{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy.stats as sps\n", "import matplotlib.pyplot as plt\n", "from scipy.misc import logsumexp\n", "#%matplotlib qt5\n", "%matplotlib inline\n", "plt.rcParams.update({'figure.figsize': (10.0, 6.0), 'font.size': 18})" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Gaussian Mixture Model (GMM)\n", "* probability density finction\n", "$$\n", "\\large\n", "\\DeclareMathOperator{\\Norm}{\\mathcal{N}}\n", "\\DeclareMathOperator{\\Gam}{Gam}\n", "\\DeclareMathOperator{\\e}{exp}\n", "p(x|\\{\\mu_c\\}, \\{\\sigma_c^2\\}, \\{\\pi_c\\}) = \\sum_{c=1}^{C} \\Norm(x|\\mu_c, \\sigma^2_c) \\pi_c $$\n", "\n", "where\n", "* $\\{\\mu_c\\}$ is the set of $C$ means\n", "* $\\{\\sigma_c^2\\}$ is the set of $C$ variances\n", "* $\\{\\pi_c\\}$ is set of $C$ weights such that $\\sum_{c=1}^C \\pi_c = 1$\n", "\n", "and single variate Gasussian distribution\n", "\n", "$$\n", "\\large\n", "p(x \\mid \\mu, \\sigma^2) = \\Norm(x \\mid \\mu, \\sigma^2) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\e\\left\\{ \\frac{-(x - \\mu)^2}{2\\sigma^2} \\right\\}\n", "$$\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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njzYJO/tsgqpWLfR5SEgIzZs31xErUmJK9EREivDyyy9TvXp1Rr6TUGZzmp1J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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot GMM pdf together with the individual components pdfs; return the GMM pdf line\n", "def plot_GMM(t, mus, sigmas, pis):\n", " p_xz = sps.norm.pdf(t[:,np.newaxis], mus, sigmas) * pis # all GMM components are evaluated at once\n", " px = np.sum(p_xz, axis=1)\n", " plt.plot(t, p_xz, ':')\n", " plt.plot(t, px, 'k')\n", " return px\n", "\n", "\n", "#Handcraft some GMM parameter \n", "mus = [-4.0, 0.0, 4.0, 5]\n", "sigmas = [1.0, 1.4, 1.2, 1]\n", "pis = [0.1, 0.4, 0.2, 0.3]\n", "\n", "t = np.linspace(-10,10,1000)\n", "true_GMM_pdf = plot_GMM(t, mus, sigmas, pis)\n", "\n", "# Generate N datapoints from this GMM\n", "N = 100\n", "Nc = sps.multinomial.rvs(N, pis) # Draw observation counts for each component from multinomial distribution\n", "x = sps.norm.rvs(np.repeat(mus, Nc), np.repeat(sigmas, Nc))\n", "np.random.shuffle(x)\n", "plt.plot(x, np.zeros_like(x), '+k');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## GMM - EM algorithm\n", "* E-step\n", "\n", "$$\n", "\\large\n", "\\DeclareMathOperator{\\Norm}{\\mathcal{N}}\n", "\\DeclareMathOperator{\\eeta}{\\boldsymbol{\\eta}}\n", "\\gamma_{nc}=P(z_n=c|x_n,\\eeta^{old})=\\frac{p(x_n|z_n=c,\\eeta^{old})P(z_n=c|\\eeta^{old})}{p(x_n|\\eeta^{old})}\n", "=\\frac{\\mathcal{N}(x_n|\\mu_c^{old}{\\sigma_c^2}^{old})\\pi_c^{old}}{\\sum_{k}\\mathcal{N}(x_n|\\mu_{k}^{old},{\\sigma_{k}^2}^{old})\\pi_{k}^{old}}\n", "$$\n", "\n", "* M-step\n", "\n", "$$\n", "\\large\n", "\\begin{align}\n", "\\mu_c^{new} & =\\frac{\\sum_n \\gamma_{nc}x_n}{\\sum_n \\gamma_{nc}}\\\\\n", "{\\sigma_c^2}^{new} & =\\frac{\\sum_n \\gamma_{nc}(x_n-\\mu_c^{new})^2}{\\sum_n \\gamma_{nc}}\\\\\n", "\\pi_c & =\\frac{\\sum_n \\gamma_{nc}}{N}\n", "\\end{align}\n", "$$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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qXHxWCsQ59tV5QjT2vXalLT9wjH8UaP7rm3MP3nntmz0Lrl/3lFKdUlVVxa5d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Uqp2kbye9MGyg+QjnbGugCxgdIqpWpEpMxKezyyW5T58+fzxBNPBNxnt9ux2+0oex0RdmFr5FYi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\nqV2h5Gnrt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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Choose some initial parameters\n", "C = 3 # number of GMM components \n", "mus = x[:C] # we choose few first observations as the initial means\n", "sigmas = np.repeat(np.std(x), C) # sigma for all components is set to std of the the training data\n", "pis = np.ones(C)/C\n", "\n", "plt.clf()\n", "plt.plot(t, true_GMM_pdf, 'gray')\n", "plot_GMM(t, mus, sigmas, pis);\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Training data log likelihood: -275.687446231\n", "Training data log likelihood: -257.756537213\n", "Training data log likelihood: -256.73326682\n", "Training data log likelihood: -255.418278557\n", "Training data log likelihood: -253.868553645\n", "Training data log likelihood: -252.588253235\n", "Training data log likelihood: -251.9249919\n", "Training data log likelihood: -251.682616958\n", "Training data log likelihood: -251.604724967\n", "Training data log likelihood: -251.57672686\n", "Training data log likelihood: -251.562926418\n", "Training data log likelihood: -251.553611058\n", "Training data log likelihood: -251.546153868\n", "Training data log likelihood: -251.539755108\n", "Training data log likelihood: -251.534101033\n", "Training data log likelihood: -251.529025116\n", "Training data log likelihood: -251.52441792\n", "Training data log likelihood: -251.520199681\n", "Training data log likelihood: -251.516309709\n", "Training data log likelihood: -251.51270094\n", "Training data log likelihood: -251.509336448\n", "Training data log likelihood: -251.506186972\n", "Training data log likelihood: -251.503229061\n", "Training data log likelihood: -251.500443693\n", "Training data log likelihood: -251.497815217\n", "Training data log likelihood: -251.495330568\n", "Training data log likelihood: -251.492978667\n", "Training data log likelihood: -251.490749977\n", "Training data log likelihood: -251.488636164\n", "Training data log likelihood: -251.486629848\n", "Training data log likelihood: -251.484724409\n", "Training data log likelihood: -251.482913848\n", "Training data log likelihood: -251.48119267\n", "Training data log likelihood: -251.479555809\n", "Training data log likelihood: -251.47799856\n", "Training data log likelihood: -251.476516528\n", "Training data log likelihood: -251.475105591\n", "Training data log likelihood: -251.473761871\n", "Training data log likelihood: -251.472481707\n", "Training data log likelihood: -251.471261635\n", "Training data log likelihood: -251.470098376\n", "Training data log likelihood: -251.468988817\n", "Training data log likelihood: -251.467930006\n", "Training data log likelihood: -251.466919136\n", "Training data log likelihood: -251.465953544\n", "Training data log likelihood: -251.465030697\n", "Training data log likelihood: -251.464148189\n", "Training data log likelihood: -251.463303737\n", "Training data log likelihood: -251.462495171\n", "Training data log likelihood: -251.461720434\n" ] }, { "data": { "image/png": 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4jCR6QgghOo3mrs8zm8386le/YvLkyWRlZfHqq6+yZMkSXnzxRQ4ePEhsbCzvvvuuw/F4\nenoSGBgoiZ5wGXtvxhBCCCHavYyMDDw8PGpG0uyhteaJJ55g0aJFPPHEEyxcuBBvb++a58899xwP\nPPAAc+fOpbKyknnz5jkUk+y8Fa4kI3pCCCE6jaysLEJDQx06KHnBggUsWrSI3/72t7z33nt1kjwA\nf39/Vq5cyZ133skzzzzD+vXrHYqpR48e5OXlUV5e7tB7QthDEj0hhBCdgtlsJisrq+ZGCnvs3r2b\n3/zmN0yfPp3XXnut0Xru7u588sknDBkyhIceesihEbrqDRnnzp2z+x0h7CWJnhBCiE4hJyeHiooK\nwsLC7KpfUlLCrFmziIyMZPHixSilmqzv6+vLkiVLuHjxIi+88ILdcYWEhACyIUO4hiR6QgghOoXq\nq8bsHdH785//TGpqKh9++CH+/v52vTN48GCef/55Pv74Y3bt2mXXO/7+/nh6ekqiJ1xCEj0hhBCd\nQmZmJp6engQFBdmse/LkSf7yl79w3333MWHCBIf6+e1vf0t4eDjz5s2z68YLuQpNuJIkekIIITqF\nzMxMuzdivPTSS7i5ufH666873E+XLl145ZVXSEhIsHtjhlyFJlxFEj0hhBAdntls5uzZs3ZN2x4+\nfJglS5Ywd+5cu9fz1Xf//ffTu3dvXnnlFbuSt5CQEMrKyrh06VKz+hOiMZLoCSGE6PDOnz9PZWWl\nXYnbH//4R/z8/BzaUFGfh4cHv/nNb9izZw/ffPONzfrBwcE1cQrhTJLoCSGE6PDs3Yhx6tQpli1b\nxty5czEajS3q86GHHiI4OJi33nrLZt3qRE+OWBHOJomeEEKIDs/ejRhvvfUWbm5uPPXUUy3u09vb\nm0ceeYQvv/ySM2fONFnX19cXPz8/GdETTieJnhBCiA4vMzOTsLCwJs/Cu3TpEh9++CH33HOPQ4cq\nN+XnP/85WmsWLVpks25wcLAkesLpJNETQgjRoZlMJrKzs20mbx988AEFBQU888wzTuu7d+/e3Hrr\nrbz//vtUVFQ0Wbc60ZOdt8KZJNETQgjRoVVvxGgq0TObzbzzzjtcd911jBo1yqn9z5kzh3PnzrFx\n48Ym6wUHB1NeXi47b4VTSaInhBCiQ8vMzARocsft1q1bOXXqFE8++aTT+58yZQpBQUF8/PHHTdbr\n0aMHIDtvhXNJoieEEKJDy8rKwsvLi8DAwEbrfPDBB/j7+3PHHXc4vX9PT0/uvfdeVq1aRX5+fqP1\n5IgV4QqS6AkhhOjQbG3EuHDhAitWrOC+++7Dx8fHJTHMnj2bsrIyli9f3mid6p23csSKcCZJ9IQQ\nQnRY9mzE+OyzzygrK2POnDkuiyM2Npa+ffuyYsWKJusFBweTk5PjsjhE5yOJnhBCiA7r3LlzmEym\nJhO9Dz/8kGHDhjFixAiXxaGUYtq0aWzevJmLFy82Wk923gpnk0RPCCFEh2VrI8bRo0dJSEjgwQcf\nbPKMPWeYNm0aFRUVrFu3rtE6wcHBlJWVUVBQ4NJYROchiZ4QQogOKysrC29vbwICAqw+X7p0KUop\n7r77bpfHcvXVV9OzZ88mp2/lKjThbHYlekopg1LqGaXUEaVUqVIqTSm1QCnlZ+f7dyul/q2UOqiU\nqlBKaaVUVCN1r1dKvauUSlJKXVJKnVdK7VRKzVRWftxSSm2tas/a12h74hNCCNExNbURQ2vN//73\nP8aPH094eLjLYzEYDNx5551s2LCBoqIiq3XkiBXhbPaO6L0BLAQOA08By4BfAl8qpexp40ngXqAE\nOGmj7l+AnwJbgeeB/we4AUuAxu6QyQFmW/k6ZUdsQgghOqDKysomN2IkJSVx5MgR7r333laLadq0\naZSUlLBhwwarz319ffH19ZVETziNu60KSqnBWJK7lVrr6bXKU4G3sCRwS2w08wCQqbWuVEq9A0Q3\nUffXwA6ttalWX28C3wCPKKXe1Fp/X++dIq31J7b+WYQQQnQe586dw2w2N5roffbZZ7i5uTF9+nSr\nz11h/PjxBAQE8OWXXzbab48ePSTRE05jz2jcTEABf69X/j5QDNxvqwGt9RmtdaU9AWmtt9VO8qrK\nzED14UNXWXuvanq5m7XpXSGEEJ1PUxsxtNZ89tlnTJ48uWZdXGtwd3fn5ptvZsOGDZjNZqt1jEaj\n7LwVTmNPohcDmIG9tQu11qXAgarnraFX1a/ZVp6FA4VAPlColFqplBrYSnEJIYS4DGVlZeHj44O/\nv3+DZ/Hx8aSmprbqtG21KVOmkJ2dTWJiotXnPXr0kJ23wmnsSfR6Ajla6zIrzzIAo1LK07lh1aWU\n6gk8hmXN3Y56j1OBvwIPA3cB7wFTgO+UUkNcGZcQQojLV2ZmJj179rS6EWPZsmV4eHi45MozW265\n5RYA1q9fb/W50WgEkIOThVPYk+j5AtaSPIDSWnVcQinlC3wBdAEe0lpX1H6utX5Ya/2i1nqp1nq5\n1voF4Kaq+gtttP2YUipBKZUg6yGEEKLjqKys5Ny5c41O265atYqJEydaHe1ztR49ejB69GhJ9ESr\nsCfRKwa8GnnmXauO0ymlvIFVwGjgYa31dnveq6r3LXCDUqrRiwu11ou01qO11qNbc42GEEII18rO\nzm50I0ZKSgonTpxok9G8alOmTGHPnj3k5eU1eNalSxc8PT0l0RNOYU+il4lletZasheOZVq33Llh\n1UnyJgOPNGNX7Q9YjmWxfkqmEEKIDqupjRirVq0C4Pbbb2/VmGqbOnUqZrOZjRs3NnimlMJoNJKb\nm9sGkYmOxp5EL76qXmztwqpEbDiQ4OygaiV5NwGPaa3/3YxmrgAqgYY/LgkhhOjQMjMz8fX1pXv3\n7g2erVq1quaWirYSExNDYGCg1UQPLNO3MqInnMGeRG8poIGn65U/imVt3qfVBUqpMKXUwKp1dc1S\nNXL4BZYk73Gt9eIm6nZXSrlZKf8JcC2wqWp3sBBCiE4kKyvL6kaM9PR04uPj23TaFsDNzY0JEyaw\nZcsWq8eoGI1GLl26RHm50yfMRCdj88BkrXWSUupdYK5SaiUQBwzCcjPGNuoelvwn4EHgBiw3WwCg\nlBoPjK/6WH0t2Vyl1MWqPl6t1canwC3AZqBYKVX/nL5DWutDVb+/AViolPoSy47cSiwjj/djuS2j\nfnIqhBCig6uoqODcuXMMGDCgwbM1a9YAtHmiBzBp0iRWrlxJamoqffv2rfOsekNGbm6u1elnIexl\nM9Gr8jSWNW+PAT/BkkS9Dfyh6jBjWyYCL9Ure67W72snetWJ4OSqr/r+CFQnekexTB3fCoQAHkA6\n8E/g/2mtM+yITQghRAeSnZ2N1trq1OyqVauIjo5m4MCWH7V67lIpf99ynNuH9eSavkEAnM0vJbS7\nt403LSZOnAjA119/3SDRCwqytJeTkyOJnmgRu+661VqbtNYLtNbRWmsvrXW41vpZrXVhvXoPaa2V\n1nprvfKXq8qtftWrG9VUXa31y7Xqpmit79Za99Nad6mKrZ/W+heS5AkhROfU2EaMixcv8s033zht\nNM/Xy51tR89zJs9y8MS2Y+cZ99ev2XHcvrV10dHRhIWF8fXXXzd4FhgYiFJK1umJFrN3RE8IIYRo\nF7KysvDz86Nbt251yuPi4qisrGxRomc2a75IzODOEeF08XJn2wsTcHezjJkMCu3Kz8f3I7ZPoF1t\nKaWYOHEimzdvRmtdZz2hu7s7AQEBkuiJFrNrRE8IIYRoLxq7EWPt2rWEhIQQGxvbyJu2bUrJ5rll\nB9ly5BxATZIH0KObN8/fHI2nu4GScpNdI3sTJ04kOzublJSUBs9k561wBkn0hBBCdBgVFRWcP3++\nwbStyWRiw4YNTJkyBYOh+d/6broyhCWPXs3kQT2arPe3r47ys4/iSb/Q9H0C1ev0tmzZ0uBZUFAQ\nubm5mM32LIUXwjpJ9IQQQnQYZ8+etboR47vvvuPChQtMnTq1We0Wl1dyvqAMpRRj+xmt3p9b27xJ\nV/DxnFh6BTR92lhUVBR9+/a1uk7PaDRiMpnIz89vVsxCgCR6QgghOpDqjRj1E724uDjc3Ny48cYb\nm9Xu3zcf58Y3tnGhyL5z7br7enB11U7c0gpTk3UnTpzI1q1bMZnq1pM7b4UzSKInhBCiw8jKyqJL\nly507dq1TnlcXBzXXnst/v7+zWp32shwnr1xAAF+ng69F5eUxbi/fsPF4sYTxAkTJnDx4kWSkpLq\nlEuiJ5xBEj0hhBAdRvVGjPpliYmJzZ62BRgY2o0HxkQ5/F6/4C5c0zeIssrG19mNGzcOgO3bt9cp\n9/X1xcfHRxI90SKS6AkhhOgQysvLrR4wvGHDBoBmJXqpOUW8vCbZ7inb+qJDu/L2zBGEdGv8EOXI\nyEgiIyPZsWNHg2dGo5Hc3Nxm9S0ESKInhBCig2hsI0ZcXBy9evXiqquucrjN+NQ8liWkUWlueB+t\nI9IvFLPt2PlGn1933XVs3769wb23csSKaClJ9IQQQnQI1m7EqKioYOPGjUydOtXmTllr7o6JYM/8\nSQR39WpRbC+vOcwLyw5iaiRhHDduHFlZWZw6dapOeVBQEEVFRZSUlLSof9F5yc0YQgjhRGazmZMn\nT3L48GHOnz9PZWUlXbt2JTIykmHDhjW4rUE4T1ZWFl27dq2zEWPnzp0UFBQ0a9q2tMKEt4cbXb09\nWhzbb6cOxNvDDTeD9WTzuuuuA2DHjh3069evprx6Q0Zubi69evVqcRyi85ERPSGEcJJTp07xj3/8\ngyVLlpCSkoKnpyf+/v4UFBTw9ddf8+abb7Ju3TrKysraOtQOydpGjLi4ODw8PJg0aZJDbZnMmhvf\n2MZ7W084JbZ+wV0I9/dp9PmVV15JQEBAgw0ZsvNWtJSM6AkhRAuZzWa+/vprdu7cSUBAADNmzCA6\nOhp39x//ir148SI7d+5k3759nDhxghkzZhAeHt6GUXcsZWVl5OTkMGTIkDrlcXFxXH/99XTp0sWh\n9korTNwyOJSBoV1tV7ZTVn4Jf9twlJ9d14erwrvXeWYwGGrW6dUWEBCAwWCQRE80m4zoCSFEC5hM\nJlasWMHOnTsZOXIkTz75JIMHD66T5AH4+/vzk5/8hIcffhitNf/5z38arMcSzZeVlQXUPSj59OnT\nJCcnN2va1s/LnRd/ciUTB4Y4LUZfT3e+PZ7DqZwiq8+vu+46jh07xrlz52rKDAYDQUFBkuiJZpNE\nTwghmslsNrNq1SoOHz7MTTfdxG233dYgwasvIiKCOXPmEBAQwJIlSzh9+nQrRduxWduIsX79egCm\nTJniUFuXSitIznT+tWPdfTzY89uJ3D6sp9Xn1efp1T9mRXbeipaQRE8IIZpp69atfP/990yaNIkx\nY8bY/V7Xrl158MEHCQgI4LPPPuP8+caP3RD2yczMpHv37vj5+dWUxcXF0adPH6Kjox1qa3ViBj95\nawfHsgucHSbubpZvuxWmhgcojxo1Cm9v7wbTt0FBQVy4cKHBFWlC2EMSPSGEaIaUlBS2b9/OiBEj\nuPbaax1+39fXl1mzZuHm5sbSpUtlg0YLZWZm1lnzWFpaypYtW5p1rMqtQ3uy8O5hDAhx3vq82p74\nZB9zl+xvUO7p6UlMTAy7d++uU240GjGbzVy4cMEl8YiOTRI9IYRw0KVLl1izZg09e/Zs9vlsYFm3\nN2PGDPLy8li3bl2Dw3KFfUpKSrhw4UKdadtvv/2W4uLiZq3PC/DzZNpI1x1lMqp3ADFRgVafjRkz\nhsTExDqJf1BQECA7b0XzSKInhBAO0FqzZs0aTCYT06ZNs7kmz5aoqCiuv/56kpKSSElJcVKUnUv1\n+rzaGzHi4uLw9vZmwoQJDrW1JSWb9UlZLk26HxnXl0fG9bX67JprrqG8vJz9+38c8at9lp4QjpJE\nTwghHHDo0CFOnjzJ5MmTa0ZaWmrcuHGEhYURFxcnNyA0g7WNGHFxcdxwww34+vo61NZ/dp/mH9tO\nNnuU1l4ms+bI2UsNyq+55hqAOtO33t7e+Pn5yYieaBZJ9IQQwk5lZWVs3ryZnj17EhMT47R2DQYD\nt912G8XFxWzcuNFp7XYWmZmZBAYG4uNjOZD4+PHjHD9+vFnTth8+OJp/zR7l7BAbWLjpKLe/vZNL\npRV1ysOyKxVGAAAgAElEQVTCwujduzd79uypU240GmVETzSLJHpCCGGnb7/9lsLCQqZMmeL0EZ+w\nsDDGjh3LgQMHOHPmjFPb7ujq34hRfaxKcxI9dzcDYd0bv8HCWe4cEc4b9wzH063ht+ExY8Y02JAh\nZ+mJ5pJETwgh7JCbm8uePXsYPny4y+4cHT9+PF27dmXjxo2yMcNOhYWFXLp0qcH6vOjoaPr2tb4O\nrjG/Xn6IFfvSnR2iVf17dOUnQ8Pw9nBr8Oyaa64hPT2d9PQfYzEajZSUlFBcXNwq8YmOQxI9IYSw\nw7Zt23Bzc3P4zlRHeHp6csMNN5CRkUFycrLL+ulI6t+IUVRUxNatWx0ezSuvNHP8XAFZ+a23RjKv\nqJzP49Morah7Pl71mYy1p29l561oLkn0hBDChnPnzpGUlERsbKzDd6Y6atiwYYSEhLB582YqKytd\n2ldHkJGRAUBoaCgA33zzDWVlZQ7fhuHpbmDlk9fyixv6Oz3GxhxMu8ivVhwi4Ye65+MNHz4cLy+v\nOtO3svNWNJckekIIYcO2bdvw9PRk7NixLu/LYDBw4403kp+fX+eIDWFdVlYWwcHBeHl5AZZpWz8/\nP8aPH+9QO9VT5a7ebVvbmH5BrJ83jmv719297enpyahRo+qM6Pn7++Pm5iYjesJhkugJIUQTsrOz\nOXz4MNdcc43DR3U0V9++fYmMjGTHjh0yqtcErXWdjRhaa+Li4pg8eXJN4mePCpOZCa9v5bO9rbsJ\nxtvDjUFh3awml2PGjGHfvn2Ul5cDlh8AAgMDZURPOEwSPSGEaMLOnTvx9PR06C7bllJKcf3111NQ\nUEBiYmKr9dveFBQUUFhYWHN+3uHDhzl9+rTD6/MKSisZFRlAaHdvV4TZpHOXSvlTXAonztW9V/ea\na66hrKyszn9/2XkrmkMSPSGEaMTFixf5/vvvGTlyJN7erZsE9OnTh4iICBnVa0L9GzHi4uIAx49V\nCfTzZOE9w5kQ3cO5Adrp3zt/4GBafp0yaxsyjEYjFy5cwGSqu3lDiKZIoieEEI3Ys2cPSqma2wpa\nU/Wo3qVLl0hKSmr1/tuDzMxMlFI1GzHi4uIYOnSow8ff5BWVuyI8u/To5s2hl29i+qi6MYeHhxMR\nEVFnQ0ZQUBBms5mLFy+2dpiiHbMr0VNKGZRSzyiljiilSpVSaUqpBUopPzvfv1sp9W+l1EGlVIVS\nSiulopqo310p9bZSKqOqv2Sl1BOqkVWySqmpSqldSqkipVSeUmqZUqqPPbEJIYQ1JSUl7N+/n6uu\nuoru3bu3SQx9+/YlJCSEXbt2ybl6VmRmZtKjRw88PDzIz89nx44dDo/mpeUVM/KVTazc3zrn51lj\n7Sw9gNjYWOLj42s+V++8lelb4Qh7R/TeABYCh4GngGXAL4EvlVL2tPEkcC9QApxsqqJSyhPYBDwO\nLK3q7yjwHvCSlfrTgLWAD/AC8DdgPLBTKdWzfn0hhLBHYmIipaWlhIeHs337dtauXcvq1avZsGED\n+/bt4/z58y6PQSnF2LFjycnJ4cSJEy7vrz3RWpORkUF4eDgAmzZtorKy0uFEz9vDjeduHEBMVKAr\nwrRL9qVSHv1vAtuP1/1/KjY2llOnTtUkdnKWnmgOd1sVlFKDsSRbK7XW02uVpwJvYUngltho5gEg\nU2tdqZR6B4huou4jQAzwS63121Vl7yulVgDzlVL/1lqfrorBA3gbSAPGaa0Lq8rXA/uAl4HHbP0z\nCiEEgMlkYvfu3axevZrly5eTkZHBK6+80mj9kJAQYmJimDx5MlOnTuWKK65wekyDBw9m8+bN7N69\n2yXtt1e5ubmUlpbWTNPGxcXh7+/v8KaZ4K5ePDWpbf+9+vt68ENOEReK6957W32fcnx8PFOmTMHH\nxwc/Pz/ZeSscYjPRA2YCCvh7vfL3gT8D92Mj0dNaO7Jn/T6guKr92v4OTAPuAf5aVXY90BP4Q3WS\nV9XfAaXUVuAepdQvtNYVCCFEI9LS0li0aBEffPABWVlZeHh4EBoaysyZMxk/fjwRERH4+/vj7u5O\nSUkJ58+f59SpUyQlJbFz507Wrl3L008/zZgxY3jwwQeZNWuW0w5WdnNz4+qrr2bz5s1kZWXV7DDt\n7KqvBwsPD8dsNrN+/Xpuvvlm3N3t+bZmYTJrDqRdYGgvfzys3DnbWrzc3dj07PUNykeNGoVSqibR\nA8uoniR6whH2/ImIAczA3tqFWutSpdSBqudOUTUNPBLYr7Uurfd4L6Dr9Vf9+900tAeYCAwA5C4h\nIUQD6enpvPbaayxevBiTycTUqVN54IEHKCwsJDc3l2eeecauxOGHH35g+fLlfPTRRzz++OPMnz+f\nZ555hrlz5+Lv79/iOEeNGsW3337L7t27mTZtWovb6wgyMjLw9PTEaDRy4MABzp496/C07fcZ+Uz/\nx27emjmC24ddHit9tNY15+p169aNQYMGsXfvj99+g4KCOHr0aFuFJ9ohe36E6QnkaK3LrDzLAIxV\n6+qcIQDLWruM+g+q+s8BwuvFhrX6tcrCrTwTQnRipaWl/O53v6N///588MEHPProo5w6dYq1a9dy\n8803k56ezsiRI+0eHYqKiuL5558nKSmJXbt2ce211/L73/+evn378u6777b4eBRvb29GjBhBcnIy\nRUVFLWqro0hPTyc8PByDwcC6detQSnHLLbc41EbfYD/+MWsk468wuihK++UUljFpwVaWJdTdFBIT\nE0N8fHzNZhyj0UhxcTElJa13J69o3+xJ9HwBa0keQGmtOs5Q3U5T/dXuq6n6NmNTSj2mlEpQSiW0\nxsJqIUTb27p1K0OHDuW1117jrrvu4vjx47z33ntERUUBsG/fPrTWjBo1yuG2lVKMGTOGNWvWkJiY\nyMiRI5k7dy6jRo3iu+++a1Hco0ePxmw2y7VoQEVFBdnZ2TUbMeLi4oiJiaFHD8fOwevq7cGUIWH4\n+zprrKL5gvw8ubJnd4xd68YSGxvLuXPnOHPGsgJKdt4KR9mT6BUDjd0l412rjjNUt9NUf7X7aqq+\nzdi01ou01qO11qODg4MdClQI0b5UVlYyf/58brjhBsxmM5s2beLjjz+md+/eNXXMZjOJiYkMGDCg\nxVOuw4cPZ9OmTSxbtoy8vDzGjh3L73//eyoqmrdk2Gg00qdPH/bt24fZbG5RbO1dVlYWWmt69epF\nTk4O3333ncPTtqUVJj5PSCO3sLFxhdallOLtmSOYODCkTnlsbCxAzfSt7LwVjrIn0cvEMj1rLZkK\nxzKt66zTJi9gOYKlwXRrVf9G6k7TZtaKw1psYH1aVwjRiWRkZHDDDTfwpz/9iUceeYRDhw4xefLk\nBvVOnjxJYWEhw4cPd0q/SilmzJjB999/z+zZs3n11VcZM2YMqampzWpv9OjR5Ofnd/qjVmpvxPjq\nq6/QWjuc6O0/fYFfLT/EoYx825VbUWmFiaKyH6f6hw4diqenZ815egEBARgMBtmQIexmT6IXX1Uv\ntnahUsobGA4kOCsYrbUZ2A+MsJJYxmLZ/Vu7v+qTJK3tp78GuAQcc1Z8Qoj2JzExkdjYWBITE/nk\nk094//338fW1vqLj4MGD+Pj4MGDAAKfG0L17dz766CNWrFjByZMnGT16NBs3bnS4nejoaLp06VLn\nEN3OKCMjA39/f7p06cK6desIDg52eKp9TL8gvnp6PNf0CXJRlI7LKypn2B838ll8Wk2Zp6cnw4cP\nrxnRMxgMBAYGSqIn7GZPorcUy27Xp+uVP4pl/dun1QVKqTCl1EClVEvW7P2vqt365989DVRWxVNt\nG5AFPKKUqjnLQCk1DJgALJOjVYTovNatW8e4ceMwGAzs2rWLWbNmNVq3pKSEI0eOMGTIENzcrN9U\n0FLTpk0jPj6e8PBwbrnlFl5//XWHbrxwc3Nj5MiRnDhxggsXLrgkxvageiNGRUUFcXFx3HrrrRgM\njh2PopQiOrQrPp6u+W/dHIF+njw5oT8jI+suG4iJiSEhIaHmjluj0ShTt8JuNv9kaK2TgHeBaUqp\nlUqpR5RSC7DclLGNumfo/QlIoeHo33il1O+UUr8DRlcVz61VVtv7WA47Xlh1zdojSqmVWM7Q+7PW\n+odasVUA84AIYLtS6kml1G+AjcB5rNykIYToHD799FNuv/12oqOj+e677xg6dGiT9ZOTkzGZTE6b\ntm1M//792b17NzNmzOCFF15g3rx5Dl1SX322WkKC0yZT2pWCggIuXbpEr169+Pbbb8nPz+enP/2p\nQ23kl1Tw5/VHOHW+0HblVjZv8hWMiAyoUxYbG0tRURFHjhwBLOv08vLyOv1aTWEfe38Eehp4HhiM\nJem7F8uNFLdWTbfaMhF4perr6qqy52qV1aha7zcZ+BeWw5rfBQZiuZ3jD/Ub1lovA27HsvP2deDX\nwHbgWq21rM8TohP68MMPmT17NuPHj2fbtm307Gn7jLQDBw7Qo0cPQkNDXR6fn58fn332Gc8++yxv\nv/02d999t93HZXTr1o3o6GgOHDjgUILYUdRen7d69Wq8vb258cYbHWrjWHYBi7efIvvS5bERozat\nNak5RXU2idTfkGE0GjGbzZ16VFfYz65ET2tt0lov0FpHa629tNbhWutna99GUVXvIa210lpvrVf+\nclW51S8r/V3UWs/VWves6u9KrfU7upE5Dq31Wq31NVprX611gNZ6hta6yTt1hRAd0+LFi5kzZw43\n3ngj69ats+uGivPnz5ORkcHw4cNrDqt1NYPBwIIFC3jjjTf44osvmDJlCoWF9o0wjRgxguLiYo4d\n63xLkDMyMjAYDISGhrJ69WpuvPHGRtdcNiYmKpCkl29mdFSA7cqt7OylUm54fSurD2TWlA0YMIBu\n3brVrM2s3nkr6/SEPdruzhchhHCy5cuX89hjjzFlyhRWr15tdwJw8OBBlFIMGTLExRE29PTTT/Pp\np5+yfft2pkyZQkFBgc13+vfvT9euXUlMTGyFCC8v6enphIaGkpyczJkzZxyetq3m4+nWpteeNSas\nuw8L7x7GzVf9OLJsMBgYPXp0nRE9kCNWhH0uv//LhRCiGTZt2sR9993H2LFjWb58Od7e3rZfwjJV\ndujQIa644gqn3U/rqJkzZ/K///2P3bt3c/PNN5Of3/SRHwaDgWHDhnHixAkuXbrUSlG2PZPJREZG\nBhEREaxevRqlFLfeeqtDbRSWVfL4x/vYdzrPRVG23LSRvQj396lTFhsby8GDByktLcXHxwdfX19J\n9IRdJNETQrR7e/fu5c4772TQoEGsXbvWoam8M2fOUFBQ0CajebXdfffdLF26tOYCe1tXnY0YMQKt\nNQcPHmylCNteVlYWlZWVREZGsnr1asaMGUNISIjtF2vJvFhCclY+xeWX7/rGknITW1Kyybz447rN\nmJgYKisra/57G41GmboVdpFETwjRrp05c4bbbruNHj16sGHDBodvtEhKSsLDw8PpZ+c1x/Tp0/ns\ns8/47rvvmD59OuXljZ9FHxgYSO/evTlw4IBDR7S0Z2lpP54vl5iY2Kxp2wEhXdn+q4lc17/t77dt\nTG5RGXP+k8BXyWdryqzdkCGJnrCHJHpCiHarsLCQ22+/ndLSUtatW0dYWJhD75tMJlJSUoiOjsbT\ns+3vOwVLsrdo0SK++uorZs+e3eTO2hEjRpCXl8fp06dbMcK2c+bMGQICAvjmm28Amr0+D2i1TTfN\n0SvAl2WPj2FmbGRNWXh4OGFhYXUSvaKiIrt3a4vOSxI9IUS7ZDabmT17NklJSSxdupRBgwY53EZq\nairFxcUMHjzYBRE235w5c3j99df5/PPPeeKJJxodsbvyyivx8vLiwIEDrRxh69Nak5aWRkREBKtW\nrWLAgAFER0c71EZphYkpb25nw/dZLorSeWKiAvH2+PEwZ6UUMTExNTtvqzdkyKiesEUSPSFEu/Ty\nyy+zatUqFixYwC233NKsNpKTk/Hy8qJ///5Ojq7lnnvuOebPn8/777/Pq6++arWOh4cHV111FcnJ\nyZSWlrZyhK0rLy+PoqIiunXrxjfffMP06dMdbuNCcTkh3bzw83J3QYTOlVNYxvvfnuJMbnFNWWxs\nLEePHuXixYuy81bYTRI9IUS7s379el555RUefvhh5s2b16w2KisrSUlJYdCgQbi7X57f+F999VUe\neOAB/vCHP/Dpp59arTNixAgqKytJTk5u5ehaV/X6vIMHD2IymbjrrrscbiOsuw8fPRzLuCuCnR2e\n0xWVVfJaXArxP/y4OzgmJgaAhIQE/P39MRgMMqInbJJETwjRrqSlpTF79myGDh3Ku+++2+y1VidO\nnKCsrOyym7atTSnF+++/z4QJE/jZz37G9u3bG9Tp2bMnwcHBHX769syZM3h7e/PVV1/Rr1+/Zl1V\nZzK3n00rkYG+7H1xEtNH9aopGz3acoNofHw8bm5uBAQEyIiesEkSPSFEu1FRUcG9995LWVkZy5Yt\nw8fHx/ZLjUhOTsbX15c+ffo4MULn8/T0ZMWKFfTp04c77riD48eP13mulGL48OGkp6d36G/6aWlp\n+Pv7s2XLFu666y6HE/zySjOjX93Ef3b94JoAnUwpRY+udc+CDAwMpH///nXW6cmInrBFEj0hRLsx\nf/58du3axeLFi1t0HEp5eTlHjx5l0KBBuLm52X6hjQUGBrJu3ToMBgNTp05t8M196NChKKU67Khe\ncXExOTk5pKamYjKZmDFjhsNtlFSYuGNEOFeEtM2h2M1xPLuA3648xLlLP66/rL0hIygoiLy8PMxm\ne66cF52VJHpCiHZh/fr1vP766zz55JPcc889LWrr2LFjVFRUcNVVVzkpOtfr168fq1ev5syZM9xz\nzz1UVlbWPOvSpQtXXHEFBw8e7JDf9KvX5+3Zs4c+ffowcuRIh9vo7uPBS7cNZmy/y/f8vPqKy02s\nPZRFas6Ph2fHxsaSnp5OVlYWRqMRk8nExYsX2zBKcbmTRE8IcdnLycnhZz/7GUOGDGHBggUtbi8l\nJQU/Pz8iIyNtV76MjB07ln/+859s2bKFX//613WeDR8+nMLCQk6ePNlG0bnOmTNnKCsrY+fOnc2a\ntgXIKypvdwdLDwnvzsE/3MTVfYNqyqo3ZMTHx8vOW2EXSfSEEJc1rTU///nPycvL45NPPrH7DtvG\nVFRUcPz4cQYOHIjB0P7+Cnz44Yd56qmnWLhwIR9//HFN+YABA/Dx8emQ07dnzpwhIyODysrKZu22\n1Voz5c1veXHV9y6IznUMBoXBUDepHTFiBG5ubsTHxxMUZEkAZZ2eaEr7+1tOCNGpfPzxx6xcuZJX\nX32VoUOHtri9kydPUlFRwZVXXumE6NrGggULmDBhAo8++igJCQkAuLm5MWTIEI4ePdqhbksoLy8n\nMzOTxMREoqOjGTVqlMNtmDXMnXgFU64KdUGErrXjeA73/Gs3hWWWqXpfX1+uuuoq9u7di6+vLz4+\nPjKiJ5okiZ4Q4rL1ww8/MHfuXMaPH8+zzz7rlDZTUlLw9vamd+/eTmmvLXh4ePD5558TEhLCnXfe\nSXZ2NmAZ7TGZTCQlJbVxhM5z5swZ8vLySEpK4v7772/WtK2bQTH7mt7t4vy8+pSy3OhxvqCspiwm\nJoaEhAS01rLzVtgkiZ4Q4rJkNpt5+OGHAfjPf/7jlN2xJpOJY8eOER0djZubGxXmCvLL8mueb0jd\nwK6MXTWfiyqKLtt1XcHBwaxatYrc3FxmzJhBeXk5oaGhhIaGdqjp2x9++IHvv7dMuc6aNatZbZw4\nV0B+SYUzw2o11/Y3snrudfQx+tWUxcTEkJeXx6lTpwgKCpIRPdEkSfSEEJelxYsXs3XrVhYuXEhU\nVJRT2kxNTSW/PL/mXtx7197LizterHn+r0P/YsXxFTWf71l7T53n5aZyp8ThLCNGjOCDDz5gx44d\nNSOew4YNIysrq2aUr71LTU0lOTmZ6667rtlnHj699ABPfrrPyZG1ndjYWODHDRlFRUUd/go80XyS\n6AkhLjsZGRm88MILTJw4kTlz5jit3T/G/5GtPbfSt29fAB4Z8gjTrphW83zxTYv5/TW/r/k8c+BM\nboq6CYCSyhImLpvIJ4c/cVo8zjBz5kyee+453n33XT766COGDh2KwWDoEKN6ZWVl7Nu3j6ysLGbP\nnt3sdl6ceiVzb7jCiZG1rs/2nmHC376h0mQ5Omfw4MF4e3uzd+/emg0ZMqonGiOJnhDisqK15okn\nnqCiooJFixY1+4ozsCRn/03+L+WmcsxmM8ZzRsb5jkO5Wdqc0mcKEyMn1tQP8gnC39u/5vOsQbOY\nEDEBgLLKMm7rexsjeowA4ELpBXZn7m52bM705z//mYkTJ/L4449z+PBhoqOjOXToECaTqa1Da5HT\np09z8OBBPD09m7XbttqYfkGM6Rdku+Jlqkc3L0ZEBtRsyPDw8GDEiBF1jliRdXqiMZLoCSEuK59/\n/jlffvklr7zyCv369WtRW4fOH+JvCX9je8Z2yxVaF/2ZPWQ27gZ3h9vy9/bn17G/ZrDRcjfupymf\n8vjmx8kszGxRjM7g7u7O0qVLCQkJYdq0aURERFBcXNzgurT25vjx4yQlJTF16lQCAgKa1caBtIsk\npefbrngZmzgwhDfuGY6/r2dNWUxMDPv376dr164YDAYZ0RONkkRPCHHZyM3N5amnnmL06NHMmzev\nWW2kF6SzNW0rAFeHXc2K21cwKXISKSkpuLm5ccUVzpnCe3Too/xj0j/o2aUnAAlnE6g0V9p4y3WM\nRiNffPEF58+fZ/78+Xh7e7f76ds1a9ZQVFTEY4891uw2/r75GM8ta9//HqqVVvw4QhsbG0txcTFH\njx4lICBARvREoxz/sVYIIVzk2Wef5cKFC2zevBl39+b99fTX+L+SnJPM2J5j8XTzZEDAALTWHDly\nhH79+uHl5eWUWL3cvBgbPhaAtEtpPLLxER4b+hhPDn/SKe03x8iRI/nXv/7Fgw8+SGBgIOXl5RQV\nFeHn52f75ctMSUkJmzdvJiQkhJtuuqnZ7fxp2pA6R5O0V/8vLoUvD2ay6zcTUUrVuSFDdt6Kpkii\nJ4S4LGzdupX//ve/zJ8/3+GDkUsqS9Ba4+vhy/yr56O1xtPtx2murKws8vPzmTBhgpOjtojoFsHf\nrv8bsaGW3ZAV5go8DB4u6cuWBx54gPj4eN555x2UUhw6dIgxY8a0SSwtsWPHDk6dOsUzzzzToqN1\nwrr7ENbdx4mRtY2r+wTSxcudSrPGw03Rv39/unfvTnx8PNOnT+fkyZOYzeZ2eduLcC35P0II0eYq\nKir4xS9+Qe/evXnxxRdtv1BLuamc2XGzeXn3ywCE+oUS1iWsTp2UlBSUUgwYMMBZITdwY+8b6e7V\nHZPZxJObn+St/W+5rC9bFi5cyLhx41izZg1r1669bM8CbMrixYtRSjV7Ch8g4Yc8ViVm1OxWbc8m\nDQrhl5OuwMPN8m3bYDAQExNTM6JnMpnIz2/faxGFa0iiJ4Roc2+++SaHDx/mrbfewtfX16F3Pd08\nmTFgBj/t91Orz7XWpKSkEBUV5XDbzWHWZiK7RhLZLdLlfTWm+uYMf39/3nvvPVJSUtosluYoLS1l\n/fr1jBgxokU3mKzYn87/rT2Mm6H5O7cvJxUmM5kXf7zeLiYmhkOHDtGlSxdAjlgR1kmiJ4RoU+np\n6bz88svceuut3H777Xa/tytjF4dzDwNw78B7uTb8Wqv1zp8/T25ubs0hya7m4ebB78f8njv63wHA\n9znfc7H0Yqv0XVtoaCjLli2joKCA2bNnt6ujVj744AMKCgr42c9+1qJ2Xr1jCKt/cW2Ljui5nDz2\n3wTm/Ceh5nNMTAyVlZVkZlp2fkuiJ6yRRE8I0aaeffZZTCYTb71l/1Rnuamc/9vzf7yVaPud6tGs\ngQMHNjvG5iqtLOWpr5+qmVZubddffz2PPPII+/fvd3hKvK1orXnzzTfp0aMH9957b4vacjMoIgJd\nP4rbWh4YG8VTE/vXfK6+ISMpKQkfHx/ZeSusks0YQog2s3HjRpYtW8b//d//OXS9laebJ4tvWoy/\nl7/NukeOHCEiIoKuXbu2JNRm8Xb35i/j/tKm07jPP/888fHx/OUvfyE2NpZp06bZfqkNbd26lePH\njzNz5syaWx+aY9/pC2w7dp451/Whu0/bbIxxthuie9T5HB4eTlhYGHv37mXChAmS6Amr7BrRU0oZ\nlFLPKKWOKKVKlVJpSqkFSim79+wrpaYqpXYppYqUUnlKqWVKqQZ/syultiqldBNfmxyoP9re+IQQ\nrausrIy5c+fSv39/XnjhBbve2ZC6gcVJiwHo1bUXXTy7NFn/woULnD17ttWmba2JDYsl1C8UrTX/\nTf4vOSWtO73Wt29f7rnnHvr168eDDz7I4cOHW7V/Ry1cuBBfX98W3YQBloOSF317Ei/3jjVxlZZX\nzJGzl2o+V2/IMBqNMnUrrLL3T8AbwELgMPAUsAz4JfClUspmG0qpacBawAd4AfgbMB7YqZTqWa/6\na8BsK19rq55/aaWLnEbeOWXnP58QopUtXLiQ48eP88477+Dt7W3XOzszd7I9fTsV5gq76rfltG19\nGYUZvHPgHVYcW9Gq/RoMBkaNGsUdd9yBr68vd9xxx2W7O/PQoUOsXbuWmJgYBg8e3KK25lzXhwN/\nuAlvj+YfzXI5evS/Cby27sfNNTExMRw9ehQvLy8KCwspK2v/ZwYK57I5dauUGowluVuptZ5eqzwV\neAu4F1jSxPsewNtAGjBOa11YVb4e2Ae8DNQce6613mSlGZRSvwPKAGs3ihdprS+vm8aFEI3Kysri\ntdde46c//Sk333yz3e+9POZlykxldp9Rl5KSQmhoaLOvz3KmXl17sfTWpUR1i2r1vocPH86OHTt4\n6aWXmDdvHrNnz2bVqlWX3Zlrr7zyCr6+vlx77bVERUW1uL2OluQB/PH2wXWuQqtep3f27FnAsiEj\nPNJvCOQAACAASURBVDy8TWITlyd7/pTPBBTw93rl7wPFwP023r8e6Aksrk7yALTWB4CtwD1VyWCj\nlFLjgGjgC611XiN1DEqpbqqjbK8SogObP38+5eXlvP766zbrHrtwjMc3Pc6F0gu4Gdzw9bBvcX1B\nQQHp6emXxWhetT7d+6CUIqckh4UJC1vtyrSgoCAiIiLQWrNw4UK+/PJLXn311Vbp217ff/89y5cv\nZ/z48URHR+Pp6Wn7pUYkZ+Yzd8l+TucWOTHCy8PVfYOIDv1xveno0ZYVSidPngSQdXqiAXsSvRjA\nDOytXai1LgUOVD239T7AbivP9gDdAFunmM6p+nVxI8/DgUIgHyhUSq1USl0+f7sLIWrs27ePjz76\niKeffpr+/fvbrH+26CxpBWmUVJbYrFvbkSNHALjyyiubFacr7crcxWdHP+PohaOt1ufw4cPJycnh\njjvu4IEHHuCll15i7dq1tl9sJa+88gpdunRh6NChLb6POPtSKftPX+iQI3pms2bbsfMcSLMc2RMY\nGEi/fv1ITk62/BAh6/REPfYkej2BHK21tYn/DMColGrqR6+etepaex8siZpVSqluwF1AKvC1lSqp\nwF+Bh6vqvQdMAb5TSg1pIi4hRCvTWjNv3jyCg4PtPu5jfK/xrLpjFT271F/O27QjR44QFBSE0Whs\nTqgudXu/24mbFsfgoJatQ3PE4MGDcXd358CBA/zzn/9k5MiRzJo1i++//77VYmjM3r17+fzzz5k2\nbRq+vr4tHoWdODCEXb+dREg3+9Z+tidKwfPLDvLRztSastjYWBISEggICJARPdGAPYmeL5a1cdaU\n1qrT1Ps00oY978+sev6htnKPj9b6Ya31i1rrpVrr5VrrF4CbgC5YNpA0Sin1mFIqQSmVcP78+aaq\nCiGc4PPPP2fnzp289tprdO/evdF6Zm3mxR0v8s2ZbwAcvje2pKSE1NRUBg4ceNkelmv0sSSg/5+9\n+46rsnwfOP65OWxZIogoLhy4RQUF9zZHajbUMi3T6ms7W1ZfK0tb5te0YZn5s7JylVvceyAOFJUh\nigsFQRBlwzn374+DgMrmHA7I/X69eMFznue5n0sFuc49rnv7pe3si95n9OdZWVnRqlUrTp8+jbm5\nOf/++y92dnY89NBDXL582ejPL4yUkjfeeAM3Nzf8/Pxwc3OrFHMqKyshBL8/15nPHsnrx/D19eXy\n5cuYm5urHj3lPiVJ9FIBq0LOWee7pqj7KaSNktz/HKAFFhdxzV2klHuBPUAfIUShu1lLKX+WUvpI\nKX1cXV1L2ryiKGWQlpbGO++8Q/v27Yvd8SA5K5lzN89x+XbZEpDw8HCklCYtq1ISWp2Wn078xG+n\nf6uQ/Wi9vb3JyMggLCyMBg0asGnTJm7fvs3gwYNJTEw0+vMLsnz5cg4cOMD06dOJi4vDy8urXO1d\nSUxlyLd7CTz/4PZstajjgJ1V3lpKX1/9DKk7u8DodFV/b1/FcEqS6F1FPzxbUKJWD/2wbmYx99+5\ntqD7oeBhXXKGXn2BACllgdcU4QKgAdRbQ0WpBL755hsuXbrEt99+i0ZT9NwpB0sHfhv8G0+3erpM\nzwoLC8PBwYG6dUs33FvRNGYafuj/A/P6zquQnsdGjRpRs2ZNjhzRb6PVrl07Vq9eTUREBCNHjiQ9\nPb2YFgwrOTk5N/nv0qULUspyD9smZ2TjXMMSR9sHo0hyQdIytSzeH8WxS/rkvEOHDmg0GqKjo9Fq\ntSQkFLhmUammSpLoBeVc1zn/i0IIa8AbOFLQTffcD+BfwDk/4BYQUci9k3I+F7YIoyjNgGxAfccr\niolFR0fz+eef8+ijj9KrV69Cr4tMjGTmoZmkZ6djqbEsU/KTmZnJuXPnKvWwbX4uNi5Ym1uToc3g\nz9A/0Unj9cYIIfDx8eHSpUu55Tj69OnDb7/9xp49exg9ejSZmUW9bzes999/n8uXL/P9998TGRmJ\ng4MDderUKVebLeo48MekLrSo42CgKCsfjZngi01h7ArXTzmqUaMGrVu35uzZswBcv37dlOEplUxJ\nEr1lgARev+f1yejnzi2984IQwl0I0UIIkX/O3W7gGjBJCGGX79r2QG9ghZTyvuqnOT2I44BY8ool\n33uNoxDivq4BIcRQoBuwNWd1sKIoJjRt2jSys7P56quvirwuMCaQbZe2cTvzdpmfFRkZSXZ2dqUf\ntr3Xtovb+Pzw5xyJKe69c/l06NABc3NzgoKCcl8bM2YM33//PWvXruWJJ56okGRv3759fPfdd7z8\n8sv4+PgQGRlpkORcpzP+ELipWZqbceC9vrw5IK9gha+vLydOnEBKiZpzruRXbKInpQwBvgdG5ZQt\nmSSE+Ab9Qofd3F0s+XMglHy9fzlJ3GtAfWCvEGKKEOI9YAsQB3xUyKNHAs7AEillYcWm+gBnhRDf\nCiFeE0K8JIRYAqxFv1vGvcmpoigV7OjRo/z++++88cYbeHp6FnntUy2fYs3INbjaln3ObGhoKLa2\ntjRoYLr9ZctiSOMh/D30bzq7dy7+4nKwsbGhbdu2nDx5krS0vJI1U6ZM4bvvvmPNmjVGT/Zu3LjB\nk08+SePGjZk1axbh4eFkZ2eXezeMlIxsvGdsYfkR0y0uqSi17O6eTdW5c2cSEhLQarUq0VPuUtKy\n6K8DbwGt0Sd9Y9DvdjFMyuLHGaSUK4Dh6FfezgbeBfYC3YqYe3endt6iIpoORz90PAz91mlzgO7A\nAsBbSlnYkLCiKBVASsnbb7+Ni4sL06ZNK/S6gKgAzibqh50cLMs+5Jadnc3Zs2fx8vKqdLs+FEcI\nQWsXfaITmRhJbEqs0Z7VuXNnsrOzCQ4Ovuv1l156KTfZGzlyJMnJyYW0UHZarZYJEyYQGxvL8uXL\nsbOz49SpUzg6OlK/fv1ytZ2WpWVkh3o0cS3xNuxVVuytdP67+hQhV/Tb2d1ZkJGUlKQSPeUuxW6B\nBiCl1ALf5HwUdd0zwDOFnFtPIUOwhVw/sATXhAJPlLRNRVEqVkBAADt37mTevHmFllPJ1Gbyv6P/\no2Wtlsztc+8GPKUTFRVFRkZGpdoNo7TSs9OZtGUS7V3b823fb43yjDp16tCgQQOCgoLw8/O7a7j0\npZdewtLSkhdffJFevXqxfv163N3dDfbst956iw0bNvDDDz/QqVMnUlNTOXfu3H1xlIWLnRUzRrQx\nUKSVm4XGjH+PR+PTqCZtPRxp06YN1tbWXL16FVdXV7RabbGLnpTqoWq95VUUpcrQarW88847NGnS\nhBdeeKHQ6yw1liwdupSP/AubxVFyoaGhWFpaFjtEXJlZm1szq8csPvT70KjP8fX1JTExkcjIyPvO\nTZ48mXXr1hEeHo6fn1/uKt3y+vzzz5k7dy6vvfYa//nPfwA4c+YMOp2Otm3LX9/+ZmrFLSQxNeca\nlpz4aCAjvPXFKywsLPD29iYqKgqdTqdW3iq5VKKnKIpRLFmyhFOnTvH5558Xum9pUEwQUkpcbFyo\naV2+Skg6nY7w8HCaN2+OuXmJBisqra51u+Jq64qUkoR04/zCbtmyJfb29hw6dKjA80OGDGHPnj1I\nKenatSvffvttmeuzSSn58MMPef/99xk7dizffJM3OHTq1ClcXFxwc3MrU9t36HSSnl/tZNbG0HK1\nU5VozO7uAe3cuTNhYWHodDo1fKvkUomeoigGl5qayn//+1+6dOnCY489VuA1gdcCmbh5IuvPG2a/\n1cuXL5Oamlqlh23vNfvIbJ7c8CTJmYafK6fRaOjSpQvnz5/n6tWrBV7TsWNHgoODGTx4MK+//jq9\nevUq9ZZpiYmJPPLII8ycOZPnnnuO33//PXdIMTExkYsXL9KmTZtyD9tm6XS8MaA5fVvULlc7Vcmp\n6CTG/RLI+Tj994evry+pqanExcWpRE/JpRI9RVEMbu7cuVy9epWvv/660F/gvnV8+azbZzzU+CGD\nPDM0NBSNRkPTpk0N0l5lMKDhAB5r/hg25oVu8FMuPj4+WFlZsX///kKvcXZ2ZvXq1fz666+Ehobi\n7e3N+PHji034MjIy+OWXX/Dy8mLDhg3MnTuXhQsX3jVv7NixYwgh6NChQ7n/LFbmGp7t1hg/z1rl\nbquqsLbQkJCSSWKqvkJZ5876FduJiYkq0VNyVe3xDUVRKp24uDi++OILRowYQY8ePe47r5M6UrNS\nsbO0Y0TTEQZ5ppSSsLAwmjRpgpVVYTs2Vj3etb3xru0N6P+Mhi4AbWVlhY+PDwcOHCAhIQFnZ+cC\nrxNC8OyzzzJ8+HBmzpzJzz//zO+//06nTp0YMmQIHTp0wNXVFZ1Ox+XLl9m/fz8rV64kLi6Orl27\nMn/+fDp27HhXmzqdjuDgYJo2bYqDQ/mLG0dev427ow01rKrPr7Wmte3Y+Frez1izZs1wdnYmNjZW\nFU1WcqkePUVRDOrTTz8lNTWVL774osDzv5/5nVFrRxGXargeh2vXrpGUlFTliiSX1OkbpxmzYQwx\nKTEGb9vPzw8zMzMOHDhQ7LW1atVizpw5XLp0idmzZ2NhYcHMmTMZNWoUPXr0oFevXowbN44//viD\n7t27ExAQwL59++5L8gAiIiJITk4u8FxZTFpyhDeWBRd/4QNMCIGfnx9RUVHcuHEDrVZr6pCUSqD6\nvPVRFMXoIiMj+fHHH5k0aVKhc+U61O7AtZRruNi4GOy5oaGhCCFo3rx58RdXQQ4WDmTpskhIT6BO\njfJtEXYvOzs72rdvT3BwMD179ixR75qzszNTp05l6tSppKamEhoamrvK093dnRYtWhS7IObYsWPY\n2dkZ5N9MSsknI9pga1n9yolsPh3DjHVnWP9Kd2rWsMTPz49NmzaRmppKQkICrq5lLz6uPBhUoqco\nisG8//77WFlZ8fHHHxd6TTvXdrRzbWewZ0opOXPmDI0aNcLW1rb4G6qg+g71WfXwKqPt3du9e3eC\ng4PZu3cvQ4cOLdW9tra2dOrUqVT3JCQkEBkZSffu3Q1S2FoIQa/m1TOhcXOwxruBE8kZ2dSsYYm/\nvz9SSq5cuUJcXJxK9BQ1dKsoimEcOnSIFStW8Pbbbxe4Mf0vIb+w4MQCpDTsXqSxsbEkJCSUe/us\nyk4IgVanZcnpJVy5fcWgbdesWZMOHTpw7NgxEhMTDdp2QQ4dOoQQInc3h/I6ejGBsJhbBmmrqvGu\n78T3T3akvrP+TU7nzp0RQnDlyhU1T08BVKKnKIoB3NnqzM3NjalTpxZ4PiopivM3zxu8V+r06dMI\nIR6osiqFiU+L58cTP7Lu/DqDt92zZ0+EEOzZs8fgbeeXlpZGcHAwbdu2xd7e3iBtztwQyof/lq7s\ny4MmPUs/H8/BwYHWrVsTGxurVt4qgBq6VRTFANauXcu+fftYsGABdnZ2950XQjCz+0yytFkGfe6d\nYdvGjRtTo8aDv7+pWw03Vjy8Ag87D4O37eDggK+vL4GBgfj7+1O7tnHq0QUFBZGVlYW/v7/B2vx2\nTAeS0gz7vVWV/LT7HPO2n+X49IFYmpvh7+/P0qVLiY013n7JStWhevQURSmX7Oxs3n33Xby8vHju\nuefuO7/5wmZiU/S/cCw0FgZ99p1h21atWhm03cqsvn19hBDEp8VzNbngQsdl1aNHD6ysrAgICDD4\nEDtAeno6Bw8epHnz5uXeCSO/+s62tKlX8F7K1YF3fSee696YjGx9r56/vz+pqalERESolbeKSvQU\nRSmfRYsWER4ezpdffnnfSsvkzGQ+OfgJ84/PN8qz7wzbPqhlVQqj1WmZsGkCHx/42KDt2tra0rdv\nX6KioggNNfxWYocOHSI9PZ3evXsbrM39kfFsOHnNKIlpVdHFsxZvDvTC3lr/RsrPzw+AS5cucePG\nDVOGplQCauhWUZQyS05O5qOPPqJHjx4MHz78vvN2lnb8PfRv7CzvH84tr/zDtg/qatvCaMw0vOP7\nDvXt6xu87U6dOnH06FG2bNlC06ZNC92nuLSSk5M5dOgQLVu2xN3d3SBtAvxx6CJhMbcZ2s5wbVZF\nWp3kWlIaHjVt8fLywtHRkcuXLxMXF2e0YXilalA9eoqilNns2bOJjY0tcKuzO8V9Gzg0wNm64B0X\nyiMmJqZarLYtTK/6vfB08gT0PXyGYmZmxuDBg0lKSmLbtm0Ga3f79u1kZWXRt29fg7UJMG9sB36b\n2NmgbVZF7646yaM/HkBKiZmZGX5+fly5ckXN01NUoqcoStlcu3aN2bNn8/jjj9OlS5e7zl1IusDQ\nf4ayMmKl0Z5fnVbbFmXO0TlM3T3VoEOXDRs2pEuXLgQFBXHu3Llyt3flyhWCg4Px8/PDxcVwhbIB\nLDRmuaVFqrPHO3kwbXBLdDnfBv7+/sTFxXHhwgWTxqWYnkr0FEUpk08++YSMjAxmzZp13zm3Gm48\n2+ZZetfvbZRn3xm29fT0rHbDtveqZV0LN1s3smW2Qdvt168fLi4urFmzhrS0tDK3k5WVxZo1a7C3\nt6dnz54GjBD2nY1n3vazuaVFqrMunrUY2aEeGjN9z/qdwslBQUEmjkwxNZXoKYpSaqGhofzyyy+8\n+OKLNG3a9L7zNuY2vNzhZYNuc5bftWvXSExMrFarbQszofUEpnWZhoWZYVc0W1hY8Mgjj5CamsqK\nFSvQ6XRlamfr1q3Ex8czcuRIrKysDBrj4agbLN4fhaVG/SoDiElK51R0EgBdunRBCEF4eDjp6ekm\njkwxJfXToShKqU2bNg1bW1umT59+1+sJ6Qm8sPUFziaeNerzQ0JC0Gg01W61bVHO3zzPr6d+NWib\ndevWZdiwYURFRbFx48ZSDw8fP36coKAg/Pz88PT0NGhsAG8O9OLgtH6YmRlna7iq5q0VJ3h75UkA\nHB0dadKkCZcvX1bz9Ko5legpilIq+/btY82aNbz33nv37aN56dYlopKiMBPG+69Fp9Nx6tQpmjVr\nho2NjdGeU9WsP7+eX0/9yo00w5bT8Pb2plu3bhw9epTNmzeXONmLjIxk/fr1eHp60r9/f4PGlJ+1\nhcZobVc1bw5szleP5u0j7e/vz5UrV7h27ZoJo1JMTSV6iqKU2J2tzurWrcvrr79+33nv2t5sGLWB\nJk5NjBZDVFQUycnJtG3b1mjPqIpeaP8Ca0asoZZNLYO33a9fP7p06UJgYCArV64kIyOjyOtPnDjB\nX3/9Re3atXn88cfRaAyfjB06f4PX/z7O9VtqWPKOjg1q0tYjr3B0nz59SE9P58iRIyaMSjE1legp\nilJi//zzD4cOHWLGjBl3LYJIz04nIEq/m4Kh54rdKyQkBCsrK5o3b27U51Q1VhoratnUQkpp8KFz\nIQSDBg2if//+hIaGsmDBAk6dOnXfvL2bN2/yzz//sHr1aho2bMiECROwtrY2aCx3xCSlczgqIbdI\nsKJ38NwNAs/re3XvLH45dOiQKUNSTExU52ri+fn4+Ej1rkdRCpeVlUXr1q2xtLQkODj4rl0w/g77\nm5mBM/lr6F+0cWlj1Bhmz55N69atCyzQrMDS0KV8HfQ1q4avMkrP6sWLF9m0aROxsbHUqFEDDw8P\nLC0tSUhIIDo6GjMzM7p3707Pnj2N0pOnFO2huXtwtbfi9+e6IKWkVq1aNGjQgGPHjmFmpvp2HiRC\niKNSSp/irlM7YyiKUiILFy7k7NmzrF+//r6tzp7weoLGjo2NmuQBhIeHk5mZqYZtizDMcxgADR0a\nGqX9hg0b8vzzzxMeHs6ZM2eIjY0lKysLBwcHevXqRceOHXFwcDDKs5XizR/bgdoO+l5UIQQ+Pj4c\nPnyYxMREatUy/LC+UvmpRE9RlGLdvn2bjz/+mN69ezNkyJDc13VSR3p2OrYWtnRx71JEC4YREhKC\nvb09jRo1MvqzqipHK0eeavkUoJ9Tee+OJYZgZmZGy5YtTbbq+ejFBGasO8PXj7enuZu9SWKorJrd\n8/fRo0cPtm7dyvHjx426KEapvFQ/rqIoxfr666+Ji4vjq6++uitxWBmxkhFrRuRud2ZMqampREZG\n0rZtW6MkLw+akLgQxmwYQ1xqnKlDMbgsrcTKQoOrnWHr8j0IsrU6fj90kf2R8QAMGjQIgJ07d5oy\nLMWEVKKnKEqRrl27xjfffMPo0aPx9fW965yXsxe9PHrhZutm9DhCQkLQ6XS0a9eu+IsV7C3tydJl\ncSPdsOVWKgM/z1osf8GfmjUsTR1KpaMxE8zbfpaNIfqSKp06dcLa2prDhw+bODLFVNTQraIoRfr4\n44/Jyspi5syZ951r79qe9q7tjR6DlJLjx49Tt25d3NyMn1Q+CBo5NmLVw6seuN5PXc5mrqpIcsGE\nEAS81gPnnCRYo9Hg5eXFqVOnTByZYiqqR09RlELd2epsypQpNGmSt4Jz75W9/Bj8I1narAqJ49q1\na8TGxuLt7V0hz3tQCCHI1mXzV9hfpGWXfb/ayuTU1SS8Z2zJLSGi3K+WndVdCb6vry8xMTFcvXrV\nhFEpplKiRE8IYSaEeEMIESaESBdCXBZCfCOEqFHSBwkhhgghDgghUoQQCUKIFUKIxgVc11sIIQv5\nWF+ethVFKZ333nsPOzs7Pvzww7teD7wWyOYLmyssjuPHj2Nubq5W25bB6RunmRU4i4CoAFOHYhA2\nFhqGtnOnsUuJf/1UO0lpWcxYd4YD5/Tz9Hr16gVAQMCD8T2glE5Jh27/B7wK/At8A7TMOe4ghOgv\npSxyt2shxChgJXACeBtwBF4H9gshfKSUBb3N+BnYe89rVwzUtqIoxdizZw9r165l1qxZuLi43HXu\nLd+3eLH9i1hojF+sNisri5CQEFq1amW04rsPsvau7fl72N+0cm5l6lAMopmbPZ+PUvM0i2JrqWF1\ncDT1nW3o2sSFAQMGYGZmxq5du5g4caKpw1MqWLEFk4UQrYEQ4F8p5aP5Xn8FmAc8JaX8s4j7LYAL\nQDbQWkqZnPO6N3AUWCSlfD7f9b2BncCzUsr/Kya2UrVdFFUwWVHySClz98mMiIjI3QUjKikKG3Mb\n6tSoU2GxnDx5kn///ZcJEyaosirllJCegJOVk1H3IjYmnU4Sn5JBbXuV8BdHq5NocuYxSilp3Lgx\n1tbWhIWFmTgyxVBKWjC5JD/tYwEBzL3n9YVAKjCumPt7AXWBX+4kYgBSymBgFzA6J2G7jxCihhCi\nqJ/oMretKErhVqxYQWBgIJ9++uldW519cvATntv8HFqdtsJiOXbsGDVr1qRhQ+MUAK4uLt+6zMP/\nPsyK8BWmDqXMzl5PpvPM7Ww4ec3UoVR6mnyLVYQQtG3blsjISFJSUkwYlWIKJUn0fAEdcNfabCll\nOhCcc764+wEOFnDuEOAAFLRp5bdAMpAmhIgQQrwm7l8+Vta2FUUpRHp6Ou+++y7t2rVj/Pjxd537\ntNunfOT/ERqzitna6vr161y8eJFOnTo9cKtHK5qHvQePNnsU3zrF/ZddedWsYcEHQ1rSsaGTqUOp\n9K7fTueZxYfZHhoLQNeuXdFqtezde++MKOVBV5JEry4QL6XMKOBcNOAihCiqmFHdfNcWdD9AvXyv\nZQFrgXeA4cCLwE30PYq/lrNtRVGK8e2333LhwgXmzJmTu1dpti4bgPr29ens3rnCYjl8+DDm5uZ0\n6NChwp75oBJC8KbPm3g6eZo6lDKrbW/N5J6euDvamDqUSq+mrSXxyRmkZup73+/M01u/vsA1jcoD\nrCSLMWyBgpI8gPR812QWcT+FtJF+zzVIKfcDI/JfJIRYCGwEnhFC/JJzTanbvpcQ4nngeYAGDRoU\ndpmiVBvXr19n5syZPPzww/Tr1y/39am7plLbtjYf+H1QYbGkp6dz8uRJ2rRpc9fwsVI+qVmpzD02\nlx71etDDo4epwykxKSVHLibStp4j1hYV06NclVlozFj/St6/b9OmTalXrx67d+82YVSKKZSkRy8V\nKGyfGet81xR1P4W0UZL7yVnV+3nO4VBDtS2l/FlK6SOl9HF1dS0qBEWpFqZPn05aWhpff/117mta\nnZbGjo2pb1+/QmMJDg4mKyuLzp0rrgexOjA3M+fwtcOEJ4abOpRSuZSQyuMLDrLi6H3FF5RiSClx\ndHSkWbNmnDlzhlu3bpk6JKUClSTRu4p+eLagZKoe+mHdwnrz7tx/59qC7oeCh17vdSHnc/46D4Zq\nW1GqvVOnTrFw4UKmTJmCl5dX7usaMw2vd3qd8a3HF3G3YUkpCQoKwsPDA3d39wp7bnVgqbFk2cPL\nmNR2kqlDKZXa9tYsmuDDgJZqZ5SSunQjlZ5f7STgVAxCCDp37oxOp1Pz9KqZkiR6QTnX3fW2Omc1\nrDdQXE2SoJzP/gWc8wNuAREliKNZzudYI7StKNWalJKpU6fi6OjI9OnTc1//7fRvhN4IrfB4IiMj\nSUhIUL15RmKl0b9vP3fzHJGJkSaOpmRsLDX0a+lGHUdVWqWk6jha07aeI062+mn03bt3x9zcnG3b\ntpk4MqUilSTRWwZI9EWI85uMfv7b0jsvCCHchRAthBD5J9TsBq4Bk4QQdvmubQ/0BlZIKbPyvV7r\n3gByehM/zjlcV9a2FUUpWEBAAFu2bGH69OnUqqX/EUzOTGbJ6SWsObemwuPZv38/9vb2tGr1YBT5\nrYyydFm8uO1FZh+ZbepQiiWlZFnQJa4lPRjbuFUUS3Mzvn+qI/5N9D/TjRs3xsPDQyV61UyxBZMB\nhBDzgZfR74yxkbydMfYDfe/sjCGE+D9gAtBHSrkr3/2Po08YT6Cvv+cAvIE+gewkpYzOd20Q+iHZ\nozmf66Kv1dcMmC+lfPWe2ErcdlFUwWSlusrKyqJ9+/ZkZ2dz6tQpLC3zFtHfyryFuTDH1qLiFkNc\nuXKFRYsWMXDgQPz9C+qsVwwl+HowDRwa4GztbOpQihR5/Tb95+zhy0fbMtpXLZwrrdTMbMyEIC35\nFo8++ii7du0iPj4eZ+fK/e+uFM2QBZNB35v3FtAa+B4YA8wHhhW3/RmAlHIF+lIpGcBs4F30y+Z/\nogAAIABJREFU25t1KyARWwnUBl4BfgTeRD/P7sl7k7wytK0oyj0WLlxIaGgoX3/9dW6SdzbxLFJK\nHCwdKjTJA31vnrW1NR07dqzQ51ZH3rW9cbZ2RkpJWnbl7S1r4mrHzrd681BrNV+ztMJibtHu4y3s\nDLuOk5MTXl5eSCnV6ttqpESJnpRSK6X8RkrpJaW0klLWk1K+mX83ipzrnpFSivy9efnOrZdS+kkp\nbaWUNaWUj0kpzxVw3ZdSSn8ppauU0kJK6SSl7COl/KuI+ErUtqIod7t58ybTp0+nd+/eDB8+HICr\nyVcZu2EsC04uqPB44uPjCQsLw9fXFyurwhb7K4b27p53eWv3W5RkhMcUhBA0dqmBo63a6Ki0mrja\n8XxPT5rUtstdkGFpacnOnTtNHZpSQUpSR09RlAfUJ598QkJCAnPmzMndeaJOjTq82/ldetbrWeHx\n7N69GwsLC7p06VLhz67OOrl1IkObgUQiqFw7kGh1kq8CwhjuXZfWdR1NHU6VY6Ex452HWuQe169f\nn/r167Njxw4TRqVUJJXoKUo1dfr0aebPn8/kyZNzd56QUmImzHi8+eMVHk9sbCynTp2ie/fu1KhR\no8KfX52NbjHa1CEU6uKNFP7vwAVa1XVQiV4ZSSmJiE3G3cmaevXq0bhxY7Zt28a1a9dU+aJqoKRz\n9BRFeYBIKXn11VdxcHBg5syZACSmJzJ6/WiCYoKKuds4du3ahZWVFV27djXJ8xU4ePUgPwb/aOow\n7uLpaseJjwYyqHUdU4dSZZ2+eotBc/ewPTQWDw8PmjRpAsCWLVtMHJlSEVSipyjV0KpVq9ixYwef\nfvopLi76GuSJ6YkAOFlV/Ibx0dHRhIWF4e/vj42N2sfUVA5cPcDGqI2kZhW5WVGFs7bQqG3PyqGV\nuwNfP9aObk1dsLe3p3nz5jg6OrJ582ZTh6ZUgBKVV6kOVHkVpbpITU2lZcuWODk5cfToUczN82Zw\nSClz5+pVFCklixcvJiEhgVdeeUUtwjCh9Ox0hBC5BZVNLTNbx5Slx3i2WyO6NXUp/galRFauXMmX\nX37JhQsXiI2NxcxM9flURSUtr6Lm6CnKAyA7O5uLFy8SHR1NYmIiWVlZaDQa7O3tqVOnDg0bNsTe\n3h6AL774gkuXLvH7779jbm5OWnYay8OX82SLJ7HQVPyqxpCQEC5fvsz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WSsOr/Zrh36RW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B3c1vE2bux1Y9V/U3c44GC67nqpnaBb4967HAaMh063Q3YWTOivgxO3Gqy7YWy5ZsJENcfuEAa+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\n7rSsF8n3m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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for _ in range(50):\n", " #E-step\n", " log_p_xz = sps.norm.logpdf(x[:,np.newaxis], mus, sigmas) + np.log(pis)\n", " log_p_x = logsumexp(log_p_xz, axis=1, keepdims=True)\n", " print \"Training data log likelihood:\", log_p_x.sum()\n", "\n", " gammas = np.exp(log_p_xz - log_p_x)\n", " #M-step\n", " Nc = gammas.sum(axis=0)\n", " mus = x.dot(gammas) / Nc\n", " sigmas = np.sqrt((x**2).dot(gammas) / Nc - mus**2) # we use std, not variance!\n", " pis = Nc / Nc.sum()\n", " \n", "plot_GMM(t, mus, sigmas, pis)\n", "\n", "plt.clf()\n", "plt.plot(t, true_GMM_pdf, 'gray')\n", "plot_GMM(t, mus, sigmas, pis);\n", "plt.plot(x, np.zeros_like(x), '+k');" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 2 }