k_medoids.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Importing Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd   \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loading the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "iris = datasets.load_iris()  #loading iris dataset\n",
    "data = pd.DataFrame(iris.data,columns = iris.feature_names)   #Converting data to a dataframe\n",
    "\n",
    "target = iris.target_names  #storing target names\n",
    "labels = iris.target  #storing target\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)\n",
       "0                  5.1               3.5                1.4               0.2\n",
       "1                  4.9               3.0                1.4               0.2\n",
       "2                  4.7               3.2                1.3               0.2\n",
       "3                  4.6               3.1                1.5               0.2\n",
       "4                  5.0               3.6                1.4               0.2\n",
       "..                 ...               ...                ...               ...\n",
       "145                6.7               3.0                5.2               2.3\n",
       "146                6.3               2.5                5.0               1.9\n",
       "147                6.5               3.0                5.2               2.0\n",
       "148                6.2               3.4                5.4               2.3\n",
       "149                5.9               3.0                5.1               1.8\n",
       "\n",
       "[150 rows x 4 columns]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data  #displaying data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Storing data and target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris['data']   #storing features in X\n",
    "y = iris['target']   #storing target in y\n",
    "m, n = X.shape   #Taking shape of data matrix\n",
    "k = 3   #number of clusters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center> Defining the input </center>"
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting the data points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fa57c81cc10>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plotting the initial data\n",
    "plt.scatter(X[:, 0], X[:,1], s=7, color = 'black')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Initialising the medoids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Function is used to randomly initialise the medoids initially\n",
    "def initialise_medoids(X,rseed,k):\n",
    "    val = np.random.RandomState(rseed)  #Generating random number\n",
    "    i = val.permutation(X.shape[0])[:k]   #Computing indices randomly\n",
    "    medoids_initial = X[i]   #assigning the initial medoids\n",
    "    return medoids_initial\n",
    "\n",
    "medoids_initial = initialise_medoids(X,2, 3)   #calling the function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.6, 3.4, 1.4, 0.3],\n",
       "       [4.6, 3.1, 1.5, 0.2],\n",
       "       [5.7, 2.5, 5. , 2. ]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "medoids_initial  #displaying initial medoids"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculating distance of data points from medoids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_distance(X, medoids):\n",
    "    m = len(X)  #taking length of input data\n",
    "    medoids_shape = medoids.shape  #taking shape of medoids\n",
    "    \n",
    "    #condition for reshaping the shape of medoids\n",
    "    if len(medoids_shape) == 1: \n",
    "        medoids = medoids.reshape((1,len(medoids)))\n",
    "    k = len(medoids)\n",
    "    \n",
    "    #creating an empty array of dimensions m,k\n",
    "    S = np.empty((m, k))\n",
    "    \n",
    "    #calculating squared distance of all datapoints from the computed medoids\n",
    "    for i in range(m):\n",
    "        dist = np.linalg.norm(X[i, :] - medoids, axis=1)\n",
    "        S[i, :] = dist**2\n",
    "\n",
    "    return S\n",
    "  \n",
    "S = compute_distance(X, medoids_initial)  #Calling the function\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.700e-01, 4.200e-01, 1.756e+01],\n",
       "       [2.600e-01, 1.100e-01, 1.709e+01],\n",
       "       [7.000e-02, 6.000e-02, 1.842e+01],\n",
       "       [1.100e-01, 0.000e+00, 1.706e+01],\n",
       "       [2.100e-01, 4.200e-01, 1.790e+01],\n",
       "       [9.900e-01, 1.360e+00, 1.550e+01],\n",
       "       [0.000e+00, 1.100e-01, 1.787e+01],\n",
       "       [1.800e-01, 2.500e-01, 1.679e+01],\n",
       "       [3.000e-01, 9.000e-02, 1.805e+01],\n",
       "       [2.300e-01, 1.000e-01, 1.686e+01],\n",
       "       [7.500e-01, 1.000e+00, 1.702e+01],\n",
       "       [9.000e-02, 1.400e-01, 1.642e+01],\n",
       "       [2.400e-01, 7.000e-02, 1.763e+01],\n",
       "       [3.800e-01, 2.700e-01, 2.103e+01],\n",
       "       [1.850e+00, 2.340e+00, 1.994e+01],\n",
       "       [2.230e+00, 2.940e+00, 1.842e+01],\n",
       "       [9.100e-01, 1.360e+00, 1.830e+01],\n",
       "       [2.600e-01, 4.300e-01, 1.721e+01],\n",
       "       [1.460e+00, 1.750e+00, 1.547e+01],\n",
       "       [4.200e-01, 7.500e-01, 1.719e+01],\n",
       "       [7.400e-01, 7.700e-01, 1.503e+01],\n",
       "       [3.600e-01, 6.500e-01, 1.661e+01],\n",
       "       [2.100e-01, 5.000e-01, 2.166e+01],\n",
       "       [3.900e-01, 4.200e-01, 1.414e+01],\n",
       "       [3.000e-01, 2.900e-01, 1.447e+01],\n",
       "       [3.700e-01, 1.800e-01, 1.554e+01],\n",
       "       [2.100e-01, 3.000e-01, 1.542e+01],\n",
       "       [3.900e-01, 5.200e-01, 1.674e+01],\n",
       "       [3.700e-01, 4.600e-01, 1.726e+01],\n",
       "       [1.000e-01, 3.000e-02, 1.629e+01],\n",
       "       [1.800e-01, 5.000e-02, 1.597e+01],\n",
       "       [6.600e-01, 7.700e-01, 1.571e+01],\n",
       "       [9.000e-01, 1.370e+00, 1.867e+01],\n",
       "       [1.460e+00, 2.030e+00, 1.913e+01],\n",
       "       [2.000e-01, 9.000e-02, 1.649e+01],\n",
       "       [2.500e-01, 2.600e-01, 1.866e+01],\n",
       "       [8.400e-01, 1.010e+00, 1.797e+01],\n",
       "       [1.700e-01, 3.600e-01, 1.842e+01],\n",
       "       [2.200e-01, 9.000e-02, 1.887e+01],\n",
       "       [2.700e-01, 3.400e-01, 1.666e+01],\n",
       "       [1.800e-01, 3.700e-01, 1.807e+01],\n",
       "       [1.230e+00, 7.000e-01, 1.806e+01],\n",
       "       [1.000e-01, 9.000e-02, 1.911e+01],\n",
       "       [3.000e-01, 4.900e-01, 1.501e+01],\n",
       "       [6.700e-01, 9.400e-01, 1.422e+01],\n",
       "       [2.000e-01, 7.000e-02, 1.691e+01],\n",
       "       [4.600e-01, 7.500e-01, 1.685e+01],\n",
       "       [5.000e-02, 2.000e-02, 1.790e+01],\n",
       "       [6.000e-01, 8.500e-01, 1.709e+01],\n",
       "       [1.800e-01, 2.100e-01, 1.733e+01],\n",
       "       [1.790e+01, 1.745e+01, 2.630e+00],\n",
       "       [1.433e+01, 1.394e+01, 1.480e+00],\n",
       "       [1.907e+01, 1.854e+01, 2.060e+00],\n",
       "       [9.780e+00, 8.910e+00, 1.570e+00],\n",
       "       [1.565e+01, 1.500e+01, 1.140e+00],\n",
       "       [1.218e+01, 1.151e+01, 8.300e-01],\n",
       "       [1.548e+01, 1.513e+01, 1.250e+00],\n",
       "       [5.190e+00, 4.460e+00, 4.540e+00],\n",
       "       [1.549e+01, 1.486e+01, 1.620e+00],\n",
       "       [8.310e+00, 7.720e+00, 1.860e+00],\n",
       "       [7.020e+00, 6.010e+00, 3.990e+00],\n",
       "       [1.113e+01, 1.068e+01, 1.180e+00],\n",
       "       [1.065e+01, 9.660e+00, 2.180e+00],\n",
       "       [1.460e+01, 1.397e+01, 7.700e-01],\n",
       "       [7.090e+00, 6.660e+00, 2.620e+00],\n",
       "       [1.471e+01, 1.426e+01, 2.080e+00],\n",
       "       [1.221e+01, 1.170e+01, 7.600e-01],\n",
       "       [9.710e+00, 9.000e+00, 1.860e+00],\n",
       "       [1.505e+01, 1.406e+01, 8.400e-01],\n",
       "       [8.700e+00, 7.930e+00, 2.030e+00],\n",
       "       [1.554e+01, 1.515e+01, 6.100e-01],\n",
       "       [1.037e+01, 9.800e+00, 1.740e+00],\n",
       "       [1.739e+01, 1.650e+01, 6.200e-01],\n",
       "       [1.431e+01, 1.358e+01, 9.800e-01],\n",
       "       [1.290e+01, 1.233e+01, 1.630e+00],\n",
       "       [1.437e+01, 1.386e+01, 1.780e+00],\n",
       "       [1.797e+01, 1.726e+01, 1.700e+00],\n",
       "       [1.949e+01, 1.892e+01, 1.340e+00],\n",
       "       [1.326e+01, 1.269e+01, 7.500e-01],\n",
       "       [6.750e+00, 6.100e+00, 3.260e+00],\n",
       "       [8.210e+00, 7.400e+00, 2.300e+00],\n",
       "       [7.590e+00, 6.780e+00, 2.740e+00],\n",
       "       [8.990e+00, 8.360e+00, 1.900e+00],\n",
       "       [1.783e+01, 1.704e+01, 3.000e-01],\n",
       "       [1.185e+01, 1.134e+01, 8.400e-01],\n",
       "       [1.326e+01, 1.301e+01, 1.310e+00],\n",
       "       [1.683e+01, 1.634e+01, 1.700e+00],\n",
       "       [1.410e+01, 1.315e+01, 1.250e+00],\n",
       "       [9.450e+00, 8.980e+00, 1.560e+00],\n",
       "       [9.380e+00, 8.630e+00, 1.530e+00],\n",
       "       [1.126e+01, 1.047e+01, 1.050e+00],\n",
       "       [1.386e+01, 1.331e+01, 9.300e-01],\n",
       "       [9.650e+00, 8.940e+00, 1.660e+00],\n",
       "       [5.470e+00, 4.680e+00, 4.420e+00],\n",
       "       [1.033e+01, 9.660e+00, 1.180e+00],\n",
       "       [1.002e+01, 9.510e+00, 1.530e+00],\n",
       "       [1.030e+01, 9.750e+00, 1.290e+00],\n",
       "       [1.222e+01, 1.165e+01, 1.390e+00],\n",
       "       [4.260e+00, 3.670e+00, 5.170e+00],\n",
       "       [9.860e+00, 9.270e+00, 1.390e+00],\n",
       "       [2.890e+01, 2.847e+01, 2.250e+00],\n",
       "       [1.818e+01, 1.745e+01, 7.000e-02],\n",
       "       [2.990e+01, 2.923e+01, 3.030e+00],\n",
       "       [2.303e+01, 2.230e+01, 9.200e-01],\n",
       "       [2.674e+01, 2.611e+01, 1.570e+00],\n",
       "       [3.944e+01, 3.863e+01, 6.430e+00],\n",
       "       [1.247e+01, 1.170e+01, 9.800e-01],\n",
       "       [3.380e+01, 3.293e+01, 4.450e+00],\n",
       "       [2.683e+01, 2.582e+01, 1.680e+00],\n",
       "       [3.373e+01, 3.346e+01, 4.920e+00],\n",
       "       [2.023e+01, 1.982e+01, 1.140e+00],\n",
       "       [2.150e+01, 2.073e+01, 6.300e-01],\n",
       "       [2.505e+01, 2.446e+01, 1.720e+00],\n",
       "       [1.787e+01, 1.706e+01, 0.000e+00],\n",
       "       [1.990e+01, 1.933e+01, 2.700e-01],\n",
       "       [2.249e+01, 2.210e+01, 1.160e+00],\n",
       "       [2.283e+01, 2.218e+01, 1.180e+00],\n",
       "       [4.147e+01, 4.114e+01, 8.620e+00],\n",
       "       [4.450e+01, 4.343e+01, 7.710e+00],\n",
       "       [1.780e+01, 1.671e+01, 4.300e-01],\n",
       "       [2.782e+01, 2.735e+01, 2.510e+00],\n",
       "       [1.650e+01, 1.589e+01, 1.100e-01],\n",
       "       [4.095e+01, 3.998e+01, 6.980e+00],\n",
       "       [1.788e+01, 1.717e+01, 4.500e-01],\n",
       "       [2.615e+01, 2.570e+01, 2.140e+00],\n",
       "       [3.021e+01, 2.958e+01, 3.780e+00],\n",
       "       [1.673e+01, 1.610e+01, 4.200e-01],\n",
       "       [1.691e+01, 1.638e+01, 4.600e-01],\n",
       "       [2.448e+01, 2.375e+01, 9.500e-01],\n",
       "       [2.797e+01, 2.722e+01, 3.300e+00],\n",
       "       [3.285e+01, 3.198e+01, 4.200e+00],\n",
       "       [3.894e+01, 3.863e+01, 8.490e+00],\n",
       "       [2.485e+01, 2.414e+01, 9.800e-01],\n",
       "       [1.838e+01, 1.763e+01, 7.100e-01],\n",
       "       [2.174e+01, 2.075e+01, 8.900e-01],\n",
       "       [3.586e+01, 3.519e+01, 5.550e+00],\n",
       "       [2.494e+01, 2.463e+01, 1.690e+00],\n",
       "       [2.239e+01, 2.180e+01, 1.140e+00],\n",
       "       [1.593e+01, 1.542e+01, 4.200e-01],\n",
       "       [2.462e+01, 2.411e+01, 1.970e+00],\n",
       "       [2.655e+01, 2.606e+01, 1.880e+00],\n",
       "       [2.307e+01, 2.266e+01, 1.900e+00],\n",
       "       [1.818e+01, 1.745e+01, 7.000e-02],\n",
       "       [2.913e+01, 2.862e+01, 2.600e+00],\n",
       "       [2.775e+01, 2.738e+01, 2.380e+00],\n",
       "       [2.301e+01, 2.252e+01, 1.380e+00],\n",
       "       [1.922e+01, 1.839e+01, 3.700e-01],\n",
       "       [2.110e+01, 2.055e+01, 9.300e-01],\n",
       "       [2.256e+01, 2.227e+01, 1.310e+00],\n",
       "       [1.779e+01, 1.722e+01, 3.400e-01]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Assigning labels to data points "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Assign labels to data points according to the minimum distance with the medoids\n",
    "def assign_labels(S):\n",
    "    return np.argmin(S, axis=1)\n",
    "  \n",
    "labels = assign_labels(S)  #calling function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Updating medoids "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "#function to update the medoids\n",
    "def update_medoids(X, medoids):\n",
    "    \n",
    "    S = compute_distance(X, medoids)  #computing distance\n",
    "    labels = assign_labels(S)   #assigning labels\n",
    "        \n",
    "    out_medoids = medoids\n",
    "                \n",
    "    for i in set(labels):\n",
    "        \n",
    "        avg_dissimilarity = np.sum(compute_distance(X, medoids[i]))  #calculating the average dissimilarity by summing over all the distances\n",
    "\n",
    "        cluster_points = X[labels == i]  #Assigning cluster points\n",
    "        \n",
    "        for datap in cluster_points:  #checking for a data point in the cluster points\n",
    "            new_medoid = datap\n",
    "            new_dissimilarity= np.sum(compute_distance(X, datap))  #calculating the new dissimilarity\n",
    "            \n",
    "            #condition to update the value of average dissimilarity\n",
    "            if new_dissimilarity < avg_dissimilarity :\n",
    "                avg_dissimilarity = new_dissimilarity\n",
    "                \n",
    "                out_medoids[i] = datap\n",
    "                \n",
    "    return out_medoids"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setting condition for convergence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "#function to set the condition for convergence by comparing the values of old medoids and new medoids\n",
    "def has_converged(old_medoids, medoids):\n",
    "    return set([tuple(x) for x in old_medoids]) == set([tuple(x) for x in medoids])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center> Algorithm for computing k medoids </center>"
   ]
  },
  {
   "attachments": {
    "image.png": {
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xsvVOSRe1nwKSlC1107OvJZmgqO1PrRX1WWyOMVq8H168m+njtZSWItL/ytmsQtDcaX94OeyBsdiyvDUEC0V9DqRVsWYu10J17wfic23pbG0UxmerQmad8Vz18Sc8Lhib1/Z/qpEkKYqQJbQ4VvsVslIWUNS7Tvai0ernFAVEsW4Preq4FVFYJUofWELrsQmarosYzcMXDJRknyVFkumrnRyu1g0KmXRaoQ/3GQ2aawTLJ9lVUWmnaRLsnm8o2dcy7GDd3wcTD73UH+HaHcVMPHktmwUEM+oJPEgsjuTC99GDju39DD1neyqQtHEOkpTVIomrJYcpq23OkczKY2MBKSvGB5gAJoAJYAKYACaACWACHzKBv3jcKy7yndYvF+tfoNwZIQhbgCwZvLoLiXYr6q0rAKwL4qrhot/aKP+Ynb6Z43+cZvUVnk/j8XVAjziY9fDsf5d22FX0EbDxfs616lBvfFs2MF/y1Otg4Gd9lC3L6A1b9KNGXexaLPybFnVBDN5LUGPO+rdyi7JN/WGcDmZ1fnq5m+81kE9dmw7qS20tLRBarSQ0gVAdlhgeZeHjgL+43zUAyFiCO+GyPpmdulN6blBA+NByclnKllJX0fJCEC1UdxcAkHVPUIkbi/pLyBUByDrHqdT9sL4Fs/w4GJFZ11jd8LMirh+ZRlct2OvgOsTFy/NC0Sqlfq7vpSAWKLo46S8KL5TySUXNMX6YTC9ejehPKHLrxYclBEHCbBqtXi7I6eeVLcChBYKshF7sBuidXuFpSgFAeS3UPjyoqK8cKcLi3RQ14bJb3tU3qmwQgz8uFneobm2Brcikqp+JJy/7px/qo0oIIUQDxdpflf7aG5UzQ8+p3G72yDAHCdYxCOPX/XFtXwBlPVfMkuYcyaw8NhaQZo3EcpgAJoAJYAKYACaACWAC75fAHu23Jf065//G4zxKglaaO+v1XQ5rO/SuLIyQ5MiCtn1tJeZ8Oug7zZIWQPa7fbdTeSHsHSTBPtZ7O5XLpYIXWNJCcZeiQjrsP8uSFpI9GwgLeVVdWRijiHbaNup79H9qbwkLzgMEbKdsY77AORvcx3pC/7t0w8cfALDX6b+VkJ5Vy0vBUQJAih13Oiec/AhLk5QnjsxbiXi5XpIgKeYoy58LanvDZuaM9nPOPwsWbb4aLe5FbGDDH4nrThpCZiKw9EpdiQWcPQD2uheSOVXNp264bV0E2cXYBp3OoyTsYH0P0CbDUtzvHGT5cSc/yHIXgppyaemak4GQGfeHn+UyEb+zF8Iepz+SyQlh/wQDLbTz6pL4LBzQcZ0LRPWtj7U0BfoJ25XSrs6VTEBHmRtO21EtriGW/z6qb57cCGElFvAOUaDd5r4cTqFtnKWlyzzToRvPua+ntJ2K86lbHq5Ho3eE5U7MoQ2fpbCnhyA6bNyFsK5cj3/lKgt7fWj7aH2b4laSvRCtcxI1nwme49gh3jnGsYPOQFxTkM8EL3E0hNSQx3cjUa0TqaqK7n8f+LguQBz1LCzn8i/C/lEKEDbPbWRq/tmCZ5Am20n6kI0b90Vf6UYV/8/fdRKkO6rblkfbaNPjgWhxn+qKZG454DykuwrnHGVgK81fWcq9TQSGKNhK0v1O/xU33UpxGtV83GdrJ8he1n0rI911M+2Q6GC4C3O+QUgccS+kizs9F7Wj/ZwJZszjOeHk+20lH0A3jX3jho/vgbCHR0BMitLKhlplw/8TPsva+nnnOM8Nct679eBVA09eUZ8GuCM2bszpHGXZ8UCiYRfqiv658MJpG2Gh+R/DmXwuccNjawfUqF/jbOg5ZapN+blkloNS1DeqZyvLn+BoSDATc1p+GzhSvqZCQE5hWB4NC0jZXHyACWACmAAmgAlgApgAJvDBEvhEVdX3O/DGsf+1BJT4eVf6fNhb9RrzX2sAjm2bBNYWh6lZ+nEmcGSbAbE4JoAJYAKYACaACWACmAAmgAloBP7idc6Y+vsmsJ6IrXMuPOh93/mwzfiVmj29thkYi2MCmAAmgAlgApgAJoAJYAL/4QTwuPc/wwEK6cV/JRWgJK/Mg3HXjjfG+s+AhVOJCWACmAAmgAlgApgAJoAJYAIfFQE87v2osnOTxGRDru6Ddv+nnunB5jcP3kQfvvXXEBBCP4YERYpdnZp/0rA78V9jAo4FE8AEMAFMABPABDABTAAT+JsTwO/3/s0zEJuPCWACmAAmgAlgApgAJoAJYAKYACawKQE837spHnwTE8AEMAFMABPABDABTAATwAQwAUzgb07gIxv3yrHzfW2fD8z8Xvxa5988d7D5u01AEUI/OLpb2k49alKznLw57TjY0nI80mSAj0hMTt6cGqZaur9N7kqilD8js18PWFvssy93Rd9fruR5ZAbZ3zfz5w6i/k92pB3gwkEwAUwAE8AEMAFMABPYZQJ7M+4tCPNf2ftsA8NfDg/Y7MMXQ8J6s3an/9H3ySeffNIysJPOcUFMPEnLrxOJNH4TclPgcsRlbWk5PCMUNhXbjZvy/VOdlGPx9W7oencdkHb+4GIszSsibKf97sPv843o9weQsJ2e4vY3z2oLSdjDe79mrduAv4XCv/r2Ad53nqO2st8kv96/I/3VuHB8mAAmgAlgApgAJoAJfEgE9mbcCyQBuMLJpeiD6NLjWfqxe/jbeFMzsIVkOGllDwCgJML3hG2DsjBTNxcCV4OBiQ9vx+L1dOif8/Gmh3/io/mZX9JNQds2JiA/jlu/dlN/BoN/bD/wNkNAK80wNNW6WTD591hybTOBD/zentrfDEAAgKkNBTH2aFtFSREexcUPnLiZedtOrJminV9vMr92HgEOiQlgApgAJoAJYAKYACawfQJ7M+61dLvOc5RuTauN6yekJ7F0E1OLynI4fWg6MMYAoCTvBpsJUpdk4ojbe4GnDefn1tKhf4Z2oLMuih2dKunLbvcPs7HV5kJnQ1MnJ/13Unsz7pVjTyB3wc13iZG7u7OEdZNUwSPecMTPEuYiBWH+nD+eNRf4wO/ssf1bAwQAmNsg35+e/EXYhiOtLk59GxGbKK0fYLZsO7HbTcNWk70AgKbya7vxYnlMABPABDABTAATwAQwgXcjsDfjXkDajhaHvci8AgAWaDgUrTVeid8T7LyN4R1oJeqfkeDvlfvK7/OnjvX12fq6qc5u5yKaj1qLz3xl7zts76M7O5nJmAyEn13dbWiR9PBNbRS1LoQuDvdR1s79Vuvnndb99kCeppXY5EEk9Ak1PHlmuG9/W0tLWzc/j6ZWf5vp+y90p409Ncnbu60tLW2dw/+MJe/MuI51tn3WYj02GSsNz8R7U8NMZydlte63n7opKCAbOt7Z8sknn3za7TjvGmA0+cOnQi/RmGTxJMv9lFYK0uJEd7dzsaRDS11BjH033MfY7Uxn53779L+B/Gh6eNATyQJlebqPRldAIRv/h6NvP4qu87Br9jcZrMem9FR81j3A2bs/b2tp67SfnE/r68lfh1yUdeAnk1m+tVgCcvZWxjFKi/fDNRPxcnL2+MAA73LxA3Z+XguPoh74wuFyDtttp0L6fLWCwA5wDtdXwwOsa+ZJKUEFMfaDSxN2DB/rs38bV9aS8+e1Vzqf61kpLur6nQN9NtfinwpQhNC3k3O/C8GLDsfFEMpWOT1/cmDgS5eDsw+cWTQYsRkKrEUm2QHHcZeLs/fxs8niOndFuDPl+GLY4XQ5vrD3fTFTfuohPZmd/LLP+llLG6PlUcXRikfZJzMu1j7Au06dOTWfLA8bm7D/yfQAO+w67ho+1jf8XdlfimqV3+cddEvLwWHXlwN22mqlB6buleZWDanWAMzGvhvo/LRt4OSk43DJwVaBAcNScrKPZz0/RsRkwPWVa/bfGtx/nRr+YtjldAwcGzj1PyVOJXnwMjJ9fja2Gpv5ynHqZtF/lNfxmZMDqDhY7VMPi3mtPA9NcgPDX7mG2QHXTw16UKlvcIZyLKUDBPmLAT13hs+Hinlt4ITAKLp6z2xIbCkagIpYZ0ubvcitrdN2av5+aObMcN/nLS3/1e0qpdTY9xQhdH7YjvL01KkfwpUnAlvnFzLAxJHKtuEDTAATwAQwAUwAE8AEMIG/hIC657+VwFFInVvKbxnR27B7yJ9RVXUj4z+EEl8JtZHy9UDyrKYkF/WMBTJqfuk0CXt9qQ1VVaXghHPhjapupPy9aMaFuyGpaj5xgQYA0BcSeXVlrh8CANnrK6qq5u860SC8nQvEU6kHXgadEM4IMnDpHFogDY96o09TS9/b0B0L7b6dSC3P8fvQHdtlZKCa9jEQwCOBTF4zFdoCgqq+mmMhABbKeSOReRp0H9CScCGB5N8G+VZ0y7tcTyF3mycgOyei6yvXePcDdJC6hCyHQws5TXzlGpoupb9J5PUoDngTG6q67EWvGkJuQVLVjZW5ITSjqiVWVV8F+Q6SvaqZWh+hKt1ye3/VciPtZyDl0Y81scxlGzke1iLNRy/PIbbLXrrLo2eedNu/gOzML52jyREUraqquV89dDs79wJdT1xiiKP+jJ7T+ajnbBgdPvMzrRofJJ6Zu1zUHx4niIkoEngRsLUy/meaOjUfPU1RE5rMRsZ/BDI6cP0m+t9EQAr6b6HMVfNLng7I3UKJyMXcFMlpNqOz4Gnv0oaqboSdrQR/ayW/oapvljw9kNLzqBKFqr6YY9sp9wMdvxo9QcCJsHZ/S/vVfMwfeKrJ1iS8oj1xgYKDcxq9fOY6RxbhmFGtBVhtvBR2d0H6UgqprmFYiUtV1ehpAo5rGaGqubtOssMdfaMJSEF+H+m8W0xjOUzuNg87PAgU+klzg5A6HZbyqrohBSdI5POohCZ8PaRWylT11QJHUN5lPdfLajZ1BuQtqirOse1MMeDGytwgoZd3Ayc0jM7AM2sSWzYFHWyEnQTkrmWkt/n8i7D7ACTH5lKvcvm3UvQsDTs0xzB2rfzSOYroD2R0IELZV5vLL1NHqrEOn2ACmAAmgAlgApgAJoAJ7DWBPZrvrQzZld8Xg685/7doSLj5T34Ylvp5NOCz0PyXDABAvB8qzkYWRPG1kn08P/tQkFs5/zU3BWTxtay8jARuxsV1kr8666hbSVsQ4k8EACB9mIGAonutACipZNUUKEHbjzHMkItDA1Qlm63aCouyc4cY9qthtF7aQtDHbMxRlwNtbqRk3yCxZCiSVgA8SNPQSlohUNKJp6XgFqLbZqMPOZ39aAgtZaXyXKFh8qXXolJIBa8uJl8r1Il5f3+jlBi5m5ABpA/SkKTQi7KriUR5vbQFthFoRO0as0MAhEdRNKW5zxkWpSVt2N+gLhtdJrhjWm708o4eKXynMuMr52RZFEQ0aQy5Sx406/5WlmRRWEWJICd87g4AlHjojtg36tBfoSb6XRyRCN4XgRJf/FnoO+4uLjKHrOdr7ZFCjQW05xKvZRQkyDZFboCjxCP3JWaEQzIW2sYQwnKiNJusKTITIJ2+E9oSA2i1toPcWg4AOXYzmOt3uzp0Cwjuoru7tE61jaSgBYB2lmNgbk2qsREA4V4wQfBu7VFC7a2t7EdPK3xe7akNaCetQJZKflGjp7j8AdInvA4iHX4omFKtCVY8KRpPciwDpAbjjULo1+TwLxGln2fbtVOSd/UrkV/ChgZWK4GElUQFgeT6+8CaJBcA+D0cWe3mhjQXIPuYDim+XJq11kM24QzivWCinXUc0VxRc2DpDirvBk5oGF2jZ1YbbXAMiQ6abIWwi+cPQwVamX0EbCW5IQauablk6FpKbPGOZJ9w0yXPKSo2KwW18Zo7Uq0cPsMEMAFMABPABDABTAAT2GMCdb253Y5tLT59IcndCjvRZOnmv2z4TizxNG69pokVFG2UGQ0+UrhRCKCd7SdC9yPTX0b8+2zuHxcDJ2h7PwMfJUNfD4S+pdizgYXL+oCqFIsFguq11dr7irC1YfRtgS2Whou6jvLabBQWgiKqPACKtKotyL3n7nzSAtYh0Y5k9fUAACAASURBVA4VpWF4C1tKpmz2l+7nKMtM8n9O2f81RY9MzV33kXVbQBVEURt2xr7t6/wR5AFBEKAxNgKNv4GSFXObxQbA62gkmQBfDc9qYso6zD4KxtY5NB0NgO24x/7LpH1/mBt3e8672Q4Ijrk9Xdzk4e7gqNN9ZtJ9lARZUVwnqH2lxwwW0vo5EF+I6LpMUPv04TAiRvdUrXXXrSpkYz/5g8+UtlYoJXPg8wZb10RxHYg33a6H6JaStdJlfbqsmcBacv7yXEJuaYP5lL4YuyBmXgDrCFXOXeIAeqhS/7MApeFdVvGFACiXwc69W9oPgPzHYuBaXLS0tRUEoQCMoqwyAVJUBwiLkilV0MCwOvS2im9BFEVg7UF+ov0gtc8K0qJYANvZ4BoFVURRVMTgRVcC6VJkSJeVFnU34QzIZ6wOspQEYp+VWBfFLOAanNA4ukbPLMbdxJ/qTLe0AJBHYQxd6zXy9r6OkreXdZuVgtr8MnWksh58gAlgApgAJoAJYAKYACbwlxAo9Tr3IrK1+PTJ+bZ/hn1HG3qNjdGthiPKdEryFrv5hfTM4b7pP7KxexF51EkA0n0rDjqmZ3+JCa+T81+7rYcTvm8iUcv0zPVw/KUY/2/35H579ES1Xpr/yh74LZ5eTiijbcmkBCyUY9ReLbHzYw0bORZcucFWlDS9V3MlCADgiD8aaZm+vBj5tyjcn3a10sJtvkYAzXxqE7BXM+Hx0pgFAIBe16z66YM31Inf7Jd9GKeuxOdGSnr+mO6zzYcfyvy4lkc9niWBjd0LLl6fHrgTX0iG3R02/7LoeBgM/jw/ORhK3k0tHNT0V48VN3QL0RBos7gBEH7iXXeH48tolXj8Yixm/B1XaDsXDI5soqlRILt4hpvfF07dYiEQZp5GouXQhS1MKgtWHzSOhPW7W9u/Hpsanc5fFoLjBMguDt/THy9U6647VkABtJRLoTHVuiAfwKlFW/9/PejWp46NLdqKfDnVdcEbnNBlEl29Z440Uc/UxVV/2uBaz2cAMC9TW+WXmSPVR4vPMQFMABPABDABTAATwAT2mMCerXPOxqbOhKjLwaYGvQCI9yK5/tIW0Gikx3AjaKmz/CgcXkNbQ8WfEu6r0cyrlegFBirpzAs5/Vjsu7Cw9ELKhNy0RRaE2pWW6GXXBf8QmX882ce4wp/xvlA0MFga770TVkh1oOG5vFa9NnqHGuV/x+VjvuDyipRGrxDLglC/6NZCUdqcpZStv1MdZVZbUA0P0PULMquFgBh+3MKiV51Lv55hrkOO3Yvpi13lbFYhaO60P7wc9sBYbFkGa9ksIJhRT+BBYnEkF76fACRFEbJUTnohK2UBRVHadSXzZ30ulGJCo2IhnQYHmcbVzxWZdopqVcSX5koMBQqZdFqhD/dVJQyt/e7eD8TnmS3X8VZiLx2hiVARTYTW/pqwfzWdWqP6Djc9ACtI4mtA7e82pVprwTudaUCqFt4r4msJ5ZzZ+NM8Mvg5RQFRLC+2b5RETrK5MwBqPwUkKVuCnH0tyQRFkaDRCY2ja/TMRjO2dcXQtUjKapHE1QYnMisFtTGaOFKtED7DBDABTAATwAQwAUwAE9h7Ansz7n0dOTXiV4Z4SkrEH8e1f0kRTf+Ii3yn9UttN+aatAmhSI4dqlkTynzJoSGcHIvczwIgLP4wjzaNhZTdRsNWpo9WUv+aRhsCA0gfY6yQoA/WrwjN3pmeXaYm76cyQiYVD/rHjD9vVGNIcyeM02VrBcrjgP++IK8r8qogNnSMazRZiDYIQCEnPBPlNbl6IkxanvFrO/oSPWwfCYmDDAUA0UagRcuikFqT5XWKH2cJoCRvzIT+yCrrcvZ5TWxoTqkghu8nFAvBHnchCmb7Ob+MxCDLVq+jttiGhyj5cTCsvUSbujYd1GetLS0QWtFrncv+6Yd62iCE2spYyDrHqdR9PQSQHwcjMusaowBk3RNU+vrU/B8lFvWrsSHRbkVjRwWAdUFc1RaXopls2AJkSX/VF9r5ESJ9YyakLe1GY+VqWEjYUAC90ys8RZ99Ul6X84LgTrisT2an7miuh3YYrldWk0dVJ8yXPPU6GPhZDyjL+i7ZoAn7CaINiCntZe+sIEilQV2V7ppD+eFirMA5R0lgRrVG3PykmmGtFLRAkJW0RyYEN87DJ5GY/qnkbCT4GPIT9e/Fo5cDZClbTHKtrvJZr4PrEBcvzwtFMaV+YnNrZwDUqItdi4V/0zK4IAbvJagxJwuBgRMaRtfomQBUJbZsa9MHhq5FsI5BGL/uj2vQlPVc0R+byy8TRwJgLXJqv9X+z3TTxmFBTAATwAQwAUwAE8AEMIF3I7AnG2fF3PUTXtAWQJu4riyMkOTIgrbxbjnmleAETVggdYjzl7c7frHgPFJ6M7Od8dz/vwOjNrqLZo4wTC/ruZ3Jq7ml7znmAEUfsjG9DHcpurKhZq7ztBYxecgTFHPBsRorIElzl6LS24R/UBsht9LO2xnpgYfRgxzxRp/McV3alGEHN/dUil5gCLTAkmDOhleeBljtFWV4gJ/Tdh5eeeDjj1AEhARJ20a9YVGKfmNDLytaCOZcVHoRdB7QVbF+tNVtPnPDyZAQQIIe9KPdmEs/KeJleymqh7H1MrZx/5K+1+6bJd+gpnwf4w5JqppbuuK0dREQQrKL4c4uoN1l9f2cLQTVS9P7CKLD5ryaKG7O+yrobNjPeeWB391PEb285+qSvhWzquZTt7zufgo9Thh0+0KZzA2n7SjLjzv5IZb/PorEnga4IzZuzOkcZdnxQDGCfCZ4jmOHeOcYxw46A/GyvpXwJZ7pIMkumjnKOS8vSc/C/rMsaSHZs4GwkFeFBecBArZTtjFf4JwN7mM9oRXkFWMU0U7bRn1LOVXNJeZO2CiSoHps7JDTH6/fcNhQQLrrZtoh0cFwF+Z8g5A44l5II+ypWx6uhyRIijnCcifmEm+lpWtO2gKZicDSK1X6NeDshbDHObdcF0s+dcNt6yLILsY26HQeJWEH63sgNWF/bukbG9lKkL2s+6qfJwl6rAStlONoP+cO1n3W7RzjbP3OQDlqI6r5GoBS4rqThkXjV2IBZw+Ave6FZK6eYSkutL913Gdr1+y5lVHVXOq6m+vn+HGe62fd11N1yUbhpLCnB7kTdyH8vw98XBcgjnoWlnP5F2H/KAUIm+d2CpF9tuAZpMl2kj5k48Z90VdVUeqHeQNnCOjOcC4Q1bZ0luJ+56Dmb4MsdyGo7wRu4ISG0Rl5Zm1iyyahTGcgZMb94We5TMSvZ7o/kskJYf8EAy20Uy8Uhr4nRX2jekpZ/gRHQ4KZmNMQGJSC2vzSPNDQkd6E3V2k7bK2F3fZTHyACWACmAAmgAlgApgAJrBnBD5RVfXdBs4fbmjlz3nH4GRM1re30naeslDeJyuBox+uzduw7N9Tnf2zInSGc0F++0tVtxERFt1VAsmLnexLn/Sg4dnQrsaClWECmAAmgAlgApgAJoAJYAKYQJnA3qxzLqt/nwdi5PJsyraAvtiJfmrmig0WcvIW+x2/T4t3FDfaGAn//mYEcJb9zTIMm4sJYAKYACaACWACmAAm8Pcm8PGOe9fT0UciKH9MaC0dT4qgy8Uf+3tnGLYeE8AEMAFMABPABDABTAATwAQwAUxgWwQ+3nFvK++/7WNf+Rmr1fq51XrYHSGmwo/nuJp3frfF6kMSVuLT3wTRtklKfPrL6eJ2zB+SgdgWQwLyv2fnnkjKs8Wp70ICnvU1ZIQvYgKYACaACWACmAAmgAlgArtN4GN+v3e3WWF9mAAmgAlgApgAJoAJYAKYACaACWACfz8CH+98798vL7DFmAAmgAlgApgAJoAJYAKYACaACWACu0/gYxv3Cjcd3Z998sknLQP/0r5Iu/vE/rM0Zp/MTh6zthybFfc83XLy5rTjYEvL8chOonoemfl6wNrSN/PnTkK/e5js49kprrNl/1RyV1cvb5v/++bw7iQ/Wg3r6dA/XH1tLcM3cdW0G5n8Xlz9vUS6G7Q206EIoR8c3S1tpx5tJrWn98RHWv1JT+9u/bljm5XnoemTLseXjtnfzHTIyZtTw1RL97dJM4m/4HoTdv4FVuxWFHL658VkzafjPwjIxeS9jM0c72v7bDgk71Z6P0g977mdysZvzjgOtrSdiX0YdOT4T5Mup8NxPvRemm3lz8gs6tnaZ18CAJqDszv1+bt1yD+MzDOzYo/GvcKi0953eGD4y+EBm33gzHxy05pC+PnUwMG2Tz755JNP27q/cM3+WwEAKE9mXFyftcXax0/HmvY4+sS0q8sssX+L60r65+lTx6wIBTsw8MXAADtgt/V1WocXm4awi+kk+72eL6y7qNBcFWE77Xcf1j56bC4ECumZY9a+7xq6Ggd433mOen/fcyIHvdNj9CaG7+zWtvm/bw7ojfNvu63srLCzBH9QoVYXhz/vPPVw08qreYNbGeelSba9+QBYclMC78XV30ukm2LYhZuQdv7gYt5f5QkAoIa8UyPULqRlV1QU0rMTAeVMMPyDXTH9AARhOz3F7d+V+HaqpM7O3a2vtjTKrC3eMqChgCIsHnfNQ5Zprb69e5DfHU4X5zthb6u27qM8rmunts9Nvn+qk3Isvt4GnaogJHva6zq4jbBIdPtGNhmBfM9z6gkzH1p0WfOmNUGTunYkBnt479estVg5Nwdnd+rz5jrkO0pUs4H2LFv3ZtxbkIXCcDC5FH0QXXoya3s6xV+MobGsyY8+sRA8b0cjHot9+m7QexQdwn5f8ME02z7sv+vnSJOQ73BZfDQ/80t6E6ua0C3Hb84s/nuXusXF+CBzwu/7qhta7N67S0u/Li3FlxLJ1ML4x7EfVxNQNxexWGmmr28/prE5ps3vKsKj+J5N4EPrfqavh9qqf7CnNmye/KbvtlqZwzbauumzmGw89vt2ahHj0cXfgUbT2LDg+yIg/x5LrjUdeUGMPdqNx1PNFIHdiqvpxFULbg8LAOBlLPrcSncAcMjrG6rWhB7I72XlWRfXVqd1djZTX22lcov71fm4m22xHDvvmO/wz41TWm37DpDNvHHHcKqTvAWdj+h2uZ3aPjdopRmGpmqeX2xBZgdBajTWGWnmAzVhmjlR4g9joIMiAMFfcu9gWmPbNU8zRpnJvA9H3dsE1mWrScJ3YMPejHstJHeCp/WSA21sv1VOxtO7uv7ThAAaL4NyiTUXAtnQ1MlJ/53Udnqs9erkR9OnvvYvLkv1N/bgvHvQ0b1p93sP4vwwVZL8tejCCaMqqJl839M0WT6MHNqSw+ri1LcRcc/KI306GL3Gb/Goao9t2J18buf8kaD30CbZqsSvTM4/fecnX38LGrvDdFe1bOnquxpbUdl7ibSZhBSE+XP+eNPLguT705O/CO/SAmpGNVUEdimuZig0yGwTCwq/lkMUDTP6gyqqdXZuUl/J6dB/h969D1abj+ZtcUMmbH5B+bd/6j7tOc8Uq9qdQzb3xk3gbGpcbZK1Huam8h/STSX7ZH7+UdM1gqHp2+cGj3jDET+7nbmJHQSpMbbGSHMfqAnTzImSW1OApaUZUQOZHdQ8BlqavdTgqM0G3LncXiewJltNzNyZDere/5bOkvCIP7NpRNINDlV5kAvmquQ2ws597uiGqib9NlKrErts3BGaIiDcx/CXl0qy+cwtD3uAJEiaOcJoz5kge11CiuI+tpdmjtiYDoLosDmvJHKqmov5uB6tULaS1AGbbxkJrtz1cr0U1UGSXTb3jUy+ygp0+GbJP2ZjDtmYAxTV64nm8omrPKN17SFJ0b2e6FtVzSUCEzaqg6L2kfSILyptYXYu5qFJxpesjwoZc42FkFt4U2cEOpXifucgy487+UEbdy6oGSpFL/M0pNy3ooHTLH3As7RREzAvBD1DLDfm5PpZ51VEQFXV1FWeHeKdEzx7iPWEVooBNlai3zvZQd45znNHGds3S3lVzfzIwF63/5KTPUDAVor9saihHEf+6ZzzEAEP8J4JliYhJGnu+2D4upc/ShGtkOz3LZUSsvLAx/dz/DjPHuV9MS2D9BT129hRp/u0mzsA4URY12yUUjUT8fM9kDgRLcaezwTPcbZ+zjnhdo/bSMj4n5XtKqqJfs9SkHQ/yIS/Yal2gjkdlt5mgmdtVDtp+6bsQpVQjWRWQh4bCakht3uI0XzP5v215Hpi2Ddqsw3xzhNuZz8Fu7yJWviqqu41f2S6GYe4j0VwnNxRhruEXFJ9EfaNUKCVYkd5942Mqq4sTLDsqNM5zjJHnAvP6r0xc8vJtENqEPkb3UFSR90VGTHqG0N+5Rxh2VFfWNQMSQd9IyUOuURglIaQcV5w2g6QEBL0+EJmo9GGCnx0tCEtXXFzQ7xznGMH3QvpepNMbJaWfuQ11+VsR9zBV0jTSsTLDSJ/447avDFdTy513c0Nck7khKz7WtmZ85mQl0fCKKXMoD+1IS1ddTME5G4V87rBMXKJG25bOyAPcfy4L4qcPLd0WSs+o6xtyBt+oacrl7jmZo+gMus+zSOFN4qeX0x2fY6oqhHYonBJJQLbygeFJf8oTbZT/I1MXgx7h2iinXbfrdWvqvlnC+4hltOSxv6YUKWluQkGWijuwtySJpuXVqS3SLW0vOAboZlx7fqbsKef5SecziEbMxpApN4s+QcpSDD8OMceosh9NP+9rqDGOr280JeWUrc8tg6CPOJdyuVS15zMPoIc9Kca8rMBrJpPzzl7CdijVykEJCjucqIYzszVa0xQc+mgd4zTkszy32ueXyuAmobaovGukRpVnqhgXuBQTTvGsf1Ofxzhbq7ClMIXbKSFtI2hqpgiKWZcy4KNlfD3HAVp31Pkb6lbPq4L0t8ktIhY0kLQgzx/IYgq9Fxq7gTLjjj5IRt7eqGuSZN+DTh7IOiw8WPOwLKqboSdrQT3TcAzwpCtkOh1B4veqxpW2iWWDUXAKL31cZnUOdJ1Fh7wNdafqiFY1bgg17s6sqcWS8l09NeooOWSc94RGlpIZoTnxwM19tQXVWluEFLjfv8JveGzeR8Ui55hnV8ds/pmKTDBsSPIMWyHmGKZNbLHrPVpsLO+vtIaUM55wsn3M1Q7xd9eUc2cRzXqQjQUkLp8NGiLG119k4JcwZGPnibh4FyRXdOQG+qNBm+sRFEHx6CxqMhWHdUlWY17qFbWe9XLH6GIVoIenSvVZoY1f5WiRp+XlvwjFLBQ3DcLKdTCSEvXPLYOxh1CJbWx0K3c9bIdkLkUDv/otHXZ/Gmtc1tbg6H4tOoR9abGOdsBkjjiS2gV++a1gWaoYTu1Nbf6RvZNYu4cS0JbQEAtcPQSR0HCdsLDH0LEqCPuuUjQf5pj9kHYTjtRD0RVa4KgNITHIXG61Mdr8MN8esFzlICD/uhtH3+I4q7/f1Utda0P/L9Rbz8JLDT/fTD1FpX3wGkbdaixU2FYmayEv3fb9gF4gOXHeG+5k1zO1c07Ko01j1HdWFZWPGhILLr+zM+02gLFCrkWTil8vaPusD5H6lC9YdAhb+goNibQ0PiShZt2Hgz5V/ueFL3EUhaCLToSJA+5g6Lm7bXVe703lmOvPQC1p3twJoXdByj+drFOM4tgi3GvqmYu2yAAaPycV1Up7NwHgIV0R1CFkY950IudXW7U9dxI+XvRAFof9+bvuvlbWtSv5lgIgIVB9YWqpi6hCUM4tFDs0qZ9DATwSCCTz/gPAVAstGVj80unSdjrS6EhjRSccGoj0pVAP7LIdlkf0eeC4yQy6UEud9dJAECeiKJBo7nZaNzb3sy4Nxe84NeiVlVxjm1nvMtaD3BjZW6QoM6hoanWa4G2C8HEs8zCOV/NuHcj4eshi13tVwscQenBE1cDWkgV9TaKo7V84hJDHNUII6xRz9lwcdx7yLf0Jo+87BpHtBoMyFEye7xRMZfP5xKXWQIy3l9XpLf5XDrAtZc6+kKAbbfp49JcxEmSznBOVV/Mse2U+0ExH6IniOK41yylqhqeKI9780vnKKI/gIZSqqoKAVtr47hXVV/Nsa2Ubdw79zSXe+AmIcOf8wWf5aRbHCS1pyrlfNYOjMho/ZvTYSmvqhsrC6Mk7J9DPcuNlP8QZL4p9shzt7gSySqNfwV/Uw75mD+A+selqhM1RWruNg87yg9HMnOXUT5ojQ1BTCCnrf1l/Ecg82MKXdyQwhMU7NH6pijthO2K7vz51PcMcajopagsl8f/Wkch8AzFkFv2MpB0/4o01dpQHSGKghya07vp0i2ePOAtjXjKYkY2L3vpLk/RpW/7F0RVfRt2kiV/EOb8Wl2Ru+skO7SKQivK/D7SeVezLeamSA6FQr9c8LQXFaKNhLerMu41cIyNhO9A6RGbqkq3ebLHq/Uz8ksXaGJoQVJVKeQkSX5BG4cXFdaNe+tomIMtpx/l1l0n0W7jzwWWpHziGxr2cO5v5lJvctETJByteXioqtLCCFF8DriRCFxZQnreLPAEoacdpXeMtF3RH37lo6f5OZ2DFPTf0i7mlzwdJQ4PnESrM6z1pfJP/TaCMKjbUSUM6UG3L5TJSwtcK2Eb9/ofrORRCdUHbNVJUQ3A6o/bytXOFRYSvJYqU1ev1ogMI2mP/mQtn/D1EvXPGlCrYVA00DO+HUZqWHnml87R5AhyA+RVv3rodnZO6740VWG+WeBaKU9cK5Fvlry9kDodRc6KKrQyxtzCkDbuRY+0qivAfPQ0RU1oRXtDK8LFdqrCKXqagOOohkc/rZ/E31rJb6CnG54eSF1IoOuGlbYeRP+/pgiYprcmLtWo/KpaS2Qw7jUEq5oUZCNXr8FSZfomBW3ZSxk1cw0VV3W7IAUnSNSFQDCN29xK3BuZQD9BX9CrK1VN+tzXV7TWxLBGrY6lqvVRVbXOzur66k3YSVJu/WHfmyDfXirsZs6DHKCmC2FYQGrzsa4tNnF14zJVgaFupHy9kDyr1Uva5drWoTr5VZBVo3qjxhurotAypVKZNzYWtbLVZzVJrm7OnvpsrYTzASpAhjV/tRLV0OeRZxL8ba351coapxdY40KHOJCDvnAyk7rm8aeNa7DUjwzsD+hVeeoSAw/5td7R1rWBaTtV7VSN3Iwa2eI4TetsoIqFgNy1jPQ2n38Rdh+A5Nhc6lUu/1aKnqVhh9bO1vZP6sa9hn6IKuoOPhBLZeJ+73WppqWu84Gkl4alWhRNKfGlVq+SPyaVCSruC0OlmrAirh810VGpqXlM68ZqxYaJbWbcq6pqjaPuuD4365CbOnCpi2XSpFanTjXpPJjyr/a96hRJYXcXpC9pndJqyIbeWGNB8WRv1jlrM9Lyw6mBY32dh6ek0bn5sS2WPZrMYTdc/oxogwCQnKufAIVs9FFCAUrsl6BYANSIm2vYMwaOLoRPaFGTVm3CWBLfNOgEIBmKpBUAD9I0tJJWCJR0ombtoiy+lpWXkcDNuLhO8ldnHY1LONZi4YdZYKFomiA+t1otIJtMVJYVGZgNiKG5zJuU/4jJKspCYvYrbV+rLzj/cl5fjSbeCybaWYcexEK5xuzSnVC8uFINdg86bT20+6qfrV6g9Xs4strNDekQ+pgOKb6MXu20XfCiBwEAkCQJZBm9sq/EF38W+o67ad0iyHq+Lq07gm1UOxrk04N2GuSyhq+QtbZRHQSEhG2UpS2w7XNKmzfg2C4grSH1wsNwYh/LHUCREoft3evJxJ9AuBdMELx7qB7opikt5aASW7wj2SfcxRX1pcv1f18ImQLBnvd7DhFQI9N30u/sIaAFglai8TVUAzKaRkhoLmShhvu7wRtJLgDwW3DxT8ZxEj2RMf39BfzNOcAhn/eQZlo7aQWyZLAgl/Zc4jX6kCDbFFkyXPeIWKGFfyR/0Um/DIV/A+D3YPA57RjVF5xDxumg/wwGfzfEAK37UAzEEc7eLueyBkaUgymP/VP3yamrHt0JyWN26nUs/Ef5vn5gZPNbWZJFYRWZT0743B0AFHLyupx5pq3yOuDxjRIAyOFfIko/X9xciuRd/Urkl7AM5NjNYK7f7erQ9RPcRXd3dSHSLps5Rsk4OXovBo5xNvReE7QfppVkPKFko79ElEGXa19Jasu/zYEVngtKa7f7Ry+rL4QpUM4fPEw74gxbiVqHzMs5RRIyiLvF5v2GRSa0Oxz9IHY/ji6uxcJPsulIBL3rqcRjMsvpHEin74S21RC0WttBTivFKKwFvU2CIjrkmRwEsXvR+hxVxMwqsA55/eM0hC0QgJZjHrQKACEl2hre+zIFW6l2bHRBktYAMHf1Kq7i4nd+cSjg1ys9aLMfhvFHWkqrhEyLxs4iNaw8lXjojtg36tAbP6LfxRGJ4P3Sm/VbVZi6sfBTjXU76zlpl+5HEoblsypdxUMlHrkvMSMccggLbWMIYTmx5XrHNlLLo3aWY2BuDb2/Y1hpN8ZWjnSz9FaCGZXfyt3aI0OwpgXZyNVr9VXOmitoFXmTo1K7QHL9fWBNaxdM6vyKgj+Ci08p10m9BQbgkNs7aN28Ri3FUtX6VNQZHT2Lx9cpRm/ACaavQxGelRzPSFy7VtOFMC0ghsE3d/XGMlWtpCCJq8Da3tgUV4RKya+CbNiHqYTY9KixsdhUvPZmqTnrHbaTioyaM8OavzYQMPL5Lpd7EKDuqyabvhenJlCB3aTQtfUO80do5tycrwcYZVA2sSxYexh9gziaocHzFNrDZuvaoLl2qpGbQSNbl3DUUBAdNNkKYRfPH4YKtDL7CNhKckMMXDPqktQqMEqmJrHPzg8xdL8vcHrTwcUhF39Ait3TK04xttzmGNT6O5VYzHoFFYnGo+Y6KlXhNi8gJUHTxJYEtvV3B/W5WYccGDpwrTVNGW/QedgG/2KKSI5lgKS1UDUmNOWNKERD565GzTudECOBpREACtnYtxzTn4488W06PthWXLCNtAIgy1lJAaIgKgBA8nMD75d/NWMx8wAAIABJREFUn5++Ekm8yrf9l5Kp2R+/OjpFWkU1j3zP3fmkBaxDoh0qSnX/grT3M/BRMvT1QOhbij0bWLisDxWqlLwWkRWFtH+wcx7kcwRBACUPQG0JqzZb7zpWaag7RPtaRd1oJJ9d/HpOvym+EIHVQZYyjdhnJdZFMQtAda+6dFcPooiiqIjBi64E6j4pMtS36VGE+7Oz9zKAaIOraQDsSDgrijJB7StjhHRP4wabEAAFbPFqaLWM9rq1Ji+JopKN+Y+LqPtbkPNdaAcL8YUAKFfjPsymKS2OTLTEvRbFdaKvo5axnuyq/7PPBbmLc2hvaUrPM3KPg0crAoAoCGB/4xbQRmSqtKFDZD9QAJBfCJJF2/6kTqDq9K/gb85B/mMxcC0uWtraCoJQAAZvRReysZ/8wWdKWyuUkjnweZXphocdlBVI4itFAaIIrNays5CU1YJcDZg9x9G11TpnYwyJ+2Gpd4rXHo4U7xZyqCBV/wxtPub2dHGTh7uDo073mUn3URIQDs/ErOM43fmzw33C4xlniIKIjO4pb1QFqX1WkEYFJPMCWEf0LVVQTMSBRlRbOUZBFF8BRZx1HV9EKmSZ7qKhIgoioGwVzdXpMDxGDrM1WKSXGAxowxpZfClaB3kWjSdF4YVMcXXRUfwZfv7MAPWEcx13e87yNJIkuFEWXAzH13n7w3jbaQ/1P+HIc6/3VTx3zFMs9mvJ+ctzCbmlDeZTxptzElSHFTwWxQKo2Q34pSAU7G79mcjzjAD6vKOayheCCCmquggjBFuBRSWu9IaVuatXYK7GIsvEcKTq/bKCAtZz1RU6yp8ti8a2IjWsPFdj4jpBaQ99kHkW0vo5QDUbqKtXjSvMSoq0I6qDguuiaPjMsU4UPcsQxXUg3nS7HqJ7StZKl4tqo3DjFQtQzCvtRvHilSyqkLdOr2H5NVNqCLaQNi7IBUNXN1bdXEEzDrv5VZM6vxJIeYFqBarcalsougsoT80KfiUgOiq1PrVXG84+hajMFJ1eyReA9gCqQczwglZLb11AqsM2mfXlMlUdVpGVbZlXDNtEvVEdS/VxY2NRfXe7x4Y1f10fydjnSdcJx/RXi6E/Pb4DyeBTxnUJ9dIMe0r1RlmMazBoAfly1AUFWCDqbm1ZGxSaa6cauTU2svWG1p6XKhZ0FTlDXdNeK6ydbe2HWokwCKlfsjCur+jZ66HEVZbNxuLtfLCuw2jWK6hr1GojaKqjUh2kuQKydWKrdTZ/XMK+pWuZdcjROG6rjuI2jS91HvSKuLFXVgCMeQL1Gaz6+01741b90HrF2z+3kNx5d/e/phcfe20j2qNrIx0QFm8VZzZ1GUVRyjeMQlX6Q4Z35YhndDK0Rnt+Tc0di7n+yxEyG/pqGMix4MoNbTKkQRv9TSRqmZ65Ho6/FOP/7Z7cb4+erhXSQUK7/8mSp6pjZ7xdpmHtX6uv6owcPukoZvMOssuCnve7rwe1IXRJ62/TjpNJT1oz9b5r8WnpeqmdLJ/v7gHscPlD3uohReSGSQzNpLSgAFDqEJuoAQBkhAzY79aG1oogiHA/rfU6ZeG5aD1A1fcGf/ObkDGKADUwpi5dDPAX8DfjsB6bGp3OXxaC4wTILg7fm21Mg/AT77o7HF9G6/zjF2Mx9I24TX9am6o9udhUbIc3s+KqXMogpELvIDpqhwnGNrfa/Mui42Ew+PP85GAoeTe1MEJw11Pi8Ujw9uL8SXs4HU9c3jSzEEbzX3OO0TY4Hbxqq2gpJOPNOEklQHNHBUEQlO6TGpeCkBEAPdSNQhYE4SWkD9TyAoCaCGaOuYO/LC5eddkf+BNPvLQFECMO9qI3/EjIPYH8NTf5cDF8P23LSfYzevDs4hlufl84dYuFQJh5Gokam4bKYB1W5UVGbKVorVsvvxDEdprSVuKIzzNyx3BxOUlZW3Ngi+Jmrl7Wpo39RVA99heFFwpBUzW9nSaKRkVlM5EiaRP/KXdDAQAbe/qouWKydgRt54LBkbqL2z5trLS3ULFVeo3L72ZKTcAaBTFwdSOxvb1mWOfXRVlNqe7Wrpz2smz7Yuyx6DlNgeex+Gt6eKi64d0qjm0VkLKy6kQ17+paW7+NPNaj21a9UbZQPzBqLOpEtntaX/PXhjfzeTjodnUEg7eTnsGgaPPYSt2erQudcQaR9kFGuRVLrrO2Vjn2OE2MBEqLCraqDVDe1VXktWkAABhxq29kr+ze9BYAwDiZDYZteoEeczE/BkJPFOplwjri3iqRm+oq3myqo2KgaPMCshuJNYi09tLmrqU/7qwNgc7MHLgiuRPjDToPFYU7OWro8pl4496sc34djz+vthrVaZWnUNV3SsfEQRqtVi2k4lWf+lWeJgSKbpwMBECRsmgVFtVFEcBKoUkqJfuqYRnX81R6DS3OtZeW65Ziq/sLqQ7U1ZPXzJZgKunHYt+FhaUXUibkpi2yIDQsGdpHoUmWgoRmX01/1WabCjXeIA8xeqeN2k8BScqWCk/2tSQTVMPQrUYB/JyigCiu1lzMPkuKJNNXft6s3yQpilAyfzYkrSbozk+sFAVWtbn5Kh1owk1E80V1v6ZSiuYYJXG1fpVlraqs8FymDtAaQEkQZIrWOt4FNMVH7ddGC1UBjMlUCVQfovn2Qj3bagHUkvwF/M04rKZTa1Tf4ZoOf615ipBOg4PF1XC1t0zOXouShab2Q0hRyBfL04CvRTSDUTfRaKLD/HJxTqLUB5Jjd6KyzcFXPUhC04OGNq9ls4BgRj2BB4nFkVz4fgIUstk1SB5xeq8vLV2xCw/DaUB17wcSWiSi/xTxtaRZja6jUZm5ZVs7hoWiPgfSqlijpDTFV4rRPILSnabAooXEBNWlDVDXReG1lerSHuC8FsR1qnt/XcuuZF/LsIN1fx9MPPRSf4Rjem1AcI5BJfavqRjBsQTjGKWF0PRsto/Tv39eyKTTCn24r05XyUz9ryKu5uB+qvR1weJNtAabLtbb2qoKWl80XvXUqaJma7AVWQDMXL1a5rPi6wzFa3+Gwn9YHaOl7p9+deuiUaWxmUgNK090UZbKrUohK2WRu1Wp3sZhdlVU2unytK1ZB6WosZ2iWhXx5btW5oaVtqnRTaXXpPyaKTUEazEpyBYTVzdS3lRBMwq45TXDOr86lPZoT0jV9JHALtvTyvl/ZKVbk67jLtcVyRGK+bRVTroZWzgP+iDqlm1HdYJQwdy5q0P08ppSM+NRq9zobHv1Rp2GxsaiTmBbp4Y1f40Gc5+HNvdxWrwzN/Vzjh0vPphoqtCZZBB9dtbzX/Hp465Txz0x0h+7rq1M3LI2aLKdauTW2Mg29OVqSGz3xCSZ21PTxbuOydE7i6GklUeb8tT+TCuTWrGas2Y6KjUBmiogu5LY2mjrzrZ0LZMOubkDlyPYtvGlzgM0q8zLqps+aNob92bcu5acv50sGauk74QTJOc4hpa1LvKd1i8XDVrj3smpMQoUsqGLrulf4uk/0sl7M66v4/ZzrppuQkFbGJGNhJ/IoNXmOm7TFuxxpAWI9+ciWQDWc+VeLSDbUIdMe9kMyEp1XU+0oVfgFFFIrcnyOmCcLlsrUB4H/PcFeV2RV4Xa3quc+tf04p9oNTV9jLFCgj5IAdBGoOWCiigIWVmWIecaJUFBiFyZT75WFDkrvsxWOrsGZgP50WS3tW/6t4pUiZjpX2rUxa7FwnqQghi8l6DGnLUduoawvQ6uQ1y8PC8U57oRB4IgYTaN1i4W5PTz0kgdsu4JKn19av6PUte9ZrF3g+ZtXqBHHMx6ePa/Sw82NOXMlzz1Ohj4GS0SR2tDSxPyTaWUYB2DMH7dH9fW/ikNSxmRykJGeAFofYq3ejZsXRBWrfSB+uleYzJmKT3GD5PpxasR/UlEbt0oK/8C/mYcCKINiCntTfWsIEilBgktrZClLEINiXYrqtIUANYFcXXLRUdK8nZE7HW5egE45HL1COH7+oIGJX03LB5wufR3ic1wVV2vsqHqKiDYEQ4mYwnNDbL3p6YfUdNXSstui4ImNi/7px/qfgsh1BYwr0X9V5J6lrRACD+nSAvBjfPwSSSmLxbNRoKPIT/hIADBnXBZn8xO3dH9EIBCveubOAZq/3KS/iUzYniUhY8D/vJ3I1DcFDfCKI9m5//QDFHy1bVQOeU1NJoBuyoIhW5a7ya9zAiAovdrygQhY6HRd0drfmLwx0VBz/3WFtiKXtbVfgQ3yoFlwTqCqhDmKwf9PJ5j+FJ9i8SEp+hLb8rruvqwpH01GHzS5tDeSStd0qtEkeiqXlWhD9ZE4WXpqVOVtAnYKonqQzNXr5bpGeY6hPgTrZFZT89cnMuOBqaHars7JkWjWk3luJlIDStPyDrHqdT9sF7Dyo+DEZl1jZUAVyJo4kgRFu+mqAmX3QIAYSUtYvqJ9vF5Wcy+LQWHsAXIkt7+QTs/QqRvzIS0N95RrjRUTuil/WzRd0sq6v8aVtq1QlVFwDy9VXGZlN9apZUzQ7DArCAbuXo1loreHdZgNUW1Wlv1sVGdX30f9Lrch8TgDzPljy2j3Gmm4Ndo2fTk+bzrW7HvpNs15nKNcTSQRL1tNXOeOmUmBaQqH2sDmGd9rZzRmYWiutDjyPK9ZiCb1BtV3lhW13jQ2FgAOXKys+3gZKzU9ykHMk1yWQIY1vyV25u3s/SE2y6HwspwaXcJ0EShA8A4g+T4t+4QdLgnXPyYi7cRij4rsHVt0FQ7BRq5GTSy1Ql/52PjZG6uttEHKMcYq9yfDpKcvbYd0BSZVSabxNJMRwWA6pqnmQKyk8RWjGzCUbd2LZMOuUmlXZ3A7Rpf6TzsgH8l1TWQm/dGo82u3vnaq7Bn0GYb5Pgxnhu0sWPeoKBvG7myMEKSIwv6dnP10eRXopfdbC9JQABbSbrfibYALQmhDTDRdiwU3UNT7QR5qPIhHPT5kCtOG9pUCRIdDKPNV8AObu5ZLnGZo9vRR4/YCY/20iAk+/3oywRvlnyD6JM0xD7GHULbbaKN449oV0jaNurVP8pSijy39D3HHKDoQzamF30PZkXbQDifDPA9KFKyh597hr4bsXBW+55BK0H1ok+klPdzNjTb7DtGmbs+N9p7nWJPeP23yt9ZKdpS9XUflrtQ/I7R0jUnbYHMuH9h2WDf7PyzBc8gTbaT9CEbN+6LvlLVt4nAEFWEfMVNt1Kc/qmP/Er4Es+gjznRzFHOeXlJehb0DpJgH+u9ncq9TQW/YUkLyX4TLm6hrBmVF8JFmetLkpRYQBuLk+yFuaVXUuKGl90HyEFvUPsaDdpkvJckSIo5yvLngv9/e2cD2kaSL/haTvsogfdogedoQQJu40Da5wFLlyxpkbzDLRxwCw+4heewhM1L5ASycoZL5ISbkWd4l5U9d1k5c8zaWUisDJecPFyClCNBCiRYOTb7pF0ySDky5w6XIW1IoMUb8yQYgxos6KNaH9ZHy5YdJ7GTEiHqj6r/x68+3KWu+lch0mDyiovpIMgOE9PrcBwmYRvrVXeD0Pb0ipfvgrCL916JI1eliBft40LSB1j+GEdDwjRc3lpANa4yfKWoxjtVA3orj700JNlzwcVClP9SSWuS+T/3fVwHIA675x5lcoK6D1Ar455HIYczj/yOAwWPOMeACbbQ/MXavZHeNH9kuzaHzMI5hmwhyG7WdcnHkwQ9qG6FIoXcXWhbL+5MSBLmHPsJ2Eoxg17/aQbuqdjUqsgEBYMlDzvcJ1yOfpYZUOtP4ZYY8Q6oeyD1s+ygN6IGAX4R9Xv6KEAwrqlg8mUyeIIhdDR/IbSYk+KXXQwB6EH/wksUkn3NhjL8gidf8swhlkN7I3nmUqVYl5VpNG1+7OcOMWhTpQGWLez4klnw9jJsvwPth9RX3rpAjZivbqbF9bCuy+oWEkh4LnnNzXWpRXmI5Y7NxF8mgxccJgJQ/R7//ReaFUNC+4GxaP+0Ht6fQMWwMMWb2gqVmXNdVje5WH0ROsPSJEF1Meygg22D5GF3sBDrsuxUDQ0tsOW0xWDOpVDklbFPX1xiYSvjvlLTaUihUyzTo25O1st5blb0vpmQ40AxCLaiLPoOs6XNEpA26abL1Ip6VO7MjLcXEodUhnccBKS5E27XsLoR1JXSRh5l+1YXfd2QuaRqWU16u0rxrlcjLhJSA75IaYOcYg7NvqjcpVxPZjJJdSsaqtjxalf1snp0gDaz6WGYPo7r4VwXi911VQpFq2n8rdSPbUmpUtd5orpb2FaksI9Rr8Nf2Meo7N36HSaK50yYBt1utBUNU+rtkdD4FEe1QKKD4c/43Ich0e3wxzJof69BimilmQEv6oMy8ZljDFWoeH0OH0pQ9cnFvEyr2jlc+3PxL8gwaptoS4xuCLscM49QFq1Ou0pOVRPQ8hdZvKZrUdFqv8V+o5VxTYXQjiOVH02whX2MahuyZlWvxlIpWbOhPY/4htAuX+wJrz9a0VgKGSua6t/ueNf+LjwP+QZQv+e+jlqERp9fqRcF5V7wDTEUSVJdJqaX94RVRVr2SI3++tTYmanur3JJfyGuW+kREbY51N3dNCvPs7pHCK0Gkqksxz8v1Pwt1iz6clWvb1MVQFBE+sPFKMTocjOQNfuN2g65pKMGTv0fCyUXv8AQkPKgbrzqs1Z1Z0Jza3/OMvErbqYVoA4NxerX6vkrxWjV+dL9TGiIdqlxoUtXNBrdi2Jlc/nmC3+ztAtICruLkwOL5U4wF9QueqPeAO1xVf936m/VlaqeW90f2dzTkO+U+gR4yh8SxIVvHSaIHk1DTzOLYV+hY/GFFzNCyIf20qMdlxbEmixXvPx+ALsd6tOvhpv/+59KD6WXIupDWLWRmnUAhTSnPeqWpWXIFQeaTwWoiNk2QHTznqlg+UGhlEuKbPigUtMhazaQkjj1W9PZkL/A87Q/8lxCjW4NTlXmtYr6Wv15TvuBXLsCV3atGsbXPIigeM7aDw9a/Kva7JP4ZQfaElP9C/Ui6nd0AdjtmktU/9Vb0nzkq6JUOPmVoiiljnFHfwtfW8xfJEDfnBh11b6k28GG71KzdzBRbNpbJiBMMuYIvxg/t6X3VG/ZWKzuTRO46zQc1welOa60FO1NK/xw5S8HbNQ0/WDRf+jDZYA93yKBbGz8eJS9Vgh9B8CrsPOIM/uFGFk/+O0Wlb12tmfTliNR5+Oq2CivLXSTAvLC5FEfdTPoqNsWZJOC3mVy4arTJ/uCpwt/rOXU16zlmiUm+Msrh9+lce9Qdz416Qhx876q+Ivv0J4PU/WOeXh4M/Oc31yhrh975s3pfU3Ju9Ts1/QaZ39vCOAK/N4U5es7kt/kUrzX1/jhStgweP6HiwZ7vg4B8epEmOTUeO9qqj10JwlBYTu6dbK9q1v73bOf5QJT9bOM35ZBK8L8eZ90zLerB71Ajk5fSFsKwfMRORTjUDvy7dviulP0PIkuHnTiQe+7L46d8fCw28a9777csAWYACaACWACmAAmgAnsVAI6fS5djqgG0vdmQ8ucq3+dGIfv1hFo+jLqJwOur2KlcCNv2R6D6WxgZnj3z2nSZaRyYBlZCFxN0CPOD/dl79L87L0skIXpS6JteDPxzN9y7cPq3i6Bf/WP//iPb1fjlrQ9mf6HL+aFf8nn/1mIv/qItX283h7nW9LwRjLtUrPfCAssdDcSkFNXv/xvtx4LUmb51+1/b6oJ3LsbPcI2vwaBV9HJ31+JLb5K//PKR//27/ft2Kfo13Bxx2QV5v/Tf735V0H8lyz4N7/97etGSt8xbmFD3goBg+m3hr9Nf/mn8P17d+ZvXAv/v87/ePW/8Ht28uIESPX8h38PxMxH1Ed/91YYVSr5u5aP/vVOhlNpa+Nj3b7f/tvl//n19Hwkeic0f+2/x/L904EzBzViOTWW8V7dyf75Pzv+YfJGwvjZrOffoTi0+PPOCOykh4dds773nZUWVowJYAKYACaACWACmAAmgAlgApgAJrCbCeB5zru59LDtmAAmgAlgApgAJoAJYAKYACaACWACGxHA496NCK13P5u4OmH/WK8fCa+XanvuyYkbgVTd5nKvL1u8Nz3OtevpiURpf9fXl7kmQRbmv7J36g2j99auvdWjZ+HJ31mNevPkj1tQ+zbLt8q89MPpsSNG/ZFpjZ2uqxKWTrbOOR27Omn/WG84GS3J+sC+V1KBs07npzbn1cJexPXuZxNXx22UvvN8eU/y+jRv/srGdr55G7AGTAATwAQwAUwAE8AEdi2BD2zcm09NHjGi/ZC250MwJ3yut7R6ApoY/azDGXgmb2y7LIS/sFtZm42321izmbFN/qVhLqrPM97/xsI5QNrx1TsNo7ef937GURut3MneHm2n7IFXNWjfePk20AvIHo/7qLHGmvVOt86ZZE94nB+vJ/u9vifHvnAGjL7gNY95pdGvSgRzYpzb924xVNu5FLDtbR+928jgbTdVjp3vNLLTjX4Y2HZ9WCAmgAlgApgAJoAJYALbTuADG/fqjLTJbF4/HktejN7bhge87A/RxPJ2lhfscMxcoGYHx6IbiJVjZ23jS/bg/UgkHIrEkiEHWHy5nZaUZTX0cZsYlhW96QNopE0mmnrrgQ9q9Dbk2cj/3ca56Ec6Fv2h4Q8xjXxt5vrmAaai9ySqwwhaWM8ZplqFLNyLNfu+vTrn9p/lq+1sMZoOMrTxjcYrqXQfGveZzF3U7ogmuP30sURMABPABDABTAATeB8IfGDjXkDy30bmjq0X0Dx7e2LshvC6T+V5Yfa0b9tD8sMD424qNH4xsZ55+VT0gUQdYcnSS06q321/E2+rGvu4PQy3q32VOKwjDx7yhMI+9q3Hp63S25hnI8t3FudGVtZel2MXx2Yfv4F3lZsHCEBGWgba21ouBcbPh8U3Mfm/Fkgz59V2tnK+cNBzQGvcm08nvpsO/9SMzHXTVLtPnwhGvuXJdXPgm5gAJoAJYAKYACaACexkAjtl3Jv6xm7l7M4Ru/Wgdez7wluWdOz3dutRu9NhszCj8+ocVPH2uO2oze6w245Yxu8VRn/Z1J9GbUdtTofdesQ6+sdE6YFaFr4ft6PETvtRi/noZCoPhNvqUsbjxaWM9UrTD6bdF8Jiwu/81Dn9F1Rw4t0JO4s0Wo/YJ+4V95ZLP5x0shYr7xw9OTpbPwiVhfnzYzM/CMGzdvvZeeSMLMyftSEHP7VZWefkw/o96tLRr6zteuPoXSF83tr+kcF8MpxeEeZ/Z2n/yGg5Hys5Rdj6zOL3wfg6A18dYWgF8Su+aHnWbhvHlx6R5WfzY5zV9qnTxlqd35RZVVbRbOxrJ8LOWy3cePkBOvtDoJDRzlvNB+2B/1vnY0lGPUMAgPRweuwTs/E3eoNpdL70UK7JtiRGjH5ha9cbLMfH7AfbDb8xtDOjs7fnJ0/azHv1+o8611ZjZlOzx63WT5x2zmI9GSj+YiEL85/ZLKzNOTI6+lVobfSiWRDLidnPrEa9ZfpZUfkG5VtIlU/H/jBq41D9tB4dDTypLpJ0bHbErP91u+3sbOHnDzktpldQzvRfAhOfdJods7HFCr31dQYAsCLMf+G00gb9b9qtv68trG3iXOJd/tZAJAu3xq17f6U3OSdvFQBnxZ/UKikL4T+MWvZZx9XrGgWaTUyPWK28E1UnflYA2cTVsYkbQvKay+6YqJu5oNFmAdBu4PKPgVHOalNbt/X3CdTEahpd2aNGDfBVbPrsdGIlm7hot386GqhcAf5TeOKz6ehSdPJT+2hp3a/8KjZ53Npp1OuNlvG7xSa8cYPKi9Gv1AaFei2z5XwMVRQNyEB+Mus0GfQf28dGrJ1Gg97Qbvta7Vxq7UzHvhk1G/S270q9wlJ4grfaRkadn1g6Kdr1mGY75NSNcVSnv0HdT/rh7NjR4nJx8da4ldKbvwiHf++07LNMPgHg4YQVtRSn7YjZ9kUUOVbtvvxkfuKTdv2+8WIIgE0ZX1kK+BgTwAQwAUwAE8AEMIF3SEDZGZ/4Jf9CDpkiXWZhhye+qiiPPHSHu3jxum9OVJRfQg7S5HuqWizM+MIZRVEyNx1kmyvys3pRCvJ7SMdN9XrURZEcyoU+meAJz8IqOgoNQ+JYpHBVQ6miRE4QcCik2qIogp9tZQoaM2EHSTpCGUV5PsO2Uq47SIuiKJFjBBwOFY7X/n/uZ1pKpiq5hdM02T8nqbcz9910KzvzfC1t8ejlDNtCMUOemceZzB0XCU38aW/waUa6xkHSFVGNRyljbgqafKm67BUXpJsOtN1jQVp0seiLoiircW8XyV1RDXk5xxGU5xG6iZjv9yLmiiJd58kuT/wXRVFyC2dook81+2WQJymHClxRlBeXXMiAKh8r1NcwXA05Wgj+2ovcqqL8vODugtSZOEqtybZSzGrIQUDu20Xpl1zueci1H5KDM8mXmdwvUuQUDdsKBZqLnKCoYVQsyuqi7xA0TS0iy09TRI9/sQBNKJdF44J46jO1MH5BVd9M+SpSaJgi+2YKcKVrPLnfE18Drcr5eY4niEJtRDVwkGQuvlBv5CIn+JlCzazSW7YTpVq8YIIHvAs/5xQlt/gtR7Rwc4VKrooo/FdVV7fMWcmFhiBxotAoGiKKn6Nhty9ZQJrymva4IqiSoHLkT6vNVKtAF6cYckgtHSUXmZpB2Vfj3v2QvVxoDRXOKEpGq802aODSXD9RFLIa919cQIIaVsiGTimojhGOO1VmFE4y13nY5i50GooizfRC6kRIyinKqhQcJuEh/2LjBlUhLhf/3EQc9hUbYS7iPhXKNe4Qqgr9IgsJPljoZmrsXI17OiB3rXDvxUwvQX+eVJW+8PdA6rRKYzXp64bMpUKVUxanGHjYr54gX8hebyixmPzW7UspuajP/1jNXVEbq91XpCtcsVvegvEVOPAhJoAJYAKYACaACWAC74rATnnfy5zxsOqsPZIkQTabAQD8kpWyorCE3o6Qw15XGwBXGyNWAAAgAElEQVT5THYlu/hUfdOy3+0dIADIhm6E5R6ebVV/OiB5Z48cvhHKgmz0ajDT43K2FX5SILizrs66+a4aSqt/gRDuhuJ7WG4/ukoctHSuJOI/AuFWME7wrr6mJ8XKsfnvRfOAvTBLkOhxckQ8eLtu5eBzYTFPsJ/53AcIqJpqPu5zdBFQB0ELsbay7iMjAURx3fW65GAw+Sjo7SfFu9NjXCd1ZFx9iQPAD6HwUifXpxpCmk1tUuxRjRnZyK0oOMIxaKUrtByk5UQsLgPx1kwUcq7+osvUkIcvgq3m1fjMQFLIqVaWM8HMsgQA0GRbJwASbTTZAmEHzx+EMjSa9hCwheT6THBZQm+75Fj4tmTq55BlOpoxEcKjeFqOBr6XLMMuuqbEmyuIZspXfuAbv02OX3LThUp7xEK9ioaeVJvfarf3gOht9V39cjT0MJ0Kh9HCcTkWzbJcMwChgWqFAEC610KDTHqDdd1I+1Y5lyxvjIj5lKd+CkXVV+Kpm2EhHQk/RG1TvBc39ltggwLNZrJZURDRi27Ife421ZRISa36rdlmGzXwXDYjS8IiqgM6xnOOrZJUc9LYqZqE659CwkhCAHQk12MGy1I230SDkmOB7wTziKtQTwBk3b8zwfXtWSt0hs5LaBr2+p+VVCwhm0yFtRuUqcso/SjUtOp6AYZuG3+INp2e8XYB2Of1HFCTtJJGkFXbVX2O0pXtNb4kFX9jApgAJoAJYAKYACbwpgms9xz6pnVXyJeF29PTtxYBYYBLKQAs6NYRl7uDGzvYGRxwuE6OuQ6TgLC7h6ftI3T7d3bXMbd7yETkRVEExq5ygBdI7TGClCjK4uJzYOxHbz0LH2J//ZpeLaWl9IVvSRTldNQ3IqIxWz6b60ACxecCoJwbhghek5QWxRWC2lMaJ+tI414gPhcBqIqinH4mZDs4uzohWXq2mO2y891IhigIYF9FRGIdhEDOrMgAlJ1bU1U+Ig44fPMOX1YI/3F8fGradd4iXOehiMgEzzrjKKuchXWRcfJoRC2L086RABKVzdIdNMwDURDBHvuayySNaG74RF62pvJAB2R1zaQm28qEtceljOi6Tg9ADh0si+IKEK+6nHfRmZw20iQArxBwc1sJeFlQcwXRTPnGb4ek7nFe/UGkKD6fkVWLytoAILgBFpwNxVZ4y92Y4YSb+mMo/MzjeRnLHHFXlX1FngaHEAAZbGqtaQnX5jivg6jbzrdNh+4K3v3Z0BLn7g0Eb0Xlfkv0sZE7heqTpiJmxG25MWbZF+KGXO7PXGxb40qb12qz+ZR2A89T/El+9qSVesg5R1zuUzy9TkyydZxqgLvJy/KGDSotilmC2lNeGAvpLgosRZvpENRK3oQhOgBLZY1S53MAwrWfyTYUoAPZJwH/tzFRZzDkBSEP6jvKKhlNwkQtFH8wAUwAE8AEMAFMABPYQQR2xrj3rz778YQ7teBuA+C2M/BYBdTC+B6J9rvB4HezY73ziZvJuX6Cu5wUR8LB64HZ45ZQKhafavwYjR4Bq5dc1mDXVFqTBgDY5vTNeyqfBcNX6hI1c6Fy0LIKQB34RWER7HOpY0tZEES4j1aHRlnhmWjcT5UfnNH4Z8NPviSfoPkvQ8aMmb0XF/I8etumo12Xg67C6/EGcgy9E8FLVbFtY3XWNsi6ucv1bDeXv5gaMqeDwf6KrM8mAWj82L1RQRSG5RXi6g/T4lK2VEDorvxcEAFlrxvLEv129qwndE/IPIT8ty7ybiB0O8VkJMvJuqT1SrbvyqY5ayLSmewD9HQ4nDqUEQ+6plvFwNlQ9Fkm3sq5Sq1QS5F7QWCjt4KByxPW72NziZBrz7qOrd9mK7JSw8HFI67gjUDgktNyxxd/WNVIKxKWDjWdKt3c4ndTDapBg90ue6DF1gMn7kWzQzyxkog+ktnfbSZA20p0fGAiNyUEhwiQDthuTTeFYruMb0oZToQJYAKYACaACWACmMA2ENgR85zTTxMiaTLXPBAvp9OAMA24/Xfigf5M6HYc5NPpZUgecnguLyxctAh3QylAde4DUloqPVrK4isJUBQF0XXxmToNsgElbaXViY0UBZYEsSS9cBO9UhbFtVBJ1Vk0zkiKIrJSuhSEJp+W0sjG6pRp4VmW2k+r7yglQchStDo1Un0JRu3rXEss52QADURpqLF2o3SUT0ycnS8pQ/NLyb0EIAyEDsC9FAVEcamUsv5bR1F7gbQkVmRHiah9FPhJENSwTPWZtnZFk+2mRbVSVIss/lQ9r5OkjDpJXKpxAoCmCgI0Ub5Qr+Iv1Yts9PtIlrFrzP0mOHuvHP3TeJTgWAKNG4X5iem0mevYtKNbzrA5zusiMvEc/Sw08Y1k6afJfjsLorPno4a+wgIFoKkom07LBM2d8IUehdwwGn1UVyhlx3RabVa9qNHAdXL6VRa2sa4vg/G7HupJKLpOrV7XqbL+LRxs3KCQannxx9r62USH0Lw5pGNqgn7qdzlGnSdnwO+iwVM1fcu6opZSyWXKfLBuckSjTG8MZiOF+DomgAlgApgAJoAJYALbQmBHjHsJgoTpVPIVmkucelaKdfzIN3G38JQMIVQnMC9HfKUtfPQQwr0UqSO4IR4+DBcDw6bDwQeQH7YTgOCOOY0Pp8e/Lw1a83JplFLkpq0UALSeNi2hFagA0P1200po+g+lULqqDNMnPPUq6P+uIDmb1RwNQqgHWakwHoesY4hK3g4VHMs+CIazrHOw+tk0vyg8B3ThFW9eEH6C9H41wYogLBnp/RWve6W0VEwoBvh24yeB6mdqZLb8OBT8seTuSipwU7R8yqNX1t12rk0MTM2WRrBy3btNwjbAwgd+XylydeHtMjXoYvMh34VouihVRiQqfSxCLX5VMqy+s3amyXbtdpNH0ML3E6krk/PqOnDkuwwAwdp7YeyyL6bOxJZXMkWrmykIAJooX4Lt52AiGi/EZ749PnGPmrioOXWZ4AY48Egw9qPBoelTO/0sljHx1WVfcrUxz1KK2u/t57w+oi6nvSMVW7GgcTvBOXtB7LGB6yn+BKNZoMlvJ4KFuOI6PYRGdYEs+tUgU2xhlR5pttlGDVwMXggIhbeOLXrYYjS2Nq6Q6ztVaULFMYQAZKVCCO6Ky9WHGzYoyLqGqdTl8dknpQG/LIMt2VOtuOIsn5oc9md6xpxDvHPIybblxFdqfdcZiY+A8CiG+ik5Lf1cMqAiKzokCAMQk+q2UmlBkEovchu6v3njU3+wGPc5w6V+vUY/PsUEMAFMABPABDABTOAtEXhXAbWq9P4S9/dRsIWkexy+iy66heK+jEiP/dwhhht0OAZYdsgfzyhKZsHby7D9DscQx/a55lKF+LmZ5GUX18PxQzzXw7ouJ4txlpVc8pqb6yIJkjIdYrljM/FfpIUrXr4Lwi7eeyUuaSpVlFzMy7QSZDfruoYitr4Ie7huVchhlj8dVEME55JXXEwHQXaYmF6H4zAJ21jvnZr4tC/mBimilWYGvAsZFJE3eJpj+3jHIMf2OvyxmsSKgoI5095CVFVRjetbiNj82EtDkj0XXCzEzkWxlBm4X413rbyY6yfJ/rliwNY1oFLkgoM7xLD9vGOQ53o418WFsr7c0zl3L022kvQBhhvyRl4qL6J+Tx8FWhnXVCiJtEgLU7ypreAd57qcLFJOzLh6aJIk6W6G7XfPodDH1T6uGVDJ8M8L3zpoHTQN+xdeKtJ9v6Mbwi7HzCNUSlpsy1KkhW8dJghNQ77Q08xi2FfI6AsvZoSQb9gEdbTjkupXJj5zjKFIgupi2D6HL6aWvxTxDhTcZPljHA0J0/AM8kSrIHJPQ75TLKkj2VP+kIASNVG+UuRLnjnEcv0sO+CZS5UqXdn88kEm5DhQDEuuKIu+w6y/FMq7Tu8az3v/FPT0kmAP67mezPySDJ5TzTsXKkaoLgmvqKuvwfmKl98PYLfDdw01Mk1EJYXK4gWGK4VizoVd9IlIZRDr+gJdvOJgDrP8kIPvY/kvI4V6mLzEkgRJ9/D+RFlw4aC+zaJg7FoNXAqdYpke3jHEc72c52ahEawBRI2u8qNV7sjTzzkaQqrPjTqEyvSoHYTcXQTRxnBnQn+74+U6AHHYPfcok3se8g1QgGDc19UKVdegasQouRehz3lTG0l20KbDnGNKNU3THiG0VuiZZPAMS+oo7vPIi1+q7cwkgxccJgJQ/R7//ReoW/ySISpXIrTQ7vvI/8x9D7MHQpJmhzy+YyZIMq4rSaHoi8s3X+gqMwvnGLJF7fEu+XiSoAfVzrbS/UIXQTCuqSDKsynjV5XkFEN2uEJ10chrQeFzTAATwAQwAUwAE8AE3iSBXymK8pZG2FjNNhAQZ1lzsC8eP1e54ngb5GIRmAAmsDsJpMMn3cLJoLewR7cszn5qniAC0nW+8VqI3ekothoTwAQwAUwAE8AEMIHXILAj5jm/hv0fVtbs3cnA6vjsaTzo/bDKHXuLCTQk8Ff/RIrmukuDXEiZOwxoAjz+YAKYACaACWACmAAmgAlUEMDj3goYO/sw/WDC9R3pv+014WfanV1S2DpM4O0R0EGQXYvsB5bmZ+5C53Ax2NjbMwNrwgQwAUwAE8AEMAFMYGcTwPOcd3b5rFknCw9Shh6GrFzIt3YXH2ECmMCHSSCb+OO4716GICDIZ7OykT3tQ+uE8QcTwAQwAUwAE8AEMAFMoIIAHvdWwMCHmAAmgAlgApgAJoAJYAKYACaACWAC7x0BPM/5vStS7BAmgAlgApgAJoAJYAKYACaACWACmEAFgV047s2m5r92mg16+40GO1JWuIcP3zSB9IPpca5dv288Udr5801r1JKfjl2dtH+sN5yMat0tXZOF+a/snXrD6L3SlffnO5u4Om6j9J3nE7vQp11t/C7kjU3GBDABTAATwAQwAUzgwyNQNe5NP5wdd5gNv/6V0WS1HrVaGXPnxxbnF2FB3klgCJPjnMtCvCOTlgK2ve2jd3fVkHtpfpQ1W1ir7ROrhbGO/imxjdaTvZ6JQc340kLAYTEftNo+sVkZi/Xk7HZqLRT+WlmQ7AmP8+ONqgSkHV85TW9ygXT29mg7ZQ+82siS7b9PMCfGuX3bL7d5ia/h+zsyPp+aPGI0f7EbfylovlhwSkwAE8AEMAFMABPABDABRKBq3Ev2uP3nOQoQ7IWFhfsLC4lk8oYt/Sen/as3/2iYjkV/2Orw+nXyNlMNKuW3GE0HGdr4ZkIqVypqxrAm02TFzOFAPLYQubMQu8ounudd32/jyLeBEfmskLcFEwuRO5GFh9PM43H+bHSrBVyhohJRk2WRF6P3hAoRb/AQGmmTiaZa3qCKHSt6C75nf4gmlt+dQzojbTKb972rn9A0HH/HQDQswpcwAUwAE8AEMAFMABN4TwhUjXvrfYLdLv4gEBNxsf7edl6RYxfHZh9vbTD2Onmb8aFafivnCwc9BzYz7s2m5v8wn9p4GnC1omZMazLNHnbcYSqkhfs5W0c29iDeZNamkmluFqojuWM8XXi5Chm2x5hNxJqAsL7CakTNlUX29sTYjbc0ZQEe8oTCPnYHjaTW57nhXTn9cHb2XnrDdACATfueF2ZP+2JNyW5G/xbSkPy3kbljmrMVNuH4FhRrZ3n3QLTtwlcxAUwAE8AEMAFMABN4DwhsMO4FICfnATAQ+pKv4t0JO2uzO+zWI/YJ9ECcDp+1GH9ttHxqtx0xtxvbzY7p8ozWusRISuobu5WzO0fs1oPWse9FALKJq2MTN4TkNZfdMRGtef+zHB5jrfYRp5OzmPk1ySVz6vNmY187rUftTt5q4cbDPwGwnJgdMet/Y599EBj/pLPdcfl/fWFt/7XBenzMfrDd8Bu98eDo/FJBnhgYsVp5p9NhNTPOwI9ynW3p2DejZoPe9l0WgHS0oRyQfjjpPGpzHnfaWXP7PnuIZGqn12YT0wVdvNXCzwoaEOodiU0ebdcbzHaHzXqw3bi30/5VcdQg/xgY5aw2h9N+1GL9fd3L+VaG2V8CBkAuDyCsH7fX+w7E78csRn07NzrKmdsNev1ey/iD0m8TS+EJ3mLh7M7jo+7vUmvS144otq9iRCHnAGEgquYYy6kb41aj3vIN+lEl/XB27KhRf2RaBI301pR1ZVmsaa05Sj+Ydl8Iiwm/81Pn9F+KN6WH02OfmI2/0RtMo/M/FS/W1dV09Gt7p7599Lvo9ElrJz0WywOQTc0et1o/cdo5i/VkoHYwvZyY/Qw5NP1MlVlbxFWmrcs2OvGp1fap0/mJ1cpPhIuVsyo7WI5Nj9isn9idn9osB82jt4rDR/lVbPK4tdOo1xst43eLF+taHJCfzDpNBv3H9rERa6fRoDe0275OFN/Gy8L8ZzYr7xx12Cw0RX8hmY+om+Jswvf1mkbRDVmYPz8284MQPGu3n50v/Kymabz8bH6MQzRsrNX5TblrqaDxcMLK2pwjTtsRs+2LaMFn8fa47SjqpmxHLOP3kGf1bUS4ra4JP15aE67leCNQ8g+zzoMGPV0AqNcbO21fzYf/NG4/onYp7ESs1I9p1CvNfqMOSL0LFT7jQ0wAE8AEMAFMABPABDCBTRJQaj4pr0lHOO4UruakO25TC+2OZoqpBD/byvieorNM2EGSjlBGUX6e41oodyyHrv684OmG1IkIyqCZWFHil/wLalrpMgs7PPFVRVmNe/dD9rJU1FL5JQV9116gC7kFdxvkrqmWrKJj/nrhuCqvdJ0nuzzxX9QMZ2iibw4JjbkpSLuuLCSFkOdcKLcacrQQ/LUXuVVFkUKuDkh/nlR1Ls5MIYcUJRcaIojhCDKzxrbVuKejbEYDOT+HHCTlihaABPlWwnFTlVrh1+IUQw4VdUWmZpJ1ELQdueMgWhwh5J2Se+xjCIK/LimKNNdPFOmtxv0XFyr01B1mgjxB1tujKFq+K9JML6ROhKScoqy+mBsgYc8MKozVpO8ANJ2Lqx4qmWtcsRzrtBUvSCHXfko1tTrFatLXDZlLavkqyuIUAw/71ZNGeqvKWqksC1RkkDgRqVaAziInCDgUKpiqVBb9zwvuLkidiaNEmnUVJYbMmWD86eLcae/Cai5ygqKG1VJbXfQdgqapxVp1T32mFsYvoMsaRVyVupGPSd8BgrlYkJxLfmkiDvhQ9aj8rC76ewj6TKEZKUrC67r8QqkqLCk4TMJD/oIUjRanKIsXTPCAd+HnnKLkFi+ykOCDaiVNXjDBnkIpKMnPTfCAbxFp35zvVZyrmliFG8/9TIup0Jk0NH417u0iuStqz/ByjiMoz6NiSZYF5aI+/2P1rAz/l5CDLEkWZnzhTKM2EhqGxLFinWngeENQqLp2eSJiJpfLxKdYApo8919Iv+QyKT/XCos2N6xXWv1PJRANF8oe4wNMABPABDABTAATwAQwgU0T0Hzfm41dsNk+sZopA/WZaL8Tm+krTtwU7obie1hOfXlIHLR0riTiPxbH2fDX6ivEVtZ93CLdDsdl0Cgxc8bDqmlJkgTZbGb9gTrp8B6jUBJoNLaCzPL6ybORW1FwhGPQAktoOUjLiVi88BpLR7GDrGk/77/AF951GkgK6gAgOdYEpGVJtYJ2f86rrkKCNMhZqfgGbF0LNeQ8jcVWKJNJ1UOYzG2y8LR2nng2k82KgriC7OQ+d9e+DQbrOAKAKhgecI/1guitSBbkshlZEhbRq1gd4znHrmOv+F0gfnB8YqB+Jm5D3yFhJCEAOsrW0wl+lrJ5AP4aDPxosh9nCiTXUZe9O249Ym4/OC4NzMwOqq8N10ldfUtDb3WCLZ8Vi6yV5UwwoxZ9o7oKAOzsdTBdtOuSj83HwrclUz+H2OloxkQIj+LrzNLdqIiR+Ro+/hAMPqPtA4VX5dDksNM/BoM/VPv6JBh4TDmPF5oRAAdcnl5jIUVJIMn1mMGyWlgANGxx0EC1QgAg3cvQeUlCryjT8UeCscukNjlAm2jwLJmSAZA353vBGI2mUe1HzZmG8T+EwkudXJ9ac0izqU2KPaptSrDP6zmgSmoljSArZQHIZ7Ir2cWnauHsd3tRbd+wjTRwvGCiBij1RouBaiMgJJgBltZBw16KbIFEN8d2AEntqRrXK7ABHA0XamjhU0wAE8AEMAFMABPABDCBTRComnhaykewX0WC/UD8o9V8Xsrp18ZIkijK6ahvREQjxnw210HVj3yoNgquiOIygNqJZeH29PStRUAY4FIKAEtJaYPv5cTs1Ew8qzfAXHLDMLl5UXwJZHHaORJA4rJZuoOGNQtrIQDVV5AvhU8+Hf3GF3wqG1qglMiAvaXrzX2vyfk1RNPCS9NG0bxifS0nZsRtuTFm2Rfihlzuz1xsW3WCZhwBBNVmBA9EMU/xJ/nZk1bqIecccblP8XSDuEryD5OjYTpwy1NcdlvpVzO+o0JHbmWfC5LOSLdV5tc+Jvr9C/0A5NPR85ypJxV+6N14rFwvqaS3/s7rXtEBNI0fgI0rtg6AtCiuAPGqy3kXZZHTRnrdgfwGRVxjeslHWRRFYDSWJZOUUSeKogwOrdUQ+bkgAoraUxKho+iO0rHGdxMtTldexwCgDs2EL37yMtBBVLGXN+d7KX/xe61p1NzY6BTRkMXgWWcceS9noUZEueyTgP/bmKgzGPKCkAfoBwPC7h6eto/Q7d/ZXcfc7iETATZuI9qO11hYAar6DkQNvsgNArU0m6pXAAHX+Gi4oJEKX8IEMAFMABPABDABTAATaJKA5jNXMS91wu++Zpk+N+186C2PlGCb0zfvqVi4CUBpJVu9So3Ef/XZjyfcqQV3GwC3nYHH9Zkqr6QDJ7nZPaHkNRYCYfJxOFJ5s8GxoXcieIlpcHO9y8I3vPOmLfbIa4IgdjYaLa38XC+P5r1ulm0NRB+I7hMUeBaNvaJtlStdC1m63AsCG70VDFyesH4fm0uEXOVhTElmE47IAKAhNTUcXDziCt4IBC45LXd88YcaI1v5ybTzq4zn1gxXHlOVFAEANuc7er5fG4ZViGlwqCO5z1ydf5oIPPAw/ZvJ2EDem7isUVfLw781fZA5HQz2r52vd1RfxE38UrCewMp7GrZV3q443lyLIy29JvlaNLHCMi3Z6IMU0e8vvVbejO8V+l/rUIderbsuB12tDcSsRMcHJnJTQnCIAOmA7da0mo7gLifFkXDwemD2uCWUisUvMhu1kXUcb6C6ucvN1at6WRou7NCWU287voIJYAKYACaACWACmMDOI6A5z7lkJjSNTzmNf/WPXS3OLTRSFFgSxHWn/6aXRLmVpkmgmTj9NCGSJnPdGK+ksvo7v5hKyfRBc7MPfDqK2gukJbEUfKla2gZnspBKgY+L05M3SLv+7RbOd4GVro05R5zOi5J9Purtrs2QTadlguZO+EKPQm4YjT6qNrkpR2RxKQP3UUadnH6VhW2s68tg/K6HehKK1kVCyv5l0nlRHp/3aw56Adic78QeI5EXxTotVU6+isUK4Z2KV1GlWXuRWJX03Z9o1tVas1opqkUWf6qdZ1ubrHS+QRGXktV8Q4qigCSVpza8EtGr3ep5FXAfTQEhWYW3Rsza6eZaHAD0qWn3R7GJEefoiDtK+qKX1Zn/m/R9Tf3rHcG9FAXWrWlLqeQyZT64NicFKcyn08uQPOTwXF5YuGgR7oZS+Y3biLbjr2d/U/VKU4WGC5rp8EVMABPABDABTAATwAQwgaYIrDvuBYDo83n7QezC+Ly6Vo7ut5tWQtN/KEVVletGwLIQuJmkhp0WHdBMTBAkTKfQjOV8NvWsvDoSTQTOSIVFtpV2ozW9wuMkWmD4SmgwnK3MS9gGWPjA7yvvvFJnYKX06mNItBrR+E8GYEUQl3Klu5XyS9fW/3426zwvmo+7nINO5yBHA0ldx1uVJ/ntRLAwttHpITSqK2grFTXhyFIw+NBgH+YIIAYvBITCC8AWPWxB0Co/2Yfj3JlFyyCTexyLPVD//aXmt4tGvleKqTg+wtvIVOBSOK0qzaxoUV5OzF4vR5aWU9+H4iRnP1L9C4bOSHwEhEcxZI2cln6uHvxXKCwdViIqXdvoG+ogSGvUrcp8mnW1MgE6hha+n0hdmZxfKvpbX/0rs2gVceX9BscHnM4uIXS7sOGwnLoZEvc7nYX1q+Uc3U7XATH41WR589t1LGnQ4sqyag6ysfOueWh3DTv5QSfPEPKSWiib9L1GqPYphHqQldZfRN9t59rEwNSsgFbCo6nOhXnpawIJwgDEpLoFWloQpEIrWI74LhbDU+shhHspUrdBGwGggeNrmrZy1FS9KguuBKLhApAfjpuNneMPtZpbWQg+wAQwAUwAE8AEMAFMABPQJFAZCSuXmPMMmAgdoHpdnouRYnjlpz6mBaCXJ/MoOuyLsIfrJgmSMh1m+dNBFOsVxXMmTINu9zEH38NwZ4KLpZCrGol/ifv7KNhC0j0O30UX3UJxXyJFyUssSZB0D+9PVFqkSDddplZItJm4MzPeXkgccs39ORGccphaAD3gnYkhG6vzSgtTvKmNIDtMTC/nupzMZZJzJxhCR/OfzyyIKBB1/LKDhtA07F94qbyI+h1dAHa75hIZRZhz7CdgK8UMev2nGbiHdc+j6MJr8u8ngxccaLFgv8d//0lDObmkvxCJp0QctjmCL6v8WrziYA6z/JCD72N5lUCVIgShzhFFUe44CEhzJ9yuYZ49zLquJFXSUugUy/TwjiGe6+U8N4vhkcv64ueqpqUjo/Z7URjtyo+W79J9H9cBiMPuuUeZnBDy9lOglXHPo+LNPPI7DhSqAecYMMEWmr+4UBW0+mXI3cswvRw/yHO9DDvoCQqlalGhN3Pfw+yBkKTZIY/vmAmSjOtKUmyst0FZ/G3hipffD2C3w3ctXmWGouRiXqaVILtZ17U/L3zroHXFopfu+x3dEHY5Zh6hHHV1VSomHvLNPSo2BSUTnznGUCRBdTFsn8MXq2sw9cIAAAOfSURBVFKVexrynWJJHcme8oeEnGYRl11fh60iRrwDLDvgcPSz7KA3gipt3eflgm+IoUiS6jIxvbwn/OLFHe9aYT0P+QYoQDDu68mcZosTQp5eEuxhPdeTmUwyeIYldRT3eeTFqiKF3aaqt6cEc0GtZpvwXWrYNKr8eDE3SBGtNDPg/R/fNzBeUXJP59y9NNlK0gcYbsgbqW5HipJZOMeQLWr5XvLxJEEP+uNLC95ehu13OIY4ts81l8qhuO21bURCdaYLwi7eeyWOoqJrOt4AlPC0BPDygiTF5xBAkj0zs/BSil/xsHsA2esJIr319apx/6OsAVnQcEHJxTw0SXsKkfOrSOITTAATwAQwAUwAE8AEMIENCPxKUZTS6Gyr38sBGzVNP1j0H9qqhPcsXzY2fjzKXvOrkX8BeBV2HnFmvxAjJ7RW1m7K97tOw3F9UJrj1luXvSmJODEmUEVAuOr0yb7g6UJEZzn1NWu5ZokJfuZ9r3IfrONVxY9PMAFMABPABDABTAATeE8JbDDPuWmvy7FMm87x/iYUr06ESa446AUA7KE7SQh01VN8t+x+PoenOW4ZHs64AQE5On0hbRkoDHrR3G56v7rd1wbZdv/tD9bx3V902ANMABPABDABTAATwASaIbBd495mdH0waXT6XDpdXquavjcbWuZc/VWTRz8YFtjR3UZAl5HSpZ9WZCFwNUGPON/7l72okD5Yx3dbDcX2YgKYACaACWACmAAmsAUCrz95UZi/MC/IknhpnFqdcPfg0R2gTs34xHH7JyGSgPJKVm6xTNzz89WxprZQVOBVdPJqQl4Bs59NwvNebhs3xdmKNTjP+0gAcr4rKc9XdjtBQCBns4DqD0ZPmd5HV6t9+mAdr8aAzzABTAATwAQwAUwAE3hfCWzH+t73lQ32CxPABDABTAATwAQwAUwAE8AEMAFMYPcTwPOcd38ZYg8wAUwAE8AEMAFMABPABDABTAATwAQaE8Dj3sZs8B1MABPABDABTAATwAQwAUwAE8AEMIHdTwCPe3d/GWIPMAFMABPABDABTAATwAQwAUwAE8AEGhPA497GbPAdTAATwAQwAUwAE8AEMAFMABPABDCB3U8Aj3t3fxliDzABTAATwAQwAUwAE8AEMAFMABPABBoTwOPexmzwHUwAE8AEMAFMABPABDABTAATwAQwgd1PAI97d38ZYg8wAUwAE8AEMAFMABPABDABTAATwAQaE/j/H/8XRi6l78YAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# k medoids procedure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "#function to compute k medoids\n",
    "def kmedoids(X, k, starting_medoids=None, max_steps=np.inf):\n",
    "    \n",
    "    #condition for setting the initial values of medoids\n",
    "    if starting_medoids is None:\n",
    "        medoids = initialise_medoids(X,2, k)\n",
    "    else:\n",
    "        medoids = starting_medoids\n",
    "    \n",
    "    #setting the converged variable initially to false\n",
    "    converged = False\n",
    "    labels = np.zeros(len(X))\n",
    "    i = 1\n",
    "    \n",
    "    #loop the till the condition of convergence is not met\n",
    "    while (not converged) and (i <= max_steps):\n",
    "        old_medoids = medoids.copy()  #copying old medoids\n",
    "        \n",
    "        S = compute_distance(X, medoids)  #computing distance \n",
    "        \n",
    "        labels = assign_labels(S)  #assigning labels\n",
    "        \n",
    "        medoids = update_medoids(X, medoids)   #updating medoids\n",
    "        \n",
    "        converged = has_converged(old_medoids, medoids)  #getting the value of converged\n",
    "        i += 1\n",
    "    return (medoids,labels)\n",
    "\n",
    "#getting the results\n",
    "results = kmedoids(X, 3)\n",
    "final_medoids = results[0]\n",
    "data['clusters'] = results[1]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[5.1, 3.8, 1.9, 0.4],\n",
       "        [5.1, 2.5, 3. , 1.1],\n",
       "        [5.6, 2.9, 3.6, 1.3]]),\n",
       " array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "        0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2,\n",
       "        2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "        2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "        2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "        2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]))"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting final results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fa57c70b2d0>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "centers, labels = kmedoids(X, 3)\n",
    "legends = ['cluster1','cluster2','cluster3']\n",
    "\n",
    "#plotting the results\n",
    "for i in range(3):\n",
    "    plt.scatter(X[:, 0], X[:, 1], c=labels,label = legends[i],\n",
    "            s=50, cmap='viridis');\n",
    "plt.scatter(centers[:,0], centers[:,1], marker='*', c='g',label = 'Centroids', s=150)\n"
   ]
  }
 ],
 "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": "3.8.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}