agrupacionMD.ipynb

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      "source": [
        "<center><h1>MINERIA DE DATOS</h1>\n",
        "<strong>Taller Agrupación</strong><br />\n",
        "PROFESORA ELIZABETH LEON GUZMAN <br />\n",
        "<strong>TEMA</strong> Algoritmos de Agrupación</center>\n",
        "\n",
        "-------\n",
        "Práctica correspondiente a Agrupación (modelamiento no supervisado) usando diferentes distancias y similitudes para los algoritmos:\n",
        "\n",
        "* K-means\n",
        "* Hierarchical clustering\n",
        "--------"
      ]
    },
    {
      "cell_type": "markdown",
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      "source": [
        "## K-means"
      ]
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      "source": [
        "###Ejemplo 1\n",
        "Ejecución del algoritmo k-means en un conjunto de datos de juguete de calificaciones de películas"
      ]
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              "   usuario  El viaje de Chihiro  Star Wars  The Matrix  Advengers  Malefica\n",
              "0     juan                    1          5           5          4         2\n",
              "1      ana                    2          4           5          3         2\n",
              "2     luis                    2          4           4          5         3\n",
              "3    jorge                    4          2           2          3         5\n",
              "4    maría                    5          1           2          3         4\n",
              "5    oscar                    4          2           1          4         5\n",
              "6  mariana                    3          5           5          5         3"
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              "      <th>1</th>\n",
              "      <td>ana</td>\n",
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              "      <td>jorge</td>\n",
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              "      <td>maría</td>\n",
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              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>oscar</td>\n",
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              "      <td>4</td>\n",
              "      <td>5</td>\n",
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              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>mariana</td>\n",
              "      <td>3</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
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      "source": [
        "#Se crea el conjunto de datos y se visualiza\n",
        "import pandas as pd\n",
        "\n",
        "titulos = ['usuario','El viaje de Chihiro','Star Wars','The Matrix','Advengers','Malefica']\n",
        "puntajes = [['juan',1,5,5,4,2],['ana',2,4,5,3,2],['luis',2,4,4,5,3],['jorge',4,2,2,3,5],['maría',5,1,2,3,4],['oscar',4,2,1,4,5],['mariana',3,5,5,5,3]]\n",
        "peliculas = pd.DataFrame(puntajes,columns=titulos)\n",
        "peliculas"
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      "source": [
        "Para este conjunto de dtaos los tres primeros usuarios y el últomo les gusta las películas de acción, mientras a los tres usuarios restantes les gusta películas de drama. La idea es aplicar el algoritmo de k-means para encontrar los dos grupos de usuarios con preferencias similares de películas. Es necesario remover la primera columna, correspondiente al usuario, ya que no es importante para la agrupación. "
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              "         ID Grupo\n",
              "usuario          \n",
              "juan            1\n",
              "ana             1\n",
              "luis            1\n",
              "jorge           0\n",
              "maría           0\n",
              "oscar           0\n",
              "mariana         1"
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              "      <th>juan</th>\n",
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              "      <th>ana</th>\n",
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              "                                                     [key], {});\n",
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      ],
      "source": [
        "# Se importa los algoritmos de grupación de la libreria de sklearn\n",
        "from sklearn import cluster\n",
        "\n",
        "data = peliculas.drop('usuario',axis=1)\n",
        "k_means = cluster.KMeans(n_clusters=2, max_iter=50, random_state=1)\n",
        "k_means.fit(data) \n",
        "labels = k_means.labels_\n",
        "# La asignación de grupo a cada usuario es visualizada como un objeto dataframe\n",
        "pd.DataFrame(labels, index=peliculas.usuario, columns=['ID Grupo'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_loqPQQx2-Vw"
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      "source": [
        "Los redultados de la agrupación son lo esperado: el algoritmo asignó los tres primeros usuarios y el último al cluster 1, y los otros tres usuarios al cluster 0."
      ]
    },
    {
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      "execution_count": null,
      "metadata": {
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      "source": [
        "#Visualización de los centroides de los grupos:"
      ]
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            "text/plain": [
              "   El viaje de Chihiro  Star Wars  The Matrix  Advengers  Malefica\n",
              "0             4.333333   1.666667    1.666667   3.333333  4.666667\n",
              "1             2.000000   4.500000    4.750000   4.250000  2.500000"
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
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              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-4851a160-4240-44df-ad56-8d42396657d2');\n",
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              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
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              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ],
      "source": [
        "centroids = k_means.cluster_centers_\n",
        "pd.DataFrame(centroids,columns=data.columns)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fWvjC0-l6sZ9"
      },
      "source": [
        "El grupo 0 corresponde con el perfil del usuario que prefiere las películas de drama, mientras el grupo 1 correponde con el perfil de usuarios que prefiere películas de acción."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I_61uSFb69f5"
      },
      "source": [
        "Estos centroides son el modelo de agrupación, por lo que pueden ser usados para predecir el perfil de un nuevo usuario de acuerdo a la calificación que le asigne a las películas. Por ejemplo, se tienen las siguientes nuevas calificaciones:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9XsnO7Az7QdY",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 241
        },
        "outputId": "bc860743-b3f6-415f-cc51-5f80d98dcd1c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/sklearn/base.py:451: UserWarning: X does not have valid feature names, but KMeans was fitted with feature names\n",
            "  \"X does not have valid feature names, but\"\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "  usuario El viaje de Chihiro Star Wars The Matrix Advengers Malefica  \\\n",
              "0   pedro                   1         4          5         4        2   \n",
              "1   marco                   5         3          2         2        4   \n",
              "2     liz                   4         2          3         3        1   \n",
              "3    nico                   3         3          2         3        3   \n",
              "4   ligia                   4         5          4         1        4   \n",
              "\n",
              "  Cluster ID  \n",
              "0          1  \n",
              "1          0  \n",
              "2          0  \n",
              "3          0  \n",
              "4          1  "
            ],
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              "\n",
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              "  <thead>\n",
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              "      <th></th>\n",
              "      <th>usuario</th>\n",
              "      <th>El viaje de Chihiro</th>\n",
              "      <th>Star Wars</th>\n",
              "      <th>The Matrix</th>\n",
              "      <th>Advengers</th>\n",
              "      <th>Malefica</th>\n",
              "      <th>Cluster ID</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>pedro</td>\n",
              "      <td>1</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>marco</td>\n",
              "      <td>5</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>liz</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>nico</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>ligia</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>4</td>\n",
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              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
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              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "import numpy as np\n",
        "\n",
        "testData = np.array([[1,4,5,4,2],[5,3,2,2,4],[4,2,3,3,1],[3,3,2,3,3],[4,5,4,1,4]])\n",
        "labels = k_means.predict(testData)\n",
        "labels = labels.reshape(-1,1)\n",
        "usernames = np.array(['pedro','marco','liz','nico','ligia']).reshape(-1,1)\n",
        "cols = peliculas.columns.tolist()\n",
        "cols.append('Cluster ID')\n",
        "newusers = pd.DataFrame(np.concatenate((usernames, testData, labels), axis=1),columns=cols)\n",
        "newusers"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Gjk5Cfch2dZ9"
      },
      "source": [
        "### Ejemplo 2\n",
        "Ejecución del algoritmo k-means a un conjunto de datos sintetico de dos dimensiones numéricas, de 1000 puntos"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GrILKJ7NsDTZ"
      },
      "outputs": [],
      "source": [
        "# Importar funciones y conjunto de datos\n",
        "\n",
        "import pandas as pd\n",
        "from sklearn import cluster\n",
        "#from sklearn.metrics import silhouette_samples, silhouette_score\n",
        "import matplotlib.cm as cm\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "tt8g8o_rCVcO"
      },
      "outputs": [],
      "source": [
        "X = pd.read_csv(\"cluster1.csv\")\n",
        "X[\"x0\"] = [float(str(i).replace(\",\", \"\")) for i in X[\"x0\"]]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sSHCibGCtO8_"
      },
      "source": [
        "La función predict asigna clusters a los ejemplos\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "df4deyxqtVHq",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b7a13cde-7bfc-4790-b327-cbbeff54085c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(500, 2)"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ],
      "source": [
        "# Lee el archivo de puntos\n",
        "\n",
        "n_clusters = 2\n",
        "# ejecuta el k-means con k=2\n",
        "km = cluster.KMeans(n_clusters=2)\n",
        "km.fit(X)\n",
        "y = km.predict(X)\n",
        "X.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "20TxHFEYurHE",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "03feb3cf-8fca-4840-87c0-1b3d8f50cb25"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 8.01615594,  9.85357474],\n",
              "       [ 4.5061742 , -0.68473232]])"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ],
      "source": [
        "#Lista los centroides de los clusters\n",
        "km.cluster_centers_\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "31j6mEtTu2gQ",
        "outputId": "8a01a39b-e101-494d-ae25-9f0482f388a0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "cmap = plt.cm.plasma\n",
        "\n",
        "cmap((y*255./(n_clusters-1)).astype(int))\n",
        "for i in np.unique(y):\n",
        "    cmap = plt.cm.bwr\n",
        "    col = cmap((i*255./(n_clusters-1)).astype(int))\n",
        "    Xr = X[y==i]\n",
        "    plt.scatter(Xr[\"x0\"], Xr[\"x1\"], color=col, label=\"cluster %d\"%i, alpha=.5)\n",
        "plt.scatter(km.cluster_centers_[:,0], km.cluster_centers_[:,1],marker=\"x\", lw=5, s=200, color=\"black\")\n",
        "plt.legend()    \n",
        "plt.xlabel(\"anchura del trilobite\")\n",
        "plt.ylabel(\"largo del trilobite\");"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4ij2TnWq-cQW"
      },
      "source": [
        "## Iteración del kmeans"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 461
        },
        "id": "zOF5Vemr9BnS",
        "outputId": "adb3b70e-248c-436b-f7b4-2a39d10b9c40"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, '$x_2$')"
            ]
          },
          "metadata": {},
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 504x504 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "from sklearn.datasets import make_blobs\n",
        "np.random.seed(2)\n",
        "# Creación de un dataset sintético de 5 grupos con 600 puntos (se incluyen valores negativos)\n",
        "X,_=make_blobs(n_samples=600,centers=5, cluster_std=0.5)\n",
        "plt.figure(figsize=(7,7))\n",
        "plt.scatter(X[:,0],X[:,1],alpha=0.4)\n",
        "plt.xlabel(\"$x_1$\")\n",
        "plt.ylabel(\"$x_2$\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9t9x4NRx80FZ"
      },
      "outputs": [],
      "source": [
        "# Definición de una funcion del simplekmeans para ver por iteraciones\n",
        "from sklearn.metrics.pairwise import euclidean_distances\n",
        "def simple_kmeans(X,k, iter=100):\n",
        "    # Inicializacion de los primeros centroides\n",
        "    init_clus=np.random.choice(np.arange(X.shape[0]),replace=False, size=k)\n",
        "    clusters=X[init_clus]\n",
        "    preds=np.argmin(euclidean_distances(X,clusters),axis=1)\n",
        "    all_clusters=[clusters.copy()]\n",
        "    all_preds=[preds]\n",
        "    for i in range(iter):\n",
        "        for clus in range(k):\n",
        "            clusters[clus]=X[preds==clus].mean(axis=0)\n",
        "            all_clusters.append(clusters.copy())\n",
        "            preds=np.argmin(euclidean_distances(X,clusters),axis=1)\n",
        "            all_preds.append(preds.copy())\n",
        "    return all_clusters,all_preds\n",
        "\n",
        "all_clusters,all_preds=simple_kmeans(X,5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 391
        },
        "id": "Er6knxTnvdGh",
        "outputId": "9fcf0856-61e8-4504-ed43-7c2f36796f7d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7fd16f92dd90>"
            ]
          },
          "metadata": {},
          "execution_count": 33
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ],
            "image/png": 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Xmzfy4C9z2HQ8hdTCAubv28Ol30xjd0ZGhdqlKErdEtIgL4RoIYRYJITYJoTYKoR4KJT3K8vrK5aWWolSSsnhvNyAr5k0jZt69qFjfALtYuOIt9sDllaY1a8v/7jmCg7HxmAAR2Jj+eDO25nb/6wKtdVjGBwvKGDunt2lnhcbFka7AAOrZk1jQtceCCHw6Dov/7nEbxWtw+PhjRWn10IvRVGqV6jTNV7gUSnlOiFEFLBWCDFfSrktxPcN6HBu4AB+kquU/HW42cLfhgzjPvdAvtu+hU3Hj9MpPoGNx1P47cC+Eg+PWf36lhhktQgRcP/YshR6PKw9eoRLOnUu9bw3zruAq2dMx6PrOLxeIiwWGkdG8dDAQQAcL8jHa/g/3CSwPuVYhdulKErdEdIgL6U8Bhw78fs8IcR2oBlQK0G+bWwcG4+nBH29tGmSo9u25VheHhdN/5I8lwtdSmadeK2s8B2orEJ52M1mWsb45/KP5uXi9HppFROLJgQd4xP44+Y7mLVzO8k52fRu3ITRbdphObFgKtYeFvQh0yQyqlJtUxSlbqixgVchRCugN7DylON3AncCJCUlhbQNTwweym2zf6jUVnzRNhv/+O1Xsp3OomOhrvpj1jQu69yl6Ocjubnc+/MsdmWkowlBlM3GG2MuYHCLJKJtNq7v0SvgdSKsVsZ37MysnTuK9nMFCFO14xWl3quRAmVCiEhgMfCClPL7YOdVtEBZZfx5KJmXlv7B9rTUCgVpu8mE2zAqlXapKJMQtGwQQ/dGjVm4fy9Or5d+TZqyPzuLtMLCEm0IM5uZd/3NNI8ufQ9Yl9fLM78vZObO7WhCYDGZ+NvZw5jQrUeoP46iKCFWWoGykAd5IYQFmAPMk1K+Udq5NRHkT/r7gnl8t31ruaZF1rRwiwX9xGYlwWrqnGTRNIa1bIWUEGm1MqFbDwY0bxH0/AK3m2ynk0aRkRXaUnBjyjG+3eZbdHVB+w6MaNXmtCrapihnsloL8sI3t28qkCmlfLis82syyB/MyWbc/76k0OOpkd55KJmEKHpYhZnN3N2vPw/0H1Rt1/9g9UreW70Cl65jSEm4xcKwpFZMuuCioNM3FUWpObVZavhs4AZgpBBiw4lfF1TnDZKzs5m48FfOnzaVB+bOZlsp8+CLS2oQw49XX8d5bdsTHxZOh/h47uzTjx6JdW8T6+LfRhxeL5NWryS1IL9arp2Sn8fbq5bj8HqLHoaFHg9/HDzAkoOq3LGinO5CPbtmKSHcE3tnRjqXf/MVLq8XXUp2Z2awcP8+Jo+7hCFJLct8f5vYOCZdcJHf8Qu/msr29PRQNNnPsKRWrDhyqNT5+ydpgKZpeE+kcrQgUzMtmsbyw4cY37H0qZflsfRgMmah4aZk+wo9Hubt3c2wlq2qfA9FUUKnTq94fXHJYgo9nqKerCElTq+XpxYtqNJ1G0XUzLRCu9nMu+eP44rOXbGUIz9uN1t4dODZdElMpHVMLF0TGwZ8ggohiAxQ46YywswWAmVkTNV4D0VRQqdO165Ze+xIwOOHc3MocLsDFvMqj4s7dmLVkcNFlSpPMp/IfVc0g28WAolvyqWUEovJhIbg1VFjibLZeGzwEJYdPkhqQUHQ6pdJ0Q34YNx4Oickcle//gDsSE/jsm++8psSahaaX735yhrRuk3A4xaTics6d62WeyiKEjp1Osg3sNkDBkWzZsJWhQ24x3XoxIxtW9lw/BiFHg9mITCbTLx07hj+tmBeuVIrAl86ZUK3nnRMSKBvk6Z4DYPfD+zHbjYzrkNHGp9YiBRjD+OX627m1727eXz+PFy6/zx+l66X2BAFoFNCIs+eM5JnFv/mmykjwWY28dn4y7EG2DmqMsItFj6+6FLumP0jQoCU4DV0nhw6nI7xCdVyD0VRQqdOb+T92fq1vL58aYmaLDaTmSu6dOW5EaOq1BbdMFh0YB8L9u0lNiyMK7t0o01sHKO+nMK+rMyg77OZTHRv2Ihbe/djcIsWRNv8K0cGY0hJu3cDzzI1CcHuBx4J+Fq+282qI4cJt1jo17RZhaZGlpfT62FJcjIu3cvZLVqqTcQV5TRS2uyaOt2Tv7lXH47k5fLV5o1YTSbcus6oNm3559DhVb62SdMY1aYdo4qV6gUY174j76xa7ne+wDdj57ruPbm5V59KBVrtxCKo5Bz/UsVtY+OCvi/SamVkkLRKdbGbLYxu267sExVFOa3U6SCvCcFTw0bwYP9B7M/OollUdNEG3aGyPT0t4HGrycxTQ4czonWbKs0d/+ew4Twwd06JPLvdbObJYcMrfU1FUc5cdTrIn9TAbqdX4yY1cq8sR2HA4y7dy71zZ9MoIpJ3zh9Hz0aNK3X9c1u35eOLLuGN5X+yPzuLdrHxPDro7FJXsRpSsmDfHmbt3IHFZOLKLt0Y3CK0dYAURakb6nROvjZ8sm4Nb6z4s9QiZ5EWK3/ccjsx9tDnraWU3PfzbP5IPlA0GyjMbOGGHr34+5BhIb+/oii1rzZXvNY7E7r1oGlUFPZSZu94pcGsnTtqpD3LDx/ij4MHSkz3dHg9TN24juTsyu8rqyhK/aCCfAVFWK3MuuYGnhg8lJYNYgIuRnJ6vRzLC76XbHX6bf/egNNIhRAsOXigRtqgKMrpSwX5Sgi3WLi5Vx/eGHM+drMl4Ov9mjWrkbZE2WwBV8tqakWqoiioIF8lvRo34axmzUqkbmwmM+3i4hnesnWNtOHSTl0wBZmueer0T0VRzjwqyFeBEIKPx13C44OH0CEunraxcdzffwDTL78qaOCtbkkNYvjPuWOwm81EWq1EWq1EWa18ctGlqievKIqaXVNf5LvdrDh8EItmYmDzFlUq66AoSt1Sb1e8Kn+JtFpVekZRFD8qXaMoilKPqSCvKIpSj6kgryiKUo+pIK8oilKPqSCvKIpSj6kgryiKUo+pIK8oilKPqSCvKIpSj6kgryiKUo+pIK8oilKPqSCvKEq94jW8ZLgycOmu2m7KaUHVrlEUpd6Yl/IrPxyZiS4NpJQMb3gOE5KuwiRMtd20WqOCvKIo9cKy9BXMOPwDbsNddGxx2h9YhJmrk66sxZbVLpWuURSlXph1dE6JAA/gNtwsTF2E1/DWUqtqnwryiqLUC1nurIDHdenFZZy5+XkV5BVFOa24dJdfj7w8Wke0Cng8whxJuCm8iq2qu1ROXlGU00KK8zif7PuMvfn7EELQOaojt7W5hThrXLnef1WLK3hpxyslHhBWzcqEFlcjhAhVs097Id/+TwgxFngbMAGfSCn/E+xctf2fopyZHLqDxzb+nQJvARJfTNIQxFrjeKXHi5i18vVHDxQk893hH0guTCbBmsilzS6me0y3CrfHpbtYlrGCHbk7aWhPZHjiMOJt8RW+Tk2pte3/hBAmYBIwGjgMrBZCzJJSbgvlfRVFqVtWZqzGY3iKAjyAgaTAW8CmnM30ie1druu0imjJox0frlJb8r35PLv1eXI8ubgMF2ZhZl7KfB7t+DAdozpU6dq1IdQ5+f7AHinlPimlG5gOjA/xPRVFqWOOO48HHBz1SA+prrQabcvsoz+R6c4sao/3xMDtR3s/Id9TwNacbRwqPFyjbaqKUOfkmwGHiv18GBhQ/AQhxJ3AnQBJSUkhbo6iKKejVhEtsWk2v0BvEWZahDWv0baszlyLV+p+x7PcWTy04REsmgVd6jS0NeSxjg8Ta42t0fZVVK3PrpFSTpZS9pNS9ktMTKzt5iiKUgv6xvahgaVBiZWpZmGmsb0JXaI712hbrJo14HEDA6/04tAduA03Rx1HeWvXuzXatsoIdZA/ArQo9nPzE8cURVGKmDUzz3R5kqEJZxNhiiDSHMnIhiOY2PnxGp0Z49SdaJTvfgYGR51HSXEeD3GrqibU6ZrVQHshRGt8wf0a4NoQ31NRlDoo0hLJLa1v4pbWN9XoffO9+eR6ckmwJfLxvk857kr1O0dDw8DwO27CRIG3oCaaWWkhDfJSSq8Q4n5gHr4plJ9JKbeG8p6Koijl4TbcfLpvCmuy1mEWJgwp8UpvwGAeZY6iUC/EIz0ljkskLcJb+J1/Ogn5Yigp5c/Az6G+j6IoSkV8vv8L1matxyu9eGXptW2EgAaWaHI8uUWB3qpZua7ltVg1S000t9LUildFUc44Dt3BqszVeMoI7uBblNU1ugvXt7yW31IXsTF7MzHWGM5rNIp2Ue1qoLVVo4K8oiinPY/hYX32Bo46juHwOoi1xtIntjcN7ZWbkVfgLUAIDcpY8G/ChM1k49LmlxBuDmdc0wsZ1/TCSt2ztqggryjKae2YI4UXtv8Hh9eBF1/PWyCYcfh7xjcbx5hGozEJU7lLHwDEWmOxCAtuShZCEwg6RXbAarKR7kqnU3RHLmxyPoW6g8/2TyXTnUmPBt0YljgUu8lerZ8zVEJeu6YiVO0aRVFO9c/Nz3DIEXiFqTgx3VETGr1ienJrq5uItESW67pL05YxNfnLooJmGhpWzcq/uj5Fk7DGReetyljDx/s/xWv4BmU1NMyamQktrmZY4pAKPVxCpbTaNbW+GEpRFCWY/fn7OeY8FvR1eeJ/utTZkLWR/+x4lfJ2XIckDubh9g/QKaojibYEBsb359luT5cI8F7Dy5QDU3Eb7qJZNwYGbsPNf5On8dKOV077DUlq/xGkKIqCbzB0fspC1mStJcwUhiEN9ubvRQ8wpTEQHZ1UVxq78/fQIap9ud7TtUEXujboEvT1I46jGDLw/XUMDhUeYkXGSoYknl2u+9UGFeQVRal1Lt3Fv7Y+R4Yr028uekWlOlPLHeTLYtNs6AHq2JzkMtysylytgryiKEpplqQvJdOdVeUAX52LkzZkbWTKgalltinCHFF2u7wHwcgCSweECKuW9pWXCvKKotS6jdmby73l36D4gcRZYlicvpRCb2FRrtwiLLSPbEfLiJLVbHWpszd/H4Y0aBfZtlwDpQcKkpm098My22TVrIxoODzo61LPQGbfA54dIMyAjox8Ai3iujLbUF1UkFcUpdbFWmOC1ocprk1EG+5uewcAoxqP4utD37IxayNmzcI5iUMZ3+ziEufvztvD27vfxWW4kVIihOD21rdiEho5nlw6RrWnebh/KeOfj83FYwTuwVuFFU1oeKWXS5peXGpqyBfgtwDev+bk572CNLdF2AaW+lmriwryiqLUulGNzmV5xsqgPWcNDYtm4YakazGkgSY04qyx3NP2zqDXdOgOXtv5Jk7D+ddBCe/v/RCTMCGkQBMavWN7cXfbOxAI/kxfxsyjc0hzpZXYpeoku2bn0ubjSbDG0zGqA1GWKL9zpPcQMv9NcC0BmYv/iisHsuAzFeQVRTlzJIW34PbWtzDlwFSk9E1TjLPG0jq8Ncddx2lqb4rTcPDCjv+gS50OUe25udUNNA1rGvSaKzNWBa1JUzSYKmF99gaWpi+jwFvA90d+9HvQJJgcjIk6QpzZzVZnIkPj+xJhCbzfq9RTkRmXgcyD0r6VGP6VLkNFBXlFUWqFIQ1WZa5mWfpyzJqZYQlDebfXWxxyHCbMFEaTsMYcKEhmefoKlmeuJN+bXxScd+bt4rltL/FyjxeJPqU3neHK5ON9n7Ijb2fA3vip3Iab344vIsWVEuCbhCTG5GJk1DFMAnqG5WLOvh4Z/y1C8190JQs/B1lIqQEeK9jOKbNd1UUFeUVRapyUknd2v8e23B1FW/5tydnGkITBTEi6mr35+5hz9GdWZq4KOrulUC9k4qYnmZB0DUMSB8O0ach//IO4Qwe5vVEE397TjxVj25arPS7DhSfgoibBXnc0phP7iJiFB/TDyMJpiMi7AlxoNVDabBwraDGIiJvL1a7qoIK8oighpUud3Xl70KVO+6h2WDUr23K3lwjw4Au0C1MX8Vvq7+XqgQPk6wVMPfAFOVPf57ynv8Xs8PXEE1IKuPWlpQBlBnqB4OyEQcw4/EPA1yWCHc4GdLLnnGwpOOdCoCCvxQW/kakt2EcjIm5GaDW3L6wK8oqihMye/L28uesdvIYXIQSGNLij9a3sKdjnt2n3SeUN8Ce5pYcBr/9YFOBPsjl1rvxgTZlBPtIcyZjGo5l3bAG5em7Ac37NbVosyAMiQKrGKADpCH6j+BBTePQAACAASURBVG/QNP+B2lBTtWsURak2Bd4C0l3pGNLApbt4beeb5HvzcRpOHLoDl+Fi8v5PEPg26q4u8ccDb8EX7Hhx/9fhIayald6xPYOcITjmDS95KPyvee7SvQEj/UJkaj/wrAh+o8Jvy2xLKKievKIoVVbgLWDyvk/YkrMNTWiEmewMjh8UsFiYLg0MKYsqSFaHjEYRJKT4B/SMRqWvRo0wRdA2sjUA5zUezeL0JQHOkiSai03DRICpBUbOs+BeCfp+IHjpgyLuTUgjD0QYohofcGVRPXlFUarsrV3vsSVnG17pxW24yfHk8uvxBQErNOpSx5A697a7C5tmw66Vry57aQ+Fb+/ph8tuKnHMZTfx7T0Bq+8WKdALeGnrv8g5fg1NcsfS1ZaNdsrMGKswuCC6eKljC2TdCI6vQd9DuQI8gGcRMnUAMrUfRu7ryFJq4lQnFeQVRamSFEcKBwoP+M1JN6SBHiAA2jQbPWN60Ce2N+/1eYsH2t9L9+hupaZvukd34/bWt2LVrAFfXzG2LZ9NHEJ64wikgPTGEXw2cUi5ZtfsKTjAz5mZSOni/sSt9A7LwIyBTehEaB5uit3tn4+X+UAFSwxLh+89shAKv0DmvV6x91eSStcoilIlGe5MTMLkd1wiaWBugNNwFg2y2jQrHaLaF5X3tWpWukR3Rpc6WZ5sUpwp6FIvMfiqobEzbxfb83bQKrwV2Z4s0t0ZCESJ81aMbVvuKZPFeTGxMK8pF0YfJtLk5f7EHRQYZgp0M/FmZ9H0yb8+WGY5r2w58cuJ/7x5BxROQ0Y9hBC2Cre5IlSQVxSlSpLCWwRMy5iFmaGJQ+gQ1Y7FaX/gMbwMih/IgPiz0IQviZDmSuc/218l35vve5OE7g26cXGTcezK380PR2bikR7c0jdzJrkwmd6xPbm/8b38N/kr9hTsrWBrJQRI+5iF5LAngk4mX489QvMSoVVlMxCz7z7mjuDdD2QHbouRBabGAV6rPirIK4pSJVGWKEY1GsnC1EUlttILM9k5r/Eooi3R9IzpEfC9b+9+jwx3Roke+c68naTGDwi4EMojPazKXMP67I3l3gGquGjNTa5h5dRA70UQYwo8pbNyTjwgvNtAiwm8AFZYQItHeveDewWIBmAfUe2liFWQVxSlyq5ucSXNw5oxN2UeBd5Cusd049JmFxNtiQ76njRXGimOFL958S7DzfSDX5PrzQv63mAVIsE3QBtniSHDk0U7ay79I1KRUrCyMJHmlgJWFDbELf9KL5kwaG3Np7HFGfSalecCIxOw+X5fxA4RDyJzXwDHd4AAYYJcDeKmICyBH4qVoYK8oihVJoRgSOLZFdoh6bgjNejWenmlBPiyaELDipPHEzfSwZ6Lhi9Jc05kCn/kN+LWuF18ldUWpzRhSEFXexZ3JOyq9P3KpuML8h58XXoBwg5aFBT8QFHwP/Gsk1l3Q+ISRIBxjspQQV5RlBq3OXsL7+yZFHD2zakDqhXV0uLksYZLsAsdUSwrYxIG50QeZ11hLG82W0mGbiNM6ESaysi9f5+LeCkDjnihmRk5MR4uC/4NxZ8NKF60TPpm5+S/GXiFrHSAZxNYe1fgHsGpIK8oSo3Spc4HeycHrB1vwoTVZMWhl1IeoBRWzcqDjfZgp2SAP0kISY/wbDQBieaT6RM7vt50gAfL97mIx1IRjhOvHfbCY6m+M8sT6EUYSBf+SXkvGGnB3kTpRc4qRs2TVxSlRh0oSA66OXacLY57296FVVgqdE2BwK7ZGd94EA1EesAAD2BCEq7pwIlUiAgHS/Aes3gp468Af/KYQ/p69ieZe/qCeQkamPtB3AyCh1kbEGSQ1dIraJsqSgV5RVFqlFmYg6Zj4q1xdG/QjWEJQyt0zftbjuX9Vke5wPw8pfWC/4r9Blh6Ixq8CbEfBL/wkSCpnKLjGthGQ+QjICJ8P2ODiNsR8dPQLO3BNgT/pIkF7JeBtZfvQXPyGHZEg1cRIvCir8pQQV5RlBqVFN6CSLN/TRmbZmNEw3MQQnBD6+uIs5ZStrcYDUlP4zmEd2uZ5/7Vw5fg2Qm2s9G0cDC1DvyGZkEy2kXHDSicDN59IHXfz3ig4Atk4Re+e0a/UCyQn+QFc0tE7BREzFsQdj1E3INInIuwn1vm56gIFeQVRalRQgge7vAgEaYI7Jodi7BgFRb6x/VjQFz/ovPCyqxpI7EJLw8nbkETlcnhe0H3bcMnop/Flzo5GRJ9TwM5MR4ZVjL3I8OEb/C16EAeOKbjW9kKvkDvhLzXkHoKGNkg/XecIv91MFIRtuFoDZ5Gi7ofYWpWic9ROjXwqihKjUsKb8FbvV9nY/ZG8rz5dIzqQLNT9muNtkRxJOjUdclF0Qc5P+owYabSttorjSza5EPYBkD8N8iCyeDdA3oayHS4LNqXWCp1dk2wmUACXL8j9TQCp5AEuBaWKFscCiEL8kKIV4GLADewF7hFShloba+iKGcgq2bhrLjgVSK7N+jG9rydQV+PN7mqEOAFhF0FsgBZ8DXSyEJYz0Y0eM23uUnmXeBe5Dv1smhkhaZMnryFhi/PXopKrNqtqFCma+YD3aSUPYBdwMQQ3ktRlHomKTwJrZQQ1dqWX8krC7BfCbZzkGnn+qpBFnyIzL4TmX0PUuqIiOsCzJgBX9AuZ9iUXrCPRNjHEjjYS7CPquRnKL+QBXkp5a9SFtUeXQE0D9W9FEWpf9pFtQ1Y3RIgzuSlhSXYrk+nDnKewjwcLN0h5xF8efQT+XLpAPdycP6EsA3zDYZiwpefFyCiThwr72YnBtK5CGFpD5F345syaQasvt9HTUSEuDgZgKhMkZ8K30SI2cDXUsr/lnZev3795Jo1a0LeHkVR6obfU//gv8lflShU1sASzYsdLiU8/wH/FaNaAiJxCTL9UtB3lHJlK748eYD4Zx0Elj5Q8CElNwSx4xtU9V/EFZSIQjRcjhBWXyEy5wJfGsd2HsJcff1eIcRaKWXA3FeVcvJCiAVAoEfRk1LKmSfOeRJfSbZpQa5xJ3AnQFJSUlWaoyhKPTO84TBaR7Tkt9TfyfXm0S+2DwPi+mPWzBjyLsh/31fNEQArIvYThDAhrX3BsYvA5R+h1EDt2Q3uVfjv+FSZAmaGb3qlpRPC3Boi76jENaompD15IcTNwF3AuVLKwrLOVz15RVEqQuppvoCsRYF1EOJEwJeenciMK6l4YLbj6+EH25pPEHg2jZXADw4rInFByNMypfXkQ5aTF0KMBZ4ALi5PgFcURakoYUpEhF3oy6EXS0wIS0eIfs43eCpK38zbF6B9q02x9CT4lMji5xZnh4g7AgzUmn2ramsg716aUM6Tfw/fSMN84VtmtkJKeXcI76co1Sr1YBrpRzJp2aU5EQ3KChQ+Gxdv5bs35pB+JJP+F/TmsocuJDo+KsQtPXNJKZEFn0LBxyCzkKY2iOgnEbahaOHjkWFjwL0Jmfs06PsDX0TYIOI+hG0QoCEzLgp+Q2GGBm9Dwbu+HZ/MrRGR/4ewDcYQYZD/nu8c6QFLN0TsOyH53BVRIwOv5aXSNcrpoDDPwXNXvc6mxdswW8143V6uemI8Nz5zFSJY5StgzuT5fPjIVFyFvuqGFpuF6IQoPlr/Kg0SKjHPuh6RUrItdzvrszcQZgrj7ITBNLY3qvJ1jby3oGAKUHwA1o6I+xRhPeuv+3sPIdNHESzVIhr+gTixMMo43ufERt2BWBGx7yFswwO+Ko188O4ELRFhrrkxxlpJ1yhKXfXqzZPY+PtW3E4PhbkO3E4PM16fzaL/LQ36HpfDxUePfVEU4AE8Lg+56bl89+acKrfp4I4jfPv6bGa9P4+s43VrTaEhDd7b8wFv736P+ccX8tPRufxz8zMsTVtWpetK6QoQ4AGcyPySPWhhbgFaqyBXEiVTOg1eJ3hodCPzgxc0E1okwtq3RgN8WVSQV5Ri8rMLWPnzWjyuktUHnQUuvn51ZtD37d98EE3z7+V7XF6Wz/J9O5VSkpmSRV5WxRbxfPz3/3JP3yf47MmvmPz4F1zf5j6WfL+yQteoTRuyN7I5Zwsuw/cA1NHxSA+fH/ii0nXjATAygr/mDbDBd+Td+Jf2tUHYeISwFR3R7CMg+tng19ZTKtTM2qaCvKIUk59dgGYK/M8iJy036PsaJEbj9QSekZG87TDv3P8Jt3R8kOtb38dVTe7g8VHPkpmSVWZ7tvy5g5nv/YLb4cbr9uJyuHE73Lx8wzsU5ARbDHR6WZGxqijAF2cSJrblbq/8hbUEghaON7fzOyTCLjkxhfHkYKwV7Ochop8OcO6lICID3RSsfSrf5lqggryiFJPYIp6wSP/l7JpJo8+o4JsrN2ndiHa9WmGy+K/QlFIy+/15HNmTgsflwev2smnxVh4b+SxljYktnLakRArorwbBgv8uKfsDnQYsWvD5HWZR+bkfQlgh4nb8e+d2RORDAc4XaJH3+xYnxU1HNFyCFvNawNrtQlgh8tFTrq2BCENEPlDpNtcGFeQVpRiTycSDk27HFm4t6iSarSYiosO56dmrS33vv354gqRO5SsVa+iSlP3H2bI0+KrM48lpLP76z4CvuQrcfPjI59zX/2+kHgy2jdzpYWjCEKxaoEAq6BzduUrXFhH3QdSjoCUCJjB3RMR+iLD2Df4eLRxh6YjQYku9thZxHSLmDbD0AK2hb5Vq/HcIc5sqtbmmqdk1yhnB4/aw9PtVbPx9K41aJjDm5hHENwn+j3z7yt188+pMju07Ts/hXbny0YtIaBYf9PyTNi7eyj8veglnfoDedwCPT7mXMTeN8DsupeSWTg9ydO9xpBH836hm0miYlMDU3e+iaf59NillqTOCasqMQ9/zS8qvvt40Agn8X4cH6RzdqbabVi+ErKyBotQFjnwHD539T47tT8WZ78Rqt/DVi9/z0twn6TYkcE+y84D2PDPjsQrfq0O/tsgKVL9NaB74wbFz9R4yj2WXGuABDN0gJz2XzX9sp+fwrmSl5rD2142kH8lgyXcr2b1uH/YIGxfeMZpbX5yAxVqxvVOryxUtLuOchkPZkrMVu2and2wv7KayNgVRqoMK8kq9N+ONORzZfQy301fk6uT/v3jd20w78EG19nTDIuzc/caNvP/wFDzOEzN0gqyEF5qg88AOJY7pXp3NS7azYdGW4IOKAWQczWTmpLlMfvxLhKaVyOM78pzM+mAeqYfSeerrRyrzsapFoi2REQ2H19r9z1QqyCv13m9fLS0K7MXlZuRzZE8Kzds3qdD1nIUu5n66kKXfrSQqPpKL7x1Ln3O7A76FVPOnLkYgMJlNGIZBbMMG5GUX4CnWBpNZ47xbRhAW8Vdvdu/GA0wc+zyuQjcSiSOvfHVXdI9OVFwUr9/xYcDPCeB2uFkxew2ph9Jp2CKhQp9XqdtUkFfqPYst8F9zKSUWa8X+CbgcLh4c9A+O7k3BVegrSLVm3kauf+pyrvnbpUx66DN2rtmLXmw6ZV5WAd2GdGLvxgM4850gBGNvHcE9b9xcdI7u1fn7ec+TnZoT/HPYLUjdQGiiaB6/LdzGiGvOZsOiLXjd3qDvBd8K3MO7jqkgf4ZRQV6p9y68azQfP/HfEikMoQmat29Co5aJFbrWr1MXc3Tv8aIAD+AqdPHFs98yeHx/fp36u19qxuPysHPVHr7PnEJOWi6RMRFY7X/NNjm2/ziz3p+HIy/AwiABCU3jiGsay9DLBjLy2iH89NF8/pixHHuEnfH3jWXMzcOZ9NBnGHrpgwEel4cWHZuWeo5S/6ggr9R74+4azcbft7Lq53UAaCYTYZF2np7xaIWvtXzW6oDz1q1WM6/eOiloAUOnw4XJZCKu8V8zeqSUTH7iS2ZN+gUppd8qW99JYDKbePqbR7HYzMQ1juWW5ydwy/MTSpw25NIB/Pr57zgLAs/qsdgsDL6kP4lBBnqV+ksFeaXeM5l8QXLfpmS2Ld9FfNNYzhrbC7Ol4n/9Yxo1QGjCb9aL0+Fm56o9wd8ooSCnoEQ1y1Vz1zPnw1+D5tFPOp6cxo3t7kPTNJI6NeOsC3qz9LuVeL06IycM4Zq/X0qvEd0YPP4sls1cHTDQSym5+d+lz/MvjSENNKGW1dRFap68olTAztV7eHTEMyXSNeWhmTQe+/Rezr1+KPs3H0RKyRf/+qaork1lWWwWmrVvzAdrX8FkNrHkuxW8MOEtv9SNyWLiwjtH8cC7t1fo+ptztjAt+X8cc6YQbgpnbOPzuKjpBSrgn2bUPHlFqYLjyWls+mMb0XGR9B3Tk7teu4l37v24QtcwdIPtq3bz2ZNfkZ9TiAA8ZQyUlofH5eH4gTSWzVzNsCsGEdc4hrBIOwU5Jffp0T0625fvqtC1d+ft4Z3dk3AbvgdaoV7InGM/4dALuSbpqiq3XakZKsgrShBSSj56bCqzPvgVs1lDCA2r3cIjn9yDLcKGK0j+O5h5ny3C7azYN4DycOQ7WfzNMgZe1I9GrRridvmnf4SApM4V2zj6hyMziwL8SW7DzcLURVzabDw2ky3IO5XTifrOpShBLJ+9hp8mL8Dj9ODId1GY5yA7LZd37v0YwxtsD9DgRIBSxNVl+ew1XNnwNnau3kPXwR39XpcSFn+7jLHWa5g49nkO7z5W5jWPOgKfIxBke+pWTfszmQryihLEnI9+DTiIWZBTSKcBHfzm39vCbdgjAvduW3Ztgddd+gBrVXhcXgrzHPzn+neCTqX0unV0r87a+Zt4cNA/yEkPXjoZoHl44GJrEkmstfTiXsrpQwV5RQki2IpToQkmTLyU3ud2x2q3EB4dhj3Cxs3/vpr317xM4zYNi0olCCE497qhPDjpNiy20NeNcTncbF5Seo12KSXOQhc/f7yg1PMua3aJX/VIq2ZlbOMxAatKKqcnlZNXlCBGXDOE3ev2+c+kkdBzeFfOOq8XGceyyErJpnnHplisZlIPpfPhulfJzyrA4/bgdnrIOJJJ8w5N6TWyOxsWbsYZqD58NSqrqBmAx+lh97p9pZ7TJrI1j3Z4mK8OTuew4zCR5igubDyWMY1HV1dTlRqggryiBDH2tpHM/3IxB7YcwlngxGQxYTabeOyze7Ge6JW7HW62r9jFzPd/YcmMFeheHd1rMODCvqQmp5K8/Qhmi4bb6WXAhX24+L7z+P2bZaQmp9fypwN7ZNlVIDtFd+Tf3Z6pgdYooaKCvKIEYbVZePOPf7P0+5WsnLueuEYNOP+2c2newVcaYMpT/2PG67MxDOlXN+bPH1YW7fp0st++9PuVmCymEnVtapOhnz5rZJTQUUFeUUphtpgZfvXZDL/67BLHtyzdzndv/hR0tWqwRYanS4DXTBoxDaNruxlKDVBBXqkRWcezWTBtCTmpOfQa2Z0+o7oH3Mmorpg39XfcjtDm1kPJYjVz3k3Da7sZSg1QQf4MkpWaw2dPfsWyH1djtpoYe8tIrvvn5SUqIobC+t828/TFL2MYBm6nh5nvz6PzwPa8+NM/KlU/piadHCS1h5ecGul1ewl1RRDNJKo9pWKxmUEI7nr9Rlp3b1np6+zZsJ+F05bgdXsZdsUgug3pdFpsM6j4U7VrzhDOQhe3dXmYjGNZRSkDq91Cl8EdeXVByYG19CMZLP1+FV6Pl0EX96NZu4ptqlGc7tW5qskd5GbklThuC7dx71u3cMHt51b62qGUejCNV295v2g6YudB7Xn8s/to2rYxACt/XsfzV78RtOpjVWgmjae+fYRVP69j7ie/Vfl6tnAbXQa2p9vQLiR1akqfUT2Ijo+q9PW+fuVHvnz2WzwuD1KCLdzKudcP5aH371SBvpaUVrtGBfkzxC+f/cakhz7zC0r2CBuvLXqWjv3aAjBv6iLeucdXl8UwJJomuPbJy7nuycsrdd8dq3bzt9HPURigVnq3szvx5pLnKnXd6rRr7V6Stx6mecemdOrfDq/Hy41t7yczJbtoYZHQBA0Sovhy3/vYw21IKXnp+rdZNnN1hYuVleX6p69k5qS5OPNdeAKUKKgooQnmeb4uVwBet2AT3731E9mpOQy6qC+XPHABkTG+ypnJ2w/z1QvfsWj6n37TNG3hNl6Z/xRdBvmvtlVCTxUoU9i6bGeQErSwd/1+OvZrS9bxbN6552O/wcT/vfg9gy7qR5seFf96r5m0oIOQmrl2c/KOAidPXvgiu9fuw9ANDEOS2Dyeq/82noLcwhIrR6XhW0C0ZMYKRt94Di6Hm76jeqJ7dJbPWfPXfq7V4KsXvitzA5CKsNos5QrwM96cw+dPTS+ql39gy0F+mbKIj9a/ys41+3h6/H9wOzwB/3u6HW6W/rBKBfnTkAryZ4gWnZphDbPidpTsdWomQePWDQFYPmtNwMFQj9vLwv8tpXX3pAp/HW/XuzXhUWE48kuuHrVH2Dj32iGkHc4goVlcrXzN/3TiNHas3FOit3xs33Heue8TAiXcnfkuju5NIe1wBvcPmEhhrgNnQfn2Ya2Iag3wdgtjbh5R5nkFuYV8/s//4Sr298Pt9JB1PJtZ789jzuQFpX5j0Uy+4m3K6afuTm9QKuS8m4f77WdqMvt2Kuo1shvgm/YnA2xtZOgG37z8I+Mb3MinT36FfqI4l2EYrFu4mXmfLyJ5++GA99U0jWd/fIKI6HDskXYsNjPWMCsRMRG8+8Cn3NzxQa5NupvVv6yv5k9ctvlfLA6YDjG8vl79qcIi7bTt1Yp37/+E7NSckAT46qJpAqvdQvdhXbjz1RvKPH/32n2YA+x363Z4WPrDKrKOl16QzGQxMfLaoZVurxI6qid/hmiQEM0bi//Nq7dMYv/mgyCgz8juPDbl3qLe+8CL+vH+w1OCXsOR7+SHt38mP6uACRMv5dHhz5CTnouhG3icHoSmEdckhsseupDRN53D1Ke/ZtH0P30LhYSvJ2yxmgmPCiMnLRevWwd00o9k8uwVr/Hu8herNOOjogJut3eSBLPVdKKNYLaaSWgez6CL+vHCNW9Wa287JIQgoVkcL8yZiGbSmPvpQr5++Uey03LpMqgjd7x8XYk/6waJ0QHn8AsB8U1j2b8pOeitzBYTd716A0mdAhc0U2qXGng9AxXkFqKZNMIi/Je1z5k8nw/+73Pf8vwgC3esdgute7QsymX7vR5mwWqz4ip0lXtjDM2kMfqGYTz22X0V+zBV8NDZT7ItyEYaQhOcf9u5LP1hJdKQDL96MLc8P4Go2EguCLu2WgZEq4vFZkH36n7/LcIi7fztiwfYs2E/3742uyjXLgTYIuy8v/o/tOj4V2C+q9djHNh6qMR1bOE2/vPLk/z3+Rms/XVTwPv3OKcLry96NgSfTCmv0gZeQ56uEUI8KoSQQoiEUN9LKZ+I6PCAAR5g3J2jeezTe7CFBZ87r5lN7F2/P2hv1u3wkJ9dUKGdjwzd4Mje4+U+vzqMKW0xkJSsmbeB8feNZfqRyTw46Q6iYiMBGHblIMwWU6nXFpqAEA8ztOnRks4DO9D/gt4E2kHcke9k+8rdfPvqrBKbj0vpGyid9sL3Jc5/4aeJtO6ehC3cWlRZ8+43bqLbkM5M+PtlaKbA4SI3PS/gceX0ENJ0jRCiBTAGOBjK+yjVJ+1wBm/c8WGp878Nr17tG2CYLWa6Du4AQG5mHht+24LVbqXPqO4hW6w15LIBvPfgp0UpmeKkhNSD6Xz98o9s/mM7ryx4umhw+N63bmbPun2kHkrH6/aimU14nB4sNguuQhf2CJvv9wWugLs0VQvhW9z2yeY3WL9wM+vmb/If3I60Yw+3YrKY4JQZrIZusGNlyW8xCc3i+XDdqxzaeYTcjHza9mpVtAis04B2WO0Wv78XZouJvmN6Vv/nU6pNqHvybwJPEKiboZyWfpnyW9HAaiC2cBuXPngB8U3jqvW+Xq+XH9+Zy78ue4UJze/i9ds+4KXr3+aqxnew6Y9t1XOTadOgVSvQNGjVigbzZnPzv6/BWsq3FrfTw45Vu9m+cnfRsei4KCZvep2nv32M21+6nmdmPMb3GVO4542bGHf3GO585Qa+2PseCS3iA14zPDqszG8CZZJQkF3AzEm/MGj8WYRFhaEVe/AK4Rt4HX3TcL/iaSeZLWb+b9hTTBz7PH/+uKpoamSLjs3oOrhjiVW+tjAbt710HbZix8wWE5ExEVz1+MVV+yxKSIUsJy+EGA+MlFI+JIQ4APSTUpZaX1Xl5Gvf67d/wC+fBV5lGRETwY3PXMmlD17A1mU7+ft5zwWdVnfyq32glI4t3Ervc3uwafFWCnP9F0mdKiwqjK+PTg6aYiqXadPgzjuhsNgG1+HhMHkyG5v3Yvb789i6fCfphzP93mq1W7jjlRu45P7zK3TLPev389jIf+FyuP0CrcliIq5RDJnHs4OOfWgmgZSl14fvNrQzby7+NykHUnnl5veKxhg69G3LE1Pvp3n7Jrx847v88d2KEtNnhSYwW814TqyJsEfYOO+WEdz/zm2lfqY1v27k29dmkX40k7PO68VVj19MXGO1S1RtC9mKVyHEAqBxgJeeBP4BjJFS5pQW5IUQdwJ3AiQlJfVNTg4+iq+E3sJpS3jr7o/8vpbbwqxMWvMyLYttBj1z0i98+OjnAdMdfUb3AClZt3Cz3/c4e6SNTv3bs2XpjqC9zOLCouw8+sm9nHPloMp9KPD14AP93WrZEg4cAOD7t3/isye/8ntwhUeFMXHaQwwc17fCt83PKeCG1veRn13g91q7Pq3peU5XZn8wz28Bmj3STosOTdi9bn/Qa2uaYOR1Q/nb1AeKjhXmOZBSEhEdXnTM4/bwwSNTmTdlEYZuYAuz4nZ6/AaPrXYLn2x5kyZtGlX4cyq1K2QDr1LKUVLKbqf+AvYBrYGNJwJ8c2CdEMLvgSClnCyl7Cel7JeYmFiV5ijFuJ1ufvvfUr7897cs/mYZS79fyZyP5rN/c+kP0aFXDKRx64YlFrbYwm0MvuSsEgEeoPPAjrWiZQAAIABJREFU9gEXT1ntFroP6UTf0T2LNtcozpnvYsNvW8oV4OHEatOqzkk/GGRYqNjxUTcM8yuYppk0ImLCOWtsrwrfMnnbIbb+uZPCvMKAr+9Zt5+fJi8ombcX0LRdY6buescvx34qi93C5Q+PK3EsPCqsRIAHsFgtPPje7fzfR3edyKs7A84O0kwaGxdXU2pMOW2EZOBVSrkZaHjy5/Kma5TKWzT9T6a98B2Zx7Jo06MlB7YexO30+PYpFSAQRYF74EX9mDjtQUwm/7yw1Wbh7T9f4Ls357Bo+p9Y7RYuunsMY28bWeK8QzuP8O8rXw86g2bDoq3sXL0naL31itC9On1H96jaRZKSAvfkk5KKfhsdF8Xrvz/Lyze+y+GdR5FS0mlgByZ++QAmc/lz6JkpWTx54Usc2nkEk9lcaiVJv4eXhKN7Uti8dIdvwDSI8OgwHvv0Xtr1bl2uNu1au5e37vqoxIrWU2maRnR8ZLmup9QdNTJPXuXkQ2vGG7P5/OmvS0yTK409wsbdr9/EhXcG3qvT7XSzd2MyUbERNO/QlNRD6cz9dCFphzLoPbI7Z1/Wn9s6P0zaoQy/OiYnBzFPLZ9QFYkt4vkq+cOqXaSUnDzXXed3ek56Liazqag4V0U8MHAiu9ftQ/dWfsGUZtYYc9Nwfp2yKODq2+lHJhPfpPy58JdvepeF05aUmt+PTohi+uGPsFhVeYK6ptYLlEkpW9XEfc5EbpeHL/71TbkDPICzwMVPk+eXCPKb/tjG/176nr0bDpCbkYfFbsHQDezhdvIy83xpdQm/f/0nnz8zndzMvICFqrxub8VXgwpKnX+Vm57H0b0pRWV+K+VkIH/ySV+KJikJXnghYIAH3wrhyjj2/+3dd2BUxfrw8e9s3/QKgQChSe+GIgJKUUEFRFERsSv2ivxQsHtVrK/9Knbv9dqxgyiCKEgv0ntvISEkIW3rvH9sDITdTQLJJmF5Pv/InrN7zuwKz87OPPPM1gy2rtoZNMBXdvs/r9tLTFJ0wI/FaDIy//slXHhz5TfUztx1MGiAt9gtxCZG868fH0QphdfrPak3dBFlSVmDk1zmrhMbAXMetaR/zpfzef6618tMOHryfV8azqKywy2OQieZO7OCBoETWu5fwY9Jo9nIoYzcqgV58AX0IEG9uuRl52MyG3GWkzRkMKiAvfNj7d92ALPF5Dfk5XF7mPbuzOMK8t0Hd2Hdwo1+/z9NFiP/+uEBImMjeOmmf7Nx6VZMZhODxvTj1pevrVpGk6gT5Ov6JBdfPw53OXntgVhsFgaM7gP4ioy9cdd7x1UT3eP2BhyLNxgNIVnl6XF7SGwYH7RkcV3SrEPjcodEPC5PpQI8QPNOTTEEmDcByl3LEMiFN59DXHKsb2eoErZIK5dPuIjUlincP+AxNizegvZqXA4Xv33yB49e9Oxx3UPUTRLkT3IR0XYGjennX4ZA+WrIlAbdkv/ao2w0btOQ4bedx59TF/LyrW+TcyCv6g1RvqBR3SWDlUHhcri4ttVdXBAxmiua3Mxb4z7i0IHcar1PdbHYLNz2ynVYIyxU5aOw2C1cdv9QImPtfuesdguDxvQ7rutFxkby72XPcem4YaS1a0THvm2Z8PGdXPv4KL59/We/bBtnsYu1f21k5/o9J/4mRJ0gBcrCgMvp4q1xH/Hz+7PRXk1UXAQ3PjcGq9XC7k37iEmIYtZnc9myYjsR0XaG3nousz6dR+bOrArT9GqTxW4JWCjNaDYSmxTDO6teJCbhxLexK0/WnoNMe/c39m3NoPPZHeg/qjdWu7XiF5ZY89cGpr78I6vnbSB736HjurfZauLpaRPJOZDHmvkbmfbOTNAaZ7ELW5SN5h2b8Pxvj1ZbuYcHBv+Lpb/87Xc8IjaCCR/dQe9h3avlPiJ0ZPu/U4TT4aIgt5DYpOjSMXOnw8UtXcezf9uB0t6a0WTA69XlDivUtmd/fZhHhj0bNOXPbDNzxQMjuOqRS6v93qvnruPBIU/5hqUcLmyRVhIbJvD6wmdwFDnZvHwb9Zok0axDkwqvtXHpFu4+86FKrQkwGA2MnjiCzv078GRJeqrb6cFgUDRomULXgR3pNqAj3Yd0CZj+eqI+fPhTvnjhe7/SyxabmXdWvVT1uRARcrWeXSNqhsVqxlIvtsyxP79aQOburDI/xyub2peUmkDWHv9l/qGmlGLbqp2YLKagQd5V7GLJL39Xe5DXWjP5qtfKrPgtLnCQseMA9w94nJ3rdmOxmXG7PDRt35inp00sd1Nsi80S8Ms0IsaO0+HCZDailEJ7NY9NHU+3QZ24rs3d5B3ML/P8fVsyGH7b4BNadVuRYbcP5ts3fsbt9JTOe1jtFtIHd5EAHwYkyIe5lX+spTi/8umVRzucnV/xk0JAo1k9d325C6mUUtRPq/4V0hk7MskJMN7vdnrY+vc2tKb0C3PLim1MHvMqT0+fFPR6370+PeCEsfZqHvv6fnIzD2Oxmel5QTfsUXZ2b9wb8IvVUehg2ju/HldGTWUlpMTz+oJn+Pd9H7Ji1hpskVYuuHlQSH4liZonQT7MpTRNxmIzn9DKU5er+janPi4aVs9dT7szWrF+0ebAawAU9BjStdpvbbGZg2a/HBur3S4PK2avJi/7cNC5gQO7sgKmlSqDwu30+NW097g9QSdsq7K4qiKNWjXkqR8nhuz6ovZIdk2YO++6/hiOWZJvKKlAaIu0YjAF/yvgDWFQqUjOgVzWL9pEdGIU9dKS/OrXa6/mlVunsH3NLoryi9i//QDuavhSSkiJp2XXpkE3yDiWwWjwlY4IIv28Llgj/CdI3U43bXqe5ne8cZvUgKtsrXYLg646vowaIUCC/Elj7YKNPHbJ89zc9X7evPcDsvYcDPg8R5GD3z+fx/dvzmDH2l0kpMTz7IyHSGlWD6vdgtlq5rTTm/Pe2pd54rsJ3Pj0laQ0q5uF4RyFTg4fzOeSey4MmElSXOjg4WGTGVnvBm7qcB8j693Aj2//UuX7PvTZvSQ3TiQi2rc7ksVuoUHzegHr10QnRFGvSfBNzwZf15+ElHi//PSht50XsCyBwWBg0mf3YouylZaIsEfZaN45jeG3D67yexOnHsmuOQn8syLVWeREa99mDfYoO/9e9lyZcelNy7byf4OewOPx+H72o+h/RR/Ou64/sz+dS1F+Mf1GnuE3eXeu6bI6nWnTKr0FuzbsCdxjPqYkgi3CyoOf3E3v4VVL+/N6vayYtZrM3Qdp0/M0ouIiubXbeApyC3EWuzAYDZitZh79ahzdB5c/bHT4UD5fv/QDf36ziKjYCEbcdT5nXda73DUFhw7k8tsnf5C15xCdz2pHj/O7VmtGjQgvkkJ5EvN4PFze4CZyj9lH02A0MGhMP8Z/4Nv42uv1MrrJrRzcW3bSzmgyYDAaSmu+W+wWht8xmJsmjyl9zjmG0EywdTunE6v+XIfb4a7SatUe53dl2a8rcVei5gv4vhTeWDT5hO8XTN7Bw/zw1gxWzF5DassURtx1PmntGlf7fYQ4XpJCeRI7sDOL4gAlB7weL8tmrix9vGnZNgrz/OuWe9zeMhN2jkIH3742nXOvPqs0QCmDCklP/oGP70Br+Py5b5n68rQTuobJYiL3QF6lAzz49qkNhZjEaK6cNJIrJ40MyfWFCAUZk6/jouIi8XoCB7i4o3LiPS53pUsKeN0eFvy4rPTxwDF9q9bIQBQ8fsmLvHHPh0x9pXIB/p/66cqgSv/s9XjZsGRL5W+rFG0DTGgKcaqSIF/HRcdH0WNItzITd+Abe75s/PDSx63SW1Q6IwQorXWzbfVO9m3OOHKiukrPaFi3cBN/fPlXpbZxt0ZaeOLbCXx98AOuefyy0k2pj6eqpVIKa6SVa58cdaKtFiLsSJA/CYz/8HY6n90ei81MZGwEFpuFS8cP4+zLe5c+x2Q2MfF/d1eqnonH7aXvyF5k7c3mnj4PseavDUeuYzLSOr0FfS7uidlqxhphwR5lo2XXpsfdbq/HW6kAD+AocJKfk09MfBRr/trgt8S+MtIHd+G1+U9XqtyAEKcKGZM/CUTGRPDM9Ic4sCuLrD3ZpLVr5LePJ0D3wV15ftaj3NfvkXJL0SY0jCOxQTwfPPSpXzB1uzxsX7OL+z+4nfveuYXD2fnUT0vG6/XyyPDnWDJjRbW/v3+8dONbpJ/Xpdy882AiYuycd21/mraXiVAhjiY9+ZNIvcZJtOvVKmCA/0fbnqfRoHm9oOdNFiODr+0PwOYV2wJu6Gw0G9m1YS/R8VE0bJGCMigK84p48vsJPDp1PNEh2gdUGQ3M/34JA67oE3ABUbm0L2ddCFGWBPkwo5Ri0qf3Ehkb4TeOb7GZSUpN5JL7hgK+cXyz1X8/T7fLQ5O2qQDM+HA2l6XcyBWNb2ZEwrWsX7AxZDn1Xo8Ht9PNedcPoFnHNGwluxIZTQaMJiNN2qbS95KepRuS/0OV1LLvfHa7kLRLiJOZ5MmHqfycAmZ/No9Ny7aSuesgoOk+uCuDrx9ARLRvI4rs/Ye4vt09FOYWltZlsdjMdD67PU9Pm8Rf3y3m6StfKVM7xmK34Cx2Vnqs/XiYrSY+3vw6SamJuF1u5k5dyMKflhERY8caYeVwdj5te7UCNP++90MMRiPa6yU6IYqnp02UnHVxypLFUCKonev38Mbd7/P372uw2i0Mvn4ANzw9GovNwi1d72fL3ztqpB3KoLjlxau5+O4LyxzftmoH9/Z7BJfTjbPIiTXCQkxiNC/NeYJ9WzOwR9lo3b1lte9IJcTJRIK8OCEjEq8l/1CB33FlLFk8dcxfnX9SOI8v7RGiE6N44tsJtO/dxu/8ben/x6Zl2/yO12+azOsLnyEuOdbvnBCnmvKCvIzJi6BadGka8Lj2aFp0bnqkMqTyDbX0Ht6dDn3aYIu0You0VirnXhkNJKTEk9gwgcU/L2fvlv2l5wryCtm6cmfA12Vsz+Tevg/j9R75QnE6XHz4yGdc1vAmLoq/hmeuejVoITchThXSkxdBrVu4ifEDHgu4O5PZaqbTWe0Ycv0ADmXk0qFvG1p2aQbAhsWb2bpyB1+99AM711W8EbTRZEAZFFa7FZfTTZf+7Xnky3FoDRfFX+O3x+s/7NE2Hv5iHN3P6wLApAufYcXs1ThL2mswGohNiuaD9a8QGetfvleIcCE9eXFC2vY8jed+e7RM+YR/uBwuVv2xjjY9T+OiO4eUBniA1t1bMuSGgYx9/upKpUJ63F7cTo+vwmORkxWzVvP2/f/BFmGl26BOQX8RuJ0e9mzcB/hW7v59VIAH37BR4eEiZnz4+/G9cSHCiAR5Ua52vVoFrZdutprI2JEZ9LU9z+/GXW/ehDXCelz3dBa7mPHhbLTWjH//NuIDfMmAr+Ry0w6+jJqtf+8IWNbBUehk3YKNx3V/IcKJBHlRoY5922Cy+NcydzlcpLVrVO5rz736bL7L/YgbnhlNYmpCpe/pKnbh9XqJrx/HLS9e43feYDKQeloDOp/dHoAGzev5bc8HvpTQJm3Lb6MQ4UyCvKjQJfcOxRphLbMFnzXCygU3n0NsUkyFrzcajYyaMILPdr3Np7ve4uzLe2OLshGdEEVy48C/ElqlN8doNJKXfZiXbnrL/wka7n5rbGnqZNterUhtmYLJXPbLyGQ2cf5Ng47j3QoRXiTIiwolN0rkjUWT6XNxT2ISfaUOxj5/Fbe+dO1xXyspNZFJn97LD3n/YWrWB1z/1Kgy+8waTQZsUTbufOMmAOZ/vwQVYBhGKZj//eKjHiue++0Rel54OiaLCaPJSMuuzXjx98cDbrMnxKlCCpSJSklt2YBHvhhXrdec9dlcXr5lSpkNww0GA0/9+ACt01sAvg2vA5VR8Hi8OIvL1t2JSYjmsa/H4yx24nF7sEfZq7W9QpyMpCcvaoXH4+GNO9/DccyuVx63h2nvzip93OP8bmiv/+Iqq91K34t7Bry2xWaRAC9ECQnyolYc2JmFo8i/AqbXq/l79urSx8mNErnmiVFY7RYMRgNKKWwRVgZd1Y92Z7SuySYLcVKS4RpRK6Ljo4Jva1i/bMrkZfcPo/t5nZn5yZ+4nW76XtKL9r0lwAtRGSEN8kqpO4HbAQ/wk9b6/0J5P3HyiIqLpNfQdBb8sLRMTXtrhJVRE0b4Pb9ZxzRumpxWk00UIiyEbLhGKdUfGA501lq3B14I1b3EyWn8+7dx+rmdsdjMvnLCdgujJ47grEvPqO2mCRE2QtmTvxWYrLV2AGitD4TwXuIkZI+y8+R3Ezi47xAH92bTuHVDmTAVopqFcuK1FdBXKbVQKTVHKdU90JOUUmOVUkuUUksyM4MvkRfhK7FBPK1ObyEBXogQqFJPXik1E0gJcGpSybUTgF5Ad+ALpVRzfUzZS631FGAK+KpQVqU9QgghyqpSkNdaB10vrpS6FZhaEtQXKaW8QBIg3XUhhKghoRyu+RboD6CUagVYgKwQ3k8IIcQxQjnx+j7wvlJqNeAErjl2qEYIIURohSzIa62dwJhQXV8IIUTFpKyBEEKEMQnyQggRxiTICyFEGJMgL4QQYUyCvBBChDEJ8kIIEcYkyAshRBiTIC+EEGFMgrwQQoQxCfJCCBHGJMgLIUQYkyAvhBBhTIK8EEKEMQnyQggRxiTICyFEGJMgL4QQYUyCvBBChDEJ8kIIEcYkyAshRBiTIC+EEGFMgrwQQoQxCfJCCBHGJMgLIUQYkyAvhBBhTIK8EEKEMQnyQggRxiTICyFEGJMgL4QQYUyCvBBChDEJ8kIIEcYkyAshRBiTIC+EEGEsZEFeKdVFKbVAKbVCKbVEKdUjVPcSQggRWCh78s8Bj2utuwCPlDwWQghRg0IZ5DUQU/LnWGBvCO8lhBAiAFMIr30PMEMp9QK+L5PegZ6klBoLjAVo0qRJCJsjxMmrqNjJ0lW7UApO79gEm9Vc200SJ4kqBXml1EwgJcCpScBA4F6t9ddKqcuA94BBxz5Raz0FmAKQnp6uq9IeIcLRHws38cQrP2Ew+H54a6154r6hnHF681pumTgZKK1DE1eVUrlAnNZaK6UUkKu1jinvNenp6XrJkiUhaY8QJ6OsQ/lcftu7OJzuMsetFhNfvz2WuJiIWmqZqEuUUku11umBzoVyTH4vcFbJnwcAm0J4LyHC0qx5GwjYEVPw+/yNFb7e69WsXL+HuYs3k5NXGIIWiroulGPyNwGvKKVMQDEl4+5CiMorLHLicnv8jrvdXgqKnOW+dve+Q9zz+JfkHS5CGRQul4erL+nFtZeeEarmijooZD15rfVcrfXpWuvOWuueWuulobqXEOGqZ9emmE1Gv+Mej5fEuMigr9Nac/9TX5ORlUdhsYuCQidOl4f/frOIRSu2h7DFoq6RFa9C1GFNGyXi9ngDnvvku8VBX7d5eyYHDxVw7EhPscPFV9OWVWcTRR0nQV6IOmzGnLV4vYGTI3bsPkhhkCGbgkIHBoMKeC4vv7ja2ifqvlCOyQtxUsovcPDbvPVkHcqnfauG9OjcNGjAPB45eYVs2JJBQlwkLZsm40s6K195QytKKSxm/6EcgDYtU/B4/L8crBYTA3q3rnSbxclPgrwQR9m4NYM7H/0cj0dT7HBht5lp0SSZVx6/DKvF/5/Lhq0Z/LFwEyaTkYFntqZJwwS/52itefezeXz63WLMZiMejyY1JZYXHx5JUnxUue2pnxyDUvgNu4BvUZQpwHg9gM1q5t4bB/LSOzNxuT14vRqb1UTD+nEMHdSxch+GCAshy5M/EZInL2qT1ppRd7zHnv05ZY5bLSauu+wMxozoWeb46x/9zjc/r8Dl8qAMCqPRwO1X9+OSId3KPG/Ogo08+ep0ih2u0mMGg6JNi/pMmTym3Dbt3JvNdeM+wuEsm2FjsRj54b3biIywlvv6DVszmDp9OQdzCujbvSWDz2qHVVbLhp3aypMX4qSyNyOXrOx8v+MOp5vps9eUObZu8z6+nbECh9ONV2s8Hi9Op5s3Pprjd40vflxWJsCDL3997ab9TH7jZ1wu/xTJfzRpmMCT9w8jLsaO1WrCZDKQlprA8xMvCdi7P1br5vV58PbBvDDpEoaf21kC/ClIgrwQJcobdz92/Pz3+Zv8VqECKINi3pItZY7l5RcFve6MP9bxr9emlduu3qe34Lt3b2XKM6MZeX43MrLyeGDyNwy74U0mvzkDd0kefV5+MZu3ZwadjBWnJhmTF6JESnIM9ZNj2Lknu8xxq8XEBQM6lDlmNCqUUn6rURUKo6Fs36lP9xbs3p8TsMfucnv4c9FmsrLzSUoIPj5vNBrYsPUA385YQbHjyJfLr3+uw2I24XS5+eWPtZhMRlwuDw3qx5IQG0G/nqcxdFBH7DZLpT8HEV6kJy9ECaUU/7p/KDFRNuw2M0aDwm4z075VA0aeX3acfVCfNgEXKXm1pk+PFmWOXTGsOwmxEQRLpjGbTX7zAIF8/PXCMgEefENJ3/6ygl//XIfT5SldIbtzTzYr1u7m1Q9mc9GNb7FleyYAm7cf4L4nvmTETW9x16Ofs2lbRsB7OZxuVm/Yy7ZdWYHLKoiThky8CnGMomIncxZsKk2h7NKuUcB0x/9+s4j3P58H+IZp0PDAbedxTt+2fs/NL3Bw35NfsnbTfr9zFrORr94aS0LJCtb9mXn8+uc6CgodnNGtOZ3apqKU4ryrXqWg8MSGYixmI+PGDmTym7/4jeVPumMIQ/q3L33885y1vDjlVwxK4fF6SUmO5bmJI2hYP+6E7i1Cr7yJVwnyQlTBvgO5/LVkCx6vxmwyYDIZ6dm1GfUSo/2eu2d/DteO+4ii4iOTsFaLiYFntmHiHYMBmD1/A/96dToerxe324vNaubM9BY8es8FjHvyKxav3HHCbTWbDLjc/qtnTSYDv/z3LixmExu2ZnDbQ5/iOOoXg8GgaJAcy2dv3FCp3H5R88oL8jImL0QVNKgXS6MG8Ux6/vuSfHaN16u57rLeXHXxkZRLl8s3hHLtpWfw58JNbNiaQUSElUvP78qYi3sBvmJkT702vcyEbrHDxV9Lt/DX0i0M6d++SkE+UIAH8Li9rNm4j67tGzN1+nK/uQOvV5OdW8CaTfvo0KrhCd+/svLyi/l2xgqWrNxBw/pxjDy/Gy2bJof8vuFKgrwQVVBY5GTS89/7pUh+8MVfWC0mLBYTVouRV9+fjaekPIHb7eGWMf24fGjZjtfyNbsC9pSLil38NGs1y1btDMl70MC4f32Fx6OJirAGLKNgUIrcvOBZQtXlUG4B1437mLyCYpxODyvW7mbm3HU8du+F9OnessLXFxU7ycouoF5ilKSLlpAgL0QVLFi+LWDqpdPl4c2P52AwKJwBsmqm/G8undqm0rZlg9Jje/YfKjOUc7StO7MocgQ+9w+FL+vHHaCcAUC9xCgOHPRfBwDgLFlslXs4cCB3uT20O61BwHPV6aOvFpJzuAh3ya8Or1dT7HAz+c0ZfPduc4zGwLkiXq/mzf/M4ZufV2Aw+LKeRg1N54ZRZ57yQ0ySXSNEFbhcnqDZJ26PN2CAB9+XwA8zV5V57kdfLQj4XIVv7D9YobJ/aAga4IGgAT4Qo/FIYLRZzYwZ0YP42NDvQvXX0i2lAf5oxQ43ezKCZyB99NX80sVpRcUuih1uPvthCV9KxU3pyQtRFT26NMUTpBRwebTWzJy7Hq9Xc/UlPdmbkRt0zFwDuoIAX93SUhOxWkzERNkYeX63GttPNioycJkGr9dLVJASDlprPvthqV96abHDzSffLOKyC06v9naeTKQnL0QVxMdGcOe1Z2O1mDAeZ6XKwiInP81axXXjPmbXvkNB8+hrmtVi4pw+bXjn2TG8+PDIgAH+cEExqzfsJfPg4Wq99+UXpmM7ZizdZDTQvnXD0hTTY3m9moJCR8BzwYafTiXSkxeiis7v34GWTesxd/Fmih0u/li0mcxKDo1oDQVFTmbNWx+wTEJt8GrN2We0CnhOa83bn/zJFz8uxWz2ra5N75TG4/ddWC2ras/t15ZN2w8wdfrykoqdXtJSE3nivguDvsZoNNC4QTy79h3yO9cyTbJyJE9eiBNUWOTkubd+Yc4C3x71SQlR/N8t5xIVaeHux77E7fHgdHqw28zERNnIL3SUu5gpKsJKfpAeaU1TClKSY+nVtRlXXdKzNO//x99W8fJ7v5UZGrGYjZzVqxWP3nNBtd0/O6eAjdsOkBQfVan0yYXLtzHxue9KvyiVAovFxEsPjaRzu0bV1q66ShZDCREC9z7xJSvW7i6TV26zmpgy+UriYyOYNmsNew/k0KlNI1IbxHH3o18E7a0Hqxlf20xGAxF2Cx+9dA3JidFcedf77Dimtg+A2WRk2ke312qNnFXr9/DBF/PZvvsgLdKSuGHUmbRpkVJr7alJshhKiOO0esNe3vtsHtt2H6RZo0RuGHUmHVofWQi0asMevwAPvqyZT79bwqQ7h3DliB6lx+cu3ozJZMARpCNfWwE+UJG1o7k9XgqKnHzy7SLuuWFg0DFupXzDTrUZ5Du2SeWlR0bW2v3rKgnyQhxjycodTHjmm9Jed1Z2PivX7+HZB0eQkhzDwy98z7ZdBwNusO316oA93dbN65dbN/54Ddq5jFvWTKdeUQ4H7HG81X4IM5t0q/iFJWKibDRMiSPSbmFpBYusPB4vS0pW2nbt0Jg5Czb5pXNGR9lIiA08MSpqlwR5IfBli3w9bTnzlmxhx+6DfsMqDqebV96fRe7hYg7lFpbb+83IymPJyh2kd0rD4XSTX+AgIS6S8/t3YPrvq/12eTpeg3YuY8Lyr7B7fIujUopymLD8KwwGmNnkdAwGFTDX/GgT7xxMn/SWrN20j1sm/q/CHPzkkjH5m0f3ZdGKHTgcLtweb+nY9/ibz62WfXBF9ZMxeXHKO1xQzHXjPiY7pyDo4iXwLUqy2y2V2pTDajHRvVMai1eka9/dAAAPnUlEQVTuwKs1dquZW6/qR0ZmHh99vbBK5Xu/mv4UKUX+C4OcDVPJXr6GbbsOMun578p9L53bNeKNJ0cB8NoHs/jip2VBh4xsVhOTHxhBeqc0wFcl83/fLWLl2j00ahjPlRd1L7NyV9Q8GZMXohxTpy2vMMAD2GzmgEM0gTicbuYetUOUy+XhxXdmkhAbWeX67PUCBHgAy769aGDymz9X+F527fUNKWmt6dimEcvX7Gb7noNYzSbiYiPIyMzDVFJC4OIhXctkuKQkx3DfjYOq9B5EzZEgL055fy3bWnGAt5q4cGBHfpi58oTv43Z7OVANi4cO2OMC9uRp0oTHXv6RgzmFFV6jaaNENmzN4O5HvyiTtul0enC5PYy5uBebtmWwcPk2vpmxgi9+XMp5Z7Vj3NhzKCp2sm7zfmIibbRqXl+Gaeo4CfLilBdfzoSh1WJCKbj0gtO56Yo+7D2Qy9KVO0rzxC0lC3Y81Vx2wGg0BC2X8Fb7IWXG5AGKTRa8Dz/K2un7KnX9ay7pxdgJ/w3Y7mKHm4+/no/RYMDp8pR+Ac74Yx3zFm8hO9f3JaKUIj7WzosPj+S0pvWO9y2KGiJlDcQp7/Khp2Ozlu3vGAyKFmnJfPz/ruWnD27n5iv7YjAonho/nJuv7EvTxok0ahDHlRf14JYx/fxeX1XNGydhCPKvc2aTbjzbdST77XF4gf32OF7qfinb+w2uVCrmA7edx89z1pT7xeR2e/0mn51Od2mAB99QT3ZOIXc/+nm1Zg6J6iU9eXHK69q+MbdddRZv/mcORqMBt9tLWmoCz0282G9zbZPRwKUXnM6lRxW90lrj8Wr+8/UCXG5PtfTsd+8/RP2kGPYdyAt4fmaTbmVSJo0GxapXp1V4XaXgzPQWfPjl/Cq172hFxS4WLN9G3x4V13sXNU+CvBD4JheH9G/Ppu2ZxEbZSGuUWOnXKqUYM6IHo4alczi/iFnzNvD6R78HrSpZGUXFLrSGpPhIsg4VVPh8j1eza69/7ZZjaQ3ZOfk0qBfD/szAXyAGgyIywsrh/OJKtdXr1VIIrA6T4RohSthtFjq1ST2uAH80k9FAfGwk5w/oQEpybGl2CnBCFSaLHS7y8qs/eP6xcDOjh/fAZAzcqAG9W/HU+GHYrKbSSVVDeW9A+X4NibpJgrwQ1cxus/DOs2O4+pJeNGucSIdWDRk1LJ0TyUExqOr/J7p01U40mrGj+2IxGzEaFUpBcmIUH790DY/dO5RuHZrwzrNjOKdPG1qkJXFOv7a0SEvy+7JSwNCBnUhNiav2dorqUaXFUEqpS4HHgLZAD631kqPOPQjcAHiAu7TWMyq6niyGEuHqz0WbeeKVn4Ju7xeM0ajwBNntyVTOVn/lUfhWqVrMRm66og8t0pJJSoiqMFAXFTt559O5/DhzFQ6nm4S4SMaO7sPgs9uf8lvs1baQVaFUSrUFvMDbwP3/BHmlVDvgU6AH0BCYCbTSWpc7BS9BXoSr/AIHw2/8d8AqlGaT4bjH7/t2b8HBnELWbqpcymQwBoOiXmI0bz0zmqT4qIpfIOqk8oJ8lX4Laq3Xaa03BDg1HPhMa+3QWm8DNuML+EKckqIirdx740CsliPj3HabmfSOTbjr+v7HtauUzWqiccMENm3PqHK7vF5N5sHDvPD2r1W+lqibQpVdkwocvSvx7pJjQpyyLhzYkfatGvDTrNXkFzjo17Mlvbr6ttZ7//P5HMqteKUqgMej2bYrC5frxLN3ylzPq5m/dCsejxejUabpwk2FQV4pNRMIVHl/ktb6u6o2QCk1FhgL0KRJk6peTog6rVnjJO645my/42Ov7MOzb/5SuYso2LC14l680aBAEXRM/2ihLFPodnuYt2QL23YdpHHDePr1OA2z2RjCO4qjVRjktdYnUoloD3B0TlWjkmOBrj8FmAK+MfkTuJcQJ730jpXv4LhcHnJyy0+ttNvMnNasHi8/eilmk5Hcw0WMnfAJGVl5fgu1DAZFjy5NQ9KLz8kr5OYH/0d2TgHFxS5sNjNvfjyHt5+50m+hmQiNUP02+x4YpZSyKqWaAacBi0J0LyFOet/9svK4UiyNpuD/dNu3asAzEy7ijSdHYTGbUEoRFxPBf165jruvH0Ck3YLZ5OtJ221mEuIiGX/zOVV8B4G99sFs9mfm+RZ34VvklZmdzwtTZA6gplRpTF4pNQJ4DUgGflJKrdBan6e1XqOU+gJYC7iB2yvKrBHiVLZs9a7jHjKxWkx+2To2q4lz+7Ytrf1+7PMvHtKVoYM68efizWzdmUmThgmc2b0lS1fu4Off19IkNZ6+3VtiMlXPcMrvCzf5FVrzlswBeL1aKljWgCoFea31N8A3Qc49BTxVlesLcapoWD+WdZv3V6rWvFLQKCWOwwXFuHI8ZXZ18ni8uL1e8gscREVaA77ebDYyoHdrBvRuTU5eITeM/5jsQwUUOVzYrWbeiLZLSmUYkal0IeqAUcPSsVjK9p7/GSM/urOrFLRsWo+XHh7JW09fSYfWDTGWlCdQSuFye3nnf3MZeesUNm0/UOF9X/tgNvsO5FFYUiunsNhF5sHDvDhlZulzDhcUs37z/kpn/xzt7J6n+Y31Gw2KM05vLr34GiLb/wkRAhlZeRzKLSStYQKz5m9g6s8rcDjcDDyzDZcPPZ0Iu8XvNXMWbuSFt2dSVOzE49Wkd0rj9mvO4o8Fm9iTkUP9xBhSkmOw2cx0apNaOnH55n/m8NVPy/w2PmnaKJH/vnIdANk5BXz501KWr9lN4wbxXD40nZZNkxk4+mUcDv8FWkaDYvbn9/Lmf/5g6vTlmM1GXC4PZ5/RigdvG1zp7JicvEJuKZl4LXK4sFnNxETZZOK1moVsxWt1kyAvTnZ5h4t46IXvWb1hLyaTEYfDhVKqdNtAi9lIowbxvPvcGCxm/9FSj8fL/sw8oiOtxETbS4/v2nuIux87souT2+3hsgtP5+Yr+3L57e+yNyPX71oWs5HP37gRj1dz/fiPKSpy4XJ7MBgUZpORf40fxkPPfx9wFa7RoLj9mrOZ8r8/SzdIAd+4/tBBnbjnhgGV/kzcbg/zlm5l284smqQm0Ld7S0mhrGYhW/EqhCjr4Rd/YNX6PThdHgqLfD3yo/eFdbo87M3IZda8QAvFfUM0qSlxZQK81prxT39NZvZhCoucFBY5cbo8fDVtOfOWbC23bowyKN79bC75BQ5cbl9P3+vVOJxunvv3L/Tt0cJvOMVQMpzy2Q9LygR48O1d+8PMlUF3rQrEZDJyVs/TuPbSMxjQu7UE+BomQV6IanLg4GFWrd9TYR2aYoeLpat2VPq6W3dmkZVd4LfrU7HDxdSfl3PBgA5YLWV/FSgFaakJJMVHsWjFjjKTs//IPVzMmBE9qZ8Ujb1kZyuT0UCk3crtV59NXpAa8W63B6fLv/cv6iYJ8kJUk5zcwkqlHppNRuonx1b6uoVFzqC1bfILHIwalk7blinYbWZMRgN2m5nYaDuP3zcUgOggWTZaaxrUi+XtZ0YTFWXDZDLg9nhxuz3cMvF/tEhLDvi6BvVisdv85xRE3SQ7QwlRTdIaJVYqBdJoVFw4sGOlr9u6Rf2AOfRWi4mBZ7bGYjbx2hOX8/fa3azdtI/kxGj69WiJ1WoGfHvYvvrB7DJDL2aTkTO6NSMywso7780jJ7cId8kvkCKHi2Kni2JHJHabGafTjcerUcp3z3FjT2QRvKgt0pMXoppYLSZuu/qsMpt6G40GDAaFxWwsWV0aweQHRpCSHFPp61rMJibcem6ZCpY2q5lGDeIZfm5nwJc+2aV9Y0Zf1INz+rYtDfAAQwd1YtigTljMRiIjLFgtJjq0bsjEO4YA8Nu89aXj9f/QGnbszua1xy/n3LPa0bRRImf1asXrT46ie+emJ/oRiVog2TVCVLPFf+/g0+8Xk3nwMD26NGX08B44nC4cTjdpqYknnB++dWcW3/6ygoPZBfROb86gPm39xuLLcyi3kC07MqmfFEPjhvGlx4fd8CbZOf458Eajgekf3REw3VPULeVl18hwjRDVrHvnNLp39i8rUFXNmyRx340nPlQSHxsRsNzBef3a8fX05WXy7A0GRYfWDSXAhwEZrhHiFHfdZb1p3iSpdOI2wm4hPjaCh+8cUttNE9VAevJCnOIi7BamTB7D0lU72LTtACn1YmXBUhiRIC+EwGBQdO/cVCZVw5AM1wghRBiTIC+EEGFMgrwQQoQxCfJCCBHGJMgLIUQYkyAvhBBhTIK8EEKEMQnyQggRxiTICyFEGJMgL4QQYaxOlRpWSmUCld8XrW5KArJquxF1gHwOR8hncYR8Fj7V/Tmkaa0DbuVVp4J8OFBKLQlW1/lUIp/DEfJZHCGfhU9Nfg4yXCOEEGFMgrwQQoQxCfLVb0ptN6COkM/hCPksjpDPwqfGPgcZkxdCiDAmPXkhhAhjEuRDRCl1p1JqvVJqjVLqudpuT21SSo1TSmmlVFJtt6W2KKWeL/n7sFIp9Y1SKq6221STlFKDlVIblFKblVIP1HZ7aotSqrFSarZSam1JbLg71PeUIB8CSqn+wHCgs9a6PfBCLTep1iilGgPnAjtruy217Fegg9a6E7AReLCW21NjlFJG4A1gCNAOuEIp1a52W1Vr3MA4rXU7oBdwe6g/CwnyoXErMFlr7QDQWh+o5fbUpv8H/B9wSk/+aK1/0Vq7Sx4uABrVZntqWA9gs9Z6q9baCXyGrxN0ytFa79NaLyv582FgHZAayntKkA+NVkBfpdRCpdQcpVT32m5QbVBKDQf2aK3/ru221DHXA9NruxE1KBXYddTj3YQ4sJ0MlFJNga7AwlDexxTKi4czpdRMICXAqUn4PtcEfD/HugNfKKWa6zBMZargc5iIb6jmlFDeZ6G1/q7kOZPw/WT/pCbbJuoWpVQU8DVwj9Y6L5T3kiB/grTWg4KdU0rdCkwtCeqLlFJefLUqMmuqfTUl2OeglOoINAP+VkqBb3himVKqh9Z6fw02scaU93cCQCl1LXAhMDAcv/DLsQdofNTjRiXHTklKKTO+AP+J1npqqO8nwzWh8S3QH0Ap1QqwcIoVZdJar9Ja19NaN9VaN8X3E71buAb4iiilBuObmximtS6s7fbUsMXAaUqpZkopCzAK+L6W21QrlK/H8x6wTmv9Uk3cU4J8aLwPNFdKrcY3yXTNKdZzE/5eB6KBX5VSK5RSb9V2g2pKyYTzHcAMfBONX2it19Ruq2rNmcBVwICSvwcrlFLnh/KGsuJVCCHCmPTkhRAijEmQF0KIMCZBXgghwpgEeSGECGMS5IUQIoxJkBdCiDAmQV4IIcKYBHkhhAhj/x99lTWJw2vh1gAAAABJRU5ErkJggg==\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# Iteración 0. Se realiza la inicialización aleatoriamente, para el ejemplo son 5 puntos, \n",
        "# y los demas puntos se asignan al cluster más cercano.\n",
        "\n",
        "iteration=11 #@param {type:\"slider\", min:0, max:40, step:1}\n",
        "plt.figure(figsize=(6,6))\n",
        "plt.scatter(X[:,0],X[:,1],c=all_preds[iteration])\n",
        "plt.scatter(all_clusters[iteration][:,0],all_clusters[iteration][:,1],c=\"r\")\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-ZkdXxNaJP5m"
      },
      "source": [
        "**Ejercicio 3.**\n",
        "\n",
        "Usar el algoritmo k-means y distancia Euclidean para agrupar los siguientes puntos en 3\n",
        "\n",
        "grupos: A1=(2,10), A2=(2,5), A3=(8,4), A4=(5,8), A5=(7,5), A6=(6,4), A7=(1,2), A8=(4,9). Asumir los centroides iniciales: A1, A4 and A7.\n",
        "\n",
        "a) Correr una iteración y mostrar: <br />\n",
        "\n",
        "> 1) Los nuevos grupos <br />\n",
        "\n",
        "> 2) Los nuevos centroides <br />\n",
        "\n",
        "b) Iterar más. ¿Cuantas iteraciones se necesita para converger? <br />\n",
        "\n",
        "c) Mostrar gráficamente (los puntos y centroides) al converger: <br />\n",
        "\n",
        "> 1) grupos finales <br />\n",
        "> 2) centroides finales <br />"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Consulta**\n",
        "\n",
        "1. En que consiste la inicialización kmeans++\n",
        "2. En que consiste el  Mini Batch K-Means"
      ],
      "metadata": {
        "id": "HNjpadmp7UbX"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kmFcElL-v7i9"
      },
      "source": [
        "## Determinar el número de k\n",
        "La distancia intra-cluster mide qué tan compacto es cada cluster, ecisten varias medidas intra-cluster, una de ellas se define como:\n",
        "\n",
        "\n",
        "\n",
        "$$\\sum_{i=0}^{n}\\min_{\\mu_j \\in C}(||x_i - \\mu_j||^2)$$\n",
        "\n",
        "k-means minimiza esta medida, y se utiliza para medir la calidad del cluster. El método consiste en  ejecutar varias veces el k-means con diferentes valores de k,  y graficar el valor de la inercia para cda k. La grafica resultante es una curva que desciende (a myor número de grupos menor la inercia). En esta gráfica se busca un valor de k tan pequeño como sea posible y que tenga un valor de la métrica bajo. A este tipo de gráfica se le conoce usualmente como gráfica de codo o *elbow*:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "49IgwKH2v8CY",
        "outputId": "bcc65cf6-d86e-4707-97d7-0c6dac6a261c"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# Creamos un conjunto sintetico\n",
        "# Se ejecuta Kmeans, para valores de k entre 2 y 15 y se grafica la inercia con respecto al número de clusters\n",
        "X,_ = make_blobs(600, cluster_std=1.2, centers=6, random_state=10)\n",
        "\n",
        "Sum_of_squared_distances = []\n",
        "K = range(2,15)\n",
        "for k in K:\n",
        "    km = cluster.KMeans(n_clusters=k)\n",
        "    km = km.fit(X)\n",
        "    Sum_of_squared_distances.append(km.inertia_)\n",
        "    \n",
        "plt.plot(K, Sum_of_squared_distances, 'bx-')\n",
        "plt.xlabel('k')\n",
        "plt.ylabel('SSE')\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "z36kg1tQxUas"
      },
      "outputs": [],
      "source": [
        "# Graficamos los clusters, para visualizar los centroides y comparar con la gráfica del codo\n",
        "#experiment_number_of_clusters(X, KMeans(), show_metric=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4vfO3d-12iFi"
      },
      "source": [
        "\n",
        "**Ejercicios:**\n",
        "\n",
        "**4.**  Calcular la gráfica del codo para el ejemplo 1 (calificaciones de películas)\n",
        "\n",
        "**5.** Entrenar un modelo K-means con un conjunto de datos en dos dimensiones, realice una exploración del parámetro $K$. Seleccione un valor apropiado (utilizando el método del codo y argumente su decisión.\n",
        "\n",
        "**6.** Aplicar el algoritmo k-means al conjunto de datos Iris (sin la clase), para k=2,3,4,5,6,7,8. Dibujar la gáfica de Elbow(codo) basada en el SSE. Explique los resultados.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IEMqCEeOI5iA"
      },
      "source": [
        "## Hierarchical Clustering\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8A-KvPVfopfE"
      },
      "source": [
        "###Ejemplo1\n",
        "Usaremos un dataset de vertebrados (ejemplo de TAN) usado para clasificación. Se ejecutaran los tres algoritmos clásicos de agrupacion jerarquica aglomerativa: **single link (MIN), complete link (MAX), y  group average**, usando scipy library de python.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "vaolZ5bipKTi"
      },
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "data = pd.read_csv('vertebrate.csv',header='infer')\n",
        "data"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# importamos las librerías\n",
        "from scipy.cluster import hierarchy\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "\n",
        "names = data['Name']\n",
        "Y = data['Class']\n",
        "# Se eliminan la columna de nombre y la clase\n",
        "X = data.drop(['Name','Class'],axis=1)"
      ],
      "metadata": {
        "id": "38lmouiia5I_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fsfUIMM93AF9"
      },
      "source": [
        "###Single Link (MIN)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "X4Oy7veCrin8",
        "outputId": "6bcd9717-5bfd-4ad3-b506-fed055a0ba9b"
      },
      "outputs": [
        {
          "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": [
        "Z = hierarchy.single(X)\n",
        "dn = hierarchy.dendrogram(Z,labels=names.tolist(),orientation='right')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JP9Fgg_DrwY9"
      },
      "source": [
        "###Complete Link (MAX)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "ZSmT0vdKqYnj",
        "outputId": "25914ee0-ea91-4871-e74a-b98c1b6dcb6c"
      },
      "outputs": [
        {
          "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": [
        "Z = hierarchy.complete(X)\n",
        "dn = hierarchy.dendrogram(Z,labels=names.tolist(),orientation='right')"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###Average - Promedio"
      ],
      "metadata": {
        "id": "s6KSbSPDcENp"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "uy5q4_LZp6r1",
        "outputId": "18176a0c-34f5-4178-d710-8cf4df0d1fbd"
      },
      "outputs": [
        {
          "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": [
        "Z = hierarchy.average(X)\n",
        "dn = hierarchy.dendrogram(Z,labels=names.tolist(),orientation='right')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PzKDnLmAbwM4"
      },
      "source": [
        "###Ward"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "c1GYP3QXsUL_",
        "outputId": "effef9f0-9437-47c7-d155-f55fb4097e67"
      },
      "outputs": [
        {
          "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": [
        "Z = hierarchy.ward(X)\n",
        "dn = hierarchy.dendrogram(Z,labels=names.tolist(),orientation='right')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c8mofjuYbwNA"
      },
      "source": [
        "**Ejercicio 1**\n",
        "\n",
        "¿Qué concluye de los cuatro métodos? con respecto al conjunto de datos usado.\n",
        "\n",
        "**Ejercicio 2**\n",
        "\n",
        "Dado un conjunto de ejemplos categóricos de 5 dimensiones:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "i2o_HtYXK0Rs",
        "outputId": "0092d649-807b-4a86-86c9-c2e81d16afb4"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[1, 0, 1, 1, 0],\n",
              "       [1, 1, 0, 1, 0],\n",
              "       [0, 0, 1, 1, 0],\n",
              "       [0, 1, 0, 1, 0],\n",
              "       [1, 0, 1, 1, 0],\n",
              "       [0, 1, 1, 0, 0]])"
            ]
          },
          "execution_count": 66,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "from scipy.spatial import distance\n",
        "\n",
        "X = np.array([\n",
        "              [ 1,0,1,1,0],\n",
        "              [ 1,1,0,1,0],\n",
        "              [ 0,0,1,1,0],\n",
        "              [ 0,1,0,1,0],\n",
        "              [ 1,0,1,1,0],\n",
        "              [ 0,1,1,0,0],\n",
        "             ])\n",
        "X"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iviV83cgK1r3"
      },
      "source": [
        "a) Aplique agrupamiento jerárquico aglomerativo, usando:\n",
        "\n",
        "1) Medida intercluster enlace simple (single link o MIN) basado en el coeficiente de Rao. Diagramar el dendograma\n",
        "\n",
        "2) Medida intercluster enlace completo (complete link o MAX) basado en coeficiente de corres-pondencia simple CCS (su sigla en inglés, SMC Simple Matching Coeficient). Diagramar el dendograma\n",
        "\n",
        "b) ¿Es posible usar el método de Ward? Explique."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZkaC9M35LBdd"
      },
      "source": [
        "**Ejercicio 3**\n",
        "\n",
        "Usar el conjunto de datos [“Perfume Data Data Set”](https://archive.ics.uci.edu/ml/datasets/Perfume+Data#) del repositorio UCI (Machine Learning), para:\n",
        "- Aplicar los algoritmos: single link, complete link average ling y Ward. Graficar dendogramas y explicar resultados.\n",
        "- Aplicar PCA y nuevamente aplicar los algoritmos y graficar los dendogramas."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R-w6SVAeKwkD"
      },
      "source": [
        "\n",
        "**Ejercicio 4**\n",
        "\n",
        "Usar el data set creado en la sección \"Determinar el número de K\" y construya un dendograma con distancia euclidiana (from sklearn.metrics.pairwise import euclidean_distances), y otro con similitud coseno (puede utilizar la función de scikit-learn [cosine similarity](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.pairwise.cosine_similarity.html)). Discuta los resultados."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## K-Nearest Neighbor\n",
        "\n",
        "**Ejercicio 1**\n",
        "\n",
        "Crear un conjunto sintetico de 5 clusters:"
      ],
      "metadata": {
        "id": "C8x4PucdjYNL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.datasets import make_blobs\n",
        "np.random.seed(2)\n",
        "# Creación de un dataset sintético de 5 grupos con 600 puntos (se incluyen valores negativos)\n",
        "X,_=make_blobs(n_samples=600,centers=5, cluster_std=0.8)\n",
        "plt.figure(figsize=(7,7))\n",
        "plt.scatter(X[:,0],X[:,1],alpha=0.4)\n",
        "plt.xlabel(\"$x_1$\")\n",
        "plt.ylabel(\"$x_2$\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 461
        },
        "id": "5vsCv8MQjWwA",
        "outputId": "e07d7847-7cb0-4cc1-9031-f3ddbc4939ce"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, '$x_2$')"
            ]
          },
          "metadata": {},
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 504x504 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Usar el algoritmo de K-Nearest Neighbor y distancia Euclidean para agrupar los datos. Probar con varios valores de umbral."
      ],
      "metadata": {
        "id": "mcLEy94Cj5Fi"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wPl1mzUFLRqd"
      },
      "source": [
        "**Ejercicio 2**\n",
        "\n",
        "Usar el algoritmo de agrupación K-Nearest Neighbor y distancia Euclidean para agrupar los datos del ejercicio 3. Usar un umbral de 4."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3LEgTQfoMx0t"
      },
      "source": [
        "---------\n",
        "**REFERENCIAS**\n",
        "\n",
        "[1] TAN y otros. Introduction to Data Mining  (segunda edición)"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "machine_shape": "hm",
      "provenance": [],
      "include_colab_link": true
    },
    "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": "3.8.5"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}