{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Variational inference for Bayesian Gaussian mixture models\n", "\n", "In this notebook, variational inference for Bayesian Gaussian mixture models, which is described in Chapter 10 of PRML, is implemented. \n", "\n", "The theory part summarize the result from Section 10.2. Note that derivation is not included in this notebook. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "%matplotlib inline\n", "plt.rcParams['axes.labelsize'] = 14\n", "plt.rcParams['xtick.labelsize'] = 12\n", "plt.rcParams['ytick.labelsize'] = 12" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1 Setting\n", "\n", "Here we consider a unsupervised learning problem. \n", "\n", "* Let$N \\in \\mathbb{N}$ be the number of data points, and\n", "* Let $D \\in \\mathbb{N}$ be the input dimension.\n", "* Denote input data by $x_0, x_1, \\dots , x_{N-1} \\in \\mathbb{R}^D$. \n", "* Denote the input data collectively by a matrix $X$, where $X_{n,i}$ is $i$-th component of $x_n$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 2 Theory\n", "\n", "## 2.1 Model\n", "\n", "A Gaussian mixture model with $K \\in \\mathbb{N}$ components, with prior on parameters, for $N$ data points is defined by \n", "\n", "$$\n", "\\begin{align}\n", " & p(\\pi) = {\\rm Dir}(\\pi | \\alpha_0)\\\\\n", " & p(Z | \\pi) = \\prod_{n=0}^{N-1} \\prod_{k=0}^{K-1} \\pi_{k}^{z_{n,k}} \\\\\n", " & p\\left(X \\middle| Z, \\mu, \\Lambda, \\pi \\right) = \n", " \\prod_{n=0}^{N-1} \\prod_{k=0}^{K-1} \\mathcal{N}\\left(x_n \\middle| \\mu_k , \\Lambda_{k}^{-1} \\right)^{z_{n,k}} \\\\\n", " & p(\\Lambda) = \\prod_{k=0}^{K-1} \\mathcal{W}\\left(\\Lambda_k \\middle| W_0, \\nu_0 \\right)\\\\\n", " & p(\\mu|\\Lambda) = \\prod_{k=0}^{K-1} \\mathcal{N}\\left(\\mu_k \\middle| m_0, (\\beta_0 \\Lambda_k)^{-1} \\right)\n", "\\end{align}\n", "$$\n", "\n", "where \n", "* $Z = (z_{n,k})_{ n \\in \\{ 0, 1, \\dots, N-1 \\} k \\in \\{ 0,1, \\dots, K-1 \\} }, \\ z_{n,k}\\in \\{0,1 \\}, \\sum_{k=0}^{K-1}z_{n,k}=1$, is the matrix that stands for latent variables, \n", "* $\\pi_k \\geq 0, \\sum_{k=0}^{K-1} \\pi_k = 1$, and we collectively denote $(\\pi_k)_{k \\in \\left\\{ 0,1,\\dots, K-1 \\right\\}}$ as $\\pi$, \n", "* $\\mathcal{N}\\left(x \\middle| \\mu_k , \\Lambda_{k}^{-1} \\right)$ is the Gaussian probability density with mean $\\mu_k \\in \\mathbb{R}^D$ and $D \\times D$ precision matrix $\\Lambda_k$, and we collectively denote $(\\mu_k)_{k \\in \\left\\{ 0,1,\\dots, K-1 \\right\\}}$ as $\\mu$ and $(\\Lambda_k)_{k \\in \\left\\{ 0,1,\\dots, K-1 \\right\\}}$ as $\\Lambda$, \n", "* ${\\rm Dir}(\\pi | \\alpha_0)$ is the probability density of the Dirichlet distribution, and \n", "* $\\mathcal{W}\\left(\\Lambda_k \\middle| W_0, \\nu_0 \\right)$ is the probability density of the Wishart distribution.\n", "\n", "With these distributions, the whole joint distribution is defined by \n", "\n", "$$\n", "\\begin{align}\n", " p\\left(X, Z, \\pi, \\mu, \\Lambda \\right)\n", " = p\\left(X \\middle| Z, \\mu, \\Lambda, \\pi \\right) \n", " p(Z | \\pi)\n", " p(\\pi)\n", " p(\\mu|\\Lambda)\n", " p(\\Lambda)\n", "\\end{align}\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.2 Variational distribution\n", "\n", "Our goal here is to approximate the posterior distribution $p(Z, \\pi,\\mu,\\Lambda| X)$ by a variational distribution $q(Z, \\pi, \\mu, \\Lambda)$. Note that although not explicitly shown, $q$ depends on the observed data $X$.\n", "\n", "The result is \n", "\n", "$$\n", "\\begin{align}\n", " q(Z, \\pi, \\mu, \\Lambda) = q(Z) q(\\pi) \\prod_{k=0}^{K-1} q(\\mu_k, \\Lambda_k), \n", "\\end{align}\n", "$$\n", "\n", "where \n", "\n", "$$\n", "\\begin{align}\n", " & q(Z) = \\prod_{n=0}^{N-1} \\prod_{k=0}^{K-1} r_{n,k}^{z_{n,k}} \\\\\n", " & q(\\pi) = {\\rm Dir}(\\pi|\\alpha) \\\\\n", " & q(\\mu_k, \\Lambda_k) = \n", " \\mathcal{N}\\left(\\mu_k \\middle| m_k, (\\beta_k \\Lambda_k)^{-1}\\right)\n", " \\mathcal{W}\\left( \\Lambda_k \\middle| W_k, \\nu_k \\right)\n", "\\end{align}\n", "$$\n", "\n", "with parameters defined by \n", "\n", "\n", "$$\n", "\\begin{align}\n", " \\mbox{For $q(Z)$} & \\\\\n", " & r_{n,k} := \\frac{\\rho_{n,k}}{\\sum_{j=0}^{K-1} \\rho_{n,j}} \\\\\n", " & \\rho_{n,k} := \\frac{\\tilde{\\pi}_k \\tilde{\\Lambda}_{k}^{1/2}}{(2\\pi)^{D/2}}\n", " \\exp\\left[ - \\frac{D}{2\\beta_k} - \\frac{\\nu_k}{2} (x_n - m_k)^T W_k (x_n - m_k) \\right] \\\\\n", " & \\tilde{\\pi}_k := \\exp \\left[ \\psi(\\alpha_k) - \\psi(\\hat{\\alpha}) \\right] \\\\ \n", " & \\tilde{\\Lambda}_k := \\exp\\left[ \\sum_{i=0}^{D-1} \\psi\\left( \\frac{\\nu_k-i}{2} \\right) + D\\log 2 + \\log(\\det W_k) \\right] \\\\\n", " & \\psi(a) := \\frac{d}{da} \\log \\Gamma(a) \\ \\ (\\mbox{digamma function}) \\\\\n", " & \\hat{\\alpha} := \\sum_{k=1}^{K} \\alpha_k \\\\\n", " \\mbox{For $q(\\pi, \\Lambda, \\mu)$} & \\\\\n", " & \\alpha_k := \\alpha_0 + N_k \\\\\n", " & \\beta_k := \\beta_0 + N_k \\\\\n", " & \\nu_k := \\nu_0 + N_k \\\\\n", " & m_k := \\frac{1}{\\beta_k}(\\beta_0 m_0 + N_k \\bar{x}_k) \\\\\n", " & W_{k}^{-1} := W_{0}^{-1} + N_k S_k \n", " {} + \\frac{\\beta_0 N_k}{\\beta_0 + N_k}(\\bar{x}_k - m_0)(\\bar{x}_k - m_0)^T \\\\\n", " & N_k := \\sum_{n=0}^{N-1} r_{n,k} \\\\\n", " & \\bar{x}_k := \\frac{1}{N_k} \\sum_{n=0}^{N-1} r_{n,k} x_n \\\\\n", " & S_k := \\frac{1}{N_k} \\sum_{n=0}^{N-1} r_{n,k}(x_n - \\bar{x}_k)(x_n - \\bar{x}_k)^T\n", "\\end{align}\n", "$$\n", "\n", "Note that the above expression is not a closed form expression, because the distributions of $Z$ and $(\\pi, \\mu, \\Lambda)$ depend on each other. \n", "\n", "The self-consistent solution can be obtained by iteration (Note: We do not discuss the convergence properties).\n", "\n", "1. Initialize parameters $\\alpha_k, \\beta_k, \\nu_k, m_k, W_k$.\n", "2. Calculate $r_{n,k}$ from $\\alpha_k, \\beta_k, \\nu_k, m_k, W_k$.\n", "3. Calculate $\\alpha_k, \\beta_k, \\nu_k, m_k, W_k$ from $r_{n,k}$.\n", "4. Repeat 2 and 3 until the variatoinal lower bound converges.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.3 Variational lower bound\n", "\n", "The variational lower bound $\\mathcal{L}(q)$ is useful for monitoring the convergence and model selection. Although an expression for $\\mathcal{L}(q)$ is given in equations (10.70)-(10.77), we can further simplify it as \n", "\n", "$$\n", "\\begin{align}\n", " \\mathcal{L}(q) = -\\sum_{n=0}^{N-1}\\sum_{k=0}^{K-1} r_{n, k} \\log r_{n, k} + \n", " \\log \\frac{C(\\alpha_0)}{C(\\alpha)} + \n", " \\frac{D}{2} \\sum_{k=0}^{K-1} \\log \\frac{\\beta_0}{\\beta_k} + \n", " \\sum_{k=0}^{K-1} \\log \\frac{B(W_0, \\nu_0)}{B(W_k, \\nu_k)} - \n", " \\frac{DN}{2} \\log(2\\pi), \n", "\\end{align}\n", "$$\n", "where \n", "$$\n", "\\begin{align}\n", " C(\\alpha) := \\frac{\\Gamma\\left( \\sum_{k=0}^{K-1} \\alpha_k \\right)}{\\prod_{k=0}^{K-1} \\Gamma(\\alpha_k)}\n", "\\end{align}\n", "$$\n", "is the normalization coefficient for Dirichlet distribution $\\mathrm{Dir}(\\pi | \\alpha)$, and \n", "$$\n", "\\begin{align}\n", " B(W, \\nu) := \\left( \\det W \\right)^{-\\nu/2} \\left[ 2^{\\nu D/2} \\pi^{D(D-1)/4} \\prod_{i=0}^{D-1} \\Gamma\\left( \\frac{\\nu - i}{2} \\right) \\right]^{-1}\n", "\\end{align}\n", "$$\n", "is the normalization coefficient for Wishart distribution $\\mathcal{W}(\\Lambda | W, \\nu)$.\n", "\n", "The derivation is lengthy but straightforward, and hence I shall omit it here. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.4 Model comparison\n", "\n", "In the formulation so far, we have fixed hyperparameters $\\alpha_0, \\beta_0, \\nu_0, m_0, W_0$, as if they were given. \n", "However, in reality, we have to choose the value of these hyperparameters. \n", "\n", "Here, we shall choose a set of hyperparameters that maximizes the variational lower bound $\\mathcal{L}$, whose expression is shown in the previous section.\n", "\n", "For the rationale of this approach, see equation (10.36) of the book. Here we assume the prior on the model $p(m)$ is uniform, and follow evidence-approximation-like approach." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.5 Predictive distribution\n", "\n", "The predictive distribution for a new data $\\hat{x}$ and the corresponding latent variable $\\hat{z}$ can be expressed as follows: \n", "\n", "$$\n", "\\begin{align}\n", " p(\\hat{z} | \\hat{x}, X) &\\propto p(\\hat{x}, \\hat{z} | X) \\simeq \\prod_{k=0}^{K-1} \\left[ \\frac{\\alpha_k}{\\sum_{j=0}^{K-1} \\alpha_j} \\mathrm{St}\\left(\\hat{x} \\middle| m_k, L_k, \\nu_k + 1 - D \\right) \\right]^{\\hat{z}_k} \\\\\n", " p(\\hat{x} | X) &\\simeq \\frac{1}{\\sum_{k=0}^{K-1} \\alpha_k} \\sum_{k=0}^{K-1} \\alpha_k \\mathrm{St}(\\hat{x} | m_k, L_k, \\nu_k + 1 - D) \\\\\n", " L_k &:= \\frac{(\\nu_k + 1 - D) \\beta_k}{ 1 + \\beta_k} W_k, \n", "\\end{align}\n", "$$\n", "where $\\mathrm{St}$ stands for Student's t distribution. \n", "\n", "For the drivation, see Section 10.2.3 of PRML. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 3 From math to code\n", "\n", "In this section, we describe `BayesianGaussianMixtureModel` class, which implements the model described above.\n", "\n", "## 3.1 Properties and methods\n", "\n", "We let `BayesianGaussianMixtureModel` has the following properties and methods.\n", "\n", "### Properties\n", "\n", "* `K` : $K$, i.e., the number of components\n", "* `D` : $D$, i.e., the input dimension\n", "* `alpha0` : $\\alpha_0$, a positive float\n", "* `beta0` : $\\beta_0$, a positive float.\n", "* `nu0` : $\\nu_0$, float satisfying `nu0` > $D - 1$\n", "* `m0` : $m_0$, a ($D$,) array.\n", "* `W0` : $W_0$, a ($D$, $D$) array, representing a symmetric positive definite matrix.\n", "* `alpha` : ($K$,) array, where `alpha[k] = ` $\\alpha_k$\n", "* `beta` : ($K$,) array, where `beta[k] = ` $\\beta_k$\n", "* `nu` : ($K$,) array, where `nu[k] = ` $\\nu_k$\n", "* `m` : ($K$, $D$) array, where `m[k, i]` = $i$ th component of $m_k$\n", "* `W` : ($K$, $D$, $D$) array, where `W[k, i, j]` = (i,j) component of $W_k$.\n", "* `lower_bound` : float, representing the variational lower bound.\n", "\n", "### Methods\n", "\n", "* `_init_params` : initializes parameters `alpha`, `beta`, `nu`, `m`, `W`.\n", "* `_e_like_step` : performs E-like-step, i.e., calculates and returns $r$ from `alpha`, `beta`, `nu`, `m`, `W`.\n", "* `_m_like_step` : peroforms M-like-step, i.e., calculates `alpha`, `beta`, `nu`, `m`, `W` from $r$.\n", "* `calc_lower_bound` : calculates and returns the variational lower bound $\\mathcal{L}$ for current parameter set.\n", "* `fit` : fits the model to the data, i.e., runs `_e_like_step` and `_m_like_step` alternately until the variational lower bound converges.\n", "* `_predict_joint_proba` : for given data points $\\hat{x}$, returns the joint probability $p(\\hat{x}, \\hat{z} | X)$.\n", "* `predict_proba` : for a given data set, returns probability over classes of latent variables.\n", "* `predict` : for a given data set, returns the predicted class, which is the argmax of the corresponding latent variables.\n", "* `calc_prob_density` : for a given data set, returns the predictive density " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.2 Calculation\n", "\n", "Here we discuss how to implement several methods, especially how we shall translate the equations described in the previous sections into codes.\n", "\n", "\n", "### 3.2.1 Initialization of the parameters\n", "\n", "We initialize parameters as follows\n", "* `alpha`, `beta`, `nu` : They are initialized as `alpha[k] = alpha0 +` $N/K$ etc. An implicit assumption here is that the cluster sizes (the number of data belonging to a cluster) are almost the same for different clusters.\n", "* `mu` : `K` vectors randomly chosen from the input $X$. \n", "* `W` : Each $W_k$ is taken to be a diagonal matrix, whose $i$th diagonal element is the 1/(variance of the $i$th component of the input data $X$). It may fail when the variance inside clusters is much smaller than the distances between clusters.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2.2 E-like-step\n", "\n", "In the E-like-step, we evaluate $r_{n,k}$ according to the following equations:\n", "$$\n", "\\begin{align}\n", " r_{n,k} &:= \\frac{\\rho_{n,k}}{\\sum_{j=0}^{K-1} \\rho_{n,j}} \\\\\n", " \\rho_{n,k} &:= \\frac{\\tilde{\\pi}_k \\tilde{\\Lambda}_{k}^{1/2}}{(2\\pi)^{D/2}}\n", " \\exp\\left[ - \\frac{D}{2\\beta_k} - \\frac{\\nu_k}{2} (x_n - m_k)^T W_k (x_n - m_k) \\right] \\\\\n", " \\tilde{\\pi}_k &:= \\exp \\left[ \\psi(\\alpha_k) - \\psi(\\hat{\\alpha}) \\right] \\\\ \n", " \\tilde{\\Lambda}_k &:= \\exp\\left[ \\sum_{i=0}^{D-1} \\psi\\left( \\frac{\\nu_k-i}{2} \\right) + D\\log 2 + \\log(\\det W_k) \\right] \\\\\n", " \\psi(a) &:= \\frac{d}{da} \\log \\Gamma(a) \\ \\ (\\mbox{digamma function}) \\\\\n", " \\hat{\\alpha} &:= \\sum_{k=1}^{K} \\alpha_k\n", "\\end{align}\n", "$$\n", "\n", "We set the following three temporal arrays.\n", "* `tpi` : (K,) array, where tpi[k] = $\\tilde{\\pi}_k$\n", "* `tlam` : (K,) array, where tlam[k] = $\\tilde{\\Lambda}_k$\n", "* `rho` : (N,K) array, where rho[n,k] = $\\rho_{n,k}$\n", "\n", "In calculating `tlam`, we define another temporal array `arg_digamma`, where `arg_digamma[k,i]` = $\\nu_k - i$\n", "\n", "In calculating `rho`, we first calculate a ($N, K, D$) array `diff`, where `diff[n,k,i]` = $(x_n - m_k)_{i}$, and then calculate a $(N, K)$ array `exponent`, where `exponent[n, k]` = $D/\\beta_k + \\nu_k (x_n-m_k)^T W_k (x_n-m_k)$. \n", "\n", "Using these quantities, `rho` can be evaluated. We shall omit the $2\\pi$ factor, because it does not affect the final result $r_{n,k}$. \n", "Also, note that because rho contains exponential factor, it often happens numerically that $\\sum_{j=0}^{K-1}\\rho_{n,j} = 0$, which hinders the normalization to obtain $r_{n, k}$.\n", "To prevent such trouble, we subtract a constant (for each $n$) as `exponent[n, k]` - $\\min_j$(`exponent[n, j]`)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2.3 M-like-step\n", "\n", "In the M-like-step, we calculate parameters using the following equations:\n", "\n", "$$\n", "\\begin{align}\n", " \\alpha_k &:= \\alpha_0 + N_k \\\\\n", " \\beta_k &:= \\beta_0 + N_k \\\\\n", " \\nu_k &:= \\nu_0 + N_k \\\\\n", " m_k &:= \\frac{1}{\\beta_k}(\\beta_0 m_0 + N_k \\bar{x}_k) \\\\\n", " W_{k}^{-1} &:= W_{0}^{-1} + N_k S_k + \\frac{\\beta_0 N_k}{\\beta_0 + N_k}(\\bar{x}_k - m_0)(\\bar{x}_k - m_0)^T \\\\\n", " N_k &:= \\sum_{n=0}^{N-1} r_{n,k} \\\\\n", " \\bar{x}_k &:= \\frac{1}{N_k} \\sum_{n=0}^{N-1} r_{n,k} x_n \\\\\n", " S_k &:= \\frac{1}{N_k} \\sum_{n=0}^{N-1} r_{n,k}(x_n - \\bar{x}_k)(x_n - \\bar{x}_k)^T\n", "\\end{align}\n", "$$\n", "\n", "* `n_samples_in_component` : ($K$,) array, where`n_samples_in_component[k]` = $N_k$\n", "* `barx` : ($K, D$) array, where `barx[k, i]` = $\\bar{x}_{k, i}$\n", "* `S` : ($K, D, D$) array, where `S[k,i,j]` = $(S_k)_{i,j}$\n", "\n", "For calculating these quantities and parameters, we use the following two temporal arrays.\n", "* `diff` : ($N,K,D$) array, where `diff[n,k,i]` = $x_{n,i} - \\bar{x}_{k,i}$\n", "* `diff2` : ($K, D$) array, where `diff2[k, i]` = $\\bar{x}_{k,i} - (m_0)_i$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2.4 Variational lower bound\n", "\n", "$$\n", "\\begin{align}\n", " \\mathcal{L}(q) = -\\sum_{n=0}^{N-1}\\sum_{k=0}^{K-1} r_{n, k} \\log r_{n, k} + \n", " \\log \\frac{C(\\alpha_0)}{C(\\alpha)} + \n", " \\frac{D}{2} \\sum_{k=0}^{K-1} \\log \\frac{\\beta_0}{\\beta_k} + \n", " \\sum_{k=0}^{K-1} \\log \\frac{B(W_0, \\nu_0)}{B(W_k, \\nu_k)} - \n", " \\frac{DN}{2} \\log(2\\pi), \n", "\\end{align}\n", "$$\n", "where \n", "$$\n", "\\begin{align}\n", " C(\\alpha) &:= \\frac{\\Gamma\\left( \\sum_{k=0}^{K-1} \\alpha_k \\right)}{\\prod_{k=0}^{K-1} \\Gamma(\\alpha_k)} \\\\\n", " B(W_k, \\nu_k) &:= \\left( \\det W_k \\right)^{-\\nu_k/2} \\left[ 2^{\\nu_k D/2} \\pi^{D(D-1)/4} \\prod_{i=0}^{D-1} \\Gamma\\left( \\frac{\\nu_k - i}{2} \\right) \\right]^{-1}\n", "\\end{align}\n", "$$\n", "\n", "To make the code readable, we define two utility functions for calculating $\\log C(\\alpha)$ and $\\log B(W, \\nu)$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from scipy.special import gamma, digamma, gammaln\n", "\n", "def logC(alpha):\n", " '''\n", " Function for calculating the natural log of C(alpha), the normalization constant for Dirichlet distributions.\n", " See equations (B.16) and (B.27) of PRML.\n", " \n", " Parameters\n", " ----------\n", " alpha : 1D numpy array\n", " 1D numpy array representing the parameter alpha for Dirichlet distribution. \n", " \n", " Returns\n", " ----------\n", " logC : flaot\n", " log of C(alpha), the normalization constant for Dirichlet distributions\n", " '''\n", " return gammaln(alpha.sum()) - gammaln(alpha).sum()\n", " \n", "def logB(W, nu):\n", " '''\n", " Function for calculating the natural log of B(W, nu), the normalization constant for Wishart distributions.\n", " See equations (B.78) and (B.79) of PRML.\n", " \n", " Parameters\n", " ----------\n", " W : 2D or 3D numpy array\n", " numpy array representing the parameter W for Wishart distributions.\n", " When W is a 2D array, it must be a (D, D) symmetric positive definite matrix, where D is a integer.\n", " When W is a 3D array, it must be a (K, D, D) array, and W[k] are symmetric positive definite matrices, where K and D are integers. \n", " In the latter case, it is understood that the function deals with several Wishart distributions at once.\n", " nu : float, or 1D numpy array\n", " Number(s) representing the degrees of freedom of Wishart distributions.\n", " When W is (K, D, D) (resp. 2D) numpy array, it must be (K,) numpy array (resp. float).\n", " \n", " Returns\n", " ----------\n", " logB : flaot or 1D numpy array\n", " log of B(alpha), the normalization constant for Wishart distributions.\n", " '''\n", " Wshape = W.shape\n", " if len(Wshape) == 2:\n", " D, _ = Wshape\n", " arg_gamma = nu - np.arange(0, D, 1)\n", " return -nu/2 * np.log(np.linalg.det(W)) - D/2 * nu * np.log(2) - D* (D - 1)/4 * np.log(np.pi) - gammaln(arg_gamma/2).sum()\n", " else:\n", " K, D, _ = Wshape\n", " arg_gamma = np.reshape(nu, (K, 1)) - np.reshape(np.arange(0, D, 1), (1, D))\n", " return -nu/2 * np.log(np.linalg.det(W)) - D/2 * nu * np.log(2) - D* (D - 1)/4 * np.log(np.pi) - gammaln(arg_gamma/2).sum(axis=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2.5 prediction\n", "\n", "$$\n", "\\begin{align}\n", " p(\\hat{z} | \\hat{x}, X) &\\propto p(\\hat{x}, \\hat{z} | X) \\simeq \\prod_{k=0}^{K-1} \\left[ \\frac{\\alpha_k}{\\sum_{j=0}^{K-1} \\alpha_j} \\mathrm{St}\\left(\\hat{x} \\middle| m_k, L_k, \\nu_k + 1 - D \\right) \\right]^{\\hat{z}_k} \\\\\n", " p(\\hat{x} | X) &\\simeq \\frac{1}{\\sum_{k=0}^{K-1} \\alpha_k} \\sum_{k=0}^{K-1} \\alpha_k \\mathrm{St}(\\hat{x} | m_k, L_k, \\nu_k + 1 - D) \\\\\n", " L_k &:= \\frac{(\\nu_k + 1 - D) \\beta_k}{ 1 + \\beta_k} W_k\n", "\\end{align}\n", "$$\n", "\n", "The probability density of the Student's t distribution is given by (equations (B.68)-(B.72) in PRML)\n", "$$\n", "\\begin{align}\n", " \\mathrm{St}\\left(x \\middle| \\mu, L, \\nu \\right) &= \\frac{\\Gamma\\left(\\frac{\\nu + D}{2} \\right)}{\\Gamma\\left(\\frac{\\nu}{2}\\right)}\n", " \\frac{(\\det L)^{1/2}}{(\\nu \\pi)^{D/2}}\n", " \\left( 1 + \\frac{\\Delta^2}{\\nu} \\right)^{-\\frac{\\nu}{2} - \\frac{D}{2}} \\\\\n", " \\Delta^2 &:= (x - \\mu)^T L (x- \\mu)\n", "\\end{align}\n", "$$\n", "\n", "For later convenience, we define a function calculating the probability density function of multivariate Students's t distribution as follows" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def multi_student_t(X, mu, L, nu):\n", " '''\n", " Function for calculating the probability density of multivariate Student's t distribution.\n", " See equations (B.68) and (B.72) of PRML.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2D numpy array representing input data points on which the density are calculated.\n", " X[n, i] represents the i-th element of n-th point in X.\n", " mu : 1D numpy array\n", " 1D numpy array representing the mean of the distribution. \n", " Its length must coincide with X.shape[1]\n", " L : 2D numpy array\n", " 2D numpy array representing \"accuracy\".\n", " It must be a (D, D) array, where D = X.shape[1]\n", " nu : float, must be positive\n", " a positive number representing the degrees of freedom of the distribution\n", " \n", " Returns\n", " ----------\n", " prob_density : 1D numpy array\n", " The probability density of the Student's t distribution with the given parameters mu, L, nu, evaluated on X, \n", " where prob_density[n] = the density on n-th data of X.\n", " '''\n", " _, D = X.shape\n", " diff = X - mu\n", " delta2 = ((diff @ L ) * diff).sum(axis=1)\n", " coeff = gamma( (nu + D)/2 )/gamma(nu/2) * (np.linalg.det(L)**0.5) / ((nu*np.pi)**(D/2))\n", " return coeff/((1 + delta2/nu)**(0.5*nu + 0.5*D)) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.3 The code for `BayesianGaussianMixtureModel` class" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class BayesianGaussianMixtureModel:\n", " \n", " def __init__(self, K, D, alpha0, beta0, nu0, m0, W0):\n", " self.K = K\n", " self.D = D\n", " self.alpha0 = alpha0\n", " self.beta0 = beta0\n", " self.nu0 = nu0\n", " self.m0 = m0\n", " self.W0 = W0\n", " \n", " self.alpha = None\n", " self.beta = None\n", " self.nu = None\n", " self.m = None\n", " self.W = None\n", " self.lower_bound = None\n", " \n", " def _init_params(self, X, random_state=None):\n", " '''\n", " Method for initializing model parameterse based on the size and variance of the input data array. \n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " random_state : int\n", " int, specifying the seed for random initialization of m\n", " '''\n", " N, D = X.shape\n", " rnd = np.random.RandomState(seed=random_state)\n", " \n", " self.alpha = (self.alpha0 + N / self.K) * np.ones(self.K)\n", " self.beta = (self.beta0 + N / self.K) * np.ones(self.K)\n", " self.nu = (self.nu0 + N / self.K) * np.ones(self.K)\n", " self.m = X[rnd.randint(low=0, high=N, size=self.K)]\n", " self.W = np.tile(np.diag(1.0/np.var(X, axis=0)), (self.K, 1, 1))\n", "\n", " def _e_like_step(self, X):\n", " '''\n", " Method for calculating the array corresponding to responsibility.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " \n", " Returns\n", " ----------\n", " r : 2D numpy array\n", " 2D numpy array representing responsibility of each component for each sample in X, \n", " where r[n, k] = $r_{n, k}$.\n", " \n", " '''\n", " N, _ = np.shape(X)\n", " \n", " tpi = np.exp( digamma(self.alpha) - digamma(self.alpha.sum()) )\n", " \n", " arg_digamma = np.reshape(self.nu, (self.K, 1)) - np.reshape(np.arange(0, self.D, 1), (1, self.D))\n", " tlam = np.exp( digamma(arg_digamma/2).sum(axis=1) + self.D * np.log(2) + np.log(np.linalg.det(self.W)) )\n", " \n", " diff = np.reshape(X, (N, 1, self.D) ) - np.reshape(self.m, (1, self.K, self.D) )\n", " exponent = self.D / self.beta + self.nu * np.einsum(\"nkj,nkj->nk\", np.einsum(\"nki,kij->nkj\", diff, self.W), diff)\n", " \n", " exponent_subtracted = exponent - np.reshape(exponent.min(axis=1), (N, 1))\n", " rho = tpi*np.sqrt(tlam)*np.exp( -0.5 * exponent_subtracted )\n", " r = rho/np.reshape(rho.sum(axis=1), (N, 1))\n", " \n", " return r\n", " \n", " \n", " def _m_like_step(self, X, r):\n", " '''\n", " Method for calculating the model parameters based on the responsibility.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " r : 2D numpy array\n", " 2-D numpy array representing responsibility of each component for each sample in X, \n", " where r[n, k] = $r_{n, k}$.\n", " '''\n", " N, _ = np.shape(X)\n", " n_samples_in_component = r.sum(axis=0)\n", " barx = r.T @ X / np.reshape(n_samples_in_component, (self.K, 1))\n", " diff = np.reshape(X, (N, 1, self.D) ) - np.reshape(barx, (1, self.K, self.D) )\n", " S = np.einsum(\"nki,nkj->kij\", np.einsum(\"nk,nki->nki\", r, diff), diff) / np.reshape(n_samples_in_component, (self.K, 1, 1))\n", " \n", " self.alpha = self.alpha0 + n_samples_in_component\n", " self.beta = self.beta0 + n_samples_in_component\n", " self.nu = self.nu0 + n_samples_in_component\n", " self.m = (self.m0 * self.beta0 + barx * np.reshape(n_samples_in_component, (self.K, 1)))/np.reshape(self.beta, (self.K, 1))\n", " \n", " diff2 = barx - self.m0\n", " Winv = np.reshape(np.linalg.inv( self.W0 ), (1, self.D, self.D)) + \\\n", " S * np.reshape(n_samples_in_component, (self.K, 1, 1)) + \\\n", " np.reshape( self.beta0 * n_samples_in_component / (self.beta0 + n_samples_in_component), (self.K, 1, 1)) * np.einsum(\"ki,kj->kij\",diff2,diff2) \n", " self.W = np.linalg.inv(Winv)\n", " \n", " def _calc_lower_bound(self, r):\n", " '''\n", " Method for calculating the variational lower bound.\n", " \n", " Parameters\n", " ----------\n", " r : 2D numpy array\n", " 2-D numpy array representing responsibility of each component for each sample in X, \n", " where r[n, k] = $r_{n, k}$.\n", " Returns\n", " ----------\n", " lower_bound : float\n", " The variational lower bound, where the final constant term is omitted.\n", " '''\n", " return - (r * np.log(r)).sum() + \\\n", " logC(self.alpha0*np.ones(self.K)) - logC(self.alpha) +\\\n", " self.D/2 * (self.K * np.log(self.beta0) - np.log(self.beta).sum()) + \\\n", " self.K * logB(self.W0, self.nu0) - logB(self.W, self.nu).sum()\n", " \n", " \n", " def fit(self, X, max_iter=1e3, tol=1e-4, random_state=None, disp_message=False):\n", " '''\n", " Method for fitting the model.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " max_iter : int\n", " The maximum number of iteration\n", " tol : float\n", " The criterion for juding the convergence. \n", " When the change of lower bound becomes smaller than tol, the iteration is stopped.\n", " random_state : int\n", " An integer specifying the random number seed for random initialization\n", " disp_message : Boolean\n", " Whether to show the message on the result.\n", " '''\n", " self._init_params(X, random_state=random_state)\n", " r = self._e_like_step(X)\n", " lower_bound = self._calc_lower_bound(r)\n", " \n", " for i in range(max_iter):\n", " self._m_like_step(X, r)\n", " r = self._e_like_step(X)\n", " \n", " lower_bound_prev = lower_bound\n", " lower_bound = self._calc_lower_bound(r)\n", " \n", " if abs(lower_bound - lower_bound_prev) < tol:\n", " break\n", " \n", " self.lower_bound = lower_bound\n", " \n", " if disp_message:\n", " print(f\"n_iter : {i}\")\n", " print(f\"convergend : {i < max_iter}\")\n", " print(f\"lower bound : {lower_bound}\")\n", " print(f\"Change in the variational lower bound : {lower_bound - lower_bound_prev}\")\n", " \n", " \n", " def _predict_joint_proba(self, X):\n", " '''\n", " Method for calculating and returning the joint probability. \n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " \n", " Returns\n", " ----------\n", " joint_proba : 2D numpy array\n", " A numpy array with shape (len(X), self.K), where joint_proba[n, k] = joint probability p(X[n], z_k=1 | training data)\n", " '''\n", " L = np.reshape( (self.nu + 1 - self.D)*self.beta/(1 + self.beta), (self.K, 1,1) ) * self.W\n", " tmp = np.zeros((len(X), self.K))\n", " for k in range(self.K):\n", " tmp[:,k] = multi_student_t(X, self.m[k], L[k], self.nu[k] + 1 - self.D)\n", " return tmp * np.reshape(self.alpha/(self.alpha.sum()), (1, self.K))\n", " \n", " def calc_prob_density(self, X):\n", " '''\n", " Method for calculating and returning the predictive density.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " \n", " Returns\n", " ----------\n", " prob_density : 1D numpy array\n", " A numpy array with shape (len(X), ), where proba[n] = p(X[n] | training data)\n", " '''\n", " joint_proba = self._predict_joint_proba(X)\n", " return joint_proba.sum(axis=1)\n", " \n", " def predict_proba(self, X):\n", " '''\n", " Method for calculating and returning the probability of belonging to each component.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " \n", " Returns\n", " ----------\n", " proba : 2D numpy array\n", " A numpy array with shape (len(X), self.K), where proba[n, k] = p(z_k=1 | X[n], training data)\n", " '''\n", " joint_proba = self._predict_joint_proba(X)\n", " return joint_proba / joint_proba.sum(axis=1).reshape(-1, 1)\n", " \n", " def predict(self, X):\n", " '''\n", " Method for predicting which component each input data belongs to.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " \n", " Returns\n", " ----------\n", " pred : 1D numpy array\n", " A numpy array with shape (len(X), ), where pred[n] = argmax_{k} p(z_k=1 | X[n], training data)\n", " '''\n", " proba = self.predict_proba(X)\n", " return proba.argmax(axis=1)\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 4 Experiment\n", "\n", "## 4.1 Preparation" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def get_meshgrid(x, y, nx, ny, margin=0.1):\n", " x_min, x_max = (1 + margin) * x.min() - margin * x.max(), (1 + margin) * x.max() - margin * x.min()\n", " y_min, y_max = (1 + margin) * y.min() - margin * y.max(), (1 + margin) * y.max() - margin * y.min()\n", " xx, yy = np.meshgrid(np.linspace(x_min, x_max, nx),\n", " np.linspace(y_min, y_max, ny))\n", " return xx, yy" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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KAwGKAgF8oRB3z5nN1tycpMYWL/IEIBqM1mlpbMyOLCwfMEI0d8nagWTp0bQZ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\nBHPX4kFsBYQLuKjG/wkPdFcgPFX1VJT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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import make_blobs\n", "\n", "X, y = make_blobs(centers=3, n_features=2, n_samples=100, cluster_std=[2.0, 2.3, 1.8], random_state=42)\n", "plt.scatter(X[:,0], X[:,1], c=y)\n", "\n", "xx, yy = get_meshgrid(X[:, 0], X[:, 1], nx=100, ny=100, margin=0.1)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_predicted_label(ax, clf, xx, yy, X, t):\n", " Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])\n", " Z = Z.reshape(xx.shape)\n", " ax.contourf(xx, yy, Z, alpha=0.7)\n", " ax.scatter(X[:,0], X[:,1], c=t, edgecolor='k')\n", " \n", "def plot_prob_density(ax, model, xx, yy, X, t):\n", " Z = model.calc_prob_density(np.c_[xx.ravel(), yy.ravel()])\n", " Z = Z.reshape(xx.shape)\n", " ax.scatter(X[:,0], X[:,1], c=t, edgecolor='k')\n", " ax.contour(xx, yy, Z)\n", " \n", "def plot_result(model, xx, yy, X, t):\n", " fig = plt.figure(figsize=(8,4))\n", " ax = fig.add_subplot(121)\n", " plot_predicted_label(ax, model, xx, yy, X, t)\n", " ax = fig.add_subplot(122)\n", " plot_prob_density(ax, model, xx, yy, X, t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4.2 Simple example\n", "\n", "First, let us see the results for simply appying the model to the above data." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n_iter : 10\n", "convergend : True\n", "lower bound : -389.1578289309176\n", "Change in the variational lower bound : -3.9195783756440505e-05\n" ] }, { "data": { "image/png": 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uCQSDnnBHFAWcpYBsujGQocI4wkt688YLx9Bo5Tz4VCQpLlvZq1nJftkGFDI5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AfZC6LEJRP6o1FcXMzQIQPYv38vdWtZc/FKPs2atWD1mk1lzl0LcgsJ2RHKya3nOLf7Ipr8IpRm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\nHVmvKA8ihHisejbOLvEPCI2Gxm9P5Ozu3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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bgmm = BayesianGaussianMixtureModel(K=3, D=2, alpha0=1.0, beta0=1.0, nu0=2.0, m0=np.zeros(2), W0=np.eye(2))\n", "bgmm.fit(X, max_iter=1000, tol=1e-4, random_state=42, disp_message=True)\n", "plot_result(bgmm, xx, yy, X, y)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It seems that the model is properly fit to the data. \n", "However, due to the random initialization, different results may be obtained, whose example is given below." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n_iter : 8\n", "convergend : True\n", "lower bound : -397.75619724106684\n", "Change in the variational lower bound : 1.2367827594061964e-05\n" ] }, { "data": { "image/png": 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TDhBkaoValM/PdMKKJsYQIk7vYn/UFpzL3GkqW+Ms3PEV/rQ2dWb70Z8oMxos2hNCoFap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\n0A6dTs/cGVs5dfwG3ft4M3/ha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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bgmm = BayesianGaussianMixtureModel(K=3, D=2, alpha0=1.0, beta0=1.0, nu0=2.0, m0=np.zeros(2), W0=np.eye(2))\n", "bgmm.fit(X, max_iter=1000, tol=1e-4, random_state=0, disp_message=True)\n", "plot_result(bgmm, xx, yy, X, y)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Intuitively speaking, the former result is more appropriate. This intuition is also supported from the fact that the former result has larger value of variational lower bound.\n", "\n", "Also note that we took a somewhat arbitrary initialization, and better result may be obtained by using different initialization scheme." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4.2 Hyperparameter tuning" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can perform hyperparameter search using the variational lower bound as our criterion." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\sokohaku\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:113: RuntimeWarning: divide by zero encountered in log\n", "C:\\Users\\sokohaku\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:113: RuntimeWarning: invalid value encountered in multiply\n" ] } ], "source": [ "best_estimator = None\n", "best_lower_bound = -np.float(\"inf\")\n", "m0 = np.zeros(2)\n", "\n", "for alpha0 in [0.1, 1.0, 10.0, 100.0]:\n", " for beta0 in [0.01, 0.1, 1.0]:\n", " for nu0 in [1.1, 2.0, 11.0]:\n", " for W0 in [0.01*np.eye(2), 0.1*np.eye(2), np.eye(2), 10.0*np.eye(2)]:\n", " for random_state in np.arange(0,10,1):\n", " bgmm = BayesianGaussianMixtureModel(K=3, D=2, alpha0=alpha0, beta0=beta0, nu0=nu0, m0=m0, W0=W0)\n", " bgmm.fit(X, max_iter=1000, tol=1e-4, random_state=random_state, disp_message=False)\n", " if bgmm.lower_bound > best_lower_bound:\n", " best_estimator = bgmm\n", " best_lower_bound = bgmm.lower_bound" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lower_bound : -367.9533872980828\n" ] }, { "data": { "image/png": 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tRjkORicyMzPZmZ/PnuIiZgf34PD2nfSO6M3oySNZuXYFKxLX8krxBu7a9wHv\nZ24kq76EraWpvHr8J2YnvsaHWZuw/GKy6xWRUQz0D+CtvXswWiykpKQwaMBAmtIysTj5s/XLfQwe\nOISdO3cyICGMpiYTGenF/FKvgeE0NxopzGybWlnWtbT3MjLVqWMqAaUkSTrAAiwDXpEkaRawGngS\nSBZCpLXn+buT/ce3EmQLx0NqecalREWkiKOEfKopx4Mzz76qKMPLuSVg2WxWlmxYSFNVA/7WUGxY\nSarZTX1jLTOGzflDbSqrLiIt9zBDrBNRSWoAvC2BHKzYyomi40QEdv5jTjl4XxpyXz6/7OQ8PPzd\n8fBzp6CggC1btjLYOBGlpARnPVJDE542HyooJlREYQrzQDKYURXWUK+vpn///nx+5DAuShWvzL0J\n/8Ye6G2uHEw9yjUH59N/0W2YsXFf5DRmBiXgpNYhhKCgqYr3MtezOGsTuY3lPNfvutY5MJIk8bdB\ng7lt5XK25Obw5v3/xrchBM8TVuqj1Pj7DkKbr2XBPf9g89ZEAFKSTxIdE2h3beH9W5Zl5iTn0SPK\nfp+sa2nvO/DHAQPwMDDv1N8fF0KUA7OA54FqYAhwfTufu1upbajGUdiPRCokBWo0HGUvFaIYkzBS\nJgrJVCYzduDlQMuwe111Nf2sw/GRAvGTejDAMpLUnIPnLEZyMXJL0/EioDV4n26Tp8WfnGI5B/Jf\njNyXz6Mgo4jgyJZERkVFRThrXFqCN4DeARoN+BFMA3WkS4cx+zsjFVaQpUmiR0QwA4cPZ2tuDnX7\nD9KzPoYeojeeki+hIoagBdOoMzTy0dB7uCFsJE7qlvSrkiQRrPfkhbg53NVrAuuLk1l2cp9du0aF\nhOLp4MDqjHS279iOr+iBuqQebAKLnzM+BHE0JRlHvRoPLyeys0rbXFtgRMsX5OLstvtkXUt7LyN7\nWggh/eLP06f2bRRCRAkhHIQQY4QQue157u4myDecKqV9wDUJI1aFlanDr6XENZ89yg1UuBdz1WU3\n0yuwLwA5Rel4WvztMp6pJDVekh95pVl/qE0OWieMkqHNdpOy+YKSw3QkuVjJpSX35fMrzi4joGdL\noIuOjqbeXEuzaAKdFhQKaDRQp6nklttvYcxNExFOOiprk7ni9qls3raJxFMZ1ip27rbL72Ca6ooq\n2p2SRVvp6ez7q+e/JXwMQ7168XraGmpMTa3bVQoFk3pGsCU3B1dXN5ppQrLYUFY2YvFxxkQzWq0O\ntVpNaJg3uTkVbY7t4OSAm48rJTll7fZ5yTqGvCK/kwyKGk2tuopMkqkXNVSIYo6odp1KczqMO694\nhIfnvsbtM/7Pbuha7+iMUdFWEtyBAAAgAElEQVQ2lWGzZED/B4NsZFA/GqRaSkVB67KTalFOOUXE\nhg/+Q8f+I+RiJbKuxGq1Ulteh4d/y1wVZ2dnHnn0EY7r91OjbSkSVGRKp1ZfzlNPPcmChx4F4Lsv\nP+DthW/j4uLCkdISHFQqLEVFmGmpACYUYLrKDZFahy79lxP97SkkBfdFTsNoM7e5Cx8YEEiT2czc\ne/9GvmM6FmFGWWPA6qIj1yGVW26+GYVCga+fKxVldec8voefG9Vl52+DrPPJAbyT6HXO3D79//CO\n8CPD8Qjl7oWMGTyd8QOvPO/7+vccSplUQKUoIUscZYdYw1axkjprFX4ef2ydpkatZe7Ev5PvkMF+\n1WYOqLaQpjnErDG34eLYtlDD2YQQFFbkkl2chsncfrmS5WIlsq6mrrIBIQRuPmdmgj/2+GO889Hb\naCNahrsTZkRy8PABgoKCOFnWUv0r2PtMHzpWVkYfbx+uv/Y6cnSpVIgSUqPTsflryF+ZyPDRw36z\nHT2dfYl3D2NjiX21vz7eLevSh8+8ghnXT2WfdgPVxmysThoGT0ngf6/9DwAvb2eqqxqxWNpmfnRw\n1ZGbkU9qaupFfjqyS0kuZtKJnB3dmDb04h4fuuo9uHLUTfyw9WPc8CSOEShRUSCy+WzdG9wz83E0\npya8mC1GVErNRSVTCfAM4d5Zz1JUmY/NZiXAK/Q3l5BV1Jby7ab3MBlNaCQtDbZaJg2axYDz5E6/\nEHKxEllX1NzQ8gXV0dm+2Md1112HwtqDxQs3sWjxQhwcNQDUnHq9h7Nj62tLGxqI9/fn+XffZmzK\nOA4e2ENMUEs50sBUH1bsX8XioYu58647ATCZTFgsFhwdHe3OGekSwLKCfQghWh+r+Tm1jMRVG418\n8NFinnv+Wd5fsY0VSUV88sUX6HQtXzJOlzY1NptRObX0cSEED/3fwyTu3IUeF4YPGkGf2D6s/GkF\nXl5e7fQJytqLHMC7uPyyLLYcWkVJdQGujh5EBMWQlLkTBQr6MQyF1BKcexHLUfMejubsx1HnzMb9\ny6gzVKNSqhkUOZoxcTNQXOBabklSEOgVekGvFcLGVxvfwc/Qg0ARhiRJNIo6Nu5fjq9HMAEXWDDl\nl+TgLeuqjIaWFKRaB02bfafTk2p1ZyaC1huMaNVKLGYTjz/6DJ9/+hm6f92LJSOL6xcu4vDBw0Qy\nABdfX4wWgUeVO2prHE889gSzZs/i7/csYPnyZVhtNuL6xbH4o/cZMGAAAL4OrjRbzdSZDbhqWoK7\ns0aLBNSeqhrm5+dHv5g+rEgqosloxkXfErg12pZf/83N5tZgvmTJEj5571NirSNQSkoGNo0j93Aq\nN869kbXr13bApyn7I+QA3oWdLDvBNxvfI9zalyFEUl9Xw8HU7TjijCuOrcH7NFeLFxknj1JQmkO0\nNR53fDBYGklLS8JiMTNp8GwAGgy17E9LpKg8D09XHwZFj8HT5fwpG39NftkJhFm0Bm8AveRCoC2M\nQxk7CRh28QFcDt6yruz0/BBJ0XZS5elMNb+oqoskSUyfMoPMfTmENsdSJpQUpRezf/XPAC3LRoUA\nqeUgLpI7dfX1TJ4wmcrUeoaaJ6NERUlSPuMuG0dKWgoBAQFYTmVdu+mG+VgajFx/w3XMvvZaBC0T\n2k6znmqz4hxtPntC7FuvvUVgY0TrjHqFpCDEFEVi4nrKy8vx9vZu835Z55GfgXdh25LWEGbtQ4AU\ngkbS4Sn5EccIGqmljiq7/MYAjapaqusqCbNG4yG1lAF0lJyItiZwKGsnJnMz1fUVvL/yBXJTM9GX\nulKeWcpHq1/+3TPYm01NaNG1qQOuEToMzb8vFa5cJlTWlSmULb82rZa2yY1UqpbAZ7We2adVqzCa\nLSQdTKJ38wCcJFcURhsuWl9c8UCFmjqqkGqsoJQQzkqaRD0qlZLszFx6mmJRSxoUkoIAQnE3+bH4\n/cUA/PDzKmwGE+nf55CzrpR/3/0QM2ddA4CL9kyq4WajGQAHzZl7NrPJAoDmrG3V1dVo0dlfL0rU\nKi21tfKktq5GDuBdWGl1gV1CFwBnyQ2BQEIigyOYhQmbsJIvsiizFmKxmnDB3e49WkmHWtLQ2NzA\nlkMr8TX3IFLE4SMF0pMYeln6s27P76sIGezdk2prRcsSmlOEEJSpCokIvvjELynlDTSEquTgLeuy\nTg+dG5uMbfY5nnru3dhwZp+LoxYhwEMT1Dpqpqw3YXHT4oEvelzI4AiGgpYlXY2RNpLZTcKgBFwV\nHm2+HDsYnTiekkZmZibZlipU+RaCpHACpBD6NA7lSEZLaXYfvb71PVX1TaiUChx1Z4b96+ubkSTQ\nOZwZ7p8ybQrl6iK789VQgaPegfDw8Iv/sGQdSg7gHayyrpTl2z/n3R+fZcn6hWQXX3jCKncnL+qo\nttvWJFruauMYiRkT21nNFpZTykn0kgtatY4qqazNe6xYcHZ0Jbs4DX9hP6ztQyCV9WU0n7We9EI5\n6pwY3X8qh5XbOSmyKBUnSVbuRuOsJTZs0EUfTybrqmw2G++//z4zLp8OwHdffd/mrtTD89QEsqrG\n1m3+Hi0JmwxOonXUTFvchCnAkTqqcMebCPqSmrwFc20TVZMFLnhwYP9BKi2l2IT9LPFGxxoGDU1g\n6fa1OPTyRbPtzLkUkgK9R08AYs6qZFZQUUuApwvKs4bVqyoacHXTt44aADz2xGMYPepplOoxCxP5\ninQyHA+z6IP35DrgXZD8E+lAFbUlfLz6FRry6glvjEFb6siPWz4mOXvfb78ZGNl/CieUx6gW5Qgh\naBT1HGUPGklHA7V4E4AeZwIIYZA0lghbX4zmZvIUGRSKbIyimSpRxjHVXkb0nYxKqUandsBIMxZh\npkjkkivSqKQUgUClVP92o85hRN9JXD32VlQ9VDT5NjBo4GhumvLP33W8Ug/5v6Ssa7rlplt56l/P\nYj2mRQhB0tZjDBs8HIPhTPIjT++WomylxTWt24J9WpaPeYaFkaNOxSxMqE/WY3XRUO1lxIYNLQ54\nW/yoXJOM2/Be9IofjavKgz4xfUhzOES9qKFZNJGjOI7RqZGbb72F/T512JpMqDfUUisqyRVpFIoc\nbL290doEwS5nlrmdKKokxNd+ZK6kuAZvX/tskH5+fiSnHMHX3weVh8So+YPZviuRK664ot0/T9kf\nJ09i60DbktYQaO1JKJEggQvu6K0ubNj/I+5OXggEgZ4hKJXn/jH0Dopl8rBr2HxwJY3NtahVWhIi\nRwOw+9gmXHCnB73wo+WOWnnqxzlv0j/YcnAV+6s24aRz5bLY6cT1bFlXGh81kn1J2zDYGnHDCx0O\nnOQgLjo3FNLvrzwU5h9JmH/k734/2Fcaa08VOdkkrVlJdUkRXsE9iJt+Je6Bcm1j2YXLyMjgxx9+\nZJBhPEqppZ+5W30oLcxj0aJFxMXFERYWRkhoS/a0vNwKhozoBUC4vyc6tYopt95NktuHrFm7GinN\nFX8e4raXnmfNMy9w/GQenvgS/I0D1hFGDA/4onrIkX/8cwEZ6Rl8uPgjmgxNTJs2lRdeeoHvKg5S\npGqi9J1tZDfk0UwT3gRQq6rFsU8P4pydW4feaxubySmpYtpg+0qFeTkVxA8KbXOtnp6e6CQHhs8c\nwr8//nsHfqoXr7m5mXffe48lS5ei1qi5bd6N3HrrrX/ZqmlyAO9ABWXZ9BEJLTNLT5GQaDY18f2m\nD1FKKkw0c8XIG+kdFHvOY8SGDaJvaAImixH1WWu6M/KT8a5ryYV+WqEih97B/Qj0CmXe5H+c83hD\nosay/cg6oonHR2opVBAhYkky7SA5ey9xEb+dQKIjdFSlsYJjyax/6384jx+DNr4v5VlZLH/mUWY8\n8hTeYT3b7TyyP7e9e/fipfRrDd6nGRoNPPTgQ/g4+1NjrGLChAl4el3GibMqeamUCvqG+ZFysoIf\nV/yA0WjEarVy/YofybHZeOPt17lj3l1ENMSiNCux/reEhteC8Xh1MqJ/AI/PuY5nnn0GgLyGct5I\nX8PO8nSmB8RjG6zmtZ/fZKiYhFJSUt/fizKdjh0ff4bt1ttRKBQcyDgJQFxEQGubqqsaqayoJ6xn\n29UnFrOFqpIaPP3d2+zrTFarlfGTJ5NWU4162GCE1cpDr/yX9Vu28N1XX3V28zqFPF7ZgZwcXGnk\nzExsq7CSxA76kMBgy3gSLGPoY05gWeKn1DZW/epxJElCq9bZPYOaMeIGslTHSFMc5qTIIlm5G4ND\nPaPjpp63TWW1xWgkDd6c6cxKSUmQtSfJWRc2tN/eOrJM6K6vPsP92lm4jr0MXc8w3CZPxHnKRPYu\n/Wt2eNnvExAQgEGyX1UhEFiwMtw2lei6wQxunsihjck0m8pIPpxvt0pkdGw4mYUVnCyvQavV4ujo\nyPz+A0irqMCpb19GjR/BUf1O8kQG+blHyHl4KQFaV97K3cBlG57hxl0LmbblRa7Z8TqHq3L4Z9Q0\nHut7Fdu37CBMRKGUlAgFVE8MRF3aRHNKFocOHQJg46FM3Jwc6B9+ps8nH26Z6Na3f9tlniW55dis\nNgJ7+XfER/m7rV69muOFBbjcciOOfaLRx/bF5c7bWLdxI4cPH+7s5nUKOYB3oGGx48lWpdAo6gEo\nIR9HnPGVglqHt9wkL3xEIMkn9l7UsQO9Qrln5hP06tsHh3BHBieM4c4rHsVRe/586C2/VKQ2M1ul\n0wtQL7HTRUo6InhbTCZq8vNw7NvHbrs+rj+l6cfb9VyyP7cxY8ag93AkX5GBTdgQQqCQFEQTj1pq\nmdmtlJSENkdzNGU7FeX1FBacmYA6bkDLcPrP+89U9ZsZGUWIqxsv7kzk82+/4rOlnzDm9qHMvHcK\nm75ZzsqZT7Jo8B1cHzocN7WewZ4R/CtqBt+NeoC5oSNRKZTYhI3TQ3y1I/0w+zniseYkkpAQQlBv\nMJJ4NJtxcRGolGd+3R8+mIuDo4ZekW373Mm0QgCCege02deZtiUmQlQk0lk3MgqNGl10JDt27OjE\nlnUeeQi9A/UJiaeusYbEI6tRo6HR2ogvbevram06mn7HmmlnR1dG9Tv/Hfcv+bkHIakkKizFeEkt\n37BtwkahKpuh4eMvug3toaPynCtVKlRaHZbqatSenq3bzRUV6FzPn9tdJjubUqlk87ZNXH/NHPYe\nXY+T5Eps8zB02Kc21aCjrGov4cGT2b09g2vmDgUgwNOFIVE9WJp4hJsmJaBWKVErlTw3bjzzl/3A\nizu3859p05g2bZrd8eI9woj3CPvVds2/5UYeO/wkLm69qLw8BMdjVRiOpKDyURAfH89XW5IwGM1c\nPfLMIzqbTbB7RwYDB4fbzUA/LfNgNpIkERb7+7IodpQAf3+Ue3a13VFVja/vr1du+zOT78A72NA+\n43jg2peYN+1ebp78ANWKcizC3LrfJmyUq4oJC4i6JO1RKBRcfdktpKkOkao4QJY4xn7VZjy8fTrt\n+XdHkRQKosdPoub75VibWmYKW+vqqV2+itiJ5/7iU11YwPbPPmT1/17g4LLvMNSdu1qT7K8nJCSE\n3ft2kZ6VRmLSZtAKTJJ94Z4yCgkN8adnL18St9iP8swbH09FbSOr9pwpEDKyRwh3Dkzgq6PJfHEk\n6aLbNH/+fGInD6PgtlBoMNCwbAU5Tkf55rtvMFlsfLnxIAm9g+gTcibAHU8poKqigRGjzz3pNP1A\nFj2iA9vkeu9s8+bNw5h6nKaUVIQQCJuNhj37oKLynLPkTSYTn3zyCVNnzuS6G25g06ZNndDqjiXf\ngV8CKqUab9eWu92YsAQO524n0BKOEiVFqjw8PX2ICLj4pCe/pbS6kN3HNlJeXYy3uz/DYyfi4xZA\nD58IFlz9DCm5B2k01DPKbzKhvr3bDKt3tNaUqR14jsHXzsH46QeceO5FNB4emKqq6DN+MrFTprd5\nbcHRI6x/6384jRiGul8UGanppD66nquffQm9h+c5ji77KwoMbBlFGzQ5jt0rD5CtSsHF7EGDqpZS\nTT4/LVpFaYGaxQs3kZ1VSnhES/AcHhNK/3B/3lmxkwkDerXmJH9g2Aiyqqp4autmyhobeWDY8DZ9\n0WQysXjxYr78dAmSJHHTbfO5/fbbOV5ZSfXk8TibjIyuqqXPM3dz/fXX4+npydvLd1Be28hLt9v/\nX1+94jAOjhqGjerd5tosZgtHE48zbs7Ijvjo/hBfX19+Wr6CufPnU71qLTaLBT9vb37csKG1QMtp\nZrOZCVOmcKykGNXAAdgMTay94QYeXLCAJx9/vJOuoP1Jv0zH2ZUEeIaIO6Y/3NnNaFdCCNLykziS\nuQeLzUJMWDz9eg79zYpfF+tk2Qm+2vguwbYIXIUHtVIVBcos5k5YQJD3rw/JXSqXOt+5oa6Ohopy\nXHz90J6Voeo0IQRfP/gPHGdMwTHmzHKb6hU/4afQctltd3d4G/+I9+dcdVAIkdDZ7TifhIQEceDA\ngc5uRrvZ8s1OXpj7BuHX+pKal0x0TBT3/+t+oqOjqaszMOeKN5kwJZb7Hz4TQNNPlnHDi18xa1Qs\nj8w588jKYrPxxOaNfJtyjKFBQTw66jL6+rQEfiEEkydO4dju4/g0BQNQ6l5C8I0zqI0Iw1uv57Mr\nZ9HTw6P1eCeKKpjz/BKmDonimfmTW7fX1jQx58o3mTI9jnv/3XYU6uj24zxw2ZM8+f2DjLp6SLt/\nZu3BZrORkpKCWq0mMjLynDce3377Lfc8+QSu99zR+szcUldHxcuvkZ2ZiZ9f1y5NLEnSBfVn+Q78\nEpMkieiQAUSHDGizTwhBbmkGOUVpOOic6BuagLOj6zmO8ts27P+RCGss/lIPkMAdbzQWLRv2/8gt\n0/51QcewWi3UG2rR65xRq9pWXvq9OqNYiYOLCw4uLr+6v6m6GkNdLZ597B9l6AcncPKTLzq6ebJu\nKGFyf9QaFXH+Cbz/zUK7fS4uDowa24t1Px3mZOlOJk+5jIkTJxIZ7MOccQNYsukQCb2DmTiw5S5Y\npVDwwviJ9PP143+7dnDF10sY6B/AxJ49aS4o5EheERF+47F66miKcscxxo0KnYoR7h68cfVsPM8q\nM1rf1My/P1iNs6OW+64c1bq9vLycJZ/sxmK2MvOac2dJ3LfmEAqlggHj+nbAJ9Y+FAoFsbHnXnZ7\n2orVq1H0j7Wb8KZyccE5KpKtW7dy/fUXV8a5q5IDeBdhs9n4fuuHFJbm4mXxx6w0kpi0mlljbici\noM9vH+AsQggKq3LpTZzddl+CSKs6dEHv35u6me1H1yEJCYswM7DXKMYPvPIPp1NMKW/oksVKVDot\nwmJBGI1IZw3HWevq0Di2vWOXyZzdnRg8PZ4t3+zgzlduRHnWhLDt27fz6pv30a/3HexcVcyXH95E\n7MC+rF2/hn/MHEFKbglPfrYOf08X+oa23A1KksSc2H5M7x3Jj8dT+CE1lZd2bAdAv+AWik8dW9Fg\nxulwJfV7dxFz13S74G22WHnow9UUlNfw7r1X4+HiSE5ODvPm3Mixo+kMjP0bJksRVdUnCQltW997\nz+qDxI6Kxsmte/+f9/L0hPTSNtutdXW4uf15JrDKk9i6iGO5+yktLWSQZSw9pRiibPH0tQ5heeKn\nWK2WizqWJEk4qPUYaLTbbqARB/X5l5kBJGfvZXfyJuLMIxhuncJg6wQyso6yNWnVRbXjXEo9FF2y\nWInWUU9wXDw1P61FWFtyT1ubDNSt+ZmYsRM7uXWyrmrS/DFUl9ayc/mZHAo2m405184lqDoURUkl\nLt7hxDKJtP0ZLF68GI1axat3XY6Xi54Fb/9I0olCu2O6aLXcHBfPqrnz2H3bncxVa7Et+Rn/RakE\nv5RE6FMH8FmajbWiyG4ouLHZxIOLV7HneD6PzZ1AQu9gzGYzY0aNoeJAPYMC56NASf2xTMaPGU9l\nZaXdefNST5J77CTDr+j+NQzuuPVWmvfsw1TSklBHCEHjgUMoGxoZP75zVtt0BDmAdxEp2QcJsITa\npTN1l7zRCC35ZScu+ngJUZeRqUzGJFqqIpmEkUxVMoOiR//me3cf3UiEJRa91DLkrJMciLQMYH96\nIjab9Tfe/es2W5u6ZPA+bcxt9+BQVUfRcy9RvuhDip57kdCovvQZP6mzmybroobMiCegpy/f/W9l\na+KWo0eP0tzQjCd+UFAKJjOKiB54G0L48tMlCCFwd3Zk0T9n4+bkwJ2vf8/yncfOeXxfJyf+NWcu\ntWn7aEhLRV3SBFZBiThJg7KG2bNnA1BQXsMtr3zDrpRcHp0zjpnDWybFrlmzBku9oIdrApKXO1JB\nKT4mb1wsnnz55Zd251r70WaUKiVj53a9CWwXKzY2lndef4OadxZTv+hDat9YiCpxB+vXrEGt/n01\nH7oieQi9i1BICsRZiVSEEOSRTr2lli82voW3sx8TBl1Fr8ALezY1ut8UGg117MlejxYdjaIBR4Ue\ntVKL1WY976S5OkMNkdg/L3ZAj9VqwWwxodVc/PKSlPIGGuI1XTZ4A2idnJj5+LNUncyjvrwcr9Bw\n9GdNDJLJfkmpVDLr/st5e8GHHNmaQtzYviiVpxOsADYbZBdAdDgiPJC9B5fi6KDnhrlzef3N1/n8\n/+bw8EerefbLDWxOyuJfsy9rU3TE3d2dtevXct3s68mrOo7RZEJINkbGjyQtI5OkUhMfr9uHWqlk\n4YKrGBJ9po/l5+fjhC+EB0OjAYpbKhWqmxzIyc5pfZ2hsZkNn29j2BUJuPv8vnk3Xc1NN93ErFmz\n2LlzJ3q9nuHDh//pKqr9ua6mG4uNGEyhKhuLaBkuzyaVMgoZxFjGczWB9eEs2/YpeaWZF3Q8hULJ\n1CHX4uniixodsQyhl6k/h4/s5LstH3C+1Qf+Hj2ooMRuWzXlOOlc0Kh1v/KuPw+P4BBC4hPk4C27\nIFNuHYtXoAefPvkNQghiYmJw93KjlJYc5MaacvJOJuLj05dxfncwyDiODV9t5fLpV+Ci1/HW36/i\n/lmjScoq5JpnP+ehD1ezOzUPs+XMaNfQoUN59/13MAsz/tYQYvUTKWkI4NY3V/Luyl0M7xPK14/N\nswveAP36xePdc2TLrUFGLohTw8lO1Qwbfibvw7qPNlNXWc+s+2d0/Ad2CTk5OTF58mRGjhz5pwve\nIN+BdxnRPQZwoiCVvXkb8LD5UUwuw5mMTmqZoOKFP2HWZnYc+ZmQSb0u6JiZhcdobjAQbxvdutTC\n3erN3rKNFFbk/upysnEDr+DL9W9js1nxED7UUU22MpVpCdf/7rXicplQ2Z+VRqdh7mOzeOtvH7B7\n5QGGzxzE98u+Z+K4idRay6lvrMehQA/6fihCg9BaBb3KdRw8tJmkpCTi4uK4ccJApg+O5uOf97F6\n73E2HMxAq1YS5udJmL8HLg5avlyygt5j/4bCyxOrXoNGCKz5RehFCv977/427TI0mVj1XTYOOg9y\ns9bg2qxFgZJSbR6ewe5cddVVABgNRr57dSUxIyLpO+LSJJSStQ/5t2oXIUkSl4+Yx41T7iM8phca\nhbY1eJ/mhieVdW1nVv6ak2XZuFt87IKuQlLgafOloCLnV98X6BXKjZPvA3/BcYeDNHrXMWvsbcSE\nDrz4C+NMsRKndi4TKpN1FVNvG0do32Deue9jDA0GBgwYQF5BHi++9xwhfYJwxxuyTkJdA/QMRvL1\nxE3pRXr6mdzoHi6OPHjNGNa9eAev3nU514zuj5uTjqPZxazedxzcA1DpnVEX1aLffgK3rw7itjaD\npMS1bdpTX2fgofuWcPRIPv96dAa33T+Thp6lVATnMue+2ezYvR2NpmVp6A+vr6b8ZCW3PDfnkn1e\nsvYh34F3MX4eQXi5+rIvbRtNlgYcpTOzxqspx9vtwgsMuOjdyFVmgs1+u0HZiLPD+Z9zBXj24Lrx\nd11U288lpbyBmn7KDilWIpN1FSq1ivveu5P7Rz3Bx49+zd/fuhW9Xs8NN9xAfl4+i//zCTTbIC0H\neodCeDD6sj5ERbVdIqpVqxgbF8H/s3ee4VEVbx++z9ZsNr1XIAkkkNAJvUSa0kUQFAQERUFQFKQJ\nKCJVUVH+iooNwRcQkCa9Kb2EXgIJCSWF9L7ZZDe7e94PK4GYQoAQoux9XXzg7Jw5c/bK7G+emad0\nbFy76JrJZMLBzpEGeW2K/SbkkIO7a/E84DFXk5n7/nqSErP4YM7ztA0LoluvJkx9r2RSrNT4dFYv\n2EDbvs1p9FTlZ4O08GixWODVEJlUTpuQLlySnSBLTMMgFpIkxnJDeoX2jbpVuJ/6fs3JlKSSJMaZ\ncweLIvHEkC/Jo5ZHIFHxF4i+FYHBWHjvzh6A2wlb7ke8RVHkxqlwtn++gM3zZ3Fhx1YMet0jGZ8F\nC5VJ/bZ16ftWdzZ+tZ2jf9zJOPfa66+hUWVxU4hEbyogL/ICmakReLqF8v3icK5F33tXTSKRMGbs\nG1y3vlQUWZIv5hGrvsK7U97l7NmzrF37O9/+bwtvvfYTeVod878YTNuw0vOdg3mufTbyG0xGE6M+\nffnhv4BSSExMZPLUqbQOC2PoiBFPbNnPR4UllWo1RRRFTkUe4OilveQWZOPh4Evn0Gep6V6x8+/b\nJKTdYOPBX9DmaxAx4WDjQoOA5hw4tw07iSMmTOSTx/MdR1LLvWRu5AflQcQb4Phv/8eVYwex6RiG\nRKVCezwclcHEszM+Qir774R/VDaWVKrVA32BnnFtppMSm8bX4Qvw9DNbxzExMbz7zrvs2r0La5Wa\nEa8Mp9szQ/n6893kaQro3K0BQ0e0x9Pbscy+DQYD74x7h59/Xoa13JoCYz5jxo7l8MEj3IrV4evR\nAYXSHrkyh+VrpuPiWv4u28avtvP1uJ9466uR9BnzTLltH4SbN2/SrGVLqBeELKgOhqRkCg4cZvXy\n5fTqVbqznL5AT9KNVNLi08lJz0Wbk4/RYEQUQWmtQGVjhaO7Ay7eTrjVcCmWPOe/REVTqVoE/AlA\nFEWyNOlIJBJMJhNL/0ceozYAACAASURBVJhHY2M7bAVzRqJ0MZnLslO8/fwclJXgZf6g4q1JT+O3\nyW/jNX0KUhtzJijRZCJ1yVJadO1JYPunHnps/1UsAl59iL+ayLhW7+HgZs8Xh+dg52RbZtvcnHx+\n/fkg2zafQVdQSKu2gTzVJZjQlv7Y2VuXek92djbx8QkYdEren7aYnDRr5Ao15BdgvBHPFf0+xk4b\nxfTp08t87rn9l5jSdTahzzRi9uapj6SQ0bBXXmHrrXjse9xZHORHRiHbvpvYmBjzbtvFOE7vOU/E\nsSiiT18n8VrFfXzkChnegZ4EhdYmuE0QoU83xK2Ga6W/x+PAIuAWSmA0Glix53/oUwqoRyjSu5LG\nXJAeo03LLjTwb/FQz3iYPOfRRw4SfnAvziOGFruec+gIjimZdB497qHG9l/GIuDViwsHLzOl60cE\ntajNvO3TUanLXxinpuSwZcMptm0+S1ZmHoIAnt6O1PJzxdFJjcpaiaHQiEZTwK2ETG5eTyVPo0MU\nTRizs5ElZ0GmufRttphBslcMNxNulPqs6xduMr7DBzh5OrL4yNxHljbVu1YthMEDUNyVLU40mdC+\n/xUTX5zE6R0XSEvIAMDT3506zfypFeKLV4AHrr7O2DnbYm2nQq4wu2rp8vVoc/LJTM4iNS6duMhb\n3LgUy5Xj0eSk5wJQq74vYQPaEDawNb5B3o/kvaqCalnMRBCEv4BWwO3coAmiKJZ9SGOh0hBFkW83\nzyVTk4YMOYfYiq9YGz/qIQgCclGBrrDg3h2Vw8MWKbGyscWQmVXiujErG5VN2YVILFQ9lrlcPg3a\n12PKinHMG7SI97rNYe6W91Dbly2Urm52jBjVkWEjw4i6ksjJ4zFcj04h9mYaVyJuoc3TIZNLsbZW\n4O7pgK+fkg0bfiMtMwqjQYcaW4JphlqwQ4ESTZ6m1OdcO3+TKV0/wkqtZP726Y8057mjsxNpmdko\nPDwQ9EbsjqZgezgJZV4L9q04TIvuTRg++0WadmmIq8/9lOst/tsiiiKxVxII336GI5vD+WXmb/wy\n8zdC2gbRe/QzhA1sjUz+3/TXfhxv9aYoij88huc+0ew5tZ4CTT6teRqVoCZfzOMCx5Aiw1OsSSqJ\n+HvVu3dHZVAZFca8Qhog5BeQc+QYtq1bIggCurh48o6doN7MuQ88NguPDMtcLoewAa0RBJj/0pdM\n6jyLjzZPxcWr/ORAUqmEeiHe1Asp23rUaDS4OLrgZwgmCHOe/ltc5zQHaSM+Q5I0lm7dSp5ph+88\ny5yBn2Ntp2Lhvg9xr/lot5vHjxnLxI/m4nFdgdORdKQaA3k2ehyaW7Fq94+o7Uo/IrhfBEGgZj0f\natbz4fkJvUlLSOfPVYfZsnQ3C4YuZtn7qxg8vT9dh4X954Tc4oX+hHD26jFCaI5KMK+4VYKaujTl\nBpGcEPYSGtQeJ9sHn9CVUWFMIpXSc/IMDIePkzj3E5I/X0za0p8IGzEKR2/fB+7XgoXHRYfnW/Ph\nhsnERd5ibOgULh6+8tB9rlu3DrXBHh8hAIkgQSJI8BECUGPHKfaTY5/CvI/nFbU3Goz839zfmdFz\nHu61XPnyyFx86ng+9DjKQxRF/NV1aZ3dEtddyeSZMrmgDsemvYFfd39faeJdGi7ezgyY2Iefr3zJ\n7M1TsXOx4/PXvuX1RhM5vu10uVko/208juXIfEEQFgCRwHRRFP96DGN44igwaLH5R35zG+wpREeI\nfxs6N+v70M+ojEQtjt4+vPDJl6TfvEFhQT5uAXWQ/oeKD/zHsMzlCtCyR1MWH53Hh/0W8u5TMxk4\n6VmGvN8fperB5ktsbCx2lPRWt8GeBMk1Ii/FFVUpi72SwKevfM3lY1d56oU2jF86Gmvb+69lcD9k\nJGXy5Rvfc2RTOLWb+DFoZl9E+0J8fX3x9/d/pM++G4lEQqtezWjZsylHNoXz/ZRfmdFrPm37Nmfc\nktdw8ijb4//fQlVb4FMAf8AbWAr8IQhCwN0NBEF4XRCEk4IgnNTqSj/HsXD/eDj4klpUUdhMGonI\nUNC5ybOPaVSlIwgCLrX88KwbbBHv6ss95zIUn8+pqalVPcZqg1/9Gnx9YgFdh4axesEGRjWexOGN\nJx7IGmzZsiU5VunF7hVFkTRu8fzz/fHw8CA3U8M345fxesN3iY+8xbSV7zBt5TuPXLzP/nmRUY0m\nEr7jLK8vHMZXJ+bToU8bwsLCqlS870YQBNr2bcH3Fz7jtY+HcGL7WUbWn1CsBOy/lcfqhS4Iwg5g\nqyiK/yvtc4sXeuVxLfEKa//8Hj9jXRxwJYtUornI0y36Exp07xKj5XG7TKiNjdKSbe0x8bi90O81\nl+HJ8kIvj9N7zvPVWz8SF3mLeq3q0P+dXrTp2xy5omKLVZPJRLvW7bl+Jg6fQvOa6TqXsfZUcGDP\nIbZ+t4cdP+1Dp9XT/dVODJ/9Io7uDo/ylRBFkfVfbGXp5BX4BHrywdp3qRlcPY+9Yq8ksGDoYq6e\nusYLk59lxJxB1S6e/F8RRiYIwnZguyiKi0v73CLglUtc6jUOnt1BavYtnO3cCWvcA1+3EkbTfXE7\nz7klVerjpRoIeLlzGSwCfjdGg5Fdv/zFyrm/k3QjFbW9NV2GdKDDgNYEtw68p7OVVqtl4cKF/Lrs\n/5Dq5XRo2Al5hpqo8BhzTe9BbRk4sQ9+VVC+VxRFvpu4nN8XbaFdv5ZM+nnsQ1n6oiiSk51PQnwG\n6am5aLV6CgsNyOUyVCoFLq62uHva4+Rs88Dx6/oCPUve/pmt3++hefcmvL9mwj1D/aqSaifggiA4\nAC2B/ZhDT17AvPXWVBTFyNLusQh49ebfIt6iyUTEnp1c+nM3ujwN3iENad5vILaubo97aJVGVQr4\ng8xlsAh4aRiNRk7tOs/u5X9xZFM4+oJCrKyVBLWoTY16PngFuGPvYofK1iwuhToD2ak5pManE3s5\nnugz14tiqWvV96Xr0DA6vdT+nt7ulcXd4t33ze688cXwByrbmZWZx5EDkZwKv07EhXjSUnPveU+h\nUYuRHNq1r8vYtwfh43s/oWhmti7dzeIx3xMYGsCcLe9h71I9wlWro4C7AtuAuoARuAK8L4ri7rLu\nsQh49eXfIt4Ah5b/xPXL57Hr2Q2pvT3ak6fJDz/NgHmfYe3waLcWq4oqFvD7nstgEfB7oc3N5+TO\ns1w4eJkrx68SH5WIJiuv1LYyuRSfQC8CGtciuHUQzbs1xtPfvdS2j5JV8zfw0/SV9H2zO2O+HHFf\nFrEoipw6cY2Na8MJPxaDySTi5m5H/Ua+BNb1wsvHEVc3O9Q2SuRyGQaDkajIGIa+PArrwMbY2Hqj\nygSlznz0UDfYi2d6NaJLt4ZYWVXcd+bIpnDmDlqEV4AHn/01CzvnsjPnVRXVTsAfBIuAVx2iKJKd\nl4FcqkCtKv8P+N8k3tqsLFa9OxavGVORqu+ErmSsWY+/uw8tBvw3Sig+7i30imAR8PsnN1NDboYG\nbU4+CCBXyrF3scXO2bZcSzcnJ4fU1FRq1KiB/BE5gp7cdY5p3efy1IttmLpi3H1Z3udO3+C7/+3h\namQSjk5quvVqTFjnYPxru5W7CHht9Gg23LiG3V3pWYX4LCTrjtCh1fPE3kjHwcGafi+2pO+A5qhU\nigqN5+yfF5nWYx4BjWryyZ4PUNk8Wme/e1EtM7FZqJ7cTL7K5pOrydNrMBkMeLv68VyLIdhZl7RO\n/23lQTNib2Dl41NMvAGU9YJIDj/7mEZlwULFsHW0wdbR5t4N/0an0/HGW2+xetUq5GprJEYT8+fM\nYfSohy8NfDdpCeksGPIlNUN8mPD9GxUW7+wsLYs/3c6BfZdxdbfj3Wm96PR0fRSKiknR0RMnULRv\nU+ya6ONAhniNMe+2QClzZeUvh/np2z/5Y/1JRo97mvYd695zZ6Bxx/rMWD2eWf0XMnvg58zePLXa\nObaVhkXAn3CyNOmsOrgUh5cG4lU/GNFgIGfXPlb8tYQx3d8r8Yef7CT514g3gI2rK7qkJESjEUF6\nZ0IW3krEye3hthx12jzObdnItVPhSOUy6rZ7ipCu3ZFIq//Et/DfZMy4cWwKP4HrtElI1Wr0txKZ\nPHMmXp6e9OnTp9Kes+Sdn8nXFLBo7btYWVcsnv3iuVjmfrCB7CwtL78WxoDBrVAq7293wN/Pj6Rb\nt7AK8Cu6ZiooID89HR8fH9zd3Zn3eQ0unovlf5/vZPaM3+nYNYS3J/dArS5/nFp1NvqgPMJ3nOXZ\nxoP4+LeZhIRU7xrplkxsTzinY45gHdoUdYMQBEFAIpdj3+Np8qUGYlOiH/fwHhoHT2/c/GuTsXY9\nRq0WURTRXrqM5uBhGnTt/sD9GgsL2TT7faLjrmPdrzeKZzpz7sh+9i75shJHb8FCxcnNzWXVypXY\nDHgOqdqccVHh5Ymq+9PM+/TTSnvOie1nOPj7cV6a8XyFC4bs3XmBSW/9ikIp48ulwxkyov19izfA\n1HffpWDffvKjzdXMjBoNuWvX06tXL9zd7yzI6zeqwZIfX2X460+xf28EY0b8UG7d9VWrV/PcoBe5\n2MSOrAZqdBEi3Vo9y/nz5+97jFWJRcCfcLLys5B6FbdEBUFA7uFBjrZ4YZFLqRqyfCq/7OCjputb\nE3CVWpEwax7x0z8kf+tOnn5zAk6+NR64z5hjh9Er5TgPeRErv1qoggJxGfUq8RHnSY+9WXmDt2Ch\ngmRkZCCzskJqU3zLXe7pTnx8fKU8w2QysXTScnyDvBgwsXeF7tmx5SwLZm0ipKEvX//4KnWC7i+N\nq8kkklegp0BvoGWrViz//nskm7eR/MFsUuYt5Nkmzfjlxx9L3CeVSXhpeDs++3oougID499YzsVz\nsaW+04TJk7EdMgjbFqFkDA1G52lNgKEx7703877GWtVYttCfcGo41eTm+fPQplXRNZNOhzY6Gq+u\ndzK03V2s5N+yfX4bpbWaLmPfobAgn8ICHSp7+4euf5wUHYUyuF6xfiRyOaqgIFKio3Cu8ejjby1Y\nuBtvb2/kEgm6+ASUPncs44KLl+nYqmWlPOPwxnBuRsTz3v+9XaHEM8cOX2XRgq00a+HPRx8PRKG8\nt+TcTM5k//kYzkQnEBWfRmq2BoPRBIBUIuDpZEe/iYsI8nSgfaPaNAzwKXc+129Ug8XfD2fq2yuZ\n+s5KZn08kGYt7mSFS0tLIzs7G/da5jkrKqSkvBSAz+cXSPwz/Z7jfZxYBPwJp6FfS47u3E/GqrWo\n27bClJ9P7rbd1PVuiLOd2TKvjEpjlYnRUEj8+bPoNBo8g+tj61KxIixyKxVyq8rxLrVxcuZWbMkj\nhsLkFNRO9x+PasHCwyKTyVgwdy7vTp9OYfeuKDw8KIi4gv7QET46fLhSnrHus8141fYgbGDre7aN\nj8tg3swNBNRxZ+a858sU7+joaA4fPkyOYMP5NCOnriYA4OvqQCN/TzycbLFXqxBFEU2BnoS0bK4m\npHL40g1+2nOWur5uvPBUY3q0rIu8DP8TN3d7PlsyjKnjV/Lh1LUs+uZlageZDRE7OzsEUcSYk4PM\n3h4AvY+a1IZK3M66c27/JRqFVc+zcIuAP+Eo5EpGdp3AwYhdXFm2BoVMSYeaLWlWp31Rm8qoNHYv\nUq/FcOXAPnRaLbUaNcWvZWukspJ/nuk3r7P1k7lInBzMMd3Lf6R+1+60GDj4oa3q+yGoQ0fOTdlE\nXlAg1o0agNFIzv6DSHU6fBo2qrJxWLBwN6+NHIm3lxdzFy4k7tAxOrdsyawjR6hbt+5D9x0XmUDE\n0SheXzgMaTmOmhqNhp9/XsbW32+BScWIN1qgsi4ZzmUymXh9zBjWbd2FV/t+WNl7Y8zPYWjXFgzt\n0Q53x/LDWVOzNPx5Loa1+88xa8Uuftl9knf7d6Btfb9S2zs6qZn/+SDefPVHPpi6hq9+eAUnZxus\nrKwYMWIEq9ZtxOaF/khtbNAnp3Az+QB+Tk/xw5RfWXx0XpX+vlQUSxy4hXK5nef8UYr3pT07Ob52\nJTbt2iCxUZMffhoHW3t6TJpeTMRFk4mVE8aieroTNqFNATBq8khZvISOL79GjSbNACjIzeHW5UvI\nlVZ4hTQodSFQGSRFXeGv75egzclGNBhwruVH59HjHkuGN0scuIVHzbL3V7NqwQZWxX1bZiWvjIwM\nQlu3QmnXCB95I24oL5F0dgcb162jc+fOxdouX76cqV/9jHtobxCgwEUk/dJhPK7f5PypU4A5P8Wx\nY8eIj48nNDQUP7+S4iyKIgfOX2PR+gPEpmTRt019pr7YEUUZ6WijI5N4Z/Qy6tX34eMvX0IiEdDr\n9bz5zjv8umIFchs16PR8MGMGIY5N+OzVJXywbiLt+1XOMURFsMSBW3hoqkK8dXl5HFu1HI8J45C7\nugBg26oFKV9/x7Vjh6nTLqyobUrMVYwSAXWzJkXXpDZq1E+15/LBP/Ft3JQjK34mYt8uVH61QKfH\nlJVNt3en4hZQp9LH7hFYlxc++RJNWioSmQy1Y9Wkr7Rg4XFwYvtpQtoElVuGc96CBeS6eFBL0Qit\ngwTjU81Q17Vh+GuvERsTU8yK/WrdTtyb9saogDxfEVEO6natufbnfqKjoykoKOCZXj3Jyi/A2seb\nvOgYXhg4kB+/+65Y3LkgCIQ1CqBNSC2+23qMn3ac4FpSOp+P6oNTKXXHawd58MbbT/PFJ9vY8ccZ\nejzbFIVCwdIlS/h0wQJSUlLw9fVFqVRiNBpZOfd31n22uUoFvKJYvNAtlEpViDdA4pUIrGrWKBJv\nAEEqxbpFKNfOFLfWDHo9EiurEltZEislhQX5rJ/5HhF/7cFrygTc3ngNt3fGYvtcb7Z/Nh+jwfBQ\n4zQaDJzasJZf3x7Fz68NY+fiT8lOSkQQBGxd3SzibeE/TU56LtFnbtC0S8Ny223cugVPnzZIdZDR\nUA6CgKpuEFm5OVy7dq2o3eFLNyj0aope0KKpaRZvAEEiQWZlxa5du2jSsiV5tQNwmzYJ25dfwm36\nZDbu/4ulS5eW+my5TMqbz7bl45E9iYpL5fUv1pKdV1BqW3cfEyZpFgvnrad23UYsWbIEURSxs7Oj\ndu3aKJXmmHGpVEq/t3sScTSKiGNRD/DNPVosAm6hBLdTpdrYVCxBw8Mgt7LClKctcd2k1aKwKl4d\nyL1OIIWpaejiE4quiSYT2qMnkMvkZKUlYxfWHrnzHScydaMGSJ0cSbh4rlhfmQnxHFr+I9sXfczZ\nLRvR5ZWec/o2f32/hMvnT2E/bDDuk98h29mOjbOmo83KfJDXtmDhX8XlY1GIokjDsOBy29nY2OCY\nZIXWXYLO+W95MRox6vSo/45Nz8jRMvOXnTgoIPnUZkTJnWPc/MirKICJU6ZgNBTi0P3pogW7xMoK\nZeeOfP3DD8WeqdfrWbZsGb3792fYKyOwLkjly7F9iUvNZtLSLRQajcXaX7x4kY5du3LFLRGpTIld\n3R5M/3QhH8yaVeo7PTPiKayslexa9td9fGNVg0XALRSjqvOce9YNBm0+mtN30poaMrPQHDhMvQ6d\nirWVKZR0eGUUqd/+QObmrWTvP0jK4iXYKVVkJCVi0umQ2paSdlKppDD/zko87twZNsyaxi1jAfl1\nA7h85QLrpk8kPzur5L1AbmoKN06dwOWVYSh9fZDZ2+PQtTPKkHpc2rPzod7fZDRSWJBPdfZFsWAh\nMjwGiUSgTtPSHcRu83yPYSgKZWT7msO+RFEkd8+fhDZvjoeH+fdk3qq9aPJ1fDluAN4mEzlLfyLn\n4GFyNv6BZuVvjHntNQRrawSZDOEf/itStTWa3DuVyvR6PR27duXdTz7mmErOtsx0uj/3HAe2ruX9\nIV04GRXHVxuLe+DPnj8fZVg7lGFNya0lwzFdjcMLL/H5okXklbKQV9moaNO3OQfWHkFfoC/3/fPy\n8igsLCy3TWViEXALRTyOIiUSqZTuE6ai2bKdlC++Iu2HZSR+/BlNe/bFI6heifYBrdvSb9Z8ato4\n4pqdT9tnB9BrygcYdToEhRLNiXDEu1bchoxMtNExeIU0AMwW+/6fl+I8ZBAOPbth06wJzsMGIw0M\n4PTmDaWOMSPuJqqaNZEoi+9IKOsEkHrz+gO9t9Fg4NiqFSx7/WWWjRrO6knjuHk6/IH6smDhUXMj\nIg7PAI97FvlwtK2NIJi4sXwReStWkfXZYlzjb7F6xQoAouJT2Xc2mpHdW9Kwdg1OHD7Ml+9No6e9\nI6PbdeDCmTM0bNiQQr0eQWlFfsTlYv3nHDpKWNu2Rf9fvXo1l1OSsXv9FWxbNMeuYxgOY17n/Q8/\npHVtd/q3b8D/7T1NdEJa0T2nz51FWTsAgMxgGRIjOGbYoLS348aNG6W+V6fB7cnNzOPcX5dK/fz4\n8eM0bt4cBycnbB0cGPbKCHJz710S9WGxOLFZAB6teJstTFCoSp/8Ln7+vPTFt9yKuEhhvhbPN0NQ\n2dmX2Z+DpzetXhxa7Jp33WCuRV1GamtL4pdfY9OyOSatlpz9h7D38ERlZ67zm5uWSqGuAKug4k5t\n6hahxP62nraMKPE8O3dPChISSuRT18fF4e7hVeHv4W4O//ozsTev4T7xbWROjuRHRrHvu6/oPmFq\nqQsXCxYeJ0nXU/D0d8NoNJKVlYW9vT2yUqI7zp+NpUloAN/9epLw8HC8vb1p06ZN0Tb4qj/PYKWQ\nMTDMHGqpVCoZMmQIQ4YMKerDyckJk16PXeenyD1+CqmtHXJXV0STCcce3civWYvVF8/Tv14IG7du\nRdq4IcJdTm0yJ0ds/f04ePAgbz7bjd2noli0/gBfv9UPgKA6gRyPjUNZwxeDrYR8Nwm2MYUUZGXj\n7V16atjGHUNQqhSc2HaG5t2aFPvs+vXrdOnWDVXvHvgMHoApP5+tW7YT//zz7Nv5cDt098JigVso\nSpFa2eKtSU9j68K5LBs1nF9GD2fTnA/IupVQalupTIZvw8b4t2xTrniXReshIzBlZmLXuSN2HTug\nu3ETQ2YWMhsbmvS8k1FObmWFUadDLCzu1GbM1ZS5wHD09sHdvzbpq9ZizMlFNBrRhJ9Ce+IU9bt2\nu++x6rR5XD3wJ85DByF3dkIQBKzrBmHb/WnObN103/1ZsPCoSYtPJzUnBXdvb3xq1cLFw4P5H39c\n7OgnP1/PtegU6jf0xc/Pj4EDB9K2bdsi8S40GNl5MpLuzetip7Yq61HY2dnxQr9+KLy9cR8xDLm7\nO/qkZPSJiQi3EokzFDJt7x4G/74WaxcXxFK2vQ0aDfb29tirrRjZvSVHI25y8UYSANMnTyZ/z59o\nIy4jmkxkuuaj0AoM7P8KDg4lKzACKFVKGoYFc2bfhRKffbVkCVahTbEJbYoglSK1scFuQD/CT58i\nIiLivr7n+8Ui4E84t7OsPYx4Z8TFcvN0OLlpqUXXjAYDm+d+QJ67M75zP6TG/I8oDPJn05wP0Ofn\nV9bwi7CytaXLm+NJ+/5ndFHRyF1dKbx+EzcvH2q37VDUTmVnj0fdYLJ37EQ0mc/pjNp8cnbuJvip\nLmX2//S4d/GycyJhzsfcnDwd8cRpekyegd0DVDTTZmQgs7NDaqMudl3p60N2UuJ992fBQmWRl5fH\nzp072b9/P4a7IjdyMnM5dv4UypdfwnPuh9iMepVPvvuWzz7/vKhN0i2zD4lvzdIzEV66mUSB3lBm\nopXbmEQR98EvYl23LnnHjpNz8BC6EyfQrFjJisFDOPzKa3zZrQdX0lK5GFwXw9UYCtPubJFrwk+h\n1BfSoYN53j/btj5KuZQ/jprFtHXr1qz9v//DZv9h4qfMIHG9OY/60089X+646rUMJPZyAvma4r9f\nlyIjEXyK78QJUinWPj7ExMSU2+fDUq230PMNRi6lakr9LMS14jVyLZTOpVTNQ5UH1Wnz2PnFQtLj\nY1F6epJ/8yb+LdsQ9uooYs+cwmRtjUO3rkXt7cLao792g+gjBwnu/HRlvgoAfqEtGfjxF1w9tJ8C\nTS4+Q1/Ft2HjYttrAJ1eH8vmuTOJPzYLuYsL+pQU6oZ1om7HsgVcbqXiqZFv0GHE65iMBmSKB/fQ\nt3F1w6jRUJiRgdzpTvhZQdRVXGqW/+NmwcKj4v9WrmTUmDGovL0wFRQgK9CxZeNGmjVrhlFvQtoo\nAKW3WagU7m6IA/qx4NNPeXfCBARBIDkpGwAPr9Kt2HMx5sVpk9rlVzBbffECG6MiGRvagoCa/vx5\n4ADe7T0Z9vvQIke43kF1CXZ1Y/Dvawl4/TUuTn8fpbMTUokEa0HCjq1bi7LF2aqUdGgYwJ7TUUx9\nsSOCINC9e3eiu3dHq9WiVCoZNex7Lp6PK3dcdZr5I4oiMeduUr/tncx2LZs149Te3dCkcdE1k05H\n7rXrNGjQoNw+H5ZqLeB6VyNxo0sJ0xEhea2ETtKSQfoW7g9NLRktH9DyPrjse/JsVXi9PxVBKsVU\nUED898u4sH0rAiJyn5LnwzJvL3JSyi7r97DYurjStG/ZK+nCgnx2f7UInV6HdYP66G7cxNbNjWbP\nDaxQqkSJVPrQ9b7lSiWNej7LpR9/wb5vb+TubmjPXyR33346fzDnofq2YOFBiIyMZNTYsTiMHonC\ny1wtLO/cBbr17En8TXN1PenffiS3UXh5kpiSgsFgQC6Xk681e2hbl1EfPDVbg7VSjuM9HOG2RkUS\n6OzMhDbm7fe+ffuW2i7AyYkuSitWafNw6toFXXw82shIFiz6ooRwNg/0YfepKG6l5+DtcueIztra\nrCG163hwoZRKZXfjE2j+XhKvJRcT8DGjR/P1N9+QvWsP6uahGHNzyd+xm2ef7UOtWrXK7fNhqdYC\n7qPKZn6DbSWuFxqNbPGsz77FoRYRf0wY9DpunDiG94fTixy7JFZW2Pd8hojfN9Fh+Ovo9pq3qW9b\nwKIooo+6imv30idkVRC+bjV5VnI83puIIJEgiiKZGzZzaMWPdB07vsrG0bTv86js7Dm/aSsZmZm4\n1q5D2Hsf4uT7csKJegAAIABJREFU+IvFWHjy+PmXZVg1b1ok3mDOoZB7PJydO3ciCiLGlHTgzg5R\nQVQ0NWsHIJebs7AU/u1XIpeXvsDN0uTjcA/xLjAUEn4rgVeaNL3ngjolJYUv3n4HtxnvoeoUhkoA\ndWoaEyZNokunTgQEBBS1Da5pNlIuxyYXE/Db+NZyYe+ui+Tn61GpSuZtB3CrYU42lXwjtdh1d3d3\nThw5wuRp09i9eAk2dnZMGDmSqVOmlDv+yqBaC7hSqiLQtqzMP2dgHPwa3qSMz4tjHSejX2LlVKL6\nL1BUYewB7zfo9SAISP6RbEVqZ4teq8UruD52js6kL1+JXddOIJWSu/8gcl0htZq3ePgXqCBGQyGx\nZ06jzcrEIzCIqMMHcB07qmhRIQgC9s905caHczCNNj60dV1RBEEguPPTj+QowYKF+yU9IxNRrS5x\nXWJrQ1ZWFmo7FcmR0WhOSrCqHYDuxk20f2zjf998U9RWqTQLeUFB6XHQCpmMQoOx1M9uIyBgMJmw\nLeOI6urVq+zduxdHR0dSUlJQ1w1EkN2Zs3JXF1RNGrF69WqmT59edN3d0XzkmpFbuv+Nk7P53XOz\n88sUcIWVAmtbFbkZJY91/f39Wbd6dbnv9iio1gJeHo5KNb2dL9K728V7thVF2JJhsdhvc/vs+2Eq\njCnVNti6e6A9fxF14zuLLM2Jk/g2aIQgCPScNJ1TG9cSvexXTEYT/s1bEvr+GKSye9cRrgyybiXw\nx/xZCI72SF2cObZuFcb8fPhH+IsglyGaTIiiCagaAbdgoTrRq3t3fh8/HrFDu6IdNaNGQ27EFTp1\n6sRh3/P42HtyJvYEl7fvIqBOHT765Rd69OhR1IetvdlAyskpXSTtbazIzitAFMUyrWulTIaNQkGa\ntrhnuSiKvDNxIj/89BPqkGBMWVloomNQNSp5xizK5RTodMWuWVuZRVlbRiIW9d9e8Xl5ulI/L+rH\nTkVedsnMkY+Lf62Ae6kC8bovg9pssa9f37zCd/xXLfZkJ8lD5zkXBIEOw19j++cL0McloPDxouBK\nFIVR0TT/cB5gDtlq9eLQEjHbFcWg1xOxZwdRxw6j02iQKxR4BNWjwdPdcfT2vef9u79ehOqpdihr\n+JL66yqQy5EgcuvzL3EfOQKrWub3zz18DM+QBlW2sLBgobrRq1cvQr/7jpPf/oC0eVPEAh2FR47x\nzrhx1KhRA/earqTGpXPk7F9l9uHmbt6aTkzIpFGTkr8tJm02eoORgCYtELXZ1KhRgxFDhjB48GAU\nijtWbwM3d3bFRDOlXXus/p6T27Zt45c1v+E88W2yd+1Fc+06UidHss+ew65PbyRqawRBwKjVUnj2\nPH3nf1zs2fpCs+Uvlz3cAl0qk2L6O3qlOvCvFfD7JcShCXCGXiPvbbEDiIhM+uGV/5yIV2aREs+6\nwfT/6GMu7t5B9qUofGv5EzLijQeK4/4nJpORbQvnkmPUY9O5AzKjiaw9+4i5dI7oo4fo+uYEfBs2\nLvP+nOQkctNS8WzWhPi5n+Ay4DmsG5l3CrQXLpG0ZCn2XTpiSkpBf+06Xd+f/dBjtmDh34pUKmXb\n5s2sXr2a39avx1plzchfltO1qzmKpEZdb07vuYDRaCyzFrinlwNKpYwbMaklPtuzZw+zp0+gVvc3\noEMXsmLOEPvnAc7ERPPTihXs3bGj6Cz9rZatGPz7Wr46cZyJbdoB8OPy5chatyT3yHH0iUn4vP8e\nUrU1xgIdUqUVWTt3IQCFp88wYugQmjVrVuz5KVnmbW83h9Kjl7Ras+VdWt3yuzEajEil1Sf6+okR\ncLgt4hUjIvsMC0f+xKQfXsEhvvw81f+WbflHUWHM3sOTtkNLZi/7JzkpyRz77Vfiz55BprKiboeO\nNHtuIFJ56VZv3NkzZGVn4D5hXNF5tVVQHRLmfYLd05058PNSBn/+dZlbcSajEYlMRt65C1j5+6Fu\n3KjoM3XD+mjrBqG6Fodfi1YEvjEBZSnnfxYsPEnIZLISWdFu49ewJoW6Qm5eisevQQ2++eYbPvli\nESmJSTQNDeXT+fNp1aoVAXU8uHShZDjWm+PHI+/aFpNURK10hWe6IlWr0UZc5mJcHOvXr+eFF14A\noJWPL/3rBbMk/ARKqYwxzVug0+kQbFTk7tqDxxuvI1VbgwhSpRLRYCD/6HFGv/IKA2Z8QJs2bUo8\n/2qCeVHh61Z6iFtmhnnL3t6+/N/ygjwdyjK87B8HT5SA3w/B9k24lHWGTs+fLLedySSyfn3zam+p\nF6VKrYIKY/+kIDeHDR9OQ9W6OR5T38Wk1XJ1y3YyvvqcbuNL99RMiryMsn5wsRhuiVyOdUgwotGI\nTpuHJj0NWxfXUu+39/RCrlBSEH0NuUvJUp8yVxe8Hdxo0K1X5bxkKYiiiDYzA6lCgZWN7SN7jgUL\nj5qQNkGAuSrZr5tX8PmPP2DdpxeuHu5EXrhIl+7dObhvH6Et/Vnx0wGyMvNwcDQvigsKCoi+cgXf\nV4ehTwNlOgiFoG7ckMwt27Hu1Z3N27cVCTjAvM5dKTSZWHTsCNujowju3Yvj336LaDQhc3GBu2wq\nERP63FwWffZZmeM/fjkWe7UVgd6l/17E3kjD1c22XAs8KzMbTVYedi7VZy5bBLwcQhya4KgsvwZs\nlj6PniMvVGtL/XEUKbmbiH27UdQJwOGZv5O62NvhMmIoCbPmkRkfh6PPnfNsvVZLZkKcuUpXUsl4\n8cK0NBQ+3pgKC5FblZ2OURAEOo16k22fzKFAqcCxZ/eiykaiwUDemXN4jB5XuS96F4lXItj/03fk\nZWYgGo141guh42tjsS4jVaMFC9UZT393HNzsObPvAp/s+BTHt8cidzYvjG1btUAs0DFr3jw+mb2Y\n5T8e4MiBSLr3acKVK1fIzs5GqlBgyMxE7+CMMl1AmSGQr01DamcLGg1OXsV9WuRSKYue6c7TAbWZ\nf/AAG/NysRsymOKR6Obf27wz5whuVHad8nx9IQcvXKNVvZpIJKXv2EVHJlHTr3Rx1+l0jH37bX5f\nsZ5Qwpj7+VyMNfIYMeLeO4+PGouA3wMvVeA9Pr+93f4zH17uU2Y70SSy/qhQ5Zb64xZvgLS4myjq\n+Be7JshkqPz9yIiLLRLw05t+58zm9ShcXclPTgZE8i5cxLp+CIgimpOn0N9KQu7igndIg3tatZ51\ng3nh0/+xetI4Ev/3DfadO4IgkPPXAUx6PXmZGY/kfXNTU9j+2XwcX3gexwYhiIWFZO/cw9aFc3h+\nzsIKJYyxYKE6IQgCzbs15simE8hU1kXifRurOgGc3fAHdYI8qOXnyoa1x5n84avEJiQgyGUUGo2k\nr/kd15eHoLdXo8yAvIOHsG7YgIJj4by2YGGpz+xRJ5DOfv5cSUvlano63/2yjCO792BV2x+Fpwe6\nazfI3vcXUifHMr3bNxy6QFZeQVEBlX+SnpbLjeupdO5Weta0MePGsfHEcTyfHwYrbmLs2Za3p0zB\n09OTbt3uvxZCZWIR8Eog2L4JUbnnmVd/a5ltDCYjphCzY1zQ+dJjISs7PWx1EG8ARw8vMm7GQ4s7\nEQCiyYQuNg57D3PiiJhjh7nw5248J41HamfLzanv4zZyBOnr1pO+dj2iwQCCgGg0YZWawVPjp1bo\n2fq8PKRKJTYtQsk5dAREEXXTxghKJZGHDxDY/qlKf9+IfbtRhzZD3bA+AIJCgUOv7iQt+JTkq5F4\nBNa9Rw8WLFQ/WvZsxu7l+1HpFBhycpDdlZlNFxtHSFAggiDQrXcjvl28h1yfYJxfHkzm9p3YFhoQ\n9XriZs1D4ehM4DOj8Qzpyo1t3/LN4i9p2LBsC1opk9HIw5NGHp78cDkShY8nhQm3yDt9FoW7Gx5v\nj0X76ypOnz5dwnktU5PPTzvCaVrHu8wUrieORgPQrEXJNMY5OTmsWrkS12mTsDpizvVOw5pYyboy\nd+FCi4D/Vyg74cwdbjvGzYwoxVIXIfKotNIs9EupGrIeskhJZRHc6WkuvjeeHG9PbFuEYsrPJ2vL\ndhw9vXHxM1vm53dvx65nN2ROjpj0hSCKWAX44TN9CoVJyRi1eeiTU8ndupPnZs6r8LONhkIkSiV2\nbVtj17Z10XXtpQgMhaXHhD4sOWkpyHyLf+eCIKDw9ESTnlbGXRYsVG9a9myKtZ2Ktl5h7Fu5BnW/\nZ5G5OJN/OZL8nXt4f/NmAGyd8ig05uMjCyFRIgGjEYlSiWPf3jj27EZhegbZmnScrWrQe+xHDB8+\nvMJjyC8oQOHrhbpr8boFOoWSgoKCYtdEUWTeyj3kaAuYPLBjmX1u33yWGrVcqB1Y8ncyJSUFuVqN\nVK1GFROL3kOFyVqGwsuT2KMnKjzuR0X18Yd/Agi2b4JCKmN+g20l/s2u/wcLR/7Ees+Hr9RVGRXG\nKhO1kxN9pn2I7GIkNydPJ2H2Ajys7eg+4Y4VXZCTjezvbTmJQo5V7QByDx/9W/g8UAUEYExKJqBV\nSQ/T8nCuUQtBX0j+1eiia6LJRN7hYwQ0ezQZ4TwCAtFdjix2zaTTkR8dg6tfQBl3WbBQvbGyVtJp\nUDvybxTyWo/nyF6ylLhJ07A9dIQ1v/5Ku3bmkK/s7AxSxatYJ5tQJRqxblAfzYlwjNp8pGo1VjV8\nMblbk3puLzHZIvNW7cVYwdjqQf37YzhxsqiSIEDB9RsYc3Jo3vyuHT5RZOnWY+w9E82Y3m0I9Cn9\nfPtqZCKXLyXQvXfjUrffa9SogWAwUBiXiNW1XPJrm3cdCiKu0Lpl1WWULAuLBV7FlGep37bQx+4c\nVurnFUkHW93E+zbONf3oO+MjjIWFCFIJEknxWFLvevVJPH0WpY95m8u5f18SFy8hP/IqVrX9KYyK\nQZKTS4uZc4vdZzIZidizkyuH9mMsLMS/WQsa9eiD4u8iBRKplI6vj2X3V59j3bQxUicnCs5fwEah\nIrjLM4/kXYPCOnFh11Yy1m1A3bolJq2WnB27qdW0edGRgQUL/0b6jO3Glu9208C+KVlpaej1eqz+\n4Uzapk0bbkS+jkuLBriGF5LfrQbWDRuYQ0DbtEQwGNGdPsPcWR8h8W3CzzvDScnS8NHL3Yi/EcNH\n8+YRfvoUtQMCmD5pMmFhYUV9jxgxgpVr1nDx6+8QQuoh5ORScPosq1asKEoGYzKJ/G/TIX7ZdZLe\nrYMZ1jW0zPdZtnQ/trZWdOtVek4JhULBvNmz+XjaV0j0wWR7Qc7eP9EfOsLMw4cr4Rt9OIS7C7I/\n8ocJghPwI/A0kAa8J4riyrLaN2zsLG7b3bOqhlctiMg+U+ZnJrH85DLVVbwrgiY9jd/fn4JVwxCs\nQoIpTE4mZ/c+/Js2R6FW41LTD/+WbZApiod57FnyBYm34rHt2hGJUonm0FHkGVn0m7WgWIx5bloq\nkfv3oc3JxrteCLVCWyKVPbr1a352Fqc2/c7Ns6eRW1lRr0NHQp7uXmLhUll8N+i5U6Iolv1LVcnc\n71wGCA0NFU+eLD8s00L1Z1rPeVw9GcPya1+jUpceCTJp6lRWrttDPbdnyXTUcCNpNw6aPPr27o21\ntTWDBw2iXr16AKzZf45P1/6FnUrOxW3LMNR2QxkUiD4unoLde1n23VL69+9f1LfBYOCPP/5gx+7d\nuLu6MmL4cPz8zOfXyZm5zF25l0MXrzOgQyOmvNCxTM/z8GMxTJuwitfGdmbgS61LbXOb0e3e5eqJ\n61zxPE2rVi2ZPXMmwcHBD/L1VQhBECo0n6tawFdh3rZ/FWgMbAXaiKJ4qbT2T6KAl0dE9pkiEf8n\nDvEiWT7CQ+U3f9zkZWRwfscfJF6NxMbJmYbP9CzX4SsjLpaNcz/Aa8ZUJAqzWIuiSNqS72nepXul\nOKhlJsRzevN6Uq7HYOviSpMeffCuf29/h6rmMQj4fc1lsAj4f4VLRyJ5p90Mhs0cyNCZA0ptI4oi\nGzdu5OvFOxB0vtRrLGPeJ29iY1O6o27EzSRenv0DRrkag0qkwEXEoIb86GhkW3cSGxNTbvRGWnYe\nq/48w29/ncVkEhnXrz0vhDUqdo/RaOTb775j6bJl6AuM+Dn1xc3diaXLR6FQlr2Yz0zOYnCN0fR+\n4xnGfFE1oWMVFfAq20IXBEEN9Afqi6KoAQ4JgrAZGApUzKX4CSfYvgkR2Wf4dOTPxa6LwIeX+yA7\n7vavFW8wn5W3HvxyhdunREdhHRRYJN7wt7NYSD0Sr0Y+tIBnxMWyafYM1B3aYfNCP3S3Etn19SLa\nD32F2m3aP1Tf/2Ysc/nJJqRNEB0GtGbNwk10e7UTrj7OJdoIgsBzzz1Hnz7PMnPKGsKPxXD+zC3a\ntC89LDe4pgcxW7/GZegYrPPV2MRJMMlEVDa1SVWd4cLVm9Sp6Y1KKUcURTT5Om6mZHElNpmDF69z\n7HIsBqORLk3q8Fbfdvi4lsy3MGTEcHYcP4GyYwdqxrqjyzRxJmoNJvFVypPCrUv3YCg00mfMozly\nexiq8gw8EDCKonh3ZpRzQFgZ7S2UQrB9yXSwUbnnmVVvM7OlfSH33yvg94u1oxOFKSXzLhtTUrH1\nKRkScr+Er/8Nm85PYd/R/Ceq9PVB7ubK0f9bQUCrtsWyxD1hWObyE87IBS9xfMspFo/9no82TinT\nOpZKJUz/qB8T31zBnBm/M2NO/zJF3N3NjSxNPIbAQOQaEUW2gDwbfDq8wPBFGwCQSSUYjMUd3jyd\n7BjQoSEDwxpRw82x1L4jIiL4Y+tWXKZOxO28gF2WkdSmMhL2p7F27VqGDi294FJupob1X2yhRY8m\n+AR6VfTrqTKq8hfIBsj+x7VsoFg2DkEQXhcE4aQgCCcz0ssv7WbBTKBtQxyVaj4I2shF21OPezhV\nhk+DRkgKdGTv+wvRaEQUzYlftOfOE9Sh00P3nxwdZU4icxfKWjXR5+eTn/PPP+UnigrNZSg+n1NT\nSy62LPw78fRz5+WPXuTYH6f4c9WhctuqrBUs+GIw/rXdmfXeWv7YUPpv1NQJE8jfso3CjHQK7SDH\nUUPc4V9orExk1rCnGde3HUM6N+W1Hi15+7n2fD66DxtnDWfLnFeYOOCpMsUb4NixY1gHBeEaIcE+\nxkhmPRk5QXLEuoH8efBgmfetXrARTZaWEXMGVeyLqWKq0gLXwD8y4Zn/n3v3BVEUlwJLwXwGXjVD\n+/fjpQpEYzjP+4EbmR0F9XOb3fumfzkSqZTe781k7zdfEr/nTyRyOUpra7q/+x5qp5L5z+8Xawcn\nClNSkLu6FF0z5uaC0Vjk5f6EUqG5DMXnc2hoqGU+/4fo904PDqw7yuKxP1CvVSCe/u5ltrW1U7Hw\nf0OY8/56Fi/cTtSVRN4Y1xVr9Z3aDMOGDSMhKZH5CxYgU6vR5eTy0ksv8fUnc4qVG30QXF09qKEL\nwSHSQFYdKRkNzdInSUunVqOmpd5z41IcG77cSpehHajd+OF39B4FVWmBRwEyQRDq3HWtEVCm04uF\n+yPQtiFyqZT3A58cS9zOzZ3nZs7jxU++pN+H8xj06Vd41jV7h149tJ9Vk95i6ZDnWT35bWKO3l/Y\nR+PuvcjetLVom96YpyVzzXrqdOiITFF9KhI9Bixz2QJSqZRpK99GEAQ+7L+QAm35O6YqawUffTKQ\nQcPasnPLWUYNW8qZk9eLPhcEgWlTppJyK5Fje/eRGBfH9998g0KhICkpiYGDB6NSq7G2tWXoiBGk\npVUsKVJ0ZBKbVsfioKhBgs1N0hpJEIG8C5coOHeBV18p6RRsNBr57NUlqGxVvL6w9O316kBVe6Gv\nxuxzNRKz5+o2LF7olU5U7nkKjUZmR/V9Iizx0og6+BdH1vwfji/0R+lXi4KYa2T+9jsdhr5CQKu2\nFe7n7JaNnFy/BkEhx6jNx7lmLXpMmoHK7p8G6OPlMXih39dcBosX+n+VE9vPMKPXfNo+14IZv40v\ns1743Vw8H8fCOZu5FZ9Jm/aBvPJGJ2rWcim1rU6nI6h+CLm1amIT1h5RNKHdux/X9Awunj1b5vOy\nMvNYtfwwG9eFY29vzfBRrZg8cwyRVyIRJRIUMhkL585l7NixJe5d8dFaln+4hvd+HUenwVXvsFpR\nL/Sq9sIZA6iAFGAV8EZ5E97Cg3HbEm/mFvPEWOL/JHzDWhwHDUAVWMdchrRuEI4v9OfkhrX31U/K\n9RgUnp7Yd38Gt1deRmerZusnczAaCh/RyP81WOayBQBadG/CG4uGc2j9cRa/8T0VMQrrN/Rl6YrX\nGTHqKc6eusHIwd8yY+JqThyNxmAoXiti/fr15FlZYd+7B1I7W2T29tg+15sUXQHbt28v0Xd8bDrf\nLt7N0P5fsWHNCbr3aswPK0fj7qXg5vUb2LZvg/OggVg/04WpH3zApk2bit1/ZHM4yz9cQ+ch7ek4\nqN3DfTmPmCrNxCaKYgbQtyqf+aQSaNuQZzkPwJEMd5rJfR7ziKoO0WRCk3gLF//i51ZW/v6k3Eqo\ncD9pN66TcPkSntMnI/k7KYyqXhCp//uW6+HHqd26ek/uR4llLlu4m+fG9SAzOYtV8zcglUl586tX\nkdwjSkOplDP45Xb06NOEPzac4o/1p5j+7mrsHaxp0TqA0JYB1G/ky8WLlzD4FC9EIggC1PAlIiKC\nrl2fIeZqMmfCr3P8SDSXLyUgkQh07BrCoJfbFVn2k2dMR9m1E3bt7qRj1jo78fakSfTp0wdBELh6\n+hofD/0fdZr5M/67UdW+cqAllep/mCIRrwtHrrR5YkRckEiw8fBEd/0mVgF3RFx3/Tp2nhUPBUm5\nGomqblCReIP5h0NZvx5JUVfKFPDspEQi/txNXmYm3nWDqdOuw5N+Zm7hCWDEnEEYDSbWLNyEJjuP\niT+NRaGU3/M+B0c1Q1/pwAtD2hB+NIb9+yI4fiSa3dsvACBXWBOcH4K4X4dJ8begmkTcsusRfgD6\nbP4Ek8ls9dcJ8mDkmE506dYAZ5fiQRHhx0/gMP6tYtdUQYEk/LwCjUZDckwaU5+Zg42jmlkbJqNU\nKdHr9axbt44/tm/HxdmZ1199lQYNSi87+jiwCPh/nP+6iOdlpHPtxFFMBiM1m4Xi4GleqYf2fZ6j\nq1bjNGggSr+aFMRcI+O332l/H4lirB2dMKSklLhuTE7Fxi+o1Htiz55iz9dfoG7ZHJm3K8mH/+TC\n7u30fX/Ok+65buE/jiAIjFzwEraOan6ctpLUuHQ+WDcRRzf7Ct0vlQpkaaIRrK4w4GV/GgS34mpU\nCtdjklmzZguS5GyUVuZMbqZ8LQhSQhr4UcvfFf8Adxo2qYGDo7rM/t08PMhLSUFmf8d/xZCRiUKh\n4OaFBD7ovQArGysW7p2Jq48zOp2Ojl27EpmSjNCoAURd5uewDiz5cjHDyogbr2osAv4EYCOzQvYf\nTDoSdfAvDi77HuuG9RFkck5t/p1G3XvT7LkBBIWZ48BPrv2dxKREbD29aDdo2H1lUPNt3BRW/ETO\nXwewbd8WJBK05y+SfymCwJdHl2hvMhn564dvcB4+BFWd2gDYtGpB+vKVXNi5lWbPlZ520oKF/wqC\nIPDi1Ofw9Hfnk+FfMbrJJKYsf4umncu3WrOzs+nQqRNxWVkI/rUQbiWiys/nyP4D9H2+OQOHNOHN\n8ePZunkzgiDQt18//rdoEW5ubhUe2+Tx45k8dw6yl4cgd3bCqNGQt34TA9sOZnLnj3D1cWLBrvfx\n9DOHw/3yyy9EZqRjN3pkUdImq4YNGPPWWzzfvz/W1WBBbhFwC/9K8nOyObjse9zfHoPCw1y4xf6Z\nLpz/7EtqNG6Kq18AQWGdCArrhCiKD3SWJZXJzHHm3y4mfvc+JDIZVmobuk+chrVDyVSNWQnxiBJJ\nkXiD+QdN3boF13fuswi4hSeGsIFt8K3rzZwXFzH16dn0H9+Llz96ASvr0o+Spn/wAfFWCuzHvVE0\nV3N27mbkG2+wc8sWvL292bDm/9k77/gaz/ePv58zcnKy9xJZIiJWELGJvfcoRVUpSlGlKLVHrVa1\nahVtUXvvvfcmQ4yQvfce55zn98f5Npqf7iLE83698odnXs/tdZ/rvq/7uj/XtuIEuX/Tnz8cMoSE\nxEQWLFqE0sSYooxc2rh1IupIMr7NqjBly1gsbJ9FC3bs24fcr2YJxUUDJ0fUjg5cvnyZFi1a/GMb\nXjSSA39LaGN+F423rsyE0SNu3cDI26vYeQPIzUwx8q/NkyuXStTd/i+JKOYOjnSf8SXZKcloNUWY\n2Tn84fMUKkO0BQWIWi3Cb7a26HLzUBj+ftUmCYmyikd1V76/Pp9V49az4+v9XNh9lY+//QD/9rWe\n60Nbtm3FaPD7JY6bBDTh9NSZ5OfnF5cs/S99WRAEpk6ZwrixYzm16xxbZ+wnPjiR3uM788G8d5Er\nSm5HMzUxQZebV+KYKIpocnL/sCjLq6bsxVUlnsNJ7YWFgTEdLANRWSVwsyi6tE3674gi8DudWRAQ\nefHaBibWNpjbO/7pD4iZnT3m9o5knjlXPFPQ5eWRdeI0Pi9A2lVC4k1DbWzIJyuHsvj0DJQGCr7o\nNJ9Pm07j7tngEtvNfk1Ce44X3JXjniTw9QcrWfreWhBh8akZfLhwwHPOG2DYBx9QdOES2sxnAoM5\n129gqlRQp06dF2vYv0Sagf8DRFHk+NFoDu17ilaro00Hd9p3dPnDerOvE05qL+Ah0yrtYdaDrpD1\nZs/CXWr6cXHjj5glJqG0swVAm51D7rWbVBg3udTsaj3qUw4smE3CrTsobW3JffiYSo2bUrGRVOfj\ndSM2NpYVK5YREnQDL+8afPTRKFxcXErbrDJJjaZVWHV3MUfWnmLjnJ2MbzaDKg0r0WtcZ+p2qEWv\nHj3YcfYCZj27Fg+Sc85fpEnz5sWz7/9CREgUWxfu5dSmCyiUcvpP7UnvzzqjNlH/4T2tW7fmk2HD\nWbRgMabeXmgzMlHm5XPo8OG/3CL3qnilSmz/lNdNiW3qpCtcuxjFxx+YoVDA8p+yqOBtx5JljV/7\n/YK/EpsznryaAAAgAElEQVT3kPTCHGY9ePNV2kLPnOTixh8x9q0BSgW5t+5QtUUb/Hu/W6p2iTod\ncaEh5KalYe9VCVPbv59o82951Ups/4bXSYktJCSEFs0b0rOjkkZ15Vy9qeWXXQUcPXYWX1/f0jav\nTFOQV8CRdafZtmgviZHJWNiZ06CbHz8f+5EoeRo6D1cU8YkoU9O4ePYs7u7/Toc8JS6NS3uvc2LD\nWUIuP8TQSEW7IS3oPaELNk5/v1ZCXFwcZ8+excrKiubNm6NQvPx5799VYpMc+N/kfnAaA/seJeRc\necxM9eGWvDwdvi2jWfBNAP71Xv6P9IuiLDnxrKREnly9hFajwa12HazKvz3lVH+L5MD/GV27tKZp\n7TuMGfosGXH1hgx2HfPk2PF/ppkv8e/QFGm4fuQOR386zbVDtykqKMLASImpqxrPOq70/KA73n4V\n/zDx7beIokhKbCpP7kUSeP4+d04HEXr1EQBuVcrT6r2mtBnUDHOb10sC+Y+QHPgLZvWKEFIiwvhu\nrm2J41/MTyZX7sz4SW/WqF3SSy9bSA78n2FsrCLypjOWFs/WPvPzdZhWeEJRkea1CZG+LeRl53Hj\n6F2uHrzFrRP3SIpOKT5n5WCBnastZtYmmFgY69erBcjPKSA3M4+U2FQSI5PJzdQnnMkVcrz8PKjb\nvjYNuvjhVtXljYmQ/srfdeDSGvjfxMxMSUiS7rnjCUki5Sr9t1J3pYGXaXUeZt2jtl3YWye1KiFh\nYW5CQpK2hANPTNZiaqp+437sywJqEzWNe9SjcY96iKJIYmQyj28/JTwoivinCSRGp5AWn070g1i0\nGh2iKGJorMLIVI1TBQeqN/HBpbIzblXL4+VXAbXx27HrQ3Lgf5N2HV35cvZNTp7PpUVj/Qb+yzfy\n2H04m+Ofu5Wucf+Ssirw8v8RRZHoe3cIPX+aosJCKtT2x7NhE+SvYC1L4vVk0AcfMmH2GrauskCt\nllFQoOOz2VkMGjRIcuCljCAI2LvaYu9qS8Ou/s+dT0xMZNny5Vy4egVvT0/e/fh9KlX6fWXEsk7Z\n//V+QZibG7BiTQADRiVTr0MsjTrH0vX9RJYsa4y9fekr8vxbzAzK/kj12vZNnFy3kgwnW/K9K3D9\nxCEOLZqHTqv965slyiRTp87E3KYJ7v5xdBiQibt/PKLCn3nzFpW2aRJ/QkREBFVq1GDF6RMEOzmw\n7fEjaterx5kzZ0rbtFJBmoL8Axo0cuDSzR5cv5qIViviX88eQ8O/rn37uuKk9qKx5gap3rllRuDl\n/5OVlEjQscM4TZ6A3ESvk2xcswaJS5cTces67nXqlbKFEqWBSqXil027ePLkCSEhIVSqVImKFSuW\ntlkSf8HkadMQfatj1q61/kCNasjLOTH045E8CAx666In0gz8H2JgIKdhY0eaBDi90c77V7xMq9PF\nOoQG3pfKhsDL/yM2JAgjb69i5w0gyOUY1qpB5L07pWiZxOuAh4cHHTt2lJz3G8Kx48dR165Z4phR\nVR+iwiNISUn5g7vKLtIMXAIThSFdrEPKZMUylbFxCSWlX9FlZqEysSwFiyTeBIoKi4h/mkhqXDqZ\nqdloCjXIZAKGJoZYOVhg72qLmbXpXz9I4oViZm5OXlZWsXgTgC4vH0TxtSgu8qqRHLgETmovYvMe\n0sEysMw58fI1aqFdt4rs23cwqanf6lcQE0vOtRt4z/iylK2TeF1Ijk3l9slAgs7fJ/jSA6IexKLT\nPr/r5LfYlLOikr8nfq19qd26enEVK4mXx6jhw5m5/HsMPngPmVqNqNWSc/Awnbt2lRy4xNvLr1Kr\nHSwDuWlV4Y2XWv0VuVJJh8++4MiSBWSfOINMpaIwIYEmg4Zi4VSutM2TKEUSI5M4+csFTm+5wNPA\nSACMzY2o0rASDbv64+zlhG15a0wsjTEwNECn1ZGblUdqXBqxj+N5ci+CwPP3ubj7GgA+9b1o834z\nWr7XFAOVsjQ/rcwyetQoQh48YOPchZi6u5IbE4dfrVqsXr68tE0rFSQhl1IgO7uI7Zsfc/tmIvaO\nxvTt74VHhddDIehh1j2m3e9U5sRddDotiY8eoiksxN7LG6Xqr9Wd3iQkIZe/z+PbT9m6cA/ntl9G\npxP1DruLPzVbVMO9ugty+d/PbRFFkYPbj7BxySYyQvPQZAjYlrem/9RetBkU8I+eJfH3iYmJITAw\nEDc3N7y9vUvbnBeOJOTympKWWkDPzofw8ZTRpY2a0MfZdO/wmG+WNyGguVNpm1dmkcnkOFSqXNpm\nSJQi968+YuPs7Vw7dBsjMzU9x3Wm4/BW/yn0vWzZUhbMn8rHg9RY9RTY+IMpSQlVWTJ0JYfXnmTs\nqmF4VH875X1fJuXKlaNcOSmCJjnwV8yq74No5Cfnh6+eaac3b6Rm2MTLnL3SvdQrm5koDP9XsYwy\nNwuXeDvJTMli1WfrOfbTGcysTRk0py9dRrbB2Nz4r2/+E1JSUpg6dTK3jtvjVl4fMh/UR6RZt/O0\n8fuMuzseMrLOREYtG0L7D1u+iE+RkCiB5MBfMefORLPyy5Lh8haN1WiKkogIz8Ldo3RD6SXLjkpO\nXOLN5uy2S3z38Rqy03PpM7Er707p/qclJEEfFk9PyyExPpPs7HwKCzUoFHJMzQyxtTPDytoEQRA4\nf/489f1Mi503gFwu8N47Cs7fus7akB+ZP+BblgxbRXhwFMO/HihprEu8UCQH/ooxNlGSnFpSAayw\nUCQ7R4eR8evx3+Gk9iJbc6+0zZCQ+NfkZOSwdMQPnN58kUp1KjBuzUe4V/v9ULYoioQ/SeLiuQcE\n3onkwf1YcrIL/vDZZuZqvH3KYWGjJTX1eSXDlFQRU3NLzG3MmHPgc1aNW8/ubw+h1Wj5+LvBb53Y\niMTL4/XwGG8RPft4MfOrOzSuq8bcTI4oisxdmoZvTes3WpJVQuJ1ITI0hhndFhLzOJ6BM9+h7+fd\n9BWs/h8pyVkcPxzIsUN3iYpIQRDAvYIdAS18cPOww87BHDMzQ5RKBUUaLdlZ+cTHpvM0LJE7t8K5\ndjkNU9Vgho19wtgRD/CumEJ4VBHf/5THzl0fAiCXy/loyfsolHK2f7UfY3MjPphbuvXqJcoOkgN/\nAWRnFxEdlY2jkzHm5n9emax3nwqEBqdSoV4YDf2NePC4EGNTQ9ZsaPSKrP37TPXaw+yHUhhd4s3h\n5vG7zOr5FQaGShaemEaNplWeuyYxIYPN6y9yZP8dNBodVao7M/qzdjRsUglLK2OePHmCTqfD09Pz\nD2fLoigSGZHChnXHOHWskDETPRHk97l9/xjTZ8yhbt26xdcKgsCHCweQk5HL5i9341nTnSY967+0\nNpB4e5Ac+H9AFEW+WnCHn9aG4mCnIC5BQ+8+FZgyww+F4vfXugRBYPocf4YMr8K9Oyk4OKrxrWXz\n2oXVfltu9CaSE5d4/Tm7/TLz+y/FpbIzs/dPwq68TYnzBQVFbN1wiS0bLyHqRNp28qXHO3VxdrEG\nICgoiFatehEXF41MBpZWDny/cj11/PxQKRUlEkwFQcDVzYYvZr3LmPG5LJy7hWsXBRrV9qW+f6fn\nbBMEgY+XDebJvQi+GrKCirU9JOEXif+MtA/8P7Bu9X327wxh9zp7nBwUJCVr6Dsikep13Bgzzhel\n8s1PWCmr+8LLGm/7PvBTm86z4L3vqNLQm1l7J2JiUTLDPDgwivkz9xIfm05ASx+GfNQce0eL4vPJ\nqenUbdOZRi1d0Bo5E5NmRkbes2Q3lVKOk7U5lZxtqefjSqMq7liZlVzyighPZu7UXUSEJzF6XDs6\ndK31nJ3x4YkMrT6OGs2qMHvvpBfcChJlBWkf+Ctg/Y/32fCtNU4O+ma0tVGwYr4Nvs1DWLEshBYt\nnZg22x/n8ialbKmERNnlwu6rLBi4jGpNfJhz4HMMjZ6J9Oh0Ils3XuKnH85gb2/Oou/641vbDdBH\n0G49jmHL6ducufMYc79uhOUWUtkiiZY+T7A1zWHzzlRCH2uwsLXFsWZ9rj/M58iNBygVctrWqcTA\nVn54OOpn8K5uNnyzciBzpu3im4WH0OlEOnUvOfB1cLOj3xc9WTNpI9eP3KZO25KFOSQk/gmSA/8P\nJCTk4+VRUjLRw1VJkUYkIciD73/MoE/3oxw/1wW1+s1t6tp2YVxKtS8z+ugSZYegi6HMe3cp3v6e\nzN43sYTzLigoYvGc/Zw5GUJACx8+mdgeYxN91vi10EiW7j7P/chELIwNqWCmQ522kdUTc5HLnkUl\no68l07CcQOc2xgwcfYSx4xfQpF0/9lwMYt/lYA5fDeWDdv4MbuuPUiHHyFjFrAW9mfn5DpZ9fYRy\nLlbU8nMvYXP3T9pzcPVxfp6+Fb82vq/d8pnEm8ObH+MtRWr7WbP7cHaJYweO51CzqgpLCzlfjLWi\nkoecwwciS8nC/46JwpAOloFlttyoxJtLfHgiM7otxM7Fhtn7JpXY352ZkcuEUb9w5mQIH45sweRZ\n3TA2MSQpPZtxK/cxfOlO0rPz+aJfSw7OG8KoTvW4ePIp6XkKLiWUY/uTSqwMqcGOuNpQtQ5Fjh4s\nW2zJ4kWz8S5vx6Q+zTk4ZzCt/LxYffAKAxduITFd/1ugUMiZPLMb5V2tmTdtNynJJavhKQ2U9Brf\nmQfXw7h3LuSVtplE2eLNnRa+BoybVJtB754gJU1HQAM1V27mMe+bNNYve5acUremkqdPMv/yWRkZ\nhVy+GI/KUE6Dhg6oVK+HhnJZLXIi8WZTmF/IzB6L0Wp0zNk/qURpz+ysfCaO2UREeBJT5/SgSXO9\nhO7pO4+ZtfE4BYUaPu7SkH4taqFSKojJzOSuUoFi0FjqHvh/JULrwqZs2HQG5IKO7NZhHHn8iJYe\nFbA0NWLuoHa0rFmRqT8dYcjX21g7rjc2ZsYEBd+lbhMTdm9OY+XS40yZ3b3EY1sPbMrP07awb/nR\n382Ul5D4O7wSBy4IwhmgHqD536EYURQrvYp3v0xq1rJh8642rF4exNrNSeRkF7B3vSP+NfUzAVEU\nOXWxgAFD/7zu9PYtj5k59Tr+NdXk5OoYP1rDijUB+Nez+9P7XhWSsIvEb3kd+vMPEzby+PZTZu+b\nhLPXsxoCebmFTBm3hfAnicxc0Bv/+p7odCIrD1xmzeGrVHaxY+6gdrg5WPE0LY3vr19lT+h9dKJI\nTU8vDOMTeHj2KFGBd2hTr4jF02zJl6l5lGHFjltWHHWswoiD+6lgacX8lq2p7eREM19PVozpwfCl\nOxm2ZDuJp1aSEPOAapUNiYrz5cxJLV1716FKtfLFdqrUKhp1r8fJX85RkFeASl22iutIvBpeZQj9\nY1EUTf7398Y771+p7GPJkmWNOX6+K3YOpvywMYuw8ELCo4r4eHIy6dlyWrct/4f3P3qYwbyZN7i0\nvxxHNjtwfq8TP31jzfAPTpOXq/nD+yQkSplS6883jt1lz7LDdBvdnnodnyWJ6XQi82fuITQkhsmz\nuuNf3xONVsf09UdZc/gqXRtU5afP+uBka86Syxdps/FnDj16yAc1a3Fu0GB2vtOXX8Z8wvVdh/l+\n4fecuqTj/KVMjIoyyA4O4cCMw8zzqsz37TuSpymi9/YtrLiuLyVazd2Rr4Z1Ijw+DdPK3tw/b8uO\nNWac2hWOSC6zp65/7jsada9Lfk4BN49Lg2OJf4cUQv8bJCflceRQFEVFOpq3LIerm+lz18jlMjZu\nb81X82/TqHM4Op1I+04ubN5Z+0+3k+3aHsagvqZ4V3wmANOmmTG+VbM4dTKGDp1ej0pGUpETideB\ngrwCvh3xA85ejgyZ36/EuW0bL3Hp/EM+GtOKxgHe6HQiMzcc4+DV+3zUqT5D2tXlaVoqA7dtJaYg\nHz9jE5b2egdHc3MS8tL5KewMt9PCCcmIJkOdi+P3w5mv1THzQhqq+GwmLG9H7069EASBxq5uTDl5\nnEWXLiATBIb51aFqeWtSQ85BlaaExIZR1TkRa2sdAY2COXuhDnGxaTg6PYvGVW/qg0ptwO2TgTTo\nXOdVN6VEGeBVzsC/FAQhWRCEi4IgBPzRRYIgDBUE4YYgCDdSU/5Yj/hFodOJnD0dy5pV9zlzKhad\nruS++IP7wmnWcA/3LocSEfyIzm0PsPzbwN99lrm5Ab36euJUzpjUtCK2b33KVwtukZtT9Ifvz8ku\nwsby+f8Ga0sZWVl/fN+rxknthYWBMdMq7SHI9GZpmyNR+vzj/pyUlPSfX7p53m7iniQwZsVQDAyf\nDXoD70Ty4+oz1G3oTkLqLVatWsWsnw9x8Op9RnRqwIft63H28SNarV1NbEYq/pHbiVs7hZadGzPy\n4mo6n13E8kfHSMzPoKm9D8M8W/Jxxda4RusojEtDW8WR9QYhdDs6n4icZEwMDPi6TTs6elViwcXz\n7Am9T35+PunBp7AxyWHxkUb8KrER0Ogxoihy/FDJmbaBSkmVhpW4d1ZKZJP4d7yqGfhEIAQoBPoA\n+wVB8BVFMez/XyiK4mpgNeiFXF6mUWlpBQzscxxRU0BDfxX7theweL4BG7a0xtJKRVpaARPHXeb0\nTidqVNGvUc0Yb0nNlkEUaURq1rKhYWMH5HK9Aw57nEnf7kcwUgv07mzC9TsFnDwaTlRkNj9vbvW7\nNgS0cGbR7ChGDTZHpdI/Jz5Rw5HTOXw63fFlfv4/RloLl/gf/6o/+/n5/af+nBiZxPav9tGsb0N8\nm1UtPp6XV8jiuftRG8tYue5j2rUwIE1VjViTDtSwVzK4nT8XIyMZcnA/Kk02B3sexsE4l1XvNmVz\ngifXkx5RR+fIBzXbUtvdp/i5nTu34+SJozSoY4jysgGBSjc0/ZrR/8K3zKjRixYO1Vjcui0J2dlM\nP32Kk++9j6dbOWpaXOR4dGtCYm2pUi6JPUcSURsXcO1yGO8NaVrim7z8PNm+eB+aIg0KpRQQlfhn\n/OcZuCAIZwRBEP/g7wKAKIpXRVHMEkWxQBTFn4GLQPv/+u5/y/2QNJYsukv/3sepUF7DjaNOfDvH\nhutHnKjvC1/Oug7AyWPRNG9kVOy8dTqRL79NRaPRERYYxldzL9Oy8V4iwvXbRCaMvUDjeoY8ve7O\nLyscCb3oSrvmRty+mcTjRxm/a0tAcyfcK9rQoFMsK35OZ9HyNOp3iGH4iCo4Ov23esUSEv+U17k/\nr/tiMwBDvnwWOs/NzWXCmOXExqRx9fY6Tu0wY+oUd1Is2lDFIZK9307k2N27DDuwF21yEmvq7kSt\n0jDsUQCbkrzIPh9I0fw1JP68gFa1/Jjz9QRCM05y6uGPpKjusndfBY5scebAOjsOjk0jYsKP6GLT\nmXJnC+cTQzGQy5nboiW5RYV8e+0K3363lp+W3UAmFrFwhyfvfpTO7iNK2nSox6MHcWRl5pX4Jhfv\ncmg1WuKeJLzs5pMog/xnBy6KYoAoisIf/P1RhQ4RKBX1gu+/uceA3kcRcqJo5q/j3KVcvlqRDuj1\niqeOtWT/Xv2+bY1WRKl8ZuaGHVlcu5VP+A13dqxx5PqRcgzvr+bTj88B8CA0nflTbIvvkckEZk+0\nJidX94cOXCYT+G5VE0aM9efcHWOCIy34enkAIz+p/jKbQULid3ld+3PckwROb7pAl5FtsXOxBSAy\nMpJaNfwIDcrEyfEelTxj6D00gS92BmCiKmRJ/1N07GLL+DOnsFKrKdq2Ga2BnA8fNSeiwJSM73cz\nzeMWl3fb8flSZxZeqoNp+1scjfuSQN0v9J7tQ7CzKxuzHAkqMKFKJRW9mkLkrG14mjowN2gXmUV5\neFpZ09OnCjtCgqnu58e1KzewV2l5kFqZOo0mcvNWCHXrV0anE3kSlljiu+zd9N+SFJXyMptPoozy\n0tfABUGwEAShjSAIhoIgKARB6Ac0AY6+7Hf/fx49zGDt6hBuHXdm4VQbvp5lx83jLiz6Po3HTwsB\nUBkIaLQioijSomU5jp7OKT73y45MPh9jhanJs2YbNdiciPAsIsKz0GrB3Kxkk5qayNBqRLKz/3g9\nWy6X0a6jC19925h5i+pTt55U5EDi9aS0+vPOJQcQZDK6f/KsNsL4cSPw9fZHbajl67mhnNrljG+r\nAB4n2TO+3QUsjfJ44NGBfERWdexC+05t+Ty+Gbk6BUNzj2Ic/pTabe1Yn+nE+XxLzBVauBVN6FoL\n8o40JuTbezRTp2Ao6DidZ8XBHBssbRQU5RUyybszGUW5fP9Q/9k9faqSr9Fw9PEjXF1dea9bOzQy\nFX3fH4KFhQXOLlYAxESllviuX/evZ6WWFISSkPg7vIokNiUwB0gCkoFRQFdRFB+8gneX4NiRKPp0\nNcHB7tlak5ODgp6dTNh3NAeAJavTadO2HIIgYGunZsq02jToGMvoL5J4Gln0nIOWy8HYSEZenoaA\nZo6s+Dm9xPm1mzKxt5MzZ9p1oqNeXCcNDkxlxJDTNPHfSd/uRzhx7NWppNW2C5NU2d5eXnl/zsnI\n4eiPp2nRvzE25fS64zqdjuPHbpGS4kmPziFYWuSTnW9ArEFTcmNDaekTxvpAD5LMKjCsSjUqWluh\n6VadAgMjClcf5Ogv4dToWZ6DObaYyLT0Momnh2kiZsnppEbk0719X7ZvzsAhO5OeJgk0VqcRrlGT\n4e2Mg20hP8z6km7l67Av+gbZRfnUcnTE0cSUM+FPAajq5gDAgyh94p6dvTmCAEmJJUWdjEz10q67\ntu+mpm9FKnu7MH78GFJTSzp6CYnf46VnTYiimAS8Fnsk5DKBIs3zeTQ5uTrOXMzl0MkcnkYLbN0d\nUHyu7wAv6jdyZP+ecJxcYlnxUyYBDdTF+sUnz+eh1cnwqmRBv/e9Gf7BaYJDC2nb3IgLV/M4eCKX\nE9vL8fO2bLZuesy4ib7Fz05IyGXBnJscORSNXA4dO7syYUptLC3/XNQhODCVfr2OMeUTcxZ8Zsu9\n+wVMmHSRtNTa9Orj+WIa6w/wMq1OF+6BN1wKbSDpo79llEZ/PrHxPPm5BXQe0bb4mCAIlHeoj4GB\nhi4dQgHYcq0q2QWGJN8+xNhZBexzqoedsZZPW7Ziw9NzBGXHMM23F7l5tQkt2oeFXwL2eZl0d0hH\nIYBGI7JuUxEfjuiNi4sLTQNaUS3gCKOHmKNUpHA115wmH3rwQb0iWjZez9FJY9kReZXLyQ9p5Vgd\n84J8Dl2/yg/du1HVtzrU7F8sryqXyzBUG5CXW/i73xh87zDfLMjH1ETGip830bTJQa5dD0StVv/u\n9RIS8JZpobfv5MK2fdmEhT/rRA/DCtl7JAcnRwWPnmqYNtsfp3Ilk8fc3E0ZNbYaP/zcnLBoBa3e\niWfFT+mMnpJE90GxZGRq6NvjKCOGnKaat4Kzl/MYMSGJo6dz+Wa2DRXclMhkIsGByfxavjU/X0uf\nbkdxtckk9EJ57p50xogU3nvn+HNb2f4/3y25w7RxFoz50JJKngb06mTK9h/s+WrBbbRa3YtvuP/H\nr/roKisp8Ubi5XN8/Rk8a7pTya9C8bG83ELsbWpgZHwfU5N8CjUyNl+pjrnmAZ62SdyR10JmZsaK\nPv1ILsjkh8cnaW5fhU4udfDv4IaFXwIGyR6MaRvCjPnpLFubTu3W0UTFZnPx9FzatfYkPuoiluYy\npi9KZeqCVNKuJ2BKEYE6C2SCDsOkfEwVhtxICWPdujU8uHQSLMxJCHZj6sh4AK7eultss8pAQUFB\nyaW04CD9FrJPhhrRuJ4a36oqVi60wNkhk82bN7+C1pV4k3mrHLiLqykTPq9FrZZR9B8Rz/uj46nf\nIYqvZ9mwcqE9nVqbEBWZjU4ncu1KIgf3RxAXl1t8v4mJku372tGpd3UWrczm7KVctq915MQ2B+7e\nTmbQO6bk5sLxbeUoiPbkx28d+HR6Ms41n3Lhah6PQlNo22wf4U+zOHwgAlcnWPCFNQ52CpydlCyf\nb4OgK+Dsmdg//Y57d1Jo17xkLWI/X0MK8rUkJ+e/lLb7LU5qLxSy10OrXaJskxybyoPrYTTpWb/E\n8csXHoIo42lMNFWbRPLBLCsy8tRkP77I3g3OFFWrhyb8KbWdnFgZdASNVkOdNEtyCzM4EfcV1io3\nPmywjNOnrxGeFMDWvTnsW+/Ak2uurPhS5PgWNTM+M2LiKCtSH1Qg7Jo7DjYyjv0SR5pMhZeXnKZN\n6iPLKCAhP4O5c6byTlsBERlylZKOLfWTgPPnTxbbXFCoQWVQsnrhjSt6TQVLm2cDb0EQaN8crl07\n/7KaVaKMUGYd+P2QNGZNvcanH59j25YwCgq0APQbWIlPxvty734hdWsbEnjGlUF9zNHpdJy8kEtB\ngY62zfYydcI5Dm67Q+ume/ly1o3imbOhoRx3d1MMFCK3TrjQJsCYsIgiGtczZMP2LDatdKBWdUPk\ncoH2LYxZMsuWWtVUXDviwuMrLgzpo2Lo+6d4EJpG03olQ+WCINC4roqHob+fsf4r5ZyNCQotGYqL\nji2iSCNibv7qNJWltXCJl821Q7cBiCkMZ+CAXowfP4bQ0FBOHw/Gzt6Mi1dPk5SmIlFWA3NVJhc2\nFBCY70ZCvhlmTx7x+ezJ7Iu9iUHwA+Z9+h5D5zUlV5tGK8cJKGQG+Pj4YGUaxpndTrg6653r0HEJ\nnDyfS4M6aga+Y4aJsQwnBwXrlzkQG5SBXClj+04Pgs44kBweTlhCFFHRSXiU1/+cFmrlaEX9EltS\noj67XKvVkZ9XiKFRSQdurrYAwNSypGxyYKiAq+vLXQ6TePMpkw58766n9Ot5FHvjJFr657F/2z3e\n7XmUvDx9JxnwvhfZeXLiE7UYqgQOncihfM1w0lI1LF96h35dDLh3qhx7frLn0SUXzp18yv69EcXP\nDw5Ko2l9vZMGMFAKZGbpHXxFD4MStjT0VxMRpX+vIAiMHmKOprAQpYGcSzdLOmFRFLl8s4AKnmZ/\n+n0fDK3K+Jmp3AvRK9XFJWgY/Gkyfft7Ymj4ambGvw2jS05c4mVx88QddAoNx8/Oo1HNcxgUbaZp\nk/R75M0AACAASURBVLrcvBZGg8aVUKkMmDp9Nik6d3wdH6Mp0jFpkx26/Hwyb11k+51DyAwUrOge\nzbXDVtTpYkbkrRzsVBUBEHU5TB6Zzm8XrW7czWf5jxlcv1MymiWTCVR21/cvrahPgHXzMCA1PgFH\nBytCoxTIBB0mykKSs/QRMtv/DahTkrIQRbC1Ldm3bU30yW6bDyWTl6dDqxXZvDuLPYfzGTRo8Mto\nUokyRJlz4Hl5GqZPvsrRLY7M/MyaIf3MOb7VASuTArZuegyAkbGSbXvaEvjEGOeaT+n9YRxLZtty\nYb8zhiqBz0ZaFiepWVnKmTzGgp1bHxa/w83dlBt3C4tn5a2aGPHoSSE6nUjoo5JO+fyVPCp7PXPq\ngiDgaK+gajVrQsO0zFicQkamluQULeNmpJBboKBZCyf+jHYdXRg6sgZt302gnG84VZpGUcHHmQmT\nX51G+W+lVaW1cImXgSiKXDl8A5VdMod+sWDwu+bM+dyCr2dUQqMRqVHLBQD/Fl0Q5EqO7gnHslIY\n6VYVaeESTaM6Ar69fXBQ5uCtTiNWqwK1AaEn47l5839ywHnbcbCTc+3WM2fdt5spDx8XcvRUTgl7\ntFqRB0/1g/H/jd3RqAzRZOUy6fPp7L1ggJksFxk6Dl3Qz7R7d+0BQFxsGgAOThYlnhnzMA5DYxV3\nIyriWCMah2oxLFljwYGDx3FwcHixDSpR5ihzDvzunRTcXQ2K1dNAP3Ie3NeUMycji485lTNm2eoA\nps/2p2MbU3p3NiU7R8TCTIZCUVKTwsZKTs5v9nE3buqIRlQycY7e+QoC9OpsSk6uSLdBsVy+kUde\nno7dh7IZOy2JCR8/K2DwNLKIu8H51G9oz9bdbbnzyAiHak9xqxNOTLo5v2xvUyzN+mf0G1iJK7d7\nsvdIJ67f7cUXM+v8adGUl4G0Fi7xMkmKTqEwS0Pj1rnFA2oApVw/wNUJ+i2boVF6cZQrJ45h4eiA\nztic+k6JZOXoSDO2oYZJsn4Ll0Y/kM4NzyMrS6+eKGoek19ownujMrhyMw9RFGnd1IjUDJGHT/R9\nPitLy9PIIvoMi8ejhn4GbSErIl8nJwFz3E0dGD58BNY+tUh/moyBcxjfbtHLIPfv2QmARw/0SW3u\nFUqWCH5w/TEVa3lw6PBpwsNjCQ55wo2b9/H393/xDSpR5ihz4rsmJkrS0jWIolii06emazEyMnju\n+sSEXLw89M1Q1duArByRS9fzaFDnWU3vNZuyaNrcvfgemUxg/ZZWzJhylXK++spj9erbsnN/Wzb8\n/JDeQ6NJTi6kSlVz5HI5fYbGozYU8K6oJPiBhvETfTEzM8DMzIDla5qh04kIAiXs/TsoFLLnMuYl\nJMoKj2/r91QbWmeVOP403AKNJhsHR/2e8LDYFOwtTTBSKclWGWMCeJql0rK5Kb8oTHAxCAcgXadA\nodMSeCebunXr6h8mZmOotmH6zNEMGPU58QkRmJkaM37CbHq2DiK/4BpuflEolIZ4eVXCyVVHcngO\nLT4Px9DHAwbIGNisGzlFRSQDo3v1YfSib5jy4xHuhMXgaKV3+CGB0Tg4mmNlbVL8Hfm5BTy69ZRe\n4zsDYGVl9fIaU6JMUuZm4FWqWmJgqGL1hmeCCQlJGhYtz6BnH6/nrvfzt2Pv0Tw0GhGFQuC7ebZ0\nHxTHpDlJ/LQ1k07vJXA/TOD9Id4l7rO1U/P9DwEEPuxD4MM+bNzWhuq+Nixa0oCrd3vzKKofKkMF\nzRqqObTJiV0/OmJqIsfSWs2AQSXLJ8tkwj923hISZZ2Yh3EA/LgvjZRUfRKqKIrcvGcI8jy8vPT9\nOT4tCydrcxQKBV6++mIkTsbZdOlmo79/TTzrNmdwI6iI9DQtXy9ZhpHR/3ZxyMuBNpL3+jXmcVgs\nCQmpxMQkM264Glf7axha9CQto5ANG7eRWhCOZz1L6joUMmKQBYmO7ihEgcYu1Tj5JAydKNKgvAta\nncjlkHD8vMoDUFSk5fbNcKrVLFkaOPBcCFqNlupNfZCQ+DeUOQcuCAIr1gawaGUOtVvH0PX9BCo3\njqJLTy+atyz33PWNmzpiY29Gp/fiOXo6B6VSwM3VgD3HNBw8r6JJm8rs3N8eU9PnZ+8AKpUctfr5\nQMa5M3HkZuWweaUdtaobUrOaIVtWOaCUaThz6s+3iUlISEBiVDJqE0PadR1ApYZx9BiSSe3WqSQm\nG+Nft1bxdVm5BZgZ6ZfMuvceAMDmrWncf6RP8oyKgz3Hq5Cb6YmJlYp+A54VQxGMBoGgRkx5F3KW\nYyw7CJkjIOd7UPdEMJsJwPRp4xm3xBW5AE3tcujewwrr5j5o7kRgojBkT+h9nExN8XMqx5X7EWTm\nFtCqtn6AcfdWONlZ+TRqWnIScOtEIEqVkupNKr+8RpQo05S5EDpABU9zTl/qypVLCaSlFTJ9sS32\n9ka/e61MJrBmfQs2/PiAWd+GIwjQuWdV+g30+k9ryvfuptAmwBCZ7NnMWiYTaNtMxb07KbRoVXYU\nzGrbhXEp1V5SZZN4oaQnZmDpYMGCBV8zatSnXLp0CXt7e5Yvvo29vXXxdYVFWlT/K8XpXbkyxEQR\n9LQOB48EwlQYMf5TPm/Qh9CMkxyN+5K4vGCcjWoAIMhtwGobYuYkxOyl+gcKFggmY8F4eHFkrNAq\niRy7aviqMjGW6Vge60ORTMn9H08SNiyVcxHhjPSvi0wQ2HspGAtjQ+pX1s+4Tx8PxsjIgNr+z5bh\nRFHk8v4bVGtSGZX61W39lChblEkHDnrpwoaN/149bZVKzpDhPgwZ/uJCWeXLG3Nwh+a543dDNLTs\nZPI7d7yZSNKqEi+L/NwC1CZ6rXBnZ2d69+4NwPKvbpdYclKrlOQX6vuanbE+J2TinEX4OZWj+7nF\npKv14fcKpg1RJZgSmLa/2IEDCMqKYLUDdIkgFoDcGUF4NnhPzn/Cu1/6YJKfRwPzdCLzTdiU5EVd\nwkjRwLdXL2OoUDCwRk1ikjM4czeMga39UCrk5OYUcO7UfZq3ropK9WwP+MObT4h5FMc7E7q8pNaT\neBsocyH014W2HVwIeaRhyap0CgtFCgtFvl2Tzt2QIjp2dv3rB7xBeJlWp4t1iLSdTOKFUlSgwcBQ\n+dxxuUxAo9EW/9tEbUBGjr7OdjlTfdJYeLo+Q72KeXnupIVTpNOglBlSxaItj7LOEZF9vcQzBUFA\nkNsjKFxKOO+n2VfYGTkOA8GIdWMeEfpEy4xIf5SihguzztN77CQOPHzAQN+aWBsZse7oNWSCQK8m\n+gHCkQN3yc8vok3HGiXed2TtSZQGChp1r/sCWkribUVy4C8JtVrBL9tbs/ck2FV5in3Vp+w8Cpt2\ntEFtVGYDHxISLwylgYKiguejWOYWxmSkP5M4drGzJDwhDVEUqWBlhZVazeUo/ZbRdk6+pBXmcCI+\nEAB/635Yq9zYF/0FwelH/vDdOZo0Tsd/x77oLzBV2vFe5ZV0aj+aPidqE5xtScQ3J+jRZSRXzUxx\nNjNnZJ26PIxOYu/FYHo1rYGDlSn5+UVs3XiJGrVc8an6LDKVkZzJ8fVnadG/CaaWZScaJ/HqkTzJ\nS8Tdw4xNO9uSlqZPpvmrKmMSEhLPUBkZkJ/zvLa/lbUJSUnPtpZ5Olmz60Ig8WlZOFqZ0aC8C+ci\nwinQaKhnU5EKJvasfHSChrbemClN6OmyhEMxszgRv5h76fuoaNoEc6UTcpkBGYUxxOWF8CT7EjpR\nSw2LLjSyGwbI0XWognF0LoMcG/LB3hlMP3+W8OAgfuneE0OFgvlbTmFqpGJoh3oA7Nl+ndSUbKbM\n6lbC/gMrj1OQV0iPsR1favtJlH2kGfgrwNJSJTlvCYl/iKW9Banx6c8dd/OwJSo8maIifRjd31uv\nyHYhUL9vvHeVqqTk5bE7NASZIOPzKt1Iys9k+r1t6EQdKrkxncvPpYXDWAAuJq3hUOws9kd/wbnE\nFcTlBeNj3oYBHusIcBhFlqaQkdfXsif6Ou97BDC8envW3L3DtuAgRtTxp355F34+doM7YbGM69UU\nc2NDUpKz2PTzBeo1qkj132wfy83KY+c3B6jboRZuVcq/5BaUKOtIM/CXQHRUNgf2RVBYqKNVG2cq\n+1j+9U1lhJtF0VIim8QLwa68DbmZeeRk5GBs/kywyMvbkaIiLU8eJVDJxwl3Bytc7Cw4cfsRvZrW\noGF5F6rZ2bPyxnW6elemuqUL4yp3ZEHIXj6/s5nPq3TFwsCYqhYdqGrRgRxNKrmadLRiIaZKW4wV\n+gx3rahjT+Q1lgYfJE8solWWI+87N2JzUCBfXb5IV+/KjKvfkLtPYlm5/zKta3vRwV+/JWzVdyfQ\nFGn5aHSrEt+0+9tDZKVm039qz1fXkBJlFmkG/hs0Gt2f1uIWRZEtGx/RJmAPNby3MLDvMW7fSi5x\nzY6tYbRvuZ+kp08oSo3gvXeOsmjerZdteqljojCUdNElXijlvfW6DU8DI0scr17TFZlM4PJFfX0C\nQRDoWM+H6w+ieBidhCAIfNagIZEZGUw9dRJRFOle3p/RldpxPjGUPheW8svTC9x9dJ8B/Xvi7uhO\nPZ+GrF60GaXOlNSCbDaHX+Sds0uYF7KHnOho6l7dwa01s6kydBBfnDpBgJs781u2JjIxnbHL9+Jg\nZcrkvi0QBIFTx4I4fTyYvgMb4uT8TF0tMTKJLV/upmHXOnj7V3x1DSlRZpFm4MDjRxnMmX6Ns2cS\nUBnI6NLNlckz6mBuXlK8ZcV3QezfGcp3c6zx8bJh39EcBr17gk07WuNT1YqU5HxmfHGNS/vL4V1R\nf+/k0ZbUbv2I5q3Lk5erIexxJl6VzKnXwL7EVpi8PA1LF99l144wcnO1NG/hxGeTa1Pe5c1IcnFS\newEPmVZpD7MeQNWsV1dYRaJs4uXnAcCD62FUbfRM7MTSypjqvi6cO3mfgUOaIggCvZvUYP2xG6zY\nfwmHzGCWfrOYfN867ATy4+L5buD79HdvjL+1J4tC9rH0wSFEjRbzzlb0+KAriqICjj54yNE9kyky\n0/ddk3QN5QPPsnVkKskFxkyp2pYHsW5YRoUzq1cfVqxex+4HuQhyJctGdcPM2JCY6FSWLjyEs4sp\nP66fwIgxd3B1cWTMJ58TdywLURT5aMmg0mhOiTLIWzMD12p13L6VzL27KSVm2WmpBfTtcZQOTTSk\nP/Tg8VUXjIRUBg84UVxtDCA/X8uq5cHs/tGBgAZG2NkoGNLPnMljzFnxnT7D9dSJGFo2MSp23gDW\nVnIG9THho8GnmTf9IhHBD5k+6QI9Ox8mM/NZ5bKPh54lJiyKE1sdCDlXnuoVcujd9Qjp6QWvoHVe\nDL8WNzEzlNb7Jf47Vg6WOFWw59bJe8+dq1XXmajIFE6fuAOAmbEh77epw9l7T9hx8jBHNpsSv+YJ\ntVShHExPZeD6n8gpLMTLzJEf6g2jeYghtqFBVC6nIUNmTJTSjnJVrch4FEUfq9psajiax5/9yPQ2\nSWx94kPbw+9wMd6ZSVXPE7xsOTXr1eeX2zFk5eURsmcJl04dITsrn6njtyKi49jZhXzQO5yIG+X4\nfq6G1TO/4vzOK7w7pQf2rravuiklyihvhQO/dCGeRnV2MumTM4z96BTNGuzmzm196Hvblse0bGzI\nmA8tUatl2NkoWLHAhtSkHG7deBYej4vNwdxUhodryX2pzRsZERqSCoAggE73/Ps1GhFHW7h9vBwr\nF9py71Q5KrtrikPrIUGpBAcms2WlPd4VDXCwUzDtUysa+xuwbfPjl9QqLxepRrjEi8C/fS3unAqi\nIE8/kC0oKOD9ge8w6pPOiGIOk8Z9y+jRw9BqtbzTpBoFyZGoKnfA3M4WhVxgU+ezNBKucD41hY6b\nNrD/QSiFWi0R127QV32TpRUusNH7BLt8jrDF5zgVLp7FLVrAUm6GrJYfQ4PfY+rNpniZp3KgzXb6\nugeitvfAq+twzM0VrB+2j+NrCxk5chiTx/1CXGwaOuV1po3T8G53MyzM5VQqb4Zjpg85inS6fdKu\nlFtUoixR5h14UmIeHw05ww+LrAg87UzIOWfmf27K4P4nycku4mlYOvVqlwyVy2QC/jUNCQt7VhDF\nzk5NarqW+MSS+1Jv3M3H1V0vHtGilTOnLuQSFPps1pyYrGHFzxnMnWxdHDKXyQSmf2rJvj3hADwI\nTaehvxqlsmRBk2YNVTy8n/rC2kJC4k2jXsfaFOYXcfWgfrA7efJ40hJP8vS6PYMHhGJuUoF7N67z\n1VcLSUtNIfPWDpRyHUN/6sLTJAsUMpEv6lyD7ZuRCTLGHDlErVXLSfSty87IapyPd+Zuih1XEx05\nEOHOXbN6/JyVQb01q5A1b0VeShY/ND7I5uZ7KW+cxeClNXFrNwxHi1x+GryLyk7JeHmoqV/jHe4H\nxfHZF525/+ASAQ301QyLCgXmDXcFUSDW/B4pqSml2ZwSZYwy78D37g6nYysjWgfos1gFQaBHR1Pq\n1FRx5FAUXpWsOHu5ZJhaoxG5cDUP78oWxceMTZT0edeTfiMTCQsvRBRFjp/N4Yv5aQz5qCpPwjJ5\n9DCDqTP9aNotlkGfJPLx5CSqN4smN0+kfm11iXeo1QKFhfrpunsFM67fzn8uge7KzULcPMxfRrNI\nSLwR+Daviq2zNUd+PI1Op2Pt2nUsnW2KsZGMbp3u4+Kcjq15K9b8sAo7OzsKs7L4vPlOdDoZQ3/q\nyo1wJ85cyqOatQXH33ufdV260c6zIqnm5txzasegsx3pcaI7/U534ZMrbZDVbUSRXEY7ewcW+9bG\n+OApJnxwh6FzzGn4RTceFzbATnObn4fsxNEim5wcJVPntqAg34Xqfiqat65KxYqeXL2l37++aoYT\n928aM2BKOFm6HGxtpfC5xIujzCexpSTn4+osf+64q7OclJR8+vTzZM2qYGYsTmH4e+ZkZumYtigN\nj4oWVK9hXeKeSVNr881iBfU6PCA3V4ubqzETv/Djm4W3eRKWgbOTkkdPCvhwuA9m5iry87Xs2F+e\nBXNu8N3adCaPeZaR+t3aDFq30WfZ1vC1xsnZjKGfJTHvcyvMTGSs25LJgRO5HD0tZatKvL3I5XJa\nvx/Aprm7CLsXTk5OPk4O+p8tA6WOT0ZcZtyUNpgbNkUuUzBh4mTGT5zH1MlbWB/UneE/dyE7zJFv\nJw5DJggEuLkT4OaOKIocvHCBOV/P5f7TGGQ6La2bNMLP05v5Y0aS4qZmV3w+LlWb4BIwmNvpRZhb\nyOnXyIvpo6aR+6kdGUXmTJvXjOgYcyLiDrByzCYAPpswgwH9uxJzqxynfrIhoFccX+8MZ9SoMahU\nUn6IxIujzDvw+g3tmTP1MVPGWBWHqHNzdew7msvqn+0xMzNg2562LJp3k8qNo1Cr5XTr6cHcz3yf\ne5ZCIWP8pJqM/awGBfla1EYK+vc6RsOaWk5tcUGhEHgSUUSTLiGUd7Pg47HV8ahgxpQZdXin21Fu\n3iuiYR0Dzl4pIDBUy/a9AYA+KrD65+bMm3Edz7oRFBTqaNTYjk072mBjq37ODgmJt4luo9uze+kh\nNs3ZhV/tKuw8mMQ7XUwBqOKdRNUqZwkMasZ3Xx9h7PjxmJlZMGPuPCJjv6ZK676Yevozfc89LscU\n0LqWF7W8nFEbKOnYuDEdGx8hLy8PhULBpUuXGDCgG2vXVCcypwIn73sQlWrBk/hUqlrLWDTuQ5wc\n7Xl66yMCup6hvH0bQCQsZiuDh/WlQoUKALRo0YKx/WZz9OsLpBDHsjMhfPLpeD77bFIptqJEWUT4\nbab160Z1X2vx0PEO/+kZOp3I0PdPkZOewejBphRpYMF3aeQVKvhwRDW69nD/3Xref4eI8Cy6dzhI\n5E3XEuvXazdlsOaXDJJToc+Aynw0qhrZ2UXs2fmEsEcZeHlb0qWbG0bGzxdq0OlEtFrxP5UyLU0e\nZt3jYFpVzoXUkwRdXiGr+na7KYqiX2nb8Wf4+fmJN27c+Ff3bpi1nfUztjFgSTfGzR7GmCFq6tRU\ncvJ8AavWZxLQ6CNy021p1b46n3zWHgPVsz4dmZjGplO32X8lhLyCIgAqOFpT3s4CtUqJTBDIyMnn\n+t1ACuVqROTIZVpqu8XStspDRn54nHq1jLgTbMThwxfZufk2p44FY2yqwcOngPcGvoOv77MB//ld\nV5nbZwk+DbyYseczTM1NSmwZlZD4KwRB+Fv9uczPwGUygRVrm7Fjaxjzvr9PZEQ2Teurad/SiG37\ngtiy8QGbd7b5XWf6V6SmFuBgr3wu+czVWYlaJeP0TnuqNw+iT38vLC1V9B9Y6W/Z+9sa4m8aJgpD\n2pjfReOtk8qLSrwweo7rxIkNZzm+9ALHjpzj+5Vfs/yTXRirRSZ/Yk5OzmZ2H6jJ8UMQHZHCpOld\nikVUXOwsmdSnOZ90b8LtxzHcfRLLg6hEopPSyS/UoNWJmBsbIuZn0tAriK6N0qjpGoe5Wp8bs9BJ\nxvABFqzdWJHRQzYgkyl4b3AT3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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_result(best_estimator, xx, yy, X, y)\n", "print(f\"lower_bound : {best_lower_bound}\")" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "alpha0 : 100.0\n", "beta0 : 0.1\n", "nu0 : 2.0\n", "m0 : [0. 0.]\n", "W0 : [[0.1 0. ]\n", " [0. 0.1]]\n" ] } ], "source": [ "print(f\"alpha0 : {best_estimator.alpha0}\")\n", "print(f\"beta0 : {best_estimator.beta0}\")\n", "print(f\"nu0 : {best_estimator.nu0}\")\n", "print(f\"m0 : {best_estimator.m0}\")\n", "print(f\"W0 : {best_estimator.W0}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4.3 Results for larger $K$\n", "\n", "Finally, let us see what happens if we choose a large value of $K$. \n", "\n", "Concretely, here we choose $K=10$. \n", "To cope with the initial conditoin dependence, for each value of `alpha0`, we try 10 random seeds, and select the best estimator.\n", "\n", "Let us first try out a large value of $\\alpha_0$, which, from the property of Dirichlet distribution, means that the model distribute the weight on many more components." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lower bound : -452.0379619828742\n" ] }, { "data": { "image/png": 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jT92/jQ0/F+PfEIkCBQv2p7N6WQ4fLRnZtGiD7JJ2SdblnBTb0p7hXVsecH/d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\nWrfyqfabIAj8OnU57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97aiS5hIwjv+QeDH1YhlcL6bVrmfuTEU2NseZEcEi9mIwgmrmbE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\nJsPYcfg3/OqEocvUE+RTnp4t38XGyk6Kt+S5pIyfO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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "alpha0 = 10.0\n", "\n", "best_estimator = None\n", "best_lower_bound = -np.float(\"inf\")\n", "\n", "for random_state in np.arange(0,10,1):\n", " bgmm = BayesianGaussianMixtureModel(K=10, D=2, alpha0=alpha0, beta0=1.0, nu0=2.0, m0=np.zeros(2), W0=np.eye(2))\n", " bgmm.fit(X, max_iter=1000, tol=1e-4, random_state=random_state, disp_message=False)\n", " if bgmm.lower_bound > best_lower_bound:\n", " best_estimator = bgmm\n", " best_lower_bound = bgmm.lower_bound\n", " \n", "plot_result(best_estimator, xx, yy, X, y)\n", "print(f\"lower bound : {best_lower_bound}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As was anticipated, the model does not work well with the data, which can also be seen from the smaller value of variational lower bound. Next, let us try out a smaller value of $\\alpha_0$, which is supposed to result in smaller numbers of components with non-negligible weight." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lower bound : -396.83871150380935\n" ] }, { "data": { "image/png": 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USiW33HILiz5ZyLPPPSsJ7xbI1RLgjsCfo4RUAE5/vlAQhPvOn70dKi0x/rn6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\nvYszNbp2KuJIBeMtaiIZSSpMdOJJc4dgE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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "alpha0 = 0.1\n", "\n", "best_estimator = None\n", "best_lower_bound = -np.float(\"inf\")\n", "\n", "for random_state in np.arange(0,10,1):\n", " bgmm = BayesianGaussianMixtureModel(K=10, D=2, alpha0=alpha0, beta0=1.0, nu0=2.0, m0=np.zeros(2), W0=np.eye(2))\n", " bgmm.fit(X, max_iter=1000, tol=1e-4, random_state=random_state, disp_message=False)\n", " if bgmm.lower_bound > best_lower_bound:\n", " best_estimator = bgmm\n", " best_lower_bound = bgmm.lower_bound\n", " \n", "plot_result(best_estimator, xx, yy, X, y)\n", "print(f\"lower bound : {best_lower_bound}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looks great! It is also much better in terms of the value of variational lower bound. \n", "\n", "Thus, we can see that, unlike the maximum likelihood estimation in Chapter 9, the Bayesian Gaussian mixture model can perform well even when we do not know the proper value of $K$, provided that we set large enough $K$ and $\\alpha_0 < 1$." ] } ], "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": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 2 }