KMeans_Introduction.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "KMeans_Introduction.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyOKIP4M9LAiqrq24de/lp+L",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/tawfiqam/MI564/blob/main/KMeans_Introduction.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bjUqXQNRLF34"
      },
      "source": [
        "#K-means and agglomerative clustersing\n",
        "\n",
        "Clustering divides data into clusters that are meaningful to your analysis. Meaningful groups are found when the cluster capture the \"natural structure of the data\" [1].\n",
        "\n",
        "K-means is an unsepervised classification method. The goal of clustering is to group data points that are similar to each and **and** different from data points in other groups. The clusters are basically labels for the data points within each of them. If a group of data points is in cluster 1, then they are distinct from data points in cluster 2 adn cluster 3. \n",
        "\n",
        "Much of this introduction is source from [here](https://heartbeat.fritz.ai/k-means-clustering-using-sklearn-and-python-4a054d67b187). \n",
        "\n",
        "References: \n",
        "\n",
        "[1] Steinbach, M., Kumar, V., & Tan, P. (2005). Cluster analysis: Basic concepts and algorithms. Introduction to Data Mining, 1st Edn. Pearson Addison Wesley.\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VtTu0yxSRmZU"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn import datasets\n",
        "from sklearn.cluster import KMeans\n",
        "\n",
        "#getting the Iris dartaset from sklearn\n",
        "#see details here: https://scikit-learn.org/stable/auto_examples/datasets/plot_iris_dataset.html\n",
        "iris = datasets.load_iris()\n"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_AQKrZayXBRJ"
      },
      "source": [
        "#these are the packages we use when plotting figures using Pandas DataFrames in a notebook. \n",
        "#check the introduction to Pandas for details (https://github.com/tawfiqam/MI564/blob/main/Pandas_Introduction.ipynb)\n",
        "import matplotlib.pyplot as plt\n",
        "plt.rcParams.update({'font.size':20,'figure.figsize':(10,8)})"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4ar5Z4gv3_et"
      },
      "source": [
        "K-means chooses K initial centroids randomly. Each data point is then assigned to the closest centroid. The centroid is then updated based on the elements assigned to the cluster. \n",
        "\n",
        "How do we asses what close means? Consider that if our data is plotted, then we can think of the \"distance\" between data points as the euclidian distance between them on the graph. \n",
        "\n",
        "We can use the sum of squared error (SSE) as the error (also known as scatter) of the data. Turns out that the centroid that minimizes the SSE of the cluster is the mean. If you want to see more details, check out [1:Page 500].\n",
        "\n",
        "For example, if we had 3 points on a graph at (1,1), (2,3), and (6,2), then the centroid should be (3,2) ==> ((1+2+6)/3),((1+3+2)/3)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 492
        },
        "id": "K__rTNUu3_0l",
        "outputId": "df04a3eb-0823-43ff-c76b-f46e4e108559"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "colors = [\"blue\", \"red\"]\n",
        "X = [1,2,6,3]\n",
        "Y = [1,3,2,2]\n",
        "\n",
        "color_indices = [0, 0, 0, 1]\n",
        "\n",
        "colormap = matplotlib.colors.ListedColormap(colors)\n",
        "\n",
        "plt.scatter(X, Y,c=color_indices, cmap=colormap)\n",
        "\n",
        "for x, y in zip(X,Y):\n",
        "    text = str(x) + ', ' + str(y)\n",
        "\n",
        "plt.text(x, y, text)\n",
        "plt.show()"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M84onq_IOQcE"
      },
      "source": [
        "##Back to the Iris dataset!\n",
        "\n",
        "Let's explore the Iris dataset. There's a data portion that includes 4 featuers. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8AN1dVRNTRK4",
        "outputId": "75eec98a-254a-4c04-961a-2ffa0c9c4bd8"
      },
      "source": [
        "print(iris['data'][0:5])"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[5.1 3.5 1.4 0.2]\n",
            " [4.9 3.  1.4 0.2]\n",
            " [4.7 3.2 1.3 0.2]\n",
            " [4.6 3.1 1.5 0.2]\n",
            " [5.  3.6 1.4 0.2]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B87rG3EYOZT2"
      },
      "source": [
        "The four features are..."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HmTxhiqyTKvB",
        "outputId": "eb188889-e98b-425c-9cfc-264f6f11b48b"
      },
      "source": [
        "iris['feature_names']"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "['sepal length (cm)',\n",
              " 'sepal width (cm)',\n",
              " 'petal length (cm)',\n",
              " 'petal width (cm)']"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M2NRKJoaOcy3"
      },
      "source": [
        "The target is basically describing three different types of flowers: Iris setosa, Iris virginica and Iris versicolor"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RNoKTkOjTNAw",
        "outputId": "90dfe04e-de45-49f0-dc5b-b8533ef4f74a"
      },
      "source": [
        "iris['target']"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
              "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
              "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
              "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
              "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kLDwAl5jOrxy"
      },
      "source": [
        "Since we always like to work with Pandas DataFrames, let's set one up using this dataset"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IEb5YzqESwwz"
      },
      "source": [
        "# np.c_ is the numpy concatenate function\n",
        "# which is used to concat iris['data'] and iris['target'] arrays \n",
        "# for pandas column argument: concat iris['feature_names'] list\n",
        "# and string list (in this case one string); you can make this anything you'd like..  \n",
        "# the original dataset would probably call this ['Species']\n",
        "df = pd.DataFrame(data= np.c_[iris['data'], iris['target']],\n",
        "                     columns= iris['feature_names'] + ['target'])"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "FgHLDCMKTD4Y",
        "outputId": "d7b0543a-886e-45df-c1fc-58a72392badc"
      },
      "source": [
        "df.head()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>sepal length (cm)</th>\n",
              "      <th>sepal width (cm)</th>\n",
              "      <th>petal length (cm)</th>\n",
              "      <th>petal width (cm)</th>\n",
              "      <th>target</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5.1</td>\n",
              "      <td>3.5</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4.9</td>\n",
              "      <td>3.0</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>4.7</td>\n",
              "      <td>3.2</td>\n",
              "      <td>1.3</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4.6</td>\n",
              "      <td>3.1</td>\n",
              "      <td>1.5</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5.0</td>\n",
              "      <td>3.6</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   sepal length (cm)  sepal width (cm)  ...  petal width (cm)  target\n",
              "0                5.1               3.5  ...               0.2     0.0\n",
              "1                4.9               3.0  ...               0.2     0.0\n",
              "2                4.7               3.2  ...               0.2     0.0\n",
              "3                4.6               3.1  ...               0.2     0.0\n",
              "4                5.0               3.6  ...               0.2     0.0\n",
              "\n",
              "[5 rows x 5 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mGKBb-DcO--C"
      },
      "source": [
        "Because we want to make the names of the columns easier for us (not to have to add the spaces and the \"cm,\" let's rename our columns..."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i2apNfrkVEeC"
      },
      "source": [
        "df.rename(columns={'sepal length (cm)':'sepal_length','sepal width (cm)':'sepal_width','petal length (cm)':'petal_length','petal width (cm)':'petal_width'}, inplace=True)"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HeY10AU4Pvze"
      },
      "source": [
        "Let's create a scatterplot with sepal length on the x-axis and sepal width on the y-axis. Let's color the different types of flowers to make things clearer. Do you see any patterns here? "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 537
        },
        "id": "gc8olyo3WkW3",
        "outputId": "d3c8019a-b6eb-4b5e-8b23-841e948a1107"
      },
      "source": [
        "col = df.target.map({0.0:'b', 1.0:'r', 2.0:'g'})\n",
        "df.plot.scatter(x='sepal_length',y='sepal_width',c=col)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7ff3d69970b8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MEslaKm7Pzeo"
      },
      "source": [
        "##Enter K-means clustering\n",
        "\n",
        "OK. Let's try this for the first time, with a K (number of clusters) = 5."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "F5rJYdd_YzQ9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "273cea41-ee84-4383-d417-e577bebebb4e"
      },
      "source": [
        "x = df[df.columns[:-1]].values\n",
        "kmeans5 = KMeans(n_clusters=5)\n",
        "y_kneas5 = kmeans5.fit(x)\n",
        "print(y_kneas5.cluster_centers_)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[6.20769231 2.85384615 4.74615385 1.56410256]\n",
            " [5.006      3.428      1.462      0.246     ]\n",
            " [5.508      2.6        3.908      1.204     ]\n",
            " [7.475      3.125      6.3        2.05      ]\n",
            " [6.52916667 3.05833333 5.50833333 2.1625    ]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_Sfcs-AknLMR",
        "outputId": "9c6e2c44-a551-4b7c-b2af-43b5c3eb5f65"
      },
      "source": [
        "k_means_test = y_kneas5.predict(x)\n",
        "print(k_means_test)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
            " 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 2 0 0 0 2 0 2 2 0 2 0 2 0 0 2 0 2 0 2 0 0\n",
            " 0 0 0 0 0 2 2 2 2 0 2 0 0 0 2 2 2 0 2 2 2 2 2 0 2 2 4 0 3 4 4 3 2 3 4 3 4\n",
            " 4 4 0 4 4 4 3 3 0 4 0 3 0 4 3 0 0 4 3 3 3 4 0 0 3 4 4 0 4 4 4 0 4 4 4 0 4\n",
            " 4 0]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        },
        "id": "rVC9Fts0sQpb",
        "outputId": "361dd2ea-11b0-43bb-e9ab-e00324e037ca"
      },
      "source": [
        "plt.scatter(x[:,0],x[:,1],c=k_means_test, cmap='rainbow')"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7ff3d68c85f8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmcAAAHfCAYAAAAVw3+UAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nOzdd5xcdb3/8dd3ypbZmt57QhJCCyT0LihWLHjRK94LyEXxiqBXQbGiIkVFELj6Q7HAVRRRBEWQEnooCQkllJDee7bP7JRzvr8/zgZ2N3NmS2Z2zmzez8cjj8mes9/5fmZ2yvt8T/kaay0iIiIiEgyhYhcgIiIiIu9QOBMREREJEIUzERERkQBROBMREREJEIUzERERkQBROBMREREJEIUzERERkQDpdzgzxpxjjLEd/y7oQzub499z/a1HREREZDCI9KeRMWYCcDPQClT34y7WAb/Nsnxjf+oRERERGSz6HM6MMQb4DbAL+CvwlX70u9Za+91+tBMREREZ1PozcvZF4FTg5I7bohg+fLidPHlysboXERER6bUXX3xxp7V2RG9+t0/hzBgzG7gGuNFa+6Qxpr/hrN4Ycz4wGmgCXrTW9ul4s8mTJ7N48eJ+di8iIiIycIwx63r7u70OZ8aYCHAHsB64oh91dXYocFu3+38Z+LS19tV9vG8RERGRktWXszW/DcwFzrXWJvahz+uB44ARQA0wH7gbL7AtMMaM82tojLnQGLPYGLN4x44d+1CCiIiISDD1KpwZY47CGy37ibX22X3p0Fr7P9bahdbandbaVmvtYmvtx4G/AMPJcYKBtfZWa+08a+28ESN6tdtWREREpKT0GM46dmfeDrwFfKuAtfyi4/bEAvYhIiIiEmi9GTmrBg4AZgPtnS8aC3yn43d+2bHshn2oZc9+yqp9uA8RERGRktabEwKSdDt4v5PD8Y5DexpYDuzLLs+jO25X78N9iIiIiJS0HsNZx8H/WadnMsZ8Fy+c/c5a+6tOy2PARCBurV3fafkhwBvW2nS3+zkEuKrjx//r42MQERERGTT6NX1TLxwJPAY8gXex2j2+DHzQGPMUsAFvVG4WcAYQBn4J3FmgmkREREQCr1DhzM/fgFrgELzZBSrwpoF6APiltfa+Aa5HREREJFCMtbbYNfTLvHnzrGYIEBERkVJgjHnRWjuvN7/bl4vQioiIiEiBKZyJiIiIBIjCmYiIiEiAKJyJiIiIBIjCmYj0aGPC4aJlLcx4fDcnPdvI/dtTxS5JRGTQGuhLaYhIidnU7nDY0400ZSwZCyvjLouXNvPDA6q4ZEplscsTERl0NHImIjldsypBc0cw2yPuwDfeaiPulOaleEREgkzhTERyWrArTTpLBgsbw5utzsAXJCIyyCmciUhOEyqyf0ykXMuocjPA1YiIDH4KZyKS02VTK4mFuy4rM3DS0CjjKsLZG4mISL8pnIlITqcOL+PG2VXURgw1YSgPwWnDo/xpbk2xSxMRGZR0tqaI9OiCiZX8x/gK3mpzGFEWYlS5tutERApF4UxEeqUsZDioRh8ZIiKFps1fERERkQBROBMREREJEIUzERERkQBROBMREREJEIUzERERkQBROBMREREJEIUzERERkQBROBMREREJEIUzERERkQBROBMREREJEIUzERERkQBROBMREREJEIUzERERkQBROBMREREJEIUzERERkQBROBMREREJEIUzERERkQBROBMREREJEIUzERERkQBROBMREREJEIUzERERkQBROBMREREJEIUzERERkQBROBMREREJEIUzkRL0XEOa059vYvQjuzjpuUae2JUudkkiIpInCmciJeaJXWne9XwTj+xKsy1leXJ3hvctauL+7alilyYiInmgcCZSYr78Ritxt+uyuAuXvN5anIJERCSvFM5ESsyrLU7W5avjLhnXDnA1IiKSbwpnIiVmVHn2t21dxBA2A1yMiIjkncKZSIn5+rRKYuGuy2Jh+MrUSoxROhMRKXWRYhcgIn1z0cQKGtOWq1fF2bMT85LJlXx9WmVR6xIRkfxQOBMpMcYYrpge43+mVLI15TKqLESF9meKiAwaCmciJao8bJhUGe75F0VEpKTomDMRERGRAFE4ExEREQkQhTMRERGRAFE4ExEREQkQhTMRERGRAFE4ExEREQkQhTMRERGRANF1zkQ6SbuWh3am2Z50OXFolGlVuo6YiIgMLIUzkQ6vt2Q45fkm2l2LY8GxcN74cm6ZU605K0VEZMBot6YIYK3lg4ub2ZGyNGegzYF2F27flOTuralilyciIvsRhTMR4NUWh20p9+2JxPdoc+AX6xNFqUlERPZPCmciQLtrCfnsuWxzBrYWERHZvymciQBzayNE2DudVYbgk2PKilCRiIjsrxTORIBoyHD7oTXEQhDtyGjVYZhTE+bCiZXFLU5ERPYrOltTpMMHRpXx6olDuG1DO1uSLmeMKOMjo8qI+u3vFBERKQCFM5FOpsbCXDWzqthliIjIfky7NUVEREQCROFMREREJEAUzkREREQCROFMREREJEAUzkREREQCROFMREREJED6Hc6MMecYY2zHvwv62PZAY8xdxpjtxph2Y8xyY8yVxhhd7VNERET2a/0KZ8aYCcDNQGs/2h4FLAI+DDwC3Ag0A98GHjbGlPenJhEREZHBoM/hzBhjgN8Au4Bf9LFtuKNtDDjLWvvv1trLgaOAvwDHAV/qa00iEkyr4w4fX9JM/UO7mLBgN9etiuNYW+yyREQCrT8jZ18ETgXOA9r62PYkYDbwpLX2vj0LrbUucFnHj5/rCIAiUsK2JV3mP9PIX7emaMpYNra7XLkyzvmv9HnAXURkv9KncGaMmQ1cA9xorX2yH/2d2nH7YPcV1trVwFvAJGBqP+5bRALk5rUJ2hyL22lZ3IG7tiTZkHCKVpeISND1OpwZYyLAHcB64Ip+9jez4/Ytn/UrOm4P6Of9i0hAPNOQIenuvbw8ZFjWonAmIuKnLyNn3wbmAudaaxP97K+u47bJZ/2e5fXZVhpjLjTGLDbGLN6xY0c/SxCRgXBgdZhIlgMUUq5lSkxX8RER8dOrT8iOMyyvAH5irX22sCX5s9beaq2dZ62dN2LEiGKVISK9cOmUSsq7fcKUh+Co+iizqiPFKUpEpAT0GM46dmfejrcr8lv72N+ekbE6n/V7ljfuYz8iUmTTq8I8OL/u7RG0MgMfG13OffNqil2aiEig9WbztZp3jgFr9zmR8pfGmF/inShwaY77Wt5x63dM2YyOW79j0kSkhBw/NMprJw6hKe1SETKUh3UitohIT3oTzpLAbT7rDsc7Du1pvODV0y7PBcA3gDOAqzuvMMZMxQtt64DVvahLREpEXVTHmImI9FaP4azj4P+s0zMZY76LF85+Z639VaflMWAiELfWru/U5AngDeBEY8yH9lzrzBgTAq7t+J1fWKurVIqIiMj+qVBH5R4JPIYXxk7es9Ba6xhjzsMbQbvbGHM33qU53gXMA54BflqgmkREREQCb8D3NVhrnwfmA/cC78abrqkO+B5wurU2OdA1iYiIiASFKdU9iPPmzbOLFy8udhkiIiIiPTLGvGitndeb39VRuiIiIiIBonAmIiIiEiAKZyIiIiIBojlURIqoPePyw1UJXm11OGFIhEsnVxAKaZtJRGR/pnAmUiQvNWWYv7CRTMc5OX/bluJbb8VZdfJQRlcooImI7K/0DSBSJO9e1PR2MNsj7sIZi5qyNxARkf2CwplIEbRmXHaksl/G5pUWZ4CrERGRIFE4EymCjOu/rjSvPCgiIvmicCZSBPVlIWp9jvicHtPbUkRkf6ZvAZEi+evhtZhuyyIG7juitij1iIhIMCiciRTJu4aXsfHUIXx6bDmH14S5aGI5u04byuwanUQtIrI/07eASBGNrQhz+2E1xS5DREQCRCNnIiIiIgGicCYiIiISIApnIiIiIgGicCYiIiISIApnIiIiIgGicCYiIiISIApnIiIiIgGicCYiIiISILoIrQw6WxMOhz7TwPaU93PUwM/nVPGZiZXFLayELWpMc8nrbSxuyjAkarh0SiWXT60kZLpPQCUi0k9bl8Abf4b4dqgcBjM/CuOOLlx/javhtT9A41qIxmDqe2Dae8EUf9xK4UwGnYmPN5C27/yctnDBsjamxcKcPLyseIWVqNdbMpzyfBNtjvfz9pTlByvjbG53uWlOdXGLE5HBYesSWPL/wO3Yqo7vgFd+A24GJhyf//5aNsGz14LT0V+qBVbcB4kGOPic/PfXR8WPhyJ59P/WxbsEs87OfaVlYIsZJK5alSDhdF0Wd+BXG9ppSLvFKUpEBpc37n4nmO3hpODNvxSmvxX/ACe9d38bnoRUW2H67AOFMxlUHtiR9l23JemT2iSnpU0ZskWwspBhdVzhTETyIL49+/JkI7hO9nX7onkdkOU7IRTxRu2KTOFMBpWTh0V9143UHs1+OagmnPWDIuVaJlfqI0RE8qByWPblZbUQCue/v5rxQJZjZt0MxIbnv78+0ierDCqXTonh9zb+1cE1A1rLYPGN6TEquj2plSH41NhyhpXpI0RE8mDmRyHUbQs6XAYHfLgw/c34AIS7bcyHymDcMVBW/GNp9ckqg86Kk4ZQ3+lUlxDwk1kx3jOyvGg1lbJDayM8ML+Og2vCGKAmbLh0ciW/OKj4H2AiMkiMOwoO+U+oGOr9XF4LB34CJp9SmP5qJ8KRX+4YQQPCFTDldDj4PwrTXx8Za0vzOJx58+bZxYsXF7sMCTDHcUgBleECDInvpxxrCQFGl9AQkUKx7sBezsK6gIECf64ZY1601s7rze/qUhoyaIXDYXRls/wKK5SJSKEN9HXGAnBds+6CV5GIiIjIfkzhTERERCRAFM5EREREAkThTERERCRAFM5EREREAkThTERERCRAFM5EREREAkTXOZNBaVvS5a4tSZozljNGlHFEXWFf6q0Zy5+3JNnY7nJUfYTThkcJ9eKaYO2O5a9bk6yMuxxaG+b9I8qIhHQtMRGR/ZnCmQw6929P8W9LmnGBtAs/XBXn7DHl3HZwdUGubP9aS4YTnmsi5VriDlSF4aCaCAuOqqMy7N/fuoTDMQsbaclY2jraTagI88yxdQyJalBbRGR/pW8AGVTijuUTS5uJu9DuggPEHbhrS5J/7kgXpM+zl7bQkPYClgVaHXi5OcNPVidytjv/lVa2pyytndqtijt8/c22gtQpIiKlQeFMBpXHd6XJtlewzYHbN7bnvb+NCYdVcWev5QkXfrfJv7+kY3lidxqn29S2KQt3bU3lu0wRESkhCmey3yjEtJCaalJERPJN4UwGlVOGRXHt3surwvAf4yry3t+4ijDTY2G6Z7TKEJw73r+/8rDh5KFRuh+SVmbg7DFlea9TRERKh8KZDCqVYcNdc2uJhbyAFAFiIfjkmHLeOyJakD7/NLeGIVFDddh7Q1WHYW5thC9PqczZ7teHVDOqLERNp3bTq8JcPbOqIHWKiEhpMNZmGWYoAfPmzbOLFy8udhkSUDu6XUpjboEvpdGWsdy99Z1LaZw6rHeX0kg6lr9tS7Ei7nBoTZj3jSwjrH2lIiKDjjHmRWvtvF79rsKZiIiISGH1JZxpt6aIiIhIgCiciYiIiASIwpmIiIhIgCiciYiIiASIwpmIiIhIgCiciYiIiASIwpmIiIhIgCicDQIZ11IK16tzrMXpR51uP9uJiASWdb1/IlkU9rLpUlCP70rxhdfaeL3VIRaG/55UyQ8OiBENBesK8xsTDp9d1sq/dqYxwPtGRPnFQTWMqci9bbAr5fL5Za3csy2Fa+GkYVFuPaiaaVXhgSlcRCTfUq3w6h2w9UUvnA2bBYecC1Uji12ZBIhmCChRLzVnOG5hI/FOG16VIfjk2HJuO6SmeIV10+5Ypj3ewLaki9OxLAKMqwyx4qQhvkHStZaDn2pkRZtDuuMlGgKGRg2rTh5CbVSDviJSYqwLT3wL2raB3fOJaCBaBadeB9Hc8/FKadMMAfuBH66Mk+g2Ip5w4Q+bk+xKBWeo/K9bkzRn3glmABlgd8rl79tTvu0e25VmfeKdYAbgAgnX8n+bkoUqV0SkcHa9CYndnYIZgAU3DZueLVpZEjwKZyVqWYtDtjHPspBhbffUVkRvtjm0OnsvjzuwPNuKDsvbHDJZHmCbA8taM3msUERkgLRu7RbMOjhJaN448PVIYCmclajD6yJZ/3gp1zItFpw/68E1EaqzHCJWGfbW+TmoJkIkyx7PqjAcXhfNY4UiIgOkZhyYLJ/P4XKonzTw9UhgBedbXPrkG9MrqewWemIh+K8JFdQH6HisM0eVMbI8RLRT0IoaGF8R5r0j/UPWCUMizKoKU97poYSB2ojhk2PKC1ewiEihDD0AqsdAqPOGaQgiFTD26KKVJcETnG9x6ZPZ1REeP6qO44ZEKDMwqszwnRkxbjiwqtildVEWMjx3TD2fGFNOVdgb+frU2HKeOaaOsPE/q9QYw4Kj6zhvfDk1EUNlCD46uoxFx9VTlW1ITUQk6IyBYy6D8Sd4gSxUBmMOh+O/AxFtdMo7dLamiIiISIHpbE0RERGREqVwJiIiIhIgCmciIiIiAaJwJiIiIhIgCmciIiIiAaJwJiIiIhIgvQ5nxphrjTGPGmM2GGMSxpjdxpilxpjvGGOG9eF+1hpjrM+/rf17GCIiIiKDg//8OXv7ErAEeBjYDlQBRwPfBS40xhxtrd3Qy/tqAm7Isry1D/WIiIiIDDp9CWe11tr27guNMVcBVwBfBz7fy/tqtNZ+tw99y37qH9uTXLsyTtLChRMquGBiZa/aPbkrxZUr4jSlLf8+rpxLJ1cQCvU8ULyl3eWOTe1sTbq8a3gZ7x0RJZRjJoNiSTiWP21JsrQpw0E1ET45tpxqzZwgIjIo7PMMAcaYQ4GXgEestaf34vfXAlhrJ+9Lv5ohYPA7a0kTf9ma7rLsoOowLx9flzNofem1Fm5Yl+yybGy5Yd0pQ4jkaPfIzhRnvtiM40LSQnXYm2D+4SPrKAsFJ/hsaXc5cmEjDWmXNoeOabEMzx1bz5RYllnmRUSk6AZ6hoAPdty+0oc25caYc4wxVxhjLjHGnGKM0beKvO2lpsxewQxgWavDLzcms7TwbG139wpmAJuTlm+8Ffdtl3Etn1jaQtzxghlAqwOLGzPctmGvAeOiuvT1Vra2e8EMoM2BnSnLZ5fpqAARkcGgL7s1ATDGfAWoBuqAecDxeMHsmj7czWjgjm7L1hhjzrPWPtHXmmTwuWFtwnfdreva+azP7s3/Xeff7vebklw7qzrruqXNGVLu3svjLty+KclFk3q3O3Ug/H17iky3ZS6wYGcax9qcE8qLiEjw9TmcAV8BRnX6+UHgXGvtjl62/w3wFPAa0AJMBb4AXAg8YIw5xlr7craGxpgLO36PiRMn9qN0KRVlOcZ0IznWlYf9g0kkR2iJhgyW7Lv4ywKWdbzHsXetxkDAShURkX7o825Na+1oa63BG/36KF64WmqMObyX7a+01i6w1m6z1sattcustZ8Drgcq8c7+9Gt7q7V2nrV23ogRI/paupSQr0/zH6n66tSY77qLJ1X4rvt8jnWH1oQZEt377VAVhgsn+rcrhk+OLdsrMEYNfHhUWSBPXhARkb7p9zFnHeHqHuDdwDDg9n2s5Rcdtyfu4/3IIDAlFuGrk8v3Wv6+4VHOGrP38j1qoyF+Onvv8HZEbZivTPEPWcYY7j2iliERQ00YKkJQGYKPjCrnk2P9+yuG62ZVcWBNmOowlIegJmyYGgvx84Oy77IVEZHSss9nawIYY5YChwEjrLU7+3kfdUAjkLTW9jhUobM19w8rWjP8cFWCpGu5ZHIlRw2J9qrd5naH762Isztt+a8JFZw+oqxX7RKO5b5tKXakXE4aGuXg2v7s+S88ay2P7UqzrNVhZlWY04cH85IfIiLi6cvZmvkKZ9uAkcBQa21DP+/jPXjHr71hrT2wp99XOBMREZFSkfdLaRhjDugY2eq+PNRxEdqRwMI9wcwYEzXGzDLGTOv2+7ONMVVZ7mcycHPHj//Xm5pEREREBqPe7rN5H3C1MeZpYA2wC++MzZPwTgjYCvxXp98fB7wBrAMmd1p+NvA/xpgnO9a1ANOA9wMVwD+BH/fzsYiIiIiUvN6Gs0eA6XjXNJsL1ANtwFt41yv7mbV2dy/u5zFgZsd9HIc3P2cj8HTH/dxh87GfVURERKRE9SqcWWuX4V2LrFestWvJcsmljgvM6iKzIiIiIj7yMX2TiIiIiOSJwpmIiIhIgCiciYiIiASIwlmJs9ayO+WScgfuPIqNCYed2WYJL5Dt7S4bE06f2yUcS2O673UmHUtD2mWgzk1pz7isaM2QcQfuOR3sUq3evwGTSEBjY9/bJZPQ0AA6D0pEOlE4K2H3b08x+bEGxjy6m7qHdvHZV1todwr3IX/X5iSxB3cy4bEGRjyym1GP7OK1lkzB+nupKcPwh3cxasFuJjzWQNW/dnLv1mSP7RrTLmctaab+oV2MfGQ3c55s4LmGdI/t4o7l/JdbqH94F6Mf2c20xxt4aEcqHw8lq4zrcspzjVQ+tJsDnmyk7MHdfGppc8H62x/sXgW/Ph6uHer9++3J0Li2gB02NsJZZ0F9PYwcCXPmwHPP9dwuHofzz/fajR4N06bBQw8VsFARKSV5mSGgGPb3GQJeaExzynNNxDsNtlSG4MxRZdw5tzbv/b3WkuGgp/YeGSgzkHjPUEKh/Ob8lOtS9a/dZLq9PA2w6uR6psT8TzQ++plGljZnSHVqWx2GZScOYVJl2LfdmYubeGhnmvZOz2ksBAuPrefQAkzjdNpzjTy6e+9we/GkCn42R/Nk9lU6DjdMgcROsB1/QxOCqlFwyRqIFGKK1KOPhqVLIdUpxFdXw7JlMGmSf7szz/TCWHv7O8tiMVi4EA49tACFikix5X2GAAmeq1clSHTbC5Zw4Z5tKbYn87977H9ez76PKGXhpnU9j2b11Y9Wt+8VzAAs8OXX23zbLW3KsKy1azADSLlwy7r27I3wdtV2D2YA7S5ctzrRh8p7J+O6WYMZwC/W+9cp/l77sxfQbKe/oXUh1QLL7y1Ah0uXeiEs1W10NZWCW27xb7dx497BDLyfr7su/3WKSMlROCtRy1sdso15locMG7snjDxYEfe/z1cLsGtzWY77XBn3P/5sTcIhnGX+75SFN1r973NdwqU8tHdDF3gzR7v+2pljb2m6NAezi65hFaSzbEOkE9CwugAdrlkD4SwjsakUvPGGf7t166A8yzCe68Kbb+avPhEpWQpnJeroIRGy7aBLuZbpsfz/WY+q998dePrwaN77O2WY/30eXe+/7tCaCNnOVagMwbE52s2uDpPMclJF1MAxOdr118gy/zdflf9TLTmMORzKsuwNjlbC6LkF6PDQQ/ceNQOorIRjj/VvN3u2dyJAd9EoHHNM/uoTkZKlcFairpgWIxbuOg1DLAxfmlxJbTT/f9brZ9dkDYPDooazx1bkvb8LxpeT7TCviIFrZ1X5tptWFeZDI8vonE/DQHXEcOFE/zqHloX43MSKLu0MUBk2fHVaZd8fQA9CoRAXTsh+ENRVB/g/PvF3wAegbiKEy95ZFi6HoTNg2ukF6HDaNPjQh7xjxd7uMOwdc3bhhf7thg6Fz32uaztjvFD31a8WoFARKTUKZyVqelWYZ4+t530jotRFDNNiIa6fXcVVM2M9N+6H0RUhlhxfz/RYCIP3wjlxSITVJw8pSH+hUIg1Jw/l6LowIbygNLMqxCvH1zO0LPfL9veH1fDN6THGV4QYEjGcPbacF4+rZ1gP7X4yu4prZ1UxtTJEfcTwoZFRXji2LudJBPvi5wfX8PVpFVR0lFUThp8dWMUlU/IfBvcHoQic/wwc8VmIjfD+zb8Izn3COzGgIH7/e/jmN2H8eBgyBM4+G158EYYNy93uJz+Ba6+FqVO9MzY/9CF44YXcJxGIyH5DZ2uKiIiIFJjO1hQREREpUQpnIiIiIgGicCYiIiISIApnIiIiIgGicCYiIiISIApnIiIiIgGicCYiIiISIApnIiIiIgGicCaBtqgxzRdea+GCV1p4aEeK3l40eVlLhi+/3sp5L7dw77YkTolebFkGr8YFq1hz9NdYP+0/WX/xnTjxdLFLyq/t2+Gcc2DKFDj1VHjppWJXJFIyNEOABNYPV8a5amWcdhdcvAnBPzyqnDsOrcYY49vu1xsSfOG1NlIuOEB1GI4dEuX+ebVEQv7tRAbKxm/9nVE/+ASGNBHSpKiiKTaL+g1PER06CKbvWr4c5swBx+m6/Ne/hvPOK05NIkWmGQKk5K1POHx/ZZx4RzADaHPgb9uSPLHbf4ShKe3yhdfaSHQEM4BWB55pSPOXramC1y3SEyeeZvhV/0GUOBG813IZbdTF32DTZ24tcnV5ctZZewcz8CZ8F5EeKZxJIP1rRzrrizPuwN+2+YesJ3aniWYZHWtz4E9bknmsUKR/dt25BGP3Di5lxIk9/IciVFQAr7+efXkqBcuWDWwtIiVI4UwCqTIM2fZAhg1Uhf13TVaGDNn21BugOkc7kYESro9h3h4P7sqJVg9wNQUSyvHVUlMzcHWIlCiFMwmkD44sy/r1FTVwzrhy33YnD4sSzfKqrgzDBRMr8legSD8N/chBxCOjcem6sZCiisz5FxWpqjw7/fTsy4cMgUmTBrYWkRKkcCaBVBcNcc/htVSFoabjX0UIfjq7itnVEd920ZDhn/NrqY8YaiOG6o52X5sa48Sh0QF8BCLZmZDBvefvJEIjSVJDkmrSVLD54PMY/6OPFbu8/Lj7bhg9uuuyaBQWLChOPSIlRmdrSqC1ZiwP7kiRci3vHlHG8LLebU8kHcuDO1M0ZyzvGhZlbEW4wJWK9I0TT7P1x4/gbNxB3TknUHfilGKXlH/33AP33w8HHghf/CJE/DesRAa7vpytqXAmIiIiUmC6lIaIiIhIiVI4ExEREQkQhTMRERGRAFE4ExEREQkQhTMRERGRAFE4ExEREQkQhTMRERGRAFE4y7OkY1kTd0g4A3P9OMda1sYdmtLZ5+rz47ouz11DEz4AACAASURBVDakWRPPFKiy/NmedNnU7lCq1+ST/rEWmjdCfGexKwme5OYWmp9ei9vex/dvPA5r1kAyWZjC8sVxYO1aaGrqWztrYf16aGjoc7MBf60lmyHRQNbJgGW/p3CWJ9Zavr8izrBHdnHwUw0Mf2QXl7/ZilvAN94fN7cz+pHdzHmqgVGP7ubsJc20ZXru76qVcaIP7ubYZ5uY+ngjIx7exYrW4IW0tXGHYxY2MmHBbqY/3sDsJxtZ3JgudlkyADY8CzfN8P5dPx5+c4L35bm/yzS2s27GeYTHjaDihDmkYiNY+5+/6rmh48CXvwzDh8PBB3u3114bzGDwxz96Uz/NmQOjRsHZZ0NbW8/t/vUvmDABZs3y2r/vfbBrV4/NBvy1Ft8JT38fHv0feOxyePwKaFxTwA6lFGmGgDy5eW2Cy5e3EXfeWRYLwdenxfjmjFje+3t6d5r3LGrq0l95CN4zPMq98+p82923NcmZS1r2Wl4Vhtb3DM97nf2VcS1THm9gc7vbZQL0mrBh1clDGFGu7YrBqmUz3DwTUq3vLDNhqJsIX1wJZj/+06+bfi5jV91FlMTby1LE2HHl3Yz79nv9G15xBdx4ozdytkcsBjffDOedV8CK++jpp+E97+laZ3m5t+zee/3bvf46zJ/ftV00CnPnwvPP+zYb8Nea68CCr0J7I9DpuzdSAadcC+W1ee5QgkQzBBTBNasSXYISQNyFn6xJFGR33NWr4nv1l3ThoZ1ptib9d3Fetjz7FmibA/dsDc6ujgd3pGlKdw1mABlruX1Te1FqkoGx5DZwug2QWscbcFjzWHFqCoLkxmbGrfpTl2AGUEacyI9/4N/QceCmm7oGF/B+vuqqAlS6D66+eu86k0l46CHYutW/3Q037L2rNp2GZcu8fz4G/LW241VIJ+gSzMALbRufKUCHUqoUzvJkeyp7IGrKWApx+NnaePb+ykKGze3+4Wxb0r+YV1uCs2tzQ7tDtj20CRdWd0+lMqg0rAQny3aCdaF5w8DXExSJ5dtxCWddF4uvz9EwAe0+GzS5Ak8xrF2bfXlZGWze7N9u5UovhHYXjcIG/xfNgL/WEru99Nedm9bBldKFwlmeHFyT/UNzWixEJGTy3t8JQyNEstxtxlpmVmWvBWBurf+6D40sz0dpeTG/LoLJ8viqw3D80LKBL0gGzKSTIFq193Lrwtj5A19PUNQcNRGbJZy5hGgce6x/w6oqGDMm+7rDD89TdXlywgkQiey9PJOBmTP9251yClRU7L28vR0OO8y32YC/1uqnkPWDLVwOQ2cUoEMpVQpnefLTA6uJdXs2YyG48cDqgvT39ekxqsOmyx8wFoZvTItRlS21dfh/B1Vn/aPPqQ5zWF2WD8UimVcf5aShUSo7FVsegvEVYT46SuFsMDvok1A9GsKd/szRGEw/A0bOKV5dxRauLmPLJ64hxTvHsLqEyBCj+hdX+jc0xtvtF4t1XRaLwXXXFbDifvj616G6GkKd3vixGHzjG17I9PP5z0NdXddgV1UFn/mMfzClCK+1+ikwdCaEOnUYikDFUBh9RAE6lFKlEwLy6PnGNN9+K86rLRlmVYX57gFVnDg0WrD+Vscdvv1WnMd2pRlVbrh8aoyzx/Y8+rWkKc05L7WwvM0lGoJ/G13Gbw+pJhQKVlZPuZYb1iT45YZ2Ui6cPbacb0yrpC4arDol/xK74cmr4PU/Q6QS5n0OjrrY+x7b32284l7KfnYVscQmGsYcS9UvvsfQD8zuueGCBXDllbBihXeg/Pe+B0cEMBCsXg3f/jY89ph3tubll3tnbPZk82bvMf3jH1BfD5dcAhdckH2kqpMBf625GVj9EKx/wtvFOXY+TP+glwplUOvLCQEKZyIiIiIFprM1RUREREqUwpmIiIhIgCiciYiIiASIwpmIiIhIgCiciYiIiASIwpmIiIhIgCiciYiIiASIwpmIiIhIgCiclbC2jOWWtQk+sKiJzy9r4bUCT1zuWMufNif5yIvNfPqlFp7cne5VO9d1+dbyNsY/uouJC3bxvRVtuK7/5OwiksNbb3lXv//AB+D666GpqdgVZdX4UgNLZv2IVWXv5+WRX2bjH1YXtL/MjmZ2nXgBifLRtNQdQMOVtxe0P5FC0gwBJaop7TLvmUY2J13iDoTx5p78v8Nq+Mjo/E9g7ljL+xc183RDmjYHDFAZhsumVvKdGf5z3rmuy4wnGlmd6BrGZleFeP2koXmvU2RQe+QROPNMSKW8ycArK2HYMFiyBEaMKHZ1b9v28BZi7z6cCpqIksAhikMZK7/4Tw688cS895fZ2ogdO46IjWOAPd9qu+b/O8Nf+H3e+xPpD80QsB/46ZoEG9u9YAbgAHEXPvNqK2k3/4H7/u0pnukIZuB9+MUduGZVgo0Jx7fdbzYl9wpmAG+0udy9JZn3OkUGLWvh3HMhHveCGUAiAdu2wQ9+UNTSutt51reIsZMoCQDCpCmjjTE/Ow/Xyf/nU9OZX3g7mIG38WiAYYv+QPKNjXnvT6TQFM5K1F+2pmjPsmcw41pea/UPS/1177YU2e42YmDBLv/dm7/flPJd9+sN7fkoTWT/sHYtNDTsvTydhr/9bcDLyWVS8/2E2fswixo2seuJbXnvr2rJA/hNb9567e/y3p9IoSmclai6aPaPooyF2ojfx1T/DYkawlmWG0zO/vzqBKjPsU5EuqmuBsdnw6u2dmBr6UGSap81lrKRlXnvz4nG8BuPM6OCs7tXpLcUzkrUFydXUtUtLYUNzKoOMzWWLUbtm/PHV1CW5dUSNnDGiDLfdt+ZHvNdd+UM/3Ui0s2IEXDssRCJdF0ei8EXv1icmnysO/gLpOj6/s4QZV3ZadQdVJf3/to/85W9llnAEmbI98/Pe38ihaZwVqI+PrqMz06ooDwEtRGoDsPUyhB/O6IwW9AH1kS4ZU4VlSFvZK42YhgaNTwwv5aKsP8I2GF1Eb45be8t5R8cEGNGdSRLCxHxdeedMHu2N4pWWwsVFfCpT8FnPlPsyro45PkvsKr6LNJU0E4tKarYYQ6m/onC7GIcdtMl7D7gvR2BbM+/EM03/RVTps8ZKT06W7PEbW53eL4xw+jyEEfXRzCmsLsKm9MuT+xOUxk2nDQ0SjTUu/52plxuWZvAGPjipErqsw3DiUjPrIXFi2HjRjjiCJg4sdgV+dr057Xs/P0SKo+YxPQrDieUY0MuH+IvrCB+7a8xY0cz5LqLCFX6j+qLDLS+nK2pcCYiIiJSYLqUhoiIiEiJUjgTERERCRCFMxEREZEAUTgTERERCRCFMxEREZEA6XU4M8Zca4x51BizwRiTMMbsNsYsNcZ8xxgzrC+dGmPGG2N+bYzZbIxJGmPWGmNuMMYM6ftDEBERERk8+jJy9iWgCngYuBH4PZABvgu8YoyZ0Js7McZMA14EzgNeAH4KrAYuAZ7ta9ATERERGUz6Es5qrbVHW2vPt9Z+zVp7sbV2PvBDYCzw9V7ez/8CI4EvWms/3HFfp+KFtJnAVX15AIWyO+XycnOGlkyW2cVzaE577RrTfWtXKjKuy31bkzy5y39C82ystSxvzbCizaGv19Zb1ebwRmsGt0SvydeTBCm20kwyy0TRhRCPO7y2vJmdffwbZnDYRjMtDMyE9W4Glt8Ha5/sWztrYedy2LXC+39frFkAy//h9T0ovfgiXHcdvPVWn5olm2Hry9De2Lfu0jvj7LzrZeLLd/atYTIJr7wCW7b0rd1AsxZat0Dr1r6/2Nq2Q8tmsIPzu4JUKzSvh0yib+3SCa9dOl6YukrEPl+E1hhzKPAS8Ii19vQefncasBJYC0yz9p1XpTGmBtgCGGCktbYt130V6iK0adfy2Vdb+cOWJOXGkLaWSydXctXMWM6r77vWctmbbdyyrp2ykCHpWs4dV87Nc6qJ9PIq+kH3o1VxvrY8zp4/WkUI7p9Xy6nDc1+Fe3Fjmo8vbWF7ygULYypC/OXwWg6tzT2tyvLWDB9d0sKauEPIQH0kxJ1zazhhaDRPj6i4HFz+wassYzNhQri4HMUUTmUmhvy/Zlxr+f0Tq1gzfyU4BspcapaM4rNzDyVWmXs+1hdZx8O8CVgcLJMZxseYSwWF+Vs88yN49GvvfG+FK+BT98OUU3O327wY7vo4xLd7P1ePgX/7C4w+NHe7FQ/Anz4MTkdeNSE440Y48gv79jgCo6kJJkyAlpZ3lo0dC+vXQ9j/b29dePgyWHQLhMsgk4TDzoX33QyhHG9f61rWnXE1Yx++CkuEMEm2TDiT0S/9lujQHiY+v/VW+ErHXJmpFJx8Mvzxj1Bf3+uHOyAa18CLt0Cq4zktr4d5/w21PczY0LoFFt8M8Z1gDERjMPdzMOyAwtc8ENwMvPI72Pyc9yJxHZjybpj1Me/x+rEuvHEXrF0AobB3P+OPh4PO8X4eBAb6IrQf7Lh9pRe/e0rH7UOdgxmAtbYFeAaIAUfnoa5+uezNNv64JUnShWbHknDhxnUJ/ndd7tGC69ck+Pn6dtpdaM5Yki7csSnJt98aHOn/2YY0l3UKZgDtLpz+QjMp13/LrzHt8q4XmlmbcIk7EHdhVdzl5OeaaMv4bxikXMuJzzXxRqtDwoU2BzYlXd67qIkt7YNjS/MR3uA1NuPgkiJDBpcXWMti1hWkvwcXbvaCWZUDtRmocGmZu43bFr+as91qdvIQb5AiQwoHB5e17ORulhSkzg3PwiOXdR1QcNrhjtMhk2Owr70RfvcuaFrrbXSn49CwCn53MqRybOqlWuEP738nmIHX9wMXw5aX9vXRBMSMGV2DGcDmzTB/fs5mz14Pi38OmXZv9MxJwit3wGPfzt3dhovvZOzDP6SMOOU0EyHJ6A33sfnIi3I3fPRR+NKXvFpbWrwRtMceg7PP7sWDHEDpODx3HSR2eS8cJ+VtESy81kuwftwMLLwGWjeDm/Ke0PYGeOH6vg9LBtUbd8HmF7zHmmkHNw1rH4Z1C3K3W/0vWPeY9/uZdq/9xoWw/J6BqTtg+hzOjDFfMcZ81xjzU2PMU8D38YLZNb1oPrPj1m9MfUXHbVE2IRxruXV9O4lu3/1xB360JvfQ7I9XJ4g73dq5cPO69j7vxguiy9/M/u3mAj9a7R9c/7QlSSbL489Yy91b/T/E/rk9RcKxdG+ZsfC7TQOzW62QXCxL2ECGri+2NA4LWV2QPpeOWOUFs84qXRrmb6G1zX8/3kJWkaZrOwfLenbTXIBdnI9cnn25dWHhj/zbLfsT2CwPw83A63f7t3vyKtjrhdbh0a/5tysZiQTs2JF93dKlOZsu/PHee5fScXjh5tx78apuu4Yyun5mRGln3Ko/ktqeIylfdx3Eu3WYSsGTT8KmTTlrHVCbn8++O9I6sGWRf7vtr3TdCujcbuMz+auvWKwL65/wgmdnTgpWPZC77eoH935u3BSsfbTvu4wHgdz7lbL7CjCq088PAudaa33e/V3Uddw2+azfszzr+LUx5kLgQoCJBZjst92BlM9rYGcq92hNQzp7w1bH4liIlPiezc05RqvWdE+lnWxpd/cKreA911uS/ve5JemSbWAt6cKGhH9/pSKDs1cw2yNO344F6y1niE8YttDcnKG6KvvHgV8ACxGijSS1VOSrRMA7DMdP4xr/da1bsh+mkm731vne51r/dc0BygP9tnVrv5u2N2Rfnmr18oTx+QapSG3LutwSIrm+kbKRVdkbbtyYfXlZGWzbBuPG9VDxAGlvyh6ynDQk/b7e8EbHbJbPLzcDid35q69YnLT/AZup1txtUz57mZx2L/SZwbFrs7f6PHJmrR1trTXAaOCjwFRgqTHm8HwXl6XvW62186y180aMGJH3+4+FYUJF9qfkqPrcx9YcXpf9U2pWVXhQHHN22nD/x/+x0f7HnB07JEp1lvdUeRiOG+J/n8cNiWY96qo6DKcMy32MWymIEqbOJ9SMy75tss+qVw6FbLm2NcLoUeW+7aYynFCWv4bFMpzqPFbomXKa/7rZH/NfN+FYKMtSTqQcJhzn3+7AHPc5/d3+60pGrg3ZSO7t8zE+n+rDZ+U+5mz3mONxs3y9pEwN1YeN8W942mkQzfK54Dgwe3bOWgfU0OkQzvKeCUdhyIwc7WZAtk+2cDkMm5W38oomXAaVPhdcqJ+au23dpOzLq8cMmmPO+qLfx5xZa7dZa+8B3g0MA27vRbM9mxR1Puv3LC/KzndjDLfMqSYWeuftEwKqwvDjWT5beh1uOLCKWPidJ9QAsRDcPCd3u1Jx3awqyrN8pkytDPHekf5f7KcNjzK3NkJlp1daLOSFr+OH+H+6H1Ib4f0jy4h1ek9WhmBGVZgzR5V+ODMY3stBRDq9BQ1eaDudwnwJfXDUTGiLQNr72bpAW5gjV8whlGMD4jimUU6kS0CLEuZUZhIl/x+ap1+X/XtvyFSY8V7/dlNPg9FzIdLpePNoDCYeBxOP92934FlQM37v5ZFKOPn7va87sMJhOOec7Ou+972cTd9zg/ccmk4fbNGYd0JALtW/+iFpqnA6Xh8WSBFj9yU3YSI5vnYuvxxqa7sGtFgMrr4aKns4kWAgDT/QCxOhTp9FoTIYMr0jgPmonQCjDvFCzNvtolA1ynvxljpjOg7g7/wZbbw39IE9HDc455Mdz8uezxnj3c9BPq/dQW6fz9YEMMYsBQ4DRlhrfc+ZNsZcAPwSuNVa+9ks6/+FF/ZOs9Y+mqvPQp2tCfB8Y5ofrozzRqvD/Poo35xeyezqnvcAv9qc4Qcr4yxtzjCnJsI3p8c4wmdErRRtbnc456UWnmnIEDFw9phybj24ikgod8ZPOpZb1iX47aYkIeD88eVcNKmSaA8jio61/Gp9O7duaCfpwqfGlnPJlEpi4dIfidxjIw08zUp20spY6jmB6YygpmD9rVnXxj/Wr6Rp/G7Kd8Y4sWw6Rx3a86UFm2nnGVayip3UUM6xTGMGIwtWZ/NmuOcc2PCMt+vsoLPhg7fmHq0B71jsRbfAS7/1AsXc82HeRd6ARs52Kbj3PHjzHi+0TjoRPvYHiA3P20Mqvm98A37yE+8g+1gMfvxjuKiHA/SBba/CUz+ALUth5Bw44Zsw9oieu2tcsIqmz15F7bqniddOJfydKxh98Yk9N9y0Ca65Bh56yDuj9LLL4L05UnmxOGnvIPcNT3uhZPwJMPmUnl+ke47LWveEtwtw3NEw9fTsWySlqmEVrPyHdzxB3RSY8UGoGdtzu+YNsOLv3qU0asbB9A9C/eSClztQ+nK2Zr7C2Ta8a5cNtdb6HKVQGpfSEBEREcm3vF9KwxhzgDFmr12RxpiQMeYqvGC2cE8wM8ZEjTGzOsLY26y1q4CHgMnAf3e7uyvxZiC4o6dgJiIiIjJY9Xaf2/uAq40xTwNrgF14Z2yehHdCwFbgvzr9/jjgDWAdXhDr7PPAQuBnxph3dfzeUXjXQHsL+EZ/HoiIiIjIYNDbcPYIMB04HpiLd6mLNrwwdQfwM2ttr84DttauMsbMA74HnIEX/Lbgzdd5Za7doiIiIiKDXa/CmbV2GdDriUystWvJer7w2+s34E18LiIiIiKd5GP6JhERERHJE4UzERERkQBROBMREREJEIUzERERkQAZPJevD4D1CYfr1yRY1Jjh0NowX54SY3rV/jcnmARXK0meZw3r2M0wqjiGqYzsxYwECdIsZi0r2UEtFRzN1ILNAbovXAeW/dGbISAUgsPOhzkf7zT9kA9rYfm98OKtkGmHQ86BQz7d88wCAKse9mYlSDR4fc39DER7M9PQwoVw442weTN84APwuc9Bnd/Mdu/Y+hI8ez00rIYpp8KRF0NV/qcaflvTeq+/TYtg9KFwzJe9qSWlCHa8BmsfhXQbjJkPE0/sOhWUDBp5mSGgGII2Q8CylgzHLmyk3YW0hYiB8hAsOKqOI3uYNF1kIDQS55c8TQoHBxeDIYLh48xjOv7f7nFS3MpTxEmRwZvUI0qY93MQh5BlUsoisRbu+qgXltIdl7GOVsHMD3lTMeVy/+fh5du7tht3FHz6odxzLj/5A3j6mnfaRWIw/AD4zLMQyT6vvedXv4JLLoFEwiu8shJGj4YlS6DeP/Qu/zv85RNegLSuN+NPRR18dmnvZsfpq+3L4LZjvf7ctDczUbgc/nMBjDsy//1JDm/dB6vuByfl/Rwqg+rRcNw3e7cVIUWX9xkCpGeXvN5Ki+MFM4CMhTYHLlrWWtzCRDo8xlu0k8bpCFgWSxqXf/AKFv+NtGdZTRvJt4MZQBqHB3jt7fsKgvVPdw1m4P1/+b2wOcd23M7l3khb93abX4CVD/q3a9sOT13VtV0mDrtWwCu/z1FoIgGXXgrxuBfM9izbsgVuusm3mXXh7xdAOt4xaT3gJCGxG57IPX95vz1wCaRavGAG3lSQ6Ta4v+cpOSWfks3eXJV7ghmAm4K2rbDp2eLVJQWjcJYnzzRksi5f2uzglOjopAwuq9mRNYLFSdFK0rfdW2zDydLSYtlOSx4r3DdrHvWCS3dOClY/6t9u7WPZl6daYeUD/u02LMy+Rynd5g1y+HrpJQhnGY5rb4f7/Bs2rvVq6s7NwIp/5uhvH2x4JvvyLUu9XcgyQBpWZh/CdVKwbenA1yMFp3CWJ9Xh7NfcrQjpSZZgqCD7rg8LlOU4/DRG9mNaXCyVPvdZDJXDsu9KDJdDbFjudqEsDz9UBlWjcrQb+s7AV2cmlLsdQ4dCJvvGHCP8dy+X1/kHosocj29flFVnXx6p6Pk4PsmjaBXZB7cNlNUOdDUyAPT2ypPPT6qgstuzWRGCz0yowBjfyRJEBszRTCFK163vMIYZjKA8Rzg7mql7tQthGE0t9cQKUmt/HPSJ7IHBGDjwLP92B3wg+6BEKAKH/od/u4nHQ0U9e82FEqmAebl2+82cCQccsPfoWSzm7e70ERvmnQAQ6paHo1XeQfqFMP/zEOl2ckOkwjvpQR9rA2joDIhmea+FozD51IGvRwpO4SxPvjU9xkdGl1MRgrqIoSIEZ4wo40ezqopdmggAhzORuUwgTIhyIkQIMZ4hfIhDc7abySiOYxqRjnZRwoykhn/jiAGqvHeqRsAn7oWKIVBeC2U13ojSv/+zI0T5iFbCpx/2jq0uq/HaltfCWXdC/ST/dibktauf7I0wldd6Qem9N8OYuT0U+/e/w4EHQlWVd4ZmZSV897vw7nfnbPbR/4Nx873v6fI6LyjNv8g7u7QQTvwWzP6I18+e/qadAe/+UWH6Ex8mBEd/BSqHe0PBkUrv9qBzoC7Hi1RKls7WzLONCYc32xxmVIWZVKnLaEjwtJFkGy3UUckwer/xkCDNFpqoprxXl98oFicNm54HDIw/Kvsuy2ysC5te8A7jGXcURMp72c7CliXeMdvjj8o+wOHbcNky2LEDjjiiV5fR2GPncmje6F3aIja81836rXkj7HzTG8DJFVilwKyFpnWQScCQqV5Ak5LRl7M1Fc5ERERECkyX0hAREREpUQpnIiIiIgGicCYiIiISIApnIiIiIgGicCYiIiISIApnIiIiIgGicCYiIiISIApnIvuZxG5Y/zQ0rutbu+aWDIte2c3qdW197DABCxfC66/3rd0Ac63l1aUtLHm+mUzG7XU7a2H7MtjwLGTa+9bnrrdg/TOQ6uNTypNPws9/Duv69kds3uT97dt29LG/AZZs8Z6X3SuLXckg0roVdq+ATLLYleSWbIbdb0F7Q7ErKapeXjtbREqdtfDI5fD8Td7V750kTDoJPv5nKO/hgv93Pr6KFUe+BZNCEHWJvlrLBWPmMWJ4D1co/+1v4eKLIRTyJvueOhX+8Q+YFKzLzL/2cit/+VAYu6sSQvD3SIZT/hDnxDNyzPsE7F4Fd34AmjZ483NaCx/4BRz877n7a90Kd34QdrzuzWDgZuBd18BRF/dQ6Pr1cNhh0NDpi+uEE+Dxx73n2EemHf7yKVj5T++i8pl2mHs+vO/m4E1gvvDH8Ni3vWkjnbQ3C8In7vOm55J+aG+CRTdAy+aOF6kDs86CKacXu7KuXAdevR02LfQmkHXTMOpwmPtfvZ/mYxAJ2NtSRApl6a9h0f+C0w7JJu8Leu3j8PcLcrd7YtF2VsxfATEX6jIQc0nPbOK2jUtyN1y0CP77v6G1FZqbIR73Rs/e8x4vxQREe7vD3aeWYddXQFsEWiLQUMZjH6th4wb/oTDrwu3v8ka/0m3eBn+qBe67ALa9krvPOz8IW16CdNxrl47Do1+DNQt6KPbII7sGM4CnnoJLLsnZ7MFLvWCW6fjbO0l4+Xfw3E976G+ArfgnPP5db3aiZLN3u/lFuOtjxa6shC26AZrWg5vynlAnBW/eDTsDNpK98n7Y/Jy3pZJJeLfblsIbfy52ZUWhcCayn3j2J16I6MxJwpv3QqrVv93z4dVQ5XRdWGZJzWxkw6aEf8ObbvJ2aXbmurBpE7z4Yt+KL6Cn7m+GtAFM1xUOLLjd/4nZsNDbRWy77QF1Ul4I9rNrBWx/DWym6/J0HJ69Pkehq1bBtm3Z1912m28zN+MFse67XNNxeO6GHP0VQbbXqJuGzYu8fCF91LrVGzEjy4t09b+KUpKvtY94dXXmpmH944HamBsoCmci+4nEruzLjfFGKfyka3yOUUmHaGxJZV8HsHlz9g/VcBh27vRvN8Cad7iQMXuvSIb5/+3deZxcVZ338c+vqqv3bJ2dLHToBJKQgEhLAkECRNlBFOPK4ggqo4I4jOIgw4Azvh4dHYHHFdxAmWF8FEWUXQkgS4hhh0ACJJ0Qsu/pdHqpqvP8catD0l1VXdV9q+6t6u/79apXJefWPed3T52q/tXdzp71acpT9mz2+q4nl4Dd6zO317bZO2SXTuuGLIFmO7+sM/P7EO/wDg+m074jS3sBaM2Qe0YroS3D+JUsOnd7hzLTyfahD0JXhh96iU5AyZmIlKkpja+1CAAAIABJREFUC9KfX1TTAPXjM6835u0x0JE+SZk2pT7zimefDTU1vcs7OrzDcyExa341vfaaAdTHOeyUDH/YgEnHQTxNThSrhWlnZG5v3Lu8vVk9Ratg2plZAj3++PTZIEBTU8bVKuugYWqaBQaT35ulvQBMO8NLxHpyDkbPLH48JW/YZO/XQk+RChhzRPHjyWZEhjE8dFL4TowsgsG3xSKD1Mn/AVVD3/njZxEvkTjr5sx/8wHOnXUIbK+Edu9FLgnsiXLkCzOprsqcvHDxxTBx4oEJWl0dXHMNNDQMfIN8ctiMOho+tgPq9suYauNUvquNE84clnG9+rFw3JUQq3unrKIGhjfCkRdmbi9WC+/7T+9533rVUDcG5mY7dayyEr785d7lZvCrX2VZ0btIIVYLlnq7IjGorIdTvpt1taI77itQM9JLVLvFauG0G72LWCRP0SqYvvDAjDcSg8qh4bsg4PBPpN74VFpiES/uWRcEGlZQzJXosdzm5ma3dOnSoMMQKSm73vbO61n9mLc3Zd5XYfy7+15vy9ZO/vTSKtaP2Uz1rmqOrzmEY47MIcHatcu75cOdd8KoUXD55XDaaQPfEJ8lneOB32znxVuiJDuMqZ/s4uyLh2dPPlNW/BmW/AD2bofDF0LzpV7i05dVi7xzvlrXe3vM5lzm7cXs0y9/CddeC9u2weGHwy23eFdw9mHTy/Dkd7zz3SbMgXlf8RLJsGnbAotvgjfuh2ETYe4/wcEh28NXcra8Cqse9K7cHHsENL4vt0FabHs2wZv3wc5VMGQSNJ0OQw4KOirfmNkzzrnmnF6r5ExERESksPJJznRYU0RERCRElJyJiIiIhIiSMxEREZEQUXImIiIiEiJKzkRERERCRMmZiIiISIgoORMREREJESVnIiIiIiFSEXQAImHyBptZzEpa6WAqYziOQ6glzWR/JWoHbTzBm7zFdkZQyzyamMiIgrW3ZnUb/3NRFx1P10N1kkmf38mnvzmqYO0luuDZn8Lzt3qzGh11MRz1aW8qwbB54wFvtobWjTDtdDjun6E2l6554gn41re8idDnz4errvKmyRKRsqEZAkRSFrOSRaygC2+i4ChGDZVcygllkaBtYw8/5XG6SJDE+9zHiHIuRzKDLDOf99O6de389OBKiBvvTCzuqJq/i689knnOyv5yDn59Cqx9ErravLJYLTSeDB+/O/v8ocW2+AZ4+Jp34oxWQe1IuPSFPhK0O+6ASy6Btu4NjEF9PTz3HBx8cMHjFpH+0wwBInnqJH5AYgaQwLGXTp5mVYCR+edhltNJfF9iBtBFgvt4BYf/P9L++3N7eyRmAEbHo0N5fXmr7+21LIK3F7+T8ID375ZFsHax7831W2frgYkZQKID2rZ6c0pmlEjAZZe9k5gBdHV585def33B4hWR4lNyJgJsZBcReu9aSeB4g00BROS/1WxNm4K100UrHb631/ZEHaTpU4Anf9Pue3stj3qJT0/xDlj9qO/N9dvGF9MfZk10wBv3ZlmxpQXa0/RbIgEPPeRXeCISAkrORIA6qkiQTLtsCNVFjqYwMh2adUBVAU4/jYyIp2rvbVST/1899eOgorZ3eUUV1I31vbl+qxvjnRuXzpAJWVZsaIB4PP2ysSHaQBEZMCVnIkADdYxlaK+9ZzGizOWQgKLy17EcQozoAWVRIsxgHJUFSM6Ouj7d3jEHlUlO/fhw39ub9VGIRHuXRypg5od9b67fGqbCuCMhEjuwPFYLx16ZZcURI+CMM6Cq6sDyujrvogARKRtKzkRSPkYzExhOBRGqqKCSKKcwg0ZGBh2aL45kInOZsm/7KojQxGjOYnZB2jvr/AZG/eNWvL1nqUdNgg883kpFxP+vnpoGOP8BGHIQVNZDrA6GToIL/wJVQ3xvbkA+9keY8B6oqIGqoV68p34PGuf3seJtt8HJJ0N1NQwdCjU18C//AgsXFiVuESkOXa0p0sMO2mijkzEMoYI0u2JKXAddbGEPQ6kuyiHb1tY4i36/g5ETKzjuZP/3mPXkkrDpZcBgzKxwXaXZ044WaNvixVmRz1vx9tuwbh3MmOFdrSkioZfP1ZpKzkREREQKTLfSEBERESlRSs5EREREQkTJmYiIiEiIKDkTERERCRElZyIiIiIhouRMREREJESUnImIiIiEiP9ztohIUWynjS200kAdI6kreHt76GAdO6mninEMxTJMat5TO12sZTvVxJjA8JzXK7ZkHNY8AYlOmHw8xGqCjkhkEGrbDLvXeRPi1o8LOprAKDkTKTEJkvye53idTUSJkCDJwYzkIxzda+5MPzgci1jOYlYRJUISx3BqOJ85fc4w8DSr+CuvESWCw1FDJedzDCMJ113t1y6GO86GeIc3o4BLwgduhZnnBR2ZyCCRjMOzN8OmF7wJcZNxGDkdmr8A0aq+1y8zOqwpUmIeZQWvs4k4STqIEyfJarbyIMsK0t5yNvI0Lfva6yLBFlr5Ddln6FjDNh5m+b71Okmwk73czhIc4ZmZpKsNbj/Nm0apczd07ILOVvjDBbB9VdDRiQwSK+6CTS9Csgvie73nra/BK78JOrJAKDkTKTHPsIY4yQPK4iR5gbUFSXoWs4ouEgeUOWATu9lBW8b1/k5Lr/UA9tLJ2+zwO8x+W/4nb09ZTy4BL9xW/HhEBqXVj0Cy88CyZBesfRxKdJrJgVByJlJiOtMkPOAlaIX4CttLZ9ryCMZeujKu15ZhmWG0Z1mv2Np3eEdQekp0envTRKQIEh3py5NxCNGe9mJRciZSYg6mIW35QQwjUoCT7aczjmiarwrDGMOQjOvNYGzac+ASJJnICF9jHIhDFpD2uz9WD4eeVfRwRAanhsPSlw9vBBt8qcrg22KREncqM6migmgqEYtgVBLlDGYXpL25HEI9VVSkvi4MiBHhTGanTdq6HckkGqg9IEGLEWUB06kmVpBY+6NhKhz9OYjtd8FrrA4mz4OmU4KLS2RQOfwTUFHjXQwAYFHvQoBZFwYbV0DMleix3ObmZrd0afYTkkXK1S7aWUIL69jBOIZyDI0Mp7Zg7XXQxbO8xRtsYig1HEMj4xnW53pdJHiBtbzKBuqopJmDmZxhz1+QnIM37oNnfwbxdpj9SZj10Xf+TohIEezdDi1/gR2rYOgkmPJ+qB0VdFS+MbNnnHPNOb1WyZmIiIhIYeWTnOmwpoiIiEiIKDkTERERCRElZyIiIiIhouRMREREJESUnImIiIiEiJIzERERkRDJKTkzs5FmdomZ/cHM3jCzvWa208weN7OLzXK/fa+ZtZiZy/DY0P9NERERESl9ud5icSHwY2A9sAhYA4wFPgT8DDjdzBa63G+athO4MU15a47ri4iIiJSlXJOzFcA5wD3OuWR3oZldDSwBzsNL1O7Msb4dzrnr8ohTSlgXCRazkhd5GwPexSSOoZGKNPMu+sHheIG1PM0qOklwGGM5nqnUUlmQ9oKwnp08ygo2sptR1DOfaTnNV7mFVh5lBWvZwXBqeC/TOIS+78C9cw08+g1Y9VeoHwfzroLp5/qxJYPXg1fC0pu9+Z4bpsEHfwUH5XR7yhKxfDlcfz089RQ0NsI118CCBUFHJVISBjxDQCpB+ybwA+fcZTm8vgXAOdc4kHY1Q0BpcDh+yZNsYBdxvLy+gggTGM6FzMUKMFH3PbzEi7xNFwkAohj1VHEp86nK+fdIeL3FNm5nyb7tA69PP0ozTYzOuN5mdvNznqCLxL55vmNEOYvZzGZCxvV2rYUfHwkdu8DFU+vVwonfgOOu9GOLBp/bFkDLwz0KDS59HsYeEUhI/lq2DObMgbY2SKZ+z9fWwi23wCc/GWxsIgEp9gwBXanneB7rVJnZ+WZ2tZl9ycxOMrPC7EaRQL3JZjaxe19iBhAnyTp2spptvre3k728wNoDEpcEjj108jxv+d5eEB5g2QHbB16f3s8rWdd7mOV07peYgbdX8wGWkSTzj7THvw2d+yVmAF1t8Mi13rPkZ9faNIkZgIO7Lyl6OIXx9a/Dnj3vJGbgJWpXXAGJROb1RAQYYHJmZhVA95Tx9+ex6jjg13h73G4EHgZeN7P5A4lHwmct2+mk95dxnARr2e57e+vZSSTNsI6TZCVbfG8vCBvZlbZ8K3tI7pcE9/RWhv7uJE4rHRnXW/UwJNP89IpUwJbXsscqva24J/OyTS8XL46CevJJbzb5nvbsgQ267kukLwPdc/YtYBZwr3PugRzX+SWwAC9BqwNmAzcDjcB9ZnZkphXN7LNmttTMlm7evHlAgUtxDKWGWJpzy2JEGUq17+3VU4VLsxcogjGCWt/bC0JNhnPnqqjIeph4CFVZ6oxlXDZ8cvryRKd3/pnkZ8zhmZfV9H3aYGkYPz59uXMwolw2UqRw+p2cmdnlwJXAa8AFua7nnLveOfewc26jc67NOfeyc+5S4HtADXBdlnVvcc41O+eaR4/OfG6NhMdMxhNJkzBEiTCDDF/gAzCB4QyjpleLUSI0c7Dv7QXhOA7plfDGiDCHKVmTs+OZ2mu9CiLMZkLaBLrbvKu8c8z2F62CxpNgyEH5xz/YTT4eqoenXzb/34obS8FcfbV3jtn+amq88816lotIL/1Kzszsi8BNwDLgJOecHycP/ST1fIIPdUlIVBPjIubSQB0VRKggwijquIhjsyYE/WUYFzCHiYyggggxotRTxULezSjqfW8vCHOYwhwaqSBCJVEqiHAUkzmBaVnXO5yDOJFpVBKlkihRIsxkPKeTZVcO0HginPEjL6GorPcSs6mnwof/18eNGmQ+9zzU7n+RrMF7vghHfzawkPz1kY/Av/871Nd7j6oqWLgQfvjDoCMTKQl5X61pZlcANwAvAwucc5t8CcRsGLAD6HDO9Xm8S1drlhaHYyd7ARhepMOLrbTTQYIGagtyVWjQOomzi3aGUJ3XVahxEuxgL/VUUZ3lcGZPiS7YvtJLKmpH9idi6Wnzq95tShrnQ4X/R/mD194OLS0wbhwMz7C7UGSQyOdqzbzuK2BmV+GdZ/Y88H7nnJ9nWM9NPa/0sU4JCcOKlpR1q6e6TPaVpVdJRb/2BlYQ7dd60RiMOizv1SSL0TO8R9mqrobp04OOQqTk5DPt0r/iJWbP4O0xy5iYmVnMzKabWVOP8hlmVpfm9Y3AD1L/vT3XmERERETKTU57zszsIuAbQAL4G3C5Wa/DRC3OuVtT/54AvAqsxrsKs9tHgSvN7LHUst1AE3AmUA3cC3y3H9shIiIiUhZyPaw5JfUcBa7I8JpHgVv7qGcRcBhwFDAP71YaO4DH8e579us85ucUERERKTs5JWepeTCvy7VS51wL9D4D2zn3KF4SJyIiIiJp+DF9k4iIiIj4RMmZiIiISIgoORMREREJkbzucybSXx3EWcUWDJjCKCo19AZsGetZzTYmMpzZTAg6HBER8Yn+QkrBLWM9d/F8ao5Nw+E4j6M4lLFBh1aS2ujkhzzCXroA+DtwDy/xeU4syGTyIiJSXDqsKQW1i3bu4nniJOkkQSdxukhwJ8+yh46gwytJt/P0vsSsWycJbuOpgCISERE/KTmTgnqFdWS6cd2rbChqLOViA7vSlm+njSTJIkcjIiJ+U3ImBdVFIm3CkMDRSTyAiMqbUjMRkdKn5EwKaiqjqSDaqzyCMZUxAURU+mqpTFteSZQKfaRFREqevsmloA5iOLM4iNh+CVqMKEcxiTEMCTCy0vVh3p22/FzeVeRIRESkEHS1phTcWcxmJuN5ibcxYDYTmcLIoMMqWY2M5AvM535eYSO7GUU9pzKTsQwNOjQREfGBkjMpOMNoYjRNjA46lLIxkno+yZygwxARkQLQYU0RERGREFFyJiIiIhIiSs5EREREQkTJmYiIiEiIKDkTERERCRElZyIiIiIhouRMREREJESUnImIiIiEiG5CGwLP7Yxz9fI9LN0ZZ1JNhGun1nLuuKqgwwpcnARPspJnWUMSxwzGcyKHUkMs6NACt4ZtLGI5m2mlgVpO5DAOYVTQYUmOnIPnfgFPfRfatsKUk+Hkb0JDU9CRiUgYmHMu6Bj6pbm52S1dujToMAbsuZ1xjl+8g7bEO2W1UbhhRh2fnVwTXGABczhuZwlvsY04SQCiGMOo4VJOSDuZ+mCxii3cwd/39QtABRE+xFFMZ1yAkUmuHvoq/P2H0NXm/d8iUDUU/vElGDox2NhEpDDM7BnnXHMur9VhzYBds2IPexMHlrUl4GvL24gnSzNx9sM6drKW7QckIAkcrXSwjPUBRha8B3n1gH4BiJPkIV4NKCLJx97tsOT77yRmAC4JnXvgye8GF5eIhIeSs4D9fWecdClYe8KxsTOZZsngsI4duDQ900mCt9geQEThsZndacu300aSwTtmSsXmZRBNc9ZCsgtWP1b8eEQkfJScBWxydea3oCE2eN+e4dQSwXqVVxBhJHUBRBQe9aQ/H7GaCixNn0m4DJsMiY40CwxGTit6OCISQoP3r39IXDutltoe70JtBC6ZVE1NdPD+oW1iFDVU9ko2okQ4gsF9Us7xTCXW45y7GFHm0aTkrAQMmwSNJ/XeexargeO+GkxMIhIuSs4Cds7YKm6aWcfImFETgZoIXDypmv+aMbj3DkWI8CmOZRIjiGBEMcYwhIuYSy2VQYcXqKOZzHymUUUFFUSIEeVYpnAcutSvVCz8fzD9g16CVlENQybAh38DBx0ddGQiEga6WjMkEs6xsSNJQyxC9SDeY5ZOO10kcYM+KespQZI2Oqmlkqh+Z5Wkzj3QuRvqxoLpYy9S1vK5WlP3OQuJqBkHVQ/e20NkU637mqUVJcIQqoMOQwagss57iIjsTz+3RUREREJEyZmIiIhIiCg5ExEREQkRJWciIiIiIaLkTERERCRElJyJiIiIhIiSMxEREZEQ0X3ORKSsbNnSyVP3tmIGx51ZT0NDYW9e3NUGK/4MHbvhkPfB8IML2pyIDAJKzkSkbNx92zaeu3QYRIeCwTNx45hfbOP0jzcUpL01T8D/nAHOgUuAS8KxV8LJ/1GQ5kRkkNBhTREpC2tW7/USs/Yo7KmA1gpoj7Lk4mFs3NDue3uJTrjjbOjY5U3B1NUG8XZYfAO0POJ7cyIyiCg5E5Gy8Phv90Ay/bLHfrfH9/ZaHvH2lvXUtRee+7nvzYnIIKLkTETKQrwdSKSZPTwBXe3O//Y6Mixw3l40EZH+UnImImXh6LOroSpNEhaF95xd43t7jfMh0dW7PFYHsz7ue3MiMogoORORsnD4kfWMv3Q71MbBkhBxUBtn8pXbmXZYne/tVQ2Fs2+GihqIxLyyynpoPBGmf9D35kRkEDHn/N/dXwzNzc1u6dKlQYchIiHz7OJdLPnfTsyMOZ+o5F3vGVLQ9raugOdvhfYdcNg50HQKmH72ikgPZvaMc645p9cqORMREREprHySM/2+ExEREQkRJWciIiIiIaLkTERERCRElJyJiIiIhIiSMxEREZEQUXImIiIiEiJKzkRERERCRMmZiIiISIgoORMREREJESVnIiIiIiGi5ExEREQkRJSciYiIiISIkjMRERGREFFyJiIiIhIiSs5EREREQkTJmYiIiEiIKDkTERERCRElZyIiIiIhouRMREREJESUnImIiIiEiJIzERERkRBRciYiIiISIjklZ2Y20swuMbM/mNkbZrbXzHaa2eNmdrGZ5ZXkmdlEM/uFma0zsw4zazGzG81sRP82Q0RERKQ8VOT4uoXAj4H1wCJgDTAW+BDwM+B0M1vonHN9VWRmTcCTwBjgj8BrwDHAl4DTzGyec25rvhsiIiIiUg5yTc5WAOcA9zjnkt2FZnY1sAQ4Dy9RuzOHun6El5hd7pz7/n51fQ/4MvBN4NIc45Iy10oHr7GBBEkOZSwjqA06JBERkYKyHHZ2Za/AS9C+CfzAOXdZH69tAt4AWoCmHoneELw9cwaMcc7tyVZXc3OzW7p06YBil3B7mXXczQsAOLyBcTxTOYFpgcYlIiKSLzN7xjnXnMtr/bggoCv1HM/htSelnh/cPzEDcM7tBp4AaoG5PsQlJayNTu7mBeIkiZMkkXp+nDfYwM6gwxMRESmYASVnZlYBXJj67/05rHJY6nlFhuWvp54PHUhcUvpWsBHDepUnSPIy6wKISEREpDgGuufsW8As4F7n3AM5vH5Y6jnTro/u8uHpFprZZ81sqZkt3bx5c36RSknJdLDdAcmMS0VEREpfv5MzM7scuBLvassLfIsoC+fcLc65Zudc8+jRo4vRpARkGmNwaZKwGFFmMj6AiERERIqjX8mZmX0RuAlYBpzknNuW46rde8aGZVjeXb6jP3FJ+ainilOZSQURIqkDnDEiHM1kJqLb4YmISPnK9VYa+5jZFcANwMvAAufcpjxWX556znROWfdleJnOSZNB5GgOZgqjeIV1JHAcxljGZ8zrRUREykNeyZmZXYV3ntnzwPudc1vybG9R6vkUM4ukuZXGPKANWJxnvVKmGqjjvbp1hoiIDCI5H9Y0s3/FS8yewdtjljExM7OYmU1P3ddsH+fcm8CDQCPwhR6rXQ/UAb/u6x5nIiIiIuUqpz1nZnYR8A0gAfwNuNys120OWpxzt6b+PQF4FViNl4jt7/N40zf9XzNbkHrdHLx7oK0Avp7vRoiIiIiUi1wPa05JPUeBKzK85lHg1r4qcs69aWbNeMneacAZeDMD3ARc75zbnmNMIiIiImUnp+TMOXcdcF2ulTrnWiDNHUTfWf4W8A+51iciIiIyWPgxfZOIiIiI+ETJmYiIiEiIKDkTERERCRElZyIiIiIhouRMREREJESUnImIiIiEiJIzERERkRBRciYiIiISIkrOREREREJEyZmIiIhIiCg5ExEREQkRc84FHUO/mNlmYHXQcRTAKGBL0EGEkPolM/VNeuqX9NQvmalv0lO/ZJZP3xzsnBudywtLNjkrV2a21DnXHHQcYaN+yUx9k576JT31S2bqm/TUL5kVqm90WFNEREQkRJSciYiIiISIkrPwuSXoAEJK/ZKZ+iY99Ut66pfM1DfpqV8yK0jf6JwzERERkRDRnjMRERGREFFyJiIiIhIiSs6KyMzONzOXelySx3ouy2NxIWMuBDNrybI9G/Ksa6KZ/cLM1plZR6ruG81sRKHiLxS/+sXP/g0TM1tgZn8wsw2p93qdmT1gZmfkUUfZjJf9DbRvym3MmNmn+vjedGaWyKO+shg3fvZLuY0ZADM708weNLO1ZrbXzFaa2W/N7Ng86xnweKnIP3zpDzObBPwAaAXq+1HFauDWNOVrBxBWkHYCN6Ypb821AjNrAp4ExgB/BF4DjgG+BJxmZvOcc1t9iLWYBtwvPtcTCmb2n8BX8Mb73Xg3fRwNHA2cCNybQx3lOF586ZuUchozzwPXZ1j2XuBk4L5cKiqzceNbv6SUzZgxs28DXwW2AnfhfY6mAh8AzjOzC51zt+dQjz/jxTmnR4EfgAF/Ad4EvgM44JI81nfAI0Fvh4/90QK0+FDPA6m+uaxH+fdS5T8JelsD6hdf6gnLA/hM6v28FahMszw2GMeLz31TVmOmj219KtVn5wzWceNTv5TNmAHGAQlgAzCmx7KTUv2yspjjRVdrFoGZfQm4Ae9X7MnAvwGfcc79LMf1HfCoc+7EQsVYTGbWAuCcaxxAHU3AG3hfEE3OueR+y4YA6/GS4jHOuT0DCLdo/OgXP+sJAzOrAt4C9gLTnHOd/aynHMeLL32TqqsFymPMZGNms4EXgbfxptLJegivHMdNOvn2S2qdFiiPMWNmc4DFwN3OuQ+kWb4L7+4WQ/qox7fxosOaBWZmM4BvATc55x4zs5P7WdVwM/s0Xoa/E3jGOVdy55vtp8rMzgcmA3vwvhgey+VLIeWk1POD+38AAJxzu83sCeAUYC7wV59iLoaB9ovf9QTt/XiH6G4EkmZ2JjALaAeWOOeeyrGechwvfvVNt3IZM9l8NvX88xy3qxzHTTr59ku3chkzrwOdwDFmNso5t2+uTDM7ARiCd6izL76NFyVnBWRmFcCvgTXA1QOs7kjg5z3qfwG4wDn30gDrDsI4vL7Z3yoz+wfn3KM5rH9Y6nlFhuWv430IDqW0vjQH2i9+1xO096Se24Hn8JKPfczsMeDDzrnNfdRTjuPFr77pVi5jJi0zqwHOxzt8ldNRC8pz3Bygn/3SrSzGjHNum5ldhXfocZmZ3YV37lkTcA7wEPC5HKrybbzoas3CuhY4CviUc27vAOr5HjAP71fyELwv5d/hJWwPm9mEgQZaZL8EFuB9sOuA2cDNQCNwn5kdmUMdw1LPOzMs7y4f3v8wi86PfvGznjAYk3r+Ct75Gu/F+wwcATwInAD8Nod6ynG8+NU3UF5jJpOP4L2/9zvn3spxnXIcNz31p1+gzMaMc+5G4EN4O60+A3wNWIh36sCtzrlNOVTj23hRclYgqWPYVwP/1Y/DCwdwzl3pnHvSObfFOdfqnFvqnFsI3AmMAv7Zh5CLxjl3vXPuYefcRudcm3PuZefcpXhJaA1wXbARBsOvfimz/u3+jorjnaj8eOoz8BLwQbwrFOfne6l7mfCtb8pszGTSfeju5kCjCJ9+9Uu5jRkz+yreTo9b8faY1eFd8bwS+O/UVdFFo+SsAFKHM3+Ft2vzXwvY1E9SzycUsI1iymd7un+BDMuwvLt8x4AiCge/3udSHC/d799zzrmW/Rc459rwrowC71L1bMpxvPjVN9mU4pjpxcwOB47DS1hzvbUIlOe42WcA/ZJNyY0ZMzsR+DbeBQH/5JxbmUo4n8X7ofM2cKWZHdJHVb6NFyVnhVGPd0x5BtC+/8358K7UBPhpqizdPWJy1X0uSd0A6giTfLZneer50AzLp6WeMx37LyV+vc+lOF663+dMX2bbU881OdZTTuPFr77JphTHTDr9PeG9HMfN/vrbL9mU4pg5K/X5UD1dAAACm0lEQVS8qOeC1A+dJXj50lF91OPbeNEFAYXRQY+T9/fzbrw3+HG8N3Ighzznpp5XDqCOMMlne7o/RKeYWSTNJcvzgDa8y6NLnV/vcymOl7/inU81s+f7nNJ9EvyqPuopx/HiV99kU4pj5gBmVg1cgHfCe6bv5UzKcdwAA+6XbEpxzFSlnkdnWN5d3tftavwbL7ncDE0PX292dx1pbkIL1ALTgck9yo8gzY0kU+VbUnV9IujtymP7ZwB1acob8a5kccDV+5XHUv3SlGadsrk5pF/9km89pfDAu8u2A77co/wUIIm3h2jYYBovfvZNOY6ZHttxQWob/pTlNYNq3Ay0X8ptzOBdFOHwbkI7ocey01Ofpb3AyGKNl8A7ZbA9yJycnUiamQDwTk7snk7i+8B3gT/jnQTsgFvwbo4X+Lblsf27gXuAH+Ed5/9dauC7VHnlfq9vTJW3pKmrCdiYWn4X8H+Ah1P/X979QSqFh1/9km89pfAAJuLdjsbhzbTxndQ2xYEu4LzBNl787JtyHDM9tu9vqe04O8trBtW4GWi/lNuYwTtk+VAq9l3AbaltuhsvMXPAl4o5XgLvlMH2IP/k7Fzg93h3Hd6Ft1t1PfAncpxmI0wPYD5wB958YztSf0A2pz4YF9Ij0cz2IUgtn4R3Sff6VN+sxrsp54igtzWIfsm3nlJ54B1W+H7q/e3E22v8B+CYwThe/Oybch0zqW2bkdrmt4BoltcNqnEz0H4pxzGDtzfsCrxDjrvwfuBswtsZckqxx4umbxIREREJEV2tKSIiIhIiSs5EREREQkTJmYiIiEiIKDkTERERCRElZyIiIiIhouRMREREJESUnImIiIiEiJIzERERkRBRciYiIiISIkrORERERELk/wMOmcwV/YjCbgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FZBJ1WqU9tpc"
      },
      "source": [
        "The graph above does not really make sense given that we know we have three  different types of flowers: Iris setosa, Iris virginica and Iris versicolor, \n",
        "it makes more sense that we should have 3 centroids (clusters), each corresponding to one of the three flower types. See the discussion of meaningful clusters on the top of this notebook.\n",
        "\n",
        "Alright, so, how do we find the best K (number of centroids) if we don't know as much about the dataset?\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vOeikAQLq90D"
      },
      "source": [
        "##Finding the best number of clusters (centroids),K: The Elbow Method"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 540
        },
        "id": "s54OVuh4nhxF",
        "outputId": "c26d5525-9432-4cc3-c6cb-a090b934c064"
      },
      "source": [
        "Error =[]\n",
        "for i in range(1, 11):\n",
        "    kmeans = KMeans(n_clusters = i).fit(x)\n",
        "    kmeans.fit(x)\n",
        "    #inertia_float:Sum of squared distances of samples to their closest cluster center\n",
        "    #remember the explanation of K-means as the average between the points\n",
        "    #the lower the error, the better\n",
        "    Error.append(kmeans.inertia_)\n",
        "\n",
        "plt.plot(range(1, 11), Error)\n",
        "plt.title('Elbow method')\n",
        "plt.xlabel('No of clusters')\n",
        "plt.ylabel('Error')\n",
        "plt.show()"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAoAAAAILCAYAAAB4ui04AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nOzde5xddX3v/9dnJskkk9mThFxmB0IICpnBOxJrBURra6tW1Cr1h6f1Xq1WvGPPOYKVWi/tOVgV8Ei1HqBiG1qsWipQj0VELiJBKCIkASHhYhJCrpPbJDPz/f2x1obtZiZzyUzW3rNfz8djHou91ve792dPYnw/vmt9v99IKSFJkqTm0VJ0AZIkSTq8DICSJElNxgAoSZLUZAyAkiRJTcYAKEmS1GQMgJIkSU3GACjpsIuISyMiRcR5NeeX5eddn6pORcTb8j+j64uupdZwf68kPZUBUNK4VP2f7Wh+PlR0vRpZHu7Oi4jnFV2LpMk1regCJDW8A8DWEdrsPhyF6JC9DXgJsA64s9BKJE0qA6CkQ3VzSumlRRchSRo9bwFLkiQ1GQOgpLoVEadExL9HxOaI2BMRd0bEWRFx0H+7IuL1EXFt3q8vIh6JiG9GxPOHaHt0/pxif0R0DnH95/n13ohoHeL6hvz6S8fwvdZV+kTE4oi4OCIejoi9EXFvRHy4+jtGxB9GxI8jYntE7IyI70XEs0b4jIUR8bm8/l0RsTsi7o6Iz0TEETVt35ZPvHlJfuqSmmc41x3kc06PiB/mte2KiJ9ExJtGqK0zf9bwv/I+uyLiroj4y4iYM0LfF0bEVRGxNe93Z0R8cKS/E5J+nf+DkVSXIuINwPXA75M9rjIdeC5wIfCtiHjKIywR0RIRlwHfAn4PmAfsAY4C/htwW0S8t7pPSulh4EGgFTil5v3mA8/MX3YAz6+5vhwoA33AT8bxNY8Ffgb8KdCZf8ce4G+BL+Wf8dfAPwMvIvs3uwS8CvhxRBw/1JtGxKnAauB/AM/K37cl/y4fB+6MiO6qLnuBTWTPcwLszF9XfjYP8zmfAP4NOC0/NRt4IfCPw038iYjjgLuATwLPASL/eTbwF8BdB/leZwI3Aa8m+7M9kH+nL5L9jiSNkgFQUr36OvAD4GkppXnAXODPgUHgdfl/1/pz4C1AAj4BzMv7LgH+hezfvIsi4rSafjfkx5fUnD+NLJz0DnO98vqnKaV9o/9qT/gCWfh8bkppDlkI/ER+7X0R8XHgI8CHgDkppU6yoLSG7Pfxmdo3jIhjgKuAI4CvAMcDs8jC2bOB7wNHA/9aGdFMKV2RUioDN+dv88GUUrnq5wVD1P48shD3CWB+SmkuWRi+Mr/+uSFGGmeQhfNjgIeB3yUL1h3A7wAPAUuBb0dEW03fpwOXkAX17wNPz/9s5wAfJfs78boh6pQ0lJSSP/7448+Yf4BLyYLWfmDjCD+dw/Q9r+b8svx8Au4G2ob43PPy6zuA9qrzHfm5BHxuiH6twI/z6zfUXHt7fv6WmvNfzM9/Jj9eVXP98vz8X43xd7cu77cVmDvE9f+s+j38xRDXX5xf2wfMGKamp/wO8uszgP/K25xRc+36/PzbDlL726pqO2eI67OAx/Lrb6m59uaqvzPPGqLvM/NrCXhHzbWv5+dXAzOH6HtuVV3nDVe/P/74k/04AijpUE0Hukb4Gc+/NZ9PKfUNcf5vyYJPJ9kIUsXL83P7gf9V2ymlNAD8Vf7yxRFRrrpcGQFcERGzq85XRvguArYDp9Y8a1a5/qORv86QLk4pbR/i/A/y436y71vrJrLfQRtwXOVkRLQDf0g2SjpUP1JK+3lylO7l4ysb8s//4hDvvxf4j/xl7XOKZ+TH76aU7h6i7y+qantj5XxEBPD6/OUX0tCjrV8ku90vaRQMgJIO1Y9SSjHCz1AhZyTXD3UypbQTuCN/Wf1MXuW//yultG2Y97wBGKjtm1L6JfAo2bOGJwNExFyyZ9RWp5Q2kI0eziV7DpGIeBrZreUDPHnrdKx+Psz5x/LjupTSrtqLKaVB4PH85byqSyeRjfAF8POI2DjUD3B23v7ocdYNcE9Kabj1HR8dojZ48nf+w4O873U1bQGeRva7h2HCdv57uv0g7yupigFQUr16dBTXFladW1hz7SnykaNKcFpYc7kSLCqjei8m+zfy+mGuV463p5TGO/K0YZjzAyNcr24zverc4vwYHHxEtjLbuX2M9VbrPci1ygjd9JrzI/4ZAY/kx/n5yF91P4BfHaTvwd5XUhUDoKSpZuY4+9VOBKm9vTtcABzv7d/JUPk3fccoRmUjFbeA93j/jCRNEAOgpHp15CiuVS9PUvnvpcN1ioiZwPwh+sKTQe43ImIWTwa86/PjHWSjXi/OR6bqMQBuyo+dI62nV5AR/4zIbqsDbEkppZp+MLq/F5JGYACUVK9ql1wBICJKPPl82M+qLlX++/iIOGqY9zyNJ7fArO5LSmk12bN3M8gml5wIrE0pbcyvD5BNvphPtg7fMrLbsDeN+htNvlVAP9kt4FeMo/9gfoyDthq/yu/8tw7S5mU1bQEeIJuEA0+uOfhr8sk7Kw6pOqmJGAAl1auP5uvG1foQ2S3EnWTrwVV8Pz83HfhYbad8zbvKGns/rgS7GpXbwOeQLRtzfc31ymjfJ/PjHfmklLqQUuolW2cP4FN5WB5SREyLiI6a05XvMre2/QSpzPB9ZUScOERNz+TJmcJPLOycjwRWvteHatcIzH2AQ3umUWoqBkBJ9aqyIPAyyJY4iYiPkq0DCPA31ZMv8hmpn81ffiAizqkEnHxE8J+AU8lGuc4d5jMrAbCy8HHt7d0fjXC9HvwPsvUFlwM3R8QrImI6ZMupRMTxEfERsvX0akfMfpEfXz9Jt5CvINsFBOA7EfE7lYkeEfHbwNVkAf4XwDdr+n6ObHLJCXnfY/N+s/JdR/6KbB1ISaPwlK2UJGmMTs6XFjmYK1JKHxzj+74TWAk8GBHbyRZ6rvyb9V2GWOsPOB94BtluIJ8G/jIidpKNaAVZ+Ht/SumGIfrCUwPd9TWvV5GtNVcZaaq7AJhSWhcRrwC+Q7YO3zXAgfz3UCK7xf1E85ru3yBbIuZU4PGIeIxsmZtHUkqnTkBt+/Mt/n5AthvI/wP25Bmw8jt9CHh97RqQKaVfRsTbyRa6fgXwQM3fi28Bu8n+7CWNwBFASYdqNAtBj3k0KaX0LbJnxb5H9qxdP9kOFu8nCwj9Q/QZSCm9lew24vfJnhvrIFtO5Z+A30gp/Z+DfOzPyUbPAO5PKf3akiMppeo1/waBG8f6vQ6HlNJtZHsK/3eyeneRheA9ZCH2AuAlKaUf1fRbTbY49LVko2llsqC2hAmSUrqfbC3FT5Ht9lJxN9ko3nNSSmuH6buSbL/m75H92c4A7iF7LOCNPDXQShpGPDnJSpIkSc3AEUBJkqQmYwCUJElqMgZASZKkJmMAlCRJajIGQEmSpCbjOoBjtGDBgrRs2bKiy5AkSRrR7bff/nhKaWHteQPgGC1btoxVq1YVXYYkSdKIImL9UOcLvwUcEW+LiDTCz8AQ/U6OiKsjYmtE7I2IuyLiQ/l+n8N91qsj4vqI2BERuyLi1oh46+R+Q0mSpPpSDyOAdwJ/Ocy1FwMvI9vK6AkR8VqybX/2ke0tuRU4HfgC2Srxf1j7RhFxFnAhsIVsK6H9ZLsFXBoRz04pnT0RX0aSJKne1fVOIBFxC/CbwGtTSv+Wn+sE7ifbWuqUlNKq/PxM4DrgRcCb8i2DKu+zjGzj893ASSmldfn5ecBtwNOBk1NKt4xU04oVK5K3gCVJUiOIiNtTSitqzxd+C3g4EfFssvD3KNm+jxVnAAuBlZXwB5BS2gecm798b83bvQNoAy6qhL+8zzbgs/nL90xk/ZIkSfWqbgMg8O78+PWUUvUzgC/Lj9cO0ecGss3OT46ItlH2uaamjSRJ0pRWlwEwImYBfwwMAH9fc7k7P66t7ZdS6gceJHu28Wmj7LOB7NbwkohoP7TKJUmS6l9dBkDgjcBc4NqU0sM11+bkxx3D9K2cnzuOPnOGuhgR746IVRGxavPmzcNXLUmS1ADqNQBWbv/+XaFV5FJKX00prUgprVi48ClrKUqSJDWUuguAEfFM4GTgEeDqIZocdLSu6vz2cfQZboRQkiRpyqi7AMjwkz8q1uTH5bUXImIacCzQDzwwyj6LgdnAIymlPeMtWpIkqVHUVQDM1/J7M9nkj68P0+y6/PiKIa6dBrQDN6eU+kbZ55U1bSRJkqa0ugqAZDt4zAOuGWLyR8WVwOPAmRHxxMKGeXj8dP7yKzV9LgH6gLPyRaErfeYBH89fXnyoxUuSJDWCetgKrlrl9u9Xh2uQUtoZEe8iC4LXR8RKsq3gXkO23MuVZNvDVfd5MCI+BlwArIqIK3hyK7glwOdHswuIJEnSVFA3ATAiTgBOZfjJH09IKX0nIl4CnAO8AZhJtj3cR4AL0hD726WULoyIdcDZwFvIRj/vAc5NKV02gV9FkiSprtVNAEwp3QvEGNrfBLxqjJ9xFXDVGEuTJEmaUurtGUBJkiRNMgNgnekfGGRzb9/IDSVJksbJAFhn3nnZKt552W1FlyFJkqYwA2CdefrCDtZu6mVg8CnzWCRJkiaEAbDO9Cwuse/AIA9tdVMSSZI0OQyAdaanXAJgzcadBVciSZKmKgNgnTl+UYkIuHdDb9GlSJKkKcoAWGdmzWhl2fzZrNloAJQkSZPDAFiHurtKrNlkAJQkSZPDAFiHehaXWLdlN3v3DxRdiiRJmoIMgHWop1wiJbjvMUcBJUnSxDMA1qHucicAq50IIkmSJoEBsA4tPaKdmdNbWO1EEEmSNAkMgHWotSVY3lVizSbXApQkSRPPAFinurtKLgUjSZImhQGwTvUs7uTxXfvZ3NtXdCmSJGmKMQDWqSe3hHMUUJIkTSwDYJ3qzgPgavcEliRJE8wAWKcWdLSxoGOGI4CSJGnCGQDrWHfZLeEkSdLEMwDWsZ5yJ2s39TIwmIouRZIkTSEGwDrWXS6x78AgD23dU3QpkiRpCjEA1rHKTODVG5wIIkmSJo4BsI4dv6hEBG4JJ0mSJpQBsI7NmtHKsvmznQksSZImlAGwzvU4E1iSJE0wA2Cd6y6XWLdlN3v3DxRdiiRJmiIMgHWup1wiJVjrKKAkSZogBsA6113uBNwTWJIkTRwDYJ1bekQ7M6e3OBNYkiRNGANgnWttCbq7SqzZ5FqAkiRpYhgAG0B3ueQtYEmSNGEMgA2gu9zJ47v2s7m3r+hSJEnSFGAAbACVLeEcBZQkSRPBANgAuit7Am/0OUBJknToDIANYEFHGws6ZjgCKEmSJoQBsEH0lDvdEk6SJE0IA2CDqMwEHhhMRZciSZIanAGwQXSXS/T1D7J+y+6iS5EkSQ3OANggnAksSZImigGwQRy/qEQEbgknSZIOmQGwQcya0cqx82c7AihJkg6ZAbCBdJdLrgUoSZIOmQGwgXSXS6zfuoc9+/uLLkWSJDUwA2AD6SmXSAnu27Sr6FIkSVIDMwA2kO5yJ+BMYEmSdGjqKgBGxG9HxLcjYmNE9EXEryLiPyLiVUO0PTkiro6IrRGxNyLuiogPRUTrQd7/1RFxfUTsiIhdEXFrRLx1cr/VxFl6RDuzprc6E1iSJB2SugmAEfG/gB8AK4B/Az4PfA9YCLy0pu1rgRuA04BvAxcBM4AvACuHef+zgKuAZwGXA18DjgQujYjzJ/wLTYLWlmB5V4cTQSRJ0iGZVnQBABHxLuBjwGXAu1NK+2uuT6/6706y8DYAvDSltCo//wngOuCMiDgzpbSyqs8y4HxgK7AipbQuP/8p4DbgoxHxrZTSLZP1HSdKd7nEf977WNFlSJKkBlb4CGBEtAGfAR5iiPAHkFI6UPXyDLJRwZWV8Je32Qecm798b81bvANoAy6qhL+8zzbgs/nL9xzaNzk8usudbNm9n829fUWXIkmSGlQ9jAC+nCzQfREYjIjfJ7tNuw/46RCjci/Lj9cO8V43AHuAkyOiLaXUN4o+19S0qWvVW8ItLLUVXI0kSWpE9RAAX5Af9wF3kIW/J0TEDcAZKaXN+anu/Li29o1SSv0R8SDwTOBpwL2j6LMhInYDSyKiPaW051C+zGSrBMDVG3dy6vELCq5GkiQ1osJvAQOL8uPHgAS8GCgBzwG+TzbR41+q2s/JjzuGeb/K+bnj6DNnqIsR8e6IWBURqzZv3jxUk8NmfkcbCzraXApGkiSNWz0EwEoN/cBrUko3ppR2pZR+DvwB8Ajwkoh4UVEFppS+mlJakVJasXDhwqLKeEJPueRSMJIkadzqIQBuz493VE/QAMhvx/5H/vI38uNBR+uqzm+vOjfaPsONENaV7nKJtZt6GRhMRZciSZIaUD0EwDX5cfsw17flx1k17ZfXNoyIacCxZKOJDwzxGUP1WQzMBh6p9+f/KrrLJfr6B1m/ZXfRpUiSpAZUDwHwP8me/XtGRAxVT2VSyIP58br8+Ioh2p4GtAM3V80AHqnPK2va1L0T3BJOkiQdgsIDYEppPdkOHUuBD1Zfi4jfBX6PbHSwsoTLlcDjwJkRsaKq7Uzg0/nLr9R8zCVAH3BWvih0pc884OP5y4sP/dscHsd3ddAS+BygJEkal3pYBgbgfcCJwN/m6wDeQXYr93VkO378SUppB0BKaWe+c8iVwPURsZJsh4/XkC33ciVwRfWbp5QejIiPARcAqyLiCmA/2aLSS4DPN8IuIBUzp7eybP5st4STJEnjUhcBMKX0SEScBPwFWZA7DdhJNjL4uZTST2vafyciXgKcA7wBmAncD3wEuCCl9JTZESmlCyNiHXA28Bay0c97gHNTSpdN1nebLN3lEvduMABKkqSxq4sACJAv9Pz+/Gc07W8CXjXGz7iKLFQ2vO5yiWt/sZE9+/tpn1E3f4ySJKkBFP4MoManp1wiJbhv066iS5EkSQ3GANigepwJLEmSxskA2KCWHtHOrOmt3OtEEEmSNEYGwAbV0hIs7+pwBFCSJI2ZAbCBdZdLBkBJkjRmBsAG1l3uZMvu/Wzu7Ru5sSRJUs4A2MBOKJcAJ4JIkqSxMQA2sO48ALojiCRJGgsDYAOb39HGgo429wSWJEljYgBscD1OBJEkSWNkAGxw3eUSazf1MjD4lO2PJUmShmQAbHA95RJ9/YOs37K76FIkSVKDMAA2uMqWcD4HKEmSRssA2OCO7+qgJQyAkiRp9AyADW7m9FaWzZ/NGpeCkSRJo2QAnALcEk6SJI2FAXAK6Cl3sn7rHvbs7y+6FEmS1AAMgFNAd7lESrB2066iS5EkSQ3AADgF9DyxJ7DPAUqSpJEZAKeApUe0M2t6qzOBJUnSqBgAp4CWlmB5V4cTQSRJ0qgYAKcIZwJLkqTRMgBOET3lTrbs3s/m3r6iS5EkSXXOADhFVCaCrHYiiCRJGoEBcIrofmImsLeBJUnSwRkAp4j5HW0s6GhzJrAkSRqRAXAK6XEiiCRJGgUD4BTSUy6xdlMvA4Op6FIkSVIdMwBOId3lEn39g6zbsrvoUiRJUh0zAE4hPeVOwIkgkiTp4AyAU8jxXR20BE4EkSRJB2UAnEJmTm9l2fzZrHEtQEmSdBAGwCmmZ7EzgSVJ0sEZAKeY7q5O1m/dw579/UWXIkmS6pQBcIrpLpdICdZu2lV0KZIkqU4ZAKeYnie2hPM5QEmSNDQD4BSz9Ih2Zk1vdSawJEkalgFwimlpCZa7JZwkSToIA+AU1NNVYvXGXlJySzhJkvRUBsApqLtcYuvu/Wze1Vd0KZIkqQ4ZAKegJyeCeBtYkiQ9lQFwCuo2AEqSpIMwAE5B8zvaWFhqcyawJEkakgFwiuopl1jtWoCSJGkIBsApqrurxH2bdjEw6ExgSZL06+oiAEbEuohIw/xsHKbPyRFxdURsjYi9EXFXRHwoIloP8jmvjojrI2JHROyKiFsj4q2T982K010u0dc/yLotu4suRZIk1ZlpRRdQZQfwxSHOP2VT24h4LfAtYB9wBbAVOB34AnAK8IdD9DkLuBDYAlwO7AfOAC6NiGenlM6emK9RH3rKnUA2EeTpCzsKrkaSJNWTegqA21NK543UKCI6ga8BA8BLU0qr8vOfAK4DzoiIM1NKK6v6LAPOJwuKK1JK6/LznwJuAz4aEd9KKd0ykV+oSMd3ddASsHpjL6969uKiy5EkSXWkLm4Bj9EZwEJgZSX8AaSU9gHn5i/fW9PnHUAbcFEl/OV9tgGfzV++Z7IKLsLM6a0sWzCb1RucCCJJkn5dPY0AtkXEHwNLgd3AXcANKaWBmnYvy4/XDvEeNwB7gJMjoi2l1DeKPtfUtJkyesolfvErA6AkSfp19RQAy8A3as49GBFvTyn9qOpcd35cW/sGKaX+iHgQeCbwNODeUfTZEBG7gSUR0Z5S2nMoX6KedHd1cs3dG9mzv5/2GfX0Ry1JkopUL7eALwF+mywEzgaeDfwdsAy4JiKeW9V2Tn7cMcx7Vc7PHUefOUNdjIh3R8SqiFi1efPm4b5D3ekul0gJ1m56yjwaSZLUxOoiAKaU/jKldF1KaVNKaU9K6e6U0nuAvwVmAecVXN9XU0orUkorFi5cWGQpY/LknsDeBpYkSU+qiwB4EBfnx9Oqzh10tK7q/PZx9BluhLAhLT2inVnTW90STpIk/Zp6D4CV+62zq86tyY/LaxtHxDTgWKAfeGCUfRbn7//IVHr+D6ClJVheLrF6gwFQkiQ9qd4D4G/mx+owd11+fMUQ7U8D2oGbq2YAj9TnlTVtppSerhJrNvWSklvCSZKkTOEBMCJOiIjZQ5xfBlyUv7y86tKVwOPAmRGxoqr9TODT+cuv1LzdJUAfcFb+vpU+84CP5y8vZgrqLpfYuns/m3f1jdxYkiQ1hXpYG+T/I9uJ4wZgPdALPB34fWAmcDXZLh4ApJR2RsS7yILg9RGxkmyHj9eQLfdyJdn2cFT1eTAiPgZcAKyKiCt4ciu4JcDnp9IuINWenAjSy6LSzIKrkSRJ9aAeAuAPyYLbiWT7+M4mm8BxI9m6gN9INfcvU0rfiYiXAOcAbyALivcDHwEuqG2f97kwItYBZwNvIRv9vAc4N6V02eR8teJ1VwXAFx/fODOYJUnS5Ck8AOaLPP9oxIZP7XcT8Kox9rkKuGqsn9XI5ne0sbDUxr1OBJEkSbnCnwHU5Ospl1izybUAJUlSxgDYBLq7Sty3aRcDg84EliRJBsCm0F0u0dc/yLotu4suRZIk1QEDYBM4YXEnkE0EkSRJMgA2geMWddASsHqDzwFKkiQDYFOYOb2VZQtmuyewJEkCDIBNI5sJbACUJEkGwKbR3dXJQ1v3sGd/f9GlSJKkghkAm0R3uURKsHbTrqJLkSRJBTMANokTFmdbwjkRRJIkGQCbxNHz2mmf0epEEEmSZABsFi0twfFdJdcClCRJBsBm0tOVzQROyS3hJElqZgbAJtJdLrF193427+oruhRJklQgA2AT6XliIoi3gSVJamYGwCbSU3ZPYEmSZABsKkfMnsHCUpszgSVJanIGwCaTbQnnWoCSJDUzA2CT6e4qcd+mXfQPDBZdiiRJKogBsMn0LO6kr3+QdVv2FF2KJEkqiAGwyfSUs5nATgSRJKl5GQCbzHGLOmgJWLPR5wAlSWpWBsAmM3N6K8sWzHYmsCRJTcwA2ISymcAGQEmSmpUBsAn1lDtZv2UPu/v6iy5FkiQVwADYhLrziSBrHQWUJKkpGQCbkDOBJUlqbgbAJnT0vHbaZ7Q6EUSSpCZlAGxCLS3B8V0lRwAlSWpSBsAmdUK5xOqNO0kpFV2KJEk6zAyATaq7XGLbngNs7u0ruhRJknSYGQCbVGUmsM8BSpLUfAyATaqn3Ak4E1iSpGZkAGxSR8yewcJSmyOAkiQ1IQNgE8u2hNtZdBmSJOkwMwA2sZ5yibWbdtE/MFh0KZIk6TAyADax7nIn+/sHWbdlT9GlSJKkw8gA2MTcEk6SpOZkAGxixy3qoCVgzUafA5QkqZkYAJvYzOmtLFsw25nAkiQ1GQNgkzuh3GkAlCSpyRgAm1x3ucRDW/ewu6+/6FIkSdJhYgBscpUt4dZuchRQkqRmYQBscs4EliSp+RgAm9zR89ppn9Hqc4CSJDWRugyAEfHHEZHynz8Zps2rI+L6iNgREbsi4taIeOsI7/vWiPhp3n5H3v/Vk/MtGkNLS7C8q8Rql4KRJKlp1F0AjIijgYuAXQdpcxZwFfAs4HLga8CRwKURcf4wfc4HLgUW5+0vB54NXJW/X9PqKZdYs7GXlFLRpUiSpMOgrgJgRARwCbAFuHiYNsuA84GtwIqU0vtSSh8GngP8EvhoRLyops/JwEfz689JKX04pfQ+4KT8fc7P37cpdZdLbNtzgM29fUWXIkmSDoO6CoDAB4CXAW8Hdg/T5h1AG3BRSmld5WRKaRvw2fzle2r6VF5/Jm9X6bMO+HL+fm8/xNobVmUmsM8BSpLUHOomAEbECcBfA19KKd1wkKYvy4/XDnHtmpo2h9KnafSUOwFnAkuS1CzqIgBGxDTgG8BDwMdHaN6dH9fWXkgpbSAbOVwSEe35e88GjgJ25ddr3Zcfl4+j9CnhiNkzWFRq414ngkiS1BTqIgACfwGcCLwtpbR3hLZz8uOOYa7vqGk32vZzh/vAiHh3RKyKiFWbN28eobzG1J1PBJEkSVNf4QEwIl5INur3+ZTSLUXXM5SU0ldTSitSSisWLlxYdDmToqdc4r7HdtE/MFh0KZIkaZIVGgDzW7//QHY79xOj7FY7wlerdsRvtO23j/Lzp6Tucif7+wdZt2VP0aVIkqRJVvQIYAfZs3cnAPuqFn9OwCfzNl/Lz30xf70mPz7lmb2IWAzMBh5JKe0BSCntBh4FOvLrtY7Pj095prCZuCWcJEnNY1rBn98HfH2Ya88ney7wRrLQV7k9fB1wCvCKqnMVr6xqU+064M15n0tG2aepHLeog5aA1Rt38vvPGSonS5KkqaLQAJhP+Bhuq7fzyALgZSmlv6+6dAnw58BZEXFJZS3AiJjHkzOIaxeRvpgsAJ4TEd+prAWYL/78PrIgWhsMm8rM6QHltvMAACAASURBVK0cu2C2awFKktQEih4BHLOU0oMR8THgAmBVRFwB7AfOAJYwxGSSlNLNEfG3wEeAuyLiSmAG8P8BRwDvr15Uuln1lDv5+aPDTZaWJElTxZifAYyIgYj45mQUM1oppQuB1wC/AN4CvBvYSLaMzNnD9Pko2W4fG/P2b8n7n55Suuhw1F3vusslHtq6h919/UWXIkmSJtF4RgB7yRZsnlQppfOA8w5y/SrgqjG+56XApYdQ1pRW2RJu7aZeTlw6r+BqJEnSZBnPLOA7gGdMdCEqnjOBJUlqDuMJgH8DvCoiXj7RxahYR89rp31GqxNBJEma4sZzC3gRcC1wTUR8B7iN7Lm6VNswpfQPh1aeDqeWlmB5V4nV7gksSdKUNp4AeClZ2Avg9fkP/HoAjPy1AbDB9JRL/McvNpJSIiKKLkeSJE2C8QTAt094Faob3eUSK297mM29fSzqnFl0OZIkaRKMOQCmlC6bjEJUHyozgVdv7DUASpI0RRW9F7DqTE+5E8DnACVJmsLGvRNIRLSTPf93IjAX2AH8DPh2Smn3xJSnw+2I2TNYVGpzJrAkSVPYuAJgRLwKuIxsG7XqmQIJ+EJEvD2l9O8TUJ8K0F0uuRagJElT2Hi2gns+8K9ko37fBN4BvDI/fjM/f2VEnDSBdeow6imXuO+xXfQPDBZdiiRJmgTjGQE8h2yk78UppZ/UXLs0Ir4MXA98HHjDoZWnInSXO9nfP8i6LXs4blFH0eVIkqQJNp5JIC8G/mWI8AdASulW4Mq8nRpQzxMzgZ0IIknSVDSeADgHeHiENg8BneN4b9WB4xZ10NoSPgcoSdIUNZ4A+CvgN0ZoswLYMI73Vh2YOb2VZfPbnQksSdIUNZ4AeDXwsoj4HxHRWn0hIloi4qPA7+Tt1KB6yp2OAEqSNEWNZxLIXwGvAz4D/GlE/JhstK8MnAosAzYCn56gGlWA7nKJ7/18A7v7+pndNu7lIiVJUh0az1ZwGyPiVOBi4OXAMTVN/h/wnpSSt4AbWGUiyJpNvTx/6byCq5EkSRNpXEM7KaUHgd+LiKPIdgKZQ7YTyB0ppUcnsD4VpLIl3JqNBkBJkqaaMQfAiHgAuCal9L487Bn4pqAl82bRPqPV5wAlSZqCxjMJZCHZaJ+msJaWYHlXybUAJUmagsYTAH8BPH2iC1H96cn3BE4pFV2KJEmaQOMJgBcAp0fEcya6GNWX7nKJbXsO8FhvX9GlSJKkCTSeSSCPAD8AboqIvwNuI1v25SnDRCmlGw6tPBWpMhFk9cZeujpnFlyNJEmaKOMJgNeThb0APsIQwa9K60Guqc49sRTMxp28ZPnCgquRJEkTZTwB8FMcPPRpipg3ewaLSm1uCSdJ0hQznoWgz5uEOlSnuvOJIJIkaeoY8ySQiHggIi6ajGJUf3rKJe57bBf9A4NFlyJJkibIeNcBdHG4JtFT7mR//yDrtuwuuhRJkjRBXAdQB9WdTwTxOUBJkqYO1wHUQR23qIPWlvA5QEmSphDXAdRBzZzeyrL57Y4ASpI0hbgOoEbUU+7k54+6/bMkSVOF6wBqRD3lEt/7+QZ29fXT0TaevzKSJKmeuA6gRlSZCLJ2Uy/PXzqv4GokSdKhGs8kEDWZyp7ATgSRJGlqGFUAjIjTImLpaN80Ip4bEW8Zf1mqJ0vmzaJ9RqsBUJKkKWK0I4A/BN5WfSIi/ntEbBmm/euASw6hLtWRlpZgeVeJ1Rtd/1uSpKlgtAEwhjg3E5g7gbWojp2wuMTqjb2k5PwfSZIanc8AalS6u0ps33OAx3r7ii5FkiQdIgOgRqU7nwjigtCSJDU+A6BGpSdfCmaNzwFKktTwDIAalXmzZ7Co1OYIoCRJU8BYAqBP/ze57nKJ1RsMgJIkNbqx7ARyXkScV3syIgYmrhzVsxMWd3LpzevoHxhkWquDx5IkNaqx/L94jPFHU0x3V4n9/YOs27K76FIkSdIhGFUATCm1jOOndbKL1+FV2RPY5wAlSWpsdXEfLyL+JiL+MyIejoi9EbE1Iu6IiE9GxPxh+pwcEVfnbfdGxF0R8aGIGDZ4RsSrI+L6iNgREbsi4taIeOvkfbOp5bhFHbS2hFvCSZLU4OoiAAIfBmYD/w/4EvBNoB84D7grIo6ubhwRrwVuAE4Dvg1cBMwAvgCsHOoDIuIs4CrgWcDlwNeAI4FLI+L8Cf9GU9DM6a0sm9/OvU4EkSSpoY1lEshk6kwp7as9GRGfAT4O/E/gz/JznWThbQB4aUppVX7+E8B1wBkRcWZKaWXV+ywDzge2AitSSuvy858CbgM+GhHfSindMllfcKroWdzJXY9sL7oMSZJ0COpiBHCo8Jf75/x4fNW5M4CFwMpK+Kt6j3Pzl++teZ93AG3ARZXwl/fZBnw2f/mecRXfZHq6Sjy8dS+7+vqLLkWSJI1TXQTAgzg9P95Vde5l+fHaIdrfAOwBTo6ItlH2uaamjQ6iMhFk7SZvA0uS1Kjq5RYwABFxNtABzAFWAKeShb+/rmrWnR/X1vZPKfVHxIPAM4GnAfeOos+GiNgNLImI9pTSnon4LlNVT74n8JqNvTx/6byCq5EkSeNRVwEQOBvoqnp9LfC2lNLmqnNz8uOOYd6jcn7uGPvMzts9JQBGxLuBdwMsXbp0uNqbwpJ5s2if0crqDe4JLElSo6qrW8AppXJKKYAy8HqyUbw7IuL5Bdf11ZTSipTSioULFxZZSuFaWiLbEs6lYCRJalh1FQArUkqbUkrfBn4XmA/8Q9XlyijenKd0/PXz1VNVR9tnuBFCVekpl1izqZeU3B5akqRGVJcBsCKltB64B3hmRCzIT6/Jj8tr20fENOBYsjUEH6i6dLA+i8lu/z7i83+j091VYvueAzzW21d0KZIkaRzqOgDmjsyPA/nxuvz4iiHanga0AzenlKrTycH6vLKmjUbQnU8E8TawJEmNqfAAGBHLI+Ipt2YjoiVfCHoRWaDbll+6EngcODMiVlS1nwl8On/5lZq3uwToA87KF4Wu9JlHttA0wMWH/m2aQ09lT2AngkiS1JDqYRbwq4DPRcSNwIPAFrKZwC8hmwSyEXhXpXFKaWdEvIssCF4fESvJdvh4DdlyL1cCV1R/QErpwYj4GHABsCoirgD2ky0qvQT4vLuAjN682TPo6mxzT2BJkhpUPQTAHwDHka35dyLZ8i27ydbs+wZwQUppa3WHlNJ3IuIlwDnAG4CZwP3AR/L2T5mdkFK6MCLWkS018xay0c97gHNTSpdNzleburrLnd4CliSpQRUeAFNKdwNnjaPfTWSjh2PpcxVw1Vg/S0/VUy5x6QNb6B8YZFpr4U8SSJKkMfD/uTUu3V0l9vcPsm7L7qJLkSRJY2QA1LhU9gT2NrAkSY3HAKhxOW5RB60tweoNBkBJkhqNAVDjMnN6K8cumO0IoCRJDcgAqHHrLpdYs8m1ACVJajQGQI1bT1eJh7fuZVdff9GlSJKkMTAAatwqE0HWbvI2sCRJjcQAqHHrqewJ7EQQSZIaigFQ47Zk3ixmz2hlzUafA5QkqZEYADVuLS3B8nLJmcCSJDUYA6AOSU+5xJpNvQyx/bIkSapTBkAdku6uEtv3HOCx3r6iS5EkSaNkANQh6c4ngty7wecAJUlqFAZAHZKefCmYNT4HKElSwzAA6pDMmz2Drs42A6AkSQ3EAKhD1l3udCawJEkNxACoQ9ZTLnH/Y7voHxgsuhRJkjQKBkAdsu6uEvsHBnnw8d1FlyJJkkbBAKhD1rM4mwjibWBJkhqDAVCH7LhFHbS2hBNBJElqEAZAHbK2aa0cu2C2I4CSJDUIA6AmRHe5xJpNLgYtSVIjMABqQvR0lXh461529fUXXYokSRqBAVATomdxtiWczwFKklT/DICaEG4JJ0lS4zAAakIcNXcWs2e0smajzwFKklTvDICaEC0twfJyyZnAkiQ1AAOgJkxPHgBTSkWXIkmSDsIAqAnT3VVix94DbNrZV3QpkiTpIAyAmjCVmcCrfQ5QkqS6ZgDUhHEmsCRJjcEAqAkzt30GXZ1tBkBJkuqcAVATqrvcyb0GQEmS6poBUBOqp1zil4/t4sDAYNGlSJKkYRgANaF6yiX2Dwyy7vHdRZciSZKGYQDUhOrOJ4K4ILQkSfXLAKgJddyiDlpbwokgkiTVMQOgJlTbtFaOXTDbEUBJkuqYAVATrrtccjFoSZLqmAFQE+6EcolHtu1lV19/0aVIkqQhGAA14brL2ZZwPgcoSVJ9MgBqwrklnCRJ9c0AqAl31NxZzJ7RyhqfA5QkqS4ZADXhWlqC5eWSW8JJklSnDICaFD3lTtZs7CWlVHQpkiSpRuEBMCLmR8SfRMS3I+L+iNgbETsi4saIeGdEDFljRJwcEVdHxNa8z10R8aGIaD3IZ706Iq7P339XRNwaEW+dvG/XvHrKJXbsPcCmnX1FlyJJkmoUHgCBPwS+BrwQuBX4IvAt4FnA3wP/HBFR3SEiXgvcAJwGfBu4CJgBfAFYOdSHRMRZwFX5+16ef+aRwKURcf6Ef6sm9+SWcD4HKElSvamHALgWeA2wJKX0Ryml/5lSegfQAzwMvAF4faVxRHSShbcB4KUppXemlD4GPA+4BTgjIs6s/oCIWAacD2wFVqSU3pdS+jDwHOCXwEcj4kWT+zWbizOBJUmqX4UHwJTSdSmlq1JKgzXnNwIX5y9fWnXpDGAhsDKltKqq/T7g3Pzle2s+5h1AG3BRSmldVZ9twGfzl+85tG+ianPbZ9DV2eaWcJIk1aHCA+AIDuTH6i0lXpYfrx2i/Q3AHuDkiGgbZZ9ratpogvSUOw2AkiTVoboNgBExDXhL/rI6uHXnx7W1fVJK/cCDwDTgaaPsswHYDSyJiPZDLFtVesolfvnYLg4MDI7cWJIkHTZ1GwCBvyabsHF1Suk/qs7PyY87hulXOT93HH3mDHUxIt4dEasiYtXmzZsPXrWe0F0usX9gkHWP7y66FEmSVKUuA2BEfAD4KLAaeHPB5ZBS+mpKaUVKacXChQuLLqdhPDkT2NvAkiTVk7oLgPlyLV8C7gF+K6W0tabJQUfrqs5vH0ef4UYINQ7HLeqgtSVcCkaSpDpTVwEwIj4EXAjcTRb+Ng7RbE1+XD5E/2nAsWSTRh4YZZ/FwGzgkZTSnvFXr1pt01o5dsFsl4KRJKnO1E0AjIj/TraQ851k4e+xYZpelx9fMcS104B24OaUUvUWFAfr88qaNppAPeWSt4AlSaozdREAI+ITZJM+bgd+O6X0+EGaXwk8DpwZESuq3mMm8On85Vdq+lwC9AFn5YtCV/rMAz6ev7wYTbiecolHtu1lV1//yI0lSdJhMa3oAvK9eD9FtrPHj4EP1Oz8BrAupXQpQEppZ0S8iywIXh8RK8l2+HgN2XIvVwJXVHdOKT0YER8DLgBWRcQVwH6yRaWXAJ9PKd0yOd+wuXWXO4FsR5CTjplXcDWSJAnqIACSPbMH0Ap8aJg2PwIurbxIKX0nIl4CnEO2VdxM4H7gI8AFKaVU+wYppQsjYh1wNtn6gi1kE03OTSldNiHfRE/RU7UnsAFQkqT6UHgATCmdB5w3jn43Aa8aY5+rgKvG+lkav6PmzmL2jFYngkiSVEfq4hlATV0tLUG3E0EkSaorBkBNuu5yJ2s29jLEnXlJklQAA6AmXU+5xI69B9i0s2/kxpIkadIZADXpKlvC3euOIJIk1QUDoCZdZSawE0EkSaoPBkBNurntMyh3zjQASpJUJwyAOiycCSxJUv0wAOqw6CmX+OVjuzgwMFh0KZIkNT0DoA6L7nKJ/QODrHt8d9GlSJLU9AyAOiyenAnsbWBJkopmANRhcdyiDlpbgjUuBSNJUuEMgDos2qa18rQFs50JLElSHTAA6rBxJrAkSfXBAKjDpqdc4pFte+ndd6DoUiRJamoGQB023eVOANZuchRQkqQiGQB12FS2hPM2sCRJxTIA6rA5au4sOtqmORFEkqSCGQB12LS0BMu7OhwBlCSpYAZAHVbd5U7WbOwlpVR0KZIkNS0DoA6rnnKJHXsPcMfD24suRZKkpmUA1GH18md0Ue6cyZu++hP+9WePFF2OJElNyQCow+rIubP49w+cyolL5/KRf/4vPvndu9nfP1h0WZIkNRUDoA67BR1tXP7OF/KuFx/LZbes501f+wmbdu4ruixJkpqGAVCFmNbawjm//wwufNOJ3LthJ6++8EZ++uDWosuSJKkpGABVqNOfeyTfed8pdLRN47997SdcetODzhCWJGmSGQBVuOVdJb571im8tHsR5111Dx++4k727h8ouixJkqYsA6DqQufM6Xz1zSdx9u8u57v/9Sv+4P/cxPotu4suS5KkKckAqLrR0hKc9bLjueRtL2DDjn2cfuGN/HD1Y0WXJUnSlGMAVN15afci/v39p7JkXjvvuOw2vvSD+xgc9LlASZImigFQdenoI9r51ntP5g+edxRf+MFa3vUPq9ix90DRZUmSNCUYAFW3Zs1o5fNvfC6feu0z+dHazbzmohtZvXFn0WVJktTwDICqaxHBW160jCv+9DfZu3+AP/jyzXz3zkeLLkuSpIZmAFRDOOmYI/j3D5zKs47q5IMr7+RTV93DgQG3kJMkaTwMgGoYi0oz+cd3/SZvP2UZ//emB/mjv7+Vx3rdQk6SpLEyAKqhTG9t4ZOnP5Mvnfk87npkO6dfeCO3r99WdFmSJDUUA6Aa0mufdxTf/rNTaJvWyplfvYVv/GS9W8hJkjRKBkA1rBMWd3LVWady6nEL+MR37ubsf7mLfQfcQk6SpJEYANXQ5rRP5+tvfQEf/O3j+dbPHuENX7mZh7fuKbosSZLqmgFQDa+lJfjwy5fz9beu4KGtezj9ohu5Ye3mosuSJKluGQA1Zfz2CV1cddaplDtn8tZLfsqXf3i/W8hJkjQEA6CmlGULZvOvf3Yypz/nSP73f6zhPZffTu8+t5CTJKmaAVBTTvuMaXzpzOfxF69+Bv+5+jFee9FN3Lept+iyJEmqGwZATUkRwTtOPZZ//JMXsnNfP6/98k18764NRZclSVJdMABqSnvh0+bz7+8/lZ5yiff948/47NX30u8WcpKkJmcA1JRXnjOTle9+EW/+zWP46g0P8Oav/5THd/UVXZYkSYUpPABGxBkRcWFE/DgidkZEiojLR+hzckRcHRFbI2JvRNwVER+KiNaD9Hl1RFwfETsiYldE3BoRb534b6R6NGNaC3/1umdx/h8+l589tI3TL7yROx/eXnRZkiQVovAACJwLnAU8D3h0pMYR8VrgBuA04NvARcAM4AvAymH6nAVcBTwLuBz4GnAkcGlEnH/oX0GN4oyTlvCt955Ma0vwxotv4Z9++lDRJUmSdNhF0funRsRvAY8A9wMvAX4IfDOl9MdDtO3M280BTkkprcrPzwSuA14EvCmltLKqzzJgNbAbOCmltC4/Pw+4DXg6cHJK6ZbR1LtixYq0atWq8XxV1ZFtu/fzwSvu5Ia1mznzBUdz3mueyczpww4gS5LUkCLi9pTSitrzhY8AppR+mFK6L40uiZ4BLARWVsJf/h77yEYSAd5b0+cdQBtwUSX85X22AZ/NX75nnOWrQc2bPYNL3vYCzvqt41h528O88e9u4dHte4suS5Kkw6LwADhGL8uP1w5x7QZgD3ByRLSNss81NW3URFpbgrN/r5uvvvkkHti8m9MvvJGb7n+86LIkSZp0jRYAu/Pj2toLKaV+4EFgGvC0UfbZQHZreElEtE9sqWoUv/vMMt896xTmz57Bm79+K3/3o19S9KMRkiRNpkYLgHPy445hrlfOzx1HnznDXFcTePrCDr7zvlN45bMW87lrVvO+f/wZu/r6iy5LkqRJ0WgBsBAR8e6IWBURqzZv3lx0OZoks9umcdF/O5FzXnUC1969kdd9+Sbuf2xX0WVJkjThGi0AjjRaVzlfvcDbaPsMN0JISumrKaUVKaUVCxcuHFWhakwRwbtOexqX/8kL2bZ7P6/78k1ce/fGosuSJGlCNVoAXJMfl9deiIhpwLFAP/DAKPssBmYDj6SU9kxsqWpkJz99AVe9/1SevqiD91x+O//r2tUMDPpcoCRpami0AHhdfnzFENdOA9qBm1NK1ft8HazPK2vaSE84cu4s/vlPf5M3/cZS/s/1v+Rtl/yUrbv3F12WJEmHrNEC4JXA48CZEfHEoob5QtCfzl9+pabPJUAfcFa+KHSlzzzg4/nLiyepXjW4tmmtfO71z+Zv3vBsbn1wK6dfeCN3Pzrs0wKSJDWEetgJ5HXA6/KXZeD3yG7h/jg/93hK6eya9lcC+8i2ftsKvIZsuZcrgTfWLiodEe8HLgC2AFcA+8kWlV4CfL76/UfiTiDN665HtvOeb9zO47v38+nXPYs3rji66JIkSTqo4XYCqYcAeB7wyYM0WZ9SWlbT5xTgHLKt32aSbQ/3f4ELUkoDw3zO6cDZwPPJRj7vIdsd5LKx1GsAbG5bdvXxgZV3cNP9W/ijFy7lL05/Bm3T3EJOklSf6jYANhoDoPoHBvnf31/D3/3oAU5cOpev/NFJlOfMLLosSZKeom73ApYazbTWFv7nK0/gK3/0fNZu7OXVF/6YnzywpeiyJEkaNQOgNE6vfPZivnvWKXTOms4f/f2t/P2PH3ALOUlSQzAASofguEUlvvu+U/idExbx6e/dy/v/6Q727HcLOUlSfTMASoeoNHM6F//xSfz5K7q5+ucb+IMv38x/3ruJHXsOFF2aJElDmlZ0AdJUEBH82UuP4zlHzeUDK+/gnZdlE4WWd3Vw0jFH8IJl81hxzBEcfcQsIqLgaiVJzc5ZwGPkLGCNZO/+Ae58eDu3r9/Kbeu28bOHttG7L7stvLDUxopj5rFi2RGsOGYezziyk+mtDsRLkibHcLOAHQGUJtisGa286OnzedHT5wMwOJhY+1gvq9ZtY9W6raxav41r7t6YtZ3eyvOOnsuKZfM46Zh5PP+YeXTOnF5k+ZKkJuAI4Bg5AqiJsHHHPlat38qqddu4ff027tmwk4HBRAR0d5VYkd8yXrFsHkfN9baxJGl8XAh6ghgANRl29/Vz58Pbs1HC9Vu546Ht7OrLbhuXO2dy0rJ5rDhmHi9YdgQ95RLTvG0sSRoFbwFLdWx22zROOW4Bpxy3AICBwcTqjTu5ff22J24df++uDQC0z2jlxKVznxghPHHpPDra/J+yJGn0HAEcI0cAVZRfbd/LqvXbuH1dNrlk9cadDCZoCegpd/KCZfM4KZ9ccuTcWUWXK0mqA94CniAGQNWL3n0HuPPh7dy2bhu357eN9+wfAODIOTOzmcb55JKecietLT5HKEnNxlvA0hRTmjmdFx+/kBcfvxCA/oFBVm/s5bZ8pvFPH9zKv/3XrwDoaJv2a7eNn3f0XGZ721iSmpYjgGPkCKAaRUqJR7fvfWJiyap121izqZeUoLUleMbiTk7KJ5asWDaPrs6ZRZcsSZpg3gKeIAZANbIdew9wx0PbnphccsfD29h3YBCAJfNmPblI9bJ5LF9UosXbxpLU0LwFLIk5s6bz0u5FvLR7EQAHBga551c7WbU+m2l80y+38J07s9vGpZnTOOmYbPmZk445gucdPZdZM1qLLF+SNEEcARwjRwA1laWUeHjrXlbl29jdvn4razftAmBaS/DMo+aw4ph5PGfJHI6cO4sj586iq9TmuoSSVKccAZQ0oohg6fx2ls5v5/XPXwLAjj0H+NlD256YXHL5T9bT1z/4RJ+WgK7OmRw5dxaL58zkqPxYCYhHzp3FvPbp7mYiSXXEACjpoOa0T+e3ehbxWz3ZbeP9/YOs37KbX+3Yx6+272XD9r08un0fG3bs5e5Hd/D9ezaxvyogAsyc3sKRc2Y9ERKzYFgJjdl/t8/wnyNJOlz8F1fSmMyY1sLxXSWO7yoNeT2lxJbd+9mwfR+Pbt+bhcQde/nV9n38asdebrhvM4/19lH79Mnc9ul5SHxy9PCJEUVvNUvShDIASppQEcGCjjYWdLTx7CVzhmxzYGCQjTv2sSEfRXy0KiQ+sm0vP31wKzv39f9an6FuNR9Zc7vZW82SNDoGQP3/7d13lKRVncbx71Ohe6Z7YBKgqyAginFNYMCwBBUUXUzo6ppwF/WoLAYMYFjDGjAjrAEVz7iurh4xr6yyCoiICbPHQJrBZQCFiUz3dFdX12//uLe6q6urpqunQ3Vbz+ecOm/Ve2+97+2pmepn7r3vfc0WXblY4KB1Axy0bqBtnV2jVW7evnvaUPNN22c31Jx6EHNIXL3SVzKbmeEAaGZL1Kr+UkdDzTdtz8PLDb2Im7e3H2peO1DO8w4b5yFO9ige4KFmM+sBDoBmtiw1DjXf78DWdSrVGn/eWQ+HI01DzcP8ZOOWtkPN61f1sXagj3WD+THQx9rBPtYPpm19/5qVZQdGM1t2HADN7K9WX6nzoebNOSTWw+LWoQpbhyrcsGWYbUMVbh+ttj3G6pXliWCYQmOZdYP9rBsss3agb1qYXNVf8lxFM+sqB0Az62kzDTXXVao1tg2nULhtqMKWoUrL15u37+Y3m7ezbWiMynit5bHKRU0JhGtzD2Pj6/WDk6Fx7WCZ/pLnLprZ/HEANDPrQF+pwB32XcEd9l3RUf2IYKgyztZdFbYON4TEoemvf3/zTrYOVdg+PNb2eKv6S6wdLE8ExYnQuKrF8PRAH6tXln0vZzNrywHQzGwBSGJVf4lV/SXusr79EHSj6niNHbvHJoaftw03hMahsYnXt+2qcPWfd7F1qMLusfGWxyoI1g5M7V1McxfT8PQ+K1LbBvtLDPYVGeyffD3QV6S/VPAwtdlfMQdAM7MlolQssH5VP+tX9Xf8nt2V8Ymh6K0Nw9JTQuSuCtfftoutN6QQOV6b+R7wpYKmhMP0KDLYl4LiQH8OjX0lBvpLrOpvqNeX6q7qrEQY6QAAEgZJREFULzGQ668oO1CaLSUOgGZmy9jKviIr+9ISNp2o1YKdI2PcPlJlqFJlaLTK0Og4Q6NVdo3m15XxvH/y+a7RKsOVcbbsGp5Sr3ktxnYKIgfDHCQnguLk61UN4XGwRe/kQF9xopdyZbnoIW6zOXAANDPrIYWCWDPQx5qBvnk53th4bXpQHB1vCIlTA+Zwfl1/vnn77oawWWVkrLNAKcFAuSEcTumdTD2SK8spTA70pfCYHqlu/b3N+7ykj/UKB0AzM9tr5WIhB8r5OV51vMZQZTwHxSq7RscZrvdOViZfT5RVpvZc3rJzZKJsd6XK8Nj4tMXA96SvVGCgL4XJKaGxr8hAf4mBcnEibK7sKzLYGCDz84my/iID5VRWdrC0JcYB0MzMloxSscDqlQVWryzPy/EigpGxGsOVNIQ9XBlnqJJ6KRv31Z9PljWWV7ll51gqH62yO9frYCrlhHJRORwWczhMw9iD/U1BckpZkZWN78nD4yv7UhDtKxUoFUW5UPBwuM2aA6CZmf3VkpTnSRZZP4/HjQhGq7WmoJh7J1vsGx6bLKsHyOHKOH+5fSTXmdzXyUU6zYoFUc5hsFQU5WIhP0SpWKBUUAqMhell5Vy/VCjQVxKlfIy+4tRjTb4315/yXlEuFSgXph93Sv1C/fnkcYsOr13hAGhmZjZLklhRLrKiXGTd4PzMp4QULCvjtRwS0zD2UEOPZOO+sfEa1VpQqdao1mpUx9N7q+PB2HiNsfGgWqtNPB9rKBuuVBveO7Ws/rySj783gXQ2CmIyHJZyEK0H1xxqyzmYlovTA+rUYDlZp1xqDsQNx5gSiut1JoPw9HDcEIQbgvZy7oF1ADQzM1siJNFfKtJfKs7bvMq5qtWCsVqLYFlN+6cExvGgOl6bGkRrad+0IJqPUa3VpgXXVGfyvVOOX6uxe2zqcZrb1hhmFzi/AqkHtrGHtB5Kp4TIhgBaD6vnPfOBrB6Yn+kOs+UAaGZmZm0VCqK/UKR/mSaGdgG2uce03hM61hA0m3tOJ+vkYNrUAztRvzZZZ6wWjDX1tFaq6WInuthxuEw/TjMzM7OZLfcAu1B8XbqZmZlZj3EANDMzM+sxDoBmZmZmPcYB0MzMzKzHOACamZmZ9RgHQDMzM7Me4wBoZmZm1mMcAM3MzMx6TE8FQEkHSvqUpJskjUraJOkcSWu73TYzMzOzxdIz62JLOgy4EjgA+BrwB+AhwMuBx0l6RERs6WITzczMzBZFL/UAfoQU/k6PiCdHxJkRcRzwQeAewDu62jozMzOzRdITATD3/h0PbAI+3FT8ZmAIeK6kwUVumpmZmdmi64kACBybtxdHRK2xICJuB34ADAAPW+yGmZmZmS22XgmA98jbq9uUX5O3hy9CW8zMzMy6qlcC4Oq83dGmvL5/TatCSS+SdJWkq2699dZ5b5yZmZnZYuqVADgnEfHxiDgyIo7cf//9u90cMzMzsznplQBY7+Fb3aa8vn/7IrTFzMzMrKt6JQD+MW/bzfG7e962myNoZmZm9ldDEdHtNiy4vAzMtaRlYA5rvBJY0j7AzYCAAyJiaIZj3QrcsHCt7Qn7Abd1uxE2J/4Mlz9/hsufP8PlbbE+v4MjYtr8tZ64E0hEXCfpYtJagC8DzmsofiswCJw/U/jLx/IkwDmSdFVEHNntdtje82e4/PkzXP78GS5v3f78eiIAZi8l3QruXEmPBn4PPJS0RuDVwBu62DYzMzOzRdMrcwCJiOuAI4ENpOB3BnAY8CHgYb4PsJmZmfWKXuoBJCL+D3hBt9thfLzbDbA582e4/PkzXP78GS5vXf38euIiEDMzMzOb1DNDwGZmZmaWOACamZmZ9RgHQFtwktZLOlXSVyRdK2m3pB2SrpD0z5L893AZkvQcSZEfp3a7PdYZSY/O/xZvkTQq6SZJ35Z0YrfbZjOT9ARJF0u6MX+XXi/pi5KO6nbbLJF0sqTzJH1f0s78HfmfM7zn4ZIukrQ1f66/lvQKScWFamdPXQRiXfN04KOkBbcvBf4E3AF4KvBJ4PGSnh6ekLpsSDoI+HdgF7Cqy82xDkl6D/Aa4Ebg66RFaPcHjgCOAS7qWuNsRpLeDbwW2AJ8lfT53Q14EvA0Sc+LiD0GDVsUbwTuT/p+vBG4554qS3oS8CVgBPgCsBX4e+CDwCNIv0PnnS8CsQUn6TjSYtvfbLoLyx2BnwAHASdHxJe61ESbBUkC/hc4FPgy8GrghRHxya42zPZI0gtJVx1+GnhRRFSayssRMdaVxtmM8vflZuBW4H4R8ZeGsmOBS4CNEXHXLjXRsvx53Ei6A9nRpI6Pz0bEc1rU3TfXWw08IiKuyvtXkD7To4BnRcTn57udHnqzBRcRl0TENxrDX95/C/Cx/PKYRW+Y7a3TgeNISyrNePcc6z5J/cA7SL3v08IfgMPfkncw6Xf2jxvDH0BEXArcTurNtS6LiEsj4poOR7VOJn1un6+Hv3yMEVJPIsBLFqCZDoDWdfVfOtWutsI6IulewNnAhyLi8m63xzr2WNIvmS8DtTyP7HWSXu65Y8vGNUAFeIik/RoLJP0dsA/wnW40zObkuLz9Vouyy4Fh4OH5P3HzynMArWsklYDn5Zet/vLbEpI/r8+QepFe3+Xm2Ow8OG9HgF8A920slHQ5aRrGrYvdMOtMRGyV9DrgA8DvJH2VNBfwMOAk0rSMF3exibZ37pG3VzcXRERV0kbgPsBdSbewnTcOgNZNZ5N+EV0UEd/udmNsRv8KPBB4ZETs7nZjbFYOyNvXAL8DHgX8kjSP833A8cAX8VSMJS0izpG0CfgU8MKGomuBDc1Dw7YsrM7bHW3K6/vXzPeJPQRsXSHpdNL9mP8APLfLzbEZSHooqdfv/RHxw263x2at/l1fBU6KiCsiYldE/AZ4CmnC+tEeDl7aJL0WuJB0T/vDSBfXHQFcD3w2X+Vt1hEHQFt0kk4DPkTqiTg2IrZ2uUm2B3no9z9IQxRv6nJzbO9sz9tfRMSmxoKIGAbqPfAPWcxGWeckHQO8G/h6RLwqIq6PiOGI+DkpxG8GzpDkq4CXl3oP3+o25fX929uU7zUHQFtUkl4BnAf8lhT+bulyk2xmq4DDgXsBIw2LPwfw5lznE3nfOV1rpe3JH/O23S+RbXm7chHaYnvniXl7aXNBDvE/If1Of+BiNsrmrP5v8/Dmgvyf70NJPffXz/eJPQfQFk2ewHw2ae7RYyPiti43yTozClzQpuxBpF84V5C+yDw8vDR9Fwjg3pIKzUsyMXlRyMbFbZbNQv0q0HZLvdT3T1vix5a0S4BnA48D/qup7O+AAeDyiBid7xO7B9AWhaQ3kcLfz4BHO/wtHxGxOyJObfUg3U0C4NN53xe62VZrLSJuAL4B3AV4eWOZpOOBE0i9g74af+n6ft6+SNKdGwskPZ50x4gR4MrFbpjNyYWkO7o8U9KR9Z15Iei355cfXYgTuwfQFpyk5wNvA8ZJX2Knp5tJTLEpIjYsctPMesnLSL21H5D0BNJyMIcCTyb92zw1ItpdiWjddyFpnb/HAL+X9BXgFtLUjCcCAs6MiC3da6IBSHoy6d8VwB3z9ihJG/Lz2yLi1QARsTPfpedC4DJJnyfdCu4k0hIxF5JuDzfvHABtMRyat0XgFW3qfI90ZZuZLYCIuFHSEaTlfE4iDS/tJPUMvisiftLN9tmeRURN0omkIP9M0oUfA6SwcBFwbkRc3MUm2qQHAM9v2nfX/AC4gXQLTQAi4quSjgbeADwNWEFa2udVpM91Qe7Z63sBm5mZmfUYzwE0MzMz6zEOgGZmZmY9xgHQzMzMrMc4AJqZmZn1GAdAMzMzsx7jAGhmZmbWYxwAzczMzHqMA6CZ2SxJKkt6q6RrJI1Kirz6/3wd/zJJXqTVzBaMA6CZdU0OTiHphnzvy1Z1NuU6S+nORWeQ7qhxE/A+4K3AH7raojmQdEj+M97Q7baY2eJYSl+oZta77kK6TeDZ3W5Ih54I7AIeGxGVbjfGzGy23ANoZt22jXQ/0zMl7dftxnToTsAWhz8zW64cAM2s24aBfwNWA2+ezRslPUPS5ZJ2SNot6TeSzpLUP8vjrJb0Lkl/lDQiaZukb0t6TFO9DXlu3qHAwQ1D2Js6PM86Se+Q9FtJw7ndv5J0tqTBGd57Sj7XKW3KQ9JlTfv2kfSmfL6dkm6XdJ2kL0g6Itd5C7Axv+X5DT/TtHNJOkHSRZJuy3Mfr5P0XklrWrRnU37sK+kD+flYPl9HbTOzheMhYDNbCj4MnAa8WNK5EXHNTG+Q9E7gLOA24HOkIdnHA+8ETpB0fCc9dDm8/AC4N/BT4BxgP+AZwMWSXhIR5+fqXwU2kYaryXUBtndwnkOBS4GDgZ8BHyX9J/xw4JXAx4ChmY7TKUkCvgU8HPgh8EmgChwIHAt8P7fjMmAN8HLgV6Sfse6XDcd7M/AWUm/tfwN/Ae4HvBo4UdJREbGzqRl9wCXAOuBiYCewcRZtM7OFEhF++OGHH115AAHcmJ+fnF9/uanOpry/1LDvqLzvT8AdG/aXgG/kstd32Ibzc/3zATXsvzuwAxgFDmnRpk2z/FmvzOc5q0XZfsCKhteXpa/nKXVOye8/ZQ9/lpc1vP7bvO8rLeoWgLUNrw/JdTe0OfaxufxKYE2bdn2wzef2HWCwqazjtvnhhx8L8/AQsJktCRFxIak36CmSHjlD9X/K27dHxC0Nx6iSrtCtAafOdE5JfcBzSL2HZ0XExNIrkXohzyX1Yj1vFj9Kq/McQQqtvwTe3VweEbdFxMhczrEHu1ucrxYR22ZxjNPz9oURMaW3MyI2kH6uZ7d57xkR0a5ncz7aZmZ7wUPAZraUnEHqZXof8LA91HtQ3l7SXBARV0u6EThU0uqI2LGH49wDGAB+EBFbW5RfArwReGAnjd+D+s/y7YiozfFYnfodKZg9S9LBwNeAK4CrYvYXrxwFjAFPl/T0FuV9wP6S1kfElob9I8CvF7htZrYXHADNbMmIiB9KuhA4WdI/RMQX2lRdnbc3tym/mbS0zBrSMG47nRyHfJy5qL9/8xyP07GIGJd0HGm9wpOZ7Hm8XdKnST2euzo83HrS74uZLtJZBTQGwL809qouUNvMbC94CNjMlpqzSL1N78pDtK3UQ90d25T/TVO9dubrODOpD5veeQ7HqPccTvuPe6urcAEiYltEvDIiDiLNaTyVtGD1aaSLUDq1A9gWEZrhcUNzE9odcB7bZmZ7wQHQzJaUiLgW+AhpqZV/aVPtF3l7THOBpLuRribd2DxfrYU/kpahuX+bEHVs3v58huPM5Ed5e4Kkvf3erc+LO6hF2ZEzvTkiro2IC4CjSXMen9RQPJ63xTZv/xGwVtJ9OmzrrMzQNjNbAA6AZrYUvY3Ua/YG0rBis0/l7Rsl7V/fKalImj9YAC6Y6SR5vtlngX1IaxFOkHQY6eKHMeAzs/8RppznZ6S5jQ8AXtdcLml9u1vhNbiK1Av4j5IGGt67DnhPi2MeKumuLY6zFuhn6gUY20i9dXdpc+4P5u0nJN2pxbkGJe1pzuZc2mZmC8BzAM1syYmIrXmdv2nBJpdfKek9wGuB3+Z5g0OkdQDvS7qg4L0dnu5M4FHAaZIeTFqrr74O4D7AaRGxcQ/v79RzSMu7vFPS0/JzkYY/jwfuSVo6paWIuFnSZ4HnAr+U9E1gX+BE4HKmX6hyf+DLkn4K/J503+L9Sb1rZRquRo6IXZJ+DDwqn+NqUq/g1yPi1xHxXUlnAu8CrpF0EWnx6FWkdQ2PJv2ZP67DP4uO22ZmC0Mt5ueamS2KfFeNzRFxYIuyftKcsEPyrnJe5qWxzjNJc8buTwoO15EWhX7/bJZVycO/ZwFPJfWC7SYtCv3eiLi4Rf1NABFxSHPZDOdZTwqtTyYFpxFS6Psm8I6IGM71LgOOjgg1vb8feDvwLOAA0jqIF5DC7hjwvYg4Jtc9EHgpKZwdRupduxX4DXBuRPxP07HvRurpe3iuK+AFeZmXep1HknpFH0kKyTtIF7ZcAnwuIq7q5M9otm0zs/nnAGhmZmbWYzwH0MzMzKzHOACamZmZ9RgHQDMzM7Me4wBoZmZm1mMcAM3MzMx6jAOgmZmZWY9xADQzMzPrMQ6AZmZmZj3GAdDMzMysxzgAmpmZmfWY/wdkDYiNLWVUUwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xvYtOdZb-lJr"
      },
      "source": [
        "As you can see in the graph above, the \"elbow\" can be seen around 3! OK. Let's change our k from 5 ro 3:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qlpDM-wynxz-",
        "outputId": "0cabc7cb-aa13-40ec-c0df-db39041ddbee"
      },
      "source": [
        "x = df[df.columns[:-1]].values\n",
        "kmeans3 = KMeans(n_clusters=3)\n",
        "y_kmeans3 = kmeans3.fit(x)\n",
        "print(y_kmeans3.cluster_centers_)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[5.006      3.428      1.462      0.246     ]\n",
            " [5.9016129  2.7483871  4.39354839 1.43387097]\n",
            " [6.85       3.07368421 5.74210526 2.07105263]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SyRgzLcurMoR",
        "outputId": "72f92271-65e0-49e7-d7c0-80cf4a9c107b"
      },
      "source": [
        "k_means_test = y_kmeans3.predict(x)\n",
        "print(k_means_test)"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
            " 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
            " 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2 2 1 2 2 2 2\n",
            " 2 2 1 1 2 2 2 2 1 2 1 2 1 2 2 1 1 2 2 2 2 2 1 2 2 2 2 1 2 2 2 1 2 2 2 1 2\n",
            " 2 1]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        },
        "id": "zRLRsmoxrOP1",
        "outputId": "001d8fa0-06c6-48be-f9dc-1b6190e78e5b"
      },
      "source": [
        "#[ : , 0 ] means (more or less) [ first_row:last_row , column_0 ]. If you have a 2-dimensional list/matrix/array, this notation will give you all the values in column 0 (from all rows)\n",
        "plt.scatter(x[:,0],x[:,1],c=k_means_test, cmap='rainbow')"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7ff3ce02a518>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GHt7DQn3BzlT"
      },
      "source": [
        "##Agglomerative Hierarchical Clustering\n",
        "\n",
        "Agglomerative clustering starts with the points as individual clusters, and step by step merges the closest clusters. \n",
        "\n",
        "This cluster usually visualized with a \"tree-like\" dendogram. [1:P.515]\n",
        "\n",
        "Ward's method (see dendogram below) assumes each cluster is represented by its centroid, and measures the proximity between any two clusters by the increase in SSE (see above) resulting from merging two clusters represented by their respective centroids. [1:P.517]\n",
        "\n",
        "Check more from [this example](https://towardsdatascience.com/machine-learning-algorithms-part-12-hierarchical-agglomerative-clustering-example-in-python-1e18e0075019)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "4Drno9-M_7vN",
        "outputId": "b3bb1cee-d409-46b1-e9bf-1edb3033fc81"
      },
      "source": [
        "import scipy.cluster.hierarchy as sch\n",
        "from sklearn.cluster import AgglomerativeClustering\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "clustering = AgglomerativeClustering(n_clusters=3,affinity='euclidean', linkage='ward')\n",
        "clustering.fit(x)\n",
        "clustering_class = clustering.fit_predict(x)\n",
        "\n",
        "display(clustering_class)\n",
        "labels = clustering.labels_\n",
        "\n",
        "plt.figure(figsize=(20,17))\n",
        "dend = sch.dendrogram(sch.linkage(x, method='ward'))\n",
        "plt.show()"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
              "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
              "       1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2,\n",
              "       2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2,\n",
              "       2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0])"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 1440x1224 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "29JdKGTTHPJf"
      },
      "source": [
        "We can also plot the resulting cluster to see what it looks like.\n",
        "\n",
        "Compare this to our earlier analysis using K-means. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        },
        "id": "CHa_SjIsEoDN",
        "outputId": "136b75e4-7dd5-43fb-8fd5-ca17e9db759d"
      },
      "source": [
        "plt.scatter(x[labels==0, 0], x[labels==0, 1], s=50, marker='o', color='red')\n",
        "plt.scatter(x[labels==1, 0], x[labels==1, 1], s=50, marker='o', color='blue')\n",
        "plt.scatter(x[labels==2, 0], x[labels==2, 1], s=50, marker='o', color='green')"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7ff3cd73cd30>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}