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@asnelt
Last active June 8, 2017 16:59
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Demonstration of Python package mixedvines
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Test of the mixed vine."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from scipy.stats import norm, gamma, poisson\n",
"import numpy as np\n",
"from mixedvines.copula import Copula, IndependenceCopula, GaussianCopula, ClaytonCopula, FrankCopula\n",
"from mixedvines.mixedvine import MixedVine\n",
"import matplotlib.pyplot as plt\n",
"import itertools\n",
"\n",
"# Define a function for visualizing 2d marginals and samples\n",
"def show_2d_marginals(pdf, samples, bnds):\n",
" comb = list(itertools.combinations(range(samples.shape[1]), 2))\n",
" for i, cmb in enumerate(comb):\n",
" # Sum over all axes not in cmb\n",
" cmb_inv = tuple(set(range(samples.shape[1])) - set(cmb))\n",
" margin = np.sum(pdf, axis=cmb_inv).T\n",
" plt.subplot(2, len(comb), i + 1)\n",
" plt.imshow(margin, aspect='auto', interpolation='none', cmap='hot',\n",
" origin='lower', extent=[bnds[cmb[0]][0], bnds[cmb[0]][1],\n",
" bnds[cmb[1]][0], bnds[cmb[1]][1]])\n",
" plt.ylabel('$x_' + str(cmb[1]) + '$')\n",
" plt.subplot(2, len(comb), len(comb) + i + 1)\n",
" plt.scatter(samples[:, cmb[0]], samples[:, cmb[1]], s=1)\n",
" plt.xlim(bnds[cmb[0]][0], bnds[cmb[0]][1])\n",
" plt.ylim(bnds[cmb[1]][0], bnds[cmb[1]][1])\n",
" plt.xlabel('$x_' + str(cmb[0]) + '$')\n",
" plt.ylabel('$x_' + str(cmb[1]) + '$')\n",
" plt.tight_layout()\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Manually construct mixed vine\n",
"dim = 3 # Dimension\n",
"vine = MixedVine(dim)\n",
"\n",
"# Specify marginals\n",
"vine.set_marginal(0, norm(0, 1))\n",
"vine.set_marginal(1, poisson(5))\n",
"vine.set_marginal(2, gamma(2, 0, 4))\n",
"# Specify pair copulas\n",
"vine.set_copula(1, 0, GaussianCopula(0.5))\n",
"vine.set_copula(1, 1, FrankCopula(4))\n",
"vine.set_copula(2, 0, ClaytonCopula(5))"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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ykRVl7baCKu4bRdYmzL4iFx30i5IQrJ0SKgss7uN2XxNWpKrM31WB7M7kU/W/r3PPr1Nm\nUq8xF02O44yMOkHcReXrnmuTUMaj3mxdIR1BbKGyLxixYEq5/gJ2gt6UaEoFhIfyYb1K4FvrUeo3\n+QuC4wwXF02O44yMqqSNZftiK0mcEbwslqnIomotS7Nk2bPruudi91cd0RIEkg3ettbSmURZ+1s8\nrslZLtM88q0JXDQ5jjN0qkz1S7UyFbnnymKZYqEUu+Csey6IKGuRigPBg1Cy+ZmsBYlE2bBuRVB8\nTurhNmhckzNdNOE2m1S3WlO04u8jIqeLyKdE5C4ROSgi5yTK/JGI3C0iu0TkcyJy4jja6jjO4NSZ\nGqRsX5GVKXbFxVghZMumhNIc/RanuejYHNlb5oro3LBvNjqeyvs0kziWiqFaDlbUVf3dne4wU2Op\ng1QsTjmtEE3AGrIpUl5NIhxARN4IvAZ4JXAqsBO4WkQGmWfPcZwJoszKlIplsg8WG6NkP+OHT1HK\nASt2pOBc6BdBVVaAugMwYhehP+ycQagSXrEVNrU0JeC6SCvcc6r6WbK094hIqv+/Dnirqn46L/Mb\nZLNXPx/46Kja6TjO4AwiFlLli9IMlE0LEscylY2IC2WCtWguUdaeU9T+MH1JKL/PlLGB3/HvsqPn\nrIsuFd9UdxoVZzqZZLHSFlr/NxaRHweOAb4Q9qnqNuB64KnjapfjOKMltq7Y9ZS4iQO+i96m5xL7\nYjeddc/NR4stG4TXTH6syBUXi7jUp6VMtDnOILgVaXm0wtJUwTFkLrv7ov335cccx2kp47IyFbka\noF/kxOv2k6gO+8CwI+espSkmNWIPeiPlQpqBGbMvHkVXlnPJg8EdiweCD58uiKYiKmcr2MdiX38w\nww+TMhO+bUf4nInWU64Bux7f4KH3tjwfHY/Xic5N1V/0GwI2wWScsDJs7zfb+8znflPHvuhzf3Ru\nqHe/qXchsW7buxvYS+/CUDwj8iSQSmYZBzzD4limqr4Y97/Zgn1xQHddDprP4H6z26E9Lnwcpxt0\nQTTdS3YPPJp+a9NRwNfLTgzmcWd6WJkvNqv4AbKRA85oqep7qeSMdc63+62YmmVxLFMctA3plwb7\nsrGC/peRWEjF7SqLIYrjlez+YGVaSKynJvm1+4qSXNq0ByG+yadTmR7qWJoGtf4u9XsmldZrClW9\nlUw4nRn2icg64DTgunG1y3GccqpGdKVGv6W2U6PP4tiLurFM1rJqY5WsFXeetJU2tcTHU+fa77Tt\nT1l3U8Hq8W8us3iVuS0dB6pjmpxyWmFpEpE1wIn07pMniMhJwBZVvRN4F/AmEfkecBvwVuCHwJVj\naK7jOBUsx8pU5lJLxRXFdaZimawrO3U8JXagZ3kKLj/73UrPQhTqjZNXhs+Uey62NlkrU5zk0kfE\nOU3EK9Up4xbJclohmoBTgC/SC0F5R77/CuDlqnqxiKwG3g9sAP4J+AVV3ZeqzHGc8bIcK1NqvSiW\nyWIFVcqVlrLilI0Ygn7LTpUVJ04VEMSP/a7UxNS2fak56cqwbfK4KKcOVaLJr6NyWmHJVdUvq+qM\nqs5Gy8tNmTer6mNUdbWqnqWq3xtnmx1nWFRlyBeRD+T77XLVuNo7KGWCKr4hlYmp2GKEWY9jmVJC\nKTW4IrY61XHRpVxzqXqr2hBIWRRacaMeE5PeH5qkyvXW1DLNtMXS5DhOj5Ah/6+ATxSU+QzwUnpa\nYu/wm1WPqptqakRr6phEx20+pjjeKRXLFMcuhekDUkInFc+E2V8UBG7bF6cKCBw0x2YL9tltOxdd\nKJvanqIA7073h1HShAvPLU3luGhynJZRI0M+wF5VvX90rWqGQWKZ4ilQ7P54tFwoU2bViQVWbFGK\nt6FfNBUJoqIHVRzLFLah/MEUxzXFKQlsO4pG1IXtOM6qi0xyfxgHVcKq69fLsJlmq6/jdJlnish9\nInKLiFwmIkeMu0EweAB4UfxSKs9SWRxTbAlKjTCLBVUoX+Y6my3YF9cT11Um2oraM0zXxxTMT9fK\n/tAkddxmRSNGB1mcctzS5Djd4zNkbopbgccDfwJcJSJPVdWxemuaeDDHQirOxVQ2hD8uE8cZEe0v\nszZBfz6nItectQhZS5K1LoVt2wab4DJVb6quOkyKhWkAWtsfRk0d0V1Vpo5wmua4JhdNS6BsSDT0\nLqj4JhnK2VgLa/5P3bDngVX5+qp8WWnWV+Vl7fbqaHsuKmsfEDOmHbadljgT9/58CRm+9+TlwnpY\n9kbbe0rK7jH12nXM94TvDlnEYzdGwA4Ft/Evk4Kq2kmqvy0i/wp8H3gm2SjUsVB2sy2LBbLrKZec\nFUJxnbPRdlGQdRBKsDg/U1hflZcpS25p22DjkMJv2Eev/was6IljmuzvSMU1Qf+1XDRRLyXHJ522\n9odx0ITgmWZBVAcXTY7TcVT1VhF5gCzXWelDYphTCw3TyhS2YyuTFSxFbrHY0mTFUnipCJPvlsU0\n2e+D/lxL0BMs++gXQnMsFlixxSm8IFhSqQRmGVwY2emLgtnl2uuvH7CW7tCW/jAO6gieWNTH7Kk4\n3nUOkH7Rrou7MB2n44jIscCRwD1VZefpTTUTlmE/IFJiqixWyVp0ynIjpepIWZni/anFBnvb/SvM\nvlT6gFikpSxdqfZB/wMutqTFD7+yY1XMkw0/W22Wp5922oC1dIe294elUiceqU7cU9Uy6axg8f98\nvvSMxee3HhGZAd4CvBg4Brgb+KCq/n9jbZjjDIGyDPn58odkMRz35uX+FPgP4OrRtzaj7GabEk2p\nAPCZaLsslim2OBVZmYJFKXxCea6lVSy2NBXFNIXvDhl24xii4Jabp+eas+kDwr6UK64qHinELNnz\nJzV4p4v9YVCaEit1rCBVZdySUk4nRBNwAfBK4DeA75BlEP+giDysqpeOtWWO0zxlGfJfBfwsWV/Y\nQPYCcTXwB6qa8vKMlUFjmWz5OrFMsQUmFktxgDfRthVKq1gcV7iCnrUpds1Bv+BZiI7Hbrk4aDz+\nnKXfTRfHP8XB4KkYpgnN3TQx/WHYNOGeq0NTsXNdHKzQFdH0VODKPF8HwB0ici5w6hjb5DhDQVW/\nTPkL38+Pqi11aOLNNDVdij1m3V+BWVM+ZWWCfnFl98Wutjjzd7gxWvdc/N3hwRELp9hdB+nz7bH9\nZj0VDD7NdK0/DIs6gqgJi9U0uOiWQ1dE03XAb4nIT6jqd3PT7NOA88fcLseZeooCwJcSy5T6tFhx\nZK0/daxMsXvOjka1o1Rt9vAVUb2BIGwORvvI91mXnF0PD6T9Zns//cIpRbAyDSqmpjD9wFRTx4o0\nSPzOcpjUa64roukiYB1wi4iE+9XvqerfjrdZjjO9VFmYlhLLFB8vi1+y+6x1Zz76tKPjID1nnBVP\nRXmaLHP0UmAEgqCZiz5j61P4DSnhlBJES7E6pcTSpKXemDaaiFeCZtxz00xXRNOvA+cCLyKLaXoy\n8D9E5G5V/euxtsxxppSyh3DZdClQHMsk9Ashe37RaLiwHQRPHPwdpxFYVbAUiSb7vYEF+r8bsoBw\nG+tkrUup0XSp9VBf2ZQrReLKcepYkdz9tjwaFU0iMjek4LuLgbep6sfy7W+LyPHAhUChaFpODo4i\n10Gow36mhhvP0J880r7lxgknQ0LKNeaTfH1tvr02sWwA5PC8sD1gTwwVprJb2sAO6N2J95v1kGky\nZKDcBezMP7fn69vzstuzZWE3bAO25ru2meKhqK1ij9lO5QixiTWrCM0MgbDKaIJi8xGezwFuUdU7\nRORJAKp68wi+vnWUTZeS2l8Vy2SP25t+0ZD+1BKPiEuNuEvlaYrjk+x1OE9v9FzqHpAaCk5UPv4t\nRVRZnKRGmVHifaJZ6oidpqxRTjFNW5p+Gfi7huuE7NEfP/uCi7+Q+aoCzsQRRkAdJLtggtjaMfyv\nvpjsWft/ichHVfUTIvIl4JnD/+rRU3YDr7IyxakFiiwu8TmxuIktTWVWppX0W4+KsuuHFxobCB7f\nJO2ouPgNsczCFL94xSPl6sQ22fIdiBmZqj7RBupYmtw9tzyWLJpE5JrofAGOYzii6dPA74nIncC3\ngZPJgsD/cgjf5ThL4UZV3QwgImeLyEZ6RoiposrKlMrDFOdkgvJcTNYqBP2j36yrzqYSiKccCoJp\nDelg8FBvSsjtT+xfoCfYQyyTjVuKR8zZZX/0OSEuOe8TDVLH0rSyoXqq6OC12BjLsTS9S1WvsjtE\nZNMy21PEa4C3Au8FjiLLxfG+fJ/jtIEZEXmVql6mqleJyCnA0eNu1DBYjpUpjmWy27FFJnadFbnU\nQtk4bUA896KNabKCKY5pWmnqtfPQBUI8U8rKFD6D+JmjN62K/b0p111cnz0nTooZji/Q/zdvWX6m\nqekTo6CO18QtTcNnYNEkIkeRhY18KXH4E8ttUApV3Qn8t3xxnNZg+sM1wLPDflX9FxF55dgaNiYG\njWUqW7fbRWkIYoEVW6Os227elA3WqFSwuI1/Cp+xa81OzFskaGKhVOcNv657zpYPtOXt3/vEcKhz\n/bggGj5LsTT9JbBDVc8VkXVkmVg/rKoPq6qbXp1pw/aHz4jIq4G/yfvD18bduKYpe9stszLNJsrF\nI+ZSgihlZbKpAkK9KStT7JoL7rnV9CxL1tIU9qUCwQM2w3cQN9bCZFMN7M/X99Mv5EK98UOwLD9V\nx5iqPjEq6oimVdVFRpanqS0ivmmW0j8/TTYHHKq6jcxlNiy3nOO0nbg/XMYE94dB0gzUGTEXW5ms\nSArbRaPQUlaiWCiFIPAgiMJ6EE5hfbXZtxqYn8mWFStgZr63rFgB89Lv+kvlfYrbmRpRR7SviiZi\nUUbEVPWJJoiv86UuRek07FJVRx0O1lgmlaVYmu4DviAifw98QVW/LSJuFXSmlanpD4NYmeKh9XEd\ncSxTLC5CWXvcCox4PrngbouFTPzAwKyHjBw2GHx2BsQOn7MNyk1JchDYD3MHetYl6D0s4nimOAA8\n9XdJ/X2K3HRtSitQwNT0iVEyqkDwll9bY2cplqYzyd4cjgU+LCLb6aUWcpxpY2r6wyBWpuXWB+lh\n+rGoistaF16IWZo323Y9nmLlkGCKC8dKLS8nUhycngqAT91sO2Q9GoSp6ROjpI6lKWX5jJcmLE3T\nzFIsTV9X1Y8DHwcQkROA/9Joq0ZIfOMNiNm2b8HxjRkWz3Fl4ylsbkno5Z5cB6ynl6QyLEcA60LF\nj8h3HAk8Kl8/Il8/MluXI/KytpK1gDzC7DicnmMC+v/te4ADZOkld+TLA6B5GsqHyTJQPgxsAR7M\nP+36/XlV+b7ZLfCILTB7INsd4jvi2JB9+bE9wN58e69Zwpv2/nx7IW9pyL1pk17G2ZPDpzJ0U/FE\n9YcilhvLlEpOGY+Yi11V4fhcdCwWPbDYHRf6ZLAgBfcc9Od8DZamuTmQlaZSa2kKhAstD2gSYH4P\nLGjvcLjO43tG/Ntji1NqBF0oY1MYdISp6BOjpqmYJg88Xh5LEU23iMhLgM2qugA8Dzi+0VY5TneY\niv6wlFim+CXE7ovFUSC2JBUFf8ej3ILesfFMcdzSGlM2CKbVwOxKkDizpVU3M/QrFxvRvQDz+VMo\nuObmWZyfqSzwu2nC33OM6Qemok+Mmjr+zdU1ylSJ7zovmR0S8I0zsGhS1a+JyHfoDRL5LvBQ0w1z\nnC4wDf2h6OGeElJlo+TCvjiRZSpQmsSxVPB3eLO2lqY4jilYesMDxQqmFXYInTVRpXyAwTxqBJMs\nwGxuHprR/jbPUWx1SlWPOTaMuahGxTT0iaapY0WqM+qtjg90e8XxaRZEdVhScst8RERY/4fmmuM4\n3WPS+0OdXEsxsRgocn3HZVJWp9TIOZtnCfqFSpxvyYYoQU9czaaCQIJrLlY1cTImm0sgLzt7oN8I\nBfUehpPIpPeJcVDH0uTR9sOn6bnnhoaIPAb4U+AXyF4Svwu8TFVvGmvDHGcKGdTKlJo6pcjKlHLP\nFaUYsEIoXoI1yVqWyD9XzYDYSa2tpSllEornRIGeyy5/Us0dWDwSEBYLqdTfy3GqaMo9V0VT7rlJ\nTTvQCdEkIhuArwJfAM4CHgB+Ajf5Os5QKXqw17EyxVOlhH1Fwd828JvoWDzSLXbPpVxyYVlNNjZi\nbShrBdOFfnbLAAAgAElEQVRa+udVsUOMAkEczZONWghj/vN9Enxpe2BOFwtB+3cpGvnnTDdNBXk3\nMUSxKfdcy6b0aYyu9NcLgDtU9RWqeqOq3q6qn1fVW8fdMMdpGhE5XUQ+JSJ3ichBETknUeaPRORu\nEdklIp8TkRNH1r7EvpSVybrh4iHNRW44a1lKBX/bTABxTiabuNIuQTytmjGCKSxBUa0jG2S6NjrJ\nDrULXxAnhDINjoO+UwHgw0aZrAdW2/vDqKiTuDK+9lPLQsUySrqYJLMroum5wL+IyEdF5D4RuUlE\nXjHuRjnOkFgDfAN4NYnnn4i8kWwS61cCp5Lli7haRBqdIWGQAPD4nNgdZ88tymdUlMsotkhVjapL\npVqaIxsh1zdKzq6nkjjZiuLo7thsFDU83tWVG21LaUV/GDd1cjDN11iqqBJV0x4o3gn3HHAC8NvA\nO4A/Bk4D3i0ie1T1w2NtmeM0jKp+FvgsgIikNMrrgLeq6qfzMr9BloX5+cBHm2pH6ouXY2WKy8Ti\nJ5X/rMzKZDOPhUFwsYEoGJLmV9Lzz1nXnM1LYGOaAnZCuT35vlX08gvY8rPFws9ZOm3pD8OkzjVT\nx/VWx4VXZb2pY91powVoVHRFNM0AN6jq7+fb3xSR/4NMSLlocqYGEflx4Biy+D4gG6kkItcDT6Wh\nh0SdWKb4Rh/H68TpBUKZIJbK5pYLZVNv06mpUYL3zLohggdubiX9QU1h3Sqr+byCWPWEeCabAyCI\nKNvA/IenRvkN6p6L3+TjB9Q0P7BiRtUf2sDa6iKN5GlyyumKaLoHuDnadzPwy2Un7WPxm/EK+uM8\n4wy9cY6YeCqG+MYN/f7k8AIblpCTe31eNk/kzZHA7BHAI8kyfB9N1vUfBXJ0XviYfAnHDjsCOC5f\njgUemx8IhY/kUAZwOTxvVfgXH8gXyF6Zd5Cl+X6ALLX3vcBdwA/z5fas6IZb+1Nz7yJL9PEg2bvc\nffQygt8Pej9s25tF6IeE4Q/TSywecoRsz6vamX/uMct+sv+d/dqiLOBxBvB9LM54O0nxHWT/aCX7\ny1vuo3cxDIWyCXmLgr/t3HGhXFEMk+1jUC2WbO6lOPh7Xf65ai6PYQqZ8qG/gx6aoTf68oAdNRe2\nQ/ZKax4DJFeCswNecEUiaIRZ7bvM2PpDk9QR1nVEUx1LU1UOMBdV5XRFNH0VeGK074kcerKnCYLH\nzeXTg50BA7K76QF6npUJRmhAH9adLiUul4phqjO3XKquOIja5mSy8U3WM5aySK0knxrFxjBBT3HN\nm8+Ua842zmYCj9Ve3PAh4cJpIBrpD6OizjOqjiCqcwlWiaI6ommahVVXRNMlwFdF5EIyc+tpwCuA\n3xprqxxn9NxL9kA4mv6366OAr1ednLK+ztK7EdRNZDmolclacKusTKGstTCFmKayLN92MNxaYEWY\n5DG2NIX14J5byeKkluGpYK1M0ItlCqkH4reyWeBA9cPLWknrklIAdUYYhTkdLddef/2A395ahtof\nRkUdsbO+ukitXE7TLr4PsLjvDaKuOyGaVPVfROQFwEXA7wO3Aq9T1b8db8scZ7So6q0ici/ZTPLf\nAhCRdWQvEu+tOt9m0Y6pa2WKb/BFwd9FCStTAeBxPiYods2F2O3gioOeBgoa6VDg93r6J7ImXw/q\nKgSAxybK8GQJAgl6sUw2Qj32PVZQFK9kXc+pcikO0p9eoOjGb39aKPP0007jo1deWeNb2s0w+8Mo\nqSOajqxRps5vqZqwtylR1VZxtoLFwucg9b0RnRBNAKp6FXDVuNvhOMNGRNYAJ9LTIyeIyEnAFlW9\nE3gX8CYR+R5wG/BWskC0ZT0Fi6xMRTfi2UQZG/ydqjNlaUqlCMBsB0uTnSbOBntDv4Vp1Rz9QikW\nTetZnH/JDtuz46rtnTQE18VKsAQrhqpilwJlD5tpdIuMqz+Mkjpi54gaZeqIL49pWh6dEU2OM0Wc\nAnyRniHhHfn+K4CXq+rFIrIaeD+ZHPgn4BdUteolspC6b9tl5axwSmX9tuVSLrrY22Xjlmy6JCuy\ngs6xWQMOxTFZP57NT7AqOqFovjnyY2Gi3nj0SEnAZJ24kbpv4qlyqX0THDA+8v4wauqInSayfUMz\n18iEXme1cNHkOC1DVb9MhY5R1TcDb27qOweNZSqyMqWyflujTDwU3worm4MJFuegjEfIBZcc+frh\n5HFMdsiq/dxgCgcrUxBOoRFBzYTH7V56I+ZCA2sGgKeEU/ywWTD7D0blwrYm6qqKwUgJqK5mCh9H\nf2iSOoKoTizSo5bbkJwqQT/NgqgOLpocZ8oZNJapaCqUosl4U7FOcRbj2EUH/cageIoIG/RN/rly\nJf2C6UjzmUo5YBNahgaGCG37RwlpB2wAVs0ETEWZlO32wYL9MYPEOwUm2Po0UdQRTUfVKLOrRpkq\n95xTjosmx5ly6sQypTJ6S3Qs5ZazGgN6+sRam1KpAkLZYF2y08HZhN7BeHQojslalaxgWs9iS1MQ\nTVYA2QRh0J/5u0gsLfSXj4O6g9UoJYhsnrEmYkm6ak2adupMb3JYDf/c1p3VZap8lh7TVM5Ei6aU\nuyBOXmk/U3lfbCBqPHLHBqHGMadH0EtiuWY1WRJLyGyseTJLyZNZ9iWwPBp4ZGjl4+klsjwWJCSz\nPNJ80+F5WZtuE3rZiXbSS2T5YH7sXnrJLG/LPvU22LEly3V5X344FL3PfN7PoSSWC1t6qTHJvyEk\ns9yef4ZcmDaJJfl2GJi03yz76HlH7Jt1/JadeksHf7MeFimBZI8VBX/HOqNIWM2xuA9ab1hsjQrW\npyCw+uKYbCyTzTpbFNOUshiFC8y642xwVpF5LlIsZe64+FqGtIiK3XbO5FHH0sS66iILNUSTX0PL\nY6JFk+M45RR5mOpYmeL9qZFx8UCzOLC76OUEit1ya8meH+vJY5ig96YSUu6vN+tH0O+es/mZrEoL\nbrgZ+lMOWCtTCXoQVPuz1dsldsNB+YuBpSg+agG3LE0CdaY/qRPUtOee6jJNjJ6bZmuUiybHmVLq\njpiLg7+LAr2L3HJxcst42jbrlovnk4vdcmFZT56LKbjcgvHVmngfRX9skxVNRQHgwRQaFMw++k1l\nmOOJuXxiV1wsnmKrUeyWi116ljho3MXS5FBrZFwd0VSjGg8EXx4umhxnSknFMtWZhDfsLxpZl3K9\npRJWpuaTC0KJaDtYl4ILfNUcSLAkQSaKYsFkrUwhNxP552H0Zza0gikksQw/tMglZ4VTfl4QQfuj\nw1ZMxaemjkFPFMXxUbFYUnMsbPuDrz3UeTmpM69cHdHkgeDDpw3JUAdGRC4UkYMi8s5xt8VxpoGi\nueVSMUo2ljB1g4nTDsSZwe3ofjuNil2XlfSbpoI5KvbnhWOHmX2HmS9YIdliE0Cl0gkUBX9HZqXY\nzVa1xFRZAZZqXfIA8XaTmow6XlhZvdS55ga9Jp1+OmdpEpH/RDbn3DfH3RbH6Sqp8JxBrEypKddS\nLjobxA1pS5ONXbKWpuCKC5amYDCaP5x+dxz0rEphoIWNb9pgKgKYnzeR4wAHYMUemN3dP1VK+PHh\nD1Gkhsz+MIghDGxIuesw66kHVmr0nf0sIhZGbnHqDnWyfR9yRZdQx9JUJ/GqU0ynRJOIHA58mGyy\n3t8fc3McZ2IoSjtgj6WCv6FfXMXWI2sxgsVuudS8ctaLZkekrgdWhqGqQRSFCbkeRb9gehT96QbW\nzIBsMDWvIrv9HcgW2ZEdmt+92NoEiwOKQiqCMOSTrJow6jMIn330RFTKPWcFUtEkvrH4see69aj9\n1ElueUydimoEPtUYPNdIIPg0i/FOiSayCRg/rar/KCIumhxnCaRu4qk54uxnnLZjlnKxFFue7Hxy\nRZPwBg+btTT1xTGFwO8gloJIgp5VKRZN64H51XkAlI0ED7e+kJojX5/bXSyY9iWWBdD8KbRwsKeh\nYktTEDr7TZXxsVg8WYGlpEWVW5Mmg8fUKVQjL0EdS1MT10sdsT6p12VnRJOIvAh4Mtk8RI7jjJgZ\nqhNhxpm/7QL9Wb/jMCIrpmCxC0/CSlhCjBL0qy6rvubncwuTnXTFiqa9+eceSm+H8RC3hLpJiZ6i\neJFUPqYq6jyoXER1kxqet1omqzqT7bn7bXl0QjSJyLFkM1n/Z1WtHfy/gvQ8nDbg1H7aG7ZNoBeP\n7LHDn6H3JryWXgjFBmDNymyHhHgL6M8d8wiyV+lVZE+jvcA2soQvAGu/C4d9n14Sy8PzXxQnsQyf\ne4AdoDtAt2U5LbfndW4lyzYJvQyUW8gyU24hS1qZr2u+kBd7KP8MVWw31YbklZCZhvfQS2Jpk1fa\nt2/ovXXb2I44ZMRSNPzaGYxUYHYcmxTvD9YiG/gdpxEoc8ul3HNxDLftVzb1UvCurTic/pFx1qIE\nvSSxYf8jgcNW5xlkg8nJZrcM7OntkxX5LzTyJOWOSy0svs7tstBf9FDsU1lOp7pJLTX6DOt2NJ27\n8cZHHffccXUqqnHTayKmyUV3OZ0QTcBGstvhjSJiQymeISKvAVaq6qL7wi4Wvx2Hm7QzmRwg7cJw\n0sTZu+NjcTxTKmFlUY4m+yISRFPqJWQ1PTecnRol5GNauZp+l5wVTkE0HWO2HwmsPCLf+UgyFXU4\nPbEUbnt7zOcq+m6H1hRkA5P20++e28Oh95Z9lAsn616Lg8Rj45VNLRCHU3k8U7eoM0T9xDoV1TAX\n1IlpclG0PLoimj4P/Ey074PAzcBFKcEE2c04ZWlyJpdgXbTYFDxOP0XTn8TTnsTHUjFNsXXJpg6w\nLrdYOKVyMYGJYzoiWoI4CkIJIsF0FGZOorwm65KDTOmEQPBVZHbUHGvqjJXPnv5F98O+/Cm0l35d\nFT4XonX7FanFxjDZJqXyM/kDsP3UsTTNPLG6jNZQRHXucz733PLohGhS1Z3Ad+w+EdkJPKiqN4+n\nVY7TbcqsTPFxm48pPidOmF2UfgAWu+zi/Es2EcBKQOwcclZhWaWFWZ+fp+fYC27tUIltZRBMK3rb\nSjYPivWNBRVjVU/ksrNCKLYqpYK8ifaFbctS5ptzEdVOar2s10hcWUcRjSpx5TRfZ50QTQW4ddpx\nlkHKyjQb7UtNbJ2au9YGclu3XF9yPsrjAzfQm1MOYMX6fONRFQtkhqW1q0GOB+KJrYOVKR4xF6xM\nJvVAUDPh6RPE0h4yU9Je+q1Ne/udfMHCFE9EHY+eq+OaS8Wex665VLySxzO1i/nqIvCEGmW2Vhdp\nIiP4NAuiOnRWNKnqs8fdBsfpKilXXGxFSsU42WPhvDK3XBBPIbi7KI4piKZHACsPzwvHKQQeReZx\nO8Z8hgQ3hwTTcaZACCO3wgjzGfs7DvS74GCRO+7QaIedoHsy19zeRFEb+mTddVXuOeuas1Yod811\nl1XVReCnapT5fHWROu45v26WR2dFk+NMKyLyh8AfRrtvUdU6t96sjoJ9sfWpaALeojxN8/Rn+U5Z\nmlJxTH3JK0PCyjgfUyycjgHWrssbezyZhelY0lYm6ImlIG1mzf58n41dCkV30a+IdpEppd39+mp/\nvjuOG08MtOuzQKXcefGDzVqjAkq/JSkVCxUTz1M3KTTRJ4bFyjqFasQ0sbm6SJ1AcI9ZWh4umhyn\nm/wbcCY9nXOgpGwfqVimeKqUojnjYpec3W8Xm34glXLAuu9Wms9FCivOernWbB+GyfJt45iCX89m\n/ob0e/gBs+xdnBsjpXpMYkubEDxOLRC24ylSUp+BIHqsZSl2tdV1t02ha27JfWKY1LI0HVldpI4i\nqiOGfRqV5eGiyXG6yQFVvX8pJ6ZimepYmWzsUpynqcgtF1ua4jgmO6fczHoW516yo+LCaLljgKOA\nuR8Djs8LH0dmZYpHzIX3fPv8DOJpgUNWJt0BB/ZlpqKd9B5QYX1X/7rugd0He6FOodY4linWWjZ9\nQCyqrCXJpidw11xtltwnhsna6iJwQo0yNX6ZpxwYPi6aHKeb/ISI3EX2nP5n4EJVvbPqpFQsk00v\nEFuSUhPwWpGEWS9yy9lBbqk4pvXkQd82hgmK45geiRFMIS3g8aZACCkPwd/B/RanHAj7dwI7equ7\n6EXUbqeXwTWs7wR291aLwp+K8jZB8bQp8fQp0O+yiwPA46DvKtfchD8wl9Qnhk2dgXH6qOo5UhYe\nrB4bVyemyZNbLo+JFk3h5h4HsNpM4SEOYwX9D4J5s9+WF3pvieENM+wP+3aQZdFevRfW3ANr7+kF\nwspqek8S+2SxUbS2/8wcJEvZvaX/7hm7EWy8xZ4sp8fC3t79fyf9mbvtPnvzD+up4Fb7Fl30ILBv\nz6lM30Trnul7SXwNeCnw78CjgTcDXxGRn87TcxRSNA2KFByPM4DHrjdYHASeysMUEsoWxjFtIJ3l\nO87JdDSw8jH0BNPxeWE7Yi6kGbBuOWtpCoJph1m29jpLSHeP2Q5Wpu2guzIrU+gnKdG03xyzbrtw\nvdexMqUsTHWFzxS65pbcJ5ZLVR6mx9apRI6tLHI/t1aWaUI0TfO8cnWYaNHkOJOIql5tNv9NRG4A\nbgdeCHygTh2pWCY7Ym422g6Z9eMUBKFsyoWXmkYlGccUhtNZlRX2hximRXmY1ptP6E0zFCpJRZLE\nUw4F19weOHBwsYkIsx38cPs5NMjuYFTUZvkOrrhUfiZYbGVKBXFbEZV6SE2B5ag2TfSJYXFEdRGy\na7ecbZUl6uVp8mtmebhocpyOo6pbReQ/qDEbw24WT4+yijymOipbZGUKxtA4YWXKLWdjmCARxxTm\nk0tNjWKtTMcAR86YtALhM+QcSI2YCxYluw49P1yYUfGBnvvNLuSfWzlkbdKdsG9/z/gULLOh1lRc\nUzyaDhZbmVJz0AWshekgi61I8Yi4+Lj93sBXr7+eSaZun9jH4ut+lmYfjHUGxtX5xjrBWk1Ymiad\n5U615aLJcTqOiBwOPB74UFXZw+i5oOOUAWUj4qxYCskrrXtuFf2uOeuWC8IJojimw/OVMD1KEE6P\nzAsHsRT2yfH5zzyenjsuOD9s8HeQdMGaZCazBnouuYdBH4AD23tCyc5MDf0zVG/PTrOCqSylU+zC\njgPBy2KZYnddzCBWpjmyG70t/7TTTuPjV15Zs4buUbdPhMnah8nJtUrtqCxxX41amsgIPumWqOVO\ntdUJ0SQiFwIvAH6S7GX5OuCNqvofY22Y44wBEfkz4NNk7ofHAm8hUwY1Mrn0k0piGfbHwd+x681m\nBrBToKyOlngS3rVEk/Da5JUpS9NRwMyP0RshZ/MxBYUV0g3Eo+WCYArRhnDIusR92fIwi5eQfTnE\nN20H3Q47Dy4eTBeLpiCS7Fx0NicT0b7YVWeDvcNnmZUplbtp2miyTwxKleh63GPq1HJXZYl7a9Ti\nyS2HTydEE3A68B7gX8ja/CfANSLyJFXdPdaWOc7oORb4CJnkuB+4Fvg/VfXBqhNTeZhseoHU3HJl\nCS6hfzTdnDlmLU82pqkvH9PqxLqNaVoNrAiR4kVzyoUKV9BzKsaiKWFp0h1ZVHeI2N5Jv6kIenor\n/yxKWgm94G4bz5SyJAXCVCl2VNxBFlualsuUxD4tuU8MGzmuuozurp4Apc4UKU3kaXLK6YRoUtWz\n7baIvBT4EbCRrHM4ztSgqpuWem5RXqaAFUJxTFMqwBt6oiiOZYpzMkHCLRdGzRVZmo6cyUcWBetS\nyMMU4peCDetw+q1M1iUX4pfC8zNYme7tWZa2kFmXgmvOuuce7lmZgpfOWplifVVmZQoCax+92Ioi\nK1MspOI0A1MihmqxnD6xXKpGz/GcGpX8oLpIHUvTvuoizjLphGhKsIHsnrFl3A1xnK5hR8zF1iNb\nJpViIE5gCT3BtJL+WKZ4Ml6A+ZX5RtA8IZYpxDVZ0XQECcEUXHJBMAVL08r8Fyk9wRTUzwNkj5wH\n8rI/BP0h7N6e3UHuJ/t8MF+20BNNW0EfhoXd/YJpV7TA4ngma5Wy1idIT5sSB4PHbriqlANVk/c6\nw6Eyw9KZNSr51+oidR52nqdp+HRONImIAO8CrlXV74y7PY7TNYqsTHEgeGoqlBAEHlxv0D9ibiW9\nOCa7rM6VmlgPmxVMNr4pjNFeeQS9aHArltbTSy8QWhEEU5AtQTA9SCaY7gN+mBXVu0Dv6QkmK5bs\nQl7FjuwjD23qszQVxTQFS1MQS0XJLVMpCOwoOEg/xOKklvbTGS2VoukZh1VX8obqKJM6fsY6gsdF\n0fLonGgCLiObE/ppVQV3sDhIbzW9jBg2wHKW7EYXOoB9YNgHR7xO4lg81UTf5Ka7YHYXsCUdQGgv\n6PjN067bPDGY9eAG2JfYF27QNtle2XdgtuN1ov0pxuE7X+5w0mnB5mWK55TDrMdZw+P0A6Fcygpl\nE15KrLDi1OGro2NAL24puN6sUIrHwAQLk41hCu65fKTcoejuh/sVjzUZRT433QP7DhZPjxIHd8f9\nKu4zgTgHUyrTN4l9gzzw3Mo0GuYrS5xSXckP/6mySJ2YJo9XGj6dEk0icilwNnC6qt5TVf5wem/H\ngUr/s9NpljucdNKJA8Dt+qzZZ2OZ4jQDQRyV6SCbj3L1DP2JmmJrU7w+F0xNsYXJBn+H/3II+N5P\nTyQFl9xdZNal/FNvy4ruuz+zMN1PZoQK68Ha9GDmkgPQbYuzDlhtlbI02elT4sBxa1mK3XKxlanM\nDediqD1Uzy13bnUl11WLpu2VJZpJOeCU0xnRlAum5wFnqOod426P43SVoszfcQZw66KLrUgrWZzl\nOxiMgmBal6+LjQS3ybw3RNtrgbUz9NIIHMlid5y9Ze2h9xq0lywbiXXJ/ZBsBPptoN+HMA3Z/RyK\nAz8kmMISXHMPZUWDky92ywXDlA0Ej3MyxVapYIWCtIU3lcSSaH/dFAMurEZH1dxyylmVddxR44lW\nRzTVsTT5dbE8OiGaROQyYBNwDrBTRI7OD21VVTciOM6A2Ml5rZUpdsMFK1NYgnCyUyTG2cCtcJpb\nSf/wuTjYKV4OBT1B/9QosXUp7vZBMG0lU0P30i+Ybu0NPwqH8zRNfaLpQdCtsC1/soRk4PFSlJ0g\nztWUCvTGbFthVDR6rkgATWtOprZxQmWJ6pwDdfKz15lAzwXR8OmEaALOI7s/fCna/zJqZEF2HKeY\nVDwTpIPCbQxUEE3zLI71C8clzk9gFVc8SfU89IujlLPVxi2FbchEU0gtEKxN4fPB/hmrrY/NZqrc\nk6VtWthbnOU7FddUNJ9cygVXlI+pSbecW5lGyzGVJYqmye5xd43vcddbO+iEaFLVYWe6d5ypIOWa\nI/EZZwOPBzcEdx30ax9raepLYhkSVtp5VeznKmBuhv5IcDvpbhBKIXHlCvrF0w6yOCYby3R7ZmXa\nti2zLIUn0915kWBpyt10ej/oQ720TZB2zcVTqIQW7KU4jiksQeLFgiqV9btq9JxbmdrBsypLfKOy\nRI2MAy6aWkInRJPjOM1R5pqzI+LCpx0tFxuKoN89Z8XTTIgMt4m741Fz1uIksWUpNW/cHlPG7rf5\nmPLgb/0+PLSvJ5jC5F1BMN1Nv2B6sJeuyea23Eov3YAVS8FFtzcvu4/F1qjUKFUoj2NKjZSLUwwU\nCSa3MjVLnYFDZ1R6395ZWUeN3Ja1Elf6/374uGhyHCfpmouDwa1rzqYcSHna5uID1pcXJ37qezLZ\npBFBFFmRZOOaQjoByKROHuGtt2V5mO7t7ToklKAXzxQE0739gsnmtjRTzx3y4lnhFKxLsDgLuE0N\nEqf9CALJuvRcMLWPOi4O+W/lx/WGD1fWUWcyXv/ftgMXTY4zxRTlZSJat4LJiqi4rr68ZPEEdfEX\nLuKAWaDfAbaCftEUJuANoskOiXtw8QS8wccG/UpoO7C7ZzkK08zZmKZUHFMc5A39AojE/tREu2Uu\ntjL3nNMiTq84flV1FXWCvJ124KLJcaaUOm/R8fQqdl8cKB7WZ4oKxlgTzB6yLJLzD7M4lmkH6dFz\nNmHlA5nJaPeuxWkErMUJ+lIN6AOwc2+/hSloLFicmymOZbKWppBqwEq/IJgOsDhRrE0hsNRpUsDF\n1TCpTlwJ+uSXlh7fd/IHK+toajJeZ/hMtGgKUxgEih4STSe8LMsAXKes44yCsjE9KaG0JOL5QoKZ\nxiqPnfTim9Ztg3lraQoiKsQ72YzfD2eqB2DHwUw/2TnkglCyAoreuj4ED+3PTnuQ3ly91ii1jZ5g\n2ms+95nPeBJeK5hSI+igWjB5PqZ2UJ24EuD/Lj36dj5YWYPnzekOEy2aHMdZGgv0z6kVi/uFaF8c\n4LwAzNphZNbfFTJDbqd/PqKgRFbn791r7sgDxOc5JJj0ABw4mJULdZB/PkQvOWUQTeEzJK4k01kL\nW3sB38HCFOdiIv+K3aTjmMIcczYnuXXbpaYminMvxYIpJYJcMI2PqsSVGatKj15Towb/P3YHF02O\nM6UsUM9FlzovtR1cTkFQzMdBQNCbZyQokF3kQ+3oiSdrlZoD5vKB/EF97Kc/vxL0zEQhNVNQQg/l\nx8JxgO09C5IdEWeFkbUe2QDvYEE6QP+oOMxnPC1KnIcplF3qnHLO6Kgnmr5fevT+0qNO1+iUaBKR\nVwOvJ8sn9k3gd1T1f4+yDXsx84k2SMg84/V27KLsOGGy6rAe9Moci60lqWBogGuB59ATHCvJPW57\nYXYn/RNAhhinoK7CSWvJRI1JT7D5K7Dp5+kXU+GLU6IptjYFM9KDoFtgd54b4APAGfRSCYRTd5rP\nMOf8bsotTPbvsCX/GUXzyqVGwRW55Kx1KWhHEuWc4fILNcps3vxiNm0qvmvVGRnX1H2viXra1Jam\n6mnyudKZ55OI/DrwDjIH8g3A+cDVIvIE1RDYMHz2MRzRtMBw/hler1PFAosHt+3P94VPm+U7aJ3w\nIL8O+LmoXFjfsBVm45imEMcU/GBBbYTMmHnFm/8XbPox09AgtPZGdWDqCtam3LKkD2diKRibAP4W\neEAGFWgAACAASURBVAL9A+jiBOEh95KdhNdanRaiT8j02iqqk1ZCsViCxe44K5pcMI2W335CdZnn\n/c4+Nr2vOItSnXilpu57TdTTprY0VU+Tz5UuPZ/OB96vqh8CEJHzgF8EXg5cPM6GOU5XsNYki3Wx\nhe3wGLAJLlMPgAP0tEvQRzbWe+2ObAGQIGzCXHM2M7hNdgmZqvl6ScXBpwZ9wUi6DXRH/7xxdkTc\nbrK8lvEEvPGUKdBvXbIT8doM3+Fvp/mxovxLsNg9VyfY2x53wdQsK6gY5PDH1XV869fgVdc21CCn\n9XRCNInIHLAReFvYp6oqIp8Hnjq2hjnOhBAe/DYT+Cw9nRJPqWJjuw/m69YDF9cd6l+3FWat8Akx\nTavJxnevNBXsJktKGb5kn/myWDTlVifdDrsPZkkKUhPtQk/kWcG0O1+CFc1m+a4STFY0WcvScqxL\nMS6YhsOi3Kox66rreAj452aa43SATogm4JFk13bsHr4PeOLom+M43cQGJfeNdCsoF8fnWAERxgzt\nIwt2DdpnO4unlwtDt1cDq3bBml2w+oHsnPng9wspxYP62kYWMGUbuw90P+jenpcO+oO5d5Z8QiaO\n7mSxZSlOZBl+W5zdOzUyDnqWprppBKBcLNn9LpiGwzoqxr5dXV3HTupNg+JMBl0RTUUI6XvOKoDD\n169nfkXvJxaNFBpkBNHubdtYt6789SN1gyu66YX9D27bxoaKepeC1wv7Dhxgz9atUDU2eLJZBbB6\n/XpW5X3CTt4b1sVsC5kgEHoJGoMwWUEv8d+ebdu4dd26Q5P4Bu1jFzuLStgOdYQ57cKceLN5j75H\nt/GJA9m1sAAcFNCVsH8lLBze7xoLsUZ2wlw76i3sB9i5bRs/WLeOAyzOraT0ElFi1jVvX2hj+LSi\nZ2bbNg5bt26REIotSlBuVYrvFfuH0Cf27DsUgzOtfWIVwE+uX88jVhQ/Bq+6orqiFXPbWLvM/09T\n970m6mlTW5qqp6qOQZ4Rotr+ubJz99wu4FdU9VNm/weB9ar6gqj8ucDfjLSRThd4sap+ZNyNGAfe\nJ5wCprJPeH9wCqjsD50QTQAi8jXgelV9Xb4twB3Au1X1z6KyRwJnAbfhyVad7O3heOBqVX1wzG0Z\nC94nnIip7hPeH5yI2v2hS6LphcAVwCvppRz4VeAnVdXzhzmO4ziOM1Q6E9Okqh8VkUcCfwQcDXwD\nOMsFk+M4juM4o6AzlibHcRzHcZxxspSppxzHcRzHcaYOF02O4ziO4zg1mHjRJCJXisjtIrJbRO4W\nkQ+JyKOXWedxIvKXIvIDEdklIt8VkTfnqRGW297/V0S+KiI7RWTLMut6tYjcmv/2r4nIf1pmfaeL\nyKdE5C4ROSgi5yynPlPvhSJyg4hsE5H7ROSTIlJj1qfKes8TkW+KyNZ8uU5Efr6JNneZae0TTfeH\nvM7G+4T3h+GznGthiP+fC/Nr6J0DnvcYEflrEXkg73vfFJGTB6xjRkTeavrv90TkTTXOq7z+ReSP\n8vvMLhH5nIicWLcOEVkhIn8qIt8SkR15mStS96tB+qKIvD8v89rqv04/Ey+agH8Efo1sjs5fBh4P\nfGyZdf4kWX673wJ+imwk33nUmqmokjngo8D7llOJ9CY4/kPgKcA3ySY4fuQyql1DFoD/asrz8w3K\n6cB7gNOA55D9Da4RkcOWWe+dwBvJpuDZSHYtXCkiT1pmvV1n6vrEkPoDDKdPeH8YIg1cC43/f3LR\n9lt5WwY5bwPwVbJcrmcBTwL+H7LZXQbhArKR6a8i68tvAN4gIq+pOK/0+heRNwKvyes+lSyB+tUi\nMl+zjtXAk4G3kP2vXkA2C8iVg7bFtOn5eVvuKipTiqpO1QI8lyzR72zD9b4e+F6D9f0msGUZ538N\n+B9mW4AfAm9oqH0HgXOG9D96ZF7/04dQ94PAy4bR7q4u09Anht0f8jqH0ie8PzT+mxu9Fpb7/wEO\nB/4deDbwReCdA5x7EfDlBv4mnwb+Itr3ceBDA9Sx6Ponmxv7fLO9jmwmoxfWrSNR5hSyyQCOHaQt\n+f7HkuV3fBJwK/DaQf9W02BpOoSIHAG8GPiqqqYme18OG4BludOaQnoTHH8h7NPsiunKBMcbyN4U\nGvt75ubnF5G9ufj8mjnT0Ce8PyxmWvvDkK6F5f5/3gt8WlX/cQnnPhf4FxH5aO4qvElEXrGEeq4D\nzhSRnwAQkZOApwFXLaEu8jp+HDiG/r/1NuB6ltfvwt/74QHbI8CHgItV9ealfvlUiCYRuUhEdgAP\nAI8Dnt9w/SeSmSAvb7LeZVA2wfExo29OffIL+13Atar6nQbq+2kR2U5mvr4MeIGq3rLcervOlPUJ\n7w+9+qa9PzR6LSz3/5ML1ycDFw56bs4JwG+TWar+C1l/e7eIvGTAei4C/g64RUT2ATcC71LVv11i\nuyD7eyoN9jsRWZm39SOqumPA0y8A9qnqpUv57kAnRZOI/EkexFW0LESBeReTXZj/mcys99cN1YuI\nPBb4DPB3qvpXTdU7JIomOG4Tl5HFxLyoofpuAU4iiz94H/AhEfnJhupuDd4nloT3hwntD0tgqdfC\nkv8/InIsmeB6iaruX8J3Q/YMv1FVf19Vv6mqfw78BZmQGoRfB84l+x1PIXOF/3cR+a9LbFcZS/pb\ni8gKsthLJYu9GuTcjcBrgZcN+r0xnckIHvF24AMVZX4QVlR1C5np9Hsicgtwp4icpqrXL6deEXkM\nWTDltar6yqba2wAPkD0Ij472H8Vi1d8aRORS4GzgdFW9p4k6VfUAvb/tTSJyKvA6Br+ptB3vE8V4\nf8iZov5QRGPXQgP/n43Ao4Abc4sVZFawZ+QB2Ctz12EZ9wCxq+lmsgEeg3Ax8DZVDQNCvi0ix5NZ\nwJIvVDW4l0wgHU3/3/Yo4OuDVGQE0+OAZy/ByvR0sr/1nb0/NbPAO0Xkd1X1hLoVdVI0aTah3lIn\nmZzNP1cup978bfofgf8NvLys7DLbOzCqul9EbgTOBD4Fh8zIZwLvHlU7BiG/AT0POENV7xjiV82Q\n+N93He8Tpd/l/aGYiewPRTR1LTT0//k88DPRvg+SiZ6LaggmyEbOPTHa90Tg9gHbsprF1p+DLMMb\npaq3isi9ZH/bbwGIyDoyK+d769ZjBNMJwLNUddCRgZDFMn0u2ndNvr/q5a2PToqmukg2jPNU4Fqy\nIZgnks1d912WEfwoWY6IL5HNkP0G4KigXlV1WW+uIvI44AjgOGBWsoA8yEYh7RygqncCV+Q3iDDB\n8WqyTrnUtq0h+xsGqX5C3r4tqnrnMuq9DNgEnAPsFJHwFrhVVZc8A7mI/DGZm+hOYC1ZwPMZZL7/\nqWSK+0Tj/SFvW+N9wvvD0FnWtdDU/ye/dvvioERkJ/DgAIHKlwBfFZELydJynAa8gix9wSB8Gvg9\nEbkT+DZwMtnf5S/LTqpx/b8LeJOIfI/s3vBWspGKV9apg2z03SfIQgl+CZgzf+8t1q1Zoy19YktE\n9gP3qup3q/88hkGH23VpAX6aLHL/fmAX8H3gUuDRy6z3N8lMvHY5CCw00OYPJOpeAJ6xhLpelV+o\nu8keiKcss21nhN8ZLX+1zHpTdS4Av7HMev+SzBWxm8xUfA2ZaXfs1+a4lmnuE033h7zOxvuE94fh\nL8u5Fob1/8nr/kcGSDmQn3M2mSVnF5ngefkSvncNmZi8lSyX0nfJciOtqDiv8voH3kwmfnYBVwMn\n1q2D7EUpPha2nzFoW6LyP2AJKQd8wl7HcRzHcZwadHL0nOM4juM4zqhx0eQ4juM4jlMDF02O4ziO\n4zg1cNHkOI7jOI5TAxdNjuM4juM4NXDR5DiO4ziOUwMXTY7jOI7jODVw0eQ4juM4jlMDF02O4ziO\n4zg1cNHkOI7jOI5TAxdNjuM4juM4NXDR5DiO4ziOUwMXTY7jOI7jODVw0eQ4juM4jlMDF02O4ziO\n4zg1cNHkOI7jOI5TAxdNjuM4juM4NXDR5DiO4ziOUwMXTY7TMkTkQhG5QUS2ich9IvJJEXlCVOZL\nInLQLAsictm42uw4w8L7g9MmXDQ5Tvs4HXgPcBrwHGAOuEZEDjNlFPhz4GjgGODRwBtG3E7HGQXe\nH5zWsGLcDXAcpx9VPdtui8hLgR8BG4FrzaFdqnr/CJvmOCPH+4PTJtzS5DjtZwPZm/SWaP+LReR+\nEflXEXlb9ObtOJOK9wdnbIiqjrsNjSMiRwJnAbcBe8bbGqcFrAKOB65W1QfH3JaBEBEBPg2sVdUz\nzP5XALcDdwM/C1wMXK+qv1pQj/cJx9LJPuH9wRkS9fuDqk7cApxL9ibiiy92OXfc1+YSruX3AT8A\nHl1R7lnAAvDj3id8GWDpVJ/A+4Mvw10q+8OkxjTdBvDhD3+YJz3pSY1WfP7553PJJZc0WqfXO9x6\nb775Zl7ykpdAfl10BRG5FDgbOF1V76kofj0gwInArYnjt4H3Ca83o4t9oq39oYn/T1P/40lrS1P1\nVNUxSH+YVNG0B+BJT3oSJ598cqMVr1+/vvE6vd7h15vTGTN8/oB4HnCGqt5R45SnkL0pFT1MvE94\nvSk60Sfa3B+a+P809T+etLY0Vc8AdVT2h0kVTY7TWfL8MpuAc4CdInJ0fmirqu4RkRPI3AtXAQ8C\nJwHvBL6sqv82jjY7zrDw/uC0iVaMnhOR00XkUyJyV56Y7JySsu/Py7x2lG10nBFyHrAO+BJZYGtY\nXpgf30eWr+Zq4Gbgz4CPkT1UHGfS8P7gtIa2WJrWAN8A/gr4RFEhEXk+cCpw14ja5TgjR1VLX2ZU\n9YfAM0fTGscZL94fnDbRCtGkqp8FPguHhpQuQkQeC7ybbJjoVaNrXT+bNm3yejtYrzM8unYteL1O\nkzTx/2nqfzxpbWmqnib7UOvyNInIQeD5qvops0+AzwOfVNVLReRW4BJVfXdBHScDN954443DDKB0\nOsJNN93Exo0bATaq6k3jbs848D7hWKa9T3h/cCyD9IdWxDTV4AJgn6peOu6GOI7jOI4znbReNInI\nRuC1wMvG3RbHcZxhcfnll3P88Sdy+eWXj7spjlPItF+nrYhpquDpwKOAO0240yzwThH5XVU9oejE\n888/n/Xr1/ft27Rpk8cITDCbN29m8+bNffu2bt06ptY4Tn0uuujt3H7797noordz3nnnjbs5jpNk\n2q/TLoimDwGfi/Zdk+//QNmJl1xyifurp4yUKDb+asdpLRdc8HouuujtXHDB68fdFMcpZNqv01aI\nJhFZQ5buPpiSThCRk4Atqnon8FBUfj9wr6p+d7QtdRzHGQ7nnXfeVL65O91i2q/TVogm4BTgi/Qm\nzXtHvv8K4OWJ8u0a8uc4juM4zsTTCtGkql9mgKD0sjgmx3Ecx3GcYdD60XOO4ziO4zhtwEWT4ziO\n4zhODVw0OY7jOI7j1MBFk+M4juM4Tg1cNDmO4ziO49TARZPjOI7jOE4NXDQ5juM4juPUwEWT4ziO\n4zhODVohmkTkdBH5lIjcJSIHReQcc2yFiPypiHxLRHbkZa4QkUePs82OMyxE5EIRuUFEtonIfSLy\nSRF5QlRmpYi8V0QeEJHtIvJxETlqXG12nGHh/cFpE60QTcAa4BvAq1k8Rcpq4MnAW4CnAC8Anghc\nOcoGOs4IOR14D3Aa8BxgDrhGRA4zZd4F/CLwK8AzgMcAnxhxOx1nFHh/cFpDW6ZR+SzwWQARkejY\nNuAsu09EXgNcLyLHquoPR9ZQxxkBqnq23RaRlwI/AjYC14rIOrI5GV+UT0GEiLwMuFlETlXVG0bc\nZMcZGt4fnDbRFkvToGwgs0g9PO6GOM4ICNf7lnx7I9kLzxdCAVX9d+AO4Kkjb53jjBbvD87Y6Jxo\nEpGVwEXAR1R1x7jb4zjDJLe8vgu4VlW/k+8+BtiXW2Et9+XHHGci8f7gjJtWuOfqIiIrgI+RvWW8\nqqr8+eefz/r16/v2bdq0iU2bNg2ngc7Y2bx5M5s3b+7bt3Xr1jG1phEuA34KeHqNssLimEDHmSS8\nPzhjpTOiyQimxwHPrmNluuSSSzj55JOH3janPaRE8U033cTGjRvH1KKlIyKXAmcDp6vq3ebQvcC8\niKyL3q6PInu7LsRfJKaPSXmR8P7gNMFy+0MnRJMRTCcAz1LVh8bcJMcZKvkD4nnAGap6R3T4RuAA\ncCbwybz8E4AfA/65rF5/kZg+JuFFwvuD0xTL7Q+tEE0isgY4kcycCnCCiJxEFuh3N9nQ0ScDvwTM\nicjRebktqrp/1O11nGEiIpcBm4BzgJ3met+qqntUdZuI/E/gnSLyELAdeDfwVR8p5Ewa3h+cNtGW\nQPBTgK+TvTEo8A7gJrLcTMcCz80/v0Emou7JP31khDOJnAesA75Edp2H5YWmzPnAPwAfN+V+ZZSN\ndIq5/PLLOf74E7n88svH3ZRJwPvDiPDrtppWiCZV/bKqzqjqbLS8XFVvTxwL218Zd9sdp2kK+sKs\nqn7IlNmrqr+jqo9U1bWq+muq+qNxttvpcdFFb+f227/PRRe9fdxN6TzeH0aHX7fVtEI0OY7jTBIX\nXPB6jjvu8VxwwevH3RTHqY1ft9W0IqbJcRxnkjjvvPM477zzxt0MxxkIv26rcUuT4ziO4zhODVw0\nTQmDBvh5QKDjOI7j9OOiaUoYNMDPAwIdpxv4C47TNib5mnTRNCUMGuDnAYGO0w38BcdpG5N8Tbpo\nmhLOO+88brvte7WD/AYt7zjOePAXHKdtTPI12QrRJCKni8inROQuETkoIuckyvyRiNwtIrtE5HMi\ncuI42uo4jtMm/AXHaRuTfE22QjQBa8iyfb+axKzUIvJG4DXAK4FTgZ3A1SIyP8pGOo7jpJjkGA5n\nevDruJpWiCZV/ayq/oGq/j29+ecsrwPeqqqfVtV/A34DeAzw/FG203EcJ8Ukx3A404Nfx9W0QjSV\nISI/DhwDfCHsU9VtwPX43HOO47SASY7hcKYHv46r6UJG8GPIXHb3Rfvvy485juOMFc+k7EwCfh1X\n03pLUwlCIv7JmXzc7+44juOMgy5Ymu4lE0hH029tOgr4etmJ559/PuvXr+/bt2nTJjZt2tR0G50R\nYv3u8VvR5s2b2bx5c9++rVu3jrJ5juM4zoTSetGkqreKyL3AmcC3AERkHXAa8N6ycy+55BJOPvnk\n4TfSGSkXXPB6Lrro7Um/e0oU33TTTWzcuHFUzXOmhMsvv/zQdeguDWcS8Gu6mla450RkjYicJCJP\nznedkG8/Lt9+F/AmEXmuiPwM8CHgh8CV42ivM14mOQeI0x18pJEzafg1XU0rRBNwCpmr7UayOKV3\nADcBbwFQ1YuB9wDvJxs1dxjwC6q6byytdRxnqkjF0flII2fSGOU13dXY1FaIJlX9sqrOqOpstLzc\nlHmzqj5GVVer6lmq+r1xttlxnOkh9QY+qMWzqw8JxxkGXbVqtUI0OY7To2paIRH5QL7fLleNq71d\nZFAB08QbeFcfEuPG+8PoGOU1+nM/dyqzs6v4uZ87dejf1SQumhynfZROK5TzGbIRpcfkiw8JHYBB\nHw5NxNG5O2/JeH8YEaO8Rq+77gYWFvZw3XU3DP27msRFk+O0jBrTCgHsVdX7VfVH+eJ5FQZg1ALG\nRyUtHe8Pk0lXXyJcNE0JbYunqNOetrW5ZTxTRO4TkVtE5DIROWLcDeoSox6B6a65oeP9oQFGeZ12\ndRS0i6YpoW037TrtaVubW8RnyCatfjbwBuAM4CoRKXoLd8ZMV9+qO4L3h4bw67QaF01TQts6Q532\ntK3NbUFVP6qq/6Cq31bVTwG/BJwKPHO8LXOK6OpbdRfw/tAcfp1WI6qTN32biJwM3HjjjTd6RnDH\nZgTfqKo3jbs9gyAiB4Hn5w+DsnI/An5PVf+i4PjJwI3PeMYzfGqhKaNoaqGvfOUr0LE+4f3BWS7L\n7Q+tn0bFcZxyRORY4EjgnqqyPrXQ9DFtUwt5f3DKWG5/6IR7TkRmROStIvIDEdklIt8TkTeNu12O\nMwzKphXKj10sIqeJyHEicibw98B/AFePr9WOMxy8PzhtoiuWpguAV5IF+32HbNqVD4rIw6p66Vhb\n5jjNcwrwRbKcNGFaIYArgFcBP0vWFzYAd5M9HP5AVfePvqmOM3S8PzitoROWJuCpwJV5vo47VPV/\nAdeQBfs5zkRRNq2Qqu5R1Z9X1WNUdZWqnqCqv62q94+73ZOOp8AYD94f6uHX52joimi6DjhTRH4C\nQEROAp4GeKp8x3FGgqfAcNqMX5+joSui6SLg74BbRGQfcCPwLlX92/E2y3GcacFTYDhtxq/P0dAV\n0fTrwLnAi4CnAL8J/HcR+a9jbVWC5ZpImzaxNlmfratoPXDuueeyYsVhnHvuucv+XsdpA57Dxmkz\nfn2OhkbzNInI3DCC70TkDuBtqnq52fd7wItV9acS5ceWg+P440/k9tu/z3HHPZ7bbvveyM8fZn22\nLiC5Hr5jxYrDWFjYw+zsKg4c2L28HzEA48pJIyIzwHOAW1T1DhF5EoCq3jyM7xsUz13mWEaRu6zN\nfcL7g2P5/9s7+yi76vLef57MDCYTS7gnIVgKnZjkonh1qZNJbLkwXkHkXpZRYzEwI9oiuEyVhaWl\nGhgpIittLiVIvZGMLau82RnlYi3QRa+gSKmkSp1YtAouQRheLJSXGgIhkkye+8feZ3Lm5Lzsc87e\nZ5999vez1l7nzDm//exnzvl9z35+b8+vET3EvXru/QTDaHHTz8G7W++nTk9ZGjk4Nm68YHZjzjTO\nT9Jeua1qzwHWr1/HTTd9nfXr17V83UZIMSfN5UAfcLaZ3eTuXzOzu1FWYpFfpAnRdTTd02RmdzA3\n6DJgwN2Xx+FY2bWuBU4CNgA/BgaBLwHXuPtFFcqrFSFmaVOresTdJ8PnpwJPA3/m7u9K4nqNIk2I\nUvKuCelBlNKIHlqZ03SVu59YcrwDGGvBXi3OBW4GvkiQp+lyYBvwJwldT4hGmWdmHwdw99sJGhFH\npOuSEKkiTYiuo+HhOTNbCuwB7q7w9tdadagS7v4S8IfhIUTHUKKHOwh2WQfA3b9vZh9LzTEhUkKa\nEN1MMz1N1wDj7r7bzA41s3PN7DAAd38lXveE6HiKengG+Acz+0SJHr6brmtCpII0IbqWZoKm24AP\nArj7CwRDZtoSWuSVcj1cjfTQVjo5TUdOkSZiJq46qbrdOs0ETU8D3zKz88zsv3kwk7wvZr+EyArS\nQ8LU+6GPOxNyub16OcnEQUgTMROljkepm2NjFzM9Pc3Y2MVN28g7zQRNJxG0HI4Cvmxmu4CFsXqV\nQxqtrHFU7qKN0dHRirbivll0qSClh4Spd8OIMxPy+Pg4u3btpFBYOiedRvH6pc+7tD7HgTQRM1Hq\neJTA6sUXdwP7wsfmbOQed2/oAH6v7O/lwIZG7SR5EKQk8KmpKc8KAwMrHPCBgRWJlK9lo6dnfkVb\npdeI83qt2GiGqamp4u7ogx5/Xet4PXhGNVFk27ZtPjCwwrdt25b4tSrV0dLrlz5Pqz7HQd41kWU9\nVCOKTsx6HXrdrLdpG91II3popqfpQTM708x6wr/fCxzbhB1RQqOt5Tha10Ub69evq2ir9BpxXq/L\n9kaSHhImye0hynuLKtXR0uuXPu/S+hwH0kSHcsYZH6Cnp5czzvhAxfe1FUsE6kVVlQ7gUGB++Pzd\nlLUs0j7owlaEaJ4kW9WeAT24NDGHtHqLOqkVn3dNZE0PUepOHHW5k+poO0m6pwl3f8Hd94TP/97d\nr2vGjhDdgPSQLUrnbSTZW1Tei1W87rnnnt/1k8qliXiJMtfo8MP/C9AXPlam3YsqupFWMoK3FTM7\n0sxuNLNnzWy3md0fpsIXQojIlAZKxeEIIPYApvwGtHHjBfT0zGdmZs9Bk8qFqEWU4H7Hjh8Be8PH\nyrRzUUXXUq8rqhMO4DDgEYKkaauAAYLds19bpXymul5FsiQ9FBH3AZwA3Ao8SbAx9XsqlPkc8Atg\nN3AnsLKOTWmiBkkM01Ua6qg2qbzdZEkT0kM0+vsXOvR6f//CqmXyOvxWj8SH51JgI/CYu5/j7lPu\nPu3u33T3R9J2TIgEWAj8K/AJAiHPwcw+TbAf48eANcBLwDfM7JB2OtlNJNHCrjSpttqkclET6SEC\nW7ZcwcDAAFu2VO+5VJ1rnawETWuB75vZTWb2tJntMLNz0nZKiCRw9//n7n/i7n9HsMlpOZ8ELnP3\n29z934APA0cC72unn91EozeTtOYjdfM8qGpID51FHutgKVkJmpYDvw/8FHgXMA58wczOTNWrEupV\npCQq2vj4OIsXH87ixUfM2o3qx+rVq+ntXcDo6GjVMsWkl9WSX1Y7r7Rc3gUWN2b2WuA1wLeKr3mw\nVcX3gN9Oy6+8kdZ8JM2Dmov0cIB21Y3c18F643edcAC/Av6p7LW/AO6tUn4Q8OHhYV+7du2cY2Ji\notlhz5rUmxORxJyJwGbvHLtR/YC+2cSW1coUk15WS35Z7bzScu1OADgxMXHQdz48PJyZ+RvlB2Vz\nOAhuBDPAEWXlvgpM1rDTdXM40iStuSFxXTdLc5pKD+mhOu2qk904L6oRPaQugigH8Cjwl2WvbQAe\nr1K+7YKoV5GSqGjbtm3zQmGJFwpLZ+1G9WNoaMh7eub7yMhI1TIjIyNzHuv5Xm/ia1pk9Qbhjd0k\nbgImatjpupuEaJ6sakJ6EEnQiB7M/aB5dR2Hmf0NcJS7v73ktc8Dq939+ArlB4GpqakpBgeVlSDv\n7Nixg1WrVgGscvcdafvTCGa2H3ifu98a/v1a4GHgLe7+w5JydwM/cPfzq9gZBKaGh4dZtGjRnPdG\nRkYYGcn2JvTj4+OzeZc0yXUuk5OTTE5Oznlt586d3HPPPZAxTUgPrSGdxKCHelFVJxzAEMEQ3YXA\nCmAU2AWcUaW8WhFilqy2qr1Cyzp87RfA+SV/Hwq8DHyghp2u1kSW94FLg6xqQnpoDemkMl2XMb5n\npQAAGGJJREFUcsDdvw+sA0aAHwFjwCfd/SupOiZEApjZQjN7s5m9JXxpefj30eHfVwGfMbO1ZvYm\n4AbgCeCWNPztBJSUr3uRHuJDOmmd3rQdiIq73w7cnrYfQrSBIeDbBC0fB7aEr18PfMTdLzezfuBL\nBIlf/wn4X+7+ShrOdgLFvEeiK5EeYkI6aZ3MBE1C5AV3/0fqpANx988Cn22HP0KkifQgOolMDM8J\nIUSSKJ+YyDqqw+1BQZMQIrcUbzRjYxfnO2Gf6GiiBES5TzrZJhQ0NUhp5W0lsq92bi2blTKAR7Xb\nyPuLFx/B4sWHH/Q/NupzFH+FSJPijQbmRZ4gqxa9aDdjY5cwPf0wY2OXVC2jSd5tot7yuiweJLic\ntHTJZivLN6udW8tmpQzgUe02+j70HvQ/NupzFH/bQVaXV8d5JKmJTqdWgtVmkq92w7LtvGsia3oo\nFJY49HqhsKRqmU5IJJxVui7lQCdRGs23EtlXO7eWzY0bL6BQOIxCYWnVa9bzKcr7hcJSCoXDDvof\nG/U5ir9CJE2tYYtmdn1Xi160m02bLmNgYIBNmy6rWkbDc22iXlSVxYOMtSJEsuS9Ve050kSnbuXT\naeRdE92oh5GRkapbY4nadH1Pk5ldaGb7zezKtH0RQnQOlVrbzfQmRUXzm0Q7iFLPtm+/j5mZPWzf\nfl8bPcsfmQuazGw18FHg/rR9EULUJ4nAoprNJIbOavmvIRHRKlH0MTbWnongagREoF5XVCcdwKuB\nnwInEmSIvbJKua7rehXNk/ehCE9ZE0lMnI7DZtRhu1rXanTor1OGCvOuiU66R0Spy/39Cx16vb9/\nYeq+dEodjpNuHp77InCbu9+VtiNCiGgt0yR6f6LajKOXqNa1Gh36U8+UKCdKXd63z4F94WO6vuS+\nDteLqjrlAM4gGJLrC/9WT5OIRN5b1Z6gJjp9+X2cvUSNUM12p7TS866JrN0jzHocet2sJ21XOqYO\nx0nX9TSZ2VEEO1mf6e570/QlSst6dHSU3t4FjI6OxnrN0dHROYknK/k0OjpKT8+rWLjw0KoJMg/Y\nOpB4cvXq1ZgdwurVqyP7E3XcW+Pk3UunLb8vr2tx9hI1QrXWeJLXFN3LggX9cx4r0a7f2dzX4XpR\nVSccwHuBGeAVYG947C95zcrKDwI+PDzsa9eunXNMTEy0FJFGaVn39Mx3wHt65rd0rfJrFu0WE09W\n8qlamcq2DiSehL7wvL7I/kTtXWhnb8TExMRB3/nw8HCuW9WewZZ1s3RKz1ent8bV05QtPUSpT51S\n97NII3pIvfJGOYCFwBvKjvuA64FjK5RPTBBRKm/c+TKK1xwZGfFCYakXCkuq5qEZGRnxefMO8f7+\nX6uZATmwtcQLhaW+bds2HxoacujzoaGhyP5kZfJr3m8QnsGbRLM0W9fSrqPtJu+a6CQ9xFX38laH\n46QRPZh7shPLksLMvg38wN3/sMJ7g8DU1NQUg4OD7XdOdBQ7duxg1apVAKvcfUfa/qSBNFGbZctW\nMj39MAMDK3j00YfSdidx8q6JTtJD3upeJ9KIHjIxp6kK2Yz2hMgBWZvH1mlzs0R+iKvuZU1zWSWz\nQZO7n1ipl0kIkT5ZWZZcvNEAVSe36mYk0iZKHcyK5rJOZoMmIUTnkpWem1o3muKNamzsEt2MRGIU\n69fYWPVs31ECoqxoLusoaBIiY5jZJeHei6XHT9L2q5S0lyVH7R2qdaMp3qhgf82bkXqi0icLmqjG\nrl0vAL3hY2WiBERpay4vKGgSIpv8G3AE8JrwOD5ddzqLqEMV1W404+PjPPPMs5j1csopJ9e8GWlY\npGPIpCb27v3VnMdKKCDqHHIbNCXZOqxmu/T1as+LFBNkrl69ejah5ejoaEs+17tmlDKlyTHVuk6V\nfe7+jLv/R3g8n7ZDEK3ut+N6rQ5VbN58Bbt378SdurvGN3Mt9U4lQkdqoj49wL7wsTKqLx1EvZwE\nWTyIkIMjyURg1WyXvl7teZEDSSqLSSd7Z19r1ud614xSpjzRZhYSqXVbThrgEmAX8CTwMPBl4Og6\n5ySSl6Y8N0yUehXFTlSS0vG2bdsq5kSLi7QTEeZdE0npoRlgXphoeF7VMoXCEodeLxSWtNGz/NB1\nyS0bPaIIIu19p6o9L1JMkDk0NDT74z0yMtKSz/WuGaVMaXLMrCRS68IbxCnA7wBvBE4G7gUeARbW\nOKcte881u+daM0FEENgcSNCaJdJORJh3TXRS0NTXd4hDr/f1HVK1TH//Ige8v39RGz3LDwqaOkgQ\nIn267QZRfgCLgF8CZ9Uo05aepmbPa8ZOI4FW2kFKp5F3TXTSPSLKDhJReppUx5snFxnBa9FJ2V5F\n+uQh+7GZ3Qfc6e5jVd4fBKaGh4dZtGjRnPdGRkYYGRlJzLfx8XE2b76CjRsvmJ3IGkcW5Ep2q5Hn\nrMuTk5NMTk7OeW3nzp3cc889kFNNtEsPUepolLoZlx0Rgx7qRVWdcAAXEuw19wLwNPB14Jga5Tum\nFSHSJwet6lcDzwHn1iiTmiYq9QhFaRXHMfyWxeHkdpB3TbRLD1F6Q6P0NEXVSxxl8kjXDc8BtwMf\nAo4F3gT8PfAosKBKeQVNYpZuu0EAfw4MAwPAccCdYWNicY1zUtNEsxtYBzec3pYmTBcKSx3wQmFp\nU+d3K3nXRLv0ECVIiTJfKa6FA2kvQOhUGtFDJlIOuPup7n6juz/g7j8Cfg/4TWBVup4JkQpHARPA\ng8BXgGeA33L351L1qgrbt9/HzMyeukv3y9m48QIKhcMoFJa2kOV4P9AbPs6lfBl3M8u6tRS8Y+hI\nTdxzzz088cSTxaGfiuzevQvoDR8rE1e2b2UNj4F6UVUnHsBKYAZ4Q5X31dMkZum2VnUzR5qaSHNI\noNa1y1vdzbTCs9pyz7sm2qWHYmqWnp75VctoZVz6dF1PUylmZsBVwHfcPRNp8oXIM2lmM6517fJW\ndzOtcLXcRS3Wr19HT8981q9fV7XMli2bGRhYwZYtm9vomWiWzAVNwNXAG4Az4jbcSld7vUzIxQza\n1TJpt3rtYtbwVoYahMgardTz8oCqmeBO21uIWkxMTLBv38tMTEyk7YqIi3pdUZ10AFuBaeA365Qb\nBHx4eNjXrl0755iYmKjaRddKV3u9TMil3bS1yrVybehtaaihG5iYmDjoOx8eHs71UIS3cTii3cRV\nz/O2qkjDc50zETyvv9WdRNetnnOfDZgeB5ZHKNuUIFr54ayXCbm45Lna0udWr12+5UPebgK1yPsN\nwtt4k2g3cdXzvN248q6JdukhSr3Sb3X6dF3QRDAk95/ACQS7WBeP+VXKd+UNQjRH3m8Q3qWaqHez\naeRm1Oz2L1kl75qISw/16sfQ0JBDnw8NDbV0HZEs3Rg07SdYLVd+fLhK+a67QYjmyfsNwiNoIovB\nQb1WfBy9R1FtZO3zy7sm4rpH1KsfUTbjFenTdavn3H2eu/dUOG5I2zchuoHNm69gevphNm++Im1X\nalK6sGLXrl0UCkuqrlwrX9nWzKTxqDay8vmJeDnuuDX09MznuOPWVCnRA+wLH0VXUC+qyuKBeppE\nCXlvVXsETaTVUxL1usVyxQzf1RZU1CLJnif1NGXriOseUb+nidms9qJz6bqeJiFEsqS1dD5qD83Y\n2MVMT0+zZ89LDAysYP36dankVKpmQ6kH8kn9OtVL0NPU20avRJIoaBJCJEKU4bDiTee449bUKTsP\n2Mf8+Qt59NGHmJiYSCWnkoIj0Qh9fb1Ab/gougEFTRFpZD5E1LL1EmKOj48nknBTiHYQpRepGIRs\n337fnLKjo6P09i5gdHQUgE2bLmVgYAWbNl3aFt+FiMLY2CVMTz/M2NglFd/v6+uZ8yi6gHrjd1k8\nSGBOUyPzIaKWrZcQc2BgRSIJN/NG3udveEKaqEcrS/6j7NklmifvmohLD4XCEodeLxSWVHk/mINX\nKCxt6ToiWTSnKQEamQ8RtWy1cqWvtzIPQ/tiiTSpNpRVqQe0vGyUPbuESJtTTjmZnp5eTjnl5Irv\nq4e0+zAPou6uwswGgampqSkGBwfTdkekzI4dO1i1ahXAKnffkbY/adBJmli2bCXT0w/T0zOfrVs/\nr/lBKZB3TcSlh8WLD+f5539JoXAYzz33THwOirbSiB7U0ySEaCsbN15AT898Zmb2sHnzFbHPvdNc\nPtEudu3aNedRdD+ZCprM7BNm9oiZvWxm3zWz1e32YXJyUnYzaFfETzE4Ofvssxs6b8OGDWzd+vnZ\noeNqE8abrQv1JqBnre5KE+kQJfiemQHYFz42T1zfcRx2OsmXuOzEqaHMBE1mdjqwBbgEeCtwP/AN\nM1vSTj+y9sMouyIpisHJ5ORXGj63dA5Ttbl3zdaFWnP5xsfHOfvscxLphZImuouxsdor4wBOP/39\nwLzwsXm6McDoJDu5DJqA84EvufsN7v4gsAHYDXwkXbeE6E7qtbSLwcnKlStauk7cuY9q2du8+Qpe\nfnm3tjsREdhPkJRyf9USw8PDLFgwn+Hh4bZ5JdIlE0GTmfUBq4BvFV/zYAb7N4HfTssvIbqZesNc\nxeBk2bJlNe3EMccornlKGzdewIIF/VpRKuqyfPkywMLHyigIzx+ZCJqAJQQ7Hj5d9vrTwGva744Q\n3U9cKSsa2cy23oa4Y2MXtxQ8bdiwgXe+8ySt2BN1mZq6H9gbPlZGQXj+yHpudyNISFXOfIAHHngg\nlovcfPPNXHvtjZx11ofYuXMnO3bEv0J3586dXHTRRbPXOe2002Kzm5S/WbFbUg/mx2o4WzSsiTVr\n1vC3f3sTwJzvpFQPp512Wt3vbHR0PddeeyOjo+vrfreXXrqJp556gksv3cQxxyyfLV+0sXv3S0xP\nP8yll25izZpqO8vXJkt1Nym70kTwf2/dupVzzz23YgH3/UAP7vurfv5r1qxh9eoh1qxZ09J3FNd3\nHIedTvIlLjv1bDSih0zkaQqH53YDv+Put5a8fh2wyN3XlZUfBf6mrU6KLPBBd59I24k0kCZEFXKp\nCelBVKGuHjIRNAGY2XeB77n7J8O/DXgM+IK7/3lZ2cXAKcCjwJ42uyo6j/nAMuAb7v5cyr6kgjQh\nysi1JqQHUUZkPWQpaFoPXA98DLiPYDXdacDr3V2pWIUQQgiRKJmZ0+TuN4U5mT4HHAH8K3CKAiYh\nhBBCtIPM9DQJIYQQQqRJVlIOCCGEEEKkStcHTWZ2i5lNh/vV/cLMbjCzX2/R5oCZXWNmPzez3Wb2\nMzP7bLjKr1V/LzKze83sJTN7vkVbse7VZ2YnmNmtZvakme03s/e0Yq/E7oVmdp+ZvWBmT5vZ183s\nmBjsbjCz+81sZ3hsN7P/GYfPWSavmkhi78okNCE9JE8rdSHB7+fCsA5d2eB5R5rZjWb2bKi9+81s\nsEEb88zsshL9PmRmn4lwXt36b2afC39ndpvZnWa2MqoNM+s1s/9tZj80sxfDMtdX+r1qRItm9qWw\nzHn1P525dH3QBNwFfAA4Bng/sAL4vy3afD1BjqiPAm8gmJS+AdjUol2APuAmYFsrRiyZvfoWEswl\n+wSV82M1ywnA/wHeBryT4DO4w8wWtGj3ceDTBNnkVxHUhVvM7NgW7Wad3GkiIT1AMpqQHhIkhroQ\n+/cTBm0fDX1p5LzDgHuBXxGsBjwW+CPgPxt0YSPBIquPE2j5U8CnzKxyEqsD1Kz/ZvZp4NzQ9hrg\nJYLP+pCINvqBtwCXEnxX64DXAbc06kuJT+8LfXmyzv9WGXfP1QGsBfYBPTHbvQB4KEZ7vws838L5\n3wX+ouRvA54APhWTf/uB9yT0HS0J7R+fgO3ngLOS8DurRx40kbQeQpuJaEJ6iP1/jrUutPr9AK8G\nfgqcCHwbuLKBczcD/xjDZ3Ib8Fdlr90M3NCAjYPqP/AL4PySvw8FXgbWR7VRocwQMAMc1Ygv4eu/\nQZCq6FjgEeC8Rj+rPPQ0zWJmBeCDwL3uPhOz+cOAlobT4sKyv1ffYQQthdg+z7D7+QyClss/x2U3\n6+RBE9LDweRVDwnVhVa/ny8Ct7n7XU2cuxb4vpndFA4V7jCzc5qwsx04ycz+K4CZvRn478DtTdgi\ntPFagm3OSj/rF4Dv0Zruip/3Lxv0x4AbgMvdventQnIRNJnZZjN7EXgWOBp4X8z2VxJ0Qba2m2h8\nZHavvrBiXwV8x91/EoO9N5rZLoLu66uBde7+YKt2s07ONCE9HLCXdz3EWhda/X7CwPUtwIWNnhuy\nHPh9gp6qdxHo7QtmdmaDdjYDXwUeNLNXgCngKnf/SpN+QfB5OjHqzsxeFfo64e4vNnj6RuAVd9/a\nzLWLZDJoMrM/CydxVTtmyibmXU5QMU8m6Na7MSa7mNlvAP8AfNXd/zouuwlRba++TuJqgjkxZ8Rk\n70HgzQTzD7YBN5jZ62Oy3TFIE00hPXSpHpqg2brQ9PdjZkcRBFxnuvveJq4NwT18yt0vdvf73f0v\ngb8iCKQa4XRglOD/eCvBUPgfm9mHmvSrFk191mbWSzD30gnmXjVy7irgPOCsRq9bTmaSW5ZxBXBt\nnTI/Lz5x9+cJuk4fMrMHgcfN7G3u/r1W7JrZkQSTKb/j7h+Ly98YeJbgRnhE2etLOTjq7xjMbCtw\nKnCCu/97HDbdfR8HPtsdZrYG+CSN/6h0OtJEdaSHkBzpoRqx1YUYvp9VwOHAVNhjBUEv2HA4AftV\n4dBhLf4dKB9qeoBggUcjXA78qbsXF4T82MyWEfSAVWxQReApggDpCOZ+tkuBHzRiqCRgOho4sYle\npuMJPuvHD3zU9ABXmtkfuPvyqIYyGTR5sDdMs/sl9YSPr2rFbtiavgv4F+Ajtcq26G/DuPteM5sC\nTgJuhdlu5JOAL7TLj0YIf4DeC7zd3R9L8FLzqPDdZx1poua1pIfqdKUeqhFXXYjp+/km8Kay164j\nCHo2RwiYIFg597qy114HTDfoSz8H9/7sp4XRKHd/xMyeIvhsfwhgZocS9HJ+MaqdkoBpOfAOd290\nZSAEc5nuLHvtjvD1eo23OWQyaIqKBcs41wDfIViCuZJgG5af0cLkRwtyRNxNsNnjp4ClxejV3Vtq\nuZrZ0UABGAB6LJiQB8EqpJcaMHUlcH34A1Hcq6+fQJTN+raQ4DMshurLQ/+ed/fHW7B7NTACvAd4\nycyKrcCd7t70ZppmtolgmOhx4NcIJjy/nWDsP5fkWBOx6yH0LXZNSA+J01JdiOv7CevunHlQZvYS\n8FwDE5U/D9xrZhcSpOV4G3AOQfqCRrgNGDOzx4EfA4MEn8s1tU6KUP+vAj5jZg8R/DZcRrBS8ZYo\nNghW332NYCrBu4G+ks/7+dJhzQi+zAm2zGwv8JS7/6z+x1NCo8vtsnQAbySYuf8MsBt4GNgK/HqL\ndn+XoIu39NgPzMTg87UVbM8Aw03Y+nhYUV8muCEOtejb24v/Z9nx1y3arWRzBvhwi3avIRiKeJmg\nq/gOgq7d1OtmWkeeNRG3HkKbsWtCekj+aKUuJPX9hLbvooGUA+E5pxL05OwmCHg+0sR1FxIEk48Q\n5FL6GUFupN4659Wt/8BnCYKf3cA3gJVRbRA0lMrfK/493KgvZeV/ThMpB7T3nBBCCCFEBDK5ek4I\nIYQQot0oaBJCCCGEiICCJiGEEEKICChoEkIIIYSIgIImIYQQQogIKGgSQgghhIiAgiYhhBBCiAgo\naBJCCCGEiICCJiGEEEKICChoEkIIIYSIgIImIYQQQogIKGgSQgghhIhAb9oOiPgws98CXg+8lWAn\n+yOAtcA57v4fafomRLuRHoSYizTROgqaugQzOxRY6e7XmdmLwB8AJwHvAPak6pwQbUZ6EGIu0kQ8\naHiue3gFmAyfrwH+zgNGgb1m9jkzO9HMLk7PRSHahvQgxFxqaWKfmZ1qZnek5142UNDUJbj7Hnef\nCf88maDrtdi6+DDwE3e/C+gzs+NTclOItiA9CDGXWppw993ufjsafaqLgqYuwczebWbnm9lygi7Y\nH5uZEdwgjgUeC4s+Brw5LT+FaAfSgxBzqaMJERFFld3DEmAZ8C7gT83sPGAv8GXgMmBfWK6n5LkQ\n3Yr0IMRcamlCRERBU5fg7tcB11V6z8x+CBwZ/rkCuL09XgmRDtKDEHOppYkSLHlPso2G5/LBBPBW\nM/sfAO5+d6reCJEu0oMQJZjZIWY2AgyY2elm1pe2T52KuXvaPgghhBBCdDzqaRJCCCGEiICCJiGE\nEEKICChoEkIIIYSIgIImIYQQQogIKGgSQgghhIiAgiYhhBBCiAgoaBJCCCGEiICCJiGEEEKICCho\nEkIIIYSIgIImIYQQQogIKGgSQgghhIiAgiYhhBBCiAj8f9QY2Iu830shAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f4b8afa19b0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Calculate probability density function on lattice\n",
"bnds = np.empty(dim, dtype=object)\n",
"bnds[0] = [-3, 3]\n",
"bnds[1] = [0, 15]\n",
"bnds[2] = [0.5, 25]\n",
"(x0, x1, x2) = np.mgrid[bnds[0][0]:bnds[0][1]:0.05, bnds[1][0]:bnds[1][1],\n",
" bnds[2][0]:bnds[2][1]:0.1]\n",
"points = np.array([x0.ravel(), x1.ravel(), x2.ravel()]).T\n",
"pdf = vine.pdf(points)\n",
"pdf = np.reshape(pdf, x1.shape)\n",
"\n",
"# Generate random variates\n",
"size = 100\n",
"samples = vine.rvs(size)\n",
"\n",
"# Plot 2d marginals\n",
"show_2d_marginals(pdf, samples, bnds)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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4PA14nxgOdSxN66qLVNYzATFzY2VFyS3zERFh+x+ba47jTB7eH4pJWVFC4HfR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\no4AEvwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f4b5cb23898>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Fit mixed vine to samples\n",
"is_continuous = np.full(dim, True, dtype=bool)\n",
"is_continuous[1] = False\n",
"vine_est = MixedVine.fit(samples, is_continuous)\n",
"\n",
"# Calculate probability density function on lattice\n",
"pdf_est = vine_est.pdf(points)\n",
"pdf_est = np.reshape(pdf_est, x1.shape)\n",
"\n",
"# Plot estimated 2d marginals\n",
"show_2d_marginals(pdf_est, samples, bnds)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Entropy of original vine: 7.84120932648 bits estimated with SEM 0.0099953040207 bits.\n",
"Entropy of estimated vine: 7.7736715245 bits estimated with SEM 0.0099678267182 bits.\n"
]
}
],
"source": [
"# Estimate entropy\n",
"(ent, sem) = vine.entropy(sem_tol=1e-2)\n",
"print(\"Entropy of original vine: \" + str(ent) + \" bits estimated with SEM \" + str(sem) + \" bits.\")\n",
"(ent_est, sem_est) = vine_est.entropy(sem_tol=1e-2)\n",
"print(\"Entropy of estimated vine: \" + str(ent_est) + \" bits estimated with SEM \" + str(sem_est) + \" bits.\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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