{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Fitting Gaussian Mixture Model with Expectatoin Maximization Algorithm\n", "\n", "In this notebook, we implement the process of fitting Gaussian mixture models using the expectatoin maximization (EM) algorithm. \n", "\n", "Note : I have not followed any convergence proof of the EM algorithm, and do not know whether the parameter set obtained by the EM algorithm is indeed a local maximum. Hence, the treatment in the notebook is non rigoirous. \n", "It seems that the following paper discusses these points: \n", "\n", "Wu, C. F. Jeff (Mar 1983). \"On the Convergence Properties of the EM Algorithm\". Annals of Statistics. 11 (1): 95-103.\n", "https://projecteuclid.org/euclid.aos/1176346060" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib as mpl\n", "from matplotlib import pyplot as plt\n", "import time\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. \n", "\n", "* $N \\in \\mathbb{N}$ be the number of data points, and\n", "* $d \\in \\mathbb{N}$ 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 $x_n$.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# 2 Theory \n", "\n", "Here we briefly summarize the analytical results needed. \n", "For the derivation, please see the book.\n", "\n", "## 2.1 Model\n", "\n", "a Gaussian mixture model with $K \\in \\mathbb{N}$ components for the $N$ data points is defined by\n", "$$\n", "\\begin{align}\n", " p\\left(X,Z \\middle| \\mu, \\Sigma, \\pi \\right) = \n", " \\prod_{n=0}^{N-1} \\prod_{k=0}^{K-1} \n", " \\left[\\pi_k \\mathcal{N}\\left(x_n \\middle| \\mu_k , \\Sigma_k \\right) \\right]^{z_{n,k}}\n", "\\end{align}\n", "$$\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 \n", "* $\\mathcal{N}\\left(x \\middle| \\mu_k , \\Sigma_k \\right)$ is a gaussian probability density with mean $\\mu_k \\in \\mathbb{R}^d$ and covariance matrix $\\Sigma_k$.\n", "\n", "By summing over $Z$, we get\n", "\n", "$$\n", "\\begin{align}\n", " p \\left( X \\middle| \\mu, \\Sigma, \\pi \\right) =\n", " \\prod_{n=0}^{N-1} \\left[ \\sum_{k=0}^{K-1} \\pi_k \\mathcal{N}\\left(x_n \\middle| \\mu_k, \\Sigma_k \\right) \\right]\n", "\\end{align}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.2 Goal\n", "\n", "Our goal is to obtain a tuple of parameter $(\\mu, \\Sigma, \\pi)$ which \"maximizes\" the likelihood $\\log p(X|\\mu, \\Sigma, \\pi)$. \n", "\n", "Note that, as was discussed in detail in Section 9.2.1 of the book, this maximization procedure is ill-posed, and hence we expect that we obtain a parameter set that locally maximizes the likelihood. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.3 Algorithm\n", "\n", "\n", "1. Initialize parameters. \n", "2. E step : Calculate the responsibility $\\gamma_{n,k}$ by \n", "$$\n", "\\begin{align}\n", " \\gamma_{n,k} := \\frac{ \\pi_{k} \\mathcal{N}\\left(x_n \\middle| \\mu_k , \\Sigma_k \\right) }{ \\sum_{l=0}^{K-1} \\pi_{l} \\mathcal{N}\\left(x_n \\middle| \\mu_l , \\Sigma_l \\right) }\n", "\\end{align}\n", "$$\n", "3. M step : Using the responsibility obtained in the previous step, calculate the new parameters by \n", "$$\n", "\\begin{align}\n", " &{} N_k := \\sum_{n=0}^{N-1} \\gamma_{n,k} \\\\\n", " &{} \\pi_k = \\frac{N_k}{N}\\\\\n", " &{} \\mu_k = \\frac{1}{N_k} \\sum_{n=0}^{N-1} \\gamma_{n,k} x_n \\\\\n", " &{} \\Sigma_k = \\frac{1}{N_k} \\sum_{n=0}^{N-1} \\gamma_{n,k} (x_n-\\mu_k)(x_n-\\mu_k)^T \\\\\n", "\\end{align}\n", "$$\n", "4. Repeat 2 and 3 until a predefined convergence criterion is met.\n", "\n", "For a convergence criterion, we can use \n", "* the change of the parameter value\n", "* the change of the log likelihood\n", "\n", "as was stated in the book. Here we employ the latter; we terminate the iteration when the change of the log-likelihood\n", "$$\n", "\\begin{align}\n", " \\log p \\left( X \\middle| \\mu, \\Sigma, \\pi \\right) =\n", " \\sum_{n=0}^{N-1} \\log \\left[ \\sum_{k=0}^{K-1} \\pi_k \\mathcal{N}\\left(x_n \\middle| \\mu_k, \\Sigma_k \\right) \\right]\n", "\\end{align}\n", "$$\n", "gets smaller than a predefined value." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 3 From math to code\n", "\n", "Here we show how we can convert the equations shown above into codes, emphasizing vectorized implementations.\n", "\n", "We define a class `GaussianMixtureModel` representing Gaussian mixture models. \n", "\n", "\n", "## 3.1 Properties and methods\n", "\n", "We give the class the following properties\n", "* `K` : $K$, i.e., the number of components\n", "* `Pi` : (K, ) array, where `Pi[k]` = $\\pi_k$\n", "* `Mu` : (K,d) array, where `Mu[k,i]` = $\\mu_{k,i}$\n", "* `Sigma` : (K, d, d) array, where `Sigma[k,i,j]` = $\\left( \\Sigma_{k} \\right)_{i,j}$\n", "\n", "We also give the class the following methods\n", "* `_init_params` : method for initializing model parameters `Pi`, `Mu`, and `Sigma`.\n", "* `_calc_nmat` : method for calculating and returning a ($N$, $K$) array `Nmat` where `Nmat[n,k]` = $\\mathcal{N}\\left(x_n \\middle| \\mu_k, \\Sigma_k \\right)$\n", "* `_Estep` : method for performing the E-step of EM algorithm. Concretely, it calculates and returns $\\gamma$\n", "* `_Mstep` : method for performing the M-step of EM algorithm. Concretely, it calculates model parameters `Pi`, `Mu`, and `Sigma`, based on $\\gamma$.\n", "* `calc_prob_density` : method for calculating the probability densities $p \\left( X \\middle| \\mu, \\Sigma, \\pi \\right) =\n", " \\prod_{n=0}^{N-1} \\left[ \\sum_{k=0}^{K-1} \\pi_k \\mathcal{N}\\left(x_n \\middle| \\mu_k, \\Sigma_k \\right) \\right]$ for a given set of samples $X$. \n", "* `calc_log_likelihood` : method for calculating the log-likelihood $\\log p \\left( X \\middle| \\mu, \\Sigma, \\pi \\right) =\n", " \\sum_{n=0}^{N-1} \\log \\left[ \\sum_{k=0}^{K-1} \\pi_k \\mathcal{N}\\left(x_n \\middle| \\mu_k, \\Sigma_k \\right) \\right]$ for a given set of samples $X$. \n", "* `fit` : method for fitting. Concretely, it runs `_Estep` and `_Mstep` alternately.\n", "* `predict_proba` : method for calculating the responsibility $\\gamma$.\n", "* `predict` : method for predicting which class a input is assigned to.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.2 Calculation\n", "\n", "Before starting coding, we first specify some details, and rewrite some equations so that they can be directly implemented.\n", "\n", "### Initializing parameters\n", "\n", "In `_init_params`, we set initial values of parameters as follows:\n", "* `Pi`: equally distributed.\n", "* `Mu`: $K$ vectors randomly chosen from the input data points, and\n", "* `Sigma`: $[\\Sigma_0, \\dots, \\Sigma_0]$, where $\\Sigma_0$ is a diagonal matrix, whose $i$-th component is the variance of the $i$-th feature of the input data.\n", "\n", "\n", "### E-step\n", "\n", "Let us define arrays as follows:\n", "\n", "* `X` : (N, d) array stands for input data, where `X[n, i]` = $i$-th component of $x_n$.\n", "* `Gam` : (N, K) array, where `Gam[n,k]` = $\\gamma_{n,k}$\n", "* `L` : (K, d, d) array, where `L[k,i,j]` = $\\left( \\Sigma_{k}^{-1} \\right)_{i,j} $\n", "* `Diff` : (N, K, d) array, where `Diff[n,k,i]` = $x_{n,i} - \\mu_{k,i}$\n", "\n", "Note that `Diff` can be easily calculated by utilizing numpy broadcasting.\n", "\n", "Then, the calculation for E-step can be rewritten as follows:\n", "\n", "First, we calculate `Nmat` by `_calc_nmat` as\n", "$$\n", "\\begin{align}\n", " \\verb| Nmat[n, k] | = \\frac{1}{\\sqrt{\\det \\verb|Sigma[k]|}} \\exp\\left( -\\frac{1}{2} \\sum_{i,j=1}^{d} \\verb| Diff[n,k,i] L[k,i,j] Diff[n,k,j] | \\right)\n", "\\end{align}\n", "$$\n", "Then, using the result, we calculate `Gam` by `_Estep` \n", "$$\n", "\\begin{align}\n", " \\verb|Gam[n,k]| = \\frac{\\verb|Nmat[n,k] Pi[k] |}{ \\sum_{l=1} \\verb| Nmat[n,l] Pi[l] |}\n", "\\end{align}\n", "$$\n", "To vectorize the summation, numpy.einsum function will be used\n", "(For detail, see https://docs.scipy.org/doc/numpy/reference/generated/numpy.einsum.html ).\n", "Also, note that the inverses of several matrices can be computed at once by numpy.linalg.inv (See https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.inv.html ). \n", "Same statement applies to determinant( https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.det.html ).\n", "\n", "### M-step\n", "\n", "The calculation in M-step can rewritten as follows:\n", "$$\n", "\\begin{align}\n", " \\verb|Pi[k]| &= \\frac{1}{N} \\sum_{n=0}^{N-1} \\verb| Gam[n,k] | \\\\\n", " \\verb| Mu[k,i]| &= \\frac{1}{N_k} \\sum_{n=0}^{N-1} \\verb| Gam[n,k] X_[n,i] | \\\\\n", " \\verb| Sigma[k,i,j]| &= \\frac{1}{N_k} \\sum_{n=0}^{N-1} \\verb| Gam[n,k] Diff[n,k,i] Diff[n,k,j]|\n", "\\end{align}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.3 Code" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class GaussianMixtureModel:\n", " def __init__(self, K):\n", " self.K = K\n", " self.Pi = None\n", " self.Mu = None\n", " self.Sigma = 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", " 2-D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " '''\n", " n_samples, n_features = np.shape(X)\n", " rnd = np.random.RandomState(seed=random_state)\n", " \n", " self.Pi = np.ones(self.K)/self.K\n", " self.Mu = X[rnd.choice(n_samples, size=self.K, replace=False)]\n", " self.Sigma = np.tile(np.diag(np.var(X, axis=0)), (self.K, 1, 1))\n", "\n", " \n", " def _calc_nmat(self, X):\n", " '''\n", " Method for calculating array corresponding $\\mathcal{N}(x_n | \\mu_k)$\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2-D 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", " Nmat : 2D numpy array\n", " 2-D numpy array representing probability density for each sample and each component, \n", " where Nmat[n, k] = $\\mathcal{N}(x_n | \\mu_k)$.\n", " \n", " '''\n", " n_samples, n_features = np.shape(X)\n", " \n", " Diff = np.reshape(X, (n_samples, 1, n_features) ) - np.reshape(self.Mu, (1, self.K, n_features) )\n", " L = np.linalg.inv(self.Sigma)\n", " exponent = np.einsum(\"nkj,nkj->nk\", np.einsum(\"nki,kij->nkj\", Diff, L), Diff)\n", " Nmat = np.exp(-0.5*exponent)/np.sqrt(np.linalg.det(self.Sigma)) / (2*np.pi)**(n_features/2)\n", " return Nmat\n", " \n", " def _Estep(self, X):\n", " '''\n", " Method for calculating the array corresponding to responsibility.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2-D 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", " Gam : 2D numpy array\n", " 2-D numpy array representing responsibility of each component for each sample in X, \n", " where Gamt[n, k] = $\\gamma_{n, k}$.\n", " \n", " '''\n", " n_samples, n_features = np.shape(X)\n", " Nmat = self._calc_nmat(X)\n", " tmp = Nmat * self.Pi\n", " Gam = tmp/np.reshape(np.sum(tmp, axis=1), (n_samples, 1) )\n", " return Gam\n", " \n", " def _Mstep(self, X, Gam):\n", " '''\n", " Method for calculating the model parameters based on the responsibility gamma.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2-D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " Gam : 2D numpy array\n", " 2-D numpy array representing responsibility of each component for each sample in X, \n", " where Gamt[n, k] = $\\gamma_{n, k}$.\n", " '''\n", " n_samples, n_features = np.shape(X)\n", " Diff = np.reshape(X, (n_samples, 1, n_features) ) - np.reshape(self.Mu, (1, self.K, n_features) )\n", " Nk = np.sum(Gam, axis=0)\n", " self.Pi = Nk/n_samples\n", " self.Mu = Gam.T @ X / np.reshape(Nk, (self.K, 1))\n", " self.Sigma = np.einsum(\"nki,nkj->kij\", np.einsum(\"nk,nki->nki\", Gam, Diff), Diff) / np.reshape(Nk, (self.K, 1, 1))\n", " \n", " def calc_prob_density(self, X):\n", " '''\n", " Method for calculating the probablity density $\\sum_k \\pi_k \\mathcal{N}(x_n | \\mu_k)$\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2-D 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 : 2D numpy array\n", "\n", " '''\n", " prob_density = self._calc_nmat(X) @ self.Pi\n", " return prob_density\n", " \n", " \n", " def calc_log_likelihood(self, X):\n", " '''\n", " Method for calculating the log-likelihood for the input X and current model parameters.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2-D numpy array representing input data, where X[n, i] represents the i-th element of n-th point in X.\n", " Returns\n", " ----------\n", " loglikelihood : float\n", " The log-likelihood of the input data X with respect to current parameter set.\n", " \n", " '''\n", " log_likelihood = np.sum(np.log(self.calc_prob_density(X)))\n", " return log_likelihood\n", " \n", " \n", " def fit(self, X, max_iter, tol, disp_message, random_state=None):\n", " '''\n", " Method for performing learning. \n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2-D 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", " Maximum number of iteration\n", " tol : float, positive\n", " Precision. If the change of parameter is below this value, the iteration is stopped\n", " disp_message : Boolean\n", " Whether or not to show the message about the number of iteration\n", " '''\n", " self._init_params(X, random_state=random_state)\n", " log_likelihood = - np.float(\"inf\")\n", " \n", " for i in range(max_iter):\n", " Gam = self._Estep(X)\n", " self._Mstep(X, Gam)\n", " log_likelihood_old = log_likelihood\n", " log_likelihood = self.calc_log_likelihood(X)\n", " \n", " if log_likelihood - log_likelihood_old < tol:\n", " break\n", " if disp_message:\n", " print(f\"n_iter : {i}\")\n", " print(f\"log_likelihood : {log_likelihood}\")\n", " \n", " def predict_proba(self, X):\n", " '''\n", " Method for calculating the array corresponding to responsibility. Just a different name for _Estep\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2-D 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", " Gam : 2D numpy array\n", " 2-D numpy array representing responsibility of each component for each sample in X, \n", " where Gamt[n, k] = $\\gamma_{n, k}$.\n", " \n", " '''\n", " Gam = self._Estep(X)\n", " return Gam\n", " \n", " def predict(self, X):\n", " '''\n", " Method for make prediction about which cluster input points are assigned to.\n", " \n", " Parameters\n", " ----------\n", " X : 2D numpy array\n", " 2-D 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", " 1D numpy array, with dtype=int, representing which class input points are assigned to.\n", " '''\n", " pred = np.argmax(self.predict_proba(X), axis=1)\n", " return pred\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 4. Experiment\n", "\n", "Here is a toy example, in which data is generated from a Gaussian mixture distribution.\n", "\n", "## 4.1 Preparation" ] }, { "cell_type": "code", "execution_count": 3, "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": 4, "metadata": { "scrolled": false }, "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": 5, "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 Results for $K=3$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n_iter : 23\n", "log_likelihood : -515.3221954638727\n" ] }, { "data": { "image/png": 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hg7DvGkVRejqrX/wfo599Aa/gkEY/nuTadOjQITzlvnXB+2I/fvUz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\nyaGZf08yclNJz0mhU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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gmm = GaussianMixtureModel(K=3)\n", "gmm.fit(X, max_iter=30, tol=1e-4, disp_message=True, random_state=0)\n", "\n", "plot_result(gmm, xx, yy, X, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the data is properly clustered as we expect intuitively. \n", "However, depending on the initialization of model parameters, different results can be obtained, as follows:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n_iter : 29\n", "log_likelihood : -533.6831531127243\n" ] }, { "data": { "image/png": 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XbNq0ifLy8lq6YlltkQN4AxuqtKn8qW6OcUmS6DHlfs6ow8gUyehEMSmcI159hh5TpuDs\n6UMWaRbHZEgpeLfvgNbFBR3FFttMwoTeWILWwbLLDaAkLxe1Ultl5TZ7nChMtwzQWQnx/PDYTI5/\nvpq4lX+w7n/PcfC7b+TMSTLZPwghyLtQwKm9Z9j02Z+kbs+jrb5z5bgSkzCRo0pH0UPH7B+nEG8X\nYXEPGYWRC1IKo+4YQRZpVe6vDJKw76ghL7OAj2Yv517fR3h5wrsc3RrOmYgotAZ7i/0VkgInK1fO\nnTtXWWY2m3ng/gfp1b03bz79Ho9OmY1/85ZyqtNGRh7E1ogMVdqw87yOI1w7GUrbfgPQ2Nhw4pdf\nOJcVi2sLf26ZtAjPNu3o89AMtr/zFjpjMfZmJ/KU2aRbJTPuvtfR5eWyM2YpTnpXbCUHTMJEnOo0\nnu0CsHN1q3Iee3d3ykUZpaLEIndxrpSFW6tWlf8WZjPb3nmLNiUBeEoV81PLhYGwXfvw6RiMf/ce\ntfRbkskaJ2O5kfRzmVxIyiYrJZf8CwUUZhdSmFNMYW4RBdlF5F8oICc1F32pofI4Jw9H+gzvSXLJ\neQ6d3QtaMw/OeIDnn38elUpFQJelnD1+FDedL2ZMZNomMeGuCdx555289spiEs9G0cLYHoWkoFDk\nkmgTxXfffkbXrl1JiEhi+8o97Ph+DwfWH8XaxQGlVQ78YyFGkzCSrc+kY8eOlWXfffcdf6zfRkjp\n0MpPcalF55hw+11EnDklD2JtJORBbI3MxWQoKpWyShDPiD7L8Z9+IjclGUdvH7rdfTfNOna6bD05\nSYlEbPqNgpQ0XNu0otNt43Hw8Kw4x7Y/OPbjKtSSFr2xBM92AQx7+lk0dnaXrev4r2uJ2vQnbfVB\n2GJPlpRGgjqaca+9gUvzijZmxkbz1xvv0rNssMXNnSoSKOuqYuTz/63/HeubPIitYaTFZ7Dj+72E\nbjtB/InzGMosu5k1WjUOrvbYu9jh6O6Ao5s9bs1ccfJyYP/xPfyxewsGSc+k+yayYOEC7O3tq5xD\nr9ezfPlyfvx+DRqNhhmPPsTEiRNRKBSkpaVx1x13ExERgVZlg0lRzieff8KkSZMs6ig3lLN/3VHW\nLvmN2NAETBgxCzOllJBsE8Ogsf358acfKvfv16sfxUcFHlKzyjIhBMds/iL0xFHatm1by79J2T9V\ndxCbHMAbocsF8dTICLa/8zatDAE4404BOcSpInFq7oskJHy6dKLjLWPRVnMkqdGgJy81Ba2D42Xf\nvP9JCEHUrh1E/LYRXWEeHq3b0WPyfbi3al25T9qZ0+x7bxkhZQMsjs0QyRQEGRiz4KXr/C3Irocc\nwOtXZmIWnzz1DYc2hiJJEoG92xLYqy2tOvvj1dID9+auOHk4orW1rnKs2WxmQN8BJJ1Mx7usJRIS\n6ZoETE56fJv54uHpwZPPPMGIESOq3Z7z58+Tl5dHx44dsbKqmsjon7av3cXSpz+lPB1MkpHWg315\n/5c3cHC+9PDQvXMI4pS2Mh0xVPwdCLfbw+6DOwkODq5222TXr7oBvFa70CVJehx4EAgGfhRCPPiP\nbcOAT4AWwBHgQSFE9UZt/cdcXII1uhOVucWPrVpFO0PHyu5pG+ywMmqISggnkK5kph4nds9u7njr\nvWoFcZVag3vL1tfcDyq+uQcOHUHg0Cv/QfFo045SUUyByMXx77SHZmEmTZNIcL8J1TqPrPGQ7+Ur\nO30gihfHvIHZZGbqy/cwevpQ3H2rn7Zz586dxEbG06msf2Vvlb3eiSOZO8jOLKQII/fsmciixS/x\n9DNPV6tOf39//P39q7XviLuHMOLuIcSdSGDVq2s5sOEYDwU8zeQXJzD20RFYqa24Z/LdfBz7OS6l\nnpVtzCUTja2aoKCga5xBVl9qexBbGrAY+OafhZIkuQHrgIWACxAKyJkxLsNkMmIymyqToRiNJo5E\nJJKVdA5XLOeLu+JJGSU440GgsSsOxQ6c3vJ7g7RbpVYzaNbjnFQfIkZ5ikQRQ5j1PmxaedJ2wOAG\naZPshsj38mWUFJSweOISnL2c+Or0Eu5/6e4rBm8hBDqdrsogs9DQUOzLXCw+NUmShDs+CKCZ1JIO\nul4seHEhRUVFdXYtbbq05OV1z/Px4Tfw79icT59ewcPBz3Hwt2M8/vjjeAe4E2l3mEQRQ7w6gjjb\nU6z64XsUCnnsc2NRq2/gQoh1AJIkhQC+/9h0JxAphFj79/aXgWxJkgKEEFXnQfwH5RfnsOXQGhIy\nowCJ1l6BjOg5AXFSiySZiFM7UlxWgBOXurtLKESDFunvTAUe5T6knjhBj0mTG+QaWvbsjaufPzF7\ndlFaUEjvrmNo0S0EhUJ57YNljYp8L1/e6sW/kpuez0eHXsfL3+Oy+wgh+OjDj3hj8Rvk5ufh7urO\nSy8vZPpD01Gr1fj5+WHQ6vjXZBCKKcCNiimeNpIdjmpnwsPDGThwYJ1eU0DPtryzYxFHt4bzxZyV\nLLrjHUJGdebn73/hWORh/tqxE1/fZkybPg1fX99rVyirN/X1KBUEnLz4DyFECRD/d/l/XrnRwLdb\nl0CmxAAxlpYikIT0aD797RW273kTQ/5JBnUeRZTyJCWi4olcJ4o5QygtaFP5JF+GDu2/kiDUNwdP\nL0LuuZcBDz+Cf0gvOXjffP7T9/KxP04QMroLAT2vPIhr2bJlvLbgdVrmdKKnaRilFww89thj2Gpt\nGXfrOHr37o1JW06yFIdZmDALM8kijkLy8KTiE5kQguLyQjw8Lv+QUNskSaLXmG58efI9Zi15kDOH\nYnis2/PoIsx8/NFHLHxpoRy8G6H6CuB2QMG/ygqAKkMuJUmaKUlSqCRJoTp98b8333SEMHMseg/q\ncg3+BJBOEukk0o2BDJMmEFDWjV3HNqFSqujdaTBhyn3sUW7hiLQDhaTClzYA6EQRiZpYgsaMaeAr\nkt3kqn0vg+X9nJWVVeeNq0ulxaUknU0hoEebK+6Tm5vLK4tepVVJMDbYcZy9uOHFYMbT33wrZ7bF\nM2LYSHbu+QvXHrYcVG/lgGozCdJZAuiKSlJhFmYSVVG0D2hPQEBAPV4hqKxU3Pn0rXwb/RGDJvZl\n9eu/8nCn5zi5O7Je2yGrnvqaB14M/HtklQNQ5QOPEOJL4EuoGIVe901rODEpEWw5tAa9vhSjKOck\nBykkj870xV6qeJN2lFxoZ+rM/lN/MvuORfTqMJTw1AziAiQubP6Jg5nbsFbaUmoqosekKRZJSWpC\nCMG5wweJ2bkLs9FI64H9aTtgMEqVvGSADLiOexks7+eQkJAmfT8X5+swmwWuPs5VthUVFTH9wYfY\nvPl3yvUmIjiMK57Y4Yi/dCkItzR1IDL7MDExMRw4vJ+cnByEEKz7dR1znvsfmcrz6MpLCAwKZP3G\nqisdXq/ExESWvLeEsGPH6dAxkGfnPFuthwJnTyfmrXySkQ8M4cNHv2DO0Je5deYIHn5nCrYONjfc\nLlntqK+/ypHAAxf/IUmSLdD67/L/pIzcFDbs/Y4OphCccceMiRhOoacUeyy7wR1woUCXC4BSoaSL\njwfRobsxmQRaDx9a9+5OpzHjUGurrqd8vfZ98Smph0/QXN8SBdZEJPxKwsFDjJ7/IpI8eEX2H76X\n7ZwrFjIqyiupsm3yxMlE7Iyil34kKsmKfJFDOPvwp32VfbV6O2JjYwFwdXXlxIkT7Nu7j3Zt2tG6\nXSsem/0YgwYNuuH2RkZG0r9Pf1zLfLAvd2Z32CHW/NiLrdu20K9fv2rV0W1YMF+cfJ+Vi37i16W/\nc+yPcOZ88xhdh8rTyBqDWv2LLEmSSpIka0AJKCVJspYkSQWsBzpKkjTh7+0vAaf+C4NeruTY2d34\nmlvhInlUJA2RVLSnC0pU5GHZ1ZjLBdzsK0agm80mVm9fRmH4YVqmueOb4kz0xu388elnN5xjPDc5\nkYRDh+im74e35Ien1Jwu+r7kxyWSfOrEDdUta1rke7kqaxsNNg5aMhIuWJSnpKSwa9duWumDUUkV\nc7CdJFfcaUY26VXWOC9S59G5c0XmsW3btjGw30COrjmF+aSWsA0R3DH+TmJiYm64vXOe+R+exX60\nNHbATfLGzxSAny6Ax2c9cV31WNtomPnuVJbuX4za2ornh7/Kp0+vwFBmuPbBsjpV269UC4BSYB4w\n5e//XiCEyAImAK8DeUAvYNKVKvkvKCjOw0ZY9kQqJAVWqIngCNkiHYPQc0GkEqs8xZDutwEV3e6F\neXl0MvXFQ2qGl9SCEEN/ssNDyYxPuKEgnhZ5GjfhXflH6GKb3Mq8SI04VeN6ZU2SfC//iyRJdOjT\njsgDls8qaWlp2KsdUEqWAza9aE4xhURL4ZSKEkpEEbGaE7Ro05yhQ4cihOCxR2bTWteJFqIdrpIn\nLY1BuBU144V5L95we/ft34enaGFR5oEvEZGn0Ov1Vzjqyjr0bsdnx9/l9sdvYf1HW5jdYx4J1UzA\nJKsbtRrAhRAvCyGkf/28/Pe2HUKIACGEVggxWAhxvjbP3dT4erYiV2kZbA1Cj0lh4pa+95DhmMRh\n5XayndO5Y9CDtG1WsU5xQlo0rkZvizmkKskKT8kbEXGO/HxdjYO4xt4evbJq5iODlR5rOVfwf4p8\nL19ep4FBnI9MJislp7IsMDCQovICyoTOYt9CdQ7TZkxj5ANDiHQ4TKxzGONm3MLOPX+hUCjIzc0l\nNS21yvoOHmZfdu/efcNtdXRwpAzLNhkoQ6OxvuZqbVdibaNh9kfTeWPLCxRkF/J4r/ls+uxPOWFR\nA5E/ajaQHgEDKbDKJZZTFIl8skU6J1UH6dF+IF1a92HmuPnMm7yEGWOfp02zSzN0bG3s0SuqBtky\nqZRuWhecUkSNg7h/954UKQrIFCmVN2SeyOKClEa7ATf+TU4ma+oG3t0bgJ0/7K8ss7e3Z/4L8zlr\ne4wLIpUikU+C4gwFtlksWvQSX69YTl5BLlm5WXy87GMc/n4YtrW1RZKgHMu34TJ0uDpXf2W3K5n9\n5GMk2URjFBXrs5uEkfPaM0x78MEbXoylx+iufHHyfToP6chHs5fz6t3vU1JQdWyArG7JAbyB2Frb\nM+PW53Fv40WMzUmynFMZ3PNWhnW//arHdW7dmwtSCjkigzgRwX6xhd1iI4WmXLxcfBmqtMEpRVBc\nfP1dZFbW1ox54SUSnOI4Yr2Lo9a7OWMbzvBn52DrcvU/KEIILsTHknL6FOVlpdd9bpmsKWjWxpsO\nfdqx7btdFm+dLy54kU++/hjrbmYymsUx6P7ehIWHXnXutLW1NZMm3UuC9RmyRQZhYg+7xW9ESIfp\nO7DPDbd17ty5jJ10C0c12znrcJSj1jvoNTqE95a8d81js7Ky2L59O2fOnLniPs4ejizeNI+Z79zP\nwd+O8VjIXOJOJNxwu2XVJyczaYKik0/x6+5vcMKVNnREiYoU6Rz51lnMGr8AtZU1fxlLKGxmpnfX\n1te9mIowm8k6F4fZbMa9VZtrTiHLT0vlz7dex1hUhlqyptiUT+8Hpl117XRZ7ZKTmdSf7Sv38M6D\ny3hj64v0GHVj0zZ1Oh1DBg0lLDSMALrhiidF5HHe5ixvLXmDmY/MBMBgMGA0GrGxuf4pXBkZGZw9\ne5bWrVvTokWLq+4rhGDu8/P4ZNkyXDQeFJXn0yG4Axt//w03tysnPTp9IIrXJy2lMKeIpz9/hBFT\n5R67GyFnI7tJJF2IY9fxTWTkpeBo40Ib3yBOxB7AWG6iP2NQSJc6USKUhwnpPgAba3t2HFtPQWke\nCpUVwaPHEDLxXhTK2l8VTZjNrHliFj55vjQTLZEkiRJRSLj6IGMWvWyRsUxWd+QAXn/KDeXc32o2\nzdv78O5fL1f7uNLSUl5e9Aorv/0OvcHArbfeSkFBPn9s+ZO2ojM+0qX0wYUij/OuEZyJPsPsWY+z\nYcN6TGYzXTp14cuvv6Br1651cGWwatUqnnn0OTqU9EItaTALM+fVZ2g3yJ+t27Ze9di8CwW8Pmkp\nJ3dHMn72aB5d8gAqK3n9iJpokGxkstqVfCGeNTs+o5WpI71oT1FhPmFn9mGDPY7YWARvAEejGzHJ\nEaRkJhBo6oYzHpSWl3Bm6wFS03LwGXU7vYL90OXnEfnnVrJi4nBs5kPHW8bg6O1TozamR58Fnbky\neAPYSg40M/oTtWMb7jNn3fDvQSZrTKzUVtwzZzyfPfstx3ecotvwTtc8RgjBraPHEns0Af+yYJSo\n2LfmMGnmRBzsffFw6g4aLViFZ4v+AAAgAElEQVSpwCxwMLfAxajhtlGPkJeQSW/zGJQmiYwTSQwd\nNJTIqEh8fHwQQrB582a+Wb4Cg97ApPsmMmnSJFQ1XHjpoyUf0aykDWpJA1TMQvEzBLB37zaysrJw\nd3e/4rHOHo68vW0hy+et5pclm0g4ncTCn5/Fyd2xRm2RXZv8DbwR23NiCy1NHfCR/FBL1rhKXnSh\nHyUUUEhulZGfJaoC8gpzaGkKxEWqSANoI9kRbAwhL/wQep2OvXvD+GXOM1zYHI7zGWtKdiawfv7/\nSI+68reuqzGUFKORtBaj4gE0ZmvKCgprfO0yWWM29tEReLRwY/n81ZjN5mvuf+zYMU6EnaBdWVfs\nJEe0ki1tbfvQp9vTdO04DaWPNzjYgUoFGjVmO2t8PHpgq+6Cb/tRWPXshqJzID4t+9Pctjcff/gl\nAM889QwPTprO2d/Ok/BHJv97dC7jxo6vVpsuJy8vDw2WOcwVKLFSaSgo+PcKulUpVUoeeW8qc1c+\nwdnDsTzecz4Jp5Nq1BbZtckBvBHLzEvBBctkBvaSEwKBhEQMJykXBszCRJKI44IpFaPJgAOWSz1q\nJGvUCjUtjheQsXMzXjpfAoxd8JCa0drcgXb6Thz46ssatdGzXSD5xiyLKTRCCDI1aTQP6V6jOmWy\nxk5treaBVyYSG3aOv1bvu+b+J0+exBn3S71mCgW09UMhFCTG7uBw6FLyj+9DRMRQciqUo+HLMGv2\nkBD1C0Sdg+R0MBjA1QnPlv0I3adi6l0fsX3zOYKVI/GVWuEj+dGhpDehB8LYtm1bja5r9JjRZFml\nWZTlk42NrZZWrVpVu57hUwaydO+rlBuMPN1vAUe3hteoPbKrkwN4HcspzGTDvpV8uu5VVm9bxrn0\n6i9Y5WznRiF5FmU6UZHgpQv9KcfAPjaziw1kkoyt5IDGyppc6UKVY0wY6e7rgy4+Bp8qizs0Iz8z\nDX3J9U8D0To40O3Ouzmu2U8ycWSKZE5qDqP0tqFNv7pNgyiT1Sez2cwXX3xB9y4hBLbrwJ7o7bTp\n5s/yeavRFV195kXr1q0pkvIv9Zo19wKNmqS4HZCdR0tTOyIJZRfrOcpOHHAhNDSMC2UJmPPyIfUC\nRCVA6GmSYjbRrqMKo7kUb/fuqIICoHsQtPRF4eSIQ4knWzdf/Xv1lby48EX0LkXEak5yQaSSpIgm\nxiacz7/67LqnnrXv0YZlR97Ep40XC297k02f/VmjNsmuTA7gdSi7IINvNr9LcWIRrUqC0GTasG7X\nN5w6d7Rax/fvPJp45WnyRBZCCEpEEREcrhjpTQHu+GCLPT740UMaQhtzR/TlZSQqYkgV59CLMnLF\nBU6rjtCv4yhUSits1TboKcMoykkT5zkvosghEwBlDRd36HL7nQyd8xymHnbkdzAQcN9YbntlMSq1\nukb1yWSN0bQHprPouVcxn7TGLtaTVUt+4mDWLvIy8lk+b/VVjx08eDAevu4kWJ2hXBgQrk7oclJI\nLArHjBkNWjzwQYmKHgylgxSCo8qFDkEdiNIep0jkUyZ0JCjOUqhMZvHbjzB+oj+xUasQ0QkYCrIx\nuzlAYCtahIwnO92NIwfjMBmvryvdy8uLU5EneeiF+3EbaMOAqT3Zd3Av48aNq9HvzN3XlSV7XqHn\nmG58NHs5Xz3/fY2792VVyaPQ69Cve75Bn6y3SGhQIHI5ow7lniEzEQiaufqhVF55wElEwjF2hm2k\npKwAK5WGkPYVb7WHTv+FA8540wIvWiBJEkUin2htOBMGP8SusE2k5Z7HztqRPsHD6dK6D5IkcTBy\nO0dP7KHUXIITblij5QKpaFwcmPjxJzdl/u7shHOc2LKRvIw03Jq3oMutt+Pc7ObKbSyPQq9bMTEx\ndO8SQo/SYSilivtVCEGU7TFu6T6e8/vSmbt2NsMnDL5iHVlZWTwy41G2bN1Mny5zQJnBI08NZ/7z\nL3AhORtXPGlBW7RSRdKUGLvjvPHZq8REx7D8y6/RleoYM+YW3nz7TVq0aIFOp6OZdzOkQivK0OEh\n+aJ0dEHr6o1/8+7o9WacXWwZOqIjI2/tRKs2nvXxq7osk9HEJ09+w6bPtzHsvgE89/UsrNTX/8JQ\nVlbGp599xuqff8ZKbcVDU+5n+vTpKOtghk1DkqeRNQIfrl1Ah7IQbKVLy5AWijzC2IONyg6lpMJA\nGeP630873ytn9xFCYDDqsVKqK7uxvvjtddwLK9ZCvyhKCsenTQtG97r7inWZTEbe+2ku7U0V38AB\nTMJEuOYAnR+8h4DBw270shuVlNOn2PbRe9gPG4ymRQvK4uIo2XeQsfMX4d7y5pniJgfwuvX999/z\n0mOv0aakc2WZEIJw9lIiFdFbGkE55biNsubHX1Zfdb62Xq/n3nEfM2BIIM/Mu5WNGzcy476ZdCzu\nW7meuk4Uc8J6H0kpibi6XnkRpUWLFrHktQ/pIYZWHntBpJLjncqaH//krz9Pc3h/DEajmVZtPBg5\npjNDR3bE2cW2ln4z1SeE4Mc317NiwY90H9mZRb/OQWtrfe0D/2YymRg4dChR+XlY9emJMJko37Of\nYSE9WPvDD3XY8vpX3QAud6HXITutIyUUV/7bJEycYD8dCKGncRghxsF0KA9h/d5vKSjJvWI9kiSh\nsbK2+AY1tt99xKlOE6UIJ1nEcUp5iFJtEQO73HLVNl0oSEctqXHn0rQxpaSkub4V4Zu33XBGs8bm\n4A/f4XzPBByHDMK6dUucRo3AfvQIjvx8c93wsrrl4+NDqVRsUZZELEZM9BYjsRIabIQdqdtzeeap\nZ65al0ajIaBjM06fSgZg7NixDBjWjwjbAySKGBIUZ4nQHuTd99+5avAG2LdrPy1FgEUiFXd80BeX\nYW1bzKI37mLNxqd5/LnRqNUqPv9oO5Nv/5A3X17PmYiUel3DXJIkJr9wJ88tn0X4jlPMG/kahbmX\nTSN/WZs3b+ZsagoO0+7HpkMgtsEdcZj5EH/s2EF4+H9zkJwcwOtQn+BhnFNFUiIq/k+aQRI22OMp\n+VZOu3KS3PAQzTgVf+S66m7m5s+s8Qtp27ED2lY29AwZzMxxL2CjsbvqcRU3rFRl2peEhHWx+YaS\noTQ2RoOB/KREbDp2sCi37dKZzOizDdQqWVM0ePBgbF1sSFLEYBZmhBAkE0d7umAlXRrr4WzyYNPK\nPzAajVetr2t3f5LOZ5OZno9CoWDturV89/MKBs/ozfgnR7P/8D4ee+yxa7bLLMzAv+5lSUJCqgzO\njk42jJ8QwsfLp7N89SPcdmcIhw/E8dQj3/LYtK/Z8ttx9Pry6/+l1NDo6UNZ8PNzxIadY86Ql8nL\nzK/WcXv27oWA9kj/eJFRqK2wDmzP/v37r3LkzUsO4HWog183+nYeQbhqL0eU24mWTlZ+3/onjdka\nXVnxZWq4OnsbRwZ0uoVx/abQrW0/rFTXHjTm5eyLpJLIFumVZWZhJlV1jh7te95QMpTGRqlSodJY\nY8yzHMlfnp2NtaNTA7VK1hQplUp27vkLl262HLHeRqjtTsolA9ZoLfYTQtC2vBOZKVlXrW/gkEAk\nCbb+fgIAhULBmDFj+PKrL3h/yXt06nTtxWEApk67nyzb5L8DeYVskY5Kq6Bbt25V9vdr6c5jT49k\nzW9P8eScWzCZzCx9ewtT7lzG6hX7KCmumiipLgy4sxeLf59Penwmzw1eRHZqzjWP8fH2Rpl/mWCf\nm4enZ8N9329IcgCvY707DOXZe95iypgneXDUs+QpsiqzA0FF8MxSpdPSJ6Be2qNQKLhz0DSiVMc5\nowglTpzmmGonLu4edGnTpzIZys0QxCWFgsBhI8n/ZQMmXcU0H1NhEQUbNhE84vKfGvJSU9j33XI2\nv/cGYevXUlooL0Yjq+Dn58ehoweJjoviWPgRxowZQ6Yi2WKfXDKxktQsm/X1VUdbe3o70aN3G7Zu\nOnFDb79Tp06l+8CunLTbRzynibU+wTm7CNasXXPVgV1aGzW33dmdL1Y+zHvLptA2wItvv9rDlAnL\nWLl8T70E8m7DO/HG1hfJScvj2UGLuJB09YeeKVOmoD9zFl3kGYQQCLOZ4sNHITvnsqPkDQYDK1as\n4Jbx45l433389ddfdXUpDUYexFbPNh9aQ9z50zQztkKJkjRVIo6uzkwePvuGU/z9W2ZeKodO7yAr\nLx13Z2/6Bo/Aw6ni27dOX0zk+TBKSovw82qLv2c7i271nSYd+b4STk42BLX0utIpGj2TsZx9335F\n/KEDqF1cMOTm0mHYKHpPmmLRFQeQEnGSbR+9h12/Plj5eFF2Jhpj3DnufPWta2Zja2jyILb6FxUV\nRd9efXEu88LB4EKxqoBMdRKvzHqTLUt28eBrk7jvxQlXPP5E2Hn+98QqHnliOHfd2/uq5zIYDHz5\n5Zes+nY1kiTxwENTmTFjBiqVCiEEe/bsYdeuXXh4eDBp0qRrfju/nLjoDFat2MeBvdHYO2i5d2pf\nxt/VA7W6blfcjjoay7xRi3Fwtee9nYvwaHHl5Vr37t3L5KlTKTYYMBuNeLm7s+6nn+jYsaPFfuXl\n5QwbNYrTGemounfFXFqKYf8h5jz+OC8tWFCn11Mb5FHojZQQgqikE5yMPYzRbCSoZTc6te6Nspan\nbyVfiOeHHZ/S3NwGR+FCgZRLijKOycMfx9e9ZbXquFmCOEBpYSHF2Vk4eHqhsa36GUMIwY9znsBm\n7GhsggIry/N++x0vhYZBDz1an829bnIAbxjJycksXfIBxw4fIzAogGeee4aAgADeuv8jdq85wFvb\nFtJ16JVnmMx9ajXxsZl8t3Y2traay+4jhGDUiNGcPnQWD11zADJtkugxuCu//f5blfEsNyouOoNv\nvtjFscPx+Pg689hTI+nVr22tnuPf/hnE39/9Cu6+V34AMZvNREZGYmVlRfv27S97/T/99BOzXlqI\n46yHKx/UjYWFZL+9hHOxsXh5Ne6/Z3IAb4KEEJzPjCEhLQqttR0d/UOwt6lZIoBvNr+LY6473v+Y\nZpYmzlPkmse0Mc9Vqw6TycifJRkY2jnh4GxfWd7Ug/nllOTmsmbuU/guXmTxB8GQnkH+iu+Z8sHn\nDdi6a5MDeOOiKyrlsR7PcyE1m4D7mzFq/AhGjBhRpZctJiqdxx/6mjvu6cmsp0Zetq6dO3cycfy9\ndCruX7kUq1mYOGG7l03bNtK3b99qtSkrKwuj0Yi3t3e19g89Es+nS7eRnJTDgMEBPP7caFxcrz5I\n9kZEHY1l7ojXcPF2YsmeV3H2rPk4lclTp7KtrASH/pa/m5Lvf+TD5+YwadKkG21unZKnkTUxZrOZ\ntbu+YsOu70iNTOLsiXA+3fAKcWnXn2RECEFq7nk8aWZR7okvqbkJ1Tr+cORfLFk7nzObP+LMkoWc\n/24N4lQRxcX6625PU6Cy1iCMRoTe8vpMhYWobep/zqysaQs7EcqW5F8oK9ET+nkUUydMY8TQkRgM\nBov92gV4c+vt3diw9hhxMZcfc7Jnzx7sS1wtsg8qJCWOenf27t17zbYkJCTQr3d//Hz9aNOyLcEd\nOlVr2lVIr9Z88f1Mpj86hMMHY5kx+XN274i85nE1FdCzLa9vnk92Si5zr3OK2b+5ubpCcdWBwabC\nQpycbp4BrI06gJcaTURmFROZdf0jtJua0+ePkZmZSg/jEFpLQQSYu9HR1IsNe7/FZLr6lJR/kyQJ\nrZUtpViubV5KCVqraz9Bnzp3hEOn/qJLeT/6mkbT2zSc0vgopIi/sDtv5EhE4nW1pynQ2NjSvEs3\n8n/fijCZADDpSinc8idBQ0Y0cOtkTYnZbObeeybTTNcaJUo0aAku6UvU0Ri+/LJq0qDpjwzBwUHL\nkjd/x2g0Vdnu7e2NWVt1oJvJ2kAmTjz5yQYmvPId976+ihe+3sKqHWGcS89BCEF5eTmDBwwmO7SI\nPoZb6KMfjThrzbDBw8jJufbIbysrJfdO7cfn3z5MsxauvP7Set5+9Td0JXXzIN+xfyCv/DaXlJh0\nFox9k9KSmg2me3j6dMoOH8WQUfFQJISgJPQ4yuIShg27eRaratQBXG+jIL6bmuhOyps+iEeeC8PH\n6I/iHwsyOEvuqIWGpAvx111fSMAgYpWnMIiKG80g9MSqTtEj8NoJRg5F7KCNMbhyBTlrSUt7Y1eO\nRe9lsKS5aYP44Idmoc0tJO21t8j6fDlpr72Jf0BHOgy7fNemTHY5ERERlBWX4cqlT02SJOFXGsiq\nb1dXWTzF3kHLk8+PITY6gx+/O1ClvokTJ1KgzOaCSK0YfS0EGSIZVbeu7EksJS2nAH8vF9wcbTl5\nLp0lv+7lrldXcvuib5n70WrMJjtamNuhkBRIkoS35IeD0ZVVq1ZV+5pa+Lux9LOp3D99ADu3neaJ\nh1eQknTtB4Ca6DYsmBd+eIroo3G8dvf7lBuuf5R+cHAwnyz9gPxPvqTo8+UUfLAM1d79bNuyBasa\n5nxojOp2eOENstWq6RXsR2RCBtGddHCqmCD3uvsG05AUkgLBpRtbCEEi0RQZC/h+x0e423sxvMcd\ntG3W8Sq1XDKw02hKSgs5fG4bGqwpEcXYKGyxUmowmU1XHTRXWJpPexwsyrTYYjIZKTca8CwwA0aO\nkEivYL8aXW9jpLGzY/yCV8lNTqQoKws3/1bYurg0dLNkTYxSqbSYlw1QLgzYSg6cCjuDjdaW+yZP\nZumHS7G3rxhbMmBwAMNGdmTVt/voGuJPx86Xxq44OzuzddtWJt41icTcs+gNBpR29rTrMJH+7b35\n4MmJKBSXxm2k5xZyIPI820Jj2B2TjNu46RTF56A9kYoqtyLtr5VOS8K5a39O+yeVSsnUGYMI7tKC\n119az+yHvmHh4jsJ6VX7SxL3v6MXT33+CEtnfs7SmV/wvxWzr3uw3gMPPMCECRM4cOAAtra29O3b\nt9Zn+jS0JnE1QS29UKmUN/WbeHCbnqSqzmEUFd3l5zjDBVLpwRCGcSfNilqxfs+3JGbGVqs+hULJ\nLb3uwdXBEyusCaYXbQ2dCT95gLW7vrrqEoreLi3IxvJ7XB5Z2Fk7oLayJsjdDs9cM0aj6aZ8E3dp\n7odftxA5eMtqJCgoCGc3JzKpmCOuF2UcZjt6UUowveipH872H3Zz262Wc5ef+N8teHk58cbLGygs\ntExP2rt3bz794hPKRTneJj8Cjd0B+HXF54SFWQ4M9HZx4K4BnfjymbtYPKEbhVFHMfg5U3B3F4pG\ntqfcRUuJXR59+vap0fV1DWnJp988hJePEwvm/MSfm0/WqJ5rGTNjGFNfvoftK/fw3aKfalSHnZ0d\no0aNon///jdd8IYmEsABegX73dRBPLBFV1q1COCIcjtnCSeRGDrRBzvJEUmScJO8aWkKZP/J6ufU\njU09TVlxKV3N/XGXfHCVPOlk6kvqhfOkZp+/4nFDu4/jnPIMycRRIgpJF4mcVYYxLOT2yqfgIHc7\n2p8y3bRBXCarKUmS+GX9L6Q7xRNtF0aE4jAueKCRtEiShFrS0FbfhZPHT3LixInK42xtNbzw6h3k\n5RTz7msbMZste+SeeeJZ2pV1obUUhEN5xZu7i8qfuXOuPFPnlmEDaWddxIVfv0I6FoXBx4GCu7rg\nMfw2+g+t+achDy9Hlnw6lU5dW/De65tY+8PhGtd1NVMW3sXoaUNYvfhXtn23u07O0ZQ1mQAON3cQ\nlySJ2/pN4f7RT9EqqC1qhQZryTKjkROu5BRmVrvO5AvncDZ6WHQ9KSQFrmZPUrKv3H3WzM2f+0c9\nBd6Cs9owStwLmTDkIYL8u1vsJwdxmezyunbtSmJKIm9+9hp+HXxxxnJxEkmScJW8iI6OtihvH+jD\nrKdGcvhALKu+uTTCvLS0lISkhMrv6opyE6qMQjRt23As9OgV2yFJEhs2rufxudMpyd9Lwe4V+Gt0\nqJu1557XV7NyeyjlpqoD56rD1lbD6+/fy6BhHfhy2Q5+XFn1+/2NkiSJpz6fSddhwSyd+Tmn98s5\nDP6pSQVwuLmDOICXiy8DOt2CUAh0wvL68sjC3cnnCkdW5WDrRJmypEp5qbIEe+3V55f7uLZg4rBH\nePKu15g6+ilaeV9+qdd/BvGmvvSqTFabbG1tue+++5h47z3otAUW24QQuOt8aduq6gIpt93ZnZFj\nOrFqxT4O7Y8BwNraGq211mJmiSbqAmZnW3wCulep4580Gg3z5s8jKu4s8efOsv7DBfy66AFC2vny\nwbp9TH59NREJ6Vet40qsrJTMX3Q7Q0cG8c3nu1jz/cEa1XM1KisVC39+Fq+WHrx857tkJl59ydX/\nkiYXwOFSEM90UdyUQVyltKJv0HAiVUfJF9kYRTkZIonzyigGdB5d7Xo6tuxBniKLDJFcOXo1hXhK\nFSX4e7UjJiWCuLQzGE03lonoYhDPz9d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SPpjYFXW2lnlfF89tIjAggLy74qgbc3PRpqbi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xiZTGDaWEtWrE/j9q0UKlcxfcIemUxg/u9N2L/nHgf3R6Knp+Dn3+pQ3+/pFZPKIg5KdyCURo6R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\nC2dXu3gtG2dXbWisZ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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gmm = GaussianMixtureModel(K=3)\n", "gmm.fit(X, max_iter=30, tol=1e-4, disp_message=True, random_state=1)\n", "plot_result(gmm, xx, yy, X, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, we can see that the former result has larger log-likelihood, and thus it is more appropriate to choose the former result. In reality, we should run fitting several times with different initialization, and choose the result with largest log-likelihood." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4.3 Results for different valeus of $K$\n", "\n", "The result for various $K$ are shown below." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "K = 2\n", "n_iter : 18\n", "log_likelihood : -562.7613810500463\n" ] }, { "data": { "image/png": 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TJGn+6XdvCRf6PvdSZrcLvvw0DcmoJ9geQTH5FJNHL4YySrqc4PJ+LHosGZ1O\nyfz7wkh13s4+7RoOKDahUigJwjHGtEHUUaRP4/pb/31jNCsajawsjSPz8x7ysqEX3wWXZWhensvK\nyi565lpD8nbHsroxwyKbpe/eno6Hp54lS54nxBiNIjwEu82KOrOUodoZuA0cDEdOcOO0y7lr2Uso\nAvRkvbeaPfY1xD5uIXqsFynP68h4V0OulE738O5072pHGD/CXn0P9ppHEcaPENZ8ABSSkn7e19DX\n6xpSa35iX/lnaJVO3N19PNn1JawqSCDMy4uBHTvx9dEjWO12xvZ2fD5sTEwHIDK6I3q9moP7mvcs\n79bH8dor/aDc47w9a60AXg+4/ibNFaj77Y5CiPeFEH2EEH3Ot4LWP8nmjScZ3HM5rz13lLKGCpLE\nHnJJowfxuEjuALhJnoSY4ljyYgrz74riYNoVbNw7hW0JlxESp+KA9ieSnTeTpNvKPY9FNVuU5K8Q\nQrB21QlumLWFOdN+ZulXGed9J99e5JuyWFXei8zPe8izrrWOCy7L0Lw8+/j4nG+XS07agUz0Ljo6\nR3U8k1ZdXcPO7akcz9hNTVUtR9mHKcSNxrwcOltCMMX6InQqOmxrwGS0sa4qhZF+PUjfsJd9uavo\nf2UAOz4tZs2qQyToNhM63MDWNX0QFZch6haBJQnMWxF1ixDlE7DXLkLYHY+8v/f1RLiOIaHiG6os\nBQz360G0eye+yt1Jbm4u5gOHKK6v56p776W6tJAewX7sSc0FwMlJSVTPTqQmN5+roXu8I4BnH8lt\nlWcq+2taK4CnAj1/+UGSJAPQ9XT6v9Lx1Erunb+LwNJeDLROZihTUKPFjAkX3Jvt64onRcWOwurk\npMDDU8umDSeRUBAe6c7VtwazL2Um1/9qKdG/6pF79rHwniQqdvhRvy+I1xZkcvPVW7Db5aZpGSCX\nZTISc+ga17lZZ645V9wCQolPpSvDpan08BqD0uCMlHcKgPpe3jiVmdDk1eM+NBKzZOP6kOG4ebhw\noOYTTGUq8n/WM3TcYDZveYO1Xwp00jYw3IbksxuF71YUvnuRfLaDbio0fIyovBphr0SSJAb5zkep\nULO79AMkSWJGx74UNFQy8MqJHHpzHVhtHDpZS9/e/fA3SKTknsJkcUyN2i0igPy8ckwmy5n7cfFw\nxjPAg9xjJ1vz0cr+pJYeRqaSJEkLKAGlJElaSZJUwA9AlCRJl5/e/gSQ/G/q9PJbn76XRoAlFE/J\nF0mSUEoquhOLEhVVNG9qrKSUriGOMddWq53rLt/Ee0/nYk4MxnyoE1++lctzjyf+7TylH69i3co8\nohuGESAF4yd1pEfDEFIT69jYCO51AAAgAElEQVS5rfBvn/9iqDr97lvWsuSyfH42m43sI7l06312\nZEVBQQHpaY5AraxzvPbTBjlG1pXmJ2JTKzCFuWI4XAlCoBoRSEdciXDrwIq9b2JSlLN5QQW2Qzoy\ntybjq36KJpsTkvcqFC73IinPtlxIygAUbv9D8vgYrCcQNY8ghMCg8qC35xVk1++mylLAKP8oaLLh\n2zuWEGM3dNl1OIV1IbghnE3Lv8Fqs5Nx0vE5Exrmj90uyD/RfG2FTuGBFGYUX9TnKft7WroGvgAw\nAQ8D15z+/wIhRBlwOfAcUAX0A2a38LUvKQV5RnQ2t2ZpCkmBGjUp7KdcFGMRZkpFITm6wzzwRCzg\naHbPPWYm0jQYX6kD/lInohqGsWZFHtmZ1X8rT/t2n8JbBKKSzq4HrJAUuBmD2L391N8698UgL1py\nUcll+TxOnSilydxE5x5nm8+LiopwM3QASxM0OSYtsvo6I2qN1JiKyepaCgoJKaOY7MB0NCHeTA0b\ngBCCw2U/UJ1th53BeEm+vPycM34+Sp54yR1JFfq7+ZA0g5BcHgTzVjA5RvH1cJuAhIK0mp/RKtXU\npxSgiXEMPdXk1WPx1+Pt1In0I/sBOFHimLMhMMhROThV3Pzzw6ejN+WFlcjarxYN4EKIhUII6Tf/\nFp7etkkIES6E0Akhhgshclvy2peaPgN9qNEUNUuzCDNC08Szr8fT2C2dBO167D2yWfLxYEaMdvQA\n3b39FG7GDs1mPFNJTnhL/hzYW/K38uTuoaFJZTon3aZpwNO7fS0vKC9acnHJZfn8Ck7XSIO6n+1r\nEhERgZPaFZup4Uya1duAtaKEuTfNpeu0/gibjfyabfS7azQAg33DyS1NxT9cQ+H3ekAisk8Dw6bW\n8OnLnnz02YH/PzP6a8GpD6L+HYQQODt5E6TvSXb9bgBsWRWIzlqEswJNgRGUEg3+SqSmBpxUSvJL\nqgDw83dUJEpONe+b6BXgQUVRlTz3eTsmD9BtI9fNC8fkUka2Mok6UU25KOaYfifXnp7mdN3OyaTk\nzeHHLRMZNvLs8A0fXy1WdcM557MoG/A8z2pif8aY8R0xKqsoEQVnCm2VKKNcUcRlM0P+1rkvBnnR\nEllrqyhyBD3fjl5n0lxcXPDy7EC1rYBSUUgt1dhcNDSYinnyySfoPqg/od4+lJUU02fqSPRKNV2c\nfahR5ABQuMNR1oZMrsbSKPH1R2q8PLzOvfhvSJICSTcd7MVgdfQq99dFUGnOx2q3MKbXQAAs/hJO\nlWYAiv3KmHv99Xi66Kioc3yO6PRqVCoFdbXNv7wb3PTYrDYsjRZk7ZMcwNuIl7eWVZsnMfBqFYWB\nB7FGZvLwoigeXtjrD4+bcWVXypQFVIhTZImj7BLr2CZ+pNJcTWSU5x8e+//RG5z49PvRlPmmcNjw\nM0mGTeS4HeCtT4biH/DHTdRCCJIOl7N7RxFG48VfN1hetETWFiqLHQHcw/9sR1Ob1U6TBUaPH4K2\nl52ykFNICgUP33cnQUFB5FZVEeLhaKbOrj9FiLMfCklBpS0Ha6OCo6fSKBeniBtbwsbtRvYZDzBw\n6IALy5Dm9CQvFket21vTBYGdKksBd82ZB0BmxzRybI5m8879I1j8ymI8nPVU1TkCtiRJODtrqas7\nO2y3rKyMvMI8ABpqz22Vk7UP8mImbcjPX88zL/X7U8d0CHLm9Q8Gcft1O3G1exPLIJSoKLJnM3vK\nRjbumYrB4IQQgoYGK1qt8k9NphIT682upMs5eqQcq00QE+uNk9MfH5+TVcO82Vuoq7SjVmios9ay\n4Nk+XHlNtz91bxdKXrRE1lbqq41oDRqc1Gf7iTQ0mBEC+g/ozYuv3U5GQRmzn/uSkE4dAKgwmegd\nePr/5npCnB2Ts9Q3lePn0pmAHrUkJ+0juFMXti/rSA/RhVXfreb9/u8z/5b5AFgsFqxWK3q9vll+\nJKUvQtIjbCVIgE7p+GJhttfhqnF8aXjxjZfxLhbccSyJa264Hq1Wi5NKidVmO3MepUqJzWZHCMFD\n/32Yt958kxApEn86M3nCFFZt/AFv7+brH8janlwDb+cO7i/hykkbiOnyDeMG/siLzyXywO17wK4k\nhgE4S27oJANd7TEoa11YtTyHDevyGNZrJb26fUtc6FJeeuYQVuuFj+VWKCR69vKhd7zv/xu87XbB\n9TM3oS/oSpxxLFH1w4kxDef5BYc4mlT+h8f+Fb9etKTb93LwlrWuxvpGdM7NX1WZGhxNzDq9Y6Ww\nepOjudqgdfxcZzbjqtFgMpkorCrlx2+W4+nuxdGMRDJScjmceJihATEoFFBRpMNL8iesIZbHH3uc\niooKZl9xFa7Orri5uhPfqy+HDx9uninJHeyODmgqhaOvSpO9ESeFo36mczEwcvjw0+mOzwGlQsL2\nq9EbCgUgBF999RWfvPMpfRpH4d/YGYCylGquvfraFnh6spYm18DbscSDpdx45RaCTTH0ojd12dV8\n8kYielzxQo9Cah5c9Q2+bPqpgIS9ZXQzxdMdX0xWIys+OkSjKZHHn48HoKy0gS8+SufIwQpCurly\n/fxwuoT8dm6OC5OwvwRznZJA0eVMxzqD5Iq/pSvffJpJ9Kst/619ZVkvun1vkGddk7U6m9WGUtV8\nmU3bL0HxdEuX/fS7HeXpceI2YUcpKZg0fjKNt/fEpcEDz5p+1FfWUV1lBAEudm+gjl/6prpKHtTW\n1TFu9DgqjtXRv2kcSlScOpLPyGEjSU1LJTAwECEETZYqNm/ZwdufTeHyW4dAd1ArdJhtjldZWqWa\nRqujd7zu9KpjjRYrzrqzHVMtFhtOahVvvPIGHYyhqKWz24KaQtmxYyNlZWX8Uybj+aeQa+Dt2KvP\nJ9PJFEWgFIxa0uIl+RPLIIzUUEvlOb1DG3VV5OfU08kUhafkhyRJ6CVnupn68u1XGRiNTeTn1jFh\nyGrWvFNH7e6O7P7CzrRRazmw76/1YK+ptqCVtOesA+5k01FZbv7L9y6TtUvSuZ0mfwnUv0x2dCZw\nnw7saqWSk4WFHEk8gsqsRKXWoJMMqIwGDAYNKpw4WVELgIe3I9A2iDpUKiU5mbl0tUTjJKlRSAoC\n6YyHxZ/333sfgEcfuhMnlYnkbUZOrC/hqy8/AUCrcKfKYgTA3UlP9ek1vN21jtaD+kYzLr8K4A1G\nMwaDhqqqKjQ0b2FQoMRJpaGm5rcz6MramhzA27G0Y5V44tsszUVyRyCQkMggiSZhwS5s5IssTjUV\nYTJZccWj2TEaSYtaoaairJHFzx7Go64LoZZe+Eod6GKLoktDHE88cAHDVs6jd19fyi0VNIqzPeOF\nEFTq8xk5ocNfOufv+WXRErn3mqytOKlVWBqbd9JUa07Xak+n6zSO9+PG0723ndUa8kpL8MAHqc6G\ncD+9f5kCj0AtBlxJNiVTXKCkW2wDRlFLMnvpE98HN4XnOV+OdWZnjqemkZmZSX7mdwCUp3YgUAom\nvGMINqtg//YkChoqAPDXuVNU5/iC4GtwRghBRW0DHi46Rz6NZpqabLi66Rg/cTxlTs2Ht1ZTjt6g\nIySk/Y1E+beTA/hFlpNdw/237WJk/CqunbGJ3TuK/v+DTuvY0YVaqpqlNYh6AGIZTBMWdrKWrayk\nhJO4Kl1xcVVTKZWec4xNsuLnr2PX9mL8bcHNtvvSgdwTNdTW/Pkas6eXlrvvj+GofjsFZFEiTnJM\ntxufEMG0GV3+9Pn+iLxoiawt2e12MnLSqamsJSIskgWPLaCmpgZnl9O12tO9uL1cHB3Nqk4P0wpw\nccGq1VInVaMobMLewRHga9OUOAcoCXD3JZQoVv9cS+ywapK1W3HFk4SDiVRYS7ALW7N8GPXVxPfv\nw+bNm5kz1YPKUhVH9zrKg1dvK2WpVjas2URGbTFqhYrOBh8yKx3BPMzTi8q6BkzmJoJ8HB3eSk+P\n//bxdeWxxx/D7FlHpiaJRtFAExYy9Id594N35HXA2yH5N3IRZWdWM2PsTxxdpcY3vxdVu/25/bqd\nrFyWfUHH3/VQFHm6ZKpEGUIIjKKOFMU+tEoN9dTgQyAGXAgkmHhpBJ3N0dTXWSjUplEocjCLRipF\nKWn6vdz2nyg0WhUuLmrMNGIVTRSJXHJFGhWUgCTQaJT/f6bO49b/RPPW54MJmViL26BCbl/YmaVr\nxqHRtlwXi6SqpDPBW551TdYW5l5/I9u2bkcSEs5Z/nzx8rcM6DuQpiYLLi5aKiscX67dXXSoFAqK\nKx3rF3RydaNGIeEb5ENtYSF2fydsOkFGsuO1VYeBTmjQsW2NAYNewUu3xBEp9cFN5Ulkj0jSdIeo\nE9U0igZOKI5jdjYyb948unepZOw4weZl7lTZKin3z8A91kruPiNe3l4crjpBN5cAVAolKWUluGu1\n+BoM5BQ7Zlfr5OsI4EUFjkqCf6A7/v7+JKcmMe/Ra9G4qHEJ0LFzzw6mTp3a2o9bdgHkAH4RvfZC\nMn4NoXS2R+IqeRAodSbcNIDnFiRwKKGUhAMlWCy23z1+5JiOPP1KH4r8DrFDtZJU5+1cd1cw19/d\nhVT2U8gJOhFGOL0BUKJCCPhyxWg8BpRw2PAz1Z2P8tBzPbj17igA5swLI1tzmN2sp4xizDRynAR8\nvA2o/p8e539k4JAA3vx4KJ+vGM2cG8LR6lo2eK/4G8G7uCKfZXs+4d0Ni1i57wvKa9rftLCy9i0j\nI4MVy1fgZ3FMoeoueRFmjqW2sJ53330Xg4uSE9mOWdqclEo6+rqTe8oRKKN8/Sisq2XFxnUE6/Sg\nlEiOTaVJpUZhcSbiKieOc4g9ewSbVzpz0wNVRPQ2ohRK7rrnTm564HpO+h0nxXUv/Wb1ZP/Bfbi7\n2hgau5rMHBv3L84ihQNEXKFGkuDn79LoHNOd1JoCBvuGA7Cv4CR9A4OQJInUXMfff2Qnx3C2nOwS\nJAmCuzg6qHl5ebFgwQIMkgvjZoyhZ8+etBeNjY288uqr9B4wgP7DhvLBBx9gs/3+Z+g/ndwL/SJK\n3F9GF/sA+NUrLAmJmqombp61EyelCotkYvHbgxg5puN5zzF1RghTpnfBaLSi050d071xdSHqrGD8\npU5n9j2lzmHspI707OXDlyvHnPd8c+dHsOTFo0TgeAcOECqiSanewYrvspl1VVgL3X3LSK1NYUVZ\nLzI//2vznecUp/Hdrg9xHjMCTXAfTmZm8dHGxVw38m4CvDr9/yeQyYD9+/fjrfRHITVvpTIZTTz0\nwEPEhc8h94QXl02ZztdLvyI00IvUPEcNO9Y/AIAccyM/vP0pYzY/w51vPcXC2CvYV/YZdqcv6BLr\nge+RaN58CHr0yuB/S7Mpurua8ePHM2fOHJ56+qkz1xSWI4iq25BEPVsSp1DT+BlD3EcTd5WRkm0q\nOhTF8NzKD3G7Kp5hvpHkVFVSUFvLvDjHF/1DWYV08nXH3dnxDjwjrZgOHT3R6dRnrlGaX05DnYng\nyLOzQLY1m83GqHHjSKuuwmlAX4TNxkMvvcjGrVv5/uuv2zp7bUKugV9EPn46jNSf+dkmbBxhFxH0\noVfDWGLqRxFa25//3LyLokLj757HMVOSU7MJWRa9OYA8QxJZ6kROiiyO6XaBfwV3Pxjzh3nKSKtG\nrVTjw9m5nJWSEn9TGCu+PvE37vbiOZwfTEDpX+u4tuHICtyvmonbyGFou3bBffwYnCeNZVPyjy2c\nS9k/WWBgICapvllaPplYsTHQPgHXGj1ajTtHtqZx73/uJbZrB4oqaimqqCXOPwBXjYbNJ7JRK1SM\n9o9ha9kxjFYzsZ7T0SpdmPl0OEcNuzlem811cwTHMi1896EXHtJ/EQ3LEJaDCNMK7NX3ISqvBHst\nkse7LF+eQhcRTo97LagMgrTXdHgrAtGPCidE5UlXFz9WpR9HAsZ37YbJ0sTB9HwG9egMOGaRSz6c\nT0xs834xaQeyAOgW//sLqrS2tWvXcrywANe516KPjMAQHYXr/Hms37Tp3LHx/xJyAL+IbvlPJPn6\noxiF413YKfLR44KfFHSmZ6m75I2PLYgVS7P+1Ll7xnnz895pzLjXg+hZDdz1TAjrtk/Bw/OP50O3\n2wUSnNOzVUJCXPhcL63qry4XarU1UV5eiD4qslm6IbYnBSUX1g9BJgMYPnw4Bk89+YoMhBAIIThJ\nFt2JxUlSQ72jw1qwUy++/PJLYrs6at37j+fhpFQysnMIm09kY7Zamd6xLyabhR9OHkCrdKW/z/V4\nhNl4ff3dDL+pPz2nTEAbsAzJ5SFoSkbUPoqonIOoeRjM20F/A5L3T0iaQdiFndBpTgRfYeHEFxrq\ns5RYx7rh5OvCaF0YVrudH9KOMaBjJ/ycndmTmou5ycbQaEeP8vS0IhqMZnr2ah7Asw7loFQp6RJ1\n/pbBtrB9xw4I7470q850CrUT2oju7Nq1qw1z1nbkJvSLaOLUzhQXNvD6S9twQk2d2YivCILfBEqV\n5a+Nmfb103PnvX9c4/6tyChPVHpBubEYb8nxIWMXdkr0Wdw9u/1824azU6Zac//apC1KhRIntQZr\nVRVOXmcXh2gqL0en/2sT18j+nZRKJVu2b2b2rKuoOlSGThhoEha0wtEMTb0R7Hac3Lxoqm+io5cz\nHbxc+flQJtMHRzMzMoqV6cf5MSONWZFRDPTuxkfZW5gQGEu0+xTyjImcYCv3Lv4vEW5jT1+1N+hv\nAFsh2PJA4Q+qrki/msDpqvuH0xC2g7I9KtJf02F3VdAw1xNLegnX3zGRdZnpFNTWsmDIcABW7z2G\nt5uB3t0cgXnPjgyUSgXx/c+ubw5wdNdxwnqHoNaqaS8CAwJQ7ttz7obKKvz8/Fo/Q+2AXAO/yObd\nFsnBY7NYun4U3/04gRqnUqzi7DhSu7BTbShg8IiAVsmPUqlgyUdDyDIkkKE9QDYpHDFsIqKfjpmz\n28/771+C96Pfz/nLy4VKkoJeYUOoXvoDtgbHggy22jpql/1I/9Ch5z2mvOYU6w4u5cvt77Dj6Doa\nGuvPu5/s3yc4OJi9B/Yw797r0OPMhDETKVGcdGy0C6itx+ahp3tYOM7OzoyLD+dAWj5lNfUMCOpI\nNy9vPj6ciF0I7g2fRKOtiTfS16OQlEwMfJyO+jh+Ll7MgfIvsdodY8glSYmk6oSkGYLkFHYmeFvt\nFvaUfYw5fDe1BQo+evgImU2plN2lBr2Cx3rOAEnBmwf2EerhyeiQUEqq6tideoIp/SNRKRUIIdi9\nI42evYJxcdWduU+TsZH0A1nEDI085xm0pWuuuQbzseM0pB5ztILY7dTvOwDlFeftJW+xWPjkk0+Y\nMG0aV86Zw+bNm9sg1xeXHMBbgUarIrSbO7G9fZg2szNH9dsoErmUiJOk6nfSPdbAsJEtO+kJQNqx\nKu69dReThq7lvtt2kZHmGC4S38+P7QnTmfdkIFPu07Dk8wF89M2I/3fe89bSEsH7F6N6TqGr5EPx\nwucp/d+rFD/7ItHu4fSLGHHOvjlFx/lww0tkB6moHxHDYWUx7657nlpj1XnOLPu36j++L0IIbpgx\njzLnk+Q4pVIuiqmozkClc+bxJ14AYOqASASCZTuSkSSJW3v3Jb2inBXHUwl29uGGkGH8VHSYZfn7\nUCnUTA56mlCXwewt/5SPs68mqWoVRqvjb89isbDkzSWMGD2QuU8O5a2kWRys+JpwtzE8PHoV33z3\nLX3fvxztoI7MDR7GFcMn8fGRRLKqKvnvoCEoJInPf05AQuLyIdEApB4toCC/kuGjmwfqxI1JWJts\n9BnXfnqfA/j5+bFm5SpUGzZTtegVKp5/CfekFLb+/DNabfNXh01NTYweP577X3qRRFcDm80NTJ8z\nh6effbaNcn9xyE3oreyZxf0YNCKP77/IwWKxc/XMMGZcEfqnVgy7EIkHS7lh1mYCzWG42juQmlXB\nzJ/W89myUcT18cXDU8u1c8Nb9Jot4Zfg/cTBy/528AZQKlVM6zeHMT2nUW2swNPFB61af85+QgjW\nJC7F49rZ6HtEAI535VUr17A95Sem9Lv6b+dF9s/QY2A3nDROlKVXkpSSxKuvvMbBfQfp1t2fgiyJ\nuipHMOnk68HgqC4s25HMDePimdo9nC+TD7No9w5Gh3RlXteRpNcW89Kx1bg56RkTEMPEDk+QV3+Q\nAxVfsa1kCdtK3kSvdKekoApVHxuXjXb87Z48VEZ5ggd3v/wAAIXBKnIa7VwWFM9tPSaQV13N6/v3\nMjYklNEhoZRV17Ni11Em948k0MsNgHU/HkanVzN8VI9m97frh/24eDq3uxo4wNChQ8nPySE1NRUn\nJye6d+9+Tn8egBUrVpBSWIDbbTefeWdujY3hhUWLmH/TTfj7+7d21i8KOYC3MkmSmDC5MxMmdz5n\nmxCCfbtPsWt7ER5eWqZO74Kv37nB5kI8+0ginU09CZA6gQQedh+cTFqeW3CIZevHX9A5LBYbZSUm\nPL206PSt96fyZOJ0un2v5zczwv4teq0zeu3vfyGoN9VgbKzDPbL5lxpDvz5kvftZy2VEdsnT6DT0\nHB7J7lUHueXl63nl1ZfPbFvwwLesX5PEtTcOpaa2CufaPKrq7Sx8dyn/u/Nqnh4xmulLv+LhTRt5\nZ9JUno+dzV0Jn/B40lLyG8q5vsswgp3j6WToQ4Ull5y6PaTnHaYwLRdtiQ/GXCVlu52ozXLliGEH\n2y7fyTaXEn4qOsxwv0j+GzkVY1MTt6/7EbVSyRPDHC1Nr/2wE7tdMLl3Z8Ax+9rWjSlMnNbrzCpq\nAMbaBnavOMCIqwafs2hLe6FQKIiOjv7DfVatXYuiZ3SzDm8qV1dcwruzbds2Zs+efbGz2SraR5up\nDJvNzq3XbuOu6/awYYmVr54vZ1S/lezYWvinzyWEIDmlFD+aN8v7EURSUunvHNX8+A/fTqVvxPdM\nGrqW+IilPPd4AjZbO+2m3gKcVBqE1YowN+9MaKutPW+NXfbvNvzKQZw6UXpmuNUvZszuR3WVkXff\nWkFoSChfPf0WTTkn2JBcyKixUwl1c+e/g4ayMSeLNw7sRatU80bvuYwOiOa9zE3ceuADUqtPIkkS\n3pou9PWeQ9aPBjbcYSTlaQMnPtdSn61EUijx6dOTp8s3sr7oCLeEjuaF2KsBif+sX0tGRTlvjJ9M\noIsrK7fu56cDaRQnbmZIrziiI2N48zXHMMor5wxolv/t3+2lscHM+HkjW+tRXhTeXl5Qf27/FVtt\nLe7u7m2Qo4tDDuDtxOofTnBkdz2xxtGE0IMwS2/CTQO4Z/7OP5yt7XwkScLNRYuJ5mPLTRhxc/3j\nYWYAP3yfzTsvptOjfih9TZPo1TiWNV+U8Mr/jvypfPxZv6z1/VeHjf0dWrWOrkFRVP+4DnF6Zidb\ng4m61euJDxnY6vmRtW+DLuuLWuvEhk+2NkuP692ZrmF+LP/mICHGGMIae+KzrxIFSkqdw3jvvfe4\nMbYXM8IjeX3/Xt5LPIBOpebZnrN5OuYKTtSXMnffO1y9+w2+OrGT1OqTuAX5Ijzs2H1VWHvqaLzB\ni/r3g3F9uB9qhYol8XOZFzoSs9XGXT+tYWtuDguHj2JocGdKK2tZ+NlG7NU1hB5UM8A8HsUJL3Zv\ny2HYqHB8/d3O5F0IwZr3NtIpogMR/dpPh9a/4uYbb6Rx3wEspxyzzgkhMCb8H3vnHVdV+cfx97kT\nuGzZAjIUJ27ce++0tNIcWVq23JZaVqbZ0PbPTK00995774U4EQeICoLsfbn7nt8fJIaAogKa3ffr\n5esV5zznPM+53ed+zvd5vuMM0hw17du3f8qjKz0sS+jPCBtX3cItN6BApicnwRW52YqwU4k0beH1\ngKsLM+jNqqz67RxVNY1RCEr0oo4b1ucYMrzqQ6/97YcI/DR1UAl5oVZWgjWBmgYs/mM/YybWRSYr\nm/e+u8VKnlat716NBrDi8HzufP4VSnd3NLGx1A5oTIOgluU+FgvPNraOKtq+2oK9Sw/x1sxB2Pxd\n2UsQBNp0qsT1yEQquNWEpFSk2TpUx25A68os2nmG99+Hrzt0Rm8y8c3RwySq1Uxq3oouXnVp6Vad\nLbfD2H7nHD9d3Z7XmQ+4Ln2R7LudG0VMF9JJWXuG3Sv34GBnz53sbN7eupFLSYl80rINrwXXwWgy\n8+73yxAUVjhuvYTULIAAbn4hmEQTEqtbBZ7p8olrRIZFM3L2sCL3lf9NBAcHM/uHH3lv5EisK3ph\n0miwFkW2bduGXC5/2sMrNSwC/owglQqI3LM8RVHkFldJy8lhYN9dBPg5MXl6A9p2KFlqww/G1yYl\nScuGNTtQYE2OXo2DQom1SorBYH6gx3liohpPCsZJW6NCrzeh0Rixsyv92NCz/yxW4vR0ipVYK1UM\n7TCapPQ4MtRpeNb1wc7m+Vlus1C6dHurAzsX7mfXwgP0/qBr/vGatT3JyonBzscL0jPBYMRwOZJs\nbz22/jVxrxpCrxZ1mfnDd7ioVCw8d4Yzd+KZ3rYDtdzcecWvGa/4NSNFm8WFjBjS9WouR19jydyF\nZN1MIjPiNqZcLS1atiA6+gbhgsh3x49gMpuZ16M37QMCMZtFpi7eRXSqBs3xo7ik/i1azg7gZE/m\nzXPExxf8LVnxzQZUDjZ0GFR0iOW/jSFDhvDSSy9x9OhRVCoVzZo1e+4qqj1fT/Mv5sUB/iTaRGEU\njQBEE0EScYTQlnbiS9jdqMGoN49w6njJCnHIZBKmftuIgMoOKEQltcTGVMpswJ/fxPDO4AOID6ip\nXSvYhRQK9pNOMi4u1tjalv7b67NWaczNqSJB3sEW8bbwQGo0CaJWi2qsmrURg/5ebodatWqRmXsa\npAL4V0QnajnLIaQHziFLUuPdpj8HDkbTp2dvPm3Vlv917UlsZga9Vixh5PYtnI6PQxRFXKzsaedR\ni5d8G/NJm0F8N3Asmedu4J7lSbCkJTcNjrywahmfHdhLTVd3Nr46kPYBgZjMZr5cvoetJy/Ts54P\nSTcOYxbNoJBDgDditmH9HgQAACAASURBVJo72ado2uze/nfEiWsc33SafuN7YW1rXdTj/iuxtbWl\nc+fOtGjR4rkTb7AI+DND1x6VaNfTjTDrnVyThRHDNWrTFFvBIc+hRfDER1uTX2aGl/ie+3ffJvmm\nmdr6VrgKXlQQ3KmhacGZE6mcC0su9roPP6tLjHU4sUShFrO4I94i0jqUydPql/rS2pNWGrNg4Wky\nYPKLJMemsuPPe3vhgiCwfPUfxCcfA2dHEjzUVMADH6Mf9tsvI03Lxb5dd65niJw7d45uVYLYP2QY\n74c0Yd/NaF5es4KQ+XMYt2s7v585zYYrEWyPvMqoufPwbdcfq/f6kjajI+Z+TZAbZLieOMOSPn0J\ncHImR6NjzJxNrD8SzptdGvHZsBdp3LwxV23OYKzihSjAzVs7qODjSJ8+fYC/nVYnLsHR1Z4XR3V7\nWh+lhcfAIuDPCIIg8M3PzVixtSM937NDqZBjJRT0fnakAtFRmSW+Z1hoErZqzwKiKxEkOJk8OPsA\nAa9T35VlGzvi3S6dm+7HsW0Ux+y/WtKtl/+jP9gDOJ9+HrMoWsTbwr+Whp3rEtyqOn99ugJ15j2n\n0Xr16nHi7Bq8K1nj69cGd/u88ESJ3oT91ghkidm4Nn+BXzafRKs3Yq9UMrZpc068OYLvOnalma8v\nx2JjmHHkIGN3bee97Vswd2iFrmNVzCoZ9kcSqPhjOBVnXiRi4yYEQSAs8javfbWM4xE3mfRqO957\noTkSiYR1G9bRttswZHaOJGYcpu87nTly/DAKRd5W2P7lR7h46DKvT3v1ubK+/wtY9sCfMarXdCYg\n0J6/5l0lV5+DjXDPmStdSKZq9ZIHR3t6qTBa3wFtweM6eQ7uHg/eSw+u48L8ZYWzlZUWd8V78pqB\nvGIRbwv/UgRBYMR3Q3i/0SQWT13NiO9fzz9nb2/H/+a/x4AXZ2Gu2hAu3QKNFonOiO2Wi9xsLuEs\nzej3xV+M6duatnUCsVUo6FO9Bn2q5yVRSdPkkqnTkavX07xeQ2okBKMS782XdLLw8KnMtCW7WX80\nHG8XB34b3ZcGVfLmtyiK/DnnIAlxIq+/1YbXXv+kwPhzMtTMnbCYoIaB//rQsf8iFgv8GURpJeOt\n92ty1eYEGWIKRtFAghhDrFUEIz98cAKDf9LrRX8ypEkkiLH5FZRucx29MoemzT3YuyuWQ/vj0Oke\nLUztSbmUFX5PvO/LtiaKIldjL7D80FwW7vuZU5f3YzDqy3V8Fiw8CkENAun+VgfW/bSN8KNXCpxT\n2Vox47v+mEQjphp+GKylqMVsIpVnqGaTy9zRfbFSyBk/dzOvTF/MmsMXSM/Ozb/e2doGf0cnarq5\nM2Lga9y0Ckcv6hAFyPFSkt0hAId2g9l8/BKNfe2YMaBZvnibjGZ+nrWdDWtCeemVxgwY0rzQ2P83\n8g8ykjIZ+etwpNLST9xy584dPpw4kaatWzNo6ND/bNnPskJ4kDPT0ya4rou4aVfPpz2Mp4IoiixZ\ncJV5P0eQnKKmRnUXJn5Rj0ZNHy0F4PmzKYx56wipyTrMohmfSna8+KofP357AUeZI2bMaIUc5vzV\nhsbNyj694MPynO85t5GzcWGoOrZBYm2N5tgp7DL0DO0wBqnUsmBUHF/8NSJMFMWGT3scD6Jhw4bi\n6dOnn/YwyoTcbA1v1xmHRCrh17BvUdkX3P46cewcn364FoPezM247fR9tT3TvpyGlZUVRpOZrScv\ns2L/Wa7eTkYQoJqPG9V93anoYo+znQq5TEJmjoZlqzdwLS4FKxdvpEprpJgRkm8QfWgLtjoZqfok\nuvXoxtx5vzNz+hZOHY/i5deaMuzddoX8V/avOMqMAT8y+LOXGfRZv1L/TG7dukWDxo2helVkVatg\nTEhEe+goKxYtokePHqXe3/OEIAglms8WAf8PIIoisbdykMoETEaRbq03E6xthZ2Q52WdKiYSpTrF\n0Qt9y8TL/C4PE+8sdTqzt0zDc8pHSG3zlglFs5mUn+fSoWJLagc2KbOx/duxCPjT5+Lhy4xv9zlN\nejTgs7XjC3k9J9zJYMr4ldy6mcyQ4W14dVCzAjUQRFHkckwiRy/d5NSVWK7Hp5Cj0WM038uAKJUI\n+Lo6UslFRbv61Vj809ec2hhKoK42giBgEk3EuMZRvXZPDDoJ74/rTI/eDQqN9ealWD5oMomAOn58\nf2BqmaRNHfzGG2yNv41Dt875xzRXryHbvpuY69f/9bHmZUlJBdxi0vwHEAQBXz879HoTg/vtxl7r\njg12+ecrCO4kCxXYsyOG3n0DH3Cnx6ckFcZikqKwqVw5X7wBBIkEZcM6RJ2/ahFwC880wS2r8/as\nwcwZs5Cl09YWsmo9PB35ef5QfvhmKwvnHeDooauMHN+FajXyUh4LgkCNSh7UqOTB8G553/UstZZs\njQ690YSdtRInO2ukf78YHDlyhDWrVhBC+zwxlMuQelfE370+WZmZzP5jJLVq+xQaZ3piBlN6foWN\nnTVTVo0ts5zne/ftw3pAwc/AKqgKSctWER8fT8WKpV+B8b9Gue6BC4JwQBAErSAIOX//u1qe/f+X\nEUWRri02c/pEMmkkc4StRIsR+fHgMpOCnBzDQ+7yeJS0wpi1UoUxPaPQcXN6JipF+Wdms1A8lrlc\nNH1GdqPj4NYsmrqKzXN2FjpvbaNg0ue9mTy1D6kp2XwwbAGfT1rN1Yj4Iu9nr7KioosD/h7OuDio\n8sV7+fLltGvVHhAIV5wl3luLWLcquFXAeCeeiKjFRYp3ToaaSV2/JCMpiy82TcTFy7lUn/+fOFVw\nxpheMGrGrNFi0uuxs7Mr5ioLj8LTsMDfF0Xx96fQ73+arz4/TdItM03phLWgQiOqucgJpMjwFCuR\nJN6hZZv6pd7v3fzmn4b2Jmi16oEVxvw9qiI5lUv2sRPYNm2MIAjoYm+jPnaS+h3HlfrYLDwxlrl8\nH4IgMGbe22Sn5/Dze78jV8rp8ka7Qm3adqxJo2aVWb3sOBvXnObowav4BbjSql116of4E1TNC7m8\naMs4Kyubd98aR233njg6BYBDnhimpl3FKcZIrCGcTn0L5/vOSsvm424zuHUpli82TaRqw7JZbbvL\nmHffY9z06Si9vZDa2SEajai3bKPnC72wt7d/+A0sPBTLEvp/hFVLrlOT5lgLecvT1oKKamJ9znKE\nOGkkg94IopJf6U6qGE0UqVp1vng/LL+5RCJlUNv3WbFnHgm7DiC1scaYnkHPkFdxdfQs1bFZsFBW\nyBVypqwcy6e9v+W7YXPITMnm5Qm9Cu35qlRKXh/ehn4DmrJ7+wUO7o1g8R+HWPT7IQQB/ALccPd0\nwMZGgVQqIVetJy01h6hr8TQMfjfvJhodxCdBUhox2r1Eo0fpLGPGNzMK9JUSl8qkrl8Sd+0OU1aP\nI6Rz3TL/HN544w2uREYy+5vvsa3ohTohgebNmvPHb3PLvO8HodcZSLiRRMrtVFLvpJOTriY3S4PZ\nZEaQCFjbWuHo5oB7JRf8a1cq5JD4LFGuTmyCIBwAagICcBX4WBTFA8W1tzixlR6BHn/RVuxdoFiK\nWTSzj3W8PKAyX//QolT7e1Tx/ieiKJKYfhu9QYeXSyVk0uen+EBZUd5ObI86l+H5d2K7H71Wz8yh\nszmw8hjdhrXnvV/eRKF88Hc5PU1N+IVYrl2J52Z0MkkJmWg1BoxGEypbKxwcbUhMusG5Aydwz3YE\n7b0Qy2viBeIk0dyOi8XD415EyfkDl/iy/w9o1TqmbviQeu1KHopaGqSmphIeHo6Pjw8BAQHl2ndK\nXCpXTkVx7fR1blyM4WZ4DIm3Uh6YSvp+AmpXokWfxrTt3xzvoEcrKvW4PJNe6IIgNAYiAD3wKvA/\noK4oitf/0eYt4C0AL29VgyNhpR/e8F+kR+utSK8E4i7cS+CSJMZxWTjN0Ysv4uJaehmY7or3hqR6\n5Myq8VQqi/3XeAoC/tC5/He7/Pns6+vb4NatW/ff6rnGbDaz4JMVrPh6PYF1/Zi8bDS+1Z7MeWvn\nzp0M6D2QetrW+Va9KIocZyc9X+7OipUrADAajCz/aj1LvlhNxSqeTFk9Dv9avk/8TM8qoigSfz2B\nc/vCuXAogvAjV0iKSQFAKpPiU9ULv2BffIK88Ax0x72SK86eTtg722JtZ4VUJkU0i+Rma8hIyiQu\nMoHr524Stvs84UeuIAjw8oQXGPT5yw99EXtSnkkBL9S5IOwAtoqi+EtR5y0WeOlx9FA8IwYdxEdb\nA0dcySCZ60I4U75uwMDXq5VqX3cri1nEu/x42mFkD5vL8N+zwP/J8c2n+e7NX9GqdfQb34uXJzx+\n0RCz2UyLpi25cTYWb0PePvYNLmPjqeD6revI5XIiTlzjpxHziL5wi7b9mzP6t7fzS54+T+g0Os7u\nDefk1jBO7zxHws28FNHOnk7UalGNms2qUq1xFQLrVEJprXzsflLvpLNwygp2/LmPyvX8+XrnJzi4\nlN0+/r9FwLcD20VR/Lmo8xYBL13OhCbx87cXibySgX+gPWM+rkODELdS7ePsM1ZZ7L/CMyDgD5zL\n8N8WcMgTgd/G/cWBFUdx9nSi/8Q+dB3W7rGEJTc3l5kzZ7Lkr6WIZpHXhrzGxIkfkXA9mb8+XcHR\nDaFU8HJi5OzhNHshpAye5umRlZrNsU2nOb4plLBd59Fp9FjbWlGvfTANOtahXvtaeAd5lUmc+fHN\np5n+yvf4B/vy07EvyyR7HTyDAi4IgiPQGDgIGIFXgHlAfVEUiwxBsQj4v4tntbKYKJo5ffUQodFH\n0epyCfCoRpvgbjjaVnjaQys1ylPAH2cug0XA7xJx/Cq/T1zKxcOXcfZwpMOg1nQY2BK/Wr6PJTrq\nTDWhO86xdf4ezu0Lx8bOmpcnvMCLo7s9N8VJ1JlqDq87xYGVRzm79yJmkxm9VIfBSUvPIZ0YO20k\nSitFuYxlz5JDfDP4FyYtHUW7/qXrO3SXZ1HAXYFtQDXABFwBpoiiuLu4aywC/u/hWRVvgO2nVxOR\nFYldr65IHRzIDT2D7vhpRnSbjK318xHOUs4C/shzGSwCfj/nD15izXebCd1xDpPRhKtPBeq0qUmd\n1jWp0iAAr0D3QgIsiiLJt1OJvRJHxLFrnD94iUtHr2A05F3f653OdB3WvkyXd8sLvc5A6Paz7F12\nmBObwzDoDLj4OHMx+SyZDd2hZQ0MaWlot+1izLBhfDZlSrmMy2w2M6LeBAw6A39e/qlMLP1nLhOb\nKIrJwPO1lvMcIYoi8bfVKK2kJXZoO59+Pv+/n9WyoDmaLM5dP4bnp5OQqvLCQRQ9upCWoyb06kHa\n1rW8ID4qlrlcOtRpnSfWGcmZHFl3ijN7znN653n2LD6U38bG3hprWytkchm6XB05GWqMhrziQ4Ig\nEFjXjxdHdadpr4ZUbxqUv6SblZVFcnIyvr6+yOX/riiOqHM32PHHPvYtP0J2Wg6OrvZ0H96B9gNb\nMuuPWSTccsS+WxsA5O5uKNzd+XbWLMaOHl0uCWIkEgld3mjHnDELyUjKxMndscz7LA5LHLgFTh1P\nYPy4U6Sl6TAZjNSt78YPPzfBw7N4Mf5nOdC7PItlQRPTb2PtVTFfvO+irFmNmF2hT2lUFizcw9HV\ngR5vd6TH2x0xm83ERyUQeeYGSTEppNxORZurw2gworRWYutog3slV7yrelG5nj929zmJ6nQ63vng\nA1YsX45cZYPEZOar6dMZ8fbbT+npSkZutoYDK4+xbf5uroZeR66U07x3CB0Ht6F+h2Bk8jypOjEi\nFEXLZgWulTk7YeXsTGRkJPXrl34yqqK4G04WF5VgEXALT4+42BzeHHIQVb9XcatVA9FoJGrvXga+\nup/dB7oXuTxUoJb3A1KjPgs4qiqgTUpCNJkQ/uFwYoiLx1v1ZHvgWr2GoxG7uRx3AZlURr1KjQip\n2hqJpGwcWyw8/0gkEryDvB473vjdkSPZGHoK18kTkKpU6OPv8OFnn+Hl6UmvXr1KebRPTtTZG2ye\ns5N9y4+gVevwq+nDez+9QfuBLQu9nAAE+PuTEB+PVaB//jGzVosmNfWJc6vv2bOH6d9+y82bNwlp\n0IDPP/mEmjVrFtnWwSXP0s9Oy3miPp8USz3w/zjLl0ZhVb8+quCaCIKARC7HrnNnUtUSQk8kFmr/\noFrezyIVHNyp6OxL+sp1mHJzEUWR3EuXUR88SqMqrR/7vkaTgQV7fuCiNBHlwN5IXurE0ZQw1h5b\nWHqDt2DhEcjOzmb5smXY9uuDVJW3Gqbw8sS6aydmzJr1lEd3D6PByMFVxxjV4hPeafAhe5ceps3L\nzfjp2JfMu/AdvT/oWqR4A0wcNw7tvoNooq4jiiKmnByyV6+jR48euLu7P/aYlq9YQZ/+r3LJrQLG\nPj3Zr8mhacuWXLhwocj2WX8Lt53z0/0NtFjg/3Fi43LBrXKBY4IgIPd05058LpAn2nfRm0z/GvG+\nS7/mb7Ll9AquffYlglSKytqBfs3fwM3p8bMqRdwMQ2uvpMLgV/NXKZQB/kRP/ZrE9DjcnSyVliyU\nL2lpacisrJDaFpybck93bh888pRGdY/0xAy2ztvDlrm7SI1PxzPAnRHfDaHT622KFez7adasGYvm\nz+eDsWNJTE9HNJnoP2AAs3/66bHHZTabGfvhh9gN7I+Vvx8AiopeZEmlTP7sM7asX1/omuS/E8Q4\nezy95XOwCPh/nkYNK3B0aTg0u1eq06zTob56neC6nfMriX0W1gcAQ7TNv0q8AawU1vRtNhR9iBa9\nUY/Kyu6JPUdjUm8ir12jwH0kcjnWVYOIS75hEXAL5U7FihWRSyTobseh9L73/dOGX6Ztk8ZPbVyx\nV+NY891mdi8+hEFnoGHnOoz+7W1CutZ9rDjqF198kd69e5OUlIS9vT02Nk+WqzwlJYXMzEzc/SoV\nOG5dqwYn5i0o8prwY1dwcLHDM+Dxrf7S4JkWcL1ZR4wmqsAxX+vKxbS28Dj06RvA/HnbyVi1Cusm\nTTFrNGj27KRTF280rrH5Nbxr/O3v9SxkVjOZjFyPj0Cjz8XPPQgH25KVRFTIrVDIrUplDA7Wjpjv\nJBQ6bkxIxL6apW65hfJHJpPx9ZdfMu7jjzF07YjCwwNtxBX0R47xxdGj5ToWURQ5f+ASa3/Ywokt\nYciVcjoNacOLo7sXSiUbFRXF0aNH8fDwoH379shkD5cliURSIN/7k2Bvb48gipiyspA5OOQfNyQk\n4VXEvrooilw8GEHN5tXKJITsUXimBTxVb8Wft6vm//2CyxmyDeHUtK/1FEf1fGGjkrNhS2dm/xLO\nzg1LUNnIGDHUn7p9DAVreD+gDGhpEJ96i7PRJ9AaNFT1qEl1v/pIi3AGS0i7zdL9s5G4OCFxsCc3\nbBUhQa1pX6dwtaeypG5gU45tmYaiehA2dYLBZCJr/2GkOToCPKuX2zgsWPgnw4cNo6KXF1/OnEns\nkRO0b9yYqceOUa1a6aZLLg6z2cze5YeY9/EiMmKykdlI6f5Be4Z83B8nN4dCbd96912Wr1yJbbUg\njCmpWBtNHNi9m8qVy89Qs7KyYujQoSxfswHbV15CamuLPjEJzdYdTC7Cd+DKqSgSbibz2pSnX6fj\nqaZSfRi2rj5icO8x+X9nt87hi5ANKKRSi4iXIU9SSexxOH3tEHsubsG2ZTMEOxXaE2G4iDYMbPNe\nAREXRTM/bfoMZY+O2IbkhYuYctQk/zCb3nX6UcU7r8pSrjaHW4mRyGUK/D2rFfkiUBrEJl1n46ml\n5OhyEI1G3Ct482KTwTjaupRJfw/iaadSLQmWRC7PLwa9gb1LDrP8m/XERyagVehJqqMkXZWK5uwZ\nNqxZQ/v2BWuUL1q0iFFTp+Lw9htIrPJWxnIOHcHjRgwXwsKAPGv3xIkT3L59m4YNG+Lv71+o79JA\nr9fz/ujRLFm8GLmtCnR6Pv3kE8aNHVuo7f8++INtv+9ldcJ8VA5lEzr7zCVyeRzsRUmBxCAXV4t8\nSm++CNlQIIkIgMwi6o/FpaxwjCZTgWNmKDfx1upz2X1mPe4TRiF3zRM+uyaNSP75NyJuniY44N7e\nXVzKTYwKKc4N6+Ufk9qqsGnfijOnT1K5Yi12nl5DWORhrP38QavFfGIx/VuPoKKLX6mP3cctkPe6\nTyFTnYpUIsfOxuHhF1mw8Byh0+jYNn8vq2dtIvl2KlZuCm4EpWEe0RUkAraApGoArw8fTsz16wVW\nyeb8+QeK1i3yxRtA1aIZ0fsPERUVhVarpXOP7mRotNh4V0QddZ1XXn6ZP+bORSIp3QAqhULBvF9/\nZdbXX5OUlISPjw9KZeEc9TkZanb9dYBW/ZqUmXg/Cs+0gN9PsJMtrIbJN18rcFzmp+aLkA1cyrIs\nrz8KMZqo/GVy482CX8YaoeWz330rMQprX9988QYQpFKsm4Zw+VR4AQE3GA1IlMpCS+USKyV6o47f\nd84kMesOXpPGIa+QF+OtPn+R5at+Y0yfL5/IEjeZTRy9tJOw68fQ67X4e1WjQ+1eONu7PRWL24KF\np4lGrWXr3N2snrWJtIQMgltVZ8z8EfQfM4DcLh2wktybo9bVqpKyZj3R0dEEBgbeu0eupoB4AwgS\nCTIrK3bt2sWoCRNQNW2MW89uCIKASqtlw+8LaTxvHiNGjHii8YeFhTF+8iRCT57C1d2dCaNG8c47\n72Bvb4+9ffFpaLfM3Y0mR0vfsc9GBsd/lYBDnqgEF/Rr42IoxVrmd7FY6HnEaKJI16qBh1jaZbzn\nfReFTIkpN7fQcbM6F4Ws4Buwt6s/hsOpBbxsRbMZzZFTVBBVxOrSsG/dMl+8AVR1gsndc4jo+MtU\n8b73/z8lM4HQyMNkaNKp5OxP/SrNsVIU78268cQSbpKK/fCBSO3tSDx5mj92fcc73Sdja22xvC38\nN8jN1rDxfztY+8NmMlOyqdOmJpOXj6ZO67yEJ7Z2tuTcP59NJkw6PSpVQSOhX+/efL9uDVZVq+S/\nlGuuRqIAxn/0ESajAceunfLPSaysULZvy+zffy8g4Hq9nmXLlrF282acHOx5+81hNG/evNhnCA8P\np02HDig7d6DChNHokpL5eNZM7iQlMe3zz4u9Tp2Vy+pZm2jQqQ6V65bNUv6j8q8T8KIozjK/i8VC\nz+Ofe9t3Le7ysrSLo5J7ZYQTueScOYdt/boAGNMzUB84Qv3mwwq0lcsU9Gj0Kptnz8emcUMkTg7o\nQs9RQbQhUZOMWa9DalfEs1gr0Ru1+X9GxV1izbEFqJo3QeZZnaQLEZzadojhnSegKqK4SUZOCldv\nX8Br6mQkfy+rOXZqT3paBqHXDtG2zuO/jZvNJowmA3JZ4ZUFCxaeFbS5Orb8touV32wgIzmLkK71\nGPjJS9RoWrVAu3ffHMZHM7/FKsAfiZUVoiiSvWc/DUNCCnmNjxo5klXr1nF73p8INapBahq6s+cZ\nN2oUM+fMwVpqi02KgFxrRKITkRjBPsMFDF4c3n+Z6rW8sXdQ0rZjR64kJyGpXwcxPZUNffrw2cSJ\nRe5fA0z76iuUrVtg/3forNTODtng1/j+hx+YOGFCoReNu6z9fgtZqdkMnd6/2M9JrVajUCjKLf/8\ncyHgULRlfpd/Wuj/TEpyP8+TuMdoosg2aAscu7tcXsDiLidLuzgkEin9W73NsnVz0Ow7jNTWFnV0\nNG1qd8fXrbAnak2/hng4+XA2+ji5d9KoHNCJar51+WnTZwgKJTmnQrFr2jg/baoxLZ3c6Gj86+a9\nDIiimS2nV+A8ZADW1YLybtqgHmmr1nH40i66NOxbqM+k9HisfXzyxfsuiqqViT948bGe22Q2se/8\nJsKuHcZoNGBv70KXun0I8qn9WPezYKEs0Gl0bPltNyu/3UB6Yib12gczdHp/qjeuUmT7YcOGcTIs\njOVffotdUBX0iUl4ODqyYseOQm1tbW05dfQoq1evZvvuQ9g51sa31XtEXIyhsf8IpBI5HDTcd5UN\nqBrxxcdrAXBwkpGYYYP98KH35nyd2kz5/HNeHzKEChUKp0s+c/4cyi4dCxyTOTuhdLDn5s2bRaZP\nTbyVzKqZG2nZtwlVGwYWOn/y5Enefv99Ll24gFQm4+VXXmb2Tz+XeXGV50bAH8RdC/1TeiNIirZy\npjZY/9xY6Hct7bvJV+4imsVycUy7H71Biwgoi4nB9qzgy+je07l55yo6g4ZKtV9HZVX8F7+Cgzsd\n6vUucMzfpTIR6ptI7ey489NsbBuHYM7NJevgEZzsXbGxynvmjJw0dCY9zlUL/gCpmoQQuXA1XYro\nz9neDW18fOF86rdicVW5lexDuI8dYWu4aojD7cPRyJyd0Fy9xvpFS+ivfKvIFxcLFsoTk9HE7sWH\nWPTZSpJvp1KvfTBTVvWjRrMgMjIyMBqNRcZrSyQS/pg7l08mTiQ0NJSKFSvSrFmzQqtLGo2eM6du\nEHoiirDQDJLifUkC4qKjCajsyukLhzD7O5N6/iSyGpXAw4mciHC016LYvmELlXyqceFcDL/P3Yy/\nqjm63QYSmwkY7CXInJ2wC/Dn8OHD9O7du9AYq1YJ4mRMLEpfn3vPm6NGm5FZbD71OWMXIggCI2YN\nLnTuxo0bdOjSBeue3fAe0A+zRsPWLdu53bcv+3bufMRP/tH4Twg43BPx4vjU/HAL/X6ehtgXZVnf\nj95kYkNSPaqsLLynW57inalOY3PoCm7FXwHAyy2AniGv4uJQOAGDVCIlsGKNx+6rU8N+hK+fhP0r\nL2HKzEQTcQVBLkdmo6JFlXtv2wq5EpNej2gwIijuLXOZsnOKfcFwcfDA27kSKUtX4di7BxKVDeoz\n58g9eZqQLhMfeaxavYbz10/g9elEpLZ5y3U21api7N6JI6F7GWARcAtPCbPZzMFVx1n0+UpuX7tD\ntUaV+WjRB9RpU5P/zZ5N235tUavVKJVKPpowgYkffljk1o+/v3+hkK/sLA3Hj1zj8P4rhIVGY9Cb\nsFEpqVu/Ei++AUoEegAAIABJREFU3Ijgur74B7ohlUoYOGg/a08docLwl8g5GYox6ipSWxXubq50\n6NgGiURC1Rpe7DiwgEO3NPjkBuF2Qk9cRyUIAsacHBwcivZN+fjDD+nYvTtSZyesq1XFmJ6Oet0m\nBg0ahKNj4dSoJ7aEcXT9KYZO74+br2uh8//79VesGtbHtmFeaKvU1hb7fi8SOuNbIiIiqFHj8X/X\nHsZ/RsDhIeL1EAv9fp6GxV6cZX0/5W1pJ6XHk5GTgruTd35WNJPZxMI9PyFpUgfv919FkEjIPnKc\nhbt/5INenxcrlo+LjZWKfs3fZO3cP7GpVwe5qyva0+fwtnIn2P9e6WqVlR2+7pVJ37YTh17dECQS\nTLkasrftol1A8cVNXm7xJjvOrCX8i68xm424ufrxWpv3cLJ7dA/07Nx05La2+eJ9F6WvN2n7jj/y\n/SxYKA3OH7zEnLELuX72Jq7+znyyaiytXmqCIAgsWLiQj7/6Ctshr2Ff0Qt9YhLfzv0NuUzG+HHj\nir2nXmfk2OGr7Nt1idATURiNZtzc7enRuwFNW1QhuK4vMlnh6JD58+YR0bo1kYuXIa8djFKhQB9x\nhRUbNxYIIXt72Jus6tYN5QuV8LysxOaOmaS4cyj1Blq1alXkmJo2bcrqpUv5YOxYbi1YjJW1NSNG\njGDGtGmF2uZkqPlxxFz8g33pN75oX5dLV68ieBesqyBIpdh4e3P9+vUyFfBnOpGLl0slcXiPyeXW\n38X0kpeGiwiBGf2WopBKsStlMSqOfyZXeRjlId5avYaVh+eTkBWP0sMDTWwMNSrVp2fIAK7dvsC2\nG7twHfNugWvS5i+ihV0wDYJalsmYMnPSuHDjJLk6NYGe1Qn0qo4gFIwZzcnN5K+9P5GpzUThXAF9\ncjJ1Kzela4N+D3UkM5tNmMwm5DLFY4/RYNTz3dqJuH00GrnzvTSwmXv243Elhb7Nhj7yPS2JXCw8\nLjfCY/hz8jJObAlDJ2hJ8EwhVZGITKdjy4YNhISEEFitGrkd22Jd5d7qkC4uHt2iZSTHxxeYN6Io\ncu3KHbZvPseBPZdQ5+hwcbWjdfsatOlQg6rVvUrksGk0GtmyZQv7Dx2ioqcngwcNKjJ96rczZ/Lp\np5/TKPh9NMZ04tN2sWPzZoKDgx/aR25uLkqlstic7N8M+YV9y47wy4kZBDUovPcN8NnUqfy6dzd2\nfe8ZVmadjqTp3xBx/jx+fn4PHcf9PBeJXMqbRxG94Ki8EKz6fjGUl/Pw09rDLo6tp1eS4W2H58uT\nEKRSzFotUb8t4OTlfQDIfArvJ0kqVST970o+ZYGDrTMtg7sWe15v0LL62AJyBQOqWjXR3byFg10F\n2tTqVqIfFYlE+sT1vuUyBU1rdCB07kLs+/ZC7u5G7oVwcvYcoFXHoj1nLVgobTKSM1nw8XJ2/LkP\npUrJLWUkmnfbIa/UBgfycih06d6duJgY4mJi8PDxLnC9wsuTO0lJGI1G5HI5uWode3eFs2XDGaIj\nE1EqZbRoU41O3WpTp74fUumjJV+RyWT07t27yH3su6xZs4ap06djX7MaWkkuErOMTz/+uETiDTyw\nEMqBlUfZs/gQgz7tV6x4A7w7YgSz58whc9ceVCENMWVno9mxmxde6PVY4v0oWAT8CQharSLSreyW\nR+7HM0l8ZsTbYNRz9dZZvN74ON+xS2JlhX2vLpxeso4eDV5Ff+4IotmM8PeSlyiKGCKu4enb9qmN\ne/+FLWS6WeM+eAKCRIIoimSs3cS2sFX0bf5GuY2jVa2u2CrtOL58M+m5mXi5+tGn/UjcLFXMLJQx\nep2BDT9vY9mMdWjVOvqM7EaUGMGxS/HYV7r3/VPVCSb7ZCg7duygenAw8VeuoqpbJ/+89loUlSoH\nkhCfxca1oezedoHcXD2BVdwZOb4r7TrVRGVbdquTSUlJDHnzTRzffhOld0Vkh3VIMw2MnTCBDu3a\nFUga86jcuZHIT+/Mp1rjKrz2yUsPbOvu7s6pY8f4cPJkdv/8K7b29owdNoyJH3302P2XFIuAPwHB\nTrYE3x/lUJY85ZCvf2I0GRChUCYlqb0dOr0WP48gnGX2pC5cin3n9iCVkrP/EFbZOqr51C23cZpM\nRiLjwsnJzcTbLZALN0KpMHpE/kuFIAjYd+3I1U+nYW5qemLruqQIgkCDoJZltpVgwcL9iKLIkfWn\nmDdhEQk3kmjcvT5vzRyMb7WKDB8xArGI+GeJnS0ZGRl8O306fV55BdFowqpyILobt5DvC6dt83d4\no/8c5HIprdpV54W+IVSrUbIl8schMjKSvXv34uTkRFJSEqoa1fKTOsmzRAwOcqzr1WHFihV8/PHH\nj9WHXmdg2svfI4oik5aMRFrEHv39BAQEsGbFisfq70mwCLiFx8JKYYOTQ97Sr6ruvdhl9cnTBHrm\nldkb2OY9DoVv5+LcRZhFM9W969K2wxik0vL52qVkJrBo3y8IFRyRuLqQu28LRp0G7gt/EeQyRNHM\ns+wPYsHCkxBzJY7fxi4kdMc5/Gr58M2uKdTvcG/e9ujalbVjxiC2apG/ombKySE74grt2rXD19eX\nzWvX8vHnX5B45BaBHk2RVexDThYMGd6a7i/Ux8m57HKDi6LI6PHj+f3PP1HVrIE5I4OcqOtY18lb\nKpdoRRTZItn+UsRMOVqd7rH7mjd+EZFh0Xy+bgJegaVTsrSssAi4hcdCEAS6N3iZFSvnYoi5jdyn\nIrqIqxgjImnbeTyQF7LVoV7vQjHbJcVoMhB69SAXYs+g0atRCHIquQXSKKgNro6eD71+zbEFKDu1\nQunrQ/KS5YhWCiRSiP/+J9yHDcXKrxIA2UdP4FuxWrm9WFiwUF7kZmtYOm0Na3/citJGwYjvhtD7\ng66FrMoePXrQcO5cTv/2O9KQ+ohaHYZjJxg9ciS+vr7odAYyU20JqPAiKkMmvn4u9BvQhHadaqFQ\nlGzehIWFMWPmTMLOnkUQRXx9fRk6cCADBgxAoXiwU+i2bdv4a9VKKowfReauveRE30Dq7ETm2XMY\nBYGABnkOZDmOBgznLtD7q28e6/PasWA/G2fv4KUxPWjeu9Fj3aM8sfxiWXhsKrlXYXjnDzl17RCp\n0Rep7uhDw+79HpiEpaSYzWaW7J9Nmi2oerfD2mQmY88+LmZFcnF3GP2avfHAuPH07GQyctPxaFCP\n219+i0u/PtjUybM4ci9eIuHXeTh0aIsYl4gh6gb9O4wp9l4WLPzbEEWRI+tO8uvoBaTEpdFlaFve\n+Oq1QjW57yKVStm2aRMrVqxg5bp12FjbMOyvRbRo3prVy46zetkJ0tPU1KztzfvjutCoaWUkJQy5\nBdizZw+9+/XDqk0rFN06obkWScz+Q5y9HsWfixezd8eOB6Yf/WPRImRNG5N97CT6Owl4T5mEVGWD\nSZ1L4rw/sAlNIlepJGHhAoYOGkiDBg0e+TO7GhrFz+/Op36HYIZ/M/CRr38aWATcwhPhbO9WZPrR\n+0nPTmH3+Y1Ex11CLldSN6AprYO7IpMWPWmj4i+RYs7GbcSo/P1qq6pViJvxLfZdO7Bl30pGen1e\n7F6byWxCIpWiPn8RqwD/As43qtq10AQFYX8mmuo+danTc9ADC5lYsPBvIi7qDr+8/wdhu84TULsS\nU1aPo0aToIdeJ5PJGDhwIAMHDkSTq2fj2tMM6vs/MjNyqR/izyfTWlC7XiVEUWTOnDl8++MPJN1J\noH7Dhsz66iuaNGlS7L3fHzMGVd/eqILz8mZY+fshVanIjbhMeGws69at45VXXin2ep1Oh2BrTfau\nPXi88xZSVd58lapsqNS5P7YXVHj5qpn5zXqaNWv2aB8YkHw7lU97f4uzhyOTl40u0b73s4BFwC2U\nObnaHP7YNQtly8a4DxmPOTeXCxu3kXx0Aa+2eqvIa2KSolDUrZkv3gASuRybmjUQTSY0Bg1Z6vT8\nxDH3U8HeHaWgQBsVjdylcBupuyv+UhWNq7crnYcsAlEUyc7NQC5TYK18+rWDLTzfGPQGVs/azJJp\na5ArZLz741B6vdv5kcRIpzOwZf0ZViw6SkZGLiFNAhk4tCU1gu+FkE378ku+/+N3bHr1wNXDnasX\nw+nQtSuH9+2jXr16he6p1WqJunIFnzcLpiFV1a1N+pbt2PToyqbt2x4o4AP69eP41M8xZecg+2d+\nc1HELVaFRpfB7wu/QS5/dOHV5GiY0utrtGot3+z6EgeXosuJqtVq0tLS8PT0LDKN7NPg2RiFheea\nM5FHkFerjOPdAgIO9lQYNpibn80gOSMeV8d7WYx0eg3JmXcwm0wY7iQXupchJQWFd0XMBj0KubLQ\n+bsIgkCfJoNYum82WhsFTt27Ivw96USjkdwz5/FtOKh0H/Qf3EqMZHPoCrI1GYgmE74eQfRuPBDb\nIqqdWbDwpJw/cImf3p1P7JU4Wr7UmHd/egMXr6JfbovCaDSxffM5li44QmpKNvVD/BkyvDU1ahWM\n/dZoNHw7axZOo95DXiHv/nZNGiFqdUydMYMNq+/lqxZFkStXrpCZmYlUocCYnl6g1K8hOQWpvR3k\n5ODs5cODeOWVV1i6ciW7ExJQnzuPXaO8HCe2MSas0iFTcv2xxNtkNDH91R+4ceEW07dMwq9m4XHo\ndDreGzWKZUuXIlUqUcpkzPzqK4YOffSES6WNRcAtlDnxWfHIGxeMyRRkMqz9/Ej6h4AfDt/BkfCd\nKF1cUacmASLqi+HY1KoJokjO6TD08QkoKrjg51ntoVatr3tl3uv1Kb9sncadX+bg0L4tCAJZBw5h\n0uvJzs0ok+fNyEll+cHfcBzQj4rBNRENBtK272HJgdm83WWipWyohVJDnalm/odL2Dp/Dx7+bkzf\nPJHG3Uu+/yuKIof2X+bP3/YTfzudGsHeTPr8BerU9yuyfWxsLDIbm3zxvotVlUDOrd+c//f169d5\noW9fYuLiEOQyDCYTqavW4jpkIFIbG4yZWaSt34hN7WC0J0IZ/vXMB45TJpOxZcMG3nzzTf5atgxj\nRgY2vgH4nq9AljqFmNRQRFF8pLkliiI/vzufU9vOMvLX4YR0Kbx6APDuyJFsOHUS10njkdraoou9\nzaiPPsLT05MuXYoqf1R+WATcQpnjautKwo1YaHQvJ7loNqONjcXZrwcAETfDOHHrGB4TxyK1t0M9\ncQpuw4aSumYdqavXIRqNIAhgMmN7PYnerd4uUd9avQaZXIFto4ZkHTkGooiqfl0EpZKzB0OpHVj8\nvt3jEhZ5BJtGDVDVztvvExQKHHt1JfHCTG4n38DHLaDU+7Tw3+Kuk9rsUX+SnpBBv3E9GTz1Faxs\nil+Vup8LZ28xf/ZerkTE4xfgyrSZr9C4WeUHiqCXlxf6nByMWVnI7O+tJuliYqlZNW+f3Ww206FL\nF3Jq16TCkAGkb9+JncGIqNcTO3VGnvNZVjYSW1s0R47x2+zZ1K798DK6EomEOykpOHRqhyk1Hafb\nmchsPEhpaYduI5w5c+aRnNeWfLGGbb/vpf+kPvQc0anINllZWSxftgzXyROQ/h0nr/TxxtClI1/O\nnGkRcAvPPw2rtOTU1i+R+nhh16ghZo2GzE3bcbN1x7OCLwDHow5i16srMmcnzHoDiCJWgf54f/wR\nhoRETLlq9InJqDdu581OxRdPuB+T2YhUqcS+eVPsmzfNP557KQKjqWyy8KRr0pDVrFTgmCAIKDw9\nyFKnARYBt/D4pMSn8fO78zm+6TSBdf2Yuv5DqoaUvILd7dg05v9vD8cOX8PF1Y5xk3vQsWvtEqU6\ntbW1ZfjwYSxetgrViy8gc6mA5vJVNDv3MHb1Oq7GJrH/6An0Tt44NmiBaBTAZEKiVOLUuydO3btg\nSE3DnJOD9uBhpr/3wSMtRWu0WhQ+XrjWaIvnYT3p1WSIQW5IFUq02gdXafwnG/63nUVTV9Hp9TYM\nnd6/2HZJSUnIVap88b6LwsuTmOOnStxfWWERcAtljp2NI0Paj2L7kTXcWr0eiVRKzYBGdP2HFa3W\nZmPz97KcRCHHqnIg2UeP49CmFQrPvGQK2rMXqeH3aOEh7k4VQaNHExmVX4hBNJvJPXScpl4Pf+t/\nHHyd/Lgdfhma3IsjNet0aK5H49n54R77FiwUhSiKbP9jH/M/XIxeq2f4NwN5aUyPEjup5WRrWfLn\nYTauDUWukDH07Ta89GpjlMriw7eK4vtvZ2KnsuXXPxcjc/TCvWo9arw+lUlrzgJnAXBv0Ati89rb\nBHUl9sAqTLkapH+LoSE1jay4eF566cFpSu+n/0sv8fns33F1qYLOUSAtWIb2xk1MWVmEhIQ8/AbA\nvmWH+XXUApq9EMLYeSMeuOLg6+uLYDSiv5OQ/zsEoI24QofGTz9O3CLgFsoFD2dvhnYYjdFkQCJI\nC5QEBAhwCyI67Fx+WsQKL/Xmzs+/orkaiVXlAIyXo5ClZNLuPuvbbDYTdu0QZ2NOYTQZqO5Vm2bV\nO6BUWAN5xUd6NxnImj/+xKZBPSQuzujOXMDRIKdBg6LLDT4pdSo35fi2A6StWoeqeRPMublkb91F\nVe/aONu7lUmfFp5vEm4m8cNbv3Fmz0Vqt67BmLlv4x3k9fALAZPJzLZNZ1k47wDZWRq69KjL62+1\nwbnCo9VVEEWRq7eT2XMmkmvyyvj1HAmAm6MtdQK9qO7rho+LI2Z9Lq/0fxWnQQORS61Qpsmo1OJl\nIn+ZgzK4MoLRhO7MWb6e8RWengUTMl26dIkvZswg9EwYlQMD+XjCh7Rufa/M76BBg1m9OApRa+C6\n6jK6zUloz5xj+eLFD00GA3B0wym+GfI/gltVZ/KyUQ99+VEoFMyYNo1JX3yBVddOyD3c0V6KQH/k\nGJ8dPfpIn19ZUK7lRAVBcAb+ADoBKcAkURSXFde+vMuJWnh6ZKrTmL/jWxT1amEVXBNDYiLZO/ZS\nwzMYpdIGTydvavg1KBQ3vvbYQm4akrDt0g6JUon60DGUt1MZ3nlCgbaZOWmcjT5OjjabALcqVPWt\ni7QM856rNVkcurSTa/HhyOVKGvg1IaRqm0IvLqVFeZcTfdS5DJZyoo+D2Wxm67w9zP9wMQDDvx1E\n97c6lPh7FH4hltnf7yTqWgK16/nyzqhOVA56tPSgKZlqNh2/xMZjl4hNzkAqEahXuSKtggNoVtMP\nfw/nQlbshIkTmb9sKYrWLZGp7HE1VgJtNu3d9ahUNgzo35/q1asXuOb8+fO0bNsWRctmKKsGoY+9\njXb3XhbOnZdvqf/2827WrjhJxx7eXL99CndXV4a+/jr+/v4PfY7Tu87zaa+vCaznzze7pmBjZ13i\nz2D9+vV89d13xN2+TZPGjZn22WdlW+e7hOVEy1vAlwMS4E2gLrAVaCaK4qWi2lsE/L9Fdm4Gx6/s\n41bqDRytHWkS1AYft+IrCiWlx/Pnvh/x/GwSEkWeWIuiSOov82jv2YLagY2feEwpmQkcurSTuPQY\nHFXOtKjaHn/Pak9839LmKQj4I81lsAj4o3InOpGZb8zm4qHL1O8QzNj57+BeybVE16al5vD7r3vZ\nvf0irm52vPV+B1q3r1FiL21RFDl97TZrDp1n/7nrGM1mGgZ50zWkGm3qVsbJ9sHiJ4oiGzZs4H/z\n5pGdk02VFn24mikldPaoYsfQtVdPQhUy7Fu1yD+miYxCtnUnMdevs3Preb6bsYUX+jbk/bGP5jx2\nZu9FpvT8CqsKSq67XkZjVNOvdx8+HD8ee/tnL7TzmasHLgiCCngJqCWKYg5wRBCETcAgYGJ5jcPC\ns4udjSOd6r9Y4vZxKTewqRqUL96Q5ywmr12DmCvRTyzgSenxLNj9Paq2LbGu0Zjs+Dus2ryA7vX6\nUsu/ZPttzyOWuVy2iKLIlrm7mTdhEVKZlHG/v0PnoW1LJL4mk5ktG86wYO5+dFoDrw5uxoAhLbC2\nfvjyMoDOYGTrycss23eG6DtpOKis6N+uHi+2CKaSe8nLIQqCQJ8+fejTJy9H+cxV+7l94vIDn+Hk\nyZPYvlMwsZNV5UDuJCVx/GgEP327jfoh/rwzsmiP8eI4f+ASn/b6GpOVkUPKc0gbN0eiVDJn5w7W\nb9xI2MmTWFmVXdnTsqQ898CDAJMoitf+cew80LqY9hYsPBA7G0eMMUmFjpsTknCwfvK95v2XtqHq\n1BaHdnlfUaWPN3I3V3b9uZyafg0QhLJZDv8XYJnLZUTirWS+GzaHs3svUr9DMOP+eBc3H5cSXRt5\n9Q4/frONa1fuUK+hHx+M64pPpQoPvxBQa/WsOXSBpXvDSMnKpaq3K58N6kTnhlWxKmGxkgdxIfoO\nFV2KzsN+F3cPTzKSkpE533tRMGVmYmvlwqzp23H3dOSTaS8ilZV83p3Ze5FPe32Nk5cDm1PW4jhi\nNJK/98qV/n4kzl/A6tWrGTSo7JI6lSXlKeC2QOZ9xzKBApUvBEF4C3gLwEFV8kxCFv57BHhWQ3p6\nJVl7D2DXpiVIJOSGXyL33AXq9pjyxPe/nRyNU3CHAseUfpVIMWpRa7OxtX7wD9JzTInmMhScz76+\nvmU/sn8poiiy668D/DpqAaIoMmrOW3R/q0OJrG5Nrp6F8w+wYXUoDo42TJ7ahzYdSrZcnqXWsmz/\nWVbsP0tWro5GVX2YNrQrjar6lFrCoci4FC7dSmR8vwe/300cO5ZRUz5B5lIBuUsFTDlqdGt30Ch4\nKDKZlK++74+dfcn3rc/sucCUXl9TsYondYdWZufqs/niDXmrBGK1IPYfPmwR8BKQA9y/2WAPZP/z\ngCiK84B5kLcHXj5Ds/BvRCKRMrjdSNYe/4u43fuRyGRYy6zp33oEdjaOT3x/WxtHDElJyF3vWUCm\n7GwwmVHKS/5D8hxSorkMBedzw4YNLfO5CNIS0vnhrbmc2BJGcKvqfLjwfTz8SraCdPJoJD/P2k5y\nUhY9ejfgjRFtsbV7+HKwRmdg+f6z/LXrNNkaHW3rBDK0SyNq+ZV+/ev5206glEvp2qj6A9sNHjyY\nuIQ7fPX118hUKow5elrWfxcJVkyb+QqeFUu+hH9yaxhT+36HT1Uvvtk9hZNnTmBOSinUTpKSil+d\n+o/8TM8K5Sng1wCZIAhVRFGM/PtYHaBYpxcLFh6Gk50LwzqNI0udjtFkxMnOJd9yuBB9koMRO8hI\nT8LJ2YO2NbtS06/kfl7Ng9qyfd1m5K6uyN1cMalzyVi+ltqBTZDLSran+JximculxPHNp/nuzV/R\n5Gh55/vXeeGDLkilD4+OyEhX8+uPu9i/+xKV/F344bch1Ax+cD5xAL3ByNrDF/lz5ylSs3JpGezP\ne72aE+RdMue4R+XUlRj2nInk3Z7NHur4JggCkz+ayJiRo4iMjGbuj8e5cT2ZqTP74eAk4eUBA9i8\n8f/snWVAFdn7xz/3Xu6lGwUERRpRBBNbxO7uNdbOtbu721XX1rW7MVFULCwUUVRUREVAuuPe+b/g\nv7j8VMB2dT7vnDtn5pzBM985z3niIBKplJatWrFo3jxMTN7dXji/5zIzOyzB1q0os7zGoWesS61a\ntdBBIMH7HDrV/7HWBZLqf5fuW7d/lbF/C76ZgAuCkCSRSPYBUyUSSQ+yPFebAh9f+01E5H/Q0875\ndX7nyVWOBxzCoEMrilgXJTX4CUe27QEkFM9nMpgS1uWIS47FZ/4SUFegTEnB1MgSD4+GX34A/yHE\nufz5JCeksGroJrzWncHWrShjtvyBlXPeAiwIAudOB/LnohMkJabSuXs12nWunGchD0EQ8L79mCX7\nLvDiTRxlHSyZ36sxrrb5iyX/FJJT05m13ZtCxnp0qp3/BEwSiRp/r7nF44fhTJjRkhKuFjiWKE5C\nUSsKjhmBIKjwOuPD9Ro1CLh9O8cHz4mNZ1nYYyXFKjow48gYtPWzMqjJZDLOnTpNoxbNCRo3GUEq\nRaGmxrwZM7CwsPjiY/9WfOtELv2A9UAEEAX0zS3sRETkUzkbcAyD39qgaZcVhqbl5AgdWnFut1e+\nBRzgVcxzFGbmaFYsi5q+PslX/Nhy7k961B6GTPZL50ES5/Incu9SELM7LSUiJJJ2o5rRaXIbFPnI\nhhYdlciSuce4dOEhjsUKMWxsI6xt8za1B4aEs3CvDzcfvcTW3JjlA5tTsZjVVy+qM2fnWUIjY/lr\ncCvU5fmbK+lpmUwatQv/m88YOaEpVao7sX37dpI0NNBv3CD7PN3mjYn48y+8vLxo1CirnsK+xUdZ\nOXQjpWuXZPK+EWhq59xKiIqKIuTpM3SrVkJepAjK+HhGT5yIpaUlTZs2/XID/4Z80zeQIAjRQLNv\neU+RXw9BUBEXE46hTc7kDho2NoTGhOX7Oq+jQ3kS+QiziaOQyrNesJrFHHmzeCUPnt+muPU3C7v+\n4RDn8sejzFSyZdoets3YS0GrAizwmUqJynnnFPhn1b1swXFSU9Pp2b8mLdu65+mNHZOQzLIDvhy4\nFIChjiZj23vSrLILavnIef65HLkSyOErgfRs4E4ZB8u8G5BVi3zKmD3c9HvK8HGNqVXPBcjKzpZp\nmXOVLJFIoEhhAgMDadiwIRsn7GDbzH1UbenO6C2D3vtBNHL8ONRre6JX5a2hKNnYiEEjRtCkSZP/\nZJXAX3oJIfJzIpFI0Tc0Je1pCBq2b0U87elTDAzz76TzIvIpmsUcs8U769oSFK7OhDwK/qCAR8dH\ncOOxL/GpcVib2OFiU/5X3zP/5Xn9LIJZHZcQePkhtTpVY8Cy7mjraeXZLi42maXzvTjvfR+n4haM\nGNeYIkVzDytTqlTs9w1g+YGLJKdm0KlWGXo0cEdXM/+Vyj4H/+BXTNt6mrIOlvRokL9cDCkp6Uwc\nmbXyHjqmIXUbumb/VqxYMdQOHcxxviAIEPoCB3sHFvZcxfH13tTvXpNBq3p+0IfA7+o1DIYMzHFM\n09GBlxv+JjExEV3dd4IoSE9PZ8+ePRz28sLE2Jhe3bvj4uKSrzF9C0QBF/lPE58Uw/3nt1CplDhY\nlsRY3xRUu1u9AAAgAElEQVSAas51ObVlJ4a/tUXd2orU4CfEbNtDw5LN831tXU19Mp+8G2euDItA\nX/P9+2aPXgSw99IGtCuUQ2ZamOc3r3PlkQ/daw/Nzs8u8mvhs/syi3qtQlAJjNk6CM/2VfJuRJaH\n+YJZR0iIT6Fbnxq06VAxz1V3UGgEM7adIeDZa8o6WDK6nSc25vmLBf8SvIiMZdhfhzEz1GVuz0bI\n8+GQl5SYyoQRO7l39wV1GltxO+A4CSmPaNasGQqFgpYtWzJ6wgTij55A26MqCCqSzpzDRCLnxoYH\nXDlyg47jWtJlattcV9EFzcxIiohATf9tAEVmdAwKhQJNzXfnZlpaGjVq1yYoIhyJqws8vM+G6tVY\nsWQpnX+QsDNRwEX+s9x5cpWjfjvRcimORCHH5+QJKjp5Ut2lAaXsKiGRSPD5ew9hMREYGJnSwKXZ\nR2VQs7MsgeTmbuLPnke3WuUsz9U7AaTeDcS18btVxVQqFYeubcWoe6fsymc6FcoTvXErVx6cpXrJ\nBu+0Efl5SUlMYcWgDRzfcBan8naM3TYYcxvTvNulpPPX0lMcPXgLa9uCzFrUAVv73NulpGew+ugV\ntpy+gYGOJjN+r0+9co7f1CwcGZdIv6X7UKpULO7XFIM8vM4hy5t+zJDtPA2OICbtKjPXrEdiUxTJ\nlr8ZNnoUl3zOU7hwYa5cuMCAIUM4OmUGEomEJg2aYxxXlqtHbzJgWXea9s87terIIUMYOWM6al1+\nQ25shDIxkaR9B+nTuzdqau9K4aZNmwiKjkKvTw8k/597XqOkC/0GDqRVy5ZoaeVtQfnaiAIu8p8k\nKTWBo9d2UHBofxRmWWZxvfq1uTJ3MQ6FSmBuXAQ324q42VZEEIRPepHJpDK6eP7B3iubeHnyDFKZ\nGlpyLTp49EVH8938yW/iwlDJZdniDVkmd63K7jzYe0oU8F+IJ3dCmN52IS8ehtFhbAs6TWqNWj4c\nuYLuv2L2lAO8DI2mdYcKdO3lgSKPTGjXH4Yy9e9TvHgTR/PKJfijeVX0tb9tatC4pFT6L9tPVEIy\nqwa1xNos7yRcEeFxjB68jYjXcZjZxOD3OBL9P/pmz9X4E6fo0bcvJ44cwcLCgv27diEIAi8fv2Zc\nw5mEvnjJxD3DqNI8f2b6nj16EB4RwZx585DraJMWn0Dnzp2ZNWPGe8/fc+gQsrKlssUbsuqAa5qb\ncfnyZWrWrJmv+35NRAEX+U/yKPQuWo4O2eININPTRbNCWe6F3MDc+G3Wr89ZhRjpFaRnnRHEJUWj\nVCpzxJn/L3I1dZRpaQhKJZJ/mQ5VySmoi3vgvwSCIHB45UlWDduErqE2c09PxK1GiTzbqVQCu7dd\nZsNf5zAy1mbu0t9wK1M01zbJqeksO+jLznO3KVzAgNVDWlHWIe9QtC9NTGIK/Zbs5Xl4DEv6NcXF\n2jzPNk+DIxg7dDvJyenMWtSBGvXLo9W9a465peNRjbMTppCampqdqzzw8kMmNp0DwLwzk3Cu6Jjv\nfkokEiaMG8ewIUN4/vw5hQoVyrWQia6ODqrklBzHBEEgMykZHZ2PK8X6tRAFXOQ/iYAA7xHSr2Uy\nzE9aX0NdE4x1CxB/9jx6NT2QSCSoUlJIPOFNJZvaX6VfIj8OyQkpLOr9F+d2+FKunhsjNg7AsGDe\n6Xaj3iQwd9ohbvo9paqHE4NHN0Qvj5Sh1x+GMmXzSV5Fx9O+RikGNKuMpiLvULQvTUxiCn0W7+F5\nRAwL+zbBvZhVnm3u3n7OxFG7UKirsWhlZ2zsTFGpPpCk71+Hz++5zOxOyyhQ2JgZR8diaZ/3h8L7\n0NLSwskpb+//3t26cbprF5QlXZDpZTm4JfldR1euRrlyP0YxI1HAPwJBEHgYeofHYVdRCUpszcpT\nzKrUr1zU4rthb+nC8YN70I2IRF4wK4uUMjGJ5CvXca7a97v1q3Xlbvx99k8i/W6hVsCE5MfBuNq4\n42JT/rv1SeT9vHr1ipUrlxMYcB0HJ1f69h34yfnag/2fMa3NQsKCX9NtRgfajmqar5rdfleCmTv1\nICkp6QwZ3ZD6jd1y/QjNyFTy5yFf/j59A0sTA9YMaU1p+/yFaX1pwqLj6b90H2HR8Szu2zRf4n32\n1D3mTT+EmbkBMxe1x8w8K+Vx65Yt2eNzEb1WzbLHn3TBl2qenqirq7Nj9n7Wjd2Gc0UHph4chb7J\n1y8BWqdOHQb37sO8OfPRdXJAGRePPCWVY15e+a7H/rX5pvXAP5YfrR74qRtbeJN0iyF9tFFTg6Wr\nk1HgSEP3Hv/JGML/OrceX+L4jT1olXIFhZyUG7cpZ1eFmq5Nvmu/BEFFSPgjEpPjsSxojYFO/qpJ\nfQ7fuh74p/Aj1QMPDAykpmdlWjWSU8VdxtUbSrbuS+PESR/c3Nw+6lpe686wfOA6dAx1GLd9MCWr\nOefZJjNTycbVPuzccomiNgUYP60FVta5pzN9EhbF+A3HeRAaQcuqLgxtWR3NfCSA+Ro8ex1N36V7\nSUrNYFHfJpTJ4yNCEAR2/n2JdavO4uJamMlz2uSwMsTExFC5enXC01JRWVuh9joCeXQMPqfOcHDO\nKU5sPItHu8qMWN8Phca33Y4KCwvDx8cHIyMjPD093+vw9qX54eqB/9cJj37B41fXeXilEHq6Wfub\nHZrrUrzqfUIjgiliapfHFUS+NKXsKmFt5kDgs5soU5U4eg6ioOH3T4sokUgpapb/vTmRb8/YMYMZ\n2U/OoF7/vwJsDA62cYwc0Z+Tp3zzdY3U5DSWDVjLyY3nKF3LhdFbBuXLZP4mMoEZE/cR4B9Kgyal\n6DekDuq5CLEgCBy8fI+5O86ioS5nYZ8meLja5m+gX4Fbj18ybNUhpFIpa4e2zjOPekaGkqXzvTh+\n+DY1ahdn+LjG7zjmGRoacufmTQ4dOsSdO3ews7OjdvU6zOm0nLvn79NxfEs6T27zXVa+5ubmtGvX\n7pvfNz+IAp5PnoQ9oGUjrWzxBtDUlNKhpQa+PvdEAf9OGOiYUKlEne/dDZH/GKdO+7BuTs5VY+fW\nuvQffRmVSpWnULwKfs2UlvN5evc5v01oxW8TW+WrCMnN60+ZNekAqanpjJncDM86uTu4JaakMXPb\nGY5fD6KcY2Gm/16PAvrfz4Hq1I2HTNh4HDMjXZb2b06RgrlX/YuPS2bquL343wyhQ5fKdOnpgVT6\nfmulmpoaLVq0oEWLFjy5E8Lw6pOJCov9qNj5Xw1RwPOJhkKTV6/f3W549RrU5drfoUciIiKfioG+\nDuGRSgwN3opuxBslurqaeW6HXT16g9mdliGRwIyjYyhXr1Se9/vHhLxh9Tksixgz/89OWOWRUe3h\ni0hGrD7Cq6g4+jWpxO91yyH7TnuvgiCw8aQfyw/64mpTiIV9muQZ5x3yNJKJI3cRGRHPqIlNs1Oj\n5sXF/VeZ03kZ2vpaLPSZglN5+y8xhJ8SUcDzSTGrUqw8tJszF5KpWTUrgP/y9RT2HU2iR4MfwyNR\n5P0IgkDwq0BuPbtKhjID50IuuNi4I5PmvWIS+Tn5vVtPRk5by86/DNDUlJKWpmLEtAR+//33Dwq4\nSqVi24x9bJ68CxtXKybtHY65dd6JWZISU5k3/TC+54PwqOnM0DGN0NTKfR/36NX7zNh6Gh0tdVYP\naU0pu++3NZSansm0Lafw8ntAvbKOTOpcJ8/iJJcvPmT25AOoa8iZv7wTzi55O9qpVCr+nrKbLdP2\n4FTejkn7RmBS6N3oj4iICJavWMHFq1dwsrNj0ICBODr+mltWooDnEw2FFs0q96Vtj9UUsUxATU3C\noyfpNKzQA12tvPe9RL4f3v6HufHCD23Pqkg1NPC+eJE7z2/wm0c/pKKI/5JMmDCFbr8/xLr8Ccq4\n6XLrTiJVqlRj5sx57z0/KT6ZeV2X43vAj5q/VWXIX71Rz0du8ZBnb5g8ehevXsbQd1Btmrcpn7uX\nuVLJwj3n2XnuNqXtLZjdvSEm+t/Pwhcek8CI1UcIePaa/k0q061euVz7r1IJbNt0kc1rfbB3NGfy\n7NYUKJi3x3hSfDJzOi/j8qHr1O1agz9W9Hivs1pISAhlK1QAB1ukdnbcefyIzRUqcGT/fjw8PD5n\nqP9JRAH/CKzNHenXZA7PIx6jElTULWmPmuz7eIGK5I/YxCiuPTyH+fhRyHSyXoTapVyJXLCch6F3\ncLLK2/wp8vOhrq7O1m37ePLkCYGBgTg6OmJv/35TbWjQSyY1n8fLR2H0XdiV5oMa5Cvq5IrvI2ZN\n2o9CXc68pb9RslTuYVaxiSmMXnuUa0Gh/FazNAObV8lXLvGvxbUHzxmz7hhpGZnM790YT7fc/XyS\nElOZM/UQly8+pGbdEgwZ3TBX57x/+Pfz7b+kG00H1Pvg8x07cSKCW0n06v+/34urCzKLQvQa0J+g\nuwG/XDSQKOAfiUymhrV53kkARH4MQl4/RMvBIVu8ASQyGerlS/Hw/n1RwH9xbGxssLGx+eDv17xu\nMaP9IhTqcuaemoirR/E8rykIAjv+vsSGv85i52DG5NmtKWiau5XuSVgUg1ccJDw2kSmd69C4Yt73\n+VqoVAKbT19n+QFfrEwNmd+7cZ6pUZ89iWTK2N2EvYyl/5C6NG1VNl9i6nvgGnO7LEeursbc0xNx\nrZ77uE+eOoVmt845jmmVcCZ0x26ioqIwMfn6IZs/EqKAi/zUaCg0UcUnvHNcFRuPluL7FyMQ+TER\nBIHd8w+xdvRWbFytmHpgJAWL5B4uBZCelsnC2Uc4cyKAGrWLM3RMIzQ0cl+F+gWFMvyvwyjkMtYM\naU1Jm0/LMPYliElIZuKmE/jee0bt0vZM7FQH7Tzirs+cuMviOcfQ1FIwb9lvuLjlnQxHmalk48Sd\n7Ji9H8dytkzcPSxfz1dPX5+UhITs5E0AqpRUEIQforjIt0YUcJGfGluL4ij9dpB46zY6pbISdKS9\nfEXy1eu41Rn+nXsn8iOSnpbB4j5/cWqTD9XbVGT4+v5oaOW93x0TncTk0bsJDHhB114edOhSOc9V\n6MFL95ix9TRFTA1Y2r8ZhYy/nz/NjUcvGLvuGHFJqYxp50mraiVz7X96WiYrl57kyP6buLgWZty0\nFhibvFtT+3+JCY9lZofF3D57jwY9atJ/abd8J2cZ2KcPU1b8iaJbZ6SamghKJUlHvWjSrJko4CIi\nPxtqMjkdPfqxY99qko97I1VXJy08gkbl22Gib5b3BUR+KWIj45jcYh73fIPoPKkNv01slS9TcMiz\nN4wftp2Y6CQmzmhJ1RrFcj3/n7CsZQd8qVCsCHN6NkI3H05xX4MMpZLVR66w4YQfFib6LOnfDKfC\nBXNt8yI0mhkT9vH44WvadKzI7709UFPLe7/+zvlAZrRfTFJsEiM29KdOF4+P6usfAwcSGBTElhlz\n0bW2IvllGGVLl2b1ihUfdZ2fBVHAvwNpGan4B18iIi4ILYUJrjbVMNbPOxxF5NMwNy7CoKZTefHm\nCZmZGRSuYotcrA4m8j+E3H/B+EaziA6LYfyOIVRvUylf7bZv8WLjX9cAFQ2aW1GhSu7OXiqVwII9\nPmw/e4v65ZyY3LkO8nyI39fgeUQs4zd4EfDsNU0qFmdEG488TebeJwNYPPcYamoyps5tQ8UqDnne\nR6VSsXv+YdaP24a5jSmzvMZhUzLv3On/i1QqZfWKFUwaN467d+9StGjRfBUm+VkRBfwbk5yayFbv\n2ZRxzWRgB3UCH75g9eaLNHTvhZ3F93Nc+dmRSqUUKShmyxN5P7e87zK11QLk6mosOJf/5CGjhs3j\nxqVkdHRi8ah2mN07Y/A6sYnDR04jl7+7961UqZi25TSHLt+jg2cphras/sHMZF8TlUpg13l/lu6/\ngFwmY06PhtQuk7sQp6Sk8+fCE5w46k/xkpaMndI8T+c8gPjoBOZ1/ZMrR25QrXVFhq7pg7be55m7\nLSwssLD4/mmTvzeigH9jrj44Qd0aStYteeuEUauaBp37/Y1toZliZTMRkW/M8Q1nWdz7LywdzJl+\nZAxmRXM3H//D5nXe3LychqN9BLMmnUNHW0r/bkbUaBHA7t276dChQ47zlSoVUzaf5MjV+/Rs4E6f\nRhW/S9jTq6g4Jm8+xfWHoVRyLsqE32phapj73vXjoNfMnLSfF6FRdOxahU7dqiFTy/tdFeD7gFkd\nlxAdFsOAZd1p0q/uLxfq9TURBfwb8zzSn9kzciZmqFlVE4k0muiESIz1RFO6iMi3QBAENk3aydbp\neylduyQTdw1FOx9JUwRBYO0Kb3ZtvYxE9ogF06+iUKgAkMkkdG6jhtfRvTkEXKUSssW7b+OK9GxQ\n4auN60OoVAK7z/uz7MBFJBIJEzrWolnlEnkmZtm74wrrV51F30CbuUt/w61M0XzcS8XOOQfZOHEH\nplYFWHxxOo7lRAvYl0YU8G+MQk2DN9EZOY6lpwskpShRqGl8p16JiPxaZKRnsKjXX5za7EO932sw\naFUv1PJIDwqgzFSxZN4xvA7fpnR5U86eX4xCkTNGOipaQFffMPvfgiAwf/c5jly9T59G30e8n4RF\nMW3LKfyfhFGhWBHGd6yVp8d7RHgc86Yd4vbNECpXd2To6Ibo6edt+n7zKpq5XZZz68xdqrepyJDV\nn28yF3k/ooB/Y4pZejBh1j6qumuirydDEASmLYrDwsRKTMkqIvINSE5IYWrrBdw46U+XKW3pOL5l\nvsy6GRlKZk3az4VzD+jYtQodf6+Mg/1EdhxIoF2zLBP0s9AM/tyYwt59PbPbrT56hR3nbvNbzdL0\nbOD+1cb1PlLTM9lw4hobTvihraFgape6NHQvlut4BUHA+2QAyxYcR6lUMXRMQ+o1cstf9rkjN5jf\n7U9Sk9IYuqYP9bp5iibzr4go4F+AtIxU4hKj0NM2RCOP5CCudhWJuvWMomWuUKGMNo+epCMo9Wle\nucc36q2IyK9LTEQc4xrOJPj2M4at60e932vk+F0QBJ48eYJKpcLOzi5bfNLTMpk2YS9XLj6izx+1\nadkuS4j3H/CiebP6LF4djZGhjKs3E5g2bRbu7lm/H7kSyF9Hr9C4ojNDWlb7pmJ2MeApc3Z48zIq\nnvrlnBjWqjpGeayE42KTWTLPiwtn7+PsYsmoCU0oZJl7FjaA9NR01o3Zxr4lR7FxtWLstsFYFcu7\ngInI5yEK+GcgCAIX7h7getBZCpooCH+ThpttRWq4tf1gkQyJRELN0h0o61CPV1Eh1HAxwMKkqPiV\nKiLylQl7Gs7outOJehnN1AMjcW9YJsfvAQEBdOncmrCwF0ilYGhYkPUbdlCypBsTR+7ipt9T/hhe\nn8Yt3rZzc3Pj0eNQfHx8SEhIYFu1ahgZZQnezUcvmLrlFOUcCzO+Y61vNsdfRMayaO95zvoHU9TM\niFWDWlLeKe/saL4+QSyee4zEhBS69/WkdYcKyGR5O6o9DXjOrI5LeHr3OU3716PXvE75Tswi8nmI\nAv4Z+AV5E5vuy31fCwqZqRH5JpPWPW5z4a4mVVya5FquUl/HCH2dvL9sRUREPp+nAc8ZXXc6Ganp\nzD0zCecKOUOmkpOTqVfXgykj1OjSxgyJBHYdSqRxo3q0bzGfe3deMnxcY+o2dH3n2mpqatSsWTPH\nsZiEZEavO0YhYz3m9Wz0TYqSJKakse74NbZ530ImlTCgaWU61SqTZ4x5fFwyKxad5MzJAGztTZmz\npAM2dnk706pUKg4s82Lt6K1o62sx/cgY3BuU/lLDEckHooB/Bv7Bp9m7yZBCZlmPsYCJGmsWGuLm\neRLfgJMUK+pMDdcOGOgYf+eeioj8uty/+ohxDWYg11CwwGcq1iXeXY3u37+fks5Sfm/3tvRl8/r6\nbNxSibu3Q4mI9ebZC2MEIff0opBlmZu46QTxSaksH9AcPe2v65yaqVRx+PI9Vhy+RFR8Mo3cizGw\nWRUKGOjk2fa8932WLThOQnwKnbtXo32XyvnKqBb5Ior53f7k5um7VGhUhqFr+mBoavAlhiPyEYgC\n/hnEJibiYGOY45iNlZyMTIHwABuWrwtnxfp5dK8/Vcz8JSLyHfD3uceExrMxKKjPnFMTMLd+/8oy\nLCwMh38VJcvMlDBzYTVUyiLY2JxkZqdndPljDFKpjJ49e+V6z6NX7+N77xmj2tbAwTLvAh2fiiAI\neN96zJ+HfHkWHoOrjTmL+zaleNG8UwRHRyWybMFxLp57gJ2DGbMXd8DWPn8hrD67L7Okz19kpGUy\neFUvGvT8dtsDIjkRs4Z8BlZmVuz3Ssxx7MipJEqVUMfQQMaEYYYUd4L7Ibe+Uw9FRH5d/I7fYmz9\nGRQobMzC81M/KN4AFStW5NiZdNLTBZRKCfOXVebytSIkph6nWcNgyrppsHahLvPmTs31nnFJqSza\ne54SRc1oXe1dc/uXQBAErj54Tuc52xmx5ggSiYT5vRuzfnjbPMVbpRI4dvAm3dqv5OqlR3Tv68ny\ntd3yJd7xUQnM7LiY6W0XYmFvzspb82jYq7Yo3t8RcQX+GVR2bsnwSYt5EyVQo4oGV26kMHNxDJuX\nv50MVSpI8TkTnue1UtOTefb6IWoyOUXNHFCT5V6CUERE5MNcOXKDqa3mY1W8MLOOj8OgQO4hmpUq\nVaKES0UadbxG6RI1ueVvg0x+Fm35Tep4ZKXsLF9Kg8fBwQiC8EHR2njSj7ikVPrXdGTv3j2UKlUK\nO7svk8BEEAQuBYawzusqt4NfYWaoy+TOdWjoXgyZNO+1WMizNyyZc5S7/qG4lrZi8MgGWBbJ3/be\n1aM3WNjrL+Ii4+kypS3tRjfLV9y8yNflm/wFJBLJOaACkPn/h14KguD4Le79NbEoYE27GiPZs/cY\ny9c8QSkkcnCzOeVLaQJZE+6EdyZFDHLP2esffIkzN3dQpqQWSSkCx65m0KxyP4qYipmLRH48fvT5\nfHH/VWa0W4StW1FmHR+PrmHee8ESiYSduw4x7I/F3PJPIzL2KmVKXWfZjELZucq9LyZTorj1B8U7\nOTWdPef9kcQ8ZVT/ybgU06B/vwQaNmzCmrV/o6b2aa9blUrg3J1g1nld5f7zCMwMdRndzpOmlYqj\nng8RTUvLYPsmX3ZuuYSmpuKj4rqT4pJYNXQTxzecpWjxwsw4Mga7UtafNA6RL8+3/IQaIAjC2m94\nv2+CqaEFDd17olKp+Pv0dP7alISxoQyZTMKcpXG8CtOktovbB9tHxobhc2cnV4+b42SftU9+4mwS\n7Xv9Sb+mc8S9c5EflR9yPvseuMb0totwKGvDLK9x+UqNmt3W5yH3/dPwqOVMMTdn/hh4jpM+yVR1\n18TXL4UBYxJYsGjxB9ufvPmQpNQMXHXPseZCAaRSCcnJOjTtepLFixcxfPiIjxpLUmo6R64Esv3s\nLZ5HxGJZQJ+Jv9WmoXuxfFcv87sSzLL5XoS9iqVmnRL0/qM2hkb5eybXT/qzoPsKosNiaDe6OZ0m\ntUahLloGfyREG0g+SEqJ58Hz2yhVSuwtS2Co+65jilQqpa3HcC7c3U/5OtdRCQLFipSmnUeLXMPJ\nAp5dpkdHnWzxBqhbQxs3l2QevbiLc9EyH2wrIiLylksH/ZjWZmGWeB8f/970nSqVCm9vb/z9/bG1\ntaVhw4bI5XIeBL5k3vTDlHAtzIjxTVAo1JDL5cyaOY7OAx/h5GjLsj9X0rRp0w/e/0HIa1SZGSwc\nkZidB0JLS8rk4Vr0H7cq3wL+JCyKPefvcPhKIEmp6ZQoasas7g2oWcoetXzEZQOEh8WycukpfH2C\nKFzEmHnL8pfDHCAxNonVI/7Ga90ZihSzYPK+EWIe8x+UbyngsyQSyWwgCBgnCMK5950kkUh6Ab0A\n9LW/fpy0IKh48uoBkXFhmOibYVuoWI6KYIHPbnDi+ibq1tBGR1vC5mP7Ke9Yj4rFG7xzLQ2FFiWK\nVuVVVDDPX7/i9uOrSCQSPFzboJCrv/f+mZmpFDB515RlYiQlLSb1yw1UROTL8tHzuUiRvJOJfCpX\nj91kWpsFWLlYYt+6EFu2/02TJk0wNzfPPichIYGGDTyJiwmmRmU1DuwRGDNam927TjJ17FGMTHSY\nNLMVCkXWa7F+/fr4+p4j4N4jbtwMZMrkUWhra1OrVq339uFFZCyZybHoaOcUWWNDGQkJie9t8w+x\niSl4337MsWv3ufnoJXI1GbVL29PWww0Xa/Nc2/6btLQMdm29zI7Nl5BKJXTv60nLdu7I5flbsV86\n6MeSfmuIjYijzYimdJ7cGnXN97+7RL4/30rARwGBQDrQDjgskUjcBEEI/t8TBUFYDawGKGRiJXzN\nTqWkJbH7/EK0deKpWlHOxSsZ+N7TpXW1oWhp6JCSlsRxv02cP2SGa/Gs/8TTRutT0uM4GZkCFgWs\nsTZzQvr/DiRRceHsPDcHbW1o21QHv9tpvIi+ysFLb2hdfch7+1DUzIX1W28ysLsKdfWs67yOyOTk\nuUS613f+msMXEflUPmk+ly1b9qvM55tn7jKl5Xx0C2mzL3gNyZez4q7HjB7K/AVL6NYtK03xlCnj\nKWz6FO+dxtn72mNnxPFH7xWoywswfHxTDAzfmpdbtGjMmdMnqFROA4VCkwtXHtKyRSPOeF+kbNmy\n7/TDplABLukas3SXHkPaJ2QfX789iXr1m7xzfmRcIhfuPuXMrUf4PQglU6XCqqAhA5tVplmlEhjq\n5r8AiCAIXDz3gNXLT/M6LI7qNZ3pNaBmvup1A8S9iWfF4A14b7uIjasV0w+Pxr60Td4NRb4rny3g\n/+/QUv0DP/sKglBFEISr/zq2SSKRtAcaAMs+9/6fQnjMSx48v0nwq9u4l0tg5xpTJBIJgiDQb2QU\nPjd2Ub98Nx6+uItHJe1s8VapBGYtjUYgE31TH+6EnOPMLTmtqw3BULcAx65uoFolDfasNUcul6BS\nCfQbFcGuQ495E/caE/13QzzsLIoT+NyG8nWf0Od3TRITBZauTsK9WF30tA3fOV9E5GvyX5vPN7z9\nGZulndAAACAASURBVNdwFjIdgZPhOzl/1JgSxbLm68NgTSo1+oNatepQpEgRdu/azrEtOtniffNO\nKie9y2Gsb4JC04t69WcwZOgIJkyYQnBwMKdPneDMXkvcS2d9EAQ8SKNqkxdMnzaOAwdPvNOXng0r\n4HXlHptuNeJG0Hnc7V9y6WIs1++oc/TEeAJDXvMsPIZ7z8K59fglD0IjALAsoE/HWqWpU8YBp8IF\nPzos63HQa1YuPcmdW8+xti34UeZyQRA4s/UCK4dsJDk+mc6T29BudDPkCnGv+7/AZwu4IAgen9IM\n+C7Bg5fuHeVW8Em6tNHGTaVk+/4kFqyMZXg/QyQSCZNGGGBX/hb1y4NKpUQuf9vNv/ckcO1mKs+u\nW6Ork7VaXrgqllXrVtOx5jjeJLxg9jiL7DZSqYRpo4zZtDOByNiw9wq4RCKlcYU+BIX6s3HTDWQS\nBbVLV8TK1P7bPBARkX/xX5rPvieuMKHhHGQa6ZRvf4ukGyra9AzjzF5LzE3VcLBV0LKRDnv37mXI\nkCEolUr+cQRXKgW6DNCmkEkFmjUMpG/3CMIjzajSZDGVKlXj/Pnz1K6ulS3eACWc1GnfXJcjp2+8\ntz+6muosHtCCgcv3EZTUmAePJWAG+mbQYcGB7PM05GoUszJlQNPKVClhjb2FySfFUr+JjGfTGh9O\nHPVHT1+LP4bXp0GTUsjU8rdPHvY0nGX91+J3/DbOFR0Y/Ffv92apE/lx+eomdIlEYgC4Az5khZ20\nBaoBg7/2vf+XyNgwbjw6ScD5QpgVzBr68H5GlKr5nGb1tbGzVqCukKBUqRAEAXtLF1Yf2cnjp7rY\nWSvYuieeMYOMssUb4I8e+sxeGkpMQiRKJejr5Zw8ujpSlEqB9Iy0D/ZLKpVSzKoUxaxKfZ2Bi4h8\nIX6U+Rz2JJwpzeejqaVkrfczTC11AB1GT3/DuFlvWL8462NZXSGQmZkV7daseUsWr97P8llyTp4F\nM6OmWFvF0L3zTQBMC6gxqIc6W/5eg6OTG0YG7+4bG+hLyVSqSE9PR6F4N0KkeFEzjs/qRdCLSB6+\niCQiNhG5TIaGuhwLYz0KFzCgqJlRvp3R3kdSUhq7t15mz/YrqFQCLdtVoGPXKujo5i9la2ZGJnsX\nHeXvKbuQyqT0W/w7TfrXRfYN8rWLfFm+xR64HJgOOAFK4AHQTBCEoG9w7xwEhfrToaVWtngDFDJT\no1VjHQ6dSGJoHwULV8XhbF0CiUSCjqYeNUq1xr3uHtq31Obp84x3BFomAy0NGRmZ6dhZFGPlphdM\nG2WS/fu6bfGYFpRx1n8HVmb2Xywv+uvoUK4+OMzr6BAMdIwoZVsfh8Ilv8i1RURy4bvP59jIOMbU\nn0F6agYLjgZjapmR/dvgXgYUqxLC+sUQFp7JrkPJXByV5Tk+ZcosPGuco2araHQ16iGRaDB6sDcK\nuSq7va6ulOTkRFq0aEGFOZOYE6XExDhL2BISVWzYHo+5mQYjRvzBkiWr3ts/hVwNF2vzfDufZWRk\nsHjxIrZtXUNqahoNGzVn7NhJ2VXN3p6n5OjBm2xdf4HY2GQ8ajrTrW8NzAvlf6styO8xi3r/RfDt\nZ1RuVo5+S7pRsLBJ3g1Ffki+uoALghAJlPva98kPUomUjPR3TVVJySrO+SZz7HQy9+4raO/ZNvu3\nUnZVsSroxL07fpDxgOVrw/GopJlt8jpzIYXUNDkFDMxxtanJsjV/cu9BOvU8tbh4NYWjp5M5vduC\n9duS8fe/SPWSb8NQEpLjOH93N/ef+SOVSnEuWprqJVuhqZ57nObr6FB2np3PxBF61Pc04M79FIZO\n2EBKemtcbSt9oaclIvIu33s+pyanMaHJHCJD33BfcQ0zKy3g7coxI0NApRIYPjmSLXvTGDJ0DA4O\nWZXHjI2N8bsewNKFWzhx6BUvIs6RlBoOZO2ZZ2YKrN+WQc9+bShSpAjVPWrj4nGcP3roI1eDPzfG\nU72iJoummVC8+mZmzVqIltZbR7PNmzcxb+4UHj0OxaWEPRMmzqZJk3ed1/6Xzp1aExl2gcWTtdDV\nkbJy0zaqVzvKNb+7aGpqolSq8D4ZwOZ153n9KpaSpYowvX8tHJ0L5fu5xUclsH7cdo6tOY2hmQGT\n9g6nSnP3fLcX+TH5peLAi1mVZvPBIwzvr4tt0Szz18PgdA4eT6JtMx2OnEijhlv7d8LXjPQKUNWl\nAeWdPNlxdh4ezSJp11xBYFAGG3fGIZUo2HpmPm/iQnEtLsPncgqHjidhbCRl8TQTbIvKkSuURMY+\ny07DmKnMYPvZOXRsJeFQX0syMwWmLQhi19kFdK49Pkco2/9y5f5Bpo7WY0D3rOo/jnYKrAvLadB+\nHy7WFbK94kVEfiZUKhWzOy0l6NpjJu4ZxtoDSqYv9mbhFINsJ9Tpi6Ip7qjgxatMLC2LMGbMhBzX\nkEnVuHszhSJFTejYqxO1Wvene3stzArCmq0JhL7MZPGimUybOgYTg2QM9aVMmheNTAqVymmyal4B\nQl4okUpUBAcH4+LiAsD69WuZPXMYq+bqUt7NirOX4ujbtyNS6XYaNWr0wTHduXOHixfO8PCSaXYU\nyqq5Chp1imPbtm042FRi4xofnj97g52DGTMXtqesu02+98wFQeD03+f5a/gmEmKSaDG4IZ0mtX5v\njLzIf49fSsANdU2o6tKSUp67aFJPCzU1OHwyiYVTTfi9nT59hShCHkYhCCpCI56QmBKHZQGbbG9w\ndbkGHWuOJuDpdabN34+xcRp71ptT0FhG9WZP6d1Zn3O+KZzaZYFrcXVOnEumy8DX9B8TiZOtgoS0\np2w4MYlmlQby8s0THOyUzJ1UMLt/q+Yb4VYjnOBX97GzKP7BcYRFh1C/Zs6PjLJuGqhUGSSlJqCr\nlb/QERGR/xLrRm/Fd/81+i7sSpXm7jhWWU6tmpUpUS2EOh5aXLiSglwOx7ZZkJEpUMLjJQDh4eFc\nvHgRIyMjEmJ0efUihilz2lCpqgPly5dj+vTJrNx0gM5ttBjRz4whE18iqODKzRQG9TSkd2d94hNU\njJwaiXPV5yjkWVUHq1Z1Z8SIUYwdO5EZ0yewZbl+ttNbw1raLJshMHPG2FwF3M/PD8+q2tniDSAI\nEkoVs2Hf1mekp4ZR2MqYCdNbUsXDKduDPj88vRvCn4M24H/uHsUq2DN4VW9sSlp90rMX+TH5aQU8\nPOYlAU8vkJaZQCGj4pSwLoeaTE5p++qkpqVz6+4xBvTQYeZYEwqZqaFSqTh9IRVr4wzWH5+MlnYy\nNlZy1nklUcquKtVdWyGRSFCTyTHWK4imZia3vQsjk0nYcySBqhU0+Ht3AhcOWWJvk7W6b1BTm0VT\nC7B2axzn9hdGEASWrI5n4YplWJu6Uad+zscvkUjwqCwn6M6rXAXcQMeQgAfp2VYEgBevMsjIFNBU\nF7+sRX4uUlJSmN5/Ltc2BmDsqkWxulnxyQUKFOD6jXuYmxsjk8GMscbUrq6FVCph8654Che2YNKk\ncSxduogq7nq8eq1CT707Do5FqFglK8rD2dmZ8NfPWTbTiA4tsmqB33uQTt0ammhqajGsb9bHu462\nlM3LzbAu94wdq82oUEaTV68zqdV6Efb2xQh9EUn5/8kRXq2CJl0HPc51bFZWVgQ8yEAQBARBgu+V\nImzdXZKnIUZoasOoiU2pUat4vj3LISt/+ebJuzmw3AttfS3+WNGThr1qiZa5n5Cf8i8a8PQau3zm\n4uF5l57dQ4nOOMDOc/PJyEwHoKxjNaKj1QkLU6GhLuHY6SQKuz0jPiGN648P0aebkvu+ZhzbbsIT\nP0vCE68Q+Oxt6Mjr6FA8Kmsgk2V9DSvkEuITsnJU/CPe/1C5vCYhoVlesBKJhEG99FCoJyGVyvG5\npMxxriAIXLyagbFe7qX93GzqM2hcLHcCszzbw8Iz6TIwmlL2VcQqZiI/FQkJCdQoXZVrm+5Q0C4G\n6ypeVK9Wjv379wMgl8uZMmU6J84J6OlKSUsTaPn7K/qNiiAqIpQ1q+YQcM6Mgxv1mDfeDTWZNtf9\nd+S4h/+de9Sq9vbDV6GAJyGZVCqnmeM8qVRCtQqaBAVnOc0VMlNj3GANNm9cibmZETfv5Iw0uXQ9\nFSfH3At/eHp6kqE0YcAoc3r+0YTp8z2IipEQ8vooKzd2o1Y9l3yLt0ql4tRmH353GsT+pceo370m\nGx8upXGfOqJ4/6T8dH/VjMx0Tt/cxpm9pkwdbUSPjvqc3V8Qa+tYbj/2BUAhV6e950iOellSqOQz\n2vQMY9H0AvgesURTA0b2N8zeYzIylDFphC73X/hk38NItyB+t7K+mgFqV9Pi0ZN0VCqBB4/Sc/Tn\nwpUUijm8FXWJRIJpATXMjApzNxAmzYkmLl7JmyglQyZE8+aNFnYWJXIdYzGrUrgWbYZn8yhMnUNx\nqvSSzKQyVCvZ8os8QxGRH4WFsxei96wQZoUz+PPAS2aMM+DARkMG9O9BRkaWkPbrN5DBw+bSbSgY\nOgYTEaXi2XVrqrjLGD/UCHPTLEvX0ZMOmBVMIDH5DjduvP0gt7O14rr/W/Ft31yXh4/TuXg1OUdf\nlEqBy9dTcP7XfC5kpkZMTBSjx0yi66B4rt5MRaUSOOubzIAxCYweM/2DY0tOSmPfzmsUK9qbx4/r\nEBScxtOXBwiJ9GLLjiVYWOTfSS3oejCDKo1jbtflmFoVYNnVWQxe1Qs9I918X0Pkv8dPZ0J/9SaE\nooUV2dnTIOvLuXcXLSbPukk5agBZedabVOxLIaPzqBt60aaJLrcD0jDQk6KmlnOfycRIRkbm27zk\nNoWcOH9XmxFTopkw1AB1hYRWjXXZsD2e5l1fsX6JKW7F1Tl+NpkhEyLZu+FtOMnT5xkEPEihWlNH\n2huP5PDRHcxZHoBUKqGEtRttPdrl62u5tH113GyrkJASh5a6jli1TOSnQ5mp5PwKPxSCgknrH6Nn\nlGWxqlBGE0P9JO7cuUOZMmWQSCT07NmLHj16YlrQgHWLDDExlpGQpMoOAUtJUePe/YK0anqP4Fdy\nEhLepjodPmIyfwzvhpGBFPfSGtSprsXCVXEcPJ7EjMVR9O1iQFyCipFT32BuqkZZ17fvli170qhV\npwl9+vRDJpPRaeBUnjx9gXMxK+bOX03z5s3fGVd4WCwH917n6MFbJCelUbJUEYaNrYStgyEZGRmY\nmb2b8OlDRIXFsH7cNk5uPIeRmQEjNw6g5m9VxRX3L8JPJ+AKuTqxcZnZ3t7/EB2rRC7TfOf8xJRY\nSlXIOq+Ek4KEJIFLfinZ5jNBEPhrUxKFC1TNbiORSGldfSjeZ7eyYkMAKkHA1sKG32r15ebD8zTt\n5E9cYgqFTU1RKtVp2/M1WpoSnOwU3L6nomrJpmgoNNFQaNK0Uj+aVFQBko/OxiSVyr5JwRcRke/B\nxok7kcZpUqHTQ2yc335AK5UCsfEZ6OrmXF0qlUqiohOwLZrlGFqvhhYbtsfTooEOAfcLolRK0dcP\n5WFwCu7ub0OoWrVqRVJSIp0GjuF1eAh6utoMHzkNe3snZs+ayMzF99HR0cTBwZH7D29TqORTrCzV\n0NFWJ+yNIQv+HIpEIqFXrz706tUHlUr1joAKgsCdWyEc2HOdS+eDQALVahSjZTt3nJwtPvrZpKWk\nsWfBEXbM2Y8yQ0mbEU3pMK6F6F3+i/HTCbiZUWFUmTr8tTmePl2yvLHDIzOZuTiRSo5V3zm/cAE7\n9hw+z8RhAmpqEpbNLECL38Po2k4XJ3t1duxL5cFDTTrU8MzRTkdTjyYV+9KgfJYp/Z8VcCGTokBW\nlbPt3nOpVU3B2MEmSCQwc3Es6jJdytjXyHGt3ELGRER+RW6fDWDnnAM4eVqzx+80/aKNMDaSIQgC\nS9fEY2lpnR3f/Q9qamqUK1ucA15vaNlIl65t9dh5IAHPli+oWDrL+3rIpMcsXLQ8R/w2QJcuXenc\nuQtJSUloaWllC3CzZs0AOH78OL93bc2iaSZULq/JxaspDJ8cy+q1C99JuPJv8Y6PT+HM8bscPXiT\nkKdv0NXVoHWHijRpUYaCZh8fLSIIAmd3+LJ+7DbCQyKp0sKdHrM7YmGX/4plIj8PP52ASyQSmlTq\nx9R5S1ix/jWWhdTwvZZEeada2Fu6vHO+TSEnbjwyp367CIb310Yul1C4kAZbdkoxNzHH3MCZ32pW\n+KCJ+kNOY8Gv7iPXfMOutWbZoR8715hSyjOcx6/u4fCevoiIiGQlHZnTeRkW9mbMOTCFqdOVOFZe\nSfXKejwNySBDqc/hIwfe23bmrCW0a9uEF69UuJdRUMdDhznLE9DSzNpP3r3nKBUrvT8PjUQiQUdH\n572/TZo4nBWzdWlaL+t3Gys5+npS5syZRIsWLXKcq1IJ3L7xlBNH/bl4Loj09EwcixVi+LjGeNRy\nRl390xxN75wPZPWIzQT5BWPjasXcdRMp5Sm+R35lfjoBBzDRN6NngxmEhD8kJS2Jng3tPhgbLZFI\naVH1D24E+TBo9FUkSLAxb0T9+tWQST89N3BYVAgNaytyxG1KpRIa15VzySdEFHARkQ+wbOA6YiPi\nWHZlFlo6msyevYABA4Zw6dIlTE1NqVr1w3u8np6eHD9xnkULZ7D9cCDFS1Th8pVxhD7NYOGso5ib\nFf2kPl2/EUh9T9scx+rV0KJ1j0Aga2Uc/DCcs6fv4X0ygDeRCejoalC3kSsNmpTCziH/+9r/S2jQ\nS9aN3Ybv/msUsDRm+Pp+1OpUTcxdLvJzCjhkmbGszZ3yda6aTI67cy3cnWt9sfsb6Bhz01/1zvHr\nt1VfLB+6iMjPhu+Ba5zb4UuXKW2x+1dctaWlJW3atMnXNUqXLs3fW/bmOGZuloBMJsXr8C36Dqrz\n0f0qamXKncA0yrq9LRhyOzAdB1sX1q305vzZ+7x6EYNMJqVcBVt6D6xFpaqOKNQ//RX75mUUW6bu\nwWu9N+qaCrpObUerYY1Q11TPu7HIL8FPK+DfG6cipVhzdC8LV8UyoFvW6n/lxjhu3lHSq2GZ79w7\nEZEfj6T4ZJb2X4utW1HajW72Ra9tbKKLZ90SHNjjh2URYxo3/7g5OGjwKPqMnMKK2TokJBTm3EVT\nrvhZYGGsze5tV3AtbUXbjhWpXN0JfYPPcyRLikti17xD7F10BGWmkiZ969JhfEsMC4oZFkVyIgr4\nV0KupqBdjeGs3biRSXOfIUGCRUFL2nkMEEO+RETew6aJO4l5HcvUg6NQk3/5V9OAIXWJj01m6Twv\nzp8JpHmb8pRxt3nvnrQgCMREJxHyNJInjyNIjLLCsuAwJvx/WHemMhmLIlp06d6ECpXs0dV7N8Ll\nY0lJTOHg8uPsmneQhJgkarSvzO/T22NunXtiJ5FfF1HAvyJGegVp6zGSlLQkgDyrjImI/Ko8uxfK\nweVeNOpdG8eytnk3+AS0tNWZMqcN+3ddY9+ua0wavRuJBPT1tTAuoItcoUZ6eibJialERSWSkf42\nU6KxiS5lyzvhWNycIkX1KFXGAQ2NL2PKTk/L4Njq02ydvofYyHjcG5am69R2ObYQRETehyjg3wBR\nuEVEcmfD+O1oaGvQZWrbvE/+DGQyKa3aV6B56/Jcu/KYx0GveROZQEx0EhkZmcjl2mjZFMDIWIeC\nZvpYFjbC1t4UQ6P3e6d/DulpGZzYcJbtM/cR+SIKV4/iTJnRHueKjl/8XiI/J6KAfwViE6MIfHYD\npSoTh8KumBp+fKIGEZFfhQDfB1w66EfXae3QN9H7JveUqUmpWMWBilUccj0vMzOTw4cP4+/vj42N\nDa1atXonhvxjyUjP4Pj6t8LtXNGBYev6UrpWyY9O5iTyayMK+L9QqZRIJJIPJlYRBIHbj325/eQE\nsQkJFC5YhIrFmmNR4K2p607wJbxv76B1Ex10tGHr3pMUL1KN6q4t3ntNEZFfnR2z96NvokvLIR8u\nu/mxCIJAZmYmcvmHY66fPn3KxAkjOHHiFLq6WnTp2ovRo8ehUGT5qMTExFCndhXk0nBqVhHY8beM\nSRNHccbbFxsbm4/uU3pqOsfXn2XHnP1EhkbhXMmRoWv7Uqa2KNwin4Yo4MCbuNec899G0PNHyNVk\nuNiWoYZrWzQUOb+0rwR68TzmDBv/NMDZwZxDJ2IZOWUxbT1GYGZkSVJqAqdv7uDqcXOc7LNeAuMG\nG+Ba4wK25q6kKzOIintNAQNzrEwdckzajMx0LgYc4t6zy6RlZOBQ2JmqJVphoGPyTZ+FiMi3JCQw\nlKtHb9JlSls0tD5/T1mlUjFv3myWLJ5PeEQsJYrbMHXaApo2bZrjvDdv3lCtanl6dJAw44QRkVFK\nxs1eTregALZszQpBmzJlPCUdw1k9/21xo3l/xvHHwO6sXbedo0ePIpVKady4MSYmOeepj48PUyaP\nxO+6P0UtLahTvC2hvhHEhMfhXMmRIav7ULaOqyjcIp/FL5PDU6VS8TLyKa+iQhCEt/HZyamJbPee\nR/euMcQ9suHp9cKUcH3I3gtLsquNAWQqM7hy/yRHthbAo5IWBU3U6NFRnwnD9PALOgLA4xcBeFbR\nzhZvAGMjGT1+0+LApZVcf7IWc+uTXA5azTbvWaSmp2Sfd/jySgwK+nHhsAkPL1vQuFEo287MyXaA\nExH5GfFa542aXEbjvh8Xm/3y5UsuXLhAREREjuPTpk1k/+75HN+uS1qoLbNGp9C3z294e3vnOG/1\n6lXUriZhwlADLAvJKeWiwb51hpw6dYJHjx4BsG/vLob31ckhsgO66XL6zAWcnKw5fWwsxw6Mxt6+\nCDt2bM8+5/Lly7Ru1ZAO9V8y//cyWL904c6+R0j1BeadmcTiC9MoV9dNFG+Rz+aXWIE/DQvC69pa\nDA0FMjMFkpMVNKrQGwuTovg/uURdTwWDexkAoKkpZfV8Y+zdX/Ei8imFC2aZyuKSotHXlWJjldMk\nV7OqJotXhmb9QyJB9W7uFjKVAlaFM/A7WRiJRIJKJfD7oCjO391LnTK/8Tr6BZHxT7m+zhK5PGtS\nTxpuxP2Hb/APvkQF59pf7+GIiHwnMjMyObv9IuUblM733ndaWhq9e3Xm8OHDONnrEPgwkU6dOrFo\n0QoyMzNZtnQJV71MsC6SNU/reWoze5ySeXMn4+n5tp7B3TvXaFA15/pFQ0NKhbI63L17F3t7+/+f\nq//X3n2HR1VmDxz/vpPMJJMeUgiBJEBCMbQgEUFaqC4C0iwIoqBIEV2FBXQRERvq6uIisLK68JMt\nuuJKURdcXZo0kYigoJSABCmB9F4myfv7IyGYECDAZJI7nM/zzPNk7sy998x57smZueW9lddfqqG0\npIQtq0Npd1PZoC77D7oTN2ICcXG9CQkJYf6c5xjesgNr5oVQWGCiy4BMug4/xfhnT/G3bm9L4xZ2\n4/S/wHPys1i7/c/8/W1vDu5oxJFdjVj0qhsff/UWRbYCMnNP071L5e8xJpOic0crqVlJFdO8rb5k\nZBWTdK640nvj9xXg711296MWjduyeUcu+w9euLfwuZRilq7IYP6cgIrCNZkUL8zy5cDP8QAkZ5yi\na6xHRfM+r3+cmfTcRPslQ4h65Medh0lLyqDf/T1rPM/s2TNIP7eB4/GhbF3rR8LORuyL/4g//vEP\nJCcnY7FQ0bzP69LJnUOHDlea1jwymvgqIyWWlGj2/pBHVFQUAHfdPYrXFudU2hO3YGkmzZtaKpo3\nQNvWbgzu78WyN9/jpVELyN/kw4n4EOKGpfOXTQd5/r3j/GaoDReXkov2GAhxPZy+ge//eTdDbvdg\nQFzZpVxKKUYO9qbzzRYOntiLv1cYG7ZUbsrFxZpt3+QR/Kuzxy1md2JadOPeR1I5erwIrTVfbsnl\n6RezuDnyDlIzz5KSmUTvmHvpPjiJsVNTeXRWKtHdT5OXp+naqfJAD1arorik7DrTBj4Nid9XQGmp\nrvSebV8X41N+EwYhnM3ejftRShHTp22N3l9aWsqyZctZ+KI3nh5l/7r8/Vx4fa4X776zmODgYEpK\nXDiUUFRpvs078mnXrvI6Jk+eygerC1ixMgubTZOcUsykmRm0vqkDkZGRbN++nfvue4CEX8LoPDCN\np19Kp/896by9ooheXS+cG2MrUmxa7Ufaphg2v/4tuz/fi6lpLkPn7mb6gpM0bVX2Zf74LzYKizRB\nQUHXkzIhKnH6Xeh5hVk0b3rxLqvmESaO/phDxxbdWP75f3nuD2lMGedDVnYpz8zPxMcaRmhARKV5\n4trfxbb9Fjr120JhkY0gf3+6R9/Dzp9WkZ5zhtAQC0ePF9K59QDSTnpyrsTG6N4d2Lp/JW+9e5Zn\npvlXLOutd7NoHVH2TyU0IAKruSETpqXy6rN++HiZWPZ+Np/8t4CHf9O9dhMkRB35addhmrULx9u/\nZtdY22w2cnMLCA2p/G8rookrKampWCwWZj01m3snzWfRy960j7awbkMec17NZc3aFyrNExYWxrr1\nG/nd9MlMmbUPV1cXRo26m4F3dCQ8vCFRTa2cSiqgWdMWTJuxkJMnTzKpZ3OaNWvGsKF9mHlEsWt9\nEJ+tCCDljIVCUy5j5wxh9Iy7+Hr3TsbeP4ymkT707+XBT4eLeGRGNo8//gRubjKOubAfp2/gEQ1b\n8a/V23jmSV2xizovr5Q16/MYcmtL3C1WRvd5iv+s+zdvLj2AxexKm6ZdGd5t6EXLMplc6Nl+ON3b\nDqW4xIbZ1cLKLW9w5+AsXv59E1xdFccSbfQY8jlWc2O6Rt9JgG9DerW/j4XvvMauPcnEdXPlf1uK\n+e57GN2n7OYMSimGd/stm/d9SLPYeGzFJbQMj2RU3GQ8rY65LlYIR0s5mUbjFjW/S5ebmxuxndrw\n8X+SuXeod8X0D9fm0KtnNwCmT5+Jj48fj86eT+KJU8R2asfKj17ntttuu2h5sbGxbPkqnvz8fFxd\nXdmxYwdjxwxh+yeBtIy0UFKief6NRGb+bjKPTHqC3r17c/rAOXo0GMmkXtmYMOETlkai3zHG9JoH\nSQAADNhJREFUz3iIR2Y/AEDfvn15e+k/mDVnOj+NPUZggA9PTpvJzJlPX2fGhKhM/fr4Tn0TGhih\nHxk8+7qWoXUpq7ctxsvvF6ZP8cRWDK8szCAt1crNUYNo17zzNY9Nnp6dzD83vsTp78MqHb9e9n4m\nf/1nJmeSXGjduD9dowdSaCtg/7FvSM85TQPvJrRtdgsW88XfxrUupVTr67qVqbjxvLBi8rda69i6\njuNyYmNjdXx8fMXzu4IfovuILjy5dGKNl7F161ZGDL+DJyZYuaWjmQ1bC/nL37IYcucInn56Dm3b\n1mx3fHXuHzOCru22M2XchZuGlJRoIm8+RfvAFmQnNMFi88DT14N2/VuR6XMWr2Ar99wzipiYmGqX\nWVhYiMVikRPXxFVRStWonp3+F7hSJoZ2m8q+hJ3Mmvc/MnOT6dXVyqCJZt7/96d8sGkzo+JmVttM\nrySvIIeGgZaLTj6LaGLG6mZi26fBtOmxnpjInljdPOnU6son6yhlwkVqXdwAPHw8yMvOu6p5evTo\nwZavdrFgwSv8+clVeFo1s5/0JS9vI337fMaixctrfNvRqlKSzxLWuOyLc7ENvt3izZcrG9AypR2F\nyS54B2bSqHMAi1YurPE167LLXNQmp2/gAC4mF9pH3srWHz5mw6pQOrYrO4N0/CjNkPuT2XPkq2u6\nVCvYvzGnkmz8eKiQ6FYXCvVfa7Lp2dVKk1AzHaI9OJVynKjGbez2eYRwBgGh/pw7kXLV80VHR9Oy\nZVvSz65n5TsXBlkZ1M+dOx+cxLBhwypGU7saPeMG8vf/W8ap7aFs+NiPzFQznr42zpl/5h//Lia1\nKJ1nXj9jlwFnhLAHpz8L/bwzqSdoEupa0byh7NjzxAc8OJm6l+SMM6z7ZhkrvpjLmu2LOHE24YrL\nNLta6NVhJP3uOsfi5Rms35DL+CeS2LYrn8cf9kNrzckzRXi42/9GCEIYXYdebfhxx2GSjl/9pVVf\nfL6K8aPcKu2ajo1xJyTYxO7du1myZAk9usdwa+doXn75RXJzqx8QSWvNz/tPsOK5Dzm04iwZm2NZ\n9W4Agc2yuHXsfvZ6rmPic6doG1tI4sligoLk1p6i/rghfoFD2WVg6ZnFlJZqTKYLRZ+SVkJpKby/\n8TVmTPViQC8re75PZs6ri+kXM45W4dUf2zqvY1QPGniFsPSvn3EuPYH7Rnix47MwfH1MvPpWBrrE\nl0YNwmv74wlhOHdM7McHr6zi4wWfMfWth65qXm8fX1JSK4+RUFqqSUu38eor88hK28PvH3PH6q5Y\n8t5CBvRfxeYt32A2mykpKeHgrgR2rN3NttW7OJ2QhMmkaN8rmsFT+vNjyh6Wr/gTvjmFLH0jiAFx\nnhz/xcZLf8pn4aJp9kyBENflhmngwX6huJp8WfTXTH77iC9KKc4mFzP/zRxKi9154SlvHnu4bDS2\n2Bh3IpuZGTd1JS3DrjxecURICyJCpvH90R38beVKNm1LJjW9GKslgGHdpsgJLEJUIzgskIEP92XN\n4vX4BfsyZs7IGs/74LhHmf3UOAb28SAo0BWtNW+9m4WffzDf7dnJ4R0huLuX7WDs0cVKr8FJvDFj\nIaYMN+I/30tGchYuri507NuWu6YPofvwzvg39Ctf+p08+sRUxowezvgn9xLeuIgjP+fx7LPPM2jQ\noFrIhBDXxi4NXCn1GDAOaAd8oLUeV+X1vsASIBzYBYzTWjt0iDGlFHd2eZTXFy/kLyuSCG9iZmd8\nLp1b9+O7hM0MGxhc6f19ulvJyDlLQVFeje/n3T7yNm6KiCUp7RfcLR4E+TWqjY8iRK1yZD0//ucJ\nFBXaeG/uv0hLSuf+uXfjH+x7xfmGDh3Knj1TaN1jId1v9SHxlyJKtB+j7nuQxENLyExx4+t4T37Y\n5cn+XZ54HLSyce8ufAK8ib29A10Gx9J5YAyevtXXdlBQEF98uY2EhATOnj1L+/bt8fb2rva9QtQV\ne/0CPw28BNwOVBpyTCkVCKwCJgCfAi8CHwJd7LTuGmvgE8yEgS9y4uxR8gpzmDi4OV5WX44mfcuh\nozaahF4YgvHk6WKUMmExu19miRczu1oIC460d+hCOJLD6tnFxYUZyx/F09eDNYvWs37ZRm75TQw9\nRnahXY+bCAoLwGS6+FQdpRTPPz+fMXePZ+O6LZRma9xKPNm59hsSf+jMA++XnWhm9Szhpk55pLsd\no3WPQTz/5nO4uNT8Es2oqKiKoVWFqG/s0sC11qsAlFKxQJMqL48ADmitPyp/zzwgRSnVWmt90B7r\nvxpKmYgIaVFpWvumA3j896tY94GZpmFmUtNKmDAtnY5R3eR6bHHDcXQ9m0wmpi58iCFTbmfdO1+y\n4Z9b2bF2NwAWdzNBYYF4+FixuJspKS6lK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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "K = 4\n", "n_iter : 50\n", "log_likelihood : -511.2771065710105\n" ] }, { "data": { "image/png": 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L8pwV/PHS+4g227+uuyWxKyNLsrj/GVJfPodju9PQuTnxwn+f48Daw/Q23sgQ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\nJGnqo5hE+8jeJBpJVx8l6vaRF7gSkn9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ux1H3ZNV9K4Ig8Pm0aYx/6y3OnDlDQEAANWve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\nxDIu6rQMLaIIPd89wCfDzPlso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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "K = 10\n", "n_iter : 115\n", "log_likelihood : -483.17586164025226\n" ] }, { "data": { "image/png": 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s16UAaJw1lObXX8DBLuL/N3siRQXFLJz1C+agClw83Hnt7vd5e/U0Ygde3oaJ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HumTR13zzIcPnyYTu1tsbQs/KdYCEHPTnDo0O5SrT/J/JV6F3p5SYi9yrnjW9HlpuJVvQlBDdpj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\noln02zkO7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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for K in [2, 4, 10]:\n", " print(f\"K = {K}\")\n", " gmm = GaussianMixtureModel(K=K)\n", " gmm.fit(X, max_iter=1000, tol=1e-4, disp_message=True, random_state=0)\n", " plot_result(gmm, xx, yy, X, y)\n", " plt.show()" ] } ], "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 }