{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### A Simple Bayesian analysis of X-ray spectrum in Sherpa" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First import Sherpa " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from sherpa.astro.ui import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are only working with spectra, so imaging with ds9 will not be shown. We will use \"matplotlib\" for visualization. \n", "\n", "Set Poisson likelihood statistics called \"cash\"in Sherpa and select an optimization method for the initial fit - simplex method which uses nelder-mead algorithm." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "set_stat('cash')\n", "set_method('neldermead')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next load the data, filter and setup a simple absorbed power law model. Note that the calibration files, ARF and RMF, which are needed for the X-ray analysis and a background fileare read and when the file \"acis.pi\" is loaded into the session. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "read ARF file acis.arf\n", "read RMF file acis.rmf\n", "read background file acis_bg.pi\n" ] } ], "source": [ "load_data(\"acis.pi\")\n", "ignore(\":0.5,7.0:\")\n", "set_model(xsphabs.abs1*xspowerlaw.p1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Run the initial fit using simplex and cash. This returns the best fit model parameters, absorption column, power law photon index and normalization." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WARNING: data set 1 has associated backgrounds, but they have not been subtracted, nor have background models been set\n", "Dataset = 1\n", "Method = neldermead\n", "Statistic = cash\n", "Initial fit statistic = 3.15508e+07\n", "Final fit statistic = -89797.1 at function evaluation 540\n", "Data points = 444\n", "Degrees of freedom = 441\n", "Change in statistic = 3.16406e+07\n", " abs1.nH 0.0716477 \n", " p1.PhoIndex 1.17604 \n", " p1.norm 0.000533859 \n" ] } ], "source": [ "fit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next get the covariance matrix with covar(). The matrix is later used in the MCMC run." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WARNING: data set 1 has associated backgrounds, but they have not been subtracted, nor have background models been set\n", "Dataset = 1\n", "Confidence Method = covariance\n", "Iterative Fit Method = None\n", "Fitting Method = neldermead\n", "Statistic = cash\n", "covariance 1-sigma (68.2689%) bounds:\n", " Param Best-Fit Lower Bound Upper Bound\n", " ----- -------- ----------- -----------\n", " abs1.nH 0.0716477 -0.00811361 0.00811361\n", " p1.PhoIndex 1.17604 -0.0242164 0.0242164\n", " p1.norm 0.000533859 -1.37268e-05 1.37268e-05\n" ] } ], "source": [ "covar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the model and the data. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WARNING: The displayed errorbars have been supplied with the data or calculated using chi2xspecvar; the errors are not used in fits with cash\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_fit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are a few samplers in Sherpa that can be used to explore the parameter space. The standard \"metropolismh\" runs MCMC with Metropolis-Metropolis-Hastings criterium for accepting parameters." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['metropolismh', 'mh', 'pragbayes', 'fullbayes']" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "list_samplers()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Select MetropolisMH and check the options:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'log': False,\n", " 'inv': False,\n", " 'defaultprior': True,\n", " 'priorshape': False,\n", " 'priors': (),\n", " 'originalscale': True,\n", " 'scale': 1,\n", " 'sigma_m': False,\n", " 'p_M': 0.5}" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "set_sampler(\"MetropolisMH\")\n", "get_sampler()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we list several options for running the MCMC sampler: \n", "\n", "defaultprior – indicates that all parameters have the default flat prior\n", "\n", "inv – indicates which parameters on the inverse scale.\n", "\n", "log – indicates which parameters are on the logarithm scale (natural log).\n", "\n", "originalscale – shows that the parameters are on the original scale.\n", "\n", "p_M – the proportion of jumps generated by the MCMC jumping rule.\n", "\n", "priorshape – indicates which parameters have user-defined prior functions.\n", "\n", "scale – A scalar multiple of the output of covar() used in the scale of the t-distribution\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We first run the MCMC with the default settings:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WARNING: data set 1 has associated backgrounds, but they have not been subtracted, nor have background models been set\n", "Using Priors:\n", "abs1.nH: \n", "p1.PhoIndex: \n", "p1.norm: \n" ] } ], "source": [ "stats, accept, params = get_draws(niter=1e4)\n", "# check the parameters at the minimum statistic value based on the sampler:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[7.16476507e-02 1.17603887e+00 5.33858688e-04]\n" ] }, { "data": { "text/plain": [ "[0.008107642152592251, 0.024272855895549304, 1.3822923361501428e-05]" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bestfit = params[::,stats.argmin()].T\n", "# print bestfit values and standard deviations\n", "print(bestfit)\n", "[params[i].std() for i in [0,1,2]]" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# visualization of the MCMC run - Cash at each iteration\n", "plot_trace(stats)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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cewKuCrtO8QgbWHzxWIZmB2PCOWVsbkqrhvbE1klXheZmEhUORVHaZfmqiphQOHmrvLbdiRDaz2hOlK+RaBUC50JaV5fX8mH1yYTvffX0ccyelM+gUNC1fXNlPaGsAOGwe2VkjyMYtH47XSwVh05SfeIsYGWez52cn3BFZa8a/MqXJPvMuio0N5MEenoAiqL0ft7yFPKzuaq0MG6bPeE/uHontzy+IbZK8Hu6L9tfz8Nr9wCW3f/7V06NCUSic2xmT8onPyeb0y1h1/a7F5Sw+OKxXFI0whXWavfRsDHAyJwQX5w2NvaeO2sbmTo2l7+YNpZnvzOf7y4ocZ3T5HmvTZX1sXt0Yq8a3tt9LM4/k+iztPGO0/u6N6ArDkUZoNg9JOwOdsm4qrTQteLIHRTklnmTfJ+c/Sb8VFcUzuKAjWdaY0/7weC5FYEtRI1nWl1jumD0UL59RQk3zyuOHTO1MNdlIrt7QQkr3tsX69tR29BM7Y7DlIwa6smlOElZ5XG+OWciD1w/I+ZvqKo7HbfyOtsa4QcvbOOdHy2KbfOuGryfZTLSjUDrCVQ4FGUA4uwhYf9OJh62QKRip/cTCT+/h7c3xkNrdnHvly7kd+sr+WN5ravqbDhaS8opNl6GDsqKiYZ9TFZAQIS28DlxWlxayA9e2EZlXVPs3BXv7aNk9DDX9Y43WcK0YMqouM/h1W0HOdzQHBO2yrombntiI09HW8p6czf8ypcko7eH5qpwKMoA5J1dR5O+9mPpNdNSmvQSOce9kUT5OdkERDDGEDGWI9ibXW4TNsQ5r71sP3iSv3/lY4zjGCsM18R1BLxrwfmuTO2Igb1HTvm+t21qssdmfw4X/v2qc5FawKbK47G/+8KqoTOocCjKAGThhaNjKw37dbokCxltL9y0bH89979R7sqNSEYwAAdPnGH6+BGIRONiPYSNNaZQVoCsgBWuG4yuOMJhy8n96zW72LivjqfvmEdV3WkeXbfPFTnVHk5H9fySApf/Yu7kka5jnasGv1IlmsehKEqfwjZLperjAPfk5/QHvLf7GFV1p8kdEkrafc+J7QdJZbIOBiASgec2VZGdFSAnO0hjNCQYiOVumOhPOBzhxrnFjM8bQuOZVtZUHOZAfRPNbYaWsGHd7mMs/OVaHvzmTBqb21i5sSo2DgEGhQJcVVrItgMnyBsSYpsjYqtg6Lks9afvmMdtT2xkU+Vx5k4eGTNT+X1u3ix0Z9/zTPXMyCQqHIoyQEmn4ZB38ps61l0JdsV7lsPYzn8YFHJPiGX763n03b0cbjjLDZcVu/wggYC4MrtDQfdru1WGMVYWd7On4951M8eTMyiLF8uqY6G1X5tVxM7aRn75x52+91NZ18RNj23gCxeOJpQVoC1stZL9i4vGcLejhtbDa/fwYfXJmLC88VENt14+Obb/qunjMNHfifAGC6RS36q3kzHhEJEngWuBI8aY6T77bwF+HH15CvhrY8yHIjIReBooBCLACmPMr6Pn3Ad8B7ANsj8xxqzK1D0oSl8nUUkNPzNJOgl6Y4cPBs49iRvjTpZzhs++vLWa5zZXxQTgw+qPeeD6GS4/yM7axqSRSzYiuPwbIsQm8q/PKnKN/9tPbUr62bS0RViz4zDBgJWJHokY3tt9lLu/cH7smPklBQSiZi+ASMTEJvpUE/VsXw4YQlkBrp4+js2VxzPeMyOTZHLF8RTwGywR8ONT4AvGmHoRuRpYAcwD2oAfGGO2ikguUCYibxtjdkTP+5/GmF9lcNyK0i9or6SG00ySboLed79wPgunjuHN7TWUjhvOU+srY7WdBKvgX35Odqx3htck9fzmKl773hWxCdjrK9lR08Cf99bFigqCVUjwrs+XuPwSArGJ3P5ZvqqCWx7bwFmfyCsvBntF43agO+9dHHVMsoISm+gTJep5Oxze94dy2qL+lmXXlnLzvOK4fhx9jYwJhzFmnYhMTrL/z46XG4Ci6PYaoCb6d6OIVAATgB1xF1EUJSGJEuj8zCQb9tXFJviW1ggvba3m5a3VGODr0TLk3kgpe8J7c3sNV5UW8sZHNTGH9O2XT+b5zVWcbfWfvMcOH0zZ/noeeXcvb0fLhby3+xhP/uenTB8/PC5pDqzeG7UNZ+NEyJ6gl6+q4JmN+2lsDsedm4xgAAKB+Axy+zOMRMVLgG/MmRi7b79ugt7S6wumjI6FDocjhvJD1iqtveCBriJTNa96i4/jDuBN78ao8FwKbHRs/p6I3AZswVqZ1HvPi557F3AXQHFx/wqFU5RUSFRs0G+bM9kuAjy/+UDMPPPilgM8e9flrsnO9lk4a0TZtZ0ixvDYe/tc5dCDAcsUZLB8GAunjuGWxzfECcueI6fYkyAstiVsXJFgAIOyArFVRiLzlpe8nJCrr8cNlxXzNYeZ63frK7njt5v5zIQRFI3MISsYcPlObPzKpd/w6PrYKqmlLcLhhrOu9+7OtnmZrHnV48IhIouwhOMKz/ZhwEvAvcaYhujmfwd+jvX5/xx4EPi233WNMSuwzF/MmTOn/7c5VBQPifIpvNvK9tfz+Pufus51hsm2ho3LfGObtbyTfkx4fP63zSrO48KxubEVjL0a6ixnWyOs3FjVbhkPJ22e9920r47S8SPYsK+Ox9bt5cQZK2LLXvVkB4Ub5xb7NoByhtw+vHaP63MLiHDDZcVU1GynNWwIBYWvO4Qn02Sy5lWPCoeIfAZ4HLjaGFPn2B7CEo1njDEv29uNMYcdxzwGvNGNw1WUPoefScS7bfmbFS5fQjDa7MKeBEMOuz4QM2ulw+bKerZU1jMoFODrs4qYX1JgrULChoDAuBGDOXjibPsX8mCAf3htOxeOGea7PyjWCso4qt2e8tSb2n30dFw/dCfhiGF83pB2TUvzSwoYFArQ0mpFit1/3fQe9Wf4mdK6ih4TDhEpBl4GbjXG7HJsF+AJoMIY8z8854yL+kAArge2d9d4FaUvk8jWvXxVBZsrz1l7Baspkf20HQDu++p0Zk/Kj+UsTMwb0iGTi+FcXaeZE/NiIbcRA/csmsLv1ldSUduY9nXDEZPwvIiBm+YVMyFvSLtVdBORauRTqhnz3UUms9czGY77LLAQGCUi1cDPgBCAMeYRYBlQAPybpRW0RZuifw64FfhYRLZFL2eH3f5CRGZi/RusBL6bqfErSn8hma3ba+IJBnA5piPA9kMnue2JjbHtu4+e7tR4KuuaXHWiwJrcLp2U3yHhSIYBpo8fARBXRbc9Rg/L5vbPnZfWSiEVkejOJk2ZqnmVyaiqm9rZfydwp8/29yGukZe979auGZ2iDByS2bq9VW/93A6Cuw5TJhCg/OBJgkLSHuMdue7anUdikVt+BABx5GrY2x65dU6XrxT6QpOmVNB+HIrSx1i+qoKFv1zL8lUVKR3v19+hbH898/95DY+9t4+cUOJpIBiA0vEjKBw+uFNjbo91u4/xYfVJwgaSDCdlAmJNboNCAY40JPad3DKvmJvmFWM8ta9EzhVVTITdS8TbiyMZfiLeF+nxqCpFUVLHGXaaSjc58A8b/fq/n0ujakrg6B6UFeBnXynlvte3u0qAeMkJBRJew2bu5HwqahpSyrFoz+9elDc41oUPICvgXikV5Q2mYNggxgwfzN1fOJ+3k/g2xucNIT8n252NTvt+DVfp9mCA/zK7KJbvkoxMOqy7ExUORelDeH0S3tatl/3T2xw91cLoYdls/uni2HZv2KgXZ39tmwUXjuaf3ih3lQ73oz3RAFhyaRFLLiVp9FIqTBk9lIMn3SsIr3mt+sTZqLCcZNHUMTQ2t+GHYEVCbdhXF7t/Aa6YMop7v3RhSkUa7V4iz26s4uWt1e0WLOwv5dZVOBSlD+H1STi7ydmiAXD0VAvn//f/y+jcQSyZOSEmLosffIc9Ps7t/JwQp1rCtLZFIGrmSeYXSJc3t9fwSU1D0mMuGDOMYdlBVzVaL+k65p/fXMX2g/7Xu27m+NgkPyh0LimyPdGAc8mVdrZ9onIlfvT2Jk2pIF7bXn9kzpw5ZsuWLT09DEXpEpavquCt8lqKR+ZgIPbkOnnp/014zt0LSnjjo0MuE48TwcrX+MaciRgsJ25PkRWw8i66wkmeNyTEiTOtrm1Bge98vsS1UutIf4yy/fW8vLWa32+xsuxDfbREejJEpCwa7epCVxyK0otIZQJbes00iguGxvXD8Nr6nfx2faWrFasXg5Uhvv3gyWjl23iSRTxlByV2jc7SBQnlMbyiAfDzJTO65InfDr39mqcq70BAhUNRegntVah14o3GWfHePr+meDGSiYaNgagTOf0kufb8IB1BgBGeulKpnOMdiQDnjx7K0EFZ3HBZMVV1p1n4y7Wx/t/pfO5+9FSCX0+i4biK0ktIVM3WD280TiTaDyMAXFI0gqx2/mcX5Q3mgetnWOVFUiQD2pAUA4xLMwzYb4gG+PYVJbz2vStivT4q65p4ZN0+lq+qSOtzVyxUOBSllzC/pICsYAABgsHk4aBVdacZmROiKG8wdy8oYXAoYOUuBKzCes9/97P86MtTfQUkJxTg2s+MZ9OndYikoRw9wCe1jQQ6METnKQGB+qYWyvbX89yWA67j3iqvjTm6g5J6eZGBjpqqFKU3YdubfOxOtv9j9+HGWHnx402tvPHRIdrChoixSpr/5JWPWTBlFE/fMY+N++riels0tUZSLkGeKfxMSn4YfD+KdgmIJb52OXS7qZS3ou9VpYWuGlP5Odls2FfHztrGlHqnD1RUOBSlB/Bzgm/YZ3W8s7rS+Zcyb2mLxE2kfpFS63Yf497nPuDpO+ax+MF3Ol1fqqtpTwvsJLzWtvjuge2dFxDLAW5Xpc3PyebN7TWuir55OSFunDPRFVl18MQZfv2n3bSFIwl7pysWKhyK0s0kcsYmarwE8Mi7exN200vEW+W1lO2v5+0fLGT6srfiyon3Zi4YPZTl/+USXtpazXObqnx7fPhhsHwx7+w8wtTCXOaXFJwTXCzbfHYowBPfuixOlL0tbpPlZnQkfLc/ocKhKN2MnzPWjszxK8u9cmNVh5LxzrZG+MYjfyZvSKhPiQZYiX6/XrOLv/3Shby+7SCn0mwHu3rHYf5j5xFumDMx9lkHxCoZ703ws78PZx9zW2ScAm5XtbV7rHc0Cqs/oMKhKN2Mc2UhAqvLa8nPyebmecW+oZ2dKYQXMZYfpC/y/p5jvr3HnYwYksVnivLYur8+rmx6W9hwpLGZrKD1WQcDwsSROXHXcH4fwYCVBFk6fkTMx/F2eS3feXoLx09bWfnOWlOpZov3N1Q4FKWbsVcWj7y7l7d3HObD6pN8WP0xVXWWH+KFLQdiT7PfnDMxrjCen2M5FBBaU7Xn9BFSuZ2TZ9pcn40XATAmlpy4MkFNqa/PKoq1tXV1R0zQyzwg7mKIA810pcKhKB2kow15Vm6s4vnNVRw47m5mFDdBtYR5ZN0+AgKDswK0RSJMyMuhuS1MbUOz69D+JhpdxYHjTXHJic2t51YJXn+Ttyd4ol7md32+hNwhoZgZqzMJhKnQnc2fUkGFQ1E6gPNJNJWGPPYTaeOZ1rRDYSMGzkbrcOw/3sTMohFxwtFfSDVMN1USdRScX1LAyo1V/K8/7YoFHTgFxcZbVHJC3mDuWTTF9V0/vHaPr8+qq+iNzZ9UOBSF9KJkyvbXs+I99+Tv7Krnd7z9RNoV7Dl6iiUzx7PtwAnyhoSSVpPta6QjGtlBSanUife44UOyeLu8Nk7ADbD7cCMPr90T+3dgh+u+VV4bK1HiJVk0XFeQrINjT6HCoQx40q1VtGFfXZz9PVlDHmcUVVfkaZ9qDrNqey3Pfmc+P37xwy64Yt8k1fpY18wYx+sfHop9ZyfPtPFoglXf6x9aiZXOfwdLr5mWtFlWomi4rqI3Nn/KWMkREXlSRI6IyPYE+28RkY+iP38WkUsc+64SkZ0iskdEljq2jxSRt0Vkd/R3//dCKRnHLzw2WVvQ+SUFDA4FYslmdy8oSfoE2Bit0GonlN29oIQLxgzr1Jhb2iK8vLXa6nGqxFgwZRTZjgJcY3KzmXteATMmjHAdl0hyjKFDNatmT8rnnkUXZMQxfvO8Yh64fgafnzKKB67vmsq+nSVj/ThEZAFwCnjaGDPdZ/9ngQpjTL2IXA3cZ4yZJyJBYBewGKgGNgM3GWN2iMgvgOPGmOVRQck3xvy4vbFoPw4lGfaKwzY1LLu2lPvfKE+6AknFtFW2v55H393LakcOxpTRQzl6uoWFF462SoV4rFfp2PgFy+aeqMfGQGJIKMiXS8fy0I2XUra/nu8/v439juCDJTPHx8q0gNXz484rSlgffWjIzgpweUkBT62vtMJy02gH259J1I8jo42cRGQy8IafcHiOywe2G2MmiMjlWCLy5ei+/w5gjPkXEdkJLDTG1IjIOOAdY8zU9sahwqEkwm6KNHNiHlPG5sZaiT64emfSpLH2sMUonWxvAfKHhjh+2j/vYvSwbMbnDUnYP3ugIcCcyVZklG2GGj44i5a2SCyYwOaSohFW8cfNVbFe5H7fp7M5U1vExD04DLSw297eyOkO4M3o3xMAZwnLamBe9O+xxpgagKh4jEl0QRG5C7gLoLi455d2Su/DGRlVWdfEkpnjAcjPySY7KxAzX72/+xibK4+nHGZZtr+eh9bsctVGSgUDCUUDrHaw/23xVD6s7lzf7v6CATZXuk2JDWf9+4tvP3SSZYW5vPa9K5Jec/ak/FjNMG+UVGf7dvQnelw4RGQRlnDY36if0TbtZZExZgWwAqwVR4cHqPRbvDH6r207hIjlGF12bSlvbq/hvd3HMECLT6imH4lWGkGB3MFZnDjjP7GlysNrd3fq/IFKOAIvba1OaaJPFCWVqFTMQKRH+3GIyGeAx4HrjDG2J6oamOg4rAiwjZOHoyYqor+PdNdYlb6P1+F9VWmha7/hnGO0vqnFFb0SwVqJtMeGfXW+5qmwodOiAXBwgPkzAnTdJJVqGIEdJfX9K6e6VhXat+McPbbiEJFi4GXgVmPMLseuzcAUETkPOAjcCNwc3fc68C1gefT3a903YqUv42dmcMboz5yYx1vlta6nzA376ggIMV9HfVNL7FqJ7NwDeTLpSkYNy+b7i6ey/dBJXiyrTpgDI8B1M8fzzq6jrhazeZ6Ws8GA8DVPVngy/GqG/XrNLiIRw8SROTz4zZkDdrUBGRQOEXkWWAiMEpFq4GdACMAY8wiwDCgA/i3ahazNGDPHGNMmIt8D/ggEgSeNMeXRyy4HXhCRO4Aq4BuZGr/Sv0hkZnDG6NuCYDfzyc/JJisgtIYNWQGJ1ST65iN/Jmws89MLd3/WNYHMnpTPzKIR/Sopryeob2phamEu9U0ttCZJnLx5XjH/fP2MuMi4J751GTtrG3ny/X0gwrc/d16nJvrbntgYK7hYWdfEr9fs4uk75rVzVv8lY8JhjLmpnf13Ancm2LcKWOWzvQ74YpcMUBlQpJLda08s9sokKxggHC2Q1xYx3P+Hck40tcZ6b4cNLH+zgt/f/VnXdV793hUsfvAd9hw93aXlMwYS4Qg8+u5eFk4dk/QzPNLYTNn++oRJeNUnztDSFuH+N8qZWpgbJx6p1oDaVHk86euBRo87xxWlO0g1u9e5MnGaRyIG3zDYvUdOuUpUgDUZ9baOe72ZIaEAZ3z8QocbzlLf1BIzF/rx9o7DvLvzCM/edXmceak9Z3ayGlBeQZk7eaSrxPvcySM7fd99GRUOpU+TTly9n93ai3NlggjhdqrOnjzbxoOrd7rCMzvTP2Mg4icaYPkvVpfXEnQoh9/X0Ro2vhFO7a0yE9WA8hOUp++Yx21PbGRT5XHmTh45oM1UoMKh9GEyEVfvXJnk52Rz3x/K4xyzM4tGcOJMK2NyB7ElmnzWGi0B8vLWas629q1ue70Vp58o2aojFJSEpsdkq8xENaASCcpAFwsnKhxKn6WjcfXt2bW9K5MV6/ZSWWeVrxBgcWkh9yy6gOWrKtiyvx4BgsEAz285QJuj8F7uoCCNabY8VfxJJBqXTc5n6dXTEn7vyVaZ9nfv/bfQG4sK9jZUOJQ+S0fKWafT26Bsf32sZhVY+QTZoUCsl4OzLPclRSPisphVNLoOu6CknWtjMzgU7NQq8+Z5xXHffyJBUc6hwqH0WTpSzjqRGcLPV+Ith15ckMNdC84H4Ferd7qus+uwf8MgJZ5U+2g4+e4Cq+OetxFWplYDfoKinEOFQ+nTeE0R7TnLvWaI0nHDE/pK7BWNLR7765q47w/lhCMRwh5/7skuyAofKIQjhimjhyaNPMvLCbHwwtHUnW6Je+ovLhiqq4EeJqPVcXsLWh13YJCqs3z5qgpWvLePiIHBoQALpozm7R2HMVhJfd+/cir3LLogds2H1uzi/WjNqq5ubTpQ+dGXp7L7cKOr1LkTu3fJQC4k2BtIVB23R2tVKUpX4ucsX76qgoW/XMvyVRWx43KHhGJ/t7RF+FPF4ZgYBINuX8nsSfnc+6ULGRRt3IR0TRe/gU7jmVbqTrfEbQ/KOXFOpZlSsoZbSuZQU5XSb/A6y51PtLZdfOk101zHGYhlggvwX2bHN+6ZPSmfq0oLrWvpcqNLKK9piDMbwrnvIpBCIUEtc95z6IpD6Res3FjFQ2t2cfvlk2NVTbcdOOE6xi6jbjvVvzhtrCtCJxB92nU+vS5fVcH8B9YkNKkoHaP84Emq6k4zs2iE7/4ZE0bwzJ3zebu8Nm7FaOO3wlS6B11xKH0eb4jtA9fPiK0SnBE43jLq3kioCPDspipe2lodm7Sc5ytdx/EmKzoqd1DQd/+OmgZ+t77Sd8Vo05FwbKVrUOFQ+jyJQmydZdOvKi1kR00DF/3Dm1w0NpdPDjfG9c0wxm1b9zZ6UrqeaGXsONrChnd2HXVte6u81iUcHQnHVroGNVUpfR5vLL/z9dJrpvHOjxaxo6aBdbuPcbY1wrbqk8l7gYtVwsK7QlE6hxXBNsq1bfjgLIZlx686QlkBFl442rXN7/uYPSmfexZdoKLRzeiKQ+nzpJLpm479OxJ1fCwuLeTRdfvUH95F3H75ZJZeM43lqyp4YcsBjje1Uu3T0XDYoCC//fY8Zk/Kp3D44NiK0bnaUHoWFQ6lT5Eowc8v03f5qopYd782T7EjEcs0lYhH392r2eBdRHZQuHjccHKHhCjbX8/Sa6ZRXtMQF1FlkxWQ2HfrbLSl9B5UOJQ+Q9n+em5asZ7WsCEUlFgPBnvfy1urMcDXZxW5HNuVdU2u3Iu8nBAnHW1Fs4PW3pawQYCsoLB6x+Fuuqv+T0vYsK36JNuqTzI4mtTnF4pr03BWs/B7OyocSp/hpa3VsRpHLWHDS1urmT0p3xKUxzbEihG+uOUAI4dmx50flHO2c2d4rX3NBVNGMa+kgNXltb5Nm5TE+GXU+zVoOtsaiXVNXLvzCG/7CPTwwTot9XbUOa70GCs3VnHrExtZubEqpeO98Tf26w376lx9qVvCJq6HxnUzx/P9K6dy0dhcXv/QPydj3e5jPPjHndSdak71FpQoI4ZkMTjLPZ0U+Ig3wObKer7xyJ9ZNHUMAZ+gqhNn2lL+N9GVaBZ66mRMOETkSRE5IiLbE+y/SETWi0iziPzQsX2qiGxz/DSIyL3RffeJyEHHvmsyNX4ls9i5F+/tPsZPXvk4pYnia7OKyM6ySn9kZwX42qwiwIrnD3hmoOMOU1RR3mAeuvFSNu6rY1v1yYS9HcDK5ag+cZag1hVJixNn2jjrEevxeUNYfPFYLikaEbeK2Fxplaz/6iXjfa/X3V0U7Sz0B1fv5JbHN6h4tEO7wiEi3xORjsS6PQVclWT/ceBvgF85NxpjdhpjZhpjZgKzgSbgFcch/9Peb4xZ1YFxKb0Av9yL9pg9KZ9nvzOfH355Ks9+51x5iZ21jUlbvFafOMvyVRVsqjye8vjSrPqt+LDtwAn+VHGYnYcb+YuLxsTtb22LMGVsLg9cP4OivMGufd3dPEmz0NMjlRVHIbBZRF4QkaskUcaOB2PMOixxSLT/iDFmM9Ca6Bjgi8BeY8z+VN5T6Tsky71IRKKIqlRE563yWuZOHpn+QBVf2ps4BoUCtIRNbCKeMjaXuxeUUDh8EEE552+aX1LAzfOKeX/pF3ng+hl8fsooHrh+RreXS7ez0IMp1MhSUnCOG2N+KiL/AFwJ/FfgNyLyAvCEMWZvhsd3I/CsZ9v3ROQ2YAvwA2OMrin7IOl2WUtW0K72xJm444dlBznVcq4DXyggVB1vYvSwbI6eiq/KqqRHkvRJAJodTnERYmK/9JppaYVUdxeahZ4eKYUvGGOMiNQCtUAbkA+8KCJvG2P+LhMDE5Fs4KvAf3ds/nfg51gBHD8HHgS+neD8u4C7AIqLtdlLbySdiSJRf/GVG6t8GwKdP2YY540aGoueStY0SMkspeNHuCbiZH3Ae5LeOq7eSCo+jr8RkTLgF8B/AjOMMX+N5X/4egbHdjWw1RgTi9czxhw2xoSNMRHgMWBuopONMSuMMXOMMXNGjx6d6DClj7D7cGPMqR0MSMyUkMhMtaOmgaYW7fndG7jhMn1w62+ksuIYBXzN62cwxkRE5NrMDAuAm/CYqURknDHGnimuB3wjtpS+SSITxvJVFXF5F7c/uZERQ0LMSeC3iEQMhxviy1konSOVDoihoHDH586L9dzQ9q79j1R8HMuS7Isvkh9FRJ4FFgKjRKQa+BkQip73iIgUYvkphgORaMjtxcaYBhHJARYD3/Vc9hciMhPr326lz36lj7JyYxXLXttOOGJiLUPBMlG9uu1g3PGNzWEam8NUbzvEyJyQK/xWsByc540aqol8XUwy0cgJBbhiymgWTh3DKx9Uc+B4E6Xjhnfb2JTuI2MpmsaYm9rZXwsUJdjXBMSFNRhjbu2a0Sm9ibL99Sx7bXusnlRLa4SXtlbz8tZqWtoi7bZqdYpGQODGucVMHz+Cn776cQZHrXhpM7Bw6hj+4dWPY+HMfn00Vm6sSjkoQumdaOa40q14s3PL9tfz0JpdrjyMQEAQiDnDAaYV5qZ0/ayA0NTcxop1e5Mm+ikdIzsoCb+LcDjCm9tr4nJgnH1NOpL4qfQ+tCiM0m14Q2qXXVvK/W+U09xq9f4WLMf3/ddNZ2phLi9trY51d5s4MoeK2var1baEjbZ57UIGBYX8odnMLylgythc5pcU8NCaXeD4LoRzPcKvnj6OP+855hIPZx+NRE23lL6FCofSbXhDat/cXkNLmyUaAeBzU0Zx75cujDnGnXH1L22t7tB7hgJCqy490sZ2greEDcdOtTD3vILYBO+tbPvdBSXkDgnFghqmFuay/M0KDhxvYsnMCS4zlffc7s4QV7oGFQ6l2/D2iL56+jg2Vx6npTVCICBcPX1cXLz/ztpG7v9DOa3h9lLO/PH24VDc5A3J4i8/M57ntxygLbpMEKzIqJawwWB9hste287UwlxmT8pvN3lz9qR8fn/3Z33fL93ET6V3IiZZN5t+wpw5c8yWLVt6ehgK8SG3djRVxJi4jPB7n/tAzU7dwKSROew/3pT0mIDAD66cyj2LLuimUSm9AREpM8bM8W7XFYfSrXizc+ubWogYE1dc7tF396bdTClvSBYnzmgToPbw5mKkIhrZWQHyc7J5eO2ehCU5EuXhKP0PFQ6lR/GarxrPtHLDo+s7ZGJS0UiN3MFZCbvsZUdNVDa2Kat0/Ajuf6Pct1YY+OfhqHj0X1Q4lIyT7EnUWVwuPyfblc+hZIaSUUMZPiTEpsrjTMwb4qrj5S1P33C2LRaY4FcrDPzzcJz7lf6HCofSae597gPe2XWUhReO5qEbL3UJBRBX1fbt8lpe2HKAnOwg/8+iKdw8r5jZk/J5eO0eIgPA59bTbD/UEJvkdx89zbTC3FioszFWNVv7a7CFwoBrZegsO75hX53rews4aokp/RMVDqVTOB3Yr247xPHTLWyqPB4Tiq/NKuJstMR2c2uEf32zgk2VVvLf8aZWfvKKld1987zimNnqbGvHIqiU1PCu6GoazjI4FIgJhFe7Q1kBvj6riK/PKnI9ENj+Dvt7a2mLEBArD0dXG/0bzRxX2iVZb/B3dh11vbZFI2LgbGuEtRXnHNwGqKhpiLuGnRQ2e1K+K1lM6Rijh/n3+k7EiaZW5k4eyfevnErJqKGufYXDB3H75ZN5aM0udtY2xqKqnG1Wwcq5+cGVU3n+u5d3OsRWe3/3fnTFoSTFLhEB8N7uY2z6tI6Hbrw0tn/hhaNdIbNzJ4/kP/fWxR5baxqaXdcbMSREY7O73PmnR0/F6hdpy87O05FGVR8dPMnffulCth04wR6Hz2N+SUGs3pSduFff1BLn77hn0QVdsspI1rBL6T3oikNJirdExKvbDrlWHg/deClLZo4nLyfEkpnjefqOeUmfeJ0FCW2qT5yN1S9q1WbfPcJnJozglsc38KeKw2QF4JKiETxw/QzqTrtF6M3tNRlts6q9v/sGKhxKUvxKQnjF5KEbL2XbsitjK5ElMye49i+YMoqivMEA2lypF1KYO4h5JQWxCdsYuLK0kJvnFfv2hrcj4b5/5dRY+fuuMi1p7+++gZqqlKTcPK+YTZ/WucxR7dUXsmsTvVVeS1s4wqbK4xgNse21jB0xOC6fxp6wE5UIsRM5u9q0pL2/+wYqHEq7PHTjpcw9ryCt+kJLr5nGhn11bEvQSGlC3mAaz7TS0KwrkK5iUFBoDRskAHlDQtSfbiWV+LQbLitOOmEn6w2fqBd8Z9De370fFQ4FaL9chN/kYZ+Tn5NNfVOL69yy/fVxohEMCBPzh3BVaSFLr5nGyo1V/PTVj119MwICQ7KDtLRFBoy/IyhWxFmqi7K5k/OZVZxPeU0DH1efiGXMN9ufVwSOn24llBUAY1yZ4AB5OSFOnW1l2OAQf/fli+JWEemQaKWi9G9UOJQOmRuc50RMtCdDQBg9LJslMyew99jpuHM+d34BT98xL3b+/W+Ux02W/7RkBuWHTvLMAGrwk44+ziwawQvRyrP3PvdBwjIrBqux0o1ziznS2MzbjrpfTrGAztWYUtPSwESFQ+mQucF5DkQnqoihtqGZR9bt8233+rdfujD290tbq2n2SfRbu/MI//FJesUNBxLbDzWwfFUFS6+ZFpdD48Tuu/61WUWxKsROU6NztZisBlUqqGlp4KHCoXTI3ODMFvYzsXg3BSAmSGX763mxrDruGIA/VRzWlq9JaIuYWF6FN4cmKJCTHeSL08bGuvXZE7rT1OhcLQZECEesvhtd5aNQ+j8ZEw4ReRK4FjhijJnus/8i4H8Ds4C/N8b8yrGvEmgEwkCbXQ9eREYCzwOTgUrgm8YYTS/tJB0xN3iLEz767t6E5bkFyA6dEyS7JawfKhqp8VZ5Le/8aBEAayoO09Qctib/iOHWyyfHfYfLV1XwVnktV5UWkjsk5BB8QzAgGGPUR6GkTMYaOYnIAuAU8HQC4RgDTAKWAPU+wjHHGHPMc84vgOPGmOUishTIN8b8uL2xaCOnzHPrExtdLUFthoSCTJ8wnKVXT4utNm56zHra9SMrKFw4Zhg7atrvLz6QKMwdRG3juSz8orzBHDvdwtzJI5lXUsCDq3fGRHfxxWN57LZzvXeWr6qIrVIAlswcz1vltbEV5rJrS+OCGxQFeqCRkzFmnYhMTrL/CHBERP4yjcteByyM/v1b4B2gXeFQ0qMjzlJvL2mbM61hNlfW83Z5LbMn5bNhXx1tSdrARiKGkwl6RQxkahubEWDooCBDQkGqT5wFYN3uYzScaSUg51Zrb+84zF1Pb+G7Xzif2ZPyeau81nWtbQdOqENb6RS9NXPcAKtFpExE7nJsH2uMqQGI/h6T6AIicpeIbBGRLUePJnYiKm5s+/eDq3dyw6PrfQsb+nHzvGIeuH4Gn58yirsXlJCXE3Ltf3XbQcCdGZydFWBaYS7ZWef+GUYMHKw/03U31I8wwOnmcFwtqk8ON1I6foRr2+odh7nl8Q2U7a+PKxx5VWkhsyfld1l9KWXg0Vud458zxhyKmrPeFpFPjDHr0rmAMWYFsAIsU1UmBtkfcUZLRYxh2WvbmVqYm9IE4831cJpHDjc0s3JjFTfPK+aZO+fz8tZqnt9yINYHQrHIG5LFqNzBYAx7j56OCyDw+4c8d/JIrpo+jg+rP3Ztt53dzkx+O4dGUTpDrxQOY8yh6O8jIvIKMBdYBxwWkXHGmBoRGQcc6clx9kfmlxQQEIk15olETFqRNraZa3FpIWVV9WyO9t4wwE9f/Zjth07y9VlFGKCtnyf4eXt7ewkGYFAwQJMjLPlUc5gbLxvD0mumsfjBd1zd+YBYDaeLxubyyeFG5k4eGcuNAXh+cxU7ahqIRNzO7qXXTFPBULqMXiccIjIUCBhjGqN/XwncH939OvAtYHn092s9M8r+y+xJ+dx/3XSWvbadSMS4oqGcePMCID6R8PbLJ7Olsj42eUaMdV6q5q++TnuyGI5As+coZ7jtkllF/PKPO2P7Fl88lrOt4YRlX+wVX2cS+hQlFTIZjvssliN7lIhUAz8DQgDGmEdEpBDYAgwHIiJyL3AxMAp4RUTs8a00xrwVvexy4AURuQOoAr6RqfEPZG6eV8zUwtyEk4+3R4d9jtPM1dIW4fH3P2138hxIBCU+S9wYw4S8wdScPOsKRX5hywEe+9ZlDA4FYomS//HJEYwxbK48ntR8qAl5SqbJZFTVTe3srwWKfHY1AJckOKcO+GLnR6e0x6/X7GJT5XE27qtzlQnZsK+OlRv3u4598v193DyvmN2HG62e1UBAJK5FqRJPxMChE2fjBLb+jNW35PbLJ8dWIOHo59naZrXgPdLYHOezcK4Ek4m/onSGXmeqUnqe257YyLroSmLd7mPc9sRG/vZLF8bMUHGpPyIsX1XhymI+ryDHZZ+fNDInYYLgQCAUFErHDXcVfhw2KMjpaOKeF8EKVCj3abWLSKxvuy0qdtFI50owFLSywrWTntLV9NZwXCVDpNLP2dt1bVPl8bjaVE7GjxjM4+9/6tp24IQ7pDYUjK9elTckC4luFoHcQcEU76L3MTgU4IHrZ7D44rGx7nlLZo5n2KAg0wpz+cevTmdxaSFTRp/r6d0SNgQT/A80BnYfbozrfXLlxWPjOizaeRreBlutYaOd9JSMoCuOAUR7VXDL9tfz0tbquDLcF43NJT8nm4AIGENWVoBwOBKz16/zSfwLBYSzjtcNZ90tYwOCq7KrMXDGp+ih8/iOWr78fAtdiQAFQ63J/LHb5rB8VQW/+uMnsTa5FbWNLHvNKh8fEIndSzgcYfqEEXzo07PEQGwFd+XFYznccJYbLrOc395M8OKROdz6xMbYGGxCQYmLrlKUrkCFYwCRrAquLSp+FWt31DRw3x/KiRhDICB84cLRrNmRvIJtY7RBU3ZQmF9SwKETZzjSeC5xzU8EkvlEerO7xAAHo33T39pe4yuksQor0c9QsCb0Gy4rZufh8ljBweFDQhx39Pl+bdshJJosObUwF3B3WCwemeN6vyUzx1N3ukV9HEpGUeEYQCSrgmuLit/8bDVUsiqoCsZygqf4ni1hw7rdx1gwZRR7jsb36EiFodlBTneiV3nu4KyEfSu6mk2Vx323WwED+NaGck7wb5fXulYTgK/Q23kZtz6x0XVs3ekWfufI61DBUDKBCscAIlkVXFtUmlvd4iFE/RMihMMREKGyLn0n93/ujX8KT5V0RWNaYa4rI72zojG5IIe6U82xVVQyJuYNiUvaA2tVMmtSfqzY4/JVFfzghW2xqCj7u7B/v1Vey8yJea5ihH7mJm+NsPb6wStKV5Cx6ri9iYFYHddZRjvVjOGy/fX84IVtLmGYXJDDg9+cCcCj7+7lnZ1H4nwgfYlUfSUBYFAoQLMjiizRaSNzQrSEI1wweljCHutgfZbv/GhRnI/i7gUlCb+jVJL5/JIxFaUr6PbquEr3Y08yuw83xhyrznDNRMc7e4bPnJjnEo6ZE/N4aM0uCoZms7odv0ZvZFCW0Nx2bspPRTQum2ytDF7eWu3bwtYuJRIArpgyKuZjSCYaQKzYoLda7VvltQmFI5VkPr9+8IqSSVQ4+gnOiCnvIvK5LQdYHK2I6ne83TM8GBRX/agpo4e6cjO6k9xBwZRMQ+2RTj0sAT4/ZRTzoiahRGfGSqjgH1Hmx4S8wTFxuKq00LXiuKq00FfE1T+h9FZUOPoJzogpb8bEyaZWbnl8gyv89uVoz297EvQrOuhnq09Ge0X9nAwKCs0JJvXBoQChYACrAWTnCETbqbYnQiOHZvPDK6dy/xvlvL/nGNlZgbhy5J3hK58Zz8Nr9zC/pCCuWu3i0kJXcyvBMpNp0p7SW1Hh6Cd4I6auKi3knV1HOdnUGtdPumx/Pb/fcsA1yQcA2rH/Txk9lNaISegcD6SRL9ESNr5Ck5Md5MIxyX0F6dAagdYUVi4jc0LUN7XExLe5NdIlq60LxgzjSxeN4an1la78GTsqqmx/Pff/odzVEVH7fyu9HRWOfoJfxJRtjvJG5WzYVxfLmRCsqquXTMwjPyebf3jtY+wGfQEsc4zN7qOnWTJzPAfqz8TqJjlJx2ee6NCmlnCXiUY6TJ8wghXr9saEM5rr6EtOKMDZtggFQ7NdTZVyBwW5tDif7YcaGBIKcM+iKdw8r5iH1+7xzZ+xv5+zPrkzmrSn9GZUOPoRXkdqovBb7+rEbjEKMLUwl399s4I9R09xoqk1boZ//UPrKTzZxNpXGBQU5pYUUDA0O251kTckFMv8dhIQ+J3DhJRKRFOi/BnbvOgkKyh8c85Evj6rSFcbSq9FhaMf45zUUhEUgJ21jbECen4Yk7ofo7czOncQv7tjXlwSHeArGmCZ8n63vjL2maUS0ZSKgAcDwjfmTORrKhhKH0CFo5+SqGeGU0zuWXRB3HneQnkAWQEYOjiLM80R2iIRy4TVAQFJx3ked24HVzhZAauboZ/vpmT0MAAaz/iLRCLWVByOObpTneT9wmqTCbii9GZUOHopHUngc+IVAPu1n5g4KR033JWJfMHooQwblOXyO4wbPogpY3NTDkW1MVgFB1MRnWGDgpxyOLU7aha784rzyB0SovFMa1wpj02Vx7n3uQ9c95ZKgmBTS5gHV+/sknLl2nRJ6YtoWfVeiJ1ZXFnXxCPr9rF8VUXa1/CWnrh6+riEYmJTtr+eRx2TqwB7jp6Oc1bXNDSzPlqmW7BqSaXKDXOL+e6CknaPO9UFORwAuUNC3LPoApZeM40RQ9zPSWdbI7zxkdu3kZ0VYGbRCN9rBQQuHmcVGtRy5cpARoWjF+KXWZwuN88r5oHrZ/D5KaN44PoZ3Dyv2FdMnHz/+W2ulUCyB+/WaAhVQGBQKHXheH5TFcUFQ8kd3PnF7rRotVibBVNGuV4HA8Qc0WX7631rXnl805xtjfDJ4UYWTBnFME9/kIiBBVNGk50VICga+aQMXFQ4eiHexLPOJKJ9evQUv/rjJymtWmpOnmn3GJtQUAgKBIMBznc0J2qPsIF/ePVjGs92vlqts5AhwPt7vKazc6mQG/bVEfGxQcW3l7JWEvNKCtj+j1dxiWf1UV7TwDN3zuf7V07VBD1lwJIx4RCRJ0XkiIhsT7D/IhFZLyLNIvJDx/aJIrJWRCpEpFxE/tax7z4ROSgi26I/12Rq/D3J0mumcfeCEiYX5CQtgJcM2zlefeIsx5ss+/6/rd3tOsY2VdldAS8eNzylay+ZOZ7n7rqcG+cWgzFsSRKF5Yed7yEQu8cffXkqS2aOT+l8v8ke4n0T4YiJmZLsCKagWH6WwuGDWDJzPINC1rbsrADZUTF0riRuuMztA7Ij1O5ZdIGKhjJgyaRz/CngN8DTCfYfB/4GWOLZ3gb8wBizVURygTIRedsYsyO6/38aY36VgfH2OM5KqHZmcUfxi45q8phqrp4+Lq4r4MyiEe0m4NWdbuHt8lpe9ukWaNNerSm7XPvnLhhFbcNZq3x4OHEHQJsAMKNoBOU1DXElUrxRW6FoEylwRzA560Hdevnk2GcOxEU42cEDWn1WUc6RMeEwxqwTkclJ9h8BjojIX3q21wA10b8bRaQCmADsiL9K/6G9tq7p4u3TAPDNORMpLhjqmgS9Wc0tKUzeAnERSk7yckJW8mAShg4K0twW8a0+68Tb9jUCfHzwJFkB4ZKic21XBbhpXjHHGpvZd/QUJaOHuRIb4VyvC+/n7AxL9vvMtfqsorjp1eG4UeG5FHBmaH1PRG4DtmCtTHztJCJyF3AXQHFx7/9Pn6yta0ewJ7p/W7ubppYw35wzMbaCcU6C3qzmquPJmzTdvaCEV7cdTHqMNxvaj1SjpsLGEg+Dlc194kyr1a87YiidMIKdhxtjY08l27qrP2dFGYj0WuEQkWHAS8C9xpiG6OZ/B36ONY/8HHgQ+Lbf+caYFcAKsBo5ZXzAnSRZW9eOkm5Wc+OZVl7+oNo1qV88Lpe/mj85ZtoBeOz9T5Ne82xrYlHICQU40+rfojYRYWNFb51qbiMrGCAcPicUwwdlxfJdUikDYn/OLa0RRIT8nOx237+zOTWK0t/olcIhIiEs0XjGGPOyvd0Yc9hxzGPAGz0wvIzgzSIG0s5Obg/nhOrscw2w7cAJ3nY0ahoSCvDl0kIeuvFS1zUeXruH9rpGJkugywoGGASxMhsLp45hzY7DtLdGsVcZN8ydyIS8IcwvKWBnbWPMZPbIun0UF1jRXcmSHGdPymfZtaUse207EWO4/41yphbmJvyMnd36kjXFUpSBRK8TDhER4AmgwhjzPzz7xkV9IADXA74RW30VO4u4q/0dAEt+837M6f3e7mNkBazJOCtg9RP3mpcKhmYzZWwuZfvrU+pN7sfIoSGmjx/hyjBvONvG3QtKyB0SclXxtTsXvv7hId96WAJx5qiH1uxyHeMXEPDk+/viVh/1TS2xMiTtmavS6danKAOFTIbjPgusB6aKSLWI3CEid4vI3dH9hSJSDXwf+Gn0mOHA54Bbgb/wCbv9hYh8LCIfAYuA/5ap8fckfnb4zuAtqwFW4lvEWIl8rT4+ieoTZ3lw9U5ueXwDZfvPuZHsldHN84oJJoqLjTIxP8c3xHf9vjpXOOvsSfk0nmll24ETfPWS8fzwy1MpHD7Idc6InFCcgPolNHq37Tl6mvd2H+Mnr3zMyqgj3hma255ZsCtzahSlv5DJqKqb2tlfCxT57HqfBKH6xphbu2BovZ6O2OGT8c6uo3HbsgLR+k92bSaf5UPEQEtrhIfW7OLq6eN45YNqDhxvYsnMCfzz9TP42qwiHnl3LztqGjhYH588eMNlxaxYtzdu+5jhg12vneagyrom7l5QwpKZE1yRWzfOmRi3KkgWKvvm9hpqTp5lz5FTrm03zytOq7igt1ufrjYUBaQ9e3V/YM6cOWbLli09PYy0WL6qghXv7cOYzrcRvfe5D1z9JoYPzmJM7iBCwYAr+3rBlFEYrEKHT62vpKU1QgT/qrZ2YmLZ/npuWrE+ls8hwPmjh/LtK0q4eV5x3HsL8OJff9Z1Lwt/udbVVXByQQ7v/GhRp53SzgrBQKz0iqIoqSEiZcaYOd7tvc7HoVg5HY+//2nMydySYtjokt+8z/ZDDUwfP5xXv3dFbLvt4F5TcZjTLWEazrbR4FPywwC/u2MeAMUFQ1mxbi/765p8fRmvbjvI4tJCHlqzKy4J8PpZRQlF45+vnxF3H1eVFrpWF7Y5yJsE6UyQTEVENXlPUTKDCkcvZMO+Oldr1oBIu+G5Tuf3tuqTLPnN+3Hi8fDaPfzyjzsTXsP2D5Ttr+f+N6w+2FFrVpx4HGlo5qbHNtDmSRi0fQbLV1X49uyub2qJ22aLw6vbDlI8MofFPn6EjgYMaPKeonQ9WuSwFzK/pIBBoQABrKin+6+b3u4kuf1QQ9LX9nVDHo/2kpnjXRV0we2cDwicP2YYF4wZxoicc88ZBstxbx9zSdEIbplXzLPfsSZ0v4q+WUHh4IkzLme7zeLSQk6caWVLVCBWbqzi4bV7Ysd2dcBAqth1vPzGrCgDFV1x9EI60hlu+vjhrsip6ePjo5lmT8rnH786nSf/81MwJuaH8OJMRgwExOVgDgWFcMQgQCAgRCKGUFaAZV8pdY0zb0jIdc3hg7M42xrmuU1VvLy1Om7F4BSGlrZILM/CXl1kIkGyPTIRFq0o/QEVjl5Kos5wiez8r37vioQ+Due5tgkqOyvAVE8/C+d728K1urw2Vg8KrBVQOGyIAEHgxrnFvn2yT3jasQYCQlskce6EUxhELHEyWP0xHnl3L4/dNqfb26xqeRJF8UeFow/R3hOwn1g4SWcitIUrPyebD6vPRSadaT3n0whHDOPzhgDxWe5eh/fCC0dbFXATrBi81WuXvfZxrMnS2zsOs3JjVSyUtrvoiVWOovQFVDh6GclCUDv7BNyRidA2Zf3ij5/EVbwNZQXIz8n2FTO//IdEqyXn9nsWXUDZ/npGDRtEbUNz7Bg7B6M76YjJUFEGAiocPYh3Im2vLpLX97C6vJb8nOyUJ9R0J0Ln+P7uyxe5ciIWXzyWu79wflIx84bT+pnfvKuoZdeWcv8b5TS3uqO1vBnh3UUik6GiDGRUOHoI54QZECtyqr26SPbE/+i7e1m94zAfVp/kw+qPqao77ar9lIxUJ0I/s9gD18/wzYnwZrmnk2/hFZ43t9e4woAnFeRw14LzNaRWUXoRKhw9xIZ9dbFCgRFjWPbadq79zDhXBrVfXaTZk/I54ylbvuI9a3XSlZE/fiuJexZdEDeBe6vN3vf6dhChLZxaJJLXfHb19HFsrjwee/3gN2fqE7+i9DJUONIg3czlZOTnZLuS6sIRw5SxubFGSRMTJMJBfHc/u5qs01TU2bGm4w9xVZsNW4WvvONJhJ/5zFnyvTtFoyu/X0Xpz6hwpEhXx/R7M6iDgXPZ4U+tr+RI9P383sdZSsOuK+Wc4LtirOn4Q5wiE4yWabebLaXigPeaz3rCr6A5G4qSOiocKdLVMf3zSwoYHLJ8AwFHdri3B3iiFYSzlMbi0kLXvkTXaA9nX4xtB06kXFzQrwlVX3ty15wNRUkdFY4U6eqY/kRP9H7v097TsPcJvSNjtd/D2aApnY53fquGvoTmbChK6mhZ9TToLhu4930eXruHB1fvJGIgKPD9K6dyz6ILunSszvdwYpc4Hwioj0NR3GhZ9S6gq2zvziQ/iG8S1BUriHTHmqgl7FWlhbEJNT8nm/qmlriWr/1lotWcDUVJDV1xdDPOJD8vdnMkP9KZpFdurOpQDwo/H8fi0kKXCSsguBL11JmsKP0XXXH0EvzKjTv3JRKOVJ+GnV3v7JDddDLLve9hO9rtxwtvol4iZ3J/W40oinIO7cfRzfgl9aWyL1Xe3F6T9HW62CYs+x9KQIgl6mVnBQgKceYz29H+4Oqd3PL4Bu1loSj9jIytOETkSeBa4IgxZrrP/ouA/w3MAv7eGPMrx76rgF9jVe5+3BizPLp9JPA8MBmoBL5pjOlTs9LSa6ZR23CWd3YdZeGFoykcPrhTfbW9eJMDO1vjyVu11unjSJSop6GtitK/yaSp6ingN8DTCfYfB/4GWOLcKCJB4GFgMVANbBaR140xO4ClwJ+MMctFZGn09Y8zMvoMUba/nrfKa2lpi/BWeS3P3Dm/SwTDJhN9thOZyRJt19BWRenfZEw4jDHrRGRykv1HgCMi8peeXXOBPcaYfQAi8hxwHbAj+nth9LjfAu/Qx4SjO57Ge7rPtpYjV5T+TW/0cUwADjheV0e3AYw1xtQARH+PSXQREblLRLaIyJajR49mbLDpYj+N+/kGFEVR+gK9MapKfLalHTNsjFkBrAArHLcjA8lEZNBAeBrXuk+K0r/pjcJRDUx0vC4CDkX/Piwi44wxNSIyDjiSqUFkcvLr74lm6hxXlP5NbzRVbQamiMh5IpIN3Ai8Ht33OvCt6N/fAl7L1CD8Jj8lNdQcpyj9m0yG4z6L5cgeJSLVwM+AEIAx5hERKQS2AMOBiIjcC1xsjGkQke8Bf8QKx33SGFMevexy4AURuQOoAr6RqfFrZFDHGQjmOEUZyGjJkSRo9rOiKAMZLTnSAfq7L0JRFKUj9EYfh6IoitKLUeFQFEVR0kKFQ1EURUkLFY5exvJVFSz85VqWr6ro6aEoiqL4os7xXoSzyVM6/b4VRVG6E11x9CK8TZ6SNX1SFEXpKVQ4ehHeRk5d0dhJURSlq1FTVS/CNkt1ZWMnRVGUrkYzxxVFURRfEmWOq6lKURRFSQsVDkVRFCUtVDgURVGUtFDhUBRFUdJChUNRFEVJCxUORVEUJS0GRDiuiBwF9qd4+CjgWAaH053ovfQ++st9gN5Lb6Ur72WSMWa0d+OAEI50EJEtfnHLfRG9l95Hf7kP0HvprXTHvaipSlEURUkLFQ5FURQlLVQ44lnR0wPoQvReeh/95T5A76W3kvF7UR+HoiiKkha64lAURVHSQoVDURRFSYsBJRwicpWI7BSRPSKy1Ge/iMj/iu7/SERmefYHReQDEXmj+0YdT2fuQ0QqReRjEdkmIj1ea76T95InIi+KyCciUiEil3fv6OPG2qF7EZGp0e/D/mkQkXu7/QbcY+3M9/LfRKRcRLaLyLMiMrh7R+8aZ2fu42+j91De099HdDzt3ctFIrJeRJpF5IfpnJs2xpgB8QMEgb1ACZANfAhc7DnmGuBNQID5wEbP/u8DK4E3+up9AJXAqJ7+PrroXn4L3Bn9OxvI66v34rlOLVbiVZ+7F2AC8CkwJPr6BeD2Pngf04HtQA5Ww7s1wJRe/p2MAS4D/hn4YTrnpvszkFYcc4E9xph9xpgW4DngOs8x1wFPG4sNQJ6IjAMQkSLgL4HHu3PQPnTqPnoZHb4XERkOLACeADDGtBhjTnTj2L101ffyRWCvMSbVSgeZoLP3kgUMEZEsrIn3UHcN3ENn7mMasMEY02SMaQPeBa7vzsF7aPdejDFHjDGbgdZ0z02XgSQcE4ADjtfV0W2pHvMQ8HdAJEPjS5XO3ocBVotImYjclbFRpkZn7qUEOAr876j58HERGZrJwbZDZ78XmxuBZ7t8dOnR4XsxxhwEfgVUATXASWPM6gyONRmd+U62AwtEpEBEcrBWJhMzONb2SOVeMnGuLwNJOMRnmzcW2fcYEbkWOGKMKev6YaVNh+8j+vtzxphZwNXAPSKyoCsHlyaduZcsYBbw78aYS4HTQOdttx2ns98LIpINfBX4fReOqyN05v9KPtbT7HnAeGCoiPxVF48vVTp8H8aYCuBfgbeBt7DMO21dO7y0SOVeMnGuLwNJOKpxPzEUEb+ETnTM54Cvikgl1jLvL0Tk/2RuqEnpzH1gjLF/HwFewVrG9hSduZdqoNoYszG6/UUsIekpOvW9RLka2GqMOZyREaZOZ+7lS8CnxpijxphW4GXgsxkcazI6+3/lCWPMLGPMAuA4sDuDY22PVO4lE+f601POnu7+wXpC3Yf1JGQ7iEo9x/wlbkfZJp/rLKRnneMdvg9gKJDr+PvPwFV98V6i+94Dpkb/vg/4ZV+9l+j+54D/2lP30EX/xuYB5Vi+DcEKYPh/+9p9RPeNif4uBj4B8nvzd+I49j7czvGUz015PD39j7SbP/xrgF1YEQZ/H912N3B39G8BHo7u/xiY43ONhfSgcHTmPrD8Ah9Gf8rtc/vivUT3zQS2AB8Br/bkf+wuuJccoA4Y0dPfSRfcyz9GJ9rtwO+AQX30Pt4DdkT/v3yxD3wnhViriwbgRPTv4YnO7cyPlhxRFEVR0mIg+TgURVGULkCFQ1EURUkLFQ5FURQlLVQ4FEVRlLRQ4VAURVHSQoVDURRFSQsVDkVRFCUtVDgUpQcQkcui/R8Gi8jQaM+H6T09LkVJBU0AVJQeQkT+CRgMDMGqu/UvPTwkRUkJFQ5F6SGi1XA3A2eBzxpjwj08JEVJCTVVKUrPMRIYBuRirTwUpU+gKw5F6SFE5HWsirjnAeOMMd/r4SEpSkpk9fQAFGUgIiK3AW3GmJUiEgT+LCJ/YYz5j54em6K0h644FEVRlLRQH4eiKIqSFiociqIoSlqocCiKoihpocKhKIqipIUKh6IoipIWKhyKoihKWqhwKIqiKGnx/wO78FzVCeZ+BQAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# dependence between parameters\n", "plot_scatter(params[0],params[1])" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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uwdTSdv5VN7Nh87bW29myfRerVyxrvR0Nb+2aQ1pvY8v2XQAG/yIwzBn/scCaqrobIMl5wJeZ5Np7LW0bNm/rJJRXr1jWSdBoeCcdtbL1QG77rwkNb6iuHgaXb97evP7FdkrRYrB6xTIuPNUx86Q92TDB/0bgy0k+x+AKn6OB17RalSSpNdMGf5L7AHcDT2DQzx/g1c1NWJKkJWja4K+qu5O8rKo+ymBkTknSEjfMkA2XJTkjyWFJDtz9aL0ySVIrhunj3z237h+OW1YszBDNkqSODTMe/+FdFCJJ6sYwN3DtA/wB8BQGZ/pfAN5dVT9uuTZJUguG6er5AHAH8I7m/YnAB4HfaasoSVJ7hgn+I6rqMePefy7JtW0VJElq1zBX9Xw5yRN2v0lyFPBP7ZUkSWrTMGf8RwEvTnJz834lcEOSrwJVVY9urTpJ0oIbJviPaaPhJHsBG4FtVfXcNtqQJN3bMJdzfqeltk8DbgAcn1eSOjRMH/+CS3Io8BzgnFG0L0l9NpLgB94GvIrBAHCTSrIuycYkG3fu3NlZYZK0p+s8+JM8F9hRVZum+1xVra+qsaoaW758eUfVSdKebxRn/E8Gjk9yE/AR4BlJPjSCOiSplzoP/qp6TVUdWlWrgBOAz1bVi7quQ5L6alR9/JKkERl2zt1WVNXlwOWjrEGS+sYzfknqGYNfknrG4JeknjH4JalnDH5J6hmDX5J6xuCXpJ4x+CWpZwx+SeoZg1+Sesbgl6SeMfglqWcMfknqGYNfknrG4JeknjH4JalnRjHZ+mFJPpfkhiTXJzmt6xokqc9GMQPXXcAfV9U1SfYHNiW5rKq2jKAWSeqdzoO/qrYD25vXdyS5ATgEMPincf5VN7Nh87ZW29iyfRerVyxrtQ1JozfSOXeTrAIeC1w1ybp1wDqAlStXdlvYIrRh87bWg3n1imWsXXNIa9uXtmzfxQvOvrL1dtauOYSTjjI3pjKy4E+yH/Bx4PSq2jVxfVWtB9YDjI2NVcflLUqrVyzjwlOfOOoypDnp6qRiy/ZBnBj8UxtJ8Ce5L4PQ/3BVXTSKGiR166SjVnYSxl38RbHUjeKqngDvBW6oqrd23b4k9d0oruN/MvC7wDOSbG4ex46gDknqpVFc1fN/gXTdriRpwDt3JalnDH5J6hmDX5J6xuCXpJ4x+CWpZwx+SeoZg1+Sesbgl6SeMfglqWcMfknqGYNfknpmpBOxSFIbupjwZSlP9mLwLwCnRZQWjy4mfFnqk70Y/AvAaRGlxaOLCV+W+mQvBv8CcVpESUuFP+5KUs+Mas7dY4C3A3sB51TVm0ZRhyTNVRc/IAOsfsgyzjrukQu6zc6DP8lewN8CzwK2Alcnubiqtix0W3/+ievZcsuuhd7svfjDq9QvS/33tlGc8f868K2quhEgyUeAtcCCB39X/OFV6pcufkBu0yiC/xDgX8e93wocNfFDSdYB6wBWrpzbDl7oP48kaU8wih93J5tove61oGp9VY1V1djy5cs7KEuS+mEUwb8VOGzc+0OBW0ZQhyT10iiC/2rg4UkOT3I/4ATg4hHUIUm91Hkff1XdleRlwD8yuJzz3Kq6vus6JKmvRnIdf1VdAlwyirYlqe+8c1eSesbgl6SeMfglqWdSda9L6BedJDuB74y6DuBg4LZRFzELS6nepVQrWG+bllKtsLjr/eWquteNUEsi+BeLJBuramzUdQxrKdW7lGoF623TUqoVll69YFePJPWOwS9JPWPwz876URcwS0up3qVUK1hvm5ZSrbD06rWPX5L6xjN+SeoZg1+Seqa3wZ/k3CQ7klw3xfpHJLkyyZ1Jzpiw7pgkX0/yrSRnjlt+YJLLknyzeT5glLUmOSzJ55LckOT6JKeNW/f6JNuSbG4exy5ErfOpt1l3U5KvNjVtHLe8lX07n3qTHDFu/21OsivJ6c26VvbvELW+MMlXmscXkzxm3LpOj9v51LuIj93p9m/nx+6cVVUvH8DRwJHAdVOsfxDweOAvgTPGLd8L+DbwUOB+wLXA6mbdXwFnNq/PBN484lpXAEc2r/cHvjGu1teP/+xi2LfNupuAgyf5Tiv7dr71TjguvsvghpnW9u8QtT4JOKB5/ZvAVaM6budZ72I9dietd1TH7lwfvT3jr6orgNunWb+jqq4Gfjph1T1zBlfVT4DdcwbTPJ/XvD4PeN4oa62q7VV1TfP6DuAGBlNftmoe+3Y6rezbpp6FqPeZwLerqtU7zIeo9YtV9W/N239mMNERjOC4nU+9i/jYnWr/Tqe1/TtXvQ3+eZhszuDdB+QvVdV2GBy4DM4UF4Ukq4DHAleNW/yy5k/WcxfFn58DBVyaZFMG8y7vtmj3beME4IIJy0a9f08BPtW8XgrH7fh677GIj92J9S6ZY9fgn72h5gxeTJLsB3wcOL2qdjWL3wU8DFgDbAf+ejTV3cuTq+pIBn9G/2GSo0dd0EwymEnueODvxi0e6f5N8nQGwfTq3Ysm+diiOW4nqXf38kV57E5R75I5dg3+2ZtuzuBbk6wAaJ53dFzbvSS5L4P/cD5cVRftXl5Vt1bVz6rqbuA9DLoCRq6qbmmedwB/z8/rWnT7dpzfBK6pqlt3Lxjl/k3yaOAcYG1Vfa9ZvGiP2ynqXbTH7lT1LqVj1+CfvenmDL4YOLl5fTKwYQT13SNJgPcCN1TVWyesWzHu7X8BJr2KoUtJHpBk/92vgWfz87oW1b6d4EQmdPOMav8mWQlcBPxuVX1j3KpFedxOVe9iPXanqXdpHbuj/nV5VA8G/6FuZ/CD3VYGf7b9HvB7zfoHN8t3Af/evF7WrDuWwVUG3wZeO26bBwGfAb7ZPB84ylqBpzD4c/4rwObmcWzznQ8CX23WXQysGPW+ZXDFybXN4/ou9u0CHAv7At8DfnHCNlvZv0PUeg7wb+P+/9447rudHrfzqXcRH7tT1TuSY3euD4dskKSesatHknrG4JeknjH4JalnDH5J6hmDX5J6xuCXpJ4x+CWpZwx+aQ6SPL4ZJGyf5q7N65M8atR1ScPwBi5pjpK8AdgHuD+wtar+x4hLkoZi8Etz1Ix5czXwY+BJVfWzEZckDcWuHmnuDgT2YzBD1D4jrkUammf80hwluZjBTFaHMxgo7GUjLkkayt6jLkBaipK8GLirqs5PshfwxSTPqKrPjro2aSae8UtSz9jHL0k9Y/BLUs8Y/JLUMwa/JPWMwS9JPWPwS1LPGPyS1DP/D/CiptqTzrrBAAAAAElFTkSuQmCC\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_cdf(params[1])\n", "print(get_cdf_plot().median)\n", "print(get_cdf_plot().upper)\n", "print(get_cdf_plot().lower) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Effects of Priors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Changing the prior - here an example of prior which has a gaussian shape. We use one of the predefined Sherpa models to set the prior." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "normgauss1d.g1\n", "g1.pos=2.\n", "g1.fwhm=0.5\n", "set_prior(p1.PhoIndex,g1)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "set_sampler_opt('defaultprior',False) \n", "set_sampler_opt('priorshape', [False, True, False]) \n", "set_sampler_opt('originalscale', [True, True, True])" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WARNING: data set 1 has associated backgrounds, but they have not been subtracted, nor have background models been set\n", "Using Priors:\n", "abs1.nH: \n", "p1.PhoIndex: normgauss1d.g1\n", " Param Type Value Min Max Units\n", " ----- ---- ----- --- --- -----\n", " g1.fwhm thawed 0.5 1.17549e-38 3.40282e+38 \n", " g1.pos thawed 2 -3.40282e+38 3.40282e+38 \n", " g1.ampl thawed 1 -3.40282e+38 3.40282e+38 \n", "p1.norm: \n" ] } ], "source": [ "#Run sampler\n", "stats, accept, params = get_draws(niter=1e4)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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qswC1B49Tvuj/smB2uaUT5WnjumLLfj7Yup+cYACMoTViYrGUTXVNPP5BNVujwoXvb9nP/fMmc9H4YTyzuobP9xzmnY17Wb5pHxNHFMbFPDKpbnfWgPhlknUXWjmuKEq34ZzU7d9+K4nGYy0ExIojBMR6v7Syhn96cyNHT7QxaWQhX+xt8g2W2zENr/GIOLZ527gCsVUPWG6ucGuER97b5lpZ2LyxYQ+/v2UGjcda+GzXISvm0WbiYh6ZFPVlq5q9M1DDoShKt+HXxGjRlRNS1mC427XC+tpDsdfOPuD/tnwLew8fJxAI0D8nQHPUEHg/892/uQiw2rh+5fSBfLT9QKyWBGNoixhCOQH2HT7uex9rth9g4bKPmT+rjNycAMfD7s+x3UyZ6nVlo5q9M1DDoShKt5FuE6NNdU2MH14Qa5T00DubfY+zg+Vew0LEmshzg0JLm7sEwf5Muwc4uN1JcDLGsamuKbaCACjIC9J0oo3mcCS2Ynnq1pk8+t423nKsTGw3U1F+LgERwPS4or5MUMOhKEqnsHDZx7yzcS+ji/L5h3mT0woMp9PEyF3fcIg544fFqdkC9M8JcOfF45hZPiShYWlps6rQBRhakMfcKaf7fqY3fmK/tn/b7qNf/OELLEk9i3c31/PQdeew+KZzfYv57nutiraIIRgQ7rmqosdoT2WKNnJSFKXD2FlJR060sbGuie/+5sOkzZqcDZ0WXTmBBbPPpGrPYd+UU7/sopqGo3HHNbdG2LK3iWljipIGku1mTfNnlaVV0+HtVX7DjFJ+f8sMbphRypyzhrqO/crpA2P3ZR8HMH9JJY+8t42WViszzBhD47EWHnh9I3N+uTxhinBPRVcciqK0G/upes12t5GIQMx/v3DZx/yhqo6CfjksvGQ840sKXAHim2eVxdxVTuVb+9pDBuS6rn3FpBEsXrHNdzx2dpQdF7BjHAahNXLSRWWApuZwrKAw0ZN/KlVe273ljI18sHW/KwPLWQ2eE7BWO6GcAFv2NsXcW4+sqKbu8HGXu6wnk1XJkZ6CSo4oSufjlchwIsDzf3k+v1+5PS5b6bKJw3ln496YBlVeToBjjmBy8Wm5/PjS8a5rz50ykoajLTG3z5S//wMHm1vjPjc/FOAmn5XE/Gg9R6KxFuWH+N65o1Oe99VRA7msosTX2Dy8fCsPvrUpdl8/vmw8q6obEp5/17Pr2d5wLO5v1pPcVz1SckRRlK6ns4TzklVHXzpxONPGFPEX0epvJ3sPH3dlSHli1Rw90RZ37Q27DjFiUH/AMlh+RgPgWDjCIyuqeWFdLQeOtjCsII9f3zgtbtXixAAHjoVjqx6n8fCe9/mew3y265BvKu3M8iHkBIRwmxXDmFk+hKL8XJfhcNZ0eBMDgJRZVj0FNRyKcgrRmc2BvE2KggGhLeoO+uPGvSxc9jHN4fj012vPK2V8SUHMeP3V0+uoPXgyzXXIgFBc8Htr/VG21h/l/S37GTt0QMqx1R9pAWDP4RN85zcfxsmyJ+LNqjourShhVXUDTc1h12pp4ogCvqhrSp5KG82Ysn67azEqRhTSeKwlVlG+6MoJ1B0+zivRz8gL9Z4sKzUcitKH8Wb2dFbf77U7Gnli5XYEa45c8PVyDp9ojQWQ2wyxCdEmFBT+/luTYpOp/blHWtpcxx1paXNNuHsOHWfrviOx/QeOhTMaq4mOJx2mjB4UM6wRzzk7Go6RmxOgpTWCiFCU716NrKpuoLXNCn63tZ38294wozQurmMb7IeuO4f5s8p6ZHvYZKjhUJQ+il9gt7OaA9kGyACYk+m0OYGTQWjvXO00Gk53mbdq285UsovfvLGUA0dbyAlYEuYCbNh9CGddn7dWQ7CqzdMxHvl5Ob5GA+BEa4T7rp7EPa9soC1iuO+1KsaXFMQm+2R/W6/BfmFdrctYeA2GU4alM9V8Ows1HIrSR/HGCZ5ZXcNlFSXcc1UFjcdaOvSE29R88qnfANsbjvHIimpmjyt29cDwBrXBMmg/ffkzSz4kAJNGDmTKqIFsP3CMOWcNjcssss9bvGJbLJjcGrFiJavuvgSIb9g099cf8NmuQwwryOO/X3wWv1+5nY11TUnvKRit77An/4hxG7/zzxxC47EWIsbEJEicK7ZkHQhdnQ0DwvNra2lt83cX+smw9DTjoVlVitJH8T6ph4JWDKKjsY1k2VRlQ/LZ0XAsNuH2DwUZPCDEmUNPo+bAMaaMHsR/frLb9+n//nmTgcTaTGt3NHLNbz50bSspzONHF5/Ffa9V0RKdlJ3Cgmt3NPK9R1fGYi8Ag/rn+AbXc4PCd88dTcXIgTHD+i/vbI4ZpL+65CxeXFfLc2t2xiRIMvk72qus3QebedrR2fDHl42PSccDzPnlcle2VdmQ/JgkSlejWVWKcorhjBP0DwVjKbAdiW3Y10vElNGD2OGY9JrDbew62MauaPDbOSF6+buXPosZHL+aiWljigh6XE51h0+4jJhTWPDNDXtYV9PoMhoAk0cNonRwPk85ig0H54doOtHK0x/VxAwrwIzyIfzVJWcBxGIUOcEA104fzTVTR2XUKtZ2Sa3d0cgL62oTugvTlWHpTtRwKEofxo4TrN3RyIot9R2ObQC+ch9guXk+rjkYF9tIF+95zv4TdpB/xMB+rgysZKxIULdxxaQRjC8p4Lm1tbREgyONx8Kxzw+3RnhxXS0vrKuNBbOvmToqFqNoa4tw+qD+CY1Gqqy1ZC4tSE+GpbtRw6EovRTvk603g8rLt6eOQqK/M3WveCe4scNOA2O4ZMJwnli5PWaQ9hxq7qzb44pJI1haWcO/Ld/iMhZ5OQFO+KjcpsP0sqLY3+bpH87koXc286et+2PBcAGCwQAbdh1yBbM3723C9uoHojUafiTLWvP+LZN9B4uunNAjDYaNGg5F6YV4n2wTyXb4HfvtqaOSXnvurz9gw+7DnDEkn50Hm11Pz14JjTOGHo0F24vyc3n0vW3sOHDSHWX30MiEgMD44QV89GVDXNU5WDpP7eUnV0xwTeALLzmL1baEekCYM34Y727ax6e1hzDRsYjAaoekSrjNsKmuyXfiT5RZ1Zn1Mz0BFTlUlF6I98nW29fCGYfwewoGt9Cgzdxff8D62kO0Rgxb6o9yPOw+zxvfePvzvdz3WhVF+bnc91oVOxstoxEUmDJqIM/dfj65wdTVd0GBnGiVXsTAxromX6MBxMmip8vQ06y6ixsfW8Wv/rCJax9dyaa6Jp66dSYXTxjOhBGFALRGrKypAPC1scVUjBwYd61EcR7bDfXjy8a7jEOi76C3oisORemFeJ9svQFVpzqs31PwTUsqYzGAfqGTT8Abdh+O+yy7x4WfhAZYE+EbG/a46h8ixmqudM1vPiQolovoI48QopNAQMjLCXDkRFvCYzrK0ROtrt7lrRHD3S99RgBLlNHiEKGgINGsqYWXnBXXgwMSt3FN5NrrrPqZnkLWDIeIPA5cBewzxkzy2X8j8JPo2yPAXxpjPhGR0cCTQAnW97nYGPMv0XPuBX4I2A2C7zbGvJ6te1CUnoo3wAqw5E9fEm4zhILC+JKChMf+fuV2V+D4ePikL37SyEJXNz2A66aX8t6mfXznNx9SlB+Kq9UQsSbSP209uc25JmgzsK6mMe48J+E2Q7gte0YDoDkcoak5jAg4vV3eaMnEEYUML+xHdf0RHn1vG7ddeCb3z5vM43/6EozhBxeUu2JIdrHelNGDeLOqztcd5RcQ7+lFfsnIWh2HiMzGMghPJjAc5wMbjTGNInIFcK8xZoaIjABGGGPWiUgBsBaYa4z5PGo4jhhjfpXJWLSOQ+krJHqi9SqzXjxhOM3hNt9A+ZT73uKgR7bjhb88n7er6nh5/S7qDp9w7XM/kcfz1VEDGdg/lNAo2Ph13+uJzJ0y0uUmCwWFZQtm+cYknMV6TvzqM5Kdd/vs8h5pPLq8jsMYs0JEypLsd1byrAJGRbfvAfZEXzeJyEbgdODzbI1VUXoDzgBrTsAqVrMzpJyukEBAYm1L/eohvBIfQ0/L5e2qOt8JEJIbDYCGIyfYtDd5VTa0Pzbhh7eeozPZsMu94gq3GV5cV+syHLYBf3n9rrjzBWLquIlI1Gu9t9BTguO3AG94N0YNzzlApWPznSLyqYg8LiIJ0xJEZIGIrBGRNfX19YkOU5RegzPA2tJmWFpZw42PrYqprdpB2YnRIK+NN5B74GiL6339kRaeXLWj3eOqPXicFh8V3GySzYXL8XC8y+y5NTtjSQS2AX/wrU3sazoRd6yBmDpuIrxFfT2xyC8Z3W44ROQiLMPxE8/204AXgIXGGDti9xvgTGAK1qrkwUTXNcYsNsaca4w5d+jQoYkOU5Reg72qsKckp14SWH70Oy4ay7XnuV1TzkCuMyjuxFtdnYj8UIBxPrLmXrMhWFIZp+UFCYi1QuhphILC7bPL47ZPGDmQ++dNpqQwL7atLWJ4YV0tDy/fyovRwsCISZxqbKvjJmLRlRO4fXY5ZUPye6ybKhndajhE5CvAY8DVxpgGx/YQltF4yhjzor3dGLPXGNNmjIkAvwWmd/WYFSVbpOo/ba8qrp9RSm5OwJXt5GR8SQE50f+zcwK4AuUfbT/ge+0ZZwxm1KB+Kcc4rWwwb981h3TswO6DzUwtLeK5289n9OD8NM5ITro9NZwU5AXjtuUFhcEDQswqH8J/VLpXWgLcfuGZ3DCjlIK8k578iIFnVu/kwbc28dyaneQEA66/QUCsWE+y78XLoisn8O7fXNTrjAZ0YzquiJQCLwLzjTGbHdsFWIIVOP9nzzkjojEQgHnAhq4ar6Jkk0SKqN5qcLvi+JqpoxJKVqyqbog9CRvj7io3vWyw74qjvulEWlIe9uol1frEYLnTVmzZnzJoni7JFkWnF/XnzOIBrs8KCjzxgxlxRYsn2gwnjoZ9xzV26ADuenY9R0+0xppB2fdjr8raIoZrp49GwCV4eM83KwB6XW+N9pDNdNyngTlAsYjUAj8DQgDGmEeAe4AhwL9ZtoLWaPT+a8B84DMRWR+9nJ12+wsRmUJUyRm4LVvjV5SuxC9YWjpkQFw/DWcTpEQTU6KaAVtq3Eu/UCBWuJeMvOgyZv6Syh6XIbXnYDOFee7pLD83yHd+82FG2llb6o+mPCYU1a6aNqaIb/sY8L5sMGxUVl1RegB+6ZlVew67iu3GDh3AgLwchhf247YLz0w6QXnTdu2KcD9Oyw0iAk1ZLL7rCk7LC2a1gBDgsonDU/7t06Gz+r5nG5VVV5QejJ8i6tLKmri+2xaHePvzvdyWJKhqr0iWVtbw0DubExoNiG/dmohU9RzdSUCgOc37AGuVdfbwArbWHyEgwuHj8f057OuOHNiPM4aeFteMKpmgZDL6gm6VGg5F6SHYiqhLK2uYv6SSihGFXDZxOHsPH+doS5ur77bhZCykoH8o9uS6cNnHvLGhjqBAQCRto5AOXqPRHgHDzkSAAXlBSgfnc9bwgoTaVn4kivU4cUqxwEltr6bmcEJByXTorL7v3YkaDkXJEu1xR/j1Ce8XstRvnYbDZvH71RhjFZz5yYVkk+40GmAZjqmlRRhgxeb4Wq3coBBuswQLvTGZbfXxf0ub2eOKmRHV5XKm1NqrBC/OviHp0Bd0q9RwKEoWaK87wk91NdwaoaB/iNtnl/PYB9U45y578m6NmC41Gj2BCImbNQF899zRjBzUn5nlQ7jr2fWu7oMNniLIoaflsj+aRfXR9gNcPmlErB2tt5GTNys4keBhIlI1cuoNqOFQlCzQXneEt7ueYGXxFOXn8ss/bMriiPsWIlaqbGu0x/rlFSUuwxEKCM7k4+ZotbhdVOlU+w23Wmq6zlXCzbPKqNpzuF0xDkieFdcbUMOhKFnAzx2RjuvK2Se8YkRhLH7xT2/4FwU6CQicWTwgrZTSvs55Y07KuB8PRxg3vIDbZ5fHkg8AVxbb0RNtsbTdYDDAFZNGxBo82em3frUzC5d9zC/+8AVzzhrKQ9ed06X32J1oOq6iOOjMNEnntYC0XVf2eU3NYZ5fV8vRE21EIhFO+NRNCJbB6EElFd3OhJICmo6HXQWNYwbn88/XTnH9zW9aUslH2w8wqF+IOofm1KUTh/Pbm85N+W9h4bKPXQH5uVNG9jnjoem4ipKCzk6TdLojHl6+NS3X1cJlH/PK+t1pF62JwBlDT/MNnPd1BEtSJWLchnNjXbxS744Dx7jxsVWx73RpZU0sPlIXdgsVDiuwNKpSuZPe9QTkve/7Mt0ucqgoPYVstve0XVdBsTKgdh9sdrVsBasI8OUkRiMvJ0BJYV6c8OoZxfGig32Z/JA1bRkgHEl/tXUiHOHR97Yxf0klj3/glpAXsQxROj3ZbeacNTTp+76MrjgUJUo20yTtTJoX1tXy/Npanv6ohhfW1caegG9aUhnXktXLhJKCWMzjtU/3EDFW4Pf2C8/kzOIBPLtmJwc8DZps+ocCHI+2TO3tmCQSi8EAtCWoUjQQ61Pi5bavl7vqYZwkclnZbql3N9drjKMvojEOJV2yLQXh7dT348vG83ZVnW8qbUFe0IpvYMmCOIv5Zo8rZlv9EXalIUwI0D8nQLNPDUJvJJVOVmG/nISV4E7GDjuNEQP7Jc2M6gtV3h1BYxyKkgbZSpO0JSoqRhS6VjVb9jYlrL9wakd5K8AzVZztK0YDUhcepmM0AH7wtTNSptL2hSrvbKCGQ1E6yAOvb3RpTHnxVoPfPttyizilK5z0ywlwvA9N9J1Naxol6xNKCsjNCTCssB8DcoOsqm6I66X+ZhoV332hyjsbqOFQFB8Sidh5tyfqo+F0eXmrwav2HOb3t8xg/pJK/FCjkRl+mllf7G3iH+dOjn13Dy/fGldAmaiplZOurPLuLYq5oIZDUeLw04u6YUap73ZvH42X1+/i0ooSl1/c20+6YkQhDy/fSsWIwpQB8b4Um8gWF4wtZvCAXFdNhTFwzysbGF9SwLQxRcwsH4LgbkA1vWxwymt31WTe22IpajgUxYN3hWCL2Pltv7yixOVuqm86wR3/sZbjYWuybwlHeO1T67yAwLe+OpInVm6PTRB2342V2xp8XTBqNJITEPirS85i2pgiSgr78eiK6phxiERMLKV6VXUD/zhvMo++t409h5qZWT6EJ2+ZkfTaXTmZ97ZYihoORfHg1YuqGFHou912V62taWR1VN6izeCqQo6A9fiLVSfQcLTFNUEU9A/x+1tmMPGnb6Tlu1cs7NWDYE26b1fVWUrBjmOCQeGldbU89M5m2qKaVZlM/l05mfe2WIoWACqKh/ElBQQdpQKPf7idtTsaGV9SQLR7KjkB67i1Oxo5a3gBuUFxnWOTExAC0e0ilrHJzQkQEBARmprDPLx8K6cP6p/9G+sjnJYbJC9kFVOGcgKxJAOv3Q23GbbWHyXcZtpV1Oks2sz2ZG7HUn582fge76YCXXEoShyrqhtck1C4NcI/vbGRzfuOxCTNjYEX19XywrpaWloj5AQDXDt9NJ/vOuRKry3slxMryrPPvXlWGYvfr6Y1YnyzqpTkbLjvcpZW1vDM6hqGF/ZjZZrGINPJv6vlz3uTYm7WDIeIPA5cBewzxkzy2X8j8JPo2yPAXxpjPonuuxz4FyAIPGaMeSC6fTDwDFAGbAe+Z4xx6zYoSgeZWT6EkKPITISY0qpNKCeAgZgro6U1wpa9Tbx85wXctKSSVdUNhNtMXCX3v/5xM3sPn+gTFdztxRukzvTctTsauffVDdHvJ70eJBNHFPAXM8tiK450J+jeNJl3JVmrHBeR2VgG4ckEhuN8YKMxplFErgDuNcbMEJEgsBm4FKgFVgPXG2M+F5FfAAeMMQ+IyCKgyBjzE++1vWjluJIpa3c08sK6WgT448a9rhqAQfkhlnz/PAC+98iHLq2k26N9wJ0V4krnUlKQ54ojeekXOpnJ5sy0CgWlXbGOU5kurxw3xqwQkbIk+z90vF0F2Mpi04GtxphqABFZBlwNfB79PSd63O+Adzm5alEUX9qTUul80tx54JjLcAzIDbKprokbZpQytCDPte/JldtZtmYnXzl9IDmB5NIYNh15Aj8VSWU0nrp1JgB3PbvetS8c/S56Q9ZST6enxDhuAd6Ivj4d2OnYVwvYeXPDjTF7AIwxe0RkWKILisgCYAFAaWnmHbqUvkGylMpERX5OnPLbNrsOHufulz6jpuEoowfnuwzHsXCEY+EIK7bsZ3B+KKHooJPTB/Vz9Y44Feks43nzrDLA6n1yIuxOZQ4FhUjEpIx19KZCvO6i2w2HiFyEZTgusDf5HJbxvyljzGJgMViuqnYPUOnVJEqp9Bbz/eoPX/C9c0fHSYb49QC3Wfx+8sB2OkYDoLB/CE5xw9FZ/4NW7TlMQf8QLa0nlYBLCvP40cVnMb6kIKVB6G2FeN1Ft6bjishXgMeAq40xdmpELTDacdgowHZU7hWREdFzRwD7umqsSu8kUUql1yAcOGaldD7wurtF6xWTRiS8dsSkFtxLh8/3xDceUuIpyAsyrCA36TFXTBrBzPIh5ARPTm0HjrbEKsjvuGhsUkOQzZ4sfYluW3GISCnwIjDfGLPZsWs1ME5EzgB2AdcBN0T3vQp8H3gg+vuVrhux0htJlFLpLeazebOqzrXqsF1YdupnefEAqvYcRshcoVbpGC1thrBH+TYUFG752hlU7Tnscjl+Z9oonq6swQBtEcOL62rTcj/1tkK87iKbWVVPYwWyi4G9wM+AEIAx5hEReQy4BtgRPaXVjt6LyJXAQ1jpuI8bY/4xun0I8CxQCtQA3zXGpFQq06wqxYmzp/drn+52xRdmjytm98Fm9h9tIQC+7iuA+Wk0XlI6H28sxO5pcsdFY13H2S6ncGuEYDAAxhBuMwQDwn1XT0qqiqsxjpMkyqrSRk5Kt5NKlrwz8fNhv11Vx8vrd9EvFGR7w7G4c6aMGsjLd17gusaj721L2E1OSU3xabnsP9KS8rgxg/PZceDkd5ITsALcESydqmRxCNsA7DrYHFt92Nd45rZZp7xRSAdt5KT0SBLJkmcLpw+7pTXCff9ZxfDCfhw4Fqal1T/Nc33tIR54fWNMLt02PMpJAkR1udJAgGZPY6qEx3pSZSaNLOTSihKK8nNpPNZCUX5uwqI+O6V67Y5Gnl29M6YFFjFG03E7iGpVKd2KV5bc+76zsX3Ydg+HT2oP8dbne1MaAntcj763jePhiBb2eUj010uUInk0DcPRLxRg/xG3Md9+4Bh3XDSWG2aUMrN8CPe9VsWDb23ixsdWsXaHv4jEtDFF3Hf1pJhuWK7GLjqMGg6lW/H2qvC+72zsYPnXxhbH7RMs90fxabkxYUKb0sH5XPLP76l7KgMK+wXbnWZ7Xpn1PV0yYbhr+5yzhsZeZ5IBdcOMUp65bRZ39RIRwZ6OuqqUbsV2S2U7xuENePplVdmrkMajLa4VxahB/TSDqh0cPp6eO8pm9rhiag4cc/07sCf4dzfXM+esoTx03Tmx4zPNgFLdqc5Dg+NKryPTYLpfQHxVdUNcK1Gle/jqqIFce15pyv7ffmgGVHbR4LjSJ2hPMN3PpZHo6dTuqZGGxFRGAWElMcML+7XLaICuIroLjXEovYr2BNNtl4ZdA9DUHOb3K7fHHTd7XDE/vmw8z95+PrfPLk95XTUancPew6e23EpvJKXhEJE7RURNutIj8AbPSwfnM39JJUsraxKeM21METfPKsNgxTAeWVHNf36y23VMTgCevGVGTJJi0ZUTGJwfysYtKB6uPU9FSHsb6biqSoDVIrIOeBz4gzkVAiNKj8QZTC8dnB8LWtuBbqfLw+n/rtpz2HUdrytq8IBcllbWuM6ffdZQVz8HpXMZNagf/99F49rtplK6j5QrDmPM/wTGAUuAm4EtInK/iJyZ5bEpii+LrpzAu39zUVyqp1O4cGllDdc+ujKW418xojDpNfc1tXD3S5+5Vi7rdx7sxFErXnKCATUavZS0YhzRFUZd9KcVKAKej3bkU5Ruwatca79fu6ORe17ZQGvEEDFwPByhoH+I++dN5uvjiinICya85jOrTxqOg8dSS2Io8QzIDVJSmJfyOKfbce2ORh5evjVhEZ/Ss0jpqhKRH2Ep0e7HkkD/G2NMWEQCwBbgb7M7REXxZ3xJAZdNHM7ew8dd6Zyrqhti8hI2W/Y28dB151DTcDSpOOGG3Yc4+6dv0BKOaPC7neTlBJg75XQurSjhh0+u4cDRkwY4GBDyQwFunDEm5nbUHhi9j3RiHMXAt40xO5wbjTEREbkqO8NSTiVS5eL77fdONuNLCmLHzywfEqeiarudUmVhtUWgLaImoyPYvU3qDh/nULN71fZzhzKt/b3uPtjs22xL6bmkNBzGmHuS7NuYaJ+ipEOqp81E+521GSfCEV5cVxvr7PfGhj18ddRA1tceil3Hzr4a1F8zpbqKP1TV0eawwdPLilxGw/5ecwJCTjBAW5v2wOgtaAGg0i04Ja+TPW3aooLg3m93ebNbhD63ZicFeTmxokA4KWExqH9IJUO6gdycAM2Ovt9jh59cFToNf1vEcO300Zw+qL9WgPcS1HAoXc7CZR/zSjTNNZQTICcgtEVM3NPm0soal6hgICCx/dPGFMV1efO6oQ41h3nwe1P47iMfZv+mTjEK+uVw9EQrxljfS5snphQQOHLipFZVTgCumToq9t6rM3XN1FFqMHoRajiUdtMenaAHXt/oqo0It0a4YUYpI32eNr19wSeOKHTtv2bqKF5cVxubfEoH57saMVXtPsSL62pJp+ooKOnJjJzqDOyfw08un0DjsRYefGuTFUcyhssmDqc53EbFiEIK+of4ZOdBl9H/xtnDXd+ds6Vvsp4aSs9EDYfSLtqbCeMXnP52gqdNr4LtsROtnP3TN5heNpgnb5nhmnzerqqLc0cZYwXI80KBmLsrEWo0UjOof4gBeUEe/9OXXHL2MNeK4bYLz3R9h3e/9Jnr3OKC+PRc+3jNqOp9qOFQ2oWfcGA6/8NfXlHiikNcPWVkwvPsQOobG/ZQd7CZLfVHAVixZT9zf/0BP/1mBauqG9iyt8kVCLcRESaNHMg1U0fx0DubtUd4BznYHOZgcxiArfuOcPvscgr6h+Ky3VZVN1CYl0MwKlMfCorLTeWkvf+OlO5FDYfSLjLthWCTaf+NG2ZY9Rln//QN1/b1tYe49tEPiRgSuqJaI4afvbqBYdGn3WAAV5aP0jGWrdnJ3/7Z2bH2rC+uq+W5NTsJtxkMVmOsYEC491uTEhqD9v47UrqXrPXjEJHHgauAfcaYST77zwb+HZgK/J0x5lfR7eOBZxyHlgP3GGMeEpF7gR8C9dF9dxtjXk81Fu3HkR26shfCTUsqOyUzKhQUwuqX6lSmjBrIJ7WHEnb7G5Qf4rpzRyd8SNCeGj2XRP04smk4ZgNHgCcTGI5hwBhgLtBoGw7PMUFgFzDDGLMjajiO+B2bDDUc3U9nTA5zf/1BnEtKsGIY/XICHGxuTXmN/qEgzeHMOtMpJ8kJQCiY/G/oLb60uX12edY6PCrZIZHhyFo/DmPMCuBAkv37jDGrgXCSy1wMbPNWrSu9CzuQbgsOtleP6OU7L+D+eZPJCUjMDXLpxOE8detM/vby9CYkNRrpIVgriX6hAP1zAgQExg0dwNb7/5yfXjUx6bnXzyjl/nmTGeSRpU+nd4rSO+jpjZyuA572bLtTRD4VkceT9QkRkQUiskZE1tTX1yc6TOkC/AKgmWKL4I0vKeC+qycRDAiRiGHFFuu79abuKpkR8swE+blB1tce4ng4QnP0u9t5sJm1Oxq5IWoYvj6umNnjil3nzZ0ykvvnTeaGGaVcd+5o1z5vLxVQccPeSo8NjotILvAt4H84Nv8G+DnWSvjnwIPAD/zON8YsBhaD5arK6mCVpKQKgM799Qds2H2YSSMLefnOC+LO96b+fnvqKCLGCsDahqipOdnCVUmGAN87r5Sl0WJKgKMt8SuzlvDJrCc7aQES94BPlQih4oa9lx5rOIArgHXGmFgVkfO1iPwWeK07BqakhzOu8dStM61iPM8xzrjF+tpDzP31BzHjkUgET8BliCqrG1yxj0A0DVRJDwOs29GISOIMNbAqxIvyc3l4+VZXrGrRlRMSxi6S7dNU3N5LTzYc1+NxU4nICGOM7ZOYB2zo8lEpSbFFBitGFPLEyu2xp8l7rqrghXW1tLRagoT20+WG3e7OfPb7Sx98N1a3ERSrJkOMIRgMUDFyIGBNeNdMHcX3H690XUONRuZsrGsiKJbv2i9jOSBw6wVncN9rVe1aIdj/Lq6YNCK2UtFU3N5L1gyHiDwNzAGKRaQW+BkQAjDGPCIiJcAaoBCIiMhCYKIx5rCI5AOXArd5LvsLEZmCNWds99mvdAP2yqCpORwr7nt/y/5Ydk24NcIbG/b4Pl1OGlnoWi1MGlnI3F9/EDMaEK3qjj4Kh1sj3PPqBiIRQ04wQH3TCY6e0IB3JpyWG+SIjytqaEEe82eV8d6mfXy03R1zyAkITSda27VCWFpZE6skd7b4dVb+aypu7yJrhsMYc32K/XWAbzmpMeYYEPf4YYyZ3zmjUzoLp5/ai0SfYEM5Aa6YNILK6gbCbYagQ6zw5TsviItxjL07cWmOAVqjdRgtrRHedughKakR4GiCzLK5U07njovGsutgc5zhaItYMaX2rBC8iQtvbNgTW3VMG1OkBqMX0pNdVUovwOmnFs++BV8/KUkBWJYEE/19Em9AvKQwj9qDx7M36FMYE/vPSQrygq6OfNdMHcXzjgpw2/hfM3UU10wdlfEKwas55m35q/Q+1HAoHcLrp755VhlVew67fNkADy/fSmtbJOa6emFdLYDvJHTG0NNchiM/FOBEm4mT7lY6jgC3zxnLHReNjW2bNqaIpxfMiinXNh5rcX1Hma4QnJpj3n8XSu9EDYfSIdLxUy+trOGtqrrYisRuvPT8mp20RkxcoDVOFTccYYqno5/iz4SSAr6oa0oo/2EjWAHvVC6n8SUFcQKG7YlHONN3ld6PGg6lwyTzUzsDo07sOIWzFuPtqrpYzv/gAbkcOHqyX/UXe5uyMva+xqa9qY0GWN7Ca6eX+jZQ8quvAJU/V07S0yvHlV6ONzAaECu9NhiUWKgjGBC27G3ikRXVbG84xiMrqsn3lDJPLxvcVUPu1aTrzTMGTh/U33fy96uv6Izqf6XvoIZDySreQOiCr5czenA+rW0mNslFIG4icsY4powayJO3zOD+eZMpyAtme8inBMlcVHbcKuhwZfltU05d1FWlZJXxJQVcNnE4ew8f54ziATy/rpb9R1pcx7S2GY751BXYrK89xMJlH1NS2I8mrdlIiwklBTSH25gyehCvfrLbynoTuGTCcIYV5CXsugiJ41aZ1lyoXHrfJWuy6j0JlVXvHh54fSOL36+OdYFL1gcjkRS3khm2zLwzBtEdE7jqUPUNEsmq64pDyQpLK2tcLWJTNU9So5EegwfkMntcMeOGFzCzfAiLnv/EVWVfOjiff752imuS7o4iO9Wh6tuo4VCygsqcdz6zxxUzIxpvsCfhnQebXcfsbTreIyZo1aHq26jhUDqNpZU1PLO6huGF/eKqyCeUFLCxzp1SO27oANfTspKcFVv2W/UtAueOKWLRFROYXjbY1VLXzj7r7viC6lD1bTTGoXQIP4FDL3OnjGT+rDKu+c2HXTy6vk9QrHa4rcYwvWwwT94yg7U7Grl+8UrCbYZQUHh6wSymjSnqdmOi9D40xqF0OskEDp00HG1h2pgiCvKCGWdFpeoR0dsQ4LyyojgRwfbSZuBIS1ssZRng0fe20WILQbaZmLyLBquVzkLrOJR24wyAJpvc7VqOG2eMyfgzhhfkceOMUnKCXudX78QATcdbCaW4HwFOL+qf9nU/23WIh5dvZWllDX/c6FYMFjqnfa+i2OiKQ2k3fgKHK6sbOHgszI4Dx2LHffRlAzfMKI2pry5bs5ODx9Jr9ZoTECpGDsREarJyD93BxromZo8r5qMvD3A8wWotFBTqD6evENxm4MG3NhEQwZnAFgwI355qdS/QYLXSWajhUOLw69bmjGXY6rcA44cXMKywH7dfeGbM9THnl8td13tl/W7mzyqL7c9kmVt78Liv1lVvxxnQ9qOlzRBwLErSaYcbiWqm5wSESMQQCAj3XT2p3QV8ipIINRyKC79ubeNLCrjxsVUcD598On7fNfEd4qLxw2KTUengfLY3nFxxGIiJGPoF0IcMCNF4LHzKt3zNDwU45vgbiwgBY2KtXAPRKslErV0FSw7knqsq4qTQQZsmKZ2HGg7FhV+3tsZjLSkD4HZXt7U7Gvlwm9t/nhMQivJz+e37/llXxlhuFKdhOtUoKczjGxOGs7TypEvuG2cP43i4jT9t3U/EWCs18Vl6TCgp4B/mTdbVhNJlqOFQXPh1axtfUkBuToAT4UjCCu+V2xqY++sPKOgfcjVcEoGppYO499UNsUwfL4eaw/x87mT++Z1N7G9q8T2mLxEgftUwd8rpXFpREuu8FwoKt194JgCrtx8g3BpBRIg4shBseZF/mDfZdzXh53JUlM4ga3UcIvI4cBWwzxgzyWf/2cC/A1OBvzPG/MqxbzvQBLQBrXYesYgMBp4ByoDtwPeMMSnzGrWOIzNSxTjerKpzuaL8sBsFSUBoi7YgTURQ4MeXjWdm+RC+85sPkx4rnOwo91Rl7wyYjx12GoPzQ2zYdYicYIAbpp9MHPCrtbC3FeXnct9rVYRbIwSDAb4zbZRvPw2I74Ny/7zJajyUjOmOOo4ngF8DTybYfwD4ETA3wf6LjDHeCOIi4I/GmAdEZFH0/U86PlTFiV+3NucT7aUVJVz76EpaEwQlAsDXxhVTOjifpz+qSWkIggFhd1Q645KJw3n7872+x9qumj9u3BvL6ErlQusJDD0tl3qHIvDIgf1OBsc97jm/lYNz2/iSgphhgZNy9N5z/FyOajiUziJrdRzGmBVYxiHR/n3GmNVAenmZFlcDv4u+/h2JjY7SSazd0cjDy7eydsfJhd20MUXcd/UkcpxpPw5yQwEWXnIW3546itycQJz8iJPhhXkY4OmParj+t6sSGg2AwqgbrO7wCV5ev5u8DGo7JP1DO536Iy3MnTKSr48r5v55k6k54F6tvVlVB/j/rb1MG1MU6w9+42OrePCtTdz42Kq4c7x9ULzvFaUj9NQYhwHeEhEDPGqMWRzdPtwYswfAGLNHRIYluoCILAAWAJSW9q0nra6SjkgmjX3DjNLY0+/bVXV8sbeJs4cXcGlFCTPLh7Cprok3Nuzh5lllNJ1o5bk1O31jHHWHT8Reh1OsHg42u58xMqlC7+7q89c+3cMzt1nSH/f/389d+6aMHpSxDHkq9Vl7daExDiUb9FTD8TVjzO6oYXhbRL6IrmDSJmpsFoMV48jGILuDruxzkGpysl0o9hPw2h2NPPreNpZW7mBXtIPf+1v2c9nE4dz7rUksXrEtYWxEgJwUPTu6k5wAXPWVkby8fne7zo8Yw6rqBhY9/wlHPE2rxg0vyFiGPB31WT+Xo6J0Bj1ScsQYszv6ex/wEjA9umuviIwAiP7e1z0j7D66UjrCr11oInfK2h2NXLd4JW99vjdmNGze+nwv9766gWEFeb6fI0C/UMCVjdWTKCnI4xtnD+f1z6y4QUAsZd9kzJ0y0iUrkhMQZpYPYdv+eDXgovzcjFuz2uqzP75svOpOKV1Oj1txiMgAIGCMaYq+vgy4L7r7VeD7wAPR3690zyi7j67sc+CVxoaTQnk5wQBzzhpKcUEe10wdxarqhqSrhZY2ExP2ywmA7ZWyRQybe3ANR13TCeocsRdrdZT8meuV9btjcRUBvnvuaKaNKeLM4ngp+cZjLe2SIdeCPqW7yJrhEJGngTlAsYjUAj8DQgDGmEdEpARYAxQCERFZCEwEioGXxPq/LgdYaox5M3rZB4BnReQWoAb4brbG31Ppqj4HdkpuxYhCCvqHAPdqp6U1wlvRyfT5NTu591uT0m7/6gxlpBt76J8ToLmHZFC1GeJ6i3gxQFAEwRDKCcT0oh74zldd8vK5DuOvhkDpLWTNcBhjrk+xvw4Y5bPrMPDVBOc0ABd3fHS9m45OMKmC636yI/1ClpSFXyFguM3w0se1cUajMyXRE4kBZpugQLphl/45AU60RTDGKszzk/5YVd0Q050S4DvT/OswFKUn0+NcVUp2SRZctw3K0sodceeFWyM0HmvhqVtn8uK6Wp5Zs5PW6IwaCgrb9h2JO6c9RiORmF93RT8yidX/9JsVjC8p4IV1texvOsGG3YfiCvS8rsbCvBzmL6nUzCelV6GG4xQjUfaO06D4Tfh2PMVe7Xx76iheXGetMiaNHMhPX9nQKePrzPh4Kuny9hAKWpXw3isGA1ZxHsDza2tjhYnPr9kZ68AHblejs2uivbJT46H0BtRwnGIkCq47DYq3Vu7SicNdsungdpc9vHwrPbEF8Yot+xl6Wi7Hj3SO/tVlE4dTXjyAZWt2cuhY2LUKaovAi+tqGTmov6sepaXNxDLfnO7BaWOKmL+k0nV9re5WegtqOE4xEgXX/Zoy2X03Uk1mTvkP54ohFIhT1MgaiQLz9R6jcV5ZEVv2HYmb+NMhPzeYsK860c+fWT6EYFBibjyA9zbt41/e2Uy4zRCM9si4YUapr6CkovQG1HCcgiTSQ0qVrZUoqG6f+5PnP2GrI9U0XaPRPxSkOZy8CjxVxpbBEg88eKyF/QlWGAGBeeeMYsPuQzwXjdF4J3mb88qKqG86EStYFODdzfWuY0oK89h/5ARtEQg6ajamjh7k6inufN0aMdzzygbGlxRodbfSa8maOm5PQtVx288Dr2/kzao6powexJtVdQkr1r1qrDbpGIVRg/rRPxSMq29oD8k65c2dMpLXP9vjkj4JCpT71FYMHhDie9NG88TK7XErKZv7501mfEkBL66rtQxRxJCbE2BUUT5bfZIFnGO867LxsYp7RempJFLH7ZGV40rP4IHXN/LIimq2Nxzj5fW7ORGO1nCEIzz0zuZY9fjSyhp+8YcvfK/xZxXD6RdKLnR4pKWNkkH9O2XMfhO8ALfPLic/LydOL6vN4Fol2Rw4agWub55VxtfGFsfGL0DZkPyYTPm0MUWMHNSf1oiJJRycUeyuKrflVIIBISDu2g1F6Y2oq+oUJ1lNh63a6sRuQvT+lv1UfnmAH5xf5uv3H5wf4nvnjmbRlRNYu6OR+/6zik9qD/mOIQB8WZ/4CT0TvC6tsiH5PPi9KUwbU8TfJehdnmzNXbXnMAsvOSvWTCmUE4hdz8YbH7r9wjO5aPwwVwGlMwlBu/QpvR11VfVgsq2Cm0ow0V5x2MydMpIv9x91GYCSwjyXwu2g/BB/+2dnx9rI2uN/cV1thxsv5QYl9mTvxe7rcd/Vk/joywbe3VzPnLOG8tB157ju9/rfriLcGiEQsM4yxgpYJ5JLsVcWqb6LrlIsVpSupDsaOSkdoCtUcFMpsi66cgJ1h4+7JuG7X/rMZTi8Uui50SCxd/z3XFVBqJ3qt6MG9eOMoafF2tj+aNnH7Gpsdh3zlVEDufa8Uv71nc3UHznB5NMHxhmNVdUN3PvNCn6/cjs7G48xtbSIGeVDXDLwdmZTsoC1n5FQuRDlVEINRw8lU5ntTFm7o5FdB5vJCQZoa/MXTFy7ozEWEH+zqo61Oxq5ZuoonlldQ1vUXjQcc/fI2NfUwt0vfcZlE4e7dK0aj7Xw99+axP2vf86RNPponD6oH3sOHccYqD14nNqDx/nT1v0MK8hjZvkQ6g42u6q6c3MCruD8+tpDTPjpG/z0Kqua2zZimJP9vlds2c/gAZYybeOxFhZecpar34itBGy3bG1pjVjNq0Robcu+rL2i9FTUcPRQsqmC61wN5ASE66aX8m2HNIb9RL37YHOc8brjorFMGjkwYbzCprr+SMylFDHQ1Bzm//zXFo57cnSnlxWx9/AJdni64lWMHGgZDse2iCHW/W/2uGL+tHU/EWNVba+rORg3huZwJM6IeXln417fbDHn3yggQlvE6ptuBdetC2XDoCtKb0ANRw8lmyq4ztVMW8QwclB/l9G48bFVHA9HECAQgCAQCAhvVdVRlJ/LteeV8kntyad73xRYR6/WAFaQ2ZbhEGDMkHwWzD4TsNxC55QOYsPuw2AMP7igHCCmvutHzYFjPHv7+TEDtzRJ/KS6/gg5QcsIe4c5uiifTXub4lZ2zr8RGAIescNAmn0zFKUvooajB5MNv/nSyhreqqojINYE7pz8llbWsHjFttiqwGBJaUwoKWBjXROf1B7ik9rPuH/eZG6fXc6bVXVcXlHCpRUlPPDGRtZsb4xNzHYdQwArFbV/KEhOwHpytzOTNtU1udxLdiAa8K0JcXJ5RUns77N2RyPPrLbqKPz4cv9RJEF/9LycAMbE/y28K77Z44by9ud7MdF7+trYYpdrS1FOJdRwnEJ4i/ScGlSJCvgA9hx2d/R7ZnUNG+uaaGmN8NsPvuTzPYdZ7aiOdjJ51EA21jXxzsa95AQDXDt9dEwx9qF3NruOdWo1eaf5scNOY9LIQtbvPMjlFSUsunJCbN+muibKhuT71mNAdDXUZnzTbtc7XG62MQL/JlYrttTHDIkaDeVURg3HKcQbG/a43h8Pt8UmP+8+J3POGurqtZ0X1aUCy9W1wqG35ESAitMH8tmuQ0QMtLZFON3hFvNqNVWMKIy9/vbUUTy7ZmcsC2v7/iPMOGNwrIIdrKyvZAbPVgEJOgLaydR31+886HrvXfF1RQMtRekNqOE4hUgmqufdF8BaLVx7Xik3zChl+hlDYimqG3YfcukvJeLqKSOZNHJgXJDc5oYZpdQ0HGXx+9VEDDyyopo/btzL23fNYdqYIr577mierqzBYHUNdNaBPLKiOrrSOeD6zNMH9SMUDMRcaM4Vw6rqBoryc1m+aR/7Dh9nYP+Qy+hdXlGS9H405VZRLLQAsA/jV29gt4T1q1H44ZNreDsakA4K/DiBnpK3MNAmIPCV0wdysDkccyc9vHwrv/zDptgxOQHhmdtmxWITD72z2WWwAEoK8nj4L6YBVo9zb8fBZIwdOoAfXFCeUjDQ1uAa1D/kGq+iKCfRAsBTjEQFhDfMKE04qd5+4Zm87/DjJ8oYqtpz2Hf7gq+Xx02+M8uHkBOQWOA6Yk72p7hu8UrfgsC6phPc+Ngqnrp1JvdcVcFPX/4s7U58W+uPxlxXie7Ta/hunx0/bkVREqMihz0Iu+DMFg/sCH4FhKk+c9qYIu65qoLzxxZzz1UVAL7jGTIg1/dafgbl7ao6CvvlEBBcAn+PvrctaRW5PebGYy2+RmPc0AHxGx0ki9l4Nbj8NLkURUlM1lYcIvI4cBWwzxgzyWf/2cC/A1OBvzPG/Cq6fTTwJFCCVeS72BjzL9F99wI/BOzGCHcbY17P1j10JZ0tMZJOAaGfLIhdIV1Z3ZCwQvrL/f7ZS95GRN4n++llRfzkiglMG1PEXk+mlhNnauzbnkn99EH9uOOicdwwo5SllTU8/kE1x8Nt7DroLhZ0Btq9XF5R4hpXqtiGoihusrnieAK4PMn+A8CPgF95trcCdxljJgAzgTtEZKJj//82xkyJ/vQJowHprxDSZdqYIm6eVcbowfncPKvM1wh5P/ONDXtOvm8zhB37XlhXG1t9DCvs57rO4PyQqwbD5uX1u1zv9zWdiI3j2vMSxyD6hSwjNm1MUdwqpnzoabHPuWFGKe/cNYfrZ4yJu0ZB/1DC6y+6cgK3zy6nbEi+uqkUpR1kbcVhjFkhImVJ9u8D9onIn3u27wH2RF83ichG4HTg82yNtSfQ2RIjSytrYk/Vj6yopnTIgLiJvSg/l4AIGKvGYeU2K0gdlJMprG1tEYIB4dk1O2lrM4SCwr3fmsTyL/bSGoGcAPz2++fFGaa1Oxqpbzrh2uZ8snd2v/tiz2FXi9fmcIT7XqtifEkBFSMKU7ZXnVk+hFBQYr020ul3sejKCWowFKWd9OjgeNTwnANUOjbfKSI3AWuwVia+AQERWQAsACgt7fktOTtbYsTr43cW14E1sd/3WhWRqNEw5qRsiN3DAqxVySc7D8bkP1raDBt2H+KZ2873HaudybXrYLPLdXReWVHcRG0H6m9aUkm9J7OqpTXCi+tqeWFdLWDFRxZ83T9batqYIp5eMIsX1tUi4NLdcqLS54rSOfRYwyEipwEvAAuNMba/4jfAz7HUMH4OPAj8wO98Y8xiYDFY6bhZH3An0Jl1AslqNgCPFpOb2sZmVwW1twGSJBirM2YSDIjr2vPOGeU7zgde3+hbQBgQsUQFHfpWydxPqf52XSFTryinCj0yq0pEQlhG4yljzIv2dmPMXmNMmzEmAvwWmN5dY+wpJMrEumFGKffPm8zXxxW74g9OqfDcnIDvP4ABeUHX+29PHUVujtX+NTcnwLen+huBVdUNsfayzoypAFC1+5DvOP0ymoIC9109iWuin2u7znYfbG5XxtnSyhruenb9ybF1QgxJUU5letyKQ0QEWAJsNMb8s2ffiGgMBGAesKGrx9eTSPUU7a3Z8B5/86wyHvvgS0zEreP0k8vdLqVpY4p4+oczeXFdbdJCvC17m1z7A1giuRIQln1UQ8RAXsg9Tm+GE0AwaJmzVdUN3HNVBRt2H+L5tbU8/VENL6yrzWi14JUk8YoZKoqSOdlMx30amAMUi0gt8DMgBGCMeURESrDiFIVAREQWAhOBrwDzgc9EZH30cnba7S9EZAqWq2o7cFu2xt8byLTZk/N4uzmTHeNwSp0nKpx7YV1tLPbgN3l7tZ6GFebxjQnDeWb1zlgtRkvYPU477rFszU4ORptCtbZFuOeVDUSMITcnwDVTR8V0pjLtgeGN9Yxx9CBXFKV9ZDOr6voU++sAP5/HB8SLo9rnzO+EofUZMs3Eso+3jcf2Bqt5kl2Yl2xCTcdIeVcPc6ecTkH/EE5Zm0BA4sa56MoJXFpRwrWPfkhrBDDQFjVodg+N9maceWM9C2afqUZDUTpIj3NVKemTaSaWffxD72zmgy37M+otkY6RslcPdp+ORVdOYO2OxpixCohw39WTfD9nU10TdvvyCFaarzGWW2nSyIEASTOmEuFM+03UQ1xRlMxQkcNTEDvWYRuBdGMG7U1nTee8+UsqXSuDr44ayGUVJa5+35oNpShdi4ocKjHaWzPS3nThdM7zupRsOfeHl2/NKI6jKEr2UcNxitLTekuMLyngsonD2Xv4eMxoQOdX1CuK0nHUcCi+2P0quqJPhTdNeHxJQWxfZ1fUK4rScdRw9GHaG5Nwqtrav7NpPFJlbPW01ZGinOr0yMpxpePYT/EPvrWJGx9blVHFdVf3q7DdUUHR4jxF6Q2o4eijdESm3dufItv9Kmx31I8vG69ZU4rSC1BXVR8l06Cy063lV4+RbdQdpSi9B63j6MOkG+NQ5VhFUfzQOo5TkHSf4jPVvFIU5dRGYxyKBqcVRckIXXEoWiuhKEpGqOFQAA1OK4qSPuqqUhRFUTJCDYeiKIqSEWo4FEVRlIxQw6EoiqJkhBoORVEUJSOyZjhE5HER2SciGxLsP1tEVorICRH5a8++y0Vkk4hsFZFFju2DReRtEdkS/Z3VNKC1Oxp5ePnWjAQCFUVR+jrZXHE8AVyeZP8B4EfAr5wbRSQIPAxcAUwErheRidHdi4A/GmPGAX+Mvs8KHVGXVRRF6ctkzXAYY1ZgGYdE+/cZY1YDYc+u6cBWY0y1MaYFWAZcHd13NfC76OvfAXM7ddAOOqIuqyiK0pfpiTGO04Gdjve10W0Aw40xewCiv4cluoiILBCRNSKypr6+PuNBqAyHoiiKPz2xclx8tmUs4WuMWQwsBksdN9PzVYZDURTFn55oOGqB0Y73o4Dd0dd7RWSEMWaPiIwA9mVzICrDoSiKEk9PdFWtBsaJyBkikgtcB7wa3fcq8P3o6+8Dr3TD+BRFUU5psrbiEJGngTlAsYjUAj8DQgDGmEdEpARYAxQCERFZCEw0xhwWkTuBPwBB4HFjTFX0sg8Az4rILUAN8N1sjV9RFEXxJ2uGwxhzfYr9dVhuKL99rwOv+2xvAC7ulAEqiqIo7aInuqoURVGUHowaDkVRFCUj1HAoiqIoGSHGZFzi0OsQkXpgR5JDioH9XTScbNIX7kPvoefQF+5D76FjjDHGDPVuPCUMRypEZI0x5tzuHkdH6Qv3offQc+gL96H3kB3UVaUoiqJkhBoORVEUJSPUcFgs7u4BdBJ94T70HnoOfeE+9B6ygMY4FEVRlIzQFYeiKIqSEWo4FEVRlIzo84YjUf9yx34RkX+N7v9URKZ69gdF5GMRea3rRh03xnbfg4hsF5HPRGS9iKzp2pG7xtiRexgkIs+LyBcislFEZnXt6F3jbNd9iMj46Hdg/xyOCnt2OR38Lv5/EakSkQ0i8rSI9Ova0cfG0ZF7+Kvo+Ku66ztwjCXVfZwtIitF5ISI/HUm52YVY0yf/cFS190GlAO5wCdYCrzOY64E3sBqIDUTqPTs/zGwFHitN94DsB0o7s3fA1ab4Fujr3OBQb3xPjzXqcMqruo194DVifNLoH/0/bPAzb3sHiYBG4B8LJHXd4BxPfjf0zDgPOAfgb/O5Nxs/vT1FUey/uU2VwNPGotVwCCxmkQhIqOAPwce68pBe+jQPfQQ2n0PIlIIzAaWABhjWowxB7tw7E4667u4GNhmjEmmZpAtOnoPOUB/EcnBmnx30/V05B4mAKuMMceMMa3Ae8C8rhy8g5T3YYzZZ4xZDYQzPTeb9HXDkax/eTrHPAT8LRDJ0vjSoaP3YIC3RGStiCzI2iiT05F7KAfqgX+PugwfE5EB2RxsEjr6XdhcBzzd6aNLj3bfgzFmF/ArrF44e4BDxpi3sjjWRHTke9gAzBaRISKSj7UyGU33kM59ZOPcDtPXDUc6/ct9jxGRq4B9xpi1nT+sjGj3PUR/f80YMxW4ArhDRGZ35uDSpCP3kANMBX5jjDkHOAp0rT/3JB39LhCrq+W3gOc6cVyZ0JH/J4qwnmrPAEYCA0TkLzp5fOnQ7nswxmwE/gl4G3gTy8XT2rnDS5t07iMb53aYvm44kvUvT3XM14Bvich2rGXgN0TkP7I31IR05B4wxti/9wEvYS1xu5qO3EMtUGuMqYxufx7LkHQHHfouolwBrDPG7M3KCFPTkXu4BPjSGFNvjAkDLwLnZ3Gsiejo/xNLjDFTjTGzgQPAliyONRnp3Ec2zu04XRkM6uofrKfVaqwnJDuAVOE55s9xB9E+8rnOHLovON7uewAGAAWO1x8Cl/eme4juex8YH319L/DL3vZdOPYvA/5bd4y/E/49zQCqsGIbgpW08N970z1E9w2L/i4FvgCKeup34Tj2XtzB8bTPzcrYu+MP1sVfzpXAZqwMhL+LbrsduD36WoCHo/s/A871ucYcuslwdOQesOIDn0R/quxze9M9RPdNwepP/ynwcnf9j94J95EPNAADu2v8nXAPfx+dbDcAvwfyeuE9vA98Hv3/4uIe/l2UYK0uDgMHo68LE53bVT8qOaIoiqJkRF+PcSiKoiidjBoORVEUJSPUcCiKoigZoYZDURRFyQg1HIqiKEpGqOFQFEVRMkINh6IoipIRajgUpRsQkfOifSL6iciAaG+ISd09LkVJBy0AVJRuQkT+AegH9MfS4/pf3TwkRUkLNRyK0k1ElXJXA8eB840xbd08JEVJC3VVKUr3MRg4DSjAWnkoSq9AVxyK0k2IyKtYarlnACOMMXd285AUJS1yunsAinIqIiI3Aa3GmKUiEgQ+FJFvGGP+q7vHpiip0BWHoiiKkhEa41AURVEyQg2HoiiKkhFqOBRFUZSMUMOhKIqiZIQaDkVRFCUj1HAoiqIoGaGGQ1EURcmI/wdigQAhtuOG9QAAAABJRU5ErkJggg==\n", 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\n", 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TxJ3tGjLGUS8tzudfK3fyzdP6MbBLTtBxTDNmjcA47667vMFZy+/yhhhatf0gP355Gacc04HvnzUwpu/tfD1N3FkjMM57+21vcNaut70hhh6ek0dmWiqPf/1EstJrvuVkYzlfTxN31giMccyKbQd4a9UuLh7di7bZGUHHMUnAGoExDjlUUs4dM1fQIj2VG884Nug4JknYUUPGOGTa/E0s2bqfRy4ZQfuWtjVg4sMagXFehw5BJ4giMzYBl+Xv55G31zFhSBemjOgRk/esifP1NHFnjcA476WXgk4QxelND6iq/Ogfy8jJSuPer0a/AX1TOF9PE3f2HYExDlj4yT7W7DzE7ecOpnOO3XvYxJc1AuO8n/zEG5y15Cfe0AR/X7CZ7IxUzh/p3y6ho5yvp4k72zVknPf++0EniKKwaQF3Hyzhv2t2c87xXWN2GYm6OF9PE3e2RWBMgI6UVXLd3xZTVFbJdV88Jug4JklZIzAmQHe9voqPt+zn518awuCurYOOY5KUNQJjAvLe+kKeW7CFC07syVWn9gs6jkli9h2BcV7PnkEniCK74QFDIeXu11fTrU0W93zF38NFq3O+niburBEY5/3tb0EniGJswwPOW1fAqh0Hufv8oTG/qFw0ztfTxJ3tGjImAPPXFZKZlsKFo+zPcxM8awTGebfe6g3OWnyrN9TTzgMlvLF8B8N7to371gAkQD1N3Pm6a0hEzgUeAVKBaap6Xw3LjAMeBtKBQlX9op+ZTOJZsiToBFHsW9KgxX/y8jL2Hynn0csH+5MnCufraeLOt0YgIqnAo8BZQD6wUERmqeqqiGXaAo8B56rqFhHp7FceY1zw4aa9/HdtAd+bMJCRvdsFHccYwN9dQ2OA9aq6UVXLgBeAKdWWuQx4WVW3AKjqbh/zGBOosooQv3p1JR1aZvCt0+1wUeMOPxtBD2BrxPP88LRIA4F2IjJXRBaLyJU1vZGIXCsii0RkUUFBgU9xjfHXX9//hJXbD/LLLx8fl0tJGFNffq6NUsM0reHzRwHjgRbA+yLygarmVXmR6lRgKkBubm719zDN3MDY3rs99nKiByytqOSJdzZy6rEdmDysWxxC1c75epq487MR5AO9Ip73BLbXsEyhqhYBRSIyDxgO5GFM2NSpQSeI4qToAf/50TYKD5dy/+nDEKnpb6T4cb6eJu783DW0EBggIv1EJAO4BJhVbZlXgNNFJE1EsoGTgNU+ZjIm7rbsKeaBt9ZybOdWjBvYKeg4xnyOb1sEqlohIjcBb+IdPvq0qq4UkevD859Q1dUi8i9gGRDCO8R0hV+ZTGK69lpv7OxfsgvCAWvZMnjk7XUUlVbyt2tGBr41AAlQTxN3URuBiGQB5wGnA92BI8AK4HVVXVnXa1V1NjC72rQnqj2/H7i/YbFNMslzfUfhodoDFpVW8ObKnUw8oaszVxd1vp4m7upsBCJyJzAZmAssAHYDWXhH+9wXbhK3qeoyf2Mak5j+/L9NHC6t4IqT+wQdxZhaRdsiWKiqd9Yy76HwCWC9YxvJmOahuKyCp97dxPjBne3kMeO0OhuBqr4O3u4hVS2JnCciHcMngNlJYMbUYPrCrewrLueGM44NOooxdarvl8ULReTbqvoBgIhcAPwGbxeRMb4aMSLoBFG0G/G5SeWVIabN38SYvu0Z1cetrQHn62nirr6N4DLgaRGZi/eFcQfgTL9CGRPp4YeDThDFqIc/N+mfH21j2/4j3HX+8fHPE4Xz9TRxV69GoKrLReQe4FngEPAFVc33NZkxCWrr3mJ+/doqTujRhjMG2XUUjfvq1QhE5CmgPzAMb3fQqyLyR1V91M9wxgB8/eve2Nk7a70XDhi+U9mT8zZQVhHisctPdOK8geqcr6eJu/ruGloBXKOqCmwSkZOBh/yLZcxn8l3f9iz+LGBRaQUvLsrn/JHd6dU+O8BQtXO+nibu6rtr6PfVnh8AvuVLImMS2Mwl2yitCHHhqF7RFzbGEfW+1pCIPBw5NsZUFQopzy3YQp8O2Yzu69aRQsbUpSEXnftCeGy3kjSmBkfvN/C9CQOd/G7AmNrY3TGM8045JegEUXQ8hT1FpfzqtVWcPqAjU0Z0DzpRnZyvp4k7awTGeb/5TdAJohjxG259agEtM/bz4NeGO7814Hw9Tdz5eT8CY5LC26t3MX9dITedeSydc7KCjmNMg9kWgXHeBRd445deCjZHTQ6VlJP6v4v4c3/ltNPeCTpOvbhcTxOMhjSC58Ljv/sRxJja7NkTdILaTV+4laGhfQzp1pr01MTYwHa5niYY9V5zVfWByLExya4ypLywcCstM9No0yI96DjGNFrURiAirUVkYrVpI0RkkH+xjHHfI3PyWL/7MN3a2PcCJrHVZ4vgEPCwiLSPmPaYT3mMSQgFh0p5ct5GvnRCNzq0ygw6jjFNEvU7AlVVEXkO+DrwBxEZHJ681vd0xgDjxwed4PNmL99BaUWIG87oj+xxMGAdXKynCZZ415GLspBIL2Cmqo4SkfuAPFV92vd0NcjNzdVFixYF8dHGALBm50G+/Mf/MaRrDjNvPNX58waMARCRxaqaW9O8+l50bquIFIjIaOArwMhYBjQmkfzf2+vJSE3hsa+PsiZgmoWGHO82DfgzME9Vi33KY8znTJzoDS5Yu/MQs1fs4Gu5vejRtoU38b8TvSFBuFRP44aGNIJXgEpgqk9ZjKnRkSPe4IK7X19Fq4w0bj4z4ob0lUe8IUG4VE/jhnqfUKaq5cBwH7MY47T3NhQyf10hPzxnEO1aZgQdx5iYqXOLQET6RpkvItIzpomMcdTzH26lbXY63zqtX9BRjImpaFsE94tICt5uocVAAZAFHAucAYwHfgnYze9Ms7Z5TxFvrtjJJWN6kZWeGnQcY2KqzkagqheJyHHA5cA3ga7AEWA1MBu4R1VLfE9pktp55wWdAO6dvZrUFOHGM479/MweDgRsABfqadxS3/MIWgA3AKcBCswHHg+iCdh5BCbe5uUVcOXTH/K9CQO5ZcKAoOMY0yhNPo8A+AtwEPhD+PmlwF+BrzU9njHuUlV+OWsl/Tu15JrT7bsB0zzVtxEMUtXII4b+KyJL/QhkTHXjxnnjuXPj/9nz1hWyqbCIBy8aTsvMWn5c5ozzxhPmxitWkwRZT+Om+p5H8LGInHz0iYicBPwv2otE5FwRWSsi60Xkx3UsN1pEKkXkwnrmMcZ3oZBy/5tr6JSTyXnDuwUdxxjf1HeL4CTgShHZEn7eG1gtIsvxLkA3rPoLRCQVeBQ4C++oooUiMktVV9Ww3G+BNxv5bzDGF1Pnb2TFtoPcf+EwMtPsSCHTfNW3EZzbiPceA6xX1Y0AIvICMAVYVW25m4GXgNGN+AxjfLFlTzEPvZXH6QM6cuEoO1XGNG/1vejc5ka8dw9ga8TzfLwti0+JSA+8i9idSR2NQESuBa4F6N27dyOiGNMw097dCMDvLhxmF5YzzZ6fN6+v6aen+rGqDwO3q2plXT9sqjqV8DWOcnNzox/vapqVr8X52LQNBYf5+4ItTBnRnW5tWkR/Qe/EOngu3vU07vOzEeQDvSKe9wS2V1smF3gh3AQ6ApNEpEJVZ/qYyySYG26I7+dNX+htyN52dj3vxjowzgGbKN71NO7zsxEsBAaISD9gG3AJcFnkAqr66YHZIvIM8Jo1AVNdcfii59nZ/n9WSXklLy7ayjnHd/nsMtPRVIQDpsUhYAzEs54mMfjWCFS1QkRuwjsaKBV4WlVXisj14flP+PXZpnmZNMkbx+O499eW7WBfcTmXn9Sn/i+aGw6YIOcRxLOeJjH4uUWAqs7GuyZR5LQaG4CqXuVnFmOiKa8M8cQ7GxjYpRVj+3cIOo4xcdOQG9MY06w9MXcD63cf5rvjB9iRQiapWCMwBu+aQq8v38HwXm05b1j3oOMYE1fWCIwB3lixkzU7D9nJYyYp+fodgTGxcNVV/r5/KKTc98YaBnRuxSWje0V/QXXHXBXzTH7yu54m8VgjMM7z+xfXO3kFbNlbzO8uHEZ6aiM2kq0RmARnu4aM8woLvcEPB0vK+cGLS+nWJovJjf1uoKTQGxKEn/U0icm2CIzzLgxfnNyP494feiuPfcVlzLzxVFpkNPIKo++GAybIeQR+1tMkJtsiMEnrcGkFryzZxsSh3RjWs23QcYwJjDUCk7R+/++88FnEdkVbk9ysEZikVHi4lGff38zk4d0Ze2zHoOMYEyhrBCYp3f+vtYRU+e6ZxwYdxZjA2ZfFxnnf+U5s32/l9gNMX7SVq0/ty4AuOU1/wwExDuizWNfTJD5rBMZ5F18cu/dSVR56K4+WGancfOaA2LxpnxgGjINY1tM0D7ZryDhv61ZviIUn523k7TW7+d5ZA2nfMiM2b1q01RsSRCzraZoH2yIwzrviCm/c1OPeNxUW8eBbaznruC5867R+0V9QX++HAybIeQSxqqdpPmyLwCSFnQdK+OYzC8nOSOPOLx9vl5k2JoI1AtPslVeGuPn5j9hx4Ah/ujK3/regNCZJ2K4h0+w9MmcdCz/Zx+8vHs6Yfu2DjmOMc2yLwDRrebsO8cQ7G/jqiT34yki714AxNbEtAuO8225r3OtUlZ/PXEHLzDR+NmlIbENFGtzIgAFpbD1N82WNwDhv8uTGve5fK3ayYNNe7ppyPB1aZcY2VKSejQwYkMbW0zRftmvIOG/tWm9oiK17i7n9pWUM6NyKi3Ibcdexhji41hsSRGPqaZo32yIwzrvuOm9c3+Pej5RVcv3fFgMw7Ru5ZKU38j4D9fVhOGCCnEfQ0Hqa5s8agWl2npy3gZXbDzLtylz6dGgZdBxjnGe7hkyzsudwKX+at5GJQ7sy4bguQccxJiFYIzDNyhPvbKCorJJbJsTognLGJAFrBKbZeG7BFv40fxOXjO7F4K6tg45jTMKw7wiM8+64I/oyOw+UcO/s1Yzp2567zh/qf6hIQ+sR0CH1qadJLtYIjPMmTKh7vqry69dWUhEKcd8FJ5CeGucN3a5RAjomWj1N8rFdQ8Z5S5Z4Q23eXLmT2ct3cu0X+nNMp1bxivWZfUu8IUFEq6dJPr5uEYjIucAjQCowTVXvqzb/cuD28NPDwHdUdamfmUziufVWb1zTce+bCov4ycvLGdw1h5uDuv/w4lu9cYKcR1BXPU1y8m2LQERSgUeBicBxwKUicly1xTYBX1TVYcBdwFS/8pjmp6wixHfCJ4794dKR8d8lZEwz4edPzhhgvapuVNUy4AVgSuQCqvqequ4LP/0AsMtDmnp78N9rWbPzEL+9YBgDY3ETemOSlJ+NoAcQeWfU/PC02nwLeKOmGSJyrYgsEpFFBQUFMYxoEtW76wqZOm8jX8vtydnHdw06jjEJzc9GUNO9ALXGBUXOwGsEt9c0X1WnqmququZ26tQphhFNIiouq+D2l5bRp302v5h8fNBxjEl4fn5ZnA9EXvaxJ7C9+kIiMgyYBkxU1T0+5jEJ6t57qz7/2web2bb/CM9cPZpWmQ4cAT383ujLOKR6PY3x86doITBARPoB24BLgMsiFxCR3sDLwBWqmudjFpPAxo797PGugyX8af4mRvdtxxcHOrJ12Gls9GUcMjax4po48K0RqGqFiNwEvIl3+OjTqrpSRK4Pz38C+AXQAXhMRAAqVDXXr0wmMb33njfOHRPiumcXU1xawU8mDSG8zgSvIBwwQRrC0XpaQzBHiWqNu+2dlZubq4sWLQo6homjceOgMhSi62UfsPCTffzh0pF8eXj3oGN9Zs44b5wg5xGMG+eN7TyC5CIii2v7Q9uBHazG1C2kyqrtB9m2eR/3ffUEt5qAMc2ANQLjvPx9xRSVVfLsZScy6YRuQccxptmxRmCcNmPRVrbvz6Zz60wmndAh6DjGNEt2Tr5x1uY9Rfx85gpaZqbSz245aYxvbIvAOGva/E1UhJTnn86ic44jRwjVZNTDQSdokIcfDjqBcY01AuOklxbn8+wHm7l0TC/OPj0r6Dh1azci6AQNMmJE0AmMa2zXkHHOjIVbue3FpYzq046ffek45syBOXOCTlWHnXO8IUE4X08Td7ZFYJwyfeEWbn9pOWP7d2DaN3LJzkjj7ru9ec7eWWtFOGCC3KnM+XqauLNGYJygqjz17ibumb2aE3u3/bQJGGP8Zz9pJnCqyu//nccf/rOeU4/twCOXjLQmYEwc2U+bCVRlSPnJy8uYsSifi0b15L4LhpGa4vARQsY0Q9YITGDKK0P88MWlzFyynctO6s095w9150JyxiQRawQmEO/kFXDP66vI23WY744fwK3jB9TaBJ58Ms7hGmqM6wGrcr6eJu6sEZi4e3v1Lr7910V0bJXJ/106kslRLiI3aFCcgjVWa9cDVuV8PU3cWSMwcVNRGeLXr63ir+9vZkDnVrx4/Sm0zc6I+rpXX/XGkyf7HLCx8sMBe7oasCrn62nizhqBiYv9xWX8+rVVvPzRNs4c3JkHLhperyYA8OCD3tjZX1xrwgETpBE4X08Td9YIjO8+KSzi8mkL2H7gCN8dP4DvnzUw6EjGmAjWCIxvVJV/fryNO2auQIDnrjmZU/rbpaSNcY01AuOLA8Xl/Oilpby5che5fdrxuwuHcUynVkHHMsbUwBqBiami0gpmLNrKA2+upaiskp9MHMw1px9jJ4kZ4zBrBCZm/rViJ3fMXEHh4VL6d2rJzWcO4PyRPZr8vs8+G4NwfjrF9YBVOV9PE3fWCEyTqCr/WbObv7y/mXl5BfRs14I/XzWacYM6xews4V69YvI2/mnpesCqnK+niTtrBKZRdh4o4U/zN/KvFTvZtv8InXMyuWX8AG44oz+Zaakx/azp073xxRfH9G1jZ3M4YB9XA1blfD1N3FkjMA2ydW8xv3tzLa8v205IoWe7FtzxpSFceUpfMtL8uc/R4497Y2d/ca0LB0yQRuB8PU3cWSMwUa3YdoA5q3cxf10hH23ZhwCTh3fntrMG0btDdtDxjDFNZI3A1Gr3oRKmvrORae9uAmB4r7bcdMaxXDy6Fz3bWQMwprmwRmCq2FhwmJlLtvPfNbtZvu0A4P31//PzhtA5x/GbyBtjGsUaQZJTVZbmH+A/a3bzztrdLM33fvmP6tOOH54ziPFDOjO4a+uAUxpj/GSNIAkVHi7l9WU7mL+ukOXb9rPrYCkAx3dvzS3jB3DhqJ70au/Orp9//CPoBFGc5nrAqpyvp4k7awTNVEVliNU7DrG+4BBb9hxh2/5iCg6VsuNACWt2HgKgb4dsxvbvyMnHtGf8kC50bJUZcOqadewYdIIoslwPWJXz9TRxZ40gwakq2w+U8MGGPeTtOsSGgiI2FR5my95iyiv10+U652TSuXUm3dpkcc7xXTn7+C4c371NgMnr75lnvPFVVwWZog4bn/HGx1wVZIp6c76eJu58bQQici7wCJAKTFPV+6rNl/D8SUAxcJWqfuRnpkRzpKySbfuL2Vdczu6DpXyyp4gte4r5ZE8ROw6UsPtQCSXlIQAy0lLo2yGbAZ1zOPv4rvTr2JL+nVpxfPfWZKXH9iSveHL+F5c1ApPgfGsEIpIKPAqcBeQDC0VklqquilhsIjAgPJwEPB4eNyuVIaW8MhQevMf7isvYc7iMfcVl7CsqY29ROXuLStl5sIR9ReUcLCnnwJFydh4sQbXq+3XKyaRvh2xG9m5L55xMerXPJrdPewZ1zbGLuxljGszPLYIxwHpV3QggIi8AU4DIRjAF+KuqKvCBiLQVkW6quiPWYd7JK+Cu11ahqiigyqePQ6rh596ynz7HG4cU4Oi0yOU/m/a59/JeQkUoFH59dDlZaXRrk0X7lhn0bp9NTlY6Pdu14JhOLWnfMoMOLTPp0yGblpm2R88YEzt+/kbpAWyNeJ7P5//ar2mZHkCVRiAi1wLXAvTu3btRYVplpjGwSysEQQREBAFSIh4jkBJ+LAKCkJLizfCeh+eHH8unj71x9fcShPRUIT01hbRUISM1hbQUIT0thdZZ6XTOyaR9ywzaZmfQNjud9FR/LtFgjDF18bMR1LSPovrfxvVZBlWdCkwFyM3Nreff11WN6tOOUX1GNealxhjTrPnZCPKByAve9gS2N2IZk+Rmzw46QRTjXA9YlfP1NHHn576IhcAAEeknIhnAJcCsasvMAq4Uz8nAAT++HzCJLTvbG5yVlu0NCcL5epq4822LQFUrROQm4E28w0efVtWVInJ9eP4TwGy8Q0fX4x0+erVfeUzieuwxb3zDDcHmqFVeOOBAVwNW5Xw9TdyJVj820XG5ubm6aNGioGOYOBo3zhvPnRtkijrMGeeNJ8wNMkW9OV9P4wsRWayquTXNs8NUjDEmyVkjMMaYJGeNwBhjkpw1AmOMSXIJ92WxiBQAmxvx0o5AYYzj+CWRsoLl9Vsi5U2krJBcefuoaqeaZiRcI2gsEVlU2zfmrkmkrGB5/ZZIeRMpK1jeo2zXkDHGJDlrBMYYk+SSqRFMDTpAAyRSVrC8fkukvImUFSwvkETfERhjjKlZMm0RGGOMqYE1AmOMSXIJ1whE5GkR2S0iK2qZP1hE3heRUhH5QbV554rIWhFZLyI/jpjeXkT+LSLrwuN2QecVkV4i8l8RWS0iK0Xkloh5d4rINhFZEh4mBZ03PO8TEVkezrQoYrqL9R0UUb8lInJQRG4Nz/OlvvXIermILAsP74nI8Ih5Lq67NeZ1eN2tq75xXXebUFt/1lvvvruJMwBfAE4EVtQyvzMwGrgH+EHE9FRgA3AMkAEsBY4Lz/sd8OPw4x8Dv3UgbzfgxPDjHCAvIu+dkcu6UN/wvE+AjjW8xrn6VlsmFdiJd8KNb/WtR9axQLvw44nAAsfX3dryurru1pg3iHW3KVn9WG8TbotAVecBe+uYv1tVFwLl1WaNAdar6kZVLQNeAKaE500B/hJ+/Bfg/KDzquoOVf0o/PgQsBrvfs6+akJ96+JcfasZD2xQ1cacsV5v9cj6nqruCz/9AO+OfeDuultjXofX3drqWxdf6hujrDFbbxOuETRBD2BrxPN8Pls5u2j4zmjhcec4Z6uTiPQFRgILIibfFN5sfDqWuwOaSIG3RGSxiFwbMd3p+uLdPe/5atOCru+3gDfCjxNh3Y3M+ymH193qeV1ed2usLTFcb5OpEUgN05w/dlZEWgEvAbeq6sHw5MeB/sAIYAfwYDDpPudUVT0Rb1P2RhH5QtCBohHvNqpfBl6MmBxofUXkDLwf/tuPTqphMWfW3RryHp3u5LpbS14n1906ahvT9TaZGkE+0CvieU9ge/jxLhHpBhAe745zthqJSDreD9LfVfXlo9NVdZeqVqpqCPgT3q6DwKnq9vB4N/BPPsvlZH3DJgIfqequoxOCrK+IDAOmAVNUdU94srPrbi15nV13a8vr4rpbW9awmK63ydQIFgIDRKRfuJteAswKz5sFfCP8+BvAKwHkq0JEBHgKWK2qD1Wb1y3i6VeAGo88iCcRaSkiOUcfA2fzWS7n6hvhUqptXgdVXxHpDbwMXKGqeRGznFx3a8vr6rpbR17n1t061oWjYrvexuIb8HgO4X/8Drwv//LxNpuuB64Pz+8ann4Q2B9+3Do8bxLeEQwbgJ9FvGcH4G1gXXjcPui8wGl4m//LgCXhYVL4Nc8Cy8PzZgHdHMh7DN7RLEuBla7XNzwvG9gDtKn2nr7Utx5ZpwH7Iv6/F0W81sV1t8a8Dq+7teWN+7rbxHUh5uutXWLCGGOSXDLtGjLGGFMDawTGGJPkrBEYY0ySs0ZgjDFJzhqBMcYkOWsExhiT5KwRGGNMkrNGYEwTicjo8IW+ssJnqa4UkaFB5zKmvuyEMmNiQETuBrKAFkC+qv4m4EjG1Js1AmNiIHwNoIVACTBWVSsDjmRMvdmuIWNioz3QCu+OXFkBZzGmQWyLwJgYEJFZeHcO64d3sa+bAo5kTL2lBR3AmEQnIlcCFar6nIikAu+JyJmq+p+gsxlTH7ZFYIwxSc6+IzDGmCRnjcAYY5KcNQJjjEly1giMMSbJWSMwxpgkZ43AGGOSnDUCY4xJcv8PK0XuOqavBaMAAAAASUVORK5CYII=\n", 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