KNN_FROM_SCRATCH.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "    \n",
    "# <center>$Machine   Learning   From   Scratch$</center>\n",
    "# <center><span style='background:yellow'> KNN (K-Vizinhos-Mais-Próximos)</span></center>\n",
    "<center>$Rafael Pavan$</center>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "    \n",
    "## 1. Introdução\n",
    "\n",
    "Este notebook irá realizar a formulação matemática do algoritmo KNN, visando classificar automaticamente a espécie de uma flor (Setoda ou Virginica) com base na medida de comprimento e largura de suas pétalas. O algoritmo realiza a classificação de uma amostra com base nas $K$ amostras mais próximas a ela. A proximidade é calculada a partir de uma métrica de distância, geralmente a Euclidiana."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import rcParams\n",
    "rcParams['font.family'] = 'sans-serif'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "    \n",
    "## 2. Importando e Pré-Visualizando os Dados\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "nbpresent": {
     "id": "b274d631-4f72-4234-89ec-444cfe36a1ac"
    }
   },
   "outputs": [],
   "source": [
    "df1 = pd.read_csv('dados.csv', sep=',', index_col=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "nbpresent": {
     "id": "e6fc786d-681a-4f29-9932-e46534412e22"
    }
   },
   "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>largura_petala</th>\n",
       "      <th>comprimento_petala</th>\n",
       "      <th>classe</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.4</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.7</td>\n",
       "      <td>4.4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.5</td>\n",
       "      <td>4.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   largura_petala  comprimento_petala  classe\n",
       "0             4.9                 3.1       0\n",
       "1             4.4                 3.0       0\n",
       "2             5.7                 4.4       0\n",
       "3             5.5                 4.2       0\n",
       "4             4.9                 3.1       0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(df1.classe)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "nbpresent": {
     "id": "66b4b9cc-ebb3-4d13-af8a-63d12cb23725"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X: [[4.9 3.1]\n",
      " [4.4 3. ]\n",
      " [5.7 4.4]\n",
      " [5.5 4.2]\n",
      " [4.9 3.1]]\n",
      "Y: [0 0 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "X = df1.iloc[:, 0:-1].values\n",
    "\n",
    "Y = df1.iloc[:, -1].values #TARGET\n",
    "\n",
    "print('X:', X[0:5,:])\n",
    "\n",
    "print('Y:', Y[0:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "e22583ed-a7a5-4a8f-945f-4342b5ca4523"
    }
   },
   "source": [
    "Agora, vamos criar uma função para plotar os dados."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "nbpresent": {
     "id": "4c0492d9-4630-45c6-acaf-83d4cb4696ed"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def visualizaDados(X,Y, nome_classe0, nome_classe1):\n",
    "\n",
    "    \"\"\"\n",
    "    Função usada para plotar os dados.\n",
    "    \"\"\"\n",
    "\n",
    "    plt.figure(figsize=(16,10))\n",
    "    plt.scatter( X[Y==0,0], X[Y==0,1], label=nome_classe0, marker='o', color='red', s=80) \n",
    "    plt.scatter( X[Y==1,0], X[Y==1,1], label=nome_classe1, marker='+', color='blue', s=80) \n",
    "    plt.xlabel(r'Comprimento da Pétala',fontsize='medium') \n",
    "    plt.ylabel(r'Largura da Pétala',fontsize='medium') \n",
    "    plt.legend()\n",
    "    plt.title('Plot 2D da Base de Dados', fontsize='x-large')\n",
    "    plt.grid()\n",
    "    \n",
    "visualizaDados(X,Y, 'Iris Setosa', 'Iris Versicolour')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "    \n",
    "## 2. Normalização\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "d8183ff0-4a56-4209-bd1e-04379658d23b"
    }
   },
   "source": [
    "<span style='font-family:serif'>\n",
    "Atributos com escalas diferentes podem gerar um $bias$ na classificação. Assim, devem ser normalizados de forma que a média ($\\mu$) seja igual a 0 e desvio padrão ($\\sigma$) igual a 1.\n",
    "    \n",
    "\n",
    "<center>$X$Normalizado = ($X$ - $\\mu$) / $\\sigma$</center>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "nbpresent": {
     "id": "521de916-1c6f-48d5-9109-d13519ca5e81"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def normaliza(X):\n",
    "    \"\"\"\n",
    "    Normaliza os atributos.\n",
    "    \n",
    "    Entrada: X não normalizado.\n",
    "    Saída: X normalizado.\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    m, n = X.shape \n",
    "    \n",
    "    X_norm = np.zeros( (m,n) ) \n",
    "    \n",
    "    mu = 0 \n",
    "    \n",
    "    sigma = 1\n",
    "    \n",
    "    mu = X.mean(axis=0)\n",
    "    \n",
    "    sigma = X.std(axis=0,ddof=1)\n",
    "    \n",
    "    colu, lin = 0, 0\n",
    "    \n",
    "    for colu in range(X.shape[1]):\n",
    "    \n",
    "        for lin in range(X.shape[0]):\n",
    "    \n",
    "            X_norm[lin,colu]=(X[lin,colu]-mu[colu])/(sigma[colu])   \n",
    "    \n",
    "    \n",
    "    return X_norm, mu, sigma\n",
    "\n",
    "X_norm, mu, sigma = normaliza(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "Caso de teste:\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "nbpresent": {
     "id": "ba149ed3-978b-47a5-9d8b-1e7f9cc14efa"
    }
   },
   "outputs": [],
   "source": [
    "x_teste = np.array(([[6.5, 3.5]]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "nbpresent": {
     "id": "0912047e-511e-4265-a675-937f69961287"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualizaDados(X,Y, 'Iris Setosa', 'Iris Versicolour')\n",
    "\n",
    "plt.scatter( x_teste[0,0], x_teste[0,1], marker='s', color='green', s=80)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "52e62aa9-4564-4907-a072-b4900b93aade"
    }
   },
   "source": [
    "<span style='font-family:serif'>\n",
    "Agora, vamos normalizar o caso de teste usando os valores de $\\mu$ e $\\sigma$ já calculados.\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "nbpresent": {
     "id": "13b33947-7b02-4c21-a346-3f170f91b1f7"
    }
   },
   "outputs": [],
   "source": [
    "x_teste_norm = (x_teste-mu) / sigma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "1d821246-7fdb-47f8-afa8-009a642b5d2e"
    }
   },
   "source": [
    "<span style='font-family:serif'>\n",
    "\n",
    "## 3. K-Vizinhos-Mais-Próximos\n",
    "\n",
    "A métrica de distância adotada será a Euclidiana:     $dist(x,y) = \\sqrt{\\sum_{i=1}^{n} (x_i-y_i)^2}$.\n",
    "\n",
    "A equação mostrada acima, também pode ser definida da seguinta forma: $dist(x,y) = \\left\\Vert x-y \\right\\Vert_2$.\n",
    "\n",
    "Nas equações mostradas acima, $x$ e $y$ são vetores que possuem a mesma dimensão ($n$).\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "nbpresent": {
     "id": "3a819928-e38c-4763-8d35-ed33e45ccb0d"
    }
   },
   "outputs": [],
   "source": [
    "def distancia(x, X):\n",
    "    \n",
    "    \"\"\"\n",
    "    Calcula um vetor de distâncias entre a amostra x e todas as amostras da base X.\n",
    "    Entrada: x (teste) e X (atributos da base de dados)\n",
    "    Saídas: D (vetor de distância)\n",
    "    \"\"\"\n",
    "      \n",
    "    m = X.shape[0]\n",
    "    D = np.zeros(m)\n",
    "\n",
    "    \n",
    "    D1 = np.zeros(m)\n",
    "    D2 = np.zeros(X.shape)\n",
    "    Daux=np.zeros(X.shape)\n",
    "    x_r=x.reshape(-1)\n",
    "\n",
    "    for p in range(X.shape[1]):\n",
    "        Daux[:,p] = X[:,p]-x_r[p]\n",
    "    \n",
    "    D2 = np.square(Daux)\n",
    "    D1 = np.sum(D2,axis=1)\n",
    "    D =  np.sqrt(D1)\n",
    "    \n",
    "    \n",
    "    return D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "883d5dc8-9fa8-4346-abf9-6e4ce493047f"
    }
   },
   "source": [
    "<span style='font-family:serif'>\n",
    "Após o cálculo das distâncias, é necessário encontrar os $K$ menores valores de $D$, que correspondem aos vizinhos mais próximos da amostra de teste. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "nbpresent": {
     "id": "62fb5523-b495-4e5e-b880-4e30d2edebbe"
    }
   },
   "outputs": [],
   "source": [
    "def knn(x, X, Y, K):\n",
    "    \n",
    "    \"\"\"\n",
    "    Parâmetros de entrada:\n",
    "        -> x : amostra a ser classificada\n",
    "        -> X : base de dados de treinamento\n",
    "        -> Y : conjunto de rótulos de cada amostra de X\n",
    "        -> K : quantidade de vizinhos mais próximos\n",
    " \n",
    "    Parâmetros de saída:\n",
    "        -> y : predição (0 ou 1) do rótulo da amostra x\n",
    "        -> ind : índice das K amostras mais próximas de x\n",
    "                            encontradas em X (da mais próxima para a menos\n",
    "                            próxima)\n",
    "    \"\"\"\n",
    "    \n",
    "    y = 0 \n",
    "    \n",
    "    ind = np.ones(K, dtype=int) \n",
    "        \n",
    "    dist = distancia(x,X)\n",
    "    \n",
    "    ind = np.argsort(dist)[:K]\n",
    "    \n",
    "    Ysel = Y[ind]\n",
    "    \n",
    "    values, counts = np.unique(Ysel, return_counts=True)\n",
    "    \n",
    "    j = counts.argmax()\n",
    "    \n",
    "    y=values[j]\n",
    "    \n",
    "    return y, ind"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "5bb869a9-a603-4c92-beda-67868d41ca38"
    }
   },
   "source": [
    "<span style='font-family:serif'>\n",
    "Testando o Algoritmo:\n",
    "</span>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "nbpresent": {
     "id": "289c9a1e-0e73-4a75-8959-e84381fb8387"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Segundo o KNN, a amostra de teste foi classificada como:\n",
      "\tClasse 1 ==> Iris Setosa.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "x_teste = np.array(([[6.5, 3.5]]))\n",
    "\n",
    "K = 10\n",
    "\n",
    "x_teste_norm = (x_teste-mu) / sigma\n",
    "\n",
    "y, ind_viz = knn(x_teste_norm, X_norm, Y, K)\n",
    "\n",
    "print('Segundo o KNN, a amostra de teste foi classificada como:')\n",
    "\n",
    "# Imprime a espécie da planta de acordo com o rótulo informado\n",
    "if y == 0:\n",
    "    print('\\tClasse 0 ==> Iris Versicolour.\\n');\n",
    "else:\n",
    "    print('\\tClasse 1 ==> Iris Setosa.\\n');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "ccb95a8b-48e3-4c8e-816b-25030fa2c3c1"
    }
   },
   "source": [
    "<span style='font-family:serif'>\n",
    "Vamos plotar o(s) vizinho(s) mais próximo(s) usado(s) na classificação:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "nbpresent": {
     "id": "8352eb00-4f87-4e04-aec7-b8575c0ddf21"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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O5z3veXznO9/hiCOO4JnPfCa/+MUv6O7u5mtf+xqHH34473vf+/jgBz/IX/3VXwF5SZrbb78dgDlz5vDDH/6Qpz3taTz66KNPquPtb3875557Lr29vYyNjTE0NMSdd97JDTfcwHe/+11SSjzvec/j3HPP5TnPec6Oz33hC1+gv7+fu+66i1/84heceeaZLFiwYI/3Y3Js+8MeWEmSJEmNobcX9rSszKxZudx+Ouuss56UvAKceeaZ3HDDDVx55ZX86Ec/mnaW4Ne//vX867/+K+Pj46xbt46LLroIgO985zvcfffdvPCFL2TevHl86lOf4v7779/xude97nU7fj7ttNO45JJL+Kd/+icOOujJ/Za33norf/ZnfwZAU1MTs2fP5vbbb6erq4vDDz+c1tZWLrjggif1EN9+++1cdNFFNDU10d7ezrnnnsv3v//9Pd6PybHtDxNYSZIkSY1hYABGR4uXGR2Fbdv2u6rDDz982v0LFizg61//OkcddRRLlixh7dq1Tyrzu7/7uxx77LHcdtttfP7zn+fCCy8E8vDd3//936e/v5/+/n7uvvtuPvnJT05b55e//GUuvfRS7rzzTs444wy2b9++x5hLWWJ1d2UOOuggxsfHd7wfnXKfd3c/9pYJrCRJkqTG0NEBzc3FyzQ3Q2dn8TL74f777+fII4/k0ksv5c1vfjM/+MEPpi130UUXcfnll/OMZzyDuXPnAvD85z+fb37zm2zevBmA4eFh7rnnnid9dnx8nAceeIAFCxZwzTXX8Oijj+54VnbCeeedx8c+9jEgT6z061//mgULFrB+/XqGh4f5zW9+Q29vLy960Yt2+dyCBQv43Oc+x9jYGA8//DBf//rXOeusszjmmGO4++67efzxx3nsscf4j//4j/2+V9PxGVhJkiRJjaGrC5YtK15mfDyXK5O+vj7e//73c/DBB9Pa2jptDyzAa1/7Wt7xjnfw0Y9+dMe+pz/96dx4441cdNFFPP744wB0d3dzwgkn7PLZsbEx3vjGN/KrX/2KiODyyy/nqU996i5l/u7v/o6lS5fyyU9+kqamJj72sY/xghe8gIsvvpizzjoLgEsuuWSX518Burq6+Pa3v83pp59ORHDNNdfQ0dEBwIUXXshpp53GM5/5zCd9bqZEKd3EB5r58+enO+64o9phaJK+vj4WLlxY7TBUR2xTmmm2Kc0025Rmmm1q/2zcuLG0tVKvvjpP1DTN5Em0tMCqVTBlHdZaNTg4OO0ztgea6b67iLgzpTR/all7YCVJkiQ1jol1UNesyRM6jY7mYcNjYzl5rfI6qSrOBFaSJElS44jIPazLl8P69XnCps7OPGx4P5fOUfmZwEqSJElqPG1tsGRJtaPQXjKBlSSpngwO5vULBwbybJtdXfmXNEmS6oAJrCRJ9SAl6Ol58jNdy5bB6tX5ma6IakcpSdJ+MYGVJKke9PTkWTVHRnbum1jzr7s7b+tkVk1JUuOaVe0AJEnSfhoczD2v0y0JAXl/d/fOhFaSVBatRSaBOvvss0s+z80338xznvMcTj/9dE4++WT+8R//sWj5vr4+vvWtb5V8/lpmD6wkSbWutzcPGy5m1qxczglLJGmHiWV3+/rKV8fY2BhNTU0lJ5hPPPEES5cu5Xvf+x5z587l8ccf57777iv6mb6+PlpbW/cqSa5V9sBKklTrBgbyM6/FjI7mpSIkSWXX19fHokWLeMMb3sCpp54K7Oyd3bZtGwsWLGDevHmccsopfOMb39jls4ODg2zfvp0jjjgCgEMPPZQTTzwRgIcffphXv/rVnHnmmZx55pl885vf5L777uO6667jQx/6EPPmzeMb3/gG999/P+eddx4veMELOO+88/j5z38OwE033cQpp5zC6aefzoIFCwC47777eNGLXsRzn/tcnvvc5x7wPbn2wEqSVOs6OvKETcWGCDc353UOJUkV8b3vfY8f//jHHHfccbvs/+xnP8v555/PFVdcwdjYGMNTHv/4nd/5HV71qldxzDHHcN555/GKV7yCiy66iFmzZvGOd7yDyy+/nHPOOYef//znnH/++WzcuJFly5bR2trKu971LgBe+cpX8sd//MdccMEF3HTTTbz97W9n/fr1XHXVVXzlK1/hqKOO4tFHHwXgyCOP5Ktf/SrNzc3ce++9XHTRRdxxxx2VuUn7wARWkqRa19WVZxsuZnw8l5OkBjcxbBjgttuevG+mhhOfddZZT0peAc4880ze9KY38cQTT/CHf/iHzJs370llPvGJT/CjH/2Ir33ta3zgAx/gq1/9KjfeeCNf+9rXuPvuu3eU+/Wvf83g4OCTPv/tb3+bL3zhC4yOjrJkyRLe8573APDCF76Qiy++mAsvvJALLrgAyEOWly9fTn9/P01NTdxzzz0zcwPKxCHEkiTVura2vFROS8v0x1taYNUqKDK5iCRpZh1++OHT7l+wYAFf//rXOeqoo1iyZAlr166dttypp57K5Zdfzle/+lU+//nPAzA+Ps63v/1t+vv76e/v58EHH6SthLW+o7CM2nXXXUd3dzcPPPAA8+bN45FHHuFDH/oQ7e3t3HXXXdxxxx389re/3ccrrgwTWEmS6sGKFTlJPeywnKgedFDeHnZY3r9iRbUjlKQDQl/fzte55+bX5H3ldv/993PkkUdy6aWX8uY3v5kf/OAHuxwfGhqib1Ig/f39HHPMMQAsXryYv//7v9/lGEBbW9suPbFnn30269atA+Azn/kM55xzDgA/+9nPeN7znsdVV13F0572NB544AEee+wxOjs7mTVrFp/+9KcZGxsry3XPFIcQS5JUDyLyOq/Ll8P69XnCps7OPGzYnldJOmD09fXx/ve/n4MPPpjW1tYn9cCmlLjmmmt4y1vewmGHHcbhhx/OjTfeCMBHPvIRLrvsMk477TS2b9/OggULuO6663jlK1/Ja17zGr74xS/y0Y9+lI985CO86U1v4n3vex/t7e3ccMMNALz73e/m3nvvJaXEeeedx+mnn85b3/pWXv3qV3PTTTexaNGi3fYcHygipVTtGPba/Pnz04H8YHEj6uvrY+Hkhwek/WSb0kyzTWmm2aY002xT+2fjxo0861nP2qvPVGIZnWoaHBwsaYhxtU333UXEnSml+VPL2gMrSZIkqSHVa+Jaz3wGVpIkSZJUE0xgJUmSJEk1wQRWkiRJUl2oxfl9Gt3efmcmsJIkSZJqXnNzM4888ohJbA1JKfHII4/Q3Nxc8mecxEmSJElSzZs7dy5btmzh4YcfrnYoB4zR0dG9Sg6robm5mblz55Zc3gRWkiRJUs07+OCDOe6446odxgGlr6+P5zznOdUOY0Y5hFiSJEmSVBNMYCVJkiRJNcEEVpIkSZJUE0xgJUmSJEk1wQRWkiRJklQTTGAlSZIkSTXBBFaSJEmSVBNMYCVJkiRJNcEEVpIkSZJUE0xgJUmSJEk1wQRWkiRJklQTTGAlSZIkSTXBBFaSJEmSVBNMYCVJkiRJNcEEVpIkSZJUE0xgJUmSJEk1wQRWkiRJklQTTGAlSZIkSTXBBFaSJEmSVBNMYCVJkiRJNcEEVpIkSZJUE0xgJUmSJEk1wQRWklTfBgdh7Vp46KG8HRysdkSSJGkfmcBKkupTSnD11dDeDpddBg8+mLft7Xl/StWOUJIk7aWDqh2AJEll0dMD3d0wMpLfpwRDQ/nn7u68XbmyOrFJkqR9Yg+sJKn+DA7CmjUwPDz98eHhnMROJLSSJKkmmMBKkupPby80NRUvM2tWLidJkmqGCawkqf4MDMDoaPEyo6OwbVtl4pEkSTPCBFaSVH86OqC5uXiZ5mbo7KxMPJIkaUaYwEqS6k9XF4yNFS8zPp7LSZKkmmECK0mqP21tsHo1tLRMf7ylBVatgtbWysYlSZL2i8voSJLq04oVebtmTZ7QKSInrGNjOXmdOC5JkmqGCawkqT5F5HVely+H9evhkEPg2mvzsGF7XiVJqkkOIZYk1be2NliyBNrb89bkVZKkmmUCK0mSJEmqCSawkiRJkqSaYAIrSZIkSaoJJrCSJEmSpJpgAitJkiRJqgkmsJIkSZKkmmACK0mSJEmqCSawkiRJkqSacFC1A5CkhjY4CL29MDAAHR3Q1QVtbdWOSpIk6YBkAitJ1ZAS9PTAmjXQ1ASjo9DcDMuWwerVsGIFRFQ7SkmSpAOKCawkVUNPD3R3w8jIzn1DQ3nb3Z23K1dWPi5JkqQDmM/ASlKlDQ7mntfh4emPDw/nJHYioZUkSRJgAitJldfbm4cNFzNrVi4nSZKkHUxgJanSBgbyM6/FjI7Ctm2ViUeSJKlGmMBKUqV1dOQJm4ppbobOzsrEI0mSVCNMYCWp0rq6YGyseJnx8VxOkiRJO5jASlKltbXlpXJaWqY/3tICq1ZBa2tl45IkSTrAuYyOJFXDihV5O3Ud2LGxnLxOHJckSdIOJrCSVA0ReZ3X5cth/fo8YVNnZx42bM+rJEnStExgJama2tpgyZJqRyFJklQTfAZWkiRJklQTTGAlSZIkSTXBBFaSJEmSVBNMYCVJkiRJNcEEVpIkSZJUE0xgJUmSJEk1wQRWkiRJklQTTGAlSZIkSTXBBFaSJEmSVBMOqnYAkiSpDgwOQm8vDAxARwd0dUFbW7WjkiTVmbL3wEZEU0T8V0TcPM2xQyPicxGxOSK+GxHHljseSZI0g1KCq6+G9na47DK44oq8bW/P+1OqdoSSpDpSiSHE7wA27ubYm4FfpZSOBz4EvK8C8UiSpJnS0wPd3TAyAkNDsH173o6M5P09PdWOUJJUR8qawEbEXODlwCd2U+QPgE8Vfv5X4LyIiHLGJEmSZsjgIKxZA8PD0x8fHs5J7NBQZeOSJNWtcvfAfhh4DzC+m+NHAQ8ApJS2A48BR5Q5JkmSNBN6e6GpqXiZWbNyOUmSZkCkMj2bEhGvAF6WUnprRCwE3pVSesWUMj8Bzk8pbSm8/xlwVkrpkWnOtxRYCtDe3n7GunXryhK39s3Q0BCtra3VDkN1xDalmWabKoOHHoIHHyz+nGsEHHVUfia2ztimNNNsU5pptdymFi1adGdKaf7U/eWchfiFwKsi4mVAM/CUiPinlNIbJ5XZAvwusCUiDgJmA7+c7mQppY8DHweYP39+WrhwYRlD197q6+vD70QzyTalmWabKoO1a+Gv/7r4EOHWVrj2WqjDe2+b0kyzTWmm1WObKtsQ4pTSypTS3JTSscDrgVunJK8AXwL+pPDzawplnK5QkqRa0NUFY2PFy4yP53KSJM2ASsxCvIuIuCoiXlV4+0ngiIjYDPw5sKLS8UiSpH3U1garV0NLy/THW1pg1arcCytJ0gwo5xDiHVJKfUBf4ee/mrR/FHhtJWKQJEllsKLwt+c1a/KETqOj0Nyce2ZXrdp5XJKkGVCRBFaSJNWpCFi5EpYvh/XrYds26OzMw4bteZUkzTATWEmStP/a2mDJkmpHIUmqcxV/BlaSJEmSpH1hAitJkiRJqgkmsJIkSZKkmmACK0mSJEmqCSawkiRJkqSaYAIrSZIkSaoJJrCSJEmSpJpgAitJkiRJqgkHVTsASVIDGRyE3l4YGICODujqgra2akclSZJqhAmsJKn8UoKeHlizBpqaYHQUmpth2TJYvRpWrICIakcpSZIOcCawkqTy6+mB7m4YGdm5b2gob7u783blysrHJUmSaorPwEqSymtwMPe8Dg9Pf3x4OCexEwmtJEnSbpjASpLKq7c3DxsuZtasXE6SJKkIE1hJUnkNDORnXosZHYVt2yoTjyRJqlkmsJKk8uroyBM2FdPcDJ2dlYlHkiTVLBNYSVJ5dXXB2FjxMuPjuZwkSVIRJrCSpPJqa8tL5bS0TH+8pQVWrYLW1srGJUmSao7L6EiSym/Firydug7s2FhOXieOS5IkFWECK0kqv4i8zuvy5bB+fZ6wqbMzDxu251WSJJXIBFaSVDltbbBkSbWjkCRJNcpnYCVJkiRJNcEEVpIkSZJUE0xgJUmSJEk1wQRWkiRJklQTTGAlSZIkSTXBBFaSJEmSVBNMYCVJkiRJNcEEVpIkSZJUEw6qdgCSdEC45x5YuhQGBqCjAz7+cTjhhGpHJe29wUHo7d3Zlru6oK4+e2MAACAASURBVK2t2lFJkjQjTGAlNbaxMTjpJNi8eee+n/4UTjwRjj8eNm2CpqbqxSeVKiXo6YE1a3KbHR2F5mZYtgxWr4YVKyCi2lFKkrRfHEIsqbFNTV4n27w5H5dqQU8PdHfDyAgMDcH27Xk7MpL39/RUO0JJkvabCaykxnXPPbtPXids3gw/+1ll4pH21eBg7nkdHp7++PBwTmKHhioblyRJM8wEVlLjWrq0tHKXXlreOKT91du756Hus2blcpIk1TATWEmNa2CgtHJbt5Y3Dml/DQzkZ16LGR2FbdsqE48kSWViAiupcXV0lFZuzpzyxiHtr46OPGFTMc3N0NlZmXgkSSoTE1hJjevjHy+t3PXXlzcOaX91deUZtYsZH8/lJEmqYSawkhrXCSfkpXKKOf54eMYzKhOPtK/a2vJSOS0t0x9vaYFVq6C1tbJxSZI0w0xgJTW2TZt2n8ROrAMr1YIVK3KSethhOVE96KC8PeywvH/FimpHKEnSfjuo2gFIUlU1NcG99+YldZYtyxM2zZmThw3b86paEgErV8Ly5bB+fZ6wqbMzDxu251WSVCdMYCUJ8nDiW2+tdhTS/mtrgyVLqh2FJEll4RBiSZIkSVJNMIGVJEmSJNUEE1hJkiRJUk0wgZUkSZIk1QQTWEmSJElSTTCBlSRJkiTVBBNYSZIkSVJNMIGVJEmSJNUEE1hJkiRJUk04qNoBSJKqYHAQenthYAA6OqCrC9ra6rdeSZJUF0xgJamRpAQ9PbBmDTQ1wegoNDfDsmWwejWsWAER9VOvJEmqKyawktRIenqguxtGRnbuGxrK2+7uvF25sn7qlSRJdcVnYCWpUQwO5h7Q4eHpjw8P52RyIrGs9XolSVLdMYGVpEbR25uH7xYza1YuVw/1SpKkumMCK0mNYmAgP3tazOgobNtWH/VKkqS6YwIrSY2ioyNPnFRMczN0dtZHvZIkqe6YwEpSo+jqgrGx4mXGx3O5eqhXkiTVHRNYSWoUbW15yZqWlumPt7TAqlXQ2lof9UqSpLrjMjqS1EhWrMjbqeuxjo3lJHLieL3UK0mS6ooJrCQ1koi83ury5bB+fZ44qbMzD98tZw9oteqVJEl1xQRWkhpRWxssWdI49UqSpLrgM7CSJEmSpJpgAitJkiRJqgkmsJIkSZKkmmACK0mSJEmqCSawkiRJkqSaYAIrSZIkSaoJJrCSJEmSpJpgAitJkiRJqgkHVTsAaZ8MDkJvLwwMQEcHdHVBW1u1o9JMmPhuDz0U1q71u5UkSdIO9sCqtqQEV18N7e1w2WVwxRV5296e96dU7Qi1r6Z+tw8+6HcrSZKkXdgDq9rS0wPd3TAysnPf0FDednfn7cqVlY9L+2/qd5uS360kSZJ2YQ+sasfgIKxZA8PD0x8fHs6JzkTSo9rhdytJkqQSmMCqdvT2QlNT8TKzZuVyqi1+t5IkSSqBCaxqx8AAjI4WLzM6Ctu2VSYezRy/W0mSJJXABFa1o6MDmpuLl2luhs7OysSjmeN3K0mSpBKYwKp2dHXB2FjxMuPjuZxqi9+tJEmSSmACq9rR1garV0NLy/THW1pg1Spoba1sXNp/freSJEkqgcvoqLasWJG3a9bkSX9GR/PQ0rGxnOBMHFftmfrdRuSE1e9WkiRJBSawqi0ReS3Q5cth/fo8qU9nZx5aau9cbZv63R5yCFx7rd+tJEmSdjCBVW1qa4MlS6odhcph4rvt64OFC6sdjSRJkg4gPgMrSZIkSaoJJrCSJEmSpJpgAitJkiRJqgkmsJIkSZKkmmACK0mSJEmqCSawkiRJkqSaYAIrSZIkSaoJJrCSJEmSpJpgAivpwLJ1KyxdCps35+3WrZWpd3AQ1q6Fa67J28HB+q63kUzc44ce8h5LklTjTGAlHRjGx+H88+Goo+D66+Gxx/L2qKPy/vHx8tSbElx9NbS3w2WXwRVX5G17e96fUn3V20im3uMHH/QeSzqgPOXqpxDvjR2vO7fducv7p1z9lGqHKB1wyprARkRzRHwvIu6KiJ9ExHunKXNxRDwcEf2F1yXljEnSAeqlL4UNG6Y/tmFDPl4OPT3Q3Q0jIzA0BNu35+3ISN7f01Nf9TaSqfc4Je+xpAPK4G+LjwjZ03GpEZW7B/Zx4MUppdOBecBLIuL505T7XEppXuH1iTLHJOlAs3Xr7pPXCRs2wMDAzNY7OAhr1sDw8PTHh4dzojM0VB/1NhLvsSRJdamsCWzKJn47OLjwcsyWpF1deeXMlitVby80NRUvM2tWLlcP9TYS77EkSXUpUpmfAYqIJuBO4HjgH1JKfznl+MXA1cDDwD3A5SmlB6Y5z1JgKUB7e/sZ69atK2vc2jtDQ0O0trZWOwzVqs2b8zOvkwzNnUvrli27lps9G44/fubqfeih/FxksX8HI/JzuO3ttV9vI5nmHj+pTXmPtZ/8v0/7685td+7yfu6hc9ny+K7/953ReUYlQ1KdqeV/pxYtWnRnSmn+1P1lT2B3VBTxVKAXeFtK6ceT9h8BDKWUHo+IZcCFKaUXFzvX/Pnz0x133FHegLVX+vr6WLhwYbXDUK1aujRP2DRJ3wc+wMJ3vWvXcm95C1x33czVu3ZtntSn2DDS1la49lpYsqT2620k09zjJ7Up77H2k//3aX/Fe2OX9x844QO8655d/+9Lf+3gRe27Wv53KiKmTWArNgtxSulRoA94yZT9j6SUHi+8vR7wz0xSo6nWEOKuLhgbK15mfDyXq4d6G4n3WJKkulTuWYifXuh5JSIOA/43sGlKmc5Jb18FbCxnTJIOQHPmwOLFxcssXgwdHTNbb1sbrF4NLS3TH29pgVWrck9dPdTbSLzHkiTVpYPKfP5O4FOF52BnAf+SUro5Iq4C7kgpfQl4e0S8CtgO/BK4uMwxSToQ3XLL7pfSWbw4Hy+HFSvyds2aPOnP6Cg0N+feu1Wrdh6vl3obydR7HJETVu+xpANE2yFtRZfKaTukrYLRSLWhYs/AziSfgT3w1PL4eh1gtm6Fq66ib/58Ft5xRx42PNM9r9MZHIT162HbNujszENLK9E7V616G0nhHvcdcggLf/tb77FmjP/3aabZpjTTarlN7e4Z2HL3wErS3pkzJ0/U1NcHl1xSuXrb2qozmU+16m0kE/e4rw9q9D9xSZKUVWwSJ0mSJEmS9ocJrCRJkiSpJpjASpIkSZJqggmsJEmSJKkmmMBKkiRJkmqCCawkSZIkqSaYwEqSJEmSaoIJrCRJkiSpJpjASpIkSZJqwkHVDkDaJ4OD0NsLAwPQ0QFdXdDWVu2oymfrVrjyStiyBebOzT/PmVPtqMpj4lrPOgs++9nKXWu12lSjteVGu15JkjSjTGBVW1KCnh5YswaammB0FJqbYdkyWL0aVqyAiGpHOXPGx+GlL4UNG3bdf/31sHgx3HILzKqTgRRTr/XEE/N1lvtaq9WmGq0tN9r1SpKksqiT33zVMHp6oLsbRkZgaAi2b8/bkZG8v6en2hHOrOmS1wkbNuTj9aJa11qtNtVobbnRrleSJJWFCaxqx+Bg7r0ZHp7++PBw/kV4aKiycZXL1q27T+gmbNiQh2LWumpda7XaVKO15Ua7XkmSVDYlJbAR8fSI+EBE/FtE3DrxKndw0i56e/PQw2Jmzcrl6sGVV85suQNZta61Wm2q0dpyo12vJEkqm1J7YD8DbASOA94L3Ad8v0wxSdMbGMjPzRUzOgrbtlUmnnLbsqW0cj//eXnjqIRqXWu12lSjteVGu15JklQ2pSawR6SUPgk8kVK6LaX0JuD5ZYxLerKOjjzpSzHNzdDZWZl4ym3u3NLKHX10eeOohGpda7XaVKO15Ua7XkmSVDalJrBPFLbbIuLlEfEcoMTfOKUZ0tUFY2PFy4yP53L1wCHE+16uVNVqU43WlhvteiVJUtmUmsB2R8Rs4C+AdwGfAC4vW1TSdNra8nIbLS3TH29pgVWroLW1snGVy5w5efmYYhYvzr1bta5a11qtNtVobbnRrleSJJVNSevAppRuLvz4GLCofOFIe7BiRd5OXUtybCz/AjxxvF7ccsvul5eZWBu1XlTrWqvVphqtLTfa9UqSpLIomsBGxEeBtLvjKaW3z3hEUjERsHIlLF8O69fnSV86O/PQw3rsvZk1C77ylbzMzFVX5UmMjj46D6Wth57XyaZe6+zZ8Ja3lP9aq9WmGq0tN9r1SpKksthTD+wdFYlC2lttbbBkSbWjqJw5c+C666odRWVMXGtfH1xySeXqrVabarS23GjXK0mSZlTRBDal9KlKBSJJkiRJUjElPQMbEU8H/hI4GdixFkJK6cVlikuSJEmSpF2UOgvxZ4CNwHHAe4H7gO+XKSZJkiRJkp6k1AT2iJTSJ4EnUkq3pZTeBDy/jHFJkiRJkrSLkoYQA08Uttsi4uXAVmBueUKSJEmSJOnJSk1guyNiNvAXwEeBpwDvLFtUkiRJkiRNUWoC+6uU0mPAY8AigIh4YdmikiRJkiRpilKfgf1oifskSZIkSSqLoj2wEfEC4Gzg6RHx55MOPQVoKmdgkhrU4CD09sKhh8LatdDVBW1tlat3YAA6OipXryRp9/o35e28k6obh6QDxp56YA8BWsmJbtuk16+B15Q3NEkNJSW4+mpob4fLLoMHH8zb9va8P6XK1HvFFZWpV5K0R/39+SVJE4r2wKaUbgNui4gbU0r3R8ThKaXfVCg2SY2kpwe6u2FkJL9PCYaG8s/d3Xm7cmX564XK1CtJkqS9ttse2Ig4eNLbORFxN7CxcOz0iLi23MFJahCDg7BmDQwPT398eDgnkxOJZa3XK0mSpH1SrAd2aUTclVK6HfgwcD7wJYCU0l0RsaASAUpqAL290LSHx+pnzcrlliyp/XolSdPr37TLkOF5x+U/IPbfuGnnvnn4TKzUwIo9A3sdcOHEm5TSA1OOj5UlIkmNZ2AARkeLlxkdhW3b6qNeSZIk7ZPd9sCmlMaAtxfePhARZwMpIg4p7N9YgfgkNYKODmhuLj5Ut7kZOjvro15J0vTmnZR7WAsmel7nXWyPq6Ss1HVglwGXAUcBW4B5hfeStP+6umBsD4M6xsdzuXqoV5IkSfuk1ASWlNIfpZTaU0pHppTemFJ6pJyBSWogbW2wejW0tEx/vKUFVq2C1tb6qFeSJEn7pOgyOhHxSuD/AtsjYgy4MKX0rYpEJqmxrFiRt2vW5ImVInLiODaWk8iJ4+Wud3Q0Dxsud72SpD2aPJxYkmAPCSzwN8CLUkqbIuJ5wDXAueUPS1LDicjrrS5fDuvXwyGHwLXX5uG75ewBnVrvtm35mddy1ytJ2jNnG5Y0xZ4S2O0ppU0AKaXvRkRbBWKS1Mja2vKSNX19sHBh5euVJEnSAWtPCeyREfHnu3ufUvpgecKSJEmSJGlXe0pgrwfairyXJEmSJKkiiiawKaX3VioQSZIkSZKKKXkZHUmSJEmSqskEVpIkSZJUE0xgJUmSJEk1YU+TOO0QES8Hng00T+xLKV1VjqAkSZIkSZqqpB7YiLgOeB3wNiCA1wLHlDEuSZIkSZJ2UWoP7NkppdMi4ocppfdGxN8CXyhnYNoHg4PQ2wsDA9DRAV1d0Fanqx5V61q3boUrr4QtW2Du3PzznDnlr7eRTHy3hx4Ka9fWdzuWNDP6N+XtvJOqG4fqh21K9aB/E4yMVjuKGVfqM7Ajhe1wRMwBngCOK09I2mspwdVXQ3s7XHYZXHFF3ra35/0pVTvCmVOtax0fh/PPh6OOguuvh1tuydujjsr7x8fLU28jmfrdPvhg/bZjSTOqvz+/pJlim1I96O+HkeFqRzHzSu2BvTkingq8H/gBkIBPlC0q7Z2eHujuhpGRnfuGhvK2uztvV66sfFzlUK1rfelLYcOG6Y9t2JCPf+UrM19vI5n63aZUv+1YkiRJ+6SkHtiU0pqU0qMppc+Tn309KaW0uryhqSSDg7BmDQzv5s8rw8P5l/+JRKCWVetat27dffI6YcOGPJxZ+6aR2rEkSZL2WdEe2Ii4oMgxUko+B1ttvb3Q1FS8zKxZudySJZWJqVyqda1XXll6ueuum7l6G0kjtWNJ+69/0y7DO+cdl/+41X/jpp375uHziyqdbUr1YJp2/OjgeN214z0NIX5lYXskcDZwa+H9IqAPJ3KqvoEBGN3Dw9mjo7BtW2XiKadqXeuWLaWV+/nPZ7beRtJI7ViSJEn7rGgCm1L6U4CIuBk4OaW0rfC+E/iH8oenPerogObm4kMrm5uhs7NyMZVLta517tzSyh199MzW20gaqR1L2n/zTsq9CAUTvQvzLq7tXgVVkW1K9WCadjzS9gsW1lk7LnUW4mMnkteCh4ATyhCP9lZXF4yNFS8zPp7L1bpqXeveDCHWvmmkdixJkqR9VmoC2xcRX4mIiyPiT4AvA/9ZxrhUqrY2WL0aWlqmP97SAqtWQWtrZeMqh2pd65w5sHhx8TKLF+deRO2bRmrHkiRJ2mclLaOTUloeEV3AgsKuj6eUessXlvbKihV5u2ZNnghndDQPtxwby7/0TxyvB9W61ltu2f1SOosX5+PaP1O/24icsNZjO5Y0oyYPmZNmgm1K9WDePHi0DqcPKXUdWAoJq0nrgSgir4+5fDmsX58nuunszMMt663HqlrXOmtWXud161a46qo8YdPRR+dhw/a8zoyp3+0hh8C119ZnO5Y0s2p8Rk0dgGxTqgfzToJH62+Zx5ITWNWAtrbGWWKkWtc6Z45L5ZTbxHfb1wcLF1Y7GkmSJB1ASn0GVpIkSZKkqjKBlSRJkiTVhJKGEEfEM4GrgZOB5on9KaXfK1NckiRJkiTtotQe2BuAjwHbgUXAWuDT5QpKkiRJkqSpSk1gD0sp/QcQKaX7U0pXAi8uX1iSJEmSJO2q1FmIRyNiFnBvRCwHHgSOLF9YkiRJkiTtqtQe2HcCLcDbgTOANwJ/Uq6gJEmSJEmaao89sBHRBFyYUno3MAT8admjkiRJkiRpij32wKaUxoAzIiIqEI8kSZIkSdMq9RnY/wK+GBE3Ab+Z2JlS+kJZopL2ZHAQenthYAA6OqCrC9raqh1V/bnnHli6dOd9/vjH4YQTqh2VJEmqdbf/IG/PeW5146iU/k15O++k6sZRB0pNYH8HeIRdZx5OgAmsKisl6OmBNWugqQlGR6G5GZYtg9WrYcUKcLDA/hsbg5NOgs2bd+776U/hxBPh+ONh06Z8/yVJkvbBY4/l7ezqhlEx/f15O29edeOoByUlsCkln3vVgaGnB7q7YWRk576hobzt7s7blSsrH1e9mZq8TrZ5cz5+772VjUmSJEkNr6QENiJuIPe47iKl9KYZj0jancHB3PM6OXmdbHg4J7Fvexu0tlY2tnpyzz27T14nbN4MP/sZPOMZlYlJkiRJovQhxDdP+rkZ6AK2znw4UhG9vXsetjprVi63ZEllYqpHS5eWVu7SS+HWW8sbiyRJqg+3/2DHsGGA2a3jADz25R/s3Deb+nkmtn/TjmHDAPOOyyMG+2/ctHPfPHwmdh+UOoT485PfR8Q/A18rS0TS7gwM5GdeixkdhW3bKhNPvRoYKK3cVv+GJUmSpMoqtQd2qmcCR89kINIedXTkCZsmnnmdTnMzdHZWLqZ61NGRJ2zakzlzyh+LJEmqD+c8d5cJmyZ6Xme/vE56XKead9IuEzZN9LzOu9ge1/21x3VgASJiMCJ+PbEF/j/gL8sbmjRFV1eeHbeY8fFcTvvu4x8vrdz115c3DkmSJGmKkhLYlFJbSukpk7YnTB1WLJVdW1teKqelZfrjLS2wapUTOO2vE07IS+UUc/zxTuAkSZKkiit1FuLp+vYfA+5PKW2f2ZCkIlasyNup68COjeXkdeK49s+mTbtfSmdiHVhJkqR9NLtRFoAtcP3XmVPqM7DXAs8FfggEcCpwF3BERCxLKW0oU3zSriLyOq/Ll8P69XnCps7OPGzYnteZ09SU13m95x5YtixP2DRnTh42bM+rJEnaX/Uy23CpnG14xpSawN4HvDml9BOAiDgZeDewBvgCYAKrymprc6mcSjjhBJfKkSRJ0gGjpGdggZMmkleAlNLdwHNSSv9dnrAkSZIkSdpVqT2w90TEx4B1hfevK+w7FHiiLJFJkiRJkjRJqT2wfwJsBt4JXA78N3AxOXldVJbIJEmSJEmaZI89sBHRBFyfUnoj8LfTFBma8agkSZIkSZpijz2wKaUx4OkRcUgF4pEkSZIkaVp7MwvxNyPiS8BvJnamlD5YjqAkSZIkSZqq1AR2a+E1C2grXziSJEmSJE2vpAQ2pfTecgciSZIkSVIxJSWwEfF04D3As4Hmif0ppReXKa7aNjgIvb0wMAAdHdDVBW0V6LiuVr0qv61b4corYcsWmDs3/zxnTvnrrUabmqjz0ENh7VrbsSRN1r8pb+edVN04VD+q1aZsy9pHpS6j8xlgE3Ac8F7yM7HfL1NMtSsluPpqaG+Hyy6DK67I2/b2vD+l+qpX5Tc+DuefD0cdBddfD7fckrdHHZX3j4+Xp95qtKmpdT74oO24Ti1cmF+NoFrX2kj3GBrrevv780uaKdVqU7Zl7atSE9gjUkqfBJ5IKd2WUnoT8Pw9fSgimiPiexFxV0T8JCKeNBQ5Ig6NiM9FxOaI+G5EHLtXV3Ag6emB7m4YGYGhIdi+PW9HRvL+np76qlfl99KXwoYN0x/bsCEfL4dqtKmpdaZkO5YkSdIuSk1gnyhst0XEyyPiOcDcEj73OPDilNLpwDzgJRExNfF9M/CrlNLxwIeA95UY04FlcBDWrIHh4emPDw/nX8KHZnjZ3GrVq/LbunX3yeuEDRvy8N6ZVI02ZTuWJElSCUqdhbg7ImYDfwF8FHgK8M49fSillICJ3zgPLrymjgP8A+DKws//Cvx9REThs7WjtxeamoqXmTUrl1uypPbrVfldeWXp5a67bubqrUabsh3XvcnDO2+77cn7+voqGEyZVetaG+keQwNdb/+mXYZZzjsu/1rVf+Omnfvm4XOEKl212pRtWTMk9jVPjIh3ppQ+XEK5JuBO4HjgH1JKfznl+I+Bl6SUthTe/wx4XkrpF1PKLQWWArS3t5+xbt26fYq7bB56KD+zV+x+RuRnF9vba7/eKYaGhmhtbS3b+RvS5s3w2GN7Ljd7Nhx//MzVW402NU2dQ3Pn0rplS/nqVEXdc8/OnwcH83by3FwnnFD+GCr171S1rvVAuMeVdCBcb0Xa1MgoI5MGpxx2aJ77YOTxnYPoDmsBDmtGta+u25RtuSpq+Xf0RYsW3ZlSmv+kAymlfXoBP9/L8k8F/hM4Zcr+nwBzJ73/GfmZ292e64wzzkgHnE99KqXW1pTyr+DTv1pbU1q7tj7qneI///M/y3r+hnTppcW/14nXW94ys/VWo01NU+d/fuADFW/Hqoxzz82vSqvGv1PVutZq1VstjdSm/uuGjem/bthY8XpVGY3UpmzLlVHLv6MDd6RpcsFSn4GdTuxN4ZTSo0Af8JIph7YAvwsQEQcBs4Ff7kdc1dHVBWNjxcuMj+dy9VCvym9vhhDPpGq0KduxJEmSSrA/Cewexx5HxNMj4qmFnw8D/jd5OZ7JvgT8SeHn1wC3FjLu2tLWBqtXQ0vL9MdbWmDVKpjpLvxq1avymzMHFi8uXmbx4rw+60yqRpuyHUuSJKkERSdxiohBpk9UAzishPN3Ap8qPAc7C/iXlNLNEXEVuUv4S8AngU9HxGZyz+vr9+YCDigrVuTtmjV5QprRUWhuzj1Lq1btPF4v9ar8brll90vpLF6cj5dDNdrU1DojcsJqO647dTO5Tgmqda2NdI+hsa533rxqR6B6U602ZVvWvtrnSZyqaf78+emOO+6odhi7NzgI69fDtm3Q2ZmHPVai56ha9QJ9fX0sbJRV5Kth61a46ir4+c/h6KPzsOGZ7nmdTjXaVKHOvkMOYeFvf1vRdqz65r9Tmmm2Kc0025RmWi23qYiYdhKnUpfR0d5oa6vOUh/VqlflN2fOzC6VU6pqtKmJOvv6dl0TQ5IkSQ1vf56BlSRJkiT9/+3de4ykV3kn4N9rD8Q7mWZHEex4FkOsIEyUG7fhthBSzk2CMCAnIAjEBLQbL5FNWDYRMgQQWhthKSsIF4FFYEPQZmMCiS0ghIUsdGO0C8E2xsZ2mHAVxjYBohlmYptd22f/qGpcU+6Z6Z7pqppT/TxSqaq/71TV+3Wd+Ua/fk9VMTMCLAAAAF0QYAEAAOiCAAsAAEAXBFgAAAC6IMACAADQBQEWAACALgiwAAAAdGHbvAtgEx08mFx+eXLbbcnppyfnnJMsLc27KgAAgE2hA7sIWkve8IZk167k/POTP/zD4fWuXcPtrc27QoAtaTAYXrbK824lg0Gyb998ntecmr6tdLxb6VhZDDqwi+CSS5KLL07uuOPebYcODa8vvnh4/cpXzr4uAACATaQD27uDB5OLLkpuv33t/bffPgyxq4EWAACgUzqwvbv88uTUU48+5pRThuPOPXc2NQFsYeNL8VZW7rtteXmxnncrmfwd79272K/tVptTW+l4t9Kxsnh0YHt3223JnXcefcyddya33jqbegAAAKZEB7Z3p5+enHba0ZcIn3Zasnv37GoC2MLGOxerHY1ZdDPm9bxbyeTveGlpsV/brTanttLxbqVjZfHowPbunHOSu+8++ph77hmOAwAA6JgA27ulpeQ1r0m2b197//btyatfnezYMdu6AAAANpklxIvgwguH1xddNPxApzvvHC4bvvvuYXhd3Q/ATM1rSZ6lgNO3vDyf37M5NRtb6Xi30rGyGATYRVA1/J7XCy5Irrhi+IFNu3cPlw3rvAIAAAtCgF0kS0u+KgcAAFhY3gMLAABAFwRYAAAAuiDAAgAA0AUBFgAAgC4IsAAAAHRBgAUAAKALAiwAAABdEGABAADoggALAABAFwRYAAAAe0EI8AAAFDxJREFUuiDAAsCC2blzeGHxeG3hxAwGwwv9EmABAADoggALAABAF7bNuwAA4MSNLys9cOC+2/bvn209bB6vLZyY8SXDKyv33ba8PMNiOGE6sAAAAHRBBxYAFsB4F261O6cztxi8tnBixjusq51XXdd+6cACAADQBQEWAACALlhCDAALxvLSxeW1hRNj6XD/dGABAADoggALAABAFwRYAAAAuiDAAgAA0AUBFgAAgC4IsAAAAHRBgAUAAKALAiwAAABdEGABAADoggALAABAFwRYAAAAuiDAAszZYDC8sHi22mu7c+fwshUMBsm+ffOuAmDrEWABAADoggALAABAF7bNuwCArWh8WenKyn23LS/PsBg21VZ7bceXDB84cN9t+/fPtp5pmnxt9+5d7NcW4GSkAwsAAEAXdGAB5mC8U7PawdG9WQxb7bUd77Cudl4Xqes6bvK1XVpa7NcW4GSkAwsAAEAXBFgAAAC6YAkxwJxZgri4ttpru6hLh9eyvLz1Xl+Ak4EOLAAAAF0QYAEAAOiCAAsAAEAXBFgAAAC6IMACAADQBQEWAACALgiwAAAAdEGABQAAoAsCLAAAAF0QYAEAAOiCAAsAAEAXBFgAAAC6IMACsPAGg2TfvnlXMTuDwfCyVZ4XgK1DgAUAAKALAiwAAABd2DbvAgBgGsaXsq6sJHv3Hr5teXnGBU3Z5PFObpvW8c7reQHYmnRgAQAA6IIOLAALabzzNxgkS0uL3Q2cPN7JbYv2vABsTTqwAAAAdEGABQAAoAuWEAOw8JaXt9ay1nkd61b6HQMwHzqwAAAAdEGABQAAoAsCLAAAAF0QYAEAAOiCAAsAAEAXBFgAAAC6IMACAADQBQEWAACALgiwAAAAdEGABQAAoAsCLAAAAF2YWoCtqodU1Ser6qaquqGqXrbGmEFVHaiqa0eX106rHoBjGQyGFwBODs7LwKRtU3zsu5L8fmvtmqpaSnJ1VX28tXbjxLgrW2vPmGIdAAAALICpdWBba7e21q4Z3T6Y5KYkD57W8wEAALDYptmB/aGqOjPJo5N8do3dT6qqLyS5JckftNZumEVNAMnhS9NWVu67bXl5hsUA4LwMHFW11qb7BFU7kqwkeX1r7a8n9j0gyT2ttUNV9fQkb26tPfwIj3NekvOSZNeuXY+97LLLplo3G3Po0KHs2LFj3mWwQGY1p/btu/f2wYPD66Wle7edddbUS2BGnKfYbObUdGzl87I5xWbreU6dffbZV7fW9kxun2qArar7Jflwkv/ZWnvjOsZ/Pcme1tp3jzZuz5497aqrrtqcItkUy8vLGfiUBTbRPObU6tP56/5icp5is5lT07fVzsvmFJut5zlVVWsG2Gl+CnEleXeSm44UXqvq9NG4VNXjR/V8b1o1AQAA0K9pvgf2yUnOTXJ9VV072vaqJA9NktbapUmeneR3q+quJHckeV6b9ppmAAAAujS1ANta+3SSOsaYtyV527RqANiIrbJEDaAXzsvApKktIQYAAIDNJMACAADQBQEWAACALgiwAAAAdEGABQAAoAsCLAAAAF0QYAEAAOiCAAsAAEAXBFgAAAC6IMACAADQBQEWAACALgiwwFENBsML9GznzuTaa+ddBQBwogRYAAAAuiDAAgAA0IVt8y4AOPmMLxleWbnvtuXlGRYDx2nnzntvHziQ3H334dv27599TQDAidGBBQAAoAs6sMB9jHdYVzuvuq70ZrzDunNncuqpuq4A0DsdWAAAALogwAIAANAFS4iBo7J0mEWwf7+5DACLQAcWAACALgiwAAAAdEGABQAAoAsCLAAAAF0QYAEAAOiCAAsAAEAXBFgAAAC6IMACAADQBQEWAACALgiwAAAAdEGABQAAoAsCLCfm4MHkve9Nvv3t4fXBg/OuCAAAWFACLMenteQNb0h27UrOPz/51reG17t2Dbe3Nu8K6dhgkOzbN+8qWCTmFPRpMBheAFZtm3cBdOqSS5KLL07uuGP4c2vJoUPD2xdfPLx+5SvnUxsAALCQdGDZuIMHk4suSm6/fe39t98+DLGrgRYAAGAT6MCycZdfnpx66tHHnHLKcNy5586mJro3vkRsZSXZu/fwbcvLMy6I7plT0KfJf7uT2/zbha1NB5aNu+225M47jz7mzjuTW2+dTT0AAMCWoAPLxp1+enLaaUdfInzaacnu3bOrie6N/0V9MEiWlvyVnRNjTkGfJv/tTm4DtjYdWDbunHOSu+8++ph77hmOAwAA2CQCLBu3tJS85jXJ9u1r79++PXn1q5MdO2ZbFwAAsNAsIeb4XHjh8Pqii4Yf6FQ1DKx33z0Mr6v74TgsL1suxuYyp6BP/t0CkwRYjk/V8HteL7ggueKK5P73T97+9uGyYZ1XAABgCiwh5sQsLQ2/KmfXruG18AoAAEyJAAsAAEAXBFgAAAC6IMACAADQBQEWAACALgiwAAAAdEGABQAAoAsCLAAAAF0QYAEAAOiCAAsAAEAXBFgAgA0aDJJ9++ZdxewMBsMLwLwJsAAAAHRBgAUAAKAL2+ZdAABAD8aX0K6sJHv3Hr5teXnGBU3Z5PFOblu04wX6oAMLAABAF3RgAQDWYbzjOBgkS0uL3YWcPN7JbQDzoAMLAABAFwRYAAAAumAJMQDABi0vb63ltFvpWIGTmw4sAAAAXRBgAQAA6IIACwAAQBcEWAAAALogwAIAANAFARYAAIAuCLAAAAB0QYAFAACgCwIsAAAAXRBgAQAA6IIACwAAQBcEWAAAALogwAIAANAFARYAAIAuCLAAAAB0QYAFAACgCwIsAAAAXRBgAQAA6IIACwAAQBcEWAAAALogwAIAANAFARYAAIAuCLAAAAB0QYAFAACgCwIsAAAAXRBgAQAA6IIACwAAQBcEWAAAALogwAIAANAFARYAAIAuCLAAAAB0QYAFAACgC1MNsFX1kKr6ZFXdVFU3VNXL1hhTVfWWqvpyVV1XVY+ZZk3AyW8wSPbtm3cVAACcbLZN+fHvSvL7rbVrqmopydVV9fHW2o1jY56W5OGjyxOSvGN0DQAAAD801Q5sa+3W1to1o9sHk9yU5METw56V5L1t6DNJdlbV7mnWBQAAQH+m3YH9oao6M8mjk3x2YteDk3xz7OebR9tunUlhwElhMLj39spKsnfv4duWl2dcEAAAJ51qrU3/Sap2JFlJ8vrW2l9P7PubJG9orX169PP/SvKK1trVE+POS3Jekuzateuxl1122dTrZv0OHTqUHTt2zLsMOjb+nteDB5MzzjiUAwfunVNnnTWHolgozlNsNnOKzWZOsdl6nlNnn3321a21PZPbp96Brar7JfmrJH8+GV5Hbk7ykLGfz0hyy+Sg1to7k7wzSfbs2dMG460Z5m55eTleE07E+PQZDJLnP3855503OMJo2DjnKTabOcVmM6fYbIs4p6b9KcSV5N1JbmqtvfEIwz6Y5IWjTyN+YpIDrTXLhwEAADjMtDuwT05ybpLrq+ra0bZXJXlokrTWLk3ykSRPT/LlJLcnefGUawIAAKBDUw2wo/e11jHGtCTnT7MOoC/Lyz60CQCA+5rqEmIAAADYLAIsAAAAXRBgAQAA6IIACwAAQBcEWAAAALogwAIAANAFARYAAIAuCLAAAAB0QYAFAACgCwIsAAAAXRBgAQAA6IIACwAAQBcEWAAAALogwAIAANAFARYAAIAuCLAAAAB0QYAFAACgCwIsAAAAXRBgAQAA6IIACwAAQBcEWAAAALogwAIAANAFARYAAIAuVGtt3jVsWFV9J8k35l0Hh3lgku/OuwgWijnFZjOn2GzmFJvNnGKz9Tynfry19qDJjV0GWE4+VXVVa23PvOtgcZhTbDZzis1mTrHZzCk22yLOKUuIAQAA6IIACwAAQBcEWDbLO+ddAAvHnGKzmVNsNnOKzWZOsdkWbk55DywAAABd0IEFAACgCwIsAAAAXRBg2bCqOrWqPl9VH15j34uq6jtVde3o8h/mUSP9qKqvV9X1o/ly1Rr7q6reUlVfrqrrquox86iTfqxjTg2q6sDYeeq186iTflTVzqr6QFX9Q1XdVFVPmtjvPMWGrGNOOU+xblX1iLG5cm1Vfb+q/tPEmIU5T22bdwF06WVJbkrygCPsf19r7YIZ1kP/zm6tHelLtp+W5OGjyxOSvGN0DUdztDmVJFe21p4xs2ro3ZuTfLS19uyqun+S7RP7nafYqGPNqcR5inVqrX0pyaOSYaMpybeSXD4xbGHOUzqwbEhVnZHk15K8a961sGU8K8l729Bnkuysqt3zLgrYGqrqAUmemuTdSdJa+7+ttf0Tw5ynWLd1zik4Xr+U5CuttW9MbF+Y85QAy0b9cZJXJLnnKGN+Y7Q04QNV9ZAZ1UW/WpKPVdXVVXXeGvsfnOSbYz/fPNoGR3KsOZUkT6qqL1TV31bVT8+yOLrzE0m+k+RPR2+feVdV/ejEGOcpNmI9cypxnuL4PC/JX6yxfWHOUwIs61ZVz0jyT621q48y7ENJzmyt/VySv0vyZzMpjp49ubX2mAyXtpxfVU+d2F9r3Mf3f3E0x5pT1yT58dbaI5O8NckVsy6QrmxL8pgk72itPTrJvyS5cGKM8xQbsZ455TzFho2Woz8zyfvX2r3Gti7PUwIsG/HkJM+sqq8nuSzJL1bVfx8f0Fr7XmvtB6Mf/yTJY2dbIr1prd0yuv6nDN+v8fiJITcnGe/kn5HkltlUR4+ONadaa99vrR0a3f5IkvtV1QNnXii9uDnJza21z45+/kCG4WNyjPMU63XMOeU8xXF6WpJrWmvfXmPfwpynBFjWrbX2ytbaGa21MzNcnvCJ1tpvjY+ZWEv/zAw/7AnWVFU/WlVLq7eT/GqSL04M+2CSF44+Pe+JSQ601m6dcal0Yj1zqqpOr6oa3X58hv8Xfm/WtdKH1tptSb5ZVY8YbfqlJDdODHOeYt3WM6ecpzhOv5m1lw8nC3Se8inEnLCq+i9JrmqtfTDJ71XVM5PcleSfk7xonrVx0tuV5PLR/9HbkvyP1tpHq+olSdJauzTJR5I8PcmXk9ye5MVzqpU+rGdOPTvJ71bVXUnuSPK81lqXy6iYmZcm+fPR8ryvJnmx8xQn6FhzynmKDamq7Ul+Jcl/HNu2kOep8m8BAACAHlhCDAAAQBcEWAAAALogwAIAANAFARYAAIAuCLAAwIZU1baquqCqfmTetQCwtQiwAHRr9F2Jl1XVV6rqxqr6SFWdNcPn/7dV9YEpP8eZVfX8E3yM91TVszcw/nVV9a2quraqvjj6erTVfZXkj5Nc11r7wWjboKr+3Toe90VV9bbjOQYASARYADo1ClKXJ1lurT2stfZTSV6V4XfBzuL5t7XWbmmtrTsYHqczk5xQgD1Ob2qtPSrJc5L8t6o6JUna0AWttU+NjR0kOWaABYATJcAC0Kuzk/y/0Re0J0laa9e21q6soT8adQ+vr6rnJj/sFK5U1V9W1b6quqSqXlBVfz8a97DRuPdU1aVVdeVo3DNG219UVe+vqg8l+dioO/rFsX1XVNWHquproyW2/7mqPl9Vn6mqHxuNe1hVfbSqrh49/k+OPedbqup/V9VXxzqmlyT5+VE39OVVdVpV/emo3s9X1dmTv5jR8b9t1JX+myT/Zmzfa6vqc6PfzTtHfwg4otbaTUnuSvLAqnpQVf3V6P6fq6onV9WZSV6S5OWjGn++qvZW1WdH9f1dVd3njwrrGQMAkwRYAHr1M0muPsK+X0/yqCSPTPLLSf6oqnaP9j0yycuS/GySc5Oc1Vp7fJJ3JXnp2GOcmeQXkvxakkur6rTR9icl+e3W2i8eoabnJ3l8ktcnub219ugk/yfJC0dj3pnkpa21xyb5gyRvH7v/7iRPSfKMDINrklyY5MrW2qNaa29Kcn6StNZ+NslvJvmzsdpWnZPkEaNj/J0c3h19W2vtca21n0nyr0bPdURV9YQk9yT5TpI3Z9iZfVyS30jyrtba15NcOtr+qNbalUk+neSJo2O/LMkr1njo9YwBgMNsm3cBADAFT0nyF621u5N8u6pWkjwuyfeTfK61dmuSVNVXknxsdJ/rM+zqrvrL1to9Sf6xqr6a5CdH2z/eWvvnIzzvJ1trB5McrKoDST409tg/V1U7MgyT7x9rfI5/ENIVo+e88SgdyackeWuStNb+oaq+keSsJNeNjXnq2PHfUlWfGNt3dlW9Isn2JD+W5IaxOse9vKp+K8nBJM9trbWq+uUkPzVW+wOqammN+56R5H2jPxrcP8nXjnMMABxGgAWgVzckOdL7T4+2LPYHY7fvGfv5nhz+/2KbuN/qz/9yAo99SpL9o/eWHuv+RzqGoy75HTNZf0ad2rcn2dNa+2ZVvS7JZPd21Ztaa/91YtspSZ7UWrtj4nEn7/vWJG9srX2wqgZJXrfG469nDAAcxhJiAHr1iSQ/UlW/s7qhqh5XVb+Q5FNJnltVp1bVgzLsSP79Bh//OVV1yuh9sT+R5EsnWnBr7ftJvlZVzxnVW1X1yGPc7WCS8S7np5K8YHT/s5I8dI3aPpXkeaPj3517O8urYfW7o27wRj+A6mNJLlj9oapWg/hkjf86ybdGt3/7CI+1njEAcBgBFoAutdZahu/1/JUafo3ODRl28W7J8NOJr0vyhQyD7itaa7dt8Cm+lGQlyd8meUlr7c5NKv0FSf59VX0hwy7ys44x/rokd1XVF6rq5Rl2UE+tquuTvC/Ji1a/zmbM5Un+McOly+8YHUdaa/uT/Mlo+xVJPrfB2n8vyZ6quq6qbszww5uS4RLkc1Y/xCnD1+H9VXVlku8e4bHWMwYADlPD//8BgFVV9Z4kH26tTfU7XgGAjdGBBQAAoAs6sAAAAHRBBxYAAIAuCLAAAAB0QYAFAACgCwIsAAAAXRBgAQAA6IIACwAAQBf+P1CZgQiU8DUeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualizaDados(X,Y, 'Iris Versicolour', 'Iris Setosa')\n",
    "\n",
    "plt.scatter( x_teste[0,0], x_teste[0,1], marker='s', color='green', s=80)\n",
    "\n",
    "for i in range(K):\n",
    "    if Y[ind_viz[i]]==0:\n",
    "        plt.scatter( X[ind_viz[i],0], X[ind_viz[i],1], label=\"Iris Versicolour\", marker='o', color='orange', s=120)\n",
    "    else:\n",
    "        plt.scatter( X[ind_viz[i],0], X[ind_viz[i],1], label=\"Iris Setosa\", marker='+', color='', s=120) \n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "Vamos agora analisar a superfície de decisão (K=3):\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dR510uvx+v9ctAgAwYPiLV2hGdYtK2nf2aR8CKACgX5qz4CO65Pqb9cjNP9H67U/JmDwVFw/Rx045W+dc+T2v2wMAYECIBc+x2iBJGhqyfdqPAAoA6Lfmf/xEzf/4iardVqPWPc0aO+lA+Xw+r9sCAKDfSwyegaplWrpqWp/3JYACAPq9UWMqvG4BAIABIXXwnKaWhmrVBwN92p8ACgAAAAADVE+GBsWu8QwU1HcKnnsbqlUXDEgKqKJ0TafXmOhHvHCaGgRQAAAAABhgYsGzJ4ODAgX1CmxOHjwrE4KnFAmaieFTSn+vTwIoAAAAAAwQ8cFzrDYoULXM8Wv3B8+NqguWK1XwjEkXNFMhgAIAAABAP5cqeC5dNU2N9SFHexSa2DWe5aoojgTPcLrzaXuBAAoAAAAA/VS64NnSUC2pWs2tzgYHNSuwL3hmCgEUAAAAALKgJwOBnEoWPPdGg2d9MDI0qKJ0S6fXOBkcZBI+p1uX7DrQVAigAAAAAJBBsVubSHI8EMiJ2LRaqXPwrAtGrt2sTAiekrPBQWFJVsmv8Uxc15PwKRFAAQAAACAj4oNnTwcCORUJnhslRQYHpQqeMU4GBzkdLsQQIgAAAADwWKrg2ZOBQE4Ums2KnGobGRpUUVzj+tAgtxFAAQAAAMAF6YJnTwcCOREbGlRRnPqIZ64hgAJAhtVuq9Gjt/9Mm9e+I39pqT726c/oI586w+u2AABAN3o6NMitgUCSs2E/bg8O6m1NhhABQI5Y+eLzuv1bl6ksVK4RHaPVanbr/re/o3889Sddc/fDXrcHAACSSLy1iVM9HQiUjhfXarpZMxUCKABk0L3XXqWJbdM0XlP3/XhwfGiqXn1juZ64+1adeuFXvW0QAAB0EjuNNhY8A1XLZGyto9cuWb2gRwOBBiMCKABkyMvP/FnB5j2qtAd2OjfFbwo1MXSQ/vnUkwRQAAByRLLguXTVNEnT1Fg/pdvX98eBQF4ggAJAhmyt3qCSvDKZcNcrI0pVpu27N3vQFQAAiJcueLY0RK7ddKI/DgTyAgEUADJk+tzD9ZfQ7QrZkHzG1+m5JlOv8lEHeNQZAABIFzz3NkSu3awo3dJlaJDUt2E/uTI4qLc1ne6VCgEUADLk4HlHaeTYcVq3dbWmh+fKmMj/mpvtTr3vW68vfv4nHncIAMDg4yR4SpHBQT3V3wcHMYQIAPq5K391v35y4Wf1cuMzGmHHqDVvrxptnY7+9Fk66sTTvG4PAIBBI33wjAwN6m3whHMEUADIoIqJk3Xbsyv0t8cXac1r/1Lp0IBOOvdLGlVR6XVrAAAMCrHgWdK+U4GC+hTXeEYGB0licFCGEUABIAuOOe1sHXPa2V63AQDAoNEleG5OFjwDqog74pns9NJkeTRxnZM1fdnLi5pu9x9DAAUAAAAwYKQLnqmu8UwXmuIDVljJg1niGrf38qKmG3slQwAFAAAA0O/1JnjG9PeBP7lcMxEBFAAAAEC/lT54Mlwo1xBAAQAAAPQ7yYKnsbVasnoBw4VyWJ8DqDFmvKTfSxqjyKnAd1lrb+3rvgAAAACQjL94hfL9VSppL9L4UJ3y3v+jJOnB5fPU3NqkxOFCUmaH/eTK4KDe1sxG/+nW91SHpCuttTMlzZf0ZWPMLBf2BQAAAABntq/d98vK0jXK0/6wk2pYTl7Cc07WdbempzWT6e1eudR/b55zxFq71Vr7evTXuyW9I2lcX/cFAAAAgL5yOnjHiwFDbtXM5f5724MjxphJkg6R9EqS5y4yxrxmjHltd2ODm2UBAAAAwJFwOHKKaLrTRMPh/ev6ulf8um7XuFQzl/t3bQiRMWaIpMclXWGt3ZX4vLX2Lkl3SdKUWXOsW3UBAAAAIF63A4fCnT6lXedkjWt7eVEzy/27EkCNMQWKhM9F1to/ubEnAAAAAMTzF6+QJM2obtFY7ZEK9shsXq4lqxeosX6eisxmNSvQ5TxPE/1IlBiUkq1zsqYve8nhuv7cfzw3puAaSfdKesda+4u+7gcAAHLH6pdf1Htvv6HKA6friKOP97odAINU5+C5QZIUqIq/32e1mlsDKi/dosrSLZ1eG5ZklTx05SWsc7LG7b1SDfvJZM1s9p/IjSOgH5Z0jqQ3jTFvRB+72lq71IW9AQCAB6r++7Zuu+JiNdRuU5kvoObwLg0JDNOXbrhFs49Y4HV7AAaR2P0+UwXPumBAlUmCZ4zbg3dycS8vavZ2mFCfA6i19h9KHpABAEA/FAqFdOMl5yiwe5iODJ8gn/UpbMPa1Piubr7iQt36zD9VWlbudZsABri+Bs9UwmHtS0/pQpSTdfuuNc3Lrb28qBm/VzquDSECAAADw5Lf/UYde9o0LfwBRa60kfJMniZphurbd+jRO27SeVdd53GXAAaqdMGzpaFa9cGAKoq3qKJ4S/fDhlLpweAdp+tydS+vaqZCAAUAAJ28++ZKjQyN3hc+443sGKOqt970oCsAg4G/eIXy/VUqaS/S0JCVAjtlbK0a66folW0f1uxhTaooXdPpNZke9pMrg4N6WzMX+o/n6n1AAQBA/1dSOkStecGkz7WaoIpKh2S5IwDYLy/uQ0o9LCd+TbrBOz3ZK68He6W67+Rg6T8VAigAAOhk4TkXq85uVYtt7vR4qw1qq6nWxz9zjkedARjcuh5Xczosx4sBPW7V7O/9J+IUXAAA0Mnk6bP1oYUn65VnFmti+CAF7HDt1k5V+97V7HlH6vCPHud1iwAGiyTncvb6uk/kBAIoAADo4kvX3axp/3Oonn/4Aa2ve1tDyst1yimX61PnXep1awAGqdnDnvW6BbiAAAoAAJI69n/P0bH/y+m2ADLPX7xCkqLTb/doaKhZZutyLX1mmhrr56nIbFazAl0GEEnuD/vJhcFBfamZK/2nQgAFAAAA4InOwXODhgZtJHiumqbG+ikqMtVqbg2oPMX9PsNKHX7yHKxLXJNuQE9v9kp2jaSTvfpSM1f6T4UACgAAACCrEoOntP9+n5HguVHNreUpg2eM24N3cnEvL2q63X88AigAAACArOgueBZGj3gOLa5RRXENA4cGIAIoAAAAgIxyHjy3qKI49RFP9H8EUAAAAAAZ0f2pttHgWbpFFUlOtc30sJxcGRzU25q53H8qBFAAAAAArnIaPLu7xjOZXL7Wsb9fq+lmzVQIoAAAAABckS54StO0t8HZcCEMXARQAAAAAH3SXfBsaahWfTCgCoYLDXoEUAAAAAC9Fgufh67fqkBBvYYGrfJq/qglqxfEBU+GCyGCAAoAAACgT/L9VZKKNDRopcBOqUZqrA+puTWgitI1ytP+4TXdXUMYdrDG6To3a9J/79YlIoACAAAAyJi8hM9O17uxLlf38qKmF/0nQwAFALhi9csv6pHbbtSWqnWSrMZNmqrTL/s/zT3qaK9bAwAAOYIACgDos5UvPa9ffuNSjeuYqCPsRyVJW9dX65YrL9alN9ymDx6z0NsGAQDZkzBgiIFDiEcABQD02SM33aDxHQdqsmbsuxP1FM2SryNff7z1pwRQABigYgOI5qwpUqCgXgpJef/9q5asXqBCU61mBSILE87XTDx9M1VGdbIuk3t5UXOg9h9DAAUA9EkoFFLN++t1lD1xX/iMGafJenHLUwru2aOi0lJvGgQAuC7xtitDQ1Zm83ItXTVNexvGSYpMv60sXdPpdakG1+QlrEl8LNW67tb0tGYyPa1J/+kRQAEAfRIKhWStlU++Ls/lySdZKRRu96AzAIDbugTPoJXZGguefknVqosGz8rSrrddydVhObm6lxc1GUIEAMhpfr9fI0ZWaHvdZo3VxE7P7dAWDRt+gErLyj3qDgDghvTBs0DSRtUFy1MGTyCGAAoA6LOF535Rj9zyU/lC+RqlCklSnbbqXd8b+vTnvu5xdwCA3koXPFuiRzzrg+WqKF6jiuIaBg6hWwRQAECfLTz7QrW1tuqZ39+rNc0rZSQVl5bppLO+rE+dd6nX7QEAeihd8Gysn6IiE7nGs6J0jSqiRzxjYwASxgF0uT7RJFnjdF2m95LDdfTfs73iEUABAK44+fzLdPL5l2n9228oHArpwNlz5fN1vS4UAJC7EoOnJAWqlnUKns2tAZWXbul0qm1YkpWzwTXJAovTdYlrrMN1Tvei/57X7G5dIgIoAMBVU2fP9boFAEAP9TZ4xjB4x9uaudx/IgIoAAAAMEj1NXimsu9a0Lz0QSUcdy8PJ+u6XeNSTfpPvs6N/gmgAAAAwCDTXfAsjAbPocVbVFG8pffDhcLprweMrYn71Le9vKhJ/z1aRwAFAAAABoBYqHSiuyOeQ0u37BsuJOXOsJxcGbzT25qDtf94BFAAAACgH/MXr9CM6hZJUkn7zm7XBwrqI5+jwVOapr0NqU+1zaVhOYmvCyd5LFVN+vem/0QEUAAAAKAfig+esVulOGE2L+8UPOuCAVWmucZzsAzLof/MrYtHAAUAAAD6kcTgGahaJknRUNm92Km23QXPVHJ1WE78Xl7UpH+lXxBFAAUAAAD6gXTBs6WhWvXBJsd79Xm4kJTTw3K8qEn/crSAAAoAAADksHTBM3IKbZOkgCpK13R6Xa4MrulLTfrfv0YO1+Vi//EIoAAAAEAOcho8KxOCp5Rbg2v6UpP++3//iQigAAAAQA5JHzw3pg2eMf19cE2u7uVFzf7efyICKIBBZcVzS3X/T65RcHezfP4CfeLMz+szl33L67aAbq1941Ut/u2vtbOuXqMnTtDpl1yp0RMme90WABc5u8azXBXFkeDZp+s3AY8Ya52Na3bTlFlz7PWLlma9LoDB7cbLz9Xqf7yo4Rql4RqtZu3SNm3SsNGj9cunX/G6PSCl+2/4rpb/6Q8abcerJDxEO30NajS1+tw3vqdjzzjH6/YA9FF3wVOS6oOBfcET6A9OfWTtSmvt4YmPcwQUwKCwfVu1Vv/jRc3WERptKvc9PtFO0yvb/6b7rv+2zr/mBg87BJJ7+9WXtfxPf9BhoY9oiAlELrYJS7W2Rotuuk4fWniSSsvKvW4TQC90d42nVB0JnqVrVJFwq5TBMLiG/ntXM1f6T6U3p+0CQL9z01e+qBIN6RQ+JanUDNU4TdY/Fj/hUWdAek/d92uNsRMi4TPOKFOhEjtET957u0edAegtf/GKfeFzrDZoRtU9ClQt09JV0/T4cn90wFBARb4tqixdozypy0eqwS+Ja5yuS6a3Nd3ci/77b/+pcAQUwKCwq7FeZUp+lKhM5drevjnLHQHO7Kqr15Dw0KT/wg8JB1S3jb+7QH/hL14hSfuCZ+JwIWmj6oLlqixdo8qEI57AQEEABTAojBxbqa0N62StlTGd38k3qU6+ogKPOgPSG1E5Tls3vqtxSYaN7Mxr0AcnH5T9pgD0SLrg2bLvVNvIcKGK4hqGC2FA4xRcAIPCN375gNrUqvf1XqfHm2ydtul9nXDOhR51BqT36YsuV622qNHWdnp8i92gjoIOnXTulzzqDEB34k+1/Vj1W51OtX1suT862TagQrOFAUMYNDgCCmBQKC8v18dOO1PLH39IW+wGjdBo7dZO7VSdxk+fqdMu/prXLQJJTZ45R6d96et6/Dc3K6DhKg0NVZOvXu0Frbr4ul/IX1TkdYsAEqQ/1bb74ULxn2NyddhMrgze6W1N+s9czVS4DQuAQaVp+3b9+LKz1bBjq4pLh+jC79yoOQs+4nVbQLcaarfryXtuU2Ptdo2bfKBOOf9yFZWWet0WgDiJwXNo0MpsXR4XPKW6YECVpRztxMB38kPJb8NCAAUAAAD6IH3w3ChJ+4YLAYNFqgDKKbgAAABAL6QLni0NfjFcCOiKAAoAAAD0gLPgGYgGT26nAsQjgAIAAAAOpD/Vdn/wjL+PZ+ygZ3e3ngg7XON0Ly9q0r+3NXOx/2QIoAAAAEAaToJnXULwjHH6Bt3JOjf38qIm/Xtb04v+kyGAAgAAAEmkC56N9VNUZDbuGy6UGDwBJEcABQAAAOIkBk9JClQt2xc8C021mlsDGlpcw3AhoIcIoAAAAIB6EDxLt6gi7ohn4qmIqfKok3XJTmt0ss7NmvTvbc2B2n8MARQAAAADlr94hWZUtzhenyx4FkWDZ3nplk6n2qYawmN+WPEAACAASURBVJLsDXl369K9aU9c53QvJ+vov3PNZOi/93slQwAFAADAgBMfPGPXbzrR+RrP5MEzJlcHxDAsx9ua9J8eARQAAAADRmLwDFQtk7G1jl67ZPWCfcOFmlvLUwZPAL1HAAWAAaqpoVb/fn6JCotL9aHjTpbf7894zeCePXr52Sdlw9L84z+l0tKyjNcEACl18FyyeoFaGiL//zNpXh85PspwISDTCKAAMMCEQiHd9o1L9MY/lqnIlCqkDj1ww/e18NwLddrFX8tY3fuuv1ov/eUxFdjIG70Hb/yBPnTCKbro+zdmrCaAgSs2EMiJVMFzb4NfdcEmSQFVlK7Zt94oeRgNS52GCyVbl5hJ0+3V3bpka+RwnZs16X//GjlcR/892yseARQABphfX/0VvfOPf+mI0NEqMUNkrVVDxw795Z7bVT7yAB1z2tmu1/zj7TfqpScf05zQhxQwwyVJu2yjViz+s0oDAZ19xTWu1wQwMMVPoi1p3+noNYGCegWqlkmSlq6a1il4VsYFTynyxtgq+ZvmxAErTta4vZeTwS/0n7m96L/nNbtbl4gACgADSHDPHr3+wvOaG/qwSswQSZIxRiM0WlNCM/X07+7JSAB94bFHND00d1/4lKShZphmhA7RS088SgAF0K3EW6D0ZGiQFAue1SmDZ0yuDmthcI23Nek/czUTEUABYABZ+/orMmGjMlPe5blRqtDG7ctdr9kWDKppZ60O1ZFdnhuhMVq1+1/a3dSksvKuPQFAuntvOuMseKYSjruXRLo31E7W7btmNC+39vKiJv17WzOX+yeAAsAAUjZ8pDpsu8I2pDzj6/Rcm4LKz3d/EJGvoEC+PJ/aw20qVFGn59rVJmOMCouKUrwawGCVLng21k9RoalWfTDgcLeAKoojwbNXg4PCnT65si5X9/KiJv17WzPX+ieAAsAAcuDsOSofPko1dRtVqQP3PW6tVXXeOk39n0Ncr+nz+TRh6kxtWveupmlOp+c2mXWqnHyQ/ARQAFHdBc/YvTeHlm7pdiCQlP1hLbky+KW3Nenf25qDtf94BFAAGGDOvPIa3fXdK9USbtbocKU61K7Nvg1qLW3V+d+5ISM1v/DdH+uGC89SW1ubKsITJUlb8zapoWCH/u/b92ekJoD+xWnwTHbvTa+GtTgZrhJO8liqmvRP/4Ox/0QEUAAYYBYc9ymVjzxAj/3q5/rve6uV5/Np+uFH6Kwrv6dRYyoyUnPq7Ln6/u8f18O33KD1b74pSZo0+2B95Yo7NfGgmRmpCaB/6D54blRza3nS4BkzWIa10H/u16T/3q2LZ6x1NmHMTVNmzbHXL1qa9boAAADIju6GC7U0RK7xjF27CWBgOfWRtSuttYcnPs4RUAAAALgmffCcFhc8t6iiOPkRTwADFwEUAAAAacVCpROpgmfkVikBVSQMF5Jye1hLLgx+6UtN+t+/Rg7X0b/7e8UjgAIAACApf/EKzahukSSVtO/sdn2goD7yOUnwrExxjWc2Bqc4XZerg1/6UpP+6b8vNd3oPxEBFAAAAJ3EB8+x2qBA1TLHr90fPDeqLlieMnjG5OrglFzdy4ua9O9tzf7efyICKAAAACSlDp6RibUhR3sUmtg1njWqKK5RuNu71gMYTAigAAAAg1y64BkZGtTkeK9mMdkWQGoEUAAAgAGmp0ODpK7BM3LtZpOkgCpKuwbKXB6c0tua9O9tTfr3tqbb/adCAAUAABggkt0CxYnE4CnFBgf17Ehmf79Wjf69rUn/3tbM5HWf8QigAAAA/Vyqe28aW+vo9UtWL9Deho2SYoOD1qQdHAQAvUUABQAA6KdSBc/YJNrG+ind7lFoNkuqVn2wXBXFaxgcBCCjCKAAAAD9THfBMzI4KOBor9jQoIpijngCyDwCKPqN1S+/qEd/9XPVVK2XMUYTps/SWd/4jqbOnut1a+iFUCikB35+rV599hm1NO9SaVlA8xaeqLOuuEY+n8/r9gDANT0ZCORUquAZGRwUUEXpFlUkOYXW7WEnuTA4pS816X//GjlcR/+Z2UsO1/Wn/lMhgKJfWPH8Yv3m6q9pXGiy5toFsrLa8maVfnzBmbrqjgc0Y+4RXreIHrru/NNVs2adpoRmaajKtbOhQX9/+BFt+u8aXXPXw163BwB91tuBQE4lC56VpVt6de1mfx92Qv/e7eVFTfr3tiZDiDAoPPKLn2hSx3RNMNP2/Xhlup2rvDafFt34A133h8XeNogeWfHcYm1c86Y+FPqECoxfklSkEg0LjdK/Xn9Wq19+UXMWfMTjLgGgd/o6EMiJJasXKBI8Y0ODehc8ASDbCKDIeQ3ba1S7fbNm6ZAuz423B+qVdc970BX64oUnH9HY8IR94TPGbwo1WpX62+MPEkAB9DvprsuMDAPqfiCQU4Umdo1nZHAQQ4MA9BcEUOS8YLBVRkZ56npdYL4KFAqHPOgKfdHR2iqfLUh6sUB+OF/tba3ZbwoAeqm74FloqtXc6mwgkFNDi7cwNAhA7kpzni4BFDlvdOUElZQOVX3zdo3UmE7PbddmjTpgnEedobdmzfuw/rr6Hk3umCFj9qdQa6125NfoyHmf8bA7AHCmu+BZFA2e5Qmnx4bV/TVUsQOaTtZlcy8vatK/tzXp39ua/b3/ZPp6DSmQcT6fT//vtDP0jm+lGm2trLWy1qrW1mi97y0df+6FXreIHjrx3C8pv6xQa/P+o3bbJklqs61ak/eaSoYN1XGfPd/jDgEgNX/xCvmLV2hGdYs+Vv2WxmqDAlXL9M8n39eiZVO0t6Faza27VeTbosrSNV1e73TIh1vDQNzcy4ua9O9tTfr3tmZ/7z8ZjoCiXzj7q9co1Nquvz/5R4XbQworrMKiYp3y+a/ouDPP87o99JDf79f3fvuobv76xfrnxqflzytSWzio8QfO0LduvYfbsADISd3de3Nvw0Y1t5Z3OeIJANjPWGuzXnTKrDn2+kVLs14X/V9bW5vefOXvKvAVaPa8IwkqA0BNdZU2rXtbk2d8QKMrJ3rdDgB0kT54Si0NkYFAFcVdj3YCwGB16iNrV1prD0983JUjoMaY+ySdKGmHtfZgN/YEkvH7/TrsqGO9bgMuqpg4WRUTJ3vdBgAkFTvVNtkRz33Bs3SLKuKOeCY7LS3ZkNrEdakG2TpZ52ZN+ve2Jv17W5P+M1czxq1TcO+X9CtJv3dpPwAAAM+kC557G6pVFwx0ufdmujdc8W/QUg3uSFyT+FhP9upLTTf3ov+e13RzL/rveU0396L/5FwJoNbavxtjJrmxFwAAgFd6Ezxj3B4C4tZeXtSkf29r0r+3Nek/vawNITLGXCTpIkkaOYbbZgAAgNzhJHhKgaRTbVMJxx1GSPdGLRx3GCHVOjf3il/X7RqXatJ/8nX0T/893St+XX/tP2sB1Fp7l6S7pMgQomzVBQAASMXJNZ7S/gFD+96I9UQ4/elxsTVxn3JnLy9q0r+3Nenf25qDoH9uwwIAAAYdp0c8K+KOeJroR7zEN1km4XO6dYlrnK5zsyb9e1uT/r2tSf/ZqxmPAAoAAAaNWPAsad+pQEG941Ntw0r+hi3xNLNwkscS14UlWQf7OakZ28tJTfrvXJP+6Z/++1bTaf+J3LoNy0OSPipppDFms6TvW2vvdWNvAACAvuoSPDf37BrPXB3w4fawEPr3bi8vatK/tzUHS/+J3JqC+1k39gEAAHBTX4NnKq4P7nC6LovDQug/wzXp39ua9O9ZTU7BBQAAA0664OnmcKG4T2nX9ddhIY738qIm/Xtbk/69rdmP+yeAAgCAAcPpEc+KhCOeTodt5MLgkb7UpP/9a+RwHf1nZi85XEf/mdlLDte5VTMeARSAZ1aveEkP3nStmhsaNXTkSJ171XWaedi8jNZsaqjVo7++SVur3lNgxAh96otf0eTpszNaM7hnjx6/62ZteHuViocM0SfOPF9z5h+V0ZqDyYrnF+vFJx9Re2ubZh4+Xyd94cvy+/1et4UsSxY8ja3VktULuj3VNiznwzZyYfBIX2rSP/33pSb9039vaiYy1mb/lpxTZs2x1y9amvW6AHLHzVdeqJXLn9MIjVZAw9WoOjWqVvMXfkqXXX9bRmr+8+kndM8PvqWycEDlHSPU4mvWDtXo4585R+d849qM1Fz7xqu66Svnq6A1XyM6Rqs1L6jtel+HfORYXXHTnRmpOViEQiFdf8FntOGtVRoTnqB8m6/a/Brll/l1zX2PqWLiZK9bRBbEgqckjdUGBarig+dG1QXLJanH13gCAPrm5IfWrrTWHp74OEdAAWTd6hUvaeXyZ3WIjtIwM0qSNElSvd2mFU//RZ/83AWaPHOOqzXbgkHdd93Vmtp2sMaaCZEf14Wl8bZJzz/ygA456hgdPM/9o5K3X3WZRrdUaIpmRWpaaZKdrtf+/oKeXnS3Fp59oes1B4sHf/FDbX5rrT4U+oQKjF8y0uSOmVq78z+67esX6SePP+d1i8igdMGzpcGv+mCTpPK+XeMJAHBdb6fnAkCvPXjTtRqhMfvCZ8wIM0blGqF7fvQt12s+9bs7VNDhj4TPOGWmXGPsRD312ztcr/nqsme0u7FBk+yMTo8XmRJNCE3TC4894nrNweTVvy7VlNCsSPiMMsZoavhg1VS/p5qq9R52h0zxF6/QnB3LNKO6RWO1QTOq7lH5hke0dNU0PfrCOL1f06T6YGS4UCx8AgByB0dAAWTd7oZGjdKYpM8FNEI7G+pcr7n9/SqV2fKkz5WFA2ravsP1mpvWvaOyvIDywl1/1lemcu1oesf1moNJS/Nulanr97TA+FWYV6yN765RxeSpHnSGTEh/qq1fdcEmOR0uJPWfwR3033mNHK6j/8zsJYfr6D8ze8nhulzsPx4BFEDWDR0xQk2NdZKmd3muSXUaNmKs6zXHTjxQq8wLSZ/bndek8jEVrtecNOsD2h3eqbANK890DqG7TKOGDhvues3BpLQsoF31jSpWaafH22yrWsN7NWnGBzzqDG5yGjxTDRdya3BHbJ2TwR1uDwuh//3r6N95TfrvjP57VtPt/p0+BwAZcd43f6QG7VC93d7p8Vpbo51q0IXf+7nrNT957pcUKghpi63q9Pgu26BtZpNOvuArrtc87KhjFRgxShvMO4of+LbX7tGmvHU6+syzXa85mMw/4SRt8K1Rm23d95i1Vuvz3lTl5IMYQtTPpTvV9rEXKvR+TZPqgpHgmWrAUJ6cvdFx+mbI6V5u1aR/b2vSv7c16d/bmm73H48joACybuZh8zTv+BP1yjOLVW5HKKARalKddqpBR51yhiYeNNP1mn6/Xxf98Of6zXe+pm2h9/dNwa3Xdp3w+Qs067D5rteUpK/c9Gv9/NJzVb93m0Z2jFGrL6gddos+eOwJ+sQZ52Wk5mBx5uXfVvXat/WvlX/VaI1XfrhAtb4aFQ0bom/e+pDX7aGXkh3xlKSlq6YxXAgABgBuwwLAM+vfekP3/fjb2tVQr/KRo3Th936ekfAZb8/uJj1+5y3asmGdAiMO0CkXXJ7xI2VtbW36y32/1LrVr6ukbKgWnn2BDppzWEZrDiZvvLxcyx5fpLbWVh0870gtPOsC+Xw+r9tCD6UPntWqDwYkicFCANBPnPpI8tuwEEABAIBn0gXPvQ3VqosFzySn2ToZkOHV4A63atJ/9+voP/U6+u9+Hf2nXtfXvbgPKAAAyBndB8/Uw4W648V1V27t5UVN+ve2Jv17W5P+M1czFQIoAADImvTBc2OfgicAIPcRQAEAQMZ1d42nVK36IMOFAGCgI4ACAICMioXPkvadGh+qk9m6XEtXTVNjfUiFJjJgqKJ4jSqKt3jdKgAgwwigAAAg40rad2rc1kLpAMnYWjXWT9Er2z6s2cOecTxgqL8M7uhJTfrfv0YO19F/ZvaSw3X0n5m95HBdf+o/FQIoAADwVC4P0cjVmvTvbU3697Ym/Xtbs69DiPr6egAAgF7iQk8AGGw4AgoAADzFwCEAGDwIoAAAIEvSJM28pL9M+8rEdU7W9GUvL2rSv7c16d/bmvTvbU23+48hgAIAgCxJfJsS+X1e9OFwkhXJXplqXeIaJ130ZC8n6+i/c00396L/ntd0cy/673lNN/fqr/0nQwBFv9IWDOq1F/6qvHyfjvjYQvl8Pq9bypjF9/9G9bXb9LFTz9KEqQd53U7GvPL8Ur3z+r80+/AFOuLohVmpWVNdpXWrXtXYSQfqoDmHZaVmQ+12vbni7xo2aozmzD8qKzW90NbWptdffFbhcFiHf+QT8hcVed0S+pH+PnAjV2vSv7c16d/bmvTvfc1EBFD0G/f86Ft6efGTygvnKWzDusf/TX3i7PN0xqX/53VrrvrtDdfohccfkQ2Hla8CPffQ/RoxpkI/fvQ5lZaWet2ea1578Xnd8a3L1draokIV6fmHf6+ioiH62q13a/YRCzJSs6mhVjdd9gVVv7tGRXmlag23aNioMbr4Rzdp5mHzM1KzLRjUTV89X2tff0WFplht4aBKA+U66xvX6MMLT81ITa88cPMP9cKjD0vtYckY3ev7po469Qydd9UPvG4NOYuLPwFgsCGAol944OfX6uU/P6EPhOYrYIbLWquGvTu09Ld3qaRsqE4852KvW3TF4kV362+PLtJMHaoxmiBjjFpss1Zte1nf/vQxuu2vK7xu0RV7mpr0yysv1ujweE3Vwco3BWq3bVoXXK2fXfp53fXPNfL7/a7Xvf4LZ6i9JqgF4ePkt0UK2ZCqd/xXN11+vm58crmGjxrtes2ffvnz2rp6nT4YOkbFplRhG9bWxo26+/tXadTYCTpobnaOwGban+6+VX/7wwP6QGieyjVSkrSzo14vPvqQSkpLdcaXr/K4Q+QyhhABwODR2yOnQNaEQiG99Oc/aWboMAXMcEmSMUYjzGhNDR2s5x6839sGXbT4nl+rUlM01kyUMZHb+ZaYITpER6qhdquq3lntcYfu+OV3vqKCcKGma67yTYEkqcD4NVOHKS/k0x3fudz1miueX6zams06OHSE/CZyWqjP+DRFs1TSPkSP3fFz12vWVK3XulWv6QOh+So2kaPXeSZP48wUjQ5X6tE7fuZ6Ta8se/hBTQ/N1TAzSsYYGWNUbkZqeugQLX/sYa/bQ85IkTTzOn/kJflIXJNsXbI1Tte5WZP+6Z/+6Z/+lVKap4DcsH1Tlfbu3a3hOqDLcwdonOrrtnrQVWbs3bVbo1XZ5fEiU6JilWrpg/d40JX7qteu0djoEd54xhiN0Xitf+s/rtd8/cW/aaTGKs90vW54VEeFNqxa5XrNV55fojLfMBWartdBjgpXqGbdetdreqEtGFRD43aNUkWX50ZprHbtrNfupiYPOkPuSXzbkbfvv929IclLWJdsfeKanqxzs6abe9E//fdlL/qn/77s1deaqXAKLnJe0ZAyWWsVUkj5CX9l29Umn2/g/DU2xqjdtnV53FqrdrVrSPlwD7pyX35BvtrUmvS5NrUqv8D902+LSkrUbrp+baXI36OCQvdrlpSVJf1+xmrmFxS4XtMLvoIC5Zk8ddh2+VXY6bkOtcsYo0KGEcGB7t7Q9GSdm3t5UZP+va1J/97WpH9va7rdv1uvA7Jm+KjROmDsBG0x73V5bpNZrwnTZnnQVWaMmjhB1XpX1tpOj9drm8IK6bNfvdqjztz10ZPPUI02qs12DqGtNqhtel+fOOMLrtc8/qwL1BjeoRa7u9PjIduhLb4qzVt4kus1P3bKWerwtavB7uj0uLVWm33v6eAjB8Y0XJ/Pp/FTpmuTWdfluffNeo2bOJVpuEgh/cWf4XD0o7tdomvSrXNzLy9q0r+3Nenf25r0721Nt/sfOIeOMKCd/X/f0y+vulStoVaNCY+XVVg1eRvV4K/T1VcPnOvLvvaLO3X1/x6v/4Re0iQ7Q34VqlZbVaV3dPgxx2VkMI8XTrvkSi177CH9u+FvmmoPVpnKtUuNWq83NXx0hRaefb7rNSsmTtaHFp6sfz+zRJNDMzVMI7VHu7XRt1ajJ03UwrMucL2mv6hIJ5x7oZ669w5NCh+kEXasWrVXm3zr5BteqLOuGBg/UJCkz3/rB/rZZeepo71dY8MTZWS0Na9aO/Jr9LWrBsap48icbocQOXjjE1vgZJ2be3lRk/69rUn/3takf29rurGXSTzSkg1TZs2x1y9amvW66N/WrFyhR3/1M21+978yJk+TDz5YZ339u5p40EyvW3PVpvXv6pYrL1T95i2yNqzCkhJ99PTP6uyvXuN1a65qa2vTjZedo/f+8x+FQh3Kzy/QtMMP17d/vSijdZ+6/w4tf/Qh7WqsV1FxiQ49+lh97v9+kNFw/+JTj+rp396lum01KvAXaub8+frCt36ssvLyjNX0wntvr9ZDN1+vTWvXSJLGT5+pz3z1m1m71ypyl794hQ5dv1XjthYq74Atyqv5ox5cPk+vbPuQZg97VhWla/atNQmfYxLfzJgka5yuS7amtzXd3MuLmvTvbU3697Ym/We25qkPrV1prT08sQ4BFAAAZFTqAPphzR72jCrjAmhY3V8fFHsD5GRdNvfyoib9e1uT/r2tSf/e1uxur5NTBFBOwQUAADmjvw/boH/v9vKiJv17W5P+va3Z22FCBFAAAOCRbq8milwfmpf+jU447sfw3a7L27c043vFr6N/+u/pXvHr6J/+e7pX/Lpc658ACgAAPOXKECKn6xwMyPBkLy9q0r+3Nenf25r071lNAigAAMgIf/EKzahukSQFCurlCy2TqanVktULVGSqNXvYs5GFCT8qz+VhG7kweKQvNel//xo5XEf/mdlLDtfRf2b2ksN1btWMRwAFAACuig+eY7VBgaplkqSlq6Zpb4NfdcEmSYFOw4diwkr+hicvYY1V8lO8kq1zsp/Tmm7uRf89r0n/9N+XmvTvTf+JCKAAAMAV6YPnxrTBM8bNwRdursvVvbyoSf/e1qR/b2vSf+/WxSOAAgCAPkkXPFsaqlUfbJJUroriSPDs9ppPAMCARQAFAAC94i9eIUmaUd2SJngG9gVPAAAIoAAAoNfy/VUqaS/S0JCVsbXS9rVqrJ+i5taAKhJOtfVqcEdva+bC4A76d2cvL2rSv7c16d/bmgwhAgAAWZd4bVA4yWOJ67watuFkiAb996wm/XdG/z2rSf+d9ff+4xFAAQBAVgyGYRu5upcXNenf25r0721N+k+NAArAE6FQSI/+6kb9a+lftGf3Lg0JlGvBSafqjEu/kdG6ix+4U8sf+YN2NtSpqKRUhx7zcX3uyu/L7/dntC4wWDFwaHDb2dqme/6zQ1V7gmrvsBpZUqATJg3Th8cHvG4NgEcIoAA88ZNLztbGN97U5NAMlWmWdgUb9dff3quNa97UVb/6XUZq/uZ7X9crTy/W5NBMTdJU7Qnu1it/ekrvvfG6fviHxfL5fBmpCwxkc9YUdfr9g2vO3fdrwufgtjPYpu+89L5mzi7Q/ZeP1gEjffrzM8362S+3q66lQydPH+F1iwA8QAAFkHWvLntG6954TfNDn5DfFEqSSjVUw0OjtWLFs3rrlZd08LyjXK25fVOVXl76pD4YPlolpmxfzRGh0Vqx4Xn99aH7dMLnLnS1JtDfxKbaOjGjukUl7TsVKKhXoGqZlq6aJmmBiky16oLRo1tJzs3K5WEbuTC4oy81c63/375Rq2kz8rX04Qrl5UVWHjyjUHNmFerCy3foxIPK9/3gLxf772lN+t+/Rg7X0X9m9pLDdZnuPxUCKICsW/6nP2hMeOK+8BlTaIp0gCr13GMPuh5Alyy6R8PyDlCJLev0uM/ka1xosv619C8EUAxaibdTcSqwORY8p2lvQyx4BlRZ2rPbrnCtlLc1M9V/VUtQd3x51L7wGXPix0tVUGj08qbd+sjk8j7X5OvvbU3697ZmLvefCgEUQNa1BveqwBYk/XFZQdivtr0trtcMtrSowCa/zrNAfu0Jul8TyHWp7uNpbK2j1y9ZvUB7GzaqLliu3gRPDGwdYavhw7pe2mCMUXkgT7vbOUcbGIwIoACybvqhH9Sy1Q9qUscMGbM/hVprVZtfo/mHn+p6zUM/coz+/cxihW1IeabzG6La/BrNnuPuEVcgl6UKnktXTVNjfUjSlG73KDSbVR9sklSuiuJI8OSaT8QbWVigxxfv1gcP6XydcPX77are3K6vfXwIf2eAQaivR1ABoMdOOf8rMqV5ejdvtTpsuySpw7Zrbd5/VDi0RJ8852LXa84/9kSNrKjU275X1WZbJUkhG9IGvaOWgmad/uWrXK8J5Bp/8Qr5i1doRnWLPlb9lqYH39t3/eZjy/1qaahWc+tuRx/1wYAqitfsC59AopOnDted9+/Sosd3KRSykqQN1e065dwafeCAEo0sZvo4MBgZa23Wi06ZNcdev2hp1usCyB2b1r+j275+qXbUVKs4r1R7w3s0dvwUffWWu1UxcXJGajY11OrnX/6CNq1bo+K8UgXDLRo2aowu+tFNmnXY/IzUBHqrJwOBnIod8RwatDJbl2vpqsi1m5JUFwyoIsUptLk8+KK3Nek/OzWfW9+oJ9+rVzAc1vCAT9t2hHTwASX6+ryxKoibPJ6r/WdjLy9q0r+3NQdL/yc/tHaltfZwJa4ngALw0ntvr1b1u2s0edYHNHn67KzUrKlar3dXv6YxEw/UjLlHZKUm4FTsCKWkHg0EciJV8OTaTWTaq5t3a2drSIePK1F5EUc+gcEgVQDlGlAAnjpw9hwdOHtOVmtWTJ6qislTs1oT6E5i8OzpQCAnIkODCiRFBgdVlq5RZekW1/YHUjmisqz7RQAGBQIoAAAeSjcQqKWhWkbjUr42/hymdPdg27+uWvXB8ui1mzUMgAEAZB0BFAAAD3QXPCNhset1mYnTA5NlyGQTBmPrKuKOePZ1r5725UVN+ve2Jv17W5P+va1JwHpN0AAAIABJREFU/8kRQAEA/Up8cOvvEoPn3rjgGX96bOwf82RvBuIfC6dY43Rd4ppUersX/fe8ppt70X/Pa7q5F/33vKabe9F/z2u6sVcyBFAAQL+QeMRwaDD7Q/TcZLYul9Q5eNYlBM8Yp/dMc3Ndru7lRU3697Ym/Xtbk/69rdnf+0+GAAoAyGmpTlV1cziPFyIDgTaKgUAAgMGEAAoAyEnJjnjGbiESuUZynMPBO84G9GRrr/3rGAgEABh8CKAAgJySPnj65XQ4j5T9YQ893SvdQKBM1czWXl7UpH9va9K/tzXp39ua9O9sP4kACgDIEemC59644Jl4qmouDXtI9g91fxpWQf99q0n/ndF/7/ai/57XTIb+e79XT2smk+y1MQRQAICnnATPVMN5pPT/yPV0nZt7eVGT/r2tSf/e1qR/b2vSv7c1c7n/RARQAIAn+ho8UwnH/Rg43T+O4bgf76Za59leXtSkf29r0r+3Nenf25r0723NLPdPAB0Agnv26Mn7blP1f9eoNFCuk869VBMPmul1Wxmx7ImHtfKFZ2Ty8nTkJz+t+ceemPGaj995s15a/JjC4bBmzztKF3/vxozXHCwattfo8btuUf32rTpg3AR9+uIrVD58lNdtIcMcX+NZvEYVxVt6P5wnnP70oNiauE+5s5cXNXOk/2B7SI++U6eNTW0a4s/TKdNHaPKwon7Tf07s5UXNHOt/086gnninQTtbOzRpWKHOmDlSRQW+Xu3V476crhvAX39P9/Kipot7vbF1t/66Yafaw1b/c0CpTpgakM+X5O9ujvbvZJ2xNvv3UZsya469ftHSrNcdiN5+9WXd8rWLlN+Wr+EdoxT07VWttuqjp56p86++3uv2XLNnd5O+/7lT1VBTo9HhSoWN1XbzvsZPm6Hv3v+4/H6/6zXb2tr01ePmqXlnk8ZognzyaZs2Ka8gXz/642JVTJzqes3B5OlFd+uRW2/UUA1XWUdAu/KbtNs06Zyrvq9jTjvb6/aQAemCZ2N9SEVms+qSDBcy6jpVNvEfNpPwOd26ZBNqnazL9F5yuG4g9//mtmbdtnKrxo/P18JjS7TuvXYteX6Pjp4Q0BcPG5Pz/fe0Jv3vXyOH65zUvHfldi3f1KSFx5Rq+rQCPf18i6o3dejSQ8bo0IqynO+/v3/96b/ne0lSOBTST1Zs0Tv1QX3mlCEaVp6nR55oltqMvrdgvEaW+nO6/2TrTn1o7Upr7eGJdQig/VgoFNJlxx6hUbvGaJKm73u82e7S674XdcmPb9H8j2f+CGE2XH/hmdr+xgbNCX1IeSZyUL/Dtus/vn9o9if+ny67/jbXa377zONV9+4mHaGjlW8KJElhG9Zqvaz2QEh3LH/d9ZqDxfbN1brq08fo4I4jNMLsf1NZa2v0TsF/dMvT/+RI6ACSGDwlKVC17P+zd97hbZXnG36OliXLtrwdO87eCYRAAgmBsAqFhhlW2aNltdACbSmlLfwolA4KZZVRoMyyCaOQkECaMNNACGQvkjhOPGNZHrJlSfbR+f3hyNG0juwjf0f2c19XLoP86n1uH8uyX53zfYoaPMsjBk+g+xdYojUmwV+GaurUrFcZ6Ez6dyPLMq7/qAI3Xu/ALdfn99y+aZsPR59WhZ9MH4a5o3I0zdS6l4hM+ofzVZUbD39Ti0//U47pUzN6bn/wn02498FmPP79MZD2n03So3+6H3/6973XM9/UY4OnDSsXl6OosPsiVVlWcMXP6rH+y07cc+zoBN30d/zPjDOAqvleEJ3yyX/egL/Ng1HKxLDbs6QcDA+MxQcvPC3ITFu87e3Yvu5rTJQP6Rk+AcAkmTFePgjrP1mRktya777DRMzoGT4BwCAZMBmHwd3SiNq9lSnJHQos/OeDyFOKwoZPACiSypCt5OKtx/8uyIxoicW2ChbbKkyu9OD4yo0oxS44Kpbji3f24qXlY9HhqkSbzw2rsTrm8Amo+yVlSKJODQOdSf9ullW0wmABfvmTvLDbp03KwE+ucGBJZZPmmVr3EpFJ/3AWV7hwzaU5YcMnANx4TS6sduCDnS269k/340//vvda29SGP99R0DN8AoDRKOGBu4uwy+VDjdureeZA9YqEa0DTmL07tiBHyockRZ9Ez1HyUNtQJcBKe/bV7oESUJApZUV9Lgf5aO9oTUlul9KFHORF3W6VMmFQjNjy9ecoHTEqJdmDHWf1XuTIeTGv/8jpysW+mr0DL0U0o/cznmNhlSrR5nMg116d1OZCAAZ844XQuoQ1GmUOVf89LX7MPCQDBkP0E8PsmVYsXNjee68+ZKa6V2id3o9/orp08W8PBDB7pjWqXpIkzDzEij3bfZpnpqpXaF26HP94dfRPnNnSIePwQ6Ifu4UFRhTmG7HT5UNZtlW3/pG9eoMDaBozfNR4fKa8AUVRooZQt9SM7IICQWbaUlBaDkkCOgLtsEn2sM+50QybNXow1QKTZIJbaUY+isNu9yodCEDG5MNmpyR3KFBQWoadG9ZELyQA0GZqweiSGQMvRfpNosEzY//gmWOr7vfmQiEfeq1TU6NZLxGZg8h/eLYZH2x0x/yd9u0GH2ySMfFjhsdfXC8RmTF62SQDvlnvwzmnZYeVKoqCtRt8OK4gL/7jSAf+fe4lIpP+mmZmW41Yu8mHUSPMYbc3NctwumSMmZER/tjVmX+sunj05awp0QnHn3MRTJlmVEk7w273KG2oMuzC9y+6QoyYxtjt2Rh30KH4zrABAeXAI1pWurDTuBEHH3VMSnJLxozBdqxHl9LVc5uiKNiOtcjKzuMmRP1gwTU3oxF1aFIawm5vVOrRAhfOufYmQWakL6i91DbDWN29wdD+a3ak/f8MEf8Q8S9Wjdq6WDV9zdSyF/2j604a54DPAzz2bEvY42tHhR+PPN2Mk0Y6dO2f7sd/sPifMioPjz3bgm07/GGPo6f+3QJ3awDzJzp07Z/ux5/+ffc/ONeO2/7oRHOL3PO4DQQU/PouJ0blWzDcYdW1f8yaOHATojRnzWfL8NitP4Oty478riJ0GDyoRxXmzj8T1901eNbRuV0u3H7xaWh3tqBELkcAAdQZ96B41Cjc9e//wGKNvmShv7S3t+PmU+bA1+5BGUbDABNqsRsBk4L/e/5NjJkyXfPMocTb/3oE7zzxIPJRgmw5F25jM1zSPvzw57di/iVXi9YjKujtjCcAdLgq424uBEB3myUk00tE5lDw/6rKjce+rcW0KRk49fvdu+C+9q4bc4dn44bDy1KSKaKXiMyh5P/E17X4vKoV552RhckTLFj8kQfrN/lw7SHDMHfkgY2s9Oqf7sef/n3LlGUZd62swh63D5f/MAd5uUa8vNANd1MAv51TjjKHVdf+sYi3CREH0EGAu7kZC/95P/Zs2wJ7bi5OvexaTJ5xuGgtzZFlGR+8/DTWfrIcBpMRc04+AycsuCDluc/dewe+/u8SyLKMSYfOwk/veSQlb/syFKmp2IG3nnoQrtpaFJaX45xrf4GScq6r1TuJB8/dcHpz4w6ehPSG29uJlzc0oqrdh0yjEWdOysPUYnviOxISwpaGdry7tQmegIzSTAsuPLgAuVb+7ib657PKZqzY3YouRcHU/EycPS0flljvA5oGcAAlhBDSb4KX2sYaPD2uSjR6HSizcfAkhBBChjoLXos9gHITIkIIIQmJP3hOCBk8uzcXIoQQQgiJBwdQQgghcelt8Ayu8SyzV6Ms4u1UJMR8l52ojfFi1cWqgcq6RJla9opXR//4dfRPXEf/+HX0T1xH//h19E9cp7V/PDiAEkIIiULN4AnE3mAoAEBB7F9Ghog6NTUKYm9woKZXrDo1vegf3ov+B+ro33sm/Xuvo3/vmfTvvS7d/OPBAZQQQkgPvQ+e3ZsLxRs8g6jZgU9tnZa9RGTSX2wm/cVm0l9sJv3FZtI/PhxACSGEqFrjCeT2bDAU943cCSGEEEJ6gQMoIYQMYYKDZ2ZnCxzmxjiDJ3e2JYQQQog2cAAlhJAhSNTgWRV7jWdZjEttB3rjhWQy9bLxAv373wsq6+ifml5QWUf/1PSCyjr6p6YXVNbRv/de8eAASgghQwi1g2dvazxjwbUuYjPpLzaT/mIz6S82k/5iM/XsHw8OoIQQMgToffBUt7kQIYQQQkh/4QBKCCGDmN4GT24uRAghhJCBhgMoSSv8fj82f/0FTEYTpsyaC6PRKFppULFs4UvYvv5rnLDgIkyecbhoHdIPLLZVAIDDdtTCYW5EjqzAsPd1LFo/F02NMtp8bnBzIUIIIX3B6fFj+a5mlGRbcOyoXNE6KUOWZWzY5wEAHFycyb87NYIDKEkbXrzvTnzy9huQ/Z1QoCDDlon5V1yNM390g2i1tOf1x+7Don89DlnpggkWrHzvLVgybPjz20tRMmyUaD3SR0yWCgBW5HgVwNEC1ABNjTK+rDsK0/KWRG0wJGrjgr5m6mXjhb5m0l9sJv3FZtJfbGZfe3X4/bh1xR44PTJysg1o3RnAi1v34fvDc3H+9GLd+ydz/F9e34CPq5vRBQUAYIKEY0oduHhGcVr46+H4x4MDKEkLXn3kz1j+2ss4SD4CuSgEADjbavHW4w/CmpmFky+4QqxgGrPms+V47+l/YAQmYDQmwySZ0KG0Y5NvNW49/UQ8t/o70YokReh544J033iB/vrPpL/YTPqLzexrr1tW7EF+iQFLnxyOSeMt8HoDeOKFFtz+l0aUZltw7Jj4Z0P14K+2buEmJz7c24SXnxiG7x+XCQBY9qkHF15bhwyThPMPKupX5lB5/KTq/oSkHFmWseKNVzFFPgx5UhEkSYIkSSiSyjBePghLnn9KtGJa89Sdv4QDhRgvHQST1P2alE2yYwaOQpfciVce/rNgQ6I9XOhJCCEkOdbXtqOxXcbil7uHTwCwWg246Zo8nH9GNl7e7BRsqB0f17bg0b8W4+Tj7T1/d550rB2P/60Yn9a2itZLe3gGlOie+qo98LS3ogDDoj5XgnJs27dWgNXgwdvchgmYHnW7STIjXynGyiXv4MKf3ybAjGhKjJmTGw4RQghRy3vbXZg2yYKyYdHjw4VnZ+P9D9sGxe8VnyyjqrETZ8/PivrcWadk4eLr6tDml5Fp4nrQvqLJACpJ0ikAHgJgBPC0oih/0aIvIQBgtWZAgYIAZBgjHrJd6ITRwCeA/qBICmSlM+bnutCJDEv2ABuR/hLcgGj6Zisc5kZABgzblmLR+rkAZEzL+7C7MOIamMhLYuL9HaGmLtblNWrqUt1LRCb9xWbSX2wm/cVmatkrwyyhri32V9bqDkCCBBj066+2zqIARgPQ1h5AviX8b8x2TwCSBJgkwBDRTC/+ej7+vfVNCkmSjAAeBfADAFMBXChJ0tT+9iUkSH5JGYpKylGNiqjP7ZV2YsT4KQKsBg8lY0ZjD75DQAl/umhX3GiFC5f88k4hXiR5LLZVPW+7cnzlxu63XalYjg+WVGHR+rnocFWizedGuX0zyu2bYcCBXwKxfhkYQv4hybpYRNaJ6EV/+venF/3p359e6e5/1SHFqK7twv++7girDQQUPPDPJmQr8c9r6cFfbZ3RaMTYwgz845nmqPpHn23GuKIMWM3RJz/04q9lZn97xUOLM6BHANihKMouAJAk6VUAZwLg3v5EM35482/wxO9uRqfsxzBlJBQEUG2oQIO5Fr++9UXRemnNb596Ez//3kysUT7GOOUgZCILLuzDd1iPnPxCzJx3gmhFkoDgGc/JlR6UYhcAwFFx4P0+O1yVcHodKLdXo9xeHXX/RL9s1NZoXafXXiIy6S82k/5iM+kvNjNYk2u3YFyWFfMvrMaffleIH3zPjuraLtzzgAubtvrxl6NHa+Ym+lhcMKkQDzxei9bWAK68KAcSgOdebcVTL7bixpmlKckciF6iMiORFEXp4133N5CkcwGcoijKVfv//1IAsxVFuSGi7hoA1wBA4bDhMx9evKpfuWTosXblCiz8x/2ortgBCQaMnDwFF978W0ycPlO0WtpTX1mBO65YgI6WVigIQIIRI6ZMxj0vLRKtRhIQPOMZPXgCHa7dcHpzUW7n64GEEEK04aGV1Vjf4kGHPwCzSUImDPjNUaUYlWsXraYpG+rb8fo2J6rcfgDA8CwLzp9ciOklg+vrTCVnvrJ1jaIosyJv12IAPQ/AyRED6BGKovws3n3GTp2u3PPS4n7lEkLIUKa3wdPjqkSj14EyGwdPQgghhIhhwWuxB1AtLsGtAjAi5P/LAdRo0JcQQkgMLLZVOGxHLQAgR1ZgqHkdANDUOBZtPjfK7NUo23+p7WB9c2v6pyaT/mIz6S82k/5iM+kvNjPV/qFoMYCuBjBBkqQxAKoBXADgIg36EkII6YXhtRlA8f7/qd8KYDaA8DUZAcReoxFZoyD2L5DIOjU1isrMRL2CdfRXn0n/cOifXCb9w6F/cpn0D4f+8en3AKooSpckSTcAWIrut2F5RlGUTf3tSwghpP+kw2YPesqkv9hM+ovNpL/YTPqLzaR/6jIj0eR9QBVFWQyAizoJIUTnBPa/pNnbL42eNxJXU2foKU15r9A6+tM/2V6hdfSnf7K9QuvoT/9ke4XW0V+jAZQQQoh+6PkFELeg97UZSdUFwj7op5eITPqLzaS/2Ez6i82kv9hM+idVxwGUEELShND3+3SYG2EoViDVrsCi9XPR4RoOq1SFNjiiXnbU82YJeth4oT+Z9D9QA5V19E9NL6iso39qekFlHf1T0wsq6+ifml5QURcKB1BCCNE5oYNnKXYhx9s9eC5eNwEdLguASji9DpTbN6N8/+63QQLQduMCrTdLGOiNF+iful70Tz6T/vTvTyb96d+fzIH0j4QDKCGE6JTeBs+mxrGwSvEHzyC9/QJIpkbrOr32EpFJf7GZ9BebSX+xmfQXmzlU/CPhAEoIITojcvAEAEfF8rDBs83nQK69Ou7gGQ+RGxcMVCb9xWbSX2wm/cVm0l9sJv3FZob26g0OoIQQohMSDZ4Z+wfPHFs1ymzViTcbikcg7EOvdWpq1PYSkUl/sZn0F5tJf7GZ9BebSX/xmfHgAEoIITrCZKlAZqcVObICOFogKQ1oahyLNp8bOfZqlIWc8RS1cUFfM7XsJSKT/mIz6S82k/5iM+kvNpP+/c8MhQOoxiz+91NY8cbLaHW5YM/JwdzTz8K51/0ypZmfLXoLHzz/FFx1NbBYbTj0hBNx8S/ugMViSWkuSQ0NNTW4/6YrUF+xG4FAALYsO06+/Gos+NENKcuUZRkvPXA31nz0IbyeduSVlOCUS3+E4868IGWZAPDWUw/hi3cXoq2lBdl5eTjm7PNxxhU/TWlmOhN5RUsgxm2RdQEM3GYDlc1e/HtjA2q8fkBRUGbNwEXTijAm35oW/mp7eTtlPLN2H7a5PfB3KcjLMOEHo/Mwb5QjZf6yLOPlDY341tUGT1cAORYjjitzYP7E/KR7hdbp8fgvr2jGR5XNaPZ3IcNkwJScTFx5aBEsRmNa+Ks9/jsaPXhlsxO1Xj8kCRhhteKyQwpRlm1NC/90P/6Dxf+D71z4uLoFLX4ZmSYDpufZcen0QhiNxpT5r9zTikUVTXD5OmExSpiQZcNVh5bAajEOueOvJpP+yX2OJMk/fnMD3njob8jam40p7Yciv7YQS/71L/zp2gtTlvnqP/6Kp+/8NUw7gcltM1DqHIEvF76H2y+YD7/fn7Jckhoaamrw67OOQ8uOfZgsH4oZylHIdxdh4T/uw+N33JySTFmWcftFp+GL1xaipKEMU9oPRUaFCc/98Xa8eP9dKckEgHtvuByLnnwcuTX5mNJ+KHKqHHjn0Yfw4C+vTVnmYEPNE7ghibr+9Nre0I47P9+L8bMMeOGJYrz45DBMmmPAH77Yg8372lOSKaKXt1PGbz+tRIPVi/v+VIi3/12K8y7KxJPr6vHqhoaUZALA3Sur8E27G3f8Pg/vvlSK636ajTd3NuLR1TVJ90qmbqCP/4tr9+G5jftw8RV2vP3vUvz57nzsMXjw+0/3QJbllGSK6PVNjRt3razCIceY8PLTw/DsYyUoPRi4/bO9qGz2piRTy14iMukfXffE6lq8/p0TV1+XjXdfKsWdd+Rhg7cNd35RpXlmsNfCTU489m0dzr7Qhrf+XYr7/1KI5mwfbvusEl6/PKSO/0Bmprt/JDwDqhE7N63HV8sWY3bgRNgkOwAgB3kolEux6puPsOqj9zHnpNM0zWx3N2PJi0/jEHkucqUCQAJykI9CuRSr9y7HO08/hPN/eoummSS13H/TFbB2ZWIWjoMkdb+e5EA+cpR8/G/Ru/jx7/+q+Znt959/HA279uAI+QQYpe6nhBzkIU8uxrLXXsDpV/4EuflFmmau/Ww5Nq36AnMCJyFDsvZkFsrDsOqTZdiyZhWmzJyjaWZaEuP6lT6v+0wxz21uwGUXZOP+uw48Vo450obb/ujEC2/tw58Kxwi0046X1juRmQ98sWgELJbun9FZM6w4arYN511ZizMn5yMj4kxdf/nvrmZUefzYunIUch3dvWceYsUpx9sx88Q9OHOiN+ysWbri9nViaWUzlrxehjkzbQC6j+1pJ9ox4/g9eHWTCxcepO1zkShe3ubEL6/Pxe9uKui57YSjM3HNL+rxr0/qcee8UQLtSDpQ3+7HJ1Wt+HLJCEydlAGg+3nh1BPtmHpUJRZvd+GU8fmaZnbKMt6vaMLr/xqG7x/X/bfu4TOAU0+048j5e/H8ugZcPXOYpplkcMIzoBqx5OWnUSSV9QyfQSxSBkoDo7D8zZdSkPksMpWs7uEzBKNkRLk8Dl9/uFTzTJJa6it2YzQm9QyfQYpQBoNiwOuP/lXzzC8/eB/D5TE9w2eQHCkP2XBgyYtPa5754RvPYxhG9gyfQaxSJkowHB++9pzmmYMBvQ6fsixjh9OHW27Ii/rcL3+Sh51OP3wRZ6/SlS2t7fjV9Xk9w2eQE47OREmxER/uaNE887PqFlx3haNn+AwycZwFx8+14d1tTZpnimDRd82YOM7cM3wGsdkMuOknudjQ1CbITFtcHj8qG/342Y9zoz53yw15qGjxCbAi6cZ/trpw9BG2nuEziCPHiJ/+2IGVtW7NMz+qaEFevgEnHZsZdrvZLOFX1+dhm9ujeSYZnPAMqEZ4OzwwBzJifs6iZMDn6dA80+NuhQVxMpGBTl+j5pkktQQCAVgQfSZDkiSYlQy0OKMv8esvPq8XWSiM+TkLrPC0tWqf6fHAErDEXDRgDmTA64l9yeaQI/IlwhgvGephswG/DPg7FRTmR5/5y88zQA4o6JIDsJmNabNZQrxeXQpQXBj7DGdxoQlt7XLU96m//rKkYFhx7MzSYSZs2xGImamHjS+SyWzvDKCkPPbXWVJoQleMBVB68lfbq60rAJMRyM6K/oEuKTLC61fCvk69+felF1TW0V99L09XACNL4vy8FJkgo/t5QUv/Np+MogJj1Ivk3ZlGdClKT+ZgP/7J9ILKusHoHw+eAdWIKYfNhtNYC0VRoj7nNNVh3CEzNM887NiT0BRogKx0RWca6zB8wkTNM0lqsWXZ0YDo93X0KR3oQBtOOPtizTNHTJoEp7E26nZZkdEYqMchx3xP88wJBx8Gp6ku6udFURQ4TXWYeMgszTMHA4aIf0D8hf+hNb1tIpCol5o6q9mIsnwTFi2LfuFg6QoPih0mZFvNqjMH2j9eZizyzSa8szj662xqlrFmvRezh9s19y/NsGDhf6LP/smygvc+bMchJbEzY6Hn43/EcDs++9KLdk/0qf63F7WhwGTWtb/a4z8i24zMDAM+W+WN+vx7H7ajNNeka/90P/6Dxf+QYZlYvMyDzs7o6rfea8OwjAzN/WcPz8b6zT40uqKvaHlncRvyzSbV/vEy0+X4J9NrKPvHw5C4hKjh5At/BGuOHdsMa9G1fyCUFRk7sRl+iw/nXHuT5pnTDp+L0tHjsNG4Gn6l+5IdRVFQrVSg0VCHc65P7e67RHtOvvxq7MEO7FOqe4Yzn9KBdVgJR34RpsycrXnm+dffgiajE3uxEwGl+w+/TsWPzcavUVI+EjPnnah55llX/RwBq4Kd0ibISvcvMlnpwneG9TDazTj18p9onjkYUfMEHvoLor+9eqs7sjgH1/1qH9asO/BH9dqNPlx1cz1mF2f3OXOg/NVmnje5AC8vdOOF11sQCHT/jDY4u3DeVbUYl2/F+ILwS9O08L/kkEKs3eDHXx52we/vzmx1y/jxTfWwSgacND78Uk4tj9lAHv9DhmWhPMeMC6+p6/kDV5YV/POFZrz/YTsumBp+pYbe/NVmGo1GHF6Uhcuur8PmbQcut/3f1x246XcNmFeao7pXMl5q69L18ZOKTD37nzAmF9kmI350Yz1aWrt/Xjo7FfztURe+WuPFRQcXau4/Jt+KCYVWnPvjWtQ3dP+tGwgoePmtVjz/qhvnTNI2U8/Hn/7J9YpEinXGLtWMnTpdueelxQOem2pqKnbg7zdejYaaPcg05sAju5FbWIzr//IIJs6YmZJMd3Mz7v3pJajcvhl2Yw68AQ+sWVm4/Ld3ab7pERkYHr/jZvxv0bswKAaYkYEOtMGRX4R731wGe270miEt+PrjpXj27t/B09oKq8GOdrkFI8ZNwi2Pv6D5BkRBdm5aj3/c8lO49tUh05gNj9yKwmHluPHBJzBy/JSUZOodi20VTJYKTN9sxQjZCWS3wLBtKf69YjbafG6U2zfrdh0oADz1TS0+r3GjuNAIgwGo2yfjyNIsXDezTLSapnxc2YzXtzsRkBSUFJmwY7cfEwutuOWIcmSatd2AKMiGfW3418Z6tPpkjCo347sKP0bkWnDTocNRkj143nKrxefH/atrsbPRiwljLKiu60KGQcKFk4pw1AiHaD1NeWRNDVbXtGH4MBP8nQpcTTKOLXPgikNLRKuRNMHZ4cfMAhQGAAAgAElEQVTfV1djT7MfE8ZYUFnViWyLEVdOK8aMYbFf+Osv3k4Z935VhW1OL8aPtqDe2QVJlnDu+EJ8b2xq/kYh6cuC17auURQl6rI2DqApYPvaNdix8RuUj5+M6XPmDUjmnh1bsOnLz1EwrBxHfO8HA5JJUoff78frj/4VLc4GnHD2xSk58xmLrz9eiobqPZg8ay7GTJo2IJmbVq9E5bZNGDPl4CG/822iAbTMtlm0YkI8nTI+29MCKMC8UY6UDWSikWUZq2ra0OSRMWNYJsodA7ML7Te1btS0dmJiQQYmFtoT3yFN2dPixfo6D4qyzJg9PDV/SOsBt7cTX1S5YTRIOGZUjuY7KJOhwU6XB1savCjLMeOw0oH5ealxe/FNjQe5mQYcWZYNIx+7JAYcQAkhROdEDaCOFhi2hAyg9ugBVC+bDehl44W+ZtJfbCb9xWbSX2wm/cVm0j91mWe+EnsA5S64hBCSJiSzzkLEuhOteonIpL/YTPqLzaS/2Ez6i82kf+oyU3V/QgghhBBCCCFEFTwDSggheiXGhkN63oSIEEIIISQRPANKCCE6wGJbBQCYvtkKh7kRAGDYthSL1s/tqeHwSQghhJB0h2dACSFEMBbbKkyu9KAUuwAz4KhYjsXrJgCYiw5XJdp8DpSHbEAUnEMTvYIYUFGjtk7LTPqLzaS/2Ez6i82kv9hM+ovNFOEfCw6ghBAiiLDBE6GD5wR0uCrh9DpQbq9Gub067H563nAg3TdMoL/+M+kvNpP+YjPpLzaT/n2ri4QDKCGEDDC9D5674fTmxhw8CSGEEELSHQ6ghBAyQPQ2eHpclWj0OgDkosy2mes9CSGEEDIo4QBKCCEpRt3g6UBZyDrPWJe1xJpJI+viza1q6lLZS0Qm/cVm0l9sJv3FZtJfbCb9xWYmeg2dAyghhKSI4OCZ2dkCh7kx5hpPIPYGQ7EIfYKPt/A/sibytr72SjYzFvTve69kM2NB/773SjYzFvTve69kM2NB/773SjYzFvTve69kM2Mh2j8SDqCDAL/fj0Uv/hO7N69HliMPZ/zoepSUjxKtRciQJWrwrEo8eAZJ9KSdTJ2WvURk6tm/ptmLt7a60N4ZwKQCK86clAej0ZgyLwBobvfjjc0uNHZ0YUSOBedNLYDVkrpMPR9/rXvJsoylO1uwrt4Dq8mA0yflYXy+LaWZAPBZZTP+t6cNkkHCSWNyMKMsu8+91Natq2vDRztbIAcUHDkiC8eMzk1JpujHT73bjze3NKLFK2NsXgbOnpoPy/6f0XTwV1vn7ZSxcIsLlc0+5NmMOHdqAYrslrTxH4heIjLp3zuSoih9vGvfGTt1unLPS4sHPHcwsn3tGvz9xh8h0BFAvlwMr9EDl7IPJ11wOS795R2i9QgZUsQ/44mezYUAxBw8Sfrw5Jo6rNjTghOPycTokWa8v7QdHW0KfnXE8KihRSsWbnLire9cOOKwDBw8NQOffNGBPXu7cO2MYZhTnp24AYlLvduPe1btRadRwYL5duxzylj0UTuOKM3CzXOGpySz3S/jri/2YF9HJ845PRs+XwBvL27H+LwM3D63POrFDC2QZRn3rKzCNpcPC+bbYbMZsPA9NwoyzLjz6JGwW7TPFMWLa/fhg4omzDvShknjLfhwuQdOp4wbZ5bh4BK7aD3NWF3lxuPr6jB8uBHHH52JjVv8WLWmA2eNz8f5BxWJ1iMEZ76ydY2iKLMib+cZ0DTn4V9dh8K2YRijTIEkSYAMtCpNWPbqC5gyczZmHXeyaEVCBj29nfGM3FwIADcYSmM+rWzG57WtWLVkBKZNygAA/P2uQtx6lxMPL6zBgyeM0zxzV3MH3vrOhXdeLMXxR2X23P7E88244091OKQkExkpGFiGCg+sqcYxx1nxrwdLYDRKAIDKvZ04cv5eLNzkxIIphZpnPvhVNYaNMeDrl8bAZus+h/D3u2Qce2YVHl1djxuOKNM885/f7EObpQu7Vo9GQX734+WBuwpx5mU1uP+ravx+7kjNM0XwbZ0bSyqb8d+3y3H4DCsAQPmDgr883IRHn6zFI98bA6Mh/X9eOgMynlhfhzt+nYcbfpzXc/tnqzpw2kU1mFGSifEFg2fYJoMLDqBpzCfvvQFPSysOVY7qHj73kyPlYXhgDN5/9p8cQAlJIWovtQ3dXEja/y+UyHlUivjYW11kjdq6VPeCyrp08/9oTwt+cV1uz/AJAJIk4Y+3FeLZV1rxVbUbR4wIPyPZX/83NzfirPn2sOETAK67PBePPdOCd7e4cP70A2c7BvPx1zqzwuXFnmY/vrhneM/wCQCjRpjxh1vzcd/9rVgw7cAAqoW/1y9jS6MXX748omf4BIC8XCMe+GMRLru2Puy6Nq2O/4amdjz1cHHP8AkAVqsBj91bjMNO2AtPl4xMizHtHz/v73Thxxfl9AyfQPfP6K0/y8Pjz7VgWUULTp6Qr1t/tcf/P1tcKCgw4Pof5YbdPm+ODeedkYU3VzbhN0fbdeuf7sef/sn3CoUDaBqze+tGOKSCsOEziEPJR219lQArQgY/fV3jGUDsJ+nIBf0KYq+riKyL1UttXaxMNXVD3b9N7sKRh0dfZmuxSDhkaga+c3VgTsgAqoW/O9CFo+fkxPgscPRsGzZ94u/pN9iPf6JeyWZub/Rg5HAzHDnRZ8TmzLTB7W8KO7Za+Ne3dUKBgknjLTEyrXC5u/qUmajO5ZYxZ6Y1qmbcaAtMJqCmxYvxRfa0f/y0BQKYOzv66zQYJMw+zIqK7T4gTq++Zop4/O9t6cTcObaYfwMeNceKLz9vBXTsn+7Hn/7hmYnqkvkc0TnDRoxCG1oQax1vm9SKrLy8GPcihPQVi20Vpu9bjsN21KIUuzCy6g3k7noNi9d1D557a5rh9HYPnn3dYMiQRJ0aBjpzsPvbDAZs2OKLul2WFWzZ4cfwnPChQpNMyYh1m6IzAWDtRh8KMw+8ljzYj38yvdTUjXJkoKq2Cx0d0a/Vb9zqR6b5QAet/IuzzAgEgL3VnTEzc+wHhmEtj1lOpgEbt/qjbq+p64LPr6A42zwoHj9WGLAhxs+LoijYuMWHYXazrv3V1hVlmuI+L6zf6IdNMujaXw30F9dL68y+OhAdcuJ5l0PKMKAGu8Nu9yoe7DXswIkXXCJGjJBBRnDwDL6XZ+jg+ebHwxMOnvEIBLpfPeztMpVA4EBdf3uF1iWs0ShzsPnPLXHg3keaUFPXFVb32LPNkLokzBvZ+4ZAffE/fUIeXny9FZu2hf+xuWhZO7Zs8+O8afHXKA6249+fXqF1QaYW21FkN+GPD7jC6pqaZfzfXxtxSF78NXR99bdbjBifb8WtdzkRCBx4AdnnC+DXf3BioiP+Rlb9Of6THJn4zd1OeL2BkFoFv7nbifEFVuRao8/IpuPj58SRDvzjmRZU7Akf8F9a6EZjYwCnTYp+cV5P/mp7nT21ADsrOvHOB21ht2/9zo9nX23FqePif5168E+2V2hdwhr6a94rtC5hjYo67oKb5qxa9j6e/P0vkR3IRV5XMbyGdtRKezDz+JPw83sfF61HSFoTvNQWAEqxC46K5ZCUBixaPzdkcyH0bC5Ehgb3fVmFjU4PfnRxDkaVm/GfJW34Zp0PPz20FIeXpWZH2n99W4ePq1pwwVnZmD4tAys+78BHn3hw8ZRCnDI+PyWZQ4Xtznbc93UNxo4144dnZWGfU8ZTL7ZiRJYFv5+Tmh1pnR4/7lq5F1l5Eq64MAc+XwBPvdiKjIARdx81Elaz9pneThn/98UeeCQZV12Sg8xMA55/pRXNjQHcPmckSrKjB9B05ZHVNVhd34bLzsvGpAkWfLCsHSu/8uLKg4tx7KjcxA3ShI92ufDiJidOmGfD947JxMatfry8sBXzynNwzaGlovUIwYLXYu+CywF0EOCqr8Ebj9+Pqu3bkenIwQ8u+jFmzDtBtBYhaY3FtgoAcNiOWoyQnYCjBYYtS/HvFbPxZd1RmJa3JGpzodCPQSJfBdTLZgNa9hKRKdr/qyo3PtzVBL+ioNRmwcXTC3rOIKXKf+u+dry9rQkdiow8kwkXHlyAsmxrSjMHopeIzMiaDr+Mlzc4UdnmhQnAMSMdOGFMbkr9u2QZb21yYVOTBxKAWcXZOHWiA1LEwKvlsVBkGR/sbMGXNW4oEjAlLxPnTMmHxZy6TFGPn29r3Fi8sxleJYAiixkXHVyIArslrEbP/moza91evLbRhcbOTtgkA86YmI9pIW81o3f/dD/+9O+914I4b8PCAZQQQmJgsa2CyVKB6ZutcQfQ0MttA0i8piH4pK2mbiB7icikv9hM+ovNpL/YTPqLzaS/2MyB9Of7gBJCiGZEr24QsfBfq14iMukvNpP+YjPpLzaT/mIz6S82U4R/JBxACSFEDYlW1IeWRry8GO/JObSutyfwQMjLi2p6JazTstf+AvonkUn/qDr6J5FJ/6g6+ieRSf+oOvonkZlkr3hwACWEkD7S80QbtyDsQ691amrU9kpYp2Wv/QX0T6KO/lF19E+ijv5RdfRPoo7+UXX0T6IuyV7x4ABKCCFqMMT4n4hX+PS82YAeNi7oTyb9D9RAZR39U9MLKuvon5peUFlH/9T0gso6+qemF1TW6dE/FA6ghBDSR0LnzwBiP0lH1iiIfWWKml79yVRTR//ee/Unk/70708m/enfn0z6078/mVr4R8IBlBBCkib6db0Eyx1U12hdp9deIjLpLzaT/mIz6S82k/5iM+kvPjMUDqCEEKKGGNeSJFwDSgghhBBCwujL0EoIIYQQQgghhCQNz4ASQogaDDH+J+IlPL0u/E/3jQvo37dM+h+ogco6+qemF1TW0T81vaCyjv6p6QWVdYPRPx4cQAkhpI/oda1Fuq8Vob/YTPqLzaS/2Ez6i82kv9jMVK771PL+hBAyBOHiTyKGHQ3tWLTdhZpmv2gVogF+vx8fVzRjZWWzaBVCdI8sy9jS0I7KZq9oFdJPeAaUEELUwE2IiEC+rXPjiXV1aPEEYLNJeHFTA/KsRvxh3kgUZlpE65E+cNfHldjl8aFLVhAIAE9u2ofpuXbcNGe4aDVCdMcz39bjf/Wt6Awo6OxUUJRtwhljCnDCmFzRaqQP8AwoIYQQomOcHj8eXFOLM061o3LNaDRuHYf1H4/CpGlm/PazStF6pA/c/UklKjp8ePmJYWj+bhyavxuHR/5cjNX72vDPNXWi9QjRFU9/W4fVTa147ZlhaNw2Fo3bxuF3v8nDcxv34ctqt2g90gd4BpQQQtSgchOi0I9B+rJBgKiNC7TKpH/iOrX+D6yqxdjRZjzxt2JIUvdnx44y470Xy1A2vQKvbdyHC6cX69Y/3Y9/Kvx3eXx47pESnHKCHQBgMAAXLsiGq6kLd/2tCdcahunaP5le8eroH7+O/gfolGWsqnPj7RdLcdQRNgCAxQL8+CIHauq68PpLjZg9Ilu3/vHq0uX4x6tT6x8PngElhJA+Yoj4F+/JPFZdon5a9opXR//08Hd2+nHlBTk9w2cQm82As+bb8cWeNl37p/vx19p/fY0bHV4F879nj/r8hQty0NIu69o/3Y8//dPLf2O9BwYTMPdwa1TdRWdno8bt17V/uh///vrHw5BELSGEEADchIgMKArg6Yj9mGtvD8BoTObXPhFNptmAgNK9ji0ST0cARgO/n4QEsRoN8HcqMfdc8HQoMEr8eUlHeAkuIYSogZsQEUFMyLbhsWdbcOPVucjIOPC6cd2+Liz+rwfXzSjhYzGNGF9gR47dgOdfb8W1l4VvoPLYcy3Ithr4/SRkP1OK7LCbDXhrcRvOOz077HOPPdOCUTkW/rykITwDSgghcZi++cAlP4ZtS7Fo/VwAwLS8D0UpkSHIjUcUw9Om4Pizq/Hp/zrgbJTx7pI2HDl/LwpsJhwzirtAphtHFjvwqzud+PNDLuyt7sTO3X78+q4GPPJ0M84aly9ajxBdccrIfFx98z48+GQTauq6sPU7P66/dR/efLcNF00pFq1H+oCkKNGXgKSasVOnK/e8tHjAcwkhQxeLbRUAYHKlR1V9ZmcLHOZGOCqWY/G6CQCADlclnF4HAKDcvrmnNoDEr+YFX6BVU6dlLxGZ9Nc+s7ndj99/shduRYbXpyDTKqHEbMFfThqddC8e/9Rmqu310tp6fFLbijZvAAYJsFsMOGt8AU6dmJ+yTB5/+qc6M1X+y3Y2Y+meJtS0dMJkBEblZOCyg4owtiAzLfwHKlNv/me+snWNoiizIm/nAEoIGdSEDp6l2IUcr7rnPKl2RcLBkxBCCCGExCbeAMo1oISQQUnk4OmoWA4AkJSGhPftvtR2Ajpcu+H05gJwcPAkhBBCCNEADqCEkEFFvMFz8boJ8LgqAQzvdavw7vOjlWj0OgDkoszWPXhykwNCCCGEkP7DAZQQMihIPHh2D5VlEWcyI9cuBOfMMnu1qrreatTWpbqXiEz6i82kv9hM+ovNpL/YTPqLzdSzfxAOoIQQzUh2ox+tiRw8O0IGz3L7ZpSHDJXxFs6H3tbbIvzIuniL8NXUxcrUshf9k8/Ushf9k8/Ushf9k8/Ushf9k8/Ushf9k8/Ushf9Y8MBlBDSbyLPPgJQvdmPlgQ3DgoOns4Yg2eQ3p4Yk6nRuk6vvURk0l9sJv3FZtJfbCb9xWbSX2ym1v6RcAAlhPSZWIOno2K5qo1+tGbR+rnocJkBdG8cFG/wJIQQQggh4uAASghJmniD5+J1E9DUOBYZkgUAVGz2o65GTV2jtxnBTYPKbDXcNIgQQgghRIdwACVkkBMcFrUk1uDZ/bYllWjzOZATceZRQvQAGTkfxqpRWxdA+KZBUsTHVGWmshdU1tE/Nb2gso7+qekFlXX0T00vqKyjf2p6QWUd/VPTCyrr6J9cr1A4gBIySAk9S5nZ2aJZX4e5sftjxODZvd6yOuqy1wBiPzFFLmJXVNap7aVm4bzWmfSnf38y6U///mTSn/79yaQ//fuTmaguEg6ghAwyIi+P1XozIKlqharBM0i6L5ynv7heIjLpLzaT/mIz6S82k/5iM+mfusxIOIASMkjobV2mtqgbPOMRCKDnGSveE1fP+k1D709uA91LRCb9xWbSX2wm/cVm0l9sJv3FZtI/dZkcQAlJcxJvCNT9PphaUmarRpmtuu8b/QTCPvRap6ZGRK9kMtfWuvHODheaurpgNkiYkmPHJdMLkWE0poW/HnuJyAzWdMoyXlrvxKbWdvgDCvJMJpwxPh+HlWar7pVspqhej62uxTpXG2RJgRESJmTZ8Ku55SnNHIhekXWb6tvx1g4nnP4umCQJE7JtuGx6MTLNRs0yB8vjX4teIjLpLzaT/mIz9ebPAZQQHZLMxkHxBk+rdGBDoMgNevSw2F3LXiIy1fZ6f7sLr25x4upLc3Da9/NRUy/jrw+7cPtnHvxx3khY9/+Bq1f/dD/+Wvt3yjJu/3wPjNkK7vh9HkaUmbF4WTseeK4W5070Y8GUAl37J5N5y0cVcPo7cduNeZh9mA0btvhw1/0u/PyjHXj45PG691fb6+OKZjyzfh8uPT8bZ5+Wj8YmGfc/2oTffVaJPx0zCjaLsddeov3720tEJv3FZtJfbOZQ9Q+FAyghOsJiW4XJlR4AULVxUOSGQKGDZ26cDYFELHZP1CtYp6ZXOvnLsoy3dzTi+UdLcOYpWT23nz3fjtmn7MWL6524emaJbv3jZabL8Y+X2R//V9Y7IdkVrP5wBKzW7nsdc6QNx8614dKf1OPUibmwGI2qeonwj+wVL3NlZTOq3H6sXT4SE8Z2v63SvDk2LJifhclH7cYbGxvww4OKdOufTK83tjvx0J8KcfkPD1wpctYpWTjh7Co8uaYeNx9Zpmv/YF26Hv9gHf3VZ9I/HPonlynCPxIOoITogNDBsxS74KhYrvq+BwbP3Wjz5cYcPIP09mSQbJ2WvURkDoT/sooWZGVJOONke9jtGRkG/Ppnebjz7qY+Z/L4i8nc2OzBbbfl9QyfQU45IRMFBQYs+a4FZ0zO1zRTRK9XNrpw6kn2nuEzSGmJCVdekIM3Xm8JG0D15q+27qsqN3yBAC45NyfsdpNJwm9uzMf1Nzdonql1LxGZ9BebSX+xmfTvW10oHEAJEUiswVNSGrBo/Vw0NcqqemQEL7W11aDMVtP3dZlEc5o6ZAwrMUGSol9DHD7MhM6Awu9XmtGpBFBWEr0uUJIkDC8xocXdNSi+pz45gFHlsf9EGFluRkAaHI/dJm8nCvNNMBpj/4z65MHxdRJCiJ7oy9BKCOknFtsqTN+3vGf95uSKp5G76zUsXjcBb3w8HHtrmtHmc6v6lyFVo8y2WfSXRGIwszQLG7b40NQc/WLC+x+2I8/E1wDTjTyTCe8vbY+6vdUt4+v1Xswstce4V/oxJi8Dby9ug6JEv43Tm++1Ic9kFmClPYcOy8Lemk5U1XRGfW7RsjYUZPBnlBBCtIbPrIQkIJkNgdQQ74xnh8sCp7cZgANl9vCBUi8Lz/uTORT9JxTaMDbPiguvqcMrTw5DXq4RiqLgP0vb8dSLrfjF4aUwGPTrH68GKusGo//Zkwpx72vVmDfXhnNOzYIkSWhukXHpT+sxKi8DU4vtuvZXm/mL2SW4aulu3PIHJ+65rQAZGQZ0dSm477EmbNzqw33Hjol6CVtP/mp7FWZZMKXIih9eXYe3ny9FcaEJiqLgv5914G+PNOOqg4vDvk69+felF1TW0T81vaCyjv6p6QWVdfTXvldYfaxXN1PN2KnTlXteWjzguYQkQ/DyWDWbASWDw9zYs8Zz8boD76kJAOX26DOZwR/gRJcrxFsEnqpeIjLT0b/dL+PPq6qwy+XFwVMyUFffhbY2BWeOLQhbK5isl9q6oX78U9Hrg+0uLNzRCJtdQtkwEzZs8WFMXgZ+M3s4sq3hZwb16K+2bmVlM57atA+dsoKpEzOwfacfUIBzJxTitInhj109+qvN9HbKuHdVNbY4O3DQ5Aw0NslwuQKYPzoX50dstJSol1ovtXXp/PjROpP+YjPpLzYzXf3PfGXrGkVRZkXezgGUkAhCB8/QYVFLugfP3XB6cwHEHjzJ4GKHqwNfV7chz2bEiWMcMBoTvL8g0TWyLGNZRSuaOrowq8yO8QWZopVSxsJNDdjU0IFx+Rm4eHqJaJ2UUdnsxZdVbmRajPj+OEfYbsaEEEKSJ94AyktwCdlP1OBZlfyGQGrIkKrQ6G0GkNuzdpObXAx+xubaMDbX1vP//J6nN5JkxElj83r+fzB/PxdMKcKCKd3/PZi/zhE5VoyYau35/8H8tRJCiEg4gJIhT9ROtCGDp8dl2T8sakcbHNw0iBBCCCGEDEk4gJIhS29vgdLbhkBA6heL62XheV8z6S82k/5iM+kvNpP+YjPpLzaT/mIz6a8ODqBkyKF28Ex2XWa6v0mwXnuJyKS/2Ez6i82kv9hM+ovNpL/YTPqLzdTaPx4cQMmQoffB09znwZMQQgghhBCiDg6gZNDT2+B5YI0nNwQihBBCCCEk1XAAJYMWi20VAGBypQel2IUcrwJDzev7d7Udizbf/jWe3BCIEEIIIYSQAYEDKBnUmCwVyOy0IkdWAEcLUAM0Ncr4su4oTMtbErXBkKjF4npYeN6fTPofqIHKOvqnphdU1tE/Nb2gso7+qekFlXX0T00vqKyjf2p6QWUd/VPTCzHq4sEBlAxpuFhcbCb9xWbSX2wm/cVm0l9sJv3FZtJfbOZQ8U/V/QlJU7jQkxBCCCGEkIGGZ0DJ0CHGzMkNhwghhBBCCBk4+jWASpJ0HoA7AUwBcISiKF9rIUXIgGKI+Z8A4p8nVVOXyl4iMukvNpP+8ev2Nnvx3jYXOmVg1nA75o1yaJ6ph+Pf4ZfxxiYnnB1dGOWw4MzJ+bAYjSn193fKeGerC1VuP0oyzTh7agHsltRmprqXiEz6i82kv9hM+ovN1JN/b32TYSOAswF82s8+hKQeQ/T/GAwHbo71w2AI+RezTZy6RDXJZsair73oT/++ZCKJuoH0f2hVNX6zohK2cTJGHqHgmU31+NXyCjR7/Wnhr7bX+1tduG7JTtTYOjDxKAlfuVtx/dJd+KbGnTL/r/a68dMPd2Gdz42JR0moMLXjJ0t2YumOpkHz+KE//RNlxoL+fe9F/6HlH49+nQFVFGULAEiS2j2PCNEniX7Y1NZoXafXXiIy6S82U4/+r25owLY2DzZ8OgqjR5gBAD5fAOdfVYf7v6rF3ceMSomX2jqtelU2e/HaNidefXIYfvA9OwBAURQ8+GQz/vpAHR4ryYTFaNQ00+uX8c91dbjn9nxcc2luz+1vL27DlT+rx4wSO0qyLaoz0/n4a91LRCb9xWbSX2wm/cVnanW/pJEk6RpJkr6WJOlrd5NroGIJiQMXfxKS7nzZ4Mafby/sGT4BICPDgCfuK8aORi/q3X6Bdtrx2mYnTjsps2f4BLpf+L3pmlzkFxjwzhbtf6e+utmJMaNNYcMnACyYn4V5c6x4ZaNT80xCCCFDg4RnQCVJWgZgWIxP/U5RlHfVBimK8iSAJwFg7NTpimpDQrSCmxARMqho8nTh6Nm2qNtLS0woyjdiu6sDRXaLADNtaenqwiVH5UTdLkkSjjsqE5s+8Wv+XFbV0onjz4o+tgDwvWMy8fzWdj5/EkII6RMJB1BFUU4cCBFCtMRiWwUAmL7ZCoe5EZABw7alWLR+LgAZ0/I+7C6MuAYg1iUBfV1srWUvEZn0F5tJ/8R1dqsBW7/zY8xIc9jn3G0BNLhklB+cEVNEL/5qMzNgwOZtvph9N27xodBq0/y5LNdqwIbNsc8gb9jiQ6bRyOfPAeolIpP+YjPpLzaT/qnL7K2ekLTFYlsFi20VJld6cHzlRjjMjXBULMcHS6rw7xWz0eGqRJvPjXL7ZpTbN8OAAz8E8X4YDCH/4tVF1sSjr73U1NGf/unhmV8AACAASURBVPF6DVb/KVmZuP3PjfB4wn/N/fGBRpQ5LBiTb9W1v9rjf+r4PDz3qhvbd4YPhMs+9WD9Zj/Onpanuf95Uwvx+Zcd+OKrjrDPb9zqwxv/acNZk/JU+6f78ad//3rRn/796UX/9PaPR3/fhmUBgEcAFAFYJEnSWkVRTu5PT0L6QvCM5+RKD0qxCwDgqFiOxesmoKlxLKxSJdp8DuTaq1Fur466f6If3GTq9NpLRCb9xWYOdv9rDi/B7Z/twdSjK/GTKx3IdRjx8ptubN3ux62Hl6UkU0SvmWXZmFvqxhEn78WPLszBQVMt+OSLDryzuB3nTipArvXAZcZaZZZkW3DGuHzMv6AG552Rhbmzrfh2vQ8vvO7G8SNyMaXowHpUPR4zrXuJyKS/2Ez6i82kv9hMrf0jkRRl4Jdjjp06XbnnpcUDnksGH70PnjKsUhWcXgfK7ZuT6hsIoOenqrcfrmBdwhqorEuQqWWv0Dr60z/ZXqF1Iv1lWcb721uwep8bAUnBCFsGLjq4ENlWc1r4J9Pr62o3Fu9qgleRkWM047wphT1neVPlv62hHW9tb0JrVydsBiPOGJeH6WXZg+bx09deoXX0p3+yvULr6E//ZHuF1und/8xXtq5RFGVWZB0HUJKWJBo8M6QqNHodKLMlN3gSQgghhBBC+s+C12IPoP26BJeQgUbtpbY59mqUhVxqK+3/F0rk4mgp4mNvdansJSKT/mIz6S82k/5iM+kvNpP+YjPpLzaT/gOXGQoHUJIW9GeNZwCxf8gMETUKYl9WEFmXqFewTk0vRaUb/dX3CtbRX30m/cOhf3KZ9A+H/sll0j8c+ieXSf9w9OofCQdQomt6GzyBCft3tY2/uRDQ+w9AMjVa1+m1l4hM+ovNpL/YTPqLzaS/2Ez6i82kv9jMoeIfCQdQokvUDJ7dmwvFHzzjMdCLxZPqJSKT/mIz6S82k/5iM+kvNpP+YjPpLzaT/sIyOYAS3RF8H89Yg6fHVbl/c6FqlNmqDzzQkyUQ9qHXOjU1mvUSkUl/sZn0F5tJf7GZ9BebSX+xmfQXm0l/YZkcQIlu6G3wDJ7xLIuxuVDoxyCRD3qtF1vrYeF5fzLpf6AGKuvon5peUFlH/9T0gso6+qemF1TW0T81vaCyjv6p6QWVdfRPTS+orNMqMxQOoEQ4agbPWJfaBtC/hdtq6yJr9LLwvD+Z9Kd/fzLpT//+ZNKf/v3JpD/9+5NJfzH+kXAAJcLoffDcDac3F4AD5fbY7+XZ2wM7VXV67SUik/5iM+kvNpP+YjPpLzaT/mIz6S82k/59qwuFAygZcNSs8QRyUWbrHjz7vM6TEEIIIYQQois4gJIBQ93g6egZPAkhhBBCCCGDCw6gJOUEB8/MzhY4zI0x13gCDpRFXGqrl8XWeli4TX9tegXrfJ0y9rV3oiDTDLvFmHb+A5lJf7GZ9BebSX/tMlu8frR5AyjNNsNoNKadf7off/rTX7R/KBxAScqIGjyrYg+esdZ46mmxdeT9Aip70T+8lx78vZ0yHlxdi81OD7oCCgIBYFyBFdcfVoKybKvu/fuSSf9w6J9cJv3DoX9ymQEA39a48fI2Jyob/TAagSyrAYcXZePaWcPSwj/djz/9w+vorz5Ta3+1nyOkT1hsqzB933IctqMWpdiFkVVv4It39mLxuu7NhfbWNO/f2XZzrxsMabWQWsteIjLpr13mPf+rgpzXhU/eK0frrvHYvmo0Zh1txl1fVKHdLyfVqy9eausG6/EX3UtEJv3FZtJfbOaOhnY8+HUtLrnMjvpNY+DeNQ6v/msY1rvb8NBXNUn1UlvH45+aXiIy6S82U2v/UHgGlGhGb2c8ubkQEc2GfW2oaPZhz4rRyMk2AgDKhpnw9IPFmHPKXry6wYkrDy0RbEkIIYOHV7c24ryzsvD7mwt6bjtubiYWvVKGo0+tQptPRqbZKNCQECICDqCk36gbPLm5EBHLx7tb8YMTMnuGzyCSJOHKi3Lw6MNuQWaEEDI4qfP6cdn5+VG3HzQ5A6UlRny2pwUnj4v+PCFkcMMBlPSZWIOnpDRg0fq5vW4uBAz8Yut0W7gdWUf/xHWJ/I0S0NkZozm6b5cAGEKuI9Gbf38y6Z+4jv7x6+ifuI7+seskSUJnlxKjAvB3AibJ0HP9nh79te4Vr47+8evon7hOz/7x4ABKkqb3wdMCp7cZ8TYX6g0tr4FXW6fXXiIyB7v/KeNzcccne1Hf0IWSogNPfV1dCp54rgXT87I1zxTVS0Qm/cVm0l9sJv1j15VbM/DEsy04bm5m2Oe/+KoDLS0y5s3JTtiTx1//mfQXm6ln/1TdnwwhgpsLBd/Lc2TVG8jd9RoWr5uANz8uU7W5ECGiGF+QiYOKMnHM6VVYsrwdHk8A36z34vRLauBtBc6bxsvACCFESy49uBArPu3Adb+qx87dfrjbAnhpYSvOuqwGx5Q6YOX6T0KGJDwDShISPOMJAKXYBUfFgTOeHpcFjd5mcHMhkg7cMrsMT3+7D1f9bB+crV3IzjRivMOKu44aAZNk5GOXEEI0pCzbit8eOQLPrajHYW/vhd8fQGm+GfNH5eGcKUV8ziVkiMIBlMRF3eDJzYVI+mA0GHHtzFLRGoQQMmQYk2vFH+aNEq1BCNERHECHEBbbKtW18QbP0DWe8TYXCv0YJNWLrfW4cDuZTPofqIHKOvqnphdU1tE/Nb2gso7+qekFlXX0T00vqKyjf2p6QWUd/VPTCyrr0sk/HhxAhwDBwTO4dlMt8QbPvqzv1Otiaz0v3Ka//jPpLzaT/mIz6S82k/5iM+kvNpP+YjP7u4kQB9BBTOTgmeNVINWugKQ0qLp/9+Bp7tfgSQghhBBCCCFBOIAOQuINnovXTUBT41hkSJZeT5EH37GLmwsRQgghhBBCtIQD6CAi1qW2jorlIYNnJdp8DuTYq8PuF3kaPThnloXUxTrVHmsejderL3VaZtJfbCb9xWbSX2wm/cVm0l9sJv3FZtJfbCb9Y8MBdBCQaPC07h88c+3VKA8ZKgOI/cAKva23B1BkndpeauriXVve10wte9E/+Uwte9E/+Uwte9E/+Uwte9E/+Uwte9E/+Uwte9E/+Uwte9E/+Uwte6Wrfyw4gKYxfR08gyR6cKitEdFLRCb9xWbSX2wm/cVm0l9sJv3FZtJfbCb9xWamu38sOICmIYkHz91o8+XGHTwJIYQQQgghRAQcQNMI1Ws8bTUos9Vw0yBCCCGEEEKIruAAmgb0NngCE+BxHdhciBsH0V+rTPqLzaS/2Ez6i82kv9hM+ovNpL/YTPqnLjMIB1BBWGyrMLnSo7o+1uDZ4aqE0+tAeYzNheIR+gDReuGz1pla9qJ/8pla9qJ/8pla9qJ/8pla9qJ/8pla9qJ/8pla9qJ/8pla9qJ/8pla9qJ/bDiADjChg2fwPTrVEHwfz94GzyC9fcOTrdOyl4hM+qurk2UZ72xtwldON/yyghyTEaePy8es4dn9yuTxF5s5FPyb2/340+c1aFI6AQkwyxKunF6Iw8tzU5YpopeITPqLzaS/2Ez6i82kv9hMrf0j4QA6QEQOno6K5QCwf6hUQ+LBMx6BkJcxenugBEJeEolXp2UvEZn0j133x5VV2Cd34tc35GL8GAv++6kHD75QizOavDh3apHu/Qcqk/5iMyN7NbT7ccuK3Rg1yoTfXVcIR44Br77txt+X1GNBSyfOnVaka//+9BKRSX+xmfQXm0l/sZn0F5uptT8H0BTT2+DpcVWi0dusuleZrRpltuq+by4U6P1UebAm5MOA9RKRSf9u3t/qQq3Pjw2fjkJerhEAcPLxdpx6kh1nXVaL+RPykWk26tY/3Y8//fve6w+f7MXB0yz46I1ymEwSAOC0k7Jw/+Mu/OWhJpw7pUjX/lr1EpFJf7GZ9BebSX+xmfQXm6lFLw6gKaK3wbP7TGYzAAfK7Jt77iNFfAwS+Q2UVNb0tZeITPqLy/yyvhU3XZfbM3wGOXZuJiaMNePdbS5cPL1It/5a9xKRSf++ZbZBxv/dUtwzfAa5/spc3Pk3F1bsbsbxY8MvxdWTv1aZ9BebSX+xmfQXm0l/sZnp5B8KB1CNUTt4locMnkD3N0lB7NPVhoi6WA+YyPsFVPZSVPRTk0n/cNLJvxMKRpabY9wTGD3CjJbtXb1mivaPrAnWpcvxj6wJ1tE/cWZnl4KRw6Mfu1arAXkOA2pafbr2j+yVbsc/shf9D9TRX30m/cOhf3KZ9A9Hr/6RcADViESDJxBcv7k55v17+yalqk6vvURkDmX/PJMZiz9qx/lnhG841Nmp4OOVHlw5tVjzzFT2EpFJfzGZVosBH37cjusuDz/LWbGnE41NARxzaJbmmXrvJSKT/mIz6S82k/5iM+kvNlNtr0g4gPaTZAZPURsHhdYlrNEok/6x6/Tof96UAty5eC9eP8mN807PgiRJ8HoDuOG2BjgsJswblatr/3Q//vTve+ZBOZn47T2NmHWIFbNmWAEAjS4ZF15bi4JMI0bk2nvpJN4/3Y8//RP3Cq2jP/2T7RVaR3/6J9srtE5v/pKiqHsbEC0ZO3W6cs9Liwc8V0sSbS4EAI1eB8pssc94EqInlu1qxmvbG5CdY8D40WZ8tdaLokwzfjGzFKXZVtF6hMTld8srUeH2YvwYM3IdBqxe60OezYj7jh+JTLNFtB4hhBAyZFnw2tY1iqLMirydA2iSWGyrAACTKz1xzngCTm/45kKA9ot99bDwuT+Z9D9QA5V1qfbvlGUs3dkCp6cT0wozMas8O6380/3407/vmXXNfjy7rh4+OYBTxjkwd1RuVI3aXr3V8fhrk0n/AzVQWUf/1PSCyjr6p6YXVNbRPzW9oLKuP5kLXok9gPISXJUkHjzjX2obgPaLfbXsFesUeaoz6a8/f7PRiNMm5ifdSy/+6X786d/3zLJcC247doSQY8Hjn3wm/enfn0z6078/mfQX4x8JB9AE9D547gawG05vbq9rPHv7BiRbp9deIjLpLzaT/mIz6S82k/5iM+kvNpP+YjPpLzaT/n2rC4UDaBx6Gzw9+894NnpzUWbbjDJbzYFFt4QQQgghhBBCYsIBNAJ1g6dj/+CpfldbQgghhBBCCBnqDIkBNDhUqiE4eOZ4FUi1K8LWeDbu31yoLOJS21Qv9tXLwue+ZtJfbCb9xWbSX2wm/cVm0l9sJv3FZtJfbCb9xWb2dnHooB5Ag2+VktnZoqreYW6MGDwtSPQ+nlov9k3UK1gnYuEz/Q/U0V99Jv3DoX9ymfQPh/7JZdI/HPonl0n/cOifXCb94zMoB9DQwdNhboSjarnq+3YPnmao2VwI0O9iX732EpFJf7GZ9BebSX+xmfQXm0l/sZn0F5tJf7GZ9I/PoBpAYw2ei9dNADABTY1ywvtnSFXg5kKEEEIIIYT8f3vnHiVnWd/x77OT7Ca7SXbZZLnkyk2uEiFQDaEcFLFcpKLYngrWKqiUorR6tAc8FG2trUfxxHqq6AFET6tGrFwVb1gVEKQRUIFAIndICIFNssnmupudp3/sbjI7+87M88687/zemfl8ztkTdua7v+9nhknOPvvO8yxAOjTFArTcwnPHptG9myFsE4cLAQAAAAAApEVDL0DLLTx3bhrduymNHhxUTJY3+2Zh43Atnfjvyygwh386sxSYwz+dWQrM4Z/OLAXm8E9nlgJz+KczS4E5/NOZpcAc/unMUmAubf9SNOQCNHThOT9i4VkO3qtt24m/bSf+tp3423bib9uJv20n/rad+Nt24p9eZykaagFafuE5emhQNQtPqI6Vawe1ct2gOqfk9OdH7ae+rnZrJWgwhkZG9IPVm7V+cEjzujv0tiN6lMvlrLWgwdgwOKQ7/rhZQyN5LZ0/QyfOnWmtBAAFvLp9SD9Ys1k7hkd00tyZWrqAv6MArUxDLECjFp7Ov6o7H1lWsMdz9OAgSRwclDJbdg/p6v9dr5e3DWuODtCQdutHTz6v0w+doUtPOshaDxqE+17com889ormzGnTktdN070PD+jOn27SJYsP1EksICCQax98SfetG9TSE6erp7tNX7x7vebP6tc/nbxQnVP5YQaANV//3Qb98oUBLVk8TQfun9NX71mv7z/ZryvfME+90/nBNUArkukF6PjCU5IO0jNFC892bdw1II0dHAT149/u3qDd27r1p/5k5dzoN3jb/Bb96plfaWHPJp1zeK+xIWSdLbuGdMMjG/SFT8/R+941S845ee/11W9u0ac++7L+s6+TxQNU5NYn+vWHge166OcLdcRho9/Ibt+R1/nvW68vrFynT56y0NgQoLW565lN+vXLW3TvDxfodcd2SJJ2787r3X+3QcsffEmfOfVgW0EAMMFkAdrWtl0dnb8pmznyufGF57PqfnbfwnPnpnb1jy085xW81daPzy4xL6ubfbOycTi0c93ALj07sEvL/Ol7F5+SNMN162B/rH6yZo3eekRvZv0b/flvFv8VqzbqhMUduuiCfSdUO+d02UU9+q+bBvW9Vf26eMkBmfVPY5ZFZ6P737dhqz579Zy9i09J6ups09f/Y38dfcrz2rhzSH1d7Zn1b/TnH3/bzkbw/8XaLbrqo717F5+S1NHRpuuX769FS57V8wO7tKh3Wmb96zXLohN/285W8S+FyQJ0xtBOvfG5VRVzpRaeUXs8Kz3grG72zfLG4ajcqv4d6nTT1a6OSfftpz6t2/V45P+LrPinOcuis1H9128f0gVv6oy878zTp+vOFbsT78z6LIvORvfftGOPTjt5+qTb58+dqr7enFb371RfV3tm/Rv9+cfftrMR/LcMjeiNyyb/Hd2vJ6fDFrVrVf8OHTK2AE2qsxFnWXTib9vZKv6lMFmATtm9WT1P31Qxd+ejy7Rz09SChedjMVqKn5qojaEhmaicj8iErvkbm4Nmdmin36S8H1Gbm/gWyR3apmm5Wl+S0Ap05XJ6Ys1Q5H2PrxlWd0emdwdARujsaNOTzwzpkIVTJ9y+fUde/ZtHdNBx7C8DsGT6lDY9+eywliyeuMgcHvZ68aVhnXf81BJfCQDNjMl3eZsHp+p/7p5XMbdx54CkHs3tHD9cqJbFTZLr+dZYbEbx2r4u9XRM0Qu7ntTBOmrv7SN+j55zq7RsQQeHQEFF3n7Ufvr0nWv1jx/erWOO3Hc1/XeP7tJPfrFd17xpEa8jqMgRMzr1qc9t1GknT1dHx75/v6/58mYdOGuqDu2ZzusIwJBjurv0r1/YpHPf0qWuzn1/R79y44BmtOe05KCZ/B0FaEFMFqDODasjt27v56WuQ86dUTpTmCuk2muaIbNq6Wwm/8veMFuf//Vqbc33q88v0LB2a517Sn0zvd6/ZL7aCsJZ9K91lkVns/kf1delNy7o1ilvXasP/PUsnXj8NK18aJduXLFVf3Zwj+b3TCs5q9rO0FwrPP+1zLLoLDXrb086QFff+4IWn/aCLv9gj7pntWnFzYP67cO79fE/mVvyZ4pZ8a9mlkUn/radjex/0fFzdPW9O/XaU5/X5R/s0QF9Od38g226+76duuyEgyYMyKJ/0rMsOvG37cQ/Gud91NtJ0+Xw2dP98jMPniBX6tpjvsL9hbmQTFKzLDqz5L9hcEjferRfz27co6k5admi6Tr/qN6yv8MxS/7Wsyw6s+i/cu2gfvTMJu3weXW1tencw3pL/g7HLPpbzbLozKr/0MiIbnl8k/6wcbvyzmtuR4cuPG7OpN9LnFV/i1kWnfjbdlr6+5ER3bZ6sx7u36Y98tp/arsuOG625s7c94PGLPs3+vOPP/6WneetWP2Q9/6k4ttNF6AAAAAAAADQfJRagBqd9OGV3MXg0IvUAAAAAAAAYInNAtS7wAOFksoAAAAAAACANTYLUKeG2HhebSf+tp3423bib9uJv20n/rad+Nt24m/bib9tJ/5h8ySzt+COio6LFW9gjXqgUQ+srShTrquaWSG5Spm4nVHgX/2suJ1R4F/9rLidUeBf/ay4nVHgX/2suJ1R4F/9rLidUeBf/ay4nVHgX/2suJ1R4F/9rLidUTSTfzGmv+29nFjcXFZnWXTib9uJv20n/rad+Nt24m/bib9tJ/62nfjbdmbZvxjTBWgxpVbaEzLjh/a68tl8wY8BKuba9kazNcuiE3/bTvxtO/G37cTfthN/2078bTvxt+3E37azzv5GhxAVCBZR7lLupBkhuXxALh/YXe9ZFp3423bib9uJv20n/rad+Nt24m/bib9tJ/62nXX2Nz+EyI19FFMsHZWLyigwl2Qn/vsyCszhn84sBebwT2eWAnP4pzNLgTn805mlwBz+6cxSYA7/dGYpMId/OrMUmMM/nVkKyBVifghRwTtqJ90/Tj7i/qiMV/Tl3pBZtXSG5PAvP6uWTvzxr6UTf/xr6cQf/1o68ce/lk788a+ls57+xXAIUUY68bftxN+2E3/bTvxtO/G37cTfthN/2078bTtbxb+YzB1CJFV+MPmCZXupbJIbbwtzFTMJdeIfncMf/7izCnP44x93VmEO/+b3H9w1rCm5NnXkcg3pHzpr19CI9kjqbM+VnVXYmSX/0FmFOfzxjzurMId/fP9yZO4QImnfQrTSjKBsPiyT2CyLTvxtO/G37cTfthN/2078E+n870c26IFXBrVhYI9yTjqkr0PvPnJ/HXdAV+xZVXuF5mro/PWLA7r96U16rn9IXtK83qk6fV6Pzjtydu1eobkmfP1kYpZFJ/62nRn3L0cmDiEq/HOcYu+sbPZNcpZFJ/62nfjbduJv24m/bSf+0bnrH3pZD24c1PVf3F9nn96lgS15fen6zVp+wzpdvWy+Dp3dmWn/0M6VLw7qut+/on++olcfeHe32qc6ff+Hg/rwla8qn/d6x7FzMu1fayf+tp3423Zmwb8Q00OIark/KheyobbUoUfVzIrbGQX+1c+K2xkF/tXPitsZBf7Vz4rbGQX+1c+K2xkF/tXPitsZRZtG34p6/0tb9ePvzdPrT5gmSZrdm9Onr5ijl18Z0Xfu6dcnT12YWf84s257ul//eHmPPnLJfntvu/D8Wepod/rolf1659gCNKv+jf784z8R/KubVU//fIxcSGfofQ1H1IOPyoTmstiJv20n/rad+Nt24m/biX/ynfevG1R3d9vexWchF184Sy/tHAqeFccrNJdk5wsDQ3rfX3VPuv3tZ8/Q5u0jen5gV/Cs0Fyzv36sZll04m/baeHfprCFYjWLyWwdQjR+rbbSIwl6IzMAAABAeXyJyxT5/Og3aeXOrGgknJx8xIP1fuxDzfNYASDb2FwBHTuEqPhjL/kKHwAAAAA1cvL8mRoczOv+3+6cdN8N39qqg6a3G1ilw4KeqbpxxdZJt9985zbNnjlFC2dNvgoMAJAG5ocQjX9afCk4C5tlk56lwBz+6cxSYA7/dGYpMId/OrMUmMM/nVkKzOGfziyVyHW05XTq3G69/b3rde3n+3TemTO0cfOIln91s+740TZ96pSFk35UnyX/OJ3vPHyOll+7Xh3tTpe8p1vTOpxW3Daoj32yX+cfPrvi92XW/nE78d+XUWAO/3RmKTDXjP6lcFFvx0ibw2dP98vPPDjxuaU2ylaTK7fZ13KWRSf+tp3423bib9uJv21nq/h/55FXdf+GrVq7cVjtU5wOm9Ohvzm2T0f3Tfw1LFn1D33+H3hxULc81a+nX92tvJcWzWnXGQt6dO4Rval0tsrrB/90OvG37YyzM7JU5rwVqx/y3p9UfHum9oDWSujKOySX1VkWnfjbduJv24m/bSf+tp2t4n/h4j5dqD4NjYwoJymXy6XeafH8L10wU0sXzNTIyIhGJLVHPM4s+zf684+/3SyLzkb3r+Y3koRiswD1bHQHAACAbDHFjS7Imv17FOdymqLmf5wAkE2a6tewAAAAAAAAQHbJ7CFEUuNvvMW/9lkKzOGfziwF5vBPZ5YCc/inM0uBOfzTmaXAHP7pzFJgDv90Zikwh386sxSYw7/8rFKY7QFN6hebJvn+5KTf64y/3SyLTvxtO/G37cTfthN/2078bTvxt+3E37Yzy/5pfT0AAAAAAABAEBxCBAAAAAAAAHWhpiugzrlrnHOrnXOPOOdudc71JCUGAAAAAAAAzUWtV0DvkvQJ7/0e59znJH1C0hUVv8pp0iFEhX+OU81mWauNt0l14l85h3/pHP6Vc/iXzuFfOYd/6Rz+lXP4l87hXzmHf+kc/pVzFv6lqGkB6r3/WcGnD0j6i9CvbeQNulne7It/9jvxt+3E37YTf9tO/G078bftxN+2E3/bTgv/UiS5B/RiSTeVutM5d4mkSySpr3OKJq+vox5G1EbR4lypzaScrwQAAAAAAJAlKi5AnXM/l3RgxF1Xee9vH8tcJWmPpG+XmuO9v07SdZJ0eO90n88ntVZnoQkAAAAAANAIVFyAeu/PKHe/c+69ks6V9GbvvQ9qdZqwbgy5ppn29dG0O/G37cTfthN/2078bTvxt+3E37YTf9tO/G078Y+mprfgOufO0uihQ6d573fE+do27ZPLa6J44X+XewDFuagnKWpWaC7JziRn4R+/M8lZ+MfvTHIW/vE7k5yFf/zOJGfhH78zyVn4x+9Mchb+8TuTnIV//M4kZzWqfxS17gH9sqQOSXc55yTpAe/9paFfXEkuNGMxy6ITf9tO/G078bftxN+2E3/bTvxtO/G37cTftrPR/aOo9RTcw6v8SiV3MTj0IjUAAAAAAABYkuQpuOF4Jw4hAgAAAAAAaC1sFqAFhxC18i9nxb98JqlO/Cvn8C+dw79yDv/SOfwr5/AvncO/cg7/0jn8K+fwL51L2r8QmwWoRtef42Jek8Wr2SwbNScqF5LxgZ1Rs6Jy+JfvxL98Dv/ynfiXz+FfvhP/8jn8y3fiXz6Hf/lO/Mvn8C/f2Sj+xZgtQKXyYnFz1qBnfwAADCpJREFUWZ1l0Ym/bSf+tp3423bib9uJv20n/rad+Nt24m/bmWX/YkwXoMWUWmlPyo0ttctl8+OXV9sCcm17o6nPKszhj3/cWYU5/PGPO6swhz/+cWcV5vD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      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def superficie_decisao(X, Y, K, ax, title = \"\"):\n",
    "    \n",
    "    h = 0.05\n",
    "        \n",
    "    x_min, x_max = X[:, 0].min() - 0.3, X[:, 0].max() + 0.3\n",
    "        \n",
    "    y_min, y_max = X[:, 1].min() - 0.3, X[:, 1].max() + 0.3\n",
    "      \n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n",
    "\n",
    "    X_teste = np.c_[xx.ravel(), yy.ravel()] \n",
    "\n",
    "    Z = np.zeros( X_teste.shape[0] )\n",
    "    \n",
    "    for i in range( X_teste.shape[0] ):\n",
    "\n",
    "        Z[i], ind_viz = knn(X_teste[i], X, Y, K)\n",
    "\n",
    "        Z2 = np.unique(Z, return_inverse=True)[1]\n",
    "\n",
    "        Z2 = Z2.reshape(xx.shape)\n",
    "        \n",
    "        ax.contourf(xx, yy, Z2, cmap=plt.cm.Paired, alpha=.4)\n",
    "\n",
    "        Y2 = np.unique(Y, return_inverse=True)[1]\n",
    "\n",
    "        ax.scatter(X[:, 0], X[:, 1], c=Y2, edgecolor='k', s=50)\n",
    "\n",
    "        ax.set_xlim(xx.min(), xx.max())\n",
    "        \n",
    "        ax.set_ylim(yy.min(), yy.max())\n",
    "        \n",
    "        ax.set_title(title, fontsize='large')\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(16, 10)) \n",
    "\n",
    "K=3\n",
    "\n",
    "superficie_decisao(X_norm, Y, K, ax, title = \"Superfície de Decisao do KNN\")\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}