{ "cells": [ { "cell_type": "code", "execution_count": 74, "metadata": { "collapsed": false }, "outputs": [], "source": [ "\n", "import numpy,scipy,scipy.ndimage,zlib,pylab\n", "from pylab import imread,imshow,savefig\n", "from scipy import linalg,ndimage\n", "from scipy.ndimage import interpolation,filters,morphology,measurements,fourier\n", "from scipy.linalg import norm\n", "from scipy.fftpack import fft,ifft,fft2,ifft2\n", "figsize(8,8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Sample Data for Line Finding" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We're going to illustrate the Hough transform for the problem of finding lines in a collection of points.\n", "\n", "Hough transforms can also be used for more general object recognition problems (see below)." ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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DAGCIEAMAYIgQAwBgiBADAGAow3oAYLzLzs6OeTwwMKBIJGI0DYBkI8SAoVmzZumTTz6J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\n0P8DC08BcoOjZ/AAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "imshow(imread(\"points.png\"))" ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": false }, "outputs": [], "source": [ "image = transpose(imread(\"points.png\")[::-1,:,0])\n", "labels,n = measurements.label(image)\n", "points = array(measurements.center_of_mass(image,labels,range(1,n)))" ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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CC3r55Zd17tw5NTQ0qKurSxs3btTJkycVDoe1Zs0ahUIhzZp143sCzg0OAEg303pu8Kyv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\niDUAAIYj1gAAGO7/AVvHGFkPnU9+AAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(points[:,0],points[:,1],'.')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Hough Transform for Lines" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The original Hough transform used the following parameterization:\n", "\n", "$$ y = mx + b $$\n", "\n", "The set of parameters corresponding to a point (x,y) is therefore:\n", "\n", "$$ m = \\frac{y-b}{x} $$" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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su3z5cm677TaWL1/OunXrmDFjBitWrKBDB82SEhHZs3UCpmI2FffLk65MgXQlrCV8Pu7L\ngMa6kcN+AGYfBE4EanC/oCC1aDYQH3nkkaxevXq37e6+27Y77riD+fPnU1ZWRnV1NUOHDqWmpoYp\nU6YUpLIiIpKUEzCrxv0/kq5IwZhdC+yD+w3A35vY7yqgEgD3XwEfpZDJS3K+RnzDDTdw8803M3Hi\nRL797W/Tu3dv1q9fXyfoVlVVsW7dukaOsCLjdt/4T0REWp95mHWJ6SvbQtKO3ph9MwbgtwhTrzKn\nKI3E7DO199y/D7wa770JvJNFGa9mPKdpOfUZX3DBBaxatYply5YxcOBALrnkkkb3NbNGHhme8U9B\nWESk9XoE9/vINrC0bpWYfTKO+F4JrCGdrOMozK7EbCbuP6j9B/+I+60BtmRZTl/qxrnG5dQiHjBg\nQO3t888/n5NOOgmAyspK1qxZU/vY2rVrqayszKUIERFpFU4kBKAnk65IAQzBbDrufwWWxm1nYlYe\nb2/G/UHgtYzHiy+nFvGGDRtqb//2t7+tHVE9Z84cbr31VrZt28aqVatYuXIlkye35XUpRUTasuMI\n05Wy6Ypt7UZgNgX3LZgNxuwszM4CwH1j/PcU8CfgiZLWrNkW8fz583nggQfYvHkzgwYN4oorruD+\n++9n2bJlmBn7778/3/ve9wAYPXo08+bNY/To0XTq1Ikbb7yxia5pERFpvaZhVon7X4B/JV2ZPA2P\no50rgb8A+2Y89ivg5URqlWLe0PDnYhdqRujuEBGR1qWMMFf4GNx/ATQ24HZPMJIJ43uydet0nn9h\nKPAisB73mxKoy10NzjYCZdYSEZE6umH24ThX+I2kK9NCZcCg2ntm/49TT92bVau2svL5uwmt39ZH\nLWIREYk6At3JfmRwa9EZ6AZUYHYZ0IuQgONt3L8LPJRk5QjDse5stEWslFciIhLtj9l3SGWR2nNM\nxewnmF0Ys12F6Ugh+cgjidYs2LfJR9U1LSIihOvCp+D+RaDkHaUtZvYpYEK8txT3TwD9MVuI++cJ\nq0K9DuxKqorRqLhu8/82uocCsYhIu3cYZofg/hPglaQr04hemH2l9l4Yzf2XeO9NoCdmc2K2rLUk\nH4CnxYUkNsTkIY1TIBYRafdW474FWJV0ReqZgNmMeHs77r/PeOxZ0pm+xmB2BO73ErJgJW0GZuWx\nvq8DLzS5twKxiEi7dgjQhdZxLTXlKMyGAe/hvjJuew94sIF9D8JsLO7PAI+VrIaNmwH0w30psDyr\nZygQi4i0WxMwG4H7iwnXoxMwm1RIMusJGO6raPoEYRwwGvc1wMPFrmQzZgNdMeuF++NkG4RBgVhE\npJ06ELPxuP8D+FsC5Q8gvRhCR8xGEaZPEbt0n2nm+aNi/V8EHihaLZvXBZiE2WigM+6/ISwmkT0F\nYhGRducAzGbg/hCl784tB/YhLMBwVNz2Pu7fJPslFqsxOzZ2/ybZpd4NGB0HiX2DXOdfKxCLiLQz\nZufG9JXZd5/mpy+p1q7ZScBhwN9w/0ILjtEB6BePcQ7ud1DqxRnSugE9gUGYzcf90ryOpkAsItKu\ndMT9q0Uuw8jMF2X2H6TWnQ/r+56Xw/H6Yvb9eIzP09Lu38IxYDpm5wMr8g7CoEAsItKOdMXsOtyv\npLiLORyM2UW199y/TjpvdS5LKu6P2edwPyfefyvP+uXjdMz2jnXZUZAjKhCLiLQLAzC7FPfrKF7S\njhPivN9VMdinrCH3oDUWsxNx/zZhTm5ywmIYO3BfXNC6KBCLiLR5gzE7FfdfAv8EdhbsyGYfB/oD\n4P487rcSgtTzBTj6RMwOxv13wOoCHC93IQi/DdRQ6BMZBWIRkTZtOGaH4/4EsKQAx6vEbE7tPff1\nhBYvhCDfdBap7B2K2bA4J7e5qUzF0hmzs4Ey3DcR3r/1BS9FgVhEpE3bgfs68p9rOxIYSxiE9XbG\n9vsJuZ4LaTJmQ2JWrccLfOxs9QKOIywesY0w13pDUUpSIBYRabMGE6ba3Jvj8ycSAhKEa8wDcV+D\n+80FqV3DJmA2CvfnCN3ASdgHmIJZv7hgw7ailqZALCLSJlUCUwjXg5/N8jl7kc52BWZHEoISuP81\nXv8tppFx8YaHgKVFLqsh5cBAwknHUNyvL0mpCsQiIm1OX8xm4/468Nss9u8B9AYGYnZu7Vb3ayjN\nICmLZX8Y95+TzApKvYFjMDsG+EccXV4aCsQiIm1KF8zOw/1p4I9N7pdOunFMHJT0Au4XFL2GaR1i\nPbpidjXuX6a485sb0xmzM3DfUuLXHygQi4i0IWaXxXV5m17IwexSwupFAH/G/aPAruJWbjejMbsM\neBf3i0lqnrDZhbivAO5JpHwFYhGRNsT9BkLmqe31HinH7OsZ+90KpAZdbSW3jFf5OBSzo2OKSCcE\n4dKeCJhdBfTG/dfAoxR7UFZjFIhFRNoIs0twv410UD0Cs1nx9taY5znleZJLFXlkXAf5N6TnIJdS\nr5hl7C7gXWAV4WQkGQrEIiJ7vO7xuvByQnA9AbOhwGbcH4z7vE0yI5HrOwazStz/RmGyb7VUOWan\nxfflccI84WQpEIuI7NH6YnYqMAOz94CTcN+J+0bgOeCpZKtXx9HAwDiQLNspVYU0CLOjcF8D/CmB\n8humQCwiskfaDxiDWX9gNmGgUSdCAo67gX8lWLeGHIbZ/jFl5dMlLns4MATYC/f3gTtLXH7TFIhF\nRPYo+xMWWRiE2eHAvsDDuN9IGPTUGo3HbFIczV3qOcIHYDYJOAD3fwK3l7j85ikQi4i0akZIVRnm\n/JrNBEYDT+H+B8wOwv3aBOvXlI6ElZ9Ox/37wIslLn8gZrNwfx74eYnLzp4CsYhIq9OZkCMaQoKO\nLxPSTxID2iJgJmZj4zq9rU0Zob57Y3YF7hcBr5WobCOVH9vsfNz/AjxUorJzo0AsItLqHIbZZ+Pt\n93D/BOkVj3ZhdibQq2S5kFvuYMy+BLyG+7nsPqe5mLpidiPhevCVwJMlLDs3CsQiIq3GfMymA8ti\n8IVw3XcLqeu/Zufg/g7wC8KCDq3NNMwmxPrvorRBuCJmFvs3wrSk0icJyYUCsYhIgsz+jbDgALjX\n4P5fhPV9NzW4v/s9hAxQW0pUw5Y4Li6V+Esaq3/xDMVsXswstpY9IQCnKBCLiJTUUMxOqb3nvoR0\nasXngfVNPPd0wqjjUk//ycYHCN3lf6W02bKmxOUatyQ0Krs5g+MJwl2N7qFALCJSEodgNh7YhvvK\njO0PE9IsNufU+P+bBa9Z/o4DegJPUNpsWam5ySuBV4DHSlh2NoZhdli9v/fuFIhFRIrmWEKAArPu\ngOG+Cbi3BcfoCMzGrBfu/0cyywQ25VjMBsSUlU0HnMKajNkBcdWkJSUsNxvjCPO9u+L+Ck0vR6lA\nLCJSQHsDY2vvmY0hPe3or8AjLTxeN0LAGYX7ImBzYapZEB0JdRuD+++A1SUs+yDMxuH+BKEV3lqM\nB3pgdgAhleczNBeEQYFYRKQA+gIDCKN2j6/dGub45jNoqUdMSPENsuu+LpXOwAjMToxTqEoxMKsT\nMBQwzGbj/gfgmRKU25xOwDCAuNJVP9wXk15iMrsjiIhIi/UhJK4AOCoG4H/i/oUCHb8zsBP3rxTo\neIXQlZAsox9mF+B+CaU5QegEVGP2eYB4YrKqBOU2p4xQr0uB3OulQCwikhUjlWYSUtOOhsd7v8X9\nvAKXNQqzj+P+yQIeNx8GTMXsM8C6EtbLgCGYfTG+x60hn3bqszAEs8/n/bdXIBYRycpgzK6svRfy\nO6+O994rcFmHYTYd9y8V+Lj5OCGOUD6H0iYSORizU3D/HK0jCANMx+xs4EXcL877aArEIiJNmorZ\n6cArMWViyloKH4Ah/MgPx/1HtJ6kHadi1h332wnZqkrhBMxmAKtw/19aw7Qtsw8DE4Gn42fhPQpR\nLwViEZHdzMdsSLy9FvdbCbmeiz1HdjZm/WNiitYyTek0ANzvp3TZsuYQckXfSgj8a0tUbsPMPkEY\nhPUMcCvhfVhdsOMrEIuIsDdmH6q95/5ynBoD8BKlG527BvcXgRdKVF5zUklEHqN02bJOIgwKW0Ly\n70NnzM7GfQPhc/AkxThBUiAWkXZqBCHxAoSBN29nPPY3mk41WQxTCdmhSpkUoyknYrYX7g8SglAx\ndSIE4E6Ydcb97yQbhMuBowiDst4H7ie/LuheTT6qQCwi7cyBhDm/AzAbGLe9jvtPkqsSEzEbGVdV\nSlpn4AjMqnH/FbCxyOXtBRyO2SCgI+6/pviBvzHVwAFAT8yqgPdx/yHpXOC52AeYQlgtq2EdGn0E\nWLNmDdOmTWPMmDEceOCBXH99WPvytddeY+bMmQwfPpxZs2bxxhtv1D7n6quvZtiwYYwcOZJ7721J\nGjcRkWLoBBxEyHo0HrMjMJtGCL7Xxn8/SbB+ozE7EvdHgWUJ1gNCUDwYs2m430zxg3APQg7uKbh/\nL45ETyII70/4fEzBbBpm+8TPxY3kH4QnYja0yb3M3RsdD75x40Y2btzI+PHj2bp1K4cccgiLFy/m\nxz/+Mf369eMLX/gC11xzDa+//joLFy5k+fLlfOhDH2LJkiWsW7eOGTNmsGLFCjp0qBvvzQw4MY8X\nJyLSlO6EhBvhdpj7Gn6H3H9Aa0qLaPZN3G8C/pVwTboBB2I2N67nW+ypQqmgPx33K4pcVlMGxPEB\nI3C/G7ijgMeegtmhuF8H3EVj4bbJrumKigoqKioA6NGjB6NGjWLdunXceeedPPDAAwAsWLCAY445\nhoULF3LHHXcwf/58ysrKqK6uZujQodTU1DBlypQCvjARkcZ0JuRAPhqzj8Ztb8ZF6ks59zUbRlgU\n4KskOz+2jBAKDo4pK4s9dzlV3tS4MlESQTi89wBmF+P+G+A7BS6jE/BEvN7d/J5ZWb16NUuXLuXQ\nQw9l06ZNlJeXA1BeXs6mTWFI+/r16+sE3aqqKtatay1D8EWkrTM7F5gG/AX3jxJ+cJ3WF4QhjNT+\nH9wvJNnFHObG9ZGXliQomp1FWDbxEdy/VfTyGtYHsxsJq2H9O/BcEco4EbN9Y/d207IKxFu3bmXu\n3Llcd9119OzZs85jZha7mhvW+GMrMm73jf9ERFqiDLOrCF3R4P574FJgK9AaBj41Zj/MPh1bn6VK\nkLG7MDXnfdwvJeSMLkaCkszyPhaXBbyU8Pcpbnm7OwizjwNvxZzgTpgTXOgTtTOAlbjfQDa5uJsN\nxNu3b2fu3Ll85CMf4eSTTwZCK3jjxo1UVFSwYcMGBgwYAEBlZSVr1qTnmq1du5bKyspGjjy8ke0i\nIk0Zh9lp8fbOOLI3NaDmJeDVZKqVtZGYfSAOhnqJpLqlzRbg/gbwKMUflJUKwuuAGsI0rVKaidmR\nwPo4RmA7xRsUNp/wedwIDMrYvqLh3Wlm1LS7c9555zF69Gg++9nP1m6fM2cOixYtAmDRokW1AXrO\nnDnceuutbNu2jVWrVrFy5UomT56c66sREclwNGYXYXYw7g/W/gsDr5bGf609CI/DbCruDxGShCQV\nhD+C+5uEoFjMINw9/s0uikkxllD6IDwL6Bs/L48QPifFStByJqGV/ygtmYfe5Kjphx56iKOOOopx\n48bVdjFfffXVTJ48mXnz5vHSSy9RXV3N7bffTu/evQG46qqr+NGPfkSnTp247rrrmD179u6FatS0\niGTlFMxS3c47gV3Ai0DzA2Bap6FABfBQQuV3AuYSrp3/heKmrOyL2fG4b4/3/0RpT5TmYNYrfm6W\nUZzrwJnmEgai/ZWGs281Pmq6yUBcLArEItKwAcAhtfdCkodwBS20Ip9KpFaFMYwwqvvZhMrvTuhV\n2A/32yjutelywgpSe+O+qIjl1NedkBGLmJCjDPf7gH8WscyuwLT4vv4WeLmR/XKcviQiUhqV8V9/\nzA6u3ep+Pa1h1Z387Y/ZZNxfJ5lA3IuQOGMs7t8hpG0shipgX8Lc3L5xfnQp9CNkxOqO2UQA3P+H\n4o9G70GY9jUxvq9v5XQUBWIRSUgVoYUIZlOAQ4Fn43SStmQgZrNwXwUkkW2wByGj2FTcv1nEcgZg\ndgwwibBM4A+LWFam3sChmM0CNpXw89OdcM1/Ou5fb2bfsiYfVSAWkRLpRGqaERCzXe0LEPMLX5RI\nrYqrJ2YMNM32AAAgAElEQVTn4v5X4MESl92NcKIzGbNJRQ7C3TE7I64cVaq/Y3fCZ2pmbH2X8vPT\nmZC6clozQbgz4e9Q0eTRFIhFpERGYPaN2nvul5CeQrIrkRoVm9k34jSlpQmU/WHgBOBB3K8pclmf\nj9fw/1zUcuqWeSGhF+W3cUpSKc3AbFwWre/D4wnnOty/3eheGqwlIkU2G7PTgVX1uitfBXYkVKdS\n6Uu4bpjPwgEtZ3ZBnC70N8J0muJdZze7Evd7CNPImk9ekX953wL64P5zYDlh+cqtRS837dS4KMSv\ngDca3COcBE0jZCv7FeFzvkiDtUSkdMwuICwpB+G6738RMikVc7pMa1KG2VfigKFSB+FP4f4vwlzW\n14pUSn/MLgXA/Q7gSYobhKtiC5g44vsdYA25Do7K3RmxDnfRUBAOdayKK2n9V9xnE2E2QOPUIhaR\nAhiA2YLae+7Pkm6lrCX5lYVKqU+8LvwEIRiWLtWm2Sdwf4mQqKNYI4b3w+yDuD8Z7z9GcV/jMMxm\n4p5KwvF3Sn1yE5xByMi1hHASkNITs08AxDq+DTxPeJ+OjPu8h/tstYhFpNAOxmxCvL0D95UZjz1K\n689yVQwDMZuN+wpC0o7tzT2hQPbC7EzcXyYEqmK1hIfG0dfPUfzBZxMxOwjYhvvyEpTXnLWEAJwK\nwtWYTQd21X72zQYQwuow4N2M70TTXecKxCLSQlOA8pjxKmTcc98CLE6yUq1AFTAF93eA35Ww3N6E\n65EdgHsILbJCG0uYp9sV982ELFnFMpXQ9R0+X+4bgfuLWF42phOSybwCjCYE2i7APoQENLfE/Yz0\nd2IFobegeQrEItKMrsDE2ntmowmDZR4CHk6qUq1QL8J80Vua27GA+gKTMpbbK8aVxlGx52NgvOTw\nhyKU0RGYDHTEbAzQO+YR/1sRymqJUC+zMbh3A97A7GjCyegK3P+EWQfMRgLEEfIbWlyKArGINGAf\nQppCCNfA5tQ+ErIlFTNl4J6oL2FgTimDcB9C9+3wmIGsGKoxOxb3ZcDNRSqjM2FFqhMJKSl/AKxs\n5jml0IWOHUcxaeIldOhwPcufO4U33xxKaBWHvNVmQ7OcGtalyUcViEUkQy9CC/hIzD4Qt70S126V\nhvUg5BruU6L5rD0JSSKmYDa4CEG4AyFlJJh9FPc7CVOTCq0r4fPWH7OPZ6yJnLSudKWM8rKudB92\nJT/60Svs1e1sPvwR45FHXo7JZ7LtFUi/xqYoEIu0ex1rb4XRn1OBxbifl1iN9hwdMAvrz5YmCHfA\n7BzgWOCPceH5QjJgH8y+R7g++wWaWkc3Nx1iOVMzkl18qsBl5FanDh2gQ4cjOIoD+d2QC9n6wFtU\nH/Bp3nqrpScIqdd4eJzStLbJlrMCsUi71hOz60ivcPQT4AeEJBDSnDBndw1hkFQpyrsU96eAn1Kc\nhRuqMbsknoQ5xZinG5JdzASW4H4OsLPgZbRUCJaHcOGnnS99sTOP/vWfDD6rGh/zKbZubfl3wews\nYAZQk9Vr1DxikXbnMMzmxdvv4f5j0ikmN1LaLEV7rrDY/T8I04WKv0KU2RdxrwEeB7YUoYQDMTsJ\n91uA1QU/utnngP1i3u2nCEE+qQQve2N2ecb9gUB3Kipg331r2LLlJlauXN/io5pdDAyKA82eJvyd\nUssiaj1iEeGEOPp1bZwHCiH13hMUZ7RtWzeGMEK2WHN2U8pi0F9KmA5TjKB/SFzK72HgmWb3bimz\nz8STljeBFwknfKU2EbPj4u33cf9r7BrvCfwS2D9u/yXwQpbHrIyXCoKQUWsL4USm/kmG1iMWaYc6\nYnY2YcAIuL8asz2tIZytS67MPoL7vRQ/CPeOiTr+QUiSUujeimMxGwG8hftjFDYID8BsLkBcArKG\nxnIzF8eZmPXJuP8W7k/EpBsnYLY1tv53YtY/vsfLyC4IHxizZr0fv1MpNeRyoqRALNKmDCLMcYQw\nWGQH6QQPS2kd00L2ZF1J9+YVe8WoAYREHVsI6xgXOq3jUZgNBN6OGaAeL9BxhwITCAOWUp+9+yh+\nqs8BwNG198w6UTe5yS6gO+7vYpZKuHIfcBjhe7KM5qflTQYGE0Ln2zG5Sf7zqhWIRdqEYYQg3Buz\nqrhtRxzJq4FXhdGTMNK3Ks6lLuaCAxWERBLd4gC6QpsS5x8/QljBqBBGE+rdD7NK3DfGBBfFNJyQ\n0QzCwMOq2kfcFxF6LDLrVVWvXofHucD3EfJDN2YKIY3ofoRkNstw/0vBXoUCscgeaxSpRAFm44Bh\nuD+N+7WJ1qrt6onZeNy/RXFbwwMIQbgf7j8q4HG7ED4zYHZUnA+b7bXQ5gzBbCowGPeaIn8GxxAy\nmIHZeGBI3P6veuWOJCy8MIkwSOzRjMfLgNGYHRMD9tp6ZfTMOG54v6BnfM+WFfj1KBCL7EG6kkq0\nAMTrv70B4pqnxW59tGddCT0M2WRRykdv4GjMehQhCI/E7OMAuF9JLqkY6zLCaOMOmM2NI4V/2Mxz\nctGNkLkslmoLCIEytSTiTzL27URo/aamEPXNmJKXqXtMIvJl6l637gnsDeyP2Ydqt7pfQTEHmCkQ\ni7R6ZYSv6kFxekTg/mnSUyOkeDoBE+LSf18qUhldCAHtdOCdOKWsUDoCYzA7G/cLCnC8DoT6dsXs\nKmAv3L9BmJJUCF1iGSkHY3ZR7T33T1B3kFwnUi3ksPrVwrjf54B1jdT/Pdw/mbGtM+F9Oh6z04Cn\nC/ReZUeBWKTV+2D8gX4S94/GbUYp17lt347BbBLulxetBLOvAsNx/zlwd4GPPhWz6bj/W4GONwqz\nrxGC2SWEtJSFG4dg9nnCak8pT2R87mH3NJgnxuxmABvivtbAfikHxKQlnyQ1bS8k9JhMmGL0UYo/\nEK8uzSMWaYXMvkx6EMpDMQnCe4SE81I6J2FWgftiivXem30D97sIrbc3KNwgsNMxmwY8Ey9d5Nt7\nMguzk4EXcf8FIYitJ/+gVY7Z12vv7Z5Q5F1g827PMvsYMB74G+73x607aLrL/aCYtOQ3mH2K9JKF\nvyak8txC8ZKzaB6xSCs3GLN0bmf3P5P+QdhAMgkQ2ruTgW64301xgnAPzD6P+x8I87oLuY7wmaRH\nzb9G/kH4hIxFLd4izEXPx5GYzYy336qXp/t5mjoZMbsU6BWTZywhJM7IJgvWoTG9Zjlmu3DPvJ69\nitLOca5LgVgkMUfFTFcQrgs+mPHYYyjVZNJWEFpj+QadhgzA7PTY0/EEhZ1idgZhzvES8q/7GbFH\nYAPuf6fpKT7ZHSvYnPF5f5swx70p5ZidCYD7M4SW75Nke4J02typdO16Cj//xa4Y9N/PoszSUSAW\nKblZmA3AfSfuqZbuK8Cfk6yU1DGd0D26qgjHrsLsaNzXEhJKFOLqYLeMLFY7CBme6k/Jye1Y4TO6\nlJYF4UGYHV1nS/pYENbzzWZw14g4/cgznvsA2S+XOIO5cysYM2YHjz66BPd1wMNZPrd0FIhFiq4n\ncETtvZDNqCvhB+HJhOokjTsCs/1wb3nS/+btB0zCfRtwR4GOuTdwJGHdW4Bfk9tiCgOAQwijh3M5\n1jigMt7eK+MYKbkcqxehG/pl4FdZPK87cFTtPbM59OzxKo8++hvuvqcYayo3p5LwWgDuanQvDdYS\nKYpK0j9KPWOygyAkEHgpiUpJkzoA42Nr9U4Kl+wipQo4lND+ua1Ax+xDWLBhLO7fIbfWdRWwL6G7\nfAKwNctjdSQMlgrrWZuNjccB938Ct+dQl7GEFnk4Vsh//ccsntcPOIAwPzh10jsOWI37Tync1Kps\nDQbKgX3jawH3QzVYS6Q0Kgip8KYQfnQhLHz+7wnWSZpXRpjWckYMQvkmu6ivfwzw2yhcEO5FCMIH\n4f7tPOp1DDCJMHe2uc9pD0LLGcKqUGeQyu4Wpl7dlEMdygjpWcHsVGCfFhyrH+F9GIXZLGAT7t8k\nZNRaEEdgr8ihTrkYTPqkZBrhRKAmq+++ArFIXjqQyvIDxCXRxuD+G+Cixp4krU5fzL6A+2co7Ojl\nnoREHfPiNeFCdEfvRQheR8U8ybkE4VS9zsB9DU1/VlPlQUi9uSDefi++X7nOZ+9MyJpVgdllALh/\ngexGQPcgrC52CmGhh4dwv4jwfeyP2Vdx/1qWx8pVGeG9ATDMvkC4TEDM5pX9SYm6pkXyUo7Z/9be\nc7+aMAp2F6VOCiD5MEJrZkdhj2rXEfIc30gYmJX/ZyIknzgWuCeOAN6ZwzGuJyxg/9+EQYKN18vs\ni6RX9HoQ9xsyHs3n/TomZsxah/tn47adZNO9bvYfhNzqNxESoHh8biVm34rZt97K6li5mxLfGwiD\nyTIzfjX0/dc8YpECmhm75ABej1/AlDco9I+5FNuImP7xKwU8ZmfM/jMGypcJiSIKEYQ/R1g393bC\nyOGWBOEKzL4BgPt1TdRrb8z+k3Syi1+Qzuf8Hvl+vkMO52OBpfG7syOLY1bH7GPEOv0PYVT4WxnP\nHRX/jp+lWEE4zPU/LN57tt53fzO5/o3VIhbJUvgBOQhYjvuSuHU7WuN3TzYhrsDzO/KbI5upXwyY\nvyRM03m/IEc1uxj3pwhzzFuafGIIZmfi/tt4/4WMes3G7NiMfd+NdU+FhjUUItuX2acJrfBHgX8Q\nEtY0lAs602Exm9dm3H+fsX0VdacwHRxXlPodhR1k1wWzr5C+Dv5QxvFbmtik8RaxArFIo7phdgGp\nARjuzwOvEs7E/5VgvaQwJmN2YByZW6hRtYMwOxn3J4BHyb93pA9m5wPEIFwDvN6C5x8al/Dbgvvj\nhCAOZueSWtEoXCPOvJa6Dfh7nvVO6RG/Q+D+LCFJzfM0f+32A5iNIQy+Wk0Ieo0l4JiC2aj4d3y6\nILUOme7mATvj3zLV0v0nuU0NAwVikayNyJj+sAv3N0i3DB4j9yQJ0rpMwewA3FeQCk75G4LZ4bhv\nAP6vAMcbiNns+BmEcC13S5bPnY5ZNaF1+w5hhHN6Xm84Zqpb+zlCgCmkwZjNIHyHUicOD9D8ScRc\nzHrjvpXQYl9F83PthxMGnz2eT4UJre/R8fZ23LcQTqTuJv8Tqt7Az3SNWKRp4wnTD7qSujYWup3v\nJJfBMNLaWezhKFQQHgocjPurFCYIVwFTcH8bWNyC580i9OT0Ikyf2UpoRTvpzzWEgWPFyK08ihAY\nu8Ty3qfp+vcH0nPsQ72NMOAxm0s+4whBMtcgPJvwnQezHqSvi79CdvOXmzKc8H5A6FX7WaN7KhBL\nO2WEZc/CtAyzIUAF7k8SFhuXtmsk8CKFm9pyACEj1TvA75vZNxtVhHm9ZcAtWT6nM6Gr/aOE1uFi\nQnAaiNlI3F+qt8hBoR0I9MZsMFCF+8pmyqsCquNzRtZuDc95NcsyR2E2HvcXW1DPvqSDI7EF3DmW\n/X+EE4B8jCdMrYKQynRwvP0qTfU9KxBLO9KLdLarDpidQOpsOCyDtiiheknpDMbs2Hi9tRCBuDIO\nEnqF/INwKqXjWEILqrkg3Id99iln5AjYtr0Xjz/+BcJAorXACNzvAG7Os05N6UDoCegYu6H3jStV\n/byJ51QRThTGYjYReB73a3Iouzr+HZcCj2Sxf39C8o/BdQamheQf+Sx72I1wQhGEpCL94rH/jPut\nWR1FgVjagR6EiffjSC8gvpOwqHmh1n6V1q8vZh+No2/z7ZLuSwhA83B/GvhTnsfrEwcHHYj7H2k8\nPWRvoDO9e0PHDtM45JDT+f733uDlV+Cwqa+wc+e/k57LWiyda+sR5gF3jUlFljfxnPT7FRLe/DEm\n78hFX8zOiScaTbVg9yEV4sxmA8cQpkzlWm5K9/gPwuC8T9Y+4v4NclkoRIO1pI3qQOp6T8gENIeQ\nfec/k6yUJMjsBzFg/CPPI3XE7HtAP9z/g+xaZE3pgNnCOLXobw2Wl2J2OTCeKy7fRZ8+u/jMRUtw\nvyrP8rNlhO/V2FiP93A/l4Yza6X2jffs+0Bf3BeS34jsjvHveDW7X0OuX+b1pHrAQr7pX+dRbubv\nyYeBU+P2FS0I7Bo1Le1MSEgQcuKGM+c/E6ZlFDJ9oexZ9ib8/fMZAbs3ZtfhfiVhBPDbhM9V7syu\nxf1m4BnCAMFMFTGLVEoPoIwePX6F2Z1s2bKd0q1bfWJs0a7E/buEAWBv0nDijENiazlw/zphcNhW\ndn+N2eoT3/uvEbrf6/8dR2P2pYwyryI91ehd8lnz2ewaYGA87l2kB+TtIPteNQViafNGYfax2nvh\nDDg11WMzxRkhKnuGnphdHrsNWzIHt75BmH0i5hFeRX4BfRBmFwOp1bj+QTpQTMcs9fv4RlwAIaSa\ndF9MmGr0Kvm9luyF/OnjgCdw/xuhBdzY9fUT4vXiVbj/IWP7avJ7v/bD7GPxvc881tyM6YZr40l3\nykvkfpI0vHb+M6QWtEj9huT63isQS5t1JGEB8s1x4EbKk+RzBixtRUVMe/ggISFErlmuhmF2fMys\ntJT80icOx+y4mGEKYGnM2lYV76/GPdXtuhdmhwPEIPgY+Q0uyp7ZZwhrAT9JSIe5nsYySYX6HxCn\nhK0iBKpCrXo0Is6n/ivhvbqI1EIrId1nqk5bCHOic3VcHEAG8FpMgJLyFHUzeeVCgVjalNMx6xdv\nvxmTE7wCLGniOdL+VGM2PWZm+jO5B88xmE2KwfHhPOs0BrPTgGF1juW+kfRJwr+AXZhNJySWSLU+\nH6T43dD9Y/0grBa1kzAgamMD+5ZhdjbQGfdNhBPff1LYFJMHYnYI7lswq6hXL4BnCVPRWqo7Zh8h\nc261+2uku5k3E+ZfF5IWfZA9Wj9gWu09sy6krvWGtHnNZd6R9mcIMCkGuPvyOM6BwFjcXyKfIHzC\nCRM5aFw1TywdwT337AvcW2+PhwgnkxNIT196O2Z3+gPFNwQ4mDAoKTWO4j52H4g1mDD/HkIQ20a4\n5vs3Cr2G8zFHH0iXridz7737ErJyNVWvbAwlvL8Q6l7/GMsofIax7CgQSys1FNgv3u6OWVXtI+4/\nI/xoiTSmO6ErMZ+5vaMwGxdbe39u4XM7AocDnZg5A444vIqBA/uwbt3bcfrUnQ08ZyxmBxJGYz8X\n5+QW22iggrBQRSUht3NDc4+HE7rO+2R8F7fFBByFWdQimALsxRGHw7RpFbzwwlbC6OgOjdSrOROA\nPvF26jUCbCWsjFVM1YRkLyl3Nbpnk4F4zZo1nH322bz88suYGR/72Mf4zGc+w+WXX84Pf/hD+vfv\nD8BVV13F8ccfD8DVV1/Nj370Izp27Mj111/PrFmz8n010q4MJSSKH0v48gO8hPu1CdZJ9iwVhLm0\n+SzkcABmU3F/Abg/y+f0IbQYIUyzOQYYy/Tpa/nLX27mnnsbW7QgZHcym4L7MuCnedQ7WyOBrvGa\n6GDcaxr5jg0jnAiPB4bEzHOF/C72IHzng7BAxXimTn2Nf/zzdm655RctPF4X6mbOOoL07IlHS/A7\nMpyQswBgZFy4glh+489q8hrxxo0b2bhxI+PHj2fr1q0ccsghLF68mNtvv52ePXty8cUX19l/+fLl\nfOhDH2LJkiWsW7eOGTNmsGLFCjp06FBnP10jlrQyoLz2Xrhus1/MdJVvkgRpf/pg9gHCQu0t/RFP\nKY8DvB6m+TnCfQnZlSBcz/xgvL0d9+vjcW5h90FEnUkFCLMLCYOivk/jKwwVQifCSQqYfZzQ8r6Z\n3ecudyQ1VSeMmN43pn29v4B16UmYTlYd5+UG7ldgdkYcyJbtfOPUsSAk+0ivERzWXc533nhjupFa\nwSolrGqVmuZ0N5A5ijvHa8QVFRVUVIQ/XI8ePRg1ahTr1q2Lhex+wDvuuIP58+dTVlZGdXU1Q4cO\npaamhilTpmT3uqSd6EQqx3PIx/rN2kfCfMN8Rj5K+9UFsw8TVj9qafIGI538/4txSlH9sQcdSK1L\nW/ssO5eQFxpCwphPxX06xzmvl1F3pHHqs1+N2RUAuH+SMDioGDK/awMxWxjLvJi6K4ll7tcbs28T\nFsb4CoVbb7sL6YQbs+Oc5KdxvyBjn66430B62cFsjnUcZqfH2+vqHa+QMssEmBhPotLc/426g9U6\nkspl3ZSsrxGvXr2apUuXMmXKFB5++GFuuOEGbr75ZiZOnMi3v/1tevfuzfr16+sE3aqqqtrALZL2\nwfglhDD376MZjxXyepO0J2aXxCknLb2eC6EVfB1ADJ4NjfytxuzqOlvc/xv4b0Ig30Hojvw68H4M\ndvXTTU4jrC+8OuNzn++0mKZ8IKPFuSGjzPpT+47F7Lx4+w3czyMEw8JNATS7jNDVDfB73M+h/spm\nZlfh/mOaW1fY7Guku7RTx3Lym1bWNLPPEwbSpTxe77fL2P1veURtCkz3XzZ67KwC8datWznttNO4\n7rrr6NGjBxdccAFf+9rXALjsssu45JJLuOmmmxqpvDW4ve4cs77Ub+JL2xMmyI8ltBwujVu3k9sI\nSJE0s6/GeaaP0fLMTcMwW5DxmdxIOkCchNnxtdvT+6S8SvrzOylOl7qUEBBeo27L7iTMyuPjxf3c\nm/0/wkClv2fUecduZYbpR1MIyTpS++2iMNOkBmP2xdp7oZchNRXrLepmueuK2TdjIp6GWuAtOVah\nVMSAnyrzFuouDPMuu7+fXyQ1TiDM+74D96ObLanZQLx9+3bmzp3LWWedxcknnwzAgAEDah8///zz\nOemkkwCorKxkzZp0N8zatWuprKykYcMb2S5tR+/a7EGQ+mD+nfBDV9ipDtK+hTEF62j5D/I4zI6J\n15PDb5fZp0kP8HkuY3TtOzSW0CK0fEbFetTdJwS7obgvx/2eJo6RP7NLgL3jNdbHCCked8+CFbpU\n+8cehB8QusYLUa8ZccAVwOv1RiavoOG/Tz/MPklYqeg50q3wpo71Twp/InMiZpMz7r9Vr8zn2T2d\nZVW9jH73U3dqWh9S1+Wb0uRgLXdnwYIF9O3bl2uvTY8227BhAwMHhgvS1157LUuWLOEXv/hF7WCt\nmpqa2sFazz///G6tYg3WassmZHx5tuOe2fOxjOJdC5P2qRNm5+H+K7JfxzblEMzG4v46ZtW1W0N2\nqNQlkhdoejWdEzAbSsjs9iQhX3SqXucDXQjr5W7N4li5KsfszFj3FYTW9lOEbFgpVZjNrb2Xfo3P\nku9JcRhguU887sukpxZuofmkGIMwOyFmyHqIsDparsdqudAd3yOWt4G6lxLeZveBbLMwG5Vx/13c\n/5Vxv4Z0at1JmE2tfcR9Zm6DtR5++GF+9rOfMW7cOCZMCBOhr7rqKm655RaWLVuGmbH//vvzve99\nD4DRo0czb948Ro8eTadOnbjxxhub6JqWtuWI+GO2KyZRgPBB1shnKZaemH0wZlZrSR7jozjhA/ux\nY+dI7r23N2Z/y/jMQkiukU0ayeMIo503EkbmPkMIijMBcE/lI071AhXa8NiC84z6P0DdluIYzCbU\n2wfgr6QDRi56YTYHAPftpF/fU2Q72HL8+AOYMOFkfvKTQzDbCpyZ87GyMwKzSXW2uG8l3Q3/BKHV\nm7I3ZmfV239nvffxVdK/cXNr35NgV719G6cUl5KjMkK2q7BEm1l/oAdhwfWHEqyXtA/7AIdjti9h\nIYCmBvl1IXxWU8vYzeb0099nx/YX+e1iCCkkF7ew/GMwGxK7IlMDu/YFDsVsILAjXscsxuDDsYTk\nGr0w64v7K0D9gUATCF2ie2O2D+7rqDuVJhcHACPi7bLaxB7h2mm2iyCEek0Y7xx3XA/efbc/112f\nmWayJcfKxmTS44/C+5Up/I1S3eWjSc8Dh8zXmN7/PkK3+OC4f5rZfmQuWen+BHWnYCnFpRREf2D/\neLssnl2G4fxhLdVnGnmeSCH1JUwdGUxYjq8hAwiZjSBMJZpICMSjgY3cfvuvaXlXZ3cgJGgIuadv\nIUwB2o8Q9AZi1hP3G1t43GyNBbrF7FuVuD8W5/dmGk94veOBctwfiddeczWaVNct7I9ZamzPq1m+\nzjLSaSWJ9ZrMkCE7ee+93/Od6/4nj7rV14uQqCQt/N1D8HVf0uj7FfYdRTqbH4TLDZmvcSRhvvJk\nwmpQmV3U4P4dGl4SMVWvxjNrqUUsWehH+DCNISxxBvAOYV3QXNcWFcnVITHr1Q31tg8knVxjLGbH\nxttvxc9qFWYfiokWlrWwzL0IA7vmA+B+edzWhbD613jgsTjqt5DKgEEAsZu0bxxYllq5qTt1E+Kc\nC/TE/UfkloO9C5AeYGt2BqnBRu5/An6XxTF6EX4zIGTJO5dUb4T77zGriq34bI7VnNRvE4TrzafW\neTRML0uNU8msV1D3GvEvSffmdSOVmCO976mk/hZhhP6vGqlTBensWhCC9im4D1GLWFqqF+muvNOA\nI4D7cb+oqSeJFFkX4Lk42rcDqeXwIBWEUq2U++JntSPhh7YnZpfG4N3SBBWdgYMJS/F9ltQPf8jg\ntH8Mvj/O/SU1WmY3YECclwzuXySMDIeQfKQL4eTg47XPCq+5pYPWUseCEDQypwl9nexWU+pOOpwc\nFQM4hNHOnyFM5+pBWM/5KXZf9CIbdf/eAGanAKnpQc/W+33qGZ+Tyrp1dEb+gsD9QkJXeKr+qX1H\nNpCs42rC4LZMqc9XZp0+AhyUseWZZn83FYilAR1jcoPeAITUez+kmJPlRbJzPGb7E3IGl2OW7jp0\n/yZwTbyXmr87mJAlKpXBKpdBU9NiV/TlhGuuNxEWIfgKobXVXBaoXByG2WeB9RlJI9LJL0Lr7HRg\nSb2kEi0ZtJY61lzgtHjvhXrH27n7Exo8xudJB5976h3D4z6X4X4nu49EzlZvzH5I3aULbwJSZdX9\nfTK7ivQazwB316sXpN6vEHQPzdj+VAP7NvReDMHsmjpb3L8FZOa0bv53U4FYoomkc7Tuwv0bpEcT\nbiGXL7hIYZ0ZR6WWEZLpv4r7JzIef526n9ODMJubsc9mWn4yeTJmA+K16CrMPov7pwnB9zUK/72Y\nT+vl4DcAACAASURBVFiHeFms9846ZZh9DhiD+/8BnyAMBsutDmGO/+iMY0G41JTN8Sow+0btvZAN\nK3W9953djmH2rXh99mladuIyjXRmsC3xZCrzb/hWLOsw0pnBUnX6DnVXaUvVa3/MvlJv359Tt1dj\n226vIbyO84DDMrasqfcZBGjpKH5dIxY+EK9xrcb9gbjNCd13Cr6SLLMvAX248grn6acr+OWvnsE9\ntT7vNupON8k0BbOJcd9/NbJPU+WeBwzHfSnwPmZTCIF/MXWzAhaG2acIi53UEKbsvEm6G7ozZl8G\nusWguZ4wR7ilc/L7Y5bODNbyYx1DOsvYljhAM+VFGk7W0Quzr8Trr8/SXDrPkJBkQMaWfxCSk0D4\nPVqRse/ZpAbPhZZ8/dkaLxBOVM7A7OCM7ZsJS1FmWsPuA60GxPqkhTIyu+rfJfu54Y2PmlYgbodC\n+rtUt/NLhAn9r6DFFiR5Q+oMuAmBcBuHT3U2b4Z/rlhL8z98R8SpRY+x+zW95pmdg/tmzA4jXA9e\ngvsqwg91IVdH6k5I+2q4P0vogXqeEBxHY3ZC3G9XnAqzk9CibMn0nkNJJ9h5j5B0JKX5Y4UBYqlB\nS+txT2XfeoeQuaspFZidGev+KA1P5Rpc57ptqF9mfuv1hPekIl57JWPfFRn130SYVrRPAy3jF6h7\notHY33FGnHOdUv/9IpaxqYHnZkOBuJ2rxOy42nshAULqesezFG51FZFcHIFZan7qNtwzWyb3AscS\nPqfZtDyOJFwXfI6Wj4zuRMhQdTxhgM2/CMFjdQ7Hasp+hKQfu+J30YEHCV3dU2K3+/sx2QSE7+rd\nZD9D4STMUq3Kd3FPJfjYSvMJdvqRXsoR3N8k3TO2kpad2PQhXHe9O2PbdDKzmIXse5mJRe4jBMqj\nMBuWsX1HrEumRwmNiIPiNCWAnfE9zfQE8FK9bXvFv3Xm9ea3qXsSkM371RKaR9wOHUTmPMrMDxz8\nH/ll1RHJR0dgFun5mz1JT2/ZRN0RtTNj0opsjntYnFv8LC0LnP2Awwk/hycT1iDeQmg1FbIbehQh\nx37q+7iNkEjECScQ+2DWg9BCXkvL1v/tSnhPDbPepN/P52l6vvQE6s6d7UTd34oHqHudNVsDCa/1\nfiAd2M3SszFC/TYTTkKmxy3Hxv161tvvDdIJSWYTXm8qL/RepF/vVhpOzjKa9MpPEEZTd6i3z1PA\n8mZfWTEoELc54wnTBIaQnv+3CvcfJlorae/6k87K1AGz0aR+ftz/SPgRzFQGTMZsTLy+2Nxyqgdj\nNo6wsEj9YzVdr9A6nU8YRFSD+80UNif6gYQRv/sBg3B/Pn4fOwNTCcFzLGH+75+Ax7M87kBgSLzd\nGbORhCD+Uxpa6CHoSAhgqYx4w6h7TXZjnr8Vgxk6dBDl5cN45JHDcO8Y6xWE68o7qTtH97A6+4T9\nfk9IEJT5Go+IdR5N5hq/7n/PGN8C9V9jeM5g6o6gfoviJV5pOQXiPV430i3fkL4vTPr/DXWX7BIp\npcHUTWpwQBwUCKGb8Rs0vnpOV2AUZnNw///snXeYV9Xxxj+zjWV3KUuvS5GOSleagkoRbNgVk9iw\nxST2ntgjGCuKGmtMfhoTNCrYGxYQBaQpvUuvS4cFlp3fH3Pu3vtdtvdy3+fhYW8/31vOnDMz7ztj\nyD2OKVgZw1Oxwg/5n8E2bVKHxMTBLF12FubKPoTqkxRPfeAorF5utBPBaYJVXvoEGyB3xFSyzsSM\n53NYwlNeaI7PW+3g4thghuVhss8Kr4XJb4K530/HBjqgOp68Y715oTUeD1nkVLoc25VevTYydeoO\nTHjlr5gxjcXuRz98vjfAFlQfPeJctk/wN+La/FcitcDrZjlfbMRvtGM+Ad4s0q8sSYQx4gqJJPxO\nLsUlfBhUHyR/H3SIEMWJGLyqOeCJXQR1e6c5Pnp+kILITajeQs5Ul1gsBhmDyN1ObCGvWbOhfr2a\nJCRW4+KLTqRx42HceNMSVP+Wz7blBa9dsS7TOd4Z99XYoPl4REa4fXfl8RvBZnW+PrKJlngu1q9R\nfSOH42rhG7SuAYGNA+6ahR1sxOMrWXltugmbVdfEZrtfoTohyz534ollmDLYVzmc62bMe+Ih+Buj\nyKqMZRjoJiAe0rDaysUxoCpOhDHiSoIozI11HhbLAliM6pW5HBMiRElB8ONsLRF5PHOL6l0ULgtf\ngLWo3pTHPh0QeQhL7rqC/Bayj46OYty4azjn7D48/sT73HDjqEK0Mac2RWEz+Qcxg3cFZgzE0ZNO\nxkQl8vpeg/e1CSK+lKeJiozJ4bigK/Y6oLdb+raIfUQUfry2LyJ/itiqegPR0WtRvYGMjHXAHkRe\nyrLPlZhnwztPdA7n+gOm3w3+ffB+V50jzmv4X4XvA0NDXIFgo8oOTp3mcrc25PqGKCucHZjdrUX1\n8sC27MTv8wNPhOMvuezTG5HB7npK9vzV7PH+u3cz/u0p3HDjK+zdm5b3AfnGcDfrXBZo1z6n7tTU\nzQL/j/xVYxoemMFuyXJfcxpw1MbU8LykpdeAF922gwX7KVkg8gfAy0qekaU9IHIX/36zIf97N5G3\n384AvjhiH9iJyF/w473ZnysyifQ8RM6IOMeR+0NkpnPFROiaLtdojMjtmUsmJrAOSyTJmqIfIkTJ\nw95HS7Qx8YkZbssBTBShKOiLSUm+m8u5Tkakg3N95s8VbTrT9/PBBOFf//c/vvhyLtu3528GnRdE\nLsMYCrNRnYrNgA86t7RX1i8VE83InakgcjlwLDDLJZ2BGdGs1BsP/Zx3DKwIy+v4MeKN5NdLEInm\nzj3sw+KrnihKe/zCLx5SaNPmVVJTl7BtG1j8dgteiME/zztEcnB3B5arIfIAvjvdkrAiE9fSMSpZ\nRUXII65A6I/IQPf3nsAHCebqC2lHIUoTKU7ByGCdozfbXUv+jWFeGIBpSP+AiSZkhyGY3OSP5Kyo\nFURbN7O0UnyDBo1j5syppKYW3QibNnEtrIDBJsw178Vu96H6vfv7Z3KOVSY516xXSnQuZrA3kJPx\nFRmJJTSBySsucn8fwviyhcFARPq7v3fhK1l51+yCn1m9AVWv3GkcIje4AcBk7BkeGzgy67k80RKw\nQdfJgW3pWEWjoIdvDTlnf1dEhIa4AmCYI7rvDBDSd2MveIgQpYUhjvrmIc1xez1MpvBu55wwEJtl\n/0LONa2HYMlgc4BFOezj4ThEemDGoycmavEvLEGoKAk89TNnoKrrgHRE6mOJk7tQ9bK792L82+zQ\nOaB0ddjxhT3M4siiFLXxSi/adTcHfsOvFFw5LNYNrIL0nx34WchxiESW/7OShV6G+zpgLg0b1uaO\n2y/hz38ZxP79U7FJwzYiZ+E7ARuQmCpWUsS2SOGNdGASlTvUFiZrlUMkAKdlLonEAXtRXUDxqviE\nCJEbqmGDYpuVee+hBzPCn5VwGw5gBiUnI3wyIvUxqcS8jHAvRNpgNXobA2+juh/4iMJXDzsK6I7d\nI+/exLvzpWPf7SJy5v+eiF8zOCbzHNauT7JpVwfgGPd38JpglYsKOktsgS9+4QmJeCpdvRDZjuov\nOVwPTBCkLkbHakfLFu245BJh585dZGQE9aZnYjrMbTChkESsQpSH4Hu1iMLP4CsfQkNcqmiOTz2I\nQ8QnmFvMq+Di9CFCFBxNsM4ejP7TnGDh9pIoapAzumIzu5yMS19E2qD6NblLsR6PaTc3R/UgZthn\n46sxFQYdMWNe132r+1C1Noh0BOJQ/TCHdkXjqXWJtMaro6s6F9VJWfbtRzA2asUGvFnpduf6LQh6\nEkkLSnbtTwB6oPoyXtKYeSfrBPqiTaj+B088w9AGkaYYdagRCYmNqVHjS+68619ue2937hbuXz23\nvw+7ZvHE5SsjQtd0qaAFxi1s4+ItYK6Zx3M5JkSI4kRr/M65FX41mn2OQ5u/urPFi/Yu+/kHjpxN\nxmBu3OFYibrsYqbV8IQcTB2rG6YNnIZJHU4sdLtMbKMHVvJutWMq1MZKFOK+3azax8n43OlorGhD\nLKr/JDKmXRM/zgsiwzGOMe7ck4mU+cwLCZicpHe+k/A53Q2BzS5RKikL3xaXGLcRf8YOEI9fcMLb\n7yNgBVZ9qTtW9tC73hC8gYbtOx34oADtryoIY8SljChsJG2zDBNRP9qN6seXYbtCVB3E4EmcApjA\nvRf7neKMW1lBMEbANViN2qz6vrGYEtefHI0pNcv2BMzQJCPyewBUX3LZvK1R/QD4mILBv18iVwMd\nUX0bkVj82eFqJxwSRF18I3o0fsGEg6jeiR/PTcZctWBJZMGKQ/dk8xtzQ/BcYPfyisy/VZ/AL5DR\nJ5AUtcnxkMEMb6z7vQOxWbmHnY4Hrlic3dMEH4rF6iPbaiJCGwrQ/qqK0BCXAqLxEyASEHkaz92k\n+gyQtVZmiBDFiVgiI00NEHksc0n1EcpH7oFgNWqfRvU+Ime6MdjvaIHILVjB9awz9RisMs+1mC7y\nn7AZ3CNu5pm1bF1u8K4H0BCRv2FKWLe6bOtj3EDhf1naH+8vyR+AXm5pivvWPVQP7DcKK+wA8BMF\nV/LK7lxe+5c7wwkiTxFUOIMJztUcRxAio/FkL237u0T2Yd5+9+LLU4KpZo0rYNtD2HvzQWiISx4D\n8aUm96F6M5YUoe7/ypwNGKKsYVmpwW9qM6p3eFsx0YOycD9nRSNEHsNkFrcSKe84CKuV/aubuWWn\nRX2Gixm/iH1bhxF5AdMqXk7BfuOZiFzi/t6E6n2IvABEOdfzfCITm8Dc07YPgGlE/4Td43R8wY5q\nbr9Et9+r+IPxw+RP2MNDTucagtXezcATtbD76s1YxbX9eDdg8GGzcC8uf8j964nIbVn2ewhY6fjS\nB7CCEgVpewhDU+DF0BCXHC5ydISfXRwFrINYR+GzNEOEyBsmpWjau6pfEVnuLp3y6S70XMDriTTC\npyPSGFWv7m4kjcdmgd0xzeoPsQSjm7BCDc9hrtj81ev1z/UjqnudkUnHXM/jMKO2BV+x6YQAhWiP\nu57X9m34A4ZeTpQD165xgXOkkn8FsCH4imVgbu7nnJFsHDjXLKyQRBDrnSBHq8C6ec5dH8RG51UI\nFktY6mLJQWxC5DJHYfqaUEiooOjt6GJbUe0eGuLig7gPwjhxqnOwTmAbOSvghAhRHGiHyG8yl6wT\nDvI7N5dFowqAloiMQPXpLOtHYK7XKWRV1DKjUtslAHm/sS4iA11SUwZGe8p7Jhw8lyVNtsIMu1d9\nKOu5RriktpXuOwcz9vPxB9kXItLZ/b0ml3Pl1barMFYFWNZ6DHBuxLlUPydS0Gcrlik+MuJcVhIw\nGMdtjkhPssJER4LvzE6yMjdErnac6ekUri5xVcTFLqsebHA3E0tmuz00xEVDm4gsQtXF+K7mRfgi\n5SFCFDdOQeRo9/duVIODve8pfxVmckJ7RE5EdT4wNbB+BBZ//Ak/wah+pnFRXYIZv18wBaseiBzj\neK/5qdvbIHM2q7oEkbOx2clcbPC8EZ+/HONmy15uxzpsBrgWn7+c4Pbx6F5r8I1j8Fy5oTWRGsqg\nusIlVbXBZBxnEin2AcYhHoLVNfaQ9Z3A0aWqB9bszOZcYDzenJPERK7EBESmUf4HeWUPey8S3fPY\njUgvbLA3H3Prnx4a4oKjHyKeeycDVW9kqxgtouILjYcoj4gGzkHEMwaH8d2g66mYSmudEOmK6gbM\nvenhdMyzNB1/JtbUzXa9ge4H+LP+noi0Q3UF8GMe12yLyPHY9+rNLj9CdadbNxubebbC6uMaVIPu\n7enY4MA7V3b7fE/+BuJ98BXLFKMwDQ9s/woTT/Ge9a9YbHZwxFnsvgS7bEEkJo99fiXv+xVEdazw\nxiGMDratAMdWNdRD5FRsYHYGvmdnHZF2YxdwfY6GOBT0OAInYu6e+vju5xXAp2XZqBCVFq3wxTXA\nOta6+GXwvuFIek9FQ1wgxgg22DgJkUbO3boaE7ppAyQ4AxCk+fXGqEp182GEjwGaOXfxAKx60buI\nfOqu+w0WZz3K/UvC51enA//EkpF6Yc+lA+ZW9PbZhxWYz23+koj1Iz5stus951WofonIJ1mOO4Qf\nR0527ayZZZ+NRHpBPCpXEP8jsrhCQVALy8iuCfyLUIQjO7QDjqJVK6Vb14a8975XeONr/AlaTUwJ\nLn8DoNAQUwsj8BvMnZCAVTr6JaeDQoQoAjriCyC0RKR9YNthF0PNLmO4IiIFm1F5MdZ4rFB9T6xU\nXzKmDd0GOApTrvpP4Pgu7pus7Yx2ZEECH8dgM7kzMLWuzXjJazaLftrtk+Liw8YZVp3nMoG9mF4X\nd0wP/ES4majmxf9vjB/jrZPJb/axkmAynUl2vuza6ukNdCUyeSoV1RkEYbHeupnLqktQfT6PtuUX\nyZjrv627X2GyaRB9erenXr2aLFp0CsuW96Nxo1T69l3Ke+/bc7XnWTgd9irqmq6HP9JMcXEjg+rD\nhEkJIYoXcYAvZ2qFA0wC0ERe3i+TVpU8GiIyDCuGMAEzwp0QucRRcNJcdnALVD8mUtM6GuMTX+4M\n9sojzm6xZTN+Vqu7Mfbt7naJSB8SKWpyOTZT+QeWFFbLbWmGyLkEofoCuetapxCcx5ji1plu6RBZ\nk86sHvFSoHZgbSImxOFRoT4iUoGrMO0qLGpiA6IumCBICIglOro5nTtDdBTceuvZdOzYjHHjhH+8\nLsBc927mF2HRB4ckTHruHHzX0TxUbyjDNoWonIjH1w9uhshdmVuMm5lTqb/KgiRncBdgLrtaWKz1\nElQfQeRhLLHlb1ipQA+xmLu1JiL3BfjGZLNPQ0Q8o7EbS0oajyU1AXR3FB1DUKXLBkMnuS0L89EH\neNfEHf8gwZmpubM9ycuNqN6GeT0kcMwZwKluKRrzfvwRLy5smdN+yUlYUEp9UzxWwrBNFTfC1YE4\n4uOhZk04nN6EQ+mP8t67O0lKVM67YAyTJ5dMmKhKzYhNaagNqq/gj75NFCBEiOLFhZisJJhAxa2B\nbYep7G4/kdFYQfkpmAjHZZhheQGRJ1C9Bos/Zr0XPRG5B9iBKWsd5Mh7dQJ+8XqbS5jBWo2J6niS\njjNRHRNo0/NAfbf/P/BlMPPTB/RC5O7ActY5zHtYqUUP0Yi8SlCK0hSsPJWuoxB5nKDQjxnBYEyx\ndPomEzWp4VyrVbcvNGnTYfzmEuWVl5VFi4Wu3Q4RGzsK2E96+mEyMory3VZZicvWER+PxVLWYaPn\nyhKDC1FeIHIffpxwkhPZAOtsq07mqcgYrJjAz8BZiFRHNRWRS4FlzuBkVdUCm5X1cjHbDI4MEV3E\n1VedQqdO8dx0c21MPex+N8BOw4rLv4tPa+qAKY4ZVB/DF6TIvQ8wsRDjB4+8WDlpYDWuuiY5cK7b\niaT+nOCyZz0ccoOANHe+y7H4s5eMtS6b2O4OSlu1ylz/+7ByjLvy2r0SobZ7bySwrgaQQFLSVOrV\ne41DB2HtOsXew+Iwk1XKEA/DRMzBMiaD4u8rqTi8yxDlG12yEVKYCHjF4bdQdXMN2gLrXO6FR7/5\nEdXvsBnusmyOGYKVMPycI0U9fs+DD6Twyy+NmPrDPBIT17NkycXuXItRfRu/rF8/LPsaTGAjWHJw\nKTmrb9XDk3f85+vKc8+1YPoMY000avQjycnvsSDglTTXdrDwwjwn3OCd6xZ3PZthWsw6+LvTKOuy\npyKjHE94Kke6/ysj+uIX5djn3htPL7w58D5WCWwHBa/5nB9UCUN8ISIpjmDv3cRdlA+h+xCVA2cg\n4lFQtqGa1aDMJP8yhpURCYhch+orPHD/cD79dDA/TvvFGajNZJ9kdB4irZzgxE/4tX0TEbmOZ8bC\nuHHdqFfva7Zua8qSJY2AGYF7Ly7DORrwqIbeAGgbJqaQHU7BKwXZsSNcNSqem285DoBTh77GnDlb\n2bDRmy01CGgK4K4zGxsIeNSkhviGNc0JhgSxmMJTioofIlc4Stl0ylO7ihOmwx2kdm1CdRWmd34h\nloGvqM7DvttllIwB9lApk7VqR2QUqu5y1IcFlG5h8xCVF/Euzut18nvwCsNbiGNGTgdWQdRF5ExU\nV3DP3SNIS9tLaupETAFreQ7HnI0VWFiKGemlQHOaNh3MVaOq8dDDJ/Lzz7Bnr7BkaWNM0W4uVgSh\nrTuHus7Vc3PPxgQsssOFiCTx298oK1cdy5QpJrCxe/cGfvnlY9dW+OTTSZgAh5fpnpb53EUSMH35\n/XjeNdVFRA749wLf5euulRVUf8XomZVJMasJVi/ZoLqDyJBQvHtv0l34w8OP+J6sskEFM8Tt8Hl2\n0UT697+nZEczIaoGWmDcTjBaSfA9m0FZuxPLJxoichoJCady5ZX/pnZt4fkXJrNyZU4zrWjMFV0L\n1S+BtfTp04Hex58JpBAXN4SoKADhlVe/wGK5vRDJcLMXxX8mh4GPODK22hLoQoMGcMlIm4W89toI\ndu1OQqKmIzIPT45y7dpDvPaP4EzlJERqYYUhUoCFWP8CqvsRmej289rwCznPvMsbYrCawpMpLOe1\n/OA4jLLmIZZIm/AV0AkvQc8gzkBPKPnmFQAVxBB3wlwMzRBp4dZtddnPIUIUFZ0xMQMwo+LFGPdj\nlXaqbiZpXmjduhFNmwxlyvdnExNziN7Ht+eGG//Oli07czgiHuOrdkL1X5x4QgMart1C52bt6NR7\nFJDKylVTuPOuOOA4VJcDOxFRLPbaAdUFOQhsdKZXr2RatVSWr+jGrFlDSUraQ+/eswF44805sBv+\n+c/FRMZEaznRkB6BdeOxgZfpOPshib3unaiIWe/VsXvfESuiUdEMsb0THuyZBMVNfnU2IdrtdzSm\n017LbZ/lMtfLH8qpIY7BEj4MFoNJQXVSub2RISoKErBZrw8TYzA3pOp0rLZtiNzRGKjNMce0o3+/\n45jyfRq7ds1j5CWPk/3ApSYmYlKD6Ohh9Oj+H6Lnr+WyEVfT7ut/8+o7O3jgHcEyoT/A3Ig1EBkA\ngOobRPKNE4iPT6F7N3/NwkVXMHhQEqedtoP33xdmzVrIypXbuPCiyBKAIidhbnEvfrgc1bec29nD\nMS6Z5/VC36HyhQTgGEQGO9GiiqCVXx9P3cyQgMiZmUtGFwsW2UjEPKaxiJwOxKL6EtknB5YvlKNk\nrer4sn+1nFKOwep6zi6dxoWohEjCF2NoESHyAKA6lshOPkTuqIXISGrXGkBU9E9s2zYdkZNQfSCH\n/ROAfsTLBTRkDXHV7uPdH94i6aILuGzJ3XyrKxGJx+f/AuxyYh5BilMSNWsmkJysHEhrT3z1W/lm\nkj+zvfQy4dvv/oclfXlogsgNBDt04zI3BvoG9tuM6l1UTniyomegek9ZNyYP1MGbH4oMBQYGtu1w\nfPygyaqBX2nqKKwCUprbr7wxZMp1slYU5tcf5LLcwDJSr8zlmBAh8oL3XoHIBfjygwvDd6vQsKQ1\nkRuJivqBG2/cSf3653P9H+JzNMJRKFEMRqQ1vfUcPmMG+9Oq07r7YbbzCaCI9Ef1LSDrc4kmJjo6\nM+yXkTGSq0adxpjRh/lusjBo8EZatr4+4giR64Fr8WOFK1C9BZGXA+2/2rkwq8J7IFji2cnl0AgL\nfnETt0YexPdOvUHOz8i+b6MQeglaP1fYb7vMZ8Qi1wD9gO9Q9VRnMvDl4kKEKDhMtagBAKoTAI9P\nmk7Fi42VB8QiMhZIQvXvPPlEF3bsSOXpsZ+za9chcqrScz9LuIpNQDSzOJqr5b8owhbqc1j/jF9C\ncD+R7tJaiIxl+jShWVProu67P5E3/z2JGjX+w8GDkJpaD5G/RFxP9d8u29njix7GxDPuJXJ2vY/S\nFs8oG5yGyFFOSay8vff9nZqVD9VH8OlUWd8JHyL3A61RfQe/NGjO72H5QDnkEYsYHcCyJhdjJOqq\nQCoPUTLoGPFRGz3BUwraiq+oFKJgOMoJHhxG9XUgjWfGnsayZct5+53v2bDhSNqHyF94WW9jK3Pp\ncdN1bMg4l7HPCHvYxGL9IrDnajwuLsA55/Th7rvOByB1WzTDT29Fxw4PERdnClZr1sLmzd0R8VzK\nO1H9r+uUvdDDZlS/INI9nY5RmipiglVRcA4iiU4kpXxwhU1h7Fi3tNj1/0FEvhORqOWeNS5+vxnj\njFeUSVs5NMTwkFtaTmiAQxQOwzNFGSyLPphHMJeKkZBSXtEbkUHAdlR/wozYLMY+fRlLlqzngw9n\nsHq1J5zRFpELqVULXn0lg49//3duu6kff/+wIbN2bmCbbmX+fLAZmS9PNfbpq2jRwqeWLF68jqlT\nTfTjwAH4/AtQ7Y8fAwRLEktxf6cBs1CdTKRi1lqM512VcR7m+p2Gl/ld+miCVZfyYUInHnd5Kzlz\nzD30DEiHHnDPWjG6WHme/WaHchkjzqmuaIgQ2aEGIr+JWKO6DSu+DTYyDgU2igf9EGnp7m0q9q1G\nI/I7pk7dwg8/eka4FyI9OfroBlx3WgPixz7KWV8o/9y/gL9Ob8EPGw+zbPlCvBKGbds04cYb/US5\nZcs2sHjx2szl+Qtq8N133YnE8UQa4jlYuUAPGa59OUlXVkWc4/736Velh+MDg+ODge/TwyxgYz7O\nczJWp3t34BxpRBbFqDwo8xhxiBA5ox1eoXZLzIiP2Gq6sEuzHhSi0DgZU8iKdSpWnnZyEnC601f+\nHNXtDOdjupxwIpLUh/ZRSxn6YD9e7fEkyoc8QSu2E8vZI3rTsaNfhzkqOorq8dUyl58dd5CNG/24\nrUg7oHeWNn1EsDiD6vxAu0IcidMRqe10vUvaCMdg/Xhs5hqRWPyKWFvxK1zlF6dig+44INq9h5Vl\n0lYuZ8QhQmSH7vjF0+sj0sT9vQsrJh+ieBEL9McGOm2wGsHfYjMXaNiwNqcOPQkyC1zYALrD1EM0\nrlcXau5A58zlpQ9bMLr6Q5x3bgpnRplx7dw5hQYNTExBaMSixbW458/vZF5Z5LeIBHmi6/CTz+hH\nSAAAIABJREFU6gyq/6ZqVQUqLOKw5KcWWAWqDSV0nUaYwBKYlyQFLxsdvOIW0wtwvmTAJ4Obpnc8\nqp8RDGNUduQ6I05LS2PAgAEcOHCAgwcPctZZZzF69GhSU1O58MIL+fXXX2nZsiXjx4+ndm3rPEeP\nHs1rr71GdHQ0zzzzDEOGDDnyouGMOEQm4oEOmUsm4GCds+pUrDxbiOJHTaA1EIfIaZjm88vYLKop\nUJ9GbOTiE2J48pvnyMiAKVPg0CGjBT3xFCz5dCWtmh6ADsLu3V+xZMk1vPXmPKJjFGjLw3/9kG+/\nNelHkWOB87O0YTFBrqfFosuX9GDFQAJwLCKnofo4xZu81JbIKlMpToUMzPXslaAsKBoATbCCGidk\nrlV9hspbtawIyVr79u0jISGB9PR0+vfvz+OPP87EiROpV68et99+O48++ijbt29nzJgxLFiwgJEj\nRzJjxgzWrVvHoEGDWLJkCVFRWblioSGu2qjp/oF9iFdlblF9ktDdXNJIxOK7FwJ7nJBFOtCApk3i\n2J92HiKncE61j7ipyX+Qf/2TQwdh1FVR7A4wYC7c+jAXnLwSue8+Fi6K49zzEt25DiNyK3BU4Jr7\niKzfi1N4qupJVcWBFq7q1V0UPTM8Do/2B16Wc5PA9mkue76wqIvF/Ps6hbPFqD5dhPNVJBTBNZ2Q\nYLSAgwcPcvjwYZKTk5k4cSLffvstAJdeeikDBw5kzJgxTJgwgYsvvpjY2FhatmxJmzZtmD59Or17\nZ437hKhaiCdSjH04Il5CyWpUryuDNlVFWNwNTkSkCyLXk5hYDXNPx7J//+089WQ7Zs2G6MMHOLbj\nCfQYdSKxx+ynWp1EfpqeQXKyf7a/PtKWLk/9TPwnt5KR0Qp4FJFxbusBIpWNvneznRDFi2hgI6p3\n5rln9vDeCQ+tMilCgBMBKcrAWLDv3y3JlUBPrPZv+N17yNMQZ2Rk0L17d5YvX851111H586d2bRp\nEw0bNgSgYcOGbNpkHLX169dHGN1mzZqxbl044q3aiEbkGTzhdcNEVC9zf1c1bmfZwWY3JwPfovoU\nRx/dnMnfjsncfupwy06+715Fx73I4j/ey2MKI1NacWjqTHr3iWJ7gI6dlnYOv7nkdJ56Uvn5lygG\nDPS3qf4VK0fqPd+wcEbJoBsi56B6d6GONsM4MLBmpfs2BXt2RaUA1kbkBbyBuMkVj8M8MCE85GmI\no6KimDNnDjt37mTo0KF8/fXXEdtNnENyOJpctgVrBtclWEUjREVHd6f5CiYE8SRWo9XDLoKZsCFK\nFiL3AE1R/Zg/XP811113ItCJVas207f/7QB8/tmDnB91La1vnU3cgyBnnMGK+8fyyO2v8/y6JsQN\ni+I/b2WQ5OTg771XePe9WN6fMI1p0/9NWhpEet02UzWUq8oSJyLSw2ml5wcNEbkvYo3qh8CtgTUH\nKZ5vs4tTTdyN6u34A7KtlD8N6JLCNswN3yWvHfOfNV2rVi1OO+00Zs6cScOGDdm4cSONGjViw4YN\nNGhgMYWmTZuyZs2azGPWrl1L06ZNczhju/xeOkSFwHkuIQdMUvBl97di1U/CEXDpog4iNwLwwvPt\nad2qOsqpTJ06hZtumgRyJg127+bJBZbFnDxyAdMWXsb/tsdzyzXNyKhxMZPX1ucfnx4DxHH4sPLI\naGH//ueBjcxfIKjC9u1b2b59Tc7NCFFCOAWR5k6+NTfVrP6IeAmzewLfpYdfyRq7LzzOQcSr5b3B\nXesQZScoUla4GJGO7u/VqOZNt8s1WWvr1q3ExMRQu3Zt9u/fz9ChQ7nvvvv47LPPqFu3LnfccQdj\nxoxhx44dEcla06dPz0zWWrZs2RGz4jBZqzIg3rm1PM7gWvxszU1YsfQQZYG27OXOBoeIGvMdADNn\nwt69cNllSo1JTzHn283IpWPYszqVJQ+8yeN6C/fIaJrd+Vtqfnk/K6QHn+sotm6DAScqsJPDh19n\n/Hgh7cCPVDxFo8qGwRizYDawKGKLfZNJgTVbUfUM9V7gh2JvjchvgTqorsOXkt2CqdtVBSQFChaB\n6mp8Xe8NmAoYFDpZa8OGDVx66aVkZGSQkZHBb3/7W0455RS6devGBRdcwKuvvppJXwLo1KkTF1xw\nAZ06dSImJobnn38+V7d1iIqGNoj4OQBG2PdQFio+IXz0oB+pDOVTlAasOHQxsb/CbbcqTz8dRdeu\nyqRJwuGve9Kzwx7O6rOYjVPf4GUVHpT7eIWrOGv9DzTbs5EvFs5lhswC6rBixRTM8H5Vxr8vhOEU\nzAjPxYxwM0QGZm5V3UPkQGkhJVPis2ZmbWDVQ5ha1k/AqhK4VnlE+wCNC1SDamHTKSgbIFTWCpEL\n+uHTjMAUbzwBhgOo/pPQ5VyWGMBZZ1Vn37wvSVzeiEuObcK5fdYxZWMbBky8lfh4WPNrBi/8XTh7\nhDJ77Hd8PzeJukN60GznPHhuDLuZy90yhsNEo7oekxBMxuJa24Avcm1BiNLECYhcDCxF1ZsJJyDS\nMHMP1X9Rch6L1kB793esq3KFK2F5ZPGPyofj8HOZaiLi/b3X9YV5IVTWCpEvJOGr5oBIT4KGWHUO\nqs+XfrNCONSmFg05AXM5izTkkT61+HJbCw4sX0G11s34cPgtbFxQh9MnfkD04Wi+/vwU/vTHWBYu\nglqrJzK8rfL5zro88nxzkItQ3QX6In5yTW0gwxnlrJVxQpQ+4omJOZZBpyhTf7ic3btTMVdoTwBU\nl5TCN9kWG5y1cjKkYDXjK3tfUB04JnPJ7rkZX9UZqP632K4UzoirPOriU4saI3JB5hZTzVmb3UEh\nSgkpzetT99BedOMGhM40l2E8FH0/nTsrCxcKBw/Ci63GMGNvZ9j8X0jeTbv6g7l9yZkcoA3D5TNe\nfGsXzzx7kO+//y/mzjwBkUaovoRxSFMcdzQNSEP1PeCbMvvNVRv1iPRCNSAh4S4++XgVV1ypLF/+\nd7LGhUsOLTD64WlAG1ey8INSunZZoTZQx/1dx8W/DarPEcn2KSjKZRnE0BCXHWoApnYmcjYwyK1f\niuoDZdWoEIAI1K1bk6gd2yE9nSdevJER6+ex54EnqBYHa5Pac1HMu8z5tQ79Tohi9Rp47FFlyA+3\noy8+i4w4j+mX/ZkzR7wYqN16F5YZG+M61XhUX8OMcBPH896P6v0UraMJUTjUxOPZipyPz+uNwWZl\nW1H9IyVP+YvFr+sMIg8DyU756qecDqokSMTu99DM2LexP+4oxmuErukQAYg8itV1BdX/Ay5zW0Jx\njbJGXFwsP88ZS/KwQfDLL8RyPqO5mYflRoadovzv/p+ZdXoXYlnO91PiUIXLrhBGjW8PnAITj4GP\n2yNyS0A05TAifwa6ozoe8OJZKYg8CcSgeislVyggRG4QeRywusyq/8D/Ho9B5FpUr6d0cjG6IXJX\n5pLqtVieQOUXYxH5I1Zy893Ad1N6CA1xlUBnRG7KXDKBjW1uaQ9hwlXZYdSVg7n7LiuGsHPNGt44\ndSg1Y5Vzoz7itlcPMPDculz/1DhG6jNM+/Yk2p5zF5raG+kUDUShjGHz5mUcyhgO8hroz+jBq7DO\n056ryP2ofgW8hD1vr2MVbCZ8G0Y5CwdiJY+B2dTVfgyf9rMbe269ETnZSUyW9Pd5tvOULHTG18NW\nKq8Rro3IY/iKX28C/8AoXqXfH4au6UoIkcuAjoE161ENZr8uwxR0QpQ2RO5g3LPJHOu0T5o2qUOr\nVg3h5585dO+9bLz9dpr26sXc+bG0bAEvvyJ88Pxr6OrX2E5fFspDwAJU3wYyEBkGNEB1BlY2bhd+\nXD8GkXtcbG8ufjbt8fTtcw5XjdrG5VdOIFKKMkRxw1Tm2rqlxahmLW6/FBO+8DAQkfaofooJbpRs\nu1RnYxSn3UBlFmfpi8hZ7u997hvysAaf+1tSCF3TlRw1XcarwYppfxTYnkpVqu1ZfnAsIkNJSYEx\no+0DFHpw8snVWPHWM6z58UdqnnYatLqERbua8MDXF0DCVGAqyGWg3zHjp7asWDMIpC2wA9VnMQN7\nKiCoLsA43MuJ5C7WRmQUqpOBOfgSo/0QOZdVv0bxn/FfYKUIQxQfmiNyUcQaoxp5sff12EA4J5zi\nEum+ofiNcJ0swhNeu1ZReTUALnQ1kwE2oer1iwcoT31iaIgrLDoHxDUOoxqskDIdI9iHKF2MyOQW\nDhms1KzVknnzunHX79Zx9k9P8h3Qj4kkHPd7nvlhDV+N/4Umy+JoOecga9fBf/dEI+M9ekg1TB96\nHr7wfhwibTF60XJsFvsjfpjBQ0NEhqG6BJiC7/3o72YEGaxf/zbr188usTtRtdAbkc7u70NZvkWA\naZj2dn6wxYlDFOcA6Sgn+pG1nyhIuyoKaiFyXuaS6q7Ab15ByYibFB2hIa5Q6IfRG8CyKb34Rhrw\nfhm1qSqjLtA/c0nkbEaclUzL5V8yROZxQFbxHd8wdOtBnn4yjW/5nOlkkHCwKR8uSWcOrWHmdpg5\nA+iJSHVghDvb15ibeTb2nNtjhlcwN+YEICObNjUF+qC6D5jo1p2EeU1OABTV9ykJqcOqgWrAUIJl\nPUWS8L/FbUR6owqCXtigakWRWuify6sjbGVIVfdSOfuJtvj6B9FEllz9HvNClG+EMeJyjQSge+aS\nyNF4nF/VnwhlB0sb7fGyWw3NSJIRDOMjlmCsy/vvULpmzGL+Ryv5cP4m1rOMZrTgTnnA8RCDyS+t\ngKZOIP5MbOZrNBHLnq0PJDvXWnM3C34nl/Y1BXohkuiST6KA45wQQaI77xSscwqRfzQC2ri/49z9\n9Dt7S4QrKr2nCyK9XLw27yIBOaMXUA2RDvjiE/OBD4vYvvKGLhgNE0zms4X7exuqr5RRm/JCyCOu\nIGiEKdh4qO14vgbVF7FYYIiSRzVM0s+HyEBa0IgapLETK6nepVoqb3V9hNtmCqccgjqsQW6/nte2\nnsmrr00nJ8PZrl0T9uy5hA0bTsRmvuuAVFQfxTr9GEQGA81col1eUpMNgAGIxDkjHAe0Q+RCp4AU\ngyWj7MjtJCEAe+7VAsvtEenr/t7tai1n540oLNogcrZLzipMsZR4bFCHE+RJdLTEylR4xf+NACJn\n4HkHVb8GPimTVhUMoSEux6iHL64xAuOyeViH6r1l0agqiBqYu99DY1dGsC41WE8U6aAvchMfczQ7\nmIw5/s5v3oT0L9/j+D7C9u048YOcO8CmTesSExPFffdezNQfuvDqqwDTncBGMqZkdDeQkOe5DMmY\n7u9pzh39PuY1sTKIxg+OQ+QqVKcCkwtzcyox4olUssI994aBNd84w1bciALqInKnGywVZJCdiOfl\nMK/KHwAcFa24yhqWB1THvs1miFyfuVb1YWBlWTWqkAgNcTmC4BleiELkZUxWDVT/DnxaRu2qiojO\n/EvkWmAoUShCBsoqVO8lWl7lWj2a2vwKCF/K3/iRG/FnRJtQvSabc/sQEaKj7ZkvmDeOVq0aMvI3\nT/D229/jvw8dnZLRIVSvxGbJeSEKkUeADs6Qf4DJV94MbHSc0GhEnnSi9LPyfWcqN6LwXcsn4NVt\n9qD6J0o+i1iwwdLL7v3Zks/jrO1W/MFLSlrmBlyVBcHncyoiV1E5fmNIXypH6OlUXMASZ/6Cz18r\naQm7ED5iEBmLF2dS/S8i73EhaVyvt/Auh6nObq7WSQylA2vlNaA9B6gBfIbqv9158nZRduzYjK++\neAiA0898mHXrtrFjh0cnOtV1qitQvRxLyMofn1HkMdeOFdi7c6rjn16OxaJjERlbDBq5lQsiv8cq\n6QDMdPcriPwMgoqKFojchuooChIuELkVONrRcLx2Vy5BHpHbAC8LfbJ7PpXrN2ZFOCMuBZiSTg+3\ntNzFgsA63VVUXvWa8oSBATI/2Ii7JRDNUL2RFN6lOzGkcSavSE+26UtEkUhDuZ8FJJOm7+NLQO7A\nVIdyx9kjenPPPRewdu1WHnrIKrXMm7+aAwcOIXIp0BWYg+r3wH7yX8M0yall/RvjQqZh1Kla7t3a\nBNRzLs/XMSNcVQVcmiFyS8Qau0eeG3g3dr9KE0cjcqZ7fqvysX+c0w2vjupETHxiG5Wn9GCDLNKa\nE/BFaXaSf29BeUfomi5lxCPyJyxhBscF9TrxVExJJ0RJwuJJwcS3RkALOrKQu/UuPsbylKsBr7ON\nRRygLrCPs5gr12M8zoNOECMDM3j5malehEgbLrpQ6dZtHd9/v5Cdu/bxzTe/RLRL9ReM672BgrlB\nGyJyqWvXLEyY4BzMufVj4FzxwLFun8o9mzgSAxxVC2AXqtOybF9K2cVReyDS0w2+5uWy39EuZwSM\n/zsZo60twoxTRUdfRE52f+91+QseKstvzIrQEJcweiByXGA5A9W1+LKBc6gIXLaKi45OsCCIgUAC\nl1+m9FjzHnxpVK99JLBI6vGLvsmxWL2Zj7mM1dLBHbfHcUHBZpGTyNv9HOVmuPEYfaQ+PXvOIDHh\nXb75dh6WkGPlJVXXYYZxNgUvstACkUGo/gpMci7tmqhuxegzXvJKY6dT/GYBz18REYPI7whmOavu\nwO/Id2GiJuUBxyHSzila5UR36o/IMZhx8rwuh7H38FAOx1QUnIOIlwS30z0nMNW3b8uoTaWJMEZc\nAhiEP+OKwZcQBNWDwGdUvZlIaaI/XgUpU5vqQ4MGcOXF+9Bx45Cr+qAfvcuFg7qydVY8077cjDKH\n1bTkNa5CuZXp7kwicXjPT3UZ+Re7qIeJZUQDp2HGYDLwDTNmzMXitudjySfe+zEJX/O5IGgNHIfq\nJneNswPnnYHv4mwO9HUZ1JUVKfjsAk/gJPitzaf8KSj1QqSNU3nKzgifjA3YYjEjvILyM4AoLOoA\np2QuiVTD/84WESYP+ggNcb5RCz/OCyJH4dXuVJ2WxbUSonhh9z4qCs4/D+Lj4atJI0hp3oq27bwR\nptK8Gfz5hnTG/30p2uogWv195kz+lf+u6s0nHOfO0xl0ixPRcEfq+xSMCpGCcT+bAhdgM+bvsYzn\n9zGD3ATj8TbDZAv/VYTf3wp799KAbzDXa3Mn+hF04aUAPTFPzHtFuF55Qw88IRtDsruvAOmovowv\nA1oe0RWRTs74eG7yGpj3xCDSBuP/fo150CoqjsKkbQASAs8JVN8ilN7NHqFrOlc0xucT1kHkpMwt\nqi8QuptLCi2AZFJSlHZtYcfOFObPv5oTT1B+/3s4aaDy6N+E5GQ4e4QSHw8LFwrKfnbtWszIS4SD\nB0H1VcwoeZ6LZogcjxVPeKKAbWoDJLm/2yIyAJsRL8VieH/DZqPVEekOtEJ1JkWXFGzu4p3xqM7C\ntHT7uutlTfLrh6lrjS/iNcsa1TEVM4OFHepmLqv+DLyd9aByig6IDHYx4VnYO9MME+vxZ4uqL1Fx\nKx91wMIyOM1tL8yzzlEyQxjCGHEB0AjPUWDJBH3c+pWu8wtRvIjFG+y0bg1xcbBh/RXs2t2LS3+n\n3HGHsmiR8PTTwrhnMxh4chSvvKx06KDcd79Qv94uGjXaxb33CfbhP4INoIyHaAkvHhViZgHl76Iy\nz2VxyObYzGw6qgsQOdaJbjRy1xoFNHSx2eJwK9ZD5Bwsbr0bkeHAWqfslBW1sUFHRUxyScYXpwBo\nRGSVoMcoHv3l0ofIvVi5vY3Yb+yOla5cjerosm1ckRCD/95fg69yNYFQCyEnhIY4B0TjZTZ7EHkU\n7wWzDnVCqbeqciMWiCE21lzMGRkp7Nv3OABzZmfQqiVc/0dhwgSb1R44AL2Ph5dfyuCYLp4QygG8\nBCrVd4B33XnBqD1PZy6rjqXg2sree1HDnSvGGb8lLkHqdGCGM8L1EXncXes2iqd0nYn0i9yM6ixE\nkoEkN2vKDnGOIpdeRBd4acJ+I+CM7omBbStRvaMsGlVsEIHExHj27RMyMrxB2gnA5wUcDJYnxOB/\nZ40RGQOA6s34dKMQOSM0xDlggCP3+1C9Cz+OcYiKn6lYvmAqOYP4zW+UZ8cqCxZE0e8Ei7XXqAFR\nUfDMWOXMM5QX/i7cfY8QHQ0JCbDbsYesk16FdeQHMXUkT91qj+sYDrntByh40lxXx2vcjeotQDoi\ndwLtUP0PJpRxsbv2FtcexeKURdUgjkXkeSwb+inn5t7hBhzZc4FFbkB1NVb1pyLwheMQeQHP1W+x\n7sn4LIMMynfMN29Ur16NRQue49ThSSxaJC5MMgV7FyvCM8oOZyEy0v29AdW73d/F8d5XBYSGOHDt\na7DKHQC/oJq1KskGwmzn4kQ0Io/wzvhEOnSABx6qy9tvJ1G7NjRpDGkHIDUVJn2ZwVlnR7FmDTRt\n8ho1a6WQmjqITZvAVKceD5xzk5thHO2W56L6sfs7A4vdF+y1tg7GK2m4HNXxWLLJ9diM+A1EhmDJ\nKF9hFXfA4rTFlStQz7kyn0PkJiAO1feA78jJ5Sxyi+Mk/0B+FblKH4Oci93DIaf2td8tpxJkHVRs\ntKVlixt5992DXHPNc/z8ywEOHICK+htN5cortvADqt+4v9MpOP2uqqNKG+JaEco6qj8SKa5RHK7E\nED76MODEYdx9t71Wh9OFS357DB06xFCjhrJwoTDgRKVBA3jqaXNNxsbCiScqP0wV9u0HWOUEDDzh\nk72YOlS0k/hLRPUHfM/FNgqrDWwekUZY+blVbu0uYC8io1D9BJEbgK0uo3UtVkw9vypY+UULRC5C\n9UtEhmHlCndiv2tbtkeI3OSM8EzKm8qSDZRS3NJSJ2rjIQMTs6gsinLDEent/k4iIaEOvY9/im+/\nm0d6ekX7jU0w3XWDGV7v3dpEmKBaFFQ5Q9zVZbWCjb6DOrtzqTySaWUPkcu44/aatGtny19+mcIP\nP7Zn4AB7rTIUxo8X0gKexi5dppGUuIvvpw52a9Jc3CzYaS3FBkltXZISmDb3Emw0Pof8yExmj5qI\nmE6v1fhNAxZixrUzIoMwekl3TOvWVLasElJJyCG2Q2QAqusc13QxFtfOi2/cD+PMlnVpw1aInBmx\nRnUlvnb6r1RONbkLEGmM6kZgGyLtMR3o/wMqEp2xLyIelWq/4zB7mEHFTAAsj6gShnhwQLUlA1Wv\nU9+HVaUJUXS0oW3b3vzut/4r8/TY0zlteCIpbvIzfQZ88YVkc+xHmLZyUzzBBf8ZHcCekbfcH5GW\n7u/gs8wAJrr9C4MWmdKHql7s/zPMkPV2XM7WGL9zOyas77W9MCIc+UFHRLqhmoFIDKpp2L3I7TfG\nI3IOpjtcUu3KC30clx5sgJQ1nPMVhR8olWdUd252cb9ZMZW0WES6oLoB+LpMW5g/nIGIcbPt+/Ji\nvKnkXfs6RMHQGJFTUL2osilr1SNIhgcQaYzHZTN3XVh3tThw6qndadmiAQCLFnVky9aTqV/ff5mi\no4X/e2MaRu1p4tZuxDqn6pjUJJh7+Ud8EZRghxWLKfBYWUKRBnh0FpuxflaEX9Al0K5ErPbsbuC/\nbl0/bIY8EOiEuZ4/wWQu/0vJogNWiKIB9r7GAO/kcUxNLPu2Fn45zZJGAjAgYo1IPfzKVb9ig5XK\nihR8Clw0vrjIu9i73hE4BtUtlF8jXIdgrXORRvgZ0NOw8EaI4sVRQDusH6yZ654VyBC3xDosMCm4\nnhFbzR20qnSbVMmQnJxE/34dI9YNHdqdlJReCA2Ii4Nnx+3kut+vwU+UAtXFiGzEOLeNsMzln7DZ\nQ4Lbq6XLOA66KGthwg2xzjUW5c73HrkL4ucHx2Izx2PxpDBVF2AF2MEyqrs6F3VD7N2Z7mLFWRP4\nSgJtEDkXe69XI1ITqxmcG2pjuuYdHHWqJOOPjfBjvAnZfG8fULEVoPKDVkB9TFSlk1u3x917bzDa\nBpFemIb4V9mdpAzRgkhBIv8ZmtBGGKIrObTAZE3bYnS853Pdu5y7plvgz5JOwjpXgMV5/rAQeaNl\niwYkJydlLh/VpjF333URfgcMN970CpMnN8R4nsnAQlTfQeSSwJmauCzjmUA3RDxOaCqqD2S5aj38\n0WELJ7ixF9X7KDpVLA5TLbLYNdRyxi2oaRtPXFwTOnWMZv6CB0lP34FVWfovpRfX8xJiUjBJzPyo\nb9XEPuweJSQsk0LkuLw7fgWjrag+VALXLK9ohlGsBgGdnSpWdmplTRE523ngykvRAv85Wp5MV7d+\nKarjyqpRVQhNgWqInITpwgcH9RUmRhyL57o0QYO/4rmBrK7ql6XRvEqIGGJiEqlTJ3Lto2MuZfiw\n/niVa2b8tIzTzxiHyENYx2+xXtXXsJfLe2brI9SdRG4E2rqlT1F9I8v1/XMZ/9ajCf1cTEYlDnP/\nNEXkbtfmm7HsZg/ViK8WT/WE9tSseQ/fT95J1+7C1q1/pnQy5wWoSd26sHv3Xzh0qLl7pz/J5/En\nOSP8eN675gnvfgVaJw8SKSP5EfBWMVyrIiCGoLKXyD3Y4PJlcjawNRG5zXkGpuewT2khGo+TLfIw\nnqSribt8XmatqjqIwgvTiNwOtMjBXlUYQ9wbEU9RR1G9Fr9uaAYhabyw6MrRne9l5k+Rj/qKUc/w\nztttwNU9VVUOHdqI6h8ReQVzhYLd9/Fu1giQgoiv1Wyz2QWBfYPPKRqRV/EHVC/hJ4MoxeNeHeT4\nvr+ieqtbd5hILvGZnH/+Zfz+WjhlcCoxMddy6JCXqFIan0BNRF5h4fxoRl0dy5QpT2L84Py+01GY\nMS+O+zUEkesi1qheT+TApSp9b0e7wafBRFxWk9s9EHnJuagXUjrvT25og8hjAKheh58kV5WeYVmi\nrusvPUGoZWR/78uxITZ5O0/PeT6q/w7suYXwRSo4RP4IdOEP1ys33ahMnlKNq67eT9OmjyI8jifr\nuXnLTvbseR9LFOrp3KWHgc2oPkpkRu5JzlUHsAnVZwLbthOpFuSdC/yCCN65duELORTlN/4JP1Tx\nk4srp5OVcytyNXfd2YuoqASeHruYGjVeZMOGw5RuRm9zRB4A6tGs6d1s2bqFtLSd5F9Y1Gn/AAAg\nAElEQVQ96kxEalMU+UrjQh/jlmY4l3gQW6k8vN784lREzsNieEHZyW3kLOpTC5HHsKIhKyg75b0R\nAQ/VukCorio+x7JEK0T+EPDspZLzO1EODbHIfAAn3ODx1nZTcSuQlBVaIPJ7oqPh3XeU5Dpw510p\nTJ1ag+bNoUUKbN8B8+cfwOK7b2OSjddgVJ1NWMezClXPDafAUid20dStm4uql5xzAFiepR0XI+LF\no448V/GolUU713OSU7by9G13kJ3QwLhnr2HChBNYtnwK8B0rV+6i9DVxO7jZZ0OsIMUiCiZxeC4i\n1ZyYSH6VjFpFiDIAqH6JL0KyvQDnqnwwXe5jgHlYhay95C880RSRq9w3tITSNsIiN+MlX1lSoVdz\neT8FK+MZoujo6xgPW92gNj88+XJoiMEbQSwi0iUWInecjkhHTh0Kv/udsnRpTe67vxsicOaZVhJw\n8mRh/XowSTqvClA9RH6LURUOo7qASEnEOi7Dz4cloQRFGY7srEw7ujaqy/Bno1swl11xoSkmQalY\nKcB0LKs69Yg9k5Kq8/xz1xIbG82UKQv48MPd/Lp6JWUhSn/yycfSq+dF/O2xhm7GNY2CeXjOc//P\nIG9DcVIgK3a3e75BZH+/qgYS3WDIy3lYit2LNeTfgB2FyFD3/k2jdNzRKYhcmLlk5R89b9IqCqsm\nF6IoGI6VetyE6irMw5df9kDOhrgM6Uvfld2lKwyS8TR677hdqVdPeeutXsya3ZxNm+fz008b2bDB\nZqGqGbz//n/wPlSRfkQa1/Qs9JhpWGzME2U46DqoIH7kSNWmZogMzVxSTcUM708Uv7E7GqsffMi1\nTTHFqSPFLjp0aMaoK4egGRnMnWud64SJ01i7Nnt5yJLGkCHd6N+vI3PmTEd1F6YFXRCMwOLC0znS\nCMcjchEeowBAdV/g+W0j5NGDGbLBmCjMcnzjOYOCS5TudYObH4uzgdmgt+vowX/vPfyAdfwhygbD\ngBrumazA90gUHRWIR1wV0AVoSefOMGSwsnVbMm+8YYlUUVFfEB3dFaQ+ALNnw6xZ6xGZGDg+Db+z\nmYNlxnqzgD2Y6MJQrAPvh0gwM3o9OfMgrV2GuMxjDF9QvJ1Df/zsXWu/6nZyUkfrfXx7+vRpT3x8\nHFFRwr60dMY+80GZavwOGtSFvn06MG/+at59r7B1iaOwjtcL1bTAp6JEceSnOw+T4Kzq6IZPv/Pe\n1YNYOdPC5pu0xFzC3xSxbTlhCF4Wu0gS/je5jcotlFIREIP1mTEuT2MqJSHXGhriMkM1gupg/fvB\nxo1DWL6iGw0abKR37y2sXXs0bzgm0COjVyJyEF/VpwkixwWSbsSJYnh1eD/DjHFDfGpRP0Q64gtn\nfICf7RyEAMdlnstmzV6N5hUUfz3VGHe9KESOweMZq85wIiDZoTM9eyQzdGgzOnVKYc6cFdx8y6vF\n3K6C44T+nRh0SldmzlzG2+8UtA4y2LPphYVrWrh/AI0C3ot9LjknTMrx0R0THmmDH0ddVgzvagug\nJzbAnVbEc3mog6m4GUwsxCiEFssPVa7KBxIw7n5HINr1RSVDdSzzrOmqgwZ4M70aNZR27Woza9Y9\nmVsfHaP8+CO8975gWa1TsbJ7PlQ/wa841Mm5bT1koPowlp3cDI/XZkUTPN7ufrdPTkkm1bHRvzjX\npycZ+i4l45JLxGYv1VwsLNop/qzIYX8B2tClSzRr1lzBVaNqs3Xb27z6allr4/rt+tMfBzNhwjQm\nflBQbmkC8fEpdO0aw8yZfyY9fTPBrGrVacD/irHNlQFxmIwgiJyN5Sq8jbmeiwONETkZ1f2YnGXR\nzuXTAZsHGAi4JL6yLtwRwkctTBa3FiKnuT6zsPr2QZTLZK3KbIgFU5AyF1O9enDo0Hns2jUMgO7d\n4NlnM+jXP6gVvJPIh73UCWkEzipXYZnO3sjZE1yIJijGIHIp0MEtTcEKr+eEJHwRlRSX1JLhuJQl\nFY9KdP/aOYnJve56OQ0QYomJSaZJk2jWr3+ciRMO8fgTh5k06V+UtaJRTEw0TZo0YN26J/nwgwP8\n7W9P8PU3+XER18Qb6Bja0iLlNr74fCu9+wqpqfcTMgiyQwKeeIXxN403rnovxVuasjYiF6O6lqIV\njamDuTXPA3q4dXNQfbbILQxR3KiBTUa6I3I+sAHVPxfj+UNDXMIQPHevCERHJ3L48Kt4He0/X1d+\n/hmeeNKLrSpZ41U2Kv4JP/7aFZG/ZNnnz/gazP41oT4ifw/s91dynxV44hAg8jvgLLd+Eap35vVj\nCwn/mnC+m3HP5kgJzCAEkSiiojrQvPloFsxLp2XrKDZvvonyQNcQEY46qhFzZz9Hy1ZRbNl6I7nr\nnfvJVUZF6Zdl+yZUryn+hlYKeO/PWe6dBesor8vlmMJfS+ReR60sqH508LsEkaeB5s7wljct6hA+\nohC5GjgV+BrVsSVwjXKZNV2ZcCYm4A/t28GE96F7z2rsc8yfP90gpEfQaJej+mCWc+xxHczJbnkR\nqpdn2SdINxrs+JBgJfuC++ZeGk/kUfw42gTAO7Y4uL45XfMB/HjnZ669efEwh3LGGSMZdWU055y7\njVZH3czWrVBeMkd79WrL889dS+s2V7ItFXJvVw1ExuJ9ciaBlzV+GYrX5ATjtB8HTAq86yUTIxd5\n2OVPFCZW2wGRuzKXVEdj4aS9xdS6ECUBkT9iNbQvp2A8/2K6fjgjLijEGZUagXV13D+Ij99I+3Zj\n+WXeA2RkmIKVaS8HP+o0YC8i90ac2UQwvBnvPrKKVIj8AS8mZjrNHkXlELknEXRwAh7edd7AL/a9\nlZKLT9XJnNWbPKanZpVKbpxWG5B0A2qTnLyW+vVfZ/HidEpHEzo/GMiQwWdxxRXrefiv45k3L7t2\nnRpB84I0Z3w947ERf8DUDZH+obsyG9g3kozqp5iIzHayqqcVH+IQud8lQM7D59DnhbPxC52sy6Ja\ntpqy6NhD5A8i92PFYT7BkvF25n5AkRC6pguJkxHpm8367vi1PLNiPzDTGUmv012OGaHjAglYaQFD\n6mEVpnTloX4WA/oT1hGBdeS5GaZhiHgxqW1OiMDDXPIvr1gYdHL85/0BQZF55DUrML3oZKANFvOe\n5gx48dMFCo9BiIygSZO9tGr1T6ZM8bPOLYbvlZ1b4birHtKxGs1ZZ729ETna0SKyy2CvamibRcRi\nCvZNeSIcJYU6iFzjvsmZ5CXDajKynn76YnxxjV0Ur5hNiOJHE0SuAED1Oyw3Zwl+31pSCA1xPlDN\nKU/5BlZ1OyIt8KsF5YSZqAazZA8Bk4ALEKkdWL/bCWCAfehZi4ifGCDz23mM3+thGnnPBs5DpL67\njufK3krpVIjp42Qu92FF0rP7jVlRJ9DxDsSScb50pPmVlK9ObTAiZwC7UJ2LSL2Iraob8Gc/S8l7\nANEXkVZOKGJ2sbe2YqGXUwbbj2pQae9rikObPHc0QWQ4qmuw7za7kElLRIZlLln9YS+Us4CwFnpF\nQSusRKHHPplEyU5KgghjxNmgI8Hi9pZkcQCL0XolrWZxZBxKsRqTQWrJz/icXc9FdQ4i0QRngTZy\nDiZReQOSeHe92Cz77wA+zuN31MWPK4NINXeO2dgor6QxDL8Em7XfpN/yUk5rhRWHSAaGu3Ufu+Mn\nUx6SsXwMBxIZMeIENmxoxfTpC7DEq6wz/G/J/6i6NyIt3TtRlY3wCRhH2nt31mKdY2khBeiD6lbg\nsyzbeuEL2WR93l8Rxn0rEo7BmCTRzgjn1a+WLqqIIRYsQzUusK4hIo0wV2g34ACqLyMSTFjqjlFI\ngh2Dovom9hEei9GU6uAZcJFm/p76Okd2zA3wBwDiZtyeCMdX5E82rQ2+elBilmu+SclrdydhiTMg\n0gpfjOA78k5w6YBx9Oogciz2Wya54/9NycZoCoIk4uOP47xzYcLEkfTvV5O+feYx6euvsPdpF6pF\n+ZjroLoImJXnnpUL1fGrrYFIa0w2cCrFJ5iRX3hiHYeB9/EU57xuUaQ5Xu6HCdnkJC4TovyiGyYV\n3BhogGnily8jDHkY4rS0NAYMGMCBAwc4ePAgZ511FqNHj+b+++/nlVdeoX59k1t85JFHGDbM3Daj\nR4/mtddeIzo6mmeeeYYhQ4bkdokSQj1M1MKHyABs5tkKi+18S+NGX9CoURtmz+mGuab/gBWh8GOv\nqj/iy8zFAp3xlKosftw4cJXlqD6VTXta4BXrtgIGvb2zE1kiMDd0xDN4pj7Vzq1fk8M1SwJ1sAFA\nTUROAnDXzk/srh2mfNQd64jXoToFkU2ojiupBhcQjfAUxKAR8dWuYeTIeUz6Op4hQ5YxYeJbfJMv\njnBeaANMpWqJOCRj30Fi5rsDXvH6ssgBaAoc72QLp2PyodGIDMQfGL9H1RsoVSZ0cGJGDVD9Aniz\nrBuUI/KMEe/bt4+EhATS09Pp378/jz/+OF999RU1atTg5ptvjth3wYIFjBw5khkzZrBu3ToGDRrE\nkiVLiIqKitiv+GPEjYgcU/RySVFx2AxUsYLNO7HycF0AGDFiL6eflsqoq3ztZCty780oaxGZHV3T\nJWl4+75A9jPYKMxAe1zds/BnwbNQfTmfvysWL/nHhDa80fl7wOf5PEdxIBkT4OiKyGmYEX04H8dF\n4w1UrO70/7d35uFVVtf+/6wMDDEBgkiICRghgCSEEEHAAcUi2ooiFqtonbEDvT+r1WvV9lqt1gGH\n1uGx1vrYW+29VVurYm+FaqsURAQRkAJqsYAyKyAzGEzW74+135xzQoYzT7yf58nzJCfv2Wfvd79n\nrz2s9V2DnUoXzst0RQo9hcXVLfjZHO3q1Qnr+9WoPozId1F9Ekv4HSu9ELkSkyA9FKQMu2E7KNWI\nTAQ+c+IbqcUc6zqhutJ9P8ESn9xM+N7SPulHHt5k2r63/4MtrtKBGM6ICwpMdam+vp6GhgaKi21l\n11KB06dP58ILLyQ/P5+KigoqKytZsGABo0aNOuja6MkldIsZF7dX6l7PBWageh3mgXkntgV8j7u6\nHs/546WXZvPii15CbSGgdOQJsE8Exgd90tY2BASC61XgPs/bsn0YeDTM9uURcBgrd/UH1WtIbg7Z\nTgQmEpOBU7EYzvYEFILr3wORB7AB7yZEDiByLqrPJ0iIIdx62d8idxA60XrJPTd1iFyE6jREHkT1\nB4R6s0eDPV8it7jJR7oMDokg+NmZhInmv5mCPm+O1atzZ2hoUA4cGI2IpEG9fGLHG39Lm8Z6+97G\nU20tcbRriBsbGzn22GP597//zdSpU6murub555/nkUce4emnn2b48OE88MADdOvWjQ0bNoQY3fLy\nctavj/eNOMkF9wdQ/RGwyYW/jMa8W08hdLXjXfsQthJRQh2xChD5JcGyg6ZbewWBjEZtbR6MdqtW\nMK/h72NGX4ksjnBCkBfxOlQvxwa1RHuOBpPrxCfM49vSJ4YjwAFwOiaxCZY0+ypEHkPkp6j+HHgw\nzHLizRkEFJnA0kJeR8CzXLB7/1vsS52PyF1ukI6HgEghIo+h+mNSkRs5mYjch+1EgeozwOWkQ4IK\nkfuBI/jVLxuZ9/Yz/OrxK0ikiI1PMjnRjf8bUzRmxka7hjgnJ4clS5awY8cOzjjjDGbNmsXUqVP5\nyU9se+mWW27h+uuv58knW858Y9vQLRHs0Xs4wVrJoe+/kYAiE8A/Uf1PbOZzS9A1X+Jt3Vqz8rCt\nxfualbiFQAeNChqc92NqV8FGcwdteUbaNvcQ99dSVy8w47udcJOHi9xEwPlqblA5B0juNllfTLu3\n0Z39em3/nPZjgK/AvEzfCap/V0TuRPUO9/7ge594RH5AIPPUgqB6eXyGF9crchFg2/4iQ1F91P1v\nJ7EngS9D5Aeo3oLN0FNvlOJPbzxFKcsM5TndbSd1W701QZNjq5fIt/jxLa+zd+8b+F7P2cIZiPR1\n3+8vSZ+jha2EKz4Tttd0165dGT9+PAsXLmTMmDFNr1911VWcffbZAJSVlbF2bUCoft26dZSVlbVS\n4oAWXqty26ABVGfhnYfa+d0o5wEXLJjvOUz9CdX3gl7fQ7BwvhnOI4P+/0nQeW0DFjLTlsxgV0Su\nD6rb2wQ8PbcSvkh/b3dG5ZXzBoHQiU0kdwsaLP73a8A2dz8UOw9tf7Ugci3mAfwO8ARm3Lohcj62\nM+CdrSZ65dHfxYEHsDCoWe6vT2ltm0rkYlT3YFvHBe4exDPhwja3q7CG2I16OvEV59wEsCPou/Qv\nUqcmNdE5BAJsCvHHEDkL1ZdZt+5dQuVifTKTC7EUhf9yEQzpliSl+QKz9XDSNg3xli1byMvLo1u3\nbuzbt4/XXnuNW2+9lU2bNtGrlx2Iv/jii9TU1AAwYcIELrroIq677jrWr1/PypUrGTFiRBufMCkk\n9MZCQgLxpyJXIXIA2MnF31T27q3ghRc9OcltHCzMvZxQI9YLkWua/lJdRajDzQbaVzMa6ra5wQQ2\nguNj38MMTzicREDpal+zct4l+frJ5yHiTZK2uvpsJ7yY1h6IfBMAVW/QXQZUusmS14/7sPjqRDEW\nEc8JbnezewqWRKM1z+Rc50DWGdVPECnCtqvnYUpo8aICkRNdWFm2cI6Lgf406J7vIjXx0HmuH72U\nneuD6vQZ9h0tQGSKm6QvJH1C5Hyiwfq7ENW1rq/XkD7yt9HRpiHeuHEjl112GY2NjTQ2NnLJJZcw\nduxYLr30UpYsWYKIcPTRR/P4448DUFVVxfnnn09VVRV5eXn88pe/bHVr2lYhX+IpnIgMxNzND9Cl\nC/zn9XDf/Tns2mWGfMuW+ezbP8+tQsG+TH9rVuqJiIwN+lsJKKgAzKX9UJtz3KDs0RhUxt4WPrM9\nxiFSgmpDUDlbSE0mlg7Y5Cc35N7bTC2cQbTShV4F39fZmELUaUFtXIuF58STQuc8FyD0nm6kfRGR\n0LJUd2Ce9AWoHgD+SXyVvCoRGYmJRWQ6uZhITcegZ2cZNvlNNhUEcmx7wjce7xIqBtMdU836FBNc\nSZdtS5/IKUDk66juxkI+55MpzljtkTKJS5HdmJThekaOVPLzhjD3rdEAdOu2n7vufJ2bfyTscJNX\nm/ksa1ZSHubN6wXgH0EgVymobqb9ZOo9sLNNr27lhMpc/hNorgndFoWYw5hXnm2j20orVQpKXhtz\nEOkDCCZMv6HttzVRjZ1hFyHSA5PP9MQNTkakksS0sQKLnwZb+fQO+a8dW0Sqz1yM7U6Uue3iYxHp\nj8WSxlPruRIThNmLKbFlIqVYfC1Y5EEfIAfV/yOgrZws6gjEeBe67zpAAyac01Li9p7YsUt319d+\ndqvMpAT7LuUi0sf1ZSae76eh1rTIFrz980svWUunThv49RPe6nlnC9vOYOe7wVvZee6MyvK8mnEJ\nR3ChAs+r05KLD2/6jzmaRJrdJbhehYgE8syq/o7U6dB69erhtsX3oxqJ13I1JsBQheVUXYIlSe+M\nScaByGhUnyc+W0NDCD37PwqRY9zvO1wYWLT0wiYTxYgMwERE7NhB9S/EV1TiaESOR3UnmWmE+2D3\nqxRTPwPbtn+Q5Dnb5WOTAC8MqhbPEKsuA15s5/09MT2BIwk/bt8nvSjHxrCeiNRhWv0PprhOsZCW\nhvgTPINguT9b2/Itw4vHtS9WcDakfZgAR0uz4eYchWewTdnHG2A+dMY3UoLrNQIRT7ZvI6r3tPKe\nZFBOIJ7Zq9cHmPhIOOTheXCLXIip0jyHbTUXAUcQekZ8B4H0hpFSQGCVAyKX42W0sbJn0f6AGw6H\nA2Pc+fUq5xF9tDs3fIT4b29Nxs6mZ8a53ERzJOawdjK2An0XU75KFl2w3RvwznW9EETV/yZ8f4Pu\nWDhhT98IZyw9MVGm47BImea5uzORNDTE8C0O9g7Oxwbn4Gt/iBe+ZEns/xjmpwSXlYPIzwikLfst\nkZ/15hK87W0hU31ceS8Bz0dYXjzJIZCo4ibAtnAjq5d3v7pjQheg+l/Yar4zZtxPcAZ4LaZAFCmH\nEeqWUOVi/3Cfdx3x18kucB7cB1D9A9bGHpiwxtXE33v2MGyCmQk5aJs/09cB/TA1omROIrzn6yQ3\n+QPbAfk+kYd6dcZScHZwxtsnsyjCxutLUf0YeDnVFYojaZl9aVMLrw1zBi6ADfiep3MkZzzDnRG3\n96l+l0AChmjOivohMi2oXjcCq2IoL54cjsivgVjqdRwiN2AShJe712wQNIGOMzBlrcuJNgTHQp2G\nB72yJOizAp8XT0zmbg0m6n88Fif9KapXkYiQKosXng+8Fvey408fRH7e9JfFOX9Asp9nyw17GvBa\nzM+D7XJsAZ6KT+V8korIXUC527VKZhau1JJCQ2yDuW0/edu6y53BDGYb4Q6YbZe1legGmLFulr62\nWXnh1ytxDMMEC7YH1S3Sen0DkTOAZa6MhpD3i1ztDNl3sfPBSMo+vNnk5XdA8BZTfYTlRYbID1Fd\njHnLj0WkqsU2xu/zbkX1dSxEJp05GROy2ZiiZzofU7k6DADTH4/m+QrFJkEfYt7RqZ4c+0RGJ0Tu\nQ/VxLOxsJ4dSH6bwjNjCHkx0wVvB7SKyoOxOiPwY70w0tKydRCslKPJtoJ/7633nUbuP9MmRe6aL\nbf7YnaMeIFJnI5HvAH1RXYiFoATfrxx3XwudYVlAeHl2vXp57EY12Gv9E8LLNBULBa7ueajOxLLn\nnOS8vf9OYuQlcxH5sSv/PRLfxmg5D5HjMAGEeVhO7VXtvCdeDA3adm7A5GM9344NxJqJyozwP2k7\ndtwn/ajExI0OuGfiA8Lz+clE0vKM+F731wdEdi44GFOBAvtCLyIwc4q0LI8emESjofo+AYGN9cRX\n4CE6RK7CS6Wo+gl2vv4ZkcW9dnIr6DxUV2ATn1UEjFMZAanHRZiBX05bXuT2JfI0qb16eezHjHiy\nOAKLT1+E7bi8B5yMnQu/Q+KMjgCjsExc6RRWkef62xO7WIU9MxtJTurBCZg+AJhojHfE1IDFgMZj\n9W1tNGGZcCeMPqlnJAHxn/exZ2E+2Sn/6pGWhjiSNIinIeLpTX/hArrBOm8m0X2ha4PClhqaiQK8\nSfSewPGk2DmeeKIF3kO6nMgG0jJEvoqdlXsa2MFtrMaEOg64kBvF7mvzmekAREaHvBJbveJJOSJj\nUf0MkwttwDJnFWIiD/FIYdgSRYhMwpLG70/QZ0RKCSJnYcIr2wlMVBeTWAWiTm7V63k67ybwDK0j\nMVv2ucBXsVj/ZKvT+UTH8YgcjepebGI4N9UVShJp6azVGsXYKiaASFe8eEJbdYWroNQSI7GQmYKg\nMndhzjzpQh8sfCQPr47m/BPpQGNqZbZ1L9iE5c8EJi7DsHCnzpjIx+fu/8F49wuC09sFiKZe8STQ\nRuvHV9zrp7nt6DdJ3I7G4UDLWb6Sz2ACxyn5WD81An8hsVt9FXj5ve0+5Ab9L5G7EGBnzKdiWvSZ\n4KV+qHMytrgodDsY76S6QmlDmhjiCgKCGEVBIg6GOXNEu9LqSKhy1iAsScE8DtYmTjX9MDWjEqdW\n9VmU8XNVWCxlb6dEs7qFcmqcSMIRqC50K7ouwEkhV3n3C0B1qYspThdMvcrauAp4AXukRyBS7Z6b\nRAnB93Cf0xPVXyXoM8JhCNAFkaMJJDRZl+C4y2q8YxLTc/cmAHsJZK1KNF0xT/+BqEYaiuiTPDoA\nJlNsuvBFrr/eTWWl0o4UGuK+eIIYtkVc415fi+q01t4UJsUEVnGHITKh6T8mj5YKfdzW6E9AovN4\n4BhU34niHghmmPIwve3eqP4dywfrkeuuyUFkHJb1aT22shuEBdGPDynVYq7jKf0YL3o7Vay1QW3s\nCAxC5GxU7ydyhbRw6Y4Z4YooxWBiJRd7bsSJHvTEZCd/l6DP60BgtQ0ip2GCNqA6Pw7f10jpgk3A\nhqXgs33CpxOmFWDjr6nZJVsaNTNImSE2r11T0THP2h+2eX37dCOgKHUCIme73z/n4Dy0qSYfmywI\nIv8PT1TBhBR+E2VZOU1lmRRkcDrIDtj9KXBxeh3cALbeOb55RwH/RjXWfkg0PbC2Xujidf+BfeG7\nYKuzK1G9nvBlPKNhuFuFJ9MId8YTbbHJ5XVALqbilqhzee++dnfx14bJDIYjJZsICjBHn2N9I5y2\neM9qOSLfdONvNqX/jD8pdNb6DrFLCwbOo0RuI7Cq/r8Eb81Fi2DnaAMQuRtznppCdJ6ezctqcGVt\nD7kmJycHkToaG291r4V6JdoOQTxkJJNBB0SeALqi+jPM+UeA05138MeoXtNmCbHjnQcnK8YxB2vj\nOCyfNpin6ZUkJubX+zywsK8fYHl9m8f3p4IcLN9wBao/b+9in6TjPTtfddEUH6XhIiiVpKWzVkvK\nWpFQ5gyQYdse3pczXePQxiFyMbAGVS9cKtrcqC2V1dxpagIXnD+JCRPyuOibAHucoQp2bEmWiH+s\n9HAB//+Fxel6nvPnIFLq7kEyQh8uQERQ/X0SPsvT3x4DvBXUz40kSnhD5Ht4Z3qwKIn3tX3MIzvf\niT74pBsWYnkSMMc9N6kWPMocMiR8KZgR7gv5ebPBcD3palTMYA4DljrRkf1ELzbSdlki1wPl3HyT\n8vnn3fnj8x9R3O0ZVn4k2IC6hszbJjoakSvc6n0NAcNwPiJ5zvkj3hrVB2P6t3uBWSQ6vM3kRo90\n5/grsAnbZwn4pEK3m+RlMPsrgVCvXcDmBHxm5Ihc7rziZ5G4s3+faLFY7rWYlkOintVMJ+PjiM9H\nZID7fQOqyzGjuzTudYsPnRD5PgHFr2WYiMImoo3jtJVK92ZlFSAyqdmVg4HDGDLkFb74YhEffPAZ\nyVNPSgRViHzFhSEFZ9+ZjJ0DzycxalmhmBHegYlGNE9WEg96Y5rehurbmCFcTfwnGXVBTnn1bkLn\nbbV/RLoZOjPC27B7H+tOmk/86IDINUBHJ6KzgPTQX0hXMs4QH4Zp4Rom0rDX/X7MMwoAABczSURB\nVLWO9DXAvZ2QQiOq6wisPJdgMn6R0h2RCwBQ3QAcQKQHnkavhYt8hoV8Xexee969tozM9lA8HpGh\nWBv/BcwL+t83MMPxDsloozmc7AXeJv5GuBZL7fkFqsFG5k3iG589HpE+7vfdqHrGth4T109PXV9T\nSttDYu69T3SUOU/oRlTXY8+Ob4TbJy3PiJtTiYlYgB34B0sFzidx8aDxYBC2Es3FzmHrMXWnaM9I\njsY8c7sBZwIg8pJTvWrAuzeWJmwZMBYvPaSFsWyL8nPThVEuLnYPlnDCM8I5wFmIdAwKvUo8ZoTn\nEt+V6SgsXWUe1s7N2DMTLwqBrzX9JdKBwHOzEjNs6UwnbLIu2KTE3+pMD47Cnt09qB7AF1OJD2lg\niKuwmN8eiJS513alqddzc4Zg4TQliPRC9WMnjBEtAxkypIyiwmremnc6NnB6qcC6INIF1RnYOUxv\nLJb0BESKUH0yloakEcciMgjVpYQG/XcCTkTkKHePkzEw52POJzOJ3f/AK8s8kk2ytRuq78ZRWKYP\nNqEF6IhIedN/VF/EztczgSLsuS5H9Tf40pXpwABMdKkYi9B4OsX1yS5SaIiHAmDZYPqg+jaqv0hd\ndcIiH1MVMmxLsRTVfzQTzggXAaoYMSKPLkXwwYcTqKnpQ2mvTbw1bwmWN/eRZu85Crt3lU4Zay2q\nv46uOWlDHjYhy0FktFvtBh8/HIZt4Z6M6r0kJ7FCZ0x9bAyqS4jeEHfBxGs6IDKGgA7zH4hPLG4l\nXhw69EdkiPt9WwZ8n1rCE+uoc32dnlvmhw79saPCoUA/VN8Dnk9xnbKPFKZBtK1mU26an+wqREhn\nTH2qCyJXN72q+hiRn1dbWfn50LevsGrVPTzz+71UV9Vz+x3CM8/OBF5u4X29MNWsc4DBzlj9IarW\npBf5QIVzbstz8aHBAhWdMSN8lgtdSgadsEQYk1G9meiOGLq4n0p3zr87hrKak4NJoYrzpegN4LzH\n/9TG+zKBGqeMdleqK+JDqQtJOhKTtp2V4vpkOhnnrJUu5GOrteHOAG9FdWqEZXTEWwV16AC5uaPY\nv/86ysuVpUv2Mqgqh02bb6J1z2bBvLDvBUqcatabUbUm/cgF+iJykxOMCFbD8u79CEROQ/WWJNUp\nDxiGyHmo3hDhewN9LXIuMBFYjOrdbb0pgnrlu9+LEHkQm7j8BDuqyAbysPvnnzmmjhwC0sO/QPUB\nUpdRLdvICGet9EPkG8A5wEJULyea+FuRG/G2s6dcqRw/KpfLroANG7ZS0fc/2LkT2k6fV4DIY6je\nisV0ZtMgNdiFBV1Nc0lKW0WeDSxA9c4k1ulkRI53Bi4yRO7Ajg4AprtnJl5iGKcg8m33+y43cfmS\n9Em9GA/GOOnKe9u/1CdBVDQJJZlUbDTRHj6R4q+ImyFyK1AC4LZ/38bOB8N1zS9FJLB6U/09Il8B\njqN79zfo3PmPrFsHNkC39ZBXOe3o/QTE0rNFqeZMF+a1CtPXDo0NNb3ondiRRST3Ph4chukZh+sM\ndrgzwDiHOc+zeifRq6YZFjs+2P21xDnqgZ2bbiDzhFna4iynkPYSvod0KjgZkcnARndcCPaMpYeq\nWnbgb023Q09n9ED1NQLyiRtoX1nobOdw5rET1b8DuGD3z51BX4sNMO2JT5yCZU/6FNW52BdhGdnj\ntDIBy0f6PmasQnMFi0xB9VPMCCdeLSuUU7Fz3entXHcCIl91v+91alRgW8SxeFcXO21nQ/UtAs/f\nFtI7hC8WJmK+AG+SvW1MZ05zHurvYXoNH6a6QlmKb4hboQqRcZiYgifr9xYB8ZCWEOfAUACA6kZC\n43Y7YrmEvXjNesyQtqcIdDYifbEcxJ9i6kaLI2tO2jMBO396l5bOxFOroDQWkRJUFwPvt3LN15zC\n29Yg8Y19WIxxtByLyGj3e717ZjyWkP0iCROxs++FmIqYT/I4F8si9ik21mSLr0G64p8RN2OEG1Ab\n3YC6A2gtufgxWL7kALZt6sU2LsJkAfth+YQ1aJCeg8kUtseZwGHufStIXYq5RDIem7y8w8FGuCPw\ndVT3YeIdyd6aPBXL6buUlo3wRLeKb3B99CGhcpuRcjoiPd3vjUHPy25afw6zkbMwD/UF+EY42ZyN\nSVNuwsYb3winkkPEEAs22HregBaKpPoBAcGMYEZg4UoQCEPxUOApAqvmakzBqNCVuQ14Low6dcay\n6oDIkS70ZE2Y7ckUgttY2kobi7DzqW5YEo/YzlWjowDL37zC/X0EEJh8mdHMA14jOg/SIkzMwyuv\nFDNAuO3AWFbUmUgucKoTwXmVzJZizSQOw8s9bvd+Jv5RQHqQ5Ya4EBOKwK1qzRCb08tCd01XYGDI\nu+zMt7u7doGLoWtONRboXgX0RvU9wksU3x0TYejUtNI2FbFs09EtxMKAvDY+wcHbzV3dNYOwZPOp\ncEYbjBnC7UCZ++mByLCmK8xZLtKc0V5ZYOFGAcNuWaQOVePTCRiKyHCnmpVsP4BDkcOBfth45X0f\nf4XvFJc+ZKkh7oo9fL1cGIy6cBRvO7kHpnYE0MfFfAawgbellU8eJiMIIhOx7cw/AL8No07dgW6Y\n+tGZmBPXbeE3KaMoxAbbMaj+tJVrirDz0eNQnZbEunkI1vcTUZ2HbY2ORGQUsALVO6Iosxwv45aV\nM9K9vj7K8rKNTphfxnnu+9iWL4ZPfOiGPddnYA6g/nOYjmSZIS7AHD/GuBjgj1D9ATboC2agQeTr\neFs0sAzVa9opN9+VXYzI7QBOYCLcc60CRM4GxmFxse19XqbSCdt1ONZJVbZkhDtjxuoERGpSYoRz\nc3Po3r2YbdvupqHhHjcxugLVF6Lomxzs+cJ53pu+s+oLQLb2czTkY3HjF7r4VJ/E4o2FpyFyRBaP\nOdlBVhlikW9hZ5KvBAlwdEfkiZDrbCv4cu+vMEoejsgPgS2uXIgkvk7kO6h+4j4zm2I/Q7Hdh4nA\nW62KcFjO3TOA151qT/Lp3bsH/3zvMfpWdmDLltudnOL9RBcidgQivwJwSlxr3OvZEm4WL0Yh8lVU\nb0x1RQ4JbFJ4PCYsk+la9NlPhhvizojcT+Ds94+IHMBmgd624A6nQhTMLsI7j5yEyNeA5a6MhjDf\nZ4jciclS/gE7h8wWQY6DEfkWqp8D38XUng6eqIh8H9XV7pp9LV6TWI7juOHf4aEHt1JT+z22bQOL\nJthOZH0zDi9PtB0xeM/X1gjLOVQ4A5EBqN6Pf38Si0nhdneOj09hCVJ8UY50J0PjiPu7WN56Z3yv\nxTxd1zvxjODwnwNE6ulqUoL9UH0XiwHeSftCHB4liFwHeKnndmJ5c1PhDZwcbMW/DlMh29rKNdc4\nEY93iNzxKVbGI3IysIaion8wYEA9Cxd+1O67ghH5LnC0+2sFqu+43yN/vg4tzkak2IncJCd/9KFJ\nESI/RvVPmPFdh58+Mt3IGkGPUZxyymhOOrEbd909BJtdz0d1EQHN3dVE55LfEZGpQH6Q6lMkZdU4\ntaV9Lh4VzOjEmsc2Xenk7lceqiuwtrbkAZuDyFRU/43Fi25r4Zr4Y8cU3QDcscBGTI6ys1sttEdP\nt42OK2MFgZjwdbSepMMnwATMb2Ah/v1KFJXO2fSAGwfnA1+kuE4+LZPhgh5XXD6W6uqj+PvrA1n7\nST4ffjg7aEUCpoa1u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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Hough space in high resolution\n", "N = 400; accumulator = zeros((N,N))\n", "x,y = points[:,0],points[:,1]\n", "for b in range(-200,200):\n", " m = (y-b)/x\n", " bi = int(b+200) \n", " for mi in array((m+2)*100.0,'i'):\n", " if bi<0 or bi>=N or mi<0 or mi>=N: continue\n", " accumulator[mi,bi] += 1\n", "imshow(accumulator,cmap=cm.seismic)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Coarse buckets:\n", "\n", "The traditional Hough transform uses \"bins\" or \"buckets\" for accumulation. That's similar to downsampling after a box filtering operation.\n", "\n" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 20\n", "hough = zeros((N,N))\n", "x,y = points[:,0],points[:,1]\n", "for bi in range(20):\n", " b = (bi-10)*20.0\n", " m = (y-b)/x \n", " for mi in array((m+2)*5.0,'i'):\n", " if bi<0 or bi>=N or mi<0 or mi>=N: continue\n", " hough[mi,bi] += 1\n", "imshow(hough,cmap=cm.seismic,interpolation='nearest')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Probabilistic Hough Transform:\n", "\n", "Bucketing is not a very good method for detecting maxima. \n", "\n", "It's better to accumulate at a high resolution, convolve with a\n", "Gaussian, and then look for the maximum. \n", "\n", "That is a technique similar to something called the probabilistic\n", "Hough tranform. \n", "\n", "However, a uniform Gaussian convolution is still not entirely justified; the actual convolution\n", "needed for a correct probabilistic treatment would have to be spatially non-uniform." ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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OdpnqK1Y+P6ofmvr6o/mo/WPUb4zPZapyvw5f7+q87go7kv1JJG3xarlC1H7+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\nHoT/H04mkBWRpw3IAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "smoothed = filters.gaussian_filter(accumulator,10.0)\n", "axis(\"off\"); imshow(smoothed,cmap=cm.gray)\n", "mi0,bi0 = measurements.maximum_position(accumulator); plot([bi0],[mi0],'o',color='yellow')\n", "mi,bi = measurements.maximum_position(smoothed); plot([bi],[mi],'o',color='green')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To identify the actual line, we need to find the bucket containing the maximum and transform back.\n", "\n" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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PKeGfCUp3psvvWj/Tc+DFiDXqTGV3KALsLO5vcVqyd4nSnelqfW1r03Pg5bjrFurM5e5Q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\nHABAPePM2uY2fbNJEz+YqDV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py5Yt6tKli4YOHVo7x6pWv8JeBSkpKVaHDh2stm3bWs8/\n/3x9P7ytjB071rrpppusRo0aWQEBAdaiRYusw4cPW+Hh4Vb79u2tiIgI6+jRoxXv/9xzz1lt27a1\nOnbsaG3cuNHg8vq1fft2y+FwWN27d7d69Ohh9ejRw9qwYQPH6iL27t1rBQcHW927d7e6du1qvfji\ni5ZlWRyry8jIyKh4NTjH6UL79++3unfvbnXv3t3q0qVLxd/ZHKeL+/zzz61evXpZ3bp1s0aMGGEV\nFRXV2rGq9Rt5AACA2lWvT4MDAIArR6wBALA5Yg0AgM0RawAAbI5YAwBgc/8/PbtW96TwX6oAAAAA\nSUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m = (mi-200)/100.0; b = bi-200.0\n", "plot(points[:,0],points[:,1],'.'); plot([0,512],[b,m*512+b])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Other Parameterization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The $ y = m x + b $ parameterization is not very good because we can't detect vertical lines.\n", "\n", "It is better to parameterize lines by $\\phi$ and $d$:\n", "\n", "$$ x \\cos \\phi + y \\sin \\phi = d $$\n", "\n", "$$ y = \\frac{d}{\\sin \\phi} - x \\frac{\\cos \\phi}{\\sin \\phi} $$" ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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SDvsxmzdjMq3j8OFvT3nsuBZ2Ts4qysruZ//+r8zJl1JpYM2aT9LevpPe3kNJ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MOGb2Bo6IhA/3qhXPx8mUz1qKz8GPbt+/Is5xAgCFLgBONOdro6xlPt37z52+jsfIkXyU/ORhJm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\n86tpQWiMAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "accumulator = zeros((400,400))\n", "for x,y in points:\n", " for p in range(-200,200):\n", " phi = (pi/2)*p/200.0\n", " d = x*cos(phi)+y*sin(phi)\n", " if d<-200 or d>=200: continue\n", " accumulator[p+200,d+200] += 1\n", "imshow(accumulator,cmap=cm.seismic)" ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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gru9nnf4uFeehzyHCO+rPqwjtAzSfF+FpwG+y1e8XAM3z8olfKuu69bVCu+6moM51d7sF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\n6AS1YI0Qv7jo4eL8AqNfh8gmR1XXfXxcAvzbt7If1U3vLun9PdKnJ3S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AZIDrjy7OgR/3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E5op1K/lNYArr8OvxrAa+67BvDa+ugceq2txa48krd/97rM6/FT54feJ8c9/SRGVeEKbQ2nHg5+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\n7y0qYfrG+r6zy+Vg8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fz9u9nXr0t4M7QBbHbdnOd+VAntVCqV+lC6Na8dOW0cS0G+t3mI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\nUncqaleLZczVRTPAb4W1B20vlx2Nle2BvByjbdurw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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "smoothed = filters.gaussian_filter(accumulator,10.0)\n", "axis(\"off\"); imshow(smoothed,cmap=cm.seismic)\n", "p,di = measurements.maximum_position(smoothed)\n", "plot([di],[p],'go')" ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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X9eKWF2W32dW9Y3ez48ANUdYAcBav/fc1Pbv5Wdltdl3a6VKz48BNUdYAcAZvbn9Tz2x6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\nSUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "phi = (pi/2)*(p-200)/200.0\n", "d = di-200\n", "plot(points[:,0],points[:,1],'.')\n", "plot([0,512],[d/sin(phi),d/sin(phi)-512*cos(phi)/sin(phi)],'g-')" ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "collapsed": false }, "outputs": [], "source": [] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 0 }