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@AustinRochford
Created March 8, 2015 21:49
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Robust Regresion with t-Distributed Residuals
{"nbformat_minor": 0, "cells": [{"execution_count": 1, "cell_type": "code", "source": "%matplotlib inline", "outputs": [], "metadata": {"collapsed": true, "trusted": false}}, {"source": "---\ntitle: Robust Regression with t-Distributed Residuals\ntags: Statistics, PyMC\n---", "cell_type": "markdown", "metadata": {}}, {"source": "Ordinarly least squares (OLS) is, without a doubt, the most-well known linear regression model. Despite its wide applicability, it often gives undesireable results when the data deviate from its underlying normal model. In particular, it is quite sensitive to outliers in the data. In this post, we will illustrate this sensitivity and then show that changing the error distribution results in a more robust regression model.\n\nWe will use one of the data sets from [Anscombe's quartet](http://en.wikipedia.org/wiki/Anscombe%27s_quartet) to illustrate these concepts. Anscombe's quartet is a well-known group of four data sets that illustrates the importance of exploratory data analysis and visualization. In particular, we will use the third dataset from Anscombe's quartet. This data set is shown below.", "cell_type": "markdown", "metadata": {}}, {"execution_count": 2, "cell_type": "code", "source": "from matplotlib import pyplot as plt\nimport numpy as np\nimport pandas as pd\nimport pymc3\nfrom scipy import stats\nimport seaborn as sns\nfrom statsmodels import api as sm", "outputs": [{"output_type": "stream", "name": "stderr", "text": ":0: FutureWarning: IPython widgets are experimental and may change in the future.\n"}], "metadata": {"collapsed": false, "trusted": false}}, {"execution_count": 3, "cell_type": "code", "source": "x = np.array([10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5])\ny = np.array([7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73])", "outputs": [], "metadata": {"collapsed": false, "trusted": false}}, {"execution_count": 4, "cell_type": "code", "source": "X_MIN, X_MAX = x.min() - 1, x.max() + 1", "outputs": [], "metadata": {"collapsed": true, "trusted": false}}, {"execution_count": 5, "cell_type": "code", "source": "fig, ax = plt.subplots()\n\nax.scatter(x, y);\n\nax.set_xlim(X_MIN, X_MAX);", "outputs": [{"output_type": "display_data", "data": {"image/png": 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UMwB0JHgBoCPBCwAdCV4A6EjwAkBHrmpmX7k4FzlZv4fWrTvAfiN42Tc2z0U+dcpcZGD/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\nZAAAAABJRU5ErkJggg==\n", "text/plain": "<matplotlib.figure.Figure at 0x7f4d0cd9e9d0>"}, "metadata": {}}], "metadata": {"collapsed": false, "trusted": false}}, {"source": "It is quite clear that this data set exhibits a highly linear relationship, with one outlier (when `x = 13`). Below, we show the results of two OLS models fit to this data. One is fit to all of the data, and the other is fit to the data with the outlier point removed.", "cell_type": "markdown", "metadata": {}}, {"execution_count": 6, "cell_type": "code", "source": "X = sm.add_constant(x)", "outputs": [], "metadata": {"collapsed": true, "trusted": false}}, {"execution_count": 7, "cell_type": "code", "source": "ols_result = sm.OLS(y, X).fit()", "outputs": [], "metadata": {"collapsed": true, "trusted": false}}, {"execution_count": 8, "cell_type": "code", "source": "x_no_outlier = x[x != 13]\nX_no_outlier = X[x != 13]\ny_no_outlier = y[x != 13]", "outputs": [], "metadata": {"collapsed": true, "trusted": false}}, {"execution_count": 9, "cell_type": "code", "source": "no_outlier_result = sm.OLS(y_no_outlier, X_no_outlier).fit()", "outputs": [], "metadata": {"collapsed": true, "trusted": false}}, {"execution_count": 10, "cell_type": "code", "source": "xs = np.linspace(X_MIN, X_MAX, 20)\nXS = sm.add_constant(xs)", "outputs": [], "metadata": {"collapsed": true, "trusted": false}}, {"execution_count": 11, "cell_type": "code", "source": "fig, ax = plt.subplots()\n\nax.scatter(x, y);\nax.plot(xs, ols_result.predict(XS), label='OLS model (full)');\nax.plot(xs, no_outlier_result.predict(XS), label='OLS model (without outlier)');\n\nax.set_xlim(X_MIN, X_MAX);\n\nax.legend(loc='upper left');", "outputs": [{"output_type": "display_data", "data": {"image/png": 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C9xEREZn3rniN93IMw/hTYMQ0zR9e7nmZmcnExcVey0dNi5yc1JkewpyhuZoYzdPEaa4m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\ny6L1XDv1o0Hb1HvyLVVtEhW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"text/plain": "<matplotlib.figure.Figure at 0x7f4d0cb15d90>"}, "metadata": {}}], "metadata": {"collapsed": false, "trusted": false}}, {"source": "One of the ways the OLS estimator can be derived is by minimizing the mean squared error (MSE) of the model on the training data. Below we show the MSE of both of these model on both the full data set and the data set without the outlier.", "cell_type": "markdown", "metadata": {}}, {"execution_count": 12, "cell_type": "code", "source": "def mse(actual, predicted):\n return ((actual - predicted)**2).mean()", "outputs": [], "metadata": {"collapsed": true, "trusted": false}}, {"execution_count": 13, "cell_type": "code", "source": "mse_df = pd.DataFrame({\n 'Full data set': [\n mse(y, ols_result.predict(X)),\n mse(y, no_outlier_result.predict(X))\n ],\n 'Data set without outlier': [\n mse(y_no_outlier, ols_result.predict(X_no_outlier)),\n mse(y_no_outlier, no_outlier_result.predict(X_no_outlier))\n ]\n },\n index=['Full model', 'No outlier mdoel']\n )\nmse_df = mse_df[mse_df.columns[::-1]]", "outputs": [], "metadata": {"collapsed": false, "trusted": false}}, {"execution_count": 14, "cell_type": "code", "source": "mse_df", "outputs": [{"execution_count": 14, "output_type": "execute_result", "data": {"text/plain": " Full data set Data set without outlier\nFull model 1.250563 0.325152\nNo outlier mdoel 1.637640 0.000008", "text/html": "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n<table border=\"1\" class=\"dataframe\">\n <thead>\n <tr style=\"text-align: right;\">\n <th></th>\n <th>Full data set</th>\n <th>Data set without outlier</th>\n </tr>\n </thead>\n <tbody>\n <tr>\n <th>Full model</th>\n <td> 1.250563</td>\n <td> 0.325152</td>\n </tr>\n <tr>\n <th>No outlier mdoel</th>\n <td> 1.637640</td>\n <td> 0.000008</td>\n </tr>\n </tbody>\n</table>\n</div>"}, "metadata": {}}], "metadata": {"collapsed": false, "trusted": false}}, {"source": "By simple visual inspection, we suspect that without the outlier (`x = 13`), the relationship between `x` and `y` is (almost) perfectly linear. This suspicion is confirmed by this model's very small MSE on the reduced data set.", "cell_type": "markdown", "metadata": {}}, {"source": "#### Toward robust regression", "cell_type": "markdown", "metadata": {}}, {"source": "Unfortunately, we will usually have many more than eleven points in our data set. In reality, the outliers may be more difficult to detect visually, and they may be harder to exclude manually. We would like a model that performs reasonably well, even in the presence of outliers.\n\nBefore we define such a robust regression model, it will be helpful to consider the OLS model mathematically. In the OLS model, we have that\n\n$$y_i = \\vec{\\beta} \\cdot \\vec{x}_i + \\varepsilon_i.$$\n\nHere, $y_i$ is the observation corresponding to the feature vector $\\vec{x}_i$, $\\vec{\\beta}$ is the vector of regression coefficients, and $\\varepsilon_i$ is noise. In the OLS model, the noise terms are independent with identical normal distributions. It is the properties of these normally distributed errors that make OLS susceptible to outliers.\n\nThe normal distribution is well-known to have [thin tails](http://en.wikipedia.org/wiki/Fat-tailed_distribution). That is, it assigns relatively little probability to observations far away from the mean. Students of basic statistics are quite familiar with the fact that approximately 95% of the mass of the normal distribution lies within two standard deviations of the mean.\n\nWe find a robust regression model by choosing an error distribution with fatter tails; a common choice is [Student's t-distribution](https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=student%27s%20t-distribution).\n\nBelow we define this model using [`pymc3`](https://github.com/pymc-devs/pymc3).", "cell_type": "markdown", "metadata": {}}, {"execution_count": 15, "cell_type": "code", "source": "with pymc3.Model() as model:\n # Regression coefficients\n alpha = pymc3.Uniform('alpha', -100, 100)\n beta = pymc3.Uniform('beta', -100, 100)\n \n # Expected value\n y_hat = alpha + beta * x\n \n # Observations with t-distributed error\n y_obs = pymc3.T('y_obs', nu=5, mu=y_hat, observed=y)", "outputs": [], "metadata": {"collapsed": true, "trusted": false}}, {"source": "Here we have given our t-distributed residuals five degrees of freedom. Customarily, these models will use [four, five, or six degrees of freedom](http://en.wikipedia.org/wiki/Robust_regression#Parametric_alternatives). It is important that the number of degrees of freedom, $\\nu$, be relatively small, because as $\\nu \\to \\infty$, the t-distribution converges to the normal distribution.\n\nWe now fit this model using [no-U-turn sampling](http://arxiv.org/abs/1111.4246).", "cell_type": "markdown", "metadata": {}}, {"execution_count": 16, "cell_type": "code", "source": "with model:\n step = pymc3.NUTS()\n trace_ = pymc3.sample(3000, step)\n \nburn = 1000\nthin = 2\ntrace = trace_[burn::thin]", "outputs": [{"output_type": "stream", "name": "stdout", "text": " [-----------------100%-----------------] 3000 of 3000 complete in 8.7 sec"}, {"output_type": "stream", "name": "stderr", "text": "/usr/local/lib/python2.7/dist-packages/theano/scan_module/scan_perform_ext.py:133: RuntimeWarning: numpy.ndarray size changed, may indicate binary incompatibility\n from scan_perform.scan_perform import *\n"}], "metadata": {"collapsed": false, "trusted": false}}, {"source": "The following plots summarize the posterior distribution of the regression intercept ($\\alpha$) and slope ($\\beta$).", "cell_type": "markdown", "metadata": {}}, {"execution_count": 17, "cell_type": "code", "source": "pymc3.plots.traceplot(trace);", "outputs": [{"output_type": "display_data", "data": {"image/png": 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4w8GA8Xy1PA+d1CoVMvkymfQgLEHxc+LnLL3GmSVQCKFJKXUp5T1t2l0H7JdS\nHq63uRO4CWgoSFLKrGX7UWDWb1uF4kyx68Acd9zzNPlihZdfu4k3//L5Kjueg4Cm8daXG1kDv/3I\nUT78ucf44C1XdfSLVihWAiHEGEZNxcbSvJTyhz7aLUsmW+sPak235G92LCD7cumzZgt0+7red7bQ\nFGKLJXchyc3Vz/lZIKBB1d0EWChalAmP4TYzGraOcSlYu8gWysymDGHKTbny2p2fUcynCgxFQp5C\n7u5DRr6vkOM3wiuRhJ8Ypaplm+dOp5nw+VyNhIItqbxnkwUGwkFPgdpzDLVay3WTypZalCvbee3Q\np3Xb44kMQ5EQ8dhgI/bNGrNU03Xfv7texzRfrDQUK7NfsN9nFUvSBc2xnYlZ961Yqba4y1VdEnp0\nuo3dsle6uwW278cN63zc7jMzns+NbrNxNjZZ4TxezaFq9ffeY8/kDSvl4DJndPZzpT4ghGiUlBZC\nTAL/7qPdBuCo5f2x+mc2hBCvE0LsxUh88TvdtFUo+s23HnqOj37xScqVGu969U5uueFCpVh5oGka\nb3nZBdx43WZOzuW47bOPNYKDFYrVghDiZmA38H3gH+v/P+Kz+VqM38QngJ9hlCjpPpOtQ7Hwkkms\nIkHFI9OWTWxoxHhYBTzj/57D887NWvtyU64ckmHDDcylD2s9LC+BRm8InO7fp3Il388NL5GpU9pp\n77G131+xVGXfsUVbKmcvnLqUVyJIP+nKndu0G6f1uwGXel7pfKmRvt1Jteadze2pg/ONOMHGuNwU\ngC4sE9Z5HU1k2HfMSLxhXmPmeXrmyAIPP3Oaaq3G7GKew6dSbZVSvyngzc2s25vp642BdO7DHIap\nPOu11nvPKzGEqYi5jdZtekZa/2RXadU7LdBY557Jl3luJm1JjNM5fs5K8znmFUfXvn2lWjMKVXsl\nnPExBut+zHvOzyLVcmc79mO5GpVSNu7Eeh0qP1XWfF3dUsq7gbuFEC8BPiOEuMhPO4Wi39z70yPc\n9YMDjI8O8L43XN4ScKpoRdM03vTS8wkGNb7xkyP8nzsf50O/drWtaJ9CscL8V+Ba4JtSyquEEC/H\nZyp2KeUhliGTrc1yVcNbuXLUq3JLaKV7vG727z8ZhT2hhfHfavGyjtFNiDZX9D0HQ1PQKZVrjSwP\nzcQCtYYS2K7mU3OMTqWjbomwZEhMLObJFytsXmuNmenYtSt5D9fFVNatTJr9bHrFtfiqH+RQrNu1\ncGav64YUrtURAAAgAElEQVS9h92VLnAvJO029k7Foa3Wr05ZG83rNFm3NlUqOodOpanWasSGB4jH\nmjFh1nPg2zLpouhbX5tKgh9dLaBp1OoWtmb39f490tN7pXA3xtr6oTy62KhZ5ZWSv6Uf3f21SbFc\nZXYxz+TYYMPqmi1UCAcDDFpd70xFVNfJFTwSnnhY4B1deLLv6CKpXIkLGV9SggndMQ4/1uHlzqDp\nR7kKCCFGTBc+IcQo4Mcp+TiwyfJ+E4YFyhUp5QP1JBnx+na+25q0C3A7G1HzWTnu+t6z3PWDA0yN\nD/G/3/0i1rsE5cLZNSc/LNd8bn3DFUQiYb78g/185K5d/O/fftGyFLHsFnV+FC5UpJQz9d8bpJTf\nFkK0lATpK04Bq6FdOaQSm4uVp7mpZXvrR26ChZes4Wa3cFccvFbWLS5I9f+5QsVm8ajVjHTV6VyJ\n0dHB+rbG1gUPd0U/6Do8eWCOWk1nrSUJwoETRpzZpjWjaJpmrM6f7i1W1sudcs+R1pJnTl3KS3hz\nE9xruk6hWG1kqGtZeW8jLGYLFWq6bsSfdalEWmtl+VFAO2W0c36dK1QaBZOt7Z1KVsMK5Jw2esO6\n5jwmbuegE8lOVtKmX6B9HK23XMPaZqZXt25nux9Na5VNEfN3j5rbV1wumkKpwpFTabauizVqyZn7\ncY7VysxCjpkFu/JvZqLcONV0qTXbHqoXBN6xcZx4bJB8sUJkIEhA0zwXidpOykKqrkRbFflcoUIw\noNnm1ImGblU/JytRzNqPcvV5jIxIf49xzN4NfNZHu0eAC4UQW4ETwM3ALdYNhBDnAwellLoQ4mpo\nWMaSndq6cS4lFzADNM8Vzqb5mBareCzCB26+gpBe8ww0Plvm5Iflns+rr9/EYirP9x47zh/93Y/4\nwFuuOqPp6tX5Wd2soKJYEEIEgP1CiPcBRwD31ZM+Ybdc6U3FySF82FfBffSl62TyZZvbkKnMePVr\n68vF6mF+FAoEqNRqlniY1lX/ssXCMpcqkC2USWVKtrifcqWGrjvG4OKe1YlaTXfMQ28IZW61vXQM\nAebo6UzLd41tOgh/pvLnpxCvsyfPmCuXOR84nmQuVeCSrXGmaT1fyZy7wgs0XP5+7uJ1viwu7SiU\nKgQDAU+XqXS+dRztDmHOUejYy3LjtFy59d3uXDm/O3AiSblcY6NL/J08usCOjeMtnwc0rRE3Y/Zm\nWwhxDCoY0HCGL5nn1s1aVXWxEnvNwbz3TNyupCOn0ixkiugnU1y0pRHJ47Akeh8zt9grpxWupuuN\ngsD7ji0SCQcplqvEo4Ps2DTe6L5cqXHgRJLNa0YJW8zt3V6O5UqVXQdnCQYCvOCiNY3PT83nGI9G\nPJNmmc8u8zgtR625buloB5NS/jlwB0ZCiV8BPl7/rFO7CvBe4H5gD/BvUsq9QohbhRC31jd7A/CU\nEOJx4KPAW9q17XZyCkW3fO+xYw3F6vdvuYo1PooIKtzRNI1fe/kOXnzZeg6fSvPRu55sGzyrUJwh\n/jsQAz4EvA74Y4xyI33h9EKOZ44seMZd6DpNi1MvO7A0qtZ0dh+a49hsU4HQ9VZlw9st0Hs3Td3A\nLtpZlYOcxYUwnSuRWMy3JFRI58stVrim8GrfZ7Fc5eRclpn5HHuPLNgsR864J2vTittE6hu4Fd51\n68MNU3mzBr97KYQRR7yTl+Wx4PJMnEsVgGbsWO/C4dKEyif2z/LovtNttyk5xm+X5Z1ak/1tw7Lj\nGKeX5cqtbSdquk5iMc9ittgyVhO3eEZN0xoXvbmrpw/N89AzM66uuG6h2OZ1qDeuvUBbV0Ar1q9D\noQBxS1p8t/pf5iVSqdZ49pjhXqfrOrPJgmufzrgoN+XfaoUDODpjX5gwf8/n08Y+zPOdL1VILOY5\nMuO9kNGW+ljMxQxnLKCOzt66pfLY6QxPHZxzfb6udssVUspPAZ/qtnMp5X0YiSqsn91hef1hwNUd\nw62tQtFPntg/y2e/vY/ocFgpVstEQNN4xysvolSp8tDe09x+927e+/rLlt2/WaHogh9LKfPAIvCy\nfu/s4Emjpk6pUmsI3LpjJbsR+F7/LJktcSKRIRy2uve09r2QLvKcxRKTdnHhq+l6i/Dokh27sa03\nhqDizORmFVzcLBlOCsWKi7tXa181XefpQ/OULMrZ4/sTXHXhdGPF3NaHpc9Mzm4hMfZh2K6CwTZW\npw4ymGmZ03V4+JnTaMCl2+Ou27azuljJ5u1jtbpEmc/JqoslrhO6rp+RFfsWT9Y215BToO9kuWpR\nwq3udW0tV8b/TL7MwRPJls+d2GIFG2O16IL1dtm65c0WA1f/bnRogJwj0URiMU8oEGAhY7jZhQIa\n1VqrNdltWNaxBjS78uO2PmB+limUyRTKzKUKbF8f4/Ris4yCTbnSHMejgzFW1w2LUTtaLrdO7+vM\nzOdIWmPmaoYV+ljC6mKpt1xrQGMhKWuJAzOPrXlM/MRcLTd+igivBd4HnG/ZXpdSvrmfA1MoziSH\nT6X4+Fd3Ew4GeP8br1CK1TISCGj81msuJluosOvAHP9y3zP85qt3+nKtUSj6wHNCiK8C/yKl/NGZ\n2qlntjjdImjV/+11jR8x4k0qVb2hpDmzvpVchMRarVXI9uMW2LSm2QUVzfL16cV8o4ivX0qVWqsA\n3hCy7W5IpUqrpaFYrrZYhZzkSxUmRiMNodayixbLlXWfhXKVxIkkW9ZG3ReA9Gb/JjPzHvVzfCo2\nTsXJGgNkxsH0svL+s70zXbex4nePHqeyp7YmbpYZY0xW5du734VMkWS2xGKmaLuGvBQ/t/smGNRa\nXGBNbHFV9f/jowNUqrWGFcfEGm8YDAagUjXuefvEWrDuM6Bp9oQomnEPyyMLjI1GOG9qxPWYZfLe\nWQU1h3bldcyt4xmKBFsUSJNKtdbyXHG6k3qdskOnUrb3x2YzNut7u7YmuaJVuap/aCpX3T2ilgU/\ny8dfAtYA3wa+YflTKM4JZpN5PvrFXZTLNW597SVsP09lBVxuQsEA7/nVS9m2PsaPd5/iru8fWOkh\nKZ6/XAQ8CXxECPGsEOKPhBAb/TYWQgSFEI8LIb7WzU5bXAHN1zXd0z3K1h7YtX+Ox59NeArbbrFG\nNV13SeVtf18sVzl8KmUT9PXGtvUXmv2/ruscPJHsOjmEjk6x7J79zk+MWTCg+cqwt35yhHCwVQnz\nspoBHDyRJLGY5+ScsUJfKFV49thiw7LhlXzCDb+WK2c8Tr7YqlBWu9FYlgm/tcecboDWazidK7P/\neLIxR6f83rRc2fflJed7xVw5288m85xezLUo517nys1yZdtvu+8sfcZj7WuHhetW02rVablq3YPT\nqmRdFNA0jWSmRDJXatx/bses5TlheevcvJMycGo+76lYgeES7Mwo2Y1VsxNu6eetn80nCzbrF1iy\nPdaPw3aPjM87t7hbn5eCH7fAcSnlf+qlcyHEjRj1Q4LAJ6SUtzm+fyvw+xjnOQ28W0q5q/7dYSAF\nVIGylPK6XsagULQjX6zw0bt2kcyWuOWGC7lqx/RKD+mcZXAgxO++6XL+4rOP8c2HniM6EuaV129Z\n6WEpnmdIKeeAvwX+VghxGfB7wCH8ZcEFeD9GLHDHjBxerj/OFXin5cq9LxrxS9Wa7pra261Okbvl\nyr7NM0cWPNOMmzhdulJtkip0whRmA03/L0rlqj3bYIdj0fqZfaU/NjJAOBSgXDWOWWIxTyQcbBE4\n3SxvpXKVSrXGoRMpkrkSGhoXbBzD7QTNLLi7SvldLbeO++Rs1u7GpZt9rYRy5XdD15dAMxZnYjTC\nRDTS4lamN5QrezsvK4qzVIDhKqb5Ttxh3Y/VtdTNQopurbfVuW9N09As221dF+OwwyITNN08aw4X\ntw7XM7o9m1+A1gQUbsfMLVbJpEXR7OBIYt5HXtjqg3ntwwWv+n1Onjo4x+BAyJY0Z9/RxcbrxWyR\nxWzRVsLBnK95HLzKIbSLw+wVP5ar3UKIrgv4CiGCwMeAG4GLgVuEEDsdmx0EfkFKeTnwZ8A/WL7T\ngV+SUl6lFCtFP6jpOp/4+h6OJ7K87OqNvPzaTZ0bKZZEdHiA33vzlUxEI3zx+wf4ye5TKz0kxfMQ\nIURACPErwJ8Arwb+xWe7jcCrgE/go6ZlxSU2w/n66OlMM5bHzyDa4CbM1PTWOknO7dopVi2Wq2XA\nHI9Wl0B04LFnExyZaVrB2hX6dV3pd9nWKjMdmUmz79hiizB3NNEadJ9I5tl9aL4hjJkr8u1kxeGI\nXTdvqcHlMkLDlar5PuOIv3Kr23Wm8G+5arUgOV2+dXT2H0+2KOSNNYUW10L3fVsXCU7MZvnZ3hl7\n0dsOWK97q0DtZrnSsVpe2liUrdYgy7RDQc1Ih2/BdJMzXIHt+2rXLzjcijWt5Tp200dbU/h7979U\n0i5xjlVnbJluKDrW493JamjFqQN5PbdaLaTG/6Bb1pE+4cdyFcfI6PcgYDqT+om5ug7YL6U8DCCE\nuBMj42Aj65+U8ieW7X8GOF0zVFCGom/c86NDPP7sLDu3THDzyy5Y6eE8b5gcG+T33nwFf/6vj/FP\n9+4lOhLm0m3+CiIqFEtFCPF/MTLTPo2hVP16PcGFH/4a+CBGtsGO2Os+uVuxckVrbaF2QpyHdtYJ\nXW+4lU3FhphLFXwJow23QEdaYy80tLZujVZMoc9cbXdbve7WcmWlXTxnSxyKR1+FUqWR6tm0ErTb\nbciRKMOpwC6mi1SqNULBAI8/m2AgHCTt0/q3FHcqP30vZkotVpZuk0dYXzvjeQKa5ip8NyxXPq8b\n63VitjkxlyXz5Alf7a2Wr0An5UpvWmt1vU2cYv2/M0GEhsaWtVFbXKSp0FVrOpq1Pq+j60MnUy0W\nUZvlSrMr3KVy1fWa97JYO9033cbQLYVyq6JjlJmw8/i+WSq1WsPC1I1y1e0iQ65QMVLI13Qjbs3j\nsdCP8G8/ytXn6n9W/MxwA3DU8v4YcH2b7d8F3OvYx3eEEFXgDinlP/rYp0Lhi0eeOc09Dx5mamyQ\nd7/uUpW97gyzYXqU33nj5fyfO5/g7768mw+99Sq2rlOxboozwjxwvZTyaMctLQghXgOcllI+LoT4\nJT9tYmPDxKKGkDQ5OcrwoGHdqAYCJNKtgvXwYIjp6SixaLLlu8nJUWJzhg4YnxxlcCDkup2T6MgA\nY2NDxDJldmyf5JkjC0TCQVudMdf9xUeYnhxhPlemWDXGFi5UiI4MEAi1jj0cCvgWlKJjQ8SyZQIa\nxKJDRGNDxAp2t6OJ+AixaKtVKTY2xEKqSCw6ZPt8Mt48PqFQgOnpKGPzeQIuGRStLddMRyl6DDtf\n0Rv7mZ6OMnY6y4BH3MnU+BAE2+vo6VKNzetGiAwaSptzDmNjg1S15m/RRNwovxaNDRIpL29Uvnn+\nD51IcnKxQGRwgEgz2zdDIxFi9X1OTo4Si6bcumFqyrgWk9kiY4NhYtE0oVDA5m45NTXKXLbccn1E\noxGmp6PkCmViM9nGuAo1WMhVGu/N63N8fJiYy30DrcfSDT0YbGw3Ho0QCHkXEA6HAkzEBinpMDQY\nIh53PwYTE8Mk8xWmJkep1nRiSaPP+OQIoWCAk4vNBBdrpqNkSjUmJoYZCAeJJXKNfVnvxz1Hk7b5\njA6HmZoaaRyT8bFBAgGtcX5OJotMTAyTr9hF86HBEMFwU8wPDYQgFGJybLBlLhMTI57HtleisUGm\nLNfO+MQw2fqYp6aMot56KOfr3IGRZGQqEm67KDE9HWUmVWzcR9mKzmh0kPBgmMmpUWILhdY2U1FG\nhvx6hfujo3IlpfyXHvv2rWIKIV4K/CbwIsvHL5JSnhRCTGMUMX5GSvlAu35WsChlX1Dz6Q+HTiT5\n5L17GRwI8if/8efZ6hHk6IfVMqfl4kzOZ3o6ihYK8heffpi/uespbnvvizlvurXI41L3cS5xrs1n\nJZBS/v89Nn0h8FohxKuAQSAmhPi0lPLtXg1OzqRIpQ2Be3Y2w1DE+MmdW8g1PrdSKoZIJNKu383O\nZpp9JTJEBoKu2zmplStQrZJK51lcyJFO5SmEAszMpDg1n2NdfNi1n7m5MMFajfn6WCulELlihVql\n0uK+BrimR/didjZAKp1nzeQoqXTedf+nLMfOymN7TrUEzht9No9bOBggkUizsJBtG4QPMBfWfB3H\n06dTLCZznnMcDHbuJ5XOczqRJpVxF+qDes323dxchjUTwywu5t1rdy2B06dTaJrG7mfd61hZ53Lw\nyLzn3GZnM8wmCxyfzTSupXAwaIvROX06zdxCtqVtrVIhkRgkX6w0+k8k0szNZxvvZ043r4ODz9Vc\nj10sOuTrHFq3GR0ItG0TCgQI1Gqk0nmKhSBP7j3Vsr2GxsK8cR/OzWep1fTGNgvzWUIh+z5SyXDj\nGoiEm/dvKBDg2PFFqrUaw4Phlv1UyxXb9aVVq7ZC0ql0HiojtnaRcJB8rtQ4D+Yx+umuY1y8Nd6y\nj7n51v36JRgIuMZ76tUqp0ea/Q5b7rWTp1KEQwFm5t2fhV7URiKkst5KcSKRZnEx17hODlcqVKqG\n9Wp+Luu6r7m5DLlIaFl/X/2kYt8B/BOwUUq5VQhxNfBaKeX/6ND0OGANYtmEYb1y9n858I/AjVLK\nhv1USnmy/j8hhPgKhpthW+Uqkegua9FqZno6qubTB1K5En/2L49QLFV5z69exkhI63lcq2VOy8VK\nzOfC9VHe9vIdfOZb+/ivtz/IH77tGiai7TMu+UWdn9XN2aYoSin/CPgjACHELwIfaKdYgb3AaqcY\nC2Mbnblk68qqs003dVtqetMdyqiLqpErVnjoGSNVt3+3nPa+M51SOVsxC5tqbQLJvQLdvZI72D9u\nul91wq+rUTJbaqs8Ot0CvVjwUKzc8JHnxJVwMGAL/HftG/9xF7PJPAFNc73udJ2GJcFMWBEIYKQi\nq+NVTNbMbtnO7dFaOLqbY2eydV2M44lMy/EYGQxzydY4Tx92K3vgGEO52kipPhwJ2RT2diGJTle9\ngMUtsMVdbn8CwJaQobEP3R5vVHa5ZlvijGq6Z6IPZ201cx+9MjYy0JKCHoxni1eW1Eq1RjgU6DpZ\ni9/7zLrPmpkA6AwGGvnxhbod+F8YBRfBSGHrp8bVI8CFQoitQogB4GbgHusGQojNwJeBt0kp91s+\nHxZCROuvR4BXAE/52KdC4UmlWuP2r+xmLlXgdS/exjVCZQZcDbz06o3c9OJtzCYL/N8vPNEo1KhQ\nrHI6SgX2lOOdtatiucqzxxfdv+xR+tEtwfOaprUIYR0VkPrXnRJqdZNwy8zO1i42yku58srsZRXQ\nzW69FKex4QEmY4YPnN9Cu888t9D2e2dNn+WgEffW5bkfjPiI+OiiS03TPM9VYjHfkqjCqWh7ZZoz\nXQdbhmKZ76zHYoNJdGig7ffhYIC18da6lZpmJFiyJjm44Lwxr2E0GBtpLv7p6G21K+elah5DI9Oh\nZT+WbbyUDXu2Tjflyr6zak13tSYBjcQxseHmsXPG3HWDV2HusltNO8v4oPtr208IR82m0DVjrrzo\nR8yVn6fBmJTyPupnU0pZBTo6ZkopK8B7gfsx0tb+m5RyrxDiViHErfXN/hiYAG6v1w15qP75OuAB\nIcQTGIkuvi6l/FY3E1MonHz+O88ijy5yjZjmNS/autLDUVh47Yu28rKrN3I8keWjd+3y7V6kUKwE\nUsp/l1K+tt02mZzd0tFtOopQwLsA53MzaY65ZLlzwxqMH9C0FktVJOwuBjgTWnRa9e2lKHh75cr9\nKHkpXfuONZVSs9fNa93djEOhQGPffpWrTgT7Ebfrkaq8EwOhANs6uLv7TSIBhuXKyy3RWiTXxK+i\nXanVWjLnOWt9dRK+rfuKhFrrmsVjEddL11RGLtgwxnmTI1y3cy1T40P83MXrGB0Ko+N+jMYdnhVm\nsVsNu5BuLGS4W65qNbt2ZZ2jV4kDa1dup8J5nPxYt3tJQe52z3rdx9VazdOCaj6Hur22fY3ZWjuu\nZhyLYMBZTKKJ9ze94yehRaVueQKgnpbdl+RTV8ruc3x2h+X1bwG/5dLuIHCln30oFH74wePH+f7j\nx9k4Pcq7Xr2zJ0FA0T80TeOWl19IplDmZ3tm+LsvP8X73nAZYZcfS4ViKQgh1gJ/BWyRUr6k7pr+\nQinlx5dzP4/J0+QK1kyAWF53ligiA0EqhaZgkrIkZljIFD1dpKzuW5FQ0Ga5CgRaha5OK8F+hZ92\nLn4mg+GQLatYu8ewV3HiTu5uRsfGvzUTw+SL1RYFYCAUbChVXqv73RLug3Jl1nLqRhECQ1i0WiW8\n+u4X3biIVhzWjb1HFmwJCzpmhgxoDYHUud9gIGB85qYQ1K/XiWikxRVdQ7PdNyZjIxHPxQivsdne\n18dR071d9rwspNa5deMW3I5uzpOJm3toO3nqqYNzjdduz8Bu5+JVq8qKtUej3IFOQPOe70pZrm7H\ncN2bEkL8KfAjjB8mheKsYM/heT777X2MDoV53xsua6k9oVgdBDSNd716J5efP8nuQ/P83Vd2d5Wm\nVaHwyT8CDwLj9fcSeM9y70TXfSoCHjhXaE/MuVkI3FeR18dHWDsxTDBoFFg1BRj3QqMewo3j406r\nu36EiUg4wBXnT9nG2g+sY3XbhVXerlSWR1C1ukYt17x0Wgs+m1x1QRu3dg0GB4LEo4O2jy/ZGme0\nnrGyv8qV/22d8UfOTHCdhG+rsO21X3fLlc8BWtiydtSzVpKmtd4hXjFXyUzJdxp+A91moXNzHbQe\nJqfV2wuvY+C8buxtWhtZn1Vb1hqxtKMu2fesSrR5Xru9DjsphLlCxWb9My2u7dqtiHIlpfwUcBvw\neYwMpm+XUjpTsysUq5Ljs1n+7iu7AXjPr17K9Li/lJ+KlSEUDPCeX72US7fF2XVgjtvv3u27grtC\n4ZMNUsrbgQqAlLII9P0icxbT7IQfAd1N8NQ02LIuyrb1MSPVsd4s5OnWZyfhtTFus6nH5m4ryudN\njrQMbnCgaY3W+lUBw+Ge5SRqseq41efpBatA26sVy+kKWavplF1cpCOhIJEBb6u+4aKmsWPTOOOW\nGKHo8IBlcXFp2lX7GJbO165mTTrSZijtLk8NeyyY8xo037kq2O0H17AaWgkGAp7xRW47suo4V14w\n1fg6nS/ZFkv8WG/6YrnyOAoXbLTHnl2yNd5QuNwMR1ar9frJEV5w0RpbbJqJbdy6y2fAxVvibcfc\nyXB1xCN2LBBojTdtsjJugdRToLfN1OeGEOJG4CNAEPiElPI2x/dvBX4fY2Zp4N1Syl1+2ioUnUhm\nS3z0i0+SL1b4j6+5GLF5YqWHpPBBOBTkva+/jL/90i6e2D/L7XfvVrXIFMtJRQjR+DUVQoy323i5\n6Dbmyo/7i2s7iwShaYbwksyUGu+dmEkfTKE7Ho24Wsk6jcZNoB4I2xUAp2tOvyxX1pV06x5Gh8Js\nXhslNjxAsk0656XuMxgMQKX7uNF03m7NeO50mkVn0WPoeDJsxWyd29bfLyXU7OKtcVKZUiPeyEnI\nx7U7MhgiUyh3jHlrp0hoGg5F2mu71i/aWjJwj7cKBLyvWU2znxbNca0PDoTIdygL0A5bzJXTtTcQ\nsI3Xb9p+t6kMhIItc4wOD5BYdE8sEtC0Fit7MBBwvUStFjdzhE6LW2xkgHXxYU7N59ixcZwDJ1I2\n191Oz0XrzMeGBxop69s9albEciWEeNjl7yEf7YLAx4AbgYuBW4QQOx2bHQR+QUp5OfBnwD900Vah\n8KRUrvK3X9rFbLLATS/exs9f2preVLF6GQgHee8bLmfnlgkef3aWj961y7W2jULRA18GPo5Rp+od\nwLeBf+77XruMuepVudJsypURH2EKW+0sV6NDYa68YKrhzuMcYafRuPXttOA4Bdp+KVq2eCNLt6ND\n4cZ31lV7q6vX6FC4YwY6N6xWinCX6aK7pZOLZluFxHzhYpnxv/8O3/s4l2ZGw2rVO6MctB+jM4uh\np+Lj8llby1v9v1Pv66SQue1jKjbUcJXr9RrXdfd9b1oTZTgSQtPaW/g897tMl6nbo8ptOFblyi3m\nypzjlrVRrhVriMcGGR6024A6XVvW68XuMqp53jf9UK78WK4+aHk9CNwCnPDR7jpgv5TyMIAQ4k7g\nJmCvuYGU8ieW7X8GbPTbVqHwolqrccc9T3PwRIqfv2Qtr1WZAc9KIuEgv/PGy/n43bt58sAcf/n5\nx3n/m67oGKitULRDSnmbEOJtGJlqXwV8VEr5r37aCiEGgX8HIsAA8FUp5R/6aat7vnEnoGlcsjXO\noZNpckX/5QmsgoJz9dTVclXzdhkEi4DZQQJxc/HrJLTYrD2BALV6yu7BgdCSFlM2rWlmCbQKY1YB\nNOBh3RoIBRkeDDWsSJvXRD2Ta1ixZgvsdyKedZOtqcWtWAXMjMPyZR4PHd2Xe5lnceg259bPwoDp\nHlqr6W0FZqPGk3uNrU4xTg3LqZsrW7shNlKmOxI31OcVjw661HXSQNOt7wC7i12vCybgrsCYluB2\np3F9fISNa0aQx1uv4eVY0AhoGrGRAYYjYSbHmrFabkqxTVnVW7czFyg0TWvWs+pS/7dbbf0t3qxI\ntkAp5Q+s74UQ92MEA3diA3DU8v4YcH2b7d8F3NtjW4UCMFZB/ukbz/D4s7Ps3DLBO165s6eMOIrV\nQSQc5D2vv4xPffMZHnzqFH/+mUf5LzdfyZSKnVMsgboy5UuhcrQrCCFeKqXMCSFCwI+EEC+WUv6o\nY2NrzJXL19HhAcLBQENoCwY0osMDrIsPcfCku3IVCgTYfl6MmYU8mXyZaq1mE+BaYlBcnoUL6WJ9\nW+dw7aPsxXKlaZpNEHVuExkINgTnUFDDlOH9uJV5EQoEPBUna1Fnr5TOAU2zWdxiI50Xcy7aPGGb\n20AXGeV6YZ1L3SYr1lPnrDFlDtMortp5X14ude3OkB+hfbCu+FRrOqcXW91QTVLZUj3bW6uC5azb\n5k4DT1YAACAASURBVNztjk2GYtOt5crEJqhb4rsu3DjGz/balatW90u349Zxl554ngfNeJ5Yx3rh\nhnEWs0WGIyHWTgx7KnXjoxFmFnL2PnsY2+BAiMvPn+y4ndUF1C2hxchgaxIMJ53G51bvznztefxX\nyHLlZAxY62M73/qmEOKlwG8CL+q2rZXp6WgvzVYtaj7does6/3D3U/zk6VOIzRP86a0vZMhPMcUl\noM7RmeFDv3Edn/rGHr70/f38r399lA/9+gu47IKpju1W63x65Vybz5lECPGXLh/r1EMspJS/76cf\nKaUpjQxgxATP+2lnW7R1WdUNBTTWxYcbikhDEOiQ5SoeGyQeG+SxfQmqNadA0VlqMOMZvLKgmdKP\ntaupsSFmk3nbZu7KlWFFcs7JFJR1HYYjRuyNbaxLEHbaCQ9WtyRrYo3JscGGkFksVxkPNhWqAR/F\ngcccCpgz1qxb/FrLvLAeg1Ag4BqDY61/1o7hiIcVcYnZ10xLX65Y8aztBM34oZGhcEuGvYBmWh3q\n1leLEnHF+VONOEJ3xcR7bGY33oK6f/dDW79LWDRwTcpRn78zXX9kIMj5Y2OtDRxEh8NcdcE0j+9P\n9Dwur1joeGywJXbTaoE3D615jDdNj7oWe+4Wq3WsncvoBRvG2H88CfRFt+qsXAkhHra8DQDb8ZeK\n/TiwyfJ+E4YFytn/5RipcW+UUi5009ZJItH7w2i1MT0dVfPpkrsfOMjXHzzMhukR3vOrl5JJ5fFX\nZrM31Dk6s7z6+s0MhQN8/jvP8t8+/mPe9NLzecULNnn+0K32+XTLuTifM0yWptzpvGi6WQwMAI8B\n5wO3Syn3uG135Y5pfvjoc80ddNhDpaq7Zrnz+8Nv3gbW+6GbJDBm/R7n/eQ27As2jLF1XZTDJ9PM\npvK2/dvH5LQsGG9MF8BKtWYoIoWyTfFxs4tYlQTraw2Ny7bH2VWvp+NMU21dLa9YXsdjg2xZGyU6\nPECxVG0oV+l8iQ3BZpbDsA/lynnM/Chk7ViKEA6d4pSM/7sOztrS4ruxaU2UNeNDJLOllnpgS7Fc\nbT9vrHFciyV/iT+sipWpnJerNU+lx5bYxaU/PwsP3ST9cCaw6NVa5oaOh4JY36+zELPfyyegaYQG\nAmxZG+XITPvfFtPSa03WMhAKsmOTez6g0aEwF2+Js+eI+9qTOVzzfj1vasR1js7EIp2mZl0IsMef\n2p9Rw5Gw63bLRbcxVxXgoJTST8zVI8CFQoitGDFaN2PEazUQQmzGCC5+m5RyfzdtFQor9/zoEPc8\neJjp8UH+y81XutZYUJz9/PLVG9m0ZpS//8pu/u17+zl0MsVv3HhR3y2UirMfKeX/WKZ+asCVQogx\n4H4hxC853ecBxkYjXCHWkitWmJnLMTk5wuTYEJlciZHRMrGSXViNjQwwNTlKbM5QVs7fEmdsNEIt\nGCSRdl/ZD4UCDSU1cjRJZNCwyJifVbQAhXo2wJGhMNPTUWLRpGtf69eNEY8NEhgIEVssMDExwvR0\nlLGFPFooyHhskKoWYHQ43Oh/bHyYh/fMADA5OUrGMaepyVEGI0FiM8YKdjw+zPR0lHgiS75QoVKt\nsXY6SgWNYFAjUgsTDgUYHAihOeKWtq6PcfikkWY5HhskOjLAkfr7TRsmOJxoujdZFfeFfIVY0Yzl\nCtq+M18nFvLMpJrZA7dvjqOFQqyJDxMbGeAFwSDPHl10rS9k7edyoZPJlVm3ZpRTSe9shE4Xtx2b\nJ9hnKR47OTnCfLa5yh+L2t2gG8c/lnRV2sdGBxrbRE+kqFZ1BsLGtZIsVsmVjUbxyVFip91d8qYn\nhrh4m+HqdTiRtdUcjMdHCEXCLZkMR4bCZPNltmycIFs2tt96XozDJ+zpsddORxkZCvPcbI6ay/y6\nIR4fIXMqTSw6xGR8BPMSXLMm2rAg6sEgpx330PR01FNxnkkVqWoBhiIhQpa6mNZrx3kfTU9FKVVq\nxGaN63BycpTxaGs68gs2lzldV+TNxY9O5UbWTg6zZjpK7JR9uXhycpSKFoBgkLGxocbcp6aM42vj\naLLlOK9ZE0XTNKano0SGBjg1l2vcI+b8tm8YY3o6yvjEMKPHkmxeF23c89dfuq5t3dCJeI1j83n3\n78aNZ8Hxhbxxr62JuW43Np8nEGqeu/jkKDGP56GTeHy48fybnBxlKj7ceBZNT48SS5ivl3+hr+uY\nK79IKStCiPcC92O4TnxSSrlXCHFr/fs7gD/GCCq+XQgBUJZSXufVtpdxKM5tdF3n7gcO8bUfH2Zq\nbJAPvuUqxkdbH2iKc4cLN47zJ+98AbffvZuH9p7m4IkUv/mqnVy0RaXaV3RGCBED/jvwy/WPvgv8\nmZSyK7OglDIphPgGcC3wA7dthoIayUKZVDrP7GyGSqHMQ8/MuPZXq1SYHwqRShvCSC5ToJQvMZ/M\nNz6zphYGw4JjWjPNbVI0vThK9X0D7NwYI5FIN96b6Y5N0skc1WKZhXSRVDrP/HyIwQAsLubJFsoE\najVSmSLVcqXRf6FUafS3EAk2XpvMz2cYijTnNBIOkBgMkc0UyOTLTI4NkskUGt9ft9OIONh7eKEl\nLfmC5dgE9RqVYnNuc3OZxutt62M2C29iNkOq7pa4cUvc1fo7n2qO4eItcebns4wNBinmiiRyRYJA\noFZjsSWJQX0f9T6HgxrD0QGy6ULLsbASDAQalqCLNk8Q0muE0BvukwsLA432sehQS1+Nc54quKYM\nr1Wa5yiZzFPTdTZMjZJIpEmnmtfTzOmUre8dG8fZd2wRaF4vAJlMwZbUYnY2Q9ZybZlsnR5h3ViE\nfLY5/1J+0OW6yFIeDrc9Rn5ZjBgKVCqdZ3QgYLsmTOVlPtl6PmZn056W3WQyTypdIJ8L2AqBW6+d\nlv7mMpQrteb+5zOUC61KQLZ+vYcCAa4R0+w+NE+2YCjSYyORlhIBW9ZGGR8MMjubadnnwsIAqWSB\nVLZICL1xnc/OZsgNtor3rcegqawtLORIpfMUw0Hbc0KrjDbmPTkSJpsuUMyXKFaqpBZzpDtYfbzO\n8VwkyHBIY2EhR6FU9fTKSCZzZPLNhYbkYs73dTMSbl4Pi0MhgrVq83k1nyWVzqOhNfa9nEqWH7fA\nBE2/dCe6lHKNV1sp5X3AfY7P7rC8/i3gt/y2VSis6LrOl/79IPf+9Ahrxof44C1X2bLVKM5dxkcj\nfPCWq7jnwcPc+5MjfPjzj3PDtRt5wy+eT2SJ8Q6Kc55/ApLA+zB+196JkYr9jZ0aCiGmgIqUclEI\nMQS8HPjTdm2sP5zW1X8wXGcagoOHC5LVRc5PLM9OSxFOq0W3JQ264yfdS9B0E97d+nAvaKy5urid\nf94YB04k2b5hjIPPNd2GGm5TLtKG1dVOM4JNXFk7YY/bMK0Ta8aHfSWn8LNNJ8KhQIsibMU69IG6\nhc56erwsZL6xNDfPi9m99TyfXrALqc40/iZOd7aa7p7hT9OMJETOek47t8TJFyscthR47aVuYSgQ\noKbrjvTdlu8tfdrTcDe32bY+Ripb8rX/TjW4rJguet1gFvkGmIwNutZfmxobJBgIoOvu1i1znzW3\nVHw9YN7Tw5EQuWLFtWjyZedPdszy2InTC3k2rRmlUtXbF2a2EAkFGR/1f3/aMqc6djEQDnLx1riv\ngu694MeX5uNAHKMGlYaR1W8B4wdKoVgRarrOF763n289fJS1E4ZiFY8pxer5RCgY4PW/sJ0rL5ji\nk9/Yw3ceOcauA3O87eU7uHR758xFiuctl0gprXUTHxRC+PWMWA98qh53FQA+I6X8btsWluxsZYf7\nz0WbJzhwPMlCxhCo7MKA1vLZ2vgwiWTeNUnB9vPGKBQrtuQKmqZxxflTnskmrHgKm7oZO+UWVNV8\naU3pXrMkwXAWNQZD6bt02yTDg2GCHQS0CzeMMzIUIhIOcuCE4arkJoxtmh51VT43rx1lcCDYonTZ\nptGFkOiVFtzJzq1xnj4037DAbZwa5fhstkVZtaafNrFmSxwZCjcsHX6Lw7rpBGb31r7NpCThYJCp\nNguTzsyKkXDQNVaqGfdn/UxjbGSAsZGBhnJlKhTdpNwfH4mwY7MR3/PQXsP6u2Z82LazkEUB94pv\nWjsx3PZasI6/puuMDoZZNzncUIK9cF4Sna6oRsyRbu5T81DOjA9DwQDr4yNEh8MN62K12lRwrNdk\nu6tz49QopUqt5Tp0trl02ySVas31uRAKBgyfsiVQrsdcNuIufbBlXdT1Xj1vcoSZhXxLXGCnGmj9\nLOviR7l6lZTyGsv79wkhHpFS/nG/BqVQtKNSrfHP9+7lJ0/PsH5ymA+85SomXHybFc8Ptp8X40/e\n8QK+/MODfOeRY/zfLzzJNWKa337TlX3JAqQ46zkhhJiWUiagYY067qehlPIp4OpudmZegzq6LbYi\noGmEggFL3SG7Jcgq4JmMDoX5uYvXceB4kkQybxOI1niUJ/CKR3QKKeZKfyNVt8scnFhlbnOcwYBG\nrWpaSxz7cBFwgh0sCGYMFjQTWbilUd8w/f/YO+84uar70H+nbO9VbVdd+iEJkEQRGGMsY4wpNjhO\nHCC245KXkEJi5yV+eU536vN7zgvxI3Fkg23AjomNDQZsLLAxGIINqCAhJB11sau2q+27s7vT7vvj\nzqxmZqfuTt39fT8fae/ce8+9v3tuOed3zq/UTltny+NkUUtN3G1TsmcyQ+FwpI5OEkNDTQUd7bX0\nDo4z6Q/EDcIQua6mqoy1HY1YFqxY1kxncxVn+j109YxERXUMi1JXVU4gaOFyOkLKXPxZRIDmhko4\nHe0v1NleQ3tT9VRY/kRlK8vcrO1stE0948zKJQq6kIgNy5vZeagn4fYFTdVTgUbimX0vaK5iaDTS\nTDb+2VL5NCXD6XTQ2pDaJ8ztdhBIwxUotoqsiIGIVFENly2MNlvzRyXljSiT5PwLW6qTz9qFCjud\nDsqds7cCceBIOPttWfagjDvZzFVE0VgfuZWLGxgYnmBRSw1n+jzEEhuKPZ+ko1zVxzREbUB8z7MY\nROQm4F5sHfd+Y8znY7ZfhG2OsRn4M2PMP0VsO4FtPh4g5IuVzjmVuc2kN8C/Pb6PN471sXJxPZ/+\n0EYNXqFQXubiznev4ZqLF/KNZw+x0/Tyu//7OW6+ainv3bJUTQWVSPqAPSLyJHZX4lbgxVCo9rRD\nsmfKpC8Y1QGKHQm3rPjhnuN2/LPQUUi3s5Fc74gwWQxdT21VWdyZuETnjKcoJRItPDuWMGz8DImd\nUYxHEovFJIUS/Z4+oh47wxe2xKgoc9kd/PpKegY8tMVRoutryulsr+Vw9yCMx9f9IsPgV5a5mfBd\nmDEKd7a98ZIFR4jrdDqoDvnyxKsHx9Tf5LUUlq/M7aTc7cLrv3DeMpdrKjfX4tYaFjZXJzTPc7uc\nUYpTVYWbzrZaGmL8rsPFy1zptQOR8ifKhxbJ2o7G0DN5QZZUs6FhpcobCvxR5nLGHXyIt661vorz\nw+NUlbsYn7DvY3hwY0FTNdVp5IuaLlDmRdLB6XQkvH/+gD2Dlq6JaOxAUU2lm/ZGW+l2OR1Rymb4\n3GHyne80HeXqXuB1EXkK+925BfiHVIVExAXcB9yAPSr4mog8EROYog/b7v0DcQ5hAVuNMWnlEFHm\nPiMeL198dC9HTw9z8cpmfu8Dl1BRrp1m5QJLF9TxPz98GT/fd5bvvnCMx188zguvn+aX37mSqzcs\nzEpGeqXk2R/6F+YrROS7yvrZQs9cV88IKxZdGJecPlob/9Tx+iXZeI5T5upJ4NcSfYwLy4taqnG7\nHLQ1VrHD9MQtF++cqUKd11Zf6Ci2N1VxbsBDQ205I2PpRQxLh3RmNsIdbqfTEdmHzoipY8QZUQ8E\nkoeiryh3sXlNW/LjR8yCJtoGUFMVX7kKB4NasTB6/DzuHUo2yxK5Kc6zEzmTsW5ZE3uOnp/6XVHm\njEp8HG/mdeOqVjwTfirKXFF+jGVuZ9wZzPbGKia8fhY1J5/BjCdzOmHxw/WXzmsZ7rOEB4XDdVFZ\n4Y5fPs66lYvraW+uor66nP7QbGM4KMayBfGDMixdWMcxrz8tZTGbJDtb+N4l87mqCuXBW9CUfMZt\n/fImegcnONN/IfpllA+ew5FS6c8m6UQL/FcReRHYiv3O/r+QaUQqtgBHjDEnAETkEeB2YEq5Cs2G\n9YrIrQmOoT0hBYBzAx7u/fYezg2Mc/WGBXzylnUzcohV5j5Oh4O3X7KIG69ZwUNPvcn2V7u4/6kD\n/HhHN3dcvxpZqlEF5zPZCsk+E6JMd2LN8Kz4nbN4M1cXymSuCy5qruFM/xj1EUrL5tXJOu3pncPp\ndEwzv5sWRCPO9VVVuFm5qJ7aqun+D/XV5VGK5LKFdSxqqaay3J1V5aq9sYrBkUmWJuiYwoVO9qyC\nTcRRPsLHjZo9m2HPZ8oENW5wkQvLKxbV0zd8IfJhWNGvKHdx9fqFcQ6c3uxi2maBEeLFKk+OyNmG\neGVDZcLlfP7glONaoj6B0+lg+cK0DK6mnTcd5SqTsY6w+W5znT0z2dFWS3fvKE215YyOT/c/i3do\np9Mx5S807dwJZFmxuIHasjRytqXcIzPcrsS+gmGFsDKJZcmyhXXUVpXR2pjcp766soxlC8toa6xi\n7zFbWY/05XI47Od7UXNNVoLWpCLd5DAngP8yxuwEEBGHMSbVF2YJ0BXxuxu4KgPZLODHIhIAthlj\nvpJBWWUOcaR7iC9+dy+j4z5ufdsyfum6lToDoaSkurKMX37nKt65aTHffeEYr+w/x+f/Yzeb17Ty\noXetZmEWssErpYeIVGPnTVzNhTYwZ+aAkZ3xyOVwNyfKzypO1yZuFL5ZdIGWLayjs7026rhRFgAx\n31Z7N0fM7+m7pjnoHpf2mAADiX28HBfy6mSxDSgvc6UMglNfXUbP4GxnrsJ/p5sFRs0UzuzwUzMA\ncU0tIwM/uJxT0eAAylIEa8j03kZNXMVNDJuYeAFQkrGguZozgxNIZxYHzSLO607DBDWeApZ4ttcR\nFVCjo62WjtBsm9MRR7nK8Dmf6bNTW13G+eHxrKeyWdvZSFfPCB3ttbwRSvQdJuzjl8y1w+1ysiCm\nrQ77XpbFUabLIxTIyAij4XsU67eWK9IJxX4LsA37c7JMRK7Ezk/1/hRFZ2te8XZjzJmQj9ezInLQ\nGPNisgK5SARWSPR64MXXT/HPj+wmELS450Mbee/Vy7Mv2CzQe1TctLXV0dZWx5+vbsec7OeBJ95k\n9+Hz7D3ax61vX8Fd772opHz25tr9KRDfw/bl3QlMkIE5oIh0Ag8B7aEyXzbGfDFZmUDEjERUQItw\nhyzct45YjqS+phx6iTJpmq1e4YwIOpEIC9sHZ3wqmtv09yQ6AEfiDn04wl5sKPpUJJOwItSJqpmJ\nf8kMaGmoZNIXoKmugnMD47icDk73jcX1gUpEXLO5EIE0zDATEZ6pWtJai99vsaTtwrNy0dImzvR5\naKmP7jRPhKL91VWVpzTNvCBP8qgJ6cqd7L4ubqmOCEee+oBNdRWsXt5CX99oyn3TJfK5dieom8vW\ntLHrcC8QP7LnjM47gwNEBvRYv7x5xr5FC5qqqK5wR5nhZoPqSndCa5Fhj5dyt4u6DGeSNq5uZcLr\nTxllsCw2fUMeSWfm6m+wTfx+CGCMeU1EVqVR7hTQGfG7E3v2Ki2MMWdCf3tF5LGQDEmVq0RJyEqR\ntra6eX09lmXx5MsnePzF41SWu/j9D17CxStbiqpO5vs9KnZir6e5uow/vmMjuw718p2fHuWJF4/x\n3I4uPnjdSq7buDgt849CMhfvT4HoNMZsmGFZH/CHxpjXRaQW2CkizyZLch/pzB2pXExr7K34Xcn6\n6nIuW9MWY+KSDZ+rBOsjlnsGUyTrTCFG+BzlbhcTPj/eDJWrZLTUVxIMWnmLFOtwOKb8eVYssjug\nHW21GX43HBH/RxNtbpjeMcNKa2SAiNUdDVH7NNZWxJ2NKC9zMeH109GW2g8pvrlf4nUpo7QlMGfd\nuKo1pkOcUjQgPdO9TIg8b1kCf6DI9zFuqoMZnHcm12Er+x7WLWueVWhxh8ORc3O5Ja21nDofrQTX\nVLoztkQqczspc8eXNSr8eoJcZ/kgLaeVsKITQTrGzjuANSKyXETKgTuAJxLsG3XZIlItInWh5Rrg\nRiAdPy9lDuD1Bdj2xJs8/uJxWuor+dOPXK55i5Ss4HA4uFza+dv/dhUf2roKXyDIQ9sNf/P11zhy\naij1AZS5wAERWTyTgsaYs8aY10PLo9g+xEmPFalcxZu5SmVCBdOTB4f3SiffUiJSmhZa0eZlne21\nVJa7Wbn4gu9Kqv5K+HIWhzrwLenmIkyjJ+RwOGhvqk5p0pZLMu0MT01WOkA6m1i1+IIiFGnilG5H\nMGwCNZkoyl8S1nY0sLajcVpkvWQkMgm9sHLaQhQXLW2ivrqclgQ5tZxOR1H4Ukd20NORZypXWapI\nHimYiQKwdEEtl65sjcpvV6x0ttey5aIFLI7wzZwy880SkXWYKs9VLknnqoZFZMrDUUS2YicRToox\nxi8i9wDbsUOxP2CMOSAid4e2bwsd9zXs0O5BEfkUsB7b5OJ7IhKW8ZvGmGcyujKlJBkcneS+773B\nsdPDrF7SwD0fvCQvzofK/KLM7eTmq5fxtosX8t3nj/Jf+87yDw/v5J2bFvPL71xVUqaCSsZ8DnhV\nRHYBYfsjyxjzq5kcRESWY6cReSXZfo21FVO5eiJDBU819lNmgVbanats9BMSHiNifaRyVVXhZtPq\n1phjJBckvL29sYrmuorMO845Cg9dMCKUj9gZt5VLGtgdMjNLl4oyF55Jf+IQ6kmorixLO2R32s9l\nnP0jFY5Es2hhisV4IDJ6XSKzwEgcMe/yTIkd8KhLYybK5XRSXVl4hTRdnE5H1KBEeRpBNjIhfC9i\nfeXy/Wylo1x9FtskcLmIvACsAW5L5+DGmKeBp2PWbYtYPku06WCYUWBTOudQ5g5HTw1x32NvMDTq\n5ZqLF/Kxmy5KaQuuKLOhsbaC33jfeq7btJiHthteeP00uw71cuf1a7h6w4K822kreeHrwOPALi6E\nJsioGx8yCXwU+FRoBishTXUVLGyu5my/Jzrc9lR/LNLpKk2yFIp9/bLmhJ0bi4xz5U4/R8RyMcxI\n5JtwUlvX1CxlYt+cipjIZunQ2V7HiMfH0hw76Yfljnwc4vm6pUqCm86ZwJ7hGhv3FeyZiRxUiBc0\nIZa4ZoEzeEUjy0hnU0nMRs2EyOckF328y9a0TQvvXlQ+VyLixHb4vR64JrT6ZWPMYK4FU+YXP9tz\nmm88YwgELX71Xat575ZO7dgqeWNNRyN/9fEreXZHF99/6ThfeWo/rx44x6/fdFHefDqUvFFmjLln\npoVFpAz4LvANY8zjyfYN+5VNBMHjs6gsd+EOmcE0N9fQ1lbHwLifiYBFRbmL9rY66k+PRJWNx0QQ\nhkJhm2fju9YWJwJ7+egk9X3jBJ1OAg4n9XVVtDVVJTxPfd3QNDnC69rbU4e/jnfcs0OTWE4n9TXl\nJR3Epa6hipNnhlm+uIGKMheNA+M43C7qquNf19JFEwyOTtLeVh81up+sDpZlM0peAvrGfHgtqKp0\nR8lSVWvPRpaH8k2FrUz8geDUc9zaWptyhqyxfpigZbFgQT0up2NG9zybz4nf4WTAY79fixY2JFQA\nws/5ggX2cz7pC1B/1h5rSee6Y5nw+qnvsfM0dS5pjJvjazYUy7sU+f1auKCepro0zYVnwNS3qK2O\nyizXZzKSnskYExSRbxhjLiEU0EJRsonPH+SRnxzmp7tPUVPp5rdvv5gNK5oLLZYyD3G7nNx81TKu\nkHa+/vRB9hzt48/vf4U7r1/NtZcuUmV/7vALEbnUGLM304Ii4gAeAPYbY+5NtX84AMnQoIfhkXE8\nzgs5X2rKnPRWuBgMbSt3uzh/fpThkfGosvEIl0m130wY8XgZHhmfOj5AR3NVwvPEk6OjuYpJXyCl\nbImCtAwOehgemyTo95d8EJfm6jKGB22z0KGhcYY93oTXtaixgoUNFVGR74ohkM1A6HnzTrinyeIF\nvKFHpddjW9n6A8Gp5+L8+dGUSsKqhbV4/QH6ZxjxL9t1NDQ0MSX/QP9owm//ivYafP7g1Ll9/kBG\n1x1LZPmB/jFGszirUwzPUZjI79fw4Dj+UL6rXBA+T1/faMrogtlUPtO584dFZIUx5nimBxeRm4B7\nsX2u7jfGfD5m+0XA17Dt1v/MGPNP6ZZVSp/ewXG+9Pg+TpwdoaOthnt++dKpBHuKUijaGqv44zs3\n8cKe03z7uSN87emD7DrUyyduWaf+f3ODq4CPi4jBtswA2+dqSxpl3w58BNgrIrtD6z5rjPlRskLh\nxKiRwS2mBQu0SNtnI++RrzJ0WJjtezJXxzHCnfREiYgdDkdRXnumIqWMFhiDHf2teMxGo6PMJb4A\nO5lx5JrZ3bzIc8Watc0lIpNcV1XkJyBNvqMBp6Nc1WM3JC9h+0JBGs6/IuIC7gNuwA7L/pqIPBET\nsrYP+H3gAzMoq5Qwuw/38sBTB/BM+nn7xQv5yHslyuZcUQqJw+Fg66YlXLqyhQd+cIA9R/v4ywde\n4eO3rJvm1K+UHJ+aaUFjzEukGWU3knC7bhGpXMU29lbaEa1y2U2Yvd/M7KmuLGNgdDJvOazyRV11\nGUNjk1PJe0uGOM9v8t0dcZdLhXAOtdpZPH+z9bnKd3S7fOIP+Z46cMxZi5CEypWI/JMx5o+AbwDf\nJjr8ejpv2BbgiDHmROh4jwC3Y4euBewcVkCviNyaaVmlNPH6Ajz6/FF+vLObMreTT9x8Ee/YOKOo\nyIqSc5rrK/mjOzfx49e6ePSFY3zx0b1s3byEO69fndLEQClOjDHP5/uc8TpK4bDkzaE8NQuaqwG4\ndGVLSkf+fHdI8t3RW9JaQ1W5i6b6ueXv2FRXQXdv9pLdlgQl2Heurizj4hUtVFdmZtY36+TeaIoD\n3QAAIABJREFUc1TRiCWc7y8fAUsKFRwl2ZNzPYAx5usistsYsznDYy8BuiJ+d2ObY+S6rFKknDw7\nwpeffJMzfR4WNlfzOx+4mM722kKLpShJcToc3LhlKeuXN/PlJ9/k+d2nONw1yG/fvmEqqahSOohI\nI/AnwEYgbIdsGWOuz9U5Y01SNq5qnfLHaKit4PK17VNmUek4weezD+bAkXXH+lQ4nQ5a56CJeE1l\nGQuaqqkpsVQPGUe0dMRdLClmm45jJjN2c3UWJ5baKjc9g9CaIN9ZNkkV/j9X5PKLOZsgrjMqWyyR\nULLFXLkefyDIf/7Y8K3tdjTA9127go/duj7ryeMKwVy5R2H0epIf61/WtvPVJ9/kB/91nL99aCe/\n9YGLufGqZXlrFOfa/SkQXwX2AwL8BfBJYGcuTxg7Ih0b/jxTf5N8mlo11qqfYTZZsSh1BMVSJ/Lp\nzLevi1L8tDdVU1nhpq7EBhkyIVnvtlJE1mO/J+HlKYwx+1Mc+xTROaw6sWeg0mFGZYslEko2KKbI\nLrPhUNcgD283nDo/RmNtOZ+8dR0Xr2hhZGicUr+6uXKPwuj1pMcvv2MFKxbU8rUfHuC+7+zh1X1n\n+NhNF+V8dH8u3p8CsdoY80ERuc0Y8x8i8l3g+VyeMLaDOVtlPKyM5cOMaLa5rpTSJxyAIN3n1uFw\ncOnKVoKWNa/ym0VVzwxfzc1r2qLybM1V6tNIkFzKJOsNVAE/CC07IpbDrEhx7B3AmlAW+9PAHcBd\nCfaNfZIyKasUIcMeL48+f5SX9p4B4Ka3LefWqzrnnIOyMj+5bG0byxbUse2JN3n1QA8nzo7wO7df\nzLIcJ/NUssJk6K9XRFqAfiCnUUpiE5HOVimqryln2YK6nJi7ZCraklY1jZ3rhBXsTJ6NTP2V5gLR\ngTxmhgb2mhskfPqNMctnc2BjjF9E7gG2Y4dTf8AYc0BE7g5t3yYiC4HXsCMSBkXkU8B6Y8xovLKz\nkUfJDxNeP8+82sWPXn2LCW+AjrZafv0m4W2bOubUqLuitDRU8j9+bTOPvXiMp3/xFn//8A7uuH4N\n11+2ZN7YzpcoJqRU/Qfwc2CINM0CReSrwK1ATyj/Y1pEhlV2ObMzkr+opSYrx0lFqokr9Zud+wQz\nnLlStK7mOzkdWjDGPA08HbNuW8TyWaLN/5KWVYqXSV+An+05zVMvn2DE46Ouuoxfum4l11+2JGud\nCUUpNtwuJx/auhrpbOL+p/bzzWcPcfDkAB+/5SKdpS1SjDEfCS3+XxF5DWgAkuapiuBrwP8DHsrk\nnG6XE6fDQdCymAcWP8ocI2wWqM9uCiLqp5jydin5Z/7N2ypZZXjMy3O7unlu1ylGx31UlLv4wLUr\neM+VnXmPMKUoheLSVS389Seu5MtP7mfnoV5OnB3m7tsvZvWShkKLpiRARJqAFuC4MSatxEPGmBdD\n5uoZ43I6CAasonfwD+egmUKdruY9F8wCi/vZLTTh2qmu0IG1+U5Oe78ichNwL7Zp3/3GmM/H2eeL\nwM2AB/i4MWZ3aP0JYBgIAD5jzJZcyqqkj2VZHD01zM/2nuaV/efw+YPUVLp53zXLueGKjjnvqKgo\n8Wiur+R/3LWZJ18+wRP/dZz/9Y1d3H7tcm552zKdvS0CROSbwP8xxrwuIs3AXmyTwDYR+TNjzFdy\neX63y4kvECz6XDZ1VWU0VJcz5PGm3lmZF1wIaFFgQYoch8PBlosWlG78eSVr5Ey5EhEXcB9wA3b0\nv9dE5IlI3ykRuQU7ctMaEbkK+BJwdWizBWw1xvTnSkYlMwZHJ3ll/zl+tuc0Z/o8ALQ1VnLjlUu5\n9pJFVJSrI6Yyv3E6Hdx+7QouWtrIl5/cz2MvHmfv0T7+2/vWTyWJVQrGZcaY10PLHwX2G2NuFJEO\n7IBNWVeuIiMitvSPMzzmpba6rOhD6i9YUM/rh3oYGvXSUFeRU3mLvS6KgULXUXf/OJbLTupcaFkS\nUaxyFRNaR/kjlzNXW4AjxpgTACLyCHA7EBmY4jbgQQBjzCsi0igiC4wx50LbVf8vMKPjPnaYHl7d\nfw7z1iAW4HY52LKunXdsXMy6ZU1FPxKrKPlGljbxN7+xhW88c4hX9p/jr772Kne8azXv3LxE35fC\nMRGxfC3wOIAxpltEgrk4YWQQn7HRCYZHJ/F7/SUR3GdoaJxhjxcCgZzJO9fSC+SCYqijwUEPoxM+\nXFaw4LLEoxjqqNjROkpNNpXPXCpXS4CuiN/dwFVp7LMEOIc9c/VjEQkA23JtsqFcYGBkkl2Hetl1\nqBfz1uBUpKDVHQ1ctW4BW9a1U6emf4qSlJrKMu6+bQOb17Ty8HbDw88c4uf7z/Gx9wpL2jTCWgGw\nRGQJduj1rcBfR2yryvXJw75WlvowKSVGUH2uFCUjcqlcpduCJHpbrzXGnBaRNuBZETlojHkx2YHm\n2pRnvq7HsixOnh3hlTfP8Mq+sxzuGpzaJkubuObSRVy7cQntszRrmmv3B+beNen1ZJ9b2+q4euMS\nvvz4G7y89wx//bXX+KWtq7njPWupLM/sE1wM11PC/COwG/ABLxlj3gQQkbcBJ9M5gIh8C3gn0CIi\nXcBfGmO+lk7Z8IxlsESUK+1GK2Ga6yrwTPporNVBVUVJh1wqV6eIDrPeiT0zlWyfjtA6jDGnQ397\nReQxbDPDpMrVXJryzPUUrs8f5FDXIK8fOc+eI+c5P2RbzLicDtYta+KytW1ctraNprpQkspZmobM\nxSnpuXZNej255b/dso4r17bxjWcO8ehzh/nxqyd5/9tX8I5LF+F2pQ54UWzXM1vyrSgaY74jIi8B\nC4HXIzadBH4zzWPMOJl9+B6XWnCT0lAFlVyypK2G5voKqjW9hKKkRS6Vqx3AmlDY2tPAHUBsw/QE\ncA/wiIhcDQwaY86JSDXgMsaMiEgNcCPwuRzKOi8YGp1k79E+9h7t480T/Ux4AwBUVbjZsq6dTWta\nuXRli35AFSVHbFzdykVLm/jBL07wzGtdPLzd8KNXTvKBa1dy5br2tJQsZeYYY84AZ2LWnc7HuZe0\n1TDpC9DaUJmP0ylK1nA4HNovUJQMyJlyZYzxi8g9wHbsUOwPGGMOiMjdoe3bjDE/FJFbROQIMAZ8\nIlR8IfA9EQnL+E1jzDO5knWuEggGOX56hDeO9fHGsT5OnL0w6t3eWMU7Lm1l0+oW1nQ2aqdOUfJE\nRbmLD163indf1sFTPz/J87tP8ZWn9vPoC0fZumkx79y0hPoaNb+Za7hdTtZ2NhZajPRR/xpFUZQZ\nkdM8V8aYp4GnY9Zti/l9T5xyx4BNuZRtLmJZFr2D4+w/McD+E/0cODnA2ISdGzNs7nfpqhYuXdXC\nwuZqdU5VlALSUFvBh9+zlvde2cn2V7v4r31neOzF4zz58gk2rWnjCmnj0lUtGftlKYqiKIpSOLTV\nLmEsy+Jsv4fD3UMc6hrEvDVI3/CFaMMt9RVceVE7F69sYd2yJqoq9HYrSrHR2ljFh29cywffuZKX\n953luV3d7DjYw46DPZS5nWxY3syGFc1cdeliqt0ODeWu5Bd1ulIURckI7W2XCJZl0T88SVfvKCfO\nDHPszDAnzowwOu6b2qem0s3l0sb65c2sX95Ee2OVzk4pSolQVeHm3Zd3cP1lS+jqGWWn6WXnoV5e\nP3Ke14+c55vPHqKm0s2qJQ10ttdO/WtrrFKzXiXraMuhKIoyM3KqXInITcC92D5X9xtjPh9nny8C\nNwMe4OPGmN3plp1rBC2LUY+P/pEJDp4a5uhb/fQMjHO6b4zT58cYnwxE7d/aUMmGFc2s7WhgTWcj\ni1trdFRbUUoch8PB0gV1LF1Qxy9dt5KeAQ/mrUFO9o6x93DvVFCaME6Hg9aGStqbq2hvrKKloZKW\nevtfU10FDbXlJRehrliZj+2SoiiKkhk5U65ExAXcB9yAHV79NRF5whhzIGKfW4DVxpg1InIV8CXg\n6nTKFjOWZTHpCzA+GWB80s+418/EZADPpJ+xCR/jE35GJ3yMenyMeHyMjHsZHPEyODpJIDjdBsPp\ncLCwpZqLV9SwpK2G5QvrWbGoThP5Kso8oL2pmvamaj4YCsU+4vHS3TNKV88oXb2jnOsfp2fAw75j\n/XHLO4D6mnIaayuorymnoaac+ppy6qvLqKkqoy70t6ayjOpKN9UVbp0Ji0Opt0szxVK7QEVRlIzI\n5czVFuCIMeYEgIg8AtwORDZEtwEPAhhjXhGRRhFZCKxIo+w0fP4A/oDFhRyNFxoFC6bWW5a9T9Cy\nCAYtgpZFIGDhDwTxh/56/UG8vgA+f5BJX4AJbwCvL8C4N8BESFma8Prt35P23/FJ/9S2TJojp8NB\nQ205SxfU0VRXQVNdBSs7Gqkqc9LeWEVbYxVlbu3sKIoCddXlrFvezLrlzVHrPRN+egfH6R+e4Pzw\nBH1DEwyOTjI4MsngqJczfWOcPJdenqwyt5PKcheV5S4qytxUlDupKHNR7nZRXuak3O2irMxJudtJ\nmdtFmdtebm+qYvOatlxcdjGQTps2Z1AjCEVRlJmRS+VqCdAV8bsbuCqNfZYAi9MoG8Wew7381Zd/\nHnfmJ9e4nA6qKtxUlrtobaiiqtxFZeh3dYWbygo3VeUuqiNGhmsq7RHj2uoyqivc03yj5lrCUEVR\nckt1pZtlC+tYtjB+cl7LspjwBhj2eBke8zLi8TE67mPE42V03Mf4pJ+xCT+eCT/jk/6pQaXR8XEm\nvUGCVnrf1vs+/Y65mhMnnTZtzhA2JVWTUkVRlMzIpXKVrpaTlfGxjWvaHI//n9uycaiioa0tfiep\nVJlr1wNz75r0eoqbuXY9JUamI3eOUr5f+ZK9lOsoX2gdpUbrKDVaR/kjl8rVKaAz4ncn9khfsn06\nQvuUpVFWURRFUfJFOm2aoiiKMs/JpXK1A1gjIsuB08AdwF0x+zwB3AM8IiJXA4PGmHMi0pdGWUVR\nFEXJF+m0aYqiKMo8J2fG1MYYP7bitB3YD/ynMeaAiNwtIneH9vkhcExEjgDbgN9NVjZXsiqKoihK\nMrRdUhRFUdLBYaXppKwoiqIoiqIoiqIkRsMAKYqiKIqiKIqiZAFVrhRFURRFURRFUbKAKleKoiiK\noiiKoihZIJfRAvOGiNwE3Au4gPuNMZ8vsEgzRkS+CtwK9BhjLim0PLNFRDqBh4B27DwxXzbGfLGw\nUs0cEakEXgAqgHLg+8aYzxZWqtkjIi7saGjdxpj3F1qe2SAiJ4BhIAD4jDFbCirQLBGRRuB+YAP2\nO/RJY8wvCivVzBERAR6JWLUS+ItS/i7EMpfapJmS6NsvIs3AfwLLgBPArxpjBkNlPgt8Evvd/QNj\nzDOFkD3fxH5/tY6iifMN/ARwGK2jKULX/BEgCLyBXUc1zOM6itefnsm7JSKXA18HKoEfGmM+lerc\nJT9zFfoo3QfcBKwH7hKRdYWValZ8Dfta5go+4A+NMRuAq4HfK+X7Y4yZAN5ljNkEXAq8S0SuLbBY\n2eBT2BHQ5kKEGwvYaozZXOqKVYh/wf6gr8N+5ko6Qp2x2WyM2QxcDniAxwosVtaYg23STEn07f+f\nwLPGmLXAT0K/EZH12OHt12PX3b+JSMn3UdIk9vurdRRN7DfwIFpHU4TSQ/wmcFlIiXABd6J1FK8/\nnUmdOEJlvgT8hjFmDXY6jpR99LlQmVuAI8aYE8YYH/aI6O0FlmnGGGNeBAYKLUe2MMacNca8Hloe\nxe4YLi6sVLPDGOMJLZZjf8T6CyjOrBGRDuAW7JFBR4rdS4U5cR0i0gC8wxjzVbDDgRtjhgosVja5\nAThqjOkqtCBZZE61STMlwbd/CXAb8GBotweBD4SWbwe+ZYzxGWNOAEew63JOk+D7q3UUIsk3UOvo\nAsPYgxnVIuIGqrFz8c3rOkrQn86kTq4SkUVAnTHm1dB+D0WUSchcMAtcAkQ2zN3AVQWSRUlCaHRl\nM/BKgUWZFaERnl3AKuBLxpj9BRZptvwz8BmgvtCCZAkL+LGIBIBtxpivFFqgWbAC6BWRrwEbgZ3A\npyIU/FLnTuA/Ci1EltE2KYaYb/8CY8y50KZzwILQ8mIg0ty1G7su5zrxvr9aRxeI9w38NFpHUxhj\n+kXkn4C3gHFguzHmWRHROppOpnXiCy2HOUUadTUXZq7mghnTnEdEaoFHsTuGo4WWZzYYY4Ihs8AO\n4DoR2VpgkWaMiLwP2x55N3Nktgd4e8jk7GZsU6R3FFqgWeAGLgP+zRhzGTBGyIyh1BGRcuD9wHcK\nLUuW0TYpgtC3/7vY3/6RyG3GGIvk9TWn6zKd7+98ryPS+AbO9zoSkVXYCudybCWhVkQ+ErnPfK+j\neKRRJzNmLihXp4DOiN+dRGuZSoERkTLsxvUbxpjHCy1PtgiZJvwAuKLQssyCa4DbROQ48C3gehF5\nqMAyzQpjzJnQ315sX55SNnfoxnZyfy30+1HsjsZc4GZgZ+g+zSW0TQoR8e1/OOLbf05EFoa2LwJ6\nQutj660jtG4uE+/7+zBaR5Ek+gae1Tqa4grgZWNMnzHGD3wPeBtaR/HI5N3qDq3viFmfsq7mgnK1\nA9vBbHloJPQO4IkCy6SECDkEPgDsN8bcW2h5ZouItIYiFyEiVcB7gN2FlWrmGGP+1BjTaYxZgW2i\n9Zwx5tcLLddMEZFqEakLLdcAN2JHTipJjDFngS4RWRtadQPwZgFFyiZ3YXco5xraJpH02/8E8LHQ\n8seAxyPW3yki5SKyAlgDvMocJsH396NoHU2R5Bv4JFpHYQ4CV4tIVei9uwE7QIrW0XQyerdCz9+w\niFwVqtuPRpRJSMn7XBlj/CJyD7AdO7jAA8aYko2mJSLfAt4JtIhIF/CXxpivFVis2fB27PCge0Uk\nrIR81hjzowLKNBsWAQ+G/K6c2COyPymwTNmk1E0DFgCP2dG+cQPfnAMhZn8f+Gaoo34UO8RuSRNS\nfG/AjnA1p5hrbdIsiPvtB/4X8G0R+Q1CoZABjDH7ReTb2J1CP/C7IbOd+UT4erWOoon3DXShdQSA\nMWZPyOJkB3Yo9l3Al4E65nEdRfSnW8P9aWb2bv0udij2KuyolSn7rw7LmnP1qSiKoiiKoiiKknfm\nglmgoiiKoiiKoihKwVHlSlEURVEURVEUJQuocqUoiqIoiqIoipIFVLlSFEVRFEVRFEXJAqpcKYqi\nKIqiKIqiZAFVrhRFURRFURRFUbKAKleKoiiKoiiKoihZQJUrRVEURVEURVGULKDKlaIoiqIoiqIo\nShZQ5UpRFEVRFEVRFCULqHKlKIqiKIqiKIqSBVS5UpQ8IiInROTdhZZDURRFUbRNUpTso8qVouQX\nK/QvI0IN4PU5kEdRFEWZv2ibpChZRpUrRSkNLMBRaCEURVEUBW2TFCUhDsvKeMBCUZQZIiLHgW3A\nR4FFwOPA7xhjJkXkfcDfAcuA/cBvG2PeEJGHgV8DJoEA8DljzBdE5DvAtUAVsCd0nP15vyhFURSl\nJNE2SVGyj85cKUp+cWA3SjcCq4C1wJ+LyGbgAeA3gWbsxu4JESkzxnwUeAt4nzGmzhjzhdCxfgCs\nBtqAXcA383oliqIoSqmjbZKiZBlVrhQlv1jAfcaYU8aYAeDvgbuwG7BtxpjXjDGWMeYh7FHBqxMd\nyBjzdWPMmDHGB3wO2CgidXm4BkVRFGVuoG2SomQZd6EFUJR5SFfE8lvAYmyzi4+JyO9HbCsLbZuG\niDiBfwB+BXuUMIjdSLYCIzmQWVEURZmbaJukKFlElStFyT9LY5ZPYzdof2+M+YcEZWKdIz8M3Aa8\n2xhzUkQagX7UwVhRFEXJDG2TFCWLqHKlKPnFAfyeiDwFjAN/BjwCPAY8JiI/Bl4DqoGtwAvGmFHg\nHLY9/HOh49Rim2j0i0gN9oihoiiKomSCtkmKkmXU50pR8ouF7eT7DHAUOAz8nTFmJ7aN+33Yo32H\ngV+PKPeP2E7GAyLy34GHgJPAKWAf8HNmkKtEURRFmddom6QoWaZgodhFxAXsALqNMe+Ps/2LwM2A\nB/i4MWZ3nkVUFEVR5gkichNwL+AC7jfGfD5meyvwDWAhttXHF4wxX8+3nIqiKEpxU8iZq09h502Y\npt2JyC3AamPMGuC3gC/lWTZFURRlnhAa7LsPuAlYD9wlIutidrsH2G2M2YRtHvVPIqKm9YqiKEoU\nBVGuRKQDuAW4n/jOjrcBDwIYY14BGkVkQf4kVBRFUeYRW4AjxpgToTDSjwC3x+xzBqgPLdcDfcYY\nfx5lVBRFUUqAQs1c/TPwGexQnfFYQnRo0G6gI9dCKYqiKPOSeG3Okph9vgJsEJHTwB5s6wtFURRF\niSLvJg0i8j6gxxizW0S2Jtk1dkYrqXOYZVmWw6ERPxVFUUqEYvpgp+N8/KfA68aYrSKyCnhWRDYa\nY+Lm8NE2SVEUpaTI2ge7EPbi1wC3hfyqKoF6EXnIGBMZheYU0BnxuyO0LiEOh4Pe3tLLU9fWVldy\ncpeizKBy55NSlBlKU+5SlBlsuYuI2DanE3v2KpJrgL8HMMYcFZHjgGAHZppGqbZJkUx6A1SUu3J2\n/FJ9dvOJ1lFqtI5So3WUmmy2SXk3CzTG/KkxptMYswK4E3guRrECeIJQyE8RuRoYNMacy7OoiqIo\nyvxgB7BGRJaLSDlwB3Y7FMlB4AaAkA+wAMfyKmUe6RkcZ/eRXs70jRVaFEVRlJKiGPJcWQAicreI\n3A1gjPkhcExEjgDbgN8toHyKoijKHCYUmOIeYDt2FNv/NMYciGyXsJOiXiEie4AfA//DGNNfGIlz\nz8DwBAB9ob+KoihKehQ0jKwx5gXghdDytpht9xREKEVRFGXeYYx5Gng6Zt22iOXzwLScjOkStCyO\ndA/R2lBJc33lzAXNEwVKgakoilLyFMPMlaIoiqLMaUbGvPSPTHCoe7DQomSEo6jijiiKohQ/qlwp\niqIoSo7xB0prKqi0pFUURSkeNLu8ouSIYY+XY6eHwYKKcheV5S4WNldTVaGvnaLMNyZ9gUKLoCiK\nouSBgvTyRKQS29eqAigHvm+M+WzMPluB73MhGtN3jTF/l085FSVTzvZ7+PGOLg6+Ncjp89OjbDkd\nDlYtqWfDimY2rW5l6YKiCketKPMWEbkJuBdwAfcbYz4fs/2PgQ+HfrqBdUCrMSYtO7+BkUnA/gaU\nBGGnqxIRV1EUpVgoiHJljJkQkXcZYzwi4gZeEpFrjTEvxez6gjHmtkLIqCiZMDbh48n/OsFPdnYT\nCFqUlznZsKKZNR0NlLtdTHj9eCb9HD89zJFTQxzuHuLxF4+zYlE979q8hCvXtVNRlrt8MoqiJEZE\nXMB92KHWTwGvicgTxpgD4X2MMV8AvhDa/33Ap9NVrAC8oZmrklGuFEVRlBlRMPskY4wntFiOPVIY\nL6SttkJK0bPjYA8PbTeMjvtoa6zkQ1tXs2lNK25XfJfGsQkf+08M8PIbZ9h7tI+vnhnmP587zNbN\nS7j+sg6a6iryfAWKMu/ZAhwxxpwAEJFHgNuBAwn2/zXgW5mcIBC0Z4L8weCMhSwE2ggriqJkRsGU\nKxFxAruAVcCXjDH7Y3axgGtCOUVOAX8cZx9FKRiWZbH91S6+/dMjVJS5+NDWVdxwRSdl7uRxYmoq\ny7jyonauvKid80Pj/GzPaZ7ffZof/PwkP3rlLbasa+f6yzpYubgeh45yK0o+WAJ0RfzuBq6Kt6OI\nVAPvJcP8i8GI2OaWZRX1uz3i8TLk8RZaDEUpOU6eHaGm0k1rY1WhRVEKSCFnroLAJhFpALaLyFZj\nzPMRu+wCOkOmgzcDjwNrkx2zra00/VdKUe5SlBmyJ3cgaHH/99/gqZeO01xfyV//5tWsWNwwI3nW\nrW7n47ddwvM7u3j8haP8/M1z/PzNc6xc3MDN1yzn2pqKkqzvUpQZSlPuUpS5yMgkON77gZfSMQkM\n3xfLsqitHZpa39Jah8tZvMrV/l3d1NfZncPGutx+f/TZTU2h6ygQCHK4e5Dm+kram6oLKksiCl1H\nAMGgxf6uIcZ8XtataS+0ONMohjqaLxQ8bJkxZkhEfgBcATwfsX4kYvlpEfk3EWk2xsQzHwSgt3ck\n0aaipa2truTkLkWZIXtyBy2Lrzy5n1f2n2NJWw1/+KGN1JY5Z33sy1a1sGllMwdODPD87lPsPnye\nf310D9se28tFy5q4Qtq5ZGVLSZgNzvdnJJ+UosyQu4ZeRG4ALjLG3CciC4AGY8yhFMVOAZ0Rvzux\nZ6/icSdpmgSG74s/EGR4ZHxqfU/PcEKz4WIgUlZHIJCz56tUn918Ugx1dLbfw4mzw1SUudi8pq2g\nssSjGOoIbOUq/O6cPTeEy1k873ix1FExk802qVDRAlsBvzFmUESqgPcAn4vZZwHQY4yxRGQL4Eim\nWClKvvj2c0d4Zf85Vnc08OlfuZTqyrKsHdvpcLBhRTMbVjQzMDLJy/vO8PrRPvYd62ffMfvxb2+s\nYm1nI6uW1NPZXseSthoNhqEogIh8FrgFWIgdoKIc+CpwbYqiO4A1IrIcOA3cAdwV5/gNwHXYPldp\nEwyWTtYoy4qRNYX5YjjEvH6D5i5hf0FNJ5A+gYBFEY+fKDmmUDNXi4AHQ35XTuBhY8xPRORuAGPM\nNuBXgN8RET/gwR4tVJSC8uxrXTzzWheLWqr5VJYVq1ia6iq49W3L+fhtl/Dm4R52mV7MWwMc6h7i\npTfO8NIbZwC777OgqZqOthqWtNXS0VbLysX1JTHDpShZ5i5sK4hXAIwxXSJSn6qQMcYvIvcA27ED\nLD1gjDkQ0yYBfADYbowZT3CouARjFJaDbw2wclF9Tr8fMyXTZMe7D/cCcPX6hbkQRykGYhXuNBgd\n9xEMWtTXlOdAoOLEirAuLp3hFCUXFCoU+xvAZXHWb4tY/lfgX/Mpl6IkY8fBHh75yWEaasr5w1/d\nSE0eO0btjVXcdNVSbrpqKcGgRXfvKCfOjtDVM0rXuRG6esc42+9hh+mdKtNUV8HKxfVn4WyjAAAg\nAElEQVRcsrKFjatbaZhHjZwybxk3xnhFJOOCxpingadj1m2L+f0g8GCmx46duRod93Goe4hNq1sz\nljPX+AOlFc1QKT4sy2Lf8T4ArpD2ojaBzSYz0EGVHOOZ8DE+GaCloTKv5y24z5WilALdPaPc/9R+\nystdfPpDG2ltKFwkIKfTwdIFdVEJiC3LYmBkku7eMbp6Rjh2epijp4fZaXrZaXpxACuX1HPNhoVc\nc/EiKsrVhEeZk7wlIu+AqdxVnwX2FVakC2ZVkUwzvysSYuUq3rAbSrES+QQFg5Y9FzzfmOHrvftQ\nL9WVbmRpU3blmafsPWYr+Y117Xn1gVPlSlFSMD7p518f34fXH+T3P3gJyxYWX8Qdh8NBc30lzfWV\nXLqqBbA7ST0D4+w5cp7Xj5znUNcQR08N890XjnHdxsXccEUHzfX5Hc1RlBzzB8BDwMXY5uQvAh8u\nqETE72cVayj2WFkHxybp6hmls7027WOc6RvDM+ln1QwiqCrFR8Z6ghV3UUmDSX+AyVH1bcs2+R7L\nUuVKUZJgWRYP/ugg5/o93LRlKZvXFl+kpEQ4HA4WNFdz45al3LhlKYOjkzy/+xTP7z7Fj159i+d2\ndXPL1cu46aqllKszujIHMMacAd4jIjWAMzLqbCGJ17DPVrUaGJmktspNmTv37+6p85kpVyfP2dWu\nypUyn7QrK0qpzPzCi3U2O1f4/EGGRidpaags2sGmmVKoaIGVwAtABXY0p+8bYz4bZ78vAjdjj0B+\n3BizO6+CKvOen+4+xasHeljd0cAH37my0OLMisbaCj7wjpXc+rbl/PzNszz2s2M8/tJxXtx7hl+7\nYU1JKY6KEg8RuZWI7lzY98oY88M0yt4E3IttxHS/MebzcfbZCvwzUAacN8ZsTUeueJ2m2XQmhsa8\nmK4BaivLuHhly4yPE49s9u+KPVnybOkZHKe+uozK8vhdqWDQYnB0ksbaCpxFnNcsJRk+E9GBHeaX\nwjAb5ltNma4BRsd9OJ2OnFvR5FtvLYiXoTFmAniXMWYTcCnwLhGJCpUrIrcAq40xa4DfAr6Uf0mV\n+cxb50Z45CeHqa0q47dv2zBnnHLL3E6u27iYf/itq7n5KntG6/997w0e3m7w+dUcQSlpPhPx7y+A\n7wJ/lqpQyD/rPuAmYD1wl4isi9mnETvI0vuNMRdjR7RNi3gN+2z62sNjXgBGJ3wzP0gemMudxdFx\nH8dOD7H3aF/Cfbp6RjnUPUh372geJcs+4WiXjjTnW+fZBEwEEUrlDOpgvs1cjY7b3698hPjPd90W\nrLdojPGEFsuxRwpjc1jdRigqkzHmFaAxlPtKUXLOpC/AtifexB+w+M33r5+TvklVFW4+9K7VfO6T\nW+hoq+Wnu0/xtw/u5EzfWKFFU5QZYYzZaox5V+jf24DLgcNpFN0CHDHGnDDG+IBHgNtj9vk14LvG\nmO7Quc6nK1e4YY90qJ7NjE6p5Jaay53FQCiqYmyY/UjCyu/YhD8vMhWKcwMejp8ZjrstnUdgbMLH\n2X4PB070M+LxZlm6mRG0LDwZ3rfZPu5z+HVJSj5mt/NdtTNWrkRku4i8X0RmVCsi4hSR14FzwE+N\nMftjdlkCdEX87gY6ZiatomTGd356hDN9Hm64vINLsmx2U2wsbq3hz3/9crZuXkJ37yh/8+AO9h1L\nPBqrKKVCqF2ZlvYjDvHamyUx+6wBmkXkpyKyQ0Q+mq4c4U5T1GxVFvoTxW5yN9POos8f5PiZ4aQj\n2nbAHk9xz7bPkc5y+D4metyOnxnm3IAn/sY0eONYHyfODjPk8WLeGpzxcbLJ8dPD7D12nqGxxMre\nsMdL7+CFlHezvd1zeTAiGfn4jOW7bmfjc7UN+DTwRRH5d2wb9bR7ZMaYILAplPF+u4hsNcY8H7Nb\nbJUnrZ22tuKL4pYOpSh3KcoM6cn92v6zPLfrFMsW1vE7H9pUFMEe8lHff/SRK7hyw0LufWQ3//Lo\nXv7gjk1cf8XSGR9vLj8jxUYpypwLYnyuXMCVQDpD4em0vGXYitq7gWrg5yLyC2NMwpmxtrY6PBM+\n9ncNUV9XRWW5iwmvrQw01lbM+L71jfnwBu3Z52zf+/LRSerPe+hor6W754I5W6Lz1NcNTdseXtfa\nWpsy4Ea84x482c+432Jg3M8lixvjluvp93B+1MdEEC6/KP9GLe7KMuoHJoDEddPQP47D7aKxPr17\nPTbuwzPhp60pOtVHorKeCR+j4z7am6ozlD4zhiYDjPmCOB2OKFmGx7y4XQ7q62x5W1trcTgc+PwB\n6k/bQU1aWmqpqUqeEzL8vIBttj6TZzrb70H4nS2vLEt47P27ugFYv6YdgAmvn/qz9jvT2lqbcZLw\nCa+f+roL5dMdPAkEggyOTtJcnzwwRLG1E+H73tJcS1trTW7P0ZL5/ZgNM1aujDHfA74Xskv/HeBN\nEXkG+BdjzM4MjjMkIj8ArgCej9h0CuiM+N0RWpeQ3t6iCAyVEW1tdSUndynKDOnJPTTm5d5v7cLt\ncvDJW9YxNDjz0bhskc/6XtfRwB/dsYkvPrqXf/7Wbt46PcQtVy/LeIR8Lj8jxUYpygw5a+g/wwVF\nyQ8cAT6URrnY9qYTe/Yqki7sIBbjwLiI/AzYSBKzw97eEXoHxxkesUe3feVuxr22qZEjEJjxfRsY\n9DA8Mo53wp31ez/i8TI8Ms5guXNKbojfvlqWNbVP5Pbwup6ekaSDU4me3fPnRxkenSTo89NbXxG3\n7OnzYwyP2HW7tCW3ykU8hsa8ca89ap+hcUbGvTiCwbTu0y/2nwVgy0ULpgJgJHu/w/tvWt2aMKhG\nMvyBIBPeALUplJ+BAbuunQ5HlCzh84fp6R3B6XDg8wen6ub8+VE8lclli3zOKssyf6Zz8Q0MyzQw\n4KbKFb/9u/CcD+NwOJj0BiKeiVGqU1x3LBNe/1T5cz3DaedlOtvv4cTZYeqry1m/vDnuPsXQTnh9\nAQZGJmlvquLY6eGIOi7HbWU/eXkw4vt0/vwoVRXJ70c226RsRAu0sGeYfMAE8JCIbDfG/PdEBUSk\nFfAbYwZFpAp4D/C5mN2eAO4BHhGRq4FBY8y5LMirKHGxLIuv//AAwx4fd16/OqPQw3OJtZ2NfPaj\nl/PP336d775wjElfkA9eV9qREpX5QbrR++KwA1gjIsuB08AdwF0x+3wfuC8U/KICuAr4v6kO7Iqw\nBXQVQcQ4nz/IiMeb0I80rJmmM6CSarovp4Y4BTahyuWdtKa6Vekx6QtSWZ75efYd62fC52fz6rak\nieXjVXVcM6spsWceLdCVQJEpFOmMK1qWvV/0tc4kFPuF5WAQ0o2h5fPbismwx1vUETr3nxxgwuvH\n7XLSO3RBoc6VuMGI5O3h53XSF6DM5cx59M4ZK1ci8ivA7wKLsKMsrTPGjIqIG3u0MKFyFSrzoIg4\nsf2+HjbG/ERE7gYwxmwzxvxQRG4RkSPAGPCJmcqqKOnwwp7T7Dnax7plTdxwZWfqAnOYJa01/OlH\nLud//8dunnr5BGVuJ++/ZnmhxVKUuMSGYI8lVSh2Y4xfRO4BtmObEz5gjDkQ0yYdFJEfAXuBIPCV\nOL7C04jsMDkiGvRCqQb7T/Qz7vWzflkz9TWJe+RpdT1SXES2/RzGJ/30Do7TUaIDX/5AkEDQShmI\nJNNq884g2tqE18+Ez55F9QeDVJCZchUvkEdYKZzNbS+GAYhI0htkmP11Q/T7Eg4stXRB6tmUKCWC\n3Cr+s2EiNGsf60uZjc9E0LKYmAxEzRZG1qeF/f7tPtxLZbmbTatbZ3/SJMxm5uoTwOeBZ4wxU1cQ\naqT+IFlBY8wbxHEyNsZsi/l9zyzkU5S0Odfv4ZGfHKa6ws1v3LoOZ5GO/OST5vpKPnPXZv7XN3fx\n2M+OUeZyctNVM/fBUpQcEmkOGI+Uea6MMU8DT8esi22TvgB8IRPBIkezI78r4XZ/fNLPnqPnWdvR\nmJeopOMJOjgXBLuwWOZy4QskCSqRQrsKX6NlWUx4AynNclJx8OQAk/5A0lmWxLIUfkTfvDXIyLiX\nK6R9WmqP2SiiYxM+vL0BFrXWpN12vX4kfrBLfyA4XbbQfY6sv0AgjnIVd4YruRynz0dHp41UrsLB\nSvKRKHs2JJrEy5QIHYnTmShX0dmLi1e7ChFbN9kYgjncNcjA6CQXr2iZMnMNRM1c2c82XFDycsls\nvnTvi1SqAETEYYyxjDFPzFIuRckb/kCQLz+5H68vyCdvXzcnw67PlJaGSj7za5v5/Dd38e2fHqGy\n3MXWzbFB1BSlsMzCHDDnRPZ7IjuO4Q5ROMra8TPDef32hMXy+YM4HEzP4+eAS1e1sPNQT0Lfj6g+\nXRzlJbz9bL+Hk+dGWLGongWzCL4wGeps+/2Z+WeMjvvYd7yPVYsbaGusSl0gHTLowIZ3HRm3Y6v0\nDIyzOMaBv2cgIupchr3Ns/32M+R2OVnQnHn9hmc+wvW0pLU22iw+jjyRHddYMhE/WZTBnYd6Abh6\n/cKo9cNjXoY9Xjracj+DGUxynWGyNUGbSsE2bw3QUFvBwph7nI6MxYQVI2+mAwvnh8bpH55kTUfD\n1DdnYHQSsIO8hJWrYMRnwj5H/rTO2eS5elFEmsI/RKQFeGH2IilKfnnq5RMcPzPM2zYsYMs6TaUW\nS3tjFZ+5azN11WU8/Izh9cNpp/dRlLwjIg0iskVErgv/K6Q8kd2GSOVq0hvAsqxpHbO9R/v4xf6z\naSXWzNSfJbqwXXbnoR52R7zTkUcscztTBjuIVy5Wvr4hO6re4MhkZiJmuD4R50LKx2yS+Q6NeXnz\neD8+f4BgcPp9S4eqUNCJodHp9RDpgzLTsXxfYGZBAcJ93cGQXKfOR9fTlB9eVJkkM1cxSncy4iUm\nHhiZTDq7sP9kP929ozmbgQg/L5A4j1kgoucevsbowYbMz5vMt80fCDIwOsmJs9PziUXN0JRA/H/P\nZPR9y7Sujpwaon9kgvHJ6fc/8lCR9y7fLpqzUa5qjTED4R+hMOzFFedRUVJwqGuQJ18+QUt9JR9+\nz9pCi1O0LGyu5lO/spEyl5N/f2JfwoSRilJIROQOYB/wU+Arob/3FlSoiFY90lnfHwxOhWW/sKuF\nZ9JOPHu4O3G+n2z4MoV9ECC6oxjGMfXXkfB8Vqw50rTt9t9w3y9ds7xE+4U74ol8gLp7pne4ff7g\nlOIyG3+e46eHGRn30tUzxqsHz3HgZH/GxwjPDsarzZqIMNHRgQ0svL4A45N+zFsDjIUSE8djpmaP\n4ZmPhKXjzVzFNQucwXMZc9JA0MJ0DSQ0W4wkGLTPOTaeuE5mwvEIBSbRrNBrB3umljO5bH8gyKGu\nQUYjZA6/f/HqL51DW1lQIvyBIN29o1nPGxe0LEY83qlvDUD/iD3YUl9t+3zO9HuWqlSUchVb1rLs\niIVJ8pjNhtkoV04RmZrXFpFa7DwgKRGRzlAixjdFZF88Hy0R2SoiQyKyO/Tvz2chq6JMY3Tcx5ef\nfBMHDu6+bUNecyCUIisX13P37Rvw+YPc+5099AyOpy6kKPnlz7DTehwyxghwE3YkwJSIyE0iclBE\nDovIn8TZPqM2KbJRj/WHiR4Vj3aIn/RO7+QEgkHO9Xvwx+nYZoyVwO8qtqOTpL+eqk90YUTf/hvP\nH8gfCNIzOB6/YxkriuPCcWP3Pj84Tvf5UQ6ejFZKI0f60w1tHY+KMrtsWPmdCWGpI33RPBN+LMuK\n9seLKHPwZD+7Dvdyps/DwOgkB04MkIh4t2rSG+BM39hU/Q6NeTlwMvoY4W2JlLN4syHxzAIvTFwl\n7tSmItFMUXwsegbG2XHg3JRpZDaoKo8MipCOFHGm7BJwtt9D/8gE5i37HpzqHeW1gz2cHxonnh6X\njuKRzEQzXU71jtHdO8qx09kdOD15doQ3T/Rz8tz0MPCtIRPdbM4qRSrD8aIFhhnx+OgZ9LB/BoMk\n6TAb5epbwLMi8pFQpvpngG+mWdYH/KExZgNwNfB7oXxZsbxgjNkc+vd3s5BVUaKwLIsHnz5I//Ak\nt127nNUdDYUWqSTYvKaND79nLSMeH//ynT14JnLvGKooGeAPpexwAxhjnsVOJJyUUHj1+7CVsfXA\nXVlrkxL4XMH0TkVkxzKeInLmvIfjZ4cZGptuVjY4OhllzpQOXl96ZmSJOj9W1HJi5Sj8N17f/djp\nYY6dHkqrcxy0opWTSMLXEo6AN7U+wj9rNuGXw2Vn5d8Srg/C/nbj7D12nrP9nulBCUL0hnyxhj32\nCLs/zixjmHj1u++43bF95YCdyebAyf5pz8/UzFWC6skoFHvs/imqK/aUcWclE9R50LpgytjdM5q1\n6JSRprDpKC5Tz3nUukSzvfZfXyDIwMgk58Mms6PepAMMyS4tGBO4IR5Do5NJ/dvC4dzH4wzqzIb+\nYfv+xM4QtTVUUeEOzeSmcd/iKd2BgEX/8ERU+ZPnRjjUZQ+wJK2XHLtfzVi5Msb8I7ANuB14P/Dv\noXXplD1rjHk9tDwKHAAWx9m1yGOeKKXKC3tOs/NQL2s7G3nf25YXWpyS4vrLOrjxyk7O9Hn49yf2\nlZwzrTKnmQil+DgiIr8vIrcBNakKAVuAI8aYE8YYH/AIdtsWS9ptkmVZnDg7PNUpBnClSFwT2UmI\nN4vgTRLI4eBbAxw/OxxlbpT0XMTv1EytCZ3fga0M+ANB3jo3Em02lMLHJLwqrPDEu6awSVesH4a9\nzjfVqRrxJDffCXeC3TGzU5FnzEaY79nMEkwVDf0dGLY71gMjkyn9ZtIJ4hFPIY+N9hhZP+H9w3Wc\ncOYqjVlFSKBgJxY3dM7U50o0m2VZ1lSSan8wyJm+7MxeRZ4tnsnsdDmi/6aL6bowg5jKjy+yXgLB\n4JRcwaDFZNQgSfyDvH6ol+NnhhNfT8x9ONvvYf+J/iworHE0T+zBivDzluoMR04N8eqBc9NkP3p6\niEPdg/TGWNH0j0wQtKxpz02kf1+uQ/7PKi6qMeZB4MHZHCOUtHEz8ErMJgu4RkT2AKeAP04np4ii\npOLE2WH+49nD1FS6+a33r895Mrm5yK++azWn+8bYd6yfb//0CHe+e02hRVIUgL8A6oE/Ab4ENGDn\nY0zFEqAr4nc3dpLgSDJqk4bHvNNmY5pqKzgRecCYxj+y3x6v09kzmLrzGBktKxmWZaWlKITF6OoZ\n5dyAh/FJP7LUjmWVOhS7FWV6GK/vPtXBSnAoz4Sf2qqyqJHveEl2wx2p2O95KuXKHwjicjoYm/Dj\ndDiornTj8wd48/gAyxbW0VRXESVfGn3tJNgHmfj/7L15mBxXeS/8q6re93UWzYx26ViW5EU2soNZ\njDGLTbAJcAGzOJAFQti++yQkuV8SLgn5LtdJyEfALL4BjIkBE8AYA3YIIYCxAW+SV8nHkrVY0oxm\neqZnet+r7h+1dFV1VXX1MptVv+eZZ7qrz/LWqVNV5z3v+/5eyVVPbopB5y57rd7CwaMZRMKi65SV\nxUpGo8WjWLG+/h43h2ZNbMvr5lCpN1UxcT2ciU2FS41CWbwntm2IgmUZZJYqtsgN8iXjpNe8IJKu\nVCSFfyFf7WBh7AsqGYxiyzqL21cq9UMsz/9soQqfQYoBxbVWdUyO97r8/DHMLpY1CnR3V11gbqmC\nRqOFCSO2Ram+7E5bb/B9pT7Qy1PTxXIxDJTB6CbzvBQzWa23EPS1NwfkZ0ul1mlt43mhwy1wJck+\nBkkiPArgQwC2qdoRKKVv6aGNEIDvAPiIZMFS4wCAKUppmRByDYC7AFgyDqTT65NPYz3KvR5lBgBf\n0Isv3n0ILZ7Hn75zP8i29GqLZAtrcbz/6vcux0c/ex/+4+FTOG9LEq+6bJPm97Uosx2sR7nXo8zL\nhF9RSisAlgC8sod6dt66Pb2TeF5QFsYAsGdbEsmoH8GIDzPzJWQWK0gmQ2gyLCpNAR43i2QyhMhZ\n8VXo97qU69riBVRrTU17AOD1cEqZSDgn/o8GNPNBEATwQluxkMvF40FwHINIQVRakskQWJYB63Eh\nslhFMhFEOh3GTK4KgeMQCHoRaQrw+d1K+/lSHZGwmI8nlQrB7eIgCO3zTiSC8HtdiISLynf9XI3H\nAyhVGohE/Mpvc4U6mtLKK50KIRTwoNISkKuKi6hYLAC3i0Ne+h4M+1A5lUMk7Iff59L0Ictv1H+j\nyeNXT0wjEfEhK1mRXr5vEidn8vD43JhZqmLnVjHZ6NlcDTzLguOYjgW3/pxyxRpm5ksIhX1gXBxi\nER/S6TAimRJckiv1YrkJhuMQCfsRlxQH+ZzDUT+eODKvjKP+uuuvuYx8tYV8tYz9u8eUnGLqMul0\nGBOlhuI+Kp93LCbOmRbLYqHY6Dins7kaWgwLt4ttz0mWVeaOjFQqhIDPjXK1gcicOC/OZCtIJIJI\nRHw4dOA0AAaM24V0IoBD0jVTw+91wa1TuM7mati5NaUoIu05HIDH50Z+Oo9I2I9UzG/6LGw0eeRL\nNSSj3an4M8U66tIlDgU9hm2qxzWRCCES9MBbqiMyL45tKhlCNOTtqFduCsirlIFQwA1XWbxWTTAd\n45FMheF1c+L9f1a7TE6lQliqNhEJNxEOeFAo15FMheDzGCztpbFOpUJ4dlqMf7pIdV4L5QbqPOCT\nniny+aVHxP7L1QYO0gx2bUkoim6t0eqaEDs8nTdUUJOJEFIxPyILFWX+GUH9PKkLDDarZJMRiwdQ\n0rk4hyJ+8ByHiDSf44kgwgEPIrPivEwmQ4hkxGu1HO/PQSxX3wVwCMBPAGUDxrZaSAhxS23cTim9\nS/87pbSg+nwvIeTzhJAEpdQ0+iyT6QyYW+tIp8PrTu71KDMg3kyfvPUhzGXLuO6KzdiUCqyL81jL\n4/2BN+zBJ257BJ/7zuMIeTgldm0ty2yF9Sj3epQZWDaF8HlCyPcBfJVSen8P9c4AmFJ9n4JovVLQ\nzzspX2i7qywslMDLCXzLdeQLFczPF7GUryrljhyfb9dpeZTrevDZDFq80GG98Lo4pYxcby7DQrW5\ni5NnC5jJlnDJzrSokEjlslkXGKZdb3YuDxfHYrFQQ75QQTbrgo8FcksV5Es1cAKPfLGGVqOJTKaA\nxUJN49aUyRThdrHgeUFpc36+CL/XpXwPeVhkvO3FWDodRiFfQbHaACfwyGRE9rClpTLyEqPYiVOL\n8PtcKJYbSjs+joHHxSrff/rgCaXNVsOtuR/yuQryUlxOwM0gk2kve0pVsU31dcpkCsjlysoxua3F\npTLypZrInqhb6ujvvyeeW9AQX+QLFbgEHku5iiF9OCfwaPGC4kI6fTav9B8J+zXyAcBvHjuNsWSg\n47iME6eySElKhP7c8vn2+crX9LFnKjj2fFbjwqo+J/nc3RyrHJ9fLHf0n8kUEfC5UK42Nb89cPAU\nLj9/TDm2tFQGmk1D+WsVrsPKAQCnp5cUpUE9v2Q67nyhgoCbwX2PPI9cqYYNyaCSgLdabyrsg+ok\ns2ZYXGzPv2a9Yfh8Vcs+P19ArSwqN2rZ6pVOV9bsYklTl280UZQYIMss23GPZ+YK8Ho4VOud4zU9\nk8NCVmqv1UK+XMd8pmhqacoXKuIc0M1tQL7nKqi5OU2Z+UwBHjeHY9N5ZJfKeOTJKi7emVbu/8lU\nCJMj5vnGcrmKoVvnkpcD02qJzxo3i7DH2GX6dKaoyJIvVMDxfMc4BNxMx7GfP3wSG0fCyvGF+SKq\nfrfm+ujHYZjvpEGUqxil9L39VCSEMAC+DOAQpdSQJleyjM1RSgVCyH4AjNVLzIGDbvjWTyiePLaA\nPVsTuO4lW1ZbnBcERuIBvP8Ne/BP33ocN3/vSXzsdy91kjA7WE2cB+DtAD5NCIkCuBXA1yilp62r\n4REAOyQ39WkAbwVwg7rAoO8kjcuV6rN63aFm1JItTeVqw3CxCRjvZuqZBGey4k5tqdpELNRedAkQ\nGfbacujiExjtf70H4XxOu5hp8Tzm5itIqe7/fsM11LLItNibRsOGv+th5eatz6lkRsOsyUfWaOHo\nmZzC3mjHtcjn4TpYBY9O5+BzGy+5GIYBr1pUd/POy+QqurxYWugp/tWQh87NsUjH/Ery1bxVTJtU\nqdHicWa+hIlU0HDy2WXN41jG1CXVzFO1UmshV6zr4qG0cUotXlDIOqYXSopylS+3r8WRU0totHi8\n6LyRrtT1bo615xZoHFZkC+rzNXL91DNMqlFv8hCkKqwSv2Qthdn4KveG7vcWL+CxI/MdRDEykcjs\nYtlSuTIDy4h/3WTW58ar90AVr3EL1P02LPITMwzCFvgUIWSiz7pXAHgngFeoaG2vIYS8jxDyPqnM\nmwE8SQh5DGKekrcNIKuDcxwPHZ7FN/6DIhnx4b2v320Y+OugP5y/OYG3XrUd+VIdN9/5JOo2kp86\ncLAcoJQuUEo/Sym9FMAbAewAcNxGvSaADwL4MUSPjG9RSg8P8k6yIqdiTMqoIS8MGhZEBuoFgkxU\noM4no/5dzyQo5tRqL5i6hvR0WYxMz5dxaq6Ao2faLjsCBMMcPHNLFRybzisui3oYHVOPg3phrleY\n3DrSEKsFtBE9NM9rl3ozCyUUyvWeFnVmwfJmCzqWYXQJTwdc+FkRI0g/7t6SsIylEQQBuWIN5WoT\nOZXidWqugFK1YWiNKJYbOD6TN7x+z6vGmp5a0sxTO8I3mi0cP5vXUOs3W7yWoc+kSZdaWW62DMkO\nNBJIv3Eca48t0OYxox+6Uc9b/dxo8h2xho8dnbck4ZieL6naVt1HxroVCuV6h2JlB80Wj+fO5EzP\nj2HahBaDxTGaj5H+njIh5FwWDGK5SkB80TwAoCodsxVzJblrWCp2lNLPAfjcAPI5cAAAOHo6hy/9\n8DD8Xhc+8uYLbAV7O+gNV186iefnCnjgybO47d8p/sd79q+2SA7OUUhsga8D8LsAXgbgq3bqUUrv\nBXCv7tgtqs+DvZPUi3yFxMH8FS+v6awWAYIAVGpN5Ev1toVJtRhUKySyhUKGXpO/8n0AACAASURB\nVNlq05wb9ygfVRRDXbGa5O6mVtgEQUdPLX07Ni0qYEuFmtKfeg1rtDhUE2OYL8zbiXoBMZehnLBU\n3T8AxZ1Mj2KloRlDvbJmB2aX1cwCyTBahXFYBKxyHJkGMnkFGFhxOT17aqljzshgdDnZZMhWRiPl\ncnqhvahv8bxprraGybU12mSYzVaQiLTjmnrJkWWnqKz0tngetTqPgM94yazcMzba1MsodLnYVkyE\nrRbfziGnGnM98YMaajp2QTAizrEUB4CW1t2s/Gy2bGldZVkGXjcHBoyhq2wvMKOYV491h5K8zNrV\nIMrVN6Q/NVaOisOBAxuYWyzjM999Ajwv4C9ufBEmk92DWR30DoZhcONrCGYWyvj102dx1y+ew0t2\nj662WA7OMRBC/gmiRelpiErVuySCixVHUedmZWS5qjdaFjl8zN2BZAgQ43vUSoN6QWFE3S7HDOkX\nsaVKQyFBANoWH7t0yUYKoyAIGmr4DoWs0VIWzbwg4NlTS3CZuGKpc3LpLRZmkBO1GvVvplwdOplF\nSJVQ3srFzgy9JcKV3QK7K352IUBUYJ49vWT4m9gpwFo4IJopVnIrVmdox9pjpSCr4XVzqDVaOJVp\nkzm4ORaNFg+W1Sp5ZhsDRtfDmvZc/M+yYt1HnslAgIB9O9IK9bsauWIdsZBXOyY2Zek2V0rVBvxe\nzpieX8WIp1Zo9dZcMxixbtrB83NaYo1mS6TBj4Y8iAQ8UtvWYBhRwfJ5OJSrTWSWKvC42E4SkAGc\njNR7NOIzxdhNUBCEri6ivaJv5YpS+tUhyuHAwdCRL9Xx6W8/gWKlgRtfQ7DvvJF1Gfi/XuB2cfjA\n7+zFJ257GF/94dOI+Fy4YFtytcVycG4hC+AySumpriWXGcen89oDRgl0Z/KdByW0eAHlqtby0lnG\nIEZDtWqoGSgGDGO87itWG4g2PaZ9qVcjeouQGurFYr7c0MRm6ReSjSavxJkIgqC06XF1LmDVlqtG\nU+vOpHX3sWcBslJgZIIBAJa77+q2fB4Os4sVlKvNnt36GEYrq1WyVztotniFrrsDiuUKYPoMDKk1\neGurqw3lysrdVQ2Pi9Nce0BtzdG69+n7bbZ4uDjWfhJk+TfpP6OLY6o3ebhdLBZ0FsGZbAmbxrRk\nCGatL0hJg/0eFyr1ZldF9LnpHKr1lpISQI1WiwcviBY2A8M4APG+0cctKTIKYo61cEDtzdP92ulj\nmRYLNZyZLyKzxGHfTpGBuVvohfy7y8WiUm/iOcmaffn5Y137twu1nE2eN1V+jSx4g6LvmCtCyE5C\nyP2EkBPS932EkI8PSS4HDgZCsdLAP95xEGezZVxz2UZceXG/4YEOekE87MWH3nQBOI7FLXc/hRmV\nK4gDB8sNSunfrQXFyggay5WNF3mrxeOJYwsdCTK7Qb3YrNT1OYTMF05zixU8+mwGc4sVjbztWIx2\nXb1FyAzlqnUOI7U7kGaX2WDBqY55arRaODOvz94id9L+qB9mdf9mbmn94PHn5jG3WMGJs3nMLZX7\ncuuzk6zWLkpV40TS6lw/DGMdj2YFemrROq7LxvlbJcRWw8UZ5CZTFHLtcf24H5M2OCyTZRtBdrXT\nHX7q+AIePDyriSs0qmcF2WIsEz/ZsXIummxkNFuicskyjKm16tDxrOKuqcdCrgp6alGMjdLlhLKC\nmfWt3myh2eIxt1Tp+oyTf7dSwvLluu2k6EaYz7efnc2WNuZKPf+WI//VIIQWXwDw/0HMJwIAjwOw\nleOKEDJFCPkZIeRpQshThJAPm5T7DCHkCCHkcULIxQPI6uAcQrnawKfueAynMyVctW8Cb75y22qL\ndE5hy3gEH37LRajUWvjn7zwx0MPRgYOVAiHktYSQZ6R3zp9blHsRIaRJCHljL+2rF7J2FrVmsSfd\noF4kyS5tAcndT16IGdaTVh5LJRN3MNX6w0g2o1b1jHkdSZPVcUaqzy2e75t0yGqZJGjcgoa7oFpS\nudHZsdyoYWa9mEiFTON8LGHSvQD1+p+xZFbsBiulwI7C0JCU5S3jEWwei5iWs7pXBGgtV/r5VZBc\nc60sV4Ig4FGaUSwnYrvd+zaWR91++7Msozwvgj433C77y2+GYTTnJt8bTZ4Hz3e6tKnLmsX5ASKD\nKAAsFevKZ0BPrtJZryM5r6rMsek8jk3num4KybGRVlPw0IlOMtZs3spd1Rwt3TNLc72XIaBpEOUq\nKgUACwBAKW0BsODy1KAB4L9TSncDuBzABwghu9QFCCHXAthOKd0B4L0QlTkHDixRrjbwT//2OE7O\nFvCyCzfg7a/aOXRfWgfdceUlU7jm8o2YW6zg89970rZ/vQMHqwFCCAfgZgCvBXA+gBv07yRVuZsA\n/DsGigZYPgiC6Fb24KFZVCXXN7fkZsfznVazuEGiUwDK2ck74sNYfwgCdG5c7d/0jGR2iST0C/ly\ntWn6vKlUmzh6OifGbEnV1PFVgyCgaqfX551+4SeDYxlctHOkZ1nsxDwxTHfXLStYLUjtKJdyDF3Y\n77YkmbJSAAXBWInpKGdSFwAK5QYarZZGGRAjkZieXcWMui9VG3jo8Cxms2VFPpHIwT4YRnsOcuLe\nRkOcx6zuVrF7r8rXSYCgbIQwjPa+1LtkAp0WQvX1ljdTyyZutzsnY9g5GUMkKLog669vt3vHyk3a\nDAwYNC3m5FpTrpqEEMVBW6JltxX5SSk9Syl9TPpcBHAYwAZdsesA3CaVeRBATMoz4sCBIbL5Kj75\n9QM4Np3HFXvGcONriUO5vop408u34ZKdaTzz/BJuu/eZZc8r4cDBANgP4Cil9ASltAHgDgDXG5T7\nEIDvAMj02oF6DdHPU8lqd18NXhBwfCYPAYISOyQHuxtZrjj9ykwP2S1Q0H7vKGbjpARB0JBVWFk4\nOgLbbaJca+DwyUVDmYrVBubzFZxdaMc0qQkKTBVNG1B3ZUe5UcNs4ccw1jv7pu2ZuDyu1DPYzvnL\nMVdcFyXaal4JOjpKs24N3QKlQ2fmDVzXhd7dJs0UStnScnK2oJTRx0h1A6vTrlwuFi6WRV2ilWd0\n7dm9zGq3OXVf6nOZNnDt17uwGlG6myEW8iIR8SnPIf3zSL53+52rRoq6SHwiWLS59twC7wSQIoT8\nDYD7AXyq10akpI0XA3hQ99MEALXv/GkAk31J6uAFjzPzJfyv2x/FmUwJr7xkEu953S5HsVplsAyD\nP3j9+dgyHsYDT53FD399crVFcvACByFklBByOyHkl9L3Cwghf2SjqtH7RhOoKW0gXo+2F0WPb2T7\n2lXAa7BA0NUZTwQNn3FGizyOY5Tf9AtGs8cko/s/jAUILwDHVSQeVguovtzhJJjFHLXlaLuTedzt\nZZARE5xdWNI+d4E+Nk0GI67we5bFLH7r4WfmlJ3/QV+PdvJEWUGOoXNzrKUCafUe11tCzWjNjQ7L\nbqGypaSf9QLLMEiExdgpszGXz0095xgWmgvAMgyiAXMyGYZhNHcfxzDwuDnUG6JbIKvKGQWI1qND\nJ7Ia1zc1jAhj1OiV0l5dXB/7tXVDVPmcjvk7LFX676VqA8VKQ5OPqxcYbRYxEK1xZmc1rNQHagzC\nFngbIeQYgNcD8AO4kVL6y17aIISEIO4CfkSyYOnREY9q1V46Hbb6ec1iPcq9lmR+8ug8bvr6ARQr\nDfzu687Hm16x3XTHaS3J3QvWo9yyzH/z3hfjTz5zH7533zFsnYzhykumVlkya6znsXaAf4GYq+pC\n6TsF8HUAX+xSz87r9dMA/oJSKhBCGNgwQEXC7dQP6XRIcR1rMiwWiuYKwNaJKI7pguaTyRDmpTqp\nmB/nb0ngV0/MdLjRcByjsQ4xDJBKhFBrAYlkCNFcDR6Vy04sFkDNYF2YSISQTgWRLTdQ40Vlx1Vt\nIhz0gHV1RgBEoz60utDPcRyLZotXxoUXBM0YqZFOhZAt9R+vmU6HET1b0FC4y0gkgqg1Wqi1gNF0\nGOWGOF6pZAiVZn8rrWgsgGJ9uO7PyWQQLAPTMRoE6XQEHMsgEhbn2Y6NMRx5vpO63Qycx2UqV9Dv\nBuu2Xl6yDAN/ABgdjaBUaSCSMWZIjMcDpteEZRlEw14s5KqIhP3wuFl4Vdfb7WKRTodRbgrIVbQK\nbCIRQiTogf9sEZwkazIZAssyiGQrcHldiEd8aFrc5h43i3hYLJNMheEp1RFZqkrtB5GK+bFYaSJS\nbbX7DJeQTAQRDngwXxDvI45jsGks0nHPK2MQ9SGZCCKSFS1NiZgfLZ7HomQVi4W9iAQ9KNTEfrKl\nBsBxqLW0c0f+HPC5TBV6AOC8btNry3EMvDrLaCweQF7qW992OhVSzjMRD3a8q3LVVsf1fX6+rJG3\nF1yyaxSPHJ7VHPO4Wbg4FqlkCJGFTmtdKhmCzztIZqpODNSapEz1pFDJIIS4AXwXwO2U0rsMipwB\noF6FTUrHTLEeabbT6fC6k3utyCwIAn780Cl85+fPgWGA33/dLlyxdwzzJixSa0XuXrEe5dbL/OE3\n7sUnbz+AT99xEHyzhb1b1yZF+wthrNcLlkkhnKCUfoEQ8l4AoJTWCCF2Vrz6980UROuVGpcAuIMQ\nAgApANcQQhqU0rvNGs0X2i/y+fmikkcqu1TR/KZHsxbo+D2b9SjHto2FMD9fRKFQ6Up8wTIMcm4W\n+UIFmUwBS7myJo7Cw8JQluyiBy6Bx5Ika73mQrXeBN9sGpLUMDyPvBkZhgliIa/pOOSWzH+zg0ym\ngHy+qmEZlLHgFvMk5QsV5HNupZ+cj+u7T7+L6bnuJTtH8Oizbcp0OWmtjMWsGxtSoYHGwQzz8wWw\nTFvm3JKnp36sytZrDVuJYb0uDplMQUyEbdJewG0+rizDgGm1AEac3y6WVZgEAdEqlskUkM2WOtrI\nzBdQLbmRXSwpY352Nge3i0NuqYxqvQWOFyzP082xYKR5lJkroFRtKOUXForg6w3Q4/NK+blMAflC\nBUE3i2atXdbFsqjHfMr3cMCjkHEAgAsCMkx7zD2saIXOy6kLGICvt8dQP48AUVGRfxda2vYBYCQW\nwNySqNQcONTbfFuQni8A0Ky7NPFWS4tl5Te/i0HGr1U7crny0OY3x7IoF6to1BoaplQ5WfF8wG3Y\nV2a+AJ/HNdR3Ut/KFSHkYYPDAqV0v426DIAvAzhEKf20SbG7AXwQ4svscgBLlNJZk7IOzjFU603c\nes8zePiZOURDHvzxG/Zgx2RstcVyYIKJdAgffvMF+NS3HsPnvvckPnrDxdimchdw4GBIaErvFwAA\nIcTuQ+ERADskN/VpAG8FcIO6AKV0q6rdWwH8wEqx0kOTh0Z1fNNoGLPZikLosH1DFB4DJjGjJMQs\ny3SNdGaZNisczwudNrouhhpF7i7lek2c261Ot1gcOzCzOTRVPkJqtySrGJuLd6Tx1LEsGi3jAe8n\nRETvweRxcVpiD1VcSj/j25MsXdziPC7OUFE1gt14GfkaW3VtlRBXdLWDcqGbOte8Rkt0mzMcO6FN\nZS6jxQtgWnw7cXQX27Sg6tuIfVKfy0vui2U7qdMDXpdynXdtiivU/kZgGUYT1MPp6OpdHGv7Wilt\nDnC7zWTbLnz6e4jrEjQ4rPANr4vDlg0RSQbtbwzDQODN+UGX49YaxHL1UdVnH8QX0bTNulcAeCeA\nJwghB6Vj/y+AjQBAKb2FUnoPIeRaQshRACUA7xlAVgcvIByfyeP/3P00Zhcr2DEZxfvfsAexAQKR\nHawMdk7F8P7r9+DmO5/Ep//tcfzFOy/BRCq42mI5eGHhTogugBFCyLsBfADArd0qUUqbhJAPAvgx\nAA7Alymlhwkh75N+v6VXQYJ+7S6pejGlzXnVDkYPeN1IxfzGjFmMtg5gzOTVUY1pL3BaBgsMu5Tk\n3crpd8JttWnRZLdFWfe2zRuv11vKwl7dj1FOJbU8ViL1k6dKv7DUx58ocW9mmZ8HgP5UrBj+ONY4\nEa8Z7JaVlQIrBUo9RAGvq4OFjucFy2TI0/MlRZ4NyaBC0CAIQofyIwjA40cX0OR5cCxrKy5Nvob6\n2COgM5eXoBBa6DZbGFEh2rs1Kc0zPUGFloyBZQFG0NGva/rt8lwwuD5W16AX6FvRbl4YlB/wPpcx\nkgio1oHtNs/bGMfzswU0LGMEhyKCBoPEXP1c/Z0Q8mMAD9isez9skGlQSj/Yl3AOXpDgeQE/+s1J\n3H3/cbR4Aa/dvxFvfPlWJV+Cg7WPi3ak8O5rzsNX7jmMf/zmQfzZ2y/GeNJRsBwMB5TSmwgh7wQQ\nB3AtgH+mlN5us+69EOO11McMlSpKadfNvgt3pDAzp9p5NjI9QctKpiTWNFhw9Lv4YRhGUSTUFOQy\nBEFcPOuVg47eVPUGtaTI7luWlqseF10Br1uTV4sXBFPLQ7XRQlBWrlTvD4+LQyriN2RR41jG0pKx\nkO+DIroLuYj8fTmomfR9W10LSX2wbG88EYTfy+HYTN625YrVzXsAmEyHcDpj7Npv9K4vVOpIJ0Om\nfeTKdQQlchR1XA0vdOZr4wVBsUzyvND1nrPaqKg3+Q7lStZfWZbRjb/42a+Sz8qKyuoILjYkgzib\nNY5ZM6xrcH2Gxf+lWP1U/Sl9GIznkHQrzcaI3CbHsoiFvDg1VxSfe6ZU/WuLLVCPKACHKt3BsuBs\ntoz//fUD+N59xxAJevDRt12Et1y13VGs1iFecsE43n71DuRKdfzDNw9idtHeS8GBAzuglN5OKX2L\n9GdLsVoOuF0c0tF2QLZ2KaVlCmN1i2gjVxn9TrddMAzgkjoQlavOhcTuzXGcvzlh2W+biZ0Z2JUn\nFRMZ1qwW9Gb5jcwWvFMj2gU2z5uXrTfa46BX4pJRX0f5dMwvWRj7P283Z8zQtt3CPVqWv59uk5HO\n8zBCNCju9vs82r12/TU2ulQulS/ZhlQQ8bDXsKzMqKeHMu9VfU2mQxiJBQzlMHvfy/0aQZ3kVn2p\nRcuVqAjIDHMlVSyhAEEZd7Oca4LQLqO/r06czXe49amp2HUtdbStlpXXM/IxjGbeej2coYIQMWAg\nHEsEDNnxhpUPVO+a2U0p91owdOrlt2JU1NzHBs9TXlgnboG6mCsWwFb0QcXuwIEVeF7ATx45hTvv\nO4ZGk8eLzhvBu15DLJMOOlj7uPrSKfC8gDv+6yj+/hsH8efv2IeR2PAZsRycGyCE/IPBYTkiQqCU\n/tkKiwRAvxMN88+K/5d1exdsTaFab/a0qcQwjFJeZhEM+dzgBSiWHpnFUO1+1hap7fakbnMQyItZ\n2U1q44gYSF6uNhWrkZkCZ7ZE0utivCCIbmcGhIMCBCwWa5Is2h3vSNCD8zcnEPK78fiRedSarbaS\nY9DvzskYnj3dybKnt+6Z7dBbxZa1F+6mRUwRDXlRq7eUXGdm2DkVRana7FjIbkgGcVoihzLKjwYA\nPg+HYlXKV8UyyqJdrzSPJQNo8QJyOsITvcVWhpoefzQRUOQwm/eW94NKMdGfg5wPzO1i0arzODaj\nVYbkegzDYONIGM/PdRIHyXOj1uC70ofLigfHad3+jKj71bIKgqCZ92L+s+7KrxHl+tRICIuFhc7z\nWA7zqI0+giZruUTY15lguIvrqtKPdE3k+gwjzsmVTLU5rJirJoBjlFK7MVcOHHTFzEIJt97zDI6e\nySEccOMPf/t8XHpe79nqHaxNvHr/RrQEAd/+2XO46esH8NEbLsZYItC9ogMHnShBbVzRYgVfqVqo\nd2XNFBJ9jhorBHyunvM/sUw7tkV2xWMYBqw0LIJOAVCceqz8AiEYxr/YlkmV1BgQ5RuNB/DsqSVV\nmXb5bRuieG46BzfHgWWNY830Y1go120tGLU73uK10Csa8sJWbi8S8CAvxZiZWU04lgGvocQ3uf7q\nmBTdb3KdTmtAd/jcnK15xbGsoYVDLYw8Z/Rwq4hXWNX56pUrQRDjpTqVKxOhVNXVfZjFxFkpVy1e\nUFjw1OfACwJaklugm2Nh5NSpvu4bUkHMLmqZNnmV5eq5M7mu16kmucx53VzX3EqMRrlC55gYuPd2\nNqL9GvK5O3JmmRQ1hN711g7kjRvA+B4ws1yFA+6O54veOrh7cwJPn8gC0JF6yO7VivLOGNaXUa41\nh75hP7SYq15ACPkKgNcBmKOU7jX4/UoA3wdwTDr0XUrp3/Xbn4P1hRbP4z8eOoXv/fI4mi0e+3eN\n4O2v2mn8AnCwrnHNZZsAAN/+2XP437c/ij9528Ud7j0OHHQDpfTjg7ZBCHktxFxWHIAvUUpv0v1+\nPYC/BcBLfx+llP6XVZtut3phqNpZVcchMIwt/3yjhUki7FOSwgImsVMMo7hvyXEZDGOscXZL2Kr+\nPIj1ilOUK0lG6bj6XNTtp2N+pCXL9uNH29TWGujEOXomZ+lypMjCmSs3eqgtGYC1YqxncvR7dUyA\ncp82hlFPMd5tkbt1PIJI0DNQsJb6vLaMR3BqtjMOSn/uZvPHLH5OsTDorTAm7ZkpUVZjqKbk9nna\n80FMQGwtn/56W1k+7CjAFUlZ8Lq5jtgkPdTnxAsC1K37PK5OQhKjOCqTA9snonjquNZ6Zed+Dvpd\nyryLBDzwe12Wbv1611S709HncWEsEcCJs1pLof4Uw6o1oUtjuZL+K0qW+N/MDfnYdG7onjODuAVm\n0Ha70EOglFqZGG4F8FkAX7Mo8wtK6XX9yudgfWJmoYQv/fAwjs/kEQl68K5XE1xC0qstloNlxDWX\nbYLPzeFf/+NZ3PT1A/jvb73QoWl30BcIIREAfw3gKunQTwF8glJqmQiMEMIBuBnA1RBzXj1MCLmb\nUnpYVew/KaXfl8rvBfA9ANut2jWiVNdDTWih1njsWIZ2TsUwmy3juBTb4ZfctNQuaQyDDqpmM/Y5\njdJnFu/DtF/8e7YkUao0lP7tQrbWCO3VKwBoXK9YhoHfY3+JYrQQscOmqFnAG5yrGvJCvcWLLuq2\n24WoGOzfNYqTZwuaBSmjK6PpXvpxciSkid/pRvYxEhc9AAaJSFb3MBoPYDZbRtMo27RZJQnjiSBC\nfjfcLlZD2Q2gzfKnq2dmYXCZ3E923b28bk6ZY4IgKDFQ+vtDL4eV1658nd0c2zXnXE1KcOx2sZq5\naSS/1nKlDboK+lxwcSymRsIISZZswzFj9F/FAyG/G143p5HBjpIvqE4vFvLC7WIxuyh+3zERw5Ez\nbctzKurHRv1GqU3tKhH2alhUlf4t6hhtknCKW6B2M2clMMi990UA34b4MnoVgDsAfAHAiwBY5rqS\nkg8vdml/BTxAHawV8IIYW/XxWx/G8Zk8Lt89ir/7g8scxeocwSv2TeIPfnsXKvUm/vGbj+HJY50+\n4Q4c2MBXACQAfAjAh6XPt9qotx/AUUrpCUppA+L77Hp1AUqpemUYAmBiQmlDjnkIeLUuJ+pFg5p2\nWf3u370lodmZNV38qI5Hgh5cvD2N7RPtzQl1zFW7T+NYKqNcN6yyMGkXFCQmvpDfbRoz0RavU3CZ\nYENe3MolNuhSM1y4PYULt6c0x6IhYw8Gq513MhU3l4/pXJR1g8/jAseymjgPPToIORhxLPWKkbr/\njaPaJKbK4r+jjrlsGvKIAayL+qrq+EE1yFQcO6Uck/reNo9FsGlMPCevm8OOCW3aObNYNrMYKZeZ\nhcnwaCdYllGsV40mrygXZtdRb7kynGPSIbdBfJMezRavWDs1ypPBGWgsV3xblh0TMeV+nkgFEQ0Z\nk4iIonXOQaVPXXkjq6N+c0P9DNDH4SWjPmUcvS4O2yei8Ogsx2azcTwR1BCqKOOtqhHyuTUKZEA3\nH9X3iGL5ZLWWUWEFtatBYq6upZReovr+IULII5TSjw0qFMSxeTEh5HGIu4h/Sik9NIR2HaxBZPNV\nfPlHh3H45CJCfjfe+/rdjlJ1DuLFe8bh87jwxe8/jc985wm8+5rzcMXe8dUWy8H6wm5K6S7V9wcI\nIYdNS7cxAeCU6vtpAJfpCxFC3gDgkwDGAby6W6Msy+CSnWnT/EVyGSO3I45lEQ95lfxRNnQrMAwD\nr4fTWLyMlo0MwwCMFHOlP658bssHdLrUyAsfq9xQgLjLriZV8Lo4JW5MWbxatqDFxtEw4mEfDp/M\n2q6jjouyopHv5hq1a1MC5WoDozZiQzuvufhdryipv3rconXrocOzANoB/FYKmR7bJiKGbduBUaJg\n2d1qy3jEkG5ePbYMIybHVWKV9GUjXqSKfsznKlL5dj07UJN/qHNWuXUWre0TUZxdKMPtYlGqNjXn\nJLdxSkX3bjaH5cV8m9Wws4x8SFaE1XLpIStXdqAntJAVQa/HWImzQ6+u/tpR3kCsdMyvIfEYSwbA\nMgzm85UO5QYQrXctnje/nibHN42FsQlh/ObQWY0o6uLnb0ngsSPiflYs6MX2SXEDKR7yYrFY09wj\nSiynitACMCYOWS4MolxFCCFpSmkGAAghaQCRLnXs4gCAKUppmRByDYC7AOzsVimdDncrsiaxHuUe\nlsy/eWoGn/nWQRTKDVy2ewwf+G8XIm5C2zoMrMexBtan3P3I/Jp0GJPjUXziKw/iyz86jIYAvPmq\nHUOjibWDc2WsX6CY1r2XUhA36LrB1luXUnoXgLsIIS8F8K8AiFV5s+vi8rkRWawqZSotAU0wCPrd\nmjo1AViqiIpSMhUyfDa2WBbzRVF5SSaCSKfDYD0uRJbE9uMRH9LpMCLhnFInEQ8gGfPh8PEsdm1J\nIh0X4w3i2Qq4kqjMJRIhpON+NMAoMgCi5Yh1cYgGvUinw2g0eURmxcXkRDqEM9KidTwVxKZxcUkw\nly1jNltGqdJALOxFOhVW6kTCfiRTIaQlV7ZXXuYDzwsIWcTYjgI4k9XmokqlQojMG8d/qM/f42ZR\nb/CGv6VTIU2/0dkiqvUWYrEA0ukw0iZ7fjs2NzC7oO07HvGCUdGvx+NiG3UwyFVbSt/lagORjFh3\nJB0Gx7GITRfA8wKSiaBS7myuTQYRj/ogmFhbRkciyvNyrlBHyyTDrtHcV7oyoAAAIABJREFUfEUs\ngF8/OSPJG8Su7SNg2ba17SKGxbEz7XkUi/k72olG84qikUgGkU5pXcNGRyL4xYHT4u/SfAWARLyA\nWEicU0vVJkoNHm4X23F95Os+PhbBHjKKswslbEgFsTARw2K+pozjru2i22a52sDDh2aVc/YF64Zz\np1jvdOmLRnxoMSzCQQ/S6TBi82W4K9pYt0QiiFy1BY+bg6fRQipp3JYM+Zz85bpmvurHUf27x83C\nF/AiUucxMd5pEQKAmVy141on4kFUmu1HmzyPASA8U0BTlYcrlQxhQXqOkE1xJCI+zGbLyr1PNsUx\nlgxi85SAYrmOaMiLzGIFEWleptNhjCxVsVSowevhNOcjX7+k6nobYfNEDdl8FRMbokjHA1isNBGR\nxnJ0JILw2SIaTR5j6SDGx6JKvzwvaDYzwvNlsC4X4tL8XKo2UeOBaCyASMXY1XrY79BBlKtPA3iM\nEPJDiIrmtQD+1zCEUvvHU0rvJYR8nhCSoJRablVlMpZu9WsS6XR43ck9DJkbzRb+7WfP4aePnobb\nxeLG1xC8/KINaFYbyHShju0X63GsgfUp9yAyj4Q9+It37MP//2+P4Wv3HMbJ6Rze8aqdK5LT7Fwb\n69XEMimECwAeJ4T8AOJ76XUAfilRtVtRsp8BMKX6PgXRemUISukvCSEuQkiSUmrqw2p2XfKlOvIF\ncYGXXSgit1RBvlBBo9bQ1FlcLKvKldA0eDZmpboAsOjjEHAxWCrWlGOcwCOTKSjfAcDLAqmQG+dN\nRIBmU+kzn68oLHjZbBFoNrGkah8AhFZLtKY1W8hkxNgV+fedG8LK51TYg7zE0uZjgaWlMir1JtyM\ngIWFIvKFCiJhP/KFChazJTA6i0lFxyzXMYYF7QJZbtMI6vPfMhbBcVXsj/q3hYUiKqW2m2MuX0Gt\n0YKXBTIBc/fHhN+FI7q+GZ5HXnUOfheDjN+lXGu572q9qXyfny+CZRlsTPoxu1hRxmRpsaQ5NxcE\n5AtaK1I06MVYIoD5+bZFZmmp3FFOfd5GUObSogs+3SN30UCOTEarBBcKVYVUJZt1w21gUZHbCHlY\nZLyiorBzPKzIJc97j4vTXJ9stqSSzwO3ICDAiZbf8agPJ6WYn4WFEngpPq7WaGnGu1JrdsyTfM5t\nOHeYVgv5ch1CS5zriYALmfmiEgMXD3mlMa4opCNLfpfpPAREy20mU0C5qpVDfz3UcrpYFpVyHdV6\nC7kl4w2EeqXR0W/QzSrHImE/crmK0k8uV9GQ32SzHqVsbskLjuc113sx6wGnKp+p1DGvm8uVsvjc\nYcBozsdqTqmRCrnhYQQw0rOlKrUX9LmRyRSQy1XQ5HkE3SwyFqypi4tlVBtNeFjp/s6Jcs6rxkOP\nTKYw1HfSIGyBnyOE/BLAlRB3/T5LKX1yGEIRQkYhMgkKhJD9AJhuipWD9YP5XAWf+95TOHm2gA2p\nIP7o+t2YTDsMcQ7amEgF8ZfvuhT//O3H8YvHpjGfq+KP37DH1O/fgQMJh6Q/Gf8CVb4ri3qPANhB\nCNkMYBrAWwHcoC5ACNkGMeWIQAjZBwBWipUl1DFXYgAUYCCgxo3FhqeNUWyI/DkVVbtjMe2+VTBy\nWeogT1AI7436MhdXzink4thlyamjbnIkFlDotzdJcUyTqZBI+Z4IoFBpKGNh3opIsHHkzBJG4tZM\nYsZMjl60WnxHnqkOFz90DlrA58aW8bYyp6VrZzrc4AAg7Hd30MIPmuxZDzvEEYzJZ8OyJvKZuYuq\nh87K5VHdrH68jTbpTNkC5b6k/+GAR0kHE/K7EVCx5bUMXDhDPjeaLUHDEsnoXNXsnAMvCKjVW/C6\nzTWTyZEgPG4Wp+aK5m6v6nPTu/l2eY4YXUx9P3KyZfN0vdZwcSwSKobB0XgA4YBHoUm326r+Wsj/\nzRgdzRJ8D4JBVyonADxAKX0UAAghDKW06/kTQr4J4OUAUoSQUwD+JwA3AFBKbwHwZgDvJ4Q0AZQB\nvG1AOR2sETx9PItb7n4axUoDV+wZwztfQ2zR5To49xAPe/Hn79iHW+5+Gk88t4BP3v4oPvLmC5GM\nLp/bqIP1jX4p2SmlTULIBwH8GCIV+5cppYcJIe+Tfr8FwJsA3EgIaQAoYkjvJZZRLa91b0+12455\nzFWncqOJ6ZIOjicDHbEuHbKoF/EmCpiVPKyJogVA2SUXFzr2Y4jso93GSNyvKFfjSdG1blLFXOYz\neefoxUhGfUhERvuSLxL0YCTux4NS/JS8Du0I8tcoDMb9+D0uhPxujMQDGIn58fxsp9XJiPEu4HMB\nvRE5DgzNKXQZN7OfFZY+xnyeBH3mlkS1gqNXnIzGyVwO8wLygl8hS9DlQpPl3bM1jpOzBWSWtMmx\nuytX2hgiXhAQdludM4vxZBAcx+LYtOSGF/VpGBrVfer1r26KsxExTSLiw+xiBRMSEU23+6TX+4hl\nGU3+qU1jYRybziEds14DNFoyUYn2GSZfg04MPxZrECr2awHcAjHfxyZCyIsAfAzA67vVpZTe0OX3\nzwH4XL+yOVh7EAQB9/zmJO78xTFwHKO4Aa5kLI2D9Qe/14UPvWkvvvmfR/BfB87gE197BB96016H\nqt2BIQghAYgWp+1ov9+s3AEVUErvBXCv7tgtqs9/D+DvhyGnRvlh2wf0O77qnVazZ6XRjrPGGCJ9\nVi/czRbxRof1ypXRItJIRv1iTN7ldruGY7lKRnwaggUra0WnnMbHu1Fi9wo5x1iT59GUaLpDfjcS\nYZ+yqWinfZZlsGdL0rKM0Tn3kxhVJqTo97x7qWdquWoL04FtG6Ko1JqWXgxq9j+GYUCm4sp4syrS\nDQYMdk7FlBixTjm0hBbGJ6H9qr5fCpU6XJyYpLmtXMnVusxRg2PhHnN9hvxuTaJdNfTPGgHAeRvj\nmFusKIyc3fRkF8di79akZRk1Br3vR2J+pKM+23PMJ80Rq+eBSHAzmFyG7Q5Q928h0tdmAYBS+jCA\nbcMQysELC7VGC7fc/TS++4tjiIW9+It3XIIrL55wFCsHtsCxLN7xqp14+9U7UCjXcdPXD+JBKUDZ\ngQMd7gTwRgCydakk/a0pMDpFh2lrVxq4e4wzNLJcqRPe6svpYcctUNb31OcwlQ51JAw1y1XkM8hd\n1c+rYMdkzPS3rvGZJh2auVP1A3ksZepv9XjsnIopFOX9nLvclDpxqpGFsR+vkN1bEkhGfF2tA4A2\nKa+MntwCTY7r80sp5RmRwU5PWa+H3joVD3sVhkq5HQCIBERXSvU1GJWIVeIhbwcVe7dzYMAYKk3q\ne0jvJtoLYiFv90IdfRsnL9dDEATEQl7snIq1nwM9zs2ulqvemuurD0C8dgAQlZRRM6r9TaNhBP1u\nU+V6EAzkFkgpnSFEQ5ZUH0wcBy80ZPNVfPbOJ3HybAHbJ6L4wBv3IhrsbffFgQOGYXD1pVMYTQTw\nhbuewi13P43p+RKuf+mWoccVOFjXmKKU7l5tIbpBrTSpk2Xq3/GT6ZBC62zObqy2FhkcY7T/ASvL\nVedxfVkjpWnCIGZWr6iMJ4KYyZYQDrg72ux3o41jWcXdUGO56kIPb7aRPdRniTLu4gez9dsgfapj\n8owWkB6LGB0zhPxuU8VVrcBtHosYKmC95A0zczkdifmxkK8q7maRgAf5ct0w1swI3SyXbQFlF712\n+S3jEWwaDYNhgOfO5FGqNgyVSH0b8sduFl0jGG2iGG0Q2D1/NcxSsU2NhHFKRbNu5BlntEljhW4l\njDZWlgM7JmNotPi2tdJkPnjdHFhGtGIOc2MFGMxylSeEjMlfCCFXontiYAfnEI5N5/GJ2x7BybMF\nvOSCcXz0hosdxcrBQNi7NYm/fNclSEV9+MGvTuAL33sKtXqre0UH5woOE0I2rLYQ3WC+6NW+4LVE\nBt1hpRxp46mM6xsmEdYtTBrNTmXGCHplYtNYGJefPyYuGnV1+1Uv9FYDGd0UFv04XbgthS3jEY11\no1dcuC2FC7YmEZJigfQ5dkyDWvo4+bFEABzLYuNoW6k1jiViFEvMMCC6Zfmxd2tSkaGz0/ZHs0Wt\nQVENoiEv9u8aRSomEons2hTHpWTEMmmzGnaVK7P8VXLuuc3jYWwaDWMiHeysLJfVtGfcr5E4arc8\no7xpLMvgUjKisQh3yykHiEQqPo9LSSRuZrGeSAVx8Y52bgFD5aJHxd+suKxUDXJ/9QKWZTRWW6vN\nFvnaDNt6NciZ/g8A9wDYTAj5BYAdAK6zU5EQ8hWIFLlzlNK9JmU+A+AaiIQW76aUHhxAVgcrjIcO\nz+LLPzqMZovH267ajle9aMpxA3QwFEykQ/jr370Un//eU3j02Qzmbn8UH3rTXqSi1oxeDs4J/A2A\nhwghBwDIPNgCpfQt3SoSQl4LMcUIB+BLlNKbdL+/A8CfQVwTFgC8n1L6RD9CMgwDjmWVF7r8aLTe\nPDWzNnV+Zo2OGZBVdPbQuRDTL1TlOLBuMSNWi5WOmkPxF+qhqK6s3+samIlUrn/+5gRaPK9YHhTL\nlUm9fixXXg+HS0kaDMPgpERuYaZQbBmPoNHkkVVRspOpeM99AuIc2jZhHe/K2ZhnAa8L5VqzayyM\nuh07ikW3fu30pYaLYxVCFPPOuvdrlLzW6+aU2DsztmQXx9q6b/V1LtqeUr6r6+vP0+vmEPS5Uao2\n4HF1cfG0MaRm8u3enECzxa9IOhUjmM0zhmGUpNLPnckpubOGgb6eJoQQFkAVwFUAXiwd/hWldMlm\nE7cC+CyAr5m0fy2A7ZTSHYSQywB8AcDl/cjqYGUhCAJ+8KsTuOuXx+HzcPjjN1yAC1U3ugMHw0A4\n4MGfvO0ifOMnz+Lnj03jE7c9gj9+wx6Qjf0tGhy8YPBViEnnD6C9nrXDYMsBuBnA1RBzXj1MCLmb\nUnpYVewYgJdRSnOSIvZ/MMB7ad/O9nOxm6JiBWPrTeeCTL2wMrOcGVkazKwP3dxozGKuZJniIS9k\nm/NybLtdvCNt7v64DP3JYFkGLNteqMrDZzUe/UC/kLWKz1Mv7uMhbwdl+zChlsNMd9q1KYFcqaah\n3R4GRmIBNJr2PRnkMfR7+2csVt+7Linnloxd0vsoGvIg4HXDzTGqWDuRTKMbZMUg3ke8ldhP+7PR\nvXzexhgWCzUkItbtD3LPuF1sXy6Nw4KVEi//tli0zqvXK/pSriilPCHkdsnqdE8f9X8p5RMxw3UA\nbpPKPkgIiRFCRimlThT7Gka90cJX7jmMhw7PIRX14cNvvsDJX+Vg2eDiWLzrNQQT6RDu+OkR/OMd\nj+HtV+9wyFLObbgppR/so95+AEcppScAgBByB4DrASjKFaX016ryDwKYHEBOQxcnq+W3ae6YLvFV\nRrdCwMRKo7F4KceM76V8yTjEevNYREywGrZeOAd8bhRqLUnGwe9XfQtWZA4r+XxQLFdmpqshQU/x\nroY6WexyMKOp4VItohmTRa3bxS6Lp8HWDZGeysvTwO1qMwn2CqtYv6ikEHEsiwu2WbM9mmEiFYLf\n60Kiy/1khm4soW4XhxET11FN8XX8TrUdgzdEDKJKHiGEbBmaJFpMADil+n4aA77IHCwvFgs13PSN\nA3jo8By2T0bxVzde6ihWDpYdDMPglZdM4k/fdhH8Xhf+9T+exW3//kxPu5cOXlD4DSHkgj7qGb1z\nJizK/z762Fg0Q9st0Hzlaydkp538s/MYILqsTaZDCJjkCGK6aWUAvNJC1Cwh51gigMt2jXaNrxjG\neseGuIYYthXJCm25lqdPn9uFsN86llntohkLLW/cs9ZytbYX5Or5fsnOEezbmbYo3b0NuzFhvcDt\nYjEaD/Rt+dEwkw5w09mpulavttV1Wa5HwSBOxhEATxBC7odIeQvY9G23Cf11WrmnoYOecGw6j5vv\nfAJLxTqu2DuGG19z3qqagB2ceyAb4/jYuy/FzXc+ifsen8Hzs0V84Hf2OgmHzz1cBuDdhBAK0XUd\nEN9L+7vUs/1+IYS8AsDvAbiiPxH7g5lCYERUod2tbpeNBDyIWOTKsbP42jYRxaGTWfgtmL9sMYt1\n2VG3B61T5J4tSVusX0YxMMuFbmyBg+KiHd3d7lstsfOQ340xA/KEYULNrLcKBoOeoJ52/a5Z1PcM\nxzLtxLVrULHs9XpoSGLWsXallj0e8mpcAOXnaj9pC6zQs3JFCPkUpfRPANwO4N+gpV8f1uPjDIAp\n1fdJ6Zgl0mnr3AdrFetRblnmnzx4Ep//7hNo8Tze89vn43eu3L6mXbLW41gD61PulZY5nQ7jU//P\ny/GF7z6B/3rkFP72tkfwZ++6BBftHOm5nfWG9SjzMuEjfdbTv3OmIFqvNJCsYv8C4LWU0q7suHav\nS7HBo1jnxTw+ujov2edGZrGCLVMxw2drsNrA8/NlAEAqGUI84oMgCDh6VtzzTCZDSNv0ImgwDLKl\nhtJWTIrNiYRzSpltm5OIxQMIBTwDLUjqYLB0agmRsB+jI2El4WcviJ4toN4QLWjpdNj2ArncFBAp\nN5V6y4lsuYE6LyodZn1t2ygmmzX7fVAZt1SbmM6UsGtzAiPLrFxFYgEsSHMonQ6bWkmHjV7GKHw6\nB0EAEvHgwGPrC9ZxJismCE4lA9i6MY5g2IdQwNNXEuflgHz/plKh3s7X5cJsXlRERmxcywbDYKHY\nvvZrCfIYvGTfJH5xQHy0J5NB8CyLGg/4h8xk2E9rVwEApfSrhJCDlNKLhyqRiLsBfBDAHYSQywEs\n2Ym3ymQK3YqsOaTT4XUndzodxszZHL75n0fws4NnEPS58L7r9mLP1iTm54vdG1glrMexBtan3Ksp\n8zteuR0TCT++8Z9H8LFbfo3XX7EZ112xxdbOmzPWK4flePlSSn/eZ9VHAOyQYoGnAbwVwA3qAoSQ\njRCTFL+TUnrUTqN2r8vSYhn5QsW0TtzvMn221hotpW42W0KzJi5u5GOLi254bO57Li1VlHoLC0U0\nqnVNW2r58vWmrTZN+1osK21ns6W+LAf5fBV1yQV4fr5gm41sfqGIfKEClmGW/d7J5cQxrbo4077S\nkque0e/DuL8jXg6uVABMq7Xs5ysIgmY+loZsETBCr2OUz1chQIDfxSDjH2xRXak1lfMNulnMzxfB\nAagUq6gUq9aVVwj5QgWRsB9LS2V4e9j7zuar7Wu5UELJKt8XgGyX59hqQi2Xen6GvC7MNJsYDQ93\n02FlSOd1IIR8E8DLAaQIIacA/E8AbgCglN5CKb2HEHItIeQogBKA96yGnA6McXahhE/e/iiOzxQw\nmQ7ig2/caxoQ6cDBSoNhGLxi3yQ2joXxxbuext0PnMCzp5bwh6/fvawsWQ5WH4SQGIA/B3AhADli\nXqCUXmVVj1LaJIR8EMCPIVKxf5lSepgQ8j7p91sAfAxAHMAXCCEA0LDhbmgPAxj71cHahvlcevAn\n0bgyqT7u2ZLEU8cX+pDOHNpYkD7b0LRnv95oPICFXBWbx3sjQOgHyYgPs4tljCdX7x3JMsyKWVGG\n4+65MhiGeGqKeMtkw2sAvV6PXu/RtXy19+1IK9dbTmge9LnhdrHYs6U/shEr9KNc+Qgh50McR/mz\nAkrpoW4NUEpvsFGmH8YnB8uMhw7P4ms/pihXm/it3aO48TXnwbvGHygOzk1s2xDFx3/vRfjKjw7j\n4JF5fPzWh/Cea3bZilFwsG7xFQCHABAAfw0xNupROxUppfcCuFd37BbV5z8A8AdDk1SFQRYlauVK\nTSbgYlk0eR7VHpJsm629loNtqxuLWa/ohc7e6+FwcR/kBf0gEvRg/3mjA5EJrFescd1qoBQIMtRk\nCcE14gZohkHus7Uc7mEHajbNTWNhbBwNLes59bNf5AfwIwA/VH1W/zl4AaJcbeLWew7ji99/Gi1e\nwO+/bhf+8PW7HcXKwZpG0OfGB9+4FzdcvQOVWguf+e4T+Oq9z6A6oEuTgzWL7ZTSvwJQopR+A2Ky\n+petskzdMaRFj5oGe9fmOAJeN0YT9imvNeQYfUvUR1/9nv86We+di4oVsPbPexhra/U5mqU4WG3I\nObLM8tuZoVuOLMsKaxzLrSz2PBMopZuXQQ4HaxhPHVvArfc+g8VCDVMjIfyPd++HzyEDdLBOwDAM\nXnXpFHZtiuNffnAI9z0+jcMns/i9a3c5SYdfeJBpoOqEkCSALIA1b6oc1mtevTMd9Ll7zq1jtoBy\nGbkbDghDF8ZBsH7WdS94pKJ+5Ev1NesWKOeMG+YC28Wya1aZ3DkVQyjiR6nQfwyYnWsZD3nBMu1E\nyecy1qaa7WBNIFeq4zs/O4oHnjoLjmVw/Uu24HW/tQnjo+szgN7BuY3JdAh/deOl+P79x3Hvgydx\n0zcO4qUXjOO/vWL7mmF1cjAwqKRUfQPArwHkYNMtcDUx6BpvLBEYSr4Wl8rFSb3wdLs47NoY74vR\nzwz+IXg9qGVcm8vacxPbJ6KrLYItDGvOXEpG1rTRhmEYBHzunpWrXpVPt4vF/l2jPdV5ocJRrhx0\noNni8Z+PnMYPfnUclVoLG0dC+L3X7cLGUWc3wsH6htvF4s1XbsMlJI2v3vsMfvnEDB4/Oo+3XLUd\nl+8eW23xHAwISuk7pY//RAh5GEAUwL+voki2MOgO+uax4RAzWFmToqHhksG4XYMrV2r33vUeE+Jg\nFTCkKWOXpdLBuYNVU64IIa8F8GmIzExfopTepPv9SgDfB3BMOvRdSunfraiQ5xh4XsCDh2dx9/3H\nMbtYQdDnwrtevRMvu2jDsmQed+BgtbBlPIK//t1L8ZOHT+Gu+4/jSz88jJ8+ehp/9KYLFVpkB+sX\nhJA4gCSA45RSWwF2Nt5J5wG4FcDFAP6SUvqpYcm7VtSC5XD/s8Ilu0aRXeg/fQfLMLaSBjtwYITl\nIGp5IcEZnf6xWlTsHICbAVwNMXnjw4SQuymlh3VFf0EpvW7FBTzH0OJ5PPzMHH7wwAnMLJTBsQyu\n2jeBN7x0q+Mu5eAFCxfH4prLN+FFu0bwnZ8/h4cOz+HPb74f+3amcd0Vmx1L7ToCIeTrAP6BUvoY\nISQB4AmILoFpQshfUkr/pUt9O++kBQAfAvCGoZ/AGlnFqDfRPH3kneoVIb8blQFcDR29ysEgWKsx\nUmsFLd65wfrFalmu9gM4Sik9AQCEkDsAXA9Ar1w5M38ZUSjXcd/j0/ivA2ewWKiBZRi89IJx/PaL\nNyMds88w5cDBekYq6scfXb8HV1+aw533HcOBZzM48GwGF+9I4bdfvBlbViAXjoOBsY9S+pj0+V0A\nDlFKX00ImYTIYmupXMHGO4lSmgGQIYS8btjCr8UXnWcFkr8OCqGXJF4OHOiwVgk31goEaffC5Xgu\n9YzVUq4mAJxSfT8N4DJdGQHAiwkhj0PcSfxTOzm0HFiD5wUcOpHFA0+dxYFnM2g0eXjdHK7aN4FX\n79+IEUepcnCOYvtEFH//oZfi5w+dxPcfOI6DR+Zx8Mg8tk1E8Mp9k7j0vBHHt37tQh2p/RIAdwEA\npfQ0IYS3Ud/OO2nZEA6IrqijayAZ++7NiXUTvyTn8to44liZHfQOxy3QGvGwF1PpEFJRZ13YK1ZL\nubKz3XQAwBSltEwIuQbiy3KnVYV0en0+YJdb7hYv4JkTWfzqyWnc/9g0snlxHbIhFcS1V2zB1S/a\n2HPyO2esVxbrUe71KDMAvOKyzbhy/yY8fiSD7993DI8+M4vnzhzCt352FC+9cAIv3zcJsim+phag\n63WshwiBEDIBkXr9SgAfV/1mZ2WwLCaQXq7LhvHomlDeVya1rqq/AebuS4NenJotYufGGLg1MHbL\nBef+7o5exigSzil1EhHfcom05tDPPBoZcTw3+sFqKVdnAEypvk9B3ClUQCktqD7fSwj5PCEkQSnN\nmjW6HunB0+nloTWv1Vs4dDKLJ55bwGNH5pEr1QGISe6uvHgCV+wZw9YNETAMg3KxinLRPkXncsm8\n3HDkXjmsR5kBrdwTcT/++PrdmHvZFvzs4Bk88ORZ/PCB4/jhA8eRivpw4fYU9m5N4ryNsVV1oVrP\nYz1EfBLAQQANAPdTSp8GAELIbwE4aaN+13dSP1iP12UlMYy5mwq5kc2WhiTR2sN6vb9XEr2OEd9o\nolhtoFyoolVrLKNkawfOPOqOYb6TVku5egTADkLIZgDTAN4K4AZ1AULIKIA5SqlACNkPgLFSrM51\n8IKA03NFPH0ii0PHs6CnltBsiZuxIb8bL7twHJeQEezaFF8Tu6MOHKwXjMQDeOtVO/Cml2/D4ZOL\nePDQLA48m8FPHz2Nnz56Gm4Xi63jEeyYimL7RAxbN0QcIpgVBqX024SQ+wGMAXhM9dNJAH9oo4mu\n7yQV1o7J0oEDBz1j1+Y4anUe3iHkWnPgwAirolxRSpuEkA8C+DFE2tsvU0oPE0LeJ/1+C4A3A3g/\nIaQJoAzgbash61qFIAiYXazgmZOLOHxyEfT5ReTL7R2YqZEQLtiWxIXbUti6IeKw4jhwMCBcHIu9\nW5PYuzWJZovH0dM5PHlsAU8ey+LZU0ugp5YgG0mSES82joYxNRLChlQQE6kgRhMBZ2NjGUEpnQEw\nozs2bbNu13cSIWQMwMMAIgB4QshHAJxPKe2fS9yBAwcrDo5lEfA5z2IHywdGeOFwmQrr0eRp11TL\nCwKmMyU8e3pJWcjlinXl91jIg/M3J7B7cwLnb44PPeFjPzKvNThyrxzWo8xA/3KXqw08N53HkdNL\nOHG2gOdni8iX6poyHMsgFfNjPBHAWDKAsYT4N5oIIBJw9x3DtY7H+oW+47Mu30krifU6d1cSzhh1\nhzNG3eGMUXcM8520akmEHVijWm/i+HQeR6fzOHo6h6NncqjU2rkwo0EP9u8awXkb4zhvUxyjcf+a\nCrB34OBcQsDnVqxaMpaKNZzOFDGdKeHMfAnTCyWcXSjjsWwZOKqt7/e6MJbwYzQRwFhcVL5G46Ly\n5biuOHDgwIEDB+sHjnK1BsDzAmYWSjg2ncexmTyOT+dxKlPUJEhuZhhDAAAMEElEQVQcifuxb2cK\nOyZjIFMxjDjKlAMHaxqxkBexkBd7tiQ1xwvlOmYWypjNlnF2sYyzC2XMLlZwaq6I4zOdO4vxsLdt\n5YqLCthoIoBU1Oe4GTpw4MCBAwdrDI5ytcJo8TxmFsp4fraAk2eLOLNQwnOnc6g1WkoZt4vFtoko\ntk9EsW1DFNsnIsvq5ufAgYOVQzjgQTjgwc6pmOY4zwuYz1dFpWuhjLPZ9t9hKbZSDYYBkhEfJkfD\niAbcSEV9SMf8SEZ9SEZ8iAQ9TpJMBw4cOHDgYIWxasoVIeS1AD4NMXj4S5TSmwzKfAbANRAJLd5N\nKT24slIOjmKlgV89OYNTmSJOZ0qYni+h0WzntGQZMd/UprEwto5HsHVDFBPpoLMj7cDBOQaWZTAS\n82Mk5te4FwJiaoXZRdHCNZsVrV5zSxXMLVbw2LMZw/ZcHINYyItE2ItYWLSiRUMexIJeRIIehANu\nSdFzO88bnDvvJAcOHDhwsLxYFeWKEMIBuBnA1RDzizxMCLmbUnpYVeZaANsppTsIIZcB+AKAy1dD\n3kFw74Mnce9vngcgso1tSAWwcTSMTaNhbBwNYd/54yjkK6sspQMHDtYyvB4OG0fD2DjamYcjFPHj\nmecymF+qIpOrYCFXRTZfxUK+imyhhiOnc10z5Po8HEJ+N4I+NwI+F4I+FwI+F/xe1Z/HBb+Xg8/j\ngs/DSX8u+LwcvG5uXSto59I7yYEDBw4cLC9Wy3K1H8BRSukJACCE3AHgegCHVWWuA3AbAFBKHySE\nxAgho5TS2ZUWdhC8dv9GbN8QleIk/OBY7QLE53XB4W9x4MBBv/B7XZhMhzCZDhn+3uJ55Ip1LBXr\nyJVqyBXryJfqKJQbyJfrKJTrKFWbKFYamMmWUG/whu10g4tjEQ648f7r92D7ZHSQU1oNnDPvJAcO\nHDhwsLxYLeVqAsAp1ffTAC6zUWYSwLp6kYUDHly8M73aYjhw4OAcBceySER8SER8tso3mjzKtSbK\n1QYqtRYqtabyV623UKmL/6v1Fmrqz40WBEGA27UuLVjnzDvJgQMHDhwsL1ZLubKbXEsfjW1Vj0mn\nO11m1gPWo9zrUWbAkXslsR5lBtan3OtR5jUG5520SnDGqDucMeoOZ4y6wxmjlcNqbTGewf9t795j\n5SjrMI5/SSlRbiISufVoK5ZHQAstCBWVFIIB0RYSiFbuSLShcpFEEPDyh7dIAgFRIFwEBE1BgUBN\nylW8BgI2tIVI+0gthBbkqhUE/qha/3jfLdvtOd13y+7M7jm/T9J0Z84059lfZ96Zd+adGRhqmh4i\nnQXc2DIT8rwQQgihm2KfFEIIoSvq6lwtBCZLmihpC+DzwPyWZeYDJwJImg6sjrHtIYQQeiD2SSGE\nELqils6V7f8ApwP3AE8At9heKmmOpDl5mQXACknLgauAuXVkDSGEMLrFPimEEEK3bLZ2belQ8xBC\nCCGEEEIIIxnIxzqFEEIIIYQQQr+JzlUIIYQQQgghdEF0rkIIIYQQQgihC+p6z9Umk3Q4cCkwDrjW\n9oXDLHMZ8GngDeBk24uqTbmhdrklfQi4HpgKfMP2xdWnXF9B5uOAc0nvfnkNOM32Y5UHbVGQ+0jg\nO8D/8p9zbD9QedD1M7Vdr/NyHwUeAj5n+/YKIw6roNYzgDuBFXnWbba/V2nIFoVtyAzgEmA88LLt\nGVVmHE5Brb8GHJcnNwf2AHawvbrSoC0Kcu8A/BzYiZT7Its3VJ2zm0q359FM0hBwI/Be0vvArrZ9\nmaTtgVuA9wNPk9qy1fnfnA98EfgvcKbte+vIXjVJ40hPrFxle2bUaH2StgOuBfYirUunAE8SNVon\nf+fjScc0j5NqtBVjuEaSrgM+A7xo+yN5XsfblqR9gRuAdwALbJ/V7ncP1JWr3AD9BDgc2BP4gqQ9\nWpY5Avig7cnAl4ErKw/aoiQ38ApwBnBRxfGGVZh5BXCQ7SnAd4Grq025ocLc99ve2/ZU4GRqzl2Y\nubHchcDdbPgy08qV5gZ+b3tq/lN3x6qkDdkOuByYafvDwDGVB21Rktv2RY06A+cDv+uDjlXJOnI6\nsMj2PsAM4GJJA3fir6GD7WK0WwOcbXsvYDrwlVyH84D7bO8O/CZPI2lP0iPw9yTV7gpJA3WM8jac\nRXpKZeMJY1Gj9f2IdFC7BzAFWEbUaB1JE4EvAdNyJ2IcMJuo0fWk79esk5o0jrOuBE7N/YrJ+eTZ\nRg1aMfcHltt+2vYa4GbgyJZlZgE/A7D9MLCdpB2rjbmBtrltv2R7IWmH1A9KMj9k+1958mHSSzXr\nVpL79abJrYGXK8w3nJL1GlLn+1bgpSrDbURp7to7gk1KMh9LusK2CsB23esHlNe64VhgXiXJNq4k\n99+BbfPnbYFX8qPRB1Wn/1ejku3nbS/On/8NLAV2pWkfnf8+Kn8+Ephne43tp4HlpFqOapImAEeQ\nrsw02sqoUSbpXcAnbV8H6bUJ+bgjavSWV0nHjlvmE1NbAs8xxmtk+4/AP1tmd1KTAyTtDGxj+5G8\n3I1N/2ZEg9a52hVY2TS9Ks9rt0zdB/0luftNp5lPBRb0NFGZotySjpK0FLgLOLOibCNpm1nSrqSN\nv3Elth/eoVBS67XAgZKWSFqQzw7VqSTzZGB7Sb+VtFDSCZWlG1nx9ihpS+Aw4LYKcrVTkvsaYC9J\nzwFLSGfxB9kgtvc9lc+sTyWdhNux6eXLLwCNk5+7kGrVMFbqdglwDmk4V0PU6C2TgJckXS/pUUnX\nSNqKqNE6tv8BXAw8Q+pUrbZ9H1Gj4XRak9b5z1JQq0HrXJUeULaeKa/7QLTu378pijNLOpg0TvXr\nvYtTrCi37TvyEIOZwE29jdRWSeZLgfNsryWt3/1wNagk96PAkO29gR8Dd/Q2UlslmccD00hnkw8D\nviVpck9TtddJGzIT+FPdQwKzktwXAItt7wLsA1wuaZvexuqpQWzve0bS1qSO/lm2X2v+WW7PNlav\nUV1LSZ8l3Q+yiBHa9LFeI9J9mNOAK2xPA14nD+VqGOs1krQb8FVgIqkzsLWk45uXGes1Gk5BTTbZ\noHWungWGmqaHWL9HOdwyE/K8OpXk7jdFmSVNIZ15nmW79fJrHTqqdb5svLmk9/Q62EaUZN4XuFnS\nU8DRpPHAsyrKN5K2uW2/ZvuN/PkuYHy+obQuJbVeCdxr+03brwB/APauKN9IOlmvZ9MfQwKhLPeB\nwK8AbP8NeApQJel6YxDb+56QNJ7UsbrJduPEyguSdso/3xl4Mc/vx313rx0IzMrt+jzgEEk3ETVq\ntor0oI8/5+lbSZ2t56NG6+wHPGi7MaT6duBjRI2G08m2tSrPn9Ayv22tBq1ztZB0M9lESVuQbj6b\n37LMfOBEAEnTSZdHX6BeJbkb+uGKBBRklvQ+0kZ8vO3lNWQcTknu3Ro3KkqaBpAPouvSNrPtD9ie\nZHsSaedymu2R1qGqlNR6x6Za7w9slocw1KVkW7wT+ISkcXmI3QGkm83rVNSG5PsTDiJ9h35QknsZ\ncCik9YXUsVrB4OqkvR+18nb/U+AJ25c2/Wg+cFL+fBJvXc2eD8yWtIWkSaThuY8witm+wPZQbtdn\nAw/YPoGo0Tq2nwdWSto9zzoU+Avwa6JGDcuA6ZLembe7Q0n7rKjRhjratvL696qkA3JtT6BgBM5A\nda5yj/x04B7SinOL7aWS5kiak5dZAKyQtBy4CphbW+CsJLeknSStBM4GvinpmTycom8zA98G3g1c\nKWmRpNo3zsLcRwOPS1pEegrR7HrSJoWZ+05h7mNItV5MGtrY97W2vYz0RMbHSPeIXGO71s5VB+vI\nUcA9tt+sI2erwtw/APaTtAS4Hzi35g742zLSd643VS0+Tno09MF5/7BI6SlbPwQ+JemvwCF5mryN\n/ZJUs7uAuXnYzljS+L5Ro/WdAfwitxFTgO8TNVrH9hLSgxYWkvZbkJ6CPKZrJGke8GD6qJWSTmHT\najKX9MCZJ0kPK7q73e/ebO3aUVfPEEIIIYQQQqjcQF25CiGEEEIIIYR+FZ2rEEIIIYQQQuiC6FyF\nEEIIIYQQQhdE5yqEEEIIIYQQuiA6VyGEEEIIIYTQBdG5CiGEEEIIIYQuiM5VCCGEEEIIIXTB/wEF\nTU05D4ta/gAAAABJRU5ErkJggg==\n", "text/plain": "<matplotlib.figure.Figure at 0x7f4d0ca6ea50>"}, "metadata": {}}], "metadata": {"collapsed": false, "trusted": false}}, {"source": "We now plot the robust model along with the previous models.", "cell_type": "markdown", "metadata": {}}, {"execution_count": 18, "cell_type": "code", "source": "alpha = trace['alpha'].mean()\nbeta = trace['beta'].mean()", "outputs": [], "metadata": {"collapsed": true, "trusted": false}}, {"execution_count": 19, "cell_type": "code", "source": "fig, ax = plt.subplots()\n\nax.scatter(x, y);\nax.plot(xs, ols_result.predict(XS), label='OLS Model (full)');\nax.plot(xs, no_outlier_result.predict(XS), label='OLS Model (without outlier)');\nax.plot(xs, alpha + beta * xs, label='Robust model');\n\nax.set_xlim(X_MIN, X_MAX);\n\nax.legend(loc='upper left');", "outputs": [{"output_type": "display_data", "data": {"image/png": 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ssz/iYx/7J1RVxeNx8+yzz1NXZ+XLX/53fv7zFy9aMWq/Vvnb394gOTmVp556GtD6+ZpM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\nit/xcyAiIpm1oYL3O989yskLT7Lz/c9Tu6+PTc1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"text/plain": "<matplotlib.figure.Figure at 0x7f4d0cb49cd0>"}, "metadata": {}}], "metadata": {"collapsed": false, "trusted": false}}, {"source": "We see right away that, although the robust model has not completely capture the linear relationship between the non-outlier points, it is much less biased by the outlier than the OLS model on the full data set. Below we compare the MSE of this model to the previous models.", "cell_type": "markdown", "metadata": {"collapsed": true}}, {"execution_count": 20, "cell_type": "code", "source": "robust_mse = pd.Series([mse(y, alpha + beta * x), mse(y_no_outlier, alpha + beta * x_no_outlier)], index=mse_df.columns)\nrobust_mse.name = 'Robust model'\nmse_df = mse_df.append(robust_mse)", "outputs": [], "metadata": {"collapsed": false, "trusted": false}}, {"execution_count": 21, "cell_type": "code", "source": "mse_df", "outputs": [{"execution_count": 21, "output_type": "execute_result", "data": {"text/plain": " Full data set Data set without outlier\nFull model 1.250563 0.325152\nNo outlier mdoel 1.637640 0.000008\nRobust model 1.432198 0.032294", "text/html": "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n<table border=\"1\" class=\"dataframe\">\n <thead>\n <tr style=\"text-align: right;\">\n <th></th>\n <th>Full data set</th>\n <th>Data set without outlier</th>\n </tr>\n </thead>\n <tbody>\n <tr>\n <th>Full model</th>\n <td> 1.250563</td>\n <td> 0.325152</td>\n </tr>\n <tr>\n <th>No outlier mdoel</th>\n <td> 1.637640</td>\n <td> 0.000008</td>\n </tr>\n <tr>\n <th>Robust model</th>\n <td> 1.432198</td>\n <td> 0.032294</td>\n </tr>\n </tbody>\n</table>\n</div>"}, "metadata": {}}], "metadata": {"collapsed": false, "trusted": false}}, {"source": "On the data set without the outlier, the robust model has a significantly larger MSE than the no outlier model, but, importantly, its MSE is an order of magnitude smaller than that of the full model.", "cell_type": "markdown", "metadata": {"collapsed": true}}, {"execution_count": null, "cell_type": "code", "source": "", "outputs": [], "metadata": {"collapsed": true, "trusted": false}}], "nbformat": 4, "metadata": {"kernelspec": {"display_name": "Python 2", "name": "python2", "language": "python"}, "language_info": {"mimetype": "text/x-python", "nbconvert_exporter": "python", "version": "2.7.6", "name": "python", "file_extension": ".py", "pygments_lexer": "ipython2", "codemirror_mode": {"version": 2, "name": "ipython"}}}}
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