Análise_de_Correspondência.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Análise de Correspondência.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "DdM1jD-HSVgO",
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        "m81wfANyR51b",
        "j-OKZ4KV5d37",
        "llkW7NGGo5ds",
        "cg6LIm4nMg_M",
        "OWmMMCBvJTjQ",
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      ]
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UXN09MDVKFIg"
      },
      "source": [
        "#Análise de Correspondência"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DdM1jD-HSVgO"
      },
      "source": [
        "##Introdução"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O43orsSRxfMn"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "75AdgmWfxvmt"
      },
      "source": [
        "A análise de correspondência simples é baseada em resultados clássicos bastante diretos na teoria de matrizes. O\n",
        "resultado central é a decomposição de valor singular (SVD), que é a base de\n",
        "muitos métodos multivariados, como análise de componente principal, \n",
        "análise de correlação canônica, todas as formas de biplots lineares e análises discriminantes."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QnSiEMdlJVJ3"
      },
      "source": [
        "##Instalar e Importar Libs "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "L8FUiiZLQfbx",
        "outputId": "c7ff6b5e-fdfa-41fa-f34f-16267bbd7ed5"
      },
      "source": [
        "!pip install adjustText"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: adjustText in /usr/local/lib/python3.7/dist-packages (0.7.3)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from adjustText) (1.19.5)\n",
            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from adjustText) (3.2.2)\n",
            "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->adjustText) (2.8.1)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->adjustText) (2.4.7)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.7/dist-packages (from matplotlib->adjustText) (0.10.0)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->adjustText) (1.3.1)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.7/dist-packages (from cycler>=0.10->matplotlib->adjustText) (1.15.0)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZsNpcBsoNxQX"
      },
      "source": [
        "import pandas as pd #Manipulção de DataFrames\n",
        "import numpy as np #Manipulações numéricas\n",
        "import math #Biblioteca matemática\n",
        "import matplotlib.pyplot as plt #Gráficos\n",
        "import seaborn as sns #Gráficos\n",
        "\n",
        "\n",
        "from numpy.linalg import norm #Encontrar o valor da norma matricial ou da norma vectorial\n",
        "from random import normalvariate #Variações normalizadas\n",
        "from scipy.stats import chi2_contingency #Criação de Matriz de Contigência\n",
        "from adjustText import adjust_text #Ajuste de labels gráficas\n",
        "\n",
        "np.set_printoptions(suppress=True) #Suprimir notação científica"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KeElzzjuJd1y"
      },
      "source": [
        "##Leitura da Base de dados"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "A6OkBN-RHlqe",
        "outputId": "df5dea76-bfe9-4822-c8de-dba4f3e63341"
      },
      "source": [
        "df=pd.read_csv('/content/drive/MyDrive/Dataset_Excel_CSV/covid_america_weekly.csv')\n",
        "df.head()"
      ],
      "execution_count": null,
      "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>country</th>\n",
              "      <th>week</th>\n",
              "      <th>cumulative_cases</th>\n",
              "      <th>cumulative_deaths</th>\n",
              "      <th>population</th>\n",
              "      <th>std_cum_cases</th>\n",
              "      <th>std_cum_deaths</th>\n",
              "      <th>lethality</th>\n",
              "      <th>lethality_Q5</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Anguilla</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>15002.0</td>\n",
              "      <td>0.0002</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>L1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Anguilla</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>15002.0</td>\n",
              "      <td>0.0002</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>L1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Anguilla</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>15002.0</td>\n",
              "      <td>0.0002</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>L1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Anguilla</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>15002.0</td>\n",
              "      <td>0.0002</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>L1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Anguilla</td>\n",
              "      <td>5</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>15002.0</td>\n",
              "      <td>0.0002</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>L1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    country  week  cumulative_cases  ...  std_cum_deaths  lethality  lethality_Q5\n",
              "0  Anguilla     1                 3  ...             0.0        0.0            L1\n",
              "1  Anguilla     2                 3  ...             0.0        0.0            L1\n",
              "2  Anguilla     3                 3  ...             0.0        0.0            L1\n",
              "3  Anguilla     4                 3  ...             0.0        0.0            L1\n",
              "4  Anguilla     5                 3  ...             0.0        0.0            L1\n",
              "\n",
              "[5 rows x 9 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iHrJq217JhVn"
      },
      "source": [
        "##Análise dos dados"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z17KThKXRr9Z"
      },
      "source": [
        "Para o exemplo, iremos utilizar 2 variáveis: Países e o grau de Letalidade. Ambas são categóricas (Extremamente importante)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k4Iw-9vj5T7D"
      },
      "source": [
        "####Verificar todos os países utilizados"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "OlhHEuhp5GgE",
        "outputId": "ccda6df4-53e3-4b7a-8652-ba9c5e5cb816"
      },
      "source": [
        "pd.DataFrame({'Países': df['country'].sort_values().unique()}) "
      ],
      "execution_count": null,
      "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>Países</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Anguilla</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Antigua And Barbuda</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Argentina</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Aruba</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Bahamas</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>Barbados</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>Belize</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>Bermuda</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>Bolivia</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>Bonaire, Saint Eustatius And Saba</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>Brazil</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>British Virgin Islands</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>Canada</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>Cayman Islands</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>Chile</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>Colombia</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>Costa Rica</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>Cuba</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>Curaçao</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>Dominica</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>Dominican Republic</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>Ecuador</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>El Salvador</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>Falkland Islands (Malvinas)</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>Greenland</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>Grenada</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td>Guatemala</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>Guyana</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td>Haiti</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td>Honduras</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>30</th>\n",
              "      <td>Jamaica</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>31</th>\n",
              "      <td>Mexico</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>32</th>\n",
              "      <td>Montserrat</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>33</th>\n",
              "      <td>Nicaragua</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>34</th>\n",
              "      <td>Panama</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>35</th>\n",
              "      <td>Paraguay</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>36</th>\n",
              "      <td>Peru</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>37</th>\n",
              "      <td>Puerto Rico</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>38</th>\n",
              "      <td>Saint Kitts And Nevis</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>39</th>\n",
              "      <td>Saint Lucia</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>40</th>\n",
              "      <td>Saint Vincent And The Grenadines</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>41</th>\n",
              "      <td>Sint Maarten</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>42</th>\n",
              "      <td>Suriname</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>43</th>\n",
              "      <td>Trinidad And Tobago</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>44</th>\n",
              "      <td>Turks And Caicos Islands</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>45</th>\n",
              "      <td>United States Of America</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>46</th>\n",
              "      <td>United States Virgin Islands</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>47</th>\n",
              "      <td>Uruguay</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>48</th>\n",
              "      <td>Venezuela</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                               Países\n",
              "0                            Anguilla\n",
              "1                 Antigua And Barbuda\n",
              "2                           Argentina\n",
              "3                               Aruba\n",
              "4                             Bahamas\n",
              "5                            Barbados\n",
              "6                              Belize\n",
              "7                             Bermuda\n",
              "8                             Bolivia\n",
              "9   Bonaire, Saint Eustatius And Saba\n",
              "10                             Brazil\n",
              "11             British Virgin Islands\n",
              "12                             Canada\n",
              "13                     Cayman Islands\n",
              "14                              Chile\n",
              "15                           Colombia\n",
              "16                         Costa Rica\n",
              "17                               Cuba\n",
              "18                            Curaçao\n",
              "19                           Dominica\n",
              "20                 Dominican Republic\n",
              "21                            Ecuador\n",
              "22                        El Salvador\n",
              "23        Falkland Islands (Malvinas)\n",
              "24                          Greenland\n",
              "25                            Grenada\n",
              "26                          Guatemala\n",
              "27                             Guyana\n",
              "28                              Haiti\n",
              "29                           Honduras\n",
              "30                            Jamaica\n",
              "31                             Mexico\n",
              "32                         Montserrat\n",
              "33                          Nicaragua\n",
              "34                             Panama\n",
              "35                           Paraguay\n",
              "36                               Peru\n",
              "37                        Puerto Rico\n",
              "38              Saint Kitts And Nevis\n",
              "39                        Saint Lucia\n",
              "40   Saint Vincent And The Grenadines\n",
              "41                       Sint Maarten\n",
              "42                           Suriname\n",
              "43                Trinidad And Tobago\n",
              "44           Turks And Caicos Islands\n",
              "45           United States Of America\n",
              "46       United States Virgin Islands\n",
              "47                            Uruguay\n",
              "48                          Venezuela"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m81wfANyR51b"
      },
      "source": [
        "####Verificar os graus de letalidade utilizados"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jAuiqDraR-DI",
        "outputId": "504cc14a-9ae0-43ce-e09e-77a988545217"
      },
      "source": [
        "pd.DataFrame({'Letalidade': df['lethality_Q5'].sort_values().unique()}) "
      ],
      "execution_count": null,
      "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>Letalidade</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>L1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>L2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>L3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>L4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>L5</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "  Letalidade\n",
              "0         L1\n",
              "1         L2\n",
              "2         L3\n",
              "3         L4\n",
              "4         L5"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j-OKZ4KV5d37"
      },
      "source": [
        "##Criação da tabela de frequências"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BLy6CfQuQvJy"
      },
      "source": [
        "A tabela de frequências busca apresentar o número de vezes que uma determinada variável assume um determinado valor.\n",
        "\n",
        "OBS: A tabela de frequências é usada para variáveis categóricas, pois no caso de variáveis contínuas a maior parte dos valores terá frequência 1, assim, não vamos conseguir atingir o objetivo de resumir os dados. Neste caso, que não será abordado no exemplo, a solução seria criar intervalos que conteriam essas variáveis, sendo que esses intervalos seriam variáveis categóricas."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oWda_O5hUFft",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "783851bc-60d6-44bd-aae0-601c1fb46098"
      },
      "source": [
        "tab=pd.crosstab(index=df['country'], columns=df['lethality_Q5']).to_numpy()\n",
        "tab"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[67,  0,  0,  0,  0],\n",
              "       [ 2,  0,  9, 42, 15],\n",
              "       [ 0,  1, 35, 28,  6],\n",
              "       [ 4, 47,  3, 13,  0],\n",
              "       [ 2,  1, 49,  1, 16],\n",
              "       [ 1, 28,  5, 11, 23],\n",
              "       [ 0, 11, 13, 26, 17],\n",
              "       [ 2, 17, 14,  2, 33],\n",
              "       [ 0,  0,  0, 15, 53],\n",
              "       [23, 32, 10,  1,  0],\n",
              "       [ 3,  0,  8, 46, 15],\n",
              "       [11, 35,  1,  1, 19],\n",
              "       [ 8,  2, 18, 19, 30],\n",
              "       [68,  0,  0,  0,  0],\n",
              "       [ 3,  9, 24, 34,  0],\n",
              "       [ 0,  2,  1, 61,  5],\n",
              "       [ 4, 66,  0,  0,  0],\n",
              "       [ 0, 33, 16, 13,  6],\n",
              "       [50, 17,  0,  0,  0],\n",
              "       [68,  0,  0,  0,  0],\n",
              "       [ 3, 33, 23,  7,  6],\n",
              "       [ 2,  0,  1,  2, 67],\n",
              "       [ 1,  0,  8, 57,  2],\n",
              "       [66,  0,  0,  0,  0],\n",
              "       [68,  0,  0,  0,  0],\n",
              "       [41, 27,  0,  0,  0],\n",
              "       [ 2,  0,  6, 52,  9],\n",
              "       [ 2,  0, 25, 24, 18],\n",
              "       [ 2,  1, 40, 19,  6],\n",
              "       [ 1,  0, 11, 47, 10],\n",
              "       [ 1, 20, 44,  2,  2],\n",
              "       [10,  1,  1,  0, 66],\n",
              "       [ 4,  0,  0,  0, 64],\n",
              "       [ 0,  0,  4, 54, 10],\n",
              "       [ 0,  1, 59,  9,  0],\n",
              "       [ 0, 16, 38,  9,  6],\n",
              "       [ 1,  0,  0,  0, 69],\n",
              "       [ 0,  0, 39, 15, 13],\n",
              "       [64,  3,  0,  0,  0],\n",
              "       [34, 27,  8,  0,  0],\n",
              "       [47, 20,  0,  0,  0],\n",
              "       [ 0, 25,  8, 13, 21],\n",
              "       [ 1,  5, 51,  2,  9],\n",
              "       [ 1,  4, 41,  4, 19],\n",
              "       [ 0, 49,  2,  3, 13],\n",
              "       [ 5,  1, 39, 18, 14],\n",
              "       [ 0, 46,  8,  1, 12],\n",
              "       [ 2, 35, 11, 21,  0],\n",
              "       [ 1, 61,  2,  4,  1]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "llkW7NGGo5ds"
      },
      "source": [
        "##Calcular Qui²"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0s0cB5-566TH"
      },
      "source": [
        "Antes de iniciar qualquer análise, devemos verificar se as relações entre as nossas variáveis se dá ou não de forma aleatória.\n",
        "\n",
        "O objetivo de se analisar a distribuição conjunta de duas variáveis qualitativas, é descrever a\n",
        "associação entre elas. Esperamos que haja uma certa dependência entre as variáveis.\n",
        "\n",
        "Ao fazer isso estamos realizando um Teste de Hipóteses:\n",
        "\n",
        "H0 (Hipótese Nula): Aleatoriedade de associação (Não há associação).\n",
        "H1 (Hipótese Alternativa): Existência de associação.\n",
        "\n",
        "Buscamos refutar a hipótese nula. Para isso usaremos o Teste de Independência (Qui²):"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KLta_CCX615P"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0zoiLAA6-C31"
      },
      "source": [
        "Onde:\n",
        "\n",
        "n: total de frequências\n",
        "nij: frequência na linha e coluna\n",
        "ni: frequência na linha\n",
        "nj: frequência na coluna\n",
        "\n",
        "O produto de ni e nj normalizado por n é a frequência esperada para nij no objetivo de independência. Quanto maior o Qui² maior é a certeza de independência."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Uu-E7Z1uWu2w"
      },
      "source": [
        "soma_total = np.sum(tab)\n",
        "\n",
        "matriz_correspondencia = np.divide(tab,soma_total)\n",
        "\n",
        "total_linha = np.sum(matriz_correspondencia, axis=1)\n",
        "\n",
        "total_colunas = np.sum(matriz_correspondencia, axis=0)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JPBDAuUv_qrN"
      },
      "source": [
        "Cálcular o produto dos vetores das linhas e colunas"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PwSP5tmvo4-P",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8f78d3f9-0e28-48dd-f322-b12a022fba6a"
      },
      "source": [
        "modelo_independencia = np.outer(total_linha, total_colunas)\n",
        "modelo_independencia"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.00396567, 0.00397154, 0.00396567, 0.00397154, 0.00396567],\n",
              "       [0.00402486, 0.00403082, 0.00402486, 0.00403082, 0.00402486],\n",
              "       [0.00414324, 0.00414937, 0.00414324, 0.00414937, 0.00414324],\n",
              "       [0.00396567, 0.00397154, 0.00396567, 0.00397154, 0.00396567],\n",
              "       [0.00408405, 0.0040901 , 0.00408405, 0.0040901 , 0.00408405],\n",
              "       [0.00402486, 0.00403082, 0.00402486, 0.00403082, 0.00402486],\n",
              "       [0.00396567, 0.00397154, 0.00396567, 0.00397154, 0.00396567],\n",
              "       [0.00402486, 0.00403082, 0.00402486, 0.00403082, 0.00402486],\n",
              "       [0.00402486, 0.00403082, 0.00402486, 0.00403082, 0.00402486],\n",
              "       [0.00390648, 0.00391227, 0.00390648, 0.00391227, 0.00390648],\n",
              "       [0.00426161, 0.00426793, 0.00426161, 0.00426793, 0.00426161],\n",
              "       [0.00396567, 0.00397154, 0.00396567, 0.00397154, 0.00396567],\n",
              "       [0.00455756, 0.00456431, 0.00455756, 0.00456431, 0.00455756],\n",
              "       [0.00402486, 0.00403082, 0.00402486, 0.00403082, 0.00402486],\n",
              "       [0.00414324, 0.00414937, 0.00414324, 0.00414937, 0.00414324],\n",
              "       [0.00408405, 0.0040901 , 0.00408405, 0.0040901 , 0.00408405],\n",
              "       [0.00414324, 0.00414937, 0.00414324, 0.00414937, 0.00414324],\n",
              "       [0.00402486, 0.00403082, 0.00402486, 0.00403082, 0.00402486],\n",
              "       [0.00396567, 0.00397154, 0.00396567, 0.00397154, 0.00396567],\n",
              "       [0.00402486, 0.00403082, 0.00402486, 0.00403082, 0.00402486],\n",
              "       [0.00426161, 0.00426793, 0.00426161, 0.00426793, 0.00426161],\n",
              "       [0.00426161, 0.00426793, 0.00426161, 0.00426793, 0.00426161],\n",
              "       [0.00402486, 0.00403082, 0.00402486, 0.00403082, 0.00402486],\n",
              "       [0.00390648, 0.00391227, 0.00390648, 0.00391227, 0.00390648],\n",
              "       [0.00402486, 0.00403082, 0.00402486, 0.00403082, 0.00402486],\n",
              "       [0.00402486, 0.00403082, 0.00402486, 0.00403082, 0.00402486],\n",
              "       [0.00408405, 0.0040901 , 0.00408405, 0.0040901 , 0.00408405],\n",
              "       [0.00408405, 0.0040901 , 0.00408405, 0.0040901 , 0.00408405],\n",
              "       [0.00402486, 0.00403082, 0.00402486, 0.00403082, 0.00402486],\n",
              "       [0.00408405, 0.0040901 , 0.00408405, 0.0040901 , 0.00408405],\n",
              "       [0.00408405, 0.0040901 , 0.00408405, 0.0040901 , 0.00408405],\n",
              "       [0.00461675, 0.00462359, 0.00461675, 0.00462359, 0.00461675],\n",
              "       [0.00402486, 0.00403082, 0.00402486, 0.00403082, 0.00402486],\n",
              "       [0.00402486, 0.00403082, 0.00402486, 0.00403082, 0.00402486],\n",
              "       [0.00408405, 0.0040901 , 0.00408405, 0.0040901 , 0.00408405],\n",
              "       [0.00408405, 0.0040901 , 0.00408405, 0.0040901 , 0.00408405],\n",
              "       [0.00414324, 0.00414937, 0.00414324, 0.00414937, 0.00414324],\n",
              "       [0.00396567, 0.00397154, 0.00396567, 0.00397154, 0.00396567],\n",
              "       [0.00396567, 0.00397154, 0.00396567, 0.00397154, 0.00396567],\n",
              "       [0.00408405, 0.0040901 , 0.00408405, 0.0040901 , 0.00408405],\n",
              "       [0.00396567, 0.00397154, 0.00396567, 0.00397154, 0.00396567],\n",
              "       [0.00396567, 0.00397154, 0.00396567, 0.00397154, 0.00396567],\n",
              "       [0.00402486, 0.00403082, 0.00402486, 0.00403082, 0.00402486],\n",
              "       [0.00408405, 0.0040901 , 0.00408405, 0.0040901 , 0.00408405],\n",
              "       [0.00396567, 0.00397154, 0.00396567, 0.00397154, 0.00396567],\n",
              "       [0.00455756, 0.00456431, 0.00455756, 0.00456431, 0.00455756],\n",
              "       [0.00396567, 0.00397154, 0.00396567, 0.00397154, 0.00396567],\n",
              "       [0.00408405, 0.0040901 , 0.00408405, 0.0040901 , 0.00408405],\n",
              "       [0.00408405, 0.0040901 , 0.00408405, 0.0040901 , 0.00408405]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OjYIiV6j_DVd"
      },
      "source": [
        "Cálculo Manual do Qui²"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LyDnZhmMpCti",
        "outputId": "49f8b4cb-9c91-4439-fd3e-7a0ccfc14a17"
      },
      "source": [
        "qui2 = soma_total*np.sum(np.square(matriz_correspondencia - modelo_independencia) / modelo_independencia)\n",
        "print('Qui²: ',qui2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Qui²:  6419.643087147196\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p_50sKsS5xbX"
      },
      "source": [
        "Comparação com o teste qui² do scipy"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "178t2-JQVw9B",
        "outputId": "6947fc62-aaed-43b5-bffe-d022135812bc"
      },
      "source": [
        "qui2, p_value, _ , _ = chi2_contingency(tab)\n",
        "print('Qui²: ',qui2)\n",
        "print('p-value: {:.20f}'.format(p_value))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Qui²:  6419.643087147197\n",
            "p-value: 0.00000000000000000000\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aMdnyXlZAuqO"
      },
      "source": [
        "As diferenças são medidas por Qui² - distâncias (distâncias euclidianas ponderadas entre linhas normalizadas). \n",
        "\n",
        "Elas são calculados dividindo as entradas das linhas por seus respectivos totais das linhas. Os pesos são inversamente proporcionais às raízes quadradas dos totais das colunas."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fHM9CNbnAOSm"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HtFBEfiFpKkx"
      },
      "source": [
        "#Normalizar matriz de Correspondência\n",
        "matriz_correspondencia_norm = np.divide(matriz_correspondencia,total_linha[:, None])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YsB8V-ohpYI5"
      },
      "source": [
        "#Criar matriz de tamanho igual à nossa de correspondência\n",
        "distancias_qui2 = np.zeros((matriz_correspondencia.shape[0], matriz_correspondencia.shape[0]))\n",
        "\n",
        "total_colunas_norm = np.sum(matriz_correspondencia_norm, axis=0)\n",
        "\n",
        "for linha in range(matriz_correspondencia.shape[0]):\n",
        "    distancias_qui2[linha]=np.sqrt(np.sum(np.square(matriz_correspondencia_norm - matriz_correspondencia_norm[linha])/total_colunas, axis=1))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0Zvc7h1xB2W6"
      },
      "source": [
        "Agora vamos salvar tudo num Dataframe e verificar as distâncias geradas."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dpalXdcGp4pK",
        "outputId": "b1092c7d-9b1d-4251-cd5f-b838f93c28f3"
      },
      "source": [
        "df_distancias_qui2 = pd.DataFrame(data=np.round(distancias_qui2 * 100).astype(int))\n",
        "df_distancias_qui2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "      <th>10</th>\n",
              "      <th>11</th>\n",
              "      <th>12</th>\n",
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              "      <th>14</th>\n",
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              "      <th>18</th>\n",
              "      <th>19</th>\n",
              "      <th>20</th>\n",
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              "      <th>22</th>\n",
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              "      <th>28</th>\n",
              "      <th>29</th>\n",
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              "      <th>31</th>\n",
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              "      <th>38</th>\n",
              "      <th>39</th>\n",
              "      <th>40</th>\n",
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              "      <th>42</th>\n",
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              "      <th>44</th>\n",
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              "      <th>46</th>\n",
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              "      <th>48</th>\n",
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              "      <td>94</td>\n",
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              "      <td>281</td>\n",
              "      <td>247</td>\n",
              "      <td>276</td>\n",
              "      <td>257</td>\n",
              "      <td>296</td>\n",
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              "      <td>191</td>\n",
              "      <td>187</td>\n",
              "      <td>140</td>\n",
              "      <td>65</td>\n",
              "      <td>156</td>\n",
              "      <td>156</td>\n",
              "      <td>193</td>\n",
              "      <td>8</td>\n",
              "      <td>183</td>\n",
              "      <td>96</td>\n",
              "      <td>264</td>\n",
              "      <td>80</td>\n",
              "      <td>74</td>\n",
              "      <td>258</td>\n",
              "      <td>149</td>\n",
              "      <td>226</td>\n",
              "      <td>264</td>\n",
              "      <td>163</td>\n",
              "      <td>208</td>\n",
              "      <td>65</td>\n",
              "      <td>264</td>\n",
              "      <td>264</td>\n",
              "      <td>216</td>\n",
              "      <td>38</td>\n",
              "      <td>80</td>\n",
              "      <td>130</td>\n",
              "      <td>23</td>\n",
              "      <td>190</td>\n",
              "      <td>200</td>\n",
              "      <td>214</td>\n",
              "      <td>46</td>\n",
              "      <td>201</td>\n",
              "      <td>156</td>\n",
              "      <td>222</td>\n",
              "      <td>134</td>\n",
              "      <td>256</td>\n",
              "      <td>200</td>\n",
              "      <td>222</td>\n",
              "      <td>128</td>\n",
              "      <td>192</td>\n",
              "      <td>163</td>\n",
              "      <td>209</td>\n",
              "      <td>120</td>\n",
              "      <td>205</td>\n",
              "      <td>142</td>\n",
              "      <td>240</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>266</td>\n",
              "      <td>100</td>\n",
              "      <td>0</td>\n",
              "      <td>191</td>\n",
              "      <td>104</td>\n",
              "      <td>152</td>\n",
              "      <td>85</td>\n",
              "      <td>148</td>\n",
              "      <td>195</td>\n",
              "      <td>176</td>\n",
              "      <td>106</td>\n",
              "      <td>188</td>\n",
              "      <td>99</td>\n",
              "      <td>266</td>\n",
              "      <td>52</td>\n",
              "      <td>153</td>\n",
              "      <td>253</td>\n",
              "      <td>129</td>\n",
              "      <td>227</td>\n",
              "      <td>266</td>\n",
              "      <td>127</td>\n",
              "      <td>233</td>\n",
              "      <td>131</td>\n",
              "      <td>266</td>\n",
              "      <td>266</td>\n",
              "      <td>215</td>\n",
              "      <td>122</td>\n",
              "      <td>52</td>\n",
              "      <td>34</td>\n",
              "      <td>100</td>\n",
              "      <td>109</td>\n",
              "      <td>223</td>\n",
              "      <td>239</td>\n",
              "      <td>133</td>\n",
              "      <td>102</td>\n",
              "      <td>78</td>\n",
              "      <td>247</td>\n",
              "      <td>50</td>\n",
              "      <td>258</td>\n",
              "      <td>187</td>\n",
              "      <td>223</td>\n",
              "      <td>136</td>\n",
              "      <td>101</td>\n",
              "      <td>91</td>\n",
              "      <td>209</td>\n",
              "      <td>45</td>\n",
              "      <td>194</td>\n",
              "      <td>137</td>\n",
              "      <td>235</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>266</td>\n",
              "      <td>191</td>\n",
              "      <td>191</td>\n",
              "      <td>0</td>\n",
              "      <td>224</td>\n",
              "      <td>101</td>\n",
              "      <td>144</td>\n",
              "      <td>157</td>\n",
              "      <td>235</td>\n",
              "      <td>93</td>\n",
              "      <td>192</td>\n",
              "      <td>88</td>\n",
              "      <td>180</td>\n",
              "      <td>266</td>\n",
              "      <td>158</td>\n",
              "      <td>216</td>\n",
              "      <td>70</td>\n",
              "      <td>69</td>\n",
              "      <td>189</td>\n",
              "      <td>266</td>\n",
              "      <td>87</td>\n",
              "      <td>263</td>\n",
              "      <td>214</td>\n",
              "      <td>266</td>\n",
              "      <td>266</td>\n",
              "      <td>146</td>\n",
              "      <td>203</td>\n",
              "      <td>185</td>\n",
              "      <td>198</td>\n",
              "      <td>196</td>\n",
              "      <td>166</td>\n",
              "      <td>248</td>\n",
              "      <td>266</td>\n",
              "      <td>209</td>\n",
              "      <td>238</td>\n",
              "      <td>157</td>\n",
              "      <td>274</td>\n",
              "      <td>203</td>\n",
              "      <td>252</td>\n",
              "      <td>128</td>\n",
              "      <td>175</td>\n",
              "      <td>104</td>\n",
              "      <td>217</td>\n",
              "      <td>202</td>\n",
              "      <td>57</td>\n",
              "      <td>190</td>\n",
              "      <td>61</td>\n",
              "      <td>57</td>\n",
              "      <td>52</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>274</td>\n",
              "      <td>187</td>\n",
              "      <td>104</td>\n",
              "      <td>224</td>\n",
              "      <td>0</td>\n",
              "      <td>173</td>\n",
              "      <td>147</td>\n",
              "      <td>137</td>\n",
              "      <td>206</td>\n",
              "      <td>186</td>\n",
              "      <td>194</td>\n",
              "      <td>195</td>\n",
              "      <td>125</td>\n",
              "      <td>274</td>\n",
              "      <td>146</td>\n",
              "      <td>252</td>\n",
              "      <td>267</td>\n",
              "      <td>158</td>\n",
              "      <td>238</td>\n",
              "      <td>274</td>\n",
              "      <td>138</td>\n",
              "      <td>221</td>\n",
              "      <td>231</td>\n",
              "      <td>274</td>\n",
              "      <td>274</td>\n",
              "      <td>227</td>\n",
              "      <td>217</td>\n",
              "      <td>108</td>\n",
              "      <td>73</td>\n",
              "      <td>194</td>\n",
              "      <td>78</td>\n",
              "      <td>209</td>\n",
              "      <td>225</td>\n",
              "      <td>228</td>\n",
              "      <td>67</td>\n",
              "      <td>73</td>\n",
              "      <td>232</td>\n",
              "      <td>56</td>\n",
              "      <td>266</td>\n",
              "      <td>195</td>\n",
              "      <td>234</td>\n",
              "      <td>161</td>\n",
              "      <td>28</td>\n",
              "      <td>31</td>\n",
              "      <td>221</td>\n",
              "      <td>68</td>\n",
              "      <td>201</td>\n",
              "      <td>185</td>\n",
              "      <td>252</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>254</td>\n",
              "      <td>140</td>\n",
              "      <td>152</td>\n",
              "      <td>101</td>\n",
              "      <td>173</td>\n",
              "      <td>0</td>\n",
              "      <td>82</td>\n",
              "      <td>64</td>\n",
              "      <td>137</td>\n",
              "      <td>114</td>\n",
              "      <td>144</td>\n",
              "      <td>56</td>\n",
              "      <td>98</td>\n",
              "      <td>254</td>\n",
              "      <td>137</td>\n",
              "      <td>193</td>\n",
              "      <td>147</td>\n",
              "      <td>69</td>\n",
              "      <td>188</td>\n",
              "      <td>254</td>\n",
              "      <td>81</td>\n",
              "      <td>165</td>\n",
              "      <td>190</td>\n",
              "      <td>254</td>\n",
              "      <td>254</td>\n",
              "      <td>157</td>\n",
              "      <td>168</td>\n",
              "      <td>121</td>\n",
              "      <td>158</td>\n",
              "      <td>156</td>\n",
              "      <td>149</td>\n",
              "      <td>152</td>\n",
              "      <td>168</td>\n",
              "      <td>174</td>\n",
              "      <td>210</td>\n",
              "      <td>127</td>\n",
              "      <td>176</td>\n",
              "      <td>151</td>\n",
              "      <td>241</td>\n",
              "      <td>136</td>\n",
              "      <td>178</td>\n",
              "      <td>17</td>\n",
              "      <td>178</td>\n",
              "      <td>143</td>\n",
              "      <td>83</td>\n",
              "      <td>138</td>\n",
              "      <td>79</td>\n",
              "      <td>87</td>\n",
              "      <td>130</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>253</td>\n",
              "      <td>65</td>\n",
              "      <td>85</td>\n",
              "      <td>144</td>\n",
              "      <td>147</td>\n",
              "      <td>82</td>\n",
              "      <td>0</td>\n",
              "      <td>98</td>\n",
              "      <td>136</td>\n",
              "      <td>147</td>\n",
              "      <td>71</td>\n",
              "      <td>128</td>\n",
              "      <td>59</td>\n",
              "      <td>253</td>\n",
              "      <td>70</td>\n",
              "      <td>128</td>\n",
              "      <td>208</td>\n",
              "      <td>92</td>\n",
              "      <td>202</td>\n",
              "      <td>253</td>\n",
              "      <td>104</td>\n",
              "      <td>180</td>\n",
              "      <td>120</td>\n",
              "      <td>253</td>\n",
              "      <td>253</td>\n",
              "      <td>183</td>\n",
              "      <td>97</td>\n",
              "      <td>54</td>\n",
              "      <td>104</td>\n",
              "      <td>79</td>\n",
              "      <td>140</td>\n",
              "      <td>169</td>\n",
              "      <td>186</td>\n",
              "      <td>105</td>\n",
              "      <td>172</td>\n",
              "      <td>106</td>\n",
              "      <td>194</td>\n",
              "      <td>102</td>\n",
              "      <td>243</td>\n",
              "      <td>161</td>\n",
              "      <td>195</td>\n",
              "      <td>67</td>\n",
              "      <td>152</td>\n",
              "      <td>119</td>\n",
              "      <td>153</td>\n",
              "      <td>88</td>\n",
              "      <td>145</td>\n",
              "      <td>98</td>\n",
              "      <td>189</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>253</td>\n",
              "      <td>156</td>\n",
              "      <td>148</td>\n",
              "      <td>157</td>\n",
              "      <td>137</td>\n",
              "      <td>64</td>\n",
              "      <td>98</td>\n",
              "      <td>0</td>\n",
              "      <td>107</td>\n",
              "      <td>141</td>\n",
              "      <td>161</td>\n",
              "      <td>92</td>\n",
              "      <td>75</td>\n",
              "      <td>253</td>\n",
              "      <td>154</td>\n",
              "      <td>222</td>\n",
              "      <td>195</td>\n",
              "      <td>110</td>\n",
              "      <td>199</td>\n",
              "      <td>253</td>\n",
              "      <td>106</td>\n",
              "      <td>122</td>\n",
              "      <td>216</td>\n",
              "      <td>253</td>\n",
              "      <td>253</td>\n",
              "      <td>177</td>\n",
              "      <td>191</td>\n",
              "      <td>109</td>\n",
              "      <td>145</td>\n",
              "      <td>174</td>\n",
              "      <td>141</td>\n",
              "      <td>108</td>\n",
              "      <td>125</td>\n",
              "      <td>198</td>\n",
              "      <td>190</td>\n",
              "      <td>120</td>\n",
              "      <td>134</td>\n",
              "      <td>128</td>\n",
              "      <td>243</td>\n",
              "      <td>155</td>\n",
              "      <td>191</td>\n",
              "      <td>63</td>\n",
              "      <td>150</td>\n",
              "      <td>108</td>\n",
              "      <td>132</td>\n",
              "      <td>119</td>\n",
              "      <td>121</td>\n",
              "      <td>138</td>\n",
              "      <td>181</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>288</td>\n",
              "      <td>156</td>\n",
              "      <td>195</td>\n",
              "      <td>235</td>\n",
              "      <td>206</td>\n",
              "      <td>137</td>\n",
              "      <td>136</td>\n",
              "      <td>107</td>\n",
              "      <td>0</td>\n",
              "      <td>227</td>\n",
              "      <td>161</td>\n",
              "      <td>171</td>\n",
              "      <td>105</td>\n",
              "      <td>288</td>\n",
              "      <td>202</td>\n",
              "      <td>217</td>\n",
              "      <td>278</td>\n",
              "      <td>196</td>\n",
              "      <td>253</td>\n",
              "      <td>288</td>\n",
              "      <td>202</td>\n",
              "      <td>55</td>\n",
              "      <td>219</td>\n",
              "      <td>288</td>\n",
              "      <td>288</td>\n",
              "      <td>243</td>\n",
              "      <td>189</td>\n",
              "      <td>144</td>\n",
              "      <td>204</td>\n",
              "      <td>179</td>\n",
              "      <td>234</td>\n",
              "      <td>59</td>\n",
              "      <td>63</td>\n",
              "      <td>191</td>\n",
              "      <td>260</td>\n",
              "      <td>206</td>\n",
              "      <td>68</td>\n",
              "      <td>185</td>\n",
              "      <td>280</td>\n",
              "      <td>231</td>\n",
              "      <td>249</td>\n",
              "      <td>136</td>\n",
              "      <td>226</td>\n",
              "      <td>179</td>\n",
              "      <td>213</td>\n",
              "      <td>176</td>\n",
              "      <td>211</td>\n",
              "      <td>212</td>\n",
              "      <td>264</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>185</td>\n",
              "      <td>193</td>\n",
              "      <td>176</td>\n",
              "      <td>93</td>\n",
              "      <td>186</td>\n",
              "      <td>114</td>\n",
              "      <td>147</td>\n",
              "      <td>141</td>\n",
              "      <td>227</td>\n",
              "      <td>0</td>\n",
              "      <td>195</td>\n",
              "      <td>82</td>\n",
              "      <td>155</td>\n",
              "      <td>185</td>\n",
              "      <td>155</td>\n",
              "      <td>235</td>\n",
              "      <td>126</td>\n",
              "      <td>91</td>\n",
              "      <td>108</td>\n",
              "      <td>185</td>\n",
              "      <td>83</td>\n",
              "      <td>247</td>\n",
              "      <td>226</td>\n",
              "      <td>185</td>\n",
              "      <td>185</td>\n",
              "      <td>69</td>\n",
              "      <td>212</td>\n",
              "      <td>167</td>\n",
              "      <td>172</td>\n",
              "      <td>201</td>\n",
              "      <td>139</td>\n",
              "      <td>224</td>\n",
              "      <td>248</td>\n",
              "      <td>223</td>\n",
              "      <td>206</td>\n",
              "      <td>135</td>\n",
              "      <td>259</td>\n",
              "      <td>177</td>\n",
              "      <td>171</td>\n",
              "      <td>39</td>\n",
              "      <td>96</td>\n",
              "      <td>115</td>\n",
              "      <td>181</td>\n",
              "      <td>168</td>\n",
              "      <td>109</td>\n",
              "      <td>160</td>\n",
              "      <td>99</td>\n",
              "      <td>97</td>\n",
              "      <td>120</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>263</td>\n",
              "      <td>8</td>\n",
              "      <td>106</td>\n",
              "      <td>192</td>\n",
              "      <td>194</td>\n",
              "      <td>144</td>\n",
              "      <td>71</td>\n",
              "      <td>161</td>\n",
              "      <td>161</td>\n",
              "      <td>195</td>\n",
              "      <td>0</td>\n",
              "      <td>186</td>\n",
              "      <td>102</td>\n",
              "      <td>263</td>\n",
              "      <td>83</td>\n",
              "      <td>67</td>\n",
              "      <td>260</td>\n",
              "      <td>153</td>\n",
              "      <td>226</td>\n",
              "      <td>263</td>\n",
              "      <td>168</td>\n",
              "      <td>213</td>\n",
              "      <td>60</td>\n",
              "      <td>263</td>\n",
              "      <td>263</td>\n",
              "      <td>216</td>\n",
              "      <td>32</td>\n",
              "      <td>87</td>\n",
              "      <td>136</td>\n",
              "      <td>21</td>\n",
              "      <td>196</td>\n",
              "      <td>204</td>\n",
              "      <td>219</td>\n",
              "      <td>40</td>\n",
              "      <td>207</td>\n",
              "      <td>162</td>\n",
              "      <td>226</td>\n",
              "      <td>141</td>\n",
              "      <td>255</td>\n",
              "      <td>201</td>\n",
              "      <td>222</td>\n",
              "      <td>132</td>\n",
              "      <td>199</td>\n",
              "      <td>170</td>\n",
              "      <td>212</td>\n",
              "      <td>127</td>\n",
              "      <td>208</td>\n",
              "      <td>144</td>\n",
              "      <td>241</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>229</td>\n",
              "      <td>183</td>\n",
              "      <td>188</td>\n",
              "      <td>88</td>\n",
              "      <td>195</td>\n",
              "      <td>56</td>\n",
              "      <td>128</td>\n",
              "      <td>92</td>\n",
              "      <td>171</td>\n",
              "      <td>82</td>\n",
              "      <td>186</td>\n",
              "      <td>0</td>\n",
              "      <td>135</td>\n",
              "      <td>229</td>\n",
              "      <td>170</td>\n",
              "      <td>231</td>\n",
              "      <td>116</td>\n",
              "      <td>85</td>\n",
              "      <td>157</td>\n",
              "      <td>229</td>\n",
              "      <td>89</td>\n",
              "      <td>188</td>\n",
              "      <td>229</td>\n",
              "      <td>229</td>\n",
              "      <td>229</td>\n",
              "      <td>120</td>\n",
              "      <td>208</td>\n",
              "      <td>162</td>\n",
              "      <td>189</td>\n",
              "      <td>197</td>\n",
              "      <td>163</td>\n",
              "      <td>170</td>\n",
              "      <td>189</td>\n",
              "      <td>215</td>\n",
              "      <td>233</td>\n",
              "      <td>150</td>\n",
              "      <td>199</td>\n",
              "      <td>183</td>\n",
              "      <td>216</td>\n",
              "      <td>104</td>\n",
              "      <td>145</td>\n",
              "      <td>68</td>\n",
              "      <td>198</td>\n",
              "      <td>170</td>\n",
              "      <td>63</td>\n",
              "      <td>169</td>\n",
              "      <td>62</td>\n",
              "      <td>101</td>\n",
              "      <td>107</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>231</td>\n",
              "      <td>96</td>\n",
              "      <td>99</td>\n",
              "      <td>180</td>\n",
              "      <td>125</td>\n",
              "      <td>98</td>\n",
              "      <td>59</td>\n",
              "      <td>75</td>\n",
              "      <td>105</td>\n",
              "      <td>155</td>\n",
              "      <td>102</td>\n",
              "      <td>135</td>\n",
              "      <td>0</td>\n",
              "      <td>231</td>\n",
              "      <td>108</td>\n",
              "      <td>168</td>\n",
              "      <td>236</td>\n",
              "      <td>126</td>\n",
              "      <td>191</td>\n",
              "      <td>231</td>\n",
              "      <td>125</td>\n",
              "      <td>141</td>\n",
              "      <td>158</td>\n",
              "      <td>231</td>\n",
              "      <td>231</td>\n",
              "      <td>181</td>\n",
              "      <td>133</td>\n",
              "      <td>50</td>\n",
              "      <td>106</td>\n",
              "      <td>115</td>\n",
              "      <td>145</td>\n",
              "      <td>126</td>\n",
              "      <td>145</td>\n",
              "      <td>141</td>\n",
              "      <td>168</td>\n",
              "      <td>114</td>\n",
              "      <td>155</td>\n",
              "      <td>93</td>\n",
              "      <td>223</td>\n",
              "      <td>160</td>\n",
              "      <td>187</td>\n",
              "      <td>87</td>\n",
              "      <td>140</td>\n",
              "      <td>97</td>\n",
              "      <td>177</td>\n",
              "      <td>77</td>\n",
              "      <td>167</td>\n",
              "      <td>141</td>\n",
              "      <td>219</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>0</td>\n",
              "      <td>264</td>\n",
              "      <td>266</td>\n",
              "      <td>266</td>\n",
              "      <td>274</td>\n",
              "      <td>254</td>\n",
              "      <td>253</td>\n",
              "      <td>253</td>\n",
              "      <td>288</td>\n",
              "      <td>185</td>\n",
              "      <td>263</td>\n",
              "      <td>229</td>\n",
              "      <td>231</td>\n",
              "      <td>0</td>\n",
              "      <td>254</td>\n",
              "      <td>299</td>\n",
              "      <td>298</td>\n",
              "      <td>258</td>\n",
              "      <td>80</td>\n",
              "      <td>0</td>\n",
              "      <td>250</td>\n",
              "      <td>301</td>\n",
              "      <td>291</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>126</td>\n",
              "      <td>277</td>\n",
              "      <td>251</td>\n",
              "      <td>262</td>\n",
              "      <td>272</td>\n",
              "      <td>271</td>\n",
              "      <td>272</td>\n",
              "      <td>298</td>\n",
              "      <td>288</td>\n",
              "      <td>296</td>\n",
              "      <td>263</td>\n",
              "      <td>312</td>\n",
              "      <td>267</td>\n",
              "      <td>14</td>\n",
              "      <td>146</td>\n",
              "      <td>94</td>\n",
              "      <td>254</td>\n",
              "      <td>279</td>\n",
              "      <td>265</td>\n",
              "      <td>281</td>\n",
              "      <td>247</td>\n",
              "      <td>276</td>\n",
              "      <td>257</td>\n",
              "      <td>296</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>254</td>\n",
              "      <td>80</td>\n",
              "      <td>52</td>\n",
              "      <td>158</td>\n",
              "      <td>146</td>\n",
              "      <td>137</td>\n",
              "      <td>70</td>\n",
              "      <td>154</td>\n",
              "      <td>202</td>\n",
              "      <td>155</td>\n",
              "      <td>83</td>\n",
              "      <td>170</td>\n",
              "      <td>108</td>\n",
              "      <td>254</td>\n",
              "      <td>0</td>\n",
              "      <td>119</td>\n",
              "      <td>225</td>\n",
              "      <td>108</td>\n",
              "      <td>208</td>\n",
              "      <td>254</td>\n",
              "      <td>116</td>\n",
              "      <td>245</td>\n",
              "      <td>98</td>\n",
              "      <td>254</td>\n",
              "      <td>254</td>\n",
              "      <td>192</td>\n",
              "      <td>92</td>\n",
              "      <td>72</td>\n",
              "      <td>79</td>\n",
              "      <td>74</td>\n",
              "      <td>127</td>\n",
              "      <td>233</td>\n",
              "      <td>251</td>\n",
              "      <td>104</td>\n",
              "      <td>142</td>\n",
              "      <td>97</td>\n",
              "      <td>259</td>\n",
              "      <td>95</td>\n",
              "      <td>244</td>\n",
              "      <td>167</td>\n",
              "      <td>202</td>\n",
              "      <td>121</td>\n",
              "      <td>141</td>\n",
              "      <td>128</td>\n",
              "      <td>186</td>\n",
              "      <td>83</td>\n",
              "      <td>176</td>\n",
              "      <td>102</td>\n",
              "      <td>206</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>299</td>\n",
              "      <td>74</td>\n",
              "      <td>153</td>\n",
              "      <td>216</td>\n",
              "      <td>252</td>\n",
              "      <td>193</td>\n",
              "      <td>128</td>\n",
              "      <td>222</td>\n",
              "      <td>217</td>\n",
              "      <td>235</td>\n",
              "      <td>67</td>\n",
              "      <td>231</td>\n",
              "      <td>168</td>\n",
              "      <td>299</td>\n",
              "      <td>119</td>\n",
              "      <td>0</td>\n",
              "      <td>285</td>\n",
              "      <td>192</td>\n",
              "      <td>264</td>\n",
              "      <td>299</td>\n",
              "      <td>212</td>\n",
              "      <td>271</td>\n",
              "      <td>28</td>\n",
              "      <td>299</td>\n",
              "      <td>299</td>\n",
              "      <td>254</td>\n",
              "      <td>37</td>\n",
              "      <td>149</td>\n",
              "      <td>187</td>\n",
              "      <td>59</td>\n",
              "      <td>244</td>\n",
              "      <td>264</td>\n",
              "      <td>278</td>\n",
              "      <td>29</td>\n",
              "      <td>253</td>\n",
              "      <td>212</td>\n",
              "      <td>284</td>\n",
              "      <td>197</td>\n",
              "      <td>292</td>\n",
              "      <td>242</td>\n",
              "      <td>260</td>\n",
              "      <td>182</td>\n",
              "      <td>253</td>\n",
              "      <td>230</td>\n",
              "      <td>246</td>\n",
              "      <td>185</td>\n",
              "      <td>246</td>\n",
              "      <td>172</td>\n",
              "      <td>266</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>298</td>\n",
              "      <td>258</td>\n",
              "      <td>253</td>\n",
              "      <td>70</td>\n",
              "      <td>267</td>\n",
              "      <td>147</td>\n",
              "      <td>208</td>\n",
              "      <td>195</td>\n",
              "      <td>278</td>\n",
              "      <td>126</td>\n",
              "      <td>260</td>\n",
              "      <td>116</td>\n",
              "      <td>236</td>\n",
              "      <td>298</td>\n",
              "      <td>225</td>\n",
              "      <td>285</td>\n",
              "      <td>0</td>\n",
              "      <td>125</td>\n",
              "      <td>218</td>\n",
              "      <td>298</td>\n",
              "      <td>133</td>\n",
              "      <td>296</td>\n",
              "      <td>283</td>\n",
              "      <td>298</td>\n",
              "      <td>298</td>\n",
              "      <td>173</td>\n",
              "      <td>272</td>\n",
              "      <td>246</td>\n",
              "      <td>254</td>\n",
              "      <td>265</td>\n",
              "      <td>205</td>\n",
              "      <td>282</td>\n",
              "      <td>298</td>\n",
              "      <td>278</td>\n",
              "      <td>284</td>\n",
              "      <td>204</td>\n",
              "      <td>305</td>\n",
              "      <td>257</td>\n",
              "      <td>284</td>\n",
              "      <td>159</td>\n",
              "      <td>204</td>\n",
              "      <td>155</td>\n",
              "      <td>259</td>\n",
              "      <td>247</td>\n",
              "      <td>67</td>\n",
              "      <td>246</td>\n",
              "      <td>76</td>\n",
              "      <td>124</td>\n",
              "      <td>22</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>258</td>\n",
              "      <td>149</td>\n",
              "      <td>129</td>\n",
              "      <td>69</td>\n",
              "      <td>158</td>\n",
              "      <td>69</td>\n",
              "      <td>92</td>\n",
              "      <td>110</td>\n",
              "      <td>196</td>\n",
              "      <td>91</td>\n",
              "      <td>153</td>\n",
              "      <td>85</td>\n",
              "      <td>126</td>\n",
              "      <td>258</td>\n",
              "      <td>108</td>\n",
              "      <td>192</td>\n",
              "      <td>125</td>\n",
              "      <td>0</td>\n",
              "      <td>188</td>\n",
              "      <td>258</td>\n",
              "      <td>30</td>\n",
              "      <td>226</td>\n",
              "      <td>183</td>\n",
              "      <td>258</td>\n",
              "      <td>258</td>\n",
              "      <td>153</td>\n",
              "      <td>170</td>\n",
              "      <td>124</td>\n",
              "      <td>133</td>\n",
              "      <td>156</td>\n",
              "      <td>107</td>\n",
              "      <td>212</td>\n",
              "      <td>230</td>\n",
              "      <td>178</td>\n",
              "      <td>176</td>\n",
              "      <td>91</td>\n",
              "      <td>238</td>\n",
              "      <td>136</td>\n",
              "      <td>246</td>\n",
              "      <td>125</td>\n",
              "      <td>177</td>\n",
              "      <td>62</td>\n",
              "      <td>152</td>\n",
              "      <td>135</td>\n",
              "      <td>82</td>\n",
              "      <td>125</td>\n",
              "      <td>68</td>\n",
              "      <td>37</td>\n",
              "      <td>106</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>80</td>\n",
              "      <td>226</td>\n",
              "      <td>227</td>\n",
              "      <td>189</td>\n",
              "      <td>238</td>\n",
              "      <td>188</td>\n",
              "      <td>202</td>\n",
              "      <td>199</td>\n",
              "      <td>253</td>\n",
              "      <td>108</td>\n",
              "      <td>226</td>\n",
              "      <td>157</td>\n",
              "      <td>191</td>\n",
              "      <td>80</td>\n",
              "      <td>208</td>\n",
              "      <td>264</td>\n",
              "      <td>218</td>\n",
              "      <td>188</td>\n",
              "      <td>0</td>\n",
              "      <td>80</td>\n",
              "      <td>181</td>\n",
              "      <td>269</td>\n",
              "      <td>257</td>\n",
              "      <td>80</td>\n",
              "      <td>80</td>\n",
              "      <td>45</td>\n",
              "      <td>242</td>\n",
              "      <td>212</td>\n",
              "      <td>224</td>\n",
              "      <td>236</td>\n",
              "      <td>217</td>\n",
              "      <td>240</td>\n",
              "      <td>267</td>\n",
              "      <td>253</td>\n",
              "      <td>261</td>\n",
              "      <td>210</td>\n",
              "      <td>280</td>\n",
              "      <td>229</td>\n",
              "      <td>66</td>\n",
              "      <td>70</td>\n",
              "      <td>14</td>\n",
              "      <td>190</td>\n",
              "      <td>240</td>\n",
              "      <td>224</td>\n",
              "      <td>203</td>\n",
              "      <td>208</td>\n",
              "      <td>199</td>\n",
              "      <td>187</td>\n",
              "      <td>216</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>0</td>\n",
              "      <td>264</td>\n",
              "      <td>266</td>\n",
              "      <td>266</td>\n",
              "      <td>274</td>\n",
              "      <td>254</td>\n",
              "      <td>253</td>\n",
              "      <td>253</td>\n",
              "      <td>288</td>\n",
              "      <td>185</td>\n",
              "      <td>263</td>\n",
              "      <td>229</td>\n",
              "      <td>231</td>\n",
              "      <td>0</td>\n",
              "      <td>254</td>\n",
              "      <td>299</td>\n",
              "      <td>298</td>\n",
              "      <td>258</td>\n",
              "      <td>80</td>\n",
              "      <td>0</td>\n",
              "      <td>250</td>\n",
              "      <td>301</td>\n",
              "      <td>291</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>126</td>\n",
              "      <td>277</td>\n",
              "      <td>251</td>\n",
              "      <td>262</td>\n",
              "      <td>272</td>\n",
              "      <td>271</td>\n",
              "      <td>272</td>\n",
              "      <td>298</td>\n",
              "      <td>288</td>\n",
              "      <td>296</td>\n",
              "      <td>263</td>\n",
              "      <td>312</td>\n",
              "      <td>267</td>\n",
              "      <td>14</td>\n",
              "      <td>146</td>\n",
              "      <td>94</td>\n",
              "      <td>254</td>\n",
              "      <td>279</td>\n",
              "      <td>265</td>\n",
              "      <td>281</td>\n",
              "      <td>247</td>\n",
              "      <td>276</td>\n",
              "      <td>257</td>\n",
              "      <td>296</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>250</td>\n",
              "      <td>163</td>\n",
              "      <td>127</td>\n",
              "      <td>87</td>\n",
              "      <td>138</td>\n",
              "      <td>81</td>\n",
              "      <td>104</td>\n",
              "      <td>106</td>\n",
              "      <td>202</td>\n",
              "      <td>83</td>\n",
              "      <td>168</td>\n",
              "      <td>89</td>\n",
              "      <td>125</td>\n",
              "      <td>250</td>\n",
              "      <td>116</td>\n",
              "      <td>212</td>\n",
              "      <td>133</td>\n",
              "      <td>30</td>\n",
              "      <td>181</td>\n",
              "      <td>250</td>\n",
              "      <td>0</td>\n",
              "      <td>227</td>\n",
              "      <td>200</td>\n",
              "      <td>250</td>\n",
              "      <td>250</td>\n",
              "      <td>148</td>\n",
              "      <td>187</td>\n",
              "      <td>124</td>\n",
              "      <td>123</td>\n",
              "      <td>170</td>\n",
              "      <td>83</td>\n",
              "      <td>211</td>\n",
              "      <td>230</td>\n",
              "      <td>196</td>\n",
              "      <td>157</td>\n",
              "      <td>73</td>\n",
              "      <td>238</td>\n",
              "      <td>124</td>\n",
              "      <td>237</td>\n",
              "      <td>115</td>\n",
              "      <td>170</td>\n",
              "      <td>75</td>\n",
              "      <td>131</td>\n",
              "      <td>117</td>\n",
              "      <td>94</td>\n",
              "      <td>114</td>\n",
              "      <td>74</td>\n",
              "      <td>62</td>\n",
              "      <td>117</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>301</td>\n",
              "      <td>208</td>\n",
              "      <td>233</td>\n",
              "      <td>263</td>\n",
              "      <td>221</td>\n",
              "      <td>165</td>\n",
              "      <td>180</td>\n",
              "      <td>122</td>\n",
              "      <td>55</td>\n",
              "      <td>247</td>\n",
              "      <td>213</td>\n",
              "      <td>188</td>\n",
              "      <td>141</td>\n",
              "      <td>301</td>\n",
              "      <td>245</td>\n",
              "      <td>271</td>\n",
              "      <td>296</td>\n",
              "      <td>226</td>\n",
              "      <td>269</td>\n",
              "      <td>301</td>\n",
              "      <td>227</td>\n",
              "      <td>0</td>\n",
              "      <td>272</td>\n",
              "      <td>301</td>\n",
              "      <td>301</td>\n",
              "      <td>260</td>\n",
              "      <td>242</td>\n",
              "      <td>183</td>\n",
              "      <td>235</td>\n",
              "      <td>231</td>\n",
              "      <td>254</td>\n",
              "      <td>30</td>\n",
              "      <td>10</td>\n",
              "      <td>245</td>\n",
              "      <td>282</td>\n",
              "      <td>231</td>\n",
              "      <td>14</td>\n",
              "      <td>213</td>\n",
              "      <td>294</td>\n",
              "      <td>250</td>\n",
              "      <td>266</td>\n",
              "      <td>167</td>\n",
              "      <td>243</td>\n",
              "      <td>196</td>\n",
              "      <td>232</td>\n",
              "      <td>206</td>\n",
              "      <td>229</td>\n",
              "      <td>247</td>\n",
              "      <td>285</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>291</td>\n",
              "      <td>65</td>\n",
              "      <td>131</td>\n",
              "      <td>214</td>\n",
              "      <td>231</td>\n",
              "      <td>190</td>\n",
              "      <td>120</td>\n",
              "      <td>216</td>\n",
              "      <td>219</td>\n",
              "      <td>226</td>\n",
              "      <td>60</td>\n",
              "      <td>229</td>\n",
              "      <td>158</td>\n",
              "      <td>291</td>\n",
              "      <td>98</td>\n",
              "      <td>28</td>\n",
              "      <td>283</td>\n",
              "      <td>183</td>\n",
              "      <td>257</td>\n",
              "      <td>291</td>\n",
              "      <td>200</td>\n",
              "      <td>272</td>\n",
              "      <td>0</td>\n",
              "      <td>291</td>\n",
              "      <td>291</td>\n",
              "      <td>247</td>\n",
              "      <td>30</td>\n",
              "      <td>133</td>\n",
              "      <td>164</td>\n",
              "      <td>45</td>\n",
              "      <td>225</td>\n",
              "      <td>264</td>\n",
              "      <td>278</td>\n",
              "      <td>31</td>\n",
              "      <td>229</td>\n",
              "      <td>193</td>\n",
              "      <td>286</td>\n",
              "      <td>176</td>\n",
              "      <td>283</td>\n",
              "      <td>233</td>\n",
              "      <td>253</td>\n",
              "      <td>178</td>\n",
              "      <td>231</td>\n",
              "      <td>212</td>\n",
              "      <td>245</td>\n",
              "      <td>165</td>\n",
              "      <td>242</td>\n",
              "      <td>165</td>\n",
              "      <td>264</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>0</td>\n",
              "      <td>264</td>\n",
              "      <td>266</td>\n",
              "      <td>266</td>\n",
              "      <td>274</td>\n",
              "      <td>254</td>\n",
              "      <td>253</td>\n",
              "      <td>253</td>\n",
              "      <td>288</td>\n",
              "      <td>185</td>\n",
              "      <td>263</td>\n",
              "      <td>229</td>\n",
              "      <td>231</td>\n",
              "      <td>0</td>\n",
              "      <td>254</td>\n",
              "      <td>299</td>\n",
              "      <td>298</td>\n",
              "      <td>258</td>\n",
              "      <td>80</td>\n",
              "      <td>0</td>\n",
              "      <td>250</td>\n",
              "      <td>301</td>\n",
              "      <td>291</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>126</td>\n",
              "      <td>277</td>\n",
              "      <td>251</td>\n",
              "      <td>262</td>\n",
              "      <td>272</td>\n",
              "      <td>271</td>\n",
              "      <td>272</td>\n",
              "      <td>298</td>\n",
              "      <td>288</td>\n",
              "      <td>296</td>\n",
              "      <td>263</td>\n",
              "      <td>312</td>\n",
              "      <td>267</td>\n",
              "      <td>14</td>\n",
              "      <td>146</td>\n",
              "      <td>94</td>\n",
              "      <td>254</td>\n",
              "      <td>279</td>\n",
              "      <td>265</td>\n",
              "      <td>281</td>\n",
              "      <td>247</td>\n",
              "      <td>276</td>\n",
              "      <td>257</td>\n",
              "      <td>296</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>0</td>\n",
              "      <td>264</td>\n",
              "      <td>266</td>\n",
              "      <td>266</td>\n",
              "      <td>274</td>\n",
              "      <td>254</td>\n",
              "      <td>253</td>\n",
              "      <td>253</td>\n",
              "      <td>288</td>\n",
              "      <td>185</td>\n",
              "      <td>263</td>\n",
              "      <td>229</td>\n",
              "      <td>231</td>\n",
              "      <td>0</td>\n",
              "      <td>254</td>\n",
              "      <td>299</td>\n",
              "      <td>298</td>\n",
              "      <td>258</td>\n",
              "      <td>80</td>\n",
              "      <td>0</td>\n",
              "      <td>250</td>\n",
              "      <td>301</td>\n",
              "      <td>291</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>126</td>\n",
              "      <td>277</td>\n",
              "      <td>251</td>\n",
              "      <td>262</td>\n",
              "      <td>272</td>\n",
              "      <td>271</td>\n",
              "      <td>272</td>\n",
              "      <td>298</td>\n",
              "      <td>288</td>\n",
              "      <td>296</td>\n",
              "      <td>263</td>\n",
              "      <td>312</td>\n",
              "      <td>267</td>\n",
              "      <td>14</td>\n",
              "      <td>146</td>\n",
              "      <td>94</td>\n",
              "      <td>254</td>\n",
              "      <td>279</td>\n",
              "      <td>265</td>\n",
              "      <td>281</td>\n",
              "      <td>247</td>\n",
              "      <td>276</td>\n",
              "      <td>257</td>\n",
              "      <td>296</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>126</td>\n",
              "      <td>216</td>\n",
              "      <td>215</td>\n",
              "      <td>146</td>\n",
              "      <td>227</td>\n",
              "      <td>157</td>\n",
              "      <td>183</td>\n",
              "      <td>177</td>\n",
              "      <td>243</td>\n",
              "      <td>69</td>\n",
              "      <td>216</td>\n",
              "      <td>120</td>\n",
              "      <td>181</td>\n",
              "      <td>126</td>\n",
              "      <td>192</td>\n",
              "      <td>254</td>\n",
              "      <td>173</td>\n",
              "      <td>153</td>\n",
              "      <td>45</td>\n",
              "      <td>126</td>\n",
              "      <td>148</td>\n",
              "      <td>260</td>\n",
              "      <td>247</td>\n",
              "      <td>126</td>\n",
              "      <td>126</td>\n",
              "      <td>0</td>\n",
              "      <td>232</td>\n",
              "      <td>201</td>\n",
              "      <td>213</td>\n",
              "      <td>225</td>\n",
              "      <td>196</td>\n",
              "      <td>233</td>\n",
              "      <td>259</td>\n",
              "      <td>243</td>\n",
              "      <td>251</td>\n",
              "      <td>190</td>\n",
              "      <td>272</td>\n",
              "      <td>218</td>\n",
              "      <td>111</td>\n",
              "      <td>36</td>\n",
              "      <td>31</td>\n",
              "      <td>160</td>\n",
              "      <td>227</td>\n",
              "      <td>211</td>\n",
              "      <td>161</td>\n",
              "      <td>198</td>\n",
              "      <td>157</td>\n",
              "      <td>152</td>\n",
              "      <td>171</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td>277</td>\n",
              "      <td>38</td>\n",
              "      <td>122</td>\n",
              "      <td>203</td>\n",
              "      <td>217</td>\n",
              "      <td>168</td>\n",
              "      <td>97</td>\n",
              "      <td>191</td>\n",
              "      <td>189</td>\n",
              "      <td>212</td>\n",
              "      <td>32</td>\n",
              "      <td>208</td>\n",
              "      <td>133</td>\n",
              "      <td>277</td>\n",
              "      <td>92</td>\n",
              "      <td>37</td>\n",
              "      <td>272</td>\n",
              "      <td>170</td>\n",
              "      <td>242</td>\n",
              "      <td>277</td>\n",
              "      <td>187</td>\n",
              "      <td>242</td>\n",
              "      <td>30</td>\n",
              "      <td>277</td>\n",
              "      <td>277</td>\n",
              "      <td>232</td>\n",
              "      <td>0</td>\n",
              "      <td>113</td>\n",
              "      <td>155</td>\n",
              "      <td>23</td>\n",
              "      <td>215</td>\n",
              "      <td>234</td>\n",
              "      <td>248</td>\n",
              "      <td>13</td>\n",
              "      <td>223</td>\n",
              "      <td>182</td>\n",
              "      <td>256</td>\n",
              "      <td>163</td>\n",
              "      <td>269</td>\n",
              "      <td>218</td>\n",
              "      <td>238</td>\n",
              "      <td>156</td>\n",
              "      <td>220</td>\n",
              "      <td>196</td>\n",
              "      <td>229</td>\n",
              "      <td>150</td>\n",
              "      <td>226</td>\n",
              "      <td>155</td>\n",
              "      <td>253</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>251</td>\n",
              "      <td>80</td>\n",
              "      <td>52</td>\n",
              "      <td>185</td>\n",
              "      <td>108</td>\n",
              "      <td>121</td>\n",
              "      <td>54</td>\n",
              "      <td>109</td>\n",
              "      <td>144</td>\n",
              "      <td>167</td>\n",
              "      <td>87</td>\n",
              "      <td>162</td>\n",
              "      <td>50</td>\n",
              "      <td>251</td>\n",
              "      <td>72</td>\n",
              "      <td>149</td>\n",
              "      <td>246</td>\n",
              "      <td>124</td>\n",
              "      <td>212</td>\n",
              "      <td>251</td>\n",
              "      <td>124</td>\n",
              "      <td>183</td>\n",
              "      <td>133</td>\n",
              "      <td>251</td>\n",
              "      <td>251</td>\n",
              "      <td>201</td>\n",
              "      <td>113</td>\n",
              "      <td>0</td>\n",
              "      <td>65</td>\n",
              "      <td>91</td>\n",
              "      <td>126</td>\n",
              "      <td>173</td>\n",
              "      <td>189</td>\n",
              "      <td>123</td>\n",
              "      <td>134</td>\n",
              "      <td>92</td>\n",
              "      <td>197</td>\n",
              "      <td>59</td>\n",
              "      <td>243</td>\n",
              "      <td>176</td>\n",
              "      <td>208</td>\n",
              "      <td>106</td>\n",
              "      <td>117</td>\n",
              "      <td>84</td>\n",
              "      <td>193</td>\n",
              "      <td>46</td>\n",
              "      <td>180</td>\n",
              "      <td>136</td>\n",
              "      <td>228</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td>262</td>\n",
              "      <td>130</td>\n",
              "      <td>34</td>\n",
              "      <td>198</td>\n",
              "      <td>73</td>\n",
              "      <td>158</td>\n",
              "      <td>104</td>\n",
              "      <td>145</td>\n",
              "      <td>204</td>\n",
              "      <td>172</td>\n",
              "      <td>136</td>\n",
              "      <td>189</td>\n",
              "      <td>106</td>\n",
              "      <td>262</td>\n",
              "      <td>79</td>\n",
              "      <td>187</td>\n",
              "      <td>254</td>\n",
              "      <td>133</td>\n",
              "      <td>224</td>\n",
              "      <td>262</td>\n",
              "      <td>123</td>\n",
              "      <td>235</td>\n",
              "      <td>164</td>\n",
              "      <td>262</td>\n",
              "      <td>262</td>\n",
              "      <td>213</td>\n",
              "      <td>155</td>\n",
              "      <td>65</td>\n",
              "      <td>0</td>\n",
              "      <td>132</td>\n",
              "      <td>85</td>\n",
              "      <td>223</td>\n",
              "      <td>240</td>\n",
              "      <td>166</td>\n",
              "      <td>71</td>\n",
              "      <td>60</td>\n",
              "      <td>248</td>\n",
              "      <td>28</td>\n",
              "      <td>254</td>\n",
              "      <td>182</td>\n",
              "      <td>220</td>\n",
              "      <td>143</td>\n",
              "      <td>69</td>\n",
              "      <td>66</td>\n",
              "      <td>211</td>\n",
              "      <td>31</td>\n",
              "      <td>194</td>\n",
              "      <td>147</td>\n",
              "      <td>237</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td>272</td>\n",
              "      <td>23</td>\n",
              "      <td>100</td>\n",
              "      <td>196</td>\n",
              "      <td>194</td>\n",
              "      <td>156</td>\n",
              "      <td>79</td>\n",
              "      <td>174</td>\n",
              "      <td>179</td>\n",
              "      <td>201</td>\n",
              "      <td>21</td>\n",
              "      <td>197</td>\n",
              "      <td>115</td>\n",
              "      <td>272</td>\n",
              "      <td>74</td>\n",
              "      <td>59</td>\n",
              "      <td>265</td>\n",
              "      <td>156</td>\n",
              "      <td>236</td>\n",
              "      <td>272</td>\n",
              "      <td>170</td>\n",
              "      <td>231</td>\n",
              "      <td>45</td>\n",
              "      <td>272</td>\n",
              "      <td>272</td>\n",
              "      <td>225</td>\n",
              "      <td>23</td>\n",
              "      <td>91</td>\n",
              "      <td>132</td>\n",
              "      <td>0</td>\n",
              "      <td>194</td>\n",
              "      <td>223</td>\n",
              "      <td>237</td>\n",
              "      <td>34</td>\n",
              "      <td>201</td>\n",
              "      <td>160</td>\n",
              "      <td>245</td>\n",
              "      <td>140</td>\n",
              "      <td>264</td>\n",
              "      <td>208</td>\n",
              "      <td>231</td>\n",
              "      <td>143</td>\n",
              "      <td>197</td>\n",
              "      <td>173</td>\n",
              "      <td>219</td>\n",
              "      <td>127</td>\n",
              "      <td>214</td>\n",
              "      <td>145</td>\n",
              "      <td>245</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>30</th>\n",
              "      <td>271</td>\n",
              "      <td>190</td>\n",
              "      <td>109</td>\n",
              "      <td>166</td>\n",
              "      <td>78</td>\n",
              "      <td>149</td>\n",
              "      <td>140</td>\n",
              "      <td>141</td>\n",
              "      <td>234</td>\n",
              "      <td>139</td>\n",
              "      <td>196</td>\n",
              "      <td>163</td>\n",
              "      <td>145</td>\n",
              "      <td>271</td>\n",
              "      <td>127</td>\n",
              "      <td>244</td>\n",
              "      <td>205</td>\n",
              "      <td>107</td>\n",
              "      <td>217</td>\n",
              "      <td>271</td>\n",
              "      <td>83</td>\n",
              "      <td>254</td>\n",
              "      <td>225</td>\n",
              "      <td>271</td>\n",
              "      <td>271</td>\n",
              "      <td>196</td>\n",
              "      <td>215</td>\n",
              "      <td>126</td>\n",
              "      <td>85</td>\n",
              "      <td>194</td>\n",
              "      <td>0</td>\n",
              "      <td>240</td>\n",
              "      <td>258</td>\n",
              "      <td>226</td>\n",
              "      <td>82</td>\n",
              "      <td>35</td>\n",
              "      <td>265</td>\n",
              "      <td>87</td>\n",
              "      <td>260</td>\n",
              "      <td>160</td>\n",
              "      <td>210</td>\n",
              "      <td>139</td>\n",
              "      <td>59</td>\n",
              "      <td>77</td>\n",
              "      <td>172</td>\n",
              "      <td>90</td>\n",
              "      <td>150</td>\n",
              "      <td>133</td>\n",
              "      <td>190</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>31</th>\n",
              "      <td>272</td>\n",
              "      <td>200</td>\n",
              "      <td>223</td>\n",
              "      <td>248</td>\n",
              "      <td>209</td>\n",
              "      <td>152</td>\n",
              "      <td>169</td>\n",
              "      <td>108</td>\n",
              "      <td>59</td>\n",
              "      <td>224</td>\n",
              "      <td>204</td>\n",
              "      <td>170</td>\n",
              "      <td>126</td>\n",
              "      <td>272</td>\n",
              "      <td>233</td>\n",
              "      <td>264</td>\n",
              "      <td>282</td>\n",
              "      <td>212</td>\n",
              "      <td>240</td>\n",
              "      <td>272</td>\n",
              "      <td>211</td>\n",
              "      <td>30</td>\n",
              "      <td>264</td>\n",
              "      <td>272</td>\n",
              "      <td>272</td>\n",
              "      <td>233</td>\n",
              "      <td>234</td>\n",
              "      <td>173</td>\n",
              "      <td>223</td>\n",
              "      <td>223</td>\n",
              "      <td>240</td>\n",
              "      <td>0</td>\n",
              "      <td>27</td>\n",
              "      <td>239</td>\n",
              "      <td>270</td>\n",
              "      <td>218</td>\n",
              "      <td>40</td>\n",
              "      <td>202</td>\n",
              "      <td>265</td>\n",
              "      <td>224</td>\n",
              "      <td>237</td>\n",
              "      <td>155</td>\n",
              "      <td>231</td>\n",
              "      <td>185</td>\n",
              "      <td>219</td>\n",
              "      <td>193</td>\n",
              "      <td>215</td>\n",
              "      <td>233</td>\n",
              "      <td>271</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>32</th>\n",
              "      <td>298</td>\n",
              "      <td>214</td>\n",
              "      <td>239</td>\n",
              "      <td>266</td>\n",
              "      <td>225</td>\n",
              "      <td>168</td>\n",
              "      <td>186</td>\n",
              "      <td>125</td>\n",
              "      <td>63</td>\n",
              "      <td>248</td>\n",
              "      <td>219</td>\n",
              "      <td>189</td>\n",
              "      <td>145</td>\n",
              "      <td>298</td>\n",
              "      <td>251</td>\n",
              "      <td>278</td>\n",
              "      <td>298</td>\n",
              "      <td>230</td>\n",
              "      <td>267</td>\n",
              "      <td>298</td>\n",
              "      <td>230</td>\n",
              "      <td>10</td>\n",
              "      <td>278</td>\n",
              "      <td>298</td>\n",
              "      <td>298</td>\n",
              "      <td>259</td>\n",
              "      <td>248</td>\n",
              "      <td>189</td>\n",
              "      <td>240</td>\n",
              "      <td>237</td>\n",
              "      <td>258</td>\n",
              "      <td>27</td>\n",
              "      <td>0</td>\n",
              "      <td>252</td>\n",
              "      <td>286</td>\n",
              "      <td>235</td>\n",
              "      <td>14</td>\n",
              "      <td>218</td>\n",
              "      <td>291</td>\n",
              "      <td>249</td>\n",
              "      <td>263</td>\n",
              "      <td>172</td>\n",
              "      <td>248</td>\n",
              "      <td>201</td>\n",
              "      <td>234</td>\n",
              "      <td>211</td>\n",
              "      <td>231</td>\n",
              "      <td>251</td>\n",
              "      <td>287</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>33</th>\n",
              "      <td>288</td>\n",
              "      <td>46</td>\n",
              "      <td>133</td>\n",
              "      <td>209</td>\n",
              "      <td>228</td>\n",
              "      <td>174</td>\n",
              "      <td>105</td>\n",
              "      <td>198</td>\n",
              "      <td>191</td>\n",
              "      <td>223</td>\n",
              "      <td>40</td>\n",
              "      <td>215</td>\n",
              "      <td>141</td>\n",
              "      <td>288</td>\n",
              "      <td>104</td>\n",
              "      <td>29</td>\n",
              "      <td>278</td>\n",
              "      <td>178</td>\n",
              "      <td>253</td>\n",
              "      <td>288</td>\n",
              "      <td>196</td>\n",
              "      <td>245</td>\n",
              "      <td>31</td>\n",
              "      <td>288</td>\n",
              "      <td>288</td>\n",
              "      <td>243</td>\n",
              "      <td>13</td>\n",
              "      <td>123</td>\n",
              "      <td>166</td>\n",
              "      <td>34</td>\n",
              "      <td>226</td>\n",
              "      <td>239</td>\n",
              "      <td>252</td>\n",
              "      <td>0</td>\n",
              "      <td>234</td>\n",
              "      <td>192</td>\n",
              "      <td>259</td>\n",
              "      <td>173</td>\n",
              "      <td>280</td>\n",
              "      <td>229</td>\n",
              "      <td>249</td>\n",
              "      <td>163</td>\n",
              "      <td>231</td>\n",
              "      <td>206</td>\n",
              "      <td>234</td>\n",
              "      <td>161</td>\n",
              "      <td>233</td>\n",
              "      <td>163</td>\n",
              "      <td>259</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>34</th>\n",
              "      <td>296</td>\n",
              "      <td>201</td>\n",
              "      <td>102</td>\n",
              "      <td>238</td>\n",
              "      <td>67</td>\n",
              "      <td>210</td>\n",
              "      <td>172</td>\n",
              "      <td>190</td>\n",
              "      <td>260</td>\n",
              "      <td>206</td>\n",
              "      <td>207</td>\n",
              "      <td>233</td>\n",
              "      <td>168</td>\n",
              "      <td>296</td>\n",
              "      <td>142</td>\n",
              "      <td>253</td>\n",
              "      <td>284</td>\n",
              "      <td>176</td>\n",
              "      <td>261</td>\n",
              "      <td>296</td>\n",
              "      <td>157</td>\n",
              "      <td>282</td>\n",
              "      <td>229</td>\n",
              "      <td>296</td>\n",
              "      <td>296</td>\n",
              "      <td>251</td>\n",
              "      <td>223</td>\n",
              "      <td>134</td>\n",
              "      <td>71</td>\n",
              "      <td>201</td>\n",
              "      <td>82</td>\n",
              "      <td>270</td>\n",
              "      <td>286</td>\n",
              "      <td>234</td>\n",
              "      <td>0</td>\n",
              "      <td>86</td>\n",
              "      <td>293</td>\n",
              "      <td>78</td>\n",
              "      <td>288</td>\n",
              "      <td>218</td>\n",
              "      <td>257</td>\n",
              "      <td>197</td>\n",
              "      <td>46</td>\n",
              "      <td>87</td>\n",
              "      <td>249</td>\n",
              "      <td>92</td>\n",
              "      <td>228</td>\n",
              "      <td>195</td>\n",
              "      <td>269</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>35</th>\n",
              "      <td>263</td>\n",
              "      <td>156</td>\n",
              "      <td>78</td>\n",
              "      <td>157</td>\n",
              "      <td>73</td>\n",
              "      <td>127</td>\n",
              "      <td>106</td>\n",
              "      <td>120</td>\n",
              "      <td>206</td>\n",
              "      <td>135</td>\n",
              "      <td>162</td>\n",
              "      <td>150</td>\n",
              "      <td>114</td>\n",
              "      <td>263</td>\n",
              "      <td>97</td>\n",
              "      <td>212</td>\n",
              "      <td>204</td>\n",
              "      <td>91</td>\n",
              "      <td>210</td>\n",
              "      <td>263</td>\n",
              "      <td>73</td>\n",
              "      <td>231</td>\n",
              "      <td>193</td>\n",
              "      <td>263</td>\n",
              "      <td>263</td>\n",
              "      <td>190</td>\n",
              "      <td>182</td>\n",
              "      <td>92</td>\n",
              "      <td>60</td>\n",
              "      <td>160</td>\n",
              "      <td>35</td>\n",
              "      <td>218</td>\n",
              "      <td>235</td>\n",
              "      <td>192</td>\n",
              "      <td>86</td>\n",
              "      <td>0</td>\n",
              "      <td>243</td>\n",
              "      <td>61</td>\n",
              "      <td>253</td>\n",
              "      <td>155</td>\n",
              "      <td>203</td>\n",
              "      <td>114</td>\n",
              "      <td>62</td>\n",
              "      <td>60</td>\n",
              "      <td>164</td>\n",
              "      <td>61</td>\n",
              "      <td>144</td>\n",
              "      <td>116</td>\n",
              "      <td>188</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>36</th>\n",
              "      <td>312</td>\n",
              "      <td>222</td>\n",
              "      <td>247</td>\n",
              "      <td>274</td>\n",
              "      <td>232</td>\n",
              "      <td>176</td>\n",
              "      <td>194</td>\n",
              "      <td>134</td>\n",
              "      <td>68</td>\n",
              "      <td>259</td>\n",
              "      <td>226</td>\n",
              "      <td>199</td>\n",
              "      <td>155</td>\n",
              "      <td>312</td>\n",
              "      <td>259</td>\n",
              "      <td>284</td>\n",
              "      <td>305</td>\n",
              "      <td>238</td>\n",
              "      <td>280</td>\n",
              "      <td>312</td>\n",
              "      <td>238</td>\n",
              "      <td>14</td>\n",
              "      <td>286</td>\n",
              "      <td>312</td>\n",
              "      <td>312</td>\n",
              "      <td>272</td>\n",
              "      <td>256</td>\n",
              "      <td>197</td>\n",
              "      <td>248</td>\n",
              "      <td>245</td>\n",
              "      <td>265</td>\n",
              "      <td>40</td>\n",
              "      <td>14</td>\n",
              "      <td>259</td>\n",
              "      <td>293</td>\n",
              "      <td>243</td>\n",
              "      <td>0</td>\n",
              "      <td>225</td>\n",
              "      <td>305</td>\n",
              "      <td>262</td>\n",
              "      <td>277</td>\n",
              "      <td>179</td>\n",
              "      <td>255</td>\n",
              "      <td>208</td>\n",
              "      <td>241</td>\n",
              "      <td>219</td>\n",
              "      <td>238</td>\n",
              "      <td>260</td>\n",
              "      <td>294</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>37</th>\n",
              "      <td>267</td>\n",
              "      <td>134</td>\n",
              "      <td>50</td>\n",
              "      <td>203</td>\n",
              "      <td>56</td>\n",
              "      <td>151</td>\n",
              "      <td>102</td>\n",
              "      <td>128</td>\n",
              "      <td>185</td>\n",
              "      <td>177</td>\n",
              "      <td>141</td>\n",
              "      <td>183</td>\n",
              "      <td>93</td>\n",
              "      <td>267</td>\n",
              "      <td>95</td>\n",
              "      <td>197</td>\n",
              "      <td>257</td>\n",
              "      <td>136</td>\n",
              "      <td>229</td>\n",
              "      <td>267</td>\n",
              "      <td>124</td>\n",
              "      <td>213</td>\n",
              "      <td>176</td>\n",
              "      <td>267</td>\n",
              "      <td>267</td>\n",
              "      <td>218</td>\n",
              "      <td>163</td>\n",
              "      <td>59</td>\n",
              "      <td>28</td>\n",
              "      <td>140</td>\n",
              "      <td>87</td>\n",
              "      <td>202</td>\n",
              "      <td>218</td>\n",
              "      <td>173</td>\n",
              "      <td>78</td>\n",
              "      <td>61</td>\n",
              "      <td>225</td>\n",
              "      <td>0</td>\n",
              "      <td>259</td>\n",
              "      <td>187</td>\n",
              "      <td>225</td>\n",
              "      <td>136</td>\n",
              "      <td>61</td>\n",
              "      <td>43</td>\n",
              "      <td>209</td>\n",
              "      <td>23</td>\n",
              "      <td>191</td>\n",
              "      <td>155</td>\n",
              "      <td>239</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>38</th>\n",
              "      <td>14</td>\n",
              "      <td>256</td>\n",
              "      <td>258</td>\n",
              "      <td>252</td>\n",
              "      <td>266</td>\n",
              "      <td>241</td>\n",
              "      <td>243</td>\n",
              "      <td>243</td>\n",
              "      <td>280</td>\n",
              "      <td>171</td>\n",
              "      <td>255</td>\n",
              "      <td>216</td>\n",
              "      <td>223</td>\n",
              "      <td>14</td>\n",
              "      <td>244</td>\n",
              "      <td>292</td>\n",
              "      <td>284</td>\n",
              "      <td>246</td>\n",
              "      <td>66</td>\n",
              "      <td>14</td>\n",
              "      <td>237</td>\n",
              "      <td>294</td>\n",
              "      <td>283</td>\n",
              "      <td>14</td>\n",
              "      <td>14</td>\n",
              "      <td>111</td>\n",
              "      <td>269</td>\n",
              "      <td>243</td>\n",
              "      <td>254</td>\n",
              "      <td>264</td>\n",
              "      <td>260</td>\n",
              "      <td>265</td>\n",
              "      <td>291</td>\n",
              "      <td>280</td>\n",
              "      <td>288</td>\n",
              "      <td>253</td>\n",
              "      <td>305</td>\n",
              "      <td>259</td>\n",
              "      <td>0</td>\n",
              "      <td>132</td>\n",
              "      <td>80</td>\n",
              "      <td>242</td>\n",
              "      <td>271</td>\n",
              "      <td>257</td>\n",
              "      <td>267</td>\n",
              "      <td>239</td>\n",
              "      <td>262</td>\n",
              "      <td>244</td>\n",
              "      <td>282</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>39</th>\n",
              "      <td>146</td>\n",
              "      <td>200</td>\n",
              "      <td>187</td>\n",
              "      <td>128</td>\n",
              "      <td>195</td>\n",
              "      <td>136</td>\n",
              "      <td>161</td>\n",
              "      <td>155</td>\n",
              "      <td>231</td>\n",
              "      <td>39</td>\n",
              "      <td>201</td>\n",
              "      <td>104</td>\n",
              "      <td>160</td>\n",
              "      <td>146</td>\n",
              "      <td>167</td>\n",
              "      <td>242</td>\n",
              "      <td>159</td>\n",
              "      <td>125</td>\n",
              "      <td>70</td>\n",
              "      <td>146</td>\n",
              "      <td>115</td>\n",
              "      <td>250</td>\n",
              "      <td>233</td>\n",
              "      <td>146</td>\n",
              "      <td>146</td>\n",
              "      <td>36</td>\n",
              "      <td>218</td>\n",
              "      <td>176</td>\n",
              "      <td>182</td>\n",
              "      <td>208</td>\n",
              "      <td>160</td>\n",
              "      <td>224</td>\n",
              "      <td>249</td>\n",
              "      <td>229</td>\n",
              "      <td>218</td>\n",
              "      <td>155</td>\n",
              "      <td>262</td>\n",
              "      <td>187</td>\n",
              "      <td>132</td>\n",
              "      <td>0</td>\n",
              "      <td>57</td>\n",
              "      <td>138</td>\n",
              "      <td>194</td>\n",
              "      <td>180</td>\n",
              "      <td>142</td>\n",
              "      <td>168</td>\n",
              "      <td>135</td>\n",
              "      <td>127</td>\n",
              "      <td>155</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>40</th>\n",
              "      <td>94</td>\n",
              "      <td>222</td>\n",
              "      <td>223</td>\n",
              "      <td>175</td>\n",
              "      <td>234</td>\n",
              "      <td>178</td>\n",
              "      <td>195</td>\n",
              "      <td>191</td>\n",
              "      <td>249</td>\n",
              "      <td>96</td>\n",
              "      <td>222</td>\n",
              "      <td>145</td>\n",
              "      <td>187</td>\n",
              "      <td>94</td>\n",
              "      <td>202</td>\n",
              "      <td>260</td>\n",
              "      <td>204</td>\n",
              "      <td>177</td>\n",
              "      <td>14</td>\n",
              "      <td>94</td>\n",
              "      <td>170</td>\n",
              "      <td>266</td>\n",
              "      <td>253</td>\n",
              "      <td>94</td>\n",
              "      <td>94</td>\n",
              "      <td>31</td>\n",
              "      <td>238</td>\n",
              "      <td>208</td>\n",
              "      <td>220</td>\n",
              "      <td>231</td>\n",
              "      <td>210</td>\n",
              "      <td>237</td>\n",
              "      <td>263</td>\n",
              "      <td>249</td>\n",
              "      <td>257</td>\n",
              "      <td>203</td>\n",
              "      <td>277</td>\n",
              "      <td>225</td>\n",
              "      <td>80</td>\n",
              "      <td>57</td>\n",
              "      <td>0</td>\n",
              "      <td>180</td>\n",
              "      <td>235</td>\n",
              "      <td>219</td>\n",
              "      <td>190</td>\n",
              "      <td>204</td>\n",
              "      <td>186</td>\n",
              "      <td>175</td>\n",
              "      <td>202</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>41</th>\n",
              "      <td>254</td>\n",
              "      <td>128</td>\n",
              "      <td>136</td>\n",
              "      <td>104</td>\n",
              "      <td>161</td>\n",
              "      <td>17</td>\n",
              "      <td>67</td>\n",
              "      <td>63</td>\n",
              "      <td>136</td>\n",
              "      <td>115</td>\n",
              "      <td>132</td>\n",
              "      <td>68</td>\n",
              "      <td>87</td>\n",
              "      <td>254</td>\n",
              "      <td>121</td>\n",
              "      <td>182</td>\n",
              "      <td>155</td>\n",
              "      <td>62</td>\n",
              "      <td>190</td>\n",
              "      <td>254</td>\n",
              "      <td>75</td>\n",
              "      <td>167</td>\n",
              "      <td>178</td>\n",
              "      <td>254</td>\n",
              "      <td>254</td>\n",
              "      <td>160</td>\n",
              "      <td>156</td>\n",
              "      <td>106</td>\n",
              "      <td>143</td>\n",
              "      <td>143</td>\n",
              "      <td>139</td>\n",
              "      <td>155</td>\n",
              "      <td>172</td>\n",
              "      <td>163</td>\n",
              "      <td>197</td>\n",
              "      <td>114</td>\n",
              "      <td>179</td>\n",
              "      <td>136</td>\n",
              "      <td>242</td>\n",
              "      <td>138</td>\n",
              "      <td>180</td>\n",
              "      <td>0</td>\n",
              "      <td>165</td>\n",
              "      <td>131</td>\n",
              "      <td>93</td>\n",
              "      <td>123</td>\n",
              "      <td>86</td>\n",
              "      <td>81</td>\n",
              "      <td>137</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>42</th>\n",
              "      <td>279</td>\n",
              "      <td>192</td>\n",
              "      <td>101</td>\n",
              "      <td>217</td>\n",
              "      <td>28</td>\n",
              "      <td>178</td>\n",
              "      <td>152</td>\n",
              "      <td>150</td>\n",
              "      <td>226</td>\n",
              "      <td>181</td>\n",
              "      <td>199</td>\n",
              "      <td>198</td>\n",
              "      <td>140</td>\n",
              "      <td>279</td>\n",
              "      <td>141</td>\n",
              "      <td>253</td>\n",
              "      <td>259</td>\n",
              "      <td>152</td>\n",
              "      <td>240</td>\n",
              "      <td>279</td>\n",
              "      <td>131</td>\n",
              "      <td>243</td>\n",
              "      <td>231</td>\n",
              "      <td>279</td>\n",
              "      <td>279</td>\n",
              "      <td>227</td>\n",
              "      <td>220</td>\n",
              "      <td>117</td>\n",
              "      <td>69</td>\n",
              "      <td>197</td>\n",
              "      <td>59</td>\n",
              "      <td>231</td>\n",
              "      <td>248</td>\n",
              "      <td>231</td>\n",
              "      <td>46</td>\n",
              "      <td>62</td>\n",
              "      <td>255</td>\n",
              "      <td>61</td>\n",
              "      <td>271</td>\n",
              "      <td>194</td>\n",
              "      <td>235</td>\n",
              "      <td>165</td>\n",
              "      <td>0</td>\n",
              "      <td>48</td>\n",
              "      <td>219</td>\n",
              "      <td>74</td>\n",
              "      <td>197</td>\n",
              "      <td>178</td>\n",
              "      <td>244</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>43</th>\n",
              "      <td>265</td>\n",
              "      <td>163</td>\n",
              "      <td>91</td>\n",
              "      <td>202</td>\n",
              "      <td>31</td>\n",
              "      <td>143</td>\n",
              "      <td>119</td>\n",
              "      <td>108</td>\n",
              "      <td>179</td>\n",
              "      <td>168</td>\n",
              "      <td>170</td>\n",
              "      <td>170</td>\n",
              "      <td>97</td>\n",
              "      <td>265</td>\n",
              "      <td>128</td>\n",
              "      <td>230</td>\n",
              "      <td>247</td>\n",
              "      <td>135</td>\n",
              "      <td>224</td>\n",
              "      <td>265</td>\n",
              "      <td>117</td>\n",
              "      <td>196</td>\n",
              "      <td>212</td>\n",
              "      <td>265</td>\n",
              "      <td>265</td>\n",
              "      <td>211</td>\n",
              "      <td>196</td>\n",
              "      <td>84</td>\n",
              "      <td>66</td>\n",
              "      <td>173</td>\n",
              "      <td>77</td>\n",
              "      <td>185</td>\n",
              "      <td>201</td>\n",
              "      <td>206</td>\n",
              "      <td>87</td>\n",
              "      <td>60</td>\n",
              "      <td>208</td>\n",
              "      <td>43</td>\n",
              "      <td>257</td>\n",
              "      <td>180</td>\n",
              "      <td>219</td>\n",
              "      <td>131</td>\n",
              "      <td>48</td>\n",
              "      <td>0</td>\n",
              "      <td>197</td>\n",
              "      <td>51</td>\n",
              "      <td>178</td>\n",
              "      <td>162</td>\n",
              "      <td>231</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>44</th>\n",
              "      <td>281</td>\n",
              "      <td>209</td>\n",
              "      <td>209</td>\n",
              "      <td>57</td>\n",
              "      <td>221</td>\n",
              "      <td>83</td>\n",
              "      <td>153</td>\n",
              "      <td>132</td>\n",
              "      <td>213</td>\n",
              "      <td>109</td>\n",
              "      <td>212</td>\n",
              "      <td>63</td>\n",
              "      <td>177</td>\n",
              "      <td>281</td>\n",
              "      <td>186</td>\n",
              "      <td>246</td>\n",
              "      <td>67</td>\n",
              "      <td>82</td>\n",
              "      <td>203</td>\n",
              "      <td>281</td>\n",
              "      <td>94</td>\n",
              "      <td>232</td>\n",
              "      <td>245</td>\n",
              "      <td>281</td>\n",
              "      <td>281</td>\n",
              "      <td>161</td>\n",
              "      <td>229</td>\n",
              "      <td>193</td>\n",
              "      <td>211</td>\n",
              "      <td>219</td>\n",
              "      <td>172</td>\n",
              "      <td>219</td>\n",
              "      <td>234</td>\n",
              "      <td>234</td>\n",
              "      <td>249</td>\n",
              "      <td>164</td>\n",
              "      <td>241</td>\n",
              "      <td>209</td>\n",
              "      <td>267</td>\n",
              "      <td>142</td>\n",
              "      <td>190</td>\n",
              "      <td>93</td>\n",
              "      <td>219</td>\n",
              "      <td>197</td>\n",
              "      <td>0</td>\n",
              "      <td>198</td>\n",
              "      <td>24</td>\n",
              "      <td>93</td>\n",
              "      <td>53</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>45</th>\n",
              "      <td>247</td>\n",
              "      <td>120</td>\n",
              "      <td>45</td>\n",
              "      <td>190</td>\n",
              "      <td>68</td>\n",
              "      <td>138</td>\n",
              "      <td>88</td>\n",
              "      <td>119</td>\n",
              "      <td>176</td>\n",
              "      <td>160</td>\n",
              "      <td>127</td>\n",
              "      <td>169</td>\n",
              "      <td>77</td>\n",
              "      <td>247</td>\n",
              "      <td>83</td>\n",
              "      <td>185</td>\n",
              "      <td>246</td>\n",
              "      <td>125</td>\n",
              "      <td>208</td>\n",
              "      <td>247</td>\n",
              "      <td>114</td>\n",
              "      <td>206</td>\n",
              "      <td>165</td>\n",
              "      <td>247</td>\n",
              "      <td>247</td>\n",
              "      <td>198</td>\n",
              "      <td>150</td>\n",
              "      <td>46</td>\n",
              "      <td>31</td>\n",
              "      <td>127</td>\n",
              "      <td>90</td>\n",
              "      <td>193</td>\n",
              "      <td>211</td>\n",
              "      <td>161</td>\n",
              "      <td>92</td>\n",
              "      <td>61</td>\n",
              "      <td>219</td>\n",
              "      <td>23</td>\n",
              "      <td>239</td>\n",
              "      <td>168</td>\n",
              "      <td>204</td>\n",
              "      <td>123</td>\n",
              "      <td>74</td>\n",
              "      <td>51</td>\n",
              "      <td>198</td>\n",
              "      <td>0</td>\n",
              "      <td>181</td>\n",
              "      <td>142</td>\n",
              "      <td>229</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>46</th>\n",
              "      <td>276</td>\n",
              "      <td>205</td>\n",
              "      <td>194</td>\n",
              "      <td>61</td>\n",
              "      <td>201</td>\n",
              "      <td>79</td>\n",
              "      <td>145</td>\n",
              "      <td>121</td>\n",
              "      <td>211</td>\n",
              "      <td>99</td>\n",
              "      <td>208</td>\n",
              "      <td>62</td>\n",
              "      <td>167</td>\n",
              "      <td>276</td>\n",
              "      <td>176</td>\n",
              "      <td>246</td>\n",
              "      <td>76</td>\n",
              "      <td>68</td>\n",
              "      <td>199</td>\n",
              "      <td>276</td>\n",
              "      <td>74</td>\n",
              "      <td>229</td>\n",
              "      <td>242</td>\n",
              "      <td>276</td>\n",
              "      <td>276</td>\n",
              "      <td>157</td>\n",
              "      <td>226</td>\n",
              "      <td>180</td>\n",
              "      <td>194</td>\n",
              "      <td>214</td>\n",
              "      <td>150</td>\n",
              "      <td>215</td>\n",
              "      <td>231</td>\n",
              "      <td>233</td>\n",
              "      <td>228</td>\n",
              "      <td>144</td>\n",
              "      <td>238</td>\n",
              "      <td>191</td>\n",
              "      <td>262</td>\n",
              "      <td>135</td>\n",
              "      <td>186</td>\n",
              "      <td>86</td>\n",
              "      <td>197</td>\n",
              "      <td>178</td>\n",
              "      <td>24</td>\n",
              "      <td>181</td>\n",
              "      <td>0</td>\n",
              "      <td>87</td>\n",
              "      <td>62</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>47</th>\n",
              "      <td>257</td>\n",
              "      <td>142</td>\n",
              "      <td>137</td>\n",
              "      <td>57</td>\n",
              "      <td>185</td>\n",
              "      <td>87</td>\n",
              "      <td>98</td>\n",
              "      <td>138</td>\n",
              "      <td>212</td>\n",
              "      <td>97</td>\n",
              "      <td>144</td>\n",
              "      <td>101</td>\n",
              "      <td>141</td>\n",
              "      <td>257</td>\n",
              "      <td>102</td>\n",
              "      <td>172</td>\n",
              "      <td>124</td>\n",
              "      <td>37</td>\n",
              "      <td>187</td>\n",
              "      <td>257</td>\n",
              "      <td>62</td>\n",
              "      <td>247</td>\n",
              "      <td>165</td>\n",
              "      <td>257</td>\n",
              "      <td>257</td>\n",
              "      <td>152</td>\n",
              "      <td>155</td>\n",
              "      <td>136</td>\n",
              "      <td>147</td>\n",
              "      <td>145</td>\n",
              "      <td>133</td>\n",
              "      <td>233</td>\n",
              "      <td>251</td>\n",
              "      <td>163</td>\n",
              "      <td>195</td>\n",
              "      <td>116</td>\n",
              "      <td>260</td>\n",
              "      <td>155</td>\n",
              "      <td>244</td>\n",
              "      <td>127</td>\n",
              "      <td>175</td>\n",
              "      <td>81</td>\n",
              "      <td>178</td>\n",
              "      <td>162</td>\n",
              "      <td>93</td>\n",
              "      <td>142</td>\n",
              "      <td>87</td>\n",
              "      <td>0</td>\n",
              "      <td>105</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>48</th>\n",
              "      <td>296</td>\n",
              "      <td>240</td>\n",
              "      <td>235</td>\n",
              "      <td>52</td>\n",
              "      <td>252</td>\n",
              "      <td>130</td>\n",
              "      <td>189</td>\n",
              "      <td>181</td>\n",
              "      <td>264</td>\n",
              "      <td>120</td>\n",
              "      <td>241</td>\n",
              "      <td>107</td>\n",
              "      <td>219</td>\n",
              "      <td>296</td>\n",
              "      <td>206</td>\n",
              "      <td>266</td>\n",
              "      <td>22</td>\n",
              "      <td>106</td>\n",
              "      <td>216</td>\n",
              "      <td>296</td>\n",
              "      <td>117</td>\n",
              "      <td>285</td>\n",
              "      <td>264</td>\n",
              "      <td>296</td>\n",
              "      <td>296</td>\n",
              "      <td>171</td>\n",
              "      <td>253</td>\n",
              "      <td>228</td>\n",
              "      <td>237</td>\n",
              "      <td>245</td>\n",
              "      <td>190</td>\n",
              "      <td>271</td>\n",
              "      <td>287</td>\n",
              "      <td>259</td>\n",
              "      <td>269</td>\n",
              "      <td>188</td>\n",
              "      <td>294</td>\n",
              "      <td>239</td>\n",
              "      <td>282</td>\n",
              "      <td>155</td>\n",
              "      <td>202</td>\n",
              "      <td>137</td>\n",
              "      <td>244</td>\n",
              "      <td>231</td>\n",
              "      <td>53</td>\n",
              "      <td>229</td>\n",
              "      <td>62</td>\n",
              "      <td>105</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "     0    1    2    3    4    5    6   ...   42   43   44   45   46   47   48\n",
              "0     0  264  266  266  274  254  253  ...  279  265  281  247  276  257  296\n",
              "1   264    0  100  191  187  140   65  ...  192  163  209  120  205  142  240\n",
              "2   266  100    0  191  104  152   85  ...  101   91  209   45  194  137  235\n",
              "3   266  191  191    0  224  101  144  ...  217  202   57  190   61   57   52\n",
              "4   274  187  104  224    0  173  147  ...   28   31  221   68  201  185  252\n",
              "5   254  140  152  101  173    0   82  ...  178  143   83  138   79   87  130\n",
              "6   253   65   85  144  147   82    0  ...  152  119  153   88  145   98  189\n",
              "7   253  156  148  157  137   64   98  ...  150  108  132  119  121  138  181\n",
              "8   288  156  195  235  206  137  136  ...  226  179  213  176  211  212  264\n",
              "9   185  193  176   93  186  114  147  ...  181  168  109  160   99   97  120\n",
              "10  263    8  106  192  194  144   71  ...  199  170  212  127  208  144  241\n",
              "11  229  183  188   88  195   56  128  ...  198  170   63  169   62  101  107\n",
              "12  231   96   99  180  125   98   59  ...  140   97  177   77  167  141  219\n",
              "13    0  264  266  266  274  254  253  ...  279  265  281  247  276  257  296\n",
              "14  254   80   52  158  146  137   70  ...  141  128  186   83  176  102  206\n",
              "15  299   74  153  216  252  193  128  ...  253  230  246  185  246  172  266\n",
              "16  298  258  253   70  267  147  208  ...  259  247   67  246   76  124   22\n",
              "17  258  149  129   69  158   69   92  ...  152  135   82  125   68   37  106\n",
              "18   80  226  227  189  238  188  202  ...  240  224  203  208  199  187  216\n",
              "19    0  264  266  266  274  254  253  ...  279  265  281  247  276  257  296\n",
              "20  250  163  127   87  138   81  104  ...  131  117   94  114   74   62  117\n",
              "21  301  208  233  263  221  165  180  ...  243  196  232  206  229  247  285\n",
              "22  291   65  131  214  231  190  120  ...  231  212  245  165  242  165  264\n",
              "23    0  264  266  266  274  254  253  ...  279  265  281  247  276  257  296\n",
              "24    0  264  266  266  274  254  253  ...  279  265  281  247  276  257  296\n",
              "25  126  216  215  146  227  157  183  ...  227  211  161  198  157  152  171\n",
              "26  277   38  122  203  217  168   97  ...  220  196  229  150  226  155  253\n",
              "27  251   80   52  185  108  121   54  ...  117   84  193   46  180  136  228\n",
              "28  262  130   34  198   73  158  104  ...   69   66  211   31  194  147  237\n",
              "29  272   23  100  196  194  156   79  ...  197  173  219  127  214  145  245\n",
              "30  271  190  109  166   78  149  140  ...   59   77  172   90  150  133  190\n",
              "31  272  200  223  248  209  152  169  ...  231  185  219  193  215  233  271\n",
              "32  298  214  239  266  225  168  186  ...  248  201  234  211  231  251  287\n",
              "33  288   46  133  209  228  174  105  ...  231  206  234  161  233  163  259\n",
              "34  296  201  102  238   67  210  172  ...   46   87  249   92  228  195  269\n",
              "35  263  156   78  157   73  127  106  ...   62   60  164   61  144  116  188\n",
              "36  312  222  247  274  232  176  194  ...  255  208  241  219  238  260  294\n",
              "37  267  134   50  203   56  151  102  ...   61   43  209   23  191  155  239\n",
              "38   14  256  258  252  266  241  243  ...  271  257  267  239  262  244  282\n",
              "39  146  200  187  128  195  136  161  ...  194  180  142  168  135  127  155\n",
              "40   94  222  223  175  234  178  195  ...  235  219  190  204  186  175  202\n",
              "41  254  128  136  104  161   17   67  ...  165  131   93  123   86   81  137\n",
              "42  279  192  101  217   28  178  152  ...    0   48  219   74  197  178  244\n",
              "43  265  163   91  202   31  143  119  ...   48    0  197   51  178  162  231\n",
              "44  281  209  209   57  221   83  153  ...  219  197    0  198   24   93   53\n",
              "45  247  120   45  190   68  138   88  ...   74   51  198    0  181  142  229\n",
              "46  276  205  194   61  201   79  145  ...  197  178   24  181    0   87   62\n",
              "47  257  142  137   57  185   87   98  ...  178  162   93  142   87    0  105\n",
              "48  296  240  235   52  252  130  189  ...  244  231   53  229   62  105    0\n",
              "\n",
              "[49 rows x 49 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cg6LIm4nMg_M"
      },
      "source": [
        "##SVD (Decomposição Singular de Vetores)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OWmMMCBvJTjQ"
      },
      "source": [
        "####Resumo"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T4b1HnYtIcJD"
      },
      "source": [
        "Qualquer vetor de força pode ser decomposto em seus componentes ao longo dos eixos x e y conforme imagem abaixo:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p_9-tiTFIaxC"
      },
      "source": [
        "<img alt=\"\" class=\"qv wg et fh fd ke v c\" width=\"338\" height=\"312\" role=\"presentation\" src=\"https://miro.medium.com/max/423/1*AP19J0U3bJUy8zbodGS_4g.gif\" srcset=\"https://miro.medium.com/max/345/1*AP19J0U3bJUy8zbodGS_4g.gif 276w, https://miro.medium.com/max/423/1*AP19J0U3bJUy8zbodGS_4g.gif 338w\" sizes=\"338px\">"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l6htvkTGIjaa"
      },
      "source": [
        "Parabéns, Agora você sabe o que é singular decomposição de valor. De forma resumida, o svd nada mais é do que decomposição de vetores em eixos ortogonais (que intercepta em ângulos retos)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jfP6lymMJWA2"
      },
      "source": [
        "####Detalhamento"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s6QjYbA-Myrp"
      },
      "source": [
        "Como vimos, a decomposição de valores singulares, é um método de decomposição de matriz para reduzir uma matriz às suas partes constituintes, a fim de tornar mais simples alguns cálculos de matriz subsequentes.\n",
        "\n",
        "A = U . Sigma . V^T\n",
        "\n",
        "Onde A é a matriz real **coluna x linha** que desejamos decompor, U é uma matriz **coluna x coluna**, Sigma (frequentemente representado pela letra grega maiúscula Sigma) é uma matriz diagonal **coluna x linha** e V^T é a transposta de uma matriz **linha x linha** onde T é um sobrescrito.\n",
        "\n",
        "Os valores diagonais na matriz Sigma são conhecidos como os valores singulares da matriz original A. As colunas da matriz U são chamadas de vetores singulares à esquerda de A, e as colunas de V são chamadas de vetores singulares à direita de A.\n",
        "\n",
        "O SVD é amplamente usado no cálculo de outras operações de matriz, como matriz inversa, mas também como um método de redução de dados em aprendizado de máquina.\n",
        " \n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qcn0ddhFJowt"
      },
      "source": [
        "####Como calcular?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ftFICzwsJsYw"
      },
      "source": [
        "Especificamente, o SVD decompõe qualquer matriz A em uma matriz ortogonal U, uma matriz diagonal Σ, e outra matriz ortogonal V^T."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XvPOrXBVJyo7"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n7mIilM2KB1H"
      },
      "source": [
        "U consiste dos autovetores de AA^T, enquanto V é uma matriz de autovetores de A^TA. Os valores singulares values em Σ são a raiz quadrada dos autovalores de AA^T.\n",
        "\n",
        "Lembre-se que a decomposição espectral só pode ser realizada em matrizes quadradas. Multiplicando A por sua transposição, você tem uma matriz que tem o mesmo número de linhas e de colunas. U também é conhecida como uma matriz de vetores singulares de esquerda, Σ como valores singulares, e V^T\n",
        "como os vetores singulares de direita. Ufa... isso é muito para digerir."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ez4rdbtUKr1f"
      },
      "source": [
        "####Analogia"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dOGp1HnMLh79"
      },
      "source": [
        "Imagine que você tenha uma mercearia que vende diferentes produtos, e você capturou todos os seus produtos como colunas em uma matriz e todos os clientes como linhas. Cada linha indica quantos itens de um determinado produto um cliente comprou. Assumimos que comprar quantidades maiores de um determinado produto indica uma preferência maior."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9-gKv0vvL1fD"
      },
      "source": [
        "Você pode pensar em U como representando a similaridade de vários produtos a certos conceitos."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qo0zzy2SMVCK"
      },
      "source": [
        "V^T encapsula um conceito como um \"amante do vinho\" ou um amante do queijo, enquanto Sigma (s) representa a força desse conceito."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ddt0Wzr7M099"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VBs1DR9FNhLC"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hwIzfXUlOYV2"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SwTGTwzBOvwv"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1_gyX5-kMb0P"
      },
      "source": [
        "Neste caso, temos um cliente que gosta muito de vinho e queijo, vou chamar esse comportamento de \"harmonização Portuguesa\" ([Veja o porque no link](https://www.wine.com.br/winepedia/harmonizacao-de-a-a-w/queijos-e-vinhos/)), mas que não gosta de doces e um amante doce que não gosta de vinho e queijo. As duas primeiras entradas de coluna em U indicam que o vinho tem uma alta semelhança com o conceito de \"harmonização portuguesa\". Sigma nos mostra que este parece ser um conceito forte, e V^T indica que os Clientes 1 e 2 associam-se fortemente a esse conceito."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LP65hx-xPlAb"
      },
      "source": [
        "####Implementação Manual"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hsorbUbjPmvX"
      },
      "source": [
        "Como esse tutorial é baseado em sua maioria em conceitos manuais, deixei uma implementação do svd para que você possa se aprofundar mais a fundo nos conceitos depurando o código. Ele é altamente baseado na biblioteca **np.linalg.svd** do Numpy. Usaremos ele mais à frente."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mxl_5wms-CJx"
      },
      "source": [
        "def vetorDeUnidadeAleatorio(vetor):\n",
        "    nao_normalizado= [normalvariate(0, 1) for _ in range(vetor)]\n",
        "    normalizacao = math.sqrt(sum(x * x for x in nao_normalizado))\n",
        "    return [x / normalizacao for x in nao_normalizado]\n",
        "\n",
        "\n",
        "def svd_1d(A, epsilon=1e-10):\n",
        "    '''SVD unidimensional'''\n",
        "\n",
        "    linhas, colunas = A.shape\n",
        "    x = vetorDeUnidadeAleatorio(min(linhas,colunas))\n",
        "    ultimoV = None\n",
        "    atualV = x\n",
        "\n",
        "    if linhas > colunas:\n",
        "        B = np.dot(A.T, A)\n",
        "    else:\n",
        "        B = np.dot(A, A.T)\n",
        "\n",
        "    iteracoes= 0\n",
        "    while True:\n",
        "        iteracoes += 1\n",
        "        ultimoV = atualV\n",
        "        atualV = np.dot(B, ultimoV)\n",
        "        atualV = atualV / norm(atualV)\n",
        "\n",
        "        if abs(np.dot(atualV, ultimoV)) > 1 - epsilon:\n",
        "            return atualV\n",
        "\n",
        "\n",
        "def svd(A, k=None, epsilon=1e-10):\n",
        "    '''\n",
        "        Calcula a decomposição de valor singular de uma matriz A\n",
        "        usando o método de potência. A é a matriz de entrada e k\n",
        "        é o número de valores singulares que você deseja calcular.\n",
        "        Se k não tiver valores, isso calcula a decomposição completa.\n",
        "    '''\n",
        "    A = np.array(A, dtype=float)\n",
        "    linhas, colunas = A.shape\n",
        "    svds = []\n",
        "    if k is None:\n",
        "        k = min(linhas, colunas)\n",
        "\n",
        "    for i in range(k):\n",
        "        matriz_1d = A.copy()\n",
        "\n",
        "        for u, valor_singular, v in svds[:i]:\n",
        "            matriz_1d -= valor_singular * np.outer(u, v)\n",
        "\n",
        "        if linhas > colunas:\n",
        "            v = svd_1d(matriz_1d, epsilon=epsilon) #próximo vetor singular\n",
        "            u_nao_normalizado = np.dot(A, v)\n",
        "            sigma = norm(u_nao_normalizado)  #próximo vetor singular\n",
        "            u = u_nao_normalizado / sigma\n",
        "        else:\n",
        "            u = svd_1d(matriz_1d, epsilon=epsilon)  #próximo vetor singular\n",
        "            vetor_nao_normalizado = np.dot(A.T, u)\n",
        "            sigma = norm(vetor_nao_normalizado)  #próximo vetor singular\n",
        "            v = vetor_nao_normalizado / sigma\n",
        "\n",
        "        svds.append((u,sigma, v))\n",
        "\n",
        "    us,valores_singulares, vs = [np.array(x) for x in zip(*svds)]\n",
        "    return us.T, valores_singulares,vs"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Dk3ZHZ3WJhPQ"
      },
      "source": [
        "OBS: Como estamos utilizando um algoritmo que gera números aleatórios, as vezes a saída poderá ser diferente da implementada pelo numpy (np.linalg.svd). O sinal poderá alternar entre + e -."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_rO3Tt28JvUz"
      },
      "source": [
        "##Scores"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WXW-cxVYCmeY"
      },
      "source": [
        "A análise de Correspondência Simples fornece uma forma de representar uma tabela de distâncias Qui² em formato gráfico (similar à uma PCA). \n",
        "\n",
        "Para calcular essa representação, precisamos transformar as distâncias em pontos em um sistema de coordenadas cartesianas. Isso é obtido por uma decomposição de valor singular (SVD) de uma matriz de resíduos padronizados"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "31HUSbUJDL2O"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vY8O4jEnqP3J"
      },
      "source": [
        "residuos_padronizados = np.divide((matriz_correspondencia-modelo_independencia),np.sqrt(modelo_independencia))\n",
        "u,s,vh = svd(residuos_padronizados)\n",
        "\n",
        "#Caso queiram Comparar basta utilizar o comando ao lado -> u,s,vh = np.linalg.svd(residuos_padronizados, full_matrices=False)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DXh9tXBwDXsJ"
      },
      "source": [
        "Estamos atrás das coordenadas das linhas. Esses pontos são organizados de forma que a distância euclidiana entre dois pontos seja igual à distância Qui² entre as duas linhas às quais eles correspondem. As pontuações das linhas são definidas como:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OzoPFzV5Dm2O"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uXgDlZOaDtzH"
      },
      "source": [
        "onde U e S são a matriz de vetores singulares à esquerda e os valores singulares na matriz diagonal de SVD. Quando ao deltaR é a matriz diagonal feita dos recíprocos das raízes quadradas dos totais da linha.\n",
        "\n",
        "OBS: No caso do vh para o cálculo dos scores das colunas deveremos fazer a transposição da matriz."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OYUXKpnkqzaa"
      },
      "source": [
        "def Calculo_Scores(total_linha_coluna,u_vhT,s):\n",
        "  delta_R=np.diag(np.divide(1.0, np.sqrt(total_linha_coluna)))\n",
        "  return np.dot(np.dot(delta_R, u_vhT), np.diag(s))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C_RrEG5ir_-X"
      },
      "source": [
        "scores_linhas = Calculo_Scores(total_linha, u, s)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7TiiYKVosKXB"
      },
      "source": [
        "scores_colunas = Calculo_Scores(total_colunas, vh.T, s)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "flkVCXSjJzEO"
      },
      "source": [
        "##Variância Explicada"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OXTcp5grGlRL"
      },
      "source": [
        "Vamos verificar quanto da variância cada componente está capturando"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lIpaP4ttGLTa",
        "outputId": "63a68a13-7684-4b79-e324-787699d80691"
      },
      "source": [
        "variancia_explicada = np.round(s**2/np.sum(s**2), decimals=3) * 100\n",
        "variancia_explicada"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([39.6, 23.2, 21.5, 15.7,  0. ])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 88
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XSebBYrfG8E_"
      },
      "source": [
        "Veja que com 4 dimensões explicamos praticamente todos os nossos dados e a quinta está muita próxima de 0. Vamos então considerar somente as 4 primeiras para plotagem da variância capturada."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Xx-spzMYHO2I",
        "outputId": "a4146043-e8aa-4ddd-93f7-1127e0315153"
      },
      "source": [
        "variancia_dimensional=variancia_explicada[0:4]\n",
        "print(f'Variâncias Dimensionais: {variancia_dimensional}')\n",
        "print(f'Variância capturada: {round(sum(variancia_dimensional),2)}%')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Variâncias Dimensionais: [39.6 23.2 21.5 15.7]\n",
            "Variância capturada: 100.0%\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2ENwiUgaGrpY"
      },
      "source": [
        "Com 2 componentes podemos explicar em média 62.8% da variância de todos os nossos dados. Vamos visualizar isso de forma gráfica:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "id": "gKavr7z6FYpP",
        "outputId": "76e45a3a-9855-48a9-91f2-c39cb9866e99"
      },
      "source": [
        "sns.barplot(x=list(range(1,len(variancia_dimensional)+1)), y=variancia_dimensional, color=\"blue\")\n",
        "plt.title(\"Quantidade de variância explicada por componente\")\n",
        "plt.xlabel('SVs', fontsize=16)\n",
        "plt.ylabel('% Variância Explicada', fontsize=16)\n",
        "plt.show();"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6Z8YH0MCEMD8"
      },
      "source": [
        "Vamos separar esses 2 componentes dos demais criando um dataframe."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6KXqd2xDmjVc"
      },
      "source": [
        "def Row_Column_Scores(n_componentes=2):\n",
        "  #Scores das linhas\n",
        "  df_linha = pd.DataFrame(data=[l[0:n_componentes] for l in scores_linhas], columns=[f'dim{i}' for i in range(1,n_componentes+1)],index=df['country'].sort_values().unique())\n",
        "  df_linha['variavel']='linha'\n",
        "\n",
        "  #Scores das colunas\n",
        "  df_coluna=pd.DataFrame(data=[l[0:n_componentes] for l in scores_colunas], columns=[f'dim{i}' for i in range(1,n_componentes+1)],index=df['lethality_Q5'].sort_values().unique())\n",
        "  df_coluna['variavel']='coluna'\n",
        "\n",
        "  #Juntar tudo\n",
        "  df_final=pd.concat([df_linha,df_coluna])\n",
        "\n",
        "  return df_final"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8VWeefxBm9P1"
      },
      "source": [
        "df_final_dois_componentes =Row_Column_Scores()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "LVxKZhUlGdcS",
        "outputId": "85cfe081-d2bc-4d9b-fda4-a7829f20cb62"
      },
      "source": [
        "df_final_dois_componentes"
      ],
      "execution_count": null,
      "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>dim1</th>\n",
              "      <th>dim2</th>\n",
              "      <th>variavel</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>Anguilla</th>\n",
              "      <td>-1.894034</td>\n",
              "      <td>0.602967</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Antigua And Barbuda</th>\n",
              "      <td>0.643029</td>\n",
              "      <td>0.511945</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Argentina</th>\n",
              "      <td>0.679111</td>\n",
              "      <td>0.185432</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Aruba</th>\n",
              "      <td>-0.035105</td>\n",
              "      <td>-1.190976</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Bahamas</th>\n",
              "      <td>0.552884</td>\n",
              "      <td>0.112795</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Barbados</th>\n",
              "      <td>0.297002</td>\n",
              "      <td>-0.385940</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Belize</th>\n",
              "      <td>0.558527</td>\n",
              "      <td>0.091646</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Bermuda</th>\n",
              "      <td>0.366923</td>\n",
              "      <td>-0.023767</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Bolivia</th>\n",
              "      <td>0.658593</td>\n",
              "      <td>0.820111</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Bonaire, Saint Eustatius And Saba</th>\n",
              "      <td>-0.620855</td>\n",
              "      <td>-0.714133</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Brazil</th>\n",
              "      <td>0.614945</td>\n",
              "      <td>0.521759</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>British Virgin Islands</th>\n",
              "      <td>-0.186723</td>\n",
              "      <td>-0.619628</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Canada</th>\n",
              "      <td>0.383126</td>\n",
              "      <td>0.461099</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Cayman Islands</th>\n",
              "      <td>-1.894034</td>\n",
              "      <td>0.602967</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Chile</th>\n",
              "      <td>0.493632</td>\n",
              "      <td>-0.017156</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Colombia</th>\n",
              "      <td>0.731804</td>\n",
              "      <td>0.455191</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Costa Rica</th>\n",
              "      <td>-0.242815</td>\n",
              "      <td>-1.738067</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Cuba</th>\n",
              "      <td>0.283564</td>\n",
              "      <td>-0.767379</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Curaçao</th>\n",
              "      <td>-1.449676</td>\n",
              "      <td>-0.027026</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Dominica</th>\n",
              "      <td>-1.894034</td>\n",
              "      <td>0.602967</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Dominican Republic</th>\n",
              "      <td>0.186736</td>\n",
              "      <td>-0.754733</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Ecuador</th>\n",
              "      <td>0.561015</td>\n",
              "      <td>0.875247</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>El Salvador</th>\n",
              "      <td>0.711636</td>\n",
              "      <td>0.442396</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Falkland Islands (Malvinas)</th>\n",
              "      <td>-1.894034</td>\n",
              "      <td>0.602967</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Greenland</th>\n",
              "      <td>-1.894034</td>\n",
              "      <td>0.602967</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Grenada</th>\n",
              "      <td>-1.198668</td>\n",
              "      <td>-0.382896</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Guatemala</th>\n",
              "      <td>0.663126</td>\n",
              "      <td>0.504362</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Guyana</th>\n",
              "      <td>0.607960</td>\n",
              "      <td>0.381312</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Haiti</th>\n",
              "      <td>0.588323</td>\n",
              "      <td>0.131986</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Honduras</th>\n",
              "      <td>0.690077</td>\n",
              "      <td>0.462510</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Jamaica</th>\n",
              "      <td>0.378744</td>\n",
              "      <td>-0.581085</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Mexico</th>\n",
              "      <td>0.293974</td>\n",
              "      <td>0.821073</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Montserrat</th>\n",
              "      <td>0.478600</td>\n",
              "      <td>0.891492</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Nicaragua</th>\n",
              "      <td>0.741694</td>\n",
              "      <td>0.526211</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Panama</th>\n",
              "      <td>0.644277</td>\n",
              "      <td>-0.076651</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Paraguay</th>\n",
              "      <td>0.473480</td>\n",
              "      <td>-0.365254</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Peru</th>\n",
              "      <td>0.590876</td>\n",
              "      <td>0.905145</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Puerto Rico</th>\n",
              "      <td>0.665734</td>\n",
              "      <td>0.210951</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Saint Kitts And Nevis</th>\n",
              "      <td>-1.815618</td>\n",
              "      <td>0.491792</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Saint Lucia</th>\n",
              "      <td>-0.915136</td>\n",
              "      <td>-0.454133</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Saint Vincent And The Grenadines</th>\n",
              "      <td>-1.371260</td>\n",
              "      <td>-0.138201</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Sint Maarten</th>\n",
              "      <td>0.368968</td>\n",
              "      <td>-0.334654</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Suriname</th>\n",
              "      <td>0.546046</td>\n",
              "      <td>-0.095173</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Trinidad And Tobago</th>\n",
              "      <td>0.560877</td>\n",
              "      <td>0.099401</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Turks And Caicos Islands</th>\n",
              "      <td>0.070803</td>\n",
              "      <td>-1.179858</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>United States Of America</th>\n",
              "      <td>0.492597</td>\n",
              "      <td>0.229749</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>United States Virgin Islands</th>\n",
              "      <td>0.101999</td>\n",
              "      <td>-1.136368</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Uruguay</th>\n",
              "      <td>0.208994</td>\n",
              "      <td>-0.804145</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Venezuela</th>\n",
              "      <td>-0.081380</td>\n",
              "      <td>-1.614739</td>\n",
              "      <td>linha</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>L1</th>\n",
              "      <td>-1.643636</td>\n",
              "      <td>0.400104</td>\n",
              "      <td>coluna</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>L2</th>\n",
              "      <td>-0.123870</td>\n",
              "      <td>-1.247455</td>\n",
              "      <td>coluna</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>L3</th>\n",
              "      <td>0.553954</td>\n",
              "      <td>-0.089373</td>\n",
              "      <td>coluna</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>L4</th>\n",
              "      <td>0.668732</td>\n",
              "      <td>0.334554</td>\n",
              "      <td>coluna</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>L5</th>\n",
              "      <td>0.544013</td>\n",
              "      <td>0.603523</td>\n",
              "      <td>coluna</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                                       dim1      dim2 variavel\n",
              "Anguilla                          -1.894034  0.602967    linha\n",
              "Antigua And Barbuda                0.643029  0.511945    linha\n",
              "Argentina                          0.679111  0.185432    linha\n",
              "Aruba                             -0.035105 -1.190976    linha\n",
              "Bahamas                            0.552884  0.112795    linha\n",
              "Barbados                           0.297002 -0.385940    linha\n",
              "Belize                             0.558527  0.091646    linha\n",
              "Bermuda                            0.366923 -0.023767    linha\n",
              "Bolivia                            0.658593  0.820111    linha\n",
              "Bonaire, Saint Eustatius And Saba -0.620855 -0.714133    linha\n",
              "Brazil                             0.614945  0.521759    linha\n",
              "British Virgin Islands            -0.186723 -0.619628    linha\n",
              "Canada                             0.383126  0.461099    linha\n",
              "Cayman Islands                    -1.894034  0.602967    linha\n",
              "Chile                              0.493632 -0.017156    linha\n",
              "Colombia                           0.731804  0.455191    linha\n",
              "Costa Rica                        -0.242815 -1.738067    linha\n",
              "Cuba                               0.283564 -0.767379    linha\n",
              "Curaçao                           -1.449676 -0.027026    linha\n",
              "Dominica                          -1.894034  0.602967    linha\n",
              "Dominican Republic                 0.186736 -0.754733    linha\n",
              "Ecuador                            0.561015  0.875247    linha\n",
              "El Salvador                        0.711636  0.442396    linha\n",
              "Falkland Islands (Malvinas)       -1.894034  0.602967    linha\n",
              "Greenland                         -1.894034  0.602967    linha\n",
              "Grenada                           -1.198668 -0.382896    linha\n",
              "Guatemala                          0.663126  0.504362    linha\n",
              "Guyana                             0.607960  0.381312    linha\n",
              "Haiti                              0.588323  0.131986    linha\n",
              "Honduras                           0.690077  0.462510    linha\n",
              "Jamaica                            0.378744 -0.581085    linha\n",
              "Mexico                             0.293974  0.821073    linha\n",
              "Montserrat                         0.478600  0.891492    linha\n",
              "Nicaragua                          0.741694  0.526211    linha\n",
              "Panama                             0.644277 -0.076651    linha\n",
              "Paraguay                           0.473480 -0.365254    linha\n",
              "Peru                               0.590876  0.905145    linha\n",
              "Puerto Rico                        0.665734  0.210951    linha\n",
              "Saint Kitts And Nevis             -1.815618  0.491792    linha\n",
              "Saint Lucia                       -0.915136 -0.454133    linha\n",
              "Saint Vincent And The Grenadines  -1.371260 -0.138201    linha\n",
              "Sint Maarten                       0.368968 -0.334654    linha\n",
              "Suriname                           0.546046 -0.095173    linha\n",
              "Trinidad And Tobago                0.560877  0.099401    linha\n",
              "Turks And Caicos Islands           0.070803 -1.179858    linha\n",
              "United States Of America           0.492597  0.229749    linha\n",
              "United States Virgin Islands       0.101999 -1.136368    linha\n",
              "Uruguay                            0.208994 -0.804145    linha\n",
              "Venezuela                         -0.081380 -1.614739    linha\n",
              "L1                                -1.643636  0.400104   coluna\n",
              "L2                                -0.123870 -1.247455   coluna\n",
              "L3                                 0.553954 -0.089373   coluna\n",
              "L4                                 0.668732  0.334554   coluna\n",
              "L5                                 0.544013  0.603523   coluna"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 94
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OMj-jU-dJ3Hl"
      },
      "source": [
        "##Visualização dos resultados"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bcYNI0HVEWDG"
      },
      "source": [
        "Vamos visualizar gráficamente nossos resultados."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "xJhXU8QHqy7E",
        "outputId": "43c44892-d03a-4104-9a81-c0552ecb8e5e"
      },
      "source": [
        "fig=plt.figure(figsize=(30,30))\n",
        "ax = sns.scatterplot(data=df_final_dois_componentes,x='dim1', y='dim2', hue='variavel')\n",
        "ax.axhline(y=0, color='k')\n",
        "ax.axvline(x=0, color='k')\n",
        "ax.get_legend().set_visible(False)\n",
        "plt.title(\"Análise de Correspondência\",fontsize=18)\n",
        "plt.xlabel(f\"Dimensão 1: {round(variancia_explicada[0],2)}%\",fontsize=18)\n",
        "plt.ylabel(f\"Dimensão 2: {round(variancia_explicada[1],2)}%\",fontsize=18)\n",
        "\n",
        "texts=[]\n",
        "\n",
        "for rotulo in df_final_dois_componentes.index:\n",
        "    texts.append(plt.annotate(rotulo, \n",
        "                 (df_final_dois_componentes.loc[rotulo,:]['dim1'],\n",
        "                  df_final_dois_componentes.loc[rotulo,:]['dim2']),\n",
        "                 horizontalalignment='center', verticalalignment='center',size=15))\n",
        "    \n",
        "adjust_text(texts, force_points=0.2, force_text=0.2,\n",
        "            expand_points=(1.5, 1.5), expand_text=(1.5, 1.5),\n",
        "            arrowprops=dict(arrowstyle=\"-\", color='black', lw=1))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "500"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 95
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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eDRs21Pz58/XQQw9lG69FixZq3769/v73v+vYsWOKjo7W5MmTHcc7dOigt956S+PHj9eUKVPUvHlzLVu2TDVq1CjwvQIAABQ1Y60t6QzFLjIy0u7YsaOkYwAAAAAASqlevXrJzc1NU6dOLekoAHIRHR0tSVq3bl2J5gAAAIXPGLPTWhuZtZ2ZZgAAAAAAFLOEhAQtWLCgpGMAAAAAuAJFMwAAAABAobDW6ty5czp9+nSe25kzZ5z2hw4dqrZt25Z0/GL1448/lnQEAAAAAFlQNAMAAACAErb397Pad/ycynl5qGZIOQX6eRV7hoyMjAIVvPLazp49Ky8vL5UvXz7PLTg42Gk/Kiqq2O8XAAAAALKiaAYAAAAAJWj7/hN65ONtSr6YLklqV6uS3rivvoL9vQs8RkZGRrbZWznN6Mqv4OXr65tvwaty5cqOz/7+/k7H/P395eHhUVSPCgAAAACKFEUzAAAAACghZ5Iv6vXl3zoKZpK0aus3Ck/6XtX8TYELXufPn5efn1++Ba+wsLBcj/n7+6tMmTIl+DQAAAAAoGRRNAMAAACAEnLuQpq+P3rWqS3px81a+M1+1b7+v0sYXnfddapWrVquBa9y5crJzc2thO4CAAAAAP4aKJoBAAAAQAkJ9PPUnfVCtPjL3xxt/k076/0nmikqIrAEkwEAAABA6cOvIgIAAABACfFyL6OBbW9Si+qZBbKynmU0snM91atSvoST4f+zd9/RVlX32oDfTZEOSjmAQUSKYveTo1EURRRRERFLxMTrxa43ftEYJbnGgiaxY7lfrNEIhthFMdiTiAWxoNcC9oKKgthACAdp+/sj13Nz5NCFA+7nGWMPzpprrjl/a63jcAxe5twAAEDpsdIMAACgBnUqa5zrDu+Wj6fPSf26tbPBeg1SKBRquiwAAICSIzQDAACoYY3r1c3GrevWdBkAAAAlzfaMAAAAAACr0JAhQ1IoFFIoFFKrVq2st9562W677fLrX/86U6dOXa21jBkzJoVCIRMmTFiu64YNG5ZCoZBZs2atosqWz6RJkyqfaaFQSOPGjbP11lvn+uuvXyPqGj169BL7DRkyJC1btqw8XtH3Any3rDQDAAAAAFjFmjVrlgcffDBJMmPGjLzwwgu5+uqrc9111+XBBx9Mt27dVksd2267bcaNG5dOnTot13V9+/bNuHHj0rBhw1VU2Yq55JJLstNOO2XmzJn505/+lGOOOSb169fPYYcdVtOlLZcVfS/Ad0toBgAAAACwitWpUyc77LBD5XGfPn1ywgknZJdddsnAgQPz+uuvp3bt2qu8jqZNm1apY1m1atUqrVq1WgUVrZxNNtmk8n722GOPjB8/PjfddNNaF5qt6HsBvlu2ZwQAAAAAqAHrrrtuLrroorz99tt55JFHKts/++yz/Pu//3tatGiRhg0bpmfPnhk/fnyVazt06JBTTz01F1xwQdq2bZtmzZrlF7/4RYrFYu6///5svvnmadKkSfbff/98+eWXlddVtw1goVDIFVdckdNPPz2tWrVKWVlZfvrTn+brr7+u7FPd9owVFRUZPHhwNtxww9SrVy8bbbRR/vM//7Py/E033ZSdd945zZs3z3rrrZfddtttkfsYNGhQysvL88gjj2SrrbZKo0aNsvPOO2fixInL/TwLhUK23HLLfPjhh1XaJ0yYkL59+6ZJkyZp0qRJDj744CrbYn7zTB5++OHsu+++adSoUdq3b59rrrmmyjg9e/bMQQcdVKVtcdsqfvXVV/m3f/u3NGnSJGVlZTnnnHOWWHt14yxYsCDnn39+Nt5449SrVy/t2rXLoEGDlueRAMtJaAYAAAAAUEN69uyZOnXq5Omnn65s23///fPQQw/lkksuyW233ZaFCxdmt912y9tvv13l2ltvvTXPPvtsbrzxxgwePDiXXnppTjnllJx55pn5zW9+k2uuuSaPPfZYlSBrcYYOHZqPP/44I0aMyGmnnZZrr702V1xxxWL7F4vF9O/fP1dffXV++tOf5v77788555yTzz77rLLPpEmTcvjhh+eOO+7IzTffnA022CA9evTIu+++W2WsDz74IKeddlp+/etf55Zbbsm0adNyyCGHpFgsLutjrDLWRhttVHn89ttvZ6eddsqcOXMyYsSIDBs2LBMnTky/fv0WGf+oo47KVlttlZEjR2afffbJCSecsNTvJluc0047LQ0bNsydd96ZY445Juecc06uvPLK5RrjuOOOy9lnn50f/ehHGT16dIYOHZrZs2evUD3AsrE9IwAAAABADalfv35atmyZTz75JEny4IMPZuzYsRkzZkx23XXXJEmvXr3SoUOHXHzxxbn22murXHvHHXekdu3a2WuvvTJq1Kj8v//3//LWWwTCshQAACAASURBVG9VBkcvvfRShg8fvsiqqW/r0KFDhg0bluSfW0eOHTs2I0eOzODBg6vt//DDD+eRRx7JqFGjst9++1W2H3744ZU/n3XWWZU/L1y4ML17986zzz6bESNGVDn3xRdfZOzYsenSpUtl3wEDBuSNN95I165dl1j3woULM3/+/MycOTPDhw/PCy+8UGXV3jnnnJM2bdrkgQceyDrrrJMk2WqrrdK1a9fcf//96du3b2XfvffeO+edd17lM3jnnXfy29/+Nvvuu+8Sa6jO5ptvXvmu+vTpk2nTpuW8887LCSeckFq1lr6W5fXXX88NN9yQK664Ij/72c8q2w855JDlrgVYdlaaAQAAAADUoH9d8fTss8+mrKysMjBLkkaNGmXffffNk08+WeW6nj17VvketM6dO6dDhw5VVlp17tw5n376aebOnbvEGvbcc88qx5tttlkmT5682P5///vf07x58yqB2be99tprGTBgQFq3bp3atWunbt26eeONN/Lmm29W6dehQ4fKwOybuZMscf5v9O/fP3Xr1k3z5s3z85//PBdffHF22WWXyvN//etfM2DAgNSqVSvz58/P/Pnzs9FGG6VDhw6LbBU5YMCAKscHHHBAnn/++SxYsGCpdXxbdWN9/PHHy3RPSfLoo48mie0YYTUTmgEAAAAA1JA5c+bk888/T+vWrZMkU6ZMSVlZ2SL9WrdunS+++KJK27rrrlvleJ111qm2rVgsLjU0q+66OXPmLLb/559/nrZt2y72/MyZM7Pnnnvmww8/zKWXXponnngizz33XLbeeutFxq1u7iRLnP8bl112WZ577rncd9996d69e0499dS89NJLlec/++yzXHjhhalbt26Vz7vvvrvId599+7mXlZVl/vz5VbacXFbVjZX88/0ui88//zyNGjVK06ZNl3tuYMXZnhEAAAAAoIY8+uijmT9/fnbcccckSdu2bTNt2rRF+n3yySdp3rz56i5vsVq0aLHEAGjcuHGZPHlyHnnkkSpbLM6YMeM7raNz584pLy9Pkuy4447p0qVLfvWrX+WBBx5IkjRv3jwDBgzI0Ucfvci1LVu2rHL87ec+bdq01KlTp7Jf/fr1Fwkfv/zyy2rrqm6sJEsMGv9VixYt8o9//CNfffWV4AxWIyvNAAAAAABqwPTp0/PLX/4ynTt3zh577JEk+eEPf5hp06bl8ccfr+w3e/bs3Hfffdl5551rqtRF7L777vniiy8yevToas9XVFQkSerVq1fZ9tRTT2XSpEmrrKb11lsvv/zlL/Pggw/m5Zdfrqxz4sSJ6datW8rLy6t8OnToUOX6u+++e5Hjbt26VW6B2a5du7z++utV+jz88MPV1vLtsUaOHJm2bdumXbt2y3QvvXr1SpLcdNNNy9Qf+G5YaQYAAAAAsIrNnz8/Tz/9dJJ/bl34/PPP5+qrr87s2bPz4IMPVgYzffr0Sffu3XPIIYfkggsuSIsWLXLJJZekoqIip512Wk3eQhW9e/dOnz598uMf/zhnnXVWtt1220yZMiWPP/54rr322uywww5p3LhxjjnmmAwePDiTJ0/OkCFD8oMf/GCV1nXCCSfkggsuyMUXX5w//elPGTJkSLbffvv07ds3Rx55ZFq2bJmPPvoojzzySAYNGpSePXtWXvvAAw/k17/+dXbdddeMHDkyjzzySEaNGlV5fsCAAbnhhhvy85//PH379s2jjz6aBx98sNo6Jk6cmOOOOy4HHnhgHn/88dxwww254oorUqvWsq1j2WSTTXLsscfmF7/4RaZNm5Zddtkl06dPz5133plbb711pZ4RsHhWmgEAAAAArGIzZszIjjvumO7du+fggw/OnXfemcMOOyyvvPJKunXrVqXvPffck969e+fkk0/OwQcfnGKxmL///e/p3LlzDVW/qEKhkLvvvjvHHntsLr/88uy9994544wzKrcybN26de64445MnTo1/fv3z+WXX55rrrlmld9D48aNc9JJJ+XWW2/Nhx9+mI033jhPP/10GjZsmGOPPTZ77713zj777NSrV2+RWq6//vq88MIL2X///TN69OhceeWV2W+//SrP9+3bN+edd17uvPPODBgwIO+//36uuOKKauu46KKL8tVXX+XAAw/MtddemzPPPDMnnnjict3LVVddlbPPPjsjRozIPvvsk5NPPjkNGzZc/ocCLLNCsVis6RpWu/Ly8uL48eNrugwAAAAA1lDfrD4ZM2ZMjdYBrHpjxozJbrvtlldeeSVbbLFFTZcDrAaFQuH5YrFY/u12K80AAAAAAAAoeb7TDAAAAABgGc2dOzdTp07Nxx9/nClTplT585ufa9eunRdeeKGmSwVgOQnNAAAAAIC11qsfz8jT736Rr+cvyA4dW2Srduumdq3Cco/zTRj27QDs2z/PmDEjrVu3zvrrr5+2bdtW/rnTTjtV/ty+fftVcKesKj179kwpfo0RsCihGQAAAACwVprw0Yz86NpxmT13QZKkTq1Cbj7mh9l+oxaVfb4dhi0uFPsmDPsmCKsuDFt//fXTsmXL1KrlW28Avo+EZgAAAADAWunhV6dWBmZJMvuTSTl80LXp0ODrTJkyJVOmTMn06dO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            "text/plain": [
              "<Figure size 2160x2160 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}