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@dniku
Created November 18, 2017 23:22
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{
"cells": [
{
"metadata": {},
"cell_type": "markdown",
"source": "# Задача 1\n\nПусть $K(x, y) = (x_1 y_1 + x_2 y_2)^n$. Тогда\n\n$$\nK(x, y) =\n\\sum_{k=0}^n C^k_n (x_1 y_1)^k (x_2 y_2)^{n-k} =\n\\sum_{k=0}^n \\sqrt{C^k_n} x_1^k x_2^{n-k} \\sqrt{C^k_n} y_1^k y_2^{n-k}\n$$\n\nпоэтому в качестве спрямляющего отображения можно взять\n\n$$\n\\varphi(x_1, x_2) = \\left( \\sqrt{C^k_n} x_1^k x_2^{n-k} \\right) \\in {\\mathbb R}^{n+1}\n$$\n\nПусть теперь $K(x, y) = (1 + x_1 y_1 + x_2 y_2)^2$. Тогда\n\n$$\nK(x, y) = 1 + 2 x_1 y_1 + 2 x_2 y_2 + x_1 x_2 y_1 y_2 + x_1^2 y_1^2 + x_2^2 y_2^2\n$$\n\nи можно взять\n\n$$\n\\varphi(x_1, x_2) = \\left( 1, \\sqrt{2} x_1, \\sqrt{2} x_2, x_1 x_2, x_1^2, x_2^2 \\right) \\in {\\mathbb R}^6\n$$"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "# Задача 3\n\nПусть $p$ — это некоторый объект. Тогда\n\n$$\n\\operatorname{class}(p) =\n\\operatorname{argmax}_{C \\in \\{ S, B, U \\}} \\mathbb P (b, w, h | p \\in C) \\cdot \\mathbb P (p \\in C) =\n\\operatorname{argmax}_{C \\in \\{ S, B, U \\}} \\left( \\ln \\mathbb P (b, w, h | p \\in C) + \\ln \\mathbb P (p \\in C) \\right)\n$$\n\nЕсли признаки $b$, $w$, $h$ распределены в каждом классе с одинаковыми ковариационными матрицами, то\n\n$$\n\\operatorname{class}(p) =\n\\operatorname{argmax}_{C \\in \\{ S, B, U \\}} \\left( - \\frac 1 2 \\left( \\begin{pmatrix} b \\\\ w \\\\ h \\end{pmatrix} - \\mu_C \\right)^T \\Sigma^{-1} \\left( \\begin{pmatrix} b \\\\ w \\\\ h \\end{pmatrix} - \\mu_C \\right) + \\ln \\mathbb P (p \\in C) \\right) =\n\\operatorname{argmin}_{C \\in \\{ S, B, U \\}} \\left( \\left( \\begin{pmatrix} b \\\\ w \\\\ h \\end{pmatrix} - \\mu_C \\right)^T \\Sigma^{-1} \\left( \\begin{pmatrix} b \\\\ w \\\\ h \\end{pmatrix} - \\mu_C \\right) - 2 \\ln \\mathbb P (p \\in C) \\right)\n$$\n\nгде $\\mu_C$ — матожидание для вектора $\\begin{pmatrix} b \\\\ w \\\\ h \\end{pmatrix}$ в классе $C$.\n\nЛегко посчитать, что для функций вида\n\n$$\n(x - x_i)^2 + (y - y_i)^2 + (z - z_i)^2 - \\alpha_i\n$$\n\nпри $i = 1, 2$ разделяющие поверхности имеют вид\n\n$$\n2(x_2 - x_1) x + 2(y_2 - y_1) y + 2(z_2 - z_1) z = (x_2 - x_1) (x_1 + x_2) + (y_2 - y_1) (y_1 + y_2) + (z_2 - z_1) (z_1 + z_2) + \\alpha_1 - \\alpha_2\n$$\n\nто есть это плоскости. Построим эти плоскости для всех трёх пар классов при фиксированных вероятностях принадлежности к каждому классу:"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "import numpy as np\nimport matplotlib.pyplot as plt\nfrom mpl_toolkits.mplot3d import Axes3D\n%matplotlib inline\n\ndef get_plane(c1, c2, a1, a2):\n return [\n 2 * (c2[0] - c1[0]),\n 2 * (c2[1] - c1[1]),\n 2 * (c2[2] - c1[2]),\n -((c2[0] - c1[0]) * (c1[0] + c2[0]) +\n (c2[1] - c1[1]) * (c1[1] + c2[1]) +\n (c2[2] - c1[2]) * (c1[2] + c2[2]) +\n a1 - a2)\n ]\n\nmu_S = np.array([6, 6, 4])\nmu_B = np.array([6, 4, 6])\nmu_U = np.array([4, 6, 6])\n\np_S = 0.1\np_B = 0.3\np_U = 0.6\n\nplane1 = get_plane(mu_S, mu_B, -2 * np.log(p_S), -2 * np.log(p_B))\nplane2 = get_plane(mu_B, mu_U, -2 * np.log(p_B), -2 * np.log(p_U))\nplane3 = get_plane(mu_U, mu_S, -2 * np.log(p_U), -2 * np.log(p_S))\n\nnormal1 = plane1[:-1]\nnormal2 = plane2[:-1]\nnormal3 = plane3[:-1]\n\nd1 = plane1[-1]\nd2 = plane2[-1]\nd3 = plane3[-1]\n\n# create x,y\nxx, yy = np.meshgrid(range(10), range(10))\nyy1, zz1 = np.meshgrid(range(10), range(10))\n\n# calculate corresponding z\nz1 = (-normal1[0]*xx - normal1[1]*yy - d1)*1./normal1[2]\nz2 = (-normal2[1]*yy1 - normal2[2]*zz1 - d2)*1./normal2[0]\nz3 = (-normal3[0]*xx - normal3[1]*yy - d3)*1./normal3[2]\n\n# plot the surface\nplt3d = plt.figure().gca(projection='3d')\nplt3d.plot_surface(xx,yy,z1, color='blue')\nplt3d.plot_surface(z2,yy1,zz1, color='yellow')\nplt3d.plot_surface(xx,yy,z3, color='cyan')\nplt.show()",
"execution_count": 1,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x7f698051bc50>",
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xiSe6TROm9+3zmWI7xYoLFwZNs30g7G3LvpqswAnKQdoKfB/46tYfks+r3LkT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QR2m8FzY930B6JsDUZ5IddBIi/T7UsgOwoIQDTr5tRkO2/efYY//5mf8IYtgxawKdTPBdu1qfk/\n5rpJpUQyGZHTp1tLiTGFgg2fTyKdziPLBdxutXRRGggotLYmsNo+rmKJUD2j685aL2HdhMNdbNmy\npfR3wzDI5XJkMhnS6TSZTIaxsTEymQyqqiLLcpnALv5ZkqSqT46LE+omG0dTUFuI9UyoF3rTiv7o\ny5cvoygKfX197N27F1mWV/yYjTahNqncLcds1kE06iQed5btpIf55jy3W8XjUQgGTYHc2mp+VIJ6\nrCG+HAvwN48f4+FzO9keirC3fRJDgKQicz7aws3uMQLOPM+Pd3Gwa4yjvcOcn20hW8gRcOYIyDkM\nBE5Pt6MbAv/jwEn+47/9G32BeK0PrURjbUq03rHEYjKxmJNkUl6wQc+8KHU4dGS5gMej4vebde5e\nr/nngYGZWi99XTSCoNa0lZ9/rMqVHmpBEHC5XLhcrkWNhIqilAnt2dlZhoaGyOVy2O32RSK70vaR\naDTabEncYJqCugEQRZFMJlPyRw8PDyNJEps3b17GH70SGm9CbRiuZSeYhhEAgui6h1RKJ5uF8+dz\naJrpPZYkc3rs9+cJBs3NeS5X5TfnrRSns34E9dnpVu577DZenOjAJylsDUVwiQWGEgFm0i52t00j\n2XWGEgG2BGMEnTkSeQlV01E1Gy6HStiV4yeXt3C0d4SP/8L/49d3n0GyW+/foJEEdbWn/Qvv2pj+\nYxFFMf3HgmD6j53Oouc/TzicJRjMEwyuzhPdCDacYqpHPdMYgnrlKR+SJCFJEsFg+XBK0zQymUxJ\nbKdSKSYnJ8lmsyX7yJXWkbXYR5oT6o2nKagtxFon1LquE4lE+MlPfkI4HGbv3r1X9UevDC+G4UAQ\nrNHOtRrM1q7gnEj2AE4MQ8QwfEA3ZmtiFrPJKwFEEIQ4EMduh0DA/OjsrNkhXJN6qCF+erSHjz9x\nC+NJH9GckzZ3Brtg8PxEF30B0+oxlvCS10S2BGJ4nHkUzc5EykdacTDQPo3s0Dgx3M/b95zioV/+\nLns7Jmt9WFelkQT1alGUYkGIk1RKJJdz4HI5SSTUkkAu+o+LG/QqeddmORrhZ1IoNIKgFmu9hHVT\niZQPu92Oz+fD5/OVfd0wDLLZbJnYjsVipNNpCoXCIvtI8fNy9pFoNMrWrVvXvd4mK6cpqOuUhf7o\nSCSCKIrceuuti16k6yMETFfw8daGYXiA0JwgdgMS4Jhr8tIwDAVByAIJBCE+J5KnEYTytev6fmy2\nFzZ8/dXA7V5dTOJG8sjFLXz2+QOMp/y8OhtioG0al6MwZ+UYZ1/HBBejIQJynu0tEXxyjtmci+cm\nuunwpOjyJnk+2c1IIsAf3vIkv7nvJfxyfRTzWHCz/5opFGyMjvpKBSG5nINCYWFBSAG3e35TbDCY\np7MzTWentTbFNsKEuliEVM+oav3LjWrG5gmCUJpGL8QwDFRVLVlHMpkMMzMzJfuIw+EoCezBwUES\niQQ33XTThk2oP/axj/HNb36Tc+fO4XK5OHbsGPfffz87duyo+nNbjfr/DW8gVjJR1jSN8fFxLl26\nVPJH9/b2cuHChQqLadNHfaUoXf9j2tA0H3Z7y5xQdmEYIoJgwzCMuYl4DsjMCeMogpDGnCav97nr\nf0JSRJJ0CgWo4SbyMgwD/uPcTv79zC7OzbZxKeZnX8cUDhtcigfZFopwU7tGIi/jsOkE5SweSSGe\nd/LjwS3sDk6xq3WakxNdHOia4Duv/wo/s/lyrQ9rTWgarMllVWUSCWku/7joPy7PHC9uivX7Tc+/\nKGqWLQhZDZXKbK8lLlf92yUKBQu+KFZJLXKoBUEo2UeuTO0o2keKYvvkyZN87WtfY2RkBMMwuHjx\nIo888gi7du1i586d7Nq1ix07dlS07OUnP/kJd999N4cPH6ZQKPBnf/Zn/MIv/AJnzpy57kplLHI6\nbnIt8vk8w8PDDA0NLfJHx+PxVRe7rIxrb0w0DCfz02MPIAPi3PRYxzBUBCEDpEoC2eEw7RUbn8jQ\nWL/u2ayIz1fbSXVBt/GN07t4+NxuHh/eRNCZod2ToaCHyBZEdrZOk1VFsqrIWNJPiytN0JnjxXgn\n01kPe9unsLUbjMb83L33af7jv32NTm99F1joulD1qaiuU6p0TyZlwEk8bixIjdFxOlXcbpVAwNyg\n5/cr+P31XayxFhphQp1MWveO1EpR1fqYssuyH1kOIUleHA4XdruIINgxDANJslaxy5X2kQ984AN8\n4AMfQFEUjh49yrve9S4kSeLcuXM88sgjnD17ll27dvH4449XbA3f//73y/7+xS9+kfb2dp577jnu\nuOOOij1PPdBYCqPOWWpCnUwmuXz5MmNjY8v6o4uxeeaEt3JvWrp+EyAC9jmBXMAw8ghCdsH0OAOM\nIwjjFXveahGPJ2mkPRq1FNRZ1cFXX76Jf3t5D0+PdrO/Y5zt4VkGo0Fa3Vn2dkwiOzRyBZEXJjrZ\n0zFJly/JM6Pd7Gmf5GDnGJfjQQqGjXvv+CldyQS3HNnYEpZqYd6eX52IKxQEIpH5gpArS3mKAtnr\nVQkGc4RCWcLhHOFw9Up5ah9BWBlcrlqvYP00guVDUWpxDAKyHECWAwsEslS6I6rrKul0HE3LoutZ\ncrko+XyCfH7pNCinsz6qx0VRZHJykl/6pV9i//79pa8bhkE6XV1LVjxupi5djxsim4LaYgiCgK7r\nzM7OlvzR3d3dV/VHS5KEYRgUCgVEsXK2BkFIYbNV7kq21rjdjXX7qRZlD/GcxOdOHuTzJw+SVEQG\n2mbY3TZNUpER7Tq9/gRuUWUoHuByLMDN3eN0eFOcnWllb/sEr99yiZm0mxtbInziF/8fN7bMAvDU\nU90bfizVQtcFcjk70aiLeFwmnZ4XyPP+48UFIe3tGdrbrdToWf+TXVhdsUuT6lGZ1nEBpzOILAcQ\nxYUT5KJAVigU8qhqmnw+PieQY+TzsXU/s83mQBTr4xyiKAqpVGpRbJ4gCCvsoVgbuq7zvve9j+PH\nj3PTTTdV7XmsSlNQW4yRkREGBwdRFIVNmzaxZ8+ea+ZH2+12BEFAVdWKCupGi86TJKnWS6goudzG\nCerJlIdPPHkrn3nuINvCETb5YyQVJ2nFwXTaTbcviezQODneRdCZZVs4SjTnYirtoceXYJM/gUss\n8Gu7zvLWPS/jFssn65pm7QncwtZKw3ARjRpomimQ52MVzYIQWS7Q2ZmhqytFV1f92lcaZUJtpvrU\nN0YDXNvk84sPQhBsyHJRIHsQRRc2W1Eg6+h6gUIhh6KkUJQ42WyUXM782GgkqT6m02BG5gEbnkN9\n99138/LLL3PixIkNfV6r0BTUFiOVStHf3093d/eK86MFQVhR/fhqabRyF6MRzkoL2Ihd84PRIH/9\n+HG+9cqNbA9F2N9pWntSiszZqRb2d03Q4s7y1GgvN3ePcqh7jFOT7aQUiQ5PirArx67Waf773pc4\n2ju67PNs9C3ttRSELNdaeSWJRONsfm0EHI76n1DXy8WNYdgwjBDgxzC8c3tsRMBGLuenq+sIqpqd\nmyDHyOVi5HIRcrlIjVd+bWqxIXGtRKNRPB4PTufGtVO+973v5Tvf+Q4//elP6e3t3bDntRJNQW0x\ndu3aha6v/gRwZVtiZWisCbUgWK8IZD0oSvUy2l6eaue+E7fx8lQbPinPtlAEp1hgNOlnJO5jf+cE\nPqfK2Zk2BtqmuK1viNGED9GWRrTrtHsyvG7zIG/fc4oW97Vzhg1j7YphNQUhxfzjtRSErJzGyM6r\nFxF3LRpDUNdmGGAY9rnBSmCBQHZg1tIbgArkEITkXGRpDJttFphd9FiKcpjx8Wc2cvkVpZ4E9ezs\nLKFQqOr15mAOqn7v936Phx9+mB//+Mdl1ezXG01BbTHWUz/enFBfi/q/9buQapQ9PDHcywNP3sJk\nyksk66TdncFuM3hhopN2T5ouX5KhWICEIrMtNItm2MioEnnNQTzv5PVbLvNntz/Kz2+9uCpBtlBQ\nK4qNaNRFOu0ikRDJZOyoqh1dp7RBrxYFIStFa5DrtlqJuErTGIK6Mo+zcPNrR0c7Ho8fEFEUlXw+\nh88nA9kFAjm+rEBeLblcfSeV1JOgjkajhMPhDRHUd999N1/5ylf4P//n/+Dz+ZiYmAAgEAjgaoQd\nwaugKagbhGoI6kabUJvTlMZBVSsnqH9wYRufP7mfibSP8zMhBtqn8UoqT432crh7lL0dk5yebqXV\nk2F32zRuUUE3bFyIhJHsGr914HnevvcU/cH4osfOZh1EIq6rFoTE4xKDg4FSQUhHh5k9Xo80QiJD\nIyGK9X+Fs1yWtqraFqTDzL+2iukwkqThdi+3+XXeZuFwwBV9IhUnm63vyMbV1I7Xmo2sHf/0pz8N\nwOte97qyr3/hC1/gne9854aswSo0BbXFWOsVpSRJzQn1NanvN/Qr0fX1CWrdEHj47E6+eXYXZ2fa\nuBzzc6BzAtFh8GqkhV2tM9zcPcZs1k3AmaPDm8HtUMgrLh4d6mcgNM1vb3mW4+FhbJrB4AtBhux+\nnE4zwcLvzxEK5fD51GsWhPz4x/1s2bJYjNcjjSKoG8XyIYr1M6FWFBuzs2Z9u3nxKVIo2IhEZH76\n076SQPZ6FUKhLIGAefFpXoBam/oX1PUzod5IQd1oe5PWQ1NQNwjNCfVKqF5mby1Yq+VD1Wx8/fQA\nD5/byePDffjEHGE5R1YVGY946bCnyBQcjE77SGsSkl3DbtdJ5SQejWzm7Xte4h/f9B32dU5W+Iga\ng0YR1I0SmyeKtTsORbHPCeSl4xNluYDLVV7f3tWVpqurXCA/80wXhw9bP+v/amQy9f3+W08T6qLl\no8nG0hTUFmM9HupKB7Y32oTaLKFpHJYaDBQ9kvG4TColk83OF4Qoho0fzWzhR9NbOB1rZ2/bBNvD\nM5yfbaXLn+JIzyg2m4Fu2HhtMswN4Vna5TTPjvVgk+B9tz7JO/a/iF+u/Ga+RhpyNIqgboQJtaLY\nkKTKTahzOfvc68ucIOfzSwlkFb9fIRTKEQjkKxKf2Ag+8EzGGnsc1ko9Taij0SidnZ21XsZ1R1NQ\nNwjNCfVKqD9Bnc/bSwL5yglXJCLz5JM91ywIiWZlPvv8zXzhhQOkFJGBtin2OidJqzJePc+WUASX\no8B0xs2LEx0c7R2lPxjj+YlufmXnOf7jN/6N12+5VNXjbATxVmQ9iSVWohF+Jqpqv6qgvpa/X5YL\ncx7k/JxAVujuTtHdvbH54vVkW1mOdLr+3n8XUk8T6kgkwsDAQK2Xcd3RFNQWYz0e6srH5vkwDHvD\nxM0ZRqrmIiGVEonH3aRSTuJx+1z+8dIFIcGgeQJfbsL14x/3c8sty2c7jye9PPDErXz2+YNsb4mw\nORAlknORViViWSctngweUeX0dDsXNRt72ifp9qW4FAvx7oPP8d23fYUuX/0Wk9SKRplQ16PlI5Mp\nF8iplIQgsOTrKxzOrsjfbwUcjvp+DzYMG9lsvU+o6+eObSwWa1o+akBTUDcI1ZlQC0CQSkQmWQGb\nTSedduDxVC4+LxaTiUZdJJMSmYyIopQXhDid5oSrvCAkDqx/A95yNonXIiH+6rHjfOuVHdzYMsPB\n7jE03UZalbgYDXFT+xStngzPjPWwq3WaPe2TnBzvwsDGA3f+gF/Z+QqODa5rFsXGyG6GxrGv2Czw\nI0mnRSIRJ4mEWcCTyznKLkBlWaO1FRyOJOFwFq+3gNudBEyBPDPjskyc4nqopG2lNrio19SeIvXW\nlLjRLYlNmoLaclgphxpMH7UgNIagBvMEvZyg1rR5/3EyKZHLiaiqbU4gL1UQkqtyQcjVsdnKlduL\nEx3c99htnJlqwy/nuTE8g1PUmEp7uDAb4nDPGC3uLM+NdXNz1xh39F3mldlW7ugf4hN3/oAdrbX7\nObtcG1ejXm2sXqO+UhyOyivqhRXupkA279CYz1ecICtzF6BZPB4Vj0elKJBXSzWy2muBJNX3hFrX\n3dS7oK4XD7VhGEQiEVpbW2u9lOuOpqC2IIIgrDqKpiioDcOocJh7/fqoDUMEQkxNORgZ0cnlHCQS\nEk6nVspodbkKeL2mKA6FsrS1ZWhrqw+vX/HHfGKojweeuIWZjJtYzkmLK4No1zk11YHLrrIlFMNu\nC7xJ2bIAACAASURBVDKa9NHnj9PlTZLXHLx1zwu8fe8p3GLt87nT6fqO1FpIo3ioC4Vri7hMRiYe\ndxOLiSSTDvJ5B4VCeYX7/B2a7Koq3CtBowhqWa7vUipd37gK7GpRTx7qpuWjNjQFdYMgiiIAhUKh\n9OfKYB3fmGG4gBCG4QfcgAw4MAyzVtwwFAQhCyQRhBiCkACm6OiAjg7zMc6caWX37plaHUJFeTra\nw99+/RZmM27OR0Lsbp3GJys8MbKJA53jDLRN8dxYN11air0dk4g2nb5Agt86+Dy3bhqp9fLLaJRW\nPqhvQZ1ISESjTpJJmfFxL8mksySQw2GRfD6NxzNvYXK787jdebq6ar3ypSlOv+udpqCuPfUyoU6n\n0+RyueaEugY0BbUFWcuE2m63IwgCiqJUVFAbRvUm1IbhA4Jzn92ABNjnBHJhTiBn5oRxdC72Losg\njK35OfP5+rYWaLrA/z67m4fP7uSFoU5mCi4Odk7gchR4cbKT/Z0T3NI7wuVYgP5gnK2hKG3uNLf1\nDfHO/S/S6rbm9P1K+0o9o1vI7hqPy8RiThIJiUxGmtsEu9jjHwzmCIWy+P0Kfr95t0DXBfbunarx\nEayPRplQu1z1Lag1Tar1EtaMLPuR5VDdCOpIxGzAbE6oN56moG4QBEGoSlsirOxNxJzKBTCMAIoi\nk8sJGIaI0+lBkkQEoYBZrJJB1yPYbHFsNnPz0EYmbyhKfQpqRbPz1VMDfPvVnTw50ovLoeAX84zl\n/UxlPNwQjhDPycRyTgwEAnKegbZpfvnGV7lz+2vYLD4BbiRBXc0JdSxmCuRk0kyxKN8Eq+F0mh7k\nokAOBPIEAmvz+DfCXYNG8LMXCkJNy2kqQaFQybum60OSfMhyEEnyUSgI2O0S7rnedU1TKRTyFApp\ncrk4uVyUfD5BPp+oG8tHNBolEAjgcDTl3UbT/Be3IFbamGgYPej6PsA550k2N+gZhjpnr0jNTZAj\nczaLGE4nOK9yh6+W6QH1NrFKKRJfPrWHb5zezZMjvezvHGd7aJZTUx0EfSqHu0dRNDvZgoPRpJ9u\nf5L/suMM//WmM2wOxmq9/BXTSIJ6NbF5ZkqMmWKRzZoC2edzEo/nEUUdWTY9x+Ym2OyGboKtdcRk\nJWgEy0cu59hQ33k1iESqd2dMFN04nSEkyYfD4cZul7DZHICBrhcoFPKoapp8PkkuF0FRkihK+SbX\nuaHuVZ7DM/eY1mcja8eblFMfvyFNVkR1kj4kbLYXK/yYtaNeTrCRjJPPnLyZf35hH9Gck70dk+zt\nmGQ646XDnWJX2zRaXiCnOTg53snrN1/igTt/wC/f+CpyHWbWNoKg1nWIx51MT7vJ5USyWQeKYi8J\nbFHUrkiJ2ViBvFqaE2pr0AiC2uVauXXQbnfidAaR5QCi6MZulxEE09Ko6wU0baFAjqKqGVS1ula2\nerF7gCmoQ6FQhcMJmqyEpqC2IOuZUFe63KXR6setXroxkvDzwBO38vmT+9kaitIfjOLJuEnkZbKq\nSJs7jUdSuBQPMRQL8Pa9p/iHN36XfZ2TtV76urDbrSfedB1iMeecB1kuCWTT0jEfo+jzzQvkUChH\nS0uOXbvqf+Or3V4fF59Xo14uoK9GvdrUihiGhKK4CYVuQBQ9OBwyNpsIGGiahqpmUZT03OQ4jqbl\nSKcnSKcnar30EvVi9wDT8tHMoK4NTUHdQDTrx6+NVUs3Xp1t4f4Tx/nWqzeyu3WGwz2jZFSRjCoz\nlvRzQ3gWt6jy7FgPXb4k7zn0LG9oeY2btte/cAOw26u/k0/XIRp1EY06SaUkCgUZRbGRzxvYbKYH\n2YxRnPcgh8Nm3vhqsOrv2GqRpPoXo6JY/6e4fN5ax2AY4txmdT+G4cEwnJibyQVAA4qbyVMIQgyb\nLYWq5olGz9d24eug3ibUTctHbbDWK7UJYDUPdWNNqK12F+zkeCcfO3E7p6fbaHFl2N06jeTQSeSd\nnJ1q5UjvKB3eNI8N9/OmHa/wzd/4Gm/YMgjA5KSnxquvHGuZUGuaQDTqnNukV17EY7OZE2SXS52z\nWJgxby0tWVpaqtucZ/W7ICsln69vmwFAJmOhyJU1Uu0JtWHYMdOWghiGB3BiJi6BWT+fB3IIghlH\nCnFstilg5Qkwqlrfr4l6a0lsCura0BTUDYQkSSSTa2sUW4pcLsfUVIIbbqjYQ9Ycq3h1f3Kpn79+\n/BixnIu06qDNnUa2a7w620JadTDQNoNXVjk708a7Dz7Pt9/6Vbp95T9bp7O+o7QW4nDoc02VTmIx\nF6mURDbrQFVt6LqAzWZ6kN1utcyD3NqatVy1tJVi89aD1S4+10IjXNyo6uruFBiGDcMIoKoecjkR\nm82DLHux20VAB1TM+NHUnECOIQizVW3ErUKJ74ZSTxPqaDTK1q1ba72M65KmoLYgtZ5Qp1IpBgcH\nGR8fp7u7vv17V+Jw1E7tGAZ859Ub+ezJA8RzTgajQXa0zOCwaTwz1sMN4Rm2hSM8NdqLIMDf3fU9\nfnXnORy2pdfscln7LFUomFXusZgT8DAzYywQyOYE2RTIeTIZO2DQ1palrc1aAnn11L+Ig8bYlNgo\ngjoadZYKdzIZB6pqL7sTs2uXh0BAARIIQhSbLYosR5HlWq/eJJ+v76vMehPUTQ91bWgK6gZiPYLa\nMAxisRgXL15kdnaWrq4ujh07htfbOFNQAFHc+Dd2TRf42ssDPHxuF5fiQS5FAxzsGp9rNezjcPcI\nR7pHOT3dzh39w3zyru+xq+3a3mhJ0lHVjcuoVVUbkYiLeFwmlZLI5Yqb9FhQ5a7i8ymlKvf29gzt\n7Rkgwo03Lv/Yly8HsDfItVujeKibE+rqUcwTL8Yl5vPlaTAuV6GUJ57P2wmFcoRCq/PyW4lcrv6S\nhxZiGDKKoiBJ1i+oiUajTctHjWgK6gZiLYLaMAwmJycZHBwknU6zadMmBgYGcJaCpA0Mw4Yg1PeE\noYgkbdwbe67g4Msv7eG752/gubFuDGBbOIqOjYuxENtDEQLOPPG8i9859Bxv3/MSHml1P79s1oEo\nru0iSlGKAtlJOi2SzZoe5KJAluWFAjlHMJijoyNNR0d6Tc93NWp556DS1HP1+EIaYUK9UT+LZFIi\nEilOkCVAwm53YLMJ2GwaNpuCJGXw+XK0tKwuLnFwsP43hufz9T2YicWynDhxAlEU8Xg8uN1uPB5P\n6UOSJEvE1BmGQSQSaU6oa0RTUFsQQRDWVD8uSdKKY/M0TWN0dJRLly6h6zr9/f1s2rRpiXYlswER\noqtai1WR5eq/sSfzEv/60l4ePreLE0ObuKl9is3BGM+OddPrT3Coa4yUItHqyfLBn3mUY5uG1/xc\n+byI6Yk0BfLsrAtV9TI9LZQ26RmGuelv4QS5mIHc2Zmms7PyAnm1SFIjCepar6AyWEAfrJu1+tnT\naZFIxEUiYTZS5vN2PB4XiUQeu92MS/R45gt3fD4Fn6+ykaVFrDplXw3ZrLXtadfixhv3MjBwB5lM\nhnQ6TTqdJhqNMjIyQjabxW63lwnsouB2Op0bLrSj0Sitra0b+pxNTJqCuoEQRZFCoYBhGMu+iBVF\nYWhoiKGhISRJYtu2bXR1dWG7an1hkEYR1NX0HU+n3Xz+5AG+fGovo0kvN3eNsb9zgqF4gO3hCIe6\nR3GJGq/bfIn/ceB52jxXLyPI5+0li0U6bW7SKxQWCuQCqmojlRIJh7MEAgpdXWkgTV9f1Q6zKtjt\n9X1LeCGNIIBM6v/KoDihzmYdC15LIvn8/GvJ4dCRZbOyPRAwrUoej4rHYw0R2AhZ2tmsNcuLVoos\n+3E4HPj9fvz+8sQPTdPIZDIlsR2PxxkfHyeTySAIwqKJttvtxuVyXeOcuzYMw2haPmpIU1BblLVM\nqEVRBEBV1UVer0wmw6VLlxgdHSUQCLBnzx5aW1tXdPVsGCEEYXBVa7Eq1ThJDsUDPPjkLXzpxX10\neZP0B2KItgKzWTeioLM5EGN7OMobt77KkdAIyYSTy2cDvJJrKTupS5KOy6Xg9yuEQkWBnKKrK7Xs\nc1+4EGLLlnjFj2mjqYW3vVo0iuWjCuf7irHwYjOVksjnHaU0jOLFpsejksk4SCZFfD6Vnp4kPT2V\nS0HaKDwe6/t2r0UmU9+C2m73oChK6e5x8cNms2G32/H5fPh8vrL/R9d1stlsaaKdTqeZmpoik8lg\nGEZJZF8pttcjtOPxOJqmNSfUNaIpqBsIu92OzWYrE9TxeJzBwUEmJyfp6OjgyJEjBAKr3bFc/x6+\nIl5v5W7Lnhzp4P4Td/Dd17azzTvLdleEeE5mJO9nVnHT5UlyuGOUt+w8zf7+Cfz+OTHfs7xAXi2K\nYmHVswo20ttebRrF8rGRzG94daKqLmIxgULBhq7P25XcbhW/P08wmCUYvPbFJsDMjBufzxqT5rWS\nSNT3+gGy2fpO7nG5QthsNgzDQF/CR7SU0LbZbCWhvBDDMMjlcmVCOxKJkE6n0TQNt9u9SGR7PB7s\nK9i1HY1GsdvtazjHN6kETUFtUdYTnZfP58lkMgwODhKPx+np6eH222/H7Xav6THNVqzGwOnUUBQB\nSVqsejIZxxW+SccVE2QNj0flYj7IZ8/dzOnZdjb5YxzqGUMHNN3GzLSbn916kV/bfY437XgFp6O6\nnu16ryUuIoqNI6gbJTZvPZnt85ni5ka9XM6MejMMc7Nj0c8/fzcmX7UNr01qTzpd34La42lBnssg\n1HW9JKwNwyh9rFRoC4KAy+XC5XKVTZINwyCfz5NOp0v2kdHRUdLpNIVCAafTueREu3hnGsxSl1Ao\nVBU7SZNr0xTUDUTxBX3q1Ck0TaOvr4/9+/dXIOqnPtsSzY1FZjRVJiORz9spFGzk8zbc7gKyXMDt\nLuD3mxuLvN4CbncSWPq28CMXt/Dnj72BeF7GMKDXF0ey64wm/YwlfLxz/wt86o3fZV/nyhvE1kuh\n0BiC2mZjQyMAq0mjFLss9FAXa9uLrZRm6U55FnKxdKdY226FTPFGuFvQCMeQTtf3hZLTOX8OLIrV\nKyfGywntpcT2ckLb6XTidDrLUjoMw0BV1dI0O5PJMDk5STqdRlEU7HY7H/nIR9iyZQuBQIBQKMTU\n1BTt7e1V3xD5qU99ir/+679mYmKCffv28clPfpIjR45U9TmtTFNQW5TVvBAKhQLDw8NcvnwZVVXp\n7OxkYGBgRbeIVoJV6sd13c3YmEg8LpV23hc37MxPkBX8/jzh8MKNReUCeXjYx6ZNK/NSGgb8x7md\nPPTczeQLIiMJH1uDUTRsnBzvos2T5j2HnuWd+04SdG28T7BQaJxJhKLYEcX6jteqJ+JxJ7OzTlIp\niUxGRFGKWcgGkqSjKAKK4iAYzG1YbXuTxdR72ophONH1+s3QhpVVj1dDaBcfV5IkJEkiFCq/W6yq\nKtFolDe96U2cO3eOZ555hpGRETo7O2lpaWH37t3s2rWL3bt387a3vY22trb1/DOU8bWvfY33v//9\nPPTQQxw9epQHH3yQO++8k1deeYX29vaKPU890RTUdUwul+Py5csMDw/j8XjYuXMnY2Nj+P3+iolp\nk+pYPjTNhc3WgmH4AA8gAcXbwgUMI48gZBCEOBDFZsvQ2wu9vet73mxWvOb3FHQbXzm1h2+e3cVk\n2sNgNMCBzklCrhw/vryFX77xVb7+lm/ws1su1vSE53Q2zktYVe1A/QvqWm1KjMfny0LSaVMgFyfI\nDoeB06mWykJaWnIEAubHcqzmwrNJ9aj3PHDDcAPWE9Si6MXtbsPtbsPjacPlai39vfyjFUnyXPsB\nl2GlQvvKry1kOaEtiiLt7e38wR/8AQCf/vSn+fGPf8zXv/51zp07x5kzZzh79iw//OEP+ZVf+ZWK\nCuoHHniAd7/73bzrXe8C4KGHHuK73/0un//85/nTP/3Tij1PPdE4Z+MG42oT6oXV4C0tLRw8eJBQ\nKIQgCMzMzFSkfnwhK51QG4YXCM0JZDdXCmTIA2kEIY5hRLDbs8DIhgvSXG75X/us6uCfX9zH9y9s\n5+WpdjKqg91t0zhsBi9OdvJbB5/nP37j3+jxW0NoJJP1fbJdSDGlod7xeK59wbYSkkmJaLRoWTI9\n/ZpmvlgcjmIWshn1Fg5nCATyBAL1nabQZDH1PqHWddeGPI8giLhcLfh8nbjd5QLZ4ymK4/bS10Vx\nY9a1HFcT2sXPV062ryW0i6UuXq+XQ4cOcejQoaqsXVEUnnvuOe65556y4/m5n/s5nnjiiao8Zz3Q\nFNR1wvLV4N6y71tP/fjyz92Orh+iXCCrzAvkBBBBEFJAakUngFqeJJbayBfPyfzLi3v59vkdPDG8\nif5AlE5fimdGe1D1KA/c+f/4LzvPItqtZZBtHL9u49hXksmlX3+5nEgk4iYWE0mlJBTFXjrm+bIQ\nMzYxHM5UtSxkJaxnU6JVqHcxCtT9vgJdd177m5ZAEOy4XOFlpsZtgIfZ2SyKIrJt2z62bdvdEJvx\nisdw5bFcKbSvtI5EIhG+853vbEhk3szMDJqm0dHRUfb1jo4Ozp07V/XntypNQW1RihPqa1eDlyOK\nYhUiitzYbM9W+DFrx0JBPZny8IUX9vON0wO8MtvC4Z5Rbmqf5OxMG6/b/BL/+MvfYXfbdA1Xe3Ua\np0Sk/ibUuZy9rLo9lzNTYaJRJ48+uglZLtDaKiCKSUKhLF6vSnd3nO7uWq98ZTSCGG0E+vu91/4m\nC6NpcunPshws2SiWs1cU/+xytSAIi98TstksFy5cYGpqir6+PjZv3lyWdNGoLCe0c7kcn/nMZ7j/\n/vvZsWMH73nPe2qxvCY0BbVl0TSNoaGhFVSDlyNJUsUn1I2UQw1mpNdgNMjfP3OEf31pL15RYUfr\nNIJgEM26ec+hZ3j73lN4pdpNB1dKI4meWieWFKvbEwlzo54Z9TY/QZYkHbdbweczN736/Srd3Sm6\nu8uzkB97rJfjx0dqcQgVpr4no9AYr4+OjrVNeDcCw3BjGG0YRivQNvfnhR+tFAqd/O7vtuB2t2K3\nrz1xSlVVBgcHGR4epqOjg2PHjuFy1da2UUt0Xefb3/429957L7Is8+Uvf5m77rprQ6rOW1tbsdvt\nTE5Oln19cnKSzs7Oqj+/VWkKaotiGAbj4+MrrAafpzqWD2ukfFSCl6fa+cjLr+PRn/Sxv3Ocm7vG\nmEh5CbnyfOD2ExzvG671EldFI0RqFam05aNQEIhEzKi3VGq+ul3XhVJZiJmFnCcUyhEM5unqSs/V\nt6+dxmlKrP9frnrf0GeycRnthiFiGK3oeguqGkJRAmSzPjIZL8mki2zWiyB04HB0I0m9uN1teL1e\n3G73shvh7Xa4okRwVWiaxvDwMIODgwQCAY4cObKolfB6wjAMXnjhBe655x7Onj3Lhz70IX77t397\nQ6f0kiRx880388gjj/Crv/qrgCnwH3nkEd773vdu2DqsRlNQWxRRFDl69Oia/r/mhHoxTwz38rET\nt/PMaDe9zjS39Q2h6nZu7xvifxw8SbunPnNSG8AyWOJagtosCzHrpotlIYpievp9PhFFyeJyFfD5\nigI5R3t7hvb2zAYdQWPRCNPdxhDUa38/Ny/uwktMjtuA1iW+Vv5eL4rmh98PHR3zxSOpVIp0Os3s\n7HCpeMTlcuH1evF4PKXPK234W3rtBhMTE1y4cAGHw8HevXvL8pmvR8bGxvjQhz7EN7/5Tf7n//yf\nfOtb3yIYrM3A6/3vfz/veMc7OHToEEeOHOHBBx8knU6XUj+uR5qC2sIIglCK01kp1RHUAQxDqMuT\n0w8ubOO+x24jlpPxiCo722ZwZDR+/+jT/NKN57HV4TEtpB5/JkV0HWIxJ9Goi1RKYnTUy8yMu6ws\nxOWaLwsJh7O0tWVoa7O2QPb51lukZA0a4WKtnl8fRcwN4PMYhu8KETxvr1hKNENlrFRXKx4pCu2i\n2B4ZGSGVSpWE9kKRXfx8NaEdiUR49dVXUVW1dJd2I6wMViWdTvPggw/yt3/7t9x111289NJLbN++\nvaZr+o3f+A2mp6f58z//cyYmJti/fz/f//73F21UvJ5oCuoGQxRFCoUCuq5XcMezDQgAsQo9XnXR\nDYFvnt3FJ58+DIbAbMbFpkCCo70j/Obelxg55eNndgzVepkVwW6x1JFYTC5FvWWzC8tCQJI0ZLmA\nz6cQCJgCORzOEQ6bGbWGAfv3T17t4euCVKr+s7RN6l+M1sNFQTbrYHrazdSUh6kpD/G4n1/8xVvx\neLrmhHEXhhGmKJxBvtZDbihXE9qKopSm2alUitHR0WWFtsfjwTAMLl68SDweZ8uWLWzatKnCnQr1\nhaZpfPWrX+XDH/4w3d3d/N//+3+5/fbbLXNx8d73vve6tnhcSVNQW5i1TqjB3MAhy5V84w1idUGt\najb+5aV9fO30ABlV5FI0yOs2X+J3Dj3Lm3edw+kwhc64vb53zS/Ebq+u6EkkJKJRF4mEVKpvd7tl\nUikFUZwXyMV2ymAwTzC4tizkYsZyvaNp9S9EoTEsH7XwgRcKAjMz8wJ5asrD9LSn7O/zX3eTTJZv\nOvziF38ZWd5Foc6vywRBQJZlZFleUmgvtI4MDw+TTCYxDAO73U4gEEBRFCYnJ0ti+1ob8hsJwzA4\nceIE99xzD9PT09x333287W1vu64vLuqB6+c39DrBbrdjt9srLqgNI4QgXKrY41WSjCry2ecO8J8X\nt3IpHiKScfHf973E3/7i9zjYNbHo+0XRWlPd9eBwrO5YUimRSMS1oCzEzEIWhPmyELdbLdVN+/1m\nLvJGoOt1ME68jmgE/VIJy0fRmnQtcVwUyLOzbmBtVyO/9ms7eMtbdq17zVZmodD2+XxcvnyZVCpF\ne3s7/f39aJpWEttjY2OkUilUVcXpdC5pHWk0oX3hwgU++MEP8sMf/pA/+qM/4n/9r/+Fx7P2psYm\nG0dj/SY2GGu9rVMdH7X1kj6iWSdfOLmf/xzcxrOj3bS4M/zekad5+56XCLqWn5KK4sbtmq82gmAw\nMuIjHjcFci7nQNNMYepw6MiyKZCLbXper4rXW+nfjcrQKBPqRkleMYz6v/Bc7g5OKiUSi/kZGXFe\ndXpcFNAbEenY0eHhE5/4+ao/jxXQdZ2RkREuXrxYavULBAKl/x4Oh8u+f6F1JJ1OMz4+TjqdRlGU\nktC+0j5Sb9nU0WiU+++/n8985jO89a1v5dy5c/T09NR6WU1WQVNQNyDVic6zTtLHRNLDF148wLdf\nuZHnxrt54w3n+cqv/Ts/t/Xiim5Ty7J176XOl4XIZLMymiaRTpuiwMxC1vB4VPx+04PsdBbo7U3S\n22uNKvT10EglNY1APVk+8nk709PuReL44sUQn/rUkTKP8tSUh4MHt/LYY9bKCv/Up+6kpaWxc5UN\nw2Bqaorz589js9kYGBigtbX1msMjSZIIh8NLCu2F1pGJiQlSqRSKoiDLcpnALv7ZakJbVVU+97nP\n8dGPfpQ9e/Zw4sQJDh48aBmfdJOV0xTUFmY9E2pFqfRt+tpPqC9Gg/zjc4f42ss3kdfs/NaB5/n6\nW/43vf7Eqh7H5do4Qa0otlKbXiolksuJFArCgizkAh6Pis+nEA7n8PvzS5aFLIcsN860vVEmu41C\nLRMyihGJV7NWLPx7PL5yIbppk4+TJ621+fU3f/Mm7rprW62XUVWi0Sjnz58nl8uxbds2uru71y0a\nJUlCkiRCofKBT1FoF8X25OQkr732WkloL2Ud2Wihres6P/jBD/jABz6Arut89rOf5U1velND1Kdf\nrzQFdQPSaBPqFyc6+PgTx/jGmd0c6Rnl/p/7T9686yziGhMuXK61/9sUCgLRqIto1Ek6bZaFqKqZ\nhSwIBrJsloX4fAqhUJZAIE9nZ5rOzurkXDeSoG6UCXWjFLtUWlDH43JJAEciPrLZEJlMkFjMx/i4\nm1dftXP+vIOpKQ8zM24Mo/LCQhAgEHAyPGydOzp9fX7+6q/eUOtlVI1UKsWFCxeIRCJs3ryZ/v7+\nqm+uW05oq6paNtGenJzk4sWL5PN5JElaJLK9Xm/FhbZhGJw+fZp77rmHkydP8sEPfpC7774bSWqM\nuM3rmaagtjBrvXqvTv34xk+oTwz18bETt3FiqI//vuclnn33PzHQPr3ux13oIdY0YS7mzUku5yIe\nt6EotrncbUptel7vfFmIlbKQPZ7GGes2ihBtFK6VkJHJOJb0Hxenx4mEH1Vt5cUXDaamPKjqtU83\nwaBMb6+fG280N1QnEnlGR5NEIrmKHNPx472cOGEdq4cgwKc//Yv4/daKwqsE+Xye1157jfHxcXp6\nerjttttqLhpFUSQYDC4qQ7lSaE9NTZFKpRYJ7YViey3HMjExwV/+5V/y1a9+lXe/+918/etfv+7L\nahqJpqBuQOq9fvx757fz0RO3E885ec+hZ/jar/9vvNLKLCy6DvG4k2jUSTIpk8mYE+RiWYjDoeNy\nFfB4TItFKJShtTVLa2sWiFb3wKqAw7G2iDor0rR81BZVtZXFvY2OeonFlrddpNNXF4HHjvXw+OOj\nq1pDLJYnFlt80dzS4qKnx4ffL2EYEIvlGB5OkEis3NrW1SXx1FOrW0+1+d3fPcjrXtdf62VUlEKh\nwOXLl7l8+TItLS3ccsstlk+puJbQLort6elpLl26RC6XQ5KkRRshvV7vkkI7m83y93//93z84x/n\n9a9/PSdPnmTnzp0bdXhNNoimoLYw6/FQZzKVnqBW1/KhGwLfOL2bB568la2hKB99wyPc3m+Wr8Ri\nMpfGAqWykHx+vixEFDWczgJe73xZSCiUIxS6+kQrkRDx+62ZdrEaNtIPXm2aE+rKousQjS4WxFf6\nj4sf0aiLtca9XcmBAx2rFtNXY3Y2y+xsdtHXOzo8dHV58HoldN0gGjWFdipV/tp2OAQ8Hjfj49bJ\n0r/hhhB/8Rd31HoZFUPXdUZHR7l48SJut5uDBw/WrBa7UiwntAuFQtlEe6HQFkWRL37xixiG6axM\nQAAAIABJREFUwY4dO9A0jX/5l3+hpaWFhx9+mDe84Q3NDYcNSlNQNyBWn1AbhodIxMX4uEAs6eRb\nl3fw/01u5WBwnA9s+QndgRSejML4uGfdZSHLkU5LDSGoRVFHVQVEsTnevR5IJKRFNgtFCTM4KDI2\nVi6ezRr3jS+CCAZlxsZWtql2vUxOppmcXLw/obvbS0eHB49HRNMMfD6JRx8d3pA1rQS7XeCf/umN\nuFzWSpxYC4ZhMD09zfnz5wHYtWsXbW1tDS0aHQ4HgUCgLOoP5oX2+fPnefTRR/n3f/93hoaGyGQy\n5HI5PvzhD/ONb3yDgYEBfvZnf5bdu3fX6AiaVIOmoLYw1sqhXn5CbRhuIIhhBDAMF/k85HLqXCWt\nA0kyEIQMghAHoghCGtmn8p+vHuTlqXZ+5cArfOyGR7BvYKtZNlv/J7IimYxIILAx5SvVpFEsH6s5\njlzOvmxZyFKT5Hy+/PdWFG1s3hzg/Hnr2JVuvLGFp58eq+kaxsZSJVG/a5e5HsOA3l4fHR0e7HaN\nZDJLMllgakpBUTY2c/t97zvCkSPdG/qc1SAWi3H+/HkymQxbt26lp6fnuk6pcDgcRKNRTpw4wfe+\n9z3+8A//kD/5kz9BEATOnj3LmTNnOH36ND/4wQ/weDxNQd1gNAW1xVlL/bgkSRWPzTOMEJp2O4JQ\nwDAUBCGNICSBCIKQATIIgnkSdbvNj6WYzbj415eOklFF3jJwhj+89cmKrnOlZLON86ufzzdGHW0j\nDLQKBYFUSuLUqfYVxb1dWTu9Wo4e7eHECetMXo8e7eapp2orphfidNrJZgulOviRkSQjI+UJH3a7\nQH9/gPZ2N06nHUXRmZrKMDwcp1Co/FXeTTe1ce+9xyv+uBtJOp3mwoULzM7O0t/fz4EDBxqusXC1\nJBIJ/uZv/oZ/+Id/4M1vfjNnzpyhv3/eH3/48GEOHz5cwxU2qTbX9yugQalWU6Ld/uia/+/RhI+f\nXu5HtOv8zqHncDpq6/01jMbZVZ/LNV/G1SQSMdv0Egk/o6Muxsfdy4rk9dROr5aBgVaeeMI6iRXt\n7W7OnZut9TLKuPnmrmsWuGiaweXLcS5fjpd9XRRtbNkSoK3NjSzbyOUKTE9nGRqKo69xoC2KNj7x\niTuumaBiVRRF4eLFi4yOjtLV1cXx48eR5cZ5L10LhUKBf/7nf+Yv/uIvuOGGG/jhD3/I0aNHG9ry\n0mRpmmdii7OWCbUoimiahq7rFbz9FpiLklvdWkYSfobiAXxSnrfueblCa1k/mtY4v/qK0hjHslHn\nn1RKvGbd9Pzfzdppux26u10MDy/eGFcLPB4HiYRSmrxagZ4eaxWm7N3bzuOPr/2CQ1V1BgdjDA6W\nb2SUZTubNvlpbXUhinYyGZWpqTQjI8lr2n3e8Y5+VHWYH/3otVJlttfrLcs9rnZG81rQNI2hoSEG\nBwcJh8McPXoUr9db62XVFMMw+NGPfsQ999xDOp3mk5/8JL/+679+XVternca40zcpIxiEL2qqhWc\nHtgBH7CyVsKUIhHLOfFJeY5tss4t6SLJ5MZ6JquJoljvBLwW1lokoii2FQvkqSkP2ezq82OPHu3i\n8cfH17S+arBvX2VTNNbLWiLyqonPJzI2Fq+KLz+f17hwIcqFC+W+dZfLwaZNflpaXNjtNjIZlYmJ\neS/3oUNdPPDAm7HbbSiKUkqISKVSjI6Okk6nUVUVl8tVJrS9Xi9ut7smQtswDMbGxnjttdeQZZkD\nBw4sKku53jAMg3PnznHvvffyxBNPcM899/AHf/AHOJ3rs281qX+agtrirOW2kc1mw263l2pW14th\nGMzOztLS4sbpvLagNgzwSsqKs6NrgaY1zu24RhHUbrf5dqRpAsmkh8lJz6LkiqUE8mpqp9fCwEAr\nTz01UdXnWA0339xpKfHa1+fjhRemar2MMnp7Jc6erU476XJkswVefTWy6Osej8gNN4T53OfeiN1u\nTi8lSSIcDhMOh0vfZxjGIqE9PDxMOp2mUCjgdrsXTbQ9Hk9VJqKGYTAzM8OFCxfQNI0dO3bQ3t5+\n3dsYZmZm+OhHP8qXvvQl3vGOd/DFL36Rjo6OWi+riUVoCuoGpRI+asMwStWs2WyW178+CFxbWNTD\ne26j1FwDFArWv8W4sHZ6OWE8Pu5ldtbNrl038tOfmhvbAgGZTZv8BALy3OPkGR5OEI9vTKGN1awV\n4bBzkde3lths4PXKDA1Zp8p79+4AZ85Y598onVZ561t3s317+KrfJwgCsiwjy3JZe55hGOTz+TKh\nPTs7SzqdRtf1JYW22+1es9COx+OcP3+eVCrF1q1b6e3tve5tDPl8noceeoi/+qu/4ujRozzzzDMM\nDAxc9xcYTcppCmqLU4v6cV3XGRsbY3BwEE3T2Lx5M729vchyB3BuTY/ZpHrUQlBns45rFoUsjINb\nqc97//52Hn10PiUiHs8Tjy9uzuvocNPd7SvlDM/OmpvFcjmtYscI1rNWbNsW4plnrGM9OXbMWlXe\noZDM5KS17ozdcccm7r775jX//2b8qBOn00lra2vp64ZhkMvlyoT29PQ06XQawzDK2vsWCu3lzinZ\nbJYLFy4wNTVFX18f+/btK9kHr1d0Xedb3/oWH/zgB3E6nXz5y1/mrrvuagrpJkvSFNQNylom1IVC\ngZGRES5duoTdbmfLli10d3eXphMbWT9ebRrp/bAS9pVCQSirnV5OGBc/UqnK7+wPBGTGx9Mr8r1O\nTmaYnCxvA7XZBPr6/HR0eJDlYvxZes2pDFazVtx8c7ulxPQNN4QsFZEHsH172FL/Rj6fxEMPVUeA\nCYKAy+XC5XLR1tZW+rphGGSz2TKhPTk5WWrPvVJoy7LM2NgYo6OjdHZ2cvz48eveD2wYBidPnuSe\ne+7hlVde4UMf+hDvfve7r/sLjCZXpymoLc5GlLsoisLQ0BCXL1/G5XKxc+dOOjo6SgkjhmGgaRo2\nWwALbkBfE3Z742xK1LTFE2pdh1jMeVVxrOutXL4sMzgoEYlUrnZ6rezYsb5CEF03GBpKMDRU7vOX\nZTt9fX7CYReiaCOTKTA+nmJ8fPk2v3DYxaVL1rENtLXJnD1rnUg6SbJhGGYShlW45ZZunnzSWgL/\nvvteT39/4NrfWEEEQcDtduO+ogxA1/UyoZ1IJBgaGip1Fng8HgzDYGJioiS4nU7ndTeNHRkZ4cMf\n/jAPP/ww733ve/n2t79d9xXqTTaGpqBuUERRvGa5Sy6X49KlSwwPDxMMBtm3bx8tLS2LhHQxtq+R\nJtQOhzU8sashlRKXFMavvRbiH//x0KLa6UJh+asfQTALJk6dWmynqAXVFEP5vDbXJFieyuDzSWza\n5CcYlLHZBBKJPCMjSSKRHFu3Bnj2WetsROzqCvDSS9bZ+HfkSLelrB6dnR7OnJmp9TLKuPPOrbzz\nnXtrvYwSNputZPuYmJhgdHQUWZYZGBjA6XSWptnxeJyxsTEymQw2m60s0q/4Z1mWG05op1IpHnzw\nQf7u7/6ON77xjZw6dYpt27bVellN6oimoLY465lQLyeo0+k0g4ODjI2N0dbWxuHDh0tX4IZhoOt6\n2ef5DSlX31RTT4hiZb22ayGfty+Ze7xc/Nta4t6W4/hx63hfu7q8NRFDyaSy5PO+7nV9RKM5brut\nF00ziEZzDA3FyWRqU0Z0223W+VmBeSFmJSsMmILaSkkj4bCTT33qzlovYxGzs7OcP38eVVXZvn07\nnZ2dpXOM1+stS6zQdb0kstPpNNFolOHhYbLZLA6Ho0xoFz9LklR3QlvTNL7yla/wkY98hJ6eHr73\nve9x22231d1xNKk9TUHdoEiSRDpdHhsVj8cZHBxkamqKrq4ujh07VgrnL06kiyK6KKTLd3dv7K3L\naiLLlRfUmiYwO3tlzJv52e3u5umnC2UCudpxb8txww0hnn7aGj5TQYC2NvdV7RcbSW+vj2eeGSed\nLrdLCYL53zo7PTidDlS1uvXURcxJuTV+VmCmnsRiOXTdOnd4jh/vvWYb4kbz8Y//HF1d1ik+SSaT\nnD9/nng8zpYtW9i0adM1c61tNhs+nw+fz1f2dU3TSKfTZYkjQ0NDZLNZRFFcsqxGkio3DKgUhmHw\n6KOPcs899zA7O8t9993H29/+9us+0aTJ2mkKaouzXg+1YRhEIhEuXrxILBajt7eX22+/HZfLFHNX\nCunicy71ptJIlg9ZXtm0MRaTl/UgX/kxO+vCMBb/u7W1uSgUzElnrXE67RQKBopS+wk9WGtSLgjm\nxsiRkcURcIYBIyPJRf9NFG1s2xYgEBDRNIVMpkAyqTMxsf5GRYdDwOGwVzy5ZD1YLfWkr8/PyZPW\nseYAvPnNO/iv/3VXrZcBmLa+CxcuMDk5yaZNm9izZ8+6N9bZ7Xb8fj9+v7/s64VCoUxoT09Pc+nS\nJXK5HJIkLTnRrtUmvwsXLnDvvffyox/9iD/+4z/m/e9/Px6PpyZradI4NAV1HbCW+nGHw0Emk+HJ\nJ58knU7T39/Pvn37SpOChR7phc9zNQHfCII6kzHj3i5eDPHqqy3XtFmo6vpfIj09fl54wRqVzDff\n3Mljj1lDEG3fbp1JOcDx45s4cWJ1rZ6qqvPaa7FFX/d4RPr6/IRC5qauVEphZCTJ7OzKhfatt/by\n6KPWaRndudNrKTFtZmBLizah1pL2djcPPvjztV4Gqqpy6dIlhoaGaG9v59ixY6UhSrVwOBwEAgEC\ngfI7mYVCgVQqVbKOTE5Okk6nyefzyLK85ETb4aiONIlGo9x333189rOf5W1vexuvvPIK3d3dVXmu\nSqFpGh/60If413/9VyYmJuju7uad73wn9957b9OWYjGagrrB0HWd8fFxLly4QC6Xo7+/n02bNpXe\noBZOpHVdL4nolb0wrVc5qyi2RXFvdns7L73EkgI5na583NvVsNLt6O3b3ZYRRJJkTvKtMik3bTCV\n2xSZTqtLpnK0tLjo6fHh80kYhnnXYng4QSpVbjHZvbuVxx+3xu8NQDAoMzW1vqKoSmO1DGyAT33q\nTlpaamPlAvP9f2RkhIsXL+Lz+Th8+PCiSfJG43A4CAaDi5IyVFUti/YbHx8nnU6jKApOp3NJob3W\n+nVFUfjc5z7HRz/6Ufbu3ctjjz3GgQMH6kKQ3n///Xz605/mS1/6EgMDAzz77LO8613vIhAI8Pu/\n//u1Xl6TBTQFdR2wkgm1pmmMjIwwODiIzWajp6eHixcvsmXLFmDxZsOirWM1bygbMaE2DAHDCJHP\nB8hkPOh6Gy5XH5LUC7RhGAs/Wkkk3Jw9O8Pp0zO8/PI0r70W5cKFqCWmVlu3BnnuOWtMYL1eOzMz\nyooynjcCK6VESJIN7f9v787jm67z/IG/cvVI0pbe95G0oVdaDgtdQGbkN96j7qqjo+PsAK6uJ6g8\ndrRFq4CAYAHZAUf0MS7Mquyg7gg7rug4zooyoBQR2vRM27RN77tN0jTX9/v7o5PYNBwtTfr9pn0/\nH48+mPla2k9omrzyyfvzfjtmpgymr8/ssUstEAAJCXLExckhlUpgtzvAsmN9tfkyoVGl4ld/Z769\nuwEAv/ylGrfemsHJ93ZOta2vr4dIJIJarXZ1bOIriUSC8PBwhIe7b9RMHL/e1tYGk8kEm82G4ODg\ni45fv1TQZhgGx48fxwsvvACWZfEf//EfuP322/2qTvrUqVP4x3/8R/z0pz8FAKSlpeG//uu/cObM\nGY5XRiaiQO3nbDabq4d0YGAgMjMzERcXB5vNhvr6etjtP9QKX22QdrraQM2yIW4h2DMYj32YzXI0\nNhrQ0dGNqKgopKWlud4+tF+i5Dk0dOyt8WXLktyu6/XD0Gh6XB+Vlb3Qavtht89M31yJRAiRSMCb\n+teMjHk4f54ffYzz82N4s2sPAEuWJHC6HpYF2tuNaG8fO5i5YkUi/va3NojFQigUYYiOliEgQITR\nURu6u03Q6w0z+sKosDCBVwNcJBJ+vbsBAMnJoSgt/X+cfO/+/n5otVpYLBakp6cjISGB10H6SgIC\nAhAREYGIiB+6SrEs6xG09Xo9TCYT7Ha7a/z6sWPHEB8fjwULFkAkEmHTpk04f/48XnzxRTz++OO8\nPBx5JcuXL8dbb72Furo6zJ8/HxcuXMDJkyexZ88erpdGJqBA7Qcu9uBosVhcNXKhoaHIy8tDVFSU\nazfb+Yq9qakJoaGhCAkJgUQimeYD7dhOAssGukIwEHXRcDw+NAOXn7plNBrR1NSErq4GxMTEoLCw\n0NV95GolJ4ciOTkUt9zyQx9Rq9WBmpq+vwfsHteuti86TBQW8mcHdtmyBJw+zY9AFBoagJ6eEd7s\nlOfnx/CqtGLx4h9q3O12BjrdEHQ69wEzUqkYKSlhCA8PglAogMlkQ1vbMHp6pn8QcqK4OBlqavjx\nQsypsDBxyrXuviQQAG+8cTNCQ2e2nMxoNEKr1WJwcBBpaWlISUm56pIIvhMIBAgMDERgYCAiIyNd\n11mWhcVicQVtrVaLY8eOobm5GRaLBfPmzcO1116LwcFBHDt2DLm5uVCpVH418bCoqAjDw8PIysqC\nSCSCw+HAtm3b8MADD3C9NDIBBWo/MzIyAp1Oh7a2NkRGRqKgoMD1ltnEYSxKpdLVO9RisSAoKAhy\nuRwhISGuP4ODg6fw9pcYIyOdAEKu+JmTMTw8DJ1Oh97eXsTHx2PZsmUe0728KSBAhPz8GOTnx7hd\n7+83u3axnWG7qqrXo3XaZPFpBzYxMQQVFfwZeJGTE8WbaXZ8C/fh4UHQ669cqjQyYr9oyJ03LxDJ\nyaEIDR3bhRsctECvH8bw8OUHPF0O3/o7Z2dH8uoFEAA88sgirFqVOmPfb3R0FI2Njejo6EBiYiJy\nc3P9cufVGwQCAYKCglw11/n5+fjLX/6CG2+8EevXr4fFYoFGo0FlZSU+/vhjVFVVYcuWLfi3f/s3\nrpc+ae+//z7ee+89HD58GLm5uTh//jyefvppJCQkYPXq1Vwvj4wjYKfaPoLMOIfDgf7+fuh0OnR1\ndSEuLg4KhcLVH9QZpC82jMW5I+18u8xoNMJgMLj+NzA2cnZ8yPZ139DBwUE0NjZiYGAASUlJSE1N\nRVDQ5XexZxrLstDpBj2CdkPD4GV78IaGBkAqlaCz03TJz5kpQiGQnR2Fykp+BOqCglicPcuPbicA\n/0oZli6N90ldcFycDPHxcshkEtjtDPr6zGhpGYbFcvmSCT4dqAWAwEABQkPF6Onhz+HIjIxwnD69\nGlKp73c87Xa7613JqKgoZGRk+HQDwl8wDIMPPvgAmzZtQkREBHbv3o1Vq1Zd9N1YhmFchx79RXJy\nMoqKivDEE0+4rm3duhXvvvsuampqOFwZmYh2qP1Ae3s7zp8/j6SkJFx77bWuB9GJHTsAXGQYy5hL\n1aWNjIy4Qvb4SVgBAQGucO0M2jKZ7KoPczj7Yet0OhgMBiQlJUGtVvN2Z0UgEECpDIdSGY477pjv\nuj4yYkNNTR8qKsYCtjNw9/aOABgLsHwJaStWJPOm7VpEhATV1fwI9gBQWBjPm58T4NvR652dJo8X\neCKRAKmpYYiJkSIwUASLxYGenhG0tAyBYYC0tDCcO8ev/s4FBYm8CvgikQBvvXWLz8M0wzBoa2tD\nY2MjpFIprrnmGo/WdHMRy7L49ttvUVRUhNbWVrz88stYs2bNZctehEKhX4VpAK4R8OOJRCLXcz7h\nD9qh9gNWqxWjo6MIDByr0bvUMBZvHURx9g0dv5NtMBjAMIzbCWtn4A4MDLzk92ZZFj09PdDpdDCb\nzUhJSUFycrJf1bBNRmenEdXVfSgv73YF7ZqavivuAvpKZmYkGhsHYLPx40F3wYIYXLjAj9KBmBgp\nrFYHBgctXC8FwNgO8siIbVqlGd4SFCRCWloYEhJCYLU6YDLZ0N5uRFcXt++4LFwYy5te7k4bNizF\nyy//2Gdf3/nYqdVqIRAIkJGRgejoaL8+cOgtTU1NeOmll/DJJ5/gmWeewXPPPecx0XG2WLNmDf7y\nl7/gzTffRG5uLr7//nv867/+Kx588EHs3LmT6+WRcShQ+wGGYVxTD30ZpC+HZVmMjo56hOyRkRFI\nJBKPkC2TyVyTsqxWK9LS0pCYmOizhv185HAw0GoH3A5AVlb2oLl5yKd1u8HBYsTGytDUNHTlT54B\n117Lr37BfAtnfHqxAVz85xUWFoikpBDMmxcEgMXwsBV6/fCMvCgJDQ1AcLCE81A/Xm5uFE6e/BUC\nAnxzCHBwcBB1dXUwm82uzh3+1OrNV4aHh1FaWoo33ngDd999N7Zt24aUlBSul+VTBoMBJSUl+Oij\nj9Dd3Y2EhATcf//9ePHFF3n7Du9cRYHaD3R0dEAgEEAul4Nl2SkOY/Eth8PhCtjOkD08PAyHw+Fa\nc1RUFEJDQyGXyxEcHMyLdXPJYLCiqqrHoz7bW+GET7WvSuU8tLcbeNM+kE8dTwB+/awAIDMzAo2N\ng5N+ZyM6OhiRkRKIRAzEYgnMZkCvN8BsvkSfy6vgy3KYqyGRCHHixC+xYEGs17+2yWRCfX09+vr6\nkJqaitTU1Dm1CXEpdrsdv//97/Hyyy8jMzMTu3btwtKlS+f8cwnhFwrUfmDdunXYv38/0tLSoFar\n3T6USuVV95X2JofDgba2NjQ1NUEkEiEpKQlSqdTVM9RgMMBkMkEoFHrsZsvl8llXAnI1WluHodH0\n/r13djfOn++ATjcMu33yv6KLF8fxpvZVIhEiLS0MWu0A10sBACQmStHTY4bVyo+HPIUiDB0dRt68\n2AgMFCExMQSNjZ6j1KdCKBQgKSkEMTFSBAeLx9VnD095UI2vDmpOx1NP5eHXvy706uOWxWJBY2Mj\n2tvbkZCQAKVS6Srxm8tYlsVf//pXFBcXw2w2Y8eOHbj77rtpt57wEgVqP8CyLNrb26HRaHD+/HlU\nVFSgoqICNTU1kEgkyMnJQW5uritk5+XlISwsbEZCtt1uh16vR0tLCwIDA6FQKBATE3PJE9bOgD2+\nRvtiLf3kcjmkUumce+B0/ns2NzdDKpUiOTkNvb1AZWWv2yHItjaDx9+NiAiGUAj09nq/H/HVuPba\nZN70CxYKgcTEIOj1o1wvBQAgFguQnh6O2tp+rpfi4uvd8sBAEZKTQxEVFQyxWIiRERs6O02ugTYT\nRUUFg2FY9Pfz42cGAGr1POzfvxhmswkWiwWBgYGux6vx0/sm2w/a4XCgubkZTU1NiIiIgEqlgkwm\n8/Gt4D+WZVFdXY0XXngB33zzDTZu3Ij169f73YFCMrdQoPZTzslR1dXVKC8vR3l5uStod3R0ICUl\nBbm5ucjNzUVeXh7UajUyMjIgEom8ErStVitaWlqg1+shl8uhUCiuetTtZFv6OQP3bKwbs9vtaGlp\nQUtLC6RSKZRK5WX/PQcGRv9em/1DyJZIhLypVc7Li0ZlZe9lWwzOpMWLI3DuHH/C68qV/OnAAgD5\n+dGoqOjhpCd3SEgAkpNDMW/e2OFmg8GK1tZhKBTz8N13/Hi3BQCCgsQ4depXyMwcGyxis9ncyt2c\nH3a7HcHBwR5Be/wGAcMwaG9vR0NDA4KDg6FSqTxGcM9VPT092L59O/7zP/8Ta9aswebNmxETE3Pl\nv0gIxyhQzzIsy6K7uxsVFRW4cOGCK2hXVVVBKBQiKyvLbSdbrVYjIiJi0kHYYrGgubkZra2tCAsL\ng0KhQHh4uNd3wye29HM+WfmipR+XnKPjW1paIJfLoVQqp/TzGI9lWTQ3D3nUZtfXD0z5rfbpCAmR\nICQk8JI7jzMtOzsSdXX9M/pvcDk5OZGoreXPevj28wKAZcsSodX2IzExBHJ5wN/bbo6ipWUIIyPe\nq8+eih07VmHduoLLfs74EdkTP1iWhVQqhUQigclkgkAggEKhQFJSkl8+dnnb6OgoDhw4gFdffRXL\nli3Drl27kJOTw3k5IyGTRYF6DmBZFjabDVqtFufPn3eFbI1GA71e75q2pVarkZubi/z8fKhUKojF\nYteDWW1tLerr6xEUFITIyEgoFApOeqFerKWf0WiEw+Fwa+nnDNqXa+nHpYlBOj093ScvTABgdNSO\n6uofRq47/+zuHvH69wKAf/iHRHzzTZtPvvZUBQeLER0tRUvLlScQzgS+rQcYC6+nT/Pj5wUACQly\nDA9bYTR6thEUCMamf8bGyiCVSmCxONDbO9Y/eypnDaZq5cpkHD/+86v+/XRudDQ0NMBsNkMmk4Fl\nWVewnrib7RyuxcfHLm9jGAbHjh1DSUkJpFIpSktLcfPNN8+J205mFwrUcxjLsujr63PtZldUVKC8\nvBxVVVVwOBzIzMxEcnIyBgYGUFZWhrVr12LLli286/fpbOk3MWibTCaIxWKP3Wy5XD7pGkdvs9ls\naG5uhl6vR0hIiGtHmgvd3Sa3nWxn7+zpdGhYsiQeZWX8OUS2fHkiTp3iT1jkW1ePgoI4nD3Ln7IK\nAMjPj0F5+dTaCEokQiQnhyI6WgqJRITRUTs6OowXPWswVXK5BGfOrEVq6tVtIIyMjKC+vh49PT1I\nTU1FWlqaq3MHwzCud+LGf5jNZkgkEo9Ngtl0gJtlWZw7dw7FxcWoq6vD5s2b8fDDD1NXE+K3KFAT\nNyzLwm634+OPP8bOnTtx9uxZzJ8/HyKRCBqNBrGxsa6dbGfZSGZmJi93UxwOB0wmk0fvbJvNBqlU\n6hGyfdnSz1lz3tLSgrCwMCiVSl7WTDIMi/r6AbedbI2mB01NV+6dHR0dDLudxcAAPw6RLVoUi++/\n50+/ab6tJyIiGAIB0NfHj0OsgPd7lkulEqSmhmLevCCIRAIMD1vR1maY0m3ev/9GrF27YMrf22q1\nQqfTobW1FXFxcUhPT5/0oTrnY9fEoH2xg5DO0M3VJsHVaG1txaZNm3D06FE8+eST2LhxI+bNm8f1\nsgiZFgrUxMP69evxu9/9Dg899BB+/etfIzk5GSzLYmhoyK0u21k2YrFYkJmZ6Ray1WqbtC8PAAAg\nAElEQVQ1YmNjeVcb6KxxnBiyfdXSz2q1unakw8LCkJ6e7pdPHEajFVVV7p1GKit73Dow8CkwhocH\nQSwWoqfHN2UtUyWXCyEWCzE4yE3978Xw7d2EmWwjGBERhKSkUISGBoBhWAwOWqDXD8FgsLl93o03\nKvDRRz+b0td2OBxoaWlBU1MT5s2bh4yMDK+9qzf+IOT4wG2z2a54EJIPjEYjXnvtNezbtw+33nor\nduzYAaVSyfWyCPEKCtTEw3fffYekpCTExl5+cIFzamNjY6MraJeXl0Oj0aCxsRGRkZEeu9lZWVkI\nCgri3W62861XZ9Cebku/8UF63rx5UCqVfhmkr6S93YCKih7odIM4c6YdlZW9qKvrh9XKbW9lvoVF\nvq2Hb8NSRCIBVKoI1NT0cbqO+Hg5EhLkCA6WQCQS4O23f4r4ePmk/i7Lsujo6EB9fT0CAgIwf/78\nGSnnutRBSJPJBIZhIJPJPEpHZnrAlsPhwHvvvYctW7YgOTkZu3btwrXXXsu754GJ2tra8Nxzz+H4\n8eMYGRlBRkYGDh48iIKCyx9OJXMTBWridSzLwmAwuHUa0Wg00Gg0MBqNUKlUHgNqEhMTebWT4jTV\nln5jnTbGuqCEh4dDqVRycniTSzabA3V1/R712a2t069nnQw+HYoEgMLCBHz7LX/Ca1ycDAaDBSYT\nf3bLV65Mwtdf86e2HAAOHrwN996bPanP7evrQ11dHex2OzIyMhAXF8d5WBx/tmRi0L7YQUiZTOb1\nQ9wsy+Lrr79GUVER+vv7sX37dvziF7/g5WP9RAMDA1i0aBFWrVqFxx57DNHR0dBqtUhPT0d6ejrX\nyyM8RIGazBiGYdDU1OR2ALK8vBwNDQ0ICwvz2M3Oycnh5ajy8S39nEHbYDBgdHSs/EEikSAyMhKR\nkZF+3dLP2wYHRycMqBkrHTEYPLs5XK2EBDkMBqtXv+Z0xMXJYDbbMTTknbHy3qBUBqOxkT9101Md\ndz4T7rorE++8c8cVP89gMKCurg7Dw8NQKpVITk7m/e/6xIOQztKRkZERiMXii3YcuZqyN61Wixde\neAEnTpzAs88+i2eeecavhtYUFRXhb3/7G77++muul0L8BAVqwiln6yiNRoPy8nJcuHABGo0GFRUV\nGBoaQnp6uttwGrVajZSUFN48aVksFjQ1Nbl2pGNjY1079ONb+kmlUo/dbL629JtJLMuipWXYbSe7\nvLwLDQ2DYKaYrwQCQK0eG1DCFwsXxuD8+al1rPCl/PwwlJcPcb0MF2+NO/emmBgpysrWIipKesnP\nMZvNaGhoQFdXF5KTk6FQKPy++8ZkDkJOLB252EHI/v5+7Ny5E7/73e/wwAMP4OWXX0Z8fDwHt2h6\ncnJycNNNN6G1tRUnTpxAYmIiHn/8cTz88MNcL43wFAVqwksMw6C1tdU1at15ELKurg5yudw1BXJ8\n2YhMJpuxgDo6Ooqmpia0tbUhMjISSqUSoaGhHp/nTy39uDY4OIiGhgYMDw8jNjYRIyMy1NQMuB2E\n7OoyXfLve7tDxHTxrUVeUpIUPT0WWCzc1rePx7efGQB88MGduPXWjIv+N5vNhqamJrS0tCA2Nhbp\n6ekIDg6e4RXOLJvNdtGgbbPZIBKJ8OqrryIzMxPZ2dno6OjA22+/jUWLFmHXrl1YuHCh324aODuy\nbNiwAffccw/Kysrw1FNP4cCBA1i9ejXHqyN8RIGa+A2WZWE2m1FZWekqF3EG7f7+figUCo9OI2lp\naV4NqOODdFRUFJRK5VWd4B+/GzT+IKTztL4zXM9ESz+uDQ0NoaGhAYODg0hJSUFqauold/t6ekY8\nOo1UV/chIUGOlpZhzg9DOqWlhaGryzStnt7eJBQCiYnB0Ov5U+rBt/H0APDLX6rx5pu3eFxnGAZ6\nvR46nQ4hISFQqVQXfQE9VzgPQnZ1deHQoUM4e/Ys6uvr0do69uJo/ERetVqN5cuX+9348ICAABQU\nFODUqVOua+vXr0dZWRlOnz7N4coIX1EHdeI3BAIBpFIplixZgiVLlriuMwyDjo4Ot04jf/rTn1Bb\nW4vAwEDk5OR4HIIMDQ2dUkA1m81oampCe3s7oqOjsXTp0mm1whKJRAgNDXV7Uh5/Wt8Zsru7u33W\n0o9rBoMBDQ0N6OvrQ3JyMtRqNQICAi77d6KjpbjuulRcd12q6xrDsNDpBlBR4T5yXacb4iSsiUQC\nBAWJeROmAWDFimR8/bWe62W4yGRiDAyM8ipMJyeHorT0/7ldY1kWnZ2dqK+vh1gsRl5eHiIjIzla\nIX8IBAIEBARgcHAQ3377LcrLy/Hiiy/ikUceQWdnp6ulqkajwQcffICNGzfi5z//OdfLnpL4+Hjk\n5OS4XcvOzsZ///d/c7Qiwne0Q01mJZZlYbFYUF1d7dY7W6PRoLOzE2lpaW5lI3l5eVAqlRCJRG5B\nu7a2FqOjo+jt7UV0dDSUSiXk8sm10fKWiS39nIF7fEu/8UGbb71nJzIajWhsbERPTw8SExOhUCgQ\nGBjo9e9jMlldI9fHH4L09SCTlSv5FV6zsiJRXz8Au50/h/74NsFSIAD+9Kd7sWrVDy/U+vv7UVdX\nB6vVioyMDMTHx8/ad4mmqrOzE1u2bMGRI0fwyCOPoKSkZNa90PjFL34BvV7vdijxmWeewbfffuu2\na02IEwVqMqewLIuuri7XAUhnfXZ1dTXEYjGys7ORm5uLxMREnD17Fl9++SVee+013HPPPTMepK/E\nZrN5hOzxLf3Gh+yQkJAr7v76mslkQmNjI7q7u5GQkACFQjHpyXHe1NFhdDsEWVnZi9raPq/UFvMt\nvAYFiRAXJ0dTE38OIi5eHIdz5/g17vyRRxZhz57rAYy94NNqtRgcHERaWhpSUlLm7LmGiUZGRrBv\n3z7s2bMHP/nJT/Dqq69i/vz5XC/LJ8rKyrB8+XJs3rwZ9957L86cOYOHH34Yb731Fh544AGul0d4\niAI1mfNYloXNZkNtbS3+/Oc/49ChQ6iqqkJGRgYGBwcREBDgKhVx7mirVCqIxWLe7VhdrKWf0WiE\n2WxGQECAR8mITCbzeVgwm81obGxEZ2cn4uLioFQqeXeQy25noNX2uwK2M3C3tAxP+msEB4sREyND\nczN/wivfDkbybYIlAGRkhOP06dUQCh1oaGhAZ2cnkpKSoFAoOH8RyhcMw+D999/Hpk2bEBUVhd27\nd+O6667j3eOft3388ccoLi6GVquFQqHAhg0bqMsHuSQK1IRg7AnjoYcewuHDh3Hffffh+eefR0ZG\nBnp7e912sysqKlBVVQWWZV0Hb3Jzc5Gfnw+1Wo3IyEhePsnY7Xa3E/rOoO1s6TdxN9sbLf1GR0fR\n2NiIjo4OxMbGQqFQ+FUfWgAYGrKgqqrHLWhXVfVetK8038LrggUxKC/vBp8e4RcsiMCFC/1cL8NF\nKBTgs8/uRUzM2GTT6OhoZGRkQCq9dMu8uYRlWXzzzTcoLi5Ga2srtm7ditWrV9OOPSEXQYGakL87\ncOAAbrjhhstOwWJZFna7HVqt1mPcektLC+Lj493a+eXl5WH+/PmQSCS8C9oTJ6k5Q7azpd/EkC2T\nySAWX/kcs8VigU6nQ1tbG2d1576m1w+7arM1mh4YjVZ88UUTb4aThIYGQCqVoLPz0m0GZxrfwjQA\nPPRQFu68c+w+rlKp5txU08vR6XR48cUX8dlnn+GZZ57Bs88+O62D2ITMdhSoCfEClmUxMDDgsZtd\nWVkJm82GzMxMty4jeXl5iImJ4V3IBibf0s8ZtJ0t/axWK5qamqDX6xEZGYn09PQ59QRstTpQU9Pn\nUZ/d0WGc8bX8wz8k4Jtv+DPuPCZGCovFwauJkQqFFK+/vgA5OZmIiori5e8iF4aGhlBaWooDBw7g\n7rvvxrZt25CSksL1sgjhPQrUhPgIy7JgGAb19fUenUYaGxsRExPj1mkkPz8fmZmZvJ2gaLFYPAbU\nGI1GCAQCiMVi2Gw2SKVSpKSkIDY21q9b+nlTX5/ZLWBrND2oru6FyWTzyfdbsiQeZWUdPvnaV2vx\n4licO9fF9TJcxGIBPvzwJvzkJ7m87ogzk2w2G37/+99j69atyMrKwq5du7BkyRJePhYRwkcUqAmZ\nYSzLYnh42G0wjbNsxGw2Y/78+R7j1uPj43n3xG+z2dDc3Izm5mbXzrXdbvfrln4zhWVZ6HSDHocg\nx0auX/1DclRUMBiGRX//qBdXOz18a5EHAC+8sBzFxSu4XgYvsCyLL774AsXFxbBYLNixYwfuuusu\n+j0lZIooUM8xr7/+OkpLS9HZ2YkFCxZg3759WLp0KdfLIhg7GKnT6XDhwgVX2YhGo0F9fT3Cw8OR\nl5fnVp+dk5ODoKCgGd9Bstvt0Ov1aGpqglwuR0ZGBsLDw90+Z2JLP+fONsuyrpA9Pmj7og+1v+nr\n64NGU4u6ugGYTHK0t9uh0fSisrIXvb2T64pxzTVx+O47/rSkS0oKwcDAqM92469GQUE8/vrXX0Ak\nmtuBkWVZVFdX4/nnn8eZM2ewceNGrF+/nn4XCblKFKjnkCNHjuBXv/oVDhw4gMLCQuzduxcffPAB\namtr/W4s7FzBsiyMRqNrF9u5k11RUYHh4WGoVCqPcetJSUk+2V1yOByuIC2VSpGeno6IiIhJB3rn\n6PiJvbPHt/QbH7JnoqUfHwwNDaG+vh7Dw8NQKBRITk72uN2dnUa3nWyNpgc1Ne69s5ctS8Tp0/zZ\nCRYIgNzcaGg0PVwvxSUgQIBDh5ZDrY513d+kUumcK2vo6enBtm3b8M4772Dt2rXYtGkTPQcQMk0U\nqOeQwsJCLFmyBPv37wcwtiOanJyMdevWoaioiOPVkalgGAYtLS2unWznn1qtFiEhIR6j1nNyciCT\nya4qODgcDrS1tUGn0yEwMBDp6elePcQ1lZZ+crmck115XzAaja7R6ykpKUhNTZ1S3bnDwUCrHUBl\n5VgrP622H2fPdqKlZYgXrfKuvTYJJ0/yp40gALz44lL8/OeprvuayTTWBcU5CGn8fS0gIGBW3M/G\nGx0dxRtvvIHS0lIsX74cpaWlyMnJmXW3kxAuUKCeI6xWK6RSKT788EP80z/9k+v66tWrMTg4iGPH\njnG4OuINzqEulZWVHt1GBgYGkJ6e7tHSLzU19ZK72Q6HA+3t7dDpdJBIJEhPT0d0dPSMPPk6R8eP\n7zJiNBoxMjICkUjkEbLlcvmkWvrxwfhBN74YvW4wWD16Z1dW9mBwcOY6bCiV89DWZvDK9ElvWbky\nGceP/9zt/jtxENL4d00kEonb/cvf7mfjMQyDo0ePoqSkBHK5HKWlpbjpppsoSBPiRRSo54j29nYk\nJibi1KlTWLZsmev6s88+ixMnTuDbb7/lcHXElxiGQVtbm1unkfLyctTV1UEqlSInJ8ftEGRGRgbe\nffddHDx4ELt27UJ+fj5iY2N58eR7tS39+MBqtUKn06G1tRWxsbFQKpUzOkCktXUYGs0PAbuysgd1\ndf1e750tFgugVIajro4/PaflcgnOnFmL1NTJ9Zl2OBxuIdv5YbVaERwc7BGy+XrYlmVZfPfddygu\nLkZ9fT02b96Mhx56yC9fFBDCd/RbRcgsJxQKkZycjOTkZNx2220AfhjqUlVV5drNPnbsGEpKSmA2\nmxEREYFFixbh9OnTMJlMUKvVUCqVEAqFnAZUkUiE0NBQhIaGul2f2NKvp6fH1dJv4m52SEjIjLb0\ns9vtrm4o4eHhWLp0KSf9uZOSQpGUFIqbb1a6rtlsDtTW9nv0zm5rM1z191m2LAlff633xpK9ZseO\nVZMO08DY/SwsLMxj0IvVanU7A9DX1wej0QiWZSGTyTzeNeGyBaZer8fmzZtx9OhRrFu3Dp988onf\nDa7ZsWMHiouL8dRTT2Hv3r1cL4eQy6JAPUdERUVBJBKhq8u9F2xXVxfi4uI4WhXhikAgQHBwMK65\n5hosWrQIH374IT777DNERkZi3bp1yMzMdB1+/PTTT1FTUwOJROLazR5fNhIWFsb5LnBgYCACAwMR\nGRnpusYwjOvtfIPBgL6+PjQ3N2N0dBSBgYEeIdvbu4zjD3HKZDIsXrwY8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jIAAAdTSURB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\nAAAASUVORK5CYII=\n"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "# Задача 4\n\n$$\n\\mathbb P (i = 1 \\ | \\ успех) =\n\\frac {\\mathbb P (успех \\ | \\ i = 1) \\cdot \\mathbb P (i = 1)} {\\mathbb P (успех)} =\n\\frac {Q_1 \\cdot P_1} {\\sum_{i = 1}^n P_i Q_i}\n$$"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "# Задача 5\n\nПрежде всего хочется заметить, что несколько вещей в постановке задачи кажутся очень странными.\n\n* Не описывается смысл `y`\n* Не предлагается находить коэффициент при свободном члене (а `y` очень сильно смещён относительно нуля)\n* Предлагается рассматривать очень короткий промежуток для $\\lambda$: $[0, 0.1]$, при том что при изменении промежутка можно увидеть, что минимум по $\\lambda$ нормы вектора ошибок находится около $\\lambda = 0.15$\n* Не уточняется, что такое \"нормировать на 1\". Это можно понимать как \"разделить на дисперсию\" и как \"разделить на разность между максимумом и минимумом\". Я выбрал первое.\n\nДальнейшая часть кода написана точно так, как описано в условии.\n\nИмпортируем нужные библиотеки и загрузим данные:"
},
{
"metadata": {
"trusted": true,
"collapsed": true
},
"cell_type": "code",
"source": "from sklearn import preprocessing\nfrom sklearn.linear_model import Ridge",
"execution_count": 2,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "x1=[58.8 ,65.2 ,70.9 ,77.4 ,79.3 ,81.0 ,71.9 ,63.9 ,54.5 ,39.5 ,44.5 ,43.6 ,56.0 ,64.7 ,73.0 ,78.9 ,79.4]\nx2=[7107,6373,6796,9208,14792,14564,11964,13526,12656,14119,16691,14571,13619,14575,14556,18573,15618]\nx3=[21 ,22 ,22 ,20 ,25 ,23 ,20 ,23 ,20 ,20 ,22 ,19 ,22 ,22 ,21 ,21 ,22]\nx4=[129 ,141 ,153 ,166 ,193 ,189 ,175 ,186 ,190 ,187 ,195 ,206 ,198 ,192 ,191 ,200 ,200]\nx5=[0.26,1.48,1.58,1.70,0.43,0.35,-0.07,-0.03,-0.73,1.88,-0.18,0.08,0.97,-0.37,0.18,-0.88,-0.89]\ny=[3067 ,2828 ,2891 ,2994 ,3082 ,3898 ,3502 ,3060 ,3211 ,3286 ,3542 ,3125 ,3022 ,2922 ,3950 ,4488 ,3295]\n\nX = np.array([x1, x2, x3, x4, x5]).T\ny = np.array(y)",
"execution_count": 3,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Вычтем среднее и отмасштабируем данные в каждой колонке:"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "X = preprocessing.scale(X, axis=0)\nX",
"execution_count": 4,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 4,
"data": {
"text/plain": "array([[-0.46181979, -1.69326173, -0.33161067, -2.47553 , -0.09087948],\n [ 0.02647946, -1.90778843, 0.373062 , -1.91316016, 1.31571786],\n [ 0.46137099, -1.78415792, 0.373062 , -1.35079031, 1.43101273],\n [ 0.95729992, -1.07920098, -1.03628334, -0.74155631, 1.56936656],\n [ 1.10226377, 0.55283863, 2.48708002, 0.52377584, 0.10512179],\n [ 1.23196826, 0.48620091, 1.07773467, 0.33631922, 0.0128859 ],\n [ 0.53766775, -0.27370292, -1.03628334, -0.31977893, -0.47135253],\n [-0.07270632, 0.18282392, 1.07773467, 0.19572676, -0.42523459],\n [-0.78989586, -0.07145159, -1.03628334, 0.38318337, -1.23229864],\n [-1.93434724, 0.35614045, -1.03628334, 0.24259091, 1.77689732],\n [-1.55286345, 1.1078607 , 0.373062 , 0.61750414, -0.59817688],\n [-1.62153053, 0.48824681, -1.74095601, 1.13300983, -0.29841024],\n [-0.67545072, 0.2100051 , 0.373062 , 0.7580966 , 0.72771406],\n [-0.01166892, 0.48941589, 0.373062 , 0.47691168, -0.81723713],\n [ 0.62159418, 0.48386275, -0.33161067, 0.43004753, -0.18311537],\n [ 1.07174506, 1.65791417, -0.33161067, 0.85182491, -1.40524093],\n [ 1.10989344, 0.79425424, 0.373062 , 0.85182491, -1.41677042]])"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Обучим гребневую регрессию на сетке от $0$ до $0.1$:"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "lbdas = np.linspace(0, 0.1, 101)\nvs = []\nnorms = []\n\nfor lbda in lbdas:\n clf = Ridge(alpha=lbda, fit_intercept=False)\n clf.fit(X, y)\n vs.append(clf.coef_)\n assert np.allclose(clf.intercept_, 0)\n norms.append(np.linalg.norm(y - X[:, :-1] @ clf.coef_[:-1] - clf.intercept_))\n\nvs = np.array(vs)",
"execution_count": 5,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Нарисуем графики:"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "ax = plt.gca()\n\nfor idx in range(5):\n ax.plot(lbdas, vs[:, idx], label=\"$v_{}$\".format(idx + 1))\n\nax.legend()\nax.set_title(\"Коэффициенты в гребневой регрессии\")\nax.set_xlabel(\"$\\lambda$\")\n\nplt.show()",
"execution_count": 6,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x7f694b07cc88>",
"image/png": 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HCxYsUFVVlSZOnKgrr7zS5xWAoLoDxLAYKbJxvi660RiGj5GLKs8g4RpIXEdC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\nSBkZGYqJiQl1OUHz7LPP6ss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TU5MaGhosNwAAAAAuFQDGGM2YMUN33nmnLr74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\nK1dx110AAAAASUVORK5CYII=\n"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "plt.plot(lbdas, norms)\nplt.title('$||y - \\hat X \\hat v_\\lambda||$')\nplt.xlabel(\"$\\lambda$\")\nplt.show()",
"execution_count": 7,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x7f694af82390>",
"image/png": 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WWlpa3rHZs2erfv36GjRokCSpZcuWql+/vlasWGGvmCiCnMwm/b1joOY9GyIP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\nublZzc1Xn47X0NDQ6TgAAICeFhkSoBVTk7ViarI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},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Ожидаемо, что коэффициент $v_5$ получился самым маленьким по модулю.\n\nКакие-то содержательные выводы из этого сделать трудно, поскольку запрещено брать свободный член и взят очень маленький отрезок для $\\lambda$, на котором, как видно из графиков, оптимальное значение $\\lambda$ находится у правой границы.\n\nЕсли разрешить брать свободный член и рассмотреть промежуток $\\lambda \\in [0, 1]$, то:\n\n* Минимум нормы вектора ошибок без $x_5$ будет достигаться при $\\lambda \\approx 0.15$\n* Минимум нормы вектора ошибок с $x_5$ будет достигаться при $\\lambda = 0$\n* Наилучшее качество по кросс-валидации без $x_5$ будет достигаться при $\\lambda \\approx 0.007$\n* Наилучшее качество по кросс-валидации с $x_5$ будет достигаться при $\\lambda \\approx 0.016$\n\nВ свете всего этого я бы рекомендовал брать $\\lambda = 0.016$ как оптимальное по кросс-валидации при реалистично имеющихся у нас данных."
}
],
"metadata": {
"kernelspec": {
"name": "python3",
"display_name": "Python 3",
"language": "python"
},
"language_info": {
"file_extension": ".py",
"mimetype": "text/x-python",
"codemirror_mode": {
"version": 3,
"name": "ipython"
},
"pygments_lexer": "ipython3",
"name": "python",
"nbconvert_exporter": "python",
"version": "3.5.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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