{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Title: Basic Clustering with $k$-Means\n", "Author: Thomas Breuel\n", "Institution: UniKL" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": true }, "outputs": [], "source": [ "\n", "from pylab import *\n", "import random as pyrandom\n", "from scipy.spatial.distance import cdist\n", "matplotlib.rc(\"image\",cmap=\"gray\")\n", "from collections import Counter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Mixture Densities\n", "================\n", "\n", "Consider a collection of points that are sampled from three different densities,\n", "in this case normal densities with the same covariances but different means.\n", "\n" ] }, { "cell_type": "code", "execution_count": 100, "metadata": { "collapsed": true }, "outputs": [], "source": [ "data = r_[10*randn(1000,2)+array([70,30]),\n", " 10*randn(1000,2)+array([10,10]),\n", " 10*randn(1000,2)+array([50,80])]\n", "data = data[pyrandom.sample(xrange(len(data)),len(data))]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is a scatterplot of this data.\n", "\n", "We clearly see three _clusters_, corresponding to the three _mixture components_.\n", "How can we recover these clusters?\n", "\n", "This is the job of _clustering algorithms_.\n", "One of the most useful clustering algorithms is the _k-means_ algorithm\n", "\n" ] }, { "cell_type": "code", "execution_count": 101, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 101, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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48SOTEGOytcB0aYfh0AtDbYVDTSwbrK9dnMAKyLTSD9hPF44tsjB5HsHVNuFF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\nYsR0H2nvq3WJxhIhijALHhXSLBRcMhkffZF9mv5iZk0eeWvPYPxraz7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ctU8WYEHYuHox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P8hDlE28hshvYW7rYs+V3R8loj/d05r9SStoZ032kasNe7EkHYSt65jJ+COjf32QEHaQ98LLlip\nkqCtJnCjFYvGchMKkG40GNNnkXEDrt3vJieN1QhWHbgQsc/SkomR0vu5ucF8VqIzZ6LdcL/yK/Xi\nCbMM4RbEzEOgRdbiol2cGlx4oXFHzs+bmZMiNiYKLl24GrVbbnzcLjekBaR7Q4qySqEsvTakiN89\n6EP3Rdz27b45pqXb2ttJxI0B7mSQLMtuJTpBclYWI58VCmNX1OQVQjqJvhdcegZc1Gr1bpCznnHn\nxig0+oSU1AoW+l9/hs8xc69YtMcH4VMoRM+Sg6B85BEzU1EHhyPRqIgVPJghCAvP5KSpc/16Uw7c\ndcWicUMi8H7LFjOrcGTEiEKsLTk0ZAP7YVkcHKyPA9NWLv3eFU46zYU7exPo5ZfwHdJO4HhE6l2J\nejIFjj9JfFa33Ri6rb2dRFLB1W247d6yxW89boYkVqis6iEkL/pecKU1J0OcaGtNiLSxAaEBNyo2\nS6TelYZ1EItF6wrTYskNWPfNstNi4bXX7CQD/QTuWtqQbBTWNlewIs5qctKUp9t18KD5XsR8Pj5u\nLUooS5epLWgA7cIMS8RgrV5tjgdiEEITIKWFiHVlQjTp2K5i0cabub8J6vYlgCUkDh0fmmah805I\nc+DGwOq2dIN7UUPBRfKk7wVXWiC0QjfcPGID3ABPLXbctAhuiofBQbN8D6w+rtXFrQef6fg0HZjv\nbqtvFJOT9dY+xJthosH8vA3En5+3AgizE1E2ji9kzdNiCCkf8H5pyUwGmJ831rWFBSOUkNRVCyOR\ncCyW/q2xve8G5rtZQvCR/iZOFLkzVotFGzsZd/NPMr74rLB5EGqLbyJSFnUl+YyQTqOvBZc7ACW5\naKOeNhuJHcjKChbabmnJxGC9//12TUNN0vaeOVMbDA5mZ20Qu/tkWyzWLji9caPI22+bz/bssQlJ\nRUR+8Qv/WpN41aJqdtYcx8SEEVM7d1qLGfptctLGfkE8hgQv4vF0LEgongYi1H2qR2D9+vXWnTgy\nUuvGJL1D0uswThT5vncforIiS8EVNW5p8jgOCi7SrVBwFe37NBdtM9OQ3c+TWsHKZSMsEEyOzwoF\n447TcUZonys2kqYhgHWnVDJ5tV5+2QTcI5GnFja+9vtiOF5+2aZ0EDEibnFR5Mc/Nu8hBu+5xwb3\no+xdu2qD7EVMW3ROHh2PhuP2iSaR2hi0Awes+MMrUk6Uy8Yih37Tmf/dIHpMDCgU7OxGnXCVN4Xe\nIW9rUTP7hMRQlu69rKz3vUy3xuSR/OhrwdUMUXELPotGI8Gy2sqCepAXCukRfCb7SsXM4oMLEWWt\nWmX+kqDdEFiWR8SKCggtbRFatcoGz7sxUktLJhv9yy+b/Y4eNYH4EFI66Wxo8EabSiVjSZqZqbUo\nrVlTG6O1c6cNtHf717ecE1yf2qUJNw/EG9oXskLAoqfjzggRSeYiTLJdXNluaABo1TJSFBkGCi7i\n0neCK60LL4qsnvJC7kj9uRYB+nv3fbls1xBEYtFCoVZMpGkXBAxmGE5MGGuaGwOlXWdIT+H2R7ks\n8slPWlEG0QOx5qtfCz8cL2KyRGwSWzcNhM5QHzrm/ftNX+kZhTpZqWutSxLYrF/ziF8h7aPZsSOp\n4MoS15WexwMARQUhyeg7wdWMSEoat9AocVawyUk7825kxLx+/OMmVglLaMCNqGf5pcEXmyQi8r73\n2dQMECgIXNcWLbzXsU44Lp3kEwtm4+/UKSt2fPFTc3MmdgtxWaOjtRMHYM2DS0/PNvT1qxZbOrZN\nWwBcweS6ULUQbkXsCmkv3ehGa8V5yHPdkuUDPek9+k5wuaQx+2Y54IYuTLjf3M+1patUqk2J4Aor\nLWywHI0b2+UeixY5WlRAkFQqIm+8YV1rsJr5+g/uvMlJI5K0KNMZ4HGcyJOlg95dlpZMVnwcf6Fg\nBCCW2hkft+0sFIwY1VYvt8ypKXscsGy5v6fPIqj7JRRY726bFXRRkLQ0GqNKGqMbRTlpHX0tuKJu\nlq0oy2fq9wXyQzToeCnX+qIFg17aplhMlpg11HaIIHexb98agrpc7V7En8/N6LYLgg/HoY/PLdet\nd3KyNlAe7XVFV6lkhJqObztxovMtVRRcnUM3/g7d2GZCeomOE1ytvKnoG3MWsw7TlBEXKK/rcUUN\nrEazsyZDO9xpWPpm27ba5KYQHHp2oy47FJs0OGjqELFuTASgu+3SebQg/opFW97UlE1sGiVsdJsq\nFVP/3Jxd9qdQMLMbMXMQMwZd16YuE4Js/34rHE+fNgH3IsY6hqSsPsvj7KzI7t22XMTJHThg+17P\niuSNrffhb0zi4DlCXPpScPluqq4rLQ5fgHujhOrUVjMtir79bRPLtGWLWf4G7kU3oanrPtSxXfge\n/yOPlJt00V0oOtRHehFsBNUPDtp1COfn7TJKelmk0PHDbahdp+iD0VHTLogegFQWOkGp/l30sj36\nGN2lfFyBi88QH4bjQV+hnXnAmBBCuhNen8Sl4wRXK/DdVBtNNqgDv3VSUQSx+7YVqbckhW6qWjTp\nNkZlSfcFrOvPdfn6ewghLdjc7XUZ+ngQsF6p2MB+iC0ch1770C3X7X/MiPSh0zxoAanL1hYz3V5X\n6M3N+evw4c74giUvzzgNxoT4oXuVENJtdITgyuMpPsmAnGSaf5I6tGCIEkJJb57aBebu7ytTpD6R\nJ1xt+/fXBuG7ay1qKhU7+w9xTvPz1hU5OmpdkrBg6RmJhYINXB8fN6+Li1aMoj4IU4gqfK7bqpcg\nmpkRuf56s0TRxo0ml9f4uHELbthg+8EVhPjcdy5gzcdQUD3cjzh2BOljpqQvKz5pHRRchJBuoyME\nVx5P8UkG5JDVKCmYpSdixMzWrdksywERUCqZmzzwxU65bjHX6uRaelxrno5/ghBaWjJCaXy8fhFp\n/KF/8R6xUYij0msYipi4st27a/dBaohSyWZ7HxysF3Cuy073gXscbnJHHLOOJ3OtZ+65Ui7b/F4o\nR7tUdX26nryhwCB5QyFLSH50hOBqJ80MLq6LCakO9IxC14oTV68WVeWyzeqetM3a4iZSu29UnBlE\nCtp/9KiJFYOIhEXHzZUFEJ+FsnT8lCvSUAb6b2LCJmnVggbfuyKnUrECF8esU0CEXJYoX+cA02s6\n6n73WcYwM7NdMVX9fiNkPFv+UHARkh8dJ7iaudibGZCT1huqA5nNNVGxYaH6kDMLcVC4yeuZdHH4\nttHrAfr6plw2S+Mg9urUKSNE9JI2AH0wMVEbtK4FValUazXTQk3nBatU7MLT8/O2b5FkFTm7dFsh\nbN3fVQvK0MQICDkcM9Y81IlU3eMZH6/vL9DumKp+ukF2Wt8TQkgaekpwNTMgJ603VEeaWYo+F5Z2\nDWKpGh2X5Qssj2qjfhUxAkULQp8VaHbWJhedmal176Gd7hqNmKmn65uYsLMLUWehYIQPYr/0DMbT\np43gGRw0Ge1HRkx74RLVa0YWi7Z/XHci2qX7TLcN4lULTjfmS3+PMuFadLftBKLOJUKSQMshIa2h\n4wRXp5D2xuXe9OKsSUlvkmmEVgi0B/+H6t2921qVYFXD4tK7dtmg+fFxmxke1iLdRv0ewmv/fiuw\nkILi6FEbJI9g+2PHRP75n81nvhmIodgtlKvdjG6sm/te74c2aCE4M2PbXyjU5/gKBeS3k05rT170\nwzG2CloOCWkNPSu4sghcb9QN2egA5j5pbttmrEVIXeCmkohzMSKoH5YfzFwcH/fPztP/FwpWDMGN\nVyjYeCeR2qV63PgmWJrm5uzsQ90viKWCyHGzzGtB5PsttPByv0sS86YF28hIrTVNx+bp2DM3Zg/f\nt/rmH2WRSLJvL4iVXjiGJPTK70UI6XDB1cxgk/UgFXXTT7KvfkXsElIq+CwnOt3CgQNGJK1fX2/Z\niWuDDjrH/3DJ+fC5BfVi1QsLNrHpqlW1bRSpbbeIXcsRZWrrH2Y0XnqpFV7z87YNV19tRVixmMzd\ngXgv3zG573UZbkJYTRp3cSsIWetcd6mvj3gD7y5a/Xvx3CAkP3pWcDVaX8hy0GhbsK9rCdGCx2c5\ncT9zUzGE0DP5sPQMUksgl9TUlLHk+FJO6D5AqgZYuhYWTGC9iBVPvjZ+85tGHLpCbXHR/A0Nme31\notWYyanb4LoofTMQNdoq5vZJyJLn288XA6fLSBPz0opzmC4hkhUUXITkR0cLrlYTdeNq1MoREgEo\nM8otiW0gNDCbrlIxgeb43hUs2Hduzs4IRHoKbS3yxTvp/7WwcN2BIcplkZ/8RGTTJrtU0MyMyOrV\nJmZrYcG6NLH2o6+8ffvqRY1vwWxNqK9Lpegbie87HDtyhKGvsH1SgZO34ErqRmRQdPfA34uQ3qTj\nBFcnDTbNtCXJvrgZR8UYaYsWttdiCQJKuy3x//y8tQwhuN21kLllh3CTier/fftisWc39YKbZsLd\nDykYzp6tza0lYlNFuNavuL7WWeFDhNyOk5O2/bqfO+XGl8TNTQtYd9Grvxfd2aTf6TjB1SmDjWst\nStuWNPvGDUI+8eV+p8UbPpuasqLFV5fPZeYLfBcxYim0T6kkcuSIyM9/bt2UExMmnuoDHxB54w0b\nmL5+vYkhm583Fi4tYMplu1g26kZMmC+Ra2iVAC3UMGHAlypCH4PG15chV26UdUyEyVEJARRcpN/p\nOMHVKeQ1MKSxfPnaFGdh8Vm49PY+16FbR0gouoJDz97TWeF1G3SbRkdt7Jeb8iHkdsW6jKHvdDsa\nwedudJds2rkz7M7sNotS0n7izbEz4G9ASO/Q0YKrkwabZtrisypBPPluxlGCSy88rfcPudKiZiNm\n4TJFrjF3CSB9HNoKFYqzcicW4D1mVfrarBfpduvC/7qdbn0hd2PUhIU4GhEqrRQ3FFzdRbf/Bp0U\nIkJIu8lNcE1PT8uuXbvk/Pnzcs8998iXvvSl1GW0+4J0Y4V8nych5LJqhEolbKXyzXSMa1fU/j5R\nptNZIGHo6tW1C2VffbV5dY8T7kJYjXw5rFCX3tZtL9qFLPYzM/WxXbo8XzZ5JDPVrksRmxEf4PNG\nhEqeIo2QbqCTrb2EtJpcBNf58+fl3nvvlaefflrWrl0r119/vWzfvl02b96cR3W5EboRNnODdGcd\nYgDC+oAi/mSWvriquKfEZm/iPrHpS2eBdoSsdRBGOkv9xIT9HnFWeI/M9L74LDeIXsQuLxQ6XtQF\nkBdMW7f0pAJdZ6OzU7FvN91gaI0ghJD8yEVwPfvss7Jx40YpvGtauOOOO+TQoUNdJ7iyQs8gFLHW\noJGR8M0saUqKJDMd9XYhGnGDaeEoIsvrP7rCERax++6zbkI3GB2vbsyZ6/LTxwqXKVysbtuQiwyf\noW0QeFu32mSyoeNPaqHyCZWo2ZHIvu/u005xQ2sEyROKdtLv5CK4Tp48KZdddtny+3Xr1skzzzxT\ns82kGs2LxaIUO+RqDN08oyxQSeKdtMiAUEhqKXMD6n0z9aKC6OGCa1ZwubFornDy1aOX8AGDg/X9\nvH69FUJRIhL4XIUaiDeIPL2fTlUxMlI/ESHtqaj30yILMWb4zude1e1NCl2QpBvhOUu6iXK5LOVm\nXBwechFcAwMDsdtMdujjs8+C4qOZ5ut4oVAbQoT2Cc1ejLs5J7l5hwSQK8D0tuWySUuh3YUjI/bY\nd+2q31+7JaOW2XGFnS9Gy9cP2sK4dav50wt0+44rKXrGZqNCKm1decKbIyGkn3ENQXu0paVBchFc\na9eulePHjy+/P378uKxbty6PqnIlScLMEHGWssnJsAUk6maHtApu2bD4+FxroeBzbBNXZyPWsWLR\nxmEhE74vl5YGVj9YuUSsWEOZenYhjs/tX33MOjhf14uyMAMyKxET14++c+LVV5uvN2souAghJFty\nEVzXXXedvPjii1KpVOTSSy+VJ554Qr7xjW/kUVWuNGKB0tu4Fpxy2YgtHTyeNmYnFMjuWoTceDHU\n5Wt/UrdjiLm5eiGhc2Rh/UaIQr3Q9eio7QO0QbtN3WPDdwcOGHehiBFVun/1MaNFAqcAABZxSURB\nVPviu3x9kAS3f0ICCuX7LIK+GKkkVjAGtBNCSHeTi+BasWKFPPLII7Jt2zY5f/683H333V0TMK9v\nbI1YoEL44rB8aRHS4HPbIZGnFhq6Lj07UKQ+h5ZuY5IbPEROKNM7GBoS2bKlvk1LS35h6h5nSEDq\nWDLXFez2ry91RFQeMxd337gg8yyFEAPaCSGku8ktD9cnPvEJ+cQnPpF5uXnHr+RxYwu1t9nj0G67\nuLghLUa0qNLrBMJNh+2T9EMoptAVmFu21Fp0fPv5YsW09Uu3xQ3Y14RyZ/mC46MElNuuLBkcTCf2\nCCGEdDcdnWneRyfN0Eozy9C10rjxRI3iK1t/p7+HJUynXtBxajqBKILJRfyxbG6ZYHCwflvtmi2X\nRU6cMJY25NHSMw59bjhs47OE+QSKW1aorT5rnVufnmEaJYzS/oboW5BG2HfK+U8IISQ5XSe4Wkno\nZhz1WVRZURajZoSktnC5aSPiZrVOTBg3pBszhRQYPnwz/tAOfQxurins8/LLZh+swYjEqNoVGerr\nKIHkcwXrdB5RbXVdmbo+3b9RSyW1CgouQgjpPrpCcLUrYDhOcEWRVqBlYbkLxT/51ijUYLFmPbtv\nZMSW6U4ecOOl3FQIQMd2YQalK9Tm5myeLi3KQv2hjyPUJpF60Rn1ne/cmp2td/mFxGCzUEARQkjv\n0xWCq5MChtMEkyex0qSpN2q/qLL1vr6ZlxBD4+NGJCGuCykWotxwlUr90jk+EDvmC3KHEJuaMu/h\n2oTlS69vCPdmpWK2g+AbHKx30wF9/D6XpRaP4NvfNnFnIja1RF7ubAouQgjpfbpCcLWLJOKqEfHn\nc4PFWe4ajReD1QhlumsY+urWdYrUpmZw8SUd9ZW7uFjfRrcfkDIDbj83pYO2kB04YLaD4IuzjGH/\nKEEaSlrqLjdECCGEpKXrBFerY2XSWNZ8YkNnlfeJqmYsd259sPbomKNQ2aGg73LZWo+wj7b8aGEj\nYoSPtl75jsnn/vO1Be33tdfXZv25bpeblkL/FnNz9ZawOMsjhRYhhJBm6QvB1SpXUBIBlXbNvCgL\nmE8kuElC41yCui43b5VveR3fdnpbjV4zMtQGN9gdwfS+WYm6DeWyyKpVxvWH8isVm9rC91tMTERP\nBgjVR8FFCCGkWbpOcDVCVgHpST7Lo/xG3Zfa0hO1ry/YXrsKQwItTtDBJehbWse3ve+9rw1umXhF\nFnsd3O7Gm+G4kojZdpDXwwEhhJD20heCKwtCN8G42XRJymikfP093IBYMkek1s0XSg2RZgJA1HY+\nQacFmc5mHydmkooNn0jzpW4ol82Mw2LRCEME5GN9Ry1mfXm4Wg0FFyGE9CY9K7halUoiK8EVR9S+\nOvWCT3QkDSKPyjEVtV0oXYLbhjjh2Mj3rhXQB2YbIhVFyIoVElyNiCAKJ0IIIZqeFVzNBqS3k5BY\nFLEWJZ8YQMyUu1/eVhu3Tb664uqNc3smFVxRcXUoI+2ah3kLrlY9HBBCCGkfPSu48iTvG2QSi5Kv\nHqR8cN18SVMmJG2b77OQ2zJN2VkQVRdmcGpc1yeOQ8el+ZY2ypJufjgghBCSjL4QXGlu+EksE62+\nQbptirJkRSVcjRIOjQguX1oKBKbreLKo+LS42LAsha2b18stq1KxyVZ1Mle9VFBU3bRUEUIICUHB\n5dBpsTfaeqTTJ9x3n/kfWdDxPSxbyKOF3FPYL4lwSNO2kPAMLfeTdP8k36f9reK21YI0lAQ1rvxm\nhXgnnXuEEEKyoy8EV54kuUE2I+K01cp3M5+crF0kembGbDcyUmttGh8XWb8+P2tLlm63UH/FxYk1\nS1wqjFZAwUUIIb0JBZc05wrKS3BFtQnf473Ori5SK8Z0OQsL4RxVjZJmlmYUcUIq5C5tFjfxqrYA\n+tqWFAonQgghGgou6cyg5STuNHzuuhyxvy4H7sWsjw0iyF1TMa0QTSJsdYC7SDZxUkl+ewouQggh\nzULBlRPNCoO4GYWlkhVQKL9cNq5DbKO3F6kXRc20Ad/DutbsMYb6a3DQukvdOnRyV0IIIaSToeBy\nyOrm3YjVLJRfS38GoYW0BUtLImvW2M9gzdL1J7UiuW0JtccXM6YTijZC0v5yA9nRriyyxFO4EUII\nyQsKLod23nSTJPfE/zpOCwIrbmZgWsEVatvSUr3w8S1oHSo3K5egtthRcBFCCOlkKLhaQJIZdyLR\n+bWixIBOHdEMOhasXE6X/DOpWGkmZqpYNNa1ublaK1+5LHLiBN2LhBBCOhcKrhYQElzu/6H8WnFl\nJpnBl8TqUypZq9HMjEktgYWeDxywoksLscHB+vY0S5TggltVxCQnRRzXnj22v3T7KMIIIYR0AhRc\n79KOhKcIOA/l14raT6eDEKkNnPeJjCTH53NJhhbGzmK2Y7P9XSjYdmlXZVbtI4QQQrKCgutdWiG4\n3PilrVvrA9xBEmtVFuksQjFVlUrt8jZ5kLS/Q2189VWRM2dqM+uLZJeEtdNWHSCEENK9UHC1EB3U\nvXWrneGnk5i62zZDkgD1kGhzxUbatkWJlUaW5IkTljr+LYt4NpRDwUUIISQLekpwpb1BtmOxYZ2I\nFK9JiGtraHZjoxawKItbqwRXmt+zE5blIYQQQkL0teDKwiXXKGlnFsa1NQtrUqcJldASPz6yans7\nRDghhJDep6cEVzfRqpt3mnUT9TZJF4pOki1ef+/7Lq1ITvN5WtopwgkhhPQuXS+4srJItMN60UxW\n9rz3SSO4UH4aK1xIyNDCRAghpBfpesGVlUWim27mcW1tVLQ0GiSeZXB5J1mYuumcIIQQ0tl0veAi\n9TQqWkqlWqFWqZg/JD4F7oLSvvQWcZnxu4FuaSchhJDOp6cEV6feIJO659qNm/hU/+9+BytaKL1F\nFoKrE/uIEEIIaQQKrhbQTsHVqPsxydqJjaS3SEOn/p6EEEJIWnpKcJF64kRLVOLTJOWkTW/RaXSq\ntZEQQkhvQcGVE67lKBQP1amz71qd/6pdUHARQghpBRRcOREVuO5bJLoTaGWaCkIIIaSfoOAiy3S6\ncMrKGsVcX4QQQloNBVcLSOqeI9E0K7h01v1OyfVFSC9A1zwh8VzQ7gb0A+7SNhyY2kM3B/cT0snw\n2iIkHlq4WkgnZHLvNvJ2//VrvxJCCGktFFxdQD8Lrmbdf3GCrV/7lZBmYSwkIemg4MoZDkrthfFa\nhOQDry1C0kHBlTONDkoUavX063ETQgjpfii4OhQ+PdbTrOCiYCMkH3htERIPZym2kKxySGVJXHm9\nNPuINwVC8oHXFiHxUHC1kCwyuVNwEUIIId0HBVcXwKdHQgghpLthDFcXkHUAfVx5DNgnhBBCsoWC\nqwvIOoA+rjwG7BNCCCHZQpdiBIxfIoQQQkgWUHBF0ImCK2uXXlx5dCESQgghzUPB1WX0muDqRFFL\nCCGEZA1juBwYMN5a+nmdSEIIIf0DBZcDA8YJIYQQkjUUXKTl0IpICCGk36DgioA3/3ygFZEQQki/\nwaD5CCi4CCGEEJIFFFykrVDUEkII6QcGqtVqteWVDgxIG6olhBBCCElNFrqlLy1czP1ECCGEkFZC\nwUUIIYQQkjMNC64vfvGLsnnzZhkZGZFbbrlFTp8+vfzd3r175YorrpBNmzbJd77znUwaSgghhBDS\nrTQcw/XUU0/JjTfeK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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,10)\n", "plot(data[:,0],data[:,1],'b+')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Mixture densities arise in both unsupervised learning and in supervised learning.\n", "In both cases, they commonly represent a problem structure in which data is\n", "generated from a number of ideal prototypes (the cluster centers) but then\n", "corrupted by noise.\n", "\n", "- When each cluster has a distinct class label, we have a regular classification\n", "problem with normal densities.\n", "\n", "- When no cluster has any labels, we can hope to recover the underlying\n", "clusters with a clustering algorithm and then assign labels to these clusters.\n", "This is a form of _semi-supervised learning_.\n", "\n", "- When there is training data with labels available, often each class is\n", "a mixture of multiple clusters. That is, each class is generated by multiple\n", "prototypes (think characters in different fonts).\n", "\n", "You can perform clustering either at the class level or across all samples and then label each cluster with its\n", "corresponding class label." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "k-Means Algorithm\n", "=================" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The _k-means algorithm_ is an example of an expectation maximization algorithm.\n", "Such algorithms generally have a form in which we need to find some parameters,\n", "but in order to find those parameters, we need to know some other values that\n", "we can't observe directly.\n", "\n", "In this case, we want to find the cluster centers (`protos` array), but\n", "in order to compute the cluster center for each cluste, we would have to\n", "know what cluster each data point belongs do, which we don't.\n", "\n", "The EM approach is to just guess the result." ] }, { "cell_type": "code", "execution_count": 102, "metadata": { "collapsed": true }, "outputs": [], "source": [ "protos = array([[30,30],[40,20],[0,90],[50,50]])\n", "start = protos.copy()" ] }, { "cell_type": "code", "execution_count": 103, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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MielIwEepiK9+1YUrkTT/C7/gSkMgl0qPx1Z7tyHHRx/tD1PqGl/drpthCacO\nOW7drruuCC+iH5y7LuEwNxdfVsg6kUn5WNgn62srS45XGlULLuaHEeKh4CKkJEVzYHCzhhsj4tfh\n29xMvlEl5V1lqdcVE21JLpsejy5oCnduackLEgioUDkDndiuz0nE7Y9woIhfn7DXE7njDpcPZoUF\njnv5ZZG/+Au/3iEmBeCahs7XznDUYghjQCL//v2uXTy+suLEHq4lxoOctFCIMRT+Qx8hQq+tJFFc\nNxEzqvwwQiYBCi5CxoS+GdlyAJbYjDQtEPI6CbaMgkjyAtl2DBB9EFg2kdy6Z/ocrfuDeldaKKFs\nBcpLzM+7Y/78z70DBiG0teX6395248dMQozJ1gLTpR26XS8MtQuHmlg2WV+HOIEVkEmlH7CfLhyb\nZ2HyLIKrbsKLEELBRUillLnRpeVeWVFl3aKiToI+FjlYob71GCB4Nje9o4TaWFrIoX0ci7/h6Fih\nAscJxVhxLrrExfHjLj/MzpTU4nV5ub+Wl94PY0FSfLsdLhQr0n8+mlYrvnZjbMakdbrsORQtL1F2\n31FRxzERMkoouAipkCI3FYSvvv51kSef7G8rFnoDeUM0IScM4qfZ9AIk1B/+X1nx+1++7I4/eHBw\n0WctuCBQQuE0jEv3pd0e3b+IEyo4RodksSQOEu6R26WdK33+usjpjTf6OlvtthO/Tz7pk+0h+FA2\nQqScK5V3IoTO9as6F2pUswcpuMheh4KLkDGjhdWHPxyvEC8ymGRv27D74xgr2iA6rOjRDtfKSjxM\nidmDEFEhp82G3EKlKpLGqX+jFAXGcvKkn0UI12t21gst3a+drYdtEGutlp/RiBpdSJLHgtYYh25b\nz5oMCcM08h6Txw3TpAkqlmsgZDRQcBEyRmwStUi4QjzQgkE7N3Yf24d2nrDNjqHb7Xe4er3B/CXb\nLoSXTvqfne1fnLrTcc7Q1pZbckjEFUfV56FDpKFzeOUVN7swNparV32RUos9d70NYurcuf7cq07H\nJei324PlG5AXZtdcDF13LViRc9Zs+uT70LmGKCOKQsdW3R4hJB0KLkJqBG7sm5vJISjtUmUl5sRA\nxLXbg2UPQsevrPjyDZcvu+1zc66aO2p04XgtOnTNrrW1fvGoK7qH+uz1/KzA0Iy+pJmZ+lrpa6DX\nj3zhBZfEjjyy1VVfMR9lK+y4er3BEhS2X/1bt2HPNWnWaazdMujwbt4QJQUXIcWg4CJkjNgQHBwl\nG+qLJW7rjsuRAAAgAElEQVTHCOVqra15YYNt6A/bMBPQujAQJ61Wf9iu2XSzAdfWnNjSN28rjCBQ\nRLyTtrHh6nVhhqE9N4hAnaSP+l64XljnEKAMBAqn6mug3SgdHlxbc47Wyoprb37etQnXD0n8KFCK\ncGS7nSxYYqsHaGLCOWnmaRpps1ZDgo8QMlxKC65HHnlEzp07J29729vkfe97n3z+85+XV199VR54\n4AHZ3t6WZrMpX/rSl6ShV70lhAwQm6UYuyEn3Xht6LHX8zWtRPorr4eOE4nflK2I2N3tX/haO0o6\nOV4nsqM9Hb60/WE/u5QPrpMea2zGom7LVsWHYNOTBc6dE3nnO/0i3a2WW/QaoUccj1yvUP8aPRtT\no5+bWD6ePY+iM09xbCzxPmmJIZAm4Agh6ZQSXL1eT/7oj/5I/vIv/1Le/va3ywMPPCBf/OIX5Wtf\n+5ocO3ZMHnroIfnUpz4lZ8+elbNnz1Y1ZkKmFp0YjpwflC8AeW5yet/Tp9OrkKflIYk4JwiODwqL\nNhpOUCEJHW3FwoSoxH7hgsilS267nmGo86Te/naR6693fe3uujAmkuRD1dxDMwK1G6UT6DG+jY3B\nAqinTvVv03lz1iGMXTM7GzM0KUDXM0uibCgvJuCyhKbLiD9CiONtZQ7+kR/5Ebn++uvlypUr8vrr\nr8uVK1fkXe96lzz++ONy8uRJERE5efKkrCHhgxASBXWZ2m3nQDWb7ia3teXXBCziKCTlFyVt0+5N\nq+XHAIHU7frQG/7X4b4YugzFpUtOaC0uivzszzoBs7Dg+15cFHntNZGbbnKlJy5fdr9RGkLnY9lr\no2cRIlyJmYg2lIucufV1J6ZOnRL5P//HCTqUu9CTA+bmXJ/NphtvXrTjBhGIsep9QJGcPX1smceL\nUHSshEwzpRyum266SX79139dbrvtNnnHO94h9913nxw7dkwuXbokM29mnM7MzMglfEIr2uorUqvV\nkhZ9abIHiYVqRMKV3cu0jTBi0gxI+38smVsn98/NeVFy9Wr/zRahOT2W1VU/WxF1sJpNlwOGfdEn\nnK6FBbeeohZ4vZ7fd3PT/ej8NJwDku7B6qo7TueGYQy6PATKQtiJBBBGGJutsG/FXFro1v6PyQF2\n1mZWEZOlTEVZpyzvGAiZNLrdrnQr/uZQSnC98MILsrKyIr1eTw4ePCj/6l/9Kzl37lzfPvv27ZN9\n+/YNHNumJ01I341WJ5Xb93la2CxL27E6WFnrNOmxQQDs7DgBNDfnl+CBE7Sx4QSYiF9zEGPBD8TT\nzo4TOFpgQCg1GiIPPyzyy7/sx4S+Oh33s7PTX7nd5mrpNRNxbSEG4bQ1m25mIhbMRjgQMyrRFlyv\nXs85ZxCNCKvqa5k0e1Kjj1lb8/lwIUEeWxhbn+8wXS0KKbIXsEbQGfuNuAClBNef/umfyk/+5E/K\nP/2n/1RERH7+539ennnmGZmdnZWdnR2ZnZ2Vb33rW3LLLbeUHigh007WBYxF8jsI2g0K5TjZ//VN\nXuc1Qbzg/3bbCSUIGv0DrAOkHaPjx11SOup0Qazpmlro78Mf7nfdEMqDOEI4015HFC+1SeqLi25s\nWuRBzOhz1nlpWJ8RTtvcnK9Qj1mU+lracGPoOUjKNwM6vJunhMQoYWI9IcmUElx33nmn/PZv/7Z8\n97vflf3798tTTz0lhw8flhtuuEFWV1fl4x//uKyursoSpkYRMiGMIySi3ZDYDblM2zHBZbE3SAgO\nHLu8PNi2dq9s0vjiYn8oE+10Ok5sYaHquTnX1v79/lqsrvpSFcifggPVbPpJBTfc0D8LU5+jTeTX\nMzc1cAAxi29x0ZeYQHu6lATyxnS7tm8rNmOCS9c22952j8/M+DIUODZGHcQOE+sJSaaU4Jqfn5df\n/MVflPe///3ytre9TX78x39c/u2//bfyne98R+6//3753Oc+91ZZCEImiVEJLpvbBKERcrvy3lRt\n2xA+VhSF2rJukM15Qn2s1VW/zI6Ic5m6Xb8WIfK7IPjQB35DeIl44WbznvA3hN7Cguv39tvdkj+X\nL7vtN9zgZznq49bX++tobW56VwzXZGmp33nD9e92XV9adIr4cGSj4cOaSMxH2QwrTJM4daq/tpkV\neEnOl/4BFDuE1I/Sdbgeeugheeihh/q23XTTTfLUU0+VbZqQWjBM8WXzrEBoYeS8N1WddzQ/7wSG\nLjGhnSnblhZeumyBDRdqkbKyEs+jSkrUh7DTobwQOg8L9bheeMGVjXjtNZFXX/XJ81bsoJbX8rJP\nrv/zP/cLXq+teQcNocGFBSeiEHqEyNJCrtXyazhqsQzRpMt7QISeO+fGjf1i10Y7npMmqPRrj+FE\nQhysNE/Im8RcHx2SGibDqP6tb9QIty0thQuMauA8wQmCy4WcJy0SV1bcdu3y4DGdOxW7hq2WX1Yn\naYaddsaaTT9DEn3ecINbc/GDHxxcZFpkUBD9wz/443XbEGf4jeT4Tsc7YfgRcRMDVlddWyJuX8zC\nPHlycD3KbndwkXId5sR4IACTRFmIOggcCi5CBqHgIuRNYi7CqNyEtBtT0bwunTeUtV99LRCO00VA\nNVjAGi6Vnc2Iv0Pjghh58kkvMqzzoxPYcRyEHNyov/kbke98x4U09ZJEGN/WltsX7lKr5RwntNnp\neCcP41pedq5Wu90f2oMQmplxSf8QX3DVdEg062vHismQm2j3TWtrHFBgERKHgouQALpEw6iSkGPO\nDigiuCAekGCOnKtQEnusTxva0iBnC0Lk+efd30tLLsyWdA11yFLPotTJ6yL9SwnpECdqi4mIXHed\nnzmIOlovv+wcL7C97UTWDTe4EOLVqz6fa2WlP7zZbrtrdeONTkjpwqnz867dd77T1/1Cwr+9Pvgf\nSfEQf7u7/jppMZflea2zoNETB0Q4W5EQDQUXIQFsnaNR58zERFBeB0HXoBIJL7WT1G5sDDrciHZn\nZpzIevjhsDC0Dlm362fmoeZVqHyFXksRN23tIK2suPHY5VpfecWLNzhHCA+jnAXyvTATEWNptZww\n+63fcoJIu3z6PHSSfZIbpZPik9zGqmenjoNJyzcjZFRQcBESoA43u5BbYMNrsXHaWYYgy0LFOD7W\nh96uhUir5ZLmk0ShPaetLSd8ZmZcHhdKInQ6Xmhtbbl+EGpEyHBtTeSJJ0TuusvtgwKkdhHwlRXn\nvG1uuhmNzz8v8tnPumKnNleq0XDt9HouCR/hUhGfk7a56fpbX3fjvHrVF04NXa8kbN5g6LqnXc+y\norwsSTNeCSEeCi5CUhjnjSMUhtHuTsyVsnWw0FZsP32jbDR8dfVYSAg3dQi4dtsJHdSvsksI2XCp\nDt8dOeLXRtToBbv1cVrgtdv9y+/ccYdvS8/0fPhhHz7EscePu8Wz221f7woTA7Qw7fVc+PDECX8e\n+jnQYcgs6LKEdgJCyIEsK7iqEGBpkx7oaBGSDgUXISlULbjSbqBWBOHmr0N4erslSaQl7Werw8cS\nv3U4TCeLi7icLoTksN/mps9Z0mUSbImKnR3nFunSDygcqvPI9PgtH/zgYDkKiKjVVeekISyoRZ5e\nTseGJlHSIUlwxEKEIULV5/GjZ3lWlfM0bMGVBF0uQjwUXISMmKJugZ7VJxKu1RVrM+u4rNjTJR3w\nN9YxRLgS6xhin9OnB8dty10gifz2272IXF93/2t3DDXE9PHnz/tzgrhDnSxbf8telyeeGNzWarmx\nIGwJEYhCqvv3+zUhcX1iYdYswiRU+gJuoZ4Nip9QmC4mypHEr/fXeXHDhgKLkDgUXISMmTyz00Li\nJe2YrG3bkKFNctePo5YXEt11Un4S2BdibXHRz/br9XxBUIQo19e94EL/jz7aP+60chc6b+zFF70g\n2dhwrhbWcYSzdd99Lq/sq1/tdxUh7BYWBhcCTxNcSdsREtWrAeiEfJFwYdrYY3gcgs1Wys8rwDG7\nVbddVtwTsheh4CIkQpW5MEmJxbF2s25LIuv+aTdQO369TNDmpr/po+zE8eN+UWt9vgsLTuRAVCBf\nrNn0Vd1FfG2rJ58cDMFlBWM/e9Y5cPv3u+R29KFnU+pZijiXhQWfz4VipFq85Xkuzp6Nixedt1VV\nGDGUbxeqj5aljXZ70LUkhOSHgouQCFUKrrRQYeyYpG3DyC3TyfZWBOgb+NKSz6/Si0ajsrot2mmT\nyyHaWi2Ru+/24s0mjXe7gyU6NDoBPcbOjvuNsKCl2/X7iLi+kHcGsXXDDb6SPqrut1o+hAmXKjbJ\nALlpEC/2eiaR9DyHnDUIw9BKAUVmUhJCqoGCi5AxkOR4lXWlio4nz2wzOEI6hJhWckILAvzWzkuo\ncGizOViXS6OX8NHo64twoc5zsvu+853+/81N32677YurQkiCWJ6adpL0uosQnc2mX/Bai7Rer7/I\nK0gKUcYEl/6N0h32eidhX5+2WC4hJD8UXIQo7I0GM+p0/SeRbDcefRMM5UJlFTeh9qrGjjX0uHa/\ndPI4hAXCiHCwgJ71p9sOCQu7DUv4iITFSBpaBG5vu8rxum+IoBde8M+BnrEo4sWKvQb2PBAyjI0B\neWtIwtduXt6lgPK8FpAfpyv067HHnNS8r09CSDIUXIQokm40sSrtMZIEVxFGNdMs1E/adRFxYbkL\nF8L72PaxRqFIv8OzuelztpJmTKahx4tZejpsKTJYLR/u0yuv9I/t5Ml4HhRCd6urvvyEdZ+0KEU5\nCpxTu+2S94ssI5XVJcXf2qGjgCJk9FBwETJmyoioYSTyawGQpQ0Rt//WVn9V9lg/yN3SwgBiBIIF\nbow+dnvbiYZQ+DMJhCVFvGNm+z53zv29uencLux/330+hyzkAuq8LBDK+2s0fIK8iLsGKGkxOzs4\nHotO1hcJl4qIHYdjUEYkj3C150MIKQ4FFyERsuTSWKy4iIWgsia/p7kYVSXya4H05JPJs+ZCeVYA\nDpLOidIiRQuNtGTxENqhSkJfl+Xl/gWxQ2Llgx/0YqzR6BdUoRwyPf5z50Ref90XLYVThjw3K0Yb\nDR+m1I5Z2vnYlQWyTrzQ1x/nkwcKLkKqgYKLkAhFBFcs9GZn7eUZwyhyaXS4VCd7x8YUA4LolVcG\nj4HAsEJjY8OJE72Uz9qa27a83O92pSV9J4mjtPplISGSJAyx/YUXXNgR5w7htrvrxaV29WJ9Z3Xt\nYuOM7RuaeYq6XISQ0UHBRciEUcUMR4vOqQqVhIihH8f6i0kipdXqd5tiobTQDMDd3fS1HW3YL3Sd\nQont2Hd93YcRAfKz1tedOETCO8TU3Fx/cn/IVbLuVGhGpnUrk8YfqqgfQ4ss5nARMj4ouAgZElnD\nhnnbq9r16nb7Z+X1en4x56zHd7sif//3ThigXhUcHztuK7jS0PleMSdI5zjZWZK2fy0GrQO0uOiX\nKcIxepaiduYg3La3/f+xIq1Ydkgn6a+tud8LC17U6XMNhZ61S5gFLQJFiiXnZ+2HjhkhyVBwETIk\n8giuLDesYd3QbN/N5mBphKTj8GPzq7Q40X3EcrCynH8o4RvbIGZ0CC90XEjEAL30UChJ3h6H87a5\nXqEwHpLvQy4TrklMPOct66DBuGwB2SpdLgouQtKh4CKkBhS9YQ3jJpc1od0KEtQsg1Okc68w8xFL\n2yBEp12wmLgJjc3O2oNrND/fL7R0sc60c+r1fMV5va8NVdrtEEtWgIK0nDMdztRt6zYQsswSEgzN\nCs3jihFChgMFFyETTNGbaCg/aGPDCY5Gw938Fxbc30tL2Sq6r6/7quxLS36WHsTEkSNOnMSW/wG2\nwKkWV1qwhcSNDaHpvKUsztDOjnerdIFXXasrFOLMQ8hhw3Wy1yP0PIVcvlD7elaoLo1RRQgxNrYq\n2ydk2qDgImRMJN2w9O9hkObC6HwhzcqKX0MxVguq3e5fDHp93SWWY78sTpNGl0TQNa8gjLRAmp93\n4hD9r676/bE8jW5Xi53NTb8MENrSgig0izOt9EfoOYxti80+tM9T1vCzzffS515VTuGwQpSETCMU\nXISMCSus7Cy9PDfFqnNoIKpC2+2N24YCbe4UXBbsg6V+QnlYIoOzJGP7iPhEdYT1EM7UyfqxMBza\nQsV5XZZiZsa1G6qTFRMaIccuz3OSdd+8bWYJDxNChg8FFyFjpCqhVKadkKh55ZVsYSLdr82d0q6U\nrfOF/WLjRj6YDiGK+LDl7q4//tQp7zrZwqq9nnPlTp2KO0vYvrzsXC6dZK73C517aFsVz0ORx0Nj\n0WFY3U7V7um4X8OETAIUXITUAJsMXiQnporE+1gICz92UWrthCWFxWwpBu2K2fBbt+tLR4gMLvIc\nSoSHsMP/NvwHwRW7xo2GE1vI4UL+VmhmI+h0+kUZKtRnfQ7yPl9FcsVwTN51QPNCwUVIOhRchIyY\nJGGVVg09qZ1YInnRcenZbTaM2O0OFiJtNHxtqdiMOyvIQkVIddmImIuE0GZsuSO9TaPHYguBooZW\nUghSn4et1h4Lw8agwCBkb0HBRUgGqrw5Fkk2jpUlsNvKuBi2vaSk79j4ITqsSLPJ7TYXS5eG0AtM\nh0ROt+vyrZaW+utt6TaPHxd5/nknAre2/D56xiXawoLYWAux1/MhSxtuFfE5X8g1g2jURU1D16kM\nZV9/ZY4dpjDkTEeyl6DgIiQDo3YjbF+x/nW4z97sQ+0kYfuIia3QcVqEiLhZiViCJiTkdFK8ze/C\n46HcMCv0QvvhMd1fyCnbv99tbzad2Fpc7D82du20K4c8Myz1gzaSct7yCIyQ8CxCmTDnMF/7Rb58\nEDKpUHARMkZiN7KsNzgdRrN1nGxl8TR0/aukm3+of2xH/3ppICsK5+e90IFA00VScUwsZGj7z4MW\nPE8+KTI762uDIZRpXa1Oxz125owLme7uOoE2N+cXq4Zw1NcgRB6BoXPIhk1Vwq7KsRAybVBwERJh\nFOGOpHby9B9ycUL5UUno/fMIrlA7Og8L49XJ7mhvft7PKux0XOJ60hI9tt8sLtzS0uBYNHDKGo3+\ntRCtCMH13dpyYqvRGMwJ0+HQssA1zCI8y2LHPI5Qn35dUHCRaYSCi5AI4w535O1fO10ig/Ws0kJc\nWfZPA8Ip1D4S8bEf+oLIaTZd+YJGY1Bo5alLZvfLsgh3SLDixo/keD0eOHC6r52dbGNNmvmIx5Gv\nZoVnkeckTcBod/TMmfByS6N47VNkkWmHgouQKSGWqwSyOAfWnUpyOvRvvW9S3adQPpcNhdo+QpRx\nQWLjRBJ9q+Vqd2Fcq6vusZdeEnnhBedubW/7ZHuET69ezd5/VgEMgaoLueYlLf8PfUHYiYz+ywWT\n58legIKLkAyM+0M/b06XyKCQCTkvdn9brynJZQvlXYkkJ4/HQpI2z+vkSV/jqtsNi72i6DFtbvrt\nq6s+v2x3189unJvrL4+hReLKisvr2tz0oiW2KHfesQFdX6woWWa5xta2HMVrf9xuMiGjgIKLkAxM\niuDSaKeq6v21AAiF10SyL3NjQ3VJjhcej4W+8oI8rG7XV6k/fdqJqPl5t8/2tu93Y6NfAEGw2YR7\nO2GhqIOTlKuWhO1Pu2qxvDuUuBh2VXpC9ioUXIRMCHnDaEjgTrvRZxUDWvDoMhSh2XRZktlDJIVF\nQ+KjiBOiF+DWNcH27/fO3NaW//u++3w/cN0aDS9Q4GzNzcUFUlYHR1/HMmIn5pTF0AJx2FXp06DA\nI9MKBRchE0JewZVVoOibc9LNVre3vDwoWtJclKwkiTV9DfLOwgR2AW78DSFmJw7ofZtNH3IU6Q+f\n3nnnoKuV9TqEyjIkJdVnaTckjtFuLLRbB+o0FkKqhIKLEBJF39y1E7a66hwdEZdvlcWxyUqS4ELp\nBYxBh/LKJtmjurztE26WSDyXTIcZQ+JQE0tgzyqwsl5TXJOkMG3sOEJI9VBwEVJjssz8Cx1j3RIc\nk4bdx7ahhQXyftKKd5a9gVuht7johNb8fHYRgRmFIoPrP4bQY7ZlJeySRXnzrELXWJdl0Pvp57Ho\ntUwK02YZHyGkGii4CKkxOqx1+nS+dRerEFy2XRE/hvV1J3x0OYVhoMUlltLp9VyeVaiyfQgbKtVL\nCWn3CjM14aKFSMqzypMcHyvLENsXExPQrl46KY0iSfcUXoRUCwUXIaSPpDpVOkcrFqbKU7uryJiw\nPND8fDjPKm0ctqJ+KASYFPZL2i9rcnxsX112Iuka2nUk06DgImT8UHARUlPsTRe5UkluCUQSEqWL\nlE7QIubkSbcN7ULwwGWK5RfFREcekWDHhHGI+GT1pFBZbBz2GH3tUA0/dJ0hMMvWxErCOmfWBdOJ\n8ISQyYKCi5CaUtQtQfgsLb8qCzoUZ9sNuSBVOyMhNwliY2nJJbrnrcsVCgH2en5BaoRKdRJ8Wp5V\nWj9ppDlmeuYkhG5VFdm1c1ekVliV0Fkj0wwFFyFTTN4bWJKrZsmaO1TmRm5nSbbbTgwh58mOI62k\nRWi7Fqq2HSzxI5J/XcM8YjSrQMwjwrMSK+cxjlpcFFxkmqHgImQCKOqWFKndpWe1ZVnqJYugquJG\nrt2enZ3B2YJpx2btQ7cVqtlVNCxadLZhmdw3Qkh9oOAiZAIoI7iKEDquikTxrH1rAYd8sWbTJ/E/\n/7zfJ2/ZDNuXzZvS6yuGKCt8ypR3qGocaSJ5lOKuDqFMQkYBBRchU0ZVN7Bh5GJlDUPGXDbkkWHG\nJPbXjxUZl25nczNc6BQ1u8qEaPW2ste3zPFpInmUQqcOoUxCRgEFFyFTRtEbWEwc5J3hGGs7r+CL\nzSZst/NVmc9LrGZXiDThlDbbsMjYR53nxLwqQqqBgosQIiLVOA1ViwebMK7zp4q6MiFhqWtz2dpj\naW3lce0w5jIuTtUCKM/EhWFDYUemGQouQqaYPCKk6ptdltBmqI5XyGVDJfms4syOI+tMP1vRP+Sy\n6bEn9ZN1fOOmTuOq01gIqRoKLkKmmKKCq4obXxHHLHaMFkCxMFxM8GQVk0kTBew+EIbr6/4xnVcW\nosxsw1EnljORnZDqoeAihAyQN9eqbCI5+gwJHOuApQmuPOPR+VUQUEkV/fU4sU/eMGHRGYqjTCxn\nIjsh1UPBRcgepYiLUbS6fNaQngZhxKWlfDP8tAslknxu2nWyAkq3p9vSye/z8+5/XbIi1A8hhFBw\nEbJHKeJiVFVDKgunTomsrbljOx23zc7ww5hEBmdW6jBk7Nz00j6rq+F1FJPCnPqxImUpijBqIUfh\nSEg1UHARQnIzzFpfoRIKet9QPldS2YW0/iHOTp+uZvzDomgZibJQcBFSDRRchJBgnpT+P01clVmu\nJwZKMnS7bmHpTscv3GxztWzZBS3C1tf7t2edSWiFXtLfaedSBayHRchkQ8FFCEkUXMNIoE5byBmP\nQWBhDcO04zRpxUutkLTJ8kmCKzQOiiFCSBIUXISQUhQtc5DlOFST14SW3bE5V3nCibbdLMRmT1ZN\nkruof48KumyEFIeCixCSOScrViYhL2kV3MHycn8fWUSSdqf0sVnodn3oEjW2MAtxeTnf7M0qSDpf\nXXU/C1WMkYKLkOJQcBFCMrs9ZW62WtRlXQsxj5OT5gbp/WLhwFBeWmi2Y1L7w6ao6KFYImS8UHAR\nQkqTN4SXVKohKyHRFBONtoxElvyrXq8/pBly+yDyRlGNvdUSWVnxpTJGVQGeVecJqYbSgmt3d1d+\n+Zd/Wb72ta/Jvn375POf/7y85z3vkQceeEC2t7el2WzKl770JWk0GlWMlxAyZIrcRDud9ONs6QY9\nc7BIv6MIp6XNaKx6MkHaWGyNsbQ+qxBLoz5PQqaV0oLr3/27fyc/8zM/I+fPn5fXX39dXn31Vfnk\nJz8px44dk4ceekg+9alPydmzZ+Xs2bNVjJcQMmSGlZNlZx+WyUfK0pdG95dVeDSb2WdEDhu7/JDe\nVidRSAiJU0pwXb58Wf77f//vsvrmmhbXXXedHDx4UB5//HFZf/NT4eTJk9JqtSi4CJkykhyrtJmC\nodmHofaLChsd7hNxOWOnT7u/Uf4h1meRyQPDFGD2Oi8uur+XlkYj/Gy9M0JIMUoJrr/927+Vf/bP\n/pl85CMfka2tLfkX/+JfyMrKily6dElmZmZERGRmZkYuXbo0cGxbfeK1Wi1p8Z1Mppy9lrSclDdl\nBVFI3JS9XjF3J8nlKeoIDfN5DblwRZyqomOk4CJ7kW63K1093bkCSgmu119/Xf7sz/5MHn30UfnA\nBz4gp06dGnCy9u3bJ/v27Rs4tk1vm+wxpk1w5UmCDwku/VtkdOGuSX8Oyrh+hJBsWCPojP5WWJBS\nguvWW2+VW2+9VT7wgQ+IiMiJEyfkkUcekdnZWdnZ2ZHZ2Vn51re+JbfcckvpgRJC6gtChDHXKinH\nS3+JrCLJO20WYp5k8boxqpmBnJlISPWUElyzs7Py7ne/W/7qr/5K3vve98pTTz0lP/qjPyo/+qM/\nKqurq/Lxj39cVldXZWlpqarxEjJRTOKNq4gTpwuU6sR4kFR3K7QmIijielW17E4dn59RjYnJ9oRU\nT+lZiv/xP/5H+df/+l/L9773Pbn99tvl85//vHz/+9+X+++/Xz73uc+9VRaCkL3IJN64igiu0P7N\nZvp6hknHE0LINFFacM3Pz8v/+l//a2D7U089VbZpQsgIqTrHLKmtLM5f3jpbk+YkTgq8foRUAyvN\nEzIi6nzjQtJ7FRXMIdzSyiikOX95+p1EJ3FSqPPrlpBJgoKLkBFR5xsXBEvWCuZJVJVDVTV5HLxp\nm1FKCBk/FFyE7GFCobgsFcyrpOp+Yu1RcBFCxgkFFyF7mFAorojYKJNDNSrBVQYKMEJIWSi4CCF9\nFC2hMIocqrzCJ48QTNqXgosQUhYKLkImhGHf9CdBUOS9BnmEYNK+Fa/wQQjZg1BwETIhTIrgmgTh\nloWypSboihFCNBRchJBKqVpkVFVjq4gzViZMOg7BRZFHSH2h4CKkxtS5oOeobu5V5YcNS5zViWkT\nXM07rX8AACAASURBVNN2PmRvQ8FFSI2pc0HPvXQzzFNOYtwCeZqel2k6F0IouAghYyXPTXVcN988\n4xu1QLYiT1f6p1ghpD5QcBEyIdTh5jkMB2cSBFfd0NcsdO3r5ITmpQ4uISHDgIKLkAlhlDebmAiq\nc4izbgzz+bLPD0RKtyuyvt4/hirGMeqVB/gaI9MIBRchZIBh32AnxcUocx1GeR64bnpZpir7Zy4V\nIeWh4CKEFKLMDbhKF2OYYqBOQiOLSLWia9KZhnMgBFBwEUJEJL/rVJeb4bSIi7TzyLruJURXFePp\ndkV6PZHV1fg4yrSfd53NaXmuyd6EgosQIiLjy52p2w10XOHOJDERe0xvr3rcOK7dFjl9uvrXQ9FF\n0uv2eiEkKxRchJCxUuQGOkxRVMekbSs0OKGBkMmDgosQMkDdXYQ6iYsyrksR4ahnJA7LgbPhxJMn\n3TXWuWJl2hXJf755jiGkjlBwEUIGmLQb2bBCTVnaLDuTMSYcY0Kj0ejfLyQ2q3L5QuFELbyKtqvb\nGsYxhNQRCi5CyESDJPFxCa4qCCW5x4RGVpFC8sMcMTJMKLgIIRNNVbPy8pA3zJV2Iy96ox+GOLDn\ndvKkyPKy+7/ZrC6sV5fz1VBwkWFCwUVIDeAHfX7GmduTN8xVpASCRocR7blWTZZzqyKsV0fBRcgw\noeAipAZQcOVn0nN78gjGU6f6/7fnytdPcZiUT0YFBRchZKK5cuWKvPj1p+WTv3xevvvii/KO226T\noydOyJF77pEDBw4Mvf+is+smodp+nQveVsWkC3cyOVBwETIm+M26PL/1wAPy9meflQ9946L85Pev\nyQERuSIiG1/4gnz60CF57fBh+cRjj41lbMO6kVf92kgSa3tBcBEyKii4CBkT/GZdjitXrsjbn31W\nfrPX69t+QETuvXZN7u315Hfe3G+YTlcV7lKe46uuLM9wpIfXgQwTCi5CyESy8fTTcvTixcR9jl68\nKBtPPy33Hj8+olGFKZMwn3RM1YJ9GsRX2bpohAwLCi5CagA/6PPzzPnz8tFr1xL3OXrtmnz6/PnK\nBdekLvQNYuPv9eo3Vk0WMTUNopFMJxRchNQA3iDy890XX5S0QOGBN/ermrqFg/O+ftKKqtZVtIxz\nXHW9JmRyoOAihEwk77jtNrkikii6rry537STVQiEREOvN1jjq9stt4RP1r6rbLvKQrSxPii4SBko\nuAghE8nREydk4wtfkHsTworPXH+9HD1xopL+YjfcSboJh85heXnQ7apabMX6znpcFjGVtL6k7Zvi\niYwDCi5CyERy5J575NOHDsm9Zpai5plDh+Rj99xTSX/TILhC2FmP7Xa9ypRkCd+mCahOZ7hij5As\nUHARQiaSAwcOyGuHD8vviJuNePSar8P1zPXXyzOHDsn3Dh8eSfHTOgPR0OuJrK767VY0tFr9zlZV\nsx5HLVhC7fZ62a+DbatOuXpksqHgIoRMLJ947DG5cuWKbDz9tHz6fH+l+Y9VUGl+GhwOjLXdFjl9\nOlk0lMkFS+oblBUsjUb/GGLPjX18fb1/gfO060DIMKDgIoRMNAcOHJB7jx8fSq2tSXA4soqfXk+k\n2czWZl1LL+zu+r9H/dxMisAm9eVt4x4AIYSQ4mjnJvQYkuBXV/2MRBwTO3ZU6zIOE7h67bbI/Lzf\nHroOWdsjpAx0uAghJAPjuOGWdZLgAiG81ukUb79seLXoeWTpN63thYXwLMY8gitpfBRjJAsUXIQQ\nkoFx3FQxuy5U1iCL+MF+3a7LY2q3nbtjS0Fg31BfmqTSC5aqhEiW0GFaP8vL4e1VjJGCi2SFgosQ\nQnIw7Busbh8VL2yfWfOXdMJ8s+l+Ly97ERZa1id2fnnPu05CxF47QsYBBRchhOSgKiERa6fT6Z9d\nh1wjbCsaAlxcHFzCR/+dJ+l82KJl2DXPbGV9tJ21OOo0zF4lo4eCixBCxkCacNPu1vq6E2JI9s7i\n2Oibv64Nu7rqZytubPgw4+qq7wszGhsNPzMwVHohdE5VCJFhCq6s7mDS8zMJs1dJ/aDgIoSQFIbt\naOj2V1ddnahm082u0zMNQ0vuZOkf4UQQWqQa++AnBNw2ChFC8kPBRQghKVQlJJKEmy5TgPZ1hfQy\nS+4kCaS8DCs3qw5V6YuMgSFEkhUKLkLInmKcydxpws2WKVhYyLfkTpZQXJpwyCssqgr/DcMdS3uu\nQ25h3jFQcJGssPApIaTWVFErqUh7oygKGupDt4/8qTyJ8mntx7CCSx9rXTaEHbUjFGuvyFiqoqo+\nxzF2Mn3Q4SKE1JpxOVLDnimHEgzoS8SHsXTf+u+8fYfOIUu9rVi/IZctj4AtGwIdJVlnLBKSFQou\nQsjUAycGs/HAOKfxa9GjxRf+Rp0svU+sPlbs3JIoUlfL9ilSvLRC0phaLZGVFZFTp7Ifm3dsaVBg\nkaqh4CKE1I6qE6h1AdDTp8O5U1roVNVviFgfKMVgBZhIf/guNA6E+E6fHhRsaFvEtY9ta2v954X+\nOp3+/UQG3bYkx0vT6cTbi4lHbO90igmuUUxwoBgjRaDgIoTUjlGXF4i5SMPoN9aHToxHvpSIq4uF\nbRBkGluZPukctIjY2uoXcRBHum8r3hYXw/3GQL2vLMVVbWgS+WtZyBomzUOVrwWGJIkIBRchZMqx\nTsXJk255m9B6gqMGhUxFBvO3tNMVq41lk9nn571wi+Wf6RIUaWsjagG4uOjEH8YE1yyttAIq3Ovi\nq6H9dYFXEZHtbd/20lKy2xUTXON+fgEFFxGh4CKE1JyyN6qQU2Edl1DIaBQ3SCv6rKO0sSGyuenC\nf1tbbp9uV2T/fpHZWecgQQTNzbkyElo4NRr9/UEotdvuuOVl9//+/b4dVJrH/lqkwbES6a9Yj7Hr\n31ak6fY0tn20eeaM33dhQQpRpdtFSFkouAghtWZYN7u00NuwSRIfmuPHnbsTC8vFlu1ptQbDcrr9\nXs8JGez/5JP+sZD712j4avS2QKtFiyj8DhFywxA27XTSQ5B6sgAcMpsLVwVF2mEOGLFQcBFC9gTa\n3UlbF1DPGBzmeLKEv5JymXBOzaYLwSHHKpR4b49rNl3bepmf2PJBGIdNsI+1rd2upDFYV0yLkTvv\njPdh982yLNGoGXUeIqk/FFyEkKkiqX5W3W6AIdFhnRvkQDUag6E17SJpZ8fOUsS+NrSnxZB2xuzY\ndBuhv9POKWm/2PP18MPxYwmZRCi4CCFTRZEEZdz4Ox0nXOzMwKoS7G2YKTY7EuPROVDW6bIlGno9\nP84kYRkLdUHMWRfLjlfEh+7sGEJkvW5WfOW53rFj6pKsXocxkPFDwUUImTrSbrSxGzO2ZyljUISQ\nOLHbENpLy4Gy5xgqGWH314Kp1XKCLkkw2ccajXA+WZ5CqEl5V7GZjGmEXMIk92zU1GEMZPxQcBFC\nJh57w19bc6UEYmIiJriGfYPWrhHERszlwjjT8qXwuE2YD7lmWpCE8rWShJOIu66h8gxZw7WhvKvl\nZT/u0DkUoS5CixANBRchZOKJuUR5yRIiy9pG7DGIHO32ZMm7wvFJgsiec9p52LbThNPamq+pVdUS\nSXpGoa5LVhRbmwxwdiAZNxRchJCpwBbQ1NXSQ46W/q2LjqYJprSbdto+IZcL4bTlZfdYFofI7pdW\nymJlxeeB6euDdmPjXllxQkvE1QJDba/77vMlIrIk01t0GBBt6JAi1lIMjSu2LW/ItGrorJEk3jbu\nARBCSJXoYpwxcGOE24RyCgjx6VpT9ri86PDdmTP9IqXd9rMQbQ5W3r7SbvQoAaHXk4yVgNDtQfQg\niR9/HzkSHmcWQar3s3loACIv6/OA69luu9UEkiruZxlfEUZRv41MLqUdru9///vy/ve/X2699Vb5\nL//lv8i3v/1teeCBB2R7e1uazaZ86UtfkoYtd0wIIRVjZ+xlDU3huDKJ8mlJ40m5WXCbrLvW6aQn\n/ifN6ktyW3Ql+aLFOYs6OTgv9L2x4Yquwu0T8TXCQF7nKGnZobIOJSFFKS24/vAP/1Duuusu+c53\nviMiImfPnpVjx47JQw89JJ/61Kfk7Nmzcvbs2dIDJYSQrIRcrqLiIstxsVCfDR9qUSHiwnPz8+5v\nuGsgbcaeduhi49a/z5zxbe7sZBu3ZWnJP54l5yyEFkM4hyNH3O+bbnKPb2668CUKuv7RH4kcO+aO\nazbT+7Q1xUBWMZVHdJURrWRvUUpwvfTSS/LEE0/Ib/7mb8of/MEfiIjI448/LutvfqKcPHlSWq0W\nBRchZIBhOgnIhdJkmUkXm9GYZQZeCDsDUSd0A13tXe+TloeWhZD71ev5cKAeZ2jc9n/MUAzNeExC\nTxCw56X5kR/pDznq8C4WtQZJ9cXyzna0oilp5qilzOuD7C1KCa6PfvSj8nu/93vyj//4j29tu3Tp\nkszMzIiIyMzMjFy6dCl4bFu9KlutlrT4VWAiof1OijLM107RdqsYT6gNfQPPm/MUaqvTGXR6UIk+\nNBEAMwvxs73dX5m+0wmLVDv+vNjj4G7psayuiszMuDFsb7v9d3dF/v7vvdhKEmkgya1LWqQ8dKw+\nnuxNut2udCtOyissuL7yla/ILbfcIj/2Yz8WHdS+fftk3759wcfafDVPBRRcZBIZtiCzN3hdDiKW\nz2UdlZhzZGf16dyzkOhYXnZiBmE6EZG5Ofc/KtPb/DWMW8+c1NgZgTEnzp4X9tNulV4QW/9++WX/\nuA7Dop+sZHWgYmHfPO4iPwunB2sEndFqvSCFBdf/+B//Qx5//HF54okn5OrVq/KP//iP8m/+zb+R\nmZkZ2dnZkdnZWfnWt74lt9xyS+lBEkKmg7rku+TJz9H7hsREqG17g9e5VjEHzAoBhMRi/XS7TjSF\n0KHL1VVXwqHRELn9dpEXXvBJ6Z2OFxih2YMQQGkTAZK+P9vnfH4+LA7t9/ZHH/Xb89bnKuIaJoV9\nh9Uv2VsUFly/+7u/K7/7u78rIiLr6+vy+7//+/Kf/tN/koceekhWV1fl4x//uKyursoSsizJ1FCX\nmyaZPCYt3wU3YitG9GNJx+LGnfY+CSXIw1nSY9Dvu8VFkRdfFDl+3OVkWVdqaal/set22/0/MyOy\nf7+vqRVLzreuVNbnKunzQbdrt/d6blz2eiH0mYeksGMIO9uzikgS3X9iqazwKUKHDz/8sNx///3y\nuc997q2yEGS6mLSbJpleRnVTCwmuNLRYEcmf5B0Td52OCwki7PX88yKzs672VKPh87J0+2Bhwbli\ns7OuDX1eOucJog3V5G3JitC4YonmNkyqH0Mx1m7X9XX6tNuOOloiyTMxs6AFa5HQYFX5a4RUIrgW\nFxdl8c3KgTfddJM89dRTVTRLCJliqrgZFbmpxWbg6f9DiefNZn+19izurhVd1kmJ5WslzZpbXvau\nD6rUg7W1fscIrpGuc3X77e5vNdeprw3tbKFAalJYUwu1pAkDaFujZ2iK+L+Xl/0ai/o5KOKixwRX\nmhMXGj8hZeDSPqQU/CAiRRnXaydNcOlcnrU1L1TW10UuXHAhvLQleCwhhyct8dxeH93X0pIbG5wu\niMAXX3T/Y8afiAs93n67E1433uhyuMDsrPv54AezjT8vNjyXtZ3l5X4xNwwXPcmp1+td5oHpFiQJ\nCi5SCn6IkFEzqptaq+WEDZLe0Tdm2CXdjGMumc2XQruhpHD0hdpVelynTrnwYKfjiphuborceafL\ny5qbc6HF664T+fCH+5P2UR5ie1vk4EGRX/mVQadNjzu0RE7IfRPxY+z13Nh2d8OLXKMNfW1E/BqN\n2C90fbG+YhoYI/qHaNalMJJeK3g+8s5YZLoFSYKCixAyURS5qVmRgHBbszkoCKzbFXOiYiuW2dCX\nFlk6V2tjw+8TSgpH39btQR/g6lWRS5eceNrcdMc1m4POEgTkyopLnEeJRMx2PHVqMPQXK0sRuv4Q\ndu22F0U6LGnbsMdjLFaM9Xr+mq6tDQqumGOpr60eWwj7PMfyyQgpAwUXqQ3MlSDDIkmk4YYcOw75\nWyL9boeeAaixr2PbfqiAZ5prYpPWIcDwGMTEZz/rH0d+V7vtxCHExPa2E1y3396fr6XHPy6Kimmd\no1Xkc0QLTSuwMY68Dio/y4iFgovUBgoukpdRvF6sW5WURB47Hvvr0GGsenrM5Tl7NrwfQo4LC861\nQoHT+fl4+EyH1kKkzUjU54bHcG42zKjDkva4pFw6OIMrK87ZQnvYZ2mp3+2KPSfYFnMkQ/trEVo0\nVM3PMmKh4CK1hiKMJFHFjTBPG7FipGl5ZRAcyG2KEZqJhxv/wkJ4iRo4bZ3OYOgsFK6D+3XffT78\niDwnEfcYFtTGOYTOWT+WFGbUj+nx2GNi73Xkq+nJDPiBwEPYMZQzhjaTrrslq/tISB4ouMhYSbtR\nUXBNFknP16iey7R+ygiu2HqDWUNh1pEJJcpblwf7bG05V0fEu0Z4/0AI6nwxLZR0jpYWK0CvqSji\nRNfSkn9vZhFGMbK6ZXa7zmtLmkmK89/edr8XF4u7Urp9/OZnEKkKCi4yVjirZ7qYBMFVpl38ZJkd\nmfZlIkv19Jgj9txz/e2HRCSW/cF+p0715zlZbL6aFnT6nHX+GP6POUIQccvLg2s56tmMIq79tTVf\nvFU7VRCSduESG/7D2pF6bKHwrN4nCe1OElIWCi5SO1jLhtQR7aqIJCfa6/2B3V8v3RN7vcccsXPn\n+nPB8Lg+tt32pRl0G6H3kXWLQnXB4LZZsRUSuLpALGb8bW66UGWj4RP6d3ezfenSszuTBJ7F5orZ\n8ZdlGOKejtr0QsFFRkKWD5GsNypSL5IEAx4PPValEzZKkZ42iy8UPrP/63Flfb1rwfH66+5v5FtB\nKEGY9Hoi//t/i/zP/+nKRoi4AqciTvBYIafzt1ot16YeF/bRy/2IhNc5DAnSUFkIXdvs+HE3Tj0L\nNK0N3Zb+HRrPsF5PRcVRHZxgMnoouMhIyCO4htE2GR5pgiGveC46rX+YIj2Lq2LLNsRCbkVfr+98\npw/BbW/74qWvvOIcpVbLFUFdW3P7vPKKO+7660V+6Iec4Nra8svpvPyyyKOPun2ylK3A/6dPe0cs\nVthUn6sWaidPDp4XxBdCmFqIZSUp3IvH9SzK0Hnp52XUryeyN6DgIrUmy4cSP7yIpWrnodMZdDys\nU6Xzo0ICLW1MacnlEEdor9kcLPtw5IgXLktLIleuiFy7JvKudzlnSxfxxOzGUL8oobCy4kKBcM9Q\nxV6v5Yh8rJ0dPwMS7Tabbhy7u67vpCr9Nrcsa9gQj4eutxZ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DEEFf6+uunIOIc64g1BoN\n16YujgrxqGuCAZ2npsE4MR5cC7sQt73GuE4vvdQvakGSMGk0/HlubbnzgDgVcZ9RmBGphZcdg+4n\n65dSQtKg4KoBVQiDIivXV3Uzsx9ERa3y0GPjEAOj6lM/7wcOHJBTDx2XUw+50g/WEdmrjOK5yOs0\nQARkeW1nGb91T3ToDCJLhxSxULSewWdBvpNeQBtODcaEZYDQJ/7GItpw6XT+lBZ8eI/rqvHacYOw\nwnFZQnNot9n0Qk5XyceSP41G+Ase1qBEOxCweqzz8869Q+0uHYoNuXSxx8oQcufI9LOnBVddYuhp\n7lGWsaStXB/L3UqaraMTdEOPr6w4Z6vXczeBhQX/7biqvIfQN+S0mUVln1N++A2PcbqOefqO7Qvh\nYF0Q/bj9Hzd+HY7UpQ5CxwCIm/Pn/XHYbve3x+mwH7YhQb/Z9CUfRFx5B/3F6aWX/ELWEGxAJ5wj\nTwxu0u5u2CWKhe+066e3N5teDDWb7rNFO2A26d+2q3PsIEi7XSe2UJkf4ksk/jxooVklFFx7kz0t\nuCYhhl7Vmz3LuYZuHtrSt6ESfLii6CDsfN1PKBd8GHldmmEluVZBVkE4rR/AdRdcWkjE9i3i0mqh\nlhSOtECUdToijz7qjoNIEBlcUif02trZcYIFwkuHK/H+OHHC/cDB+vrX/fHHj/e/j3TpBRH3ZQv5\nXrEvNmfPDp4vrrGe4WgnGuj1IEPCLMtzoX/3ek4YaocuzW2zJAm9aX3fkmrY04JrnFThxAzLoct6\nYwp9+GW5YQ3zg6muH3qh3B2R0c7Am2aq/GJS5b72PQqxBNGTVTToLy4LC9m+VOhwIep2ffWrrlDp\n88/7diHYMBabnnD1av//NjcLrhHCb5htqc8L/elzAnDMsB3unBaJIq5dnBMKmWrhGvosDPWHbUnC\nKZY4b8t22OOSnsu6RFTI+KDgkvHcpPW3LpsYmscFKeLQxT6AAL7B6v5jpSMw1v37+8eKD9GqZ/fk\nea7q9CFW9jVWVyGZhVHcaJJugln7zjvOLGPXx4ZmzuG9nzR23PjvuMNXdY8dEwIz9JDz9eEPu3bv\nvLM/ZKZDcPp6Ypz62ui6YSJ+TUWbe4jHUVNLC0e9wDcmDiSdE/Kzut3+mlp5csR0H0nPqw2JxiZC\n5GESIipkuFBwyWhi9Hn2GfYbM+3mkbX2DMa/tORn/yB3An9rwYa2y9x0rTjFttiNss7kPe+6n0+M\ncd5o8vSdtG+R62+PaTb731s2tKhZWXEiBseJiLz+ugvdPfywHy8EnKXRGKyVNTvrSk3MzjrhNj/v\nhM7mpnsP6/fO2bM+f9POKhTx72frLml0CQa9z913u/AlvpStr4dz0kJhRB2eFck2gzD0+aDbTXtu\n9YQF3YZI/yQBulYkDQquN6n6hpbVXsYUZXxwFH2jlh177AMloR7nW+eIDxxdQRrfPjEl246vyptu\nXb85pjkm/EAuxzCcsyrzc7RzBKcKSev6f6DHjTIrIUGjBQfee3Z8p075WXwLCz7fcnXVJciLOOGl\ny1HosLeuYq9/oy8dEu12XYX4J5/0jhVClXfe6frRzxVEJs5jba1fOOEH1yr0ftGOnD1/+zylfT6k\n5et1OvE27LFlogxk+tkzgiuUcKk/rHU+wDDfDLrfNFEiMrrwWdIHSlbsArNJ3+CTSHuu9AK1OqRQ\nN8oKwWnM+ahy3Hmvb5a+bS5iFejXKRwuFAq2brJlZcXd8L/+dVcAVcQXA8X7AK8T+56x7hocK+RH\nzc66x+BgPf+8G9PSktuGpYC0uNLFWkXc/rOzznU7csSXYcD+umL+8nJ/CYss7r5IPN1Cf1HVXwyr\nfu7S3LNxfEEmk8meFVz6m6PNB9CP5+0j7QYZukkkiZJxvzFt//bbuv1Ga48pIiJjYQRNLNwz7utV\nJXV17sowzucnT9/amRIpt3QWjoHgEQmXcUGZFZH+5XiWl51AQpV4hPlef92FC9fW/AxFjFvnYW5t\niXzgA/3iCTlX+jPv0iXvRs3MuP/1eYm4GY86qV6XlgBaROIc7r5b5OabXTs2qR2hU91XaGkk63TZ\nfDD9+ZP2eZr23BZ57qfps4cMhz0juEJoW1vb9GXbA3W3l5NyyGLoc9RJsrF6RGVcuyLU9UOvruOa\nFrJe39BrPunmmrfESOgzQCd12yKlsTBgyFmB2Go2/ZfEUAFPfPmxYS9bmwqhMggVXaMKYguunB6T\n/YJoz7nR8AVTtWDCLD8cA1EYEkvdrk/ej325ypprqkn64mv3iz2ux2Tzufg+J0lMteDK+i0lzTYe\nFuN2ZYoIrqwUCSNm+cap82D00iN2/7pRRciXxCkjuIbpJGqBokNgWohgDGksLfkCoFq4oQI7HB/t\nPuu+2u3+Wl32fdPreedrbc2JLzsu5J+99JJf63F93e2PEKWuAI9x6vIO2onTk2ws1mnSx+LxGDFh\nXdVnW+j1Mg0ONBkuUy24sn6QDuNmlmWpnUm/iVYpGPN847TfbNPyYKYBfW3qmrM2zRT5ApH0Zcbm\nINrjlpYGj7VCRgsXPQt4ddUJMB2+RIgSyfMiIp/9bP97R+d4AQgincgu4hLv77jDJcqj6PG3vz14\nzrYsTNJrN/SlS6+GkdROFnFV9Asm32ukKqZacOWh6jdV2lI74yLJSdK/szBMh26YomLSBcukj78I\nZc45q9OdNlstD2fPuiRyES925ub60xi0YNK5Ra1W+kLw+r2H8FunEw6xtdt+uS0tni5d6nfgbI2q\njY3BtpBfFRqH3m4fBxBPnc5gHS6R/ok3unCrdetsaLPM+6GM4MLqGiLTM7GFDI89I7j44nckOUlF\nZhQOA3sTCj2e9H8ae1GwTDplnrOsTncstJWXbtdVZ7fvLZ3kres3FcXmI2mRlpQysbHhK79jwgtC\niBh/q+VDhDoBH2FRrLP4538u8g//4IXQwoL7ia0TaR005JHZYqu9nqsjtrPTvzj2zEz/LGVNSFhv\nbPjyF8MQRFYYT7vTTspBwVUhkz6NP6nm1ihJy6krKrhCTsKkMOmvrWEzzudTO1X4sSULtAvV7XqB\no383GuFZeVnCcN2ua8cKO7SDfTsdJ7aQFH/wYL/giVVU1+ei9/m1XxP5ylfc39vb7hxQUV/3GwoV\n6qKt9v2ux4Mq9DgG4skm2oeEtZ3QU1QQTdrnBakne0ZwjYJhJt8OA5uUivwMnV9ShKIfTlWGO+0Y\ndAjizBn/+KQIlkl7bVVBHpGZ9TWXxRWJ9ZE0zqR9UTHdJogvLfnFlG31+VD7GGfauGy+E46B4Dp+\n3O2zu+tnFFrBaMu+6HZRQ0zELah9881+e+iLkr6WWkSJuN9w2ba3w+4Vtukirfr3sMj7BW0SPkfI\neKHgGhPD/saU5wNCf6jEEtBj7WVJTs2awFpVuBM3DRtWQe5MqH1SP8qKzNhrrKo+dPsrKz5EiHIN\nuj+IDC1i5uf7k9iz9IfK65Y0d7rb9XW8dDHSV1/1xU5R1gDtQ/i02/1hxXbbCy6dsH/5sr9+jUY4\nD2131y8n9P+3d/YxclXn/X+M7MQFUm9oirfY4I1sqG0guzS8mCqNp5CNCQrWFhABK8SbQKo0oqmT\nKo3Vn/RjXf3ApqjCRBRFikLHqaVARdU1jVwTiDSbpGVxUrKbJsbipZ6NbbJODawrx3FszPz+OHz3\nPHPmnPsyc++87Hw/0mrn5d5zzj1z77nf+zzPec7kpNlu2TIjtpYts3m9SiWb5BjCEMI1dHx6HIMl\nTidKTjKRKVRmEuLGPEK6SnBleRHElRVXTzsILmznBqT6Mu6Hnq6T1JNmxpCuq170/niqhxsCgzHW\nlxNpjTWvETiQG+KsU1n/Nu5NXVtM+/uNaNExSNoqpVeVwAxEndLEveZ8x1Yq1cZ96QeJ/v7omdiw\npEFIYckf1O8e6+hodVC7607U9YsYseSzPmmr2eSkqXNqyrS3UKjOmI9s9agf+4yOmj+MUXDT+ixQ\nvuu5nocrfbxpEt/mce756iCdBwVXndvGXVh53cCTuhWSoges/v7ojPtJYklEGl9A2o2J8ZXpE3C6\nHW6eI30jwDZZBUjX6+qsd+DsxsE2dI1l6WZN8+DgWkz1+YR4LV/7RkaM0BkdtS6ykAsQ14AWPvgO\nSUR1+W7GdrSlVLJrHRaLRuw89ZQp933vMwtZu/UWCibYfM0aU9f0tBUgOgs+Fq4XsUH2PtA3OFZY\n0wsFaz1zH/i0xU3PWAwlQo36LCluiMW995rXGzcmO7+aIYYouDqXrhJcaUhjIUrr6hKJTu5Zr+Cq\nNx5Ff6/jSXRMhl5vUs+wilrCCO3RgbIiyWYM6XJA1IDnTsNfu7a6HW7ZjVrR6iULwdWNZHWNNVqH\nW762mGp3WqgstANCxRX+vizuSEY6MWHcdvh+YqK6LRAF7nWI11rw4drGteCzSO3fb/NsiZhj1JYu\n9xi1hUv3Pa57CCtYlzFTUgvFsTEb1nDoUO06t9p16loZffWJWCtiuVwrUl1CIj6p2EKbfGu+EjLn\nBVcjA3CSspKIpFCdPjN+IzT6xO8KEcSXlErV603icz2Qp2mLjgXRnzXyO7nT8PWCu1rw4bdKG8+h\nyfKcItkQcic1avWK+q1xQ0WAedL2idgZej7rlgtEgi8xqUZb2ELALamvCz2G6eNFXFVPj13yRyQs\nKOEOdNujxRlmH7rLD2E7BMfjoQwJXPG76v5yrV9ufRA/qKeRtDdR44UbllEo2Ae+rOJEOebMDea8\n4EozAMed1K4lSsRcYHrAqteF5nOF6frcxVxHR6vz3WRByG0DMHDhWLdvr90+ifj03RDifif0g97G\nDVQeGbF5d9x+cctrJAdS2pu6zyoi4v+tSX3k1XdxDw54PzERtob4rgk8EECAQIS4y+1MTNgFraem\nRI4erbaQ+YgKcygURD7+8VoXe6j/enrskkKwbGnxEWr77t32NcbS0dHqJKY+y5PrmnXHXL3PwoXG\nAoeyIeJcIVkvuk+ixgvfOZL1hJysHyRIa5jzgisNSU/q0JNV2rpEasWbdoWF3AIYiKLqbeQG5LoF\nSiUz6OKpHPWPjvpvLu5nWL/NdZWkcanhePX2yMmj2b/fTHtvJ/ES5abgwJkfeZ8Dadycvgc1/PY4\nt0dGTMyQPicKheoYqRtu8D9kJbWwi9g0Dr599etSyYgaEfuwh5xYWgyh/brtboA9jn/TJutCxFjh\nXtdaJOk6gL5+YFXDrEi3j4tFM074xGxcn9Vz/uC466mPzH26SnBlecL7ykorIIB7083iJpzEyhT1\nFOyWs2lTsqU7fMzMVE8rR3xDKBYkaR9qlwSWNcGgro/PJ27rMcv7+oyDaDJaEa+WdX1Rv31vb3hG\nW724Qm1mxi7cHiVEkp7boc9xjei8V9u3Vz/0xaGD47X1XovMENgG3oNiMd6SDzepFoBYh1G3Kc3Y\nWs94oduZtr6kcMzpXCi46tzWvZmL1HdT8Vl+QtvhaW1y0g5GmK0Uta+vnri2YrBxM2IvWSLy2mtm\n4dsjR+zTam+v+cMNwQ0W9Q0+2MbFbadPqOkp9ePjpi2Fgo2hKJeN8Nq0yW8pFEk/GKIdSX6vEI3s\n20pOnDgh49/7njz35JPy65//XH7roovk2ltvlTUf/rCcffbZsfu3QnBljdt+fW4+/bSdtLFxY7VQ\nCk2Q0TNmsZ0OfEfZ+P+b3/gt4MAXP+Vrq26P77jcawwWLcRWhcpct86Upa9NuP5OnqyuA1YnBJjr\ntqAebflDG921C9FfOj4T2za6ckY940UzzvFOv466mYYE18GDB+VTn/qU/PKXv5R58+bJn/7pn8oX\nvvAFeeONN+QTn/iETE1NSV9fn/zTP/2T9DQSpdwC6rFUZVFn1NOo+4QZmt3ku7mlveFhsCsWbZDs\n5KTIZz9b7QrQ5n+4FbA/rE56wdmFC81sJncZk1CixCSD3po15oYHoaUtXZokIrNey2BSOlFw/d9P\nfELevXevXHv4sHzx9Gk5W0ROiMj4N78pDy1ZIr+5+mr5myeeaHUzm47v3AzFc/oeNkJlAH1tQTxg\nRiQsxlrARZ1Pce3xxYmKmLULjx61711xFBJ5EEwQalu2mLJ8bcFn7nixbFmtaNLXNEShiBF4ejYj\n2uDWocn7IaBTrm/SPBoSXAsWLJCHHnpIBgYG5Pjx4/LBD35QBgcH5R/+4R9kcHBQ/uqv/koeeOAB\n2bZtm2zbti2rNrcV9Zido/bJAiwIG1cvBrOBgeqBTG+HgUzEJlb0xVz4BlBXIGIARnxDVOoGXWZo\nYHStZhi0o6wKPstk1HG4faYH9W4YUE+cOCHv3rtX/o9z5ztbRK47fVquK5fl/72znWvpatSF24kk\nvYnDKu3b371GYcXWDxNR1pZ6nm31b4K6+vqM+Pn2t43I6+uzyUqTHKO7nS/mU2+r94FYgljzCVQt\n6jCLGmOCts752iJSfwhIUubqOU7qpyHB1dvbK73vZLs799xzZdWqVXL48GF56qmnZOydx5SNGzdK\noVCYs4IrjdnZDTRNso8PvcyFzqIOdHC7e8PDjCCApTM0bvvwHvdcfDc0ZAd/DHAXXGBcjr410dzB\nUiQ8lV2LRp/FQLdDv4cbUZftI+1Aqwd1LRDzHlRb7Yob/9735NrDhyO3ufbwYRn/3vfkuhtuqPq8\n0fO8k4iyXPoeHHy/qW9s0MHnWmCgPJ+gda1C7rkadz7BpTcyYsYSZMaPetCIuzZF7Jjl2xbjSKFQ\nvXaj+9Dmq0M/BLpWtqzOOYonkgWZxXCVy2X58Y9/LNdcc40cOXJEFr9jP168eLEcwdL0XU69Liv3\nM73+GgYqPchOTlZblXwDEwZhbZYPoZ988V677DDQTUwYMfjZz1YPdBMT/izYbjyGrs8XfxE1qOO1\nz40YZWUJfa9dnNjWN6jnTasF13NPPilfPH06cptrT5+Wh558skZwtTtZ9a0bhwVcAZXE7eeirwM3\nVjMkaH3uwlD5oXZMTJj6ZmaqLbuYtejbx/ce/QKrti/gX//HWIb0ET7rt65Di8DQdpputLqS9iET\nwXX8+HG55ZZb5OGHH5b3vOc9Vd/NmzdP5s2bV7PPiBoVCoWCFDrkbI8aNOs15ceVX8+NIRQwWi6b\nqeWvvGKX9BgbC+f1cl+jLe6sQ5TtE2+uQERZoSddzGjC90nyVYUGfL193FpwItGpPpIO6nOJX//8\n5xIXEn/2O9tF0Y6Xd1aCKytLnhYYECm+mX0hYZZ0lmSS496zx8RaTk2Z2KuZGVPH00/7H+ZCRFm1\n0RbfOOKW4UNfi0nGBLc9vvdpaPXDEMmXUqkkpYwH/IYF1+nTp+WWW26RO++8U4besT0vXrxYpqen\npbe3V37xi1/I+eefX7PfSDPNBBkSdZG5rjl3llHU02+SenU5eB1KlKpjFzB4j4yYp8z+fpGlS0XO\nPddmkMbCu3GuARw/zPWlksjOnUaAHTtmypuetkkOfRYnkWpXYqgP9ECtbzZJgt99ZDFrqRm001P4\nb110kZwQiRRdJ97ZLopuvTGl+S3d8zrO8qzRD0qwIoUmrUSteYi2IbfVvfdWH0M9bjptAdSLT/vW\nm4R1W1sL3VAGX3n6+9B77Ks/b0Q0UXDNbVxD0BZ3em8dNCS4KpWK3HXXXbJ69WrZpO6s69evlx07\ndshXvvIV2bFjx6wQa0fyvGh0XIIrNNzttNldJHrdQV2OL3kmBmotMNwcWiMjZsCDVc596vRZpNBO\nPZW7XDbCbWjIzkT63OfseovutG9ffIkWn6gXNwu0zW1HlJsmtG3cDSzKxRllXciarCwmWXDtrbfK\n+De/KddFuBWfW7BArr311ia2qn7yFrO+m37a31LvExcg70O77VCnnuUYFUyO/tm/36RawX8kPK3n\noUU/COJ4fPn33Haj7e622Cbk4o8a0904um6zWJPW0pDg+vd//3fZuXOnfOADH5ArrrhCRES2bt0q\nmzdvlttuu02+8Y1vzKaFaFeibt6uiV+kdpCemAgv5OzWE0IPIG6maRCaLu7WsW2bsTBp4TYzY+Mx\n8FRYLhu3wbnnGteiO5NQ9wmeOEWq1wrTA6lrSdMgr4+ecu66H93+0u7ZqIExTjDD9ZnkRuNa41oh\ndJr11Jy0njUf/rA8tGSJXBdxp31uyRL50oc/nFXTciVvMZvWehI1togkt3LFPVjoWX8+kSJikpsW\ni2acQNjt8eMiy5dXL71TL3r/eq3Nbn+5qSCSWsDrFd3tZH0mnUdDgutDH/qQvP32297vnn322UaK\nbgkhwRU1SLtPoFqguZad0FTwtLhPe27dOkcW3kNM6M+Gh21wapygc/PtaBeGHuh9QbUY5DHQj47a\nffSUb1jFRIxrcnjYzricnDT/i0UTV6IXDkZ73TxCpZIVm6VSWMxi23YYMN125Gl9TVL22WefLb+5\n+mr5f2JmI16r8nA9t2CBPLdkiZy6+upEyU/bjUZdzHEk+S2jxhZcZ0nq0Q867oNFT49NNIrlw3wz\nDjHDV48HaYRMknaOj9vQBvfhRwtFfUy+3F/aiq0teSE3YpSoTSO628n6TDqPzGYpdhKhCzCLAVgP\nULo8nbHZdRloC4zONB1yY0UN4hikkBm+ULAWrb4+u66hHvRKpeqFoLdsMfvPzBhxg3JDT9u6P31B\ntYWCtTShXfAyL18enZvH50Lt7a1OeIip67g5QXgVCjbeTce1oc2oI1S37zjbQZQ1m7954onZTPMP\nOZnmv5Qw07yPbuvPeo7VZyl3xw5YrZF0GGMIttELvK9dax6KoiwyuH56emqzuTfye+kHQv3f94CK\nMQPEzbz0hTvge/dY3fG3HvJ0RXbbddFNdKXg0hecK4rwGfJK4b0O8AwJNrjBcMG4AaahmW9x7sSQ\nyxPo9uzYYcoZGDDCZM+e2jivgQFTDixNvsHXjZ9C+T7xovf3BdXqgXZ83NSPbYpFI/Z8WeajBp6Q\nlXFkpHppEO0KRdu0+1P/jr4lieLixbIg6gk8yzobcYecffbZct0NN2Sa+iHrY0tbVpqg9DTtqLeP\no8YWPfboBzGMHdpN6F5/uP43bqydTFMo2OtPj1tYZNq9ttxjTdPn27fb8tzZl/rBKmm5bn/5wh18\nuH1YD3mKIgquuUtXCi5NlCjCd26MgP7vi1kC9Vw0votNx0j5ypyY8B9DVIB+qWQsTZs2WWuTPib3\n6dkNvE2SqsF389i/v7ptU1PWuuZa9fRT5NGjIj/4gfkMazjOzIjMn18dg6Zdt/qG5PYHRKPv5uQe\nQ96DX5SbIssn6bnsDkn6O6UVRGl//0b62CcColzgbiwTQgT0/vr8QW4t/fCEBy8R+wC2ZYudnTg+\nbgPm3eTJoRCMUFsxlhQKZnJN0j53rVg4Zv29Fmwh1yK21X3SyEMNRRFJS9cLrkZFEURIaDBAHb4c\nXe4+MN27A0aclWV0NLwOof6P13i/c2f1zDx3XwxGesagSHh2UKgufZxTUyIrV5r3vnivUD/eeqvI\nI4+Y1319dhJAuWwEl2vJArrfcSxunJcOKHaJym+U5xNuvVaSdqfVx5ZWELWDtSFJn/mEgyt0zjnH\nWpfccvHA4z6c4GFIf66txG47fX3lWuJCbY0SSe7x6jaGtnfb1qgVuZ5zN0qE+n6rNGWTzoOCq2D+\n+y6AUNCm3lbfpKPch26OLpTlDiA+saVjE1B36EKM+0yLjldfNX9wI+Dp2HUXog16GaF6ZgeBNWvM\nk/PEhMiiRUaEoY6hoer4Ez1Aa6sYnsax7hsGq+Fhv4VI95ke3PC+XLa/8/i4jRODi1boJu/BAAAg\nAElEQVSkOjYmL3y/bR51tmoQz/LY2v0m1Wgb0giNQsHGPLlutmXLzB/WQyyXRXbvFvnhD0Vuv91Y\njH/0I5Ff/cqc+ydPWjejL7egHo/ctrq4saHLltmJL9qliLGlVKr/t/Q9YIbKqceKXM+5m1RwzWXr\nM7F0veAC+oYuEn0BaIuPDjyPMmVH1avrd5P99fVVxyYgxki7EXVWdiQwRZmuENLfIcdOoWDqCy38\nfPSovxxtxg8JLnymt9FPy+WydRWG+sUVIePjRrShHC0QQxMffGLajdfSLuSkLlofjVhFoiyZWdbV\nDoKkURq9SUVZJbIQclkJLuATBvrBUM/8w4zf/n6b3BjgPIfIgQBau9ZcV5jViHgqTLrRMx0xHqGe\nkFDS1jF8juMIxWG63/lI+rAZot3FOpmbUHAlRF+gPquHL84ryUVdLFoBpwWMxg3sx2wh10Qf1W5f\nm44csQOxu05iaPDTlqFQfa640dsvXFjtolu3TuTQoWpxqN0gqF+3/+TJ6v7U6zRC/CYZTOMGVrdP\nkw7EcX2UtIwkg387uLzqpdXtDtXfTtaGuHAC3Vb3ugV4CIPI0tfayIhdFULEiiyIMcxsdC3gGPN0\nKENUPKt7TSLmTMRazXWqlzgaOXfqtSL7HlxD2/nGH532ppFxiXQuXS240tyYfRcoBqyQeT3JRe0u\nW+EDA9z27WFR5goWkeolgHyWItStLTi+p2rtWsXgC1cB0lkg3cPoaO0yQXqg2ry5ViC+8opfrK5d\na5+mtaUMNwTtenQtjiJ2aRLsgz8ch8+tqH9LuDjdY0hCnCshaXlzefDN8tjmaj/5XE/6O/3fN/NP\nn2t6hqL+j6V+enpsgDxSt+B6j4vXFImPZx0aql0Q3gXXap7Ue64kFVxJxVyWk61IZ9DVgivphRG6\nQWorU9T+Lm6MhTtIuiB3FnJjIQko9hkaqhVUbh3a0qVdaFrgYLbS2JhZ4Hr/flP31JQROIsWWQGk\nZxVqgVMo2PZqceNa47ZtszMWp6Zsmb29xq2BJ2vfFG/0u37v+x3dbbAqgCvkQmXoJ/g4geR7gtfH\nrLcLnU9JHwBa4Q5pd0taXm1r9TFHTdpwwxhGR2vHIN3+UBLVNWvsuYPzXj9M+sY9t2yRsKBLItaS\nfpeEtOdqq39jkfa/vkg2dLXgSkPo6SbpRdLIdlrclMvVgeXYB4NkoWCtTxBna9fa7XxtR1n6qXbz\n5up93NgrEXvT10v3aCuYiF/cFIvGLbhypUmUumyZ34oIE7yvT3wzCn1ocYN4kqhZlhAzsHQldXNE\nWeb093FlJH0ASLJdlnTrDaEVAjYufEFvp/HNhBbxj1tarEHIFYt2ZQc3FYyvPF9bcV1GJUn17a/X\nkcU2+prKwrocIs2DlN6nEQu172GrG6+vboOC6x0avUDj9neFjh5Mom6YrgBYu7Z6Vp4eDODOQwA8\nxJlI9FMm/heL1Z+5T7c6BgHbY5CG1W3ZMrucji5Du/X0EiNr19YG1oKZmepksvjvrovY02MtUb4F\nqN0+1kLI1ydoM0QkZiuGnuD1vu4x6/rRbsSn+QL3SXcQdYONsti6AkCfo661XP8P1eGKKjx09fcn\nOy/jrMs+625oLPS5LrVlvhU0+nCTVHCR7oCC6x18F0Cap5t6L6CQpcZ1CYoYMTM2ZgLNfTFZ2g2g\ny/YNer56MFUbgecAos1nbUIQLgQe2oty9SwmfTywuvX1VQe9o03YDwJPH2+pZJ769U0DuPnItGDz\nrQrgQ98A9E3AnUgQNZjq/vPdVNyZkKE2xJHnwN0K1yUJ47MC63NIn6shoeL7TXUi0/5+v1hKQsj9\nibJ8Y09cHUniuXwPn7redj1Xu+n6ogXPQMEVQTNcN6G4Cl/dvpmDGCgRtD4wYP7v3GlybK1bV11m\n3ImPQPhisdrErwc+N0C9VKq21LiJUl2xpIVXX5+pUy8vgn31Qruw6uk1HZO6ZVBP3JIf7r7azZHm\nSTvtwBKKD0xCnoNYK1yXc5l6brCuNSiq7Kj3obp0KEKpZB9w6jmv3Cz3ceeLe977HgRhDdbb+ESk\n+wCUx7ma9bXWTdcXBZeBgqvFpHVlhgZSCK2hIWO96esT+eQnk+ezKZWMBW1y0saMrFtXLZJCQbsj\nI6ZOrNEYFbirn9K1uNJpKfr6jJty+XI72I6NmeVATp4UOXbMtG3//nDsR6Fg+mJiotq6lLS/tZUQ\nM0T15/VaPH2uHg5G3UE9N9io88J3DoWEina7a2CdHhmx2+MajKs/SVujRGZo/5A1vNWWH16jpFEo\nuBLSyotNz/rTcUAiZkC6914zQC5ebAZOTO0GGFSR7wZocVIoWCuSb2o5ysGgXizawPCxMeOKgOsx\nLqBdCy6Add70sjuLFhnRtXChzZQtIvLud4tMT9vM2a7lyr3pYMDWszld9Oe+bdy1HkVqJw8kwSe4\nOoFOa28epBHGeQd6i4TPY5FaoeI7R91rBvtl8Vvr89w3fvge4Hz7iPjze+XtjoPFXdeXtzV5rtFN\nLtOkUHAlpFUniDbzu1YXfIYTeOdO835iwogyzGrCE6svFgl1FArGQqXjIXzCyb1Y8HSsc/DA1YjY\nkJA1Rwe4wzqHuCm4DmGVQmzZ2JhJHTE0ZNrrm7qONkLAIegd5WD7OJGFsuKoZzDutMGoHdvUbLIU\nXD63WJbnEPA9FGgXv68tWbi2oiy8WbjR8nbHuevTUnClp5tcpkmh4GpT9NOgfu+Cp79CwcRsiRgh\ns3FjbVZp4D69bdtmysBSP4irOnbM1hGaBYUYEFjayuXa7PshYaMFnohZsmd62vwdOWItZ+PjIpdd\nJvLTn1Zbusrl6mSwKN9doLpctrOudNt1W3wBv1pExomitANyXoMR3ZPtQdI0ImnRv69rPXLjJn0z\ndtG20PmbJMt7Glz3YNqA/JB1jpBOhIKriaS5GUIsabeYL5EmguYLBbt4LYTG8LCxdg0NVYuIiYlq\nwdXba1NCrFxpB+/RUVumSO20bZSDdkJkuYN2lPUInxeLph179lS7QPWMvu3bzfdYoNoXyK7LRFv0\n9vrGs3u3fR23SLXvhqZvZtpqkLXgydOVRaJJY4nU27ppRELuv7RWzjQTN0KWq6j8bo3ie7hK+mDh\n7pu0b7I637dvr07+PDBgHjyRLzCqDSQa9peBgquJJB0sEaslYi58pIPAjEAdByESvayQnt2ony7d\nmDDk0jrnHPP92JiJofKJPIB0D255WPgW7RodtQtO67YePSryvveZ11NTZv/h4doYNF0fliHRxxGF\ndkmKVIvBH/5Q5MYbzWstspIGM2fliok7J7pZRLX62NMIhiiLU6Nl+4iyHrl9BguunmSCa8GN7UQZ\n9ZDETR+qI2S9E8kmhUocmzZVLz2kx5a4NC4kmm4dv1wouFoELmY9OOn/CF5F1nakatC4wguiZXTU\nBsBjIN2503ze02PK3rTJvH7ve42gO37cbLd6tfnf32+Tmbpt9R0HBnRY4+DGEzHl9PRUuxtFql2O\nqA/tPnrUtAnCTSd41Gu+ubmEXGuXfu0KKn1T1Ok5XFeuiP+G5gbn6/3TuByTivDQdlhZQKQz4sHS\n0GrBlYYkAijrWC1fqhgfOhEx1hd168jbrd1Ov2Oah992ajfpbCi4ciY0WOos49jOl0sGn0W5AVwx\n4Xs61J8VCjYgvVQyQm3RIiO8NmywlitfXa5lDDOhBgbMZ3pZm6jlPVx0ItJy2ZQHd+XXvmZciYjr\nKpdNGwcG7M3D7Tu012V6ujrPF15PT1fvp59otYvSLV/3SVJ3SRLc8ybKZelm6ueTeD7E/X76t/HN\nrBOpT4wksfbkFTOWBPdcRThA3EOIb1/f9nm0Pe56dBetp+giWUDBVQdpbp6hwTLJTbFUMq44kehl\nO0JCQ4smdxuIPW1dQrB8oWAFkNt+LT4groC74PTkZG0c2sKFfuvUwoV2cWwR45ZEXq+VK81nn/uc\nrXtkpHqZoRCu9QdWNwhCn4VLk+S3TuLaTEqUsOoWIVVPbFMzSFN3XGqURsoO4TtXXUvtli3WyqyX\n6opzSUYROlfxF2fdjROTrfjN3ZxlFFwkCyi46qBeMzPcXnoGXbFoBj6470Sqb7jacuJaMeKEV7Fo\nhYQeeE+cMAMvstGfc4757vhxO7tpZqY6Zgz76raNj1e7J9AmBODjPSxSmMkoYuq4917zH67SFSvs\nQIeAfbgpRcwsSvTjjh1WPLnJT5HksVSyArJUsgIR+bi0tUvHtSCNBI45qehyaTQoOsplie/dsqOW\nLOoU0sTvtCu6/VkKyND27rWq6/ZZzn000s++c1V/1g6CJenv0K6Cn3Q+FFxNBG4ykVoR1WhQpm9Q\n0y49PfD6UjYMD4u88ordF8Hr2nKzbVv1QITM726wq441wyA1MGCyw7vHjcWvRYz4277dpqMQMSJw\n+XLz3Q03WNcfxJNvZqGO0dJt8H2v+wftdictRFkKoz5vVDjEuSw7XZTMZVyrcFa/VZQwCM1kbga+\ncxXXV1Lrb95tTvo7zAXBT9oTCq6EZPHUk8QFFqoLOadCwdF6cPMF7sI16YqM8XGzzfz5tfFZsMTB\n6qMtQtjfFS/bt9vXOmv1//xPbWwY2ov0D3v2GFGFemGJmpkxNxMdFO/GtmGAR1/hPdoPt6XuE2Tw\nd/sqJNDyIu7cytJl2Wl0q0UhjVVVW2/xwBNaWSJkAc2qn/UYhL961o0UCfdBu1jMCEkLBVcMoZia\nem7COrDVfVINPRGHgm/dNoRuyK6g0JauUslatVasqK23VKpO0TA5aQTR/v3GsnXkiJ1qfv75JsVC\nuWyC8IeHzXYIzh8bMzMih4dFTp8Wee01c1OYmhL50Y/M6yNHbLuXL7eWOJ2AVFvS9DEjyePMjGkn\n4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G7yeiZdHL5t9HqAvr4plczSOIi9OnLECBG9pA1AHwwPVweta0FVLFZbzbRQ03nBymW7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\nj3WXunXo5K6EEEJIO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ZeQpUuXytKlS+Wqq64SEZFbb71Vtm7dKr29vey/BPzoRz+SP/zD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\nSM78f4wQHIScyHXMAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,10)\n", "plot(data[:,0],data[:,1],'b+')\n", "plot(protos[:,0],protos[:,1],'ro',markersize=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Obviously, those centers are wildly wrong, but let's keep going.\n", "\n", "Now, we compute the assignment of the data points to the prototypes\n", "(array `closest`).\n", "This is also wildly wrong, but we're going to be using it anyay." ] }, { "cell_type": "code", "execution_count": 104, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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nyw8bdd1KIOVdkBWB29vXfC8XEBQYsoqx1XLx7rtv+GGl2rtltgdFaOhNrhuN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l8LFUGLE8oPGrEbZypy1v5fzBJmknDJlWsEnobjrWMoOpXESgDoFpYTVMQiSToxTq9Er3Oj0qum\niVwmg+zcHF7/yEe6dF65TAZ5wxCRJpVYXtZPkaO8irzw8aoWPjzyVt3fRy6bDfVA3NrdVbrMxxGc\nqCgjeYJRVM0KxldcFyYjs3Kq9FpgBCu3JEpiwDos4v4CH+Uv32HSIfPz8/jk5csjtX4Y9bn1O1c/\novR+9jHoNeY6p6jxsgZJpWWSbSFIB3Vl9UooqkRzbVW3RGSLIk3UZJpryFR2E/1c863qliBFcvUl\njzYlnVe+XpVGBXkzj/Xl9djr3csPLQnGSYo04Tq5mEnCxRFHiug97qwu/1RplgiD3JzjbCGibvi1\nVkt5DiprAyJMlutip9XC5s2bItrEz4kfVwkiYjaLdiWxalAR0/rBQWhvDc8T0TU5qsdTm80HD/Dm\n3buwXFf0cHQ7HaQeeyykQeOpW0Fm6XpIJE1FDuXnRxHViktTjPIv6ZOcDkl6k+qXEPV78xvmGqtI\nQNR4lZapUC50NXnm35+aUxP+VvRe3syjXC8D8J3g82Ye1yrXRHVidbcqBPO8apD7ZPG14lJ6FInL\nm3ksnl1MfM3lKBadM3+fE7ao1CIdK9tJDEpwNCnS6BczT7iGJUVEQqKiXrSGyqNLHkPpRKpsVK2n\nIgDlZjOyD6F8jpzUvLK351fmxUTeLNcNVQwCiDUAVa1lua6INDU8Dyvz87BcV6n3irqOL7z//fjq\nBz4AADCrVVEEYHsebt2/HxL18+gbv+50LrLOi45XpUwpRSvvJ4pkjgInWZh73OfWLyGahGhDkmum\nIg4y0Tn7+Nkumwia1/XccJQs+LlV3YLruaHX5ebafL04nZpsUpqErNF4+Xz5HqOOl/c2bBR5kO9u\nHAlVfVb9zK0xfdCEK6ZCkW628o02ymogLn0oe3TRXLIYX9WnkFsxWCwFqLrh93qNk45bgflpvlaD\nmU6LtKmcLqQ98DZCvKeg6rrEYe3cOVT391FrtXA+lUKDRdQ2Fha6PLpESpJFxSgdWshm/YhckPIs\n1OvKAgB+zTip4+lF+pyr+/vIzs2JtDI15L7CUqHjgkpzMo5I1HH9Eh/luU36TWrYPfRDNPKm77sF\nhK9LpVHB8vllLJ9fFv0QbdfGN3/0Tfz9O3+PF197EXv39nDjnRu49+AeqrtVeB1PpBlJ/0WI00qp\nQIQN8D+j5fPLKNVKaNxthFKKpVoJpmEqtVxJr2NcmnAUUeRBvrtJCddJjj5rHGLmCRdBVW0YVZlY\nchxx8+fCczkylXRdsb7kbwX4hI5bMZDGqMba93BXdjIwpTllIsTfqx8cYK/dFgL/qMbPzQcPwvME\n58kF7VGEi17jfmQ85Wl7np8qDAiT6rrIBLO6v4+1c+fEPJwgRhU+qMi0rNfiKeSkKVoVhklD8vRJ\n0r+6ZzUdMuxNKi4qMQoiNyrCxfclg1fz8co/I23A9VysLq5iZ28Hy+eXxRgyLyWSQwRofXkda0tr\noqqxaBVFdMx27VClI2mlaJ0oosSjY/Q6nYdMekIVmj0+yyhSlRSTTtY1TiY04UoIlTAdOIx6qHRe\ncf5ddEzJcVBaWQmRNZWPFWGbVeDRmHyt1kVY5H2r9rTXbmM5ICtyn0Q5hcjn4+eoWk8mN/z49KlT\noRTd8xcuYPfdd0PkkGvHaH2+f+/Ro9D15H0aifz2uu5x5yDvPenxoXFubahf3ESkes0xCSmvQXHc\n+45LYU1KtEGuSpT3zPcqkxbCxsqGSOmVNkpiHjq+XC8L+wkSrRMZo8pG0zCFPowIW9EqYnNtU6zD\nG22rzkOlOQMg9GG2ayc2Vx3muzNoFDmp2D6KzBE5lV+X93Lc/y80xoeZJlz93JhVES+KSqnSjqp5\nVOkoIlNxN3OKvGzt7kaSMpmw0DlZjKjI50Fr8wiOKkLFU6sUZSOhO9lZkN1DOZPpahPESdhLTz11\nKIgP1r15/76SrK4bhoju8UiZrCvj6UZubmqkUqLykxM5Og9VWpF/lpTilM8hCXqlEvqpxDqpGOW5\nndTrFCUgp/f4T1XlH/+u8QpF/pNa/RhpQwjkd/Z2sLGyIchWVBqTg4hSFOHYWNkQBC3qjwnusTUu\nDPpdSUq4kpK5fjRoGicDM024khAiOk51w+VRprjxMjgpqjCyEKXLIu8s8sYiE1Aas7Gw0EWouFC9\nwsiGnELjBKfcbIrjL7/1FuoHBzACjVXJcXA+lfIJkGmGqgo5wckbhtgvJzfcW8xyfUd8qlhseB7y\ntRrcTgfZuTmsnTuHSkC4uKN96LrHEGRVCpDSsG6n00XkouaQDWPjCJdMdNeDz1WeN45wJU1zHEc6\nZNIjaePa23Gfc1xTaopQ0R7L9XLXTZzvP8pEdW1pLSRs5z5Zqoq/KNIRReiSkLWk7yXBIJWlx41J\n//+lMRrMNOHqByodlPw4DsMcx8mN7XkhYTmNIb+svGGI6BORs/WIiBvXYAEQhqTrhoGXgmbEPGXJ\nzUeBw5Qbb93Do2AAlOSm5DjwHj3Cyvw8rt+5g2WmpeL7I+d51TXp1ReRnyNdF7fTCaV/4/paUqSL\nO9r3WgduDZZtYd11Udn5ir82ACQkQkn/Mj6OlNes3hCOg8ByQr29s600NKXjOIy0+neMiiCR8D1v\n5gWRK9VKqDm+FpSiZar0XhT55xqyOJNU1Xjq8ciP6VfPyOccFeEa9o+bJNeA1pnF/1+zBk24AvST\nLlId22u8KkUJdIv1ZcgEYD0gXVxUDgTu8EE6z/Y8lFZWBDkDok1X+c+S44Rek1OMvPUOHV8KnN4p\n6racTot2OnwOntYjWwaKYBERkuF2OiEzWfop90U0UikRiepqQE2pX0X7JRV41JJIJFUr8j6M/KcY\nS1ECOmfm9k03r+2d7ZAQmXrb6V+2s4VeNggqQk0idk4AbNcW3yM5pch/Rq1RzIdJFaUSVxdXE30v\n4/Yqr6/SJfLnqtQlne9x/f8Y9o+bpIRLYzagCVcAFWFKqvGKGp8ESdrlkHh8OahYfP7CBaUmi4gF\nEQ6ZINAx8nNapxFomEh4TiDSpoo2lVZWQlYTtF+al0iafD4UdTPT6ZDonfZE44jgyRYRV1mlJE8d\nyn5knLDxz1Dli0bgKVdujqryIosab/HnipsKpW4i95DwF/I4f3HrSq7JQi+xNycsUURF9ZlyI9PV\nxVUxR7+fcVT6k+bqx3uLH9MLspZtWr6rs/T/y3UtGEb+uLdx7NCEKwZJNV7DIKqhdZSmSN5LoV4X\n+qudVgu5Gzew02rhlb093Lp/H89fuBCas5cWiYTwJccRrY2AcMWeyhKDWyzIRqkyWeLaMjMwMKX2\nPlwAT8SM7CO4nQOfVwWZ4JnptFIPFjeWImn8tSTEOm8YwJApkEkgXMeRujzJGOQGm7R6TWVCGjWf\n/JlyXSFV0Q3yvZJd7vs1lVWlGikaHLV/OpZr2ZKsPQhG/X9tlv5/acLlQxOuY0a/qcyoVFgukxEa\nLCOVgplO4zcXF3uSRB4dW06nsdNqCcuL5y9cCFU+UopO7CVIvxVtG0YqJXo0yn5VqnQqzcuJI71v\nptOotVp4+swZEd2ruC4W5+bgPXqEu50Onr9wAfWDgxApkuffWFhArdVCnvl1Jb3e3OOLKkQBhNOV\n0pqhc+5xA+33L32N6ccgN9ik4nJOmlRExUgbIQsHPq5UK4Uc6POl7orGJFAdG0cyo8bLxq3ry+vi\n/eP8f6L/j2oMC024EmLQlOEowKv+iGDw6M1V04SZTmNxbg5F00ShXg+lKinlRy7xBE5OSLPESVC+\nVutKWRJRKjmOMFytuC5WA/0Y0FvQzgkXodZqoVCvh9runE+l8PSZM0ifOoXldBqNIGX5xKlTcNpt\nNIJolxy5kr28KH3JqzllyF5l8jFyr0eAFQ/YFpDwr7de2ppJxbTtdxzohxiPW+gNRBMcoJuoqCJe\nsjCdxo3is+bfc1n8ToQqrk0R34PK32vc6Thy2ufrjTuafNLguhZc1wIA2DbzIzPyMxvt0oQrIY6L\ncFmuK3RMctQFQMh64JW9PRRtG7VWC9uOI3ozUtRIpUWiNfKGgVwmExKnq4iTTDpKKyuhxtaW64pU\nIzWSjtKQcYE7RedIN0WpQ4pKkbas4rrIzs1hY2EBuUxG2Q6J9lio12EHc2wHBQG8V2UvkkVz9fyM\nBvhlPG36jUnc01FjlIRrFFVqSaJHXNMlrxVF/keR2uq3IGCQ+ceZjivXy5pwDQmZWJlm8dj2MinQ\nhGtCwaNJ/LkMMuvMGwZu3b8PwCcyV7JZIWiXo0mklyK8fPs2irYtWv2Y1SrcTgd3A6JH5Ef2DAMg\n7Cgo0mZ7Xpf7fhSx4QQP8Fv2OO02nHYbe+02KgBWMxlU9/fx4bNn8f1790KRLtvzQmawNL/coNr2\nPKwG6U6+d74XVZNqTiKv1coANsR4+bMYpBR9HDcMnZ6cDPRySx/0M5LNN3n0SLaMMNKGUsSusmyg\neZO4vPe73yhj1iSIis5paEwjNOE6QvTjVk59DXlaTGWkWchmxbylICJVcV0giPDUgsgRJxG1VitE\nuLJzcyitrCBfq2Flfl54bpWbTZRWVsRxPEoGQMwjrCsCkiV7VsVFj7glRXZuDq9/5COhFCjvbbi1\nu4vX79xBISB0KiE7n5P2UggifXKl4jd/9jPxuFeTaqsW7q9o2RaKNQuAfzPjUYNRE55xprI04tFP\nJDLKkyrqOzFIlLOfDgVRkSsiPaoxw4LvT2UDEfeHhTw26bUZ1fd9q7qFcr0MwCeHua/l4HouVhZW\ncP3W9dg9aMRjVlOIMjThOkIkJVyk1QJ88kR2EFQRyIXsALrE7Ly5NG/EzLVZsiaMvLTOnj4tdFnn\ng5RfVGUf2T3w/RCh4y1yys2maDjNCU/zwQMsPP44AN+SwnJdFOp1FLJZZTqTnOgJcUUEBJGSDM7d\nZlWhf/9P/4TPvO99AMIkK0mT6rgbWr9IUho/q7/gj/vc+yEMcRGnYedWIS56JF8zsmzgBqMUzaJe\nhvLeBoGKcEUhLq3a73UfBTbXNg9bD5XysArW4fo9bFw04qEJlw9NuI4JvKUMf87F8HnTFK7tZGbK\nIdssEGkpN5tCAE8E55W9PZSbTRhBe57NmzdhpFJ4byqF5XQarYcPAQAfmp8H4KfyyMxU3qvqPCgl\nR9E4SuMBvj7LCF6TiQ2dA61H+24+eIDWw4chx3dKbRqplCgM4JE7WS8mP1Y55ctVkuK6St4+lZ2v\noEgpyeBm0G/peq/KxTjEjd+qbiVqijuNOG7C1Q+SEKBRa7U4CYgjBGTZULSKuLp+VSlCH3dae5I+\nx6SfwzR9/zQmH5pwjRlR5qlEHjjh4n0ZAYR0UFFRFxHJYlEsVTUdfy1fqwlBuuW6aHgezgfE679f\nXBSRK9VacmSMKgBzmQxszzts5RPouSji1gvciNT2POQyGZGu/NrcHF6/c0foumzDd6fPZTKiObXK\niFRFEJ12O+TzRY+ddjs0rlizugwgVX3qOPFKmi5JAvkmG5eydD038Y1XY3D0+vz4Z6OqrAMGIyNJ\noj3j0owlgfxdLdVKwvmerz9oWnUce+/1/3FjZSN0nCZdGqOAJlwDoB8tVpSVQJK0leW6qO7vA+hu\ncq36ydek8fJrBCJ7PLpkBm158oYhCJC8f66PInJFkBtO77RaXTq09KlT4ehUQMzSp06J5tgw/EbT\n5Ou1EkTdfv/JJ8U1LNp2qM1QFKivJOATXoq65Q0DNou28QgXRxKiNEphbxyxmhUiNakVnP2sTfqt\nccwdhShnef7zWuWa35PRKsJIGyIy2islGYeo7ypvhD1M1eJxfOayZ5kmXBqjgCZcA6AfwsVhe16X\n11TJcWCkUiJ9BxySHCJEvVrLRBGvkuMIJ3uesjx4+BDXbBuvnDmDW/fv4+zp0wCA1sOHobY6XDPG\nz5v+Vff3RYSJ76nELBjI38vNZEQlI+BHtK6aJoxUSqRKL333u0LMX242fcf6IE0JAPWDA3Edtx1H\nkCfZ/JR6K5KlBl1HIojkx8WjXduOA7g12E7Vt5H47p/75xzc/JOQLhnDiqLjUruECUYAACAASURB\nVJb0vjx3VAPjacK4S/6PAnz/oySQUcebhhlJuJK6sA9znVXfVf7aJBCWpJ/DpBJ+jemHJlxHCEqT\nAejSE3Fx+yBQkUCR0kM4ZamybCjU67j58Y+LsSRe51Gyl2/fDqVHyfmdr02Ei0DkLHfjBp6/cKEr\nwkfNrwHg1v372NrdFXYUgE8Cnw6I4eULF0Tqj8iTqrKQ5ubasygNF78+pVwewIuwbAu2UwXg/+XP\no1f96LCGJQ69UpbTTkpOMvhnM0oCGUcM1pfXUbSKx0IMVN9VbnSadI6j2CMh6nM4CYRfYzKhCVdC\nRGmxoir4VEiSAotaizyneHqM70FVvcjTkJSalElGdX8fRdNE6rHHuvRZFIkjvZnTbnf1SJTJy9bu\nrv84qHTM12oAgJ+2213aMNov2T+8fucOLl+4INalSJTb6WDdMEKieKFtYyRLFvBTKpME9+lTp0LX\nhBz85WuVN3IhQfK4f+H2+ot6lCnLacOsRhT6iapatoX15XXhEl+qlYSOSv4+RUVAR3Wd5WKSOEf5\nXnuIugaTEjHT0OgXmnD1gJxGIwwSjeL+VLJZZ5SXlO15kWvJ5Cdq/8AhoeCRLst1cTMwS7105kzX\nulYuF2oTtNNq4fJbb6F+cADv0SPsBSk52/PwS48/js+8732wPQ+NoGKwfnAgxPkV18V7g+rCB48e\n4Z12G6XAxPTGP/0TSo6DPSZcf/rMmS5fLzmSxs+ZXOvdTgc7rZbQpT195gzMdFqQtUK9rryeXdc5\n4S/0JL/8445J6lXUS1R9UnFc5zaum3rSOfv126LIlkozJRuiDrOvJFBpEAf5o2WchCtp6v0k/9/S\nOHpowtUDg+q1+HgiBtTyBgiTKh4pksFJmsp9Pi7qVnIcWLkcAMCsVkWfRT6GvLayc3PK6Bil+2jf\na+fOYe3cORipFMrNZoiUEUGi1GG52YTTbos5f97p4BGA9KlT+Nh73oPPvO99+No772Cv3cZH3/Me\nNAIPr+zcHH7SbosoGeDbVNRarUi92ubSkoj+bSwswPa8UO9EOj6qz6P8etIKqSQ3hbgKxn5urIO8\npzEYjptwDTIvF8hPS3HBcYGKBXphGs5FY3ow84RLbnOTBF1tXWJIWVJiFQUiAtxVPWnULfXYYyJC\n1PA8QWA+9p734CcPHiBz+jTudjooOQ4angen3cbauXOhCr6o/Vuui5dv3w6RIkr/EckqZLPYXFrC\n1u4uXr59G96jR7jb6eAufNJlex6yc3M+2cvlRLNsIoallRXkbtyAkUohbxi4FkToys0mti5dEtdC\nbuWznE7De/QIly9c6BL+k8eW/Is08vMb8Bdu0pueXM4/6b/gj/tmfpIxjFg7Lk131CJw+TvSzxpR\ne+UVlVrIrjGtmHnCVW42uwhXr8gRJz10fNQNO0pTRZWAqjVoHHAYFSOtE9AthpfTkzT21v37XZop\n2/OE11bJcdB6+FCI41966qnQvDT3F3/0I3z1Ax/oigK99NRT2Fxa6iJFi3NzoSIAt9MR2iyanyoJ\niYwVbRu7774rSBWRJ/LbEi75kl6NE0KqAE2fOoXrd+4I93xuBUEeW7L4mEejot7jr0VpZOhYcvYG\n1I2F6aaSpAXMJOEkE67jrk4bJg3XSzN1lCLwYQhX0r0OmqLs9fme5O+3xvFj5gmXCnGRI7rJk/VB\nP3Ml1WPROBpjex7cTickZAcgHOjj9svb+VD/QSKYtueh3GwqjUNJUJ43DHzjZz/DVz/wAWExAeCw\n16FtC61UyXGQPnVKaLGKti3Se4VsFrVWS5BMav8DQBz/ifPn8Ynz50XvQ5M1qi7U63jz7l1BxmQ9\nGge1/zECM9edoJ9kpM6tB+EC0HUD4WlC+mnZliBZ2zvbuLJ6BaZh+r5HERWGo3T41hgO01ydNs17\nPyokuUaacGmMEzNJuLZ2d1FuNgEgVEm3sbDQM71IRIsTBh6hosiNClH6oShQxSDgC9bJUNTtdIR3\nlWyGqop4EdEhT6vcjRtwOx1BZvK1GtKnToXGyhWV8ry8kTURKgDY+P73sTg3h4bnYWV+HuVmU/SB\npOuTy2RC1hEcZPtAqUVqaUTnoQKlhbnn2LphiCbcAJCH7f+FC3XESYV+NTGqSAgZQMrz9moBM0k4\n7sjPLGKcWq9xIC4VKJuIJkXUXlWCd02UNKYBM0m4NpeWBCnK12pCWB7VzoZAaTaK6mwsLABI3vg4\nTucV9TpFpSiaBfjki0hiRUoZyuPpnLYuXfJflIxKq/v7eP0jH+k6x3/7zjt4p90Wvli//h//IzKn\nT+OpJ57AZ973vhDJ/MG9e2Kdu52OiCzJHmNka2G5LrYdR3horQaO8rwYgJzuqbfiy7dviz6Q54Po\nWyXYa8lxhCs9jefFCaX668ivvaiMUlEKhhMg27VhuzZcz8XO3o7wNzLSBmpOLZRKtF078pc96bO6\n9GJy6nHCoxGzGD057pv3MOsfR4FF1HdE/mOj3zlVUAne+yVcchRb/0GhcRSYScIVBZUWi3tbkfic\n+z0ljVr1Etarjuc6MmpiTYJ2HuHi4vFtyXSUP1aRQe/RI+Wa77TbIqL2b3Z38QdLS11pT3r+zZ/9\nDMBhRWXqscdw6/59bN68KSJpqhQgj5DRunQ9KcJGkbf6wQEaQa9Gt9MRRJR+0rWg63UlSEsare8D\nbg2WnVVGn+THvB1J0SoKfyPTMIXWKs6fi355264d0mcB6htIvy1gNI4Gx3mjHSRaw8ccN0no1ddx\nEiD/8TVrf1BoHA9mnnBRlCoJeNSE0mhk9qlKL8oVfv3YS8i6LHku1bFF28bVgNDIbXGogvAT58+H\nxsneYKooUStoBcSP45g/fTpMngKriNLKiqiSpMpDAidZTrstmlMTzp4+jXKziZ1WC2vnzgHwI4lE\nOmutlm97wTRdgP95Urshy7ZgNW8AntN1Q4qLStFf5ZVGBevL61hfXgegTg+qQL+wk0Svjvvm2C+m\nbb+ThF5EijuzD0O4jhtOy4ksGBmm6leOQhGxiyte0dCYJMw84cplMj3JksoagVfcyZqtQVv0JI2C\nRT1W7Z0q96iCkF4DfAIZ5Q0GQBDKr+7u4osswkUpP7puRHioQpCigUXbxjXbxnI6LewjaC8/uHdP\nCO/Xzp3D9Tt3sJrJwA1SkjuBH5cd+H1RZNFIpQ51YCzKR2lh8ZwJ2Ik48bYnUe16ctlcSHOSN33n\nbiJiUalEelyqlUSEK4k+a9puDNO230lCUsI1bZD3vba0poweD4MkUahRraOhMS7MPOHq5WUlg8gJ\nr9iLQr/tgKIIV5w2C+hOpVEfxHyQhuQCd8t1BVER49l7MokCgJ91OqLIQLZl4CCzUdKeyYQ1d+OG\neK/cbIb29creHnKBfYOZTmNjYUFUTxZNU1RZciJJETT5+hmt78Nq3hAarPNPnEelUUE6lYZlWzAN\nE9s722KckTbEL1rShxBp4tquvJnH6uKqkjzRTcc0TBEJe/7p53V6QiMRRA9CRuqB+GjNpNgc8OIS\neS/TkF7k0IRLY5yYecLVL4hoRZmfRqUBgcEjX7Jwn5Md2RZBtngwUincvH8/1FtQrmxU7Zfr0yoS\nseLHWq4LyzhsiC1H+2zPE+nNncAXi4T4O62WSF06LJ3Izy8qmsdTkmT5YLku4NbgNm+gulvFzt4O\nls8vo3G3gdXFVawtrYmbEREjQC3stWwLhVzBX5cdH+XLJd8sLdtK7GatcXLRixTJFat5M4/15fVE\nabF+bQ7GSb6i9jKOHqAnIVKsMZuYacKl6mHYC3EGp1GRq157GEUULOo4t9NB6+FDLDz+uN/TUDou\n6X5bDx+KVCEX5lf394XlBN8/pQ55w+lL3/0uOr/4BQrZLK7ZtjAkBYB7Dx8qe03ST06qqvv7qLgu\nCvU6Gp6HK9msiJjlV/xf/EWriLWlNX8vrh0iWDJs10ahXAhpQaL0NCRyl/+qJ2H98vllkU5cXVwN\npTE1Tg4GtQpR+bHJ79N3ZtQYJeGKI5Ic4zgPTbg0phWacPVJuKLG9kKcNitpFIza2pCYnF4z02nk\nMpmQbsoK5qVIFRe1J4m0USSv5DhYnJvDrfv38Ynz52Gm07gSkCgS6ov9S5YT4pyCx7fu3xeWDoBP\n4px2G28F50KRtN/54Q+FuJ/r5LjIHvBTj2QfAQDb9ddDbvxmOh0pQjbSRsikdHVxFQDEz0qjIm4q\nW9UtoeGiykMyLJW1KkTcqLpxY2VDaZ6qMd0Yd7RomDFRZGiU6T1d2dcb06rJ0xgfZppwDQPuGQX0\njk7FkbMo8sbTh7QOGaCSPQIXixPsoAk0b5FjuS7Sp04hfepUovPjRQLUlgeAqDYkonXNtoHAmiF9\n6pQQz/MoGLUxevrMGdy6fx95w0D94ABfvHhREKmN739fpCOjCCHtqeQ4WE6nUXFdLAf+ZBXXxeKd\n/wdWzXeo3/7un+PK6hVYthXSaBFkM0bLtlDaKInogpzmMQ1TzBEXhSjkCiLCljfz+kakIZAkRZjk\nuF5zyz5vhKNqI6VJhg9NuDRkzBzh6jeFF4dRabSi0pFyk2rLdQGpzZB8PDmy77RawljUTKeFwLzf\nKB5F0CquCzudRqFeRy6TCUXNuG6M21PI18NyXfzm4qKo8iSCRWQt6rrwvQBAw/P8dGQ6LUxsfY3a\nfwlrYwsAYDtVlDZKsb/0tqpbqDm1UEUhNytVte7pJWyWrSc0Tg6GNchMSrhGCTmVPo4/ADSp0NBI\nhpkjXMOQpDiyNqq9xa1dtG24gdh8NZPBTquFy2+9hbVz50RLIUoj8iq/fiBH7iquCxgG3ptKCWsG\niijZ7Pm244hIFxfcc9LETWKpYTb922u3RRRNbk4N+L0Xq/v7wpMrl8kIkXzx5r/zo3k7X0EBLkzD\nDFUbqm4InGyZholKw1e38QiATJiIhHFSFZWy1Dehk4dpTKMdxfdQf9cPoV3rNeIwc4RLRj9arFFF\ntGhdFXmj9Jv8Oo90lRwnZIkgEytObIxUSvR95Nou+Vw4yeGVj0SebM/DzzsdYTxKUTPV9dt2HOH0\nXt3fD5Ey4QDPzrPiuiEnfdXn4XY68B498s8/sLpoeB5qaME0C9hIpWDCFQRqZ28HRasofgHKv+zK\n9XKo+lBlUqpKG/JUTS+jylH/gtUpCo1+IacaNcaLaSTlGkeHmSZcchTlqOfihI17YclCfiJnXC+l\n8sBStbbJG0YiY9aovRMJKjebQJBapCiaPIbPy9OLRAhVaUZ5X9wLTK56DM1L89gWiuaL/vibptBa\ncQ2WTLpKtRJqTk1EtSzbwu7+7sRHqjThmhxM4+cwjXvW0DhJmDjCNSoClATc72kUVYf9zNFLKM/X\nkUkNRY2q+/u4fueOEMdT65vnL1wImZsSQePVjXxuel+2djBSKVT39wFApDGNoEm0vC/uo0XkT4jq\nAZSbTWFsqjp3bgNBe7KzWVT391HbfRN78x8CAJjVKlqNV7GV+R9gO1WYOAzjU/9CMScTuQN+GrFc\nLwMA7r57F8vnlwEAGysbyGVzXb5IlBKo7lbx0ideOryetoWaU8P2zjYs2xINr4ns6RvbyYf+jDV6\nQX9HNGTMJOFSpfPkVFovqATugyLOMkKuVCzaNq7fuYO1c+ewdu4csnNzIr1IUZ98rSb2xMkR13bR\n+9xZ3kynRcNq2pPcKDpKeM+bYJOo3kilsB4cu9NqiTZKvC1S1PlT25/SygqKd/4PwPyMfw1yOeRq\nvw/35nnUbn4L229/W4who1JuUMp1WLxtT750SIzkVj5ySoCOJcsHANjZ2xEGlaZhorRRUnyCw0Nr\nQjQ0phP6/6eGjIkjXEcBVdSo3wo+Ahd+c0d2ErGrjgW6dVtRYnxOmjghVPldEVSCdf46n5+/T0SI\nVwbKx/M5+PmQEanteULYv86iVpZhhHofyvPK15+ag6vAbR42Lv2LcBUW613IfwLdKbm8mUfNqSnX\nUEGu+CLdV5KG1oNCa0LU0OlVDQ2NacNEEK5RWjXwOXuNjUqlJV03RIYCwhBHhJKK7un1rd3drvGq\nOQGEmklTQ2rLdbG1uxsS4cu9FjlszxPVfyXHEfYSlIrM3bghUpIUweIVidS3kSJptufBabcFGaXI\nGxFTIlW0D77Xyvf/HYq2//Ws7HwFH7PfxM2f/RCX3ngCt35+Cxv/fgN3372Lp9/7tH8dAmJCEShx\nfSJE7RsrG6EUovw+pR/L9TJ29nZgbplo3G2gulvF2tJayN9I3/iPHppwaWhoTBsmgnCNsvqPkIRw\nRUWNkqLkOCGiuK6I1AwCIoIlx0FDancjXyt6zD2trOC1CrsGecMQTvB8j7QWWT0AfhrRabexsbDQ\n1USaftL1pefU3JqqEZeDKkJq3/P8hQt46amnQmMK9bo4z23H8TViqZRP4DotmNnLMLNrfmrx8suH\n58zSgbxPnGVbXeaOwGG1IaXkbNcW6UcaK0fCNtc2Q+lHq+D7b8meXHydcUMTDI1xQxNZDY3xYSII\n13FiGHLEzT+BQ0sHUVGI7ihOr3U5qbJcF4VstosIxu1ZruLjY+N0ZhSlov3XDw5w/c4dQSKpSlD2\nyiLkMhmxFlU20npE1GgMzUHXr1CvC5NWoS+rpWF6dRTNF1G0gxQpE8dfq1zD+vK6f86BP5YwJlX0\nq+MmpoVyQRx7rXJNtPORfbXkmw9ZQRyXpmrWb4RazzZ+aMKloTE+TBzhGoYADZOa7Ke6ULWG7Xmh\nykAgXhsWtR55ZpEOiuwXNhYWkAsqBHtBdczW7m6o1yI/lsjR4tyc0F7ttdtYDcTvqgIBK9Bs8RY+\nnFCVHCcUNeNEjfuC2Z4nGk/v7L4Jq+bvrfHD/xWWt46iVYSRDqJ0wY3VSBtwPbfrRssF8qqbM73G\nrSOo52Eum+syOqWbz8bKxuH1mjBN1SzdICft2mtoaGj0gxNFuIZJTfZTnahao58qRTk6xJ/zVjVG\nKnVYedhHujKURgzgdjohQqiKmlX394W5aMV1D9N7bJ+hHo2GIaoa+XqFbBYlx0HRNFEKCJmZTuOa\nbQvtF69gvNvpIJfJwDDzeO9//p+x+t6LcC/+16KPoeu5ofTd5tpmyJSUiBRZNHDhPE89UoSKR0dk\nzRd/n+ak1KJ87CRAlQ6dFQKmMRroyKGGxtFg4gjXpGAYXy7SRMVFk6IIl2reYXVhtB96HLXuS089\nJewfKKpGzaU3b95ELmgntLGwIJzhKQLG98ifE/Ha2t0VBIssKOoHB0IkT2L7//yz/xf/53/3bwGo\nKxCjtFuAb3LK04xRDX3pOR8H+ITKSBtijkqjglLNb2htGmaXx1ecy/xxYdL2My7MwjkeFXTkUEPj\naHBiCdcohOuDpiEHjbTJ6crnL1xAoV5HLagMlK0keqUYSdRPESmqXNxYWBCvR/lhmem0IEN5wxDR\nLhLBA+EWPpT65DYRRdtGrdUS1YfiugTi/UK9LiJewuur5n8lOSGKc4BX/RWu0nDJ4IRtdXE1FE3j\n9g/c00u2hQDU7X/GjbiIRJKxJ4GsnIRzSIKT8nlpaGhMOOEaxgR11Oapce7oScbyn6RdIksFroPi\nJqWUztt2HGwsLGCZ6alUhEkF3meRHlPKUoWutGCwV2pW3QisI8x0GukLF0J7BBDaN3DYy5Hm5NE/\nqmh88qf/F8zq78NIpbDz9reRL+UBAB/+pQ/7InipyhCITneQ3it0TgnI2sbKRqgCkUN+ftyIitbJ\n6VLVNdI38OnCUX9e+ruhoTE+nFjCNeh6vQxI+wWNlV3sedRLrnZUvSZbMfQ6ByIzlusKawmzWkUj\nEKm7nY7ScoJfA7JqoEhXw/OwODcH4JA8qfb42k9/iuUgRVhxXdiBRYTTbsNpt5GdmwPcGipe1k9N\nZn8Xhez/6O8hsGDgNxpehRiX7pCd5cU1URiexo3rZZraj+blKG6YOiWkMSpowqWhMT5MNOE6asSl\nAgdt3cPtEWT00m7RMWTOWnFd5G7cgO15uBuQICtIFZL1BD+HWquF2kc/KqJJBdbQmnzD5PPmj6mV\nDgDka7VEfmWW6+L79+5hZX5etAqquC7Op1KoHxyg4XnYME1Y/18VV1Z+X0k2AeDlN1/uIjUkeo+6\nKUQRrlKtFHsjUb1HpKpUK2F7Z1vouuj4pARn3IQraRpRi6KnB/rz0tA4mZg4wjUO1/nj2EuSsdyp\nXkZIgE6VkMGxnCxR5IynLenxTmC/QKRM9uii8XwvUaA0oUrzpRr70lNPifeIdOW4zYRhAArLCbJg\n8DpeyFsLABp3G13O8DydBqhvUNwVPgpRaceiVRTWEZzQTcqNL2rf8ms6AjY9OKmfl05na8w6Jo5w\nDWPtMI59DGMzkXRsUnG+TJb4e3KjagAoN5sizadaS1UpqRK+A76xadSYkuPgB/fu4ScPHog0ZaFe\nh5FK4b9Ip/HzTgermQwqtoVlr47N7zexc+t/xxXPg5VOA6ziz/VcFK2isHewXbtLxC6uKROsh15n\nRC3OKgJQ3wToNdlWQnXji4uOAdocVUODoAmXxqxj4gjXpGBc0bR+Il+qPdHYqP2pIlz8eFXqUF4j\niijK2jHaJ9lDcEd5SkXyPeU6WRRWCrBqW9hY+nCIwEQJ023XDhmPyu/R2EF/kavSjaVaKUSYrqxe\niUxnTltEKel10jfHyYD+DDQ0Tg4mmnAddQoxDsMassqPuZheRhzh4o2nLRaBUpE32/MiI2tyNGvQ\nlCl5jcktgAAWKaL0Z62K/NqLsFTzBYJ4Lkwv5osoWsXDnoZS+pD6JvI0o1yBGNXuh45XpRtl+wdu\nDdELgxCVoyQ3mnBNF6b9M9B6NA2NQ4yNcL3++uvY3NzEw4cP8Tu/8zv40pe+1Pccx024OPFJalSq\ngnzsMNWXtudFRqlUlY699hU3XkXKuJ0Fte05n0qFGmV/+OxZANJN263Bbd5A0SqKqJHKw4p+OVNq\nUfVLmohUqVYC4BuUytouPp/KTZ7MTHnqEvDJFl+TXh+EqIyTpGloTAMmOdqroXHUGAvhevjwIb74\nxS/iW9/6Fi5evIiPfexj+OxnP4sPfvCD41hubIgiRsMQJrnqkCJU1Pga6I420TggrKvqFYkalrCq\nyKbKzoIqGJXROkaMdt7+NjYu/QusL6+jkCuI90lnRc+L+SK2Lm8p9VmyiB4A1pfXY/9iprUINacG\nAKHoFvVXlNccxoOrl43FpEFHIzQ0NDTGh7EQru9973u4dOkSzOAG/OKLL+Jv/uZvpo5wjQqy8SlF\ng1YDp3gVMUpqSZGk0pEfF4V+yZlMHAFf42W0vg+3eQNA2M7BNExcXb8q0oQhMXrwnN6j12lsaJ/s\n5m+7Nor5IgrlQpcQ3rIt2K4t2vFYtiWaXhPBW19ex/L55VhCMYztQlx15FZ1C67ndo05TnKjoxEa\n44Qm7RqzjrEQrrfffhu/8iu/Ip4vLS3hu9/9buiYYrEoHufzeeTz+XFspW9E6ZriIlBJ9E7c+JS0\nVUkjZbKgXhayx+2BVx8OS7hkLRo/J9qDZdvIf7h4uL+AEPG0npE2ukjK8vllQYRkPZbyvBSpQg4i\nb0Ty+DjLtoTVw+riapfVQ783Bj6OkyzSmNF7fF7Xc7t0YkmhU5Aa0wj9ndWYJliWBcuyRjrnWAjX\nY4891vMYTrgmCZy8xInOh7GrIGF5lMYqiR+WjKjqxV5EKwnpi4qiKT25AjJg2RbK9XIoXbi6uCoI\nyebaZpf7O0W7gOiUHp+fxqs0Wiotl9zken15HRsrG9hc21Q6zfeDqH6L44gSHZV7vYaGhsasQg4E\nXbt2LfrghBgL4bp48SJ+/OMfi+c//vGPsbS0NI6lxgpecdcvekXKiraNbccJGYqqNFMyqKWOPDc3\nN5X3QJWEBDli1mvNQaJjeTMvdFjmlolCrnDopRWQKhlFqxiKcgEQZI3m5NWFqv6BFD1TifM5+aG5\nqAJyVCSmV1ROlXpsHjSHXnfU0IRLQ0NDY7QYC+H66Ec/ih/96EewbRtPPvkkXn31VfzVX/3VOJYa\nKwaJQPFj5AiQ5bpwOx3stFrYWFjAusJcNcm88h54g+oovdh6DKFLmnaMQq1egiXpkbhHVuNuQ0S7\nTMMUuirbtZHL5rqqD7nYvGgVQ9EuIlPbO9u4un4VAHBl9UrIOJVc4UmcL+u7gOGiWPy5ikDR/CrP\nLpVGKoqAymtrQbuGhobG9GIshCuVSuGrX/0qnn/+eTx8+BBf+MIXpkYwLzdv7jcCFQWVDov0V8Ps\ntdxswnJdIVwvBVEu8uoCEFqrUK+LsQC6PLT4HpN4dAl3+Aind0I2k8Xa0lqoCrBoFeF6bldqUZVG\n5BEvIlM8DakS08u2EyrrCCI7SUiMPLaXyHyUREgL2jU0NDSmG2Pz4fr0pz+NT3/60yOfdxhLhiTo\n5U016Jz9vN7PvFuXLvkCdkaKVHvmujROqqjPIRml8hRjkusQZZvACYJlW1hbWgtFdFTjVGJ5Hv0S\ne1FUOnJEeWepxPFxBEre1yhhpI2+yJ6GhoaGxnRjop3mVRg34eoH/VQZRvUopPcHhWpu/h5/nyJh\n3MfL9jy/kXQwlo7bWFjAZqC7U2nZ5F6FBCPdfS5c1G7ZFnb3d1EoF4SPFq84VKXh6BhVJExFUOS5\novYqj1WZllIKM2/mY4lRvySJtGOEfiJWmpBpaGhoTB+mjnAdJXr5WPVD/npFjIYhktx0VLaNiPPw\nAnwRfslxxBhKP5IFhgqqij+gm4TIXlM05tbPb2F9eR2mYcI0TJQ2Sv7aVlGZ9qM1exEkueUPAOG9\n1WuvciqTr8cF91HE6ChJkCZcGhoaGtOHqSBcw/T8GwbDtPPpl6CNInJH0Sx5Xu6XperfWHKcrorG\n1UxGzCkXD8h6KdkKgcC1XeTkLhO1mlMTPl2clEWl8TjBitoT0O1OH/eeSoxe3a12pfyiyOCw0ARK\nQ0ND4+RjKgjXOHRVgyKxmDyGcA1CrJL6afVqRaSqvCQ7iY2FBbidjtB1IjRNfAAAFFxJREFUGalU\nSJCvOk/btbta56hgu3akyJ37dgGHvRGpJRDvb0j6LNu1UWlUBOEz0kZXmk6cPyNJcZWD3LT0+q3r\nWFtaA+BXQfbTwLpfaMKloaGhcfIxFYTruJCEXA1C/vqtBKRjB9GLXbNtWMx+opDN9lxbrJnLAfDd\n7KPOU2U6qooYOS3ncA3JuJTGuJ6Lnb0dkfaTLR14hGx7Zxvry+uC8PWKjNH4OFF8lGmp3G5IQ0ND\nQ0OjX0wd4TpKwXy/kTUVieGu8ipSNUzkTl7P9jwRrZLnkp+rfMJoTtvzQuJ6LprnxAbwiQ+PXqlS\ne6r0n/yczEyJwKlSlFGEiRMx8vBSET/btVFzal2RsF6thDTR0tDQ0NAYFjNBuMZV2ahqddOLQPVD\nqnpFwFSRMC6e55WJUXvka3GtlzyXOC4gNDIJUREk27VD7vFiD5JlhBy1Mg1TWZXI92DZFtKpNK7f\nui7mt11bONCriF+hXBACehWi1tOES0NDQ0NjWEwd4RoEoxKkJ3ltHPMPmr6kBtkqoby8jiy251ov\nJUFLYLVAKUFVax3V8arn/HX+mEifmNsqChd7Lm7n43gErZdz+3GRLN2YWkNDQ+NkYiYI1yjQb3Vh\nvwRt0OpFIlS252HbOdRJkcGpikzJY4HebvJx5IS34pHHUK/D9eX1LrG8CknJhoqkqawbLNtCdbeK\nfCmPSqMiBPmmYYY0YrIo/riIjyZcGhoaGicTJ5ZwHZWVxKgIVy/EjaXolZlOH/ppJTBWTaohi7Nc\nAKLtEuRm0XFEohfR6GUTETeWqg3JiiIqihVFuAYhQZo4aWhoaGhwnFjCNUlWEv0iiiwCh+k/LnLn\nbXuIaKkqD8emZZOqDgG1M3wcVFEy+f0khCvO9oHm6Lfn4bgJl25MraGhoXHycWIJ1zgx7ujZoK70\nZPlApEwWvccRrsSO+T2qBJOOGRfi1iLzVQ459cmNWQncn2sc6BVB1NDQ0NCYfswE4RrWIV4131FG\nz+Q9xUWy4gxXVT0R+dgkUFULAn5khqoESbyuGhPaVwJt2CgjP7KvlzyX7dqizVChXBDH8FZBcWvr\nSJWGhoaGRhQ04ZIwSc2xgXAFIf3cdhxcDUjelWy2ywqiaNvCR8v2PNRaLTGOqg9HEY2Li8xEtftJ\nOj7J+/2m+nodyyNZUSaoveYfNlKliZnG/9/e/cc2Vf1/HH9t2cgSf01UNtmAGjbcCrihCGpimEIx\nIdmCQAgsQQT0DwlG1JAY//mOP8ZAYgQT+cdIRiRxJJowNLNhkJSQKExF/MEwA13NNhzJBywGcU7w\nfv+QXtquv3tvf6zPR9K43ra3ZyeWvnbOue8DYHzKi8Blp3hCS6obU4fbtidwcfyuwUFzs+ljN59b\nd/vtZiHUfcPDWnrvvZp2syiqHYHSymm3SEEq1jqxVAVWzc9U8CFwAcD4ROBSamuy7Apcsbbe8T8W\nuF7L4/NJDsetMOavw3XzNb+OjJjntSp4xVrMHq9YQSrcwnwrhBZeDZw6DNe2eBGcAACBCFzKzisa\n41k47z8eOuXof33geVocjv/Wfln8uwXuQxjU/jgCR7RNpUMFrumycp1UPNOABC4AQKoIXDZJ9UrG\nWFcUtg8Pm4vn/ef3+Hxaeu+95nMCny8FV4+P63eIozaWx+tRi6clqfATbgNrKThIlZaUmtvxhL5H\n4B6OAABkMwJXCKvWNyUzahapvlbgMX/Q8u+P6Lt+XWUTJpjHGkpL1eL1Br1/6H/jEVrMNPDnXSd2\nmSHo2K/H1OBoCCoomox4F5wHLWT33KoOb0WVeIIbAMAuBK4QmbxCMVbV+sAQ5S8L0eJwmAErsNJ8\nOIkGrtD7/kDiG/GNuYLPv21PPOe1akowcBqTwAUAyGYErjQIu/lzmHAVrb5WrH0YI+2XmAh/EAq3\nKXWsqxAT2QMx2TVTDY4G7TqxS6eHT8vr85rt83g9GvxjkOlFAEDWInClQaTAFfpzpPpasc4ZqeBp\n0PvFMerTfrrdHDU69usx1ZXVmRs97/tunxm6AoNYacnN0TcLg060wOXxeoKKk/rXcW09tlUtnpYx\n7SOEAQCyAYHrpkwUPPWXc4hUXyva68xyEIEjYjevWAw3IhZP4ApXrNR/P/CxFk+LJdvPpBqEHKUO\ns10er0ee5z2Wtg8AAKsQuG5KR+AKvXJxQZgF7n5RR6sCQlWq5Swirany+rx6vv75hM+XiFQ3d/7f\ntf/p6uhVtXhadOzXY+YIl1VFWO2o+wUAyE8ErjQKvNpwQWmpeVVhYBHT0OemIp4F6pHWVIWGjUQL\ngUYLK8lsyRNr3ZfX5w1quxUIXAAAq4yrwJXoKFWqtbKSYRYivTmyFe+oVKy2hr26MYW9/cJVeo/0\nWNj2WhC4Egk82bAtDwAAkeR14MpkhflEryyM1dZIv3cioSXbgkqkLX7CsartVleyBwBAGmeBK5ek\na4G+P7TEExai7WcYz4bS0cKK//FwjyU6vZjI8USlMioIAEAkOR+4rJoWzETB02TfM5nXJRpIEglc\n/vPHCivxBBlGmAAA41HOBy6rpgUzWWE+UbHammxoSXaRuJWLy7NphImABwCwSs4HLoyVbGhpP90e\nFNS8Pq+8Pq9Z+NQvdEPpBdMWmFv7BF79GK19uSBX2gkAyH7jKnBl6yhV6GL+TBRZjUdo4dPAn0Mf\n84+iLZi2wNzAOnR6MZJcXcQPAECyCFxpkMnAFSu0RCt8Guu8DY4Gc2TLjqk/AhcAYLwYV4ELY8UK\nLdEKn8ZznsCRrVxEcVMAQDoQuGwSevWkd2RE3pEROUpKtG942HyenUVWU5Hu+leZQuACAKQDgcsm\n0a6edJSUpLXIarySDR4EFgAAoiNwwZTtwcmq0ShqfQEA0o3AlQahU4bZOIWYC1INXIFV97Ol1hcw\nHjA1D8RWmOkG5AN/wPKv6SJwZUYuL+4HshmfLSA2RrjSKNlyEPn816Pd03/52q8AgPQicOWAfA5c\nqU7/xQps+dqvQKpYCwkkhsBlM6s210ZyWK8F2IPPFpAYApfNkt1cm78ex8rX3xsAkPsIXFmKvx7H\nSjVwEdgAe/DZAmLjKsU0smIK0eqrgWKdbzxdfcSXAmAPPltAbASuNEo2cAX+Y0bgAgAg9xC4cgB/\nPQIAkNtYw5UDrF5AH+t8LNgHAMBaBK4cYPUC+ljnY8E+AADWYkoxCn/9LAAAgFQQuKLIxsBl9ZRe\nrPMxhQgAQOoIXDlmvAUuroIEAOQD1nCFYCue9MrnfSIBAPmDwBUi2a14AAAAIiFwIe0oOwEAyDcE\nriiYQrQHZScAAPmGRfNRELgAAIAVCFzIKKYQAQD5oMAwDCPtb1pQoAy8LQAAQMKsyC15OcKVjQVN\nAQDA+EXgAgAAsFnSgWvLli2qra1VXV2dli1bpitXrpiPtbW1qbq6WjU1NTp8+LAlDQUAAMhVSa/h\n6u7u1sKFC1VYWKg33nhDkrR9+3b19vaqublZX331lYaGhrRo0SL19fWpsPBWtsvEGq7QCvL/d7Og\nKRXkAQBANFbklqTrcLlcLvPn+fPn65NPPpEkdXZ2avXq1SouLpbD4VBVVZV6enr02GOPpdTQVFFB\nHgAAZIolhU/37t2r1atXS5IuXLgQFK4qKys1NDQ05jUtLS3mzw0NDWpoaLCiKQAAACnxeDzyeDyW\nnjNq4HK5XBoeHh5zfNu2bWpsbJQktba2asKECWpubo54noKCgjHHAgNXujGFCAAAIgkdCNq6dWvk\nJ8cpauDq7u6O+uL29nZ1dXXp6NGj5rGKigoNDAyY9wcHB1VRUZFiM61F4AIAAOmU9FWKbrdbO3fu\nVGdnp0pKSszjTU1N6ujo0OjoqPr7+3Xu3DnNmzfPksYCAADkoqTXcL388ssaHR01F88//vjj2rNn\nj5xOp1auXCmn06mioiLt2bMn7JQiAABAvmBrHwAAgCjY2gcAACAHELgAAABsRuACAACwGYELAADA\nZgQuAAAAmxG4AAAAbEbgAgAAsBmBCwAAwGYELgAAAJsRuAAAAGxG4AIAALAZgQsAAMBmBC4AAACb\nEbiQdTxeT6abAACApQhcyDoELgDAeEPgAgAAsFlRphsASP+NavlHtrYe22oeb3A0qMHRkJlGAQBg\nEQIXskJosGppaMlYWwAAsBpTigAAADYjcCHrMIUIABhvCgzDMNL+pgUFysDbAgAAJMyK3MIIFwAA\ngM0IXAAAADYjcAEAANiMwAUAAGAzAhcAAIDNCFzIaey7CADIBQQu5DQCFwAgFxC4AAAAbMZeisg5\nbHQNAMg1BC7kHDa6BgDkGqYUAQAAbEbgQk5jChEAkAvYvBoAACAKNq8GAADIAQQuAAAAmxG4AAAA\nbEbgAgAAsBmBCwAAwGYELgAAAJsRuAAAAGxG4AIAALAZgQsAAMBmBC4AAACbEbgAAABsRuACAACw\nGYELAADAZgQuAAAAmxG4AAAAbEbgAgAAsBmBCwAAwGYELgAAAJsRuAAAAGxG4AIAALAZgQsAAMBm\nBC4AAACbEbgAAABsRuACAACwGYELAADAZgQuAAAAmxG4cpDH48l0E3Ia/Zca+i959F1q6L/U0H+Z\nlXLgevvtt1VYWKjLly+bx9ra2lRdXa2amhodPnw41bdACD40qaH/UkP/JY++Sw39lxr6L7OKUnnx\nwMCAuru7NW3aNPNYb2+vDhw4oN7eXg0NDWnRokXq6+tTYSGDaQAAID+llIJee+01vfXWW0HHOjs7\ntXr1ahUXF8vhcKiqqko9PT0pNRIAACCnGUk6ePCgsXnzZsMwDMPhcBiXLl0yDMMwNm3aZOzfv998\n3oYNG4yPP/446LWSuHHjxo0bN27ccuaWqqhTii6XS8PDw2OOt7a2qq2tLWh91n85KryCgoKg+9Ge\nCwAAMN5EDVzd3d1hj//444/q7+9XXV2dJGlwcFCPPPKITp48qYqKCg0MDJjPHRwcVEVFhYVNBgAA\nyC0FhgXDTQ888IC++eYbTZw4Ub29vWpublZPT4+5aP78+fNjRrkAAADyRUpXKfoFhimn06mVK1fK\n6XSqqKhIe/bsIWwBAIC8Zkmthl9++UUTJ04077/55ps6f/68fvrpJz3zzDPm8S1btqi2tlZ1dXVa\ntmyZrly5Yj5G7a74uN1u1dTUqLq6Wjt27Mh0c7LewMCAnnrqKc2cOVOzZs3Su+++K0m6fPmyXC6X\nZsyYocWLF8vn82W4pdnrxo0bmjNnjhobGyXRd4nw+XxasWKFamtr5XQ6dfLkSfovAW1tbZo5c6Zm\nz56t5uZm/f333/RfFOvXr1dZWZlmz55tHovWX3zv3hKu76zOLGktjrV48WKdOXNG3333nWbMmKG2\ntjZJwbW73G63Nm7cqH///TedTcsJN27c0KZNm+R2u9Xb26uPPvpIZ8+ezXSzslpxcbHeeecdnTlz\nRidOnNB7772ns2fPavv27XK5XOrr69PChQu1ffv2TDc1a+3evVtOp9Mcqabv4vfKK69oyZIlOnv2\nrL7//nvV1NTQf3Hyer16//33derUKf3www+6ceOGOjo66L8o1q1bJ7fbHXQsUn/xvRssXN9ZnVnS\nGrhcLpdZAHX+/PkaHByURO2uePX09KiqqkoOh0PFxcVatWqVOjs7M92srFZeXq76+npJ0u23367a\n2loNDQ3p0KFDWrt2rSRp7dq1OnjwYCabmbUGBwfV1dWlF154wby6mL6Lz5UrV3T8+HGtX79eklRU\nVKS77rqL/ovTnXfeqeLiYl27dk3Xr1/XtWvXNHnyZPoviieffFJ333130LFI/cX3brBwfWd1ZslY\n+fe9e/dqyZIlkqQLFy6osrLSfKyyslJDQ0OZalrWGhoa0pQpU8z79FNivF6vvv32W82fP18XL15U\nWVmZJKmsrEwXL17McOuy06uvvqqdO3cG7RRB38Wnv79f9913n9atW6eHH35YL774ov7880/6L04T\nJ07U66+/rqlTp2ry5MkqLS2Vy+Wi/xIUqb/43k2MFZnF8sDlcrk0e/bsMbdPP/3UfE5ra6smTJig\n5ubmiOdhof1Y9Enyrl69quXLl2v37t264447gh4rKCigb8P47LPPNGnSJM2ZMydi7Tz6LrLr16/r\n1KlT2rhxo06dOqXbbrttzPQX/RfZzz//rF27dsnr9erChQu6evWq9u/fH/Qc+i8xsfqLvgzPqsxi\nyVWKgSLV7vJrb29XV1eXjh49ah6jdld8QvtpYGAgKGUjvH/++UfLly/XmjVrtHTpUkn//aU3PDys\n8vJy/fbbb5o0aVKGW5l9vvjiCx06dEhdXV0aGRnRH3/8oTVr1tB3caqsrFRlZaUeffRRSdKKFSvU\n1tam8vJy+i8OX3/9tZ544gndc889kqRly5bpyy+/pP8SFOnzyvdufKzMLGmdUnS73dq5c6c6OztV\nUlJiHm9qalJHR4dGR0fV39+vc+fOad68eelsWk6YO3euzp07J6/Xq9HRUR04cEBNTU2ZblZWMwxD\nGzZskNPp1ObNm83jTU1N2rdvnyRp3759ZhDDLdu2bdPAwID6+/vV0dGhp59+Wh9++CF9F6fy8nJN\nmTJFfX19kqQjR45o5syZamxspP/iUFNToxMnTuivv/6SYRg6cuSInE4n/ZegSJ9XvndjszyzpLw5\nUAKqqqqMqVOnGvX19UZ9fb3x0ksvmY+1trYa06dPNx588EHD7Xans1k5paury5gxY4Yxffp0Y9u2\nbZluTtY7fvy4UVBQYNTV1Zn/333++efGpUuXjIULFxrV1dWGy+Uyfv/990w3Nat5PB6jsbHRMAyD\nvkvA6dOnjblz5xoPPfSQ8eyzzxo+n4/+S8COHTsMp9NpzJo1y3juueeM0dFR+i+KVatWGffff79R\nXFxsVFZWGnv37o3aX3zv3hLadx988IHlmcWSSvMAAACILGNXKQIAAOQLAhcAAIDNCFwAAAA2I3AB\nAADYjMAFAABgMwIXAACAzf4f3y5oBwNM4SgAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,10)\n", "dists = cdist(protos,data)\n", "closest = argmin(dists,axis=0)\n", "for i in range(len(protos)):\n", " plot(data[closest==i,0],data[closest==i,1],['c+','g+','b+','y+'][i])\n", "plot(protos[:,0],protos[:,1],'ro',markersize=10)" ] }, { "cell_type": "code", "execution_count": 105, "metadata": { "collapsed": true }, "outputs": [], "source": [ "history = [protos.copy()]\n", "\n", "for i in range(len(protos)):\n", " protos[i,:] = average(data[closest==i],axis=0)\n", " \n", "history.append(protos.copy())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we pretend that the cluster assignments are correct and\n", "recompute the location of the centers." ] }, { "cell_type": "code", "execution_count": 106, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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iuVQUXGSjQ8FFSJewb5pR6wnGZcuW+P1PTibv67LLmpPKtfiTWlQHDwI7djTn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\nLeRcJIwqEwBcNblEBGrEOaxUmheMlnOyRVgS2vm50M68M1IcKLj6hCT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Xxw2Xz5tybGEn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\nF7oUQ2D8EiGEEELSgIIrhEYUX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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,10)\n", "plot(data[:,0],data[:,1],'b+')\n", "harray = array(history)\n", "for i in range(len(protos)):\n", " plot(harray[:,i,0],harray[:,i,1],'r')\n", "plot(harray[0,:,0],harray[0,:,1],'ko',markersize=10)\n", "plot(protos[:,0],protos[:,1],'ro',markersize=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the centers have moved, and it looks like they have generally\n", "moved in the right direction.\n", "\n", "Now let's just repeat this process multiple times." ] }, { "cell_type": "code", "execution_count": 107, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "0 100 200 300 400 500 600 700 800 900 " ] } ], "source": [ "for round in range(1000):\n", " if round%100==0: sys.stderr.write(\"%d \"%round)\n", " dists = cdist(protos,data)\n", " closest = argmin(dists,axis=0)\n", " for i in range(len(protos)):\n", " protos[i,:] = average(data[closest==i],axis=0)\n", " history.append(protos.copy())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now plot the path that the prototype guesses have taken." ] }, { "cell_type": "code", "execution_count": 108, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 108, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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7pYWniLEzzjDjOXIEeOop4OSTzTV45SuBvXvN8ZWKGWehEIg1CUPK2o9DQ6Y/\nuVa+Yqr2tXPhEs5aFNvHuhL4XW26cr/CaNZnkhBSDwUXITkSZxaZbxZY2LFJb4qufC/dxqFDRjwc\nOdI4q82H9LWwUD9uETerVhmnqL/fbB8ZMcJl165gXz3Dz7hQJ2Fy3yfx579+Dt75pRL6r/wbfK+0\n3nmN9CxEO3fKlywuvOxlwXMpu+ASS1L3S0KYkpAv2ySfzRVedIkk+3lYHlba/V3H+3LLfPv7PpN5\nkjSETkivQcFFSI6kvalUq/Wz81xtht0U9evSlo3L7XKJLd/4ZfvBg/VJ9MLoaCBExCEaHDT7FgqN\n1ddlPwD45jmbcf9jK7HlLzfi/znyJ6hW3woAOO204FztxHY53pUsLi7V/HxjkU8pRSHnVK2aNmU/\nLapmZ40TKO3biea2ILK32ejXwiq9h00CcPWr3U09yaCTXCoKLrLUoeAipE3YN82o9QTjsnx5/P5H\nR5P3dcYZ9UnlWvxJLapt24B16+pziKQEhO5fMALxdfjWTXfjzz7yRuw6vA+Pvv33sXCor05AyGMZ\nqyDhxz17TH0vySmTkOTmzcE4JeypxyBFS2Ws0r6EGkulwLErlcx5aBcxrhOlxZFOoPcJUh+uUKMv\nxyuJ6KIgIqR5UHARkpG0OTD6JikOSpzCpnKc7/WBgegxy7H2TT6uuNP7aUdNzmF6Olgf0c49smfQ\naRdsaupX8MIL/gl/sOc3ceKjNXzyjD/BAw88iW98fTeOm9+J4ZP2Yd+R1dj02xtx3svW43d+ZwXG\nx+vHY1d7t0OON9xQH6bUNb6qVTPDUpw6yXGrVs11lfCi9CPnrks4rFnjX1bIdiLD8rFkn7ifrTg5\nXlHkLbiYH0ZIAAUXIRlJmwMjN2txY4BgHb6ZmfAbVVjeVZx6XT7RFuay6fGIUNEzFkdHA0EiAspV\nzkAntutzAsz+hcIqvH3/N3Dz4Y14+XdW47S55+HPDz2C1+AoVhwBFgF882e3YO/DK/HTe9cC4zuw\nsGCcq+9+N1jvUCYFyDV1na89w1GLIbkWtZr5Wb7ctCuvT0wYwSrXUt53mVnpCjG6wn9h19312QoT\nxZ0mYlqVH0ZIN0DBRUib0DcjuxyAjW9GmhYISZ0Eu4wCEL5Atj0GEX0isOxEcts90+douz9S7+qY\nUHroBbgIf4Pfxypcd+hwXTsrAGx45ig21Gr4H48CGzYsYnZ2BRYWjMAqFoOZhDImHQIF6ks7VKuB\nMNQunNQsMHy9AAAgAElEQVTEspP1dYhTsAVkWOkH2U8Xjk2yMHkcwdVpwosQQsFFSK5kudFF5V7Z\nosp2i9I6CfpYycFy9a3HIDW3ZmYCR0lqY2khJ+3LsfJYHB1bqIjjNDYGHPfUvbjky08Az/jH/uZn\n9qPvo7tx9OhInXgdG6uv5aXPVcYiSfHlsrtQLFB/PppSyb92o2/GpO10rVsXrz6X3X4cOlFwdeKY\nCGklFFyE5Eiam4qErx54ALjrrvq2fKE3IWmIxuWEifgpFgMB4upPnk9MBPsfOmSOP/XUxkWfteAS\ngeIKp8m4dF/FIvBvt+/Erz9zNPR8Ljp6FK+7YifunR85tiROrWZCiJLbpZ0rff66yOlppwV1tspl\nI37vuitIthc3T8pGANlcqaQTIXSuX965UK2aPUjBRZY6FFyEtBktrN7xDn+FeKAxyd5uw95fjrFF\nm4gOW/Roh2tiwh+mlFpcIqJcTpsdcnOVqggb50/u2IcV4YdgBYBLLtyHFwyapHYRWrpfe7aebJP8\nuVIpmNEoNbokSV4WtJZx6bb1rElbmMYh6TFJ3DBNlKBiuQZCWgMFFyFtxE6iBtwV4gUtGLRzY+9j\n92EnyWsxpEWcdrhqtcb8JbtdEV466X9gwNS6km2VinGGZmfNkkOAKY6qz0OHSOUcvjm0GovfRqjo\nWgRw0urVOPJAUKTUxj53vU3E1Pbt9blXlYop2FouN5ZvkLwwe81F13XXglWS74vFIPlexhJFFlHk\nOjbv9ggh0VBwEdJByI19ZiY8BKVdqrj4nBgRceVyY9kD1/ETE8G6gocOme1r1phq7lKjS47XokPX\n7JqaqhePuqK7cNHGjfinyi143dP+sOK9y5bhoo0b8YOv+M9bXyt9DfT6kQ8+aJLYJY9scjKomC9l\nK+xrUas1lqCw+9W/dRv2ucat9q/by4IO7yYNUVJwEZIOCi5C2ogdghNHyQ71+RK3fbhytaamAmEj\n26Q/2TY4WC86BBEnpVJ92K5YNLMBp6aM2NI3b7vUgQgUIHDS9uwx9bpkhqE+tyexHnecsBKve9pq\nSHH781biH69aj3/7t2CblIEYGqpf1Fmui4gbHR6cmjKO1sSEEbuDg2aM4vqNjQWLfI+PB+HIcjlc\nsPhWD9D4hHPYzNMoomatugQfIaS5ZBZc1113HbZv347jjjsOF154IW6++WY8/vjj2LRpE+bm5lAs\nFnHrrbeioFe9JYQ04Jul6Lshh9147dBjrWaEg1SW15XXXccB/puyLSIWFuoXvtaOkk6O14ns0p4O\nX9r9VasrMPuCtfg/F4A3Hd2PYRzFCpgw4r3LluHelStx6tq1+M6OFXXHuVwaEVq2kJV6YiIAt28H\nTjklWKS7VDKLXkvoUY6XXC+Xe6XRszE1+r3x5ePZ55F25qkc60u8D1tiSEhTdoQQUk8mwVWr1fAX\nf/EX+Pd//3eceOKJ2LRpE77yla/ge9/7HjZs2ICrrroK119/PbZt24Zt27blNWZCehZdJ0pyfqR8\ngZDkJqf33bIlugp5VB4SYJwgcXyksGihYASVJKFLW7aIkjalEvuuXcCBA2a7nmEoztQ9P9mBvc9b\nROW43Rh4ZifOOn4fHnl6NQYu3IizX7IeV17ZmOHlmhGo3SidQC/j27OnsQDq+Hj9Np03ZzuEvmtm\nz8a0w4wi4rSY85E1lOcTcHFC01nEHyHEkElwveAFL8CyZcuwuLiI448/HouLizjrrLNw3XXXYfq5\nf9k2b96MUqlEwUVIBLoukzg+EuqTNQHTOAqufK+wnCP7uZ2LJQKpWg1Cb8PD5rks5xMmDnQZigMH\njNAqFk0O2A031OdbDQ8D09Mr0N8/gv86MoLaIVOCYvN/rxd3IvjkOPktjyVcKTMRbQdQcuamp83P\n1BTwH/9hRKGUuwCCx2vWmD4lzJgUW8gODzdOlrAnEaQVXFHHNMOhYp4XIY1kElynn346PvrRj2L1\n6tU46aSTcOmll2LDhg04cOAA+p/LOO3v78cB+YZWlNW/SKVSCSX+dZIliC9UA7gru2dpW8KIYTMg\n7ee+ZG6d3L9mTSBEjhypF3ciRvRYJieD2YpSB6tYNDlgsq/0KU7X0BBwzz2BwAOM4JJ9Z2bMj85P\nk3MolerDZpOT5jhZmkgLQF0eQspC2BMJRIDK2OwK+7Zoigrd2s9lySCX4IpDnDIVWZ2ypGMgpNuo\nVquoJp2ZFEEmwfXggw9iYmICtVoNp556Kt7ylrdg+/btdfv09fWhr6+v4dgyPWlC6m60Oqk8ypGK\nc0Oz2/bVwYpbp0mPTQTA/LwRQGvWGFdIcqGmp02Y7sgRc4ysOShjkR8RT/PzRuBogSFCqVAArrkG\nuPLKYEzSV6Vifubn6x1CO1dLr5ko11bEoDhtxaKZmbiwEKxvWS4HMyqlLXG9ajXjnIloFJdNX0tX\nmQoX+pipqSAfziXIfQtj6/NtpqtFIUWWArYRtNX+jzgFmQTXv/zLv+DVr341fuEXfgEA8OY3vxn3\n3nsvBgYGMD8/j4GBATz66KM488wzMw+UkF4n7gLGQHIHQbtBrhwn+7m+yeu8JhEv8rxcNkJJBI3+\nEWwHSDtGIyMmKV3qdIlY0zW1pL93vKPedZMQoogjCWfa11GKl9pJ6sPDZmxa5ImY0eesQ5eyPqM4\nbWvWBBXqZakjfS1ljPra2u9BWL6ZoMO7SUpItBIm1hMSTibBdf755+OTn/wkfv7zn2P58uW4++67\nsXbtWpx88smYnJzE1VdfjcnJSYzK1ChCuoR2hES0G+K7IWdp2ye4bOwbpAgOOXZsrLFt7V7ZSeN2\nfpK0U6kYsTU3Z34kl2v58uBaTE4GpSpkJp84UMViMKng5JPrZ2Hqc7QT+fXMTY04gDKLb3g4KDEh\n7elSEoWCO+TnCokKPsGla5vNzZnX+/uDMhRyrI9OEDtMrCcknEyCa3BwEO9617vwile8Ascddxx+\n9Vd/Fe9973vx2GOP4bLLLsNNN910rCwEId1EqwSXndskQsPldiW9qdpti/CxRZGrLdsNsnOepEjq\n5KTJDZO25ufNY1mLUPK7RPBJH/JbhBcQCDc770kei9AbGjL9nn02cPCgKb4KGNElsxz1cdPT9XW0\nZmYCV0yuyehovfMm179aNX1p0QkE4chCIQhrSmK+lM2whWkY4+P1tc1sgRfmfOkfgWKHkM4jcx2u\nq666CldddVXdttNPPx1333131qYJ6QiaKb7sPCvBtTBy0puqzjsaHDQCQ5eY0M6Ua/1GLX4klGeH\nC7VImZjw51GFJeqLsNOhPBc6D6tWM6LuwQeBE08EnngCePzxIHneFjszM+b32FiQXP+d7+DYgtdT\nU4GDJqHBoSEjoiT0KCJLC7lSKVjDUYtlEU26vIeI0O3bzbhlP9+10Y5ntwkq/dljOJEQAyvNE/Ic\nPtdHh6SaSTOqf+sbtYTbRkcbk8ptxHkSJ0hcLsl50iJxYsJs1y6PvKZzp3zXsFQKltUJm2GnnbFi\nMZghKX2efDJw+DBw8cWNi0wDjYLov/4rOF63LeJMfktyfKUSOGHyA5iJAZOTpi3A7CuzMDdvblyP\nslptXKRchzllPCIAw0SZi04QOBRchDRCwUXIc/hchFa5CVE3prR5XTpvKG6/+lpIOE4XAdXIAtbi\nUtmzGeWxa1wiRu66KxAZtvOjE9jlOBFy4kb98IfAY4+ZkKZekkjGNztr9hV3qVQyjpO0WakETp6M\na2zMuFrlcn1oT4RQf79J+hfxJa6aDonG/ezYYtLlJtr7RrXVDiiwCPFDwUWIA12ioVVJyD5nR0gj\nuEQ8SIK55Fy5kth9fdqhLY3kbIkQuf9+83h01ITZwq6hDlnqWZQ6eR2oX0pIhzilthgAnHBCfRHW\nYtHkdx0+HPQ7N2dE1sknmxDikSNBPtfERH14s1w21+q004yQ0oVTBwdNu6ecEtT9koR/+/rIc0mK\nF/G3sBBcJy3m4ryvnSxo9MQBgLMVCdFQcBHiwK5z1OqcGZ8ISuog6BpUgHupnbB2fWPQ4UZpt7/f\niKxrrnELQ9shq1aDmXlS88pVvkJCe9Ke5JNJmxMTZjx2xffDhwPxJs6RhIelnIXke8lMRBlLqWSE\n2R/+oRFE2uXT56GT7MPcKJ0UH+Y25j07tR10W74ZIa2CgosQB51ws3O5BXZ4zTdOe5ahEGehYjne\n14feroVIqWSS5sNEoX1Os7NG+PT3mzwuKYlQqQRCa3bW9COhRgkZTk0Bd94JXHCB2UcKkNqLgE9M\nGOdtZsbMaLz/fuCLXzTFTu1cqULBtFOrmSR8CZcCQU7azIzpb3rajPPIkaBwqut6hWHnDbque9T1\nzCrKsxI245UQEkDBRUgE7bxxuMIw2t3xuVJ2HSxpy7efvlEWCkF1dV9ISG7qIuDKZSN0fOsC2uFS\nHb5bt8782OgFu/VxWuCVy/XL75xzTtCWnul5zTVB+FCOHRkxi2eXy0G9K5kYoIVprWbChxs3Bueh\n3wMdhoyDLktoT0BwOZBZBVceAixq0gMdLUKioeAiJIK8BVfUDdQWQXLz1yE8vd0mTKSF7WdXh/cl\nfutwmE4WB0xOl4TkZL+ZmSBnSZdJsEtUzM8bt0iXfpDCoTqPTI/f5uKLG8tRiIianDROmoQFtcjT\ny+nYoUkp6RAmOHwhQheu6vPyo2d55pXz1GzBFQZdLkICKLgIaTFp3QI9qw9w1+rytRl3XLbY0yUd\n5LGsYyjhSlnHUPbZsqVx3Ha5C0kiP/vsQEROT5vn2h2TGmL6+J07g3MScSd1suz6W/Z1ufPOxm2l\nkhmLhC1FBEoh1eXLgzUh5fr4wqxxhImr9IW4hXo2qPy4wnQ+US5J/Hp/nRfXbCiwCPFDwUVIm0ky\nO80lXqKOidu2HTK0k9z161LLSxLddVJ+GLKviLXh4WC2X60WFASVEOX0dCC4pP8bbqgfd1S5C503\ntm9fIEj27DGulqzjKM7WpZeavLJ77ql3FUXYDQ01LgQeJbjCtktIVK8GoBPyAXdhWt9r8roINrtS\nflIBLrNbddtZxT0hSxEKLkI85JkLE5ZY7Gs37rYw4u4fdQO1x6+XCZqZCW76UnZiZCRY1Fqf79CQ\nETkiKiRfrFgMqroDQW2ru+5qDMHFRca+bZtx4JYvN8nt0oeeTalnKcq5DA0F+VxSjFSLtyTvxbZt\nfvGi87byCiO68u1c9dHitFEuN7qWhJDkUHAR4iFPwRUVKvQdE7atGbllOtneFgH6Bj46GuRX6UWj\npbK6XbTTTi4X0VYqAS97WSDe7KTxarWxRIdGJ6D7mJ83vyUsaFOtBvsApi/JOxOxdfLJQSV9qbpf\nKgUhTHGpfJMMJDdNxIt9PcMIe59dzpoIQ9dKAWlmUhJC8oGCi5A2EOZ4ZXWl0o4nyWwzcYR0CDGq\n5IQWBPJbOy+uwqHFYmNdLo1ewkejr6+EC3Wek73vKacEz2dmgnbL5aC4qghJwZenpp0kve6iiM5i\nMVjwWou0Wq2+yKsQFqL0CS79W0p32Nc7DPvzaRfLJYQkh4KLEIV9o5EZdbr+ExDvxqNvgq5cqLji\nxtVe3thjdb2u3S+dPC7CQsKI4mAJetafbtslLOxtsoQP4BYjUWgRODdnKsfrvkUEPfhg8B7oGYtA\nIFbsa2Cfh4QMfWOQvDVJwtduXtKlgJJ8FiQ/Tlfo12P3OalJP5+EkHAouAhRhN1ofFXafYQJrjS0\naqaZq5+o6wKYsNyuXe597PZljUKg3uGZmQlytsJmTEahxyuz9HTYEmisli/u0+HD9WPbvNmfByWh\nu8nJoPyE7T5pUSrlKOScymWTvJ9mGam4Lqk81g4dBRQhrYeCi5A2k0VENSORXwuAOG0AZv/Z2fqq\n7L5+JHdLCwMRIyJYxI3Rx87NGdHgCn+GIWFJIHDM7L63bzePZ2aM2yX7X3ppkEPmcgF1Xpbgyvsr\nFIIEecBcAylpMTDQOB4bnawPuEtF+I6TY6SMSBLhap8PISQ9FFyEeIiTS2NjiwtfCCpu8nuUi5FX\nIr8WSHfdFT5rzpVnJYiDpHOitEjRQiMqWdyFdqjC0NdlbKx+QWyXWLn44kCMFQr1gsqVQ6bHv307\n8NRTQdFSccokz80Wo4VCEKbUjlnU+dgrC8SdeKGvv5xPEii4CMkHCi5CPKQRXL7Qmz1rL8kYWpFL\no8OlOtnbNyYfIogOH248RgSGLTT27DHiRC/lMzVlto2N1btdUUnfYeIoqn6ZS4iECUPZ/uCDJuwo\n5y7CbWEhEJfa1fP1Hde1843Tt69r5qnU5SKEtA4KLkK6jDxmONronCpXSQgf+nVZfzFMpJRK9W6T\nL5TmmgG4sBC9tqMd9nNdJ1diu+w7PR2EEQXJz5qeNuJQEt5FTK1ZU5/c73KVbHfKNSPTdivDxu+q\nqO9DiyzmcBHSPii4CGkSccOGSdvL2/WqVutn5dVqwWLOcY+vVoGf/MQIA6lXJY6PPW5bcEWh8718\nTpDOcbJnSdr9azFoO0DDw8EyRXKMnqWonTkRbnNzwXNfkVZZdkgn6U9Nmd9DQ4Go0+fqCj1rlzAO\nWgQC6ZLz4/ZDx4yQcCi4CGkSSQRXnBtWs25odt/FYmNphLDj5MfOr9LiRPfhy8GKc/6uhG/ZJmJG\nh/Bcx7lEjKCXHnIlydvHyXnbuV6uMJ4k37tcJrkmPvGctKyDRsZlF5DN0+Wi4CIkGgouQjqAtDes\nZtzk4ia024JEapaJU6Rzr2TmoyxtIyE67YL5xI1rbPasPXGNBgfrhZYu1hl1TrVaUHFe72uHKu3t\nIpZsASpE5ZzpcKZuW7chIcs4IUHXrNAkrhghpDlQcBHSxaS9ibryg/bsMYKjUDA3/6Eh83h0NF5F\n9+npoCr76GgwS0/ExLp1Rpz4lv8R7AKnWlxpweYSN3YITectxXGG5ucDt0oXeNW1ulwhziS4HDa5\nTvb1cL1PLpfP1b6eFapLY+QRQvSNLc/2Cek1KLgIaRNhNyz9uxlEuTA6X0gzMRGsoeirBVUu1y8G\nPT1tEstlvzhOk0aXRNA1r0QYaYE0OGjEofQ/ORnsL8vT6Ha12JmZCZYBkra0IHLN4owq/eF6D33b\nfLMP7fcpbvjZzvfS555XTmGzQpSE9CIUXIS0CVtY2bP0ktwU886hEVHl2m7fuO1QoJ07JS6L7CNL\n/bjysIDGWZK+fYAgUV3CehLO1Mn6vjCctCUV53VZiv5+066rTpZPaLgcuyTvSdx9k7YZJzxMCGk+\nFFyEtJG8hFKWdlyi5vDheGEi3a+dO6VdKbvOl+znG7fkg+kQIhCELRcWguPHxwPXyS6sWqsZV258\n3O8syfaxMeNy6SRzvZ/r3F3b8ngf0rzuGosOw+p28nZP2/0ZJqQboOAipAOwk8HT5MTkkXjvC2HJ\nj70otXbCwsJidikG7YrZ4bdqNSgdATQu8uxKhBdhJ8/t8J8ILt81LhSM2JIcLsnfcs1sFCqVelEm\nFerjvgdJ3680uWJyTNJ1QJNCwUVINBRchLSYMGEVVQ09rB1fInnacenZbXYYsVptLERaKAS1pXwz\n7mxB5ipCqstG+FwkCW36ljvS2zR6LHYhUKmhFRaC1OdhV2v3hWF9UGAQsrSg4CIkBnneHNMkG/vK\nEtjbsrgYdnthSd++8YvosEWandxu52Lp0hB6gWmXyKlWTb7V6Gh9vS3d5sgIcP/9RgTOzgb76BmX\n0pYsiC1rIdZqQcjSDrcCQc6X5JqJaNRFTV3XKQtZP39Zjm2mMORMR7KUoOAiJAatdiPsvnz963Cf\nfbN3tROG3YdPbLmO0yIEMLMSZQkal5DTSfF2fpe87soNs4Weaz95TffncsqWLzfbi0UjtoaH64/1\nXTvtykmemSz1I22E5bwlERgu4ZmGLGHOZn720/zzQUi3QsFFSBvx3cji3uB0GM2u42RXFo9C178K\nu/m7+pft0r9eGsgWhYODgdARgaaLpMoxvpCh3X8StOC56y5gYCCoDSahTNvVqlTMa1u3mpDpwoIR\naGvWBItVi3DU18BFEoGhc8iaTV7CLs+xENJrUHAR4qEV4Y6wdpL073JxXPlRYej9kwguVzs6D0vG\nq5Pdpb3BwWBWYaViEtfDluix+43jwo2ONo5FI05ZoVC/FqItQuT6zs4asVUoNOaE6XBoVsQ1jCM8\ns2KPuR2hPv25oOAivQgFFyEe2h3uSNq/drqAxnpWUSGuOPtHIcLJ1b4k4st+0peInGLRlC8oFBqF\nVpK6ZPZ+cRbhdglWufFLcrwejzhwuq/5+XhjDZv5KK9LvpotPNO8J1ECRrujW7e6l1tqxWefIov0\nOhRchPQIvlwlIY5zYLtTYU6H/q33Dav75MrnskOhdh8usrggvnFKEn2pZGp3ybgmJ81rDz8MPPig\ncbfm5oJkewmfHjkSv/+4AlgEqi7kmpSo/D/pS4Qd0Pp/Lpg8T5YCFFyExKDdX/pJc7qARiHjcl7s\n/e16TWEumyvvCghPHveFJO08r82bgxpX1apb7KVFj2lmJtg+ORnkly0sBLMb16ypL4+hReLEhMnr\nmpkJRItvUe6kYxN0fbG0xJnl6lvbshWf/Xa7yYS0AgouQmLQLYJLo52qvPfXAsAVXgPiL3Njh+rC\nHC953Rf6SorkYVWrQZX6LVuMiBocNPvMzQX97tlTL4BEsNkJ9/aEhbQOTliuWhh2f9pV8+XdSYmL\nZlelJ2SpQsFFSJeQNIwmCdxRN/q4YkALHl2GwjWbLk4yu4uwsKhLfKRxQvQC3Lom2PLlgTM3Oxs8\nvvTSoB9x3QqFQKCIs7VmjV8gxXVw9HXMInZ8TpkPLRCbXZU+Cgo80qtQcBHSJSQVXHEFir45h91s\ndXtjY42iJcpFiUuYWNPXIOksTMFegFseixCzJw7ofYvFIOQI1IdPzz+/0dWKex1cZRnCkurjtOsS\nx9KuL7TbCXTSWAjJEwouQogXfXPXTtjkpHF0AJNvFcexiUuY4JLSCzIGHcrLmmQv1eXtPsXNAvy5\nZDrM6BKHGl8Ce1yBFfeayjUJC9P6jiOE5A8FFyEdTJyZf65jbLdEjonC3sduQwsLyfuJKt6Z9QZu\nC73hYSO0BgfjiwiZUQg0rv/oQo/ZLithL1mUNM/KdY11WQa9n34f017LsDBtnPERQvKBgouQDkaH\ntbZsSbbuYh6Cy24XCMYwPW2Ejy6n0Ay0uJSldGo1k2flqmzvwg6V6qWEtHslMzXFRXMRlmeVJDne\nV5bBt69MTJB29dJJUaRJuqfwIiRfKLgIIXWE1anSOVq+MFWS2l1pxiTLAw0OuvOsosZhV9R3hQDD\nwn5h+8VNjvftq8tOhF1Dex3JKCi4CGk/FFyEdCj2TVdypcLcEhFJkiidpnSCFjGbN5tt0q4IHnGZ\nfPlFPtGRRCTYY5JxAEGyeliozDcO+xh97aQavus6i8DMWhMrDNs5s10wnQhPCOkuKLgI6VDSuiUS\nPovKr4qDDsXZ7bpckLydEZebJGJjdNQkuiety+UKAdZqwYLUEirVSfBReVZR/UQR5ZjpmZMidPOq\nyK6duzS1wvKEzhrpZSi4COlhkt7Awlw1m7i5Q1lu5PYsyXLZiCHJebLHEVXSwrVdC1W7HVniB0i+\nrmESMRpXICYR4XHxlfNoRy0uCi7Sy1BwEdIFpHVL0tTu0rPa4iz1EkdQ5XEj127P/HzjbMGoY+P2\nodty1exKGxZNO9swS+4bIaRzoOAipAvIIrjS4Douj0TxuH1rASf5YsVikMR///3BPknLZth92XlT\nen1FF1mFT5byDnmNI0okt1LcdUIok5BWQMFFSI+R1w2sGblYccOQPpdN8shkxqTsr19LMy7dzsyM\nu9Cp1OzKEqLV27Je3yzHR4nkVgqdTghlEtIKKLgI6THS3sB84iDpDEdf20kFn282YbmcrMp8Unw1\nu1xECaeo2YZpxt7qPCfmVRGSDxRchBAA+TgNeYsHO2Fc50+ldWVcwlLX5rJrj0W1lcS1kzFncXHy\nFkBJJi40Gwo70stQcBHSwyQRIXnf7OKENl11vFwum1SSjyvO7HHEnelnV/R3uWx67GH9xB1fu+mk\ncXXSWAjJGwouQnqYtIIrjxtfGsfMd4wWQL4wnE/wxBWTYRMF7H1EGE5PB6/pvDIXWWYbtjqxnIns\nhOQPBRchpIGkuVZZE8mlT5fAsR2wKMGVZDw6v0oEVFhFfz1O2SdpmDDtDMVWJpYzkZ2Q/KHgImSJ\nksbFSFtdPm5ITyNhxNHRZDP8tAsFhJ+bdp1sAaXb023p5PfBQfNcl6xw9UMIIRRchCxR0rgYedWQ\nisP4ODA1ZY6tVMw2e4afjAlonFmpw5C+c9NL+0xOutdRDAtz6tfSlKVIQ6uFHIUjIflAwUUISUwz\na325SijofV35XGFlF6L6F3G2ZUs+428WactIZIWCi5B8oOAihDjzpPTzKHGVZbkeH1KSoVo1C0tX\nKsHCzXaull12QYuw6en67XFnEtpCL+xx1LnkAethEdLdUHARQkIFVzMSqKMWcpbXRGDJGoZRx2mi\nipfaQtJOlg8TXK5xUAwRQsKg4CKEZCJtmYM4x0k1eY1r2R075ypJONFuNw6+2ZN5E+Yu6t+tgi4b\nIemh4CKExM7J8pVJSEpUBXdhbKy+jzgiSbtT+tg4VKtB6FJqbMksxLGxZLM38yDsfHXV/TjkMUYK\nLkLSQ8FFCInt9mS52WpRF3ctxCROTpQbpPfzhQNdeWmu2Y5h7TebtKKHYomQ9kLBRQjJTNIQXlip\nhri4RJNPNNplJOLkX9Vq9SFNl9snIq8V1dhLJWBiIiiV0aoK8Kw6T0g+ZBZcCwsLuPLKK/G9730P\nfX19uPnmm3Huuedi06ZNmJubQ7FYxK233opCoZDHeAkhTSbNTbRSiT7OLt2gZw6m6bcV4bSoGY2R\nruBttwHXXgvccQfwwhcmH4DVn11jLEq05iGWmjFpgpClSGbB9aEPfQhveMMbsHPnTjz11FN4/PHH\n8TSFVPMAACAASURBVOlPfxobNmzAVVddheuvvx7btm3Dtm3b8hgvIaTJNCsny559mCUfKU5fGt1f\nXOFRLMafEenkH/4B+N3fBUZGTLn8r38dWL48xoGN2MsP6W2ZRSEhpCVkElyHDh3CN77xDUw+t6bF\nCSecgFNPPRW33347pp/7Vti8eTNKpRIFFyE9RphjFTVT0DX70NV+WhGmw32AyRnbssU8lvIPvj7T\nTB5oGOfevcBb3wr8zd8Ar3kNcPnlwBVXAH/918BxxyU6F/s6Dw+bx6OjrQnp2fXOCCHpyCS4fvSj\nH+GFL3whrrjiCszOzuLXfu3XMDExgQMHDqC/vx8A0N/fjwMHDjQcW1bfeKVSCSX+JZMeZ6klLYfl\nTdmCyCVusl4vn7sT5vKkdYTqxvnd7wJvehNw882BOqpUgEsuMarvk5+M16hnTEnG5R1jAii4yFKk\nWq2iqqc750AmwfXUU0/hX//1X3HDDTfgla98JcbHxxucrL6+PvT19TUcW6a3TZYYvSa4kiTBuwSX\n/g20LtzV1Pfghz80IcTPfQ74zd8Mtp90ksnnuugi4JxzjM2WkiyuHyEkHrYRtFX/V5iSTIJr1apV\nWLVqFV75ylcCADZu3IjrrrsOAwMDmJ+fx8DAAB599FGceeaZmQdKCOlcJEToc63Ccrz0P5F5JHlH\nzUJMkiyeiEceATZsAP7gD0wI0ebMM03yfKkErFmTSgG1amYgZyYSkj+ZBNfAwABe9KIX4fvf/z7O\nO+883H333XjpS1+Kl770pZicnMTVV1+NyclJjI6O5jVeQrqKbrxxpXHidIFSnRgvhNXdcq2JKKRx\nvfJadifRMf/5n0Zs/e7vAu97n3+/l7wE+PKXgU2bgN27gRe/uHljygCT7QnJn8yzFL/whS/g7W9/\nO5588kmcffbZuPnmm/H000/jsssuw0033XSsLAQhS5FuvHGlEVyu/YvF6PUMw47vGh57DPhv/w14\n4xuBa66J3v+SS4Bt20zI8d57M5eLIIR0B5kF1+DgIL71rW81bL/77ruzNk0IaSF555iFtRXH+Uta\nZ6stTuKRI8Bv/Rbw8pcbERWXK64AHnggc7mIVtDVYpiQDqLv2Weffbblnfb1oQ3dEtJWOjlpXpLe\npYK5lFBII1hc5xl27uVyvs5f3u3ZLC4uYs/u3bj31lvx869+FSc9//m46IYbsK5UwooVK+I39Mwz\nwNveBvT1pSoXQQhpHXnoFi7tQ0iL6FSxBQTCKm4F8zDyyqHKmySC17fvH27ahBP37sVF+/fjw0eP\nYgWAxYMHsWd0FJ9buRJPrF2LT+zYEa+T444zpSNe+9pU5SIIId0FBRchSxhXKC5OBfM8ybsfX3tZ\nBdfi4iJO3LsXH7emXK4AcMnRo7ikVsOnntsvttMl5SLWrctcLoIQ0tlQcBGyhHEl9acRW1lyqFol\nuLJQrQLPHNmNi/bvD93vov37sWf3blwyMhK/8Re+MHO5CEJI50PBRQipI20JhVbMxkwqBpMIwbB9\nq1Vg2cM78eGjR0P7u+joUXxu585kggvIXC6CENL5UHAR0iU0O8zXDcZK0muQRAiG7VutAj+/915E\nBQpXAPj5TTeZ3Kw0PPOMyeXavj3d8YSQjoWCi5AuoVsEVzcItzhox+t7W/8GLz3hR1gEQkXXIoCT\n3v1u4M//PP37xdmKhPQkFFyEkFzJW3DlVWMrjTNWKgHYtQuHT/4A9v7RZ7FnfByXhIQV7122DBe9\n5S3A8cej+g2g9Nr4feZBJ5ceIWSpQ8FFSAfTyUsDtermnld+WCpx9s1vAu96F3ZsmsLlY0P43Gc+\ng0tCFoa8d+VKfGT9+nQDzIFeE1y9dj5kaUPBRUgH08lLA/X8zXBmBvjt3wb+6q9w9omvxooVwBNr\n1+JTMLMRL5I6XDDO1r0rV+Lh4lr80R+ZoGO7BHIvvS+9dC6EUHARQtpKkptqy26+3/8+8IY3ADfe\nCFx6KaTbT+zYcazS/Od27sTP9+3DSatX46KNG/GR9esb6m+1QiDbLqhcz05wQQkhARRchHQJnXDz\nbEaIs+ME1759wOtfD3zqU8DGjQ0vr1ixApeMjCQv/ZAj+pq5rn0nOaFJ6eQwOiFZoOAipEto5c3G\nJ4I6OcSZCz/+MbBhA/ChDwHvfnemppr5ftnvj4iUahWYnq4fQx7jaPXKAz39GSNLFgouQkgDzb7B\ndqSLcegQMDJiio9++MMAsl2HVp6HXDe9LFOe/TOXipDsUHARQlKR5Qacp4uRixhYXATe+Ebg4ovr\nFGAnCY04ItUWXd1OL5wDIQIFFyEEQHLXqVNuhpnFxZNPAr/zO8Av/RIwMQH09eU0smREnUfcdS9F\ndOUxnmoVqNWAyUn/OLK0n3SdzV4RkmRpQsFFCAHQvtyZtt5An34aeOc7gRNPBL70JeC449oW7gwT\nE77X9Pa8xy3HlcvAli35fx7SLpJOwUW6FQouQkhbSXMDzUVcPPss8L73AQcPAn/3d8AJJzjb6ISk\nbVtoLMkJDYR0ORRchJAGOt1FyCwunn0WuPpq4DvfAe6+G1i+PPVYsrguaYSjnpHYLAfODidu3myu\nsc4Vy9IukPx8kxxDSCdCwUUIaaDbbmSJRc+2bcCddwK7dwPPf753tzhtZp3J6BOOPqFRKNTv5xKb\nWd+/sHCiFl5p29VtNeMYQjoRCi5CSFcjSeKxRcCf/inwl38JfOMbwOmnR7bdClxJ7j6hEVekkOQw\nR4w0EwouQkhXk2hW3v/+38C11xpn66yzUveZNMwVdSNPe6Nvhjiwz23zZmBszDwvFvML63XK+Woo\nuEgzoeAipAPgF31yEuf2fPWrwEc+Anz966YERAaShrnSlEDQ6DCifa55E+fc8gjrdaLgIqSZUHAR\n0gFQcCUnkeipVoH3vAe44w7gpS9t6rjikkQwjo/XP7fPlZ+f9DApn7QKCi5CSFezuLiIBx7YjSuv\n3Il9+/Zh9erV2LhxI9avX48VK1YA3/oWcNllwI4dwNq1ufefdnZdx1Xbd9DJBW/zgkn5pFVQcBHS\nJvifdXY2bdqEvXv34qGH9uPpp48e237LLbdg5cqVWPviF2PHzIxJkv+N32jp2Jp1I8/7sxEm1paC\n4CKkVVBwEdIm+J91NhYXF7F3717UarWG144ePWq2P/QQFv/sz7DiTW9q2jjycJeSHJ93ZXmGIwN4\nHUgzoeAihHQlu3fvxv79+0P32f/ss9i9ciVGWjQmH1kS5sOOyVuw94L4yloXjZBmQcFFSAfAL/rk\n7Ny5E0ePHg3d5+gzz2Dnzp0YGclXcnXrQt+Cb/y1WueNVRNHTPWCaCS9CQUXIR0AbxDJ2bdvX677\nJaHTwsFJPz9RRVU7VbS0c1ydek1I90DBRQjpSlavXp3rft1MXCHgEg21WmONr2o12xI+cfvOs+08\nC9H6+qDgIlmg4CKEdCUbN27ELbfcEhpWXLZsGTZu3JhLf74bbjfdhF3nMDbW6HblLbZ8fcc9Lo6Y\nCltf0u6b4om0AwouQkhXsn79eqxcudI5S1FYuXIl1q9fn0t/vSC4XNizHsvlzipTEid8GyWgKpXm\nij1C4kDBRQjpSlasWIG1zxUy3b9/f53TtWzZMlOHa+1aU/x0CSOioVYDJieD7bZoKJXqna28Zj22\nWrC42q3V4l8Hu61OytUj3Q0FFyGka9mxYwcWFxexe/du7NzpqTSfgV5wOGSs5TKwZUu4aMiSCxbW\nt5BVsBQK9WPwvTf269PT9QucR10HQpoBBRchpKtZsWIFRkZGci/9AHSHwxFX/NRqQLEYr81OLb2w\nsBA8bvV70y0Cm3Qux7V7AIQQQtKjnRvXa5IEPzkZzEiUY3zHtmpdxmYirl65DAwOBttd1yFue4Rk\ngQ4XIYTEoB033KxOkrhAEl6rVNK3nzW8mvY84vQb1fbQkHsWYxLBFTY+ijESBwouQgiJQTtuqjK7\nzlXWII74kf2qVZPHVC4bd8cuBSH7uvrShJVesMlLiMQJHUb1Mzbm3p7HGCm4SFwouAghJAHNvsHq\n9qXihd1n3PwlnTBfLJrfY2OBCHMt6+M7v6Tn3UlCxL52hLQDCi5CCElAXkLC106lUj+7TnKNZFva\nEODwcOMSPvpxkqTzZouWZtc8syvrS9txi6P2wuxV0noouAghpA1ECTftbk1PGyEmyd5xHBt989e1\nYScng9mKe/YEYcbJyaAvmdFYKAQzA12lF1znlIcQaabgiusOhr0/3TB7lXQeFFyEEBJBsx0N3f7k\npKkTVSya2XV6pqFryZ04/Us4UXAtUi37yI8LcdsoRAhJDgUXIYREkJeQCBNuukyBtK8rpGdZcidM\nICWlWblZnVCVPs0YGEIkcaHgIoQsKdqZzB0l3OwyBUNDyZbciROKixIOSYVFXuG/ZrhjUe+1yy1M\nOgYKLhIXFj4lhHQ0edRKStNeK4qCuvrQ7Uv+VJJE+aj2fdiCSx9ru2wSdtSOkK+9NGPJi7z6bMfY\nSe9Bh4sQ0tG0y5Fq9kw5KcEgfQFBGEv3rR8n7dt1DnHqbfn6dblsSQRs1hBoK4k7Y5GQuFBwEUJ6\nHnFiZDae0M5p/Fr0aPElj6VOlt7HVx/Ld25hpKmrZfcJpC+tEDamUgmYmADGx+Mfm3RsUVBgkbyh\n4CKEdBx5J1DrAqBbtrhzp7TQyatfF74+pBSDLcCA+vCdaxwS4tuypVGwSduAaV+2TU3Vn5f0V6nU\n7wc0um1hjpemUvG35xOPsr1SSSe4WjHBgWKMpIGCixDScbS6vIDPRWpGv74+dGK85EsBpi6WbBNB\nprEr04edgxYRs7P1Ik7Eke7bFm/Dw+5+fUi9rzjFVe3QpOSvxSFumDQJeX4WGJIkAAUXIaTHsZ2K\nzZvN8jau9QRbjRQyBRrzt7TT5auNZSezDw4Gws2Xf6ZLUEStjagF4PCwEX8yJnHNokorSIV7XXzV\ntb8u8AoAc3NB26Oj4W6XT3C1+/0VKLgIQMFFCOlwst6oXE6F7bi4QkatuEHaos92lPbsAWZmTPhv\ndtbsU60Cy5cDAwPGQRIRtGaNKSOhhVOhUN+fCKVy2Rw3NmaeL18etCOV5mV/LdLEsQLqK9bL2PVv\nW6Tp9jR2+9Lm1q3BvkNDSEWebhchWaHgIoR0NM262UWF3ppNmPjQjIwYd8cXlvMt21MqNYbldPu1\nmhEysv9ddwWvudy/QiGoRm8XaLXRIkp+u3C5YRI2rVSiQ5B6soA4ZHYuXB6kaYc5YMSGgosQsiTQ\n7k7UuoB6xmAzxxMn/BWWyyTnVCyaEJzkWLkS7+3jikXTtl7mx7d8kIzDTrD3ta3drrAx2K6YFiPn\nn+/vw943zrJErabVeYik86HgIoT0FGH1szrtBugSHbZzIzlQhUJjaE27SNrZsWcpyr52aE+LIe2M\n2WPTbbgeR51T2H6+9+uaa/zHEtKNUHARQnqKNAnKcuOvVIxwsWcG5pVgb4eZfLMjZTw6B8p2uuwS\nDbVaMM4wYekLdYmYs10se7xAELqzx+Ai7nWzxVeS6+07plOS1TthDKT9UHARQnqOqBut78Ys2+OU\nMUiDS5zY2yS0F5UDZZ+jq2SEvb8WTKWSEXRhgsl+rVBw55MlKYQalnflm8kYhcslDHPPWk0njIG0\nHwouQkjXY9/wp6ZMKQGfmPAJrmbfoLVrJGLD53LJOKPypeR1O2He5ZppQeLK1woTToC5rq7yDHHD\nta68q7GxYNyuc0hDpwgtQjQUXISQrsfnEiUlTogsbhu+10TkaLcnTt6VHB8miOxzjjoPu+0o4TQ1\nFdTUymuJJD2jUNclS4tdm0zg7EDSbii4CCE9gV1AU1dLdzla+rcuOholmKJu2lH7uFwuCaeNjZnX\n4jhE9n5RpSwmJoI8MH19pF3fuCcmjNACTC0wqe116aVBiYg4yfQ2OgwobeiQoqyl6BqXb1vSkGne\n0FkjYRzX7gEQQkie6GKcPuTGKG6TlFOQEJ+uNWUflxQdvtu6tV6klMvBLEQ7BytpX1E3eikBodeT\n9JWA0O2J6JEkfnm8bp17nHEEqd7PzkMTROTFfR/kepbLZjWBsIr7ccaXhlbUbyPdS2aH6+mnn8Yr\nXvEKrFq1Cl/96lfx05/+FJs2bcLc3ByKxSJuvfVWFOxyx4QQkjP2jL24oSk5LkuifFTSeFhulrhN\ntrtWqUQn/ofN6gtzW3Ql+bTFOdM6OXJe0veePaboqrh9QFAjTEjqHIUtO5TVoSQkLZkF1+c//3lc\ncMEFeOyxxwAA27Ztw4YNG3DVVVfh+uuvx7Zt27Bt27bMAyWEkLi4XK604iLOcb5Qnx0+1KICMOG5\nwUHzWNw1IWrGnnbofOPWv7duDdqcn483bpvR0eD1ODlnLrQYknNYt878Pv108/rMjAlfSkHXv/gL\nYMMGc1yxGN2nXVNMiCumkoiuLKKVLC0yCa6HH34Yd955Jz7+8Y/jj//4jwEAt99+O6af+0bZvHkz\nSqUSBRchpIFmOgmSC6WJM5PON6Mxzgw8F/YMRJ3QLehq73qfqDy0OLjcr1otCAfqcbrGbT+XGYqu\nGY9h6AkC9nlpXvCC+pCjDu/KotZCWH2xpLMdbdEUNnPUJsvngywtMgmuD3/4w/jMZz6Dn/3sZ8e2\nHThwAP39/QCA/v5+HDhwwHlsWX0qS6USSvxXoCuh/U7S0szPTtp28xiPqw19A0+a8+Rqq1JpdHqk\nEr1rIoDMLJSfubn6yvSViluk2uNPin2cuFt6LJOTQH+/GcPcnNl/YQH4yU8CsRUm0oQwty5skXLX\nsfp4sjSpVquo5pyUl1pw3XHHHTjzzDPx8pe/3Duovr4+9PX1OV8r89PcE1BwkW6k2YLMvsHrchC+\nfC7bUfE5R/asPp175hIdY2NGzEiYDgDWrDHPpTK9nb8m49YzJzX2jECfE2efl+yn3Sq9ILb+ffBg\n8LoOw0o/cYnrQPnCvkncRX4X9g62EbRVq/WUpBZc//RP/4Tbb78dd955J44cOYKf/exneOc734n+\n/n7Mz89jYGAAjz76KM4888zMgySE9Aadku+SJD9H7+sSE6627Ru8zrXyOWC2EJCQmK+fatWIJhc6\ndDk5aUo4FArA2WcDDz4YJKVXKoHAcM0eFAEUNREg7P9n+z0fHHSLQ/v/9htuCLYnrc+VxjUMC/s2\nq1+ytEgtuK699lpce+21AIDp6Wl89rOfxV/91V/hqquuwuTkJK6++mpMTk5iVLIsSc/QKTdN0n10\nW76L3IhtMaJfCztWbtxRfyeuBHlxlvQY9N/d8DCwbx8wMmJysmxXanS0frHrctk87+8Hli8Pamr5\nkvNtVyruexX2/aDbtbfXamZc9vWS0GcSwsKOLuzZnnlEkuj+E5vcCp9K6PCaa67BZZddhptuuulY\nWQjSW3TbTZP0Lq26qbkEVxRarADJk7x94q5SMSFBCXvdfz8wMGBqTxUKQV6Wbl8YGjKu2MCAaUOf\nl855EtEm1eTtkhWucfkSze0wqX5NirFWq6avLVvMdqmjBYTPxIyDFqxpQoN55a8RkovgGh4exvBz\nlQNPP/103H333Xk0SwjpYfK4GaW5qflm4OnnrsTzYrG+Wnscd9cWXbaT4svXCps1NzYWuD5SpV6Y\nmqp3jMQ10nWuzj7bPFZznera0M6WFEgNC2tqoRY2YUDa1ugZmkDweGwsWGNRvwdpXHSf4Ipy4lzj\nJyQLXNqHZIJfRCQt7frsRAkuncszNRUIlelpYNcuE8KLWoLHxuXwRCWe29dH9zU6asYmTpeIwH37\nzHOZ8QeY0OPZZxvhddppJodLGBgwPxdfHG/8SbHDc3HbGRurF3PNcNHDnHq93mUSmG5BwqDgIpng\nlwhpNa26qZVKRthI0rv0LTPswm7GPpfMzpeSdl1J4dKX1K7S4xofN+HBSsUUMZ2ZAc4/3+RlrVlj\nQosnnAC84x31SftSHmJuDjj1VOB972t02vS4XUvkuNw3IBhjrWbGtrDgXuRa2tDXBgjWaJT9XNdX\n1leMQsYo/Yto1qUwwj4r8n4knbHIdAsSBgUXIaSrSHNTs0WChNuKxUZBYLtdPifKt2KZHfrSIkvn\nau3ZE+zjSgqXvm23R/oQjhwBDhww4mlmxhxXLDY6SyIgJyZM4ryUSJTZjuPjjaE/X1kK1/UXYVcu\nB6JIhyXtNuzjZSy2GKvVgms6NdUouHyOpb62emwu7PfZl09GSBYouEjHwFwJ0izCRJrckH3HSf4W\nUO926BmAGvtzbLfvKuAZ5ZrYSesiwOQ1ERNf/GLwuuR3lctGHIqYmJszguvss+vztfT420VaMa1z\ntNJ8j2ihaQtsGUdSB5XfZcSGgot0DBRcJCmt+LzYblVYErnveNlfhw591dN9Ls+2be79JOQ4NGRc\nKylwOjjoD5/p0JqLqBmJ+tzkNTk3O8yow5L2cWG5dOIMTkwYZ0vak31GR+vdLt97Itt8jqRrfy1C\n04aq+V1GbCi4SEdDEUbCyONGmKQNXzHSqLwyERyS2+TDNRNPbvxDQ+4lasRpq1QaQ2eucJ24X5de\nGoQfJc8JMK/JgtpyDq5z1q+FhRn1a3o89jG+v3XJV9OTGeRHBJ6EHV05Y9Jm2HW3ies+EpIECi7S\nVqJuVBRc3UXY+9Wq9zKqnyyCy7feYNxQmO3IuBLlbZdH9pmdNa4OELhG8vcjQlDni2mhpHO0tFgR\n9JqKgBFdo6PB32YcYeQjrltmb9d5bWEzSeX85+bM7+Hh9K6Ubl9+8zuI5AUFF2krnNXTW3SD4MrS\nrvzEmR0Z9c9EnOrpPkfsvvvq23eJSFn2R/YbH6/Pc7Kx89W0oNPnrPPH5LnPERIRNzbWuJajns0I\nmPanpoLirdqpEiFpL1xih/9k7Ug9Nld4Vu8ThnYnCckKBRfpOFjLhnQi2lUBwhPt9f6Cvb9eusf3\nefc5Ytu31+eCyev62HI5KM2g23D9HdlukasumLhttthyCVxdIFZm/M3MmFBloRAk9C8sxPunS8/u\nDBN4NnaumD3+rDRD3NNR610ouEhLiPMlEvdGRTqLMMEgr7tey9MJa6VIj5rF5wqf2c/1uOJ+3rXg\neOop81jyrUQoiTCp1YBvfxv45382ZSMAU+AUMILHFnI6f6tUMm3qcck+erkfwL3OoUuQuspC6Npm\nIyNmnHoWaFQbui392zWeZn2e0oqjTnCCSeuh4CItIYngakbbpHlECYak4jnttP5mivQ4ropdtsEX\nckv7eT3llCAENzcXFC89fNg4SqWSKYI6NWX2OXzYHLdsGXD88UZwzc4Gy+kcPAjccIPZJ07ZCnm+\nZUvgiPkKm+pz1UJt8+bG8xLxJSFMLcTiEhbuldf1LErXeen3pdWfJ7I0oOAiHU2cLyV+eRGbvJ2H\nSqXR8bCdKp0f5RJoUWOKSi4XcSTtFYuNZR/WrQuEy+gosLgIHD0KnHWWcbZ0EU+Z3ejqV0ooTEyY\nUKC4Z1LFXq/lKPlY8/PBDEhpt1g041hYMH2HVem3c8vihg3lddf11gJMl8FwCSifMLZXB0jjpsZ5\n75lG0ftQcJGmkceXCL9suos4+TQu8rzhxBE3YeNwOR6+4qW+NvTsQl22oFTyly2wZw7aY7Cfu5K/\nS6WgbtWRI0ZsnXyyWajaLuKpk/G1eNT5V3qf4eEg5KjFS7UaCClpX/+Wx/YMSld9rYWFxpCn7K+J\nen/lXFzhzbjOma+PNO6X9Bn2GWcaRe9DwUWaRjO/RPgfYWeSVnDl+VmxnZK0uFwtoDEJXe8jYmtu\nrn5pGF0jyxZvScSh7Ds6GizjY7Nrl/n9xBPm9xlnmP1mZoCXvcy0MTUVlFGYmzNJ+O94h9lvaip8\nPJIjptd5tJc7EoGpr83gYH1drvHxQFglfc/CrpktUO397dfD8g+BeLNJ44xRf8Zda2eS3oeCi3Ql\n/I+Q2KQV4b7jgCA8J49lf7ttHUbcutW4QYARIDMz9blD1WqwCLO4WnIcEAi6YrHxPPSNWs/c0y5J\npRLMAJydDRypmRngnHOMAAPMa2NjZv+LLw7O4/77jYiqVIwYA4xYGhgIRJMvfCqPK5X6beKO+Wp7\nZSEqv84ej/26XYy1UjE/cRa9DjsHn2B3hSnt8ZLehIKLtAR+iZC4pP2spBXhtvOgF7UuFoNcpLDx\nSRuusKMILtmmBZ59nGvMWtjEXVRZ+nn+84Oxz84G7lWpBPzJnwT760rzBw6YvKxiETjzTOANbwja\nlIW0dQhSnmtR4jo/+/oIkm/mwhZzLgGjFwH37efKq7Pbl/GKCBYnUlfuDzvWJiwMHeaa8buyd6Hg\nIrkSlveQ5fgwkuZ3kM6mne+dLvoJ+F0RF64bt25TvyYhRsAvCmzRIoQt2wMY8VSrGafqsceCfTZv\nDkSAdunm5uqrs4+PGwHkqlclgktTKBghd//9RqyJK7Rnj0nit/OpbFy5a/o1+z2Q33byv2ALQTlH\nl1C0j0uCT8D5wtD2e2S7k3HaJ90NBVeP0q4/1qz9UnCRPLBDXEmOkxuj/OhZd2HhSZ8gkOP37DGC\nRdwz26myxyoV2l24zkvakPCZ1Ojas8eEA+0SDmvXuh2Y+Xlz/Ac+EBROFRFXqwWhylrNuHeHDwMP\nPmiOFWdMfppVTsFe8sgu0hrGzp2N762E+KrV+tBums+PSxy7PjtR14bfY71HTwgufjAb4TUhS5mk\ngsvlTGgHIolwcDkyruPtMKM95lqtcZt+rtvU+UKSdzU8XC987NmEd91VX0JCOP54s+2OO0xbo6PB\nYtaSazY4aNodGjLu1qpVQfV4SarX49bXQ7bb11uW+hkaik5kj1oEXPYXl05fLx0mjHpv9Hht1yxJ\nniC/iwlAwUVyIO2XUF7H59UGWRq4xI2dxyVMThrhomfXRbWnZ+8BQZ0qKeHgCmVVKsYtGhoK+tKz\n/0R8+T7LIqomJgLHTIsN6ccWaq5JAY88Eryu88TsEKYcq5cPkppbQDBr076+Mhbb7SmX3Uv9TM6C\nYAAAIABJREFUaKHjmlggz115UdKOvCbtyCSGqPdWn6/rPMKEeBoBxu+x3qYnBBcxtOuPNalVnvfx\nebWxlOmlf1qi/g5cgkujk6WlqnrUzVi3r0OKcnO33R1bUEidKjsfKey87AR/IAgnShK7FilAULZB\nUyoZoQaY8KO0MzdnSkyUSqachGb58uD8JHQJmPFrkROn/EHYjD0Zn329gHrh6hNcgghZIKj5NTxs\nBGJUza+0pBFc/B7rbbpWcPE/gUa68Y+1l2703UwvvQ9x/w58Sdz2dYjr0kbldtnb9HfY9LRZpqdc\nDgRBf3/jjEndnj5PHTbUxVDtfCffuGS5Hz22YrG+nIJUnQdMOHLdOvNYkvG1oNU5UmHJ4dUq8Pd/\nHzh6gAlRDg01FnXVx2gRKzMvw77vbFElgtreLuOUfsLuMS7xSkgYXSu4ulFcdBNpb8BJj3H9t5+V\nbhcOvSR+OgX75ikOkOQ7AY032q1bg5Ca/X1jt6dDU/K6Lgrqqq1VqwH33Qf8+Mfm+aFDZlt/v7mZ\nj4y4K7jr/sWdkhwuHYZcvjwQXPo4LcZ8Dp++JrKPhArHxgJ3TWpUzc3VJ5lr8ecrqSDtn3tuY6jT\n94+zDpFm/ac7ap+oe0xUDllWsn4H8Huk8+hawUXCadcfa9Z+Kbha90XZCpe43V/6LjcIqK+tZN9I\n4/wjp4WVXvLGlesTJylbtyfOix0ys/eX14eGAmGmc7JkhqMWUHY41VV0dX7ebJ+bqw+LyutyblKr\nqlQKioXqdgHThszM1Ndk2zaz9JA4W9KPJN3bn5s4YWLXTE8X+jPRyVBw9R49Ibj4oWokKuekndes\nW8LBrbxOi4uL2L17N3bu3Il//Md9ePjh1di4cSPWr1+PFStWNKXPVrjE7f6suUJYaZKm5VjbjRXh\nYYe0ZJvPXbLRM/vCBIHrb0dmGS4sBKFBKeUwM2PKJszPm9IQGj1+GbNNqWRCdhLqBIzAGxiod6nC\nPjuu/Kr5+fqQnJSbmJ93T1RwfVZt8ahdvzCy/CPZLd9dpDOh4FqC+L6UWvVlov8rBTo3HNwqsbBp\n0ybs3r0XP/7xfjzzzFEAwA9/CNx88y0488yVWL9+LXbs2NH8gSwBtECS57732CXWosJcNi536eDB\nerECGBdI8qNcfdhhPhFCsq8O90lekgidoaH6EKB+TZLtbbGivwtmZ40AWrPGOFaFQpC/Jfu7xqfP\nWYcYazXTptDfH5z/zEyjY+i7Jnq8hUJ9qDHvv9swp7SToCDsbHpCcJFspJnynFe/S53FxUXs3bsX\n8/O1hteeeeYo5udr2LvX7NcspwvI98s4y5d+kptlHmHvsOPjtm2LFHGXJKcKqHewvvvdYD3DMOFn\ntyfbdCmE8XEjXkQMXXqpEWLFYv0agFoQ6bwwnWzvEkl6fNVq0LYcU60G6w5KH4VCUEtrYaGxlIOE\nEaW6veSa6ZCi6/tIcF2nqSnzeHra/X3Wbqe1VXS6IFzqUHAtEcJugu38Muq0L8FW/4e4e/du7N+/\nP3Sf/fv3Y/fu3RgZGcl/AMj//c/ypd8KwSXEOTbu58EOA4ookfwlIBAlupyDr08tGMbGTHkKaU+S\n0w8dMoKmvz9YnmfdOiN4FhaAs882FeCPHAmE36mnmjbsGYB2vpTeVqsFIk1CfnIeQ0PmsYwPaAwF\n2gnx2k3TOWd6LL7woC3y7Or3smi46zjf9rSfoU777iKdDwXXEiHsJuhympr1ZeLLQQnLW2klrf4P\ncefOnTh69GjoPkePHsXOnTu7RnDlSTPHFqddl7BKMh5dkPS004AvftGsNyiO1fbtwDnnANdc43dj\nJNSmHTMJP87NGRElld+187RqlRFcIyPm+cGDRqRJUnrYNZAxyH5aQEqZCSlU6sPnYIuTJe3LupJ6\nCaXly93HyvUvl4NyFDLzc82a+vUc9aQAPR5bXKYV+J36NyN0+viWIhRcPULSG5N80elp6kC4lZ8H\nYYLGLhAJtEcMtLLPffv25bpfp5HVRUo6W63ZxP1s2LlF4+Mm7KXdK6C+IrxQqwU1r4pF49xocSFi\nRY7Ti0RL33Lt3vpWs61YDFwwvY8+L31dh4eNUJufN9smJwOxCBhna34eOOUUI+ouvdS0Z+eFFYvu\n9SDtWmFyLeRcJIwqEwBcNblEBGrEOSyV6heMlnOyRVgSmvm90My8M9I5UHD1CEn+YF1Wf6fG+tsp\nuFrR7+rVq3PdLy6tnCARZ5+47ms7c1TCQl2C/dlZWAi2+UKItsCS2YULC8D557v3r1SCtqenzaxB\nCftpIXP88YEIEQcJMO3b5yDnNzho9l2zxmzXQm1oCHjgASMkZ2eNADv1VNO/iCIRQnYhVZ+zrcdx\n5EjgpK1ZU9+O/U+irpEm/Ug9Mrkumzebc5VzGh4OSlj4/tkUolzAPOlkl5nkBwXXEqRT/rB9X8Ty\nWrvH2Yr+N27ciFtuuSU0rLhs2TJs3Lgx137bKVyiaOdnIixvSMbjm2TiOl5yjMrlIPdp+XIT3jt8\nONguCeVjY/Vt1GpGeOhwoYgFcY7K5SAsZ/9NPfKIKSxaLJpcL13Cwk6Ul9f+9m8XserM3TjriZ14\nan4fzjh9NQ7/dCPO/5X1OOecFcfE3f/f3rvH11WV+f+flAZLARsQaSSFhKEwpVwShltFbI9ibcGh\nE6Fy+woNF6+DWpkBKipNZywtMg5FEW8jpFiGdqaOKTK1XPR3AiixKCSopXKxp7SFFLmkY6mFUs7v\nj9Un+zkra1/OOXufS87n/XrlleScvddae52z1/6s53nWs3T8lc7BJZY87SKU9orlyS8FRW+vV67O\nAyYi0zVJlPfTadOXc+aY/2fMMOeIG1SvftQbgwftRCDlApU3PpHqg4KriinkweQ6R2eIjpugcl1x\nWzoGRVwB+vhSxpYlXScATP3zn9G0ezcyAcc0NTVh6tSpyTWignAJmbDko3Hi+r66vgOuYG9dhr2B\nNWCsLCJ27ONbWowlRlYdynn77gvsvXeue6yvz1sFCeQmDrVFVHOzJzKiXOunP3A+TntqLT761ha8\nH7swFsCOV4GHX7sT//27JvQ2n4JnR6/AzJkmXkoy9Ytlq6PDWOtSKW/BgMvtZ7dDxM199+WWK3s6\nDg66XZNStxaaYiUUCxmQm1hVu3H1ik0XdvvjnJhU8mSTJAMF1x6q0aRbiJXCFTcB+D88hLD+WbLE\nvS9ZIf0adl1RyyzEzepXZ+y8+irwj/+IsX19OOUDHwCeew5btmzJsXTV19ejqakJp5xyStWkhCiW\nfNpSynbrSYC23Nj3jzw4RXzI69o1Jsd3dXmJSaXM1lbgkEOAffYxFrCtW4HXXzcCYs0a47qT1Xip\nlLciEfBSIoiIkLitcePM61u3mnu0ocHbcFoLlP/5nx04bd1afHd3JufaxwKYkd2FGcjga3XAiefv\nwMKFY3OEpSsuym8lpv2aFkxieVqwwCwyaGkBRo821zw4mLsVkyuIXQRtJuMtLNCrKmXxgZxv4xLL\n0kdxU8lWZpIMFFx7qEbBVSh+bpOg6w+LW+nudguufIja/0kIrpLys58Bn/gENr33Yzj08cexYp99\nsGPHDtx660NYvnwltm17Hn/602E477zZaG6eiunTkxNbQIX20R5KFT8TZmmwrSh2sHuUGDQ537bi\n6dQReiUgYESSxE9JfTpoPp02WeZdbjZxnYl1TISI1NXTY9I5AMYNd8kFDwGztgC74cvJG7fg7Bse\nQn29t2JWx6lppJ3SHukLeyNuu4+lnzZvzhW1QpAwaWjwrrO/3/SNiFPAjFGyIlILL7sNup6ok1JC\nwqDgqgDiEAaF7Fwf18PMHogKNZW73iuHGEiszr/8BfinfwLuvx/40Y/ww54PoHMf89bYsWNxzTUz\ncc015kFmW0RqlVJ8/vlaGkQERPluR2m/bT3RrjO9RZDcV7JRtF7BZyPxTnoDbbHUSJtkGyCp89vX\nrcSPQlKUvD+7C2efsBKp1Myhe1xnjdcWNxFWMr5Fcc2J2Gpp8YSczpIvW/40NLgneLIHpZQjAla3\ntbXVuBsld5d2xbqsdH7vFYPLOkdGPjUtuCrFhx5mPYrSlrCd6/1it4JW6+gAXdf7S5YYy1YmYx4C\nbW1mINQzbqA44eCaIYetLCr2M03ks3/4YWNG+MAHgCefBN75TqAn/LSRRjmtjvnU7XesCAfbCqLf\nt/+XB792R+pUB65zBBFIK1d658nr9vH2eTrIXl6TAP2WFi/lA2DSOwxseB5httSxAHYPPD8sTkys\nSYODbiuRn/tOW/3065IOQ/5ua8u1gNlB/3a5OsZOBGk6bcSWZOYX8QX4fw4iXOP+zlJw1SY1Lbiq\nwYce180e5VpdDw9t0rddJTK4StJBMefreuwAWTk37rguTVJBrgWxcyfw1a8Cd90FfO97SO9/NtL/\nbt6Kkrl8pFHpgksLCb9jC7HSaqEW5I60EVHW1QXceqs5T0QCMHxLHddkY2DACBYRXtpdKffH7NnA\nyg2HYcdqBIquHQD+uu9hORObjRu9FBJ+E5vFi4dfr/SxXuFoLzTQ+0G6hFmUz0L/zmSMMJSxDQi3\nttkECb2Ret+SeKhpwVVO4rDEJGWhi/pgcg1+UR5YSQ5MFTXoPf44cMklwNFH45ffeRLvO/sgpBBN\nOFbMNVQJcU5M4jzWvkdFLInoiSoa9MSlrS3apEK7CyVv1yOPmESl69d75Ypg23HAbPTW34kPBrgV\nH62vR9Ops3Puc7EaiftNVlvq65L69DUJEigvr4t1TotEwJQr1ySJTF2Z5PVY6KpPXgsSTn6B83ba\nDvu8oM+yUjwqpHxQcKE8D2k967IDQ6PemIVa6PwGIEHM6Lp+v9QR0tYxY3LbKoNo3Kt78vmsyjaI\nvfUWsGgR8K1vGb/rhRfigQV1eN8/FF5kRQnJPCnFgyboIRi17nzbGaXt+lzXyjm594PaLg/+iRO9\nrO75ZEuXFXoS8/Xxj5tyJ03KdZk98MBUPPqe9+CDAbsarB7bhDvumoq39zw5xF0neyrasYfyvuTU\n0sJRb/AtCweCrknis9Lp3Jxa+cSI6TqCPlfbJeq3ECIfqsGjQpKFggul8dHnc0zSN2bYwyNq7hlp\nf3u7t/pHYifkby3YpOxiHrquVUtBD8qSs369sWodeCDwxBNAU5Pvofled7UKrnI+aPKpO+jYQvrf\nPqelJffesl2LmiVLjIiR8wCj45ubzb6L0l4RcDYNDRiWK6ux0aSaaGw0wq211Qidvj5zD3/jhlG4\ncp/X8ZV3vBOnv/lXTM3uycMF4JFR9bhv/ya8fsIpmD9t7ND9bFuXNDoFgz7m2GONC1MmZT097pg0\nlxtRu2eBaCsIXeODLjfss9ULFnQZQO4iAVqtSBgUXHuI+4EW1bwsS5Rl4Cj0Ri227X4DiisGS5+T\nSnkDjs4gLbNPWZJtty/Oh25FzBzffhv45jeBr33N/HzqU0j31CH9A/N2KferrBWSsJzFGZ+jg8LF\nUiVB6/p/Qbdb0qy4BI0WHHLv2e2bO9dbxdfW5sVbLl1qAuQBI7yG0lHMz+L071yG4yd/EPv99HZ8\n7KOP4ObMSpx8+PN46uXD8I83zMa/Tp2KsWPH5liq5Np6e03SUrFYiaty0iRTj/6sRGTKdXR35won\n+ZG+ct0v0q92X8t7mrDxISxer6vLvwz73GK8DGTkUzOCyxVwqQdrHQ+Q5M2g6w0TJUDp3GdBA0pU\n7A1mg2bwQYR9VnqDWu1SKBuZDHDppcCbb5onz8SJAIoXgiMx5iPOdufbv1HqtmMR40B/T8XCJYmC\nbWuyzZIl5oH/7LMmASrgJQOV+0C+J/Y9Y1vXZMWxxEc1Npr3li4FLt0wHw2vbcDZr/wCZ/7bPlj9\n4EyMHz8T7z0N2D8DfHCmF9skyVoBcw2NjcbqNmWKl4ZB2qAz5nd05KawiGLdB/zDLfREVU8M4/7s\nwqxn5Zggk+qkZgWXnjna8QD6/XzrCHtAuh4SQaKk3DemXb89W7dntPY5hYhIPzeCxs/dU9L+ymbN\nE+iaa4CrrzY5tvbaK7biK8JyFzPl/D7nU7e2TAHFbZ0l54jgAdxpXCTNCpC7HU9HhxFIkiVe0ju8\n9ZZxF3Z3eysUpd06DrO/Hzj55NwYKom5SqWAvZffieOfXIa/3dWLQ0btg3Ta7Lu4dWvudQFmxaPO\n+adTSwhaRMo1HHsscNBBphw7qF1cp7ou19ZItqXLjgdzJVO10eN+0GdbyGdf7rGaVD41I7hcaLO2\nNtMXW55Q6ebloBgyP/Q16iBZv3xExVjtCqFkfTkwAHzyk8DzzwO/+AVw3HGBh3MwTpao/Ru08AMY\n/nDNN8WIawzQQd12klI/N6DLsiJiq6XFmyS6EnjK5Md2e9m5qbq6gBTS+LuN/4w7L+vBIb88eChH\nlYgtscrpNtkTRPuaGxq8bPlaMMkqPzlHRKFLLKXT3opAv8lV1FhTTdDE1z7O733dJjuei/c5CWJE\nC66os5Qws3FSlMUqoyhEcEWlEDdilBmnjoORB4tfHExirFwJXHklcMUV5u+99w49JQ6XL/GnGMGV\npCVRCxTtAtNCRNoQRnu7lwBUCzfJwC4WH2191nV1dubm6np06R+xbcUF+O7Uu3Hqx45G2+ue5au7\n24g4u10Sf7Z5s7fXY0+POV5clDoDvLRTp3fQlji9yMbGtjTpc+V9P/yEdVxjm+v7MhIs0CRZRrTg\nijqQJvEwi7LVTrU/ROMUjPnMOO2ZbVgcTGy89hrwuc8Bjz0GrFoFnHpqCSo16L4pe8xaDVLIBCJo\nMmPHINrntbcPP9cWMlq46FXAS5caAabdl+KilOD5+m0vY85eH0H6wzfg2lVnAMiN8RJEEOlAdsAE\n3k+caALlJenxq68Ov2Y7LUzQd9c16dK7YQSVE0VcFTrB5L1G4mJEC658iPumCttqp1wEWZL07ygk\naaFLUlQUVPZ99xmL1kc/atI9jE12Q+kgalFwFXPNUS3dYavV8mHxYhNEDnhip7k5N4xBCyYdW5RK\nhW8Er+89cb91dbldbJ2d3nZb6TTwyIM78Q/fasfy3R/DfdsuwxOdphw7R1Vv7/CyJL7K1Q79uv2+\nIOKpq2t4Hi4gd+GNTtxqW+ts12Yx90Mxgkt21wBGzsIWkhw1I7j45TcEWZIKWVGYBPZDyPV+0P9h\n5PXw3r7dBMSvXm2eEmeckV9lJBaKEVxRLd1+rq18SafNjk72vaWDvHX+pkKx45G0SPMNmchm8b4f\nXoYNbxyCL2MhsnsWvIgLUdqfSnkuQh2AL27RTMaEMT75pDH8ihBqazM/fvtE2hY0SblgZ3DPZEwe\nsYGB3M2xx4/PXaWscQnr3l4v/UUSgsgWxnQrkiAouGKk2pfxB+XcKiVhMXWFCi6XJSGQX/7SbDh9\n+unmyTJuXLSKEqDav1tJU06rn7ZUyY+dskBbodJpT+Do3w0N7lV5Udxw6bQpxxZ2Uo4cu23ufBz6\n6gac9eYvkMUojBuXK3j8Mqrra9HHXHklcO+95u+NG801SEZ9Xa/LVaiTttr3u26PZKGXc0Q82YH2\nLmFtL+gpVBDVolWZxE/NCK5SkGTwbRLYQakSn6HjSwqh0MEpTnen3QbtgliwwHvfeZ1vvAHMn286\n5DvfcQfUlJhq+27FQT4iM+p3LopVxK+OoHYGHSsZ0+0A8fZ2bzNlO/u8q3xpZ1i77HgnOeepL92J\n1F+W4fzTenFqdh8MDnorCm3BaKd90eVKDjHAbKh90EHe666Jku5LLaIA81vSymzc6LZeyWtDSVo7\nc38nRb4TNAoyEgYFV5lIesaUzwChBxW/AHS/8qIEp0YNYI3L3SkPDdutIrEzrvKH6OszW/NMnGhM\nBgcfHK1SEjvFiky/71hcdejylyzxXISSrkHXJyJDi5jWVi+IPWp9knndJsw63bckjcP+7Z9xSVsP\n/ittvtP77muSqc6da0SfpDWQ8kX4dHbmuhU7Oz3BpQP2t23z+q+hwR2HNjjobSfU32+Oa242Yqu5\n2cvrlU57SY5FGIpw9esbPY6JJU4nSo6ykMmvzCiEjXmE1JTgivMmCCsrrJ5KEFxynB2Q6sq47ze7\njlJPvku0g9yJUbBXfUmgrli2ZDYtpFJA6vS3gBtvBG65BfjGN8wOv3V1keoq9cDKgdwQZp2K+7Ox\nH+raYtraakSLjkHSVim9q4QYTHVKE/uec11bOj087ktPJFpbfQTjH/+ItkXnY+mFd+POO4/GQy3m\nHNnyR+q3r7W7Ozeo3XYn6voBI5Zc1idtNevvN3Vu3Gjam0rlZsyXbPVSv5zT3W1+ZIwSN63LAuWy\nThZiDdPXm0/i2yS+e646SPVBwVXgsWE3VlLuuKhuhajoAau1NTjjfpRYEqD4DaTtmBhXmS4Bp9th\n5znSDwI5ZmgQfvpp4PRLgP33B377W+DQQ/NuayHHFzpw1uJg63ePxelmzWfiYFtM9fdJ4rVc7evs\nNEKnu9tzkfm5AOUe0MJH3pMkorp8O2M7APTevQFH/eNHsPSQG3DVj87A/IeM2LnnHlPuQQeZjazt\nelMpE2w+ZYqpa2DAEyA6C75sXA94QfYupG/kWsWankp51jN7wqctbnrFol8i1KDXomKHWMyfb/6e\nMyfa96sUYoiCq3qpKcGVD/lYiPJ1dQHByT0LFVyFxqPo93U8iY7J0PtN6hVWQVsYSXt0oCwQbcWQ\nLkcIGvDsZfjTpuW2wy47nYbZcPrb3zaNWbAA+MxngFGj/CuJgTgEVy0S1z1WbB12+dpiqt1pfmVJ\nO0So5Ah/uLO4SzLSvj7jtpP3+/py2yKiIJUCUsf8GVi4EFN+9CPg+q/ii3Mvx7ZOT/DJvS33gssi\ntX69l2cLMNeoLV32NWoLl+57ue9FWIl1ef1681sLxZ4eL6xh8+bh+9xq16ltZXTVB3hWxExmuEi1\n8RPxUcWWtMm15yshI15wFTMARykrikjyq9Nlxi+GYmf8tjiR+JJ0One/SXld6vLLEu3XFh0Lol8r\n5nOyl+HLoGsLPvmsDs0+D0y/FNixA/jVr4CjjgqvJKa2kvjxcycVa/UK+qzlgSoB5lHbB3gr9FzW\nLRsRCa7EpJrOTgB/+Qs2fP7fgZ9+C7joImDdOpNLQV3P4GDufaHHMH29ElfV0IChLX8Af0Ep7sCc\n9iBXnMnqQ3v7ITlOguNlUiYJXOVz1f1lW7/s+kT8SD3FpL0Jiv+ywzJSKW/CF1dgP8eckcGIF1z5\nDMBhX2rbEgWYG0wPWIW60FyuMF2fvZlrd3duvps48HPbCDJwybUuWTL8+Cji0yUswz4n6Qd9jB2o\n3Nnp5d2x+2WovGwWWHonLvi3q4GvfNHk2Bqd322Q70PdZRWRNvuVSfIjqb4LmzjI/319/tYQ1z0h\nEwIRICJC7G2q+vq8Da03bgRefjnXQibstftN4FvfA264AX959xnA2rXA3/yN81r+/u+Hu9j9+q+h\nwdtSSCxbWnz4tX31au9vGUu7u3OTmLosT7Zr1h5z9TljxhgLnJQtIs4WkoWi+yQoZ5rrOxL3Csq4\nJxKkPIx4wZUPUb/UfjOrfOsChos37Qpzzdr1ABlUbzEPINstkE6bQVdm5VJ/d7f74WK/Jvu32a6S\nfFxqcr36eMnJo1m/3iRMdJb70kvApz4FPPcc7rz4AXzmS63RKi+SIDcFB87kSFrA5uPmdE3U5LOX\n73Znp4kZ0t+JVCo3RmrmTGsy8fbbwN13459/+FWgbRLws5/hf7rbcHyu1sppr6RxcF2H/judNqIG\n8CZ7khNLiyFpv267HWAv1z93rudClLHCvq+1SNJ1CPr+EauarIq0+7iry4wTLjEb9vkV8v2R6y6k\nPjLyqSnBFecX3lVWvgJCsB+6cTyEo1iZ/CxargF47txoW3e4GBzMXVYu8Q1+sSBR+1C7JGRbExnU\n9fWlUgB+8hO8ccVnsXZyB9KzluP6he/A1kbv/Sh1uvqMg2g0yhGvFnd9QZ99Y6P/irZCsYXa4KC3\ncXtqWhbnjF2D4+/+EjBmDNZfcwdWDU4DuqO7nPxel/tU571asiR30heGDo7X1nstMv2QY8R70NUV\nbskXN6kWgLIPo25TPmNrIW483c5864sKx5zqhYKrwGNzHuZ7KOSh4rL8+B0ns7X+fm8wktVKQee6\n6glrqww2dkbspibghReA734X2LrVm602NpofeSDYwaKuwUeOsbHb6RJqekl9b69pSyrlxVBkMkZ4\nze0YROr2zwOPPop3/PTHeP9pp+H9AHaPzn8wlHZE+bz8KObccrJjxw489NBDWLlyJZ5//nkcdthh\nmD17NqZOnYqxEfaVHAkLBOz26+/mffd5izbmzMkVSn4LZPSKWTlOB75L2fL7jTeMBXzy//Vi7qp5\naHhjK3DDDUB7O7b11KFTtc9leXaJB9d12feYWLQktsqvzBkzTFn63hTX386duXWI1UkCzHVbpB5t\n+ZM22nsXSn/p+Ew5ttidMwpx45XiO17t91EtU5Tg2rRpEy655BK89NJLqKurwyc/+Ul8/vOfx6uv\nvorzzz8fGzduREtLC/7rv/4LDflmnSszhViq4qgzaDZqzzD9Vje5Hm75PvBksOvq8oJk+/uBT3wi\n1xWgzf/iVpDzxeqkN5wdM8asZrK3MfFLlBhl0JsyxTzwRGgNWbqOeQA4/nLg7LOBvj6kH9sXQV0Q\nNf6smM+8GgXX+eefj7Vr12LLli3YtWvX0Ot33nknmpqacMopp2DFihVlbGF5cH03/eI5XZMNvzIE\nfW9lMsAkPIV5a7+MY/76GH58Wie2zJqDqQeMRqou/HsZ1h5XnChg4u1fftn73xZHriB5wBNMItQW\nLPBi913jnGu8aG4eLpr0GCGiEDACT69mlDbYdWiSngRUy/1NSkdRgqu+vh4333wz2trasH37dpx4\n4omYPn067rjjDkyfPh3XXHMNbrzxRixevBiLFy+Oq80VRSFm56Bz4kA2hA2rVwaztrYvWcBVAAAg\nAElEQVTcgUwfJwMZ4CVWdMVcuAZQWyDKACzxDUGpG3SZfgOjbTWTQfuX97+OgxZdi23vXIV7Zv0Q\nh37sw0jt63AzWvgJVd1nelCvhQF1x44dWLt2LTIOc8GuXbuGXt+xY8cwS1ch90a1E/UhLlZp1/n2\nPXr8AZuw6M8LMKb+Hrw65xosPfAufGXhPr5lFzK31Z+JpH5oaTHi5957TcB+S4uXrDTKNdrHuWI+\n9bH6HBFLItZcAlWLOllFLWOCts652gIUHgISlZH6HSeFU5TgamxsROOebHf77bcfjj76aGzZsgX3\n3HMPevZMU+bMmYNUKjViBVc+Zmc70DTKOS70Nhc6i7qgg9vtB56sCBJk6wyN3T75X5658l57u2ft\nkgHukEOMy9G1J5o9WAK5K5I0WjS6LAa6Hfr/xe2P4oKVc9B//KkYl34SFx9wAFzkO9DqQV0LxKQH\n1XK74h566CFs2bIl8JgtW7bgoYcewsyZM3NeL/Z7Xk0EWS5dEwfXZ2qPDfv89VUc97+LcNaLtwOf\n+hQ+O+5p3PadBrzV6ZXnErS2Nra/q2HfJ3HpdXaasUQy4wdNNMLuTcAbs1zHyjiSSuXu3WhP2lx1\n6EmgbWWL6ztH8UTiILYYrkwmgyeeeAKnnnoqtm7divF77Mfjx4/H1q1b46qmqinUZWW/pvdfk4FK\nD7L9/blWJdfAJIOwNsv7oWe+8r8Ep8v/Mjg3NBi3ox7o+vrcWbDteAxdnyv+ImhQ/8D73gSu68QF\ny28HbrsNP3nyHLQeEG5l8XtfuzjlWNegnjTlFlwrV67McSO62LVrF1auXDlMcFU6cfWtHYcl2AIq\nitsPgMkNd8stuPLWf8fPx50L/O53wCGH4Lx07nF+gtblLswpP4RUytyzHR1mrNGWXVm16Nt263/p\nF7Fqy5ZHuu36t4xlkj7CZf3WdWgR6HecphatrqRyiEVwbd++Heeeey5uueUW7L///jnv1dXVoc6x\nJ12nGhVSqRRSVfJtDxo0CzXlh5VfyIPBL2A0kzFLy5991tvSo6fHP6+X/be0xV51KGW7xJstEKUs\nv5murGiS90PzVT35JKZdfYkJ+ujvB8aPR+rA4ceH7QUHBKf6iDqojySef/75WI6rxNs7LsEVlyWv\n58FdmPbc7XjjK/+CZw9+H+788C/x9e6jMP/7Xj36tyZo3z+bKNe9Zo2Jtdy40cReDQ6aOu67zz2Z\n8yPIqi1tcY0jdhku9L0Yxepmt8f1fz6UezJEkiWdTiMd84BftODatWsXzj33XFx88cVo32N7Hj9+\nPAYGBtDY2IgXX3wRBx988LDzOktpJoiRoJvMds3Zq4yCZr9R6tXlyN9+iVJ17ILMMDs7zSyztRWY\nMAHYbz8vg7RsvBvmGpDrF3N9Og0sW2YE2LZtpryBAS/JoR0IL+22kxu60AO1ftgMnbN7N3DTTWaz\n6ZtuMkuW6up8RVEcq5ZKQSXNwg877LBYjqvVB1OkzzKbBVauxLGf/jJwwmH4/ddW4acvnoR9AKA7\nWj16oiRWJL9FK0F7HkrbJLfV/Pm511CIm05bAPXm0679JsW6ra2FdiiDqzz9vt//cq5+vRjRRME1\nsrENQQvs5b0FUJTgymazuPzyyzF58mTMVU/WWbNmYenSpbj22muxdOnSISFWiSR50+i4BFto2Mdp\nszsQvO+gLseVPFPElhYYdg6tzk4z4IlVzp51uixS0k69lDuTMcKtvd1bifTpT3v7LdrLvl3xJVp8\nSr3ysJC22e1INT0DzJmD13aOwQG/+Y2374ijzfYM248gF2eQdSFu4rKYxMHs2bNx5513BroV60eP\nxuzZs0vYqsJJWsy6HvqBn+WDDwLz5gEA/vcjt+GSOz+EEwGcqNqb7+ev3XZSp9x3Msb4BZNL/6xf\nb1KtyG9JeFrIpEVPBOV6XPn37HZL2+1j5Rg/F3/QmG7H0dWaxZqUl6IE1y9/+UssW7YMxx9/PE44\n4QQAwKJFizBv3jycd955+OEPfziUFqJSCVoNp2MI/Abpvj7/jZztevzQA4idaVrwWy5u17F4sbEw\naeE2OOjFY8isMJMxboP99jOuRXsloe4TmXECuXuF6YHUtqRpJK+PXnJuux/t/tLu2ZyBMZvFyY99\nB7j1euD66/HNV67E/OZR7g6B5/qM8qCxrXHlEDqlmjVHrWfq1KloampyrlIUmt5+G1N37IiraYmS\ntJiNbD357W+BefOw46kM/ve9C7Fu8mx0/sso/OlvcssJmyS46nKdo1f9uUQKYJKbdnWZcULCbrdv\nB444InfrnULR5xdqbbbHYjsVhD1+RSlDty/snqgk6zOpPooSXKeffjrefvtt53sPPvhgMUWXBT/B\nFTRI2zNQLdBsy47fUvB8sWd7dt06R5b8L2JCv9bR4QWnhgk6O9+OdmHogd4VVCuDvAz03d3eOXrJ\nt1jFAOOa7OjwVlz29wNN2IwP3ngZDtq5DV9qfwTveHUSMhu99tp5hNJpT2ym0/5iVo6thAHTbkeS\n1tcoZY8dOxannHIKAAzLw1VfX2/ycB1+OMZ+/vPmQ7r+emCvvZJpdMwU62IOw/lZPvMM8JWvAA8/\nDFx/PcZefjk+Vl8PAMjWue+zKPXoiY49sWho8BKNyvZhrhWHc+d6uzToCZj8LvYeSadNkmIJbbAn\nP1oo6mty5f5yxYK6rGZSlp9IkvOiUknWZ1J9xLZKsZrwuwHjGID1AKXL0xmb9U1ruxN1pmk/N1bQ\nA1kGKckMn0p5Fq2WFm9fQz3opdO5G0EvWGDOHxw0QbNSrt9sW/enK6g2lfIsTdIu8TIfcURwbp5U\nCkA2i/859y7MuO8q7Pulz6PpW/PwiVbz1V261Fu6Lg8nEV6plBfvpuPapM2u/tN1u66zEkRZqVmx\nYkV4pvmBAeCCC8zOyMuWAe96V2i5NdWfL76I1Ip/Af77v4GrrgJuvx3Yd9/Q01yWcnvsEKu1JB2W\nMUSO0Ru8T5tmJkVBFhm5fxoahmdzL+bz0hNC/ds1QZUxQwhbeekKd5D37Wu1x99CSNIVWVP3RY1R\nk4JL33C2KJLXJK+U/K8DPP0Em7jB5IaxA0z9Vr6FuRP9XJ6Cbs/SpaactjYTHLtmzfA4r7Y2U45Y\nmlyDrx0/JeW7xIs+3xVUqwfa3l5TvxzT1WXEnivLfDoNpI75M/DpT+P0R/6IH338Pnz6Kydg963+\nVkbJCaaTIgK5SRG1+1N/jq4tiYJcznERNAOPs85i3CFjx47FzJkz/VM/NDaaeKQvfQk48URg5Urg\npJNC2xPnteVbVlR3Xb7t0H08ZucgTvvVTXhv/3dR/8nLgD/+0VeMBo0ttvtev2bHMtn3n9z/c+YM\nX0yTSnn3nx63ZJNp+96yrzWfPl+yxCvP3ldRW5uilmv3lyvcwYXdh4WQpCii4Bq51KTg0gSJInnP\njhHQv10xS0IhN43rZtMxUq4y+/rc1xAUoJ9OG0vT3LmetUlfkz17tgNvQ1M1wP3wWL8+t20bN3rW\nNduq9+L37gFaPw18/OO44d13Id07BstT3h6Og4PA6NG5MWjadasfSHZ/iGh0PZzsa0h68AtyU8Q5\nk07cHTJ6tFkteuqpwJlnAosWAVdcEXMlbqJ+TvmKznw//6Fydu7Eab+6FR++/etma6m7+oBDDw09\nV/8Ggl3gdiyThAjo8/X3R3Jr6cmTTLwAbwK2YIG3OrG31wuYt5Mn+4Vg+LVVxpJUyiyuidrnthVL\nrlm/rwWbn2tRjtV9UsykhqKI5EvNC65iRZGIEL/BQOpw5eiyzxHTvT1ghFlZurv99yHUv+Vv+X/Z\nstyVefa5MhjpFYOA/+ogv7r0dW7cCEyaZP53xXul08Cja7Zh5n1zcWjfQ7i9YwWeH/t+tJ8FLPmu\nOaalxVsEkMkYwWVbsgTd73ItdpyXDii2CcpvlOQMt1BLVEUwezZw7LHAOecAjz4K3HorsI/Ziqbc\n15av6Mz7YfzWW8CddwKdnTh03xNNAZMn59nK4W0I6zOXcLCFzr77etYlu1yZ8NiTE5kM6de1ldhu\np6uvbEucX1uDRJJ9vbqNfsfbbSvWilzIdzdIhLo+q3zKJtUHBVfK/HbdAH5Bm/pY/ZAOch/aObqk\nLHsAcYktHZsgdfvdiGGvadHx3HPmR9wIMju23YXSBr2NUCGrg4QpU8zMua8PGDfOiDCp48pjfoEv\n3XspcOaZOHO/flw7Zz9clsp1bWzc6M3GZd83Gaw6OtwWIt1nenCT/zMZ73Pu7TUeMnEru2JjksL1\n2SZRZ+KD+KRJwNq1xsL1vvcBP/4xcPjhsV5bRT2ksllg1SrguuuAd78bWLECW994L44uQmvlIzRS\nKS/myXazNTebH9kPMZMBVq8GHnvMhN1t3Qr85jfA66+b7/7OnZ6b0ZVbUI9Hdltt7NjQ5mbTzo0b\nc12KMrak04V/lq4Jpl85hViRC/nuRhVcpbjnSfmpecEl6Ac6EHwDaIuPDjwPMmUH1avrt5P9tbTk\nxiZIjJF2I+qs7JLAVMq0hZB+T3LspFKmPglstwe8l192l6PN+H6CS17Tx+jZciYDPPIIkF69w8T/\n/PjHwH/8B9JjZuKvnW6B2dtrRJuUowWi38IHl5i247W0Czmqi9ZFMW7IIEtmnHWVRJDstx9w993A\nN79pPrA77gDOOiu24ot9SAVZJfIScg89ZHJpvf468G//ZtypdXXwKb7g9rmEgZ4Y6pV/suK3tdVL\nbizI91xEjgigadPMxySrGiWeShbd6JWOMh5JPX5CSVvH5HW5Dr84TPs9F1Enm35UlFgnNQMFV0T0\nDeqyerjivKLc1F1dnoDTAkZjB/bLaiHbRB/Ublebtm71BmJ7n0S/wU9bhvzqs8WNPn7MmFwX3YwZ\nQOPza7Fj0sUYe/qJeOS2J/Fg74FDA73Ur9u/c2duf+p9GkX8RhlMwwZWu0+jDsRhfRS1jCiDfzHi\nriTU1QFf+IIJpL/gAuDyy4dSR5S73X71RxZy/f1mkvDUU8C//itw0UXAqFGxtjEsnEC31b5vBZmE\nicjSE7HOTm9XCMATWSLGZGWjbQGXMU+HMgTFs9r3pMScAZ7VXCZBUVaLF/PdKdSK7Jq4+h3nGn90\n2ptixiVSvdS04Mrnwey6QWXA8jOvR7mp7W0rXMgAt2SJvyjTg6i+Jm1Bs69D6tYWHNesWrtWZfAV\nV4Gks5B0D93dw7cJ0gPVvHleO/fa/SamPvSvmPz2DzD2G98CPvYxnA7grXea96dN82bT2lImDwRp\nt37Q2LN8Wfmp41nkOlxuRf1ZptPegoJ8hU2YKyFqeSNm8D39dOO3uuAC4CMfAe66C6lUeOqIqJS0\nnzZsAL76VbMq88tfBn7yE+Ad70ikKpfrSb+nf7tW/unvml6hqH/LVj8NDV6AvKRukfs9LF4TCI9n\nbW8fviG8jdyrSVLodyWq4Ioq5uJcbEWqg5oWXFFvDL8HpLYyBZ1vY8dY2IOkjeTOktxY/f25bWhv\nHy6o7Dq0pUu70LQoktVKPT1mg+v1603dGzcagTNunCeA9KpCLXBSKa+9WtzY1ri7v/x7fO43l2Dr\nXofg+N1P4G+//R4MLjSD/5Qp3szatcRb+l3/7/oc7WNkVwBbyPmVoWfwYQLJNYPX16yP8/s+RZ0A\nlMMdEoslrYDUEVFJ6rpzyn3pJeBrXwP+8z+Bz30O+M53gP33T6biPQQt2rDDGLq7h49Buv1+SVSn\nTPG+O/K915NJ17hnlw34C7ooYi3qe1HI97taCQKn4i3VJBZqWnDlg9/sJupNUsxxWtxkMkZg2WJC\nBslUyrM+iTibNs07ztV2KUvPavds75YjkmwhIw99vXWPtoIBDnGzeze2XvvvuPHJr+OOoxbjqj9c\nhubmOqcVUUzwrj5xrSh0ocWNxJMErbIUMSOWrqhuDi1c/QRdlLZGnQBEOS5OYnsgjB5dttQRhZBK\nAfjLX8wG6d/6FvDxjwPr1gEHH1xUuUH9GRa+oI/TuFZCA+5xS4s1EXJdXd7ODnYqGFd5rrbKfRmU\nJNV1vt5HVo5xWcijEKfgKnZyE6UPpB4KrpEPBdceir1Bw863hY4eTIIemLYAmDYtd1WeHgzEnScB\n8CLOgOBZpvzu6sp9zZ7d6hgEOV4GabG6NTd72+noMjo7gd67nsN7LutAw7a9cMKutWg+6HBMmzY8\nsFYYHMxNJiu/7X0RGxo8S5RrA2q7j7UQcvWJtFlEpKxW9JvB63Pta9b1S7slPs0VuF8zBKSOqBje\neAP43veAG24Apk83LtHDD4+l6KAHbJDF1hYA+jtqW8v1b786bFElk67W1mjfyzDrssu66zcWulyX\n2jJfDoqd3EQVXKQ2oODag+sGyGd2U+gN5GepsV2CgBEzPT0m0NwVk6XdALps16DnqkeWakvguSCi\nzWVtkiBcEXjSXim3oQEYfC2Lp6/6Ho773lfx8OnX4az7v4Cp00YNtVEHvUubRNyJwNPXm06bWb9+\naAh2PjIt2Fy7ArjQDwD9ELAXEgQNprr/XA8VeyWkXxvCSHLgTtx16ZM6ouzs3m3chtdfb3Jo3X8/\ncPzx5W6V0wqsv0P6u+onVFyfqU5k2trqFktR8HN/SlmusSesjijxXK7Jp663UsVNOUIDygUteAYK\nrgBK4brxi6tw1e1aOSgDpQStt7WZ38uWmRxbM2bklhn2xZdA+K6uXBO/HvjsAPV0OtdSk5ModcsW\nvHLOFXjX7j8Dj/VgzEuTMfUN85YkKR0czN1eRM7VG+2KVU/v6RjVLSP1hG35YZ+r3Rz5zLTzHVj8\n4gOjkOQgVhLXZcKpI/IimzUJqq67zmQJXboUmDo1tuILecDa1qCgsoP+96tLhyKk094Ep5DvlZ3l\nPuz7Yn/vXRNBsQbrY1wi0p4AJfFdjfteK8n9VSFQcBkouMpMvq5Mv4FUhFZ7u7HetLSYcJOwm1hb\nx5qbTRkSMzJjhlenbSGS10UINjR4ezR2dsI8vJYvB+bOxbs++1nzEKuvR2pyrqVKC0cpt6XFuCmP\nOMIbbHt6zHYgO3cC27aZtq1f7x/7kUqZvujry7UuRe1vbSWUFaL69UItni5XT80PRgGpI0rGo48C\n114LvPKKcSHOmmXaFSOFPGCDvheu75CfUNFud41Ypzs7vePlHgyrP0pbg0Sm3/n2ZMkvBrXU1PQ9\nSmKBgisi5bzZ9Ko/HQcEmAFp/nwzQI4fbwZOWdotyKAq+W4ELU5SKc+K5FpaLuXIoN7V5QWG9/QY\nV4S4Ho9tfBk4/7PA738P/O//DluJpgWXIPu86W13xo0zomvMGC9TNmBW4A8MeJmzbcuV/dCRAVuv\n5rTRr7uOsfd6BIYvHoiCS3BVAyVpryN1hN9Gz7Gxbp2ZDDz+uLk5LrnEV+jlI4yTDvQG/L/HwHCh\n4vqO2veMnBfHZ62/567xwzWBc50DuPN7Je2OE4u7ri9pa/JIo5ZcplGh4IpIub4g2sxvW13kNfkC\nL1tm/u/rM6JMVjXJjNUViyR1pFLGQqXjIVzxZfbNIrNjid964fv34ksrPoVfvfcC3PF3S/H/tu8D\ndXjOwKUD3MU6J3FT4joUq5TElvX0mOwC7e2mva6l69JGEXAS9C7lyPFhIkvKCqOQwbjaBqOStSnB\n1BE5bNpkZir33mssW8uXuzf3VMQpuFxusTi/Q4JrUmAHr9v1xuHaCrLwxuFGS9odZ+9PS8GVP7Xk\nMo0KBVeFomeD+n8bmf2lUiZmCzBCZs6c4VmlBXv2tnixKUO2+pG4qm3bvDr8VkFJDMjjPf+H9AlX\nYcIzv8APZ/wnvrRmGu7vDBY2WuABZsuegQHzs3WrZznr7TUL2n7/+1xLVyaTmwxWyrc3qM5kvFVX\nuu26La6AX53IMUwU5TsgJzUYjQj3ZJKpI155xZR3xx3AZz4DPPOMMaXGTNQ0IvmiP1/bemSnjHCt\n2JW2+X1/o2R5zwfbPZhvQL6fdY6QaoSCq4Tk8zAUsaTdYtqaJUjQfCrlbV4rQqOjw1i72ttzRURf\nX67gamz0UkJMmuQN3t3dXpnA8GXbUk7fkjSa+y/FASd+CDfM6MfTL+YmgwyyHsnrXV2mHWvW5LpA\n9Yq+JUvM+7JBtSuQXZcpljd9vH7wrF7t/R22SbXrgaYfZtpqELfgSdKVVdHEmTri9dfNF+jmm4Hz\nzjPq/T3vCT0tH0ukPtZOI+Ln/svXypnPwg0/y1VQfrdicU2uok4s7HOj9k1c3/clS3KTP7e1mYnn\npEnAffcFt4EEw/4yUHCVkKiDpcRqAebGl3QQsiJQx0EAwdsK6dWNenZpx4RJLq199zXv9/SYib9L\n5Anb//xXbPrYdWj71X/hrjO/j6b/9xE83eVtfCvt6u72NpzWbX35ZeCgg8zfGzea9nR0DI9BEwYH\nvW1I9HUEoV2SQO4M/rHHvAVxWmRFDWaOyxUT9p0YUSIqT9IDk5AqJnXErl3Af/yH2etw6lQj3I48\nMvLp+QiGIItTsWW7CLIe2d8XseDqRSZyL9ixnVJGIURx0/vV4We9A+JJoRLG3Lm5Ww/psSUsjQsJ\nplbHLxsKrjIhN7MenPRvCV6VrO2SqkFjCy8RLd3dXgC8DKTLlpnXGxpM2XPnmr8POMAIuu3bzXGT\nJ5vfra1eMlO7rQCA3/wGn/r+xdg6/nhsvO1JPPCTdyHT6VnjxI0HmHIaGsxrtrCRa5D6pN0vv2za\nJMJNJ3jUe77ZuYRsa5f+2xZU+qGo03PYrlzA/UCzg/P1+fm4HKOKcL/jZGcBoDriwfLBXHcBqSPe\nfhv47/8GvvIVI9B++lMTE5ZwW8MEUNyxWq5UMS50ImLZX9SuI2m3diV9F/OZ/FZSu0l1Q8GVMH6D\npc4yLse5csnIa0FuAFtMuGaH+rVUygtIT6eNUBs3zgiviy4yD2+/VU09D+5C9msLccKvv4PP7bwF\nA8dcgNQTxvyeyeRuaxO0vYeNTkSayZjyJC/Xd79rXIkS15XJmDa2tXkPD7vvpL02AwO5eb7k74GB\n3PP0jFa7KO3ytfCK6i6Jgv29CXJZ2pn6R+RMPJ/UEQ88YPamGjXKfHnOOCOWJoR9fvqzca2sAwoT\nI1GsPUnFjEXB/q5KOEDYJMR1ruv4JNoedj/am9ZTdJE4oOAqgHwenn6DZZSHYjptXHFA8LYdfkJD\niyb7GBF72rokwfKplCeActq/bh2mzbsEr+z1blzW9gReecchOYOqveF0f//wOLQxY9zWqTFjvM2x\nAeOWlLxekyaZ1z79afNbxJDeZsgP2/ojVjcRhC4LlybKZx3FtRmVIGE1IoWUg+CHcEDqiMceM6sb\nn38eWLjQxIDFmEsrn4euyyUeV9l+uL6rtqV2wQLPyqy36gpzSQbh912VnzDrbpiYLIfYsXOWUXCR\nOKDgKoBCzczi9tIr6Lq6zMAn7jsg94GrLSe2FSNMeHV1eUJCD7w7dpiBV7LR77uveW/7dm910+Cg\nihl7/25gyRK8+a+LsffXF+Jdn/gEjltQh97eXPeEtEkC8OV/sUhJzjDA1DF/vvktrtKJE72BTgL2\nOzu9vlq/3uvHpUs98WQnP5Ukj+m0JyDTac/6Jvm4tLVLx7VIGgnpr6iiy6bYoOggl6W8b5cdtGVR\ntRD6ELZTR9x8s9mK51e/Mlavyy4D6utL12AHuv2FfA+ilKvR8Z0aP8u5i2IEveu7ql+rBMES9XOI\n8/MiREPBVULETQYMF1HFBmW6BjXt0tMDrysXVUcH8Oyz3rkSvJ5OwyQv/epX8ekT+3HYC0cCC8xA\nJJnf7WBXHWsmg1Rbm8kOb1+3bH4NGPG3ZImXjgIwIvCII8x7M2d6rj8RT66VhXbuIZfb1e6zdNpr\nt71oIchSGPR6lNl7EGEuy2LKrnokdcSUKcCXv2wSli5dCowdW+6WAcj9bIr9HviVawsDv5XMpcD1\nXdULfKKWkSRRP4c4Py9CNBRcEYlj1hPFBeZXl+Sc8guO1oObK3BXXJO2yOjtNceMHu2dKxYjscRt\nvPgj+Grje3HqMz/Cpx7+l5x22uJlyRLvb521+s9/Hh4bJu2V9A9r1hhRJfWKJWpw0DxMdFC8Hdsm\nA7z0lfwvMV/ittR9Ihn87b7yE2hJEfbditNlWW2E3lvnnmt+Rhj5WFW19VYmPH47S/hZQOMSO3oM\nkp9C9o0E/PugUixmhOQLBVcIfjE1hTyEdWCrPVP1mxH7Bd/abfB7INuCQlu60mnPqjVx4vB602kj\ncppb9sKPD/5PXPiNE/Hlk96Hu16egZ07TRC7LDU/+GCzcCyTMUH4HR3GBSjB+T09ZkVkR4dZqf/C\nC+ahsHGjCcnp6jLlCUcc4VnidAJSbUnT1yxJHgcHjXtW4tKOOMLUL2JNcnLZBPVzEFEG/6BjXEG5\n+caxjOSHT7muLamHetQyo9avJwfy2z43yjgR57XGNV4mKbiiut5H8r1FSg8FVwjF3tzaeuGXDNHl\nLhK0SLNN9GGWEUmeCnhWpCE34Z5zJNdWY6PbOibuvpaW8bgI/4nV68/Duz7xGEY1H4rubk+U6SSl\n4jrs7jYuQCnztdfMav0xY4CTTzYC7bvfNULrpJOM+OrrM2156SXPSgYYAaU3orY/k7lzPetfe7vp\nN713ohzvF8xsv+5Xj02Uh0LQ55vPg7WQ90hhlFtwFVKuHhfK+Z2ohu9jVG9DNVwLqR5qXnDZ29xE\nIarpW46N8uD1Q4SADj6NanUbPdqzEG3c6AmYk082gma//Uy8lFiaBgZMSEwqlbtlkNf+qdjvzC/i\nqlXno+cjPVi8uD5HFIn7T0RWR4fp2yVLzPZBO3ea+rZtM6IrkzHiSsSenq13dJh2tbWZ2Wgq5aVH\n6O72tvSR2Cu9EKG52dQ1c+bwYGLdf5p8YrOiEPWhZy/nr/QBvtwP85FMMWELQd/fUgeBuyz2+Zzr\ntxhkpOaaI7VDzQsue5NSIHpMjRZSQS4jV5xQ0AAi5wGeVUxinYDhwfC2e1LOffEnzFcAACAASURB\nVO654TFTmYyXa6urywSli9Vr3rzccqXsK680u6q0tAC4+mrgkUfwntuuwsf+4SNo3L0Se/32efx1\nv8PwNxNm446eqRg/fmzOIoDBQS82S8qXlYQixjo7gc2bPVEl4knyben4KpfwBLwVoGPGmK04JHu+\nTgWh3S+6z4L60yWw/WJkXK7gKJ+vfX6lMpIFV6mFiU0xbriwmKli3Xv5UIzgitrWQl2UYZ/vSP5+\nk/JT84LLRdBNLzekpD7Ip6yo8VhynpwjaRV0IDvgZaAPaq8WKhLfIQIzkzGCU69aFCSgPJUC7r3X\nCK6ODgCjRuH6vfbC6O7v4h/wHZyW3Y0vA9ixHXj4rjuxV10THtp6CtZjBTo7Pfee7OsoIlO2/wG8\n2K3TTzc/EmfV0uJtVN3RATzyiCfG7Hg0jWz/09BgrF39/Z570UWY4JL+E0TsuVY96jQTc+aYa3Dt\nzViM1ZMkQ6mFSZxUc9tLRZQ+ouAiSVKTgsvepFRusPb2cPeiCC0tGGzTt18Z+SZDTKc9l1N/v5dQ\nVKxTwPBkqC7BIEJHclrJpqwiZlIpYxXS59oxDvLejh078I7+fnw5+1bO+2MBzMAuzMhm8Km9gO9v\n3YFJk8aiu9vbBxIw/dPWNnybIkHSPohAlC2N5DpciFtY5xybNi1XzGjXisvi5CLfmBiXJcSV7sPP\n6lmpFq5yW35qkSRjvZIgyBWYb8iG4NdWV8A7hRKpBmpScPltUuqygLjcdZ2dntUEiL7xcb5xQtoq\nJdYswNQt57gSYur/5ZqWLPFe123t7TXpGAS5xh/8wKwklLxYf//3JubroHc+hJuf3+JzhYaP7t6C\n1Qc/hM7OmUP1dHZ6aS3SaWMBkhxara3DPwcZVGW15OLF3j6Q48Z5li5x70lWejlfu+lEJLusVCLA\ntADSVkURup2dpv6+vuFZ8v0Ge/m8XJ9LFKtnpVCL1pNyP7yLqT/o3CSFnOs7ElfOMY0r4D1fweUX\nhsEJBUmSmhRcfvgFU8sNKcHncnNKVvJCy9Z1uI7Xg4BsYi1xWNrCJW3s6srNuG4LDNfgt3Onu84X\nXvAsat/8JvD5z5vzF16xEu97Zpf7QvYwFbsw+qWVmDt35pAlzeUClPaIaAG8/pRBVSxv69ebcqZN\n86x1Up6cqy2OevsSuTaX9cn+W8ShlC35jSS9hX2sjf6u6PgswP0552v1JKWhnA/aQqw19sKQchK2\nr2MlYI+NtTahIOWh5gWXWKmioK0mEpeUShnLjV+AdKHBmC6LjB1wbb/X2WmsRmLVEReinDM4aGKk\n9Hl2bjCXlWj7du+6/vj/PY+wXN5jAbS+53l093luQVl5KGiRNTDgbU4t7Luvcfv295uVk4AXEyUu\nXXE1ardce7u33ZAWkPYDKcgqJWXpvSEBt3vQhRaSYceX++GYL9XW3koibAywF4PEWXYp0VtmxWUx\nclmhZOwKWrxCSCVR84JLr4AL2q3eDnLWK+7sGIVCZ0hRrWB+f+vX5HVZuZdKedcnwqelJXiVnAjK\nW281KxU7O4GFmw/Djj8hUHTtAPBS9jB0dpo6m5tNOeKuS6WAdeu8lX5TpphVha2tRhTK3pKNjV5g\nv1gWGxqGx4FpK5f+3xZOOs2FvXpT0NsvyXuSdkKuBxjuStSLKcTCFSU+q9oeDNXW3koiquCqNux2\nT5nith4XQxQrVFz1EJIUNS+48jUnizjR1ho/8o0N8Btwg2KzgOGuNNkHMZXyXGF6JZ0dsO5aZafF\nwiuveIsMGo6ajV+OuhPT3/Z3Kz5aX4/zvjgbc6/x2ptKeXFWkhRVt2vZMvM+YF5vb/csSiKUtDtS\n8nS5VpDKCkuJwRo3zlyPuCdFaAqS5wvwXJkimnRsVyrlxZvZn4nU7UoAS0gYOj40n43OKyHNgR0D\nq9tSDe5FDQUXSZKaF1z5IkLL74GbRGyAHeCpBZedFsFO8dDQYLbvEauPbXWx65HXdHyaDsyfdPxU\n3PfOJkwfzPi299GmJpx0/NShckQY9febHwnE7+/3BJCsTpR2+KVjELQYkpQP8v/goFkM0N9vrGsb\nNxqhJEldtTAC/GOx9Gctx7seYK6HpQg+UtuEiSJ7xWoq5cVOhj38o4wvLitsEvi1xbUQKY66orxG\nSKVR04LLHoCi3LRBs81CYgfisoL5HTc4aGKwDjrI29NQE7W927eL1WcsHh08BdlxwIy/bMHpb+/C\nWBg3Yg/q8eC4JmTGnoJnl4/FzJm5G05PnAi89ZZ5bcECLyEpALz+unuvSfmtRVVvr7mOjg4jpubM\n8SxmOp5NYr9EPPoJXonH07EgfvE0IkLtWb0E1jc3e+7E1tZcNyYZOUS9D8NEket9V265OIhTcAWN\nW5okroOCi1QrFFwp7/98btpiliHbr0e1gqXTRlhIMLm81tJi3HE6zkjaZ4uNqGkIxLrT1QWMH2+y\n1p9++h7BMWcFpl+wA6PxEC6+biUaRz2PuvGHYccBs3Hr96di7NixzhiO557zUjoARsQNDABPPmn+\nFzF4xRVecL+Ok9NB9oBpi87Jo+PR5LpdognwNruW80T8yW9JOZFOG4uc9JvO/G8H0cvCgJYWb3Wj\nTrjKh8LIIWlrUTHn+ImhON17cVnvRzLVGpNHkqOmBVcxBMUtuCwahQTLaiuL1CN5oSQ9gstkn8mY\nVXziQpSyxowxP1HQbgjZlgfwRMXixWORSs3E/zwxE/Pn7yl/N/D1r3spEQTZxuiII4zoSqVMmocr\nr/SElE466zd4S5u6uowlqacn16I0fnxujNacOV6gvd2/ru2cxPWpXZri5hHxJu3zs0KIRU/HnREC\nRHMRRjkurGw7NEAo1TZSFBkGCi5iU3OCK18XXhBxzfL83JH6dS0C9Pv2/+m0t4egJBZtackVE/m0\nSwSMrDDs6DDWNDsGSrvOJD2F3R/pNPDxj3urPEX0iBh01a+Fn1yvxGQBXhJbOw2EzlDvd81Llpi+\n0isKdbJSO8YrSmCz/p1E/AopH8WOHVEFV5zYrvQkJgAUFYREo+YEVzEiKWrcQqGEWcE6O72Vd62t\n5vfMmSZWSbbQEDeiXuWXD67YJAA44AAvNYMIFAlc1xYt+V/HOsl16SSfsmG2/Gzd6okdV/xUX5+J\n3ZK4rLa23IUDYs0Tl55ebejqVy22dGybtgDYgklbruR/P5clH0Ijj2p0o5Xie8jvukecE3oy8qg5\nwWWTj9k3zgHX78YU95v9urZ0dXXlpkSwhZUWNrIdjR3bZV+LFjlaVIggyWSA117zXGtiNXP1n7jz\nOjuNSNKiTGeAl+uUPFk66N1mcNBkxZfrb2kxAlC22mlv99rZ0mLEqLZ62WV2d3vXoZOzalwWQd0v\nfoH19rFxQRcFyZdCY1RJYVSjKCelo6YFV9DDshRluUz9rkB+EQ16BZ1tfdGCQW9tk0pFS8zq13YR\nQfZm3649BHW52r0oPy43o90uEXxyHfr67HLtejs7cwPlpb226OrqMkJNx7dt3lz5lioKrsqhGj+H\namwzISOJihNcpXyo6AdzHKsO8ykjLFBe12OLGrEa9faaDO3iTpOtb2bMyE1uKoJDr27UZfvFJjU0\nmDoAz40pAeh2u3QeLRF/qZRXXne3l9g0SNjoNmUypv6+Pm/bn5YWs7pRVg7KikHbtanLFEG2ZIkn\nHLdtMwH3gLGOSVJWl+WxtxeYN88rV+Lkli71+l6viuSDbeTDz5iEwe8IsalJweV6qNqutDBcAe6F\n4lentpppUXTffSaWacoUs/2NuBfthKa2+1DHdsn7OrO8pDPQosHeKNqvj/Qm2BJU39Dg7UPY3+9t\no6S3RfK7fnEbatep9EFbm2mXiB5BUlnoBKX6c9Hb9uhrtLfysQWuvCbxYXI90lfSziRgTAgh1Qnv\nT2JTcYKrFLgeqoUmG9SB3zqpqASxu44FhluS/B6qWjTpNgZlSXcFrOvXdfn6fRFCWrDZx+sy9PVI\nwHom4wX2i9iS69B7H9rl2v0vKyJd6DQPWkDqsrXFTLfXFnp9fe46XNgrvsSSl2ScBmNC3NC9Sgip\nNipCcCUxi48yIEdZ5h+lDi0YgoRQ1IendoHZ57vKBIYn8hRX25IluUH49l6LmkzGW/0ncU79/Z4r\nsq3Nc0mKBUuvSGxp8QLX29vN74EBT4xKfSJMRVTJ67qteguinh7g5JPNFkUTJ5pcXu3txi14xBFe\nP9iCUF53fRfa23Mth/b74n6Ua5cgfVkp6cqKT0oHBRchpNqoCMGVxCw+yoDsZzWKiqzSA4yYmTYt\nnm05RAR0dZmHvOCKnbLdYrbVybb02NY8Hf8kQmhw0Ail9vbhm0jLj/Sv/C+xURJHpfcwBExc2bx5\nuedIaoiuLi/be0PDcAFnu+x0H9jXYSd3lGvW8WS29cz+rqTTXn4vKUe7VHV9up6kocAgSUMhS0hy\nVITgKifFDC62i0lSHegVhbYVJ6xeLarSaXOuywXnh7a4AbnnBsWZiUiR9q9fb2LFRESKRcfOlSVI\nfJaUpeOnbJEmZUj/dXR4SVq1oJH3bZGTyXgCV65Zp4Dwc1lK+ToHmN7TUfe7yzImKzPLFVNV6w9C\nxrMlDwUXIclRcYKrmJu9mAE5ar1+dUhmc01QbJhffZIzS+Kg5CGvV9KF4TpG7wfo6pt02myNI7FX\nW7caIaK3tBGkDzo6coPWtaDq6sq1mmmhpvOCZTLextP9/V7fSpJVydml2yrC1v5ctaD0WxghQk6u\nWfY81IlU7etpbx/eX0K5Y6pq6QFZaX1PCCH5MKIEVzEDctR6/erIZ5Wiy4WlXYOyVY2Oy3IFlge1\nUf8GjEDRgtBlBert9ZKL9vTkuveknfYejbJST9fX0eGtLpQ6W1qM8JHYL72Ccds2I3gaGkxG+9ZW\n015xieo9I1Mpr39sd6K0S/eZbpuIVy047Zgv/b6UKa5F+9hKIOi7REgUaDkkpDRUnOCqFPJ9cNkP\nvTBrUtSHZD5Cyw9pj/ztV++8eZ5VSaxqsrn03Lle0Hx7u5cZXqxFuo36fxFeS5Z4AktSUKxf7wXJ\nS7D9hg3AT35iXnOtQPSL3ZJytZvRjnWz/9fnSRu0EOzp8drf0jI8x5dfQH45qbT2JEUtXGOpoOWQ\nkNIwYgVXHIHrhbohCx3A7JnmjBnGWiSpC+xUEmEuRgnqF8uPrFxsb3evztN/t7R4YkjceC0tXrwT\nkLtVjx3fJJamvj5v9aHuF4mlEpFjZ5nXgsj1WWjhZb8XJeZNC7bW1lxrmo7N07FndsyevF/qh3+Q\nRSLKuSNBrIyEa4jCSPm8CCEVLriKGWziHqSCHvpRztW/JXZJUiq4LCc63cLSpUYkNTcPt+yEtUEH\nncvf4pJz4XIL6s2qN270EpuOGZPbRiC33YC3l6OUqa1/sqLxkEM84dXf77Xh2GM9EZZKRXN3SLyX\n65rs/3UZdkJYTT7u4lLgZ62z3aWuPuIDvLoo9efF7wYhyTFiBVeh9flZDgpti5xrW0K04HFZTuzX\n7FQMfuiVfLL1jKSWkFxS3d3GkuNKOaH7QFI1iKVr40YTWA944snVxpUrjTi0hdrAgPlpbDTH602r\nZSWnboPtonStQNRoq5jdJ36WPNd5rhg4XUY+MS+l+A7TJUTigoKLkOSoaMFVaoIeXIVaOfxEgJQZ\n5JaUY0RoyGq6TMYEmsv7tmCRc/v6vBWBkp5CW4tc8U76by0sbHegH+k08PvfA5MmeVsF9fQA48aZ\nmK2NGz2Xpuz96Cpv8eLhosa1YbbGr6+7uoIfJK735NolR5j0lRwfVeAkLbiiuhEZFF098PMiZGRS\ncYKrkgabYtoS5Vx5GAfFGGmLlhyvxZIIKO22lL/7+z3LkAS32xYyu2w/7GSi+m/XubLZs516wU4z\nYZ8nKRh27szNrQV4qSJs61dYX+us8H74uR07O732636ulAdfFDc3LWDVxUj9vOjOJrVOxQmuShls\nbGtRvm3J59ywQcglvuz3tHiT17q7PdHiqsvlMnMFvgNGLPmd09UFrFsHvPSS56bs6DDxVIcfDrz2\nmheY3txsYsj6+42FSwuYdNrbLFvqlpgwVyJXv10CtFCTBQOuVBH6GjSuvvRz5QZZxwAmRyVEoOAi\ntU7FCa5KIamBIR/Ll6tNYRYWl4VLH+9yHdp1+AlFW3Do1Xs6K7xug25TW5sX+2WnfPBzu8q+jH7v\n6XYUgsvdaG/ZNGeOvzuz2ixKUfuJD8fKgJ8BISOHihZclTTYFNMWl1VJxJPrYRwkuPTG0/p8P1da\n0GrEOFymkmvM3gJIX4e2QvnFWdkLC+R/WVXparPepNuuS/7W7bTr83M3Bi1YCKMQoVJKcUPBVV1U\n+2dQSSEihJSbxATXmjVrMHfuXOzevRtXXHEFrr322rzLKPcNaccKuV6Pgp/LqhAyGX8rlWulY1i7\ngs53iTKdzkISho4bl7tR9rHHmt/2dYq7UKxGrhxWUpc+1m6vtEuy2Pf0DI/t0uW5sslLMlPtugS8\njPiCvF6IUElSpBFSDVSytZeQUpOI4Nq9ezeuvPJKPPjgg2hqasLJJ5+MWbNm4eijj06iusTwexAW\n84C0Vx3KACT7AwLuZJauuKqwWWKxD3GX2HSls5B2+FnrRBjpLPUdHd77Emcl/0tmeld8lh1ED3jb\nC/ldr9QlSF4wbd3Siwp0nYWuTpVzq+kBQ2sEIYQkRyKCa+3atZg4cSJa9pgWLrjgAqxatarqBFdc\n6BWEgGcNam31f5hFTUkRZaWjPs6PQtxgWjgCGNr/0RaOYhGbP99zE9rB6PLbjjmzXX76WsVlKi5W\nu22Si0xek7aJwJs2zUsm63f9US1ULqEStDpSsu/b55RT3NAaQZKEop3UOokIri1btuDQQw8d+n/C\nhAn49a9/nXNMpxrNU6kUUhVyN/o9PIMsUFHinbTIEKEQ1VJmB9S7VuoFBdGLC65YwWXHotnCyVWP\n3sJHaGgY3s/NzZ4QChKRgstVqBHxJiJPn6dTVbS2Dl+IkO9XUZ+nRZbEmMl7Lveqbm9U6IIk1Qi/\ns6SaSKfTSBfj4nCQiOCqq6sLPaazQqfPLguKi2Kar+OF/Nrgh985fqsXwx7OUR7efgLIFmD62HTa\npKXQ7sLWVu/a584dfr52SwZts2MLO1eMlqsftIVx2jTzozfodl1XVPSKzUKFVL51JQkfjoSQWsY2\nBC3QlpYCSURwNTU1YdOmTUP/b9q0CRMmTEiiqkSJkjDTjzBLWWenvwUk6GEnaRXsssXi43Kt+QWf\nyzFhdRZiHUulvDgsyYTvyqWlEaufWLkAT6xJmXp1oVyf3b/6mnVwvq5XypIVkHGJmLB+dH0nXn65\n+HrjhoKLEELiJRHBddJJJ+GZZ55BJpPBIYccghUrVuDuu+9OoqpEKcQCpY+xLTjptBFbOng835gd\nv0B22yJkx4tJXa72R3U7+tHXN1xI6BxZsn+jiEK90XVbm9cH0gbtNrWvTd5butS4CwEjqnT/6mt2\nxXe5+iAKdv/4CSgp32URdMVIRbGCMaCdEEKqm0QE1+jRo3HrrbdixowZ2L17Ny6//PKqCZjXD7ZC\nLFB+uOKwXGkR8sHltpNEnlpo6Lr06kBgeA4t3cYoD3gROX6Z3oXGRmDKlOFtGhx0C1P7Ov0EpI4l\ns13Bdv+6UkcE5TGzsc8NCzKPUwgxoJ0QQqqbxPJwnXnmmTjzzDNjLzfp+JUkHmx+7S32OrTbLixu\nSIsRLar0PoHippPjo/SDX0yhLTCnTMm16LjOc8WKaeuXbosdsK/xy53lCo4PElB2u+KkoSE/sUcI\nIaS6qehM8y4qaYVWPqsMbSuNHU9UKK6y9Xv6fbGE6dQLOk5NJxCVYHLAHctmlyk0NAw/Vrtm02lg\n82ZjaZM8WnrFocsNJ8e4LGEugWKX5ddWl7XOrk+vMA0SRvl+htK3Qj7CvlK+/4QQQqJTdYKrlPg9\njINeCyoryGJUjJDUFi47bUTYqtaODuOGtGOmJAWGC9eKP2mHvgY715Sc89xz5hzZg1ESo2pXpF9f\nBwkklytYp/MIaqvtytT16f4N2iqpVFBwEUJI9VEVgqtcAcNhgiuIfAVaHJY7v/gn1x6FGtmsWa/u\na231yrQXD9jxUnYqBEHHdskKSluo9fV5ebq0KPPrD30dfm0ChovOoPdc363e3uEuPz8xWCwUUIQQ\nMvKpCsFVSQHD+QSTR7HS5FNv0HlBZetzXSsvRQy1txuRJHFdkmIhyA2XyQzfOseFxI65gtxFiHV3\nm//FtSmWL72/obg3MxlznAi+hobhbjpBX7/LZanFo3DffSbuDPBSSyTlzqbgIoSQkU9VCK5yEUVc\nFSL+XG6wMMtdofFiYjWSMu09DF116zqB3NQMNq6ko65yBwaGt9HuB0mZIW4/O6WDtpAtXWqOE8EX\nZhmT84MEqV/SUnu7IUIIISRfqk5wlTpWJh/Lmkts6KzyLlFVjOXOrk+sPTrmyK9sv6DvdNqzHsk5\n2vKjhQ1ghI+2XrmuyeX+c7VF2u9qr6vN+nXdLjsthf4s+vqGW8LCLI8UWoQQQoqlJgRXqVxBUQRU\nvnvmBVnAXCLBThIa5hLUddl5q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b349re/jaeeegqLFy/G9OnT8fTTT+OMM87A4sWLy93U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\nCCGEEEIShoKLEEIIISRh/n9kCWcVt5l5SwAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,10)\n", "plot(data[:,0],data[:,1],'b+')\n", "history = array(history)\n", "for i in range(len(protos)):\n", " plot(history[:,i,0],history[:,i,1],'r')\n", "plot(history[0,:,0],history[0,:,1],'ko',markersize=10)\n", "plot(protos[:,0],protos[:,1],'ro',markersize=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the final location of the prototype centers (red) are nicely\n", "in the center of the classes.\n", "The algorithm doesn't give us exactly the cluster centers because there are\n", "three clusters but we postulated four cluster centers." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also look at the partition of the data induced by these cluster centers." ] }, { "cell_type": "code", "execution_count": 110, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 110, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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F5Po8EVxANH2oI2zmmHmxzTFuIYJeiSljard3s73tvmZNd45D/RkhJBkKLkLGjEFGLPJE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\n0c7MdtVU9brgEo+j1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YUFdQxvFeR3bYlUCYIgCF6I4NLotNobHj3i9gknqiKPXNDp/VzV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\nXEREREQLxsJFREREtGBvhD6T5idQi6IAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,10)\n", "dists = cdist(protos,data)\n", "closest = argmin(dists,axis=0)\n", "for i in range(len(protos)):\n", " plot(data[closest==i,0],data[closest==i,1],['c+','g+','b+','y+'][i])\n", "plot(protos[:,0],protos[:,1],'ro',markersize=10)" ] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 0 }