{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Counterintuitive problem: Everyone in a room keeps giving dollars to random others. \n", "------------\n", "\n", "from http://www.decisionsciencenews.com/2017/06/19/counterintuitive-problem-everyone-room-keeps-giving-dollars-random-others-youll-never-guess-happens-next/\n", " \n", "Intentionally written in very basic python.\n", "\n", "July, 2017 - Roger Allen" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "from random import randint" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# There are 100 people\n", "N=100\n", "# They initially have 100 dollars each\n", "dollars = [100]*N\n", "# Every turn they transfer 1 dollar each through this array\n", "temp_dollars = [0]*N" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# initialize the arrays\n", "def init():\n", " global dollars, temp_dollars\n", " dollars = [100]*N\n", " temp_dollars = [0]*N\n", "\n", "# one step in the simulation\n", "def step():\n", " global dollars, temp_dollars\n", " # everyone picks a random person to transfer their money to\n", " # go through a temporary array to avoid modifying the initial\n", " # state of the simulation step. E.g if a person has $0 at the\n", " # start of the step, they shouldn't transfer money in that step.\n", " # But, without this temp array someone prior could transfer\n", " # money & they would be able to further move that money.\n", " for i in range(N):\n", " if dollars[i] > 0:\n", " j = randint(0,N-1) # randint is inclusive of top value\n", " while j == i: # you cannot give money to yourself\n", " j = randint(0,N-1) \n", " temp_dollars[j] += 1 # credit a dollar to them\n", " temp_dollars[i] -= 1 # debit a dollar from yourself\n", " # actually do the transfers\n", " for i in range(N):\n", " dollars[i] += temp_dollars[i]\n", " temp_dollars[i] = 0\n", "\n", "# show each person's number of dollars\n", "def show():\n", " global dollars\n", " fig, (ax1, ax2) = plt.subplots(2, sharex=True, figsize=(10,6))\n", " ax1.plot(dollars)\n", " ax1.set_title(\"ordered by person\")\n", " ax1.set_ylabel(\"$\")\n", " sorted_dollars = sorted(dollars)\n", " ax2.plot(sorted_dollars)\n", " ax2.set_title(\"ordered by value\")\n", " ax2.set_ylabel(\"$\")\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# initialize the simulation\n", "init()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# show that everyone has the same amount of money\n", "show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Y+c2EUorD035s6Myd3mS02Y0FrVDcgRgISQc45dBqNcBq0NZk4eQNxTIsNuTH\nADRWgMau0cuL5W+7uA/NFj1++NRoPQ6r6iwpqJyAsHAIx5NlK+/sfG6XNQnEkxSxRO2aMHyROLQa\ngjabkStoHOCkO4hJTxjbB9sAAO0OY0PVoHlDuVvfgcpTnHaTLmPQeq/TAncgdkbUcIzOB3DV+nY0\nmfXYO954dWjuQBQ2o66souWhDhsANFQdGvtMBGPJup0fwVgSyRTNmCIApD0B1UhxzvqiWAzGsLE7\nf4DmshmLUtBaLAZFJa4YCCFY3WqtiReaJ5z75s/S9I3kzTfjFY5luf2QxaDD7Rf14bFDs2es2Wk+\nlIJoANIowGiZAdW8P5qxoGB1krVU0bzhOBwmHQZcVq6gcYDnRHuN7euEAK2jQRW05WkdoLIUJzOp\nlcOsNsYbXEVbDMawFIpjXbsNW3qbG1NBC5Q25kmO3aTHqmZzQ3Vyzvkjsq/z36gj8ST2jXuwd2wp\n41+lKVulz4KaTQKHc4x4ykWb3VCEghatqP6M0ee04HSVFbRoIolQLJkzxcnGPVVDQSv3WjvjFRaY\n1hzdjLdf0g+jToP/fPqNp6ItKTRyAJDsUcqtQ5sPROGULSisRmF/wRrWofnCQkPcQLutIUtXClFT\no9qVwDPH3ehpMUu1Hh0OI54fcRd4Vu3whNgA4+wLvb2CFOeUJ4zu5szVpzRaZiGE4QIpHkBIB/3h\n1UmsajbX1JpjVPzgDrhsCEQT+M7O4whEExlqYL1ZCEbLSm8y1nc21kxOeVA2748qFtADwNd3HMHP\nnj+V9bjFoMXeL15Xtgl0rjFPgLoKGpvBOZzDA02Oy2bEc4GFvNu4AzEpuKmEvlYLdh2ZQzJFodVk\nd++pgRT85rjOOG3VGZi+b9yDd/zf57DjU5cVDIiXM+OLZKlnjDabEe/Z2ovfvjyOz7xpCB11tIVR\nk0g8iXA8iRaFAI0paOUGaG6ZBxqQVtDCtVbQzHqsbbPCE4pjMRirqESg1nAFTUUSyRReGFnAZYNt\nUttyu8MEXyRRUbGlmnikm1J28GE3lm+zMe2NZNSfAaXN/qOU4v/8+Sg++7v9+MQ9r6ru5J4PtrJa\n67Li3NUtoBR4bbyxVDRBQSv/5jzUYRf9uBrDhFOe9perabkYdQcx4LLip391gfTvQ5etQSiWxKy3\n/DSZT0FBsxq00JC0C3klHJr2oddpzgoCl9NmM8IbjiOaUL5OuANRyWKjEla3WhBLpqqq7OctpTDq\nYNBqVB8aJlnWAAAgAElEQVSYztTKiaXSldUZXxSdOcxaGR+6bC0SqRR+8tzJso+vUhLJFN7zwxfw\nX8+oo+TlC6IBYdQTUH5ANR+IZtgCMUUuWMOB6b5IXFLQAJxxKhoP0MogEk/mdBnfP+GFP5rA9nXp\nGaFstVXoJlQrvOE47EZdzjoWu0knjaYqhUg8icVgLKODExA6Re1GXcELJqUUX3noEH7w5Aiu29iB\nhWAMP3hypKRjqITR+SAMWg16WizY0tMMANjbYAGaOxCrKL013GlHPElxskHqMOb8ESm1UqhGc8Yb\nxrp2G65a3y79u2JI8Bic8paf5lRqmCGEwGbUqbJIODztK9ggAKS9zfKpSm6/WilOQa2sZidnvm5x\nNo9T7YHprCGpnMHzM96wooIGCEHtW87uwj0vjknmp7Xm/r2T2H1qEU8dm1dlf2xWakEFLVZ+DVou\nBa2WA9OFGjQ9BtqEAG2UB2hvbFIpiuv//Wnc9uPdWcWOz51wgxDgEll6jnUGzjZIo4A3x5gnhjQw\nvUQVTergXFaDRghBbwGrjWSK4h/++Dp+9vwp3Ll9DX502/l457mr8ONnT9bMFmJkPoD+Ngu0GoIm\nix4DLmtDGdamUhSLwWhF6a2hjsbq5JzzRzHUbodeSwrWoE17I1nnFpv5Ol1BgMbU4lzqllCPWdmN\nJBRL4KQ7WLBBAEhbESg1CoRjSQRjyZKNinPByi/GFqsXrEuD0s25A8pWm/oD08cXhXOh1AAtIdq9\n5FPQAOAjVwzAH03gnpfGyj7GcokmkvjO48cBCAtKNVgSy12UbDYqqUGjlGYFaKwGLVRLBS2cgMOs\nx6oWMww6DUZUeu9qBQ/QSuTkQhCnF0J49oQbt/94d8Zq6tnjbpzV3YQWWY6bKWiN0iiQyzmdUe7A\n9LRJbfYFLp8XWiKZwmd/tx/37h7HJ65ah//91g0ghOCz168HBfCtPx8t6TjKZXQ+iAGXTfr+vNUt\neHXMo9osxkrxhONI0fJMahkD7VZoNaRxAjRfBO0OI1w2Y151ORBNwB9JZN08WUPKlKf8z1W+hhmH\nWV+xD9rRGT8oLdwgAKQVNKVGATU80BhdTSboNKS6CppU65r7WuO0GuBWO0ArU0FzB2JIURSsLTtr\nVRO2r2vDT549WXKWoVJ++/I4Jj1hbOt3YtITVqVkhgXRSvcDUwU1aIFoAtFEKkPxlbo4a2RQTCmF\nLxyHw6yDVkOwptXKFbQ3OqzD79PXDmHfuAfv/6+X4AnFEIgm8OrYkmSvweiwN1aApmQeCZTfvcaU\nrlXLatAAoNdpxvhiKMtLh1KKz9y3H3/cO4m/u349Pnv9eqlub1WzGXduX4P7907iwKS3pGMplVgi\nhdOLIax1pYvUz13dgsVgrGFMdisxqWUYdVqsabM2zND0OX8U7XYTXA5TXnuJGUmdzbx5mg1aNFv0\nlSlo4o3clqse01R5ivPwtPBeK414kiNNE1B4L+alMU+Vpzh1Wg16WsxV7eRM1zflvta02YxYVHlg\nuqSghUoL/OQmtYX48BVrMeeP4k97J0s/wDIJx5L43q4T2LbGidsv6QOgzvBvFkS3KBTNp1OcpS9U\n5pdNEQDkClptUpyReAqxZEoKQNe6rFxBe6Ozd2wJdqMOn7x6HX74/vNxZNqPW370Ih55fRqJFMVl\n6zIDNIdZB6NOUzCNUys8oZhi2qHc7jWW4syVIljttCCaSGWNsXlxdBEP7p/Cp64ZxMevWpf1vI9e\nOQCn1YB/efhQVZWsscUQkimaoaCdu1qsQ2sQuw02JLutwu6j9Z32hrDaCEQTCMWSaHcY0W7P7//F\nArRc9UFdTeaKFDRfJA67SZezk9FRgScg4+CUF3aTDj0t2QuX5bAOXUUFTRrzVLmCBgCrW60Yq6KC\nthRSHsINqD+PMxxLSu9dqQqaZFJbRHfm9nVt2NTtwH88NYpkjUan/eKFU5j3R/F316+XrlNqpDml\nOkEFBc1cQYozPUUg/Z5a9KwGrTYKGstusRKGAZcNY4uhmhrlVgoP0Epk75gHW1Y3Q6MhuHZjB378\nga04tRDE5/7wGow6Dc7ra8nYnhCCDkfjeKF5xZx8LiQFrcQVzrQ3jDabIafdQa9CJ+d3dx5Hu92I\nj145kHOfDpMef3PtIF4cXcTOw3MlHU8ppDs40wHaUIddsHBokDq0hWDlChoAbOi0Y2wxVNMO2Vyw\n6QHtdiNcdmPexUta3cgOclY1mzBVQZ0iKyDOhd2khz9a2ft0cMqHTd2OnIOol2PSa2E36aRgfDlS\nkK5SgNbntFTVrNYTEkoplH73VpsBoVhSte72SU/6+lJqgDaTZ4G5HEIIPnblOoy6g3j49enSDrIM\nfJE4fvDUCK4YcuGCfifWtFlBSOFuxHAsKXXSKrEUisGg1Ui1ZsuppElAOl9lii8L+GqloC0vYVjr\nsiKZolWtvVQbHqCVQCiWwJEZH87tbZYeu2zQhZ//1TZY9FpcNtiW0+m9w2FsiACNUgpvOKZ6inPK\nk13EzWBWG+OyAG3PqUW8MLqAuy5fm9cZ/9Ztq7HWZcXXdhyumj0EW4nKU5xaDcHmnuaG6eRkxdSV\n1KAB6VqoeqtoLCBrt5vQbjdiMRhTXNWym2e7Izsw6WoyS+ptOfgKLFYqUdASyRQOT/twVndT0c9x\n5VET3VKaWx0Pp75WC3yRhJTmUhulKQIMphguqJTmZOlNi0FbcoA27YvAoNXAqVAsv5wbzurEYLsN\n3991vOwxSMXy42dOwhOK47NvWg9ACORXNZsLKmhffvAgbvvJS3m3YQ1jSkF0ZQqa8LmU10wadBoY\ntJraKWjLAjSmPp5JaU4eoJXA/nEvUlSoUZJz4dpWPPF3V+JbN2/J+bx2h6khxj2FYknEk1Txwll+\nijOsWL+xqsUMQjIVtO/uOoFWqwF/eWFf3v3qtRp84YYNGJ0P4u4nRqqi/IzMB+CyG7OUlHNXN+PQ\nlA+RGhW05oPNYFTqtiqWYTFAY7VR9UIK0BxGtIs1mkqpvWlfBK1WQ85AvqvZBG84XvboGGFQeu4U\nHAvQyk2vj8wHEU2ksGlV8YapbTZjVikAwx2IwmHSlW3Kuxy2cKq0UeCl0YWcwXW+bnEgPU1ArTQn\naxDY1O0oPcXpFRpWNEWa9mo0BJ+4eh2OzQbw6KGZko+1WJaCMfz42ZN486ZOnN2TDvQHXIVd8Xef\nWiwYxC2FYooWG0CFNWiBKLQaknXNshi1NTOqXW6jwxbhZ5IXGg/QSoDNaNwiU9AY7XaT4gWpUcY9\n5etaA9JdnKXabEx5IujO0SAACMXpXQ6TFKDtG/fg6WPz+NDla6UVWj6u3dCOywbb8O3Hj2HzVx7F\n2773DL7y0EHseH26oIRfDKPzAQy4sl3sz13dgkSKVr1JoRgWxJEplbq+dzeZ4DDpJEPPeiFPcbYX\nKI6f8UYUU0/FdnIqBXC+SP4UZzJFESpztX9wSjhvSlXQ3HkUNDVMahl9raIXWgWNAqPzAbz3Ry/i\n1y+dzvqZJxzLr6DZ1B2YPr4YglGnwYDLBm+JBsP5pggo8bZzurGmzYrv7jxRtRrZHz41gmAsgb99\n01DG42tdVozOBxXVO38kjpPuoFjrqfxeCIPSlRd9ei2BVkPKUtDc/hharYasoNei19a8Bo3d7+wm\nPdrtRtVsSmoBD9BKYO+YB2varIpdL0p0OIwIxpJlj1FSC8mbSCGQNOg0MOo0JdWg+SJxBKKJrDFP\ncnqdFinF+b2dx9Fs0eP9F+VXzxiEEPzXHVvxqzsvxCeuHoTdqMc9L43ho79+FW/+ztMVDdqmlGJk\nPphRf8ZgQXgjNApUModTDiEEw12OundyzvujMOg0aDLrpdSlUh2a4IGW+9xij+erQzs648c5X34U\nr+aoJ/TlsZypdB7ngUkfTHpNznNLCVdeBS2mWv0ZIHRXA8BYBXVoTIl9/PBs1s88objiEG4graCp\nNTB9fDGMnhYzmix6+MLxkoKmGW8EHUXUn8nRagg+ftU6HJr2VaVG9uiMHz97/hTeuWUVBjsyx4QN\nuGwIx5OYUVj0yxVyt185APbmmcMJCNcLs15bVg3afCDTA41hMepqNiydLeDlU3OETk6uoL3hoJRi\n75gno/6sWBrFC03JOV1OqQPTpz25TWrlMLPaA5Ne7Dwyhw9uX1PSnEujTovtg234zHVDuPeui/D6\nl6/HD99/Hqa9kZwzGotlMRiDNxzP6OBkuOxG9DrNOW/stWahQpNaORvEmZzVrp3Jx5w/CpfNCEKI\ndBFX8kKb8YaVFTRRtc1ntbF/3INEiuKxQ9lBBJvTl4tK53EenPJiQ5ejJNWzzWaAP5LImVZXa1A6\nw2LQwWU3VpTiZLWML40uZr1P3pBy8Auor6BNeELoabGgyaxHLJlCJF5cUEEpxYwvgq4y5mvetKUb\nvU4zvrfruKoqWjCawMd+/QrsJj0+/5bhrJ+zVJ2SEsTUWwCYDyjfc5ZCyvXIDLNBW3YXZ64AzWrQ\n5h31FIolVOsuloyoZefhgMuG0flgw3hcFqKoAI0Q0k4IsYpfmwkh/0gI+TohpKu6h9c4TCyF4Q5E\nce6yLs1iaJemCdQ7QBPNI/PI2g5TafM42aidfAraaqcFs74ovvnoUThMOtx+SX/R+8+FQafBm8/q\nwjXD7fiPp0bKGu0CCDMegcwGATnn9ra8oRQ0QKhDC0QTZc0rVIs5f0T6TLTZjCAk97inSDyJpVBc\nMfjvcJhASP4UJ/sbP3vcnfF4IplCMJbMk+IUFhDlmNWmUhSHxA7OUnDlMasVxjypp6ABYidnBSnO\nY7N+6LUEiRTFM7L3N55MwR9N5K2ZtBi0MOrUm8c5vhhGr9MsBYXFXhN84QQi8VRRHZzL0Ws1+NiV\n67B/wqva+CVKhckqJ91BfPfWLVKNppx1rvxzJQ9MpksYlGqfKaXwhOMF61oFBa30z4A7kPt8tRjy\nK2g/enoUb/3eM6pYmHjDcVgMWuhlYw3XumzwhuOqT7GoFsUqaL8BwOYXfQXAOgBLAO6pxkE1Iqyj\nrxIFrd6NAoVSnIBg2llKDRpLL+VT0FhB8pNH5/GBS9cUHBxdLJ950xB8kQT+8+nyhgePzAkXuHUK\naahzVzdjxhepyAxVDZQuduXAOjkPz9SvDm3OF5Vqz/Ri91yuFGc+DzRACNRdNmPevw9zDj8w5cWS\n7KLMAi+lJgFHBQra+FII/miipPozIG2hsdxqI5pIwhdJqB6grW61VKRWHJv144ohF5ot+ow0H+ue\nK5Q+a7MZVWkS8EXi8Ibj6BUVNKD4AG3aJ5w7xXig5eLd5/Wgu8mE7+1Spxbt3t3jeGDfFD597RAu\nGWjLuY3LboTNqFN0xT845cVZYnOKUso8HE8ilkjlTUMDYoBWooKWSlG4lVKcBm3eus7JpTD8kURF\n9jmMXCUMA1KjwJlRh1YwQCOE3AFgAMCV4tfvBbAHwAyAPkLI7YSQc6p7mPVn79gSTHoNhjvthTde\nRqOlOPOlHkp1UJ/2RKDVEOmGmwvmhWYz6vDXl/YXve9CbOpuwlvP6cJPnjtZVi3LqDsIg06j2ODA\nunXrqaLFEin4IgnJlqBShjpsIAQ4UsdOTjZFgKFkLzGtMEVATldzfquNUXcQnQ4TKAWeG0mrPL4C\n6X5HBTVoTME4a1VpAZrSNIEFlT3QGH1OK2Z8kbI6laOJJE4thLChy4Erh1x44uicpHrkG5Qux2k1\nqFKDxupbe52lB2hKkyqKxaDT4KNXDuCV00t4YWRBejyRTGHSE86wFyrEgUkvvvzQQVw+5Mpp3s0g\nhGBAwRU/Ek/i+FwAlw26oNUQxeabYhbrAGAyaBEuMl3M8IbjiCdpzrFkQg2a8vnG5oOedFceQOXy\nOUwb/Z4ZdWjFKGhPAggCeA3ABIBZAA+Jj7vF/7PbeN5g7B3z4JyeZui0pZft2Yw6WA3aug9M94Tj\n0GuJojEhANiNpQ2JnvKG0WE35n1f1rRZodMQ3HFJX8EVW6l85rohROJJ/ODJkZKfOzIXwNo2q2Kd\n0MYuB4w6DV4cXcj581qQ9kBT5+ZsMejQ32qtWydnJJ6ENxzPCOjbHSbJN0kOU8bypZ+6m0zSqLHl\nJJIpnF4I4sYt3bCbdBlpzuUdXstJ16CVEaBNeaHTEAx2FN8gAMgVtMzrBPtezRo0ID00fWKpdBVt\ndD6IZIpiqMOOqzd0YDEYwz4xy1BoxiOj12lWxSyXeaCVo6CVMkVAiZu39qLdbsTn7n8N7/nhC7j0\n67uw/p/+B5d+fReu/OaTRQVpvkgcH7/nVTgtBnz7PZsLWn6sddlyBhlHZ/xIpijOWdWEVqtBMUBL\nD0rP/zey6LWIlNh1KZ2vijVo+TtLAXUCNF8kW0HrbjbDqNOcMY0CBaMNSulpAN8D8GcAvwLwz5TS\nMQAUwAKldIxSmuVFQAj5CSFkjhByQPaYkxDyGCHkuPh/i+xnXyCEnCCEHCWEXK/GL6cW0UQSh6Z8\n0gigcuhwmDCbZyh0LRAGpRvyOpvbTLqSuk2nPRF0KShQDKfVgB2fugyfvnYo73blMOCy4d3n9eCX\nL54uORU56g4q1p8Bwur4qvXteOT1GSQKGOWOL4ZUuagsR22DUgDY0GXHkTqlOOdlHmgMYWC6soKW\nL0DrajJj2hPJmV6a9IQRT1Ksa7fh4rWteOa4W9quUMNMuouz9BTnwSkfhjrsJXuWsb/x8ptqvhte\nJaxuLd8LjTUIDHXYcYWo1uw6IjRiSLWuBRZjQx12nF4MVTxNgAWYPS2l16Cxc6ySAM2k1+Jzbx4G\ngXBd3bbGiY9eMYB/eMswkimKnTm6XOVQSvH5P7yGiaUwvv++c4tajA24rJjyRrLquQ5OpdXbfMbH\nXimILpDiNGgRipe2SEmPeVKqQcujoAXVVNAScCwrYdBqCNa0Wc8Yq42i5CBK6Q8gpDkHKKX/LT68\nAODWPE/7GYA3L3vs8wB2UkoHAewUvwchZCOAWwBsEp9zNyFEHUdGFTg45UMsmcK5vaU3CDDaHUbJ\n/6leCJ1V+bsnS3VQz2dSK2eww16W+lgM/+uaQVBK8d2dJ4p+TiyRwthiKGcHp5wbt3TDHYjipZOL\nittQSvGhX+zBJ+99tejXLxZWRK2mejLc6cDpxVBFFiXlwro122U3xHaHcCNZ3lk6442gyayHxaB8\nznY3mxAWVbnlSFMi2qzYPtiGSU9YCkZ8YVaDljtAsxi00GpIyQoapRQHJ70lNwgAQrdyk1mfraCJ\nVgm5bniV0FeBWe2xWT904s2uyaLH1r4WqQ5NSp8VUNCGO+2gFDgxV5maMbEUhs2oQ7NFX5aC1mYz\nwKCr7Nr07vN78PTfX4X7PnIxvv3eLfjs9etx1+UDGHBZsfNIfhuOV8c8eOT1GXzmuiFs7XcW9Xpr\nFWZyHpjywiHOf803Ro0pVS3WAl2cem3JATSre8vZxWnUIhRTNoBmyt4pFZRVn0KX9plktVH0WUkp\nDVBKQ7Lvg5RSxeIcSunTAJbf1W4C8HPx658DeIfs8d9QSqOU0pMATgDYVuyxVRtWg1Sxglb3FGes\n4KrWbtIjEE0U1UVDKcWUV9mktlb0Oi24ddtq/G7PeNEpk7FFIUWTT0EDgKuH22E1aPHgvinFbfaN\ne3Bkxo9jMwHVR1ItMAVNJZsNIH1jPFqHkU+sUSYjxWk3IpGi0sWZkc8DjcHOvVydnPI5q9vXCQXX\nz5wQ0pySgqbQsEIIgc2ok1KhcvacWlRMe8/6olgIxkquP2O02bLrsualFKe6AZrTaoDNqMuak1sM\nR2cCWNNmlQKbaza048iMH5OecNH1TUOiv1elau74Ygg9LWYQQqTUdCk1aJWoZ4W4ZkMHXhpdzJuV\nePi1aRh0Gtx+cXHekIB8bFFmoCHMf20SLGxsygqap4iOfkBQB4u1LGHkU9DMBi1SFIjmmD6RTFGp\nflGVFKfCrN0Blw3jS2FEE/WfElOIWvugdVBK2YTZGQAd4terAIzLtpsQH8uCEHIXIWQPIWTP/Lw6\nrc2F2Du2hFXN5oo+yGxgej39VzwFvIkAwC76kwWLaK1eEGcodpdZYKsmn7hqHXRagn9//HhR25+Y\nEy4AhRQ0k16LN23qxI4D04of6Ht3jwEAYmLNk5qwAnF1U5yCulOPRgH5HE4G+3p5x9mMT9kDjcEC\nuFzp7VF3EM0WPZxWA9a0WbGq2YxnjwvXDBZ4LU+ByFFSk//u96/hE/e8mvN8YJMnylHQgNwNE+5A\nFFaDtqjJG6VACMHqMoemH5/zY0jWMHX1sHAp33VkDp5wHISk6/iU6Gu1wqjTVDwbdnwpJDUiaTUE\ndpNOagIpxLS39CkCpXD1cDtiyVSWzQsjlaJ45PVpXD7oKvh+yelrtYCQTAUtkUzhyHTa3qXdYYQ7\nkK1MA8U3CVjK8EGbD0Rh0GpyfrasohqeS70XDIaFz93EUlhxPm8xJFMU/mgi5/1OGpqukt9aNamb\nUS0VIpWSoxVK6Y8opVsppVtdLlcVjiybvWMebKlAPQMElSCaSEmplVqTSlGccgclywslSnFQl0xq\n66ygAULK7I6L+/GnfZOKReNyRt3CynNNW34FDQBu3NwNXySBp49lX2T9kTge2j+NzeKsPLVd+t1B\nwXW/FGPfQvS0mGEz6upShzbnF7p+5V2p0jSBZQrzTEkKWvbf/OR8UPr7EkKwfV0bnh9ZQCKZgk9s\nmDHnmPHJyGXaPDIfwEl3EO5ADP9zIHsO44EpLwhJB8Gl0mYzZtlsuAMx1evPGH2tpXuhhWNJjC2G\nMNSeDtAGXFb0t1qw6/AsvKEYHCZ9QZNerdhIUclnhlKKiaUwelvS17Vmi76kFGc5HmjFcn5fCxwm\nnWId2t7xJcz4InjrOZ0l7dek16K3xZKhoLH5r0y9ddkEZdqT473whGIw6TU5Z9zKMRu0JTv/M5Pa\nXLXOrEEtVx3aoqigb+ltRjJFpfmq5eCPKNeYnklD02sdoM0yc1vxf5acnwTQK9uuR3ys7sz5Ipj0\nhMvyP5MjWW3UqVFgfCmEYCxZ0CakFAd1VifQnccDrZa8/6I+UArc/8pEwW1H5oJotxuLWrVuH2xD\ni0WPh/Znpzkf2DeFcDyJf3zrRmgIcEzlAG0hEEObNX9jR6kQQjDcaa9LJ+ecT3DEl3epsVSIvF4m\nmkjCHYih05H/3GqzGaHTEEzlsNoYdQewti2tkF462AZ/JIHXJ71SC36+99Wew7R5l1hn5bIb8csX\nspvXD075sLbNCmuZAXVOBa0KJrWMvlYrJhbDJd2ET8wFQCmwvjP93hJCcPVwB54bWcCUN1JQmWEM\nddgrUtAWgzGEYkn0tKTPkyZzcQEaM0KupoKm12pwxfp2PHF0LqeS9fBrMzDoNLh2Q0eOZ+eHzeRk\nMPWWeaC5RGU615SOpVBhk1ogneIsZfKIMJYs976teTI0rEHgPNHe6FQFac58NaZs0XYm1KHVOkB7\nEMAd4td3AHhA9vgthBAjIWQNgEEAu2t8bDmRDGpXl98gANTfC43NZxsusLIvRUH788EZtFj0GO4q\n3RuuGvQ6Lbh4bSt+/+pEwVTyqDtQML3J0Gs1uOHsLjx2aDbrRnbv7jFs6HLggv4W9LdZVVfQFgJR\n1Sw25GzocuDItL/mKfflHmiATEGT3UiYmlZIQdNqCDqbTJhepqAFognM+qIZNYaXDghe288ed8MX\nyZ3+kOMwZVvO7Dwyi+FOOz58+VrsOb2EQ1OZQa7QIFBe/RkgBJyBaOa4J7XHPMlhKbiHX5suvLEI\nq11cPiPymg3tiCVSePrYfMEGAcZwpx2zvig8ofIMa8fFiRi9ssxAk1lf1P4ki40ql2hcM9wOdyCG\n1yYzzQ5SKYodB0pPbzIGXDaMugNS8HRgyguzXos14qJEyVcPKK7cBYCkMOeqGVNCacwTAClNn0tB\nY40L54nTeiqpQ0vXmGYvlOwmPVx2Y0UBYK2oWoBGCLkXwAsA1hNCJgghdwL4OoDrCCHHAVwrfg9K\n6UEA9wE4BOB/AHycUtoQFXx7xzzQa0nZNSWMDmncU30aBY7M+EAIsL4jfzBlE0/oQtMEQrEEdh6e\nw1vO7soYpVFvbt7ag9MLIewu0HU5Mhco2CAg58bN3QjHk3hc5pj++oQXB6d8eN+2XkmVqrSeZjkL\nQfXGPMkZ7rLDH00UlQ5WEyFAy7x4Www62Iy6jBSnZFKbZ4QYo7vJnKWgnZxnNYbpv3GrzYhN3Q48\nc8INbzgOe8EALdO02RuO4+VTS7h6uB03n98Lk16DX754Svr5YjCGKW9EUjDKgamJ8puqu0pBOgBc\n0N+CAZdVqqMshuOzfhi0GqkLNL0vJ2xGHaKJFJqK9DtkjQJHy1zYpE1qS1fQKjWpLZYrhlzQEGDX\nsjTn3vElTHtLT28y1rqsiMRTmBYDzYNTPmzoskup5fa8AVqsKAWNpSQL1aEtBmP4xQun8M67n8Ph\naZ/iZBlWgxbKMY+TKWhr26xoMusrCtAK+Rz2tJhrfu0rh6rdWSmlt1JKuyilekppD6X0x5TSBUrp\nNZTSQUrptZTSRdn2X6WUDlBK11NKd1TruEpl79gSNnY3FczVF4KpBvVT0HxY02otWGjskGYQ5r/A\nPXZoFuF4Ejdu7lbtGNXghrO6YDPq8Ls8ac6FYAy+SKJoBQ0AtvU70eEwZnRz3rN7DCa9BjedK/Sz\nMF+nUms28rEQiKnawckY7hRHPtW4UWBeNodTTrvdmNEkwIr+i7l5djWbspoE0jWGmX/j7YNt2Du2\nhBlvOOfqWs7yJoGnj80jmaK4ZkM7mix63LR5Ff60d0oKBtiQ6koUNEn1EN+LRDKFpVC8ailOQghu\n3bYar455ig6Sjs76MdBuy7LNMeg0uHxI6JYtVkFbL5ZclLuwYXVK8ho0IUAr/Bmc8eUfJaYWLVYD\nzu9rybLbePi1GRi0GlxTRnoTkNVSzQVk81/T514+BW0pFCtosQGkFTSla9quI7P44M9fxravPo4v\nPlOC88UAACAASURBVHAQ4VgSX7hhGJ990/qc27OAL2eKk5nnWg3ob7NWZLVRyOdwVfMKD9DeCCSS\nKbw24a24/gwQpF2HSVeSF5qaN/ojM/6iUpHFOqg/tH8KnQ4TLijSt6dWmA1avO2cLjzy+rSiz9cO\nsbi7lEJujYbgbed046ljc/CG4ghGE3hw3yTedk631Mqtlq8Tg1JatfQWq0U8UsM6tEQyhYVgTKqN\nkdNmN2JepqBJcziLqG/sajJjxhvJqJMZnQ+CkLRbPmP7ujbEkxTHZgOFO5pFyxmWBt55eBZOqwFb\nRD/E2y7uQziexB/ExQAzCa1EbZemCYg3VTZJwlWlFCcAvOu8Hhi0mqJVtOOzAQwpTElg3ZzF1qB1\nOkxwmHRllwZMLIXhtBoyav4cZr3YEZg/fc/OsWqnOAHhfTk45ZNeU0pvDrnKnk3MMgCj8wGMLYYQ\niCYy1FurUQeLQZszQGOm5YUwiQFVrnFgoVgCH/z5Hrw24cWd29dgx6cuw//8zeX48BUDaFL4+7O/\nU65722IoBoNWA6tBi7VtVpxyl98kUGis4apmweC6lNq6esADtDx4wnFs7W/BxQOthTcuglK80J4f\ncWPzVx5VxQ8mGE3g9EIIGzoL3zhYt2A+3x5PKIanjs3jbed0FRxJUg9u3tqDUCyJh1/PrqtZCsbw\nrUeP4qK1Tly0trTg8sbN3YgnKf58cAYP7Z9CMJbErdvSvS2VpmuWE4wlEU2kqpLitBp16Gu11HRo\nujsQA6XIObe13W7MqEGb9kZgN+qK6l7tbjYhnqQZ/mGj7iB6WsxZyvcF/U7Ju0tpdc2wm3RIpihC\nsSQSyRSePDaPK9e7pBTSWauacO7qZvzqxdOglOLApBc9LeaKxpktV9Cq5YEmx2k14PqzOvHHvZMF\n53L6I3FMesLSub6cq9a7oCswm1cOIQTrKygNYB5ocprMesSSqYL+XTO+CKwGrWQtVE2u2dAOQLAh\nAYTa5krSm4CQDrebdBiZD+KAgnqby6yWUgpPKF5wzBOQVtDCsez3ct4fRYoCf//mYXzhLRuKWvBa\n89SgeYJxNFuExp3+VismPeGy5sQChWftrmoxI5ZMKQ6TbxR4gJaHNpsRv7zzQly/qfwPkZxSxj29\nOLKAeJLimeOVe72x1WmhBgFA7qCunOL8nwMziCcpbtzSWOlNxnmrW7C2zYrf78lOc/7/jx6FP5LA\nV248q+TOyHN6mtDXasGD+6dw78vjGOqwSR1HQNrXSa0ArRomtXI2dDpq6oUmTRHIGaCZMm4kM97i\n7Q9YvYu8Dm10PrODk2HSa7FNVH2LUdAAId2/d9wDTyiOa4Yz01G3XdSHUXcQz51YEE1CK6tVZcE4\nmx7ALDeqZbPBuPWCXnjDcew4kL9Z4LioDisFaK02I/74sUtx+yX9Rb/2+k47js6U17Cy3GIDQNHT\nBGZ9EXQ0mVTtkFZisN2GnhazNA7rkdenK0pvAkJwu1ZsFDgw6YNemz3/NZdZbSCaQCJFi1I589Wg\nSYa0JZybUpNAjhq0xVAMTtF+p7+t/CkXgPC312qIFBAuZ5VozzOx1NhpTh6g1RBh3FNxETtLl7w0\nqlzsXizM76qQxQaQdlDPl+J8cP8U+lstOLtMt/RqQwjBu8/vwe5TixmdOq9PeHHv7jF84JJ+qfal\n1P3euLkbz424sX/cg1suWJ1xcWe+Tmo59LurYFIrZ7jLjpMLwYpnIRaLNEUgR81Pu8OIUCwpKbfT\nJfhTdYuNBKyTk1KKk+6gosfd9kGhTqpQakne0bzz8Bx0GoLLxBorxlvO7oLTasAPnjqBk+4gzqqg\n/gwQOoabLelxTyzVWU0FDQAuWtuK/lYL7t09nnc7ZiOTr9no7J6mktJ26zvs8EUSUk1YsaRSFJNL\nYfQ4sxU0oHCAVm2TWjmEEFy7oQPPnnAjFEsI5rRDbWWnNxkDotXGwSlvzvmv7Q5jlkqUNqktzmYD\nyJ2SzDcxQAk2ti1XDZonFJOCRra4Oukur1zEF4nDYdIpBt+rWpT9ExsJHqDVkA6HCXP+4vLeTLJ+\n6eRCxVYIR6b9sBt1WakAJfIFaHO+CF4YXcCNm7trsvIsl3ef1wMNAX4v1gelUhT/9MABtFqN+NS1\ng2Xv98bN3aBUKIh+13nZwy6GOuyqK2jVujkPdzpqOvJpNq+CllnQPFPkjFcg7cPHFLRZXxShWDKj\ng1POZWKA5ixQJC0fmL7ryCy2rXFm3VBNei3ee0EvnjshjH7aVEEHJ0OuekiD0qtYgwYINZbvvWA1\ndp9czFtDeWw2ALNeW/S1pBjKLQ2Y9UcQS6bKV9BKUGnV4OrhdkTiKdz9xAimvRG85eyuivc54LJh\n2hvBvnFPTvU2l4JW7KxUIJ3izJVqzDdzUwmthsCk1+Q2qg1mK2gny6xD84bz2+gwBa3RGwV4gFZD\nOuxGxJPZMweXM++PYtYXxWC7De5ArGLH48PTPgx32YsOqPINTH/49WlQioZNbzI6m0y4bNCFP7w6\ngWSK4vevTmDfuAdfuGG4olXrYIcd2/qduPn8npwr0OFOO+b8UallvBLYoPRqKWgbpZFPtalDYwpa\nroCTXeTnfBHEkynM+aNFNQgAQkG6Sa+RVsOjshmcudjU3YQf37EVbzsn/znMUpyHpv04NhvA1cPt\nObd737bVYB+tShU0gE0TSAdoRpUnSSjxF+f3QKch+O3Lys0Cx2b9GOywqVp7ytRspQBt5+FZfOzX\nr2SN/pnI4YEGFBegJVNUOMdqpKABwIVrnbAYtPiPp0dg0Gpw7cby05sMtgjxRxI557+67EZ4w/GM\nsWTybslCmAukODUEUlBVLFaDLmcDlycUl66pdpMebTZD2V5lSoPSGXaTHg6TDpM8xclhpM1q86c5\nWbv+X29fAwB5Pb0KQSkVOjiLaBBgOHKMuGE8uH8KG7ocWNfeGOa0+bh5aw+mvRHsODCNb+w4gvP7\nWvDOc3OOeC2J+z5yMf7lHWfl/BlTA9TwQ2MKWqkXwGLpaTHDatCqbq6rxJw/CqfVIBXpy2mXXM+j\nmPdHQWnx/lSEEHQ3mSWrjRHxop7P5+6aDR0F3f6ZDccDeyel5+Si12nBtRs6sKrZnDN9WyoumeWI\n4Mqee2yO2rjsRly3sQO/f2VCce7ssVk/BlX+7DdbDOhwGBWV3O/uOoFHXp/BT587mfE480DL1SQA\n5A/QFgJRJFK0pgqaUafFZYNCF7Ea6U0gcxGSU0HLYbXBRj8Vo6BJNWgKTQKtNmPBkV7LMRu0WWUV\nqZQgXDhli941bdaym+SELtX8v9+qFgtX0Dhp2osc98Tqz95ydhdcdiNeOrlQ9mtOLIURiCZKspSw\nKSho44sh7B3z4O2bK5fma8G1GzrQZNbjb+/bj6VQDP980ybVVv5KN0wWCKuRNnQHYrCbdFl1JWqh\n0QgddIdqpKDN+yOK3X3s8Tl/VDKpLeXm2dVswpQ4G/bkfBBmvRYdOew8SoGtwPecXsJalzXv3NZv\n3rwZv/3wRRW9HqPNZpRqz9yBaNUbBOTcum01lkJxPHowe3akJxTDnD+aMeJJLdZ3OnIuao7P+rF/\n3AO7UYfv7jwu2VQAwPiicHNd1Vx6gFYrD7TlsCYTNdKbgGAjoyFQnP/KFj4ZAZqooKlRg1ZK/RnD\natBl1aD5IwmkaKaq199qxckyvdCEGrQCAVqzmStonDQdjnQaJx8Hp7xY7bSgyazHhWuceGl0sew6\nNDZvsZRxTHaTLqfNxoPiLMq3F0gNNQomvRY3belGNJHCX17YV5GBaLF0OIxwmHSq1KEtBGNVLw7f\n1N2Eg5PerPRRNZjzRxUVpmaLHgatBnP+SFkO73IFbdQdwJo2a8XBuF1mZHuNQnqT0WTWo2dZLVS5\nuOxGBGNJhGIJ8SZY3fozOdvXtaGnxZzTE+3YrJA6Xj7iSQ3Wd9hwfDaA5LL63N+/MgGthuDnd25D\nPEXxrzsOSz8bXwqhw2HMslJhqem8AVoZiwA1uHFLN/6/mzYVTK8Xi1GnRa/TggGXTSrAl5NTQQvl\n9wiTU6gGrZT6M4bFqM2qQWOD0uXWH2tcVsz7o0XNhV5OoRQnkJ4mUOtxd6XAA7Qawk7mwilOn2Q4\neOHaVsz4ItJqsVSOzPiLGvEkp8ViwPhSCH/10914YN+kJEc/tH8K561uzqr5aGTu3L4GN23pxt++\naagmryeMfHIoBmjT3rBkbFqIhUAUrVVKbzK2D7YhGEvildNLVX0dQKhBU1LQCCHSoHBpikCBQely\nuprNmPNHEU+mMDofLGmMlxJmvVZK31w9XHm9ULG0yaw2WIqzVmg0BLdc0IvnRxbwJzG1y2CqcCnX\nkmIZ6rAjmkjhtEwxSSRTuH/vJK5a347zVrfgI1cM4IF9U3hxVMgojC+GshoEAKEQ3W7SSV5YuaiX\ngmbSa3Hbxf050/zlctfla/Hhy9fm/NlyXz1AqEGzGXVFHYNeS6DVEMUatHICtFw1aMyQWa6grWkV\nPsOlWm1QSuELJ+Aw5y9h6G42IRBNSIPVGxEeoNUQo04Lp9WQd9yTNxzH6YWQpPZcuEbwbHqxzDTn\nkRkf+pyWgvU2cj521QA+csUAjs748anf7MPWf3kMH/3VKzgy42+40U6F6Gu14ju3nFuReWipDHUK\nVhu5VmZfffgw/vZ3+6VC9nwsBKozh1POpevaoNcSPHl0rvDGFZBKCUay+QxM28QAbcYbgVmvLXiB\nldPdZAKlwk17Yimk2CBQCoQIN3q7SYet/S2Fn6ASLKU5649gMRit+jmwnL/evgYXr23Fp+/bl9Ew\ncHxW6AavxuxKqTRAtrB56tg85v1R3Ly1BwDw0SsGsKrZjC89cBCJZErwQFNYLBaaxznjjUCrIVWb\ncVpL/vLCPty8tTfnz5xWAwhBhr2TNxQvetIDIQQWvTarBo1NOSknQDMbshU0j6SgyVKcYklBqXVo\nkXgKsWSqcA1as3DuTHjKn1hQbXiAVmPa7ca8CtqhZeNiBtttcFoNZfuhHZ7+f+3deXydZZ3//9cn\n5+QkJ/ueNGnThK60hbbQllVlcRQVKKCDMKOioui4fmd0FJdxmRlndBydcX4yCzOD4gLIKBVEFBFQ\nBIG2ULZCS0vXpGmaZt+Xc67fH+c+6cm+55wk7+fjwSPn3Oc+d670Dsk71/K5JrZAINLGVD572Woe\n/+wl3PnBc7n8zFIe33eSFH8Sbz1zbsw/i6dVxZm0dvX1z6WKOtbU2b/N1CN7xg5E9e0zt0l2VEaK\nn80Vefxu79QLIo+moaOHvrAbNaAVZUbqBNa0dLFoggVEF3nzkJ460EDYRTZcng6Lc4O8aU0Jyb7Z\n+1EZndezr7aNsJv5GmiDpQX8fO99m3n9ikI++7MX+b43OX/v8cgKzplYsLC8KAOzgXM3/29nFfnp\ngf7Vs8GAj7+5fA17a1v53hOHqGnuHLHcx5gBraWL4syJT3Cfa5J9SeSlBYb0oI03oEFku6fO3oG9\nTM2dvfSG3CTnoA0zxOn1oMUuEqjIn1xAG2uj9KhoLbREnoemgDbLorXQRjJ4w2UzY0tFHtsPDd+D\n5pzj96/WDTtnrKOnj0P17ROafxYrKck4b1k+33jHmez44hv5/V9f3D/pVEa2aoSFAj94MrIl0KLs\nVB5+ZfSAFgo7Gtp7KJjhIU6Ai1cVsbe2dUaLNo5WpDYqut3TRHYRiCr1zn9i/0lg9BWcE/HjG8/l\na1cPv2J3pkR7JaIFpmc7oEFkKO7W95zNm9cW85VfvMx//v41Xq1tHXEHgakKBnxU5Kf3LxRoaO/h\n4T21XLWxbEA4fvPaYl6/spBvPriXsGPYIU6IzGkcqwdtNvbgTATRqQNRTZ29A3qqxhJMHrrqcjK7\nCESlpfiHLDror80WU5swGPCxKDt1wqU2+jdKH8ciAUjsYrUKaLOsOCuFY01dI05M3H2sheKslAHf\n+Fsq8zja0DnsN9Lv9tZxw23b+fK9u4e89mptG85NbFPwkaQm+2Z9Qu1cFZ2j82rMcE1HTx93bj/C\nZetKuGpjGTsONYz6C6Spo4ewY1aGYC5aVQgwbb1oNc1DJ96Ots1TVFFmKo0dvRxp6Jjw91q0B+2J\n1yIBbbQVlxORnZY8ZBL6TIsOS0W34YpHQIPIlIzv/tlZXLm+lK//ag+NHb0zFtAAVhZn9Jd8+fmu\nanpDjnecvXjAOWbGl69YgyPy/TV4F4Go8fSgzfb8s3gZEtA6xi5BESuY7BsyB20qAS094KO9e+gi\nAX+SDdkXtSI/nQMT7UEbY6P0qIKMACn+pIQutaGANsvOXJzDybbu/lIag+0+1jyk2OU53qbeg8tt\n9IXC/MMDkVVN23ZVsf/EwB6b6ArO8WySLtMnOy2ZkqzUAfNp7nm2mubOXt5/QSWXri6iLzz6Pqsz\nXaQ21vKiDMpygjw6DfPQTrZ187pvPMoXf/7SgJAW3WdztB7YoqxTK84mOs8pI8VPVqqfpo5eijJT\n+lfyzUXJviRy0wL9G9kXZs7uHLTBbfmXd27gWm8e2FT3Gh3NquJMDp1sp6s3xP89U8W6sqxh/7hc\nVpjBB153GmYMu98qjB7QnHOT6qWdqwYHtMaOnon1oAV8dA7aeH4yuwhEpQX8dPaGBuyo09TRQ256\nYMjweWVhOocmWGqjeYyN0qPMLFJqQwFNot52xiKSfca2QSukADp7Quw/0Tbkh+DqkiyyUv1DCtbe\nvbOKfSfa+IerzyCY7ONfHto34PU9NS2kB6Z3WxYZn5Ulmf1DnOGw47YnDnLm4mzOXprLxvJcctKS\neWSUYc7oUN2yaZjsPhYz46JVhfxx/8kRC5SO14G6dvrCjh8/fYQfPHm4/3j0F0Q0hA0ndj7LeHcR\niFXq9aJNV+9ZPBVkBPprEcarBy3Kl2R8/Zozuf/jF7LFW7Q0E1aVZBF2kXI+r9S08KdnDz/xHeDT\nb1rFrz75uhFDVlYwmeaO3mFHKpo7e+noCfVvETbfRQOac45w2NHcOf5FAhAd4hw4JDmlIc5hdido\naO8ZUGIjqjI/naaO3gntzDLeOWgQmYemOWjSLzc9wMWrirjv+WP0hQb+VbLneAthB2sHbdnhSzI2\nV+QNWCjQ1t3Htx96lU1Lc7l+yxJufN1p/PLFGl6qbu4/55XjraxelDWt27LI+KwuyWTfiTb6QmF+\nv6+OA3Xt3HhhJWaRZesXryri0b0nhtR9gshf+D986jAbluRMy/D0eFy8qoj2nhA7D02t3Ea0uvv6\nxdl89Re7eezVSC/hiZYuMlP9ow4Xxoa3RZMYfor2uk3HCs54i/7iS/bZhIajZkpSkrGuLHtGdzSI\nFsD91m/2EvAlsXWU7eR8STbq4qfsYDI9oTBdvUPr+x3yyjZUzIMgPx5Fman0hMK0dPbR0tWLc+Mr\nUhsV6UEbOsSZ4k8aMiQ5HmkpQzdMb+wYfl5c/0rOCfSiNXdE56CN3Tb1oMkQ15xVRl1rN0+8NnDI\n8iVv2HO4PdXOOS2PAyfb+4vc3vr71zjZ1s0X3nY6ZsYHXldJdjCZb/1mLxD5Jf9KTQurSxJ/S6b5\naGVxJj19YQ43dHDb4wcpzkrhLetOrYC9ZHURjR29PHd0aCD642v1HKhr5z3nLZ219p6/PJ+AL2nE\nchtNHT386KnDYxZ1PNLQgRl8/31bWFmcyUfveJb9J9qoHaUGWlTs8Odkhp+i89BG2iR9Lon2muWn\nz842T4mgIj+dgC+J2pZu/mRN8ZRK44y2m0B00nlF/typ5zgVp2qhdU1oo/SokRYJFGZO7nsz3etB\n64iZh9bYPvywa7Q3fCILBVq8nuexhjgh0ut+sq1n2EK8iUABLQ4uXl1EVqqfbc8OLFj68rFmctKS\n+1ekxTqnMh+A7YcaON7cxa1/OMAV60vZWB6pz5SVmsyH37CMR/fW8czhBo41d9Ha1cfqWeqBkYGi\nwfj+52v4w76TvGdQccrXryzEl2TDrub84ZOHyUsPTNt2MOORFvBzzml5PDrCQoEvbHuJL/78pRHn\nTkYdbeygJCuV3PQA/3PDJgK+JD5w+w4OnGwbcwVwQUagf9PxydTaiq7Kmq4VnPEUHe4tiOP8s9nm\n9yWxrCjSi/aOTYvHOHt0owa0+nbMhm6yPl9Fv5dOtHbHbJQ+gYAW8A3piZzsLgJA/44HQ3rQhlmx\nXp4X2cpqIqU2mjt7SQv4xlUaJ/ozI1F70RTQ4iDF7+NtZ5by4O7aARWVX6puYV3p8MMIa0uzSA/4\nePpAA9/6zV7CYfjMm1cNOOeG85dSkJHCNx/cyyveL9I1kyyxIVMTrev077/bT4o/ieu3lA94PTuY\nzOaK3CEBraa5k4deqeXaTUtmffXgG1YWsv9EW/8wZdRvdh/nly/WAIw5Ybeq4VTx0MW5afzXu8/m\nWFMXr9a2jTr/DCK/oPO9zdQns0H8yuJM/GMMfc0V0WK18Z5/Nts2LMlhcW6Q168onNJ1Rgtoh+s7\nWJSVOuv/f8VL7HZPTf0rHCdWZmNwWYzJ7sMJp+agRWuhOee8hQtDQ2PAn8Ti3LQJBbSWcWyUHpXo\ntdAU0OLkmrPK6OwN8eDuSOHS3lCYvcdbR1wl5fclcXZFHr96qYafPlvFey+oGPIXYFrAz8cuXsZT\nBxq4zSsuOZPL4mVkqcmRuk7dfWGuOats2MBx6epi9ta2DghEdz59hLBz/Pk55UPOn2kXewVBf/fq\nqV60lq5e/ubel1jh9WyMNdRwZND2O5sq8vjHa84AxjdsWZCRMuEitVFvPL2IP958Sf9igbksGswW\nWkD70uVruP/jF065gOxYPWhL8+d+L+t4DQhow+x5OZaR5qAVTLIHLT1lYEBr6eojFHYj/lFWUTCx\nlZzNnWNvlB6lHjQZ1tnluSzODfav5txX20ZPKDxkgUCscyrzONnWQ3YwmY9etHzYc64/p5yynCB/\nfK2eJXnBOV1uYK6L1kN73wWVw75+yemRQBQtb9HTF+aO7Ue5ZFVRXIZfTitIZ0lekN/HzEP7p1/v\noa61m2/+6XpKslI5eHLkbVG6+0LUtnaxZFBtqrefvZjvvW8zN47w7xBrY3kuZ5VPblslMxu1EO5c\nUrhAe9CCAd+0bMs2Vg/aQlkgAJHJ8in+JC+gRf49JlJmIzU5MsQZLYvRGwrT0NEzhR60yBBnhzd6\nNNw2T7Eq89M4WNc+7IKq4TRPoAetJDuVJEvcYrVxCWhmdsjMXjSz58xsp3csz8weMrN93sfZ2/wu\nDpKSjKs3lvHE/pPUtnTxkreDwLpR6gxdsLwAgE9csoLsEf4CSvH7+OSlKwDVP4u3911QwRfeevqI\nvZjLCjOoLEjvH+Z8cPdxTrZ1865ZXBwQyyyyuvSJ/fV09YbYcaiBHz11hPddUMmGJTlUFKSN+pds\ndWMnboTq7hevKhpXePrHa87gX965YUpfx3wQ3TC9YJb34ZwvRgpozZ29NLT3LJgFAhD5/zpaaqOx\noxez8U2gj4oOSXb3ReahNbT34NzkSmxAZLN0gHavB+3URunDt2lFcSbtPSHWf/U33HDbdm55dD/b\nDzaMOLG/pWvsjdKjkn1JlGSlaohzGBc75zY45zZ5z28GHnbOrQAe9p7Pa1dtLIvU/XnuGC8fi9Qs\nqxil633Dkhwe+MTreN8FFaNe95qzyrh4VeGsTjKXoc45LZ8Pvv60Uc+5ZHURT75WT3t3Hz988jDl\neWm8YYrzb6biolWFdPaGeHzfSW7+2Qsszg3yqTetBCIrqkYb4jzq/ZArX0C//GbKaQUZbKnI49zT\n8uPdlDkpOnIwOKAd8UpsLKQhTvBqobV109zRQ1Zq8oSGkIPJ0SHJSI/XVGqgAaSlDLzeWL16125a\nwneu28DWDaXUNHfyzQf3cu1/Pcl5//gwVY1De/RbOnsnFEDLcoNUJWgP2sSLmMycrcBF3uPbgd8B\nn41XY2bDssIM1i/O5p5d1aQHfKwpHbtm2ZpxVPL2+5L43vu2TFczZQZdurqI/338ILc9fpDthxr4\n/FtXx7Vu3XmnFRDwJ/GZn71AQ3sPt79/S/+QxNL8dOrbe2jpGn6OxxFvLt1I+yPK+AUDPu7+8Hnx\nbsac5UsyMlP9/dv+REV7gCsKFtb3aGFGCofrO8hNC0yoSC2cCmjReWhTDmiDFgn096CNENAC/iS2\nbihj64ay/vP/sK+OT971HA+9XDtkCknLBOagQWQe2o4p1n+cKfHqQXPAb83sGTO7yTtW7Jyr8R4f\nB4qHe6OZ3WRmO81sZ13d9OwdGE9XbyzjlZoWnjva1L9BuiwcmyryyEzx868P7yPFnzRq9fTZEAz4\nOPe0fBrae7hmYxlvWHmqNy/au3t4hHloVQ0dBPxJY9Y7E5kNw233dNgLaOULpMRGVFFWpAetqbN3\nwnP8Ur1A1TU4oE1yDlqq34fZqTlop0p/jK9deekBtm4oozwvjSf2D6wlGgo7Wrv7JlTcuSw3yPGW\nriGF4xNBvALahc65DcBbgI+a2etjX3SRapjDzgh0zt3qnNvknNtUWBi/oaDpcvn6UnxJRl/Yzeg+\nd5KYAv4kXr+ykFDYccX60nH/kJpJbz+rjOVFGXzx8jUDjleOUdX7aGMHi3OD2rlCEsJwAe3gyQ6K\ns1L6e4UXisKMVBrae6hr7Z5QkVqI6UHriQSYqezDCZH512nJvv45aI0dPfiSbFyV/2Odvyyfpw/U\nDwhWrV3j24czVmlOkFDYURuzX2miiEtAc85Vex9PANuALUCtmS0C8D5OfefmOaAgI6W/l2K4HQRk\n/rtsXQlJBjecVxHvpgCwdUMZv/2rNwxZ9h7tdRhpHtrgEhsi8TRSD9pCm38Gp8LUgbq2CZXYgNgh\nyVNz0Mbatm3Ma6b4+68X2eYpecKldc5fXkBrd1//Djxwas7hhHrQchK3FtqsBzQzSzezzOhj4E3A\nS8B9wA3eaTcA98522+LlLy5axmVrS/prTcnCcvmZi3ji5ks4Y3FiB/RgwMei7NQRV3Iebegck39W\nVgAAIABJREFUUmJDJF6GC2iH6juoXMABrbsvPPEhzmHmoE229ywqLeCj3dvqaaRtnsZynreA5o+v\nnew/1tLpbfM0gd64xdFitU0jlxCKl3j08xYD27y07AfucM792sx2AHeb2Y3AYeDaOLQtLjZX5LG5\nIi/ezZA4MTMWZc+NYFORP/xKzpauXpo7exfc3B5JXDlpAwNaW3cfJ9u6WbrAFgjAwOHIyS4SiJ2D\nNtn5Z1FpAX//IoHILgITD2iFmSmsKs7kj/vr+YhXF3QyPWjRwtbHmrom3IaZNusBzTl3AFg/zPF6\n4NLZbo+IjF9FQXr/7hexjmoFpySYrEE9aNEFAqOVMpqvYhfuTHgOWmBQD1pb95TnS6cHTm0f1dje\nO+lVtecvz+eOp4/Q1RsiNdlHyyTmoKUF/OSlB6jSEKeIzGUV+Wk0tPcMGTrqD2jqQZMEkR1Mpqcv\n3N/zc7i/BtrC+x7Njyl4PNGFSIPLYkzLEGeKf8Aigcn0oAFcsKyA7r4wu440AZPrQYPIPLRE3O5J\nAU1Exi26Rc7gYc6jDZEfbupBk0QxeDeB6NzJhbhIIMXv6x/anGh46Z+D1hOisydEW3ff1ANaso+O\n7r5TG6VPcvX6ltPySLJT89Cide8m0oMGXkAbpuhtvCmgici4RUttDF4ocLSxg6xU/4hbkInMtsEB\n7fDJDgoyUshIWVglNqKi88Ym2lsVOwftZNvUaqBFpaX46PDCXm/ITXhlaVRWajJnLs7hj69F6qE1\nd/biSzLSAxNbYVqWG+lBi1T4ShwKaCIybuV5aZjBoUHFao80dGh4UxJKNKBFtxI6VN++oPbgHKwo\na3IBLdln+JKMzt4QJ6a4i0BUeiBSZmMym7cPdv6yfJ4/2kRbd5+3y4l/wiU7ynKCdPWG+3c1SBQK\naCIybqnJPhZlDS21cVQ10CTBDOlBq+/oH6JfiKK9XhPt5TaLFJbt6AlNeZunqLSUSKHaaCAaXHNx\nIi5YXkBf2LH9YD3NnRPbRSAqupIz0eahKaCJyIRUFKRzMGYOmnOOqsZObZIuCSU2oHX2hDje0rWg\ne9BKsoME/ElkTmKINzXgo6s3NOVdBKLSA356+sL9gW+itdlinb00l4A/iT/ur5/wRulR/bXQEmwl\n58IcjBeRSasoSOdXL9b0P69r7aa7L8yS3LlRy00WhtiAdrhh4S4QiLrxwkouWlU4qa3Ygsk+Or0e\ntCSD/PSpF6oFONYcCURT6UFLTfZxdnkuT7xWT4o/aVI9aGXqQROR+aAyP53Gjl6avfkjR7wSG4s1\nB00SSGbqqYAWnTO5EGugRRVmpnCuV31/ooLJPjp7IwEtLz0F3xT3243uhRrtsZrsIoGoC5bn80pN\nC0cbOshKnfi1ctKSSQv4FNBEZG6L1pGKbpp+1Fuerl0EJJH4kozMVD8tnb39RWo1DD85wcCpOWhT\nHd4ESE+J9KBVNXaSZEwqVMU6f3kBAPXtPZMa4jQzr9RGYgU0DXGKyIRUxtRC27Akp78GWnSYQCRR\nRPfj7O4Lk5cemNTwl0R60Lp6Q7R0Tb0GGpzqQatq6iQnLTCpYddYZ5Zlk5Hip627j6zg5GLNe85b\n2t+uRJFYrRGRhLckWmrD65U40tBBcVZKf0FLkUQRDWi1C3yBwFQFAz5OtPbS2N7L8sKMKV8vOget\nurFzysObAH5fEudU5vHwnhOTDuHvPq9iyu2YbhriFJEJSU32UZod7N9NQCU2JFFFA9rh+o4FPf9s\nqoLJ0zvEGQ1oJ9u6p7RAINZ5yyLz6+ZTL6kCmohMWEVBGge9vQ2rGjs1/0wSUnYwmbrWbo41dy7o\nFZxTFQz4qG3uoicUnqY5aKcG76ZSYiPWRauK8CUZi+fRH4sKaCIyYRX56Rw62U5PX5ia5k6t4JSE\nlB1M5khDB85F/qiQyQkm+/o3Ny/ImHqgSovZiilvmgLa8qIM/njzJbx+RcG0XC8RaA6aiExYZUE6\nzZ29vFzTQtihGmiSkGKHu9SDNnnBmEA1LT1oMZPxc9Knb0iyOCt12q6VCNSDJiITFv1l94dX6wCV\n2JDEFLutkRYJTF7sAqCiaQhowRnoQZuPFNBEZMIqveGiP+w/CaCN0iUhRXvQsoPJ0zbXaSGKHZIs\nzJh6L1WKP6m/2O1UNkqf7xTQRGTCluSlkWTw7OFGkn0274YWZH6IBrSFvEn6dAh6PWgBX9Kk64zF\nMrP+0Jc7Tas45yMFNBGZsBS/j9KcIH1hx+LctClv/SIyE/oDmoY3pyQa0AozUzCbnv/Xo/PQ8qZx\nDtp8o4AmIpMSrSu1WAsEJEFFA5oWCExNqtfbVTAN88+ioj1oGnoemQKaiExKtGyB5p9JoirJTsWf\nZKwtzYp3U+a0tGgPWsY0BjRvP04tEhhZwgU0M7vMzPaa2X4zuzne7RGR4UV70LSLgCSqosxU/njz\nJbxpTXG8mzKnRVddTkeJjai0gB8zJrW5+UKRUAHNzHzALcBbgDXA9Wa2Jr6tEpHhRDdNV4kNSWRF\nWanTNm9qoUpNnv6Alh7wkRNM1vzVUSRUQAO2APudcweccz3AXcDWOLdJRIZx3rJ83n9BJa9bOX8q\nd4vIUMEZCGhFmamUaf7qqBJtJ4Ey4GjM8yrgnDi1RURGkRbw86Ur1MEtMt+V56dxVnkO51TmTds1\nP//W0+nsDU3b9eajRAtoYzKzm4CbAMrLy+PcGhERkfktI8XPPR+5YFqvmZ2WTDaafzaaRBvirAaW\nxDxf7B3r55y71Tm3yTm3qbCwcFYbJyIiIjIbEi2g7QBWmFmlmQWA64D74twmERERkVmVUEOczrk+\nM/sY8CDgA25zzu2Oc7NEREREZlVCBTQA59wDwAPxboeIiIhIvCTaEKeIiIjIgmfOuXi3YdLMrA44\nPAufqgA4OQufRyZG9yVx6d4kJt2XxKV7k5im+74sdc6Na4XjnA5os8XMdjrnNsW7HTKQ7kvi0r1J\nTLoviUv3JjHF875oiFNEREQkwSigiYiIiCQYBbTxuTXeDZBh6b4kLt2bxKT7krh0bxJT3O6L5qCJ\niIiIJBj1oImIiIgkGAU0ERERkQSjgCYiIiKSYBTQRERERBKMApqIiIhIglFAExEREUkwCmgiIiIi\nCUYBTURERCTBKKCJSMIws/ea2eOz+PmcmS0f4bXfmdkHZqstI7ThK2b2o3i2QUTiQwFNREREJMEo\noIlIXJiZL5GvJyISTwpoIjJtzOx0b2iwycx2m9mVMa9938z+w8weMLN24GIzyzez+8ysxcy2A8sG\nXW+1mT1kZg1mttfMrh3jeilm9s9mdsTMas3sP80sGPOevzazGjM7ZmbvH8eXtMzMtnvtu9fM8rzr\n/NLMPj6orS+Y2dXD/Jv8ysw+NujY82Z2jff4O2Z21Pscz5jZ60b4t73IzKoGHTtkZm/0HieZ2c1m\n9pqZ1ZvZ3dH2isjco4AmItPCzJKBXwC/AYqAjwM/NrNVMaf9GfA1IBN4HLgF6AIWAe/3/oteLx14\nCLjDu951wL+b2ZpRrvd1YCWwAVgOlAFf8q53GfBp4E+AFcAbx/Flvcdr0yKgD/g37/jtwLti2rre\n+1y/HOYadwLXx5y7Blgac+4Or7153tf6f2aWOo62DfZx4CrgDUAp0Ejk31dE5iAFNBGZLucCGcDX\nnXM9zrlHgPuJCSfAvc65J5xzYaAXeDvwJedcu3PuJSLBJ+py4JBz7nvOuT7n3C7gZ8CfjnC9buAm\n4C+dcw3OuVbgH4gEO4Brge85515yzrUDXxnH1/TDmPP/BrjWG0q9D1hpZiu8894N/MQ51zPMNbYB\nG8xsqff8z4F7nHPdAM65Hznn6r2v8VtACrBqmOuM5cPAF5xzVd61vwK8w8z8k7iWiMSZApqITJdS\n4KgXlqIOE+lZijoa87gQ8A86djjm8VLgHG+4tMnMmoiEm5JRrpcGPBNz/q+94/3tG+FzjWTw+clA\ngXOuC/gJ8C4zSyISQn843AW8oPhLTgXF64EfR183s0+b2Stm1uy1ORsoGEfbBlsKbIv52l8BQkDx\nJK4lInGmv6xEZLocA5aYWVJMSCsHXo05x8U8riMybLgE2BNzftRR4PfOuT8Z5XPGXu8k0Amsdc5V\nD3Nujfe5osqHOWewwef3ep8HIr19PyQytNrhnHtylOvcCXzZzB4DUoFHAbz5Zp8BLgV2O+fCZtYI\n2DDXaCcSQPHe6+NU+ITIv9f7nXNPjOPrEpEEpx40EZkuTwMdwGfMLNnMLgKuAO4a7mTnXAi4B/iK\nmaV5c7NuiDnlfiLDiO/2rpdsZpvN7PQRrhcG/hv4FzMrAjCzMjN7s3fK3cB7zWyNmaUBXx7H1/Su\nmPP/Fvip1268QBYGvsUIvWcxHiDSw/W3RIZCowE2k0hIrQP8ZvYlIGuEa7wKpJrZ27z5fl8kMhwa\n9Z/A16JDqWZWaGZbx/E1ikgCUkATkWnhzb+6AngLkV6mfwfe45zbM8rbPkZk3tpx4PvA92Ku1wq8\nicjQ4DHvnG8wMJQM9llgP/CUmbUAv8Wbz+Wc+xXwr8Aj3jmPjOPL+qHXruNEer4+Mej1HwBnAKMW\nk/XmhN1DZGHCHTEvPUhkGPZVIkOoXQwcVo29RjPwEeB/gGoiPWqxqzq/Q2Ru3G/MrBV4CjhnjK9P\nRBKUOefGPktERIYws/cANznnLox3W0RkflEPmojIJHjDnh8Bbo13W0Rk/lFAExGZIG9eWx1Qy8Ah\nSxGRaaEhThEREZEEox40ERERkQSjgCYiIiKSYOZ0odqCggJXUVER72aIiIiIjOmZZ5456ZwrHPvM\nOR7QKioq2LlzZ7ybISIiIjImMxvPFnOAhjhFREREEo4CmoiIiEiCUUATERERSTAKaCIiIrKg/fql\nGh7ZUxvvZgyggCYiIiILknOOWx7dz4d/9Czfe+IQiVS8f06v4hQRERGZjO6+EJ+750XuebaaK9eX\n8k/vOBMzi3ez+imgiYiIyIJS39bNh374DDsPN/KXb1zJJy5dnlDhDBTQREREZAF5tbaVG2/fwYmW\nbr77Zxu5/MzSeDdpWApoIiIiMu8drm/nP3//Gj99porsYICffOg8NizJiXezRqSAJiIiIvPWq7Wt\n3PLofn7x/DH8viTeuXkJH79kBcVZqfFu2qgU0ERERGRe6ekL8+jeE/zfzip++0otaQEfN15YyQdf\ndxpFCR7MohTQREREZM5zzvHskUbuebaaX75YQ1NHL/npAT5xyXLed0EluemBeDdxQhTQREREZE5r\nbO/hnbc+yau1baQmJ/GmNSVcfVYZFy4vINk3N0u+zlhAM7MlwA+AYsABtzrnvmNmecBPgArgEHCt\nc67Re8/ngBuBEPAJ59yDM9U+ERERmR9+/lw1r9a28fdXreOqjWVkpMz9/qeZjJV9wKecc2uAc4GP\nmtka4GbgYefcCuBh7znea9cBa4HLgH83M98Mtk9ERETmgW27qlmzKIt3nbt0XoQzmMGA5pyrcc49\n6z1uBV4ByoCtwO3eabcDV3mPtwJ3Oee6nXMHgf3Alplqn4iIiMx9+0+08UJVM9ecVRbvpkyrWRmY\nNbMKYCPwNFDsnKvxXjpOZAgUIuHtaMzbqrxjIiIiIsP6+a5qkgyuXJ+YBWcna8YDmpllAD8D/p9z\nriX2NRfZlXRCO5Oa2U1mttPMdtbV1U1jS0VERGQuCYcd23ZVc8HygjlTPmO8ZjSgmVkykXD2Y+fc\nPd7hWjNb5L2+CDjhHa8GlsS8fbF3bADn3K3OuU3OuU2FhYUz13gRERFJaDsPN1Ld1DnvhjdhBgOa\nRXYd/V/gFefct2Neug+4wXt8A3BvzPHrzCzFzCqBFcD2mWqfiIiIzG3bdlURTPbxpjUl8W7KtJvJ\npQ4XAO8GXjSz57xjnwe+DtxtZjcCh4FrAZxzu83sbuBlIitAP+qcC81g+0RERGSO6uoNcf8LNVy2\nroT0ebJyM9aMfUXOuccBG+HlS0d4z9eAr81Um0RERGR+eHTPCVq7+rh64/wb3oRZWsUpIiIiMp3u\n2VVNYWYK5y/Lj3dTZoQCmoiIiMwpje09/G7vCbauL8U/R7dyGsv8/KpERERk3rr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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# simulate as many steps as you'd like\n", "# repeatedly call this cell to see how it changes over time\n", "for i in range(2000):\n", " step()\n", "# show that an unequal distribution is the result of the random transfers.\n", "# did you expect this? or did you expect a more equal distribution?\n", "show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.0" } }, "nbformat": 4, "nbformat_minor": 2 }