{ "cells": [ { "cell_type": "code", "execution_count": 124, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy.stats as sps\n", "import matplotlib.pyplot as plt\n", "from scipy.special import logsumexp\n", "from scipy.special import digamma\n", "from scipy.special import gamma \n", "from scipy.special import loggamma \n", "%matplotlib inline\n", "#%matplotlib qt5\n", "plt.rcParams.update({'figure.figsize': (8.0, 6.0), 'font.size': 11})" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Gaussian Mixture Model (GMM)\n", "* probability density finction\n", "\n", "$$\n", "\\large\n", "\\DeclareMathOperator{\\NormalGamma}{NormalGamma}\n", "\\DeclareMathOperator{\\Norm}{\\mathcal{N}}\n", "\\DeclareMathOperator{\\Gam}{Gam}\n", "\\DeclareMathOperator{\\e}{exp}\n", "p(x|\\boldsymbol{\\mu}, \\boldsymbol{\\sigma^2}, \\boldsymbol{\\pi}) = \\sum_{k=1}^{K} \\Norm(x|\\mu_k, \\sigma^2_k) \\pi_k\n", "$$\n", "\n", "* $\\boldsymbol{\\mu}$ is the vector of $K$ means\n", "* $\\boldsymbol{\\sigma}^2$ is the vector of $K$ variances\n", "* $\\boldsymbol{\\pi}$ is the vector of $K$ weights such that $\\sum_{k=1}^K \\pi_k = 1$ " ] }, { "cell_type": "code", "execution_count": 125, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot GMM pdf together with the individual components pdfs; return the GMM pdf line\n", "t = np.linspace(-10,10,1000)\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', label='ML estimate')\n", " return px\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", "\n", "plt.clf()\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')\n", "\n", "#Log likelihood of the training data evaluated using the true distribution\n", "true_tll = np.sum(logsumexp(sps.norm.logpdf(x[:,np.newaxis], mus, sigmas) + np.log(pis), axis=1))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## GMM - EM algorithm\n", "* E-step\n", "\n", "$$\n", "\\DeclareMathOperator{\\Norm}{\\mathcal{N}}\n", "\\DeclareMathOperator{\\eeta}{\\boldsymbol{\\eta}}\n", "\\gamma_{nc}=P(z_n=c|x_n,\\eeta^{old})=\\frac{p(x_n|z_n=c,\\eeta^{old})P(z_n=c|\\eeta^{old})}{p(x_n|\\eeta^{old})}\n", "=\\frac{\\mathcal{N}(x_n|\\mu_c^{old}{\\sigma_c^2}^{old})\\pi_c^{old}}{\\sum_{k}\\mathcal{N}(x_n|\\mu_{k}^{old},{\\sigma_{k}^2}^{old})\\pi_{k}^{old}}\n", "$$\n", "\n", "* M-step\n", "\n", "$$\n", "\\begin{align}\n", "\\mu_c^{new} & =\\frac{\\sum_n \\gamma_{nc}x_n}{\\sum_n \\gamma_{nc}}\\\\\n", "{\\sigma_c^2}^{new} & =\\frac{\\sum_n \\gamma_{nc}(x_n-\\mu_c^{new})^2}{\\sum_n \\gamma_{nc}}\\\\\n", "\\pi_c & =\\frac{\\sum_n \\gamma_{nc}}{N}\n", "\\end{align}\n", "$$" ] }, { "cell_type": "code", "execution_count": 126, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#Choose some initial parameters\n", "C = 6 # 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", "tll=[]\n", "\n", "plt.clf()\n", "plt.plot(t, true_GMM_pdf, 'r')\n", "plot_GMM(t, mus, sigmas, pis);\n" ] }, { "cell_type": "code", "execution_count": 138, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 138, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for _ in range(500):\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", " tll.append(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, 'r', label='true distribution')\n", "ml_GMM_pdf=plot_GMM(t, mus, sigmas, pis);\n", "plt.plot(x, np.zeros_like(x), '+r')\n", "plt.legend()\n", "\n", "plt.figure()\n", "plt.plot(tll, label='ML trained GMM')\n", "log_p_xz = sps.norm.logpdf(x[:,np.newaxis], mus, sigmas) + np.log(pis)\n", "plt.plot(np.repeat(true_tll, len(tll)), label='Grand truth GMM')\n", "plt.ylabel('training data log likelihood')\n", "plt.xlabel('iteration');\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Variational Bayes \n", "\n", "$$\n", "\\DeclareMathOperator{\\aalpha}{\\boldsymbol{\\alpha}}\n", "\\DeclareMathOperator{\\bbeta}{\\boldsymbol{\\beta}}\n", "\\DeclareMathOperator{\\NN}{\\mathbf{N}}\n", "\\DeclareMathOperator{\\ppi}{\\boldsymbol{\\pi}}\n", "\\DeclareMathOperator{\\mmu}{\\boldsymbol{\\mu}}\n", "\\DeclareMathOperator{\\llambda}{\\boldsymbol{\\lambda}}\n", "\\DeclareMathOperator{\\diff}{\\mathop{}\\mathrm{d}}\n", "\\DeclareMathOperator{\\zz}{\\mathbf{z}}\n", "\\DeclareMathOperator{\\XX}{\\mathbf{X}}\n", "\\DeclareMathOperator{\\xx}{\\mathbf{x}}\n", "\\DeclareMathOperator{\\YY}{\\mathbf{Y}}\n", "\\DeclareMathOperator{\\NormalGamma}{\\mathcal{NG}}\n", "ln\\ p(\\mathbf{X})=\\mathcal{L}(q) + KL (q||p)\n", "$$\n", "\n", "\\begin{equation}\n", "\\begin{split}\n", "& {\\mathcal{L}(q) = \\int q(\\YY)\\ \\ln\\left\\{ \\frac{p(\\XX,\\YY)}{q(\\YY)} \\right \\}d\\YY}\\\\\n", "& {KL (q||p)=-\\int q(\\YY)\\ \\ln\\left\\{ \\frac{p(\\YY|\\XX)}{q(\\YY)}\\right\\}d\\YY}\n", "\\end{split}\n", "\\end{equation}\n", "\n", "where $\\XX=\\{x_1, x_2,...,x_N\\}$ is the data (i.e. all observed variables), $\\YY=\\{\\zz,\\mmu, \\llambda,\\ppi\\}=\\{z_1, z_2,\\dots,z_N,\\mu_1, \\lambda_1,\\mu_2, \\lambda_2,\\dots,\\mu_C, \\lambda_C,\\pi_1,\\pi_2,\\dots,\\pi_C\\}$ is the collection of all the hidden variables (incluting GMM parameters) and the approximate posterior distribution\n", "$p(\\ppi,\\mmu, \\llambda,\\zz | \\XX)\\approx q(\\ppi,\\mmu,\\llambda)q(\\zz)=q(\\ppi)\\prod_{c=1}^C q(\\mu_c,\\lambda_c)\\prod_{n=1}^N q(z_n)$\n", "\n", "* VB GMM update for $q(\\mmu, \\llambda)=\\prod_{c=1}^C q(\\mu_c,\\lambda_c)$\n", "\n", "\\begin{equation*}\n", "\\begin{split}\n", "q(\\mu_c, \\lambda_c)^* \n", "&= \\NormalGamma\\left(\\mu_c,\\lambda_c \\,\\middle|\\, \\frac{\\kappa m +N_c \\bar{x}_c}{\\kappa+N_c}, \\kappa+N_c, a+\\frac{N_c}{2},\n", "b+\\frac{N_c}{2}\\left(v_c+\\frac{\\kappa (\\bar{x}_c-m)^2}{\\kappa+N_c}\\right)\\right)\\\\\n", "&= \\NormalGamma\\left(\\mu_c,\\lambda_c \\,\\middle|\\, \\frac{\\kappa m + f_c}{\\kappa+N_c}, \\kappa+N_c, a+\\frac{N_c}{2},\n", "b+\\frac{1}{2}\\left(s_c+\\kappa m^2 - \\frac{(\\kappa m + f_c)^2}{\\kappa+N_c} \\right)\n", "\\right)\\\\\n", "&= \\NormalGamma\\left(\\mu_c,\\lambda_c \\,\\middle|\\, m_c^*, \\kappa_c^*, a_c^*, b_c^*, \\right)\n", "\\end{split}\n", "\\end{equation*}\n", "\n", "\\begin{equation*}\n", "\\begin{split}\n", "N_c & = \\sum_n \\gamma_{nc} \\\\\n", "\\bar{x}_c &=\\frac{\\sum_n \\gamma_{nc}x_n}{\\sum_n \\gamma_{nc}} \\\\\n", "v_c &=\\frac{\\sum_n \\gamma_{nc}(x_n-\\bar{x}_n)^2}{\\sum_n \\gamma_{nc}}\\\\\n", "f_c &=\\sum_n \\gamma_{nc}x_n \\\\\n", "s_c &=\\sum_n \\gamma_{nc}x_n^2\n", "\\end{split}\n", "\\end{equation*}\n", "\n", "\n", "* VB GMM update for $q(\\ppi)$\n", "\n", "\\begin{equation*}\n", "\\begin{split}\n", "q(\\ppi)^* &=\\sum_c \\sum_N \\gamma_{nc} \\ln \\mathrm{Cat}(z_n=c|\\ppi)+ \\ln \\mathrm{Dir}(\\ppi|\\aalpha)+const\\\\\n", "&=\\mathrm{Dir}(\\ppi|\\aalpha+\\NN)\\\\\n", "&=\\mathrm{Dir}(\\ppi|\\aalpha^*)\\\\\n", "\\end{split}\n", "\\end{equation*}\n", "\n", "\\begin{equation*}\n", "\\begin{split}\n", "\\NN&=[N_1,N_2\\dots,N_C]\\\\\n", "N_c&=\\sum_n \\gamma_{nc}\n", "\\end{split}\n", "\\end{equation*}\n", "\n", "* VB GMM update for $q(\\mathbf{z})=\\prod_{n=1}^N q(z_n)$\n", "\n", "\\begin{equation*}\n", "\\begin{split}\n", "q(z_n=c)^* &= \\gamma_{nc} = \\frac{\\rho_{nc}}{\\sum_k{\\rho_{nk}}}\\\\\\\\\\\n", "\\ln \\rho_{nc} &= \\iint q(\\mu_c, \\lambda_c) \\ln \\mathcal{N}(x;\\mu_c,\\lambda_c^{-1}) \\diff\\mu_c \\diff\\lambda_c &+&\\int q(\\ppi)\\ln \\mathrm{Cat}(z_n=c|\\ppi) \\diff\\ppi\\\\\n", "&= \\frac{1}{2}\\left(\\psi(a_c^*)-\\ln b_c^*-\\frac{1}{\\kappa_c^*}-\\frac{a_c^*}{b_c^*}(x_n-m_c^*)^2-\\ln(2\\pi)\\right)&+&\\ \\psi(\\alpha_c^*)-\\psi\\Big(\\sum_c\\alpha_c^*\\Big)\\\\\\\\\n", "%\\ln q(z_n=c)^* &= \\ln \\rho_{nc} + const\n", "\\end{split}\n", "\\end{equation*}\n", "\n", "* VB GMM approximate posterior predictive distribution\n", "$$\\begin{align*}\n", "\\\\\n", "p(x' \\mid \\mathbf{x}) \n", "\\approx \\iiint p(x'|\\mmu, \\llambda,\\ppi) q(\\mmu, \\llambda,\\ppi) \\diff\\mmu \\diff\\llambda \\diff\\ppi \n", "=\\sum_c St\\left(x'|m_c^*,2a_c^*,\\frac{a_c^* \\kappa_c^*}{b_c^*(\\kappa_c^*+1)}\\right)\\frac{\\alpha_c^*}{\\sum_c \\alpha_c^*}\\\\\n", "\\\\\n", "\\end{align*}$$\n", "\n", "\n", "* Calculation of Evidence Lower Bound (ELBO)\n", "\n", "\\begin{equation}\n", "\\begin{split}\n", "\\mathcal{L}(q) &= E_{q(\\zz,\\ppi,\\mmu,\\llambda)}\\left\\lbrace \\ln\\left(\\frac{p(\\xx,\\zz,\\ppi,\\mmu,\\llambda)}{q(\\zz,\\ppi,\\mmu,\\llambda)}\\right)\\right\\rbrace\\\\\n", "&= E_{q(\\zz)}\\left\\{ E_{q(\\mmu,\\llambda)}\\left\\{\\ln\\ p(\\xx|\\zz,\\mmu,\\llambda)\\} \n", " + E_{q(\\ppi)}\\{\\ln p(\\zz|\\ppi)\\right\\}\\right\\}\n", " - E_{q(\\zz)}\\{\\ln q(\\zz)\\}\n", " - E_{q(\\ppi})\\left\\{\\ln \\frac{q(\\ppi)}{p(\\ppi)}\\right\\} \n", " - E_{q(\\mmu,\\llambda)}\\left\\{\\ln \\frac{q(\\mmu,\\llambda)}{p(\\mmu,\\llambda)}\\right\\}\\\\\n", "&= \\sum_n\\sum_c\\left\\{\\gamma_{nc} \\ln \\rho_{nc} \\right\\}\n", " - \\sum_n\\sum_c\\left\\{\\gamma_{nc} \\ln \\gamma_{nc} \\right\\}\n", " - KL(q(\\ppi)||p(\\ppi)) \n", " - KL(q(\\mmu,\\llambda)||p(\\mmu,\\llambda))\\\\\n", "&= \\sum_n \\ln \\sum_c \\rho_{nc}\n", " - KL(q(\\ppi)||p(\\ppi)) \n", " - KL(q(\\mmu,\\llambda)||p(\\mmu,\\llambda))\n", "\\end{split}\n", "\\end{equation}\n", "\n", "where the Kulback-Leibrer divergences\n", "\n", "$$\n", "KL(\\mathrm{Dir}(\\ppi|\\aalpha)\\,||\\,\\mathrm{Dir}(\\ppi|\\bbeta)) = \n", "\\log \\Gamma\\Big(\\sum_c\\alpha_c\\Big) – \\sum_c \\log \\Gamma(\\alpha_c) -\\log \\Gamma\\Big(\\sum_c\\beta_c\\Big) + \\sum_c \\log \\Gamma(\\beta_c) + \\sum_c (\\alpha_c – \\beta_c) \\left(\\psi(\\alpha_c)-\\psi\\Big(\\sum_c\\alpha_c\\Big)\\right)\n", "$$\n", "\n", "\\begin{equation}\n", "\\begin{split}\n", "KL\\left(\\NormalGamma(\\mu,\\lambda|m_1,\\kappa_1,a_1,b_1)\\,||\\NormalGamma(\\mu,\\lambda|m_2,\\kappa_2,a_2,b_2)\\right)\n", "=\\frac{1}{2} \\left(\\frac{a_1}{b_1} \\kappa_2 (m_2-m_1)^2 + \\frac{\\kappa_2}{\\kappa_1} - \\ln\\frac{\\kappa_2}{\\kappa_1} - 1\\right) + a_2 \\ln\\frac{b_1}{b_2} - \\ln\\frac{\\Gamma(a_1)}{\\Gamma(a_2)} + (a_1-a_2) \\psi(a_1)-(b_1-b_2) \\frac{a_1}{b_1}\n", "\\end{split}\n", "\\end{equation}\n" ] }, { "cell_type": "code", "execution_count": 139, "metadata": {}, "outputs": [], "source": [ "def NormalGamma(mu, lmbd, m, kappa, a, b):\n", " # sps.norm.pdf takes mean and std (not precision), therefore 1.0/np.sqrt()\n", " # sps.gamma.pdf takes shape and scale (not rate), therefore 1.0/b\n", " return sps.norm.pdf(mu, m, 1.0/np.sqrt(lmbd*kappa))* sps.gamma.pdf(lmbd, a, scale=1.0/b)\n", "\n", "def NormalGamma_plot(m0, kappa0, a0, b0, limits):\n", " mu_vals, lmbd_vals = np.meshgrid(np.linspace(limits[0], limits[1], 500), np.linspace(limits[2], limits[3], 500))\n", " pdf = NormalGamma(mu_vals, lmbd_vals, m0, kappa0, a0, b0)\n", " plt.imshow(pdf, origin='lower', cmap='Greys', extent=limits)\n", " plt.xlabel('$\\mu$'); plt.ylabel('$\\lambda$')\n", "\n", "def plot_VB_GMM(t, mN, kappaN, aN, bN, alphaN):\n", " # VB approximate posterior predictive for GMM (i.e. mixture of student's-t)\n", " pis = alphaN/alphaN.sum()\n", " p_xz = sps.t.pdf(t[:,np.newaxis], loc=mN, df=2*aN, scale=np.sqrt(bN*(kappaN+1)/aN/kappaN)) * pis \n", " px = np.sum(p_xz, axis=1)\n", " plt.plot(t, p_xz, ':')\n", " plt.plot(t, px, 'k', label='VB posterior predictive')\n", " return px\n", "\n", "def NormalGamma_rvs(m, kappa, a, b, N):\n", " # Sample from NormalGamma distribution\n", " lmbd = sps.gamma.rvs(a, scale=1.0/b, size=N)\n", " mu = sps.norm.rvs(m, 1.0/np.sqrt(lmbd*kappa), N)\n", " return mu, lmbd\n", "\n", "def NormalGamma_KL(m1, kappa1, a1, b1, m2, kappa2, a2, b2):\n", " # Calculates KL(p1||p2) for two NormalGamma distributions \n", " return 0.5 * (a1/b1 * kappa2*(m2-m1)**2 + kappa2/kappa1 - np.log(kappa2/kappa1) - 1\n", " ) + a2*np.log(b1/b2) - loggamma(a1) + loggamma(a2) + (a1-a2)*digamma(a1)-(b1-b2)*a1/b1\n", "\n", "def Dirichlet_KL(alpha1, alpha2):\n", " # Calculates KL(p1||p2) for two Dirichlet distributions \n", " return (loggamma(np.sum(alpha1)) - np.sum(loggamma(alpha1)) \n", " - loggamma(np.sum(alpha2)) + np.sum(loggamma(alpha2))\n", " + np.sum((alpha1 - alpha2)*(digamma(alpha1)-digamma(np.sum(alpha1)))))\n", "\n", "#Choose some initial parameters\n", "C = 6 # number of GMM components \n", "\n", "#hyperparameters for gamma distribution for precission term (lambda)\n", "[a,b]=[0.05,0.05] \n", "#hyper parameters for normal distribution for mean term (mu)\n", "kap=0.05\n", "ms=0.0 #dummy initialization of m terms\n", "\n", "#hyperparameter for the weights\n", "alpha=np.ones(C)\n", "\n", "#use the statistics that come from the EM to initialize the model\n", "gammas = np.exp(log_p_xz - log_p_x)\n", "ELBO = []" ] }, { "cell_type": "code", "execution_count": 142, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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eeuklTCYT+/fvJyUlhV69ehEcHEzPnj2ZO3cu8fHxeHp6kpKSgqenJ/PmzeP9999ny5Yt+Pj4ADB9+nQGDBjAxx9/jMlkYuLEiXzyySc88MADABw4cIC1a9fi5uZmDS2A+Ph4Jk+ezKZNm+jUqRP/+9//mDhxItu3bwdg//79fPDBB7z77rs2P9Ply5cJDg5m7ty5bNq0iQkTJnDixAnrsY4dOzJnzhwAXn75Zfz8/NixYwcATzzxBK+++iqvvPIKDz/8MP379+ef//wnJ0+eJCQkhJEjR173vFdffZWTJ08SFRWFu7s7ly5dwt/fnxdffJGffvqJZcuWXXfN2LFjefTRR7l06RL16tVj9erVdOjQgcDAQJYsWcLx48fZtm0bLi4ufPDBBzz++ON8/vnndv87Cucl4S2cRZE1b611PBDNtZr0BGCP1jpftVgpFQEsBcZpraMKHGua5/sRQC5wlirg/vvvZ/HixeTk5LB06VL69u1L06bWj2ttNj9+/DgrVqzg7rvvJj093ea9br75Zho2bGi9r6V/PDIykgceeAClFL6+vkyYMIHIyEh8fX1p3749kyZNYsGCBaSmpuLmZvv3sR9++IF///vf1r733bt3c/ToUevxe+65x+a127dvJyQkhE6dOgEwdepUoqOjSUlJAaBt27b06tXL7p+Pu7s7kyZNAmDAgAF4enpy5Ijxe52Hhwd33nlnvjIuWbLEOkbghx9+sAb9hg0bmD59OmCs4DZkyBCbz/vpp5945JFHcHd3B8jXgmCPl5cXt912G1988QUAixYtsrae/PDDD0RGRhIWFkZoaCjz5s3L98uNqFokvIWzcHS0+UzgU6XU80ACRp82SqlVwPNa613A+4An8JFSynLdZK31fvO1DQETkAzcqrUu9f8WRdWMy0NISAiNGzdmzZo1LFy4kEcffdTuuQMHDiQ7O5uDBw8SERFR6H211lj+HPN+b6GUwtXVlW3btvH777+zfv16wsPDWbNmDcHBwTbvt3z5clq1amXzeZYaemHlKM519uS9n7e3d757a615//33GTy44IsMxbt/SUyZMoVHHnmEiRMnsmnTJuuSp1prnn32WaZNm1biMgnnIeEtnIVDfd5a68Na6x5a63bm7RHz/tHm4EZrHaG1rq+1Ds3ztd98bKjWuovWOkRr3U9rve3GfaTyN23aNObMmcPRo0e59dZb7Z5nafYODAy0eXzlypVY+vkXLVpkHfE9bNgwPv74Y7TWpKSk8NVXXzF06FBSUlK4ePEiAwYM4IUXXiAoKIgDBw4AUKtWrXzrcN9666289tpr1n7uS5cucerUqSI/W69evYiOjubw4cMAfPrpp3Tt2pVatWoV/QeD0QdtqdFu3ryZjIwM2rdvb/PcW2+9lTfffNM6AjwlJcXaBTF48GDr4MBTp06xbt06m/e45ZZbePvtt62D9Sx940Wtfd6vXz+Sk5N56qmnGDNmDF7mWTpuvfVW3n//fRISEgDIzMxk7969Dn124XwkvIWzkBnWysDEiRM5ePAgEydOtDbXWlj6vENCQpg4cSKLFi2ifv36Nu8zZMgQpk2bRufOnbly5Yp1ze/nnnsOrTVdunShV69eTJ48mZEjR5KUlMSYMWMIDg4mKCiIRo0acccddwDw+OOPM3jwYOuAtbfffhtXV1dCQkLo0qULI0eO5OzZonsu6tevz+LFi7nnnnsIDg5myZIlLFmyxOE/G39/f44dO0aPHj148MEH+fLLL6/7M7J48sknCQkJISIiguDgYPr27WsN73feeYcNGzYQEhLCE088wbBhw+zeIzAw0Nr0PnPmTOufbVpaGiEhIdYBawXdd999LFiwgClTplj3TZ48mYkTJzJgwACCg4MJDw/n999/d/jzC+ci4S2chaznXUnMmTOH1NRU5s6dW9FFKTOnT5+mW7du+UaGV2VV9e9mdfLRRzBzJixdCnfdBb/8AkOHVnSpRHUi63kLIUQxyXvewlk4OmBN3GCW16WqksDAwGpT6xZVg2WeIQlvUdlJzVsIIcwsYV2zZv6fhahsnDK8K3M/vaie5O9k1VDWNe8DB+CFFyA+vnT3EaIgp2s29/Dw4PLly/j7+xf6/rEQ5UVrzeXLl/Gw/IsvnFZZ1rwzM2H4cDh/HrZtgwKzBwtRKk4X3gEBAcTGxlLZ5z0X1YuHhwcBAQEVXQxRSmVZ81650gjuAQNgzRo4fhzatCl9GYUAJwzvGjVq0LJly4ouhhCiCirLmvfGjcb74h9+CB07Gq+dSXiLsuKUfd5CCHEj5OaCUmCZ5r804b15M/TsCe3bQ9OmsGlT2ZRRCJDwFkIIq9xcI7hLG97JybBvH/TrZ/wyMGCAEd4yrlGUFQlvIYQwy8kBV9fSh/ehQ2AyQXi48XPv3hAXBw7MSCyEQyS8hRDCrGDN2zKArbiOHTO2ljV4goKM7cGDpSufEBYS3kIIYVZWNe+jR437WMbWdu5sbM2L/glRahLeQghhVlZ93kePQmAgWBbQq1cPGjaUmrcoOxLeQghhVpY173bt8u/r3Flq3qLsSHgLIYRZbq4R3q6uxs8lCW+tbU/I0r69sV+IsiDhLYQQZpZmcxcX46sk4Z2cDKmp0Lx5/v0tW0JCAiQmlk1ZRfUm4S2EEGaWZnMwQrwk4W15HazgbLmWwWunTpW8fEJYSHgLIYSZpeYNJQ/v2FhjWzC8W7UythLeoixIeAshhFlZ1LzthbfUvEVZkvAWQggzy4A1KH14N2mSf3+dOuDnBydPlq6MQoCEtxBCWOXklE2zecOG197xzqtVK6l5i7Ih4S2EEGZlUfM+e9ZYRcyWli0lvEXZkPAWQgizshiwFhcHjRrZPmYJb5Op5GUUAiS8hRDCqiwGrF28CA0a2D4WGAiZmXDhQomLKAQg4S2EEFalrXlrDfHxUL++7ePNmhlbWRpUlJaEtxBCmJW25p2aatSs7YW35fUxy4h0IUpKwlsIIcxKO2Dt4kVjay+8LQPZpOYtSkvCWwghzPK+KubqWvbh3aCBcX+peYvSkvAWQgiz0ta84+ONrb0Bay4uRu1bwluUloS3EEKYlXbAWlE1bzD6vSW8RWlJeAshhFnBAWu5ucW73pHwbtpU+rxF6Ul4CyGEWVnUvD09wdvb/jmWmrfWJS+nEBLeQghhVtpXxeLj7fd3WwQEwNWrkJBQsjIKARLeQghhVRavihXWZA7yrrcoGxLeQghhVtpVxYoT3tLvLUpDwlsIIczKo+ZtmahFat6iNCS8hRDCrCwGrBUV3o0bg1IS3qJ0JLyFEMKsNAPWMjKMgWh16xZ+Xo0axpKhEt6iNCS8hRDCrDQ178REY1unTtHnyixrorQkvIUQwqw0NW/Lq1+1axd9bkCADFgTpSPhLYQQZqUZsGYJb0dr3hLeojQkvIUQwqw0r4oVN7wTEyE9vfhlFAIkvIUQwqo0Ne/i9nmD1L5FyTkU3kqpdkqprUqpo+ZtWxvnPKeUOqiU2quU2q2UGpHnmJdSaqlS6rhS6rBS6uay/BBCCFEWCg5Yy852/Nri1rxBBq2JknO05v0hME9r3Q6YB3xk45wdQITWOgSYBixVSnmaj80GUrTWbYBbgI+VUj6lK7oQQpQdk8lYLMRS83Z1Ld6qYsUdsAZS8xYlV2R4K6UaAGHAl+ZdXwJhSql8UxForddqrS09OPsABfibf74L4xcAtNbHgF3AqFKXXgghyoglqPPWvIsb3t7exnvcRZFmc1FajtS8mwFntda5AObtOfN+e+4FTmitLY1CzYE/8hw/U8T1QghRriz926Xp83akyRzAxwd8fSW8RcmV+YA1pdQA4CVgQgmvn6GU2qWU2nXRsrK9EELcYJZadt7wNpmML0ckJDge3iCvi4nScSS8/wSaKqVcAczbJub9+SilegFLgDFa6yN5Dp0BWuT5ubmt6wG01vO11t201t3qFzVJsBBClBFLLTtvszk43nRekvCWAWuipIoMb611PBDNtZr0BGCP1jpftVgpFQEsBcZpraMK3OYb4C/m89oCEcCa0hVdCCHKTsGat2XraNN5QoJjg9UsZJY1URqONpvPBB5SSh0FHjL/jFJqlVKqm/mc9wFP4COlVLT5q4v52L+B2kqp48BPwAytdUqZfQohhCglWwPWoHjhXdyad1xc8QbFCWHh5shJWuvDQA8b+0fn+T6ikOvTgPElKaAQQpQHWwPWwPFwLc6ANTDCOzcXLlyAJk0cv04IkBnWhBACKF3NOycHUlKKH94g/d6iZCS8hRAC+zVvR8K7OFOjWhjhncjBg/GOXySEmYS3EEJQugFrxZldDSAuLo7ZT9wC1GXatIYEdY0gKnpvscorqjcJbyGEwP6rYsUJb0dq3nFxcXTqGsGvv/6Ci8uTDBjwKkeOn6BX777s3r27+AUX1ZKEtxBCYHuSlrz7C+Nos3lubi533nknGckJ/N/cxQQ0e4XmzZ/k4+9+pr5/HcaOHUui5WZCFELCWwghKN2ANUdr3h9++CGbN2/mww/e552Hx9O0iSI2Fu4b1o1vl31DbGwss598umQfQFQrEt5CCEHpBqw5Et6pqanMfvo52oX2YPLkyUD+KVJ79OhB+Ihx/G/BfPYcOFSCTyCqEwlvIYTg+pp3WQ9Ye/Ott8lITuCuv/4DpRRwbZY1rY1zXn3pRWrW9OD1V14qwScQ1YmEtxBCUPpXxWrWBE9P28ezsrL44P15jBw5khdn3GHd37QppKVBcrLx8+Cwdjw4cwbfLlvGWZk7VRRCwlsIISjdgLWi5jVfuOQr4uLiePjhh/PttzVRy6xZ/4fJZOIfL/3bwZKL6kjCWwghsB/ejtS8k5PBz8/+8X/95x1q1GlM7wGD8+23hHfeSnarVi2p16k3333xGTnFWVBcVCsS3kIIQelGmxcW3qdPn+bMoSjumngffl418x0LCDC2ecNbKcXrTz1ERkoCkZGRxfgEojqR8BZCCErX552cDL6+to99/fXXALzw6APXHbMsSFKwe3vC2NuoU6cOixcvLvrholqS8BZCCEo3PWpSkv3w/vCTxXQOCaNVq1bXHfPwgPr14cyZ/Ptr1qxJr2G3sHTZtySnpDr4CUR1IuEthBCUbsCavWbzw4ePcOrIAeqHDLJ7bWAg/PHH9ft7DRlNblYm369cXXQBRLUj4S2EEJS+z9tWzfu7774F4K2nZtq9NjAQTp++fv8TU+/Az8+PzZFriy6AqHYkvIUQgpL3eWttP7xXrlxJt27dCO3Qxu71lpq3yZR/f40aNRg1ahQ//vgjpoIHRbUn4S2EEJT8VbG0NCN4C4b3pUuX2bp1G0E9BhR6fYsWkJkJFy5cf6x1twHEx8ez4pdNDnwCUZ1IeAshBCUfsGaZHa1gn/e3P65CaxPtI/oXen1goLG11e991+23oFxc+XnVysILIaodCW8hhMB+n3dRA9aSkoxtwZr3lo2R+Pv78/g9owu93hLetvq9u7RqSr++fdjx24bCCyGqHQlvIYSg5H3elpp33vA2mUysWbOG4cOHU6OGW6HXt2hhbG2FN8CQIUPYs2cPcfGXCi+IqFYkvIUQgpL3edtqNt8RtYf4+HiaBPUs8rk+PlCvnu1mc4B67cLRWrNwmTSdi2skvIUQgpKHt61m87WRRjN3334DHXp2YCCcOmX72J2jB1LTw4sjUVscupeoHiS8hRCCayFd3PW8bTWbR2//ndatWzOmX7BDz27dGo4ft32snq83gwcNYNtvMuJcXCPhLYQQlF2zuclkYtOmTQwcONDhZ7dta/R5Z2UBGRmQkpLv+IBBgzhy5AjHTtppWxfVjoS3EEJQ8ulRLc3mtWoZ2x2795CQkIB7QJDDz27XznjOqcH3g7e3UY0PD4e1xuxqDdqFAfDpd6scvqeo2iS8hRCC0tW8vb2vXbdhw0YAbhoxxOFnt7v4OwBH92fCP/4BL78MqakwciS89RbjhvXF08ub+OP7Hb6nqNoKf4dBCCGqiYJ93sUJ73wjzbf+RuvWrbmpVxfHHrxlC22fuAO4wNHHPoR/+hj7H3sM7r0XHnuMWk2b0rtXT3Zu3+rw5xFVm9S8hRCCks+wlnc5UK01m3/7nT59+jj20EuX4K67qNvcB/+6Jo4XglMVAAAgAElEQVSd97l2zNMTvvgCevaEGTMIbtuBvfv2cSUxyfEPJaosCW8hhOD68HZxAaUcq3lbwvvIseNcvnSRpFqBjj307383JjX/+mvatXfh6NECx2vUMALcZKL20fNok4llq2W2NSHhLYQQwPXhDUbTeVED1vI2m2/dYjRrT7h5aNEP3LoVFi2CRx+F8HDatYMjR2yc17IlPPUU0zavQinF+aN7i763qPIkvIUQAqOGbaltW7i5Fa/ZfNfO7fj4+DBuWO/CL9IanngCGjeGZ58FoEMHOHcOEhNtnP/IIwQ0bkAXT0+2bJHJWoSEtxBCAEYNO2+tGxwL77zN5hs2/07X8G64FrxRQRs3wubN8NRT1nfMQkKMQ3ttVaw9PeEf/6C9rsGvm38jp6hCiSpPwlsIIbAd3q6ujo82T0tLI+bgftJrty76YS+/bNS6H3jAuis01NjaDG+AqVOp06wDGVfT2bxzT9HPEFWahLcQQmCEt1uBl2eLqnmbTMZkaL6+sHPnTjCZuG/MsMIfdOAArF8Pf/sbeHhYdzdqBPXrQ3S0neu8vHhoaAQAxzatc+ATiapMwlsIITBC2lazeWED1lJTje5rX1/Ytm0bAPfcUsRgtXnzoGZNuP/+fLuVMmrfdmveQOfZj1EH2LVsWeHPEFWehLcQQlCyPu+885qvWf8rzVu2xt/f3/4FSUmweDFMmGCsA1pASIhRMc/Otn25atmS5g2bsfLYH0a1X1RbEt5CCEHpwtvXF3bs2El23VaFP2TJEkhLg1mzbB4ODTUWJ4mJsX+LWp0jOJ9yhfRffin8WaJKk/AWQghK1udtWZQkJ+c8V5MuMfmWQYU/ZPFio3rdrZvNw716GdvffrN/i0fuH4vWJvYtWFD4s0SVJuEthBDY7vMuarS5peZ99uxuAG4e3Nf+yceOwfbtMGmS3VNatoSAAPj1V/u36dG/PwA7f/656BlkRJUl4S2EENhvNi8sHy3hHRXzO0opOgYF2z/588+NUWkTJtg9RSno3x82bTIGwtnStGlTfGrVZknNuvD77/afJ6o0CW8hhKBkfd6WZvPd+7bjVjcAX8ui3gVpbYT3oEHQtGmh5ejfH+Li4Phx28eVUvi36sypq0nw9deF3ktUXRLeQghByfq8LTXvlHNHuHlQb9zd7PyTumOHkcaFNJlbDBhgbDcUsv7ItDuGcyktkZTly+1X0UWVJuEthBDYf8+76PCOI+78Ofr17mH/xK++And3uOOOIsvRvj0EBsKKFfbP6datGxqIOnsWDh4s8p6i6nEovJVS7ZRSW5VSR83btjbOGa6U2qWUylRKzS1wbI5SKl4pFW3+mldWH0AIIcpCSaZHTUoCrzrGQiHN2na2fZLWsHw5DBt2bfmxQihlZHxk5LWafUHtOhkToS9s2AZWrSrynqLqcbTm/SEwT2vdDpgHfGTjnJPAA8C/7dzjM611qPnL9kuOQghRQUo6YM3NczugCGjTyfZJe/fC6dNw++0Ol2XcOON9b3sTqbVu0QRPv3r86ZILK1c6fF9RdRQZ3kqpBkAY8KV515dAmFKqft7ztNbHtdZ7AFnuRgjhdEra561TjtCuXTsi2tkZiPb998Zao7fc4nBZevaEjh1h/nzbx5VSDOwdwaXcNGPEuc11REVV5kjNuxlwVmudC2DenjPvL467lVL7lFI/K6V6FfNaIYS4oUrS552UBJmZu+nWLRxXF2X7pO+/hz59oEEDh8uiFMycabwWbm/CltDQUA5dvkxGbi7IbGvVTnkNWPsQaKm1DsZoVl+hlLI5AbBSaoa573zXxYsXy6l4QojqriSvil2+HE9WVizeTa4bBmQ4cQL27y9Wk7nF9OnQsCE884ztAeXuDVuRk5vLzw2aGauUiWrFkfD+E2iqlHIFMG+bmPc7RGsdp7XONn//i/naIDvnztdad9Nad6tfv76tU4QQosyVZMBa/MWdAHg1tRPeliHjY8YUuzxeXvDii8Zsa7ZmQu3bw5hi9XDTxhLe1VCR4a21jgeiAcu0QBOAPVprh6vFSqmmeb4PBQKBI8UqqRBC3EAlmts8cQ8AL0y92fYJK1dC587GvKcl8MADMHgwPP64UYHPa3D3YLy9vYn1doejR+HcuRI9QzgnR5vNZwIPKaWOAg+Zf0YptUop1c38fV+lVCzwGPAXpVSsUmqE+fp/KaUOKKX2AguAyVrruDL9JEIIUQolWc87PT2K2rXb4mfrFbCUFNi8GUaPLnGZlIJPPzVWLRs1CmJjrx1zcXEhJCSE3Smpxo7CZnURVY5b0aeA1vowcN0MBFrr0Xm+/w0IsHP9fSUtoBBClIfi9nnn5oLJbTcejTrYPmH9emNh7lGjSlWugABYvRr69oURI4zfB+rWNZehTgt27l6BqXZtXNavh4kTS/Us4TxkhjUhhKD44X3uXAo68wyejeys4b16Nfj4GCPNSyk4GH74wRj/dtNNxpLgAH17dsOUmc7xiAipeVczEt5CCIHtPu/CBqzt3Gl0Qt8UZKNZXGsjvIcONaZFLQMDBxqzrO7YYSxMZjLB3SON5UH3N2sGp04Zk8GIakHCWwghKP573tHR+wDo1MnGMqCHDsGZM6VuMi9ozBh46y348Ud4800ICgrC1dWV37X5n3KpfVcbEt5CCEHxp0fduGMbqkYtfBvXu/7g6tXGtozDG+Chh4zXxp9+Gs6c8aBm/eZ8t+ew0REu63tXGxLeQghB8fu8z5w4iFud1jStV/P6g6tXQ1AQNCvuRJRFUwo++AA8PY0gjwjrSvr5E9CrF2zZUubPE5WThLcQQlC897xNJhMXYg+THd+Xhv4FLkpLM+Y0HTnyhpW1YUNjApeff4Z2TXtz8cJ5LoaEQEwMXLlyw54rKg8JbyGEwHaft70Ba6dOnSIjIxUIwde3wMHffjOWBBs27EYVFTDmPg8IgK1bjeVBN/ua3x/buvWGPldUDhLeQghB8ZrNd+w2ZlbzaNXo+vCOjDRGmPfte2MKalazJvzjHxDzRxsAvo+9YhRY+r2rBQlvIYSgeAPW9kRHg3JBZwfj41Pg4Lp10Lu3MTn5DTZ9Ovi6taCGRz2yE/6Erl2l37uakPAWQgjs93nn5l6/qtexmIPUqd0Wj+TmqLwrgV66BHv2GO93lwNPT7jvPkVOZghHDsYYvzTs2GHM7CaqNAlvIYTA/nvecH3te+/evfj5hXDdlOaW1b2GDLkhZbRlxgzQrp3Zf+AAOT17wdWrEB1dbs8XFUPCWwghsN9sDvn7vZOTk40Baw3rXd/fvW6dsYpIt243tKx5dewIASEB5OZksL22+Z1z6feu8iS8hRAC++t5Q/7w3m9em9OnRrfra96RkcY8pgXb32+w2wb0BmDroSvQooX0e1cDEt5CCIER0Lb6vCF/s/nevXsB8Eoemr/mfeoUnDxZbv3deT02qyvgwg/LDxj93hLeVZ6EtxBC4Hiz+a6oPdSpU4f09ID8Ne9164xtOfZ3W7Rq5YWHd0uiDu2C7t3h7Fk4f77cyyHKj4S3ENXQ7t0wdiz4+UGNGsYbRh98YH8e7+rA0fDeuHUXV2sFkHI1N3/NOzISGjc2OqErgE/z5mRk7eVEk37Gjp07K6QconxIeAtRjWgNr74KPXrApk1w993w+OPGnCIPPgj9+0N8fEWXsvxp7Vh4m0wm4k4fo2e3riRddrtW8zaZjJHmQ4eS/92x8nPrgN7kppzju+OtjA+yY0eFlEOUDwlvIaqRZ54xVqMaNw5OnICPPoLXXoNt22DxYuMV5QED4MKFii5p+TKZjK2t9bzhWnifOHGCq+lpTBgxgIwMroX3/v1w8WKFNJlb3Dw8HNB8+8MxY1EUqXlXaRLeQlQTn3xi1LpnzIAvviBff61SMGmSsRjWH3/A+PHVa54PS3dBUe95R5nfn24R2AXgWrN5ZKSxrcDwbtu+EwB7jm4ntWs/I7wLzi4jqgwJbyGqgQMHYNYsI1vefx9c7PyfP2AALFgAmzfDc8+VbxkrUlHhbal5b/h9JygXTmUZi4BYfwFatw7atzdWCqkgbdq0RtWoCZ67iPS8BRISjOYVUSVJeAtRxZlM8MAD4ONj1LgLBlRBEyfC/ffD3LkQFVU+Zaxo9sK7Rg1jm5VlbP84FkPTwFa0rdsUMNe8s7Lg118rtNYN4OHuRkiXLuTE/ckvl8OMndLvXWVJeAtRxX38sdGn/dZb0KCBY9fMnWucO3Nm9Wh5tdSsC/Z5u7sbW0sXwuFDB+jbPRy3bA/AXPPescNYw7sC3u8uKLxrCK6u+1m/r64x8bn0e1dZEt5CVGHp6fDPf0K/fjBgQCwPPfQQbdq0wcfHh06dOvH888+TlJR03XW1axv94zt3wrJlFVDwcmav5m0J76wsSEpK4vTp07Tu0BnLH5mvL8Yoc6WMPocK1jCwHdnZlzh84izng4ZJzbsKk/AWogp77z2Ii4N+/T6lfft2LFiwgI5NmzLez48mPj68/PLLtG/fnk2bNl137aRJ0LmzMUK9qg9ec6TZfN++fQAczqxjDW8/P4z+7q5doW7d8ilsIeo2aw2Aq9cuNvqPNfo9qvp/vGpKwluIKiopyXgNrH37N/jXv6YQ0aEDhw8f5vvly/nXtGms+uYbdu7cSR1vb4YPG8aKFSvyXe/qCv/6Fxw7Bp99VkEfopxYwttes3lWFkSbR5o/OHYwycnGfl+3dNi6tcL7uy3uGWlM0FIj8yTrM3tDRgYcPFjBpRI3goS3EFXUxx9DQsJijhx5gpubNGFhRHcCAwNxq1OHxi+9hHuLFoSHh/N1/wF08PTk7rvvZtu2bfnuccstEBIC//nPtXehqyJLn3dhzeb79++nbt26DA7veK3mfXCLUbMdPLj8CluIxg0b0LhxY+rX38+GE82NndJ0XiVJeAtRBeXkwNy5B3FxmcGgQYP4es8eWr73rs1zO7z2Gj+tXk2TJk0YP348CQkJ1mNKwezZEBMDa9aUV+nLnyN93tt2RtGynfEudXKycazmb+uM6nrfvuVY2sLVb96WlJwdnDjjTqxfZwnvKkrCW4gqaOnSbK5cGItfTTe++OwzPBs0QFk6cAuo0bABzXr35uuvvybu/HlmzpiR7/hdd0HTpsYI9KqqqPDOyMglJuYgsS71UUqRlJSnv7tHD+M9vErCq1FLki+eAHLY0vxuYyJ7UeVIeAtRBT3zzLtk6SO83CKAejVrOnRNkK8vD9apy9fLlvHzzz9b99eoAQ8/DBs2VN3u06L6vGNjT5CTmcGDdxh928nJ4OuTawRjJenvtvjLmIGYcrLw8DjO7+6DjBl6MjMruliijEl4C1HFbNoUxx9/zKFjx9H8Zds23OrXd+i6mm3b8s9vvqZ169b87W9/IzvPKOWpU40Q//jjG1XqilVUn/fJk8Ya3jcN7AkYgwH9XFKMgQCVpL/bIiQkBIBWrfazJbGj8eEOHKjgUomyJuEtRBXzt7/OBjJZuPBtXPMtOF20ugMH8vbbb3P48GHmzZtn3V+/Ptx+uzHqPCOjjAtcCRTVbH7k5G5cXF1pHNgWMNe8My+Chwf07FmOJS1au/YdUC6uUPs39pyuQxpe0nReBUl4C1GFHD58kv0xX3J3ndpEBDUp0T2Gh4fTq25dXnvhRa5evWrd/8ADcOUKfPddWZW28igqvE/8EYVr7aYkmxsjkpLAL+lPY6Cag90S5cXbyxOfBs3ISD1Ibq5ip/eg6jPPbTUi4S1EFTJr1iuYcGf89Ddw8fYu/g2Skqhx/jyz+/ThQmIC8+fPtx4aPBhatoSFC8uwwJVEUX3eSXFHGdm/O23qGwPTkhNy8Uv5s9L1d1uM6t+d3KSTAPze4HapeVdBEt5CVBGnTp1iw4ZP8fb+C7e9ep/jF2ZnG53ZERFQuzYqPJw7fvyRgcDrf/87V995BzIzcXExFi1Zvx7On79Rn6JiFN7nnUhCwh/07h6Om6vxT2bSlRx8Sa50/d0WwcHB/PHHKdq3T2ELvWHfPplprYqR8BaiinjjhddRWjNz/KQiVw6z2rXLmIXlgQeMl5lfeMGYzPzbb3nm3ns5n53N5488Ap06wcaN3HOPMUbr669v6Ecpd4VPj7ofAM9GrQBjoZbkdDf83DMgLKz8ClkMPo2NsjbruJ0tF1pjysquuq8KVFMS3kJUAampqXz21RKG+NRm4oTGjl30v/9Bnz6QmgorVkB0NDz/PIwdC3fcQcTEibSvWZO3GzdGAwwZQsef36FrV83nn9/IT1P+7IW3qyu41DD6izNqGcuApqdDrnbFt3X969vZK4nQkGAAvDz3k5juzhHaS793FSPhLUQV8Nlnn5Gemcbx2t8ROqxp0Re89RZMn26shBUVBbfeakynlofvkCH87YknOHj+PBvffRduuw0eeYR7av3Ezp3GnOdVhb0+bwBlOoiHR13+7+buACQdjAXAL6hZeRWv2PqHdaJWrVp4cwKAnR79pd+7ipHwFsLJmUwm3nrzv0AEE+7tXzCDr/fRR/DYY0YNe+VKqFfP5mnK1ZWpTz1FvXr1eGf+fKM5fdYs7v71ryg0X3xR5h+lwtjr8zbspV69ELxrGjPUJa8z1sj2DW9bPoUrAaUUwcHB/PnnPry9YWfdEVLzrmIkvIVwcuvWreP4iSPcXCuQu+8uIrnXr4dZs+Cmm+DLL6+teWmHh4cHE7p146cff+T8hQvw3/8SMG0E/fiVZQuulOGnqFj2ms1zc3Mx6f241mth3Zf0qzFhi1/ngPIqXom4+Ldg2649hIVpdprCYO/ea7+lCKcn4S2Ek1v4v//h6epF7cb3EhRUyIlnzsC4cdChg0PBbXFX23bkmkwsWrQIXFxg/nzuaH+IA2frcuyb6DL5DBXNXnifOHECbbqKbmAOaq1J3nEYAN/alfufz85BQeRkpNKh4xn2XGpG1tUcOHy4ooslykjl/tsnhChUYmIi369YwdXcKbS552b7TeYmE0yZYrwutHw51Krl8DN6v/M2/fv3Z+HChWitwdWV27+eAMD301dCnlXInJW9Pu99+/YB0NntNmPH0aMkXTFqr8WcvK7cTRrdH4C6dQ6QlePKfrpI03kVIuEthBP7ctEiMjIygCmMHVvIiW+/baws8s470KZNsZ6hlOL+++/n2LFjbN68GYDmwbUJ75jGd8lD4f/+r+QfoJKw1+e9d+9ewBVvL3OTRmQkyfgC4OtbfuUriSBzM0xOjtHMv7NGHxm0VoVIeAvhxD6ZN4827u70b16Lzp3tnHTkCDz1lDFafOrUEj1nZKNG+Li48NGbb1r33THJm+304OwXG53+xW97zeYbt+7C3a8FGZibNNauJamu8Q51Za95+/n54Vm3ESu3bcbfH3bWGSY17ypEwlsIJxUTE8Ou48dxdZtGp9EdbDeZa23UjD09jVHmRQ5Ft61uRARjwsJY8csvpKWlAcZCJQDLWzwCDz4Ily6V8JNUPHvhfeTQAWo0bEFuhpsxic2GDSS27AoUq+ehwrTp0Im0uFNERMCOnHDYs+fahxVOTcJbCCf16aef4uLiypH0fzJqlJ2Tvv0WIiPh5ZehYcMSP8utTh2mz51LWno6P/74IwAdOxpj375v9FdITDRq907KVp93UlISF8/HUvfqcHIyXWHbNkhNJaFRB/z87L1WVrncOqgX504fJywsk0MJjUhL01XrBf1qzKHwVkq1U0ptVUodNW+ve8FRKTVcKbVLKZWplJpb4JirUmqeUuqEUuq4Ump6WX0AIaojk8nE5//7H50ahODu3sj2FNtpafDoo8b0pzNnlvqZ/fr1o2nDhizJs6j37bfDxl0+XJn5tDE/+tatpX5ORbDV520ZrObnF0xWFvDzz+DqSoJ3M+rUKf8ylkSXLl3Izc2lbr0DmLQLUYRJv3cV4WjN+0Ngnta6HTAP+MjGOSeBB4B/2zg2EWgDtAV6AXOUUoHFLawQwrB9+3ZiL11iIJ707w8+PjZOeucdiI2F994rm2k8c3IYDvy8YQNXrhjveN96q1FrXRv+NDRtajSfO2GzrK1m8x279wDg3qzptfDu2ZOENHenCW/LHOfHL28BYIdbH+n3riKKDG+lVAMgDPjSvOtLIEwpVT/veVrr41rrPYCtWQDuAhZorU1a64vAcmB8qUouRDW2dOlS3N1r8umFL203mV+5Am+8AbfcYqw5XQZc3N2Z9sq/yDaZ+PbbbwFjIbJ69WDlOg/4z3+M+dEXLy6T55UnW+G9e0807t6+eHs3ISs9x1jEZfhwEhJwmvAeEBGMWw13sq8cJyAAovwGSnhXEY7UvJsBZ7XWuQDm7Tnzfkc1B/7I8/OZYl4vhDAzmUx88803dOw4khTdjNGjbZz0+uuQnAyvvFKmz+4zbSrt2rXjC/PcqK6uMGoUrFkDuWPvhO7d4dlnjdU7nIitPu+TRw7Rp3s4/jn1yUpINQb/jRjhVOHt41mT4C5B/HniMOHhEJUbaoS3yVTRRROlVOkGrCmlZpj7znddvHixoosjRKXz2+bNnDt3jlZZbQkMhPbtC5xw7hz897/G4ttdupTps5VSjOvXj02bNnH27FnAmGn18mXYvkPB3Llw9qzxXrkTKdjnnZuby/79+wkODsbdHbKT0qF2bejWjcRE5wlvMGZai967j7AwOJLUkJRkE5w8WdHFEqXkSHj/CTRVSrmCMfgMaGLe76gzQIs8Pze3d73Wer7WupvWulv9+vVtnSJEtfbVkiXUdHUlK74Xo0fbePvrX/8y0uiFF27I80d6eqK1Zpn53e7hw43QW7kS6NfPeJ/8tdcgPv6GPP9GKNhsfvToUdLT04l1aYi7uyYrNRuGDjUGrDlRzRsgxasJ8RfiCAg8j9aKvYTIoLUqoMjw1lrHA9HABPOuCcAec9+1o74BHlBKuZj7yscA3xa3sEJUd7m5uXz344907z2GlZfvuL6/Oy7OGPU9ZQq0anVDytD75Zfp3KkT369YARhB1ru3ObzBCO60NGPrJCw1b0uz+Z49xmC1LiGhuKcnkZXrAsOHk5EBGRnOFd63De4FgHuNAwBEuXaX8K4CHG02nwk8pJQ6Cjxk/hml1CqlVDfz932VUrHAY8BflFKxSqkR5usXY4xGPwZsA17UWku7jRDF9Ouvv3LhwgV8fe+iZk0YNKjACW+/bcxf/sQTN6wMrn5+jB03js2bNxNvrl3fdJOxaFVsLMbL35MnwwcfwPnzN6wcZckS3pa1WqKioqhZsyZP3zMU97gzZOFuHawGRgu6sxjVvwcAly4comFDiKo9SAatVQEOhbfW+rDWuofWup15e8S8f7TWepf5+9+01gFaa1+tdS3z92vNx3K11n/VWrc2f82/cR9JiKpr6Sef4Klc8D3qxYAB4O2d52BiIrz/PowfX+z5y4trZMuWmEwmvl+2DDDCG2DVKvMJzz1n/BLx+us3tBxlJTvb2OateQcHB1OjRg3c/zxBlosHtGhhDW9nqnk3bNiQevXrs3n7LsLCIEp3NWreWld00UQpVLoBa0II20wmEz9FRtKvbUc2nQq9vsl83jxISYEnn7zhZQlq3YYW3t58u3QpAJ07Q/PmecK7dWu491748ENjAF0llze8tdZs3bGLWJeG5CYl4372JFmungBOGd5grO29YasR3ocSm3A1MUMGrTk5CW8hnMTu3bs5GxdHo57/4FxO0/yviKWnG03mo0ZBaOgNL0utfn2588EH2bBlC4mJiShl1L4jIyEz03zSs88aI8FeffWGl6e0cnKMpcpdXOCPP/7gamoyEeFhuK6LxMOUztWcGmjtvOE9tE93rl74g5CQXHJNLsbyoNLv7dQkvIVwEt9/8w2urq7Exd1Eq1bQNu8kxQsXGguDlOP84mPHjiUnJ4cfzAPXRowwxqlt2WI+oVUrY+Dc/PnmzvDKKzs7f383wDP33QQ//YSXh0ZrRWam84b3sL4RZGRcxd//BABRLhES3k5OwlsIJ7F86VLC3WsSt+1i/lfEtDamQI2IMF7VKiddvL1p6O7ON598AhiD59zcYO3aPCc984wxIUglr33n5FwL7127o3B1daVL586wciVeHY23XNPTnTe8O3Qy1os9fHoHdepAVJ0hEt5OTsJbCCdw4sQJYs6coWf/cexLbp+/v3v9ejh8GGbNKtcyebRqxejOQURu305qaiq+vsYrY/nCOzAQpk0zXl8zT+pSGWVnXxustnHLdlzqBnBgUzTEx+MdZsyCkze8nWm0OUCrdh1AufDjxm3GoDUVZow4l0FrTkvCWwgnsMLcNJ3SZA41ayoGDsxzcN488PeHu+4q1zK5eHlx75v/ISMzk9WrVwNG03l0NFy4kOfEp54yat+VeOR53pr3iZgDBAeH0nrrOnBxwSvCqLVawrtWrbJZ56U8Nahdi5Zt2qIvnSI8HPYnNjOmfD11qqKLJkpIwlsIJ/D9l18S1KoV234PYNAg8PIyHzhzBlasgOnTwcOj3MvVr18/6vn7891XXwHGbGsAv/yS56TAQGPk+fz5lfa9b0vNOy4ujvgLcUy6eSB1Vy6H3r3xalgLMPrznW1q1Lz69IjgwL69hIVBVo4rB+ksTedOTMJbiEru0qVLbNm9m35pVzl+TOdvMv/oI6PpswzW6y6Rqxn0zzWxctUqsrKyCAszVhnL13QO8PTTRvX237ZWDK54lgFrlpnVghs1gj174JZbrO/Sp6cbi7U5a3i36hDE2bNnadjU+AUqylUGrTkzCW8hKrmffvoJk9Y0uG0e2dr92itimZmwYAHcfLNRu60Arj7ejJ/5F1IyMtiwYQMuLjBsmLH0db6Fq1q3hkmTjPe+87WpVw6WZvOdu4ww27Qv0Tgwdqy1lSM93Sh6w4YVVMhS8g0wJu7Zd3ILtWpBVJ2hxjKnwilJeAtRya1YsYJmzZqx488xtGmTZ/K0Zcvg4sVyH6hW0Jh//hNvb2++//57wOj3jo+HffsKnM8UBMEAACAASURBVPj008YvHHPnln8hi2BpNo+O3kOjgBaM3f0LhIRA69bW8E5LM6aOd9bwnjByAABpZ4/StStEuYTLoDUnJuEtRCWWnp7O2lWrGNqmHRs3qvwTs8ybZ7zsPWxYhZUPoGbNmgzv1Yvl336LyWSy9ntf13Terh1MmGBM4VrJlvu11Lz3REXRL7QLwT9/B+PGAdemoE1LM2rejRpVYEFLoUnDegQGBhIdHU1YGOxNaE5OQrIMWnNSEt5CVGKRkZFczcqiW7orV69yrb87Kgq2boUHHzSmBatASin6XYjnwqVLbN++ncaNjWXErwtvMGZdu3oV3nyz3MtZGGN61IucPn2a9i7mYedjxwLg42P8ePas0XDgrDVvgOZtO7Nxyw7CwuBqdg2O0F76vZ2UhLcQldiKFSvw8/PjSNdv8PCAAQPMB+bNM4acT5lSkcWzmrBgPm5ubixfvhwwms5/+w1SUwuc2KGD8Urbe+/B5cvlX1A7srMhM3MnAOtdWkPHjsYX1waoxcQYW2cOb4/GrYmPPU2btkmALA/qzCS8haikcnNz+fHHHxk9ejSr1/kyeDB4emIMef7iC5g4sdLMFtKoRw8GDx7M999/j9aaESOMQNy0ycbJzz5rtEG/9Va5l9OenBy4enUHLi4uvLh7tbXJHIw/c0/PqhHef7l9CACZGfvx9IQo/6ES3k5KwluISmrr1q1cvHiRCJM3x47laTJfuBAyMip8oFpBI9q249ixY8TExNC3rxF4NpvOO3c2wvG//702ZVkFy86G9PSddGzUiCF/HrQ2mVvUqXMtvJ21zxugZ/duAOzbF0VISJ45zmXQmtOR8Baiklq+fDk1XFxo7NoFwBisZjLBBx9A377GaOhKZEBuLgDfffedtYnfZniDUftOSTFWQqsEsrM1yanbCXTxILtTZwgOzne8bl1ITja+d+aad+PGjalVx59lP28mLAz2JAZiSkiE06crumiimCS8haiEtNasWLGCwcOG8emVh2nXzliki7Vr4cSJSlfrBgj99xv07NkzX7/30aN2ciE4GG6/Hd55x5i2rIKlpZ0mJ+syOzoMwzRxUp5VXwx16xrbGjWMmWidlVIK78ZtiDmwj/BwSMlw5wStpencCUl4C1EJxcTEcPz4cUaNuo2NG/M0mb/3nlH1u+OOiiyeTa4+PowZM4bdu3fz559/MmKEsf/nn+1c8PzzkJQE775bbmW0JynJGKz25t611Jw44brjAQHGtl07cHUtz5KVvftuGUji2ZMEBRkLr+927SGTtTghCW8hKqHl334LQIsjGWRkmJvMT56E1athxgxwd6/YAtoxxNt4r2r58uV06ADNmhXSdB4aCrfeagxcs7RJV5DU1O24UIM7OzSDFi2uO96pk7Ft0qScC3YDhIeHk5OTg8l0AHd32O0/XGreTkjCW4hKaMUPPxDarBkHUwbi5QX9+2P0dbu4wF/+UtHFs6tVndq08fNj+bffopTRdB4ZaXmP2obnnjMGrb33XrmWs6C0tG14e7UkaeJUm8ctq7j93/+VX5lulFbtjVXSlv2yiZAQ+P/2zjs8quJrwO/sphNIQgu9SQfpHQEpUlRAUKnSBBFEREXABqg/9EMFC0VQVBCkg4BIEQWkF6nSS+glIYEACWmb3fP9cTcQYJNsIGRT5n2e++zemXPnnrllz86ZmTO7E6aL6UFrmQptvDWaDMbly5fZuWsXz/fvz/Rt1WnWDLwkGn7+2egnLlzY1SomSe7u3ek0aBAbNm/m6tWrtG5tNKp37EjigFq1DLfC+PHGADYXYLVaiYndBxXKcbFRC4cyDRsaf0DatUtn5R4BlSuUxezpw8ED+6lZE3aHlzIGrZ065WrVNKlAG2+NJoPxu33t7qpV2hIUZO/vnjfPmN+dAQeq3UuHDh2wWq388ccfNG9u9BEn6ToHo+/72jXDs+ACjvz7L2KLomJIFSqWTfqPUWZbwzspPN3daFCnJjfOH6dWLbiZMGgtyX9YmoyINt4aTQZj6Zw5FHF3J3LNBQDatBbDrVypUqIQaxmX0pcuUcDDgyULF+LvD/XqwerVyRxQt67hXx83zgjeks5snTABgKJln8XDLXv8JNauXZt9+/ZRpYrRn7HLo6E23pmM7PGkajSZhMjISNbv3Enb1q1ZcOwJypeHkld2GLHMX3vtvilMGRHPUo/RpmpV1qxbR1RUFK1bG12qya5FMmqUITB1arrpCYAIW1atwuQegKlsmfQ9twvJU6ICMTExXAzfiacn7MrXBnbudLVamlSgjbdGk4FYs2YNsbGxtB34Fqs2+Rku88mTIWdO6NHD1eo5hXflSnT/v/8jOjqaNWvW0KqVMRbqr7+SOahBA2jRAr74wlg4O73YupVNN27iWbw8t7xc0+fuCurVrQPA3r3/Uq0a7Fa1YO9eiItzsWYaZ9HGW6PJQCyZNw9/X18sETWIjYU29cNhwQLo2dMw4JmExo0bE+Dnx5LFi6lZE/LmTcF1DvDRR8ZC4Om43nfI2LGcFhu2C8/xmCqabud1NU1rP06ePHm4eOIgNWvCnqvFsMXGwf79rlZN4yTaeGs0GYT4+HhWrFxFI5OJzSsj8fWFxkenGa2hTDBQLTFxu3bRSITly5ZhtVp46ikjWIvNlsxBDRsaMc8//xwuXHj0Sp44wdY//gBAbE/g6ZbJo6+kAqUUtWvXZufOndSqBRHR7pygjO73zkRo463RZBC2bNlC+K1Iunz0MXPXFuapFjY8f5wMzZrdXp4ys+BdrRrP9+hBeEQEmzZtonVrCAlxomH35ZdgtcJ77z16JcePZ4vJhJu7Bx7l8uPu/uhPmZHwKlSWAwcPUba80V2wy6+FNt6ZCG28NZoMwrJly/Dw8KBkvb5cuADPFt4H585lulY3gMnbmxe++AJvb2+WLFlCy5ZGeoqu8xIlYOhQ+PVX2L790Sl46RLMmMHWvHnJVbQc7oExWWYqmLPUr1sXxEb4zV14ecHuvC218c5EaOOt0WQARISl8+fT6LHSbPjLaAI+vWcMFCuWaSODeLu706xmLZYuXkxgoFCtWgrzvRN47z0oWNAYXR8f/2iU++QTYuLj2X39On06tCH870rZruXdq72xtvexg3uoVg12WavDiRPGnHtNhkcbb40mA3D48GFOX7pEY2s8y1d7UrNiFAW2LTEMWCZtElpv3KBh0EkuXL7M7t27ad0atmxxIoy5r6+xWMnevUbktbTm5En46Sd2tWtHXFwcdeo0AFS2M96BgYEUK1aMbTuMfu+9IYWwYoJ//3W1ahon0MZbo8kALLNHVeswZzXbdyie9VoLXl7Qr5+LNXtw3PLm5aVffsFsNrN06VJatzYa0uvXO3Hw888boWA/+shYVzQtef998PDgnzJlUEqx5VZeQ9/M+R/pofAoWJaVazdRqxZERrtxnHLadZ5J0MZbkymwWl0SfCvdWLJkCbVr12b/kZLYbPDMoS+ge/fMvXg0UPSpp2jcuDFLliyhfn2jUZ1iv3cCkyaBpyf06pXMyiap5M8/YeFCGDGCdf/+S4GS5bCYcwBku5Y3QJOG9Yi+dplSpcIA2FWonTbemQRtvDUZno0bjfWUc+aEl19+dN2gruLs2bPs2rWLlrn8WLECAn1vUTN2Cwwe7GrVHhqJj6dlkaIcPnyYM2eO07y5YbydWsCqUCH4/ntj4NoHHzy8MtHRxuC/smWJGTKErVu30qV9G0a3qgZkz5Z3j3bGQizh4Tvw8YHd/s2N661XGMvwaOOtydCcPAmtW4O/PwwcCNOnw9tvu1qrtGWxfe3upys/zurVwtOswNS4EVSt6mLN0gCzmQanTwPcdp2fOWOMi3KKzp1hwABjCtmKFQ+ny/DhEBQEU6awfe9eYmNjadq06e1GfXZsedeuXRs3NzfW/POPMWgt7nFjwNqxY65WTZMC2nhrMjQDB4KHh7Em9OTJxnrKkyYZob6zCosWLaJatWpEt/2K69cVbSPnZolWNxjBQBou/52aNWuyZMkSWrUy0p12nQN8/TVUqwZduz54BLDFi40H5623oFkz1q9fjzKZmHLUnVsxViB7Gm8fHx98CpZm0Yq1xqC1i/mNQWubN7taNU0KaOOtybBs324Y7ZEj7yxhPWYM5M4NH3/sWt3SigsXLrBt2zZeeOEFfvsNvE0xtCp0EJ57ztWqpRlmf3+ee+45tm/fjqfnJcqWdXLKWAJeXrB8Ofj5GeujBgWlToF9+4z+ljp1YOxYANavX89j5R+nZOH8mMSIrJYd3eYAzZ9sRPjZI1SvbiEq2sRh/4bGtABNhkYbb02G5dtvDXf5q6/eSfPzM7yoy5eD3RubqUlwmTe+EsaSBXG0sa3A561Xs5wlaWpfbGTRokW0bm2MOI+JSUUBRYrAqlUQGwtPPAH//efccQcPGgbfzw8WLQIPD6Kioti+fTsdnmnJ5G41srXbHKBbu5bExcaQM+deALYX76yNdyZAG29NhiQiApYtMzylvr535w0YYHzOmJHuaqU5ixctokLhwniVb8flMA86eq+C/v1drVaaU8rsRqX8gcyePZs2bYyxY05NGUtM5cqGO9fNzYiD/vPPyQ+sWr7cMPRKGU39osbCI1u2bMFisdCkyZPAnQGQWez/ktPUr18fgF0H15InD2z3aGQMSggJcbFmmuTQxluTIVm61PiB7979/rwiRaBJE2PGT2YeFBscHMzmLVvo/MorLNhTHXfieKZ/EciVy9WqpTkF//cJvYe9w86dOylS5AQ5chi2NdVUqADbtkHt2tC3Lzz5JPz+u/GwgGGJN2825om3awfFixvyiWLDr169Gjd3D97dGs/lG9HZvuVdqFAhPPwDWbRqLfXqwfbQ0kbG1q2uVUyTLNp4azIkc+YYYa4bNHCc36kTHDkChw6lq1ppypIlSxAROrZvz28LLLRQa/EfnvVa3Ql07doVpRSLF8+hZUv4448H/PNVpMidEYwnT0L79oZ7JjDQ+GzUCNauNQK87NxpGPBErFq1ipp1G9CxTikK5PK63fLOrsZbKUXTJo24eeYgdesKh8/4cN0jv3adZ3C08dZkOCIjYd06o/GklGOZjh3BZDKWus6sLPj1V0p5eGBduI1TN/PRsUGIMbc5i+L5++/U9fdn9uzZPPuscP78QywfbTIZoWNPnzaGrn/wgWHEBw82Hopz52D0aCPISyLOnDnDkSNH6PJ8ez5uXxml1O2Wd3Z1mwO0b9WMKyEhlChxBoB/y3TTI84zONp4azIc69cbS1i3aZO0TGCg0SpfuTL99EpLgoOD2bh9O8+/+CIL/yqOB7E8P66+q9V6pHiWK0+nZs05ceIEhQvvQinD4/1QeHhAq1bwySfwww/GfPAXX0yy62HVqlUA1G3c/HZadnebA9SqUxeAU8F/oxRsD2hjzMdM6I7QZDi08dZkOFatghw5jLFGydGqFezeDVeupI9eacm8efOw2Wz0GPg6P+2qyTOF9hJQr5yr1Xqk5GzWlD4/TsPDw4NVq2ZTr94D9ns/BCtXrqRAkeJ0mX+WgxdvAMYAdrivkZ6tqFS5MiZPH1au/5uKFWF7TFXjX83Ona5WTZMEThlvpVRZpdQ2pdRx+2cZBzJmpdRkpVSQUuqkUqpforyPlFJXlFL77NvktKyEJusgYhjv5s1T/jFNCPjx11+PXq+0ZvbMmVQpUYLLE/YTIoG8NLSAq1VKF/z8/GjT5Enmzp3L00/Hs2uXsbR2ehATE8O6deto1boNHz5TkXIFcgKGlweMRnx2xcfTgycaNuTm6f+MQWtB+RAUbNjgatU0SeBsy3sqMFlEygKTge8dyHQHSgNlgPrAR0qpEonyZ4pINfs26MFV1mRlzpwxtpYtU5atUcNYtyNVAT8yACdOnGDX3r20unWLlcvj8HeP5JlBJVytVroQsXo1zQ8d4sqVK/j7Gy7sh4166iwbNmwgKiqKTh3a8krjUribjZ8/3fI2aNumJUePHqV8+UtcCzdxsmI7Y/CJJkOSovFWSuUHagBz7UlzgRpKqXz3iHYGpomITURCgaXAi2mprCbrkzA7JSWXOYDZDC1aGAOLM9OUsdmzZ6OUolfrDvwY3YdO7WOzjeHI0bAhnb/4ggKBgaxZM40SJdKg39tJlixZQo4cOfAtWZUYi/V2ekLLO7vcg6So06ARAOev/wHA9uKdjGl2ut87Q+JMy7socFFErAD2z0v29MQUA84m2j93j0wXpdR/Sqk1SqmsPTJH88Bs2WKsHla5snPyTZoYbtfMEm1NRJg9ezZPNmjA1gUe3MKXnm9m7mU/U4M5Vy7yd+9Gn5dfZsWKFTRteoG//wZ7ALZHhtVq5bfffqN24xb0/GUfe86G387TLW+DWjWrY/LyZdfev8mVCzZLQ+OfzbZtrlZN44D0GrA2FSgpIlWAL4FlSimHv1hKqf5KqV1KqV2hoaHppJ4mo7B1K9SrZ7SqnaFxY+Nz48ZHp1Na8u+//3Ly5EmevXaNqbG9qVIuNsm57FkVW2wsncuWw2azYbX+TEyMMW37UbJp0yZCQ0N5+aUu/NCjJjWKB9zOSzDe2bnPG4x+76dbNufykV088QRsOl3EeBFTHQpPkx44Y7zPA4WVUmYwBqYBhezpiTkHJI6GUCxBRkSCRcRi//6XPd1h20pEfhCRWiJSK1++ez3zmqzMzZtw4EDSgVkcUaGCsVBJZjHeM2bMwMvNjboRwh5q8tpbnknOZc+q2KKi8PjySxqXK8c///yEv78Ve4j3R8aiRYvw9vamY/u2tKxUAC/3O/8Otdv8Dk81b8bp06epXPkMR46ZCa3aQvd7Z1BSNN4icgXYB3S1J3UF9tr7tROzEHhFKWWy94c/BywGUEoVThBSSlUDSgB6wVjNXezYATabEbbaWUwmI6DWpk2PTq+0Iioqijlz5vBC/vxMDRlFTl+bw/CvWR23gABKLJjPoI8/5ty5c9Sq9SfLlt0xomlNgsu8+VOtWHbwKtdu3X0i7Ta/Q816Rr/3pVvLANhcvLsxXSwy0pVqaRzgrNt8ADBYKXUcGGzfRym1UilVyy4zCzgFnAC2A5+IyCl73mdKqYNKqf3ANKCHiASnVSU0WYOtW42IanXrpu64Ro2MKJnpNeXoQVm8eDE3btzg6Us25lo707ef6b5FV7IL3pUq8VyHDgQGBhIePokbN4yBh4+Cv//+m8uXL1O5URveX3KA89fu7mDXbvM71KlRBfcc/pwO2oCXF2yksREvXodKzXA4FRBQRI4C9/2kisjTib5bgYFJHN/rQRXUZB+2boXHH0/9uhwJ/d6bNkHnzmmvV1rx4/ffU8Ldnbj8z+IWphg2zNUauZbI+QvoU6cuY5f/To4ch1m0qGKyUfUelF9++YWAgABGv96TvjfjKZk3x135cXGGByc7h0dNwN3NTIdnWrJlyxbq1RM2ni5ihJ5bv/5OYAVNhkBHWNNkCKxWY1Crsy7zoKAgFi9ezIIFC4C9+PhIhnadHz9+nI1btvC8R05+j2pDv34qK4cxd4roA//ROcAfb29vChT4iqVL74QqTSuuX7/OkiVL6Nq1K15eXpTO74vZdPcgg9hY7TJPTLNmzbh48SIVKhxh339mbtRs9uhHFGpSjTbemgzBoUPGGt4pDVbbsmULTzzxBKVLl+aFF16gc+fO1KlTA5utFEuX/ozNZksfhVPJzx9/jBk4nX8WK6I6MmKEqzVyPYU+/ZRqv/xCr169OHt2FteuhaT5wOYFCxYQExNDmw5dGPPH4ftc5mAYb+0yv0P9xs0ACLo+F5sNtpbplXnjEGdhtPHWZAgSgrMkZbxtNhsjR46kUaNG/HfiP5q+1pTdu3dz8OBBun3UjVz5vLh4sS/NmrUiJCQk/RR3gtjgYKbPm0d9rwL8dvpphg2DovdGSciGKPtKIG++8QZWqwV39wksWpR25YsIU6ZMoXLlypgDSzNz+1lsDqL5xMXplndiHi9fmoDCJQkJ2oCbG2w0PWlkrFnjSrU096CNtyZDsGULFCgAJUven2ez2Xj55ZcZM2YMffr0YdRvo+j1Wi9q1KhB2fJluVnlJt3H9QWmsX3TBp4oWZKzFStCpUpGFJfevWHqVGMB8PRGhHlt23LFZqN3Xnc6Ft/Au++mvxoZlRsrVmDq/yrPP/ccIhNYvDjs9vraD8uGDRvYt28fQ4YMoc3jBdk/qiXF8+S4T067ze9GKUXfrs9zZN8OqlePZNPJApAvn7H0qibjICIZdqtZs6ZosgelSol07Hh/us1mk0GDBwkgA94ZIDab7W6BoCCxvDZQruXMI27ESaeAPuLnZpYiXl5ypnVrkcaNRfLnFzEiqIpUriwydqxIWFi61Ms2ZoxUBwnwKimd/WbL+jUx6XLezELUfwfkwjvDZN+GDaKUEhguf/6ZNmW3b99e8uTJI1FRUcnKdesm8thjaXPOrMLatWsFkPYdF4u7u0hE574iefOKWK2uVi3LA+wSJ+yjbnlrXE5wMJw65dhlPmXKFCZPnMxjbR+jw6AOqISIJlFR8N57UKECbj/+RMDzbalRMYKjo67yxNetifD0pM3Zs4QvXWqcICgIJk0CPz94913Dbz1woDHH7FGxcCGbPvyQvUB4zLuUfaMbTz6lm3iJ8X68MoW//IKqjRvTuXM3YBLff3/5ocs9ceIEv//+OwMGDGD7uQj6TN/JlZsxDmVjYsDb+6FPmaWoW78BJg9vjl+Zj8UCG4p0h7AwY41vTcbAGQvvqk23vLMHixcbjeJt2+5O37Vrl3h4eMgzzzwjsZbYOxkHDohUqmQc1LOnyIULIiIydKiIf+Wdsv/yEVm/fr14eHhI06ZNxWKx3F3wwYMiffuKeHqKmEwiXbqI/Pdf2lZq6VKJM3tJaa864kYuGdXmd7HG61ZLUsQFB8uR7TvEZPIQs7mXREQ8XHk9evQQb29vuXz5svy+76K0+WajxFocX/82bURq136482VFqjVqKfkLFhFPT5sM6X9LRCmRTz5xtVpZHpxsebvcQCe3aeOdPRg61LCjMYk8yhERERJYLFD88vvJ5SuX72TMnSvi5SUSGCj3+leXLDGe6M2bjf0vvvtCAHn33Xcdn/jyZZHhw0V8fY0D27UT2b79oesT8/NsWWx+Ucp6rRRQ0rlIdTn59DP3u/w1IiJijYyUI1WryeVPP5Xu3d8VQEaO3PrA5R0+fFhMJpMMGzbMKfknnzR6VzR3M23aNAGkfv39UqGCGP9w6tVztVpZHm28NZmGevVEnnji7rQhQ4YIIG3HtxWrzSpis4l88YXxyDZuLBIcfF85V64Y2WPHiqw/t14en/G4dOzRUQBZunRp0gpcvSry0UciAQFGAc2bi6xda5zTSWw2kS3rYuTVKlskgKsCIj4+3cXT00dCLl2S2PMXnC4rO3J9+R8Se/as3LwZIWZzIfH1rSqxsbEpH3gPNptNWrVqJTlz5pTQ0FCJtVhT/NNUt65Iq1YPqnnWJTg4WJRS0rD5uwIi54d+bbS+L11ytWpZGm28NZmC6GgRd3ejAZzA1q1bRSklgwYNkjhrnGEZ33vPeFw7d767iX4P5cqJPPusSLQlWqbumyrXIq5JrVq1JFeuXHLy5Mnklbl5U+TLL0UKFDDOVa+eyO+/J2vEb90SmTTRKmULRwiIeHNLupfdIT//cERMJpMMHTo0tZck29Op0zIBZNCgEak+dvHixQLIN998IyIiX64+Ks3H/5Oky1xEpEoVkeeee2B1szQBj1UV3wKlBESm/++88V5MnepqtbI02nhrMgWbNxtPYULDODY2VkqUKSEFixSUmzdvGokffWQIvfpqiqNd+/Y1GtCJxU6dOiX+/v5So0YNiUnG8N8mOlrku+9Eihc3zluqlMigQSLz54vs2ydy+rTI8ePy99h/pYTfNQGRumyT6fmGyc2la0VE5OWXXxYvLy/Z2badRCT48TXJEnXwoIT9+KMcPy4Cr4hSSv7++2+nj798+bLky5dPqlatenucw8r/Lsn/rTyS7HGlS4t07fpQqmdZ3hr5mQCSJ88x6drVZlys1q1drVaWRhtvTabg88+Np/DKFWN/3LhxAkiLj1sYCWPHGgIvv+zUNJXp0w3xgweN/YsRF6XbH91k3Ixx9tbcIOeVi4sTmTnTaMr7+Mjt6WYgkxkoJuKlHEdkXeXBIrNmGfJi9LmazWYZ1Lu3nHqxk9zavScVVyT7Evr9D3K0eg2xhIVJnTqR4uFRQQICAuTo0aMpHhsbGyvNmzcXLy8vOZhw852kcGHj8dLcz7lz5wSQatX+T/LlE7EOHWa4yq5fd7VqWRZtvDWZgvbtRcqUMb6HhIRIrly5pHnL5nLmxhmRX381HtFu3UTi450q7+RJucuzF2WJkm5/dJMN5zfI0KFDBZD58+enXtGYGJG9e0UWLJAfem8WEGnbIFQizl69T7Rt27aSK1cuuZLwj0TjFPERkRJv97bMmCECp8TfP58ULlxYDh8+nORxFotFunXrJoBMnz79dvqJkJtyK9aS5HEJ5M5tOFY0jqlcrabkL1ZFQGTr9/uNF2zOHFerlWXRxluT4bHZRPLlE+nVy9jv07ePuLm5yZEjR0Q2bBDx8DCGAqdi4JLNZnRZv/RS4jSjzzouLk7q1asnOXPmlBMnTjyQzmvXGrPL2rS53dC+i3Xr1gkgn37wgVijox/oHBqRW7ds4u8v0rr1fxIYGCh+fn4ye/bs+wafXbhwQZ566ikB5LPPPrsrr8X4f+SlH1OePeDtLeLkwPRsSZs+bwsgbh4n5d0RNmOmx4svulqtLIs23poMj9G3KfLDDyJ79uwRFFK3c12RY8eMjuvy5UWuXUt1uS+8IFKixN1pNptNlgctl91Hd0tAQIBUq1ZNolNpXMPCDBdruXLicB5yTEyMlC9fXkqUKCHH+/aToGef1dPDUok1JkbO9ukjYT/+KEOGGB7anTtPFf5dUgAAIABJREFUSb169QSQqlWryocffijjx4+Xnj17ire3t3h4eMhPP/10Vzk2m022ngyTbUHJR9Kz2YxncNSoR1mrzM2eg0cFkFKlxkjFiiIyYIDRjfSwk/E1DtHGW5PhSeifPnDAJo0aNxLfAF+ZveUnwzrmyycSFPRA5X7zjVHu+fN30i5HXpYaM2vIt7u/leXLlwsgAwcOTFW5nToZxmRPEl3Yo0ePFkBWr14tkdt3yI0VKx5I/+zOhWHD5Nq8+XL4sHEfP//ccI1Pnz5datWqJSaTSQDJnTu39OnTR06dOvXA54qONs7xf/+XhhXIgjRu3Fjy5y8nYJMTc3YaF23WLFerlSXRxluT4Xn5ZaO/cf78hQLI1ClTRDp0EDGbRf7554HL3bXLeLLnzbs7/VDYIWPOuIgMGzZMAJk7d65TZW7ZYpSZVICpPXv2iLu7u3Tv3v2B9dbcT+PGxmD/xGMVo6Ki5Pr162JNYgBjvNUmU/85KZeuJx/TXMSY4g8i336bVhpnTcaMnyiAmHOul/HjrCLFiulR548Ibbw1GZ4yZUSeeSZK8hbKK6Urlpb4Tz81Hsmvvnqoci0WkZw5jZlljoiyRElUTJQ0aNBAfHx8ZHsKUdVsNsOIBAaKREben3/jxg0pXbq0FC5cWC6fOCGh330n8eHhD1WH7I7NZpPIbdtl3hyrgMiyZc4fu/dcuBQf8Yes+C/lYCJnzhiP3M8/P4Sy2YDj54JFublLQOG+0qSJiLz7rvEnOyTE1aplOZw13nphEo1LCA6GEyfAYv2SsEthNHyxLOaRI6FzZ3jzzYcq280NmjaFv/66P+9K1BXaL23PstPL+O233yhQoADPPPMMx48fT7K8P/+EjRth5EjIcc+Kkjabjb59+3L69Gnmzp2L96FDhE6cRPzVqw9Vh+xO5Lp1nOvdm1b5NlCsGIwb5/yx1Yr6s2l4U5pXyJ+ibESE8Zkz5wMqmk0oUzSQFzt2IObaUjZujCOkVU+wWmHBAlerln1xxsK7atMt76zLggUicEG8vHzkudat5GbhvMZiI2k0CGbSJKNFde+gcpvNJv/b9j/ZHbxbRESOHz8uefPmlWLFisnx48fvK8dqFaleXaRkyfsHvdtsNhk8eLAAMm7cuNvpcRcvpkkdsjM2i0WuL1smtthY+fpr416mQdj5+9i61Sh71aq0LzursWLFCgEEtzkycaIYoenq1HG1WlkOtNtck5EZPFjEPUcH8fT0lFOVK4vkymUMP08jTpwwnu7Jk1OW3bNnj+TNm1cCAwNl165dd+XNny8Ox+ZYrdbb88bffvttsdlsYn2AWNyalLl5U8TPz5hFkBKzt5+VdxbskxiLc3EB/vxT7lrMRpM08fHx4pOnoHgF1pD69cXo3gIj6qAmzXDWeGu3ucYlrPprA5ZbS6jZIJCSBw/CrFlQpkyalf/YY1CyJKxZ4zg/1hrLD//9wJGrR6hevTqbNm3Cw8ODBg0a8O2332K1WrFY4MMPoXJl6Nr1zrGhoaF06NCB8ePHM2jQIL788ktsN29ysnlzri9dmmZ10EDEuvVEjHmXgQOE336DZHo3AAiPiuPSjWg83czOla/d5k5jNptp26UXMSF72LbtAKea9AFPT/j+e1erli3RxluT7oSH2zh5dDg+Pn6MP30F3n8f2rVL03MoBS1bwrp1YLHcnx9rjWX2kdn8c/4fAMqXL8+ePXto2bIlb775JjVr1uTVV2dx4sR1Pv0UTCbh9OnTjBkzhnLlyrF69Wq+/fZbJk6ciMlkQiwWfBs0wKtCxTStR3bHeu0qMYcPMaT3Vby84OOPk5cf1LQ0v/at63T52ninjskfv4OnpxfwHfNW+0OnTvDrrxAZ6WrVsh/ONM9dtWm3edZk6NCZAshw8+MiLVo4Hfo0tSSs753U2hZhUfcH8LDZbDJ37lx57LHSRv8eSP78+cXPz+/2/tNPPy0HDhx4JDpr7sYWHy82+/MxYoSxImVSocsvX099RLsJE4xnJDT0YbTMXvTo2UtMZh8pW+Gq2Dbb51D+8IOr1coyoN3mmoxIREQEE6cNxJyjDCMDo2HOHDA75+JMLS1bgo8PLF7sOD+Pdx4AQqNCuWW5BYBSii5duvDqq8eAjfTtO4YOHTrQvXt3vv32W4KCglixYgWVK1e+XU74vHnEXbj4SOqQ3VFmM8psxhYXx1sdj+PrCx99dL/cqdBIGoxdy+LdF1JV/o0bxmeuXA+va3ahcYce2KxRnA4dx79u9eHxx2HKFGPJHk364YyFd9WmW95Zj0GDXxNAHq/R99EMH76HF14wYp0ntSDZtehrUm92Pflq15255devG8FjWrVKuXzL1atypHoNCfnq6zTSWOOIC28PlWP16svH70YKiOzceXf+9ag4+fqvYxJyM3Wt7zffNGICaJzHZrNJ7YbNBfJJjx63jFZ3ci4uTapAjzbXZDR2794tJqUE+svnHdJneO/cucZTvnFj0jJzjsyRczfO3d4fOdI4Zvdu584Rd+GCxOs4z4+U6KPHJGLjJrlxwwiWU7euUyvEpshLL90fB1+TMps3bxZA3N2/kfDgGJGCBY0uMM1D46zx1m5zTbpgtVrp0qkdvuIJfE6rUQ3S5bzPPgu+vjB9etIyXct3pWiuooARPOarr4xxODVqJF92fFgYAO6FC2P29U0rlTUO8CpXFt9GT5ArF3w+Vtixw5igADBr2xl2nr72QOVevQp58qSdntmFhg0b8ljl+ljdxvDTrwJvvQV//w27d7tatWyDNt6adOHTEW9yIugiRRs0JTC/H49XUelyXl9f6NYN5s2707/piOj4aEZuGcnACX8QFweffZZ8uZaQEIJat+HqjBlpqq8mea4vXkyTdb1pUMfCiBEQEmZl6oZTLNv3YGMOtPF+cHq/8Sa26DD+74sJWPu9Cn5+MHasq9XKNmjjrXnkHNm2jf/7ajJP+Hlx5dQ8nmqpMKXjk9e/P0RH32mpOcLD5MHR4PNsORDM668b88STwxwQQED37uRs1ixtldUkiylXLkzu7nw7NpLQUBjxjpk1bzVmWKtyD1ReWJg23g/KB/1epFq11ly98hm/LImDwYNh0SLYu9fVqmUPnPGtu2rTfd6Zn9iICKmSy1fygiz7fL2AyJw56a9H/foiRYoYS0A6Ij5epMETFgkIMFaaSg69RrdrSbj+77wfK2CTpUsftBwRT0+Rd95JQ+WyGfv3HxQwS56ifcUWfl0kTx6R5s2Ni6t5INB93hqXI0K/FrX472Ykw4d0Z+OVJ/HwgGeeSX9VPv0ULlwwZrQ4YsIE2LrZjW++gWA5zOrTqx3KxZ48ydkuXYk9dfoRaqtJDqUUsddvUOb4Wzz+0mb69zfGKqSW0FCIjYWiRdNex+xClSqVKFanI1cvTOe7+Wdh1ChYu9ZYzUfzSNHGW/PI+Kt7d2bvOEbNOsV4Y9zP/PYbNG/umjm1TZtCq1YwejScOnV33tq1MHw4tG0LPXrAlP1TmLB3Ahbr/aHZrNevY4uKwuSb4748TfoRH3SShkc3M7pqGBER8OKLEBeXujLOnzc+tfF+OBb89CUmkz/D336FuJf7QalSMGyY49CGmrTDmea5qzbtNs+8HBv5vuQGqRwQIJEREbJnj7g8ENOZMyL+/iJly4ocO2Z49n77zZjnW6mSMb9bRCQ8OlyuRiftO7elxRwlzUNjuXJFRO5MB3zlldR5a+fNM47bu/cRKZiNGDhwrgDSuev/3Qlt+PnnrlYrU4J2m2tcRcT339N48pdEeplZtGUzOXx9mTkTPDzg+eddp1fx4vDHHxASAhUqQP780LGjMTht9WpjsCyAv5c/ub1yIyKsOr2KeFs8V77+hvCFCwFQ6TnaTnMX8VYb/X75l3VHQ3DLlw+AdqV3MbnnWqZNMxaScZYDB4zgfhUqPCJlsxETJnTGN7AV8xeM4q/cReG55ww3V1CQq1XLsuhfIU2aYpk2jRcHDOBKuIV+Y/tRrkJFLBaYPdtwS+fO7Vr9GjaEI0dg5Eho3x5+/BF27IAiRe6X3X55O8M3DmfF8d+JOXyYmEOH0l9hzV1ci4rj8o0YImOtgOE5DJ0wkdY3J9O/n5XPPoP33gObLeWydu0yDLen5yNWOhvg5qb4bOxklDkXnTt05cZnnxn/1nv1gvh4V6uXNXGmee6qTbvNMxfWqVOli9lYvGNaooW0ly0zvGi//+5C5R6Q7Re2is1mE1tc3O0FMjSuxRJ/d7eF5do1sVy7JvHxIv37G89ap053ukEcERkp4uUlMmTII1Y2m/HUUxsEzPJk03ZinTnTuBkffuhqtTIVaLe5Jt0QIX7UKJ4aOZh5VnhrxGD6vfba7eyJE6FQIWjd2oU6PgDhc+dScOQ0JDaWMMt15hyfh/FuadKbgxdv8NHvh7BYbbiZ7/7ZcgsIwC0gAJNJ+OSxL5k2dC+LFhnrsC9d6ni9jEmTICYGOndOpwpkE379tTE+uT7nn/W/88yKjUivXsZUj5UrXa1alkMbb83DERdHbK9edP/f/1gXaqHJy435bMwXt7MPHDCiJg4eDO7uLtTzAVDe3igfHzCZWHh8Id/u+ZbLty67Wq1sydagMNYcCuZ6VNIjmG03bhC5di3tS25l61Zjje4OHQwjPmoUzJ8Pc+fCq6/eWUK+fv10rEQ2IH9+mDXjTbxKvcjq+T8ypmhRqFbN+Jf033+uVi9r4Uzz3FWbdptncM6elfM1qknFHGYB5MsvvrhP5KWXRHx8Ug58klGwRkZK1IE7C0YnBASx2qwSdD3odnq8VbvQ04N4653h49ej4lKWDw+/PRsg6vxl+WWGVRo1MtYBN9rgIh4eIgMHGq5zzaPhjSHxAj0FkGGD3xRbwYLG4iXHj7tatQwP2m2ueaQsX876ypWpdug/jlhsfD7tc94ZNuwukf37jYFqgwa5fqCas1weNZrzfftijYwEjIAgACZlopRfKQD+PPMn3VZ2Iyw6zGV6Zge2n7pKy683cCE8CgA/75RdN2Z/f5TJhC0qiou9e9Di2Eg2boSbN43n8eBBuH4dvvsOcuip+o+ML78w06zZT5i9u/DlxG9oWbkWlrg4I+DCsWOuVi9LoI23JnWEhRHRuRMDn29Ps4gIchcsytSlUxneb/hdYiJG4BN/f2P0b0bGFhV121jne2MwhSdMSHaVMG83bwI8A/Dz9EsvFbMluXN4kDuHByaV+kVslLc3eQe8iv8LxtzEHJ4WHq9so1Il8PZOa0019+LhAb/95kaFsrPwKfUqf/+1nCZFinAmOtroq1i3ztUqZn6caZ67atNu8wxEXJzET5woM319Jae3SQB5tX8/iUzC9/jzz4aLcsKEdNYzlVhv3ZITTZvJ5U/+90DHR1uiZci6IXIw9GDKwpoUOXf1lszZcfb2flrFkQ/9/gc59cKLEh+hfeXpSUiISLVqImbzXPH2ziWePr7yfunKYjWbRb74wlhUQHMXaLe5Jk2wWIidMYPPyhehwuDB9IyMpEiJEoyeM5pJU6aQw4Hv8fBhGDIEmjQxXOYZDVtcHFG7dgFg8vEh4KWXyPWAAdfPRZzjQNgBouIN1268LV6PSH8IZu84x5g/DhN8Iwa4023xsHgULYJXxYqY7WFt486e1fcpHcifH9avhyZNuhCrdmDKXYrPTh6kbs6crB0+HGnUyPjB0KQeZyy8qzbd8nYdtvPnZedrr8ngHDkkQBlzt4uXDJT58+aJNZnwoBcuiJQoIRIYKHL2bJJi6Y7NZrvdirsyYaIcrlhJ4i5cSJOyY+Njb3+fsm+KdFvRTeLiUx5cpRG5FWuRL1YfkV1njBGNkTEWuXQ96pGe03LtmhypXkNCxn/1SM+juYPFIjJihIhyj5OA3LMkIKCQABIYUFCmu3tJdK9eIqdOuVrNDAFp2fJWSpVVSm1TSh23f5ZxIGNWSk1WSgUppU4qpfo5k6fJGIgIZzZvZl6/fvQpWJCc5UpQ57vv+CE6mqeeaMQHP77P3kNH6NS5M6YkwoPu2QP16sHVq0YY0mLF0rkS9yD2llXMkSMEtXiK6D17APB/4XmK/vA9boUKpcl5PMwet78X8i1E+YDyuJuNwVVT909lyYklaXKerEJoRCxHg28CYDYp5u48z87T4QDk8HSjoN+j7ZQ25chBwdGjyPWs4W2JPXmS0x2fJ/rAwUd63uyMmxuMHQvbNrlTvNhLhIcHkf/xT7mOoo8lhgK//EKHytX5sUFTIubNg+hoV6uc8XHGwgPrgJfs318C1jmQ6Qn8iTEILh9wASiRUl5ym255pz0Wi0XOnTsnvy9fLP97Z6AMbdFCni5aVHJ4G9O9APEzmaRS9ULSZ/iLcu3atRTLvHBB5O23RcxmkcKFRfbtc1KZ0aONLak8J4+32WwS/9ZbEnf5soiIWEeMkKBnn5Vr8+eLiEj8zZtybuBrEpWcYs6cLyXZxOl2vXqu7Cmjt9xJH7ZhmBwd3OX2fnh0uOERuOfY+86R1DmbNLkj36RJ0vIJ+4nLvvc8jtKLF09aj+LF7+wnc+5ToZGy6Xjo7bx2EzdJx++23M6/fisZL0WCLo7qn5p7lgxRe/fK6a7dJP7tt0VEJOallyQqb16JHzpUZPRosVy7JrYGDZLWLfE9SKxXQnria5iQlvA9cdq99zCxzL33qXjx+8977zH3lpXc9XLmmUuj622xiMyaJTIp72gBi3h5/Skli3UVk7uXAOIG0tBkkvYVasjYzj1l/9y5EnXzZpqcOzOAky1vJSn0+yil8gPHgTwiYlVKmYGrQBkRCU0ktwKYLiKL7PuTgLMi8mVyecmdu1atWrLL3jeZ2XF08ZNKFxGsVisWi4W4uLjbnwlbfHw8kdGR3Ii+gY/ywRIXx6XQ81wMOYdfnDcR4eGcCgni4rVL5Ivw5EpYGMduhBAWEUnMrXgS33EvoIzZTM7yeQisUpQPOoyg6nPP4ZZERJWYGAgLM2Z77N8Pa9YYA0etViOM8bhxqZgWltCfKYJYLIYryMPjdp4lOBj3wEAAItauxZQzJznq1AHg0gcfUOizz4zDrVaU2UzIZ58R+N57oBQX33qLXM8+S85mzZzXxdk+0KRkE6cn+h5vi8fN5EacNY4+q/sw+9k5IEKsNZbav9bmjRpv0K/KK8RYohm5ZSRfPjkOgGhLFH+e+ZMa+WtQzK84lvg4ztw8Q4EcBcjpkdMo13zPfXJw/rv27dfcFhuHydPj9ncbNtw8ve6WiY/H5OZGfGwMtrg43Lx9MLm5EXEjkus3IyhatCAAR88EU75EAUPebAalePvH9XzV90kARszezr/HL7H2ow4ok4mth87hbRKqlzdcM/Fxsdji4/HwMfqjbXFGIBaTh/udZyRx3VK6Dw/KPdcogdCJk8g3+HVs0dGYvLy4sWwZt3buvP383YX9eMulS7gn8uyI1WosaJPomU/qfEnet8T31tF5kzsmcXpSdU+qHGeOfxCUYv06YfZsWLIEbsSHg9qCd+wGzLa/uGk7gsTfWefV0zsXRXxyUjV3LvLnzU2YXwHKF8lP+ceKkTNfPmK8chJYIC/+eXLj7eODj48P3t7euLu7Yzab79qS8h5mBJRSu0WkVkpybk6UVRS4KCJWALsBv2RPD00kVww4m2j/nF0mpbx0ITBnMWLiw7ChiI31xs0tFrPJgmAiNtYLN/dYTCoemygsFg/c3OJQyoaIwhLvjtlsub0fbzVjNsWDEkTAZjOhlBUQo+kqCrChgDR81FOFm9mMl5sbMbH5MZOHsoX9KFogL0fOtsVsLkjX+v/gn9OdX/fNJ9LNg9cqDSTGFskLw1+E4TCizqvEqii+3j4LgBF1X8GiYhkyfyYAkzu9gpuK4/TpX3jjDSh9sR+WqHhy554BwJSufbFi4/W50wH4rmtfBBuD7PuTu/Qh8Vi2yT1ewYyJgfN+vp3205D3GTDvJwCmT/sFT+XBq3MN470w6BxD7HIJq3wtO3me/va0hcHB5FiwlFfsxvvrrl3IFRBI3+++BeCrLp3wz1uElyd9dft80994hz4TxhEXE8PE3t3IU7AMvb/+nOtXwvjpjf7kK1yOnuP/D4DxnTsQWKISL30+hjMHD7H4fx8y1F7OsR3/Ug6YN+oTunwyikMbtvD31K8pWqkOs0fNBuYwvvNzFK1SjxEdR+C515imtuyrbzlS5shtfZZNnMSnuWcyIPIFBgG/TZ7EGL+fGRjekehteyj8ZAu63HPf68yuQ79zrekPLJg1hYnuc+hx/En6A4sW/sQLdrmve3S4re/PH4/ixskDDAU6LOtAgpN/+aaFtAd+fv9DIs4focxbvWkHzBk1isjLx24fv2HcWMoDq06s4pcTM1kAFF4znj+evMXMw7/wzI5C5A85zfIgN9oBJ6eMIzT0PGf+14MFxxbQemVerl67TNFPOrPkxBKeWh7A9RuhFBzd8a76/Xr4V/45/w/1FrpxKzqCIcCAvwZQc56N6NhofEY0Yd+VfTw+OxaLxYL5nbocu3aM8jMjsdlsWN+szrmb5yg1/RpKKaJfr0RIVAjFfryCu5s7rwAfbv6QMfdc0/nbd/I68OneL1FK4Tf/OD5Wd/pyP+N3jWcoMGfwB/RKlD6rUz/2ve5PwtM2p8srdAO+3/89r95TxtddulDE3Z+/etj4wb7/FtD3z7408a1DTwfn/eOVwcztcI22Ho3pAqwcMISngQWrp3JxxgYq5C5Aa2Dh8u+4MHsTFfMXYmbrYDrGNuDc/M28ZS/nt4WTOLt4C48XKUYLYMmcCZz5fRvVSpakKbB01recXrGd6mUfY1q903QKrsWpNTupWaks39c8Sadz1Tj1z15qVCnHD9WO0/lkFYK27qdmrQp8X/EonY5U4vS/B6lR/3EaAzd3/o/KkUfoNaYaX+XdT6sNZYkJu8ipGy+xsu6/tNwcQGTUAXaf8+Ni0UPIKcWm4AtcP3UWiy3q4X5gTQo3TJiUwqbM2NyteFnNgGARMzYPK14WE0oJsWLG5hGPj8UMSoix5/vEudO14Wt8v3bsQyjyYDjT8q4JzBSRSonSDmO40fckSjsAvCwi/9r3hwNFROSN5PIcnK8/GL/BxYoVq3n27Nl7RR6IWkWb4+FxHovNg+DLZckVEExAjmvE2ff981zC3zucGKsXV4LLkTvvOXJ5XSc6PgdXgkuTN/8ZfD0jiI73JTS4DPkKnMTXI5LI2FxcvVKa/AWP4+N+i4iYAK6FPkbBQkfwdo/memRerl8tScEiB/FyiyE8ogA3w4tRqMhBPE3RhEUUIfJ6EYoU3YeHKY7Q8BLciihIsWJ78TbHc/lqReJuFeKxUjvwcrNw7mIdLDGBVCi7AU+3OI6fb4nNmp8aZVeTwyOOfedfw8OjAI1K/IAy3WBz5HiUpxcN3UeiCGeL248APGF9B+Q6W9yN/Ybxb6Mkgi0e01AKGsS9BRLJNq9pANSPHYKSaMKq/EDu3OC57Q2s8bH0m/09ALNeHozFYuHlWVMBmNnndazxVvrMmgLAL70HISL0LpkfPv7Y4T0KLlCIAsGX7s8YPZofg8Px8PWlp697ksc7ZPRo+Ogjvh/wBn5FitDlQ2M++vf9B/NE0DEqrfvrvkNsH3zIDyHXyF+hPB3fHkzkjZscbdaCWnv+vb/8Jk1gw4ZkVQh/7TWCtv/r+PgHIDpfXrxDM0eAmJU9alMlshBFliy7L+/EG934qm0uepypRtjZi6jetVlxegXvf3OeYitSFwv7WOMm7PjuZQ5ePUjzLQFYYmMJfaE4J8JP0Ogfb6xWG5c7FuJ8xHnq/GVCmUyca5+PihMW0OTnf9KotpmHsw0b8V/JW7T9dU/Kwg4437wpY0aUocONmpxZvIOqtUozo8oZOoZW4/TyXVSrW5bplU7x/KUqnFq9h2qNKjC9zAmGTTxH6eWr7y+vXWvGvF6MjkfKcHrbYao+U4MZ+Q/Qdk8pzu87Rs7qtZlfYB8ddhcn5spJwnLXZE3p7TyzLT8xkWc4fCs/+ysco+mR3Ij1Gkdu5uZ02TPUCfJDEUFQlD/Bj12m5rlcKKIIisnF1RIhVL2QE4jhdFwOwouE8fhlX5SycNqag4iC4VQK9saEhVOSg8jAG1QK8cKEhSByEJXvJiUv+dOuYU9Gzxv8kHfkDs62vLXbXOM6HLnqEuel5KJz5IJ09tgHOV9Kss7q4CjPkVvUGZdlUi7XFNzm931PTiYpPR7k+qf23mQAt7nD63Cvbo5kHemu3eaPrrwsgrPGO0XHv4hcAfYBXe1JXYG9iQ23nYXAK0opk1IqH/AcsNiJPI1Go9FoNKnAmT5vgAHAL0qpUUA4xuhxlFIrgVEisguYBdQFTtiP+URETtm/J5enya6MHv1geY5kkvqeFro4K+usDo7yUjo2qfKaNIEnnzS+//NP0vIJ+8mdx5FM8eJJ61G8OPTufUePlHRNKS+18g9yn5051+jRxrVMuK5wd/3ulb9XNiE94d7MmHF3OQmyCWUmdQ8Ty9x732bMgBIl7j7vvcfcq/PDPJMpHf8gpHV52YwU3eauRLvNNRqNRpOdSDO3uUaj0Wg0moyFNt4ajUaj0WQytPHWaDQajSaToY23RqPRaDSZDG28NRqNRqPJZGjjrdFoNBpNJkMbb41Go9FoMhnaeGs0Go1Gk8nQxluj0Wg0mkyGNt4ajUaj0WQyMnR4VKVUKHevA/6w5AUyx1qKKZNV6pJV6gG6LhmVrFKXrFIP0HVJjuIiki8loQxtvNMapdQuZ2LGZgaySl2ySj1A1yWjklXqklXqAbouaYF2m2s0Go1Gk8nQxluj0Wg0mkxGdjPeP7hagTQkq9Qlq9QDdF0yKlmlLlmlHqDr8tBkqz5vjUaj0WiyAtmt5a3RaDQaTaYnSxlvpdRLSqn/lFLxSqnX78nzUUrNV0qdVEodVUo9m0w5r9jlgpRSk5RSLr1OSqm/lVL77NtBpZQopao4kHv8BESxAAAFzUlEQVRSKRWVSHaHK/RNDqXUDKXUhUQ6fpCM7Ej7PQhSSo1MTz2dQSk12f4s7VdKbVFKORxxqpTqrZS6nqjOS9JbV0copcoqpbYppY7bP8s4kDHb6xlkfyf6uULX5FBK5VFKrVRKHbO//78ppe6bapOaZ89VKKXO2J+pBB1bOZBx+rfMVSilSiSqwz57va45kPtIKXUlkdxkV+h7L0qpcUqp0/bf2sqJ0lN8Z+xyj/69EZEsswGVgYrATOD1e/JGAT/av5cBggFfB2WUBC4A+TD+3PwJ9HR13RLp9xxwMIm8J4FdrtYxBf1n3HtvkpBrDPwHeNu3/4DGrtb/Hh2fBdwTfQ9KQq43sMjV+jrQax3wkv37S8A6BzI97e+Ayf5OXABKuFr3e3TMDTyZaP9L4CcHck49ey6uyxmgcgoyTv2WZaQN+AaY5CD9I2Ccq/VzoNcTQNF774cz74w975G/N1mq5S0iB0XkMGBzkN0ZmGqXOwHsAto4kHsBWCoioSJiA6bZj80ovAz87Gol0oHOwEwRiRaRaIw/ZBnpPiAif4iIxb67DSjiai+Nsyil8gM1gLn2pLlADQct1s7ANBGxiUgosBR4Mf00TRkRuSYi/yRK2g4Ud5E66YGzv2UZAqWUB9CdTPS7JSKbReR84rRUvDOQDu9NpvihSSOKcXe0tnMY/6weVC7dUUoFAi2AWcmIlVVK7VFK7VBK9Uon1VLL20qpA0qppUqpCknIZNj7kASvAyvsf/gc0cTuFtyolHomPRVLgqLARRGxAtg/L3H/Nc5U98H+52kg8HsSIs48e65mtt39/51Syt9Bfqa6J0A7jGdtTxL5Xez1XaOUqp+eiqUSZ98ZSId75JaWhT1qlFJ7MC6KIwITLmpmIxX16gWstv+Tc8QeoKiI3FBKlQT+VkpdFJG/01jlJEmpLsAHwGURsSmlegKrlVKlMuK9c/a+KKW6AN0wXP2O+AOYLyLRSqnqGHV+UkSOpLnSmolAJDDJQV5mePYaich5pZQndlczhns2M5Oct3Aq8KmIWJRSTwHLlFIVRORq+qmXOclULW8RqSEieZPYUnoBz3G3K60YcP4h5NKMVNSrD8m4nkTkpojcsH8/jeGqafgodXegQ7J1EZGLCa1TEZkJ+AJFHBSV7vfhXpy5L0qpDsCnQCsRCUminDC76x8R2QtsBuqkVz2S4DxQWCllBmOADVCI+6+xy++DsyilxmH0AXd25AFJxbPnMhJctSISC3yH4/c3M92TQkATYLajfBEJTuh6EpG/MOpR2ZFsBsDZdwbS4R5lKuP9kCwEXgWwjxCsDax2ILcYeE4plc/ugnsFWJBuWiaBUqoB4AesSkamoFJK2b/nBloC+9JHQ+dQShVO9L0VYAUuOhBdCPRUSnkrpbwxBoC4/D4kxj7K9ysMw30mGbnEdS4O1MMYgOcyROQKxrPR1Z7UFdjrwKuzEHhFKWWy9+09h/GOZCiUUp8CNYHn7IbPkYyzz55LUErlUEr52b8roAuO319nf8syAr0xupMctqTvuSfVgBLAsXTRLJWk4p2B9Hhv0nL0m6s3+8W8ANwCwu3fK9rzctgv6EmMh6N9ouM+AQYk2n8VCLJvUwBzBqjbNGCsg/TbumP0ux7CeMAOAsNdrbcDff8GDgD7gU1AvUR5PwLtEu1/ZL8Hp4CPXK27g7qEYvz470u05bm3LsBn9vuy3771crXudr3KAzuA4/bPcvb0lUAt+3ez/R1IeB/6u1pvB/WoBIj9vU64D0vsefuAQik9exlhA0oBezH+2B2y/14VdFCPJH/LMtpmf7Za35OW+Pn6xf5btR/4F3ja1Trb9Zpgtx/xGKP5D9nTHb4zDur1yN8bHWFNo9FoNJpMRnZym2s0Go1GkyXQxluj0Wg0mkyGNt4ajUaj0WQytPHWaDQajSaToY23RqPRaDSZDG28NRqNRqPJZGjjrdFoNBpNJkMbb41Go9FoMhn/D1vMR2Vd9jqqAAAAAElFTkSuQmCC\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for _ in range(500):\n", " #statistics\n", " Nc = gammas.sum(axis=0)\n", " fc = x.dot(gammas)\n", " sc = (x**2).dot(gammas)\n", "\n", " #hyperparameters for the normal gamma distribution\n", " kn = kap + Nc\n", " mn = (kap*ms + fc) / kn\n", " an = a + 0.5*Nc\n", " bn = b + 0.5 * (sc + kap * ms**2 - kn * mn**2)\n", " \n", " #update for the weights\n", " alphan=alpha+Nc\n", " \n", " #update for the assignments of frames to gaussians\n", " logRho= 0.5* (digamma(an)-np.log(bn) - 1/kn - an/bn*(x[:,np.newaxis]-mn)**2 - np.log(2*np.pi)\n", " ) + digamma(alphan)-digamma(np.sum(alphan)) \n", " logsumRho = logsumexp(logRho, axis=1, keepdims=True)\n", " gammas=np.exp(logRho-logsumRho)\n", " #print(np.sum(NormalGamma_KL(mn, kn, an, bn, ms, kap, a, b)))\n", " #print(Dirichlet_KL(alphan, alpha))\n", " #print((alphan, alpha))\n", " ELBO.append(sum(logsumRho) - np.sum(NormalGamma_KL(mn, kn, an, bn, ms, kap, a, b)) - Dirichlet_KL(alphan, alpha))\n", "\n", "\n", "\n", "#plot update of mu and labmda parameters\n", "#plt.figure()\n", "#plt.clf()\n", "plt.figure(1)\n", "for i in range(C):\n", " plt.subplot(3,2,i+1)\n", " plt.title(alphan[i])\n", " NormalGamma_plot(mn[i], kn[i], an[i], bn[i], limits=[-6, 6, 0.001, 5])\n", "plt.figure(2)\n", "plt.plot(t, true_GMM_pdf, 'r', label='true distribution')\n", "plt.plot(t, ml_GMM_pdf, 'b', label='ML estimate')\n", "vb_GMM_pdf=plot_VB_GMM(t, mn, kn, an, bn, alphan);\n", "plt.plot(x, np.zeros_like(x), '+r');\n", "plt.legend()\n", "plt.figure(3)\n", "plt.plot(ELBO)\n", "plt.ylabel('ELBO')\n", "plt.xlabel('iteration');" ] }, { "cell_type": "code", "execution_count": 143, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Samples from posterior')" ] }, "execution_count": 143, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(4)\n", "for i in range(50):\n", " mus_sampled, lmbds_sampled = NormalGamma_rvs(mn, kn, an, bn, 6)\n", " pis_sampled = sps.dirichlet.rvs(alphan)\n", " #plot_GMM(t, mus_sampled, lmbds_sampled, pis_sampled)\n", " plt.plot(t, sps.norm.pdf(t[:,np.newaxis], mus_sampled, 1./np.sqrt(lmbds_sampled)).dot(pis_sampled.T), lw=0.5)\n", "plt.plot(t, true_GMM_pdf, 'r', lw=2, label='true distribution')\n", "plt.plot(t, vb_GMM_pdf, 'k',lw=2, label='VB posterior predictive')\n", "plt.plot(x, np.zeros_like(x), '+r')\n", "plt.legend()\n", "plt.title('Samples from posterior')" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [], "source": [ "# This code allows to \"remove\" one of the components.\n", "# If we got stuck in a local optimum, this might improve ELBO (after few more iterations).\n", "logRho[:,3]=-100\n", "logsumRho = logsumexp(logRho, axis=1, keepdims=True)\n", "gammas=np.exp(logRho-logsumRho)" ] } ], "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }