfMdgfnrzfe4+tGkpen7EYSSdcTrRIXILgsRKsERI1a+YI0wdHIgkQpW/67Z9SzwwAw4boU3HZrmm4wKWX409N99e2h2KGTvdprF/g8GhsR1IIxMKguKPD1KhcgoGtXBxobffc1I+AeNFD9EDRggLFDkxmLhImIiKzEYJuQm+PEyOHagUmkAY28xKWiwuMfpuJwQLO/thapvCWwnAUARo9yYe16ZR2z3JWXu1C+Wf92H350Bvn5SejW1YvGRihKZsI5ObAT+a8Kas9Dek+kBaTykyHpFxCprGf2zDRc0McVVZ10v74uXDs2WVGzbbSEJNpFwkRERFbjBEkTxWqCpNXUJg4KAvDeiixFQKpV1621jXA/fXNmtwXogcGfVUJNXowlvf7eg3/hxJe7WlXr3UNN7ZQmSRp9vma0i9y334Pdu1swYED43UhYs01ERHbGzDaFJO9fDfgC3EnFp4KCOUB9vDignh2X2vOFEyy/+FLwQkKrBZbMhFsfboTR5692uwv7OVG1R702+c9f+i6fcF0ybrs1PejER+95eL3ApvJmjBiebPj5mtEusl9fV8Qt/6JZJExERGQ1/tZKhhQUuIIWUgLBixkffaJBd6Ga1gK8Sy9RP9+7dXqq4vHCDczHXG1Ov2apZEbtOUTrxhtSDW3znruUmVqtQDvQhx81Y/2G4D7iB/6iX0rz3AuNGDriBLbvULYq1CKKvimTsRLpImEiIiKrMdgmQ0JlOUVRWdIgBamALxgaOzo56Pqhv3Lhsz+pB2jZ2Q7cOystqAtG4H8bsXa9RxGwBxpzdbLu9YHS0nzPYfbMNOM7YMCI4cnYvDEbQy7S/5FpwSL97i96XnypyX/SU1vXivkLmkLco62LSliE9qlIq61rxY6dHnYcISKiuMAyEjIkPV3/ekHw/U9roVptXatiSIt8CmKg515oVF2wB/ha5RmlVaoiCMAVlyfjv//baWiRZtlqN/r1deGCPi4Axh8/lE8/a8Y337Ri+w7rssKBQ4q0TpquGZPsH6oTeD+jBCG4L7lVQ2ZYn01ERPGGmW0ypFG7Wx4cDt8COb1+zJHUO0sTHwMD7bQIEstaQePcB+oxf0ETisanhNzGhx81o7au1fRSktffcGOdgU4q0XA4gB07m7Fvv0eznCcrK7rtB/ZmD7cnu1HsqU1ERPGImW0yRGvaJODLPkvZRa2Fanr31xPYYlA+1jsagfXmq0rP6N/43zaVN2PggCQUjU8xfJ9Yk35teH2xG68vdiOvvzPo5EPK+q9YqXxdjdTIlzyfga4/dfp7bwMIuye7UeypTURE8YiZbTJE6kiiltWdv6CtJlhroZratEqj9h/wqI71bm/PvdCIiVNOxU2gXVCQpAiWq/a0Bl0WOLUzXBOuS8G+fa2YVHzKn8VevsKtW7sfDa2s/LFjXma3iYjIthhsk2FFhal47ulMxeWBwVSoxWuRBNvzFzTh062xDbTjUUVFdHXgUr27llWlZ7DsHXfQrwTvrHAr7uNw+Mp/ol3UKD/hkzLvcx+oN7VchYiIyEwMtiksAwYkqWYXu3d34K1lvpZxarW68nrbcHi9QErosmqygCgCD/9GfXWsWkbc6w1uZ+hwAGNHJ2Py1FOm1HAXFaZi88ZslDyfEbQPrN8mIiK7YrBNYbuhuK0HtrQQcv2GMyiZ36Tovb1vv2/xX7QDYRYsZNbSbIIADB+q34vc4QDEMN43hwMonpKKlcuzcP/cdCx8KRNr1jWbuqgxN8eJLtlORbAv/cLC1oBERGQnXCBJQfRatsnbrt14QyqKp/gWRg4dcUKxLWnK5OOPZODkKZvMOCc/UdRvvygIwNCrXHjqWZ1WNLLbP/ZwBioqPP7PidoiS71FjUZbBqotuHU4fPX9t9zaxNaARERkG8xsd0BamT+9lm1qbdeWvePG7ioPdu9u0VxkJ43yfvEl83pTA8BN05QTJvV0/WkExeIdnCgC5Zs9hn6RGDkiGVs2ZaOgwBX0OVH7XAT2Xw8UTstAef221JM9sGc6S0uIiMgOGGzHATN/FtcKaEL1MFYrAxFFYO79DbjvwXrdx4ym44WW8/7LgfdWZGHkCGNTII9+a3wHunWLYsc6qPvmpOsOzdHqvy6JpIe2VL+9dEkWNm/MxgV9XJZ1QiEiIooUy0hszsyJeVoBTUGBK2QPY70JkmYH0kb89lFjpQ2ROHLEsk3H1FVXuvDH/9MfoGOkt7bafSRa5R0rl2ehqQmK/uuSSHto5+Y4g65Xe2y1LDoREVF74beQjZk9MU8voNHqYSwFKnoTJCk+fPJp6EmVkZw4SePgAfXyjscezkC/vi7V/uuSA39R7lu4gbLWY3PgDRERxRIz2zZm9sQ8rayjlG187OEMRRZdepxwJkAKAlA8KQVn/YeAlxe5Y5L5JiWr3ofAoLi2rhXdujlDZrKl21ZXe5Ge7uulLjd7ZlrYn/OiwlTNKaZERESxwGDbxvSC40ioBdQ3FLeVpOgFKvL7apHKEJav9E1ZvHZsclDrN0osgSdlgSVPggDcOysN3bunYMdOj6K7iPy2aicCTqeA2rrWsANmeWkJERFRLAmiyLyjWSorKzFo0CDs2rULAwcONGWbZtZsS2rrWrHiXbd/+l84262ta0VNjRfrN5wxPLb8/XezsKm8OWjaIMW/229LxRWXJaNfXxdq61oxbOQJxUmVFEgHfsa0bquG7fuIiCjeMdg2kRXBNtAW4Jr1s7hasONwAJs3ZiM3x2mo13FtXSuGjjhhKHh++KF0TLw+Dfv2e1C5uwVZncxb4Djz7lQOvIkhKRju1s2Jm2ec0r2tIABbNmWjutqrelutDHfgZ5OIiCjecIFkHMjNceouLguXXi24vDXg8yXqCzJzc5y4d1aaocf74UffdidPPYXnXmg0tZPIj8dFjBiuPwWRrCMt2k1PR8gWjKIIVO3xaC7GfW+Fb+qk2mNICzA5HZKIiOINg+0OSCvYSUuD6uCaoSPUB4xc0MdYkHvypBiy1jtSDQ0ienRnxjOWvF6gqQnGTr5EQbdjyYjhyZpdccIZekNERGQXXCDZAWl1HmlsVO82Iopt/bgDy0zS05V9jdW89/4Zy2q1y1Y3hzVJkswnBcP5g31Z6cApjnJ5eb5DjrQYt6qqBSJEDMjznbhpfTYB5YngY082oHdvJxobEXK8OxERUaww2O6g1DqP1Na1agbP0k/5FRWeoEBo7Ohk/O+aZt3HsnpVAFcdxFZgi76bb0zH1aNS8OnWZjz5u+ByIflJkfyzJC2EVPts7tipHBvv9QKTik8FLcAsKHBh9+4WQPAF8AzAiYgo1hhsJzi9xY7yFml67f20ykxCBdrSfS8pSMJnf2qJ+vmQ/fS9ILicqKLCg3lPKevypeE30omd1jRT6XMZ+NnU6vMunWh5vcCjTzQEnXgJAvD4I+xkQkREscWa7QQWSY1rUWEqZs8Mrr0VBP0yEz2C4Mt8bqtgoB1PJlyXgjFXh67Jl/d9l4JotV8bBMF3wlZb14qNm5S91wMXQsqp1XnLyR9TKn/iYkoiIoolZrYTVKjMod79XnxJOc2voMAXeBmdIimZNDEFF/RxwetVbpPsa1VpcJ39rTNScfFFyXi+pAF/+aoteL2wX3AGWq3TjUQU28o+1IQa2BRYXpKWBkyeeirkZzGaiatERERmYGY7Qem195MLbKe2u8qjmiGs2uPxZxfD8d77Z/Dtt8xqx8qF/SILMuWfgd8vcePo0ZagQBsAqva0Yt9+j/8zJC2aNbrdQKHGs0slUd27O9Cvrytkplu6PNKJq0RERGZgZjtBGRn1XlvXitcXN2LVR83+64vGp6hvUPStbisqTEWzx4t5TxnLVIuieQNsKHx795lTQqH3Pj77Qj127/Z90BwOYMhFSfhiewtEUXtQjRq98exak1QDF1JWVHiC6ral8idmtYmIKJY4QdJEVk2QjJTeqPfSMrdiQRnQ1jFCvtBsy6a2CX7hTI+kjkkQgBtvSMWI4cm6pSNyauPZQ008DVRb14qqKl83krz+7EZCRESxZ+vfV/fu3YsZM2Zg8ODByMvLw3XXXYc1a9aEtY3m5mYsWrQII0aMQL9+/XDJJZfgN7/5Db7//nvV27vdbixduhTjx4/H4MGD8Ytf/ALXXHMNXnvtNZw+fdqMp9VuigpTsXljNpYuycLmjdn+AEZvEZsoAiOGtS2Mkzo6yLuWPP5IBvtbkyZR9A1EOvtsh+FJo0Db2oLARY3hlETl5jgxckQKRg5PNTXQ5uRKIiKKlG2D7R07dmDy5Mn48ssvMWLECEyaNAnHjx/H3Llz8frrrxvahtfrxR133IGFCxeic+fOmDZtGgYOHIiysjJMmDBBEXB7PB7ccMMNeOaZZyCKIsaNG4fCwkIIgoCXXnoJkyZNQlNTfC30Uxv1rreIDQA2lnvgcAA3TUvFlk3BQfqOnR7s2+9Bt25OPPlYOgNu0iSKwIp33Rj8Cxcuv6ytYk36bL3/rvZ49qo9Hn9wqzXxtL1qsTm5koiIomHLMpKWlhaMGjUKtbW1+OCDD9CnTx8AQH19PSZOnIjDhw9j3bp1OPfcc3W3U1paioceegijR49GSUkJhH9HhtLl48aNw7PPPuu//fr16zF79mwMHz4cCxcuDNrWXXfdhS1btuDZZ5/FuHHjVB/PTmUkev211X6WVxP4U31gSQpRpAp+mYQnHssMKkmSfxYDS5nUJkiqlZpYJZwSFiIiIjW2zGxv374dNTU1GDNmjD/QBoDMzEzceeedaGlpQVlZWcjtrFq1CgAwZ84cf6ANAEVFRTjvvPOwfv161NfX+y8/cuQIAOCyyy5TbOvyyy8HABw7diyyJ9WOQmXipK4iobLS0k/1tXWtePQJBtoUvYrPW3DwYFt3mtwcJ2bPTPN/FqUMduCwGqllpVpJlNXCKWEhIiJSY8tge+fOnQCASy65RHFdQUFB0G20nDlzBnv27EHPnj3RtWtX1e00Nzdjz549/st69eoFAPjTn/6kuP1nn30GQRCQn59v/InEgFZ/bXmtaVFhKt5bkYXbb03FzLvVAxfpp3q1doBEkfqfmfX+E8DSMjdefKnJ//kaNSJZ8VkL7JUtL4myWqxLWIiIKP7ZsvXf119/DQDo0aOH4rrOnTujS5cuqK6u1t1GTU0NvF6vZqmJdPnXX3/tD+CvvPJKXHnlldi0aRMKCwsxePBgAL7Avrq6Go8++ij69esX2ZNqJ3qZuMAgJbAsRCvDPW2qb5HZieOhR7ITGSVNduzd26noiLNug/KzJgjAsR9bUVunLImymvQrkLyEhSUkRERklC2Dbam0o1OnTqrXZ2Zmora2VncbUueQzMxM1eszMjKCHgsABEHAK69k8E2uAAAgAElEQVS8ghdeeAFLly7FgQMH/Ndde+21uPTSS40/iRgx2l87MMjRGq1dPCUVpWVuPPUs+2RTm4d/k4Z5TzVF9WuH1wt8urVZ87MHwN+nGwDm3t/QrrXageT9vBloExFROEwJto8ePYo33ngD+/btQ0tLC7p27Ypf/epXKCwsRFKSLeN5VW63G7Nnz8bevXtRUlKCX/7ylxAEAV988QV+97vf4bPPPsOHH36I7t27x3pXNWll4gBgx04PevRwYPkKt2qQIwXpaovSiABf8HvF5SnYvKUZ23cYb4MnH27jcAD/+Z/qP6mIIlDyfAYgCrjvwXpFSVRBQfv3z87NcTLIJiKiiBiOhP/+979jxYoVOHr0KDp37oxLL70U48aNw5EjRzBx4kT88MMPQbfdunUrPv74YyxbtgzJyclh7ZSUjdbqa11fX6+Z9ZZI1wdmrgM1NDQEPRYAvPHGG/jkk0/w6quv4qqrrvJfPmrUKGRkZGDGjBl45ZVXgjqY2JHaZD2po4LDoZ3JXrk8C01N8Gfvduz0MNCmIJdf5kJ1tRf5v3CFFWxfV5SM0rLmoJO5I0fV7+9wAHn9XSFLovQ67hAREdmFoWD7wIEDKC4uDuoxvX79evzf//0fkpOT8cMPP+DGG2/Er3/9azgcDvz1r3/FK6+8gt27d2PJkiW48847w9opqZ66uroaffv2Dbru5MmTOH78OAYMGKC7je7du8PhcPjrv+WkywNrurdu3QoAuOiiixS3HzJkCARBCCotsTMpE6e2YFLNjTekol9fV9BlPXo4FBlJQQDunZWG+Quaguq9uYAyMQgCUDw5BcvfPaN6/dbPPPh0qyfs/uqrPmqGIPj6axdPScX6DWeweImyX7V8xLpWSZTedFQiIiI7MbSk/o033kBTUxPuu+8+rF27FosWLUL37t1RXl6OtWvXYvTo0XjwwQdx3nnnoWfPnhg5ciTefvttZGVlYePGjWHvlLQwcdu2bYrrKioqACBkV5CUlBRceOGFOHz4MI4ePaq6neTkZPTv399/mcfjAQAcP35ccfvjx49DFMWws/SxFmqADeALVoqnGA9Urh6V4m/DtmVTNh5/JEPRsYHikygCZ52lHUnr1fkb2fbby934/nsvXnxJfTjUC89m+oNmqSRK+mw5HMDsmb5plEY67hAREdmBoRCpsrISeXl5uOWWW9CrVy8MHToUS5YsgePf34LXXXed4j5nnXUW8vLyUFNTE/ZOXXzxxTjnnHOwdu1afPXVV/7L6+vr8eqrryIpKQnjx4/3X/7dd9/h0KFDirKTCRMmAABKSkoQOLuntLQUhw4dwtVXXx1URiJlyxctWoTW1rYvbq/XiwULFgBQz3rbmVrrMnlWUhSBigqP4r7V1V5FUCWKyjZs0lj46yekmLz3FAsLFlo3IdHrBZa+rb64UvoVJTBoLipM9ffh9nqB+QuasHyF27Le1xzLTkREZjNURnLixAlFJvmcc87BhRdeiKqqKpx//vmq93O5XPBGUPSblJSEefPmYfr06Zg8eTLGjBmDzMxMlJeX48iRI5g1axZ69uzpv/2LL76I1atX4+mnn0ZhYaH/8nHjxmH9+vVYt24djhw5gvz8fHzzzTcoLy/HT37yE8ydOzfoce+44w588skn+Pjjj3HgwAEMGTIEgG90/N/+9jd07doVM2bMCPv5WE2vdlVtweTsmWlBvY2lVmzyhWdanU3S0toWW0q3z81xYvy1KfjgQ/XyAyLJpnKP4nMlmftAPRwO4IbiVEwt9mW45y9oChpy8/Zyd8iOO5FgaQoREVnB0LdTRkYG/vGPfyguHzRoEPr06YPOnTsrrmtsbMSf//xn1YEyRgwZMgQrV67EoEGDsGHDBqxcuRLZ2dl4/vnncccddxjahtPpxGuvvYa7774bJ06cwLJly/Dll19i/Pjx+PDDD3H22WcH3f4nP/kJVq9ejalTp6K5uRnvv/8+PvjgAzQ3N+Omm25CaWkpzjrrrIiej1VCTYsEfNnBlcuzcP/cdKxcnoUL+rg0B4cE+v57L4YNdQVN9xs7OhmTp55Sfby3lqqXBlDiu+rK8LoOTZuaqvjFJTCgXvaOG0NHnFDNYoti8P3N6H1tdBgUERFRuARRDF19edttt+Gzzz7D9OnTceeddyItLU339lILvU8//RQzZ87E7bffbtoO21llZSUGDRqEXbt2YeDAgZY8Rm1dK3ZXeQBRQLduDkyeekqR4du8MVtzgI3DAUy/JRWLf68Myt9/N8u/SPKh357G/65pGzBS8Msk3H1Xuubjff+9FxOnnAq5/4IAvLciCytWNmHtOmXpCtmDfGFsqNtu2ZSN9RvOoGR+6BMu6TMD+E7wjv3Yirn3N2huWyoh0bq/lNGOpjPJjp0e3DxD+flduiQL+YNdKvcgIiIyxlA66q677sIXX3yBJUuW4M0338R//Md/6C4UbGhowMmTJwEAH3zwAVatWuW/ThAEbNmyJcrd7phKy9yKiXty8mmRahm7JW+q1+RKzWb27fcEBdoAUPF5C668vEW1VrZqjweffmoscBZF4NgxL9atZ6BtVw4HMP3mVCx5S5lVVvProhRUVHgwf4HvA6TXoUbKQn//vRe7KlswaGASBuS5NMtKRNHXKeft5W7NCY7LV7jx9nK3fwjOtKm+EpRwgm4jw6CIiIgiYSjYvvDCC/H+++/j1VdfRWVlJY4dO2a4Fvtf//pXVDtIPlLQHCrbKA8QtHoVqw0ZkWqxd/5ZfTz7seNeRUAiCL7pfuF0p7jrHvXe52QPXi/w+zfVBx+p+e//dgad0ElBr/QZk9YJ9L3Ahe7dHXh5YSMeebwtk53X36n5WFKnnOIpqYoJjoG/2EhE0VeC8s4Kd1g11xzLTkREVjFcaNmnTx8sWrTIyn3pcMIZyqHXwk8++dHIIsfZM9t6ZQfWYgf2zpa7/NJk/CSnLbAKp9SAYuee/0mFyyUYKvGQhPO+HjzYqlpXXfJ8Bs7q4gwKkNV+Nanaoz3cJvDzHPi5lv9iIxfJtMmCAheeeyYDAgTk5SUx0CYiIlPEzyz1BBNu5wO1oBlQn/wYSCtjV1SYiqtHpaCmxou0NATVYqsFWn1+7kRjI3DkaKvu7ch+Xl7k694xZ3Ya/vrXVqxdr/7LRShaJ1erSs+o/lKS118Z6O6qbDH0WA/MTcfw4cmaAa+R/vHykio96n+PDLaJiCh6hhZIkjFGF0jW1rX6x6dL1BY2yslrtgUBePwRYz+V19a1Kn6Gl2gtDiOSOBzA0F+5UL4ldK293ufy061nQpYRyf8W1H4BUvsbUvPHcv2/Ka1tGfl7JCIiMoKZ7RjQqqMOlYUrKkxFQYELVXt83UjC+albGt+uRitrHi6jo9tZfhJfpLIjo2Uoogj07q3+WUtLU19wGFjfHVg6ovULkPwXGy0VFZ6QGepI/x6JiIiM4FL7GFCb6mi080FujhMjh6di5IgU0wIBXz/tZP8+adVsaxEE4I5bU/HeiizcOytN8/6C4KvjfW9FFse7xxFRBL7YHl73mEnFp1R7vmt99t9bkYWlS7KweWO2PyO+b78Hjz6h3ftamlx60zTtX3aM9MqO5u+RiIgoFH6bxICUlTNzKEekHvrtaUyccgqbypvh9QIFFyfhvRVZYQfcry12Y+KUU0GTKQM5HL7SgpHDU9GvrwtF4znaPV6IIvD5F8ZqrQPvoxboan32+/V1IX+wKyijPan4VMjhS7k5Tsy9NwN/LM/GHbcpg24jY9zt9PdIRESJh2UkMSKVhGjVUbcH1X7aX7TgyitawhpoEnhbtfvJF7uVlrlRuppj3ROd1wv8YY0b/S9MDqq3DvXZ12tzKQjAsR9bUVsXfL/cHCeuK0rFG793K2qvjWSo7fD3SEREiYmZ7RjKzXEGZfPaU21dK1Z/rB7wSv20jTDS9zsw0JaXBhhxzVgXXnk5M+xsO7UvtfdnwUI3bp5xCsNGnggqK8nN8bUErK72KrLfoTqNzL2/QbE9aZvRZKhj+fdIRESJi91ITNQe49rNsGBhAxYvUZ8iCfjGtv/tb/p9jI2QtzQ0MgGTiyfj0/BhLmze4tF97wI7fOi1vlTrDqK2+FarY4he5x0iIqL2xsx2BzN77indQPvascm+mup/Lz57+DdpqrcLlWV++DfpQYvdQpUGlDzvq7t9/JEMZrDjUKhAG2irn5YPpJEvfFTLUE+bmhqyflvCDDUREdkJa7Y7kH37PSjfrN5VQhCARQsycf75Sdix0+OvsXW71SPf4skpePe9M5qZ73lPNcKVJPjbroUqDWio9wVJBQVhPSWyCSO/Rkj100Za7clrqAHgnRXh1WOHM6GViIjIKgy2OxC96X2iCGz9UzP+Z2Z9UL/jk6fUI+QhF7nws15JmqPbRRF49Im2cdnp6dr7Jd22d28ndlUaX5xJ8WXoVW3ZZnlfd7XAWd4bXm0SqlYQHe6EViIiIquwZttEdqrZVsvq7dvvwcQpxidF6g2pkQIYKft46J8ezHtKOfRkwnUpePThTENTKlmvndgEAdiyKXTNth4j9dicCElERHbCmu0EVFrmxrCRJxRdIPr1dSGvvzLY0Oo8Iorawa9UZwsA+YNdyM5W38iHH51BbV2r6uAQtcej2Pv5+dYcFkSxrcZaWhMgH2QTipF6bL0yFSIiovbGYDvB6C0+q61rxd59wW3WHA7goQd0ajx0eL3Aind9gfyAPJfmwkapFvexhzMiehxqX/fPzcSc2W2TQAUhsqmicvJSEXn7v9q6VuzY6Qk58TEUToQkIiI7Yc12gpDKRn78UTurJ4pQve7Yj17NEg69UhIAWPq2Gxdc4MSAPBfunZWGkvnBpSQOB9DY6MWyd5pw+lR0QRRZTwpK8wenY/AvXKjc3YITJ734vU4HGzlB8I1fL1vtxocfNfsvu6E4Fd9/7/WXN1VUeIJq/gEErReItMZaOrEzWt9NRERkJdZsmyhWNdvy+ld5+YdUrwpAUcsq0auXFgTghecysH17C1aVqg/CCVxQKY1sdziAC/s5UbWHQXa8GD7MhfkvZAV9psIl1WZXVHg0+6qrfU7l10dbY81+20REZAf8XTXOqZWNAAgqAbih2JchlPcvDiQFx8VTUlSvO6uLE7fflqZZTiCVq1w9KgVbNvlqcRe+lMlAO85s+aMH+/Z7ohpoJIpA1R6PZl91wPd50TvNN6PGmv22iYjIDhhsxympvnV3lUcRFImiLxN907RUCAKw7B23f6GktDDt/rnKOm2vF8jMFBQBtVRakJvjxOOPqAfr0v2l+uz8wS58XR1esMRhNrHn9QJbtzZHPTlU9ApRbyOaGmuz6r+JiIiixWA7DgV2G7nvgQbV4LjrT514e7lbdaFkbo4TI4YnqwbNr7/hq82Vtimvd5WC9ZLnMlUXoR075vUHOIMGhrckQMquP/ybNJxvUUcMCu313xuvz5aTPi8DBiSF7D4TuPAy8N/R1lhrdeMhIiKKBS6QjDPyshFR9AUp0pAQKVBpbFRfDCllnuWLyAJJQe9v/186RIhIz4A/SAd8P8+PHOFEQ4OoGGoz94H6oAVu145Nxv+uaTb8/Lxe4MgREX/7W9tODbkoCf/1X0689/4ZtgcMQ8nzGTh+3Kva/1xPpK/xHbel4rqiVP/nROvzBSj7tHfv7sD333tRubsFAwckoV9fV0T7oNWNRxquRERE1N4YbMcZtR7Cogi88GwmzjrL4S/3qK1rDTmlTxqJvam8Gc+90Bi0Ta8XePKp4MtuvCEVU4tTg7LcBQUuVO3xYO79bfW5gQHOU/M6YdJED3bvbkGnTsC2z1uwcZN28O1w+MpeAgO+7TtasH2H9vRLUldXJyI52fztqnWoEQTg8suSgwLaosLUoAWzggDMuCUVFw9JDlq0GM2QGzkjo+CJiIjaE3+rjzNaPYTz8pKCFoPJF0Nq/TSvV1IiF1j7HXj/LtlORTY0cIFbv74u3DA1DePHpeG+Oem6tdlDLkpi9tokz73QGHZWW83woa6gz9Hjj2QoavdFEZg89VTQZ6O2rhXzFzT5309RBJa85VZ0B9HrDR8u9tgmIiK74TdQnDEaRAPGp/SpbVOLWiCkFuAIgnqAU13t1Q2mv9jODLbdbPnEg5XLs4I+R0WFqVi5PCvoxEn+2Qg1yVFvkW+k3UjC+fsgIiJqDywjiUNS+YaRHsJSfXY420xLAyYVn9Jt2xb4s7wU4Mh7KldUeFBUGPzY6en6Pb2NZLX17k/m83qBpiYgf3BwHXVjo/J98HqBTeXNGDE82X8SplbKFFg2Ii2OlPeGjzQbHc7fBxERkdWY2Y5TVvQQlrbZr68Ljz+SoVnuoRYIFRQEj2sXRWUGvLTMjclTtYN4I6Qyhnv+J7LpghSZ/Qc8isvUftEAfOUrw0ae8E2IVMkyA1As8pWuD7xdNJ9t9tgmIiK7YGa7A5BGuffoYTzL51/8WNWCHX9uxkelzbqjr0MtTJPX5QJtC+aWvOVW7VgRaN7j6UhLc0CEiAF5LgAuvLyILd2iNWVSCgYOTMKc+xp0bzd/QROuHpUS9L7rdbSRSko2b8zG5o3ZQVnmHTs1esPLFvkSERElAgbbCU6vy0OoIFxq8TdyRApum6EcfR14f72SAUC7i8rFQ5Jx/YRU1NR48c9/tig6oADALwY54fUKuO/B+qDn8cSjGXjkcf0gMRDLT5Te++AMbr4pDXNmp6FkvvZiSq2OHqE62tTUeP0ZZqlGOz0dqp+VvLykmAXZkZyQEhERGcEykgSm1+WhtMyNoSN8gz+Gjgg9+EP+s7x8cIhWyYB0e70uEdK2r7giWVG6IgjA3HszNHsnz3tcOQlTzfvvZgV10HA4gJumpWLO7DRD909UUkB8843puq+FwwGkpUF1KqNWR5vAk63Az8vkqacwdnSybRYxcggOERFZSRBF5vrMUllZiUGDBmHXrl0YOHBgrHcHO3Z6cPOMU4rLS57PCOqLDfiC2vdWZKGxESGze7V1rRg28oQiM7l5YzYAaC5MM9JLWe023bo5VZ9HwcVJ+Hx7i262OvBxautasbvKAwEC8vJ8P+pUV3uRng688GIDvtyVGKO95Rl8vYy+IABbNmX7M8/y91Vy7dhkrFnXrPvePfTb00EDjK4dm4yn5nXS/LysXJ6FpibEtGxE77PMDDcREZmBZSQJTK20AwA++cSjCL5EEZg4xRfQhhoqolefrbcozUiXCLXbqA3oAYCKL9TbBKoFcvIgfshFSfji34G6IADTpqYiJQWo+Dz+A+5hV7mw5ROPv9PH8GEubCpXLnAEfDXz0vug9r4Cvm38YW2z6tCiwJKiNeuChxWtWdeMe+5u1fy8qHU4aW8cgkNERFZjGUkCy81xYvZMZWnA+o3649NDDRXRKglJ06nIkOp1AYTsEiEvWcnNceKGYmPdRwQBmD0zDf36uoJqheVlKJ9/0RI0bGXZO27bBtqC4Ct5mTIpxdDty7e0LUAURWgG2oCvZl7So4dDtQONKKq3+Avsg60XtKptV6sPe3vjEBwiIrIav1ES3AV9lJlDI4VDekNF5INDpNvLJwhKzKiJnVqcqjt5UiKKvs4ZgY+hlbG1i549tZ+Yw+Er7ymekoqV758x9XHlQWVujhP3zlKeMTkcULz28vvGa9DKIThERGQ1e38TUtS0gqA5s9OCAoxQwZSckQmCgHmjuHNznEG9vwXBN0ZcjfwxtPpBh8Ph8JVjWOHwYe2zn7Gjk9Gvrwuvv9FkSicV6fVzOHy/AMiDSmmhpDz4lC8ulQekekGr2tRQUYxsQqQVjE5aJSIiigRrthOcvBdyYD321aNS/LXRFRUexW1CZfe0JggG1ruaXRMbuNivc7Z2RjjwMbQmXBr18EPpuOKKZFRUeFC+Wbskwwpr1jVj+LAzWFVqTlb70kuS8KdtLfB6fb8AdM5yKFpBXj0qJeizIb1PRurte/d2onJ3CwYOSEK/vr6Tk1BtIe3A6KRVIiKicLEbiYns1o0kUG2dsk92JLeR3z5UJwezuj1odcrQ6rSh9hj79nv8i0DDsXRJFrp3d2h26rBaqP7gN96QiuQUYMmbbv+iSMBYuZDUheZvf2sN2SkmFL1uM0Y60RARESUiBtsmsnOwbZVI2/mFG2hptTEUBN//5MG81mME7otRr7yciX37W/D6Yvv2X5bKQvpe4PJnjD8qdeO1N4ztszygD/eEyOiJVzgnc0RERImAZSQUlUjb+YWrRw/1kgNRBG6/NRW9ejnR9adONDX5uqI0NvqCO7WJh717O7H07SbdLh2B/mdmve0nT0plIZs3to1UP+88469zqHIgLVLpyY/HW0OWC7FUg4iIOiIG22SKUMGokUBLb2R2RYVHs5zitTfc/mw2AN0semmZO+za7UgDbUEAfvtQOg4ebMVHZWcsD9i9XqBqjwcjh/teu25dIw9sjdRUB/5KIP3CIM+O26kum4iIKBYYbFNUzKrF1duO1NFEL1j1eoFHn2gIKimRupL07u1EYyOQno6Q24nUtWOTgwa/CAJwzZhk/O7pxqA6aqvNua8BDfW+fz/2ZENY95WCZSMLZOVdZqThQNJCyFDb0DuxIiIiSiSs2TZRR6vZtnLxY+B2tOq1wxVqoaHkjtvaylImFZ8KeZ/AUfVVVS2AIKLrT52YPPVUzPp7q03cDEUQgBeey0Bef/2hQ4B2DX3Jc5k46yyHbrkQF0sSEVFHwt94KWJ6bf2AtqmRoXpqh9qO0T7ZUimDFiOBtsMBXFeUipHDU3H22cb+PLxeX5Cdm+PEyBEpGDk8FY2N4Qe7gK+X9/UT1CdFXnGZ8T7feo+t9RqJInBWF/VyH/l7qdW/PS8vSXdCqFl914mIiOIFg21SZSRQ1psaGM7UyFDTB9UmVkoCh7SoTT80InBQTuCgF7VhLFrue7A+6DlGOkhnyx89uOwS9aD69tvS8MJzGYa2o/Z6vv9uFpYuycKWTdl4/90sw4OM1N7LSCcvhjqxIiIiSjSs2SYFoz/zaw3MAaCavSwoUM94am0n8LaBHU3S0oCmprbAULpsV2VL2PXYDgcw/ZZU/H6J2z/qXRr0ojaMRYv8OebmODF2dDL+d01zWPvj9QLp6Q5cOzb4vteO9U2SPPts/X0SBODxR9QXikpDZgDfglP5/dSCZa1MdEGBK6IuM2qvqSD4OsiEi3XfREQUD1izbaJEqNmOpA5b3j9Zq55XGg6jFSBF2oc5nN7Zl12ahG0VLf4gdPbMNMxf0KT5fMPty710SRbyB7s0h/AEUqshl4bM9Ovrwr79Huze3YIBAdMY5c9Xeg4//akDEAXk5SWF7Guttm+CAGzZpHyP9d7L/MHhj6+vrWvF8hVuvL3crehcEk7tNuu+iYgoXjCzTUEiGa8ub+unNZ57/wEPbrm1STNAiqQPszzzqmf4MBfmv5AVFIT6nm+T5vOVsrdVezyYc59+d4/AMgy111FO6uAh/Vv6/8lTT/lfm8AgW2I0o6z1eqrtmyiqv8dmjlrXaxUY6tePQHrZdma4iYjIblizTUFC1U8boVbPK88gR7swTqop3727xVCg/fBv0jD/hSz//kmL+LSe77FjXv++5eY4MXJ4Km68QTtzKi996dHDYajdnyj6enEH3tbIaxP4HMIVznscaW22nFqrQK1BOqHEY9230cXCRESUeBhsUxCzgquiwlRs3piNpUuysHljNi7o4zItQApcsHf//6sPGdQ6HMAVlwd3+JCCHwBBz1fKts59oF6xsHNqcapqkFryXCY2b8xWZOmNLNh0OABRFCMOPOWMBHXhvsfy9zKScg0jmX6jJ3VmnBC2p3AWCxMRUeJhzbaJEqFmWxJp/bTe9qzqyR1YiuFwAGNHJ2PNumbdKZLyel+pVGTu/Q2KWuLAfQy3VvitZY148aUm1X1T2/9Ac2an4eYb0w2/NuHuW7TvcTgLFLXeN2kIUaLWbJv1uSciovjFYNtEiRRsW8GMAElzmMrzGTiri9MfOGoFkvv2ezBxSvD9peCnutpraDFguEFq4O0rKjx45HFjkx3DCcraO6iL5L3UOsnRei1DBfNmnxBawewFpkREFH+4QJLaTSSt4uS0FuzJpx6qLQ4sLXOrBrpSyYaRxYCRtJuT9kWqWzYq1MLUQJEsbI1UpAsUtd5/tfsYCeYjWVDb3sxcYEpERPGJR3xqV9Es7JPuH0lNeW1dKx59Qj3QFQT4gz+9bUdbe2ukblltv7Sej5GJjlYEddEsUDTy/ifSlEmz1kAQEVH8Ymab4k44GXIpE/3j8VbNgTc33pDq34bWtiPN5gZmwrWG5Kj125bvVyCtrG+owUBmsTpb255Z+vZgxi86REQUvxhsU1wyUkIg7+usxuEAiqfolyfU1rVi46Zm1QBwxbtuzL1XfYS6WlD82MMZePSJtkWYggBMmpiC994/o1iYKd8vaV/0Jjr27u1E5e4WDJQNwjGTkYmf0UjE0ot4KHkhIiJrMNimhLRvvycoqFUbIKM1ojxQqAmSy95xo3iKMgOtFRSvXJ4VlMkWRWDle2eC7qsXvOplfSsqPO3WocPKbK3VwTwREVF7YrBNpopkAaHZ2ystcwcF2hJR9PXEBgAIomJRpdpjh5pOqTV5USsorgwxhEcQgJXLfePa1Z67VtY3LQ2mTFUM5/W2MlvL0gsiIkoUDLbJNGb3Po5ke1KArFYD7XAAeXlJhlvMRTOIRSsoHjggSbVuWyKKQFOT9nPXyvo2Niq3GW6ds916V7P0goiIEkH8FkGSrZjdQSLS7WkFyFqlCHodRtQ6fAgCNDtLBHYI0epC0a+vK+hytf3UylJLz11tomO03UgSqQMIERGRnTCzTaYwu4NEpNtTyygHlmYECtVhRCuLrFbeoJUVVrtt4OX7D3gwf0FT2FlqedY32jrnROsAQkREZBcMtskUZneQiHR7WkGnWmcOIwGmkUEsRm6dcf8AACAASURBVIJ2tf2Uek5fPSolaPu1da0RPfdo6pwTsQMIERGRHfCblExh9vCOaLanVmahxmjpRahBLKGGvMgH0MjJtx/Nc490aBCHrxAREVlDEEWtUR8UrsrKSgwaNAi7du3CwIEDY707MVFb1xp1B4nABYsALO1IYcaiwH37PZhUfErRJ3vzxmzNdnxGun6Y8VqGIt+P9nhMIiKijoRlJGSqaDtItHdHjGhbzEn7Kw+0H3vYN+hGrbzk5Cmvok5b7Tla3Y1Dr+MJERERmYOZbRMxsx2d2rpWDBt5QlE3vHljti0DQK39lRZj7tjpwc0zTinuJx/PHovnGG+vNRERUbxizTbZRqjaZ7vR2t+mJt+/tWrC5ae3sXiO8fZaExERxSsG22Qb0faKbm+h9ldt0eHsmWm2eI7x9loTERHFK36zkm3k5jiDgtFYdMQI1TkkkJEOHvLOKDffmG6Lrh/sPkJERNQ+WLNtItZsRydwwZ4gAPfOSsPNN6bH5PHDWZwpdfBISwMaG6HbYUR+n1h3/bDLfhARESUqBtsmYrAdOaML9oy0zLPy8bW0dxcVIiIiig8sIyFbMLJgr7TMjWEjT+DmGacwbOQJlJa52/XxtWhNkDRSihJO2QoRERHFH1v32d67dy8WLlyIqqoqeDwe9OrVC9OmTcPYsWMNb6O5uRmLFy/GmjVr8O2336Jz5864/PLLMWvWLJx99tlBt33wwQexevVq3e3dc889uOuuuyJ6PqQt1LjwUCPRrX58PUbGvqthNpyIiCjx2TbY3rFjB2655Ra4XC6MHj0anTp1Qnl5OebOnYujR4/i9ttvD7kNr9eLO+64A9u2bUP//v0xbNgw1NTUoKysDJ9//jk+/PDDoIB76NCh6Nq1q+q23nrrLTQ2NuLSSy817TlSG2nBnjz4lILVSANasx5fTySButUnD3qsKsUhIiIiJVvWbLe0tGDUqFGora3FBx98gD59+gAA6uvrMXHiRBw+fBjr1q3Dueeeq7ud0tJSPPTQQxg9ejRKSkogCELQ5ePGjcOzzz4bcn/279+PoqIi9O7dG2vWrNG8HWu2o6e1YK+9hrBEumAw3Cy11sCbpUuykD/YFdG+W7GfREREFB1b1mxv374dNTU1GDNmjD/QBoDMzEzceeedaGlpQVlZWcjtrFq1CgAwZ84cf6ANAEVFRTjvvPOwfv161NfXG97OddddF+5ToTDl5jiRP1iZ3W2vVnVajx+KvMVfqAA2Fn2uo6ktJyIiosjYMtjeuXMnAOCSSy5RXFdQUBB0Gy1nzpzBnj170LNnT9XSkIKCAjQ3N2PPnj2623G73Vi3bh2Sk5Nx7bXXGn0KZIFwA9r2Fk6gHos+15waSURE1P5sWbP99ddfAwB69OihuK5z587o0qULqqurdbdRU1MDr9erWWoiXf7111/7A3g1GzduxOnTpzF69GhkZ2cb2n+yTm6OM2HqjIsKU1FQ4Gq3PtfRLAIlIiKiyNjyW1Yq7ejUqZPq9ZmZmTh9+rTuNqTrMzMzVa/PyMgIeiwtpaWlAIBf//rXurcjMkLe6i/SspVIcGokERFR+7NlZtsuqqur8ec//xndunXDkCFDYr07FOfssDixvbPpREREHZ0tM9tSNlore11fX6+Z9ZZI12tlrhsaGoIeS81HH30EURRRVFQUtMCSKFx2WpzYntl0IiKijs6WwbZUT61Wl33y5EkcP35ctZ47UPfu3eFwOPz133LS5Vo13a2trVi9ejWcTieKioqM7jqRKi5OJCIi6phsGWwPHjwYALBt2zbFdRUVFQCA/Px83W2kpKTgwgsvxOHDh3H06FHV7SQnJ6N///6q99+6dSu+//57XHrppcjJyQn3KRAFiUWrPyIiIoo9W37TX3zxxTjnnHOwdu1afPXVV/7L6+vr8eqrryIpKQnjx4/3X/7dd9/h0KFDirKTCRMmAABKSkoQOLuntLQUhw4dwtVXX61ZRvLRRx8BYG9tMgcXJxIREXVMtpwgCfgG20yfPh0ulwtjxoxBZmYmysvLceTIEcyaNQt33HGH/7YPPvggVq9ejaeffhqFhYX+y1tbW3Hrrbf6x7Xn5+fjm2++QXl5OXJycrBq1aqgce2SH374AZdffjmys7OxdetWJCUZW0fKCZIUSqQTKomIiCg+2bYbyZAhQ7By5Uq8/PLL2LBhAzweD3r16oWZM2fimmuuMbQNp9OJ1157DYsXL8Yf/vAHLFu2DJ07d8b48eMxa9Ys1UAbAFavXo2WlhaMGzfOcKBNZEQi9QknIiKi0Gyb2Y5HzGwTERERUSBb1mwTERERESUCBttERERERBZhQbKJmpqaACCogwoRUaTOP/98pKenx3o3iIgoCgy2TSQNyikuLo7tjhBRQuD6DyKi+McFkib64YcfsGnTJpx77rlIS0uL9e4QUZxjZpuIKP4x2CYiIiIisggXSBIRERERWYTBNhERERGRRRhsExERERFZhME2EREREZFFGGwTEREREVmEwTYRERERkUUYbBMRERERWYTBNhERERGRRRhsExERERFZhME2EREREZFFGGwTEREREVmEwTYRERERkUUYbBMRERERWYTBNhERERGRRRhsExERERFZhME2EREREZFFGGwTEREREVmEwTYRERERkUUYbBMRERERWYTBNhERERGRRRhsExERERFZhME2EREREZFFGGwTEREREVmEwTYRERERkUUYbBMRERERWYTBNhERERGRRRhsExERERFZhME2EREREZFFGGwTEREREVmEwTYRERERkUUYbBMRERERWYTBNhERERGRRRhsExERERFZhMG2iRobG1FZWYnGxsZY7woRUdzjMZWIEgGDbRMdPHgQgwYNwsGDB2O9K0REcY/HVCJKBAy2iYiIiIgswmCbiIiIiMgiDLaJiIiIiCzCYJuIiIiIyCIMtokMqK1rxY6dHtTWtcZ6V4iIyAb4vUBGMdgmCqG0zI1hI0/g5hmnMGzkCZSWuWO9S0REFEP8XqBwMNhOEDzDtkZtXSsee7IBXq/vv71e4LEnG/g6E1GHxO8afi9Q+BhsJwCeYVunutrrP6BKvF6gpsarfgciogTF7xoffi9QuBhsxzmeYVurRw8HHLK/EocD6N6dfzpE1HHwu6YNvxcoXPxkxDmeYVsrN8eJxx7O8B9YHQ7gsYczkJvjjO2OERG1I37XtOH3AoUrKdY7QNGRzrADD4I8wzZXUWEqCgpcqKnxont3Bw+oRNTh8LsmGL8XKBwd868kgfAMu33k5jiRP9jF15WIOiR+1yjxe4GMYmY7AfAMm4iIrMbvGqLIMNhOELk5Th74iIjIUvyuIQofy0iIiIiIiCzCYJviDocqEFFHx+MgUfxgsE1xhUMViKij43GQKL4w2Ka4kYhDFZidIqJw2P04yGMakRKDbYobiTZUgdkpIgqXnY+DPKYRqWOwTXEjkUbk2j07RUT2ZNfjII9pRNriL0qhDiuRhirYOTtFRPZl1+Mgj2lE2thnm+JKogxV4OhjIoqUHY+DPKYRaeNfAcWdRBiRa9fsFBHFB7sdB3lMI9LGzDZRjLRHdqq2rhXV1V706GGP7BcRJS47ZtzNxOMpRYrBNlEMWTn6uLTM7V+wJGWZigpTLXksIiIgcce583hK0WAZCSUc9nllZwAiaj+Jfszl8ZSixWCbEood+rza4YuHnQGIqD2UlrkxdITvmDt0RGL21ubxlKLFYJsShh2yD3YI9gFfZwBBCL5MENgZgIjMU1vXikefaIAo+v5bFIFHn0i8jO+Bv3gUl7HTCoWDnxRKGLHOPtgh2Cciai+7d7f4A22JKAJVVS2x2SEL1Na1Yv6CJsXls2emJWRtOlmDwTYlDDMmq0VTAhLrYF++L2pfgonws6cdynSICIAghnd5HNq9u0VxXAeAvhe4TH8sHtsSF4NtShjR9nmNtgTETmOU7bQvZrJLmQ4RAQPyXKrlann9zQ9EY6G0zI37/1+94nIrjqU8tiW2+P7mJZIpKkzF5o3ZWLokC5s3ZitaM6llDmrrWrFh4xlDJSB6mYdog30zsxqJOGCCZToU7xItc5mb48TjjwQfZx5/RHmcicfnLT/eSAQh9LE03OfLY1viY59tSjhafV7V+qQCUD2gAm0lINK2jPRZjXSogxU9XGMxYMLKoQ96ZTrxfBJBHYOVfZpjOWwl1HEmXvtTqx1vAOCF5zIwcrj2/kfyfLWObSvedWPuvRmR7D7ZjCCK8spOilRlZSUGDRqEXbt2YeDAgbHeHQpQW9eKYSNPBB3QHA5fHbPWX4DDAWzemI3cHKfm/aXrrdg3M7bdnqz+Uk2U14mMS5RjqpWfXTsHs/H8NxvJvkf6fNXuB/iy6Fs22f+1otBYRkIdglbmQC/QDvyp0MrFj3ZaWBmp9vgZNBFLY6hjsOpv3O7lB/F8bIvkeBPp883NceKGYuUJUqIsaqcEKyPZu3cvFi5ciKqqKng8HvTq1QvTpk3D2LFjDd2/vLwca9euxcGDB/HDDz9AFEX89Kc/xS9/+UtMnz4dOTk5Fj8Dsoq0YDBUZlsQfD8T5vV3BR1Ute5vxiIZK7fdXtqrxCMWpTFE0bLqb9zupVXxfmwL93gTzfOdWpyKt5e7g76P4um1In0J8y7u2LEDkydPxpdffokRI0Zg0qRJOH78OObOnYvXX3/d0DY2b96MgwcPol+/fpgwYQKuv/56/Od//ieWL1+OMWPG4O9//7vFz4KsopWlUFvcM3J4quKgamVW1U4LKyPdfnt2P8nNcSJ/sMsWwQSREVYdP6z8uzPjuJIIv0aFc7yJ5vmqLTaNt9eKdIgJwOPxiEOHDhX79u0rHjhwwH/56dOnxdGjR4t9+vQRDx8+HHI7brdb9fIPP/xQ7N27t3j33Xfr3n/Xrl0iAHHXrl1h7T+1n3/Vtog7djaL/6pt0b0snPtbuW+hfFTaJPbN+0Hsc+EPYt+8H8SPSptM3adwtm/1vlDHk2jHVCuOH1b83Zm9TSuPm3bzUWmTeEF/32t3Qf/wX7uO9Fp1JAmxQHLbtm245ZZbUFhYiKeffjrouvXr12P27Nm47bbbcO+990a0/fr6egwaNAg///nP8fHHH2veLlEW81B8sHrxUaQLhFjiQWbhMdUYM//u4nlRY6zxtSMtCVFGsnPnTgDAJZdcoriuoKAg6DaR+PTTTwEAP/vZzyLeBpHZrF58FMn2Y1XiEY99fIn0hPOZNvPvLp4XNcZae752PObFl4RYIPn1118DAHr06KG4rnPnzujSpQuqq6sNb2/Lli346quv0NTUhH/84x/Ytm0bunXrhnvuucesXSaKmtWLj9S2DwBfbG9G/mD7TIizc+szokjE8jMd74sarabX07y9Xjse8+JPQvz11Nf7xql26tRJ9frMzEycPn3a8Pa2bNmCRYsW4c0338TWrVvx85//HEuXLsU555xjyv4SmcHqxUe5OU7MnpmmuHzxEjfeWtZoymNES6312aNPNGDDJjczPhSXYt3OLxEWNVol1Eh1tddu9sw0VFd7TXv/Yv35oMgkRGbbbM888wyeeeYZnD59Gn/5y18wf/58FBYWYuHChbj44otjvXuU4MKZBmd1K7wL+rgANCkun7+gCVePSon5F7Daz7aiCMy9v4EZH4pLdmjnZ6cWm7GcjinfD7Ugt6AguHwn8LXbf8CD+Qua4PU2mXY8ssPng8KXEJntzMxMANDMXtfX12tmvfV06tQJF110EZYsWYLU1FQ88MAD8Hg8Ue1rR8X6MmNCZU7UWFkn3aOHA4KgvNzrBaqqWkx/vHCptT6TMOND8ag922jqMXJcsfq4Hsnx0Kp9CqceOzfHie7dHf8OtNtua8bxyC6fDwpPQrw75557LgCo1mWfPHkSx48fV63nNiozMxP9+/dHXV0dampqIt5ORxXJAbMjsuPPg7k5Ttw7S1lKAgD3PVgf8/dS/rOtHBd2UbyJlzIOq4/rkRwPrdyncINcqxZLxsvng4IlRLA9ePBgAL4WgHIVFRUAgPz8/Kge47vvvgMAOJ38QIfDjgGkXe2u8tiyC8DNN6Zjzuw0RYbbLu9lUWEqNm/MRslzmcz4UEKQPtNLl2Rh88Zs25VCtcdxPdxg1ep9CjfItTIDbffPByklxLfQxRdfjHPOOQdr167FV1995b+8vr4er776KpKSkjB+/Hj/5d999x0OHToUVHbS3NyMqqoq1e2XlpZi79696NGjhz+LTsawjZQ+6SfPt5Y14r4HGhTX2yVYvPnGdDz/bIbicru8l7k5TowckcKMDyUMO09KbY/jul0yyXLSZJJQE0raYwG71Z8Pln+aJyEWSCYlJWHevHmYPn06Jk+ejDFjxiAzMxPl5eU4cuQIZs2ahZ49e/pv/+KLL2L16tV4+umnUVhYCABwu924/vrr0bt3b5x//vnIycnB6dOnsW/fPhw4cADp6el46qmnYvUU41JtXSt+PN4KQQg+MNklgIy1wPZNauwWLA7Ic5ne1srsxU92WthFFAm7LAjU0x4t7qRgVd7iLlQmWWufon1dpcx5YLCttkAyUDwfj9he0FwJEWwDwJAhQ7By5Uq8/PLL2LBhA/4/e+ceHlV17v/v3pNJZpIQAudQEBS1KvXHNYGC2vTiqRAiFz2CWi7hjmhbNQQRqAoIIlgQI8VzqogIJAStgLUIBIJ3cxQqEAU8Ty/WBtSTlGIh5j6Z2b8/tmtnX9bal7llLuvzPOdUJnv27Nmz9rve9a73/b4+nw9XX301ioqKcMstt1i+3+v14r777sORI0fwwQcf4MKFC0hJSUGfPn0wY8YMzJw5E717947CN0kM1A+qIEBxuGPNgews9FueNNY9kYmC0WnRuygLnE5+VkTKmPfq6Ur68cWJT+LFwQmnLTBzgp04q2bXFI77GqwKSDzaI7vKKxz7JES79liBtxaWYbWsXfdEJnJyUiL+sMZqZEh9XTU1Acy+q555bCy3+A1Ha2je1phjh2SyqaxnYu2aTOTmRt5uBoPeFji1vZFYXNCuKRy2JhI2K1bnqiNHfdT56cXNWTHV0CyeSJjINid2YEUAunePvEGxY7ydGrhwGMQNzzTi+c0tSnR/5E3mBqu4yBtTxldNOCI1XCuWw9HCeiYWLm6I2Si32hY4dZwjFT3V2yentqa2zo8TJ9px8WIAXbuKykInXnb2zLA7l/EuouGHO9ucsNNZD6od480ycCwjFA7nvfiBehw63KHPHggAhyrN9doHDnDbOreT64gluDHncLTQnglCrG/jnzzlw/KVHfnMdq7XrhMcql1zYmt272nRfA9AToFcsUy2++HKwQ52oRHKvXDi3NtZWMTTfBML8JmNE3asqrA7q+kAy8Bt2dpE1Wa1IyVlpet68pRP42jbgUwETjRj403LnGvFcjha4lUzfveeFkwurDeoc1hdrx21ESu7ZmcusWtrauv8BkcbkGuNlq/ssPvhUAEJRjklFBsfjCyimbxgvM03sQCPbHMiAisCEKmts9o6P/72udGpVRtvloF76ulmakTGKvLCMmD9+rkwaKAcmT523FmXRXJPANiOfMRrMUs8V+pzOEDk1HSqP/Zh4aLGiKg4hfOa9Qodaqyu1yp6ambXAKC0rAXbSls0hfesucSOrampCTDl/CTJPMWNdk/N7rPTnb1QbXw4izvjdb7pbLiznaREYwtI/6CG8pCaXS9t648wfmyqcjzNwOllCcl1nTkTQHo6/Vq83zZUZBmwyYX1yrbjsKH0R+yaa0R89llAmWSKi7wYOMCtTARHjrIb3Oi/fzznP8djpT6HA0RWTacg34XGBphu40fzmln2l2Z7ANmukusNVm2EZdfKdshOtvpvduYSluNIru3yy0XqfEDw0hvpUu8pYPzt1PfZaf53qDY+nGl78TzfdCbc2U5COkteKtiH1Ox6WVt/hL372jB5kg9NTbLB0Ru44iIvSjY0U41QTQ19S6+5Wf5fVo4l0V8lEe78UW5DjvZnnwVQXpqF5mZQIy00wy8IdOOYnm5cNPD8Zw4nckQjuhfunZ9gr9nM/rKcuPLSLAwa6LY11xAnmKSEEKecFRzRO9oEq7lE7/TTrm3FsgwsW2FsLgZ02H0799TOQsDJ7xuqsxzO4k5ebxMc/O7EIaHkPEejzS7r+oJpX2t1vWZbf+T4yYX1Sm4ZACUPrbw0CwP6u1Fc5KXm81ldLzFg+jbm6s/dvacFk+40hkQCAdl4s3L/zp1jfy/1/d29pwVTptUbHG2e/8zhRI5IdSvU285w5AcTgrlmK/tbVeUzBAQeXZqBQQPdjuYadQ7wyNEXsG59I86dC2B6oUdjm2dM81AdbfL3vn1F5R6ePOXT2El1jvGWrU3MhcdLO7KY57Z7T/UEAkB1tTGl0O7vG44al3C1eOf1NsHBI9txRqhR6UhvAW3Z2qTkQOuvL5jVtdX1Wm39ATDkY1dWZOPsWb8hwq1O4yBREHXkm5ZTmJ7B/mwS4S4vzXIUCSBpMbTzqbdQiZOvd7RJVInD4USGSET3wr3jqI/kBnPNVg46LV+b5FQ7URtRO76SBGzd3oKt2+WiO0EAZs3wYHR+Kr74IkDdTSROflWVzxBZ1tvJQACG3Uz1tY0Y7sbK5R3zlCAA0wvpv4OZgoyeB5c0oLFRsvxNWWk34djpCFfaHq+3cQ6PbMcR4YhKm0VrQ1UJ2bK1CetLjMWG6vM5XV3biS6vWEaPLtMIBIDqj32G+1iyoVk557r1jRg5Wo6ClGxoRnGR13C9JFKycBF9y1H9eV9+5cf0Qo/mGiVJjgrpMSs40m+hShI935y23RnrREqhhsOJBOGO7oV7x5GmFhHMNZvZX5ozLUkdEVyS3kZ7rxpW3rf6nFu3y4onCxc3QJI6ziuKsiO+sywL6Rmyagjtmmh20uzayDw1a4Zst7dub6Gqbujvqdk8ZOc3tVL5oEXCO8t2hnPXJRngke04IhxRaVZ0WR0RCCaqUlvnx1NPG7082vU5XV1PL/QYqs5pK/7q6nb85bN2PPscW4ZIFAEpIDgqvCnZ0IzKijRmlbwZggCDqgDQISfVr59LySfv1dNlWnA0Y5pHifaYfb9w5s5Fo5A2XlpUczhqwhndY9n26up2dOvm7Pkzy812es1Wu5G0qO6DSxrw7ntt2LuvzZBiUlzkVWphzArX9ajPQ5ztpQ+no2uWiP+r9WPKtHpb9pigr9dhLTzU84Gd3GuvF6bXYjZfB5NTz21n/MCd7TgiXFuXeoMLQNOGNphiH1budCjOn96QzJzuQeFUD1NaqWC0Czl1Kdj0PL2Ahmw15uamUO/j1u0t1O+gN5BWkRj1OWlRFYIkQdGnJYYyL8/NLDjq0UPE9jLtdxME+f/UxhaAptAoWMxSgsIFl5HixDPh2pZnFQM+uKSB6Ug5UQhR2zCn18xy0Ikjri9QDwSA1/a2Uc8l25NmzfdhnccMSQJWrW6yfTzNTk6c4MGYm9NQXd0OCRJyc7Spd06CW+fOBfDp/8pdJ82uyWw+DKbTJbed8QNPI4kjwrl1qd4CCkexD227EQi+7TjNkGwr7Yjqsrbb9PdIDzFE48emal6//roUppHUG0jWd1UfP2uGB2vXZFpOBvqUG6DDYSaQgiPa779iWYYmLQdAWJoN2EkJCgeRKjTjcOIJVjoCK63ELN0gmEJ0NbS0BFbKwMQJHqz7dYb+FFTUgQf995k4wYPDB7NRMDrV5AzG89lBFIEF871YuyYT69dloLw0C5deKtflVFX58OCSBixc1Bj0fXzokW8waWo91q1vwqbNxoCNOuXFbL52+rtx2xlf8Mh2nBGJwgQnMnMs9NuNgiAbuNkzGWLVFtgpzGGt6CdO8CA9XcDCxQ2a95PGBIAsCajmgw/bTQtv9Gkw0wvZKR1kYVBemmVZvEn7fseOa3O5jx33KREtsyhTuFoAO0kJChUuI8XhyKif7fNf+w31IHbtXygyb8GkJeTmGHfj7BAIAAcPtWF0fqpy3TOne1Bx0BgVnzfXg81bOgrDrWzqnbenYcJtaWhuBk6d9inpIupiSVrhpNP7ePKUjxnFJzy5NgPdu7ks52unvxu3nfEF/1XikGgUJkgScKLaWdGFuvjx8MFsg6Otj5jQIijktfR0OCrMITnXBJIqYvf9kiTnRKujxrNmyNEW2mQzTVfwqIcUKs6Y5izt4ssv2w3G+7W9bTh5qsMBJ78/AM39C1cLYFZKkNMFmB24jBSH0wF5tokDq8bK/qmf82Bk3oIp0qyt86O0jJ62Z4e1TzZpIspNTfTjbrg+Vfk+O8uyTHcWAeCV3a3o0UNE376iRnlEHV1nFU4ePNSG2jr/t12J/Zrj9Vh1CCY1QnYDY6zfjbXbwG1n/MAj20mCWaEby7lauKjRca4uKx9QHzEZPzYVe/e1GXKNrY4xK8zZur1Fyek2ixKcO0efGUbnp6JwqsfWrgFRQWEVSpKJcVqhx5BnLYrAw0vS8dhq48zy+72t1M87caJdI+dHi0D160e/XlbnM9bkSpMqBIC75ngMxU3hgMtIcThanBYm0iKaTnOzneYMq22QHVgRaXVE2WyXVf191PeGBlFF6dZNdLwQWPtkE9atN+aDEylX9U4hq0MwuW5JAhYubnA0j+p/N7PdBm474wce2U4CrOSEzHKQw5GrS3PqXtvbZnDy1LJNgYCc6lFemmVY5ZM0Dj3qNBFANkTlpVlYtDAd5aVZyMtz48hRH774kv5diGSe3bQPdRTigWJ6YxxW9OHGG1OpkauPPqJfW25uh1FnOclW30sPa3JtbobhmvNHubF5S0vIueBq1NEaLiPF4Wgh9mX9ugysXZOp6FdHKqLpJGfYSpFJbzuAjtSNgnxjDwCnucZqaT4mgmRZXyMIxh1Ucq009Nc5aKAbt47X5pn/+EcpWL8uQ3OeYOdRO7sN3HbGBzyyneDYyePVR1H0Tf9AAAAAIABJREFUBAKyNnW37OAk4Oyod7A+l3RZ1DNNJQeo5vzXfpw8JW9Hnv6UnatHa29+6rQPc+Y1UyMILIhD3beviEt6uSCIEvr0luX8iBNJiz7U1sna2yTqLYpg5oH36SNootosJ1mA4CiHzyznb8RwN1POKhxV7/EmWRUNCURO4hHquKFJsubluXHppS6Ul2ahuRlhi2haRdPV38XKpj+0xItu3UT06e3C5MJ65XVJAioO+ah25/z5AM6fN+6ySpKc2jE0N0Ujkwpoi+bVCAKQM8RtOreR73exPqCoLllBs6erV3VBz16NeP7b4sj33m+nRvHVjrrdMeFkt4H8PunpMNwnTufDne0Ex+7DqtaqJnJTBLVWdDCOkZMuW2rMHEWSxqGXi2I1mdHrtKoh+q/q3D4zh1Jv1Myc+hnTPJhW2JHaAmgdTdIdrXCqfD9pC4gvv5RQvLAeJU/KbYRf+p0xVC0IwFf/5zfc4/FjU00Nrt7hV0+u5JqPHPU52l62It4kq+JtYcCJDUIdN7TnZPnKRoOEHS0YESwTJ3jQr58Lx0+0Y2huirLI13+X4iKvqU1ftVqW95t4WxrVib19Qhp27WnVFDySdAuao7r2yY6UO/K9L73UZZpG8ut1jZh0pxd5eW5UVmQbuu8WF8l/G1VwwbajTdtBOHnKpzja5LPfedeYyy0IwAcftmHOvBbbY8JuESQtpYfbqtiCp5EkOE62BmWt6jTDFiUQ2naYlRwfDZph0xeJ5OW5bXeOtOKSXkbDTdvaVKfkTJpaj9l31WN9CbsAR915rLbOjwMVrYbWxCQ606uni1lQeajSh5On5P87VGnsPClJoCqI/OF1bXElYcvWJowcfUHRFp81w8MspDr9qfH9Zgshq45mTgs5O7O7ZLg7+3GSg3CMG1YhdyTH4u49LZgyrR5rn2zClGn1it2iddwlDjeLQADYtYdeg3LddSmorMjG0ofTDZKAVo4v+d60Ino1hyp9Strb/gOthu67JRua8coue8Wds2bIKYnpGcCBilaNBCPplWCFJAGbNhub5Jj9fjSZWn0AhZXSw21VbMEj2wmO2dYga4tTI0F1PmCQ0AsmqknOefBQmyZKQWPxwnTk58sG5sDBFkAS8H+1fkO3L7PIhhMkCRBEyTKC4KRzpBoSkSKfRfs7cTQHDmA/kidOtCNgYtRp55YkYNLUeqxc3hHhIBra6mO2lbYo0XU1J0/5NMcSWPrpdqJ5TiSrOjuqHI6urZzkIxzjxs6OoJNzWqW0sBYI9/3CQ/0uAwe4UV7qNnU2yQ6fvuAxZ4gbVVU+PPa4+VzAQl1bYmWTyeKA9h2e3WSv9qS1TcKkqR3pMETatmSDvfQTs2tT/340GVa9TO3efW24/z6/8h6zlB5uq2IHHtlOAmhyQlZFk4oElYmEHgtWJLJXTxdG56eaRqNFEcjPT0VVlQ8jR1/AwkWNWLi4QRM9Js6rVWRDD+tzRVE2/lZFR3Y7R9Iw6yQJyNuLowouGBY2av51IYCuWcF9/vKVjThQ0YqTp3xMDe3qau3W5+49LZoJRs3AAcata7vRPLsFXnbOF+mod6gNQjjJidPdIBq0Rjd6G2Z3h8nK3gOgSvgFAsCGZ4zHks8dNNCNBfMZckfoaCijvm5JAl7+XYsSgAgG8vlkblv6kHk/B7t2mzVHlO/URuglCZo5KVgEAfjsb+zfiLVoI/KEgLnAAbdVsYMgSaGsyzhqjh8/jmHDhuHYsWMYOnRoZ18Ok9o6v6Y9OyA/lJUV2UFHK50cq4+sqrl1fCruvy/dcH00Zs3w4MorXJaRDVHsaHd+5kxA0+RAf421dX6mjBLtvoULJ81vIvU5giB3pJw4wYPaOj9GjqbnMgoCcPigcawcOSpv2+p5cXMWNa/U7F7bOV+0ot6dHV1PZuLFpqph2YkHioNr8qV+TmgFk7SxqB+z+sW+3t6bPe961HYCkNMqaEECclxentv2ue2g/t7q+hlWYIBci9XnL16Yjr59RfzyfnbAI1LoG+wAHfOWujhdjfo+2MnZ5kXenQtPI0lCWKtlWZfUPK3ErPLdbuEbmXBoFeB797XhRz9y23Jot5W2oLIiG5UV2YpqRnOzHCUm3cZIMQ9pljBiuBsjhrsx5uY05vdhGWUr1ZZgCaZ4lPCzO9y45mo3Vq2xtx1rNuGodWRZ2usAMHO6hzoG0tPpKi9mRa5mRt8s3SSaRZZcy5bjBNYOWO/ewUUY1c/JxAkuy7FIezb06NMLzJ53PRNudSvtznv1dAEC/Y2PPOTFxAkeHKhoDcnRXrUiHX36pCj2nXxvJzrfw4a68NEx9u4X2VHt1dOFW8e3WXaFZDFvrgff+54LkARcuBCg9lKgwUovNEuVUds8tY3S3yeABwxiAe5sJyhmq1iaEyMIUFRI1BJT6nOEU6Zo9sx0XNLLRc0Hp0nY0SDn1muMjhjuxs/u9ChRbNmpb9ZEZGjfZ/eeFkXdRB/lJfdBb9QOHmpTigyDgSwGaDmFdnj5FR/uuD1MVaLouKe05hKAfL203G5izPWOdij6v2b1BuFWSLFzLdzJ5tiBlWu9cFEjGhsQspNjNRbtpLvpF8FOFKN2/96H3b/3mTbTEgTgxp+kKXYhFCrf8GHZI/aKAlkcP2HuaKvt1LCh7qCdbZ8PKMjviCQ//kRT0IEUQZClbImaCq3eSW3zWOMiXIEJHhkPDZ5GEkZiZcvTzipWLz8HGItYyGt2V8K09BCz9BSzdJaqKp9G1o+1zcY6Nzm/fvtSnQKhNh4AcFP+BcM5Hij2MlNO1J9jp/BTTf5INyZP8sLrBb740o8jR9qx+9XWoAxzOFNQ1PdUvfggn0NbgAAw/I6CAOwsy9LogwcLLd3EaSoUJz6JFZvqFFbUNRpjlPZs2LHn+nlj7mwPNm02LyBk2Z47bk/F965Jwepfmzub99/rgSAAbW1AZgaw7im2bvaC+V4M6C93mSwta6H2JKBxx+2peGWX0Xlevy4D3bu54PV26FIDRlumv46xN6ciNycFq9YYu0wSu0fOp077IZgtalgBDhL8CsbmOU3vo8Ej46HDne0wEgsTgxMnhDgx57/2M/WpCVbOU7B5imYPcW2dH9Uf+wBJQE5Oiu18RQIrl3D92kw0Nkqac2VnC/j6a+tHgZbrSHIGabl1q1ak45OTfvxuV6vhPHPneDT6rKFw5+1phs9wCu2e1tb55cJJQVKaROgXavmj3Dh4yFgQ5sSYBwOfABKfWLCpwcKyP5F+LgD6Lp3dVEB9XUukEQTglnGptqPJTtPuaLaR5EP/+c9+jQ1hNRYD5Bqh7t0FTU8FVk2LelFDS+/4zcYmw/clC4qzZwPU6yVBKKc2L9TABA9shAeeRpJgOEnlINtOtXXWW4iSBEwurNcUxlh9LmBUrdBvRbG6K5JjyJYcYJ6vqI+01tQEcPEi/QtduBjA42s6Ii6BAGw52uRYci/1zt74sanYu69Ncx8eWU6PdgcCwKbnQ295TvjJj90hOduCIE8++sWUrL3O3r6Vu7uFrrwQDDyXmhPLECUnWs1BNCBOH4lqd9h7WaVEnQ6gtp99+4pKJ101Uyan4aWXg9t9M0OS4Chtw+nnv7LbaBcDASidLdUa39vLWqh1J+WlsgyUWubQTO6QnG/5ykbsLNMurmhyfuR9rAUOUSAZnZ+K8tIsQ9MhM6w6g1rB5U/DA3e2EwwnGsYE2sNIk6pTF9DZyQPXfy4rEsnqrkhbubNyrWkpMSwZp65ZYkgTRlNTwNCcJhCQizs3Pp2Je4saoqIsoqaG0RCGYJVqMnO6x5bhtpsPGkquthN4LjUnVgnVyQkWVo5uv34uQyT30aUZAGCI7tKe8Z0vtSra0mbzRKxh5RSrCQTkCDZpgEPu0Z//7Dd0K7b72foglZUuNou1TzZh3fom5bxOdvNCCUwE41NwjHBnO8EI1sDrH0Z9zjTBLEqu/9zphdp0BKsijdo6rUEjkQH9MepW6enpMERaCepcY/V//1+tPyQFEJYzHQjITm+0Jx9BAIZSomgEkn/5/AvslJUB/VM61AVMsCqkIg2Jgm3jzgtwOIlEZ+y+sCKRk6bWa2whscH6Do7bSo3RXUD+98ABblRWdCg5vfy7Fsu87niCFIAXTvUo3xEAs6U7rZZIDwlS9evnUuYsM1tttcNMcFroGGxgorMWjYkGd7YTECcGXu/gqCWm+vVzGbqDiSLg9cKwDan+3LIdcvHK1u0t2F7WgkeXZuBvn/upE8Aru1tw9XdTkJubgrffbqMa+LffacOVV6Tg9KfGPEI7xYF6B5y0GlZHaPr0FnD2C3teMuvzRFF2eqOlmU3IH+VGjx4iUyLq2u+5sHmLeW74wsUNilPetauIKy4X4fWKht+YGF7aQkwtn6WG5USrX99/oFWRguT515xEIpy7L3YWpGYLYlrwhHYMqwbk1Gkf+vZNU87Ttavz6Ob116XgwyPt1gd+y3evEDDs+25qkaNd7NhkogwFQAno1NQE8PW/jHMX4boRLnx4xLqhFlnskM+hpRyKIjB4kAvVH9tv0KVOL4mk88tT9kKHF0iGkXgq5qmt86O0THaG7aqW6I0Eq6DOrBI+Vli0MB1Dc1M0eqRbtzUyq+GtUBfDhLOBg5PPH3mTG4cqjfnToZ6XpcBStqNFs906vdCDaYVaDW5WWpA+9YfmuPMCHE482dRIY1VMrnbCnWhQ03hpRxbefKvNELUmXSzJc3vrLan4/WtGJ/imn6ZgTIEHf/pLOza/0OI4QEK7Hn0Beii7kyyi2VxsZ1kWmpvltMSTp9rR2ibhxa3B1d3Ec4CCtoBMxF1O7myHkXiZGPSSbgQr1RKv16i4oX8PS2Yo0qiLgeyOaH0nsoqDbUpOnJPPvfsuD278SSoGDXRH5Ptfdqn9qHskIL8xAKpRJDsZ+gr8EyfasehXDYaJ9pkNmbhvfoPlRBkN1YZokYiTRzSIF5saLHbHhZVMKs0JP3nKR+2qSJxUM2d1/dpMdOsmBm3LQu0fQLuek6faleBQLAZwnFI4NRU9v+OiNncLhngMUNAWkAAcK67EAzyNJMkgudOsnGMz1RI7jURYzVAiHTEYU5CKn/7UjT69Xcz2tnpIztvF+kDQk4IkAc9ukvMWWQ0enECbACPlaI8bm4r9B9osv3cgAJQ83Yh9B3zKgmbB/A5Jx22lHSkqJM8eoP/eksTOeVcjCIlTgMMlCpMPO060k3Fh1vWXVQvTowfdFs+d7cEN16figw+NkWsFQaJ2hLVLIEDvEBwsDyySJRQFARg3xo3X94d3B68zKNsRfFoMjXhTCKHVcS1f2ajsnJDXItUZONokxmzGsY2VmsSp07IRI/JQtXUd+WPE+KpR53DX1vlRVcU2gix1kHCw70AbHniwEX/8yIdHl2bY/iwyKYQafSGG4u13nBtQ9bWGe1vUjP0H2lBc5IVowwq8vt+nkbxaX9KMDRsbUXHQ6KxbKRTYmYAXzPfGvXEF2IXB6ueKk1js3tOCUQUXMPuueowquIDde4wOrdW40NtfkoetRhQBCRIzAMJqwb5pcwu8XuD5F9gNZL76KmCo13FCsE76jT82j/9JEhLC0bbLZZcKtueyeFMIofkikmScA8l4jnd4ZDtJUKt4mBnCkg3Nyv/Stnb0xZLjx6YqRtnsvCTFYNjQFHx0jF4co9eFDcZYry9pxpTJabaPD2fEnUS5nUDks5zCKrJxQiAAnDrdjvJSOXdw58vNjnK+I6FCQLafzRohmRFr6Rpcoza5sNsa22xcsNJCiou8hiLi3Bx3ULJs+/a3Mu3OlElphk7A0WL8OA/eeS/60qlmkKY7e19vQyDK1/XlVxJ2lmXh9KfteOxxbYqjfp6UJKCqyoeJE+LDrtAKedU1AYR4W0SwiP9vwLFEHWmZMq0eN1zPXmPpI71ksli+stHwUGx8OhN/eL1N87CbEQiA6mjf9NMUPFDsVf4tScAN16cEHQkv38meSPR0plEfne/GQ4vTg7qGjU9n4v770vHQ4nRMuC2VeVxBvnnO88FDPkwurMfZs36UPJmF//pNZkg7EKIY/A7G4oXpqKzIDtrRthNRjDasiGQiTB4cI2ZOtBrWuPB6QXXWt2xtQsmGZiUYUVzkVXoUPLo0QzmXOjhSWhbc+N+x03mRnv67BGPTBAHIyUnBgvle64OjyIL5Xqxe1QUDB0b/mQ0E5K6Tk+70YuVy7Y6tfgeRSAzGy64ZbeyuWJZBHc+JEJjgke1OJBpROFqk5YMP2y1bzaphyUOdOt3uyKiyPvPNt9rxxptaJ/x/PmiPaNpJLHDwkI/afdEOHx1rxy/vN7aCViMIwMwZXhw6bMy1V6NuVvTHj5z9pmqIxjZLo119XeRzCSzZQLvYjShGG65Rm1ywZPdOnfZpin1pEpqSBGpaViAATaSZyJeOuTmN2oW3qspnqogkCMDYMWko3RF8x1n9+Sbelkbt1OiU0rIWTCv04JtvpJjR737q6WZ89jc/PjkZ/VQG9cI8L8+6WFy9a6b3L6z+3RmwJAUTUWYw4ku11tZWlJSUYOTIkRg8eDB++tOfYvXq1Th37hzzPb/61a/Qv3//SF9apxKtKBwrL2rmdA81srJgvjGHlxatFEXg3//N/vARReCuOfTiHycdvgjx5IhH4lpf3GZvvPToISrasWaQYqttpcFLH+bmpiiT/86yLOax+nEgCME7oCS39cSJ9pjN9Zs4wYPKimy8uDkLlRXZvDgygenV00V93ko2NBsijnrnSZLkYmO9/aXZD/3Y7tXTpTjzrAJ4wi3jZOWkmdPDMw4lid4SPZjzbN3egpGjL6AtvLWDISFJoMobRhr9wpyVg69/T9++osG/eOiRb0z/3Zm7gGTs6vs56F+LdyIa2W5vb8ecOXNw7NgxEIXBr776CqWlpXjttdewevVq3HTTTdT3JrIiYTSjcKxWq+ouWV4vNHrTXbNEqhyPvrtjU7P5b0Rk3tLTReXcb73Thr/8JXQHaExBKvYdCK4YMdpDa+BAF4YPS8GWIDVUg0WSgOqPfRBFa2+fFFvR7s2QwS58/Ilxa1LfjW7KtHolv5SlhDBujNvQyVKSEJSKi17NQf95sZSuwdvKJw8D+rsBaHOeaXn6NOdJkoA7JqZh155WS3k+L2UNbVUADwB797Xh/vv8mFboUaT0OgMBAM0Uk0VHImI1/yxemI5cXf8HglWOs9lc/drejrmS9u9o7ALGQiS9M4noTFReXo6PPvoIl1xyCdavX499+/bh2WefxfXXX4+LFy/ivvvuw44dOyJ5CTGJ3by+cMDK6SOT/4jhbgwa6NasImmRuLw8t8FIWBXRSBJw3/wGnD0rtwHfsrUpLI42AOyvoDva11xjPqQj7WiPG2Pc6jt50h91RxuQjfDCRY2W2uEkspyb4zZE0QQBGD+WXnBKSzciOYOsKIxa1UTN5MJ6R9EV2oKVXC/A0zU4zqEpMAWD3Tx92nEAsGtPK4qLvHhxcxbWrslkfk4zxfyyzqlG7fg7UW4KN2amuDNjbVddFd4bop57p0xiF++TVLpBA93o21dETU1AMxZZOc76ufpENd3GmhHpXcBYrKeJNhGNbL/++utIS0vD1q1b0bdvXwDAVVddhRtvvBE7d+7E6tWrsWrVKly8eBG/+MUvInkpMQUr2hypKFwwrVbVW1cAcOKE/fa6aogD1q+fLN5vxY0/cePd98xzjAG6Mf7PW1Pxh72du/8YK7JUThRdnlybgYJ8j8EACoJszPPy3Hj8iSZb5yJG26xlNA2SN96vnwtNTfIzAhib6BBY6VHr12WgezdXQuX6cSJPOLXQ7ebp0/K2gW917Tc0o7IiDX370p8jlg49OeeyFY3M61PPNRfrrVMTko3PPgvvDRlTkIr+/VMwNDcFTU3sAtQZ0zyG7p/6sciayzVjS3K+WAjF/7CKWMdqPU20iaiz/de//hVDhw5VHG01kydPxlVXXYVf/vKX2LhxI+rr67FkyZJIXk7M0BlFU6xtbNaDon/gJ06gK17YScsIBIDjJ+wV3i19WN4Gq65uVxoZ2KUz8upikZ/8OAVDBqfgN8/Yix58eMSHPr1dhlxPQYBiEG8Zl6rZemRBnAD9GLdDIACNjCTQIRmpd35YC9acIcllwDmhEy5nQG1L7QY4Jk7wID1D3oFSQxatI4a7DQ45WQTTOv3W1ASQl+fG0ofS8dhq444WUTKpqQng5VdasOn55IswRpvX97fh9f1tiqwpa84snOqxNRatUtJyc1McNZYLxf+ws0iNlPxpvKWlRNTZliQJ3bt3Z/59xIgRKC0txdy5c7Ft2zY0NDTgsccei+QlxQzBRJvDDetBoT3wr+wyOlqCIBe7WVWNiyIwlGEA9OcDZGPy4VFnbdM5Hbzzbjveedf+TsQru9qov696a9GOow3IcobqdKS8PDeqq9vx4BLr9uyAVjNWfR20CYerfHDCQTicAZYttfN+K61s5Tn62AdIAvr0EdHUBCXFoKYmgNOf+jS9ESb9jJ6ucOstqd8e1zk62skM2bFYMN9r6K4pCMD+A604dZpd6G13LPbq6cKC+V5Dmidt/hVFoLw0C4MGWiud6LG7SI3ETn48duWNqLPdu3dv1NTUmB5z7bXXory8HLNmzcLu3bvR1NQE0U5LuwSgM4umzB4UVpGNPto4fmwqNm8xd7RJPnCPHta/qSTJRmX/gVaq88eJLsQgPvuc/Yl55nRt1Vavni4UjHahsVFSxhtL+s/MGadNOLGwYOXEP6E6A6FGxu0sHHv1dKEgX04xmDKtnvkckc8vZ6QqhLL7JwjAFVcI+PxznncSLIEAMHCAGzvL3JoOnaQrLw3WWFRHdgFtyh2rSJd2PbTcfzvYXaSGOzASr2kpEXW2r732WlRUVOAf//gHvvOd7zCP69u3L8rLyzF37lwcOHAALlfs3rBEoLbOz9RzNcu3JU72k7/ORJ8+oq12vmRCsCNbBAC79jRj/4HYyHtONJY+nA5IwONPNFlGmdWV7bv22Cvu/MENsjk5ctRnmAD0jjEAjRKO1wvFiWBdDytHNZYNLCf2CdUZCEdk3M7CUe9kRDrXWj0H3PhjN3r3EZlOPMcexI7ZnQ+BjlxuNerILi3lLi+Pvluib4QTSoTZapEaTFqVHeK1K29EQ8g33ngj/H4/ysvLLY/t2bMnduzYgcGDB6O9PbhiPA4bUmm/ZWsTRhVcoCpUkA5mZlXqgQDQvbuIL7702y6Ye/SxRqSnG7uM0djHUKvghM53r0zBpJ95LXW3SSfHiRM8tiaFK751rP/ng3ZMmlqP2XfVY+ToCxg5Wlt93qunS5loAGiUcAYNdDPHXCg63ByOHULRQrerPqJWO2Epn5g9a3Zk/dSfnz9KmxqQP8ptywYD8jM3d3bHPXj7XR93tMNAcZEXvXq6bKnGAPLvUDhVOxZpiy61zN+jjzXi3LkAVYVsxbLwdWc0UzqjqY+ESzs7XrvyRjSyfeONN+Kee+5Berq99stZWVnYtm0bnnrqKXzzzTeRvLSkQr0KNkOvldyvn4savT512odLetl/YMhWlTp6FKzeNVlJd4ZedqwzeKCIT07Rf2S1MTp/nn3j9J0cWbsc8+Z64PPJTSj+XmP8TFrO9cX6gJJXKghyA6UxN6cp0Q9WhzRJklUTOJxIEuwuiT4yTooQWQXntEgkAMscVLsKP+r3nzwlN3zKzU3BoIFubNnapMkXFgRg0EAXPjlpdPpjpYNjInH+vITaOr/tAnJaIazVoosUmhNZwEh2Z6RFrCOd5hGv9TqClMjdY6LM8ePHMWzYMBw7dgxDhw6N6GfZrcStrfNjVMEFR40LRBGorMhWtLH1uWSkqMJOGgkgG/TDB7OVB5GkD0yaWm//or5l3lwPvvc9FxYuMu+SZoeJt7lRXy9PLG+8FV8R9csuFXD2i44L/vGPUvB+lbG4BjAWv96Uf4F6Tv1xZHzp26/fcXsqJt7mMU37cIooAtMLPdi6nT7Bq8ckJ3mIpk0NFbUjq3+WzGywujEJgTXezZz24iIvel/iggQJuTlGx2b3nhaDzCAncnx/mAsfHTNqtqtTPU6caMfZL9qxYaNRdnVnGb1w0cmc/uTaDOpYiCRHjvow+y7j3P7i5iyly2k4IL5EvNTrRDSyreef//wnPv/8c1x55ZX493//d+X1s2fPoqSkBH/+85/Ru3dv3HvvvRg8eHA0Ly2ucFKJ62TrkaDOf2IVWjQ3y6tuO8b7jokdkVISPdq9pyWo6PTmLS1YuyYz5AlDEIDdr/qU/75rjgcX6yW8/Lv42CpVO9oA8O577NQr9b2qoUShCVMnpyIvz20YX+PHpmp+q1d2tWHX7rawTtqBALC9jB1Ji4ecPE7iYkdLuGRDs2E736zgnKDPoyXvp433vDw31j6RAQECvvo/v9K7QJKAv/7Vr1EkUc8LJNrIHe3IMzRHxKIHM9HUBKrTGQjIHR4B+vxHpB1ZCiG0nRTW77pwUWPU1Tqi1Uck3up1oupsb9q0CaWlpdi3b5/ibDc2NmLKlCn45z//CUmS8Ne//hV//OMf8Yc//AGXXXZZNC8vLnC6ReO0uQigfTBYD47XC1x6qQs7y7Lw9jtteHYT21GacFuHwa+pCSA9HUEb/kAAeOe90B1ifbvwRN4yJQ1j8vLcuPxyeht1ACjd0Yay8jblPYCxta/6nOEmEABmzfDgxW3G3yIecvI48YeZogMhFC3h6up2JfLsNLKtH+/661A76ZJEb8Gdni4gNzcFJ07Qd7044efExwG8+VYben6Hba/M7OczGzJx40+M0o36gsOL9QFlJ8XM4Vb7CACUOZg0Dwu3wxqvaR6RJqrO9tGjR3HVVVfhu9/9rvLaq6++inPnzmHcuHG499578c4772DNmjV44YUX8Oijj0bz8uICp5W4tIE/d7YHz7/QYilwTx7u4iKvJmIyfmyqkkICNkjiAAAgAElEQVRg1vCG0Nxs3P4MxVnb+7pWrYTnb1ujbpJB02AlOL2P5N6Lolw139YmMTuk2WF0fioKp3rw3KZmvLK7VbMln+zGmhNerPKoWT0H7GoJCwIUfXniULMaNgHGnG31+Wvr/JpdRDuOcyAALFzc0Gnt2JOVUIM39xY1YMF8Pwb0dyvOsH6hVVyk1eq201iubEcLtpW2GBZ1kYh6c1lWI1F1tuvq6jBkyBDNa2+99RZSUlLw8MMPo1u3brjiiivw+9//HkeOHInmpcUNwWzRqLcec3JS0KunC5f2cRke3oED3MqDQXu4Bw5wGyTaAgFg1+420+5UXi80E1Y4HeMJ/+lG12wRL26Nj/SPzoJ0dqyt8+PTT8Oj9kNy95ubO8bfqALzfPCL9QGmow90FPYsX5qJu+d5ubHmRAQzGT2rFBA7WsLEwVWfXxCA9esykDNEjjA6KVwrLaMHR+zAAxHxRYfmdrMy95JgFyCPKX1THCtEUS5mp6UrPfpYI/r1cwXV2MaMeEvziDRRdbYbGxuRkZGh/FuSJHzyyScYMGAAunXrprx+5ZVX4q233ormpcUNTrdo6FugLkVt5PiJdgz9tlKdQIvmlGxoRmVFGnXykSR5+1//MBPJtqYmZ2ksTtjze67JbZdnn5OjxVYI3/4/M2NOJgH1VuSRoz7q77x4YbpG4WT4993M4lp1ygs31pxIYUfRgdVzgBXcUEfzzn/tN7RglyQAkqAZ06SGgox1Vj44q55BvbM0fmwq9u4z9k/gxC8sx5plm1kNw8yKzwMBWaxg5nQPphV2aHo7EWGIp7bpnUVUne2ePXviyy+/VP598uRJfPPNNxgxYoTmuPb2dqSmmqcmJDO0BiGkkYh+65G2BdqvnwsVB9uwrbTFsG0KmKeqsCaf0fmphodZkqDkiTnNG+eEF0mCLUcbAO64PQ0/+bEbv7y/wfC3++/14PLLXfjqq4DS9pkY84LRqdSxoXa0AWDQQDdWLGPLXpFc14LR9g23ndxbDodgVctCHGqnwQ3iMNfW0c//4JIGNDbKnlCoRe6zZnhQONWjiYbff58fJU834vX9PAiRKFjlZOuPveduD3r8m2wHs7NF5OTIbt72shbTOXjr9hZsL2uxLUUJxGfb9M4iqs52Tk4O9u3bh8OHD+P666/Hb3/7WwiCgP/4j//QHPe3v/3NtOMkR6vqwRrsLKdZH1XU5yGyHOrz52WjTpt8WE1uqj/2IWeIG2MK3HwCiBMamyTcW6R1tEnE5DfPtBiiJ4GAbKi3lbbglnEd0TUzx4TsrLDkH4lTolZTYDnQdnJvORw1rLQPWo1AMPmn5Px6tSZia2mNSIj91Y911sKge3dBEw2vrfPj2U1NVDvL61riF0EA7prrweYXWqjFsXqefa4j6KW2gXZ0ve2MT0K8tk3vLKKqs/3ZZ59h4sSJaG2VI2ySJOG6667Dtm3blGO++OILjBw5ErfffjtWrVoVrUsLC9HWhKXpbar1WZ1qbKt1MO20g1VPPjtfasaqNcaulOPGpGJ/Bd/aTBb0edxWRtdM+5eM5aoqH3NBaTXGuT53fBNpm1pb50f1xz5IAQGXXiraHrd2OXCwxZBOwuLFzVk4e9ZPHeusfgdkbFs1Lps2JQ2f1/jxfhXvzhzrXDciBUeOan8ndXHtgvledM0SbTWqA4x9M5zmexP0OtnR0tNOFKIa2b7qqqtQXl6O7du34+uvv8aAAQMwZ84czTHvv/8+rr32WowcOTKalxaXWBXv0LZArbZNCSSaU/2xT9NAhqxeKyuyNQ8Uq+L99f1G2ThO4kI02PXGlhaZrq3zK/KR77zTht/q5CMDAXlnxCx6Yjf3ljvbHBq0hVw4HYXcHDd1l1AfmaQVkqvHOqvfwZkz8sFWjldpOS8gjxf0jjaglXiU66eyle6QXi9w/EQ71j5pDHYB2nGi1oJnwRqf+jqFaOlpJwpRdbYBoH///njiiSeYf580aRImTZoU1Lk/+eQTbNy4EdXV1fD5fLj66qsxY8YMjB8/3vK9kiTh3XffxZtvvonjx4/jq6++Qnt7Oy6//HKMGTMGs2bNQlqaUfuyM7Ez2NVboHolEQIpZNQ7JL16utAtO2Cr4ULXruF7wGhFHpz4gKUPTKLXpGEDoM0JLC7y0p2SgGC6oDTTDWddD4cDON8GD6YQjJXzDRhzYmmF5GTBmTOE7rT37StyDe0kQy3jSsZhjx4innyqiToOyDix0+BOEGRbrI6cs9IBuZ62M6LubEeKI0eOYM6cOXC73Rg7diy6dOmCQ4cOYeHChfjyyy9xzz33mL6/ra0N8+bNQ2pqKkaMGIEf/vCHaGtrw/vvv4+SkhIcPnwYZWVl8HhiJ//T7mBX5/Xpj58xTS6yYT0gVg49mYC8Xvo1OskVXLUiHX36pFAr+TnxgX78nTzlw7IVHb+lJBm7pxG1G72e+/RCDy69NPjoiSDI5+BwaDjpWRBKIRgr51v/Wm2dn7r7uHBRI1Ysy8D4samaxjUjf+pWIvOc5IHYP3WTuKYmo/Y2oA2kvfw7a+1vEjl/dGmGEjk3S6vietr2iWrOdqRob2/HzTffjNraWrz88svo378/AKChoQGTJk3C559/jn379uGKK65gnsPn8+GFF17AlClTkJWVpXn9vvvuw1tvvYUHH3wQc+fOZZ4j2jnbhNo6v6PB7vR4dZ6XeqKx06imYHQqKg7aSyUhuV61dX6MHH2BR7bjkB/ckILHVmQqeaRqR9uKFzdnoW9fEWU7WhQZSb2kmb7hSMXBNqxbb9w+LRidikOVxvdw4otI2lSrmpdgjgtVEYeVe83a7eOFj8kFCUL8278JGu1tgD4WyDjdf6DVtL8B7XN4rUt4SYj91Q8//BBnzpzBuHHjFEcbADIzM/GLX/wC7e3t2LNnj+k53G437rnnHo2jTV6/++67AQB//OMfw3/xDqmt8+PIUR9q6/zKa716ujRbSk6PVx+jP373nhYlz4tsMdE6q7EM/g9/YG/zhDRdIdc3Yxp3jOKR//mgHTflX8DqJxqUCLYd1NFqIkkJyFG+vfvaUF6ahRc3Z6GyIltZ6I0quEB1tAUBiqNNzvHoY42aZ4DDITuD4rezIGtn0CwCTiDjcfZd9Rg5+gJGjpb/e1TBBezeY7+b4MQJHqxdk2l4naU+wR3t5OH661yK8tP6kmbDmKSNBSKj+tTT9h1t8j71+OaETkKkkRw9ehQA8MMf/tDwt7y8PM0xwZCSIt8ml6tzV3lOtzLtHG+mOqLvXEW2mIZ/341jx+3lCS59lF60oUYQoHGu5cI53mM4nrFq2X7n7WnYtadVk7NdUxPA11/THRt10aV+oaeG1cCBF0pyaNjZBreTSmenGyVN1o9Gbm4K70vAMfDhEefBAkEA/vLXdseLMn2qCu9ZEDoJ4Wz//e9/BwBcfvnlhr917doV3bp1Q01NTdDn3717N4AOx70zCKaYx+p4q0mCJhFE0+k2w+q4wYNEnDwVUAT1eRe02CPcW9WCANw9z6u0Yz912qc0yKGp2uhztFmFPqRT5blzAU10nHYODodg1amUVhtTXORV3mNXEcdMwlLP9EKPMoZ5qgjHLoIg/586ePbsJvs7K0DH2HQyXjnWJMTs09AgN+Do0qUL9e+ZmZn45ptvgjr3u+++i5dffhlXXXUV7rjjjqCvMVTsbGU6Pd5qkiCGnvZ6uPjkZECTMvDaXu5oxxJLH0oPu6O9YlmG4uD07Ssadk/U0Lb2iQKJ/rz5+amoqvJhyrR6g6PNq+Q5oTBxggfFRV7FkSnZ0Kykh5DINwszWT99ahNJR9m6XW4edecdoXdSnlaYxpRm5SQOoijb1sqKbKxfm+l4kVZ0n0dJ1evXz4XlK63HK8c+CeFsR4qTJ0+iuLgYXbp0wYYNGzqthXxtnR9ffx0wGHSzaB3LIVEf39xs7tWKoiygr85p5CQWdiZhq9+96D4PbvyJ9SaZIAA7y7I00RHWgk8QgPVrM5UcbTucOxcwpJeQJjs8IsMJhdo6v0ajWO186HO/SXQRsJb1Uwc/aLuRu3a3hbTYFUVgyOAUHhlPYAQBmDXDo9jKXj1d6NZNdBy06ntZCkYMlxVuJk017l7zPO7QSIg0ksxMuaCEFb1uaGhgRr1ZfPrpp5gzZw4EQcDmzZtxzTXXhHydwaDPqSar1VCjdQ898o1GRgow5mxPL/RgzM1pGHNzGqo/9uFf/wrg8TXBdZ/ixB52Ih+PP9GEkTe5UXnYxzx243/J6T9mkPE6aKC2YcjpT42tpQH5urp3p+cJ1tQYtd8lSW7swMr35nD0OMlHtZIJ1Od+AzDI+umfN33wg/UZ+veJIjDyJjcOVWqfHdpxxUVevPU2byyWyEiSXDQ5Oj9VGce0OgMrcnJSUFvnZxa281S80EgIZ5tI+tXU1GDgwIGav128eBH/+te/kJuba/t8p0+fxuzZs+H3+7FlyxYMHjw4nJdrG1pOtSAA69dlIGcIPVebwHJIzpwJ4Ny5gMHRBoBnNmTi2mtTFOk1Wh41345MHOwsmgIBaCb1wYNc+OSk33AMbTwR8n6QgpWPZhrGK4kW0rDataEVrA2lFJbxCYJDw2mxuZ0GYvrcb6eBENZn6PXni4u8uOQS0eBsA/Lc4EkTcPJUO85+4Q+6NTcnvpAkuZZqxbIM5OW5UVMTMAgcmEHmdZrfQJgxjd2Pg2NNQsxCw4cPByC3etdTVVUFABgxYoStc50+fRqzZs2Cz+fD5s2bMWTIkPBdqENokQ5JArp3My/oAeh5hGRyOHbc2A4WAE6dll/XS6+p86hZedyc5EDvaNvhgw/p480shcRs14Yl2TZooNuWlBsnuWEVj5vlo9qVCWTBCn5UV7crUqu0zyC7i5UV2Xhxc5biQNGafkkScOqUH/cWNeDZTS3Yt5+9G8VJPCQJWLaiETfly7KTpFHYi5uzMG+uR5m3WXVYZ84EqOmn5D2FU81T8Wgyw5wOEiKyfcMNN+Cyyy7D66+/junTp+P//b//B0BOH/nv//5vpKSk4LbbblOO/8c//oFvvvkG3/nOdzTpJXpH20k0PBLYiaawMOsuOWwo/Wf/7XMt+Nvn1i1dWQZ8wm2p2PMq37LkaCEtpwvytY4Ja3yXl2YZ0k30sCTbeEczjhVOOkeqCWVs0ca6IAAPLmkwRNfz8tyG3cVHl8oRyznzzCOVL25zpjzBSVxIIW9lRRpGDM/Az+70oLq6Hf+64MfqJ5qpfkWvni6sWJaB5SsblXleXdTOIpQOq8lCQnSQBOTGNnPnzoXb7ca4ceOQmZmJQ4cO4YsvvsD8+fPx85//XDl2yZIlePXVV7FmzRpMmDABAHDhwgXk5+fj4sWL+NGPfkSNaHfp0gUzZ85kXkMkup2FOohZ3SKLH6jHocP0fNlQ4DJVyYcgALeMM5dsJAbbTOc9VCPNNWETj3DaVHV76ynT6i07QoYbVk8D/TUAoHasXPtEBjWizeGYQTozm/XU0Nvd2jo/qqvbAUGyTFm122FVfXwy2umEiGwDwPXXX4/y8nL85je/wYEDB+Dz+XD11VejqKgIt9xyi+X7GxoacPHiRQDAe++9h/fee89wTJ8+fUyd7UgQaqSOpSE76WdeW842aZf9h9ftV8VzhzsxGDfGje99L8Uy71OSgKuvdqGyIhtnzgSw8+VmQz6pJNF14cMVieaRFY4Z+vGhrkOJVrqReqyf/9pvcJxJdF2S6MolAgTe7IbjCEGQZScPVLQ6qv/q1dOFgtH2U6Ts7hQls51OGGcbAAYPHozNmzdbHvfEE0/giSee0Lx26aWX4k9/+lOkLi0krJouBAPJzTJzokiTkKoqH/7wur30EEmSpeA2bOTbmfHOvgM+jBieip1lWZaNjNaXNOOSS0Rc2seFw2/QF3EsAxzq+Hba8ImTXNDGx959bSgvzUJzMyKSbsSK3pGxXltHT6HyeoEvvjQql4gi0KePqGl2w+FYMeomt2EXh0By/AvyPSFFm+2muya7nU6IAslkJ5jChF49XVgw38v8uygCPXqIinaxXeMuisBllyX+g5MMSBKwfGUjDlW24i5VgQ2LhYsaMbmQbtiByCmDOG34ZAYv8kk8WOOjuRkYMTz8Ez1pTDP7rnqMKrigNL9RQyuGHD82FVOm1VNTRUjnXtLspmC0s54PvKg9uRAEYN5dHhx+02e6E7J1ewu2bG2yHK9m2C0eDqedjkcSKrKdjLC2ZeysVC+5hO74kKjKwsUNjq6FqEjk5rgjnkrCU1WigyQBW7a2OjqehtVWfTQiK1Zs2dqkpMwk2xZnIhOu8WGGOh/cbvQuL8+NtWsyIYgS+vR2aSKQtOdIrRB1qNJ+Ifr3h6Vg0p0ex/acE788+etMdOsmYtPz5o6zJEGTJhhstNlOOmA0nsNYJjm+ZYLC2paxs1LdvacFDy5mF9sE48g+syFT6WBlFjUPB9zRjg/03c1o2IkEmkEiK+ronSQBVVX2C4C3bG3C+hJ6h0BOfBOqbJ8V6vFL29kh0Tv1rsnuPS0YOfoCFi5uwMJFjag4yC4upuHk2I+OtaOlJTmihxx5fOfkpDAbhumPDVenyF49XaY7RZF+DmMdHtmOY1jbMlYrVeKk6x8yUQRGjXTj4KHgVErS0zvWbrNnpuPMmQBe2W0/KspJLAQBWDDfi9kz05nHhCuPLy9PKxXIKshkXcNTTxub69iRg+PEB5GShKQ1HtMjisCp0z5Ftk8f3SMdACNZ/PjI8qbInJgTNVjjI3+UG4ff8Gl2twFQG4blj3QrqSX6hknqz6HlW4dDQSSZpVm5sx3HsLZlrCqDWc1EAgEE7WjTHtB77vZi155WQ4tiHpVODiRJNvhjbk4DAKqxDlbzWA+taYjd87C6punbaXPim0gUmrNsKbHDNIeG5VDfPiENu/a0Mhs9Adx2JjNzZ3vQpYuA9SVaJ7rysA+P/Cod2dkicnJS0KunC0eO0nO1J0/yYvGiDI2z2zVLpPbjIIRbQSQSz2E8wGeSOIa2LVNc5GV2jiTQukuGAms7iAjkq69vxbIMzJvL82CThUAAKNvRsc0+cvQFbNnaEWVjjcVTp50t+sw6pgbzXkCOyifjpMCxD2vclZdm4cXNWaisyMaA/m5bEevrrkvBxqczDcWMoiin6HGSm+dfaMH588bVliQBj61uwoNLGpTUOTN7SNI9AODIUR/y8txKh1J9ul8w3VY5dLizHedMnODRPCizZ6Zb5kXRnPRQKC7yMle6+uu7WB/Aps1cFjCeEARg3lwPZs2wViTRI4ryFrl6m319SbPicPfq6UJxkTG/v2RDs2N1nWDzAWnvfaDYPP2FwwHY427QQLeSv2onuCEIwFdfBXBvUQN1h6bmDH33hUXRvR7cMt68CysnvpAkYFtpC3MsqR1hK3uor5OpqvJp8q1JfcGJE+1JrSASThKmg2QsEIkOksHC6hxJO6apKYBf3h98pbrd7mu1dX6MHH2Bb4XGIeQ33n+g1bLJjZrvD03BR8fbmecjW56z76o3HEM6n6mxyh20M+5ZhPJeTmSIJZtqhtXYsWqqQ8udJZBIOUsvmQUpfuP2NrEYN9aN1/exd/7UdpM2Lq06PurHqn4MRaPbaiLCc7YTFDt5UeSYI0dDa9su53q3YXR+qulnvv22/S6UnNgiEADefqfNkaMNAMdOGB1tcj6ST21XEsqONF8o+YDJmkvICR11PYz63wRaYdj993U4QnLut7GgTR0pnzvb42hXUO46yUk0zBxtvd2k2TQrvWt92oggdNRaJZuCSDjhaSQcpZukHciDp2ftk02msm2797TgsdW8Ij6eeezxJseLJUkC7rw9zfC6elKwkwLCpfk4sYzdRjbqrXr1v2mpJoIgR7TJgrLmjPOxznpce/VyfCpOjEP6XFg5wmb53DRHXJKAJ9dmUHO6OfbhzjZHKWS043ATZ4d2LMsBIkUWnORDEIB+17gwbqxbGTM0Z1qf268v0jGT5uNwOpNwFJHRFpwrlskRbfIZhypD24HUXHNt2E7F6STUczCRWaU5wvquuCxhBdKUieaI5wxxMzW0eddde/A0kiSElvdKtjmf29SM3+0y18aWJPnhHj/Ojb2vaycAmtwaSx6Lk/hIErBqjbyjQRrcFE71UI02K42DJc0HAN7I9k7icCxhbctXV7ejYHR4uvCxnoHLLxdw5ozE0/OSDH2wSy2zqt8RpKXeqcfaqdO+b+sFmiGKwMifulH5hs9W2ki4ZQETGR7ZTjKstjt37bHXhEaSYHC0CU1N2pkn3FKDnNhkyuQ05Xem7XyQanqnmKU5NRsD3hxOVGHZtweXNATVDZUWQfzwCL09+69Xd8Hhg/KO0H/9JhPTphpTtghOlYQ4scs1V4uWnR+tUu969XShb1/RoAF/6LBPCaiZKY1xWUBncBcoibB6OErLWqgR6KUPpztyln95fwM2bGxUtpZY8m6cxOLSPi5FX3jdE3Rd4GBSP3r1dGHBfOP4saujbQe+Fcoxw2x8kG15vTMbivOh/rzaOj+ef4HutDc3dzjo589L2LGTHizhzcTiBzuLoj//xWhD1fbQbuqd2a4ziZazxq9VoSVHC3e2kwizh6O2zk+NOooicONPUjU5XnbYtLlFEz0f0J9rviY6a59swpRp9Th71o/c3BTqpBGsgzx7ZjoeKPYaiigBUJ0gJ86zneI2TvJiZ3xMnODBul9nGF4PxvnQf15pWQuzDbzauVIHUtRwRzu+kCTgnnnOUjH06R52u+Ja7Tqbjd9QGoklI/yuJBFWVci0h3PGNDm/lhSwLX3YWYSaRHeam/lqNxGYNjUNbxzKxq3jU6l/J7/3uXMBQzTabrU8i9kz0zVFlACoTpAT55lvhSYW4d6hcDI+cnPcITsftM9jpV5NvK0jZcQqQsmCpS7F6Tz0MqhW/PweD9auyUReXkdAK53Rj+uuObITr951NgukmY3fUBqJJSO8QDKJIA+HvqCBPBz6h1wQgMKpHSvsqiofHl/jPEmWdECjQSuy5MQurW3yzL13Hz2HFJB/70lT6zWT+J23p+LueenKWDt5yodjx9sxbGiKorhgB1JEyXKC+vVzUV/Py6NX0pvt9vBJI76IRLGWk/FhZV+tqK3zo+JgG1V6jcYru1uxa08rVizLQF6eO6gI9l1zPRAF4Nw//Nj9e26HY4FAAMy0IT2CAPz22Rblv1csk8d8E0Nl1+eD0tBG/YwYiyXtjV+zol6OFu5sJxmsh4M2URA5IAJrm9IOFy4EqI1LhgxO4c52HLFrdxv6XeOyNQ7UE/+uPW24e54cbnnokW/w2t4OZ/0HN6TgsRWZjgw1ywk6btJemHZ+uw11OLENa/HFWmTZxen4CNb5UC8UnCBJwPKVjTh8MBsL5nuxvsR+MOS64S5sep6nTMUidhZN+sUVGQt5eW7muN26vcVQMEmeEZL7P+bmNEfjlzcDswefUZIQVsW7WuuYtA9W5w2GIt+3eUsLiou0ObfFRV5A4nuY8UQgAKxaHdzuxpkzAZw85dM42gDwPx+0Y+RoZ7nSrJSoobkpjrby+VZoYhCpYq1gxgfLvrIwy7e2gyQBW7c14ZJeLsy7y2Ortua6ESk48keeKhXP0BxySZIlJ2njdnqhx1LBBHA+fs3ghecd8Mg2RwN5wObM08oBbSttcZxLpiYQAL7+WkJlRTaqq9vx4VHnrb/NIKL+Xm9wziAnshCHt+IgPf1EkpxFIllb9oMGuh1v5fOt0PgnkjsUkR4fZvnWdlNDSne0oXRHGwQBmDwpDeUMVRLCFVe4cORoexBXy4l5BHnA6MctAGzXBc0iuYvHNbi1cGebY4DVsnXmdA+2lcoPK8nHdeIsb93egu7dBY2uZ7ggMkXlpVkAuLMdS6gd3mFD2SbHaa40ywkKxjniW6HxTaj50nbOH65z6ZuKER15VqTSCZIES0dbFAEXH+oJiSDI3R4J+nEbyWdETaTSuuIZ7mxzDLCiRN27Cxrjv2C+Fy6XgLVPMqoxdEgSwhrN1hMIAGU7eA5iZ0EcBrXjoG6MUFvnR1MTkD/SjUOHjXn6ogicPx9QquTtwHKCuPOcfMTDDgUr2kfLtyZKIfqidSA0Kb+JE1Kx8yV7zcs48YMoANOn0du1k8VdtJ4RXnhuhOdscwzQ8r1IDjcx8iSSTMuRJe/RE269V5pk1ev72SoZnMixfl0GDh+UpSH1RTslG5qxZWuTIsdX+YYPUyenoWB0qqbjpCQBCxc3cK1rTtCEM99UTThyT81kBImOPLFpoigrS+jt8IplGVixzFnPAz2v7GrjutsJSECSd4+tZFAj9Yyo4RrcRpL3m3NMURdLVlZkY0B/N3Wl2twMzYQgCMCsGfJ7Vy7XThQL5ntDmiTUkBxts/bgHGcIAnDHRHa7ZxaiCPTp7UJVlY+aLx8IyDsaZPxIErBjZysG9HehsiIb69dlKK+T49VaxrzIhtOZhKvpkVUR5+yZ6Urr9cqKbEyc4DHYYfLayJ/yJmEc+rxH7OfJU76I9hCw01WVF553wNNIOEz0W/GsAqQRw92M3FkX8vLcqK5uhwQJl/ZxYXqhpBRpiIK8Gg+GQQNFDOjvRnmpG19+GcCDSxp4tEbHwP4CTn3q7KZMnJCG3a+2OsqpDwSAyYX1AOg7F6wdjaeebsaYm9PQLdvFrJKvqvLxIhtOpxHO3FM7RZy09Cf9aydP+ahpWEX3epDijkxNDKdzmHeXB10yBaakI2vOC0YG1Ql2ih/jIa0rmvDINscWrNQStU43bWuqqsqHB5c0YOGiRkyaWq/ofObdkIJQfONPTgYw+656TJlWj5OnjEaFA8eOtiTJOxXFRc66hJL3shztBfO91AiMJMmGn7Xl6PUiopEZDseKcEoKhivad+w4XUWk7h8SxtycpuwW8d2++GbeXNnRfupp5wX/wcig2sVJV9VopKzEC9zZ5thm4gMlULIAACAASURBVAQPiou8StFOyYZmR62wCZIEVH3QHpZIdCAgyxnxiSV0iCEe0D88W9SiCOwsy8LsmemG1u3qz2M5IU1NRqnJcGgnczh2CXfuKS0txCksRZ+XfteKUQUXUFXlQ0G+x1Zud6zYTUEAfnA932hXc/y4D+tLnAsK6GVQw53KESlN+0SHj26ObWrr/JoiSf2Wql7Sykw/NpwEAnKeuLo7FscZgqA1xKEWs6oNPiDnowIdajR6w0/bcqyt8/PujpxOJRKSgqEq5fTowR7/aptMnqnq6nYsXGxMsyO7Tl2zRCxf2diptlOSgA+OJL7utxO7+tFx5zt4ixemIz8/NSQZVCt4193g4HeHYxuzFS2tiIgWFYoEoggUTvVg8iTnxX0cmUceSleibL16urBiWUbQ5xJFoLw0yxC1oxWAqdFvOfIiG04sEI5odDipqTGPYKijjL16ulAwOk0T5VbLB5ZskFMUDh/MxqwZnk6NdMdKoOS/fpOJlcuDt39qlj6sTaFjfUent53IQqoRRWgcbUK4Uzm4XQ4O7mxzbOMkt3b5ykYAWqUS9XtuHZ+qeVjzfpAStKEfeZMb+w+0WjZzIIwd446Z7dNY4bHHm7Bla4de+sQJHrxxKBt33p6m3Cv9PRMEYNyYVMO5iEoNDaeGP9YcHU5yEku5p6QJDgtBMEYZyXO09OF0jcNHIuGAHLDgdhFITxeRlxd6Kp0oAl27irYWEU7WGTQJyGg7vNwuO4enkSQh+nQPu7C2VGm5tZIELHmoAQ8Up6OyIhtnzgTg9cpOGNnOuv8+vyFt4MyZAD440oZNzxtzwW/6jxS88ZZxq/FQpQ+HKo3V+Sz27ffxSYUCqXgnKR+9erqwfGkm7p7n1bT8ra5uBwQJfXq78MUXAeyvaIvoliJvUMPhdFBVZW7rFszvKFxX23pZmtPYgIxEwiXJaMeTEa/XevfADnNnewBJMKRcmEHSTEQRGD82FXv3ddjWKZPTMOqmNE06SGeqfXC77AzubCcZdiR7zJg4wYN+/Vw4fqIdQ3NTMGigm6kO8ceP2jFpaj1uHZ+K1au6GP6uf1jJv0cMd1Pljt58O3w5fbGyZWlFbo4LJ6qjp75RskGW46P9LoSC0S7s3tOCKdPqqZPI+LHGrUwOh+MMWlDk5CkfM7+aKESRxbLa1pt1nhRFoKkpgA8+9IW98Vg46d9fxKefRn41MLmwHrdPTA35Xjz/QovSUdcuT67NQPduLsV5vvrqJqXO5aWXW3FtvxSMGM5ux86JXQRJitVHK/44fvw4hg0bhmPHjmHo0KGdfTkGauv8GFVwwRCFrKzItv3A0px1AJYFNi/tyEKPHqKjiPrJUz5MLqyPqPGP5cmls3hxc5bGoOuhjSM1ggCs+3UGcnNiY9udE7/Euk2NFE7trL4wzuoZVZMzxIXqj40LelEEphfKheecyKOfi8MxX3NiB56znUSEKtnD0te0U8lO2sg66cLW1BR5RzhRHe1VK9It8zrnzTXuaNDyPfVYqcxIErBwUSNvu87hBIFTO0srjHOiBEVztAE5DWJaoScqRe6xTjTSDtV9KwBn83UoXXZ5h97owB+jJCJUzVjWw2/HYT14qM0webAebvLwp6eDG/og+eSk36BAQCYMUmBTdF8G8kdpI9iSZJ0Taldlhjeh4XCc48TOsgrjaM+oIDizp8+/IC+UH12aeA1yBEEu0rf7vdTpIKII3Hl7GnUu/fnd9lIyc4a4NLb5gWIvvnulCytXNeDtd+RCf7vzNU0JTA/LobbzXk544K5MEhGqZA/r4bcyWD+4IYXZjluP+uGfMq0e48emRsThTrTJQ8/vdrUiL88tF+mgY6KeNcOjVI/X1vlRSWn7bOUgk3Gkvoes+8mbHXA4zrBrZwWBLrEJ0G39imUZWLsm0/Z1kA6vEyd4cNecxFGbIPriw4a6Da+bIUnA+nUZqKzIxvKlmdS59PaJ9J0A/bk/OelHeWkWXtychcMHs/HGm2345f0NePmVVvzy/gZMnX7B1nxtp5sjy6F20gmSEzq8QDLJCEXknqVGAsDwWr9+Lpw40Y7c3BT06CFSc8/0K3Taw793XxvmzvZg0+bwrrgTNX1EzeIl32gaI0gSsK20BYVT5YmzpiZAvQ/EQaaNDVK0dbE+oKmcLy7yovclLjy4pIE3O+BwQsCJnSVNo2jYbRTFqlshz25tnV+JcicCkiQ319J/b0kCvj/MhWPH/cz5oXs3bUEiOY78r/630x9HIPKoI4a78fY7rYZUnuqP/Xj7nVaqIIEas1QT8nvTHOq8PLfleznhhTvbSUgoFcwsZ532mtow2OnCxnr4zQz9vLke/OxOD4qKv8Gp08YVOW0iMavMjyVEERhTkIp9B9qCulZaBzK1MSV6vfpzsxxkddGW/pwlG5pRWZEd9m57HE4y4sTO0lArmejVK2jPaL9+Ljz7XBPefldWfFI/uwcOJl5nXkmi2/9jx/3YWZaFPa+24He72jR/U9tF4sSqnW11585+/Vymxf3qc737Hj1t7/33fTh/XjJVD7Pq5mjmUPNOkNGFO9tJTCh627QuVWbnsBNRZz38ZoU+Pp/82RtKuuCm/AuGv0uSnDqxrbRFMVjFRV489TSj60oMIIrAuicykZOTgpqaAF7f32b9JpuoCyBJp0h14ZW+bTtBHyHRQwx4JNoDczjJSDB2FrCWd2U9o/+1savS60D9+oUL9tPA8ke5MXumF++814bUFKDv5S786U/+oHYm16/LwG+eaUJNTfg9fVbARZLkiPPypV1w2WUdsnv6wIFVVNisuF9/rh//yI2XXzE2ZBswwIVlK+hRaX2XXVaAw8yhtnovJ7xwZztJCVVvOxisJgrawz/xtjTsfrWV6eSRtIhePV14oNhr0OYmrdwLp3qUSUROnwiPs02LDOePdOMQJRfa7vkeXZqBgtEdreetFhyiCEz6WZrtDppVVT7k5ckTRl6eG4cPZiuNanKG0OX6rNQN1BERrv3K4XQOZmkDZtr5rNd372nB42vs28rJP/Ni0EC3RuY1Z4hb0Zx2wsFDbTh7tuNN/3lrKrpli9i6PfRI+4L5XgCgzhfEjs2emY4xN6ehurodEiTk5nTsEJz+1GjfRRE4fz6A2jo/1ckVBFlHW29jb/xJGnKGNBtSSf76mb00D7MAh5VDzYMj0YM720mIXYNMe18wkXAnkIe/bEcLtm5vwSu7WxUlDav8YtLMoWRDM9WwqK/ZSVcvFj+/x4Nnn9NGbAQBmD3Li8o3fEFNCJIEQ6vgiRNSsWs3PZVEEOS/73zJ6Gj37+/C//6v35CXuHxlo/LfdhdatMmFwCMiHE5s4CQP18qe61MlrCCOqj6QM73QE5Qt1HcF/sPeNlRWZGN0fireebcNVf/Thk9OBmfEBw5wK+k1JHotCEb5vaoqn8FRzctzo2SDcQESCAALFzcox9Gc3IJ8up1dsigDk6bWa17bXtZimPdYaR5mAQ4rh5oHR6IDd7aTkGAKI4KNhAfroG8rbdHkwwkCsPRhL1atbjY1PiQaYbZSr6oyd4Tt5HSLInDVlUaVFUkC3nk3uBxrQvXHPuQMAUrLWiwbSkgS8MoueprJ//6vH4/8Kh2P6Vo0q6+NLLT69XMxi61q6/zUyWXeXA9uuD6VR0Q4nBjBbh6ulT2vrfOj4mAbNSDBqoN5dGkGzp0LaNLSAgHZlocjuBEIAGU7WpSUwFAUpbxyYFsJ0BCHu2RDM7pmiYpaEy0otXZNpul3IcdVVmSjsiIbZ84E4PXKfSNq6/wGW7l7T4sSANGfR58CGWxQgzvUnQ/PhE9CzPQ7aXqcwUoEBavhSVsMSBLw3SvdGu1olvEhLd+DjdbcPiENC+Z7qVJb5H+nF3oUg63nz3+h35dxY9jKAWp2vtSKUQUXQu7cJklAdra1JnYgILcoZv0+rBSSG65PZd5nDocTfezKxS1fqbXny1c24sDBFtTW+RW7vW59k+H8ggDcPjFVc/5ZMzw4fDAbF+sDmDTVWBQoScB3rxA17wkGUZSbo5HrDiWgQewdCSSoFwfLVzYqQSJaUEoQJVs2lQSvzp71Y8q0euo8aDYfkRTIyopsvLg5S5Fs5cQnPLKdhLDyuGhbZhMneIKKhAebqgKYR2f69hWxdk0mBJGdX2yGWe4xidiQ1JUF873o3VsEJAE5OfKjQiIrW7e3YFsp/TxvvElPudh3wF4e90fH2m0dZ4UoAjk5KYbfmlaJr66mZzXI4FXrHE7sY5U2UFpmzHkmXV/NdvXI317Z1QZBkJ1sUi+zZWuTIf9ZzV//FsCqFeno0ycFXi8wZVq9o0g3CXCEq3U8sXe0KLUkyXa+cKqHavdyhrht2dQPPmxD376i6Tx44kQ79T6YpUBy4hM+WyYpEydoV8x5eW5m9DqYzpOhtIZnRWeqqnwYVXABCxc34MHFjZadDmmkp9ObQyx9ON2Q2/zU083IGeJGweg0xdiRLT1yjB6zrc1Iy2epP1ttrPW/tXp3QI3Z7zNd1baZ52hzOLENa3evts6P7WVsh5Uliffzuz2a9BGi2U/OaUfd6ZHlTTh71o9BA92OulKKIrCzLMuydbwoyp0Y7Z6XRKlpx5Pvxtol0NtUUnCpZtPmFjz7XDNzHty9pwWLftVgeJ9ZsyJO/MIj20mMOo/ryFEf0yiMGG5cyVs5W6FGQ/XRGQCaxjhOIuUEkqeoz/l+dGkG0tONFleSgOrqdhSMZss9qVHLCkZDl1YdhVIX77Cq0jsq0F1UHVir3E59NIvD4cQXVjaMhigCV303hTk/sBx0GmotalIIr8/B1p+ruMir1JOo5yGa/Zs4wYMxN6fh7Xda8djj5gsAEqWeMc0YMbcjZaq2qQP6uwEYP2/XnlZqkaPXC01wS8+f/+w3bVjEiT+4s80BYO0cO5UICoeGp93FgJ1z0nSiRRHY+HQmvF4Rn3/OSN0QOqwkqwkMACxemI78/FTlWsy2VK2wW6BZXpqFHj1Ew29i534MGijnv5v9Pvp7pu9AyeFw4guanddD1J/UdiE3N8V0frBbAKm22b16urBwQYYiy3r+az8WLjIWCg4c0OF06uehc+cChu6KvXq6MOnOdLhTRE2xpv47Ens3rdCD7WUtzO9mp7iQNTfQ+jw8ujQDTU3s+2WW0seJX7izzQFgzzl2WtEcTg3PUCPlrLSWe4saFLUTPYIgRz4IvXq6sGA+Xctb7WjrK9xFERh5k9sgZUVDH6H2emV1k98+Z4y8HD/RjtH5qZoOcU6w+n14O18OJ7Gg2fnxY1Oxd1+bQd5ObxdY80NtnR/TKQ4rDZrNJvNKbZ09G0+Ot9O8Jz0DVAf+ybUdMnzhCgyx5gZ9nwdyz8wWKNzOJh6CJCVaI9bO4/jx4xg2bBiOHTuGoUOHdvblBAWtg1isEEojnto6vyYNhQYtokM7/5atxs5iRCpKLXOov5fq9+m3QIuLvBg4wE2972bXHsmGRLTPFUWgsiI75sYGJzFJBJsai+htkx27X1vnx4kT7ZridH2a2bBcFz46TldjsmOr7Np4u7bJiQ0Lx9y3ZWuToc8D6/uqv6sebmcTD+5shxE+MUSeUAyi3pDTjNz6tZno3l20PL/+OpxMEuo8dLvfpbMMc2d0GuVwCNymxgY0O5CX56Y6snPneLD5hY60CbNAAg07Nv7IUR9m31VveP3FzVmGnb5o2zAncxQ59tRpn20nnROfcGc7jPCJIfYhxo0mPxWs0xqtCHBtnR8HD7Vh7ZNG/VvaJBPOz43V3Q5OYsNtaufDsm9rn8igpmi8uDkLffsaa0micU0smxsPNiwerpETPFz6j5PQ6Jv0EEksIj8VDjm7UGQOndCrpwuj8zsaShAirXlt1iSIw+EkNszmLhCYtshMelDfNC0Y7DTv0R8f6zYsHq6REzy8QJKTsNgpoAlHAWe4m76YtbgPRzEPh8Ph2IVl32gNs8xsUbjTOcJZgB9JzOw5J3ngaSRhhG95xg7RLu4L10QSTO43N+CcRIXb1NjAzC7ZLa5MxmJrXvPCIfDINichibZsnZMoCyvS4aTFvVMZRg6Hw3EKsVV5eW5UVmRbNndhkYwyok7sOSfx4c42JyEJd2qHHexMOmaRjmSckDgcTmwSzqhsZ9jjzobbc46axB3pnKTGaQFNNGBFOkixEJmQ1CT6hMThcGIPK1vllFi0x5GG23OOmoSKbH/yySfYuHEjqqur4fP5cPXVV2PGjBkYP368rfefOXMGr732Gk6fPo3Tp0/jH//4B/r06YM333wzwlfOiQSxVkBjFengxY8cDicWiERUNtbscaTh9pyjJmGc7SNHjmDOnDlwu90YO3YsunTpgkOHDmHhwoX48ssvcc8991ie46OPPsIzzzwDl8uFq666Cv/85z+jcOWcSBJLuc12tlKTbULicDixR6TSPmLJHkcDbs85hITYz2hvb8cjjzwCQRCwY8cOrFq1CosXL8Zrr72Ga665Bhs3bsTf//53y/MM///t3WtUVFUbB/D/IBDJKOJdQcSFDl7wggmaCMbSlSIoCim2IkpFSRQVW14+VK5Wr8vwUnlBk8pbaslFVFCRzAQxwdIQRM1EGEBJvCGgAsNw3g+smdd5B3CAGQ7g//ep9jnuec7ZhzPP7LPP3k5OOHToEC5fvoy4uDgYG7eZ3yLUAuj6KJXzrRKRmF7FYR+Gwvs5AW2kZzs1NRV5eXnw8fHB4MGD1eVSqRTBwcEIDQ3F4cOHsXz58nrr6dOnD/r06WPocOkVxp4OImoNeK8i0p82kWxfvHgRADBu3DitbS4uLhr7EIntVXuUSkStE+9VRPrRJoaRqIaI9O3bV2ubhYUFLC0tIZfLmzkqIiIiInrVtYlku6ysDADQoUOHWrdLpVKUlpY2Z0hERERERG0j2SYiIiIiaonaxJhtqVQKAHX2XpeVldXZ661Pz58/BwBcv37d4J9FRG3fwIED0b59e7HDEA3vqUSkT2LdU9tEsm1rawsAkMvlcHBw0Nj25MkTPH78GI6OjgaPQzV23N/f3+CfRURt36VLlzBy5EixwxAN76lEpE9i3VPbRLLt5OSEnTt3IiUlBZ6enhrbzp8/DwBwdnY2eByTJk3C/v37YWtri9dff93gn0dEbdvAgQPFDkFUvKcSkT6JdU+VCIIgiPLJelRVVYXJkyfj3r17iIyMxKBBgwDUDB+ZPXs2cnJyEB8fj379+gEAioqKUFpaiu7du9c7vGTo0KHo1q0bl2snIiIiokZpE8k2ULOwTWBgIExMTODl5QWpVIrExEQUFBRg2bJlWLhwoXrf1atXIzY2FuvWrYOPj4+6/NGjR1i/fr36/48ePQozMzNMmjRJXfbll182zwERERERUavXJoaRAMCYMWNw8OBBbNmyBSdPnoRCoUD//v2xdOlSTJs2Tac6nj17htjY2HrLmGwTERERka7aTM82EREREVFL02Z6ton0qaCgABMmTKh3HyMjI52mJMvNzUVCQgLOnTsHuVyO4uJidOnSBaNHj0ZQUBDs7Oz0FTYZiD6vB5Vz584hIiICWVlZEAQBDg4OWLBgAVxdXZsabpuQkZGBrVu3Ij09Xf2k8oMPPsDUqVN1rqOyshIRERGIi4vD3bt3YWFhgfHjx2PZsmXo1q2bxr6q4YX1WbJkCRYtWtSo4yHdNXfbA0B5eTl++uknHDt2DAUFBRAEAb1794aHhwf8/f2bZfpgqiFG+z958gTffvstTp8+jcLCQkilUjg7OyMkJAQDBgxo8jGxZ5uoFiUlJdi7d2+t265evYqzZ8/Czc0N33333UvrCg0NxYkTJyCTyTBy5EhIpVLcvHkTycnJMDMzww8//IBRo0bp+xBIj/R5PQDAsWPHsGLFClhaWsLT0xMSiQQnT57EgwcPsGHDBp2HvrVVaWlpmDdvHkxMTODp6YkOHTqo38EJDQ3FRx999NI6qqurMX/+fKSkpGD48OFwdnZGXl4efvnlF/Ts2RORkZEaX7qnT5+u88fSrl278OzZM0RFRWHYsGF6O07SJkbbKxQKvPfee7hy5QoGDRoEJycnSCQSpKWl4caNGxgwYACioqI4I04zEKP9Hz9+jNmzZyM3NxeOjo4YMWIE7t+/j1OnTsHY2Bh79+7F8OHDm3ZgAhE1SFBQkCCTyYRTp07ptH9MTIxw/fp1rfL4+HhBJpMJU6ZM0XeI1Iwaej0UFxcLo0aNEkaPHi3cvXtXXX7v3j3BxcVFGDVqlFBcXGyocFs8hUIhTJw4UXBwcBCysrLU5aWlpYKnp6cwePBgIScn56X1REdHCzKZTAgNDRWqq6u1yleuXKlTPJmZmYJMJhO8vLwafCzUMGK1/fHjxwWZTCYsXrxYq67g4GBBJpMJsbGxjT8w0olY7f/5558LMplMWLdunUb55cuXhUGDBglTpkwRlEplk46Ny7UTNcC9e/eQnJyMLl26wN3dXad/4+PjU+vcnp6enrC1tcWtW7fw6NEjfYdKzaAx10NCQgJKSkrg7++PXr16qcu7d++OgIAAlJSUICEhwVAht3ipqanIy8uDl5cXBg8erC6XSqUIDg5GVVUVDh8+/NJ6oqKiAAAff/wxJBKJutzX1xd2dnY4ceIEysrKdK7nnXfeaeihUAOJ1fYFBQUAADc3N626xo8fDwB4+PBh4w6KdCZW+58+fRpGRkYICQnRqMfR0RHu7u64desWLl682KRjY7JN1ACxsbFQKpXw9vaGiYlJk+tT1WFszNcnWqPGXA+qm/a4ceO0tqnGazf1xt6a1Xd+XFxcNPapS0VFBa5cuYJ+/frBysqq1noqKytx5cqVeuspLy/H8ePHYWpqCm9vb10PgRpJrLbv378/gJr3KP5fcnIyJBJJsyyM96oTq/0fPnwIS0tLmJuba+1vbW0NoOaHQFPwG55IR4IgICYmBoB+erkyMjLwzz//YOjQoejYsWOT66Pm1djrQbUEed++fbW2qcrkcnnTA2yl6js/FhYWsLS0fOn5ycvLQ3V1NWxtbWvdrirPzc1Vf4nXJiEhAaWlpfD09ESnTp10ip8aT6y2d3d3h7u7O06dOgUfHx84OTkBqEns5HI51qxZg6FDhzbuoEhnYrW/paUlHj58iKdPn2ol3KqnHqrYGos920Q6unjxIvLy8vDGG280eQaR0tJSrFq1CkZGRlixYoWeIqTm1NjrQfX4srbZDdq3b4927dqhtLRUb3G2NvWdH6DmkfLLzo9qu1QqrXW76gv1ZcNIVD+mZs6cWe9+pB9itb1EIkF4eDjmzp2La9euYc+ePdizZw+uXbuGiRMncoagZiJW+7u5uaG6uhrbtm3T2DcjIwNnz57VqLex2LNNbdro0aNRXFys8/779u3D6NGja90WHR0NoOm92hUVFVi8eDFu376N0NDQOj+P9K8lXg/UMsnlcvzxxx+wtrbGmDFjxA6HDKi8vByhoaHIyMjApk2bMHbsWEgkEly4cAFr165FcnIyIiMjYWNjI3aoZABLlixBcnIydu3ahfT0dIwYMQJFRUU4deoU7Ozs8Pfff8PIqGl900y2qU3z8vLC06dPdd6/a9eutZaXlJQgMTERUqkUHh4ejY6nsrISixYtQmpqKoKCgnSaxoj0pyVcD6oel9LSUlhaWmpse/bsGZRK5Ss9p++L56c2ZWVlLz0/qu119VyrroG6er+Amh9TgiDA19dX4yUrMhyx2n7nzp04c+YMtm/frjGfvoeHB8zNzTF//nyEh4cjLCxM94OhBhOr/Xv27ImYmBhs2bIFycnJyMzMRM+ePbFkyRJYW1sjNDQUnTt3bvDxvIjJNrVpn376qV7qiYuLQ3l5Ofz8/Bo912pFRQWCg4ORkpKCwMBALF++XC+xke5awvVga2uLq1evQi6XayXbqvGItY1ZfFWoxlTK5XI4ODhobHvy5AkeP34MR0fHeuuwsbGBkZFRneMsVeV1jetUKpWIjY1Fu3bt4Ovr25DwqQnEavukpCQAqPUp1pgxYyCRSJCVlaXbQVCjifm336NHD6xdu1Zr/61btwKAVjwNxTHbRDpo6tjNFxPtuXPncpx2K9eU60H18lVKSorWNtVsCK/yzAf1nZ/z588DePn5ee211zBs2DDk5OTgzp07tdZjampa50IVSUlJuH//PlxdXdGjR4+GHgI1klhtr1AoANQsbvL/Hj9+DEEQYGpqqvuBUKO0hL/9FymVShw/fhzGxsZ4++23dTmEOjHZJnqJ69evIysrC/b29vW+kf78+XNkZ2fj7t27GuUvJtpz5szBqlWrDB0yGVBTrwcPDw906NAB+/fvR2Fhobq8qKgI+/btQ8eOHTF58mSDxd/Svfnmm+jTpw/i4+M1VnQsKyvD9u3bYWxsjBkzZqjLi4qKkJ2drfXoedasWQCATZs2QXhhoeSYmBhkZ2djypQpdQ4j4Xh8cYjV9qre0m3btkGpVKrLq6ursXnzZgC193qTfonV/gqFAuXl5Rp1VFdXIywsDDk5OfD392/yj24u1070El988QX279+PTz75BO+//36d+6WlpSEgIADOzs748ccf1eWrV69GbGwsunXrBj8/v1r/7YwZM9TzeVLL1tTrAQCOHj2KlStX1rpc+/r161/5OZ1TU1MRGBgIExMTeHl5QSqVqpdsXrZsGRYuXKjeV/X3tW7dOvj4+KjLlUolFixYoLFkc35+PhITE9GjRw9ERUVpLNms8uDBA4wfPx6dOnVCUlIS58BvZmK0fWFhIWbOnIn79+9jwIAB6hdi09LScPPmTVhZWSE6OrrJ43bp5cRo/3///Reenp5wcXGBtbU1FAoFUlJScPv2bbz11lvYunVrk59s8C5CVI+KigrExcXB1NQU06ZNa1QdqkdZ9+/f15paSMXZ2ZnJdiugj+sBALy9vWFpaYmIiAj1imhDhgzBl19+yWnGUDNO9uDBg9iyZQtOnjwJhUKByiYawgAABOlJREFU/v37Y+nSpTqf93bt2mHHjh2IiIjAsWPHsGfPHlhYWGDGjBlYtmxZrYk2ULNQUVVVFaZPn85EWwRitH2vXr0QGxuLnTt3Ijk5GT///DMkEgl69+6NOXPmICgoSOv9CjIMMdpfKpViwoQJuHz5Ms6ePQtjY2PIZDL85z//ga+vb5NnIgHYs01EREREZDAcs01EREREZCBMtomIiIiIDITJNhERERGRgTDZJiIiIiIyECbbREREREQGwmSbiIiIiMhAmGwTERERERkIk20iIiIiIgNhsk1EREREZCBci5aIiIhalYyMDISHhyM9PR1lZWXo1KkTRo4ciaCgIDg4OIgdHpEGLtdORERErUZWVhZmz56NyspKyGQy2NnZobCwEOnp6TAzM0NkZCTs7e3FDpNIjcNIiIiIqNXYsWMHKisrMW/ePMTFxeGbb77BoUOHsGLFCpSXl+PAgQNih0ikgck2ERERtRqXLl2CRCLBokWLNMrHjx8PALhz544YYRHVick2UTP49ddf8e6772LEiBEYO3YsQkJCkJubCwAICwuDvb09vyCIiHRQXFyMrl27wtzcXKNcLpcDADp27ChGWER14guSRAb2/fffY8OGDTA3N4ebmxuKioqQmJiIzMxMHDlyBImJiRg0aBCsrKzEDpWIqMWrrq6GqampRll+fj42bNgAAHB1dRUjLKI6MdkmMqAbN25g06ZNMDc3x5EjR2BjYwMA2Lx5M7Zv346wsDAUFBQgJCRE5EiJiFqfjRs34s8//0RGRgaUSiUmTZqE6dOnix0WkQYOIyEyoMOHD6O6uhre3t7qRBsAAgMDYWpqisOHDwMAJk6cKFaIRESt1u+//46//voLSqUSAGBiYsIhedTiMNkmMqDMzEwA2sm0ubk5hgwZAgCwtrbGwIEDmz02IqLWLjIyEhcuXMDu3bvh6emJ+Ph4+Pn5IT8/X+zQiNSYbBMZ0KNHjwAAvXv31tqmSrDZq01E1DjGxsbo3Lkzxo4di6+++goffvghHj58iIiICLFDI1Jjsk3UDMzMzLTKunTpAoAv8xAR6cusWbMA1KwwSdRSMNkmMiBVQl1UVKS17bfffgPwv95vIiJqGolEAgCoqqoSORKi/2GyTWRAqnHZFy5c0CjPzs5GVlYWAODmzZvNHhcRUWv29OlTPHv2TKtcdT/lVKrUkjDZJjKgqVOnAgB2796NnJwcADVzxG7cuBFAzZvzCQkJ7IUhImqA4uJiLF++HE+fPlWXPXr0COHh4QAAd3d3sUIj0iIRBEEQOwiituyzzz7DoUOH0L59e4wbNw75+fm4fv06XF1dYWNjgwMHDmD48OHw8vJCQECA2OESEbVo9vb26v+2sLCAk5MTFAoF0tPT8eTJEzg6OmLfvn1aC98QiYWL2hAZ2Jo1a2BnZ4fo6GgkJSUBANzc3PD1118DAEpLS5GYmIiuXbsy2SYi0kHPnj3h5+eHo0ePIikpCUZGRujbty8CAgLU6xgQtRTs2SYiIqJWw97eHlZWVjhz5ozYoRDphGO2iYiIiIgMhMk2EREREZGBMNkmIiIiIjIQjtkmIiIiIjIQ9mwTERERERkIk20iIiIiIgNhsk1EREREZCBMtomIiIiIDITJNhERERGRgTDZJiIiIiIyECbbREREREQGwmSbiIiIiMhA/gszepbFRWJbrgAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "az.plot_pair(keepers);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summarize the marginal distributions in a table" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
meansdmc errorhpd 3%hpd 97%
α-7.190.050.0-7.29-7.09
β0.080.000.00.070.08
s20.190.030.00.140.26
\n", "
" ], "text/plain": [ " mean sd mc error hpd 3% hpd 97%\n", "α -7.19 0.05 0.0 -7.29 -7.09\n", "β 0.08 0.00 0.0 0.07 0.08\n", "s2 0.19 0.03 0.0 0.14 0.26" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "summary = az.summary(keepers)\n", "summary" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot the marginal posterior $f(\\beta \\mid Y)$" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "az.plot_posterior(keepers, var_names=[\"β\"], round_to=2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot the fitted regression line" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(yr, Y, \".\")\n", "plt.plot(yr, summary[\"mean\"][\"α\"] + summary[\"mean\"][\"β\"] * X, \"C1\");" ] } ], "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": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 2 }