label-shift 0-1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning under Label Shift - GMM, 0-1 responses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import mxnet as mx\n",
    "from mxnet import nd, autograd, gluon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First let's set the centroids of our two classes and the marginal distributions during training and testing. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "means = np.array([[1, 1], [-1, -1]])\n",
    "variance = 1\n",
    "py_train = [.5, .5]\n",
    "py_test = [.2, .8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "num_train = 90000\n",
    "num_valid = 1000\n",
    "num_test = 1000\n",
    "num_features = 2\n",
    "num_classes = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train = np.zeros((num_train, num_features))\n",
    "X_valid = np.zeros((num_valid, num_features))\n",
    "X_test = nd.zeros((num_test, num_features))\n",
    "\n",
    "Y_train = np.random.choice(num_classes, num_train, p=py_train)\n",
    "Y_valid = np.random.choice(num_classes, num_valid, p=py_train)\n",
    "Y_test = np.random.choice(num_classes, num_test, p=py_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for i in range(num_train):\n",
    "    X_train[i] = np.random.multivariate_normal(means[Y_train[i]], np.identity(num_features))\n",
    "    \n",
    "for i in range(num_valid):\n",
    "    X_valid[i] = np.random.multivariate_normal(means[Y_valid[i]], np.identity(num_features))\n",
    "    \n",
    "for i in range(num_test):\n",
    "    X_test[i] = np.random.multivariate_normal(means[Y_test[i]], np.identity(num_features))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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nkFBb475Xd9Cjb0FYEQ+HUMDnBZNFsmh6LRZNr4WuQ9cz8nHmq6xfUX1ziqJI\ndF1gjdGIjdPRNNi/w1rtfg2OT37++Fe2/rODxm0a0P+ui+h4RjsAPnpwckgRGJ/Hz8wP5/LFjvfD\n9nVgx0FG93uBzP1ZgbqrXj/DXr6RK0eE2u+PBNUOUBJCNAQaSin/EULEAyuBK6WU6yOdYwQoHRn0\n7JHg+Q0odROLelB3AUKYkQXvIAveR/NLVBU8bsHqP+Jo0cFJnfoaaiWnAVJCbqbK3f3aovsFWWml\nN6ZK32/VE+BLb8ogP1dl48oYMg+a0fxF/RnCblA+FrulWIgvsQ8Om1pXKIKfHFOwWIM3VqWU/K/D\nvezbmhqUJtgaY+WlOY/T+cwOh23clQ1QqvaMXUp5ADhQ+O98IcQGoDEQUdgNah7p2xAq6gAyDbKH\nIrV0pLYdIcBUeB/bYiRdzyhg3je16H9rVkifmgbffliXHycmY7XpDH96P/O+rs3aP2NJaeXh0XG7\naHeyiwO7LDx3W3P2brNRbdEVEiEkUlc4d0AWzw5tSX52RZ431XG3PB440T9/KF6Xl/EPf86CKUsi\n1uGNSbBjtoRK5NZ/d5CxPzsk97vX5WH6u7MPq7BXlqhungohmgOnAH9Fs98TCSn9SN9apG9LxPzS\nh4Lf5+fLsd9zY+uxXNulDW8+lEJWWpmb1fcX6NvRQjOPYo+VNG3tYd+OUI+Bd0c3Zsob9clMtdCg\nmZcXbm/O77OTyMs2s35FHKOubcXav2Jp0sbDuQOyqf6mpgwUz9MFCMmo61pXIOoSi0XHFqtF4drH\nMoaoh8Pn8UUMOLLFWrn2of5hy+Pt3XIAzRf6Y5ESstNyoz7OqhA1YRdCxAHfAfdJKfPCvD9cCLFC\nCLEiPT09Wpc9rpCehci0M5BZNyOzrkZmXIj0b6tWn2MGvcmUMd+RtsdFbqaJeV/XYkS/NjgLQv/r\nI5laTBbJpn+DN4ay003Mm1abRs29PPnxDu55eS83PZSKUEoEVPMrPHVzC7LTTMTE6RHC/g9NcKUs\n9JqRAs1XvgcNQJN2LpKStQrbGRgUYbFbGHj/ZWELYWxfs4s3h32IzxMq7Fa7hd5Xhve6qWmiIuxC\nCDMBUZ8ipfw+XBsp5XgpZXcpZfe6detG47LHBVL60fPfRU/tjsweDjIXpAOkC7TdyKybkDL8UrEi\ndm3Yy/I5q4I2hjS/QkGuyryva4W0D7cxKiXkpJtIrFMyBp8XVi6Ko1UnF2/N3EKvfnk0aOJj1uQ6\ngdl0KfwjFYikAAAgAElEQVQ+weevNaDvVdmIsHfboQhuoK09VgsaT3ntt62N4eDu6lefNzgxsMXa\nuO/D4Qx5bhCKEnrDvnXHeFwF7rDnmqwmLr7tvMM9xEpRbWEXgbXKRGCDlPKN6g/pxELmPgqOj4GQ\nRQ4gQc9HehYder/u39iycBiqEpoy1+NS+e+v8HVMyyIEuJ0CZ76KzyvwuAULvk/irUdScDoUHhvc\nkt+mJ5GRaiIrPTR6LzZBp0kbNwm1ND76dRMXXpeJLdZfOLM/tNl6fJKfZz7ZwTfr1vHFig1MWrqR\nzqcVVPQJCmf5BgYVI6VO61PCVwXT/Boby8kV43X7ys03U5NEw4+9N3ATsFYIsarw2GNSyp+j0Pdx\njdRSwT2HkA3NIDyQ+zTS0hOhxFeuX+9yZM491G+sAi1D3jdbdFJaR67oHtSXhD5X5PH7z4lc2aYz\nfl/JXGDPFjsA2/6z0/OCPMpuCVhsGu/O3kzdhj4UBZq08XL/63vp2quAtx9ugs9b3ryirPeM5MWp\n22nRwYW5cALeuKWXMVN2cMd5bUndXdZ3vfwIVgODsggh6NSrPS06Nw37vqIqmCymiJutqqqwdvF6\nUto0PJzDrBTVnrFLKZdKKYWUsquU8uTCP4aoVwb/dhCVCKaROciC95F6VqXMMjL/DcBDxx5O6qV4\nUU3ByY1MZsmlN2aGP7kMQoDZIsnPU8JGmAK4nSrLfkmk3cnOoGt53SqPXteSRTMSi236igIrFybg\n81ZWcAPtWnV20aSNG3OZr8tk1uk/JDhvvFAk9ljDrm5waEgpSaqfwMJpv+MvtTmak57Lirmr2blu\nD+fdcBaKGl42FUUhsW5CTQ23XIyUAkcSUzOQ5c3Wi/CBcxIyrTfyYBf0tPPR3b+V03wdEBDlV77d\nRrezCzCZdUwWnaZt3Lz09TbqNAjjAhOBjFQTk15oiKug/JS9Z1yYR1Kyn9Kz7bS9Vl67rylXdejM\ngwNbkbrHjN8PFYuuICZBw2oL5A+on+IrLKwdjNkCbbqUmJvaneJg+ua1aEYaX4MqsGDKUl4f9iH3\n9n4Ct9PN+EcmM7jZnTx/7euMPP0xtq7aEbEItdlmpke/k2t4xOEx7v4jiFAbg6VnJVtLQAN00HdD\nzt3oBeMitC3Z3EmqozHmi4BdeurK9Xy8aBPtT3FVOoIUIC5Ro0//nHLbKIokO0MluaGPF6Zs57sN\na5mweCPnXx3wf9c1wfq/Y3igfxv6XJ6DxVZxEY4zL8kpXCVItq2zYbGFplWVEpp3cFH0MLn0pkws\nNln4gDEwOHTcBW52rd/D23eMZ+YHc/G5fTjzXHicHnau3U1crVhGjBuKLdaKLcaKLdZKgxb1eG3B\nM0dNCT0jV0wNI/Vc8CwBBFjPhrgRkPUHcKhC5IeCD5ExgxFKScku3bcpbOuYOB3iqjZmm11y8Q1Z\nNGntoWuvAh64ok2ZfC8St1NhxYIE3p61FatdR1EgLtHDiLF7qdPQx+ZVMdz8SCopLT3oOtxw/0Gm\nvhXIGxOwzYc+aXRN8NTEnYy6phUH91jJz1GpXS/4gVBkKmrRwc2ODXYSavlRFBg08iAfPdOosPB2\nyTirkxe+biMvthjJnq1G2oLjHY/Ty5If/sbjCN6L8vs01v2+icem3Mulw85n6787sNgstOjSNKzP\n+5HCEPYaRHfOgLzHQRR+7VID2zUcuqgXYQbvKrD1LTmU/2Z1hxmWZu3ctOjgxmKVPPvpDsbe2QyP\nW+BxKRSJ3A0PHMRiC4h6EfZYyY33H0TXJbZSrvCDRqbT++JcprxZn6WzkkJs7kJI6jTw0ai5h1e+\n3cb+nRZyMkwhwg6g66J4Nr9hZQynX5jPJTdmkZtpYtq4QFEFn0cEHiCCsCadihEkJWu8+t1WMlLN\njLqmFZmphhvl8YzuD7+qVE0Kjlwnteon0f60o7PohmGKqSGktj8g6ngK/dQdgBvcn1ejVz8oJf7o\nUs8Cb8WukYca0KppoIhAnnWAbmcX8NWadbw1YwvX3Jle7FPevpuTcDWDTZZgUS8ipZWXPv1zUM2B\nNAGlSW7o5ZQzHei6oOsZDs6/JpumbTz4w+wdSx22ro0BJLOn1kHXAzP5wfel8c26dXw4fxP3vbaX\n6Vv+Y9auNYz7ZTPtTnEc2pcApO0zs32dnUbNvdz/2h5O7GjW459wQUgAVruVhq3qs2vDXj544FNe\nuP5Nfv1iMT5v1eJNDgfVTgJWFY6XJGBSS0MWvA2eBSBiwH4DIvYWhFCR0guexaBngaUHeBYg89+k\nfNfGQ0QkIur9XbwE1B2TIX9M9PqvACkDM2EIbLA2bOaLGOQUKbXvVR0743aolBZJ1SRRFDBbdfxe\nhZPPyufxD3dji9HR9UCAlNUW+FvzC54Z0px/lxR5I0gm/72e+inBP0qPW2C1lVzD5VC464K27N95\nKCl+JSaLpG4jHzc/fIB3RjXBVVCyYjE4/rHGWHhsyn34vH5evXUcfp8fza9ji7XSpF0j3lzyPFb7\n4UsbXdkkYMaMvYpIPQ+ZOQBcP4CeCdoeKHgLmftIIM9L2tnI3IeReS8gM/ojXT8B0XyiC4gdjhAC\nKb1I189QMCGK/VdiBAIsNonFJiOKus8b+BOO7HRToahDSYENgeYX+LwKznwTXo/Cv0viGfdYIwA8\nLsEnLzZk7rRafDWuHoNO6lhK1ANMeaMBXg+4HAKvJ/BgKS3qEPDlHzDsUFNbCPxehQM7rbx+X1NU\nk069FC+Bh5Ixez/uEfDk1w/Qvd/JvHHbB3hcXjR/wATodnjYvWEfP0+YH3SK3+cnbU8GHlfl4kai\nhWFjryLS+Q3o+QTbx93gnoP0/A6yTDZE/1YCX3e0xD0GEXN9oChGxlWgH4xi34dOpH0jcwQztMcl\nmPpW/Ui9Bb3yeRQWTq/FPS/vw2KV/PFLIj9MCC1IXHTuohlJnDMgm7ZdXSyakcjZl+URE1/Wlx9a\ndgyNyq0sfp9CQY7AmS8RSiDbpMFxjgTVpLJ5xbawizSPy8vCaX9wzrW9+HXKEv6etbIkyZiEy26/\ngGGv3BRUrONwYdyNVcW3nNJuhaXeCBV1ADyAufBPaaq4jE96B6HEIfPGgr6XIynqVWHW5Dr8/EWd\nSreXEjwuBSHg3lf2ltvW41JYMjMJ1SRJ3WVFNYfOpn0e2LSquhVvBLomQvLjGBx7mMwqlkoUtP5v\n6UZssVZ0LdT1FkDzadzcegQTR09h1W/r8Di9gT8uLz+Nn8ekJ76M9tDDYgh7VTG15NAXPOEqnFdx\nCZ/7CHru0+CeUbXzK0Gk7ZdobMuoZonVHv7HEY66jXzEJWooKnQ+zUGj5uUvbYUS8MhJaeVh6axE\n3M4S8dV18HoVfpgQjWR0FWeYNDjKEdB74GmYrRULe0GOg1YnNSepXmLIKtUaY2Hv5v24HR40X6hH\njcfpZca4OWgRvG2iiSHsVUTYrwdRlWCEKM2sZSa4vgQqL46HiqaFF/FouOteelMmXc9wYLEWFZ8O\n/7RQFB2rXeeel/cWX9fnFdRvEnkT2myVnHdVNm6nYOcmG6/f35RvPqhHTqaK1y1YtTSO529rzuW3\nZPD0pB0MHJ5GTPzh/7EZHKVIWDRtGUIp/8a2xdo44/LuCCEY89NoatVPIibejj3ehtlq5qyrzog4\nky/C79Nw5lfdBFhZDK+YaiC9KwLZGbVUiqNCj5NNNF0LCHj4VLvRQUpYsyyWxTOT+PmL2oX+5SU/\nruSGXrqcXsB1I9Jp0aHE7OV1C245oz1ZB8sa8CVCwLV3p3Hro6k48xWG9O5AXlbJyiqllZvbn9lP\n93PzQYKiBrJXOvJVRlzUtkwZPwODQgSYLSbandaaW565jpPP7Yzm11j123/kZuTT5awOFGQXcE+v\nx3E7Iq8mazdI4qt946sczGR4xdQAwtIdkTwPUXchWK/gWBb1gOsgOB0CV4FCbpaKx125m0/Kqpln\nhICTejm47YkDnHNFbuAhUsqfXdcFd7+wn6ZtS0Td7RTM/65WGVEPzPhVUyCoaft6Oz9/UZsHrmgT\nJOotOrgYN3szPfrmoygBUYdACcDE2n5ueeRAcX9dz8jnqYk7eOCN3bQ7OZwJzeCEQgb82v9bspEn\nLh/LHz8uRzWpdOzVDrfDw1cv/8B/v28krnbkdNjWGAu3v3FLjUSoGl4x1UQIgdTTwRMpoaWVwMbp\n0Y3ZErA9m1SY+nZddmyw8ci75QfhFPmnF92nmgbZaSZq1/cTpkZBROyxOmf3z2HpzwmFqQoC18w6\naGbkxW247Yn9nHxmAY58lekTkpkeZBuXmC06Qgj8fkHGAQsZB8wsXxCaZW/Yk/uxxsiwpiSTGU6/\nsDAnvoCLrs+i98V5aBr06Z/DpBcb8uOkytvkFVXS/dw8YuM1tq+zs2tz2XqvRh3SYxWP08sH939K\nm1NbMqLnaJx5TtwOD7ZYKyaLiZgEO1KX+Dx+NE3DZDbR6uTm3Pz0NfTod0qNjNEQ9igg3fMIH3hk\nAqU16OtqekhVQlECfulX35HODd07FJaeC0+4oCNVhcRkPwU5Cgm1wyfs0vwlxbKL0HVwOwRX35FG\n34HZzPqiDjM/qYvfJziwy8rzw8IXPiiapddL8bF/h7VUQY3w4+5wqrPcB47bqRZ1y+kX5BV/JjVG\nMvTxA8z7phbO/Ip/MrEJGve8sodxj6bgcSt43eE2WAM55g1xP8oo+m+pgIO70xk3ciI5abnFdnW3\nw4Pi8nLSuZ3p97++5KTl0vXsjhELdxxODFNMOUj/bqR/K1JWtEGpEv6rNIGtG2CL/uAOI4oK9Rv7\nGXVdSzIPmtAPYX/WZIL4WnpY00ykfoSAc67M5eaH02jS2sftT6fy+vSt1EspWulE3lzV/Ar7tlvD\nVklSVclJvfKL0xXkZkUWZbdTMOPTOoCkR9884hKDB+v3BVIblBD513/jgwcYNzqF/BxT4Qokkngb\non60YTJXbq5rtppZPmdVyGaprktW//Yfp17YlYH3XnpERB0MYQ+L9O9ET78UmXEZMvMqZPrZSO/f\nEdsL+8UExD2kJ4i5HWz9OJa+apNZ4ihQEARMK+FmuUJE9pgp+qNpsHebhT9+iSd1twVVBU0TuBwC\nR76CzxNszilaAQgB7U528dGCTZwzIIt6jb2AoFFzD517FhCXWBQUVv4MXTFJRn+4ixe/3AZC8s37\ndXE5gj9M0Sriz3kJ/PBxXWrV9fPoe7vDfDBw5hf9H0tiEzQiiXtyA3+5qx2DoxNrrJXnfnyEpHqJ\nWGPLT/B22sWnoJrC/6Z1XTKo8XCe6P8SBTmHnpMoGhw7alNDSOlDZt0A2lbAHSgqrachs4cFStmF\nQZhaQvyDBOzpNsAe+HfCcyimeojEl0FtXmOfobqYTJLxv23i/XlbaN0lfOFeCBb3cCKvqlC/iY9n\nhzRn6NntePLm5iBhzzYbr9/fBKFEdp0UAmLiJKPf28O5A3J47YctfDh/E89+uoMv/13PTQ8doLxZ\ns6JKWrR34fcq7NhoR1Uksz6vw4+T6uBxCRx5Ap8H1v4Zwx3ntWHsnc3RtYAbpalMQJOUgYyQW9bY\nqF3PxzV3pZXr8ul2Gj+rYw0hBE9Oe4AeF53CV/s+otMZ7SJucgpFcN9Hwzn3+jMxW8LP8P1ejZVz\nV/Nk/5cO57AjYtjYy+JZCtJJiGhIDen6DhF3d9jTlNhbkbaLwD0/kJbXeh5CLdps84G267AOOxoU\nibOiQmx85ewvQgSyK5ZvbRD4vYJ/F8fzxRv16T8kg+x0E36fCBHRsuNxu6DXJTm07ODGYgWrPdD+\nqtsz2LXJzuKZSaXPQDVJNL9A12DbOjs39+xATJy/uKLSJ2Mb8dU79WnY3EvGAXOh10zJGDb+E8un\nLzdgyOhU/F5BTLyOEBCfpDF9yzrW/hXLpy81oCBXjfihsw6a8Bkz9mMKa4yV+s0Cv1dVVdmxdjeR\nXMHvensIiXUSuP3Vm9iycjv7thzA4/KGmGX8Xj9bVm5n7+b9pLRtdNg/Q2mMqUVZ9LRCpSqLF7QD\nYY6XINSGiNgbETGDSok6hTfI4QskijaH6roYydfd74O/5sZTtCN115i93PhgKskN/bzyzbZikY7Y\nrwCbHdqdFBD10thjda6+Iy3oWKC+K5QkE1PQNUFBbvD8xeVQ2b7OXsoVMnjH7IeP63FDt468el8T\nfphQh9wshbS9Zp6+tTkPD2zFf3/FUZ59fNp79blyaDpWm45QivqtKFHYsesqezygaRq1GiQWv06q\nnxi2ncli4sKbzwEgNjGW91e8zHM/jqJe0+SI7dP2VK6+cDQxhL0s5m6E/5HFICynH1JX0rcePfM6\nSOsaoc/oIvXqhfuXtnNX5VwIbEJKCc58hcyDZt57PAUI5GRv382B1VZU9Sj4/LS9Zr7/OJlvP6zL\nvh2WoH4jjSmhTnBq3rS9ljKVnYp7CXpVv4kHk1nHatMwW0uLbwn5OSZcBQqX3JCF5lcYcXEb/pyb\nULhJK2naxk2T1m7C/b8681W++7Aerbo4adnRRd1GHhS1PA8YWcp/38gUeSTwuX0Manw7Q9rfy9ev\n/sjV91+GLSY0/a7m1/juzZ+KXwshOPnczvS9/sywKQkcuU4mPzONLf9sP6zjL4sReQpILRPp+Bg8\nC0sKV/jWA0Whv1YwNUfU+Q4hKlc1R2r7kBmXFRbUOHH4c148O9bb2bHBxu+zE/H7AkLboKmHT5dt\nDCvSedkqX71Tj1lf1MHvEygK3PhAKteNiJxW1++HjP1mTGbJvh1WPn+tAWv/LAoOifx0at3Fye7N\nNrye4AeAokj0Msm8Xvp6G6ecWcBHzzRkxifJ+H0K7bs5ePyjXcQnaQghyU4389xtzdm+zl65Lygi\nRcJvuEAeaax2C516t6NT7/Z8/tw3Ic9ZW6yVZ75/mFMvOKn4WHZaLsM6309+dgG6Fqqptlgr7/45\nluadmlRrbEbkaSWRejYysz84PwdtO/hWBkTd0gtMHUFtBXF3ImpPq7SoA0jHpyCjWFTjGKHb2QWs\nWBjPX/MT8PsEFptGTJzGE+N3RZ5519K4+eFUnhy/C80H/a7PpO/A7IjukT5vYGO2XoqP5IZ+Turl\n4LJbMgpNQuWLYufTCsI2CcyoJXGJfoY8eoCPF22kU48CAP5ZFI/fpxCf5GfsV9up19iHPVbHFiOp\n38RbaFaqbq6Z8j18DGoOj8vL+mWbqd+sLtYws3a3w8OP780JOpZUN4FuF5wUccXscXkDD4ka4oTf\nPJWOL0DPJTg5lwu8SxH1fkcowRGMUrpBS0NKN0LbA6ZmCFPr0I696zjWUulGA4tV8up32/h3SRzr\nV8RSu56Pc67IITah/D0GW4yk02kOnpq0kx7n5GMOU4RGSnDkC7xuhdr1tKAHxT+L4iuVPrdWXS3s\nForUBfZYjXG/bKZOfX9xGUApoXYDHzs32elzRQ5KGbONogQqPp15SS7zv6sd2nG1KLqWIfY1jd/n\nZ9nMFSgRZiNl3RgXTF3KshnLkXp4ZZe6DORxryFOeGHHu4SwUaPCEpi5WwN2dSklsuBNcHxa2F5H\nYgZUpOUURNIHCCWmsK0H9DC+0EGoBBKHVZ9IpeeOFIoCp/Yp4NQ+BYd0ntmic1rf/JDI1NLY7BKr\nVUMrTFJW5GMfX0tDVSVaBYWq257sCLvZq5olvfrlUiu5RNQhcI2r70jnv78CD6lwG75mi069xl6s\ndq2wuDdEQ4xVU2GqBMPDpsbxezX+/vmfsHVPrTEW+lzbK+jYjA9+KTf5F0BK24ZRHWN5nPCmGNRG\nhP0RSh+U9mxxTATHZwSKaxRN+XyB196/kXlPlWo7BfScCi5cPVGXEhx5CutX2HHmV6urowZ/oZti\nJIQIpCMwWykMdgpUYgK4aFBW2IIapVFNOtlpKtfedRCrTUdRJYoisdh02p3soM8VudhiQvs4qVcB\nV/4vnXV/x4YEOEGg7mqnng6uviMd1VRZG3lFe1sSza8YRTyOIOFE3WRRadKuMf2GnBt03OMsX9St\ndgs3PHF1VMdXHie8sIuYIYSG/JvA1BZhalVyqOBDSjZTy6KBewa6v3Czzz2dqBatDoMQUJCn8Plr\nDfhrfuIhhf0fjeh6IGz/UPbyzeYSV8uUlh5GvrQHq13HFhMaFZrcyMNr323lo2dTKMhTGTttK1ff\nnsbA29O47OYMWndxklDbjxamML3Po7BycQL/LI5n61p7UNEOt1OwZlksO9bbiE3wo/kPRYjL+7AC\ni02nY4+CKNjvDcrjgpv7kNK2YaUqKAkheHXBUyEFq88d1BuLPfz59Zom8/hX99O5d/uojLcyGF4x\ngO6cAfnPAjpIP5i7IGqNQyi1kVoqMnsY+DdV3JH9FoS1BzL3SZDZh33cRfh9oJqOLnNMJEqbjTQt\n4KKpmgJh/fO/q0W3s/NIbqhV+rMEUhMIEmpp+LwCXRf893csqbssLJ6ZyPb1ds64KI/7X9vD1v/s\njLqmFS6HimqSJCX7yctW8XkUOp1WwEtfbws8LEpd2++D/TusDDunHSAwW3QuvSmTC67LQtcEc6bW\nZvbUOgghUZRAEZDKztjrN/FwcE95eYQCVab8PkFSsh9dE2SnG/nio4ktzsaz3z/MKed1IX1PBkM7\nP4C7IHK0NUDn3u15fdGzKKVybbgcbu478wn2b03F7fBgsqgoqsroz0fSe0DPqKXqraxXTFSEXQjR\nD3ibgOF4gpSy3Djao03YAaT0gn8HKIkItUHhMYnMvBz826ic6cQKQi2MXDUojbNAYcKYhiz4vhaa\nT9C9bx47N1oBhVe/20pygzBT5UrgdkJelol6Kf7AqkWW5Fkvy+bVdh65OiDsZencs4DnJu9g5W9x\nnHK2A9UkMZkkedkqVrvGlDcb8MPHkQpoV0Q484zkgdf38MaDTSvVg82uYY3VyM2ovGeWQfnYYq10\n6t2Ocwedyazxv+L3+nA7vezdtK/claMt1soT0x6g5yXdgo77vD6WfPsny+eupl6TOvT7X18atohU\nsL1qVFbYq715KoRQgfeAC4C9wHIhxAwp5frq9l2TCGEBc7vgg/4t4N9D5e3h3ugUBD3OkBJGD2rJ\ntv/sIKDL6Q68LoX8bBNN2rhJqOUP2QCuzIawlAGbe93G/uLXf/8az3cfJXPtiHQ2rIzlz18SSajt\nZ+DwdHr0zccWo+NyKHTu6eD0C/Jw5iv8PieRvldlM6JfW1wFSqE5R8fnhfOvzmHwfWkMffwA2elm\nFk6vdaifvszfAV/1Dt0dnN0/J0jYVZOO5i/KRx/84d0uFbfr8Fe3P1FIqpvArWOuZ/Vv/zFu5MTi\njU+z1YxQAgnwIpW5czs8/PPrmhBhN1vM9B18Fn0Hn3W4h18h0fCKOQ3YKqXcDiCE+Aq4AjimhD0s\nenYg70ultLqSiZxPQDasjGHnRhsn9Srg8Y92FT/7hAKLZyaEpAuAUFEPJ/RFm6lF76sqnH5hPl1O\nd3Dn+e3IzjDhKwxE2rAyhuvvSeOpiTtI32/htPPysNolmh9ueOAgq5bGMvypfZx6TgG6Fkjk9c6o\nxiyakUT//2UQl6AzaGRaFYRdEJfop04DL3u32dD8UKeBj0Ej0vhzXnDYekorD42ae1i+IMHwhDnM\nOAvcbPhjE7//uByvq2Q/zOfxYYmx0PWsjmxeuY28jFDPBLPVTK0IKQeOFqIh7I2BPaVe7wV6RqHf\nGkV6VyLzXwvY0tVGiLiRYOkd8I4JwQJKMugZBMRcA2KB48Q9Jcrs3GQjvpafJyfsDPE6Oe+q3Er1\nUdHsvXTK358m1yEns0TUATwulalv1eeyWzLpcKqruL1SaNnodrYDv18UuzraYjSe+Hg3Pm8gx7yU\nAXNSVSjINQUlDctMtfDC7c2x2oNnhLs22bjvlT2sWRZXHLFbghGRGk28Li+/Tl2CyRS6CvI6vTRq\nXZ+nv3uIQY2H48gNNq0qqsL5N/WpqaFWiRrzihFCDBdCrBBCrEhPjxwqfiSQ3pXIrCGBqFNZAP7N\nyJxHkO45EHc/UNquaQJhBlMXAlsKeuGf40fUq1rDNBJNWnk469LwAi5E9Fc5yxckhM0ZY7JItqyx\nhzwkUndbmD4xmVmf1yFtb8nmpBBgtZVsTLfq5KJ+Sllvp8qOP/iiXo9Cfk7ZeZVg9PWtaHeKs/B7\nKW3GMUQ92mg+DS2MO5nZaia5cW1sMVZenf80ySl1sMfZiIm3E187jmd/eJjkRtEORosu0Zix7wNK\nJ0BIKTwWhJRyPDAeApunUbhu1JD5rxLwTy+NC/JeBVtvgn9U/oDnjPeXmhtgDbJiYTwTnm/AOz9v\nCTKRbN9gpUlLL2brof/Xde7pYPs6GyZL6LnqYQiRS27gQwgZUlVJ80NScvAm7ffjk/lkbMPAg0zA\npBcacvuz+7js5qwwpf8k/QZn8tkrRYEm0bmNY+IDbpKaT+BxC/5ZVJQRswhD1A8X/jC+6qpJ4YLC\nDI5turVk6q4P2LZqJz6vn7antkQNM8s/2ojGjH050EYI0UIEkqkMAmZEod+oIH1bkO65SP/OyI38\nmyO8kRfIr34MFKOOBlJCh24Ozr86JyjsftdmK/O/qY1QKy9kpWf8QsD512ajh4kKPRwumgOGZWCx\nlQn9VyWNW3hp0aHkAb5vu4VPXmqI16Pg8yr4PApej8JHTzcOmrkXYbZC3UZlTXORP0DTNm569csl\npVWo+5w9VqPnBbm88s1Wpv6znikrN3DbU/sL8+CH61NiMkeu2mRQNWxxNuo0qoUtxoo9zkZSvQSe\n+3FU0IxcCEHrU1rQoWebIFHftX4P37w+k5kfziUnvXImxZqi2vMlKaVfCDEC+IWAbWKSlPKIV2+W\nugOZfTv41hRugPqQ1t6IpHdCk3mpDQMeMCEIIgclHX8IAbEJOlcOS0dRSjYsp42rR6ceBaiVnKj4\nfaEFq4sKdxzO9AdFfbfv5mTEi3t5/8nGCAKRoc3au3hm0s6gay+dlRQ20lUCv89OZMCwjKDjfh8k\nJUDXiaAAACAASURBVPto2dHF9vWRszla7TrPTNpBxx4ONH+gmMi/S+MYM7w5Po/ChddlcvcL+0CA\n1SYLx6Rx5dBMPns5ctj5O7O38OvXtfl+fF2MWXyU0CVj5zyBoir4vX6ad26CWsGNLqXko4c+Y+aH\n89A1HdWk8NGDn/H4V/dzxuUVeiLWCFFZCEspfwZ+jkZf0ULmjwHfKgIuiIUHPb8jC95FxD8Y1FbE\n3YPMeZhgc4wdTO3Av5Zo5XQ5VjCVuSvuen5fcSWhitC1UFEv4nDntCkOfPLDf3/FcOGgTPoOyCGh\nlkaj5qGRwJLglUVcop9nP91Bh+7OkDqvRa6V3c4uoMvpW5j4QkNmfpYcNqHY8Kf30amnA6utxE5+\nypkF3PLIAeZ/W5u7X9gXNnWBEFCvsY9dm0OFRQho3tbDwOEZzPo8uTiVQtUx7PYAiXUTaN6pySEF\nEK1ZvJ5Z438t9qbxF95aL17/Fl+nfow9rropnKvPcZlSQEodXDMJDev3gHNaSHthuwgSngRRCzCD\niIHY/0Hic4HXJzhxiXrYgtYQuskaLjioaDO2plz8HXkqC6fXpstpDtqd7Aor6gC9+uUW2/gVRfLp\nsg10Os2Jqkb2qVdNgUyUw548QL8b0gvTFxS3BCQXXJNdKOolWO2SiwdncfHgTMxh9hqKuOmh1DAp\nBCSnXxQYa91GPp6auJOYuOpMNgxzThFNOjQKEnUpJRv/3sLczxayafnWsOXxfv1icdjcMIqqsGLu\nmsM63spynGZ31IAIkYwyvGlFibkGab8KZD6IWNAzwfcP0n4tuL4i8FUZEaVlqcxEp7QrYk2gmnQ8\nboUupzvCXrNIqJu28TD43oN88UZ9zrsqm7jE8KuS0sdSd1uY93US+bkmel+UR/O2Hr77sB65WSoe\nl4IQIuIGs9Uuia+tlbthfNb/2zvvMCmqrA+/p6pzTx5yBnEREBTMiqiomDC7Kq665px2zWEVTGvO\numbXsOrqGtDPiDlnxYzkrORJnbvu90dN6unqMImBmfs+Dw/TXVW3bs10nzp17jm/M6mC6kqDR67t\nQ021UVtJq7jo7ga10FHbVDPpmJU8c1dLqxq1p16HP9gg6RCqCnPRHlcz74eG/sRDNhvIda9fluKF\nK0s5OikKhVpPRJs6pccu4gbXSIctht1AI+NxBkgRqupm1IrdUBWXQuQ5MMogcAzae8/N+vC5tizB\ndCnWrnS2oI0N9eSzl3PHK7M44MTcKbgfvFzMiTsP4+k7ezLtoW5cfdIgvnm/iEc+/ZVnf/oZj8/+\nwv/ydSDti29Z8P0nQT57o4hwjnz4vY5Yw9Pf/8S/P/mFYWNC3PjcnPr8+mhYWL3Cxf896txjs+3I\nx6tvuo+isHTD6UFgGJJSJXrvuY8y+9u5RGqi9f9mfT2X+857LOW4CZPH4QumV9VZCYstJm6W9n5H\n0CkNO4AUX2V73vU56F6QAqTokuwHRqdD+Ekgaue0qxqw/oDQPXTFxhnNZX0QIvP6FDvsVcEzd/cg\nnEdnwiEjIwwZHs0690jI4Oa/9ScWMWqLh4RIyGTGJwV8/Gox/76uV23Wj7B4TurivFKQjAv3X9mb\nj14tZvaPfuKxhm11/5KNoivRsMF3HxXw0xcF3D+1Dx+/WsyPXwR44paenLrrMEJV7Z1y1/iXkdnI\nu9z2ndzjtQgWWVzx0Py0ZiTrA04x9E3HD2e7/RoWO9/5z4dpUr3xaIK3nvgw5b0xu45iwhHj8Aa8\niCG4vS48fg/nP3I6waJA+1xAM+mkoRgQ9wjo9hoq9DjEfwP3aCRwBGKWZz1OhZ5wCNesfx/U9ZX1\nwbB7fIpxe6/l7sv6EI+Z+AK2WqTT4m2+C7o/fBZ0XD+IhEzefq6UQ05ZwW8zAsz8NsBO+1WkjCkC\nbq/iuv/O5fyDh/LQNb248bk59dvqsBLCF28XkIgLn75RzMCNw4Dipy9sA99xOKdflvWKc8CxK5n9\no5/BIyLs/ZfVeP0WvQbGWDrPQSeiA2kaKzddJhuPGZySAROPOYdvE7FUh05E+Nt9p7D3ibvzxavf\n4Av62Pmw7eneL7ttWZd0WsMOIGYvpPD8jNtV9BNU9R2QXAiu4UjhOWA1r+uPZv1k7E5VXHLvQvwF\nyawx/nxvRKZLZbi/K7w+i9Hb1XDNf+Zy+wV9MTPk+5d2T3L/ezNZvtjtGGdPxOGzN4oZtV01p121\niBcf6lF7bgvLqtWqV5kmvG7b6G08OsTUR+dT3jPVGMaiQk3l+h8ISCaSfPT8F5xy8zH1742ZsCnf\nvP1DSns7MYQxE0Y5jjFsy40YtuVGjts6mvX/L9BOWOE3UGtOgfg3tuZL7EPUqr+AezTpjTc0GxqF\nJRab71CD22FZJFd2jtP2Uds63/B9AYs9J6+u/Vlx6lVLcWVR1jUM6DUg7phlZLqg75AoX71bxNcf\nFPGfW3sBQjIheDxWxhuGTb468C0h/bz9NooRKEhdUInH7CebilUbxlpU00bVZ959AgUlQbx++w/o\n9XsoKAly5t0ndMT0WsUG7bErK4QK/w+ib4NRjgSOQjxjch+nFFRdS7qMQAQSP4GrPyQWYxcntV1v\nUs36QTYvPZPRd3tg6r/ncfkxgwGwkoKyYO8jVzFmfDU/fxXgu4+CHHrGilaFo154sDtrlrt4f1pJ\no4VoIRppr5h6Pp5++rZ3Xyhh8PAwB56wklhMcLkU837xc93pA3Ocaz2I1WEb9f1O3yPlvb5De/Pv\n3+7g9YffZc538xg6ZjB7HLsLRWWFHTTLlrPBdlBSVgi16mBILsE20AJ4ofAijOAROY6tQS3fEmeD\n7Ud6fg7hl1HR98DoBeFn6CqyAl2ZRALCNQZut4XPYQ0smbTb5H36RhE1VSZjdqyiz6AYz9/XjUdv\n7MXQTcNc9fg8gkXNSw1Syg5hPHxtL158MHczj8LSBFvuXEUyIXz5TqFj45C2IbchLipLsNHIMCuX\nuVk0O58n3Q427gIer5txB23LBY+enrPKtLksmb2Mb6Z/T6AowPb7b9nmxUrrrNFGR6HCzzQy6mB/\nYCJQdR3Kvz9iBDMfLD4Qr3OnI7MbIj4I/BkJ/BkAK/EjxL9t60vQrCNyLZDakrzC28+V8fGrhUx5\nZAFNww91eu9mwGKXAxsalSsLynvHSCaElb+7cTk01G7sO0VCBnN/9lHaPVFfOLVkrpupxw1h4azc\nhnHioas4459LSCalNsfdYtpD3Rk2NoRS8PqT5XzwUglWmzTBzj1G5WoX336Yn0frclv0HhS1bwAZ\n1wraF0G48/N/MmRUtieL5qOU4oELn2DaXa+BCKZpcPtp93P1yxczevyINj1XPmy4MfbIm6SHUrB1\nYeLZq79ETAj8lfRYuheCp9e/smLfYK29EKSMVOlezYZAfUOPPLTcZ/8QoFf/GFMfXYDL5Vzu7/Rw\nKwZst0cV1z87h5XLPPzyTYBYNP2Ebz1bzKVHDOLPm47ksiOHcMqEYZyz31DWrjJ59IbeLJzllEWS\nesI+g6Kc8c8leP2KQIFFoNB+sjj0jBVsvkMNY8bV8PdbFnHp/fOxpaQzj7WuMV0WwUKLG/83lx33\nWZv7gHbC7XUxcES/Nh/327d/4OV/vUEsEicWjhGujhCuinD5/tcTj637NOkN17AbGfSQlQVG7u4m\nUnAWBA4j9VeQgMh0LCuEtXx3WH04RF6A2NvYOezN7Z6jWRe0tigqkQBfMMnmO1Th8yvcGTL1Mhl3\nr08xcqsQZ12/iCuPH8y3HxYQiwrJRMNxgULFtx8WEY8ahKpMohGDWd/5mXrsIPY6chVev2pyrvQT\n7XzAGgyHBdTGNy6vT7HdxEpGbNX0aXQdd/gSRa8Bdkeonv2i7DF5NfdMn0lp90RaJs26JJm0ePq6\nF9t83Ncefqe+vV5jlFLMeG/dN5PboEIxSkXsUn+jOxI4ChX9kFT1RQPMHuAannMsEbP2Y+6iQVMm\nCbGPYPkEYHXTswNrwBwOyV9afS2atmHGJ0GGbV7jGBPPF9OE/kMjeHzZwzaWlXmbCEw8bA2Vq1xc\nfvRgevSP8dAHv9anNb70SLe08EgiYfDzV0GuOHoIG28WYtaMAC6PQlngcqu0Rhy+gJWXfr1hwl5H\nrOLnL5vmvostXzwkwtL5XpJpXZraDsOAu16fRWFJ6jqWlYQ+g1u3XmUY9u/Rspp/o0rGkzx36//x\nl0sPbtUcmtI01z31nOv+RrZBeOxKJbEqr0X9sTVq5d6o5dug4j9CwdnUVZQiATD7IaUP5q/UFn4W\nR6GwNKPeCG3U1yv+NDqMYTR4x3VkM8JNUQp8tWtc2Y7JNZ5hwCGnreCSexdwzvWLUhqVrF2RySIL\nlgU9+sY4ZepiLrl3AVc+NidFN77O0/70jeK8VR0zLahaSWHAxlEe//xn/MH2MzhWUnjw6t5EQtLo\nPYhGDF55vOWFPKbHZI/jJtB7aK8Wj1G9psZR3Ks1TJi8o6PMQDKRZPRO6z7GvkF47KrqVgg9DUQa\nniar74CiKUiPjyE+ww6/uEblbdSVUhkFwTQbDv4Ci1hUCFUbmC47Euf2Kn791s/obVPDEZm88Trt\neScax+nz+WgZBozftyJt3y0nVLJ4npdELNWXMl0Wj3zyCwVFFi63wu1RhGuE37734Qska718RSxi\n8MvXAd6bVsrO+6+pD91kmtdHrxbhlIEioggWJintkeTKx+Zz/sFD6660fv4ut6JbnyhL5/nSjm8O\nrz9Zzprlbiaf8zs9+sb55esAj93QmwW/tbxOJFDg4+s3Z7B80cqs+3XrV4ZhGCxfmL5fsNjfLJne\npliWxSv3v8VLd79OJBRlx4O34dALDmDsbqP55q0fiNREcHlMDNPkvIdO6xAZ3/U+3VGpJGr5Fhky\nWAZidJ/e4nlYqybbfU41Gzwrl7m48oRBlJQn+e17H/sft4rJZy2v355M4tgopO7jb1nO2+v2aa1U\nwtpVJqfuOoyqtSbxmAEovH6Lk6cuZa8jVqcULCXi8OW7hcz+IcDeR64iEYPLjhrCkrk+lKXYfFw1\nO06qQFmKvf6yBjHS5xeqFA7ffFOiTXq/ev1J/vnUXEZuHcJKwj4DR+PxWVx8zwJmfFyAy6PY+YC1\nzPnRxy1/H5DWXrCjMUwDK5l5UcUX8HLNq5cwevwIrj78Ft5/5tO0fVxuk8fm3N1iCYDr/3onHz73\neb10r9vrorxPGffNuIlfP5/N5//3FcGSILsftRO9h7RUgdOZzpPuqMKgnPW0sVrWFFvFf0OF/muH\nb/DSIPProqE5tWZDQilh5rd2iqvHZzFu79RWZXN/8rHRyIij3svqFSbFZcmMBrwt9G9KypPc+/ZM\nXnigO1+9W0h57ziHnLKCTbdJlxZ2uWHEliHWrHBx63n9OOyM5dz12m94fBCqNjh9j425/YJ+jNmx\nml0OqkirAAUIFCmmPjqXiw/fCK/fwlJ2eOTwM5czcmvbSUom7DDQrgevYbMdqtl2ot2Q/eFrezHt\n4W5ZjLr9ZBGPtWe1qzPZjDpALBqn75/sLlSrlq5x3Mcb8LLwl8UtMuxLZi/jg2c/JRZpiKnHownW\nLq/g7Sc+ZN9TJjJ2V2cJgnXJ+h9jlyAYGf4ArubHrqzQ86hVh0D4PxD7EBA7w8a1NRg92BB+JZpU\nYlF45/kSXG4Lj8/iqL//Tv+hqQt0n75RlNFoF5cmcdWGcdqT4vIkx1z0O3e9MYup/57PqG0zS08W\nlSbZc/Iapjw8n5LyRL1MwSWTh7BiiYdhm4c5+4bF+IOZJz1kZNgufooYKEsQgaq1JpZlP8G8/1Ix\nIIzYqgZ/0H50WbnMxfP3dycScn588fiSHHvJUo67ZBlb71pJW2faePweSnrkzmrLjOKRS58CYMjo\ngY6Np+PROH1aGKOf+eUcTHf6mJGaKDPe/bFFY7YH670VExEovIT0nHMfUnhhs8ZSVggqp2Lnv9d9\nISJ2cw3/brZmTKYGHZr1FsO0FR2PufB37n17Joeekf4k12+jGIkMf9q6TBPJEmt3Qik7hJPtmFyd\no7Jl2djxbnvuIrB0nof5M3107xPn+mfn0HtgLOPx8RhcduQQwNanj0ftZt2vPF7Os/d0xzDg8Zvt\nMMGi2b76RdkfPy9wLLIC8AcTnHfbIg4/YyUHnbSSS+9bQLfeccfUzJZgmAYXPnoGd3x2reP2fOLi\nVlLxzlMfsXLpag46Zx/c3tSghMfnZuxuo+k9uGUhkm59ndOsXR6TXkNyVw2vK9Z7ww5g+PdCSv8F\n7rFgdAfPeKT8ScTTTFH7+DcgToHWMETesIubnJBCNpBfVZfE5YIDT1jJn09bQd/BdtiuqTEdt09F\n1gbU0LAQmckYN32vzvhmszfhGoM3ny7jydt68O2HBTkXaR2LoKROPCyGP5jkoJNX4PZk9tSVgu8+\nCvLbdwGahkqiYZPn7u2BCEw+ewUeX5LXnywjkbD3KyxNZLyegcOibL1rVf1rl1txzZNzcGWZS3M4\n8h+HMP6Q7Zh60I2O2/tv0gdvIHehoMfrZuHPi+k7tDc3vHUFQ8cMRgzB4/ewx7G7cNl//9biOW46\nbhPKepVgmKn2wOVyMenkiS0et61Z/2PstYh3B8S7Q6vGUIn5mTNhjG44d0hygXd3iLyMjr1vODQ1\nTh6vou/gKPGYncttmg0pkU33zeZFN4c5P/o4/5CNSCaEaMTA67cYummYfz49t74jUtOxc51jzLhq\nBg8PZ2wYDhCNwEPX9CVT/Ltqre3cTDh4NT98GuSt50q54JCNOPfWRYzcqgav3yJUbaQd/+s3AW49\nrx+HnLKC4rIEX71XyJO39SQebb3eiukyOfIfh/DsLS8x57v5jvvEown+euXhfPDsJ8ydsQDTZRIJ\nRVNkdsHWVe812Paeh2+zMf/6+gYS8QSGaWBkat6bJ4ZhcNM7U7j68Fv57au5GKZQVFbIhY+dSa9B\n64/HvsEY9tZiVT9op0hmEv4KTEb59oKKi7Bz2RXgAaMQKfw7Skog/AgdXZqtaTkFxak35lZ+x7Oi\nFFx98iBqKk3qDGSkxmTWjADTHi7nz6dmT9dzwjDB67OY+5OPTcaEcDdxXuu8/R8/D7J0fuZGF0NG\n2s6NIXDq1Uv45ZsAs38IcOpuwygoThCNZFoUFd6fVsL709q2AltEGLvbaESEZ26YlnG/ZXP/4LEr\n/svOh+3AnZ/+k0Uzl3DqFhemNJZ2e92MHj+cPhulxtBd7rYzdd36lnPbh1ez+vc1REMxeg3u0ar0\nyfagS8QXlLUGqm/HUVsGFwSPR7zbY/j3RsqfAN/e4N4Mgicg3V5BzB5I0YXg3tHheI0mnWULPKxa\n5iYtFBIxePO/ZS3ShBeBk6cuYa+/rMHldg4NicCobUNc+9QcnHqSev0Wp165FLDj94ECK6VRdnWF\nK4cH7txNqeFf8zAMg0CRn92O2pHzJkxh7fLKrPtHaqK8+/THzPxqDv2H9eW61y9lwPC+mC4Dt9fN\nLpN34PL/ndfsebSEsl6l9B7Sc70z6tBVPPbY1yBuUA6lzJ5tMArPqn8p7tFIya3p+1nLIJ6eE6vR\ntISW2gJ/EHIZUK9PMXRkmBFb1fDzlwW4PRamS1HSLcE/HljA0FEN4UjDgCEjwgQKkoSqmxr0XBK7\nTbXc8zfsvgIvvQb1YNT44axYtIrrj7ozb4mAeCTGl699y7AtN2LTccN56KfbCFeHcXvdbeqZb8h0\njd+CUVeFl7YBzNxpT1bsO1h9Al25mXXTHO+2KNrpzPQeGKO8d5yl8zw0No5en8XEw7JIVtSSrWAq\nH7wBxbVPzuXdF0rY5cC1KEvw+C1cGb7xyQy9ZDw+i1h9kVNTQ9/0A5D/B2LSyRPZYvfNmHLQjSmh\nlHww3S78BT5mfzeP79/7mcLyAsYduLU26o1Y7ytP2wKlkqgVO4G1vMkWH1L+BOIenX5MYiEq9CiE\n3wb1O3rhNJ18ZXG7KnN+9HHBIRuRqFs89Vn8abMw1zyZvnjalFC1gWEqfP7WfT8jIeGVx8s58MSV\njmsKyYSdu26Ytvf+3rQSnrilF6Eqg5Fb1zBoWISPXi2mYpWLtipGcrlNpr54ATcddw9r/qjIfUAT\nvH4PW+65OV+98R1W0sLldmEYBte9eRmbbL1xm8xxfSXfytMuYdgBVGI2avVxds46AioOhRc7dltS\nsa9Ra44H1TjfXdMUK4ljJaemgVC1wYf/V8yq392M2DLEZjtU57wRRiPCwlleeg+MUlDU+u/nH4vd\nLJjpq09VzBS/B7uT07IFHk7dbRjJRPvcsXsP6cmVL13Imdtc7Ch1mwm3141hGuxz0m68+sBbaceW\n9SrhqcX3tTrzZX2m80gKtBHiGgrd34P4d6CqwT0WMZrKmtqoikudtWk0KdQV9GiPPTOBAos9Dncu\nbW+KUlC52uS1J8t46ZFuPP6ls5Joc3/nZT0S/PeuopQc9EzHe7yK7n3iHHbGH4zevoZ+g6PM/tHP\nYzf1Yu5PrRezMt0mV718Ef6gl2Qi/17CLo+LM+8+np0P24HL97ve8YYQrokw6+u5DNtqqMMIXYtW\nGXYRuRHYF1v7dg5wrFKq49qj5EDEAM/YrPsoqwqSC7PukxP/GRB+FKjKueuGjDbobYNSkIgJ0/9X\nyu3n92eTsdXc9vKsrKJljV/n+jssnuNJ00XPRqDA4qhz/6h/GivvHWfMjlVccMhQZn6Xv/C9GBbK\nEnwBO3XYsoRTbz2GgcPtDkbF3YtYuTj7eoOI4PKajD94O166+3Vef/hdKlc5f68EIZlDS6ar0FqP\nfTpwsVIqISLXAxcDzavzX98QL62LJQqE/4VzvrxmQ6U9n0zsalfFiw+Ws//xKzh5ytKMC6dOc6ib\nW53EQeNjIyHhket6c/IVS0kmare7cveAbRxiMwzwBRQn/mMp5x2c3Rse8KcIhmFRU+liq10rOeC4\nlcz6IUBS9WHbQx+htGdJ/b6Vq6ozjuMLehm+zZ/Y5YgdePGO1/jo+c+Jhu2qYpfHheEysBKpRtx0\nmwzbcqOs8+sqtMqwK6XebPTyM+CQ1k2n4xHxoHwTITKd9CYc+aDQRr3z0NYLxBk14V1w/7uzmj1e\n47Hqfl4w00v3PnGWzPPy4NW9CNeY/PptgC/fKeSHzws4//aFtV50OtkalAwd7Vy1bbpNJh69M8de\nNZ5iJpPa1cyWIsDwY/RoMOprV1QQC2f+fj2/6hHcHjfvPPURS+f8Xm/UARKxhC0REPAQC8Xw+NyI\nYXDZ039zFP3qirRljP044L9tOF6HIUVXoZLLa5tiJ9CGuutSZ+TaymMPVQlBhwXROomD1q77mabd\neu7Hzwv46r0CvvuokNIeCW46ZwBW0r6AYWNC7HfMStxeBSnevrB0vocBGzsvaK5d6WwukvEkbz/5\nISfd9BeI+sFqegNwgXen+leLZy3jx49+xTDEMXfd5TZxe2zNhK+nz3CMp3v9HiadvDum20Vx9yJ2\nPWIcZb10T+I6chp2EXkLcEr2vlQpNa12n0uxLeB/soxzEnASwIABA1o02fZEJZegQi+AtQrxjkfK\nHoPkPFR8IUgCqh+DxBcdPU1NB1Fn/Fpt3DOMk2+HpnxwuWHUdtXM+CTIkef+QWFJgoev7U00bHuz\nD13dhw9eKmH8vmsxDMXSBV6WzvWw3R6VTDx8jeM8ImGDp+/IrIXicpt8//6vbLv7VVBxLvbTrkW9\nLEfB6axcuprL97+ehT8vtkMpGQqSRu3Y0LO4W98yXB6TRCzVuTIMg80njGKbvTOvmcWicT6d9iXL\n5i1n47GDGbPrqE6dMdOYnIZdKbVbtu0icgwwCdhVZcmdVErdD9wPdrpj86bZvqjIu6i1Z2N75nFU\n+AVwj0LKHsZwDUWpuN1Kr+JHQGfLdFXawrj7AqpdwzpK2WmoLhdsuk0NI7eu4aWHu5GIpe446/sA\ns773M+noVZx13RLHscEeP5mwjfrrTzlL1gIk4km8fg+Gf3eU62lUzSOQXASe7ZHgkYhRxmWTzmfe\nDwuzNsvw+NyccdcJ9a/3On5Xnrv1lRTDLiJ4A162nJhZ3fX3+cs5e4fLCFeHiYXjeHxu+g3rw83v\nTumQVnXrmlbdvkRkT+ACYD+lNsz8QKViqIpzsXVk6ipLQ3YYJjzNLlRasQtUXoQOyWhaa5RbU01a\nh2XZxjvTXOoWPseOr8bnV4wdX13fqKMxXr/F7oc6p2I2foKY9kg3nrq9J9mSCmLhGMO2thdWxT0C\no+RGjPKnMQrPQowy5v+0iCW/LXM06m6vG7fXxabjNuG2j65mwCZ967f1GtSDK547j6JuhfgLfXgD\nHvr+qTc3vzclazz9+r/eydo/1hKuipBMJAlXR5j/4yIev/J/GY/pTLT2ueQuoBCYLiLfici9bTCn\ndUt8RoYNYVR4GmrtWXYDDlWDrfoI4AKj3zqaoEbTgFKweK6HNSudjZqVtGV7oUErfuPRYcbvuwZf\noMEx8QWSbLdHJcPG5PbHQlW570begIffvpyTcfva5RWOnYcANh47mNs/voai8kKu/PPNXH7A9cz6\nZm799q322Jxnlj3ALe9dyT1f3cDDP99G/2F9HccCqKkM8etns9JCPfFonLee+CDntXQGWpsV0wkq\nATxkFi9SkJhDevVpAqzF7TstjSYD/Tdy7pykLJg/08uAodG0MM25ty5m+z0refOZUrCE3Q5dw/Z7\nVuT1BDL92cwhmDoM08AXzCwVvPEWQ0jE0ltYeXweBo7sz9/G/4NYOIZS8Mf85Xzz1vdc88olbLbT\nSABM02TomMG5JwtZW1Y11W7vrHSNlYRsuEfVNrVugvjBtw/rulmvRpONpl2eUmyY2BkxYjovzm6/\nZyVTHl7AlH/PZ9zeFc7aMUn49Vs/v34TqBUG8/HHotz+X6DQzybbZNZpCRYFOHrqYSnG3+11U9Kj\niF8/m0U0FEvpIhUNxbjnnEdyntfxXMVBNh47JE1O1+VxscvhrWvWs6HQZSQFMiFiQOl9qNV/WQjB\n2QAAGw1JREFUBRXDjqMb4DsA/IdB6AFIau9c03FkyqJpigj48y8MBSAaFp6+owfTny0jGjGIhu2m\n12KA26O47N/96dYnxorFqxxOaBt0l8fFNa9ckjPj5NDz9mPwqAE8f9srrF1ewbb7bsFBZ+/Dwd2P\nc9x/3g8trwC/4NEzOHvcZcQicSLVEfwFPnoM6MZfpx7a4jE3JLq8YQfAWm2LgtWHZBSY3TEMA1V8\nC2rNMaAS5C5YMtCiYZqWkinjpr0qXpWCiw4fwuzvA8Si6UY5DFx++BKO++fxPHTxf4iGGj7/Hr+H\nCUeMY9wBW7PFxM3ylszdao/N2WqPzVPeKywNOlahFpYGm3dBjej3pz48Me8e3n/mU5bN/YM/bTGE\nbSdt0WUKmLp8KEZZNai1Z2JnxcSw0/HjUH0/KjYD8WwORdeA+MgeljFBWv5B1HRtkkmoqZScnZXy\noXKt8O2HgZxjff9pkLk/+R2Neh12Japw2m3HUtqzGDGE0p7FnHbbMZz7wKlss88WrdZBP/hv++IN\npMbnvQEvB50zqVXj+oM+9jx2F4696nB2OGDrLmPUQXvsEPsQ5/tbzM5nFzdUXIxzW71GePcCwhB9\nu+3nqOn01FSYHL3NJlx41wK22Kkaj69l4ygFp+0+DEPggfd/xZslZfu3GQES8eyPA7GoQcXKSv46\n5TD2On5XEvEELrerTdvBHX7RAVSurOTle6fjcpsk4gkmnbQbky8+sM3O0dXQhl2lr9TbWEAcVfMA\nmUMwArjAdxBGyVWo+EyUNuyaFhAsTiIiXHPKYM7852J2OWAtlrLb3DXHhlauMVmxxIvHZ2F/PjO7\n7T37xXG5IZGlMZgv4GbzXTYFbM+9rtQf7GY0RN/B/g5MRMzMlanZMAyDU245hqOnHsbyhSvpMaAb\ngcLOX0TUnnT5UAzeHZyNuwQQ396QmIdz3NwDvoOR8mdto26FUJVT8jihzrLpCjQ3pCKA158kHjW4\n5e8DOHTUSE7aeRiX/3UQsUj+461dYftqsYjB60+VEQll/rxtO7ECf0ESw2j8+W44kS/gYbOdRzF6\n/Ii0Y63qe1Er90FV3Yiquga1YiesKodewc0gUOhn0Mj+2qi3AV3esItRCkX/ALzYDzAC+MG7B3i2\nB/dYMj3YSNEFiNv+0Kuqa7MUO9UdUGiHbLz6EbOz09xIhVIQjTTEgMM1Jn8s8vDFW0VcccxAkpke\nLJuM8dIj5fWv75vSlzeeLiMaFqLh9Am5PYpbXpjNsDFhXG4Ll8eiR78Yf9o8zKhxfTjz7hOZ+sIF\naWEXFZ8J1fdgF+zFsTPJklDzL6yKy5p34Zp2ocu0xsuFSsxHhV8CFUJ8u4F7C0QElVyKWrlvbeVp\nnWfjh8BhGEWX2McqhfpjFNmzZnwYvb6394+8jVp7OjqDRtOYeb/4uOrEgaxY6kEp6DckylnXLyZQ\nmKD/0FhecgTXnd6fj14pIR5r8NkKixMc8fffOehEh5TFWirXmCgLisuTIEGkaCri389xX6vqFqi5\nH+fPrwspfx5xb5J7sppmo1vjNRNxDUIKz0p/3+wD5f9DVd0EsS/AKIbAcUhgMkrFILkcZRTToDOT\nAd9eDT97d7CLolTmRgOarsfg4REe+nAmK5a4MUxFt955uOlNOPO6JaxY4mHWD35Ml92Zacz4KvY7\nxtmo1/WtLSptpIOkYuDZOstZkmR2SpIQfRe0Ye9QtGHPA3ENRkrvTnnPqnkYqu8ELLuWW8pAOX15\nBIyeSOEFDe+ID0rvRa05ufZJQNPZyVcVUgR69MvhJGQhWGhx84uLmf+r3ZR60CYReg+M4bSQGosK\nLlfqe0qBuIchppNSd+0cfXvZ6o043XhctV3INB1Jl4ixK2Whkr+jrLYxolZoGlTdbhtlFQaitd63\nC6jLGjDs18EzkG6vI2Z5yhji2RqKrgK6Tm5tV6S+9H+dRt2iDNokwnZ7VNYadSBwfG1KrgckgKKA\nitUFKS3woPbmk5iFsjKLg4l7U/AfnmGrAb692+IiNK2g03vsVvgNqJoKVjVgoXx7IEVXIUYza68b\nU3MPTdt/2QtJPvBPhuRv4N4MCRyRNQVMrOUonSXTqanTdWlqQNc5VhVG6e0oqwKsNSDFdJeJGbIh\nDbsaO8t3xCi+HMvsA9U32/tjAgqKrsnq7WvWDZ3asKvYN1BxPinFRZE3USqMlN7TsjET8yG5LMPW\nJFJ4OmIU5TeYawSIJ0suvaYz0F6SAM0iOh24CjGKsSJvQeUUnEMp2EIxeeSkGwUnoAKHQvQDQIF3\nPGIUt+GkNS2lcxv26vtIrxiNQvQDVHJ5swoqbOmB0yH2NRm/EEapndKYL55twLUxxH9EN/HQtCu1\nCqYqMRsqp9LQW6Dpfn4InoaIQ2cOp92NIvC3rvRf0/Z07hh7cpHz++IB649mDaUqp0DsK+wvhJMR\n9kHhxc0qtRYRu7eqObBZc9Fomk3wJABU6DkyZnAZ3aFwChI8wXm7ZoOhcxt2z5Y4PpSoBJh5ivZj\nt88j8hrOeeoGuMcipf/C8O/T7CmqxBJIzs29o6ZL06pyE6MfEqiVq1WVODomEkAKz8UIHNimOjCa\njqFTh2Kk4GRU5JX04qKCExGjIP+BVF3HdaeTBDDKn85+uFWNSs6HyBtg1SC+3cGzrf0FCj2R/zw0\nXZaW21o3FE1BVV2PEj+4RoK8Ak1bFKuEXWmt6RR0bsNu9oXy51HVt0HsMzDKkeCJ4HOuqMs4jlGA\nMgc4eNZG1i+Dis9CVVwIiZ9pfGNQkefAszMqcJSdfaDRtBeuMVAvS20CLjD7gbW01rgL4IOCE3Q2\nSydCSwrkiYp9iVp9AnY4JomdD+xDyp9DXOkxcmVVoFbsCqqKzAp7fur13zWaJuRX1JRFwVG6gVrp\nsMELhf+A2Pt2CCZwKOLZqnWT1awTtKRAGyOeraDbi6iaf0NiNnjGIIGjM2bWqPCLtSGcbDfOprnw\nmi6Ha1P7qS/0JEhtJZPZG/zHk1h9GW5P+ufHNvgu8IwHszsYvaHmXmynw8Ju0O7NUAkNIIjhTaum\n1nQetGFvBuIajBRPzW/nxDxyNudIwQVGTxAXJJeQMaVS07lI/AhWFRRdAWZ/xCwCcyMgTnL5P9IM\nu1JgJQWzx7MYnpEN7/t2RYX+C9ZK8IyBqpvJ7FTE0F/9zk3nzorpQMSzWX3ucH6YEDwBo/t08E1C\nf/G6ENYCqDwf1hyBCr8JKJQVw+MzU7Jh6n5e8Pv1KUYdbH0Xo/hyjNI7ENfGduevzCcE705tfhma\n9Qdt2FuIin6KterPWH+MxVp5ACr6XuoOvr3BKCN/Ax2FquuxVh0JBWeD2avRjSFA5j+VDyhEN/Do\nDFhQcxtqxSRYezyGEU+JsYuAwmTIJjlqMFyDa5uzZ8Do07ysMM0GhzbsLUBFP7aVGeMzbPGvxM+o\nNWdhhV+r30fEi5T/D/yHgJTa6o85f90Re8zQo7ZwWNFVEDgeKboMvLtlOD4CZFug1WxwWHMg/p3j\nJkOSkMhe9yBmX/DujLPAnBspurDVU9Ss32jD3gJU1XWkx88jUHV9yjtilGEUX4nR83Ok/FnsRa1c\nRCH8AiIexL8vRtGFSOAQpPAcEB+pnrkb7al3RhSZb9QC7tE5R5CSW8B/JA1PjAIEoPBCpHFvAE2n\nRAdyW0Imj8lahlJxxCm+afYDowSs3/M4QXqFq7iGQtlTqKqbbW/O6Gar9Kk1zZu7ZgPHg/j3z7mX\niAcpvhSKL8WyQohaC0Z358+mptOhPfaWkEk8TIrJ2B9VBCm+kdwetoDHeWFL3MMxyh7E6PkVFN9Q\nmyPfFgiYw/OYmyYVD+3jGxl2hSi+Ju+7oOyJZsfHDSOAmH20Ue9CtIlhF5FzRUSJSLe2GG+9J3gG\ndnFRY/xQcHJWnQ3xbpPRaNfuAUYZUnRx1tMrFYOK88icEun0Bc4iCC7FSNnDUHgB+l6fL3VhsNam\npTb9vPjB6IGU3oeU3gnurcDsD/5DkG5vYng2a+X5NF2BVrsbItIfmAgsbP10NgyMwMFYKgTVd9hl\n2eKF4MlI4Licx0rRRahVXzq0xAtAwalI4C85PTIVej6LJrwLAqeBd1OofgCsGvDvDfGfIfpKhgHt\nG4oRPB4r8jbEN6yq4HWPD7zjbJkKlUH+Ni+8YPaB0ieQ2Huo+Pfg2tiuBBUfmD0QnZaoaQFt8Rx5\nK3ABMK0NxtpgMIJHoQJH2OEQKUQkvxY54hpS2xz7Nlvb3SiCwDEYwUytxkBZq1E1D0LkPTuFUq0l\no542PqTgCMQoTclVtlafkWVWVZD4AaUs3WDbCe++EHsXSNqVof6DIXgMrGyBDrlrMzDL7fUR70Qk\ncBhYv6NCj9ev3ajwc1ByC+LaqE0vQ9N1aJVhF5H9gSVKqRldUepTxAQpyWtfpRTEv4HkAnBtglF6\nZ37HWWtQK/ezDQHxHP04TCi5wTbqTcnaClChYj9A1Q1omQMHXP2Rks/AWgFSWt9W0fJOgOhrOQ5u\njA8pOB7x7Vn/jrJCqFWTa+V0azNhEr+iVh0BPd5DpGnIT6PJTU7DLiJvAU6yb5cCl2CHYXIiIicB\nJwEMGDCgGVPseFTsa1v7hSTimwSe7ZqlWa2stajVR0NyYd0bKM8WSOm9SI6O7qrmcbDWkpdQmNEd\n8U5w3hb7Mvux0eloo56BxEK7o5DZN+VtKbkJ9cdb5CfiZoJvd/A2+bpEXq8tJmqc3qiAqC3z7D+g\ndXPXdElyGnal1G5O74vIKGAwUOet9wO+EZGtlVJpOX1KqfuB+8FWd2zNpNclVuWNEH4CVARQqMir\n4JuEFF+d9xiq4h+QmEOKAYh9haq+Cyk8N/vB0Q9xbvDRlCKk9AFE7MVPFf8ZVf0vW7DMNRysJZkP\nDZ4GNY/kcY7OSBZ1xDqi/4dV2QMpPD8l5CbiRpkjIDkjy8GGLdJV/E8M77bpm62lON5QVSTLOopG\nk50Wp0AopX5QSvVQSg1SSg0CFgNjnYz6hopKzIXQY6DC1H/5VQjCL6Ni2b7MjcZQMYi+TbpXF4XQ\ns7kHMHuROw3RDYVnIe5h9jmjn6FWHQ7RNyE5J/OiKQABJHg00HQxt5m4NgH3Dq0bY53jBvc48ioc\nCz2JqnYIn1kZ2i9iQtEtSLdXMHq862zUwS42cgq3iC+vQiSNxgmd25aNuu7r6RtQ0XfzHCSZYQx7\nnFxI8Fgge7gG8SBmv/qXqnIqdmVs3Xnr/m96g/BCwSm1TwU5zpEVN1J8Dfh2IT0NtIUELwT31m0z\nliN+u8enuMivkXgEQo/aC8y1WDUPZSkQcyHerdIWQJW1BhV9HxX/wV538YyrVXNs/Pv32k3OPds1\n85o0Gps2M+y1nruTqv+Gi/hwzv82EQnmN4T4wTXCcQy8u+Q+3jMWiqaS1WuXAvCOB2qfEJLzsozo\nBSkEPODf1+4ohQF5ZvU44hlnP9X49rdTPx3naoK5sX1egtjFN5nO6UG8o5Hia8lPhiEfBIy+4N3P\n1j8X0167iH1Ifoad2ic3OyymVBSq7yTjTdvsi5g9U96yqu9CLR+PWvs31OqjUCv3Aut3pOxxCJ5g\nz8/oB8ETkbLH6sNqGk1z0ZIC2fBNhMprHTYYdm54nkjxtajVk2sXyaLY3mIQKbwgr+ONwIFY1iqo\nvp00L9/ogZQ/bTdeAOw/qQdHLXijmy1MllwE5mDE7A6A8o4HladxS0Mg9h5qzefg2RnKnoaqK2oX\naw07pa94CmLY2UNW5U0QehDbIDoZdgNcQ1DKgOpbwLURJBbS6lARCqw/7LWG5LKWpXUavaj3rJNL\ns+woSMnNqWePvAs1DwDRhtz35HzUmpMxur2MFJ4NhWc3f04ajQPasGdBjDIouQ219m9Q5z2pBBRd\nbSvo5TuOexh0m44KP2MvZro3Q/wHNas0XILHo6w1dsxf3HZ3Jt9eSPG19aXiKrEIVXkpziEePwSO\nQ8zedoeelOssQBXfDBV1C7kWILZCYOKXhmweRxqtPcTeQ5L7IWWPo1QCMFK8Tqv6EQjd3+jYuqpN\ng3pD7xlvK2GuOQbbO1aAD4z+9pNJciYZG4vnJAHxH2jZg6pA8LSGbCijm/1ZcMK1OeJO1UtX9Ws1\njbEgsQCVmKNz1jVtijbsORDfBOjxif3IrpLg3RExipo/jlmOFJza8nmIIEXnowpOheRiMHsjRnH9\ndmWFUKsPrc13dwgP+CbWxuudMfy7o7zvQeRN2wB5d0JcQ7AqLofwYvIypiqEiryE+CYg4kIlFmHV\nPGhLEZtDIPp6prND0XUQ+wIiL5C+0BwBazn4d4NoZZYMH9OWN/aOh+r7wHK6IWWTVuhul++rECRn\nkRqiEQg9gAr82f5bGIUo/74QfoXUpyOf7X03xVqb4Zwuu4OSRtOGaMOeB2IEoVFRSUciRgEYm6Rv\niLwGVpiMBji5OGfMVowyCKRWwErgz7U5/Pm2+at9eojPsm80KgokIPFr5rmRhOi7EH2HzDnhUQg/\nRvYMIdNOSXQNwEourE3hbJoqamUYwwcFZ2AEJ2NV3Qg1s9OPs1bacgu1jZ+laCoKN4RfsHcxCqDw\nEsS7vcPwu0P1bNKfphS4h2e5Jo2m+ejVmU6CSswFQpl3iH+LytZVJwPiHlUrDua1QyESBEpwzn7x\nI/6D7flUXWd7vvXhlhwef/x7chdIWWQX3fLaHje12URGESmCaOKHgjOh6Ersxdu6j7+/VqPlIPtl\nYpHzeVQEFfu6YTjxYBRfifT8Eun+DtL9Ywz/vo4zk8DRtamrdYqNhv1z4RU5i9Q0muaiPfZOgriH\noyRQa0ydMHG6j6vYDFTVjXYs3eyNFJyRUvIOYASPtMMOsS9sw+7ZGmJfoNaeaguI1YUsAkcgdfna\n8a/Iu6uTZzwkfs51hXmMV4PtEfvsp4/yaaia++20VaMcCR6H+Ox6O+XepLb58yrEt6u9XiG1GTie\n7SD6Puk3miRU34JlVWA06kJkC3Y1ldhtMnujAMpfRIWfheh7YPREgkfaN06Npo0RpdZ9EeiWW26p\nvvpKKwi2JUrF7PS55BLSvWMX+PbCaJqpEf8etepIUsMsfii8ECN4RO5zWlW2FIFVY689uAbVb7OW\n72hnoTjior5LkG8SUnwjqvKy2pBGU09ZAA+Yg2sXTrN8Xo1uSPePmyX34ISt3zLJXstwRJDShxDv\nuFadR6NpLiLytVJqy1z76VBMJ0HEY7ff8+1HwwKhCfjAtQlSdEXaMarqFtJj52GovhWVR/qjGIV2\ndk/wqBSjDkDgGNIbRXjBf7jdz7XsCaTHVxglN9mLkQVn2R2m6gt1DPvngnORHp8gJdeQvYjKBwV/\na7VRt68rAGX/y7KHstU2NZr1FB2K6USIUYaU3ADcgIr/DInfbE/XPdrZ4MUzhD9UBKzVUJvn3qK5\nBI9FJRdB+H920ZKK2Zk2RZfWxpRTheDE7AndXkGFnrJz4M2BSPBoW+YYwBiF8h0EkSebnsluOxg8\nGyOwX4vnmzZ/oxSFn4xx/0QmKQGNpuPRhr2TIu4R4HaqeG2E2RcSTml4BjRKpWzR+cVAiqegCs+y\ndcbNfojpJBLa6BijFCk4zXGbSi6FyHMOWzxI2X9yjt1cRAQVmAyhh513sFaiVDJvHX6NZl2iQzFd\nGCk4k/RwiQ8CkxsWElt7DqMM8WzZesMbeY2M8fXIG60bOwNSeG4WvX2x9fU1mvUQbdi7MOKbAEVT\nQEqxZQj8EDgSKTy/g2fmgIrjrOlikZ8eevMRcWdWWBQjSwaSRtOx6FBMF8cIHITyHwCqAqRg/e1k\n790Vqu8h3bibkKm5SBsg/n1QsS9Ji7WrBLhzJidoNB2C9tg1djzcKF1/jTog7o3tPqP1hUW1BT7B\nExoWWNsD3yRwjwSpay1Ye96iK+yK5Ayo5HKsiilYy3fBWnkgKvwSHZFarOmaaI9ds8FgFP4d5ZuI\nCr8KIohvH3uRuB0RcUPZYxCdjoq8BVKCBA6tb2rihLJWo1btD1YFkABrid1FKz4TKVoPw1yaToc2\n7JoNCnFvirg3XbfnFLvAS3x75bW/3ae2itRiqzCEHkMVnODcbFyjaUN0KEajaWtin+LYp1bcEP9l\nnU9H0/XQhl2jaWvM/jh+tVQCmnRV0mjaA23YNZo2xta9b1oH4AL3cN1QQ7NO0IZdo2ljxD0Cim+u\nrQ/wAx7wbIuU3tvRU9N0EfTiqUbTDhj+3VG+CbZCpFFoywhrNOsIbdg1mnZCxATXwI6ehqYLokMx\nGo1G08nQhl2j0Wg6GdqwazQaTSdDG3aNRqPpZGjDrtFoNJ2MDmlmLSIrgAXr/MTtTzdgZUdPYh2h\nr7Vzoq91/WagUipnz8oOMeydFRH5Kp8O4p0Bfa2dE32tnQMditFoNJpOhjbsGo1G08nQhr1tub+j\nJ7AO0dfaOdHX2gnQMXaNRqPpZGiPXaPRaDoZ2rC3AyJyrogoEenW0XNpL0TkRhH5VUS+F5EXRKSk\no+fU1ojIniIyU0Rmi8hFHT2f9kJE+ovIuyLys4j8JCJnd/Sc2hsRMUXkWxH5v46eS3ugDXsbIyL9\ngYnAwo6eSzszHdhUKTUa+A24uIPn06aIiAncDewFjAAmi0j7ds7uOBLAuUqpEcC2wOmd+FrrOBvo\ntH0KtWFve24FLgA69eKFUupNpVRdt+bPgH4dOZ92YGtgtlJqrlIqBjwN7N/Bc2oXlFLLlFLf1P5c\nhW3w+nbsrNoPEekH7AM82NFzaS+0YW9DRGR/YIlSakZHz2UdcxzwWkdPoo3pCyxq9HoxndjY1SEi\ng4AxwOcdO5N25TZs58vq6Im0F7rRRjMRkbeAXg6bLgUuwQ7DdAqyXatSalrtPpdiP8r/Z13OTdP2\niEgB8BxwjlKqsqPn0x6IyCRguVLqaxHZuaPn015ow95MlFK7Ob0vIqOAwcAMEQE7NPGNiGytlPp9\nHU6xzch0rXWIyDHAJGBX1fnyZpcA/Ru97lf7XqdERNzYRv0/SqnnO3o+7cgOwH4isjfgA4pE5Aml\n1JEdPK82ReextxMiMh/YUim1oYkM5YWI7AncAuyklFrR0fNpa0TEhb0ovCu2Qf8SOEIp9VOHTqwd\nENsTeRRYrZQ6p6Pns66o9djPU0pN6ui5tDU6xq5pKXcBhcB0EflORO7t6Am1JbULw2cAb2AvJj7T\nGY16LTsARwETav+W39V6tJoNFO2xazQaTSdDe+wajUbTydCGXaPRaDoZ2rBrNBpNJ0Mbdo1Go+lk\naMOu0Wg0nQxt2DUajaaToQ27RqPRdDK0YddoNJpOxv8DJPAo7hAXs50AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa3e06bff28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_train[:,0], X_train[:,1], c=Y_train)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now we'll train a simple logistic regression model to predict Y. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data_ctx = mx.cpu()\n",
    "model_ctx = mx.cpu()\n",
    "\n",
    "net = gluon.nn.Dense(2)\n",
    "net.collect_params().initialize(mx.init.Normal(sigma=1.), ctx=model_ctx)\n",
    "\n",
    "ce_loss = gluon.loss.SoftmaxCrossEntropyLoss()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "trainer = gluon.Trainer(net.collect_params(), 'sgd', {'learning_rate': 0.01})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "batch_size = 1024\n",
    "\n",
    "train_data = gluon.data.DataLoader(gluon.data.ArrayDataset(nd.array(X_train), nd.array(Y_train)),\n",
    "                                      batch_size=batch_size, shuffle=True)\n",
    "\n",
    "valid_data = gluon.data.DataLoader(gluon.data.ArrayDataset(nd.array(X_valid), nd.array(Y_valid)),\n",
    "                                      batch_size=batch_size, shuffle=True)\n",
    "\n",
    "test_data = gluon.data.DataLoader(gluon.data.ArrayDataset(nd.array(X_test), nd.array(Y_test)),\n",
    "                                      batch_size=batch_size, shuffle=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0, loss: 51128.0938721\n",
      "Epoch 1, loss: 30212.545105\n",
      "Epoch 2, loss: 24620.7541046\n",
      "Epoch 3, loss: 22134.5193329\n",
      "Epoch 4, loss: 20752.161499\n",
      "Epoch 5, loss: 19884.4256744\n",
      "Epoch 6, loss: 19297.2088623\n",
      "Epoch 7, loss: 18878.3023376\n",
      "Epoch 8, loss: 18567.8334503\n",
      "Epoch 9, loss: 18330.8624115\n",
      "Epoch 10, loss: 18145.8636932\n",
      "Epoch 11, loss: 17998.6114502\n",
      "Epoch 12, loss: 17879.6465607\n",
      "Epoch 13, loss: 17782.2668304\n",
      "Epoch 14, loss: 17701.6795502\n",
      "Epoch 15, loss: 17634.3476257\n",
      "Epoch 16, loss: 17577.6451263\n",
      "Epoch 17, loss: 17529.5833435\n",
      "Epoch 18, loss: 17488.5479431\n",
      "Epoch 19, loss: 17453.2896423\n",
      "Epoch 20, loss: 17422.8839874\n",
      "Epoch 21, loss: 17396.6068878\n",
      "Epoch 22, loss: 17373.7073212\n",
      "Epoch 23, loss: 17353.7559814\n",
      "Epoch 24, loss: 17336.2953949\n",
      "Epoch 25, loss: 17320.9209137\n",
      "Epoch 26, loss: 17307.3816528\n",
      "Epoch 27, loss: 17295.4575653\n",
      "Epoch 28, loss: 17284.9480591\n",
      "Epoch 29, loss: 17275.5889587\n"
     ]
    }
   ],
   "source": [
    "epochs = 30\n",
    "loss_sequence = []\n",
    "\n",
    "for e in range(epochs):\n",
    "    cumulative_loss = 0\n",
    "    for i, (data, label) in enumerate(train_data):\n",
    "        data = data.as_in_context(model_ctx)\n",
    "        label = label.as_in_context(model_ctx)\n",
    "        with autograd.record():\n",
    "            output = net(data)\n",
    "            loss = ce_loss(output, label)\n",
    "        loss.backward()\n",
    "        trainer.step(batch_size)\n",
    "        cumulative_loss += nd.sum(loss).asscalar()\n",
    "    print(\"Epoch %s, loss: %s\" % (e, cumulative_loss ))\n",
    "    loss_sequence.append(cumulative_loss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now let's go through the valdiation set and put together the response matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def softmax_to_onehot(preds):\n",
    "    onehots = np.zeros_like(preds)\n",
    "    argmaxes = np.argmax(preds, axis=1)\n",
    "    onehots[np.arange(preds.shape[0]), argmaxes] = 1\n",
    "    return onehots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "response_matrix = nd.zeros((2,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "valid_preds = nd.softmax(net(nd.array(X_valid)), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "valid_onehots = nd.array(softmax_to_onehot(valid_preds.asnumpy()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "[ 499.37445068  500.62554932]\n",
       "<NDArray 2 @cpu(0)>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nd.sum(valid_preds, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "[ 501.  499.]\n",
       "<NDArray 2 @cpu(0)>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nd.sum(valid_onehots, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "test_preds = nd.softmax(net(nd.array(X_test)), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "test_onehots =  nd.array(softmax_to_onehot(test_preds.asnumpy()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# calculating the response using the onehots\n",
    "\n",
    "test_response = nd.sum(test_onehots, axis=0) / num_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "[ 0.245  0.755]\n",
       "<NDArray 2 @cpu(0)>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_response"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Building the reponse matrix\n",
    "\n",
    "Now we will build the response matric based on the classifier's output on the validation set. \n",
    "We will use the 0-1 one-hot responses, not the softmax outputs here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "YV = nd.array(Y_valid)\n",
    "valid_counts = nd.zeros(num_classes)\n",
    "\n",
    "for i in range(num_valid):\n",
    "    response_matrix[:,int(Y_valid[i])] += valid_onehots[i] \n",
    "    valid_counts[int(Y_valid[i])] += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for j in range(num_classes):\n",
    "    if valid_counts[j] > 0:\n",
    "        response_matrix[:,j] /= valid_counts[j]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "[[ 0.91566265  0.08964144]\n",
       " [ 0.08433735  0.91035855]]\n",
       "<NDArray 2x2 @cpu(0)>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "response_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Invert the response matrix and estimate the test set marginal P(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "R_inv = np.linalg.inv(response_matrix.asnumpy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.18808059,  0.81191933], dtype=float32)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_inv.dot(test_response.asnumpy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Scratch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "z = nd.array([[.1,.4,.5],\n",
    "    [.4,.35,.25]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def softmax_to_onehot(preds):\n",
    "    onehots = np.zeros_like(preds)\n",
    "    argmaxes = np.argmax(preds, axis=1)\n",
    "    onehots[np.arange(2), argmaxes] = 1\n",
    "    return onehots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  1.],\n",
       "       [ 1.,  0.,  0.]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = np.array([[.1,.4,.5],\n",
    "    [.4,.35,.25]])\n",
    "\n",
    "softmax_to_onehot(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "ename": "MXNetError",
     "evalue": "Required parameter depth of int is not presented, in operator one_hot(name=\"\")",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mMXNetError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-30-9239e8cfd29e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m nd.one_hot(nd.argmax(nd.array([[.1,.4,.5],\n\u001b[0;32m----> 2\u001b[0;31m     [.4,.35,.25]]), axis=1))\n\u001b[0m",
      "\u001b[0;32m/usr/local/lib/python3.4/dist-packages/mxnet/ndarray/register.py\u001b[0m in \u001b[0;36mone_hot\u001b[0;34m(indices, depth, on_value, off_value, dtype, out, name, **kwargs)\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.4/dist-packages/mxnet/_ctypes/ndarray.py\u001b[0m in \u001b[0;36m_imperative_invoke\u001b[0;34m(handle, ndargs, keys, vals, out)\u001b[0m\n\u001b[1;32m     90\u001b[0m         \u001b[0mc_array\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mctypes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mc_char_p\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mc_str\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mkey\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mkeys\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     91\u001b[0m         \u001b[0mc_array\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mctypes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mc_char_p\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mc_str\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mval\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mval\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mvals\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 92\u001b[0;31m         ctypes.byref(out_stypes)))\n\u001b[0m\u001b[1;32m     93\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     94\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0moriginal_output\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.4/dist-packages/mxnet/base.py\u001b[0m in \u001b[0;36mcheck_call\u001b[0;34m(ret)\u001b[0m\n\u001b[1;32m    144\u001b[0m     \"\"\"\n\u001b[1;32m    145\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mret\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 146\u001b[0;31m         \u001b[0;32mraise\u001b[0m \u001b[0mMXNetError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpy_str\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_LIB\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mMXGetLastError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    147\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    148\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0msys\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mversion_info\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mMXNetError\u001b[0m: Required parameter depth of int is not presented, in operator one_hot(name=\"\")"
     ]
    }
   ],
   "source": [
    "nd.one_hot(nd.argmax(nd.array([[.1,.4,.5],\n",
    "    [.4,.35,.25]]), axis=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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