blahut-arimoto-algorithm.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Blahut-Arimoto Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.spatial import distance_matrix\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.text import OffsetFrom\n",
    "import random as ran\n",
    "import math as math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def read_and_convert_data_points(filename):\n",
    "    \"\"\"\n",
    "    read_and_convert_data_points is a function that takes  a text file as an argument\n",
    "    and converts it into an array containing all the datapoints.\n",
    "    =============================================================================================\n",
    "    :param filename: text file name in directory.\n",
    "    :return: Npts x 2 array. \n",
    "    =============================================================================================\n",
    "    \"\"\"\n",
    "    splits = []\n",
    "    with open(filename, 'r') as f:\n",
    "        data_points = f.readlines()\n",
    "    \n",
    "    for data_point in data_points:\n",
    "        splits.append(data_point.split())\n",
    "    \n",
    "    return np.array(splits, dtype=np.float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scatter_plot(data, output_file_name='none',i=0):\n",
    "    \"\"\"\n",
    "    scatter_plot is a function that plots the data and differenciate up to two clusters.\n",
    "    =============================================================================================\n",
    "    :param data: Npts x 2, data set array.\n",
    "    :param output_file_name: \n",
    "    :i: idx of the first datapoint of the second cluster. \n",
    "    :return:\n",
    "    =============================================================================================\n",
    "    \"\"\"\n",
    "    if i != 0:\n",
    "        x_1, y_1 = data[0:i].T\n",
    "        x_2, y_2 = data[i:data.shape[0]].T\n",
    "        plt.scatter(x_1, y_1, color='r')\n",
    "        plt.scatter(x_2, y_2, color = 'g')\n",
    "        \n",
    "        if output_file_name =='none': \n",
    "            plt.show()\n",
    "        else:\n",
    "            plt.savefig(output_file_name)\n",
    "            plt.show() \n",
    "    else:\n",
    "        x, y = data.T\n",
    "        plt.scatter(x,y)\n",
    "        if output_file_name =='none': \n",
    "            plt.show()\n",
    "        else:\n",
    "            plt.savefig(output_file_name)\n",
    "            plt.show()    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def initial_clustering_membership_probability(clusters_number):\n",
    "    \"\"\"\n",
    "    initial_clustering_membership_probability is a function that takes as an argument the \n",
    "    number of clusters 'C' and generates a randon cluster membership probability per element 'i' \n",
    "    in the dataset composed by 'N'elements.\n",
    "    The sum of an element cluster membership probabilities is be 1.\n",
    "    =============================================================================================\n",
    "    :param clusters_number: 'C'\n",
    "    :return initial_cond_prob: C x N matrix. \n",
    "    =============================================================================================\n",
    "    \"\"\" \n",
    "    initial_cond_prob = np.zeros((Npts,clusters_number))\n",
    "    for i in range(Npts):\n",
    "        x = np.random.rand(clusters_number)\n",
    "        initial_cond_prob[i] = x/np.sum(x)\n",
    "    return initial_cond_prob.transpose()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm implementation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def blahut_algorithm_imp(clusters_number,\n",
    "                              priors,\n",
    "                              distance_matrix,\n",
    "                              beta, \n",
    "                              rounds=20,\n",
    "                              threshold=1e-10\n",
    "                             ):\n",
    "    \"\"\"\n",
    "    the blahut_algorithm_imp function implements the Blahut Arimoto Algorithm for a given number \n",
    "    of clusters and a given value of beta.\n",
    "    For each round it will:\n",
    "    *firstly initialize the clustering membership probabilities randomly,\n",
    "    *compute the evidence for each cluster 'C'(returns a vector), \n",
    "    *Compute the posterior probability per cluster: returns a matrix C x Npts\n",
    "    *Compute the element to cluster distance: returns a matrix Npts x C\n",
    "    After performing all the previous operations for all clusters 'C' the normalization (partition)\n",
    "    function is created and posteriori to this the clustering membership probabilities are updated.\n",
    "    The function will later try to minimize the Lagrange multiplier function until convergence \n",
    "    i.e, there is no improvement or the improvement is less than the threshold. When the function\n",
    "    reaches this condition it gets out of the loop and starts the next round.\n",
    "    \n",
    "    =============================================================================================\n",
    "    :param clusters_number: \n",
    "    :priors: prior probability for each data point, if uniformly distributed = 1/Npts\n",
    "    :distance_matrix: Matrix containing the distance from every vector in x to every vector in y.\n",
    "    :beta: distortion tradeoff parameter\n",
    "    :rounds: number on rounds (iterations) perform for averaging results.\n",
    "    :threshold: if the minimization of the lagrange multiplier result compared \n",
    "    to the previous iteration's result is less than the threshold the round will exit the loop.\n",
    "    :returns: scalar value, mean of the expected distortion for each round.\n",
    "    =============================================================================================\n",
    "    \"\"\"\n",
    "\n",
    "    priors_matrix = np.full((Npts, 1), 1/float(Npts))\n",
    "    D_results=[]\n",
    "     \n",
    "    for round in range(rounds): \n",
    "        D = []\n",
    "        app_membership_funct = []\n",
    "        lagrange_multiplier=[]\n",
    "        diff_elem_value=1\n",
    "        membership_prob = initial_clustering_membership_probability(clusters_number)\n",
    "        evidence_vector = np.zeros((clusters_number,))\n",
    "        posteriori_prob = np.zeros((Npts, clusters_number)).transpose()\n",
    "        element_cluster_distance_matrix = np.zeros((Npts, clusters_number))\n",
    "        normalization_partition_funct = np.zeros((Npts, ))\n",
    "\n",
    "        while (diff_elem_value > threshold):\n",
    "  \n",
    "            for c in range(clusters_number):\n",
    "\n",
    "            #     Computes the evidence for each cluster 'C': returns a vector   \n",
    "                evidence_vector[c] = np.sum(np.dot(membership_prob[c], priors))\n",
    "            #     Computes the posterior probability: returns a matrix C x Npts\n",
    "                posteriori_prob[c] = (np.dot(priors, membership_prob[c]))/evidence_vector[c]    \n",
    "\n",
    "            #     Compute element to cluster distance:\n",
    "                element_cluster_distance_matrix.transpose()[c] =(\n",
    "                                                                np.multiply(\n",
    "                                                                    posteriori_prob[c], distance_matrix_\n",
    "                                                                           )\n",
    "                                                                ).sum(axis=1,dtype='float')\n",
    "            #compute partition function:\n",
    "            exponential_beta_matrix = np.exp(-beta * element_cluster_distance_matrix)\n",
    "            normalization_partition_funct = (np.multiply(evidence_vector, exponential_beta_matrix)).sum(axis=1)\n",
    "\n",
    "            #update conditionnal cluster_proba\n",
    "            membership_prob = (np.multiply\n",
    "                                (evidence_vector, \n",
    "                                 exponential_beta_matrix)/ normalization_partition_funct[:,None]\n",
    "                               ).transpose()\n",
    "\n",
    "            #Compute averaged element to cluster distance:\n",
    "            joint_probability = np.multiply(evidence_vector, posteriori_prob.transpose())\n",
    "            d =np.sum(np.multiply(joint_probability,element_cluster_distance_matrix))\n",
    "\n",
    "            D.append(d)\n",
    "            ##Compute Compression rate:       \n",
    "            ratios = posteriori_prob.transpose()/priors\n",
    "            compression_rate_ = np.sum(np.multiply(joint_probability, np.log2(ratios)))\n",
    "\n",
    "            ##Compute Lagrange Multiplier:\n",
    "            lagrange_multiplier_ = compression_rate_ + beta*d\n",
    "            lagrange_multiplier.append(lagrange_multiplier_)     \n",
    "\n",
    "            if len(lagrange_multiplier) > 1:\n",
    "                diff_elem_value = lagrange_multiplier[-2]-lagrange_multiplier[-1]\n",
    "            app_membership_funct.append(membership_prob)\n",
    "        D_results.append(D[-1])\n",
    "        prob = app_membership_funct[-1]\n",
    "        mean_D_results = sum(D_results)/float(rounds)\n",
    "    return mean_D_results\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def batch_perform_algorithm(range_betas_, prior_, distance_matrix, range_clusters=range(2, 5)):\n",
    "    \"\"\"\n",
    "    batch_perform_algorithm will recursively call the blahut_algorithm_imp fuction for a number of\n",
    "    clusters and distortion trade-off values (beta) it will return the coordenates of the value that\n",
    "    minimizes the expected distortion for a given distortion trade-off. \n",
    "    =============================================================================================\n",
    "    :param range_betas_:range of betas = list of the given betas (distortion trade-off values) \n",
    "    that want to be evaluated.\n",
    "    :param prior_: prior probability for each data point, if uniformly distributed = 1/Npts\n",
    "    :param distance_matrix: Matrix containing the distance from every vector in x to every vector in y.\n",
    "    :range_clusters: range of clusters = list of the given range.\n",
    "    =============================================================================================\n",
    "    \"\"\"\n",
    "    results = np.zeros((len(range_clusters),len(range_betas_)))\n",
    "    betas=np.zeros((len(range_betas_)))   \n",
    "    coordenates = np.zeros((len(range_clusters), len(range_betas_),2))\n",
    "    \n",
    "    for idx, cluster_n in enumerate(range_clusters):\n",
    "        for idx_beta, beta in enumerate(range_betas_):\n",
    "            results[idx, idx_beta] = blahut_algorithm_imp(cluster_n,prior,distance_matrix,beta)\n",
    "            betas[idx_beta]=beta\n",
    "    \n",
    "    for idx, cluster in enumerate(range_clusters):\n",
    "        coordenates[idx].transpose()[0] = (-results[idx])\n",
    "        coordenates[idx].transpose()[1] = betas\n",
    "\n",
    "    return coordenates "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_batch_information_curve(coordenates_, range_clusters=range(2, 5), out_filename='none'):\n",
    "    \"\"\"\n",
    "    plot_batch_information_curve generates a plot with the given coordenates, where the x axis is\n",
    "    the value of the distortion trade-off parameter and the y axis the (negative) expected distortion.\n",
    "    =============================================================================================\n",
    "    :param coordenates_: output of batch_perform_algorithm function, (C, Beta, 2) array.\n",
    "    :param range_clusters: range of clusters = list of the given range\n",
    "    :return: information curves plot\n",
    "    =============================================================================================\n",
    "    \"\"\"\n",
    "    colors = ['#e6194b', '#3cb44b', '#ffe119', '#4363d8', '#f58231', '#911eb4']\n",
    "    fig, ax1 = plt.subplots(figsize=(15, 5))\n",
    "    plt.style.use('seaborn-darkgrid')\n",
    "    for i_coord, i_cluster in zip(range(coordenates_.shape[0]), range_clusters):\n",
    "        y,x = coordenates_[i_coord].T\n",
    "        plt.plot(x, y, marker='o', linestyle='--', color=colors[i_coord], label= f'Nc:{i_cluster}')    \n",
    "    plt.xlabel(r'$\\beta$')\n",
    "    plt.ylabel(r'$<-D>$')\n",
    "    plt.title('Information Curve',fontsize = 16)\n",
    "    plt.legend(loc='best')\n",
    "    bbox_args = dict(boxstyle=\"round\", fc=\"0.8\")\n",
    "    arrow_args = dict(arrowstyle=\"->\")\n",
    "\n",
    "    ax1.annotate('more compressed',\n",
    "                xy=(110, 20), xycoords='figure pixels',fontsize = 13)\n",
    "    ax1.annotate('less compressed',\n",
    "                xy=(850, 18), xycoords='figure pixels',fontsize = 13)\n",
    "    ax1.annotate('less relevant',\n",
    "                xy=(30, 300), xycoords='figure pixels',fontsize = 13,rotation=89)\n",
    "    ax1.annotate('more relevant',\n",
    "                xy=(30, 125), xycoords='figure pixels',fontsize = 13,rotation=89)\n",
    "    ax1.annotate('', xy=(0, -0.15), xycoords='axes fraction', xytext=(1, -0.15), \n",
    "                arrowprops=dict(arrowstyle=\"<->\", color='b'))\n",
    "    ax1.annotate('', xy=(-0.075, 0), xycoords='axes fraction', xytext=(-0.075, 1), \n",
    "                arrowprops=dict(arrowstyle=\"<->\", color='b'))\n",
    "    if out_filename=='none':\n",
    "        plt.show()\n",
    "    else:\n",
    "        plt.savefig(out_filename)\n",
    "        plt.show() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_points = read_and_convert_data_points('Data_Exercise4_2019')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Without knowing the data, by sight we can say there're two clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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e65z+QNIIQ5xARc9pdr4DcLeQSxDmufNfXII3rD7X/0fz8ahCOIFuQXfbcMWkIbe6sNE/3nlVYdc9i1AXnWsnep+7KTYI/+baDaWmfPC9zkDeIbdVQMQf6h8CA/jGoRcL+bHqRNZEnECpzqmzyFizauWyIjWmfDxBnP+6SAZTne9A1SElFcMic9XkIdRF59qJi0TLY7CSpV2+iKusTxCzDwD9DQ/q7Ob94MRF5USxEai4H7etvXt06zD2TR5f1knoUHVIaUxmRTkQ8zLnFekA9VXEfG1XgKxPEPEHYLYzF/VjDQRDV3d3gAiLzNYCFffjTvJw2lyDuNG8r3bUvNpWlL3bVxHztV0Bsj5BzD4AYKx4VfSPVWeK+MIHr4ydwoeX9s+dWUBrBfXtJ+zMVaF6X7ftAJGkEVZQlL17YrqNuTMLfe/7IGK+1xko2jznI8SamPKyGRkZ4ampqcKOd9fEUXzj0IvL7NmDrYFSfhBpRo2qxVGtAcL5q1bitflO7NoCQH++um2D9Bbt2XkM9BamuY7I8RndfdLN3oaHBq1WhNseWxXWOTTYwt4b3adySPub9DXap84Q0WFmHondTsT/HD7+WG3blEZwkq68DW+rKyAPlNdpFomp89w1PqN0ihOA58ducHL8IjqYgCQDBaF8bMVfbP4hfLNNJ4lFTuNgS3K+0W23jR3ULiZqQkpfk8PcVd1nE0U6VOuQttnHgV3ZiM3fQwLb/Z3jM7nF02fFtspXXTGJr6nusyu7f5H3O66jKTvtdhy+rzkoCxH/nEj7QIR/qDpUD+P2Lev7nNZ5OtjiRMaXqI68MInv6FZ93WdXce5FOlR157p2sFUJYbVdc+B7J+YaEf8cuGviKHaNz6R6INIkNgvqDYTtzATg5qvzM2OZFqb5FNWhI+uDHie+urrPQXK+rMJS9GK4aOQYAJw+s4B7Hj3m9WIuwM5EVoVOzDVObP5E9B4AXwQwAOB+Zh6LfH4bgH0Agiv5JWa+38WxfWNiut0XNQTY20jTJDbTrVB+4pmTts1OTHRhWpWifZIUPYnmRyLqpre4eGjQWMzHtHbEVR4Z1z4qnV18dOsw7nn0WN9Cv85Z1i7+s0k/UpQN3mbNQR38GknJLP5ENADgywB+C8AJAE8T0QFm/mFk03FmviPr8Xxn3+TxROkPgPhc/gE6YS1rNaWPDvK0mUaB/qIn0U5iNjSab8/OY//htna0HZdh00ZY8hLIien2MjEfGmzhfVdetCx6K9pBzVqs8A5jMvsVnVTNZkGX7yuS88CF2ecaAM8y83PMfAbANwHc5GC/lcT0YzEVdw+mmyrhj0tsVrSz10d0yfk2Ksw6cUVP9h44pnW4R7fVmTfCZhkdpnbkZYaYmG5j98NHlo3YZ+c7+PqhF43mG91vaWiwldj3UHTeHxsTWROfIRfiPwzgpdDrE733otxMRH9PRA8T0SWqHRHR7UQ0RURTJ0/mZ7LIE92PhYBExd2TrJ7Nw/lXNeeXzvQF9Atn3AM9O9+xrn0QF0r75J7rtB2AqR15CeS+yePKCm46gvPT/cb23nh5Yt9DGaPsuKy8vq9IzoOi4vwfBfAgM79ORL8L4KsA+laiMPN9AO4Duou8CmqbU1RTTALwkWs3JCpesshsvSDIdYKyKuY6jxOOsJklziSTBJuRYZo8MnkJZNLvB+cX9xtzUViozFF23jU7fMSF+LcBhEfyb8Y5xy4AgJl/EXp5P4A/cnDc0jHZZG1/RK4eBJf29yo6v2wqlQXCF5zD3gPHltnxk2I7MkwjLHkJpOk6EdCX3iR8fq5+Y2k6wyIcxL75sPLGhfg/DeAyItqErujfCuDD4Q2I6CJmfqX38kYAP3Jw3FKJGx3b/oh8zC7om/PL5sG3Gc2HhTO4R9F9z51Z0EawDEWifdLUUrYlr9/F7h2bsfvhI32mn9YKws5rLtFGL7kkaWdYxZloFcgs/sy8QER3AJhEN9TzAWY+RkSfBTDFzAcA/AER3QhgAcCrAG7LetyycTU69nG66dO0PEmRdeBc6GncKDb8vWhopw95bPKsNQCgL9onSAYX7gwD/0JeHYDtfqs4E60CktgtJZv2PJZ78q6y8EUAgfQJzLKYCXzOAxO0LY+1FT7d9zB1ftbyQBK75YxPo2PX+DQbSWuCymK/9dX2GxXnICzYlRnE1xF2nZ+1MhHxT4mPtnqX+CKAdXnwXcwmTKk/XIi0b76egLo/a2Uh4p8Sn0bHdaYOD74rh2XemVSL7GiTdIZ1ftbKNDGK+GfAl9FxnUnz4Ptms3dlTlk72DKGpmYR6SJLQibpDKP38t6dV9XmmSs7iknEX/CeJJ1s2Q+UClfmlDML+jBWQjetd1KieX7C2JSETNPR2naGPt7LgLzMeEX6WCSls1Ar8s4bkybthW5EzoD1Piam25jrLGo/ZwD7D7cTpeEIxFW3ruH881bGCn+a/EO2nWHROYBscZV3qWwfi4i/UCvyfKDSPvSm2ge2+7ARvKTCGFc7Iu6apRVn2yRqvlYQc9UplZ1MTsRfqBV5PlBpH/q4DJ+6fYTFzUWiuaTbxl0zU70CE7ZJ1Ez3ssziK64GGGUnkxPxF2pFng9Uloc+yCrZXw9LvY+ouNmSpJMzbWtzzQZIfTa69wN0KZYBLBvJb9+yXnsvyzQJuRpg2KSazhNx+Aq5U2T0TZ5hgS5CIW33YVPOM0rSTm77lvXKqnM2jl5AXXvC9H6YuLQaQbEcXbW0XeMzyv0WYS93GX5cZsSgiL+QK2VEbNg8UGk6JBcPve0+4kRseGgQ27esT52ITVf3+SPXbsDnRq/Qfid8zdataWmdxdvGDiZqj24k/8QzJ5dG+uF8Q2Uu/qvLugMRfyFXyg5nU3HXxNFlI95whwTE56zP8tDb7GNium0s5zlAhJdn55eEUXX8uM4tad1nVSfeWkFoDZCyOEzSTl7X2QX7iQ4ebr56eFnZSaBYe3kd1viI+Au5UnY4W5SJ6bbS1DHfOYt7Hj2GX3UWjbMUFw+9aR+ByJpMJ3E5fWxmWyaxVaHqLDqLjKHBFs4/b6Xye0k6ed1IfoBIOyP4/AeuqPzou0xE/IVcSTs9d+EnUO1j3+RxrQNVZcKIEzDX/oyktn5V+2xmW7r7QujOjKLmJF1n8dp8BzN3X6/NvGnbyevMYbpr8fLsfKmjb99WkadBon2EXEkTfeMijE+3D9uQyTA6Abtr4ih2jc84CzecmG47aZ/NbGv3js3KyCMG8I1DL/ad09CalnKfQSeeNQJGF/mSpv5x3pQZZuoSEX8hV9KEs7kI49PtQxeGSOhGuahQCY3JfJQm3DAQFBO6tkfbZyPEo1uHtTMg1Tkxw9iJuwixDcJhw0XWy46FV+HryuOkiNlHyJ2k03ObkWvctFu3j7PMfeaEIMpl5NILlKUg584sLI3qgmOuINKKZ3t2HtvGDmbOdxMQFFQBYBUpZBtRNGxR9zjgtfkO7t15Va7OcBU+Rtb45sdKi4i/4B1xfgIbh6ZuH8Mh279OTKKF3U/NdbD7L48AhKXIFpNDlnDOcWpyyobbYBLh6Ewp+N7awRY6Zxdx5/gM7hyf6YvPT1P3OFr+MuDiocHYTjwvG7xvkTV5hZkW7UcQ8Re8I27kauPQ3L5lPb5+6MW+fW/fst4oJqNbh7Fv8nhf6uTOov06W50pKDimqvPSiW7U0BO0fWK63VeIfXa+10nBTjBVncT2LetLDaF0SV5imkeNiTLWw4j4C94RN3K1mXbr4tV17+v2kwSdgEf3qYuxV8G97aMCsG/yuDK+vrPIidZQqDqJkUsv8MrMkoY4Mc3SMeRhiipjPYyIv+AlppGrzbTbJiOk7uGNM8OEGSDCIvOyUNK0bdOh2t60j/bsPCam26lFI68V0kUS55TNOsp2bYoqw48g4i9UDptpt6mDMI0KASgrWqloDRD23XJlnwikbZuOoM1hsY2r6uXCZKATeJ+LrASYxDRJMZmiOrgy0lVIqKdQOWzCR3Uhgtu3rMcnHzqifPj3HjhmLG7Sh8JWk7ZtJrZvWd8XV376zAJWGJJnZg09NMWy+1Iwx7SdKdzVNpqsyFj+MkJaiS0y8JXByMgIT01Nld0MocJER24qZ2ZWhocG8eSe6zK37fTrC8qR/Lo1LaxZpU6fsK638MrUWf1k7IbEbQO6idl06RZ0kU4E4PmUxwuIziqArghGs3vqHNNBR6vbT5ASQhcJFtxL3fmnvd82uJppENFhZh6J207MPkJtidplt40ddCr8QHKbrK4guU6s7n7/5dr0xbNzHTw/dgN+/VOPKwU5Lq++CdM6CVM4aFZ0s4poIj7TArvwfdeJaZxprgwbfNEhrU7En4jeA+CLAAYA3M/MY5HPzwPwNQBXA/gFgJ3M/BMXxxYEW0wP7mBrAKtbK5Sj6HVrWvin+QWlwCYRPBtbuUqsdCPVFUTanDqAXV59HSa/BKM/sinvgjnRM7GJqtKJqU20Tpkpo4sis/gT0QCALwP4LQAnADxNRAeY+YehzT4G4BQz/3MiuhXAHwLYmfXYgpAEU+ZI0wrau99/ufazQPBspuxxjkadWKkc3EC8uEfz4iQxK+iOGcC9/RdVMCfJ921QXevw9Vk72OpLV13V9Q46XIz8rwHwLDM/BwBE9E0ANwEIi/9NAPb2/n4YwJeIiNhXh4OQC2WHB+qihHQraHV58NNGv6Q1JURHqqZc/+Hz2r1j89I1jy4ki4vQCd775ENHlMfKy/adZNWxy9lH9B7OznfQWkFYt6aF2bmOl+GsWXEh/sMAXgq9PgHgN3TbMPMCEb0G4NcA/Dy8ERHdDuB2ANiwYYODpgm+4EN4oM10P271r+oz29DBLKaE8LE37XksdvvVrRWYeuHVZU7RuJXHqmMCdvmEXJFk1bGuxGMadPUK1qxaienPXJ/+hDzGK4cvM98H4D6gG+1TcnMEh/hS0SsPp5rtiN5VWgBTLv7goTk111E6RePaGBA1gaxurcDsXAdrB1sgAnaNz2Df5PFcRsNlrDquS7K2JLgQ/zaAS0Kv39x7T7XNCSJaCWAtuo5foSHU+eGyHdG7SgtgaxqxGT3p0lVHTSCDrQF85NoNy0bgRc7e8o6EaYKDN4oL8X8awGVEtAldkb8VwIcj2xwA8FEAfwfgFgAHxd7fLKr6cNn4KZKM6F2ImKoTSeMk1bVRN0t78KmX+uz/ZddjdoXrZG1l+7dsyCz+PRv+HQAm0Q31fICZjxHRZwFMMfMBAH8G4C+I6FkAr6LbQQgNIo9MiHlj66coI+d8uBOZmG5j1/iMlVM0eD1saKMpxl9FHWZvLu+hD/4tG2SFr1AY4dHQ0JoWmLtFQnwdGZWxyhNIPmrUtTMoUpPEKTox3dZG+OhW9+Z9PapGWb+bAFnhK3hHOBd9FUZGrvwUScQ8zbUxLYz63OgVidr5qW8dVQp8EF1Tl1z/eVIV/5YkdhMKp4waqLbJwsJkLUoeHDdJgrA018bUHttz1R0bOLcI7nOjVySux5yVNPetbFz8bopAxF8onKJHRmkzNG7fsj7R+yqSinmaa2PKEpokG6XJ1r9v8jg27XlsKbwzXGQ9L4rOrOkKH4vOqxDxFwqn6JFR2plGlmpgAUnFPM21CaeRVmE7q9IdI6hJXLQA6+7bJx864vVMwCattw+IzV/IBZOdu+jIH1sBti2qnmSGotsPo2uSCdclTptTJtxuHe3ZeWwbO2j0O+jqHiddGaxqVxqnflzUka++IsC/ovMqRPwF58Q5LYsOjbRZY5CkqLqqsla4/XEJwgLas/PY/fARgM8ViE+aU0aVClpFMHoPjqsSTRczGl270gi1zfqFuqwzKAMJ9RScU3aoWxRTYY9ANHRtjqKLemmtILxh9Uqcmuv0dRrhz2yxvVY27dZ1YtFjmNJDJ22fi9+AbccW7NfHcOEysA31FJu/4BzfQt1sbLCmtq1b01r2vSeeOalMAhaIe1RAgwRhSUqr2F4rk/AHbbbJfQ/Y+1wIiDXRufgNRO+bqThNVZzBPiFmH8E5PqZyiLPBmkwM0cyOuspaJtqz88YSiKr2xDEx3bYa1etG4dFjxOXwD2DEm25c/QaiK5lN7RMTUDJk5C84x+dQN13cuKlt0dHqUK92blJA8wxgAAAOhklEQVRUwt8aILQildhtr9W+yePalA7h79veD9uRti6qKEwev4G4qCbAv4VUPiMjf8E5ZeS6sSHOCbn3wDFlEfXoaNWlm6xzlrEuQaqLsDNZ14zoyDzufuic1zpfiY2A5/UbCGYCtrMZG6qQhC0PRPyFXPAx1C2upsDeGy+3ErvXFB1ElHACtTiH7Km5bsrkoJi7DlsHqGpkrLsfaesK25Dnb8BVuHBVUo3kgYi/0BjinJC2YhcXgjhAhC988Mql7220qLxlY6/WpV8Ik1QA09YVLhtXMwtfigyVgYi/4BV5TMGDferMJGFTgY3YmRyjqprAQ4MtpTkpSpy92vQ5AdZZO10vZCsLFx2Tb5FpRSLiL3hDHlPwOFNJGlNBeNQZjuLRxZrvvfFy7P7LI0sLuXTE2at1Ym0bO590IVsT8CEyrSyfg4i/4A15TMFNppIsC4OSjDqjJoq1gy2cPrOQKIUDYGfnNgmJ6low+heBDbYGsH3L+th0EHWg7CJDZfocRPwFb8hjCq77LgGFrjaOdhZpRns2UTsmITHl/R8eGlza5/Yt60ur1asiz5Fx2ZFpZfocRPwFb8hjCu7DtF5F3MxBJ3im78UJia3ZaNvYQW+coEWMjMt0apfpc5BFXoI35LEwyOcFZzrS5rGPExLba6HbT3t2vpBUyuGFeJ986EjhhX+KpMzCLyL+gje4yoMeFo99k8dx89XD3udWD5O2/kCckNheX5Pw5J3TP9rx1bloPFDu4ETMPoJXZJ2Cq8wE+w+3vRf8MGlNATbOy6yhrAF5mYFs1jIA5ZvtXFGmz0HEX6gVtg40n5f0p/VTmITElMLBFB1kSiORx+jbZp++m+2SUpbPQcRfqBU2o2bfl/TrRt5zZxYwMd02tlElJLrznXrhVWNUT1ytg7WD+gR3aTtXXcc3QIRFZu866iojNn/BW3QZOE3YONDS2tSLIrDND0XE9dRcJ5WtXXe+Dz71ktV12L1jc1/mUQA43euMomQpvK6zgX/hg1cWUjS+SWQSfyK6gIj+moj+offvOs12Z4lopvffgSzHFJpBWgGxcaBVYUn/6NZhnH9e/8Rc10mZOsq4WrhRotuPbh3GG1b3t6VzlpVtydK5unL6C/FkNfvsAfC/mXmMiPb0Xv9nxXbzzHxVxmMJNcDWHJB28YuNA83X2P8oSQrPm8xYJlOKqgNQXYfZOXVuIlUbdfmCbMpkAn5mhK0jWcX/JgDv6v39VQB/A7X4C0IiW3uW0XmceJS9pF9HtGNcq0kIFxXnuI5Sd76qWsS665Ckw9R1KqYyjELxZLX5v5GZX+n9/Y8A3qjZbjURTRHRISIazXhMoaIkMQekXfxi4yfw0bSgMnOdPrNgVeXLJlW16nw/N3qF9XVIEo+uMyfZlrAUiiF25E9E3wXwJsVHnw6/YGYmIt3dvZSZ20T0FgAHiegoM/9YcazbAdwOABs2bIhtvOCGosIek4zm04zOk8wsfDMtqDrGoMrXmlUrl7KHhjvLoP02o3Ld+dpeh6g5bahXfWzX+Az2TR5f9pvRFbCxKf8oFEfsyJ+Z383Mb1f89wiAnxLRRQDQ+/dnmn20e/8+h65paKtmu/uYeYSZR9avX5/ylIQkZInMSEqS0Xya0bnvUTwmdB3j7FxnadQdjJyj98g0Kk8TMaVjdOswntxzHe7deRV+1VnE7HxH+ZupYkqNJpLV7HMAwEd7f38UwCPRDYhoHRGd1/v7QgDbAPww43EFRxQpmElFIRAb2xC/KkTx6DB1jHH3SNdRAujr2O8cn8FV9/yvTJ1A2va4mGm57MyaTlaH7xiAh4joYwBeAPBBACCiEQCfYOaPA3grgD8lokV0O5sxZhbx94QiBTPvpexVieJRYTJz7RqfUX4nfI9U5htVdk4AmJ3vZFrUZvObycOs5vvivKqRSfyZ+RcAflPx/hSAj/f+/lsAV2Q5jpAfRQtmElFI6ovwNYrHBlPHGFQMixJ3j0wdeJbcPGV1sk2ut5sHssK34fhqn03ji/AxiicJOjOX6h4BwOnX1StsA+LEuD07n8qEUtZvpspmPR+R3D4Np+xKRjqyLPIqu+2uCc7nnkeP4VRosVWc+SYuOyfh3MKrJCaUsn4zVTbr+Qixp7G3IyMjPDU1VXYzhJLYtOcxZTZJAvD82A1FN8cLdAnWTAXc75o4iq8fetH6GLbF4MsgavMHujOOKs3uioCIDjPzSNx2YvYRvKTMCke+ksbs8cQzJ50cwweqbtbzDTH7CF5SZedtXqQxeyQV87I6V1vnfh3NemUhI3/BS/Ie5VUxXjyNo1Un5uvWtLxx9Be50FA4h9j8hcYQjC7bs/MgYJlPoSq246ThryY7OeCHoz+NL0PQY2vzF7OP0AiiIhgd8lQlXjwaaRPN8xO3fVTkfThfCeEsBxF/oRHYFAavgtikWeXqu51c58tgdGcFPoQe1xERf6GWhE08uvzyUaoQSVTHVa6m9QiSwiE/xOEr1I6wAxGwyyNflUiiOppIws59FVXJzFo1RPyF2mFj4glTpXjxuq5/CFJb6Gp9Vblz8xUx+wi1w1Yo1q1pYfoz1+fcGrfUff2DpHAoDhn5C7XDVih0Rcl9pu6rXH1NNFhHZOQv1I64hGYBVR1N+h69kwVfEw3WERF/oXaEBUS1oAuQ0aTP1Llz8wkRf6GWRAWkqCL1glAVRPyFRiCjSUFYjoi/IAiVQ2Zy2RHxFwShUkghdzdIqKcgCJXClOJCsEfEXxCESlHHFBdlIGafBiL2UqHKyCpgN8jIv2FI1SSh6sgqYDfIyL9h1DElsNAsXK0CbvoMOJP4E9HvANgL4K0ArmFmZd1FInoPgC8CGABwPzOPZTmukB6xlwp1IOu6DYkYym72+QGADwD4nm4DIhoA8GUAvw3gbQA+RERvy3hcISV1TQksCEmQiKGM4s/MP2LmuKt1DYBnmfk5Zj4D4JsAbspyXCE9Yi8VBJkBA8U4fIcBvBR6faL3nlACdU8JLAg2yAzYwuZPRN8F8CbFR59m5kdcNoaIbgdwOwBs2LDB5a6FEJLnRmg6dS+KY0Os+DPzuzMeow3gktDrN/feUx3rPgD3AcDIyEh84VVBEIQUSN2AYkI9nwZwGRFtQlf0bwXw4QKOKwiCoKXpM+BMNn8i+tdEdALAOwE8RkSTvfcvJqLHAYCZFwDcAWASwI8APMTMx7I1WxAEQchCppE/M/8VgL9SvP8ygPeGXj8O4PEsxxIEQRDcIekdBEEQGoiIvyAIQgMR8RcEQWggIv6CIAgNRMRfEAShgYj4C4IgNBARf0EQhAYi4i8IgtBARPwFQRAaiIi/IAhCAxHxFwRBaCBSwF2oJU0vzi0IcYj4C7VDinMLQjxi9hFqhxTnFoR4RPyF2iHFuQUhHhF/oXZIcW5BiEfEX6gdu3dsxmBrYNl7TSvOLQhxiMNXqB1SnFsQ4hHxF2pJ04tzC0IcYvYRBEFoICL+giAIDUTEXxAEoYGI+AuCIDQQEX9BEIQGIuIvCILQQIiZy26DEiI6CeAFx7u9EMDPHe/TZ+R8602TzrdJ5wpkO99LmXl93Ebein8eENEUM4+U3Y6ikPOtN0063yadK1DM+YrZRxAEoYGI+AuCIDSQpon/fWU3oGDkfOtNk863SecKFHC+jbL5C4IgCF2aNvIXBEEQUHPxJ6ILiOiviegfev+u02x3lohmev8dKLqdWSGi9xDRcSJ6loj2KD4/j4jGe58/RUQbi2+lGyzO9TYiOhm6nx8vo52uIKIHiOhnRPQDzedERH/Sux5/T0TvKLqNLrE433cR0Wuh+/uZotvoCiK6hIieIKIfEtExIvqPim3yu7/MXNv/APwRgD29v/cA+EPNdr8su60ZznEAwI8BvAXAKgBHALwtss3vA/hK7+9bAYyX3e4cz/U2AF8qu60Oz/lfAXgHgB9oPn8vgO8AIADXAniq7DbnfL7vAvDtstvp6FwvAvCO3t//DMD/Vfyec7u/tR75A7gJwFd7f38VwGiJbcmLawA8y8zPMfMZAN9E97zDhK/DwwB+k4iowDa6wuZcawUzfw/Aq4ZNbgLwNe5yCMAQEV1UTOvcY3G+tYGZX2Hm7/f+/n8AfgQgWoQit/tbd/F/IzO/0vv7HwG8UbPdaiKaIqJDRFS1DmIYwEuh1yfQ/wNa2oaZFwC8BuDXCmmdW2zOFQBu7k2RHyaiS4ppWmnYXpM68U4iOkJE3yGiy8tujAt6ptitAJ6KfJTb/a18JS8i+i6ANyk++nT4BTMzEelCmy5l5jYRvQXAQSI6ysw/dt1WoRAeBfAgM79ORL+L7oznupLbJLjj++g+r78kovcCmABwWcltygQRvQHAfgB3MvM/FXXcyos/M79b9xkR/ZSILmLmV3pTpZ9p9tHu/fscEf0Nuj1wVcS/DSA8un1z7z3VNieIaCWAtQB+UUzznBJ7rswcPq/70fX71Bmb+18bwuLIzI8T0X8noguZuZJ5f4ioha7wf4OZv6XYJLf7W3ezzwEAH+39/VEAj0Q3IKJ1RHRe7+8LAWwD8MPCWpidpwFcRkSbiGgVug7daMRS+DrcAuAg97xJFSP2XCP20BvRtaPWmQMA/l0vKuRaAK+FTJ21g4jeFPiriOgadDWsigMZ9M7jzwD8iJn/q2az3O5v5Uf+MYwBeIiIPoZuhtAPAgARjQD4BDN/HMBbAfwpES2i+0MaY+bKiD8zLxDRHQAm0Y2GeYCZjxHRZwFMMfMBdH9gf0FEz6LrTLu1vBanx/Jc/4CIbgSwgO653lZagx1ARA+iG+FyIRGdAHA3gBYAMPNXADyObkTIswDmAPz7clrqBovzvQXA7xHRAoB5ALdWdCADdAea/xbAUSKa6b33XwBsAPK/v7LCVxAEoYHU3ewjCIIgKBDxFwRBaCAi/oIgCA1ExF8QBKGBiPgLgiA0EBF/QRCEBiLiLwiC0EBE/AVBEBrI/weyamcAi+ahLgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter_plot(data_points, 'scatter_plot.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DZdjxubGxPXNlnkRF5eiIEyiVSWNjw8vjs7XlnXNubnvitrW17cfrktr95jfqc4Y7pDTmsrxnWVnrF0EZDlCViK1vrmPH8I5cTEtZ6uWSuMoaBXH4ekRlwCzq+vgOYV0KiCAmTsm4Fc6mzlzdcSpUjuAoR7cLuF6/GAbuHQCj/z6X7eB1tV4+dV6dLA7fquGblXRhmYODyUbCcSYNU3u3qf1bN2LO01xmg5zqV5S929WFVq7Wy0fWKIj4e7Rayd7PE50pYm4uXqDCDt40ztzw+7rjWi10397C+F3AwN3A+J+PoPv7UQ1rDkXYu/3OZWl1qS/CxwURc11cZY0CapzSOQnz88zDw9vTEQ8PJ0v7bLs+SfccVqWwHh729vFVlaPbVzh8Ls1x88cO96Wfxj3g1idajUnrq0tnnPe+uqrU33QPXTyH7eufNm2zpHsuBximdBabv4+rtl/TeqVZkGVatuK48RdmtAuKqpyp0pSoDJ0HHzyYq727SHt13TKRNgFTm7+Iv8skWYFqM4W1ATqHnk8dHGdRRAkwAOVnrZEWXvzwi5nPXaQztS6O0TxXVruGOHyrjG+7v+028xWolmPW44hz3NU9ZC4qVLCzv4PhweG+z86+fNaK3b9IZ6pJSKTLi7kA99cclIWIf14kTWgW/J6/OEuHKgLnwIH+kFVLOfVVqBx6QVyJ6siLKAGe3DuJVwy/ou+zja0NK3HuRTpTde0coAF0F7uVEFbTNQeud2K2EfHPgzvuAA4eTJcN0yTPT3g07+83EDT7EHkLtHLyW/jREq2R/ogol6I6lKTtmAPECfCZtTPK7y2tLmUWliIjVXSd/CZvYvrhaRx55EjixVxFi6zp7MX1Tsw2Vmz+RPROAEcBDAK4n5k/Hvr8/QD+K4Dnem99mpnvjyqzsjb/btcTftV1NcmGGZd9U2XzL3kbxUrZU0N+lO5eYOYdhOWdjLGd7b66B9u2a2QXAE/Yx3aO4cCeAzj15Cllu6MybAJuOk1197G72MXUQ1PY5E3jsnT+hzIcyCZ+i7r4NoACHb5ENAjgHwD8awDPAvg+gPcx848Dx7wfwAQz32labmXFP2pFrM75GoymGRi4tGNYGF0654Kdva5i1AkF7k93LzB9I3A+YJ4PCpFKqIJEiVbcd4F4YcmrU+0udnHkkSNYWfNSe7RGWrj1zbdi7rE5rSjHOfjD6NpWhsiadDiur0hOQpEO3+sBPMXMTzPzOoAvAbjZQrnVxDBj5UXCCdhUwj86CszP6xd4FezsdRHdFoZ0L203LQTuz8z+7cIPeCaLI48cwfh947jtwf6dxMLH6swbQdOMjiineF5miO5iFx/86gcvCj8ArKyt4LMLn4003+hs/62RViL/Qxk5dUzMZK6vSM4DG+J/DYCfB14/23svzJ8Q0eNE9BUiep2qICKaJqIFIlp44YUXLFStBHSCS6R2vups/EnSOeSxgboFu3iR6LYwBLBdOAP3R7dT2MraSqTJJkiUaPm5+3UdQJSw5JUYbeb0DNY31+MP7OG3T+fjOHrD0UT+h7JENm4fBddXJOdBUQ7fhwGMM/PvA/gGgDnVQcw8y8wTzDxx1VVXFVQ1y+jSIB86pBZw3Uxha8s834ztTJg2tm8smLiR40XhDNyfsdXs5zURrTTCktcIOen3/fZFjZ6TbFDjqsg2Md2DDfF/DkBwJP9aXHLsAgCYeYWZX+69vB/APgvnLR/V6FglxCdOAMeOqcuwZbKxmaDM8g5XRWAiwsury9vuT+c0MHohIqNrDKailUZY8hohR30/LkeQjV3I0opsERFCee6y5iI2HL6XwXP47ocn+t8H8O+Z+UeBY65m5ud7z98N4D8z81ujynXe4Wtr/1fL+8hawTEHsonjM62DNVz2ufVz2+zhQfywVj/aJ8+opryiYnybf9j0MzQwhNuvu10bvVQmkmIiGYWmdyCiAwDugxfq+QAzd4joY/ASDJ0kor8AcBOACwDOADjMzP83qkznxd9meKVreYVKDh0NkuQf3xdyP9NlMHrDVCxcEpoio32O3nD0YoSTa2G7dQrDLALJ7ZM3jo2OreLQbCTtP34WEXNRAH2CHdwgDWKTN9FWrE9IW7YrHV+QOoVhFoGIf944NDrOBUdmI/KPf4ko05YNkXZ1hO1qvVxFErvlTR7hlS7hyA5cdYm/tuGwVIV/+tgIA3V1X1tXI4SyUnYuIRH/tBS50XiDqcM/vq0FW3FrD7KKdJEdranw+Wau8xvnMUiDAFCLMEwXcgmJ+GfBkdFxnUkTGlj2iCqMjQVb3cVuXyhmmCwi3V3s4tz6ub738+hoTYUveBzgJZPz61O28Gf9jeW1iC8JYvMXaoWLTksbfou4RHEEwqGJQzj2Ls16Eg3hyJ8gwSigqO8ndY6b2vBdtfXb+I3l6csSm7/QSPIcUaUd7elG5Aw2LifO5MNgzD02l2gE6ouYbl3DjuEdscKfxnRh6ltw1Qdh4zfmgi9LxF+oFXkJRhYbbdTGN6bl+PbuKJIKUJQDGYi/ZmlF0FT44o4ry7xn4zfmgi9LxF+oFXmNqLKM9uIyfOrKCYqbaS79JAIUd2zcNdPNRuJmKabCF3VcmQ5TG78xF3IJifgLtSKvEVXW0Z6fN0bntA2XExY3U5IIUNSxJtdMNxuJm6WohG/q2inMnJ7ZNoqPEsgyHaa2fmNl5xK6rNCzCY2kyBWzfrm2zze2c0w5ok06ozAtJ84koyKpAB3YcwDHF473dS4mjl4A2tmIySzFzwYK9DtQ/VF8+LggZfoD8vqNFY2M/IVcKWN6bjKiSmovtjXaMy0nTsTaO9s4PHE4tdmgu9jF3GNz24SfQDg8cRgvfvhFo2um2r/ZJ4kNPm4Ur7pXZTtMyx6120BCPYVccS1cTxfa6IfqAfoRna0ZTFw5JnvmEigyw2lcPZPeF1V449DAEIhIuzmMafhjVNjjiVtOKMMqp66ditx2sslIbh/BCVzKzROX9rk10sLahbVSBcUkNXWQcP1MY9CT3hddZ9EaaWHH8A6tk9ekk4/qiAC1A9lPZld100seSJy/4ARpp+c2wvjCZRx55EikqK6srSR2ItoON0xq6w/Xz9QRumtkl7K8K4avULZHZ4Y6s3YmkSNbRZQpLMq2X5bpxbUV5GkR8RdyJY2t3IafQFWGbjFTHCoB6i52sfuTu3Hbg7dZ82d0F7vGewfr6pfVEXpu/ZyyPXGdeBYbfFRUT9m2/TAu5OSxhYi/kCtp4plthPElHUGPDo1qHZhhoYlaGZs23NAvU0d7Z9toI3hTsTyzdsaoXn574jrxrA5x3SjehcVQQVzIyWMLEX8hd5JOz01Gr3FT7yQhf62RFmZvnMXRG44qV+KeWz+HO752x8XzTT00FdmxLK0uJTYLRHVWvtiZCKGpWCYZOfsmlqhOPK9FSy4shgriasqJNIjDV3COuEgUE6dmnIMyKtJGl+jMlLgtJFXROAcfPKhdzHV44vDFhG2qnbzCO3oB8THoqmsYrrdP2YnUXCLP6DVb0WTi8BUqS9zo1WTqfWDPAWXZt7751shZyOTeSewY3pG67ioBDcesq2zGOgcsAJx68tS2+vnXxw8F9f8GF0fFzbRUI+pDE4ecMrFkIS+nbF5mqDJ8CSL+gnPETfVNpt5BwQyie19XThJaIy3t6N0vU9dxJamPrR29wua4Y+865pSJJS1xQpqlY8jLDFWGL0HMPkLlMJl6x8WxR02x43Ln+wzSILZ4a9v34+qmq1cUYZOCSRnzt8znJtoub3APRP8+Ovs7xrn4i2ynzfUwYvYRaovJ1Dsq6iVqZKjb0SoMgTC9bzpxdIquXrpkaAS6mMXSH60OUPy/rQ2TgWqEXIVQx6iZoekIu+h2lhHSKuIvVA6TqbdOhA/sOaCM1jm/cR5HHjkSublJEN3mKXF109VLl8rBHw0GhcgkcVpWk4FO/FQL5WybJ3SdTvC9YPRV2HQTJaSm0TpFm2HKCGkVs49QW8LT9gN7DvTlg8lKmigPlTnBj+BRlQ+oUxz4UT5R8N3p/r9NTV8+ttJ1pMkhBGw33URFg0VdZxPTWp5pSYqO9rGS0pmI3gngKIBBAPcz88dDn18O4AsA9gFYAfDvmPkZG+cWBB3hdMDj941bFX4guXM46h9cJVh+GKiKTd7UhmcCZrt/6UjaLlvmCdWIe2NrI/Z7/qg8eM+TXucgtlJ4J0GXvjovMpt9iGgQwGcA3ADgTQDeR0RvCh32IQD/yMxvBPApAJ/Iel5BSEqUoEWt8I0S0SRiEGVHTpPiAECk49d09y8VSdpl0zyRZbFU8Lu6hYWm0TqurSzOAxs2/+sBPMXMTzPzOoAvAbg5dMzNAOZ6z78CYD8RqTNBCUJORDlbdSt8R4dGMffuOczfMh8pBibhg3F25CQpDkwIp4NIEuJocs48wkGzjKxNv6u7zsHrM3N6BlPXTlU+7DUKG2afawD8PPD6WQBv0R3DzBeIaBVAC8CLFs4vVISyQwRNw/yi6qj6LG4nKp+0qQHCZgyTUFEC4Y273ojx+8axvLqMXSO78NL6Sxft5ro6hs+p21cgr1W/qntkavPPMipX3cO5x+ZqJ/hBMjt8ieg9AN7JzLf3Xh8E8BZmvjNwzBO9Y57tvf5Z75gXQ2VNA5gGgLGxsX1LS8kzHApuYppnvoh62O6ATJf820oNkNQZG0Xcucu4b6p7BKDPeX/qyVPW7qNrmw5lobDNXIjobQDuYeZ/03v9XwCAmf8icMzXe8f8byK6DMAvAFzFESeXaJ96Uad/rjCmkSG2hDRJXp44dNErQQH2U0+cWTuz7bmLC7zS4tKmQ1kpcpHX9wHsIaLXE9EwgPcCOBk65iSAqd7z9wD4VpTwC/WjTtkQw5gu0LGVGkBVThrh19U97JheWVvB2oU1HJo4hLULa1hZW3F2gVdaXNs3oAgyiz8zXwBwJ4CvA/gJgC8z84+I6GNEdFPvsM8DaBHRUwD+DMBHsp5XqBZV/ecycZImiQyxtftUsJzO/k6qsE5dHXWO6dlHZ2uTyz6Mzeiequz0ZWWFLzOfYubfZeZ/ysyd3nsfZeaTvee/ZeY/ZeY3MvP1zPy0jfMK1aGKoXOmS/zLzDnv19EkrHNoYAitkVZsHXWzMd056jB7s3UPq5D+wkdW+AqFobMju2o7LsNPkdQhravjIA1iet90Yqdod7GrjfDRrSiug9/GFi74tiSxm+AcvqnixC0nKmE7tuWnMDUDpBk1Ro3Sjy8cBwCcuOWEkYkpahYxOjSK6X3Thc/eqmJC8amSb0vEXyicMnKXpxER3QYrtlb1hklzXeJW/ybpWHX7BPiL4IrO918lE4pPlXxbIv5C4RQ9OkojIt3FLl5af6nv/aGBoUQj3SSCnua6mKzENe1Yo2YRM6dnLq587ezvZHZYm1DFzdKr5NsS8RcKp+jRURoRmTk9o1xReuXlVyYSvCSCnua6hB2VSesRRDfTIVDi0bcNc42uzkurS86agFzbcD4KEX8hF6L++YseHZkKcLDOuhW0Z9bOJDq3TrgZ3JeX/tz6OQwPDm87Lul10YV8DtBApBB3F7s4+/JZbV2DxHWctsw1UZ2eyyYgW+G8eSPiL1gn7p+/6NGRyYg6XOe4sqI6t+BnKkH3WVpdwmcXPrttMRUzG4Vj6uqtC8fc5M1IIZ45PWOUOtknaiZhy1wTZ9I6v3EeUw9NVcYZ7BoS6ilYx4VwtyAmaRVM8uX43wH6c8L76RVaIy2cffnsNiEdGhjClZdfabRDGJDsOkWFem7xFgZowCg8M+newlF1tJkqwQ99NcllVEauKBeRUE+hNFwLdzOZacTVLfgd1cjWF7uVtZW+EfTG1gZ2DO+ItMkHSXKddKK4xVvYunsLW6wW2/A5kvhb/H2Fddj06fgmlHB6ahWuO4NdQ8RfsI6L4W5xdtiouvmjXP87aTqxpdUlo43X4+oSpLvY1XYofhmm9yLJngEMjhxd5+HTMa2fi/H0riLiL1jH1XC3OCe0jrCg6KJi4jBJwRB1ncL1P/LIEa15xS/D9F6oZke6nc3iRuF5+HTCZeoc2y7G07uK2PyFXCh74xZVfeLs/rs/uVtplw/bt3XHZaU10sLRG44qr5Oq/lEEN27K/b/KAAAN8klEQVSPuhdxn7mwB4MKm3Vz7bealcLy+eeFiL9gExMntKmgmDhHWyOti3mLTDdeiXKiJtnAxdRhbNJel4XRRt1c7uDSIuIvCAGSbLgSJyhxQtwaaeHFD1/apI7uNXP0RkXDmEbjJBEu16KyyqCO10CifYRKkkcir+5iV+tsVW24ErdAJ8r5ODo0iqM3HN32ns52HlcXk89aIy1j23r42uo6sCY5TV2LTCsSEX/BGfJI5BWXqTKNEzrofAQurarVie/RG45iaGAossy4uugct0dvOLqtswKg7DxV11YXKbRrZFelMmlmwYXItLIyl4rZR3CGPKbgUYug5t49V5hdN2xOSrMBeZxJKsp+rVsoFd77d2hgCES0La9R1W3gUZRt88/j/GLzFypHHpto12lj7jiiOs/l1WWtz8D/fGznGM6tnzOKeCqSvJ3OZTq18xjwmIr/ZalKF4Qc0EXGZJmC51FmEaQRpCj7te46qNI8JCk7b8IjY98UCMCaQE/unSxtVlOmz0Fs/oIzFLUy1IUFZ1Gk9X1E2a9Nr4OujCL9AEEb+NRDU5XL6Z+EMn0OIv6CM9jcRNsXj5nTM5i6dqoS+dV90mbFjBJ402urKmN4cBhnXz5byI5apllK6xKNU+bgRGz+Qq0o24Fngyx+iqTmItXxALa9V6QfwHQxW5Xj8MPY9jmIw1doJKYONJdXrtqOUNK1NeuK5jyc5iaL2arWmReNLPISGomJA831jcF1i8g2eTNxPaPaampeivIDRJ03jY9Ad65BGqyM2a4qiPgLzpJGQEwcaK5vDO7b51WZK5PWM6qtppEmnf0d5SK1l9Zf0m4JmbZz1dnA59495/y2iFUjk/gT0S4i+gYRPdn7+yrNcZtE9MPe42SWcwrVJYmYpxUQEwdaFZb0T+6dNN6IBdBf27jwTxWqlBdXXn5l33Hrm+vKjihL51qlDdCrTtaR/0cAnGbmPQBO916rWGPmf9573JTxnEIFSSrmaQXERDxcWNKvIizgOrNKuJ5R19ZG+Ceg37he1bnoHLamWUmrsgF61ckq/jcDmOs9nwPwxxnLE2pKUjFPMzr3xfPggwcBACduOaEUDxdj/1UC/tL6S33mFlU9o66tjfBPIFmHqdtoRfe+UA5Zxf/VzPx87/kvALxac9zvENECEX2XiKSDcIwiEkslFfOko/MkMwsXTQsqAV/fXMeVl1+5LSvoyGUjfd+NurZxbTUdZas6EQJhaXWp7zeji8032clMKI7YUE8i+iaA1yg+mgEwx8yvDBz7j8zcZ/cnomuY+TkiegOAbwHYz8w/Uxw3DWAaAMbGxvYtLZlNE4X0FBUXnzSHSdJ6VT0ve1SI4+jQaOR1KKrtfoSQnxE0WN9gnap+L6qOtVBPZn4HM/8zxeOrAH5JRFf3Tng1gF9pyniu9/dpAH8H4A80x80y8wQzT1x11VVxVRMsUFTkS1JTS9LReRWcuFFEhTjG3R/dtT2w54DVGZ0/S2jvbPd1VME6uWhWE/rJavY5CWCq93wKwFfDBxDRq4jo8t7z3QD+EMCPM55XsERRopnG1JLE8eeqE9cUnWCapDdQXdupa6cw99jcNjPYwQcPgu6lzB1B3G8mT7NaWbnv60imFb5E1ALwZQBjAJYA3MrMZ4hoAsAhZr6diP4FgM8B2ILX2dzHzJ+PK1tW+BZDXabodUjroFqJq8vDH3d/4tIkZLk2Zf1m6nCPi6CQFb7MvMLM+5l5T888dKb3/gIz3957/vfMvJeZr+39jRV+oThcnqInGeW56MRNimqmk/b+xM3cspj2yvrNuL44r2pIbh/ByTw3Msq7RPD++LH/Z9bORN6rJAnS0tz3Mn4zTdqYJwuS2E2oNHUxR9kkSYeoOjZMVMSOi8hvwgxJ7CZUmqpH7+RBErPH5N5JTF07pd2kPSz8UWW5gssmyioi4i84SdWjd/IgaYd46slTSjPJIA1q1xS43LnWwa/jEiL+gpPIKK+fpB2iTsi3eAvtne1EZeVJUse+5P2xg4i/4CR5j/KqGC+etEO0ldQtT1zfW6HOiMNXaAym6QlcJkmUTZyD2IUoL3Hi2keifQQhgEn0S1UEJ2kHULbARyHhm/YR8RcaTVj0dJuQB6mC4NRt/UPUfsVbvOVkh+U6EuopNBaVHTlO+IFqRBLVbZVr1H7F4gPIFxF/oXaoBDKOqkQS1W39Q9ixb2PfYsEMEX+hdiQVwirFi9dx/UMwfDPJvsVCNkT8hdqRRAj5bq5UvLgrIZp5UcfOzVVE/IXa0dnf0aY1CKJb6OQydV/lWvfOzSUuK7sCgmCbyb2T+M7yd3B84Xjk1ohVFZTJvZO1EfswfrtcDk+tCxLqKdSWNKmQBaHqSJy/IAhCA5E4f0EQBEGLiL8gCJWjion5XEMcvoIgVIpwigt/FTAA8eMkQEb+giBUirqluCgLEf8GIlNmocrULcVFWYj4NwzZPEOoOrIK2A4i/g1DpsxC1bGxClhmvyL+jUOmzELVyZriQma/HpkWeRHRnwK4B8DvAbiemZWrsojonQCOAhgEcD8zfzyubFnklQ+ybZ7QdOr+P1DUIq8nANwC4NsRFRkE8BkANwB4E4D3EdGbMp5XSIkkzhKajsx+PTKJPzP/hJl/GnPY9QCeYuanmXkdwJcA3JzlvEJ66p4VUhDiEIexRxGLvK4B8PPA62cBvKWA8woa6pwVUhDi6OzvKPdBbtrsN1b8ieibAF6j+GiGmb9qszJENA1gGgDGxprVCwuCUAySNtojVvyZ+R0Zz/EcgNcFXr+2957qXLMAZgHP4ZvxvIIgCEpk9ltMqOf3AewhotcT0TCA9wI4WcB5BUEQBA2ZxJ+I3k1EzwJ4G4CvEdHXe+//EyI6BQDMfAHAnQC+DuAnAL7MzD/KVm1BEAQhC5kcvsz8EICHFO//PwAHAq9PATiV5VyCIAiCPWSFryAIQgMR8RcEQWggIv6CIAgNRMRfEAShgYj4C4IgNBARf0EQhAYi4i8IgtBARPwFQRAaiIi/IAhCAxHxFwRBaCAi/oIgCA1ExF+oJd3FLsbvG8fAvQMYv2+8cZtzC0IcRezkJQiF0l3sbtupaWl1CdMPTwNA43O4C4KPjPyF2jFzembbFn0AcH7jPGZOz5RUI0FwDxF/oXYsry4nel8QmoiIv1A7xnaq93/WvS8ITUTEX6gdnf0djA6NbntvdGgUnf2dkmokCO4h4i/Ujsm9k5i9cRbtnW0QCO2dbczeOCvOXkEIQMxcdh2UTExM8MLCQtnVEARBqBRE9CgzT8QdJyN/QRCEBiLiLwiC0EBE/AVBEBqIiL8gCEIDEfEXBEFoICL+giAIDcTZUE8iegHAkuVidwN40XKZLiPtrS9Naisg7U1Cm5mvijvIWfHPAyJaMIl/rQvS3vrSpLYC0t48ELOPIAhCAxHxFwRBaCBNE//ZsitQMNLe+tKktgLSXus0yuYvCIIgeDRt5C8IgiCg5uJPRLuI6BtE9GTv76s0x20S0Q97j5NF1zMLRPROIvopET1FRB9RfH45Ef1V7/PvEdF48bW0h0F7309ELwTu5+1l1NMWRPQAEf2KiJ7QfE5E9Je96/E4EV1XdB1tYdDWtxPRauDefrToOtqEiF5HRP+TiH5MRD8ioiOKY/K7v8xc2weATwL4SO/5RwB8QnPcubLrmrJ9gwB+BuANAIYBPAbgTaFj7gBwvPf8vQD+qux659ze9wP4dNl1tdjmPwJwHYAnNJ8fAPAIAALwVgDfK7vOObb17QD+tux6Wmzv1QCu6z1/BYB/UPyec7u/tR75A7gZwFzv+RyAPy6xLnlwPYCnmPlpZl4H8CV4bQ4SvAZfAbCfiKjAOtrEpL21gpm/DeBMxCE3A/gCe3wXwCuJ6OpiamcXg7bWCmZ+npl/0Hv+EoCfALgmdFhu97fu4v9qZn6+9/wXAF6tOe53iGiBiL5LRFXqIK4B8PPA62fR/+O5eAwzXwCwCqBVSO3sY9JeAPiT3hT5K0T0umKqVhqm16QuvI2IHiOiR4jozWVXxhY9c+wfAPhe6KPc7u9lNgopEyL6JoDXKD6aCb5gZiYiXWhTm5mfI6I3APgWES0y889s11UohIcBfJGZXyai/whv1vOvSq6TYIcfwPtfPUdEBwD8DYA9JdcpM0S0A8BfA7iLmc8Wdd7Kiz8zv0P3GRH9koiuZubne1OlX2nKeK7392ki+jt4PXAVxP85AMGR7Wt776mOeZaILgOwE8BKMdWzTmx7mTnYtvvh+X3qjMlvoBYEhZGZTxHRMSLazcyVzflDREPwhL/LzA8qDsnt/tbd7HMSwFTv+RSAr4YPIKJXEdHlvee7AfwhgB8XVsNsfB/AHiJ6PRENw3PohqOVgtfgPQC+xT1PUgWJbW/IHnoTPDtqnTkJ4D/0okLeCmA1YOqsFUT0Gt9fRUTXw9Ovqg5k0GvL5wH8hJn/m+aw3O5v5Uf+MXwcwJeJ6EPwMoTeCgBENAHgEDPfDuD3AHyOiLbg/Zg+zsyVEH9mvkBEdwL4OrxImAeY+UdE9DEAC8x8Et6P6wQRPQXPmfbe8mqcDcP2/iciugnABXjtfX9pFbYAEX0RXpTLbiJ6FsDdAIYAgJmPAzgFLyLkKQDnAXygnJpmx6Ct7wFwmIguAFgD8N4KD2QAb6B5EMAiEf2w996fAxgD8r+/ssJXEAShgdTd7CMIgiAoEPEXBEFoICL+giAIDUTEXxAEoYGI+AuCIDQQEX9BEIQGIuIvCILQQET8BUEQGsj/B5q/+9ZyX1HmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter_plot(data_points, output_file_name='scatter_plot_color.png', i=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "Npts, Ndim = data_points.shape\n",
    "prior = 1/float(Npts)\n",
    "distance_matrix_= distance_matrix(data_points,data_points) # define similarities\n",
    "range_clusters= range(2,5)\n",
    "range_betas = [1,5,10,15,20,25,30,35,40,45,50]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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uR+lsUku6VzhFoWM8Rc6TUdqB126Mi18qv5a9o9q8r2lp3irbJOE9SgYOHMjAgQMjto0ePZrCwkIACgsLSUhIiGhPTU3l8ssvx+FwkJKSQqtWrfj1118jEt6D4Xjmjqoba6dCZUlvnVQAVFLC/o8/gBo1Ehk7dhKzZt1Ju3bt8fsDtGrVBtM0MU2TMWMmVDgmI2MXt9wyhYsvvpRzzun7l68thBBCCCHEcUEXY+gsDJ0FyknQaAtAvH8Wpt4eaiPUXmL2p8B1D2DgDdyMIoDGga1SsUkFgqFTkkS+8zZslYZNauizSgUVH2pXKeS555Bc0gdT76gQkq3qHK27PyRRn6X566+/rlDZBPjmm2/IycmJQkRHT6dOnVixYgUAK1eupHPnzhHtq1atYty4cUAoId6wYQNNmzY9rDGoMYMgxhW5McYV2n6Y9OzZiwYNGrFs2du43S5++WU9tm0TDAYZP34Ufn95l+o9e7KZOHE0I0eOoX///ztsMQghhBBCCFHdKJ2Jw/4Bl7WCmOCrxAWeICa4KNxew3cdKcWdSCvpQIrvLJL8lxMfeDTc7rTXYurf0cpDwOhCsWMYfrN0CKRS7HX/h6yY/5EV8z17YlaQE/NvShzDStsNShxX4Df7EjS7YBuNwsnuvgodE9HERGzTxFDomHj4H8gREJUKr9aaTZs2kZyczMSJExkzZgxnn302BQUFOBwOkpOTmTJlCjNmzOC0006LRohHxeDBg5k6dSqDBw/G6XTy8MMPA/DAAw/Qt29fevfuzaeffspll12GYRhMnDixwizOh8o8vycWlM7SnA21Uw7LLM1/NG7cJL766ks8Hi/dup3GyJHXYds2F198KS6Xi5kz72DEiFG89NK/yM/P57nnnua550IzUj/88OO43TEHuIIQQgghhBBRpm0U+WhVAwCn9TkO++fSbsWhCqzGTZ77CQAS/BNx2V9EnCKg0ilxXBH62mhPUDUJV1+1SsVS9cP75sT8e7/hWMahF8vKJqaKDz6CoXdiH2OzNCuttT7wboffFVdcwZo1a0JBlM7gq7VGKYVt27Ro0YJ//OMfNGjQYL/nyc6GFi1Cn09EmZkVq+Pi+CTjekR1J++oqO7kHRXVnbyjh094GZ3DkaBpjaIQQ5eOhSUTv9EXlCIm+Cou6/1wMmuQDbjIiv0aAK//ZmKsN9G4S5PWNCzVkHzXAwA4rVUoisLdjUNdiqtvoae6vqPVcgzv888/j1KKYcOGMWHCBDp37kxubi62bQOQmJh4xJbiEUIIIYQQQhyf/swyOkrnYOqtpclsadKqMyl0TkKrBGIDzxIffCx8rjJZMV+iSUDpPRg6C1ulEjROLh8Hq21QBgXOaRQ470ATD5XkNgGz4qRR4vCKWoUXyiu6Pp8Pv9+PYRg4HA4Mw8A0TQzjwEOMpcIrFd4TRXX9i5oQZeQdFdWdvKOiupN39DDQVmiSJTIqNNnEEDTSMXQmea7HsIyWxARfwhu48w/7JZHjfgnLaIzT+gyX/Wm4+lqW0FqqKagTb/7f6vqOVssKL4S6Mq9bt47HH3+cdevWhRNg0zTJzs7mzTffPGCXZiGEEEIIIcRxTheXVmEzMcgkqNpgGw0w7V+IDzwYrswaZKOwKz1FqEprEzRaUpYG+Y3TyXU9WZ7MkgzKGT4mYPYgYPY4CjcojpSoJby2bWMYBvfccw8JCQnccccdxMfHEwwG0VpTXFxMWlpatMITQgghhBBCHGk6iKk3liespR9+sxcB83RMewuJvkswKIw4LN/5d0qMwYCBobOxVU2CRmtslUZs8EUMcitcylZ1yXW/ELnNqIefekfyDkWURb0Ov2XLFhYtWkSjRo2iHYoQQgghhBDiUGkfCh9aJYC2ibEW75PQhj77zHMpdl6PoohkX+RSlDbx2KouAfN0bJVCiTkgPOFTebfi0EzFltGcnJjXIo63VLOIMbxwbC2jIw6vqCW8ZRNSdejQgR9//JGaNWvicDhQSmEYxkGN3xVCCCGEEEIcBVqjyAknreAiYHYBwOO/A1NvKU9oyaPEvJB814OgDDyBh4ASbFLCCatWSaHT4iXX9VjpGNmapbMUx5VfVnkpdN36p0I91pfREYdX1BPeFi1acOutt9K1a1fq16+PUgqHw4HP52PKlCnExcUd4EziUK3M+pQXti0hy59FqiuVofUH0Sv10NbhXbt2DdOnT+L555dQq1ZtAObPn0OjRo3p16/qHzaWZXH//Xfz++9bAcWUKdNp2rT5IcUihBBCCCGqZujdGHpX6edQBVYTS7FzOAA1fNfgtL9EEQgf4ze6kmsuAsDU21EEsNRJBIzu2CqVgNEmvG92zEdoaoAyK15cKfxm38N+Tz7HBZLgCqAadGkuKSlh0KBB2LZNIBDAtm38fj9FRdVv9q/j0cqsT5m/ZQE+2w9Apj+L+VsWABxy0ut0urjnnhnMnv2Pg15i6rPPPgFg/vxnWbt2DU89NY/77nvkkOIQQgghhDihlK4bq5UHAKf1BQ77RwzKE1owyXU/A4DXPx2X/WnEKQIqPZzw+o3uBI02pWvF1iydpbhOeN+y81QZjko+jDcnxJ8T9YR38uTJ0Q7huHf7zzMqbOuefCrn1TqHf217KZzslvHZfp7ZupBeqT3JC+Tx4MbZEe0zW91xUNft3LkLtq157bWXGTBgUHj7c889zSefrMCyLC66aAAXXTSAmTPvYMSIUfTq9Te6dw8l2hkZu/B4qp5iXAghhBDieOAOvhXqfrtzJ8n7636rAxjsCVdi/UYvUCbu4Nu4rXfDMxiHuhzbZMV8B8rAbb1JrPUqGlfpTMRpWEb98GmLHDdQzLDS7sY1K8xUXOwccRSeghBHRtQT3m3btvGvf/2LXbt2hcfvAqxfv55XX32VmJiYKEd4fMvyV76Acb5VcFjOP3nyNEaMuIpu3UKLaufn57F69Sqeeuo5bNvmiSfmorXm9tvLk3KHw8Hdd9/JypXLufvu+w9LHEIIIYQQ1ZE7+FbEBEum3oE3MA13cCn57nvRKomY4EvEB2ZjsDfi2KyYz9CkYugMTL0l1JVYdQ4ntWABBoXOSRQ6p6LxQiW97gJm16Nwp0JER9QT3mnTpqGUIjk5mR07dtCmTRuWLl3KhRdeiMvlinZ4x4X9VWTTXKlk+rMq3Q6Q4Ew46IpuZWrUSGTs2EnMmnUn7dq1x+8P0KpVG0zTxDRNxoyZUOlxt912F9nZWVx//dX861+vEBsb+5djEEIIIYSIJqX34LTXYOjdmDqjtEKbQYFzOvHBRyJmEwZQBHHpjzF0BpZKwlIN8Jnn7DNTcehDkwBAsfM6ip3XVXl96VIsTmRRnwr5xx9/5Mknn+Tmm2/G4/Fw5513Mm/ePH744Qdsu/JFo8XhM7T+INxG5B8W3IaLofUHVXHEn9ezZy8aNGjEsmVv43a7+OWX9di2TTAYZPz4Ufj95V2q3313KYsW/ROAmJiY0hm7D278rxBCCCHEUaFtlN6D0vkAGDqDuMBcPP47SPDdSGLJxaQU98BlfQCAw15HDf8YvIGZxAafxWl/gdLFKHwYemcVF1FYxskABMweFLhmUOQcQ4njcvzmmQSNdFBSHBLiQKJe4U1ISMAwDGrWrMkvv/yCZVl06dKFX3/9VZYmOgrKJqYKzdKcTaor5bDM0vxH48ZN4quvvsTj8dKt22mMHHkdtm1z8cWX4nK5wmN4e/c+g3vuuYubbhpBMBhk7NiJuN3SrV0IIYQQR4fSBRilVVhb1cQymqH0Hrz+v5dO+hT6UAQocN5KseNKlC4gPjgHm2QsVQtb1SRotMVWNQEIGunsdb+OpWqhSQJV/juurepg6h0V4rD3mRRKCPHXKa21jmYAo0eP5uSTT2bkyJFcdNFF3H777cTHxzNixAhWrVp1wOOzs6FFi9DnE1FmZn60QxBHSWJiHDk5Mnu5qL7kHRXVnbyjJzjtDyerBhmYejeWaojf7APaT5LvgtK28nekyHEthc6poAtJ8g0sXSc29GGpWgSMrlhGS9A2EPxLFdc/juEF0MSQ77xbltUR1U51/Tmallb1RLdRr/BOmzaNsWPHcskllzBmzBiuvfZalFKMGTMm2qEJIYQQQohjhGmvw9Q7ypNanYGlGlHsvB6AlJLTMciJOKbE7B9KeJWLoNEBmxr7JLW1sIzGoR1VPHtjllV9cWUAf617cVlSGx98BEPvxN7fLM1CRMnKrE+PeI/QIyXqFd7du3dTs2bN8Pc5OTkUFBRQv379/RxVTiq8UuE9UVTXv6gJUUbeUVHdyTt6jNEaKAIVD4DL+hiHvT6czJZ1Oc5z/wOApJILcej1oUNR2KTiN3tR4LoHgJjgi4Az3OXYVrXQJFY6a3G0yDsqqqOVWZ8yf8uCiKVM3YaLkY1HVJukt9pWeH0+H//3f//H+eefz3nnnUebNm3wer0kJiZGMywhhBBCCLEf4XVj/2pFUpeUrhm7h6DRvvSc/8Zlrwons6bOwFZJ7IlZDkBMcDFue8U+VdhaWEaj8CnznXeBMrFVLWxSQEX+mlviGHLI9y3E8cTSNn7bj0M5cBoOiq1ithfvwGf78Nn+8Od//b44ItkF8Nl+Xti2pNokvPsT1YTX7XazYMECXnnlFW666Sbq1q3LhRdeSL9+/SKqvkIIIYQQonqofN3Y2wDwmedhkB1OWg29mxLzMlAOYoKLiA2+XDpONtS1WGOSFfM9KBOHvQ6n/R1W6YRPfnUGtqobvm6+6z7yiAVV+VKFQbPjEb5zIY6eoB0sTTh9uAwXHoeHgB1gXcF6fJY/Iilt4TmJZvFNyAnk8Mr21/HbfkpKj/XbfvrXOo8uSZ34tWgrs9Y/gL/02IAOADCp2Vh6pJzGhoJN/H39rIOOMct/bHSxjfoY3rZt29K2bVvuuusuPvzwQ15//XUee+wxTj/9dB5//PFohyeEEEIIIfYRH3i4knVjS/AEZuAN3IwicllJv3kmNrXQxGGpBgSMLuFJn0KzGIdG1xW6bqWQW6u8rqwlK/6M8jGnWaS6Ug/bmFOtNX4dwG+VJ5xOw0lNdxoAa3LWUmwVh9pK96kfW5euSV3QWjP31ycoscqTUZ/t47TkblxU5wJ8lo/rvhmJz/ZjaSt8zUvrXsyQ+pdRaBVy57qKCemw+oNpFt8En+3nk+xVuE0XbsON23DhMtxYhM7lMePpWCMdl+HCbbqJMdy4DDeN4hoC0DiuIbe0mFJ6bOh4t+HmjnUzK01uU10ph/w8j4aoJ7y2bVNUVEReXh579+5FKUV8fDzx8fHRDk0IIYQQQpQy7Q3EBedjUPm6sYp8ihwjIyZ9slVNbFIB8DkG4HMMOJohixPU8sxPeGLL0/h1qBtupj+L+VsWAOBxeMjyZ4erpz7LTw1nAv1rnwfAM1sXsr1kRygZLU1Ym8U3ZVyzUQCM+m48Gb7dEdfrlnQKU0+aCMDczU+QF4ycY6d3Sk+6JnVBKcUvBRtRqFAyabqJd8QTa4aW4HQaTvqk9ibGiAknrS7DRbO4JqHYTQ8zT74jfGxZe7wZB0Atd02e77ygyueS5k7lpqY3VNme4EygS2KnCtuH1b+80jG8Q+sPqvJc1UlUE16/38/LL7/MihUrWLt2Lenp6Vx88cU89NBDxMTI2qtHyyGPw6nE2rVrmD59Es8/v4RatWoDMH/+HBo1aky/fgc+9969e7juuit49NF/0KhR40OKRQghhBB/krZw2N/islcSMLoRME8DNC5rNZpYFMUVDrFVHYqc445+rOK4ZmmbIqsIr8MDwC8FG/mt+HfyAvnkB0MfAKOb3gjAgxtm8/ne1RXOUzbmtJa7Jj/k/xTebmDQwnNSOOHNCeRSGCzEbbhJdCbiNl3Uiy1fE7l/rfPw2b5wsuk23OHqLsBdJ9+OQ5nhhNRtuHAqZ7h9TvrDVd6roQyua3RVle0Ow0GbhFb7fV5HQlll/FidpTmqCW9ubi4LFy7k+uuv59FHH8Xj8UQznBPSfsfhHGLS63S6uOeeGcye/Q/Un5gBMRgM8sAD9+ByuQ/p+kIIIYT4E7SF23oLl70Sl/UpBrloDIocbgLmaVjqJLJjPsFtLa103dhCx8QoBi+OFcVWCXsDe8kP5JMXDH3kBwu4oPZ5mMp+LzvRAAAgAElEQVTkvd0fsCLrM/KD+eQF8ygIFqJQvHLKv1BK8UHmf/ko82MAnMpJgtMb0bW2S1KnShNeCI05vbf1DIBwMuowItOhSc3H7jf+82v33W97o7gGB3wGx6JeqT3pldrzmJxJPKoJb1paGh988AF+v5/MzEy2b99OixYtCAQCuFx/bS0zUVEN3xUVtvnMvpQ4hu5nHE5osXOl95Dgj/xrba570UFdt3PnLti25rXXXmbAgPIuD8899zSffLICy7K46KIBXHTRAGbOvIMRI0ZRu3Zt5s6dzUUXDWDRon/+hbsVQgghxEEpreIa7MZv9gUM4oOPg/bjN8/Eb5yO3+yBVjVC+ysFKFk3VgChsaxFVlE4YW0QW59YM4aNBZv4394vSxPWUAU2L5DPnSffQoormaUZ7/DitpcrnO9vqaeT6KyB1uA0HDSKa0iCw0uCw4vX4cXGxsRkcL1LGVj3YhIcXtyGu0JRpU9qL17a9gqZ/qwK10h1pZDsSjpiz0RUT1Efw7tu3Truvvtu1qxZQ9OmTbnvvvuYMmUKL730EklJ8kIeaQa7Kt2u/rAw+181efI0Roy4im7dugOQn5/H6tWreOqp57BtmyeemIvWmttvD/21bdmyt0hMTKRbt9Mk4RVCCCEOM6WzcFmf4rJX4LI+wyAXizT2xJwLSpHjXoxNGihjv+fxOS6QBPc4orVGozGUQX6wgA0FGyskrP1qnUvDuAas2buWeVueIj9YEDGx0r2tZ9DScxK/FW/jzV1v4y1NVhMcXhrE1kfr0ORkpyR2Js2VGm73OkOfY4zQcMa+tc6mb62zq4w12XXgycuG1h90TI85FYdXVBPejIwM7rnnHvr06cP06dOZPHky6enppKenM2vWLB566KFohnfc2F9F1lZ1MPWOSraHlgHQKvmgK7qVqVEjkbFjJzFr1p20a9cevz9Aq1ZtME0T0zQZM2ZCxP5Ll/4HpRRr1nzBxo2/cPfdd3DffY+QkpL6l2MQQgghTlg6iMP+NrTWrXIQF3iCOGsRFmkRVVxKq2S2qhXlgE9M5TMKH/r4SK01JbYvPL41r7TrcNP4xjSIrU+GbzeLfn8xPAa2LKkd23QUPVO681vRb9z9y/3h8xkYeB0eTk3uSkMakOJK5pTELngdnoiEtV5MaJxr79TT6ZPaq8rhbI3iGoZnBT5SjvUxp+LwikrCq7VGKUVmZiYZGRlcd911fPvttwSDQQAGDx7M9OnToxHaCafQMfGIj8Pp2bMXK1d+zLJlb3Plldfwyy/rsW0b27aZPHksDzwwO9yF/R//KJ9ZbvTo65ky5RZJdoUQQog/QelMXNYnpWNxV2GQy17XYoJmJ4odV+BzXEJQnXzAKq44OlZmfRpRjdx3RuFeqT3x2X7yA/mYyiTJlUjADvBB5n8rJKynp3TnzLQ+ZPmzueHbMRWuc1WDoTSIrQ/A1qLf8Tq81HLXormnOQkOL3VKE9Ym8Y25t/WM0q7EHuLMOIx93pUm8Y0Z2WR4lfdjVpP3qmzMqRBRrfCapklsbCyWZREMBnE6QzOY7d69W7ozHyVHaxzOuHGT+OqrL/F4vHTrdhojR16HbdtcfPGluFyuiDG8QgghhPgTdBBFCVp5cNjfkOQLddvct4prGS0AsI1Gf1glVxwttrbDieMvBRvJC+SRbxXw7NbnI7reQmhG4cc3z2f+lqfx2T4Azqt5DiMaX4NC8fTW54DQMjUJzlBiapd2Ga7hTOCKBoPDY18THAkkOLwklY5dreWuud+ZguPMOFp6Tjrcty9E1Chd1qE+CvLz83n00UfZunUrnTt35o033mDy5MksWLCAoUOHctFFFx3wHNnZ0KJF6POJKDMz/8A7iePCsTgrnjixyDsqqrvj6R2NrOJ+RoljEIXOyaD9xAb/ScA8Xaq4R9Ae/15yA7kUWAUUBAspCBYQY8ZwekoPAJ7e+hy/Ff1OgRVqKwgW0NrbittaTgXg+m9Gk+U/8C+vF9Y+P5y4No5ryEme5gDkBfKId8RjKvPI3aQQlaiuP0fT0rxVtkW1wuv1epkyZQpPPvkkb775JoWFhTz77LNcd9119O27/ym/hRBCCCFORDV8V+KyQ8uuWKThM8/Cb4Qmh0S5KHbeEMXojg2WtikKFpK/T8LqtwOcmnwKAO/t/pD1+b9QYBWSX5qwehwe7m19FwCPbHqcn/LXRZyzcVyjcMKbF8jD0haprhSaxDXCY3pouM9yNROajcGhHHgdHm7/eQbZgT0VYkxzpXJ1w2GVxp/gTDgsz0GIE0FUEl7LsigqKsIwDAzDYPz48YwfPz4aoQghhBBCVEv7VnFNvZsc94sABIwu+I0e+M1eWOrk8IRTJyKf7acwWEB+adJ6srclpjL4Nvd7fsj7iQKrIJywFlsl3Nd6Bkop5v36FB9nrYg4V5wZG054NxZu5sf8n/E4PHgdHlLiGlDTlRbed2DdSyi2SvA64ol3xIf2Mz3h9okHWMu1lbdl+OsrGgyWGYWFOIKikvBu2bKFxx57jKSkpPAU5Uqp8My9fr+f1q1bM2iQ/EMXQgghxInFHVxGbHABTv0TUDYW93TQAVBOipz7T6aOhvJZhbNIdaUe0gy4trYptorJDxaQ7ErCZbjYVrydH/N/CieyoY9CbmwynERnDf6zcykvbluCXwcizrWw41N4nV5+yPuJ13f+J5ywehzxeB0egtrCqRz0TD6NpnGN8ZQmq39MWG9qcv1+Y25fo91futfKyIzCQhxZUUl4DcMgMTGRuLi48MzMWmssy8Lv91NQUEBxcXE0QhNCCCGEOGoMvRtnaRW30DEZ22gABNEqjgJzYrWs4lY1q3BQW/RK6YHDcJAXyGN9wYZQomoVhrsNn1frHOrH1mNtzjc8s3Uh+cECiqxCbEIFkPtb381Jnmb8nL+eJ7c8C4DbcIcSU9NDiVUCzho0iW9Ev1rn4nF4iC9NZj2mhxgztJbroHoDGFL/siqXxumY2J6OtD8KT+vglM0oXF3HRwpxLItKwtukSRNmzJgRsc3v94eXphFCCCGEOF4pnU1ccCFOayVO/TMQquKa5jZsGuBzXIjPcWGUo4xka5ssfzZuw80L25ZUOqvw3F+fwG246JFyGluLf+PeDQ+F2xWKeDOerkldqB9bD6/DQ7P4JuXVVYcHjxlPmju0FGHPlNPoktgJjyMep+GsEE+7hLa0S2hbZbwOI6rT1AghqpGo/TSwbRvDMNi0aRMvvPACb7/9Nueccw79+/fnk08+YcqUKdEKTQghhBDisCmr4mqVit/sDShig88SMNpXuyqu1hqlFMVWMW/tWsb24h1sK9nO9pKd+G0/VzUYSpY/q8rj65eu89osvin3t7473J34j2u5nuRpvt9xrrFmLLFm7OG7MSHECSsqCa/WGsMw2Lx5M/fccw8NGjTgkksuISMjg+TkZJYvX07jxo0ZOHBgNMITQgghhDgkDmstbnt5RBW3xOyH3+yNVslkxawGFR+1+LTWrCtYz7ayhLZ4B9tLdtA1qQvXNLwCh3Lwyo7XSXWlUC+mLm29bagXW5c23lYsy3iPzEqS3jRXKo1KZyKOM+M4ydPsaN+WEEJUELWEVynFmjVrcDgc/P3vf+eFF15gy5YttGjRggsvvJCVK1dKwiuEEEKIY4Khd+Owfy6t4IIn+CAO+1sCRicKzEmlVdzymXmPRrJraZtMX2ZEQpvkTGJw/YEopXhw42PkBHJwKSd1Y+tyUnwzmsY1AcBpOHmh87O4jIrDzYbWHySzCgshjhlRHeBgWVb460AggNNZPkZDxvMKIYQQotrSQZz2N7jsleEqrsZJdsz/0MpDvnMWtkpDK+8RD6XEKmFHyU62l+ygyCrm3JpnAXDbz39nfcGG8H41HAl0SuwY/n7aSZNIdNYg1ZUS0d24TGXJLsiswkKIY0tUEt6yGfPatm3L+++/z7///W8KCgpwu938+uuvrF69mv79+0cjNCGEEEKIShk6A5sEULHEBp/HE7wfjRlRxdWEKreW0fSwXltrTU4gl12+jPAarku2v8pHmSsixtR6HR7OSTsTpRT9ap3LWWl9qBdTj3qxdfE6PBHnbOFp/pfjKZtVWAghqruoJrzt2rVjxIgR3HXXXWzfvh2lFJ988gk33XQTl1xySTRCE0IIIYQI0YFwFddlrcSh15Hrmo3fPA+feS6WUY+A0f2wVnEtbaFQGMrg29zvWZn9Wbg7cqFVCMALnZ8l1owlwZFAa29L6sX0oV5sPerH1KVOTO3w71mnp/Q4bHEJIcSxKqpdmtetW0eNGjV477332LlzJz6fj/r16+NwHP9TyZeUlDBlyhSys7OJj4/n/vvvJzk5OWKf1157jcWLF2NZFmeeeSY33XRTlKIVQgghThA6CMqBoXeTVHIeBgURVdygCi2FYxv18FPvkC6V7d/D93k/sq14O9tLdrC9eAe7fLt4pO391I+tx46SnXyT+y31Yupyekp36sXUpV5sXRwq9HvSebXO4bxa5xzyLQshxPEsKpmlZVmYpsk777zDrl27uP/++6lTp040QomaxYsX06JFC8aMGcPSpUuZN28et912W7j9t99+Y/HixSxatAiXy8Xjjz9eYZyzEEIIIQ7MHXyL+OAjGDt3kqzqUOiYiM9xQajxD1XcoNGSfNcD2KRR4riMgNHhL1dxtdZkB/aEK7RlnwfVG0Ar78lsKtzM45vnYSqT2u5a1IutS9ekzsQYMQD0rXm2JLRCCHGIotqluUmTJvzyyy98+eWXtG7dGgCn04lhGMd9lferr75i+PDhAPTq1Yt58+ZFtK9atYq2bdsydepUMjMzufHGGytNdj0eNw6HeVRiFtFlmgaJiXHRDkOIKsk7KqojVfQ6ZvHtKIoBMPUOvIHbiYtzoYLfYRQtQel8NA60qwvOmG4kxpe9x3dxMH9mDtgBthft5LfC7fxeuI12Sa1JT2rDL3kbufHLSeH94h1xNIirhzMu9G+lh6cLz9X8B3Vja+Mwju/fe8TBkZ+joro7Ft/RqP50DQaDfP7556xcuRKXy4Xb7cbhcJCVlcXNN9/MtddeG83wDptXXnmFhQsXRmxLSUnB6w39tTg+Pp78/PyI9r1797JmzRoWL16Mz+djyJAhdOjQgYSEhIj9Cgp8RzZ4UW0kJsaRk1MU7TCEqJK8o6I6Si65L5zsllEUo/Luo8QciGH0xW/2Kq3ieiAAVPEeFwQL2F68A5fppklcI4qsIqb8cCsZvt3Y2OH9BtcbSEPVhAQrmRGNrqF+bF3qxdQjyZkY/qN/2b+VBJIpCPgBf2WXFCcY+Tkqqrvq+o6mpVXdCycqCa9hhKa+7927N61atcLhcGBZFpZlobWmuLiYRo0aRSO0I2LgwIEV1hQePXo0hYWhyScKCwsrJLKJiYl07doVj8eDx+OhadOmbNmyhfT09KMWtxBCCHEsc9jfY+gdlbYZeidFzlEVttvaptgqJt4Rmm35ma0L2VK0lW3F28kN5gHQK6UH45uNJtaIpYXnJHqknEa9mLrUj61H3Zg6xJqhLskxZox0SRZCiCiLaoU3LS2NtLS0aIYQNZ06dWLFihWkp6ezcuVKOnfuXKH9xRdfxOfzYVkWmzZtomHDhlGKVgghhKjmtMahf8ZlrcBv9iZotA51VdYKpXSF3Yvs0ESRa3O+YWPhpvKJo0p2clJ8M2a2ugOAX4u2YGmbLkmdQ0ltTF0axjUAQkO0xjWrmDQLIYSoPmTASJQMHjyYqVOnMnjwYJxOJw8//DAADzzwAH379iU9PZ0BAwYwePBgtNaMGjWKxMTEKEcthBBCVCM6gMtegctajstagcnu0GYVR9BoTcA4lcd2tuHG2j8Sa5QnvcW24qlddRjWDJZlvMfXud9S051GvZi6tPW2oVl8+Rq6d7e686jflhBCiMNHaa0r/tnzGJKdDS1ahD6fiDIz8w+8kzguVNcxE0KUkXdUHA2GvRVDZxI0u4AOkFJyKgABowc+82/4zV4U2R5iDDdKKS75YjBn1cjmhto7qOkMsDvg5MlddfkoN5V/d32Rvf4c4hxxuA1XlO9MCPk5Kqq/6vqOVrsxvPsqy7eVUuExvMf7DM1CCCGEOEjaj9P+KlTFtZfj0FsIqubsNZeCcpLjXoxP12dD0e98l/c93+XO5ZfCjTzW7kHqxtShhiOBD3Phw9yUiNOmuULfJ7mk95QQQhzPjGgH8Prrr7N+/Xq01jz00EMMHjyY5cuXRzssIYQQQkSJ0uXdtryB20j0X02s9QK2qk+B81ZynfMI2EEAfii0uerr0dz68995eftrBHSQ/6vdH5cKVWyvaXhFheqt23AxtP6go3dDQgghoiYqpVTbtjEMg5deeomnnnqKefPmsWDBAr799lvat2/PM888Q1xcHF27do1GeEIIIYQ4mrSNQ/9QOhZ3OU79I9nuD7GNBhSbg/GZ55IRPJlv8zfzXe73fJd3P/1r9+OiOv2pH1OPXqk9SE9oS9uENngdnohT90rtCcAL25aQ5c8m1ZXC0PqDwtuFEEIc36KS8JZ1Y16+fDnjxo3j5JNPZvr06fTr148RI0Zw5ZVX8vvvv0vCK4QQQhznHNbX1PDfhEE2GoOg0Z5CcwI2bgB8Rntu/vEWfi16GoAEh5d2CW1pFBuaKdnr9HJD4+v2e41eqT3pldqz2o49E0IIceREdbBsIBDAsizWrVuHUoqWLVuGt8fGxkYzNCGEEEIcTlpj6s24rBW47OX4zHMpcQzFMhrhN0+jWJ3OzyV1+Sr3N77L+wGn8RR3nXwbpjJol9CW01N60D6hHY3iGmKoqI/IEkIIcYyISsKrlAKgT58+vP/++8yfP58uXbrQvHlzHn74YbTWNG/ePBqhCSGEEOJw0pr4wL247f9i6t8BCKoWaB2q4GqVzILdp/GfXW9SYpegUDSLb0q6p234FFc3HBaV0IUQQhz7opLwGkboL7PDhg2jdu3a/PzzzwwZMoSYmBhM0+SWW26hRYsW0QhNCCGEEIfA0LtwWSsw9C6KnONAKRx6E0HVjEwuZ01hCv/L2cn3eR/zaNtz8Tq91HSn0Tu1J+0T2tE2oTWeP4zDFUIIIf6qqK/DW1BQgMcT+h/bDz/8gG3btGzZErfbfVDHyzq8sg7viULGnonqTt7RE5dpr8dtLcNtLceh1wEQVI3Z614KysFP+T/zxK/PsK1kOwAJjgTSE9owrMFgarrTjlqc8o6K6k7e0cPHWvopes4S2JUFtVNRYwZhni+T1f1V5c8zG2qnVLvnWW3X4V23bh0jR45k7ty5ZGVlceedd7Jr1y6uuuoqxowZE06EhRBCCFF9KJ2Dy/oEv/k3tPLislYSF1yAX3XkN+sqVuXXYPneDPrW/B+9U3uS6Egk1Z3CGWl/o32NdjSKbSDjcIXYR1kykVVNk4ljjbX0U/SMBVDiD23YmYWesQAL5Ln+Bcf684xKwmtZFqZpMnv2bC655BLatGnDgAEDGDZsGEOHDmXIkCFs3LiRDh06RCM8IYQQQuxLa0z9Cy5rBW57OQ77axQ2uepx/Oa55BkXMev3XazJ20yJ/T1G6Thcp+EEoG5sHe5oOT3KNyFE9XSsJxN/hbZtAJRhoC0bikvAtsGyyz9741GxbnSJP1Sl3bfNtqF+TVSCB51bABt+C52ntE0/uKj8eZYp8aMfeB5ba9CgerRHJSegt+xAf/Uz2Bq0Dn22bVS/HqhEL/qnzegvfixtt0vbNWpIX5Q3DvvLn9Crvw9vL9vHGDUQFevG/ngN+vPvIts1GLcPR5kG9n9WoD//vvza2gbTxLxvDAD2omXo1T+Utpde3xOL+fAEAKw5S0Lx7xt7WhLm7Emh9hkL0N9uCB1buo9qXAfz8Smh9rEPotdtKb9/rVFtmmHOCbUHh9wGP20Otf3xec5ZAsfAOxrVCu+WLVsYM2YM+fn5ZGRk0LFjR2JjYyksLMQu/YcghBBCiCjQxRjkY6uamPpXkn0XAlBCCzb4z2NlbhzZ9m9c3xicZhpF2lU6DjedtgmtZBzucU66i1ZN2zYELbBsVGzp5Gx786DIB4EgBIOhdoeJat4g9BwrS84eWhROJuyPvoScvNKEToc+107BOPOUUPvi9yCvMHTt0qRPNauPUXq89eiLUFQMVmnSZFmoji0xLjkj1H7z4+APlCZUoXOov3XGGHQO2h/AGnF3hYTTuLgPxpC+6NwCrCG3VkhYjeEXYwzti96eiXXJ5MjjAWP6NajLz4GNv2NdNq3CczTuHom6oBf8tBnrmrsqtj88AXVWV/QPG7FH3X9w/3Fy8rFvnQeAuWgGJCegv16PPePpCruaXdtAojfU/uiLFdsv7AXeOPj2F/Sz/wGlwDDAUKGvh18EsW5YvxX9/v9C25QqbTdCz8I00Nt2o7/fGHm8yxm+js4rRGfnhI4xQscrp7nPgzBQTkf5eQ0F3vjy9rQkVKM65XEZCuqUDyVRbZpBUkJ5u1KohrXLT3/mKdg/bqr8ee46NsaURnWW5gYNGvDTTz/x9ttv07JlSxo0aMDGjRtxu914vVX3wxZCCCHE4WfY23DZK3BZy3HZq/GZfcl3PYClmvBx4RBeztjND4V7gJ0kOBI4LblJ+NjbWk6NXuDiqDqSFUmtdSgZDJQmhXExKIeJzi+C7NzyZLFsn9ZNUG4X+rdd6E3bStuC4ePV+T1D7V/9jP5mPQQsdDAIgdA5jAlDUA4T++1P0J99W37uoAUQrnLZT/wbe/lXkdePi8Hx8n2hZzJ9LvqjL8KJLgB1U3G8Myd0/LQ56P/9EHmzzerjeO3B0B8NKrMnL/ylPe8V2Ph7RLM6tR2UJbzPvw07Ss+jFJgGnNk1nDDrj76AgqLShMoAhwmJ5b9r61+3hyp4hhE61jBQZf99lUK5XRFtmAYklCZVDhOVflJkm2FA49KkyROLGnRO5LlNhWrTNNSeloQxcWiF41W7k0Ltjeti3Dv6D9dXoUSNUMJmPHUryjTANME0sCY8DFm5FZ9pWhLmM7eHzlEzKXT8uadhdm8fTibDSaMnLtR+2dmYF/eJTGbLvgaM4RdhDL+o8v+GgHHjAIwbB1TZbo4aCKMGVt1+00C46QDt+2GOvHS/7cYNl+y//br/w37lQ9hZyXtaO2W/x1YXUZ2ledKkSUyaNImtW7fy1FNP4fP5uPbaaxk2bBhNmjQ5wFmEEEIIcUi0Dv3yBiT4bsRtfwxAka7DtyWd+CiniMGNgzgNBz+UtMHliOHqBv1Ir9GWhjIO97iiA0HI3BtKYn1+KPahfX5Uk3qo2ino7Bz0+6vB50cveL3yiuSMBVgffRmRcBpjLkelN8de/QP2g89HJrNBC3P2JFS75thLP8W+44lwolnGfPk+aNkIvfRT7Hv/WSFu8+3Z0KAW+oPV2I+/VLG9dydwu7A//w694I3QRkOBwxFK+sYMCn3eloH+bkP5docJ7vIqG/GxqNTE0HanGdrPExtuVqe1CyVQDkeo+uZwlCeEgLrifFS/nqXHh66hytprp1aeTKQlld/HE9NDFUFjn6Rwnyqg+Z9Hw4luWWFpX463Z1c8/77tr1RdIVVOB+ZTt1bdHh+Lee/oqttreDAnDq26PTkBdVX//bf361F1e6IX1a1t5LaJwyL/KAMQ40JNGBKqdu67b1wMxMVUfX6nI/Tf7ASmxgyq/HmOGRS9oP6EqM/SDGDbNpZlYVkWxcXFJCYmVvqPtTIyS7PM0nyikJkbRXUn7+ixQek9uKyVuOzlOO0f2eN+F5RJbsFjfJ+3hjez/GwqMUrH4TZjUvOxR3Um5SOhus8u+kfhKmexL9R90RMX2vb9JrTPDyW+0C+eJT5Uo7qo9OZonx97wetQXNru80OJH3VmV4zzuqOzc7FumAW+QOi8pe3GmEEYV56P/nU71kWTK8Ri3D4c49Iz0T9txhpcddIT1qz+PkmdA3PCEFSHFujvN2I/82Z5suhwgNPEuLI/qnEd9Lot2B+sDiWCZQmnwxEaR5lSIzTO8sfN4e1l11AdW4bGeWblhBJ2hyOcUOI0ITUJZRqhhN62Q+c0q9cfaipUzCGUTNwxolq/p9Xdsfbvvrqr7s9zf7M0Rz3h/fnnn3nvvff4/vvvmTlzJp9//jlnnXUWNWrUOKjjJeGVhPdEIcmEqO7kHa3enNZnxAcew6G/Q6EpthP4sbg+Ra5ptEroxs/565j36wLSE9qSXqMtbb2tiXfEH/jE1dzhTCa0bZcmmqVV0BJfqOtlacXIXv0D7MmN3KdmMkZpdcp65IVQUlYcSli1z4/q0AJz3GAAghdMgKyc0Hnt0K9n6qK/Yd51A1prrM7DyrvLllKDz8WcdjXa58c69WqIcUOMK/zZGHhWaJxlfhH27fNDYwrdrvA+xukdUJ1boQuK0B+s3ud4V6gba6PaqJTEUMJYUARuF9YlUyqvSNZJxfHu/7N3n4FRVvnbx7/3zGTSO4FQQk8ERDpSpCgiKiyKCgooLOq6rgI2ZC1redy1LCjWlbUjq2JB/FNcFQtIB10QEOkQagKkkp5MuZ8XI3GzoAICZ5Jcnzcx95m555rJMfrLaS+c0GcqAcFeTIgcEaz/rQ/aY4mWL1/OvffeywUXXMA333xDeXk57733HuvWreMvf/nLcZ/FKyIiIj+x7CJC/Ctw+76mzHUNXkc7yv1eiisOsawglfm5DraVhRMbEsfvUypoDbSKOosX2k0xHf2UscsqIL8Q++l3jj399vE38G1Kh1A3zh+n5fn+8QGs3YJd7qkcRbXqJeB87cFA+/WPwNqtVe/VtgWudx4FwP/UW7B1T5Vmq2sb+LHgtddtCxTEYW4IdWOFubH+a9qs1a8LeP0Q/mOxGRYKqSmBNsvC8cKfwR0SaAv/sT32xz9KuENwrnnnZ2fIWdERlbu2HrM9KgLrigt+vj3EFdjYhuo/vTEYOQf1gkG9graYEKnOjBS8tm1jWYVljgQAACAASURBVBZPPPEEjz76KH369GHBggWEh4fzzjvvMGDAAMaOHUu9evVMxBMREal+7FLCfe/j9i0ixP8NFl7K/aGsK3Bzdp124OrN+J3nkBLeiPPqnsMtMYF1uEcKpONdSmSSfSAHe3cm5BVCfiHkF2AfLsbx59FYloX/pQ/x/9/Xgbb/LXL/V1Ep9odfQf06gXWcAGXl2F4fVmQ4JMYGCtP6dSqf4hh6IZzfueooauJPM9KcT94eWBcd+tMIK6HuynbX9P/3i5Gcd/78OkcAx3ntf7btTP78nIN64QONSIpItWB0hDcvL69yc6ojZ/O63W4qKipwOp2/8mwREZFazK4gxP8fLMqocPYDnIRWPEOON5TFh5NYUhDFD8XRdEuI5+w64LAc/LP9c8Y3mrLLKyC/KDD6mh8oXK3z2mNFReBfvh573mLI+6mNvEKcnzyLlRiHf9YC7Fc+qnrDmEgYdzVEhkP9JKwfjxKx4qIhLgr/C+8HCuT/dYzpt867R/1idsfgPr/YbjVtcDwfQY1wZERSRCTYGT2WqEePHsyYMYM777wTn8+HZVl8+eWXNG3alLCwn98tTUREpKYK9c4j0vs0DjsTv1WfYtddlLsGA+CwD+H2LcLtW4TLvxQnpRzw1MURfQGW5WbKwTGsLdxHu5i2XNLgHCZEtyHSFVF571Nd7NoVnkBRGhWBFRGGnZmNveS7qgVrfiGOu67DSk3BP28x/gf+edR9nO8/Aa2aQnZe4DzKuGisOrHQslHg6JQf/wjuuKwPdG8buBYXDbFRgQ2Ojry/y/vC5X2rZgwL1fRbEZFazOimVTk5OVx//fX4fD4yMjJo1aoVu3bt4sUXX6RTp07HeQ9tWiW1g9b1SLBTH/3tQr3ziKi4H5f1U3Hms0Modj9BuWswjpKbSLQWk+0JY2lBFCsKY9hRnsJjbSaR4I7H6/ficpz837LtCg/sPvBfo6sFgRHY3h2xWjfD3rYH38MvB0ZMDxdBcSkAjil34uh/Lv7l6/Hf8kTgZlHhPxal0TjvG4N1TkvsbXuxF63+sWCN+nEUNhpS6gXWpZ4m2hBIqgv9HpVgF6x9NGg3rUpMTGTu3LmsWrWK3bt3ExMTQ58+fYiIiPj1J4uIiNQwrvLHcTmqrj11Wh6c5X8F12C+L7+UGfvyiXB3oV3sOQxrcg6NwxtVzpw6UuzaHm+gID1SuCbGYjVriF1cin/qzJ+mFP+4FtYxehCO4QMgMxvf0D8flcsRF43VuhmEhQaK1KYNID66smC1WjUBwOrUCudX/wyMvB7j3EorNQXrx02YziRtCCQiUnsZKXg3btyIw+EgJCQEh8NB48aNad68OU6nk7KyMrxeLzExMSaiiYiInBGWXYTLvxmX/QPlVi/8zhaEW7nHfGy4VUAJkBZ7GQ+tbUhIzpGC9Wv8hwux2qXiuPoibK8P3/l/hMKqRZ113UCcE0eBw4H90cLAqGp8NFZsFDRJhuTEwAPrJeJ46o5AwRr/X9OG3YGdhK2Uejin3vvz7+nH42xERESChZGCd/To0Xg8Hmzbxu/3V349wrbtyqJYRESk2rP9YDkCa3DL/4bDv4EIMrGswKqiFYW/o0PdKWR5Qqjr9hz19EOeEJxAiMOF95E38OcVBBrCQyE+GpLiAbBcTqyr+mGFhwWuHxmBTQmcemCFh+JaMe1nY1phbqyLup3a9y4iImKQkYJ3xYoVlUWuz+cLHKbu8+H3+yuvqdgVEZHqyLKzCPFvxOn/AZ93DSH+Tezz9SA+5in8dgTF5YvYUhrG1tJkDuTH4kmP5uwtNtwHb29vwC2t9hDu+Gl7jVK/xYxtDRjVJfC9c9pDEBEGsdGBEdX/8WtH24iIiNQmRgrekJCQX3+QiIhIMLNtHHYGLnsTftuH13Ux2DbRpf0JtcoA2FMeyrbSCDZk7WBkO8ARxfJplxG1Ygd99kFMeBxWamM4pyUAjd5rwtNj4MZGGdQN8XDIE8Lr+xqQ+n4T+LHgtZo1NPN+RUREqiGjm1aJiIhUC7YNP24M5Sx/BbxfEsE2whyBtbI7SqOIir4QR4iLeVu7sD03B2udmwY7nDTdC0NyQrA/K8GKiqBXvzHYPcsDGzjFV92vos/5v4cXX+KW3yWSkwiJOTDiYyd9Bv3+jL9lERGRmkAFr4iIyH+zvTjtdFz+H/B414BvHU47i6KwBYS6wsg4PB+Xcydby8LZeziJkh3huNeFMfTqvbjTmtE764/0+mQZpDXGGpISGMFtVA/LGViqY7VrifUzL+0c1Is+QO/ndYSOiIjIqaCCV0REai+7Ape9DYdvAyWOwbicEZSV/IUUx2wAyvwW20oj2FoWQcqhJTTrdBFlW28ma+o0Ug9H0DW5CVZqY6w2jbGSAjsdOy7qBr9h46cjR+iIiIjIb6eCV0REahXbux5/+Su47U3EOjJwWoFTAtbvO0yr1D9y6NA5fJKxlorN4UR/H0aT/U46hjQg8k+BgrZx5740fqYL1I2vPP9WREREgpMKXhERqXEsuxCXfyMe72o8ntWEsY1d/htJifk9BWU7qWMvZGtpOOmFSRTsisC/MYL2zgpIhZSG19BwjhMrrTFWn8bQtD5WyE//ubTCQwPHAYmIiEjQU8ErIiLVmmXn4vT9QIkdhTukI/i2U6diUGX7IX8IG0sj2LdmISmX/p6oiN+xeOJnNCuJp0/95jhSG2P1bAypjQP3c4fgvGOEqbcjIiIip5AKXhERqV5sP+Wlj4N3HdFWOrGuQgB+yGzCWc0/B0dT5m1sQs4uF671ESTn1qNpVDNSO3UAwOlw0f2pf2o6soiISC2ggldERIKPbeOw9+H1rqG0YhVO3wbyS0NJTp4JloPQ8g8pxmZ1UTjZGQ2p2BZB7NZk+CtguehmPQ+tQmBgo8AU5P+hYldERKR2UMErIiJm2T4c/l0UezYTHhaYilyeewmNInYB4HVAekU42/JiSIoqxhkVyc7FdxP6w0FaN0zDkdoE65LGcG1s5S2tTq1MvBMREREJMip4RUTkjCspm09FySzC/VupE3aIMKePCL+DfbtSiWuaxq70s/gm14+9O56YvJY0jm7Fec1SsZoG/rPV/PLr4HKz70FERESCnwpeERH5TXasnUDzJp/jLKnALnezc/cAWnSYAnY5Pu96CkqXYpf+hyhnOrnFU0hu0oPDGR/Ssu5StpeEs2lXAsW7o7AONKRdjwoA0lr9nTQbrAERht+diIiIVGcqeEVE5KTtWDuBDi3/TZjTBqBuWAUxLf/Nlm07adtwI04LkkOgwHKyoyiCwk3LSG7Sg6jwiWz8qAcNGp9DclpTOLtOlXW1VpQKXREREfntVPCKiMhJa9l0fmWxe0SY06ZR0jYW/NAA76F6hBa3IjmiCw2at8G6oBEA0fXTiB6dZiKyiIiI1CIqeEVE5MTZHrL23UjrRM8xm+PdHjp0XXiGQ4mIiIhUpYLXoLKyMiZOnEhOTg6RkZFMmjSJhISEyvbFixfz6quvAmDbNqtXr+bjjz+mRYsWpiKLSC3n9eXgciaCFUII2yjzOwh3+o96XHa5G0uzkkVERMQwh+kAtdm7775LWloaM2bMYMiQIUydOrVKe58+fXjrrbd46623OP/887nppptU7IqIEaXl68jZexlxpb3I3PY5AGFhs1i35RLKfFXPtC3zWezcPcBETBEREZEqNMJr0OrVq/nDH/4ABIrb/y14jzhw4ABz5sxh1qxZR7VFRYXicjlPa04JDk6ng7g4DZnJmXW4cBl5e++nRdxOyhMcrNpej4YuO9AX41qSnPoy65eNI6XBp9QJrSC73M3ejEvpfP4/TEcXOYp+j0qwUx+VYFcd+6gK3jNk5syZTJ8+vcq1xMREoqOjAYiMjKSwsPCYz502bRpjxozB7XYf1VZUVH7qw0pQiouLID+/xHQMqUUqPHtI9gwnLMbBwo2NiC+4gTZ9hmO5nFX6YuOzJwOT8cVFYOWX0Dge9VUJSvo9KsFOfVSCXbD20aSk6J9tU8F7hgwbNoxhw4ZVuTZu3DiKi4sBKC4uJiYm5qjn+f1+vv76a+68884zklNEajHbprBwDjkHZtK45Vu4QxrzzerfEVnem3N6X4bl0CoYERERqV5U8BrUqVMnFi1aRLt27Vi8eDGdO3c+6jFbt26lWbNmhIWFGUgoIrWCbXP48AxCy1+geUwe0fVCyPz+a+q370fL7lNMpxMRERE5afpzvUEjRoxg27ZtjBgxgvfff59x48YBMHnyZNavXw9Aeno6KSkpJmOKSA1WXLAMT3ZXWob+FVdoMfO/aU3e9pep376f6WgiIiIiv5ll27ZtOsRvkZMDaWmBr7VRVtax1/1KzROsayakGrI9lJTtICK8FRWleyktuIztP6TSMuk+Ys/peNK3VR+VYKc+KsFOfVSCXbD2Ua3hFRERbH8ZOYcmkxQ6i4oKJ27HctzhKTg9S+jcL8p0PBEREZFTTlOaRURqOn8RWZn34i7sSuvYd8iqcJL+XUf8ZaUAOGNU7IqIiEjNpIJXRKSGO7hnEm3i/o89RaF8vrA/Mb6P6XjJ67hj401HExERETmtNKVZRKSG8fsOkpP5AHl54aSd8zx1Gt3LokU2ae3upP7ARNPxRERERM4YFbwiIjWE17eH/Mz7aR63mqQEPwvykvF7fThdkbS58FHT8URERETOOBW8IiI1QNaeCaQm/pukBJuV++rg2zaQc/rcgcPlNB1NRERExBgVvCIi1VR5+TrKyyOIiUnFX9GEZbuScO2+itTz/4QjLcx0PBERERHjtGnVSfr++++pqKgwHUNEaqGyslXk77+YRv6r2Zd+BwD1Wt5Gm7O+5qyBd+CIULErIiIiAip4T8qhQ4cYMWIEn332mekoIlKLlJR8RWFGP1Ls0STH7uWLjY2IyLm2st3S9GURERGRKlTwnoTZs2czZMgQZs6caTqKiNQipVl/Iz7qIPPXN2X76kdp3/ELmvYbaTqWiIiISNBSwXsS5syZw1133YXH42HPnj2m44hITWT7Kcx/h9KDPdi9YQYATtck9n3/DB3P/YxGfa/EcuhXuIiIiMgv0f8tnaCVK1fSvHlzEhISuOKKK/jwww9NRxKRmsT2cTj3Zbw559I89K+43EXkZ34LQFzDbiSfNwDLsgyHFBEREakeVPCeoFmzZjF06FAABg0axGeffYbf7zecSkRqBNuLL7s7LcOfptzy8OmK9hTvnU77i54xnUxERESkWlLBewIKCgpYu3Ytffr0ASAqKor27duzaNEiw8lEpLqy/aUcOvACPq8XLBe797Xi06VdsbPepUu/D4hr18l0RBEREZFqy7Jt2zYd4rfIyYG0tMDX2igrq9B0BDlD4uIiyM8vMR1DThV/ITkHH6d+xDxi3R4WrfsDbbpPxLbtajtlWX1Ugp36qAQ79VEJdsHaR5OSon+2zXUGc4iI1Hq2v5DcA3+hUdRXtIrzsjY3mgPr+tC2fWC35epa7IqIiIgEIxW8IiJngu0Dy4nftqkf+RWb8iPJ/b43bbveS8OBSabTiYiIiNRIKnhP0IEDBzh8+DApKSlERESYjiMiQc7v20N+5v2EuzdiRXxFWFQ8+zKm0ii5A00HxZqOJyIiIlKjqeA9Tvv27WP8+PFkZ2cTGhpKdnY23bt355577qFZs2am44lIkPF6tlJw8H6ax28gMcFm+b46JBxaR1jb86nbuq/peCIiIiK1ggre4/TUU09xzTXXMHz4cAC8Xi+zZs3ipptu4rXXXqNp06ZmA4pI0CjOn0+K+zYS4i2W7k7CsfsKWvW9FUdEmOloIiIiIrWKCt7jtGvXLp599tnK710uF9dccw0NGzbkxRdf5MknnzSYTkRMKy9bwaGMRaQ0v5eImAtZtqYVrpyBnH3BDVhtQkzHExEREamVdA7vcfq5nVN79erFjh07znAaEQkWpSVfUpx5AY3sMdSNn0Hxof1YDhetu8wh9eKbsdwqdkVERERMUcF7nLKyspg5cybr1q2juLi4SpuOERGpfYoLF1J6oBeNrbHERB7i03VNObjuYSLq1DcdTURERER+pCnNx2n8+PFs3ryZOXPmsG3bNiIjI0lNTSU1NZXs7GzT8UTkTLD9+O0SHI4oyvMPEB+TzydrWtKQ8XTuebH++CUiIiISZFTwHqdrrrmmyvcHDhxgy5YtbNmyha5duxpKJSJnhO2lMP91InyvsjMnntSzviAhZQQF29rTpWdrFboiIiIiQUoF70nauHEj/fr1o29fHS8iUmPZFRzO+QdxjrdoHl5CekkY2XsTadHMg8MdQkxqG9MJRUREROQXaA3vSXrmmWdMRxCR0yx79w20jHyZXB/MW9oVf9Y79Oj/Hg5tRCUiIiJSLajgFRE5wl9I3oF72bv1XwCERd3Gx0t64S78kO4XvU1Mq7aGA4qIiIjIidCUZhGpVUK984j0Po3DzsRv1afYdRdljp7kH3yEhpFfkRTr5dOMNaQwmqg659JtwLmmI4uIiIjISVLBKyK1Rqh3HhFl9+J0egFw2hlElk8kDJu6cbAqK5ac73vRvuu9hpOKiIiIyKmggldEag1n4V9xhXmrXnPYeHwO5n91Je3Om0jzQXGG0omIiIjIqaaC9yTVqVPHdAQROUHhoQXHvO52+On0u8fOcBoREREROd20adVJmjZtmukIInKCDnmOvbvyz10XERERkepNBa+I1BpfZCRh21WvlfotZuxsZCaQiIiIiJxWmtIsIrWCz1fAhXVzKPA5KPM7SQrxcMgTwuv7GpCWc7XpeCIiIiJyGqjgFZFaISt9Kq0blPP2kq7MsWxyYv0kHnYw0nEh5/e/wXQ8ERERETkNVPCegNLSUnbv3k2rVq0qr2VkZOB0OqlXr57BZCLya5Jb3ssPa1tw6YVXMsjlNB1HRERERM4AreE9AS6Xi3HjxlFSUlJ57YEHHuDQoUMGU4nILykt/p59218BoEGHYThU7IqIiIjUGip4T0BISAgXXXQRn376KRAY3c3NzeWcc84xnExEjsX2l0PhjTSv9yx5ezaYjiMiIiIiZ5gK3hM0dOhQPvroIwBmz57NlVdeeVL3KSsrY/z48YwcOZKbbrqJ3Nzcox7zxBNPMHToUK6++mpWr179m3KL1EaHdt9E49jDrFrdg/jGbU3HEREREZEzTAXvCWrRogW2bZOens4nn3zC5ZdfflL3effdd0lLS2PGjBkMGTKEqVOnVmnfvHkz3333HTNnzmTy5Mk89thjpyK+SK2Rd+Bt2iavYumuerTrMfXXnyAiIiIiNY42rToJQ4cO5YEHHiAtLY3Y2NiTusfq1av5wx/+AECfPn2OKnjr1q1LWFgYFRUVFBUV4XId+0cVFRWKS2sSawWn00FcXITpGNVCeVkGIeF/Z3dJGC0SXyWxXrzpSLWC+qgEO/VRCXbqoxLsqmMfVcF7Ei699FIee+wxxo4de1yPnzlzJtOnT69yLTExkejoaAAiIyMpLCys0u5yuXA4HFx66aUUFhbyt7/97Zj3LioqP4l3INVRXFwE+fklv/5AweeJYPfOdniLOpPW+yx9bmeI+qgEO/VRCXbqoxLsgrWPJiVF/2ybCt6TEB4efkJraocNG8awYcOqXBs3bhzFxcUAFBcXExMTU6V99uzZ1KlTh9dff53i4mJGjhxJhw4dSE5O/u1vQKQG8/qKcYVE0rzjDNNRRERERMQwreE1pFOnTixatAiAxYsX07lz5yrtMTExRERE4HQ6iYyMxO12VzkOSUSOVpD7BWFF3di14UXTUUREREQkCGiE15ARI0Zwzz33MGLECEJCQpgyZQoAkydP5pJLLmHw4MGsWbOG4cOH4/P5GDx4MM2bNzecWiR4+XyHibLvxmtDhN3adBwRERERCQKWbdu26RC/RU4OpKUFvtZGWVmFv/4gqRGCdc1EsMjeNYi0uttZvOoK2l7wd9NxaiX1UQl26qMS7NRHJdgFax/9pTW8mtIsItVe1u6/07redhZtbsbZfR83HUdEREREgoQKXhGp9irKvmZTfhQtGr2G5dCvNREREREJ0BpeEan26rf8N8WZ24io38h0FBEREREJIhoKEZFqa//2CRzc8ykOp5PoRq1MxxERERGRIKOCV0SqpZyM6XRo+DF5hU+ajiIiIiIiQUoFr4hUO+Vle0iOfJLdxWHUj/yH6TgiIiIiEqRU8IpI9WL7Kc2+jnCXl/1bbiC2aRvTiUREREQkSKngFZFqJXPHw6QmHmTJunNIPe9203FEREREJIhpl2YRqVYSk29n8do9tGmvqcwiIiIi8stU8IpIteD15lNeXkRkVCNa95huOo6IiIiIVAOa0iwi1ULe3hGElg+k6FC66SgiIiIiUk2o4BWRoHdo1+O0Sd7J5vSGRCY1NR1HRERERKoJFbwiEtSKC9bQrM5bbMqLokXTN7Asy3QkEREREakmVPCKSNCy/eU4Sm7Ga1uUHbyP8MT6piOJiIiISDWigldEglZZcQalXvj2uz406jjUdBwRERERqWa0S7OIBK3w6GaEuJfStp7TdBQRERERqYY0wisiQaesdDeZOy/kcM73uEJDcYTob3MiIiIicuJU8IpIcLH9lGVfx1n19pOzfanpNCIiIiJSjangFZGgkrHjdlLrHGLp+vY073aL6TgiIiIiUo2p4BWRoJGf9Qlt6n/B6gMJtGn/huk4IiIiIlLNqeAVkeBR/lfyPC4ivU/hiog0nUZEREREqjntBCMiQcPlfoM92xfTpMt5pqOIiIiISA2ggldEjMvOmEtMnQuJqtuGqLptTMcRERERkRpCU5pFxKiiw9/SJOYe9uwYYjqKiIiIiNQwKnhFxBifrxRn2S14bYuIirGm44iIiIhIDaOCV0SMOZg+hsYxhaxeez4N2muEV0REREROLRW8ImJE1p5Xad9wLcvSG9Cmxwum44iIiIhIDaSCV0SM8JfFsiYjkfpxr+BwOU3HEREREZEaSLs0i8iZZdtgWdRLuxrbHoZlWaYTiYiIiEgNpRFeETmj9m8fy55t/SkrzVexKyIiIiKnlfGC1+Px4Pf7TccQkTMg98Bc2jb4CpzFuAg1HUdEREREajgjBa9t25SWlgLw5ptvsmzZMiBQ/Hq9XgDeeOMNVqxYYSKeiJwGnooc4kIeJNcTQpT9LK7wcNORRERERKSGM7KG1+/388knn5Cbm8u7775LWloau3fvpqSkBJfLRXh4ONOnT2fChAkm4onIqWbb5O0fQat6Zaxcey1pPbuZTiQiIiIitYCRgtfpdOLxeNiwYQMej4dDhw6xYsUKysrKgMBI71VXXUXPnj1NxBORU6wofy1N6+xl6aZUWvd40HQcEREREakljO3SPHz4cIYPH87s2bPp1KkTjRs3NhVFRE6zqPiO7Nv5Ii1adtBGVSIiIiJyxhg9lsjn8zFkyBD27t3LokWL8Hg8hISE4HK58Hq9dOjQgdjYWJMRReQ38PlK2bf9cVJa/j8SmvczHUdEREREahljBa9t2zidTj755BMef/xxiouLiYmJwefz4XQ6OXjwIG+//TZdunQxFVFEfqMDO0fTpfF6Vq6Lo0UnrckXERERkTPLWMHr9/txOp3MmDGDkSNHcuutt5qKIiKnwcFdL9Gh0XqW7WxAy/Z3mI4jIiIiIrWQ0SnNEBjpbdeunekYRpSVlTFx4kRycnKIjIxk0qRJJCQkVHnMo48+ypo1a4iMjOTuu++mffv2htKKHL/S4h00in+BXUXhNKzzBg6n03QkEREREamFjJzDC+BwBF56wIABzJ07ly1btlBeXk5ZWRkejwe/328q2hlz5EimGTNmMGTIEKZOnVqlfeHChaSnp/Phhx/y3HPP8cgjjxhKKnICbJvS3NGEuXzk7B1PZL1mphOJiIiISC1ldA2vZVls3ryZzz77jHnz5hEVFYXD4cDlcpGTk8PcuXNJS0szFfG0W716NX/4wx8A6NOnz1EF7/bt2+nduzcOh4OEhAScTidZWVkkJSWZiCtyfCyLouzf8e2+dFr1uNF0GhERERGpxYwVvEdGeP/4xz9y/fXX43A48Hq9eL1e/H4/JSUlpKSkmIp3ys2cOZPp06dXuZaYmEh0dDQAkZGRFBYWVmlv3bo106ZN49prr+XAgQNs376d0tLSKo+JigrF5dJ00drA6XQQFxdhOsYvqvAU4A6JIe6Cv5mOIgZUhz4qtZv6qAQ79VEJdtWxjxpfw9usWTOKiooqd20+MsK7Y8cOnDVo3d+wYcMYNmxYlWvjxo2juLgYoHKX6v/Wq1cvvv/+e0aNGkVqaipnn302cXFxVR5TVFR+eoNL0IiLiyA/v8R0jJ9VUZ6Fo6g/6fs7k9ruDdNxxIBg76Mi6qMS7NRHJdgFax9NSor+2TbjBe/ixYt54oknSE9PP6rtiy++qFGjvP+rU6dOLFq0iHbt2rF48WI6d+5cpT09PZ369evz3nvvkZmZyZ///OejimKRoGDb5GWMpHW9MnaVpJpOIyIiIiICGD6WyOFwMGXKFAYOHEhqaipffPEF1113HdOnT6dBgwbUqVPHVLwzYsSIEdxzzz2MGDGCkJAQpkyZAsDkyZO55JJLOOuss3j66aeZMWMGoaGhPPTQQ4YTixzb/u0P0qHRHhZvOovW3e8zHUdEREREBADLtm3bxAsfKXh79uzJ//3f/1GvXj2uuuoqXnrpJZKSkrj44ouZPn06ycnJv3ifnBxISwt8rY2ysgp//UFSIwTrFJKC7OU0CLuR3YcjiY75And0vOlIYkiw9lGRI9RHJdipj0qwC9Y++ktTmo0dS2RZFgDJyclkZmYCcOjQoco1rYcPH658jIgEr9yM2ZT6HPgKHlWxKyIiIiJBxdiU5iPF7KBBg3jkkUd4+eWX6dWrF6+++ip16tQhMTGRsLAwU/FE5Dg1bTeZgkM3U7d1C9NRRERERESqMDbCe8SNN97ILpPE+wAAIABJREFU8OHDcblc3H///ZSUlLB06VIefPBBYmNjTccTkZ9xIH0q6Rv/CkBkXRW7IiIiIhJ8jO/SPHv2bC666CKio6MJCQnhmWeeMR1JRH5FccEWUhJe5HBFCBUlt+OO0B+nRERERCT4GB/hfeuttyqnNa9cuZLS0lIM7aMlIsfB9vuoKLieMJePnP13qtgVERERkaBlfIR31qxZ7Nixg7lz53LfffcRERHBpZdeypAhQ2jUqJHpeCLyP/ZuvZnOTXJYvL4brbv93nQcEREREZGfZexYomOxbZv58+czefJkMjIy2LRp06/u1KxjiXQsUW0RDNvA5x9YRLOYP7I+M5EGjRbiDA01mkeCSzD0UZFfoj4qwU59VIJdsPbRXzqWyPgIb1FREXl5eSxZsoSvvvqKdevW0bNnT+6//34dSyQSZGKSevGf7y4mse71KnZFREREJOgZLXht2+aOO+5gzZo1nHPOOVxxxRW8+OKLOo5IJNjYNoWHvyc6rh0tujxvOo2IiIiIyHExXvD27NmTp59+mpiYGJNRROQX7N16P60bzmbzpvto1Hq06TgiIiIiIsfF6C7NDoeDG264gaysLF555RWmTJlCUVERS5YsMRlLRP5L/qEltG44m12HI6mbcrnpOCIiIiIix834sUSff/45I0aMYNWqVXzwwQfk5eUxfvx4Pv74Y9PRRGo9r7cYt307HtvCLv477igdQSQiIiIi1YfRgrewsJBnn32Wf/3rX0ydOhWHw0FKSgrPP/88U6dONRlNRIADO6+jSUwx328YSFJaf9NxREREREROiNGCt6Kigry8PFq1akVhYWHlrsxnnXUWeXl5JqOJ1Hq234/PU8aKHSmkdn/SdBwRERERkRNmdNMqp9NJs2bNWLBgAampqZUF77Jly0hNTTUZTaTWsxwOmpz9Kb7ych0RJiIiIiLVktGCNy4ujptvvpmJEyfStm1bKioquO2221i/fj0vvfSSyWgitZbt97F/5yAsayQNW4zWebsiIiIiUm0Z37Sqb9++fPbZZ/Tp04fhw4fTs2dPZs+eTatWrUxHE6mV9my9iY4N0ynKWWg6ioiIiIjIb2JkhNfr9ZKZmYnb7cbhcOByubjmmmtwOp2VUydt29Y0SpEz7NCe9+nQeBnfZdQhtcMrpuOIiIiIiPwmRgre/fv3c+mll5KQkIDX68W27co2y7IoKyujVatWvPfeeybiidRKZaWZ1Il6jJxyNzHhL+Nwh5iOJCIiIiLymxgpeBs0aMCcOXNwOBz4/X4sy8Lj8eDxeADweDyEh4ebiCZSax3YMYGOzctZs+lmmnVuazqOiIiIiMhvZqTgDQkJqbILc25uLlu2bMHhcNClSxcKCgqIj483EU2k1mqU+hprN0ylWee7TEcRERERETkljG9atWjRIq6++mquv/56nn/+eZYvX87gwYM5ePCg6WgitULeweUczvkeV2gETTrfbTqOiIiIiMgpY6TgPbJmd+vWrfzjH//gkUceYdasWZSWltK7d2/69evHU089ZSKaSK3i8RQRyjjc9ii8FeWm44iIiIiInFJGR3gzMzPx+Xycd955VUZ0+/bty44dOwwmE6kdMndeS5OYYvbvuASXW+ftioiIiEjNYrTgjYiIwO12U15ejt/vx+UKLCnOyMggOTnZZDSRGm/f1il0bryZVTsb0+LcJ0zHERERERE55YxsWnXkfN02bdrQvn17Ro8eTcuWLSktLWXq1Kl8+eWX3HPPPSaiidQKhXk/0Dz5DXYXhtOg4b905rWIiIiI1EhGR3gjIyO55ZZbuOyyy9izZw+hoaHs27ePv/71r3Tr1s1kNJEazfI6ST+YwOGs+wiLq286joiIiIjIaWFkhNe2bSzLYsWKFSxfvpwJEyZw7bXXmogiUuvYfj9RSa2ISlpiOoqIiIiIyGlldJfmgwcPsmnTJgAqKioqr4vI6XFw1wwOH+hGbuYK01FERERERE47o2t4W7RoQVFREbfddht9+/YlPDwcl8uF1+ulWbNmtG7d2kQ8kRqptGQ/STF/B8umpDzWdBwRERERkdPO6JTmgwcPkpGRQUVFBa+99hp+vx+Hw0F2djbXXHONCl6RU8W2yT9wHW2Sy1m7ZSxNOrYxnUhERERE5LQzUvA6HIGZ1P3796d///4mIojUKrs23U3XZhks39SW1E63mY4jIiIiInJGGN2lGQKjvVq7K3L6+H1e6iQsZHNODM3a/Mt0HBERERGRM8bICO9/0/mfIqeXw+kiJPxjfIWZuMIiTccRERERETljjI/wisjpk77xQcpKswiNbUBso86m44iIiIiInFFBUfAWFxeTm5tLWVmZpjiLnCJ7N0/m3GYfsHfrraajiIiIiIgYYXxK89dff83rr7/Ot99+yx133EFYWBi5ubncddddpqOJVFsFuetp0WA6uwrDSWn2D9NxRERERESMMDLC6/f7AViwYAH//Oc/GTlyJJdddhmWZdGxY0cWL17M559/biKaSLXn81XgLbkJt8NPUc6DhMXUMx1JRERERMQIIwXvkSnLX3/9Neeeey6XXnopTqeTkpIS2rdvT8uWLdm6dauJaCLV3p7Nf+CsxHzWbu5NvdZXmY4jIiIiImKM0TW8oaGhlJWVAYFRX7fbDQQK4vDwcJPRzpgvvviCCRMmHLPtgw8+4Morr+Tqq69m4cKFZziZVFcxYaNYubkNzTtMNR1FRERERMQoI2t4HY5AnX3RRRfx3HPPMXPmTPLy8mjQoEHlP3fp0sVEtDPq0UcfZenSpbRu3fqotqysLN566y1mzZpFeXk5I0eO5Lzzzqv8o4DI/yovz8cdEkNii4tI5CLTcUREREREjDNS8FqWhW3bnHvuudx8881MmTKF3bt3s3z5clq1asV9991H+/btTUQ7ozp16kT//v15//33j2pbv349HTt2xO1243a7ady4MZs3b6Zdu3YGkkqws/1+cvYPActPcsoCHC7j+9GJiIiIiBhn5P+KbdvGsiw+++wzGjVqxJw5c/B6vTidTizLMhHptJo5cybTp0+vcu3xxx9n4MCBrFq16pjPKSoqIjo6uvL7yMhIioqKjnpcVFQoLpfz1AaWoOR0OoiLizhm2/qVt9C5SSartrYnoU7MGU4mEvBLfVQkGKiPSrBTH5VgVx37qJGC1+/343Q6mTt3Lueeey5t27bFVYNHpIYNG8awYcNO6DlRUVEUFxdXfl9cXFylAD6iqKj8N+eT6iEuLoL8/JKjrmfvm0+bRp+wOTuWxq2mH/MxImfCz/VRkWChPirBTn1Ugl2w9tGkpKPrpCOMTWkG6N69O6tWraJevXq0a9cOt9uNy+XCsiyio6NxOmvvyGW7du149tlnKS8vp6Kigh07dpCWlmY6lgSZivLDRLjvpcJv4eRZXKG1Y7M3EREREZHjYWxKM8C2bdtYsGABy5cvx+PxYNs2DocDj8fD1KlT6devn4l4Rk2bNo3GjRtz4YUXMmrUKEaOHIlt29x5552EhoaajidBJn/fQhrUqWDLtqE069zTdBwRERERkaBi2UeqTwPKysrw+Xx4vd4qBW9FRQWJiYnHtSNxTg6kpQW+1kZZWYWmI8gZ8nNTSErz9hAe39hAIpGqgnWak8gR6qMS7NRHJdgFax8NuinNR4SFhXHw4EGWLl3K9u3bCQ0NpXfv3nTo0KFWT2cW+TWHs9eQffBpmpz1mopdEREREZGf4TD54nv37uXmm2/mtddeIz8/n23btjF69GjefPNNfD6fyWgiQcvrq8Bbdgvtm6zm8N4lpuOIiIiIiAQtIyO8Pp8Pp9PJk08+yYUXXsj48eMr2zZs2MDDDz9M9+7dOfvss03EEwlquzddT/cW+azc2I8WnS8yHUdEREREJGgZHeHduXMn3bp1AwIbWfl8Ptq2bUtJSckxz5wVqe32b5tGl+b/Yd3+ujTr8A/TcUREREREgpqRgvfIsUQtWrRg9erVFBUV4ff7cTgc7Ny5k/DwcGJjY01EEwla3ooS6iY8S06Zm9i4aTi0zl1ERERE5BcZmdLscATq7HHjxjF27Fi+++472rdvT3FxMR9++CFjxoyhefPmJqLJb7Rj7QSaN/mcOqEVZJe72bl7AC06TDEdq1o78pmGllQQ5nKxeVcbUtu3NB1LRERERCToGT2WCCAjI4OZM2eyY8cOoqOjGThwID169Kgsin+NjiUKnmOJdqydQIeW/ybM+VOXKvNbrNnah+RGt+NwhRIZHyjUinK34POWAX4g8HinK5KohLMAKMhaj99fAfZPm5c5Q2KITmwNQP6Bb/HbFVVe3+VOIObH9pyMxYH72nbl/d1hyUQntsbv85GTuQAAywb7x/awiEZEJ7bB6y0nN2PBj3f1V94/PKo50Qmt8VQUkXtgYeX9jzw/MvosohNaU16WR96BwPOPtAFExbYjOj6NspJD5B1c+GP7T/ePSehKVGxLSgr3kZ/1NTZQWjyXTs3XE+r4r8/UZ7F2+yD9IUGCTrAeVSByhPqoBDv1UQl2wdpHg/ZYIp/PR1RUFKNGjcKyLBwOB7ZtU1hYqCnN1VDzJp9XKXYBwhw2PVstAhax83AksAYAyzOcljFV/2XZkhMLCd8AEOG4jvpR5VXaNxxMJDpxOQB1wscQ7/ZWaV+7P5mYxEUANIm5mXCnv0r7f/Y0ITrxc2xs2iSOOyr/NzvTiE6cR0XxQc5OuuOo9lXb2xGdMJPi7I20Tbr7qPaVW7sRnfAvDmcu45zk+49u39KP6Ph/krfnU9o1efzo+2+5nKgOk8neM5POzV86qv2IMKdN8yaf/2y7iIiIiIgEGC14v/jiCyZNmkRmZiaWZWHbNi6XC6/Xy1dffUXDhg1NxpMTVCe04pjXbRtWbeuNg0SikwPXDmZewoHMI8PygTXdTqsBCY0CV/bsvYTddsGPzYF2l7Np5T23pl+CTRkWFrYduENISGpl+/ptlwC+yntjQ1hY2x9fzWLV5oH/FdDCAsIiOwEQEhbPNxsHV2kHiIzuDkB4bDO+2TSkSnaAmPi+AEQntOPbTUP/6xMIPCY+sT8AsUnn8e2ma/7r/oEvCcmXBh5X92L+synw3ju3mnHk7VdRJ7SCWjqpQURERETkuBmZ0nxkg6p+/foxevRoLr/8chwOBz6fD7/fj9frpW7dusc1rVlTmoNnSrOddw51w44ueg+VubHivzeQqPrTZyrVSbBOcxI5Qn1Ugp36qAS7YO2jvzSl2eguzWFhYfTr14/4+HhiY2NJSEigTp06JCcnH/caXgkeO3cPoMxXdTiyzGexc/cAQ4mqP32mIiIiIiInz2jB+8c//pHnnnuONWvWcPDgQbKzs8nNzaWgoMBELPmNWnSYwtrtgzhU5sZvB0YhtbnSb6PPVERERETk5BnftGrJkiV8+umnWJZVOdXZ5/PxzTffEBMT87PPtW148UUYPjzwfWkpvP023HTTGQovx3SkEMsBrAhoEW82T01w5DP1xUVg5ZfoMxUREREROU5GCl7btrEsiyeeeIIHHniAvn37VlnD6/P5frHYPWLqVEj+cROkV1+FBQtU8IqIiIiIiEiAkYL3yJTmevXq0bdvX+LjT3zIyrLgoYdg8uTAaO+kSTBv3qlOKiIiIiIiItWV0Z2hrrjiCh555BHWr19PZmbmCa/hHTYMDh+GoiLo0gU6dTrNgUVERERERKTaMLqG97333iM/P58vv/wSv9/PkROSbNtm48aNv7pTs9MJd98Nf/wjPPzwmUgsIiIiIiIi1YXRgnfu3LnYto1t25Xrd4+s4T3eY4muvx6KizW6KyIiIiIiIlUZLXgjIiJ+8z1cLrjjjlMQRkRERERERGoUo2t4RURERERERE4Xyz6ycFZERERERESkBtEIr4iIiIiIiNRIKnhFRERERESkRlLBKyIiIiIiIjWSCl6RIObxeJg4cSIjR45k6NChfPXVV6YjiRxTTk4Offv2ZceOHaajiBzTyy+/zDXXXMOVV17JzJkzTccRqcLj8TBhwgSGDx/OyJEj9btUgsq6desYNWoUALt372bEiBGMHDmShx9+GL/fbzjdr1PBKxLE5s6dS1xcHDNmzOC1117jb3/7m+lIIkfxeDw89NBDhIWFmY4ickyrVq3iu+++49133+Wtt97iwIEDpiOJVLFo0SK8Xi/vvfceY8eO5dlnnzUdSQSAV199lQceeIDy8nIAnnjiCe644w5mzJiBbdvVYjBGBa9IELvkkku4/fbbAbBtG6fTaTiRyNEmTZrE8OHDqVu3rukoIse0dOlS0tLSGDt2LH/60584//zzTUcSqaJZs2b4fD78fj9FRUW4XC7TkUQAaNy4MS+88ELl9z/88APnnnsuAH369GH58uWmoh03/dskEsQiIyMBKCoq4rbbbuOOO+4wnEikqo8++oiEhAR69+7NK6+8YjqOyDHl5eWRkZHBSy+9xL59+7jlllv47LPPsCzLdDQRACIiIti/fz+XXnopeXl5vPTSS6YjiQBw8cUXs2/fvsrvbduu/N0ZGRlJYWGhqWjHTSO8IkEuMzOT0aNHc/nllzN48GDTcUSqmDVrFsuXL2fUqFFs2rSJe+65h6ysLNOxRKqIi4ujV69euN1umjdvTmhoKLm5uaZjiVR688036dWrF/Pnz2fOnDnce++9lVNIRYKJw/FT+VhcXExMTIzBNMdHBa9IEMvOzuaGG25g4sSJDB061HQckaO88847vP3227z11lu0bt2aSZMmkZSUZDqWSBWdO3dmyZIl2LbNwYMHKS0tJS4uznQskUoxMTFER0cDEBsbi9frxefzGU4lcrQ2bdqwatUqABYvXkyXLl0MJ/p1mtIsEsReeuklCgoKmDp1KlOnTgUCmwdocyARkeN3wQUX8O233zJ06FBs2+ahhx7SnggSVMaMGcP999/PyJEj8Xg83HnnnURERJiOJXKUe+65hwcffJCnn36a5s2bc/HFF5uO9Kss27Zt0yFERERERERETjVNaRYREREREZEaSQWviIiIiIiI1EgqeEVERERERKRGUsErIiIiIiIiNZIKXhEREREREamRVPCKiIiIiIhIjaSCV0RERERERGokFbwiIiJy0p577jkGDx7MxRdfzPvvv286joiISBUqeEVEROSkLFmyhE2bNjF79myef/55vvzyS9ORREREqlDBKyIiIidlwYIFXHHFFXi9Xt555x0GDBhgOpKIiEgVKnhFTqFu3bqxatUq0zFERM6IH374geLiYrp168bq1av53e9+ZzqSiIhIFSp4RURE5IT5/X4OHDjAlVdeycqVKzn77LOZNm2a6VgiIiJVqOCtpvbt20e3bt2YNm0aPXr0oFu3bsycOZOXX36Z7t27c9555zFv3rzKx3/88ccMHDiQzp07M3z4cNatW1d5n86dO3PvvffSpUsX5syZQ1lZGY8++ii9e/emV69eTJo0iYqKimPmyMzM5E9/+hOdOnWid+/eVf5nZ/r06Vx44YV07dqVG264gZ07dwKwatUqrrjiCiZPnkzXrl3p06cPCxYs4LHHHqNLly7069ePFStWAPDRRx8xZswYbrvtNjp06MCgQYMq2040e0ZGBqNHj6ZLly7079+fyZMnY9s2AG+++Sbnn38+3bp149prr2XDhg2V72PGjBkMGDCAbt26MXbsWLKysirb5s2bx4UXXkinTp148sknf/PPVUSkukhPT6dJkyYAhIWF0alTJ/x+v+FUIiJnzr59+zjrrLMoLi42HaXWWbhwIf369Tuux6rgrcby8/PZv38/ixcvZsKECTz88MPk5uayZMkSxo4dy2OPPQYENhV56KGHeOSRR1i1ahVDhw7lxhtvrCzcioqKaNiwIcuXL2fAgAFMmjSJnTt3MnfuXObOncuGDRt46aWXjpnh9ttvJykpiWXLlvH222/z2muvsXTpUt5//31ef/11XnzxRZYtW0anTp246aabKCsrA2Djxo0kJiZWFr/jxo2jYcOGrFixgkGDBvHUU09VvsaKFSto37493377LTfeeCNjx44lNzf3hLM/88wzpKWl8c033/D222/z73//mxUrVrB7926ee+453nnnHVauXEn37t154oknAPj000955ZVXePHFF1m8eDEpKSnceeedAGzevJkHHniAxx9/nJUrV2JZFvn5+afhJy0iEnw2btyIx+PB5/NRUVHBxx9/TP/+/U3HEhERqUIFbzV3/fXXExISQvfu3fH5fJXf9+7dm7y8PEpLS5k7dy5XXHEFXbt2xeVyMXToUFq0aFFlN83BgwfjdrsJCwvjo48+4u677yY+Pp6EhATGjx/PBx98cNRr7927l3Xr1vHnP/+Z8PBwmjRpwvTp02nTpg1z5sxhzJgxtGrVCrfbza233kpFRQXffPMNACEhIfz+97/H4XDQvXt3HA4Ho0ePJiQkhJ49e5KRkVH5Ok2bNuXGG28kJCSEK6+8kpSUFBYuXHjC2UNDQ/n222+ZP38+ERERLFy4kJ49e+JyufB4PHzwwQds3ryZsWPH8s477wDw4YcfMmbMGFJTUwkNDeWuu+5i3bp1pKenM3/+fHr37k23bt1wu93cdtttREREnJafs4hIsNm0aRNlZWVcdNFFDB8+nCFDhtCqVSvTsUREjNmyZQujRo2iS5cuDB48mEWLFlW2zZs3jwEDBtC1a1euuuoqli5dCkBBQQG33nor5557LhdccAF/+ctfKC8vP+b958+fz6BBg+jYsSNDhw6tnJGYnZ3NhAkT6NatG3379mXy5MmVMxzvvfdeJk+ezPDhw+nQoQPXXXcd69evZ/jw4XTs2JHrr7+eoqIiAEaNGsXkyZO5+OKL6dixI+PHj68czHnhhRe4+eabGThwIH369KGoqOiUv9/8/HwmTpxIjx496NevH6+88krlbMzy8nIeeOABOnfuTL9+/U5ozxwVvNVcbGwsAA5H4EcZHR0NgGVZQGCNVW5uLg0aNKjyvAYNGnDgwIHK7+vUqQNAbm4uZWVllZ23S5cu3HLLLRQUFBz1L19OTg4RERGVrwnQsmVLEhISyMnJqfKaDoeD+vXrc/DgQQAiIyNxuVyVbZGRkZXvweFwVJkWl5KSUuV1k5OTyc7OPuHsf/nLX+jZsydPP/003bt359ZbbyU7O5uGDRvy6quvsmHDBoYPH87555/PrFmzgMCU7Weffbbyfj179sSyLDIyMsjOzqZevXqVOdxuN0lJST/7sxIRqUk2bdrE5MmTWbBgAR999BFDhw41HUlExJiioiJuvPFGLrnkElauXMkDDzzAxIkTSU9Pp7S0lPvuu4+nn36ab7/9lpEjR/Lggw9i2zZvvPEGTqeTpUuXMnv2bH744Qfmzp171P23bt3KxIkTuef/t3f/MVWWfRzH3wR59GSCGhi11tPRsWmyMM+KFbiIGhvWDsJoOdEypYbkMn+BMzSCGMsTEiu1kbnMamERliy25kyb1LJf/zDHBs4fcEQ6SAgcQg5czx/M+5GH1gNG4XP8vP67D/f1Pd9r93bO/T3X977IyeHHH3+0OiT7+/t5/vnnATh06BAVFRV8//33lJWVWWMrKyspLCzk2LFjeL1eVq1axauvvsrXX3+Nx+PhwIED1rkHDhzgjTfe4JtvvuHSpUvk5+dbf/vuu+8oLS2luroaYMznu3HjRoKCgjh06BB79+7l888/p7KyEoDS0lIaGhr46quv+PDDDzl27NiIr03IKK6jXIMuF7Z/JjIykubm5iGvNTU1ce+99w6LExYWxo033khVVZVVaPp8PrxeLzabbUiMGTNm4PP56OzstIregwcPMmXKFG677bYh7zkwMIDH42H69OmjnmNra+uQY4/HQ3Jy8qhz/+WXX8jMzCQnJ4czZ86wefNmysrKWLNmDXa7nd27d9Pb20tNTQ05OTnExcURHh7OM888M+RGrrGxkTvuuIOffvqJuro663W/309bW9uo5yci8v/o5MmTOByO8U5DROSacOTIEaZNm8aSJUuAwf/ckZiYyGeffUZWVhY2m42Kigr6+vpwuVykpqYSFBSEzWajrq6O6upq4uPjqaystBaBrlRTU0N8fDwLFiwAYPHixcyZM4fTp0/z888/s2PHDiZPnszkyZN54YUXyM3NZf369QAkJCQwa9YsAKKjo5kwYQIzZ84E4J577hlyz56RkWF166xZs4b09HRrtXj27NlERUUBUF1dPabz/fXXXzl69Cjffvstdrsdu93OihUr+Pjjj0lLS+PLL78kLy+PadOmAZCZmUlpaemIro1WeK8DKSkpVFVVcfz4cfx+P5988gkNDQ1/+KxVcHAwjz/+OG63m4sXL+Lz+diyZQu5ubnDzo2MjMTpdPL666/T29vLqVOnKC4uJiQkhJSUFN577z3q6+u5dOkSO3bsACA2NnbU+dfX11NVVYXf72f//v20trby0EMPjTr3nTt34na76e3tZfr06QQHBzN16lSam5tZvnw5dXV12Gw2pk6dis1mw263s2jRIvbs2cPp06cZGBjg/fff54knnqCnp4fk5GRqa2s5fPgwfX19vPXWW1ZLiIhIoDty5IjVqSMicr3zeDw0NjZaXYFOp5OamhpaWlqYNGkSe/fu5cKFC6xcuZIHH3yQ8vJyAJ599lnS09N59913iY+PZ9myZZw6dWpYfK/Xy6233mod33DDDcybN4+Ojg7sdrtVCMJgJ6fX66Wvrw/4T0coDN4vT5kyZUicy23DgLUZIQwubvX19VltzVd2Mo71fM+dO4cxhkcffdSKV1BQYC18/Xdn5e233z7ia6NvquuA0+kkPz+frVu3cu7cOWbOnEl5eTmRkZE0NTUNO3/z5s243W4WLlzI77//zvz589m+ffsfxi4pKeGVV15hwYIFTJo0iezsbB544AEA2tvbyc7Opq2tjejoaPbs2XNVz7g6HA4OHz5MYWEhd97szwZsAAAEQ0lEQVR5J+Xl5YSGhtLZ2Tmq3F9++WXy8vKIi4sDBn/teu6557Db7axbt47Vq1db7d+lpaXcfPPNuFwufvvtNzIzM/F6vTgcDt5++21CQ0MJDQ2lpKSE4uJiWltbSU5OHvIhISIiIiLXh/DwcGJiYqx9YABaWlqw2Wx0dXXR3d3Nm2++id/vp7a2luzsbO677z4mTpyIy+UiKyuL8+fPU1RUREFBAbt37x4Sf8aMGZw4ccI6Nsawbds2lixZgs/n48KFC1bR29TUZHU+wsg6Qi+7srPS4/EwceJEwsLChsUZ6/kWFhYSEhJCbW0tEyZMAKCjo8PaATsiIgKPx8PcuXMBrMckR8SIXMM+/fRTs2jRovFOQ0RERERkiLNnz5qoqCjT1dVl2tvbTWxsrPniiy+M3+83DQ0NJi4uzlRUVJjz58+b6Ohoc/ToUWOMMSdOnDDR0dHm5MmTJj8/36xcudJ0dnaa3t5es3HjRrN27dph79XY2GhiYmJMbW2t6e/vN/v27TMJCQnG7/ebp556yqxdu9Z0dXWZlpYWk5qaagoKCowxxuTk5Jji4mIrzp8dZ2RkmMTERHPmzBlz8eJFs2LFCpObm2uMMaasrMysXr3aGvd3zHfp0qWmsLDQ9PT0mPb2drNs2TKzfv16Y4wx27dvNy6Xy7S0tJjW1laTkpJiEhISRnSd1NIsIiIiIiLyF4SFhfHOO+/w0Ucfcf/997N8+XIWL15Meno6ERERvPbaaxQVFTFv3jxWrVrFli1buOuuu3jxxRe56aabSExMJDY2lo6ODjZt2jQsvsPhoKSkhKKiIpxOJwcPHmTXrl0EBwfjdrsZGBggMTERl8vF/Pnz2bBhw1XNIyYmhqysLBISEggPD+ell176x+ZbUlJCW1sbDz/8MElJSURERLB161YAsrOzcTqdPPbYY6SlpVkdpSMRZMwVTdsi15jKykr27dtn7dAmIiIiIiJjb+nSpSQlJZGRkTHeqYwprfDKNS01NVXFroiIiIiIXBUVvCIiIiIiIhKQ1NIsIiIiIiIiAUkrvCIiIiIiIhKQVPAGoP5++OADcLvHOxMREREREZG/5ocfYNMmaGkZ/VgVvAHkcqF7992wcyeMYrduERERERGRa9KsWeDzwZw5sG7d6ApfPcMbIM6eHSx0BwZg7ly45RYIChrvrERERERERMZGTw/U14PHAxs2QHHx/x4T8venJf+EyEh48knYvx+CgyEpCf71r/HOSkRERERE5K/z+aC6erC9OS4O0tJGNk4rvAGmuxt27YJt2+Dpp0f2q4eIiIiIiMi16vhxWLgQHnkE8vJg9uyRj1XBG6C6u6G5GaKixjsTERERERGRq9fRAW1t4HCMfqwKXhEREREREQlI2qVZREREREREApIKXhEREREREQlIKnhFREREREQkIKngFRERERERkYCkgldEREREREQC0r8BodaO9Z8BDfEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coordenates_beta_range_10 = batch_perform_algorithm(range(1,11), prior, distance_matrix_)\n",
    "plot_batch_information_curve(coordenates_beta_range_10, range_clusters, out_filename='beta_range_10.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coordenates_beta_range_50 = batch_perform_algorithm(range_betas, prior, distance_matrix_)\n",
    "plot_batch_information_curve(coordenates_beta_range_50, range_clusters, out_filename='beta_range_50.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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
}