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},
{
"cell_type": "code",
"execution_count": 349,
"metadata": {},
"outputs": [
{
"data": {
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R4uPuOjqC4rrCBHj9dTh7VkWIeBdB66C7O3TpkqksAdzcYNcuFTt95YpS/EWZmBh11lq1qvIcCA93tkTKi+Hrr6FvX1i+vJCnlhZvf6/FXqPp3Kb4fOrDO3++k2/7rMoyPyr4VKC+X3289F546b0Y2nioxX0tpWmFprzT7h1Ke5ameYXmfNHtC7vPAeo1TU7LtUKL3eZ4bcNreE7ypOHshlyJsWFn5+w6v3ldzZs3ly5yITpaykuXpDSZHDfHt99K6ekpJUip00n50UeOm8tSFiyQ0mBQMhkMUu7cWSjThseFy1pf15Laj7Wy/YL2MjE1Mc/2T694Wmo/1krGI70mecn/rvxnV3niU+LlkqNL5KbgTdLkyP8BBxIcGSwrTqsoNR9r5BPLnpBGk9Eh8+y6tEt6TfKSjEdqP9bKQSsGSWCftEInFd8V5r3Mli1QoQLUqQNPPpk9JNGe+PpmGq90Oihd2jHzFIRDhzKDDABO2G6MiEmOyYiSMUkTIbdC7ogdn7F7BheiLmCURg6GHuS343knCElOS87mCpSeGMNeGPQGBjQcQLea3WyOGMqPFGMKk7dPZsSaERwJP2K3cccFjSM0NhSTNLHp3Cb+vvC33cbOijGjPLxaIKZ7Q1iDS2E6kqtXoX17CAiABXZMiPDOO0ppJCXB+vXKY8AR9O8Pgwcrv9Q+feDFFx0zT0EYPBi8vKBECfDwsDkGfdnxZfhP9afyl5V5c/ObdFnUhYazG1JxekV2X9md0c6gN2RYrYF8Y8o/7fop5bzLoREaetftTbuAdjbJaQtSSsb+OZaaX9fkpbUvkWYqWGXkMRvHMPGficw/OJ8OCzpwK/GWXeTy0HlkeCdIKXHXudtl3NtpF9COfoH90AgNAb4BTOk6xeqxiqcfZnHhscdgwwZl0ff0VIqtShXbx+3RAzZvVuN6eEBIiFpx3itcuKCyI7VuDf7+Ng1VaXolrsVeA0ArtHjoPIhPVYEG3Wp2Y9PgTYDyR3x82ePsubqHvvX6sqD3gnx9E9NXMwU5n3QEvx3/jeGrhxOfGo9BZ2B69+m82MLyL7+mc5tyKFzl1fFx8+HvZ/62i09oeFw4PZf05PSN07zQ/AWmPjTVoatlkzRlvGfW+mEWTyt5ceHGjUz3JyGUEcUezJ+vVlqXLsHEifeWsgSoVk1ddqC0Z2lCY0ORSHQaXcY22k3rRkXvTHc1bzdvNg/ZXKCxhRBOV5agknSkb0tTTCmExxfMeDei2Qje3vI2QgjKeZUjsGygXeQq512OvSP22mWsdM7dPEf/3/pzPf46U7tNZWDDgRn37OF871phOpIdO1RC3NRUeOIJ+PlnpThd2E58POzfDzVrKtctKzl14xSDVg4iJimGmT1mcjXmKp/t/Iz6fvVZ2GdhsUoMkRs3E2/SYl4LwuPDKeFegn0j9lGpRMFes12Xd3E5+jKP1H6EEu4lHCSp7bT9vi27r+xWyZm1Hlx54wplDGUAOBh6kCd/e5Kw+DDi3ouzaoXpUpiOJjERYmNt3jq6yEJMjAqFvXlTreA3bYJ2zjsjtIXZ/83myz1fcp//fSzss9BhyijVmMql6EtULlHZYWeFRYHAbwI5eeMkAO5ad4JfC6aSTyVeWvsS8w7My2w4nnsoNLI44enpUpb2JigIIiOV4oyPV36ZxZDDYYcZu2UswTeDWXd2He9tdVyorF6rp2bpmkVCWS4/sZzK0yvTcHZDTt2wr8Hy60e+xqA3oNfoGdFsBJVLVObUjVP8dOQnu4x/dyjMgwehd28YMUIV4bIGkwmmT1cO0atX21c+F/alevXMs2FPT2hg/4JfhUFEQkTGuVqKMYWrMTmWubqriEmOYfDKwVyNvcqJiBM8veJpu47/YI0HuTH2BmFvhTGzx0xAeTRkzW1qC8VfYSYmqqS1a9bAjz8qY4g1zJsHH34Iv/8OTz9tWfEuF86hUSOV/alzZ3jlFXg37zjnM5FnimTyiI5VO9LQvyGeOk9KuJXgg44fOFskh5OclpyhvCRSVc+0M556T0p7ZvoMVy5Rmc7VOqPX6KnqW5Wzr561euzirzBv3FCJLABSUlTKN2s4eDB71nU7OEQXeaRUoZpBQWqFnZUzZ5RjfIkS8OWXzpHvdjZuhM8+U19m588r96qPPsqzlO+EvyfQZG4TWsxrweiNowtR2Pxx07qx89mdHHn5CFfeuELzikWzvLCUkm0XtrH+7PoC+3DeTlmvsoxuNRq9Ro+nzpNvenxjJylzZ+rOqfxz8R9STalEJETYlt3JmvCgwrosCo00maTs3FlKb28VKjd0qJTjxkl56pQFQVNZ2LVL9S9RQko/PynDwgrWvzjyxhtSenmp165//+z3OnaUUggVgujhIeXFi86RMZ3Fi9X7o9NJqdFI6eYmpbu7lO3b59ktPSSO8UgxXsj6s+rLKTumFGjq0zdOyxbzWsjaX9eWG89utOWvKJaM2ThGek3ykt6TvWWPxT3sMmZUYlS+4aX24rFfHsv4H/CZ7COXH19udWjk3WElT0uD7dtVEa70+jw+PmqVVJDs6SEhaoXapo3KznO34+OTmbFeo1HHG25mv8HWrWHPHvXY01Pl9KxZ0zlygqr7vmzZnc/r9WpnkQu1Z9bm3M1z2c6wvPRe/D7gd4vr0zSe25ij4UeRSDx1nkS+HWmX6pHFhZJTSmZsnbVCS8y7MRj0xaNI4IWoCwR+E5hRR8jP4MfZV89SyrPUPWwl1+nUOebhw8pqmv4lcOxYwcapUUNF59wLyhJUJiWdTinLChWyb21nzYJSpVRKt5EjnassAXr2VLlFtVp1eXqq3x/MW+ltGLSBh2o8RCWf7H6H6dE9lhCZEJmhcNNMaXaPC8+Pfy//S6eFnej/a3/C4wo/Y1RD/4boNXo0QkM573J46orPl8Vf5//KFj3Uu27vO5IxF4S7K9KnXz+VhzItTX2omjRxtkRFm3XrVNb3pCT45JPsTvUtWijXndTUzFWnMxk8WCnwI0dUMMCBA0rRDxqUZ7dapWuxacgmzkSeodX8VqSZ0ijnVY7edS2vsDi9+3SG/T4MKSUv3/+yTR+4gpKQmkC3xd2IS4lDp9ERmRjJX8P+KrT5AVYPWM34v8cTnxLPuE7jHJ7sw540r9Cc9M2FQW+wuerl3bElz8qGDWor3revfeK2reH4cRgyRG1333lHGU1iYmDmTOX+5MIpxCbHcin6ErXL1C5wyGJUUhRJaUmU9y7vIOly5lrsNWrMqJGxqi3MekN3C39f+Jtfj/9Kh6odGNBwAGB9LPndpzCLAvXqqbo9oFZt6a+xh4eKTvG0w5bm0iWV0b15c2XNLi5IqSKffHzsEyYaF6eSSZ86Bf/7nzpSuYuQUtJ3WV+2hGzBJE3MeGQGI5qNcLZYxR5rFaZdrNnAAuA6cCyX+52BaOCQ+RpnybjFNoFw2bLKunz7pddLGRUl5d9/S9mihZQPPWSd9Tk4WEofH3UZDFLu3Wv/v8ERhIZKWb26snS3aiVlQoLtY44Yoazl6QmFL1y4o0lMUoyct2+eXHp0qcOS1DoSo8ko913dJ4Mjg50tyl0DTk4gvBB4OJ8226WUTcxXESvCY2emTVMlKtzc1Lmqh4d6PHas+tmjh/Il3LpVJQAuKBs2KN/T2FjlEbBihf3/Bkfw9ddw+bI6Yz52DH7LOwmvRZw+nemHq9HcUVjOJE20/6E9ozeN5rk1zzFy3Ujb5yxkNEJD84rNqVnayYY3OxOVFMXFqIvpi6pigV0UppTyH+CmPca6KxgyBMLC1If3t9+U8SQ8HCZNUlb8VHPGZ5PJusqRVatmd6UJDraP3JZw/ryKirLmqMTbO3shNS8v2+V57z1lLff2Vlb/++/Pdvtm4k1O3ThFQmoC8anxrDq1yvY57xKklBy7foxL0ZcK3M9WJbf53GYqTqtIvW/q0e/XfsVGaRamW1EbIcRhIcQGIUTxDP4tCCVLqnLAoD7QJc2WVT8/GDhQnWN6eKh8lgWlVCk1ZjqhobbLawkXL6osQaNHQ6dOKktQboSHqyJwVavCd9+p515/Hbp2VfIPGKAMc7bSvbsy8m3dCv/+e4dFv5RHKSp4V0AndHjoPOhYpaPtc95GRHwE03ZN48fDP2I0GfPvUEQYuGIgrea3ou6suiw4mH9FAJM0MeC3Aeg+0VH689LZMtIXlHe2vENiWiJJaUlsPLeR05GnrR6rULFmH5/TBVQj9zPMEoC3+XEP4Gwe47wA7AP2ValSxb4HF0UFk0lFIl25Yl3/mBgpy5dXZ3ZeXlLOmWObPEePSrlqlTpfzYtFi1RUUPqZ7HPP5d62Xz91VgmqkNq5c7bJaANhsWHyo6CP5PRd02VSapJdx05OS5ZVvqwi3T5xk4ZJBvnKulfsOr6jCIsNk26fuGVEwARMD8i3z8trX85oz3hkvZn1rJ7/kcWPZBSJ85joIUNjQ60eyxqw8gyzUPwwpZQxWR6vF0LMFkL4SSlv5NB2HjAPlJW8MOQrdITIXn63oPj4KCf9NWuUQ/kDD+TdPjhYZWmvUkXV5cm6Lf79d+XLqNWqVfDx42r8nGjePDPm3GBQyS9y4/p1dVYJ6mwxKsriP8/elPMux/jO4x0y9tWYq0TER5BiTCHFmMK6M+uY1WOWQ+ayJ7HJsQiUl4JWaKnqWzXfPltCtmT7PWtxsYLyfa/vGbJqCJdjLjPxgYmF7q5lLYWiMIUQ5YFwKaUUQrREHQVE5tvx0CH1wZw5E557ztFiFi/8/eH55/NvFxMDLVtCdLQ6Ajh3Thml0pkzJ3vSkd274aGHch6rQQNVS2j5chU+mpfB6tNP1XY5NVVF4zgiiEBKpzvW+7j7ZIv8qeNX9F28rsdfp+X8loAyKDUu35hl/XMIO72NPvX6MGPPDFKMKWiEhoW9F1otQwWfCmwZuiX/hhaQlJbE1pCtVPCpQLMKzewyZm7YRWEKIZagXIf8hBBXgI8APYCUci7QD3hZCJEGJAIDzMvivDEaVXzzyJEq5Zo9/BfvNUJC1ErPZFKKcevW7Pfvv1/F4Scmqnb5+XS2a2dZdvO2bdU5ZnQ0lC9v/9IcwcHqHDUsjOgnexH+9afU8qtjl7otBeFg6EEMegNxKSom35J/a2ez+8pujNKY6QxfogoVfSpmayOlylCUbEzmoRoPodVomfLgFJqWb0poXCiD7htEOe8C5GnIgcvRlxmyagjhceFM7TaVnnV6WtQvxZiCXqNHCEGaKY2237fl7M2zmKSJqQ9OZWRLx3lC2EVhSikH5nN/FlD09yl3I3XrqvriRqNSWgMGZL8/frz6IjpyROWWrJr/1sxiDIbsxil7sWOHiqAKC2N3RRMP1fgd09wNNK3UgqBhQei1uad7szd1/epmKEmD3kDbgLaFNre1NCrXKMM4ZdAb6FK9yx1tXt/4OgsOLkAIQZdqXVg9cDUaoWHgfXl+1AvE4JWD2XF5ByZp4snfnuTam9fyDDs1moz0XdaXdWfXUblEZbYP305CagJnIs9kVPqcuXdm0VeYDkOrVQkhZs60fHUZGwtjxqiV1QcfKEutPdizR+VirFZNxV3bwyWmMPD0VLk+V65U9dEfvs1dVqeD9993jmzWMHUqfPyx8r00mZjQCeLcAFMyh8MPs+vyLjpV61Ro4lTxrcLmIZuZs3cOjco14o02bxTa3NZSrWQ1tj2zjZ+P/EyT8k0Y2njoHW0WHlqYoYTWnl1Lclqy3ctbhMWFZVTplEhik2PzVJibz20m6EIQJmniasxVJvw9gYldJpKcplbKWqGlaXnby//mRdFWmE2aFNzf7+WX1RlbcrJSciEhBUvxlhM3b6pzuLg4dQ4YGQmLFtk2ZmHi5wcvvKAeh4SobXLjxsoY40y2bVNnpt27Q1ML/9HnzVO+rABCUDlBi5s0kSJMGE1G/L0Kv35S24C2xWJlmZUWFVvQomLukYGBZQM5EHoAozRSyaeSQ8oFT+02laeWPwXAkw2epHKJynm2d9e5Z6zmNUKDp86T2Xtno9FowKiey0n525O7I71bVk6ezIz8EMI+PopXr2bGgyclKWNUcWH/flV6Y/Vq+P57aNgQOnRQZX+ded62aRM8+qjaBbRvb3mm/JYt1ZeWEODry9T5F+n+FomNAAAgAElEQVQZ2Ie6Zeoyq8cs6pet71i5syClJOh8EKtOrspY5RQmYXFhdF3Uldoza7Pk2JIC9b0YdZFtF7blmn187dNreb7Z8wxrPIztw7c7JENRr7q9uPbGNU6POs3C3gvzneOBag8wrPEwvN28aVahGR91/oiwuDBSjSoQxF3nnnGW7DCs8UUqrMuqWPLfflN+fz4+UrZsKWVqasHHuJ2UFCmbNMmM3V6wwPYxC4PTp5W86XHWZcpk+lC6u0t59arzZBszJlMWT0/LfUkTEqT84AMpn31WyuPHHStjPnyw9YOMTORt5reRJpOpUOfv+XPPDF9Gz4me8mqMZe/n1pCt0jDJIH0m+8jaX9eWcclxDpbUcZyKOCVLTSklDZMMsvGcxjI+Jd6ifhRlP8xCpV8/aNZMrSxbtlRndLai16sokm3boGJFVYSrOPDff5nb7vQs9Dqdsobr9coY5Cy6dVPZ8ZOT1WqxfXvL+nl6qjPkIsD8g/MzzvkOhB7gevx1my3HBSEsLizDF1IIQVRS1B3W7pyY/u/0zJVlHOy4tIPutbo7UlSHUdevLlffuEpoXChVfaui1Wjz72QDd9+WHFTm9EqVlPJ85BG1TbcVDw9lMCkuyhIylZC7u7JWT50KvXqp5zdtcq7h6uGHVUmRCROUW1PDhs6TxUpaVGyBu9YdgaCEe4lslQoLgykPTsGgN+Ch8+Dhmg9T38+y44j0SpWgnM+rlayWa1uTNLHz0k4OhRXdYyhPvSc1StVwuLKEuzkfZmCgymQjpYrp7t9fneFVrw5//aV8A+8FzpxR2Y2aNVNnly7sRmxyLBP/mUhkYiTvtn/XKdmEYpJjiEqKIqBEgMXnjMlpybz313scDD3I6Naj6VW3V65t+//Wnw1nNyCR/K/9//iw44f2Et2puBIIZ2X9eujTJzMrkBDKRSk9VK9ZM2UMceHCRa7EpcRR6rNSGaV1S3uWJvLt/AP0igPWKszitSUPDlauRpUqwZJcrILr1qnVZLqy9PBQ2/K0LPWUjxxxvKwuXNjArcRbfLHrC+bum0uKMTOV36XoSwxaOYghK4dwOfpynmP8cfoPxgWNY/816xYHnjpPfN19EQi0Qkvt0rWtGuduongZfQYPVspOSnj2WeW/V/q2c6O//86MjXZzUynFJk5U53XpOSQr5+3v5cKFM5FS0ub7NpyPOo9WaAm6EMSyfirWu8uiLpyPOo9AsPfaXk6NOpXjGL8e/5Xhq4eTkJrAtH+nsf+F/dTzq1cgObQaLf8M/4d3trxDCbcSTOs+Lf9OdznFa4UZHZ3pOyilin++nfRyrB4eyhI8bJiyDO/bBx07qsQSf/6prLOzZqkkEZF3xzajSLN/v/IwMBhU5nUXuRKdHE3IrRBSjCkkpiWyNUTF/0spuRB1AZM0YZRGQm6F5DrG5nObMyzhGjT8d/U/q2QJLBvIHwP/4Ocnfi42GYUAUo2pXIy6mOGjaS+Kl8KcOVN94PR6laasUqU723TsqFaZU6fC3r1Q32w5vO8+9fzmzVCrlkppNnYsfPSRyrxThM9yrSYkRL0ejRpBUJBzZXn2WeXqlZgIb78NN+7I7OfCjK+7L3XK1MFD64FBb8hw+RFCMKzJMLz0XnjpvXiuae4ZvPrU64NBb8iI0GlfxUK3rbuA6/HXqTWzFvW/qU+dWXW4kWC//7XiZ/RJSlJXSRtrQ5cpo0IeQSng69dtH7Oo0ayZyptpMqkjichI5WLkDBo2zIzmcXNTpTnSM9K7uIPopGgWHV6Et5s3QxsPRadRp2dSSnZe3olA0Dag7R2W8YTUBAatHMSuy7voENCBdlXa0aN2D+r62ZB/1QIiEyJ5bMljHLt+jKGNhzLzkZlOq18+dedU3v/rfVJNqbhr3fm066eMaTMmW5t7w+gDaqttD8X26KNqterpqVahznTitoaICFXuISDgzi3u8uXKSf3QocyEvykpmWe7zuD779V5s06nHM9dyjJPfD18ea3Vazzb9NkMZQlqldm+SnvaVWmXo0L68t8v2Ri8kevx19l4biM1S9e0SVn+ee5PBiwfwJf/fpmRKCMnxv89nn3X9hGbEsvCQwv56/xfVs9pK2UMZTIyVmk1WsoYytht7OJl9LEnCxZkJtQYMuTOfI2HDqntY6tWzk9SkRNvvAH//KOs///7n/pbAgPV0cLQodnPdz08YPhwVUvHWbRqpVa4Uto/N6aLDKKSo7Kd20UnRVs91omIE/RZ1oeE1AT+OPMHQghGtx6dY9uktKQMhSqEyJZUubAZ1ngY/139jw3BG3i09qMMum+Q3ca+dxWmTqcUS05MmKBSuQmhVqLL8s9GXejcuJHpKqXVZi8BkfWYpUQJtS2vVq1QxcsVl7J0KK+3ep0lR5cQkRBBXb+6PBH4hNVjnYg4gVao6JmE1AT2XN2Ta9sPO37I5nObuRJzhU5VO9GtZjer57UVrUbL3J5zAUhMTSTVlGq/KCBrAtAL67Iq+YY9KFUqMzGEVitlXAGSE1y/LmWvXlI2bSrl+vWOk3HfPilLlFBJNHr0kDItLfPe0qUq2YaPj5Rr1jhOBhdFkjRjmrwed93mZCAR8RGy7Odlpc9kH2mYZJCbgzfn2d5kMsnE1ESb5rQn8/bNk26fuEm3T9zk9we+z3YPK5NvFD+jT2HQsiUcOKDO/8qUUaUWLN2WP/YYbNyoVn+enqo0raPO65KS1MqyXDnXyq0IkZiqjkM89cW/pMqNhBv8feFv6petT2DZQGeLYzFSSjwneWYcDRh0BuLfj8+4f+8YfQqD1atVtNCjjypXpIKcYV68mLlVFsKxPp4eHo6pl+PCar4/+D0lPytJyc9K8t3+75wtjsWkGFN4Zd0rNJ7TmC93f5nxvJ/BjycCnyhWyjKd9AQjYL8vL5fCzIkKFVTo5R9/KENKQZg4Ua0s08vQ2lJO10Wx4XDYYb7b/x2j1o3KKLn72sbX7DJ2qjGVD//6kB4/92DdmXV2GfN2ZuyewQ+HfuDI9SN8+NeHbLuwzSHzFBZCCFYNWEWVElWo6luVlU+ttMu4967Rx1H06qUcxiMjlbuSa/V317Pz0k66LVZGjiRjUsbzHjqPbO2Czgdx7tY5etXtVaBSGpO3T1Y5LNMS+Pvi33mGOcanxHMl5go1StUoUDG4C1EXSEzL9Ky4EnPF4r5FiXe3vMusvbOoWaom655ex8UxF+06vmuF6QjKl1c1vIuKO9KRI6q8bqp9w8QKndWroWZN5aJ07pyzpclgzek1JKQmkJCagJvWjdIepaniW4VVT63KaDNv/zx6LunJ6xtfp9GcRsQkx1g8/qHwQySkKR9ardASfDM4x3bBN4Op8lUVms9rToPZDQo0xystX8HX3RdvN2/KeZXjsTqPWdy3qPDr8V/5bOdnxKXEcST8CG9uftPucxSRT7QLhzF7tgr97NNHHRGYcnc+tjuLFinH+tat4dKlgvePiVG1h2rXhi++UCWCQ0JUyOvTT9tfXitpV6UdBr0qJ6zT6NgweAMXR1+kc7XOGW0WH1mcoVQT0xLzTcgblxLHsuPL+P3U77zc4mUMegMl3EpQyrMUHat2zLHP7L2zuZV4i/jUeK7FXmPVyVU5tsuJwLKBXBx9kZ3P7uTEKyfw9ShmgRzA+3+9j0QZsdOrUNqbu2NL/uefykiTkqLKHgwZ4myJig7Tp2dG+Bw8COfPq1Wao7l2DV56SVnyr12D555T71NBeP99la4vORnGjVO11UE5fDkhFn1LyBZG/DECN60bPz/+c0bVxV51e7G472K2XdxGrzq9aFmp5R19u1bvyv7Q/SSkJiClzDNzUKoxlebzmnM28iwSia+7L1uGbCEmOYa2AW3xcffJsV9Fn4p46DwyttYFTZbh6+FLI49iVFHgNgTZj78+7GT/ZMd3xwpzyBCVySgxEZ5/Pnvuy3ud++5TsdugnPVtLTlsKfHxmee3JlNm3H5BuHYtswKoTqfS+bm5Ke+Ar76yn6wWYJIm+iztw4WoC5yJPMPjyx7Pdr9v/b7MeHgGXWt0zbH/h50+5MvuXzKm9Rh2PbcrzzPMM5FnuBh1MWO1FJ0czYbgDXSv1T1XZQnwWqvXePq+p6lTpg7vtHun0JzHD4YepPL0ynhN9mLG7hmFMmdOzO05F4PegE6j44MOH9C6cmu7z2GXFaYQYgHQE7gupbyjOItQQa8zgB5AAvCMlPKAPeY2T2C3oe46Fi1SoZPXrqlyu97ehTNvrVrw1FPwyy8qucn06QUf4/33YcsWdfbaoAGsWAG3bikPBJ/cFUd+nL91npjkGBqVa2RxggijyZgt3K+g5Vw1QsMLzV+wqG2Ab4CKTDEvqLVCa1G9IDetG/N7zS+QXLZgkiae+f0ZfjryU8Zz72x5hwENBxS4GNzZyLNM3j6ZUp6lGN95PCXcSxRYni7VuxD9v2jSTGl3GNzshb1WmAuBh/O4/whQ23y9AMyx07yKxYtVQg6DQcWI26NS5N1CiRLqHPP336F588KbVwj44QelqG/cgE6dCj5Gs2aqJvzRo7Bzp1pdlitnk7Kcf2A+gbMDabugLU8tf8rifnqtnsldJ6PX6NFpdAxsOJBbibesliMvSriXYPdzu6nvVx8fNx+eqP8EL7d42SFz2cL2i9tZderOc9K8knTkRKoxlbYL2rLo8CK+2fsNA5cPtFomnUbnMGUJdlphSin/EUJUy6NJb+BHc0jSbiFESSFEBSllqD3mp2tXtfJwUfQoY2OmGG9vu66KJ/w9gaQ05fqz5vQawuPCLV4NjW07Fl93X8ZsGsOPR35kzZk1nHzlJN5u9l+131fuPk68csLu49oTrUZLTpGCIbdCqOBTweJxbibeJDY5FokkxZjCwbCDFvdNTksm2Zh8x4rUJE1sv7gdg97A/ZXut3i8/CisM8xKQNYCJFfMzxUuJpNKILx5c+Fai10UGar6Vs1IKKHX6gu89fvpyE8kpCYQlxJHTHIMB0Ltd7JU3GgX0I5nmjyDuzYzx2qyMZnn1zxfoHH8vfy5v9L9eLt546X34vlmlvXfFLyJUp+Vwu9zP/635X/Z7vX7tR89l/Sk86LOjAsaVyB58qLIGX2EEC8IIfYJIfZFRETYd/AhQ5SbyhNPwDPP2HfsooqUKjlysvPSbRUGNxNvsv/a/ozVY2782v9XetbpSduAtmwavClbyFxcSly+Z5MdqnTAoFMuREaT8Z4uDCaEYFaPWYS+GZpNaeq0Bdu4CiHYOnQrvzz+C+sHrWfCAxMs6vfK+ldITFPZiL7c/SUR8UpfxKXE8ceZP4hLiSMhNYFZ/80qkDx5UViHfVeBgCy/VzY/dwdSynnAPFDJN+wqxbJlma4pS5bAjz/m3G7NGlUOo1kzlew23crsbJKSYO1aldeyS5f8jV1Go/K//PNPlWl9yBDlVvTss+pL4y7hcNhhOvygaq77e/lz4MUDua4cK/hU4PcBv9/x/Lx983h146sgYcB9A4hJiqFH7R483+z5bIahCQ9MoJRHKU7dOEWT8k14bcNrtKzckjfbvIlGFLn1R6FQyrMUX3X/irf+fIuSHiVZ1GdRgfpLKdl5aSdajZa2AW0t7pf1PRYIrsReYdT6Ubjr3CnpXpLIxEi0Gi11y9gxPNmaFEc5XUA14Fgu9x4FNgACaA38Z8mYdk/vVr++Stem00kZGJhzmxMnVGo0kNLTU8oPP7SvDNZiMknZsqWU3t5SenlJ+d57+ffZsUO1T09Vp9GonwaDlHv3Ol7mQuK51c9JxiMZj/Se7C2XHl1a4DE8J3pmjJF+eU3ykitOrMix/bHwY9IwySAZjzRMMshpu6bZ+mfcs7y6/lXpNclLek/2lo/+/KjF/U5cPyEDvwmUFb6oIJceXSrLf1Feaj7WSN0EnWzwTQPZb1k/OWzVMBkeF35HX6xM72Yvt6IlQGfATwhxBfgI0JsV8lxgPcqlKBjlVjTcHvMWmK1bYfx4tTIbP16lbdu2TdWbadBAtQkJUQl5Qfl1FpUa5mFhKhFw+tb6hx9g0qS8+/j6Zp7VCpH5WKOB06ehRYGzWxVJapSqgafOk8S0REzSRIBvQP6dbsPLzStbLDWopLlHw4/yeP3H72h/6sapbMl1911zQhrCQiAuJQ53rXuB4tILysJDC4lPVanXNgRvICktySJLd/2y9Tk+UtWJSk5L5umVT2OSJkzSxKXoSxwbeczustrLSp6nH4BZo79ij7lsokIFFQkESlk2aKCig4xGFaf84IOqyqKfn2pjNKq65kUBPz+lAG/cUH6N91tg+WvYUCnVqVOVO87p08rlysMDujkvI7a9eavtW4TGhrLr8i5GNB9RoG1dqjGVP0P+ZELnCUz7dxopxhQiEyPRaXSYpIl+gf1y7Ne5WueM80+jNOZZwbG4MnrjaL7Z+w3uWnfWPb2OTtWscA2zgIb+Ddl3bR9GaaSST6Vs56GW4q5zp19gP9afXY+U0mFuWPduAuFly1RUUJz5kH/IkMwzzfh42L1bOV9XrVqwcaVUOTF9fe1fQyckBD7/XCnP//2v4O42Fy7AyZMqttuZ9X2KCFJKHlj0APtD9yOlZGzbsXzU+SNCY0PZe20vTcs3zXO1GpkQyfZL26nvV9/hVRkLm8vRl6kzq06GEe0+//s48rJjdluRCZGM3zaehNQExnUaR9WSBfzMmUl3JfLQedCqcqs821qbQPjeVZjHj6vM6gkJyuH9s89g1CjbxpRSJYhYs0ZtgVesgEcesY+8dzPXr0Pv3moF/Oqr8PHHhTNt/HWqfFklI4KnvHd5Qt+0j2twced6/HWqflWVpLQkBII2AW3Y+exOZ4tlN1wZ1wtKgwZqGz5okFKWr9jhxODcOZV0OClJnX++847tY9pCWBj06wcPPAD//edcWfJi7FjYt08FH0yaBDVqwG+/OXzaUh6l8HH3QSBw07rRuFxjh89ZXPD38md2j9n4e/nToGwDFvZe6GyRigbWWIoK63JaETRruX5dWdbTi6c99JBz5WnfXskBqiBaYtEpUJWNxx+XUohMa366h8LlyxYPkZyWLJ9f87ys/XVt+fG2jy0uAHYq4pQcvGKwfG3DazIqMeqO++vPrJcj1oyQS44usVgWF0UfrLSSO10p5nUVmsJMTFRuOv36Sfnvv7aNtXKllHXrStmli5RXr9pHPmupWDFTAbm5SRl+p3uFPHdOykaNpCxbVsq5cwtfRimlPHlSzZ9VYXp5SXnwoMVDfLHziwzXIK9JXnLD2Q02i7Xr0i5pmJjpOrTq5Cqbx3RRNLBWYd67W/KsvPEGfPklLF+uLOXXr1s/Vt++cOqUcmGqWNF+MlrD+++r+kJeXqqapX8OKcWeew6OHYOICBg9WiW7KGzq1VPHB2vWqPNkgwHat4dGludmvBZ7LVuUT1hcmM1i7Q/dn5FIIiE1gT1Xcq/LXZiYpIk3Nr1B3Vl1eWvzWwVOdlGUkFJyI+EGRpPR2aJYhEthAuzfr84cQfkoXrRvHRCnMXKk8iP95x/49dec28TGZvfVTEzMuZ2j0WiUUr98WSU63rAh1xIfl6Mv0/zb5pT5vAzTdk0DYOT9IyntWRovvRcVfSrSt15fm0XqXrM7Oq0OL70XBr2BPvX62DymlJLIhMh8FURkQiQj141k6KqhnLuZvRzH4iOL+Xb/t5yJPMPcfXNZcnSJzXI5g4TUBO7/7n4qTa9E1a+qcjXGCV/WBcSlMEFZx9NzLFasWKCVTaGzZo0yVP3wg9q85ketWirEM7f6Ql9/rf5unU7F19eqZVdxC0zp0lCnTp5hn6+sf4VD4Ye4mXiTD4M+5EzkGWqWrsmlMZfY/8J+jo88nmOJhfiUeEauG8lDPz7E1pCt+YpSu0xtjrx0hNmPzmbfiH35uqrkR2JqIq3mt6LCtApUm1EtTwXRe2lv5h+Yz+Iji2n/Q/tsq8iwuDBSjao+U6opldC44mnZX3lyJadunCLFmEJYXBhf7SncpNDWcHcljjx/HkaMULVgZsyApk3VVrNSpbwLkg0ZopTk5cvKouxecMfZQmHnThg4ULlC/f672mo/+aRtY7Ztq7KhJyUVXnJhG4lLictQIEIIElJVCQ6D3pCnP+TrG19n8ZHFJBuT2XVlF8GvBuebhqx6qepUL1XdLnKvPLmSExEnlJKLDeXL3V/yRbcvcmyb3g7gRsINElITMtLIDW08lK92f0VMcgy+Hr4MaVQ8S7JkjQXXaXSUdC/pRGkso3isMI1GGDZMOYN3764cy3Oib1/46y9VJOuhh1RkT506Sinkl62ncWPo2VMpoaLK4cOZq8qEBOWKYw90usJXln/+qZIKP/88REUVqOu0btMo5VEKnUZH/8D+FrsDHY84nuFzqRGaQi8le7uC8HXPvdDY882ex0vvhbebN91rds+Wc7O8d3lCXg9h/wv7OffauQJnNy8qPFbnMYY3GU5ZQ1m61+zOmDZjnC1S/lhjKSqsK8NK/uuvymoKUrq7SzlpUs6mr6yW1qxuKt7eUq5ZY40xrWgREiJliRLKRchgkPK//5wtkXVs3JjdIv7IIwUeIs2YJuOS4wrUZ8WJFdIw0SB9JvvIJnObyOS05ALPawsmk0mOWjdK+n3uJ3v+0lPGp8Tn2Xb7xe1yU/AmmWZMK0QpHcfR8KOy4eyGssqXVeQfp/9wqizc1W5FixZlKkydTsr338/5VZgzR0oPD+XD16iRUq7pLio7dlj3yhY1Ll+WculSKc+ccbYk1tOpU3aFmZ6BqUYNKU+dcujUwZHBctv5bTIpNcmh87i4k/qz6mdkgvKc6CkTU53nF2ytwiweW/L+/dUZo1YL1arBa6/l3O6ll+DMGTh0CLZvh4cfVnWx330X2rUrVJEdRuXKqrhYbSclro2NVYXJrKkznk6jRtmNOklJ6pjl/Hl48UXbZcyDmqVr0qlaJ9x1RfScOhf2XNnD6lOrSUx1kheDHYhJjsl4nGZKyzBcFSeKh8L09IRdu5Qx58yZTH/CtDSVTCI6OrNtQIA6tyxRQhlGLl1S/oj3Gnv3wqOPKiNYAc8IcyUqCgIDVfLhwEBlhLKGKVNg+HDlf/n22yr7Eqj1ZmoOH6KYGGjVSp21dutm1+zxJmni2PVjhMeF221MezPrv1l0+bELg1cNpvX3rUkzFc8y0l8/8jUeOg/cNG680+6dPEsGF1msWZYW1pVnpE9iopRNm6qtnI+PlPv2Wbc2vxuJjVWvSXqEz2OP2Wfc337LnpB44ED7jDt2rArh9PPLObrn00/V35Ge/HjBArtMazQZ5YM/Pii9JnlJz4mecu3ptXYZ197Um1UvW1LjE9dPOFskq4lPiZe3Em85W4y7dEseFqbSmcXlUGclKAiCg9VWLjYWPv208OUrqkREqNU3qHyfJ2yoPvjXX8rv86uvoGbNTCd3gwHuu892WUG9x8nJKsKqSZP829upDv3x68f59/K/xKfGk5iWyLht9iuWZU/ur3h/RkJdrUZLpRKFXz/QXhj0Bkp6KPehczfP8fLalxkXNI74lFw8X4oYRdsP89o1GDdOOWvv2JH9XvnymfV53N0LnrfybqZqVZVg+MAB9Rq99ZZ145w6paJv0v0+J05UOUPnzlU5NceOtZ/M6Vnuc+KVV9T/wN69KsHz00/bZcqyXmUz/Dn1Gj3VS9rH39LefNvzWyqXqMyl6EuMbTu2wJUuiyIpxhTafN+GyIRI9Fo9x64fY+VTK60eb1PwJl5e9zIGvYGfH/+ZxuUdk3mqaOfDFELuA3V2ldPZ1ty58MUX6mzN3x9mz4bOnQtZyhy4eVMpm4YN1VmqNUgJ33+vDFjPPFPwchJpaeqM0c8vs/xGQVm5Us0dG6t+798/9xDLYsofp//go20fUb1Udeb1nEcZg4111F1YxNWYq9SaWSsj/r+STyWuvGGdX2yqMZWSU0qSkKYCGGqVrsXZV8/m2cfafJhFe4Wp0ahyCh065Hz/pZdg1iyloCIjleP5rVuZRgRncPasWt1JqWQ/dEg50BeU6dPV6johARYuVAmPC7KK1umUY7gtdOyo/gZQK9Xnin8ZhqikKHr83IMDoQfoU68PPz/+M4/VfczZYhUr5uydwyf/fEJV36osf3K5VUcEFXwq0KBsA05HnkZKyTNNnrFanjRTGimmlIzfY5Ji8mhtG0X7DDMgQJW7Xb069zYREZnRL8nJzq+//eOPakUWE6OuFSusG2fbNqUsQW1Xj9m/oFO++PkpRT1/PuzZo6KsijnTdk1j/7X9JBuTWXtmLatOrXK2SMWKkFshvLH5DULjVBmPketGWjWORmjYPnw7C3otYPWA1XzywCdWy+Sp9+TDjh/ipnXDXevOV484Lia9aCtMPz9VQzuv2O7PP1f33d2Vf6a9Q/ykhDlz1NZ02zb13Lp1Kit406Zq652VmjUzV2VarWpnDUOGZKY60+uVW40zKFtWxas3bFiwfiaTOiopYkc+qaZUJJkyFVcXHWdxLPxYxjbaKI1EJkZaPZan3pP+DfrTtUbXbLXfrWFcp3GEvxXOjbdvMLBhnjUZbaJob8ktYdgw5W+YnKySbNibWbNUwbGEBFU2Yft2VfYhKUlZawcMUNvudIYOVenhNm5UDuY9elg375NPqhX2yZOqLlB6JcviwNWr0KYNhIaquklbt2Z+iTiZt9q+xdozazkRcYL2VdrzRP0nnCKHSZoyKhz2qN0DrSYPo1cR4tfj2c+wcypB7CzSre+OpPgrTHCsMtm5M/vW+PDhTOu8lOr8NCsaDXz0kbpspU0bdRU3pk1THg5Go3q9fv9dfbHYg4QEFchg5YrEz+DHsZHHMEkTGuG8DdaQlUNYc2YNUko6Vu3ImoFr0GmK/sextKE0blo3UowpGHQGWldu7WyRCpWivSW3B6mpypo+aZKqRV5Qhg9X22Jvb3BzU6vZ119Xjz08lH+ii+xk9QxITMzZw6GgGLzaht0AACAASURBVI3w+ONq7IoVlXHNBpypLAF+O/EbcSlxxKfGsyF4Aw1nN8wWOlhU+eSBT3ig2gNU8K7A2+3fLlANeHuQYkzh233f8tXur4hOis6/g50p2m5F9iiz+9xzsGSJcrMpV07V9i6oFf3IEWX86NJFjQFw44ZSmMUkh2Sh8vff0LWrUnJCwODBmTXfrSUoCHr1UkEMGo1ycVq61D7yOoEmc5tw9PrRDD9Qg97ArEdmMbzpcIfOm5CawA8HfwBgeNPhGPQGh85nD8Ljwtl1eRdNyjfhzc1vsjF4IyZpoq5fXQ69eMiq80+nuhUJIR4GZgBaYL6Ucspt958BpgLpKaZnSSnn22NuQG2N9+5VUS3t2mXfrv35Z2bZhchIFT0UEFCw8Rs1ujMLe3E6UyxshFDb5vQILXuUvfD0zDQgaTQOyVuaakxlyKohbD63mW41u/FT35/QazO/XI0mI29tfotN5zbxeP3H+eSBT6w2Vvw55E+eWPYEu67swiiNCAR+Bsf/T/X4uQd7rqraRMtPLCfomSCHz2kLl6Mv02huI0zSlFHWIzFN/T8dv36cxLTEQlX6Nu9LhBBa4BvgESAQGCiECMyh6TIpZRPzZT9lCar+d5cuyjgyeHD2e716qQ+Xh4faylnjE3k7SUmZIYL3Mnv2KJev2xVi+/bqvdBoVEDBpEm2z9WqlSol4usLzZs7JBR24aGFrDm9hltJt1hzeg0LDy284/68A/M4eeMkX+3+ipUnrY9MKetVlj+H/smg+wZRzbcao1qOomednjb+BXdy7Poxgs4HZWQG2nFpB0lpSSSlJbHj8o58ehceIbdC2H1l9x1eCxuCN5CclkxMcgzxqfFU8K6AQW/AXetOA/8GeOo8C1VOe6wwWwLBUsoQACHEUqA3YEMAcwGZMyczC/vSpcrRO33b/fXXatUZGalionVZ/uSkJLVd12hU6Qc3t7znkVIVFvvuO3WWtnWrci1KJzISTp+2LcKnKLFtmyqg9uCDKmt9VmbNUl9UGg1Ur67CMNNfW41GRQQlJSl3L3vEfguhshxNmZJ/WyvJWvrCJE3EpWTPYXA19irJacrP12gyci32mk3zuevcWdR3kU1j5MW3+79lzMYxaDVaGpdrzD/D/6F9lfbsuboHgaBVJctc1RJTE1l9ejWlPUvzUI2HbHYBup1fjv7C82ueR6vR0qxCM4KGBWWcMTf0b5gxn0Fv4P2O75OclkxiWiLPNn3W7rLkizUZO7JeQD/UNjz99yGoLXfWNs8AocARYDkQYMnYFtclb9JEZbvRaFQtbpPJsn5du6rsNwaDlI8+mn/7Y8dU2/RsPR07Zt47dUpKX1+VEb1cOSlDQy2ToagSFKT+ViFUQuY9e7Lfr18/83Xw8pLyRPHNoJPOrcRbMvCbQKmboJOB3wTekVXnUtQl6f+5v/Se7C0rT68sr8ddd5KkllHr61rZEvYGRwbL+JR4OXPPTDlzz8w8M76nYzQZZbNvm0nvyd7Sa5KXfHfLu3aXs8E3DTLkNEwy3JGNafnx5fLxZY/Lb/77Rpos/WznA0U8W9EfQDUpZSPgTyDXr1UhxAtCiH1CiH0RERGWjb5unXJbefxx9fjAgZwzHGVFSmVISEhQ1+bN+c/j7p69JK1nlu3AokWZ0T0xMbCqmESQHD6sQii7dVPZn9LZtk1ttaVUBrPt27P3u//+7A76jvCBLWRKepTk2MvHuDH2BsdePnaHX1+AbwDnR59n93O7OfvqWcp6lXWSpJbR0L8hblq1a9JpdPh7+WPQGxjVchSjWo6y6OwvNDaUExEnMiz6Px620XiXA3X96mbIKRB31Ch6IvAJVjy5gpH3j8xxRRkWF0bvJb1p9V0rgs47+EzWGi2b9QLaAJuy/P4u8G4e7bVAtCVjW7zCTOfiRSnLlFG5IP39pbx6Ne/2LVqoPIvu7lK2b2/ZHJ9/rlaSDRqoGjvpzJ+fufr08lJ1a4o6JpN6vdJrINWpk3lvxw719+j16ueBA9n7JiRI+e67Ug4eLOWhQ4UrtwuLiEqMki/88YLs+UtP+d8V6+o/JaclS//P/aVmvEa6f+IuH1/2uJ2lVCv7YauGyU4/dJLbzm8rcP+ui7pK7cfajBVqTFJMvn1wVk0f1DloCFAdcAMOAw1ua1Mhy+O+wG5Lxi6wwpw8WdX8SU+cO21a3u2jolSfKVNU0l1bMBql/OgjKdu0kXLGDNvGKixSU9VRRtbaOlnZvVvKqVOl3L/fOfJZydaQrXLg8oFy2q5p0mgyOlucYk/IzRD5yrpX5Pig8RZt4wubmjNqZmzpPSZ6yItRF/Pt4zSFqeamB3AGOAe8b35uAtDL/PhT4LhZmQYB9SwZt8AKc/HizGJpXl4qQ7iLvHntNbWC9PBQXx7FnJMRJ6VhkiFjtTF151Rni+TCwSw+slh6TPSQhkkG2fq71rLPkj75fllaqzDt4ocppVwPrL/tuXFZHr9r3qo7lqefVlbqtWuhTx9Ve8ZF3syYodLk6fVQq5azpbGZkxEn0QoVl52QmsCeK3ucLFHepBhT0Gl0To88Ks4Mum8Qnap24t/L/zJs1TB2G3ezOWQzHjoPRt5vXTal3Li73iUhYMIEZfQZN85upQzueurXL1bKMiktiVc3vEqHHzqw4kT29Hkdq3bEU++Jj5sPBr2B55s97yQp8+fNTW9imGSgzOdl2Ht1r7PFKdZULlGZFGMKWm3ml+X+a/vtPk/Rj/Z3YX/i45WHQEAANHZMKn9H8lHQR8w/MJ+ktCQOhB6ggX8D6vnVA6CMoQwnRp4g6EIQ9f3q08A/72zz8SnxvLj2RQ6HHWZMmzE82/TZwvgTCLkVwpx9czBKI1FJUYxaP4o9I4r2ario81DNh/DQeaARGtJMaQ4JM3UpzHuN5GRV7uLqVRXrPWeOSklXjAgNPsgn65JI0MO3nTVcjLqYoTBBKc1+gf0sGuu9re+x/MRyko3JjFo/ivsr3s995exU3C0P9Bp9Rl5OgcBDXzTS3xVn/L38OfnKSXZc2kFD/4bUKm3/XdPdtSW/F4iJURE01nL0KFy5orLCJySojPbFCSn59tNjvL4H3tkJK5aY6FA1lxImFnAx+iLJRhW9o9PoCI0LtZekeRLgG8CnXT7F192X2mVq891j31nUL82Uxvht43n0l0dZe2atg6UsfvgZ/OhTr49DlCW4FGbxYtw4lfSjdGll2LKGqlUzk1h4eKi47OJEUhKeV8PRm8DdCK3CtTYlX3ivw3t4u3njpfeidpnadKpqYx2kAjC6zWii/hfF6VGnqVOmjkV9PtvxGVN3TmX92fU8tfwpTkQUXgSyC5fCLD5ER6s46tRUFYEz8v/snXd8U2UXx383oyNdlGmhjLJBQSh77yUOQJwIiCjIEl4FREFFlgqCgiCCoGxFkL2H7L1KoUBZhbZQSvdK04x73j8OTSh0ZNyMln753E+T3Huf5ySlJ88453es3P0rU4Zz4Pv2BcaMcQ09z1u3OM//ww+5NnkeHLpzCAsvL4OmRVMWVPHygtD3DZu6blqhKSLHROLE4BM4Ofgk3BX5lENxAUIehBirI8oFOW4k2KYLWtTIFhaxF66/hknEoS9btwKvvQaMGlXw7rdOx0IQRWmXXKnkFMRsMd6CxD30eiAqitWZniwP0awZl9twBYi4OmVMDL+/0FDg9OmnLlt9aTWGbB0CkUR828MD4R/Ohp//c1w33Ub2RezDwI0DAQDLey/HG3Vtc8L2ZHiT4dhxcwcUMgV83X3Rvkp7Z5tkNiKJSMxMREnPknYJo1p6YamxKNtvPX+zy6aP648wN24EJk0C/vsP+PJLLneQF3o9y7m5u3Mxsnv38r62sKFSAatXc852nTr5i+empgL16rFqUqVKwJ07DjPTYrKyWKOUHuWsP1lU7hF/X/4bap0aGr0GmXIRR1pW4C9QWT7/hZOSeEOrfXtWXcqDQZsGIVOfiUx9JgZtsq+Ar610COqAS8Mu4Z++/yBseBj8PPycbZJZpGhSUG9hPVSYUwE15tVAXIaZOhEWMHLHSGgNWmgNWozYMULy9oHC4DCvXzeVzs3Kyr80wc6dHC5DBERGAlOtL91pF/R6lj37+2/ryjb06cMbNleu5F/FccMGfv9qNUvOzZ9vvc32xsODkwy8vXmaPWRIrpd1qdrFuFZpEA14sZwZ4VAffMCf9aFDrM+ZlJTrZY+PdgpDAHlV/6roVr0bfN0Lj4Tg6kurEZEUAa1Bi6jUKPx+3rxNLkvwUHjk+lhKXH9K/uabvHZHxFPsN/KZLrm55VTldpFKhUbeegvYvZsfr1pl/cZNQZQpY1qOcHMzldVwVdatY3Ukd/endTcfMarpKJT0LInQ2FC8W+9dVPQzQzU/PDznF9PDh4C//1OXremzBv039QcArOy10pp3UEwB+Lr7Gr+MFDIF/NylHxlveHMDBmziELmVve30e7Qmn9JRhzGXPC6OaP9+/pkfokg0ZAjnkTdrRhQfn//1jkapNAldyGTm63ZaiigSTZxIFBRENGAAkUZj3n2ZmSzIUVRYtYq1PL29idq3Z4GUYpyC3qCnDzZ9QGVnlaW31r1FWfosp9oDK3PJi34RNFeiWTPgwgWemnt4cCnesmV55KlycjGq777jsCWlEvj3X57CFgVu3wbi4jhYX144an8/C0w+OBkzj81EgHcAdr630+ywKqmwtghascN0JElJXFcoO/A8W4S4Xj3g5Enn2ZWWBpQqZZq+VqzIa6DFFGMHridcR4PfGiBTnwkBAjpX7Yw9/c0Q8JYQax2m669wFyX8/Hh0mQ0Rb8ycPWuqSeQMFIqcu82eji0sVcyzRXb1x2yeLHzmyhQ7TEcik3GIlLs7P5bLeQocFOTcKbmnJ5fYKFMGqFq1UNf7lhS1mss05xeZUYzF1ClTB8ObDIdckKOcdzn80qPwpOcWT8mdwb17PC3/918eWY4cyc6qGNchM5OVnB48YJGStWuBl6Uvg1sQIolYe3kt4tRxeLfeuw6pXW4O4/aMw7zT81DRtyL29N+Dqv5VLW5DJNFpYVzFa5i2EhnJI6vq1TkuML+A6GJyEhbGReeaNCkyn1vKrs1Q9X0HyoxHNdc7duSU0nzYdG0T1l9Zjy7VumDgiwMlseOTnZ9g0dlF0IpaCBCw5Z0t6FG9B1KyUuDn7oeVoSsRkxaDgQ0GorxPeUn6LIiLDy6i5R8todapIRNk6FmjJ7a8s8UhfUuFtQ7T9eMwn0SvB06d4hFZTYl21s6eBVq0MK0vvvIKsKVw/QdwGjNnAt9+yxtYPXq4TsqlDTxIf4AehwfhmDYTSgAGD3fIGzTI956jkUfRb0M/qHVqbLy2EV5KL7Ml5vJj07VN0IpaAACBMHDjQCjkCiRlJuE57+cQr46HTtRh7qm5iBgdAU+l/defs2u3AxyW+PjzbDK0GRiwaQDO3j+LDxt+iK/afWV3uxxB4RoOiCLQqRPQvTvQoAGvu0nBn3/m3IzZts26TJxnkR9/5LW+jAzcPrgRk3dNwPKQ5bn+ERUW9tzagxveWrz2NrCjOrDvpVrAjBn53hPyIMT4nvNT+z589zBmHJlhtsJ6p6BOOZ5r9BrEZcRBJ+oQnRqNTH0m9KIeGboM3Em+Y1abttLguQYY3HAw5IIcgb6B+KnbT09dM+3wNGy/vh2RKZH44dgPOHw379TUwkThcpi3bvFoMD2d15i+/16aduvXzynUUbYsb8YUUzDVqgFyOZI9gMYfiph6ehaG7xiOyQcnO9sy1h+YPh04Z1mpgjql64BA2FcNeGOQChFfDOONunx4qcZLUMqU8HHzyXN0eSDiAHqs7oGvD3yN9sva43zM+QJtWfzKYnzY8EN4KDxQ1qssetbsCaWM/28qZAp4yD3gLneHn7sfgvyDzHp/yZpkdFvVDeVnl8eMI/l/EeSGIAiY12MedF/pEPm/SNQoVeOpax6qH0Jr0Bqvj1fHW9yPK1K4puRly+ZM+attUtkGEW+geHlZrlL00Ueco71sGe9Yr5C+WH2RZcMGYMwYhIuRMHhfgqjPgFqnxq6buzClwxTn2bVrFxfB02h4dHjyJMe7mkGTCk2wqvcqLLu4DG0rt8WQRrnntz9OVf+qCBsehmNRx9AooFGuTuS/iP+g1rE0m4EMOHL3CIIDgvNtVylX4vdXf8fvr3LudbImGYmZibgYexEfNvwQ9cvVx4P0B+hXv5/Z+dMT90/EgYgD0Ik6TD8yHZ2COqFZYDOz7n0cIZ+/s89bfY5N1zZBrVOjVqlaeKnGSxa374oULofp58e52N98AwQGmrQc4+OBVq14BNqwIecle3mZ365MxkIdribWURgICADWrkXdrDR4/FIdWhggF+TOl0jbu5eXCgD+Mj12zGyHCQC96/RG7zq9Leqyol9FvO33dp7nO1XthNknZnOxLkGOtpXbWtQ+AJTwKIF9A/ZZfN/jJGQmGGMfZYIMKVkpNrWXGzVL1cS9T+8hLiMOFXwrFApRE3MoGrvk06ZxtUidjuMZf/6ZR43FOJSYtBisv7IelUtUxis1X8l3BGJ39uwBevcGtFqejZw+DTyff0E0R3A08iiORh5F56qd0bi8xZu0knA17ipa/9kaGdoMtKzYErvf2w2l/Nlagnp2dslzw9PTJK4rCJaNLouRjACfAIxqNsrZZjBdu7Lc38mT/NgFnCUAtK7UGq0rtXaqDXXK1EHMZzFIykxCWa+yzv1iK2QUjXHy8OFA5848Ze/Vi8UsCgspKUDr1jwyfvttDpIuxnIOHOA17hIlgPXr+bW2bYHx4zmiohCzMnQl6v1aD2+tewupWamStOkmd0M573LFztJCJHGYgiB0FwQhXBCEm4IgTMjlvLsgCGsfnT8lCEIVKfo14unJJSySk1lnsjCp0syZA5w5w7v+27bxJkoxlvPOO6xKlJIC9O9fZL54wuPDMXTrUFyOu4xN4Zswds9Y8268e5cjSorI5+Aq2OwwBUGQA1gAoAeAugDeEQSh7hOXDQaQRETVAfwE4Adb+y0y6PUm0ePs57YiFt4YSKt53DGIYs7PtBATmxELuYwHAFqDFndT7hZ80/r1XMakfXueebnq/4eMDC45c8a8mFRXQIoRZlMAN4noNhFpAfwN4LUnrnkNQHaU+XoAnYQiNBdQ69R4e/3bqDq3quVxbf/7H2csCQKrjb/+uvWGxMRwqJVCwRsez9Lo4s8/eVnDzQ1YuJA/gyJAi8AWqFe2HlRKFbyUXviq/iguVdKoEa/R5saUKTxjycjgza486iQ5Fa2WU2n792fHvmiRsy0yD2tUhx8/APQFsOSx5/0BzH/imssAAh97fgtA6YLaNiquuziT9k8i96nuhMkgr+ledOjOIcsb0ettN2TkSCKFghXdvb2JNm/OcXrhmYXUY1UPWnhmoe19uSKiWCRV1fUGPV15eIUS1YlEr75q+h17ehI9fPj0DX36mNT9VaqCKxXYC52O6MsviTp2JFq3Lue5kBD+P5pdgaB+fYeaBisV113ua1gQhCEAhgBApUqVnGyNedxPv58jq6GginjHo44jMTMRXat1hZvcjV+UYt1VLs8ZtP/YKGtL+BZ8tuczqHVqHL57GAHeAXit9pMTgUKOIBSt0sqPkMvkqFOmDj+JiDAt2wgCxyA/qXS1ZAkrYN29y3n+pZ2kcDRzJvDTTzzaPXkSqFGDFaAArmaa/bvy8ODRZiFAiin5PQCPV6QKfPRartcIgqAA4AcgIbfGiGgxETUmosZlnCR5phf12Hd7n1mpawAwruU4lPAoAU+FJ6qXrJ5nVsP3R7+H9wxvtPmzDd5e/zbaL2svbc71pEmc5unhwdO27t2Np67EXTE69SxDFq7GX5Wu32Icx9SpvMmpUnEUQK1aT1/j788lmY8eZe0FR3L3Li8LqVTAypXsLAH+Mr91K6eNhw4B/foBn33m2pVNH8PmwPVHDvA6gE5gx3gGwLtEFPbYNSMA1COijwVBeBtAHyJ6s6C28wtcv/jgIs7cP4OOQR3N1uI7FnkMs47PQs1SNTGlw5RcU8mICB1XdMTZ+2chkogp7afgs5afFdh2pi4TD9IfoJJfJeMi/ZP2ZktiZeOh8MCNUTcQ6Btolv22cDPxJhotbmR8fm7IOVQvWd3u/ZoFEe9w+/q6XqVPVyQmhssn163renJ6ffoAmzfzRlO2ULZSySF/ly7xTxfAaYHrRKQXBGEkgN0A5AD+IKIwQRCmgNcJtgBYCmClIAg3ASQCyDt/7DH0oh7Dtg1DliEL37T7BpVLVAYAHLl7BN1X8+hJJshwYeiFAv/4Y9Nj0W1VN2ToMuCh8EBaVhoWvrzwqevup93HyaiT0Bi47s7Pp342y2F6Kj3zFT9I06Y9lR7mqfB0mCBs9ZLVcX3kdZyPOY+GAQ3xnPdzDum3QEQR6NsX2L6d/8D27uViccXkTUAAH0/y8CFnvQE82yhb1rF2AZw8kj0IUyhYY1alApo25drzhRxJ1jCJaAeAHU+89vVjjzUALE4uvpF4A2EXwiCSiP0R+3Fn9B0IgoCN1zYaR2qeCk/sv72/QId5N+WuMUhXo9fkOd0upSoFD4UHNAYN3ORuqFfW/Pzj/GhZsSU6VumInTd3QibI0LlqZ8zqMgvucnfEpseilKoUFDL7LimX8y6HHjVcrBrkhQucxqjV8vHFF6wyVIzldOpk2hE/eBAIDXW8DbNn8+80JgZ47z2gZ88ita7sYuP5nGj0GuhFPUQSEZUSZRQMaFWxFVRKroEjCIJZObkvlnsRFX0rwsfNB54KT4xuPjrH+dtJt7Ho7CJcfngZhwYdQp86fTCowSCseX2Nze+DiDD/9HwoZAr88eofSPsiDdve3YYqJaqg6ZKmqPxzZQTOCXSYnqFL4etrihOUy7l6ZTHWcfUqbwjp9fzYGdSsycpfOh3w22/sLFNTeb21CGSzudwu+eOU8iwFtVINQeBSnNkCAa/XfR0EwsE7B9GnTh80Kt+ogJYAd4U7zg45i0N3DqGiX0W8UPYF47k7yXfQ4LcGXM1OADa/vRn/vvmvZO9jyYUl+GL/Fyx7dmsXapWuhSYVmmBL+BZci7uGLEMW4tRxmH18Nn55qfAUhJKEGjWQPms6Euf9gIrP1YTwyzP2/qXk9deBHY8mek6oP5SDx9dW587lKglaLWez/fsv8GaBWxguiUs7zEp+lTDrnVnQGrToXLVzjnN96/a1uASASqnKdUp68M5BiCRCredp/vor65/qzxYuxFwwLiEIEBAWF4YmFZqghEcJEHi9RylToqRnScn6LCwcjzqObqlfQz9Aj/aVvbCtbBkUosRW12LNGlMw+0supD+p1ebMvCrE1QxcekoOAB2COqBb9W657jxLRaOARkbHpVKq0K5yO0nb71+/P1RKFXzcfOCucEe3at0AAF2rdcXwJsMR4B2AbtW7YXyr8ZL26yjmnpqLZr83w8T9E5+qOV0Qk/6bhHRtOjR6DY5GHcW5GMvU0Yt5DLmcR5Yvv+xau+ejR5uy2Zo1402+QkrR0MO0gNSsVESnRqNmqZo5NlmORh7Fhqsb0CKwBd54Xnrx21uJt3Dp4SW0qtgKZbycX1L3yN0j+O3cb3ix3Iv4rMVnVn8h7b65G6//8zoydBlQKVX4qdtPZimUZ/PO+nfw79V/oRN18FR4InRYqOuEOxV1Ll1i55qQwKU8Ro8u+B5b0OtdJmX12dbDNJOLDy6i7bK2MIgGVPWvipMfnjRuHkmpU/hP2D/45fQvaFK+Cb7v/D3c5G6oVrIaqpWsJkn7thKRFIHuq7tDrVNj07VN0Og1+Lrd1wXfmAt3ku8Yg+8zdZm4lXirgDty8stLvyBRk4ibCTfxZZsvi52lI/ngAy4vDQCff86yiM/ZMdzMRZylLRT+d2ABs47PMuoJ3km+g7239uaZHnjxwUXcSLyBTkGd4O/pb3YfobGhGLR5kLFyoLebt3Nr2+RCeEI4FAL/6tU6NU7dO2VxG1n6LOhEHXrX6Y3JhyZDqVNCgIAPGn5gUTulVaWx+73dFvdfjAQ8qYxViHevHUWhdZhEZIyrVOvUOBV9CkH+QahSokqe91Tyq8QxlnoNDGRAgE8uwb8ANl7diHc3vAu9QQ+FTIFjg48VWKwqmzvJdyAXeHqbqc90yRTEFoEt4OXmBQLBQAb0qd0HSZlJZn8x7LixA33/6QudqMMXrb/AjVE3EPYwDDVK1XgmN64KLYsWcfpsairHv1ao4GyLXJ5Ct4ZJRHh/8/tYHboaVf2rYtu729BzdU/EZsTCQAZsfntznjvcmbpMfLztY5y5fwbDmwzHyKYjc72u+6ru2H3LNOop5VkK8ePNKxOark1Hg98a4GHGQ4gkYvd7u9GqUisz37HjSMpMwv6I/VgVusr4Xv9+/W+zBDmq/FzFqMvoJnPDg7EPLBqFF+NCEHEcrKuIbmcXrMvMBDp2tJtd1q5hutBWmnkcvHMQG65ugIEMuJ10GyO2j0BsRizStGlQ69T46eTTReWz8VR6Ynnv5bgy4kqezhIAmgc2z/E8MTPR7N1fbzdvhA4LxY5+O3B91HWHOcsNVzdg+Pbh2HNrj1nX+3v6o0VgC+y6uQsavQYavQbj9o4z614fdx/jY5kgMykuFRaIWJhix45CHeIiCYLATkmr5VjJe0/q5jiYCRN41NunD2u6uhiFzmHKBFm2piYECPB19zU6M0+FpySpjJPaTkK7yu0gF+TwUHjgg4YfWLSLrFKq0LpSa5T3KW+zLeawJXwL+m/sj4VnF6L32t44EXXCrPu83byN+e0yyFDWy7zc479e/wu1S9VGgHcAVvZZCS+3QlZ07quv+I/yrbeAbt2KjDq71WRlca53584c/rPPtjK+NrF4MQsfp6fzF1p6uvNsyQ1rRDQddeQmICyKIg3ePJiUU5RUZ34dik6Jpq3hW6nT8k40dvdY0ug0Eo4ntwAAIABJREFU5mqIFsiFmAt0Ovo0iaIoWZv24It9XxAmgzAZ5DHNg+adnGf2vVvDt1LlnyqT/Fs5yb6VUa+/e7n8+7WZsmVNwrVubkQJCfbrKyWFaNAgonbtiPbutV8/tnDoEJGPj+kz8fEhSkx0ji0tW7L4sSCYfrZtS5SRIWk3sFJAuNCtYRbzNCejT6LTik4QwJtg54acQ63SuegkPsaD9AdYF7YOlfwqYeSOkYhOizaeW/fGOouzqAoVnTsDR47wLnHp0jwNtVfIS79+XGNHq+Vc6tu3gXLl7NOXtdy+zTWAtKyXCkEAvvzSpHzkSOLjgYkTgXPnOE5Uq2X9z9mzgWHDJOvmmVnDLAoYRAN+OPYD3lz3Jv6LsF2Zp3lgc5z68BTm9ZiHkI9DCnSWGdoMNPitAcbvG49+G/ohXp1zQ+tB+gObbQIAkURsu74Nm69ttjgDyK6sXw8MHcrO7OhR+8YHhofndEQxMdK0q9cDy5YBP/8MJCXZ1lbVqsAnn5iyg+RyaQunxcVxgPwLL7BWZn6ULs279wMG5MxWcpXMJWuGpY46pKzpo9aq6c8Lf9Ka0DWkM+gka7cgNDoNhceH51gqmH54OqmmqwiTQarpKroef91h9hARnbl3hnxm+Bin8ZV+qmR8XOqHUpShlWb68+6/75L3DG/ynuFNvf/uLUmbduf2baLLl7k+kBSsX8+1d7y9iZo14zo3UvDBB1yvx92dqHp122tCabVcL0guJ2rQQNpliifrEMXEFHxPRgZRhw48Le/ShSgzUzp7qAjV9LEXXVd1xfmY8xAgYHP4Zvzd92+79xmbHovgxcFI0aTAz8MP54ecRznvcjh977RRjEMhKBCeEI4apWrY3Z5sapaqCaVcCbkgh7vCHe/Vew+ftfwMkcmRqP9c/aeEjq1l/ZX1xrIYm8M354iddQkyMrjCpMEAfPwxsGIFMH48j2beegv44w/r2755k0ewiYnAggVcSqJJE+lGszt2AOpH6v1RUTyKsyVLR6nk0R8Rj4TPnuXPo317oEED22yNispZhyghoWBbVSqX1EV9Jhxmlj4LxyKPGQU2tl3f5pB+V4auRLw6HlqDFjpRhxUXV2Bcq3EY2mgo9t7eC7kgh8pNJVlKprn4uvvi7EdnseLiClQuURkDXhwAmSCTPOj8hbIv4FLsJRAINUrWcC1nKYpAtWpAbCz/Ea9Zw9NlDSvtY+VKnu76+lrX/ltvsZAuETBiBK/NKZXS2d+tG7BuHTuiChWeLoRmLYLABcs6deIvErmcly0aNrS+zRkzOExIEIAOHXi9VCqiooBevfjnxIl2z4d/Jhymu8IdtUvXxs3Em5AJMrQIbOGQfst5lYNCpoDWoIVCpjCWhehRowfOfHQG4fHhaF+lPUp4lHCIPY8T5B+Eb9p/Y9c+9ry3B9OPTIeBDPiy9Zd27cti/vuPnSXATi00lJ1CQgI7U5WKD2uJjzeFKxkMHIhtbnsGAztur3zCtZYsAVq3BpKTgUGDLAvwzh5F5sXevWwvETv5/ftNDnPyZGDOHCAoiLUtK1bMu51sunfnnPWEBJNqkVQMGwaEhPDv7IsveK20mh01G6yZxzvqkHINMz4jniYfmEzfHfmO0rPSJWs3NzQ6Da0IWUGrLq6i0TtHU/V51WnMzjFkEItezexCy759vF6XHUrz3HNEd+8SvfQSUatWRKdP29b+unVEHh68xjhqlPn3nTtHVKIEr/kNGiTdWioRUWQkr3fKZET9++ddw/3AAV5rzF5zPH6cXw8N5XVTgD+7Pn2ks81a2rQx/Q5VKrbRDGDlGqbTnWJ+h5QO05F0Wt6JvKZ7kdd0L3p97evONqeY3BBFdhpyOVFAAG/2SE1SEtH9+5bd07atVQ7ALAYONH1JeHsT7d+f97X79xNNmsQxmtmcOUPk5cX3CwJRjx7S2WYtZ84Q+fnxF8zAgWZ/wVjrMJ+JKXk2BtEArUELT6Wn3foQScR/Ef8Z10u339hut76KsQFB4E2NFSssu48I2LIFuH+fyyw8WYMoMpLTLatVA0qU4MMSvL1500kUuS9PCf+vPh6aQ5R/qE7Hjnw8TqNGwBtv8GdWqhTw44/S2WYtjRvz8kdmJuDjU/D1NuIiwU3258y9Myg1sxR8vvPBiO0j7NaPTJChXtl6UMqUcJO7mVWgrZhCxLff8u73Z58BwcGmTSKA1/Zq1QLq1ePz1rBwIfDii0DJkizqW11CfdBp04DatQE3N34P7SysLCAIwJ9/8u58bCzXRXcFFAqHOEugEKoVWUuLpS1wMvokAM45D/k4BDVL1ZSk7SdJzEzEvFPzoJAp8EmzT+DrbuVOayHiZuJN9FzTEzFpMfi63dcY23Kss02SFiJg9WoO8M4OFPf25h3l55/n576+QFoaP5bJeNTjVsiESQoLWVnAlClcVvh//+MNMAsoVlwvAC+lF2SCDCKJIBDc5e5266ukZ0lMbj/Zbu27IkO2DsGNhBsgEL468BX61u2brzZpoeO334CxY02xjzIZ4OEBVKliuubx3V9R5Kli+ScEWBYv5nCgl14CxowpUjW7Hcr48cDvv/OX0u7dwPXrT3/WduCZmZIvfmUx6pauC38Pf/zQ+QdULlHZ2SYVKbL0WcZ1WwGCMWBdCi4+uIih24Zi9onZxtr05hCZEokuK7ug0eJGOHTnkG1GHDhgcpbu7iw9dvZsztCfoCDTY5WKYwMfZ+VKHg3t28eKSWvX2mbTs8y5c+wsAf7yiohwTL/W7BRlHwBKAtgL4Majn/55XGcAEPLo2GJu+4V1l/xZ5Nz9c+T/vT/Jv5XTmF1jJGv3YfpDYxqn5zRPGrdnnNn3Nvu9Gcm+lREmg7yme5Faq7bekA0beNdapeKwn9x2v//5h8/7+BA9/zyR5jHlrAkTTOmB2bvMX39tvT3ORhSJVqzgkKkTJxzf/9q1ps+6Rg0itWW/WzhDrUgQhJkAEonoe0EQJjxymJ/ncl06EXlb2n5RVSuKTImEm9zNGMheVCAi6EU9lHLpMlqORx1Hj1U9kKrlWkwtAlvg+ODjZt1b8aeKiE5lFSY3mRvufXYPpVWlrTfmxAng8mUOxM4rYPvaNR5Ztm5t2uHW6fjx4zVzfHyA06d5E6YwsmgR8OmnPOpWqYCLF6XdoDKHsDDgzh1O38wvyD8XnKVW9BqA5Y8eLwfQy8b2ijzj9oxDrfm1UOXnKvjtzG/ONkdSBEGQ1FkCwIvlXoSfhx+8lF5QKVUWFVmb1mEaPBQe8FR44p167+R0liEhrO7999/mCwi3aAF89FH+2S21awNduuQMB1IoeIMom4AAXnMrrM4SyLlEIZfz5+lonn8e6NmTnaXBwHn79t7EtmZYmn0ASH7ssfD48yeu0wM4C+AkgF7mtl/UpuSZukySfys3KgP5f+/vbJOcyqXYS/TSqpforXVv0f3UvAO8E9WJtPLiSjp696jFfdxLvUfX46/nFEWOiDAFYKtURAsXWmG9hZw8SdSwIVHz5kRXrti/P3uzeXPBSxSO4u5dovLlWdmoVaucSyFPotEQJSTYL3BdEIR9AHKbO058wvGSIAh5uffKRHRPEISqAP4TBOESEeVawFoQhCEAhgBApUqVCjKvUKGUKaFSqpCmTYMAAeW8XUxI1g4kZSYhLC4MdcvUzSHuYRANaLesHRIzEyEX5IhIisCpj3Iv9+vv6Y/36r9nVf+5lgm5cMGUe61Wc+70xx+bzt+7xyIOGRnAzJkcV2krzZoB58/b3o6r8OqrnI9/6RILgQTkXoHVIcyaxXGhBgMvDWzdCvTNRQD7+HG2NSvL6q4KdJhElHsJRgCCIMQKghBARDGCIAQAeJhHG/ce/bwtCMJBAA0B5OowiWgxgMUAr2EW+A4KEXKZHLve24URO0ZApVThj1dzyoeJJCJLn2XXTCRHEpkSiYaLGkIv6iEX5Dg35ByC/HknWa1TG2vEG8iAm0k3HWdY8+YczuPhwTusb76Z8/yrr/IfnsHA64xxca4jYOtKNGvGhyWkp7OAs78/f85ShFX5+vKyh8HAU/K8gtg//dTmGkG2/i/YAmDgo8cDATwlpywIgr8gCO6PHpcG0ArAFRv7dUkS1AmYeWwmfj3za55hNS0rtsSFoRdw7INjOZTRQx6EoPTM0vD5zgcfbf0oeymjUPNP2D9Iy0pDalYq0rRp+PuySYPUx90Hfer0Ma5NftbCysyYR2RXvjSLgABec/vxR9aVfOutnOcjIkwbNMnJgJ8fhwxdvmyTjc88osjrwCNGcKbRWImSGyZMYNm40qV5jblr19yvK1HC9i8+a+bx2QeAUgD2g8OK9gEo+ej1xgCWPHrcEsAlABcf/RxsbvuWrmFGJEXQ/FPz6dCdQwVfLDGiKFLNX2qS21Q38pzmSW/884ZF97df1t64tqmarqKLDy7ayVLH8e+Vf8lrupcxrGft5bU5zouiSCeiTlDoA9sEJpaeX0puU93Ibaob/X7ud5vaIiKi6dNZpUelYmWf7FCgJk1sb/tZJjqaFZyyP88KFRzbf2QkUdOmRAEBz0YRNJ1BhxPRJxDgHfCUQvn9tPuou6AusgxZkAkyLO+13KGFvJI1ySg7qyx0Ite5LuVZCvHj4wu4y0TPNT2x68YuiBDtnrrpKIgIs0/MxsZrG/FKzVfweavPbRYRjlfH45+wf1Depzxeq/UaBEGA13QvqPW8Y+uh8ID6S7XtYsVhYSyk0auXqSbPiy86Zze4qKDTAZUrAw8fss5mr17AX385xZQinxqpF/Vo82cbhMWFwSAasPS1pXjnhXeM509GnwQRGadl/4T941CH6efuh1qlaxlFintU72H2vdfiryEqJQoKuQJKmRJft/vaZmep1qnx88mfkaJJwejmox1WI/1xBEHA2JZjJcsr1+g1CF4UjHh1PGSCDGNbjsXk9pPhofQwOUy5hzTK7s8/z8eECSyC4ePDsYfFWI9SCZw6xSU7SpcGRo50tkUWU2hGmJdiL6HF0hbI0GUA4Pi8kI9N3/YRSRGot7AeMnQZ8FJ64aduP+GjRh851N7UrFSsuLgCPm4+6Fe/HxQy876PXvj1BVyJuwICwVPhiaTPk+CusC3X/dW/XsWeW3ugF/Wo4FsBEaMjJKvV4yzCHoah+dLmSNfywn3dMnURNjwMh+4cwoBNA0BEWN5rOToEdZC2Y4OB176K876LDEV+hBngYwpbcJe74/kyz+c4H+QfhMODDmPt5bUIDgjGm8+/+WQTdkMkEYfuHIJCpsCIJiMsHuEkZiYa87D1oh5ZhiybHeaJqBPIMnD4RExqDJI1yZLX7LEUvajHHxf+QGx6LD5o+AEq+Faw6P4qJarAQ+GBTF0m3BXu6FyVAzjaVWmHuyNv8Y62oaz0hltS/qGYIk2hcZilVaWxo98OTD00FUH+QZjddfZT1wQHBCM4INjhtg3cOBCbwjeBiDDwxYFY0HOBRffP7jYbgzYNAoHwSVNp5OB61OiBlaErAXDYzpWHV9C6smOLrT3JJzs/wfKLy6E1aPHrmV8RMSYCHgoPs+/3cvPC2Y/OYumFpQj0DcTghoP5hChy0a7z53k0uGgR0L+/nd5FESUmxlT0bcwYi1MNnxUKzZTcVRFJhHKqEiJx4XsPhQcyJ2Za3E6yJhlZ+izJgtmXXliKEdtHGEeZwxoPw689f5WkbWupNq8abifdBsByeyEfh6B6SQnyj8PDWcw3O1WvTh3gSpGMXLMPoghUrQpER3M8Y+fOXOCsCOOsXPJnHpkgQyW/SpAJMsgFOWqUtK6+eAmPEpJm/jQo1wBygaeSKqUKTSs0laxta8mOu/RQeKCMVxlU8pMok6tsWdP6optb4c7RdgapqVxyw2DgLJgTJ5xtkctSaKbkrszBgQcx6b9JUMgUmNFphkP7NogG/H7+d1xPuI4Pgz9E3TJcNqBR+UZY9+Y6rA5djXZV2mHgiwMLaMn+zOw8E03LN8XDjId4+4W34SaXSI3c3x/YtQv45hugUiXgp5+kafdZwc+Py+iGhfHzN95wrj2ujDXBm446GjVqRJm6TPrmwDc0YOMAuhBzQYrwVbNQa9WUqct0WH/5kanLpPD4cNLonhYVmLh/IqmmqwiTQT4zfCguI84JFj7jJCZy1UlbSuKKItGsWUTNmhFNnixteV1zUKtZ33LDhrzL7+ZGZCRR3bockD56tPl2z5nDgesdOxLFxRGlpBB98QXRiBEspmFnUFQD14O/Ccaq0FXI1GfCx80Hkf+LRAkPCyvxmcm5++dwPuY8olOjMe3wNIgQUdG3Io5+cFS66aOF3E+7j0aLGyEtKw3+nv44P+Q8yniVMZ5vubQlTkTzFMrX3Rc73t2BVpVaOcXWZ5Ldu1l9HWCdzH//tS78aMsW4N13WfBDpeKSGIVh4+qdd7jkhsHAG0X79xecX37pEl+Tmcmxme++y5tOBw9yO+XKsaaoHfP3i+wa5qnoU8jU8yYKgRCZElngPXpRj3F7x6HJ4iaYf3q+Wf3su70Pbf9si9G7RmPK4SkQwZs4UalRGLVjlPVvwEaWhyxHvDoeGboMxGXEYfWl1TnO96/fHyqlynjUL1ffSZY+o0yYwH/4j9eWsYaICED/qPxGVhZw+7Z0NtqTbMGLbPRmlBBJTjaFaul0XPvo3DnOqDIYWOwkNTX3e2Nj+Yupbl1g40bb7bcQl3eYHzf5GCqlCt5u3gj0DUTt0jkX9Pfc2oOvD3yN41EmFe6FZxZiwekFOBtzFp/t+QwzjswoUMxi3ZV1UOvVRuf8OLm99iTx6ng0/b0pVNNVGLxlsGTiGeW8yxnX+hQyxVMq7cOaDMPWd7Zibve5CP04FD7ujik3Wswjypc3/fGLouV1yLN54w0O6fH15ayiwjC6BIDvvwcCA02qTy1bFnxPy5asSO/uzuunU6cC773HI1Rvbx59+vnlfu/gwTyKvXqVBTxiY6V9PwVhzTzeUUe2+MbJqJO0Pmw9pWWl5ViH2Hljp3H9TjVdRefunyMiotE7RxuFLDAZ5D7Vnb7Y90W+axqrLq4ytuU2xY08pnkQJoP8vvMzSxxi9M7RpJyiJEwGec/wpl03dhV4jzmkZKbQy6tfpkpzKtHYPWPJIFqwvuSirA5dTZ2Xd6ZvD35LeoPe2ebYxv37RJ06EdWuTbR+vW1tpaRwfZzERGlscySWrHsS8VrngwcmsV9RJNq1i2jdOqKsrLzva9DAJN6hUrEYs17Pwh5ardndw14Cwq5As8BmaIan10UORByAWsexd6Io4njUcQQHBGNIoyFYemGpMYUuy5CFNZfW5LuD/W69dyGXyXEi6gT61u2LNpXbIEufBTe5m1mZO1qD1hiLCcAowmELGr0GTZY0QUxaDAxkQHBAcKFPbzwVfQofbf0Iap0ax6OPo4RHCXzS7BNnm2UdFy8CbdqwxuLAgUCfPra15+vLWp2FEUvXGwWB1yoff96tW8H3zZgBvP46P+7ShaX6nn8euHsXKFWKs73sWG63UP/19ajRA54KT7jL3SGXydGhCucQ1y1TF9dHXoe/hz9kggweCg+0rdw237YEQcDbL7yNuT3mok3lNgAAd4W72WmOk9pOQpUSVSBAQKegThaJb+RFyIMQxKTFIE2bBrVOjXmn5tncZjYavQaT/puE9za8hwsxFyRrtyBuJN6AAP5M1To1Lj8sxBqTPXsCaWk83lmxoljJyBH06MEB9pcu8Rrm2rWsKqXR8PTczgIphWKEmRftq7THgYEHcCL6BDoFdcLzZU355QE+Abgw9ALmn5mPcl7lMKqpfTduyvuUx81PbsIgGiCXFZx7LJKIyJRIlFGVgZdb7mloVUpUyZFB1CigkWT2jto5CqtCV0Gj12BL+BbcHXMX/p7+krWfF92rd4ePmw/kMjkMogEfBTtWIEVSHj5WYEAUeQOjGOtZvx5YsgRo1Qr48su8c/hLluQj+3H26Fap5CiD/v2BWrWAzz/n16TEmnm8o46iVgQtG61eS63/aE2e0zzJ9ztfOn//fJ7XHos8Rn3W9qEv932ZaxymtdT/tb5xjdd7hjeFxIRI1nZBJGcm075b+ygqJcphfdqFDh24vjhA5Odn+TpeYUCvd0xM6NmzvCaZvTY5Z4559xkMXBu9QgWivn1NbXh6En36aZ63wco1zEI9JS+sHL57GCEPQpCpz0RqViqmHJqS57UtK7bEv2/+i+mdptusYPQ4w5sON0YfVPStiDpl6kjWdkH4efihU9VOCPQNfOrc7aTb6L22N3qv7Y2IpAiH2ZQnGRmmHPUn2bqVd3jHj+dd26JW9+frr3knu1Qp4MwZ+/Z1/brp81OrgdBQ8+6TyYB583iaPmYM58IDHOZ1KveierZQqKfkhZXSqtLGqbab3O2pUKHcCI8Ph4EMxtRHWxnaaCiCnwtGdGo0ulbrKl2aoo10WdkFEUkRECDgUuwl3PzEgcXRnmTePGDcOH78++/AgAE5z3t5ARMnPn1fUSAqiitmGgxAUhIwbBhgTyGcrl05pEgm4z6HDCn4nvh4VmwvW5bDsho25Ck6EbcxdKjkZrp8po+rqxVZy/zT8/Hj8R9Rzb8a1r2xDiVVeWtVTj44GTOPzQQAfNz4Y8zpNsdRZjoc5VQl9CIHPytlSmi/yr2YnF0gMmXpiCJXlcxel/T2BhITpV8Tc1Xu3weqVePNFIBjI0+etG+fyck8Kqxdm0tZ5IdWC9SsyRs9cjk79FmzOOB9714uWhect9Rjkc30eZLt17dj1rFZuJWYa5XeQkPj8o2RkJmAU/dOoedfPfOsMgkAM4/NRKY+E5n6TMw7NS9H+JLUaA1a3Ei4gSy99bWbbeHjRh/DS+kFL6UXPm78ccE3SIFOB7zyCk/n6tfnkYsg8HQ0m/R0DmEJD3eMTc6mfHngu+94FF2lCrB0qf37LFGCQ4sKcpYA74zHx7NDz8gwZf34+nLYUT7O0hYKlcNccn4J3lr/Fib+NxHBi4PxIP2Bs02ymqmHpiJdm44MXQbCHobhWOSxPK8t71MewqN/ZbzK2C0WM14djxq/1EDDRQ0RNDcI99PuW9VO2MMwrAtbh3i1+UXgspnXYx4Ovn8QB98/iLnd51rVv8Vs3gwcOMCjymvXeKQiCPx6mTKmUWdiIjBtmmNscgXGjOEviogIjnV0Fg8fcnlef3/TEkjFipwRpVBw7r05MZwSUKgc5qZrm5ChyzAGhZ+POe9ki6ynkl8luMt5BKMX9flqYe7stxNdqnZBhyodsK//PrvZtObSGsSmx3LeujoOy0OWW9zG7pu70XRJUwzeMhjPL3jeYqcpCAIal2+MxuUbS1PMzByerNeTvfnQsSOPXDw9+blSyRsgRRW9ntdtx4zhTSxXYcIEzjVPTgbmzuVpu7s7v/bNN6wUP0+6GOX8KFSbPi/XfBkH7xyERq8BEaHhcw2dbZLV/NDlByRmJuLSw0sY13Jcvps5NUrVwOZ3NsNdbn4gvTWU9SoLhUyBLANnOJX1srw+ztILS43ZVwBw5O4R9K7TW0ozpee11zggevNmLqU7frzpXKtW/HzRIj737bfOs9PejB/PKkkaDbBsGXDnjvW58VKSkWES9RAEU9RC+fLApEkONaVQbfoQETaHb8aVuCt4vc7rqFW6lhOtcwzxGfFou6wtwuPDUaNUDRz94ChKq0rbpS+RRIzfOx6brm1C9+rdMbf7XLOC8B9nzok5+OrAV1Dr1FApVTg35NxTginFuCjBwcCFR1lfPj68TNFIumQJq7l+HWjbltcsX3mFJfRsDOGydtOnUDnMZ40MbQaC5gYhTh0HAJALckxqOwmT2092rmH5IJKIeafm4cy9M/ig4QfoVLWTs00qxlx+/tk0YitVitdzs5cjnI0ocmylRMXZnFJmVxCENwBMBlAHQFMiytW7CYLQHcBcAHIAS4joe1v6fVY4HnUcaVlpxudEXLfclZEJMoxpPsbZZhRjDWPGcJRAZCQvU7iKswR4RGmrs9TreTrva31VVls3fS4D6APgcF4XCIIgB7AAQA8AdQG8IwiCNNHXRZyq/lWNQhUAbxSNbDrSiRYVU+Tp2BF4/33ekQbMEwS2lrVrWQj45Zd5um1PLl3iAPdSpWyqWWSTwySiq0RUUGBaUwA3ieg2EWkB/A3gNVv6fVaoVrIaNr69Ed2rdcfnrT5H+KjwPIU6iilGUjIyOJTHzQ1o0iRvBXRriYoCBg3i3fjduznw3J5MmMAZS3o9sHOn1c04Ype8AoCox55HA7mIW+aCTtQhJi0GAT4BdjGsMNCtejd0q+6YGLNiijGybBnrfRLx6GzpUuB//5Ou/YQE08aNXs+54PbE15czgp4sqWEhBY4wBUHYJwjC5VwOu4wSBUEYIgjCWUEQzobeDkXQ3CB8f7R4ybMYJzNtGq+hVatmfd2e3MjK4s2VvAQ+nIVSaYpNFQTpU0Lr12fxZU9PDjy3d0LATz/xSLl0aeCrr6xuRpJdckEQDgIYm9umjyAILQBMJqJuj55/AQBE9F2B7ZYXCENZoCJrknNS9QoL6dp07L65G5X8KqFJhSbONqdocesW8MILHJ8oCLzOt0+CBIKEBA7bSUhgx3H2LNdVdwWysjjF8L//OKRn0ybOrZcSIv5sS5UyrZk6CFfOJT8DoIYgCEGCILgBeBvAFksasFdZ3aJClj4LwYuC8f7m99F+eXssOb/E2SYVLfR602iLyDKhYCLgjz+A4cOB48dznvvnH077S0/ntMslLvR7c3cHtm3jke+uXdI7S4A/0+rVLXeWej2wYAELBN9yrKaETQ5TEITegiBEA2gBYLsgCLsfvV5eEIQdAEBEegAjAewGcBXAP0QUZk77KqUKDZ9riB3v7rDFzCLP5YeX8SD9AdK16VDr1Fh4ZqGzTSpa1KrFDk8u553WX34x/95ffwVGjQIWLuQaNDdumM4995xpHc/d3fpaNKLI7Y8w4V7hAAAgAElEQVQa9WyUyRg7lmX3fvyRp9lpaQXfIxXWqA476pBCcT0mLYZeWfMKNVrUiPbe2mtze65IfEY8+czwIUwGeU7zpGHbhjnbJCManYaWhyyn5SHLKUufTzVAW7hzh2jGDKK//rKvOrg16uNvvmmqcujjk7OypCgSTZxIVLMm0YgRRDqddXZNnWpSGvf2Jrp3z7p2QkKIatUiCgwk2ryZ7UlKsq4te1KvXs7P9OJFi5uAlYrrTneK+R1SOMwuK7qQYorC6EySMl3wP4AEnLt/jvpv6E+TD0yWtJSFrXRb2Y28pnuR13Qvemn1S9J3kJxMVLIkkULBTmPqVOn7sIUtW9guLy8if38uLSs1nTqZHIivL9G+fda1U7OmqR03N7ZXqSTq08e1ym/MmMGfp6cnUaVKRJmZFjdhrcMsVOIb1nA35a5RkBYAkjKTiuSaaHBAMFb0XuFsM3JARNh7e69Rv3PPrT3Sd3L1Kq9pZR9btzpckCFfXnkFOHQIuHyZp+Tl8lalspoBA4ATJ3hN0MPD+vzvlBTTY52O4xYBYM8eVghq0eLpezQa3gArU4ZFhh3BhAkshBIdzRtT9lhfzYNC4zCjUqKgF/UI8g+y6L6pHabi/U3vQxAEdKnaBVVKVLGPgbmQoknBzGMzoTFoMK7lOLNKURQlBEFAo4BGuBh7EQA79WyORx3HgYgDaF+lPVpVamV9J3XrcnC1mxuHvrzmgjkRjRvzYS8GDACqVuX10Z49rVMYOnHC5CAB/lzDw/lLSBRZcf5JDAagdWsOszIYuL7Rp59a/z7MRRCAl16yfz+5Yc2w1FFH9pR8zvE55DHNgzymedC4PeMsHn7fS71Hl2Mvk+iI6neP0eaPNuQ21Y0UUxRUY14Nh/btKiRnJtO0Q9No+uHplKJJISKi45HHSTVdRbJvZeQ5zZOO3j1qWyeRkUSzZhGtW+eYCodFkddfN03Hvb2JVq4katmSqEwZou++y/2eW7d4Wpx9X7VqjrXZBlCUp+TfHPwGGj3XFplzYg6md5wOpdz8QNryPuVR3od3INOy0qCUK/H7ud8RkRyBIY2G2E1+7HzMeWPpiZuJN6E1aF2m2Jij8PPww8S2OQuFHb57GFqDFiKJ0Bq0OHjnoG2jzIoVeee0GOupXp2nthoNjyjr1weO5V0FAAAvL7i58T1ubnYrC+FKFAqHWc67HNIT00Eg+Lr7QiGz3GwiwqDNg7D60mrIBdZ41Bq0+OPCH4gYHQF/T+kDZ9+o+wbWXVkHAGgR2EJSZzn18FTMPDYTgb6B2P7udlT1rypZ2/amQ1AHuB3mz0IpU6JjUEcnW1QMJk/mfPGzZ4FPPmGHWRBeXsCRI8D333NI1Dff2N1MZ1Mo9DDD48Px4dYPodVrsaDnAjQub/l6UGhsKFosbZFDDRwAfNx88N/A/6xqsyBEErE1fCuyDFnoVbuXZA4zPD4cDRc1RKY+EzJBhq7VumJnv9wFBa7EXcHtpNtoX6U9vN1yWYeyESJCpj4TKqXKovtO3zuNg3cOol3ldmgW6KDNgmKKeYRT9DAdRa3StXBk0BGb2lApVU9VW/RQeKCERwnJan0D7EDCE8LhofBAlRJV8Fpt6TchtAatsVSFSGKeFR43Xt2I9za8B7lMjjKqMggdFiqp2lF0ajRa/9Ea0anRaFelHXb222n2l0LTCk3RtEJTyWwpphhHUKiKoNlC9ZLV0atWrxyvNQ9sjgtDL1g8OsqPYduHIXhRMOosqIN5p+xTmOmFsi/g/Rffh0yQoYyqTJ7VFeefng+1Xo00bRri1HE4c/+MpHb8cPQHRKdGw0AGnI4+jW3Xt0nafpEnORk4f56VxIsx8fAhMHo0Hw8f8m79hQs2qQxJxTPjMAHgfy3+Z3SOXkov9KvXD6VU0lUBVOvUWHJ+CTL1mdDoNfj2kH0KZgmCgAU9F0AzUYPYsbGoV65ertcFlw82KrQbyCD5OqdKqTLW/CGQpF88RZ5r17jed/v2QJ06OUN6rCUrCxg8mNv78Ufb23MWnTpxSumvv3K8ZcOGrGw0cKCzLXu2HGbTCk2xqvcq9K7dG9M7TsfghoMlbd9d7m6c8soEGSr4VJC0/SdRypX5VpGc3nE6xrYciz61+2DHuztQyU9aJZwv23yJFoEt4OfuhwEvDkC3aibdzqORR7EsZBniMuIk7bPIsHAhb7KkpbHa+ObNtrf544/AmjXsjCdP5oD5wsjjyQgPHvAIPCMD+OsvFiqxBLUaOHkSiJPm/2GhWMOUkt51etut7KtcJse+/vswZtcYeLl5YdHLi+zSj7m4yd0wpcOUp14XScS/V/5FalYq3nrhLas3g/w8/HDw/YNPvb7swjKM2DkCAgR84fYFwkeFw9fd+joqdkejASIieMTnqDo2VapwGE/2dLxiRdvbjIriUSbAwd0xMba36Qxefx3Y8UhwR6nkLxaDgYPnLfn9pKQADRqwfB4RcPgwj1Zt4JlzmPamSYUmODa4gPg1JzNi+wisDF0JAuGX07/gwtALktY7X35xuTEaQS6T43zMebSv0l6y9iXl4UOOH0xJ4TCZs2eBwED79ztqFHD3Lo8CBwzgaaitjBnDdXJ0OqBCBa6VUxhZs8bkMOvX57XMtDQeQcstKPu8cyeP3rNHpfPns3K8DRQ7zGeQDdc2IEOXAQC4Gn8VCZkJudY614t6pGvTLc69b1elHU7fPw21Tg2RRNeuS/7XX/xHlZXFI83ly4GJEwu+z1YUCi5rKyW1a/MoMyqKA9GlVkl3FHI55+Bns2mTde1UqcJB+ACPTGvWtNm0YofpIC4/vIzQ2FB0DOro9JzyNpXaYPuN7dCLejzn/Rz8PZ4O2r8adxVt/myD1KxUdK3WFZvf3mzc4CmIr9p+hTJeZXA17io+DP7Q6e83XwIC2HllZXG2irWalK6Ctzdv+hQDNG/O2qWLFwOtWkmS517sMB3A/tv78erfr0ImyOAmd0PY8DCnOpFVfVZhwekFSNYkY0TTEbk6wq8OfIXEzEQQCIfuHsKRyCNmT6vlMjlGNBkhsdV24o03WHR3wwagRw+eHhdT+FmyBJg+nWswbdnCws8SUOwwJYKIsCxkGUJiQ9CvXr8cQdkrQlcY1/S83bxxIOIA3qn3jrNMhYfCA5+1/Czfa7JTUHWiDiKJ8HHzcZB1DkYQgBkz+CimaHDrFqd3ZmayBNyoUby2KwHPVFiRPZl/ej5G7hyJeafmoePyjriddNt4rkVgC2OMokhinnGT9kYkEaN3jUbQ3CAM2zYsh07ok/zQ+Qc0D2yO0qrSGN9qPBqVt1Jj0VmIIv+xaLXOtiR/jh4FSpbkHfNff3W2NUWDpKScJXwfPJCs6eIRpkQcuHPAOIqUCTKExoYaA8WHNhoKADgRfQID6g/AC2VfcIqNf1/+G0vPL0WGLgMrQlegUflG+DD4w1yvLeNVBocHHXawhRKRmcmBzmFhgI8Px+FVdVFxkvffNwWt/+9/QP/+bHMx1hMcDHTowMLGCgXwXYEFas2meIRpA0mZSQh5EIIsfRb61esHlVIFlVIFhUyBlhVbGq8TBAEfN/4Yy3stR6eqEoSPWElcRpxxVKkz6FwmqDw1KxXtlrWD1wwv9NvQDwbRYFuDW7dyOp1GwzF4rpL1kpTEYUTx8c62xL7cusXOf+ZMU1yoI5HJeN3yxg0eXbZsWfA9ZlI8wrSS0NhQtPmjDUSICPAOwLkh57B/wH5cfngZPar3QFkvaRaZpaRf/X74+eTPeKh+CH8PfwxqOKjAeyKSIjD/9HyU9SqLMc3HwF3hLrldc07Mwcnok9AatNh8bTM2XtuIvnX7Wt9gyZKmvGOlEij9dMiUw4mO5iBqnY7XTc+cAWrUAFasYJX49HQOM8pvdHnvHofY1KgBdO3qONstITOTS1UkJXHUwdWrwJ9/Ot4OQbBLPG2xw7SSuSfnIlWbCgCISY/Bzps78ebzb6J5YHMnW5Y3pVWlcX3UdUSnRqOCb4UClYU0eg2aLWmGBHUC3BRuCIsLs0vdoCx9Vg4lqWzR5YJYdG4RfjvzG5oFNsPc7nNNzrxTJw7iXr6c/3gnTJDcZotZv56dYlYWj4DWrGH9yJYtzUvbS0zkvOqMDI5TnD0bGDrU/nZbyr177DRFkUf4R2xTGXM1iqfkVhLkH2QUthBJRKCvA7JDJEApVyLIP8gsGbaYtBika9MhQoRGr8HRyKN2senTFp+imn81CBDQLLCZWaPL0/dO49PdnyIkNgTLLy7Hd0cfW6cSBGDaNA7gXr8eUD0mChIWxoejqV6d19MA3uCpUcOy+0NCeHSq0bDT/Ocf6W2UgipVOM3Ty4uP/v2ta+fAAf6Mnn+elYpchOIRppWMazkO91Lv4WT0SXwU/FGONUtXISkzCe4Kd6tVhCr6VUTlEpURlRIFAHi33rtSmmekjFcZXBt5zaISHtGp0UblfI1ekyMqIU/Gj+f0OAAYOZLX2J7k2DEgNJSLbFWubO5bKJiXX+bQpfXrue13LAwre/55XmYQBM5a6dat4HsAfj9Dh/L0+M8/eZRqMADHjwO+vvxcCohY6MLLi5cbNm3i2Edrlg5EEXj1VVNKY69enEZqCZGRwPDhnFI5e7Z0ReisKQTkqEOKuuTPKp/v/ZyUU5TkMc2DNl/bbHU7qZpUWh6ynHZc3+HwInL5kZaVRjV/qUneM7zJZ4YPnb9/vuCbFApTwS6F4unz//7LNcQ9PYn8/Iju3ZPecFu4coVo4kSiFSvMK/YmilynPPs9V67Mr730Ehc6U6mIZs603a7YWC6AJpdz4TQr6oTnQKvN+bsqUcLyNoKDiWQyvt/Pj0in49rqOh0RWV8EzSaHBuANAGEARACN87nuDoBLAEIsMbTYYVpHojqRlFOUhMkgTAZV+qmSs02yCxqdhi7EXKAEdYJ5N1SqRCQIfFSu/PT5N980/ZH6+HAVysKMTpfT8fj4ED18SOTmZnrtueds7+fLL039eHmxQ09PJ1q6lOjvv4n0esvbnDGD7XR3J/rzz9yv+fdfosBAohde4C+TxyldOueX4/bt/CWhUBB9953VDtPWNczLAPoAMCdgrwMRNSAr6mgUkzsG0YBph6fhpdUvYdM1k0CBm9wtR7qjAAFX4q44w0S74q5wR4PnGqCkZ0nzbti7l6eIXbsCe/Y8fb5LF55SAjwttFEKzOkoFMBXXwHu7nzMnAn4+Zneo1LJgh22olLlVBHy8ADateMMm8GDgY8+srzNL77gkKCHDzlW9UnS04F+/Tj64PLlp5c4Jk3ipQuVCnjvPVY8Sk/nQHZbirVZ42WfPAAcRMEjzNKWtls8wsyfH4/9SKrpKsJkkGq6ii7EXDCe23h1IwXOCSTFFAV5Tfci1XQV7bi+w4nWWse1uGt06M4h0uq19u9MFIn++otoyBCi+fOJUlPt36cjePCAKD7e9PziRaJXXiEaOJAoLs729tPTibp14+n/++8TJSbmHNn6+5vXzsWLRL/8QhQS8vS5Y8eIpk4lOvqohn1CApFSaeqjSpWn77l5kyg0lH+vdeuarnV3d86U3NhIwQ4zAsB5AOcADDG33WKHmT/9N/Q3Tru9Z3jT2strc5zfcm0L+c7wNV7T669eTrKUSBRFSlQnkt5g/vRsxcUV5DnNk7xneFPzJc0tutdqDh7ktT1fX6KKFYmSk+3fZ1FDFImqVmWn6eHBzrkgzp3jz93Dg3+eOWM6d/w4vyaT8fpyttMcP56dpocH0dat+bd//jwvyfj5Ef3xh/2m5IIg7BME4XIuhyXlEFsTUTCAHgBGCILQNp/+hgiCcFYQhLNxEsnKF1WGNhoKlVIFX3dfeLt5o3PVzjnO1y5dG3rizB6VUuW0Ko0avQat/2yNcj+WQ6WfKxl33Qti1rFZyNRnIl2bjkuxlxCeEG5nSwEsWMC7vampXKTswAH79nfuHDBnDv8sKggCcOIE8OWXwJQp5glf7N3Lef8aDR+7d5vOHTrE50SRf2aX3vjhB56yJyYWLJbcsCHvtCcnA4MKTtjIiwLDioioc0HXmNHGvUc/HwqCsBFAU+Sx7klEiwEsBrguua19uzpEhFE7R2FV6Co0eK4BNr29yWzB3laVWuHysMsITwhH88DmT91Xo1QNbH1nKxadW4TggGCMbTHWHm+hQLaGb0Xog1DoRB1i02Mx6/gszOtRcEXNumXqIjwh3BjI7hBJvPr1ge3b2WkaDBw/aS9On+acZ72e1wAPHQKaNLFff46kbFngWwuKALZsyaFPej2vgbZqZTrXoQOfA/hnx46mcyUsE7e2FbvHYQqC4AVARkRpjx53BfB0oZlnlD239mBZyDJk6DJwIuoEph+ZjlldZpl9f5B/EIL8g/I83zGoIzoGdczzvCPwdvMGgb/7FDIF/Nz9zLpv8SuL4evui7spd/FV26/M39yxhQkTOBvn9GmO43vBjkIp+/ZxXwYDb9Ds3190HKaltGnD+d979gCdO3M1zWyaNeOR/sGDvJnUrJmzrLTNYQqC0BvALwDKANguCEIIEXUTBKE8gCVE9BKAcgA2PqoZowCwhoh22Wi3UzgRdQK3k26jR40ekv3xZuozjfV0DGRAepaFVfEKAd2rd8fg4MFYc2kNGgc0xvhW4826z9fdF4tfWWxn655AoQCmTnVMX23b8ohJo+Ed6zZtHNOvq9KpU961jZo25cPJCESuO+tt3LgxnT171tlmADBVQpQJMpTwKIGrI65aXW3xcXQGHXqs7oGDdw6ivE95HPvgGCr65V1BcPv17fjh2A+oU7oO5nSbYyzrW0wh5dAh4L//eJrZrp2zrXlmEAThHFkR4ujSDtOtohst3rIY7zd839mmoPUfrXEsiqtB+rr7Yts729CmsnQjggxtBlRKVb7VG+8m30XdBXWh1qvhLnfHoAaDsPDlhZLZUEwx+ULElRgjIrgU7nNWrCknJwO7dgFBQU6dWlvrMF1afENn0GHYjmG4n3bf2aagbeW2RrENnUGHOSfnYN6peTlUdmzBy82rwFK30anRxoD0LEMWrsZflaTvwoDWoEWCOsHZZjzb/PQT8OabwNixLFWXlmbZ/RkZvKn20Uc8ol62zC5m2hOXdpgAZ6lkaDOcbQamdJiCaR2noW+dviAibLq2CV/s/wILziwAANxPu4/3N72P9za8hzvJd+xiQ5MKTVCtZDX4uPlApVRhQmsXkC1zAOdjzqPsrLIoP7s8Xl/7+v/bO/MoqYp7j39+szLMwr5DZBUFhijyBJUIkkBGeIIvYAT1gQJq3KKRnKBHg74gR1GDz6gkKvIwgqOgBtAgaxRQZJFlWAdlABWGNeAMzD7Tv/dH9SwMPdPd07cXoD7n3DO3u++t+t7qnrq3qn6LYzcpi5/Mm2c6vcJCE8LN36hPW7ea/O9nzhgrhDff9Hycq8r3q+6gHhFCRHeYIsKoHqPo3DiIph0+EhMVw6PXPMot3W8hNtrke84vyWf9wfUApM1JY862OaTvSGfA7AFB0RAXHcf6CetZcscSdj+wm7TOaUGpJ9J4bMVj5BTlUOwqZmnWUr7Ojox57QuW/fvNanVu7tnvDx5sXA1FzNa1q3/ldu58dp7wqqZDYIINt25tFsAefNDYV6ammqhKvXtXRi8KIxEd3q1ni57MGj4r3DLO4ob2N1QEqi3TMu66whjBfnvyW8rUpFb4IfcHXOoiSpy/H8VFx0VkKLlg0qheI2KiYih1leJSFynxKeGWdOHy+ecwdKixFkhJMX7aDdxmYE8/beYes7Jg7FhodG4++1pp0cKUP2OG6Wyr5wn/3e+M/7iqCUUXE2PSTJSVwa5dJjr9/fc7cJF1J6I7zJioyJPXLLEZu+7fxarvVtGtWTe6NesGwPgrxzN762xEhOFdhwels7xYefnGlzl0+hBZJ7OY1G8SlzV1IGCExTMzZlQOgVWN/ePNN5vXUVEBeckAcNVV8NZbnj+LiTFPruUL0fXrV2Z/LH//llsgM9ME57gtOPFZayOiV8kjyazIG6rKlz98SamrlOsvud52mBb/2bLFzA/27Ws6iHAwdaoJdJyfbzqsDRtM8OJQsG8fpKWZCEQTJ8ITT5gOcvVqEzA5IQHee8+4RyYkwPbt0KmTb2V/8ol5Sh0xAjp1qvMquSPBN4K12eAbFx5ZJ7N0yNwhOvjvg3XXsV3eT7hYePJJE2AiMVH19tvDp6OkRHXyZNUbb1RdWPfA00Fh4MDKiENJSSaCkS+8/rpp29hYE1Tl8OE6B9+wT5iWkHLpK5eSdSoLVaVlUkuyJ4bfZCwiaNCgcpElKso84cU7n6HzvGbVKjO/CiaYxmefVeZJqo2hQ2HxYrOfkgLvvYcMGXLh2WGGk9yiXEZ/MJper/di/s754ZZzwXAw9yAudaEoR/OOWhOhcjp1MgE4RExa4DjfchtdVPTvbyIObdhgFo986SwBbrqpMsixakCBoSNvVSVCeGTJI3yU+RHFZcWMXTCW3q171xrkwuIbE6+ZyJ+/+jMiwrgrxtm53nI+/tjM2xUUmLBl4ZrDjHSaNDGbP9x7r/FK2rLFPGFu317n6m2HWQP7Tu2rCCsWHRXNkTNHbIfphfQd6by/431+0fEXPPAfD3j0XJoycAqjU0dT6ioltXlqGFQ6RHGx8XpZudKEH5s/P7AhdJs2ZkHD4jwi5inzySfhwIGAirIdZg1M7j+Zm9JvQhBSm6fSu7VNRVQbqw6sYsKiCeSX5LN833IaJzSuMS1vuSnWec3s2ca4u6DAhGmbNQvuuy/cqiw18f33xiA/QK8hOx6qgYEdBrL/4f2sHb+WNXetqfDuuRjILcpl4rKJjFs4jr0n9/p0zq7juyrmI/NL8sk4khFMieGnsLDSXtDlMnEtLZFLq1bGg0gkoJGA7TBroXlic3q26HlWBsbzkTc2vcHw9OHM3jLbp+N/Pf/XvLrhVWZvnc21b11LSVmJ13OGXjqUejH1SIlPITE2kWFdh7H2h7WcyD8RoPoI5a67oFs3s6J9+eUwblzgZWZnm8yOc+ac7U9dG9u3w623GlfCnJzANZSTmQlz58IPvqUTCRnffw9/+AO8+KJ/N6m//tUcHxNj3C/riB2SX+AsyFzAo0sfJa8kj5X7V9IiqQU3drmx1nO2HtlaMX+bU5TDj4U/0iyxWa3n/KTBT8h8IJMNhzbQJqUNQ+cOJb/UDH/WjV/H5c0ud+aCIoXkZJOHp7DQpFQIlPx86NXL+E/HxhqXxOeeq/2cggIThPjHH82q+nffmcWjQFm3zgTyjYoy29atxiUy3BQVmSDCx4+b683IgHfe8e3cl14y3xXA4cN1lnBRPmGqKqcKTl0UJi07ju2goLQAMCHSdh73HmFmQq8JJMYmkhSXRJ82fWhav6lPdbVIasFNXW9iU/YmcopyyC3K5XTRaWZtiaB4AJs3m46oPJFWoDjRWYLxz87Ph5IS8/eTT7yfc+JEZSdQXAzbtjmjZd48o+HMGaOnakKycHLkiLFVdbnMda/2mBbMMz16VJpq2SG57+QV53HVG1fR4sUWdP5LZ47lHQu3pKAysttIEmMTSYlPISEmgZsvu9nrOVNumMLi2xcz91dzWTFmBSLC/lP76f5adxo+15BpX06r9fwOjTpUmAvVi6lHo4RGkXFz2r7dpIH44x9hyBCTqTBS6NTJ2ArGxZm/w4Z5P6dtWxPFJznZnPPQQ85o6dPHlAdmzi8Au0VHadsW2rc32hITYdQo38999124807jFx/IzbIu7kGh2oLhGjlz00ytP7W+8jQa86cYfeqzpxyvI9I4mHNQF2Uu0uzc7HM+m7p6qjZ4toGmzkjVA6cO1FhG2pw0ladFeRpNeCZBvznxjcfjVh1YpfN3ztfpa6drzxk9NW5KnCY8k6DXvXWdFpcWO3ZNteJyGXe4sWNVV6yofP+110xe63L3ut//PjR6qvPuu6r33KO6bNnZ72dnq77wgurcueYafKG4WHXp0rPzeAeKy6U6e7Zpv3/+07lynSA3V3XWLNVFi3xvIw9QR9fIi24OMykuCcHYB8ZExZAclxxmRcGnTUob2qS0Oef9zBOZPLP6GQpKC9h5fCcPffoQi0Yv8lhGYUlhReZHEamY46zKtC+nMWXVFESEjo060qFRB7YdM8PEjKMZrPpu1Tm504PCzJkmVFh+vrGPXLfOxFX82c/ME1N0tBmWDRpUeznFxaZrddJFcf58mDDBaJszx3islGeKbNXKRDP3h9hYE6cyEMrKYONGYxDepYtpo7FjzeY0quaaT50yT/n+TmkkJwceMSkALroh+chuI7m1+600SWjCLzv9kgeufiDcksJGYWlhhXG5S13kl9Rso/ZS2ks0TmhMlEQxpucYj7aUb256k7ySPM4Un2Hvyb0kxSYRFx1XUb6vc6EB89VXlfZ2UVGVc3upqWbea8oUk3u8to4mPd14hSQnw+uvO6dt7dqzw6dt2eJc2XVB1UQIGjQIfvpTE4cymEyebIzIx441ro6+WgNECnV5LA3VZqMVBReXy6XjF47X6P+J1ibTmmjGkQyvxxeWFNb4+W0f3Kb1ptRTeVq04XMN9VDOIR2ePlw7/m9HfWX9K07Lr5mVK010mqQk1UaNVA8d8r+MlJTKoXtcnGpZmTPavviiMipRcrJqVpYz5daVffvOnqbo0iW49bVuXVlXfLyZhggD2GhF/pNblMvHez6mbUpb+rcPXYrT43nHKdMyWibVIeteECgsLSQ+Ot5rEjZvFJQU8OwXz5J9OpuJ10wMrynRjh3G7GTgQDPU9ZeWLeHoUbOfmGgSfjnl371jB3z9NQwYYBYxwsnp06Z98vIqh/e+rNDXleHDzap7cbGZAjh0KCyBRmw8TD8pLCnUTi930sSpiVp/an2d/tX0oNVVlRkbZmj8lHiNnxJ/USw4+UJecZ7uObEndItCvrBmjWq7dqqtWplFlQuZL74wsdpIfiwAAAenSURBVCbvuEP1xIng1nX6tOrjj6vefbfqt98Gt65a4EJ8wux5ZU/97Vu/5YqWVzjuy51xJIN+/9ePM8UmsVJKXAqT+k1i0nWTgurZk/JsCqeLTXrSaImm8MnCiEzFESr2ntxLn5l9KCwtpF1KOzbevZHk+At/Ic4SIC4XPPWUyZM+YgQ89phfI4Cw5CUXkRdEJFNEtonIP0SkYQ3HpYnIHhHZKyI+54bdeXwnDy95mP6z+7Nk75JApJ5D+4btiZbKjjG3OJepa6by/JfPO1pPdZrUrwxNlRiXeJaGSOZY3jFGfTCKwe8MZvPhzY6V+8r6VzhVcIr8knwO5h5kQeYCx8q2XMDMmQPTpxtvq6lTYeHCkFQb6Cr5cqCHqvYEvgEer36AiEQDrwE3At2A0SLiW7gaNYEc8kvymbdzXoBSz6ZBvQasHb+WtM5pxEcbs5H8knw2Zm90tJ7qLBq1iF6tetGjeQ+W3L4k4HnDUDFy3kg+3P0hy/ctZ+DbAykqdSbYROvk1hVZOMF4C1ksXjlwoNKXvLTUuIWGgIDGgqq6rMrLdcBID4ddDexV1X0AIvIeMBzY5Ws99WPrc/0l1wci1SPdmnUjfUQ63Wd053TRacq0jPt6BzdEV2qLVDbdsymodQSDvSf3UuoqBaCgtIDcolyaxdTuX+4Lj/R9hD3/3sOa79cwpucYBnX0YhtpsQCMGQMvv2xcNxMSTGzSEODk5Nk44H0P77cBqoY8OQj08aXALk26MPjqwfRt25fRPUY7IPFcGtZryM77d7L6u9V0bdKVrk39TE5/kTCp3yQeX/E4URLFoE6DvAbj8JX4mPiIyz1vOQ9o395kmfzmGxMtKikpJNV6XfQRkRWAJ/uXJ1R1ofuYJ4DewK+0WoEiMhJIU9UJ7tf/DfRR1QdrqO8e4B73yx7ADt8vJ2g0BSIlTpnV4hmrxTNWi2e6qqrfq4tenzBVtVZfNhG5E/hP4OfVO0s3h4B2VV63db9XU31vAG+4y/66LitZThMpOsBqqQmrxTNWi2dEpE4G3oGukqcBfwCGqWpNfnUbgS4i0kFE4oBRgGeHZYvFYolgAl0lfxVIBpaLyFYR+RuAiLQWkcUAqloKPAgsBXYD81TVe1BGi8ViiTACXSXvXMP72cCQKq8XA4vrUMUbdZTmNJGiA6yWmrBaPGO1eKZOWiLa08disVgiiYsuvJvFYrHUlYjqMIPtaumHjltEZKeIuESkxlU9ETkgItvd87dBCavkh5agtom7jsYislxEvnX/bVTDcWXuNtkqIo4u8Hm7ThGJF5H33Z+vF5H2Ttbvp5Y7ReR4lbaYECQds0TkmIh4NMETw1/cOreJSK9g6PBRywARyanSJpODpKOdiHwmIrvc/z8PezjG/3apS8SOYG3AYCDGvT8NmObhmGggC+gIxAEZQDeHdVwOdAU+B3rXctwBoGmQ28SrllC0ibue54HH3PuPefp+3J+dCVJbeL1O4H7gb+79UcD7YdRyJ/BqMH8f7nquB3oBO2r4fAjwKSBAX2B9GLUMAD4JQZu0Anq595MxrtvVvx+/2yWinjBVdZmaVXUwrpZtPRxW4WqpqsVAuaulkzp2q+oeJ8usKz5qCXqbuBkOvO3efxvwnlHNWXy5zqoaPwB+LsFx2A9Vm3tFVVcDJ2s5ZDjwdzWsAxqKSB2ChDqiJSSo6mFV3ezeP42x0Kmep8XvdomoDrMa4zC9f3U8uVqem7AmNCiwTEQ2uT2UwkWo2qSFqpYndT4C1BQpo56IfC0i60TEyU7Vl+usOMZ9880BmuA8vrb5CPdw7wMRaefh81AQSf8zANeISIaIfCoi3YNdmXta5kpgfbWP/G6XkAdi9MPVshSYG04dPtBPVQ+JSHOMLWqm+w4bDi2OUJuWqi9UVUWkJhOLS9zt0hH4l4hsV9Usp7WeB3wMpKtqkYjci3nyHRhmTeFmM+b3cUZEhgALgC7BqkxEkoAPgUdUNTfQ8kLeYWqIXS3rqsPHMg65/x4TkX9ghml+d5gOaHGkTbxpEZGjItJKVQ+7hy4ek7pXaZd9IvI55u7uRIfpy3WWH3NQRGKABsC/Hajbby2qWrXemZg54HDg2O8jUKp2Wqq6WERmiEhTVXXcx1xEYjGd5VxV/cjDIX63S0QNyeU8crUUkUQRSS7fxyxYhStQSKjaZBFQnnt1LHDO06+INBKRePd+U+A6/Ajl5wVfrrOqxpHAv2q48QZdS7X5sGGYebRwsAgY414V7gvkVJlaCSki0rJ8TllErsb0QY7f0Nx1vAXsVtXpNRzmf7sEe7XKz5WtvZg5ha3urXy1szWwuNrq1jeYp5YngqDjvzDzGUXAUWBpdR2Y1dEM97YzGDp81RKKNnHX0QRYCXwLrAAau9/vDcx0718LbHe3y3ZgvMMazrlO4E+YmyxAPWC++7e0AegYxN+rNy3Pun8bGcBnwGVB0pEOHAZK3L+V8cBvgN+4PxdMEO8s93dSo+VHCLQ8WKVN1gHXBklHP8waw7Yq/cmQQNvFevpYLBaLj0TUkNxisVgiGdthWiwWi4/YDtNisVh8xHaYFovF4iO2w7RYLBYfsR2mxWKx+IjtMC0Wi8VHbIdpsVgsPvL/Ag5dcMAYNMUAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"xv = xor[\"x\"]\n",
"yv = xor[\"y\"]\n",
"\n",
"colors = [\"rg\"[i] for i in xor[\"label\"]]\n",
"plt.figure(figsize=(5, 5))\n",
"plt.xlim([-2, 2])\n",
"plt.ylim([-2, 2])\n",
"plt.title(\"green points have label True\")\n",
"plt.scatter(xv, yv, color=colors, marker=\".\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Again, this example data set can not be separated by a line. But we see that points where the sign of x and y are the same appear to form one class, and point with different signs for x and y belong to the other class.\n",
"\n",
"How can we engineer a more descriptive feature which describes \"x and y have the same sign\" ? We just have to recall that the product of two numbers is postive if and only if both numbers have the same sign.\n",
"\n",
"So lets plot a histogram over `x * y`:"
]
},
{
"cell_type": "code",
"execution_count": 350,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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eXgU8Oqssq0mym6V/pr21qv5n1nlOM16qYkJJAtwCHK2qT8w6z2qSDF5Y/ZXkpcCVzNmf46p6f1VtrartLP0+/HIfZQ4W+kof7XYdHAbexNJR6HnyN8ArgP3d0sq/m3WglZK8LcljwOuBf0ly76wzwdKlKljahXYvSwfz7pi3S1Uk+TTwVeDiJI8luX7WmVa4HLgWuKL7/Xeom2XOky3Age7P8NdZ2ofe27LAeeeZopLUCGfoktQIC12SGmGhS1IjLHRJaoSFLkmNsNAlqREWuiQ1wkKXpEb8H34J5hL8mzEZAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"products = xor[\"x\"] * xor[\"y\"]\n",
"\n",
"features_class_true = products[xor[\"label\"]]\n",
"features_class_false = products[~xor[\"label\"]]\n",
"\n",
"plt.hist(features_class_true, bins=30, color=\"g\", alpha=.5, histtype=\"stepfilled\")\n",
"plt.hist(features_class_false, bins=30, color=\"r\", alpha=.5, histtype=\"stepfilled\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this case a simple classifier would just introduce a threshold of 0 to distinguish both classes."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Other examples for feature engineering\n",
"\n",
"Feature engineering requires understanding your data to extract meaningful and discriminative information.\n",
"\n",
"Proper feature engineering can boost the performance of a classifier significantly.\n",
"\n",
"Examples:\n",
"\n",
"- nudity classifier: color histograms of full image and image patches\n",
"\n",
"\n",
"- spam classifier: choice of dictionary, extra feature which counts words only in capital cases or words with unusual characters (like \"pill$\")\n",
"\n",
"\n",
"- to distinguish background noise from speach audio samples, the frequency distribution might help. Also std deviation or a histogram of loudness / energy of a sample might help.\n",
"\n",
"\n",
"- to classify DNA sequences, n-gram histograms (n>=1) can be benefitial (-> GC content).\n",
"\n",
"\n",
"- for geopolitical data a feature \"state\" can be enhanced by \"political system\" and or \"GBP\".\n",
"\n",
"\n",
"- for sales data add a feature \"is week day\".\n",
"\n",
"\n",
"Most cases are beyond the 2- or 3D case and visual inspection can be difficult. Thus engineering features as we did in the 2D examples before becomes tricky. But here are some general recommendations:\n",
"\n",
"- use statistics (mean, std deviations, higher order features) as well as histograms if applicable.\n",
"\n",
"- polynomial features (e.g. extend `x, y` to `x, y, x * y, x ** 2, y ** 2`) (see examples section also).\n",
"\n",
"- image classification: dig into *computer vision* to learn about image descriptors.\n",
"\n",
"- audio classification: learn about FFT, wavelets, filter banks, power spectrum, ...\n",
"\n",
"- try to incorporate external data.\n",
"\n",
"*Comment*: \n",
"\n",
"We will see later that many features can introduce other problems (-> *overfitting*) but there are also methods for feature selection in this case (see https://scikit-learn.org/stable/modules/feature_selection.html)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise section"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. Modify the weights in the beer classifiers and check if you can improve separation in the histogram.\n",
"\n",
"Try weights `[-0.05837955, 3.69479038, 0.6666397 , 1.62751838]` in the beer classifier. These are the weights the `LogisticRegression` classifier in the previous script computed.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2. The following script learns classifiers on different data sets and plots decision surfaces."
]
},
{
"cell_type": "code",
"execution_count": 358,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"487 out of 500 predicted correctly\n"
]
},
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 432x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from sklearn.linear_model import LogisticRegression\n",
"from sklearn.svm import LinearSVC, SVC\n",
"from sklearn.preprocessing import PolynomialFeatures\n",
"from sklearn.tree import DecisionTreeClassifier\n",
"from sklearn.neighbors import KNeighborsClassifier\n",
"\n",
"\n",
"def train_and_plot_decision_surface(clf, preproc, features, labels, marker=\".\", N=400):\n",
" \n",
" features = np.array(features)\n",
" xmin, ymin = features.min(axis=0)\n",
" xmax, ymax = features.max(axis=0)\n",
" \n",
" x = np.linspace(xmin, xmax, N)\n",
" y = np.linspace(ymin, ymax, N) \n",
" points = np.array(np.meshgrid(x, y)).T.reshape(-1, 2)\n",
" \n",
"\n",
" if preproc is not None:\n",
" points_for_clf = preproc.fit_transform(points)\n",
" features = preproc.fit_transform(features)\n",
" else:\n",
" points_for_clf = points\n",
" \n",
" clf.fit(features, labels)\n",
" predicted = clf.predict(features)\n",
" print(sum(predicted == labels), \"out of\", len(labels), \"predicted correctly\")\n",
" classes = np.array(clf.predict(points_for_clf), dtype=bool) \n",
" plt.plot(points[classes][:, 0], points[classes][:, 1], \"g\" + marker, markersize=1, alpha=.05);\n",
" plt.plot(points[~classes][:, 0], points[~classes][:, 1], \"r\" + marker, markersize=1, alpha=.05);\n",
"\n",
"\n",
"df = pd.read_csv(\"2d_points.csv\")\n",
"df = pd.read_csv(\"xor.csv\")\n",
"\n",
"features = df.iloc[:, :-1]\n",
"labels = df.iloc[:, -1]\n",
"\n",
"plt.figure(figsize=(6, 6));\n",
"\n",
"clf = LinearSVC()\n",
"# clf = LogisticRegression()\n",
"# clf = SVC(gamma=.1)\n",
"# clf = DecisionTreeClassifier(max_depth=6)\n",
"# clf = KNeighborsClassifier(10)\n",
"\n",
"preproc = PolynomialFeatures()\n",
"# preproc = None\n",
"\n",
"train_and_plot_decision_surface(clf, preproc, features, labels)\n",
"\n",
"colors = [\"rg\"[i] for i in labels]\n",
"plt.scatter(features.iloc[:, 0], features.iloc[:, 1], color=colors, marker='.');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- modify the script to use the `xor.csv` data set.\n",
"\n",
"- play with the other classifiers which are outcommented in the script and play with their parameters and deactivate the feature engineering step.\n"
]
},
{
"cell_type": "code",
"execution_count": 369,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/uweschmitt/Projects/machinelearning-introduction-workshop/venv3.6/lib/python3.6/site-packages/ipykernel_launcher.py:9: UserWarning: get_ipython_dir has moved to the IPython.paths module since IPython 4.0.\n",
" if __name__ == '__main__':\n"
]
},
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" }\n",
" \n",
" div#maintoolbar {display: none !important;}\n",
" </style>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"execution_count": 369,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#REMOVEBEGIN\n",
"# THE LINES BELOW ARE JUST FOR STYLING THE CONTENT ABOVE !\n",
"\n",
"from IPython import utils\n",
"from IPython.core.display import HTML\n",
"import os\n",
"def css_styling():\n",
" \"\"\"Load default custom.css file from ipython profile\"\"\"\n",
" base = utils.path.get_ipython_dir()\n",
" styles = \"\"\"<style>\n",
" \n",
" @import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
" \n",
" @import url('http://fonts.googleapis.com/css?family=Kameron');\n",
" @import url('http://fonts.googleapis.com/css?family=Crimson+Text');\n",
" \n",
" @import url('http://fonts.googleapis.com/css?family=Lato');\n",
" @import url('http://fonts.googleapis.com/css?family=Source+Sans+Pro');\n",
" \n",
" @import url('http://fonts.googleapis.com/css?family=Lora'); \n",
"\n",
" \n",
" body {\n",
" font-family: 'Lora', Consolas, sans-serif;\n",
" \n",
" -webkit-print-color-adjust: exact important !;\n",
" \n",
" \n",
" \n",
" }\n",
" .rendered_html code\n",
" {\n",
" color: black;\n",
" background: #eaf0ff;\n",
" background: #f5f5f5; \n",
" padding: 1pt;\n",
" font-family: 'Source Code Pro', Consolas, monocco, monospace;\n",
" }\n",
" \n",
" p {\n",
" line-height: 140%;\n",
" }\n",
" \n",
" strong code {\n",
" background: red;\n",
" }\n",
" \n",
" em {\n",
" color: green;\n",
" }\n",
" \n",
" .rendered_html strong code\n",
" {\n",
" background: #f5f5f5;\n",
" }\n",
" \n",
" .CodeMirror pre {\n",
" font-family: 'Source Code Pro', monocco, Consolas, monocco, monospace;\n",
" }\n",
" \n",
" .cm-s-ipython span.cm-keyword {\n",
" font-weight: normal;\n",
" }\n",
" \n",
" strong {\n",
" background: #f5f5f5;\n",
" margin-top: 4pt;\n",
" margin-bottom: 4pt;\n",
" padding: 2pt;\n",
" border: 0.5px solid #a0a0a0;\n",
" font-weight: bold;\n",
" color: darkred;\n",
" }\n",
" \n",
" \n",
" div #notebook {\n",
" # font-size: 10pt; \n",
" line-height: 145%;\n",
" }\n",
" \n",
" li {\n",
" line-height: 145%;\n",
" }\n",
"\n",
" div.output_area pre {\n",
" background: #fff9d8 !important;\n",
" padding: 5pt;\n",
" \n",
" -webkit-print-color-adjust: exact; \n",
" \n",
" }\n",
" \n",
" \n",
" \n",
" h1, h2, h3, h4 {\n",
" font-family: Kameron, arial;\n",
" }\n",
" \n",
" div#maintoolbar {display: none !important;}\n",
" </style>\"\"\"\n",
" return HTML(styles)\n",
"css_styling()\n",
"#REMOVEEND"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"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": "3.6.6"
}
},
"nbformat": 4,
"nbformat_minor": 2
}